1,1,122,0,0.473037," ","integrate(sinh(d*x+c)^4*(a+b*sinh(d*x+c)^2),x, algorithm=""fricas"")","\frac{3 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + 2 \, {\left(5 \, b \cosh\left(d x + c\right)^{3} + 3 \, {\left(2 \, a - 3 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 6 \, {\left(6 \, a - 5 \, b\right)} d x + 3 \, {\left(b \cosh\left(d x + c\right)^{5} + 2 \, {\left(2 \, a - 3 \, b\right)} \cosh\left(d x + c\right)^{3} - {\left(16 \, a - 15 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{96 \, d}"," ",0,"1/96*(3*b*cosh(d*x + c)*sinh(d*x + c)^5 + 2*(5*b*cosh(d*x + c)^3 + 3*(2*a - 3*b)*cosh(d*x + c))*sinh(d*x + c)^3 + 6*(6*a - 5*b)*d*x + 3*(b*cosh(d*x + c)^5 + 2*(2*a - 3*b)*cosh(d*x + c)^3 - (16*a - 15*b)*cosh(d*x + c))*sinh(d*x + c))/d","A",0
2,1,102,0,0.455219," ","integrate(sinh(d*x+c)^3*(a+b*sinh(d*x+c)^2),x, algorithm=""fricas"")","\frac{3 \, b \cosh\left(d x + c\right)^{5} + 15 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} + 5 \, {\left(4 \, a - 5 \, b\right)} \cosh\left(d x + c\right)^{3} + 15 \, {\left(2 \, b \cosh\left(d x + c\right)^{3} + {\left(4 \, a - 5 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 30 \, {\left(6 \, a - 5 \, b\right)} \cosh\left(d x + c\right)}{240 \, d}"," ",0,"1/240*(3*b*cosh(d*x + c)^5 + 15*b*cosh(d*x + c)*sinh(d*x + c)^4 + 5*(4*a - 5*b)*cosh(d*x + c)^3 + 15*(2*b*cosh(d*x + c)^3 + (4*a - 5*b)*cosh(d*x + c))*sinh(d*x + c)^2 - 30*(6*a - 5*b)*cosh(d*x + c))/d","B",0
3,1,64,0,0.661118," ","integrate(sinh(d*x+c)^2*(a+b*sinh(d*x+c)^2),x, algorithm=""fricas"")","\frac{b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} - {\left(4 \, a - 3 \, b\right)} d x + {\left(b \cosh\left(d x + c\right)^{3} + 4 \, {\left(a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{8 \, d}"," ",0,"1/8*(b*cosh(d*x + c)*sinh(d*x + c)^3 - (4*a - 3*b)*d*x + (b*cosh(d*x + c)^3 + 4*(a - b)*cosh(d*x + c))*sinh(d*x + c))/d","A",0
4,1,48,0,1.008469," ","integrate(sinh(d*x+c)*(a+b*sinh(d*x+c)^2),x, algorithm=""fricas"")","\frac{b \cosh\left(d x + c\right)^{3} + 3 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + 3 \, {\left(4 \, a - 3 \, b\right)} \cosh\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(b*cosh(d*x + c)^3 + 3*b*cosh(d*x + c)*sinh(d*x + c)^2 + 3*(4*a - 3*b)*cosh(d*x + c))/d","A",0
5,1,30,0,0.453716," ","integrate(a+b*sinh(d*x+c)^2,x, algorithm=""fricas"")","\frac{{\left(2 \, a - b\right)} d x + b \cosh\left(d x + c\right) \sinh\left(d x + c\right)}{2 \, d}"," ",0,"1/2*((2*a - b)*d*x + b*cosh(d*x + c)*sinh(d*x + c))/d","A",0
6,1,126,0,0.576470," ","integrate(csch(d*x+c)*(a+b*sinh(d*x+c)^2),x, algorithm=""fricas"")","\frac{b \cosh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b \sinh\left(d x + c\right)^{2} - 2 \, {\left(a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) + 2 \, {\left(a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) + b}{2 \, {\left(d \cosh\left(d x + c\right) + d \sinh\left(d x + c\right)\right)}}"," ",0,"1/2*(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 - 2*(a*cosh(d*x + c) + a*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) + 1) + 2*(a*cosh(d*x + c) + a*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) - 1) + b)/(d*cosh(d*x + c) + d*sinh(d*x + c))","B",0
7,1,36,0,0.519279," ","integrate(csch(d*x+c)^2*(a+b*sinh(d*x+c)^2),x, algorithm=""fricas"")","-\frac{a \cosh\left(d x + c\right) - {\left(b d x + a\right)} \sinh\left(d x + c\right)}{d \sinh\left(d x + c\right)}"," ",0,"-(a*cosh(d*x + c) - (b*d*x + a)*sinh(d*x + c))/(d*sinh(d*x + c))","B",0
8,1,484,0,0.588312," ","integrate(csch(d*x+c)^3*(a+b*sinh(d*x+c)^2),x, algorithm=""fricas"")","-\frac{2 \, a \cosh\left(d x + c\right)^{3} + 6 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + 2 \, a \sinh\left(d x + c\right)^{3} + 2 \, a \cosh\left(d x + c\right) - {\left({\left(a - 2 \, b\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a - 2 \, b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a - 2 \, b\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(a - 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a - 2 \, b\right)} \cosh\left(d x + c\right)^{2} - a + 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a - 2 \, b\right)} \cosh\left(d x + c\right)^{3} - {\left(a - 2 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + a - 2 \, b\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) + {\left({\left(a - 2 \, b\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a - 2 \, b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a - 2 \, b\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(a - 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a - 2 \, b\right)} \cosh\left(d x + c\right)^{2} - a + 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a - 2 \, b\right)} \cosh\left(d x + c\right)^{3} - {\left(a - 2 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + a - 2 \, b\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} + a\right)} \sinh\left(d x + c\right)}{2 \, {\left(d \cosh\left(d x + c\right)^{4} + 4 \, d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + d \sinh\left(d x + c\right)^{4} - 2 \, d \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, d \cosh\left(d x + c\right)^{2} - d\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(d \cosh\left(d x + c\right)^{3} - d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + d\right)}}"," ",0,"-1/2*(2*a*cosh(d*x + c)^3 + 6*a*cosh(d*x + c)*sinh(d*x + c)^2 + 2*a*sinh(d*x + c)^3 + 2*a*cosh(d*x + c) - ((a - 2*b)*cosh(d*x + c)^4 + 4*(a - 2*b)*cosh(d*x + c)*sinh(d*x + c)^3 + (a - 2*b)*sinh(d*x + c)^4 - 2*(a - 2*b)*cosh(d*x + c)^2 + 2*(3*(a - 2*b)*cosh(d*x + c)^2 - a + 2*b)*sinh(d*x + c)^2 + 4*((a - 2*b)*cosh(d*x + c)^3 - (a - 2*b)*cosh(d*x + c))*sinh(d*x + c) + a - 2*b)*log(cosh(d*x + c) + sinh(d*x + c) + 1) + ((a - 2*b)*cosh(d*x + c)^4 + 4*(a - 2*b)*cosh(d*x + c)*sinh(d*x + c)^3 + (a - 2*b)*sinh(d*x + c)^4 - 2*(a - 2*b)*cosh(d*x + c)^2 + 2*(3*(a - 2*b)*cosh(d*x + c)^2 - a + 2*b)*sinh(d*x + c)^2 + 4*((a - 2*b)*cosh(d*x + c)^3 - (a - 2*b)*cosh(d*x + c))*sinh(d*x + c) + a - 2*b)*log(cosh(d*x + c) + sinh(d*x + c) - 1) + 2*(3*a*cosh(d*x + c)^2 + a)*sinh(d*x + c))/(d*cosh(d*x + c)^4 + 4*d*cosh(d*x + c)*sinh(d*x + c)^3 + d*sinh(d*x + c)^4 - 2*d*cosh(d*x + c)^2 + 2*(3*d*cosh(d*x + c)^2 - d)*sinh(d*x + c)^2 + 4*(d*cosh(d*x + c)^3 - d*cosh(d*x + c))*sinh(d*x + c) + d)","B",0
9,1,159,0,0.412371," ","integrate(csch(d*x+c)^4*(a+b*sinh(d*x+c)^2),x, algorithm=""fricas"")","\frac{4 \, {\left({\left(a - 3 \, b\right)} \cosh\left(d x + c\right)^{2} - 2 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a - 3 \, b\right)} \sinh\left(d x + c\right)^{2} - 3 \, a + 3 \, b\right)}}{3 \, {\left(d \cosh\left(d x + c\right)^{4} + 4 \, d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + d \sinh\left(d x + c\right)^{4} - 4 \, d \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, d \cosh\left(d x + c\right)^{2} - 2 \, d\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(d \cosh\left(d x + c\right)^{3} - d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + 3 \, d\right)}}"," ",0,"4/3*((a - 3*b)*cosh(d*x + c)^2 - 2*a*cosh(d*x + c)*sinh(d*x + c) + (a - 3*b)*sinh(d*x + c)^2 - 3*a + 3*b)/(d*cosh(d*x + c)^4 + 4*d*cosh(d*x + c)*sinh(d*x + c)^3 + d*sinh(d*x + c)^4 - 4*d*cosh(d*x + c)^2 + 2*(3*d*cosh(d*x + c)^2 - 2*d)*sinh(d*x + c)^2 + 4*(d*cosh(d*x + c)^3 - d*cosh(d*x + c))*sinh(d*x + c) + 3*d)","B",0
10,1,238,0,0.455131," ","integrate(sinh(d*x+c)^4*(a+b*sinh(d*x+c)^2)^2,x, algorithm=""fricas"")","\frac{3 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + 3 \, {\left(7 \, b^{2} \cosh\left(d x + c\right)^{3} + 8 \, {\left(a b - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + {\left(21 \, b^{2} \cosh\left(d x + c\right)^{5} + 80 \, {\left(a b - b^{2}\right)} \cosh\left(d x + c\right)^{3} + 12 \, {\left(4 \, a^{2} - 12 \, a b + 7 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 3 \, {\left(48 \, a^{2} - 80 \, a b + 35 \, b^{2}\right)} d x + 3 \, {\left(b^{2} \cosh\left(d x + c\right)^{7} + 8 \, {\left(a b - b^{2}\right)} \cosh\left(d x + c\right)^{5} + 4 \, {\left(4 \, a^{2} - 12 \, a b + 7 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - 8 \, {\left(8 \, a^{2} - 15 \, a b + 7 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{384 \, d}"," ",0,"1/384*(3*b^2*cosh(d*x + c)*sinh(d*x + c)^7 + 3*(7*b^2*cosh(d*x + c)^3 + 8*(a*b - b^2)*cosh(d*x + c))*sinh(d*x + c)^5 + (21*b^2*cosh(d*x + c)^5 + 80*(a*b - b^2)*cosh(d*x + c)^3 + 12*(4*a^2 - 12*a*b + 7*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 3*(48*a^2 - 80*a*b + 35*b^2)*d*x + 3*(b^2*cosh(d*x + c)^7 + 8*(a*b - b^2)*cosh(d*x + c)^5 + 4*(4*a^2 - 12*a*b + 7*b^2)*cosh(d*x + c)^3 - 8*(8*a^2 - 15*a*b + 7*b^2)*cosh(d*x + c))*sinh(d*x + c))/d","A",0
11,1,213,0,0.637403," ","integrate(sinh(d*x+c)^3*(a+b*sinh(d*x+c)^2)^2,x, algorithm=""fricas"")","\frac{15 \, b^{2} \cosh\left(d x + c\right)^{7} + 105 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + 21 \, {\left(8 \, a b - 7 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 105 \, {\left(5 \, b^{2} \cosh\left(d x + c\right)^{3} + {\left(8 \, a b - 7 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 35 \, {\left(16 \, a^{2} - 40 \, a b + 21 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 105 \, {\left(3 \, b^{2} \cosh\left(d x + c\right)^{5} + 2 \, {\left(8 \, a b - 7 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(16 \, a^{2} - 40 \, a b + 21 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 105 \, {\left(48 \, a^{2} - 80 \, a b + 35 \, b^{2}\right)} \cosh\left(d x + c\right)}{6720 \, d}"," ",0,"1/6720*(15*b^2*cosh(d*x + c)^7 + 105*b^2*cosh(d*x + c)*sinh(d*x + c)^6 + 21*(8*a*b - 7*b^2)*cosh(d*x + c)^5 + 105*(5*b^2*cosh(d*x + c)^3 + (8*a*b - 7*b^2)*cosh(d*x + c))*sinh(d*x + c)^4 + 35*(16*a^2 - 40*a*b + 21*b^2)*cosh(d*x + c)^3 + 105*(3*b^2*cosh(d*x + c)^5 + 2*(8*a*b - 7*b^2)*cosh(d*x + c)^3 + (16*a^2 - 40*a*b + 21*b^2)*cosh(d*x + c))*sinh(d*x + c)^2 - 105*(48*a^2 - 80*a*b + 35*b^2)*cosh(d*x + c))/d","B",0
12,1,149,0,0.658336," ","integrate(sinh(d*x+c)^2*(a+b*sinh(d*x+c)^2)^2,x, algorithm=""fricas"")","\frac{3 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + 2 \, {\left(5 \, b^{2} \cosh\left(d x + c\right)^{3} + 3 \, {\left(4 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 6 \, {\left(8 \, a^{2} - 12 \, a b + 5 \, b^{2}\right)} d x + 3 \, {\left(b^{2} \cosh\left(d x + c\right)^{5} + 2 \, {\left(4 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(16 \, a^{2} - 32 \, a b + 15 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{96 \, d}"," ",0,"1/96*(3*b^2*cosh(d*x + c)*sinh(d*x + c)^5 + 2*(5*b^2*cosh(d*x + c)^3 + 3*(4*a*b - 3*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 - 6*(8*a^2 - 12*a*b + 5*b^2)*d*x + 3*(b^2*cosh(d*x + c)^5 + 2*(4*a*b - 3*b^2)*cosh(d*x + c)^3 + (16*a^2 - 32*a*b + 15*b^2)*cosh(d*x + c))*sinh(d*x + c))/d","A",0
13,1,122,0,0.652171," ","integrate(sinh(d*x+c)*(a+b*sinh(d*x+c)^2)^2,x, algorithm=""fricas"")","\frac{3 \, b^{2} \cosh\left(d x + c\right)^{5} + 15 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} + 5 \, {\left(8 \, a b - 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 15 \, {\left(2 \, b^{2} \cosh\left(d x + c\right)^{3} + {\left(8 \, a b - 5 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 30 \, {\left(8 \, a^{2} - 12 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)}{240 \, d}"," ",0,"1/240*(3*b^2*cosh(d*x + c)^5 + 15*b^2*cosh(d*x + c)*sinh(d*x + c)^4 + 5*(8*a*b - 5*b^2)*cosh(d*x + c)^3 + 15*(2*b^2*cosh(d*x + c)^3 + (8*a*b - 5*b^2)*cosh(d*x + c))*sinh(d*x + c)^2 + 30*(8*a^2 - 12*a*b + 5*b^2)*cosh(d*x + c))/d","B",0
14,1,80,0,0.672309," ","integrate((a+b*sinh(d*x+c)^2)^2,x, algorithm=""fricas"")","\frac{b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} d x + {\left(b^{2} \cosh\left(d x + c\right)^{3} + 4 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{8 \, d}"," ",0,"1/8*(b^2*cosh(d*x + c)*sinh(d*x + c)^3 + (8*a^2 - 8*a*b + 3*b^2)*d*x + (b^2*cosh(d*x + c)^3 + 4*(2*a*b - b^2)*cosh(d*x + c))*sinh(d*x + c))/d","A",0
15,1,492,0,0.474458," ","integrate(csch(d*x+c)*(a+b*sinh(d*x+c)^2)^2,x, algorithm=""fricas"")","\frac{b^{2} \cosh\left(d x + c\right)^{6} + 6 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + b^{2} \sinh\left(d x + c\right)^{6} + 3 \, {\left(8 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(5 \, b^{2} \cosh\left(d x + c\right)^{2} + 8 \, a b - 3 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, b^{2} \cosh\left(d x + c\right)^{3} + 3 \, {\left(8 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 3 \, {\left(8 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 3 \, {\left(5 \, b^{2} \cosh\left(d x + c\right)^{4} + 6 \, {\left(8 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 8 \, a b - 3 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} + b^{2} - 24 \, {\left(a^{2} \cosh\left(d x + c\right)^{3} + 3 \, a^{2} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, a^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + a^{2} \sinh\left(d x + c\right)^{3}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) + 24 \, {\left(a^{2} \cosh\left(d x + c\right)^{3} + 3 \, a^{2} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, a^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + a^{2} \sinh\left(d x + c\right)^{3}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) + 6 \, {\left(b^{2} \cosh\left(d x + c\right)^{5} + 2 \, {\left(8 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{24 \, {\left(d \cosh\left(d x + c\right)^{3} + 3 \, d \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + d \sinh\left(d x + c\right)^{3}\right)}}"," ",0,"1/24*(b^2*cosh(d*x + c)^6 + 6*b^2*cosh(d*x + c)*sinh(d*x + c)^5 + b^2*sinh(d*x + c)^6 + 3*(8*a*b - 3*b^2)*cosh(d*x + c)^4 + 3*(5*b^2*cosh(d*x + c)^2 + 8*a*b - 3*b^2)*sinh(d*x + c)^4 + 4*(5*b^2*cosh(d*x + c)^3 + 3*(8*a*b - 3*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 3*(8*a*b - 3*b^2)*cosh(d*x + c)^2 + 3*(5*b^2*cosh(d*x + c)^4 + 6*(8*a*b - 3*b^2)*cosh(d*x + c)^2 + 8*a*b - 3*b^2)*sinh(d*x + c)^2 + b^2 - 24*(a^2*cosh(d*x + c)^3 + 3*a^2*cosh(d*x + c)^2*sinh(d*x + c) + 3*a^2*cosh(d*x + c)*sinh(d*x + c)^2 + a^2*sinh(d*x + c)^3)*log(cosh(d*x + c) + sinh(d*x + c) + 1) + 24*(a^2*cosh(d*x + c)^3 + 3*a^2*cosh(d*x + c)^2*sinh(d*x + c) + 3*a^2*cosh(d*x + c)*sinh(d*x + c)^2 + a^2*sinh(d*x + c)^3)*log(cosh(d*x + c) + sinh(d*x + c) - 1) + 6*(b^2*cosh(d*x + c)^5 + 2*(8*a*b - 3*b^2)*cosh(d*x + c)^3 + (8*a*b - 3*b^2)*cosh(d*x + c))*sinh(d*x + c))/(d*cosh(d*x + c)^3 + 3*d*cosh(d*x + c)^2*sinh(d*x + c) + 3*d*cosh(d*x + c)*sinh(d*x + c)^2 + d*sinh(d*x + c)^3)","B",0
16,1,89,0,0.443853," ","integrate(csch(d*x+c)^2*(a+b*sinh(d*x+c)^2)^2,x, algorithm=""fricas"")","\frac{b^{2} \cosh\left(d x + c\right)^{3} + 3 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} - {\left(8 \, a^{2} + b^{2}\right)} \cosh\left(d x + c\right) + 4 \, {\left({\left(4 \, a b - b^{2}\right)} d x + 2 \, a^{2}\right)} \sinh\left(d x + c\right)}{8 \, d \sinh\left(d x + c\right)}"," ",0,"1/8*(b^2*cosh(d*x + c)^3 + 3*b^2*cosh(d*x + c)*sinh(d*x + c)^2 - (8*a^2 + b^2)*cosh(d*x + c) + 4*((4*a*b - b^2)*d*x + 2*a^2)*sinh(d*x + c))/(d*sinh(d*x + c))","A",0
17,1,902,0,2.067869," ","integrate(csch(d*x+c)^3*(a+b*sinh(d*x+c)^2)^2,x, algorithm=""fricas"")","\frac{b^{2} \cosh\left(d x + c\right)^{6} + 6 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + b^{2} \sinh\left(d x + c\right)^{6} - {\left(2 \, a^{2} + b^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(15 \, b^{2} \cosh\left(d x + c\right)^{2} - 2 \, a^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, b^{2} \cosh\left(d x + c\right)^{3} - {\left(2 \, a^{2} + b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - {\left(2 \, a^{2} + b^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(15 \, b^{2} \cosh\left(d x + c\right)^{4} - 6 \, {\left(2 \, a^{2} + b^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, a^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{2} + b^{2} + {\left({\left(a^{2} - 4 \, a b\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(a^{2} - 4 \, a b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} + {\left(a^{2} - 4 \, a b\right)} \sinh\left(d x + c\right)^{5} - 2 \, {\left(a^{2} - 4 \, a b\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(5 \, {\left(a^{2} - 4 \, a b\right)} \cosh\left(d x + c\right)^{2} - a^{2} + 4 \, a b\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(5 \, {\left(a^{2} - 4 \, a b\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{2} - 4 \, a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{2} - 4 \, a b\right)} \cosh\left(d x + c\right) + {\left(5 \, {\left(a^{2} - 4 \, a b\right)} \cosh\left(d x + c\right)^{4} - 6 \, {\left(a^{2} - 4 \, a b\right)} \cosh\left(d x + c\right)^{2} + a^{2} - 4 \, a b\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) - {\left({\left(a^{2} - 4 \, a b\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(a^{2} - 4 \, a b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} + {\left(a^{2} - 4 \, a b\right)} \sinh\left(d x + c\right)^{5} - 2 \, {\left(a^{2} - 4 \, a b\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(5 \, {\left(a^{2} - 4 \, a b\right)} \cosh\left(d x + c\right)^{2} - a^{2} + 4 \, a b\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(5 \, {\left(a^{2} - 4 \, a b\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{2} - 4 \, a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{2} - 4 \, a b\right)} \cosh\left(d x + c\right) + {\left(5 \, {\left(a^{2} - 4 \, a b\right)} \cosh\left(d x + c\right)^{4} - 6 \, {\left(a^{2} - 4 \, a b\right)} \cosh\left(d x + c\right)^{2} + a^{2} - 4 \, a b\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) + 2 \, {\left(3 \, b^{2} \cosh\left(d x + c\right)^{5} - 2 \, {\left(2 \, a^{2} + b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(2 \, a^{2} + b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{2 \, {\left(d \cosh\left(d x + c\right)^{5} + 5 \, d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} + d \sinh\left(d x + c\right)^{5} - 2 \, d \cosh\left(d x + c\right)^{3} + 2 \, {\left(5 \, d \cosh\left(d x + c\right)^{2} - d\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(5 \, d \cosh\left(d x + c\right)^{3} - 3 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + d \cosh\left(d x + c\right) + {\left(5 \, d \cosh\left(d x + c\right)^{4} - 6 \, d \cosh\left(d x + c\right)^{2} + d\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"1/2*(b^2*cosh(d*x + c)^6 + 6*b^2*cosh(d*x + c)*sinh(d*x + c)^5 + b^2*sinh(d*x + c)^6 - (2*a^2 + b^2)*cosh(d*x + c)^4 + (15*b^2*cosh(d*x + c)^2 - 2*a^2 - b^2)*sinh(d*x + c)^4 + 4*(5*b^2*cosh(d*x + c)^3 - (2*a^2 + b^2)*cosh(d*x + c))*sinh(d*x + c)^3 - (2*a^2 + b^2)*cosh(d*x + c)^2 + (15*b^2*cosh(d*x + c)^4 - 6*(2*a^2 + b^2)*cosh(d*x + c)^2 - 2*a^2 - b^2)*sinh(d*x + c)^2 + b^2 + ((a^2 - 4*a*b)*cosh(d*x + c)^5 + 5*(a^2 - 4*a*b)*cosh(d*x + c)*sinh(d*x + c)^4 + (a^2 - 4*a*b)*sinh(d*x + c)^5 - 2*(a^2 - 4*a*b)*cosh(d*x + c)^3 + 2*(5*(a^2 - 4*a*b)*cosh(d*x + c)^2 - a^2 + 4*a*b)*sinh(d*x + c)^3 + 2*(5*(a^2 - 4*a*b)*cosh(d*x + c)^3 - 3*(a^2 - 4*a*b)*cosh(d*x + c))*sinh(d*x + c)^2 + (a^2 - 4*a*b)*cosh(d*x + c) + (5*(a^2 - 4*a*b)*cosh(d*x + c)^4 - 6*(a^2 - 4*a*b)*cosh(d*x + c)^2 + a^2 - 4*a*b)*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) + 1) - ((a^2 - 4*a*b)*cosh(d*x + c)^5 + 5*(a^2 - 4*a*b)*cosh(d*x + c)*sinh(d*x + c)^4 + (a^2 - 4*a*b)*sinh(d*x + c)^5 - 2*(a^2 - 4*a*b)*cosh(d*x + c)^3 + 2*(5*(a^2 - 4*a*b)*cosh(d*x + c)^2 - a^2 + 4*a*b)*sinh(d*x + c)^3 + 2*(5*(a^2 - 4*a*b)*cosh(d*x + c)^3 - 3*(a^2 - 4*a*b)*cosh(d*x + c))*sinh(d*x + c)^2 + (a^2 - 4*a*b)*cosh(d*x + c) + (5*(a^2 - 4*a*b)*cosh(d*x + c)^4 - 6*(a^2 - 4*a*b)*cosh(d*x + c)^2 + a^2 - 4*a*b)*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) - 1) + 2*(3*b^2*cosh(d*x + c)^5 - 2*(2*a^2 + b^2)*cosh(d*x + c)^3 - (2*a^2 + b^2)*cosh(d*x + c))*sinh(d*x + c))/(d*cosh(d*x + c)^5 + 5*d*cosh(d*x + c)*sinh(d*x + c)^4 + d*sinh(d*x + c)^5 - 2*d*cosh(d*x + c)^3 + 2*(5*d*cosh(d*x + c)^2 - d)*sinh(d*x + c)^3 + 2*(5*d*cosh(d*x + c)^3 - 3*d*cosh(d*x + c))*sinh(d*x + c)^2 + d*cosh(d*x + c) + (5*d*cosh(d*x + c)^4 - 6*d*cosh(d*x + c)^2 + d)*sinh(d*x + c))","B",0
18,1,174,0,0.392292," ","integrate(csch(d*x+c)^4*(a+b*sinh(d*x+c)^2)^2,x, algorithm=""fricas"")","\frac{2 \, {\left(a^{2} - 3 \, a b\right)} \cosh\left(d x + c\right)^{3} + 6 \, {\left(a^{2} - 3 \, a b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + {\left(3 \, b^{2} d x - 2 \, a^{2} + 6 \, a b\right)} \sinh\left(d x + c\right)^{3} - 6 \, {\left(a^{2} - a b\right)} \cosh\left(d x + c\right) - 3 \, {\left(3 \, b^{2} d x - {\left(3 \, b^{2} d x - 2 \, a^{2} + 6 \, a b\right)} \cosh\left(d x + c\right)^{2} - 2 \, a^{2} + 6 \, a b\right)} \sinh\left(d x + c\right)}{3 \, {\left(d \sinh\left(d x + c\right)^{3} + 3 \, {\left(d \cosh\left(d x + c\right)^{2} - d\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"1/3*(2*(a^2 - 3*a*b)*cosh(d*x + c)^3 + 6*(a^2 - 3*a*b)*cosh(d*x + c)*sinh(d*x + c)^2 + (3*b^2*d*x - 2*a^2 + 6*a*b)*sinh(d*x + c)^3 - 6*(a^2 - a*b)*cosh(d*x + c) - 3*(3*b^2*d*x - (3*b^2*d*x - 2*a^2 + 6*a*b)*cosh(d*x + c)^2 - 2*a^2 + 6*a*b)*sinh(d*x + c))/(d*sinh(d*x + c)^3 + 3*(d*cosh(d*x + c)^2 - d)*sinh(d*x + c))","B",0
19,1,406,0,0.475080," ","integrate(sinh(d*x+c)^4*(a+b*sinh(d*x+c)^2)^3,x, algorithm=""fricas"")","\frac{5 \, b^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + 10 \, {\left(6 \, b^{3} \cosh\left(d x + c\right)^{3} + {\left(6 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + {\left(126 \, b^{3} \cosh\left(d x + c\right)^{5} + 70 \, {\left(6 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 15 \, {\left(16 \, a^{2} b - 32 \, a b^{2} + 15 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 10 \, {\left(6 \, b^{3} \cosh\left(d x + c\right)^{7} + 7 \, {\left(6 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(16 \, a^{2} b - 32 \, a b^{2} + 15 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(8 \, a^{3} - 36 \, a^{2} b + 42 \, a b^{2} - 15 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 30 \, {\left(32 \, a^{3} - 80 \, a^{2} b + 70 \, a b^{2} - 21 \, b^{3}\right)} d x + 5 \, {\left(b^{3} \cosh\left(d x + c\right)^{9} + 2 \, {\left(6 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(16 \, a^{2} b - 32 \, a b^{2} + 15 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 8 \, {\left(8 \, a^{3} - 36 \, a^{2} b + 42 \, a b^{2} - 15 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 2 \, {\left(128 \, a^{3} - 360 \, a^{2} b + 336 \, a b^{2} - 105 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{2560 \, d}"," ",0,"1/2560*(5*b^3*cosh(d*x + c)*sinh(d*x + c)^9 + 10*(6*b^3*cosh(d*x + c)^3 + (6*a*b^2 - 5*b^3)*cosh(d*x + c))*sinh(d*x + c)^7 + (126*b^3*cosh(d*x + c)^5 + 70*(6*a*b^2 - 5*b^3)*cosh(d*x + c)^3 + 15*(16*a^2*b - 32*a*b^2 + 15*b^3)*cosh(d*x + c))*sinh(d*x + c)^5 + 10*(6*b^3*cosh(d*x + c)^7 + 7*(6*a*b^2 - 5*b^3)*cosh(d*x + c)^5 + 5*(16*a^2*b - 32*a*b^2 + 15*b^3)*cosh(d*x + c)^3 + 4*(8*a^3 - 36*a^2*b + 42*a*b^2 - 15*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 + 30*(32*a^3 - 80*a^2*b + 70*a*b^2 - 21*b^3)*d*x + 5*(b^3*cosh(d*x + c)^9 + 2*(6*a*b^2 - 5*b^3)*cosh(d*x + c)^7 + 3*(16*a^2*b - 32*a*b^2 + 15*b^3)*cosh(d*x + c)^5 + 8*(8*a^3 - 36*a^2*b + 42*a*b^2 - 15*b^3)*cosh(d*x + c)^3 - 2*(128*a^3 - 360*a^2*b + 336*a*b^2 - 105*b^3)*cosh(d*x + c))*sinh(d*x + c))/d","A",0
20,1,373,0,0.507017," ","integrate(sinh(d*x+c)^3*(a+b*sinh(d*x+c)^2)^3,x, algorithm=""fricas"")","\frac{35 \, b^{3} \cosh\left(d x + c\right)^{9} + 315 \, b^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{8} + 135 \, {\left(4 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 105 \, {\left(28 \, b^{3} \cosh\left(d x + c\right)^{3} + 9 \, {\left(4 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} + 756 \, {\left(4 \, a^{2} b - 7 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 315 \, {\left(14 \, b^{3} \cosh\left(d x + c\right)^{5} + 15 \, {\left(4 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 12 \, {\left(4 \, a^{2} b - 7 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 420 \, {\left(16 \, a^{3} - 60 \, a^{2} b + 63 \, a b^{2} - 21 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 315 \, {\left(4 \, b^{3} \cosh\left(d x + c\right)^{7} + 9 \, {\left(4 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 24 \, {\left(4 \, a^{2} b - 7 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(16 \, a^{3} - 60 \, a^{2} b + 63 \, a b^{2} - 21 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 1890 \, {\left(32 \, a^{3} - 80 \, a^{2} b + 70 \, a b^{2} - 21 \, b^{3}\right)} \cosh\left(d x + c\right)}{80640 \, d}"," ",0,"1/80640*(35*b^3*cosh(d*x + c)^9 + 315*b^3*cosh(d*x + c)*sinh(d*x + c)^8 + 135*(4*a*b^2 - 3*b^3)*cosh(d*x + c)^7 + 105*(28*b^3*cosh(d*x + c)^3 + 9*(4*a*b^2 - 3*b^3)*cosh(d*x + c))*sinh(d*x + c)^6 + 756*(4*a^2*b - 7*a*b^2 + 3*b^3)*cosh(d*x + c)^5 + 315*(14*b^3*cosh(d*x + c)^5 + 15*(4*a*b^2 - 3*b^3)*cosh(d*x + c)^3 + 12*(4*a^2*b - 7*a*b^2 + 3*b^3)*cosh(d*x + c))*sinh(d*x + c)^4 + 420*(16*a^3 - 60*a^2*b + 63*a*b^2 - 21*b^3)*cosh(d*x + c)^3 + 315*(4*b^3*cosh(d*x + c)^7 + 9*(4*a*b^2 - 3*b^3)*cosh(d*x + c)^5 + 24*(4*a^2*b - 7*a*b^2 + 3*b^3)*cosh(d*x + c)^3 + 4*(16*a^3 - 60*a^2*b + 63*a*b^2 - 21*b^3)*cosh(d*x + c))*sinh(d*x + c)^2 - 1890*(32*a^3 - 80*a^2*b + 70*a*b^2 - 21*b^3)*cosh(d*x + c))/d","B",0
21,1,269,0,1.027205," ","integrate(sinh(d*x+c)^2*(a+b*sinh(d*x+c)^2)^3,x, algorithm=""fricas"")","\frac{3 \, b^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + 3 \, {\left(7 \, b^{3} \cosh\left(d x + c\right)^{3} + 4 \, {\left(3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + {\left(21 \, b^{3} \cosh\left(d x + c\right)^{5} + 40 \, {\left(3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 12 \, {\left(12 \, a^{2} b - 18 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 3 \, {\left(64 \, a^{3} - 144 \, a^{2} b + 120 \, a b^{2} - 35 \, b^{3}\right)} d x + 3 \, {\left(b^{3} \cosh\left(d x + c\right)^{7} + 4 \, {\left(3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 4 \, {\left(12 \, a^{2} b - 18 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(16 \, a^{3} - 48 \, a^{2} b + 45 \, a b^{2} - 14 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{384 \, d}"," ",0,"1/384*(3*b^3*cosh(d*x + c)*sinh(d*x + c)^7 + 3*(7*b^3*cosh(d*x + c)^3 + 4*(3*a*b^2 - 2*b^3)*cosh(d*x + c))*sinh(d*x + c)^5 + (21*b^3*cosh(d*x + c)^5 + 40*(3*a*b^2 - 2*b^3)*cosh(d*x + c)^3 + 12*(12*a^2*b - 18*a*b^2 + 7*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 - 3*(64*a^3 - 144*a^2*b + 120*a*b^2 - 35*b^3)*d*x + 3*(b^3*cosh(d*x + c)^7 + 4*(3*a*b^2 - 2*b^3)*cosh(d*x + c)^5 + 4*(12*a^2*b - 18*a*b^2 + 7*b^3)*cosh(d*x + c)^3 + 4*(16*a^3 - 48*a^2*b + 45*a*b^2 - 14*b^3)*cosh(d*x + c))*sinh(d*x + c))/d","A",0
22,1,234,0,0.561298," ","integrate(sinh(d*x+c)*(a+b*sinh(d*x+c)^2)^3,x, algorithm=""fricas"")","\frac{5 \, b^{3} \cosh\left(d x + c\right)^{7} + 35 \, b^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + 7 \, {\left(12 \, a b^{2} - 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 35 \, {\left(5 \, b^{3} \cosh\left(d x + c\right)^{3} + {\left(12 \, a b^{2} - 7 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 35 \, {\left(16 \, a^{2} b - 20 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 35 \, {\left(3 \, b^{3} \cosh\left(d x + c\right)^{5} + 2 \, {\left(12 \, a b^{2} - 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(16 \, a^{2} b - 20 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 35 \, {\left(64 \, a^{3} - 144 \, a^{2} b + 120 \, a b^{2} - 35 \, b^{3}\right)} \cosh\left(d x + c\right)}{2240 \, d}"," ",0,"1/2240*(5*b^3*cosh(d*x + c)^7 + 35*b^3*cosh(d*x + c)*sinh(d*x + c)^6 + 7*(12*a*b^2 - 7*b^3)*cosh(d*x + c)^5 + 35*(5*b^3*cosh(d*x + c)^3 + (12*a*b^2 - 7*b^3)*cosh(d*x + c))*sinh(d*x + c)^4 + 35*(16*a^2*b - 20*a*b^2 + 7*b^3)*cosh(d*x + c)^3 + 35*(3*b^3*cosh(d*x + c)^5 + 2*(12*a*b^2 - 7*b^3)*cosh(d*x + c)^3 + 3*(16*a^2*b - 20*a*b^2 + 7*b^3)*cosh(d*x + c))*sinh(d*x + c)^2 + 35*(64*a^3 - 144*a^2*b + 120*a*b^2 - 35*b^3)*cosh(d*x + c))/d","B",0
23,1,165,0,0.467291," ","integrate((a+b*sinh(d*x+c)^2)^3,x, algorithm=""fricas"")","\frac{3 \, b^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + 2 \, {\left(5 \, b^{3} \cosh\left(d x + c\right)^{3} + 9 \, {\left(2 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 6 \, {\left(16 \, a^{3} - 24 \, a^{2} b + 18 \, a b^{2} - 5 \, b^{3}\right)} d x + 3 \, {\left(b^{3} \cosh\left(d x + c\right)^{5} + 6 \, {\left(2 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(16 \, a^{2} b - 16 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{96 \, d}"," ",0,"1/96*(3*b^3*cosh(d*x + c)*sinh(d*x + c)^5 + 2*(5*b^3*cosh(d*x + c)^3 + 9*(2*a*b^2 - b^3)*cosh(d*x + c))*sinh(d*x + c)^3 + 6*(16*a^3 - 24*a^2*b + 18*a*b^2 - 5*b^3)*d*x + 3*(b^3*cosh(d*x + c)^5 + 6*(2*a*b^2 - b^3)*cosh(d*x + c)^3 + 3*(16*a^2*b - 16*a*b^2 + 5*b^3)*cosh(d*x + c))*sinh(d*x + c))/d","A",0
24,1,1128,0,0.561096," ","integrate(csch(d*x+c)*(a+b*sinh(d*x+c)^2)^3,x, algorithm=""fricas"")","\frac{3 \, b^{3} \cosh\left(d x + c\right)^{10} + 30 \, b^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + 3 \, b^{3} \sinh\left(d x + c\right)^{10} + 5 \, {\left(12 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 5 \, {\left(27 \, b^{3} \cosh\left(d x + c\right)^{2} + 12 \, a b^{2} - 5 \, b^{3}\right)} \sinh\left(d x + c\right)^{8} + 40 \, {\left(9 \, b^{3} \cosh\left(d x + c\right)^{3} + {\left(12 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 30 \, {\left(24 \, a^{2} b - 18 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 10 \, {\left(63 \, b^{3} \cosh\left(d x + c\right)^{4} + 72 \, a^{2} b - 54 \, a b^{2} + 15 \, b^{3} + 14 \, {\left(12 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(189 \, b^{3} \cosh\left(d x + c\right)^{5} + 70 \, {\left(12 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 45 \, {\left(24 \, a^{2} b - 18 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 30 \, {\left(24 \, a^{2} b - 18 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 10 \, {\left(63 \, b^{3} \cosh\left(d x + c\right)^{6} + 35 \, {\left(12 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 72 \, a^{2} b - 54 \, a b^{2} + 15 \, b^{3} + 45 \, {\left(24 \, a^{2} b - 18 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 40 \, {\left(9 \, b^{3} \cosh\left(d x + c\right)^{7} + 7 \, {\left(12 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 15 \, {\left(24 \, a^{2} b - 18 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(24 \, a^{2} b - 18 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 3 \, b^{3} + 5 \, {\left(12 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{2} + 5 \, {\left(27 \, b^{3} \cosh\left(d x + c\right)^{8} + 28 \, {\left(12 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 90 \, {\left(24 \, a^{2} b - 18 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 12 \, a b^{2} - 5 \, b^{3} + 36 \, {\left(24 \, a^{2} b - 18 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} - 480 \, {\left(a^{3} \cosh\left(d x + c\right)^{5} + 5 \, a^{3} \cosh\left(d x + c\right)^{4} \sinh\left(d x + c\right) + 10 \, a^{3} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right)^{2} + 10 \, a^{3} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{3} + 5 \, a^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} + a^{3} \sinh\left(d x + c\right)^{5}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) + 480 \, {\left(a^{3} \cosh\left(d x + c\right)^{5} + 5 \, a^{3} \cosh\left(d x + c\right)^{4} \sinh\left(d x + c\right) + 10 \, a^{3} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right)^{2} + 10 \, a^{3} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{3} + 5 \, a^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} + a^{3} \sinh\left(d x + c\right)^{5}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) + 10 \, {\left(3 \, b^{3} \cosh\left(d x + c\right)^{9} + 4 \, {\left(12 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 18 \, {\left(24 \, a^{2} b - 18 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 12 \, {\left(24 \, a^{2} b - 18 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(12 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{480 \, {\left(d \cosh\left(d x + c\right)^{5} + 5 \, d \cosh\left(d x + c\right)^{4} \sinh\left(d x + c\right) + 10 \, d \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right)^{2} + 10 \, d \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{3} + 5 \, d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} + d \sinh\left(d x + c\right)^{5}\right)}}"," ",0,"1/480*(3*b^3*cosh(d*x + c)^10 + 30*b^3*cosh(d*x + c)*sinh(d*x + c)^9 + 3*b^3*sinh(d*x + c)^10 + 5*(12*a*b^2 - 5*b^3)*cosh(d*x + c)^8 + 5*(27*b^3*cosh(d*x + c)^2 + 12*a*b^2 - 5*b^3)*sinh(d*x + c)^8 + 40*(9*b^3*cosh(d*x + c)^3 + (12*a*b^2 - 5*b^3)*cosh(d*x + c))*sinh(d*x + c)^7 + 30*(24*a^2*b - 18*a*b^2 + 5*b^3)*cosh(d*x + c)^6 + 10*(63*b^3*cosh(d*x + c)^4 + 72*a^2*b - 54*a*b^2 + 15*b^3 + 14*(12*a*b^2 - 5*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 4*(189*b^3*cosh(d*x + c)^5 + 70*(12*a*b^2 - 5*b^3)*cosh(d*x + c)^3 + 45*(24*a^2*b - 18*a*b^2 + 5*b^3)*cosh(d*x + c))*sinh(d*x + c)^5 + 30*(24*a^2*b - 18*a*b^2 + 5*b^3)*cosh(d*x + c)^4 + 10*(63*b^3*cosh(d*x + c)^6 + 35*(12*a*b^2 - 5*b^3)*cosh(d*x + c)^4 + 72*a^2*b - 54*a*b^2 + 15*b^3 + 45*(24*a^2*b - 18*a*b^2 + 5*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 40*(9*b^3*cosh(d*x + c)^7 + 7*(12*a*b^2 - 5*b^3)*cosh(d*x + c)^5 + 15*(24*a^2*b - 18*a*b^2 + 5*b^3)*cosh(d*x + c)^3 + 3*(24*a^2*b - 18*a*b^2 + 5*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 + 3*b^3 + 5*(12*a*b^2 - 5*b^3)*cosh(d*x + c)^2 + 5*(27*b^3*cosh(d*x + c)^8 + 28*(12*a*b^2 - 5*b^3)*cosh(d*x + c)^6 + 90*(24*a^2*b - 18*a*b^2 + 5*b^3)*cosh(d*x + c)^4 + 12*a*b^2 - 5*b^3 + 36*(24*a^2*b - 18*a*b^2 + 5*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - 480*(a^3*cosh(d*x + c)^5 + 5*a^3*cosh(d*x + c)^4*sinh(d*x + c) + 10*a^3*cosh(d*x + c)^3*sinh(d*x + c)^2 + 10*a^3*cosh(d*x + c)^2*sinh(d*x + c)^3 + 5*a^3*cosh(d*x + c)*sinh(d*x + c)^4 + a^3*sinh(d*x + c)^5)*log(cosh(d*x + c) + sinh(d*x + c) + 1) + 480*(a^3*cosh(d*x + c)^5 + 5*a^3*cosh(d*x + c)^4*sinh(d*x + c) + 10*a^3*cosh(d*x + c)^3*sinh(d*x + c)^2 + 10*a^3*cosh(d*x + c)^2*sinh(d*x + c)^3 + 5*a^3*cosh(d*x + c)*sinh(d*x + c)^4 + a^3*sinh(d*x + c)^5)*log(cosh(d*x + c) + sinh(d*x + c) - 1) + 10*(3*b^3*cosh(d*x + c)^9 + 4*(12*a*b^2 - 5*b^3)*cosh(d*x + c)^7 + 18*(24*a^2*b - 18*a*b^2 + 5*b^3)*cosh(d*x + c)^5 + 12*(24*a^2*b - 18*a*b^2 + 5*b^3)*cosh(d*x + c)^3 + (12*a*b^2 - 5*b^3)*cosh(d*x + c))*sinh(d*x + c))/(d*cosh(d*x + c)^5 + 5*d*cosh(d*x + c)^4*sinh(d*x + c) + 10*d*cosh(d*x + c)^3*sinh(d*x + c)^2 + 10*d*cosh(d*x + c)^2*sinh(d*x + c)^3 + 5*d*cosh(d*x + c)*sinh(d*x + c)^4 + d*sinh(d*x + c)^5)","B",0
25,1,169,0,0.702617," ","integrate(csch(d*x+c)^2*(a+b*sinh(d*x+c)^2)^3,x, algorithm=""fricas"")","\frac{b^{3} \cosh\left(d x + c\right)^{5} + 5 \, b^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} + 3 \, {\left(8 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(10 \, b^{3} \cosh\left(d x + c\right)^{3} + 9 \, {\left(8 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 8 \, {\left(8 \, a^{3} + 3 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right) + 8 \, {\left(8 \, a^{3} + 3 \, {\left(8 \, a^{2} b - 4 \, a b^{2} + b^{3}\right)} d x\right)} \sinh\left(d x + c\right)}{64 \, d \sinh\left(d x + c\right)}"," ",0,"1/64*(b^3*cosh(d*x + c)^5 + 5*b^3*cosh(d*x + c)*sinh(d*x + c)^4 + 3*(8*a*b^2 - 3*b^3)*cosh(d*x + c)^3 + (10*b^3*cosh(d*x + c)^3 + 9*(8*a*b^2 - 3*b^3)*cosh(d*x + c))*sinh(d*x + c)^2 - 8*(8*a^3 + 3*a*b^2 - b^3)*cosh(d*x + c) + 8*(8*a^3 + 3*(8*a^2*b - 4*a*b^2 + b^3)*d*x)*sinh(d*x + c))/(d*sinh(d*x + c))","A",0
26,1,1814,0,0.562159," ","integrate(csch(d*x+c)^3*(a+b*sinh(d*x+c)^2)^3,x, algorithm=""fricas"")","\frac{b^{3} \cosh\left(d x + c\right)^{10} + 10 \, b^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + b^{3} \sinh\left(d x + c\right)^{10} + {\left(36 \, a b^{2} - 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + {\left(45 \, b^{3} \cosh\left(d x + c\right)^{2} + 36 \, a b^{2} - 11 \, b^{3}\right)} \sinh\left(d x + c\right)^{8} + 8 \, {\left(15 \, b^{3} \cosh\left(d x + c\right)^{3} + {\left(36 \, a b^{2} - 11 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} - 2 \, {\left(12 \, a^{3} + 18 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(105 \, b^{3} \cosh\left(d x + c\right)^{4} - 12 \, a^{3} - 18 \, a b^{2} + 5 \, b^{3} + 14 \, {\left(36 \, a b^{2} - 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(63 \, b^{3} \cosh\left(d x + c\right)^{5} + 14 \, {\left(36 \, a b^{2} - 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(12 \, a^{3} + 18 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 2 \, {\left(12 \, a^{3} + 18 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(105 \, b^{3} \cosh\left(d x + c\right)^{6} + 35 \, {\left(36 \, a b^{2} - 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 12 \, a^{3} - 18 \, a b^{2} + 5 \, b^{3} - 15 \, {\left(12 \, a^{3} + 18 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(15 \, b^{3} \cosh\left(d x + c\right)^{7} + 7 \, {\left(36 \, a b^{2} - 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 5 \, {\left(12 \, a^{3} + 18 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - {\left(12 \, a^{3} + 18 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + b^{3} + {\left(36 \, a b^{2} - 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{2} + {\left(45 \, b^{3} \cosh\left(d x + c\right)^{8} + 28 \, {\left(36 \, a b^{2} - 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} - 30 \, {\left(12 \, a^{3} + 18 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 36 \, a b^{2} - 11 \, b^{3} - 12 \, {\left(12 \, a^{3} + 18 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 12 \, {\left({\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{7} + 7 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + {\left(a^{3} - 6 \, a^{2} b\right)} \sinh\left(d x + c\right)^{7} - 2 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{5} - {\left(2 \, a^{3} - 12 \, a^{2} b - 21 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{5} + 5 \, {\left(7 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{3} - 2 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{3} + {\left(35 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{4} + a^{3} - 6 \, a^{2} b - 20 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + {\left(21 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{5} - 20 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(7 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{6} - 10 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) - 12 \, {\left({\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{7} + 7 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + {\left(a^{3} - 6 \, a^{2} b\right)} \sinh\left(d x + c\right)^{7} - 2 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{5} - {\left(2 \, a^{3} - 12 \, a^{2} b - 21 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{5} + 5 \, {\left(7 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{3} - 2 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{3} + {\left(35 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{4} + a^{3} - 6 \, a^{2} b - 20 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + {\left(21 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{5} - 20 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(7 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{6} - 10 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) + 2 \, {\left(5 \, b^{3} \cosh\left(d x + c\right)^{9} + 4 \, {\left(36 \, a b^{2} - 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} - 6 \, {\left(12 \, a^{3} + 18 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 4 \, {\left(12 \, a^{3} + 18 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(36 \, a b^{2} - 11 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{24 \, {\left(d \cosh\left(d x + c\right)^{7} + 7 \, d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + d \sinh\left(d x + c\right)^{7} - 2 \, d \cosh\left(d x + c\right)^{5} + {\left(21 \, d \cosh\left(d x + c\right)^{2} - 2 \, d\right)} \sinh\left(d x + c\right)^{5} + 5 \, {\left(7 \, d \cosh\left(d x + c\right)^{3} - 2 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + d \cosh\left(d x + c\right)^{3} + {\left(35 \, d \cosh\left(d x + c\right)^{4} - 20 \, d \cosh\left(d x + c\right)^{2} + d\right)} \sinh\left(d x + c\right)^{3} + {\left(21 \, d \cosh\left(d x + c\right)^{5} - 20 \, d \cosh\left(d x + c\right)^{3} + 3 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(7 \, d \cosh\left(d x + c\right)^{6} - 10 \, d \cosh\left(d x + c\right)^{4} + 3 \, d \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"1/24*(b^3*cosh(d*x + c)^10 + 10*b^3*cosh(d*x + c)*sinh(d*x + c)^9 + b^3*sinh(d*x + c)^10 + (36*a*b^2 - 11*b^3)*cosh(d*x + c)^8 + (45*b^3*cosh(d*x + c)^2 + 36*a*b^2 - 11*b^3)*sinh(d*x + c)^8 + 8*(15*b^3*cosh(d*x + c)^3 + (36*a*b^2 - 11*b^3)*cosh(d*x + c))*sinh(d*x + c)^7 - 2*(12*a^3 + 18*a*b^2 - 5*b^3)*cosh(d*x + c)^6 + 2*(105*b^3*cosh(d*x + c)^4 - 12*a^3 - 18*a*b^2 + 5*b^3 + 14*(36*a*b^2 - 11*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 4*(63*b^3*cosh(d*x + c)^5 + 14*(36*a*b^2 - 11*b^3)*cosh(d*x + c)^3 - 3*(12*a^3 + 18*a*b^2 - 5*b^3)*cosh(d*x + c))*sinh(d*x + c)^5 - 2*(12*a^3 + 18*a*b^2 - 5*b^3)*cosh(d*x + c)^4 + 2*(105*b^3*cosh(d*x + c)^6 + 35*(36*a*b^2 - 11*b^3)*cosh(d*x + c)^4 - 12*a^3 - 18*a*b^2 + 5*b^3 - 15*(12*a^3 + 18*a*b^2 - 5*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(15*b^3*cosh(d*x + c)^7 + 7*(36*a*b^2 - 11*b^3)*cosh(d*x + c)^5 - 5*(12*a^3 + 18*a*b^2 - 5*b^3)*cosh(d*x + c)^3 - (12*a^3 + 18*a*b^2 - 5*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 + b^3 + (36*a*b^2 - 11*b^3)*cosh(d*x + c)^2 + (45*b^3*cosh(d*x + c)^8 + 28*(36*a*b^2 - 11*b^3)*cosh(d*x + c)^6 - 30*(12*a^3 + 18*a*b^2 - 5*b^3)*cosh(d*x + c)^4 + 36*a*b^2 - 11*b^3 - 12*(12*a^3 + 18*a*b^2 - 5*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 12*((a^3 - 6*a^2*b)*cosh(d*x + c)^7 + 7*(a^3 - 6*a^2*b)*cosh(d*x + c)*sinh(d*x + c)^6 + (a^3 - 6*a^2*b)*sinh(d*x + c)^7 - 2*(a^3 - 6*a^2*b)*cosh(d*x + c)^5 - (2*a^3 - 12*a^2*b - 21*(a^3 - 6*a^2*b)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 5*(7*(a^3 - 6*a^2*b)*cosh(d*x + c)^3 - 2*(a^3 - 6*a^2*b)*cosh(d*x + c))*sinh(d*x + c)^4 + (a^3 - 6*a^2*b)*cosh(d*x + c)^3 + (35*(a^3 - 6*a^2*b)*cosh(d*x + c)^4 + a^3 - 6*a^2*b - 20*(a^3 - 6*a^2*b)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + (21*(a^3 - 6*a^2*b)*cosh(d*x + c)^5 - 20*(a^3 - 6*a^2*b)*cosh(d*x + c)^3 + 3*(a^3 - 6*a^2*b)*cosh(d*x + c))*sinh(d*x + c)^2 + (7*(a^3 - 6*a^2*b)*cosh(d*x + c)^6 - 10*(a^3 - 6*a^2*b)*cosh(d*x + c)^4 + 3*(a^3 - 6*a^2*b)*cosh(d*x + c)^2)*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) + 1) - 12*((a^3 - 6*a^2*b)*cosh(d*x + c)^7 + 7*(a^3 - 6*a^2*b)*cosh(d*x + c)*sinh(d*x + c)^6 + (a^3 - 6*a^2*b)*sinh(d*x + c)^7 - 2*(a^3 - 6*a^2*b)*cosh(d*x + c)^5 - (2*a^3 - 12*a^2*b - 21*(a^3 - 6*a^2*b)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 5*(7*(a^3 - 6*a^2*b)*cosh(d*x + c)^3 - 2*(a^3 - 6*a^2*b)*cosh(d*x + c))*sinh(d*x + c)^4 + (a^3 - 6*a^2*b)*cosh(d*x + c)^3 + (35*(a^3 - 6*a^2*b)*cosh(d*x + c)^4 + a^3 - 6*a^2*b - 20*(a^3 - 6*a^2*b)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + (21*(a^3 - 6*a^2*b)*cosh(d*x + c)^5 - 20*(a^3 - 6*a^2*b)*cosh(d*x + c)^3 + 3*(a^3 - 6*a^2*b)*cosh(d*x + c))*sinh(d*x + c)^2 + (7*(a^3 - 6*a^2*b)*cosh(d*x + c)^6 - 10*(a^3 - 6*a^2*b)*cosh(d*x + c)^4 + 3*(a^3 - 6*a^2*b)*cosh(d*x + c)^2)*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) - 1) + 2*(5*b^3*cosh(d*x + c)^9 + 4*(36*a*b^2 - 11*b^3)*cosh(d*x + c)^7 - 6*(12*a^3 + 18*a*b^2 - 5*b^3)*cosh(d*x + c)^5 - 4*(12*a^3 + 18*a*b^2 - 5*b^3)*cosh(d*x + c)^3 + (36*a*b^2 - 11*b^3)*cosh(d*x + c))*sinh(d*x + c))/(d*cosh(d*x + c)^7 + 7*d*cosh(d*x + c)*sinh(d*x + c)^6 + d*sinh(d*x + c)^7 - 2*d*cosh(d*x + c)^5 + (21*d*cosh(d*x + c)^2 - 2*d)*sinh(d*x + c)^5 + 5*(7*d*cosh(d*x + c)^3 - 2*d*cosh(d*x + c))*sinh(d*x + c)^4 + d*cosh(d*x + c)^3 + (35*d*cosh(d*x + c)^4 - 20*d*cosh(d*x + c)^2 + d)*sinh(d*x + c)^3 + (21*d*cosh(d*x + c)^5 - 20*d*cosh(d*x + c)^3 + 3*d*cosh(d*x + c))*sinh(d*x + c)^2 + (7*d*cosh(d*x + c)^6 - 10*d*cosh(d*x + c)^4 + 3*d*cosh(d*x + c)^2)*sinh(d*x + c))","B",0
27,1,281,0,0.592574," ","integrate(csch(d*x+c)^4*(a+b*sinh(d*x+c)^2)^3,x, algorithm=""fricas"")","\frac{3 \, b^{3} \cosh\left(d x + c\right)^{5} + 15 \, b^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} + {\left(16 \, a^{3} - 72 \, a^{2} b - 9 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 4 \, {\left(4 \, a^{3} - 18 \, a^{2} b - 3 \, {\left(6 \, a b^{2} - b^{3}\right)} d x\right)} \sinh\left(d x + c\right)^{3} + 3 \, {\left(10 \, b^{3} \cosh\left(d x + c\right)^{3} + {\left(16 \, a^{3} - 72 \, a^{2} b - 9 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 6 \, {\left(8 \, a^{3} - 12 \, a^{2} b - b^{3}\right)} \cosh\left(d x + c\right) + 12 \, {\left(4 \, a^{3} - 18 \, a^{2} b - 3 \, {\left(6 \, a b^{2} - b^{3}\right)} d x - {\left(4 \, a^{3} - 18 \, a^{2} b - 3 \, {\left(6 \, a b^{2} - b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)}{24 \, {\left(d \sinh\left(d x + c\right)^{3} + 3 \, {\left(d \cosh\left(d x + c\right)^{2} - d\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"1/24*(3*b^3*cosh(d*x + c)^5 + 15*b^3*cosh(d*x + c)*sinh(d*x + c)^4 + (16*a^3 - 72*a^2*b - 9*b^3)*cosh(d*x + c)^3 - 4*(4*a^3 - 18*a^2*b - 3*(6*a*b^2 - b^3)*d*x)*sinh(d*x + c)^3 + 3*(10*b^3*cosh(d*x + c)^3 + (16*a^3 - 72*a^2*b - 9*b^3)*cosh(d*x + c))*sinh(d*x + c)^2 - 6*(8*a^3 - 12*a^2*b - b^3)*cosh(d*x + c) + 12*(4*a^3 - 18*a^2*b - 3*(6*a*b^2 - b^3)*d*x - (4*a^3 - 18*a^2*b - 3*(6*a*b^2 - b^3)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c))/(d*sinh(d*x + c)^3 + 3*(d*cosh(d*x + c)^2 - d)*sinh(d*x + c))","B",0
28,1,3242,0,0.629911," ","integrate(sinh(d*x+c)^7/(a+b*sinh(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{10} + 30 \, {\left(a b^{3} - b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + 3 \, {\left(a b^{3} - b^{4}\right)} \sinh\left(d x + c\right)^{10} - 5 \, {\left(4 \, a^{2} b^{2} + a b^{3} - 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{8} - 5 \, {\left(4 \, a^{2} b^{2} + a b^{3} - 5 \, b^{4} - 27 \, {\left(a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{8} + 40 \, {\left(9 \, {\left(a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{3} - {\left(4 \, a^{2} b^{2} + a b^{3} - 5 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 30 \, {\left(8 \, a^{3} b - 2 \, a^{2} b^{2} - a b^{3} - 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 10 \, {\left(63 \, {\left(a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{4} + 24 \, a^{3} b - 6 \, a^{2} b^{2} - 3 \, a b^{3} - 15 \, b^{4} - 14 \, {\left(4 \, a^{2} b^{2} + a b^{3} - 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(189 \, {\left(a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{5} - 70 \, {\left(4 \, a^{2} b^{2} + a b^{3} - 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + 45 \, {\left(8 \, a^{3} b - 2 \, a^{2} b^{2} - a b^{3} - 5 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 30 \, {\left(8 \, a^{3} b - 2 \, a^{2} b^{2} - a b^{3} - 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 10 \, {\left(63 \, {\left(a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{6} - 35 \, {\left(4 \, a^{2} b^{2} + a b^{3} - 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 24 \, a^{3} b - 6 \, a^{2} b^{2} - 3 \, a b^{3} - 15 \, b^{4} + 45 \, {\left(8 \, a^{3} b - 2 \, a^{2} b^{2} - a b^{3} - 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 3 \, a b^{3} - 3 \, b^{4} + 40 \, {\left(9 \, {\left(a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{7} - 7 \, {\left(4 \, a^{2} b^{2} + a b^{3} - 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + 15 \, {\left(8 \, a^{3} b - 2 \, a^{2} b^{2} - a b^{3} - 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(8 \, a^{3} b - 2 \, a^{2} b^{2} - a b^{3} - 5 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 5 \, {\left(4 \, a^{2} b^{2} + a b^{3} - 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{2} + 5 \, {\left(27 \, {\left(a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{8} - 28 \, {\left(4 \, a^{2} b^{2} + a b^{3} - 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 90 \, {\left(8 \, a^{3} b - 2 \, a^{2} b^{2} - a b^{3} - 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} - 4 \, a^{2} b^{2} - a b^{3} + 5 \, b^{4} + 36 \, {\left(8 \, a^{3} b - 2 \, a^{2} b^{2} - a b^{3} - 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} - 240 \, {\left(a^{3} \cosh\left(d x + c\right)^{5} + 5 \, a^{3} \cosh\left(d x + c\right)^{4} \sinh\left(d x + c\right) + 10 \, a^{3} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right)^{2} + 10 \, a^{3} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{3} + 5 \, a^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} + a^{3} \sinh\left(d x + c\right)^{5}\right)} \sqrt{-a b + b^{2}} \log\left(\frac{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} - 2 \, {\left(2 \, a - 3 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} - 2 \, a + 3 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} - {\left(2 \, a - 3 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + 4 \, {\left(\cosh\left(d x + c\right)^{3} + 3 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{3} + {\left(3 \, \cosh\left(d x + c\right)^{2} + 1\right)} \sinh\left(d x + c\right) + \cosh\left(d x + c\right)\right)} \sqrt{-a b + b^{2}} + b}{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b}\right) + 10 \, {\left(3 \, {\left(a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{9} - 4 \, {\left(4 \, a^{2} b^{2} + a b^{3} - 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{7} + 18 \, {\left(8 \, a^{3} b - 2 \, a^{2} b^{2} - a b^{3} - 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + 12 \, {\left(8 \, a^{3} b - 2 \, a^{2} b^{2} - a b^{3} - 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} - {\left(4 \, a^{2} b^{2} + a b^{3} - 5 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{480 \, {\left({\left(a b^{4} - b^{5}\right)} d \cosh\left(d x + c\right)^{5} + 5 \, {\left(a b^{4} - b^{5}\right)} d \cosh\left(d x + c\right)^{4} \sinh\left(d x + c\right) + 10 \, {\left(a b^{4} - b^{5}\right)} d \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right)^{2} + 10 \, {\left(a b^{4} - b^{5}\right)} d \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{3} + 5 \, {\left(a b^{4} - b^{5}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} + {\left(a b^{4} - b^{5}\right)} d \sinh\left(d x + c\right)^{5}\right)}}, \frac{3 \, {\left(a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{10} + 30 \, {\left(a b^{3} - b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + 3 \, {\left(a b^{3} - b^{4}\right)} \sinh\left(d x + c\right)^{10} - 5 \, {\left(4 \, a^{2} b^{2} + a b^{3} - 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{8} - 5 \, {\left(4 \, a^{2} b^{2} + a b^{3} - 5 \, b^{4} - 27 \, {\left(a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{8} + 40 \, {\left(9 \, {\left(a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{3} - {\left(4 \, a^{2} b^{2} + a b^{3} - 5 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 30 \, {\left(8 \, a^{3} b - 2 \, a^{2} b^{2} - a b^{3} - 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 10 \, {\left(63 \, {\left(a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{4} + 24 \, a^{3} b - 6 \, a^{2} b^{2} - 3 \, a b^{3} - 15 \, b^{4} - 14 \, {\left(4 \, a^{2} b^{2} + a b^{3} - 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(189 \, {\left(a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{5} - 70 \, {\left(4 \, a^{2} b^{2} + a b^{3} - 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + 45 \, {\left(8 \, a^{3} b - 2 \, a^{2} b^{2} - a b^{3} - 5 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 30 \, {\left(8 \, a^{3} b - 2 \, a^{2} b^{2} - a b^{3} - 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 10 \, {\left(63 \, {\left(a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{6} - 35 \, {\left(4 \, a^{2} b^{2} + a b^{3} - 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 24 \, a^{3} b - 6 \, a^{2} b^{2} - 3 \, a b^{3} - 15 \, b^{4} + 45 \, {\left(8 \, a^{3} b - 2 \, a^{2} b^{2} - a b^{3} - 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 3 \, a b^{3} - 3 \, b^{4} + 40 \, {\left(9 \, {\left(a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{7} - 7 \, {\left(4 \, a^{2} b^{2} + a b^{3} - 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + 15 \, {\left(8 \, a^{3} b - 2 \, a^{2} b^{2} - a b^{3} - 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(8 \, a^{3} b - 2 \, a^{2} b^{2} - a b^{3} - 5 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 5 \, {\left(4 \, a^{2} b^{2} + a b^{3} - 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{2} + 5 \, {\left(27 \, {\left(a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{8} - 28 \, {\left(4 \, a^{2} b^{2} + a b^{3} - 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 90 \, {\left(8 \, a^{3} b - 2 \, a^{2} b^{2} - a b^{3} - 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} - 4 \, a^{2} b^{2} - a b^{3} + 5 \, b^{4} + 36 \, {\left(8 \, a^{3} b - 2 \, a^{2} b^{2} - a b^{3} - 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} - 480 \, {\left(a^{3} \cosh\left(d x + c\right)^{5} + 5 \, a^{3} \cosh\left(d x + c\right)^{4} \sinh\left(d x + c\right) + 10 \, a^{3} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right)^{2} + 10 \, a^{3} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{3} + 5 \, a^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} + a^{3} \sinh\left(d x + c\right)^{5}\right)} \sqrt{a b - b^{2}} \arctan\left(-\frac{b \cosh\left(d x + c\right)^{3} + 3 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{3} + {\left(4 \, a - 3 \, b\right)} \cosh\left(d x + c\right) + {\left(3 \, b \cosh\left(d x + c\right)^{2} + 4 \, a - 3 \, b\right)} \sinh\left(d x + c\right)}{2 \, \sqrt{a b - b^{2}}}\right) + 480 \, {\left(a^{3} \cosh\left(d x + c\right)^{5} + 5 \, a^{3} \cosh\left(d x + c\right)^{4} \sinh\left(d x + c\right) + 10 \, a^{3} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right)^{2} + 10 \, a^{3} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{3} + 5 \, a^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} + a^{3} \sinh\left(d x + c\right)^{5}\right)} \sqrt{a b - b^{2}} \arctan\left(-\frac{\sqrt{a b - b^{2}} {\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right)}}{2 \, {\left(a - b\right)}}\right) + 10 \, {\left(3 \, {\left(a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{9} - 4 \, {\left(4 \, a^{2} b^{2} + a b^{3} - 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{7} + 18 \, {\left(8 \, a^{3} b - 2 \, a^{2} b^{2} - a b^{3} - 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + 12 \, {\left(8 \, a^{3} b - 2 \, a^{2} b^{2} - a b^{3} - 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} - {\left(4 \, a^{2} b^{2} + a b^{3} - 5 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{480 \, {\left({\left(a b^{4} - b^{5}\right)} d \cosh\left(d x + c\right)^{5} + 5 \, {\left(a b^{4} - b^{5}\right)} d \cosh\left(d x + c\right)^{4} \sinh\left(d x + c\right) + 10 \, {\left(a b^{4} - b^{5}\right)} d \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right)^{2} + 10 \, {\left(a b^{4} - b^{5}\right)} d \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{3} + 5 \, {\left(a b^{4} - b^{5}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} + {\left(a b^{4} - b^{5}\right)} d \sinh\left(d x + c\right)^{5}\right)}}\right]"," ",0,"[1/480*(3*(a*b^3 - b^4)*cosh(d*x + c)^10 + 30*(a*b^3 - b^4)*cosh(d*x + c)*sinh(d*x + c)^9 + 3*(a*b^3 - b^4)*sinh(d*x + c)^10 - 5*(4*a^2*b^2 + a*b^3 - 5*b^4)*cosh(d*x + c)^8 - 5*(4*a^2*b^2 + a*b^3 - 5*b^4 - 27*(a*b^3 - b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 40*(9*(a*b^3 - b^4)*cosh(d*x + c)^3 - (4*a^2*b^2 + a*b^3 - 5*b^4)*cosh(d*x + c))*sinh(d*x + c)^7 + 30*(8*a^3*b - 2*a^2*b^2 - a*b^3 - 5*b^4)*cosh(d*x + c)^6 + 10*(63*(a*b^3 - b^4)*cosh(d*x + c)^4 + 24*a^3*b - 6*a^2*b^2 - 3*a*b^3 - 15*b^4 - 14*(4*a^2*b^2 + a*b^3 - 5*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 4*(189*(a*b^3 - b^4)*cosh(d*x + c)^5 - 70*(4*a^2*b^2 + a*b^3 - 5*b^4)*cosh(d*x + c)^3 + 45*(8*a^3*b - 2*a^2*b^2 - a*b^3 - 5*b^4)*cosh(d*x + c))*sinh(d*x + c)^5 + 30*(8*a^3*b - 2*a^2*b^2 - a*b^3 - 5*b^4)*cosh(d*x + c)^4 + 10*(63*(a*b^3 - b^4)*cosh(d*x + c)^6 - 35*(4*a^2*b^2 + a*b^3 - 5*b^4)*cosh(d*x + c)^4 + 24*a^3*b - 6*a^2*b^2 - 3*a*b^3 - 15*b^4 + 45*(8*a^3*b - 2*a^2*b^2 - a*b^3 - 5*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 3*a*b^3 - 3*b^4 + 40*(9*(a*b^3 - b^4)*cosh(d*x + c)^7 - 7*(4*a^2*b^2 + a*b^3 - 5*b^4)*cosh(d*x + c)^5 + 15*(8*a^3*b - 2*a^2*b^2 - a*b^3 - 5*b^4)*cosh(d*x + c)^3 + 3*(8*a^3*b - 2*a^2*b^2 - a*b^3 - 5*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 - 5*(4*a^2*b^2 + a*b^3 - 5*b^4)*cosh(d*x + c)^2 + 5*(27*(a*b^3 - b^4)*cosh(d*x + c)^8 - 28*(4*a^2*b^2 + a*b^3 - 5*b^4)*cosh(d*x + c)^6 + 90*(8*a^3*b - 2*a^2*b^2 - a*b^3 - 5*b^4)*cosh(d*x + c)^4 - 4*a^2*b^2 - a*b^3 + 5*b^4 + 36*(8*a^3*b - 2*a^2*b^2 - a*b^3 - 5*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - 240*(a^3*cosh(d*x + c)^5 + 5*a^3*cosh(d*x + c)^4*sinh(d*x + c) + 10*a^3*cosh(d*x + c)^3*sinh(d*x + c)^2 + 10*a^3*cosh(d*x + c)^2*sinh(d*x + c)^3 + 5*a^3*cosh(d*x + c)*sinh(d*x + c)^4 + a^3*sinh(d*x + c)^5)*sqrt(-a*b + b^2)*log((b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 - 2*(2*a - 3*b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 - 2*a + 3*b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 - (2*a - 3*b)*cosh(d*x + c))*sinh(d*x + c) + 4*(cosh(d*x + c)^3 + 3*cosh(d*x + c)*sinh(d*x + c)^2 + sinh(d*x + c)^3 + (3*cosh(d*x + c)^2 + 1)*sinh(d*x + c) + cosh(d*x + c))*sqrt(-a*b + b^2) + b)/(b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 + 2*(2*a - b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 + 2*a - b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 + (2*a - b)*cosh(d*x + c))*sinh(d*x + c) + b)) + 10*(3*(a*b^3 - b^4)*cosh(d*x + c)^9 - 4*(4*a^2*b^2 + a*b^3 - 5*b^4)*cosh(d*x + c)^7 + 18*(8*a^3*b - 2*a^2*b^2 - a*b^3 - 5*b^4)*cosh(d*x + c)^5 + 12*(8*a^3*b - 2*a^2*b^2 - a*b^3 - 5*b^4)*cosh(d*x + c)^3 - (4*a^2*b^2 + a*b^3 - 5*b^4)*cosh(d*x + c))*sinh(d*x + c))/((a*b^4 - b^5)*d*cosh(d*x + c)^5 + 5*(a*b^4 - b^5)*d*cosh(d*x + c)^4*sinh(d*x + c) + 10*(a*b^4 - b^5)*d*cosh(d*x + c)^3*sinh(d*x + c)^2 + 10*(a*b^4 - b^5)*d*cosh(d*x + c)^2*sinh(d*x + c)^3 + 5*(a*b^4 - b^5)*d*cosh(d*x + c)*sinh(d*x + c)^4 + (a*b^4 - b^5)*d*sinh(d*x + c)^5), 1/480*(3*(a*b^3 - b^4)*cosh(d*x + c)^10 + 30*(a*b^3 - b^4)*cosh(d*x + c)*sinh(d*x + c)^9 + 3*(a*b^3 - b^4)*sinh(d*x + c)^10 - 5*(4*a^2*b^2 + a*b^3 - 5*b^4)*cosh(d*x + c)^8 - 5*(4*a^2*b^2 + a*b^3 - 5*b^4 - 27*(a*b^3 - b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 40*(9*(a*b^3 - b^4)*cosh(d*x + c)^3 - (4*a^2*b^2 + a*b^3 - 5*b^4)*cosh(d*x + c))*sinh(d*x + c)^7 + 30*(8*a^3*b - 2*a^2*b^2 - a*b^3 - 5*b^4)*cosh(d*x + c)^6 + 10*(63*(a*b^3 - b^4)*cosh(d*x + c)^4 + 24*a^3*b - 6*a^2*b^2 - 3*a*b^3 - 15*b^4 - 14*(4*a^2*b^2 + a*b^3 - 5*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 4*(189*(a*b^3 - b^4)*cosh(d*x + c)^5 - 70*(4*a^2*b^2 + a*b^3 - 5*b^4)*cosh(d*x + c)^3 + 45*(8*a^3*b - 2*a^2*b^2 - a*b^3 - 5*b^4)*cosh(d*x + c))*sinh(d*x + c)^5 + 30*(8*a^3*b - 2*a^2*b^2 - a*b^3 - 5*b^4)*cosh(d*x + c)^4 + 10*(63*(a*b^3 - b^4)*cosh(d*x + c)^6 - 35*(4*a^2*b^2 + a*b^3 - 5*b^4)*cosh(d*x + c)^4 + 24*a^3*b - 6*a^2*b^2 - 3*a*b^3 - 15*b^4 + 45*(8*a^3*b - 2*a^2*b^2 - a*b^3 - 5*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 3*a*b^3 - 3*b^4 + 40*(9*(a*b^3 - b^4)*cosh(d*x + c)^7 - 7*(4*a^2*b^2 + a*b^3 - 5*b^4)*cosh(d*x + c)^5 + 15*(8*a^3*b - 2*a^2*b^2 - a*b^3 - 5*b^4)*cosh(d*x + c)^3 + 3*(8*a^3*b - 2*a^2*b^2 - a*b^3 - 5*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 - 5*(4*a^2*b^2 + a*b^3 - 5*b^4)*cosh(d*x + c)^2 + 5*(27*(a*b^3 - b^4)*cosh(d*x + c)^8 - 28*(4*a^2*b^2 + a*b^3 - 5*b^4)*cosh(d*x + c)^6 + 90*(8*a^3*b - 2*a^2*b^2 - a*b^3 - 5*b^4)*cosh(d*x + c)^4 - 4*a^2*b^2 - a*b^3 + 5*b^4 + 36*(8*a^3*b - 2*a^2*b^2 - a*b^3 - 5*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - 480*(a^3*cosh(d*x + c)^5 + 5*a^3*cosh(d*x + c)^4*sinh(d*x + c) + 10*a^3*cosh(d*x + c)^3*sinh(d*x + c)^2 + 10*a^3*cosh(d*x + c)^2*sinh(d*x + c)^3 + 5*a^3*cosh(d*x + c)*sinh(d*x + c)^4 + a^3*sinh(d*x + c)^5)*sqrt(a*b - b^2)*arctan(-1/2*(b*cosh(d*x + c)^3 + 3*b*cosh(d*x + c)*sinh(d*x + c)^2 + b*sinh(d*x + c)^3 + (4*a - 3*b)*cosh(d*x + c) + (3*b*cosh(d*x + c)^2 + 4*a - 3*b)*sinh(d*x + c))/sqrt(a*b - b^2)) + 480*(a^3*cosh(d*x + c)^5 + 5*a^3*cosh(d*x + c)^4*sinh(d*x + c) + 10*a^3*cosh(d*x + c)^3*sinh(d*x + c)^2 + 10*a^3*cosh(d*x + c)^2*sinh(d*x + c)^3 + 5*a^3*cosh(d*x + c)*sinh(d*x + c)^4 + a^3*sinh(d*x + c)^5)*sqrt(a*b - b^2)*arctan(-1/2*sqrt(a*b - b^2)*(cosh(d*x + c) + sinh(d*x + c))/(a - b)) + 10*(3*(a*b^3 - b^4)*cosh(d*x + c)^9 - 4*(4*a^2*b^2 + a*b^3 - 5*b^4)*cosh(d*x + c)^7 + 18*(8*a^3*b - 2*a^2*b^2 - a*b^3 - 5*b^4)*cosh(d*x + c)^5 + 12*(8*a^3*b - 2*a^2*b^2 - a*b^3 - 5*b^4)*cosh(d*x + c)^3 - (4*a^2*b^2 + a*b^3 - 5*b^4)*cosh(d*x + c))*sinh(d*x + c))/((a*b^4 - b^5)*d*cosh(d*x + c)^5 + 5*(a*b^4 - b^5)*d*cosh(d*x + c)^4*sinh(d*x + c) + 10*(a*b^4 - b^5)*d*cosh(d*x + c)^3*sinh(d*x + c)^2 + 10*(a*b^4 - b^5)*d*cosh(d*x + c)^2*sinh(d*x + c)^3 + 5*(a*b^4 - b^5)*d*cosh(d*x + c)*sinh(d*x + c)^4 + (a*b^4 - b^5)*d*sinh(d*x + c)^5)]","B",0
29,1,1725,0,0.628229," ","integrate(sinh(d*x+c)^6/(a+b*sinh(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{b^{2} \cosh\left(d x + c\right)^{8} + 8 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + b^{2} \sinh\left(d x + c\right)^{8} + 8 \, {\left(8 \, a^{2} + 4 \, a b + 3 \, b^{2}\right)} d x \cosh\left(d x + c\right)^{4} - 8 \, {\left(a b + b^{2}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, b^{2} \cosh\left(d x + c\right)^{2} - 2 \, a b - 2 \, b^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, b^{2} \cosh\left(d x + c\right)^{3} - 6 \, {\left(a b + b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, b^{2} \cosh\left(d x + c\right)^{4} + 4 \, {\left(8 \, a^{2} + 4 \, a b + 3 \, b^{2}\right)} d x - 60 \, {\left(a b + b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, b^{2} \cosh\left(d x + c\right)^{5} + 4 \, {\left(8 \, a^{2} + 4 \, a b + 3 \, b^{2}\right)} d x \cosh\left(d x + c\right) - 20 \, {\left(a b + b^{2}\right)} \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right)^{3} + 8 \, {\left(a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, b^{2} \cosh\left(d x + c\right)^{6} + 12 \, {\left(8 \, a^{2} + 4 \, a b + 3 \, b^{2}\right)} d x \cosh\left(d x + c\right)^{2} - 30 \, {\left(a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, a b + 2 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} + 32 \, {\left(a^{2} \cosh\left(d x + c\right)^{4} + 4 \, a^{2} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, a^{2} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, a^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a^{2} \sinh\left(d x + c\right)^{4}\right)} \sqrt{\frac{a}{a - b}} \log\left(\frac{b^{2} \cosh\left(d x + c\right)^{4} + 4 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{2} \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(d x + c\right)^{2} + 2 \, a b - b^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, a^{2} - 8 \, a b + b^{2} + 4 \, {\left(b^{2} \cosh\left(d x + c\right)^{3} + {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + 4 \, {\left({\left(a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a b - b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a b - b^{2}\right)} \sinh\left(d x + c\right)^{2} + 2 \, a^{2} - 3 \, a b + b^{2}\right)} \sqrt{\frac{a}{a - b}}}{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b}\right) - b^{2} + 8 \, {\left(b^{2} \cosh\left(d x + c\right)^{7} + 4 \, {\left(8 \, a^{2} + 4 \, a b + 3 \, b^{2}\right)} d x \cosh\left(d x + c\right)^{3} - 6 \, {\left(a b + b^{2}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(a b + b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{64 \, {\left(b^{3} d \cosh\left(d x + c\right)^{4} + 4 \, b^{3} d \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, b^{3} d \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, b^{3} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{3} d \sinh\left(d x + c\right)^{4}\right)}}, \frac{b^{2} \cosh\left(d x + c\right)^{8} + 8 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + b^{2} \sinh\left(d x + c\right)^{8} + 8 \, {\left(8 \, a^{2} + 4 \, a b + 3 \, b^{2}\right)} d x \cosh\left(d x + c\right)^{4} - 8 \, {\left(a b + b^{2}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, b^{2} \cosh\left(d x + c\right)^{2} - 2 \, a b - 2 \, b^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, b^{2} \cosh\left(d x + c\right)^{3} - 6 \, {\left(a b + b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, b^{2} \cosh\left(d x + c\right)^{4} + 4 \, {\left(8 \, a^{2} + 4 \, a b + 3 \, b^{2}\right)} d x - 60 \, {\left(a b + b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, b^{2} \cosh\left(d x + c\right)^{5} + 4 \, {\left(8 \, a^{2} + 4 \, a b + 3 \, b^{2}\right)} d x \cosh\left(d x + c\right) - 20 \, {\left(a b + b^{2}\right)} \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right)^{3} + 8 \, {\left(a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, b^{2} \cosh\left(d x + c\right)^{6} + 12 \, {\left(8 \, a^{2} + 4 \, a b + 3 \, b^{2}\right)} d x \cosh\left(d x + c\right)^{2} - 30 \, {\left(a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, a b + 2 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} - 64 \, {\left(a^{2} \cosh\left(d x + c\right)^{4} + 4 \, a^{2} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, a^{2} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, a^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a^{2} \sinh\left(d x + c\right)^{4}\right)} \sqrt{-\frac{a}{a - b}} \arctan\left(\frac{{\left(b \cosh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b \sinh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sqrt{-\frac{a}{a - b}}}{2 \, a}\right) - b^{2} + 8 \, {\left(b^{2} \cosh\left(d x + c\right)^{7} + 4 \, {\left(8 \, a^{2} + 4 \, a b + 3 \, b^{2}\right)} d x \cosh\left(d x + c\right)^{3} - 6 \, {\left(a b + b^{2}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(a b + b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{64 \, {\left(b^{3} d \cosh\left(d x + c\right)^{4} + 4 \, b^{3} d \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, b^{3} d \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, b^{3} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{3} d \sinh\left(d x + c\right)^{4}\right)}}\right]"," ",0,"[1/64*(b^2*cosh(d*x + c)^8 + 8*b^2*cosh(d*x + c)*sinh(d*x + c)^7 + b^2*sinh(d*x + c)^8 + 8*(8*a^2 + 4*a*b + 3*b^2)*d*x*cosh(d*x + c)^4 - 8*(a*b + b^2)*cosh(d*x + c)^6 + 4*(7*b^2*cosh(d*x + c)^2 - 2*a*b - 2*b^2)*sinh(d*x + c)^6 + 8*(7*b^2*cosh(d*x + c)^3 - 6*(a*b + b^2)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*b^2*cosh(d*x + c)^4 + 4*(8*a^2 + 4*a*b + 3*b^2)*d*x - 60*(a*b + b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(7*b^2*cosh(d*x + c)^5 + 4*(8*a^2 + 4*a*b + 3*b^2)*d*x*cosh(d*x + c) - 20*(a*b + b^2)*cosh(d*x + c)^3)*sinh(d*x + c)^3 + 8*(a*b + b^2)*cosh(d*x + c)^2 + 4*(7*b^2*cosh(d*x + c)^6 + 12*(8*a^2 + 4*a*b + 3*b^2)*d*x*cosh(d*x + c)^2 - 30*(a*b + b^2)*cosh(d*x + c)^4 + 2*a*b + 2*b^2)*sinh(d*x + c)^2 + 32*(a^2*cosh(d*x + c)^4 + 4*a^2*cosh(d*x + c)^3*sinh(d*x + c) + 6*a^2*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*a^2*cosh(d*x + c)*sinh(d*x + c)^3 + a^2*sinh(d*x + c)^4)*sqrt(a/(a - b))*log((b^2*cosh(d*x + c)^4 + 4*b^2*cosh(d*x + c)*sinh(d*x + c)^3 + b^2*sinh(d*x + c)^4 + 2*(2*a*b - b^2)*cosh(d*x + c)^2 + 2*(3*b^2*cosh(d*x + c)^2 + 2*a*b - b^2)*sinh(d*x + c)^2 + 8*a^2 - 8*a*b + b^2 + 4*(b^2*cosh(d*x + c)^3 + (2*a*b - b^2)*cosh(d*x + c))*sinh(d*x + c) + 4*((a*b - b^2)*cosh(d*x + c)^2 + 2*(a*b - b^2)*cosh(d*x + c)*sinh(d*x + c) + (a*b - b^2)*sinh(d*x + c)^2 + 2*a^2 - 3*a*b + b^2)*sqrt(a/(a - b)))/(b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 + 2*(2*a - b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 + 2*a - b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 + (2*a - b)*cosh(d*x + c))*sinh(d*x + c) + b)) - b^2 + 8*(b^2*cosh(d*x + c)^7 + 4*(8*a^2 + 4*a*b + 3*b^2)*d*x*cosh(d*x + c)^3 - 6*(a*b + b^2)*cosh(d*x + c)^5 + 2*(a*b + b^2)*cosh(d*x + c))*sinh(d*x + c))/(b^3*d*cosh(d*x + c)^4 + 4*b^3*d*cosh(d*x + c)^3*sinh(d*x + c) + 6*b^3*d*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*b^3*d*cosh(d*x + c)*sinh(d*x + c)^3 + b^3*d*sinh(d*x + c)^4), 1/64*(b^2*cosh(d*x + c)^8 + 8*b^2*cosh(d*x + c)*sinh(d*x + c)^7 + b^2*sinh(d*x + c)^8 + 8*(8*a^2 + 4*a*b + 3*b^2)*d*x*cosh(d*x + c)^4 - 8*(a*b + b^2)*cosh(d*x + c)^6 + 4*(7*b^2*cosh(d*x + c)^2 - 2*a*b - 2*b^2)*sinh(d*x + c)^6 + 8*(7*b^2*cosh(d*x + c)^3 - 6*(a*b + b^2)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*b^2*cosh(d*x + c)^4 + 4*(8*a^2 + 4*a*b + 3*b^2)*d*x - 60*(a*b + b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(7*b^2*cosh(d*x + c)^5 + 4*(8*a^2 + 4*a*b + 3*b^2)*d*x*cosh(d*x + c) - 20*(a*b + b^2)*cosh(d*x + c)^3)*sinh(d*x + c)^3 + 8*(a*b + b^2)*cosh(d*x + c)^2 + 4*(7*b^2*cosh(d*x + c)^6 + 12*(8*a^2 + 4*a*b + 3*b^2)*d*x*cosh(d*x + c)^2 - 30*(a*b + b^2)*cosh(d*x + c)^4 + 2*a*b + 2*b^2)*sinh(d*x + c)^2 - 64*(a^2*cosh(d*x + c)^4 + 4*a^2*cosh(d*x + c)^3*sinh(d*x + c) + 6*a^2*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*a^2*cosh(d*x + c)*sinh(d*x + c)^3 + a^2*sinh(d*x + c)^4)*sqrt(-a/(a - b))*arctan(1/2*(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + 2*a - b)*sqrt(-a/(a - b))/a) - b^2 + 8*(b^2*cosh(d*x + c)^7 + 4*(8*a^2 + 4*a*b + 3*b^2)*d*x*cosh(d*x + c)^3 - 6*(a*b + b^2)*cosh(d*x + c)^5 + 2*(a*b + b^2)*cosh(d*x + c))*sinh(d*x + c))/(b^3*d*cosh(d*x + c)^4 + 4*b^3*d*cosh(d*x + c)^3*sinh(d*x + c) + 6*b^3*d*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*b^3*d*cosh(d*x + c)*sinh(d*x + c)^3 + b^3*d*sinh(d*x + c)^4)]","B",0
30,1,1668,0,0.657202," ","integrate(sinh(d*x+c)^5/(a+b*sinh(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{{\left(a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{6} + 6 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(a b^{2} - b^{3}\right)} \sinh\left(d x + c\right)^{6} - 3 \, {\left(4 \, a^{2} b - a b^{2} - 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 3 \, {\left(4 \, a^{2} b - a b^{2} - 3 \, b^{3} - 5 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(4 \, a^{2} b - a b^{2} - 3 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + a b^{2} - b^{3} - 3 \, {\left(4 \, a^{2} b - a b^{2} - 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{2} + 3 \, {\left(5 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{4} - 4 \, a^{2} b + a b^{2} + 3 \, b^{3} - 6 \, {\left(4 \, a^{2} b - a b^{2} - 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} - 12 \, {\left(a^{2} \cosh\left(d x + c\right)^{3} + 3 \, a^{2} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, a^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + a^{2} \sinh\left(d x + c\right)^{3}\right)} \sqrt{-a b + b^{2}} \log\left(\frac{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} - 2 \, {\left(2 \, a - 3 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} - 2 \, a + 3 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} - {\left(2 \, a - 3 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) - 4 \, {\left(\cosh\left(d x + c\right)^{3} + 3 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{3} + {\left(3 \, \cosh\left(d x + c\right)^{2} + 1\right)} \sinh\left(d x + c\right) + \cosh\left(d x + c\right)\right)} \sqrt{-a b + b^{2}} + b}{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b}\right) + 6 \, {\left({\left(a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{5} - 2 \, {\left(4 \, a^{2} b - a b^{2} - 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - {\left(4 \, a^{2} b - a b^{2} - 3 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{24 \, {\left({\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + {\left(a b^{3} - b^{4}\right)} d \sinh\left(d x + c\right)^{3}\right)}}, \frac{{\left(a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{6} + 6 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(a b^{2} - b^{3}\right)} \sinh\left(d x + c\right)^{6} - 3 \, {\left(4 \, a^{2} b - a b^{2} - 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 3 \, {\left(4 \, a^{2} b - a b^{2} - 3 \, b^{3} - 5 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(4 \, a^{2} b - a b^{2} - 3 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + a b^{2} - b^{3} - 3 \, {\left(4 \, a^{2} b - a b^{2} - 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{2} + 3 \, {\left(5 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{4} - 4 \, a^{2} b + a b^{2} + 3 \, b^{3} - 6 \, {\left(4 \, a^{2} b - a b^{2} - 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 24 \, {\left(a^{2} \cosh\left(d x + c\right)^{3} + 3 \, a^{2} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, a^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + a^{2} \sinh\left(d x + c\right)^{3}\right)} \sqrt{a b - b^{2}} \arctan\left(-\frac{b \cosh\left(d x + c\right)^{3} + 3 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{3} + {\left(4 \, a - 3 \, b\right)} \cosh\left(d x + c\right) + {\left(3 \, b \cosh\left(d x + c\right)^{2} + 4 \, a - 3 \, b\right)} \sinh\left(d x + c\right)}{2 \, \sqrt{a b - b^{2}}}\right) - 24 \, {\left(a^{2} \cosh\left(d x + c\right)^{3} + 3 \, a^{2} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, a^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + a^{2} \sinh\left(d x + c\right)^{3}\right)} \sqrt{a b - b^{2}} \arctan\left(-\frac{\sqrt{a b - b^{2}} {\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right)}}{2 \, {\left(a - b\right)}}\right) + 6 \, {\left({\left(a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{5} - 2 \, {\left(4 \, a^{2} b - a b^{2} - 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - {\left(4 \, a^{2} b - a b^{2} - 3 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{24 \, {\left({\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + {\left(a b^{3} - b^{4}\right)} d \sinh\left(d x + c\right)^{3}\right)}}\right]"," ",0,"[1/24*((a*b^2 - b^3)*cosh(d*x + c)^6 + 6*(a*b^2 - b^3)*cosh(d*x + c)*sinh(d*x + c)^5 + (a*b^2 - b^3)*sinh(d*x + c)^6 - 3*(4*a^2*b - a*b^2 - 3*b^3)*cosh(d*x + c)^4 - 3*(4*a^2*b - a*b^2 - 3*b^3 - 5*(a*b^2 - b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 4*(5*(a*b^2 - b^3)*cosh(d*x + c)^3 - 3*(4*a^2*b - a*b^2 - 3*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 + a*b^2 - b^3 - 3*(4*a^2*b - a*b^2 - 3*b^3)*cosh(d*x + c)^2 + 3*(5*(a*b^2 - b^3)*cosh(d*x + c)^4 - 4*a^2*b + a*b^2 + 3*b^3 - 6*(4*a^2*b - a*b^2 - 3*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - 12*(a^2*cosh(d*x + c)^3 + 3*a^2*cosh(d*x + c)^2*sinh(d*x + c) + 3*a^2*cosh(d*x + c)*sinh(d*x + c)^2 + a^2*sinh(d*x + c)^3)*sqrt(-a*b + b^2)*log((b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 - 2*(2*a - 3*b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 - 2*a + 3*b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 - (2*a - 3*b)*cosh(d*x + c))*sinh(d*x + c) - 4*(cosh(d*x + c)^3 + 3*cosh(d*x + c)*sinh(d*x + c)^2 + sinh(d*x + c)^3 + (3*cosh(d*x + c)^2 + 1)*sinh(d*x + c) + cosh(d*x + c))*sqrt(-a*b + b^2) + b)/(b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 + 2*(2*a - b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 + 2*a - b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 + (2*a - b)*cosh(d*x + c))*sinh(d*x + c) + b)) + 6*((a*b^2 - b^3)*cosh(d*x + c)^5 - 2*(4*a^2*b - a*b^2 - 3*b^3)*cosh(d*x + c)^3 - (4*a^2*b - a*b^2 - 3*b^3)*cosh(d*x + c))*sinh(d*x + c))/((a*b^3 - b^4)*d*cosh(d*x + c)^3 + 3*(a*b^3 - b^4)*d*cosh(d*x + c)^2*sinh(d*x + c) + 3*(a*b^3 - b^4)*d*cosh(d*x + c)*sinh(d*x + c)^2 + (a*b^3 - b^4)*d*sinh(d*x + c)^3), 1/24*((a*b^2 - b^3)*cosh(d*x + c)^6 + 6*(a*b^2 - b^3)*cosh(d*x + c)*sinh(d*x + c)^5 + (a*b^2 - b^3)*sinh(d*x + c)^6 - 3*(4*a^2*b - a*b^2 - 3*b^3)*cosh(d*x + c)^4 - 3*(4*a^2*b - a*b^2 - 3*b^3 - 5*(a*b^2 - b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 4*(5*(a*b^2 - b^3)*cosh(d*x + c)^3 - 3*(4*a^2*b - a*b^2 - 3*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 + a*b^2 - b^3 - 3*(4*a^2*b - a*b^2 - 3*b^3)*cosh(d*x + c)^2 + 3*(5*(a*b^2 - b^3)*cosh(d*x + c)^4 - 4*a^2*b + a*b^2 + 3*b^3 - 6*(4*a^2*b - a*b^2 - 3*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 24*(a^2*cosh(d*x + c)^3 + 3*a^2*cosh(d*x + c)^2*sinh(d*x + c) + 3*a^2*cosh(d*x + c)*sinh(d*x + c)^2 + a^2*sinh(d*x + c)^3)*sqrt(a*b - b^2)*arctan(-1/2*(b*cosh(d*x + c)^3 + 3*b*cosh(d*x + c)*sinh(d*x + c)^2 + b*sinh(d*x + c)^3 + (4*a - 3*b)*cosh(d*x + c) + (3*b*cosh(d*x + c)^2 + 4*a - 3*b)*sinh(d*x + c))/sqrt(a*b - b^2)) - 24*(a^2*cosh(d*x + c)^3 + 3*a^2*cosh(d*x + c)^2*sinh(d*x + c) + 3*a^2*cosh(d*x + c)*sinh(d*x + c)^2 + a^2*sinh(d*x + c)^3)*sqrt(a*b - b^2)*arctan(-1/2*sqrt(a*b - b^2)*(cosh(d*x + c) + sinh(d*x + c))/(a - b)) + 6*((a*b^2 - b^3)*cosh(d*x + c)^5 - 2*(4*a^2*b - a*b^2 - 3*b^3)*cosh(d*x + c)^3 - (4*a^2*b - a*b^2 - 3*b^3)*cosh(d*x + c))*sinh(d*x + c))/((a*b^3 - b^4)*d*cosh(d*x + c)^3 + 3*(a*b^3 - b^4)*d*cosh(d*x + c)^2*sinh(d*x + c) + 3*(a*b^3 - b^4)*d*cosh(d*x + c)*sinh(d*x + c)^2 + (a*b^3 - b^4)*d*sinh(d*x + c)^3)]","B",0
31,1,859,0,0.732171," ","integrate(sinh(d*x+c)^4/(a+b*sinh(d*x+c)^2),x, algorithm=""fricas"")","\left[-\frac{4 \, {\left(2 \, a + b\right)} d x \cosh\left(d x + c\right)^{2} - b \cosh\left(d x + c\right)^{4} - 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} - b \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, {\left(2 \, a + b\right)} d x - 3 \, b \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} - 4 \, {\left(a \cosh\left(d x + c\right)^{2} + 2 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a}{a - b}} \log\left(\frac{b^{2} \cosh\left(d x + c\right)^{4} + 4 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{2} \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(d x + c\right)^{2} + 2 \, a b - b^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, a^{2} - 8 \, a b + b^{2} + 4 \, {\left(b^{2} \cosh\left(d x + c\right)^{3} + {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) - 4 \, {\left({\left(a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a b - b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a b - b^{2}\right)} \sinh\left(d x + c\right)^{2} + 2 \, a^{2} - 3 \, a b + b^{2}\right)} \sqrt{\frac{a}{a - b}}}{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b}\right) + 4 \, {\left(2 \, {\left(2 \, a + b\right)} d x \cosh\left(d x + c\right) - b \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right) + b}{8 \, {\left(b^{2} d \cosh\left(d x + c\right)^{2} + 2 \, b^{2} d \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b^{2} d \sinh\left(d x + c\right)^{2}\right)}}, -\frac{4 \, {\left(2 \, a + b\right)} d x \cosh\left(d x + c\right)^{2} - b \cosh\left(d x + c\right)^{4} - 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} - b \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, {\left(2 \, a + b\right)} d x - 3 \, b \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} - 8 \, {\left(a \cosh\left(d x + c\right)^{2} + 2 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a}{a - b}} \arctan\left(\frac{{\left(b \cosh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b \sinh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sqrt{-\frac{a}{a - b}}}{2 \, a}\right) + 4 \, {\left(2 \, {\left(2 \, a + b\right)} d x \cosh\left(d x + c\right) - b \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right) + b}{8 \, {\left(b^{2} d \cosh\left(d x + c\right)^{2} + 2 \, b^{2} d \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b^{2} d \sinh\left(d x + c\right)^{2}\right)}}\right]"," ",0,"[-1/8*(4*(2*a + b)*d*x*cosh(d*x + c)^2 - b*cosh(d*x + c)^4 - 4*b*cosh(d*x + c)*sinh(d*x + c)^3 - b*sinh(d*x + c)^4 + 2*(2*(2*a + b)*d*x - 3*b*cosh(d*x + c)^2)*sinh(d*x + c)^2 - 4*(a*cosh(d*x + c)^2 + 2*a*cosh(d*x + c)*sinh(d*x + c) + a*sinh(d*x + c)^2)*sqrt(a/(a - b))*log((b^2*cosh(d*x + c)^4 + 4*b^2*cosh(d*x + c)*sinh(d*x + c)^3 + b^2*sinh(d*x + c)^4 + 2*(2*a*b - b^2)*cosh(d*x + c)^2 + 2*(3*b^2*cosh(d*x + c)^2 + 2*a*b - b^2)*sinh(d*x + c)^2 + 8*a^2 - 8*a*b + b^2 + 4*(b^2*cosh(d*x + c)^3 + (2*a*b - b^2)*cosh(d*x + c))*sinh(d*x + c) - 4*((a*b - b^2)*cosh(d*x + c)^2 + 2*(a*b - b^2)*cosh(d*x + c)*sinh(d*x + c) + (a*b - b^2)*sinh(d*x + c)^2 + 2*a^2 - 3*a*b + b^2)*sqrt(a/(a - b)))/(b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 + 2*(2*a - b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 + 2*a - b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 + (2*a - b)*cosh(d*x + c))*sinh(d*x + c) + b)) + 4*(2*(2*a + b)*d*x*cosh(d*x + c) - b*cosh(d*x + c)^3)*sinh(d*x + c) + b)/(b^2*d*cosh(d*x + c)^2 + 2*b^2*d*cosh(d*x + c)*sinh(d*x + c) + b^2*d*sinh(d*x + c)^2), -1/8*(4*(2*a + b)*d*x*cosh(d*x + c)^2 - b*cosh(d*x + c)^4 - 4*b*cosh(d*x + c)*sinh(d*x + c)^3 - b*sinh(d*x + c)^4 + 2*(2*(2*a + b)*d*x - 3*b*cosh(d*x + c)^2)*sinh(d*x + c)^2 - 8*(a*cosh(d*x + c)^2 + 2*a*cosh(d*x + c)*sinh(d*x + c) + a*sinh(d*x + c)^2)*sqrt(-a/(a - b))*arctan(1/2*(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + 2*a - b)*sqrt(-a/(a - b))/a) + 4*(2*(2*a + b)*d*x*cosh(d*x + c) - b*cosh(d*x + c)^3)*sinh(d*x + c) + b)/(b^2*d*cosh(d*x + c)^2 + 2*b^2*d*cosh(d*x + c)*sinh(d*x + c) + b^2*d*sinh(d*x + c)^2)]","B",0
32,1,746,0,0.577681," ","integrate(sinh(d*x+c)^3/(a+b*sinh(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{{\left(a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a b - b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a b - b^{2}\right)} \sinh\left(d x + c\right)^{2} - \sqrt{-a b + b^{2}} {\left(a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right)\right)} \log\left(\frac{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} - 2 \, {\left(2 \, a - 3 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} - 2 \, a + 3 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} - {\left(2 \, a - 3 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + 4 \, {\left(\cosh\left(d x + c\right)^{3} + 3 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{3} + {\left(3 \, \cosh\left(d x + c\right)^{2} + 1\right)} \sinh\left(d x + c\right) + \cosh\left(d x + c\right)\right)} \sqrt{-a b + b^{2}} + b}{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b}\right) + a b - b^{2}}{2 \, {\left({\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right) + {\left(a b^{2} - b^{3}\right)} d \sinh\left(d x + c\right)\right)}}, \frac{{\left(a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a b - b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a b - b^{2}\right)} \sinh\left(d x + c\right)^{2} - 2 \, \sqrt{a b - b^{2}} {\left(a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right)\right)} \arctan\left(-\frac{b \cosh\left(d x + c\right)^{3} + 3 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{3} + {\left(4 \, a - 3 \, b\right)} \cosh\left(d x + c\right) + {\left(3 \, b \cosh\left(d x + c\right)^{2} + 4 \, a - 3 \, b\right)} \sinh\left(d x + c\right)}{2 \, \sqrt{a b - b^{2}}}\right) + 2 \, \sqrt{a b - b^{2}} {\left(a \cosh\left(d x + c\right) + a \sinh\left(d x + c\right)\right)} \arctan\left(-\frac{\sqrt{a b - b^{2}} {\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right)}}{2 \, {\left(a - b\right)}}\right) + a b - b^{2}}{2 \, {\left({\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right) + {\left(a b^{2} - b^{3}\right)} d \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[1/2*((a*b - b^2)*cosh(d*x + c)^2 + 2*(a*b - b^2)*cosh(d*x + c)*sinh(d*x + c) + (a*b - b^2)*sinh(d*x + c)^2 - sqrt(-a*b + b^2)*(a*cosh(d*x + c) + a*sinh(d*x + c))*log((b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 - 2*(2*a - 3*b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 - 2*a + 3*b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 - (2*a - 3*b)*cosh(d*x + c))*sinh(d*x + c) + 4*(cosh(d*x + c)^3 + 3*cosh(d*x + c)*sinh(d*x + c)^2 + sinh(d*x + c)^3 + (3*cosh(d*x + c)^2 + 1)*sinh(d*x + c) + cosh(d*x + c))*sqrt(-a*b + b^2) + b)/(b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 + 2*(2*a - b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 + 2*a - b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 + (2*a - b)*cosh(d*x + c))*sinh(d*x + c) + b)) + a*b - b^2)/((a*b^2 - b^3)*d*cosh(d*x + c) + (a*b^2 - b^3)*d*sinh(d*x + c)), 1/2*((a*b - b^2)*cosh(d*x + c)^2 + 2*(a*b - b^2)*cosh(d*x + c)*sinh(d*x + c) + (a*b - b^2)*sinh(d*x + c)^2 - 2*sqrt(a*b - b^2)*(a*cosh(d*x + c) + a*sinh(d*x + c))*arctan(-1/2*(b*cosh(d*x + c)^3 + 3*b*cosh(d*x + c)*sinh(d*x + c)^2 + b*sinh(d*x + c)^3 + (4*a - 3*b)*cosh(d*x + c) + (3*b*cosh(d*x + c)^2 + 4*a - 3*b)*sinh(d*x + c))/sqrt(a*b - b^2)) + 2*sqrt(a*b - b^2)*(a*cosh(d*x + c) + a*sinh(d*x + c))*arctan(-1/2*sqrt(a*b - b^2)*(cosh(d*x + c) + sinh(d*x + c))/(a - b)) + a*b - b^2)/((a*b^2 - b^3)*d*cosh(d*x + c) + (a*b^2 - b^3)*d*sinh(d*x + c))]","B",0
33,1,464,0,0.610856," ","integrate(sinh(d*x+c)^2/(a+b*sinh(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{2 \, d x + \sqrt{\frac{a}{a - b}} \log\left(\frac{b^{2} \cosh\left(d x + c\right)^{4} + 4 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{2} \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(d x + c\right)^{2} + 2 \, a b - b^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, a^{2} - 8 \, a b + b^{2} + 4 \, {\left(b^{2} \cosh\left(d x + c\right)^{3} + {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + 4 \, {\left({\left(a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a b - b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a b - b^{2}\right)} \sinh\left(d x + c\right)^{2} + 2 \, a^{2} - 3 \, a b + b^{2}\right)} \sqrt{\frac{a}{a - b}}}{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b}\right)}{2 \, b d}, \frac{d x - \sqrt{-\frac{a}{a - b}} \arctan\left(\frac{{\left(b \cosh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b \sinh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sqrt{-\frac{a}{a - b}}}{2 \, a}\right)}{b d}\right]"," ",0,"[1/2*(2*d*x + sqrt(a/(a - b))*log((b^2*cosh(d*x + c)^4 + 4*b^2*cosh(d*x + c)*sinh(d*x + c)^3 + b^2*sinh(d*x + c)^4 + 2*(2*a*b - b^2)*cosh(d*x + c)^2 + 2*(3*b^2*cosh(d*x + c)^2 + 2*a*b - b^2)*sinh(d*x + c)^2 + 8*a^2 - 8*a*b + b^2 + 4*(b^2*cosh(d*x + c)^3 + (2*a*b - b^2)*cosh(d*x + c))*sinh(d*x + c) + 4*((a*b - b^2)*cosh(d*x + c)^2 + 2*(a*b - b^2)*cosh(d*x + c)*sinh(d*x + c) + (a*b - b^2)*sinh(d*x + c)^2 + 2*a^2 - 3*a*b + b^2)*sqrt(a/(a - b)))/(b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 + 2*(2*a - b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 + 2*a - b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 + (2*a - b)*cosh(d*x + c))*sinh(d*x + c) + b)))/(b*d), (d*x - sqrt(-a/(a - b))*arctan(1/2*(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + 2*a - b)*sqrt(-a/(a - b))/a))/(b*d)]","B",0
34,1,502,0,0.721150," ","integrate(sinh(d*x+c)/(a+b*sinh(d*x+c)^2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-a b + b^{2}} \log\left(\frac{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} - 2 \, {\left(2 \, a - 3 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} - 2 \, a + 3 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} - {\left(2 \, a - 3 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) - 4 \, {\left(\cosh\left(d x + c\right)^{3} + 3 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{3} + {\left(3 \, \cosh\left(d x + c\right)^{2} + 1\right)} \sinh\left(d x + c\right) + \cosh\left(d x + c\right)\right)} \sqrt{-a b + b^{2}} + b}{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b}\right)}{2 \, {\left(a b - b^{2}\right)} d}, \frac{\sqrt{a b - b^{2}} \arctan\left(-\frac{b \cosh\left(d x + c\right)^{3} + 3 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{3} + {\left(4 \, a - 3 \, b\right)} \cosh\left(d x + c\right) + {\left(3 \, b \cosh\left(d x + c\right)^{2} + 4 \, a - 3 \, b\right)} \sinh\left(d x + c\right)}{2 \, \sqrt{a b - b^{2}}}\right) - \sqrt{a b - b^{2}} \arctan\left(-\frac{\sqrt{a b - b^{2}} {\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right)}}{2 \, {\left(a - b\right)}}\right)}{{\left(a b - b^{2}\right)} d}\right]"," ",0,"[-1/2*sqrt(-a*b + b^2)*log((b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 - 2*(2*a - 3*b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 - 2*a + 3*b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 - (2*a - 3*b)*cosh(d*x + c))*sinh(d*x + c) - 4*(cosh(d*x + c)^3 + 3*cosh(d*x + c)*sinh(d*x + c)^2 + sinh(d*x + c)^3 + (3*cosh(d*x + c)^2 + 1)*sinh(d*x + c) + cosh(d*x + c))*sqrt(-a*b + b^2) + b)/(b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 + 2*(2*a - b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 + 2*a - b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 + (2*a - b)*cosh(d*x + c))*sinh(d*x + c) + b))/((a*b - b^2)*d), (sqrt(a*b - b^2)*arctan(-1/2*(b*cosh(d*x + c)^3 + 3*b*cosh(d*x + c)*sinh(d*x + c)^2 + b*sinh(d*x + c)^3 + (4*a - 3*b)*cosh(d*x + c) + (3*b*cosh(d*x + c)^2 + 4*a - 3*b)*sinh(d*x + c))/sqrt(a*b - b^2)) - sqrt(a*b - b^2)*arctan(-1/2*sqrt(a*b - b^2)*(cosh(d*x + c) + sinh(d*x + c))/(a - b)))/((a*b - b^2)*d)]","B",0
35,1,430,0,0.596494," ","integrate(1/(a+b*sinh(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{\log\left(\frac{b^{2} \cosh\left(d x + c\right)^{4} + 4 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{2} \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(d x + c\right)^{2} + 2 \, a b - b^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, a^{2} - 8 \, a b + b^{2} + 4 \, {\left(b^{2} \cosh\left(d x + c\right)^{3} + {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) - 4 \, {\left(b \cosh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b \sinh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sqrt{a^{2} - a b}}{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b}\right)}{2 \, \sqrt{a^{2} - a b} d}, -\frac{\sqrt{-a^{2} + a b} \arctan\left(-\frac{{\left(b \cosh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b \sinh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sqrt{-a^{2} + a b}}{2 \, {\left(a^{2} - a b\right)}}\right)}{{\left(a^{2} - a b\right)} d}\right]"," ",0,"[1/2*log((b^2*cosh(d*x + c)^4 + 4*b^2*cosh(d*x + c)*sinh(d*x + c)^3 + b^2*sinh(d*x + c)^4 + 2*(2*a*b - b^2)*cosh(d*x + c)^2 + 2*(3*b^2*cosh(d*x + c)^2 + 2*a*b - b^2)*sinh(d*x + c)^2 + 8*a^2 - 8*a*b + b^2 + 4*(b^2*cosh(d*x + c)^3 + (2*a*b - b^2)*cosh(d*x + c))*sinh(d*x + c) - 4*(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + 2*a - b)*sqrt(a^2 - a*b))/(b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 + 2*(2*a - b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 + 2*a - b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 + (2*a - b)*cosh(d*x + c))*sinh(d*x + c) + b))/(sqrt(a^2 - a*b)*d), -sqrt(-a^2 + a*b)*arctan(-1/2*(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + 2*a - b)*sqrt(-a^2 + a*b)/(a^2 - a*b))/((a^2 - a*b)*d)]","B",0
36,1,586,0,0.559619," ","integrate(csch(d*x+c)/(a+b*sinh(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{\sqrt{-\frac{b}{a - b}} \log\left(\frac{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} - 2 \, {\left(2 \, a - 3 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} - 2 \, a + 3 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} - {\left(2 \, a - 3 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) - 4 \, {\left({\left(a - b\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a - b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + {\left(a - b\right)} \sinh\left(d x + c\right)^{3} + {\left(a - b\right)} \cosh\left(d x + c\right) + {\left(3 \, {\left(a - b\right)} \cosh\left(d x + c\right)^{2} + a - b\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{b}{a - b}} + b}{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b}\right) - 2 \, \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) + 2 \, \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right)}{2 \, a d}, -\frac{\sqrt{\frac{b}{a - b}} \arctan\left(\frac{1}{2} \, \sqrt{\frac{b}{a - b}} {\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right)}\right) - \sqrt{\frac{b}{a - b}} \arctan\left(\frac{{\left(b \cosh\left(d x + c\right)^{3} + 3 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{3} + {\left(4 \, a - 3 \, b\right)} \cosh\left(d x + c\right) + {\left(3 \, b \cosh\left(d x + c\right)^{2} + 4 \, a - 3 \, b\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{b}{a - b}}}{2 \, b}\right) + \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) - \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right)}{a d}\right]"," ",0,"[1/2*(sqrt(-b/(a - b))*log((b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 - 2*(2*a - 3*b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 - 2*a + 3*b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 - (2*a - 3*b)*cosh(d*x + c))*sinh(d*x + c) - 4*((a - b)*cosh(d*x + c)^3 + 3*(a - b)*cosh(d*x + c)*sinh(d*x + c)^2 + (a - b)*sinh(d*x + c)^3 + (a - b)*cosh(d*x + c) + (3*(a - b)*cosh(d*x + c)^2 + a - b)*sinh(d*x + c))*sqrt(-b/(a - b)) + b)/(b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 + 2*(2*a - b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 + 2*a - b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 + (2*a - b)*cosh(d*x + c))*sinh(d*x + c) + b)) - 2*log(cosh(d*x + c) + sinh(d*x + c) + 1) + 2*log(cosh(d*x + c) + sinh(d*x + c) - 1))/(a*d), -(sqrt(b/(a - b))*arctan(1/2*sqrt(b/(a - b))*(cosh(d*x + c) + sinh(d*x + c))) - sqrt(b/(a - b))*arctan(1/2*(b*cosh(d*x + c)^3 + 3*b*cosh(d*x + c)*sinh(d*x + c)^2 + b*sinh(d*x + c)^3 + (4*a - 3*b)*cosh(d*x + c) + (3*b*cosh(d*x + c)^2 + 4*a - 3*b)*sinh(d*x + c))*sqrt(b/(a - b))/b) + log(cosh(d*x + c) + sinh(d*x + c) + 1) - log(cosh(d*x + c) + sinh(d*x + c) - 1))/(a*d)]","B",0
37,1,675,0,0.608622," ","integrate(csch(d*x+c)^2/(a+b*sinh(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{{\left(b \cosh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b \sinh\left(d x + c\right)^{2} - b\right)} \sqrt{a^{2} - a b} \log\left(\frac{b^{2} \cosh\left(d x + c\right)^{4} + 4 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{2} \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(d x + c\right)^{2} + 2 \, a b - b^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, a^{2} - 8 \, a b + b^{2} + 4 \, {\left(b^{2} \cosh\left(d x + c\right)^{3} + {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + 4 \, {\left(b \cosh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b \sinh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sqrt{a^{2} - a b}}{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b}\right) - 4 \, a^{2} + 4 \, a b}{2 \, {\left({\left(a^{3} - a^{2} b\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{3} - a^{2} b\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{3} - a^{2} b\right)} d \sinh\left(d x + c\right)^{2} - {\left(a^{3} - a^{2} b\right)} d\right)}}, \frac{{\left(b \cosh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b \sinh\left(d x + c\right)^{2} - b\right)} \sqrt{-a^{2} + a b} \arctan\left(-\frac{{\left(b \cosh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b \sinh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sqrt{-a^{2} + a b}}{2 \, {\left(a^{2} - a b\right)}}\right) - 2 \, a^{2} + 2 \, a b}{{\left(a^{3} - a^{2} b\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{3} - a^{2} b\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{3} - a^{2} b\right)} d \sinh\left(d x + c\right)^{2} - {\left(a^{3} - a^{2} b\right)} d}\right]"," ",0,"[1/2*((b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 - b)*sqrt(a^2 - a*b)*log((b^2*cosh(d*x + c)^4 + 4*b^2*cosh(d*x + c)*sinh(d*x + c)^3 + b^2*sinh(d*x + c)^4 + 2*(2*a*b - b^2)*cosh(d*x + c)^2 + 2*(3*b^2*cosh(d*x + c)^2 + 2*a*b - b^2)*sinh(d*x + c)^2 + 8*a^2 - 8*a*b + b^2 + 4*(b^2*cosh(d*x + c)^3 + (2*a*b - b^2)*cosh(d*x + c))*sinh(d*x + c) + 4*(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + 2*a - b)*sqrt(a^2 - a*b))/(b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 + 2*(2*a - b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 + 2*a - b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 + (2*a - b)*cosh(d*x + c))*sinh(d*x + c) + b)) - 4*a^2 + 4*a*b)/((a^3 - a^2*b)*d*cosh(d*x + c)^2 + 2*(a^3 - a^2*b)*d*cosh(d*x + c)*sinh(d*x + c) + (a^3 - a^2*b)*d*sinh(d*x + c)^2 - (a^3 - a^2*b)*d), ((b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 - b)*sqrt(-a^2 + a*b)*arctan(-1/2*(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + 2*a - b)*sqrt(-a^2 + a*b)/(a^2 - a*b)) - 2*a^2 + 2*a*b)/((a^3 - a^2*b)*d*cosh(d*x + c)^2 + 2*(a^3 - a^2*b)*d*cosh(d*x + c)*sinh(d*x + c) + (a^3 - a^2*b)*d*sinh(d*x + c)^2 - (a^3 - a^2*b)*d)]","B",0
38,1,1837,0,0.531690," ","integrate(csch(d*x+c)^3/(a+b*sinh(d*x+c)^2),x, algorithm=""fricas"")","\left[-\frac{2 \, a \cosh\left(d x + c\right)^{3} + 6 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + 2 \, a \sinh\left(d x + c\right)^{3} - {\left(b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} - 2 \, b \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} - b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b\right)} \sqrt{-\frac{b}{a - b}} \log\left(\frac{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} - 2 \, {\left(2 \, a - 3 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} - 2 \, a + 3 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} - {\left(2 \, a - 3 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + 4 \, {\left({\left(a - b\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a - b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + {\left(a - b\right)} \sinh\left(d x + c\right)^{3} + {\left(a - b\right)} \cosh\left(d x + c\right) + {\left(3 \, {\left(a - b\right)} \cosh\left(d x + c\right)^{2} + a - b\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{b}{a - b}} + b}{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b}\right) + 2 \, a \cosh\left(d x + c\right) - {\left({\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a + 2 \, b\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} - a - 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{3} - {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + a + 2 \, b\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) + {\left({\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a + 2 \, b\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} - a - 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{3} - {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + a + 2 \, b\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} + a\right)} \sinh\left(d x + c\right)}{2 \, {\left(a^{2} d \cosh\left(d x + c\right)^{4} + 4 \, a^{2} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a^{2} d \sinh\left(d x + c\right)^{4} - 2 \, a^{2} d \cosh\left(d x + c\right)^{2} + a^{2} d + 2 \, {\left(3 \, a^{2} d \cosh\left(d x + c\right)^{2} - a^{2} d\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a^{2} d \cosh\left(d x + c\right)^{3} - a^{2} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}, -\frac{2 \, a \cosh\left(d x + c\right)^{3} + 6 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + 2 \, a \sinh\left(d x + c\right)^{3} - 2 \, {\left(b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} - 2 \, b \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} - b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b\right)} \sqrt{\frac{b}{a - b}} \arctan\left(\frac{1}{2} \, \sqrt{\frac{b}{a - b}} {\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right)}\right) + 2 \, {\left(b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} - 2 \, b \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} - b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b\right)} \sqrt{\frac{b}{a - b}} \arctan\left(\frac{{\left(b \cosh\left(d x + c\right)^{3} + 3 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{3} + {\left(4 \, a - 3 \, b\right)} \cosh\left(d x + c\right) + {\left(3 \, b \cosh\left(d x + c\right)^{2} + 4 \, a - 3 \, b\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{b}{a - b}}}{2 \, b}\right) + 2 \, a \cosh\left(d x + c\right) - {\left({\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a + 2 \, b\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} - a - 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{3} - {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + a + 2 \, b\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) + {\left({\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a + 2 \, b\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} - a - 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{3} - {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + a + 2 \, b\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} + a\right)} \sinh\left(d x + c\right)}{2 \, {\left(a^{2} d \cosh\left(d x + c\right)^{4} + 4 \, a^{2} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a^{2} d \sinh\left(d x + c\right)^{4} - 2 \, a^{2} d \cosh\left(d x + c\right)^{2} + a^{2} d + 2 \, {\left(3 \, a^{2} d \cosh\left(d x + c\right)^{2} - a^{2} d\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a^{2} d \cosh\left(d x + c\right)^{3} - a^{2} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[-1/2*(2*a*cosh(d*x + c)^3 + 6*a*cosh(d*x + c)*sinh(d*x + c)^2 + 2*a*sinh(d*x + c)^3 - (b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 - 2*b*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 - b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 - b*cosh(d*x + c))*sinh(d*x + c) + b)*sqrt(-b/(a - b))*log((b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 - 2*(2*a - 3*b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 - 2*a + 3*b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 - (2*a - 3*b)*cosh(d*x + c))*sinh(d*x + c) + 4*((a - b)*cosh(d*x + c)^3 + 3*(a - b)*cosh(d*x + c)*sinh(d*x + c)^2 + (a - b)*sinh(d*x + c)^3 + (a - b)*cosh(d*x + c) + (3*(a - b)*cosh(d*x + c)^2 + a - b)*sinh(d*x + c))*sqrt(-b/(a - b)) + b)/(b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 + 2*(2*a - b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 + 2*a - b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 + (2*a - b)*cosh(d*x + c))*sinh(d*x + c) + b)) + 2*a*cosh(d*x + c) - ((a + 2*b)*cosh(d*x + c)^4 + 4*(a + 2*b)*cosh(d*x + c)*sinh(d*x + c)^3 + (a + 2*b)*sinh(d*x + c)^4 - 2*(a + 2*b)*cosh(d*x + c)^2 + 2*(3*(a + 2*b)*cosh(d*x + c)^2 - a - 2*b)*sinh(d*x + c)^2 + 4*((a + 2*b)*cosh(d*x + c)^3 - (a + 2*b)*cosh(d*x + c))*sinh(d*x + c) + a + 2*b)*log(cosh(d*x + c) + sinh(d*x + c) + 1) + ((a + 2*b)*cosh(d*x + c)^4 + 4*(a + 2*b)*cosh(d*x + c)*sinh(d*x + c)^3 + (a + 2*b)*sinh(d*x + c)^4 - 2*(a + 2*b)*cosh(d*x + c)^2 + 2*(3*(a + 2*b)*cosh(d*x + c)^2 - a - 2*b)*sinh(d*x + c)^2 + 4*((a + 2*b)*cosh(d*x + c)^3 - (a + 2*b)*cosh(d*x + c))*sinh(d*x + c) + a + 2*b)*log(cosh(d*x + c) + sinh(d*x + c) - 1) + 2*(3*a*cosh(d*x + c)^2 + a)*sinh(d*x + c))/(a^2*d*cosh(d*x + c)^4 + 4*a^2*d*cosh(d*x + c)*sinh(d*x + c)^3 + a^2*d*sinh(d*x + c)^4 - 2*a^2*d*cosh(d*x + c)^2 + a^2*d + 2*(3*a^2*d*cosh(d*x + c)^2 - a^2*d)*sinh(d*x + c)^2 + 4*(a^2*d*cosh(d*x + c)^3 - a^2*d*cosh(d*x + c))*sinh(d*x + c)), -1/2*(2*a*cosh(d*x + c)^3 + 6*a*cosh(d*x + c)*sinh(d*x + c)^2 + 2*a*sinh(d*x + c)^3 - 2*(b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 - 2*b*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 - b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 - b*cosh(d*x + c))*sinh(d*x + c) + b)*sqrt(b/(a - b))*arctan(1/2*sqrt(b/(a - b))*(cosh(d*x + c) + sinh(d*x + c))) + 2*(b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 - 2*b*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 - b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 - b*cosh(d*x + c))*sinh(d*x + c) + b)*sqrt(b/(a - b))*arctan(1/2*(b*cosh(d*x + c)^3 + 3*b*cosh(d*x + c)*sinh(d*x + c)^2 + b*sinh(d*x + c)^3 + (4*a - 3*b)*cosh(d*x + c) + (3*b*cosh(d*x + c)^2 + 4*a - 3*b)*sinh(d*x + c))*sqrt(b/(a - b))/b) + 2*a*cosh(d*x + c) - ((a + 2*b)*cosh(d*x + c)^4 + 4*(a + 2*b)*cosh(d*x + c)*sinh(d*x + c)^3 + (a + 2*b)*sinh(d*x + c)^4 - 2*(a + 2*b)*cosh(d*x + c)^2 + 2*(3*(a + 2*b)*cosh(d*x + c)^2 - a - 2*b)*sinh(d*x + c)^2 + 4*((a + 2*b)*cosh(d*x + c)^3 - (a + 2*b)*cosh(d*x + c))*sinh(d*x + c) + a + 2*b)*log(cosh(d*x + c) + sinh(d*x + c) + 1) + ((a + 2*b)*cosh(d*x + c)^4 + 4*(a + 2*b)*cosh(d*x + c)*sinh(d*x + c)^3 + (a + 2*b)*sinh(d*x + c)^4 - 2*(a + 2*b)*cosh(d*x + c)^2 + 2*(3*(a + 2*b)*cosh(d*x + c)^2 - a - 2*b)*sinh(d*x + c)^2 + 4*((a + 2*b)*cosh(d*x + c)^3 - (a + 2*b)*cosh(d*x + c))*sinh(d*x + c) + a + 2*b)*log(cosh(d*x + c) + sinh(d*x + c) - 1) + 2*(3*a*cosh(d*x + c)^2 + a)*sinh(d*x + c))/(a^2*d*cosh(d*x + c)^4 + 4*a^2*d*cosh(d*x + c)*sinh(d*x + c)^3 + a^2*d*sinh(d*x + c)^4 - 2*a^2*d*cosh(d*x + c)^2 + a^2*d + 2*(3*a^2*d*cosh(d*x + c)^2 - a^2*d)*sinh(d*x + c)^2 + 4*(a^2*d*cosh(d*x + c)^3 - a^2*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
39,1,1972,0,0.732515," ","integrate(csch(d*x+c)^4/(a+b*sinh(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{12 \, {\left(a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right)^{4} + 48 \, {\left(a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + 12 \, {\left(a^{2} b - a b^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, a^{3} + 4 \, a^{2} b - 12 \, a b^{2} - 24 \, {\left(a^{3} - a b^{2}\right)} \cosh\left(d x + c\right)^{2} - 24 \, {\left(a^{3} - a b^{2} - 3 \, {\left(a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 3 \, {\left(b^{2} \cosh\left(d x + c\right)^{6} + 6 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + b^{2} \sinh\left(d x + c\right)^{6} - 3 \, b^{2} \cosh\left(d x + c\right)^{4} + 3 \, {\left(5 \, b^{2} \cosh\left(d x + c\right)^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{4} + 3 \, b^{2} \cosh\left(d x + c\right)^{2} + 4 \, {\left(5 \, b^{2} \cosh\left(d x + c\right)^{3} - 3 \, b^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 3 \, {\left(5 \, b^{2} \cosh\left(d x + c\right)^{4} - 6 \, b^{2} \cosh\left(d x + c\right)^{2} + b^{2}\right)} \sinh\left(d x + c\right)^{2} - b^{2} + 6 \, {\left(b^{2} \cosh\left(d x + c\right)^{5} - 2 \, b^{2} \cosh\left(d x + c\right)^{3} + b^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{a^{2} - a b} \log\left(\frac{b^{2} \cosh\left(d x + c\right)^{4} + 4 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{2} \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(d x + c\right)^{2} + 2 \, a b - b^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, a^{2} - 8 \, a b + b^{2} + 4 \, {\left(b^{2} \cosh\left(d x + c\right)^{3} + {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) - 4 \, {\left(b \cosh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b \sinh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sqrt{a^{2} - a b}}{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b}\right) + 48 \, {\left({\left(a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(a^{3} - a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{6 \, {\left({\left(a^{4} - a^{3} b\right)} d \cosh\left(d x + c\right)^{6} + 6 \, {\left(a^{4} - a^{3} b\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(a^{4} - a^{3} b\right)} d \sinh\left(d x + c\right)^{6} - 3 \, {\left(a^{4} - a^{3} b\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(5 \, {\left(a^{4} - a^{3} b\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{4} - a^{3} b\right)} d\right)} \sinh\left(d x + c\right)^{4} + 3 \, {\left(a^{4} - a^{3} b\right)} d \cosh\left(d x + c\right)^{2} + 4 \, {\left(5 \, {\left(a^{4} - a^{3} b\right)} d \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{4} - a^{3} b\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 3 \, {\left(5 \, {\left(a^{4} - a^{3} b\right)} d \cosh\left(d x + c\right)^{4} - 6 \, {\left(a^{4} - a^{3} b\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{4} - a^{3} b\right)} d\right)} \sinh\left(d x + c\right)^{2} - {\left(a^{4} - a^{3} b\right)} d + 6 \, {\left({\left(a^{4} - a^{3} b\right)} d \cosh\left(d x + c\right)^{5} - 2 \, {\left(a^{4} - a^{3} b\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{4} - a^{3} b\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}, \frac{6 \, {\left(a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right)^{4} + 24 \, {\left(a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + 6 \, {\left(a^{2} b - a b^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, a^{3} + 2 \, a^{2} b - 6 \, a b^{2} - 12 \, {\left(a^{3} - a b^{2}\right)} \cosh\left(d x + c\right)^{2} - 12 \, {\left(a^{3} - a b^{2} - 3 \, {\left(a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} - 3 \, {\left(b^{2} \cosh\left(d x + c\right)^{6} + 6 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + b^{2} \sinh\left(d x + c\right)^{6} - 3 \, b^{2} \cosh\left(d x + c\right)^{4} + 3 \, {\left(5 \, b^{2} \cosh\left(d x + c\right)^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{4} + 3 \, b^{2} \cosh\left(d x + c\right)^{2} + 4 \, {\left(5 \, b^{2} \cosh\left(d x + c\right)^{3} - 3 \, b^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 3 \, {\left(5 \, b^{2} \cosh\left(d x + c\right)^{4} - 6 \, b^{2} \cosh\left(d x + c\right)^{2} + b^{2}\right)} \sinh\left(d x + c\right)^{2} - b^{2} + 6 \, {\left(b^{2} \cosh\left(d x + c\right)^{5} - 2 \, b^{2} \cosh\left(d x + c\right)^{3} + b^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-a^{2} + a b} \arctan\left(-\frac{{\left(b \cosh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b \sinh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sqrt{-a^{2} + a b}}{2 \, {\left(a^{2} - a b\right)}}\right) + 24 \, {\left({\left(a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(a^{3} - a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{3 \, {\left({\left(a^{4} - a^{3} b\right)} d \cosh\left(d x + c\right)^{6} + 6 \, {\left(a^{4} - a^{3} b\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(a^{4} - a^{3} b\right)} d \sinh\left(d x + c\right)^{6} - 3 \, {\left(a^{4} - a^{3} b\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(5 \, {\left(a^{4} - a^{3} b\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{4} - a^{3} b\right)} d\right)} \sinh\left(d x + c\right)^{4} + 3 \, {\left(a^{4} - a^{3} b\right)} d \cosh\left(d x + c\right)^{2} + 4 \, {\left(5 \, {\left(a^{4} - a^{3} b\right)} d \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{4} - a^{3} b\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 3 \, {\left(5 \, {\left(a^{4} - a^{3} b\right)} d \cosh\left(d x + c\right)^{4} - 6 \, {\left(a^{4} - a^{3} b\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{4} - a^{3} b\right)} d\right)} \sinh\left(d x + c\right)^{2} - {\left(a^{4} - a^{3} b\right)} d + 6 \, {\left({\left(a^{4} - a^{3} b\right)} d \cosh\left(d x + c\right)^{5} - 2 \, {\left(a^{4} - a^{3} b\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{4} - a^{3} b\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[1/6*(12*(a^2*b - a*b^2)*cosh(d*x + c)^4 + 48*(a^2*b - a*b^2)*cosh(d*x + c)*sinh(d*x + c)^3 + 12*(a^2*b - a*b^2)*sinh(d*x + c)^4 + 8*a^3 + 4*a^2*b - 12*a*b^2 - 24*(a^3 - a*b^2)*cosh(d*x + c)^2 - 24*(a^3 - a*b^2 - 3*(a^2*b - a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 3*(b^2*cosh(d*x + c)^6 + 6*b^2*cosh(d*x + c)*sinh(d*x + c)^5 + b^2*sinh(d*x + c)^6 - 3*b^2*cosh(d*x + c)^4 + 3*(5*b^2*cosh(d*x + c)^2 - b^2)*sinh(d*x + c)^4 + 3*b^2*cosh(d*x + c)^2 + 4*(5*b^2*cosh(d*x + c)^3 - 3*b^2*cosh(d*x + c))*sinh(d*x + c)^3 + 3*(5*b^2*cosh(d*x + c)^4 - 6*b^2*cosh(d*x + c)^2 + b^2)*sinh(d*x + c)^2 - b^2 + 6*(b^2*cosh(d*x + c)^5 - 2*b^2*cosh(d*x + c)^3 + b^2*cosh(d*x + c))*sinh(d*x + c))*sqrt(a^2 - a*b)*log((b^2*cosh(d*x + c)^4 + 4*b^2*cosh(d*x + c)*sinh(d*x + c)^3 + b^2*sinh(d*x + c)^4 + 2*(2*a*b - b^2)*cosh(d*x + c)^2 + 2*(3*b^2*cosh(d*x + c)^2 + 2*a*b - b^2)*sinh(d*x + c)^2 + 8*a^2 - 8*a*b + b^2 + 4*(b^2*cosh(d*x + c)^3 + (2*a*b - b^2)*cosh(d*x + c))*sinh(d*x + c) - 4*(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + 2*a - b)*sqrt(a^2 - a*b))/(b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 + 2*(2*a - b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 + 2*a - b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 + (2*a - b)*cosh(d*x + c))*sinh(d*x + c) + b)) + 48*((a^2*b - a*b^2)*cosh(d*x + c)^3 - (a^3 - a*b^2)*cosh(d*x + c))*sinh(d*x + c))/((a^4 - a^3*b)*d*cosh(d*x + c)^6 + 6*(a^4 - a^3*b)*d*cosh(d*x + c)*sinh(d*x + c)^5 + (a^4 - a^3*b)*d*sinh(d*x + c)^6 - 3*(a^4 - a^3*b)*d*cosh(d*x + c)^4 + 3*(5*(a^4 - a^3*b)*d*cosh(d*x + c)^2 - (a^4 - a^3*b)*d)*sinh(d*x + c)^4 + 3*(a^4 - a^3*b)*d*cosh(d*x + c)^2 + 4*(5*(a^4 - a^3*b)*d*cosh(d*x + c)^3 - 3*(a^4 - a^3*b)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 3*(5*(a^4 - a^3*b)*d*cosh(d*x + c)^4 - 6*(a^4 - a^3*b)*d*cosh(d*x + c)^2 + (a^4 - a^3*b)*d)*sinh(d*x + c)^2 - (a^4 - a^3*b)*d + 6*((a^4 - a^3*b)*d*cosh(d*x + c)^5 - 2*(a^4 - a^3*b)*d*cosh(d*x + c)^3 + (a^4 - a^3*b)*d*cosh(d*x + c))*sinh(d*x + c)), 1/3*(6*(a^2*b - a*b^2)*cosh(d*x + c)^4 + 24*(a^2*b - a*b^2)*cosh(d*x + c)*sinh(d*x + c)^3 + 6*(a^2*b - a*b^2)*sinh(d*x + c)^4 + 4*a^3 + 2*a^2*b - 6*a*b^2 - 12*(a^3 - a*b^2)*cosh(d*x + c)^2 - 12*(a^3 - a*b^2 - 3*(a^2*b - a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - 3*(b^2*cosh(d*x + c)^6 + 6*b^2*cosh(d*x + c)*sinh(d*x + c)^5 + b^2*sinh(d*x + c)^6 - 3*b^2*cosh(d*x + c)^4 + 3*(5*b^2*cosh(d*x + c)^2 - b^2)*sinh(d*x + c)^4 + 3*b^2*cosh(d*x + c)^2 + 4*(5*b^2*cosh(d*x + c)^3 - 3*b^2*cosh(d*x + c))*sinh(d*x + c)^3 + 3*(5*b^2*cosh(d*x + c)^4 - 6*b^2*cosh(d*x + c)^2 + b^2)*sinh(d*x + c)^2 - b^2 + 6*(b^2*cosh(d*x + c)^5 - 2*b^2*cosh(d*x + c)^3 + b^2*cosh(d*x + c))*sinh(d*x + c))*sqrt(-a^2 + a*b)*arctan(-1/2*(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + 2*a - b)*sqrt(-a^2 + a*b)/(a^2 - a*b)) + 24*((a^2*b - a*b^2)*cosh(d*x + c)^3 - (a^3 - a*b^2)*cosh(d*x + c))*sinh(d*x + c))/((a^4 - a^3*b)*d*cosh(d*x + c)^6 + 6*(a^4 - a^3*b)*d*cosh(d*x + c)*sinh(d*x + c)^5 + (a^4 - a^3*b)*d*sinh(d*x + c)^6 - 3*(a^4 - a^3*b)*d*cosh(d*x + c)^4 + 3*(5*(a^4 - a^3*b)*d*cosh(d*x + c)^2 - (a^4 - a^3*b)*d)*sinh(d*x + c)^4 + 3*(a^4 - a^3*b)*d*cosh(d*x + c)^2 + 4*(5*(a^4 - a^3*b)*d*cosh(d*x + c)^3 - 3*(a^4 - a^3*b)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 3*(5*(a^4 - a^3*b)*d*cosh(d*x + c)^4 - 6*(a^4 - a^3*b)*d*cosh(d*x + c)^2 + (a^4 - a^3*b)*d)*sinh(d*x + c)^2 - (a^4 - a^3*b)*d + 6*((a^4 - a^3*b)*d*cosh(d*x + c)^5 - 2*(a^4 - a^3*b)*d*cosh(d*x + c)^3 + (a^4 - a^3*b)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
40,1,5809,0,0.650084," ","integrate(csch(d*x+c)^5/(a+b*sinh(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(3 \, a^{2} + 4 \, a b\right)} \cosh\left(d x + c\right)^{7} + 14 \, {\left(3 \, a^{2} + 4 \, a b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + 2 \, {\left(3 \, a^{2} + 4 \, a b\right)} \sinh\left(d x + c\right)^{7} - 2 \, {\left(11 \, a^{2} + 4 \, a b\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(21 \, {\left(3 \, a^{2} + 4 \, a b\right)} \cosh\left(d x + c\right)^{2} - 11 \, a^{2} - 4 \, a b\right)} \sinh\left(d x + c\right)^{5} + 10 \, {\left(7 \, {\left(3 \, a^{2} + 4 \, a b\right)} \cosh\left(d x + c\right)^{3} - {\left(11 \, a^{2} + 4 \, a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(11 \, a^{2} + 4 \, a b\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(35 \, {\left(3 \, a^{2} + 4 \, a b\right)} \cosh\left(d x + c\right)^{4} - 10 \, {\left(11 \, a^{2} + 4 \, a b\right)} \cosh\left(d x + c\right)^{2} - 11 \, a^{2} - 4 \, a b\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(21 \, {\left(3 \, a^{2} + 4 \, a b\right)} \cosh\left(d x + c\right)^{5} - 10 \, {\left(11 \, a^{2} + 4 \, a b\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(11 \, a^{2} + 4 \, a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b^{2} \cosh\left(d x + c\right)^{8} + 8 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + b^{2} \sinh\left(d x + c\right)^{8} - 4 \, b^{2} \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, b^{2} \cosh\left(d x + c\right)^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{6} + 6 \, b^{2} \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, b^{2} \cosh\left(d x + c\right)^{3} - 3 \, b^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, b^{2} \cosh\left(d x + c\right)^{4} - 30 \, b^{2} \cosh\left(d x + c\right)^{2} + 3 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} - 4 \, b^{2} \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, b^{2} \cosh\left(d x + c\right)^{5} - 10 \, b^{2} \cosh\left(d x + c\right)^{3} + 3 \, b^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, b^{2} \cosh\left(d x + c\right)^{6} - 15 \, b^{2} \cosh\left(d x + c\right)^{4} + 9 \, b^{2} \cosh\left(d x + c\right)^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{2} + b^{2} + 8 \, {\left(b^{2} \cosh\left(d x + c\right)^{7} - 3 \, b^{2} \cosh\left(d x + c\right)^{5} + 3 \, b^{2} \cosh\left(d x + c\right)^{3} - b^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{b}{a - b}} \log\left(\frac{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} - 2 \, {\left(2 \, a - 3 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} - 2 \, a + 3 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} - {\left(2 \, a - 3 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) - 4 \, {\left({\left(a - b\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a - b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + {\left(a - b\right)} \sinh\left(d x + c\right)^{3} + {\left(a - b\right)} \cosh\left(d x + c\right) + {\left(3 \, {\left(a - b\right)} \cosh\left(d x + c\right)^{2} + a - b\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{b}{a - b}} + b}{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b}\right) + 2 \, {\left(3 \, a^{2} + 4 \, a b\right)} \cosh\left(d x + c\right) - {\left({\left(3 \, a^{2} + 4 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(3 \, a^{2} + 4 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(3 \, a^{2} + 4 \, a b + 8 \, b^{2}\right)} \sinh\left(d x + c\right)^{8} - 4 \, {\left(3 \, a^{2} + 4 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(3 \, a^{2} + 4 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 3 \, a^{2} - 4 \, a b - 8 \, b^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(3 \, a^{2} + 4 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(3 \, a^{2} + 4 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 6 \, {\left(3 \, a^{2} + 4 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(3 \, a^{2} + 4 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} - 30 \, {\left(3 \, a^{2} + 4 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 9 \, a^{2} + 12 \, a b + 24 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(3 \, a^{2} + 4 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} - 10 \, {\left(3 \, a^{2} + 4 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(3 \, a^{2} + 4 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 4 \, {\left(3 \, a^{2} + 4 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(3 \, a^{2} + 4 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} - 15 \, {\left(3 \, a^{2} + 4 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 9 \, {\left(3 \, a^{2} + 4 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 3 \, a^{2} - 4 \, a b - 8 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} + 3 \, a^{2} + 4 \, a b + 8 \, b^{2} + 8 \, {\left({\left(3 \, a^{2} + 4 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} - 3 \, {\left(3 \, a^{2} + 4 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 3 \, {\left(3 \, a^{2} + 4 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(3 \, a^{2} + 4 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) + {\left({\left(3 \, a^{2} + 4 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(3 \, a^{2} + 4 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(3 \, a^{2} + 4 \, a b + 8 \, b^{2}\right)} \sinh\left(d x + c\right)^{8} - 4 \, {\left(3 \, a^{2} + 4 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(3 \, a^{2} + 4 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 3 \, a^{2} - 4 \, a b - 8 \, b^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(3 \, a^{2} + 4 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(3 \, a^{2} + 4 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 6 \, {\left(3 \, a^{2} + 4 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(3 \, a^{2} + 4 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} - 30 \, {\left(3 \, a^{2} + 4 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 9 \, a^{2} + 12 \, a b + 24 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(3 \, a^{2} + 4 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} - 10 \, {\left(3 \, a^{2} + 4 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(3 \, a^{2} + 4 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 4 \, {\left(3 \, a^{2} + 4 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(3 \, a^{2} + 4 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} - 15 \, {\left(3 \, a^{2} + 4 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 9 \, {\left(3 \, a^{2} + 4 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 3 \, a^{2} - 4 \, a b - 8 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} + 3 \, a^{2} + 4 \, a b + 8 \, b^{2} + 8 \, {\left({\left(3 \, a^{2} + 4 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} - 3 \, {\left(3 \, a^{2} + 4 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 3 \, {\left(3 \, a^{2} + 4 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(3 \, a^{2} + 4 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) + 2 \, {\left(7 \, {\left(3 \, a^{2} + 4 \, a b\right)} \cosh\left(d x + c\right)^{6} - 5 \, {\left(11 \, a^{2} + 4 \, a b\right)} \cosh\left(d x + c\right)^{4} - 3 \, {\left(11 \, a^{2} + 4 \, a b\right)} \cosh\left(d x + c\right)^{2} + 3 \, a^{2} + 4 \, a b\right)} \sinh\left(d x + c\right)}{8 \, {\left(a^{3} d \cosh\left(d x + c\right)^{8} + 8 \, a^{3} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + a^{3} d \sinh\left(d x + c\right)^{8} - 4 \, a^{3} d \cosh\left(d x + c\right)^{6} + 6 \, a^{3} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(7 \, a^{3} d \cosh\left(d x + c\right)^{2} - a^{3} d\right)} \sinh\left(d x + c\right)^{6} - 4 \, a^{3} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, a^{3} d \cosh\left(d x + c\right)^{3} - 3 \, a^{3} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, a^{3} d \cosh\left(d x + c\right)^{4} - 30 \, a^{3} d \cosh\left(d x + c\right)^{2} + 3 \, a^{3} d\right)} \sinh\left(d x + c\right)^{4} + a^{3} d + 8 \, {\left(7 \, a^{3} d \cosh\left(d x + c\right)^{5} - 10 \, a^{3} d \cosh\left(d x + c\right)^{3} + 3 \, a^{3} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, a^{3} d \cosh\left(d x + c\right)^{6} - 15 \, a^{3} d \cosh\left(d x + c\right)^{4} + 9 \, a^{3} d \cosh\left(d x + c\right)^{2} - a^{3} d\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left(a^{3} d \cosh\left(d x + c\right)^{7} - 3 \, a^{3} d \cosh\left(d x + c\right)^{5} + 3 \, a^{3} d \cosh\left(d x + c\right)^{3} - a^{3} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}, \frac{2 \, {\left(3 \, a^{2} + 4 \, a b\right)} \cosh\left(d x + c\right)^{7} + 14 \, {\left(3 \, a^{2} + 4 \, a b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + 2 \, {\left(3 \, a^{2} + 4 \, a b\right)} \sinh\left(d x + c\right)^{7} - 2 \, {\left(11 \, a^{2} + 4 \, a b\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(21 \, {\left(3 \, a^{2} + 4 \, a b\right)} \cosh\left(d x + c\right)^{2} - 11 \, a^{2} - 4 \, a b\right)} \sinh\left(d x + c\right)^{5} + 10 \, {\left(7 \, {\left(3 \, a^{2} + 4 \, a b\right)} \cosh\left(d x + c\right)^{3} - {\left(11 \, a^{2} + 4 \, a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(11 \, a^{2} + 4 \, a b\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(35 \, {\left(3 \, a^{2} + 4 \, a b\right)} \cosh\left(d x + c\right)^{4} - 10 \, {\left(11 \, a^{2} + 4 \, a b\right)} \cosh\left(d x + c\right)^{2} - 11 \, a^{2} - 4 \, a b\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(21 \, {\left(3 \, a^{2} + 4 \, a b\right)} \cosh\left(d x + c\right)^{5} - 10 \, {\left(11 \, a^{2} + 4 \, a b\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(11 \, a^{2} + 4 \, a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 8 \, {\left(b^{2} \cosh\left(d x + c\right)^{8} + 8 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + b^{2} \sinh\left(d x + c\right)^{8} - 4 \, b^{2} \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, b^{2} \cosh\left(d x + c\right)^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{6} + 6 \, b^{2} \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, b^{2} \cosh\left(d x + c\right)^{3} - 3 \, b^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, b^{2} \cosh\left(d x + c\right)^{4} - 30 \, b^{2} \cosh\left(d x + c\right)^{2} + 3 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} - 4 \, b^{2} \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, b^{2} \cosh\left(d x + c\right)^{5} - 10 \, b^{2} \cosh\left(d x + c\right)^{3} + 3 \, b^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, b^{2} \cosh\left(d x + c\right)^{6} - 15 \, b^{2} \cosh\left(d x + c\right)^{4} + 9 \, b^{2} \cosh\left(d x + c\right)^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{2} + b^{2} + 8 \, {\left(b^{2} \cosh\left(d x + c\right)^{7} - 3 \, b^{2} \cosh\left(d x + c\right)^{5} + 3 \, b^{2} \cosh\left(d x + c\right)^{3} - b^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{b}{a - b}} \arctan\left(\frac{1}{2} \, \sqrt{\frac{b}{a - b}} {\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right)}\right) + 8 \, {\left(b^{2} \cosh\left(d x + c\right)^{8} + 8 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + b^{2} \sinh\left(d x + c\right)^{8} - 4 \, b^{2} \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, b^{2} \cosh\left(d x + c\right)^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{6} + 6 \, b^{2} \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, b^{2} \cosh\left(d x + c\right)^{3} - 3 \, b^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, b^{2} \cosh\left(d x + c\right)^{4} - 30 \, b^{2} \cosh\left(d x + c\right)^{2} + 3 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} - 4 \, b^{2} \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, b^{2} \cosh\left(d x + c\right)^{5} - 10 \, b^{2} \cosh\left(d x + c\right)^{3} + 3 \, b^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, b^{2} \cosh\left(d x + c\right)^{6} - 15 \, b^{2} \cosh\left(d x + c\right)^{4} + 9 \, b^{2} \cosh\left(d x + c\right)^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{2} + b^{2} + 8 \, {\left(b^{2} \cosh\left(d x + c\right)^{7} - 3 \, b^{2} \cosh\left(d x + c\right)^{5} + 3 \, b^{2} \cosh\left(d x + c\right)^{3} - b^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{b}{a - b}} \arctan\left(\frac{{\left(b \cosh\left(d x + c\right)^{3} + 3 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{3} + {\left(4 \, a - 3 \, b\right)} \cosh\left(d x + c\right) + {\left(3 \, b \cosh\left(d x + c\right)^{2} + 4 \, a - 3 \, b\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{b}{a - b}}}{2 \, b}\right) + 2 \, {\left(3 \, a^{2} + 4 \, a b\right)} \cosh\left(d x + c\right) - {\left({\left(3 \, a^{2} + 4 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(3 \, a^{2} + 4 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(3 \, a^{2} + 4 \, a b + 8 \, b^{2}\right)} \sinh\left(d x + c\right)^{8} - 4 \, {\left(3 \, a^{2} + 4 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(3 \, a^{2} + 4 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 3 \, a^{2} - 4 \, a b - 8 \, b^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(3 \, a^{2} + 4 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(3 \, a^{2} + 4 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 6 \, {\left(3 \, a^{2} + 4 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(3 \, a^{2} + 4 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} - 30 \, {\left(3 \, a^{2} + 4 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 9 \, a^{2} + 12 \, a b + 24 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(3 \, a^{2} + 4 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} - 10 \, {\left(3 \, a^{2} + 4 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(3 \, a^{2} + 4 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 4 \, {\left(3 \, a^{2} + 4 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(3 \, a^{2} + 4 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} - 15 \, {\left(3 \, a^{2} + 4 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 9 \, {\left(3 \, a^{2} + 4 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 3 \, a^{2} - 4 \, a b - 8 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} + 3 \, a^{2} + 4 \, a b + 8 \, b^{2} + 8 \, {\left({\left(3 \, a^{2} + 4 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} - 3 \, {\left(3 \, a^{2} + 4 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 3 \, {\left(3 \, a^{2} + 4 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(3 \, a^{2} + 4 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) + {\left({\left(3 \, a^{2} + 4 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(3 \, a^{2} + 4 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(3 \, a^{2} + 4 \, a b + 8 \, b^{2}\right)} \sinh\left(d x + c\right)^{8} - 4 \, {\left(3 \, a^{2} + 4 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(3 \, a^{2} + 4 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 3 \, a^{2} - 4 \, a b - 8 \, b^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(3 \, a^{2} + 4 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(3 \, a^{2} + 4 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 6 \, {\left(3 \, a^{2} + 4 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(3 \, a^{2} + 4 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} - 30 \, {\left(3 \, a^{2} + 4 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 9 \, a^{2} + 12 \, a b + 24 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(3 \, a^{2} + 4 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} - 10 \, {\left(3 \, a^{2} + 4 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(3 \, a^{2} + 4 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 4 \, {\left(3 \, a^{2} + 4 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(3 \, a^{2} + 4 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} - 15 \, {\left(3 \, a^{2} + 4 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 9 \, {\left(3 \, a^{2} + 4 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 3 \, a^{2} - 4 \, a b - 8 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} + 3 \, a^{2} + 4 \, a b + 8 \, b^{2} + 8 \, {\left({\left(3 \, a^{2} + 4 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} - 3 \, {\left(3 \, a^{2} + 4 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 3 \, {\left(3 \, a^{2} + 4 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(3 \, a^{2} + 4 \, a b + 8 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) + 2 \, {\left(7 \, {\left(3 \, a^{2} + 4 \, a b\right)} \cosh\left(d x + c\right)^{6} - 5 \, {\left(11 \, a^{2} + 4 \, a b\right)} \cosh\left(d x + c\right)^{4} - 3 \, {\left(11 \, a^{2} + 4 \, a b\right)} \cosh\left(d x + c\right)^{2} + 3 \, a^{2} + 4 \, a b\right)} \sinh\left(d x + c\right)}{8 \, {\left(a^{3} d \cosh\left(d x + c\right)^{8} + 8 \, a^{3} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + a^{3} d \sinh\left(d x + c\right)^{8} - 4 \, a^{3} d \cosh\left(d x + c\right)^{6} + 6 \, a^{3} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(7 \, a^{3} d \cosh\left(d x + c\right)^{2} - a^{3} d\right)} \sinh\left(d x + c\right)^{6} - 4 \, a^{3} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, a^{3} d \cosh\left(d x + c\right)^{3} - 3 \, a^{3} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, a^{3} d \cosh\left(d x + c\right)^{4} - 30 \, a^{3} d \cosh\left(d x + c\right)^{2} + 3 \, a^{3} d\right)} \sinh\left(d x + c\right)^{4} + a^{3} d + 8 \, {\left(7 \, a^{3} d \cosh\left(d x + c\right)^{5} - 10 \, a^{3} d \cosh\left(d x + c\right)^{3} + 3 \, a^{3} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, a^{3} d \cosh\left(d x + c\right)^{6} - 15 \, a^{3} d \cosh\left(d x + c\right)^{4} + 9 \, a^{3} d \cosh\left(d x + c\right)^{2} - a^{3} d\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left(a^{3} d \cosh\left(d x + c\right)^{7} - 3 \, a^{3} d \cosh\left(d x + c\right)^{5} + 3 \, a^{3} d \cosh\left(d x + c\right)^{3} - a^{3} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[1/8*(2*(3*a^2 + 4*a*b)*cosh(d*x + c)^7 + 14*(3*a^2 + 4*a*b)*cosh(d*x + c)*sinh(d*x + c)^6 + 2*(3*a^2 + 4*a*b)*sinh(d*x + c)^7 - 2*(11*a^2 + 4*a*b)*cosh(d*x + c)^5 + 2*(21*(3*a^2 + 4*a*b)*cosh(d*x + c)^2 - 11*a^2 - 4*a*b)*sinh(d*x + c)^5 + 10*(7*(3*a^2 + 4*a*b)*cosh(d*x + c)^3 - (11*a^2 + 4*a*b)*cosh(d*x + c))*sinh(d*x + c)^4 - 2*(11*a^2 + 4*a*b)*cosh(d*x + c)^3 + 2*(35*(3*a^2 + 4*a*b)*cosh(d*x + c)^4 - 10*(11*a^2 + 4*a*b)*cosh(d*x + c)^2 - 11*a^2 - 4*a*b)*sinh(d*x + c)^3 + 2*(21*(3*a^2 + 4*a*b)*cosh(d*x + c)^5 - 10*(11*a^2 + 4*a*b)*cosh(d*x + c)^3 - 3*(11*a^2 + 4*a*b)*cosh(d*x + c))*sinh(d*x + c)^2 + 4*(b^2*cosh(d*x + c)^8 + 8*b^2*cosh(d*x + c)*sinh(d*x + c)^7 + b^2*sinh(d*x + c)^8 - 4*b^2*cosh(d*x + c)^6 + 4*(7*b^2*cosh(d*x + c)^2 - b^2)*sinh(d*x + c)^6 + 6*b^2*cosh(d*x + c)^4 + 8*(7*b^2*cosh(d*x + c)^3 - 3*b^2*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*b^2*cosh(d*x + c)^4 - 30*b^2*cosh(d*x + c)^2 + 3*b^2)*sinh(d*x + c)^4 - 4*b^2*cosh(d*x + c)^2 + 8*(7*b^2*cosh(d*x + c)^5 - 10*b^2*cosh(d*x + c)^3 + 3*b^2*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*b^2*cosh(d*x + c)^6 - 15*b^2*cosh(d*x + c)^4 + 9*b^2*cosh(d*x + c)^2 - b^2)*sinh(d*x + c)^2 + b^2 + 8*(b^2*cosh(d*x + c)^7 - 3*b^2*cosh(d*x + c)^5 + 3*b^2*cosh(d*x + c)^3 - b^2*cosh(d*x + c))*sinh(d*x + c))*sqrt(-b/(a - b))*log((b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 - 2*(2*a - 3*b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 - 2*a + 3*b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 - (2*a - 3*b)*cosh(d*x + c))*sinh(d*x + c) - 4*((a - b)*cosh(d*x + c)^3 + 3*(a - b)*cosh(d*x + c)*sinh(d*x + c)^2 + (a - b)*sinh(d*x + c)^3 + (a - b)*cosh(d*x + c) + (3*(a - b)*cosh(d*x + c)^2 + a - b)*sinh(d*x + c))*sqrt(-b/(a - b)) + b)/(b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 + 2*(2*a - b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 + 2*a - b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 + (2*a - b)*cosh(d*x + c))*sinh(d*x + c) + b)) + 2*(3*a^2 + 4*a*b)*cosh(d*x + c) - ((3*a^2 + 4*a*b + 8*b^2)*cosh(d*x + c)^8 + 8*(3*a^2 + 4*a*b + 8*b^2)*cosh(d*x + c)*sinh(d*x + c)^7 + (3*a^2 + 4*a*b + 8*b^2)*sinh(d*x + c)^8 - 4*(3*a^2 + 4*a*b + 8*b^2)*cosh(d*x + c)^6 + 4*(7*(3*a^2 + 4*a*b + 8*b^2)*cosh(d*x + c)^2 - 3*a^2 - 4*a*b - 8*b^2)*sinh(d*x + c)^6 + 8*(7*(3*a^2 + 4*a*b + 8*b^2)*cosh(d*x + c)^3 - 3*(3*a^2 + 4*a*b + 8*b^2)*cosh(d*x + c))*sinh(d*x + c)^5 + 6*(3*a^2 + 4*a*b + 8*b^2)*cosh(d*x + c)^4 + 2*(35*(3*a^2 + 4*a*b + 8*b^2)*cosh(d*x + c)^4 - 30*(3*a^2 + 4*a*b + 8*b^2)*cosh(d*x + c)^2 + 9*a^2 + 12*a*b + 24*b^2)*sinh(d*x + c)^4 + 8*(7*(3*a^2 + 4*a*b + 8*b^2)*cosh(d*x + c)^5 - 10*(3*a^2 + 4*a*b + 8*b^2)*cosh(d*x + c)^3 + 3*(3*a^2 + 4*a*b + 8*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 - 4*(3*a^2 + 4*a*b + 8*b^2)*cosh(d*x + c)^2 + 4*(7*(3*a^2 + 4*a*b + 8*b^2)*cosh(d*x + c)^6 - 15*(3*a^2 + 4*a*b + 8*b^2)*cosh(d*x + c)^4 + 9*(3*a^2 + 4*a*b + 8*b^2)*cosh(d*x + c)^2 - 3*a^2 - 4*a*b - 8*b^2)*sinh(d*x + c)^2 + 3*a^2 + 4*a*b + 8*b^2 + 8*((3*a^2 + 4*a*b + 8*b^2)*cosh(d*x + c)^7 - 3*(3*a^2 + 4*a*b + 8*b^2)*cosh(d*x + c)^5 + 3*(3*a^2 + 4*a*b + 8*b^2)*cosh(d*x + c)^3 - (3*a^2 + 4*a*b + 8*b^2)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) + 1) + ((3*a^2 + 4*a*b + 8*b^2)*cosh(d*x + c)^8 + 8*(3*a^2 + 4*a*b + 8*b^2)*cosh(d*x + c)*sinh(d*x + c)^7 + (3*a^2 + 4*a*b + 8*b^2)*sinh(d*x + c)^8 - 4*(3*a^2 + 4*a*b + 8*b^2)*cosh(d*x + c)^6 + 4*(7*(3*a^2 + 4*a*b + 8*b^2)*cosh(d*x + c)^2 - 3*a^2 - 4*a*b - 8*b^2)*sinh(d*x + c)^6 + 8*(7*(3*a^2 + 4*a*b + 8*b^2)*cosh(d*x + c)^3 - 3*(3*a^2 + 4*a*b + 8*b^2)*cosh(d*x + c))*sinh(d*x + c)^5 + 6*(3*a^2 + 4*a*b + 8*b^2)*cosh(d*x + c)^4 + 2*(35*(3*a^2 + 4*a*b + 8*b^2)*cosh(d*x + c)^4 - 30*(3*a^2 + 4*a*b + 8*b^2)*cosh(d*x + c)^2 + 9*a^2 + 12*a*b + 24*b^2)*sinh(d*x + c)^4 + 8*(7*(3*a^2 + 4*a*b + 8*b^2)*cosh(d*x + c)^5 - 10*(3*a^2 + 4*a*b + 8*b^2)*cosh(d*x + c)^3 + 3*(3*a^2 + 4*a*b + 8*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 - 4*(3*a^2 + 4*a*b + 8*b^2)*cosh(d*x + c)^2 + 4*(7*(3*a^2 + 4*a*b + 8*b^2)*cosh(d*x + c)^6 - 15*(3*a^2 + 4*a*b + 8*b^2)*cosh(d*x + c)^4 + 9*(3*a^2 + 4*a*b + 8*b^2)*cosh(d*x + c)^2 - 3*a^2 - 4*a*b - 8*b^2)*sinh(d*x + c)^2 + 3*a^2 + 4*a*b + 8*b^2 + 8*((3*a^2 + 4*a*b + 8*b^2)*cosh(d*x + c)^7 - 3*(3*a^2 + 4*a*b + 8*b^2)*cosh(d*x + c)^5 + 3*(3*a^2 + 4*a*b + 8*b^2)*cosh(d*x + c)^3 - (3*a^2 + 4*a*b + 8*b^2)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) - 1) + 2*(7*(3*a^2 + 4*a*b)*cosh(d*x + c)^6 - 5*(11*a^2 + 4*a*b)*cosh(d*x + c)^4 - 3*(11*a^2 + 4*a*b)*cosh(d*x + c)^2 + 3*a^2 + 4*a*b)*sinh(d*x + c))/(a^3*d*cosh(d*x + c)^8 + 8*a^3*d*cosh(d*x + c)*sinh(d*x + c)^7 + a^3*d*sinh(d*x + c)^8 - 4*a^3*d*cosh(d*x + c)^6 + 6*a^3*d*cosh(d*x + c)^4 + 4*(7*a^3*d*cosh(d*x + c)^2 - a^3*d)*sinh(d*x + c)^6 - 4*a^3*d*cosh(d*x + c)^2 + 8*(7*a^3*d*cosh(d*x + c)^3 - 3*a^3*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*a^3*d*cosh(d*x + c)^4 - 30*a^3*d*cosh(d*x + c)^2 + 3*a^3*d)*sinh(d*x + c)^4 + a^3*d + 8*(7*a^3*d*cosh(d*x + c)^5 - 10*a^3*d*cosh(d*x + c)^3 + 3*a^3*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*a^3*d*cosh(d*x + c)^6 - 15*a^3*d*cosh(d*x + c)^4 + 9*a^3*d*cosh(d*x + c)^2 - a^3*d)*sinh(d*x + c)^2 + 8*(a^3*d*cosh(d*x + c)^7 - 3*a^3*d*cosh(d*x + c)^5 + 3*a^3*d*cosh(d*x + c)^3 - a^3*d*cosh(d*x + c))*sinh(d*x + c)), 1/8*(2*(3*a^2 + 4*a*b)*cosh(d*x + c)^7 + 14*(3*a^2 + 4*a*b)*cosh(d*x + c)*sinh(d*x + c)^6 + 2*(3*a^2 + 4*a*b)*sinh(d*x + c)^7 - 2*(11*a^2 + 4*a*b)*cosh(d*x + c)^5 + 2*(21*(3*a^2 + 4*a*b)*cosh(d*x + c)^2 - 11*a^2 - 4*a*b)*sinh(d*x + c)^5 + 10*(7*(3*a^2 + 4*a*b)*cosh(d*x + c)^3 - (11*a^2 + 4*a*b)*cosh(d*x + c))*sinh(d*x + c)^4 - 2*(11*a^2 + 4*a*b)*cosh(d*x + c)^3 + 2*(35*(3*a^2 + 4*a*b)*cosh(d*x + c)^4 - 10*(11*a^2 + 4*a*b)*cosh(d*x + c)^2 - 11*a^2 - 4*a*b)*sinh(d*x + c)^3 + 2*(21*(3*a^2 + 4*a*b)*cosh(d*x + c)^5 - 10*(11*a^2 + 4*a*b)*cosh(d*x + c)^3 - 3*(11*a^2 + 4*a*b)*cosh(d*x + c))*sinh(d*x + c)^2 - 8*(b^2*cosh(d*x + c)^8 + 8*b^2*cosh(d*x + c)*sinh(d*x + c)^7 + b^2*sinh(d*x + c)^8 - 4*b^2*cosh(d*x + c)^6 + 4*(7*b^2*cosh(d*x + c)^2 - b^2)*sinh(d*x + c)^6 + 6*b^2*cosh(d*x + c)^4 + 8*(7*b^2*cosh(d*x + c)^3 - 3*b^2*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*b^2*cosh(d*x + c)^4 - 30*b^2*cosh(d*x + c)^2 + 3*b^2)*sinh(d*x + c)^4 - 4*b^2*cosh(d*x + c)^2 + 8*(7*b^2*cosh(d*x + c)^5 - 10*b^2*cosh(d*x + c)^3 + 3*b^2*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*b^2*cosh(d*x + c)^6 - 15*b^2*cosh(d*x + c)^4 + 9*b^2*cosh(d*x + c)^2 - b^2)*sinh(d*x + c)^2 + b^2 + 8*(b^2*cosh(d*x + c)^7 - 3*b^2*cosh(d*x + c)^5 + 3*b^2*cosh(d*x + c)^3 - b^2*cosh(d*x + c))*sinh(d*x + c))*sqrt(b/(a - b))*arctan(1/2*sqrt(b/(a - b))*(cosh(d*x + c) + sinh(d*x + c))) + 8*(b^2*cosh(d*x + c)^8 + 8*b^2*cosh(d*x + c)*sinh(d*x + c)^7 + b^2*sinh(d*x + c)^8 - 4*b^2*cosh(d*x + c)^6 + 4*(7*b^2*cosh(d*x + c)^2 - b^2)*sinh(d*x + c)^6 + 6*b^2*cosh(d*x + c)^4 + 8*(7*b^2*cosh(d*x + c)^3 - 3*b^2*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*b^2*cosh(d*x + c)^4 - 30*b^2*cosh(d*x + c)^2 + 3*b^2)*sinh(d*x + c)^4 - 4*b^2*cosh(d*x + c)^2 + 8*(7*b^2*cosh(d*x + c)^5 - 10*b^2*cosh(d*x + c)^3 + 3*b^2*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*b^2*cosh(d*x + c)^6 - 15*b^2*cosh(d*x + c)^4 + 9*b^2*cosh(d*x + c)^2 - b^2)*sinh(d*x + c)^2 + b^2 + 8*(b^2*cosh(d*x + c)^7 - 3*b^2*cosh(d*x + c)^5 + 3*b^2*cosh(d*x + c)^3 - b^2*cosh(d*x + c))*sinh(d*x + c))*sqrt(b/(a - b))*arctan(1/2*(b*cosh(d*x + c)^3 + 3*b*cosh(d*x + c)*sinh(d*x + c)^2 + b*sinh(d*x + c)^3 + (4*a - 3*b)*cosh(d*x + c) + (3*b*cosh(d*x + c)^2 + 4*a - 3*b)*sinh(d*x + c))*sqrt(b/(a - b))/b) + 2*(3*a^2 + 4*a*b)*cosh(d*x + c) - ((3*a^2 + 4*a*b + 8*b^2)*cosh(d*x + c)^8 + 8*(3*a^2 + 4*a*b + 8*b^2)*cosh(d*x + c)*sinh(d*x + c)^7 + (3*a^2 + 4*a*b + 8*b^2)*sinh(d*x + c)^8 - 4*(3*a^2 + 4*a*b + 8*b^2)*cosh(d*x + c)^6 + 4*(7*(3*a^2 + 4*a*b + 8*b^2)*cosh(d*x + c)^2 - 3*a^2 - 4*a*b - 8*b^2)*sinh(d*x + c)^6 + 8*(7*(3*a^2 + 4*a*b + 8*b^2)*cosh(d*x + c)^3 - 3*(3*a^2 + 4*a*b + 8*b^2)*cosh(d*x + c))*sinh(d*x + c)^5 + 6*(3*a^2 + 4*a*b + 8*b^2)*cosh(d*x + c)^4 + 2*(35*(3*a^2 + 4*a*b + 8*b^2)*cosh(d*x + c)^4 - 30*(3*a^2 + 4*a*b + 8*b^2)*cosh(d*x + c)^2 + 9*a^2 + 12*a*b + 24*b^2)*sinh(d*x + c)^4 + 8*(7*(3*a^2 + 4*a*b + 8*b^2)*cosh(d*x + c)^5 - 10*(3*a^2 + 4*a*b + 8*b^2)*cosh(d*x + c)^3 + 3*(3*a^2 + 4*a*b + 8*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 - 4*(3*a^2 + 4*a*b + 8*b^2)*cosh(d*x + c)^2 + 4*(7*(3*a^2 + 4*a*b + 8*b^2)*cosh(d*x + c)^6 - 15*(3*a^2 + 4*a*b + 8*b^2)*cosh(d*x + c)^4 + 9*(3*a^2 + 4*a*b + 8*b^2)*cosh(d*x + c)^2 - 3*a^2 - 4*a*b - 8*b^2)*sinh(d*x + c)^2 + 3*a^2 + 4*a*b + 8*b^2 + 8*((3*a^2 + 4*a*b + 8*b^2)*cosh(d*x + c)^7 - 3*(3*a^2 + 4*a*b + 8*b^2)*cosh(d*x + c)^5 + 3*(3*a^2 + 4*a*b + 8*b^2)*cosh(d*x + c)^3 - (3*a^2 + 4*a*b + 8*b^2)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) + 1) + ((3*a^2 + 4*a*b + 8*b^2)*cosh(d*x + c)^8 + 8*(3*a^2 + 4*a*b + 8*b^2)*cosh(d*x + c)*sinh(d*x + c)^7 + (3*a^2 + 4*a*b + 8*b^2)*sinh(d*x + c)^8 - 4*(3*a^2 + 4*a*b + 8*b^2)*cosh(d*x + c)^6 + 4*(7*(3*a^2 + 4*a*b + 8*b^2)*cosh(d*x + c)^2 - 3*a^2 - 4*a*b - 8*b^2)*sinh(d*x + c)^6 + 8*(7*(3*a^2 + 4*a*b + 8*b^2)*cosh(d*x + c)^3 - 3*(3*a^2 + 4*a*b + 8*b^2)*cosh(d*x + c))*sinh(d*x + c)^5 + 6*(3*a^2 + 4*a*b + 8*b^2)*cosh(d*x + c)^4 + 2*(35*(3*a^2 + 4*a*b + 8*b^2)*cosh(d*x + c)^4 - 30*(3*a^2 + 4*a*b + 8*b^2)*cosh(d*x + c)^2 + 9*a^2 + 12*a*b + 24*b^2)*sinh(d*x + c)^4 + 8*(7*(3*a^2 + 4*a*b + 8*b^2)*cosh(d*x + c)^5 - 10*(3*a^2 + 4*a*b + 8*b^2)*cosh(d*x + c)^3 + 3*(3*a^2 + 4*a*b + 8*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 - 4*(3*a^2 + 4*a*b + 8*b^2)*cosh(d*x + c)^2 + 4*(7*(3*a^2 + 4*a*b + 8*b^2)*cosh(d*x + c)^6 - 15*(3*a^2 + 4*a*b + 8*b^2)*cosh(d*x + c)^4 + 9*(3*a^2 + 4*a*b + 8*b^2)*cosh(d*x + c)^2 - 3*a^2 - 4*a*b - 8*b^2)*sinh(d*x + c)^2 + 3*a^2 + 4*a*b + 8*b^2 + 8*((3*a^2 + 4*a*b + 8*b^2)*cosh(d*x + c)^7 - 3*(3*a^2 + 4*a*b + 8*b^2)*cosh(d*x + c)^5 + 3*(3*a^2 + 4*a*b + 8*b^2)*cosh(d*x + c)^3 - (3*a^2 + 4*a*b + 8*b^2)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) - 1) + 2*(7*(3*a^2 + 4*a*b)*cosh(d*x + c)^6 - 5*(11*a^2 + 4*a*b)*cosh(d*x + c)^4 - 3*(11*a^2 + 4*a*b)*cosh(d*x + c)^2 + 3*a^2 + 4*a*b)*sinh(d*x + c))/(a^3*d*cosh(d*x + c)^8 + 8*a^3*d*cosh(d*x + c)*sinh(d*x + c)^7 + a^3*d*sinh(d*x + c)^8 - 4*a^3*d*cosh(d*x + c)^6 + 6*a^3*d*cosh(d*x + c)^4 + 4*(7*a^3*d*cosh(d*x + c)^2 - a^3*d)*sinh(d*x + c)^6 - 4*a^3*d*cosh(d*x + c)^2 + 8*(7*a^3*d*cosh(d*x + c)^3 - 3*a^3*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*a^3*d*cosh(d*x + c)^4 - 30*a^3*d*cosh(d*x + c)^2 + 3*a^3*d)*sinh(d*x + c)^4 + a^3*d + 8*(7*a^3*d*cosh(d*x + c)^5 - 10*a^3*d*cosh(d*x + c)^3 + 3*a^3*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*a^3*d*cosh(d*x + c)^6 - 15*a^3*d*cosh(d*x + c)^4 + 9*a^3*d*cosh(d*x + c)^2 - a^3*d)*sinh(d*x + c)^2 + 8*(a^3*d*cosh(d*x + c)^7 - 3*a^3*d*cosh(d*x + c)^5 + 3*a^3*d*cosh(d*x + c)^3 - a^3*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
41,1,4540,0,0.614727," ","integrate(csch(d*x+c)^6/(a+b*sinh(d*x+c)^2),x, algorithm=""fricas"")","\left[-\frac{60 \, {\left(a^{2} b^{2} - a b^{3}\right)} \cosh\left(d x + c\right)^{8} + 480 \, {\left(a^{2} b^{2} - a b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + 60 \, {\left(a^{2} b^{2} - a b^{3}\right)} \sinh\left(d x + c\right)^{8} - 120 \, {\left(a^{3} b + a^{2} b^{2} - 2 \, a b^{3}\right)} \cosh\left(d x + c\right)^{6} - 120 \, {\left(a^{3} b + a^{2} b^{2} - 2 \, a b^{3} - 14 \, {\left(a^{2} b^{2} - a b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 240 \, {\left(14 \, {\left(a^{2} b^{2} - a b^{3}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{3} b + a^{2} b^{2} - 2 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 40 \, {\left(8 \, a^{4} - a^{3} b + 2 \, a^{2} b^{2} - 9 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} + 40 \, {\left(105 \, {\left(a^{2} b^{2} - a b^{3}\right)} \cosh\left(d x + c\right)^{4} + 8 \, a^{4} - a^{3} b + 2 \, a^{2} b^{2} - 9 \, a b^{3} - 45 \, {\left(a^{3} b + a^{2} b^{2} - 2 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 32 \, a^{4} + 8 \, a^{3} b + 20 \, a^{2} b^{2} - 60 \, a b^{3} + 160 \, {\left(21 \, {\left(a^{2} b^{2} - a b^{3}\right)} \cosh\left(d x + c\right)^{5} - 15 \, {\left(a^{3} b + a^{2} b^{2} - 2 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{4} - a^{3} b + 2 \, a^{2} b^{2} - 9 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 40 \, {\left(4 \, a^{4} + a^{3} b + a^{2} b^{2} - 6 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2} + 40 \, {\left(42 \, {\left(a^{2} b^{2} - a b^{3}\right)} \cosh\left(d x + c\right)^{6} - 45 \, {\left(a^{3} b + a^{2} b^{2} - 2 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} - 4 \, a^{4} - a^{3} b - a^{2} b^{2} + 6 \, a b^{3} + 6 \, {\left(8 \, a^{4} - a^{3} b + 2 \, a^{2} b^{2} - 9 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} - 15 \, {\left(b^{3} \cosh\left(d x + c\right)^{10} + 10 \, b^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + b^{3} \sinh\left(d x + c\right)^{10} - 5 \, b^{3} \cosh\left(d x + c\right)^{8} + 10 \, b^{3} \cosh\left(d x + c\right)^{6} + 5 \, {\left(9 \, b^{3} \cosh\left(d x + c\right)^{2} - b^{3}\right)} \sinh\left(d x + c\right)^{8} + 40 \, {\left(3 \, b^{3} \cosh\left(d x + c\right)^{3} - b^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} - 10 \, b^{3} \cosh\left(d x + c\right)^{4} + 10 \, {\left(21 \, b^{3} \cosh\left(d x + c\right)^{4} - 14 \, b^{3} \cosh\left(d x + c\right)^{2} + b^{3}\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(63 \, b^{3} \cosh\left(d x + c\right)^{5} - 70 \, b^{3} \cosh\left(d x + c\right)^{3} + 15 \, b^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 5 \, b^{3} \cosh\left(d x + c\right)^{2} + 10 \, {\left(21 \, b^{3} \cosh\left(d x + c\right)^{6} - 35 \, b^{3} \cosh\left(d x + c\right)^{4} + 15 \, b^{3} \cosh\left(d x + c\right)^{2} - b^{3}\right)} \sinh\left(d x + c\right)^{4} + 40 \, {\left(3 \, b^{3} \cosh\left(d x + c\right)^{7} - 7 \, b^{3} \cosh\left(d x + c\right)^{5} + 5 \, b^{3} \cosh\left(d x + c\right)^{3} - b^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - b^{3} + 5 \, {\left(9 \, b^{3} \cosh\left(d x + c\right)^{8} - 28 \, b^{3} \cosh\left(d x + c\right)^{6} + 30 \, b^{3} \cosh\left(d x + c\right)^{4} - 12 \, b^{3} \cosh\left(d x + c\right)^{2} + b^{3}\right)} \sinh\left(d x + c\right)^{2} + 10 \, {\left(b^{3} \cosh\left(d x + c\right)^{9} - 4 \, b^{3} \cosh\left(d x + c\right)^{7} + 6 \, b^{3} \cosh\left(d x + c\right)^{5} - 4 \, b^{3} \cosh\left(d x + c\right)^{3} + b^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{a^{2} - a b} \log\left(\frac{b^{2} \cosh\left(d x + c\right)^{4} + 4 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{2} \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(d x + c\right)^{2} + 2 \, a b - b^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, a^{2} - 8 \, a b + b^{2} + 4 \, {\left(b^{2} \cosh\left(d x + c\right)^{3} + {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + 4 \, {\left(b \cosh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b \sinh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sqrt{a^{2} - a b}}{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b}\right) + 80 \, {\left(6 \, {\left(a^{2} b^{2} - a b^{3}\right)} \cosh\left(d x + c\right)^{7} - 9 \, {\left(a^{3} b + a^{2} b^{2} - 2 \, a b^{3}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(8 \, a^{4} - a^{3} b + 2 \, a^{2} b^{2} - 9 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} - {\left(4 \, a^{4} + a^{3} b + a^{2} b^{2} - 6 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{30 \, {\left({\left(a^{5} - a^{4} b\right)} d \cosh\left(d x + c\right)^{10} + 10 \, {\left(a^{5} - a^{4} b\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + {\left(a^{5} - a^{4} b\right)} d \sinh\left(d x + c\right)^{10} - 5 \, {\left(a^{5} - a^{4} b\right)} d \cosh\left(d x + c\right)^{8} + 5 \, {\left(9 \, {\left(a^{5} - a^{4} b\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{5} - a^{4} b\right)} d\right)} \sinh\left(d x + c\right)^{8} + 10 \, {\left(a^{5} - a^{4} b\right)} d \cosh\left(d x + c\right)^{6} + 40 \, {\left(3 \, {\left(a^{5} - a^{4} b\right)} d \cosh\left(d x + c\right)^{3} - {\left(a^{5} - a^{4} b\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 10 \, {\left(21 \, {\left(a^{5} - a^{4} b\right)} d \cosh\left(d x + c\right)^{4} - 14 \, {\left(a^{5} - a^{4} b\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{5} - a^{4} b\right)} d\right)} \sinh\left(d x + c\right)^{6} - 10 \, {\left(a^{5} - a^{4} b\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(63 \, {\left(a^{5} - a^{4} b\right)} d \cosh\left(d x + c\right)^{5} - 70 \, {\left(a^{5} - a^{4} b\right)} d \cosh\left(d x + c\right)^{3} + 15 \, {\left(a^{5} - a^{4} b\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 10 \, {\left(21 \, {\left(a^{5} - a^{4} b\right)} d \cosh\left(d x + c\right)^{6} - 35 \, {\left(a^{5} - a^{4} b\right)} d \cosh\left(d x + c\right)^{4} + 15 \, {\left(a^{5} - a^{4} b\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{5} - a^{4} b\right)} d\right)} \sinh\left(d x + c\right)^{4} + 5 \, {\left(a^{5} - a^{4} b\right)} d \cosh\left(d x + c\right)^{2} + 40 \, {\left(3 \, {\left(a^{5} - a^{4} b\right)} d \cosh\left(d x + c\right)^{7} - 7 \, {\left(a^{5} - a^{4} b\right)} d \cosh\left(d x + c\right)^{5} + 5 \, {\left(a^{5} - a^{4} b\right)} d \cosh\left(d x + c\right)^{3} - {\left(a^{5} - a^{4} b\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 5 \, {\left(9 \, {\left(a^{5} - a^{4} b\right)} d \cosh\left(d x + c\right)^{8} - 28 \, {\left(a^{5} - a^{4} b\right)} d \cosh\left(d x + c\right)^{6} + 30 \, {\left(a^{5} - a^{4} b\right)} d \cosh\left(d x + c\right)^{4} - 12 \, {\left(a^{5} - a^{4} b\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{5} - a^{4} b\right)} d\right)} \sinh\left(d x + c\right)^{2} - {\left(a^{5} - a^{4} b\right)} d + 10 \, {\left({\left(a^{5} - a^{4} b\right)} d \cosh\left(d x + c\right)^{9} - 4 \, {\left(a^{5} - a^{4} b\right)} d \cosh\left(d x + c\right)^{7} + 6 \, {\left(a^{5} - a^{4} b\right)} d \cosh\left(d x + c\right)^{5} - 4 \, {\left(a^{5} - a^{4} b\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{5} - a^{4} b\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}, -\frac{30 \, {\left(a^{2} b^{2} - a b^{3}\right)} \cosh\left(d x + c\right)^{8} + 240 \, {\left(a^{2} b^{2} - a b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + 30 \, {\left(a^{2} b^{2} - a b^{3}\right)} \sinh\left(d x + c\right)^{8} - 60 \, {\left(a^{3} b + a^{2} b^{2} - 2 \, a b^{3}\right)} \cosh\left(d x + c\right)^{6} - 60 \, {\left(a^{3} b + a^{2} b^{2} - 2 \, a b^{3} - 14 \, {\left(a^{2} b^{2} - a b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 120 \, {\left(14 \, {\left(a^{2} b^{2} - a b^{3}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{3} b + a^{2} b^{2} - 2 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 20 \, {\left(8 \, a^{4} - a^{3} b + 2 \, a^{2} b^{2} - 9 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} + 20 \, {\left(105 \, {\left(a^{2} b^{2} - a b^{3}\right)} \cosh\left(d x + c\right)^{4} + 8 \, a^{4} - a^{3} b + 2 \, a^{2} b^{2} - 9 \, a b^{3} - 45 \, {\left(a^{3} b + a^{2} b^{2} - 2 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 16 \, a^{4} + 4 \, a^{3} b + 10 \, a^{2} b^{2} - 30 \, a b^{3} + 80 \, {\left(21 \, {\left(a^{2} b^{2} - a b^{3}\right)} \cosh\left(d x + c\right)^{5} - 15 \, {\left(a^{3} b + a^{2} b^{2} - 2 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{4} - a^{3} b + 2 \, a^{2} b^{2} - 9 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 20 \, {\left(4 \, a^{4} + a^{3} b + a^{2} b^{2} - 6 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2} + 20 \, {\left(42 \, {\left(a^{2} b^{2} - a b^{3}\right)} \cosh\left(d x + c\right)^{6} - 45 \, {\left(a^{3} b + a^{2} b^{2} - 2 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} - 4 \, a^{4} - a^{3} b - a^{2} b^{2} + 6 \, a b^{3} + 6 \, {\left(8 \, a^{4} - a^{3} b + 2 \, a^{2} b^{2} - 9 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} - 15 \, {\left(b^{3} \cosh\left(d x + c\right)^{10} + 10 \, b^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + b^{3} \sinh\left(d x + c\right)^{10} - 5 \, b^{3} \cosh\left(d x + c\right)^{8} + 10 \, b^{3} \cosh\left(d x + c\right)^{6} + 5 \, {\left(9 \, b^{3} \cosh\left(d x + c\right)^{2} - b^{3}\right)} \sinh\left(d x + c\right)^{8} + 40 \, {\left(3 \, b^{3} \cosh\left(d x + c\right)^{3} - b^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} - 10 \, b^{3} \cosh\left(d x + c\right)^{4} + 10 \, {\left(21 \, b^{3} \cosh\left(d x + c\right)^{4} - 14 \, b^{3} \cosh\left(d x + c\right)^{2} + b^{3}\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(63 \, b^{3} \cosh\left(d x + c\right)^{5} - 70 \, b^{3} \cosh\left(d x + c\right)^{3} + 15 \, b^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 5 \, b^{3} \cosh\left(d x + c\right)^{2} + 10 \, {\left(21 \, b^{3} \cosh\left(d x + c\right)^{6} - 35 \, b^{3} \cosh\left(d x + c\right)^{4} + 15 \, b^{3} \cosh\left(d x + c\right)^{2} - b^{3}\right)} \sinh\left(d x + c\right)^{4} + 40 \, {\left(3 \, b^{3} \cosh\left(d x + c\right)^{7} - 7 \, b^{3} \cosh\left(d x + c\right)^{5} + 5 \, b^{3} \cosh\left(d x + c\right)^{3} - b^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - b^{3} + 5 \, {\left(9 \, b^{3} \cosh\left(d x + c\right)^{8} - 28 \, b^{3} \cosh\left(d x + c\right)^{6} + 30 \, b^{3} \cosh\left(d x + c\right)^{4} - 12 \, b^{3} \cosh\left(d x + c\right)^{2} + b^{3}\right)} \sinh\left(d x + c\right)^{2} + 10 \, {\left(b^{3} \cosh\left(d x + c\right)^{9} - 4 \, b^{3} \cosh\left(d x + c\right)^{7} + 6 \, b^{3} \cosh\left(d x + c\right)^{5} - 4 \, b^{3} \cosh\left(d x + c\right)^{3} + b^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-a^{2} + a b} \arctan\left(-\frac{{\left(b \cosh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b \sinh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sqrt{-a^{2} + a b}}{2 \, {\left(a^{2} - a b\right)}}\right) + 40 \, {\left(6 \, {\left(a^{2} b^{2} - a b^{3}\right)} \cosh\left(d x + c\right)^{7} - 9 \, {\left(a^{3} b + a^{2} b^{2} - 2 \, a b^{3}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(8 \, a^{4} - a^{3} b + 2 \, a^{2} b^{2} - 9 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} - {\left(4 \, a^{4} + a^{3} b + a^{2} b^{2} - 6 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{15 \, {\left({\left(a^{5} - a^{4} b\right)} d \cosh\left(d x + c\right)^{10} + 10 \, {\left(a^{5} - a^{4} b\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + {\left(a^{5} - a^{4} b\right)} d \sinh\left(d x + c\right)^{10} - 5 \, {\left(a^{5} - a^{4} b\right)} d \cosh\left(d x + c\right)^{8} + 5 \, {\left(9 \, {\left(a^{5} - a^{4} b\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{5} - a^{4} b\right)} d\right)} \sinh\left(d x + c\right)^{8} + 10 \, {\left(a^{5} - a^{4} b\right)} d \cosh\left(d x + c\right)^{6} + 40 \, {\left(3 \, {\left(a^{5} - a^{4} b\right)} d \cosh\left(d x + c\right)^{3} - {\left(a^{5} - a^{4} b\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 10 \, {\left(21 \, {\left(a^{5} - a^{4} b\right)} d \cosh\left(d x + c\right)^{4} - 14 \, {\left(a^{5} - a^{4} b\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{5} - a^{4} b\right)} d\right)} \sinh\left(d x + c\right)^{6} - 10 \, {\left(a^{5} - a^{4} b\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(63 \, {\left(a^{5} - a^{4} b\right)} d \cosh\left(d x + c\right)^{5} - 70 \, {\left(a^{5} - a^{4} b\right)} d \cosh\left(d x + c\right)^{3} + 15 \, {\left(a^{5} - a^{4} b\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 10 \, {\left(21 \, {\left(a^{5} - a^{4} b\right)} d \cosh\left(d x + c\right)^{6} - 35 \, {\left(a^{5} - a^{4} b\right)} d \cosh\left(d x + c\right)^{4} + 15 \, {\left(a^{5} - a^{4} b\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{5} - a^{4} b\right)} d\right)} \sinh\left(d x + c\right)^{4} + 5 \, {\left(a^{5} - a^{4} b\right)} d \cosh\left(d x + c\right)^{2} + 40 \, {\left(3 \, {\left(a^{5} - a^{4} b\right)} d \cosh\left(d x + c\right)^{7} - 7 \, {\left(a^{5} - a^{4} b\right)} d \cosh\left(d x + c\right)^{5} + 5 \, {\left(a^{5} - a^{4} b\right)} d \cosh\left(d x + c\right)^{3} - {\left(a^{5} - a^{4} b\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 5 \, {\left(9 \, {\left(a^{5} - a^{4} b\right)} d \cosh\left(d x + c\right)^{8} - 28 \, {\left(a^{5} - a^{4} b\right)} d \cosh\left(d x + c\right)^{6} + 30 \, {\left(a^{5} - a^{4} b\right)} d \cosh\left(d x + c\right)^{4} - 12 \, {\left(a^{5} - a^{4} b\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{5} - a^{4} b\right)} d\right)} \sinh\left(d x + c\right)^{2} - {\left(a^{5} - a^{4} b\right)} d + 10 \, {\left({\left(a^{5} - a^{4} b\right)} d \cosh\left(d x + c\right)^{9} - 4 \, {\left(a^{5} - a^{4} b\right)} d \cosh\left(d x + c\right)^{7} + 6 \, {\left(a^{5} - a^{4} b\right)} d \cosh\left(d x + c\right)^{5} - 4 \, {\left(a^{5} - a^{4} b\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{5} - a^{4} b\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[-1/30*(60*(a^2*b^2 - a*b^3)*cosh(d*x + c)^8 + 480*(a^2*b^2 - a*b^3)*cosh(d*x + c)*sinh(d*x + c)^7 + 60*(a^2*b^2 - a*b^3)*sinh(d*x + c)^8 - 120*(a^3*b + a^2*b^2 - 2*a*b^3)*cosh(d*x + c)^6 - 120*(a^3*b + a^2*b^2 - 2*a*b^3 - 14*(a^2*b^2 - a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 240*(14*(a^2*b^2 - a*b^3)*cosh(d*x + c)^3 - 3*(a^3*b + a^2*b^2 - 2*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^5 + 40*(8*a^4 - a^3*b + 2*a^2*b^2 - 9*a*b^3)*cosh(d*x + c)^4 + 40*(105*(a^2*b^2 - a*b^3)*cosh(d*x + c)^4 + 8*a^4 - a^3*b + 2*a^2*b^2 - 9*a*b^3 - 45*(a^3*b + a^2*b^2 - 2*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 32*a^4 + 8*a^3*b + 20*a^2*b^2 - 60*a*b^3 + 160*(21*(a^2*b^2 - a*b^3)*cosh(d*x + c)^5 - 15*(a^3*b + a^2*b^2 - 2*a*b^3)*cosh(d*x + c)^3 + (8*a^4 - a^3*b + 2*a^2*b^2 - 9*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 - 40*(4*a^4 + a^3*b + a^2*b^2 - 6*a*b^3)*cosh(d*x + c)^2 + 40*(42*(a^2*b^2 - a*b^3)*cosh(d*x + c)^6 - 45*(a^3*b + a^2*b^2 - 2*a*b^3)*cosh(d*x + c)^4 - 4*a^4 - a^3*b - a^2*b^2 + 6*a*b^3 + 6*(8*a^4 - a^3*b + 2*a^2*b^2 - 9*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - 15*(b^3*cosh(d*x + c)^10 + 10*b^3*cosh(d*x + c)*sinh(d*x + c)^9 + b^3*sinh(d*x + c)^10 - 5*b^3*cosh(d*x + c)^8 + 10*b^3*cosh(d*x + c)^6 + 5*(9*b^3*cosh(d*x + c)^2 - b^3)*sinh(d*x + c)^8 + 40*(3*b^3*cosh(d*x + c)^3 - b^3*cosh(d*x + c))*sinh(d*x + c)^7 - 10*b^3*cosh(d*x + c)^4 + 10*(21*b^3*cosh(d*x + c)^4 - 14*b^3*cosh(d*x + c)^2 + b^3)*sinh(d*x + c)^6 + 4*(63*b^3*cosh(d*x + c)^5 - 70*b^3*cosh(d*x + c)^3 + 15*b^3*cosh(d*x + c))*sinh(d*x + c)^5 + 5*b^3*cosh(d*x + c)^2 + 10*(21*b^3*cosh(d*x + c)^6 - 35*b^3*cosh(d*x + c)^4 + 15*b^3*cosh(d*x + c)^2 - b^3)*sinh(d*x + c)^4 + 40*(3*b^3*cosh(d*x + c)^7 - 7*b^3*cosh(d*x + c)^5 + 5*b^3*cosh(d*x + c)^3 - b^3*cosh(d*x + c))*sinh(d*x + c)^3 - b^3 + 5*(9*b^3*cosh(d*x + c)^8 - 28*b^3*cosh(d*x + c)^6 + 30*b^3*cosh(d*x + c)^4 - 12*b^3*cosh(d*x + c)^2 + b^3)*sinh(d*x + c)^2 + 10*(b^3*cosh(d*x + c)^9 - 4*b^3*cosh(d*x + c)^7 + 6*b^3*cosh(d*x + c)^5 - 4*b^3*cosh(d*x + c)^3 + b^3*cosh(d*x + c))*sinh(d*x + c))*sqrt(a^2 - a*b)*log((b^2*cosh(d*x + c)^4 + 4*b^2*cosh(d*x + c)*sinh(d*x + c)^3 + b^2*sinh(d*x + c)^4 + 2*(2*a*b - b^2)*cosh(d*x + c)^2 + 2*(3*b^2*cosh(d*x + c)^2 + 2*a*b - b^2)*sinh(d*x + c)^2 + 8*a^2 - 8*a*b + b^2 + 4*(b^2*cosh(d*x + c)^3 + (2*a*b - b^2)*cosh(d*x + c))*sinh(d*x + c) + 4*(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + 2*a - b)*sqrt(a^2 - a*b))/(b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 + 2*(2*a - b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 + 2*a - b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 + (2*a - b)*cosh(d*x + c))*sinh(d*x + c) + b)) + 80*(6*(a^2*b^2 - a*b^3)*cosh(d*x + c)^7 - 9*(a^3*b + a^2*b^2 - 2*a*b^3)*cosh(d*x + c)^5 + 2*(8*a^4 - a^3*b + 2*a^2*b^2 - 9*a*b^3)*cosh(d*x + c)^3 - (4*a^4 + a^3*b + a^2*b^2 - 6*a*b^3)*cosh(d*x + c))*sinh(d*x + c))/((a^5 - a^4*b)*d*cosh(d*x + c)^10 + 10*(a^5 - a^4*b)*d*cosh(d*x + c)*sinh(d*x + c)^9 + (a^5 - a^4*b)*d*sinh(d*x + c)^10 - 5*(a^5 - a^4*b)*d*cosh(d*x + c)^8 + 5*(9*(a^5 - a^4*b)*d*cosh(d*x + c)^2 - (a^5 - a^4*b)*d)*sinh(d*x + c)^8 + 10*(a^5 - a^4*b)*d*cosh(d*x + c)^6 + 40*(3*(a^5 - a^4*b)*d*cosh(d*x + c)^3 - (a^5 - a^4*b)*d*cosh(d*x + c))*sinh(d*x + c)^7 + 10*(21*(a^5 - a^4*b)*d*cosh(d*x + c)^4 - 14*(a^5 - a^4*b)*d*cosh(d*x + c)^2 + (a^5 - a^4*b)*d)*sinh(d*x + c)^6 - 10*(a^5 - a^4*b)*d*cosh(d*x + c)^4 + 4*(63*(a^5 - a^4*b)*d*cosh(d*x + c)^5 - 70*(a^5 - a^4*b)*d*cosh(d*x + c)^3 + 15*(a^5 - a^4*b)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 10*(21*(a^5 - a^4*b)*d*cosh(d*x + c)^6 - 35*(a^5 - a^4*b)*d*cosh(d*x + c)^4 + 15*(a^5 - a^4*b)*d*cosh(d*x + c)^2 - (a^5 - a^4*b)*d)*sinh(d*x + c)^4 + 5*(a^5 - a^4*b)*d*cosh(d*x + c)^2 + 40*(3*(a^5 - a^4*b)*d*cosh(d*x + c)^7 - 7*(a^5 - a^4*b)*d*cosh(d*x + c)^5 + 5*(a^5 - a^4*b)*d*cosh(d*x + c)^3 - (a^5 - a^4*b)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 5*(9*(a^5 - a^4*b)*d*cosh(d*x + c)^8 - 28*(a^5 - a^4*b)*d*cosh(d*x + c)^6 + 30*(a^5 - a^4*b)*d*cosh(d*x + c)^4 - 12*(a^5 - a^4*b)*d*cosh(d*x + c)^2 + (a^5 - a^4*b)*d)*sinh(d*x + c)^2 - (a^5 - a^4*b)*d + 10*((a^5 - a^4*b)*d*cosh(d*x + c)^9 - 4*(a^5 - a^4*b)*d*cosh(d*x + c)^7 + 6*(a^5 - a^4*b)*d*cosh(d*x + c)^5 - 4*(a^5 - a^4*b)*d*cosh(d*x + c)^3 + (a^5 - a^4*b)*d*cosh(d*x + c))*sinh(d*x + c)), -1/15*(30*(a^2*b^2 - a*b^3)*cosh(d*x + c)^8 + 240*(a^2*b^2 - a*b^3)*cosh(d*x + c)*sinh(d*x + c)^7 + 30*(a^2*b^2 - a*b^3)*sinh(d*x + c)^8 - 60*(a^3*b + a^2*b^2 - 2*a*b^3)*cosh(d*x + c)^6 - 60*(a^3*b + a^2*b^2 - 2*a*b^3 - 14*(a^2*b^2 - a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 120*(14*(a^2*b^2 - a*b^3)*cosh(d*x + c)^3 - 3*(a^3*b + a^2*b^2 - 2*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^5 + 20*(8*a^4 - a^3*b + 2*a^2*b^2 - 9*a*b^3)*cosh(d*x + c)^4 + 20*(105*(a^2*b^2 - a*b^3)*cosh(d*x + c)^4 + 8*a^4 - a^3*b + 2*a^2*b^2 - 9*a*b^3 - 45*(a^3*b + a^2*b^2 - 2*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 16*a^4 + 4*a^3*b + 10*a^2*b^2 - 30*a*b^3 + 80*(21*(a^2*b^2 - a*b^3)*cosh(d*x + c)^5 - 15*(a^3*b + a^2*b^2 - 2*a*b^3)*cosh(d*x + c)^3 + (8*a^4 - a^3*b + 2*a^2*b^2 - 9*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 - 20*(4*a^4 + a^3*b + a^2*b^2 - 6*a*b^3)*cosh(d*x + c)^2 + 20*(42*(a^2*b^2 - a*b^3)*cosh(d*x + c)^6 - 45*(a^3*b + a^2*b^2 - 2*a*b^3)*cosh(d*x + c)^4 - 4*a^4 - a^3*b - a^2*b^2 + 6*a*b^3 + 6*(8*a^4 - a^3*b + 2*a^2*b^2 - 9*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - 15*(b^3*cosh(d*x + c)^10 + 10*b^3*cosh(d*x + c)*sinh(d*x + c)^9 + b^3*sinh(d*x + c)^10 - 5*b^3*cosh(d*x + c)^8 + 10*b^3*cosh(d*x + c)^6 + 5*(9*b^3*cosh(d*x + c)^2 - b^3)*sinh(d*x + c)^8 + 40*(3*b^3*cosh(d*x + c)^3 - b^3*cosh(d*x + c))*sinh(d*x + c)^7 - 10*b^3*cosh(d*x + c)^4 + 10*(21*b^3*cosh(d*x + c)^4 - 14*b^3*cosh(d*x + c)^2 + b^3)*sinh(d*x + c)^6 + 4*(63*b^3*cosh(d*x + c)^5 - 70*b^3*cosh(d*x + c)^3 + 15*b^3*cosh(d*x + c))*sinh(d*x + c)^5 + 5*b^3*cosh(d*x + c)^2 + 10*(21*b^3*cosh(d*x + c)^6 - 35*b^3*cosh(d*x + c)^4 + 15*b^3*cosh(d*x + c)^2 - b^3)*sinh(d*x + c)^4 + 40*(3*b^3*cosh(d*x + c)^7 - 7*b^3*cosh(d*x + c)^5 + 5*b^3*cosh(d*x + c)^3 - b^3*cosh(d*x + c))*sinh(d*x + c)^3 - b^3 + 5*(9*b^3*cosh(d*x + c)^8 - 28*b^3*cosh(d*x + c)^6 + 30*b^3*cosh(d*x + c)^4 - 12*b^3*cosh(d*x + c)^2 + b^3)*sinh(d*x + c)^2 + 10*(b^3*cosh(d*x + c)^9 - 4*b^3*cosh(d*x + c)^7 + 6*b^3*cosh(d*x + c)^5 - 4*b^3*cosh(d*x + c)^3 + b^3*cosh(d*x + c))*sinh(d*x + c))*sqrt(-a^2 + a*b)*arctan(-1/2*(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + 2*a - b)*sqrt(-a^2 + a*b)/(a^2 - a*b)) + 40*(6*(a^2*b^2 - a*b^3)*cosh(d*x + c)^7 - 9*(a^3*b + a^2*b^2 - 2*a*b^3)*cosh(d*x + c)^5 + 2*(8*a^4 - a^3*b + 2*a^2*b^2 - 9*a*b^3)*cosh(d*x + c)^3 - (4*a^4 + a^3*b + a^2*b^2 - 6*a*b^3)*cosh(d*x + c))*sinh(d*x + c))/((a^5 - a^4*b)*d*cosh(d*x + c)^10 + 10*(a^5 - a^4*b)*d*cosh(d*x + c)*sinh(d*x + c)^9 + (a^5 - a^4*b)*d*sinh(d*x + c)^10 - 5*(a^5 - a^4*b)*d*cosh(d*x + c)^8 + 5*(9*(a^5 - a^4*b)*d*cosh(d*x + c)^2 - (a^5 - a^4*b)*d)*sinh(d*x + c)^8 + 10*(a^5 - a^4*b)*d*cosh(d*x + c)^6 + 40*(3*(a^5 - a^4*b)*d*cosh(d*x + c)^3 - (a^5 - a^4*b)*d*cosh(d*x + c))*sinh(d*x + c)^7 + 10*(21*(a^5 - a^4*b)*d*cosh(d*x + c)^4 - 14*(a^5 - a^4*b)*d*cosh(d*x + c)^2 + (a^5 - a^4*b)*d)*sinh(d*x + c)^6 - 10*(a^5 - a^4*b)*d*cosh(d*x + c)^4 + 4*(63*(a^5 - a^4*b)*d*cosh(d*x + c)^5 - 70*(a^5 - a^4*b)*d*cosh(d*x + c)^3 + 15*(a^5 - a^4*b)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 10*(21*(a^5 - a^4*b)*d*cosh(d*x + c)^6 - 35*(a^5 - a^4*b)*d*cosh(d*x + c)^4 + 15*(a^5 - a^4*b)*d*cosh(d*x + c)^2 - (a^5 - a^4*b)*d)*sinh(d*x + c)^4 + 5*(a^5 - a^4*b)*d*cosh(d*x + c)^2 + 40*(3*(a^5 - a^4*b)*d*cosh(d*x + c)^7 - 7*(a^5 - a^4*b)*d*cosh(d*x + c)^5 + 5*(a^5 - a^4*b)*d*cosh(d*x + c)^3 - (a^5 - a^4*b)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 5*(9*(a^5 - a^4*b)*d*cosh(d*x + c)^8 - 28*(a^5 - a^4*b)*d*cosh(d*x + c)^6 + 30*(a^5 - a^4*b)*d*cosh(d*x + c)^4 - 12*(a^5 - a^4*b)*d*cosh(d*x + c)^2 + (a^5 - a^4*b)*d)*sinh(d*x + c)^2 - (a^5 - a^4*b)*d + 10*((a^5 - a^4*b)*d*cosh(d*x + c)^9 - 4*(a^5 - a^4*b)*d*cosh(d*x + c)^7 + 6*(a^5 - a^4*b)*d*cosh(d*x + c)^5 - 4*(a^5 - a^4*b)*d*cosh(d*x + c)^3 + (a^5 - a^4*b)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
42,1,1772,0,1.046909," ","integrate(sinh(d*x+c)^4/(a+b*sinh(d*x+c)^2)^2,x, algorithm=""fricas"")","\left[\frac{4 \, {\left(a b - b^{2}\right)} d x \cosh\left(d x + c\right)^{4} + 16 \, {\left(a b - b^{2}\right)} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + 4 \, {\left(a b - b^{2}\right)} d x \sinh\left(d x + c\right)^{4} + 4 \, {\left(a b - b^{2}\right)} d x + 4 \, {\left(2 \, {\left(2 \, a^{2} - 3 \, a b + b^{2}\right)} d x + 2 \, a^{2} - a b\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(6 \, {\left(a b - b^{2}\right)} d x \cosh\left(d x + c\right)^{2} + 2 \, {\left(2 \, a^{2} - 3 \, a b + b^{2}\right)} d x + 2 \, a^{2} - a b\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(2 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(2 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(2 \, a b - 3 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(4 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(2 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} + 2 \, a b - 3 \, b^{2} + 4 \, {\left({\left(2 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(4 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a}{a - b}} \log\left(\frac{b^{2} \cosh\left(d x + c\right)^{4} + 4 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{2} \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(d x + c\right)^{2} + 2 \, a b - b^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, a^{2} - 8 \, a b + b^{2} + 4 \, {\left(b^{2} \cosh\left(d x + c\right)^{3} + {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + 4 \, {\left({\left(a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a b - b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a b - b^{2}\right)} \sinh\left(d x + c\right)^{2} + 2 \, a^{2} - 3 \, a b + b^{2}\right)} \sqrt{\frac{a}{a - b}}}{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b}\right) + 4 \, a b + 8 \, {\left(2 \, {\left(a b - b^{2}\right)} d x \cosh\left(d x + c\right)^{3} + {\left(2 \, {\left(2 \, a^{2} - 3 \, a b + b^{2}\right)} d x + 2 \, a^{2} - a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{4 \, {\left({\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a b^{3} - b^{4}\right)} d \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a^{2} b^{2} - 3 \, a b^{3} + b^{4}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{2} b^{2} - 3 \, a b^{3} + b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a b^{3} - b^{4}\right)} d + 4 \, {\left({\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{2} b^{2} - 3 \, a b^{3} + b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}, \frac{2 \, {\left(a b - b^{2}\right)} d x \cosh\left(d x + c\right)^{4} + 8 \, {\left(a b - b^{2}\right)} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + 2 \, {\left(a b - b^{2}\right)} d x \sinh\left(d x + c\right)^{4} + 2 \, {\left(a b - b^{2}\right)} d x + 2 \, {\left(2 \, {\left(2 \, a^{2} - 3 \, a b + b^{2}\right)} d x + 2 \, a^{2} - a b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(6 \, {\left(a b - b^{2}\right)} d x \cosh\left(d x + c\right)^{2} + 2 \, {\left(2 \, a^{2} - 3 \, a b + b^{2}\right)} d x + 2 \, a^{2} - a b\right)} \sinh\left(d x + c\right)^{2} - {\left({\left(2 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(2 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(2 \, a b - 3 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(4 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(2 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} + 2 \, a b - 3 \, b^{2} + 4 \, {\left({\left(2 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(4 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{a}{a - b}} \arctan\left(\frac{{\left(b \cosh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b \sinh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sqrt{-\frac{a}{a - b}}}{2 \, a}\right) + 2 \, a b + 4 \, {\left(2 \, {\left(a b - b^{2}\right)} d x \cosh\left(d x + c\right)^{3} + {\left(2 \, {\left(2 \, a^{2} - 3 \, a b + b^{2}\right)} d x + 2 \, a^{2} - a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{2 \, {\left({\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a b^{3} - b^{4}\right)} d \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a^{2} b^{2} - 3 \, a b^{3} + b^{4}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{2} b^{2} - 3 \, a b^{3} + b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a b^{3} - b^{4}\right)} d + 4 \, {\left({\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{2} b^{2} - 3 \, a b^{3} + b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[1/4*(4*(a*b - b^2)*d*x*cosh(d*x + c)^4 + 16*(a*b - b^2)*d*x*cosh(d*x + c)*sinh(d*x + c)^3 + 4*(a*b - b^2)*d*x*sinh(d*x + c)^4 + 4*(a*b - b^2)*d*x + 4*(2*(2*a^2 - 3*a*b + b^2)*d*x + 2*a^2 - a*b)*cosh(d*x + c)^2 + 4*(6*(a*b - b^2)*d*x*cosh(d*x + c)^2 + 2*(2*a^2 - 3*a*b + b^2)*d*x + 2*a^2 - a*b)*sinh(d*x + c)^2 + ((2*a*b - 3*b^2)*cosh(d*x + c)^4 + 4*(2*a*b - 3*b^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (2*a*b - 3*b^2)*sinh(d*x + c)^4 + 2*(4*a^2 - 8*a*b + 3*b^2)*cosh(d*x + c)^2 + 2*(3*(2*a*b - 3*b^2)*cosh(d*x + c)^2 + 4*a^2 - 8*a*b + 3*b^2)*sinh(d*x + c)^2 + 2*a*b - 3*b^2 + 4*((2*a*b - 3*b^2)*cosh(d*x + c)^3 + (4*a^2 - 8*a*b + 3*b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(a/(a - b))*log((b^2*cosh(d*x + c)^4 + 4*b^2*cosh(d*x + c)*sinh(d*x + c)^3 + b^2*sinh(d*x + c)^4 + 2*(2*a*b - b^2)*cosh(d*x + c)^2 + 2*(3*b^2*cosh(d*x + c)^2 + 2*a*b - b^2)*sinh(d*x + c)^2 + 8*a^2 - 8*a*b + b^2 + 4*(b^2*cosh(d*x + c)^3 + (2*a*b - b^2)*cosh(d*x + c))*sinh(d*x + c) + 4*((a*b - b^2)*cosh(d*x + c)^2 + 2*(a*b - b^2)*cosh(d*x + c)*sinh(d*x + c) + (a*b - b^2)*sinh(d*x + c)^2 + 2*a^2 - 3*a*b + b^2)*sqrt(a/(a - b)))/(b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 + 2*(2*a - b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 + 2*a - b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 + (2*a - b)*cosh(d*x + c))*sinh(d*x + c) + b)) + 4*a*b + 8*(2*(a*b - b^2)*d*x*cosh(d*x + c)^3 + (2*(2*a^2 - 3*a*b + b^2)*d*x + 2*a^2 - a*b)*cosh(d*x + c))*sinh(d*x + c))/((a*b^3 - b^4)*d*cosh(d*x + c)^4 + 4*(a*b^3 - b^4)*d*cosh(d*x + c)*sinh(d*x + c)^3 + (a*b^3 - b^4)*d*sinh(d*x + c)^4 + 2*(2*a^2*b^2 - 3*a*b^3 + b^4)*d*cosh(d*x + c)^2 + 2*(3*(a*b^3 - b^4)*d*cosh(d*x + c)^2 + (2*a^2*b^2 - 3*a*b^3 + b^4)*d)*sinh(d*x + c)^2 + (a*b^3 - b^4)*d + 4*((a*b^3 - b^4)*d*cosh(d*x + c)^3 + (2*a^2*b^2 - 3*a*b^3 + b^4)*d*cosh(d*x + c))*sinh(d*x + c)), 1/2*(2*(a*b - b^2)*d*x*cosh(d*x + c)^4 + 8*(a*b - b^2)*d*x*cosh(d*x + c)*sinh(d*x + c)^3 + 2*(a*b - b^2)*d*x*sinh(d*x + c)^4 + 2*(a*b - b^2)*d*x + 2*(2*(2*a^2 - 3*a*b + b^2)*d*x + 2*a^2 - a*b)*cosh(d*x + c)^2 + 2*(6*(a*b - b^2)*d*x*cosh(d*x + c)^2 + 2*(2*a^2 - 3*a*b + b^2)*d*x + 2*a^2 - a*b)*sinh(d*x + c)^2 - ((2*a*b - 3*b^2)*cosh(d*x + c)^4 + 4*(2*a*b - 3*b^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (2*a*b - 3*b^2)*sinh(d*x + c)^4 + 2*(4*a^2 - 8*a*b + 3*b^2)*cosh(d*x + c)^2 + 2*(3*(2*a*b - 3*b^2)*cosh(d*x + c)^2 + 4*a^2 - 8*a*b + 3*b^2)*sinh(d*x + c)^2 + 2*a*b - 3*b^2 + 4*((2*a*b - 3*b^2)*cosh(d*x + c)^3 + (4*a^2 - 8*a*b + 3*b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-a/(a - b))*arctan(1/2*(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + 2*a - b)*sqrt(-a/(a - b))/a) + 2*a*b + 4*(2*(a*b - b^2)*d*x*cosh(d*x + c)^3 + (2*(2*a^2 - 3*a*b + b^2)*d*x + 2*a^2 - a*b)*cosh(d*x + c))*sinh(d*x + c))/((a*b^3 - b^4)*d*cosh(d*x + c)^4 + 4*(a*b^3 - b^4)*d*cosh(d*x + c)*sinh(d*x + c)^3 + (a*b^3 - b^4)*d*sinh(d*x + c)^4 + 2*(2*a^2*b^2 - 3*a*b^3 + b^4)*d*cosh(d*x + c)^2 + 2*(3*(a*b^3 - b^4)*d*cosh(d*x + c)^2 + (2*a^2*b^2 - 3*a*b^3 + b^4)*d)*sinh(d*x + c)^2 + (a*b^3 - b^4)*d + 4*((a*b^3 - b^4)*d*cosh(d*x + c)^3 + (2*a^2*b^2 - 3*a*b^3 + b^4)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
43,1,1889,0,0.576358," ","integrate(sinh(d*x+c)^3/(a+b*sinh(d*x+c)^2)^2,x, algorithm=""fricas"")","\left[-\frac{4 \, {\left(a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right)^{3} + 12 \, {\left(a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + 4 \, {\left(a^{2} b - a b^{2}\right)} \sinh\left(d x + c\right)^{3} + {\left({\left(a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a b - 2 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a^{2} - 5 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, a^{2} - 5 \, a b + 2 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} + a b - 2 \, b^{2} + 4 \, {\left({\left(a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{2} - 5 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-a b + b^{2}} \log\left(\frac{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} - 2 \, {\left(2 \, a - 3 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} - 2 \, a + 3 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} - {\left(2 \, a - 3 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) - 4 \, {\left(\cosh\left(d x + c\right)^{3} + 3 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{3} + {\left(3 \, \cosh\left(d x + c\right)^{2} + 1\right)} \sinh\left(d x + c\right) + \cosh\left(d x + c\right)\right)} \sqrt{-a b + b^{2}} + b}{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b}\right) + 4 \, {\left(a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right) + 4 \, {\left(a^{2} b - a b^{2} + 3 \, {\left(a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)}{4 \, {\left({\left(a^{2} b^{3} - 2 \, a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{2} b^{3} - 2 \, a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{2} b^{3} - 2 \, a b^{4} + b^{5}\right)} d \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a^{3} b^{2} - 5 \, a^{2} b^{3} + 4 \, a b^{4} - b^{5}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} b^{3} - 2 \, a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{3} b^{2} - 5 \, a^{2} b^{3} + 4 \, a b^{4} - b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{2} b^{3} - 2 \, a b^{4} + b^{5}\right)} d + 4 \, {\left({\left(a^{2} b^{3} - 2 \, a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{3} b^{2} - 5 \, a^{2} b^{3} + 4 \, a b^{4} - b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}, -\frac{2 \, {\left(a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right)^{3} + 6 \, {\left(a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b - a b^{2}\right)} \sinh\left(d x + c\right)^{3} - {\left({\left(a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a b - 2 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a^{2} - 5 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, a^{2} - 5 \, a b + 2 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} + a b - 2 \, b^{2} + 4 \, {\left({\left(a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{2} - 5 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{a b - b^{2}} \arctan\left(-\frac{b \cosh\left(d x + c\right)^{3} + 3 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{3} + {\left(4 \, a - 3 \, b\right)} \cosh\left(d x + c\right) + {\left(3 \, b \cosh\left(d x + c\right)^{2} + 4 \, a - 3 \, b\right)} \sinh\left(d x + c\right)}{2 \, \sqrt{a b - b^{2}}}\right) + {\left({\left(a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a b - 2 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a^{2} - 5 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, a^{2} - 5 \, a b + 2 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} + a b - 2 \, b^{2} + 4 \, {\left({\left(a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{2} - 5 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{a b - b^{2}} \arctan\left(-\frac{\sqrt{a b - b^{2}} {\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right)}}{2 \, {\left(a - b\right)}}\right) + 2 \, {\left(a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right) + 2 \, {\left(a^{2} b - a b^{2} + 3 \, {\left(a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)}{2 \, {\left({\left(a^{2} b^{3} - 2 \, a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{2} b^{3} - 2 \, a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{2} b^{3} - 2 \, a b^{4} + b^{5}\right)} d \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a^{3} b^{2} - 5 \, a^{2} b^{3} + 4 \, a b^{4} - b^{5}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} b^{3} - 2 \, a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{3} b^{2} - 5 \, a^{2} b^{3} + 4 \, a b^{4} - b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{2} b^{3} - 2 \, a b^{4} + b^{5}\right)} d + 4 \, {\left({\left(a^{2} b^{3} - 2 \, a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{3} b^{2} - 5 \, a^{2} b^{3} + 4 \, a b^{4} - b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[-1/4*(4*(a^2*b - a*b^2)*cosh(d*x + c)^3 + 12*(a^2*b - a*b^2)*cosh(d*x + c)*sinh(d*x + c)^2 + 4*(a^2*b - a*b^2)*sinh(d*x + c)^3 + ((a*b - 2*b^2)*cosh(d*x + c)^4 + 4*(a*b - 2*b^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (a*b - 2*b^2)*sinh(d*x + c)^4 + 2*(2*a^2 - 5*a*b + 2*b^2)*cosh(d*x + c)^2 + 2*(3*(a*b - 2*b^2)*cosh(d*x + c)^2 + 2*a^2 - 5*a*b + 2*b^2)*sinh(d*x + c)^2 + a*b - 2*b^2 + 4*((a*b - 2*b^2)*cosh(d*x + c)^3 + (2*a^2 - 5*a*b + 2*b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-a*b + b^2)*log((b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 - 2*(2*a - 3*b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 - 2*a + 3*b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 - (2*a - 3*b)*cosh(d*x + c))*sinh(d*x + c) - 4*(cosh(d*x + c)^3 + 3*cosh(d*x + c)*sinh(d*x + c)^2 + sinh(d*x + c)^3 + (3*cosh(d*x + c)^2 + 1)*sinh(d*x + c) + cosh(d*x + c))*sqrt(-a*b + b^2) + b)/(b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 + 2*(2*a - b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 + 2*a - b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 + (2*a - b)*cosh(d*x + c))*sinh(d*x + c) + b)) + 4*(a^2*b - a*b^2)*cosh(d*x + c) + 4*(a^2*b - a*b^2 + 3*(a^2*b - a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c))/((a^2*b^3 - 2*a*b^4 + b^5)*d*cosh(d*x + c)^4 + 4*(a^2*b^3 - 2*a*b^4 + b^5)*d*cosh(d*x + c)*sinh(d*x + c)^3 + (a^2*b^3 - 2*a*b^4 + b^5)*d*sinh(d*x + c)^4 + 2*(2*a^3*b^2 - 5*a^2*b^3 + 4*a*b^4 - b^5)*d*cosh(d*x + c)^2 + 2*(3*(a^2*b^3 - 2*a*b^4 + b^5)*d*cosh(d*x + c)^2 + (2*a^3*b^2 - 5*a^2*b^3 + 4*a*b^4 - b^5)*d)*sinh(d*x + c)^2 + (a^2*b^3 - 2*a*b^4 + b^5)*d + 4*((a^2*b^3 - 2*a*b^4 + b^5)*d*cosh(d*x + c)^3 + (2*a^3*b^2 - 5*a^2*b^3 + 4*a*b^4 - b^5)*d*cosh(d*x + c))*sinh(d*x + c)), -1/2*(2*(a^2*b - a*b^2)*cosh(d*x + c)^3 + 6*(a^2*b - a*b^2)*cosh(d*x + c)*sinh(d*x + c)^2 + 2*(a^2*b - a*b^2)*sinh(d*x + c)^3 - ((a*b - 2*b^2)*cosh(d*x + c)^4 + 4*(a*b - 2*b^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (a*b - 2*b^2)*sinh(d*x + c)^4 + 2*(2*a^2 - 5*a*b + 2*b^2)*cosh(d*x + c)^2 + 2*(3*(a*b - 2*b^2)*cosh(d*x + c)^2 + 2*a^2 - 5*a*b + 2*b^2)*sinh(d*x + c)^2 + a*b - 2*b^2 + 4*((a*b - 2*b^2)*cosh(d*x + c)^3 + (2*a^2 - 5*a*b + 2*b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(a*b - b^2)*arctan(-1/2*(b*cosh(d*x + c)^3 + 3*b*cosh(d*x + c)*sinh(d*x + c)^2 + b*sinh(d*x + c)^3 + (4*a - 3*b)*cosh(d*x + c) + (3*b*cosh(d*x + c)^2 + 4*a - 3*b)*sinh(d*x + c))/sqrt(a*b - b^2)) + ((a*b - 2*b^2)*cosh(d*x + c)^4 + 4*(a*b - 2*b^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (a*b - 2*b^2)*sinh(d*x + c)^4 + 2*(2*a^2 - 5*a*b + 2*b^2)*cosh(d*x + c)^2 + 2*(3*(a*b - 2*b^2)*cosh(d*x + c)^2 + 2*a^2 - 5*a*b + 2*b^2)*sinh(d*x + c)^2 + a*b - 2*b^2 + 4*((a*b - 2*b^2)*cosh(d*x + c)^3 + (2*a^2 - 5*a*b + 2*b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(a*b - b^2)*arctan(-1/2*sqrt(a*b - b^2)*(cosh(d*x + c) + sinh(d*x + c))/(a - b)) + 2*(a^2*b - a*b^2)*cosh(d*x + c) + 2*(a^2*b - a*b^2 + 3*(a^2*b - a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c))/((a^2*b^3 - 2*a*b^4 + b^5)*d*cosh(d*x + c)^4 + 4*(a^2*b^3 - 2*a*b^4 + b^5)*d*cosh(d*x + c)*sinh(d*x + c)^3 + (a^2*b^3 - 2*a*b^4 + b^5)*d*sinh(d*x + c)^4 + 2*(2*a^3*b^2 - 5*a^2*b^3 + 4*a*b^4 - b^5)*d*cosh(d*x + c)^2 + 2*(3*(a^2*b^3 - 2*a*b^4 + b^5)*d*cosh(d*x + c)^2 + (2*a^3*b^2 - 5*a^2*b^3 + 4*a*b^4 - b^5)*d)*sinh(d*x + c)^2 + (a^2*b^3 - 2*a*b^4 + b^5)*d + 4*((a^2*b^3 - 2*a*b^4 + b^5)*d*cosh(d*x + c)^3 + (2*a^3*b^2 - 5*a^2*b^3 + 4*a*b^4 - b^5)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
44,1,1523,0,0.529531," ","integrate(sinh(d*x+c)^2/(a+b*sinh(d*x+c)^2)^2,x, algorithm=""fricas"")","\left[-\frac{4 \, a^{2} b - 4 \, a b^{2} + 4 \, {\left(2 \, a^{3} - 3 \, a^{2} b + a b^{2}\right)} \cosh\left(d x + c\right)^{2} + 8 \, {\left(2 \, a^{3} - 3 \, a^{2} b + a b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + 4 \, {\left(2 \, a^{3} - 3 \, a^{2} b + a b^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left(b^{2} \cosh\left(d x + c\right)^{4} + 4 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{2} \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(d x + c\right)^{2} + 2 \, a b - b^{2}\right)} \sinh\left(d x + c\right)^{2} + b^{2} + 4 \, {\left(b^{2} \cosh\left(d x + c\right)^{3} + {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{a^{2} - a b} \log\left(\frac{b^{2} \cosh\left(d x + c\right)^{4} + 4 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{2} \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(d x + c\right)^{2} + 2 \, a b - b^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, a^{2} - 8 \, a b + b^{2} + 4 \, {\left(b^{2} \cosh\left(d x + c\right)^{3} + {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) - 4 \, {\left(b \cosh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b \sinh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sqrt{a^{2} - a b}}{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b}\right)}{4 \, {\left({\left(a^{3} b^{2} - 2 \, a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{3} b^{2} - 2 \, a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{3} b^{2} - 2 \, a^{2} b^{3} + a b^{4}\right)} d \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a^{4} b - 5 \, a^{3} b^{2} + 4 \, a^{2} b^{3} - a b^{4}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{3} b^{2} - 2 \, a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{4} b - 5 \, a^{3} b^{2} + 4 \, a^{2} b^{3} - a b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{3} b^{2} - 2 \, a^{2} b^{3} + a b^{4}\right)} d + 4 \, {\left({\left(a^{3} b^{2} - 2 \, a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{4} b - 5 \, a^{3} b^{2} + 4 \, a^{2} b^{3} - a b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}, -\frac{2 \, a^{2} b - 2 \, a b^{2} + 2 \, {\left(2 \, a^{3} - 3 \, a^{2} b + a b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(2 \, a^{3} - 3 \, a^{2} b + a b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + 2 \, {\left(2 \, a^{3} - 3 \, a^{2} b + a b^{2}\right)} \sinh\left(d x + c\right)^{2} - {\left(b^{2} \cosh\left(d x + c\right)^{4} + 4 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{2} \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(d x + c\right)^{2} + 2 \, a b - b^{2}\right)} \sinh\left(d x + c\right)^{2} + b^{2} + 4 \, {\left(b^{2} \cosh\left(d x + c\right)^{3} + {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-a^{2} + a b} \arctan\left(-\frac{{\left(b \cosh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b \sinh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sqrt{-a^{2} + a b}}{2 \, {\left(a^{2} - a b\right)}}\right)}{2 \, {\left({\left(a^{3} b^{2} - 2 \, a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{3} b^{2} - 2 \, a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{3} b^{2} - 2 \, a^{2} b^{3} + a b^{4}\right)} d \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a^{4} b - 5 \, a^{3} b^{2} + 4 \, a^{2} b^{3} - a b^{4}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{3} b^{2} - 2 \, a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{4} b - 5 \, a^{3} b^{2} + 4 \, a^{2} b^{3} - a b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{3} b^{2} - 2 \, a^{2} b^{3} + a b^{4}\right)} d + 4 \, {\left({\left(a^{3} b^{2} - 2 \, a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{4} b - 5 \, a^{3} b^{2} + 4 \, a^{2} b^{3} - a b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[-1/4*(4*a^2*b - 4*a*b^2 + 4*(2*a^3 - 3*a^2*b + a*b^2)*cosh(d*x + c)^2 + 8*(2*a^3 - 3*a^2*b + a*b^2)*cosh(d*x + c)*sinh(d*x + c) + 4*(2*a^3 - 3*a^2*b + a*b^2)*sinh(d*x + c)^2 + (b^2*cosh(d*x + c)^4 + 4*b^2*cosh(d*x + c)*sinh(d*x + c)^3 + b^2*sinh(d*x + c)^4 + 2*(2*a*b - b^2)*cosh(d*x + c)^2 + 2*(3*b^2*cosh(d*x + c)^2 + 2*a*b - b^2)*sinh(d*x + c)^2 + b^2 + 4*(b^2*cosh(d*x + c)^3 + (2*a*b - b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(a^2 - a*b)*log((b^2*cosh(d*x + c)^4 + 4*b^2*cosh(d*x + c)*sinh(d*x + c)^3 + b^2*sinh(d*x + c)^4 + 2*(2*a*b - b^2)*cosh(d*x + c)^2 + 2*(3*b^2*cosh(d*x + c)^2 + 2*a*b - b^2)*sinh(d*x + c)^2 + 8*a^2 - 8*a*b + b^2 + 4*(b^2*cosh(d*x + c)^3 + (2*a*b - b^2)*cosh(d*x + c))*sinh(d*x + c) - 4*(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + 2*a - b)*sqrt(a^2 - a*b))/(b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 + 2*(2*a - b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 + 2*a - b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 + (2*a - b)*cosh(d*x + c))*sinh(d*x + c) + b)))/((a^3*b^2 - 2*a^2*b^3 + a*b^4)*d*cosh(d*x + c)^4 + 4*(a^3*b^2 - 2*a^2*b^3 + a*b^4)*d*cosh(d*x + c)*sinh(d*x + c)^3 + (a^3*b^2 - 2*a^2*b^3 + a*b^4)*d*sinh(d*x + c)^4 + 2*(2*a^4*b - 5*a^3*b^2 + 4*a^2*b^3 - a*b^4)*d*cosh(d*x + c)^2 + 2*(3*(a^3*b^2 - 2*a^2*b^3 + a*b^4)*d*cosh(d*x + c)^2 + (2*a^4*b - 5*a^3*b^2 + 4*a^2*b^3 - a*b^4)*d)*sinh(d*x + c)^2 + (a^3*b^2 - 2*a^2*b^3 + a*b^4)*d + 4*((a^3*b^2 - 2*a^2*b^3 + a*b^4)*d*cosh(d*x + c)^3 + (2*a^4*b - 5*a^3*b^2 + 4*a^2*b^3 - a*b^4)*d*cosh(d*x + c))*sinh(d*x + c)), -1/2*(2*a^2*b - 2*a*b^2 + 2*(2*a^3 - 3*a^2*b + a*b^2)*cosh(d*x + c)^2 + 4*(2*a^3 - 3*a^2*b + a*b^2)*cosh(d*x + c)*sinh(d*x + c) + 2*(2*a^3 - 3*a^2*b + a*b^2)*sinh(d*x + c)^2 - (b^2*cosh(d*x + c)^4 + 4*b^2*cosh(d*x + c)*sinh(d*x + c)^3 + b^2*sinh(d*x + c)^4 + 2*(2*a*b - b^2)*cosh(d*x + c)^2 + 2*(3*b^2*cosh(d*x + c)^2 + 2*a*b - b^2)*sinh(d*x + c)^2 + b^2 + 4*(b^2*cosh(d*x + c)^3 + (2*a*b - b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-a^2 + a*b)*arctan(-1/2*(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + 2*a - b)*sqrt(-a^2 + a*b)/(a^2 - a*b)))/((a^3*b^2 - 2*a^2*b^3 + a*b^4)*d*cosh(d*x + c)^4 + 4*(a^3*b^2 - 2*a^2*b^3 + a*b^4)*d*cosh(d*x + c)*sinh(d*x + c)^3 + (a^3*b^2 - 2*a^2*b^3 + a*b^4)*d*sinh(d*x + c)^4 + 2*(2*a^4*b - 5*a^3*b^2 + 4*a^2*b^3 - a*b^4)*d*cosh(d*x + c)^2 + 2*(3*(a^3*b^2 - 2*a^2*b^3 + a*b^4)*d*cosh(d*x + c)^2 + (2*a^4*b - 5*a^3*b^2 + 4*a^2*b^3 - a*b^4)*d)*sinh(d*x + c)^2 + (a^3*b^2 - 2*a^2*b^3 + a*b^4)*d + 4*((a^3*b^2 - 2*a^2*b^3 + a*b^4)*d*cosh(d*x + c)^3 + (2*a^4*b - 5*a^3*b^2 + 4*a^2*b^3 - a*b^4)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
45,1,1628,0,0.600240," ","integrate(sinh(d*x+c)/(a+b*sinh(d*x+c)^2)^2,x, algorithm=""fricas"")","\left[\frac{4 \, {\left(a b - b^{2}\right)} \cosh\left(d x + c\right)^{3} + 12 \, {\left(a b - b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + 4 \, {\left(a b - b^{2}\right)} \sinh\left(d x + c\right)^{3} + {\left(b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b\right)} \sqrt{-a b + b^{2}} \log\left(\frac{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} - 2 \, {\left(2 \, a - 3 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} - 2 \, a + 3 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} - {\left(2 \, a - 3 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + 4 \, {\left(\cosh\left(d x + c\right)^{3} + 3 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{3} + {\left(3 \, \cosh\left(d x + c\right)^{2} + 1\right)} \sinh\left(d x + c\right) + \cosh\left(d x + c\right)\right)} \sqrt{-a b + b^{2}} + b}{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b}\right) + 4 \, {\left(a b - b^{2}\right)} \cosh\left(d x + c\right) + 4 \, {\left(3 \, {\left(a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} + a b - b^{2}\right)} \sinh\left(d x + c\right)}{4 \, {\left({\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} d \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} d + 4 \, {\left({\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} d \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}, \frac{2 \, {\left(a b - b^{2}\right)} \cosh\left(d x + c\right)^{3} + 6 \, {\left(a b - b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + 2 \, {\left(a b - b^{2}\right)} \sinh\left(d x + c\right)^{3} + {\left(b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b\right)} \sqrt{a b - b^{2}} \arctan\left(-\frac{b \cosh\left(d x + c\right)^{3} + 3 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{3} + {\left(4 \, a - 3 \, b\right)} \cosh\left(d x + c\right) + {\left(3 \, b \cosh\left(d x + c\right)^{2} + 4 \, a - 3 \, b\right)} \sinh\left(d x + c\right)}{2 \, \sqrt{a b - b^{2}}}\right) - {\left(b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b\right)} \sqrt{a b - b^{2}} \arctan\left(-\frac{\sqrt{a b - b^{2}} {\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right)}}{2 \, {\left(a - b\right)}}\right) + 2 \, {\left(a b - b^{2}\right)} \cosh\left(d x + c\right) + 2 \, {\left(3 \, {\left(a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} + a b - b^{2}\right)} \sinh\left(d x + c\right)}{2 \, {\left({\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} d \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} d + 4 \, {\left({\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} d \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[1/4*(4*(a*b - b^2)*cosh(d*x + c)^3 + 12*(a*b - b^2)*cosh(d*x + c)*sinh(d*x + c)^2 + 4*(a*b - b^2)*sinh(d*x + c)^3 + (b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 + 2*(2*a - b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 + 2*a - b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 + (2*a - b)*cosh(d*x + c))*sinh(d*x + c) + b)*sqrt(-a*b + b^2)*log((b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 - 2*(2*a - 3*b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 - 2*a + 3*b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 - (2*a - 3*b)*cosh(d*x + c))*sinh(d*x + c) + 4*(cosh(d*x + c)^3 + 3*cosh(d*x + c)*sinh(d*x + c)^2 + sinh(d*x + c)^3 + (3*cosh(d*x + c)^2 + 1)*sinh(d*x + c) + cosh(d*x + c))*sqrt(-a*b + b^2) + b)/(b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 + 2*(2*a - b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 + 2*a - b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 + (2*a - b)*cosh(d*x + c))*sinh(d*x + c) + b)) + 4*(a*b - b^2)*cosh(d*x + c) + 4*(3*(a*b - b^2)*cosh(d*x + c)^2 + a*b - b^2)*sinh(d*x + c))/((a^2*b^2 - 2*a*b^3 + b^4)*d*cosh(d*x + c)^4 + 4*(a^2*b^2 - 2*a*b^3 + b^4)*d*cosh(d*x + c)*sinh(d*x + c)^3 + (a^2*b^2 - 2*a*b^3 + b^4)*d*sinh(d*x + c)^4 + 2*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*d*cosh(d*x + c)^2 + 2*(3*(a^2*b^2 - 2*a*b^3 + b^4)*d*cosh(d*x + c)^2 + (2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*d)*sinh(d*x + c)^2 + (a^2*b^2 - 2*a*b^3 + b^4)*d + 4*((a^2*b^2 - 2*a*b^3 + b^4)*d*cosh(d*x + c)^3 + (2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*d*cosh(d*x + c))*sinh(d*x + c)), 1/2*(2*(a*b - b^2)*cosh(d*x + c)^3 + 6*(a*b - b^2)*cosh(d*x + c)*sinh(d*x + c)^2 + 2*(a*b - b^2)*sinh(d*x + c)^3 + (b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 + 2*(2*a - b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 + 2*a - b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 + (2*a - b)*cosh(d*x + c))*sinh(d*x + c) + b)*sqrt(a*b - b^2)*arctan(-1/2*(b*cosh(d*x + c)^3 + 3*b*cosh(d*x + c)*sinh(d*x + c)^2 + b*sinh(d*x + c)^3 + (4*a - 3*b)*cosh(d*x + c) + (3*b*cosh(d*x + c)^2 + 4*a - 3*b)*sinh(d*x + c))/sqrt(a*b - b^2)) - (b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 + 2*(2*a - b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 + 2*a - b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 + (2*a - b)*cosh(d*x + c))*sinh(d*x + c) + b)*sqrt(a*b - b^2)*arctan(-1/2*sqrt(a*b - b^2)*(cosh(d*x + c) + sinh(d*x + c))/(a - b)) + 2*(a*b - b^2)*cosh(d*x + c) + 2*(3*(a*b - b^2)*cosh(d*x + c)^2 + a*b - b^2)*sinh(d*x + c))/((a^2*b^2 - 2*a*b^3 + b^4)*d*cosh(d*x + c)^4 + 4*(a^2*b^2 - 2*a*b^3 + b^4)*d*cosh(d*x + c)*sinh(d*x + c)^3 + (a^2*b^2 - 2*a*b^3 + b^4)*d*sinh(d*x + c)^4 + 2*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*d*cosh(d*x + c)^2 + 2*(3*(a^2*b^2 - 2*a*b^3 + b^4)*d*cosh(d*x + c)^2 + (2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*d)*sinh(d*x + c)^2 + (a^2*b^2 - 2*a*b^3 + b^4)*d + 4*((a^2*b^2 - 2*a*b^3 + b^4)*d*cosh(d*x + c)^3 + (2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
46,1,1617,0,0.756405," ","integrate(1/(a+b*sinh(d*x+c)^2)^2,x, algorithm=""fricas"")","\left[\frac{4 \, a^{2} b - 4 \, a b^{2} + 4 \, {\left(2 \, a^{3} - 3 \, a^{2} b + a b^{2}\right)} \cosh\left(d x + c\right)^{2} + 8 \, {\left(2 \, a^{3} - 3 \, a^{2} b + a b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + 4 \, {\left(2 \, a^{3} - 3 \, a^{2} b + a b^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(2 \, a b - b^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(4 \, a^{2} - 4 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, a^{2} - 4 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{2} + 2 \, a b - b^{2} + 4 \, {\left({\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(4 \, a^{2} - 4 \, a b + b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{a^{2} - a b} \log\left(\frac{b^{2} \cosh\left(d x + c\right)^{4} + 4 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{2} \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(d x + c\right)^{2} + 2 \, a b - b^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, a^{2} - 8 \, a b + b^{2} + 4 \, {\left(b^{2} \cosh\left(d x + c\right)^{3} + {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) - 4 \, {\left(b \cosh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b \sinh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sqrt{a^{2} - a b}}{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b}\right)}{4 \, {\left({\left(a^{4} b - 2 \, a^{3} b^{2} + a^{2} b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{4} b - 2 \, a^{3} b^{2} + a^{2} b^{3}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{4} b - 2 \, a^{3} b^{2} + a^{2} b^{3}\right)} d \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a^{5} - 5 \, a^{4} b + 4 \, a^{3} b^{2} - a^{2} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{4} b - 2 \, a^{3} b^{2} + a^{2} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{5} - 5 \, a^{4} b + 4 \, a^{3} b^{2} - a^{2} b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{4} b - 2 \, a^{3} b^{2} + a^{2} b^{3}\right)} d + 4 \, {\left({\left(a^{4} b - 2 \, a^{3} b^{2} + a^{2} b^{3}\right)} d \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{5} - 5 \, a^{4} b + 4 \, a^{3} b^{2} - a^{2} b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}, \frac{2 \, a^{2} b - 2 \, a b^{2} + 2 \, {\left(2 \, a^{3} - 3 \, a^{2} b + a b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(2 \, a^{3} - 3 \, a^{2} b + a b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + 2 \, {\left(2 \, a^{3} - 3 \, a^{2} b + a b^{2}\right)} \sinh\left(d x + c\right)^{2} - {\left({\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(2 \, a b - b^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(4 \, a^{2} - 4 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, a^{2} - 4 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{2} + 2 \, a b - b^{2} + 4 \, {\left({\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(4 \, a^{2} - 4 \, a b + b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-a^{2} + a b} \arctan\left(-\frac{{\left(b \cosh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b \sinh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sqrt{-a^{2} + a b}}{2 \, {\left(a^{2} - a b\right)}}\right)}{2 \, {\left({\left(a^{4} b - 2 \, a^{3} b^{2} + a^{2} b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{4} b - 2 \, a^{3} b^{2} + a^{2} b^{3}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{4} b - 2 \, a^{3} b^{2} + a^{2} b^{3}\right)} d \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a^{5} - 5 \, a^{4} b + 4 \, a^{3} b^{2} - a^{2} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{4} b - 2 \, a^{3} b^{2} + a^{2} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{5} - 5 \, a^{4} b + 4 \, a^{3} b^{2} - a^{2} b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{4} b - 2 \, a^{3} b^{2} + a^{2} b^{3}\right)} d + 4 \, {\left({\left(a^{4} b - 2 \, a^{3} b^{2} + a^{2} b^{3}\right)} d \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{5} - 5 \, a^{4} b + 4 \, a^{3} b^{2} - a^{2} b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[1/4*(4*a^2*b - 4*a*b^2 + 4*(2*a^3 - 3*a^2*b + a*b^2)*cosh(d*x + c)^2 + 8*(2*a^3 - 3*a^2*b + a*b^2)*cosh(d*x + c)*sinh(d*x + c) + 4*(2*a^3 - 3*a^2*b + a*b^2)*sinh(d*x + c)^2 + ((2*a*b - b^2)*cosh(d*x + c)^4 + 4*(2*a*b - b^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (2*a*b - b^2)*sinh(d*x + c)^4 + 2*(4*a^2 - 4*a*b + b^2)*cosh(d*x + c)^2 + 2*(3*(2*a*b - b^2)*cosh(d*x + c)^2 + 4*a^2 - 4*a*b + b^2)*sinh(d*x + c)^2 + 2*a*b - b^2 + 4*((2*a*b - b^2)*cosh(d*x + c)^3 + (4*a^2 - 4*a*b + b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(a^2 - a*b)*log((b^2*cosh(d*x + c)^4 + 4*b^2*cosh(d*x + c)*sinh(d*x + c)^3 + b^2*sinh(d*x + c)^4 + 2*(2*a*b - b^2)*cosh(d*x + c)^2 + 2*(3*b^2*cosh(d*x + c)^2 + 2*a*b - b^2)*sinh(d*x + c)^2 + 8*a^2 - 8*a*b + b^2 + 4*(b^2*cosh(d*x + c)^3 + (2*a*b - b^2)*cosh(d*x + c))*sinh(d*x + c) - 4*(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + 2*a - b)*sqrt(a^2 - a*b))/(b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 + 2*(2*a - b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 + 2*a - b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 + (2*a - b)*cosh(d*x + c))*sinh(d*x + c) + b)))/((a^4*b - 2*a^3*b^2 + a^2*b^3)*d*cosh(d*x + c)^4 + 4*(a^4*b - 2*a^3*b^2 + a^2*b^3)*d*cosh(d*x + c)*sinh(d*x + c)^3 + (a^4*b - 2*a^3*b^2 + a^2*b^3)*d*sinh(d*x + c)^4 + 2*(2*a^5 - 5*a^4*b + 4*a^3*b^2 - a^2*b^3)*d*cosh(d*x + c)^2 + 2*(3*(a^4*b - 2*a^3*b^2 + a^2*b^3)*d*cosh(d*x + c)^2 + (2*a^5 - 5*a^4*b + 4*a^3*b^2 - a^2*b^3)*d)*sinh(d*x + c)^2 + (a^4*b - 2*a^3*b^2 + a^2*b^3)*d + 4*((a^4*b - 2*a^3*b^2 + a^2*b^3)*d*cosh(d*x + c)^3 + (2*a^5 - 5*a^4*b + 4*a^3*b^2 - a^2*b^3)*d*cosh(d*x + c))*sinh(d*x + c)), 1/2*(2*a^2*b - 2*a*b^2 + 2*(2*a^3 - 3*a^2*b + a*b^2)*cosh(d*x + c)^2 + 4*(2*a^3 - 3*a^2*b + a*b^2)*cosh(d*x + c)*sinh(d*x + c) + 2*(2*a^3 - 3*a^2*b + a*b^2)*sinh(d*x + c)^2 - ((2*a*b - b^2)*cosh(d*x + c)^4 + 4*(2*a*b - b^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (2*a*b - b^2)*sinh(d*x + c)^4 + 2*(4*a^2 - 4*a*b + b^2)*cosh(d*x + c)^2 + 2*(3*(2*a*b - b^2)*cosh(d*x + c)^2 + 4*a^2 - 4*a*b + b^2)*sinh(d*x + c)^2 + 2*a*b - b^2 + 4*((2*a*b - b^2)*cosh(d*x + c)^3 + (4*a^2 - 4*a*b + b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-a^2 + a*b)*arctan(-1/2*(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + 2*a - b)*sqrt(-a^2 + a*b)/(a^2 - a*b)))/((a^4*b - 2*a^3*b^2 + a^2*b^3)*d*cosh(d*x + c)^4 + 4*(a^4*b - 2*a^3*b^2 + a^2*b^3)*d*cosh(d*x + c)*sinh(d*x + c)^3 + (a^4*b - 2*a^3*b^2 + a^2*b^3)*d*sinh(d*x + c)^4 + 2*(2*a^5 - 5*a^4*b + 4*a^3*b^2 - a^2*b^3)*d*cosh(d*x + c)^2 + 2*(3*(a^4*b - 2*a^3*b^2 + a^2*b^3)*d*cosh(d*x + c)^2 + (2*a^5 - 5*a^4*b + 4*a^3*b^2 - a^2*b^3)*d)*sinh(d*x + c)^2 + (a^4*b - 2*a^3*b^2 + a^2*b^3)*d + 4*((a^4*b - 2*a^3*b^2 + a^2*b^3)*d*cosh(d*x + c)^3 + (2*a^5 - 5*a^4*b + 4*a^3*b^2 - a^2*b^3)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
47,1,2529,0,0.724718," ","integrate(csch(d*x+c)/(a+b*sinh(d*x+c)^2)^2,x, algorithm=""fricas"")","\left[-\frac{4 \, a b \cosh\left(d x + c\right)^{3} + 12 \, a b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + 4 \, a b \sinh\left(d x + c\right)^{3} + 4 \, a b \cosh\left(d x + c\right) - {\left({\left(3 \, a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(3 \, a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(3 \, a b - 2 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(6 \, a^{2} - 7 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(3 \, a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 6 \, a^{2} - 7 \, a b + 2 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} + 3 \, a b - 2 \, b^{2} + 4 \, {\left({\left(3 \, a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(6 \, a^{2} - 7 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{b}{a - b}} \log\left(\frac{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} - 2 \, {\left(2 \, a - 3 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} - 2 \, a + 3 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} - {\left(2 \, a - 3 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) - 4 \, {\left({\left(a - b\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a - b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + {\left(a - b\right)} \sinh\left(d x + c\right)^{3} + {\left(a - b\right)} \cosh\left(d x + c\right) + {\left(3 \, {\left(a - b\right)} \cosh\left(d x + c\right)^{2} + a - b\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{b}{a - b}} + b}{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b}\right) + 4 \, {\left({\left(a b - b^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a b - b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a b - b^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a^{2} - 3 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, a^{2} - 3 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{2} + a b - b^{2} + 4 \, {\left({\left(a b - b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{2} - 3 \, a b + b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) - 4 \, {\left({\left(a b - b^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a b - b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a b - b^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a^{2} - 3 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, a^{2} - 3 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{2} + a b - b^{2} + 4 \, {\left({\left(a b - b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{2} - 3 \, a b + b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) + 4 \, {\left(3 \, a b \cosh\left(d x + c\right)^{2} + a b\right)} \sinh\left(d x + c\right)}{4 \, {\left({\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{3} b - a^{2} b^{2}\right)} d \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a^{4} - 3 \, a^{3} b + a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{4} - 3 \, a^{3} b + a^{2} b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{3} b - a^{2} b^{2}\right)} d + 4 \, {\left({\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{4} - 3 \, a^{3} b + a^{2} b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}, -\frac{2 \, a b \cosh\left(d x + c\right)^{3} + 6 \, a b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + 2 \, a b \sinh\left(d x + c\right)^{3} + 2 \, a b \cosh\left(d x + c\right) + {\left({\left(3 \, a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(3 \, a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(3 \, a b - 2 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(6 \, a^{2} - 7 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(3 \, a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 6 \, a^{2} - 7 \, a b + 2 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} + 3 \, a b - 2 \, b^{2} + 4 \, {\left({\left(3 \, a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(6 \, a^{2} - 7 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{b}{a - b}} \arctan\left(\frac{1}{2} \, \sqrt{\frac{b}{a - b}} {\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right)}\right) - {\left({\left(3 \, a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(3 \, a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(3 \, a b - 2 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(6 \, a^{2} - 7 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(3 \, a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 6 \, a^{2} - 7 \, a b + 2 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} + 3 \, a b - 2 \, b^{2} + 4 \, {\left({\left(3 \, a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(6 \, a^{2} - 7 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{b}{a - b}} \arctan\left(\frac{{\left(b \cosh\left(d x + c\right)^{3} + 3 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{3} + {\left(4 \, a - 3 \, b\right)} \cosh\left(d x + c\right) + {\left(3 \, b \cosh\left(d x + c\right)^{2} + 4 \, a - 3 \, b\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{b}{a - b}}}{2 \, b}\right) + 2 \, {\left({\left(a b - b^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a b - b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a b - b^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a^{2} - 3 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, a^{2} - 3 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{2} + a b - b^{2} + 4 \, {\left({\left(a b - b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{2} - 3 \, a b + b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) - 2 \, {\left({\left(a b - b^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a b - b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a b - b^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a^{2} - 3 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, a^{2} - 3 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{2} + a b - b^{2} + 4 \, {\left({\left(a b - b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{2} - 3 \, a b + b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) + 2 \, {\left(3 \, a b \cosh\left(d x + c\right)^{2} + a b\right)} \sinh\left(d x + c\right)}{2 \, {\left({\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{3} b - a^{2} b^{2}\right)} d \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a^{4} - 3 \, a^{3} b + a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{4} - 3 \, a^{3} b + a^{2} b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{3} b - a^{2} b^{2}\right)} d + 4 \, {\left({\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{4} - 3 \, a^{3} b + a^{2} b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[-1/4*(4*a*b*cosh(d*x + c)^3 + 12*a*b*cosh(d*x + c)*sinh(d*x + c)^2 + 4*a*b*sinh(d*x + c)^3 + 4*a*b*cosh(d*x + c) - ((3*a*b - 2*b^2)*cosh(d*x + c)^4 + 4*(3*a*b - 2*b^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (3*a*b - 2*b^2)*sinh(d*x + c)^4 + 2*(6*a^2 - 7*a*b + 2*b^2)*cosh(d*x + c)^2 + 2*(3*(3*a*b - 2*b^2)*cosh(d*x + c)^2 + 6*a^2 - 7*a*b + 2*b^2)*sinh(d*x + c)^2 + 3*a*b - 2*b^2 + 4*((3*a*b - 2*b^2)*cosh(d*x + c)^3 + (6*a^2 - 7*a*b + 2*b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-b/(a - b))*log((b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 - 2*(2*a - 3*b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 - 2*a + 3*b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 - (2*a - 3*b)*cosh(d*x + c))*sinh(d*x + c) - 4*((a - b)*cosh(d*x + c)^3 + 3*(a - b)*cosh(d*x + c)*sinh(d*x + c)^2 + (a - b)*sinh(d*x + c)^3 + (a - b)*cosh(d*x + c) + (3*(a - b)*cosh(d*x + c)^2 + a - b)*sinh(d*x + c))*sqrt(-b/(a - b)) + b)/(b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 + 2*(2*a - b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 + 2*a - b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 + (2*a - b)*cosh(d*x + c))*sinh(d*x + c) + b)) + 4*((a*b - b^2)*cosh(d*x + c)^4 + 4*(a*b - b^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (a*b - b^2)*sinh(d*x + c)^4 + 2*(2*a^2 - 3*a*b + b^2)*cosh(d*x + c)^2 + 2*(3*(a*b - b^2)*cosh(d*x + c)^2 + 2*a^2 - 3*a*b + b^2)*sinh(d*x + c)^2 + a*b - b^2 + 4*((a*b - b^2)*cosh(d*x + c)^3 + (2*a^2 - 3*a*b + b^2)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) + 1) - 4*((a*b - b^2)*cosh(d*x + c)^4 + 4*(a*b - b^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (a*b - b^2)*sinh(d*x + c)^4 + 2*(2*a^2 - 3*a*b + b^2)*cosh(d*x + c)^2 + 2*(3*(a*b - b^2)*cosh(d*x + c)^2 + 2*a^2 - 3*a*b + b^2)*sinh(d*x + c)^2 + a*b - b^2 + 4*((a*b - b^2)*cosh(d*x + c)^3 + (2*a^2 - 3*a*b + b^2)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) - 1) + 4*(3*a*b*cosh(d*x + c)^2 + a*b)*sinh(d*x + c))/((a^3*b - a^2*b^2)*d*cosh(d*x + c)^4 + 4*(a^3*b - a^2*b^2)*d*cosh(d*x + c)*sinh(d*x + c)^3 + (a^3*b - a^2*b^2)*d*sinh(d*x + c)^4 + 2*(2*a^4 - 3*a^3*b + a^2*b^2)*d*cosh(d*x + c)^2 + 2*(3*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^2 + (2*a^4 - 3*a^3*b + a^2*b^2)*d)*sinh(d*x + c)^2 + (a^3*b - a^2*b^2)*d + 4*((a^3*b - a^2*b^2)*d*cosh(d*x + c)^3 + (2*a^4 - 3*a^3*b + a^2*b^2)*d*cosh(d*x + c))*sinh(d*x + c)), -1/2*(2*a*b*cosh(d*x + c)^3 + 6*a*b*cosh(d*x + c)*sinh(d*x + c)^2 + 2*a*b*sinh(d*x + c)^3 + 2*a*b*cosh(d*x + c) + ((3*a*b - 2*b^2)*cosh(d*x + c)^4 + 4*(3*a*b - 2*b^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (3*a*b - 2*b^2)*sinh(d*x + c)^4 + 2*(6*a^2 - 7*a*b + 2*b^2)*cosh(d*x + c)^2 + 2*(3*(3*a*b - 2*b^2)*cosh(d*x + c)^2 + 6*a^2 - 7*a*b + 2*b^2)*sinh(d*x + c)^2 + 3*a*b - 2*b^2 + 4*((3*a*b - 2*b^2)*cosh(d*x + c)^3 + (6*a^2 - 7*a*b + 2*b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(b/(a - b))*arctan(1/2*sqrt(b/(a - b))*(cosh(d*x + c) + sinh(d*x + c))) - ((3*a*b - 2*b^2)*cosh(d*x + c)^4 + 4*(3*a*b - 2*b^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (3*a*b - 2*b^2)*sinh(d*x + c)^4 + 2*(6*a^2 - 7*a*b + 2*b^2)*cosh(d*x + c)^2 + 2*(3*(3*a*b - 2*b^2)*cosh(d*x + c)^2 + 6*a^2 - 7*a*b + 2*b^2)*sinh(d*x + c)^2 + 3*a*b - 2*b^2 + 4*((3*a*b - 2*b^2)*cosh(d*x + c)^3 + (6*a^2 - 7*a*b + 2*b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(b/(a - b))*arctan(1/2*(b*cosh(d*x + c)^3 + 3*b*cosh(d*x + c)*sinh(d*x + c)^2 + b*sinh(d*x + c)^3 + (4*a - 3*b)*cosh(d*x + c) + (3*b*cosh(d*x + c)^2 + 4*a - 3*b)*sinh(d*x + c))*sqrt(b/(a - b))/b) + 2*((a*b - b^2)*cosh(d*x + c)^4 + 4*(a*b - b^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (a*b - b^2)*sinh(d*x + c)^4 + 2*(2*a^2 - 3*a*b + b^2)*cosh(d*x + c)^2 + 2*(3*(a*b - b^2)*cosh(d*x + c)^2 + 2*a^2 - 3*a*b + b^2)*sinh(d*x + c)^2 + a*b - b^2 + 4*((a*b - b^2)*cosh(d*x + c)^3 + (2*a^2 - 3*a*b + b^2)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) + 1) - 2*((a*b - b^2)*cosh(d*x + c)^4 + 4*(a*b - b^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (a*b - b^2)*sinh(d*x + c)^4 + 2*(2*a^2 - 3*a*b + b^2)*cosh(d*x + c)^2 + 2*(3*(a*b - b^2)*cosh(d*x + c)^2 + 2*a^2 - 3*a*b + b^2)*sinh(d*x + c)^2 + a*b - b^2 + 4*((a*b - b^2)*cosh(d*x + c)^3 + (2*a^2 - 3*a*b + b^2)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) - 1) + 2*(3*a*b*cosh(d*x + c)^2 + a*b)*sinh(d*x + c))/((a^3*b - a^2*b^2)*d*cosh(d*x + c)^4 + 4*(a^3*b - a^2*b^2)*d*cosh(d*x + c)*sinh(d*x + c)^3 + (a^3*b - a^2*b^2)*d*sinh(d*x + c)^4 + 2*(2*a^4 - 3*a^3*b + a^2*b^2)*d*cosh(d*x + c)^2 + 2*(3*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^2 + (2*a^4 - 3*a^3*b + a^2*b^2)*d)*sinh(d*x + c)^2 + (a^3*b - a^2*b^2)*d + 4*((a^3*b - a^2*b^2)*d*cosh(d*x + c)^3 + (2*a^4 - 3*a^3*b + a^2*b^2)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
48,1,2988,0,0.945459," ","integrate(csch(d*x+c)^2/(a+b*sinh(d*x+c)^2)^2,x, algorithm=""fricas"")","\left[-\frac{4 \, {\left(4 \, a^{3} b - 7 \, a^{2} b^{2} + 3 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} + 16 \, {\left(4 \, a^{3} b - 7 \, a^{2} b^{2} + 3 \, a b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + 4 \, {\left(4 \, a^{3} b - 7 \, a^{2} b^{2} + 3 \, a b^{3}\right)} \sinh\left(d x + c\right)^{4} + 8 \, a^{3} b - 20 \, a^{2} b^{2} + 12 \, a b^{3} + 8 \, {\left(4 \, a^{4} - 11 \, a^{3} b + 10 \, a^{2} b^{2} - 3 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2} + 8 \, {\left(4 \, a^{4} - 11 \, a^{3} b + 10 \, a^{2} b^{2} - 3 \, a b^{3} + 3 \, {\left(4 \, a^{3} b - 7 \, a^{2} b^{2} + 3 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} - {\left({\left(4 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 6 \, {\left(4 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(4 \, a b^{2} - 3 \, b^{3}\right)} \sinh\left(d x + c\right)^{6} + {\left(16 \, a^{2} b - 24 \, a b^{2} + 9 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + {\left(16 \, a^{2} b - 24 \, a b^{2} + 9 \, b^{3} + 15 \, {\left(4 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, {\left(4 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(16 \, a^{2} b - 24 \, a b^{2} + 9 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 4 \, a b^{2} + 3 \, b^{3} - {\left(16 \, a^{2} b - 24 \, a b^{2} + 9 \, b^{3}\right)} \cosh\left(d x + c\right)^{2} + {\left(15 \, {\left(4 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 16 \, a^{2} b + 24 \, a b^{2} - 9 \, b^{3} + 6 \, {\left(16 \, a^{2} b - 24 \, a b^{2} + 9 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(4 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(16 \, a^{2} b - 24 \, a b^{2} + 9 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - {\left(16 \, a^{2} b - 24 \, a b^{2} + 9 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{a^{2} - a b} \log\left(\frac{b^{2} \cosh\left(d x + c\right)^{4} + 4 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{2} \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(d x + c\right)^{2} + 2 \, a b - b^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, a^{2} - 8 \, a b + b^{2} + 4 \, {\left(b^{2} \cosh\left(d x + c\right)^{3} + {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + 4 \, {\left(b \cosh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b \sinh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sqrt{a^{2} - a b}}{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b}\right) + 16 \, {\left({\left(4 \, a^{3} b - 7 \, a^{2} b^{2} + 3 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(4 \, a^{4} - 11 \, a^{3} b + 10 \, a^{2} b^{2} - 3 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{4 \, {\left({\left(a^{5} b - 2 \, a^{4} b^{2} + a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{6} + 6 \, {\left(a^{5} b - 2 \, a^{4} b^{2} + a^{3} b^{3}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(a^{5} b - 2 \, a^{4} b^{2} + a^{3} b^{3}\right)} d \sinh\left(d x + c\right)^{6} + {\left(4 \, a^{6} - 11 \, a^{5} b + 10 \, a^{4} b^{2} - 3 \, a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{4} + {\left(15 \, {\left(a^{5} b - 2 \, a^{4} b^{2} + a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + {\left(4 \, a^{6} - 11 \, a^{5} b + 10 \, a^{4} b^{2} - 3 \, a^{3} b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{4} - {\left(4 \, a^{6} - 11 \, a^{5} b + 10 \, a^{4} b^{2} - 3 \, a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + 4 \, {\left(5 \, {\left(a^{5} b - 2 \, a^{4} b^{2} + a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{3} + {\left(4 \, a^{6} - 11 \, a^{5} b + 10 \, a^{4} b^{2} - 3 \, a^{3} b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(15 \, {\left(a^{5} b - 2 \, a^{4} b^{2} + a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 6 \, {\left(4 \, a^{6} - 11 \, a^{5} b + 10 \, a^{4} b^{2} - 3 \, a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{2} - {\left(4 \, a^{6} - 11 \, a^{5} b + 10 \, a^{4} b^{2} - 3 \, a^{3} b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{2} - {\left(a^{5} b - 2 \, a^{4} b^{2} + a^{3} b^{3}\right)} d + 2 \, {\left(3 \, {\left(a^{5} b - 2 \, a^{4} b^{2} + a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{5} + 2 \, {\left(4 \, a^{6} - 11 \, a^{5} b + 10 \, a^{4} b^{2} - 3 \, a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{3} - {\left(4 \, a^{6} - 11 \, a^{5} b + 10 \, a^{4} b^{2} - 3 \, a^{3} b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}, -\frac{2 \, {\left(4 \, a^{3} b - 7 \, a^{2} b^{2} + 3 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} + 8 \, {\left(4 \, a^{3} b - 7 \, a^{2} b^{2} + 3 \, a b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + 2 \, {\left(4 \, a^{3} b - 7 \, a^{2} b^{2} + 3 \, a b^{3}\right)} \sinh\left(d x + c\right)^{4} + 4 \, a^{3} b - 10 \, a^{2} b^{2} + 6 \, a b^{3} + 4 \, {\left(4 \, a^{4} - 11 \, a^{3} b + 10 \, a^{2} b^{2} - 3 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(4 \, a^{4} - 11 \, a^{3} b + 10 \, a^{2} b^{2} - 3 \, a b^{3} + 3 \, {\left(4 \, a^{3} b - 7 \, a^{2} b^{2} + 3 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} - {\left({\left(4 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 6 \, {\left(4 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(4 \, a b^{2} - 3 \, b^{3}\right)} \sinh\left(d x + c\right)^{6} + {\left(16 \, a^{2} b - 24 \, a b^{2} + 9 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + {\left(16 \, a^{2} b - 24 \, a b^{2} + 9 \, b^{3} + 15 \, {\left(4 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, {\left(4 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(16 \, a^{2} b - 24 \, a b^{2} + 9 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 4 \, a b^{2} + 3 \, b^{3} - {\left(16 \, a^{2} b - 24 \, a b^{2} + 9 \, b^{3}\right)} \cosh\left(d x + c\right)^{2} + {\left(15 \, {\left(4 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 16 \, a^{2} b + 24 \, a b^{2} - 9 \, b^{3} + 6 \, {\left(16 \, a^{2} b - 24 \, a b^{2} + 9 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(4 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(16 \, a^{2} b - 24 \, a b^{2} + 9 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - {\left(16 \, a^{2} b - 24 \, a b^{2} + 9 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-a^{2} + a b} \arctan\left(-\frac{{\left(b \cosh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b \sinh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sqrt{-a^{2} + a b}}{2 \, {\left(a^{2} - a b\right)}}\right) + 8 \, {\left({\left(4 \, a^{3} b - 7 \, a^{2} b^{2} + 3 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(4 \, a^{4} - 11 \, a^{3} b + 10 \, a^{2} b^{2} - 3 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{2 \, {\left({\left(a^{5} b - 2 \, a^{4} b^{2} + a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{6} + 6 \, {\left(a^{5} b - 2 \, a^{4} b^{2} + a^{3} b^{3}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(a^{5} b - 2 \, a^{4} b^{2} + a^{3} b^{3}\right)} d \sinh\left(d x + c\right)^{6} + {\left(4 \, a^{6} - 11 \, a^{5} b + 10 \, a^{4} b^{2} - 3 \, a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{4} + {\left(15 \, {\left(a^{5} b - 2 \, a^{4} b^{2} + a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + {\left(4 \, a^{6} - 11 \, a^{5} b + 10 \, a^{4} b^{2} - 3 \, a^{3} b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{4} - {\left(4 \, a^{6} - 11 \, a^{5} b + 10 \, a^{4} b^{2} - 3 \, a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + 4 \, {\left(5 \, {\left(a^{5} b - 2 \, a^{4} b^{2} + a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{3} + {\left(4 \, a^{6} - 11 \, a^{5} b + 10 \, a^{4} b^{2} - 3 \, a^{3} b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(15 \, {\left(a^{5} b - 2 \, a^{4} b^{2} + a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 6 \, {\left(4 \, a^{6} - 11 \, a^{5} b + 10 \, a^{4} b^{2} - 3 \, a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{2} - {\left(4 \, a^{6} - 11 \, a^{5} b + 10 \, a^{4} b^{2} - 3 \, a^{3} b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{2} - {\left(a^{5} b - 2 \, a^{4} b^{2} + a^{3} b^{3}\right)} d + 2 \, {\left(3 \, {\left(a^{5} b - 2 \, a^{4} b^{2} + a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{5} + 2 \, {\left(4 \, a^{6} - 11 \, a^{5} b + 10 \, a^{4} b^{2} - 3 \, a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{3} - {\left(4 \, a^{6} - 11 \, a^{5} b + 10 \, a^{4} b^{2} - 3 \, a^{3} b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[-1/4*(4*(4*a^3*b - 7*a^2*b^2 + 3*a*b^3)*cosh(d*x + c)^4 + 16*(4*a^3*b - 7*a^2*b^2 + 3*a*b^3)*cosh(d*x + c)*sinh(d*x + c)^3 + 4*(4*a^3*b - 7*a^2*b^2 + 3*a*b^3)*sinh(d*x + c)^4 + 8*a^3*b - 20*a^2*b^2 + 12*a*b^3 + 8*(4*a^4 - 11*a^3*b + 10*a^2*b^2 - 3*a*b^3)*cosh(d*x + c)^2 + 8*(4*a^4 - 11*a^3*b + 10*a^2*b^2 - 3*a*b^3 + 3*(4*a^3*b - 7*a^2*b^2 + 3*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - ((4*a*b^2 - 3*b^3)*cosh(d*x + c)^6 + 6*(4*a*b^2 - 3*b^3)*cosh(d*x + c)*sinh(d*x + c)^5 + (4*a*b^2 - 3*b^3)*sinh(d*x + c)^6 + (16*a^2*b - 24*a*b^2 + 9*b^3)*cosh(d*x + c)^4 + (16*a^2*b - 24*a*b^2 + 9*b^3 + 15*(4*a*b^2 - 3*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 4*(5*(4*a*b^2 - 3*b^3)*cosh(d*x + c)^3 + (16*a^2*b - 24*a*b^2 + 9*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 - 4*a*b^2 + 3*b^3 - (16*a^2*b - 24*a*b^2 + 9*b^3)*cosh(d*x + c)^2 + (15*(4*a*b^2 - 3*b^3)*cosh(d*x + c)^4 - 16*a^2*b + 24*a*b^2 - 9*b^3 + 6*(16*a^2*b - 24*a*b^2 + 9*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 2*(3*(4*a*b^2 - 3*b^3)*cosh(d*x + c)^5 + 2*(16*a^2*b - 24*a*b^2 + 9*b^3)*cosh(d*x + c)^3 - (16*a^2*b - 24*a*b^2 + 9*b^3)*cosh(d*x + c))*sinh(d*x + c))*sqrt(a^2 - a*b)*log((b^2*cosh(d*x + c)^4 + 4*b^2*cosh(d*x + c)*sinh(d*x + c)^3 + b^2*sinh(d*x + c)^4 + 2*(2*a*b - b^2)*cosh(d*x + c)^2 + 2*(3*b^2*cosh(d*x + c)^2 + 2*a*b - b^2)*sinh(d*x + c)^2 + 8*a^2 - 8*a*b + b^2 + 4*(b^2*cosh(d*x + c)^3 + (2*a*b - b^2)*cosh(d*x + c))*sinh(d*x + c) + 4*(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + 2*a - b)*sqrt(a^2 - a*b))/(b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 + 2*(2*a - b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 + 2*a - b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 + (2*a - b)*cosh(d*x + c))*sinh(d*x + c) + b)) + 16*((4*a^3*b - 7*a^2*b^2 + 3*a*b^3)*cosh(d*x + c)^3 + (4*a^4 - 11*a^3*b + 10*a^2*b^2 - 3*a*b^3)*cosh(d*x + c))*sinh(d*x + c))/((a^5*b - 2*a^4*b^2 + a^3*b^3)*d*cosh(d*x + c)^6 + 6*(a^5*b - 2*a^4*b^2 + a^3*b^3)*d*cosh(d*x + c)*sinh(d*x + c)^5 + (a^5*b - 2*a^4*b^2 + a^3*b^3)*d*sinh(d*x + c)^6 + (4*a^6 - 11*a^5*b + 10*a^4*b^2 - 3*a^3*b^3)*d*cosh(d*x + c)^4 + (15*(a^5*b - 2*a^4*b^2 + a^3*b^3)*d*cosh(d*x + c)^2 + (4*a^6 - 11*a^5*b + 10*a^4*b^2 - 3*a^3*b^3)*d)*sinh(d*x + c)^4 - (4*a^6 - 11*a^5*b + 10*a^4*b^2 - 3*a^3*b^3)*d*cosh(d*x + c)^2 + 4*(5*(a^5*b - 2*a^4*b^2 + a^3*b^3)*d*cosh(d*x + c)^3 + (4*a^6 - 11*a^5*b + 10*a^4*b^2 - 3*a^3*b^3)*d*cosh(d*x + c))*sinh(d*x + c)^3 + (15*(a^5*b - 2*a^4*b^2 + a^3*b^3)*d*cosh(d*x + c)^4 + 6*(4*a^6 - 11*a^5*b + 10*a^4*b^2 - 3*a^3*b^3)*d*cosh(d*x + c)^2 - (4*a^6 - 11*a^5*b + 10*a^4*b^2 - 3*a^3*b^3)*d)*sinh(d*x + c)^2 - (a^5*b - 2*a^4*b^2 + a^3*b^3)*d + 2*(3*(a^5*b - 2*a^4*b^2 + a^3*b^3)*d*cosh(d*x + c)^5 + 2*(4*a^6 - 11*a^5*b + 10*a^4*b^2 - 3*a^3*b^3)*d*cosh(d*x + c)^3 - (4*a^6 - 11*a^5*b + 10*a^4*b^2 - 3*a^3*b^3)*d*cosh(d*x + c))*sinh(d*x + c)), -1/2*(2*(4*a^3*b - 7*a^2*b^2 + 3*a*b^3)*cosh(d*x + c)^4 + 8*(4*a^3*b - 7*a^2*b^2 + 3*a*b^3)*cosh(d*x + c)*sinh(d*x + c)^3 + 2*(4*a^3*b - 7*a^2*b^2 + 3*a*b^3)*sinh(d*x + c)^4 + 4*a^3*b - 10*a^2*b^2 + 6*a*b^3 + 4*(4*a^4 - 11*a^3*b + 10*a^2*b^2 - 3*a*b^3)*cosh(d*x + c)^2 + 4*(4*a^4 - 11*a^3*b + 10*a^2*b^2 - 3*a*b^3 + 3*(4*a^3*b - 7*a^2*b^2 + 3*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - ((4*a*b^2 - 3*b^3)*cosh(d*x + c)^6 + 6*(4*a*b^2 - 3*b^3)*cosh(d*x + c)*sinh(d*x + c)^5 + (4*a*b^2 - 3*b^3)*sinh(d*x + c)^6 + (16*a^2*b - 24*a*b^2 + 9*b^3)*cosh(d*x + c)^4 + (16*a^2*b - 24*a*b^2 + 9*b^3 + 15*(4*a*b^2 - 3*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 4*(5*(4*a*b^2 - 3*b^3)*cosh(d*x + c)^3 + (16*a^2*b - 24*a*b^2 + 9*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 - 4*a*b^2 + 3*b^3 - (16*a^2*b - 24*a*b^2 + 9*b^3)*cosh(d*x + c)^2 + (15*(4*a*b^2 - 3*b^3)*cosh(d*x + c)^4 - 16*a^2*b + 24*a*b^2 - 9*b^3 + 6*(16*a^2*b - 24*a*b^2 + 9*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 2*(3*(4*a*b^2 - 3*b^3)*cosh(d*x + c)^5 + 2*(16*a^2*b - 24*a*b^2 + 9*b^3)*cosh(d*x + c)^3 - (16*a^2*b - 24*a*b^2 + 9*b^3)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-a^2 + a*b)*arctan(-1/2*(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + 2*a - b)*sqrt(-a^2 + a*b)/(a^2 - a*b)) + 8*((4*a^3*b - 7*a^2*b^2 + 3*a*b^3)*cosh(d*x + c)^3 + (4*a^4 - 11*a^3*b + 10*a^2*b^2 - 3*a*b^3)*cosh(d*x + c))*sinh(d*x + c))/((a^5*b - 2*a^4*b^2 + a^3*b^3)*d*cosh(d*x + c)^6 + 6*(a^5*b - 2*a^4*b^2 + a^3*b^3)*d*cosh(d*x + c)*sinh(d*x + c)^5 + (a^5*b - 2*a^4*b^2 + a^3*b^3)*d*sinh(d*x + c)^6 + (4*a^6 - 11*a^5*b + 10*a^4*b^2 - 3*a^3*b^3)*d*cosh(d*x + c)^4 + (15*(a^5*b - 2*a^4*b^2 + a^3*b^3)*d*cosh(d*x + c)^2 + (4*a^6 - 11*a^5*b + 10*a^4*b^2 - 3*a^3*b^3)*d)*sinh(d*x + c)^4 - (4*a^6 - 11*a^5*b + 10*a^4*b^2 - 3*a^3*b^3)*d*cosh(d*x + c)^2 + 4*(5*(a^5*b - 2*a^4*b^2 + a^3*b^3)*d*cosh(d*x + c)^3 + (4*a^6 - 11*a^5*b + 10*a^4*b^2 - 3*a^3*b^3)*d*cosh(d*x + c))*sinh(d*x + c)^3 + (15*(a^5*b - 2*a^4*b^2 + a^3*b^3)*d*cosh(d*x + c)^4 + 6*(4*a^6 - 11*a^5*b + 10*a^4*b^2 - 3*a^3*b^3)*d*cosh(d*x + c)^2 - (4*a^6 - 11*a^5*b + 10*a^4*b^2 - 3*a^3*b^3)*d)*sinh(d*x + c)^2 - (a^5*b - 2*a^4*b^2 + a^3*b^3)*d + 2*(3*(a^5*b - 2*a^4*b^2 + a^3*b^3)*d*cosh(d*x + c)^5 + 2*(4*a^6 - 11*a^5*b + 10*a^4*b^2 - 3*a^3*b^3)*d*cosh(d*x + c)^3 - (4*a^6 - 11*a^5*b + 10*a^4*b^2 - 3*a^3*b^3)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
49,1,8059,0,0.764834," ","integrate(csch(d*x+c)^3/(a+b*sinh(d*x+c)^2)^2,x, algorithm=""fricas"")","\left[-\frac{4 \, {\left(a^{2} b - 2 \, a b^{2}\right)} \cosh\left(d x + c\right)^{7} + 28 \, {\left(a^{2} b - 2 \, a b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + 4 \, {\left(a^{2} b - 2 \, a b^{2}\right)} \sinh\left(d x + c\right)^{7} + 4 \, {\left(4 \, a^{3} - 5 \, a^{2} b + 2 \, a b^{2}\right)} \cosh\left(d x + c\right)^{5} + 4 \, {\left(4 \, a^{3} - 5 \, a^{2} b + 2 \, a b^{2} + 21 \, {\left(a^{2} b - 2 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{5} + 20 \, {\left(7 \, {\left(a^{2} b - 2 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(4 \, a^{3} - 5 \, a^{2} b + 2 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(4 \, a^{3} - 5 \, a^{2} b + 2 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(35 \, {\left(a^{2} b - 2 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, a^{3} - 5 \, a^{2} b + 2 \, a b^{2} + 10 \, {\left(4 \, a^{3} - 5 \, a^{2} b + 2 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(21 \, {\left(a^{2} b - 2 \, a b^{2}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(4 \, a^{3} - 5 \, a^{2} b + 2 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(4 \, a^{3} - 5 \, a^{2} b + 2 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - {\left({\left(5 \, a b^{2} - 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(5 \, a b^{2} - 4 \, b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(5 \, a b^{2} - 4 \, b^{3}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(5 \, a^{2} b - 9 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(5 \, a^{2} b - 9 \, a b^{2} + 4 \, b^{3} + 7 \, {\left(5 \, a b^{2} - 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(5 \, a b^{2} - 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(5 \, a^{2} b - 9 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 2 \, {\left(20 \, a^{2} b - 31 \, a b^{2} + 12 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(5 \, a b^{2} - 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 20 \, a^{2} b + 31 \, a b^{2} - 12 \, b^{3} + 30 \, {\left(5 \, a^{2} b - 9 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(5 \, a b^{2} - 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(5 \, a^{2} b - 9 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - {\left(20 \, a^{2} b - 31 \, a b^{2} + 12 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 5 \, a b^{2} - 4 \, b^{3} + 4 \, {\left(5 \, a^{2} b - 9 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(5 \, a b^{2} - 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(5 \, a^{2} b - 9 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 5 \, a^{2} b - 9 \, a b^{2} + 4 \, b^{3} - 3 \, {\left(20 \, a^{2} b - 31 \, a b^{2} + 12 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left({\left(5 \, a b^{2} - 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(5 \, a^{2} b - 9 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - {\left(20 \, a^{2} b - 31 \, a b^{2} + 12 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(5 \, a^{2} b - 9 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{b}{a - b}} \log\left(\frac{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} - 2 \, {\left(2 \, a - 3 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} - 2 \, a + 3 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} - {\left(2 \, a - 3 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + 4 \, {\left({\left(a - b\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a - b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + {\left(a - b\right)} \sinh\left(d x + c\right)^{3} + {\left(a - b\right)} \cosh\left(d x + c\right) + {\left(3 \, {\left(a - b\right)} \cosh\left(d x + c\right)^{2} + a - b\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{b}{a - b}} + b}{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b}\right) + 4 \, {\left(a^{2} b - 2 \, a b^{2}\right)} \cosh\left(d x + c\right) - 2 \, {\left({\left(a^{2} b + 3 \, a b^{2} - 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{2} b + 3 \, a b^{2} - 4 \, b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{2} b + 3 \, a b^{2} - 4 \, b^{3}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{3} + 2 \, a^{2} b - 7 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(a^{3} + 2 \, a^{2} b - 7 \, a b^{2} + 4 \, b^{3} + 7 \, {\left(a^{2} b + 3 \, a b^{2} - 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} b + 3 \, a b^{2} - 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{3} + 2 \, a^{2} b - 7 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 2 \, {\left(4 \, a^{3} + 9 \, a^{2} b - 25 \, a b^{2} + 12 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} b + 3 \, a b^{2} - 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 4 \, a^{3} - 9 \, a^{2} b + 25 \, a b^{2} - 12 \, b^{3} + 30 \, {\left(a^{3} + 2 \, a^{2} b - 7 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} b + 3 \, a b^{2} - 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{3} + 2 \, a^{2} b - 7 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - {\left(4 \, a^{3} + 9 \, a^{2} b - 25 \, a b^{2} + 12 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + a^{2} b + 3 \, a b^{2} - 4 \, b^{3} + 4 \, {\left(a^{3} + 2 \, a^{2} b - 7 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} b + 3 \, a b^{2} - 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{3} + 2 \, a^{2} b - 7 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + a^{3} + 2 \, a^{2} b - 7 \, a b^{2} + 4 \, b^{3} - 3 \, {\left(4 \, a^{3} + 9 \, a^{2} b - 25 \, a b^{2} + 12 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left({\left(a^{2} b + 3 \, a b^{2} - 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{3} + 2 \, a^{2} b - 7 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - {\left(4 \, a^{3} + 9 \, a^{2} b - 25 \, a b^{2} + 12 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{3} + 2 \, a^{2} b - 7 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) + 2 \, {\left({\left(a^{2} b + 3 \, a b^{2} - 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{2} b + 3 \, a b^{2} - 4 \, b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{2} b + 3 \, a b^{2} - 4 \, b^{3}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{3} + 2 \, a^{2} b - 7 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(a^{3} + 2 \, a^{2} b - 7 \, a b^{2} + 4 \, b^{3} + 7 \, {\left(a^{2} b + 3 \, a b^{2} - 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} b + 3 \, a b^{2} - 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{3} + 2 \, a^{2} b - 7 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 2 \, {\left(4 \, a^{3} + 9 \, a^{2} b - 25 \, a b^{2} + 12 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} b + 3 \, a b^{2} - 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 4 \, a^{3} - 9 \, a^{2} b + 25 \, a b^{2} - 12 \, b^{3} + 30 \, {\left(a^{3} + 2 \, a^{2} b - 7 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} b + 3 \, a b^{2} - 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{3} + 2 \, a^{2} b - 7 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - {\left(4 \, a^{3} + 9 \, a^{2} b - 25 \, a b^{2} + 12 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + a^{2} b + 3 \, a b^{2} - 4 \, b^{3} + 4 \, {\left(a^{3} + 2 \, a^{2} b - 7 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} b + 3 \, a b^{2} - 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{3} + 2 \, a^{2} b - 7 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + a^{3} + 2 \, a^{2} b - 7 \, a b^{2} + 4 \, b^{3} - 3 \, {\left(4 \, a^{3} + 9 \, a^{2} b - 25 \, a b^{2} + 12 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left({\left(a^{2} b + 3 \, a b^{2} - 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{3} + 2 \, a^{2} b - 7 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - {\left(4 \, a^{3} + 9 \, a^{2} b - 25 \, a b^{2} + 12 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{3} + 2 \, a^{2} b - 7 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) + 4 \, {\left(7 \, {\left(a^{2} b - 2 \, a b^{2}\right)} \cosh\left(d x + c\right)^{6} + 5 \, {\left(4 \, a^{3} - 5 \, a^{2} b + 2 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} + a^{2} b - 2 \, a b^{2} + 3 \, {\left(4 \, a^{3} - 5 \, a^{2} b + 2 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)}{4 \, {\left({\left(a^{4} b - a^{3} b^{2}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{4} b - a^{3} b^{2}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{4} b - a^{3} b^{2}\right)} d \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{5} - 2 \, a^{4} b + a^{3} b^{2}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{4} b - a^{3} b^{2}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{5} - 2 \, a^{4} b + a^{3} b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{6} - 2 \, {\left(4 \, a^{5} - 7 \, a^{4} b + 3 \, a^{3} b^{2}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{4} b - a^{3} b^{2}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{5} - 2 \, a^{4} b + a^{3} b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a^{4} b - a^{3} b^{2}\right)} d \cosh\left(d x + c\right)^{4} + 30 \, {\left(a^{5} - 2 \, a^{4} b + a^{3} b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(4 \, a^{5} - 7 \, a^{4} b + 3 \, a^{3} b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{5} - 2 \, a^{4} b + a^{3} b^{2}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a^{4} b - a^{3} b^{2}\right)} d \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{5} - 2 \, a^{4} b + a^{3} b^{2}\right)} d \cosh\left(d x + c\right)^{3} - {\left(4 \, a^{5} - 7 \, a^{4} b + 3 \, a^{3} b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a^{4} b - a^{3} b^{2}\right)} d \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{5} - 2 \, a^{4} b + a^{3} b^{2}\right)} d \cosh\left(d x + c\right)^{4} - 3 \, {\left(4 \, a^{5} - 7 \, a^{4} b + 3 \, a^{3} b^{2}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{5} - 2 \, a^{4} b + a^{3} b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{4} b - a^{3} b^{2}\right)} d + 8 \, {\left({\left(a^{4} b - a^{3} b^{2}\right)} d \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{5} - 2 \, a^{4} b + a^{3} b^{2}\right)} d \cosh\left(d x + c\right)^{5} - {\left(4 \, a^{5} - 7 \, a^{4} b + 3 \, a^{3} b^{2}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{5} - 2 \, a^{4} b + a^{3} b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}, -\frac{2 \, {\left(a^{2} b - 2 \, a b^{2}\right)} \cosh\left(d x + c\right)^{7} + 14 \, {\left(a^{2} b - 2 \, a b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + 2 \, {\left(a^{2} b - 2 \, a b^{2}\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(4 \, a^{3} - 5 \, a^{2} b + 2 \, a b^{2}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(4 \, a^{3} - 5 \, a^{2} b + 2 \, a b^{2} + 21 \, {\left(a^{2} b - 2 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{5} + 10 \, {\left(7 \, {\left(a^{2} b - 2 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(4 \, a^{3} - 5 \, a^{2} b + 2 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(4 \, a^{3} - 5 \, a^{2} b + 2 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(35 \, {\left(a^{2} b - 2 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, a^{3} - 5 \, a^{2} b + 2 \, a b^{2} + 10 \, {\left(4 \, a^{3} - 5 \, a^{2} b + 2 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(21 \, {\left(a^{2} b - 2 \, a b^{2}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(4 \, a^{3} - 5 \, a^{2} b + 2 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(4 \, a^{3} - 5 \, a^{2} b + 2 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - {\left({\left(5 \, a b^{2} - 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(5 \, a b^{2} - 4 \, b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(5 \, a b^{2} - 4 \, b^{3}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(5 \, a^{2} b - 9 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(5 \, a^{2} b - 9 \, a b^{2} + 4 \, b^{3} + 7 \, {\left(5 \, a b^{2} - 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(5 \, a b^{2} - 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(5 \, a^{2} b - 9 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 2 \, {\left(20 \, a^{2} b - 31 \, a b^{2} + 12 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(5 \, a b^{2} - 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 20 \, a^{2} b + 31 \, a b^{2} - 12 \, b^{3} + 30 \, {\left(5 \, a^{2} b - 9 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(5 \, a b^{2} - 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(5 \, a^{2} b - 9 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - {\left(20 \, a^{2} b - 31 \, a b^{2} + 12 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 5 \, a b^{2} - 4 \, b^{3} + 4 \, {\left(5 \, a^{2} b - 9 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(5 \, a b^{2} - 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(5 \, a^{2} b - 9 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 5 \, a^{2} b - 9 \, a b^{2} + 4 \, b^{3} - 3 \, {\left(20 \, a^{2} b - 31 \, a b^{2} + 12 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left({\left(5 \, a b^{2} - 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(5 \, a^{2} b - 9 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - {\left(20 \, a^{2} b - 31 \, a b^{2} + 12 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(5 \, a^{2} b - 9 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{b}{a - b}} \arctan\left(\frac{1}{2} \, \sqrt{\frac{b}{a - b}} {\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right)}\right) + {\left({\left(5 \, a b^{2} - 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(5 \, a b^{2} - 4 \, b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(5 \, a b^{2} - 4 \, b^{3}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(5 \, a^{2} b - 9 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(5 \, a^{2} b - 9 \, a b^{2} + 4 \, b^{3} + 7 \, {\left(5 \, a b^{2} - 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(5 \, a b^{2} - 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(5 \, a^{2} b - 9 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 2 \, {\left(20 \, a^{2} b - 31 \, a b^{2} + 12 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(5 \, a b^{2} - 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 20 \, a^{2} b + 31 \, a b^{2} - 12 \, b^{3} + 30 \, {\left(5 \, a^{2} b - 9 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(5 \, a b^{2} - 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(5 \, a^{2} b - 9 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - {\left(20 \, a^{2} b - 31 \, a b^{2} + 12 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 5 \, a b^{2} - 4 \, b^{3} + 4 \, {\left(5 \, a^{2} b - 9 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(5 \, a b^{2} - 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(5 \, a^{2} b - 9 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 5 \, a^{2} b - 9 \, a b^{2} + 4 \, b^{3} - 3 \, {\left(20 \, a^{2} b - 31 \, a b^{2} + 12 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left({\left(5 \, a b^{2} - 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(5 \, a^{2} b - 9 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - {\left(20 \, a^{2} b - 31 \, a b^{2} + 12 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(5 \, a^{2} b - 9 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{b}{a - b}} \arctan\left(\frac{{\left(b \cosh\left(d x + c\right)^{3} + 3 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{3} + {\left(4 \, a - 3 \, b\right)} \cosh\left(d x + c\right) + {\left(3 \, b \cosh\left(d x + c\right)^{2} + 4 \, a - 3 \, b\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{b}{a - b}}}{2 \, b}\right) + 2 \, {\left(a^{2} b - 2 \, a b^{2}\right)} \cosh\left(d x + c\right) - {\left({\left(a^{2} b + 3 \, a b^{2} - 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{2} b + 3 \, a b^{2} - 4 \, b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{2} b + 3 \, a b^{2} - 4 \, b^{3}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{3} + 2 \, a^{2} b - 7 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(a^{3} + 2 \, a^{2} b - 7 \, a b^{2} + 4 \, b^{3} + 7 \, {\left(a^{2} b + 3 \, a b^{2} - 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} b + 3 \, a b^{2} - 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{3} + 2 \, a^{2} b - 7 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 2 \, {\left(4 \, a^{3} + 9 \, a^{2} b - 25 \, a b^{2} + 12 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} b + 3 \, a b^{2} - 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 4 \, a^{3} - 9 \, a^{2} b + 25 \, a b^{2} - 12 \, b^{3} + 30 \, {\left(a^{3} + 2 \, a^{2} b - 7 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} b + 3 \, a b^{2} - 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{3} + 2 \, a^{2} b - 7 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - {\left(4 \, a^{3} + 9 \, a^{2} b - 25 \, a b^{2} + 12 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + a^{2} b + 3 \, a b^{2} - 4 \, b^{3} + 4 \, {\left(a^{3} + 2 \, a^{2} b - 7 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} b + 3 \, a b^{2} - 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{3} + 2 \, a^{2} b - 7 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + a^{3} + 2 \, a^{2} b - 7 \, a b^{2} + 4 \, b^{3} - 3 \, {\left(4 \, a^{3} + 9 \, a^{2} b - 25 \, a b^{2} + 12 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left({\left(a^{2} b + 3 \, a b^{2} - 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{3} + 2 \, a^{2} b - 7 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - {\left(4 \, a^{3} + 9 \, a^{2} b - 25 \, a b^{2} + 12 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{3} + 2 \, a^{2} b - 7 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) + {\left({\left(a^{2} b + 3 \, a b^{2} - 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{2} b + 3 \, a b^{2} - 4 \, b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{2} b + 3 \, a b^{2} - 4 \, b^{3}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{3} + 2 \, a^{2} b - 7 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(a^{3} + 2 \, a^{2} b - 7 \, a b^{2} + 4 \, b^{3} + 7 \, {\left(a^{2} b + 3 \, a b^{2} - 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} b + 3 \, a b^{2} - 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{3} + 2 \, a^{2} b - 7 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 2 \, {\left(4 \, a^{3} + 9 \, a^{2} b - 25 \, a b^{2} + 12 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} b + 3 \, a b^{2} - 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 4 \, a^{3} - 9 \, a^{2} b + 25 \, a b^{2} - 12 \, b^{3} + 30 \, {\left(a^{3} + 2 \, a^{2} b - 7 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} b + 3 \, a b^{2} - 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{3} + 2 \, a^{2} b - 7 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - {\left(4 \, a^{3} + 9 \, a^{2} b - 25 \, a b^{2} + 12 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + a^{2} b + 3 \, a b^{2} - 4 \, b^{3} + 4 \, {\left(a^{3} + 2 \, a^{2} b - 7 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} b + 3 \, a b^{2} - 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{3} + 2 \, a^{2} b - 7 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + a^{3} + 2 \, a^{2} b - 7 \, a b^{2} + 4 \, b^{3} - 3 \, {\left(4 \, a^{3} + 9 \, a^{2} b - 25 \, a b^{2} + 12 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left({\left(a^{2} b + 3 \, a b^{2} - 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{3} + 2 \, a^{2} b - 7 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - {\left(4 \, a^{3} + 9 \, a^{2} b - 25 \, a b^{2} + 12 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{3} + 2 \, a^{2} b - 7 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) + 2 \, {\left(7 \, {\left(a^{2} b - 2 \, a b^{2}\right)} \cosh\left(d x + c\right)^{6} + 5 \, {\left(4 \, a^{3} - 5 \, a^{2} b + 2 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} + a^{2} b - 2 \, a b^{2} + 3 \, {\left(4 \, a^{3} - 5 \, a^{2} b + 2 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)}{2 \, {\left({\left(a^{4} b - a^{3} b^{2}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{4} b - a^{3} b^{2}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{4} b - a^{3} b^{2}\right)} d \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{5} - 2 \, a^{4} b + a^{3} b^{2}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{4} b - a^{3} b^{2}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{5} - 2 \, a^{4} b + a^{3} b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{6} - 2 \, {\left(4 \, a^{5} - 7 \, a^{4} b + 3 \, a^{3} b^{2}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{4} b - a^{3} b^{2}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{5} - 2 \, a^{4} b + a^{3} b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a^{4} b - a^{3} b^{2}\right)} d \cosh\left(d x + c\right)^{4} + 30 \, {\left(a^{5} - 2 \, a^{4} b + a^{3} b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(4 \, a^{5} - 7 \, a^{4} b + 3 \, a^{3} b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{5} - 2 \, a^{4} b + a^{3} b^{2}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a^{4} b - a^{3} b^{2}\right)} d \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{5} - 2 \, a^{4} b + a^{3} b^{2}\right)} d \cosh\left(d x + c\right)^{3} - {\left(4 \, a^{5} - 7 \, a^{4} b + 3 \, a^{3} b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a^{4} b - a^{3} b^{2}\right)} d \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{5} - 2 \, a^{4} b + a^{3} b^{2}\right)} d \cosh\left(d x + c\right)^{4} - 3 \, {\left(4 \, a^{5} - 7 \, a^{4} b + 3 \, a^{3} b^{2}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{5} - 2 \, a^{4} b + a^{3} b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{4} b - a^{3} b^{2}\right)} d + 8 \, {\left({\left(a^{4} b - a^{3} b^{2}\right)} d \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{5} - 2 \, a^{4} b + a^{3} b^{2}\right)} d \cosh\left(d x + c\right)^{5} - {\left(4 \, a^{5} - 7 \, a^{4} b + 3 \, a^{3} b^{2}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{5} - 2 \, a^{4} b + a^{3} b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[-1/4*(4*(a^2*b - 2*a*b^2)*cosh(d*x + c)^7 + 28*(a^2*b - 2*a*b^2)*cosh(d*x + c)*sinh(d*x + c)^6 + 4*(a^2*b - 2*a*b^2)*sinh(d*x + c)^7 + 4*(4*a^3 - 5*a^2*b + 2*a*b^2)*cosh(d*x + c)^5 + 4*(4*a^3 - 5*a^2*b + 2*a*b^2 + 21*(a^2*b - 2*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 20*(7*(a^2*b - 2*a*b^2)*cosh(d*x + c)^3 + (4*a^3 - 5*a^2*b + 2*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^4 + 4*(4*a^3 - 5*a^2*b + 2*a*b^2)*cosh(d*x + c)^3 + 4*(35*(a^2*b - 2*a*b^2)*cosh(d*x + c)^4 + 4*a^3 - 5*a^2*b + 2*a*b^2 + 10*(4*a^3 - 5*a^2*b + 2*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 4*(21*(a^2*b - 2*a*b^2)*cosh(d*x + c)^5 + 10*(4*a^3 - 5*a^2*b + 2*a*b^2)*cosh(d*x + c)^3 + 3*(4*a^3 - 5*a^2*b + 2*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^2 - ((5*a*b^2 - 4*b^3)*cosh(d*x + c)^8 + 8*(5*a*b^2 - 4*b^3)*cosh(d*x + c)*sinh(d*x + c)^7 + (5*a*b^2 - 4*b^3)*sinh(d*x + c)^8 + 4*(5*a^2*b - 9*a*b^2 + 4*b^3)*cosh(d*x + c)^6 + 4*(5*a^2*b - 9*a*b^2 + 4*b^3 + 7*(5*a*b^2 - 4*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(5*a*b^2 - 4*b^3)*cosh(d*x + c)^3 + 3*(5*a^2*b - 9*a*b^2 + 4*b^3)*cosh(d*x + c))*sinh(d*x + c)^5 - 2*(20*a^2*b - 31*a*b^2 + 12*b^3)*cosh(d*x + c)^4 + 2*(35*(5*a*b^2 - 4*b^3)*cosh(d*x + c)^4 - 20*a^2*b + 31*a*b^2 - 12*b^3 + 30*(5*a^2*b - 9*a*b^2 + 4*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(7*(5*a*b^2 - 4*b^3)*cosh(d*x + c)^5 + 10*(5*a^2*b - 9*a*b^2 + 4*b^3)*cosh(d*x + c)^3 - (20*a^2*b - 31*a*b^2 + 12*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 + 5*a*b^2 - 4*b^3 + 4*(5*a^2*b - 9*a*b^2 + 4*b^3)*cosh(d*x + c)^2 + 4*(7*(5*a*b^2 - 4*b^3)*cosh(d*x + c)^6 + 15*(5*a^2*b - 9*a*b^2 + 4*b^3)*cosh(d*x + c)^4 + 5*a^2*b - 9*a*b^2 + 4*b^3 - 3*(20*a^2*b - 31*a*b^2 + 12*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((5*a*b^2 - 4*b^3)*cosh(d*x + c)^7 + 3*(5*a^2*b - 9*a*b^2 + 4*b^3)*cosh(d*x + c)^5 - (20*a^2*b - 31*a*b^2 + 12*b^3)*cosh(d*x + c)^3 + (5*a^2*b - 9*a*b^2 + 4*b^3)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-b/(a - b))*log((b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 - 2*(2*a - 3*b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 - 2*a + 3*b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 - (2*a - 3*b)*cosh(d*x + c))*sinh(d*x + c) + 4*((a - b)*cosh(d*x + c)^3 + 3*(a - b)*cosh(d*x + c)*sinh(d*x + c)^2 + (a - b)*sinh(d*x + c)^3 + (a - b)*cosh(d*x + c) + (3*(a - b)*cosh(d*x + c)^2 + a - b)*sinh(d*x + c))*sqrt(-b/(a - b)) + b)/(b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 + 2*(2*a - b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 + 2*a - b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 + (2*a - b)*cosh(d*x + c))*sinh(d*x + c) + b)) + 4*(a^2*b - 2*a*b^2)*cosh(d*x + c) - 2*((a^2*b + 3*a*b^2 - 4*b^3)*cosh(d*x + c)^8 + 8*(a^2*b + 3*a*b^2 - 4*b^3)*cosh(d*x + c)*sinh(d*x + c)^7 + (a^2*b + 3*a*b^2 - 4*b^3)*sinh(d*x + c)^8 + 4*(a^3 + 2*a^2*b - 7*a*b^2 + 4*b^3)*cosh(d*x + c)^6 + 4*(a^3 + 2*a^2*b - 7*a*b^2 + 4*b^3 + 7*(a^2*b + 3*a*b^2 - 4*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(a^2*b + 3*a*b^2 - 4*b^3)*cosh(d*x + c)^3 + 3*(a^3 + 2*a^2*b - 7*a*b^2 + 4*b^3)*cosh(d*x + c))*sinh(d*x + c)^5 - 2*(4*a^3 + 9*a^2*b - 25*a*b^2 + 12*b^3)*cosh(d*x + c)^4 + 2*(35*(a^2*b + 3*a*b^2 - 4*b^3)*cosh(d*x + c)^4 - 4*a^3 - 9*a^2*b + 25*a*b^2 - 12*b^3 + 30*(a^3 + 2*a^2*b - 7*a*b^2 + 4*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(7*(a^2*b + 3*a*b^2 - 4*b^3)*cosh(d*x + c)^5 + 10*(a^3 + 2*a^2*b - 7*a*b^2 + 4*b^3)*cosh(d*x + c)^3 - (4*a^3 + 9*a^2*b - 25*a*b^2 + 12*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 + a^2*b + 3*a*b^2 - 4*b^3 + 4*(a^3 + 2*a^2*b - 7*a*b^2 + 4*b^3)*cosh(d*x + c)^2 + 4*(7*(a^2*b + 3*a*b^2 - 4*b^3)*cosh(d*x + c)^6 + 15*(a^3 + 2*a^2*b - 7*a*b^2 + 4*b^3)*cosh(d*x + c)^4 + a^3 + 2*a^2*b - 7*a*b^2 + 4*b^3 - 3*(4*a^3 + 9*a^2*b - 25*a*b^2 + 12*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((a^2*b + 3*a*b^2 - 4*b^3)*cosh(d*x + c)^7 + 3*(a^3 + 2*a^2*b - 7*a*b^2 + 4*b^3)*cosh(d*x + c)^5 - (4*a^3 + 9*a^2*b - 25*a*b^2 + 12*b^3)*cosh(d*x + c)^3 + (a^3 + 2*a^2*b - 7*a*b^2 + 4*b^3)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) + 1) + 2*((a^2*b + 3*a*b^2 - 4*b^3)*cosh(d*x + c)^8 + 8*(a^2*b + 3*a*b^2 - 4*b^3)*cosh(d*x + c)*sinh(d*x + c)^7 + (a^2*b + 3*a*b^2 - 4*b^3)*sinh(d*x + c)^8 + 4*(a^3 + 2*a^2*b - 7*a*b^2 + 4*b^3)*cosh(d*x + c)^6 + 4*(a^3 + 2*a^2*b - 7*a*b^2 + 4*b^3 + 7*(a^2*b + 3*a*b^2 - 4*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(a^2*b + 3*a*b^2 - 4*b^3)*cosh(d*x + c)^3 + 3*(a^3 + 2*a^2*b - 7*a*b^2 + 4*b^3)*cosh(d*x + c))*sinh(d*x + c)^5 - 2*(4*a^3 + 9*a^2*b - 25*a*b^2 + 12*b^3)*cosh(d*x + c)^4 + 2*(35*(a^2*b + 3*a*b^2 - 4*b^3)*cosh(d*x + c)^4 - 4*a^3 - 9*a^2*b + 25*a*b^2 - 12*b^3 + 30*(a^3 + 2*a^2*b - 7*a*b^2 + 4*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(7*(a^2*b + 3*a*b^2 - 4*b^3)*cosh(d*x + c)^5 + 10*(a^3 + 2*a^2*b - 7*a*b^2 + 4*b^3)*cosh(d*x + c)^3 - (4*a^3 + 9*a^2*b - 25*a*b^2 + 12*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 + a^2*b + 3*a*b^2 - 4*b^3 + 4*(a^3 + 2*a^2*b - 7*a*b^2 + 4*b^3)*cosh(d*x + c)^2 + 4*(7*(a^2*b + 3*a*b^2 - 4*b^3)*cosh(d*x + c)^6 + 15*(a^3 + 2*a^2*b - 7*a*b^2 + 4*b^3)*cosh(d*x + c)^4 + a^3 + 2*a^2*b - 7*a*b^2 + 4*b^3 - 3*(4*a^3 + 9*a^2*b - 25*a*b^2 + 12*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((a^2*b + 3*a*b^2 - 4*b^3)*cosh(d*x + c)^7 + 3*(a^3 + 2*a^2*b - 7*a*b^2 + 4*b^3)*cosh(d*x + c)^5 - (4*a^3 + 9*a^2*b - 25*a*b^2 + 12*b^3)*cosh(d*x + c)^3 + (a^3 + 2*a^2*b - 7*a*b^2 + 4*b^3)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) - 1) + 4*(7*(a^2*b - 2*a*b^2)*cosh(d*x + c)^6 + 5*(4*a^3 - 5*a^2*b + 2*a*b^2)*cosh(d*x + c)^4 + a^2*b - 2*a*b^2 + 3*(4*a^3 - 5*a^2*b + 2*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c))/((a^4*b - a^3*b^2)*d*cosh(d*x + c)^8 + 8*(a^4*b - a^3*b^2)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^4*b - a^3*b^2)*d*sinh(d*x + c)^8 + 4*(a^5 - 2*a^4*b + a^3*b^2)*d*cosh(d*x + c)^6 + 4*(7*(a^4*b - a^3*b^2)*d*cosh(d*x + c)^2 + (a^5 - 2*a^4*b + a^3*b^2)*d)*sinh(d*x + c)^6 - 2*(4*a^5 - 7*a^4*b + 3*a^3*b^2)*d*cosh(d*x + c)^4 + 8*(7*(a^4*b - a^3*b^2)*d*cosh(d*x + c)^3 + 3*(a^5 - 2*a^4*b + a^3*b^2)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^4*b - a^3*b^2)*d*cosh(d*x + c)^4 + 30*(a^5 - 2*a^4*b + a^3*b^2)*d*cosh(d*x + c)^2 - (4*a^5 - 7*a^4*b + 3*a^3*b^2)*d)*sinh(d*x + c)^4 + 4*(a^5 - 2*a^4*b + a^3*b^2)*d*cosh(d*x + c)^2 + 8*(7*(a^4*b - a^3*b^2)*d*cosh(d*x + c)^5 + 10*(a^5 - 2*a^4*b + a^3*b^2)*d*cosh(d*x + c)^3 - (4*a^5 - 7*a^4*b + 3*a^3*b^2)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^4*b - a^3*b^2)*d*cosh(d*x + c)^6 + 15*(a^5 - 2*a^4*b + a^3*b^2)*d*cosh(d*x + c)^4 - 3*(4*a^5 - 7*a^4*b + 3*a^3*b^2)*d*cosh(d*x + c)^2 + (a^5 - 2*a^4*b + a^3*b^2)*d)*sinh(d*x + c)^2 + (a^4*b - a^3*b^2)*d + 8*((a^4*b - a^3*b^2)*d*cosh(d*x + c)^7 + 3*(a^5 - 2*a^4*b + a^3*b^2)*d*cosh(d*x + c)^5 - (4*a^5 - 7*a^4*b + 3*a^3*b^2)*d*cosh(d*x + c)^3 + (a^5 - 2*a^4*b + a^3*b^2)*d*cosh(d*x + c))*sinh(d*x + c)), -1/2*(2*(a^2*b - 2*a*b^2)*cosh(d*x + c)^7 + 14*(a^2*b - 2*a*b^2)*cosh(d*x + c)*sinh(d*x + c)^6 + 2*(a^2*b - 2*a*b^2)*sinh(d*x + c)^7 + 2*(4*a^3 - 5*a^2*b + 2*a*b^2)*cosh(d*x + c)^5 + 2*(4*a^3 - 5*a^2*b + 2*a*b^2 + 21*(a^2*b - 2*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 10*(7*(a^2*b - 2*a*b^2)*cosh(d*x + c)^3 + (4*a^3 - 5*a^2*b + 2*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^4 + 2*(4*a^3 - 5*a^2*b + 2*a*b^2)*cosh(d*x + c)^3 + 2*(35*(a^2*b - 2*a*b^2)*cosh(d*x + c)^4 + 4*a^3 - 5*a^2*b + 2*a*b^2 + 10*(4*a^3 - 5*a^2*b + 2*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 2*(21*(a^2*b - 2*a*b^2)*cosh(d*x + c)^5 + 10*(4*a^3 - 5*a^2*b + 2*a*b^2)*cosh(d*x + c)^3 + 3*(4*a^3 - 5*a^2*b + 2*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^2 - ((5*a*b^2 - 4*b^3)*cosh(d*x + c)^8 + 8*(5*a*b^2 - 4*b^3)*cosh(d*x + c)*sinh(d*x + c)^7 + (5*a*b^2 - 4*b^3)*sinh(d*x + c)^8 + 4*(5*a^2*b - 9*a*b^2 + 4*b^3)*cosh(d*x + c)^6 + 4*(5*a^2*b - 9*a*b^2 + 4*b^3 + 7*(5*a*b^2 - 4*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(5*a*b^2 - 4*b^3)*cosh(d*x + c)^3 + 3*(5*a^2*b - 9*a*b^2 + 4*b^3)*cosh(d*x + c))*sinh(d*x + c)^5 - 2*(20*a^2*b - 31*a*b^2 + 12*b^3)*cosh(d*x + c)^4 + 2*(35*(5*a*b^2 - 4*b^3)*cosh(d*x + c)^4 - 20*a^2*b + 31*a*b^2 - 12*b^3 + 30*(5*a^2*b - 9*a*b^2 + 4*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(7*(5*a*b^2 - 4*b^3)*cosh(d*x + c)^5 + 10*(5*a^2*b - 9*a*b^2 + 4*b^3)*cosh(d*x + c)^3 - (20*a^2*b - 31*a*b^2 + 12*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 + 5*a*b^2 - 4*b^3 + 4*(5*a^2*b - 9*a*b^2 + 4*b^3)*cosh(d*x + c)^2 + 4*(7*(5*a*b^2 - 4*b^3)*cosh(d*x + c)^6 + 15*(5*a^2*b - 9*a*b^2 + 4*b^3)*cosh(d*x + c)^4 + 5*a^2*b - 9*a*b^2 + 4*b^3 - 3*(20*a^2*b - 31*a*b^2 + 12*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((5*a*b^2 - 4*b^3)*cosh(d*x + c)^7 + 3*(5*a^2*b - 9*a*b^2 + 4*b^3)*cosh(d*x + c)^5 - (20*a^2*b - 31*a*b^2 + 12*b^3)*cosh(d*x + c)^3 + (5*a^2*b - 9*a*b^2 + 4*b^3)*cosh(d*x + c))*sinh(d*x + c))*sqrt(b/(a - b))*arctan(1/2*sqrt(b/(a - b))*(cosh(d*x + c) + sinh(d*x + c))) + ((5*a*b^2 - 4*b^3)*cosh(d*x + c)^8 + 8*(5*a*b^2 - 4*b^3)*cosh(d*x + c)*sinh(d*x + c)^7 + (5*a*b^2 - 4*b^3)*sinh(d*x + c)^8 + 4*(5*a^2*b - 9*a*b^2 + 4*b^3)*cosh(d*x + c)^6 + 4*(5*a^2*b - 9*a*b^2 + 4*b^3 + 7*(5*a*b^2 - 4*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(5*a*b^2 - 4*b^3)*cosh(d*x + c)^3 + 3*(5*a^2*b - 9*a*b^2 + 4*b^3)*cosh(d*x + c))*sinh(d*x + c)^5 - 2*(20*a^2*b - 31*a*b^2 + 12*b^3)*cosh(d*x + c)^4 + 2*(35*(5*a*b^2 - 4*b^3)*cosh(d*x + c)^4 - 20*a^2*b + 31*a*b^2 - 12*b^3 + 30*(5*a^2*b - 9*a*b^2 + 4*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(7*(5*a*b^2 - 4*b^3)*cosh(d*x + c)^5 + 10*(5*a^2*b - 9*a*b^2 + 4*b^3)*cosh(d*x + c)^3 - (20*a^2*b - 31*a*b^2 + 12*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 + 5*a*b^2 - 4*b^3 + 4*(5*a^2*b - 9*a*b^2 + 4*b^3)*cosh(d*x + c)^2 + 4*(7*(5*a*b^2 - 4*b^3)*cosh(d*x + c)^6 + 15*(5*a^2*b - 9*a*b^2 + 4*b^3)*cosh(d*x + c)^4 + 5*a^2*b - 9*a*b^2 + 4*b^3 - 3*(20*a^2*b - 31*a*b^2 + 12*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((5*a*b^2 - 4*b^3)*cosh(d*x + c)^7 + 3*(5*a^2*b - 9*a*b^2 + 4*b^3)*cosh(d*x + c)^5 - (20*a^2*b - 31*a*b^2 + 12*b^3)*cosh(d*x + c)^3 + (5*a^2*b - 9*a*b^2 + 4*b^3)*cosh(d*x + c))*sinh(d*x + c))*sqrt(b/(a - b))*arctan(1/2*(b*cosh(d*x + c)^3 + 3*b*cosh(d*x + c)*sinh(d*x + c)^2 + b*sinh(d*x + c)^3 + (4*a - 3*b)*cosh(d*x + c) + (3*b*cosh(d*x + c)^2 + 4*a - 3*b)*sinh(d*x + c))*sqrt(b/(a - b))/b) + 2*(a^2*b - 2*a*b^2)*cosh(d*x + c) - ((a^2*b + 3*a*b^2 - 4*b^3)*cosh(d*x + c)^8 + 8*(a^2*b + 3*a*b^2 - 4*b^3)*cosh(d*x + c)*sinh(d*x + c)^7 + (a^2*b + 3*a*b^2 - 4*b^3)*sinh(d*x + c)^8 + 4*(a^3 + 2*a^2*b - 7*a*b^2 + 4*b^3)*cosh(d*x + c)^6 + 4*(a^3 + 2*a^2*b - 7*a*b^2 + 4*b^3 + 7*(a^2*b + 3*a*b^2 - 4*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(a^2*b + 3*a*b^2 - 4*b^3)*cosh(d*x + c)^3 + 3*(a^3 + 2*a^2*b - 7*a*b^2 + 4*b^3)*cosh(d*x + c))*sinh(d*x + c)^5 - 2*(4*a^3 + 9*a^2*b - 25*a*b^2 + 12*b^3)*cosh(d*x + c)^4 + 2*(35*(a^2*b + 3*a*b^2 - 4*b^3)*cosh(d*x + c)^4 - 4*a^3 - 9*a^2*b + 25*a*b^2 - 12*b^3 + 30*(a^3 + 2*a^2*b - 7*a*b^2 + 4*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(7*(a^2*b + 3*a*b^2 - 4*b^3)*cosh(d*x + c)^5 + 10*(a^3 + 2*a^2*b - 7*a*b^2 + 4*b^3)*cosh(d*x + c)^3 - (4*a^3 + 9*a^2*b - 25*a*b^2 + 12*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 + a^2*b + 3*a*b^2 - 4*b^3 + 4*(a^3 + 2*a^2*b - 7*a*b^2 + 4*b^3)*cosh(d*x + c)^2 + 4*(7*(a^2*b + 3*a*b^2 - 4*b^3)*cosh(d*x + c)^6 + 15*(a^3 + 2*a^2*b - 7*a*b^2 + 4*b^3)*cosh(d*x + c)^4 + a^3 + 2*a^2*b - 7*a*b^2 + 4*b^3 - 3*(4*a^3 + 9*a^2*b - 25*a*b^2 + 12*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((a^2*b + 3*a*b^2 - 4*b^3)*cosh(d*x + c)^7 + 3*(a^3 + 2*a^2*b - 7*a*b^2 + 4*b^3)*cosh(d*x + c)^5 - (4*a^3 + 9*a^2*b - 25*a*b^2 + 12*b^3)*cosh(d*x + c)^3 + (a^3 + 2*a^2*b - 7*a*b^2 + 4*b^3)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) + 1) + ((a^2*b + 3*a*b^2 - 4*b^3)*cosh(d*x + c)^8 + 8*(a^2*b + 3*a*b^2 - 4*b^3)*cosh(d*x + c)*sinh(d*x + c)^7 + (a^2*b + 3*a*b^2 - 4*b^3)*sinh(d*x + c)^8 + 4*(a^3 + 2*a^2*b - 7*a*b^2 + 4*b^3)*cosh(d*x + c)^6 + 4*(a^3 + 2*a^2*b - 7*a*b^2 + 4*b^3 + 7*(a^2*b + 3*a*b^2 - 4*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(a^2*b + 3*a*b^2 - 4*b^3)*cosh(d*x + c)^3 + 3*(a^3 + 2*a^2*b - 7*a*b^2 + 4*b^3)*cosh(d*x + c))*sinh(d*x + c)^5 - 2*(4*a^3 + 9*a^2*b - 25*a*b^2 + 12*b^3)*cosh(d*x + c)^4 + 2*(35*(a^2*b + 3*a*b^2 - 4*b^3)*cosh(d*x + c)^4 - 4*a^3 - 9*a^2*b + 25*a*b^2 - 12*b^3 + 30*(a^3 + 2*a^2*b - 7*a*b^2 + 4*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(7*(a^2*b + 3*a*b^2 - 4*b^3)*cosh(d*x + c)^5 + 10*(a^3 + 2*a^2*b - 7*a*b^2 + 4*b^3)*cosh(d*x + c)^3 - (4*a^3 + 9*a^2*b - 25*a*b^2 + 12*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 + a^2*b + 3*a*b^2 - 4*b^3 + 4*(a^3 + 2*a^2*b - 7*a*b^2 + 4*b^3)*cosh(d*x + c)^2 + 4*(7*(a^2*b + 3*a*b^2 - 4*b^3)*cosh(d*x + c)^6 + 15*(a^3 + 2*a^2*b - 7*a*b^2 + 4*b^3)*cosh(d*x + c)^4 + a^3 + 2*a^2*b - 7*a*b^2 + 4*b^3 - 3*(4*a^3 + 9*a^2*b - 25*a*b^2 + 12*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((a^2*b + 3*a*b^2 - 4*b^3)*cosh(d*x + c)^7 + 3*(a^3 + 2*a^2*b - 7*a*b^2 + 4*b^3)*cosh(d*x + c)^5 - (4*a^3 + 9*a^2*b - 25*a*b^2 + 12*b^3)*cosh(d*x + c)^3 + (a^3 + 2*a^2*b - 7*a*b^2 + 4*b^3)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) - 1) + 2*(7*(a^2*b - 2*a*b^2)*cosh(d*x + c)^6 + 5*(4*a^3 - 5*a^2*b + 2*a*b^2)*cosh(d*x + c)^4 + a^2*b - 2*a*b^2 + 3*(4*a^3 - 5*a^2*b + 2*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c))/((a^4*b - a^3*b^2)*d*cosh(d*x + c)^8 + 8*(a^4*b - a^3*b^2)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^4*b - a^3*b^2)*d*sinh(d*x + c)^8 + 4*(a^5 - 2*a^4*b + a^3*b^2)*d*cosh(d*x + c)^6 + 4*(7*(a^4*b - a^3*b^2)*d*cosh(d*x + c)^2 + (a^5 - 2*a^4*b + a^3*b^2)*d)*sinh(d*x + c)^6 - 2*(4*a^5 - 7*a^4*b + 3*a^3*b^2)*d*cosh(d*x + c)^4 + 8*(7*(a^4*b - a^3*b^2)*d*cosh(d*x + c)^3 + 3*(a^5 - 2*a^4*b + a^3*b^2)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^4*b - a^3*b^2)*d*cosh(d*x + c)^4 + 30*(a^5 - 2*a^4*b + a^3*b^2)*d*cosh(d*x + c)^2 - (4*a^5 - 7*a^4*b + 3*a^3*b^2)*d)*sinh(d*x + c)^4 + 4*(a^5 - 2*a^4*b + a^3*b^2)*d*cosh(d*x + c)^2 + 8*(7*(a^4*b - a^3*b^2)*d*cosh(d*x + c)^5 + 10*(a^5 - 2*a^4*b + a^3*b^2)*d*cosh(d*x + c)^3 - (4*a^5 - 7*a^4*b + 3*a^3*b^2)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^4*b - a^3*b^2)*d*cosh(d*x + c)^6 + 15*(a^5 - 2*a^4*b + a^3*b^2)*d*cosh(d*x + c)^4 - 3*(4*a^5 - 7*a^4*b + 3*a^3*b^2)*d*cosh(d*x + c)^2 + (a^5 - 2*a^4*b + a^3*b^2)*d)*sinh(d*x + c)^2 + (a^4*b - a^3*b^2)*d + 8*((a^4*b - a^3*b^2)*d*cosh(d*x + c)^7 + 3*(a^5 - 2*a^4*b + a^3*b^2)*d*cosh(d*x + c)^5 - (4*a^5 - 7*a^4*b + 3*a^3*b^2)*d*cosh(d*x + c)^3 + (a^5 - 2*a^4*b + a^3*b^2)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
50,1,7110,0,0.785596," ","integrate(csch(d*x+c)^4/(a+b*sinh(d*x+c)^2)^2,x, algorithm=""fricas"")","\left[\frac{12 \, {\left(6 \, a^{3} b^{2} - 11 \, a^{2} b^{3} + 5 \, a b^{4}\right)} \cosh\left(d x + c\right)^{8} + 96 \, {\left(6 \, a^{3} b^{2} - 11 \, a^{2} b^{3} + 5 \, a b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + 12 \, {\left(6 \, a^{3} b^{2} - 11 \, a^{2} b^{3} + 5 \, a b^{4}\right)} \sinh\left(d x + c\right)^{8} + 24 \, {\left(6 \, a^{4} b - 23 \, a^{3} b^{2} + 27 \, a^{2} b^{3} - 10 \, a b^{4}\right)} \cosh\left(d x + c\right)^{6} + 24 \, {\left(6 \, a^{4} b - 23 \, a^{3} b^{2} + 27 \, a^{2} b^{3} - 10 \, a b^{4} + 14 \, {\left(6 \, a^{3} b^{2} - 11 \, a^{2} b^{3} + 5 \, a b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 48 \, {\left(14 \, {\left(6 \, a^{3} b^{2} - 11 \, a^{2} b^{3} + 5 \, a b^{4}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(6 \, a^{4} b - 23 \, a^{3} b^{2} + 27 \, a^{2} b^{3} - 10 \, a b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 16 \, a^{4} b + 16 \, a^{3} b^{2} - 92 \, a^{2} b^{3} + 60 \, a b^{4} - 8 \, {\left(24 \, a^{5} - 14 \, a^{4} b - 89 \, a^{3} b^{2} + 124 \, a^{2} b^{3} - 45 \, a b^{4}\right)} \cosh\left(d x + c\right)^{4} - 8 \, {\left(24 \, a^{5} - 14 \, a^{4} b - 89 \, a^{3} b^{2} + 124 \, a^{2} b^{3} - 45 \, a b^{4} - 105 \, {\left(6 \, a^{3} b^{2} - 11 \, a^{2} b^{3} + 5 \, a b^{4}\right)} \cosh\left(d x + c\right)^{4} - 45 \, {\left(6 \, a^{4} b - 23 \, a^{3} b^{2} + 27 \, a^{2} b^{3} - 10 \, a b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 32 \, {\left(21 \, {\left(6 \, a^{3} b^{2} - 11 \, a^{2} b^{3} + 5 \, a b^{4}\right)} \cosh\left(d x + c\right)^{5} + 15 \, {\left(6 \, a^{4} b - 23 \, a^{3} b^{2} + 27 \, a^{2} b^{3} - 10 \, a b^{4}\right)} \cosh\left(d x + c\right)^{3} - {\left(24 \, a^{5} - 14 \, a^{4} b - 89 \, a^{3} b^{2} + 124 \, a^{2} b^{3} - 45 \, a b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 8 \, {\left(8 \, a^{5} - 2 \, a^{4} b - 47 \, a^{3} b^{2} + 71 \, a^{2} b^{3} - 30 \, a b^{4}\right)} \cosh\left(d x + c\right)^{2} + 8 \, {\left(42 \, {\left(6 \, a^{3} b^{2} - 11 \, a^{2} b^{3} + 5 \, a b^{4}\right)} \cosh\left(d x + c\right)^{6} + 8 \, a^{5} - 2 \, a^{4} b - 47 \, a^{3} b^{2} + 71 \, a^{2} b^{3} - 30 \, a b^{4} + 45 \, {\left(6 \, a^{4} b - 23 \, a^{3} b^{2} + 27 \, a^{2} b^{3} - 10 \, a b^{4}\right)} \cosh\left(d x + c\right)^{4} - 6 \, {\left(24 \, a^{5} - 14 \, a^{4} b - 89 \, a^{3} b^{2} + 124 \, a^{2} b^{3} - 45 \, a b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 3 \, {\left({\left(6 \, a b^{3} - 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{10} + 10 \, {\left(6 \, a b^{3} - 5 \, b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + {\left(6 \, a b^{3} - 5 \, b^{4}\right)} \sinh\left(d x + c\right)^{10} + {\left(24 \, a^{2} b^{2} - 50 \, a b^{3} + 25 \, b^{4}\right)} \cosh\left(d x + c\right)^{8} + {\left(24 \, a^{2} b^{2} - 50 \, a b^{3} + 25 \, b^{4} + 45 \, {\left(6 \, a b^{3} - 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{8} + 8 \, {\left(15 \, {\left(6 \, a b^{3} - 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(24 \, a^{2} b^{2} - 50 \, a b^{3} + 25 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} - 2 \, {\left(36 \, a^{2} b^{2} - 60 \, a b^{3} + 25 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(105 \, {\left(6 \, a b^{3} - 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} - 36 \, a^{2} b^{2} + 60 \, a b^{3} - 25 \, b^{4} + 14 \, {\left(24 \, a^{2} b^{2} - 50 \, a b^{3} + 25 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(63 \, {\left(6 \, a b^{3} - 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + 14 \, {\left(24 \, a^{2} b^{2} - 50 \, a b^{3} + 25 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(36 \, a^{2} b^{2} - 60 \, a b^{3} + 25 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(36 \, a^{2} b^{2} - 60 \, a b^{3} + 25 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(105 \, {\left(6 \, a b^{3} - 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 35 \, {\left(24 \, a^{2} b^{2} - 50 \, a b^{3} + 25 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 36 \, a^{2} b^{2} - 60 \, a b^{3} + 25 \, b^{4} - 15 \, {\left(36 \, a^{2} b^{2} - 60 \, a b^{3} + 25 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} - 6 \, a b^{3} + 5 \, b^{4} + 8 \, {\left(15 \, {\left(6 \, a b^{3} - 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{7} + 7 \, {\left(24 \, a^{2} b^{2} - 50 \, a b^{3} + 25 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} - 5 \, {\left(36 \, a^{2} b^{2} - 60 \, a b^{3} + 25 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(36 \, a^{2} b^{2} - 60 \, a b^{3} + 25 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - {\left(24 \, a^{2} b^{2} - 50 \, a b^{3} + 25 \, b^{4}\right)} \cosh\left(d x + c\right)^{2} + {\left(45 \, {\left(6 \, a b^{3} - 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{8} + 28 \, {\left(24 \, a^{2} b^{2} - 50 \, a b^{3} + 25 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} - 30 \, {\left(36 \, a^{2} b^{2} - 60 \, a b^{3} + 25 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} - 24 \, a^{2} b^{2} + 50 \, a b^{3} - 25 \, b^{4} + 12 \, {\left(36 \, a^{2} b^{2} - 60 \, a b^{3} + 25 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(5 \, {\left(6 \, a b^{3} - 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{9} + 4 \, {\left(24 \, a^{2} b^{2} - 50 \, a b^{3} + 25 \, b^{4}\right)} \cosh\left(d x + c\right)^{7} - 6 \, {\left(36 \, a^{2} b^{2} - 60 \, a b^{3} + 25 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + 4 \, {\left(36 \, a^{2} b^{2} - 60 \, a b^{3} + 25 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} - {\left(24 \, a^{2} b^{2} - 50 \, a b^{3} + 25 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{a^{2} - a b} \log\left(\frac{b^{2} \cosh\left(d x + c\right)^{4} + 4 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{2} \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(d x + c\right)^{2} + 2 \, a b - b^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, a^{2} - 8 \, a b + b^{2} + 4 \, {\left(b^{2} \cosh\left(d x + c\right)^{3} + {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) - 4 \, {\left(b \cosh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b \sinh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sqrt{a^{2} - a b}}{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b}\right) + 16 \, {\left(6 \, {\left(6 \, a^{3} b^{2} - 11 \, a^{2} b^{3} + 5 \, a b^{4}\right)} \cosh\left(d x + c\right)^{7} + 9 \, {\left(6 \, a^{4} b - 23 \, a^{3} b^{2} + 27 \, a^{2} b^{3} - 10 \, a b^{4}\right)} \cosh\left(d x + c\right)^{5} - 2 \, {\left(24 \, a^{5} - 14 \, a^{4} b - 89 \, a^{3} b^{2} + 124 \, a^{2} b^{3} - 45 \, a b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{5} - 2 \, a^{4} b - 47 \, a^{3} b^{2} + 71 \, a^{2} b^{3} - 30 \, a b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{12 \, {\left({\left(a^{6} b - 2 \, a^{5} b^{2} + a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{10} + 10 \, {\left(a^{6} b - 2 \, a^{5} b^{2} + a^{4} b^{3}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + {\left(a^{6} b - 2 \, a^{5} b^{2} + a^{4} b^{3}\right)} d \sinh\left(d x + c\right)^{10} + {\left(4 \, a^{7} - 13 \, a^{6} b + 14 \, a^{5} b^{2} - 5 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{8} + {\left(45 \, {\left(a^{6} b - 2 \, a^{5} b^{2} + a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + {\left(4 \, a^{7} - 13 \, a^{6} b + 14 \, a^{5} b^{2} - 5 \, a^{4} b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{8} - 2 \, {\left(6 \, a^{7} - 17 \, a^{6} b + 16 \, a^{5} b^{2} - 5 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{6} + 8 \, {\left(15 \, {\left(a^{6} b - 2 \, a^{5} b^{2} + a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{3} + {\left(4 \, a^{7} - 13 \, a^{6} b + 14 \, a^{5} b^{2} - 5 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(105 \, {\left(a^{6} b - 2 \, a^{5} b^{2} + a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 14 \, {\left(4 \, a^{7} - 13 \, a^{6} b + 14 \, a^{5} b^{2} - 5 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{2} - {\left(6 \, a^{7} - 17 \, a^{6} b + 16 \, a^{5} b^{2} - 5 \, a^{4} b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(6 \, a^{7} - 17 \, a^{6} b + 16 \, a^{5} b^{2} - 5 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(63 \, {\left(a^{6} b - 2 \, a^{5} b^{2} + a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{5} + 14 \, {\left(4 \, a^{7} - 13 \, a^{6} b + 14 \, a^{5} b^{2} - 5 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{3} - 3 \, {\left(6 \, a^{7} - 17 \, a^{6} b + 16 \, a^{5} b^{2} - 5 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(105 \, {\left(a^{6} b - 2 \, a^{5} b^{2} + a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{6} + 35 \, {\left(4 \, a^{7} - 13 \, a^{6} b + 14 \, a^{5} b^{2} - 5 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{4} - 15 \, {\left(6 \, a^{7} - 17 \, a^{6} b + 16 \, a^{5} b^{2} - 5 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + {\left(6 \, a^{7} - 17 \, a^{6} b + 16 \, a^{5} b^{2} - 5 \, a^{4} b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{4} - {\left(4 \, a^{7} - 13 \, a^{6} b + 14 \, a^{5} b^{2} - 5 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(15 \, {\left(a^{6} b - 2 \, a^{5} b^{2} + a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{7} + 7 \, {\left(4 \, a^{7} - 13 \, a^{6} b + 14 \, a^{5} b^{2} - 5 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{5} - 5 \, {\left(6 \, a^{7} - 17 \, a^{6} b + 16 \, a^{5} b^{2} - 5 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{3} + {\left(6 \, a^{7} - 17 \, a^{6} b + 16 \, a^{5} b^{2} - 5 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(45 \, {\left(a^{6} b - 2 \, a^{5} b^{2} + a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{8} + 28 \, {\left(4 \, a^{7} - 13 \, a^{6} b + 14 \, a^{5} b^{2} - 5 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{6} - 30 \, {\left(6 \, a^{7} - 17 \, a^{6} b + 16 \, a^{5} b^{2} - 5 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 12 \, {\left(6 \, a^{7} - 17 \, a^{6} b + 16 \, a^{5} b^{2} - 5 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{2} - {\left(4 \, a^{7} - 13 \, a^{6} b + 14 \, a^{5} b^{2} - 5 \, a^{4} b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{2} - {\left(a^{6} b - 2 \, a^{5} b^{2} + a^{4} b^{3}\right)} d + 2 \, {\left(5 \, {\left(a^{6} b - 2 \, a^{5} b^{2} + a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{9} + 4 \, {\left(4 \, a^{7} - 13 \, a^{6} b + 14 \, a^{5} b^{2} - 5 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{7} - 6 \, {\left(6 \, a^{7} - 17 \, a^{6} b + 16 \, a^{5} b^{2} - 5 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{5} + 4 \, {\left(6 \, a^{7} - 17 \, a^{6} b + 16 \, a^{5} b^{2} - 5 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{3} - {\left(4 \, a^{7} - 13 \, a^{6} b + 14 \, a^{5} b^{2} - 5 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}, \frac{6 \, {\left(6 \, a^{3} b^{2} - 11 \, a^{2} b^{3} + 5 \, a b^{4}\right)} \cosh\left(d x + c\right)^{8} + 48 \, {\left(6 \, a^{3} b^{2} - 11 \, a^{2} b^{3} + 5 \, a b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + 6 \, {\left(6 \, a^{3} b^{2} - 11 \, a^{2} b^{3} + 5 \, a b^{4}\right)} \sinh\left(d x + c\right)^{8} + 12 \, {\left(6 \, a^{4} b - 23 \, a^{3} b^{2} + 27 \, a^{2} b^{3} - 10 \, a b^{4}\right)} \cosh\left(d x + c\right)^{6} + 12 \, {\left(6 \, a^{4} b - 23 \, a^{3} b^{2} + 27 \, a^{2} b^{3} - 10 \, a b^{4} + 14 \, {\left(6 \, a^{3} b^{2} - 11 \, a^{2} b^{3} + 5 \, a b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 24 \, {\left(14 \, {\left(6 \, a^{3} b^{2} - 11 \, a^{2} b^{3} + 5 \, a b^{4}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(6 \, a^{4} b - 23 \, a^{3} b^{2} + 27 \, a^{2} b^{3} - 10 \, a b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 8 \, a^{4} b + 8 \, a^{3} b^{2} - 46 \, a^{2} b^{3} + 30 \, a b^{4} - 4 \, {\left(24 \, a^{5} - 14 \, a^{4} b - 89 \, a^{3} b^{2} + 124 \, a^{2} b^{3} - 45 \, a b^{4}\right)} \cosh\left(d x + c\right)^{4} - 4 \, {\left(24 \, a^{5} - 14 \, a^{4} b - 89 \, a^{3} b^{2} + 124 \, a^{2} b^{3} - 45 \, a b^{4} - 105 \, {\left(6 \, a^{3} b^{2} - 11 \, a^{2} b^{3} + 5 \, a b^{4}\right)} \cosh\left(d x + c\right)^{4} - 45 \, {\left(6 \, a^{4} b - 23 \, a^{3} b^{2} + 27 \, a^{2} b^{3} - 10 \, a b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 16 \, {\left(21 \, {\left(6 \, a^{3} b^{2} - 11 \, a^{2} b^{3} + 5 \, a b^{4}\right)} \cosh\left(d x + c\right)^{5} + 15 \, {\left(6 \, a^{4} b - 23 \, a^{3} b^{2} + 27 \, a^{2} b^{3} - 10 \, a b^{4}\right)} \cosh\left(d x + c\right)^{3} - {\left(24 \, a^{5} - 14 \, a^{4} b - 89 \, a^{3} b^{2} + 124 \, a^{2} b^{3} - 45 \, a b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(8 \, a^{5} - 2 \, a^{4} b - 47 \, a^{3} b^{2} + 71 \, a^{2} b^{3} - 30 \, a b^{4}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(42 \, {\left(6 \, a^{3} b^{2} - 11 \, a^{2} b^{3} + 5 \, a b^{4}\right)} \cosh\left(d x + c\right)^{6} + 8 \, a^{5} - 2 \, a^{4} b - 47 \, a^{3} b^{2} + 71 \, a^{2} b^{3} - 30 \, a b^{4} + 45 \, {\left(6 \, a^{4} b - 23 \, a^{3} b^{2} + 27 \, a^{2} b^{3} - 10 \, a b^{4}\right)} \cosh\left(d x + c\right)^{4} - 6 \, {\left(24 \, a^{5} - 14 \, a^{4} b - 89 \, a^{3} b^{2} + 124 \, a^{2} b^{3} - 45 \, a b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} - 3 \, {\left({\left(6 \, a b^{3} - 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{10} + 10 \, {\left(6 \, a b^{3} - 5 \, b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + {\left(6 \, a b^{3} - 5 \, b^{4}\right)} \sinh\left(d x + c\right)^{10} + {\left(24 \, a^{2} b^{2} - 50 \, a b^{3} + 25 \, b^{4}\right)} \cosh\left(d x + c\right)^{8} + {\left(24 \, a^{2} b^{2} - 50 \, a b^{3} + 25 \, b^{4} + 45 \, {\left(6 \, a b^{3} - 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{8} + 8 \, {\left(15 \, {\left(6 \, a b^{3} - 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(24 \, a^{2} b^{2} - 50 \, a b^{3} + 25 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} - 2 \, {\left(36 \, a^{2} b^{2} - 60 \, a b^{3} + 25 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(105 \, {\left(6 \, a b^{3} - 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} - 36 \, a^{2} b^{2} + 60 \, a b^{3} - 25 \, b^{4} + 14 \, {\left(24 \, a^{2} b^{2} - 50 \, a b^{3} + 25 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(63 \, {\left(6 \, a b^{3} - 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + 14 \, {\left(24 \, a^{2} b^{2} - 50 \, a b^{3} + 25 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(36 \, a^{2} b^{2} - 60 \, a b^{3} + 25 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(36 \, a^{2} b^{2} - 60 \, a b^{3} + 25 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(105 \, {\left(6 \, a b^{3} - 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 35 \, {\left(24 \, a^{2} b^{2} - 50 \, a b^{3} + 25 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 36 \, a^{2} b^{2} - 60 \, a b^{3} + 25 \, b^{4} - 15 \, {\left(36 \, a^{2} b^{2} - 60 \, a b^{3} + 25 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} - 6 \, a b^{3} + 5 \, b^{4} + 8 \, {\left(15 \, {\left(6 \, a b^{3} - 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{7} + 7 \, {\left(24 \, a^{2} b^{2} - 50 \, a b^{3} + 25 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} - 5 \, {\left(36 \, a^{2} b^{2} - 60 \, a b^{3} + 25 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(36 \, a^{2} b^{2} - 60 \, a b^{3} + 25 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - {\left(24 \, a^{2} b^{2} - 50 \, a b^{3} + 25 \, b^{4}\right)} \cosh\left(d x + c\right)^{2} + {\left(45 \, {\left(6 \, a b^{3} - 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{8} + 28 \, {\left(24 \, a^{2} b^{2} - 50 \, a b^{3} + 25 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} - 30 \, {\left(36 \, a^{2} b^{2} - 60 \, a b^{3} + 25 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} - 24 \, a^{2} b^{2} + 50 \, a b^{3} - 25 \, b^{4} + 12 \, {\left(36 \, a^{2} b^{2} - 60 \, a b^{3} + 25 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(5 \, {\left(6 \, a b^{3} - 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{9} + 4 \, {\left(24 \, a^{2} b^{2} - 50 \, a b^{3} + 25 \, b^{4}\right)} \cosh\left(d x + c\right)^{7} - 6 \, {\left(36 \, a^{2} b^{2} - 60 \, a b^{3} + 25 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + 4 \, {\left(36 \, a^{2} b^{2} - 60 \, a b^{3} + 25 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} - {\left(24 \, a^{2} b^{2} - 50 \, a b^{3} + 25 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-a^{2} + a b} \arctan\left(-\frac{{\left(b \cosh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b \sinh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sqrt{-a^{2} + a b}}{2 \, {\left(a^{2} - a b\right)}}\right) + 8 \, {\left(6 \, {\left(6 \, a^{3} b^{2} - 11 \, a^{2} b^{3} + 5 \, a b^{4}\right)} \cosh\left(d x + c\right)^{7} + 9 \, {\left(6 \, a^{4} b - 23 \, a^{3} b^{2} + 27 \, a^{2} b^{3} - 10 \, a b^{4}\right)} \cosh\left(d x + c\right)^{5} - 2 \, {\left(24 \, a^{5} - 14 \, a^{4} b - 89 \, a^{3} b^{2} + 124 \, a^{2} b^{3} - 45 \, a b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{5} - 2 \, a^{4} b - 47 \, a^{3} b^{2} + 71 \, a^{2} b^{3} - 30 \, a b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{6 \, {\left({\left(a^{6} b - 2 \, a^{5} b^{2} + a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{10} + 10 \, {\left(a^{6} b - 2 \, a^{5} b^{2} + a^{4} b^{3}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + {\left(a^{6} b - 2 \, a^{5} b^{2} + a^{4} b^{3}\right)} d \sinh\left(d x + c\right)^{10} + {\left(4 \, a^{7} - 13 \, a^{6} b + 14 \, a^{5} b^{2} - 5 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{8} + {\left(45 \, {\left(a^{6} b - 2 \, a^{5} b^{2} + a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + {\left(4 \, a^{7} - 13 \, a^{6} b + 14 \, a^{5} b^{2} - 5 \, a^{4} b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{8} - 2 \, {\left(6 \, a^{7} - 17 \, a^{6} b + 16 \, a^{5} b^{2} - 5 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{6} + 8 \, {\left(15 \, {\left(a^{6} b - 2 \, a^{5} b^{2} + a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{3} + {\left(4 \, a^{7} - 13 \, a^{6} b + 14 \, a^{5} b^{2} - 5 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(105 \, {\left(a^{6} b - 2 \, a^{5} b^{2} + a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 14 \, {\left(4 \, a^{7} - 13 \, a^{6} b + 14 \, a^{5} b^{2} - 5 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{2} - {\left(6 \, a^{7} - 17 \, a^{6} b + 16 \, a^{5} b^{2} - 5 \, a^{4} b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(6 \, a^{7} - 17 \, a^{6} b + 16 \, a^{5} b^{2} - 5 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(63 \, {\left(a^{6} b - 2 \, a^{5} b^{2} + a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{5} + 14 \, {\left(4 \, a^{7} - 13 \, a^{6} b + 14 \, a^{5} b^{2} - 5 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{3} - 3 \, {\left(6 \, a^{7} - 17 \, a^{6} b + 16 \, a^{5} b^{2} - 5 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(105 \, {\left(a^{6} b - 2 \, a^{5} b^{2} + a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{6} + 35 \, {\left(4 \, a^{7} - 13 \, a^{6} b + 14 \, a^{5} b^{2} - 5 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{4} - 15 \, {\left(6 \, a^{7} - 17 \, a^{6} b + 16 \, a^{5} b^{2} - 5 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + {\left(6 \, a^{7} - 17 \, a^{6} b + 16 \, a^{5} b^{2} - 5 \, a^{4} b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{4} - {\left(4 \, a^{7} - 13 \, a^{6} b + 14 \, a^{5} b^{2} - 5 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(15 \, {\left(a^{6} b - 2 \, a^{5} b^{2} + a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{7} + 7 \, {\left(4 \, a^{7} - 13 \, a^{6} b + 14 \, a^{5} b^{2} - 5 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{5} - 5 \, {\left(6 \, a^{7} - 17 \, a^{6} b + 16 \, a^{5} b^{2} - 5 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{3} + {\left(6 \, a^{7} - 17 \, a^{6} b + 16 \, a^{5} b^{2} - 5 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(45 \, {\left(a^{6} b - 2 \, a^{5} b^{2} + a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{8} + 28 \, {\left(4 \, a^{7} - 13 \, a^{6} b + 14 \, a^{5} b^{2} - 5 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{6} - 30 \, {\left(6 \, a^{7} - 17 \, a^{6} b + 16 \, a^{5} b^{2} - 5 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 12 \, {\left(6 \, a^{7} - 17 \, a^{6} b + 16 \, a^{5} b^{2} - 5 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{2} - {\left(4 \, a^{7} - 13 \, a^{6} b + 14 \, a^{5} b^{2} - 5 \, a^{4} b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{2} - {\left(a^{6} b - 2 \, a^{5} b^{2} + a^{4} b^{3}\right)} d + 2 \, {\left(5 \, {\left(a^{6} b - 2 \, a^{5} b^{2} + a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{9} + 4 \, {\left(4 \, a^{7} - 13 \, a^{6} b + 14 \, a^{5} b^{2} - 5 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{7} - 6 \, {\left(6 \, a^{7} - 17 \, a^{6} b + 16 \, a^{5} b^{2} - 5 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{5} + 4 \, {\left(6 \, a^{7} - 17 \, a^{6} b + 16 \, a^{5} b^{2} - 5 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)^{3} - {\left(4 \, a^{7} - 13 \, a^{6} b + 14 \, a^{5} b^{2} - 5 \, a^{4} b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[1/12*(12*(6*a^3*b^2 - 11*a^2*b^3 + 5*a*b^4)*cosh(d*x + c)^8 + 96*(6*a^3*b^2 - 11*a^2*b^3 + 5*a*b^4)*cosh(d*x + c)*sinh(d*x + c)^7 + 12*(6*a^3*b^2 - 11*a^2*b^3 + 5*a*b^4)*sinh(d*x + c)^8 + 24*(6*a^4*b - 23*a^3*b^2 + 27*a^2*b^3 - 10*a*b^4)*cosh(d*x + c)^6 + 24*(6*a^4*b - 23*a^3*b^2 + 27*a^2*b^3 - 10*a*b^4 + 14*(6*a^3*b^2 - 11*a^2*b^3 + 5*a*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 48*(14*(6*a^3*b^2 - 11*a^2*b^3 + 5*a*b^4)*cosh(d*x + c)^3 + 3*(6*a^4*b - 23*a^3*b^2 + 27*a^2*b^3 - 10*a*b^4)*cosh(d*x + c))*sinh(d*x + c)^5 + 16*a^4*b + 16*a^3*b^2 - 92*a^2*b^3 + 60*a*b^4 - 8*(24*a^5 - 14*a^4*b - 89*a^3*b^2 + 124*a^2*b^3 - 45*a*b^4)*cosh(d*x + c)^4 - 8*(24*a^5 - 14*a^4*b - 89*a^3*b^2 + 124*a^2*b^3 - 45*a*b^4 - 105*(6*a^3*b^2 - 11*a^2*b^3 + 5*a*b^4)*cosh(d*x + c)^4 - 45*(6*a^4*b - 23*a^3*b^2 + 27*a^2*b^3 - 10*a*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 32*(21*(6*a^3*b^2 - 11*a^2*b^3 + 5*a*b^4)*cosh(d*x + c)^5 + 15*(6*a^4*b - 23*a^3*b^2 + 27*a^2*b^3 - 10*a*b^4)*cosh(d*x + c)^3 - (24*a^5 - 14*a^4*b - 89*a^3*b^2 + 124*a^2*b^3 - 45*a*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 8*(8*a^5 - 2*a^4*b - 47*a^3*b^2 + 71*a^2*b^3 - 30*a*b^4)*cosh(d*x + c)^2 + 8*(42*(6*a^3*b^2 - 11*a^2*b^3 + 5*a*b^4)*cosh(d*x + c)^6 + 8*a^5 - 2*a^4*b - 47*a^3*b^2 + 71*a^2*b^3 - 30*a*b^4 + 45*(6*a^4*b - 23*a^3*b^2 + 27*a^2*b^3 - 10*a*b^4)*cosh(d*x + c)^4 - 6*(24*a^5 - 14*a^4*b - 89*a^3*b^2 + 124*a^2*b^3 - 45*a*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 3*((6*a*b^3 - 5*b^4)*cosh(d*x + c)^10 + 10*(6*a*b^3 - 5*b^4)*cosh(d*x + c)*sinh(d*x + c)^9 + (6*a*b^3 - 5*b^4)*sinh(d*x + c)^10 + (24*a^2*b^2 - 50*a*b^3 + 25*b^4)*cosh(d*x + c)^8 + (24*a^2*b^2 - 50*a*b^3 + 25*b^4 + 45*(6*a*b^3 - 5*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 8*(15*(6*a*b^3 - 5*b^4)*cosh(d*x + c)^3 + (24*a^2*b^2 - 50*a*b^3 + 25*b^4)*cosh(d*x + c))*sinh(d*x + c)^7 - 2*(36*a^2*b^2 - 60*a*b^3 + 25*b^4)*cosh(d*x + c)^6 + 2*(105*(6*a*b^3 - 5*b^4)*cosh(d*x + c)^4 - 36*a^2*b^2 + 60*a*b^3 - 25*b^4 + 14*(24*a^2*b^2 - 50*a*b^3 + 25*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 4*(63*(6*a*b^3 - 5*b^4)*cosh(d*x + c)^5 + 14*(24*a^2*b^2 - 50*a*b^3 + 25*b^4)*cosh(d*x + c)^3 - 3*(36*a^2*b^2 - 60*a*b^3 + 25*b^4)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(36*a^2*b^2 - 60*a*b^3 + 25*b^4)*cosh(d*x + c)^4 + 2*(105*(6*a*b^3 - 5*b^4)*cosh(d*x + c)^6 + 35*(24*a^2*b^2 - 50*a*b^3 + 25*b^4)*cosh(d*x + c)^4 + 36*a^2*b^2 - 60*a*b^3 + 25*b^4 - 15*(36*a^2*b^2 - 60*a*b^3 + 25*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 - 6*a*b^3 + 5*b^4 + 8*(15*(6*a*b^3 - 5*b^4)*cosh(d*x + c)^7 + 7*(24*a^2*b^2 - 50*a*b^3 + 25*b^4)*cosh(d*x + c)^5 - 5*(36*a^2*b^2 - 60*a*b^3 + 25*b^4)*cosh(d*x + c)^3 + (36*a^2*b^2 - 60*a*b^3 + 25*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 - (24*a^2*b^2 - 50*a*b^3 + 25*b^4)*cosh(d*x + c)^2 + (45*(6*a*b^3 - 5*b^4)*cosh(d*x + c)^8 + 28*(24*a^2*b^2 - 50*a*b^3 + 25*b^4)*cosh(d*x + c)^6 - 30*(36*a^2*b^2 - 60*a*b^3 + 25*b^4)*cosh(d*x + c)^4 - 24*a^2*b^2 + 50*a*b^3 - 25*b^4 + 12*(36*a^2*b^2 - 60*a*b^3 + 25*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 2*(5*(6*a*b^3 - 5*b^4)*cosh(d*x + c)^9 + 4*(24*a^2*b^2 - 50*a*b^3 + 25*b^4)*cosh(d*x + c)^7 - 6*(36*a^2*b^2 - 60*a*b^3 + 25*b^4)*cosh(d*x + c)^5 + 4*(36*a^2*b^2 - 60*a*b^3 + 25*b^4)*cosh(d*x + c)^3 - (24*a^2*b^2 - 50*a*b^3 + 25*b^4)*cosh(d*x + c))*sinh(d*x + c))*sqrt(a^2 - a*b)*log((b^2*cosh(d*x + c)^4 + 4*b^2*cosh(d*x + c)*sinh(d*x + c)^3 + b^2*sinh(d*x + c)^4 + 2*(2*a*b - b^2)*cosh(d*x + c)^2 + 2*(3*b^2*cosh(d*x + c)^2 + 2*a*b - b^2)*sinh(d*x + c)^2 + 8*a^2 - 8*a*b + b^2 + 4*(b^2*cosh(d*x + c)^3 + (2*a*b - b^2)*cosh(d*x + c))*sinh(d*x + c) - 4*(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + 2*a - b)*sqrt(a^2 - a*b))/(b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 + 2*(2*a - b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 + 2*a - b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 + (2*a - b)*cosh(d*x + c))*sinh(d*x + c) + b)) + 16*(6*(6*a^3*b^2 - 11*a^2*b^3 + 5*a*b^4)*cosh(d*x + c)^7 + 9*(6*a^4*b - 23*a^3*b^2 + 27*a^2*b^3 - 10*a*b^4)*cosh(d*x + c)^5 - 2*(24*a^5 - 14*a^4*b - 89*a^3*b^2 + 124*a^2*b^3 - 45*a*b^4)*cosh(d*x + c)^3 + (8*a^5 - 2*a^4*b - 47*a^3*b^2 + 71*a^2*b^3 - 30*a*b^4)*cosh(d*x + c))*sinh(d*x + c))/((a^6*b - 2*a^5*b^2 + a^4*b^3)*d*cosh(d*x + c)^10 + 10*(a^6*b - 2*a^5*b^2 + a^4*b^3)*d*cosh(d*x + c)*sinh(d*x + c)^9 + (a^6*b - 2*a^5*b^2 + a^4*b^3)*d*sinh(d*x + c)^10 + (4*a^7 - 13*a^6*b + 14*a^5*b^2 - 5*a^4*b^3)*d*cosh(d*x + c)^8 + (45*(a^6*b - 2*a^5*b^2 + a^4*b^3)*d*cosh(d*x + c)^2 + (4*a^7 - 13*a^6*b + 14*a^5*b^2 - 5*a^4*b^3)*d)*sinh(d*x + c)^8 - 2*(6*a^7 - 17*a^6*b + 16*a^5*b^2 - 5*a^4*b^3)*d*cosh(d*x + c)^6 + 8*(15*(a^6*b - 2*a^5*b^2 + a^4*b^3)*d*cosh(d*x + c)^3 + (4*a^7 - 13*a^6*b + 14*a^5*b^2 - 5*a^4*b^3)*d*cosh(d*x + c))*sinh(d*x + c)^7 + 2*(105*(a^6*b - 2*a^5*b^2 + a^4*b^3)*d*cosh(d*x + c)^4 + 14*(4*a^7 - 13*a^6*b + 14*a^5*b^2 - 5*a^4*b^3)*d*cosh(d*x + c)^2 - (6*a^7 - 17*a^6*b + 16*a^5*b^2 - 5*a^4*b^3)*d)*sinh(d*x + c)^6 + 2*(6*a^7 - 17*a^6*b + 16*a^5*b^2 - 5*a^4*b^3)*d*cosh(d*x + c)^4 + 4*(63*(a^6*b - 2*a^5*b^2 + a^4*b^3)*d*cosh(d*x + c)^5 + 14*(4*a^7 - 13*a^6*b + 14*a^5*b^2 - 5*a^4*b^3)*d*cosh(d*x + c)^3 - 3*(6*a^7 - 17*a^6*b + 16*a^5*b^2 - 5*a^4*b^3)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(105*(a^6*b - 2*a^5*b^2 + a^4*b^3)*d*cosh(d*x + c)^6 + 35*(4*a^7 - 13*a^6*b + 14*a^5*b^2 - 5*a^4*b^3)*d*cosh(d*x + c)^4 - 15*(6*a^7 - 17*a^6*b + 16*a^5*b^2 - 5*a^4*b^3)*d*cosh(d*x + c)^2 + (6*a^7 - 17*a^6*b + 16*a^5*b^2 - 5*a^4*b^3)*d)*sinh(d*x + c)^4 - (4*a^7 - 13*a^6*b + 14*a^5*b^2 - 5*a^4*b^3)*d*cosh(d*x + c)^2 + 8*(15*(a^6*b - 2*a^5*b^2 + a^4*b^3)*d*cosh(d*x + c)^7 + 7*(4*a^7 - 13*a^6*b + 14*a^5*b^2 - 5*a^4*b^3)*d*cosh(d*x + c)^5 - 5*(6*a^7 - 17*a^6*b + 16*a^5*b^2 - 5*a^4*b^3)*d*cosh(d*x + c)^3 + (6*a^7 - 17*a^6*b + 16*a^5*b^2 - 5*a^4*b^3)*d*cosh(d*x + c))*sinh(d*x + c)^3 + (45*(a^6*b - 2*a^5*b^2 + a^4*b^3)*d*cosh(d*x + c)^8 + 28*(4*a^7 - 13*a^6*b + 14*a^5*b^2 - 5*a^4*b^3)*d*cosh(d*x + c)^6 - 30*(6*a^7 - 17*a^6*b + 16*a^5*b^2 - 5*a^4*b^3)*d*cosh(d*x + c)^4 + 12*(6*a^7 - 17*a^6*b + 16*a^5*b^2 - 5*a^4*b^3)*d*cosh(d*x + c)^2 - (4*a^7 - 13*a^6*b + 14*a^5*b^2 - 5*a^4*b^3)*d)*sinh(d*x + c)^2 - (a^6*b - 2*a^5*b^2 + a^4*b^3)*d + 2*(5*(a^6*b - 2*a^5*b^2 + a^4*b^3)*d*cosh(d*x + c)^9 + 4*(4*a^7 - 13*a^6*b + 14*a^5*b^2 - 5*a^4*b^3)*d*cosh(d*x + c)^7 - 6*(6*a^7 - 17*a^6*b + 16*a^5*b^2 - 5*a^4*b^3)*d*cosh(d*x + c)^5 + 4*(6*a^7 - 17*a^6*b + 16*a^5*b^2 - 5*a^4*b^3)*d*cosh(d*x + c)^3 - (4*a^7 - 13*a^6*b + 14*a^5*b^2 - 5*a^4*b^3)*d*cosh(d*x + c))*sinh(d*x + c)), 1/6*(6*(6*a^3*b^2 - 11*a^2*b^3 + 5*a*b^4)*cosh(d*x + c)^8 + 48*(6*a^3*b^2 - 11*a^2*b^3 + 5*a*b^4)*cosh(d*x + c)*sinh(d*x + c)^7 + 6*(6*a^3*b^2 - 11*a^2*b^3 + 5*a*b^4)*sinh(d*x + c)^8 + 12*(6*a^4*b - 23*a^3*b^2 + 27*a^2*b^3 - 10*a*b^4)*cosh(d*x + c)^6 + 12*(6*a^4*b - 23*a^3*b^2 + 27*a^2*b^3 - 10*a*b^4 + 14*(6*a^3*b^2 - 11*a^2*b^3 + 5*a*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 24*(14*(6*a^3*b^2 - 11*a^2*b^3 + 5*a*b^4)*cosh(d*x + c)^3 + 3*(6*a^4*b - 23*a^3*b^2 + 27*a^2*b^3 - 10*a*b^4)*cosh(d*x + c))*sinh(d*x + c)^5 + 8*a^4*b + 8*a^3*b^2 - 46*a^2*b^3 + 30*a*b^4 - 4*(24*a^5 - 14*a^4*b - 89*a^3*b^2 + 124*a^2*b^3 - 45*a*b^4)*cosh(d*x + c)^4 - 4*(24*a^5 - 14*a^4*b - 89*a^3*b^2 + 124*a^2*b^3 - 45*a*b^4 - 105*(6*a^3*b^2 - 11*a^2*b^3 + 5*a*b^4)*cosh(d*x + c)^4 - 45*(6*a^4*b - 23*a^3*b^2 + 27*a^2*b^3 - 10*a*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 16*(21*(6*a^3*b^2 - 11*a^2*b^3 + 5*a*b^4)*cosh(d*x + c)^5 + 15*(6*a^4*b - 23*a^3*b^2 + 27*a^2*b^3 - 10*a*b^4)*cosh(d*x + c)^3 - (24*a^5 - 14*a^4*b - 89*a^3*b^2 + 124*a^2*b^3 - 45*a*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(8*a^5 - 2*a^4*b - 47*a^3*b^2 + 71*a^2*b^3 - 30*a*b^4)*cosh(d*x + c)^2 + 4*(42*(6*a^3*b^2 - 11*a^2*b^3 + 5*a*b^4)*cosh(d*x + c)^6 + 8*a^5 - 2*a^4*b - 47*a^3*b^2 + 71*a^2*b^3 - 30*a*b^4 + 45*(6*a^4*b - 23*a^3*b^2 + 27*a^2*b^3 - 10*a*b^4)*cosh(d*x + c)^4 - 6*(24*a^5 - 14*a^4*b - 89*a^3*b^2 + 124*a^2*b^3 - 45*a*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - 3*((6*a*b^3 - 5*b^4)*cosh(d*x + c)^10 + 10*(6*a*b^3 - 5*b^4)*cosh(d*x + c)*sinh(d*x + c)^9 + (6*a*b^3 - 5*b^4)*sinh(d*x + c)^10 + (24*a^2*b^2 - 50*a*b^3 + 25*b^4)*cosh(d*x + c)^8 + (24*a^2*b^2 - 50*a*b^3 + 25*b^4 + 45*(6*a*b^3 - 5*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 8*(15*(6*a*b^3 - 5*b^4)*cosh(d*x + c)^3 + (24*a^2*b^2 - 50*a*b^3 + 25*b^4)*cosh(d*x + c))*sinh(d*x + c)^7 - 2*(36*a^2*b^2 - 60*a*b^3 + 25*b^4)*cosh(d*x + c)^6 + 2*(105*(6*a*b^3 - 5*b^4)*cosh(d*x + c)^4 - 36*a^2*b^2 + 60*a*b^3 - 25*b^4 + 14*(24*a^2*b^2 - 50*a*b^3 + 25*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 4*(63*(6*a*b^3 - 5*b^4)*cosh(d*x + c)^5 + 14*(24*a^2*b^2 - 50*a*b^3 + 25*b^4)*cosh(d*x + c)^3 - 3*(36*a^2*b^2 - 60*a*b^3 + 25*b^4)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(36*a^2*b^2 - 60*a*b^3 + 25*b^4)*cosh(d*x + c)^4 + 2*(105*(6*a*b^3 - 5*b^4)*cosh(d*x + c)^6 + 35*(24*a^2*b^2 - 50*a*b^3 + 25*b^4)*cosh(d*x + c)^4 + 36*a^2*b^2 - 60*a*b^3 + 25*b^4 - 15*(36*a^2*b^2 - 60*a*b^3 + 25*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 - 6*a*b^3 + 5*b^4 + 8*(15*(6*a*b^3 - 5*b^4)*cosh(d*x + c)^7 + 7*(24*a^2*b^2 - 50*a*b^3 + 25*b^4)*cosh(d*x + c)^5 - 5*(36*a^2*b^2 - 60*a*b^3 + 25*b^4)*cosh(d*x + c)^3 + (36*a^2*b^2 - 60*a*b^3 + 25*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 - (24*a^2*b^2 - 50*a*b^3 + 25*b^4)*cosh(d*x + c)^2 + (45*(6*a*b^3 - 5*b^4)*cosh(d*x + c)^8 + 28*(24*a^2*b^2 - 50*a*b^3 + 25*b^4)*cosh(d*x + c)^6 - 30*(36*a^2*b^2 - 60*a*b^3 + 25*b^4)*cosh(d*x + c)^4 - 24*a^2*b^2 + 50*a*b^3 - 25*b^4 + 12*(36*a^2*b^2 - 60*a*b^3 + 25*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 2*(5*(6*a*b^3 - 5*b^4)*cosh(d*x + c)^9 + 4*(24*a^2*b^2 - 50*a*b^3 + 25*b^4)*cosh(d*x + c)^7 - 6*(36*a^2*b^2 - 60*a*b^3 + 25*b^4)*cosh(d*x + c)^5 + 4*(36*a^2*b^2 - 60*a*b^3 + 25*b^4)*cosh(d*x + c)^3 - (24*a^2*b^2 - 50*a*b^3 + 25*b^4)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-a^2 + a*b)*arctan(-1/2*(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + 2*a - b)*sqrt(-a^2 + a*b)/(a^2 - a*b)) + 8*(6*(6*a^3*b^2 - 11*a^2*b^3 + 5*a*b^4)*cosh(d*x + c)^7 + 9*(6*a^4*b - 23*a^3*b^2 + 27*a^2*b^3 - 10*a*b^4)*cosh(d*x + c)^5 - 2*(24*a^5 - 14*a^4*b - 89*a^3*b^2 + 124*a^2*b^3 - 45*a*b^4)*cosh(d*x + c)^3 + (8*a^5 - 2*a^4*b - 47*a^3*b^2 + 71*a^2*b^3 - 30*a*b^4)*cosh(d*x + c))*sinh(d*x + c))/((a^6*b - 2*a^5*b^2 + a^4*b^3)*d*cosh(d*x + c)^10 + 10*(a^6*b - 2*a^5*b^2 + a^4*b^3)*d*cosh(d*x + c)*sinh(d*x + c)^9 + (a^6*b - 2*a^5*b^2 + a^4*b^3)*d*sinh(d*x + c)^10 + (4*a^7 - 13*a^6*b + 14*a^5*b^2 - 5*a^4*b^3)*d*cosh(d*x + c)^8 + (45*(a^6*b - 2*a^5*b^2 + a^4*b^3)*d*cosh(d*x + c)^2 + (4*a^7 - 13*a^6*b + 14*a^5*b^2 - 5*a^4*b^3)*d)*sinh(d*x + c)^8 - 2*(6*a^7 - 17*a^6*b + 16*a^5*b^2 - 5*a^4*b^3)*d*cosh(d*x + c)^6 + 8*(15*(a^6*b - 2*a^5*b^2 + a^4*b^3)*d*cosh(d*x + c)^3 + (4*a^7 - 13*a^6*b + 14*a^5*b^2 - 5*a^4*b^3)*d*cosh(d*x + c))*sinh(d*x + c)^7 + 2*(105*(a^6*b - 2*a^5*b^2 + a^4*b^3)*d*cosh(d*x + c)^4 + 14*(4*a^7 - 13*a^6*b + 14*a^5*b^2 - 5*a^4*b^3)*d*cosh(d*x + c)^2 - (6*a^7 - 17*a^6*b + 16*a^5*b^2 - 5*a^4*b^3)*d)*sinh(d*x + c)^6 + 2*(6*a^7 - 17*a^6*b + 16*a^5*b^2 - 5*a^4*b^3)*d*cosh(d*x + c)^4 + 4*(63*(a^6*b - 2*a^5*b^2 + a^4*b^3)*d*cosh(d*x + c)^5 + 14*(4*a^7 - 13*a^6*b + 14*a^5*b^2 - 5*a^4*b^3)*d*cosh(d*x + c)^3 - 3*(6*a^7 - 17*a^6*b + 16*a^5*b^2 - 5*a^4*b^3)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(105*(a^6*b - 2*a^5*b^2 + a^4*b^3)*d*cosh(d*x + c)^6 + 35*(4*a^7 - 13*a^6*b + 14*a^5*b^2 - 5*a^4*b^3)*d*cosh(d*x + c)^4 - 15*(6*a^7 - 17*a^6*b + 16*a^5*b^2 - 5*a^4*b^3)*d*cosh(d*x + c)^2 + (6*a^7 - 17*a^6*b + 16*a^5*b^2 - 5*a^4*b^3)*d)*sinh(d*x + c)^4 - (4*a^7 - 13*a^6*b + 14*a^5*b^2 - 5*a^4*b^3)*d*cosh(d*x + c)^2 + 8*(15*(a^6*b - 2*a^5*b^2 + a^4*b^3)*d*cosh(d*x + c)^7 + 7*(4*a^7 - 13*a^6*b + 14*a^5*b^2 - 5*a^4*b^3)*d*cosh(d*x + c)^5 - 5*(6*a^7 - 17*a^6*b + 16*a^5*b^2 - 5*a^4*b^3)*d*cosh(d*x + c)^3 + (6*a^7 - 17*a^6*b + 16*a^5*b^2 - 5*a^4*b^3)*d*cosh(d*x + c))*sinh(d*x + c)^3 + (45*(a^6*b - 2*a^5*b^2 + a^4*b^3)*d*cosh(d*x + c)^8 + 28*(4*a^7 - 13*a^6*b + 14*a^5*b^2 - 5*a^4*b^3)*d*cosh(d*x + c)^6 - 30*(6*a^7 - 17*a^6*b + 16*a^5*b^2 - 5*a^4*b^3)*d*cosh(d*x + c)^4 + 12*(6*a^7 - 17*a^6*b + 16*a^5*b^2 - 5*a^4*b^3)*d*cosh(d*x + c)^2 - (4*a^7 - 13*a^6*b + 14*a^5*b^2 - 5*a^4*b^3)*d)*sinh(d*x + c)^2 - (a^6*b - 2*a^5*b^2 + a^4*b^3)*d + 2*(5*(a^6*b - 2*a^5*b^2 + a^4*b^3)*d*cosh(d*x + c)^9 + 4*(4*a^7 - 13*a^6*b + 14*a^5*b^2 - 5*a^4*b^3)*d*cosh(d*x + c)^7 - 6*(6*a^7 - 17*a^6*b + 16*a^5*b^2 - 5*a^4*b^3)*d*cosh(d*x + c)^5 + 4*(6*a^7 - 17*a^6*b + 16*a^5*b^2 - 5*a^4*b^3)*d*cosh(d*x + c)^3 - (4*a^7 - 13*a^6*b + 14*a^5*b^2 - 5*a^4*b^3)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
51,1,5186,0,0.633452," ","integrate(sinh(d*x+c)^4/(a+b*sinh(d*x+c)^2)^3,x, algorithm=""fricas"")","\left[-\frac{4 \, {\left(8 \, a^{4} b - 24 \, a^{3} b^{2} + 21 \, a^{2} b^{3} - 5 \, a b^{4}\right)} \cosh\left(d x + c\right)^{6} + 24 \, {\left(8 \, a^{4} b - 24 \, a^{3} b^{2} + 21 \, a^{2} b^{3} - 5 \, a b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + 4 \, {\left(8 \, a^{4} b - 24 \, a^{3} b^{2} + 21 \, a^{2} b^{3} - 5 \, a b^{4}\right)} \sinh\left(d x + c\right)^{6} + 8 \, a^{3} b^{2} - 28 \, a^{2} b^{3} + 20 \, a b^{4} + 4 \, {\left(16 \, a^{5} - 72 \, a^{4} b + 102 \, a^{3} b^{2} - 61 \, a^{2} b^{3} + 15 \, a b^{4}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(16 \, a^{5} - 72 \, a^{4} b + 102 \, a^{3} b^{2} - 61 \, a^{2} b^{3} + 15 \, a b^{4} + 15 \, {\left(8 \, a^{4} b - 24 \, a^{3} b^{2} + 21 \, a^{2} b^{3} - 5 \, a b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 16 \, {\left(5 \, {\left(8 \, a^{4} b - 24 \, a^{3} b^{2} + 21 \, a^{2} b^{3} - 5 \, a b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(16 \, a^{5} - 72 \, a^{4} b + 102 \, a^{3} b^{2} - 61 \, a^{2} b^{3} + 15 \, a b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(8 \, a^{4} b - 40 \, a^{3} b^{2} + 47 \, a^{2} b^{3} - 15 \, a b^{4}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(8 \, a^{4} b - 40 \, a^{3} b^{2} + 47 \, a^{2} b^{3} - 15 \, a b^{4} + 15 \, {\left(8 \, a^{4} b - 24 \, a^{3} b^{2} + 21 \, a^{2} b^{3} - 5 \, a b^{4}\right)} \cosh\left(d x + c\right)^{4} + 6 \, {\left(16 \, a^{5} - 72 \, a^{4} b + 102 \, a^{3} b^{2} - 61 \, a^{2} b^{3} + 15 \, a b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} - 3 \, {\left(b^{4} \cosh\left(d x + c\right)^{8} + 8 \, b^{4} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + b^{4} \sinh\left(d x + c\right)^{8} + 4 \, {\left(2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, b^{4} \cosh\left(d x + c\right)^{2} + 2 \, a b^{3} - b^{4}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, b^{4} \cosh\left(d x + c\right)^{3} + 3 \, {\left(2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(8 \, a^{2} b^{2} - 8 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, b^{4} \cosh\left(d x + c\right)^{4} + 8 \, a^{2} b^{2} - 8 \, a b^{3} + 3 \, b^{4} + 30 \, {\left(2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + b^{4} + 8 \, {\left(7 \, b^{4} \cosh\left(d x + c\right)^{5} + 10 \, {\left(2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{2} b^{2} - 8 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, b^{4} \cosh\left(d x + c\right)^{6} + 15 \, {\left(2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, a b^{3} - b^{4} + 3 \, {\left(8 \, a^{2} b^{2} - 8 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left(b^{4} \cosh\left(d x + c\right)^{7} + 3 \, {\left(2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{5} + {\left(8 \, a^{2} b^{2} - 8 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{a^{2} - a b} \log\left(\frac{b^{2} \cosh\left(d x + c\right)^{4} + 4 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{2} \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(d x + c\right)^{2} + 2 \, a b - b^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, a^{2} - 8 \, a b + b^{2} + 4 \, {\left(b^{2} \cosh\left(d x + c\right)^{3} + {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) - 4 \, {\left(b \cosh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b \sinh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sqrt{a^{2} - a b}}{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b}\right) + 8 \, {\left(3 \, {\left(8 \, a^{4} b - 24 \, a^{3} b^{2} + 21 \, a^{2} b^{3} - 5 \, a b^{4}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(16 \, a^{5} - 72 \, a^{4} b + 102 \, a^{3} b^{2} - 61 \, a^{2} b^{3} + 15 \, a b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{4} b - 40 \, a^{3} b^{2} + 47 \, a^{2} b^{3} - 15 \, a b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{16 \, {\left({\left(a^{4} b^{4} - 3 \, a^{3} b^{5} + 3 \, a^{2} b^{6} - a b^{7}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{4} b^{4} - 3 \, a^{3} b^{5} + 3 \, a^{2} b^{6} - a b^{7}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{4} b^{4} - 3 \, a^{3} b^{5} + 3 \, a^{2} b^{6} - a b^{7}\right)} d \sinh\left(d x + c\right)^{8} + 4 \, {\left(2 \, a^{5} b^{3} - 7 \, a^{4} b^{4} + 9 \, a^{3} b^{5} - 5 \, a^{2} b^{6} + a b^{7}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{4} b^{4} - 3 \, a^{3} b^{5} + 3 \, a^{2} b^{6} - a b^{7}\right)} d \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{5} b^{3} - 7 \, a^{4} b^{4} + 9 \, a^{3} b^{5} - 5 \, a^{2} b^{6} + a b^{7}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(8 \, a^{6} b^{2} - 32 \, a^{5} b^{3} + 51 \, a^{4} b^{4} - 41 \, a^{3} b^{5} + 17 \, a^{2} b^{6} - 3 \, a b^{7}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{4} b^{4} - 3 \, a^{3} b^{5} + 3 \, a^{2} b^{6} - a b^{7}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(2 \, a^{5} b^{3} - 7 \, a^{4} b^{4} + 9 \, a^{3} b^{5} - 5 \, a^{2} b^{6} + a b^{7}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a^{4} b^{4} - 3 \, a^{3} b^{5} + 3 \, a^{2} b^{6} - a b^{7}\right)} d \cosh\left(d x + c\right)^{4} + 30 \, {\left(2 \, a^{5} b^{3} - 7 \, a^{4} b^{4} + 9 \, a^{3} b^{5} - 5 \, a^{2} b^{6} + a b^{7}\right)} d \cosh\left(d x + c\right)^{2} + {\left(8 \, a^{6} b^{2} - 32 \, a^{5} b^{3} + 51 \, a^{4} b^{4} - 41 \, a^{3} b^{5} + 17 \, a^{2} b^{6} - 3 \, a b^{7}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(2 \, a^{5} b^{3} - 7 \, a^{4} b^{4} + 9 \, a^{3} b^{5} - 5 \, a^{2} b^{6} + a b^{7}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a^{4} b^{4} - 3 \, a^{3} b^{5} + 3 \, a^{2} b^{6} - a b^{7}\right)} d \cosh\left(d x + c\right)^{5} + 10 \, {\left(2 \, a^{5} b^{3} - 7 \, a^{4} b^{4} + 9 \, a^{3} b^{5} - 5 \, a^{2} b^{6} + a b^{7}\right)} d \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{6} b^{2} - 32 \, a^{5} b^{3} + 51 \, a^{4} b^{4} - 41 \, a^{3} b^{5} + 17 \, a^{2} b^{6} - 3 \, a b^{7}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a^{4} b^{4} - 3 \, a^{3} b^{5} + 3 \, a^{2} b^{6} - a b^{7}\right)} d \cosh\left(d x + c\right)^{6} + 15 \, {\left(2 \, a^{5} b^{3} - 7 \, a^{4} b^{4} + 9 \, a^{3} b^{5} - 5 \, a^{2} b^{6} + a b^{7}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(8 \, a^{6} b^{2} - 32 \, a^{5} b^{3} + 51 \, a^{4} b^{4} - 41 \, a^{3} b^{5} + 17 \, a^{2} b^{6} - 3 \, a b^{7}\right)} d \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{5} b^{3} - 7 \, a^{4} b^{4} + 9 \, a^{3} b^{5} - 5 \, a^{2} b^{6} + a b^{7}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{4} b^{4} - 3 \, a^{3} b^{5} + 3 \, a^{2} b^{6} - a b^{7}\right)} d + 8 \, {\left({\left(a^{4} b^{4} - 3 \, a^{3} b^{5} + 3 \, a^{2} b^{6} - a b^{7}\right)} d \cosh\left(d x + c\right)^{7} + 3 \, {\left(2 \, a^{5} b^{3} - 7 \, a^{4} b^{4} + 9 \, a^{3} b^{5} - 5 \, a^{2} b^{6} + a b^{7}\right)} d \cosh\left(d x + c\right)^{5} + {\left(8 \, a^{6} b^{2} - 32 \, a^{5} b^{3} + 51 \, a^{4} b^{4} - 41 \, a^{3} b^{5} + 17 \, a^{2} b^{6} - 3 \, a b^{7}\right)} d \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{5} b^{3} - 7 \, a^{4} b^{4} + 9 \, a^{3} b^{5} - 5 \, a^{2} b^{6} + a b^{7}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}, -\frac{2 \, {\left(8 \, a^{4} b - 24 \, a^{3} b^{2} + 21 \, a^{2} b^{3} - 5 \, a b^{4}\right)} \cosh\left(d x + c\right)^{6} + 12 \, {\left(8 \, a^{4} b - 24 \, a^{3} b^{2} + 21 \, a^{2} b^{3} - 5 \, a b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + 2 \, {\left(8 \, a^{4} b - 24 \, a^{3} b^{2} + 21 \, a^{2} b^{3} - 5 \, a b^{4}\right)} \sinh\left(d x + c\right)^{6} + 4 \, a^{3} b^{2} - 14 \, a^{2} b^{3} + 10 \, a b^{4} + 2 \, {\left(16 \, a^{5} - 72 \, a^{4} b + 102 \, a^{3} b^{2} - 61 \, a^{2} b^{3} + 15 \, a b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(16 \, a^{5} - 72 \, a^{4} b + 102 \, a^{3} b^{2} - 61 \, a^{2} b^{3} + 15 \, a b^{4} + 15 \, {\left(8 \, a^{4} b - 24 \, a^{3} b^{2} + 21 \, a^{2} b^{3} - 5 \, a b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(5 \, {\left(8 \, a^{4} b - 24 \, a^{3} b^{2} + 21 \, a^{2} b^{3} - 5 \, a b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(16 \, a^{5} - 72 \, a^{4} b + 102 \, a^{3} b^{2} - 61 \, a^{2} b^{3} + 15 \, a b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(8 \, a^{4} b - 40 \, a^{3} b^{2} + 47 \, a^{2} b^{3} - 15 \, a b^{4}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(8 \, a^{4} b - 40 \, a^{3} b^{2} + 47 \, a^{2} b^{3} - 15 \, a b^{4} + 15 \, {\left(8 \, a^{4} b - 24 \, a^{3} b^{2} + 21 \, a^{2} b^{3} - 5 \, a b^{4}\right)} \cosh\left(d x + c\right)^{4} + 6 \, {\left(16 \, a^{5} - 72 \, a^{4} b + 102 \, a^{3} b^{2} - 61 \, a^{2} b^{3} + 15 \, a b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 3 \, {\left(b^{4} \cosh\left(d x + c\right)^{8} + 8 \, b^{4} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + b^{4} \sinh\left(d x + c\right)^{8} + 4 \, {\left(2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, b^{4} \cosh\left(d x + c\right)^{2} + 2 \, a b^{3} - b^{4}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, b^{4} \cosh\left(d x + c\right)^{3} + 3 \, {\left(2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(8 \, a^{2} b^{2} - 8 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, b^{4} \cosh\left(d x + c\right)^{4} + 8 \, a^{2} b^{2} - 8 \, a b^{3} + 3 \, b^{4} + 30 \, {\left(2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + b^{4} + 8 \, {\left(7 \, b^{4} \cosh\left(d x + c\right)^{5} + 10 \, {\left(2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{2} b^{2} - 8 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, b^{4} \cosh\left(d x + c\right)^{6} + 15 \, {\left(2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, a b^{3} - b^{4} + 3 \, {\left(8 \, a^{2} b^{2} - 8 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left(b^{4} \cosh\left(d x + c\right)^{7} + 3 \, {\left(2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{5} + {\left(8 \, a^{2} b^{2} - 8 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-a^{2} + a b} \arctan\left(-\frac{{\left(b \cosh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b \sinh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sqrt{-a^{2} + a b}}{2 \, {\left(a^{2} - a b\right)}}\right) + 4 \, {\left(3 \, {\left(8 \, a^{4} b - 24 \, a^{3} b^{2} + 21 \, a^{2} b^{3} - 5 \, a b^{4}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(16 \, a^{5} - 72 \, a^{4} b + 102 \, a^{3} b^{2} - 61 \, a^{2} b^{3} + 15 \, a b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{4} b - 40 \, a^{3} b^{2} + 47 \, a^{2} b^{3} - 15 \, a b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{8 \, {\left({\left(a^{4} b^{4} - 3 \, a^{3} b^{5} + 3 \, a^{2} b^{6} - a b^{7}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{4} b^{4} - 3 \, a^{3} b^{5} + 3 \, a^{2} b^{6} - a b^{7}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{4} b^{4} - 3 \, a^{3} b^{5} + 3 \, a^{2} b^{6} - a b^{7}\right)} d \sinh\left(d x + c\right)^{8} + 4 \, {\left(2 \, a^{5} b^{3} - 7 \, a^{4} b^{4} + 9 \, a^{3} b^{5} - 5 \, a^{2} b^{6} + a b^{7}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{4} b^{4} - 3 \, a^{3} b^{5} + 3 \, a^{2} b^{6} - a b^{7}\right)} d \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{5} b^{3} - 7 \, a^{4} b^{4} + 9 \, a^{3} b^{5} - 5 \, a^{2} b^{6} + a b^{7}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(8 \, a^{6} b^{2} - 32 \, a^{5} b^{3} + 51 \, a^{4} b^{4} - 41 \, a^{3} b^{5} + 17 \, a^{2} b^{6} - 3 \, a b^{7}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{4} b^{4} - 3 \, a^{3} b^{5} + 3 \, a^{2} b^{6} - a b^{7}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(2 \, a^{5} b^{3} - 7 \, a^{4} b^{4} + 9 \, a^{3} b^{5} - 5 \, a^{2} b^{6} + a b^{7}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a^{4} b^{4} - 3 \, a^{3} b^{5} + 3 \, a^{2} b^{6} - a b^{7}\right)} d \cosh\left(d x + c\right)^{4} + 30 \, {\left(2 \, a^{5} b^{3} - 7 \, a^{4} b^{4} + 9 \, a^{3} b^{5} - 5 \, a^{2} b^{6} + a b^{7}\right)} d \cosh\left(d x + c\right)^{2} + {\left(8 \, a^{6} b^{2} - 32 \, a^{5} b^{3} + 51 \, a^{4} b^{4} - 41 \, a^{3} b^{5} + 17 \, a^{2} b^{6} - 3 \, a b^{7}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(2 \, a^{5} b^{3} - 7 \, a^{4} b^{4} + 9 \, a^{3} b^{5} - 5 \, a^{2} b^{6} + a b^{7}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a^{4} b^{4} - 3 \, a^{3} b^{5} + 3 \, a^{2} b^{6} - a b^{7}\right)} d \cosh\left(d x + c\right)^{5} + 10 \, {\left(2 \, a^{5} b^{3} - 7 \, a^{4} b^{4} + 9 \, a^{3} b^{5} - 5 \, a^{2} b^{6} + a b^{7}\right)} d \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{6} b^{2} - 32 \, a^{5} b^{3} + 51 \, a^{4} b^{4} - 41 \, a^{3} b^{5} + 17 \, a^{2} b^{6} - 3 \, a b^{7}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a^{4} b^{4} - 3 \, a^{3} b^{5} + 3 \, a^{2} b^{6} - a b^{7}\right)} d \cosh\left(d x + c\right)^{6} + 15 \, {\left(2 \, a^{5} b^{3} - 7 \, a^{4} b^{4} + 9 \, a^{3} b^{5} - 5 \, a^{2} b^{6} + a b^{7}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(8 \, a^{6} b^{2} - 32 \, a^{5} b^{3} + 51 \, a^{4} b^{4} - 41 \, a^{3} b^{5} + 17 \, a^{2} b^{6} - 3 \, a b^{7}\right)} d \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{5} b^{3} - 7 \, a^{4} b^{4} + 9 \, a^{3} b^{5} - 5 \, a^{2} b^{6} + a b^{7}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{4} b^{4} - 3 \, a^{3} b^{5} + 3 \, a^{2} b^{6} - a b^{7}\right)} d + 8 \, {\left({\left(a^{4} b^{4} - 3 \, a^{3} b^{5} + 3 \, a^{2} b^{6} - a b^{7}\right)} d \cosh\left(d x + c\right)^{7} + 3 \, {\left(2 \, a^{5} b^{3} - 7 \, a^{4} b^{4} + 9 \, a^{3} b^{5} - 5 \, a^{2} b^{6} + a b^{7}\right)} d \cosh\left(d x + c\right)^{5} + {\left(8 \, a^{6} b^{2} - 32 \, a^{5} b^{3} + 51 \, a^{4} b^{4} - 41 \, a^{3} b^{5} + 17 \, a^{2} b^{6} - 3 \, a b^{7}\right)} d \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{5} b^{3} - 7 \, a^{4} b^{4} + 9 \, a^{3} b^{5} - 5 \, a^{2} b^{6} + a b^{7}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[-1/16*(4*(8*a^4*b - 24*a^3*b^2 + 21*a^2*b^3 - 5*a*b^4)*cosh(d*x + c)^6 + 24*(8*a^4*b - 24*a^3*b^2 + 21*a^2*b^3 - 5*a*b^4)*cosh(d*x + c)*sinh(d*x + c)^5 + 4*(8*a^4*b - 24*a^3*b^2 + 21*a^2*b^3 - 5*a*b^4)*sinh(d*x + c)^6 + 8*a^3*b^2 - 28*a^2*b^3 + 20*a*b^4 + 4*(16*a^5 - 72*a^4*b + 102*a^3*b^2 - 61*a^2*b^3 + 15*a*b^4)*cosh(d*x + c)^4 + 4*(16*a^5 - 72*a^4*b + 102*a^3*b^2 - 61*a^2*b^3 + 15*a*b^4 + 15*(8*a^4*b - 24*a^3*b^2 + 21*a^2*b^3 - 5*a*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 16*(5*(8*a^4*b - 24*a^3*b^2 + 21*a^2*b^3 - 5*a*b^4)*cosh(d*x + c)^3 + (16*a^5 - 72*a^4*b + 102*a^3*b^2 - 61*a^2*b^3 + 15*a*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(8*a^4*b - 40*a^3*b^2 + 47*a^2*b^3 - 15*a*b^4)*cosh(d*x + c)^2 + 4*(8*a^4*b - 40*a^3*b^2 + 47*a^2*b^3 - 15*a*b^4 + 15*(8*a^4*b - 24*a^3*b^2 + 21*a^2*b^3 - 5*a*b^4)*cosh(d*x + c)^4 + 6*(16*a^5 - 72*a^4*b + 102*a^3*b^2 - 61*a^2*b^3 + 15*a*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - 3*(b^4*cosh(d*x + c)^8 + 8*b^4*cosh(d*x + c)*sinh(d*x + c)^7 + b^4*sinh(d*x + c)^8 + 4*(2*a*b^3 - b^4)*cosh(d*x + c)^6 + 4*(7*b^4*cosh(d*x + c)^2 + 2*a*b^3 - b^4)*sinh(d*x + c)^6 + 8*(7*b^4*cosh(d*x + c)^3 + 3*(2*a*b^3 - b^4)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(8*a^2*b^2 - 8*a*b^3 + 3*b^4)*cosh(d*x + c)^4 + 2*(35*b^4*cosh(d*x + c)^4 + 8*a^2*b^2 - 8*a*b^3 + 3*b^4 + 30*(2*a*b^3 - b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + b^4 + 8*(7*b^4*cosh(d*x + c)^5 + 10*(2*a*b^3 - b^4)*cosh(d*x + c)^3 + (8*a^2*b^2 - 8*a*b^3 + 3*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(2*a*b^3 - b^4)*cosh(d*x + c)^2 + 4*(7*b^4*cosh(d*x + c)^6 + 15*(2*a*b^3 - b^4)*cosh(d*x + c)^4 + 2*a*b^3 - b^4 + 3*(8*a^2*b^2 - 8*a*b^3 + 3*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*(b^4*cosh(d*x + c)^7 + 3*(2*a*b^3 - b^4)*cosh(d*x + c)^5 + (8*a^2*b^2 - 8*a*b^3 + 3*b^4)*cosh(d*x + c)^3 + (2*a*b^3 - b^4)*cosh(d*x + c))*sinh(d*x + c))*sqrt(a^2 - a*b)*log((b^2*cosh(d*x + c)^4 + 4*b^2*cosh(d*x + c)*sinh(d*x + c)^3 + b^2*sinh(d*x + c)^4 + 2*(2*a*b - b^2)*cosh(d*x + c)^2 + 2*(3*b^2*cosh(d*x + c)^2 + 2*a*b - b^2)*sinh(d*x + c)^2 + 8*a^2 - 8*a*b + b^2 + 4*(b^2*cosh(d*x + c)^3 + (2*a*b - b^2)*cosh(d*x + c))*sinh(d*x + c) - 4*(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + 2*a - b)*sqrt(a^2 - a*b))/(b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 + 2*(2*a - b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 + 2*a - b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 + (2*a - b)*cosh(d*x + c))*sinh(d*x + c) + b)) + 8*(3*(8*a^4*b - 24*a^3*b^2 + 21*a^2*b^3 - 5*a*b^4)*cosh(d*x + c)^5 + 2*(16*a^5 - 72*a^4*b + 102*a^3*b^2 - 61*a^2*b^3 + 15*a*b^4)*cosh(d*x + c)^3 + (8*a^4*b - 40*a^3*b^2 + 47*a^2*b^3 - 15*a*b^4)*cosh(d*x + c))*sinh(d*x + c))/((a^4*b^4 - 3*a^3*b^5 + 3*a^2*b^6 - a*b^7)*d*cosh(d*x + c)^8 + 8*(a^4*b^4 - 3*a^3*b^5 + 3*a^2*b^6 - a*b^7)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^4*b^4 - 3*a^3*b^5 + 3*a^2*b^6 - a*b^7)*d*sinh(d*x + c)^8 + 4*(2*a^5*b^3 - 7*a^4*b^4 + 9*a^3*b^5 - 5*a^2*b^6 + a*b^7)*d*cosh(d*x + c)^6 + 4*(7*(a^4*b^4 - 3*a^3*b^5 + 3*a^2*b^6 - a*b^7)*d*cosh(d*x + c)^2 + (2*a^5*b^3 - 7*a^4*b^4 + 9*a^3*b^5 - 5*a^2*b^6 + a*b^7)*d)*sinh(d*x + c)^6 + 2*(8*a^6*b^2 - 32*a^5*b^3 + 51*a^4*b^4 - 41*a^3*b^5 + 17*a^2*b^6 - 3*a*b^7)*d*cosh(d*x + c)^4 + 8*(7*(a^4*b^4 - 3*a^3*b^5 + 3*a^2*b^6 - a*b^7)*d*cosh(d*x + c)^3 + 3*(2*a^5*b^3 - 7*a^4*b^4 + 9*a^3*b^5 - 5*a^2*b^6 + a*b^7)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^4*b^4 - 3*a^3*b^5 + 3*a^2*b^6 - a*b^7)*d*cosh(d*x + c)^4 + 30*(2*a^5*b^3 - 7*a^4*b^4 + 9*a^3*b^5 - 5*a^2*b^6 + a*b^7)*d*cosh(d*x + c)^2 + (8*a^6*b^2 - 32*a^5*b^3 + 51*a^4*b^4 - 41*a^3*b^5 + 17*a^2*b^6 - 3*a*b^7)*d)*sinh(d*x + c)^4 + 4*(2*a^5*b^3 - 7*a^4*b^4 + 9*a^3*b^5 - 5*a^2*b^6 + a*b^7)*d*cosh(d*x + c)^2 + 8*(7*(a^4*b^4 - 3*a^3*b^5 + 3*a^2*b^6 - a*b^7)*d*cosh(d*x + c)^5 + 10*(2*a^5*b^3 - 7*a^4*b^4 + 9*a^3*b^5 - 5*a^2*b^6 + a*b^7)*d*cosh(d*x + c)^3 + (8*a^6*b^2 - 32*a^5*b^3 + 51*a^4*b^4 - 41*a^3*b^5 + 17*a^2*b^6 - 3*a*b^7)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^4*b^4 - 3*a^3*b^5 + 3*a^2*b^6 - a*b^7)*d*cosh(d*x + c)^6 + 15*(2*a^5*b^3 - 7*a^4*b^4 + 9*a^3*b^5 - 5*a^2*b^6 + a*b^7)*d*cosh(d*x + c)^4 + 3*(8*a^6*b^2 - 32*a^5*b^3 + 51*a^4*b^4 - 41*a^3*b^5 + 17*a^2*b^6 - 3*a*b^7)*d*cosh(d*x + c)^2 + (2*a^5*b^3 - 7*a^4*b^4 + 9*a^3*b^5 - 5*a^2*b^6 + a*b^7)*d)*sinh(d*x + c)^2 + (a^4*b^4 - 3*a^3*b^5 + 3*a^2*b^6 - a*b^7)*d + 8*((a^4*b^4 - 3*a^3*b^5 + 3*a^2*b^6 - a*b^7)*d*cosh(d*x + c)^7 + 3*(2*a^5*b^3 - 7*a^4*b^4 + 9*a^3*b^5 - 5*a^2*b^6 + a*b^7)*d*cosh(d*x + c)^5 + (8*a^6*b^2 - 32*a^5*b^3 + 51*a^4*b^4 - 41*a^3*b^5 + 17*a^2*b^6 - 3*a*b^7)*d*cosh(d*x + c)^3 + (2*a^5*b^3 - 7*a^4*b^4 + 9*a^3*b^5 - 5*a^2*b^6 + a*b^7)*d*cosh(d*x + c))*sinh(d*x + c)), -1/8*(2*(8*a^4*b - 24*a^3*b^2 + 21*a^2*b^3 - 5*a*b^4)*cosh(d*x + c)^6 + 12*(8*a^4*b - 24*a^3*b^2 + 21*a^2*b^3 - 5*a*b^4)*cosh(d*x + c)*sinh(d*x + c)^5 + 2*(8*a^4*b - 24*a^3*b^2 + 21*a^2*b^3 - 5*a*b^4)*sinh(d*x + c)^6 + 4*a^3*b^2 - 14*a^2*b^3 + 10*a*b^4 + 2*(16*a^5 - 72*a^4*b + 102*a^3*b^2 - 61*a^2*b^3 + 15*a*b^4)*cosh(d*x + c)^4 + 2*(16*a^5 - 72*a^4*b + 102*a^3*b^2 - 61*a^2*b^3 + 15*a*b^4 + 15*(8*a^4*b - 24*a^3*b^2 + 21*a^2*b^3 - 5*a*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(5*(8*a^4*b - 24*a^3*b^2 + 21*a^2*b^3 - 5*a*b^4)*cosh(d*x + c)^3 + (16*a^5 - 72*a^4*b + 102*a^3*b^2 - 61*a^2*b^3 + 15*a*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 2*(8*a^4*b - 40*a^3*b^2 + 47*a^2*b^3 - 15*a*b^4)*cosh(d*x + c)^2 + 2*(8*a^4*b - 40*a^3*b^2 + 47*a^2*b^3 - 15*a*b^4 + 15*(8*a^4*b - 24*a^3*b^2 + 21*a^2*b^3 - 5*a*b^4)*cosh(d*x + c)^4 + 6*(16*a^5 - 72*a^4*b + 102*a^3*b^2 - 61*a^2*b^3 + 15*a*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 3*(b^4*cosh(d*x + c)^8 + 8*b^4*cosh(d*x + c)*sinh(d*x + c)^7 + b^4*sinh(d*x + c)^8 + 4*(2*a*b^3 - b^4)*cosh(d*x + c)^6 + 4*(7*b^4*cosh(d*x + c)^2 + 2*a*b^3 - b^4)*sinh(d*x + c)^6 + 8*(7*b^4*cosh(d*x + c)^3 + 3*(2*a*b^3 - b^4)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(8*a^2*b^2 - 8*a*b^3 + 3*b^4)*cosh(d*x + c)^4 + 2*(35*b^4*cosh(d*x + c)^4 + 8*a^2*b^2 - 8*a*b^3 + 3*b^4 + 30*(2*a*b^3 - b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + b^4 + 8*(7*b^4*cosh(d*x + c)^5 + 10*(2*a*b^3 - b^4)*cosh(d*x + c)^3 + (8*a^2*b^2 - 8*a*b^3 + 3*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(2*a*b^3 - b^4)*cosh(d*x + c)^2 + 4*(7*b^4*cosh(d*x + c)^6 + 15*(2*a*b^3 - b^4)*cosh(d*x + c)^4 + 2*a*b^3 - b^4 + 3*(8*a^2*b^2 - 8*a*b^3 + 3*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*(b^4*cosh(d*x + c)^7 + 3*(2*a*b^3 - b^4)*cosh(d*x + c)^5 + (8*a^2*b^2 - 8*a*b^3 + 3*b^4)*cosh(d*x + c)^3 + (2*a*b^3 - b^4)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-a^2 + a*b)*arctan(-1/2*(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + 2*a - b)*sqrt(-a^2 + a*b)/(a^2 - a*b)) + 4*(3*(8*a^4*b - 24*a^3*b^2 + 21*a^2*b^3 - 5*a*b^4)*cosh(d*x + c)^5 + 2*(16*a^5 - 72*a^4*b + 102*a^3*b^2 - 61*a^2*b^3 + 15*a*b^4)*cosh(d*x + c)^3 + (8*a^4*b - 40*a^3*b^2 + 47*a^2*b^3 - 15*a*b^4)*cosh(d*x + c))*sinh(d*x + c))/((a^4*b^4 - 3*a^3*b^5 + 3*a^2*b^6 - a*b^7)*d*cosh(d*x + c)^8 + 8*(a^4*b^4 - 3*a^3*b^5 + 3*a^2*b^6 - a*b^7)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^4*b^4 - 3*a^3*b^5 + 3*a^2*b^6 - a*b^7)*d*sinh(d*x + c)^8 + 4*(2*a^5*b^3 - 7*a^4*b^4 + 9*a^3*b^5 - 5*a^2*b^6 + a*b^7)*d*cosh(d*x + c)^6 + 4*(7*(a^4*b^4 - 3*a^3*b^5 + 3*a^2*b^6 - a*b^7)*d*cosh(d*x + c)^2 + (2*a^5*b^3 - 7*a^4*b^4 + 9*a^3*b^5 - 5*a^2*b^6 + a*b^7)*d)*sinh(d*x + c)^6 + 2*(8*a^6*b^2 - 32*a^5*b^3 + 51*a^4*b^4 - 41*a^3*b^5 + 17*a^2*b^6 - 3*a*b^7)*d*cosh(d*x + c)^4 + 8*(7*(a^4*b^4 - 3*a^3*b^5 + 3*a^2*b^6 - a*b^7)*d*cosh(d*x + c)^3 + 3*(2*a^5*b^3 - 7*a^4*b^4 + 9*a^3*b^5 - 5*a^2*b^6 + a*b^7)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^4*b^4 - 3*a^3*b^5 + 3*a^2*b^6 - a*b^7)*d*cosh(d*x + c)^4 + 30*(2*a^5*b^3 - 7*a^4*b^4 + 9*a^3*b^5 - 5*a^2*b^6 + a*b^7)*d*cosh(d*x + c)^2 + (8*a^6*b^2 - 32*a^5*b^3 + 51*a^4*b^4 - 41*a^3*b^5 + 17*a^2*b^6 - 3*a*b^7)*d)*sinh(d*x + c)^4 + 4*(2*a^5*b^3 - 7*a^4*b^4 + 9*a^3*b^5 - 5*a^2*b^6 + a*b^7)*d*cosh(d*x + c)^2 + 8*(7*(a^4*b^4 - 3*a^3*b^5 + 3*a^2*b^6 - a*b^7)*d*cosh(d*x + c)^5 + 10*(2*a^5*b^3 - 7*a^4*b^4 + 9*a^3*b^5 - 5*a^2*b^6 + a*b^7)*d*cosh(d*x + c)^3 + (8*a^6*b^2 - 32*a^5*b^3 + 51*a^4*b^4 - 41*a^3*b^5 + 17*a^2*b^6 - 3*a*b^7)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^4*b^4 - 3*a^3*b^5 + 3*a^2*b^6 - a*b^7)*d*cosh(d*x + c)^6 + 15*(2*a^5*b^3 - 7*a^4*b^4 + 9*a^3*b^5 - 5*a^2*b^6 + a*b^7)*d*cosh(d*x + c)^4 + 3*(8*a^6*b^2 - 32*a^5*b^3 + 51*a^4*b^4 - 41*a^3*b^5 + 17*a^2*b^6 - 3*a*b^7)*d*cosh(d*x + c)^2 + (2*a^5*b^3 - 7*a^4*b^4 + 9*a^3*b^5 - 5*a^2*b^6 + a*b^7)*d)*sinh(d*x + c)^2 + (a^4*b^4 - 3*a^3*b^5 + 3*a^2*b^6 - a*b^7)*d + 8*((a^4*b^4 - 3*a^3*b^5 + 3*a^2*b^6 - a*b^7)*d*cosh(d*x + c)^7 + 3*(2*a^5*b^3 - 7*a^4*b^4 + 9*a^3*b^5 - 5*a^2*b^6 + a*b^7)*d*cosh(d*x + c)^5 + (8*a^6*b^2 - 32*a^5*b^3 + 51*a^4*b^4 - 41*a^3*b^5 + 17*a^2*b^6 - 3*a*b^7)*d*cosh(d*x + c)^3 + (2*a^5*b^3 - 7*a^4*b^4 + 9*a^3*b^5 - 5*a^2*b^6 + a*b^7)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
52,1,6087,0,0.945056," ","integrate(sinh(d*x+c)^3/(a+b*sinh(d*x+c)^2)^3,x, algorithm=""fricas"")","\left[\frac{4 \, {\left(a^{2} b^{2} - 5 \, a b^{3} + 4 \, b^{4}\right)} \cosh\left(d x + c\right)^{7} + 28 \, {\left(a^{2} b^{2} - 5 \, a b^{3} + 4 \, b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + 4 \, {\left(a^{2} b^{2} - 5 \, a b^{3} + 4 \, b^{4}\right)} \sinh\left(d x + c\right)^{7} - 4 \, {\left(4 \, a^{3} b + 5 \, a^{2} b^{2} - 13 \, a b^{3} + 4 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} - 4 \, {\left(4 \, a^{3} b + 5 \, a^{2} b^{2} - 13 \, a b^{3} + 4 \, b^{4} - 21 \, {\left(a^{2} b^{2} - 5 \, a b^{3} + 4 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{5} + 20 \, {\left(7 \, {\left(a^{2} b^{2} - 5 \, a b^{3} + 4 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} - {\left(4 \, a^{3} b + 5 \, a^{2} b^{2} - 13 \, a b^{3} + 4 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} - 4 \, {\left(4 \, a^{3} b + 5 \, a^{2} b^{2} - 13 \, a b^{3} + 4 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(35 \, {\left(a^{2} b^{2} - 5 \, a b^{3} + 4 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} - 4 \, a^{3} b - 5 \, a^{2} b^{2} + 13 \, a b^{3} - 4 \, b^{4} - 10 \, {\left(4 \, a^{3} b + 5 \, a^{2} b^{2} - 13 \, a b^{3} + 4 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(21 \, {\left(a^{2} b^{2} - 5 \, a b^{3} + 4 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} - 10 \, {\left(4 \, a^{3} b + 5 \, a^{2} b^{2} - 13 \, a b^{3} + 4 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(4 \, a^{3} b + 5 \, a^{2} b^{2} - 13 \, a b^{3} + 4 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(a b^{2} - 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(a b^{2} - 4 \, b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a b^{2} - 4 \, b^{3}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(2 \, a^{2} b - 9 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(2 \, a^{2} b - 9 \, a b^{2} + 4 \, b^{3} + 7 \, {\left(a b^{2} - 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(a b^{2} - 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(2 \, a^{2} b - 9 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(8 \, a^{3} - 40 \, a^{2} b + 35 \, a b^{2} - 12 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(a b^{2} - 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 8 \, a^{3} - 40 \, a^{2} b + 35 \, a b^{2} - 12 \, b^{3} + 30 \, {\left(2 \, a^{2} b - 9 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a b^{2} - 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(2 \, a^{2} b - 9 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{3} - 40 \, a^{2} b + 35 \, a b^{2} - 12 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + a b^{2} - 4 \, b^{3} + 4 \, {\left(2 \, a^{2} b - 9 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(a b^{2} - 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(2 \, a^{2} b - 9 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 2 \, a^{2} b - 9 \, a b^{2} + 4 \, b^{3} + 3 \, {\left(8 \, a^{3} - 40 \, a^{2} b + 35 \, a b^{2} - 12 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left({\left(a b^{2} - 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(2 \, a^{2} b - 9 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + {\left(8 \, a^{3} - 40 \, a^{2} b + 35 \, a b^{2} - 12 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{2} b - 9 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-a b + b^{2}} \log\left(\frac{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} - 2 \, {\left(2 \, a - 3 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} - 2 \, a + 3 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} - {\left(2 \, a - 3 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + 4 \, {\left(\cosh\left(d x + c\right)^{3} + 3 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{3} + {\left(3 \, \cosh\left(d x + c\right)^{2} + 1\right)} \sinh\left(d x + c\right) + \cosh\left(d x + c\right)\right)} \sqrt{-a b + b^{2}} + b}{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b}\right) + 4 \, {\left(a^{2} b^{2} - 5 \, a b^{3} + 4 \, b^{4}\right)} \cosh\left(d x + c\right) + 4 \, {\left(7 \, {\left(a^{2} b^{2} - 5 \, a b^{3} + 4 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} - 5 \, {\left(4 \, a^{3} b + 5 \, a^{2} b^{2} - 13 \, a b^{3} + 4 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + a^{2} b^{2} - 5 \, a b^{3} + 4 \, b^{4} - 3 \, {\left(4 \, a^{3} b + 5 \, a^{2} b^{2} - 13 \, a b^{3} + 4 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)}{16 \, {\left({\left(a^{3} b^{4} - 3 \, a^{2} b^{5} + 3 \, a b^{6} - b^{7}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{3} b^{4} - 3 \, a^{2} b^{5} + 3 \, a b^{6} - b^{7}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{3} b^{4} - 3 \, a^{2} b^{5} + 3 \, a b^{6} - b^{7}\right)} d \sinh\left(d x + c\right)^{8} + 4 \, {\left(2 \, a^{4} b^{3} - 7 \, a^{3} b^{4} + 9 \, a^{2} b^{5} - 5 \, a b^{6} + b^{7}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{3} b^{4} - 3 \, a^{2} b^{5} + 3 \, a b^{6} - b^{7}\right)} d \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{4} b^{3} - 7 \, a^{3} b^{4} + 9 \, a^{2} b^{5} - 5 \, a b^{6} + b^{7}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(8 \, a^{5} b^{2} - 32 \, a^{4} b^{3} + 51 \, a^{3} b^{4} - 41 \, a^{2} b^{5} + 17 \, a b^{6} - 3 \, b^{7}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{3} b^{4} - 3 \, a^{2} b^{5} + 3 \, a b^{6} - b^{7}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(2 \, a^{4} b^{3} - 7 \, a^{3} b^{4} + 9 \, a^{2} b^{5} - 5 \, a b^{6} + b^{7}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a^{3} b^{4} - 3 \, a^{2} b^{5} + 3 \, a b^{6} - b^{7}\right)} d \cosh\left(d x + c\right)^{4} + 30 \, {\left(2 \, a^{4} b^{3} - 7 \, a^{3} b^{4} + 9 \, a^{2} b^{5} - 5 \, a b^{6} + b^{7}\right)} d \cosh\left(d x + c\right)^{2} + {\left(8 \, a^{5} b^{2} - 32 \, a^{4} b^{3} + 51 \, a^{3} b^{4} - 41 \, a^{2} b^{5} + 17 \, a b^{6} - 3 \, b^{7}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(2 \, a^{4} b^{3} - 7 \, a^{3} b^{4} + 9 \, a^{2} b^{5} - 5 \, a b^{6} + b^{7}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a^{3} b^{4} - 3 \, a^{2} b^{5} + 3 \, a b^{6} - b^{7}\right)} d \cosh\left(d x + c\right)^{5} + 10 \, {\left(2 \, a^{4} b^{3} - 7 \, a^{3} b^{4} + 9 \, a^{2} b^{5} - 5 \, a b^{6} + b^{7}\right)} d \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{5} b^{2} - 32 \, a^{4} b^{3} + 51 \, a^{3} b^{4} - 41 \, a^{2} b^{5} + 17 \, a b^{6} - 3 \, b^{7}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a^{3} b^{4} - 3 \, a^{2} b^{5} + 3 \, a b^{6} - b^{7}\right)} d \cosh\left(d x + c\right)^{6} + 15 \, {\left(2 \, a^{4} b^{3} - 7 \, a^{3} b^{4} + 9 \, a^{2} b^{5} - 5 \, a b^{6} + b^{7}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(8 \, a^{5} b^{2} - 32 \, a^{4} b^{3} + 51 \, a^{3} b^{4} - 41 \, a^{2} b^{5} + 17 \, a b^{6} - 3 \, b^{7}\right)} d \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{4} b^{3} - 7 \, a^{3} b^{4} + 9 \, a^{2} b^{5} - 5 \, a b^{6} + b^{7}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{3} b^{4} - 3 \, a^{2} b^{5} + 3 \, a b^{6} - b^{7}\right)} d + 8 \, {\left({\left(a^{3} b^{4} - 3 \, a^{2} b^{5} + 3 \, a b^{6} - b^{7}\right)} d \cosh\left(d x + c\right)^{7} + 3 \, {\left(2 \, a^{4} b^{3} - 7 \, a^{3} b^{4} + 9 \, a^{2} b^{5} - 5 \, a b^{6} + b^{7}\right)} d \cosh\left(d x + c\right)^{5} + {\left(8 \, a^{5} b^{2} - 32 \, a^{4} b^{3} + 51 \, a^{3} b^{4} - 41 \, a^{2} b^{5} + 17 \, a b^{6} - 3 \, b^{7}\right)} d \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{4} b^{3} - 7 \, a^{3} b^{4} + 9 \, a^{2} b^{5} - 5 \, a b^{6} + b^{7}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}, \frac{2 \, {\left(a^{2} b^{2} - 5 \, a b^{3} + 4 \, b^{4}\right)} \cosh\left(d x + c\right)^{7} + 14 \, {\left(a^{2} b^{2} - 5 \, a b^{3} + 4 \, b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + 2 \, {\left(a^{2} b^{2} - 5 \, a b^{3} + 4 \, b^{4}\right)} \sinh\left(d x + c\right)^{7} - 2 \, {\left(4 \, a^{3} b + 5 \, a^{2} b^{2} - 13 \, a b^{3} + 4 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} - 2 \, {\left(4 \, a^{3} b + 5 \, a^{2} b^{2} - 13 \, a b^{3} + 4 \, b^{4} - 21 \, {\left(a^{2} b^{2} - 5 \, a b^{3} + 4 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{5} + 10 \, {\left(7 \, {\left(a^{2} b^{2} - 5 \, a b^{3} + 4 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} - {\left(4 \, a^{3} b + 5 \, a^{2} b^{2} - 13 \, a b^{3} + 4 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(4 \, a^{3} b + 5 \, a^{2} b^{2} - 13 \, a b^{3} + 4 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(35 \, {\left(a^{2} b^{2} - 5 \, a b^{3} + 4 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} - 4 \, a^{3} b - 5 \, a^{2} b^{2} + 13 \, a b^{3} - 4 \, b^{4} - 10 \, {\left(4 \, a^{3} b + 5 \, a^{2} b^{2} - 13 \, a b^{3} + 4 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(21 \, {\left(a^{2} b^{2} - 5 \, a b^{3} + 4 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} - 10 \, {\left(4 \, a^{3} b + 5 \, a^{2} b^{2} - 13 \, a b^{3} + 4 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(4 \, a^{3} b + 5 \, a^{2} b^{2} - 13 \, a b^{3} + 4 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(a b^{2} - 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(a b^{2} - 4 \, b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a b^{2} - 4 \, b^{3}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(2 \, a^{2} b - 9 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(2 \, a^{2} b - 9 \, a b^{2} + 4 \, b^{3} + 7 \, {\left(a b^{2} - 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(a b^{2} - 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(2 \, a^{2} b - 9 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(8 \, a^{3} - 40 \, a^{2} b + 35 \, a b^{2} - 12 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(a b^{2} - 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 8 \, a^{3} - 40 \, a^{2} b + 35 \, a b^{2} - 12 \, b^{3} + 30 \, {\left(2 \, a^{2} b - 9 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a b^{2} - 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(2 \, a^{2} b - 9 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{3} - 40 \, a^{2} b + 35 \, a b^{2} - 12 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + a b^{2} - 4 \, b^{3} + 4 \, {\left(2 \, a^{2} b - 9 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(a b^{2} - 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(2 \, a^{2} b - 9 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 2 \, a^{2} b - 9 \, a b^{2} + 4 \, b^{3} + 3 \, {\left(8 \, a^{3} - 40 \, a^{2} b + 35 \, a b^{2} - 12 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left({\left(a b^{2} - 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(2 \, a^{2} b - 9 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + {\left(8 \, a^{3} - 40 \, a^{2} b + 35 \, a b^{2} - 12 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{2} b - 9 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{a b - b^{2}} \arctan\left(-\frac{b \cosh\left(d x + c\right)^{3} + 3 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{3} + {\left(4 \, a - 3 \, b\right)} \cosh\left(d x + c\right) + {\left(3 \, b \cosh\left(d x + c\right)^{2} + 4 \, a - 3 \, b\right)} \sinh\left(d x + c\right)}{2 \, \sqrt{a b - b^{2}}}\right) - {\left({\left(a b^{2} - 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(a b^{2} - 4 \, b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a b^{2} - 4 \, b^{3}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(2 \, a^{2} b - 9 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(2 \, a^{2} b - 9 \, a b^{2} + 4 \, b^{3} + 7 \, {\left(a b^{2} - 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(a b^{2} - 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(2 \, a^{2} b - 9 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(8 \, a^{3} - 40 \, a^{2} b + 35 \, a b^{2} - 12 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(a b^{2} - 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 8 \, a^{3} - 40 \, a^{2} b + 35 \, a b^{2} - 12 \, b^{3} + 30 \, {\left(2 \, a^{2} b - 9 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a b^{2} - 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(2 \, a^{2} b - 9 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{3} - 40 \, a^{2} b + 35 \, a b^{2} - 12 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + a b^{2} - 4 \, b^{3} + 4 \, {\left(2 \, a^{2} b - 9 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(a b^{2} - 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(2 \, a^{2} b - 9 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 2 \, a^{2} b - 9 \, a b^{2} + 4 \, b^{3} + 3 \, {\left(8 \, a^{3} - 40 \, a^{2} b + 35 \, a b^{2} - 12 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left({\left(a b^{2} - 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(2 \, a^{2} b - 9 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + {\left(8 \, a^{3} - 40 \, a^{2} b + 35 \, a b^{2} - 12 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{2} b - 9 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{a b - b^{2}} \arctan\left(-\frac{\sqrt{a b - b^{2}} {\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right)}}{2 \, {\left(a - b\right)}}\right) + 2 \, {\left(a^{2} b^{2} - 5 \, a b^{3} + 4 \, b^{4}\right)} \cosh\left(d x + c\right) + 2 \, {\left(7 \, {\left(a^{2} b^{2} - 5 \, a b^{3} + 4 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} - 5 \, {\left(4 \, a^{3} b + 5 \, a^{2} b^{2} - 13 \, a b^{3} + 4 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + a^{2} b^{2} - 5 \, a b^{3} + 4 \, b^{4} - 3 \, {\left(4 \, a^{3} b + 5 \, a^{2} b^{2} - 13 \, a b^{3} + 4 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)}{8 \, {\left({\left(a^{3} b^{4} - 3 \, a^{2} b^{5} + 3 \, a b^{6} - b^{7}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{3} b^{4} - 3 \, a^{2} b^{5} + 3 \, a b^{6} - b^{7}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{3} b^{4} - 3 \, a^{2} b^{5} + 3 \, a b^{6} - b^{7}\right)} d \sinh\left(d x + c\right)^{8} + 4 \, {\left(2 \, a^{4} b^{3} - 7 \, a^{3} b^{4} + 9 \, a^{2} b^{5} - 5 \, a b^{6} + b^{7}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{3} b^{4} - 3 \, a^{2} b^{5} + 3 \, a b^{6} - b^{7}\right)} d \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{4} b^{3} - 7 \, a^{3} b^{4} + 9 \, a^{2} b^{5} - 5 \, a b^{6} + b^{7}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(8 \, a^{5} b^{2} - 32 \, a^{4} b^{3} + 51 \, a^{3} b^{4} - 41 \, a^{2} b^{5} + 17 \, a b^{6} - 3 \, b^{7}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{3} b^{4} - 3 \, a^{2} b^{5} + 3 \, a b^{6} - b^{7}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(2 \, a^{4} b^{3} - 7 \, a^{3} b^{4} + 9 \, a^{2} b^{5} - 5 \, a b^{6} + b^{7}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a^{3} b^{4} - 3 \, a^{2} b^{5} + 3 \, a b^{6} - b^{7}\right)} d \cosh\left(d x + c\right)^{4} + 30 \, {\left(2 \, a^{4} b^{3} - 7 \, a^{3} b^{4} + 9 \, a^{2} b^{5} - 5 \, a b^{6} + b^{7}\right)} d \cosh\left(d x + c\right)^{2} + {\left(8 \, a^{5} b^{2} - 32 \, a^{4} b^{3} + 51 \, a^{3} b^{4} - 41 \, a^{2} b^{5} + 17 \, a b^{6} - 3 \, b^{7}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(2 \, a^{4} b^{3} - 7 \, a^{3} b^{4} + 9 \, a^{2} b^{5} - 5 \, a b^{6} + b^{7}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a^{3} b^{4} - 3 \, a^{2} b^{5} + 3 \, a b^{6} - b^{7}\right)} d \cosh\left(d x + c\right)^{5} + 10 \, {\left(2 \, a^{4} b^{3} - 7 \, a^{3} b^{4} + 9 \, a^{2} b^{5} - 5 \, a b^{6} + b^{7}\right)} d \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{5} b^{2} - 32 \, a^{4} b^{3} + 51 \, a^{3} b^{4} - 41 \, a^{2} b^{5} + 17 \, a b^{6} - 3 \, b^{7}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a^{3} b^{4} - 3 \, a^{2} b^{5} + 3 \, a b^{6} - b^{7}\right)} d \cosh\left(d x + c\right)^{6} + 15 \, {\left(2 \, a^{4} b^{3} - 7 \, a^{3} b^{4} + 9 \, a^{2} b^{5} - 5 \, a b^{6} + b^{7}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(8 \, a^{5} b^{2} - 32 \, a^{4} b^{3} + 51 \, a^{3} b^{4} - 41 \, a^{2} b^{5} + 17 \, a b^{6} - 3 \, b^{7}\right)} d \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{4} b^{3} - 7 \, a^{3} b^{4} + 9 \, a^{2} b^{5} - 5 \, a b^{6} + b^{7}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{3} b^{4} - 3 \, a^{2} b^{5} + 3 \, a b^{6} - b^{7}\right)} d + 8 \, {\left({\left(a^{3} b^{4} - 3 \, a^{2} b^{5} + 3 \, a b^{6} - b^{7}\right)} d \cosh\left(d x + c\right)^{7} + 3 \, {\left(2 \, a^{4} b^{3} - 7 \, a^{3} b^{4} + 9 \, a^{2} b^{5} - 5 \, a b^{6} + b^{7}\right)} d \cosh\left(d x + c\right)^{5} + {\left(8 \, a^{5} b^{2} - 32 \, a^{4} b^{3} + 51 \, a^{3} b^{4} - 41 \, a^{2} b^{5} + 17 \, a b^{6} - 3 \, b^{7}\right)} d \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{4} b^{3} - 7 \, a^{3} b^{4} + 9 \, a^{2} b^{5} - 5 \, a b^{6} + b^{7}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[1/16*(4*(a^2*b^2 - 5*a*b^3 + 4*b^4)*cosh(d*x + c)^7 + 28*(a^2*b^2 - 5*a*b^3 + 4*b^4)*cosh(d*x + c)*sinh(d*x + c)^6 + 4*(a^2*b^2 - 5*a*b^3 + 4*b^4)*sinh(d*x + c)^7 - 4*(4*a^3*b + 5*a^2*b^2 - 13*a*b^3 + 4*b^4)*cosh(d*x + c)^5 - 4*(4*a^3*b + 5*a^2*b^2 - 13*a*b^3 + 4*b^4 - 21*(a^2*b^2 - 5*a*b^3 + 4*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 20*(7*(a^2*b^2 - 5*a*b^3 + 4*b^4)*cosh(d*x + c)^3 - (4*a^3*b + 5*a^2*b^2 - 13*a*b^3 + 4*b^4)*cosh(d*x + c))*sinh(d*x + c)^4 - 4*(4*a^3*b + 5*a^2*b^2 - 13*a*b^3 + 4*b^4)*cosh(d*x + c)^3 + 4*(35*(a^2*b^2 - 5*a*b^3 + 4*b^4)*cosh(d*x + c)^4 - 4*a^3*b - 5*a^2*b^2 + 13*a*b^3 - 4*b^4 - 10*(4*a^3*b + 5*a^2*b^2 - 13*a*b^3 + 4*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 4*(21*(a^2*b^2 - 5*a*b^3 + 4*b^4)*cosh(d*x + c)^5 - 10*(4*a^3*b + 5*a^2*b^2 - 13*a*b^3 + 4*b^4)*cosh(d*x + c)^3 - 3*(4*a^3*b + 5*a^2*b^2 - 13*a*b^3 + 4*b^4)*cosh(d*x + c))*sinh(d*x + c)^2 + ((a*b^2 - 4*b^3)*cosh(d*x + c)^8 + 8*(a*b^2 - 4*b^3)*cosh(d*x + c)*sinh(d*x + c)^7 + (a*b^2 - 4*b^3)*sinh(d*x + c)^8 + 4*(2*a^2*b - 9*a*b^2 + 4*b^3)*cosh(d*x + c)^6 + 4*(2*a^2*b - 9*a*b^2 + 4*b^3 + 7*(a*b^2 - 4*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(a*b^2 - 4*b^3)*cosh(d*x + c)^3 + 3*(2*a^2*b - 9*a*b^2 + 4*b^3)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(8*a^3 - 40*a^2*b + 35*a*b^2 - 12*b^3)*cosh(d*x + c)^4 + 2*(35*(a*b^2 - 4*b^3)*cosh(d*x + c)^4 + 8*a^3 - 40*a^2*b + 35*a*b^2 - 12*b^3 + 30*(2*a^2*b - 9*a*b^2 + 4*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(7*(a*b^2 - 4*b^3)*cosh(d*x + c)^5 + 10*(2*a^2*b - 9*a*b^2 + 4*b^3)*cosh(d*x + c)^3 + (8*a^3 - 40*a^2*b + 35*a*b^2 - 12*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 + a*b^2 - 4*b^3 + 4*(2*a^2*b - 9*a*b^2 + 4*b^3)*cosh(d*x + c)^2 + 4*(7*(a*b^2 - 4*b^3)*cosh(d*x + c)^6 + 15*(2*a^2*b - 9*a*b^2 + 4*b^3)*cosh(d*x + c)^4 + 2*a^2*b - 9*a*b^2 + 4*b^3 + 3*(8*a^3 - 40*a^2*b + 35*a*b^2 - 12*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((a*b^2 - 4*b^3)*cosh(d*x + c)^7 + 3*(2*a^2*b - 9*a*b^2 + 4*b^3)*cosh(d*x + c)^5 + (8*a^3 - 40*a^2*b + 35*a*b^2 - 12*b^3)*cosh(d*x + c)^3 + (2*a^2*b - 9*a*b^2 + 4*b^3)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-a*b + b^2)*log((b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 - 2*(2*a - 3*b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 - 2*a + 3*b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 - (2*a - 3*b)*cosh(d*x + c))*sinh(d*x + c) + 4*(cosh(d*x + c)^3 + 3*cosh(d*x + c)*sinh(d*x + c)^2 + sinh(d*x + c)^3 + (3*cosh(d*x + c)^2 + 1)*sinh(d*x + c) + cosh(d*x + c))*sqrt(-a*b + b^2) + b)/(b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 + 2*(2*a - b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 + 2*a - b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 + (2*a - b)*cosh(d*x + c))*sinh(d*x + c) + b)) + 4*(a^2*b^2 - 5*a*b^3 + 4*b^4)*cosh(d*x + c) + 4*(7*(a^2*b^2 - 5*a*b^3 + 4*b^4)*cosh(d*x + c)^6 - 5*(4*a^3*b + 5*a^2*b^2 - 13*a*b^3 + 4*b^4)*cosh(d*x + c)^4 + a^2*b^2 - 5*a*b^3 + 4*b^4 - 3*(4*a^3*b + 5*a^2*b^2 - 13*a*b^3 + 4*b^4)*cosh(d*x + c)^2)*sinh(d*x + c))/((a^3*b^4 - 3*a^2*b^5 + 3*a*b^6 - b^7)*d*cosh(d*x + c)^8 + 8*(a^3*b^4 - 3*a^2*b^5 + 3*a*b^6 - b^7)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^3*b^4 - 3*a^2*b^5 + 3*a*b^6 - b^7)*d*sinh(d*x + c)^8 + 4*(2*a^4*b^3 - 7*a^3*b^4 + 9*a^2*b^5 - 5*a*b^6 + b^7)*d*cosh(d*x + c)^6 + 4*(7*(a^3*b^4 - 3*a^2*b^5 + 3*a*b^6 - b^7)*d*cosh(d*x + c)^2 + (2*a^4*b^3 - 7*a^3*b^4 + 9*a^2*b^5 - 5*a*b^6 + b^7)*d)*sinh(d*x + c)^6 + 2*(8*a^5*b^2 - 32*a^4*b^3 + 51*a^3*b^4 - 41*a^2*b^5 + 17*a*b^6 - 3*b^7)*d*cosh(d*x + c)^4 + 8*(7*(a^3*b^4 - 3*a^2*b^5 + 3*a*b^6 - b^7)*d*cosh(d*x + c)^3 + 3*(2*a^4*b^3 - 7*a^3*b^4 + 9*a^2*b^5 - 5*a*b^6 + b^7)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^3*b^4 - 3*a^2*b^5 + 3*a*b^6 - b^7)*d*cosh(d*x + c)^4 + 30*(2*a^4*b^3 - 7*a^3*b^4 + 9*a^2*b^5 - 5*a*b^6 + b^7)*d*cosh(d*x + c)^2 + (8*a^5*b^2 - 32*a^4*b^3 + 51*a^3*b^4 - 41*a^2*b^5 + 17*a*b^6 - 3*b^7)*d)*sinh(d*x + c)^4 + 4*(2*a^4*b^3 - 7*a^3*b^4 + 9*a^2*b^5 - 5*a*b^6 + b^7)*d*cosh(d*x + c)^2 + 8*(7*(a^3*b^4 - 3*a^2*b^5 + 3*a*b^6 - b^7)*d*cosh(d*x + c)^5 + 10*(2*a^4*b^3 - 7*a^3*b^4 + 9*a^2*b^5 - 5*a*b^6 + b^7)*d*cosh(d*x + c)^3 + (8*a^5*b^2 - 32*a^4*b^3 + 51*a^3*b^4 - 41*a^2*b^5 + 17*a*b^6 - 3*b^7)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^3*b^4 - 3*a^2*b^5 + 3*a*b^6 - b^7)*d*cosh(d*x + c)^6 + 15*(2*a^4*b^3 - 7*a^3*b^4 + 9*a^2*b^5 - 5*a*b^6 + b^7)*d*cosh(d*x + c)^4 + 3*(8*a^5*b^2 - 32*a^4*b^3 + 51*a^3*b^4 - 41*a^2*b^5 + 17*a*b^6 - 3*b^7)*d*cosh(d*x + c)^2 + (2*a^4*b^3 - 7*a^3*b^4 + 9*a^2*b^5 - 5*a*b^6 + b^7)*d)*sinh(d*x + c)^2 + (a^3*b^4 - 3*a^2*b^5 + 3*a*b^6 - b^7)*d + 8*((a^3*b^4 - 3*a^2*b^5 + 3*a*b^6 - b^7)*d*cosh(d*x + c)^7 + 3*(2*a^4*b^3 - 7*a^3*b^4 + 9*a^2*b^5 - 5*a*b^6 + b^7)*d*cosh(d*x + c)^5 + (8*a^5*b^2 - 32*a^4*b^3 + 51*a^3*b^4 - 41*a^2*b^5 + 17*a*b^6 - 3*b^7)*d*cosh(d*x + c)^3 + (2*a^4*b^3 - 7*a^3*b^4 + 9*a^2*b^5 - 5*a*b^6 + b^7)*d*cosh(d*x + c))*sinh(d*x + c)), 1/8*(2*(a^2*b^2 - 5*a*b^3 + 4*b^4)*cosh(d*x + c)^7 + 14*(a^2*b^2 - 5*a*b^3 + 4*b^4)*cosh(d*x + c)*sinh(d*x + c)^6 + 2*(a^2*b^2 - 5*a*b^3 + 4*b^4)*sinh(d*x + c)^7 - 2*(4*a^3*b + 5*a^2*b^2 - 13*a*b^3 + 4*b^4)*cosh(d*x + c)^5 - 2*(4*a^3*b + 5*a^2*b^2 - 13*a*b^3 + 4*b^4 - 21*(a^2*b^2 - 5*a*b^3 + 4*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 10*(7*(a^2*b^2 - 5*a*b^3 + 4*b^4)*cosh(d*x + c)^3 - (4*a^3*b + 5*a^2*b^2 - 13*a*b^3 + 4*b^4)*cosh(d*x + c))*sinh(d*x + c)^4 - 2*(4*a^3*b + 5*a^2*b^2 - 13*a*b^3 + 4*b^4)*cosh(d*x + c)^3 + 2*(35*(a^2*b^2 - 5*a*b^3 + 4*b^4)*cosh(d*x + c)^4 - 4*a^3*b - 5*a^2*b^2 + 13*a*b^3 - 4*b^4 - 10*(4*a^3*b + 5*a^2*b^2 - 13*a*b^3 + 4*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 2*(21*(a^2*b^2 - 5*a*b^3 + 4*b^4)*cosh(d*x + c)^5 - 10*(4*a^3*b + 5*a^2*b^2 - 13*a*b^3 + 4*b^4)*cosh(d*x + c)^3 - 3*(4*a^3*b + 5*a^2*b^2 - 13*a*b^3 + 4*b^4)*cosh(d*x + c))*sinh(d*x + c)^2 + ((a*b^2 - 4*b^3)*cosh(d*x + c)^8 + 8*(a*b^2 - 4*b^3)*cosh(d*x + c)*sinh(d*x + c)^7 + (a*b^2 - 4*b^3)*sinh(d*x + c)^8 + 4*(2*a^2*b - 9*a*b^2 + 4*b^3)*cosh(d*x + c)^6 + 4*(2*a^2*b - 9*a*b^2 + 4*b^3 + 7*(a*b^2 - 4*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(a*b^2 - 4*b^3)*cosh(d*x + c)^3 + 3*(2*a^2*b - 9*a*b^2 + 4*b^3)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(8*a^3 - 40*a^2*b + 35*a*b^2 - 12*b^3)*cosh(d*x + c)^4 + 2*(35*(a*b^2 - 4*b^3)*cosh(d*x + c)^4 + 8*a^3 - 40*a^2*b + 35*a*b^2 - 12*b^3 + 30*(2*a^2*b - 9*a*b^2 + 4*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(7*(a*b^2 - 4*b^3)*cosh(d*x + c)^5 + 10*(2*a^2*b - 9*a*b^2 + 4*b^3)*cosh(d*x + c)^3 + (8*a^3 - 40*a^2*b + 35*a*b^2 - 12*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 + a*b^2 - 4*b^3 + 4*(2*a^2*b - 9*a*b^2 + 4*b^3)*cosh(d*x + c)^2 + 4*(7*(a*b^2 - 4*b^3)*cosh(d*x + c)^6 + 15*(2*a^2*b - 9*a*b^2 + 4*b^3)*cosh(d*x + c)^4 + 2*a^2*b - 9*a*b^2 + 4*b^3 + 3*(8*a^3 - 40*a^2*b + 35*a*b^2 - 12*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((a*b^2 - 4*b^3)*cosh(d*x + c)^7 + 3*(2*a^2*b - 9*a*b^2 + 4*b^3)*cosh(d*x + c)^5 + (8*a^3 - 40*a^2*b + 35*a*b^2 - 12*b^3)*cosh(d*x + c)^3 + (2*a^2*b - 9*a*b^2 + 4*b^3)*cosh(d*x + c))*sinh(d*x + c))*sqrt(a*b - b^2)*arctan(-1/2*(b*cosh(d*x + c)^3 + 3*b*cosh(d*x + c)*sinh(d*x + c)^2 + b*sinh(d*x + c)^3 + (4*a - 3*b)*cosh(d*x + c) + (3*b*cosh(d*x + c)^2 + 4*a - 3*b)*sinh(d*x + c))/sqrt(a*b - b^2)) - ((a*b^2 - 4*b^3)*cosh(d*x + c)^8 + 8*(a*b^2 - 4*b^3)*cosh(d*x + c)*sinh(d*x + c)^7 + (a*b^2 - 4*b^3)*sinh(d*x + c)^8 + 4*(2*a^2*b - 9*a*b^2 + 4*b^3)*cosh(d*x + c)^6 + 4*(2*a^2*b - 9*a*b^2 + 4*b^3 + 7*(a*b^2 - 4*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(a*b^2 - 4*b^3)*cosh(d*x + c)^3 + 3*(2*a^2*b - 9*a*b^2 + 4*b^3)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(8*a^3 - 40*a^2*b + 35*a*b^2 - 12*b^3)*cosh(d*x + c)^4 + 2*(35*(a*b^2 - 4*b^3)*cosh(d*x + c)^4 + 8*a^3 - 40*a^2*b + 35*a*b^2 - 12*b^3 + 30*(2*a^2*b - 9*a*b^2 + 4*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(7*(a*b^2 - 4*b^3)*cosh(d*x + c)^5 + 10*(2*a^2*b - 9*a*b^2 + 4*b^3)*cosh(d*x + c)^3 + (8*a^3 - 40*a^2*b + 35*a*b^2 - 12*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 + a*b^2 - 4*b^3 + 4*(2*a^2*b - 9*a*b^2 + 4*b^3)*cosh(d*x + c)^2 + 4*(7*(a*b^2 - 4*b^3)*cosh(d*x + c)^6 + 15*(2*a^2*b - 9*a*b^2 + 4*b^3)*cosh(d*x + c)^4 + 2*a^2*b - 9*a*b^2 + 4*b^3 + 3*(8*a^3 - 40*a^2*b + 35*a*b^2 - 12*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((a*b^2 - 4*b^3)*cosh(d*x + c)^7 + 3*(2*a^2*b - 9*a*b^2 + 4*b^3)*cosh(d*x + c)^5 + (8*a^3 - 40*a^2*b + 35*a*b^2 - 12*b^3)*cosh(d*x + c)^3 + (2*a^2*b - 9*a*b^2 + 4*b^3)*cosh(d*x + c))*sinh(d*x + c))*sqrt(a*b - b^2)*arctan(-1/2*sqrt(a*b - b^2)*(cosh(d*x + c) + sinh(d*x + c))/(a - b)) + 2*(a^2*b^2 - 5*a*b^3 + 4*b^4)*cosh(d*x + c) + 2*(7*(a^2*b^2 - 5*a*b^3 + 4*b^4)*cosh(d*x + c)^6 - 5*(4*a^3*b + 5*a^2*b^2 - 13*a*b^3 + 4*b^4)*cosh(d*x + c)^4 + a^2*b^2 - 5*a*b^3 + 4*b^4 - 3*(4*a^3*b + 5*a^2*b^2 - 13*a*b^3 + 4*b^4)*cosh(d*x + c)^2)*sinh(d*x + c))/((a^3*b^4 - 3*a^2*b^5 + 3*a*b^6 - b^7)*d*cosh(d*x + c)^8 + 8*(a^3*b^4 - 3*a^2*b^5 + 3*a*b^6 - b^7)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^3*b^4 - 3*a^2*b^5 + 3*a*b^6 - b^7)*d*sinh(d*x + c)^8 + 4*(2*a^4*b^3 - 7*a^3*b^4 + 9*a^2*b^5 - 5*a*b^6 + b^7)*d*cosh(d*x + c)^6 + 4*(7*(a^3*b^4 - 3*a^2*b^5 + 3*a*b^6 - b^7)*d*cosh(d*x + c)^2 + (2*a^4*b^3 - 7*a^3*b^4 + 9*a^2*b^5 - 5*a*b^6 + b^7)*d)*sinh(d*x + c)^6 + 2*(8*a^5*b^2 - 32*a^4*b^3 + 51*a^3*b^4 - 41*a^2*b^5 + 17*a*b^6 - 3*b^7)*d*cosh(d*x + c)^4 + 8*(7*(a^3*b^4 - 3*a^2*b^5 + 3*a*b^6 - b^7)*d*cosh(d*x + c)^3 + 3*(2*a^4*b^3 - 7*a^3*b^4 + 9*a^2*b^5 - 5*a*b^6 + b^7)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^3*b^4 - 3*a^2*b^5 + 3*a*b^6 - b^7)*d*cosh(d*x + c)^4 + 30*(2*a^4*b^3 - 7*a^3*b^4 + 9*a^2*b^5 - 5*a*b^6 + b^7)*d*cosh(d*x + c)^2 + (8*a^5*b^2 - 32*a^4*b^3 + 51*a^3*b^4 - 41*a^2*b^5 + 17*a*b^6 - 3*b^7)*d)*sinh(d*x + c)^4 + 4*(2*a^4*b^3 - 7*a^3*b^4 + 9*a^2*b^5 - 5*a*b^6 + b^7)*d*cosh(d*x + c)^2 + 8*(7*(a^3*b^4 - 3*a^2*b^5 + 3*a*b^6 - b^7)*d*cosh(d*x + c)^5 + 10*(2*a^4*b^3 - 7*a^3*b^4 + 9*a^2*b^5 - 5*a*b^6 + b^7)*d*cosh(d*x + c)^3 + (8*a^5*b^2 - 32*a^4*b^3 + 51*a^3*b^4 - 41*a^2*b^5 + 17*a*b^6 - 3*b^7)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^3*b^4 - 3*a^2*b^5 + 3*a*b^6 - b^7)*d*cosh(d*x + c)^6 + 15*(2*a^4*b^3 - 7*a^3*b^4 + 9*a^2*b^5 - 5*a*b^6 + b^7)*d*cosh(d*x + c)^4 + 3*(8*a^5*b^2 - 32*a^4*b^3 + 51*a^3*b^4 - 41*a^2*b^5 + 17*a*b^6 - 3*b^7)*d*cosh(d*x + c)^2 + (2*a^4*b^3 - 7*a^3*b^4 + 9*a^2*b^5 - 5*a*b^6 + b^7)*d)*sinh(d*x + c)^2 + (a^3*b^4 - 3*a^2*b^5 + 3*a*b^6 - b^7)*d + 8*((a^3*b^4 - 3*a^2*b^5 + 3*a*b^6 - b^7)*d*cosh(d*x + c)^7 + 3*(2*a^4*b^3 - 7*a^3*b^4 + 9*a^2*b^5 - 5*a*b^6 + b^7)*d*cosh(d*x + c)^5 + (8*a^5*b^2 - 32*a^4*b^3 + 51*a^3*b^4 - 41*a^2*b^5 + 17*a*b^6 - 3*b^7)*d*cosh(d*x + c)^3 + (2*a^4*b^3 - 7*a^3*b^4 + 9*a^2*b^5 - 5*a*b^6 + b^7)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
53,1,5519,0,0.824868," ","integrate(sinh(d*x+c)^2/(a+b*sinh(d*x+c)^2)^3,x, algorithm=""fricas"")","\left[-\frac{4 \, {\left(4 \, a^{3} b^{2} - 5 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(d x + c\right)^{6} + 24 \, {\left(4 \, a^{3} b^{2} - 5 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + 4 \, {\left(4 \, a^{3} b^{2} - 5 \, a^{2} b^{3} + a b^{4}\right)} \sinh\left(d x + c\right)^{6} + 8 \, a^{3} b^{2} - 4 \, a^{2} b^{3} - 4 \, a b^{4} + 4 \, {\left(16 \, a^{5} - 24 \, a^{4} b + 6 \, a^{3} b^{2} + 5 \, a^{2} b^{3} - 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(16 \, a^{5} - 24 \, a^{4} b + 6 \, a^{3} b^{2} + 5 \, a^{2} b^{3} - 3 \, a b^{4} + 15 \, {\left(4 \, a^{3} b^{2} - 5 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 16 \, {\left(5 \, {\left(4 \, a^{3} b^{2} - 5 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(16 \, a^{5} - 24 \, a^{4} b + 6 \, a^{3} b^{2} + 5 \, a^{2} b^{3} - 3 \, a b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(16 \, a^{4} b - 20 \, a^{3} b^{2} + a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(16 \, a^{4} b - 20 \, a^{3} b^{2} + a^{2} b^{3} + 3 \, a b^{4} + 15 \, {\left(4 \, a^{3} b^{2} - 5 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(d x + c\right)^{4} + 6 \, {\left(16 \, a^{5} - 24 \, a^{4} b + 6 \, a^{3} b^{2} + 5 \, a^{2} b^{3} - 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(4 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(4 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(4 \, a b^{3} - b^{4}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(8 \, a^{2} b^{2} - 6 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(8 \, a^{2} b^{2} - 6 \, a b^{3} + b^{4} + 7 \, {\left(4 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(4 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(8 \, a^{2} b^{2} - 6 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(32 \, a^{3} b - 40 \, a^{2} b^{2} + 20 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(4 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{4} + 32 \, a^{3} b - 40 \, a^{2} b^{2} + 20 \, a b^{3} - 3 \, b^{4} + 30 \, {\left(8 \, a^{2} b^{2} - 6 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, a b^{3} - b^{4} + 8 \, {\left(7 \, {\left(4 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(8 \, a^{2} b^{2} - 6 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(32 \, a^{3} b - 40 \, a^{2} b^{2} + 20 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(8 \, a^{2} b^{2} - 6 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(4 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(8 \, a^{2} b^{2} - 6 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{4} + 8 \, a^{2} b^{2} - 6 \, a b^{3} + b^{4} + 3 \, {\left(32 \, a^{3} b - 40 \, a^{2} b^{2} + 20 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left({\left(4 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(8 \, a^{2} b^{2} - 6 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{5} + {\left(32 \, a^{3} b - 40 \, a^{2} b^{2} + 20 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{2} b^{2} - 6 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{a^{2} - a b} \log\left(\frac{b^{2} \cosh\left(d x + c\right)^{4} + 4 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{2} \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(d x + c\right)^{2} + 2 \, a b - b^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, a^{2} - 8 \, a b + b^{2} + 4 \, {\left(b^{2} \cosh\left(d x + c\right)^{3} + {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) - 4 \, {\left(b \cosh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b \sinh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sqrt{a^{2} - a b}}{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b}\right) + 8 \, {\left(3 \, {\left(4 \, a^{3} b^{2} - 5 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(16 \, a^{5} - 24 \, a^{4} b + 6 \, a^{3} b^{2} + 5 \, a^{2} b^{3} - 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(16 \, a^{4} b - 20 \, a^{3} b^{2} + a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{16 \, {\left({\left(a^{5} b^{3} - 3 \, a^{4} b^{4} + 3 \, a^{3} b^{5} - a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{5} b^{3} - 3 \, a^{4} b^{4} + 3 \, a^{3} b^{5} - a^{2} b^{6}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{5} b^{3} - 3 \, a^{4} b^{4} + 3 \, a^{3} b^{5} - a^{2} b^{6}\right)} d \sinh\left(d x + c\right)^{8} + 4 \, {\left(2 \, a^{6} b^{2} - 7 \, a^{5} b^{3} + 9 \, a^{4} b^{4} - 5 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{5} b^{3} - 3 \, a^{4} b^{4} + 3 \, a^{3} b^{5} - a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{6} b^{2} - 7 \, a^{5} b^{3} + 9 \, a^{4} b^{4} - 5 \, a^{3} b^{5} + a^{2} b^{6}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(8 \, a^{7} b - 32 \, a^{6} b^{2} + 51 \, a^{5} b^{3} - 41 \, a^{4} b^{4} + 17 \, a^{3} b^{5} - 3 \, a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{5} b^{3} - 3 \, a^{4} b^{4} + 3 \, a^{3} b^{5} - a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(2 \, a^{6} b^{2} - 7 \, a^{5} b^{3} + 9 \, a^{4} b^{4} - 5 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a^{5} b^{3} - 3 \, a^{4} b^{4} + 3 \, a^{3} b^{5} - a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{4} + 30 \, {\left(2 \, a^{6} b^{2} - 7 \, a^{5} b^{3} + 9 \, a^{4} b^{4} - 5 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{2} + {\left(8 \, a^{7} b - 32 \, a^{6} b^{2} + 51 \, a^{5} b^{3} - 41 \, a^{4} b^{4} + 17 \, a^{3} b^{5} - 3 \, a^{2} b^{6}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(2 \, a^{6} b^{2} - 7 \, a^{5} b^{3} + 9 \, a^{4} b^{4} - 5 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a^{5} b^{3} - 3 \, a^{4} b^{4} + 3 \, a^{3} b^{5} - a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{5} + 10 \, {\left(2 \, a^{6} b^{2} - 7 \, a^{5} b^{3} + 9 \, a^{4} b^{4} - 5 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{7} b - 32 \, a^{6} b^{2} + 51 \, a^{5} b^{3} - 41 \, a^{4} b^{4} + 17 \, a^{3} b^{5} - 3 \, a^{2} b^{6}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a^{5} b^{3} - 3 \, a^{4} b^{4} + 3 \, a^{3} b^{5} - a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{6} + 15 \, {\left(2 \, a^{6} b^{2} - 7 \, a^{5} b^{3} + 9 \, a^{4} b^{4} - 5 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(8 \, a^{7} b - 32 \, a^{6} b^{2} + 51 \, a^{5} b^{3} - 41 \, a^{4} b^{4} + 17 \, a^{3} b^{5} - 3 \, a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{6} b^{2} - 7 \, a^{5} b^{3} + 9 \, a^{4} b^{4} - 5 \, a^{3} b^{5} + a^{2} b^{6}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{5} b^{3} - 3 \, a^{4} b^{4} + 3 \, a^{3} b^{5} - a^{2} b^{6}\right)} d + 8 \, {\left({\left(a^{5} b^{3} - 3 \, a^{4} b^{4} + 3 \, a^{3} b^{5} - a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{7} + 3 \, {\left(2 \, a^{6} b^{2} - 7 \, a^{5} b^{3} + 9 \, a^{4} b^{4} - 5 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{5} + {\left(8 \, a^{7} b - 32 \, a^{6} b^{2} + 51 \, a^{5} b^{3} - 41 \, a^{4} b^{4} + 17 \, a^{3} b^{5} - 3 \, a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{6} b^{2} - 7 \, a^{5} b^{3} + 9 \, a^{4} b^{4} - 5 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}, -\frac{2 \, {\left(4 \, a^{3} b^{2} - 5 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(d x + c\right)^{6} + 12 \, {\left(4 \, a^{3} b^{2} - 5 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + 2 \, {\left(4 \, a^{3} b^{2} - 5 \, a^{2} b^{3} + a b^{4}\right)} \sinh\left(d x + c\right)^{6} + 4 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 2 \, a b^{4} + 2 \, {\left(16 \, a^{5} - 24 \, a^{4} b + 6 \, a^{3} b^{2} + 5 \, a^{2} b^{3} - 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(16 \, a^{5} - 24 \, a^{4} b + 6 \, a^{3} b^{2} + 5 \, a^{2} b^{3} - 3 \, a b^{4} + 15 \, {\left(4 \, a^{3} b^{2} - 5 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(5 \, {\left(4 \, a^{3} b^{2} - 5 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(16 \, a^{5} - 24 \, a^{4} b + 6 \, a^{3} b^{2} + 5 \, a^{2} b^{3} - 3 \, a b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(16 \, a^{4} b - 20 \, a^{3} b^{2} + a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(16 \, a^{4} b - 20 \, a^{3} b^{2} + a^{2} b^{3} + 3 \, a b^{4} + 15 \, {\left(4 \, a^{3} b^{2} - 5 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(d x + c\right)^{4} + 6 \, {\left(16 \, a^{5} - 24 \, a^{4} b + 6 \, a^{3} b^{2} + 5 \, a^{2} b^{3} - 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} - {\left({\left(4 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(4 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(4 \, a b^{3} - b^{4}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(8 \, a^{2} b^{2} - 6 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(8 \, a^{2} b^{2} - 6 \, a b^{3} + b^{4} + 7 \, {\left(4 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(4 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(8 \, a^{2} b^{2} - 6 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(32 \, a^{3} b - 40 \, a^{2} b^{2} + 20 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(4 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{4} + 32 \, a^{3} b - 40 \, a^{2} b^{2} + 20 \, a b^{3} - 3 \, b^{4} + 30 \, {\left(8 \, a^{2} b^{2} - 6 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, a b^{3} - b^{4} + 8 \, {\left(7 \, {\left(4 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(8 \, a^{2} b^{2} - 6 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(32 \, a^{3} b - 40 \, a^{2} b^{2} + 20 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(8 \, a^{2} b^{2} - 6 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(4 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(8 \, a^{2} b^{2} - 6 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{4} + 8 \, a^{2} b^{2} - 6 \, a b^{3} + b^{4} + 3 \, {\left(32 \, a^{3} b - 40 \, a^{2} b^{2} + 20 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left({\left(4 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(8 \, a^{2} b^{2} - 6 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{5} + {\left(32 \, a^{3} b - 40 \, a^{2} b^{2} + 20 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{2} b^{2} - 6 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-a^{2} + a b} \arctan\left(-\frac{{\left(b \cosh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b \sinh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sqrt{-a^{2} + a b}}{2 \, {\left(a^{2} - a b\right)}}\right) + 4 \, {\left(3 \, {\left(4 \, a^{3} b^{2} - 5 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(16 \, a^{5} - 24 \, a^{4} b + 6 \, a^{3} b^{2} + 5 \, a^{2} b^{3} - 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(16 \, a^{4} b - 20 \, a^{3} b^{2} + a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{8 \, {\left({\left(a^{5} b^{3} - 3 \, a^{4} b^{4} + 3 \, a^{3} b^{5} - a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{5} b^{3} - 3 \, a^{4} b^{4} + 3 \, a^{3} b^{5} - a^{2} b^{6}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{5} b^{3} - 3 \, a^{4} b^{4} + 3 \, a^{3} b^{5} - a^{2} b^{6}\right)} d \sinh\left(d x + c\right)^{8} + 4 \, {\left(2 \, a^{6} b^{2} - 7 \, a^{5} b^{3} + 9 \, a^{4} b^{4} - 5 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{5} b^{3} - 3 \, a^{4} b^{4} + 3 \, a^{3} b^{5} - a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{6} b^{2} - 7 \, a^{5} b^{3} + 9 \, a^{4} b^{4} - 5 \, a^{3} b^{5} + a^{2} b^{6}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(8 \, a^{7} b - 32 \, a^{6} b^{2} + 51 \, a^{5} b^{3} - 41 \, a^{4} b^{4} + 17 \, a^{3} b^{5} - 3 \, a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{5} b^{3} - 3 \, a^{4} b^{4} + 3 \, a^{3} b^{5} - a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(2 \, a^{6} b^{2} - 7 \, a^{5} b^{3} + 9 \, a^{4} b^{4} - 5 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a^{5} b^{3} - 3 \, a^{4} b^{4} + 3 \, a^{3} b^{5} - a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{4} + 30 \, {\left(2 \, a^{6} b^{2} - 7 \, a^{5} b^{3} + 9 \, a^{4} b^{4} - 5 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{2} + {\left(8 \, a^{7} b - 32 \, a^{6} b^{2} + 51 \, a^{5} b^{3} - 41 \, a^{4} b^{4} + 17 \, a^{3} b^{5} - 3 \, a^{2} b^{6}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(2 \, a^{6} b^{2} - 7 \, a^{5} b^{3} + 9 \, a^{4} b^{4} - 5 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a^{5} b^{3} - 3 \, a^{4} b^{4} + 3 \, a^{3} b^{5} - a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{5} + 10 \, {\left(2 \, a^{6} b^{2} - 7 \, a^{5} b^{3} + 9 \, a^{4} b^{4} - 5 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{7} b - 32 \, a^{6} b^{2} + 51 \, a^{5} b^{3} - 41 \, a^{4} b^{4} + 17 \, a^{3} b^{5} - 3 \, a^{2} b^{6}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a^{5} b^{3} - 3 \, a^{4} b^{4} + 3 \, a^{3} b^{5} - a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{6} + 15 \, {\left(2 \, a^{6} b^{2} - 7 \, a^{5} b^{3} + 9 \, a^{4} b^{4} - 5 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(8 \, a^{7} b - 32 \, a^{6} b^{2} + 51 \, a^{5} b^{3} - 41 \, a^{4} b^{4} + 17 \, a^{3} b^{5} - 3 \, a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{6} b^{2} - 7 \, a^{5} b^{3} + 9 \, a^{4} b^{4} - 5 \, a^{3} b^{5} + a^{2} b^{6}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{5} b^{3} - 3 \, a^{4} b^{4} + 3 \, a^{3} b^{5} - a^{2} b^{6}\right)} d + 8 \, {\left({\left(a^{5} b^{3} - 3 \, a^{4} b^{4} + 3 \, a^{3} b^{5} - a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{7} + 3 \, {\left(2 \, a^{6} b^{2} - 7 \, a^{5} b^{3} + 9 \, a^{4} b^{4} - 5 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{5} + {\left(8 \, a^{7} b - 32 \, a^{6} b^{2} + 51 \, a^{5} b^{3} - 41 \, a^{4} b^{4} + 17 \, a^{3} b^{5} - 3 \, a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{6} b^{2} - 7 \, a^{5} b^{3} + 9 \, a^{4} b^{4} - 5 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[-1/16*(4*(4*a^3*b^2 - 5*a^2*b^3 + a*b^4)*cosh(d*x + c)^6 + 24*(4*a^3*b^2 - 5*a^2*b^3 + a*b^4)*cosh(d*x + c)*sinh(d*x + c)^5 + 4*(4*a^3*b^2 - 5*a^2*b^3 + a*b^4)*sinh(d*x + c)^6 + 8*a^3*b^2 - 4*a^2*b^3 - 4*a*b^4 + 4*(16*a^5 - 24*a^4*b + 6*a^3*b^2 + 5*a^2*b^3 - 3*a*b^4)*cosh(d*x + c)^4 + 4*(16*a^5 - 24*a^4*b + 6*a^3*b^2 + 5*a^2*b^3 - 3*a*b^4 + 15*(4*a^3*b^2 - 5*a^2*b^3 + a*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 16*(5*(4*a^3*b^2 - 5*a^2*b^3 + a*b^4)*cosh(d*x + c)^3 + (16*a^5 - 24*a^4*b + 6*a^3*b^2 + 5*a^2*b^3 - 3*a*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(16*a^4*b - 20*a^3*b^2 + a^2*b^3 + 3*a*b^4)*cosh(d*x + c)^2 + 4*(16*a^4*b - 20*a^3*b^2 + a^2*b^3 + 3*a*b^4 + 15*(4*a^3*b^2 - 5*a^2*b^3 + a*b^4)*cosh(d*x + c)^4 + 6*(16*a^5 - 24*a^4*b + 6*a^3*b^2 + 5*a^2*b^3 - 3*a*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((4*a*b^3 - b^4)*cosh(d*x + c)^8 + 8*(4*a*b^3 - b^4)*cosh(d*x + c)*sinh(d*x + c)^7 + (4*a*b^3 - b^4)*sinh(d*x + c)^8 + 4*(8*a^2*b^2 - 6*a*b^3 + b^4)*cosh(d*x + c)^6 + 4*(8*a^2*b^2 - 6*a*b^3 + b^4 + 7*(4*a*b^3 - b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(4*a*b^3 - b^4)*cosh(d*x + c)^3 + 3*(8*a^2*b^2 - 6*a*b^3 + b^4)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(32*a^3*b - 40*a^2*b^2 + 20*a*b^3 - 3*b^4)*cosh(d*x + c)^4 + 2*(35*(4*a*b^3 - b^4)*cosh(d*x + c)^4 + 32*a^3*b - 40*a^2*b^2 + 20*a*b^3 - 3*b^4 + 30*(8*a^2*b^2 - 6*a*b^3 + b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 4*a*b^3 - b^4 + 8*(7*(4*a*b^3 - b^4)*cosh(d*x + c)^5 + 10*(8*a^2*b^2 - 6*a*b^3 + b^4)*cosh(d*x + c)^3 + (32*a^3*b - 40*a^2*b^2 + 20*a*b^3 - 3*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(8*a^2*b^2 - 6*a*b^3 + b^4)*cosh(d*x + c)^2 + 4*(7*(4*a*b^3 - b^4)*cosh(d*x + c)^6 + 15*(8*a^2*b^2 - 6*a*b^3 + b^4)*cosh(d*x + c)^4 + 8*a^2*b^2 - 6*a*b^3 + b^4 + 3*(32*a^3*b - 40*a^2*b^2 + 20*a*b^3 - 3*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((4*a*b^3 - b^4)*cosh(d*x + c)^7 + 3*(8*a^2*b^2 - 6*a*b^3 + b^4)*cosh(d*x + c)^5 + (32*a^3*b - 40*a^2*b^2 + 20*a*b^3 - 3*b^4)*cosh(d*x + c)^3 + (8*a^2*b^2 - 6*a*b^3 + b^4)*cosh(d*x + c))*sinh(d*x + c))*sqrt(a^2 - a*b)*log((b^2*cosh(d*x + c)^4 + 4*b^2*cosh(d*x + c)*sinh(d*x + c)^3 + b^2*sinh(d*x + c)^4 + 2*(2*a*b - b^2)*cosh(d*x + c)^2 + 2*(3*b^2*cosh(d*x + c)^2 + 2*a*b - b^2)*sinh(d*x + c)^2 + 8*a^2 - 8*a*b + b^2 + 4*(b^2*cosh(d*x + c)^3 + (2*a*b - b^2)*cosh(d*x + c))*sinh(d*x + c) - 4*(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + 2*a - b)*sqrt(a^2 - a*b))/(b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 + 2*(2*a - b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 + 2*a - b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 + (2*a - b)*cosh(d*x + c))*sinh(d*x + c) + b)) + 8*(3*(4*a^3*b^2 - 5*a^2*b^3 + a*b^4)*cosh(d*x + c)^5 + 2*(16*a^5 - 24*a^4*b + 6*a^3*b^2 + 5*a^2*b^3 - 3*a*b^4)*cosh(d*x + c)^3 + (16*a^4*b - 20*a^3*b^2 + a^2*b^3 + 3*a*b^4)*cosh(d*x + c))*sinh(d*x + c))/((a^5*b^3 - 3*a^4*b^4 + 3*a^3*b^5 - a^2*b^6)*d*cosh(d*x + c)^8 + 8*(a^5*b^3 - 3*a^4*b^4 + 3*a^3*b^5 - a^2*b^6)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^5*b^3 - 3*a^4*b^4 + 3*a^3*b^5 - a^2*b^6)*d*sinh(d*x + c)^8 + 4*(2*a^6*b^2 - 7*a^5*b^3 + 9*a^4*b^4 - 5*a^3*b^5 + a^2*b^6)*d*cosh(d*x + c)^6 + 4*(7*(a^5*b^3 - 3*a^4*b^4 + 3*a^3*b^5 - a^2*b^6)*d*cosh(d*x + c)^2 + (2*a^6*b^2 - 7*a^5*b^3 + 9*a^4*b^4 - 5*a^3*b^5 + a^2*b^6)*d)*sinh(d*x + c)^6 + 2*(8*a^7*b - 32*a^6*b^2 + 51*a^5*b^3 - 41*a^4*b^4 + 17*a^3*b^5 - 3*a^2*b^6)*d*cosh(d*x + c)^4 + 8*(7*(a^5*b^3 - 3*a^4*b^4 + 3*a^3*b^5 - a^2*b^6)*d*cosh(d*x + c)^3 + 3*(2*a^6*b^2 - 7*a^5*b^3 + 9*a^4*b^4 - 5*a^3*b^5 + a^2*b^6)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^5*b^3 - 3*a^4*b^4 + 3*a^3*b^5 - a^2*b^6)*d*cosh(d*x + c)^4 + 30*(2*a^6*b^2 - 7*a^5*b^3 + 9*a^4*b^4 - 5*a^3*b^5 + a^2*b^6)*d*cosh(d*x + c)^2 + (8*a^7*b - 32*a^6*b^2 + 51*a^5*b^3 - 41*a^4*b^4 + 17*a^3*b^5 - 3*a^2*b^6)*d)*sinh(d*x + c)^4 + 4*(2*a^6*b^2 - 7*a^5*b^3 + 9*a^4*b^4 - 5*a^3*b^5 + a^2*b^6)*d*cosh(d*x + c)^2 + 8*(7*(a^5*b^3 - 3*a^4*b^4 + 3*a^3*b^5 - a^2*b^6)*d*cosh(d*x + c)^5 + 10*(2*a^6*b^2 - 7*a^5*b^3 + 9*a^4*b^4 - 5*a^3*b^5 + a^2*b^6)*d*cosh(d*x + c)^3 + (8*a^7*b - 32*a^6*b^2 + 51*a^5*b^3 - 41*a^4*b^4 + 17*a^3*b^5 - 3*a^2*b^6)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^5*b^3 - 3*a^4*b^4 + 3*a^3*b^5 - a^2*b^6)*d*cosh(d*x + c)^6 + 15*(2*a^6*b^2 - 7*a^5*b^3 + 9*a^4*b^4 - 5*a^3*b^5 + a^2*b^6)*d*cosh(d*x + c)^4 + 3*(8*a^7*b - 32*a^6*b^2 + 51*a^5*b^3 - 41*a^4*b^4 + 17*a^3*b^5 - 3*a^2*b^6)*d*cosh(d*x + c)^2 + (2*a^6*b^2 - 7*a^5*b^3 + 9*a^4*b^4 - 5*a^3*b^5 + a^2*b^6)*d)*sinh(d*x + c)^2 + (a^5*b^3 - 3*a^4*b^4 + 3*a^3*b^5 - a^2*b^6)*d + 8*((a^5*b^3 - 3*a^4*b^4 + 3*a^3*b^5 - a^2*b^6)*d*cosh(d*x + c)^7 + 3*(2*a^6*b^2 - 7*a^5*b^3 + 9*a^4*b^4 - 5*a^3*b^5 + a^2*b^6)*d*cosh(d*x + c)^5 + (8*a^7*b - 32*a^6*b^2 + 51*a^5*b^3 - 41*a^4*b^4 + 17*a^3*b^5 - 3*a^2*b^6)*d*cosh(d*x + c)^3 + (2*a^6*b^2 - 7*a^5*b^3 + 9*a^4*b^4 - 5*a^3*b^5 + a^2*b^6)*d*cosh(d*x + c))*sinh(d*x + c)), -1/8*(2*(4*a^3*b^2 - 5*a^2*b^3 + a*b^4)*cosh(d*x + c)^6 + 12*(4*a^3*b^2 - 5*a^2*b^3 + a*b^4)*cosh(d*x + c)*sinh(d*x + c)^5 + 2*(4*a^3*b^2 - 5*a^2*b^3 + a*b^4)*sinh(d*x + c)^6 + 4*a^3*b^2 - 2*a^2*b^3 - 2*a*b^4 + 2*(16*a^5 - 24*a^4*b + 6*a^3*b^2 + 5*a^2*b^3 - 3*a*b^4)*cosh(d*x + c)^4 + 2*(16*a^5 - 24*a^4*b + 6*a^3*b^2 + 5*a^2*b^3 - 3*a*b^4 + 15*(4*a^3*b^2 - 5*a^2*b^3 + a*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(5*(4*a^3*b^2 - 5*a^2*b^3 + a*b^4)*cosh(d*x + c)^3 + (16*a^5 - 24*a^4*b + 6*a^3*b^2 + 5*a^2*b^3 - 3*a*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 2*(16*a^4*b - 20*a^3*b^2 + a^2*b^3 + 3*a*b^4)*cosh(d*x + c)^2 + 2*(16*a^4*b - 20*a^3*b^2 + a^2*b^3 + 3*a*b^4 + 15*(4*a^3*b^2 - 5*a^2*b^3 + a*b^4)*cosh(d*x + c)^4 + 6*(16*a^5 - 24*a^4*b + 6*a^3*b^2 + 5*a^2*b^3 - 3*a*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - ((4*a*b^3 - b^4)*cosh(d*x + c)^8 + 8*(4*a*b^3 - b^4)*cosh(d*x + c)*sinh(d*x + c)^7 + (4*a*b^3 - b^4)*sinh(d*x + c)^8 + 4*(8*a^2*b^2 - 6*a*b^3 + b^4)*cosh(d*x + c)^6 + 4*(8*a^2*b^2 - 6*a*b^3 + b^4 + 7*(4*a*b^3 - b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(4*a*b^3 - b^4)*cosh(d*x + c)^3 + 3*(8*a^2*b^2 - 6*a*b^3 + b^4)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(32*a^3*b - 40*a^2*b^2 + 20*a*b^3 - 3*b^4)*cosh(d*x + c)^4 + 2*(35*(4*a*b^3 - b^4)*cosh(d*x + c)^4 + 32*a^3*b - 40*a^2*b^2 + 20*a*b^3 - 3*b^4 + 30*(8*a^2*b^2 - 6*a*b^3 + b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 4*a*b^3 - b^4 + 8*(7*(4*a*b^3 - b^4)*cosh(d*x + c)^5 + 10*(8*a^2*b^2 - 6*a*b^3 + b^4)*cosh(d*x + c)^3 + (32*a^3*b - 40*a^2*b^2 + 20*a*b^3 - 3*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(8*a^2*b^2 - 6*a*b^3 + b^4)*cosh(d*x + c)^2 + 4*(7*(4*a*b^3 - b^4)*cosh(d*x + c)^6 + 15*(8*a^2*b^2 - 6*a*b^3 + b^4)*cosh(d*x + c)^4 + 8*a^2*b^2 - 6*a*b^3 + b^4 + 3*(32*a^3*b - 40*a^2*b^2 + 20*a*b^3 - 3*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((4*a*b^3 - b^4)*cosh(d*x + c)^7 + 3*(8*a^2*b^2 - 6*a*b^3 + b^4)*cosh(d*x + c)^5 + (32*a^3*b - 40*a^2*b^2 + 20*a*b^3 - 3*b^4)*cosh(d*x + c)^3 + (8*a^2*b^2 - 6*a*b^3 + b^4)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-a^2 + a*b)*arctan(-1/2*(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + 2*a - b)*sqrt(-a^2 + a*b)/(a^2 - a*b)) + 4*(3*(4*a^3*b^2 - 5*a^2*b^3 + a*b^4)*cosh(d*x + c)^5 + 2*(16*a^5 - 24*a^4*b + 6*a^3*b^2 + 5*a^2*b^3 - 3*a*b^4)*cosh(d*x + c)^3 + (16*a^4*b - 20*a^3*b^2 + a^2*b^3 + 3*a*b^4)*cosh(d*x + c))*sinh(d*x + c))/((a^5*b^3 - 3*a^4*b^4 + 3*a^3*b^5 - a^2*b^6)*d*cosh(d*x + c)^8 + 8*(a^5*b^3 - 3*a^4*b^4 + 3*a^3*b^5 - a^2*b^6)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^5*b^3 - 3*a^4*b^4 + 3*a^3*b^5 - a^2*b^6)*d*sinh(d*x + c)^8 + 4*(2*a^6*b^2 - 7*a^5*b^3 + 9*a^4*b^4 - 5*a^3*b^5 + a^2*b^6)*d*cosh(d*x + c)^6 + 4*(7*(a^5*b^3 - 3*a^4*b^4 + 3*a^3*b^5 - a^2*b^6)*d*cosh(d*x + c)^2 + (2*a^6*b^2 - 7*a^5*b^3 + 9*a^4*b^4 - 5*a^3*b^5 + a^2*b^6)*d)*sinh(d*x + c)^6 + 2*(8*a^7*b - 32*a^6*b^2 + 51*a^5*b^3 - 41*a^4*b^4 + 17*a^3*b^5 - 3*a^2*b^6)*d*cosh(d*x + c)^4 + 8*(7*(a^5*b^3 - 3*a^4*b^4 + 3*a^3*b^5 - a^2*b^6)*d*cosh(d*x + c)^3 + 3*(2*a^6*b^2 - 7*a^5*b^3 + 9*a^4*b^4 - 5*a^3*b^5 + a^2*b^6)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^5*b^3 - 3*a^4*b^4 + 3*a^3*b^5 - a^2*b^6)*d*cosh(d*x + c)^4 + 30*(2*a^6*b^2 - 7*a^5*b^3 + 9*a^4*b^4 - 5*a^3*b^5 + a^2*b^6)*d*cosh(d*x + c)^2 + (8*a^7*b - 32*a^6*b^2 + 51*a^5*b^3 - 41*a^4*b^4 + 17*a^3*b^5 - 3*a^2*b^6)*d)*sinh(d*x + c)^4 + 4*(2*a^6*b^2 - 7*a^5*b^3 + 9*a^4*b^4 - 5*a^3*b^5 + a^2*b^6)*d*cosh(d*x + c)^2 + 8*(7*(a^5*b^3 - 3*a^4*b^4 + 3*a^3*b^5 - a^2*b^6)*d*cosh(d*x + c)^5 + 10*(2*a^6*b^2 - 7*a^5*b^3 + 9*a^4*b^4 - 5*a^3*b^5 + a^2*b^6)*d*cosh(d*x + c)^3 + (8*a^7*b - 32*a^6*b^2 + 51*a^5*b^3 - 41*a^4*b^4 + 17*a^3*b^5 - 3*a^2*b^6)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^5*b^3 - 3*a^4*b^4 + 3*a^3*b^5 - a^2*b^6)*d*cosh(d*x + c)^6 + 15*(2*a^6*b^2 - 7*a^5*b^3 + 9*a^4*b^4 - 5*a^3*b^5 + a^2*b^6)*d*cosh(d*x + c)^4 + 3*(8*a^7*b - 32*a^6*b^2 + 51*a^5*b^3 - 41*a^4*b^4 + 17*a^3*b^5 - 3*a^2*b^6)*d*cosh(d*x + c)^2 + (2*a^6*b^2 - 7*a^5*b^3 + 9*a^4*b^4 - 5*a^3*b^5 + a^2*b^6)*d)*sinh(d*x + c)^2 + (a^5*b^3 - 3*a^4*b^4 + 3*a^3*b^5 - a^2*b^6)*d + 8*((a^5*b^3 - 3*a^4*b^4 + 3*a^3*b^5 - a^2*b^6)*d*cosh(d*x + c)^7 + 3*(2*a^6*b^2 - 7*a^5*b^3 + 9*a^4*b^4 - 5*a^3*b^5 + a^2*b^6)*d*cosh(d*x + c)^5 + (8*a^7*b - 32*a^6*b^2 + 51*a^5*b^3 - 41*a^4*b^4 + 17*a^3*b^5 - 3*a^2*b^6)*d*cosh(d*x + c)^3 + (2*a^6*b^2 - 7*a^5*b^3 + 9*a^4*b^4 - 5*a^3*b^5 + a^2*b^6)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
54,1,5152,0,0.982628," ","integrate(sinh(d*x+c)/(a+b*sinh(d*x+c)^2)^3,x, algorithm=""fricas"")","\left[\frac{12 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{7} + 84 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + 12 \, {\left(a b^{2} - b^{3}\right)} \sinh\left(d x + c\right)^{7} + 4 \, {\left(20 \, a^{2} b - 31 \, a b^{2} + 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 4 \, {\left(20 \, a^{2} b - 31 \, a b^{2} + 11 \, b^{3} + 63 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{5} + 20 \, {\left(21 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(20 \, a^{2} b - 31 \, a b^{2} + 11 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(20 \, a^{2} b - 31 \, a b^{2} + 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(105 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{4} + 20 \, a^{2} b - 31 \, a b^{2} + 11 \, b^{3} + 10 \, {\left(20 \, a^{2} b - 31 \, a b^{2} + 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(63 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(20 \, a^{2} b - 31 \, a b^{2} + 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(20 \, a^{2} b - 31 \, a b^{2} + 11 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 3 \, {\left(b^{2} \cosh\left(d x + c\right)^{8} + 8 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + b^{2} \sinh\left(d x + c\right)^{8} + 4 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, b^{2} \cosh\left(d x + c\right)^{2} + 2 \, a b - b^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, b^{2} \cosh\left(d x + c\right)^{3} + 3 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, b^{2} \cosh\left(d x + c\right)^{4} + 30 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, b^{2} \cosh\left(d x + c\right)^{5} + 10 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, b^{2} \cosh\left(d x + c\right)^{6} + 15 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, a b - b^{2}\right)} \sinh\left(d x + c\right)^{2} + b^{2} + 8 \, {\left(b^{2} \cosh\left(d x + c\right)^{7} + 3 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{5} + {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-a b + b^{2}} \log\left(\frac{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} - 2 \, {\left(2 \, a - 3 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} - 2 \, a + 3 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} - {\left(2 \, a - 3 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) - 4 \, {\left(\cosh\left(d x + c\right)^{3} + 3 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{3} + {\left(3 \, \cosh\left(d x + c\right)^{2} + 1\right)} \sinh\left(d x + c\right) + \cosh\left(d x + c\right)\right)} \sqrt{-a b + b^{2}} + b}{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b}\right) + 12 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(d x + c\right) + 4 \, {\left(21 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{6} + 5 \, {\left(20 \, a^{2} b - 31 \, a b^{2} + 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 3 \, a b^{2} - 3 \, b^{3} + 3 \, {\left(20 \, a^{2} b - 31 \, a b^{2} + 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)}{16 \, {\left({\left(a^{3} b^{3} - 3 \, a^{2} b^{4} + 3 \, a b^{5} - b^{6}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{3} b^{3} - 3 \, a^{2} b^{4} + 3 \, a b^{5} - b^{6}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{3} b^{3} - 3 \, a^{2} b^{4} + 3 \, a b^{5} - b^{6}\right)} d \sinh\left(d x + c\right)^{8} + 4 \, {\left(2 \, a^{4} b^{2} - 7 \, a^{3} b^{3} + 9 \, a^{2} b^{4} - 5 \, a b^{5} + b^{6}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{3} b^{3} - 3 \, a^{2} b^{4} + 3 \, a b^{5} - b^{6}\right)} d \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{4} b^{2} - 7 \, a^{3} b^{3} + 9 \, a^{2} b^{4} - 5 \, a b^{5} + b^{6}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(8 \, a^{5} b - 32 \, a^{4} b^{2} + 51 \, a^{3} b^{3} - 41 \, a^{2} b^{4} + 17 \, a b^{5} - 3 \, b^{6}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{3} b^{3} - 3 \, a^{2} b^{4} + 3 \, a b^{5} - b^{6}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(2 \, a^{4} b^{2} - 7 \, a^{3} b^{3} + 9 \, a^{2} b^{4} - 5 \, a b^{5} + b^{6}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a^{3} b^{3} - 3 \, a^{2} b^{4} + 3 \, a b^{5} - b^{6}\right)} d \cosh\left(d x + c\right)^{4} + 30 \, {\left(2 \, a^{4} b^{2} - 7 \, a^{3} b^{3} + 9 \, a^{2} b^{4} - 5 \, a b^{5} + b^{6}\right)} d \cosh\left(d x + c\right)^{2} + {\left(8 \, a^{5} b - 32 \, a^{4} b^{2} + 51 \, a^{3} b^{3} - 41 \, a^{2} b^{4} + 17 \, a b^{5} - 3 \, b^{6}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(2 \, a^{4} b^{2} - 7 \, a^{3} b^{3} + 9 \, a^{2} b^{4} - 5 \, a b^{5} + b^{6}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a^{3} b^{3} - 3 \, a^{2} b^{4} + 3 \, a b^{5} - b^{6}\right)} d \cosh\left(d x + c\right)^{5} + 10 \, {\left(2 \, a^{4} b^{2} - 7 \, a^{3} b^{3} + 9 \, a^{2} b^{4} - 5 \, a b^{5} + b^{6}\right)} d \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{5} b - 32 \, a^{4} b^{2} + 51 \, a^{3} b^{3} - 41 \, a^{2} b^{4} + 17 \, a b^{5} - 3 \, b^{6}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a^{3} b^{3} - 3 \, a^{2} b^{4} + 3 \, a b^{5} - b^{6}\right)} d \cosh\left(d x + c\right)^{6} + 15 \, {\left(2 \, a^{4} b^{2} - 7 \, a^{3} b^{3} + 9 \, a^{2} b^{4} - 5 \, a b^{5} + b^{6}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(8 \, a^{5} b - 32 \, a^{4} b^{2} + 51 \, a^{3} b^{3} - 41 \, a^{2} b^{4} + 17 \, a b^{5} - 3 \, b^{6}\right)} d \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{4} b^{2} - 7 \, a^{3} b^{3} + 9 \, a^{2} b^{4} - 5 \, a b^{5} + b^{6}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{3} b^{3} - 3 \, a^{2} b^{4} + 3 \, a b^{5} - b^{6}\right)} d + 8 \, {\left({\left(a^{3} b^{3} - 3 \, a^{2} b^{4} + 3 \, a b^{5} - b^{6}\right)} d \cosh\left(d x + c\right)^{7} + 3 \, {\left(2 \, a^{4} b^{2} - 7 \, a^{3} b^{3} + 9 \, a^{2} b^{4} - 5 \, a b^{5} + b^{6}\right)} d \cosh\left(d x + c\right)^{5} + {\left(8 \, a^{5} b - 32 \, a^{4} b^{2} + 51 \, a^{3} b^{3} - 41 \, a^{2} b^{4} + 17 \, a b^{5} - 3 \, b^{6}\right)} d \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{4} b^{2} - 7 \, a^{3} b^{3} + 9 \, a^{2} b^{4} - 5 \, a b^{5} + b^{6}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}, \frac{6 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{7} + 42 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + 6 \, {\left(a b^{2} - b^{3}\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(20 \, a^{2} b - 31 \, a b^{2} + 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(20 \, a^{2} b - 31 \, a b^{2} + 11 \, b^{3} + 63 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{5} + 10 \, {\left(21 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(20 \, a^{2} b - 31 \, a b^{2} + 11 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(20 \, a^{2} b - 31 \, a b^{2} + 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(105 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{4} + 20 \, a^{2} b - 31 \, a b^{2} + 11 \, b^{3} + 10 \, {\left(20 \, a^{2} b - 31 \, a b^{2} + 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(63 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(20 \, a^{2} b - 31 \, a b^{2} + 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(20 \, a^{2} b - 31 \, a b^{2} + 11 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 3 \, {\left(b^{2} \cosh\left(d x + c\right)^{8} + 8 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + b^{2} \sinh\left(d x + c\right)^{8} + 4 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, b^{2} \cosh\left(d x + c\right)^{2} + 2 \, a b - b^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, b^{2} \cosh\left(d x + c\right)^{3} + 3 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, b^{2} \cosh\left(d x + c\right)^{4} + 30 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, b^{2} \cosh\left(d x + c\right)^{5} + 10 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, b^{2} \cosh\left(d x + c\right)^{6} + 15 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, a b - b^{2}\right)} \sinh\left(d x + c\right)^{2} + b^{2} + 8 \, {\left(b^{2} \cosh\left(d x + c\right)^{7} + 3 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{5} + {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{a b - b^{2}} \arctan\left(-\frac{b \cosh\left(d x + c\right)^{3} + 3 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{3} + {\left(4 \, a - 3 \, b\right)} \cosh\left(d x + c\right) + {\left(3 \, b \cosh\left(d x + c\right)^{2} + 4 \, a - 3 \, b\right)} \sinh\left(d x + c\right)}{2 \, \sqrt{a b - b^{2}}}\right) - 3 \, {\left(b^{2} \cosh\left(d x + c\right)^{8} + 8 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + b^{2} \sinh\left(d x + c\right)^{8} + 4 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, b^{2} \cosh\left(d x + c\right)^{2} + 2 \, a b - b^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, b^{2} \cosh\left(d x + c\right)^{3} + 3 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, b^{2} \cosh\left(d x + c\right)^{4} + 30 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, b^{2} \cosh\left(d x + c\right)^{5} + 10 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, b^{2} \cosh\left(d x + c\right)^{6} + 15 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, a b - b^{2}\right)} \sinh\left(d x + c\right)^{2} + b^{2} + 8 \, {\left(b^{2} \cosh\left(d x + c\right)^{7} + 3 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{5} + {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{a b - b^{2}} \arctan\left(-\frac{\sqrt{a b - b^{2}} {\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right)}}{2 \, {\left(a - b\right)}}\right) + 6 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(d x + c\right) + 2 \, {\left(21 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{6} + 5 \, {\left(20 \, a^{2} b - 31 \, a b^{2} + 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 3 \, a b^{2} - 3 \, b^{3} + 3 \, {\left(20 \, a^{2} b - 31 \, a b^{2} + 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)}{8 \, {\left({\left(a^{3} b^{3} - 3 \, a^{2} b^{4} + 3 \, a b^{5} - b^{6}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{3} b^{3} - 3 \, a^{2} b^{4} + 3 \, a b^{5} - b^{6}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{3} b^{3} - 3 \, a^{2} b^{4} + 3 \, a b^{5} - b^{6}\right)} d \sinh\left(d x + c\right)^{8} + 4 \, {\left(2 \, a^{4} b^{2} - 7 \, a^{3} b^{3} + 9 \, a^{2} b^{4} - 5 \, a b^{5} + b^{6}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{3} b^{3} - 3 \, a^{2} b^{4} + 3 \, a b^{5} - b^{6}\right)} d \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{4} b^{2} - 7 \, a^{3} b^{3} + 9 \, a^{2} b^{4} - 5 \, a b^{5} + b^{6}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(8 \, a^{5} b - 32 \, a^{4} b^{2} + 51 \, a^{3} b^{3} - 41 \, a^{2} b^{4} + 17 \, a b^{5} - 3 \, b^{6}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{3} b^{3} - 3 \, a^{2} b^{4} + 3 \, a b^{5} - b^{6}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(2 \, a^{4} b^{2} - 7 \, a^{3} b^{3} + 9 \, a^{2} b^{4} - 5 \, a b^{5} + b^{6}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a^{3} b^{3} - 3 \, a^{2} b^{4} + 3 \, a b^{5} - b^{6}\right)} d \cosh\left(d x + c\right)^{4} + 30 \, {\left(2 \, a^{4} b^{2} - 7 \, a^{3} b^{3} + 9 \, a^{2} b^{4} - 5 \, a b^{5} + b^{6}\right)} d \cosh\left(d x + c\right)^{2} + {\left(8 \, a^{5} b - 32 \, a^{4} b^{2} + 51 \, a^{3} b^{3} - 41 \, a^{2} b^{4} + 17 \, a b^{5} - 3 \, b^{6}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(2 \, a^{4} b^{2} - 7 \, a^{3} b^{3} + 9 \, a^{2} b^{4} - 5 \, a b^{5} + b^{6}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a^{3} b^{3} - 3 \, a^{2} b^{4} + 3 \, a b^{5} - b^{6}\right)} d \cosh\left(d x + c\right)^{5} + 10 \, {\left(2 \, a^{4} b^{2} - 7 \, a^{3} b^{3} + 9 \, a^{2} b^{4} - 5 \, a b^{5} + b^{6}\right)} d \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{5} b - 32 \, a^{4} b^{2} + 51 \, a^{3} b^{3} - 41 \, a^{2} b^{4} + 17 \, a b^{5} - 3 \, b^{6}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a^{3} b^{3} - 3 \, a^{2} b^{4} + 3 \, a b^{5} - b^{6}\right)} d \cosh\left(d x + c\right)^{6} + 15 \, {\left(2 \, a^{4} b^{2} - 7 \, a^{3} b^{3} + 9 \, a^{2} b^{4} - 5 \, a b^{5} + b^{6}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(8 \, a^{5} b - 32 \, a^{4} b^{2} + 51 \, a^{3} b^{3} - 41 \, a^{2} b^{4} + 17 \, a b^{5} - 3 \, b^{6}\right)} d \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{4} b^{2} - 7 \, a^{3} b^{3} + 9 \, a^{2} b^{4} - 5 \, a b^{5} + b^{6}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{3} b^{3} - 3 \, a^{2} b^{4} + 3 \, a b^{5} - b^{6}\right)} d + 8 \, {\left({\left(a^{3} b^{3} - 3 \, a^{2} b^{4} + 3 \, a b^{5} - b^{6}\right)} d \cosh\left(d x + c\right)^{7} + 3 \, {\left(2 \, a^{4} b^{2} - 7 \, a^{3} b^{3} + 9 \, a^{2} b^{4} - 5 \, a b^{5} + b^{6}\right)} d \cosh\left(d x + c\right)^{5} + {\left(8 \, a^{5} b - 32 \, a^{4} b^{2} + 51 \, a^{3} b^{3} - 41 \, a^{2} b^{4} + 17 \, a b^{5} - 3 \, b^{6}\right)} d \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{4} b^{2} - 7 \, a^{3} b^{3} + 9 \, a^{2} b^{4} - 5 \, a b^{5} + b^{6}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[1/16*(12*(a*b^2 - b^3)*cosh(d*x + c)^7 + 84*(a*b^2 - b^3)*cosh(d*x + c)*sinh(d*x + c)^6 + 12*(a*b^2 - b^3)*sinh(d*x + c)^7 + 4*(20*a^2*b - 31*a*b^2 + 11*b^3)*cosh(d*x + c)^5 + 4*(20*a^2*b - 31*a*b^2 + 11*b^3 + 63*(a*b^2 - b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 20*(21*(a*b^2 - b^3)*cosh(d*x + c)^3 + (20*a^2*b - 31*a*b^2 + 11*b^3)*cosh(d*x + c))*sinh(d*x + c)^4 + 4*(20*a^2*b - 31*a*b^2 + 11*b^3)*cosh(d*x + c)^3 + 4*(105*(a*b^2 - b^3)*cosh(d*x + c)^4 + 20*a^2*b - 31*a*b^2 + 11*b^3 + 10*(20*a^2*b - 31*a*b^2 + 11*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 4*(63*(a*b^2 - b^3)*cosh(d*x + c)^5 + 10*(20*a^2*b - 31*a*b^2 + 11*b^3)*cosh(d*x + c)^3 + 3*(20*a^2*b - 31*a*b^2 + 11*b^3)*cosh(d*x + c))*sinh(d*x + c)^2 - 3*(b^2*cosh(d*x + c)^8 + 8*b^2*cosh(d*x + c)*sinh(d*x + c)^7 + b^2*sinh(d*x + c)^8 + 4*(2*a*b - b^2)*cosh(d*x + c)^6 + 4*(7*b^2*cosh(d*x + c)^2 + 2*a*b - b^2)*sinh(d*x + c)^6 + 8*(7*b^2*cosh(d*x + c)^3 + 3*(2*a*b - b^2)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(8*a^2 - 8*a*b + 3*b^2)*cosh(d*x + c)^4 + 2*(35*b^2*cosh(d*x + c)^4 + 30*(2*a*b - b^2)*cosh(d*x + c)^2 + 8*a^2 - 8*a*b + 3*b^2)*sinh(d*x + c)^4 + 8*(7*b^2*cosh(d*x + c)^5 + 10*(2*a*b - b^2)*cosh(d*x + c)^3 + (8*a^2 - 8*a*b + 3*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(2*a*b - b^2)*cosh(d*x + c)^2 + 4*(7*b^2*cosh(d*x + c)^6 + 15*(2*a*b - b^2)*cosh(d*x + c)^4 + 3*(8*a^2 - 8*a*b + 3*b^2)*cosh(d*x + c)^2 + 2*a*b - b^2)*sinh(d*x + c)^2 + b^2 + 8*(b^2*cosh(d*x + c)^7 + 3*(2*a*b - b^2)*cosh(d*x + c)^5 + (8*a^2 - 8*a*b + 3*b^2)*cosh(d*x + c)^3 + (2*a*b - b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-a*b + b^2)*log((b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 - 2*(2*a - 3*b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 - 2*a + 3*b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 - (2*a - 3*b)*cosh(d*x + c))*sinh(d*x + c) - 4*(cosh(d*x + c)^3 + 3*cosh(d*x + c)*sinh(d*x + c)^2 + sinh(d*x + c)^3 + (3*cosh(d*x + c)^2 + 1)*sinh(d*x + c) + cosh(d*x + c))*sqrt(-a*b + b^2) + b)/(b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 + 2*(2*a - b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 + 2*a - b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 + (2*a - b)*cosh(d*x + c))*sinh(d*x + c) + b)) + 12*(a*b^2 - b^3)*cosh(d*x + c) + 4*(21*(a*b^2 - b^3)*cosh(d*x + c)^6 + 5*(20*a^2*b - 31*a*b^2 + 11*b^3)*cosh(d*x + c)^4 + 3*a*b^2 - 3*b^3 + 3*(20*a^2*b - 31*a*b^2 + 11*b^3)*cosh(d*x + c)^2)*sinh(d*x + c))/((a^3*b^3 - 3*a^2*b^4 + 3*a*b^5 - b^6)*d*cosh(d*x + c)^8 + 8*(a^3*b^3 - 3*a^2*b^4 + 3*a*b^5 - b^6)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^3*b^3 - 3*a^2*b^4 + 3*a*b^5 - b^6)*d*sinh(d*x + c)^8 + 4*(2*a^4*b^2 - 7*a^3*b^3 + 9*a^2*b^4 - 5*a*b^5 + b^6)*d*cosh(d*x + c)^6 + 4*(7*(a^3*b^3 - 3*a^2*b^4 + 3*a*b^5 - b^6)*d*cosh(d*x + c)^2 + (2*a^4*b^2 - 7*a^3*b^3 + 9*a^2*b^4 - 5*a*b^5 + b^6)*d)*sinh(d*x + c)^6 + 2*(8*a^5*b - 32*a^4*b^2 + 51*a^3*b^3 - 41*a^2*b^4 + 17*a*b^5 - 3*b^6)*d*cosh(d*x + c)^4 + 8*(7*(a^3*b^3 - 3*a^2*b^4 + 3*a*b^5 - b^6)*d*cosh(d*x + c)^3 + 3*(2*a^4*b^2 - 7*a^3*b^3 + 9*a^2*b^4 - 5*a*b^5 + b^6)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^3*b^3 - 3*a^2*b^4 + 3*a*b^5 - b^6)*d*cosh(d*x + c)^4 + 30*(2*a^4*b^2 - 7*a^3*b^3 + 9*a^2*b^4 - 5*a*b^5 + b^6)*d*cosh(d*x + c)^2 + (8*a^5*b - 32*a^4*b^2 + 51*a^3*b^3 - 41*a^2*b^4 + 17*a*b^5 - 3*b^6)*d)*sinh(d*x + c)^4 + 4*(2*a^4*b^2 - 7*a^3*b^3 + 9*a^2*b^4 - 5*a*b^5 + b^6)*d*cosh(d*x + c)^2 + 8*(7*(a^3*b^3 - 3*a^2*b^4 + 3*a*b^5 - b^6)*d*cosh(d*x + c)^5 + 10*(2*a^4*b^2 - 7*a^3*b^3 + 9*a^2*b^4 - 5*a*b^5 + b^6)*d*cosh(d*x + c)^3 + (8*a^5*b - 32*a^4*b^2 + 51*a^3*b^3 - 41*a^2*b^4 + 17*a*b^5 - 3*b^6)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^3*b^3 - 3*a^2*b^4 + 3*a*b^5 - b^6)*d*cosh(d*x + c)^6 + 15*(2*a^4*b^2 - 7*a^3*b^3 + 9*a^2*b^4 - 5*a*b^5 + b^6)*d*cosh(d*x + c)^4 + 3*(8*a^5*b - 32*a^4*b^2 + 51*a^3*b^3 - 41*a^2*b^4 + 17*a*b^5 - 3*b^6)*d*cosh(d*x + c)^2 + (2*a^4*b^2 - 7*a^3*b^3 + 9*a^2*b^4 - 5*a*b^5 + b^6)*d)*sinh(d*x + c)^2 + (a^3*b^3 - 3*a^2*b^4 + 3*a*b^5 - b^6)*d + 8*((a^3*b^3 - 3*a^2*b^4 + 3*a*b^5 - b^6)*d*cosh(d*x + c)^7 + 3*(2*a^4*b^2 - 7*a^3*b^3 + 9*a^2*b^4 - 5*a*b^5 + b^6)*d*cosh(d*x + c)^5 + (8*a^5*b - 32*a^4*b^2 + 51*a^3*b^3 - 41*a^2*b^4 + 17*a*b^5 - 3*b^6)*d*cosh(d*x + c)^3 + (2*a^4*b^2 - 7*a^3*b^3 + 9*a^2*b^4 - 5*a*b^5 + b^6)*d*cosh(d*x + c))*sinh(d*x + c)), 1/8*(6*(a*b^2 - b^3)*cosh(d*x + c)^7 + 42*(a*b^2 - b^3)*cosh(d*x + c)*sinh(d*x + c)^6 + 6*(a*b^2 - b^3)*sinh(d*x + c)^7 + 2*(20*a^2*b - 31*a*b^2 + 11*b^3)*cosh(d*x + c)^5 + 2*(20*a^2*b - 31*a*b^2 + 11*b^3 + 63*(a*b^2 - b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 10*(21*(a*b^2 - b^3)*cosh(d*x + c)^3 + (20*a^2*b - 31*a*b^2 + 11*b^3)*cosh(d*x + c))*sinh(d*x + c)^4 + 2*(20*a^2*b - 31*a*b^2 + 11*b^3)*cosh(d*x + c)^3 + 2*(105*(a*b^2 - b^3)*cosh(d*x + c)^4 + 20*a^2*b - 31*a*b^2 + 11*b^3 + 10*(20*a^2*b - 31*a*b^2 + 11*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 2*(63*(a*b^2 - b^3)*cosh(d*x + c)^5 + 10*(20*a^2*b - 31*a*b^2 + 11*b^3)*cosh(d*x + c)^3 + 3*(20*a^2*b - 31*a*b^2 + 11*b^3)*cosh(d*x + c))*sinh(d*x + c)^2 + 3*(b^2*cosh(d*x + c)^8 + 8*b^2*cosh(d*x + c)*sinh(d*x + c)^7 + b^2*sinh(d*x + c)^8 + 4*(2*a*b - b^2)*cosh(d*x + c)^6 + 4*(7*b^2*cosh(d*x + c)^2 + 2*a*b - b^2)*sinh(d*x + c)^6 + 8*(7*b^2*cosh(d*x + c)^3 + 3*(2*a*b - b^2)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(8*a^2 - 8*a*b + 3*b^2)*cosh(d*x + c)^4 + 2*(35*b^2*cosh(d*x + c)^4 + 30*(2*a*b - b^2)*cosh(d*x + c)^2 + 8*a^2 - 8*a*b + 3*b^2)*sinh(d*x + c)^4 + 8*(7*b^2*cosh(d*x + c)^5 + 10*(2*a*b - b^2)*cosh(d*x + c)^3 + (8*a^2 - 8*a*b + 3*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(2*a*b - b^2)*cosh(d*x + c)^2 + 4*(7*b^2*cosh(d*x + c)^6 + 15*(2*a*b - b^2)*cosh(d*x + c)^4 + 3*(8*a^2 - 8*a*b + 3*b^2)*cosh(d*x + c)^2 + 2*a*b - b^2)*sinh(d*x + c)^2 + b^2 + 8*(b^2*cosh(d*x + c)^7 + 3*(2*a*b - b^2)*cosh(d*x + c)^5 + (8*a^2 - 8*a*b + 3*b^2)*cosh(d*x + c)^3 + (2*a*b - b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(a*b - b^2)*arctan(-1/2*(b*cosh(d*x + c)^3 + 3*b*cosh(d*x + c)*sinh(d*x + c)^2 + b*sinh(d*x + c)^3 + (4*a - 3*b)*cosh(d*x + c) + (3*b*cosh(d*x + c)^2 + 4*a - 3*b)*sinh(d*x + c))/sqrt(a*b - b^2)) - 3*(b^2*cosh(d*x + c)^8 + 8*b^2*cosh(d*x + c)*sinh(d*x + c)^7 + b^2*sinh(d*x + c)^8 + 4*(2*a*b - b^2)*cosh(d*x + c)^6 + 4*(7*b^2*cosh(d*x + c)^2 + 2*a*b - b^2)*sinh(d*x + c)^6 + 8*(7*b^2*cosh(d*x + c)^3 + 3*(2*a*b - b^2)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(8*a^2 - 8*a*b + 3*b^2)*cosh(d*x + c)^4 + 2*(35*b^2*cosh(d*x + c)^4 + 30*(2*a*b - b^2)*cosh(d*x + c)^2 + 8*a^2 - 8*a*b + 3*b^2)*sinh(d*x + c)^4 + 8*(7*b^2*cosh(d*x + c)^5 + 10*(2*a*b - b^2)*cosh(d*x + c)^3 + (8*a^2 - 8*a*b + 3*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(2*a*b - b^2)*cosh(d*x + c)^2 + 4*(7*b^2*cosh(d*x + c)^6 + 15*(2*a*b - b^2)*cosh(d*x + c)^4 + 3*(8*a^2 - 8*a*b + 3*b^2)*cosh(d*x + c)^2 + 2*a*b - b^2)*sinh(d*x + c)^2 + b^2 + 8*(b^2*cosh(d*x + c)^7 + 3*(2*a*b - b^2)*cosh(d*x + c)^5 + (8*a^2 - 8*a*b + 3*b^2)*cosh(d*x + c)^3 + (2*a*b - b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(a*b - b^2)*arctan(-1/2*sqrt(a*b - b^2)*(cosh(d*x + c) + sinh(d*x + c))/(a - b)) + 6*(a*b^2 - b^3)*cosh(d*x + c) + 2*(21*(a*b^2 - b^3)*cosh(d*x + c)^6 + 5*(20*a^2*b - 31*a*b^2 + 11*b^3)*cosh(d*x + c)^4 + 3*a*b^2 - 3*b^3 + 3*(20*a^2*b - 31*a*b^2 + 11*b^3)*cosh(d*x + c)^2)*sinh(d*x + c))/((a^3*b^3 - 3*a^2*b^4 + 3*a*b^5 - b^6)*d*cosh(d*x + c)^8 + 8*(a^3*b^3 - 3*a^2*b^4 + 3*a*b^5 - b^6)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^3*b^3 - 3*a^2*b^4 + 3*a*b^5 - b^6)*d*sinh(d*x + c)^8 + 4*(2*a^4*b^2 - 7*a^3*b^3 + 9*a^2*b^4 - 5*a*b^5 + b^6)*d*cosh(d*x + c)^6 + 4*(7*(a^3*b^3 - 3*a^2*b^4 + 3*a*b^5 - b^6)*d*cosh(d*x + c)^2 + (2*a^4*b^2 - 7*a^3*b^3 + 9*a^2*b^4 - 5*a*b^5 + b^6)*d)*sinh(d*x + c)^6 + 2*(8*a^5*b - 32*a^4*b^2 + 51*a^3*b^3 - 41*a^2*b^4 + 17*a*b^5 - 3*b^6)*d*cosh(d*x + c)^4 + 8*(7*(a^3*b^3 - 3*a^2*b^4 + 3*a*b^5 - b^6)*d*cosh(d*x + c)^3 + 3*(2*a^4*b^2 - 7*a^3*b^3 + 9*a^2*b^4 - 5*a*b^5 + b^6)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^3*b^3 - 3*a^2*b^4 + 3*a*b^5 - b^6)*d*cosh(d*x + c)^4 + 30*(2*a^4*b^2 - 7*a^3*b^3 + 9*a^2*b^4 - 5*a*b^5 + b^6)*d*cosh(d*x + c)^2 + (8*a^5*b - 32*a^4*b^2 + 51*a^3*b^3 - 41*a^2*b^4 + 17*a*b^5 - 3*b^6)*d)*sinh(d*x + c)^4 + 4*(2*a^4*b^2 - 7*a^3*b^3 + 9*a^2*b^4 - 5*a*b^5 + b^6)*d*cosh(d*x + c)^2 + 8*(7*(a^3*b^3 - 3*a^2*b^4 + 3*a*b^5 - b^6)*d*cosh(d*x + c)^5 + 10*(2*a^4*b^2 - 7*a^3*b^3 + 9*a^2*b^4 - 5*a*b^5 + b^6)*d*cosh(d*x + c)^3 + (8*a^5*b - 32*a^4*b^2 + 51*a^3*b^3 - 41*a^2*b^4 + 17*a*b^5 - 3*b^6)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^3*b^3 - 3*a^2*b^4 + 3*a*b^5 - b^6)*d*cosh(d*x + c)^6 + 15*(2*a^4*b^2 - 7*a^3*b^3 + 9*a^2*b^4 - 5*a*b^5 + b^6)*d*cosh(d*x + c)^4 + 3*(8*a^5*b - 32*a^4*b^2 + 51*a^3*b^3 - 41*a^2*b^4 + 17*a*b^5 - 3*b^6)*d*cosh(d*x + c)^2 + (2*a^4*b^2 - 7*a^3*b^3 + 9*a^2*b^4 - 5*a*b^5 + b^6)*d)*sinh(d*x + c)^2 + (a^3*b^3 - 3*a^2*b^4 + 3*a*b^5 - b^6)*d + 8*((a^3*b^3 - 3*a^2*b^4 + 3*a*b^5 - b^6)*d*cosh(d*x + c)^7 + 3*(2*a^4*b^2 - 7*a^3*b^3 + 9*a^2*b^4 - 5*a*b^5 + b^6)*d*cosh(d*x + c)^5 + (8*a^5*b - 32*a^4*b^2 + 51*a^3*b^3 - 41*a^2*b^4 + 17*a*b^5 - 3*b^6)*d*cosh(d*x + c)^3 + (2*a^4*b^2 - 7*a^3*b^3 + 9*a^2*b^4 - 5*a*b^5 + b^6)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
55,1,5925,0,0.604721," ","integrate(1/(a+b*sinh(d*x+c)^2)^3,x, algorithm=""fricas"")","\left[\frac{4 \, {\left(8 \, a^{4} b - 16 \, a^{3} b^{2} + 11 \, a^{2} b^{3} - 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{6} + 24 \, {\left(8 \, a^{4} b - 16 \, a^{3} b^{2} + 11 \, a^{2} b^{3} - 3 \, a b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + 4 \, {\left(8 \, a^{4} b - 16 \, a^{3} b^{2} + 11 \, a^{2} b^{3} - 3 \, a b^{4}\right)} \sinh\left(d x + c\right)^{6} + 24 \, a^{3} b^{2} - 36 \, a^{2} b^{3} + 12 \, a b^{4} + 12 \, {\left(16 \, a^{5} - 40 \, a^{4} b + 38 \, a^{3} b^{2} - 17 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{4} + 12 \, {\left(16 \, a^{5} - 40 \, a^{4} b + 38 \, a^{3} b^{2} - 17 \, a^{2} b^{3} + 3 \, a b^{4} + 5 \, {\left(8 \, a^{4} b - 16 \, a^{3} b^{2} + 11 \, a^{2} b^{3} - 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 16 \, {\left(5 \, {\left(8 \, a^{4} b - 16 \, a^{3} b^{2} + 11 \, a^{2} b^{3} - 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(16 \, a^{5} - 40 \, a^{4} b + 38 \, a^{3} b^{2} - 17 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(40 \, a^{4} b - 80 \, a^{3} b^{2} + 49 \, a^{2} b^{3} - 9 \, a b^{4}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(40 \, a^{4} b - 80 \, a^{3} b^{2} + 49 \, a^{2} b^{3} - 9 \, a b^{4} + 15 \, {\left(8 \, a^{4} b - 16 \, a^{3} b^{2} + 11 \, a^{2} b^{3} - 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{4} + 18 \, {\left(16 \, a^{5} - 40 \, a^{4} b + 38 \, a^{3} b^{2} - 17 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(8 \, a^{2} b^{2} - 8 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(8 \, a^{2} b^{2} - 8 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(8 \, a^{2} b^{2} - 8 \, a b^{3} + 3 \, b^{4}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(16 \, a^{3} b - 24 \, a^{2} b^{2} + 14 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(16 \, a^{3} b - 24 \, a^{2} b^{2} + 14 \, a b^{3} - 3 \, b^{4} + 7 \, {\left(8 \, a^{2} b^{2} - 8 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(8 \, a^{2} b^{2} - 8 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(16 \, a^{3} b - 24 \, a^{2} b^{2} + 14 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(64 \, a^{4} - 128 \, a^{3} b + 112 \, a^{2} b^{2} - 48 \, a b^{3} + 9 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(8 \, a^{2} b^{2} - 8 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 64 \, a^{4} - 128 \, a^{3} b + 112 \, a^{2} b^{2} - 48 \, a b^{3} + 9 \, b^{4} + 30 \, {\left(16 \, a^{3} b - 24 \, a^{2} b^{2} + 14 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, a^{2} b^{2} - 8 \, a b^{3} + 3 \, b^{4} + 8 \, {\left(7 \, {\left(8 \, a^{2} b^{2} - 8 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(16 \, a^{3} b - 24 \, a^{2} b^{2} + 14 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(64 \, a^{4} - 128 \, a^{3} b + 112 \, a^{2} b^{2} - 48 \, a b^{3} + 9 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(16 \, a^{3} b - 24 \, a^{2} b^{2} + 14 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(8 \, a^{2} b^{2} - 8 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(16 \, a^{3} b - 24 \, a^{2} b^{2} + 14 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 16 \, a^{3} b - 24 \, a^{2} b^{2} + 14 \, a b^{3} - 3 \, b^{4} + 3 \, {\left(64 \, a^{4} - 128 \, a^{3} b + 112 \, a^{2} b^{2} - 48 \, a b^{3} + 9 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left({\left(8 \, a^{2} b^{2} - 8 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(16 \, a^{3} b - 24 \, a^{2} b^{2} + 14 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + {\left(64 \, a^{4} - 128 \, a^{3} b + 112 \, a^{2} b^{2} - 48 \, a b^{3} + 9 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(16 \, a^{3} b - 24 \, a^{2} b^{2} + 14 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{a^{2} - a b} \log\left(\frac{b^{2} \cosh\left(d x + c\right)^{4} + 4 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{2} \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(d x + c\right)^{2} + 2 \, a b - b^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, a^{2} - 8 \, a b + b^{2} + 4 \, {\left(b^{2} \cosh\left(d x + c\right)^{3} + {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) - 4 \, {\left(b \cosh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b \sinh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sqrt{a^{2} - a b}}{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b}\right) + 8 \, {\left(3 \, {\left(8 \, a^{4} b - 16 \, a^{3} b^{2} + 11 \, a^{2} b^{3} - 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{5} + 6 \, {\left(16 \, a^{5} - 40 \, a^{4} b + 38 \, a^{3} b^{2} - 17 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(40 \, a^{4} b - 80 \, a^{3} b^{2} + 49 \, a^{2} b^{3} - 9 \, a b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{16 \, {\left({\left(a^{6} b^{2} - 3 \, a^{5} b^{3} + 3 \, a^{4} b^{4} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{6} b^{2} - 3 \, a^{5} b^{3} + 3 \, a^{4} b^{4} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{6} b^{2} - 3 \, a^{5} b^{3} + 3 \, a^{4} b^{4} - a^{3} b^{5}\right)} d \sinh\left(d x + c\right)^{8} + 4 \, {\left(2 \, a^{7} b - 7 \, a^{6} b^{2} + 9 \, a^{5} b^{3} - 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{6} b^{2} - 3 \, a^{5} b^{3} + 3 \, a^{4} b^{4} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{7} b - 7 \, a^{6} b^{2} + 9 \, a^{5} b^{3} - 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(8 \, a^{8} - 32 \, a^{7} b + 51 \, a^{6} b^{2} - 41 \, a^{5} b^{3} + 17 \, a^{4} b^{4} - 3 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{6} b^{2} - 3 \, a^{5} b^{3} + 3 \, a^{4} b^{4} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(2 \, a^{7} b - 7 \, a^{6} b^{2} + 9 \, a^{5} b^{3} - 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a^{6} b^{2} - 3 \, a^{5} b^{3} + 3 \, a^{4} b^{4} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 30 \, {\left(2 \, a^{7} b - 7 \, a^{6} b^{2} + 9 \, a^{5} b^{3} - 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(8 \, a^{8} - 32 \, a^{7} b + 51 \, a^{6} b^{2} - 41 \, a^{5} b^{3} + 17 \, a^{4} b^{4} - 3 \, a^{3} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(2 \, a^{7} b - 7 \, a^{6} b^{2} + 9 \, a^{5} b^{3} - 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a^{6} b^{2} - 3 \, a^{5} b^{3} + 3 \, a^{4} b^{4} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{5} + 10 \, {\left(2 \, a^{7} b - 7 \, a^{6} b^{2} + 9 \, a^{5} b^{3} - 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{8} - 32 \, a^{7} b + 51 \, a^{6} b^{2} - 41 \, a^{5} b^{3} + 17 \, a^{4} b^{4} - 3 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a^{6} b^{2} - 3 \, a^{5} b^{3} + 3 \, a^{4} b^{4} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{6} + 15 \, {\left(2 \, a^{7} b - 7 \, a^{6} b^{2} + 9 \, a^{5} b^{3} - 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(8 \, a^{8} - 32 \, a^{7} b + 51 \, a^{6} b^{2} - 41 \, a^{5} b^{3} + 17 \, a^{4} b^{4} - 3 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{7} b - 7 \, a^{6} b^{2} + 9 \, a^{5} b^{3} - 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{6} b^{2} - 3 \, a^{5} b^{3} + 3 \, a^{4} b^{4} - a^{3} b^{5}\right)} d + 8 \, {\left({\left(a^{6} b^{2} - 3 \, a^{5} b^{3} + 3 \, a^{4} b^{4} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{7} + 3 \, {\left(2 \, a^{7} b - 7 \, a^{6} b^{2} + 9 \, a^{5} b^{3} - 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{5} + {\left(8 \, a^{8} - 32 \, a^{7} b + 51 \, a^{6} b^{2} - 41 \, a^{5} b^{3} + 17 \, a^{4} b^{4} - 3 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{7} b - 7 \, a^{6} b^{2} + 9 \, a^{5} b^{3} - 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}, \frac{2 \, {\left(8 \, a^{4} b - 16 \, a^{3} b^{2} + 11 \, a^{2} b^{3} - 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{6} + 12 \, {\left(8 \, a^{4} b - 16 \, a^{3} b^{2} + 11 \, a^{2} b^{3} - 3 \, a b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + 2 \, {\left(8 \, a^{4} b - 16 \, a^{3} b^{2} + 11 \, a^{2} b^{3} - 3 \, a b^{4}\right)} \sinh\left(d x + c\right)^{6} + 12 \, a^{3} b^{2} - 18 \, a^{2} b^{3} + 6 \, a b^{4} + 6 \, {\left(16 \, a^{5} - 40 \, a^{4} b + 38 \, a^{3} b^{2} - 17 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{4} + 6 \, {\left(16 \, a^{5} - 40 \, a^{4} b + 38 \, a^{3} b^{2} - 17 \, a^{2} b^{3} + 3 \, a b^{4} + 5 \, {\left(8 \, a^{4} b - 16 \, a^{3} b^{2} + 11 \, a^{2} b^{3} - 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(5 \, {\left(8 \, a^{4} b - 16 \, a^{3} b^{2} + 11 \, a^{2} b^{3} - 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(16 \, a^{5} - 40 \, a^{4} b + 38 \, a^{3} b^{2} - 17 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(40 \, a^{4} b - 80 \, a^{3} b^{2} + 49 \, a^{2} b^{3} - 9 \, a b^{4}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(40 \, a^{4} b - 80 \, a^{3} b^{2} + 49 \, a^{2} b^{3} - 9 \, a b^{4} + 15 \, {\left(8 \, a^{4} b - 16 \, a^{3} b^{2} + 11 \, a^{2} b^{3} - 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{4} + 18 \, {\left(16 \, a^{5} - 40 \, a^{4} b + 38 \, a^{3} b^{2} - 17 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} - {\left({\left(8 \, a^{2} b^{2} - 8 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(8 \, a^{2} b^{2} - 8 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(8 \, a^{2} b^{2} - 8 \, a b^{3} + 3 \, b^{4}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(16 \, a^{3} b - 24 \, a^{2} b^{2} + 14 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(16 \, a^{3} b - 24 \, a^{2} b^{2} + 14 \, a b^{3} - 3 \, b^{4} + 7 \, {\left(8 \, a^{2} b^{2} - 8 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(8 \, a^{2} b^{2} - 8 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(16 \, a^{3} b - 24 \, a^{2} b^{2} + 14 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(64 \, a^{4} - 128 \, a^{3} b + 112 \, a^{2} b^{2} - 48 \, a b^{3} + 9 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(8 \, a^{2} b^{2} - 8 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 64 \, a^{4} - 128 \, a^{3} b + 112 \, a^{2} b^{2} - 48 \, a b^{3} + 9 \, b^{4} + 30 \, {\left(16 \, a^{3} b - 24 \, a^{2} b^{2} + 14 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, a^{2} b^{2} - 8 \, a b^{3} + 3 \, b^{4} + 8 \, {\left(7 \, {\left(8 \, a^{2} b^{2} - 8 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(16 \, a^{3} b - 24 \, a^{2} b^{2} + 14 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(64 \, a^{4} - 128 \, a^{3} b + 112 \, a^{2} b^{2} - 48 \, a b^{3} + 9 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(16 \, a^{3} b - 24 \, a^{2} b^{2} + 14 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(8 \, a^{2} b^{2} - 8 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(16 \, a^{3} b - 24 \, a^{2} b^{2} + 14 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 16 \, a^{3} b - 24 \, a^{2} b^{2} + 14 \, a b^{3} - 3 \, b^{4} + 3 \, {\left(64 \, a^{4} - 128 \, a^{3} b + 112 \, a^{2} b^{2} - 48 \, a b^{3} + 9 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left({\left(8 \, a^{2} b^{2} - 8 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(16 \, a^{3} b - 24 \, a^{2} b^{2} + 14 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + {\left(64 \, a^{4} - 128 \, a^{3} b + 112 \, a^{2} b^{2} - 48 \, a b^{3} + 9 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(16 \, a^{3} b - 24 \, a^{2} b^{2} + 14 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-a^{2} + a b} \arctan\left(-\frac{{\left(b \cosh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b \sinh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sqrt{-a^{2} + a b}}{2 \, {\left(a^{2} - a b\right)}}\right) + 4 \, {\left(3 \, {\left(8 \, a^{4} b - 16 \, a^{3} b^{2} + 11 \, a^{2} b^{3} - 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{5} + 6 \, {\left(16 \, a^{5} - 40 \, a^{4} b + 38 \, a^{3} b^{2} - 17 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(40 \, a^{4} b - 80 \, a^{3} b^{2} + 49 \, a^{2} b^{3} - 9 \, a b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{8 \, {\left({\left(a^{6} b^{2} - 3 \, a^{5} b^{3} + 3 \, a^{4} b^{4} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{6} b^{2} - 3 \, a^{5} b^{3} + 3 \, a^{4} b^{4} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{6} b^{2} - 3 \, a^{5} b^{3} + 3 \, a^{4} b^{4} - a^{3} b^{5}\right)} d \sinh\left(d x + c\right)^{8} + 4 \, {\left(2 \, a^{7} b - 7 \, a^{6} b^{2} + 9 \, a^{5} b^{3} - 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{6} b^{2} - 3 \, a^{5} b^{3} + 3 \, a^{4} b^{4} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{7} b - 7 \, a^{6} b^{2} + 9 \, a^{5} b^{3} - 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(8 \, a^{8} - 32 \, a^{7} b + 51 \, a^{6} b^{2} - 41 \, a^{5} b^{3} + 17 \, a^{4} b^{4} - 3 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{6} b^{2} - 3 \, a^{5} b^{3} + 3 \, a^{4} b^{4} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(2 \, a^{7} b - 7 \, a^{6} b^{2} + 9 \, a^{5} b^{3} - 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a^{6} b^{2} - 3 \, a^{5} b^{3} + 3 \, a^{4} b^{4} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 30 \, {\left(2 \, a^{7} b - 7 \, a^{6} b^{2} + 9 \, a^{5} b^{3} - 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(8 \, a^{8} - 32 \, a^{7} b + 51 \, a^{6} b^{2} - 41 \, a^{5} b^{3} + 17 \, a^{4} b^{4} - 3 \, a^{3} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(2 \, a^{7} b - 7 \, a^{6} b^{2} + 9 \, a^{5} b^{3} - 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a^{6} b^{2} - 3 \, a^{5} b^{3} + 3 \, a^{4} b^{4} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{5} + 10 \, {\left(2 \, a^{7} b - 7 \, a^{6} b^{2} + 9 \, a^{5} b^{3} - 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{8} - 32 \, a^{7} b + 51 \, a^{6} b^{2} - 41 \, a^{5} b^{3} + 17 \, a^{4} b^{4} - 3 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a^{6} b^{2} - 3 \, a^{5} b^{3} + 3 \, a^{4} b^{4} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{6} + 15 \, {\left(2 \, a^{7} b - 7 \, a^{6} b^{2} + 9 \, a^{5} b^{3} - 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(8 \, a^{8} - 32 \, a^{7} b + 51 \, a^{6} b^{2} - 41 \, a^{5} b^{3} + 17 \, a^{4} b^{4} - 3 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{7} b - 7 \, a^{6} b^{2} + 9 \, a^{5} b^{3} - 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{6} b^{2} - 3 \, a^{5} b^{3} + 3 \, a^{4} b^{4} - a^{3} b^{5}\right)} d + 8 \, {\left({\left(a^{6} b^{2} - 3 \, a^{5} b^{3} + 3 \, a^{4} b^{4} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{7} + 3 \, {\left(2 \, a^{7} b - 7 \, a^{6} b^{2} + 9 \, a^{5} b^{3} - 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{5} + {\left(8 \, a^{8} - 32 \, a^{7} b + 51 \, a^{6} b^{2} - 41 \, a^{5} b^{3} + 17 \, a^{4} b^{4} - 3 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{7} b - 7 \, a^{6} b^{2} + 9 \, a^{5} b^{3} - 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[1/16*(4*(8*a^4*b - 16*a^3*b^2 + 11*a^2*b^3 - 3*a*b^4)*cosh(d*x + c)^6 + 24*(8*a^4*b - 16*a^3*b^2 + 11*a^2*b^3 - 3*a*b^4)*cosh(d*x + c)*sinh(d*x + c)^5 + 4*(8*a^4*b - 16*a^3*b^2 + 11*a^2*b^3 - 3*a*b^4)*sinh(d*x + c)^6 + 24*a^3*b^2 - 36*a^2*b^3 + 12*a*b^4 + 12*(16*a^5 - 40*a^4*b + 38*a^3*b^2 - 17*a^2*b^3 + 3*a*b^4)*cosh(d*x + c)^4 + 12*(16*a^5 - 40*a^4*b + 38*a^3*b^2 - 17*a^2*b^3 + 3*a*b^4 + 5*(8*a^4*b - 16*a^3*b^2 + 11*a^2*b^3 - 3*a*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 16*(5*(8*a^4*b - 16*a^3*b^2 + 11*a^2*b^3 - 3*a*b^4)*cosh(d*x + c)^3 + 3*(16*a^5 - 40*a^4*b + 38*a^3*b^2 - 17*a^2*b^3 + 3*a*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(40*a^4*b - 80*a^3*b^2 + 49*a^2*b^3 - 9*a*b^4)*cosh(d*x + c)^2 + 4*(40*a^4*b - 80*a^3*b^2 + 49*a^2*b^3 - 9*a*b^4 + 15*(8*a^4*b - 16*a^3*b^2 + 11*a^2*b^3 - 3*a*b^4)*cosh(d*x + c)^4 + 18*(16*a^5 - 40*a^4*b + 38*a^3*b^2 - 17*a^2*b^3 + 3*a*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((8*a^2*b^2 - 8*a*b^3 + 3*b^4)*cosh(d*x + c)^8 + 8*(8*a^2*b^2 - 8*a*b^3 + 3*b^4)*cosh(d*x + c)*sinh(d*x + c)^7 + (8*a^2*b^2 - 8*a*b^3 + 3*b^4)*sinh(d*x + c)^8 + 4*(16*a^3*b - 24*a^2*b^2 + 14*a*b^3 - 3*b^4)*cosh(d*x + c)^6 + 4*(16*a^3*b - 24*a^2*b^2 + 14*a*b^3 - 3*b^4 + 7*(8*a^2*b^2 - 8*a*b^3 + 3*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(8*a^2*b^2 - 8*a*b^3 + 3*b^4)*cosh(d*x + c)^3 + 3*(16*a^3*b - 24*a^2*b^2 + 14*a*b^3 - 3*b^4)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(64*a^4 - 128*a^3*b + 112*a^2*b^2 - 48*a*b^3 + 9*b^4)*cosh(d*x + c)^4 + 2*(35*(8*a^2*b^2 - 8*a*b^3 + 3*b^4)*cosh(d*x + c)^4 + 64*a^4 - 128*a^3*b + 112*a^2*b^2 - 48*a*b^3 + 9*b^4 + 30*(16*a^3*b - 24*a^2*b^2 + 14*a*b^3 - 3*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*a^2*b^2 - 8*a*b^3 + 3*b^4 + 8*(7*(8*a^2*b^2 - 8*a*b^3 + 3*b^4)*cosh(d*x + c)^5 + 10*(16*a^3*b - 24*a^2*b^2 + 14*a*b^3 - 3*b^4)*cosh(d*x + c)^3 + (64*a^4 - 128*a^3*b + 112*a^2*b^2 - 48*a*b^3 + 9*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(16*a^3*b - 24*a^2*b^2 + 14*a*b^3 - 3*b^4)*cosh(d*x + c)^2 + 4*(7*(8*a^2*b^2 - 8*a*b^3 + 3*b^4)*cosh(d*x + c)^6 + 15*(16*a^3*b - 24*a^2*b^2 + 14*a*b^3 - 3*b^4)*cosh(d*x + c)^4 + 16*a^3*b - 24*a^2*b^2 + 14*a*b^3 - 3*b^4 + 3*(64*a^4 - 128*a^3*b + 112*a^2*b^2 - 48*a*b^3 + 9*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((8*a^2*b^2 - 8*a*b^3 + 3*b^4)*cosh(d*x + c)^7 + 3*(16*a^3*b - 24*a^2*b^2 + 14*a*b^3 - 3*b^4)*cosh(d*x + c)^5 + (64*a^4 - 128*a^3*b + 112*a^2*b^2 - 48*a*b^3 + 9*b^4)*cosh(d*x + c)^3 + (16*a^3*b - 24*a^2*b^2 + 14*a*b^3 - 3*b^4)*cosh(d*x + c))*sinh(d*x + c))*sqrt(a^2 - a*b)*log((b^2*cosh(d*x + c)^4 + 4*b^2*cosh(d*x + c)*sinh(d*x + c)^3 + b^2*sinh(d*x + c)^4 + 2*(2*a*b - b^2)*cosh(d*x + c)^2 + 2*(3*b^2*cosh(d*x + c)^2 + 2*a*b - b^2)*sinh(d*x + c)^2 + 8*a^2 - 8*a*b + b^2 + 4*(b^2*cosh(d*x + c)^3 + (2*a*b - b^2)*cosh(d*x + c))*sinh(d*x + c) - 4*(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + 2*a - b)*sqrt(a^2 - a*b))/(b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 + 2*(2*a - b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 + 2*a - b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 + (2*a - b)*cosh(d*x + c))*sinh(d*x + c) + b)) + 8*(3*(8*a^4*b - 16*a^3*b^2 + 11*a^2*b^3 - 3*a*b^4)*cosh(d*x + c)^5 + 6*(16*a^5 - 40*a^4*b + 38*a^3*b^2 - 17*a^2*b^3 + 3*a*b^4)*cosh(d*x + c)^3 + (40*a^4*b - 80*a^3*b^2 + 49*a^2*b^3 - 9*a*b^4)*cosh(d*x + c))*sinh(d*x + c))/((a^6*b^2 - 3*a^5*b^3 + 3*a^4*b^4 - a^3*b^5)*d*cosh(d*x + c)^8 + 8*(a^6*b^2 - 3*a^5*b^3 + 3*a^4*b^4 - a^3*b^5)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^6*b^2 - 3*a^5*b^3 + 3*a^4*b^4 - a^3*b^5)*d*sinh(d*x + c)^8 + 4*(2*a^7*b - 7*a^6*b^2 + 9*a^5*b^3 - 5*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)^6 + 4*(7*(a^6*b^2 - 3*a^5*b^3 + 3*a^4*b^4 - a^3*b^5)*d*cosh(d*x + c)^2 + (2*a^7*b - 7*a^6*b^2 + 9*a^5*b^3 - 5*a^4*b^4 + a^3*b^5)*d)*sinh(d*x + c)^6 + 2*(8*a^8 - 32*a^7*b + 51*a^6*b^2 - 41*a^5*b^3 + 17*a^4*b^4 - 3*a^3*b^5)*d*cosh(d*x + c)^4 + 8*(7*(a^6*b^2 - 3*a^5*b^3 + 3*a^4*b^4 - a^3*b^5)*d*cosh(d*x + c)^3 + 3*(2*a^7*b - 7*a^6*b^2 + 9*a^5*b^3 - 5*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^6*b^2 - 3*a^5*b^3 + 3*a^4*b^4 - a^3*b^5)*d*cosh(d*x + c)^4 + 30*(2*a^7*b - 7*a^6*b^2 + 9*a^5*b^3 - 5*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)^2 + (8*a^8 - 32*a^7*b + 51*a^6*b^2 - 41*a^5*b^3 + 17*a^4*b^4 - 3*a^3*b^5)*d)*sinh(d*x + c)^4 + 4*(2*a^7*b - 7*a^6*b^2 + 9*a^5*b^3 - 5*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)^2 + 8*(7*(a^6*b^2 - 3*a^5*b^3 + 3*a^4*b^4 - a^3*b^5)*d*cosh(d*x + c)^5 + 10*(2*a^7*b - 7*a^6*b^2 + 9*a^5*b^3 - 5*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)^3 + (8*a^8 - 32*a^7*b + 51*a^6*b^2 - 41*a^5*b^3 + 17*a^4*b^4 - 3*a^3*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^6*b^2 - 3*a^5*b^3 + 3*a^4*b^4 - a^3*b^5)*d*cosh(d*x + c)^6 + 15*(2*a^7*b - 7*a^6*b^2 + 9*a^5*b^3 - 5*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)^4 + 3*(8*a^8 - 32*a^7*b + 51*a^6*b^2 - 41*a^5*b^3 + 17*a^4*b^4 - 3*a^3*b^5)*d*cosh(d*x + c)^2 + (2*a^7*b - 7*a^6*b^2 + 9*a^5*b^3 - 5*a^4*b^4 + a^3*b^5)*d)*sinh(d*x + c)^2 + (a^6*b^2 - 3*a^5*b^3 + 3*a^4*b^4 - a^3*b^5)*d + 8*((a^6*b^2 - 3*a^5*b^3 + 3*a^4*b^4 - a^3*b^5)*d*cosh(d*x + c)^7 + 3*(2*a^7*b - 7*a^6*b^2 + 9*a^5*b^3 - 5*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)^5 + (8*a^8 - 32*a^7*b + 51*a^6*b^2 - 41*a^5*b^3 + 17*a^4*b^4 - 3*a^3*b^5)*d*cosh(d*x + c)^3 + (2*a^7*b - 7*a^6*b^2 + 9*a^5*b^3 - 5*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c))*sinh(d*x + c)), 1/8*(2*(8*a^4*b - 16*a^3*b^2 + 11*a^2*b^3 - 3*a*b^4)*cosh(d*x + c)^6 + 12*(8*a^4*b - 16*a^3*b^2 + 11*a^2*b^3 - 3*a*b^4)*cosh(d*x + c)*sinh(d*x + c)^5 + 2*(8*a^4*b - 16*a^3*b^2 + 11*a^2*b^3 - 3*a*b^4)*sinh(d*x + c)^6 + 12*a^3*b^2 - 18*a^2*b^3 + 6*a*b^4 + 6*(16*a^5 - 40*a^4*b + 38*a^3*b^2 - 17*a^2*b^3 + 3*a*b^4)*cosh(d*x + c)^4 + 6*(16*a^5 - 40*a^4*b + 38*a^3*b^2 - 17*a^2*b^3 + 3*a*b^4 + 5*(8*a^4*b - 16*a^3*b^2 + 11*a^2*b^3 - 3*a*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(5*(8*a^4*b - 16*a^3*b^2 + 11*a^2*b^3 - 3*a*b^4)*cosh(d*x + c)^3 + 3*(16*a^5 - 40*a^4*b + 38*a^3*b^2 - 17*a^2*b^3 + 3*a*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 2*(40*a^4*b - 80*a^3*b^2 + 49*a^2*b^3 - 9*a*b^4)*cosh(d*x + c)^2 + 2*(40*a^4*b - 80*a^3*b^2 + 49*a^2*b^3 - 9*a*b^4 + 15*(8*a^4*b - 16*a^3*b^2 + 11*a^2*b^3 - 3*a*b^4)*cosh(d*x + c)^4 + 18*(16*a^5 - 40*a^4*b + 38*a^3*b^2 - 17*a^2*b^3 + 3*a*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - ((8*a^2*b^2 - 8*a*b^3 + 3*b^4)*cosh(d*x + c)^8 + 8*(8*a^2*b^2 - 8*a*b^3 + 3*b^4)*cosh(d*x + c)*sinh(d*x + c)^7 + (8*a^2*b^2 - 8*a*b^3 + 3*b^4)*sinh(d*x + c)^8 + 4*(16*a^3*b - 24*a^2*b^2 + 14*a*b^3 - 3*b^4)*cosh(d*x + c)^6 + 4*(16*a^3*b - 24*a^2*b^2 + 14*a*b^3 - 3*b^4 + 7*(8*a^2*b^2 - 8*a*b^3 + 3*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(8*a^2*b^2 - 8*a*b^3 + 3*b^4)*cosh(d*x + c)^3 + 3*(16*a^3*b - 24*a^2*b^2 + 14*a*b^3 - 3*b^4)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(64*a^4 - 128*a^3*b + 112*a^2*b^2 - 48*a*b^3 + 9*b^4)*cosh(d*x + c)^4 + 2*(35*(8*a^2*b^2 - 8*a*b^3 + 3*b^4)*cosh(d*x + c)^4 + 64*a^4 - 128*a^3*b + 112*a^2*b^2 - 48*a*b^3 + 9*b^4 + 30*(16*a^3*b - 24*a^2*b^2 + 14*a*b^3 - 3*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*a^2*b^2 - 8*a*b^3 + 3*b^4 + 8*(7*(8*a^2*b^2 - 8*a*b^3 + 3*b^4)*cosh(d*x + c)^5 + 10*(16*a^3*b - 24*a^2*b^2 + 14*a*b^3 - 3*b^4)*cosh(d*x + c)^3 + (64*a^4 - 128*a^3*b + 112*a^2*b^2 - 48*a*b^3 + 9*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(16*a^3*b - 24*a^2*b^2 + 14*a*b^3 - 3*b^4)*cosh(d*x + c)^2 + 4*(7*(8*a^2*b^2 - 8*a*b^3 + 3*b^4)*cosh(d*x + c)^6 + 15*(16*a^3*b - 24*a^2*b^2 + 14*a*b^3 - 3*b^4)*cosh(d*x + c)^4 + 16*a^3*b - 24*a^2*b^2 + 14*a*b^3 - 3*b^4 + 3*(64*a^4 - 128*a^3*b + 112*a^2*b^2 - 48*a*b^3 + 9*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((8*a^2*b^2 - 8*a*b^3 + 3*b^4)*cosh(d*x + c)^7 + 3*(16*a^3*b - 24*a^2*b^2 + 14*a*b^3 - 3*b^4)*cosh(d*x + c)^5 + (64*a^4 - 128*a^3*b + 112*a^2*b^2 - 48*a*b^3 + 9*b^4)*cosh(d*x + c)^3 + (16*a^3*b - 24*a^2*b^2 + 14*a*b^3 - 3*b^4)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-a^2 + a*b)*arctan(-1/2*(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + 2*a - b)*sqrt(-a^2 + a*b)/(a^2 - a*b)) + 4*(3*(8*a^4*b - 16*a^3*b^2 + 11*a^2*b^3 - 3*a*b^4)*cosh(d*x + c)^5 + 6*(16*a^5 - 40*a^4*b + 38*a^3*b^2 - 17*a^2*b^3 + 3*a*b^4)*cosh(d*x + c)^3 + (40*a^4*b - 80*a^3*b^2 + 49*a^2*b^3 - 9*a*b^4)*cosh(d*x + c))*sinh(d*x + c))/((a^6*b^2 - 3*a^5*b^3 + 3*a^4*b^4 - a^3*b^5)*d*cosh(d*x + c)^8 + 8*(a^6*b^2 - 3*a^5*b^3 + 3*a^4*b^4 - a^3*b^5)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^6*b^2 - 3*a^5*b^3 + 3*a^4*b^4 - a^3*b^5)*d*sinh(d*x + c)^8 + 4*(2*a^7*b - 7*a^6*b^2 + 9*a^5*b^3 - 5*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)^6 + 4*(7*(a^6*b^2 - 3*a^5*b^3 + 3*a^4*b^4 - a^3*b^5)*d*cosh(d*x + c)^2 + (2*a^7*b - 7*a^6*b^2 + 9*a^5*b^3 - 5*a^4*b^4 + a^3*b^5)*d)*sinh(d*x + c)^6 + 2*(8*a^8 - 32*a^7*b + 51*a^6*b^2 - 41*a^5*b^3 + 17*a^4*b^4 - 3*a^3*b^5)*d*cosh(d*x + c)^4 + 8*(7*(a^6*b^2 - 3*a^5*b^3 + 3*a^4*b^4 - a^3*b^5)*d*cosh(d*x + c)^3 + 3*(2*a^7*b - 7*a^6*b^2 + 9*a^5*b^3 - 5*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^6*b^2 - 3*a^5*b^3 + 3*a^4*b^4 - a^3*b^5)*d*cosh(d*x + c)^4 + 30*(2*a^7*b - 7*a^6*b^2 + 9*a^5*b^3 - 5*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)^2 + (8*a^8 - 32*a^7*b + 51*a^6*b^2 - 41*a^5*b^3 + 17*a^4*b^4 - 3*a^3*b^5)*d)*sinh(d*x + c)^4 + 4*(2*a^7*b - 7*a^6*b^2 + 9*a^5*b^3 - 5*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)^2 + 8*(7*(a^6*b^2 - 3*a^5*b^3 + 3*a^4*b^4 - a^3*b^5)*d*cosh(d*x + c)^5 + 10*(2*a^7*b - 7*a^6*b^2 + 9*a^5*b^3 - 5*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)^3 + (8*a^8 - 32*a^7*b + 51*a^6*b^2 - 41*a^5*b^3 + 17*a^4*b^4 - 3*a^3*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^6*b^2 - 3*a^5*b^3 + 3*a^4*b^4 - a^3*b^5)*d*cosh(d*x + c)^6 + 15*(2*a^7*b - 7*a^6*b^2 + 9*a^5*b^3 - 5*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)^4 + 3*(8*a^8 - 32*a^7*b + 51*a^6*b^2 - 41*a^5*b^3 + 17*a^4*b^4 - 3*a^3*b^5)*d*cosh(d*x + c)^2 + (2*a^7*b - 7*a^6*b^2 + 9*a^5*b^3 - 5*a^4*b^4 + a^3*b^5)*d)*sinh(d*x + c)^2 + (a^6*b^2 - 3*a^5*b^3 + 3*a^4*b^4 - a^3*b^5)*d + 8*((a^6*b^2 - 3*a^5*b^3 + 3*a^4*b^4 - a^3*b^5)*d*cosh(d*x + c)^7 + 3*(2*a^7*b - 7*a^6*b^2 + 9*a^5*b^3 - 5*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)^5 + (8*a^8 - 32*a^7*b + 51*a^6*b^2 - 41*a^5*b^3 + 17*a^4*b^4 - 3*a^3*b^5)*d*cosh(d*x + c)^3 + (2*a^7*b - 7*a^6*b^2 + 9*a^5*b^3 - 5*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
56,1,9815,0,0.888563," ","integrate(csch(d*x+c)/(a+b*sinh(d*x+c)^2)^3,x, algorithm=""fricas"")","\left[-\frac{4 \, {\left(7 \, a^{2} b^{2} - 4 \, a b^{3}\right)} \cosh\left(d x + c\right)^{7} + 28 \, {\left(7 \, a^{2} b^{2} - 4 \, a b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + 4 \, {\left(7 \, a^{2} b^{2} - 4 \, a b^{3}\right)} \sinh\left(d x + c\right)^{7} + 4 \, {\left(36 \, a^{3} b - 31 \, a^{2} b^{2} + 4 \, a b^{3}\right)} \cosh\left(d x + c\right)^{5} + 4 \, {\left(36 \, a^{3} b - 31 \, a^{2} b^{2} + 4 \, a b^{3} + 21 \, {\left(7 \, a^{2} b^{2} - 4 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{5} + 20 \, {\left(7 \, {\left(7 \, a^{2} b^{2} - 4 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(36 \, a^{3} b - 31 \, a^{2} b^{2} + 4 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(36 \, a^{3} b - 31 \, a^{2} b^{2} + 4 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(35 \, {\left(7 \, a^{2} b^{2} - 4 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} + 36 \, a^{3} b - 31 \, a^{2} b^{2} + 4 \, a b^{3} + 10 \, {\left(36 \, a^{3} b - 31 \, a^{2} b^{2} + 4 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(21 \, {\left(7 \, a^{2} b^{2} - 4 \, a b^{3}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(36 \, a^{3} b - 31 \, a^{2} b^{2} + 4 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(36 \, a^{3} b - 31 \, a^{2} b^{2} + 4 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - {\left({\left(15 \, a^{2} b^{2} - 20 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(15 \, a^{2} b^{2} - 20 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(15 \, a^{2} b^{2} - 20 \, a b^{3} + 8 \, b^{4}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(30 \, a^{3} b - 55 \, a^{2} b^{2} + 36 \, a b^{3} - 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(30 \, a^{3} b - 55 \, a^{2} b^{2} + 36 \, a b^{3} - 8 \, b^{4} + 7 \, {\left(15 \, a^{2} b^{2} - 20 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(15 \, a^{2} b^{2} - 20 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(30 \, a^{3} b - 55 \, a^{2} b^{2} + 36 \, a b^{3} - 8 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(120 \, a^{4} - 280 \, a^{3} b + 269 \, a^{2} b^{2} - 124 \, a b^{3} + 24 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(15 \, a^{2} b^{2} - 20 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 120 \, a^{4} - 280 \, a^{3} b + 269 \, a^{2} b^{2} - 124 \, a b^{3} + 24 \, b^{4} + 30 \, {\left(30 \, a^{3} b - 55 \, a^{2} b^{2} + 36 \, a b^{3} - 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 15 \, a^{2} b^{2} - 20 \, a b^{3} + 8 \, b^{4} + 8 \, {\left(7 \, {\left(15 \, a^{2} b^{2} - 20 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(30 \, a^{3} b - 55 \, a^{2} b^{2} + 36 \, a b^{3} - 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(120 \, a^{4} - 280 \, a^{3} b + 269 \, a^{2} b^{2} - 124 \, a b^{3} + 24 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(30 \, a^{3} b - 55 \, a^{2} b^{2} + 36 \, a b^{3} - 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(15 \, a^{2} b^{2} - 20 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(30 \, a^{3} b - 55 \, a^{2} b^{2} + 36 \, a b^{3} - 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 30 \, a^{3} b - 55 \, a^{2} b^{2} + 36 \, a b^{3} - 8 \, b^{4} + 3 \, {\left(120 \, a^{4} - 280 \, a^{3} b + 269 \, a^{2} b^{2} - 124 \, a b^{3} + 24 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left({\left(15 \, a^{2} b^{2} - 20 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(30 \, a^{3} b - 55 \, a^{2} b^{2} + 36 \, a b^{3} - 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + {\left(120 \, a^{4} - 280 \, a^{3} b + 269 \, a^{2} b^{2} - 124 \, a b^{3} + 24 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(30 \, a^{3} b - 55 \, a^{2} b^{2} + 36 \, a b^{3} - 8 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{b}{a - b}} \log\left(\frac{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} - 2 \, {\left(2 \, a - 3 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} - 2 \, a + 3 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} - {\left(2 \, a - 3 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) - 4 \, {\left({\left(a - b\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a - b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + {\left(a - b\right)} \sinh\left(d x + c\right)^{3} + {\left(a - b\right)} \cosh\left(d x + c\right) + {\left(3 \, {\left(a - b\right)} \cosh\left(d x + c\right)^{2} + a - b\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{b}{a - b}} + b}{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b}\right) + 4 \, {\left(7 \, a^{2} b^{2} - 4 \, a b^{3}\right)} \cosh\left(d x + c\right) + 16 \, {\left({\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4} + 7 \, {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(8 \, a^{4} - 24 \, a^{3} b + 27 \, a^{2} b^{2} - 14 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{4} + 8 \, a^{4} - 24 \, a^{3} b + 27 \, a^{2} b^{2} - 14 \, a b^{3} + 3 \, b^{4} + 30 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + a^{2} b^{2} - 2 \, a b^{3} + b^{4} + 8 \, {\left(7 \, {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{4} - 24 \, a^{3} b + 27 \, a^{2} b^{2} - 14 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4} + 3 \, {\left(8 \, a^{4} - 24 \, a^{3} b + 27 \, a^{2} b^{2} - 14 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left({\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{5} + {\left(8 \, a^{4} - 24 \, a^{3} b + 27 \, a^{2} b^{2} - 14 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) - 16 \, {\left({\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4} + 7 \, {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(8 \, a^{4} - 24 \, a^{3} b + 27 \, a^{2} b^{2} - 14 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{4} + 8 \, a^{4} - 24 \, a^{3} b + 27 \, a^{2} b^{2} - 14 \, a b^{3} + 3 \, b^{4} + 30 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + a^{2} b^{2} - 2 \, a b^{3} + b^{4} + 8 \, {\left(7 \, {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{4} - 24 \, a^{3} b + 27 \, a^{2} b^{2} - 14 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4} + 3 \, {\left(8 \, a^{4} - 24 \, a^{3} b + 27 \, a^{2} b^{2} - 14 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left({\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{5} + {\left(8 \, a^{4} - 24 \, a^{3} b + 27 \, a^{2} b^{2} - 14 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) + 4 \, {\left(7 \, {\left(7 \, a^{2} b^{2} - 4 \, a b^{3}\right)} \cosh\left(d x + c\right)^{6} + 5 \, {\left(36 \, a^{3} b - 31 \, a^{2} b^{2} + 4 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} + 7 \, a^{2} b^{2} - 4 \, a b^{3} + 3 \, {\left(36 \, a^{3} b - 31 \, a^{2} b^{2} + 4 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)}{16 \, {\left({\left(a^{5} b^{2} - 2 \, a^{4} b^{3} + a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{5} b^{2} - 2 \, a^{4} b^{3} + a^{3} b^{4}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{5} b^{2} - 2 \, a^{4} b^{3} + a^{3} b^{4}\right)} d \sinh\left(d x + c\right)^{8} + 4 \, {\left(2 \, a^{6} b - 5 \, a^{5} b^{2} + 4 \, a^{4} b^{3} - a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{5} b^{2} - 2 \, a^{4} b^{3} + a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{6} b - 5 \, a^{5} b^{2} + 4 \, a^{4} b^{3} - a^{3} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(8 \, a^{7} - 24 \, a^{6} b + 27 \, a^{5} b^{2} - 14 \, a^{4} b^{3} + 3 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{5} b^{2} - 2 \, a^{4} b^{3} + a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(2 \, a^{6} b - 5 \, a^{5} b^{2} + 4 \, a^{4} b^{3} - a^{3} b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a^{5} b^{2} - 2 \, a^{4} b^{3} + a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 30 \, {\left(2 \, a^{6} b - 5 \, a^{5} b^{2} + 4 \, a^{4} b^{3} - a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(8 \, a^{7} - 24 \, a^{6} b + 27 \, a^{5} b^{2} - 14 \, a^{4} b^{3} + 3 \, a^{3} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(2 \, a^{6} b - 5 \, a^{5} b^{2} + 4 \, a^{4} b^{3} - a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a^{5} b^{2} - 2 \, a^{4} b^{3} + a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{5} + 10 \, {\left(2 \, a^{6} b - 5 \, a^{5} b^{2} + 4 \, a^{4} b^{3} - a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{7} - 24 \, a^{6} b + 27 \, a^{5} b^{2} - 14 \, a^{4} b^{3} + 3 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a^{5} b^{2} - 2 \, a^{4} b^{3} + a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{6} + 15 \, {\left(2 \, a^{6} b - 5 \, a^{5} b^{2} + 4 \, a^{4} b^{3} - a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(8 \, a^{7} - 24 \, a^{6} b + 27 \, a^{5} b^{2} - 14 \, a^{4} b^{3} + 3 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{6} b - 5 \, a^{5} b^{2} + 4 \, a^{4} b^{3} - a^{3} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{5} b^{2} - 2 \, a^{4} b^{3} + a^{3} b^{4}\right)} d + 8 \, {\left({\left(a^{5} b^{2} - 2 \, a^{4} b^{3} + a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{7} + 3 \, {\left(2 \, a^{6} b - 5 \, a^{5} b^{2} + 4 \, a^{4} b^{3} - a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{5} + {\left(8 \, a^{7} - 24 \, a^{6} b + 27 \, a^{5} b^{2} - 14 \, a^{4} b^{3} + 3 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{6} b - 5 \, a^{5} b^{2} + 4 \, a^{4} b^{3} - a^{3} b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}, -\frac{2 \, {\left(7 \, a^{2} b^{2} - 4 \, a b^{3}\right)} \cosh\left(d x + c\right)^{7} + 14 \, {\left(7 \, a^{2} b^{2} - 4 \, a b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + 2 \, {\left(7 \, a^{2} b^{2} - 4 \, a b^{3}\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(36 \, a^{3} b - 31 \, a^{2} b^{2} + 4 \, a b^{3}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(36 \, a^{3} b - 31 \, a^{2} b^{2} + 4 \, a b^{3} + 21 \, {\left(7 \, a^{2} b^{2} - 4 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{5} + 10 \, {\left(7 \, {\left(7 \, a^{2} b^{2} - 4 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(36 \, a^{3} b - 31 \, a^{2} b^{2} + 4 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(36 \, a^{3} b - 31 \, a^{2} b^{2} + 4 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(35 \, {\left(7 \, a^{2} b^{2} - 4 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} + 36 \, a^{3} b - 31 \, a^{2} b^{2} + 4 \, a b^{3} + 10 \, {\left(36 \, a^{3} b - 31 \, a^{2} b^{2} + 4 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(21 \, {\left(7 \, a^{2} b^{2} - 4 \, a b^{3}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(36 \, a^{3} b - 31 \, a^{2} b^{2} + 4 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(36 \, a^{3} b - 31 \, a^{2} b^{2} + 4 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(15 \, a^{2} b^{2} - 20 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(15 \, a^{2} b^{2} - 20 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(15 \, a^{2} b^{2} - 20 \, a b^{3} + 8 \, b^{4}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(30 \, a^{3} b - 55 \, a^{2} b^{2} + 36 \, a b^{3} - 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(30 \, a^{3} b - 55 \, a^{2} b^{2} + 36 \, a b^{3} - 8 \, b^{4} + 7 \, {\left(15 \, a^{2} b^{2} - 20 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(15 \, a^{2} b^{2} - 20 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(30 \, a^{3} b - 55 \, a^{2} b^{2} + 36 \, a b^{3} - 8 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(120 \, a^{4} - 280 \, a^{3} b + 269 \, a^{2} b^{2} - 124 \, a b^{3} + 24 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(15 \, a^{2} b^{2} - 20 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 120 \, a^{4} - 280 \, a^{3} b + 269 \, a^{2} b^{2} - 124 \, a b^{3} + 24 \, b^{4} + 30 \, {\left(30 \, a^{3} b - 55 \, a^{2} b^{2} + 36 \, a b^{3} - 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 15 \, a^{2} b^{2} - 20 \, a b^{3} + 8 \, b^{4} + 8 \, {\left(7 \, {\left(15 \, a^{2} b^{2} - 20 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(30 \, a^{3} b - 55 \, a^{2} b^{2} + 36 \, a b^{3} - 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(120 \, a^{4} - 280 \, a^{3} b + 269 \, a^{2} b^{2} - 124 \, a b^{3} + 24 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(30 \, a^{3} b - 55 \, a^{2} b^{2} + 36 \, a b^{3} - 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(15 \, a^{2} b^{2} - 20 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(30 \, a^{3} b - 55 \, a^{2} b^{2} + 36 \, a b^{3} - 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 30 \, a^{3} b - 55 \, a^{2} b^{2} + 36 \, a b^{3} - 8 \, b^{4} + 3 \, {\left(120 \, a^{4} - 280 \, a^{3} b + 269 \, a^{2} b^{2} - 124 \, a b^{3} + 24 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left({\left(15 \, a^{2} b^{2} - 20 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(30 \, a^{3} b - 55 \, a^{2} b^{2} + 36 \, a b^{3} - 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + {\left(120 \, a^{4} - 280 \, a^{3} b + 269 \, a^{2} b^{2} - 124 \, a b^{3} + 24 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(30 \, a^{3} b - 55 \, a^{2} b^{2} + 36 \, a b^{3} - 8 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{b}{a - b}} \arctan\left(\frac{1}{2} \, \sqrt{\frac{b}{a - b}} {\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right)}\right) - {\left({\left(15 \, a^{2} b^{2} - 20 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(15 \, a^{2} b^{2} - 20 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(15 \, a^{2} b^{2} - 20 \, a b^{3} + 8 \, b^{4}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(30 \, a^{3} b - 55 \, a^{2} b^{2} + 36 \, a b^{3} - 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(30 \, a^{3} b - 55 \, a^{2} b^{2} + 36 \, a b^{3} - 8 \, b^{4} + 7 \, {\left(15 \, a^{2} b^{2} - 20 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(15 \, a^{2} b^{2} - 20 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(30 \, a^{3} b - 55 \, a^{2} b^{2} + 36 \, a b^{3} - 8 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(120 \, a^{4} - 280 \, a^{3} b + 269 \, a^{2} b^{2} - 124 \, a b^{3} + 24 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(15 \, a^{2} b^{2} - 20 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 120 \, a^{4} - 280 \, a^{3} b + 269 \, a^{2} b^{2} - 124 \, a b^{3} + 24 \, b^{4} + 30 \, {\left(30 \, a^{3} b - 55 \, a^{2} b^{2} + 36 \, a b^{3} - 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 15 \, a^{2} b^{2} - 20 \, a b^{3} + 8 \, b^{4} + 8 \, {\left(7 \, {\left(15 \, a^{2} b^{2} - 20 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(30 \, a^{3} b - 55 \, a^{2} b^{2} + 36 \, a b^{3} - 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(120 \, a^{4} - 280 \, a^{3} b + 269 \, a^{2} b^{2} - 124 \, a b^{3} + 24 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(30 \, a^{3} b - 55 \, a^{2} b^{2} + 36 \, a b^{3} - 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(15 \, a^{2} b^{2} - 20 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(30 \, a^{3} b - 55 \, a^{2} b^{2} + 36 \, a b^{3} - 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 30 \, a^{3} b - 55 \, a^{2} b^{2} + 36 \, a b^{3} - 8 \, b^{4} + 3 \, {\left(120 \, a^{4} - 280 \, a^{3} b + 269 \, a^{2} b^{2} - 124 \, a b^{3} + 24 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left({\left(15 \, a^{2} b^{2} - 20 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(30 \, a^{3} b - 55 \, a^{2} b^{2} + 36 \, a b^{3} - 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + {\left(120 \, a^{4} - 280 \, a^{3} b + 269 \, a^{2} b^{2} - 124 \, a b^{3} + 24 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(30 \, a^{3} b - 55 \, a^{2} b^{2} + 36 \, a b^{3} - 8 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{b}{a - b}} \arctan\left(\frac{{\left(b \cosh\left(d x + c\right)^{3} + 3 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{3} + {\left(4 \, a - 3 \, b\right)} \cosh\left(d x + c\right) + {\left(3 \, b \cosh\left(d x + c\right)^{2} + 4 \, a - 3 \, b\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{b}{a - b}}}{2 \, b}\right) + 2 \, {\left(7 \, a^{2} b^{2} - 4 \, a b^{3}\right)} \cosh\left(d x + c\right) + 8 \, {\left({\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4} + 7 \, {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(8 \, a^{4} - 24 \, a^{3} b + 27 \, a^{2} b^{2} - 14 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{4} + 8 \, a^{4} - 24 \, a^{3} b + 27 \, a^{2} b^{2} - 14 \, a b^{3} + 3 \, b^{4} + 30 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + a^{2} b^{2} - 2 \, a b^{3} + b^{4} + 8 \, {\left(7 \, {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{4} - 24 \, a^{3} b + 27 \, a^{2} b^{2} - 14 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4} + 3 \, {\left(8 \, a^{4} - 24 \, a^{3} b + 27 \, a^{2} b^{2} - 14 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left({\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{5} + {\left(8 \, a^{4} - 24 \, a^{3} b + 27 \, a^{2} b^{2} - 14 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) - 8 \, {\left({\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4} + 7 \, {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(8 \, a^{4} - 24 \, a^{3} b + 27 \, a^{2} b^{2} - 14 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{4} + 8 \, a^{4} - 24 \, a^{3} b + 27 \, a^{2} b^{2} - 14 \, a b^{3} + 3 \, b^{4} + 30 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + a^{2} b^{2} - 2 \, a b^{3} + b^{4} + 8 \, {\left(7 \, {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{4} - 24 \, a^{3} b + 27 \, a^{2} b^{2} - 14 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4} + 3 \, {\left(8 \, a^{4} - 24 \, a^{3} b + 27 \, a^{2} b^{2} - 14 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left({\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{5} + {\left(8 \, a^{4} - 24 \, a^{3} b + 27 \, a^{2} b^{2} - 14 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) + 2 \, {\left(7 \, {\left(7 \, a^{2} b^{2} - 4 \, a b^{3}\right)} \cosh\left(d x + c\right)^{6} + 5 \, {\left(36 \, a^{3} b - 31 \, a^{2} b^{2} + 4 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} + 7 \, a^{2} b^{2} - 4 \, a b^{3} + 3 \, {\left(36 \, a^{3} b - 31 \, a^{2} b^{2} + 4 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)}{8 \, {\left({\left(a^{5} b^{2} - 2 \, a^{4} b^{3} + a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{5} b^{2} - 2 \, a^{4} b^{3} + a^{3} b^{4}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{5} b^{2} - 2 \, a^{4} b^{3} + a^{3} b^{4}\right)} d \sinh\left(d x + c\right)^{8} + 4 \, {\left(2 \, a^{6} b - 5 \, a^{5} b^{2} + 4 \, a^{4} b^{3} - a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{5} b^{2} - 2 \, a^{4} b^{3} + a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{6} b - 5 \, a^{5} b^{2} + 4 \, a^{4} b^{3} - a^{3} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(8 \, a^{7} - 24 \, a^{6} b + 27 \, a^{5} b^{2} - 14 \, a^{4} b^{3} + 3 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{5} b^{2} - 2 \, a^{4} b^{3} + a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(2 \, a^{6} b - 5 \, a^{5} b^{2} + 4 \, a^{4} b^{3} - a^{3} b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a^{5} b^{2} - 2 \, a^{4} b^{3} + a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 30 \, {\left(2 \, a^{6} b - 5 \, a^{5} b^{2} + 4 \, a^{4} b^{3} - a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(8 \, a^{7} - 24 \, a^{6} b + 27 \, a^{5} b^{2} - 14 \, a^{4} b^{3} + 3 \, a^{3} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(2 \, a^{6} b - 5 \, a^{5} b^{2} + 4 \, a^{4} b^{3} - a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a^{5} b^{2} - 2 \, a^{4} b^{3} + a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{5} + 10 \, {\left(2 \, a^{6} b - 5 \, a^{5} b^{2} + 4 \, a^{4} b^{3} - a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{7} - 24 \, a^{6} b + 27 \, a^{5} b^{2} - 14 \, a^{4} b^{3} + 3 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a^{5} b^{2} - 2 \, a^{4} b^{3} + a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{6} + 15 \, {\left(2 \, a^{6} b - 5 \, a^{5} b^{2} + 4 \, a^{4} b^{3} - a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(8 \, a^{7} - 24 \, a^{6} b + 27 \, a^{5} b^{2} - 14 \, a^{4} b^{3} + 3 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{6} b - 5 \, a^{5} b^{2} + 4 \, a^{4} b^{3} - a^{3} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{5} b^{2} - 2 \, a^{4} b^{3} + a^{3} b^{4}\right)} d + 8 \, {\left({\left(a^{5} b^{2} - 2 \, a^{4} b^{3} + a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{7} + 3 \, {\left(2 \, a^{6} b - 5 \, a^{5} b^{2} + 4 \, a^{4} b^{3} - a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{5} + {\left(8 \, a^{7} - 24 \, a^{6} b + 27 \, a^{5} b^{2} - 14 \, a^{4} b^{3} + 3 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{6} b - 5 \, a^{5} b^{2} + 4 \, a^{4} b^{3} - a^{3} b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[-1/16*(4*(7*a^2*b^2 - 4*a*b^3)*cosh(d*x + c)^7 + 28*(7*a^2*b^2 - 4*a*b^3)*cosh(d*x + c)*sinh(d*x + c)^6 + 4*(7*a^2*b^2 - 4*a*b^3)*sinh(d*x + c)^7 + 4*(36*a^3*b - 31*a^2*b^2 + 4*a*b^3)*cosh(d*x + c)^5 + 4*(36*a^3*b - 31*a^2*b^2 + 4*a*b^3 + 21*(7*a^2*b^2 - 4*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 20*(7*(7*a^2*b^2 - 4*a*b^3)*cosh(d*x + c)^3 + (36*a^3*b - 31*a^2*b^2 + 4*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^4 + 4*(36*a^3*b - 31*a^2*b^2 + 4*a*b^3)*cosh(d*x + c)^3 + 4*(35*(7*a^2*b^2 - 4*a*b^3)*cosh(d*x + c)^4 + 36*a^3*b - 31*a^2*b^2 + 4*a*b^3 + 10*(36*a^3*b - 31*a^2*b^2 + 4*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 4*(21*(7*a^2*b^2 - 4*a*b^3)*cosh(d*x + c)^5 + 10*(36*a^3*b - 31*a^2*b^2 + 4*a*b^3)*cosh(d*x + c)^3 + 3*(36*a^3*b - 31*a^2*b^2 + 4*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^2 - ((15*a^2*b^2 - 20*a*b^3 + 8*b^4)*cosh(d*x + c)^8 + 8*(15*a^2*b^2 - 20*a*b^3 + 8*b^4)*cosh(d*x + c)*sinh(d*x + c)^7 + (15*a^2*b^2 - 20*a*b^3 + 8*b^4)*sinh(d*x + c)^8 + 4*(30*a^3*b - 55*a^2*b^2 + 36*a*b^3 - 8*b^4)*cosh(d*x + c)^6 + 4*(30*a^3*b - 55*a^2*b^2 + 36*a*b^3 - 8*b^4 + 7*(15*a^2*b^2 - 20*a*b^3 + 8*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(15*a^2*b^2 - 20*a*b^3 + 8*b^4)*cosh(d*x + c)^3 + 3*(30*a^3*b - 55*a^2*b^2 + 36*a*b^3 - 8*b^4)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(120*a^4 - 280*a^3*b + 269*a^2*b^2 - 124*a*b^3 + 24*b^4)*cosh(d*x + c)^4 + 2*(35*(15*a^2*b^2 - 20*a*b^3 + 8*b^4)*cosh(d*x + c)^4 + 120*a^4 - 280*a^3*b + 269*a^2*b^2 - 124*a*b^3 + 24*b^4 + 30*(30*a^3*b - 55*a^2*b^2 + 36*a*b^3 - 8*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 15*a^2*b^2 - 20*a*b^3 + 8*b^4 + 8*(7*(15*a^2*b^2 - 20*a*b^3 + 8*b^4)*cosh(d*x + c)^5 + 10*(30*a^3*b - 55*a^2*b^2 + 36*a*b^3 - 8*b^4)*cosh(d*x + c)^3 + (120*a^4 - 280*a^3*b + 269*a^2*b^2 - 124*a*b^3 + 24*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(30*a^3*b - 55*a^2*b^2 + 36*a*b^3 - 8*b^4)*cosh(d*x + c)^2 + 4*(7*(15*a^2*b^2 - 20*a*b^3 + 8*b^4)*cosh(d*x + c)^6 + 15*(30*a^3*b - 55*a^2*b^2 + 36*a*b^3 - 8*b^4)*cosh(d*x + c)^4 + 30*a^3*b - 55*a^2*b^2 + 36*a*b^3 - 8*b^4 + 3*(120*a^4 - 280*a^3*b + 269*a^2*b^2 - 124*a*b^3 + 24*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((15*a^2*b^2 - 20*a*b^3 + 8*b^4)*cosh(d*x + c)^7 + 3*(30*a^3*b - 55*a^2*b^2 + 36*a*b^3 - 8*b^4)*cosh(d*x + c)^5 + (120*a^4 - 280*a^3*b + 269*a^2*b^2 - 124*a*b^3 + 24*b^4)*cosh(d*x + c)^3 + (30*a^3*b - 55*a^2*b^2 + 36*a*b^3 - 8*b^4)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-b/(a - b))*log((b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 - 2*(2*a - 3*b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 - 2*a + 3*b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 - (2*a - 3*b)*cosh(d*x + c))*sinh(d*x + c) - 4*((a - b)*cosh(d*x + c)^3 + 3*(a - b)*cosh(d*x + c)*sinh(d*x + c)^2 + (a - b)*sinh(d*x + c)^3 + (a - b)*cosh(d*x + c) + (3*(a - b)*cosh(d*x + c)^2 + a - b)*sinh(d*x + c))*sqrt(-b/(a - b)) + b)/(b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 + 2*(2*a - b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 + 2*a - b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 + (2*a - b)*cosh(d*x + c))*sinh(d*x + c) + b)) + 4*(7*a^2*b^2 - 4*a*b^3)*cosh(d*x + c) + 16*((a^2*b^2 - 2*a*b^3 + b^4)*cosh(d*x + c)^8 + 8*(a^2*b^2 - 2*a*b^3 + b^4)*cosh(d*x + c)*sinh(d*x + c)^7 + (a^2*b^2 - 2*a*b^3 + b^4)*sinh(d*x + c)^8 + 4*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*cosh(d*x + c)^6 + 4*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4 + 7*(a^2*b^2 - 2*a*b^3 + b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(a^2*b^2 - 2*a*b^3 + b^4)*cosh(d*x + c)^3 + 3*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(8*a^4 - 24*a^3*b + 27*a^2*b^2 - 14*a*b^3 + 3*b^4)*cosh(d*x + c)^4 + 2*(35*(a^2*b^2 - 2*a*b^3 + b^4)*cosh(d*x + c)^4 + 8*a^4 - 24*a^3*b + 27*a^2*b^2 - 14*a*b^3 + 3*b^4 + 30*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + a^2*b^2 - 2*a*b^3 + b^4 + 8*(7*(a^2*b^2 - 2*a*b^3 + b^4)*cosh(d*x + c)^5 + 10*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*cosh(d*x + c)^3 + (8*a^4 - 24*a^3*b + 27*a^2*b^2 - 14*a*b^3 + 3*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*cosh(d*x + c)^2 + 4*(7*(a^2*b^2 - 2*a*b^3 + b^4)*cosh(d*x + c)^6 + 15*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*cosh(d*x + c)^4 + 2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4 + 3*(8*a^4 - 24*a^3*b + 27*a^2*b^2 - 14*a*b^3 + 3*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((a^2*b^2 - 2*a*b^3 + b^4)*cosh(d*x + c)^7 + 3*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*cosh(d*x + c)^5 + (8*a^4 - 24*a^3*b + 27*a^2*b^2 - 14*a*b^3 + 3*b^4)*cosh(d*x + c)^3 + (2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) + 1) - 16*((a^2*b^2 - 2*a*b^3 + b^4)*cosh(d*x + c)^8 + 8*(a^2*b^2 - 2*a*b^3 + b^4)*cosh(d*x + c)*sinh(d*x + c)^7 + (a^2*b^2 - 2*a*b^3 + b^4)*sinh(d*x + c)^8 + 4*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*cosh(d*x + c)^6 + 4*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4 + 7*(a^2*b^2 - 2*a*b^3 + b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(a^2*b^2 - 2*a*b^3 + b^4)*cosh(d*x + c)^3 + 3*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(8*a^4 - 24*a^3*b + 27*a^2*b^2 - 14*a*b^3 + 3*b^4)*cosh(d*x + c)^4 + 2*(35*(a^2*b^2 - 2*a*b^3 + b^4)*cosh(d*x + c)^4 + 8*a^4 - 24*a^3*b + 27*a^2*b^2 - 14*a*b^3 + 3*b^4 + 30*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + a^2*b^2 - 2*a*b^3 + b^4 + 8*(7*(a^2*b^2 - 2*a*b^3 + b^4)*cosh(d*x + c)^5 + 10*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*cosh(d*x + c)^3 + (8*a^4 - 24*a^3*b + 27*a^2*b^2 - 14*a*b^3 + 3*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*cosh(d*x + c)^2 + 4*(7*(a^2*b^2 - 2*a*b^3 + b^4)*cosh(d*x + c)^6 + 15*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*cosh(d*x + c)^4 + 2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4 + 3*(8*a^4 - 24*a^3*b + 27*a^2*b^2 - 14*a*b^3 + 3*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((a^2*b^2 - 2*a*b^3 + b^4)*cosh(d*x + c)^7 + 3*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*cosh(d*x + c)^5 + (8*a^4 - 24*a^3*b + 27*a^2*b^2 - 14*a*b^3 + 3*b^4)*cosh(d*x + c)^3 + (2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) - 1) + 4*(7*(7*a^2*b^2 - 4*a*b^3)*cosh(d*x + c)^6 + 5*(36*a^3*b - 31*a^2*b^2 + 4*a*b^3)*cosh(d*x + c)^4 + 7*a^2*b^2 - 4*a*b^3 + 3*(36*a^3*b - 31*a^2*b^2 + 4*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c))/((a^5*b^2 - 2*a^4*b^3 + a^3*b^4)*d*cosh(d*x + c)^8 + 8*(a^5*b^2 - 2*a^4*b^3 + a^3*b^4)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^5*b^2 - 2*a^4*b^3 + a^3*b^4)*d*sinh(d*x + c)^8 + 4*(2*a^6*b - 5*a^5*b^2 + 4*a^4*b^3 - a^3*b^4)*d*cosh(d*x + c)^6 + 4*(7*(a^5*b^2 - 2*a^4*b^3 + a^3*b^4)*d*cosh(d*x + c)^2 + (2*a^6*b - 5*a^5*b^2 + 4*a^4*b^3 - a^3*b^4)*d)*sinh(d*x + c)^6 + 2*(8*a^7 - 24*a^6*b + 27*a^5*b^2 - 14*a^4*b^3 + 3*a^3*b^4)*d*cosh(d*x + c)^4 + 8*(7*(a^5*b^2 - 2*a^4*b^3 + a^3*b^4)*d*cosh(d*x + c)^3 + 3*(2*a^6*b - 5*a^5*b^2 + 4*a^4*b^3 - a^3*b^4)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^5*b^2 - 2*a^4*b^3 + a^3*b^4)*d*cosh(d*x + c)^4 + 30*(2*a^6*b - 5*a^5*b^2 + 4*a^4*b^3 - a^3*b^4)*d*cosh(d*x + c)^2 + (8*a^7 - 24*a^6*b + 27*a^5*b^2 - 14*a^4*b^3 + 3*a^3*b^4)*d)*sinh(d*x + c)^4 + 4*(2*a^6*b - 5*a^5*b^2 + 4*a^4*b^3 - a^3*b^4)*d*cosh(d*x + c)^2 + 8*(7*(a^5*b^2 - 2*a^4*b^3 + a^3*b^4)*d*cosh(d*x + c)^5 + 10*(2*a^6*b - 5*a^5*b^2 + 4*a^4*b^3 - a^3*b^4)*d*cosh(d*x + c)^3 + (8*a^7 - 24*a^6*b + 27*a^5*b^2 - 14*a^4*b^3 + 3*a^3*b^4)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^5*b^2 - 2*a^4*b^3 + a^3*b^4)*d*cosh(d*x + c)^6 + 15*(2*a^6*b - 5*a^5*b^2 + 4*a^4*b^3 - a^3*b^4)*d*cosh(d*x + c)^4 + 3*(8*a^7 - 24*a^6*b + 27*a^5*b^2 - 14*a^4*b^3 + 3*a^3*b^4)*d*cosh(d*x + c)^2 + (2*a^6*b - 5*a^5*b^2 + 4*a^4*b^3 - a^3*b^4)*d)*sinh(d*x + c)^2 + (a^5*b^2 - 2*a^4*b^3 + a^3*b^4)*d + 8*((a^5*b^2 - 2*a^4*b^3 + a^3*b^4)*d*cosh(d*x + c)^7 + 3*(2*a^6*b - 5*a^5*b^2 + 4*a^4*b^3 - a^3*b^4)*d*cosh(d*x + c)^5 + (8*a^7 - 24*a^6*b + 27*a^5*b^2 - 14*a^4*b^3 + 3*a^3*b^4)*d*cosh(d*x + c)^3 + (2*a^6*b - 5*a^5*b^2 + 4*a^4*b^3 - a^3*b^4)*d*cosh(d*x + c))*sinh(d*x + c)), -1/8*(2*(7*a^2*b^2 - 4*a*b^3)*cosh(d*x + c)^7 + 14*(7*a^2*b^2 - 4*a*b^3)*cosh(d*x + c)*sinh(d*x + c)^6 + 2*(7*a^2*b^2 - 4*a*b^3)*sinh(d*x + c)^7 + 2*(36*a^3*b - 31*a^2*b^2 + 4*a*b^3)*cosh(d*x + c)^5 + 2*(36*a^3*b - 31*a^2*b^2 + 4*a*b^3 + 21*(7*a^2*b^2 - 4*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 10*(7*(7*a^2*b^2 - 4*a*b^3)*cosh(d*x + c)^3 + (36*a^3*b - 31*a^2*b^2 + 4*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^4 + 2*(36*a^3*b - 31*a^2*b^2 + 4*a*b^3)*cosh(d*x + c)^3 + 2*(35*(7*a^2*b^2 - 4*a*b^3)*cosh(d*x + c)^4 + 36*a^3*b - 31*a^2*b^2 + 4*a*b^3 + 10*(36*a^3*b - 31*a^2*b^2 + 4*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 2*(21*(7*a^2*b^2 - 4*a*b^3)*cosh(d*x + c)^5 + 10*(36*a^3*b - 31*a^2*b^2 + 4*a*b^3)*cosh(d*x + c)^3 + 3*(36*a^3*b - 31*a^2*b^2 + 4*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^2 + ((15*a^2*b^2 - 20*a*b^3 + 8*b^4)*cosh(d*x + c)^8 + 8*(15*a^2*b^2 - 20*a*b^3 + 8*b^4)*cosh(d*x + c)*sinh(d*x + c)^7 + (15*a^2*b^2 - 20*a*b^3 + 8*b^4)*sinh(d*x + c)^8 + 4*(30*a^3*b - 55*a^2*b^2 + 36*a*b^3 - 8*b^4)*cosh(d*x + c)^6 + 4*(30*a^3*b - 55*a^2*b^2 + 36*a*b^3 - 8*b^4 + 7*(15*a^2*b^2 - 20*a*b^3 + 8*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(15*a^2*b^2 - 20*a*b^3 + 8*b^4)*cosh(d*x + c)^3 + 3*(30*a^3*b - 55*a^2*b^2 + 36*a*b^3 - 8*b^4)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(120*a^4 - 280*a^3*b + 269*a^2*b^2 - 124*a*b^3 + 24*b^4)*cosh(d*x + c)^4 + 2*(35*(15*a^2*b^2 - 20*a*b^3 + 8*b^4)*cosh(d*x + c)^4 + 120*a^4 - 280*a^3*b + 269*a^2*b^2 - 124*a*b^3 + 24*b^4 + 30*(30*a^3*b - 55*a^2*b^2 + 36*a*b^3 - 8*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 15*a^2*b^2 - 20*a*b^3 + 8*b^4 + 8*(7*(15*a^2*b^2 - 20*a*b^3 + 8*b^4)*cosh(d*x + c)^5 + 10*(30*a^3*b - 55*a^2*b^2 + 36*a*b^3 - 8*b^4)*cosh(d*x + c)^3 + (120*a^4 - 280*a^3*b + 269*a^2*b^2 - 124*a*b^3 + 24*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(30*a^3*b - 55*a^2*b^2 + 36*a*b^3 - 8*b^4)*cosh(d*x + c)^2 + 4*(7*(15*a^2*b^2 - 20*a*b^3 + 8*b^4)*cosh(d*x + c)^6 + 15*(30*a^3*b - 55*a^2*b^2 + 36*a*b^3 - 8*b^4)*cosh(d*x + c)^4 + 30*a^3*b - 55*a^2*b^2 + 36*a*b^3 - 8*b^4 + 3*(120*a^4 - 280*a^3*b + 269*a^2*b^2 - 124*a*b^3 + 24*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((15*a^2*b^2 - 20*a*b^3 + 8*b^4)*cosh(d*x + c)^7 + 3*(30*a^3*b - 55*a^2*b^2 + 36*a*b^3 - 8*b^4)*cosh(d*x + c)^5 + (120*a^4 - 280*a^3*b + 269*a^2*b^2 - 124*a*b^3 + 24*b^4)*cosh(d*x + c)^3 + (30*a^3*b - 55*a^2*b^2 + 36*a*b^3 - 8*b^4)*cosh(d*x + c))*sinh(d*x + c))*sqrt(b/(a - b))*arctan(1/2*sqrt(b/(a - b))*(cosh(d*x + c) + sinh(d*x + c))) - ((15*a^2*b^2 - 20*a*b^3 + 8*b^4)*cosh(d*x + c)^8 + 8*(15*a^2*b^2 - 20*a*b^3 + 8*b^4)*cosh(d*x + c)*sinh(d*x + c)^7 + (15*a^2*b^2 - 20*a*b^3 + 8*b^4)*sinh(d*x + c)^8 + 4*(30*a^3*b - 55*a^2*b^2 + 36*a*b^3 - 8*b^4)*cosh(d*x + c)^6 + 4*(30*a^3*b - 55*a^2*b^2 + 36*a*b^3 - 8*b^4 + 7*(15*a^2*b^2 - 20*a*b^3 + 8*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(15*a^2*b^2 - 20*a*b^3 + 8*b^4)*cosh(d*x + c)^3 + 3*(30*a^3*b - 55*a^2*b^2 + 36*a*b^3 - 8*b^4)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(120*a^4 - 280*a^3*b + 269*a^2*b^2 - 124*a*b^3 + 24*b^4)*cosh(d*x + c)^4 + 2*(35*(15*a^2*b^2 - 20*a*b^3 + 8*b^4)*cosh(d*x + c)^4 + 120*a^4 - 280*a^3*b + 269*a^2*b^2 - 124*a*b^3 + 24*b^4 + 30*(30*a^3*b - 55*a^2*b^2 + 36*a*b^3 - 8*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 15*a^2*b^2 - 20*a*b^3 + 8*b^4 + 8*(7*(15*a^2*b^2 - 20*a*b^3 + 8*b^4)*cosh(d*x + c)^5 + 10*(30*a^3*b - 55*a^2*b^2 + 36*a*b^3 - 8*b^4)*cosh(d*x + c)^3 + (120*a^4 - 280*a^3*b + 269*a^2*b^2 - 124*a*b^3 + 24*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(30*a^3*b - 55*a^2*b^2 + 36*a*b^3 - 8*b^4)*cosh(d*x + c)^2 + 4*(7*(15*a^2*b^2 - 20*a*b^3 + 8*b^4)*cosh(d*x + c)^6 + 15*(30*a^3*b - 55*a^2*b^2 + 36*a*b^3 - 8*b^4)*cosh(d*x + c)^4 + 30*a^3*b - 55*a^2*b^2 + 36*a*b^3 - 8*b^4 + 3*(120*a^4 - 280*a^3*b + 269*a^2*b^2 - 124*a*b^3 + 24*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((15*a^2*b^2 - 20*a*b^3 + 8*b^4)*cosh(d*x + c)^7 + 3*(30*a^3*b - 55*a^2*b^2 + 36*a*b^3 - 8*b^4)*cosh(d*x + c)^5 + (120*a^4 - 280*a^3*b + 269*a^2*b^2 - 124*a*b^3 + 24*b^4)*cosh(d*x + c)^3 + (30*a^3*b - 55*a^2*b^2 + 36*a*b^3 - 8*b^4)*cosh(d*x + c))*sinh(d*x + c))*sqrt(b/(a - b))*arctan(1/2*(b*cosh(d*x + c)^3 + 3*b*cosh(d*x + c)*sinh(d*x + c)^2 + b*sinh(d*x + c)^3 + (4*a - 3*b)*cosh(d*x + c) + (3*b*cosh(d*x + c)^2 + 4*a - 3*b)*sinh(d*x + c))*sqrt(b/(a - b))/b) + 2*(7*a^2*b^2 - 4*a*b^3)*cosh(d*x + c) + 8*((a^2*b^2 - 2*a*b^3 + b^4)*cosh(d*x + c)^8 + 8*(a^2*b^2 - 2*a*b^3 + b^4)*cosh(d*x + c)*sinh(d*x + c)^7 + (a^2*b^2 - 2*a*b^3 + b^4)*sinh(d*x + c)^8 + 4*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*cosh(d*x + c)^6 + 4*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4 + 7*(a^2*b^2 - 2*a*b^3 + b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(a^2*b^2 - 2*a*b^3 + b^4)*cosh(d*x + c)^3 + 3*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(8*a^4 - 24*a^3*b + 27*a^2*b^2 - 14*a*b^3 + 3*b^4)*cosh(d*x + c)^4 + 2*(35*(a^2*b^2 - 2*a*b^3 + b^4)*cosh(d*x + c)^4 + 8*a^4 - 24*a^3*b + 27*a^2*b^2 - 14*a*b^3 + 3*b^4 + 30*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + a^2*b^2 - 2*a*b^3 + b^4 + 8*(7*(a^2*b^2 - 2*a*b^3 + b^4)*cosh(d*x + c)^5 + 10*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*cosh(d*x + c)^3 + (8*a^4 - 24*a^3*b + 27*a^2*b^2 - 14*a*b^3 + 3*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*cosh(d*x + c)^2 + 4*(7*(a^2*b^2 - 2*a*b^3 + b^4)*cosh(d*x + c)^6 + 15*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*cosh(d*x + c)^4 + 2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4 + 3*(8*a^4 - 24*a^3*b + 27*a^2*b^2 - 14*a*b^3 + 3*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((a^2*b^2 - 2*a*b^3 + b^4)*cosh(d*x + c)^7 + 3*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*cosh(d*x + c)^5 + (8*a^4 - 24*a^3*b + 27*a^2*b^2 - 14*a*b^3 + 3*b^4)*cosh(d*x + c)^3 + (2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) + 1) - 8*((a^2*b^2 - 2*a*b^3 + b^4)*cosh(d*x + c)^8 + 8*(a^2*b^2 - 2*a*b^3 + b^4)*cosh(d*x + c)*sinh(d*x + c)^7 + (a^2*b^2 - 2*a*b^3 + b^4)*sinh(d*x + c)^8 + 4*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*cosh(d*x + c)^6 + 4*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4 + 7*(a^2*b^2 - 2*a*b^3 + b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(a^2*b^2 - 2*a*b^3 + b^4)*cosh(d*x + c)^3 + 3*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(8*a^4 - 24*a^3*b + 27*a^2*b^2 - 14*a*b^3 + 3*b^4)*cosh(d*x + c)^4 + 2*(35*(a^2*b^2 - 2*a*b^3 + b^4)*cosh(d*x + c)^4 + 8*a^4 - 24*a^3*b + 27*a^2*b^2 - 14*a*b^3 + 3*b^4 + 30*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + a^2*b^2 - 2*a*b^3 + b^4 + 8*(7*(a^2*b^2 - 2*a*b^3 + b^4)*cosh(d*x + c)^5 + 10*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*cosh(d*x + c)^3 + (8*a^4 - 24*a^3*b + 27*a^2*b^2 - 14*a*b^3 + 3*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*cosh(d*x + c)^2 + 4*(7*(a^2*b^2 - 2*a*b^3 + b^4)*cosh(d*x + c)^6 + 15*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*cosh(d*x + c)^4 + 2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4 + 3*(8*a^4 - 24*a^3*b + 27*a^2*b^2 - 14*a*b^3 + 3*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((a^2*b^2 - 2*a*b^3 + b^4)*cosh(d*x + c)^7 + 3*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*cosh(d*x + c)^5 + (8*a^4 - 24*a^3*b + 27*a^2*b^2 - 14*a*b^3 + 3*b^4)*cosh(d*x + c)^3 + (2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) - 1) + 2*(7*(7*a^2*b^2 - 4*a*b^3)*cosh(d*x + c)^6 + 5*(36*a^3*b - 31*a^2*b^2 + 4*a*b^3)*cosh(d*x + c)^4 + 7*a^2*b^2 - 4*a*b^3 + 3*(36*a^3*b - 31*a^2*b^2 + 4*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c))/((a^5*b^2 - 2*a^4*b^3 + a^3*b^4)*d*cosh(d*x + c)^8 + 8*(a^5*b^2 - 2*a^4*b^3 + a^3*b^4)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^5*b^2 - 2*a^4*b^3 + a^3*b^4)*d*sinh(d*x + c)^8 + 4*(2*a^6*b - 5*a^5*b^2 + 4*a^4*b^3 - a^3*b^4)*d*cosh(d*x + c)^6 + 4*(7*(a^5*b^2 - 2*a^4*b^3 + a^3*b^4)*d*cosh(d*x + c)^2 + (2*a^6*b - 5*a^5*b^2 + 4*a^4*b^3 - a^3*b^4)*d)*sinh(d*x + c)^6 + 2*(8*a^7 - 24*a^6*b + 27*a^5*b^2 - 14*a^4*b^3 + 3*a^3*b^4)*d*cosh(d*x + c)^4 + 8*(7*(a^5*b^2 - 2*a^4*b^3 + a^3*b^4)*d*cosh(d*x + c)^3 + 3*(2*a^6*b - 5*a^5*b^2 + 4*a^4*b^3 - a^3*b^4)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^5*b^2 - 2*a^4*b^3 + a^3*b^4)*d*cosh(d*x + c)^4 + 30*(2*a^6*b - 5*a^5*b^2 + 4*a^4*b^3 - a^3*b^4)*d*cosh(d*x + c)^2 + (8*a^7 - 24*a^6*b + 27*a^5*b^2 - 14*a^4*b^3 + 3*a^3*b^4)*d)*sinh(d*x + c)^4 + 4*(2*a^6*b - 5*a^5*b^2 + 4*a^4*b^3 - a^3*b^4)*d*cosh(d*x + c)^2 + 8*(7*(a^5*b^2 - 2*a^4*b^3 + a^3*b^4)*d*cosh(d*x + c)^5 + 10*(2*a^6*b - 5*a^5*b^2 + 4*a^4*b^3 - a^3*b^4)*d*cosh(d*x + c)^3 + (8*a^7 - 24*a^6*b + 27*a^5*b^2 - 14*a^4*b^3 + 3*a^3*b^4)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^5*b^2 - 2*a^4*b^3 + a^3*b^4)*d*cosh(d*x + c)^6 + 15*(2*a^6*b - 5*a^5*b^2 + 4*a^4*b^3 - a^3*b^4)*d*cosh(d*x + c)^4 + 3*(8*a^7 - 24*a^6*b + 27*a^5*b^2 - 14*a^4*b^3 + 3*a^3*b^4)*d*cosh(d*x + c)^2 + (2*a^6*b - 5*a^5*b^2 + 4*a^4*b^3 - a^3*b^4)*d)*sinh(d*x + c)^2 + (a^5*b^2 - 2*a^4*b^3 + a^3*b^4)*d + 8*((a^5*b^2 - 2*a^4*b^3 + a^3*b^4)*d*cosh(d*x + c)^7 + 3*(2*a^6*b - 5*a^5*b^2 + 4*a^4*b^3 - a^3*b^4)*d*cosh(d*x + c)^5 + (8*a^7 - 24*a^6*b + 27*a^5*b^2 - 14*a^4*b^3 + 3*a^3*b^4)*d*cosh(d*x + c)^3 + (2*a^6*b - 5*a^5*b^2 + 4*a^4*b^3 - a^3*b^4)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
57,1,9102,0,0.958697," ","integrate(csch(d*x+c)^2/(a+b*sinh(d*x+c)^2)^3,x, algorithm=""fricas"")","\left[-\frac{12 \, {\left(8 \, a^{4} b^{2} - 20 \, a^{3} b^{3} + 17 \, a^{2} b^{4} - 5 \, a b^{5}\right)} \cosh\left(d x + c\right)^{8} + 96 \, {\left(8 \, a^{4} b^{2} - 20 \, a^{3} b^{3} + 17 \, a^{2} b^{4} - 5 \, a b^{5}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + 12 \, {\left(8 \, a^{4} b^{2} - 20 \, a^{3} b^{3} + 17 \, a^{2} b^{4} - 5 \, a b^{5}\right)} \sinh\left(d x + c\right)^{8} + 24 \, {\left(24 \, a^{5} b - 76 \, a^{4} b^{2} + 91 \, a^{3} b^{3} - 49 \, a^{2} b^{4} + 10 \, a b^{5}\right)} \cosh\left(d x + c\right)^{6} + 24 \, {\left(24 \, a^{5} b - 76 \, a^{4} b^{2} + 91 \, a^{3} b^{3} - 49 \, a^{2} b^{4} + 10 \, a b^{5} + 14 \, {\left(8 \, a^{4} b^{2} - 20 \, a^{3} b^{3} + 17 \, a^{2} b^{4} - 5 \, a b^{5}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 32 \, a^{4} b^{2} - 136 \, a^{3} b^{3} + 164 \, a^{2} b^{4} - 60 \, a b^{5} + 48 \, {\left(14 \, {\left(8 \, a^{4} b^{2} - 20 \, a^{3} b^{3} + 17 \, a^{2} b^{4} - 5 \, a b^{5}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(24 \, a^{5} b - 76 \, a^{4} b^{2} + 91 \, a^{3} b^{3} - 49 \, a^{2} b^{4} + 10 \, a b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 8 \, {\left(64 \, a^{6} - 296 \, a^{5} b + 548 \, a^{4} b^{2} - 509 \, a^{3} b^{3} + 238 \, a^{2} b^{4} - 45 \, a b^{5}\right)} \cosh\left(d x + c\right)^{4} + 8 \, {\left(64 \, a^{6} - 296 \, a^{5} b + 548 \, a^{4} b^{2} - 509 \, a^{3} b^{3} + 238 \, a^{2} b^{4} - 45 \, a b^{5} + 105 \, {\left(8 \, a^{4} b^{2} - 20 \, a^{3} b^{3} + 17 \, a^{2} b^{4} - 5 \, a b^{5}\right)} \cosh\left(d x + c\right)^{4} + 45 \, {\left(24 \, a^{5} b - 76 \, a^{4} b^{2} + 91 \, a^{3} b^{3} - 49 \, a^{2} b^{4} + 10 \, a b^{5}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 32 \, {\left(21 \, {\left(8 \, a^{4} b^{2} - 20 \, a^{3} b^{3} + 17 \, a^{2} b^{4} - 5 \, a b^{5}\right)} \cosh\left(d x + c\right)^{5} + 15 \, {\left(24 \, a^{5} b - 76 \, a^{4} b^{2} + 91 \, a^{3} b^{3} - 49 \, a^{2} b^{4} + 10 \, a b^{5}\right)} \cosh\left(d x + c\right)^{3} + {\left(64 \, a^{6} - 296 \, a^{5} b + 548 \, a^{4} b^{2} - 509 \, a^{3} b^{3} + 238 \, a^{2} b^{4} - 45 \, a b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 8 \, {\left(32 \, a^{5} b - 144 \, a^{4} b^{2} + 219 \, a^{3} b^{3} - 137 \, a^{2} b^{4} + 30 \, a b^{5}\right)} \cosh\left(d x + c\right)^{2} + 8 \, {\left(42 \, {\left(8 \, a^{4} b^{2} - 20 \, a^{3} b^{3} + 17 \, a^{2} b^{4} - 5 \, a b^{5}\right)} \cosh\left(d x + c\right)^{6} + 32 \, a^{5} b - 144 \, a^{4} b^{2} + 219 \, a^{3} b^{3} - 137 \, a^{2} b^{4} + 30 \, a b^{5} + 45 \, {\left(24 \, a^{5} b - 76 \, a^{4} b^{2} + 91 \, a^{3} b^{3} - 49 \, a^{2} b^{4} + 10 \, a b^{5}\right)} \cosh\left(d x + c\right)^{4} + 6 \, {\left(64 \, a^{6} - 296 \, a^{5} b + 548 \, a^{4} b^{2} - 509 \, a^{3} b^{3} + 238 \, a^{2} b^{4} - 45 \, a b^{5}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} - 3 \, {\left({\left(8 \, a^{2} b^{3} - 12 \, a b^{4} + 5 \, b^{5}\right)} \cosh\left(d x + c\right)^{10} + 10 \, {\left(8 \, a^{2} b^{3} - 12 \, a b^{4} + 5 \, b^{5}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + {\left(8 \, a^{2} b^{3} - 12 \, a b^{4} + 5 \, b^{5}\right)} \sinh\left(d x + c\right)^{10} + {\left(64 \, a^{3} b^{2} - 136 \, a^{2} b^{3} + 100 \, a b^{4} - 25 \, b^{5}\right)} \cosh\left(d x + c\right)^{8} + {\left(64 \, a^{3} b^{2} - 136 \, a^{2} b^{3} + 100 \, a b^{4} - 25 \, b^{5} + 45 \, {\left(8 \, a^{2} b^{3} - 12 \, a b^{4} + 5 \, b^{5}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{8} + 8 \, {\left(15 \, {\left(8 \, a^{2} b^{3} - 12 \, a b^{4} + 5 \, b^{5}\right)} \cosh\left(d x + c\right)^{3} + {\left(64 \, a^{3} b^{2} - 136 \, a^{2} b^{3} + 100 \, a b^{4} - 25 \, b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(64 \, a^{4} b - 192 \, a^{3} b^{2} + 224 \, a^{2} b^{3} - 120 \, a b^{4} + 25 \, b^{5}\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(64 \, a^{4} b - 192 \, a^{3} b^{2} + 224 \, a^{2} b^{3} - 120 \, a b^{4} + 25 \, b^{5} + 105 \, {\left(8 \, a^{2} b^{3} - 12 \, a b^{4} + 5 \, b^{5}\right)} \cosh\left(d x + c\right)^{4} + 14 \, {\left(64 \, a^{3} b^{2} - 136 \, a^{2} b^{3} + 100 \, a b^{4} - 25 \, b^{5}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(63 \, {\left(8 \, a^{2} b^{3} - 12 \, a b^{4} + 5 \, b^{5}\right)} \cosh\left(d x + c\right)^{5} + 14 \, {\left(64 \, a^{3} b^{2} - 136 \, a^{2} b^{3} + 100 \, a b^{4} - 25 \, b^{5}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(64 \, a^{4} b - 192 \, a^{3} b^{2} + 224 \, a^{2} b^{3} - 120 \, a b^{4} + 25 \, b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 8 \, a^{2} b^{3} + 12 \, a b^{4} - 5 \, b^{5} - 2 \, {\left(64 \, a^{4} b - 192 \, a^{3} b^{2} + 224 \, a^{2} b^{3} - 120 \, a b^{4} + 25 \, b^{5}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(105 \, {\left(8 \, a^{2} b^{3} - 12 \, a b^{4} + 5 \, b^{5}\right)} \cosh\left(d x + c\right)^{6} - 64 \, a^{4} b + 192 \, a^{3} b^{2} - 224 \, a^{2} b^{3} + 120 \, a b^{4} - 25 \, b^{5} + 35 \, {\left(64 \, a^{3} b^{2} - 136 \, a^{2} b^{3} + 100 \, a b^{4} - 25 \, b^{5}\right)} \cosh\left(d x + c\right)^{4} + 15 \, {\left(64 \, a^{4} b - 192 \, a^{3} b^{2} + 224 \, a^{2} b^{3} - 120 \, a b^{4} + 25 \, b^{5}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(15 \, {\left(8 \, a^{2} b^{3} - 12 \, a b^{4} + 5 \, b^{5}\right)} \cosh\left(d x + c\right)^{7} + 7 \, {\left(64 \, a^{3} b^{2} - 136 \, a^{2} b^{3} + 100 \, a b^{4} - 25 \, b^{5}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(64 \, a^{4} b - 192 \, a^{3} b^{2} + 224 \, a^{2} b^{3} - 120 \, a b^{4} + 25 \, b^{5}\right)} \cosh\left(d x + c\right)^{3} - {\left(64 \, a^{4} b - 192 \, a^{3} b^{2} + 224 \, a^{2} b^{3} - 120 \, a b^{4} + 25 \, b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - {\left(64 \, a^{3} b^{2} - 136 \, a^{2} b^{3} + 100 \, a b^{4} - 25 \, b^{5}\right)} \cosh\left(d x + c\right)^{2} + {\left(45 \, {\left(8 \, a^{2} b^{3} - 12 \, a b^{4} + 5 \, b^{5}\right)} \cosh\left(d x + c\right)^{8} + 28 \, {\left(64 \, a^{3} b^{2} - 136 \, a^{2} b^{3} + 100 \, a b^{4} - 25 \, b^{5}\right)} \cosh\left(d x + c\right)^{6} - 64 \, a^{3} b^{2} + 136 \, a^{2} b^{3} - 100 \, a b^{4} + 25 \, b^{5} + 30 \, {\left(64 \, a^{4} b - 192 \, a^{3} b^{2} + 224 \, a^{2} b^{3} - 120 \, a b^{4} + 25 \, b^{5}\right)} \cosh\left(d x + c\right)^{4} - 12 \, {\left(64 \, a^{4} b - 192 \, a^{3} b^{2} + 224 \, a^{2} b^{3} - 120 \, a b^{4} + 25 \, b^{5}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(5 \, {\left(8 \, a^{2} b^{3} - 12 \, a b^{4} + 5 \, b^{5}\right)} \cosh\left(d x + c\right)^{9} + 4 \, {\left(64 \, a^{3} b^{2} - 136 \, a^{2} b^{3} + 100 \, a b^{4} - 25 \, b^{5}\right)} \cosh\left(d x + c\right)^{7} + 6 \, {\left(64 \, a^{4} b - 192 \, a^{3} b^{2} + 224 \, a^{2} b^{3} - 120 \, a b^{4} + 25 \, b^{5}\right)} \cosh\left(d x + c\right)^{5} - 4 \, {\left(64 \, a^{4} b - 192 \, a^{3} b^{2} + 224 \, a^{2} b^{3} - 120 \, a b^{4} + 25 \, b^{5}\right)} \cosh\left(d x + c\right)^{3} - {\left(64 \, a^{3} b^{2} - 136 \, a^{2} b^{3} + 100 \, a b^{4} - 25 \, b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{a^{2} - a b} \log\left(\frac{b^{2} \cosh\left(d x + c\right)^{4} + 4 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{2} \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(d x + c\right)^{2} + 2 \, a b - b^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, a^{2} - 8 \, a b + b^{2} + 4 \, {\left(b^{2} \cosh\left(d x + c\right)^{3} + {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + 4 \, {\left(b \cosh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b \sinh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sqrt{a^{2} - a b}}{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b}\right) + 16 \, {\left(6 \, {\left(8 \, a^{4} b^{2} - 20 \, a^{3} b^{3} + 17 \, a^{2} b^{4} - 5 \, a b^{5}\right)} \cosh\left(d x + c\right)^{7} + 9 \, {\left(24 \, a^{5} b - 76 \, a^{4} b^{2} + 91 \, a^{3} b^{3} - 49 \, a^{2} b^{4} + 10 \, a b^{5}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(64 \, a^{6} - 296 \, a^{5} b + 548 \, a^{4} b^{2} - 509 \, a^{3} b^{3} + 238 \, a^{2} b^{4} - 45 \, a b^{5}\right)} \cosh\left(d x + c\right)^{3} + {\left(32 \, a^{5} b - 144 \, a^{4} b^{2} + 219 \, a^{3} b^{3} - 137 \, a^{2} b^{4} + 30 \, a b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{16 \, {\left({\left(a^{7} b^{2} - 3 \, a^{6} b^{3} + 3 \, a^{5} b^{4} - a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{10} + 10 \, {\left(a^{7} b^{2} - 3 \, a^{6} b^{3} + 3 \, a^{5} b^{4} - a^{4} b^{5}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + {\left(a^{7} b^{2} - 3 \, a^{6} b^{3} + 3 \, a^{5} b^{4} - a^{4} b^{5}\right)} d \sinh\left(d x + c\right)^{10} + {\left(8 \, a^{8} b - 29 \, a^{7} b^{2} + 39 \, a^{6} b^{3} - 23 \, a^{5} b^{4} + 5 \, a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{8} + {\left(45 \, {\left(a^{7} b^{2} - 3 \, a^{6} b^{3} + 3 \, a^{5} b^{4} - a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(8 \, a^{8} b - 29 \, a^{7} b^{2} + 39 \, a^{6} b^{3} - 23 \, a^{5} b^{4} + 5 \, a^{4} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{8} + 2 \, {\left(8 \, a^{9} - 36 \, a^{8} b + 65 \, a^{7} b^{2} - 59 \, a^{6} b^{3} + 27 \, a^{5} b^{4} - 5 \, a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{6} + 8 \, {\left(15 \, {\left(a^{7} b^{2} - 3 \, a^{6} b^{3} + 3 \, a^{5} b^{4} - a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{8} b - 29 \, a^{7} b^{2} + 39 \, a^{6} b^{3} - 23 \, a^{5} b^{4} + 5 \, a^{4} b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(105 \, {\left(a^{7} b^{2} - 3 \, a^{6} b^{3} + 3 \, a^{5} b^{4} - a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 14 \, {\left(8 \, a^{8} b - 29 \, a^{7} b^{2} + 39 \, a^{6} b^{3} - 23 \, a^{5} b^{4} + 5 \, a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(8 \, a^{9} - 36 \, a^{8} b + 65 \, a^{7} b^{2} - 59 \, a^{6} b^{3} + 27 \, a^{5} b^{4} - 5 \, a^{4} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{6} - 2 \, {\left(8 \, a^{9} - 36 \, a^{8} b + 65 \, a^{7} b^{2} - 59 \, a^{6} b^{3} + 27 \, a^{5} b^{4} - 5 \, a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(63 \, {\left(a^{7} b^{2} - 3 \, a^{6} b^{3} + 3 \, a^{5} b^{4} - a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{5} + 14 \, {\left(8 \, a^{8} b - 29 \, a^{7} b^{2} + 39 \, a^{6} b^{3} - 23 \, a^{5} b^{4} + 5 \, a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(8 \, a^{9} - 36 \, a^{8} b + 65 \, a^{7} b^{2} - 59 \, a^{6} b^{3} + 27 \, a^{5} b^{4} - 5 \, a^{4} b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(105 \, {\left(a^{7} b^{2} - 3 \, a^{6} b^{3} + 3 \, a^{5} b^{4} - a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{6} + 35 \, {\left(8 \, a^{8} b - 29 \, a^{7} b^{2} + 39 \, a^{6} b^{3} - 23 \, a^{5} b^{4} + 5 \, a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 15 \, {\left(8 \, a^{9} - 36 \, a^{8} b + 65 \, a^{7} b^{2} - 59 \, a^{6} b^{3} + 27 \, a^{5} b^{4} - 5 \, a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{2} - {\left(8 \, a^{9} - 36 \, a^{8} b + 65 \, a^{7} b^{2} - 59 \, a^{6} b^{3} + 27 \, a^{5} b^{4} - 5 \, a^{4} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{4} - {\left(8 \, a^{8} b - 29 \, a^{7} b^{2} + 39 \, a^{6} b^{3} - 23 \, a^{5} b^{4} + 5 \, a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(15 \, {\left(a^{7} b^{2} - 3 \, a^{6} b^{3} + 3 \, a^{5} b^{4} - a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{7} + 7 \, {\left(8 \, a^{8} b - 29 \, a^{7} b^{2} + 39 \, a^{6} b^{3} - 23 \, a^{5} b^{4} + 5 \, a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{5} + 5 \, {\left(8 \, a^{9} - 36 \, a^{8} b + 65 \, a^{7} b^{2} - 59 \, a^{6} b^{3} + 27 \, a^{5} b^{4} - 5 \, a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{3} - {\left(8 \, a^{9} - 36 \, a^{8} b + 65 \, a^{7} b^{2} - 59 \, a^{6} b^{3} + 27 \, a^{5} b^{4} - 5 \, a^{4} b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(45 \, {\left(a^{7} b^{2} - 3 \, a^{6} b^{3} + 3 \, a^{5} b^{4} - a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{8} + 28 \, {\left(8 \, a^{8} b - 29 \, a^{7} b^{2} + 39 \, a^{6} b^{3} - 23 \, a^{5} b^{4} + 5 \, a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{6} + 30 \, {\left(8 \, a^{9} - 36 \, a^{8} b + 65 \, a^{7} b^{2} - 59 \, a^{6} b^{3} + 27 \, a^{5} b^{4} - 5 \, a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{4} - 12 \, {\left(8 \, a^{9} - 36 \, a^{8} b + 65 \, a^{7} b^{2} - 59 \, a^{6} b^{3} + 27 \, a^{5} b^{4} - 5 \, a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{2} - {\left(8 \, a^{8} b - 29 \, a^{7} b^{2} + 39 \, a^{6} b^{3} - 23 \, a^{5} b^{4} + 5 \, a^{4} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{2} - {\left(a^{7} b^{2} - 3 \, a^{6} b^{3} + 3 \, a^{5} b^{4} - a^{4} b^{5}\right)} d + 2 \, {\left(5 \, {\left(a^{7} b^{2} - 3 \, a^{6} b^{3} + 3 \, a^{5} b^{4} - a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{9} + 4 \, {\left(8 \, a^{8} b - 29 \, a^{7} b^{2} + 39 \, a^{6} b^{3} - 23 \, a^{5} b^{4} + 5 \, a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{7} + 6 \, {\left(8 \, a^{9} - 36 \, a^{8} b + 65 \, a^{7} b^{2} - 59 \, a^{6} b^{3} + 27 \, a^{5} b^{4} - 5 \, a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{5} - 4 \, {\left(8 \, a^{9} - 36 \, a^{8} b + 65 \, a^{7} b^{2} - 59 \, a^{6} b^{3} + 27 \, a^{5} b^{4} - 5 \, a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{3} - {\left(8 \, a^{8} b - 29 \, a^{7} b^{2} + 39 \, a^{6} b^{3} - 23 \, a^{5} b^{4} + 5 \, a^{4} b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}, -\frac{6 \, {\left(8 \, a^{4} b^{2} - 20 \, a^{3} b^{3} + 17 \, a^{2} b^{4} - 5 \, a b^{5}\right)} \cosh\left(d x + c\right)^{8} + 48 \, {\left(8 \, a^{4} b^{2} - 20 \, a^{3} b^{3} + 17 \, a^{2} b^{4} - 5 \, a b^{5}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + 6 \, {\left(8 \, a^{4} b^{2} - 20 \, a^{3} b^{3} + 17 \, a^{2} b^{4} - 5 \, a b^{5}\right)} \sinh\left(d x + c\right)^{8} + 12 \, {\left(24 \, a^{5} b - 76 \, a^{4} b^{2} + 91 \, a^{3} b^{3} - 49 \, a^{2} b^{4} + 10 \, a b^{5}\right)} \cosh\left(d x + c\right)^{6} + 12 \, {\left(24 \, a^{5} b - 76 \, a^{4} b^{2} + 91 \, a^{3} b^{3} - 49 \, a^{2} b^{4} + 10 \, a b^{5} + 14 \, {\left(8 \, a^{4} b^{2} - 20 \, a^{3} b^{3} + 17 \, a^{2} b^{4} - 5 \, a b^{5}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 16 \, a^{4} b^{2} - 68 \, a^{3} b^{3} + 82 \, a^{2} b^{4} - 30 \, a b^{5} + 24 \, {\left(14 \, {\left(8 \, a^{4} b^{2} - 20 \, a^{3} b^{3} + 17 \, a^{2} b^{4} - 5 \, a b^{5}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(24 \, a^{5} b - 76 \, a^{4} b^{2} + 91 \, a^{3} b^{3} - 49 \, a^{2} b^{4} + 10 \, a b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 4 \, {\left(64 \, a^{6} - 296 \, a^{5} b + 548 \, a^{4} b^{2} - 509 \, a^{3} b^{3} + 238 \, a^{2} b^{4} - 45 \, a b^{5}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(64 \, a^{6} - 296 \, a^{5} b + 548 \, a^{4} b^{2} - 509 \, a^{3} b^{3} + 238 \, a^{2} b^{4} - 45 \, a b^{5} + 105 \, {\left(8 \, a^{4} b^{2} - 20 \, a^{3} b^{3} + 17 \, a^{2} b^{4} - 5 \, a b^{5}\right)} \cosh\left(d x + c\right)^{4} + 45 \, {\left(24 \, a^{5} b - 76 \, a^{4} b^{2} + 91 \, a^{3} b^{3} - 49 \, a^{2} b^{4} + 10 \, a b^{5}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 16 \, {\left(21 \, {\left(8 \, a^{4} b^{2} - 20 \, a^{3} b^{3} + 17 \, a^{2} b^{4} - 5 \, a b^{5}\right)} \cosh\left(d x + c\right)^{5} + 15 \, {\left(24 \, a^{5} b - 76 \, a^{4} b^{2} + 91 \, a^{3} b^{3} - 49 \, a^{2} b^{4} + 10 \, a b^{5}\right)} \cosh\left(d x + c\right)^{3} + {\left(64 \, a^{6} - 296 \, a^{5} b + 548 \, a^{4} b^{2} - 509 \, a^{3} b^{3} + 238 \, a^{2} b^{4} - 45 \, a b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(32 \, a^{5} b - 144 \, a^{4} b^{2} + 219 \, a^{3} b^{3} - 137 \, a^{2} b^{4} + 30 \, a b^{5}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(42 \, {\left(8 \, a^{4} b^{2} - 20 \, a^{3} b^{3} + 17 \, a^{2} b^{4} - 5 \, a b^{5}\right)} \cosh\left(d x + c\right)^{6} + 32 \, a^{5} b - 144 \, a^{4} b^{2} + 219 \, a^{3} b^{3} - 137 \, a^{2} b^{4} + 30 \, a b^{5} + 45 \, {\left(24 \, a^{5} b - 76 \, a^{4} b^{2} + 91 \, a^{3} b^{3} - 49 \, a^{2} b^{4} + 10 \, a b^{5}\right)} \cosh\left(d x + c\right)^{4} + 6 \, {\left(64 \, a^{6} - 296 \, a^{5} b + 548 \, a^{4} b^{2} - 509 \, a^{3} b^{3} + 238 \, a^{2} b^{4} - 45 \, a b^{5}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} - 3 \, {\left({\left(8 \, a^{2} b^{3} - 12 \, a b^{4} + 5 \, b^{5}\right)} \cosh\left(d x + c\right)^{10} + 10 \, {\left(8 \, a^{2} b^{3} - 12 \, a b^{4} + 5 \, b^{5}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + {\left(8 \, a^{2} b^{3} - 12 \, a b^{4} + 5 \, b^{5}\right)} \sinh\left(d x + c\right)^{10} + {\left(64 \, a^{3} b^{2} - 136 \, a^{2} b^{3} + 100 \, a b^{4} - 25 \, b^{5}\right)} \cosh\left(d x + c\right)^{8} + {\left(64 \, a^{3} b^{2} - 136 \, a^{2} b^{3} + 100 \, a b^{4} - 25 \, b^{5} + 45 \, {\left(8 \, a^{2} b^{3} - 12 \, a b^{4} + 5 \, b^{5}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{8} + 8 \, {\left(15 \, {\left(8 \, a^{2} b^{3} - 12 \, a b^{4} + 5 \, b^{5}\right)} \cosh\left(d x + c\right)^{3} + {\left(64 \, a^{3} b^{2} - 136 \, a^{2} b^{3} + 100 \, a b^{4} - 25 \, b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(64 \, a^{4} b - 192 \, a^{3} b^{2} + 224 \, a^{2} b^{3} - 120 \, a b^{4} + 25 \, b^{5}\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(64 \, a^{4} b - 192 \, a^{3} b^{2} + 224 \, a^{2} b^{3} - 120 \, a b^{4} + 25 \, b^{5} + 105 \, {\left(8 \, a^{2} b^{3} - 12 \, a b^{4} + 5 \, b^{5}\right)} \cosh\left(d x + c\right)^{4} + 14 \, {\left(64 \, a^{3} b^{2} - 136 \, a^{2} b^{3} + 100 \, a b^{4} - 25 \, b^{5}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(63 \, {\left(8 \, a^{2} b^{3} - 12 \, a b^{4} + 5 \, b^{5}\right)} \cosh\left(d x + c\right)^{5} + 14 \, {\left(64 \, a^{3} b^{2} - 136 \, a^{2} b^{3} + 100 \, a b^{4} - 25 \, b^{5}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(64 \, a^{4} b - 192 \, a^{3} b^{2} + 224 \, a^{2} b^{3} - 120 \, a b^{4} + 25 \, b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 8 \, a^{2} b^{3} + 12 \, a b^{4} - 5 \, b^{5} - 2 \, {\left(64 \, a^{4} b - 192 \, a^{3} b^{2} + 224 \, a^{2} b^{3} - 120 \, a b^{4} + 25 \, b^{5}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(105 \, {\left(8 \, a^{2} b^{3} - 12 \, a b^{4} + 5 \, b^{5}\right)} \cosh\left(d x + c\right)^{6} - 64 \, a^{4} b + 192 \, a^{3} b^{2} - 224 \, a^{2} b^{3} + 120 \, a b^{4} - 25 \, b^{5} + 35 \, {\left(64 \, a^{3} b^{2} - 136 \, a^{2} b^{3} + 100 \, a b^{4} - 25 \, b^{5}\right)} \cosh\left(d x + c\right)^{4} + 15 \, {\left(64 \, a^{4} b - 192 \, a^{3} b^{2} + 224 \, a^{2} b^{3} - 120 \, a b^{4} + 25 \, b^{5}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(15 \, {\left(8 \, a^{2} b^{3} - 12 \, a b^{4} + 5 \, b^{5}\right)} \cosh\left(d x + c\right)^{7} + 7 \, {\left(64 \, a^{3} b^{2} - 136 \, a^{2} b^{3} + 100 \, a b^{4} - 25 \, b^{5}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(64 \, a^{4} b - 192 \, a^{3} b^{2} + 224 \, a^{2} b^{3} - 120 \, a b^{4} + 25 \, b^{5}\right)} \cosh\left(d x + c\right)^{3} - {\left(64 \, a^{4} b - 192 \, a^{3} b^{2} + 224 \, a^{2} b^{3} - 120 \, a b^{4} + 25 \, b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - {\left(64 \, a^{3} b^{2} - 136 \, a^{2} b^{3} + 100 \, a b^{4} - 25 \, b^{5}\right)} \cosh\left(d x + c\right)^{2} + {\left(45 \, {\left(8 \, a^{2} b^{3} - 12 \, a b^{4} + 5 \, b^{5}\right)} \cosh\left(d x + c\right)^{8} + 28 \, {\left(64 \, a^{3} b^{2} - 136 \, a^{2} b^{3} + 100 \, a b^{4} - 25 \, b^{5}\right)} \cosh\left(d x + c\right)^{6} - 64 \, a^{3} b^{2} + 136 \, a^{2} b^{3} - 100 \, a b^{4} + 25 \, b^{5} + 30 \, {\left(64 \, a^{4} b - 192 \, a^{3} b^{2} + 224 \, a^{2} b^{3} - 120 \, a b^{4} + 25 \, b^{5}\right)} \cosh\left(d x + c\right)^{4} - 12 \, {\left(64 \, a^{4} b - 192 \, a^{3} b^{2} + 224 \, a^{2} b^{3} - 120 \, a b^{4} + 25 \, b^{5}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(5 \, {\left(8 \, a^{2} b^{3} - 12 \, a b^{4} + 5 \, b^{5}\right)} \cosh\left(d x + c\right)^{9} + 4 \, {\left(64 \, a^{3} b^{2} - 136 \, a^{2} b^{3} + 100 \, a b^{4} - 25 \, b^{5}\right)} \cosh\left(d x + c\right)^{7} + 6 \, {\left(64 \, a^{4} b - 192 \, a^{3} b^{2} + 224 \, a^{2} b^{3} - 120 \, a b^{4} + 25 \, b^{5}\right)} \cosh\left(d x + c\right)^{5} - 4 \, {\left(64 \, a^{4} b - 192 \, a^{3} b^{2} + 224 \, a^{2} b^{3} - 120 \, a b^{4} + 25 \, b^{5}\right)} \cosh\left(d x + c\right)^{3} - {\left(64 \, a^{3} b^{2} - 136 \, a^{2} b^{3} + 100 \, a b^{4} - 25 \, b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-a^{2} + a b} \arctan\left(-\frac{{\left(b \cosh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b \sinh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sqrt{-a^{2} + a b}}{2 \, {\left(a^{2} - a b\right)}}\right) + 8 \, {\left(6 \, {\left(8 \, a^{4} b^{2} - 20 \, a^{3} b^{3} + 17 \, a^{2} b^{4} - 5 \, a b^{5}\right)} \cosh\left(d x + c\right)^{7} + 9 \, {\left(24 \, a^{5} b - 76 \, a^{4} b^{2} + 91 \, a^{3} b^{3} - 49 \, a^{2} b^{4} + 10 \, a b^{5}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(64 \, a^{6} - 296 \, a^{5} b + 548 \, a^{4} b^{2} - 509 \, a^{3} b^{3} + 238 \, a^{2} b^{4} - 45 \, a b^{5}\right)} \cosh\left(d x + c\right)^{3} + {\left(32 \, a^{5} b - 144 \, a^{4} b^{2} + 219 \, a^{3} b^{3} - 137 \, a^{2} b^{4} + 30 \, a b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{8 \, {\left({\left(a^{7} b^{2} - 3 \, a^{6} b^{3} + 3 \, a^{5} b^{4} - a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{10} + 10 \, {\left(a^{7} b^{2} - 3 \, a^{6} b^{3} + 3 \, a^{5} b^{4} - a^{4} b^{5}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + {\left(a^{7} b^{2} - 3 \, a^{6} b^{3} + 3 \, a^{5} b^{4} - a^{4} b^{5}\right)} d \sinh\left(d x + c\right)^{10} + {\left(8 \, a^{8} b - 29 \, a^{7} b^{2} + 39 \, a^{6} b^{3} - 23 \, a^{5} b^{4} + 5 \, a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{8} + {\left(45 \, {\left(a^{7} b^{2} - 3 \, a^{6} b^{3} + 3 \, a^{5} b^{4} - a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(8 \, a^{8} b - 29 \, a^{7} b^{2} + 39 \, a^{6} b^{3} - 23 \, a^{5} b^{4} + 5 \, a^{4} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{8} + 2 \, {\left(8 \, a^{9} - 36 \, a^{8} b + 65 \, a^{7} b^{2} - 59 \, a^{6} b^{3} + 27 \, a^{5} b^{4} - 5 \, a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{6} + 8 \, {\left(15 \, {\left(a^{7} b^{2} - 3 \, a^{6} b^{3} + 3 \, a^{5} b^{4} - a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{8} b - 29 \, a^{7} b^{2} + 39 \, a^{6} b^{3} - 23 \, a^{5} b^{4} + 5 \, a^{4} b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(105 \, {\left(a^{7} b^{2} - 3 \, a^{6} b^{3} + 3 \, a^{5} b^{4} - a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 14 \, {\left(8 \, a^{8} b - 29 \, a^{7} b^{2} + 39 \, a^{6} b^{3} - 23 \, a^{5} b^{4} + 5 \, a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(8 \, a^{9} - 36 \, a^{8} b + 65 \, a^{7} b^{2} - 59 \, a^{6} b^{3} + 27 \, a^{5} b^{4} - 5 \, a^{4} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{6} - 2 \, {\left(8 \, a^{9} - 36 \, a^{8} b + 65 \, a^{7} b^{2} - 59 \, a^{6} b^{3} + 27 \, a^{5} b^{4} - 5 \, a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(63 \, {\left(a^{7} b^{2} - 3 \, a^{6} b^{3} + 3 \, a^{5} b^{4} - a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{5} + 14 \, {\left(8 \, a^{8} b - 29 \, a^{7} b^{2} + 39 \, a^{6} b^{3} - 23 \, a^{5} b^{4} + 5 \, a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(8 \, a^{9} - 36 \, a^{8} b + 65 \, a^{7} b^{2} - 59 \, a^{6} b^{3} + 27 \, a^{5} b^{4} - 5 \, a^{4} b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(105 \, {\left(a^{7} b^{2} - 3 \, a^{6} b^{3} + 3 \, a^{5} b^{4} - a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{6} + 35 \, {\left(8 \, a^{8} b - 29 \, a^{7} b^{2} + 39 \, a^{6} b^{3} - 23 \, a^{5} b^{4} + 5 \, a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 15 \, {\left(8 \, a^{9} - 36 \, a^{8} b + 65 \, a^{7} b^{2} - 59 \, a^{6} b^{3} + 27 \, a^{5} b^{4} - 5 \, a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{2} - {\left(8 \, a^{9} - 36 \, a^{8} b + 65 \, a^{7} b^{2} - 59 \, a^{6} b^{3} + 27 \, a^{5} b^{4} - 5 \, a^{4} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{4} - {\left(8 \, a^{8} b - 29 \, a^{7} b^{2} + 39 \, a^{6} b^{3} - 23 \, a^{5} b^{4} + 5 \, a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(15 \, {\left(a^{7} b^{2} - 3 \, a^{6} b^{3} + 3 \, a^{5} b^{4} - a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{7} + 7 \, {\left(8 \, a^{8} b - 29 \, a^{7} b^{2} + 39 \, a^{6} b^{3} - 23 \, a^{5} b^{4} + 5 \, a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{5} + 5 \, {\left(8 \, a^{9} - 36 \, a^{8} b + 65 \, a^{7} b^{2} - 59 \, a^{6} b^{3} + 27 \, a^{5} b^{4} - 5 \, a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{3} - {\left(8 \, a^{9} - 36 \, a^{8} b + 65 \, a^{7} b^{2} - 59 \, a^{6} b^{3} + 27 \, a^{5} b^{4} - 5 \, a^{4} b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(45 \, {\left(a^{7} b^{2} - 3 \, a^{6} b^{3} + 3 \, a^{5} b^{4} - a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{8} + 28 \, {\left(8 \, a^{8} b - 29 \, a^{7} b^{2} + 39 \, a^{6} b^{3} - 23 \, a^{5} b^{4} + 5 \, a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{6} + 30 \, {\left(8 \, a^{9} - 36 \, a^{8} b + 65 \, a^{7} b^{2} - 59 \, a^{6} b^{3} + 27 \, a^{5} b^{4} - 5 \, a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{4} - 12 \, {\left(8 \, a^{9} - 36 \, a^{8} b + 65 \, a^{7} b^{2} - 59 \, a^{6} b^{3} + 27 \, a^{5} b^{4} - 5 \, a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{2} - {\left(8 \, a^{8} b - 29 \, a^{7} b^{2} + 39 \, a^{6} b^{3} - 23 \, a^{5} b^{4} + 5 \, a^{4} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{2} - {\left(a^{7} b^{2} - 3 \, a^{6} b^{3} + 3 \, a^{5} b^{4} - a^{4} b^{5}\right)} d + 2 \, {\left(5 \, {\left(a^{7} b^{2} - 3 \, a^{6} b^{3} + 3 \, a^{5} b^{4} - a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{9} + 4 \, {\left(8 \, a^{8} b - 29 \, a^{7} b^{2} + 39 \, a^{6} b^{3} - 23 \, a^{5} b^{4} + 5 \, a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{7} + 6 \, {\left(8 \, a^{9} - 36 \, a^{8} b + 65 \, a^{7} b^{2} - 59 \, a^{6} b^{3} + 27 \, a^{5} b^{4} - 5 \, a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{5} - 4 \, {\left(8 \, a^{9} - 36 \, a^{8} b + 65 \, a^{7} b^{2} - 59 \, a^{6} b^{3} + 27 \, a^{5} b^{4} - 5 \, a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{3} - {\left(8 \, a^{8} b - 29 \, a^{7} b^{2} + 39 \, a^{6} b^{3} - 23 \, a^{5} b^{4} + 5 \, a^{4} b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[-1/16*(12*(8*a^4*b^2 - 20*a^3*b^3 + 17*a^2*b^4 - 5*a*b^5)*cosh(d*x + c)^8 + 96*(8*a^4*b^2 - 20*a^3*b^3 + 17*a^2*b^4 - 5*a*b^5)*cosh(d*x + c)*sinh(d*x + c)^7 + 12*(8*a^4*b^2 - 20*a^3*b^3 + 17*a^2*b^4 - 5*a*b^5)*sinh(d*x + c)^8 + 24*(24*a^5*b - 76*a^4*b^2 + 91*a^3*b^3 - 49*a^2*b^4 + 10*a*b^5)*cosh(d*x + c)^6 + 24*(24*a^5*b - 76*a^4*b^2 + 91*a^3*b^3 - 49*a^2*b^4 + 10*a*b^5 + 14*(8*a^4*b^2 - 20*a^3*b^3 + 17*a^2*b^4 - 5*a*b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 32*a^4*b^2 - 136*a^3*b^3 + 164*a^2*b^4 - 60*a*b^5 + 48*(14*(8*a^4*b^2 - 20*a^3*b^3 + 17*a^2*b^4 - 5*a*b^5)*cosh(d*x + c)^3 + 3*(24*a^5*b - 76*a^4*b^2 + 91*a^3*b^3 - 49*a^2*b^4 + 10*a*b^5)*cosh(d*x + c))*sinh(d*x + c)^5 + 8*(64*a^6 - 296*a^5*b + 548*a^4*b^2 - 509*a^3*b^3 + 238*a^2*b^4 - 45*a*b^5)*cosh(d*x + c)^4 + 8*(64*a^6 - 296*a^5*b + 548*a^4*b^2 - 509*a^3*b^3 + 238*a^2*b^4 - 45*a*b^5 + 105*(8*a^4*b^2 - 20*a^3*b^3 + 17*a^2*b^4 - 5*a*b^5)*cosh(d*x + c)^4 + 45*(24*a^5*b - 76*a^4*b^2 + 91*a^3*b^3 - 49*a^2*b^4 + 10*a*b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 32*(21*(8*a^4*b^2 - 20*a^3*b^3 + 17*a^2*b^4 - 5*a*b^5)*cosh(d*x + c)^5 + 15*(24*a^5*b - 76*a^4*b^2 + 91*a^3*b^3 - 49*a^2*b^4 + 10*a*b^5)*cosh(d*x + c)^3 + (64*a^6 - 296*a^5*b + 548*a^4*b^2 - 509*a^3*b^3 + 238*a^2*b^4 - 45*a*b^5)*cosh(d*x + c))*sinh(d*x + c)^3 + 8*(32*a^5*b - 144*a^4*b^2 + 219*a^3*b^3 - 137*a^2*b^4 + 30*a*b^5)*cosh(d*x + c)^2 + 8*(42*(8*a^4*b^2 - 20*a^3*b^3 + 17*a^2*b^4 - 5*a*b^5)*cosh(d*x + c)^6 + 32*a^5*b - 144*a^4*b^2 + 219*a^3*b^3 - 137*a^2*b^4 + 30*a*b^5 + 45*(24*a^5*b - 76*a^4*b^2 + 91*a^3*b^3 - 49*a^2*b^4 + 10*a*b^5)*cosh(d*x + c)^4 + 6*(64*a^6 - 296*a^5*b + 548*a^4*b^2 - 509*a^3*b^3 + 238*a^2*b^4 - 45*a*b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - 3*((8*a^2*b^3 - 12*a*b^4 + 5*b^5)*cosh(d*x + c)^10 + 10*(8*a^2*b^3 - 12*a*b^4 + 5*b^5)*cosh(d*x + c)*sinh(d*x + c)^9 + (8*a^2*b^3 - 12*a*b^4 + 5*b^5)*sinh(d*x + c)^10 + (64*a^3*b^2 - 136*a^2*b^3 + 100*a*b^4 - 25*b^5)*cosh(d*x + c)^8 + (64*a^3*b^2 - 136*a^2*b^3 + 100*a*b^4 - 25*b^5 + 45*(8*a^2*b^3 - 12*a*b^4 + 5*b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 8*(15*(8*a^2*b^3 - 12*a*b^4 + 5*b^5)*cosh(d*x + c)^3 + (64*a^3*b^2 - 136*a^2*b^3 + 100*a*b^4 - 25*b^5)*cosh(d*x + c))*sinh(d*x + c)^7 + 2*(64*a^4*b - 192*a^3*b^2 + 224*a^2*b^3 - 120*a*b^4 + 25*b^5)*cosh(d*x + c)^6 + 2*(64*a^4*b - 192*a^3*b^2 + 224*a^2*b^3 - 120*a*b^4 + 25*b^5 + 105*(8*a^2*b^3 - 12*a*b^4 + 5*b^5)*cosh(d*x + c)^4 + 14*(64*a^3*b^2 - 136*a^2*b^3 + 100*a*b^4 - 25*b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 4*(63*(8*a^2*b^3 - 12*a*b^4 + 5*b^5)*cosh(d*x + c)^5 + 14*(64*a^3*b^2 - 136*a^2*b^3 + 100*a*b^4 - 25*b^5)*cosh(d*x + c)^3 + 3*(64*a^4*b - 192*a^3*b^2 + 224*a^2*b^3 - 120*a*b^4 + 25*b^5)*cosh(d*x + c))*sinh(d*x + c)^5 - 8*a^2*b^3 + 12*a*b^4 - 5*b^5 - 2*(64*a^4*b - 192*a^3*b^2 + 224*a^2*b^3 - 120*a*b^4 + 25*b^5)*cosh(d*x + c)^4 + 2*(105*(8*a^2*b^3 - 12*a*b^4 + 5*b^5)*cosh(d*x + c)^6 - 64*a^4*b + 192*a^3*b^2 - 224*a^2*b^3 + 120*a*b^4 - 25*b^5 + 35*(64*a^3*b^2 - 136*a^2*b^3 + 100*a*b^4 - 25*b^5)*cosh(d*x + c)^4 + 15*(64*a^4*b - 192*a^3*b^2 + 224*a^2*b^3 - 120*a*b^4 + 25*b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(15*(8*a^2*b^3 - 12*a*b^4 + 5*b^5)*cosh(d*x + c)^7 + 7*(64*a^3*b^2 - 136*a^2*b^3 + 100*a*b^4 - 25*b^5)*cosh(d*x + c)^5 + 5*(64*a^4*b - 192*a^3*b^2 + 224*a^2*b^3 - 120*a*b^4 + 25*b^5)*cosh(d*x + c)^3 - (64*a^4*b - 192*a^3*b^2 + 224*a^2*b^3 - 120*a*b^4 + 25*b^5)*cosh(d*x + c))*sinh(d*x + c)^3 - (64*a^3*b^2 - 136*a^2*b^3 + 100*a*b^4 - 25*b^5)*cosh(d*x + c)^2 + (45*(8*a^2*b^3 - 12*a*b^4 + 5*b^5)*cosh(d*x + c)^8 + 28*(64*a^3*b^2 - 136*a^2*b^3 + 100*a*b^4 - 25*b^5)*cosh(d*x + c)^6 - 64*a^3*b^2 + 136*a^2*b^3 - 100*a*b^4 + 25*b^5 + 30*(64*a^4*b - 192*a^3*b^2 + 224*a^2*b^3 - 120*a*b^4 + 25*b^5)*cosh(d*x + c)^4 - 12*(64*a^4*b - 192*a^3*b^2 + 224*a^2*b^3 - 120*a*b^4 + 25*b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 2*(5*(8*a^2*b^3 - 12*a*b^4 + 5*b^5)*cosh(d*x + c)^9 + 4*(64*a^3*b^2 - 136*a^2*b^3 + 100*a*b^4 - 25*b^5)*cosh(d*x + c)^7 + 6*(64*a^4*b - 192*a^3*b^2 + 224*a^2*b^3 - 120*a*b^4 + 25*b^5)*cosh(d*x + c)^5 - 4*(64*a^4*b - 192*a^3*b^2 + 224*a^2*b^3 - 120*a*b^4 + 25*b^5)*cosh(d*x + c)^3 - (64*a^3*b^2 - 136*a^2*b^3 + 100*a*b^4 - 25*b^5)*cosh(d*x + c))*sinh(d*x + c))*sqrt(a^2 - a*b)*log((b^2*cosh(d*x + c)^4 + 4*b^2*cosh(d*x + c)*sinh(d*x + c)^3 + b^2*sinh(d*x + c)^4 + 2*(2*a*b - b^2)*cosh(d*x + c)^2 + 2*(3*b^2*cosh(d*x + c)^2 + 2*a*b - b^2)*sinh(d*x + c)^2 + 8*a^2 - 8*a*b + b^2 + 4*(b^2*cosh(d*x + c)^3 + (2*a*b - b^2)*cosh(d*x + c))*sinh(d*x + c) + 4*(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + 2*a - b)*sqrt(a^2 - a*b))/(b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 + 2*(2*a - b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 + 2*a - b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 + (2*a - b)*cosh(d*x + c))*sinh(d*x + c) + b)) + 16*(6*(8*a^4*b^2 - 20*a^3*b^3 + 17*a^2*b^4 - 5*a*b^5)*cosh(d*x + c)^7 + 9*(24*a^5*b - 76*a^4*b^2 + 91*a^3*b^3 - 49*a^2*b^4 + 10*a*b^5)*cosh(d*x + c)^5 + 2*(64*a^6 - 296*a^5*b + 548*a^4*b^2 - 509*a^3*b^3 + 238*a^2*b^4 - 45*a*b^5)*cosh(d*x + c)^3 + (32*a^5*b - 144*a^4*b^2 + 219*a^3*b^3 - 137*a^2*b^4 + 30*a*b^5)*cosh(d*x + c))*sinh(d*x + c))/((a^7*b^2 - 3*a^6*b^3 + 3*a^5*b^4 - a^4*b^5)*d*cosh(d*x + c)^10 + 10*(a^7*b^2 - 3*a^6*b^3 + 3*a^5*b^4 - a^4*b^5)*d*cosh(d*x + c)*sinh(d*x + c)^9 + (a^7*b^2 - 3*a^6*b^3 + 3*a^5*b^4 - a^4*b^5)*d*sinh(d*x + c)^10 + (8*a^8*b - 29*a^7*b^2 + 39*a^6*b^3 - 23*a^5*b^4 + 5*a^4*b^5)*d*cosh(d*x + c)^8 + (45*(a^7*b^2 - 3*a^6*b^3 + 3*a^5*b^4 - a^4*b^5)*d*cosh(d*x + c)^2 + (8*a^8*b - 29*a^7*b^2 + 39*a^6*b^3 - 23*a^5*b^4 + 5*a^4*b^5)*d)*sinh(d*x + c)^8 + 2*(8*a^9 - 36*a^8*b + 65*a^7*b^2 - 59*a^6*b^3 + 27*a^5*b^4 - 5*a^4*b^5)*d*cosh(d*x + c)^6 + 8*(15*(a^7*b^2 - 3*a^6*b^3 + 3*a^5*b^4 - a^4*b^5)*d*cosh(d*x + c)^3 + (8*a^8*b - 29*a^7*b^2 + 39*a^6*b^3 - 23*a^5*b^4 + 5*a^4*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^7 + 2*(105*(a^7*b^2 - 3*a^6*b^3 + 3*a^5*b^4 - a^4*b^5)*d*cosh(d*x + c)^4 + 14*(8*a^8*b - 29*a^7*b^2 + 39*a^6*b^3 - 23*a^5*b^4 + 5*a^4*b^5)*d*cosh(d*x + c)^2 + (8*a^9 - 36*a^8*b + 65*a^7*b^2 - 59*a^6*b^3 + 27*a^5*b^4 - 5*a^4*b^5)*d)*sinh(d*x + c)^6 - 2*(8*a^9 - 36*a^8*b + 65*a^7*b^2 - 59*a^6*b^3 + 27*a^5*b^4 - 5*a^4*b^5)*d*cosh(d*x + c)^4 + 4*(63*(a^7*b^2 - 3*a^6*b^3 + 3*a^5*b^4 - a^4*b^5)*d*cosh(d*x + c)^5 + 14*(8*a^8*b - 29*a^7*b^2 + 39*a^6*b^3 - 23*a^5*b^4 + 5*a^4*b^5)*d*cosh(d*x + c)^3 + 3*(8*a^9 - 36*a^8*b + 65*a^7*b^2 - 59*a^6*b^3 + 27*a^5*b^4 - 5*a^4*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(105*(a^7*b^2 - 3*a^6*b^3 + 3*a^5*b^4 - a^4*b^5)*d*cosh(d*x + c)^6 + 35*(8*a^8*b - 29*a^7*b^2 + 39*a^6*b^3 - 23*a^5*b^4 + 5*a^4*b^5)*d*cosh(d*x + c)^4 + 15*(8*a^9 - 36*a^8*b + 65*a^7*b^2 - 59*a^6*b^3 + 27*a^5*b^4 - 5*a^4*b^5)*d*cosh(d*x + c)^2 - (8*a^9 - 36*a^8*b + 65*a^7*b^2 - 59*a^6*b^3 + 27*a^5*b^4 - 5*a^4*b^5)*d)*sinh(d*x + c)^4 - (8*a^8*b - 29*a^7*b^2 + 39*a^6*b^3 - 23*a^5*b^4 + 5*a^4*b^5)*d*cosh(d*x + c)^2 + 8*(15*(a^7*b^2 - 3*a^6*b^3 + 3*a^5*b^4 - a^4*b^5)*d*cosh(d*x + c)^7 + 7*(8*a^8*b - 29*a^7*b^2 + 39*a^6*b^3 - 23*a^5*b^4 + 5*a^4*b^5)*d*cosh(d*x + c)^5 + 5*(8*a^9 - 36*a^8*b + 65*a^7*b^2 - 59*a^6*b^3 + 27*a^5*b^4 - 5*a^4*b^5)*d*cosh(d*x + c)^3 - (8*a^9 - 36*a^8*b + 65*a^7*b^2 - 59*a^6*b^3 + 27*a^5*b^4 - 5*a^4*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^3 + (45*(a^7*b^2 - 3*a^6*b^3 + 3*a^5*b^4 - a^4*b^5)*d*cosh(d*x + c)^8 + 28*(8*a^8*b - 29*a^7*b^2 + 39*a^6*b^3 - 23*a^5*b^4 + 5*a^4*b^5)*d*cosh(d*x + c)^6 + 30*(8*a^9 - 36*a^8*b + 65*a^7*b^2 - 59*a^6*b^3 + 27*a^5*b^4 - 5*a^4*b^5)*d*cosh(d*x + c)^4 - 12*(8*a^9 - 36*a^8*b + 65*a^7*b^2 - 59*a^6*b^3 + 27*a^5*b^4 - 5*a^4*b^5)*d*cosh(d*x + c)^2 - (8*a^8*b - 29*a^7*b^2 + 39*a^6*b^3 - 23*a^5*b^4 + 5*a^4*b^5)*d)*sinh(d*x + c)^2 - (a^7*b^2 - 3*a^6*b^3 + 3*a^5*b^4 - a^4*b^5)*d + 2*(5*(a^7*b^2 - 3*a^6*b^3 + 3*a^5*b^4 - a^4*b^5)*d*cosh(d*x + c)^9 + 4*(8*a^8*b - 29*a^7*b^2 + 39*a^6*b^3 - 23*a^5*b^4 + 5*a^4*b^5)*d*cosh(d*x + c)^7 + 6*(8*a^9 - 36*a^8*b + 65*a^7*b^2 - 59*a^6*b^3 + 27*a^5*b^4 - 5*a^4*b^5)*d*cosh(d*x + c)^5 - 4*(8*a^9 - 36*a^8*b + 65*a^7*b^2 - 59*a^6*b^3 + 27*a^5*b^4 - 5*a^4*b^5)*d*cosh(d*x + c)^3 - (8*a^8*b - 29*a^7*b^2 + 39*a^6*b^3 - 23*a^5*b^4 + 5*a^4*b^5)*d*cosh(d*x + c))*sinh(d*x + c)), -1/8*(6*(8*a^4*b^2 - 20*a^3*b^3 + 17*a^2*b^4 - 5*a*b^5)*cosh(d*x + c)^8 + 48*(8*a^4*b^2 - 20*a^3*b^3 + 17*a^2*b^4 - 5*a*b^5)*cosh(d*x + c)*sinh(d*x + c)^7 + 6*(8*a^4*b^2 - 20*a^3*b^3 + 17*a^2*b^4 - 5*a*b^5)*sinh(d*x + c)^8 + 12*(24*a^5*b - 76*a^4*b^2 + 91*a^3*b^3 - 49*a^2*b^4 + 10*a*b^5)*cosh(d*x + c)^6 + 12*(24*a^5*b - 76*a^4*b^2 + 91*a^3*b^3 - 49*a^2*b^4 + 10*a*b^5 + 14*(8*a^4*b^2 - 20*a^3*b^3 + 17*a^2*b^4 - 5*a*b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 16*a^4*b^2 - 68*a^3*b^3 + 82*a^2*b^4 - 30*a*b^5 + 24*(14*(8*a^4*b^2 - 20*a^3*b^3 + 17*a^2*b^4 - 5*a*b^5)*cosh(d*x + c)^3 + 3*(24*a^5*b - 76*a^4*b^2 + 91*a^3*b^3 - 49*a^2*b^4 + 10*a*b^5)*cosh(d*x + c))*sinh(d*x + c)^5 + 4*(64*a^6 - 296*a^5*b + 548*a^4*b^2 - 509*a^3*b^3 + 238*a^2*b^4 - 45*a*b^5)*cosh(d*x + c)^4 + 4*(64*a^6 - 296*a^5*b + 548*a^4*b^2 - 509*a^3*b^3 + 238*a^2*b^4 - 45*a*b^5 + 105*(8*a^4*b^2 - 20*a^3*b^3 + 17*a^2*b^4 - 5*a*b^5)*cosh(d*x + c)^4 + 45*(24*a^5*b - 76*a^4*b^2 + 91*a^3*b^3 - 49*a^2*b^4 + 10*a*b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 16*(21*(8*a^4*b^2 - 20*a^3*b^3 + 17*a^2*b^4 - 5*a*b^5)*cosh(d*x + c)^5 + 15*(24*a^5*b - 76*a^4*b^2 + 91*a^3*b^3 - 49*a^2*b^4 + 10*a*b^5)*cosh(d*x + c)^3 + (64*a^6 - 296*a^5*b + 548*a^4*b^2 - 509*a^3*b^3 + 238*a^2*b^4 - 45*a*b^5)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(32*a^5*b - 144*a^4*b^2 + 219*a^3*b^3 - 137*a^2*b^4 + 30*a*b^5)*cosh(d*x + c)^2 + 4*(42*(8*a^4*b^2 - 20*a^3*b^3 + 17*a^2*b^4 - 5*a*b^5)*cosh(d*x + c)^6 + 32*a^5*b - 144*a^4*b^2 + 219*a^3*b^3 - 137*a^2*b^4 + 30*a*b^5 + 45*(24*a^5*b - 76*a^4*b^2 + 91*a^3*b^3 - 49*a^2*b^4 + 10*a*b^5)*cosh(d*x + c)^4 + 6*(64*a^6 - 296*a^5*b + 548*a^4*b^2 - 509*a^3*b^3 + 238*a^2*b^4 - 45*a*b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - 3*((8*a^2*b^3 - 12*a*b^4 + 5*b^5)*cosh(d*x + c)^10 + 10*(8*a^2*b^3 - 12*a*b^4 + 5*b^5)*cosh(d*x + c)*sinh(d*x + c)^9 + (8*a^2*b^3 - 12*a*b^4 + 5*b^5)*sinh(d*x + c)^10 + (64*a^3*b^2 - 136*a^2*b^3 + 100*a*b^4 - 25*b^5)*cosh(d*x + c)^8 + (64*a^3*b^2 - 136*a^2*b^3 + 100*a*b^4 - 25*b^5 + 45*(8*a^2*b^3 - 12*a*b^4 + 5*b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 8*(15*(8*a^2*b^3 - 12*a*b^4 + 5*b^5)*cosh(d*x + c)^3 + (64*a^3*b^2 - 136*a^2*b^3 + 100*a*b^4 - 25*b^5)*cosh(d*x + c))*sinh(d*x + c)^7 + 2*(64*a^4*b - 192*a^3*b^2 + 224*a^2*b^3 - 120*a*b^4 + 25*b^5)*cosh(d*x + c)^6 + 2*(64*a^4*b - 192*a^3*b^2 + 224*a^2*b^3 - 120*a*b^4 + 25*b^5 + 105*(8*a^2*b^3 - 12*a*b^4 + 5*b^5)*cosh(d*x + c)^4 + 14*(64*a^3*b^2 - 136*a^2*b^3 + 100*a*b^4 - 25*b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 4*(63*(8*a^2*b^3 - 12*a*b^4 + 5*b^5)*cosh(d*x + c)^5 + 14*(64*a^3*b^2 - 136*a^2*b^3 + 100*a*b^4 - 25*b^5)*cosh(d*x + c)^3 + 3*(64*a^4*b - 192*a^3*b^2 + 224*a^2*b^3 - 120*a*b^4 + 25*b^5)*cosh(d*x + c))*sinh(d*x + c)^5 - 8*a^2*b^3 + 12*a*b^4 - 5*b^5 - 2*(64*a^4*b - 192*a^3*b^2 + 224*a^2*b^3 - 120*a*b^4 + 25*b^5)*cosh(d*x + c)^4 + 2*(105*(8*a^2*b^3 - 12*a*b^4 + 5*b^5)*cosh(d*x + c)^6 - 64*a^4*b + 192*a^3*b^2 - 224*a^2*b^3 + 120*a*b^4 - 25*b^5 + 35*(64*a^3*b^2 - 136*a^2*b^3 + 100*a*b^4 - 25*b^5)*cosh(d*x + c)^4 + 15*(64*a^4*b - 192*a^3*b^2 + 224*a^2*b^3 - 120*a*b^4 + 25*b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(15*(8*a^2*b^3 - 12*a*b^4 + 5*b^5)*cosh(d*x + c)^7 + 7*(64*a^3*b^2 - 136*a^2*b^3 + 100*a*b^4 - 25*b^5)*cosh(d*x + c)^5 + 5*(64*a^4*b - 192*a^3*b^2 + 224*a^2*b^3 - 120*a*b^4 + 25*b^5)*cosh(d*x + c)^3 - (64*a^4*b - 192*a^3*b^2 + 224*a^2*b^3 - 120*a*b^4 + 25*b^5)*cosh(d*x + c))*sinh(d*x + c)^3 - (64*a^3*b^2 - 136*a^2*b^3 + 100*a*b^4 - 25*b^5)*cosh(d*x + c)^2 + (45*(8*a^2*b^3 - 12*a*b^4 + 5*b^5)*cosh(d*x + c)^8 + 28*(64*a^3*b^2 - 136*a^2*b^3 + 100*a*b^4 - 25*b^5)*cosh(d*x + c)^6 - 64*a^3*b^2 + 136*a^2*b^3 - 100*a*b^4 + 25*b^5 + 30*(64*a^4*b - 192*a^3*b^2 + 224*a^2*b^3 - 120*a*b^4 + 25*b^5)*cosh(d*x + c)^4 - 12*(64*a^4*b - 192*a^3*b^2 + 224*a^2*b^3 - 120*a*b^4 + 25*b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 2*(5*(8*a^2*b^3 - 12*a*b^4 + 5*b^5)*cosh(d*x + c)^9 + 4*(64*a^3*b^2 - 136*a^2*b^3 + 100*a*b^4 - 25*b^5)*cosh(d*x + c)^7 + 6*(64*a^4*b - 192*a^3*b^2 + 224*a^2*b^3 - 120*a*b^4 + 25*b^5)*cosh(d*x + c)^5 - 4*(64*a^4*b - 192*a^3*b^2 + 224*a^2*b^3 - 120*a*b^4 + 25*b^5)*cosh(d*x + c)^3 - (64*a^3*b^2 - 136*a^2*b^3 + 100*a*b^4 - 25*b^5)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-a^2 + a*b)*arctan(-1/2*(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + 2*a - b)*sqrt(-a^2 + a*b)/(a^2 - a*b)) + 8*(6*(8*a^4*b^2 - 20*a^3*b^3 + 17*a^2*b^4 - 5*a*b^5)*cosh(d*x + c)^7 + 9*(24*a^5*b - 76*a^4*b^2 + 91*a^3*b^3 - 49*a^2*b^4 + 10*a*b^5)*cosh(d*x + c)^5 + 2*(64*a^6 - 296*a^5*b + 548*a^4*b^2 - 509*a^3*b^3 + 238*a^2*b^4 - 45*a*b^5)*cosh(d*x + c)^3 + (32*a^5*b - 144*a^4*b^2 + 219*a^3*b^3 - 137*a^2*b^4 + 30*a*b^5)*cosh(d*x + c))*sinh(d*x + c))/((a^7*b^2 - 3*a^6*b^3 + 3*a^5*b^4 - a^4*b^5)*d*cosh(d*x + c)^10 + 10*(a^7*b^2 - 3*a^6*b^3 + 3*a^5*b^4 - a^4*b^5)*d*cosh(d*x + c)*sinh(d*x + c)^9 + (a^7*b^2 - 3*a^6*b^3 + 3*a^5*b^4 - a^4*b^5)*d*sinh(d*x + c)^10 + (8*a^8*b - 29*a^7*b^2 + 39*a^6*b^3 - 23*a^5*b^4 + 5*a^4*b^5)*d*cosh(d*x + c)^8 + (45*(a^7*b^2 - 3*a^6*b^3 + 3*a^5*b^4 - a^4*b^5)*d*cosh(d*x + c)^2 + (8*a^8*b - 29*a^7*b^2 + 39*a^6*b^3 - 23*a^5*b^4 + 5*a^4*b^5)*d)*sinh(d*x + c)^8 + 2*(8*a^9 - 36*a^8*b + 65*a^7*b^2 - 59*a^6*b^3 + 27*a^5*b^4 - 5*a^4*b^5)*d*cosh(d*x + c)^6 + 8*(15*(a^7*b^2 - 3*a^6*b^3 + 3*a^5*b^4 - a^4*b^5)*d*cosh(d*x + c)^3 + (8*a^8*b - 29*a^7*b^2 + 39*a^6*b^3 - 23*a^5*b^4 + 5*a^4*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^7 + 2*(105*(a^7*b^2 - 3*a^6*b^3 + 3*a^5*b^4 - a^4*b^5)*d*cosh(d*x + c)^4 + 14*(8*a^8*b - 29*a^7*b^2 + 39*a^6*b^3 - 23*a^5*b^4 + 5*a^4*b^5)*d*cosh(d*x + c)^2 + (8*a^9 - 36*a^8*b + 65*a^7*b^2 - 59*a^6*b^3 + 27*a^5*b^4 - 5*a^4*b^5)*d)*sinh(d*x + c)^6 - 2*(8*a^9 - 36*a^8*b + 65*a^7*b^2 - 59*a^6*b^3 + 27*a^5*b^4 - 5*a^4*b^5)*d*cosh(d*x + c)^4 + 4*(63*(a^7*b^2 - 3*a^6*b^3 + 3*a^5*b^4 - a^4*b^5)*d*cosh(d*x + c)^5 + 14*(8*a^8*b - 29*a^7*b^2 + 39*a^6*b^3 - 23*a^5*b^4 + 5*a^4*b^5)*d*cosh(d*x + c)^3 + 3*(8*a^9 - 36*a^8*b + 65*a^7*b^2 - 59*a^6*b^3 + 27*a^5*b^4 - 5*a^4*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(105*(a^7*b^2 - 3*a^6*b^3 + 3*a^5*b^4 - a^4*b^5)*d*cosh(d*x + c)^6 + 35*(8*a^8*b - 29*a^7*b^2 + 39*a^6*b^3 - 23*a^5*b^4 + 5*a^4*b^5)*d*cosh(d*x + c)^4 + 15*(8*a^9 - 36*a^8*b + 65*a^7*b^2 - 59*a^6*b^3 + 27*a^5*b^4 - 5*a^4*b^5)*d*cosh(d*x + c)^2 - (8*a^9 - 36*a^8*b + 65*a^7*b^2 - 59*a^6*b^3 + 27*a^5*b^4 - 5*a^4*b^5)*d)*sinh(d*x + c)^4 - (8*a^8*b - 29*a^7*b^2 + 39*a^6*b^3 - 23*a^5*b^4 + 5*a^4*b^5)*d*cosh(d*x + c)^2 + 8*(15*(a^7*b^2 - 3*a^6*b^3 + 3*a^5*b^4 - a^4*b^5)*d*cosh(d*x + c)^7 + 7*(8*a^8*b - 29*a^7*b^2 + 39*a^6*b^3 - 23*a^5*b^4 + 5*a^4*b^5)*d*cosh(d*x + c)^5 + 5*(8*a^9 - 36*a^8*b + 65*a^7*b^2 - 59*a^6*b^3 + 27*a^5*b^4 - 5*a^4*b^5)*d*cosh(d*x + c)^3 - (8*a^9 - 36*a^8*b + 65*a^7*b^2 - 59*a^6*b^3 + 27*a^5*b^4 - 5*a^4*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^3 + (45*(a^7*b^2 - 3*a^6*b^3 + 3*a^5*b^4 - a^4*b^5)*d*cosh(d*x + c)^8 + 28*(8*a^8*b - 29*a^7*b^2 + 39*a^6*b^3 - 23*a^5*b^4 + 5*a^4*b^5)*d*cosh(d*x + c)^6 + 30*(8*a^9 - 36*a^8*b + 65*a^7*b^2 - 59*a^6*b^3 + 27*a^5*b^4 - 5*a^4*b^5)*d*cosh(d*x + c)^4 - 12*(8*a^9 - 36*a^8*b + 65*a^7*b^2 - 59*a^6*b^3 + 27*a^5*b^4 - 5*a^4*b^5)*d*cosh(d*x + c)^2 - (8*a^8*b - 29*a^7*b^2 + 39*a^6*b^3 - 23*a^5*b^4 + 5*a^4*b^5)*d)*sinh(d*x + c)^2 - (a^7*b^2 - 3*a^6*b^3 + 3*a^5*b^4 - a^4*b^5)*d + 2*(5*(a^7*b^2 - 3*a^6*b^3 + 3*a^5*b^4 - a^4*b^5)*d*cosh(d*x + c)^9 + 4*(8*a^8*b - 29*a^7*b^2 + 39*a^6*b^3 - 23*a^5*b^4 + 5*a^4*b^5)*d*cosh(d*x + c)^7 + 6*(8*a^9 - 36*a^8*b + 65*a^7*b^2 - 59*a^6*b^3 + 27*a^5*b^4 - 5*a^4*b^5)*d*cosh(d*x + c)^5 - 4*(8*a^9 - 36*a^8*b + 65*a^7*b^2 - 59*a^6*b^3 + 27*a^5*b^4 - 5*a^4*b^5)*d*cosh(d*x + c)^3 - (8*a^8*b - 29*a^7*b^2 + 39*a^6*b^3 - 23*a^5*b^4 + 5*a^4*b^5)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
58,-1,0,0,0.000000," ","integrate(csch(d*x+c)^3/(a+b*sinh(d*x+c)^2)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
59,-1,0,0,0.000000," ","integrate(csch(d*x+c)^4/(a+b*sinh(d*x+c)^2)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
60,1,20,0,1.045171," ","integrate(1/(1+sinh(x)^2),x, algorithm=""fricas"")","-\frac{2}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1}"," ",0,"-2/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)","B",0
61,1,84,0,1.029733," ","integrate(1/(1+sinh(x)^2)^2,x, algorithm=""fricas"")","-\frac{8 \, {\left(2 \, \cosh\left(x\right) + \sinh\left(x\right)\right)}}{3 \, {\left(\cosh\left(x\right)^{5} + 5 \, \cosh\left(x\right) \sinh\left(x\right)^{4} + \sinh\left(x\right)^{5} + {\left(10 \, \cosh\left(x\right)^{2} + 3\right)} \sinh\left(x\right)^{3} + 3 \, \cosh\left(x\right)^{3} + {\left(10 \, \cosh\left(x\right)^{3} + 9 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{2} + {\left(5 \, \cosh\left(x\right)^{4} + 9 \, \cosh\left(x\right)^{2} + 2\right)} \sinh\left(x\right) + 4 \, \cosh\left(x\right)\right)}}"," ",0,"-8/3*(2*cosh(x) + sinh(x))/(cosh(x)^5 + 5*cosh(x)*sinh(x)^4 + sinh(x)^5 + (10*cosh(x)^2 + 3)*sinh(x)^3 + 3*cosh(x)^3 + (10*cosh(x)^3 + 9*cosh(x))*sinh(x)^2 + (5*cosh(x)^4 + 9*cosh(x)^2 + 2)*sinh(x) + 4*cosh(x))","B",0
62,1,185,0,2.197474," ","integrate(1/(1+sinh(x)^2)^3,x, algorithm=""fricas"")","-\frac{16 \, {\left(11 \, \cosh\left(x\right)^{2} + 18 \, \cosh\left(x\right) \sinh\left(x\right) + 11 \, \sinh\left(x\right)^{2} + 5\right)}}{15 \, {\left(\cosh\left(x\right)^{8} + 8 \, \cosh\left(x\right) \sinh\left(x\right)^{7} + \sinh\left(x\right)^{8} + {\left(28 \, \cosh\left(x\right)^{2} + 5\right)} \sinh\left(x\right)^{6} + 5 \, \cosh\left(x\right)^{6} + 2 \, {\left(28 \, \cosh\left(x\right)^{3} + 15 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 5 \, {\left(14 \, \cosh\left(x\right)^{4} + 15 \, \cosh\left(x\right)^{2} + 2\right)} \sinh\left(x\right)^{4} + 10 \, \cosh\left(x\right)^{4} + 4 \, {\left(14 \, \cosh\left(x\right)^{5} + 25 \, \cosh\left(x\right)^{3} + 10 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(28 \, \cosh\left(x\right)^{6} + 75 \, \cosh\left(x\right)^{4} + 60 \, \cosh\left(x\right)^{2} + 11\right)} \sinh\left(x\right)^{2} + 11 \, \cosh\left(x\right)^{2} + 2 \, {\left(4 \, \cosh\left(x\right)^{7} + 15 \, \cosh\left(x\right)^{5} + 20 \, \cosh\left(x\right)^{3} + 9 \, \cosh\left(x\right)\right)} \sinh\left(x\right) + 5\right)}}"," ",0,"-16/15*(11*cosh(x)^2 + 18*cosh(x)*sinh(x) + 11*sinh(x)^2 + 5)/(cosh(x)^8 + 8*cosh(x)*sinh(x)^7 + sinh(x)^8 + (28*cosh(x)^2 + 5)*sinh(x)^6 + 5*cosh(x)^6 + 2*(28*cosh(x)^3 + 15*cosh(x))*sinh(x)^5 + 5*(14*cosh(x)^4 + 15*cosh(x)^2 + 2)*sinh(x)^4 + 10*cosh(x)^4 + 4*(14*cosh(x)^5 + 25*cosh(x)^3 + 10*cosh(x))*sinh(x)^3 + (28*cosh(x)^6 + 75*cosh(x)^4 + 60*cosh(x)^2 + 11)*sinh(x)^2 + 11*cosh(x)^2 + 2*(4*cosh(x)^7 + 15*cosh(x)^5 + 20*cosh(x)^3 + 9*cosh(x))*sinh(x) + 5)","B",0
63,1,66,0,1.443021," ","integrate(1/(1-sinh(x)^2),x, algorithm=""fricas"")","\frac{1}{4} \, \sqrt{2} \log\left(-\frac{3 \, {\left(2 \, \sqrt{2} - 3\right)} \cosh\left(x\right)^{2} - 4 \, {\left(3 \, \sqrt{2} - 4\right)} \cosh\left(x\right) \sinh\left(x\right) + 3 \, {\left(2 \, \sqrt{2} - 3\right)} \sinh\left(x\right)^{2} - 2 \, \sqrt{2} + 3}{\cosh\left(x\right)^{2} + \sinh\left(x\right)^{2} - 3}\right)"," ",0,"1/4*sqrt(2)*log(-(3*(2*sqrt(2) - 3)*cosh(x)^2 - 4*(3*sqrt(2) - 4)*cosh(x)*sinh(x) + 3*(2*sqrt(2) - 3)*sinh(x)^2 - 2*sqrt(2) + 3)/(cosh(x)^2 + sinh(x)^2 - 3))","B",0
64,1,216,0,1.421149," ","integrate(1/(1-sinh(x)^2)^2,x, algorithm=""fricas"")","-\frac{24 \, \cosh\left(x\right)^{2} - 3 \, {\left(\sqrt{2} \cosh\left(x\right)^{4} + 4 \, \sqrt{2} \cosh\left(x\right) \sinh\left(x\right)^{3} + \sqrt{2} \sinh\left(x\right)^{4} + 6 \, {\left(\sqrt{2} \cosh\left(x\right)^{2} - \sqrt{2}\right)} \sinh\left(x\right)^{2} - 6 \, \sqrt{2} \cosh\left(x\right)^{2} + 4 \, {\left(\sqrt{2} \cosh\left(x\right)^{3} - 3 \, \sqrt{2} \cosh\left(x\right)\right)} \sinh\left(x\right) + \sqrt{2}\right)} \log\left(-\frac{3 \, {\left(2 \, \sqrt{2} - 3\right)} \cosh\left(x\right)^{2} - 4 \, {\left(3 \, \sqrt{2} - 4\right)} \cosh\left(x\right) \sinh\left(x\right) + 3 \, {\left(2 \, \sqrt{2} - 3\right)} \sinh\left(x\right)^{2} - 2 \, \sqrt{2} + 3}{\cosh\left(x\right)^{2} + \sinh\left(x\right)^{2} - 3}\right) + 48 \, \cosh\left(x\right) \sinh\left(x\right) + 24 \, \sinh\left(x\right)^{2} - 8}{16 \, {\left(\cosh\left(x\right)^{4} + 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4} + 6 \, {\left(\cosh\left(x\right)^{2} - 1\right)} \sinh\left(x\right)^{2} - 6 \, \cosh\left(x\right)^{2} + 4 \, {\left(\cosh\left(x\right)^{3} - 3 \, \cosh\left(x\right)\right)} \sinh\left(x\right) + 1\right)}}"," ",0,"-1/16*(24*cosh(x)^2 - 3*(sqrt(2)*cosh(x)^4 + 4*sqrt(2)*cosh(x)*sinh(x)^3 + sqrt(2)*sinh(x)^4 + 6*(sqrt(2)*cosh(x)^2 - sqrt(2))*sinh(x)^2 - 6*sqrt(2)*cosh(x)^2 + 4*(sqrt(2)*cosh(x)^3 - 3*sqrt(2)*cosh(x))*sinh(x) + sqrt(2))*log(-(3*(2*sqrt(2) - 3)*cosh(x)^2 - 4*(3*sqrt(2) - 4)*cosh(x)*sinh(x) + 3*(2*sqrt(2) - 3)*sinh(x)^2 - 2*sqrt(2) + 3)/(cosh(x)^2 + sinh(x)^2 - 3)) + 48*cosh(x)*sinh(x) + 24*sinh(x)^2 - 8)/(cosh(x)^4 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4 + 6*(cosh(x)^2 - 1)*sinh(x)^2 - 6*cosh(x)^2 + 4*(cosh(x)^3 - 3*cosh(x))*sinh(x) + 1)","B",0
65,1,575,0,0.566329," ","integrate(1/(1-sinh(x)^2)^3,x, algorithm=""fricas"")","-\frac{152 \, \cosh\left(x\right)^{6} + 912 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + 152 \, \sinh\left(x\right)^{6} + 456 \, {\left(5 \, \cosh\left(x\right)^{2} - 3\right)} \sinh\left(x\right)^{4} - 1368 \, \cosh\left(x\right)^{4} + 608 \, {\left(5 \, \cosh\left(x\right)^{3} - 9 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 8 \, {\left(285 \, \cosh\left(x\right)^{4} - 1026 \, \cosh\left(x\right)^{2} + 89\right)} \sinh\left(x\right)^{2} + 712 \, \cosh\left(x\right)^{2} - 19 \, {\left(\sqrt{2} \cosh\left(x\right)^{8} + 8 \, \sqrt{2} \cosh\left(x\right) \sinh\left(x\right)^{7} + \sqrt{2} \sinh\left(x\right)^{8} + 4 \, {\left(7 \, \sqrt{2} \cosh\left(x\right)^{2} - 3 \, \sqrt{2}\right)} \sinh\left(x\right)^{6} - 12 \, \sqrt{2} \cosh\left(x\right)^{6} + 8 \, {\left(7 \, \sqrt{2} \cosh\left(x\right)^{3} - 9 \, \sqrt{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(35 \, \sqrt{2} \cosh\left(x\right)^{4} - 90 \, \sqrt{2} \cosh\left(x\right)^{2} + 19 \, \sqrt{2}\right)} \sinh\left(x\right)^{4} + 38 \, \sqrt{2} \cosh\left(x\right)^{4} + 8 \, {\left(7 \, \sqrt{2} \cosh\left(x\right)^{5} - 30 \, \sqrt{2} \cosh\left(x\right)^{3} + 19 \, \sqrt{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(7 \, \sqrt{2} \cosh\left(x\right)^{6} - 45 \, \sqrt{2} \cosh\left(x\right)^{4} + 57 \, \sqrt{2} \cosh\left(x\right)^{2} - 3 \, \sqrt{2}\right)} \sinh\left(x\right)^{2} - 12 \, \sqrt{2} \cosh\left(x\right)^{2} + 8 \, {\left(\sqrt{2} \cosh\left(x\right)^{7} - 9 \, \sqrt{2} \cosh\left(x\right)^{5} + 19 \, \sqrt{2} \cosh\left(x\right)^{3} - 3 \, \sqrt{2} \cosh\left(x\right)\right)} \sinh\left(x\right) + \sqrt{2}\right)} \log\left(-\frac{3 \, {\left(2 \, \sqrt{2} - 3\right)} \cosh\left(x\right)^{2} - 4 \, {\left(3 \, \sqrt{2} - 4\right)} \cosh\left(x\right) \sinh\left(x\right) + 3 \, {\left(2 \, \sqrt{2} - 3\right)} \sinh\left(x\right)^{2} - 2 \, \sqrt{2} + 3}{\cosh\left(x\right)^{2} + \sinh\left(x\right)^{2} - 3}\right) + 16 \, {\left(57 \, \cosh\left(x\right)^{5} - 342 \, \cosh\left(x\right)^{3} + 89 \, \cosh\left(x\right)\right)} \sinh\left(x\right) - 72}{128 \, {\left(\cosh\left(x\right)^{8} + 8 \, \cosh\left(x\right) \sinh\left(x\right)^{7} + \sinh\left(x\right)^{8} + 4 \, {\left(7 \, \cosh\left(x\right)^{2} - 3\right)} \sinh\left(x\right)^{6} - 12 \, \cosh\left(x\right)^{6} + 8 \, {\left(7 \, \cosh\left(x\right)^{3} - 9 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(35 \, \cosh\left(x\right)^{4} - 90 \, \cosh\left(x\right)^{2} + 19\right)} \sinh\left(x\right)^{4} + 38 \, \cosh\left(x\right)^{4} + 8 \, {\left(7 \, \cosh\left(x\right)^{5} - 30 \, \cosh\left(x\right)^{3} + 19 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(7 \, \cosh\left(x\right)^{6} - 45 \, \cosh\left(x\right)^{4} + 57 \, \cosh\left(x\right)^{2} - 3\right)} \sinh\left(x\right)^{2} - 12 \, \cosh\left(x\right)^{2} + 8 \, {\left(\cosh\left(x\right)^{7} - 9 \, \cosh\left(x\right)^{5} + 19 \, \cosh\left(x\right)^{3} - 3 \, \cosh\left(x\right)\right)} \sinh\left(x\right) + 1\right)}}"," ",0,"-1/128*(152*cosh(x)^6 + 912*cosh(x)*sinh(x)^5 + 152*sinh(x)^6 + 456*(5*cosh(x)^2 - 3)*sinh(x)^4 - 1368*cosh(x)^4 + 608*(5*cosh(x)^3 - 9*cosh(x))*sinh(x)^3 + 8*(285*cosh(x)^4 - 1026*cosh(x)^2 + 89)*sinh(x)^2 + 712*cosh(x)^2 - 19*(sqrt(2)*cosh(x)^8 + 8*sqrt(2)*cosh(x)*sinh(x)^7 + sqrt(2)*sinh(x)^8 + 4*(7*sqrt(2)*cosh(x)^2 - 3*sqrt(2))*sinh(x)^6 - 12*sqrt(2)*cosh(x)^6 + 8*(7*sqrt(2)*cosh(x)^3 - 9*sqrt(2)*cosh(x))*sinh(x)^5 + 2*(35*sqrt(2)*cosh(x)^4 - 90*sqrt(2)*cosh(x)^2 + 19*sqrt(2))*sinh(x)^4 + 38*sqrt(2)*cosh(x)^4 + 8*(7*sqrt(2)*cosh(x)^5 - 30*sqrt(2)*cosh(x)^3 + 19*sqrt(2)*cosh(x))*sinh(x)^3 + 4*(7*sqrt(2)*cosh(x)^6 - 45*sqrt(2)*cosh(x)^4 + 57*sqrt(2)*cosh(x)^2 - 3*sqrt(2))*sinh(x)^2 - 12*sqrt(2)*cosh(x)^2 + 8*(sqrt(2)*cosh(x)^7 - 9*sqrt(2)*cosh(x)^5 + 19*sqrt(2)*cosh(x)^3 - 3*sqrt(2)*cosh(x))*sinh(x) + sqrt(2))*log(-(3*(2*sqrt(2) - 3)*cosh(x)^2 - 4*(3*sqrt(2) - 4)*cosh(x)*sinh(x) + 3*(2*sqrt(2) - 3)*sinh(x)^2 - 2*sqrt(2) + 3)/(cosh(x)^2 + sinh(x)^2 - 3)) + 16*(57*cosh(x)^5 - 342*cosh(x)^3 + 89*cosh(x))*sinh(x) - 72)/(cosh(x)^8 + 8*cosh(x)*sinh(x)^7 + sinh(x)^8 + 4*(7*cosh(x)^2 - 3)*sinh(x)^6 - 12*cosh(x)^6 + 8*(7*cosh(x)^3 - 9*cosh(x))*sinh(x)^5 + 2*(35*cosh(x)^4 - 90*cosh(x)^2 + 19)*sinh(x)^4 + 38*cosh(x)^4 + 8*(7*cosh(x)^5 - 30*cosh(x)^3 + 19*cosh(x))*sinh(x)^3 + 4*(7*cosh(x)^6 - 45*cosh(x)^4 + 57*cosh(x)^2 - 3)*sinh(x)^2 - 12*cosh(x)^2 + 8*(cosh(x)^7 - 9*cosh(x)^5 + 19*cosh(x)^3 - 3*cosh(x))*sinh(x) + 1)","B",0
66,1,3037,0,1.371494," ","integrate(sinh(f*x+e)^3*(a+b*sinh(f*x+e)^2)^(1/2),x, algorithm=""fricas"")","\left[-\frac{2 \, {\left({\left(a^{2} + 2 \, a b - 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left(a^{2} + 2 \, a b - 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{3} \sinh\left(f x + e\right) + 6 \, {\left(a^{2} + 2 \, a b - 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} \sinh\left(f x + e\right)^{2} + 4 \, {\left(a^{2} + 2 \, a b - 3 \, b^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(a^{2} + 2 \, a b - 3 \, b^{2}\right)} \sinh\left(f x + e\right)^{4}\right)} \sqrt{b} \log\left(\frac{a^{2} b \cosh\left(f x + e\right)^{8} + 8 \, a^{2} b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + a^{2} b \sinh\left(f x + e\right)^{8} + 2 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(f x + e\right)^{6} + 2 \, {\left(14 \, a^{2} b \cosh\left(f x + e\right)^{2} + a^{3} + a^{2} b\right)} \sinh\left(f x + e\right)^{6} + 4 \, {\left(14 \, a^{2} b \cosh\left(f x + e\right)^{3} + 3 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + {\left(9 \, a^{2} b - 4 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{4} + {\left(70 \, a^{2} b \cosh\left(f x + e\right)^{4} + 9 \, a^{2} b - 4 \, a b^{2} + b^{3} + 30 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(14 \, a^{2} b \cosh\left(f x + e\right)^{5} + 10 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(f x + e\right)^{3} + {\left(9 \, a^{2} b - 4 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + b^{3} + 2 \, {\left(3 \, a b^{2} - b^{3}\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(14 \, a^{2} b \cosh\left(f x + e\right)^{6} + 15 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(f x + e\right)^{4} + 3 \, a b^{2} - b^{3} + 3 \, {\left(9 \, a^{2} b - 4 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{2} + \sqrt{2} {\left(a^{2} \cosh\left(f x + e\right)^{6} + 6 \, a^{2} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + a^{2} \sinh\left(f x + e\right)^{6} + 3 \, a^{2} \cosh\left(f x + e\right)^{4} + 3 \, {\left(5 \, a^{2} \cosh\left(f x + e\right)^{2} + a^{2}\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(5 \, a^{2} \cosh\left(f x + e\right)^{3} + 3 \, a^{2} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + {\left(4 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{2} + {\left(15 \, a^{2} \cosh\left(f x + e\right)^{4} + 18 \, a^{2} \cosh\left(f x + e\right)^{2} + 4 \, a b - b^{2}\right)} \sinh\left(f x + e\right)^{2} + b^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(f x + e\right)^{5} + 6 \, a^{2} \cosh\left(f x + e\right)^{3} + {\left(4 \, a b - b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} + 4 \, {\left(2 \, a^{2} b \cosh\left(f x + e\right)^{7} + 3 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(f x + e\right)^{5} + {\left(9 \, a^{2} b - 4 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{3} + {\left(3 \, a b^{2} - b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)}{\cosh\left(f x + e\right)^{6} + 6 \, \cosh\left(f x + e\right)^{5} \sinh\left(f x + e\right) + 15 \, \cosh\left(f x + e\right)^{4} \sinh\left(f x + e\right)^{2} + 20 \, \cosh\left(f x + e\right)^{3} \sinh\left(f x + e\right)^{3} + 15 \, \cosh\left(f x + e\right)^{2} \sinh\left(f x + e\right)^{4} + 6 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + \sinh\left(f x + e\right)^{6}}\right) + 2 \, {\left({\left(a^{2} + 2 \, a b - 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left(a^{2} + 2 \, a b - 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{3} \sinh\left(f x + e\right) + 6 \, {\left(a^{2} + 2 \, a b - 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} \sinh\left(f x + e\right)^{2} + 4 \, {\left(a^{2} + 2 \, a b - 3 \, b^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(a^{2} + 2 \, a b - 3 \, b^{2}\right)} \sinh\left(f x + e\right)^{4}\right)} \sqrt{b} \log\left(-\frac{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + a - b\right)} \sinh\left(f x + e\right)^{2} + \sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} - 1\right)} \sqrt{b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}{\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}\right) - \sqrt{2} {\left(b^{2} \cosh\left(f x + e\right)^{6} + 6 \, b^{2} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + b^{2} \sinh\left(f x + e\right)^{6} + {\left(2 \, a b - 7 \, b^{2}\right)} \cosh\left(f x + e\right)^{4} + {\left(15 \, b^{2} \cosh\left(f x + e\right)^{2} + 2 \, a b - 7 \, b^{2}\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(5 \, b^{2} \cosh\left(f x + e\right)^{3} + {\left(2 \, a b - 7 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + {\left(2 \, a b - 7 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + {\left(15 \, b^{2} \cosh\left(f x + e\right)^{4} + 6 \, {\left(2 \, a b - 7 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + 2 \, a b - 7 \, b^{2}\right)} \sinh\left(f x + e\right)^{2} + b^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(f x + e\right)^{5} + 2 \, {\left(2 \, a b - 7 \, b^{2}\right)} \cosh\left(f x + e\right)^{3} + {\left(2 \, a b - 7 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{64 \, {\left(b^{2} f \cosh\left(f x + e\right)^{4} + 4 \, b^{2} f \cosh\left(f x + e\right)^{3} \sinh\left(f x + e\right) + 6 \, b^{2} f \cosh\left(f x + e\right)^{2} \sinh\left(f x + e\right)^{2} + 4 \, b^{2} f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b^{2} f \sinh\left(f x + e\right)^{4}\right)}}, \frac{4 \, {\left({\left(a^{2} + 2 \, a b - 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left(a^{2} + 2 \, a b - 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{3} \sinh\left(f x + e\right) + 6 \, {\left(a^{2} + 2 \, a b - 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} \sinh\left(f x + e\right)^{2} + 4 \, {\left(a^{2} + 2 \, a b - 3 \, b^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(a^{2} + 2 \, a b - 3 \, b^{2}\right)} \sinh\left(f x + e\right)^{4}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{2} {\left(a \cosh\left(f x + e\right)^{2} + 2 \, a \cosh\left(f x + e\right) \sinh\left(f x + e\right) + a \sinh\left(f x + e\right)^{2} + b\right)} \sqrt{-b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{a b \cosh\left(f x + e\right)^{4} + 4 \, a b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + a b \sinh\left(f x + e\right)^{4} + {\left(3 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{2} + {\left(6 \, a b \cosh\left(f x + e\right)^{2} + 3 \, a b - b^{2}\right)} \sinh\left(f x + e\right)^{2} + b^{2} + 2 \, {\left(2 \, a b \cosh\left(f x + e\right)^{3} + {\left(3 \, a b - b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)}\right) + 4 \, {\left({\left(a^{2} + 2 \, a b - 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left(a^{2} + 2 \, a b - 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{3} \sinh\left(f x + e\right) + 6 \, {\left(a^{2} + 2 \, a b - 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} \sinh\left(f x + e\right)^{2} + 4 \, {\left(a^{2} + 2 \, a b - 3 \, b^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(a^{2} + 2 \, a b - 3 \, b^{2}\right)} \sinh\left(f x + e\right)^{4}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} - 1\right)} \sqrt{-b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + 2 \, a - b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}\right) + \sqrt{2} {\left(b^{2} \cosh\left(f x + e\right)^{6} + 6 \, b^{2} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + b^{2} \sinh\left(f x + e\right)^{6} + {\left(2 \, a b - 7 \, b^{2}\right)} \cosh\left(f x + e\right)^{4} + {\left(15 \, b^{2} \cosh\left(f x + e\right)^{2} + 2 \, a b - 7 \, b^{2}\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(5 \, b^{2} \cosh\left(f x + e\right)^{3} + {\left(2 \, a b - 7 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + {\left(2 \, a b - 7 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + {\left(15 \, b^{2} \cosh\left(f x + e\right)^{4} + 6 \, {\left(2 \, a b - 7 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + 2 \, a b - 7 \, b^{2}\right)} \sinh\left(f x + e\right)^{2} + b^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(f x + e\right)^{5} + 2 \, {\left(2 \, a b - 7 \, b^{2}\right)} \cosh\left(f x + e\right)^{3} + {\left(2 \, a b - 7 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{64 \, {\left(b^{2} f \cosh\left(f x + e\right)^{4} + 4 \, b^{2} f \cosh\left(f x + e\right)^{3} \sinh\left(f x + e\right) + 6 \, b^{2} f \cosh\left(f x + e\right)^{2} \sinh\left(f x + e\right)^{2} + 4 \, b^{2} f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b^{2} f \sinh\left(f x + e\right)^{4}\right)}}\right]"," ",0,"[-1/64*(2*((a^2 + 2*a*b - 3*b^2)*cosh(f*x + e)^4 + 4*(a^2 + 2*a*b - 3*b^2)*cosh(f*x + e)^3*sinh(f*x + e) + 6*(a^2 + 2*a*b - 3*b^2)*cosh(f*x + e)^2*sinh(f*x + e)^2 + 4*(a^2 + 2*a*b - 3*b^2)*cosh(f*x + e)*sinh(f*x + e)^3 + (a^2 + 2*a*b - 3*b^2)*sinh(f*x + e)^4)*sqrt(b)*log((a^2*b*cosh(f*x + e)^8 + 8*a^2*b*cosh(f*x + e)*sinh(f*x + e)^7 + a^2*b*sinh(f*x + e)^8 + 2*(a^3 + a^2*b)*cosh(f*x + e)^6 + 2*(14*a^2*b*cosh(f*x + e)^2 + a^3 + a^2*b)*sinh(f*x + e)^6 + 4*(14*a^2*b*cosh(f*x + e)^3 + 3*(a^3 + a^2*b)*cosh(f*x + e))*sinh(f*x + e)^5 + (9*a^2*b - 4*a*b^2 + b^3)*cosh(f*x + e)^4 + (70*a^2*b*cosh(f*x + e)^4 + 9*a^2*b - 4*a*b^2 + b^3 + 30*(a^3 + a^2*b)*cosh(f*x + e)^2)*sinh(f*x + e)^4 + 4*(14*a^2*b*cosh(f*x + e)^5 + 10*(a^3 + a^2*b)*cosh(f*x + e)^3 + (9*a^2*b - 4*a*b^2 + b^3)*cosh(f*x + e))*sinh(f*x + e)^3 + b^3 + 2*(3*a*b^2 - b^3)*cosh(f*x + e)^2 + 2*(14*a^2*b*cosh(f*x + e)^6 + 15*(a^3 + a^2*b)*cosh(f*x + e)^4 + 3*a*b^2 - b^3 + 3*(9*a^2*b - 4*a*b^2 + b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^2 + sqrt(2)*(a^2*cosh(f*x + e)^6 + 6*a^2*cosh(f*x + e)*sinh(f*x + e)^5 + a^2*sinh(f*x + e)^6 + 3*a^2*cosh(f*x + e)^4 + 3*(5*a^2*cosh(f*x + e)^2 + a^2)*sinh(f*x + e)^4 + 4*(5*a^2*cosh(f*x + e)^3 + 3*a^2*cosh(f*x + e))*sinh(f*x + e)^3 + (4*a*b - b^2)*cosh(f*x + e)^2 + (15*a^2*cosh(f*x + e)^4 + 18*a^2*cosh(f*x + e)^2 + 4*a*b - b^2)*sinh(f*x + e)^2 + b^2 + 2*(3*a^2*cosh(f*x + e)^5 + 6*a^2*cosh(f*x + e)^3 + (4*a*b - b^2)*cosh(f*x + e))*sinh(f*x + e))*sqrt(b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + 4*(2*a^2*b*cosh(f*x + e)^7 + 3*(a^3 + a^2*b)*cosh(f*x + e)^5 + (9*a^2*b - 4*a*b^2 + b^3)*cosh(f*x + e)^3 + (3*a*b^2 - b^3)*cosh(f*x + e))*sinh(f*x + e))/(cosh(f*x + e)^6 + 6*cosh(f*x + e)^5*sinh(f*x + e) + 15*cosh(f*x + e)^4*sinh(f*x + e)^2 + 20*cosh(f*x + e)^3*sinh(f*x + e)^3 + 15*cosh(f*x + e)^2*sinh(f*x + e)^4 + 6*cosh(f*x + e)*sinh(f*x + e)^5 + sinh(f*x + e)^6)) + 2*((a^2 + 2*a*b - 3*b^2)*cosh(f*x + e)^4 + 4*(a^2 + 2*a*b - 3*b^2)*cosh(f*x + e)^3*sinh(f*x + e) + 6*(a^2 + 2*a*b - 3*b^2)*cosh(f*x + e)^2*sinh(f*x + e)^2 + 4*(a^2 + 2*a*b - 3*b^2)*cosh(f*x + e)*sinh(f*x + e)^3 + (a^2 + 2*a*b - 3*b^2)*sinh(f*x + e)^4)*sqrt(b)*log(-(b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(a - b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + a - b)*sinh(f*x + e)^2 + sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 - 1)*sqrt(b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + 4*(b*cosh(f*x + e)^3 + (a - b)*cosh(f*x + e))*sinh(f*x + e) + b)/(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) - sqrt(2)*(b^2*cosh(f*x + e)^6 + 6*b^2*cosh(f*x + e)*sinh(f*x + e)^5 + b^2*sinh(f*x + e)^6 + (2*a*b - 7*b^2)*cosh(f*x + e)^4 + (15*b^2*cosh(f*x + e)^2 + 2*a*b - 7*b^2)*sinh(f*x + e)^4 + 4*(5*b^2*cosh(f*x + e)^3 + (2*a*b - 7*b^2)*cosh(f*x + e))*sinh(f*x + e)^3 + (2*a*b - 7*b^2)*cosh(f*x + e)^2 + (15*b^2*cosh(f*x + e)^4 + 6*(2*a*b - 7*b^2)*cosh(f*x + e)^2 + 2*a*b - 7*b^2)*sinh(f*x + e)^2 + b^2 + 2*(3*b^2*cosh(f*x + e)^5 + 2*(2*a*b - 7*b^2)*cosh(f*x + e)^3 + (2*a*b - 7*b^2)*cosh(f*x + e))*sinh(f*x + e))*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/(b^2*f*cosh(f*x + e)^4 + 4*b^2*f*cosh(f*x + e)^3*sinh(f*x + e) + 6*b^2*f*cosh(f*x + e)^2*sinh(f*x + e)^2 + 4*b^2*f*cosh(f*x + e)*sinh(f*x + e)^3 + b^2*f*sinh(f*x + e)^4), 1/64*(4*((a^2 + 2*a*b - 3*b^2)*cosh(f*x + e)^4 + 4*(a^2 + 2*a*b - 3*b^2)*cosh(f*x + e)^3*sinh(f*x + e) + 6*(a^2 + 2*a*b - 3*b^2)*cosh(f*x + e)^2*sinh(f*x + e)^2 + 4*(a^2 + 2*a*b - 3*b^2)*cosh(f*x + e)*sinh(f*x + e)^3 + (a^2 + 2*a*b - 3*b^2)*sinh(f*x + e)^4)*sqrt(-b)*arctan(sqrt(2)*(a*cosh(f*x + e)^2 + 2*a*cosh(f*x + e)*sinh(f*x + e) + a*sinh(f*x + e)^2 + b)*sqrt(-b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/(a*b*cosh(f*x + e)^4 + 4*a*b*cosh(f*x + e)*sinh(f*x + e)^3 + a*b*sinh(f*x + e)^4 + (3*a*b - b^2)*cosh(f*x + e)^2 + (6*a*b*cosh(f*x + e)^2 + 3*a*b - b^2)*sinh(f*x + e)^2 + b^2 + 2*(2*a*b*cosh(f*x + e)^3 + (3*a*b - b^2)*cosh(f*x + e))*sinh(f*x + e))) + 4*((a^2 + 2*a*b - 3*b^2)*cosh(f*x + e)^4 + 4*(a^2 + 2*a*b - 3*b^2)*cosh(f*x + e)^3*sinh(f*x + e) + 6*(a^2 + 2*a*b - 3*b^2)*cosh(f*x + e)^2*sinh(f*x + e)^2 + 4*(a^2 + 2*a*b - 3*b^2)*cosh(f*x + e)*sinh(f*x + e)^3 + (a^2 + 2*a*b - 3*b^2)*sinh(f*x + e)^4)*sqrt(-b)*arctan(sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 - 1)*sqrt(-b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/(b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(2*a - b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 2*a - b)*sinh(f*x + e)^2 + 4*(b*cosh(f*x + e)^3 + (2*a - b)*cosh(f*x + e))*sinh(f*x + e) + b)) + sqrt(2)*(b^2*cosh(f*x + e)^6 + 6*b^2*cosh(f*x + e)*sinh(f*x + e)^5 + b^2*sinh(f*x + e)^6 + (2*a*b - 7*b^2)*cosh(f*x + e)^4 + (15*b^2*cosh(f*x + e)^2 + 2*a*b - 7*b^2)*sinh(f*x + e)^4 + 4*(5*b^2*cosh(f*x + e)^3 + (2*a*b - 7*b^2)*cosh(f*x + e))*sinh(f*x + e)^3 + (2*a*b - 7*b^2)*cosh(f*x + e)^2 + (15*b^2*cosh(f*x + e)^4 + 6*(2*a*b - 7*b^2)*cosh(f*x + e)^2 + 2*a*b - 7*b^2)*sinh(f*x + e)^2 + b^2 + 2*(3*b^2*cosh(f*x + e)^5 + 2*(2*a*b - 7*b^2)*cosh(f*x + e)^3 + (2*a*b - 7*b^2)*cosh(f*x + e))*sinh(f*x + e))*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/(b^2*f*cosh(f*x + e)^4 + 4*b^2*f*cosh(f*x + e)^3*sinh(f*x + e) + 6*b^2*f*cosh(f*x + e)^2*sinh(f*x + e)^2 + 4*b^2*f*cosh(f*x + e)*sinh(f*x + e)^3 + b^2*f*sinh(f*x + e)^4)]","B",0
67,1,2130,0,0.556574," ","integrate(sinh(f*x+e)*(a+b*sinh(f*x+e)^2)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left({\left(a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(a - b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) + {\left(a - b\right)} \sinh\left(f x + e\right)^{2}\right)} \sqrt{b} \log\left(\frac{a^{2} b \cosh\left(f x + e\right)^{8} + 8 \, a^{2} b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + a^{2} b \sinh\left(f x + e\right)^{8} + 2 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(f x + e\right)^{6} + 2 \, {\left(14 \, a^{2} b \cosh\left(f x + e\right)^{2} + a^{3} + a^{2} b\right)} \sinh\left(f x + e\right)^{6} + 4 \, {\left(14 \, a^{2} b \cosh\left(f x + e\right)^{3} + 3 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + {\left(9 \, a^{2} b - 4 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{4} + {\left(70 \, a^{2} b \cosh\left(f x + e\right)^{4} + 9 \, a^{2} b - 4 \, a b^{2} + b^{3} + 30 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(14 \, a^{2} b \cosh\left(f x + e\right)^{5} + 10 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(f x + e\right)^{3} + {\left(9 \, a^{2} b - 4 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + b^{3} + 2 \, {\left(3 \, a b^{2} - b^{3}\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(14 \, a^{2} b \cosh\left(f x + e\right)^{6} + 15 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(f x + e\right)^{4} + 3 \, a b^{2} - b^{3} + 3 \, {\left(9 \, a^{2} b - 4 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{2} - \sqrt{2} {\left(a^{2} \cosh\left(f x + e\right)^{6} + 6 \, a^{2} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + a^{2} \sinh\left(f x + e\right)^{6} + 3 \, a^{2} \cosh\left(f x + e\right)^{4} + 3 \, {\left(5 \, a^{2} \cosh\left(f x + e\right)^{2} + a^{2}\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(5 \, a^{2} \cosh\left(f x + e\right)^{3} + 3 \, a^{2} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + {\left(4 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{2} + {\left(15 \, a^{2} \cosh\left(f x + e\right)^{4} + 18 \, a^{2} \cosh\left(f x + e\right)^{2} + 4 \, a b - b^{2}\right)} \sinh\left(f x + e\right)^{2} + b^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(f x + e\right)^{5} + 6 \, a^{2} \cosh\left(f x + e\right)^{3} + {\left(4 \, a b - b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} + 4 \, {\left(2 \, a^{2} b \cosh\left(f x + e\right)^{7} + 3 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(f x + e\right)^{5} + {\left(9 \, a^{2} b - 4 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{3} + {\left(3 \, a b^{2} - b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)}{\cosh\left(f x + e\right)^{6} + 6 \, \cosh\left(f x + e\right)^{5} \sinh\left(f x + e\right) + 15 \, \cosh\left(f x + e\right)^{4} \sinh\left(f x + e\right)^{2} + 20 \, \cosh\left(f x + e\right)^{3} \sinh\left(f x + e\right)^{3} + 15 \, \cosh\left(f x + e\right)^{2} \sinh\left(f x + e\right)^{4} + 6 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + \sinh\left(f x + e\right)^{6}}\right) + {\left({\left(a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(a - b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) + {\left(a - b\right)} \sinh\left(f x + e\right)^{2}\right)} \sqrt{b} \log\left(-\frac{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + a - b\right)} \sinh\left(f x + e\right)^{2} - \sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} - 1\right)} \sqrt{b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}{\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}\right) - \sqrt{2} {\left(b \cosh\left(f x + e\right)^{2} + 2 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right) + b \sinh\left(f x + e\right)^{2} + b\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{8 \, {\left(b f \cosh\left(f x + e\right)^{2} + 2 \, b f \cosh\left(f x + e\right) \sinh\left(f x + e\right) + b f \sinh\left(f x + e\right)^{2}\right)}}, -\frac{2 \, {\left({\left(a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(a - b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) + {\left(a - b\right)} \sinh\left(f x + e\right)^{2}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{2} {\left(a \cosh\left(f x + e\right)^{2} + 2 \, a \cosh\left(f x + e\right) \sinh\left(f x + e\right) + a \sinh\left(f x + e\right)^{2} + b\right)} \sqrt{-b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{a b \cosh\left(f x + e\right)^{4} + 4 \, a b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + a b \sinh\left(f x + e\right)^{4} + {\left(3 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{2} + {\left(6 \, a b \cosh\left(f x + e\right)^{2} + 3 \, a b - b^{2}\right)} \sinh\left(f x + e\right)^{2} + b^{2} + 2 \, {\left(2 \, a b \cosh\left(f x + e\right)^{3} + {\left(3 \, a b - b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)}\right) + 2 \, {\left({\left(a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(a - b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) + {\left(a - b\right)} \sinh\left(f x + e\right)^{2}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} - 1\right)} \sqrt{-b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + 2 \, a - b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}\right) - \sqrt{2} {\left(b \cosh\left(f x + e\right)^{2} + 2 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right) + b \sinh\left(f x + e\right)^{2} + b\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{8 \, {\left(b f \cosh\left(f x + e\right)^{2} + 2 \, b f \cosh\left(f x + e\right) \sinh\left(f x + e\right) + b f \sinh\left(f x + e\right)^{2}\right)}}\right]"," ",0,"[-1/8*(((a - b)*cosh(f*x + e)^2 + 2*(a - b)*cosh(f*x + e)*sinh(f*x + e) + (a - b)*sinh(f*x + e)^2)*sqrt(b)*log((a^2*b*cosh(f*x + e)^8 + 8*a^2*b*cosh(f*x + e)*sinh(f*x + e)^7 + a^2*b*sinh(f*x + e)^8 + 2*(a^3 + a^2*b)*cosh(f*x + e)^6 + 2*(14*a^2*b*cosh(f*x + e)^2 + a^3 + a^2*b)*sinh(f*x + e)^6 + 4*(14*a^2*b*cosh(f*x + e)^3 + 3*(a^3 + a^2*b)*cosh(f*x + e))*sinh(f*x + e)^5 + (9*a^2*b - 4*a*b^2 + b^3)*cosh(f*x + e)^4 + (70*a^2*b*cosh(f*x + e)^4 + 9*a^2*b - 4*a*b^2 + b^3 + 30*(a^3 + a^2*b)*cosh(f*x + e)^2)*sinh(f*x + e)^4 + 4*(14*a^2*b*cosh(f*x + e)^5 + 10*(a^3 + a^2*b)*cosh(f*x + e)^3 + (9*a^2*b - 4*a*b^2 + b^3)*cosh(f*x + e))*sinh(f*x + e)^3 + b^3 + 2*(3*a*b^2 - b^3)*cosh(f*x + e)^2 + 2*(14*a^2*b*cosh(f*x + e)^6 + 15*(a^3 + a^2*b)*cosh(f*x + e)^4 + 3*a*b^2 - b^3 + 3*(9*a^2*b - 4*a*b^2 + b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^2 - sqrt(2)*(a^2*cosh(f*x + e)^6 + 6*a^2*cosh(f*x + e)*sinh(f*x + e)^5 + a^2*sinh(f*x + e)^6 + 3*a^2*cosh(f*x + e)^4 + 3*(5*a^2*cosh(f*x + e)^2 + a^2)*sinh(f*x + e)^4 + 4*(5*a^2*cosh(f*x + e)^3 + 3*a^2*cosh(f*x + e))*sinh(f*x + e)^3 + (4*a*b - b^2)*cosh(f*x + e)^2 + (15*a^2*cosh(f*x + e)^4 + 18*a^2*cosh(f*x + e)^2 + 4*a*b - b^2)*sinh(f*x + e)^2 + b^2 + 2*(3*a^2*cosh(f*x + e)^5 + 6*a^2*cosh(f*x + e)^3 + (4*a*b - b^2)*cosh(f*x + e))*sinh(f*x + e))*sqrt(b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + 4*(2*a^2*b*cosh(f*x + e)^7 + 3*(a^3 + a^2*b)*cosh(f*x + e)^5 + (9*a^2*b - 4*a*b^2 + b^3)*cosh(f*x + e)^3 + (3*a*b^2 - b^3)*cosh(f*x + e))*sinh(f*x + e))/(cosh(f*x + e)^6 + 6*cosh(f*x + e)^5*sinh(f*x + e) + 15*cosh(f*x + e)^4*sinh(f*x + e)^2 + 20*cosh(f*x + e)^3*sinh(f*x + e)^3 + 15*cosh(f*x + e)^2*sinh(f*x + e)^4 + 6*cosh(f*x + e)*sinh(f*x + e)^5 + sinh(f*x + e)^6)) + ((a - b)*cosh(f*x + e)^2 + 2*(a - b)*cosh(f*x + e)*sinh(f*x + e) + (a - b)*sinh(f*x + e)^2)*sqrt(b)*log(-(b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(a - b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + a - b)*sinh(f*x + e)^2 - sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 - 1)*sqrt(b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + 4*(b*cosh(f*x + e)^3 + (a - b)*cosh(f*x + e))*sinh(f*x + e) + b)/(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) - sqrt(2)*(b*cosh(f*x + e)^2 + 2*b*cosh(f*x + e)*sinh(f*x + e) + b*sinh(f*x + e)^2 + b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/(b*f*cosh(f*x + e)^2 + 2*b*f*cosh(f*x + e)*sinh(f*x + e) + b*f*sinh(f*x + e)^2), -1/8*(2*((a - b)*cosh(f*x + e)^2 + 2*(a - b)*cosh(f*x + e)*sinh(f*x + e) + (a - b)*sinh(f*x + e)^2)*sqrt(-b)*arctan(sqrt(2)*(a*cosh(f*x + e)^2 + 2*a*cosh(f*x + e)*sinh(f*x + e) + a*sinh(f*x + e)^2 + b)*sqrt(-b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/(a*b*cosh(f*x + e)^4 + 4*a*b*cosh(f*x + e)*sinh(f*x + e)^3 + a*b*sinh(f*x + e)^4 + (3*a*b - b^2)*cosh(f*x + e)^2 + (6*a*b*cosh(f*x + e)^2 + 3*a*b - b^2)*sinh(f*x + e)^2 + b^2 + 2*(2*a*b*cosh(f*x + e)^3 + (3*a*b - b^2)*cosh(f*x + e))*sinh(f*x + e))) + 2*((a - b)*cosh(f*x + e)^2 + 2*(a - b)*cosh(f*x + e)*sinh(f*x + e) + (a - b)*sinh(f*x + e)^2)*sqrt(-b)*arctan(sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 - 1)*sqrt(-b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/(b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(2*a - b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 2*a - b)*sinh(f*x + e)^2 + 4*(b*cosh(f*x + e)^3 + (2*a - b)*cosh(f*x + e))*sinh(f*x + e) + b)) - sqrt(2)*(b*cosh(f*x + e)^2 + 2*b*cosh(f*x + e)*sinh(f*x + e) + b*sinh(f*x + e)^2 + b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/(b*f*cosh(f*x + e)^2 + 2*b*f*cosh(f*x + e)*sinh(f*x + e) + b*f*sinh(f*x + e)^2)]","B",0
68,1,4423,0,1.245536," ","integrate(csch(f*x+e)*(a+b*sinh(f*x+e)^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{b} \log\left(\frac{a^{2} b \cosh\left(f x + e\right)^{8} + 8 \, a^{2} b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + a^{2} b \sinh\left(f x + e\right)^{8} + 2 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(f x + e\right)^{6} + 2 \, {\left(14 \, a^{2} b \cosh\left(f x + e\right)^{2} + a^{3} + a^{2} b\right)} \sinh\left(f x + e\right)^{6} + 4 \, {\left(14 \, a^{2} b \cosh\left(f x + e\right)^{3} + 3 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + {\left(9 \, a^{2} b - 4 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{4} + {\left(70 \, a^{2} b \cosh\left(f x + e\right)^{4} + 9 \, a^{2} b - 4 \, a b^{2} + b^{3} + 30 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(14 \, a^{2} b \cosh\left(f x + e\right)^{5} + 10 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(f x + e\right)^{3} + {\left(9 \, a^{2} b - 4 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + b^{3} + 2 \, {\left(3 \, a b^{2} - b^{3}\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(14 \, a^{2} b \cosh\left(f x + e\right)^{6} + 15 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(f x + e\right)^{4} + 3 \, a b^{2} - b^{3} + 3 \, {\left(9 \, a^{2} b - 4 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{2} + \sqrt{2} {\left(a^{2} \cosh\left(f x + e\right)^{6} + 6 \, a^{2} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + a^{2} \sinh\left(f x + e\right)^{6} + 3 \, a^{2} \cosh\left(f x + e\right)^{4} + 3 \, {\left(5 \, a^{2} \cosh\left(f x + e\right)^{2} + a^{2}\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(5 \, a^{2} \cosh\left(f x + e\right)^{3} + 3 \, a^{2} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + {\left(4 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{2} + {\left(15 \, a^{2} \cosh\left(f x + e\right)^{4} + 18 \, a^{2} \cosh\left(f x + e\right)^{2} + 4 \, a b - b^{2}\right)} \sinh\left(f x + e\right)^{2} + b^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(f x + e\right)^{5} + 6 \, a^{2} \cosh\left(f x + e\right)^{3} + {\left(4 \, a b - b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} + 4 \, {\left(2 \, a^{2} b \cosh\left(f x + e\right)^{7} + 3 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(f x + e\right)^{5} + {\left(9 \, a^{2} b - 4 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{3} + {\left(3 \, a b^{2} - b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)}{\cosh\left(f x + e\right)^{6} + 6 \, \cosh\left(f x + e\right)^{5} \sinh\left(f x + e\right) + 15 \, \cosh\left(f x + e\right)^{4} \sinh\left(f x + e\right)^{2} + 20 \, \cosh\left(f x + e\right)^{3} \sinh\left(f x + e\right)^{3} + 15 \, \cosh\left(f x + e\right)^{2} \sinh\left(f x + e\right)^{4} + 6 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + \sinh\left(f x + e\right)^{6}}\right) + 2 \, \sqrt{a} \log\left(-\frac{{\left(a + b\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(a + b\right)} \sinh\left(f x + e\right)^{4} + 2 \, {\left(3 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(f x + e\right)^{2} + 3 \, a - b\right)} \sinh\left(f x + e\right)^{2} - 2 \, \sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} + 1\right)} \sqrt{a} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(f x + e\right)^{3} + {\left(3 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + a + b}{\cosh\left(f x + e\right)^{4} + 4 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + \sinh\left(f x + e\right)^{4} + 2 \, {\left(3 \, \cosh\left(f x + e\right)^{2} - 1\right)} \sinh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right)^{2} + 4 \, {\left(\cosh\left(f x + e\right)^{3} - \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + 1}\right) + \sqrt{b} \log\left(-\frac{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + a - b\right)} \sinh\left(f x + e\right)^{2} + \sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} - 1\right)} \sqrt{b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}{\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}\right)}{4 \, f}, \frac{4 \, \sqrt{-a} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} + 1\right)} \sqrt{-a} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + 2 \, a - b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}\right) + \sqrt{b} \log\left(\frac{a^{2} b \cosh\left(f x + e\right)^{8} + 8 \, a^{2} b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + a^{2} b \sinh\left(f x + e\right)^{8} + 2 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(f x + e\right)^{6} + 2 \, {\left(14 \, a^{2} b \cosh\left(f x + e\right)^{2} + a^{3} + a^{2} b\right)} \sinh\left(f x + e\right)^{6} + 4 \, {\left(14 \, a^{2} b \cosh\left(f x + e\right)^{3} + 3 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + {\left(9 \, a^{2} b - 4 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{4} + {\left(70 \, a^{2} b \cosh\left(f x + e\right)^{4} + 9 \, a^{2} b - 4 \, a b^{2} + b^{3} + 30 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(14 \, a^{2} b \cosh\left(f x + e\right)^{5} + 10 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(f x + e\right)^{3} + {\left(9 \, a^{2} b - 4 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + b^{3} + 2 \, {\left(3 \, a b^{2} - b^{3}\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(14 \, a^{2} b \cosh\left(f x + e\right)^{6} + 15 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(f x + e\right)^{4} + 3 \, a b^{2} - b^{3} + 3 \, {\left(9 \, a^{2} b - 4 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{2} + \sqrt{2} {\left(a^{2} \cosh\left(f x + e\right)^{6} + 6 \, a^{2} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + a^{2} \sinh\left(f x + e\right)^{6} + 3 \, a^{2} \cosh\left(f x + e\right)^{4} + 3 \, {\left(5 \, a^{2} \cosh\left(f x + e\right)^{2} + a^{2}\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(5 \, a^{2} \cosh\left(f x + e\right)^{3} + 3 \, a^{2} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + {\left(4 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{2} + {\left(15 \, a^{2} \cosh\left(f x + e\right)^{4} + 18 \, a^{2} \cosh\left(f x + e\right)^{2} + 4 \, a b - b^{2}\right)} \sinh\left(f x + e\right)^{2} + b^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(f x + e\right)^{5} + 6 \, a^{2} \cosh\left(f x + e\right)^{3} + {\left(4 \, a b - b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} + 4 \, {\left(2 \, a^{2} b \cosh\left(f x + e\right)^{7} + 3 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(f x + e\right)^{5} + {\left(9 \, a^{2} b - 4 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{3} + {\left(3 \, a b^{2} - b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)}{\cosh\left(f x + e\right)^{6} + 6 \, \cosh\left(f x + e\right)^{5} \sinh\left(f x + e\right) + 15 \, \cosh\left(f x + e\right)^{4} \sinh\left(f x + e\right)^{2} + 20 \, \cosh\left(f x + e\right)^{3} \sinh\left(f x + e\right)^{3} + 15 \, \cosh\left(f x + e\right)^{2} \sinh\left(f x + e\right)^{4} + 6 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + \sinh\left(f x + e\right)^{6}}\right) + \sqrt{b} \log\left(-\frac{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + a - b\right)} \sinh\left(f x + e\right)^{2} + \sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} - 1\right)} \sqrt{b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}{\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}\right)}{4 \, f}, -\frac{\sqrt{-b} \arctan\left(\frac{\sqrt{2} {\left(a \cosh\left(f x + e\right)^{2} + 2 \, a \cosh\left(f x + e\right) \sinh\left(f x + e\right) + a \sinh\left(f x + e\right)^{2} + b\right)} \sqrt{-b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{a b \cosh\left(f x + e\right)^{4} + 4 \, a b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + a b \sinh\left(f x + e\right)^{4} + {\left(3 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{2} + {\left(6 \, a b \cosh\left(f x + e\right)^{2} + 3 \, a b - b^{2}\right)} \sinh\left(f x + e\right)^{2} + b^{2} + 2 \, {\left(2 \, a b \cosh\left(f x + e\right)^{3} + {\left(3 \, a b - b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)}\right) + \sqrt{-b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} - 1\right)} \sqrt{-b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + 2 \, a - b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}\right) - \sqrt{a} \log\left(-\frac{{\left(a + b\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(a + b\right)} \sinh\left(f x + e\right)^{4} + 2 \, {\left(3 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(f x + e\right)^{2} + 3 \, a - b\right)} \sinh\left(f x + e\right)^{2} - 2 \, \sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} + 1\right)} \sqrt{a} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(f x + e\right)^{3} + {\left(3 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + a + b}{\cosh\left(f x + e\right)^{4} + 4 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + \sinh\left(f x + e\right)^{4} + 2 \, {\left(3 \, \cosh\left(f x + e\right)^{2} - 1\right)} \sinh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right)^{2} + 4 \, {\left(\cosh\left(f x + e\right)^{3} - \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + 1}\right)}{2 \, f}, \frac{2 \, \sqrt{-a} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} + 1\right)} \sqrt{-a} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + 2 \, a - b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}\right) - \sqrt{-b} \arctan\left(\frac{\sqrt{2} {\left(a \cosh\left(f x + e\right)^{2} + 2 \, a \cosh\left(f x + e\right) \sinh\left(f x + e\right) + a \sinh\left(f x + e\right)^{2} + b\right)} \sqrt{-b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{a b \cosh\left(f x + e\right)^{4} + 4 \, a b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + a b \sinh\left(f x + e\right)^{4} + {\left(3 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{2} + {\left(6 \, a b \cosh\left(f x + e\right)^{2} + 3 \, a b - b^{2}\right)} \sinh\left(f x + e\right)^{2} + b^{2} + 2 \, {\left(2 \, a b \cosh\left(f x + e\right)^{3} + {\left(3 \, a b - b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)}\right) - \sqrt{-b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} - 1\right)} \sqrt{-b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + 2 \, a - b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}\right)}{2 \, f}\right]"," ",0,"[1/4*(sqrt(b)*log((a^2*b*cosh(f*x + e)^8 + 8*a^2*b*cosh(f*x + e)*sinh(f*x + e)^7 + a^2*b*sinh(f*x + e)^8 + 2*(a^3 + a^2*b)*cosh(f*x + e)^6 + 2*(14*a^2*b*cosh(f*x + e)^2 + a^3 + a^2*b)*sinh(f*x + e)^6 + 4*(14*a^2*b*cosh(f*x + e)^3 + 3*(a^3 + a^2*b)*cosh(f*x + e))*sinh(f*x + e)^5 + (9*a^2*b - 4*a*b^2 + b^3)*cosh(f*x + e)^4 + (70*a^2*b*cosh(f*x + e)^4 + 9*a^2*b - 4*a*b^2 + b^3 + 30*(a^3 + a^2*b)*cosh(f*x + e)^2)*sinh(f*x + e)^4 + 4*(14*a^2*b*cosh(f*x + e)^5 + 10*(a^3 + a^2*b)*cosh(f*x + e)^3 + (9*a^2*b - 4*a*b^2 + b^3)*cosh(f*x + e))*sinh(f*x + e)^3 + b^3 + 2*(3*a*b^2 - b^3)*cosh(f*x + e)^2 + 2*(14*a^2*b*cosh(f*x + e)^6 + 15*(a^3 + a^2*b)*cosh(f*x + e)^4 + 3*a*b^2 - b^3 + 3*(9*a^2*b - 4*a*b^2 + b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^2 + sqrt(2)*(a^2*cosh(f*x + e)^6 + 6*a^2*cosh(f*x + e)*sinh(f*x + e)^5 + a^2*sinh(f*x + e)^6 + 3*a^2*cosh(f*x + e)^4 + 3*(5*a^2*cosh(f*x + e)^2 + a^2)*sinh(f*x + e)^4 + 4*(5*a^2*cosh(f*x + e)^3 + 3*a^2*cosh(f*x + e))*sinh(f*x + e)^3 + (4*a*b - b^2)*cosh(f*x + e)^2 + (15*a^2*cosh(f*x + e)^4 + 18*a^2*cosh(f*x + e)^2 + 4*a*b - b^2)*sinh(f*x + e)^2 + b^2 + 2*(3*a^2*cosh(f*x + e)^5 + 6*a^2*cosh(f*x + e)^3 + (4*a*b - b^2)*cosh(f*x + e))*sinh(f*x + e))*sqrt(b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + 4*(2*a^2*b*cosh(f*x + e)^7 + 3*(a^3 + a^2*b)*cosh(f*x + e)^5 + (9*a^2*b - 4*a*b^2 + b^3)*cosh(f*x + e)^3 + (3*a*b^2 - b^3)*cosh(f*x + e))*sinh(f*x + e))/(cosh(f*x + e)^6 + 6*cosh(f*x + e)^5*sinh(f*x + e) + 15*cosh(f*x + e)^4*sinh(f*x + e)^2 + 20*cosh(f*x + e)^3*sinh(f*x + e)^3 + 15*cosh(f*x + e)^2*sinh(f*x + e)^4 + 6*cosh(f*x + e)*sinh(f*x + e)^5 + sinh(f*x + e)^6)) + 2*sqrt(a)*log(-((a + b)*cosh(f*x + e)^4 + 4*(a + b)*cosh(f*x + e)*sinh(f*x + e)^3 + (a + b)*sinh(f*x + e)^4 + 2*(3*a - b)*cosh(f*x + e)^2 + 2*(3*(a + b)*cosh(f*x + e)^2 + 3*a - b)*sinh(f*x + e)^2 - 2*sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 + 1)*sqrt(a)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + 4*((a + b)*cosh(f*x + e)^3 + (3*a - b)*cosh(f*x + e))*sinh(f*x + e) + a + b)/(cosh(f*x + e)^4 + 4*cosh(f*x + e)*sinh(f*x + e)^3 + sinh(f*x + e)^4 + 2*(3*cosh(f*x + e)^2 - 1)*sinh(f*x + e)^2 - 2*cosh(f*x + e)^2 + 4*(cosh(f*x + e)^3 - cosh(f*x + e))*sinh(f*x + e) + 1)) + sqrt(b)*log(-(b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(a - b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + a - b)*sinh(f*x + e)^2 + sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 - 1)*sqrt(b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + 4*(b*cosh(f*x + e)^3 + (a - b)*cosh(f*x + e))*sinh(f*x + e) + b)/(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/f, 1/4*(4*sqrt(-a)*arctan(sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 + 1)*sqrt(-a)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/(b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(2*a - b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 2*a - b)*sinh(f*x + e)^2 + 4*(b*cosh(f*x + e)^3 + (2*a - b)*cosh(f*x + e))*sinh(f*x + e) + b)) + sqrt(b)*log((a^2*b*cosh(f*x + e)^8 + 8*a^2*b*cosh(f*x + e)*sinh(f*x + e)^7 + a^2*b*sinh(f*x + e)^8 + 2*(a^3 + a^2*b)*cosh(f*x + e)^6 + 2*(14*a^2*b*cosh(f*x + e)^2 + a^3 + a^2*b)*sinh(f*x + e)^6 + 4*(14*a^2*b*cosh(f*x + e)^3 + 3*(a^3 + a^2*b)*cosh(f*x + e))*sinh(f*x + e)^5 + (9*a^2*b - 4*a*b^2 + b^3)*cosh(f*x + e)^4 + (70*a^2*b*cosh(f*x + e)^4 + 9*a^2*b - 4*a*b^2 + b^3 + 30*(a^3 + a^2*b)*cosh(f*x + e)^2)*sinh(f*x + e)^4 + 4*(14*a^2*b*cosh(f*x + e)^5 + 10*(a^3 + a^2*b)*cosh(f*x + e)^3 + (9*a^2*b - 4*a*b^2 + b^3)*cosh(f*x + e))*sinh(f*x + e)^3 + b^3 + 2*(3*a*b^2 - b^3)*cosh(f*x + e)^2 + 2*(14*a^2*b*cosh(f*x + e)^6 + 15*(a^3 + a^2*b)*cosh(f*x + e)^4 + 3*a*b^2 - b^3 + 3*(9*a^2*b - 4*a*b^2 + b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^2 + sqrt(2)*(a^2*cosh(f*x + e)^6 + 6*a^2*cosh(f*x + e)*sinh(f*x + e)^5 + a^2*sinh(f*x + e)^6 + 3*a^2*cosh(f*x + e)^4 + 3*(5*a^2*cosh(f*x + e)^2 + a^2)*sinh(f*x + e)^4 + 4*(5*a^2*cosh(f*x + e)^3 + 3*a^2*cosh(f*x + e))*sinh(f*x + e)^3 + (4*a*b - b^2)*cosh(f*x + e)^2 + (15*a^2*cosh(f*x + e)^4 + 18*a^2*cosh(f*x + e)^2 + 4*a*b - b^2)*sinh(f*x + e)^2 + b^2 + 2*(3*a^2*cosh(f*x + e)^5 + 6*a^2*cosh(f*x + e)^3 + (4*a*b - b^2)*cosh(f*x + e))*sinh(f*x + e))*sqrt(b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + 4*(2*a^2*b*cosh(f*x + e)^7 + 3*(a^3 + a^2*b)*cosh(f*x + e)^5 + (9*a^2*b - 4*a*b^2 + b^3)*cosh(f*x + e)^3 + (3*a*b^2 - b^3)*cosh(f*x + e))*sinh(f*x + e))/(cosh(f*x + e)^6 + 6*cosh(f*x + e)^5*sinh(f*x + e) + 15*cosh(f*x + e)^4*sinh(f*x + e)^2 + 20*cosh(f*x + e)^3*sinh(f*x + e)^3 + 15*cosh(f*x + e)^2*sinh(f*x + e)^4 + 6*cosh(f*x + e)*sinh(f*x + e)^5 + sinh(f*x + e)^6)) + sqrt(b)*log(-(b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(a - b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + a - b)*sinh(f*x + e)^2 + sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 - 1)*sqrt(b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + 4*(b*cosh(f*x + e)^3 + (a - b)*cosh(f*x + e))*sinh(f*x + e) + b)/(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/f, -1/2*(sqrt(-b)*arctan(sqrt(2)*(a*cosh(f*x + e)^2 + 2*a*cosh(f*x + e)*sinh(f*x + e) + a*sinh(f*x + e)^2 + b)*sqrt(-b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/(a*b*cosh(f*x + e)^4 + 4*a*b*cosh(f*x + e)*sinh(f*x + e)^3 + a*b*sinh(f*x + e)^4 + (3*a*b - b^2)*cosh(f*x + e)^2 + (6*a*b*cosh(f*x + e)^2 + 3*a*b - b^2)*sinh(f*x + e)^2 + b^2 + 2*(2*a*b*cosh(f*x + e)^3 + (3*a*b - b^2)*cosh(f*x + e))*sinh(f*x + e))) + sqrt(-b)*arctan(sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 - 1)*sqrt(-b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/(b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(2*a - b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 2*a - b)*sinh(f*x + e)^2 + 4*(b*cosh(f*x + e)^3 + (2*a - b)*cosh(f*x + e))*sinh(f*x + e) + b)) - sqrt(a)*log(-((a + b)*cosh(f*x + e)^4 + 4*(a + b)*cosh(f*x + e)*sinh(f*x + e)^3 + (a + b)*sinh(f*x + e)^4 + 2*(3*a - b)*cosh(f*x + e)^2 + 2*(3*(a + b)*cosh(f*x + e)^2 + 3*a - b)*sinh(f*x + e)^2 - 2*sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 + 1)*sqrt(a)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + 4*((a + b)*cosh(f*x + e)^3 + (3*a - b)*cosh(f*x + e))*sinh(f*x + e) + a + b)/(cosh(f*x + e)^4 + 4*cosh(f*x + e)*sinh(f*x + e)^3 + sinh(f*x + e)^4 + 2*(3*cosh(f*x + e)^2 - 1)*sinh(f*x + e)^2 - 2*cosh(f*x + e)^2 + 4*(cosh(f*x + e)^3 - cosh(f*x + e))*sinh(f*x + e) + 1)))/f, 1/2*(2*sqrt(-a)*arctan(sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 + 1)*sqrt(-a)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/(b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(2*a - b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 2*a - b)*sinh(f*x + e)^2 + 4*(b*cosh(f*x + e)^3 + (2*a - b)*cosh(f*x + e))*sinh(f*x + e) + b)) - sqrt(-b)*arctan(sqrt(2)*(a*cosh(f*x + e)^2 + 2*a*cosh(f*x + e)*sinh(f*x + e) + a*sinh(f*x + e)^2 + b)*sqrt(-b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/(a*b*cosh(f*x + e)^4 + 4*a*b*cosh(f*x + e)*sinh(f*x + e)^3 + a*b*sinh(f*x + e)^4 + (3*a*b - b^2)*cosh(f*x + e)^2 + (6*a*b*cosh(f*x + e)^2 + 3*a*b - b^2)*sinh(f*x + e)^2 + b^2 + 2*(2*a*b*cosh(f*x + e)^3 + (3*a*b - b^2)*cosh(f*x + e))*sinh(f*x + e))) - sqrt(-b)*arctan(sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 - 1)*sqrt(-b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/(b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(2*a - b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 2*a - b)*sinh(f*x + e)^2 + 4*(b*cosh(f*x + e)^3 + (2*a - b)*cosh(f*x + e))*sinh(f*x + e) + b)))/f]","B",0
69,1,1277,0,0.664242," ","integrate(csch(f*x+e)^3*(a+b*sinh(f*x+e)^2)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left({\left(a - b\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left(a - b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(a - b\right)} \sinh\left(f x + e\right)^{4} - 2 \, {\left(a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, {\left(a - b\right)} \cosh\left(f x + e\right)^{2} - a + b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left({\left(a - b\right)} \cosh\left(f x + e\right)^{3} - {\left(a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + a - b\right)} \sqrt{a} \log\left(-\frac{{\left(a + b\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(a + b\right)} \sinh\left(f x + e\right)^{4} + 2 \, {\left(3 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(f x + e\right)^{2} + 3 \, a - b\right)} \sinh\left(f x + e\right)^{2} - 2 \, \sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} + 1\right)} \sqrt{a} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(f x + e\right)^{3} + {\left(3 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + a + b}{\cosh\left(f x + e\right)^{4} + 4 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + \sinh\left(f x + e\right)^{4} + 2 \, {\left(3 \, \cosh\left(f x + e\right)^{2} - 1\right)} \sinh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right)^{2} + 4 \, {\left(\cosh\left(f x + e\right)^{3} - \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + 1}\right) + 2 \, \sqrt{2} {\left(a \cosh\left(f x + e\right)^{2} + 2 \, a \cosh\left(f x + e\right) \sinh\left(f x + e\right) + a \sinh\left(f x + e\right)^{2} + a\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{4 \, {\left(a f \cosh\left(f x + e\right)^{4} + 4 \, a f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + a f \sinh\left(f x + e\right)^{4} - 2 \, a f \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, a f \cosh\left(f x + e\right)^{2} - a f\right)} \sinh\left(f x + e\right)^{2} + a f + 4 \, {\left(a f \cosh\left(f x + e\right)^{3} - a f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)}}, -\frac{{\left({\left(a - b\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left(a - b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(a - b\right)} \sinh\left(f x + e\right)^{4} - 2 \, {\left(a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, {\left(a - b\right)} \cosh\left(f x + e\right)^{2} - a + b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left({\left(a - b\right)} \cosh\left(f x + e\right)^{3} - {\left(a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + a - b\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} + 1\right)} \sqrt{-a} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + 2 \, a - b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}\right) + \sqrt{2} {\left(a \cosh\left(f x + e\right)^{2} + 2 \, a \cosh\left(f x + e\right) \sinh\left(f x + e\right) + a \sinh\left(f x + e\right)^{2} + a\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{2 \, {\left(a f \cosh\left(f x + e\right)^{4} + 4 \, a f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + a f \sinh\left(f x + e\right)^{4} - 2 \, a f \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, a f \cosh\left(f x + e\right)^{2} - a f\right)} \sinh\left(f x + e\right)^{2} + a f + 4 \, {\left(a f \cosh\left(f x + e\right)^{3} - a f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)}}\right]"," ",0,"[-1/4*(((a - b)*cosh(f*x + e)^4 + 4*(a - b)*cosh(f*x + e)*sinh(f*x + e)^3 + (a - b)*sinh(f*x + e)^4 - 2*(a - b)*cosh(f*x + e)^2 + 2*(3*(a - b)*cosh(f*x + e)^2 - a + b)*sinh(f*x + e)^2 + 4*((a - b)*cosh(f*x + e)^3 - (a - b)*cosh(f*x + e))*sinh(f*x + e) + a - b)*sqrt(a)*log(-((a + b)*cosh(f*x + e)^4 + 4*(a + b)*cosh(f*x + e)*sinh(f*x + e)^3 + (a + b)*sinh(f*x + e)^4 + 2*(3*a - b)*cosh(f*x + e)^2 + 2*(3*(a + b)*cosh(f*x + e)^2 + 3*a - b)*sinh(f*x + e)^2 - 2*sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 + 1)*sqrt(a)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + 4*((a + b)*cosh(f*x + e)^3 + (3*a - b)*cosh(f*x + e))*sinh(f*x + e) + a + b)/(cosh(f*x + e)^4 + 4*cosh(f*x + e)*sinh(f*x + e)^3 + sinh(f*x + e)^4 + 2*(3*cosh(f*x + e)^2 - 1)*sinh(f*x + e)^2 - 2*cosh(f*x + e)^2 + 4*(cosh(f*x + e)^3 - cosh(f*x + e))*sinh(f*x + e) + 1)) + 2*sqrt(2)*(a*cosh(f*x + e)^2 + 2*a*cosh(f*x + e)*sinh(f*x + e) + a*sinh(f*x + e)^2 + a)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/(a*f*cosh(f*x + e)^4 + 4*a*f*cosh(f*x + e)*sinh(f*x + e)^3 + a*f*sinh(f*x + e)^4 - 2*a*f*cosh(f*x + e)^2 + 2*(3*a*f*cosh(f*x + e)^2 - a*f)*sinh(f*x + e)^2 + a*f + 4*(a*f*cosh(f*x + e)^3 - a*f*cosh(f*x + e))*sinh(f*x + e)), -1/2*(((a - b)*cosh(f*x + e)^4 + 4*(a - b)*cosh(f*x + e)*sinh(f*x + e)^3 + (a - b)*sinh(f*x + e)^4 - 2*(a - b)*cosh(f*x + e)^2 + 2*(3*(a - b)*cosh(f*x + e)^2 - a + b)*sinh(f*x + e)^2 + 4*((a - b)*cosh(f*x + e)^3 - (a - b)*cosh(f*x + e))*sinh(f*x + e) + a - b)*sqrt(-a)*arctan(sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 + 1)*sqrt(-a)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/(b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(2*a - b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 2*a - b)*sinh(f*x + e)^2 + 4*(b*cosh(f*x + e)^3 + (2*a - b)*cosh(f*x + e))*sinh(f*x + e) + b)) + sqrt(2)*(a*cosh(f*x + e)^2 + 2*a*cosh(f*x + e)*sinh(f*x + e) + a*sinh(f*x + e)^2 + a)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/(a*f*cosh(f*x + e)^4 + 4*a*f*cosh(f*x + e)*sinh(f*x + e)^3 + a*f*sinh(f*x + e)^4 - 2*a*f*cosh(f*x + e)^2 + 2*(3*a*f*cosh(f*x + e)^2 - a*f)*sinh(f*x + e)^2 + a*f + 4*(a*f*cosh(f*x + e)^3 - a*f*cosh(f*x + e))*sinh(f*x + e))]","B",0
70,1,3395,0,3.405278," ","integrate(csch(f*x+e)^5*(a+b*sinh(f*x+e)^2)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left({\left(3 \, a^{2} - 2 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{8} + 8 \, {\left(3 \, a^{2} - 2 \, a b - b^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + {\left(3 \, a^{2} - 2 \, a b - b^{2}\right)} \sinh\left(f x + e\right)^{8} - 4 \, {\left(3 \, a^{2} - 2 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{6} + 4 \, {\left(7 \, {\left(3 \, a^{2} - 2 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{2} - 3 \, a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(f x + e\right)^{6} + 8 \, {\left(7 \, {\left(3 \, a^{2} - 2 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{3} - 3 \, {\left(3 \, a^{2} - 2 \, a b - b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + 6 \, {\left(3 \, a^{2} - 2 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{4} + 2 \, {\left(35 \, {\left(3 \, a^{2} - 2 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{4} - 30 \, {\left(3 \, a^{2} - 2 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{2} + 9 \, a^{2} - 6 \, a b - 3 \, b^{2}\right)} \sinh\left(f x + e\right)^{4} + 8 \, {\left(7 \, {\left(3 \, a^{2} - 2 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{5} - 10 \, {\left(3 \, a^{2} - 2 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(3 \, a^{2} - 2 \, a b - b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} - 4 \, {\left(3 \, a^{2} - 2 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{2} + 4 \, {\left(7 \, {\left(3 \, a^{2} - 2 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{6} - 15 \, {\left(3 \, a^{2} - 2 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{4} + 9 \, {\left(3 \, a^{2} - 2 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{2} - 3 \, a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(f x + e\right)^{2} + 3 \, a^{2} - 2 \, a b - b^{2} + 8 \, {\left({\left(3 \, a^{2} - 2 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{7} - 3 \, {\left(3 \, a^{2} - 2 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{5} + 3 \, {\left(3 \, a^{2} - 2 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{3} - {\left(3 \, a^{2} - 2 \, a b - b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{a} \log\left(-\frac{{\left(a + b\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(a + b\right)} \sinh\left(f x + e\right)^{4} + 2 \, {\left(3 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(f x + e\right)^{2} + 3 \, a - b\right)} \sinh\left(f x + e\right)^{2} + 2 \, \sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} + 1\right)} \sqrt{a} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(f x + e\right)^{3} + {\left(3 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + a + b}{\cosh\left(f x + e\right)^{4} + 4 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + \sinh\left(f x + e\right)^{4} + 2 \, {\left(3 \, \cosh\left(f x + e\right)^{2} - 1\right)} \sinh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right)^{2} + 4 \, {\left(\cosh\left(f x + e\right)^{3} - \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + 1}\right) - 2 \, \sqrt{2} {\left({\left(3 \, a^{2} - a b\right)} \cosh\left(f x + e\right)^{6} + 6 \, {\left(3 \, a^{2} - a b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + {\left(3 \, a^{2} - a b\right)} \sinh\left(f x + e\right)^{6} - {\left(11 \, a^{2} - a b\right)} \cosh\left(f x + e\right)^{4} + {\left(15 \, {\left(3 \, a^{2} - a b\right)} \cosh\left(f x + e\right)^{2} - 11 \, a^{2} + a b\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(5 \, {\left(3 \, a^{2} - a b\right)} \cosh\left(f x + e\right)^{3} - {\left(11 \, a^{2} - a b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} - {\left(11 \, a^{2} - a b\right)} \cosh\left(f x + e\right)^{2} + {\left(15 \, {\left(3 \, a^{2} - a b\right)} \cosh\left(f x + e\right)^{4} - 6 \, {\left(11 \, a^{2} - a b\right)} \cosh\left(f x + e\right)^{2} - 11 \, a^{2} + a b\right)} \sinh\left(f x + e\right)^{2} + 3 \, a^{2} - a b + 2 \, {\left(3 \, {\left(3 \, a^{2} - a b\right)} \cosh\left(f x + e\right)^{5} - 2 \, {\left(11 \, a^{2} - a b\right)} \cosh\left(f x + e\right)^{3} - {\left(11 \, a^{2} - a b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{16 \, {\left(a^{2} f \cosh\left(f x + e\right)^{8} + 8 \, a^{2} f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + a^{2} f \sinh\left(f x + e\right)^{8} - 4 \, a^{2} f \cosh\left(f x + e\right)^{6} + 6 \, a^{2} f \cosh\left(f x + e\right)^{4} + 4 \, {\left(7 \, a^{2} f \cosh\left(f x + e\right)^{2} - a^{2} f\right)} \sinh\left(f x + e\right)^{6} + 8 \, {\left(7 \, a^{2} f \cosh\left(f x + e\right)^{3} - 3 \, a^{2} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} - 4 \, a^{2} f \cosh\left(f x + e\right)^{2} + 2 \, {\left(35 \, a^{2} f \cosh\left(f x + e\right)^{4} - 30 \, a^{2} f \cosh\left(f x + e\right)^{2} + 3 \, a^{2} f\right)} \sinh\left(f x + e\right)^{4} + 8 \, {\left(7 \, a^{2} f \cosh\left(f x + e\right)^{5} - 10 \, a^{2} f \cosh\left(f x + e\right)^{3} + 3 \, a^{2} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + a^{2} f + 4 \, {\left(7 \, a^{2} f \cosh\left(f x + e\right)^{6} - 15 \, a^{2} f \cosh\left(f x + e\right)^{4} + 9 \, a^{2} f \cosh\left(f x + e\right)^{2} - a^{2} f\right)} \sinh\left(f x + e\right)^{2} + 8 \, {\left(a^{2} f \cosh\left(f x + e\right)^{7} - 3 \, a^{2} f \cosh\left(f x + e\right)^{5} + 3 \, a^{2} f \cosh\left(f x + e\right)^{3} - a^{2} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)}}, \frac{{\left({\left(3 \, a^{2} - 2 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{8} + 8 \, {\left(3 \, a^{2} - 2 \, a b - b^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + {\left(3 \, a^{2} - 2 \, a b - b^{2}\right)} \sinh\left(f x + e\right)^{8} - 4 \, {\left(3 \, a^{2} - 2 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{6} + 4 \, {\left(7 \, {\left(3 \, a^{2} - 2 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{2} - 3 \, a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(f x + e\right)^{6} + 8 \, {\left(7 \, {\left(3 \, a^{2} - 2 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{3} - 3 \, {\left(3 \, a^{2} - 2 \, a b - b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + 6 \, {\left(3 \, a^{2} - 2 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{4} + 2 \, {\left(35 \, {\left(3 \, a^{2} - 2 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{4} - 30 \, {\left(3 \, a^{2} - 2 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{2} + 9 \, a^{2} - 6 \, a b - 3 \, b^{2}\right)} \sinh\left(f x + e\right)^{4} + 8 \, {\left(7 \, {\left(3 \, a^{2} - 2 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{5} - 10 \, {\left(3 \, a^{2} - 2 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(3 \, a^{2} - 2 \, a b - b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} - 4 \, {\left(3 \, a^{2} - 2 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{2} + 4 \, {\left(7 \, {\left(3 \, a^{2} - 2 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{6} - 15 \, {\left(3 \, a^{2} - 2 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{4} + 9 \, {\left(3 \, a^{2} - 2 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{2} - 3 \, a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(f x + e\right)^{2} + 3 \, a^{2} - 2 \, a b - b^{2} + 8 \, {\left({\left(3 \, a^{2} - 2 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{7} - 3 \, {\left(3 \, a^{2} - 2 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{5} + 3 \, {\left(3 \, a^{2} - 2 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{3} - {\left(3 \, a^{2} - 2 \, a b - b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} + 1\right)} \sqrt{-a} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + 2 \, a - b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}\right) + \sqrt{2} {\left({\left(3 \, a^{2} - a b\right)} \cosh\left(f x + e\right)^{6} + 6 \, {\left(3 \, a^{2} - a b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + {\left(3 \, a^{2} - a b\right)} \sinh\left(f x + e\right)^{6} - {\left(11 \, a^{2} - a b\right)} \cosh\left(f x + e\right)^{4} + {\left(15 \, {\left(3 \, a^{2} - a b\right)} \cosh\left(f x + e\right)^{2} - 11 \, a^{2} + a b\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(5 \, {\left(3 \, a^{2} - a b\right)} \cosh\left(f x + e\right)^{3} - {\left(11 \, a^{2} - a b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} - {\left(11 \, a^{2} - a b\right)} \cosh\left(f x + e\right)^{2} + {\left(15 \, {\left(3 \, a^{2} - a b\right)} \cosh\left(f x + e\right)^{4} - 6 \, {\left(11 \, a^{2} - a b\right)} \cosh\left(f x + e\right)^{2} - 11 \, a^{2} + a b\right)} \sinh\left(f x + e\right)^{2} + 3 \, a^{2} - a b + 2 \, {\left(3 \, {\left(3 \, a^{2} - a b\right)} \cosh\left(f x + e\right)^{5} - 2 \, {\left(11 \, a^{2} - a b\right)} \cosh\left(f x + e\right)^{3} - {\left(11 \, a^{2} - a b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{8 \, {\left(a^{2} f \cosh\left(f x + e\right)^{8} + 8 \, a^{2} f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + a^{2} f \sinh\left(f x + e\right)^{8} - 4 \, a^{2} f \cosh\left(f x + e\right)^{6} + 6 \, a^{2} f \cosh\left(f x + e\right)^{4} + 4 \, {\left(7 \, a^{2} f \cosh\left(f x + e\right)^{2} - a^{2} f\right)} \sinh\left(f x + e\right)^{6} + 8 \, {\left(7 \, a^{2} f \cosh\left(f x + e\right)^{3} - 3 \, a^{2} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} - 4 \, a^{2} f \cosh\left(f x + e\right)^{2} + 2 \, {\left(35 \, a^{2} f \cosh\left(f x + e\right)^{4} - 30 \, a^{2} f \cosh\left(f x + e\right)^{2} + 3 \, a^{2} f\right)} \sinh\left(f x + e\right)^{4} + 8 \, {\left(7 \, a^{2} f \cosh\left(f x + e\right)^{5} - 10 \, a^{2} f \cosh\left(f x + e\right)^{3} + 3 \, a^{2} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + a^{2} f + 4 \, {\left(7 \, a^{2} f \cosh\left(f x + e\right)^{6} - 15 \, a^{2} f \cosh\left(f x + e\right)^{4} + 9 \, a^{2} f \cosh\left(f x + e\right)^{2} - a^{2} f\right)} \sinh\left(f x + e\right)^{2} + 8 \, {\left(a^{2} f \cosh\left(f x + e\right)^{7} - 3 \, a^{2} f \cosh\left(f x + e\right)^{5} + 3 \, a^{2} f \cosh\left(f x + e\right)^{3} - a^{2} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)}}\right]"," ",0,"[-1/16*(((3*a^2 - 2*a*b - b^2)*cosh(f*x + e)^8 + 8*(3*a^2 - 2*a*b - b^2)*cosh(f*x + e)*sinh(f*x + e)^7 + (3*a^2 - 2*a*b - b^2)*sinh(f*x + e)^8 - 4*(3*a^2 - 2*a*b - b^2)*cosh(f*x + e)^6 + 4*(7*(3*a^2 - 2*a*b - b^2)*cosh(f*x + e)^2 - 3*a^2 + 2*a*b + b^2)*sinh(f*x + e)^6 + 8*(7*(3*a^2 - 2*a*b - b^2)*cosh(f*x + e)^3 - 3*(3*a^2 - 2*a*b - b^2)*cosh(f*x + e))*sinh(f*x + e)^5 + 6*(3*a^2 - 2*a*b - b^2)*cosh(f*x + e)^4 + 2*(35*(3*a^2 - 2*a*b - b^2)*cosh(f*x + e)^4 - 30*(3*a^2 - 2*a*b - b^2)*cosh(f*x + e)^2 + 9*a^2 - 6*a*b - 3*b^2)*sinh(f*x + e)^4 + 8*(7*(3*a^2 - 2*a*b - b^2)*cosh(f*x + e)^5 - 10*(3*a^2 - 2*a*b - b^2)*cosh(f*x + e)^3 + 3*(3*a^2 - 2*a*b - b^2)*cosh(f*x + e))*sinh(f*x + e)^3 - 4*(3*a^2 - 2*a*b - b^2)*cosh(f*x + e)^2 + 4*(7*(3*a^2 - 2*a*b - b^2)*cosh(f*x + e)^6 - 15*(3*a^2 - 2*a*b - b^2)*cosh(f*x + e)^4 + 9*(3*a^2 - 2*a*b - b^2)*cosh(f*x + e)^2 - 3*a^2 + 2*a*b + b^2)*sinh(f*x + e)^2 + 3*a^2 - 2*a*b - b^2 + 8*((3*a^2 - 2*a*b - b^2)*cosh(f*x + e)^7 - 3*(3*a^2 - 2*a*b - b^2)*cosh(f*x + e)^5 + 3*(3*a^2 - 2*a*b - b^2)*cosh(f*x + e)^3 - (3*a^2 - 2*a*b - b^2)*cosh(f*x + e))*sinh(f*x + e))*sqrt(a)*log(-((a + b)*cosh(f*x + e)^4 + 4*(a + b)*cosh(f*x + e)*sinh(f*x + e)^3 + (a + b)*sinh(f*x + e)^4 + 2*(3*a - b)*cosh(f*x + e)^2 + 2*(3*(a + b)*cosh(f*x + e)^2 + 3*a - b)*sinh(f*x + e)^2 + 2*sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 + 1)*sqrt(a)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + 4*((a + b)*cosh(f*x + e)^3 + (3*a - b)*cosh(f*x + e))*sinh(f*x + e) + a + b)/(cosh(f*x + e)^4 + 4*cosh(f*x + e)*sinh(f*x + e)^3 + sinh(f*x + e)^4 + 2*(3*cosh(f*x + e)^2 - 1)*sinh(f*x + e)^2 - 2*cosh(f*x + e)^2 + 4*(cosh(f*x + e)^3 - cosh(f*x + e))*sinh(f*x + e) + 1)) - 2*sqrt(2)*((3*a^2 - a*b)*cosh(f*x + e)^6 + 6*(3*a^2 - a*b)*cosh(f*x + e)*sinh(f*x + e)^5 + (3*a^2 - a*b)*sinh(f*x + e)^6 - (11*a^2 - a*b)*cosh(f*x + e)^4 + (15*(3*a^2 - a*b)*cosh(f*x + e)^2 - 11*a^2 + a*b)*sinh(f*x + e)^4 + 4*(5*(3*a^2 - a*b)*cosh(f*x + e)^3 - (11*a^2 - a*b)*cosh(f*x + e))*sinh(f*x + e)^3 - (11*a^2 - a*b)*cosh(f*x + e)^2 + (15*(3*a^2 - a*b)*cosh(f*x + e)^4 - 6*(11*a^2 - a*b)*cosh(f*x + e)^2 - 11*a^2 + a*b)*sinh(f*x + e)^2 + 3*a^2 - a*b + 2*(3*(3*a^2 - a*b)*cosh(f*x + e)^5 - 2*(11*a^2 - a*b)*cosh(f*x + e)^3 - (11*a^2 - a*b)*cosh(f*x + e))*sinh(f*x + e))*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/(a^2*f*cosh(f*x + e)^8 + 8*a^2*f*cosh(f*x + e)*sinh(f*x + e)^7 + a^2*f*sinh(f*x + e)^8 - 4*a^2*f*cosh(f*x + e)^6 + 6*a^2*f*cosh(f*x + e)^4 + 4*(7*a^2*f*cosh(f*x + e)^2 - a^2*f)*sinh(f*x + e)^6 + 8*(7*a^2*f*cosh(f*x + e)^3 - 3*a^2*f*cosh(f*x + e))*sinh(f*x + e)^5 - 4*a^2*f*cosh(f*x + e)^2 + 2*(35*a^2*f*cosh(f*x + e)^4 - 30*a^2*f*cosh(f*x + e)^2 + 3*a^2*f)*sinh(f*x + e)^4 + 8*(7*a^2*f*cosh(f*x + e)^5 - 10*a^2*f*cosh(f*x + e)^3 + 3*a^2*f*cosh(f*x + e))*sinh(f*x + e)^3 + a^2*f + 4*(7*a^2*f*cosh(f*x + e)^6 - 15*a^2*f*cosh(f*x + e)^4 + 9*a^2*f*cosh(f*x + e)^2 - a^2*f)*sinh(f*x + e)^2 + 8*(a^2*f*cosh(f*x + e)^7 - 3*a^2*f*cosh(f*x + e)^5 + 3*a^2*f*cosh(f*x + e)^3 - a^2*f*cosh(f*x + e))*sinh(f*x + e)), 1/8*(((3*a^2 - 2*a*b - b^2)*cosh(f*x + e)^8 + 8*(3*a^2 - 2*a*b - b^2)*cosh(f*x + e)*sinh(f*x + e)^7 + (3*a^2 - 2*a*b - b^2)*sinh(f*x + e)^8 - 4*(3*a^2 - 2*a*b - b^2)*cosh(f*x + e)^6 + 4*(7*(3*a^2 - 2*a*b - b^2)*cosh(f*x + e)^2 - 3*a^2 + 2*a*b + b^2)*sinh(f*x + e)^6 + 8*(7*(3*a^2 - 2*a*b - b^2)*cosh(f*x + e)^3 - 3*(3*a^2 - 2*a*b - b^2)*cosh(f*x + e))*sinh(f*x + e)^5 + 6*(3*a^2 - 2*a*b - b^2)*cosh(f*x + e)^4 + 2*(35*(3*a^2 - 2*a*b - b^2)*cosh(f*x + e)^4 - 30*(3*a^2 - 2*a*b - b^2)*cosh(f*x + e)^2 + 9*a^2 - 6*a*b - 3*b^2)*sinh(f*x + e)^4 + 8*(7*(3*a^2 - 2*a*b - b^2)*cosh(f*x + e)^5 - 10*(3*a^2 - 2*a*b - b^2)*cosh(f*x + e)^3 + 3*(3*a^2 - 2*a*b - b^2)*cosh(f*x + e))*sinh(f*x + e)^3 - 4*(3*a^2 - 2*a*b - b^2)*cosh(f*x + e)^2 + 4*(7*(3*a^2 - 2*a*b - b^2)*cosh(f*x + e)^6 - 15*(3*a^2 - 2*a*b - b^2)*cosh(f*x + e)^4 + 9*(3*a^2 - 2*a*b - b^2)*cosh(f*x + e)^2 - 3*a^2 + 2*a*b + b^2)*sinh(f*x + e)^2 + 3*a^2 - 2*a*b - b^2 + 8*((3*a^2 - 2*a*b - b^2)*cosh(f*x + e)^7 - 3*(3*a^2 - 2*a*b - b^2)*cosh(f*x + e)^5 + 3*(3*a^2 - 2*a*b - b^2)*cosh(f*x + e)^3 - (3*a^2 - 2*a*b - b^2)*cosh(f*x + e))*sinh(f*x + e))*sqrt(-a)*arctan(sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 + 1)*sqrt(-a)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/(b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(2*a - b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 2*a - b)*sinh(f*x + e)^2 + 4*(b*cosh(f*x + e)^3 + (2*a - b)*cosh(f*x + e))*sinh(f*x + e) + b)) + sqrt(2)*((3*a^2 - a*b)*cosh(f*x + e)^6 + 6*(3*a^2 - a*b)*cosh(f*x + e)*sinh(f*x + e)^5 + (3*a^2 - a*b)*sinh(f*x + e)^6 - (11*a^2 - a*b)*cosh(f*x + e)^4 + (15*(3*a^2 - a*b)*cosh(f*x + e)^2 - 11*a^2 + a*b)*sinh(f*x + e)^4 + 4*(5*(3*a^2 - a*b)*cosh(f*x + e)^3 - (11*a^2 - a*b)*cosh(f*x + e))*sinh(f*x + e)^3 - (11*a^2 - a*b)*cosh(f*x + e)^2 + (15*(3*a^2 - a*b)*cosh(f*x + e)^4 - 6*(11*a^2 - a*b)*cosh(f*x + e)^2 - 11*a^2 + a*b)*sinh(f*x + e)^2 + 3*a^2 - a*b + 2*(3*(3*a^2 - a*b)*cosh(f*x + e)^5 - 2*(11*a^2 - a*b)*cosh(f*x + e)^3 - (11*a^2 - a*b)*cosh(f*x + e))*sinh(f*x + e))*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/(a^2*f*cosh(f*x + e)^8 + 8*a^2*f*cosh(f*x + e)*sinh(f*x + e)^7 + a^2*f*sinh(f*x + e)^8 - 4*a^2*f*cosh(f*x + e)^6 + 6*a^2*f*cosh(f*x + e)^4 + 4*(7*a^2*f*cosh(f*x + e)^2 - a^2*f)*sinh(f*x + e)^6 + 8*(7*a^2*f*cosh(f*x + e)^3 - 3*a^2*f*cosh(f*x + e))*sinh(f*x + e)^5 - 4*a^2*f*cosh(f*x + e)^2 + 2*(35*a^2*f*cosh(f*x + e)^4 - 30*a^2*f*cosh(f*x + e)^2 + 3*a^2*f)*sinh(f*x + e)^4 + 8*(7*a^2*f*cosh(f*x + e)^5 - 10*a^2*f*cosh(f*x + e)^3 + 3*a^2*f*cosh(f*x + e))*sinh(f*x + e)^3 + a^2*f + 4*(7*a^2*f*cosh(f*x + e)^6 - 15*a^2*f*cosh(f*x + e)^4 + 9*a^2*f*cosh(f*x + e)^2 - a^2*f)*sinh(f*x + e)^2 + 8*(a^2*f*cosh(f*x + e)^7 - 3*a^2*f*cosh(f*x + e)^5 + 3*a^2*f*cosh(f*x + e)^3 - a^2*f*cosh(f*x + e))*sinh(f*x + e))]","B",0
71,0,0,0,3.120016," ","integrate(sinh(f*x+e)^4*(a+b*sinh(f*x+e)^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{b \sinh\left(f x + e\right)^{2} + a} \sinh\left(f x + e\right)^{4}, x\right)"," ",0,"integral(sqrt(b*sinh(f*x + e)^2 + a)*sinh(f*x + e)^4, x)","F",0
72,0,0,0,4.955406," ","integrate(sinh(f*x+e)^2*(a+b*sinh(f*x+e)^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{b \sinh\left(f x + e\right)^{2} + a} \sinh\left(f x + e\right)^{2}, x\right)"," ",0,"integral(sqrt(b*sinh(f*x + e)^2 + a)*sinh(f*x + e)^2, x)","F",0
73,0,0,0,0.762220," ","integrate((a+b*sinh(f*x+e)^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{b \sinh\left(f x + e\right)^{2} + a}, x\right)"," ",0,"integral(sqrt(b*sinh(f*x + e)^2 + a), x)","F",0
74,0,0,0,2.078994," ","integrate(csch(f*x+e)^2*(a+b*sinh(f*x+e)^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{b \sinh\left(f x + e\right)^{2} + a} \operatorname{csch}\left(f x + e\right)^{2}, x\right)"," ",0,"integral(sqrt(b*sinh(f*x + e)^2 + a)*csch(f*x + e)^2, x)","F",0
75,0,0,0,2.874738," ","integrate(csch(f*x+e)^4*(a+b*sinh(f*x+e)^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{b \sinh\left(f x + e\right)^{2} + a} \operatorname{csch}\left(f x + e\right)^{4}, x\right)"," ",0,"integral(sqrt(b*sinh(f*x + e)^2 + a)*csch(f*x + e)^4, x)","F",0
76,1,4608,0,2.047308," ","integrate(sinh(f*x+e)^3*(a+b*sinh(f*x+e)^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{6 \, {\left({\left(a^{3} + 3 \, a^{2} b - 9 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(f x + e\right)^{6} + 6 \, {\left(a^{3} + 3 \, a^{2} b - 9 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(f x + e\right)^{5} \sinh\left(f x + e\right) + 15 \, {\left(a^{3} + 3 \, a^{2} b - 9 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} \sinh\left(f x + e\right)^{2} + 20 \, {\left(a^{3} + 3 \, a^{2} b - 9 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} \sinh\left(f x + e\right)^{3} + 15 \, {\left(a^{3} + 3 \, a^{2} b - 9 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(f x + e\right)^{2} \sinh\left(f x + e\right)^{4} + 6 \, {\left(a^{3} + 3 \, a^{2} b - 9 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + {\left(a^{3} + 3 \, a^{2} b - 9 \, a b^{2} + 5 \, b^{3}\right)} \sinh\left(f x + e\right)^{6}\right)} \sqrt{b} \log\left(\frac{a^{2} b \cosh\left(f x + e\right)^{8} + 8 \, a^{2} b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + a^{2} b \sinh\left(f x + e\right)^{8} + 2 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(f x + e\right)^{6} + 2 \, {\left(14 \, a^{2} b \cosh\left(f x + e\right)^{2} + a^{3} + a^{2} b\right)} \sinh\left(f x + e\right)^{6} + 4 \, {\left(14 \, a^{2} b \cosh\left(f x + e\right)^{3} + 3 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + {\left(9 \, a^{2} b - 4 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{4} + {\left(70 \, a^{2} b \cosh\left(f x + e\right)^{4} + 9 \, a^{2} b - 4 \, a b^{2} + b^{3} + 30 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(14 \, a^{2} b \cosh\left(f x + e\right)^{5} + 10 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(f x + e\right)^{3} + {\left(9 \, a^{2} b - 4 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + b^{3} + 2 \, {\left(3 \, a b^{2} - b^{3}\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(14 \, a^{2} b \cosh\left(f x + e\right)^{6} + 15 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(f x + e\right)^{4} + 3 \, a b^{2} - b^{3} + 3 \, {\left(9 \, a^{2} b - 4 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{2} - \sqrt{2} {\left(a^{2} \cosh\left(f x + e\right)^{6} + 6 \, a^{2} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + a^{2} \sinh\left(f x + e\right)^{6} + 3 \, a^{2} \cosh\left(f x + e\right)^{4} + 3 \, {\left(5 \, a^{2} \cosh\left(f x + e\right)^{2} + a^{2}\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(5 \, a^{2} \cosh\left(f x + e\right)^{3} + 3 \, a^{2} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + {\left(4 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{2} + {\left(15 \, a^{2} \cosh\left(f x + e\right)^{4} + 18 \, a^{2} \cosh\left(f x + e\right)^{2} + 4 \, a b - b^{2}\right)} \sinh\left(f x + e\right)^{2} + b^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(f x + e\right)^{5} + 6 \, a^{2} \cosh\left(f x + e\right)^{3} + {\left(4 \, a b - b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} + 4 \, {\left(2 \, a^{2} b \cosh\left(f x + e\right)^{7} + 3 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(f x + e\right)^{5} + {\left(9 \, a^{2} b - 4 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{3} + {\left(3 \, a b^{2} - b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)}{\cosh\left(f x + e\right)^{6} + 6 \, \cosh\left(f x + e\right)^{5} \sinh\left(f x + e\right) + 15 \, \cosh\left(f x + e\right)^{4} \sinh\left(f x + e\right)^{2} + 20 \, \cosh\left(f x + e\right)^{3} \sinh\left(f x + e\right)^{3} + 15 \, \cosh\left(f x + e\right)^{2} \sinh\left(f x + e\right)^{4} + 6 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + \sinh\left(f x + e\right)^{6}}\right) + 6 \, {\left({\left(a^{3} + 3 \, a^{2} b - 9 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(f x + e\right)^{6} + 6 \, {\left(a^{3} + 3 \, a^{2} b - 9 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(f x + e\right)^{5} \sinh\left(f x + e\right) + 15 \, {\left(a^{3} + 3 \, a^{2} b - 9 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} \sinh\left(f x + e\right)^{2} + 20 \, {\left(a^{3} + 3 \, a^{2} b - 9 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} \sinh\left(f x + e\right)^{3} + 15 \, {\left(a^{3} + 3 \, a^{2} b - 9 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(f x + e\right)^{2} \sinh\left(f x + e\right)^{4} + 6 \, {\left(a^{3} + 3 \, a^{2} b - 9 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + {\left(a^{3} + 3 \, a^{2} b - 9 \, a b^{2} + 5 \, b^{3}\right)} \sinh\left(f x + e\right)^{6}\right)} \sqrt{b} \log\left(-\frac{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + a - b\right)} \sinh\left(f x + e\right)^{2} - \sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} - 1\right)} \sqrt{b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}{\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}\right) + \sqrt{2} {\left(b^{3} \cosh\left(f x + e\right)^{10} + 10 \, b^{3} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{9} + b^{3} \sinh\left(f x + e\right)^{10} + {\left(7 \, a b^{2} - 8 \, b^{3}\right)} \cosh\left(f x + e\right)^{8} + {\left(45 \, b^{3} \cosh\left(f x + e\right)^{2} + 7 \, a b^{2} - 8 \, b^{3}\right)} \sinh\left(f x + e\right)^{8} + 8 \, {\left(15 \, b^{3} \cosh\left(f x + e\right)^{3} + {\left(7 \, a b^{2} - 8 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{7} + {\left(6 \, a^{2} b - 51 \, a b^{2} + 37 \, b^{3}\right)} \cosh\left(f x + e\right)^{6} + {\left(210 \, b^{3} \cosh\left(f x + e\right)^{4} + 6 \, a^{2} b - 51 \, a b^{2} + 37 \, b^{3} + 28 \, {\left(7 \, a b^{2} - 8 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{6} + 2 \, {\left(126 \, b^{3} \cosh\left(f x + e\right)^{5} + 28 \, {\left(7 \, a b^{2} - 8 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(6 \, a^{2} b - 51 \, a b^{2} + 37 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + {\left(6 \, a^{2} b - 51 \, a b^{2} + 37 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} + {\left(210 \, b^{3} \cosh\left(f x + e\right)^{6} + 70 \, {\left(7 \, a b^{2} - 8 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} + 6 \, a^{2} b - 51 \, a b^{2} + 37 \, b^{3} + 15 \, {\left(6 \, a^{2} b - 51 \, a b^{2} + 37 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(30 \, b^{3} \cosh\left(f x + e\right)^{7} + 14 \, {\left(7 \, a b^{2} - 8 \, b^{3}\right)} \cosh\left(f x + e\right)^{5} + 5 \, {\left(6 \, a^{2} b - 51 \, a b^{2} + 37 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} + {\left(6 \, a^{2} b - 51 \, a b^{2} + 37 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + b^{3} + {\left(7 \, a b^{2} - 8 \, b^{3}\right)} \cosh\left(f x + e\right)^{2} + {\left(45 \, b^{3} \cosh\left(f x + e\right)^{8} + 28 \, {\left(7 \, a b^{2} - 8 \, b^{3}\right)} \cosh\left(f x + e\right)^{6} + 15 \, {\left(6 \, a^{2} b - 51 \, a b^{2} + 37 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} + 7 \, a b^{2} - 8 \, b^{3} + 6 \, {\left(6 \, a^{2} b - 51 \, a b^{2} + 37 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{2} + 2 \, {\left(5 \, b^{3} \cosh\left(f x + e\right)^{9} + 4 \, {\left(7 \, a b^{2} - 8 \, b^{3}\right)} \cosh\left(f x + e\right)^{7} + 3 \, {\left(6 \, a^{2} b - 51 \, a b^{2} + 37 \, b^{3}\right)} \cosh\left(f x + e\right)^{5} + 2 \, {\left(6 \, a^{2} b - 51 \, a b^{2} + 37 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} + {\left(7 \, a b^{2} - 8 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{384 \, {\left(b^{2} f \cosh\left(f x + e\right)^{6} + 6 \, b^{2} f \cosh\left(f x + e\right)^{5} \sinh\left(f x + e\right) + 15 \, b^{2} f \cosh\left(f x + e\right)^{4} \sinh\left(f x + e\right)^{2} + 20 \, b^{2} f \cosh\left(f x + e\right)^{3} \sinh\left(f x + e\right)^{3} + 15 \, b^{2} f \cosh\left(f x + e\right)^{2} \sinh\left(f x + e\right)^{4} + 6 \, b^{2} f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + b^{2} f \sinh\left(f x + e\right)^{6}\right)}}, \frac{12 \, {\left({\left(a^{3} + 3 \, a^{2} b - 9 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(f x + e\right)^{6} + 6 \, {\left(a^{3} + 3 \, a^{2} b - 9 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(f x + e\right)^{5} \sinh\left(f x + e\right) + 15 \, {\left(a^{3} + 3 \, a^{2} b - 9 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} \sinh\left(f x + e\right)^{2} + 20 \, {\left(a^{3} + 3 \, a^{2} b - 9 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} \sinh\left(f x + e\right)^{3} + 15 \, {\left(a^{3} + 3 \, a^{2} b - 9 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(f x + e\right)^{2} \sinh\left(f x + e\right)^{4} + 6 \, {\left(a^{3} + 3 \, a^{2} b - 9 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + {\left(a^{3} + 3 \, a^{2} b - 9 \, a b^{2} + 5 \, b^{3}\right)} \sinh\left(f x + e\right)^{6}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{2} {\left(a \cosh\left(f x + e\right)^{2} + 2 \, a \cosh\left(f x + e\right) \sinh\left(f x + e\right) + a \sinh\left(f x + e\right)^{2} + b\right)} \sqrt{-b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{a b \cosh\left(f x + e\right)^{4} + 4 \, a b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + a b \sinh\left(f x + e\right)^{4} + {\left(3 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{2} + {\left(6 \, a b \cosh\left(f x + e\right)^{2} + 3 \, a b - b^{2}\right)} \sinh\left(f x + e\right)^{2} + b^{2} + 2 \, {\left(2 \, a b \cosh\left(f x + e\right)^{3} + {\left(3 \, a b - b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)}\right) + 12 \, {\left({\left(a^{3} + 3 \, a^{2} b - 9 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(f x + e\right)^{6} + 6 \, {\left(a^{3} + 3 \, a^{2} b - 9 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(f x + e\right)^{5} \sinh\left(f x + e\right) + 15 \, {\left(a^{3} + 3 \, a^{2} b - 9 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} \sinh\left(f x + e\right)^{2} + 20 \, {\left(a^{3} + 3 \, a^{2} b - 9 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} \sinh\left(f x + e\right)^{3} + 15 \, {\left(a^{3} + 3 \, a^{2} b - 9 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(f x + e\right)^{2} \sinh\left(f x + e\right)^{4} + 6 \, {\left(a^{3} + 3 \, a^{2} b - 9 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + {\left(a^{3} + 3 \, a^{2} b - 9 \, a b^{2} + 5 \, b^{3}\right)} \sinh\left(f x + e\right)^{6}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} - 1\right)} \sqrt{-b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + 2 \, a - b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}\right) + \sqrt{2} {\left(b^{3} \cosh\left(f x + e\right)^{10} + 10 \, b^{3} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{9} + b^{3} \sinh\left(f x + e\right)^{10} + {\left(7 \, a b^{2} - 8 \, b^{3}\right)} \cosh\left(f x + e\right)^{8} + {\left(45 \, b^{3} \cosh\left(f x + e\right)^{2} + 7 \, a b^{2} - 8 \, b^{3}\right)} \sinh\left(f x + e\right)^{8} + 8 \, {\left(15 \, b^{3} \cosh\left(f x + e\right)^{3} + {\left(7 \, a b^{2} - 8 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{7} + {\left(6 \, a^{2} b - 51 \, a b^{2} + 37 \, b^{3}\right)} \cosh\left(f x + e\right)^{6} + {\left(210 \, b^{3} \cosh\left(f x + e\right)^{4} + 6 \, a^{2} b - 51 \, a b^{2} + 37 \, b^{3} + 28 \, {\left(7 \, a b^{2} - 8 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{6} + 2 \, {\left(126 \, b^{3} \cosh\left(f x + e\right)^{5} + 28 \, {\left(7 \, a b^{2} - 8 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(6 \, a^{2} b - 51 \, a b^{2} + 37 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + {\left(6 \, a^{2} b - 51 \, a b^{2} + 37 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} + {\left(210 \, b^{3} \cosh\left(f x + e\right)^{6} + 70 \, {\left(7 \, a b^{2} - 8 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} + 6 \, a^{2} b - 51 \, a b^{2} + 37 \, b^{3} + 15 \, {\left(6 \, a^{2} b - 51 \, a b^{2} + 37 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(30 \, b^{3} \cosh\left(f x + e\right)^{7} + 14 \, {\left(7 \, a b^{2} - 8 \, b^{3}\right)} \cosh\left(f x + e\right)^{5} + 5 \, {\left(6 \, a^{2} b - 51 \, a b^{2} + 37 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} + {\left(6 \, a^{2} b - 51 \, a b^{2} + 37 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + b^{3} + {\left(7 \, a b^{2} - 8 \, b^{3}\right)} \cosh\left(f x + e\right)^{2} + {\left(45 \, b^{3} \cosh\left(f x + e\right)^{8} + 28 \, {\left(7 \, a b^{2} - 8 \, b^{3}\right)} \cosh\left(f x + e\right)^{6} + 15 \, {\left(6 \, a^{2} b - 51 \, a b^{2} + 37 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} + 7 \, a b^{2} - 8 \, b^{3} + 6 \, {\left(6 \, a^{2} b - 51 \, a b^{2} + 37 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{2} + 2 \, {\left(5 \, b^{3} \cosh\left(f x + e\right)^{9} + 4 \, {\left(7 \, a b^{2} - 8 \, b^{3}\right)} \cosh\left(f x + e\right)^{7} + 3 \, {\left(6 \, a^{2} b - 51 \, a b^{2} + 37 \, b^{3}\right)} \cosh\left(f x + e\right)^{5} + 2 \, {\left(6 \, a^{2} b - 51 \, a b^{2} + 37 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} + {\left(7 \, a b^{2} - 8 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{384 \, {\left(b^{2} f \cosh\left(f x + e\right)^{6} + 6 \, b^{2} f \cosh\left(f x + e\right)^{5} \sinh\left(f x + e\right) + 15 \, b^{2} f \cosh\left(f x + e\right)^{4} \sinh\left(f x + e\right)^{2} + 20 \, b^{2} f \cosh\left(f x + e\right)^{3} \sinh\left(f x + e\right)^{3} + 15 \, b^{2} f \cosh\left(f x + e\right)^{2} \sinh\left(f x + e\right)^{4} + 6 \, b^{2} f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + b^{2} f \sinh\left(f x + e\right)^{6}\right)}}\right]"," ",0,"[1/384*(6*((a^3 + 3*a^2*b - 9*a*b^2 + 5*b^3)*cosh(f*x + e)^6 + 6*(a^3 + 3*a^2*b - 9*a*b^2 + 5*b^3)*cosh(f*x + e)^5*sinh(f*x + e) + 15*(a^3 + 3*a^2*b - 9*a*b^2 + 5*b^3)*cosh(f*x + e)^4*sinh(f*x + e)^2 + 20*(a^3 + 3*a^2*b - 9*a*b^2 + 5*b^3)*cosh(f*x + e)^3*sinh(f*x + e)^3 + 15*(a^3 + 3*a^2*b - 9*a*b^2 + 5*b^3)*cosh(f*x + e)^2*sinh(f*x + e)^4 + 6*(a^3 + 3*a^2*b - 9*a*b^2 + 5*b^3)*cosh(f*x + e)*sinh(f*x + e)^5 + (a^3 + 3*a^2*b - 9*a*b^2 + 5*b^3)*sinh(f*x + e)^6)*sqrt(b)*log((a^2*b*cosh(f*x + e)^8 + 8*a^2*b*cosh(f*x + e)*sinh(f*x + e)^7 + a^2*b*sinh(f*x + e)^8 + 2*(a^3 + a^2*b)*cosh(f*x + e)^6 + 2*(14*a^2*b*cosh(f*x + e)^2 + a^3 + a^2*b)*sinh(f*x + e)^6 + 4*(14*a^2*b*cosh(f*x + e)^3 + 3*(a^3 + a^2*b)*cosh(f*x + e))*sinh(f*x + e)^5 + (9*a^2*b - 4*a*b^2 + b^3)*cosh(f*x + e)^4 + (70*a^2*b*cosh(f*x + e)^4 + 9*a^2*b - 4*a*b^2 + b^3 + 30*(a^3 + a^2*b)*cosh(f*x + e)^2)*sinh(f*x + e)^4 + 4*(14*a^2*b*cosh(f*x + e)^5 + 10*(a^3 + a^2*b)*cosh(f*x + e)^3 + (9*a^2*b - 4*a*b^2 + b^3)*cosh(f*x + e))*sinh(f*x + e)^3 + b^3 + 2*(3*a*b^2 - b^3)*cosh(f*x + e)^2 + 2*(14*a^2*b*cosh(f*x + e)^6 + 15*(a^3 + a^2*b)*cosh(f*x + e)^4 + 3*a*b^2 - b^3 + 3*(9*a^2*b - 4*a*b^2 + b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^2 - sqrt(2)*(a^2*cosh(f*x + e)^6 + 6*a^2*cosh(f*x + e)*sinh(f*x + e)^5 + a^2*sinh(f*x + e)^6 + 3*a^2*cosh(f*x + e)^4 + 3*(5*a^2*cosh(f*x + e)^2 + a^2)*sinh(f*x + e)^4 + 4*(5*a^2*cosh(f*x + e)^3 + 3*a^2*cosh(f*x + e))*sinh(f*x + e)^3 + (4*a*b - b^2)*cosh(f*x + e)^2 + (15*a^2*cosh(f*x + e)^4 + 18*a^2*cosh(f*x + e)^2 + 4*a*b - b^2)*sinh(f*x + e)^2 + b^2 + 2*(3*a^2*cosh(f*x + e)^5 + 6*a^2*cosh(f*x + e)^3 + (4*a*b - b^2)*cosh(f*x + e))*sinh(f*x + e))*sqrt(b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + 4*(2*a^2*b*cosh(f*x + e)^7 + 3*(a^3 + a^2*b)*cosh(f*x + e)^5 + (9*a^2*b - 4*a*b^2 + b^3)*cosh(f*x + e)^3 + (3*a*b^2 - b^3)*cosh(f*x + e))*sinh(f*x + e))/(cosh(f*x + e)^6 + 6*cosh(f*x + e)^5*sinh(f*x + e) + 15*cosh(f*x + e)^4*sinh(f*x + e)^2 + 20*cosh(f*x + e)^3*sinh(f*x + e)^3 + 15*cosh(f*x + e)^2*sinh(f*x + e)^4 + 6*cosh(f*x + e)*sinh(f*x + e)^5 + sinh(f*x + e)^6)) + 6*((a^3 + 3*a^2*b - 9*a*b^2 + 5*b^3)*cosh(f*x + e)^6 + 6*(a^3 + 3*a^2*b - 9*a*b^2 + 5*b^3)*cosh(f*x + e)^5*sinh(f*x + e) + 15*(a^3 + 3*a^2*b - 9*a*b^2 + 5*b^3)*cosh(f*x + e)^4*sinh(f*x + e)^2 + 20*(a^3 + 3*a^2*b - 9*a*b^2 + 5*b^3)*cosh(f*x + e)^3*sinh(f*x + e)^3 + 15*(a^3 + 3*a^2*b - 9*a*b^2 + 5*b^3)*cosh(f*x + e)^2*sinh(f*x + e)^4 + 6*(a^3 + 3*a^2*b - 9*a*b^2 + 5*b^3)*cosh(f*x + e)*sinh(f*x + e)^5 + (a^3 + 3*a^2*b - 9*a*b^2 + 5*b^3)*sinh(f*x + e)^6)*sqrt(b)*log(-(b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(a - b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + a - b)*sinh(f*x + e)^2 - sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 - 1)*sqrt(b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + 4*(b*cosh(f*x + e)^3 + (a - b)*cosh(f*x + e))*sinh(f*x + e) + b)/(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + sqrt(2)*(b^3*cosh(f*x + e)^10 + 10*b^3*cosh(f*x + e)*sinh(f*x + e)^9 + b^3*sinh(f*x + e)^10 + (7*a*b^2 - 8*b^3)*cosh(f*x + e)^8 + (45*b^3*cosh(f*x + e)^2 + 7*a*b^2 - 8*b^3)*sinh(f*x + e)^8 + 8*(15*b^3*cosh(f*x + e)^3 + (7*a*b^2 - 8*b^3)*cosh(f*x + e))*sinh(f*x + e)^7 + (6*a^2*b - 51*a*b^2 + 37*b^3)*cosh(f*x + e)^6 + (210*b^3*cosh(f*x + e)^4 + 6*a^2*b - 51*a*b^2 + 37*b^3 + 28*(7*a*b^2 - 8*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^6 + 2*(126*b^3*cosh(f*x + e)^5 + 28*(7*a*b^2 - 8*b^3)*cosh(f*x + e)^3 + 3*(6*a^2*b - 51*a*b^2 + 37*b^3)*cosh(f*x + e))*sinh(f*x + e)^5 + (6*a^2*b - 51*a*b^2 + 37*b^3)*cosh(f*x + e)^4 + (210*b^3*cosh(f*x + e)^6 + 70*(7*a*b^2 - 8*b^3)*cosh(f*x + e)^4 + 6*a^2*b - 51*a*b^2 + 37*b^3 + 15*(6*a^2*b - 51*a*b^2 + 37*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^4 + 4*(30*b^3*cosh(f*x + e)^7 + 14*(7*a*b^2 - 8*b^3)*cosh(f*x + e)^5 + 5*(6*a^2*b - 51*a*b^2 + 37*b^3)*cosh(f*x + e)^3 + (6*a^2*b - 51*a*b^2 + 37*b^3)*cosh(f*x + e))*sinh(f*x + e)^3 + b^3 + (7*a*b^2 - 8*b^3)*cosh(f*x + e)^2 + (45*b^3*cosh(f*x + e)^8 + 28*(7*a*b^2 - 8*b^3)*cosh(f*x + e)^6 + 15*(6*a^2*b - 51*a*b^2 + 37*b^3)*cosh(f*x + e)^4 + 7*a*b^2 - 8*b^3 + 6*(6*a^2*b - 51*a*b^2 + 37*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^2 + 2*(5*b^3*cosh(f*x + e)^9 + 4*(7*a*b^2 - 8*b^3)*cosh(f*x + e)^7 + 3*(6*a^2*b - 51*a*b^2 + 37*b^3)*cosh(f*x + e)^5 + 2*(6*a^2*b - 51*a*b^2 + 37*b^3)*cosh(f*x + e)^3 + (7*a*b^2 - 8*b^3)*cosh(f*x + e))*sinh(f*x + e))*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/(b^2*f*cosh(f*x + e)^6 + 6*b^2*f*cosh(f*x + e)^5*sinh(f*x + e) + 15*b^2*f*cosh(f*x + e)^4*sinh(f*x + e)^2 + 20*b^2*f*cosh(f*x + e)^3*sinh(f*x + e)^3 + 15*b^2*f*cosh(f*x + e)^2*sinh(f*x + e)^4 + 6*b^2*f*cosh(f*x + e)*sinh(f*x + e)^5 + b^2*f*sinh(f*x + e)^6), 1/384*(12*((a^3 + 3*a^2*b - 9*a*b^2 + 5*b^3)*cosh(f*x + e)^6 + 6*(a^3 + 3*a^2*b - 9*a*b^2 + 5*b^3)*cosh(f*x + e)^5*sinh(f*x + e) + 15*(a^3 + 3*a^2*b - 9*a*b^2 + 5*b^3)*cosh(f*x + e)^4*sinh(f*x + e)^2 + 20*(a^3 + 3*a^2*b - 9*a*b^2 + 5*b^3)*cosh(f*x + e)^3*sinh(f*x + e)^3 + 15*(a^3 + 3*a^2*b - 9*a*b^2 + 5*b^3)*cosh(f*x + e)^2*sinh(f*x + e)^4 + 6*(a^3 + 3*a^2*b - 9*a*b^2 + 5*b^3)*cosh(f*x + e)*sinh(f*x + e)^5 + (a^3 + 3*a^2*b - 9*a*b^2 + 5*b^3)*sinh(f*x + e)^6)*sqrt(-b)*arctan(sqrt(2)*(a*cosh(f*x + e)^2 + 2*a*cosh(f*x + e)*sinh(f*x + e) + a*sinh(f*x + e)^2 + b)*sqrt(-b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/(a*b*cosh(f*x + e)^4 + 4*a*b*cosh(f*x + e)*sinh(f*x + e)^3 + a*b*sinh(f*x + e)^4 + (3*a*b - b^2)*cosh(f*x + e)^2 + (6*a*b*cosh(f*x + e)^2 + 3*a*b - b^2)*sinh(f*x + e)^2 + b^2 + 2*(2*a*b*cosh(f*x + e)^3 + (3*a*b - b^2)*cosh(f*x + e))*sinh(f*x + e))) + 12*((a^3 + 3*a^2*b - 9*a*b^2 + 5*b^3)*cosh(f*x + e)^6 + 6*(a^3 + 3*a^2*b - 9*a*b^2 + 5*b^3)*cosh(f*x + e)^5*sinh(f*x + e) + 15*(a^3 + 3*a^2*b - 9*a*b^2 + 5*b^3)*cosh(f*x + e)^4*sinh(f*x + e)^2 + 20*(a^3 + 3*a^2*b - 9*a*b^2 + 5*b^3)*cosh(f*x + e)^3*sinh(f*x + e)^3 + 15*(a^3 + 3*a^2*b - 9*a*b^2 + 5*b^3)*cosh(f*x + e)^2*sinh(f*x + e)^4 + 6*(a^3 + 3*a^2*b - 9*a*b^2 + 5*b^3)*cosh(f*x + e)*sinh(f*x + e)^5 + (a^3 + 3*a^2*b - 9*a*b^2 + 5*b^3)*sinh(f*x + e)^6)*sqrt(-b)*arctan(sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 - 1)*sqrt(-b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/(b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(2*a - b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 2*a - b)*sinh(f*x + e)^2 + 4*(b*cosh(f*x + e)^3 + (2*a - b)*cosh(f*x + e))*sinh(f*x + e) + b)) + sqrt(2)*(b^3*cosh(f*x + e)^10 + 10*b^3*cosh(f*x + e)*sinh(f*x + e)^9 + b^3*sinh(f*x + e)^10 + (7*a*b^2 - 8*b^3)*cosh(f*x + e)^8 + (45*b^3*cosh(f*x + e)^2 + 7*a*b^2 - 8*b^3)*sinh(f*x + e)^8 + 8*(15*b^3*cosh(f*x + e)^3 + (7*a*b^2 - 8*b^3)*cosh(f*x + e))*sinh(f*x + e)^7 + (6*a^2*b - 51*a*b^2 + 37*b^3)*cosh(f*x + e)^6 + (210*b^3*cosh(f*x + e)^4 + 6*a^2*b - 51*a*b^2 + 37*b^3 + 28*(7*a*b^2 - 8*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^6 + 2*(126*b^3*cosh(f*x + e)^5 + 28*(7*a*b^2 - 8*b^3)*cosh(f*x + e)^3 + 3*(6*a^2*b - 51*a*b^2 + 37*b^3)*cosh(f*x + e))*sinh(f*x + e)^5 + (6*a^2*b - 51*a*b^2 + 37*b^3)*cosh(f*x + e)^4 + (210*b^3*cosh(f*x + e)^6 + 70*(7*a*b^2 - 8*b^3)*cosh(f*x + e)^4 + 6*a^2*b - 51*a*b^2 + 37*b^3 + 15*(6*a^2*b - 51*a*b^2 + 37*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^4 + 4*(30*b^3*cosh(f*x + e)^7 + 14*(7*a*b^2 - 8*b^3)*cosh(f*x + e)^5 + 5*(6*a^2*b - 51*a*b^2 + 37*b^3)*cosh(f*x + e)^3 + (6*a^2*b - 51*a*b^2 + 37*b^3)*cosh(f*x + e))*sinh(f*x + e)^3 + b^3 + (7*a*b^2 - 8*b^3)*cosh(f*x + e)^2 + (45*b^3*cosh(f*x + e)^8 + 28*(7*a*b^2 - 8*b^3)*cosh(f*x + e)^6 + 15*(6*a^2*b - 51*a*b^2 + 37*b^3)*cosh(f*x + e)^4 + 7*a*b^2 - 8*b^3 + 6*(6*a^2*b - 51*a*b^2 + 37*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^2 + 2*(5*b^3*cosh(f*x + e)^9 + 4*(7*a*b^2 - 8*b^3)*cosh(f*x + e)^7 + 3*(6*a^2*b - 51*a*b^2 + 37*b^3)*cosh(f*x + e)^5 + 2*(6*a^2*b - 51*a*b^2 + 37*b^3)*cosh(f*x + e)^3 + (7*a*b^2 - 8*b^3)*cosh(f*x + e))*sinh(f*x + e))*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/(b^2*f*cosh(f*x + e)^6 + 6*b^2*f*cosh(f*x + e)^5*sinh(f*x + e) + 15*b^2*f*cosh(f*x + e)^4*sinh(f*x + e)^2 + 20*b^2*f*cosh(f*x + e)^3*sinh(f*x + e)^3 + 15*b^2*f*cosh(f*x + e)^2*sinh(f*x + e)^4 + 6*b^2*f*cosh(f*x + e)*sinh(f*x + e)^5 + b^2*f*sinh(f*x + e)^6)]","B",0
77,1,2977,0,4.829221," ","integrate(sinh(f*x+e)*(a+b*sinh(f*x+e)^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{6 \, {\left({\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{3} \sinh\left(f x + e\right) + 6 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{2} \sinh\left(f x + e\right)^{2} + 4 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(a^{2} - 2 \, a b + b^{2}\right)} \sinh\left(f x + e\right)^{4}\right)} \sqrt{b} \log\left(\frac{a^{2} b \cosh\left(f x + e\right)^{8} + 8 \, a^{2} b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + a^{2} b \sinh\left(f x + e\right)^{8} + 2 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(f x + e\right)^{6} + 2 \, {\left(14 \, a^{2} b \cosh\left(f x + e\right)^{2} + a^{3} + a^{2} b\right)} \sinh\left(f x + e\right)^{6} + 4 \, {\left(14 \, a^{2} b \cosh\left(f x + e\right)^{3} + 3 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + {\left(9 \, a^{2} b - 4 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{4} + {\left(70 \, a^{2} b \cosh\left(f x + e\right)^{4} + 9 \, a^{2} b - 4 \, a b^{2} + b^{3} + 30 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(14 \, a^{2} b \cosh\left(f x + e\right)^{5} + 10 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(f x + e\right)^{3} + {\left(9 \, a^{2} b - 4 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + b^{3} + 2 \, {\left(3 \, a b^{2} - b^{3}\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(14 \, a^{2} b \cosh\left(f x + e\right)^{6} + 15 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(f x + e\right)^{4} + 3 \, a b^{2} - b^{3} + 3 \, {\left(9 \, a^{2} b - 4 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{2} + \sqrt{2} {\left(a^{2} \cosh\left(f x + e\right)^{6} + 6 \, a^{2} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + a^{2} \sinh\left(f x + e\right)^{6} + 3 \, a^{2} \cosh\left(f x + e\right)^{4} + 3 \, {\left(5 \, a^{2} \cosh\left(f x + e\right)^{2} + a^{2}\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(5 \, a^{2} \cosh\left(f x + e\right)^{3} + 3 \, a^{2} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + {\left(4 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{2} + {\left(15 \, a^{2} \cosh\left(f x + e\right)^{4} + 18 \, a^{2} \cosh\left(f x + e\right)^{2} + 4 \, a b - b^{2}\right)} \sinh\left(f x + e\right)^{2} + b^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(f x + e\right)^{5} + 6 \, a^{2} \cosh\left(f x + e\right)^{3} + {\left(4 \, a b - b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} + 4 \, {\left(2 \, a^{2} b \cosh\left(f x + e\right)^{7} + 3 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(f x + e\right)^{5} + {\left(9 \, a^{2} b - 4 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{3} + {\left(3 \, a b^{2} - b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)}{\cosh\left(f x + e\right)^{6} + 6 \, \cosh\left(f x + e\right)^{5} \sinh\left(f x + e\right) + 15 \, \cosh\left(f x + e\right)^{4} \sinh\left(f x + e\right)^{2} + 20 \, \cosh\left(f x + e\right)^{3} \sinh\left(f x + e\right)^{3} + 15 \, \cosh\left(f x + e\right)^{2} \sinh\left(f x + e\right)^{4} + 6 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + \sinh\left(f x + e\right)^{6}}\right) + 6 \, {\left({\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{3} \sinh\left(f x + e\right) + 6 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{2} \sinh\left(f x + e\right)^{2} + 4 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(a^{2} - 2 \, a b + b^{2}\right)} \sinh\left(f x + e\right)^{4}\right)} \sqrt{b} \log\left(-\frac{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + a - b\right)} \sinh\left(f x + e\right)^{2} + \sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} - 1\right)} \sqrt{b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}{\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}\right) + \sqrt{2} {\left(b^{2} \cosh\left(f x + e\right)^{6} + 6 \, b^{2} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + b^{2} \sinh\left(f x + e\right)^{6} + {\left(10 \, a b - 7 \, b^{2}\right)} \cosh\left(f x + e\right)^{4} + {\left(15 \, b^{2} \cosh\left(f x + e\right)^{2} + 10 \, a b - 7 \, b^{2}\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(5 \, b^{2} \cosh\left(f x + e\right)^{3} + {\left(10 \, a b - 7 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + {\left(10 \, a b - 7 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + {\left(15 \, b^{2} \cosh\left(f x + e\right)^{4} + 6 \, {\left(10 \, a b - 7 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + 10 \, a b - 7 \, b^{2}\right)} \sinh\left(f x + e\right)^{2} + b^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(f x + e\right)^{5} + 2 \, {\left(10 \, a b - 7 \, b^{2}\right)} \cosh\left(f x + e\right)^{3} + {\left(10 \, a b - 7 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{64 \, {\left(b f \cosh\left(f x + e\right)^{4} + 4 \, b f \cosh\left(f x + e\right)^{3} \sinh\left(f x + e\right) + 6 \, b f \cosh\left(f x + e\right)^{2} \sinh\left(f x + e\right)^{2} + 4 \, b f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b f \sinh\left(f x + e\right)^{4}\right)}}, -\frac{12 \, {\left({\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{3} \sinh\left(f x + e\right) + 6 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{2} \sinh\left(f x + e\right)^{2} + 4 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(a^{2} - 2 \, a b + b^{2}\right)} \sinh\left(f x + e\right)^{4}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{2} {\left(a \cosh\left(f x + e\right)^{2} + 2 \, a \cosh\left(f x + e\right) \sinh\left(f x + e\right) + a \sinh\left(f x + e\right)^{2} + b\right)} \sqrt{-b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{a b \cosh\left(f x + e\right)^{4} + 4 \, a b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + a b \sinh\left(f x + e\right)^{4} + {\left(3 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{2} + {\left(6 \, a b \cosh\left(f x + e\right)^{2} + 3 \, a b - b^{2}\right)} \sinh\left(f x + e\right)^{2} + b^{2} + 2 \, {\left(2 \, a b \cosh\left(f x + e\right)^{3} + {\left(3 \, a b - b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)}\right) + 12 \, {\left({\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{3} \sinh\left(f x + e\right) + 6 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{2} \sinh\left(f x + e\right)^{2} + 4 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(a^{2} - 2 \, a b + b^{2}\right)} \sinh\left(f x + e\right)^{4}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} - 1\right)} \sqrt{-b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + 2 \, a - b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}\right) - \sqrt{2} {\left(b^{2} \cosh\left(f x + e\right)^{6} + 6 \, b^{2} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + b^{2} \sinh\left(f x + e\right)^{6} + {\left(10 \, a b - 7 \, b^{2}\right)} \cosh\left(f x + e\right)^{4} + {\left(15 \, b^{2} \cosh\left(f x + e\right)^{2} + 10 \, a b - 7 \, b^{2}\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(5 \, b^{2} \cosh\left(f x + e\right)^{3} + {\left(10 \, a b - 7 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + {\left(10 \, a b - 7 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + {\left(15 \, b^{2} \cosh\left(f x + e\right)^{4} + 6 \, {\left(10 \, a b - 7 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + 10 \, a b - 7 \, b^{2}\right)} \sinh\left(f x + e\right)^{2} + b^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(f x + e\right)^{5} + 2 \, {\left(10 \, a b - 7 \, b^{2}\right)} \cosh\left(f x + e\right)^{3} + {\left(10 \, a b - 7 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{64 \, {\left(b f \cosh\left(f x + e\right)^{4} + 4 \, b f \cosh\left(f x + e\right)^{3} \sinh\left(f x + e\right) + 6 \, b f \cosh\left(f x + e\right)^{2} \sinh\left(f x + e\right)^{2} + 4 \, b f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b f \sinh\left(f x + e\right)^{4}\right)}}\right]"," ",0,"[1/64*(6*((a^2 - 2*a*b + b^2)*cosh(f*x + e)^4 + 4*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^3*sinh(f*x + e) + 6*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^2*sinh(f*x + e)^2 + 4*(a^2 - 2*a*b + b^2)*cosh(f*x + e)*sinh(f*x + e)^3 + (a^2 - 2*a*b + b^2)*sinh(f*x + e)^4)*sqrt(b)*log((a^2*b*cosh(f*x + e)^8 + 8*a^2*b*cosh(f*x + e)*sinh(f*x + e)^7 + a^2*b*sinh(f*x + e)^8 + 2*(a^3 + a^2*b)*cosh(f*x + e)^6 + 2*(14*a^2*b*cosh(f*x + e)^2 + a^3 + a^2*b)*sinh(f*x + e)^6 + 4*(14*a^2*b*cosh(f*x + e)^3 + 3*(a^3 + a^2*b)*cosh(f*x + e))*sinh(f*x + e)^5 + (9*a^2*b - 4*a*b^2 + b^3)*cosh(f*x + e)^4 + (70*a^2*b*cosh(f*x + e)^4 + 9*a^2*b - 4*a*b^2 + b^3 + 30*(a^3 + a^2*b)*cosh(f*x + e)^2)*sinh(f*x + e)^4 + 4*(14*a^2*b*cosh(f*x + e)^5 + 10*(a^3 + a^2*b)*cosh(f*x + e)^3 + (9*a^2*b - 4*a*b^2 + b^3)*cosh(f*x + e))*sinh(f*x + e)^3 + b^3 + 2*(3*a*b^2 - b^3)*cosh(f*x + e)^2 + 2*(14*a^2*b*cosh(f*x + e)^6 + 15*(a^3 + a^2*b)*cosh(f*x + e)^4 + 3*a*b^2 - b^3 + 3*(9*a^2*b - 4*a*b^2 + b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^2 + sqrt(2)*(a^2*cosh(f*x + e)^6 + 6*a^2*cosh(f*x + e)*sinh(f*x + e)^5 + a^2*sinh(f*x + e)^6 + 3*a^2*cosh(f*x + e)^4 + 3*(5*a^2*cosh(f*x + e)^2 + a^2)*sinh(f*x + e)^4 + 4*(5*a^2*cosh(f*x + e)^3 + 3*a^2*cosh(f*x + e))*sinh(f*x + e)^3 + (4*a*b - b^2)*cosh(f*x + e)^2 + (15*a^2*cosh(f*x + e)^4 + 18*a^2*cosh(f*x + e)^2 + 4*a*b - b^2)*sinh(f*x + e)^2 + b^2 + 2*(3*a^2*cosh(f*x + e)^5 + 6*a^2*cosh(f*x + e)^3 + (4*a*b - b^2)*cosh(f*x + e))*sinh(f*x + e))*sqrt(b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + 4*(2*a^2*b*cosh(f*x + e)^7 + 3*(a^3 + a^2*b)*cosh(f*x + e)^5 + (9*a^2*b - 4*a*b^2 + b^3)*cosh(f*x + e)^3 + (3*a*b^2 - b^3)*cosh(f*x + e))*sinh(f*x + e))/(cosh(f*x + e)^6 + 6*cosh(f*x + e)^5*sinh(f*x + e) + 15*cosh(f*x + e)^4*sinh(f*x + e)^2 + 20*cosh(f*x + e)^3*sinh(f*x + e)^3 + 15*cosh(f*x + e)^2*sinh(f*x + e)^4 + 6*cosh(f*x + e)*sinh(f*x + e)^5 + sinh(f*x + e)^6)) + 6*((a^2 - 2*a*b + b^2)*cosh(f*x + e)^4 + 4*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^3*sinh(f*x + e) + 6*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^2*sinh(f*x + e)^2 + 4*(a^2 - 2*a*b + b^2)*cosh(f*x + e)*sinh(f*x + e)^3 + (a^2 - 2*a*b + b^2)*sinh(f*x + e)^4)*sqrt(b)*log(-(b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(a - b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + a - b)*sinh(f*x + e)^2 + sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 - 1)*sqrt(b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + 4*(b*cosh(f*x + e)^3 + (a - b)*cosh(f*x + e))*sinh(f*x + e) + b)/(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + sqrt(2)*(b^2*cosh(f*x + e)^6 + 6*b^2*cosh(f*x + e)*sinh(f*x + e)^5 + b^2*sinh(f*x + e)^6 + (10*a*b - 7*b^2)*cosh(f*x + e)^4 + (15*b^2*cosh(f*x + e)^2 + 10*a*b - 7*b^2)*sinh(f*x + e)^4 + 4*(5*b^2*cosh(f*x + e)^3 + (10*a*b - 7*b^2)*cosh(f*x + e))*sinh(f*x + e)^3 + (10*a*b - 7*b^2)*cosh(f*x + e)^2 + (15*b^2*cosh(f*x + e)^4 + 6*(10*a*b - 7*b^2)*cosh(f*x + e)^2 + 10*a*b - 7*b^2)*sinh(f*x + e)^2 + b^2 + 2*(3*b^2*cosh(f*x + e)^5 + 2*(10*a*b - 7*b^2)*cosh(f*x + e)^3 + (10*a*b - 7*b^2)*cosh(f*x + e))*sinh(f*x + e))*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/(b*f*cosh(f*x + e)^4 + 4*b*f*cosh(f*x + e)^3*sinh(f*x + e) + 6*b*f*cosh(f*x + e)^2*sinh(f*x + e)^2 + 4*b*f*cosh(f*x + e)*sinh(f*x + e)^3 + b*f*sinh(f*x + e)^4), -1/64*(12*((a^2 - 2*a*b + b^2)*cosh(f*x + e)^4 + 4*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^3*sinh(f*x + e) + 6*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^2*sinh(f*x + e)^2 + 4*(a^2 - 2*a*b + b^2)*cosh(f*x + e)*sinh(f*x + e)^3 + (a^2 - 2*a*b + b^2)*sinh(f*x + e)^4)*sqrt(-b)*arctan(sqrt(2)*(a*cosh(f*x + e)^2 + 2*a*cosh(f*x + e)*sinh(f*x + e) + a*sinh(f*x + e)^2 + b)*sqrt(-b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/(a*b*cosh(f*x + e)^4 + 4*a*b*cosh(f*x + e)*sinh(f*x + e)^3 + a*b*sinh(f*x + e)^4 + (3*a*b - b^2)*cosh(f*x + e)^2 + (6*a*b*cosh(f*x + e)^2 + 3*a*b - b^2)*sinh(f*x + e)^2 + b^2 + 2*(2*a*b*cosh(f*x + e)^3 + (3*a*b - b^2)*cosh(f*x + e))*sinh(f*x + e))) + 12*((a^2 - 2*a*b + b^2)*cosh(f*x + e)^4 + 4*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^3*sinh(f*x + e) + 6*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^2*sinh(f*x + e)^2 + 4*(a^2 - 2*a*b + b^2)*cosh(f*x + e)*sinh(f*x + e)^3 + (a^2 - 2*a*b + b^2)*sinh(f*x + e)^4)*sqrt(-b)*arctan(sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 - 1)*sqrt(-b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/(b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(2*a - b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 2*a - b)*sinh(f*x + e)^2 + 4*(b*cosh(f*x + e)^3 + (2*a - b)*cosh(f*x + e))*sinh(f*x + e) + b)) - sqrt(2)*(b^2*cosh(f*x + e)^6 + 6*b^2*cosh(f*x + e)*sinh(f*x + e)^5 + b^2*sinh(f*x + e)^6 + (10*a*b - 7*b^2)*cosh(f*x + e)^4 + (15*b^2*cosh(f*x + e)^2 + 10*a*b - 7*b^2)*sinh(f*x + e)^4 + 4*(5*b^2*cosh(f*x + e)^3 + (10*a*b - 7*b^2)*cosh(f*x + e))*sinh(f*x + e)^3 + (10*a*b - 7*b^2)*cosh(f*x + e)^2 + (15*b^2*cosh(f*x + e)^4 + 6*(10*a*b - 7*b^2)*cosh(f*x + e)^2 + 10*a*b - 7*b^2)*sinh(f*x + e)^2 + b^2 + 2*(3*b^2*cosh(f*x + e)^5 + 2*(10*a*b - 7*b^2)*cosh(f*x + e)^3 + (10*a*b - 7*b^2)*cosh(f*x + e))*sinh(f*x + e))*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/(b*f*cosh(f*x + e)^4 + 4*b*f*cosh(f*x + e)^3*sinh(f*x + e) + 6*b*f*cosh(f*x + e)^2*sinh(f*x + e)^2 + 4*b*f*cosh(f*x + e)*sinh(f*x + e)^3 + b*f*sinh(f*x + e)^4)]","B",0
78,1,5565,0,3.118780," ","integrate(csch(f*x+e)*(a+b*sinh(f*x+e)^2)^(3/2),x, algorithm=""fricas"")","\left[-\frac{{\left({\left(3 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, a - b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) + {\left(3 \, a - b\right)} \sinh\left(f x + e\right)^{2}\right)} \sqrt{b} \log\left(\frac{a^{2} b \cosh\left(f x + e\right)^{8} + 8 \, a^{2} b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + a^{2} b \sinh\left(f x + e\right)^{8} + 2 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(f x + e\right)^{6} + 2 \, {\left(14 \, a^{2} b \cosh\left(f x + e\right)^{2} + a^{3} + a^{2} b\right)} \sinh\left(f x + e\right)^{6} + 4 \, {\left(14 \, a^{2} b \cosh\left(f x + e\right)^{3} + 3 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + {\left(9 \, a^{2} b - 4 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{4} + {\left(70 \, a^{2} b \cosh\left(f x + e\right)^{4} + 9 \, a^{2} b - 4 \, a b^{2} + b^{3} + 30 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(14 \, a^{2} b \cosh\left(f x + e\right)^{5} + 10 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(f x + e\right)^{3} + {\left(9 \, a^{2} b - 4 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + b^{3} + 2 \, {\left(3 \, a b^{2} - b^{3}\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(14 \, a^{2} b \cosh\left(f x + e\right)^{6} + 15 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(f x + e\right)^{4} + 3 \, a b^{2} - b^{3} + 3 \, {\left(9 \, a^{2} b - 4 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{2} - \sqrt{2} {\left(a^{2} \cosh\left(f x + e\right)^{6} + 6 \, a^{2} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + a^{2} \sinh\left(f x + e\right)^{6} + 3 \, a^{2} \cosh\left(f x + e\right)^{4} + 3 \, {\left(5 \, a^{2} \cosh\left(f x + e\right)^{2} + a^{2}\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(5 \, a^{2} \cosh\left(f x + e\right)^{3} + 3 \, a^{2} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + {\left(4 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{2} + {\left(15 \, a^{2} \cosh\left(f x + e\right)^{4} + 18 \, a^{2} \cosh\left(f x + e\right)^{2} + 4 \, a b - b^{2}\right)} \sinh\left(f x + e\right)^{2} + b^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(f x + e\right)^{5} + 6 \, a^{2} \cosh\left(f x + e\right)^{3} + {\left(4 \, a b - b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} + 4 \, {\left(2 \, a^{2} b \cosh\left(f x + e\right)^{7} + 3 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(f x + e\right)^{5} + {\left(9 \, a^{2} b - 4 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{3} + {\left(3 \, a b^{2} - b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)}{\cosh\left(f x + e\right)^{6} + 6 \, \cosh\left(f x + e\right)^{5} \sinh\left(f x + e\right) + 15 \, \cosh\left(f x + e\right)^{4} \sinh\left(f x + e\right)^{2} + 20 \, \cosh\left(f x + e\right)^{3} \sinh\left(f x + e\right)^{3} + 15 \, \cosh\left(f x + e\right)^{2} \sinh\left(f x + e\right)^{4} + 6 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + \sinh\left(f x + e\right)^{6}}\right) - 4 \, {\left(a \cosh\left(f x + e\right)^{2} + 2 \, a \cosh\left(f x + e\right) \sinh\left(f x + e\right) + a \sinh\left(f x + e\right)^{2}\right)} \sqrt{a} \log\left(-\frac{{\left(a + b\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(a + b\right)} \sinh\left(f x + e\right)^{4} + 2 \, {\left(3 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(f x + e\right)^{2} + 3 \, a - b\right)} \sinh\left(f x + e\right)^{2} - 2 \, \sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} + 1\right)} \sqrt{a} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(f x + e\right)^{3} + {\left(3 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + a + b}{\cosh\left(f x + e\right)^{4} + 4 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + \sinh\left(f x + e\right)^{4} + 2 \, {\left(3 \, \cosh\left(f x + e\right)^{2} - 1\right)} \sinh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right)^{2} + 4 \, {\left(\cosh\left(f x + e\right)^{3} - \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + 1}\right) + {\left({\left(3 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, a - b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) + {\left(3 \, a - b\right)} \sinh\left(f x + e\right)^{2}\right)} \sqrt{b} \log\left(-\frac{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + a - b\right)} \sinh\left(f x + e\right)^{2} - \sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} - 1\right)} \sqrt{b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}{\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}\right) - \sqrt{2} {\left(b \cosh\left(f x + e\right)^{2} + 2 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right) + b \sinh\left(f x + e\right)^{2} + b\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{8 \, {\left(f \cosh\left(f x + e\right)^{2} + 2 \, f \cosh\left(f x + e\right) \sinh\left(f x + e\right) + f \sinh\left(f x + e\right)^{2}\right)}}, \frac{8 \, {\left(a \cosh\left(f x + e\right)^{2} + 2 \, a \cosh\left(f x + e\right) \sinh\left(f x + e\right) + a \sinh\left(f x + e\right)^{2}\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} + 1\right)} \sqrt{-a} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + 2 \, a - b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}\right) - {\left({\left(3 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, a - b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) + {\left(3 \, a - b\right)} \sinh\left(f x + e\right)^{2}\right)} \sqrt{b} \log\left(\frac{a^{2} b \cosh\left(f x + e\right)^{8} + 8 \, a^{2} b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + a^{2} b \sinh\left(f x + e\right)^{8} + 2 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(f x + e\right)^{6} + 2 \, {\left(14 \, a^{2} b \cosh\left(f x + e\right)^{2} + a^{3} + a^{2} b\right)} \sinh\left(f x + e\right)^{6} + 4 \, {\left(14 \, a^{2} b \cosh\left(f x + e\right)^{3} + 3 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + {\left(9 \, a^{2} b - 4 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{4} + {\left(70 \, a^{2} b \cosh\left(f x + e\right)^{4} + 9 \, a^{2} b - 4 \, a b^{2} + b^{3} + 30 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(14 \, a^{2} b \cosh\left(f x + e\right)^{5} + 10 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(f x + e\right)^{3} + {\left(9 \, a^{2} b - 4 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + b^{3} + 2 \, {\left(3 \, a b^{2} - b^{3}\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(14 \, a^{2} b \cosh\left(f x + e\right)^{6} + 15 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(f x + e\right)^{4} + 3 \, a b^{2} - b^{3} + 3 \, {\left(9 \, a^{2} b - 4 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{2} - \sqrt{2} {\left(a^{2} \cosh\left(f x + e\right)^{6} + 6 \, a^{2} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + a^{2} \sinh\left(f x + e\right)^{6} + 3 \, a^{2} \cosh\left(f x + e\right)^{4} + 3 \, {\left(5 \, a^{2} \cosh\left(f x + e\right)^{2} + a^{2}\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(5 \, a^{2} \cosh\left(f x + e\right)^{3} + 3 \, a^{2} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + {\left(4 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{2} + {\left(15 \, a^{2} \cosh\left(f x + e\right)^{4} + 18 \, a^{2} \cosh\left(f x + e\right)^{2} + 4 \, a b - b^{2}\right)} \sinh\left(f x + e\right)^{2} + b^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(f x + e\right)^{5} + 6 \, a^{2} \cosh\left(f x + e\right)^{3} + {\left(4 \, a b - b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} + 4 \, {\left(2 \, a^{2} b \cosh\left(f x + e\right)^{7} + 3 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(f x + e\right)^{5} + {\left(9 \, a^{2} b - 4 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{3} + {\left(3 \, a b^{2} - b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)}{\cosh\left(f x + e\right)^{6} + 6 \, \cosh\left(f x + e\right)^{5} \sinh\left(f x + e\right) + 15 \, \cosh\left(f x + e\right)^{4} \sinh\left(f x + e\right)^{2} + 20 \, \cosh\left(f x + e\right)^{3} \sinh\left(f x + e\right)^{3} + 15 \, \cosh\left(f x + e\right)^{2} \sinh\left(f x + e\right)^{4} + 6 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + \sinh\left(f x + e\right)^{6}}\right) - {\left({\left(3 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, a - b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) + {\left(3 \, a - b\right)} \sinh\left(f x + e\right)^{2}\right)} \sqrt{b} \log\left(-\frac{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + a - b\right)} \sinh\left(f x + e\right)^{2} - \sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} - 1\right)} \sqrt{b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}{\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}\right) + \sqrt{2} {\left(b \cosh\left(f x + e\right)^{2} + 2 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right) + b \sinh\left(f x + e\right)^{2} + b\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{8 \, {\left(f \cosh\left(f x + e\right)^{2} + 2 \, f \cosh\left(f x + e\right) \sinh\left(f x + e\right) + f \sinh\left(f x + e\right)^{2}\right)}}, -\frac{2 \, {\left({\left(3 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, a - b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) + {\left(3 \, a - b\right)} \sinh\left(f x + e\right)^{2}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{2} {\left(a \cosh\left(f x + e\right)^{2} + 2 \, a \cosh\left(f x + e\right) \sinh\left(f x + e\right) + a \sinh\left(f x + e\right)^{2} + b\right)} \sqrt{-b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{a b \cosh\left(f x + e\right)^{4} + 4 \, a b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + a b \sinh\left(f x + e\right)^{4} + {\left(3 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{2} + {\left(6 \, a b \cosh\left(f x + e\right)^{2} + 3 \, a b - b^{2}\right)} \sinh\left(f x + e\right)^{2} + b^{2} + 2 \, {\left(2 \, a b \cosh\left(f x + e\right)^{3} + {\left(3 \, a b - b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)}\right) + 2 \, {\left({\left(3 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, a - b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) + {\left(3 \, a - b\right)} \sinh\left(f x + e\right)^{2}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} - 1\right)} \sqrt{-b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + 2 \, a - b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}\right) - 4 \, {\left(a \cosh\left(f x + e\right)^{2} + 2 \, a \cosh\left(f x + e\right) \sinh\left(f x + e\right) + a \sinh\left(f x + e\right)^{2}\right)} \sqrt{a} \log\left(-\frac{{\left(a + b\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(a + b\right)} \sinh\left(f x + e\right)^{4} + 2 \, {\left(3 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(f x + e\right)^{2} + 3 \, a - b\right)} \sinh\left(f x + e\right)^{2} - 2 \, \sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} + 1\right)} \sqrt{a} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(f x + e\right)^{3} + {\left(3 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + a + b}{\cosh\left(f x + e\right)^{4} + 4 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + \sinh\left(f x + e\right)^{4} + 2 \, {\left(3 \, \cosh\left(f x + e\right)^{2} - 1\right)} \sinh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right)^{2} + 4 \, {\left(\cosh\left(f x + e\right)^{3} - \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + 1}\right) - \sqrt{2} {\left(b \cosh\left(f x + e\right)^{2} + 2 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right) + b \sinh\left(f x + e\right)^{2} + b\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{8 \, {\left(f \cosh\left(f x + e\right)^{2} + 2 \, f \cosh\left(f x + e\right) \sinh\left(f x + e\right) + f \sinh\left(f x + e\right)^{2}\right)}}, \frac{8 \, {\left(a \cosh\left(f x + e\right)^{2} + 2 \, a \cosh\left(f x + e\right) \sinh\left(f x + e\right) + a \sinh\left(f x + e\right)^{2}\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} + 1\right)} \sqrt{-a} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + 2 \, a - b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}\right) - 2 \, {\left({\left(3 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, a - b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) + {\left(3 \, a - b\right)} \sinh\left(f x + e\right)^{2}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{2} {\left(a \cosh\left(f x + e\right)^{2} + 2 \, a \cosh\left(f x + e\right) \sinh\left(f x + e\right) + a \sinh\left(f x + e\right)^{2} + b\right)} \sqrt{-b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{a b \cosh\left(f x + e\right)^{4} + 4 \, a b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + a b \sinh\left(f x + e\right)^{4} + {\left(3 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{2} + {\left(6 \, a b \cosh\left(f x + e\right)^{2} + 3 \, a b - b^{2}\right)} \sinh\left(f x + e\right)^{2} + b^{2} + 2 \, {\left(2 \, a b \cosh\left(f x + e\right)^{3} + {\left(3 \, a b - b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)}\right) - 2 \, {\left({\left(3 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, a - b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) + {\left(3 \, a - b\right)} \sinh\left(f x + e\right)^{2}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} - 1\right)} \sqrt{-b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + 2 \, a - b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}\right) + \sqrt{2} {\left(b \cosh\left(f x + e\right)^{2} + 2 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right) + b \sinh\left(f x + e\right)^{2} + b\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{8 \, {\left(f \cosh\left(f x + e\right)^{2} + 2 \, f \cosh\left(f x + e\right) \sinh\left(f x + e\right) + f \sinh\left(f x + e\right)^{2}\right)}}\right]"," ",0,"[-1/8*(((3*a - b)*cosh(f*x + e)^2 + 2*(3*a - b)*cosh(f*x + e)*sinh(f*x + e) + (3*a - b)*sinh(f*x + e)^2)*sqrt(b)*log((a^2*b*cosh(f*x + e)^8 + 8*a^2*b*cosh(f*x + e)*sinh(f*x + e)^7 + a^2*b*sinh(f*x + e)^8 + 2*(a^3 + a^2*b)*cosh(f*x + e)^6 + 2*(14*a^2*b*cosh(f*x + e)^2 + a^3 + a^2*b)*sinh(f*x + e)^6 + 4*(14*a^2*b*cosh(f*x + e)^3 + 3*(a^3 + a^2*b)*cosh(f*x + e))*sinh(f*x + e)^5 + (9*a^2*b - 4*a*b^2 + b^3)*cosh(f*x + e)^4 + (70*a^2*b*cosh(f*x + e)^4 + 9*a^2*b - 4*a*b^2 + b^3 + 30*(a^3 + a^2*b)*cosh(f*x + e)^2)*sinh(f*x + e)^4 + 4*(14*a^2*b*cosh(f*x + e)^5 + 10*(a^3 + a^2*b)*cosh(f*x + e)^3 + (9*a^2*b - 4*a*b^2 + b^3)*cosh(f*x + e))*sinh(f*x + e)^3 + b^3 + 2*(3*a*b^2 - b^3)*cosh(f*x + e)^2 + 2*(14*a^2*b*cosh(f*x + e)^6 + 15*(a^3 + a^2*b)*cosh(f*x + e)^4 + 3*a*b^2 - b^3 + 3*(9*a^2*b - 4*a*b^2 + b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^2 - sqrt(2)*(a^2*cosh(f*x + e)^6 + 6*a^2*cosh(f*x + e)*sinh(f*x + e)^5 + a^2*sinh(f*x + e)^6 + 3*a^2*cosh(f*x + e)^4 + 3*(5*a^2*cosh(f*x + e)^2 + a^2)*sinh(f*x + e)^4 + 4*(5*a^2*cosh(f*x + e)^3 + 3*a^2*cosh(f*x + e))*sinh(f*x + e)^3 + (4*a*b - b^2)*cosh(f*x + e)^2 + (15*a^2*cosh(f*x + e)^4 + 18*a^2*cosh(f*x + e)^2 + 4*a*b - b^2)*sinh(f*x + e)^2 + b^2 + 2*(3*a^2*cosh(f*x + e)^5 + 6*a^2*cosh(f*x + e)^3 + (4*a*b - b^2)*cosh(f*x + e))*sinh(f*x + e))*sqrt(b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + 4*(2*a^2*b*cosh(f*x + e)^7 + 3*(a^3 + a^2*b)*cosh(f*x + e)^5 + (9*a^2*b - 4*a*b^2 + b^3)*cosh(f*x + e)^3 + (3*a*b^2 - b^3)*cosh(f*x + e))*sinh(f*x + e))/(cosh(f*x + e)^6 + 6*cosh(f*x + e)^5*sinh(f*x + e) + 15*cosh(f*x + e)^4*sinh(f*x + e)^2 + 20*cosh(f*x + e)^3*sinh(f*x + e)^3 + 15*cosh(f*x + e)^2*sinh(f*x + e)^4 + 6*cosh(f*x + e)*sinh(f*x + e)^5 + sinh(f*x + e)^6)) - 4*(a*cosh(f*x + e)^2 + 2*a*cosh(f*x + e)*sinh(f*x + e) + a*sinh(f*x + e)^2)*sqrt(a)*log(-((a + b)*cosh(f*x + e)^4 + 4*(a + b)*cosh(f*x + e)*sinh(f*x + e)^3 + (a + b)*sinh(f*x + e)^4 + 2*(3*a - b)*cosh(f*x + e)^2 + 2*(3*(a + b)*cosh(f*x + e)^2 + 3*a - b)*sinh(f*x + e)^2 - 2*sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 + 1)*sqrt(a)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + 4*((a + b)*cosh(f*x + e)^3 + (3*a - b)*cosh(f*x + e))*sinh(f*x + e) + a + b)/(cosh(f*x + e)^4 + 4*cosh(f*x + e)*sinh(f*x + e)^3 + sinh(f*x + e)^4 + 2*(3*cosh(f*x + e)^2 - 1)*sinh(f*x + e)^2 - 2*cosh(f*x + e)^2 + 4*(cosh(f*x + e)^3 - cosh(f*x + e))*sinh(f*x + e) + 1)) + ((3*a - b)*cosh(f*x + e)^2 + 2*(3*a - b)*cosh(f*x + e)*sinh(f*x + e) + (3*a - b)*sinh(f*x + e)^2)*sqrt(b)*log(-(b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(a - b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + a - b)*sinh(f*x + e)^2 - sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 - 1)*sqrt(b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + 4*(b*cosh(f*x + e)^3 + (a - b)*cosh(f*x + e))*sinh(f*x + e) + b)/(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) - sqrt(2)*(b*cosh(f*x + e)^2 + 2*b*cosh(f*x + e)*sinh(f*x + e) + b*sinh(f*x + e)^2 + b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/(f*cosh(f*x + e)^2 + 2*f*cosh(f*x + e)*sinh(f*x + e) + f*sinh(f*x + e)^2), 1/8*(8*(a*cosh(f*x + e)^2 + 2*a*cosh(f*x + e)*sinh(f*x + e) + a*sinh(f*x + e)^2)*sqrt(-a)*arctan(sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 + 1)*sqrt(-a)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/(b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(2*a - b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 2*a - b)*sinh(f*x + e)^2 + 4*(b*cosh(f*x + e)^3 + (2*a - b)*cosh(f*x + e))*sinh(f*x + e) + b)) - ((3*a - b)*cosh(f*x + e)^2 + 2*(3*a - b)*cosh(f*x + e)*sinh(f*x + e) + (3*a - b)*sinh(f*x + e)^2)*sqrt(b)*log((a^2*b*cosh(f*x + e)^8 + 8*a^2*b*cosh(f*x + e)*sinh(f*x + e)^7 + a^2*b*sinh(f*x + e)^8 + 2*(a^3 + a^2*b)*cosh(f*x + e)^6 + 2*(14*a^2*b*cosh(f*x + e)^2 + a^3 + a^2*b)*sinh(f*x + e)^6 + 4*(14*a^2*b*cosh(f*x + e)^3 + 3*(a^3 + a^2*b)*cosh(f*x + e))*sinh(f*x + e)^5 + (9*a^2*b - 4*a*b^2 + b^3)*cosh(f*x + e)^4 + (70*a^2*b*cosh(f*x + e)^4 + 9*a^2*b - 4*a*b^2 + b^3 + 30*(a^3 + a^2*b)*cosh(f*x + e)^2)*sinh(f*x + e)^4 + 4*(14*a^2*b*cosh(f*x + e)^5 + 10*(a^3 + a^2*b)*cosh(f*x + e)^3 + (9*a^2*b - 4*a*b^2 + b^3)*cosh(f*x + e))*sinh(f*x + e)^3 + b^3 + 2*(3*a*b^2 - b^3)*cosh(f*x + e)^2 + 2*(14*a^2*b*cosh(f*x + e)^6 + 15*(a^3 + a^2*b)*cosh(f*x + e)^4 + 3*a*b^2 - b^3 + 3*(9*a^2*b - 4*a*b^2 + b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^2 - sqrt(2)*(a^2*cosh(f*x + e)^6 + 6*a^2*cosh(f*x + e)*sinh(f*x + e)^5 + a^2*sinh(f*x + e)^6 + 3*a^2*cosh(f*x + e)^4 + 3*(5*a^2*cosh(f*x + e)^2 + a^2)*sinh(f*x + e)^4 + 4*(5*a^2*cosh(f*x + e)^3 + 3*a^2*cosh(f*x + e))*sinh(f*x + e)^3 + (4*a*b - b^2)*cosh(f*x + e)^2 + (15*a^2*cosh(f*x + e)^4 + 18*a^2*cosh(f*x + e)^2 + 4*a*b - b^2)*sinh(f*x + e)^2 + b^2 + 2*(3*a^2*cosh(f*x + e)^5 + 6*a^2*cosh(f*x + e)^3 + (4*a*b - b^2)*cosh(f*x + e))*sinh(f*x + e))*sqrt(b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + 4*(2*a^2*b*cosh(f*x + e)^7 + 3*(a^3 + a^2*b)*cosh(f*x + e)^5 + (9*a^2*b - 4*a*b^2 + b^3)*cosh(f*x + e)^3 + (3*a*b^2 - b^3)*cosh(f*x + e))*sinh(f*x + e))/(cosh(f*x + e)^6 + 6*cosh(f*x + e)^5*sinh(f*x + e) + 15*cosh(f*x + e)^4*sinh(f*x + e)^2 + 20*cosh(f*x + e)^3*sinh(f*x + e)^3 + 15*cosh(f*x + e)^2*sinh(f*x + e)^4 + 6*cosh(f*x + e)*sinh(f*x + e)^5 + sinh(f*x + e)^6)) - ((3*a - b)*cosh(f*x + e)^2 + 2*(3*a - b)*cosh(f*x + e)*sinh(f*x + e) + (3*a - b)*sinh(f*x + e)^2)*sqrt(b)*log(-(b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(a - b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + a - b)*sinh(f*x + e)^2 - sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 - 1)*sqrt(b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + 4*(b*cosh(f*x + e)^3 + (a - b)*cosh(f*x + e))*sinh(f*x + e) + b)/(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + sqrt(2)*(b*cosh(f*x + e)^2 + 2*b*cosh(f*x + e)*sinh(f*x + e) + b*sinh(f*x + e)^2 + b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/(f*cosh(f*x + e)^2 + 2*f*cosh(f*x + e)*sinh(f*x + e) + f*sinh(f*x + e)^2), -1/8*(2*((3*a - b)*cosh(f*x + e)^2 + 2*(3*a - b)*cosh(f*x + e)*sinh(f*x + e) + (3*a - b)*sinh(f*x + e)^2)*sqrt(-b)*arctan(sqrt(2)*(a*cosh(f*x + e)^2 + 2*a*cosh(f*x + e)*sinh(f*x + e) + a*sinh(f*x + e)^2 + b)*sqrt(-b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/(a*b*cosh(f*x + e)^4 + 4*a*b*cosh(f*x + e)*sinh(f*x + e)^3 + a*b*sinh(f*x + e)^4 + (3*a*b - b^2)*cosh(f*x + e)^2 + (6*a*b*cosh(f*x + e)^2 + 3*a*b - b^2)*sinh(f*x + e)^2 + b^2 + 2*(2*a*b*cosh(f*x + e)^3 + (3*a*b - b^2)*cosh(f*x + e))*sinh(f*x + e))) + 2*((3*a - b)*cosh(f*x + e)^2 + 2*(3*a - b)*cosh(f*x + e)*sinh(f*x + e) + (3*a - b)*sinh(f*x + e)^2)*sqrt(-b)*arctan(sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 - 1)*sqrt(-b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/(b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(2*a - b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 2*a - b)*sinh(f*x + e)^2 + 4*(b*cosh(f*x + e)^3 + (2*a - b)*cosh(f*x + e))*sinh(f*x + e) + b)) - 4*(a*cosh(f*x + e)^2 + 2*a*cosh(f*x + e)*sinh(f*x + e) + a*sinh(f*x + e)^2)*sqrt(a)*log(-((a + b)*cosh(f*x + e)^4 + 4*(a + b)*cosh(f*x + e)*sinh(f*x + e)^3 + (a + b)*sinh(f*x + e)^4 + 2*(3*a - b)*cosh(f*x + e)^2 + 2*(3*(a + b)*cosh(f*x + e)^2 + 3*a - b)*sinh(f*x + e)^2 - 2*sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 + 1)*sqrt(a)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + 4*((a + b)*cosh(f*x + e)^3 + (3*a - b)*cosh(f*x + e))*sinh(f*x + e) + a + b)/(cosh(f*x + e)^4 + 4*cosh(f*x + e)*sinh(f*x + e)^3 + sinh(f*x + e)^4 + 2*(3*cosh(f*x + e)^2 - 1)*sinh(f*x + e)^2 - 2*cosh(f*x + e)^2 + 4*(cosh(f*x + e)^3 - cosh(f*x + e))*sinh(f*x + e) + 1)) - sqrt(2)*(b*cosh(f*x + e)^2 + 2*b*cosh(f*x + e)*sinh(f*x + e) + b*sinh(f*x + e)^2 + b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/(f*cosh(f*x + e)^2 + 2*f*cosh(f*x + e)*sinh(f*x + e) + f*sinh(f*x + e)^2), 1/8*(8*(a*cosh(f*x + e)^2 + 2*a*cosh(f*x + e)*sinh(f*x + e) + a*sinh(f*x + e)^2)*sqrt(-a)*arctan(sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 + 1)*sqrt(-a)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/(b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(2*a - b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 2*a - b)*sinh(f*x + e)^2 + 4*(b*cosh(f*x + e)^3 + (2*a - b)*cosh(f*x + e))*sinh(f*x + e) + b)) - 2*((3*a - b)*cosh(f*x + e)^2 + 2*(3*a - b)*cosh(f*x + e)*sinh(f*x + e) + (3*a - b)*sinh(f*x + e)^2)*sqrt(-b)*arctan(sqrt(2)*(a*cosh(f*x + e)^2 + 2*a*cosh(f*x + e)*sinh(f*x + e) + a*sinh(f*x + e)^2 + b)*sqrt(-b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/(a*b*cosh(f*x + e)^4 + 4*a*b*cosh(f*x + e)*sinh(f*x + e)^3 + a*b*sinh(f*x + e)^4 + (3*a*b - b^2)*cosh(f*x + e)^2 + (6*a*b*cosh(f*x + e)^2 + 3*a*b - b^2)*sinh(f*x + e)^2 + b^2 + 2*(2*a*b*cosh(f*x + e)^3 + (3*a*b - b^2)*cosh(f*x + e))*sinh(f*x + e))) - 2*((3*a - b)*cosh(f*x + e)^2 + 2*(3*a - b)*cosh(f*x + e)*sinh(f*x + e) + (3*a - b)*sinh(f*x + e)^2)*sqrt(-b)*arctan(sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 - 1)*sqrt(-b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/(b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(2*a - b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 2*a - b)*sinh(f*x + e)^2 + 4*(b*cosh(f*x + e)^3 + (2*a - b)*cosh(f*x + e))*sinh(f*x + e) + b)) + sqrt(2)*(b*cosh(f*x + e)^2 + 2*b*cosh(f*x + e)*sinh(f*x + e) + b*sinh(f*x + e)^2 + b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/(f*cosh(f*x + e)^2 + 2*f*cosh(f*x + e)*sinh(f*x + e) + f*sinh(f*x + e)^2)]","B",0
79,1,6622,0,4.081025," ","integrate(csch(f*x+e)^3*(a+b*sinh(f*x+e)^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} - 2 \, b \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} - b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} - b \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b\right)} \sqrt{b} \log\left(\frac{a^{2} b \cosh\left(f x + e\right)^{8} + 8 \, a^{2} b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + a^{2} b \sinh\left(f x + e\right)^{8} + 2 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(f x + e\right)^{6} + 2 \, {\left(14 \, a^{2} b \cosh\left(f x + e\right)^{2} + a^{3} + a^{2} b\right)} \sinh\left(f x + e\right)^{6} + 4 \, {\left(14 \, a^{2} b \cosh\left(f x + e\right)^{3} + 3 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + {\left(9 \, a^{2} b - 4 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{4} + {\left(70 \, a^{2} b \cosh\left(f x + e\right)^{4} + 9 \, a^{2} b - 4 \, a b^{2} + b^{3} + 30 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(14 \, a^{2} b \cosh\left(f x + e\right)^{5} + 10 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(f x + e\right)^{3} + {\left(9 \, a^{2} b - 4 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + b^{3} + 2 \, {\left(3 \, a b^{2} - b^{3}\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(14 \, a^{2} b \cosh\left(f x + e\right)^{6} + 15 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(f x + e\right)^{4} + 3 \, a b^{2} - b^{3} + 3 \, {\left(9 \, a^{2} b - 4 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{2} + \sqrt{2} {\left(a^{2} \cosh\left(f x + e\right)^{6} + 6 \, a^{2} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + a^{2} \sinh\left(f x + e\right)^{6} + 3 \, a^{2} \cosh\left(f x + e\right)^{4} + 3 \, {\left(5 \, a^{2} \cosh\left(f x + e\right)^{2} + a^{2}\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(5 \, a^{2} \cosh\left(f x + e\right)^{3} + 3 \, a^{2} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + {\left(4 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{2} + {\left(15 \, a^{2} \cosh\left(f x + e\right)^{4} + 18 \, a^{2} \cosh\left(f x + e\right)^{2} + 4 \, a b - b^{2}\right)} \sinh\left(f x + e\right)^{2} + b^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(f x + e\right)^{5} + 6 \, a^{2} \cosh\left(f x + e\right)^{3} + {\left(4 \, a b - b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} + 4 \, {\left(2 \, a^{2} b \cosh\left(f x + e\right)^{7} + 3 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(f x + e\right)^{5} + {\left(9 \, a^{2} b - 4 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{3} + {\left(3 \, a b^{2} - b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)}{\cosh\left(f x + e\right)^{6} + 6 \, \cosh\left(f x + e\right)^{5} \sinh\left(f x + e\right) + 15 \, \cosh\left(f x + e\right)^{4} \sinh\left(f x + e\right)^{2} + 20 \, \cosh\left(f x + e\right)^{3} \sinh\left(f x + e\right)^{3} + 15 \, \cosh\left(f x + e\right)^{2} \sinh\left(f x + e\right)^{4} + 6 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + \sinh\left(f x + e\right)^{6}}\right) - {\left({\left(a - 3 \, b\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left(a - 3 \, b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(a - 3 \, b\right)} \sinh\left(f x + e\right)^{4} - 2 \, {\left(a - 3 \, b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, {\left(a - 3 \, b\right)} \cosh\left(f x + e\right)^{2} - a + 3 \, b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left({\left(a - 3 \, b\right)} \cosh\left(f x + e\right)^{3} - {\left(a - 3 \, b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + a - 3 \, b\right)} \sqrt{a} \log\left(-\frac{{\left(a + b\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(a + b\right)} \sinh\left(f x + e\right)^{4} + 2 \, {\left(3 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(f x + e\right)^{2} + 3 \, a - b\right)} \sinh\left(f x + e\right)^{2} - 2 \, \sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} + 1\right)} \sqrt{a} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(f x + e\right)^{3} + {\left(3 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + a + b}{\cosh\left(f x + e\right)^{4} + 4 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + \sinh\left(f x + e\right)^{4} + 2 \, {\left(3 \, \cosh\left(f x + e\right)^{2} - 1\right)} \sinh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right)^{2} + 4 \, {\left(\cosh\left(f x + e\right)^{3} - \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + 1}\right) + {\left(b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} - 2 \, b \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} - b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} - b \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b\right)} \sqrt{b} \log\left(-\frac{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + a - b\right)} \sinh\left(f x + e\right)^{2} + \sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} - 1\right)} \sqrt{b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}{\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}\right) - 2 \, \sqrt{2} {\left(a \cosh\left(f x + e\right)^{2} + 2 \, a \cosh\left(f x + e\right) \sinh\left(f x + e\right) + a \sinh\left(f x + e\right)^{2} + a\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{4 \, {\left(f \cosh\left(f x + e\right)^{4} + 4 \, f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + f \sinh\left(f x + e\right)^{4} - 2 \, f \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, f \cosh\left(f x + e\right)^{2} - f\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(f \cosh\left(f x + e\right)^{3} - f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + f\right)}}, -\frac{2 \, {\left({\left(a - 3 \, b\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left(a - 3 \, b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(a - 3 \, b\right)} \sinh\left(f x + e\right)^{4} - 2 \, {\left(a - 3 \, b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, {\left(a - 3 \, b\right)} \cosh\left(f x + e\right)^{2} - a + 3 \, b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left({\left(a - 3 \, b\right)} \cosh\left(f x + e\right)^{3} - {\left(a - 3 \, b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + a - 3 \, b\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} + 1\right)} \sqrt{-a} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + 2 \, a - b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}\right) - {\left(b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} - 2 \, b \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} - b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} - b \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b\right)} \sqrt{b} \log\left(\frac{a^{2} b \cosh\left(f x + e\right)^{8} + 8 \, a^{2} b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + a^{2} b \sinh\left(f x + e\right)^{8} + 2 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(f x + e\right)^{6} + 2 \, {\left(14 \, a^{2} b \cosh\left(f x + e\right)^{2} + a^{3} + a^{2} b\right)} \sinh\left(f x + e\right)^{6} + 4 \, {\left(14 \, a^{2} b \cosh\left(f x + e\right)^{3} + 3 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + {\left(9 \, a^{2} b - 4 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{4} + {\left(70 \, a^{2} b \cosh\left(f x + e\right)^{4} + 9 \, a^{2} b - 4 \, a b^{2} + b^{3} + 30 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(14 \, a^{2} b \cosh\left(f x + e\right)^{5} + 10 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(f x + e\right)^{3} + {\left(9 \, a^{2} b - 4 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + b^{3} + 2 \, {\left(3 \, a b^{2} - b^{3}\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(14 \, a^{2} b \cosh\left(f x + e\right)^{6} + 15 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(f x + e\right)^{4} + 3 \, a b^{2} - b^{3} + 3 \, {\left(9 \, a^{2} b - 4 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{2} + \sqrt{2} {\left(a^{2} \cosh\left(f x + e\right)^{6} + 6 \, a^{2} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + a^{2} \sinh\left(f x + e\right)^{6} + 3 \, a^{2} \cosh\left(f x + e\right)^{4} + 3 \, {\left(5 \, a^{2} \cosh\left(f x + e\right)^{2} + a^{2}\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(5 \, a^{2} \cosh\left(f x + e\right)^{3} + 3 \, a^{2} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + {\left(4 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{2} + {\left(15 \, a^{2} \cosh\left(f x + e\right)^{4} + 18 \, a^{2} \cosh\left(f x + e\right)^{2} + 4 \, a b - b^{2}\right)} \sinh\left(f x + e\right)^{2} + b^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(f x + e\right)^{5} + 6 \, a^{2} \cosh\left(f x + e\right)^{3} + {\left(4 \, a b - b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} + 4 \, {\left(2 \, a^{2} b \cosh\left(f x + e\right)^{7} + 3 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(f x + e\right)^{5} + {\left(9 \, a^{2} b - 4 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{3} + {\left(3 \, a b^{2} - b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)}{\cosh\left(f x + e\right)^{6} + 6 \, \cosh\left(f x + e\right)^{5} \sinh\left(f x + e\right) + 15 \, \cosh\left(f x + e\right)^{4} \sinh\left(f x + e\right)^{2} + 20 \, \cosh\left(f x + e\right)^{3} \sinh\left(f x + e\right)^{3} + 15 \, \cosh\left(f x + e\right)^{2} \sinh\left(f x + e\right)^{4} + 6 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + \sinh\left(f x + e\right)^{6}}\right) - {\left(b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} - 2 \, b \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} - b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} - b \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b\right)} \sqrt{b} \log\left(-\frac{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + a - b\right)} \sinh\left(f x + e\right)^{2} + \sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} - 1\right)} \sqrt{b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}{\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}\right) + 2 \, \sqrt{2} {\left(a \cosh\left(f x + e\right)^{2} + 2 \, a \cosh\left(f x + e\right) \sinh\left(f x + e\right) + a \sinh\left(f x + e\right)^{2} + a\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{4 \, {\left(f \cosh\left(f x + e\right)^{4} + 4 \, f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + f \sinh\left(f x + e\right)^{4} - 2 \, f \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, f \cosh\left(f x + e\right)^{2} - f\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(f \cosh\left(f x + e\right)^{3} - f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + f\right)}}, -\frac{2 \, {\left(b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} - 2 \, b \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} - b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} - b \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{2} {\left(a \cosh\left(f x + e\right)^{2} + 2 \, a \cosh\left(f x + e\right) \sinh\left(f x + e\right) + a \sinh\left(f x + e\right)^{2} + b\right)} \sqrt{-b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{a b \cosh\left(f x + e\right)^{4} + 4 \, a b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + a b \sinh\left(f x + e\right)^{4} + {\left(3 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{2} + {\left(6 \, a b \cosh\left(f x + e\right)^{2} + 3 \, a b - b^{2}\right)} \sinh\left(f x + e\right)^{2} + b^{2} + 2 \, {\left(2 \, a b \cosh\left(f x + e\right)^{3} + {\left(3 \, a b - b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)}\right) + 2 \, {\left(b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} - 2 \, b \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} - b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} - b \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} - 1\right)} \sqrt{-b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + 2 \, a - b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}\right) + {\left({\left(a - 3 \, b\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left(a - 3 \, b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(a - 3 \, b\right)} \sinh\left(f x + e\right)^{4} - 2 \, {\left(a - 3 \, b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, {\left(a - 3 \, b\right)} \cosh\left(f x + e\right)^{2} - a + 3 \, b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left({\left(a - 3 \, b\right)} \cosh\left(f x + e\right)^{3} - {\left(a - 3 \, b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + a - 3 \, b\right)} \sqrt{a} \log\left(-\frac{{\left(a + b\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(a + b\right)} \sinh\left(f x + e\right)^{4} + 2 \, {\left(3 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(f x + e\right)^{2} + 3 \, a - b\right)} \sinh\left(f x + e\right)^{2} - 2 \, \sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} + 1\right)} \sqrt{a} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(f x + e\right)^{3} + {\left(3 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + a + b}{\cosh\left(f x + e\right)^{4} + 4 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + \sinh\left(f x + e\right)^{4} + 2 \, {\left(3 \, \cosh\left(f x + e\right)^{2} - 1\right)} \sinh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right)^{2} + 4 \, {\left(\cosh\left(f x + e\right)^{3} - \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + 1}\right) + 2 \, \sqrt{2} {\left(a \cosh\left(f x + e\right)^{2} + 2 \, a \cosh\left(f x + e\right) \sinh\left(f x + e\right) + a \sinh\left(f x + e\right)^{2} + a\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{4 \, {\left(f \cosh\left(f x + e\right)^{4} + 4 \, f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + f \sinh\left(f x + e\right)^{4} - 2 \, f \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, f \cosh\left(f x + e\right)^{2} - f\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(f \cosh\left(f x + e\right)^{3} - f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + f\right)}}, -\frac{{\left({\left(a - 3 \, b\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left(a - 3 \, b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(a - 3 \, b\right)} \sinh\left(f x + e\right)^{4} - 2 \, {\left(a - 3 \, b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, {\left(a - 3 \, b\right)} \cosh\left(f x + e\right)^{2} - a + 3 \, b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left({\left(a - 3 \, b\right)} \cosh\left(f x + e\right)^{3} - {\left(a - 3 \, b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + a - 3 \, b\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} + 1\right)} \sqrt{-a} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + 2 \, a - b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}\right) + {\left(b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} - 2 \, b \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} - b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} - b \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{2} {\left(a \cosh\left(f x + e\right)^{2} + 2 \, a \cosh\left(f x + e\right) \sinh\left(f x + e\right) + a \sinh\left(f x + e\right)^{2} + b\right)} \sqrt{-b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{a b \cosh\left(f x + e\right)^{4} + 4 \, a b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + a b \sinh\left(f x + e\right)^{4} + {\left(3 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{2} + {\left(6 \, a b \cosh\left(f x + e\right)^{2} + 3 \, a b - b^{2}\right)} \sinh\left(f x + e\right)^{2} + b^{2} + 2 \, {\left(2 \, a b \cosh\left(f x + e\right)^{3} + {\left(3 \, a b - b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)}\right) + {\left(b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} - 2 \, b \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} - b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} - b \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} - 1\right)} \sqrt{-b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + 2 \, a - b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}\right) + \sqrt{2} {\left(a \cosh\left(f x + e\right)^{2} + 2 \, a \cosh\left(f x + e\right) \sinh\left(f x + e\right) + a \sinh\left(f x + e\right)^{2} + a\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{2 \, {\left(f \cosh\left(f x + e\right)^{4} + 4 \, f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + f \sinh\left(f x + e\right)^{4} - 2 \, f \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, f \cosh\left(f x + e\right)^{2} - f\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(f \cosh\left(f x + e\right)^{3} - f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + f\right)}}\right]"," ",0,"[1/4*((b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 - 2*b*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 - b)*sinh(f*x + e)^2 + 4*(b*cosh(f*x + e)^3 - b*cosh(f*x + e))*sinh(f*x + e) + b)*sqrt(b)*log((a^2*b*cosh(f*x + e)^8 + 8*a^2*b*cosh(f*x + e)*sinh(f*x + e)^7 + a^2*b*sinh(f*x + e)^8 + 2*(a^3 + a^2*b)*cosh(f*x + e)^6 + 2*(14*a^2*b*cosh(f*x + e)^2 + a^3 + a^2*b)*sinh(f*x + e)^6 + 4*(14*a^2*b*cosh(f*x + e)^3 + 3*(a^3 + a^2*b)*cosh(f*x + e))*sinh(f*x + e)^5 + (9*a^2*b - 4*a*b^2 + b^3)*cosh(f*x + e)^4 + (70*a^2*b*cosh(f*x + e)^4 + 9*a^2*b - 4*a*b^2 + b^3 + 30*(a^3 + a^2*b)*cosh(f*x + e)^2)*sinh(f*x + e)^4 + 4*(14*a^2*b*cosh(f*x + e)^5 + 10*(a^3 + a^2*b)*cosh(f*x + e)^3 + (9*a^2*b - 4*a*b^2 + b^3)*cosh(f*x + e))*sinh(f*x + e)^3 + b^3 + 2*(3*a*b^2 - b^3)*cosh(f*x + e)^2 + 2*(14*a^2*b*cosh(f*x + e)^6 + 15*(a^3 + a^2*b)*cosh(f*x + e)^4 + 3*a*b^2 - b^3 + 3*(9*a^2*b - 4*a*b^2 + b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^2 + sqrt(2)*(a^2*cosh(f*x + e)^6 + 6*a^2*cosh(f*x + e)*sinh(f*x + e)^5 + a^2*sinh(f*x + e)^6 + 3*a^2*cosh(f*x + e)^4 + 3*(5*a^2*cosh(f*x + e)^2 + a^2)*sinh(f*x + e)^4 + 4*(5*a^2*cosh(f*x + e)^3 + 3*a^2*cosh(f*x + e))*sinh(f*x + e)^3 + (4*a*b - b^2)*cosh(f*x + e)^2 + (15*a^2*cosh(f*x + e)^4 + 18*a^2*cosh(f*x + e)^2 + 4*a*b - b^2)*sinh(f*x + e)^2 + b^2 + 2*(3*a^2*cosh(f*x + e)^5 + 6*a^2*cosh(f*x + e)^3 + (4*a*b - b^2)*cosh(f*x + e))*sinh(f*x + e))*sqrt(b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + 4*(2*a^2*b*cosh(f*x + e)^7 + 3*(a^3 + a^2*b)*cosh(f*x + e)^5 + (9*a^2*b - 4*a*b^2 + b^3)*cosh(f*x + e)^3 + (3*a*b^2 - b^3)*cosh(f*x + e))*sinh(f*x + e))/(cosh(f*x + e)^6 + 6*cosh(f*x + e)^5*sinh(f*x + e) + 15*cosh(f*x + e)^4*sinh(f*x + e)^2 + 20*cosh(f*x + e)^3*sinh(f*x + e)^3 + 15*cosh(f*x + e)^2*sinh(f*x + e)^4 + 6*cosh(f*x + e)*sinh(f*x + e)^5 + sinh(f*x + e)^6)) - ((a - 3*b)*cosh(f*x + e)^4 + 4*(a - 3*b)*cosh(f*x + e)*sinh(f*x + e)^3 + (a - 3*b)*sinh(f*x + e)^4 - 2*(a - 3*b)*cosh(f*x + e)^2 + 2*(3*(a - 3*b)*cosh(f*x + e)^2 - a + 3*b)*sinh(f*x + e)^2 + 4*((a - 3*b)*cosh(f*x + e)^3 - (a - 3*b)*cosh(f*x + e))*sinh(f*x + e) + a - 3*b)*sqrt(a)*log(-((a + b)*cosh(f*x + e)^4 + 4*(a + b)*cosh(f*x + e)*sinh(f*x + e)^3 + (a + b)*sinh(f*x + e)^4 + 2*(3*a - b)*cosh(f*x + e)^2 + 2*(3*(a + b)*cosh(f*x + e)^2 + 3*a - b)*sinh(f*x + e)^2 - 2*sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 + 1)*sqrt(a)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + 4*((a + b)*cosh(f*x + e)^3 + (3*a - b)*cosh(f*x + e))*sinh(f*x + e) + a + b)/(cosh(f*x + e)^4 + 4*cosh(f*x + e)*sinh(f*x + e)^3 + sinh(f*x + e)^4 + 2*(3*cosh(f*x + e)^2 - 1)*sinh(f*x + e)^2 - 2*cosh(f*x + e)^2 + 4*(cosh(f*x + e)^3 - cosh(f*x + e))*sinh(f*x + e) + 1)) + (b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 - 2*b*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 - b)*sinh(f*x + e)^2 + 4*(b*cosh(f*x + e)^3 - b*cosh(f*x + e))*sinh(f*x + e) + b)*sqrt(b)*log(-(b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(a - b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + a - b)*sinh(f*x + e)^2 + sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 - 1)*sqrt(b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + 4*(b*cosh(f*x + e)^3 + (a - b)*cosh(f*x + e))*sinh(f*x + e) + b)/(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) - 2*sqrt(2)*(a*cosh(f*x + e)^2 + 2*a*cosh(f*x + e)*sinh(f*x + e) + a*sinh(f*x + e)^2 + a)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/(f*cosh(f*x + e)^4 + 4*f*cosh(f*x + e)*sinh(f*x + e)^3 + f*sinh(f*x + e)^4 - 2*f*cosh(f*x + e)^2 + 2*(3*f*cosh(f*x + e)^2 - f)*sinh(f*x + e)^2 + 4*(f*cosh(f*x + e)^3 - f*cosh(f*x + e))*sinh(f*x + e) + f), -1/4*(2*((a - 3*b)*cosh(f*x + e)^4 + 4*(a - 3*b)*cosh(f*x + e)*sinh(f*x + e)^3 + (a - 3*b)*sinh(f*x + e)^4 - 2*(a - 3*b)*cosh(f*x + e)^2 + 2*(3*(a - 3*b)*cosh(f*x + e)^2 - a + 3*b)*sinh(f*x + e)^2 + 4*((a - 3*b)*cosh(f*x + e)^3 - (a - 3*b)*cosh(f*x + e))*sinh(f*x + e) + a - 3*b)*sqrt(-a)*arctan(sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 + 1)*sqrt(-a)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/(b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(2*a - b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 2*a - b)*sinh(f*x + e)^2 + 4*(b*cosh(f*x + e)^3 + (2*a - b)*cosh(f*x + e))*sinh(f*x + e) + b)) - (b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 - 2*b*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 - b)*sinh(f*x + e)^2 + 4*(b*cosh(f*x + e)^3 - b*cosh(f*x + e))*sinh(f*x + e) + b)*sqrt(b)*log((a^2*b*cosh(f*x + e)^8 + 8*a^2*b*cosh(f*x + e)*sinh(f*x + e)^7 + a^2*b*sinh(f*x + e)^8 + 2*(a^3 + a^2*b)*cosh(f*x + e)^6 + 2*(14*a^2*b*cosh(f*x + e)^2 + a^3 + a^2*b)*sinh(f*x + e)^6 + 4*(14*a^2*b*cosh(f*x + e)^3 + 3*(a^3 + a^2*b)*cosh(f*x + e))*sinh(f*x + e)^5 + (9*a^2*b - 4*a*b^2 + b^3)*cosh(f*x + e)^4 + (70*a^2*b*cosh(f*x + e)^4 + 9*a^2*b - 4*a*b^2 + b^3 + 30*(a^3 + a^2*b)*cosh(f*x + e)^2)*sinh(f*x + e)^4 + 4*(14*a^2*b*cosh(f*x + e)^5 + 10*(a^3 + a^2*b)*cosh(f*x + e)^3 + (9*a^2*b - 4*a*b^2 + b^3)*cosh(f*x + e))*sinh(f*x + e)^3 + b^3 + 2*(3*a*b^2 - b^3)*cosh(f*x + e)^2 + 2*(14*a^2*b*cosh(f*x + e)^6 + 15*(a^3 + a^2*b)*cosh(f*x + e)^4 + 3*a*b^2 - b^3 + 3*(9*a^2*b - 4*a*b^2 + b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^2 + sqrt(2)*(a^2*cosh(f*x + e)^6 + 6*a^2*cosh(f*x + e)*sinh(f*x + e)^5 + a^2*sinh(f*x + e)^6 + 3*a^2*cosh(f*x + e)^4 + 3*(5*a^2*cosh(f*x + e)^2 + a^2)*sinh(f*x + e)^4 + 4*(5*a^2*cosh(f*x + e)^3 + 3*a^2*cosh(f*x + e))*sinh(f*x + e)^3 + (4*a*b - b^2)*cosh(f*x + e)^2 + (15*a^2*cosh(f*x + e)^4 + 18*a^2*cosh(f*x + e)^2 + 4*a*b - b^2)*sinh(f*x + e)^2 + b^2 + 2*(3*a^2*cosh(f*x + e)^5 + 6*a^2*cosh(f*x + e)^3 + (4*a*b - b^2)*cosh(f*x + e))*sinh(f*x + e))*sqrt(b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + 4*(2*a^2*b*cosh(f*x + e)^7 + 3*(a^3 + a^2*b)*cosh(f*x + e)^5 + (9*a^2*b - 4*a*b^2 + b^3)*cosh(f*x + e)^3 + (3*a*b^2 - b^3)*cosh(f*x + e))*sinh(f*x + e))/(cosh(f*x + e)^6 + 6*cosh(f*x + e)^5*sinh(f*x + e) + 15*cosh(f*x + e)^4*sinh(f*x + e)^2 + 20*cosh(f*x + e)^3*sinh(f*x + e)^3 + 15*cosh(f*x + e)^2*sinh(f*x + e)^4 + 6*cosh(f*x + e)*sinh(f*x + e)^5 + sinh(f*x + e)^6)) - (b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 - 2*b*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 - b)*sinh(f*x + e)^2 + 4*(b*cosh(f*x + e)^3 - b*cosh(f*x + e))*sinh(f*x + e) + b)*sqrt(b)*log(-(b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(a - b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + a - b)*sinh(f*x + e)^2 + sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 - 1)*sqrt(b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + 4*(b*cosh(f*x + e)^3 + (a - b)*cosh(f*x + e))*sinh(f*x + e) + b)/(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + 2*sqrt(2)*(a*cosh(f*x + e)^2 + 2*a*cosh(f*x + e)*sinh(f*x + e) + a*sinh(f*x + e)^2 + a)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/(f*cosh(f*x + e)^4 + 4*f*cosh(f*x + e)*sinh(f*x + e)^3 + f*sinh(f*x + e)^4 - 2*f*cosh(f*x + e)^2 + 2*(3*f*cosh(f*x + e)^2 - f)*sinh(f*x + e)^2 + 4*(f*cosh(f*x + e)^3 - f*cosh(f*x + e))*sinh(f*x + e) + f), -1/4*(2*(b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 - 2*b*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 - b)*sinh(f*x + e)^2 + 4*(b*cosh(f*x + e)^3 - b*cosh(f*x + e))*sinh(f*x + e) + b)*sqrt(-b)*arctan(sqrt(2)*(a*cosh(f*x + e)^2 + 2*a*cosh(f*x + e)*sinh(f*x + e) + a*sinh(f*x + e)^2 + b)*sqrt(-b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/(a*b*cosh(f*x + e)^4 + 4*a*b*cosh(f*x + e)*sinh(f*x + e)^3 + a*b*sinh(f*x + e)^4 + (3*a*b - b^2)*cosh(f*x + e)^2 + (6*a*b*cosh(f*x + e)^2 + 3*a*b - b^2)*sinh(f*x + e)^2 + b^2 + 2*(2*a*b*cosh(f*x + e)^3 + (3*a*b - b^2)*cosh(f*x + e))*sinh(f*x + e))) + 2*(b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 - 2*b*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 - b)*sinh(f*x + e)^2 + 4*(b*cosh(f*x + e)^3 - b*cosh(f*x + e))*sinh(f*x + e) + b)*sqrt(-b)*arctan(sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 - 1)*sqrt(-b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/(b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(2*a - b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 2*a - b)*sinh(f*x + e)^2 + 4*(b*cosh(f*x + e)^3 + (2*a - b)*cosh(f*x + e))*sinh(f*x + e) + b)) + ((a - 3*b)*cosh(f*x + e)^4 + 4*(a - 3*b)*cosh(f*x + e)*sinh(f*x + e)^3 + (a - 3*b)*sinh(f*x + e)^4 - 2*(a - 3*b)*cosh(f*x + e)^2 + 2*(3*(a - 3*b)*cosh(f*x + e)^2 - a + 3*b)*sinh(f*x + e)^2 + 4*((a - 3*b)*cosh(f*x + e)^3 - (a - 3*b)*cosh(f*x + e))*sinh(f*x + e) + a - 3*b)*sqrt(a)*log(-((a + b)*cosh(f*x + e)^4 + 4*(a + b)*cosh(f*x + e)*sinh(f*x + e)^3 + (a + b)*sinh(f*x + e)^4 + 2*(3*a - b)*cosh(f*x + e)^2 + 2*(3*(a + b)*cosh(f*x + e)^2 + 3*a - b)*sinh(f*x + e)^2 - 2*sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 + 1)*sqrt(a)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + 4*((a + b)*cosh(f*x + e)^3 + (3*a - b)*cosh(f*x + e))*sinh(f*x + e) + a + b)/(cosh(f*x + e)^4 + 4*cosh(f*x + e)*sinh(f*x + e)^3 + sinh(f*x + e)^4 + 2*(3*cosh(f*x + e)^2 - 1)*sinh(f*x + e)^2 - 2*cosh(f*x + e)^2 + 4*(cosh(f*x + e)^3 - cosh(f*x + e))*sinh(f*x + e) + 1)) + 2*sqrt(2)*(a*cosh(f*x + e)^2 + 2*a*cosh(f*x + e)*sinh(f*x + e) + a*sinh(f*x + e)^2 + a)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/(f*cosh(f*x + e)^4 + 4*f*cosh(f*x + e)*sinh(f*x + e)^3 + f*sinh(f*x + e)^4 - 2*f*cosh(f*x + e)^2 + 2*(3*f*cosh(f*x + e)^2 - f)*sinh(f*x + e)^2 + 4*(f*cosh(f*x + e)^3 - f*cosh(f*x + e))*sinh(f*x + e) + f), -1/2*(((a - 3*b)*cosh(f*x + e)^4 + 4*(a - 3*b)*cosh(f*x + e)*sinh(f*x + e)^3 + (a - 3*b)*sinh(f*x + e)^4 - 2*(a - 3*b)*cosh(f*x + e)^2 + 2*(3*(a - 3*b)*cosh(f*x + e)^2 - a + 3*b)*sinh(f*x + e)^2 + 4*((a - 3*b)*cosh(f*x + e)^3 - (a - 3*b)*cosh(f*x + e))*sinh(f*x + e) + a - 3*b)*sqrt(-a)*arctan(sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 + 1)*sqrt(-a)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/(b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(2*a - b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 2*a - b)*sinh(f*x + e)^2 + 4*(b*cosh(f*x + e)^3 + (2*a - b)*cosh(f*x + e))*sinh(f*x + e) + b)) + (b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 - 2*b*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 - b)*sinh(f*x + e)^2 + 4*(b*cosh(f*x + e)^3 - b*cosh(f*x + e))*sinh(f*x + e) + b)*sqrt(-b)*arctan(sqrt(2)*(a*cosh(f*x + e)^2 + 2*a*cosh(f*x + e)*sinh(f*x + e) + a*sinh(f*x + e)^2 + b)*sqrt(-b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/(a*b*cosh(f*x + e)^4 + 4*a*b*cosh(f*x + e)*sinh(f*x + e)^3 + a*b*sinh(f*x + e)^4 + (3*a*b - b^2)*cosh(f*x + e)^2 + (6*a*b*cosh(f*x + e)^2 + 3*a*b - b^2)*sinh(f*x + e)^2 + b^2 + 2*(2*a*b*cosh(f*x + e)^3 + (3*a*b - b^2)*cosh(f*x + e))*sinh(f*x + e))) + (b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 - 2*b*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 - b)*sinh(f*x + e)^2 + 4*(b*cosh(f*x + e)^3 - b*cosh(f*x + e))*sinh(f*x + e) + b)*sqrt(-b)*arctan(sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 - 1)*sqrt(-b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/(b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(2*a - b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 2*a - b)*sinh(f*x + e)^2 + 4*(b*cosh(f*x + e)^3 + (2*a - b)*cosh(f*x + e))*sinh(f*x + e) + b)) + sqrt(2)*(a*cosh(f*x + e)^2 + 2*a*cosh(f*x + e)*sinh(f*x + e) + a*sinh(f*x + e)^2 + a)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/(f*cosh(f*x + e)^4 + 4*f*cosh(f*x + e)*sinh(f*x + e)^3 + f*sinh(f*x + e)^4 - 2*f*cosh(f*x + e)^2 + 2*(3*f*cosh(f*x + e)^2 - f)*sinh(f*x + e)^2 + 4*(f*cosh(f*x + e)^3 - f*cosh(f*x + e))*sinh(f*x + e) + f)]","B",0
80,1,3133,0,1.242570," ","integrate(csch(f*x+e)^5*(a+b*sinh(f*x+e)^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{8} + 8 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + {\left(a^{2} - 2 \, a b + b^{2}\right)} \sinh\left(f x + e\right)^{8} - 4 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{2} - a^{2} + 2 \, a b - b^{2}\right)} \sinh\left(f x + e\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{3} - 3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + 6 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{4} - 30 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{2} + 3 \, a^{2} - 6 \, a b + 3 \, b^{2}\right)} \sinh\left(f x + e\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{5} - 10 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} - 4 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{6} - 15 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{4} + 9 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{2} - a^{2} + 2 \, a b - b^{2}\right)} \sinh\left(f x + e\right)^{2} + a^{2} - 2 \, a b + b^{2} + 8 \, {\left({\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{7} - 3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{5} + 3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{3} - {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{a} \log\left(-\frac{{\left(a + b\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(a + b\right)} \sinh\left(f x + e\right)^{4} + 2 \, {\left(3 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(f x + e\right)^{2} + 3 \, a - b\right)} \sinh\left(f x + e\right)^{2} - 2 \, \sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} + 1\right)} \sqrt{a} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(f x + e\right)^{3} + {\left(3 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + a + b}{\cosh\left(f x + e\right)^{4} + 4 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + \sinh\left(f x + e\right)^{4} + 2 \, {\left(3 \, \cosh\left(f x + e\right)^{2} - 1\right)} \sinh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right)^{2} + 4 \, {\left(\cosh\left(f x + e\right)^{3} - \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + 1}\right) + 2 \, \sqrt{2} {\left({\left(3 \, a^{2} - 5 \, a b\right)} \cosh\left(f x + e\right)^{6} + 6 \, {\left(3 \, a^{2} - 5 \, a b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + {\left(3 \, a^{2} - 5 \, a b\right)} \sinh\left(f x + e\right)^{6} - {\left(11 \, a^{2} - 5 \, a b\right)} \cosh\left(f x + e\right)^{4} + {\left(15 \, {\left(3 \, a^{2} - 5 \, a b\right)} \cosh\left(f x + e\right)^{2} - 11 \, a^{2} + 5 \, a b\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(5 \, {\left(3 \, a^{2} - 5 \, a b\right)} \cosh\left(f x + e\right)^{3} - {\left(11 \, a^{2} - 5 \, a b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} - {\left(11 \, a^{2} - 5 \, a b\right)} \cosh\left(f x + e\right)^{2} + {\left(15 \, {\left(3 \, a^{2} - 5 \, a b\right)} \cosh\left(f x + e\right)^{4} - 6 \, {\left(11 \, a^{2} - 5 \, a b\right)} \cosh\left(f x + e\right)^{2} - 11 \, a^{2} + 5 \, a b\right)} \sinh\left(f x + e\right)^{2} + 3 \, a^{2} - 5 \, a b + 2 \, {\left(3 \, {\left(3 \, a^{2} - 5 \, a b\right)} \cosh\left(f x + e\right)^{5} - 2 \, {\left(11 \, a^{2} - 5 \, a b\right)} \cosh\left(f x + e\right)^{3} - {\left(11 \, a^{2} - 5 \, a b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{16 \, {\left(a f \cosh\left(f x + e\right)^{8} + 8 \, a f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + a f \sinh\left(f x + e\right)^{8} - 4 \, a f \cosh\left(f x + e\right)^{6} + 4 \, {\left(7 \, a f \cosh\left(f x + e\right)^{2} - a f\right)} \sinh\left(f x + e\right)^{6} + 6 \, a f \cosh\left(f x + e\right)^{4} + 8 \, {\left(7 \, a f \cosh\left(f x + e\right)^{3} - 3 \, a f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(35 \, a f \cosh\left(f x + e\right)^{4} - 30 \, a f \cosh\left(f x + e\right)^{2} + 3 \, a f\right)} \sinh\left(f x + e\right)^{4} - 4 \, a f \cosh\left(f x + e\right)^{2} + 8 \, {\left(7 \, a f \cosh\left(f x + e\right)^{5} - 10 \, a f \cosh\left(f x + e\right)^{3} + 3 \, a f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 4 \, {\left(7 \, a f \cosh\left(f x + e\right)^{6} - 15 \, a f \cosh\left(f x + e\right)^{4} + 9 \, a f \cosh\left(f x + e\right)^{2} - a f\right)} \sinh\left(f x + e\right)^{2} + a f + 8 \, {\left(a f \cosh\left(f x + e\right)^{7} - 3 \, a f \cosh\left(f x + e\right)^{5} + 3 \, a f \cosh\left(f x + e\right)^{3} - a f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)}}, \frac{3 \, {\left({\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{8} + 8 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + {\left(a^{2} - 2 \, a b + b^{2}\right)} \sinh\left(f x + e\right)^{8} - 4 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{2} - a^{2} + 2 \, a b - b^{2}\right)} \sinh\left(f x + e\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{3} - 3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + 6 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{4} - 30 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{2} + 3 \, a^{2} - 6 \, a b + 3 \, b^{2}\right)} \sinh\left(f x + e\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{5} - 10 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} - 4 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{6} - 15 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{4} + 9 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{2} - a^{2} + 2 \, a b - b^{2}\right)} \sinh\left(f x + e\right)^{2} + a^{2} - 2 \, a b + b^{2} + 8 \, {\left({\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{7} - 3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{5} + 3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{3} - {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} + 1\right)} \sqrt{-a} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + 2 \, a - b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}\right) + \sqrt{2} {\left({\left(3 \, a^{2} - 5 \, a b\right)} \cosh\left(f x + e\right)^{6} + 6 \, {\left(3 \, a^{2} - 5 \, a b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + {\left(3 \, a^{2} - 5 \, a b\right)} \sinh\left(f x + e\right)^{6} - {\left(11 \, a^{2} - 5 \, a b\right)} \cosh\left(f x + e\right)^{4} + {\left(15 \, {\left(3 \, a^{2} - 5 \, a b\right)} \cosh\left(f x + e\right)^{2} - 11 \, a^{2} + 5 \, a b\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(5 \, {\left(3 \, a^{2} - 5 \, a b\right)} \cosh\left(f x + e\right)^{3} - {\left(11 \, a^{2} - 5 \, a b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} - {\left(11 \, a^{2} - 5 \, a b\right)} \cosh\left(f x + e\right)^{2} + {\left(15 \, {\left(3 \, a^{2} - 5 \, a b\right)} \cosh\left(f x + e\right)^{4} - 6 \, {\left(11 \, a^{2} - 5 \, a b\right)} \cosh\left(f x + e\right)^{2} - 11 \, a^{2} + 5 \, a b\right)} \sinh\left(f x + e\right)^{2} + 3 \, a^{2} - 5 \, a b + 2 \, {\left(3 \, {\left(3 \, a^{2} - 5 \, a b\right)} \cosh\left(f x + e\right)^{5} - 2 \, {\left(11 \, a^{2} - 5 \, a b\right)} \cosh\left(f x + e\right)^{3} - {\left(11 \, a^{2} - 5 \, a b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{8 \, {\left(a f \cosh\left(f x + e\right)^{8} + 8 \, a f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + a f \sinh\left(f x + e\right)^{8} - 4 \, a f \cosh\left(f x + e\right)^{6} + 4 \, {\left(7 \, a f \cosh\left(f x + e\right)^{2} - a f\right)} \sinh\left(f x + e\right)^{6} + 6 \, a f \cosh\left(f x + e\right)^{4} + 8 \, {\left(7 \, a f \cosh\left(f x + e\right)^{3} - 3 \, a f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(35 \, a f \cosh\left(f x + e\right)^{4} - 30 \, a f \cosh\left(f x + e\right)^{2} + 3 \, a f\right)} \sinh\left(f x + e\right)^{4} - 4 \, a f \cosh\left(f x + e\right)^{2} + 8 \, {\left(7 \, a f \cosh\left(f x + e\right)^{5} - 10 \, a f \cosh\left(f x + e\right)^{3} + 3 \, a f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 4 \, {\left(7 \, a f \cosh\left(f x + e\right)^{6} - 15 \, a f \cosh\left(f x + e\right)^{4} + 9 \, a f \cosh\left(f x + e\right)^{2} - a f\right)} \sinh\left(f x + e\right)^{2} + a f + 8 \, {\left(a f \cosh\left(f x + e\right)^{7} - 3 \, a f \cosh\left(f x + e\right)^{5} + 3 \, a f \cosh\left(f x + e\right)^{3} - a f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)}}\right]"," ",0,"[1/16*(3*((a^2 - 2*a*b + b^2)*cosh(f*x + e)^8 + 8*(a^2 - 2*a*b + b^2)*cosh(f*x + e)*sinh(f*x + e)^7 + (a^2 - 2*a*b + b^2)*sinh(f*x + e)^8 - 4*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^6 + 4*(7*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^2 - a^2 + 2*a*b - b^2)*sinh(f*x + e)^6 + 8*(7*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^3 - 3*(a^2 - 2*a*b + b^2)*cosh(f*x + e))*sinh(f*x + e)^5 + 6*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^4 + 2*(35*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^4 - 30*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^2 + 3*a^2 - 6*a*b + 3*b^2)*sinh(f*x + e)^4 + 8*(7*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^5 - 10*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^3 + 3*(a^2 - 2*a*b + b^2)*cosh(f*x + e))*sinh(f*x + e)^3 - 4*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^2 + 4*(7*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^6 - 15*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^4 + 9*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^2 - a^2 + 2*a*b - b^2)*sinh(f*x + e)^2 + a^2 - 2*a*b + b^2 + 8*((a^2 - 2*a*b + b^2)*cosh(f*x + e)^7 - 3*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^5 + 3*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^3 - (a^2 - 2*a*b + b^2)*cosh(f*x + e))*sinh(f*x + e))*sqrt(a)*log(-((a + b)*cosh(f*x + e)^4 + 4*(a + b)*cosh(f*x + e)*sinh(f*x + e)^3 + (a + b)*sinh(f*x + e)^4 + 2*(3*a - b)*cosh(f*x + e)^2 + 2*(3*(a + b)*cosh(f*x + e)^2 + 3*a - b)*sinh(f*x + e)^2 - 2*sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 + 1)*sqrt(a)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + 4*((a + b)*cosh(f*x + e)^3 + (3*a - b)*cosh(f*x + e))*sinh(f*x + e) + a + b)/(cosh(f*x + e)^4 + 4*cosh(f*x + e)*sinh(f*x + e)^3 + sinh(f*x + e)^4 + 2*(3*cosh(f*x + e)^2 - 1)*sinh(f*x + e)^2 - 2*cosh(f*x + e)^2 + 4*(cosh(f*x + e)^3 - cosh(f*x + e))*sinh(f*x + e) + 1)) + 2*sqrt(2)*((3*a^2 - 5*a*b)*cosh(f*x + e)^6 + 6*(3*a^2 - 5*a*b)*cosh(f*x + e)*sinh(f*x + e)^5 + (3*a^2 - 5*a*b)*sinh(f*x + e)^6 - (11*a^2 - 5*a*b)*cosh(f*x + e)^4 + (15*(3*a^2 - 5*a*b)*cosh(f*x + e)^2 - 11*a^2 + 5*a*b)*sinh(f*x + e)^4 + 4*(5*(3*a^2 - 5*a*b)*cosh(f*x + e)^3 - (11*a^2 - 5*a*b)*cosh(f*x + e))*sinh(f*x + e)^3 - (11*a^2 - 5*a*b)*cosh(f*x + e)^2 + (15*(3*a^2 - 5*a*b)*cosh(f*x + e)^4 - 6*(11*a^2 - 5*a*b)*cosh(f*x + e)^2 - 11*a^2 + 5*a*b)*sinh(f*x + e)^2 + 3*a^2 - 5*a*b + 2*(3*(3*a^2 - 5*a*b)*cosh(f*x + e)^5 - 2*(11*a^2 - 5*a*b)*cosh(f*x + e)^3 - (11*a^2 - 5*a*b)*cosh(f*x + e))*sinh(f*x + e))*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/(a*f*cosh(f*x + e)^8 + 8*a*f*cosh(f*x + e)*sinh(f*x + e)^7 + a*f*sinh(f*x + e)^8 - 4*a*f*cosh(f*x + e)^6 + 4*(7*a*f*cosh(f*x + e)^2 - a*f)*sinh(f*x + e)^6 + 6*a*f*cosh(f*x + e)^4 + 8*(7*a*f*cosh(f*x + e)^3 - 3*a*f*cosh(f*x + e))*sinh(f*x + e)^5 + 2*(35*a*f*cosh(f*x + e)^4 - 30*a*f*cosh(f*x + e)^2 + 3*a*f)*sinh(f*x + e)^4 - 4*a*f*cosh(f*x + e)^2 + 8*(7*a*f*cosh(f*x + e)^5 - 10*a*f*cosh(f*x + e)^3 + 3*a*f*cosh(f*x + e))*sinh(f*x + e)^3 + 4*(7*a*f*cosh(f*x + e)^6 - 15*a*f*cosh(f*x + e)^4 + 9*a*f*cosh(f*x + e)^2 - a*f)*sinh(f*x + e)^2 + a*f + 8*(a*f*cosh(f*x + e)^7 - 3*a*f*cosh(f*x + e)^5 + 3*a*f*cosh(f*x + e)^3 - a*f*cosh(f*x + e))*sinh(f*x + e)), 1/8*(3*((a^2 - 2*a*b + b^2)*cosh(f*x + e)^8 + 8*(a^2 - 2*a*b + b^2)*cosh(f*x + e)*sinh(f*x + e)^7 + (a^2 - 2*a*b + b^2)*sinh(f*x + e)^8 - 4*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^6 + 4*(7*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^2 - a^2 + 2*a*b - b^2)*sinh(f*x + e)^6 + 8*(7*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^3 - 3*(a^2 - 2*a*b + b^2)*cosh(f*x + e))*sinh(f*x + e)^5 + 6*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^4 + 2*(35*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^4 - 30*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^2 + 3*a^2 - 6*a*b + 3*b^2)*sinh(f*x + e)^4 + 8*(7*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^5 - 10*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^3 + 3*(a^2 - 2*a*b + b^2)*cosh(f*x + e))*sinh(f*x + e)^3 - 4*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^2 + 4*(7*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^6 - 15*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^4 + 9*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^2 - a^2 + 2*a*b - b^2)*sinh(f*x + e)^2 + a^2 - 2*a*b + b^2 + 8*((a^2 - 2*a*b + b^2)*cosh(f*x + e)^7 - 3*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^5 + 3*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^3 - (a^2 - 2*a*b + b^2)*cosh(f*x + e))*sinh(f*x + e))*sqrt(-a)*arctan(sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 + 1)*sqrt(-a)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/(b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(2*a - b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 2*a - b)*sinh(f*x + e)^2 + 4*(b*cosh(f*x + e)^3 + (2*a - b)*cosh(f*x + e))*sinh(f*x + e) + b)) + sqrt(2)*((3*a^2 - 5*a*b)*cosh(f*x + e)^6 + 6*(3*a^2 - 5*a*b)*cosh(f*x + e)*sinh(f*x + e)^5 + (3*a^2 - 5*a*b)*sinh(f*x + e)^6 - (11*a^2 - 5*a*b)*cosh(f*x + e)^4 + (15*(3*a^2 - 5*a*b)*cosh(f*x + e)^2 - 11*a^2 + 5*a*b)*sinh(f*x + e)^4 + 4*(5*(3*a^2 - 5*a*b)*cosh(f*x + e)^3 - (11*a^2 - 5*a*b)*cosh(f*x + e))*sinh(f*x + e)^3 - (11*a^2 - 5*a*b)*cosh(f*x + e)^2 + (15*(3*a^2 - 5*a*b)*cosh(f*x + e)^4 - 6*(11*a^2 - 5*a*b)*cosh(f*x + e)^2 - 11*a^2 + 5*a*b)*sinh(f*x + e)^2 + 3*a^2 - 5*a*b + 2*(3*(3*a^2 - 5*a*b)*cosh(f*x + e)^5 - 2*(11*a^2 - 5*a*b)*cosh(f*x + e)^3 - (11*a^2 - 5*a*b)*cosh(f*x + e))*sinh(f*x + e))*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/(a*f*cosh(f*x + e)^8 + 8*a*f*cosh(f*x + e)*sinh(f*x + e)^7 + a*f*sinh(f*x + e)^8 - 4*a*f*cosh(f*x + e)^6 + 4*(7*a*f*cosh(f*x + e)^2 - a*f)*sinh(f*x + e)^6 + 6*a*f*cosh(f*x + e)^4 + 8*(7*a*f*cosh(f*x + e)^3 - 3*a*f*cosh(f*x + e))*sinh(f*x + e)^5 + 2*(35*a*f*cosh(f*x + e)^4 - 30*a*f*cosh(f*x + e)^2 + 3*a*f)*sinh(f*x + e)^4 - 4*a*f*cosh(f*x + e)^2 + 8*(7*a*f*cosh(f*x + e)^5 - 10*a*f*cosh(f*x + e)^3 + 3*a*f*cosh(f*x + e))*sinh(f*x + e)^3 + 4*(7*a*f*cosh(f*x + e)^6 - 15*a*f*cosh(f*x + e)^4 + 9*a*f*cosh(f*x + e)^2 - a*f)*sinh(f*x + e)^2 + a*f + 8*(a*f*cosh(f*x + e)^7 - 3*a*f*cosh(f*x + e)^5 + 3*a*f*cosh(f*x + e)^3 - a*f*cosh(f*x + e))*sinh(f*x + e))]","B",0
81,1,7369,0,1.347633," ","integrate(csch(f*x+e)^7*(a+b*sinh(f*x+e)^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{12} + 12 \, {\left(5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{11} + {\left(5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \sinh\left(f x + e\right)^{12} - 6 \, {\left(5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{10} - 6 \, {\left(5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3} - 11 \, {\left(5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{10} + 20 \, {\left(11 \, {\left(5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{3} - 3 \, {\left(5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{9} + 15 \, {\left(5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{8} + 15 \, {\left(33 \, {\left(5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{4} + 5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3} - 18 \, {\left(5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{8} + 24 \, {\left(33 \, {\left(5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{5} - 30 \, {\left(5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{3} + 5 \, {\left(5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{7} - 20 \, {\left(5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{6} + 4 \, {\left(231 \, {\left(5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{6} - 315 \, {\left(5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{4} - 25 \, a^{3} + 45 \, a^{2} b - 15 \, a b^{2} - 5 \, b^{3} + 105 \, {\left(5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{6} + 24 \, {\left(33 \, {\left(5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{7} - 63 \, {\left(5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{5} + 35 \, {\left(5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{3} - 5 \, {\left(5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + 15 \, {\left(5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{4} + 15 \, {\left(33 \, {\left(5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{8} - 84 \, {\left(5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{6} + 70 \, {\left(5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{4} + 5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3} - 20 \, {\left(5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{4} + 20 \, {\left(11 \, {\left(5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{9} - 36 \, {\left(5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{7} + 42 \, {\left(5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{5} - 20 \, {\left(5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3} - 6 \, {\left(5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{2} + 6 \, {\left(11 \, {\left(5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{10} - 45 \, {\left(5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{8} + 70 \, {\left(5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{6} - 50 \, {\left(5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{4} - 5 \, a^{3} + 9 \, a^{2} b - 3 \, a b^{2} - b^{3} + 15 \, {\left(5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{2} + 12 \, {\left({\left(5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{11} - 5 \, {\left(5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{9} + 10 \, {\left(5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{7} - 10 \, {\left(5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{5} + 5 \, {\left(5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{3} - {\left(5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{a} \log\left(-\frac{{\left(a + b\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(a + b\right)} \sinh\left(f x + e\right)^{4} + 2 \, {\left(3 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(f x + e\right)^{2} + 3 \, a - b\right)} \sinh\left(f x + e\right)^{2} + 2 \, \sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} + 1\right)} \sqrt{a} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(f x + e\right)^{3} + {\left(3 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + a + b}{\cosh\left(f x + e\right)^{4} + 4 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + \sinh\left(f x + e\right)^{4} + 2 \, {\left(3 \, \cosh\left(f x + e\right)^{2} - 1\right)} \sinh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right)^{2} + 4 \, {\left(\cosh\left(f x + e\right)^{3} - \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + 1}\right) - 2 \, \sqrt{2} {\left({\left(15 \, a^{3} - 22 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(f x + e\right)^{10} + 10 \, {\left(15 \, a^{3} - 22 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{9} + {\left(15 \, a^{3} - 22 \, a^{2} b + 3 \, a b^{2}\right)} \sinh\left(f x + e\right)^{10} - {\left(85 \, a^{3} - 122 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(f x + e\right)^{8} - {\left(85 \, a^{3} - 122 \, a^{2} b + 9 \, a b^{2} - 45 \, {\left(15 \, a^{3} - 22 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{8} + 8 \, {\left(15 \, {\left(15 \, a^{3} - 22 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(f x + e\right)^{3} - {\left(85 \, a^{3} - 122 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{7} + 2 \, {\left(99 \, a^{3} - 50 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(f x + e\right)^{6} + 2 \, {\left(105 \, {\left(15 \, a^{3} - 22 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(f x + e\right)^{4} + 99 \, a^{3} - 50 \, a^{2} b + 3 \, a b^{2} - 14 \, {\left(85 \, a^{3} - 122 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{6} + 4 \, {\left(63 \, {\left(15 \, a^{3} - 22 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(f x + e\right)^{5} - 14 \, {\left(85 \, a^{3} - 122 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(99 \, a^{3} - 50 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(99 \, a^{3} - 50 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(f x + e\right)^{4} + 2 \, {\left(105 \, {\left(15 \, a^{3} - 22 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(f x + e\right)^{6} - 35 \, {\left(85 \, a^{3} - 122 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(f x + e\right)^{4} + 99 \, a^{3} - 50 \, a^{2} b + 3 \, a b^{2} + 15 \, {\left(99 \, a^{3} - 50 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{4} + 8 \, {\left(15 \, {\left(15 \, a^{3} - 22 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(f x + e\right)^{7} - 7 \, {\left(85 \, a^{3} - 122 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(f x + e\right)^{5} + 5 \, {\left(99 \, a^{3} - 50 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(f x + e\right)^{3} + {\left(99 \, a^{3} - 50 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 15 \, a^{3} - 22 \, a^{2} b + 3 \, a b^{2} - {\left(85 \, a^{3} - 122 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(f x + e\right)^{2} + {\left(45 \, {\left(15 \, a^{3} - 22 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(f x + e\right)^{8} - 28 \, {\left(85 \, a^{3} - 122 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(f x + e\right)^{6} + 30 \, {\left(99 \, a^{3} - 50 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(f x + e\right)^{4} - 85 \, a^{3} + 122 \, a^{2} b - 9 \, a b^{2} + 12 \, {\left(99 \, a^{3} - 50 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{2} + 2 \, {\left(5 \, {\left(15 \, a^{3} - 22 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(f x + e\right)^{9} - 4 \, {\left(85 \, a^{3} - 122 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(f x + e\right)^{7} + 6 \, {\left(99 \, a^{3} - 50 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(f x + e\right)^{5} + 4 \, {\left(99 \, a^{3} - 50 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(f x + e\right)^{3} - {\left(85 \, a^{3} - 122 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{96 \, {\left(a^{2} f \cosh\left(f x + e\right)^{12} + 12 \, a^{2} f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{11} + a^{2} f \sinh\left(f x + e\right)^{12} - 6 \, a^{2} f \cosh\left(f x + e\right)^{10} + 15 \, a^{2} f \cosh\left(f x + e\right)^{8} + 6 \, {\left(11 \, a^{2} f \cosh\left(f x + e\right)^{2} - a^{2} f\right)} \sinh\left(f x + e\right)^{10} + 20 \, {\left(11 \, a^{2} f \cosh\left(f x + e\right)^{3} - 3 \, a^{2} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{9} - 20 \, a^{2} f \cosh\left(f x + e\right)^{6} + 15 \, {\left(33 \, a^{2} f \cosh\left(f x + e\right)^{4} - 18 \, a^{2} f \cosh\left(f x + e\right)^{2} + a^{2} f\right)} \sinh\left(f x + e\right)^{8} + 24 \, {\left(33 \, a^{2} f \cosh\left(f x + e\right)^{5} - 30 \, a^{2} f \cosh\left(f x + e\right)^{3} + 5 \, a^{2} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{7} + 15 \, a^{2} f \cosh\left(f x + e\right)^{4} + 4 \, {\left(231 \, a^{2} f \cosh\left(f x + e\right)^{6} - 315 \, a^{2} f \cosh\left(f x + e\right)^{4} + 105 \, a^{2} f \cosh\left(f x + e\right)^{2} - 5 \, a^{2} f\right)} \sinh\left(f x + e\right)^{6} + 24 \, {\left(33 \, a^{2} f \cosh\left(f x + e\right)^{7} - 63 \, a^{2} f \cosh\left(f x + e\right)^{5} + 35 \, a^{2} f \cosh\left(f x + e\right)^{3} - 5 \, a^{2} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} - 6 \, a^{2} f \cosh\left(f x + e\right)^{2} + 15 \, {\left(33 \, a^{2} f \cosh\left(f x + e\right)^{8} - 84 \, a^{2} f \cosh\left(f x + e\right)^{6} + 70 \, a^{2} f \cosh\left(f x + e\right)^{4} - 20 \, a^{2} f \cosh\left(f x + e\right)^{2} + a^{2} f\right)} \sinh\left(f x + e\right)^{4} + 20 \, {\left(11 \, a^{2} f \cosh\left(f x + e\right)^{9} - 36 \, a^{2} f \cosh\left(f x + e\right)^{7} + 42 \, a^{2} f \cosh\left(f x + e\right)^{5} - 20 \, a^{2} f \cosh\left(f x + e\right)^{3} + 3 \, a^{2} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + a^{2} f + 6 \, {\left(11 \, a^{2} f \cosh\left(f x + e\right)^{10} - 45 \, a^{2} f \cosh\left(f x + e\right)^{8} + 70 \, a^{2} f \cosh\left(f x + e\right)^{6} - 50 \, a^{2} f \cosh\left(f x + e\right)^{4} + 15 \, a^{2} f \cosh\left(f x + e\right)^{2} - a^{2} f\right)} \sinh\left(f x + e\right)^{2} + 12 \, {\left(a^{2} f \cosh\left(f x + e\right)^{11} - 5 \, a^{2} f \cosh\left(f x + e\right)^{9} + 10 \, a^{2} f \cosh\left(f x + e\right)^{7} - 10 \, a^{2} f \cosh\left(f x + e\right)^{5} + 5 \, a^{2} f \cosh\left(f x + e\right)^{3} - a^{2} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)}}, -\frac{3 \, {\left({\left(5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{12} + 12 \, {\left(5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{11} + {\left(5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \sinh\left(f x + e\right)^{12} - 6 \, {\left(5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{10} - 6 \, {\left(5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3} - 11 \, {\left(5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{10} + 20 \, {\left(11 \, {\left(5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{3} - 3 \, {\left(5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{9} + 15 \, {\left(5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{8} + 15 \, {\left(33 \, {\left(5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{4} + 5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3} - 18 \, {\left(5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{8} + 24 \, {\left(33 \, {\left(5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{5} - 30 \, {\left(5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{3} + 5 \, {\left(5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{7} - 20 \, {\left(5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{6} + 4 \, {\left(231 \, {\left(5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{6} - 315 \, {\left(5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{4} - 25 \, a^{3} + 45 \, a^{2} b - 15 \, a b^{2} - 5 \, b^{3} + 105 \, {\left(5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{6} + 24 \, {\left(33 \, {\left(5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{7} - 63 \, {\left(5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{5} + 35 \, {\left(5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{3} - 5 \, {\left(5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + 15 \, {\left(5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{4} + 15 \, {\left(33 \, {\left(5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{8} - 84 \, {\left(5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{6} + 70 \, {\left(5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{4} + 5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3} - 20 \, {\left(5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{4} + 20 \, {\left(11 \, {\left(5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{9} - 36 \, {\left(5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{7} + 42 \, {\left(5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{5} - 20 \, {\left(5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3} - 6 \, {\left(5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{2} + 6 \, {\left(11 \, {\left(5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{10} - 45 \, {\left(5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{8} + 70 \, {\left(5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{6} - 50 \, {\left(5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{4} - 5 \, a^{3} + 9 \, a^{2} b - 3 \, a b^{2} - b^{3} + 15 \, {\left(5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{2} + 12 \, {\left({\left(5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{11} - 5 \, {\left(5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{9} + 10 \, {\left(5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{7} - 10 \, {\left(5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{5} + 5 \, {\left(5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{3} - {\left(5 \, a^{3} - 9 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} + 1\right)} \sqrt{-a} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + 2 \, a - b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}\right) + \sqrt{2} {\left({\left(15 \, a^{3} - 22 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(f x + e\right)^{10} + 10 \, {\left(15 \, a^{3} - 22 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{9} + {\left(15 \, a^{3} - 22 \, a^{2} b + 3 \, a b^{2}\right)} \sinh\left(f x + e\right)^{10} - {\left(85 \, a^{3} - 122 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(f x + e\right)^{8} - {\left(85 \, a^{3} - 122 \, a^{2} b + 9 \, a b^{2} - 45 \, {\left(15 \, a^{3} - 22 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{8} + 8 \, {\left(15 \, {\left(15 \, a^{3} - 22 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(f x + e\right)^{3} - {\left(85 \, a^{3} - 122 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{7} + 2 \, {\left(99 \, a^{3} - 50 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(f x + e\right)^{6} + 2 \, {\left(105 \, {\left(15 \, a^{3} - 22 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(f x + e\right)^{4} + 99 \, a^{3} - 50 \, a^{2} b + 3 \, a b^{2} - 14 \, {\left(85 \, a^{3} - 122 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{6} + 4 \, {\left(63 \, {\left(15 \, a^{3} - 22 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(f x + e\right)^{5} - 14 \, {\left(85 \, a^{3} - 122 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(99 \, a^{3} - 50 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(99 \, a^{3} - 50 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(f x + e\right)^{4} + 2 \, {\left(105 \, {\left(15 \, a^{3} - 22 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(f x + e\right)^{6} - 35 \, {\left(85 \, a^{3} - 122 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(f x + e\right)^{4} + 99 \, a^{3} - 50 \, a^{2} b + 3 \, a b^{2} + 15 \, {\left(99 \, a^{3} - 50 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{4} + 8 \, {\left(15 \, {\left(15 \, a^{3} - 22 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(f x + e\right)^{7} - 7 \, {\left(85 \, a^{3} - 122 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(f x + e\right)^{5} + 5 \, {\left(99 \, a^{3} - 50 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(f x + e\right)^{3} + {\left(99 \, a^{3} - 50 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 15 \, a^{3} - 22 \, a^{2} b + 3 \, a b^{2} - {\left(85 \, a^{3} - 122 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(f x + e\right)^{2} + {\left(45 \, {\left(15 \, a^{3} - 22 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(f x + e\right)^{8} - 28 \, {\left(85 \, a^{3} - 122 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(f x + e\right)^{6} + 30 \, {\left(99 \, a^{3} - 50 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(f x + e\right)^{4} - 85 \, a^{3} + 122 \, a^{2} b - 9 \, a b^{2} + 12 \, {\left(99 \, a^{3} - 50 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{2} + 2 \, {\left(5 \, {\left(15 \, a^{3} - 22 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(f x + e\right)^{9} - 4 \, {\left(85 \, a^{3} - 122 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(f x + e\right)^{7} + 6 \, {\left(99 \, a^{3} - 50 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(f x + e\right)^{5} + 4 \, {\left(99 \, a^{3} - 50 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(f x + e\right)^{3} - {\left(85 \, a^{3} - 122 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{48 \, {\left(a^{2} f \cosh\left(f x + e\right)^{12} + 12 \, a^{2} f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{11} + a^{2} f \sinh\left(f x + e\right)^{12} - 6 \, a^{2} f \cosh\left(f x + e\right)^{10} + 15 \, a^{2} f \cosh\left(f x + e\right)^{8} + 6 \, {\left(11 \, a^{2} f \cosh\left(f x + e\right)^{2} - a^{2} f\right)} \sinh\left(f x + e\right)^{10} + 20 \, {\left(11 \, a^{2} f \cosh\left(f x + e\right)^{3} - 3 \, a^{2} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{9} - 20 \, a^{2} f \cosh\left(f x + e\right)^{6} + 15 \, {\left(33 \, a^{2} f \cosh\left(f x + e\right)^{4} - 18 \, a^{2} f \cosh\left(f x + e\right)^{2} + a^{2} f\right)} \sinh\left(f x + e\right)^{8} + 24 \, {\left(33 \, a^{2} f \cosh\left(f x + e\right)^{5} - 30 \, a^{2} f \cosh\left(f x + e\right)^{3} + 5 \, a^{2} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{7} + 15 \, a^{2} f \cosh\left(f x + e\right)^{4} + 4 \, {\left(231 \, a^{2} f \cosh\left(f x + e\right)^{6} - 315 \, a^{2} f \cosh\left(f x + e\right)^{4} + 105 \, a^{2} f \cosh\left(f x + e\right)^{2} - 5 \, a^{2} f\right)} \sinh\left(f x + e\right)^{6} + 24 \, {\left(33 \, a^{2} f \cosh\left(f x + e\right)^{7} - 63 \, a^{2} f \cosh\left(f x + e\right)^{5} + 35 \, a^{2} f \cosh\left(f x + e\right)^{3} - 5 \, a^{2} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} - 6 \, a^{2} f \cosh\left(f x + e\right)^{2} + 15 \, {\left(33 \, a^{2} f \cosh\left(f x + e\right)^{8} - 84 \, a^{2} f \cosh\left(f x + e\right)^{6} + 70 \, a^{2} f \cosh\left(f x + e\right)^{4} - 20 \, a^{2} f \cosh\left(f x + e\right)^{2} + a^{2} f\right)} \sinh\left(f x + e\right)^{4} + 20 \, {\left(11 \, a^{2} f \cosh\left(f x + e\right)^{9} - 36 \, a^{2} f \cosh\left(f x + e\right)^{7} + 42 \, a^{2} f \cosh\left(f x + e\right)^{5} - 20 \, a^{2} f \cosh\left(f x + e\right)^{3} + 3 \, a^{2} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + a^{2} f + 6 \, {\left(11 \, a^{2} f \cosh\left(f x + e\right)^{10} - 45 \, a^{2} f \cosh\left(f x + e\right)^{8} + 70 \, a^{2} f \cosh\left(f x + e\right)^{6} - 50 \, a^{2} f \cosh\left(f x + e\right)^{4} + 15 \, a^{2} f \cosh\left(f x + e\right)^{2} - a^{2} f\right)} \sinh\left(f x + e\right)^{2} + 12 \, {\left(a^{2} f \cosh\left(f x + e\right)^{11} - 5 \, a^{2} f \cosh\left(f x + e\right)^{9} + 10 \, a^{2} f \cosh\left(f x + e\right)^{7} - 10 \, a^{2} f \cosh\left(f x + e\right)^{5} + 5 \, a^{2} f \cosh\left(f x + e\right)^{3} - a^{2} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)}}\right]"," ",0,"[1/96*(3*((5*a^3 - 9*a^2*b + 3*a*b^2 + b^3)*cosh(f*x + e)^12 + 12*(5*a^3 - 9*a^2*b + 3*a*b^2 + b^3)*cosh(f*x + e)*sinh(f*x + e)^11 + (5*a^3 - 9*a^2*b + 3*a*b^2 + b^3)*sinh(f*x + e)^12 - 6*(5*a^3 - 9*a^2*b + 3*a*b^2 + b^3)*cosh(f*x + e)^10 - 6*(5*a^3 - 9*a^2*b + 3*a*b^2 + b^3 - 11*(5*a^3 - 9*a^2*b + 3*a*b^2 + b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^10 + 20*(11*(5*a^3 - 9*a^2*b + 3*a*b^2 + b^3)*cosh(f*x + e)^3 - 3*(5*a^3 - 9*a^2*b + 3*a*b^2 + b^3)*cosh(f*x + e))*sinh(f*x + e)^9 + 15*(5*a^3 - 9*a^2*b + 3*a*b^2 + b^3)*cosh(f*x + e)^8 + 15*(33*(5*a^3 - 9*a^2*b + 3*a*b^2 + b^3)*cosh(f*x + e)^4 + 5*a^3 - 9*a^2*b + 3*a*b^2 + b^3 - 18*(5*a^3 - 9*a^2*b + 3*a*b^2 + b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^8 + 24*(33*(5*a^3 - 9*a^2*b + 3*a*b^2 + b^3)*cosh(f*x + e)^5 - 30*(5*a^3 - 9*a^2*b + 3*a*b^2 + b^3)*cosh(f*x + e)^3 + 5*(5*a^3 - 9*a^2*b + 3*a*b^2 + b^3)*cosh(f*x + e))*sinh(f*x + e)^7 - 20*(5*a^3 - 9*a^2*b + 3*a*b^2 + b^3)*cosh(f*x + e)^6 + 4*(231*(5*a^3 - 9*a^2*b + 3*a*b^2 + b^3)*cosh(f*x + e)^6 - 315*(5*a^3 - 9*a^2*b + 3*a*b^2 + b^3)*cosh(f*x + e)^4 - 25*a^3 + 45*a^2*b - 15*a*b^2 - 5*b^3 + 105*(5*a^3 - 9*a^2*b + 3*a*b^2 + b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^6 + 24*(33*(5*a^3 - 9*a^2*b + 3*a*b^2 + b^3)*cosh(f*x + e)^7 - 63*(5*a^3 - 9*a^2*b + 3*a*b^2 + b^3)*cosh(f*x + e)^5 + 35*(5*a^3 - 9*a^2*b + 3*a*b^2 + b^3)*cosh(f*x + e)^3 - 5*(5*a^3 - 9*a^2*b + 3*a*b^2 + b^3)*cosh(f*x + e))*sinh(f*x + e)^5 + 15*(5*a^3 - 9*a^2*b + 3*a*b^2 + b^3)*cosh(f*x + e)^4 + 15*(33*(5*a^3 - 9*a^2*b + 3*a*b^2 + b^3)*cosh(f*x + e)^8 - 84*(5*a^3 - 9*a^2*b + 3*a*b^2 + b^3)*cosh(f*x + e)^6 + 70*(5*a^3 - 9*a^2*b + 3*a*b^2 + b^3)*cosh(f*x + e)^4 + 5*a^3 - 9*a^2*b + 3*a*b^2 + b^3 - 20*(5*a^3 - 9*a^2*b + 3*a*b^2 + b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^4 + 20*(11*(5*a^3 - 9*a^2*b + 3*a*b^2 + b^3)*cosh(f*x + e)^9 - 36*(5*a^3 - 9*a^2*b + 3*a*b^2 + b^3)*cosh(f*x + e)^7 + 42*(5*a^3 - 9*a^2*b + 3*a*b^2 + b^3)*cosh(f*x + e)^5 - 20*(5*a^3 - 9*a^2*b + 3*a*b^2 + b^3)*cosh(f*x + e)^3 + 3*(5*a^3 - 9*a^2*b + 3*a*b^2 + b^3)*cosh(f*x + e))*sinh(f*x + e)^3 + 5*a^3 - 9*a^2*b + 3*a*b^2 + b^3 - 6*(5*a^3 - 9*a^2*b + 3*a*b^2 + b^3)*cosh(f*x + e)^2 + 6*(11*(5*a^3 - 9*a^2*b + 3*a*b^2 + b^3)*cosh(f*x + e)^10 - 45*(5*a^3 - 9*a^2*b + 3*a*b^2 + b^3)*cosh(f*x + e)^8 + 70*(5*a^3 - 9*a^2*b + 3*a*b^2 + b^3)*cosh(f*x + e)^6 - 50*(5*a^3 - 9*a^2*b + 3*a*b^2 + b^3)*cosh(f*x + e)^4 - 5*a^3 + 9*a^2*b - 3*a*b^2 - b^3 + 15*(5*a^3 - 9*a^2*b + 3*a*b^2 + b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^2 + 12*((5*a^3 - 9*a^2*b + 3*a*b^2 + b^3)*cosh(f*x + e)^11 - 5*(5*a^3 - 9*a^2*b + 3*a*b^2 + b^3)*cosh(f*x + e)^9 + 10*(5*a^3 - 9*a^2*b + 3*a*b^2 + b^3)*cosh(f*x + e)^7 - 10*(5*a^3 - 9*a^2*b + 3*a*b^2 + b^3)*cosh(f*x + e)^5 + 5*(5*a^3 - 9*a^2*b + 3*a*b^2 + b^3)*cosh(f*x + e)^3 - (5*a^3 - 9*a^2*b + 3*a*b^2 + b^3)*cosh(f*x + e))*sinh(f*x + e))*sqrt(a)*log(-((a + b)*cosh(f*x + e)^4 + 4*(a + b)*cosh(f*x + e)*sinh(f*x + e)^3 + (a + b)*sinh(f*x + e)^4 + 2*(3*a - b)*cosh(f*x + e)^2 + 2*(3*(a + b)*cosh(f*x + e)^2 + 3*a - b)*sinh(f*x + e)^2 + 2*sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 + 1)*sqrt(a)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + 4*((a + b)*cosh(f*x + e)^3 + (3*a - b)*cosh(f*x + e))*sinh(f*x + e) + a + b)/(cosh(f*x + e)^4 + 4*cosh(f*x + e)*sinh(f*x + e)^3 + sinh(f*x + e)^4 + 2*(3*cosh(f*x + e)^2 - 1)*sinh(f*x + e)^2 - 2*cosh(f*x + e)^2 + 4*(cosh(f*x + e)^3 - cosh(f*x + e))*sinh(f*x + e) + 1)) - 2*sqrt(2)*((15*a^3 - 22*a^2*b + 3*a*b^2)*cosh(f*x + e)^10 + 10*(15*a^3 - 22*a^2*b + 3*a*b^2)*cosh(f*x + e)*sinh(f*x + e)^9 + (15*a^3 - 22*a^2*b + 3*a*b^2)*sinh(f*x + e)^10 - (85*a^3 - 122*a^2*b + 9*a*b^2)*cosh(f*x + e)^8 - (85*a^3 - 122*a^2*b + 9*a*b^2 - 45*(15*a^3 - 22*a^2*b + 3*a*b^2)*cosh(f*x + e)^2)*sinh(f*x + e)^8 + 8*(15*(15*a^3 - 22*a^2*b + 3*a*b^2)*cosh(f*x + e)^3 - (85*a^3 - 122*a^2*b + 9*a*b^2)*cosh(f*x + e))*sinh(f*x + e)^7 + 2*(99*a^3 - 50*a^2*b + 3*a*b^2)*cosh(f*x + e)^6 + 2*(105*(15*a^3 - 22*a^2*b + 3*a*b^2)*cosh(f*x + e)^4 + 99*a^3 - 50*a^2*b + 3*a*b^2 - 14*(85*a^3 - 122*a^2*b + 9*a*b^2)*cosh(f*x + e)^2)*sinh(f*x + e)^6 + 4*(63*(15*a^3 - 22*a^2*b + 3*a*b^2)*cosh(f*x + e)^5 - 14*(85*a^3 - 122*a^2*b + 9*a*b^2)*cosh(f*x + e)^3 + 3*(99*a^3 - 50*a^2*b + 3*a*b^2)*cosh(f*x + e))*sinh(f*x + e)^5 + 2*(99*a^3 - 50*a^2*b + 3*a*b^2)*cosh(f*x + e)^4 + 2*(105*(15*a^3 - 22*a^2*b + 3*a*b^2)*cosh(f*x + e)^6 - 35*(85*a^3 - 122*a^2*b + 9*a*b^2)*cosh(f*x + e)^4 + 99*a^3 - 50*a^2*b + 3*a*b^2 + 15*(99*a^3 - 50*a^2*b + 3*a*b^2)*cosh(f*x + e)^2)*sinh(f*x + e)^4 + 8*(15*(15*a^3 - 22*a^2*b + 3*a*b^2)*cosh(f*x + e)^7 - 7*(85*a^3 - 122*a^2*b + 9*a*b^2)*cosh(f*x + e)^5 + 5*(99*a^3 - 50*a^2*b + 3*a*b^2)*cosh(f*x + e)^3 + (99*a^3 - 50*a^2*b + 3*a*b^2)*cosh(f*x + e))*sinh(f*x + e)^3 + 15*a^3 - 22*a^2*b + 3*a*b^2 - (85*a^3 - 122*a^2*b + 9*a*b^2)*cosh(f*x + e)^2 + (45*(15*a^3 - 22*a^2*b + 3*a*b^2)*cosh(f*x + e)^8 - 28*(85*a^3 - 122*a^2*b + 9*a*b^2)*cosh(f*x + e)^6 + 30*(99*a^3 - 50*a^2*b + 3*a*b^2)*cosh(f*x + e)^4 - 85*a^3 + 122*a^2*b - 9*a*b^2 + 12*(99*a^3 - 50*a^2*b + 3*a*b^2)*cosh(f*x + e)^2)*sinh(f*x + e)^2 + 2*(5*(15*a^3 - 22*a^2*b + 3*a*b^2)*cosh(f*x + e)^9 - 4*(85*a^3 - 122*a^2*b + 9*a*b^2)*cosh(f*x + e)^7 + 6*(99*a^3 - 50*a^2*b + 3*a*b^2)*cosh(f*x + e)^5 + 4*(99*a^3 - 50*a^2*b + 3*a*b^2)*cosh(f*x + e)^3 - (85*a^3 - 122*a^2*b + 9*a*b^2)*cosh(f*x + e))*sinh(f*x + e))*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/(a^2*f*cosh(f*x + e)^12 + 12*a^2*f*cosh(f*x + e)*sinh(f*x + e)^11 + a^2*f*sinh(f*x + e)^12 - 6*a^2*f*cosh(f*x + e)^10 + 15*a^2*f*cosh(f*x + e)^8 + 6*(11*a^2*f*cosh(f*x + e)^2 - a^2*f)*sinh(f*x + e)^10 + 20*(11*a^2*f*cosh(f*x + e)^3 - 3*a^2*f*cosh(f*x + e))*sinh(f*x + e)^9 - 20*a^2*f*cosh(f*x + e)^6 + 15*(33*a^2*f*cosh(f*x + e)^4 - 18*a^2*f*cosh(f*x + e)^2 + a^2*f)*sinh(f*x + e)^8 + 24*(33*a^2*f*cosh(f*x + e)^5 - 30*a^2*f*cosh(f*x + e)^3 + 5*a^2*f*cosh(f*x + e))*sinh(f*x + e)^7 + 15*a^2*f*cosh(f*x + e)^4 + 4*(231*a^2*f*cosh(f*x + e)^6 - 315*a^2*f*cosh(f*x + e)^4 + 105*a^2*f*cosh(f*x + e)^2 - 5*a^2*f)*sinh(f*x + e)^6 + 24*(33*a^2*f*cosh(f*x + e)^7 - 63*a^2*f*cosh(f*x + e)^5 + 35*a^2*f*cosh(f*x + e)^3 - 5*a^2*f*cosh(f*x + e))*sinh(f*x + e)^5 - 6*a^2*f*cosh(f*x + e)^2 + 15*(33*a^2*f*cosh(f*x + e)^8 - 84*a^2*f*cosh(f*x + e)^6 + 70*a^2*f*cosh(f*x + e)^4 - 20*a^2*f*cosh(f*x + e)^2 + a^2*f)*sinh(f*x + e)^4 + 20*(11*a^2*f*cosh(f*x + e)^9 - 36*a^2*f*cosh(f*x + e)^7 + 42*a^2*f*cosh(f*x + e)^5 - 20*a^2*f*cosh(f*x + e)^3 + 3*a^2*f*cosh(f*x + e))*sinh(f*x + e)^3 + a^2*f + 6*(11*a^2*f*cosh(f*x + e)^10 - 45*a^2*f*cosh(f*x + e)^8 + 70*a^2*f*cosh(f*x + e)^6 - 50*a^2*f*cosh(f*x + e)^4 + 15*a^2*f*cosh(f*x + e)^2 - a^2*f)*sinh(f*x + e)^2 + 12*(a^2*f*cosh(f*x + e)^11 - 5*a^2*f*cosh(f*x + e)^9 + 10*a^2*f*cosh(f*x + e)^7 - 10*a^2*f*cosh(f*x + e)^5 + 5*a^2*f*cosh(f*x + e)^3 - a^2*f*cosh(f*x + e))*sinh(f*x + e)), -1/48*(3*((5*a^3 - 9*a^2*b + 3*a*b^2 + b^3)*cosh(f*x + e)^12 + 12*(5*a^3 - 9*a^2*b + 3*a*b^2 + b^3)*cosh(f*x + e)*sinh(f*x + e)^11 + (5*a^3 - 9*a^2*b + 3*a*b^2 + b^3)*sinh(f*x + e)^12 - 6*(5*a^3 - 9*a^2*b + 3*a*b^2 + b^3)*cosh(f*x + e)^10 - 6*(5*a^3 - 9*a^2*b + 3*a*b^2 + b^3 - 11*(5*a^3 - 9*a^2*b + 3*a*b^2 + b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^10 + 20*(11*(5*a^3 - 9*a^2*b + 3*a*b^2 + b^3)*cosh(f*x + e)^3 - 3*(5*a^3 - 9*a^2*b + 3*a*b^2 + b^3)*cosh(f*x + e))*sinh(f*x + e)^9 + 15*(5*a^3 - 9*a^2*b + 3*a*b^2 + b^3)*cosh(f*x + e)^8 + 15*(33*(5*a^3 - 9*a^2*b + 3*a*b^2 + b^3)*cosh(f*x + e)^4 + 5*a^3 - 9*a^2*b + 3*a*b^2 + b^3 - 18*(5*a^3 - 9*a^2*b + 3*a*b^2 + b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^8 + 24*(33*(5*a^3 - 9*a^2*b + 3*a*b^2 + b^3)*cosh(f*x + e)^5 - 30*(5*a^3 - 9*a^2*b + 3*a*b^2 + b^3)*cosh(f*x + e)^3 + 5*(5*a^3 - 9*a^2*b + 3*a*b^2 + b^3)*cosh(f*x + e))*sinh(f*x + e)^7 - 20*(5*a^3 - 9*a^2*b + 3*a*b^2 + b^3)*cosh(f*x + e)^6 + 4*(231*(5*a^3 - 9*a^2*b + 3*a*b^2 + b^3)*cosh(f*x + e)^6 - 315*(5*a^3 - 9*a^2*b + 3*a*b^2 + b^3)*cosh(f*x + e)^4 - 25*a^3 + 45*a^2*b - 15*a*b^2 - 5*b^3 + 105*(5*a^3 - 9*a^2*b + 3*a*b^2 + b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^6 + 24*(33*(5*a^3 - 9*a^2*b + 3*a*b^2 + b^3)*cosh(f*x + e)^7 - 63*(5*a^3 - 9*a^2*b + 3*a*b^2 + b^3)*cosh(f*x + e)^5 + 35*(5*a^3 - 9*a^2*b + 3*a*b^2 + b^3)*cosh(f*x + e)^3 - 5*(5*a^3 - 9*a^2*b + 3*a*b^2 + b^3)*cosh(f*x + e))*sinh(f*x + e)^5 + 15*(5*a^3 - 9*a^2*b + 3*a*b^2 + b^3)*cosh(f*x + e)^4 + 15*(33*(5*a^3 - 9*a^2*b + 3*a*b^2 + b^3)*cosh(f*x + e)^8 - 84*(5*a^3 - 9*a^2*b + 3*a*b^2 + b^3)*cosh(f*x + e)^6 + 70*(5*a^3 - 9*a^2*b + 3*a*b^2 + b^3)*cosh(f*x + e)^4 + 5*a^3 - 9*a^2*b + 3*a*b^2 + b^3 - 20*(5*a^3 - 9*a^2*b + 3*a*b^2 + b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^4 + 20*(11*(5*a^3 - 9*a^2*b + 3*a*b^2 + b^3)*cosh(f*x + e)^9 - 36*(5*a^3 - 9*a^2*b + 3*a*b^2 + b^3)*cosh(f*x + e)^7 + 42*(5*a^3 - 9*a^2*b + 3*a*b^2 + b^3)*cosh(f*x + e)^5 - 20*(5*a^3 - 9*a^2*b + 3*a*b^2 + b^3)*cosh(f*x + e)^3 + 3*(5*a^3 - 9*a^2*b + 3*a*b^2 + b^3)*cosh(f*x + e))*sinh(f*x + e)^3 + 5*a^3 - 9*a^2*b + 3*a*b^2 + b^3 - 6*(5*a^3 - 9*a^2*b + 3*a*b^2 + b^3)*cosh(f*x + e)^2 + 6*(11*(5*a^3 - 9*a^2*b + 3*a*b^2 + b^3)*cosh(f*x + e)^10 - 45*(5*a^3 - 9*a^2*b + 3*a*b^2 + b^3)*cosh(f*x + e)^8 + 70*(5*a^3 - 9*a^2*b + 3*a*b^2 + b^3)*cosh(f*x + e)^6 - 50*(5*a^3 - 9*a^2*b + 3*a*b^2 + b^3)*cosh(f*x + e)^4 - 5*a^3 + 9*a^2*b - 3*a*b^2 - b^3 + 15*(5*a^3 - 9*a^2*b + 3*a*b^2 + b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^2 + 12*((5*a^3 - 9*a^2*b + 3*a*b^2 + b^3)*cosh(f*x + e)^11 - 5*(5*a^3 - 9*a^2*b + 3*a*b^2 + b^3)*cosh(f*x + e)^9 + 10*(5*a^3 - 9*a^2*b + 3*a*b^2 + b^3)*cosh(f*x + e)^7 - 10*(5*a^3 - 9*a^2*b + 3*a*b^2 + b^3)*cosh(f*x + e)^5 + 5*(5*a^3 - 9*a^2*b + 3*a*b^2 + b^3)*cosh(f*x + e)^3 - (5*a^3 - 9*a^2*b + 3*a*b^2 + b^3)*cosh(f*x + e))*sinh(f*x + e))*sqrt(-a)*arctan(sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 + 1)*sqrt(-a)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/(b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(2*a - b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 2*a - b)*sinh(f*x + e)^2 + 4*(b*cosh(f*x + e)^3 + (2*a - b)*cosh(f*x + e))*sinh(f*x + e) + b)) + sqrt(2)*((15*a^3 - 22*a^2*b + 3*a*b^2)*cosh(f*x + e)^10 + 10*(15*a^3 - 22*a^2*b + 3*a*b^2)*cosh(f*x + e)*sinh(f*x + e)^9 + (15*a^3 - 22*a^2*b + 3*a*b^2)*sinh(f*x + e)^10 - (85*a^3 - 122*a^2*b + 9*a*b^2)*cosh(f*x + e)^8 - (85*a^3 - 122*a^2*b + 9*a*b^2 - 45*(15*a^3 - 22*a^2*b + 3*a*b^2)*cosh(f*x + e)^2)*sinh(f*x + e)^8 + 8*(15*(15*a^3 - 22*a^2*b + 3*a*b^2)*cosh(f*x + e)^3 - (85*a^3 - 122*a^2*b + 9*a*b^2)*cosh(f*x + e))*sinh(f*x + e)^7 + 2*(99*a^3 - 50*a^2*b + 3*a*b^2)*cosh(f*x + e)^6 + 2*(105*(15*a^3 - 22*a^2*b + 3*a*b^2)*cosh(f*x + e)^4 + 99*a^3 - 50*a^2*b + 3*a*b^2 - 14*(85*a^3 - 122*a^2*b + 9*a*b^2)*cosh(f*x + e)^2)*sinh(f*x + e)^6 + 4*(63*(15*a^3 - 22*a^2*b + 3*a*b^2)*cosh(f*x + e)^5 - 14*(85*a^3 - 122*a^2*b + 9*a*b^2)*cosh(f*x + e)^3 + 3*(99*a^3 - 50*a^2*b + 3*a*b^2)*cosh(f*x + e))*sinh(f*x + e)^5 + 2*(99*a^3 - 50*a^2*b + 3*a*b^2)*cosh(f*x + e)^4 + 2*(105*(15*a^3 - 22*a^2*b + 3*a*b^2)*cosh(f*x + e)^6 - 35*(85*a^3 - 122*a^2*b + 9*a*b^2)*cosh(f*x + e)^4 + 99*a^3 - 50*a^2*b + 3*a*b^2 + 15*(99*a^3 - 50*a^2*b + 3*a*b^2)*cosh(f*x + e)^2)*sinh(f*x + e)^4 + 8*(15*(15*a^3 - 22*a^2*b + 3*a*b^2)*cosh(f*x + e)^7 - 7*(85*a^3 - 122*a^2*b + 9*a*b^2)*cosh(f*x + e)^5 + 5*(99*a^3 - 50*a^2*b + 3*a*b^2)*cosh(f*x + e)^3 + (99*a^3 - 50*a^2*b + 3*a*b^2)*cosh(f*x + e))*sinh(f*x + e)^3 + 15*a^3 - 22*a^2*b + 3*a*b^2 - (85*a^3 - 122*a^2*b + 9*a*b^2)*cosh(f*x + e)^2 + (45*(15*a^3 - 22*a^2*b + 3*a*b^2)*cosh(f*x + e)^8 - 28*(85*a^3 - 122*a^2*b + 9*a*b^2)*cosh(f*x + e)^6 + 30*(99*a^3 - 50*a^2*b + 3*a*b^2)*cosh(f*x + e)^4 - 85*a^3 + 122*a^2*b - 9*a*b^2 + 12*(99*a^3 - 50*a^2*b + 3*a*b^2)*cosh(f*x + e)^2)*sinh(f*x + e)^2 + 2*(5*(15*a^3 - 22*a^2*b + 3*a*b^2)*cosh(f*x + e)^9 - 4*(85*a^3 - 122*a^2*b + 9*a*b^2)*cosh(f*x + e)^7 + 6*(99*a^3 - 50*a^2*b + 3*a*b^2)*cosh(f*x + e)^5 + 4*(99*a^3 - 50*a^2*b + 3*a*b^2)*cosh(f*x + e)^3 - (85*a^3 - 122*a^2*b + 9*a*b^2)*cosh(f*x + e))*sinh(f*x + e))*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/(a^2*f*cosh(f*x + e)^12 + 12*a^2*f*cosh(f*x + e)*sinh(f*x + e)^11 + a^2*f*sinh(f*x + e)^12 - 6*a^2*f*cosh(f*x + e)^10 + 15*a^2*f*cosh(f*x + e)^8 + 6*(11*a^2*f*cosh(f*x + e)^2 - a^2*f)*sinh(f*x + e)^10 + 20*(11*a^2*f*cosh(f*x + e)^3 - 3*a^2*f*cosh(f*x + e))*sinh(f*x + e)^9 - 20*a^2*f*cosh(f*x + e)^6 + 15*(33*a^2*f*cosh(f*x + e)^4 - 18*a^2*f*cosh(f*x + e)^2 + a^2*f)*sinh(f*x + e)^8 + 24*(33*a^2*f*cosh(f*x + e)^5 - 30*a^2*f*cosh(f*x + e)^3 + 5*a^2*f*cosh(f*x + e))*sinh(f*x + e)^7 + 15*a^2*f*cosh(f*x + e)^4 + 4*(231*a^2*f*cosh(f*x + e)^6 - 315*a^2*f*cosh(f*x + e)^4 + 105*a^2*f*cosh(f*x + e)^2 - 5*a^2*f)*sinh(f*x + e)^6 + 24*(33*a^2*f*cosh(f*x + e)^7 - 63*a^2*f*cosh(f*x + e)^5 + 35*a^2*f*cosh(f*x + e)^3 - 5*a^2*f*cosh(f*x + e))*sinh(f*x + e)^5 - 6*a^2*f*cosh(f*x + e)^2 + 15*(33*a^2*f*cosh(f*x + e)^8 - 84*a^2*f*cosh(f*x + e)^6 + 70*a^2*f*cosh(f*x + e)^4 - 20*a^2*f*cosh(f*x + e)^2 + a^2*f)*sinh(f*x + e)^4 + 20*(11*a^2*f*cosh(f*x + e)^9 - 36*a^2*f*cosh(f*x + e)^7 + 42*a^2*f*cosh(f*x + e)^5 - 20*a^2*f*cosh(f*x + e)^3 + 3*a^2*f*cosh(f*x + e))*sinh(f*x + e)^3 + a^2*f + 6*(11*a^2*f*cosh(f*x + e)^10 - 45*a^2*f*cosh(f*x + e)^8 + 70*a^2*f*cosh(f*x + e)^6 - 50*a^2*f*cosh(f*x + e)^4 + 15*a^2*f*cosh(f*x + e)^2 - a^2*f)*sinh(f*x + e)^2 + 12*(a^2*f*cosh(f*x + e)^11 - 5*a^2*f*cosh(f*x + e)^9 + 10*a^2*f*cosh(f*x + e)^7 - 10*a^2*f*cosh(f*x + e)^5 + 5*a^2*f*cosh(f*x + e)^3 - a^2*f*cosh(f*x + e))*sinh(f*x + e))]","B",0
82,0,0,0,0.834429," ","integrate(sinh(f*x+e)^4*(a+b*sinh(f*x+e)^2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sinh\left(f x + e\right)^{6} + a \sinh\left(f x + e\right)^{4}\right)} \sqrt{b \sinh\left(f x + e\right)^{2} + a}, x\right)"," ",0,"integral((b*sinh(f*x + e)^6 + a*sinh(f*x + e)^4)*sqrt(b*sinh(f*x + e)^2 + a), x)","F",0
83,0,0,0,0.786563," ","integrate(sinh(f*x+e)^2*(a+b*sinh(f*x+e)^2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sinh\left(f x + e\right)^{4} + a \sinh\left(f x + e\right)^{2}\right)} \sqrt{b \sinh\left(f x + e\right)^{2} + a}, x\right)"," ",0,"integral((b*sinh(f*x + e)^4 + a*sinh(f*x + e)^2)*sqrt(b*sinh(f*x + e)^2 + a), x)","F",0
84,0,0,0,0.789115," ","integrate((a+b*sinh(f*x+e)^2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sinh\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}}, x\right)"," ",0,"integral((b*sinh(f*x + e)^2 + a)^(3/2), x)","F",0
85,0,0,0,1.040583," ","integrate(csch(f*x+e)^2*(a+b*sinh(f*x+e)^2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \operatorname{csch}\left(f x + e\right)^{2} \sinh\left(f x + e\right)^{2} + a \operatorname{csch}\left(f x + e\right)^{2}\right)} \sqrt{b \sinh\left(f x + e\right)^{2} + a}, x\right)"," ",0,"integral((b*csch(f*x + e)^2*sinh(f*x + e)^2 + a*csch(f*x + e)^2)*sqrt(b*sinh(f*x + e)^2 + a), x)","F",0
86,0,0,0,0.739605," ","integrate(csch(f*x+e)^4*(a+b*sinh(f*x+e)^2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \operatorname{csch}\left(f x + e\right)^{4} \sinh\left(f x + e\right)^{2} + a \operatorname{csch}\left(f x + e\right)^{4}\right)} \sqrt{b \sinh\left(f x + e\right)^{2} + a}, x\right)"," ",0,"integral((b*csch(f*x + e)^4*sinh(f*x + e)^2 + a*csch(f*x + e)^4)*sqrt(b*sinh(f*x + e)^2 + a), x)","F",0
87,0,0,0,1.298519," ","integrate((a+b*sinh(d*x+c)^2)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b^{2} \sinh\left(d x + c\right)^{4} + 2 \, a b \sinh\left(d x + c\right)^{2} + a^{2}\right)} \sqrt{b \sinh\left(d x + c\right)^{2} + a}, x\right)"," ",0,"integral((b^2*sinh(d*x + c)^4 + 2*a*b*sinh(d*x + c)^2 + a^2)*sqrt(b*sinh(d*x + c)^2 + a), x)","F",0
88,1,2,0,3.466149," ","integrate((1+sinh(x)^2)^(1/2),x, algorithm=""fricas"")","\sinh\left(x\right)"," ",0,"sinh(x)","A",0
89,1,14,0,0.730385," ","integrate((-1-sinh(x)^2)^(1/2),x, algorithm=""fricas"")","\frac{1}{2} \, {\left(i \, e^{\left(2 \, x\right)} - i\right)} e^{\left(-x\right)}"," ",0,"1/2*(I*e^(2*x) - I)*e^(-x)","C",0
90,0,0,0,1.879135," ","integrate((1-sinh(x)^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{-\sinh\left(x\right)^{2} + 1}, x\right)"," ",0,"integral(sqrt(-sinh(x)^2 + 1), x)","F",0
91,0,0,0,3.096303," ","integrate((-1+sinh(x)^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{\sinh\left(x\right)^{2} - 1}, x\right)"," ",0,"integral(sqrt(sinh(x)^2 - 1), x)","F",0
92,0,0,0,4.814698," ","integrate((a+b*sinh(x)^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{b \sinh\left(x\right)^{2} + a}, x\right)"," ",0,"integral(sqrt(b*sinh(x)^2 + a), x)","F",0
93,1,17,0,2.911715," ","integrate((1+sinh(x)^2)^(3/2),x, algorithm=""fricas"")","\frac{1}{12} \, \sinh\left(x\right)^{3} + \frac{1}{4} \, {\left(\cosh\left(x\right)^{2} + 3\right)} \sinh\left(x\right)"," ",0,"1/12*sinh(x)^3 + 1/4*(cosh(x)^2 + 3)*sinh(x)","A",0
94,1,26,0,0.601822," ","integrate((-1-sinh(x)^2)^(3/2),x, algorithm=""fricas"")","\frac{1}{24} \, {\left(-i \, e^{\left(6 \, x\right)} - 9 i \, e^{\left(4 \, x\right)} + 9 i \, e^{\left(2 \, x\right)} + i\right)} e^{\left(-3 \, x\right)}"," ",0,"1/24*(-I*e^(6*x) - 9*I*e^(4*x) + 9*I*e^(2*x) + I)*e^(-3*x)","C",0
95,0,0,0,0.980986," ","integrate((1-sinh(x)^2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(-\sinh\left(x\right)^{2} + 1\right)}^{\frac{3}{2}}, x\right)"," ",0,"integral((-sinh(x)^2 + 1)^(3/2), x)","F",0
96,0,0,0,0.522155," ","integrate((-1+sinh(x)^2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(\sinh\left(x\right)^{2} - 1\right)}^{\frac{3}{2}}, x\right)"," ",0,"integral((sinh(x)^2 - 1)^(3/2), x)","F",0
97,0,0,0,1.291822," ","integrate((a+b*sinh(x)^2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sinh\left(x\right)^{2} + a\right)}^{\frac{3}{2}}, x\right)"," ",0,"integral((b*sinh(x)^2 + a)^(3/2), x)","F",0
98,1,2116,0,2.924849," ","integrate(sinh(f*x+e)^3/(a+b*sinh(f*x+e)^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(a + b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(a + b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) + {\left(a + b\right)} \sinh\left(f x + e\right)^{2}\right)} \sqrt{b} \log\left(\frac{a^{2} b \cosh\left(f x + e\right)^{8} + 8 \, a^{2} b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + a^{2} b \sinh\left(f x + e\right)^{8} + 2 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(f x + e\right)^{6} + 2 \, {\left(14 \, a^{2} b \cosh\left(f x + e\right)^{2} + a^{3} + a^{2} b\right)} \sinh\left(f x + e\right)^{6} + 4 \, {\left(14 \, a^{2} b \cosh\left(f x + e\right)^{3} + 3 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + {\left(9 \, a^{2} b - 4 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{4} + {\left(70 \, a^{2} b \cosh\left(f x + e\right)^{4} + 9 \, a^{2} b - 4 \, a b^{2} + b^{3} + 30 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(14 \, a^{2} b \cosh\left(f x + e\right)^{5} + 10 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(f x + e\right)^{3} + {\left(9 \, a^{2} b - 4 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + b^{3} + 2 \, {\left(3 \, a b^{2} - b^{3}\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(14 \, a^{2} b \cosh\left(f x + e\right)^{6} + 15 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(f x + e\right)^{4} + 3 \, a b^{2} - b^{3} + 3 \, {\left(9 \, a^{2} b - 4 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{2} - \sqrt{2} {\left(a^{2} \cosh\left(f x + e\right)^{6} + 6 \, a^{2} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + a^{2} \sinh\left(f x + e\right)^{6} + 3 \, a^{2} \cosh\left(f x + e\right)^{4} + 3 \, {\left(5 \, a^{2} \cosh\left(f x + e\right)^{2} + a^{2}\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(5 \, a^{2} \cosh\left(f x + e\right)^{3} + 3 \, a^{2} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + {\left(4 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{2} + {\left(15 \, a^{2} \cosh\left(f x + e\right)^{4} + 18 \, a^{2} \cosh\left(f x + e\right)^{2} + 4 \, a b - b^{2}\right)} \sinh\left(f x + e\right)^{2} + b^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(f x + e\right)^{5} + 6 \, a^{2} \cosh\left(f x + e\right)^{3} + {\left(4 \, a b - b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} + 4 \, {\left(2 \, a^{2} b \cosh\left(f x + e\right)^{7} + 3 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(f x + e\right)^{5} + {\left(9 \, a^{2} b - 4 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{3} + {\left(3 \, a b^{2} - b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)}{\cosh\left(f x + e\right)^{6} + 6 \, \cosh\left(f x + e\right)^{5} \sinh\left(f x + e\right) + 15 \, \cosh\left(f x + e\right)^{4} \sinh\left(f x + e\right)^{2} + 20 \, \cosh\left(f x + e\right)^{3} \sinh\left(f x + e\right)^{3} + 15 \, \cosh\left(f x + e\right)^{2} \sinh\left(f x + e\right)^{4} + 6 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + \sinh\left(f x + e\right)^{6}}\right) + {\left({\left(a + b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(a + b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) + {\left(a + b\right)} \sinh\left(f x + e\right)^{2}\right)} \sqrt{b} \log\left(-\frac{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + a - b\right)} \sinh\left(f x + e\right)^{2} - \sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} - 1\right)} \sqrt{b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}{\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}\right) + \sqrt{2} {\left(b \cosh\left(f x + e\right)^{2} + 2 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right) + b \sinh\left(f x + e\right)^{2} + b\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{8 \, {\left(b^{2} f \cosh\left(f x + e\right)^{2} + 2 \, b^{2} f \cosh\left(f x + e\right) \sinh\left(f x + e\right) + b^{2} f \sinh\left(f x + e\right)^{2}\right)}}, \frac{2 \, {\left({\left(a + b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(a + b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) + {\left(a + b\right)} \sinh\left(f x + e\right)^{2}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{2} {\left(a \cosh\left(f x + e\right)^{2} + 2 \, a \cosh\left(f x + e\right) \sinh\left(f x + e\right) + a \sinh\left(f x + e\right)^{2} + b\right)} \sqrt{-b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{a b \cosh\left(f x + e\right)^{4} + 4 \, a b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + a b \sinh\left(f x + e\right)^{4} + {\left(3 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{2} + {\left(6 \, a b \cosh\left(f x + e\right)^{2} + 3 \, a b - b^{2}\right)} \sinh\left(f x + e\right)^{2} + b^{2} + 2 \, {\left(2 \, a b \cosh\left(f x + e\right)^{3} + {\left(3 \, a b - b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)}\right) + 2 \, {\left({\left(a + b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(a + b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) + {\left(a + b\right)} \sinh\left(f x + e\right)^{2}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} - 1\right)} \sqrt{-b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + 2 \, a - b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}\right) + \sqrt{2} {\left(b \cosh\left(f x + e\right)^{2} + 2 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right) + b \sinh\left(f x + e\right)^{2} + b\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{8 \, {\left(b^{2} f \cosh\left(f x + e\right)^{2} + 2 \, b^{2} f \cosh\left(f x + e\right) \sinh\left(f x + e\right) + b^{2} f \sinh\left(f x + e\right)^{2}\right)}}\right]"," ",0,"[1/8*(((a + b)*cosh(f*x + e)^2 + 2*(a + b)*cosh(f*x + e)*sinh(f*x + e) + (a + b)*sinh(f*x + e)^2)*sqrt(b)*log((a^2*b*cosh(f*x + e)^8 + 8*a^2*b*cosh(f*x + e)*sinh(f*x + e)^7 + a^2*b*sinh(f*x + e)^8 + 2*(a^3 + a^2*b)*cosh(f*x + e)^6 + 2*(14*a^2*b*cosh(f*x + e)^2 + a^3 + a^2*b)*sinh(f*x + e)^6 + 4*(14*a^2*b*cosh(f*x + e)^3 + 3*(a^3 + a^2*b)*cosh(f*x + e))*sinh(f*x + e)^5 + (9*a^2*b - 4*a*b^2 + b^3)*cosh(f*x + e)^4 + (70*a^2*b*cosh(f*x + e)^4 + 9*a^2*b - 4*a*b^2 + b^3 + 30*(a^3 + a^2*b)*cosh(f*x + e)^2)*sinh(f*x + e)^4 + 4*(14*a^2*b*cosh(f*x + e)^5 + 10*(a^3 + a^2*b)*cosh(f*x + e)^3 + (9*a^2*b - 4*a*b^2 + b^3)*cosh(f*x + e))*sinh(f*x + e)^3 + b^3 + 2*(3*a*b^2 - b^3)*cosh(f*x + e)^2 + 2*(14*a^2*b*cosh(f*x + e)^6 + 15*(a^3 + a^2*b)*cosh(f*x + e)^4 + 3*a*b^2 - b^3 + 3*(9*a^2*b - 4*a*b^2 + b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^2 - sqrt(2)*(a^2*cosh(f*x + e)^6 + 6*a^2*cosh(f*x + e)*sinh(f*x + e)^5 + a^2*sinh(f*x + e)^6 + 3*a^2*cosh(f*x + e)^4 + 3*(5*a^2*cosh(f*x + e)^2 + a^2)*sinh(f*x + e)^4 + 4*(5*a^2*cosh(f*x + e)^3 + 3*a^2*cosh(f*x + e))*sinh(f*x + e)^3 + (4*a*b - b^2)*cosh(f*x + e)^2 + (15*a^2*cosh(f*x + e)^4 + 18*a^2*cosh(f*x + e)^2 + 4*a*b - b^2)*sinh(f*x + e)^2 + b^2 + 2*(3*a^2*cosh(f*x + e)^5 + 6*a^2*cosh(f*x + e)^3 + (4*a*b - b^2)*cosh(f*x + e))*sinh(f*x + e))*sqrt(b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + 4*(2*a^2*b*cosh(f*x + e)^7 + 3*(a^3 + a^2*b)*cosh(f*x + e)^5 + (9*a^2*b - 4*a*b^2 + b^3)*cosh(f*x + e)^3 + (3*a*b^2 - b^3)*cosh(f*x + e))*sinh(f*x + e))/(cosh(f*x + e)^6 + 6*cosh(f*x + e)^5*sinh(f*x + e) + 15*cosh(f*x + e)^4*sinh(f*x + e)^2 + 20*cosh(f*x + e)^3*sinh(f*x + e)^3 + 15*cosh(f*x + e)^2*sinh(f*x + e)^4 + 6*cosh(f*x + e)*sinh(f*x + e)^5 + sinh(f*x + e)^6)) + ((a + b)*cosh(f*x + e)^2 + 2*(a + b)*cosh(f*x + e)*sinh(f*x + e) + (a + b)*sinh(f*x + e)^2)*sqrt(b)*log(-(b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(a - b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + a - b)*sinh(f*x + e)^2 - sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 - 1)*sqrt(b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + 4*(b*cosh(f*x + e)^3 + (a - b)*cosh(f*x + e))*sinh(f*x + e) + b)/(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + sqrt(2)*(b*cosh(f*x + e)^2 + 2*b*cosh(f*x + e)*sinh(f*x + e) + b*sinh(f*x + e)^2 + b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/(b^2*f*cosh(f*x + e)^2 + 2*b^2*f*cosh(f*x + e)*sinh(f*x + e) + b^2*f*sinh(f*x + e)^2), 1/8*(2*((a + b)*cosh(f*x + e)^2 + 2*(a + b)*cosh(f*x + e)*sinh(f*x + e) + (a + b)*sinh(f*x + e)^2)*sqrt(-b)*arctan(sqrt(2)*(a*cosh(f*x + e)^2 + 2*a*cosh(f*x + e)*sinh(f*x + e) + a*sinh(f*x + e)^2 + b)*sqrt(-b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/(a*b*cosh(f*x + e)^4 + 4*a*b*cosh(f*x + e)*sinh(f*x + e)^3 + a*b*sinh(f*x + e)^4 + (3*a*b - b^2)*cosh(f*x + e)^2 + (6*a*b*cosh(f*x + e)^2 + 3*a*b - b^2)*sinh(f*x + e)^2 + b^2 + 2*(2*a*b*cosh(f*x + e)^3 + (3*a*b - b^2)*cosh(f*x + e))*sinh(f*x + e))) + 2*((a + b)*cosh(f*x + e)^2 + 2*(a + b)*cosh(f*x + e)*sinh(f*x + e) + (a + b)*sinh(f*x + e)^2)*sqrt(-b)*arctan(sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 - 1)*sqrt(-b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/(b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(2*a - b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 2*a - b)*sinh(f*x + e)^2 + 4*(b*cosh(f*x + e)^3 + (2*a - b)*cosh(f*x + e))*sinh(f*x + e) + b)) + sqrt(2)*(b*cosh(f*x + e)^2 + 2*b*cosh(f*x + e)*sinh(f*x + e) + b*sinh(f*x + e)^2 + b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/(b^2*f*cosh(f*x + e)^2 + 2*b^2*f*cosh(f*x + e)*sinh(f*x + e) + b^2*f*sinh(f*x + e)^2)]","B",0
99,1,1654,0,3.907283," ","integrate(sinh(f*x+e)/(a+b*sinh(f*x+e)^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{b} \log\left(\frac{a^{2} b \cosh\left(f x + e\right)^{8} + 8 \, a^{2} b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + a^{2} b \sinh\left(f x + e\right)^{8} + 2 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(f x + e\right)^{6} + 2 \, {\left(14 \, a^{2} b \cosh\left(f x + e\right)^{2} + a^{3} + a^{2} b\right)} \sinh\left(f x + e\right)^{6} + 4 \, {\left(14 \, a^{2} b \cosh\left(f x + e\right)^{3} + 3 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + {\left(9 \, a^{2} b - 4 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{4} + {\left(70 \, a^{2} b \cosh\left(f x + e\right)^{4} + 9 \, a^{2} b - 4 \, a b^{2} + b^{3} + 30 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(14 \, a^{2} b \cosh\left(f x + e\right)^{5} + 10 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(f x + e\right)^{3} + {\left(9 \, a^{2} b - 4 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + b^{3} + 2 \, {\left(3 \, a b^{2} - b^{3}\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(14 \, a^{2} b \cosh\left(f x + e\right)^{6} + 15 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(f x + e\right)^{4} + 3 \, a b^{2} - b^{3} + 3 \, {\left(9 \, a^{2} b - 4 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{2} + \sqrt{2} {\left(a^{2} \cosh\left(f x + e\right)^{6} + 6 \, a^{2} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + a^{2} \sinh\left(f x + e\right)^{6} + 3 \, a^{2} \cosh\left(f x + e\right)^{4} + 3 \, {\left(5 \, a^{2} \cosh\left(f x + e\right)^{2} + a^{2}\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(5 \, a^{2} \cosh\left(f x + e\right)^{3} + 3 \, a^{2} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + {\left(4 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{2} + {\left(15 \, a^{2} \cosh\left(f x + e\right)^{4} + 18 \, a^{2} \cosh\left(f x + e\right)^{2} + 4 \, a b - b^{2}\right)} \sinh\left(f x + e\right)^{2} + b^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(f x + e\right)^{5} + 6 \, a^{2} \cosh\left(f x + e\right)^{3} + {\left(4 \, a b - b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} + 4 \, {\left(2 \, a^{2} b \cosh\left(f x + e\right)^{7} + 3 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(f x + e\right)^{5} + {\left(9 \, a^{2} b - 4 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{3} + {\left(3 \, a b^{2} - b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)}{\cosh\left(f x + e\right)^{6} + 6 \, \cosh\left(f x + e\right)^{5} \sinh\left(f x + e\right) + 15 \, \cosh\left(f x + e\right)^{4} \sinh\left(f x + e\right)^{2} + 20 \, \cosh\left(f x + e\right)^{3} \sinh\left(f x + e\right)^{3} + 15 \, \cosh\left(f x + e\right)^{2} \sinh\left(f x + e\right)^{4} + 6 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + \sinh\left(f x + e\right)^{6}}\right) + \sqrt{b} \log\left(-\frac{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + a - b\right)} \sinh\left(f x + e\right)^{2} + \sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} - 1\right)} \sqrt{b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}{\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}\right)}{4 \, b f}, -\frac{\sqrt{-b} \arctan\left(\frac{\sqrt{2} {\left(a \cosh\left(f x + e\right)^{2} + 2 \, a \cosh\left(f x + e\right) \sinh\left(f x + e\right) + a \sinh\left(f x + e\right)^{2} + b\right)} \sqrt{-b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{a b \cosh\left(f x + e\right)^{4} + 4 \, a b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + a b \sinh\left(f x + e\right)^{4} + {\left(3 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{2} + {\left(6 \, a b \cosh\left(f x + e\right)^{2} + 3 \, a b - b^{2}\right)} \sinh\left(f x + e\right)^{2} + b^{2} + 2 \, {\left(2 \, a b \cosh\left(f x + e\right)^{3} + {\left(3 \, a b - b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)}\right) + \sqrt{-b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} - 1\right)} \sqrt{-b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + 2 \, a - b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}\right)}{2 \, b f}\right]"," ",0,"[1/4*(sqrt(b)*log((a^2*b*cosh(f*x + e)^8 + 8*a^2*b*cosh(f*x + e)*sinh(f*x + e)^7 + a^2*b*sinh(f*x + e)^8 + 2*(a^3 + a^2*b)*cosh(f*x + e)^6 + 2*(14*a^2*b*cosh(f*x + e)^2 + a^3 + a^2*b)*sinh(f*x + e)^6 + 4*(14*a^2*b*cosh(f*x + e)^3 + 3*(a^3 + a^2*b)*cosh(f*x + e))*sinh(f*x + e)^5 + (9*a^2*b - 4*a*b^2 + b^3)*cosh(f*x + e)^4 + (70*a^2*b*cosh(f*x + e)^4 + 9*a^2*b - 4*a*b^2 + b^3 + 30*(a^3 + a^2*b)*cosh(f*x + e)^2)*sinh(f*x + e)^4 + 4*(14*a^2*b*cosh(f*x + e)^5 + 10*(a^3 + a^2*b)*cosh(f*x + e)^3 + (9*a^2*b - 4*a*b^2 + b^3)*cosh(f*x + e))*sinh(f*x + e)^3 + b^3 + 2*(3*a*b^2 - b^3)*cosh(f*x + e)^2 + 2*(14*a^2*b*cosh(f*x + e)^6 + 15*(a^3 + a^2*b)*cosh(f*x + e)^4 + 3*a*b^2 - b^3 + 3*(9*a^2*b - 4*a*b^2 + b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^2 + sqrt(2)*(a^2*cosh(f*x + e)^6 + 6*a^2*cosh(f*x + e)*sinh(f*x + e)^5 + a^2*sinh(f*x + e)^6 + 3*a^2*cosh(f*x + e)^4 + 3*(5*a^2*cosh(f*x + e)^2 + a^2)*sinh(f*x + e)^4 + 4*(5*a^2*cosh(f*x + e)^3 + 3*a^2*cosh(f*x + e))*sinh(f*x + e)^3 + (4*a*b - b^2)*cosh(f*x + e)^2 + (15*a^2*cosh(f*x + e)^4 + 18*a^2*cosh(f*x + e)^2 + 4*a*b - b^2)*sinh(f*x + e)^2 + b^2 + 2*(3*a^2*cosh(f*x + e)^5 + 6*a^2*cosh(f*x + e)^3 + (4*a*b - b^2)*cosh(f*x + e))*sinh(f*x + e))*sqrt(b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + 4*(2*a^2*b*cosh(f*x + e)^7 + 3*(a^3 + a^2*b)*cosh(f*x + e)^5 + (9*a^2*b - 4*a*b^2 + b^3)*cosh(f*x + e)^3 + (3*a*b^2 - b^3)*cosh(f*x + e))*sinh(f*x + e))/(cosh(f*x + e)^6 + 6*cosh(f*x + e)^5*sinh(f*x + e) + 15*cosh(f*x + e)^4*sinh(f*x + e)^2 + 20*cosh(f*x + e)^3*sinh(f*x + e)^3 + 15*cosh(f*x + e)^2*sinh(f*x + e)^4 + 6*cosh(f*x + e)*sinh(f*x + e)^5 + sinh(f*x + e)^6)) + sqrt(b)*log(-(b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(a - b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + a - b)*sinh(f*x + e)^2 + sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 - 1)*sqrt(b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + 4*(b*cosh(f*x + e)^3 + (a - b)*cosh(f*x + e))*sinh(f*x + e) + b)/(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/(b*f), -1/2*(sqrt(-b)*arctan(sqrt(2)*(a*cosh(f*x + e)^2 + 2*a*cosh(f*x + e)*sinh(f*x + e) + a*sinh(f*x + e)^2 + b)*sqrt(-b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/(a*b*cosh(f*x + e)^4 + 4*a*b*cosh(f*x + e)*sinh(f*x + e)^3 + a*b*sinh(f*x + e)^4 + (3*a*b - b^2)*cosh(f*x + e)^2 + (6*a*b*cosh(f*x + e)^2 + 3*a*b - b^2)*sinh(f*x + e)^2 + b^2 + 2*(2*a*b*cosh(f*x + e)^3 + (3*a*b - b^2)*cosh(f*x + e))*sinh(f*x + e))) + sqrt(-b)*arctan(sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 - 1)*sqrt(-b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/(b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(2*a - b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 2*a - b)*sinh(f*x + e)^2 + 4*(b*cosh(f*x + e)^3 + (2*a - b)*cosh(f*x + e))*sinh(f*x + e) + b)))/(b*f)]","B",0
100,1,572,0,0.622514," ","integrate(csch(f*x+e)/(a+b*sinh(f*x+e)^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{\log\left(-\frac{{\left(a + b\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(a + b\right)} \sinh\left(f x + e\right)^{4} + 2 \, {\left(3 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(f x + e\right)^{2} + 3 \, a - b\right)} \sinh\left(f x + e\right)^{2} - 2 \, \sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} + 1\right)} \sqrt{a} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(f x + e\right)^{3} + {\left(3 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + a + b}{\cosh\left(f x + e\right)^{4} + 4 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + \sinh\left(f x + e\right)^{4} + 2 \, {\left(3 \, \cosh\left(f x + e\right)^{2} - 1\right)} \sinh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right)^{2} + 4 \, {\left(\cosh\left(f x + e\right)^{3} - \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + 1}\right)}{2 \, \sqrt{a} f}, \frac{\sqrt{-a} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} + 1\right)} \sqrt{-a} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + 2 \, a - b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}\right)}{a f}\right]"," ",0,"[1/2*log(-((a + b)*cosh(f*x + e)^4 + 4*(a + b)*cosh(f*x + e)*sinh(f*x + e)^3 + (a + b)*sinh(f*x + e)^4 + 2*(3*a - b)*cosh(f*x + e)^2 + 2*(3*(a + b)*cosh(f*x + e)^2 + 3*a - b)*sinh(f*x + e)^2 - 2*sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 + 1)*sqrt(a)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + 4*((a + b)*cosh(f*x + e)^3 + (3*a - b)*cosh(f*x + e))*sinh(f*x + e) + a + b)/(cosh(f*x + e)^4 + 4*cosh(f*x + e)*sinh(f*x + e)^3 + sinh(f*x + e)^4 + 2*(3*cosh(f*x + e)^2 - 1)*sinh(f*x + e)^2 - 2*cosh(f*x + e)^2 + 4*(cosh(f*x + e)^3 - cosh(f*x + e))*sinh(f*x + e) + 1))/(sqrt(a)*f), sqrt(-a)*arctan(sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 + 1)*sqrt(-a)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/(b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(2*a - b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 2*a - b)*sinh(f*x + e)^2 + 4*(b*cosh(f*x + e)^3 + (2*a - b)*cosh(f*x + e))*sinh(f*x + e) + b))/(a*f)]","B",0
101,1,1285,0,1.089710," ","integrate(csch(f*x+e)^3/(a+b*sinh(f*x+e)^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(a + b\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(a + b\right)} \sinh\left(f x + e\right)^{4} - 2 \, {\left(a + b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(f x + e\right)^{2} - a - b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(f x + e\right)^{3} - {\left(a + b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + a + b\right)} \sqrt{a} \log\left(-\frac{{\left(a + b\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(a + b\right)} \sinh\left(f x + e\right)^{4} + 2 \, {\left(3 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(f x + e\right)^{2} + 3 \, a - b\right)} \sinh\left(f x + e\right)^{2} + 2 \, \sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} + 1\right)} \sqrt{a} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(f x + e\right)^{3} + {\left(3 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + a + b}{\cosh\left(f x + e\right)^{4} + 4 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + \sinh\left(f x + e\right)^{4} + 2 \, {\left(3 \, \cosh\left(f x + e\right)^{2} - 1\right)} \sinh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right)^{2} + 4 \, {\left(\cosh\left(f x + e\right)^{3} - \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + 1}\right) - 2 \, \sqrt{2} {\left(a \cosh\left(f x + e\right)^{2} + 2 \, a \cosh\left(f x + e\right) \sinh\left(f x + e\right) + a \sinh\left(f x + e\right)^{2} + a\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{4 \, {\left(a^{2} f \cosh\left(f x + e\right)^{4} + 4 \, a^{2} f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + a^{2} f \sinh\left(f x + e\right)^{4} - 2 \, a^{2} f \cosh\left(f x + e\right)^{2} + a^{2} f + 2 \, {\left(3 \, a^{2} f \cosh\left(f x + e\right)^{2} - a^{2} f\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(a^{2} f \cosh\left(f x + e\right)^{3} - a^{2} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)}}, -\frac{{\left({\left(a + b\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(a + b\right)} \sinh\left(f x + e\right)^{4} - 2 \, {\left(a + b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(f x + e\right)^{2} - a - b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(f x + e\right)^{3} - {\left(a + b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + a + b\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} + 1\right)} \sqrt{-a} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + 2 \, a - b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}\right) + \sqrt{2} {\left(a \cosh\left(f x + e\right)^{2} + 2 \, a \cosh\left(f x + e\right) \sinh\left(f x + e\right) + a \sinh\left(f x + e\right)^{2} + a\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{2 \, {\left(a^{2} f \cosh\left(f x + e\right)^{4} + 4 \, a^{2} f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + a^{2} f \sinh\left(f x + e\right)^{4} - 2 \, a^{2} f \cosh\left(f x + e\right)^{2} + a^{2} f + 2 \, {\left(3 \, a^{2} f \cosh\left(f x + e\right)^{2} - a^{2} f\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(a^{2} f \cosh\left(f x + e\right)^{3} - a^{2} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)}}\right]"," ",0,"[1/4*(((a + b)*cosh(f*x + e)^4 + 4*(a + b)*cosh(f*x + e)*sinh(f*x + e)^3 + (a + b)*sinh(f*x + e)^4 - 2*(a + b)*cosh(f*x + e)^2 + 2*(3*(a + b)*cosh(f*x + e)^2 - a - b)*sinh(f*x + e)^2 + 4*((a + b)*cosh(f*x + e)^3 - (a + b)*cosh(f*x + e))*sinh(f*x + e) + a + b)*sqrt(a)*log(-((a + b)*cosh(f*x + e)^4 + 4*(a + b)*cosh(f*x + e)*sinh(f*x + e)^3 + (a + b)*sinh(f*x + e)^4 + 2*(3*a - b)*cosh(f*x + e)^2 + 2*(3*(a + b)*cosh(f*x + e)^2 + 3*a - b)*sinh(f*x + e)^2 + 2*sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 + 1)*sqrt(a)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + 4*((a + b)*cosh(f*x + e)^3 + (3*a - b)*cosh(f*x + e))*sinh(f*x + e) + a + b)/(cosh(f*x + e)^4 + 4*cosh(f*x + e)*sinh(f*x + e)^3 + sinh(f*x + e)^4 + 2*(3*cosh(f*x + e)^2 - 1)*sinh(f*x + e)^2 - 2*cosh(f*x + e)^2 + 4*(cosh(f*x + e)^3 - cosh(f*x + e))*sinh(f*x + e) + 1)) - 2*sqrt(2)*(a*cosh(f*x + e)^2 + 2*a*cosh(f*x + e)*sinh(f*x + e) + a*sinh(f*x + e)^2 + a)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/(a^2*f*cosh(f*x + e)^4 + 4*a^2*f*cosh(f*x + e)*sinh(f*x + e)^3 + a^2*f*sinh(f*x + e)^4 - 2*a^2*f*cosh(f*x + e)^2 + a^2*f + 2*(3*a^2*f*cosh(f*x + e)^2 - a^2*f)*sinh(f*x + e)^2 + 4*(a^2*f*cosh(f*x + e)^3 - a^2*f*cosh(f*x + e))*sinh(f*x + e)), -1/2*(((a + b)*cosh(f*x + e)^4 + 4*(a + b)*cosh(f*x + e)*sinh(f*x + e)^3 + (a + b)*sinh(f*x + e)^4 - 2*(a + b)*cosh(f*x + e)^2 + 2*(3*(a + b)*cosh(f*x + e)^2 - a - b)*sinh(f*x + e)^2 + 4*((a + b)*cosh(f*x + e)^3 - (a + b)*cosh(f*x + e))*sinh(f*x + e) + a + b)*sqrt(-a)*arctan(sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 + 1)*sqrt(-a)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/(b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(2*a - b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 2*a - b)*sinh(f*x + e)^2 + 4*(b*cosh(f*x + e)^3 + (2*a - b)*cosh(f*x + e))*sinh(f*x + e) + b)) + sqrt(2)*(a*cosh(f*x + e)^2 + 2*a*cosh(f*x + e)*sinh(f*x + e) + a*sinh(f*x + e)^2 + a)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/(a^2*f*cosh(f*x + e)^4 + 4*a^2*f*cosh(f*x + e)*sinh(f*x + e)^3 + a^2*f*sinh(f*x + e)^4 - 2*a^2*f*cosh(f*x + e)^2 + a^2*f + 2*(3*a^2*f*cosh(f*x + e)^2 - a^2*f)*sinh(f*x + e)^2 + 4*(a^2*f*cosh(f*x + e)^3 - a^2*f*cosh(f*x + e))*sinh(f*x + e))]","B",0
102,0,0,0,1.892454," ","integrate(sinh(f*x+e)^4/(a+b*sinh(f*x+e)^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sinh\left(f x + e\right)^{4}}{\sqrt{b \sinh\left(f x + e\right)^{2} + a}}, x\right)"," ",0,"integral(sinh(f*x + e)^4/sqrt(b*sinh(f*x + e)^2 + a), x)","F",0
103,0,0,0,0.531202," ","integrate(sinh(f*x+e)^2/(a+b*sinh(f*x+e)^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sinh\left(f x + e\right)^{2}}{\sqrt{b \sinh\left(f x + e\right)^{2} + a}}, x\right)"," ",0,"integral(sinh(f*x + e)^2/sqrt(b*sinh(f*x + e)^2 + a), x)","F",0
104,0,0,0,2.433606," ","integrate(1/(a+b*sinh(f*x+e)^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{b \sinh\left(f x + e\right)^{2} + a}}, x\right)"," ",0,"integral(1/sqrt(b*sinh(f*x + e)^2 + a), x)","F",0
105,0,0,0,0.835256," ","integrate(csch(f*x+e)^2/(a+b*sinh(f*x+e)^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{csch}\left(f x + e\right)^{2}}{\sqrt{b \sinh\left(f x + e\right)^{2} + a}}, x\right)"," ",0,"integral(csch(f*x + e)^2/sqrt(b*sinh(f*x + e)^2 + a), x)","F",0
106,0,0,0,2.085546," ","integrate(csch(f*x+e)^4/(a+b*sinh(f*x+e)^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{csch}\left(f x + e\right)^{4}}{\sqrt{b \sinh\left(f x + e\right)^{2} + a}}, x\right)"," ",0,"integral(csch(f*x + e)^4/sqrt(b*sinh(f*x + e)^2 + a), x)","F",0
107,1,3038,0,1.105681," ","integrate(sinh(f*x+e)^3/(a+b*sinh(f*x+e)^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(a b - b^{2}\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left(a b - b^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(a b - b^{2}\right)} \sinh\left(f x + e\right)^{4} + 2 \, {\left(2 \, a^{2} - 3 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, {\left(a b - b^{2}\right)} \cosh\left(f x + e\right)^{2} + 2 \, a^{2} - 3 \, a b + b^{2}\right)} \sinh\left(f x + e\right)^{2} + a b - b^{2} + 4 \, {\left({\left(a b - b^{2}\right)} \cosh\left(f x + e\right)^{3} + {\left(2 \, a^{2} - 3 \, a b + b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{b} \log\left(\frac{a^{2} b \cosh\left(f x + e\right)^{8} + 8 \, a^{2} b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + a^{2} b \sinh\left(f x + e\right)^{8} + 2 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(f x + e\right)^{6} + 2 \, {\left(14 \, a^{2} b \cosh\left(f x + e\right)^{2} + a^{3} + a^{2} b\right)} \sinh\left(f x + e\right)^{6} + 4 \, {\left(14 \, a^{2} b \cosh\left(f x + e\right)^{3} + 3 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + {\left(9 \, a^{2} b - 4 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{4} + {\left(70 \, a^{2} b \cosh\left(f x + e\right)^{4} + 9 \, a^{2} b - 4 \, a b^{2} + b^{3} + 30 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(14 \, a^{2} b \cosh\left(f x + e\right)^{5} + 10 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(f x + e\right)^{3} + {\left(9 \, a^{2} b - 4 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + b^{3} + 2 \, {\left(3 \, a b^{2} - b^{3}\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(14 \, a^{2} b \cosh\left(f x + e\right)^{6} + 15 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(f x + e\right)^{4} + 3 \, a b^{2} - b^{3} + 3 \, {\left(9 \, a^{2} b - 4 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{2} + \sqrt{2} {\left(a^{2} \cosh\left(f x + e\right)^{6} + 6 \, a^{2} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + a^{2} \sinh\left(f x + e\right)^{6} + 3 \, a^{2} \cosh\left(f x + e\right)^{4} + 3 \, {\left(5 \, a^{2} \cosh\left(f x + e\right)^{2} + a^{2}\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(5 \, a^{2} \cosh\left(f x + e\right)^{3} + 3 \, a^{2} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + {\left(4 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{2} + {\left(15 \, a^{2} \cosh\left(f x + e\right)^{4} + 18 \, a^{2} \cosh\left(f x + e\right)^{2} + 4 \, a b - b^{2}\right)} \sinh\left(f x + e\right)^{2} + b^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(f x + e\right)^{5} + 6 \, a^{2} \cosh\left(f x + e\right)^{3} + {\left(4 \, a b - b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} + 4 \, {\left(2 \, a^{2} b \cosh\left(f x + e\right)^{7} + 3 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(f x + e\right)^{5} + {\left(9 \, a^{2} b - 4 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{3} + {\left(3 \, a b^{2} - b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)}{\cosh\left(f x + e\right)^{6} + 6 \, \cosh\left(f x + e\right)^{5} \sinh\left(f x + e\right) + 15 \, \cosh\left(f x + e\right)^{4} \sinh\left(f x + e\right)^{2} + 20 \, \cosh\left(f x + e\right)^{3} \sinh\left(f x + e\right)^{3} + 15 \, \cosh\left(f x + e\right)^{2} \sinh\left(f x + e\right)^{4} + 6 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + \sinh\left(f x + e\right)^{6}}\right) + {\left({\left(a b - b^{2}\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left(a b - b^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(a b - b^{2}\right)} \sinh\left(f x + e\right)^{4} + 2 \, {\left(2 \, a^{2} - 3 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, {\left(a b - b^{2}\right)} \cosh\left(f x + e\right)^{2} + 2 \, a^{2} - 3 \, a b + b^{2}\right)} \sinh\left(f x + e\right)^{2} + a b - b^{2} + 4 \, {\left({\left(a b - b^{2}\right)} \cosh\left(f x + e\right)^{3} + {\left(2 \, a^{2} - 3 \, a b + b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{b} \log\left(-\frac{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + a - b\right)} \sinh\left(f x + e\right)^{2} + \sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} - 1\right)} \sqrt{b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}{\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}\right) - 4 \, \sqrt{2} {\left(a b \cosh\left(f x + e\right)^{2} + 2 \, a b \cosh\left(f x + e\right) \sinh\left(f x + e\right) + a b \sinh\left(f x + e\right)^{2} + a b\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{4 \, {\left({\left(a b^{3} - b^{4}\right)} f \cosh\left(f x + e\right)^{4} + 4 \, {\left(a b^{3} - b^{4}\right)} f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(a b^{3} - b^{4}\right)} f \sinh\left(f x + e\right)^{4} + 2 \, {\left(2 \, a^{2} b^{2} - 3 \, a b^{3} + b^{4}\right)} f \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, {\left(a b^{3} - b^{4}\right)} f \cosh\left(f x + e\right)^{2} + {\left(2 \, a^{2} b^{2} - 3 \, a b^{3} + b^{4}\right)} f\right)} \sinh\left(f x + e\right)^{2} + {\left(a b^{3} - b^{4}\right)} f + 4 \, {\left({\left(a b^{3} - b^{4}\right)} f \cosh\left(f x + e\right)^{3} + {\left(2 \, a^{2} b^{2} - 3 \, a b^{3} + b^{4}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)}}, -\frac{{\left({\left(a b - b^{2}\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left(a b - b^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(a b - b^{2}\right)} \sinh\left(f x + e\right)^{4} + 2 \, {\left(2 \, a^{2} - 3 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, {\left(a b - b^{2}\right)} \cosh\left(f x + e\right)^{2} + 2 \, a^{2} - 3 \, a b + b^{2}\right)} \sinh\left(f x + e\right)^{2} + a b - b^{2} + 4 \, {\left({\left(a b - b^{2}\right)} \cosh\left(f x + e\right)^{3} + {\left(2 \, a^{2} - 3 \, a b + b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{2} {\left(a \cosh\left(f x + e\right)^{2} + 2 \, a \cosh\left(f x + e\right) \sinh\left(f x + e\right) + a \sinh\left(f x + e\right)^{2} + b\right)} \sqrt{-b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{a b \cosh\left(f x + e\right)^{4} + 4 \, a b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + a b \sinh\left(f x + e\right)^{4} + {\left(3 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{2} + {\left(6 \, a b \cosh\left(f x + e\right)^{2} + 3 \, a b - b^{2}\right)} \sinh\left(f x + e\right)^{2} + b^{2} + 2 \, {\left(2 \, a b \cosh\left(f x + e\right)^{3} + {\left(3 \, a b - b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)}\right) + {\left({\left(a b - b^{2}\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left(a b - b^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(a b - b^{2}\right)} \sinh\left(f x + e\right)^{4} + 2 \, {\left(2 \, a^{2} - 3 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, {\left(a b - b^{2}\right)} \cosh\left(f x + e\right)^{2} + 2 \, a^{2} - 3 \, a b + b^{2}\right)} \sinh\left(f x + e\right)^{2} + a b - b^{2} + 4 \, {\left({\left(a b - b^{2}\right)} \cosh\left(f x + e\right)^{3} + {\left(2 \, a^{2} - 3 \, a b + b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} - 1\right)} \sqrt{-b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + 2 \, a - b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}\right) + 2 \, \sqrt{2} {\left(a b \cosh\left(f x + e\right)^{2} + 2 \, a b \cosh\left(f x + e\right) \sinh\left(f x + e\right) + a b \sinh\left(f x + e\right)^{2} + a b\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{2 \, {\left({\left(a b^{3} - b^{4}\right)} f \cosh\left(f x + e\right)^{4} + 4 \, {\left(a b^{3} - b^{4}\right)} f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(a b^{3} - b^{4}\right)} f \sinh\left(f x + e\right)^{4} + 2 \, {\left(2 \, a^{2} b^{2} - 3 \, a b^{3} + b^{4}\right)} f \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, {\left(a b^{3} - b^{4}\right)} f \cosh\left(f x + e\right)^{2} + {\left(2 \, a^{2} b^{2} - 3 \, a b^{3} + b^{4}\right)} f\right)} \sinh\left(f x + e\right)^{2} + {\left(a b^{3} - b^{4}\right)} f + 4 \, {\left({\left(a b^{3} - b^{4}\right)} f \cosh\left(f x + e\right)^{3} + {\left(2 \, a^{2} b^{2} - 3 \, a b^{3} + b^{4}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)}}\right]"," ",0,"[1/4*(((a*b - b^2)*cosh(f*x + e)^4 + 4*(a*b - b^2)*cosh(f*x + e)*sinh(f*x + e)^3 + (a*b - b^2)*sinh(f*x + e)^4 + 2*(2*a^2 - 3*a*b + b^2)*cosh(f*x + e)^2 + 2*(3*(a*b - b^2)*cosh(f*x + e)^2 + 2*a^2 - 3*a*b + b^2)*sinh(f*x + e)^2 + a*b - b^2 + 4*((a*b - b^2)*cosh(f*x + e)^3 + (2*a^2 - 3*a*b + b^2)*cosh(f*x + e))*sinh(f*x + e))*sqrt(b)*log((a^2*b*cosh(f*x + e)^8 + 8*a^2*b*cosh(f*x + e)*sinh(f*x + e)^7 + a^2*b*sinh(f*x + e)^8 + 2*(a^3 + a^2*b)*cosh(f*x + e)^6 + 2*(14*a^2*b*cosh(f*x + e)^2 + a^3 + a^2*b)*sinh(f*x + e)^6 + 4*(14*a^2*b*cosh(f*x + e)^3 + 3*(a^3 + a^2*b)*cosh(f*x + e))*sinh(f*x + e)^5 + (9*a^2*b - 4*a*b^2 + b^3)*cosh(f*x + e)^4 + (70*a^2*b*cosh(f*x + e)^4 + 9*a^2*b - 4*a*b^2 + b^3 + 30*(a^3 + a^2*b)*cosh(f*x + e)^2)*sinh(f*x + e)^4 + 4*(14*a^2*b*cosh(f*x + e)^5 + 10*(a^3 + a^2*b)*cosh(f*x + e)^3 + (9*a^2*b - 4*a*b^2 + b^3)*cosh(f*x + e))*sinh(f*x + e)^3 + b^3 + 2*(3*a*b^2 - b^3)*cosh(f*x + e)^2 + 2*(14*a^2*b*cosh(f*x + e)^6 + 15*(a^3 + a^2*b)*cosh(f*x + e)^4 + 3*a*b^2 - b^3 + 3*(9*a^2*b - 4*a*b^2 + b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^2 + sqrt(2)*(a^2*cosh(f*x + e)^6 + 6*a^2*cosh(f*x + e)*sinh(f*x + e)^5 + a^2*sinh(f*x + e)^6 + 3*a^2*cosh(f*x + e)^4 + 3*(5*a^2*cosh(f*x + e)^2 + a^2)*sinh(f*x + e)^4 + 4*(5*a^2*cosh(f*x + e)^3 + 3*a^2*cosh(f*x + e))*sinh(f*x + e)^3 + (4*a*b - b^2)*cosh(f*x + e)^2 + (15*a^2*cosh(f*x + e)^4 + 18*a^2*cosh(f*x + e)^2 + 4*a*b - b^2)*sinh(f*x + e)^2 + b^2 + 2*(3*a^2*cosh(f*x + e)^5 + 6*a^2*cosh(f*x + e)^3 + (4*a*b - b^2)*cosh(f*x + e))*sinh(f*x + e))*sqrt(b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + 4*(2*a^2*b*cosh(f*x + e)^7 + 3*(a^3 + a^2*b)*cosh(f*x + e)^5 + (9*a^2*b - 4*a*b^2 + b^3)*cosh(f*x + e)^3 + (3*a*b^2 - b^3)*cosh(f*x + e))*sinh(f*x + e))/(cosh(f*x + e)^6 + 6*cosh(f*x + e)^5*sinh(f*x + e) + 15*cosh(f*x + e)^4*sinh(f*x + e)^2 + 20*cosh(f*x + e)^3*sinh(f*x + e)^3 + 15*cosh(f*x + e)^2*sinh(f*x + e)^4 + 6*cosh(f*x + e)*sinh(f*x + e)^5 + sinh(f*x + e)^6)) + ((a*b - b^2)*cosh(f*x + e)^4 + 4*(a*b - b^2)*cosh(f*x + e)*sinh(f*x + e)^3 + (a*b - b^2)*sinh(f*x + e)^4 + 2*(2*a^2 - 3*a*b + b^2)*cosh(f*x + e)^2 + 2*(3*(a*b - b^2)*cosh(f*x + e)^2 + 2*a^2 - 3*a*b + b^2)*sinh(f*x + e)^2 + a*b - b^2 + 4*((a*b - b^2)*cosh(f*x + e)^3 + (2*a^2 - 3*a*b + b^2)*cosh(f*x + e))*sinh(f*x + e))*sqrt(b)*log(-(b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(a - b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + a - b)*sinh(f*x + e)^2 + sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 - 1)*sqrt(b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + 4*(b*cosh(f*x + e)^3 + (a - b)*cosh(f*x + e))*sinh(f*x + e) + b)/(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) - 4*sqrt(2)*(a*b*cosh(f*x + e)^2 + 2*a*b*cosh(f*x + e)*sinh(f*x + e) + a*b*sinh(f*x + e)^2 + a*b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/((a*b^3 - b^4)*f*cosh(f*x + e)^4 + 4*(a*b^3 - b^4)*f*cosh(f*x + e)*sinh(f*x + e)^3 + (a*b^3 - b^4)*f*sinh(f*x + e)^4 + 2*(2*a^2*b^2 - 3*a*b^3 + b^4)*f*cosh(f*x + e)^2 + 2*(3*(a*b^3 - b^4)*f*cosh(f*x + e)^2 + (2*a^2*b^2 - 3*a*b^3 + b^4)*f)*sinh(f*x + e)^2 + (a*b^3 - b^4)*f + 4*((a*b^3 - b^4)*f*cosh(f*x + e)^3 + (2*a^2*b^2 - 3*a*b^3 + b^4)*f*cosh(f*x + e))*sinh(f*x + e)), -1/2*(((a*b - b^2)*cosh(f*x + e)^4 + 4*(a*b - b^2)*cosh(f*x + e)*sinh(f*x + e)^3 + (a*b - b^2)*sinh(f*x + e)^4 + 2*(2*a^2 - 3*a*b + b^2)*cosh(f*x + e)^2 + 2*(3*(a*b - b^2)*cosh(f*x + e)^2 + 2*a^2 - 3*a*b + b^2)*sinh(f*x + e)^2 + a*b - b^2 + 4*((a*b - b^2)*cosh(f*x + e)^3 + (2*a^2 - 3*a*b + b^2)*cosh(f*x + e))*sinh(f*x + e))*sqrt(-b)*arctan(sqrt(2)*(a*cosh(f*x + e)^2 + 2*a*cosh(f*x + e)*sinh(f*x + e) + a*sinh(f*x + e)^2 + b)*sqrt(-b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/(a*b*cosh(f*x + e)^4 + 4*a*b*cosh(f*x + e)*sinh(f*x + e)^3 + a*b*sinh(f*x + e)^4 + (3*a*b - b^2)*cosh(f*x + e)^2 + (6*a*b*cosh(f*x + e)^2 + 3*a*b - b^2)*sinh(f*x + e)^2 + b^2 + 2*(2*a*b*cosh(f*x + e)^3 + (3*a*b - b^2)*cosh(f*x + e))*sinh(f*x + e))) + ((a*b - b^2)*cosh(f*x + e)^4 + 4*(a*b - b^2)*cosh(f*x + e)*sinh(f*x + e)^3 + (a*b - b^2)*sinh(f*x + e)^4 + 2*(2*a^2 - 3*a*b + b^2)*cosh(f*x + e)^2 + 2*(3*(a*b - b^2)*cosh(f*x + e)^2 + 2*a^2 - 3*a*b + b^2)*sinh(f*x + e)^2 + a*b - b^2 + 4*((a*b - b^2)*cosh(f*x + e)^3 + (2*a^2 - 3*a*b + b^2)*cosh(f*x + e))*sinh(f*x + e))*sqrt(-b)*arctan(sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 - 1)*sqrt(-b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/(b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(2*a - b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 2*a - b)*sinh(f*x + e)^2 + 4*(b*cosh(f*x + e)^3 + (2*a - b)*cosh(f*x + e))*sinh(f*x + e) + b)) + 2*sqrt(2)*(a*b*cosh(f*x + e)^2 + 2*a*b*cosh(f*x + e)*sinh(f*x + e) + a*b*sinh(f*x + e)^2 + a*b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/((a*b^3 - b^4)*f*cosh(f*x + e)^4 + 4*(a*b^3 - b^4)*f*cosh(f*x + e)*sinh(f*x + e)^3 + (a*b^3 - b^4)*f*sinh(f*x + e)^4 + 2*(2*a^2*b^2 - 3*a*b^3 + b^4)*f*cosh(f*x + e)^2 + 2*(3*(a*b^3 - b^4)*f*cosh(f*x + e)^2 + (2*a^2*b^2 - 3*a*b^3 + b^4)*f)*sinh(f*x + e)^2 + (a*b^3 - b^4)*f + 4*((a*b^3 - b^4)*f*cosh(f*x + e)^3 + (2*a^2*b^2 - 3*a*b^3 + b^4)*f*cosh(f*x + e))*sinh(f*x + e))]","B",0
108,1,296,0,0.978832," ","integrate(sinh(f*x+e)/(a+b*sinh(f*x+e)^2)^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} + 1\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{{\left(a b - b^{2}\right)} f \cosh\left(f x + e\right)^{4} + 4 \, {\left(a b - b^{2}\right)} f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(a b - b^{2}\right)} f \sinh\left(f x + e\right)^{4} + 2 \, {\left(2 \, a^{2} - 3 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, {\left(a b - b^{2}\right)} f \cosh\left(f x + e\right)^{2} + {\left(2 \, a^{2} - 3 \, a b + b^{2}\right)} f\right)} \sinh\left(f x + e\right)^{2} + {\left(a b - b^{2}\right)} f + 4 \, {\left({\left(a b - b^{2}\right)} f \cosh\left(f x + e\right)^{3} + {\left(2 \, a^{2} - 3 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)}"," ",0,"sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 + 1)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/((a*b - b^2)*f*cosh(f*x + e)^4 + 4*(a*b - b^2)*f*cosh(f*x + e)*sinh(f*x + e)^3 + (a*b - b^2)*f*sinh(f*x + e)^4 + 2*(2*a^2 - 3*a*b + b^2)*f*cosh(f*x + e)^2 + 2*(3*(a*b - b^2)*f*cosh(f*x + e)^2 + (2*a^2 - 3*a*b + b^2)*f)*sinh(f*x + e)^2 + (a*b - b^2)*f + 4*((a*b - b^2)*f*cosh(f*x + e)^3 + (2*a^2 - 3*a*b + b^2)*f*cosh(f*x + e))*sinh(f*x + e))","B",0
109,1,1641,0,1.954044," ","integrate(csch(f*x+e)/(a+b*sinh(f*x+e)^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(a b - b^{2}\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left(a b - b^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(a b - b^{2}\right)} \sinh\left(f x + e\right)^{4} + 2 \, {\left(2 \, a^{2} - 3 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, {\left(a b - b^{2}\right)} \cosh\left(f x + e\right)^{2} + 2 \, a^{2} - 3 \, a b + b^{2}\right)} \sinh\left(f x + e\right)^{2} + a b - b^{2} + 4 \, {\left({\left(a b - b^{2}\right)} \cosh\left(f x + e\right)^{3} + {\left(2 \, a^{2} - 3 \, a b + b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{a} \log\left(-\frac{{\left(a + b\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(a + b\right)} \sinh\left(f x + e\right)^{4} + 2 \, {\left(3 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(f x + e\right)^{2} + 3 \, a - b\right)} \sinh\left(f x + e\right)^{2} - 2 \, \sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} + 1\right)} \sqrt{a} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(f x + e\right)^{3} + {\left(3 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + a + b}{\cosh\left(f x + e\right)^{4} + 4 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + \sinh\left(f x + e\right)^{4} + 2 \, {\left(3 \, \cosh\left(f x + e\right)^{2} - 1\right)} \sinh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right)^{2} + 4 \, {\left(\cosh\left(f x + e\right)^{3} - \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + 1}\right) - 2 \, \sqrt{2} {\left(a b \cosh\left(f x + e\right)^{2} + 2 \, a b \cosh\left(f x + e\right) \sinh\left(f x + e\right) + a b \sinh\left(f x + e\right)^{2} + a b\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{2 \, {\left({\left(a^{3} b - a^{2} b^{2}\right)} f \cosh\left(f x + e\right)^{4} + 4 \, {\left(a^{3} b - a^{2} b^{2}\right)} f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(a^{3} b - a^{2} b^{2}\right)} f \sinh\left(f x + e\right)^{4} + 2 \, {\left(2 \, a^{4} - 3 \, a^{3} b + a^{2} b^{2}\right)} f \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, {\left(a^{3} b - a^{2} b^{2}\right)} f \cosh\left(f x + e\right)^{2} + {\left(2 \, a^{4} - 3 \, a^{3} b + a^{2} b^{2}\right)} f\right)} \sinh\left(f x + e\right)^{2} + {\left(a^{3} b - a^{2} b^{2}\right)} f + 4 \, {\left({\left(a^{3} b - a^{2} b^{2}\right)} f \cosh\left(f x + e\right)^{3} + {\left(2 \, a^{4} - 3 \, a^{3} b + a^{2} b^{2}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)}}, \frac{{\left({\left(a b - b^{2}\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left(a b - b^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(a b - b^{2}\right)} \sinh\left(f x + e\right)^{4} + 2 \, {\left(2 \, a^{2} - 3 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, {\left(a b - b^{2}\right)} \cosh\left(f x + e\right)^{2} + 2 \, a^{2} - 3 \, a b + b^{2}\right)} \sinh\left(f x + e\right)^{2} + a b - b^{2} + 4 \, {\left({\left(a b - b^{2}\right)} \cosh\left(f x + e\right)^{3} + {\left(2 \, a^{2} - 3 \, a b + b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} + 1\right)} \sqrt{-a} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + 2 \, a - b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}\right) - \sqrt{2} {\left(a b \cosh\left(f x + e\right)^{2} + 2 \, a b \cosh\left(f x + e\right) \sinh\left(f x + e\right) + a b \sinh\left(f x + e\right)^{2} + a b\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{{\left(a^{3} b - a^{2} b^{2}\right)} f \cosh\left(f x + e\right)^{4} + 4 \, {\left(a^{3} b - a^{2} b^{2}\right)} f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(a^{3} b - a^{2} b^{2}\right)} f \sinh\left(f x + e\right)^{4} + 2 \, {\left(2 \, a^{4} - 3 \, a^{3} b + a^{2} b^{2}\right)} f \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, {\left(a^{3} b - a^{2} b^{2}\right)} f \cosh\left(f x + e\right)^{2} + {\left(2 \, a^{4} - 3 \, a^{3} b + a^{2} b^{2}\right)} f\right)} \sinh\left(f x + e\right)^{2} + {\left(a^{3} b - a^{2} b^{2}\right)} f + 4 \, {\left({\left(a^{3} b - a^{2} b^{2}\right)} f \cosh\left(f x + e\right)^{3} + {\left(2 \, a^{4} - 3 \, a^{3} b + a^{2} b^{2}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)}\right]"," ",0,"[1/2*(((a*b - b^2)*cosh(f*x + e)^4 + 4*(a*b - b^2)*cosh(f*x + e)*sinh(f*x + e)^3 + (a*b - b^2)*sinh(f*x + e)^4 + 2*(2*a^2 - 3*a*b + b^2)*cosh(f*x + e)^2 + 2*(3*(a*b - b^2)*cosh(f*x + e)^2 + 2*a^2 - 3*a*b + b^2)*sinh(f*x + e)^2 + a*b - b^2 + 4*((a*b - b^2)*cosh(f*x + e)^3 + (2*a^2 - 3*a*b + b^2)*cosh(f*x + e))*sinh(f*x + e))*sqrt(a)*log(-((a + b)*cosh(f*x + e)^4 + 4*(a + b)*cosh(f*x + e)*sinh(f*x + e)^3 + (a + b)*sinh(f*x + e)^4 + 2*(3*a - b)*cosh(f*x + e)^2 + 2*(3*(a + b)*cosh(f*x + e)^2 + 3*a - b)*sinh(f*x + e)^2 - 2*sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 + 1)*sqrt(a)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + 4*((a + b)*cosh(f*x + e)^3 + (3*a - b)*cosh(f*x + e))*sinh(f*x + e) + a + b)/(cosh(f*x + e)^4 + 4*cosh(f*x + e)*sinh(f*x + e)^3 + sinh(f*x + e)^4 + 2*(3*cosh(f*x + e)^2 - 1)*sinh(f*x + e)^2 - 2*cosh(f*x + e)^2 + 4*(cosh(f*x + e)^3 - cosh(f*x + e))*sinh(f*x + e) + 1)) - 2*sqrt(2)*(a*b*cosh(f*x + e)^2 + 2*a*b*cosh(f*x + e)*sinh(f*x + e) + a*b*sinh(f*x + e)^2 + a*b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/((a^3*b - a^2*b^2)*f*cosh(f*x + e)^4 + 4*(a^3*b - a^2*b^2)*f*cosh(f*x + e)*sinh(f*x + e)^3 + (a^3*b - a^2*b^2)*f*sinh(f*x + e)^4 + 2*(2*a^4 - 3*a^3*b + a^2*b^2)*f*cosh(f*x + e)^2 + 2*(3*(a^3*b - a^2*b^2)*f*cosh(f*x + e)^2 + (2*a^4 - 3*a^3*b + a^2*b^2)*f)*sinh(f*x + e)^2 + (a^3*b - a^2*b^2)*f + 4*((a^3*b - a^2*b^2)*f*cosh(f*x + e)^3 + (2*a^4 - 3*a^3*b + a^2*b^2)*f*cosh(f*x + e))*sinh(f*x + e)), (((a*b - b^2)*cosh(f*x + e)^4 + 4*(a*b - b^2)*cosh(f*x + e)*sinh(f*x + e)^3 + (a*b - b^2)*sinh(f*x + e)^4 + 2*(2*a^2 - 3*a*b + b^2)*cosh(f*x + e)^2 + 2*(3*(a*b - b^2)*cosh(f*x + e)^2 + 2*a^2 - 3*a*b + b^2)*sinh(f*x + e)^2 + a*b - b^2 + 4*((a*b - b^2)*cosh(f*x + e)^3 + (2*a^2 - 3*a*b + b^2)*cosh(f*x + e))*sinh(f*x + e))*sqrt(-a)*arctan(sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 + 1)*sqrt(-a)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/(b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(2*a - b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 2*a - b)*sinh(f*x + e)^2 + 4*(b*cosh(f*x + e)^3 + (2*a - b)*cosh(f*x + e))*sinh(f*x + e) + b)) - sqrt(2)*(a*b*cosh(f*x + e)^2 + 2*a*b*cosh(f*x + e)*sinh(f*x + e) + a*b*sinh(f*x + e)^2 + a*b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/((a^3*b - a^2*b^2)*f*cosh(f*x + e)^4 + 4*(a^3*b - a^2*b^2)*f*cosh(f*x + e)*sinh(f*x + e)^3 + (a^3*b - a^2*b^2)*f*sinh(f*x + e)^4 + 2*(2*a^4 - 3*a^3*b + a^2*b^2)*f*cosh(f*x + e)^2 + 2*(3*(a^3*b - a^2*b^2)*f*cosh(f*x + e)^2 + (2*a^4 - 3*a^3*b + a^2*b^2)*f)*sinh(f*x + e)^2 + (a^3*b - a^2*b^2)*f + 4*((a^3*b - a^2*b^2)*f*cosh(f*x + e)^3 + (2*a^4 - 3*a^3*b + a^2*b^2)*f*cosh(f*x + e))*sinh(f*x + e))]","B",0
110,1,4441,0,3.000304," ","integrate(csch(f*x+e)^3/(a+b*sinh(f*x+e)^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(a^{2} b + 2 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{8} + 8 \, {\left(a^{2} b + 2 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + {\left(a^{2} b + 2 \, a b^{2} - 3 \, b^{3}\right)} \sinh\left(f x + e\right)^{8} + 4 \, {\left(a^{3} + a^{2} b - 5 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{6} + 4 \, {\left(a^{3} + a^{2} b - 5 \, a b^{2} + 3 \, b^{3} + 7 \, {\left(a^{2} b + 2 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} b + 2 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(a^{3} + a^{2} b - 5 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} - 2 \, {\left(4 \, a^{3} + 5 \, a^{2} b - 18 \, a b^{2} + 9 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} b + 2 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} - 4 \, a^{3} - 5 \, a^{2} b + 18 \, a b^{2} - 9 \, b^{3} + 30 \, {\left(a^{3} + a^{2} b - 5 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} b + 2 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{5} + 10 \, {\left(a^{3} + a^{2} b - 5 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} - {\left(4 \, a^{3} + 5 \, a^{2} b - 18 \, a b^{2} + 9 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + a^{2} b + 2 \, a b^{2} - 3 \, b^{3} + 4 \, {\left(a^{3} + a^{2} b - 5 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} b + 2 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{6} + 15 \, {\left(a^{3} + a^{2} b - 5 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} + a^{3} + a^{2} b - 5 \, a b^{2} + 3 \, b^{3} - 3 \, {\left(4 \, a^{3} + 5 \, a^{2} b - 18 \, a b^{2} + 9 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{2} + 8 \, {\left({\left(a^{2} b + 2 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{7} + 3 \, {\left(a^{3} + a^{2} b - 5 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{5} - {\left(4 \, a^{3} + 5 \, a^{2} b - 18 \, a b^{2} + 9 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} + {\left(a^{3} + a^{2} b - 5 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{a} \log\left(-\frac{{\left(a + b\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(a + b\right)} \sinh\left(f x + e\right)^{4} + 2 \, {\left(3 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(f x + e\right)^{2} + 3 \, a - b\right)} \sinh\left(f x + e\right)^{2} + 2 \, \sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} + 1\right)} \sqrt{a} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(f x + e\right)^{3} + {\left(3 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + a + b}{\cosh\left(f x + e\right)^{4} + 4 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + \sinh\left(f x + e\right)^{4} + 2 \, {\left(3 \, \cosh\left(f x + e\right)^{2} - 1\right)} \sinh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right)^{2} + 4 \, {\left(\cosh\left(f x + e\right)^{3} - \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + 1}\right) - 2 \, \sqrt{2} {\left({\left(a^{2} b - 3 \, a b^{2}\right)} \cosh\left(f x + e\right)^{6} + 6 \, {\left(a^{2} b - 3 \, a b^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + {\left(a^{2} b - 3 \, a b^{2}\right)} \sinh\left(f x + e\right)^{6} + {\left(4 \, a^{3} - 5 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(f x + e\right)^{4} + {\left(4 \, a^{3} - 5 \, a^{2} b + 3 \, a b^{2} + 15 \, {\left(a^{2} b - 3 \, a b^{2}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(5 \, {\left(a^{2} b - 3 \, a b^{2}\right)} \cosh\left(f x + e\right)^{3} + {\left(4 \, a^{3} - 5 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + a^{2} b - 3 \, a b^{2} + {\left(4 \, a^{3} - 5 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(f x + e\right)^{2} + {\left(15 \, {\left(a^{2} b - 3 \, a b^{2}\right)} \cosh\left(f x + e\right)^{4} + 4 \, a^{3} - 5 \, a^{2} b + 3 \, a b^{2} + 6 \, {\left(4 \, a^{3} - 5 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} b - 3 \, a b^{2}\right)} \cosh\left(f x + e\right)^{5} + 2 \, {\left(4 \, a^{3} - 5 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(f x + e\right)^{3} + {\left(4 \, a^{3} - 5 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{4 \, {\left({\left(a^{4} b - a^{3} b^{2}\right)} f \cosh\left(f x + e\right)^{8} + 8 \, {\left(a^{4} b - a^{3} b^{2}\right)} f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + {\left(a^{4} b - a^{3} b^{2}\right)} f \sinh\left(f x + e\right)^{8} + 4 \, {\left(a^{5} - 2 \, a^{4} b + a^{3} b^{2}\right)} f \cosh\left(f x + e\right)^{6} + 4 \, {\left(7 \, {\left(a^{4} b - a^{3} b^{2}\right)} f \cosh\left(f x + e\right)^{2} + {\left(a^{5} - 2 \, a^{4} b + a^{3} b^{2}\right)} f\right)} \sinh\left(f x + e\right)^{6} - 2 \, {\left(4 \, a^{5} - 7 \, a^{4} b + 3 \, a^{3} b^{2}\right)} f \cosh\left(f x + e\right)^{4} + 8 \, {\left(7 \, {\left(a^{4} b - a^{3} b^{2}\right)} f \cosh\left(f x + e\right)^{3} + 3 \, {\left(a^{5} - 2 \, a^{4} b + a^{3} b^{2}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(35 \, {\left(a^{4} b - a^{3} b^{2}\right)} f \cosh\left(f x + e\right)^{4} + 30 \, {\left(a^{5} - 2 \, a^{4} b + a^{3} b^{2}\right)} f \cosh\left(f x + e\right)^{2} - {\left(4 \, a^{5} - 7 \, a^{4} b + 3 \, a^{3} b^{2}\right)} f\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(a^{5} - 2 \, a^{4} b + a^{3} b^{2}\right)} f \cosh\left(f x + e\right)^{2} + 8 \, {\left(7 \, {\left(a^{4} b - a^{3} b^{2}\right)} f \cosh\left(f x + e\right)^{5} + 10 \, {\left(a^{5} - 2 \, a^{4} b + a^{3} b^{2}\right)} f \cosh\left(f x + e\right)^{3} - {\left(4 \, a^{5} - 7 \, a^{4} b + 3 \, a^{3} b^{2}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 4 \, {\left(7 \, {\left(a^{4} b - a^{3} b^{2}\right)} f \cosh\left(f x + e\right)^{6} + 15 \, {\left(a^{5} - 2 \, a^{4} b + a^{3} b^{2}\right)} f \cosh\left(f x + e\right)^{4} - 3 \, {\left(4 \, a^{5} - 7 \, a^{4} b + 3 \, a^{3} b^{2}\right)} f \cosh\left(f x + e\right)^{2} + {\left(a^{5} - 2 \, a^{4} b + a^{3} b^{2}\right)} f\right)} \sinh\left(f x + e\right)^{2} + {\left(a^{4} b - a^{3} b^{2}\right)} f + 8 \, {\left({\left(a^{4} b - a^{3} b^{2}\right)} f \cosh\left(f x + e\right)^{7} + 3 \, {\left(a^{5} - 2 \, a^{4} b + a^{3} b^{2}\right)} f \cosh\left(f x + e\right)^{5} - {\left(4 \, a^{5} - 7 \, a^{4} b + 3 \, a^{3} b^{2}\right)} f \cosh\left(f x + e\right)^{3} + {\left(a^{5} - 2 \, a^{4} b + a^{3} b^{2}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)}}, -\frac{{\left({\left(a^{2} b + 2 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{8} + 8 \, {\left(a^{2} b + 2 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + {\left(a^{2} b + 2 \, a b^{2} - 3 \, b^{3}\right)} \sinh\left(f x + e\right)^{8} + 4 \, {\left(a^{3} + a^{2} b - 5 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{6} + 4 \, {\left(a^{3} + a^{2} b - 5 \, a b^{2} + 3 \, b^{3} + 7 \, {\left(a^{2} b + 2 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} b + 2 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(a^{3} + a^{2} b - 5 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} - 2 \, {\left(4 \, a^{3} + 5 \, a^{2} b - 18 \, a b^{2} + 9 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} b + 2 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} - 4 \, a^{3} - 5 \, a^{2} b + 18 \, a b^{2} - 9 \, b^{3} + 30 \, {\left(a^{3} + a^{2} b - 5 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} b + 2 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{5} + 10 \, {\left(a^{3} + a^{2} b - 5 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} - {\left(4 \, a^{3} + 5 \, a^{2} b - 18 \, a b^{2} + 9 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + a^{2} b + 2 \, a b^{2} - 3 \, b^{3} + 4 \, {\left(a^{3} + a^{2} b - 5 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} b + 2 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{6} + 15 \, {\left(a^{3} + a^{2} b - 5 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} + a^{3} + a^{2} b - 5 \, a b^{2} + 3 \, b^{3} - 3 \, {\left(4 \, a^{3} + 5 \, a^{2} b - 18 \, a b^{2} + 9 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{2} + 8 \, {\left({\left(a^{2} b + 2 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{7} + 3 \, {\left(a^{3} + a^{2} b - 5 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{5} - {\left(4 \, a^{3} + 5 \, a^{2} b - 18 \, a b^{2} + 9 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} + {\left(a^{3} + a^{2} b - 5 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} + 1\right)} \sqrt{-a} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + 2 \, a - b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}\right) + \sqrt{2} {\left({\left(a^{2} b - 3 \, a b^{2}\right)} \cosh\left(f x + e\right)^{6} + 6 \, {\left(a^{2} b - 3 \, a b^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + {\left(a^{2} b - 3 \, a b^{2}\right)} \sinh\left(f x + e\right)^{6} + {\left(4 \, a^{3} - 5 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(f x + e\right)^{4} + {\left(4 \, a^{3} - 5 \, a^{2} b + 3 \, a b^{2} + 15 \, {\left(a^{2} b - 3 \, a b^{2}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(5 \, {\left(a^{2} b - 3 \, a b^{2}\right)} \cosh\left(f x + e\right)^{3} + {\left(4 \, a^{3} - 5 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + a^{2} b - 3 \, a b^{2} + {\left(4 \, a^{3} - 5 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(f x + e\right)^{2} + {\left(15 \, {\left(a^{2} b - 3 \, a b^{2}\right)} \cosh\left(f x + e\right)^{4} + 4 \, a^{3} - 5 \, a^{2} b + 3 \, a b^{2} + 6 \, {\left(4 \, a^{3} - 5 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} b - 3 \, a b^{2}\right)} \cosh\left(f x + e\right)^{5} + 2 \, {\left(4 \, a^{3} - 5 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(f x + e\right)^{3} + {\left(4 \, a^{3} - 5 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{2 \, {\left({\left(a^{4} b - a^{3} b^{2}\right)} f \cosh\left(f x + e\right)^{8} + 8 \, {\left(a^{4} b - a^{3} b^{2}\right)} f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + {\left(a^{4} b - a^{3} b^{2}\right)} f \sinh\left(f x + e\right)^{8} + 4 \, {\left(a^{5} - 2 \, a^{4} b + a^{3} b^{2}\right)} f \cosh\left(f x + e\right)^{6} + 4 \, {\left(7 \, {\left(a^{4} b - a^{3} b^{2}\right)} f \cosh\left(f x + e\right)^{2} + {\left(a^{5} - 2 \, a^{4} b + a^{3} b^{2}\right)} f\right)} \sinh\left(f x + e\right)^{6} - 2 \, {\left(4 \, a^{5} - 7 \, a^{4} b + 3 \, a^{3} b^{2}\right)} f \cosh\left(f x + e\right)^{4} + 8 \, {\left(7 \, {\left(a^{4} b - a^{3} b^{2}\right)} f \cosh\left(f x + e\right)^{3} + 3 \, {\left(a^{5} - 2 \, a^{4} b + a^{3} b^{2}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(35 \, {\left(a^{4} b - a^{3} b^{2}\right)} f \cosh\left(f x + e\right)^{4} + 30 \, {\left(a^{5} - 2 \, a^{4} b + a^{3} b^{2}\right)} f \cosh\left(f x + e\right)^{2} - {\left(4 \, a^{5} - 7 \, a^{4} b + 3 \, a^{3} b^{2}\right)} f\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(a^{5} - 2 \, a^{4} b + a^{3} b^{2}\right)} f \cosh\left(f x + e\right)^{2} + 8 \, {\left(7 \, {\left(a^{4} b - a^{3} b^{2}\right)} f \cosh\left(f x + e\right)^{5} + 10 \, {\left(a^{5} - 2 \, a^{4} b + a^{3} b^{2}\right)} f \cosh\left(f x + e\right)^{3} - {\left(4 \, a^{5} - 7 \, a^{4} b + 3 \, a^{3} b^{2}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 4 \, {\left(7 \, {\left(a^{4} b - a^{3} b^{2}\right)} f \cosh\left(f x + e\right)^{6} + 15 \, {\left(a^{5} - 2 \, a^{4} b + a^{3} b^{2}\right)} f \cosh\left(f x + e\right)^{4} - 3 \, {\left(4 \, a^{5} - 7 \, a^{4} b + 3 \, a^{3} b^{2}\right)} f \cosh\left(f x + e\right)^{2} + {\left(a^{5} - 2 \, a^{4} b + a^{3} b^{2}\right)} f\right)} \sinh\left(f x + e\right)^{2} + {\left(a^{4} b - a^{3} b^{2}\right)} f + 8 \, {\left({\left(a^{4} b - a^{3} b^{2}\right)} f \cosh\left(f x + e\right)^{7} + 3 \, {\left(a^{5} - 2 \, a^{4} b + a^{3} b^{2}\right)} f \cosh\left(f x + e\right)^{5} - {\left(4 \, a^{5} - 7 \, a^{4} b + 3 \, a^{3} b^{2}\right)} f \cosh\left(f x + e\right)^{3} + {\left(a^{5} - 2 \, a^{4} b + a^{3} b^{2}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)}}\right]"," ",0,"[1/4*(((a^2*b + 2*a*b^2 - 3*b^3)*cosh(f*x + e)^8 + 8*(a^2*b + 2*a*b^2 - 3*b^3)*cosh(f*x + e)*sinh(f*x + e)^7 + (a^2*b + 2*a*b^2 - 3*b^3)*sinh(f*x + e)^8 + 4*(a^3 + a^2*b - 5*a*b^2 + 3*b^3)*cosh(f*x + e)^6 + 4*(a^3 + a^2*b - 5*a*b^2 + 3*b^3 + 7*(a^2*b + 2*a*b^2 - 3*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^6 + 8*(7*(a^2*b + 2*a*b^2 - 3*b^3)*cosh(f*x + e)^3 + 3*(a^3 + a^2*b - 5*a*b^2 + 3*b^3)*cosh(f*x + e))*sinh(f*x + e)^5 - 2*(4*a^3 + 5*a^2*b - 18*a*b^2 + 9*b^3)*cosh(f*x + e)^4 + 2*(35*(a^2*b + 2*a*b^2 - 3*b^3)*cosh(f*x + e)^4 - 4*a^3 - 5*a^2*b + 18*a*b^2 - 9*b^3 + 30*(a^3 + a^2*b - 5*a*b^2 + 3*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^4 + 8*(7*(a^2*b + 2*a*b^2 - 3*b^3)*cosh(f*x + e)^5 + 10*(a^3 + a^2*b - 5*a*b^2 + 3*b^3)*cosh(f*x + e)^3 - (4*a^3 + 5*a^2*b - 18*a*b^2 + 9*b^3)*cosh(f*x + e))*sinh(f*x + e)^3 + a^2*b + 2*a*b^2 - 3*b^3 + 4*(a^3 + a^2*b - 5*a*b^2 + 3*b^3)*cosh(f*x + e)^2 + 4*(7*(a^2*b + 2*a*b^2 - 3*b^3)*cosh(f*x + e)^6 + 15*(a^3 + a^2*b - 5*a*b^2 + 3*b^3)*cosh(f*x + e)^4 + a^3 + a^2*b - 5*a*b^2 + 3*b^3 - 3*(4*a^3 + 5*a^2*b - 18*a*b^2 + 9*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^2 + 8*((a^2*b + 2*a*b^2 - 3*b^3)*cosh(f*x + e)^7 + 3*(a^3 + a^2*b - 5*a*b^2 + 3*b^3)*cosh(f*x + e)^5 - (4*a^3 + 5*a^2*b - 18*a*b^2 + 9*b^3)*cosh(f*x + e)^3 + (a^3 + a^2*b - 5*a*b^2 + 3*b^3)*cosh(f*x + e))*sinh(f*x + e))*sqrt(a)*log(-((a + b)*cosh(f*x + e)^4 + 4*(a + b)*cosh(f*x + e)*sinh(f*x + e)^3 + (a + b)*sinh(f*x + e)^4 + 2*(3*a - b)*cosh(f*x + e)^2 + 2*(3*(a + b)*cosh(f*x + e)^2 + 3*a - b)*sinh(f*x + e)^2 + 2*sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 + 1)*sqrt(a)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + 4*((a + b)*cosh(f*x + e)^3 + (3*a - b)*cosh(f*x + e))*sinh(f*x + e) + a + b)/(cosh(f*x + e)^4 + 4*cosh(f*x + e)*sinh(f*x + e)^3 + sinh(f*x + e)^4 + 2*(3*cosh(f*x + e)^2 - 1)*sinh(f*x + e)^2 - 2*cosh(f*x + e)^2 + 4*(cosh(f*x + e)^3 - cosh(f*x + e))*sinh(f*x + e) + 1)) - 2*sqrt(2)*((a^2*b - 3*a*b^2)*cosh(f*x + e)^6 + 6*(a^2*b - 3*a*b^2)*cosh(f*x + e)*sinh(f*x + e)^5 + (a^2*b - 3*a*b^2)*sinh(f*x + e)^6 + (4*a^3 - 5*a^2*b + 3*a*b^2)*cosh(f*x + e)^4 + (4*a^3 - 5*a^2*b + 3*a*b^2 + 15*(a^2*b - 3*a*b^2)*cosh(f*x + e)^2)*sinh(f*x + e)^4 + 4*(5*(a^2*b - 3*a*b^2)*cosh(f*x + e)^3 + (4*a^3 - 5*a^2*b + 3*a*b^2)*cosh(f*x + e))*sinh(f*x + e)^3 + a^2*b - 3*a*b^2 + (4*a^3 - 5*a^2*b + 3*a*b^2)*cosh(f*x + e)^2 + (15*(a^2*b - 3*a*b^2)*cosh(f*x + e)^4 + 4*a^3 - 5*a^2*b + 3*a*b^2 + 6*(4*a^3 - 5*a^2*b + 3*a*b^2)*cosh(f*x + e)^2)*sinh(f*x + e)^2 + 2*(3*(a^2*b - 3*a*b^2)*cosh(f*x + e)^5 + 2*(4*a^3 - 5*a^2*b + 3*a*b^2)*cosh(f*x + e)^3 + (4*a^3 - 5*a^2*b + 3*a*b^2)*cosh(f*x + e))*sinh(f*x + e))*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/((a^4*b - a^3*b^2)*f*cosh(f*x + e)^8 + 8*(a^4*b - a^3*b^2)*f*cosh(f*x + e)*sinh(f*x + e)^7 + (a^4*b - a^3*b^2)*f*sinh(f*x + e)^8 + 4*(a^5 - 2*a^4*b + a^3*b^2)*f*cosh(f*x + e)^6 + 4*(7*(a^4*b - a^3*b^2)*f*cosh(f*x + e)^2 + (a^5 - 2*a^4*b + a^3*b^2)*f)*sinh(f*x + e)^6 - 2*(4*a^5 - 7*a^4*b + 3*a^3*b^2)*f*cosh(f*x + e)^4 + 8*(7*(a^4*b - a^3*b^2)*f*cosh(f*x + e)^3 + 3*(a^5 - 2*a^4*b + a^3*b^2)*f*cosh(f*x + e))*sinh(f*x + e)^5 + 2*(35*(a^4*b - a^3*b^2)*f*cosh(f*x + e)^4 + 30*(a^5 - 2*a^4*b + a^3*b^2)*f*cosh(f*x + e)^2 - (4*a^5 - 7*a^4*b + 3*a^3*b^2)*f)*sinh(f*x + e)^4 + 4*(a^5 - 2*a^4*b + a^3*b^2)*f*cosh(f*x + e)^2 + 8*(7*(a^4*b - a^3*b^2)*f*cosh(f*x + e)^5 + 10*(a^5 - 2*a^4*b + a^3*b^2)*f*cosh(f*x + e)^3 - (4*a^5 - 7*a^4*b + 3*a^3*b^2)*f*cosh(f*x + e))*sinh(f*x + e)^3 + 4*(7*(a^4*b - a^3*b^2)*f*cosh(f*x + e)^6 + 15*(a^5 - 2*a^4*b + a^3*b^2)*f*cosh(f*x + e)^4 - 3*(4*a^5 - 7*a^4*b + 3*a^3*b^2)*f*cosh(f*x + e)^2 + (a^5 - 2*a^4*b + a^3*b^2)*f)*sinh(f*x + e)^2 + (a^4*b - a^3*b^2)*f + 8*((a^4*b - a^3*b^2)*f*cosh(f*x + e)^7 + 3*(a^5 - 2*a^4*b + a^3*b^2)*f*cosh(f*x + e)^5 - (4*a^5 - 7*a^4*b + 3*a^3*b^2)*f*cosh(f*x + e)^3 + (a^5 - 2*a^4*b + a^3*b^2)*f*cosh(f*x + e))*sinh(f*x + e)), -1/2*(((a^2*b + 2*a*b^2 - 3*b^3)*cosh(f*x + e)^8 + 8*(a^2*b + 2*a*b^2 - 3*b^3)*cosh(f*x + e)*sinh(f*x + e)^7 + (a^2*b + 2*a*b^2 - 3*b^3)*sinh(f*x + e)^8 + 4*(a^3 + a^2*b - 5*a*b^2 + 3*b^3)*cosh(f*x + e)^6 + 4*(a^3 + a^2*b - 5*a*b^2 + 3*b^3 + 7*(a^2*b + 2*a*b^2 - 3*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^6 + 8*(7*(a^2*b + 2*a*b^2 - 3*b^3)*cosh(f*x + e)^3 + 3*(a^3 + a^2*b - 5*a*b^2 + 3*b^3)*cosh(f*x + e))*sinh(f*x + e)^5 - 2*(4*a^3 + 5*a^2*b - 18*a*b^2 + 9*b^3)*cosh(f*x + e)^4 + 2*(35*(a^2*b + 2*a*b^2 - 3*b^3)*cosh(f*x + e)^4 - 4*a^3 - 5*a^2*b + 18*a*b^2 - 9*b^3 + 30*(a^3 + a^2*b - 5*a*b^2 + 3*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^4 + 8*(7*(a^2*b + 2*a*b^2 - 3*b^3)*cosh(f*x + e)^5 + 10*(a^3 + a^2*b - 5*a*b^2 + 3*b^3)*cosh(f*x + e)^3 - (4*a^3 + 5*a^2*b - 18*a*b^2 + 9*b^3)*cosh(f*x + e))*sinh(f*x + e)^3 + a^2*b + 2*a*b^2 - 3*b^3 + 4*(a^3 + a^2*b - 5*a*b^2 + 3*b^3)*cosh(f*x + e)^2 + 4*(7*(a^2*b + 2*a*b^2 - 3*b^3)*cosh(f*x + e)^6 + 15*(a^3 + a^2*b - 5*a*b^2 + 3*b^3)*cosh(f*x + e)^4 + a^3 + a^2*b - 5*a*b^2 + 3*b^3 - 3*(4*a^3 + 5*a^2*b - 18*a*b^2 + 9*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^2 + 8*((a^2*b + 2*a*b^2 - 3*b^3)*cosh(f*x + e)^7 + 3*(a^3 + a^2*b - 5*a*b^2 + 3*b^3)*cosh(f*x + e)^5 - (4*a^3 + 5*a^2*b - 18*a*b^2 + 9*b^3)*cosh(f*x + e)^3 + (a^3 + a^2*b - 5*a*b^2 + 3*b^3)*cosh(f*x + e))*sinh(f*x + e))*sqrt(-a)*arctan(sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 + 1)*sqrt(-a)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/(b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(2*a - b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 2*a - b)*sinh(f*x + e)^2 + 4*(b*cosh(f*x + e)^3 + (2*a - b)*cosh(f*x + e))*sinh(f*x + e) + b)) + sqrt(2)*((a^2*b - 3*a*b^2)*cosh(f*x + e)^6 + 6*(a^2*b - 3*a*b^2)*cosh(f*x + e)*sinh(f*x + e)^5 + (a^2*b - 3*a*b^2)*sinh(f*x + e)^6 + (4*a^3 - 5*a^2*b + 3*a*b^2)*cosh(f*x + e)^4 + (4*a^3 - 5*a^2*b + 3*a*b^2 + 15*(a^2*b - 3*a*b^2)*cosh(f*x + e)^2)*sinh(f*x + e)^4 + 4*(5*(a^2*b - 3*a*b^2)*cosh(f*x + e)^3 + (4*a^3 - 5*a^2*b + 3*a*b^2)*cosh(f*x + e))*sinh(f*x + e)^3 + a^2*b - 3*a*b^2 + (4*a^3 - 5*a^2*b + 3*a*b^2)*cosh(f*x + e)^2 + (15*(a^2*b - 3*a*b^2)*cosh(f*x + e)^4 + 4*a^3 - 5*a^2*b + 3*a*b^2 + 6*(4*a^3 - 5*a^2*b + 3*a*b^2)*cosh(f*x + e)^2)*sinh(f*x + e)^2 + 2*(3*(a^2*b - 3*a*b^2)*cosh(f*x + e)^5 + 2*(4*a^3 - 5*a^2*b + 3*a*b^2)*cosh(f*x + e)^3 + (4*a^3 - 5*a^2*b + 3*a*b^2)*cosh(f*x + e))*sinh(f*x + e))*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/((a^4*b - a^3*b^2)*f*cosh(f*x + e)^8 + 8*(a^4*b - a^3*b^2)*f*cosh(f*x + e)*sinh(f*x + e)^7 + (a^4*b - a^3*b^2)*f*sinh(f*x + e)^8 + 4*(a^5 - 2*a^4*b + a^3*b^2)*f*cosh(f*x + e)^6 + 4*(7*(a^4*b - a^3*b^2)*f*cosh(f*x + e)^2 + (a^5 - 2*a^4*b + a^3*b^2)*f)*sinh(f*x + e)^6 - 2*(4*a^5 - 7*a^4*b + 3*a^3*b^2)*f*cosh(f*x + e)^4 + 8*(7*(a^4*b - a^3*b^2)*f*cosh(f*x + e)^3 + 3*(a^5 - 2*a^4*b + a^3*b^2)*f*cosh(f*x + e))*sinh(f*x + e)^5 + 2*(35*(a^4*b - a^3*b^2)*f*cosh(f*x + e)^4 + 30*(a^5 - 2*a^4*b + a^3*b^2)*f*cosh(f*x + e)^2 - (4*a^5 - 7*a^4*b + 3*a^3*b^2)*f)*sinh(f*x + e)^4 + 4*(a^5 - 2*a^4*b + a^3*b^2)*f*cosh(f*x + e)^2 + 8*(7*(a^4*b - a^3*b^2)*f*cosh(f*x + e)^5 + 10*(a^5 - 2*a^4*b + a^3*b^2)*f*cosh(f*x + e)^3 - (4*a^5 - 7*a^4*b + 3*a^3*b^2)*f*cosh(f*x + e))*sinh(f*x + e)^3 + 4*(7*(a^4*b - a^3*b^2)*f*cosh(f*x + e)^6 + 15*(a^5 - 2*a^4*b + a^3*b^2)*f*cosh(f*x + e)^4 - 3*(4*a^5 - 7*a^4*b + 3*a^3*b^2)*f*cosh(f*x + e)^2 + (a^5 - 2*a^4*b + a^3*b^2)*f)*sinh(f*x + e)^2 + (a^4*b - a^3*b^2)*f + 8*((a^4*b - a^3*b^2)*f*cosh(f*x + e)^7 + 3*(a^5 - 2*a^4*b + a^3*b^2)*f*cosh(f*x + e)^5 - (4*a^5 - 7*a^4*b + 3*a^3*b^2)*f*cosh(f*x + e)^3 + (a^5 - 2*a^4*b + a^3*b^2)*f*cosh(f*x + e))*sinh(f*x + e))]","B",0
111,0,0,0,2.926371," ","integrate(sinh(f*x+e)^6/(a+b*sinh(f*x+e)^2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sinh\left(f x + e\right)^{2} + a} \sinh\left(f x + e\right)^{6}}{b^{2} \sinh\left(f x + e\right)^{4} + 2 \, a b \sinh\left(f x + e\right)^{2} + a^{2}}, x\right)"," ",0,"integral(sqrt(b*sinh(f*x + e)^2 + a)*sinh(f*x + e)^6/(b^2*sinh(f*x + e)^4 + 2*a*b*sinh(f*x + e)^2 + a^2), x)","F",0
112,0,0,0,1.966620," ","integrate(sinh(f*x+e)^4/(a+b*sinh(f*x+e)^2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sinh\left(f x + e\right)^{2} + a} \sinh\left(f x + e\right)^{4}}{b^{2} \sinh\left(f x + e\right)^{4} + 2 \, a b \sinh\left(f x + e\right)^{2} + a^{2}}, x\right)"," ",0,"integral(sqrt(b*sinh(f*x + e)^2 + a)*sinh(f*x + e)^4/(b^2*sinh(f*x + e)^4 + 2*a*b*sinh(f*x + e)^2 + a^2), x)","F",0
113,0,0,0,2.731460," ","integrate(sinh(f*x+e)^2/(a+b*sinh(f*x+e)^2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sinh\left(f x + e\right)^{2} + a} \sinh\left(f x + e\right)^{2}}{b^{2} \sinh\left(f x + e\right)^{4} + 2 \, a b \sinh\left(f x + e\right)^{2} + a^{2}}, x\right)"," ",0,"integral(sqrt(b*sinh(f*x + e)^2 + a)*sinh(f*x + e)^2/(b^2*sinh(f*x + e)^4 + 2*a*b*sinh(f*x + e)^2 + a^2), x)","F",0
114,0,0,0,0.748428," ","integrate(1/(a+b*sinh(f*x+e)^2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sinh\left(f x + e\right)^{2} + a}}{b^{2} \sinh\left(f x + e\right)^{4} + 2 \, a b \sinh\left(f x + e\right)^{2} + a^{2}}, x\right)"," ",0,"integral(sqrt(b*sinh(f*x + e)^2 + a)/(b^2*sinh(f*x + e)^4 + 2*a*b*sinh(f*x + e)^2 + a^2), x)","F",0
115,0,0,0,3.194289," ","integrate(csch(f*x+e)^2/(a+b*sinh(f*x+e)^2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sinh\left(f x + e\right)^{2} + a} \operatorname{csch}\left(f x + e\right)^{2}}{b^{2} \sinh\left(f x + e\right)^{4} + 2 \, a b \sinh\left(f x + e\right)^{2} + a^{2}}, x\right)"," ",0,"integral(sqrt(b*sinh(f*x + e)^2 + a)*csch(f*x + e)^2/(b^2*sinh(f*x + e)^4 + 2*a*b*sinh(f*x + e)^2 + a^2), x)","F",0
116,1,7938,0,5.989821," ","integrate(sinh(f*x+e)^5/(a+b*sinh(f*x+e)^2)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \cosh\left(f x + e\right)^{8} + 8 \, {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \sinh\left(f x + e\right)^{8} + 4 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} \cosh\left(f x + e\right)^{6} + 4 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4} + 7 \, {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(8 \, a^{4} - 24 \, a^{3} b + 27 \, a^{2} b^{2} - 14 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(f x + e\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \cosh\left(f x + e\right)^{4} + 8 \, a^{4} - 24 \, a^{3} b + 27 \, a^{2} b^{2} - 14 \, a b^{3} + 3 \, b^{4} + 30 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{4} + a^{2} b^{2} - 2 \, a b^{3} + b^{4} + 8 \, {\left(7 \, {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \cosh\left(f x + e\right)^{5} + 10 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} \cosh\left(f x + e\right)^{3} + {\left(8 \, a^{4} - 24 \, a^{3} b + 27 \, a^{2} b^{2} - 14 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 4 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} \cosh\left(f x + e\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \cosh\left(f x + e\right)^{6} + 15 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} \cosh\left(f x + e\right)^{4} + 2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4} + 3 \, {\left(8 \, a^{4} - 24 \, a^{3} b + 27 \, a^{2} b^{2} - 14 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{2} + 8 \, {\left({\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \cosh\left(f x + e\right)^{7} + 3 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} \cosh\left(f x + e\right)^{5} + {\left(8 \, a^{4} - 24 \, a^{3} b + 27 \, a^{2} b^{2} - 14 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(f x + e\right)^{3} + {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{b} \log\left(\frac{a^{2} b \cosh\left(f x + e\right)^{8} + 8 \, a^{2} b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + a^{2} b \sinh\left(f x + e\right)^{8} + 2 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(f x + e\right)^{6} + 2 \, {\left(14 \, a^{2} b \cosh\left(f x + e\right)^{2} + a^{3} + a^{2} b\right)} \sinh\left(f x + e\right)^{6} + 4 \, {\left(14 \, a^{2} b \cosh\left(f x + e\right)^{3} + 3 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + {\left(9 \, a^{2} b - 4 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{4} + {\left(70 \, a^{2} b \cosh\left(f x + e\right)^{4} + 9 \, a^{2} b - 4 \, a b^{2} + b^{3} + 30 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(14 \, a^{2} b \cosh\left(f x + e\right)^{5} + 10 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(f x + e\right)^{3} + {\left(9 \, a^{2} b - 4 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + b^{3} + 2 \, {\left(3 \, a b^{2} - b^{3}\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(14 \, a^{2} b \cosh\left(f x + e\right)^{6} + 15 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(f x + e\right)^{4} + 3 \, a b^{2} - b^{3} + 3 \, {\left(9 \, a^{2} b - 4 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{2} + \sqrt{2} {\left(a^{2} \cosh\left(f x + e\right)^{6} + 6 \, a^{2} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + a^{2} \sinh\left(f x + e\right)^{6} + 3 \, a^{2} \cosh\left(f x + e\right)^{4} + 3 \, {\left(5 \, a^{2} \cosh\left(f x + e\right)^{2} + a^{2}\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(5 \, a^{2} \cosh\left(f x + e\right)^{3} + 3 \, a^{2} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + {\left(4 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{2} + {\left(15 \, a^{2} \cosh\left(f x + e\right)^{4} + 18 \, a^{2} \cosh\left(f x + e\right)^{2} + 4 \, a b - b^{2}\right)} \sinh\left(f x + e\right)^{2} + b^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(f x + e\right)^{5} + 6 \, a^{2} \cosh\left(f x + e\right)^{3} + {\left(4 \, a b - b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} + 4 \, {\left(2 \, a^{2} b \cosh\left(f x + e\right)^{7} + 3 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(f x + e\right)^{5} + {\left(9 \, a^{2} b - 4 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{3} + {\left(3 \, a b^{2} - b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)}{\cosh\left(f x + e\right)^{6} + 6 \, \cosh\left(f x + e\right)^{5} \sinh\left(f x + e\right) + 15 \, \cosh\left(f x + e\right)^{4} \sinh\left(f x + e\right)^{2} + 20 \, \cosh\left(f x + e\right)^{3} \sinh\left(f x + e\right)^{3} + 15 \, \cosh\left(f x + e\right)^{2} \sinh\left(f x + e\right)^{4} + 6 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + \sinh\left(f x + e\right)^{6}}\right) + 3 \, {\left({\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \cosh\left(f x + e\right)^{8} + 8 \, {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \sinh\left(f x + e\right)^{8} + 4 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} \cosh\left(f x + e\right)^{6} + 4 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4} + 7 \, {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(8 \, a^{4} - 24 \, a^{3} b + 27 \, a^{2} b^{2} - 14 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(f x + e\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \cosh\left(f x + e\right)^{4} + 8 \, a^{4} - 24 \, a^{3} b + 27 \, a^{2} b^{2} - 14 \, a b^{3} + 3 \, b^{4} + 30 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{4} + a^{2} b^{2} - 2 \, a b^{3} + b^{4} + 8 \, {\left(7 \, {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \cosh\left(f x + e\right)^{5} + 10 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} \cosh\left(f x + e\right)^{3} + {\left(8 \, a^{4} - 24 \, a^{3} b + 27 \, a^{2} b^{2} - 14 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 4 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} \cosh\left(f x + e\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \cosh\left(f x + e\right)^{6} + 15 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} \cosh\left(f x + e\right)^{4} + 2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4} + 3 \, {\left(8 \, a^{4} - 24 \, a^{3} b + 27 \, a^{2} b^{2} - 14 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{2} + 8 \, {\left({\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \cosh\left(f x + e\right)^{7} + 3 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} \cosh\left(f x + e\right)^{5} + {\left(8 \, a^{4} - 24 \, a^{3} b + 27 \, a^{2} b^{2} - 14 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(f x + e\right)^{3} + {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{b} \log\left(-\frac{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + a - b\right)} \sinh\left(f x + e\right)^{2} + \sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} - 1\right)} \sqrt{b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}{\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}\right) - 8 \, \sqrt{2} {\left({\left(2 \, a^{2} b^{2} - 3 \, a b^{3}\right)} \cosh\left(f x + e\right)^{6} + 6 \, {\left(2 \, a^{2} b^{2} - 3 \, a b^{3}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + {\left(2 \, a^{2} b^{2} - 3 \, a b^{3}\right)} \sinh\left(f x + e\right)^{6} + 3 \, {\left(2 \, a^{3} b - 4 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(f x + e\right)^{4} + 3 \, {\left(2 \, a^{3} b - 4 \, a^{2} b^{2} + a b^{3} + 5 \, {\left(2 \, a^{2} b^{2} - 3 \, a b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{4} + 2 \, a^{2} b^{2} - 3 \, a b^{3} + 4 \, {\left(5 \, {\left(2 \, a^{2} b^{2} - 3 \, a b^{3}\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(2 \, a^{3} b - 4 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 3 \, {\left(2 \, a^{3} b - 4 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(f x + e\right)^{2} + 3 \, {\left(5 \, {\left(2 \, a^{2} b^{2} - 3 \, a b^{3}\right)} \cosh\left(f x + e\right)^{4} + 2 \, a^{3} b - 4 \, a^{2} b^{2} + a b^{3} + 6 \, {\left(2 \, a^{3} b - 4 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{2} + 6 \, {\left({\left(2 \, a^{2} b^{2} - 3 \, a b^{3}\right)} \cosh\left(f x + e\right)^{5} + 2 \, {\left(2 \, a^{3} b - 4 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(f x + e\right)^{3} + {\left(2 \, a^{3} b - 4 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{12 \, {\left({\left(a^{2} b^{5} - 2 \, a b^{6} + b^{7}\right)} f \cosh\left(f x + e\right)^{8} + 8 \, {\left(a^{2} b^{5} - 2 \, a b^{6} + b^{7}\right)} f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + {\left(a^{2} b^{5} - 2 \, a b^{6} + b^{7}\right)} f \sinh\left(f x + e\right)^{8} + 4 \, {\left(2 \, a^{3} b^{4} - 5 \, a^{2} b^{5} + 4 \, a b^{6} - b^{7}\right)} f \cosh\left(f x + e\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} b^{5} - 2 \, a b^{6} + b^{7}\right)} f \cosh\left(f x + e\right)^{2} + {\left(2 \, a^{3} b^{4} - 5 \, a^{2} b^{5} + 4 \, a b^{6} - b^{7}\right)} f\right)} \sinh\left(f x + e\right)^{6} + 2 \, {\left(8 \, a^{4} b^{3} - 24 \, a^{3} b^{4} + 27 \, a^{2} b^{5} - 14 \, a b^{6} + 3 \, b^{7}\right)} f \cosh\left(f x + e\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} b^{5} - 2 \, a b^{6} + b^{7}\right)} f \cosh\left(f x + e\right)^{3} + 3 \, {\left(2 \, a^{3} b^{4} - 5 \, a^{2} b^{5} + 4 \, a b^{6} - b^{7}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(35 \, {\left(a^{2} b^{5} - 2 \, a b^{6} + b^{7}\right)} f \cosh\left(f x + e\right)^{4} + 30 \, {\left(2 \, a^{3} b^{4} - 5 \, a^{2} b^{5} + 4 \, a b^{6} - b^{7}\right)} f \cosh\left(f x + e\right)^{2} + {\left(8 \, a^{4} b^{3} - 24 \, a^{3} b^{4} + 27 \, a^{2} b^{5} - 14 \, a b^{6} + 3 \, b^{7}\right)} f\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(2 \, a^{3} b^{4} - 5 \, a^{2} b^{5} + 4 \, a b^{6} - b^{7}\right)} f \cosh\left(f x + e\right)^{2} + 8 \, {\left(7 \, {\left(a^{2} b^{5} - 2 \, a b^{6} + b^{7}\right)} f \cosh\left(f x + e\right)^{5} + 10 \, {\left(2 \, a^{3} b^{4} - 5 \, a^{2} b^{5} + 4 \, a b^{6} - b^{7}\right)} f \cosh\left(f x + e\right)^{3} + {\left(8 \, a^{4} b^{3} - 24 \, a^{3} b^{4} + 27 \, a^{2} b^{5} - 14 \, a b^{6} + 3 \, b^{7}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 4 \, {\left(7 \, {\left(a^{2} b^{5} - 2 \, a b^{6} + b^{7}\right)} f \cosh\left(f x + e\right)^{6} + 15 \, {\left(2 \, a^{3} b^{4} - 5 \, a^{2} b^{5} + 4 \, a b^{6} - b^{7}\right)} f \cosh\left(f x + e\right)^{4} + 3 \, {\left(8 \, a^{4} b^{3} - 24 \, a^{3} b^{4} + 27 \, a^{2} b^{5} - 14 \, a b^{6} + 3 \, b^{7}\right)} f \cosh\left(f x + e\right)^{2} + {\left(2 \, a^{3} b^{4} - 5 \, a^{2} b^{5} + 4 \, a b^{6} - b^{7}\right)} f\right)} \sinh\left(f x + e\right)^{2} + {\left(a^{2} b^{5} - 2 \, a b^{6} + b^{7}\right)} f + 8 \, {\left({\left(a^{2} b^{5} - 2 \, a b^{6} + b^{7}\right)} f \cosh\left(f x + e\right)^{7} + 3 \, {\left(2 \, a^{3} b^{4} - 5 \, a^{2} b^{5} + 4 \, a b^{6} - b^{7}\right)} f \cosh\left(f x + e\right)^{5} + {\left(8 \, a^{4} b^{3} - 24 \, a^{3} b^{4} + 27 \, a^{2} b^{5} - 14 \, a b^{6} + 3 \, b^{7}\right)} f \cosh\left(f x + e\right)^{3} + {\left(2 \, a^{3} b^{4} - 5 \, a^{2} b^{5} + 4 \, a b^{6} - b^{7}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)}}, -\frac{3 \, {\left({\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \cosh\left(f x + e\right)^{8} + 8 \, {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \sinh\left(f x + e\right)^{8} + 4 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} \cosh\left(f x + e\right)^{6} + 4 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4} + 7 \, {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(8 \, a^{4} - 24 \, a^{3} b + 27 \, a^{2} b^{2} - 14 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(f x + e\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \cosh\left(f x + e\right)^{4} + 8 \, a^{4} - 24 \, a^{3} b + 27 \, a^{2} b^{2} - 14 \, a b^{3} + 3 \, b^{4} + 30 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{4} + a^{2} b^{2} - 2 \, a b^{3} + b^{4} + 8 \, {\left(7 \, {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \cosh\left(f x + e\right)^{5} + 10 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} \cosh\left(f x + e\right)^{3} + {\left(8 \, a^{4} - 24 \, a^{3} b + 27 \, a^{2} b^{2} - 14 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 4 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} \cosh\left(f x + e\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \cosh\left(f x + e\right)^{6} + 15 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} \cosh\left(f x + e\right)^{4} + 2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4} + 3 \, {\left(8 \, a^{4} - 24 \, a^{3} b + 27 \, a^{2} b^{2} - 14 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{2} + 8 \, {\left({\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \cosh\left(f x + e\right)^{7} + 3 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} \cosh\left(f x + e\right)^{5} + {\left(8 \, a^{4} - 24 \, a^{3} b + 27 \, a^{2} b^{2} - 14 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(f x + e\right)^{3} + {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{2} {\left(a \cosh\left(f x + e\right)^{2} + 2 \, a \cosh\left(f x + e\right) \sinh\left(f x + e\right) + a \sinh\left(f x + e\right)^{2} + b\right)} \sqrt{-b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{a b \cosh\left(f x + e\right)^{4} + 4 \, a b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + a b \sinh\left(f x + e\right)^{4} + {\left(3 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{2} + {\left(6 \, a b \cosh\left(f x + e\right)^{2} + 3 \, a b - b^{2}\right)} \sinh\left(f x + e\right)^{2} + b^{2} + 2 \, {\left(2 \, a b \cosh\left(f x + e\right)^{3} + {\left(3 \, a b - b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)}\right) + 3 \, {\left({\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \cosh\left(f x + e\right)^{8} + 8 \, {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \sinh\left(f x + e\right)^{8} + 4 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} \cosh\left(f x + e\right)^{6} + 4 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4} + 7 \, {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(8 \, a^{4} - 24 \, a^{3} b + 27 \, a^{2} b^{2} - 14 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(f x + e\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \cosh\left(f x + e\right)^{4} + 8 \, a^{4} - 24 \, a^{3} b + 27 \, a^{2} b^{2} - 14 \, a b^{3} + 3 \, b^{4} + 30 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{4} + a^{2} b^{2} - 2 \, a b^{3} + b^{4} + 8 \, {\left(7 \, {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \cosh\left(f x + e\right)^{5} + 10 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} \cosh\left(f x + e\right)^{3} + {\left(8 \, a^{4} - 24 \, a^{3} b + 27 \, a^{2} b^{2} - 14 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 4 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} \cosh\left(f x + e\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \cosh\left(f x + e\right)^{6} + 15 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} \cosh\left(f x + e\right)^{4} + 2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4} + 3 \, {\left(8 \, a^{4} - 24 \, a^{3} b + 27 \, a^{2} b^{2} - 14 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{2} + 8 \, {\left({\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \cosh\left(f x + e\right)^{7} + 3 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} \cosh\left(f x + e\right)^{5} + {\left(8 \, a^{4} - 24 \, a^{3} b + 27 \, a^{2} b^{2} - 14 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(f x + e\right)^{3} + {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} - 1\right)} \sqrt{-b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + 2 \, a - b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}\right) + 4 \, \sqrt{2} {\left({\left(2 \, a^{2} b^{2} - 3 \, a b^{3}\right)} \cosh\left(f x + e\right)^{6} + 6 \, {\left(2 \, a^{2} b^{2} - 3 \, a b^{3}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + {\left(2 \, a^{2} b^{2} - 3 \, a b^{3}\right)} \sinh\left(f x + e\right)^{6} + 3 \, {\left(2 \, a^{3} b - 4 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(f x + e\right)^{4} + 3 \, {\left(2 \, a^{3} b - 4 \, a^{2} b^{2} + a b^{3} + 5 \, {\left(2 \, a^{2} b^{2} - 3 \, a b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{4} + 2 \, a^{2} b^{2} - 3 \, a b^{3} + 4 \, {\left(5 \, {\left(2 \, a^{2} b^{2} - 3 \, a b^{3}\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(2 \, a^{3} b - 4 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 3 \, {\left(2 \, a^{3} b - 4 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(f x + e\right)^{2} + 3 \, {\left(5 \, {\left(2 \, a^{2} b^{2} - 3 \, a b^{3}\right)} \cosh\left(f x + e\right)^{4} + 2 \, a^{3} b - 4 \, a^{2} b^{2} + a b^{3} + 6 \, {\left(2 \, a^{3} b - 4 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{2} + 6 \, {\left({\left(2 \, a^{2} b^{2} - 3 \, a b^{3}\right)} \cosh\left(f x + e\right)^{5} + 2 \, {\left(2 \, a^{3} b - 4 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(f x + e\right)^{3} + {\left(2 \, a^{3} b - 4 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{6 \, {\left({\left(a^{2} b^{5} - 2 \, a b^{6} + b^{7}\right)} f \cosh\left(f x + e\right)^{8} + 8 \, {\left(a^{2} b^{5} - 2 \, a b^{6} + b^{7}\right)} f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + {\left(a^{2} b^{5} - 2 \, a b^{6} + b^{7}\right)} f \sinh\left(f x + e\right)^{8} + 4 \, {\left(2 \, a^{3} b^{4} - 5 \, a^{2} b^{5} + 4 \, a b^{6} - b^{7}\right)} f \cosh\left(f x + e\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} b^{5} - 2 \, a b^{6} + b^{7}\right)} f \cosh\left(f x + e\right)^{2} + {\left(2 \, a^{3} b^{4} - 5 \, a^{2} b^{5} + 4 \, a b^{6} - b^{7}\right)} f\right)} \sinh\left(f x + e\right)^{6} + 2 \, {\left(8 \, a^{4} b^{3} - 24 \, a^{3} b^{4} + 27 \, a^{2} b^{5} - 14 \, a b^{6} + 3 \, b^{7}\right)} f \cosh\left(f x + e\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} b^{5} - 2 \, a b^{6} + b^{7}\right)} f \cosh\left(f x + e\right)^{3} + 3 \, {\left(2 \, a^{3} b^{4} - 5 \, a^{2} b^{5} + 4 \, a b^{6} - b^{7}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(35 \, {\left(a^{2} b^{5} - 2 \, a b^{6} + b^{7}\right)} f \cosh\left(f x + e\right)^{4} + 30 \, {\left(2 \, a^{3} b^{4} - 5 \, a^{2} b^{5} + 4 \, a b^{6} - b^{7}\right)} f \cosh\left(f x + e\right)^{2} + {\left(8 \, a^{4} b^{3} - 24 \, a^{3} b^{4} + 27 \, a^{2} b^{5} - 14 \, a b^{6} + 3 \, b^{7}\right)} f\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(2 \, a^{3} b^{4} - 5 \, a^{2} b^{5} + 4 \, a b^{6} - b^{7}\right)} f \cosh\left(f x + e\right)^{2} + 8 \, {\left(7 \, {\left(a^{2} b^{5} - 2 \, a b^{6} + b^{7}\right)} f \cosh\left(f x + e\right)^{5} + 10 \, {\left(2 \, a^{3} b^{4} - 5 \, a^{2} b^{5} + 4 \, a b^{6} - b^{7}\right)} f \cosh\left(f x + e\right)^{3} + {\left(8 \, a^{4} b^{3} - 24 \, a^{3} b^{4} + 27 \, a^{2} b^{5} - 14 \, a b^{6} + 3 \, b^{7}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 4 \, {\left(7 \, {\left(a^{2} b^{5} - 2 \, a b^{6} + b^{7}\right)} f \cosh\left(f x + e\right)^{6} + 15 \, {\left(2 \, a^{3} b^{4} - 5 \, a^{2} b^{5} + 4 \, a b^{6} - b^{7}\right)} f \cosh\left(f x + e\right)^{4} + 3 \, {\left(8 \, a^{4} b^{3} - 24 \, a^{3} b^{4} + 27 \, a^{2} b^{5} - 14 \, a b^{6} + 3 \, b^{7}\right)} f \cosh\left(f x + e\right)^{2} + {\left(2 \, a^{3} b^{4} - 5 \, a^{2} b^{5} + 4 \, a b^{6} - b^{7}\right)} f\right)} \sinh\left(f x + e\right)^{2} + {\left(a^{2} b^{5} - 2 \, a b^{6} + b^{7}\right)} f + 8 \, {\left({\left(a^{2} b^{5} - 2 \, a b^{6} + b^{7}\right)} f \cosh\left(f x + e\right)^{7} + 3 \, {\left(2 \, a^{3} b^{4} - 5 \, a^{2} b^{5} + 4 \, a b^{6} - b^{7}\right)} f \cosh\left(f x + e\right)^{5} + {\left(8 \, a^{4} b^{3} - 24 \, a^{3} b^{4} + 27 \, a^{2} b^{5} - 14 \, a b^{6} + 3 \, b^{7}\right)} f \cosh\left(f x + e\right)^{3} + {\left(2 \, a^{3} b^{4} - 5 \, a^{2} b^{5} + 4 \, a b^{6} - b^{7}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)}}\right]"," ",0,"[1/12*(3*((a^2*b^2 - 2*a*b^3 + b^4)*cosh(f*x + e)^8 + 8*(a^2*b^2 - 2*a*b^3 + b^4)*cosh(f*x + e)*sinh(f*x + e)^7 + (a^2*b^2 - 2*a*b^3 + b^4)*sinh(f*x + e)^8 + 4*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*cosh(f*x + e)^6 + 4*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4 + 7*(a^2*b^2 - 2*a*b^3 + b^4)*cosh(f*x + e)^2)*sinh(f*x + e)^6 + 8*(7*(a^2*b^2 - 2*a*b^3 + b^4)*cosh(f*x + e)^3 + 3*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*cosh(f*x + e))*sinh(f*x + e)^5 + 2*(8*a^4 - 24*a^3*b + 27*a^2*b^2 - 14*a*b^3 + 3*b^4)*cosh(f*x + e)^4 + 2*(35*(a^2*b^2 - 2*a*b^3 + b^4)*cosh(f*x + e)^4 + 8*a^4 - 24*a^3*b + 27*a^2*b^2 - 14*a*b^3 + 3*b^4 + 30*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*cosh(f*x + e)^2)*sinh(f*x + e)^4 + a^2*b^2 - 2*a*b^3 + b^4 + 8*(7*(a^2*b^2 - 2*a*b^3 + b^4)*cosh(f*x + e)^5 + 10*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*cosh(f*x + e)^3 + (8*a^4 - 24*a^3*b + 27*a^2*b^2 - 14*a*b^3 + 3*b^4)*cosh(f*x + e))*sinh(f*x + e)^3 + 4*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*cosh(f*x + e)^2 + 4*(7*(a^2*b^2 - 2*a*b^3 + b^4)*cosh(f*x + e)^6 + 15*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*cosh(f*x + e)^4 + 2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4 + 3*(8*a^4 - 24*a^3*b + 27*a^2*b^2 - 14*a*b^3 + 3*b^4)*cosh(f*x + e)^2)*sinh(f*x + e)^2 + 8*((a^2*b^2 - 2*a*b^3 + b^4)*cosh(f*x + e)^7 + 3*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*cosh(f*x + e)^5 + (8*a^4 - 24*a^3*b + 27*a^2*b^2 - 14*a*b^3 + 3*b^4)*cosh(f*x + e)^3 + (2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*cosh(f*x + e))*sinh(f*x + e))*sqrt(b)*log((a^2*b*cosh(f*x + e)^8 + 8*a^2*b*cosh(f*x + e)*sinh(f*x + e)^7 + a^2*b*sinh(f*x + e)^8 + 2*(a^3 + a^2*b)*cosh(f*x + e)^6 + 2*(14*a^2*b*cosh(f*x + e)^2 + a^3 + a^2*b)*sinh(f*x + e)^6 + 4*(14*a^2*b*cosh(f*x + e)^3 + 3*(a^3 + a^2*b)*cosh(f*x + e))*sinh(f*x + e)^5 + (9*a^2*b - 4*a*b^2 + b^3)*cosh(f*x + e)^4 + (70*a^2*b*cosh(f*x + e)^4 + 9*a^2*b - 4*a*b^2 + b^3 + 30*(a^3 + a^2*b)*cosh(f*x + e)^2)*sinh(f*x + e)^4 + 4*(14*a^2*b*cosh(f*x + e)^5 + 10*(a^3 + a^2*b)*cosh(f*x + e)^3 + (9*a^2*b - 4*a*b^2 + b^3)*cosh(f*x + e))*sinh(f*x + e)^3 + b^3 + 2*(3*a*b^2 - b^3)*cosh(f*x + e)^2 + 2*(14*a^2*b*cosh(f*x + e)^6 + 15*(a^3 + a^2*b)*cosh(f*x + e)^4 + 3*a*b^2 - b^3 + 3*(9*a^2*b - 4*a*b^2 + b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^2 + sqrt(2)*(a^2*cosh(f*x + e)^6 + 6*a^2*cosh(f*x + e)*sinh(f*x + e)^5 + a^2*sinh(f*x + e)^6 + 3*a^2*cosh(f*x + e)^4 + 3*(5*a^2*cosh(f*x + e)^2 + a^2)*sinh(f*x + e)^4 + 4*(5*a^2*cosh(f*x + e)^3 + 3*a^2*cosh(f*x + e))*sinh(f*x + e)^3 + (4*a*b - b^2)*cosh(f*x + e)^2 + (15*a^2*cosh(f*x + e)^4 + 18*a^2*cosh(f*x + e)^2 + 4*a*b - b^2)*sinh(f*x + e)^2 + b^2 + 2*(3*a^2*cosh(f*x + e)^5 + 6*a^2*cosh(f*x + e)^3 + (4*a*b - b^2)*cosh(f*x + e))*sinh(f*x + e))*sqrt(b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + 4*(2*a^2*b*cosh(f*x + e)^7 + 3*(a^3 + a^2*b)*cosh(f*x + e)^5 + (9*a^2*b - 4*a*b^2 + b^3)*cosh(f*x + e)^3 + (3*a*b^2 - b^3)*cosh(f*x + e))*sinh(f*x + e))/(cosh(f*x + e)^6 + 6*cosh(f*x + e)^5*sinh(f*x + e) + 15*cosh(f*x + e)^4*sinh(f*x + e)^2 + 20*cosh(f*x + e)^3*sinh(f*x + e)^3 + 15*cosh(f*x + e)^2*sinh(f*x + e)^4 + 6*cosh(f*x + e)*sinh(f*x + e)^5 + sinh(f*x + e)^6)) + 3*((a^2*b^2 - 2*a*b^3 + b^4)*cosh(f*x + e)^8 + 8*(a^2*b^2 - 2*a*b^3 + b^4)*cosh(f*x + e)*sinh(f*x + e)^7 + (a^2*b^2 - 2*a*b^3 + b^4)*sinh(f*x + e)^8 + 4*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*cosh(f*x + e)^6 + 4*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4 + 7*(a^2*b^2 - 2*a*b^3 + b^4)*cosh(f*x + e)^2)*sinh(f*x + e)^6 + 8*(7*(a^2*b^2 - 2*a*b^3 + b^4)*cosh(f*x + e)^3 + 3*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*cosh(f*x + e))*sinh(f*x + e)^5 + 2*(8*a^4 - 24*a^3*b + 27*a^2*b^2 - 14*a*b^3 + 3*b^4)*cosh(f*x + e)^4 + 2*(35*(a^2*b^2 - 2*a*b^3 + b^4)*cosh(f*x + e)^4 + 8*a^4 - 24*a^3*b + 27*a^2*b^2 - 14*a*b^3 + 3*b^4 + 30*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*cosh(f*x + e)^2)*sinh(f*x + e)^4 + a^2*b^2 - 2*a*b^3 + b^4 + 8*(7*(a^2*b^2 - 2*a*b^3 + b^4)*cosh(f*x + e)^5 + 10*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*cosh(f*x + e)^3 + (8*a^4 - 24*a^3*b + 27*a^2*b^2 - 14*a*b^3 + 3*b^4)*cosh(f*x + e))*sinh(f*x + e)^3 + 4*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*cosh(f*x + e)^2 + 4*(7*(a^2*b^2 - 2*a*b^3 + b^4)*cosh(f*x + e)^6 + 15*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*cosh(f*x + e)^4 + 2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4 + 3*(8*a^4 - 24*a^3*b + 27*a^2*b^2 - 14*a*b^3 + 3*b^4)*cosh(f*x + e)^2)*sinh(f*x + e)^2 + 8*((a^2*b^2 - 2*a*b^3 + b^4)*cosh(f*x + e)^7 + 3*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*cosh(f*x + e)^5 + (8*a^4 - 24*a^3*b + 27*a^2*b^2 - 14*a*b^3 + 3*b^4)*cosh(f*x + e)^3 + (2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*cosh(f*x + e))*sinh(f*x + e))*sqrt(b)*log(-(b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(a - b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + a - b)*sinh(f*x + e)^2 + sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 - 1)*sqrt(b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + 4*(b*cosh(f*x + e)^3 + (a - b)*cosh(f*x + e))*sinh(f*x + e) + b)/(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) - 8*sqrt(2)*((2*a^2*b^2 - 3*a*b^3)*cosh(f*x + e)^6 + 6*(2*a^2*b^2 - 3*a*b^3)*cosh(f*x + e)*sinh(f*x + e)^5 + (2*a^2*b^2 - 3*a*b^3)*sinh(f*x + e)^6 + 3*(2*a^3*b - 4*a^2*b^2 + a*b^3)*cosh(f*x + e)^4 + 3*(2*a^3*b - 4*a^2*b^2 + a*b^3 + 5*(2*a^2*b^2 - 3*a*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^4 + 2*a^2*b^2 - 3*a*b^3 + 4*(5*(2*a^2*b^2 - 3*a*b^3)*cosh(f*x + e)^3 + 3*(2*a^3*b - 4*a^2*b^2 + a*b^3)*cosh(f*x + e))*sinh(f*x + e)^3 + 3*(2*a^3*b - 4*a^2*b^2 + a*b^3)*cosh(f*x + e)^2 + 3*(5*(2*a^2*b^2 - 3*a*b^3)*cosh(f*x + e)^4 + 2*a^3*b - 4*a^2*b^2 + a*b^3 + 6*(2*a^3*b - 4*a^2*b^2 + a*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^2 + 6*((2*a^2*b^2 - 3*a*b^3)*cosh(f*x + e)^5 + 2*(2*a^3*b - 4*a^2*b^2 + a*b^3)*cosh(f*x + e)^3 + (2*a^3*b - 4*a^2*b^2 + a*b^3)*cosh(f*x + e))*sinh(f*x + e))*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/((a^2*b^5 - 2*a*b^6 + b^7)*f*cosh(f*x + e)^8 + 8*(a^2*b^5 - 2*a*b^6 + b^7)*f*cosh(f*x + e)*sinh(f*x + e)^7 + (a^2*b^5 - 2*a*b^6 + b^7)*f*sinh(f*x + e)^8 + 4*(2*a^3*b^4 - 5*a^2*b^5 + 4*a*b^6 - b^7)*f*cosh(f*x + e)^6 + 4*(7*(a^2*b^5 - 2*a*b^6 + b^7)*f*cosh(f*x + e)^2 + (2*a^3*b^4 - 5*a^2*b^5 + 4*a*b^6 - b^7)*f)*sinh(f*x + e)^6 + 2*(8*a^4*b^3 - 24*a^3*b^4 + 27*a^2*b^5 - 14*a*b^6 + 3*b^7)*f*cosh(f*x + e)^4 + 8*(7*(a^2*b^5 - 2*a*b^6 + b^7)*f*cosh(f*x + e)^3 + 3*(2*a^3*b^4 - 5*a^2*b^5 + 4*a*b^6 - b^7)*f*cosh(f*x + e))*sinh(f*x + e)^5 + 2*(35*(a^2*b^5 - 2*a*b^6 + b^7)*f*cosh(f*x + e)^4 + 30*(2*a^3*b^4 - 5*a^2*b^5 + 4*a*b^6 - b^7)*f*cosh(f*x + e)^2 + (8*a^4*b^3 - 24*a^3*b^4 + 27*a^2*b^5 - 14*a*b^6 + 3*b^7)*f)*sinh(f*x + e)^4 + 4*(2*a^3*b^4 - 5*a^2*b^5 + 4*a*b^6 - b^7)*f*cosh(f*x + e)^2 + 8*(7*(a^2*b^5 - 2*a*b^6 + b^7)*f*cosh(f*x + e)^5 + 10*(2*a^3*b^4 - 5*a^2*b^5 + 4*a*b^6 - b^7)*f*cosh(f*x + e)^3 + (8*a^4*b^3 - 24*a^3*b^4 + 27*a^2*b^5 - 14*a*b^6 + 3*b^7)*f*cosh(f*x + e))*sinh(f*x + e)^3 + 4*(7*(a^2*b^5 - 2*a*b^6 + b^7)*f*cosh(f*x + e)^6 + 15*(2*a^3*b^4 - 5*a^2*b^5 + 4*a*b^6 - b^7)*f*cosh(f*x + e)^4 + 3*(8*a^4*b^3 - 24*a^3*b^4 + 27*a^2*b^5 - 14*a*b^6 + 3*b^7)*f*cosh(f*x + e)^2 + (2*a^3*b^4 - 5*a^2*b^5 + 4*a*b^6 - b^7)*f)*sinh(f*x + e)^2 + (a^2*b^5 - 2*a*b^6 + b^7)*f + 8*((a^2*b^5 - 2*a*b^6 + b^7)*f*cosh(f*x + e)^7 + 3*(2*a^3*b^4 - 5*a^2*b^5 + 4*a*b^6 - b^7)*f*cosh(f*x + e)^5 + (8*a^4*b^3 - 24*a^3*b^4 + 27*a^2*b^5 - 14*a*b^6 + 3*b^7)*f*cosh(f*x + e)^3 + (2*a^3*b^4 - 5*a^2*b^5 + 4*a*b^6 - b^7)*f*cosh(f*x + e))*sinh(f*x + e)), -1/6*(3*((a^2*b^2 - 2*a*b^3 + b^4)*cosh(f*x + e)^8 + 8*(a^2*b^2 - 2*a*b^3 + b^4)*cosh(f*x + e)*sinh(f*x + e)^7 + (a^2*b^2 - 2*a*b^3 + b^4)*sinh(f*x + e)^8 + 4*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*cosh(f*x + e)^6 + 4*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4 + 7*(a^2*b^2 - 2*a*b^3 + b^4)*cosh(f*x + e)^2)*sinh(f*x + e)^6 + 8*(7*(a^2*b^2 - 2*a*b^3 + b^4)*cosh(f*x + e)^3 + 3*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*cosh(f*x + e))*sinh(f*x + e)^5 + 2*(8*a^4 - 24*a^3*b + 27*a^2*b^2 - 14*a*b^3 + 3*b^4)*cosh(f*x + e)^4 + 2*(35*(a^2*b^2 - 2*a*b^3 + b^4)*cosh(f*x + e)^4 + 8*a^4 - 24*a^3*b + 27*a^2*b^2 - 14*a*b^3 + 3*b^4 + 30*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*cosh(f*x + e)^2)*sinh(f*x + e)^4 + a^2*b^2 - 2*a*b^3 + b^4 + 8*(7*(a^2*b^2 - 2*a*b^3 + b^4)*cosh(f*x + e)^5 + 10*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*cosh(f*x + e)^3 + (8*a^4 - 24*a^3*b + 27*a^2*b^2 - 14*a*b^3 + 3*b^4)*cosh(f*x + e))*sinh(f*x + e)^3 + 4*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*cosh(f*x + e)^2 + 4*(7*(a^2*b^2 - 2*a*b^3 + b^4)*cosh(f*x + e)^6 + 15*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*cosh(f*x + e)^4 + 2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4 + 3*(8*a^4 - 24*a^3*b + 27*a^2*b^2 - 14*a*b^3 + 3*b^4)*cosh(f*x + e)^2)*sinh(f*x + e)^2 + 8*((a^2*b^2 - 2*a*b^3 + b^4)*cosh(f*x + e)^7 + 3*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*cosh(f*x + e)^5 + (8*a^4 - 24*a^3*b + 27*a^2*b^2 - 14*a*b^3 + 3*b^4)*cosh(f*x + e)^3 + (2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*cosh(f*x + e))*sinh(f*x + e))*sqrt(-b)*arctan(sqrt(2)*(a*cosh(f*x + e)^2 + 2*a*cosh(f*x + e)*sinh(f*x + e) + a*sinh(f*x + e)^2 + b)*sqrt(-b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/(a*b*cosh(f*x + e)^4 + 4*a*b*cosh(f*x + e)*sinh(f*x + e)^3 + a*b*sinh(f*x + e)^4 + (3*a*b - b^2)*cosh(f*x + e)^2 + (6*a*b*cosh(f*x + e)^2 + 3*a*b - b^2)*sinh(f*x + e)^2 + b^2 + 2*(2*a*b*cosh(f*x + e)^3 + (3*a*b - b^2)*cosh(f*x + e))*sinh(f*x + e))) + 3*((a^2*b^2 - 2*a*b^3 + b^4)*cosh(f*x + e)^8 + 8*(a^2*b^2 - 2*a*b^3 + b^4)*cosh(f*x + e)*sinh(f*x + e)^7 + (a^2*b^2 - 2*a*b^3 + b^4)*sinh(f*x + e)^8 + 4*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*cosh(f*x + e)^6 + 4*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4 + 7*(a^2*b^2 - 2*a*b^3 + b^4)*cosh(f*x + e)^2)*sinh(f*x + e)^6 + 8*(7*(a^2*b^2 - 2*a*b^3 + b^4)*cosh(f*x + e)^3 + 3*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*cosh(f*x + e))*sinh(f*x + e)^5 + 2*(8*a^4 - 24*a^3*b + 27*a^2*b^2 - 14*a*b^3 + 3*b^4)*cosh(f*x + e)^4 + 2*(35*(a^2*b^2 - 2*a*b^3 + b^4)*cosh(f*x + e)^4 + 8*a^4 - 24*a^3*b + 27*a^2*b^2 - 14*a*b^3 + 3*b^4 + 30*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*cosh(f*x + e)^2)*sinh(f*x + e)^4 + a^2*b^2 - 2*a*b^3 + b^4 + 8*(7*(a^2*b^2 - 2*a*b^3 + b^4)*cosh(f*x + e)^5 + 10*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*cosh(f*x + e)^3 + (8*a^4 - 24*a^3*b + 27*a^2*b^2 - 14*a*b^3 + 3*b^4)*cosh(f*x + e))*sinh(f*x + e)^3 + 4*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*cosh(f*x + e)^2 + 4*(7*(a^2*b^2 - 2*a*b^3 + b^4)*cosh(f*x + e)^6 + 15*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*cosh(f*x + e)^4 + 2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4 + 3*(8*a^4 - 24*a^3*b + 27*a^2*b^2 - 14*a*b^3 + 3*b^4)*cosh(f*x + e)^2)*sinh(f*x + e)^2 + 8*((a^2*b^2 - 2*a*b^3 + b^4)*cosh(f*x + e)^7 + 3*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*cosh(f*x + e)^5 + (8*a^4 - 24*a^3*b + 27*a^2*b^2 - 14*a*b^3 + 3*b^4)*cosh(f*x + e)^3 + (2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*cosh(f*x + e))*sinh(f*x + e))*sqrt(-b)*arctan(sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 - 1)*sqrt(-b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/(b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(2*a - b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 2*a - b)*sinh(f*x + e)^2 + 4*(b*cosh(f*x + e)^3 + (2*a - b)*cosh(f*x + e))*sinh(f*x + e) + b)) + 4*sqrt(2)*((2*a^2*b^2 - 3*a*b^3)*cosh(f*x + e)^6 + 6*(2*a^2*b^2 - 3*a*b^3)*cosh(f*x + e)*sinh(f*x + e)^5 + (2*a^2*b^2 - 3*a*b^3)*sinh(f*x + e)^6 + 3*(2*a^3*b - 4*a^2*b^2 + a*b^3)*cosh(f*x + e)^4 + 3*(2*a^3*b - 4*a^2*b^2 + a*b^3 + 5*(2*a^2*b^2 - 3*a*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^4 + 2*a^2*b^2 - 3*a*b^3 + 4*(5*(2*a^2*b^2 - 3*a*b^3)*cosh(f*x + e)^3 + 3*(2*a^3*b - 4*a^2*b^2 + a*b^3)*cosh(f*x + e))*sinh(f*x + e)^3 + 3*(2*a^3*b - 4*a^2*b^2 + a*b^3)*cosh(f*x + e)^2 + 3*(5*(2*a^2*b^2 - 3*a*b^3)*cosh(f*x + e)^4 + 2*a^3*b - 4*a^2*b^2 + a*b^3 + 6*(2*a^3*b - 4*a^2*b^2 + a*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^2 + 6*((2*a^2*b^2 - 3*a*b^3)*cosh(f*x + e)^5 + 2*(2*a^3*b - 4*a^2*b^2 + a*b^3)*cosh(f*x + e)^3 + (2*a^3*b - 4*a^2*b^2 + a*b^3)*cosh(f*x + e))*sinh(f*x + e))*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/((a^2*b^5 - 2*a*b^6 + b^7)*f*cosh(f*x + e)^8 + 8*(a^2*b^5 - 2*a*b^6 + b^7)*f*cosh(f*x + e)*sinh(f*x + e)^7 + (a^2*b^5 - 2*a*b^6 + b^7)*f*sinh(f*x + e)^8 + 4*(2*a^3*b^4 - 5*a^2*b^5 + 4*a*b^6 - b^7)*f*cosh(f*x + e)^6 + 4*(7*(a^2*b^5 - 2*a*b^6 + b^7)*f*cosh(f*x + e)^2 + (2*a^3*b^4 - 5*a^2*b^5 + 4*a*b^6 - b^7)*f)*sinh(f*x + e)^6 + 2*(8*a^4*b^3 - 24*a^3*b^4 + 27*a^2*b^5 - 14*a*b^6 + 3*b^7)*f*cosh(f*x + e)^4 + 8*(7*(a^2*b^5 - 2*a*b^6 + b^7)*f*cosh(f*x + e)^3 + 3*(2*a^3*b^4 - 5*a^2*b^5 + 4*a*b^6 - b^7)*f*cosh(f*x + e))*sinh(f*x + e)^5 + 2*(35*(a^2*b^5 - 2*a*b^6 + b^7)*f*cosh(f*x + e)^4 + 30*(2*a^3*b^4 - 5*a^2*b^5 + 4*a*b^6 - b^7)*f*cosh(f*x + e)^2 + (8*a^4*b^3 - 24*a^3*b^4 + 27*a^2*b^5 - 14*a*b^6 + 3*b^7)*f)*sinh(f*x + e)^4 + 4*(2*a^3*b^4 - 5*a^2*b^5 + 4*a*b^6 - b^7)*f*cosh(f*x + e)^2 + 8*(7*(a^2*b^5 - 2*a*b^6 + b^7)*f*cosh(f*x + e)^5 + 10*(2*a^3*b^4 - 5*a^2*b^5 + 4*a*b^6 - b^7)*f*cosh(f*x + e)^3 + (8*a^4*b^3 - 24*a^3*b^4 + 27*a^2*b^5 - 14*a*b^6 + 3*b^7)*f*cosh(f*x + e))*sinh(f*x + e)^3 + 4*(7*(a^2*b^5 - 2*a*b^6 + b^7)*f*cosh(f*x + e)^6 + 15*(2*a^3*b^4 - 5*a^2*b^5 + 4*a*b^6 - b^7)*f*cosh(f*x + e)^4 + 3*(8*a^4*b^3 - 24*a^3*b^4 + 27*a^2*b^5 - 14*a*b^6 + 3*b^7)*f*cosh(f*x + e)^2 + (2*a^3*b^4 - 5*a^2*b^5 + 4*a*b^6 - b^7)*f)*sinh(f*x + e)^2 + (a^2*b^5 - 2*a*b^6 + b^7)*f + 8*((a^2*b^5 - 2*a*b^6 + b^7)*f*cosh(f*x + e)^7 + 3*(2*a^3*b^4 - 5*a^2*b^5 + 4*a*b^6 - b^7)*f*cosh(f*x + e)^5 + (8*a^4*b^3 - 24*a^3*b^4 + 27*a^2*b^5 - 14*a*b^6 + 3*b^7)*f*cosh(f*x + e)^3 + (2*a^3*b^4 - 5*a^2*b^5 + 4*a*b^6 - b^7)*f*cosh(f*x + e))*sinh(f*x + e))]","B",0
117,1,1214,0,3.783255," ","integrate(sinh(f*x+e)^3/(a+b*sinh(f*x+e)^2)^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left({\left(a - 3 \, b\right)} \cosh\left(f x + e\right)^{6} + 6 \, {\left(a - 3 \, b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + {\left(a - 3 \, b\right)} \sinh\left(f x + e\right)^{6} - 3 \, {\left(3 \, a - b\right)} \cosh\left(f x + e\right)^{4} + 3 \, {\left(5 \, {\left(a - 3 \, b\right)} \cosh\left(f x + e\right)^{2} - 3 \, a + b\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(5 \, {\left(a - 3 \, b\right)} \cosh\left(f x + e\right)^{3} - 3 \, {\left(3 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} - 3 \, {\left(3 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 3 \, {\left(5 \, {\left(a - 3 \, b\right)} \cosh\left(f x + e\right)^{4} - 6 \, {\left(3 \, a - b\right)} \cosh\left(f x + e\right)^{2} - 3 \, a + b\right)} \sinh\left(f x + e\right)^{2} + 6 \, {\left({\left(a - 3 \, b\right)} \cosh\left(f x + e\right)^{5} - 2 \, {\left(3 \, a - b\right)} \cosh\left(f x + e\right)^{3} - {\left(3 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + a - 3 \, b\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{3 \, {\left({\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} f \cosh\left(f x + e\right)^{8} + 8 \, {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} f \sinh\left(f x + e\right)^{8} + 4 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} f \cosh\left(f x + e\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} f \cosh\left(f x + e\right)^{2} + {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} f\right)} \sinh\left(f x + e\right)^{6} + 2 \, {\left(8 \, a^{4} - 24 \, a^{3} b + 27 \, a^{2} b^{2} - 14 \, a b^{3} + 3 \, b^{4}\right)} f \cosh\left(f x + e\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} f \cosh\left(f x + e\right)^{3} + 3 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(35 \, {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} f \cosh\left(f x + e\right)^{4} + 30 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} f \cosh\left(f x + e\right)^{2} + {\left(8 \, a^{4} - 24 \, a^{3} b + 27 \, a^{2} b^{2} - 14 \, a b^{3} + 3 \, b^{4}\right)} f\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} f \cosh\left(f x + e\right)^{2} + 8 \, {\left(7 \, {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} f \cosh\left(f x + e\right)^{5} + 10 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} f \cosh\left(f x + e\right)^{3} + {\left(8 \, a^{4} - 24 \, a^{3} b + 27 \, a^{2} b^{2} - 14 \, a b^{3} + 3 \, b^{4}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 4 \, {\left(7 \, {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} f \cosh\left(f x + e\right)^{6} + 15 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} f \cosh\left(f x + e\right)^{4} + 3 \, {\left(8 \, a^{4} - 24 \, a^{3} b + 27 \, a^{2} b^{2} - 14 \, a b^{3} + 3 \, b^{4}\right)} f \cosh\left(f x + e\right)^{2} + {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} f\right)} \sinh\left(f x + e\right)^{2} + {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} f + 8 \, {\left({\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} f \cosh\left(f x + e\right)^{7} + 3 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} f \cosh\left(f x + e\right)^{5} + {\left(8 \, a^{4} - 24 \, a^{3} b + 27 \, a^{2} b^{2} - 14 \, a b^{3} + 3 \, b^{4}\right)} f \cosh\left(f x + e\right)^{3} + {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)}}"," ",0,"1/3*sqrt(2)*((a - 3*b)*cosh(f*x + e)^6 + 6*(a - 3*b)*cosh(f*x + e)*sinh(f*x + e)^5 + (a - 3*b)*sinh(f*x + e)^6 - 3*(3*a - b)*cosh(f*x + e)^4 + 3*(5*(a - 3*b)*cosh(f*x + e)^2 - 3*a + b)*sinh(f*x + e)^4 + 4*(5*(a - 3*b)*cosh(f*x + e)^3 - 3*(3*a - b)*cosh(f*x + e))*sinh(f*x + e)^3 - 3*(3*a - b)*cosh(f*x + e)^2 + 3*(5*(a - 3*b)*cosh(f*x + e)^4 - 6*(3*a - b)*cosh(f*x + e)^2 - 3*a + b)*sinh(f*x + e)^2 + 6*((a - 3*b)*cosh(f*x + e)^5 - 2*(3*a - b)*cosh(f*x + e)^3 - (3*a - b)*cosh(f*x + e))*sinh(f*x + e) + a - 3*b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/((a^2*b^2 - 2*a*b^3 + b^4)*f*cosh(f*x + e)^8 + 8*(a^2*b^2 - 2*a*b^3 + b^4)*f*cosh(f*x + e)*sinh(f*x + e)^7 + (a^2*b^2 - 2*a*b^3 + b^4)*f*sinh(f*x + e)^8 + 4*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*f*cosh(f*x + e)^6 + 4*(7*(a^2*b^2 - 2*a*b^3 + b^4)*f*cosh(f*x + e)^2 + (2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*f)*sinh(f*x + e)^6 + 2*(8*a^4 - 24*a^3*b + 27*a^2*b^2 - 14*a*b^3 + 3*b^4)*f*cosh(f*x + e)^4 + 8*(7*(a^2*b^2 - 2*a*b^3 + b^4)*f*cosh(f*x + e)^3 + 3*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*f*cosh(f*x + e))*sinh(f*x + e)^5 + 2*(35*(a^2*b^2 - 2*a*b^3 + b^4)*f*cosh(f*x + e)^4 + 30*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*f*cosh(f*x + e)^2 + (8*a^4 - 24*a^3*b + 27*a^2*b^2 - 14*a*b^3 + 3*b^4)*f)*sinh(f*x + e)^4 + 4*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*f*cosh(f*x + e)^2 + 8*(7*(a^2*b^2 - 2*a*b^3 + b^4)*f*cosh(f*x + e)^5 + 10*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*f*cosh(f*x + e)^3 + (8*a^4 - 24*a^3*b + 27*a^2*b^2 - 14*a*b^3 + 3*b^4)*f*cosh(f*x + e))*sinh(f*x + e)^3 + 4*(7*(a^2*b^2 - 2*a*b^3 + b^4)*f*cosh(f*x + e)^6 + 15*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*f*cosh(f*x + e)^4 + 3*(8*a^4 - 24*a^3*b + 27*a^2*b^2 - 14*a*b^3 + 3*b^4)*f*cosh(f*x + e)^2 + (2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*f)*sinh(f*x + e)^2 + (a^2*b^2 - 2*a*b^3 + b^4)*f + 8*((a^2*b^2 - 2*a*b^3 + b^4)*f*cosh(f*x + e)^7 + 3*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*f*cosh(f*x + e)^5 + (8*a^4 - 24*a^3*b + 27*a^2*b^2 - 14*a*b^3 + 3*b^4)*f*cosh(f*x + e)^3 + (2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*f*cosh(f*x + e))*sinh(f*x + e))","B",0
118,1,1186,0,3.213110," ","integrate(sinh(f*x+e)/(a+b*sinh(f*x+e)^2)^(5/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{2} {\left(b \cosh\left(f x + e\right)^{6} + 6 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + b \sinh\left(f x + e\right)^{6} + 3 \, {\left(2 \, a - b\right)} \cosh\left(f x + e\right)^{4} + 3 \, {\left(5 \, b \cosh\left(f x + e\right)^{2} + 2 \, a - b\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(5 \, b \cosh\left(f x + e\right)^{3} + 3 \, {\left(2 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 3 \, {\left(2 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 3 \, {\left(5 \, b \cosh\left(f x + e\right)^{4} + 6 \, {\left(2 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, a - b\right)} \sinh\left(f x + e\right)^{2} + 6 \, {\left(b \cosh\left(f x + e\right)^{5} + 2 \, {\left(2 \, a - b\right)} \cosh\left(f x + e\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{3 \, {\left({\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} f \cosh\left(f x + e\right)^{8} + 8 \, {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} f \sinh\left(f x + e\right)^{8} + 4 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} f \cosh\left(f x + e\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} f \cosh\left(f x + e\right)^{2} + {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} f\right)} \sinh\left(f x + e\right)^{6} + 2 \, {\left(8 \, a^{4} - 24 \, a^{3} b + 27 \, a^{2} b^{2} - 14 \, a b^{3} + 3 \, b^{4}\right)} f \cosh\left(f x + e\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} f \cosh\left(f x + e\right)^{3} + 3 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(35 \, {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} f \cosh\left(f x + e\right)^{4} + 30 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} f \cosh\left(f x + e\right)^{2} + {\left(8 \, a^{4} - 24 \, a^{3} b + 27 \, a^{2} b^{2} - 14 \, a b^{3} + 3 \, b^{4}\right)} f\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} f \cosh\left(f x + e\right)^{2} + 8 \, {\left(7 \, {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} f \cosh\left(f x + e\right)^{5} + 10 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} f \cosh\left(f x + e\right)^{3} + {\left(8 \, a^{4} - 24 \, a^{3} b + 27 \, a^{2} b^{2} - 14 \, a b^{3} + 3 \, b^{4}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 4 \, {\left(7 \, {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} f \cosh\left(f x + e\right)^{6} + 15 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} f \cosh\left(f x + e\right)^{4} + 3 \, {\left(8 \, a^{4} - 24 \, a^{3} b + 27 \, a^{2} b^{2} - 14 \, a b^{3} + 3 \, b^{4}\right)} f \cosh\left(f x + e\right)^{2} + {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} f\right)} \sinh\left(f x + e\right)^{2} + {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} f + 8 \, {\left({\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} f \cosh\left(f x + e\right)^{7} + 3 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} f \cosh\left(f x + e\right)^{5} + {\left(8 \, a^{4} - 24 \, a^{3} b + 27 \, a^{2} b^{2} - 14 \, a b^{3} + 3 \, b^{4}\right)} f \cosh\left(f x + e\right)^{3} + {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)}}"," ",0,"2/3*sqrt(2)*(b*cosh(f*x + e)^6 + 6*b*cosh(f*x + e)*sinh(f*x + e)^5 + b*sinh(f*x + e)^6 + 3*(2*a - b)*cosh(f*x + e)^4 + 3*(5*b*cosh(f*x + e)^2 + 2*a - b)*sinh(f*x + e)^4 + 4*(5*b*cosh(f*x + e)^3 + 3*(2*a - b)*cosh(f*x + e))*sinh(f*x + e)^3 + 3*(2*a - b)*cosh(f*x + e)^2 + 3*(5*b*cosh(f*x + e)^4 + 6*(2*a - b)*cosh(f*x + e)^2 + 2*a - b)*sinh(f*x + e)^2 + 6*(b*cosh(f*x + e)^5 + 2*(2*a - b)*cosh(f*x + e)^3 + (2*a - b)*cosh(f*x + e))*sinh(f*x + e) + b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/((a^2*b^2 - 2*a*b^3 + b^4)*f*cosh(f*x + e)^8 + 8*(a^2*b^2 - 2*a*b^3 + b^4)*f*cosh(f*x + e)*sinh(f*x + e)^7 + (a^2*b^2 - 2*a*b^3 + b^4)*f*sinh(f*x + e)^8 + 4*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*f*cosh(f*x + e)^6 + 4*(7*(a^2*b^2 - 2*a*b^3 + b^4)*f*cosh(f*x + e)^2 + (2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*f)*sinh(f*x + e)^6 + 2*(8*a^4 - 24*a^3*b + 27*a^2*b^2 - 14*a*b^3 + 3*b^4)*f*cosh(f*x + e)^4 + 8*(7*(a^2*b^2 - 2*a*b^3 + b^4)*f*cosh(f*x + e)^3 + 3*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*f*cosh(f*x + e))*sinh(f*x + e)^5 + 2*(35*(a^2*b^2 - 2*a*b^3 + b^4)*f*cosh(f*x + e)^4 + 30*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*f*cosh(f*x + e)^2 + (8*a^4 - 24*a^3*b + 27*a^2*b^2 - 14*a*b^3 + 3*b^4)*f)*sinh(f*x + e)^4 + 4*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*f*cosh(f*x + e)^2 + 8*(7*(a^2*b^2 - 2*a*b^3 + b^4)*f*cosh(f*x + e)^5 + 10*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*f*cosh(f*x + e)^3 + (8*a^4 - 24*a^3*b + 27*a^2*b^2 - 14*a*b^3 + 3*b^4)*f*cosh(f*x + e))*sinh(f*x + e)^3 + 4*(7*(a^2*b^2 - 2*a*b^3 + b^4)*f*cosh(f*x + e)^6 + 15*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*f*cosh(f*x + e)^4 + 3*(8*a^4 - 24*a^3*b + 27*a^2*b^2 - 14*a*b^3 + 3*b^4)*f*cosh(f*x + e)^2 + (2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*f)*sinh(f*x + e)^2 + (a^2*b^2 - 2*a*b^3 + b^4)*f + 8*((a^2*b^2 - 2*a*b^3 + b^4)*f*cosh(f*x + e)^7 + 3*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*f*cosh(f*x + e)^5 + (8*a^4 - 24*a^3*b + 27*a^2*b^2 - 14*a*b^3 + 3*b^4)*f*cosh(f*x + e)^3 + (2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*f*cosh(f*x + e))*sinh(f*x + e))","B",0
119,1,5342,0,5.094240," ","integrate(csch(f*x+e)/(a+b*sinh(f*x+e)^2)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \cosh\left(f x + e\right)^{8} + 8 \, {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \sinh\left(f x + e\right)^{8} + 4 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} \cosh\left(f x + e\right)^{6} + 4 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4} + 7 \, {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(8 \, a^{4} - 24 \, a^{3} b + 27 \, a^{2} b^{2} - 14 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(f x + e\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \cosh\left(f x + e\right)^{4} + 8 \, a^{4} - 24 \, a^{3} b + 27 \, a^{2} b^{2} - 14 \, a b^{3} + 3 \, b^{4} + 30 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{4} + a^{2} b^{2} - 2 \, a b^{3} + b^{4} + 8 \, {\left(7 \, {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \cosh\left(f x + e\right)^{5} + 10 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} \cosh\left(f x + e\right)^{3} + {\left(8 \, a^{4} - 24 \, a^{3} b + 27 \, a^{2} b^{2} - 14 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 4 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} \cosh\left(f x + e\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \cosh\left(f x + e\right)^{6} + 15 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} \cosh\left(f x + e\right)^{4} + 2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4} + 3 \, {\left(8 \, a^{4} - 24 \, a^{3} b + 27 \, a^{2} b^{2} - 14 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{2} + 8 \, {\left({\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \cosh\left(f x + e\right)^{7} + 3 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} \cosh\left(f x + e\right)^{5} + {\left(8 \, a^{4} - 24 \, a^{3} b + 27 \, a^{2} b^{2} - 14 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(f x + e\right)^{3} + {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{a} \log\left(-\frac{{\left(a + b\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(a + b\right)} \sinh\left(f x + e\right)^{4} + 2 \, {\left(3 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(f x + e\right)^{2} + 3 \, a - b\right)} \sinh\left(f x + e\right)^{2} - 2 \, \sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} + 1\right)} \sqrt{a} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(f x + e\right)^{3} + {\left(3 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + a + b}{\cosh\left(f x + e\right)^{4} + 4 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + \sinh\left(f x + e\right)^{4} + 2 \, {\left(3 \, \cosh\left(f x + e\right)^{2} - 1\right)} \sinh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right)^{2} + 4 \, {\left(\cosh\left(f x + e\right)^{3} - \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + 1}\right) - 2 \, \sqrt{2} {\left({\left(5 \, a^{2} b^{2} - 3 \, a b^{3}\right)} \cosh\left(f x + e\right)^{6} + 6 \, {\left(5 \, a^{2} b^{2} - 3 \, a b^{3}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + {\left(5 \, a^{2} b^{2} - 3 \, a b^{3}\right)} \sinh\left(f x + e\right)^{6} + 3 \, {\left(8 \, a^{3} b - 7 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(f x + e\right)^{4} + 3 \, {\left(8 \, a^{3} b - 7 \, a^{2} b^{2} + a b^{3} + 5 \, {\left(5 \, a^{2} b^{2} - 3 \, a b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{4} + 5 \, a^{2} b^{2} - 3 \, a b^{3} + 4 \, {\left(5 \, {\left(5 \, a^{2} b^{2} - 3 \, a b^{3}\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(8 \, a^{3} b - 7 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 3 \, {\left(8 \, a^{3} b - 7 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(f x + e\right)^{2} + 3 \, {\left(5 \, {\left(5 \, a^{2} b^{2} - 3 \, a b^{3}\right)} \cosh\left(f x + e\right)^{4} + 8 \, a^{3} b - 7 \, a^{2} b^{2} + a b^{3} + 6 \, {\left(8 \, a^{3} b - 7 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{2} + 6 \, {\left({\left(5 \, a^{2} b^{2} - 3 \, a b^{3}\right)} \cosh\left(f x + e\right)^{5} + 2 \, {\left(8 \, a^{3} b - 7 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(f x + e\right)^{3} + {\left(8 \, a^{3} b - 7 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{6 \, {\left({\left(a^{5} b^{2} - 2 \, a^{4} b^{3} + a^{3} b^{4}\right)} f \cosh\left(f x + e\right)^{8} + 8 \, {\left(a^{5} b^{2} - 2 \, a^{4} b^{3} + a^{3} b^{4}\right)} f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + {\left(a^{5} b^{2} - 2 \, a^{4} b^{3} + a^{3} b^{4}\right)} f \sinh\left(f x + e\right)^{8} + 4 \, {\left(2 \, a^{6} b - 5 \, a^{5} b^{2} + 4 \, a^{4} b^{3} - a^{3} b^{4}\right)} f \cosh\left(f x + e\right)^{6} + 4 \, {\left(7 \, {\left(a^{5} b^{2} - 2 \, a^{4} b^{3} + a^{3} b^{4}\right)} f \cosh\left(f x + e\right)^{2} + {\left(2 \, a^{6} b - 5 \, a^{5} b^{2} + 4 \, a^{4} b^{3} - a^{3} b^{4}\right)} f\right)} \sinh\left(f x + e\right)^{6} + 2 \, {\left(8 \, a^{7} - 24 \, a^{6} b + 27 \, a^{5} b^{2} - 14 \, a^{4} b^{3} + 3 \, a^{3} b^{4}\right)} f \cosh\left(f x + e\right)^{4} + 8 \, {\left(7 \, {\left(a^{5} b^{2} - 2 \, a^{4} b^{3} + a^{3} b^{4}\right)} f \cosh\left(f x + e\right)^{3} + 3 \, {\left(2 \, a^{6} b - 5 \, a^{5} b^{2} + 4 \, a^{4} b^{3} - a^{3} b^{4}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(35 \, {\left(a^{5} b^{2} - 2 \, a^{4} b^{3} + a^{3} b^{4}\right)} f \cosh\left(f x + e\right)^{4} + 30 \, {\left(2 \, a^{6} b - 5 \, a^{5} b^{2} + 4 \, a^{4} b^{3} - a^{3} b^{4}\right)} f \cosh\left(f x + e\right)^{2} + {\left(8 \, a^{7} - 24 \, a^{6} b + 27 \, a^{5} b^{2} - 14 \, a^{4} b^{3} + 3 \, a^{3} b^{4}\right)} f\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(2 \, a^{6} b - 5 \, a^{5} b^{2} + 4 \, a^{4} b^{3} - a^{3} b^{4}\right)} f \cosh\left(f x + e\right)^{2} + 8 \, {\left(7 \, {\left(a^{5} b^{2} - 2 \, a^{4} b^{3} + a^{3} b^{4}\right)} f \cosh\left(f x + e\right)^{5} + 10 \, {\left(2 \, a^{6} b - 5 \, a^{5} b^{2} + 4 \, a^{4} b^{3} - a^{3} b^{4}\right)} f \cosh\left(f x + e\right)^{3} + {\left(8 \, a^{7} - 24 \, a^{6} b + 27 \, a^{5} b^{2} - 14 \, a^{4} b^{3} + 3 \, a^{3} b^{4}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 4 \, {\left(7 \, {\left(a^{5} b^{2} - 2 \, a^{4} b^{3} + a^{3} b^{4}\right)} f \cosh\left(f x + e\right)^{6} + 15 \, {\left(2 \, a^{6} b - 5 \, a^{5} b^{2} + 4 \, a^{4} b^{3} - a^{3} b^{4}\right)} f \cosh\left(f x + e\right)^{4} + 3 \, {\left(8 \, a^{7} - 24 \, a^{6} b + 27 \, a^{5} b^{2} - 14 \, a^{4} b^{3} + 3 \, a^{3} b^{4}\right)} f \cosh\left(f x + e\right)^{2} + {\left(2 \, a^{6} b - 5 \, a^{5} b^{2} + 4 \, a^{4} b^{3} - a^{3} b^{4}\right)} f\right)} \sinh\left(f x + e\right)^{2} + {\left(a^{5} b^{2} - 2 \, a^{4} b^{3} + a^{3} b^{4}\right)} f + 8 \, {\left({\left(a^{5} b^{2} - 2 \, a^{4} b^{3} + a^{3} b^{4}\right)} f \cosh\left(f x + e\right)^{7} + 3 \, {\left(2 \, a^{6} b - 5 \, a^{5} b^{2} + 4 \, a^{4} b^{3} - a^{3} b^{4}\right)} f \cosh\left(f x + e\right)^{5} + {\left(8 \, a^{7} - 24 \, a^{6} b + 27 \, a^{5} b^{2} - 14 \, a^{4} b^{3} + 3 \, a^{3} b^{4}\right)} f \cosh\left(f x + e\right)^{3} + {\left(2 \, a^{6} b - 5 \, a^{5} b^{2} + 4 \, a^{4} b^{3} - a^{3} b^{4}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)}}, \frac{3 \, {\left({\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \cosh\left(f x + e\right)^{8} + 8 \, {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \sinh\left(f x + e\right)^{8} + 4 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} \cosh\left(f x + e\right)^{6} + 4 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4} + 7 \, {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(8 \, a^{4} - 24 \, a^{3} b + 27 \, a^{2} b^{2} - 14 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(f x + e\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \cosh\left(f x + e\right)^{4} + 8 \, a^{4} - 24 \, a^{3} b + 27 \, a^{2} b^{2} - 14 \, a b^{3} + 3 \, b^{4} + 30 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{4} + a^{2} b^{2} - 2 \, a b^{3} + b^{4} + 8 \, {\left(7 \, {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \cosh\left(f x + e\right)^{5} + 10 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} \cosh\left(f x + e\right)^{3} + {\left(8 \, a^{4} - 24 \, a^{3} b + 27 \, a^{2} b^{2} - 14 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 4 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} \cosh\left(f x + e\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \cosh\left(f x + e\right)^{6} + 15 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} \cosh\left(f x + e\right)^{4} + 2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4} + 3 \, {\left(8 \, a^{4} - 24 \, a^{3} b + 27 \, a^{2} b^{2} - 14 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{2} + 8 \, {\left({\left(a^{2} b^{2} - 2 \, a b^{3} + b^{4}\right)} \cosh\left(f x + e\right)^{7} + 3 \, {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} \cosh\left(f x + e\right)^{5} + {\left(8 \, a^{4} - 24 \, a^{3} b + 27 \, a^{2} b^{2} - 14 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(f x + e\right)^{3} + {\left(2 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - b^{4}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} + 1\right)} \sqrt{-a} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + 2 \, a - b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}\right) - \sqrt{2} {\left({\left(5 \, a^{2} b^{2} - 3 \, a b^{3}\right)} \cosh\left(f x + e\right)^{6} + 6 \, {\left(5 \, a^{2} b^{2} - 3 \, a b^{3}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + {\left(5 \, a^{2} b^{2} - 3 \, a b^{3}\right)} \sinh\left(f x + e\right)^{6} + 3 \, {\left(8 \, a^{3} b - 7 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(f x + e\right)^{4} + 3 \, {\left(8 \, a^{3} b - 7 \, a^{2} b^{2} + a b^{3} + 5 \, {\left(5 \, a^{2} b^{2} - 3 \, a b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{4} + 5 \, a^{2} b^{2} - 3 \, a b^{3} + 4 \, {\left(5 \, {\left(5 \, a^{2} b^{2} - 3 \, a b^{3}\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(8 \, a^{3} b - 7 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 3 \, {\left(8 \, a^{3} b - 7 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(f x + e\right)^{2} + 3 \, {\left(5 \, {\left(5 \, a^{2} b^{2} - 3 \, a b^{3}\right)} \cosh\left(f x + e\right)^{4} + 8 \, a^{3} b - 7 \, a^{2} b^{2} + a b^{3} + 6 \, {\left(8 \, a^{3} b - 7 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{2} + 6 \, {\left({\left(5 \, a^{2} b^{2} - 3 \, a b^{3}\right)} \cosh\left(f x + e\right)^{5} + 2 \, {\left(8 \, a^{3} b - 7 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(f x + e\right)^{3} + {\left(8 \, a^{3} b - 7 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{3 \, {\left({\left(a^{5} b^{2} - 2 \, a^{4} b^{3} + a^{3} b^{4}\right)} f \cosh\left(f x + e\right)^{8} + 8 \, {\left(a^{5} b^{2} - 2 \, a^{4} b^{3} + a^{3} b^{4}\right)} f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + {\left(a^{5} b^{2} - 2 \, a^{4} b^{3} + a^{3} b^{4}\right)} f \sinh\left(f x + e\right)^{8} + 4 \, {\left(2 \, a^{6} b - 5 \, a^{5} b^{2} + 4 \, a^{4} b^{3} - a^{3} b^{4}\right)} f \cosh\left(f x + e\right)^{6} + 4 \, {\left(7 \, {\left(a^{5} b^{2} - 2 \, a^{4} b^{3} + a^{3} b^{4}\right)} f \cosh\left(f x + e\right)^{2} + {\left(2 \, a^{6} b - 5 \, a^{5} b^{2} + 4 \, a^{4} b^{3} - a^{3} b^{4}\right)} f\right)} \sinh\left(f x + e\right)^{6} + 2 \, {\left(8 \, a^{7} - 24 \, a^{6} b + 27 \, a^{5} b^{2} - 14 \, a^{4} b^{3} + 3 \, a^{3} b^{4}\right)} f \cosh\left(f x + e\right)^{4} + 8 \, {\left(7 \, {\left(a^{5} b^{2} - 2 \, a^{4} b^{3} + a^{3} b^{4}\right)} f \cosh\left(f x + e\right)^{3} + 3 \, {\left(2 \, a^{6} b - 5 \, a^{5} b^{2} + 4 \, a^{4} b^{3} - a^{3} b^{4}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(35 \, {\left(a^{5} b^{2} - 2 \, a^{4} b^{3} + a^{3} b^{4}\right)} f \cosh\left(f x + e\right)^{4} + 30 \, {\left(2 \, a^{6} b - 5 \, a^{5} b^{2} + 4 \, a^{4} b^{3} - a^{3} b^{4}\right)} f \cosh\left(f x + e\right)^{2} + {\left(8 \, a^{7} - 24 \, a^{6} b + 27 \, a^{5} b^{2} - 14 \, a^{4} b^{3} + 3 \, a^{3} b^{4}\right)} f\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(2 \, a^{6} b - 5 \, a^{5} b^{2} + 4 \, a^{4} b^{3} - a^{3} b^{4}\right)} f \cosh\left(f x + e\right)^{2} + 8 \, {\left(7 \, {\left(a^{5} b^{2} - 2 \, a^{4} b^{3} + a^{3} b^{4}\right)} f \cosh\left(f x + e\right)^{5} + 10 \, {\left(2 \, a^{6} b - 5 \, a^{5} b^{2} + 4 \, a^{4} b^{3} - a^{3} b^{4}\right)} f \cosh\left(f x + e\right)^{3} + {\left(8 \, a^{7} - 24 \, a^{6} b + 27 \, a^{5} b^{2} - 14 \, a^{4} b^{3} + 3 \, a^{3} b^{4}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 4 \, {\left(7 \, {\left(a^{5} b^{2} - 2 \, a^{4} b^{3} + a^{3} b^{4}\right)} f \cosh\left(f x + e\right)^{6} + 15 \, {\left(2 \, a^{6} b - 5 \, a^{5} b^{2} + 4 \, a^{4} b^{3} - a^{3} b^{4}\right)} f \cosh\left(f x + e\right)^{4} + 3 \, {\left(8 \, a^{7} - 24 \, a^{6} b + 27 \, a^{5} b^{2} - 14 \, a^{4} b^{3} + 3 \, a^{3} b^{4}\right)} f \cosh\left(f x + e\right)^{2} + {\left(2 \, a^{6} b - 5 \, a^{5} b^{2} + 4 \, a^{4} b^{3} - a^{3} b^{4}\right)} f\right)} \sinh\left(f x + e\right)^{2} + {\left(a^{5} b^{2} - 2 \, a^{4} b^{3} + a^{3} b^{4}\right)} f + 8 \, {\left({\left(a^{5} b^{2} - 2 \, a^{4} b^{3} + a^{3} b^{4}\right)} f \cosh\left(f x + e\right)^{7} + 3 \, {\left(2 \, a^{6} b - 5 \, a^{5} b^{2} + 4 \, a^{4} b^{3} - a^{3} b^{4}\right)} f \cosh\left(f x + e\right)^{5} + {\left(8 \, a^{7} - 24 \, a^{6} b + 27 \, a^{5} b^{2} - 14 \, a^{4} b^{3} + 3 \, a^{3} b^{4}\right)} f \cosh\left(f x + e\right)^{3} + {\left(2 \, a^{6} b - 5 \, a^{5} b^{2} + 4 \, a^{4} b^{3} - a^{3} b^{4}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)}}\right]"," ",0,"[1/6*(3*((a^2*b^2 - 2*a*b^3 + b^4)*cosh(f*x + e)^8 + 8*(a^2*b^2 - 2*a*b^3 + b^4)*cosh(f*x + e)*sinh(f*x + e)^7 + (a^2*b^2 - 2*a*b^3 + b^4)*sinh(f*x + e)^8 + 4*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*cosh(f*x + e)^6 + 4*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4 + 7*(a^2*b^2 - 2*a*b^3 + b^4)*cosh(f*x + e)^2)*sinh(f*x + e)^6 + 8*(7*(a^2*b^2 - 2*a*b^3 + b^4)*cosh(f*x + e)^3 + 3*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*cosh(f*x + e))*sinh(f*x + e)^5 + 2*(8*a^4 - 24*a^3*b + 27*a^2*b^2 - 14*a*b^3 + 3*b^4)*cosh(f*x + e)^4 + 2*(35*(a^2*b^2 - 2*a*b^3 + b^4)*cosh(f*x + e)^4 + 8*a^4 - 24*a^3*b + 27*a^2*b^2 - 14*a*b^3 + 3*b^4 + 30*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*cosh(f*x + e)^2)*sinh(f*x + e)^4 + a^2*b^2 - 2*a*b^3 + b^4 + 8*(7*(a^2*b^2 - 2*a*b^3 + b^4)*cosh(f*x + e)^5 + 10*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*cosh(f*x + e)^3 + (8*a^4 - 24*a^3*b + 27*a^2*b^2 - 14*a*b^3 + 3*b^4)*cosh(f*x + e))*sinh(f*x + e)^3 + 4*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*cosh(f*x + e)^2 + 4*(7*(a^2*b^2 - 2*a*b^3 + b^4)*cosh(f*x + e)^6 + 15*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*cosh(f*x + e)^4 + 2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4 + 3*(8*a^4 - 24*a^3*b + 27*a^2*b^2 - 14*a*b^3 + 3*b^4)*cosh(f*x + e)^2)*sinh(f*x + e)^2 + 8*((a^2*b^2 - 2*a*b^3 + b^4)*cosh(f*x + e)^7 + 3*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*cosh(f*x + e)^5 + (8*a^4 - 24*a^3*b + 27*a^2*b^2 - 14*a*b^3 + 3*b^4)*cosh(f*x + e)^3 + (2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*cosh(f*x + e))*sinh(f*x + e))*sqrt(a)*log(-((a + b)*cosh(f*x + e)^4 + 4*(a + b)*cosh(f*x + e)*sinh(f*x + e)^3 + (a + b)*sinh(f*x + e)^4 + 2*(3*a - b)*cosh(f*x + e)^2 + 2*(3*(a + b)*cosh(f*x + e)^2 + 3*a - b)*sinh(f*x + e)^2 - 2*sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 + 1)*sqrt(a)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + 4*((a + b)*cosh(f*x + e)^3 + (3*a - b)*cosh(f*x + e))*sinh(f*x + e) + a + b)/(cosh(f*x + e)^4 + 4*cosh(f*x + e)*sinh(f*x + e)^3 + sinh(f*x + e)^4 + 2*(3*cosh(f*x + e)^2 - 1)*sinh(f*x + e)^2 - 2*cosh(f*x + e)^2 + 4*(cosh(f*x + e)^3 - cosh(f*x + e))*sinh(f*x + e) + 1)) - 2*sqrt(2)*((5*a^2*b^2 - 3*a*b^3)*cosh(f*x + e)^6 + 6*(5*a^2*b^2 - 3*a*b^3)*cosh(f*x + e)*sinh(f*x + e)^5 + (5*a^2*b^2 - 3*a*b^3)*sinh(f*x + e)^6 + 3*(8*a^3*b - 7*a^2*b^2 + a*b^3)*cosh(f*x + e)^4 + 3*(8*a^3*b - 7*a^2*b^2 + a*b^3 + 5*(5*a^2*b^2 - 3*a*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^4 + 5*a^2*b^2 - 3*a*b^3 + 4*(5*(5*a^2*b^2 - 3*a*b^3)*cosh(f*x + e)^3 + 3*(8*a^3*b - 7*a^2*b^2 + a*b^3)*cosh(f*x + e))*sinh(f*x + e)^3 + 3*(8*a^3*b - 7*a^2*b^2 + a*b^3)*cosh(f*x + e)^2 + 3*(5*(5*a^2*b^2 - 3*a*b^3)*cosh(f*x + e)^4 + 8*a^3*b - 7*a^2*b^2 + a*b^3 + 6*(8*a^3*b - 7*a^2*b^2 + a*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^2 + 6*((5*a^2*b^2 - 3*a*b^3)*cosh(f*x + e)^5 + 2*(8*a^3*b - 7*a^2*b^2 + a*b^3)*cosh(f*x + e)^3 + (8*a^3*b - 7*a^2*b^2 + a*b^3)*cosh(f*x + e))*sinh(f*x + e))*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/((a^5*b^2 - 2*a^4*b^3 + a^3*b^4)*f*cosh(f*x + e)^8 + 8*(a^5*b^2 - 2*a^4*b^3 + a^3*b^4)*f*cosh(f*x + e)*sinh(f*x + e)^7 + (a^5*b^2 - 2*a^4*b^3 + a^3*b^4)*f*sinh(f*x + e)^8 + 4*(2*a^6*b - 5*a^5*b^2 + 4*a^4*b^3 - a^3*b^4)*f*cosh(f*x + e)^6 + 4*(7*(a^5*b^2 - 2*a^4*b^3 + a^3*b^4)*f*cosh(f*x + e)^2 + (2*a^6*b - 5*a^5*b^2 + 4*a^4*b^3 - a^3*b^4)*f)*sinh(f*x + e)^6 + 2*(8*a^7 - 24*a^6*b + 27*a^5*b^2 - 14*a^4*b^3 + 3*a^3*b^4)*f*cosh(f*x + e)^4 + 8*(7*(a^5*b^2 - 2*a^4*b^3 + a^3*b^4)*f*cosh(f*x + e)^3 + 3*(2*a^6*b - 5*a^5*b^2 + 4*a^4*b^3 - a^3*b^4)*f*cosh(f*x + e))*sinh(f*x + e)^5 + 2*(35*(a^5*b^2 - 2*a^4*b^3 + a^3*b^4)*f*cosh(f*x + e)^4 + 30*(2*a^6*b - 5*a^5*b^2 + 4*a^4*b^3 - a^3*b^4)*f*cosh(f*x + e)^2 + (8*a^7 - 24*a^6*b + 27*a^5*b^2 - 14*a^4*b^3 + 3*a^3*b^4)*f)*sinh(f*x + e)^4 + 4*(2*a^6*b - 5*a^5*b^2 + 4*a^4*b^3 - a^3*b^4)*f*cosh(f*x + e)^2 + 8*(7*(a^5*b^2 - 2*a^4*b^3 + a^3*b^4)*f*cosh(f*x + e)^5 + 10*(2*a^6*b - 5*a^5*b^2 + 4*a^4*b^3 - a^3*b^4)*f*cosh(f*x + e)^3 + (8*a^7 - 24*a^6*b + 27*a^5*b^2 - 14*a^4*b^3 + 3*a^3*b^4)*f*cosh(f*x + e))*sinh(f*x + e)^3 + 4*(7*(a^5*b^2 - 2*a^4*b^3 + a^3*b^4)*f*cosh(f*x + e)^6 + 15*(2*a^6*b - 5*a^5*b^2 + 4*a^4*b^3 - a^3*b^4)*f*cosh(f*x + e)^4 + 3*(8*a^7 - 24*a^6*b + 27*a^5*b^2 - 14*a^4*b^3 + 3*a^3*b^4)*f*cosh(f*x + e)^2 + (2*a^6*b - 5*a^5*b^2 + 4*a^4*b^3 - a^3*b^4)*f)*sinh(f*x + e)^2 + (a^5*b^2 - 2*a^4*b^3 + a^3*b^4)*f + 8*((a^5*b^2 - 2*a^4*b^3 + a^3*b^4)*f*cosh(f*x + e)^7 + 3*(2*a^6*b - 5*a^5*b^2 + 4*a^4*b^3 - a^3*b^4)*f*cosh(f*x + e)^5 + (8*a^7 - 24*a^6*b + 27*a^5*b^2 - 14*a^4*b^3 + 3*a^3*b^4)*f*cosh(f*x + e)^3 + (2*a^6*b - 5*a^5*b^2 + 4*a^4*b^3 - a^3*b^4)*f*cosh(f*x + e))*sinh(f*x + e)), 1/3*(3*((a^2*b^2 - 2*a*b^3 + b^4)*cosh(f*x + e)^8 + 8*(a^2*b^2 - 2*a*b^3 + b^4)*cosh(f*x + e)*sinh(f*x + e)^7 + (a^2*b^2 - 2*a*b^3 + b^4)*sinh(f*x + e)^8 + 4*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*cosh(f*x + e)^6 + 4*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4 + 7*(a^2*b^2 - 2*a*b^3 + b^4)*cosh(f*x + e)^2)*sinh(f*x + e)^6 + 8*(7*(a^2*b^2 - 2*a*b^3 + b^4)*cosh(f*x + e)^3 + 3*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*cosh(f*x + e))*sinh(f*x + e)^5 + 2*(8*a^4 - 24*a^3*b + 27*a^2*b^2 - 14*a*b^3 + 3*b^4)*cosh(f*x + e)^4 + 2*(35*(a^2*b^2 - 2*a*b^3 + b^4)*cosh(f*x + e)^4 + 8*a^4 - 24*a^3*b + 27*a^2*b^2 - 14*a*b^3 + 3*b^4 + 30*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*cosh(f*x + e)^2)*sinh(f*x + e)^4 + a^2*b^2 - 2*a*b^3 + b^4 + 8*(7*(a^2*b^2 - 2*a*b^3 + b^4)*cosh(f*x + e)^5 + 10*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*cosh(f*x + e)^3 + (8*a^4 - 24*a^3*b + 27*a^2*b^2 - 14*a*b^3 + 3*b^4)*cosh(f*x + e))*sinh(f*x + e)^3 + 4*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*cosh(f*x + e)^2 + 4*(7*(a^2*b^2 - 2*a*b^3 + b^4)*cosh(f*x + e)^6 + 15*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*cosh(f*x + e)^4 + 2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4 + 3*(8*a^4 - 24*a^3*b + 27*a^2*b^2 - 14*a*b^3 + 3*b^4)*cosh(f*x + e)^2)*sinh(f*x + e)^2 + 8*((a^2*b^2 - 2*a*b^3 + b^4)*cosh(f*x + e)^7 + 3*(2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*cosh(f*x + e)^5 + (8*a^4 - 24*a^3*b + 27*a^2*b^2 - 14*a*b^3 + 3*b^4)*cosh(f*x + e)^3 + (2*a^3*b - 5*a^2*b^2 + 4*a*b^3 - b^4)*cosh(f*x + e))*sinh(f*x + e))*sqrt(-a)*arctan(sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 + 1)*sqrt(-a)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/(b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(2*a - b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 2*a - b)*sinh(f*x + e)^2 + 4*(b*cosh(f*x + e)^3 + (2*a - b)*cosh(f*x + e))*sinh(f*x + e) + b)) - sqrt(2)*((5*a^2*b^2 - 3*a*b^3)*cosh(f*x + e)^6 + 6*(5*a^2*b^2 - 3*a*b^3)*cosh(f*x + e)*sinh(f*x + e)^5 + (5*a^2*b^2 - 3*a*b^3)*sinh(f*x + e)^6 + 3*(8*a^3*b - 7*a^2*b^2 + a*b^3)*cosh(f*x + e)^4 + 3*(8*a^3*b - 7*a^2*b^2 + a*b^3 + 5*(5*a^2*b^2 - 3*a*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^4 + 5*a^2*b^2 - 3*a*b^3 + 4*(5*(5*a^2*b^2 - 3*a*b^3)*cosh(f*x + e)^3 + 3*(8*a^3*b - 7*a^2*b^2 + a*b^3)*cosh(f*x + e))*sinh(f*x + e)^3 + 3*(8*a^3*b - 7*a^2*b^2 + a*b^3)*cosh(f*x + e)^2 + 3*(5*(5*a^2*b^2 - 3*a*b^3)*cosh(f*x + e)^4 + 8*a^3*b - 7*a^2*b^2 + a*b^3 + 6*(8*a^3*b - 7*a^2*b^2 + a*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^2 + 6*((5*a^2*b^2 - 3*a*b^3)*cosh(f*x + e)^5 + 2*(8*a^3*b - 7*a^2*b^2 + a*b^3)*cosh(f*x + e)^3 + (8*a^3*b - 7*a^2*b^2 + a*b^3)*cosh(f*x + e))*sinh(f*x + e))*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/((a^5*b^2 - 2*a^4*b^3 + a^3*b^4)*f*cosh(f*x + e)^8 + 8*(a^5*b^2 - 2*a^4*b^3 + a^3*b^4)*f*cosh(f*x + e)*sinh(f*x + e)^7 + (a^5*b^2 - 2*a^4*b^3 + a^3*b^4)*f*sinh(f*x + e)^8 + 4*(2*a^6*b - 5*a^5*b^2 + 4*a^4*b^3 - a^3*b^4)*f*cosh(f*x + e)^6 + 4*(7*(a^5*b^2 - 2*a^4*b^3 + a^3*b^4)*f*cosh(f*x + e)^2 + (2*a^6*b - 5*a^5*b^2 + 4*a^4*b^3 - a^3*b^4)*f)*sinh(f*x + e)^6 + 2*(8*a^7 - 24*a^6*b + 27*a^5*b^2 - 14*a^4*b^3 + 3*a^3*b^4)*f*cosh(f*x + e)^4 + 8*(7*(a^5*b^2 - 2*a^4*b^3 + a^3*b^4)*f*cosh(f*x + e)^3 + 3*(2*a^6*b - 5*a^5*b^2 + 4*a^4*b^3 - a^3*b^4)*f*cosh(f*x + e))*sinh(f*x + e)^5 + 2*(35*(a^5*b^2 - 2*a^4*b^3 + a^3*b^4)*f*cosh(f*x + e)^4 + 30*(2*a^6*b - 5*a^5*b^2 + 4*a^4*b^3 - a^3*b^4)*f*cosh(f*x + e)^2 + (8*a^7 - 24*a^6*b + 27*a^5*b^2 - 14*a^4*b^3 + 3*a^3*b^4)*f)*sinh(f*x + e)^4 + 4*(2*a^6*b - 5*a^5*b^2 + 4*a^4*b^3 - a^3*b^4)*f*cosh(f*x + e)^2 + 8*(7*(a^5*b^2 - 2*a^4*b^3 + a^3*b^4)*f*cosh(f*x + e)^5 + 10*(2*a^6*b - 5*a^5*b^2 + 4*a^4*b^3 - a^3*b^4)*f*cosh(f*x + e)^3 + (8*a^7 - 24*a^6*b + 27*a^5*b^2 - 14*a^4*b^3 + 3*a^3*b^4)*f*cosh(f*x + e))*sinh(f*x + e)^3 + 4*(7*(a^5*b^2 - 2*a^4*b^3 + a^3*b^4)*f*cosh(f*x + e)^6 + 15*(2*a^6*b - 5*a^5*b^2 + 4*a^4*b^3 - a^3*b^4)*f*cosh(f*x + e)^4 + 3*(8*a^7 - 24*a^6*b + 27*a^5*b^2 - 14*a^4*b^3 + 3*a^3*b^4)*f*cosh(f*x + e)^2 + (2*a^6*b - 5*a^5*b^2 + 4*a^4*b^3 - a^3*b^4)*f)*sinh(f*x + e)^2 + (a^5*b^2 - 2*a^4*b^3 + a^3*b^4)*f + 8*((a^5*b^2 - 2*a^4*b^3 + a^3*b^4)*f*cosh(f*x + e)^7 + 3*(2*a^6*b - 5*a^5*b^2 + 4*a^4*b^3 - a^3*b^4)*f*cosh(f*x + e)^5 + (8*a^7 - 24*a^6*b + 27*a^5*b^2 - 14*a^4*b^3 + 3*a^3*b^4)*f*cosh(f*x + e)^3 + (2*a^6*b - 5*a^5*b^2 + 4*a^4*b^3 - a^3*b^4)*f*cosh(f*x + e))*sinh(f*x + e))]","B",0
120,0,0,0,1.045090," ","integrate(sinh(f*x+e)^6/(a+b*sinh(f*x+e)^2)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sinh\left(f x + e\right)^{2} + a} \sinh\left(f x + e\right)^{6}}{b^{3} \sinh\left(f x + e\right)^{6} + 3 \, a b^{2} \sinh\left(f x + e\right)^{4} + 3 \, a^{2} b \sinh\left(f x + e\right)^{2} + a^{3}}, x\right)"," ",0,"integral(sqrt(b*sinh(f*x + e)^2 + a)*sinh(f*x + e)^6/(b^3*sinh(f*x + e)^6 + 3*a*b^2*sinh(f*x + e)^4 + 3*a^2*b*sinh(f*x + e)^2 + a^3), x)","F",0
121,0,0,0,0.892060," ","integrate(sinh(f*x+e)^4/(a+b*sinh(f*x+e)^2)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sinh\left(f x + e\right)^{2} + a} \sinh\left(f x + e\right)^{4}}{b^{3} \sinh\left(f x + e\right)^{6} + 3 \, a b^{2} \sinh\left(f x + e\right)^{4} + 3 \, a^{2} b \sinh\left(f x + e\right)^{2} + a^{3}}, x\right)"," ",0,"integral(sqrt(b*sinh(f*x + e)^2 + a)*sinh(f*x + e)^4/(b^3*sinh(f*x + e)^6 + 3*a*b^2*sinh(f*x + e)^4 + 3*a^2*b*sinh(f*x + e)^2 + a^3), x)","F",0
122,0,0,0,1.966507," ","integrate(sinh(f*x+e)^2/(a+b*sinh(f*x+e)^2)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sinh\left(f x + e\right)^{2} + a} \sinh\left(f x + e\right)^{2}}{b^{3} \sinh\left(f x + e\right)^{6} + 3 \, a b^{2} \sinh\left(f x + e\right)^{4} + 3 \, a^{2} b \sinh\left(f x + e\right)^{2} + a^{3}}, x\right)"," ",0,"integral(sqrt(b*sinh(f*x + e)^2 + a)*sinh(f*x + e)^2/(b^3*sinh(f*x + e)^6 + 3*a*b^2*sinh(f*x + e)^4 + 3*a^2*b*sinh(f*x + e)^2 + a^3), x)","F",0
123,0,0,0,2.949253," ","integrate(1/(a+b*sinh(f*x+e)^2)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sinh\left(f x + e\right)^{2} + a}}{b^{3} \sinh\left(f x + e\right)^{6} + 3 \, a b^{2} \sinh\left(f x + e\right)^{4} + 3 \, a^{2} b \sinh\left(f x + e\right)^{2} + a^{3}}, x\right)"," ",0,"integral(sqrt(b*sinh(f*x + e)^2 + a)/(b^3*sinh(f*x + e)^6 + 3*a*b^2*sinh(f*x + e)^4 + 3*a^2*b*sinh(f*x + e)^2 + a^3), x)","F",0
124,0,0,0,0.631070," ","integrate(csch(f*x+e)^2/(a+b*sinh(f*x+e)^2)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sinh\left(f x + e\right)^{2} + a} \operatorname{csch}\left(f x + e\right)^{2}}{b^{3} \sinh\left(f x + e\right)^{6} + 3 \, a b^{2} \sinh\left(f x + e\right)^{4} + 3 \, a^{2} b \sinh\left(f x + e\right)^{2} + a^{3}}, x\right)"," ",0,"integral(sqrt(b*sinh(f*x + e)^2 + a)*csch(f*x + e)^2/(b^3*sinh(f*x + e)^6 + 3*a*b^2*sinh(f*x + e)^4 + 3*a^2*b*sinh(f*x + e)^2 + a^3), x)","F",0
125,1,8,0,0.962402," ","integrate(1/(1+sinh(x)^2)^(1/2),x, algorithm=""fricas"")","2 \, \arctan\left(\cosh\left(x\right) + \sinh\left(x\right)\right)"," ",0,"2*arctan(cosh(x) + sinh(x))","A",0
126,0,0,0,1.435987," ","integrate(1/(1-sinh(x)^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(-\frac{\sqrt{-\sinh\left(x\right)^{2} + 1}}{\sinh\left(x\right)^{2} - 1}, x\right)"," ",0,"integral(-sqrt(-sinh(x)^2 + 1)/(sinh(x)^2 - 1), x)","F",0
127,0,0,0,0.539128," ","integrate(1/(-1+sinh(x)^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{\sinh\left(x\right)^{2} - 1}}, x\right)"," ",0,"integral(1/sqrt(sinh(x)^2 - 1), x)","F",0
128,1,13,0,1.025044," ","integrate(1/(-1-sinh(x)^2)^(1/2),x, algorithm=""fricas"")","\log\left(e^{x} + i\right) - \log\left(e^{x} - i\right)"," ",0,"log(e^x + I) - log(e^x - I)","C",0
129,0,0,0,0.620007," ","integrate(1/(a+b*sinh(x)^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{b \sinh\left(x\right)^{2} + a}}, x\right)"," ",0,"integral(1/sqrt(b*sinh(x)^2 + a), x)","F",0
130,0,0,0,0.816411," ","integrate((d*sinh(f*x+e))^m*(a+b*sinh(f*x+e)^2)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sinh\left(f x + e\right)^{2} + a\right)}^{p} \left(d \sinh\left(f x + e\right)\right)^{m}, x\right)"," ",0,"integral((b*sinh(f*x + e)^2 + a)^p*(d*sinh(f*x + e))^m, x)","F",0
131,0,0,0,1.987315," ","integrate(sinh(f*x+e)^5*(a+b*sinh(f*x+e)^2)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sinh\left(f x + e\right)^{2} + a\right)}^{p} \sinh\left(f x + e\right)^{5}, x\right)"," ",0,"integral((b*sinh(f*x + e)^2 + a)^p*sinh(f*x + e)^5, x)","F",0
132,0,0,0,1.146165," ","integrate(sinh(f*x+e)^3*(a+b*sinh(f*x+e)^2)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sinh\left(f x + e\right)^{2} + a\right)}^{p} \sinh\left(f x + e\right)^{3}, x\right)"," ",0,"integral((b*sinh(f*x + e)^2 + a)^p*sinh(f*x + e)^3, x)","F",0
133,0,0,0,0.898294," ","integrate(sinh(f*x+e)*(a+b*sinh(f*x+e)^2)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sinh\left(f x + e\right)^{2} + a\right)}^{p} \sinh\left(f x + e\right), x\right)"," ",0,"integral((b*sinh(f*x + e)^2 + a)^p*sinh(f*x + e), x)","F",0
134,0,0,0,0.975307," ","integrate(csch(f*x+e)*(a+b*sinh(f*x+e)^2)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sinh\left(f x + e\right)^{2} + a\right)}^{p} \operatorname{csch}\left(f x + e\right), x\right)"," ",0,"integral((b*sinh(f*x + e)^2 + a)^p*csch(f*x + e), x)","F",0
135,0,0,0,1.105225," ","integrate(csch(f*x+e)^3*(a+b*sinh(f*x+e)^2)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sinh\left(f x + e\right)^{2} + a\right)}^{p} \operatorname{csch}\left(f x + e\right)^{3}, x\right)"," ",0,"integral((b*sinh(f*x + e)^2 + a)^p*csch(f*x + e)^3, x)","F",0
136,0,0,0,0.943579," ","integrate(csch(f*x+e)^5*(a+b*sinh(f*x+e)^2)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sinh\left(f x + e\right)^{2} + a\right)}^{p} \operatorname{csch}\left(f x + e\right)^{5}, x\right)"," ",0,"integral((b*sinh(f*x + e)^2 + a)^p*csch(f*x + e)^5, x)","F",0
137,0,0,0,0.787792," ","integrate(sinh(f*x+e)^4*(a+b*sinh(f*x+e)^2)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sinh\left(f x + e\right)^{2} + a\right)}^{p} \sinh\left(f x + e\right)^{4}, x\right)"," ",0,"integral((b*sinh(f*x + e)^2 + a)^p*sinh(f*x + e)^4, x)","F",0
138,0,0,0,2.125024," ","integrate(sinh(f*x+e)^2*(a+b*sinh(f*x+e)^2)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sinh\left(f x + e\right)^{2} + a\right)}^{p} \sinh\left(f x + e\right)^{2}, x\right)"," ",0,"integral((b*sinh(f*x + e)^2 + a)^p*sinh(f*x + e)^2, x)","F",0
139,0,0,0,0.982712," ","integrate(csch(f*x+e)^2*(a+b*sinh(f*x+e)^2)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sinh\left(f x + e\right)^{2} + a\right)}^{p} \operatorname{csch}\left(f x + e\right)^{2}, x\right)"," ",0,"integral((b*sinh(f*x + e)^2 + a)^p*csch(f*x + e)^2, x)","F",0
140,0,0,0,0.656292," ","integrate(csch(f*x+e)^4*(a+b*sinh(f*x+e)^2)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sinh\left(f x + e\right)^{2} + a\right)}^{p} \operatorname{csch}\left(f x + e\right)^{4}, x\right)"," ",0,"integral((b*sinh(f*x + e)^2 + a)^p*csch(f*x + e)^4, x)","F",0
141,1,188,0,1.539028," ","integrate(sinh(d*x+c)^4*(a+b*sinh(d*x+c)^3),x, algorithm=""fricas"")","\frac{5 \, b \cosh\left(d x + c\right)^{7} + 35 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} - 49 \, b \cosh\left(d x + c\right)^{5} + 280 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + 35 \, {\left(5 \, b \cosh\left(d x + c\right)^{3} - 7 \, b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 245 \, b \cosh\left(d x + c\right)^{3} + 840 \, a d x + 35 \, {\left(3 \, b \cosh\left(d x + c\right)^{5} - 14 \, b \cosh\left(d x + c\right)^{3} + 21 \, b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 1225 \, b \cosh\left(d x + c\right) + 280 \, {\left(a \cosh\left(d x + c\right)^{3} - 4 \, a \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{2240 \, d}"," ",0,"1/2240*(5*b*cosh(d*x + c)^7 + 35*b*cosh(d*x + c)*sinh(d*x + c)^6 - 49*b*cosh(d*x + c)^5 + 280*a*cosh(d*x + c)*sinh(d*x + c)^3 + 35*(5*b*cosh(d*x + c)^3 - 7*b*cosh(d*x + c))*sinh(d*x + c)^4 + 245*b*cosh(d*x + c)^3 + 840*a*d*x + 35*(3*b*cosh(d*x + c)^5 - 14*b*cosh(d*x + c)^3 + 21*b*cosh(d*x + c))*sinh(d*x + c)^2 - 1225*b*cosh(d*x + c) + 280*(a*cosh(d*x + c)^3 - 4*a*cosh(d*x + c))*sinh(d*x + c))/d","A",0
142,1,135,0,0.865984," ","integrate(sinh(d*x+c)^3*(a+b*sinh(d*x+c)^3),x, algorithm=""fricas"")","\frac{3 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + 8 \, a \cosh\left(d x + c\right)^{3} + 24 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + 2 \, {\left(5 \, b \cosh\left(d x + c\right)^{3} - 9 \, b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 30 \, b d x - 72 \, a \cosh\left(d x + c\right) + 3 \, {\left(b \cosh\left(d x + c\right)^{5} - 6 \, b \cosh\left(d x + c\right)^{3} + 15 \, b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{96 \, d}"," ",0,"1/96*(3*b*cosh(d*x + c)*sinh(d*x + c)^5 + 8*a*cosh(d*x + c)^3 + 24*a*cosh(d*x + c)*sinh(d*x + c)^2 + 2*(5*b*cosh(d*x + c)^3 - 9*b*cosh(d*x + c))*sinh(d*x + c)^3 - 30*b*d*x - 72*a*cosh(d*x + c) + 3*(b*cosh(d*x + c)^5 - 6*b*cosh(d*x + c)^3 + 15*b*cosh(d*x + c))*sinh(d*x + c))/d","A",0
143,1,105,0,1.469325," ","integrate(sinh(d*x+c)^2*(a+b*sinh(d*x+c)^3),x, algorithm=""fricas"")","\frac{3 \, b \cosh\left(d x + c\right)^{5} + 15 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} - 25 \, b \cosh\left(d x + c\right)^{3} - 120 \, a d x + 120 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right) + 15 \, {\left(2 \, b \cosh\left(d x + c\right)^{3} - 5 \, b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 150 \, b \cosh\left(d x + c\right)}{240 \, d}"," ",0,"1/240*(3*b*cosh(d*x + c)^5 + 15*b*cosh(d*x + c)*sinh(d*x + c)^4 - 25*b*cosh(d*x + c)^3 - 120*a*d*x + 120*a*cosh(d*x + c)*sinh(d*x + c) + 15*(2*b*cosh(d*x + c)^3 - 5*b*cosh(d*x + c))*sinh(d*x + c)^2 + 150*b*cosh(d*x + c))/d","A",0
144,1,63,0,1.821510," ","integrate(sinh(d*x+c)*(a+b*sinh(d*x+c)^3),x, algorithm=""fricas"")","\frac{b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + 3 \, b d x + 8 \, a \cosh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right)^{3} - 4 \, b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{8 \, d}"," ",0,"1/8*(b*cosh(d*x + c)*sinh(d*x + c)^3 + 3*b*d*x + 8*a*cosh(d*x + c) + (b*cosh(d*x + c)^3 - 4*b*cosh(d*x + c))*sinh(d*x + c))/d","A",0
145,1,47,0,1.207142," ","integrate(a+b*sinh(d*x+c)^3,x, algorithm=""fricas"")","\frac{b \cosh\left(d x + c\right)^{3} + 3 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + 12 \, a d x - 9 \, b \cosh\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(b*cosh(d*x + c)^3 + 3*b*cosh(d*x + c)*sinh(d*x + c)^2 + 12*a*d*x - 9*b*cosh(d*x + c))/d","A",0
146,1,258,0,2.183695," ","integrate(csch(d*x+c)*(a+b*sinh(d*x+c)^3),x, algorithm=""fricas"")","-\frac{4 \, b d x \cosh\left(d x + c\right)^{2} - b \cosh\left(d x + c\right)^{4} - 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} - b \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, b d x - 3 \, b \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left(a \cosh\left(d x + c\right)^{2} + 2 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a \sinh\left(d x + c\right)^{2}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) - 8 \, {\left(a \cosh\left(d x + c\right)^{2} + 2 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a \sinh\left(d x + c\right)^{2}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) + 4 \, {\left(2 \, b d x \cosh\left(d x + c\right) - b \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right) + b}{8 \, {\left(d \cosh\left(d x + c\right)^{2} + 2 \, d \cosh\left(d x + c\right) \sinh\left(d x + c\right) + d \sinh\left(d x + c\right)^{2}\right)}}"," ",0,"-1/8*(4*b*d*x*cosh(d*x + c)^2 - b*cosh(d*x + c)^4 - 4*b*cosh(d*x + c)*sinh(d*x + c)^3 - b*sinh(d*x + c)^4 + 2*(2*b*d*x - 3*b*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*(a*cosh(d*x + c)^2 + 2*a*cosh(d*x + c)*sinh(d*x + c) + a*sinh(d*x + c)^2)*log(cosh(d*x + c) + sinh(d*x + c) + 1) - 8*(a*cosh(d*x + c)^2 + 2*a*cosh(d*x + c)*sinh(d*x + c) + a*sinh(d*x + c)^2)*log(cosh(d*x + c) + sinh(d*x + c) - 1) + 4*(2*b*d*x*cosh(d*x + c) - b*cosh(d*x + c)^3)*sinh(d*x + c) + b)/(d*cosh(d*x + c)^2 + 2*d*cosh(d*x + c)*sinh(d*x + c) + d*sinh(d*x + c)^2)","B",0
147,1,40,0,0.928564," ","integrate(csch(d*x+c)^2*(a+b*sinh(d*x+c)^3),x, algorithm=""fricas"")","-\frac{a \cosh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right) + a\right)} \sinh\left(d x + c\right)}{d \sinh\left(d x + c\right)}"," ",0,"-(a*cosh(d*x + c) - (b*cosh(d*x + c) + a)*sinh(d*x + c))/(d*sinh(d*x + c))","A",0
148,1,521,0,0.622594," ","integrate(csch(d*x+c)^3*(a+b*sinh(d*x+c)^3),x, algorithm=""fricas"")","\frac{2 \, b d x \cosh\left(d x + c\right)^{4} + 2 \, b d x \sinh\left(d x + c\right)^{4} - 4 \, b d x \cosh\left(d x + c\right)^{2} - 2 \, a \cosh\left(d x + c\right)^{3} + 2 \, {\left(4 \, b d x \cosh\left(d x + c\right) - a\right)} \sinh\left(d x + c\right)^{3} + 2 \, b d x + 2 \, {\left(6 \, b d x \cosh\left(d x + c\right)^{2} - 2 \, b d x - 3 \, a \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 2 \, a \cosh\left(d x + c\right) + {\left(a \cosh\left(d x + c\right)^{4} + 4 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a \sinh\left(d x + c\right)^{4} - 2 \, a \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} - a\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \cosh\left(d x + c\right)^{3} - a \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + a\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) - {\left(a \cosh\left(d x + c\right)^{4} + 4 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a \sinh\left(d x + c\right)^{4} - 2 \, a \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a \cosh\left(d x + c\right)^{2} - a\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a \cosh\left(d x + c\right)^{3} - a \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + a\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) + 2 \, {\left(4 \, b d x \cosh\left(d x + c\right)^{3} - 4 \, b d x \cosh\left(d x + c\right) - 3 \, a \cosh\left(d x + c\right)^{2} - a\right)} \sinh\left(d x + c\right)}{2 \, {\left(d \cosh\left(d x + c\right)^{4} + 4 \, d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + d \sinh\left(d x + c\right)^{4} - 2 \, d \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, d \cosh\left(d x + c\right)^{2} - d\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(d \cosh\left(d x + c\right)^{3} - d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + d\right)}}"," ",0,"1/2*(2*b*d*x*cosh(d*x + c)^4 + 2*b*d*x*sinh(d*x + c)^4 - 4*b*d*x*cosh(d*x + c)^2 - 2*a*cosh(d*x + c)^3 + 2*(4*b*d*x*cosh(d*x + c) - a)*sinh(d*x + c)^3 + 2*b*d*x + 2*(6*b*d*x*cosh(d*x + c)^2 - 2*b*d*x - 3*a*cosh(d*x + c))*sinh(d*x + c)^2 - 2*a*cosh(d*x + c) + (a*cosh(d*x + c)^4 + 4*a*cosh(d*x + c)*sinh(d*x + c)^3 + a*sinh(d*x + c)^4 - 2*a*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 - a)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 - a*cosh(d*x + c))*sinh(d*x + c) + a)*log(cosh(d*x + c) + sinh(d*x + c) + 1) - (a*cosh(d*x + c)^4 + 4*a*cosh(d*x + c)*sinh(d*x + c)^3 + a*sinh(d*x + c)^4 - 2*a*cosh(d*x + c)^2 + 2*(3*a*cosh(d*x + c)^2 - a)*sinh(d*x + c)^2 + 4*(a*cosh(d*x + c)^3 - a*cosh(d*x + c))*sinh(d*x + c) + a)*log(cosh(d*x + c) + sinh(d*x + c) - 1) + 2*(4*b*d*x*cosh(d*x + c)^3 - 4*b*d*x*cosh(d*x + c) - 3*a*cosh(d*x + c)^2 - a)*sinh(d*x + c))/(d*cosh(d*x + c)^4 + 4*d*cosh(d*x + c)*sinh(d*x + c)^3 + d*sinh(d*x + c)^4 - 2*d*cosh(d*x + c)^2 + 2*(3*d*cosh(d*x + c)^2 - d)*sinh(d*x + c)^2 + 4*(d*cosh(d*x + c)^3 - d*cosh(d*x + c))*sinh(d*x + c) + d)","B",0
149,1,652,0,2.925391," ","integrate(csch(d*x+c)^4*(a+b*sinh(d*x+c)^3),x, algorithm=""fricas"")","-\frac{12 \, a \cosh\left(d x + c\right)^{2} + 24 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right) + 12 \, a \sinh\left(d x + c\right)^{2} + 3 \, {\left(b \cosh\left(d x + c\right)^{6} + 6 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + b \sinh\left(d x + c\right)^{6} - 3 \, b \cosh\left(d x + c\right)^{4} + 3 \, {\left(5 \, b \cosh\left(d x + c\right)^{2} - b\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, b \cosh\left(d x + c\right)^{3} - 3 \, b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 3 \, b \cosh\left(d x + c\right)^{2} + 3 \, {\left(5 \, b \cosh\left(d x + c\right)^{4} - 6 \, b \cosh\left(d x + c\right)^{2} + b\right)} \sinh\left(d x + c\right)^{2} + 6 \, {\left(b \cosh\left(d x + c\right)^{5} - 2 \, b \cosh\left(d x + c\right)^{3} + b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) - b\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) - 3 \, {\left(b \cosh\left(d x + c\right)^{6} + 6 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + b \sinh\left(d x + c\right)^{6} - 3 \, b \cosh\left(d x + c\right)^{4} + 3 \, {\left(5 \, b \cosh\left(d x + c\right)^{2} - b\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, b \cosh\left(d x + c\right)^{3} - 3 \, b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 3 \, b \cosh\left(d x + c\right)^{2} + 3 \, {\left(5 \, b \cosh\left(d x + c\right)^{4} - 6 \, b \cosh\left(d x + c\right)^{2} + b\right)} \sinh\left(d x + c\right)^{2} + 6 \, {\left(b \cosh\left(d x + c\right)^{5} - 2 \, b \cosh\left(d x + c\right)^{3} + b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) - b\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) - 4 \, a}{3 \, {\left(d \cosh\left(d x + c\right)^{6} + 6 \, d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + d \sinh\left(d x + c\right)^{6} - 3 \, d \cosh\left(d x + c\right)^{4} + 3 \, {\left(5 \, d \cosh\left(d x + c\right)^{2} - d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, d \cosh\left(d x + c\right)^{3} - 3 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 3 \, d \cosh\left(d x + c\right)^{2} + 3 \, {\left(5 \, d \cosh\left(d x + c\right)^{4} - 6 \, d \cosh\left(d x + c\right)^{2} + d\right)} \sinh\left(d x + c\right)^{2} + 6 \, {\left(d \cosh\left(d x + c\right)^{5} - 2 \, d \cosh\left(d x + c\right)^{3} + d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) - d\right)}}"," ",0,"-1/3*(12*a*cosh(d*x + c)^2 + 24*a*cosh(d*x + c)*sinh(d*x + c) + 12*a*sinh(d*x + c)^2 + 3*(b*cosh(d*x + c)^6 + 6*b*cosh(d*x + c)*sinh(d*x + c)^5 + b*sinh(d*x + c)^6 - 3*b*cosh(d*x + c)^4 + 3*(5*b*cosh(d*x + c)^2 - b)*sinh(d*x + c)^4 + 4*(5*b*cosh(d*x + c)^3 - 3*b*cosh(d*x + c))*sinh(d*x + c)^3 + 3*b*cosh(d*x + c)^2 + 3*(5*b*cosh(d*x + c)^4 - 6*b*cosh(d*x + c)^2 + b)*sinh(d*x + c)^2 + 6*(b*cosh(d*x + c)^5 - 2*b*cosh(d*x + c)^3 + b*cosh(d*x + c))*sinh(d*x + c) - b)*log(cosh(d*x + c) + sinh(d*x + c) + 1) - 3*(b*cosh(d*x + c)^6 + 6*b*cosh(d*x + c)*sinh(d*x + c)^5 + b*sinh(d*x + c)^6 - 3*b*cosh(d*x + c)^4 + 3*(5*b*cosh(d*x + c)^2 - b)*sinh(d*x + c)^4 + 4*(5*b*cosh(d*x + c)^3 - 3*b*cosh(d*x + c))*sinh(d*x + c)^3 + 3*b*cosh(d*x + c)^2 + 3*(5*b*cosh(d*x + c)^4 - 6*b*cosh(d*x + c)^2 + b)*sinh(d*x + c)^2 + 6*(b*cosh(d*x + c)^5 - 2*b*cosh(d*x + c)^3 + b*cosh(d*x + c))*sinh(d*x + c) - b)*log(cosh(d*x + c) + sinh(d*x + c) - 1) - 4*a)/(d*cosh(d*x + c)^6 + 6*d*cosh(d*x + c)*sinh(d*x + c)^5 + d*sinh(d*x + c)^6 - 3*d*cosh(d*x + c)^4 + 3*(5*d*cosh(d*x + c)^2 - d)*sinh(d*x + c)^4 + 4*(5*d*cosh(d*x + c)^3 - 3*d*cosh(d*x + c))*sinh(d*x + c)^3 + 3*d*cosh(d*x + c)^2 + 3*(5*d*cosh(d*x + c)^4 - 6*d*cosh(d*x + c)^2 + d)*sinh(d*x + c)^2 + 6*(d*cosh(d*x + c)^5 - 2*d*cosh(d*x + c)^3 + d*cosh(d*x + c))*sinh(d*x + c) - d)","B",0
150,1,355,0,0.701782," ","integrate(sinh(d*x+c)^3*(a+b*sinh(d*x+c)^3)^2,x, algorithm=""fricas"")","\frac{35 \, b^{2} \cosh\left(d x + c\right)^{9} + 315 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{8} - 405 \, b^{2} \cosh\left(d x + c\right)^{7} + 5040 \, a b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + 2268 \, b^{2} \cosh\left(d x + c\right)^{5} + 105 \, {\left(28 \, b^{2} \cosh\left(d x + c\right)^{3} - 27 \, b^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} + 315 \, {\left(14 \, b^{2} \cosh\left(d x + c\right)^{5} - 45 \, b^{2} \cosh\left(d x + c\right)^{3} + 36 \, b^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} - 50400 \, a b d x + 420 \, {\left(16 \, a^{2} - 21 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3360 \, {\left(5 \, a b \cosh\left(d x + c\right)^{3} - 9 \, a b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 315 \, {\left(4 \, b^{2} \cosh\left(d x + c\right)^{7} - 27 \, b^{2} \cosh\left(d x + c\right)^{5} + 72 \, b^{2} \cosh\left(d x + c\right)^{3} + 4 \, {\left(16 \, a^{2} - 21 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 1890 \, {\left(32 \, a^{2} - 21 \, b^{2}\right)} \cosh\left(d x + c\right) + 5040 \, {\left(a b \cosh\left(d x + c\right)^{5} - 6 \, a b \cosh\left(d x + c\right)^{3} + 15 \, a b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{80640 \, d}"," ",0,"1/80640*(35*b^2*cosh(d*x + c)^9 + 315*b^2*cosh(d*x + c)*sinh(d*x + c)^8 - 405*b^2*cosh(d*x + c)^7 + 5040*a*b*cosh(d*x + c)*sinh(d*x + c)^5 + 2268*b^2*cosh(d*x + c)^5 + 105*(28*b^2*cosh(d*x + c)^3 - 27*b^2*cosh(d*x + c))*sinh(d*x + c)^6 + 315*(14*b^2*cosh(d*x + c)^5 - 45*b^2*cosh(d*x + c)^3 + 36*b^2*cosh(d*x + c))*sinh(d*x + c)^4 - 50400*a*b*d*x + 420*(16*a^2 - 21*b^2)*cosh(d*x + c)^3 + 3360*(5*a*b*cosh(d*x + c)^3 - 9*a*b*cosh(d*x + c))*sinh(d*x + c)^3 + 315*(4*b^2*cosh(d*x + c)^7 - 27*b^2*cosh(d*x + c)^5 + 72*b^2*cosh(d*x + c)^3 + 4*(16*a^2 - 21*b^2)*cosh(d*x + c))*sinh(d*x + c)^2 - 1890*(32*a^2 - 21*b^2)*cosh(d*x + c) + 5040*(a*b*cosh(d*x + c)^5 - 6*a*b*cosh(d*x + c)^3 + 15*a*b*cosh(d*x + c))*sinh(d*x + c))/d","B",0
151,1,274,0,1.534650," ","integrate(sinh(d*x+c)^2*(a+b*sinh(d*x+c)^3)^2,x, algorithm=""fricas"")","\frac{15 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + 48 \, a b \cosh\left(d x + c\right)^{5} + 240 \, a b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} + 15 \, {\left(7 \, b^{2} \cosh\left(d x + c\right)^{3} - 8 \, b^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 400 \, a b \cosh\left(d x + c\right)^{3} + 5 \, {\left(21 \, b^{2} \cosh\left(d x + c\right)^{5} - 80 \, b^{2} \cosh\left(d x + c\right)^{3} + 84 \, b^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 15 \, {\left(64 \, a^{2} - 35 \, b^{2}\right)} d x + 2400 \, a b \cosh\left(d x + c\right) + 240 \, {\left(2 \, a b \cosh\left(d x + c\right)^{3} - 5 \, a b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 15 \, {\left(b^{2} \cosh\left(d x + c\right)^{7} - 8 \, b^{2} \cosh\left(d x + c\right)^{5} + 28 \, b^{2} \cosh\left(d x + c\right)^{3} + 8 \, {\left(8 \, a^{2} - 7 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{1920 \, d}"," ",0,"1/1920*(15*b^2*cosh(d*x + c)*sinh(d*x + c)^7 + 48*a*b*cosh(d*x + c)^5 + 240*a*b*cosh(d*x + c)*sinh(d*x + c)^4 + 15*(7*b^2*cosh(d*x + c)^3 - 8*b^2*cosh(d*x + c))*sinh(d*x + c)^5 - 400*a*b*cosh(d*x + c)^3 + 5*(21*b^2*cosh(d*x + c)^5 - 80*b^2*cosh(d*x + c)^3 + 84*b^2*cosh(d*x + c))*sinh(d*x + c)^3 - 15*(64*a^2 - 35*b^2)*d*x + 2400*a*b*cosh(d*x + c) + 240*(2*a*b*cosh(d*x + c)^3 - 5*a*b*cosh(d*x + c))*sinh(d*x + c)^2 + 15*(b^2*cosh(d*x + c)^7 - 8*b^2*cosh(d*x + c)^5 + 28*b^2*cosh(d*x + c)^3 + 8*(8*a^2 - 7*b^2)*cosh(d*x + c))*sinh(d*x + c))/d","A",0
152,1,220,0,0.468725," ","integrate(sinh(d*x+c)*(a+b*sinh(d*x+c)^3)^2,x, algorithm=""fricas"")","\frac{5 \, b^{2} \cosh\left(d x + c\right)^{7} + 35 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} - 49 \, b^{2} \cosh\left(d x + c\right)^{5} + 560 \, a b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + 245 \, b^{2} \cosh\left(d x + c\right)^{3} + 35 \, {\left(5 \, b^{2} \cosh\left(d x + c\right)^{3} - 7 \, b^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 1680 \, a b d x + 35 \, {\left(3 \, b^{2} \cosh\left(d x + c\right)^{5} - 14 \, b^{2} \cosh\left(d x + c\right)^{3} + 21 \, b^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 35 \, {\left(64 \, a^{2} - 35 \, b^{2}\right)} \cosh\left(d x + c\right) + 560 \, {\left(a b \cosh\left(d x + c\right)^{3} - 4 \, a b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{2240 \, d}"," ",0,"1/2240*(5*b^2*cosh(d*x + c)^7 + 35*b^2*cosh(d*x + c)*sinh(d*x + c)^6 - 49*b^2*cosh(d*x + c)^5 + 560*a*b*cosh(d*x + c)*sinh(d*x + c)^3 + 245*b^2*cosh(d*x + c)^3 + 35*(5*b^2*cosh(d*x + c)^3 - 7*b^2*cosh(d*x + c))*sinh(d*x + c)^4 + 1680*a*b*d*x + 35*(3*b^2*cosh(d*x + c)^5 - 14*b^2*cosh(d*x + c)^3 + 21*b^2*cosh(d*x + c))*sinh(d*x + c)^2 + 35*(64*a^2 - 35*b^2)*cosh(d*x + c) + 560*(a*b*cosh(d*x + c)^3 - 4*a*b*cosh(d*x + c))*sinh(d*x + c))/d","A",0
153,1,160,0,0.474029," ","integrate((a+b*sinh(d*x+c)^3)^2,x, algorithm=""fricas"")","\frac{3 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + 16 \, a b \cosh\left(d x + c\right)^{3} + 48 \, a b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + 2 \, {\left(5 \, b^{2} \cosh\left(d x + c\right)^{3} - 9 \, b^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 6 \, {\left(16 \, a^{2} - 5 \, b^{2}\right)} d x - 144 \, a b \cosh\left(d x + c\right) + 3 \, {\left(b^{2} \cosh\left(d x + c\right)^{5} - 6 \, b^{2} \cosh\left(d x + c\right)^{3} + 15 \, b^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{96 \, d}"," ",0,"1/96*(3*b^2*cosh(d*x + c)*sinh(d*x + c)^5 + 16*a*b*cosh(d*x + c)^3 + 48*a*b*cosh(d*x + c)*sinh(d*x + c)^2 + 2*(5*b^2*cosh(d*x + c)^3 - 9*b^2*cosh(d*x + c))*sinh(d*x + c)^3 + 6*(16*a^2 - 5*b^2)*d*x - 144*a*b*cosh(d*x + c) + 3*(b^2*cosh(d*x + c)^5 - 6*b^2*cosh(d*x + c)^3 + 15*b^2*cosh(d*x + c))*sinh(d*x + c))/d","A",0
154,1,1052,0,0.487238," ","integrate(csch(d*x+c)*(a+b*sinh(d*x+c)^3)^2,x, algorithm=""fricas"")","\frac{3 \, b^{2} \cosh\left(d x + c\right)^{10} + 30 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + 3 \, b^{2} \sinh\left(d x + c\right)^{10} - 25 \, b^{2} \cosh\left(d x + c\right)^{8} - 480 \, a b d x \cosh\left(d x + c\right)^{5} + 120 \, a b \cosh\left(d x + c\right)^{7} + 5 \, {\left(27 \, b^{2} \cosh\left(d x + c\right)^{2} - 5 \, b^{2}\right)} \sinh\left(d x + c\right)^{8} + 150 \, b^{2} \cosh\left(d x + c\right)^{6} + 40 \, {\left(9 \, b^{2} \cosh\left(d x + c\right)^{3} - 5 \, b^{2} \cosh\left(d x + c\right) + 3 \, a b\right)} \sinh\left(d x + c\right)^{7} + 10 \, {\left(63 \, b^{2} \cosh\left(d x + c\right)^{4} - 70 \, b^{2} \cosh\left(d x + c\right)^{2} + 84 \, a b \cosh\left(d x + c\right) + 15 \, b^{2}\right)} \sinh\left(d x + c\right)^{6} + 150 \, b^{2} \cosh\left(d x + c\right)^{4} + 4 \, {\left(189 \, b^{2} \cosh\left(d x + c\right)^{5} - 350 \, b^{2} \cosh\left(d x + c\right)^{3} - 120 \, a b d x + 630 \, a b \cosh\left(d x + c\right)^{2} + 225 \, b^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 120 \, a b \cosh\left(d x + c\right)^{3} + 10 \, {\left(63 \, b^{2} \cosh\left(d x + c\right)^{6} - 175 \, b^{2} \cosh\left(d x + c\right)^{4} - 240 \, a b d x \cosh\left(d x + c\right) + 420 \, a b \cosh\left(d x + c\right)^{3} + 225 \, b^{2} \cosh\left(d x + c\right)^{2} + 15 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} - 25 \, b^{2} \cosh\left(d x + c\right)^{2} + 40 \, {\left(9 \, b^{2} \cosh\left(d x + c\right)^{7} - 35 \, b^{2} \cosh\left(d x + c\right)^{5} - 120 \, a b d x \cosh\left(d x + c\right)^{2} + 105 \, a b \cosh\left(d x + c\right)^{4} + 75 \, b^{2} \cosh\left(d x + c\right)^{3} + 15 \, b^{2} \cosh\left(d x + c\right) - 3 \, a b\right)} \sinh\left(d x + c\right)^{3} + 5 \, {\left(27 \, b^{2} \cosh\left(d x + c\right)^{8} - 140 \, b^{2} \cosh\left(d x + c\right)^{6} - 960 \, a b d x \cosh\left(d x + c\right)^{3} + 504 \, a b \cosh\left(d x + c\right)^{5} + 450 \, b^{2} \cosh\left(d x + c\right)^{4} + 180 \, b^{2} \cosh\left(d x + c\right)^{2} - 72 \, a b \cosh\left(d x + c\right) - 5 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} + 3 \, b^{2} - 480 \, {\left(a^{2} \cosh\left(d x + c\right)^{5} + 5 \, a^{2} \cosh\left(d x + c\right)^{4} \sinh\left(d x + c\right) + 10 \, a^{2} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right)^{2} + 10 \, a^{2} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{3} + 5 \, a^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} + a^{2} \sinh\left(d x + c\right)^{5}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) + 480 \, {\left(a^{2} \cosh\left(d x + c\right)^{5} + 5 \, a^{2} \cosh\left(d x + c\right)^{4} \sinh\left(d x + c\right) + 10 \, a^{2} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right)^{2} + 10 \, a^{2} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{3} + 5 \, a^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} + a^{2} \sinh\left(d x + c\right)^{5}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) + 10 \, {\left(3 \, b^{2} \cosh\left(d x + c\right)^{9} - 20 \, b^{2} \cosh\left(d x + c\right)^{7} - 240 \, a b d x \cosh\left(d x + c\right)^{4} + 84 \, a b \cosh\left(d x + c\right)^{6} + 90 \, b^{2} \cosh\left(d x + c\right)^{5} + 60 \, b^{2} \cosh\left(d x + c\right)^{3} - 36 \, a b \cosh\left(d x + c\right)^{2} - 5 \, b^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{480 \, {\left(d \cosh\left(d x + c\right)^{5} + 5 \, d \cosh\left(d x + c\right)^{4} \sinh\left(d x + c\right) + 10 \, d \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right)^{2} + 10 \, d \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{3} + 5 \, d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} + d \sinh\left(d x + c\right)^{5}\right)}}"," ",0,"1/480*(3*b^2*cosh(d*x + c)^10 + 30*b^2*cosh(d*x + c)*sinh(d*x + c)^9 + 3*b^2*sinh(d*x + c)^10 - 25*b^2*cosh(d*x + c)^8 - 480*a*b*d*x*cosh(d*x + c)^5 + 120*a*b*cosh(d*x + c)^7 + 5*(27*b^2*cosh(d*x + c)^2 - 5*b^2)*sinh(d*x + c)^8 + 150*b^2*cosh(d*x + c)^6 + 40*(9*b^2*cosh(d*x + c)^3 - 5*b^2*cosh(d*x + c) + 3*a*b)*sinh(d*x + c)^7 + 10*(63*b^2*cosh(d*x + c)^4 - 70*b^2*cosh(d*x + c)^2 + 84*a*b*cosh(d*x + c) + 15*b^2)*sinh(d*x + c)^6 + 150*b^2*cosh(d*x + c)^4 + 4*(189*b^2*cosh(d*x + c)^5 - 350*b^2*cosh(d*x + c)^3 - 120*a*b*d*x + 630*a*b*cosh(d*x + c)^2 + 225*b^2*cosh(d*x + c))*sinh(d*x + c)^5 - 120*a*b*cosh(d*x + c)^3 + 10*(63*b^2*cosh(d*x + c)^6 - 175*b^2*cosh(d*x + c)^4 - 240*a*b*d*x*cosh(d*x + c) + 420*a*b*cosh(d*x + c)^3 + 225*b^2*cosh(d*x + c)^2 + 15*b^2)*sinh(d*x + c)^4 - 25*b^2*cosh(d*x + c)^2 + 40*(9*b^2*cosh(d*x + c)^7 - 35*b^2*cosh(d*x + c)^5 - 120*a*b*d*x*cosh(d*x + c)^2 + 105*a*b*cosh(d*x + c)^4 + 75*b^2*cosh(d*x + c)^3 + 15*b^2*cosh(d*x + c) - 3*a*b)*sinh(d*x + c)^3 + 5*(27*b^2*cosh(d*x + c)^8 - 140*b^2*cosh(d*x + c)^6 - 960*a*b*d*x*cosh(d*x + c)^3 + 504*a*b*cosh(d*x + c)^5 + 450*b^2*cosh(d*x + c)^4 + 180*b^2*cosh(d*x + c)^2 - 72*a*b*cosh(d*x + c) - 5*b^2)*sinh(d*x + c)^2 + 3*b^2 - 480*(a^2*cosh(d*x + c)^5 + 5*a^2*cosh(d*x + c)^4*sinh(d*x + c) + 10*a^2*cosh(d*x + c)^3*sinh(d*x + c)^2 + 10*a^2*cosh(d*x + c)^2*sinh(d*x + c)^3 + 5*a^2*cosh(d*x + c)*sinh(d*x + c)^4 + a^2*sinh(d*x + c)^5)*log(cosh(d*x + c) + sinh(d*x + c) + 1) + 480*(a^2*cosh(d*x + c)^5 + 5*a^2*cosh(d*x + c)^4*sinh(d*x + c) + 10*a^2*cosh(d*x + c)^3*sinh(d*x + c)^2 + 10*a^2*cosh(d*x + c)^2*sinh(d*x + c)^3 + 5*a^2*cosh(d*x + c)*sinh(d*x + c)^4 + a^2*sinh(d*x + c)^5)*log(cosh(d*x + c) + sinh(d*x + c) - 1) + 10*(3*b^2*cosh(d*x + c)^9 - 20*b^2*cosh(d*x + c)^7 - 240*a*b*d*x*cosh(d*x + c)^4 + 84*a*b*cosh(d*x + c)^6 + 90*b^2*cosh(d*x + c)^5 + 60*b^2*cosh(d*x + c)^3 - 36*a*b*cosh(d*x + c)^2 - 5*b^2*cosh(d*x + c))*sinh(d*x + c))/(d*cosh(d*x + c)^5 + 5*d*cosh(d*x + c)^4*sinh(d*x + c) + 10*d*cosh(d*x + c)^3*sinh(d*x + c)^2 + 10*d*cosh(d*x + c)^2*sinh(d*x + c)^3 + 5*d*cosh(d*x + c)*sinh(d*x + c)^4 + d*sinh(d*x + c)^5)","B",0
155,1,142,0,0.446868," ","integrate(csch(d*x+c)^2*(a+b*sinh(d*x+c)^3)^2,x, algorithm=""fricas"")","\frac{b^{2} \cosh\left(d x + c\right)^{5} + 5 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} - 9 \, b^{2} \cosh\left(d x + c\right)^{3} + {\left(10 \, b^{2} \cosh\left(d x + c\right)^{3} - 27 \, b^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 8 \, {\left(8 \, a^{2} - b^{2}\right)} \cosh\left(d x + c\right) + 8 \, {\left(3 \, b^{2} d x + 16 \, a b \cosh\left(d x + c\right) + 8 \, a^{2}\right)} \sinh\left(d x + c\right)}{64 \, d \sinh\left(d x + c\right)}"," ",0,"1/64*(b^2*cosh(d*x + c)^5 + 5*b^2*cosh(d*x + c)*sinh(d*x + c)^4 - 9*b^2*cosh(d*x + c)^3 + (10*b^2*cosh(d*x + c)^3 - 27*b^2*cosh(d*x + c))*sinh(d*x + c)^2 - 8*(8*a^2 - b^2)*cosh(d*x + c) + 8*(3*b^2*d*x + 16*a*b*cosh(d*x + c) + 8*a^2)*sinh(d*x + c))/(d*sinh(d*x + c))","A",0
156,1,1616,0,0.678863," ","integrate(csch(d*x+c)^3*(a+b*sinh(d*x+c)^3)^2,x, algorithm=""fricas"")","\frac{b^{2} \cosh\left(d x + c\right)^{10} + 10 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + b^{2} \sinh\left(d x + c\right)^{10} + 48 \, a b d x \cosh\left(d x + c\right)^{7} - 11 \, b^{2} \cosh\left(d x + c\right)^{8} - 96 \, a b d x \cosh\left(d x + c\right)^{5} + {\left(45 \, b^{2} \cosh\left(d x + c\right)^{2} - 11 \, b^{2}\right)} \sinh\left(d x + c\right)^{8} + 8 \, {\left(15 \, b^{2} \cosh\left(d x + c\right)^{3} + 6 \, a b d x - 11 \, b^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 48 \, a b d x \cosh\left(d x + c\right)^{3} - 2 \, {\left(12 \, a^{2} - 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(105 \, b^{2} \cosh\left(d x + c\right)^{4} + 168 \, a b d x \cosh\left(d x + c\right) - 154 \, b^{2} \cosh\left(d x + c\right)^{2} - 12 \, a^{2} + 5 \, b^{2}\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(63 \, b^{2} \cosh\left(d x + c\right)^{5} + 252 \, a b d x \cosh\left(d x + c\right)^{2} - 154 \, b^{2} \cosh\left(d x + c\right)^{3} - 24 \, a b d x - 3 \, {\left(12 \, a^{2} - 5 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 2 \, {\left(12 \, a^{2} - 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(105 \, b^{2} \cosh\left(d x + c\right)^{6} + 840 \, a b d x \cosh\left(d x + c\right)^{3} - 385 \, b^{2} \cosh\left(d x + c\right)^{4} - 240 \, a b d x \cosh\left(d x + c\right) - 15 \, {\left(12 \, a^{2} - 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 12 \, a^{2} + 5 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} - 11 \, b^{2} \cosh\left(d x + c\right)^{2} + 8 \, {\left(15 \, b^{2} \cosh\left(d x + c\right)^{7} + 210 \, a b d x \cosh\left(d x + c\right)^{4} - 77 \, b^{2} \cosh\left(d x + c\right)^{5} - 120 \, a b d x \cosh\left(d x + c\right)^{2} + 6 \, a b d x - 5 \, {\left(12 \, a^{2} - 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(12 \, a^{2} - 5 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(45 \, b^{2} \cosh\left(d x + c\right)^{8} + 1008 \, a b d x \cosh\left(d x + c\right)^{5} - 308 \, b^{2} \cosh\left(d x + c\right)^{6} - 960 \, a b d x \cosh\left(d x + c\right)^{3} + 144 \, a b d x \cosh\left(d x + c\right) - 30 \, {\left(12 \, a^{2} - 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} - 12 \, {\left(12 \, a^{2} - 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 11 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} + b^{2} + 12 \, {\left(a^{2} \cosh\left(d x + c\right)^{7} + 7 \, a^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + a^{2} \sinh\left(d x + c\right)^{7} - 2 \, a^{2} \cosh\left(d x + c\right)^{5} + {\left(21 \, a^{2} \cosh\left(d x + c\right)^{2} - 2 \, a^{2}\right)} \sinh\left(d x + c\right)^{5} + a^{2} \cosh\left(d x + c\right)^{3} + 5 \, {\left(7 \, a^{2} \cosh\left(d x + c\right)^{3} - 2 \, a^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + {\left(35 \, a^{2} \cosh\left(d x + c\right)^{4} - 20 \, a^{2} \cosh\left(d x + c\right)^{2} + a^{2}\right)} \sinh\left(d x + c\right)^{3} + {\left(21 \, a^{2} \cosh\left(d x + c\right)^{5} - 20 \, a^{2} \cosh\left(d x + c\right)^{3} + 3 \, a^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(7 \, a^{2} \cosh\left(d x + c\right)^{6} - 10 \, a^{2} \cosh\left(d x + c\right)^{4} + 3 \, a^{2} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) - 12 \, {\left(a^{2} \cosh\left(d x + c\right)^{7} + 7 \, a^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + a^{2} \sinh\left(d x + c\right)^{7} - 2 \, a^{2} \cosh\left(d x + c\right)^{5} + {\left(21 \, a^{2} \cosh\left(d x + c\right)^{2} - 2 \, a^{2}\right)} \sinh\left(d x + c\right)^{5} + a^{2} \cosh\left(d x + c\right)^{3} + 5 \, {\left(7 \, a^{2} \cosh\left(d x + c\right)^{3} - 2 \, a^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + {\left(35 \, a^{2} \cosh\left(d x + c\right)^{4} - 20 \, a^{2} \cosh\left(d x + c\right)^{2} + a^{2}\right)} \sinh\left(d x + c\right)^{3} + {\left(21 \, a^{2} \cosh\left(d x + c\right)^{5} - 20 \, a^{2} \cosh\left(d x + c\right)^{3} + 3 \, a^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(7 \, a^{2} \cosh\left(d x + c\right)^{6} - 10 \, a^{2} \cosh\left(d x + c\right)^{4} + 3 \, a^{2} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) + 2 \, {\left(5 \, b^{2} \cosh\left(d x + c\right)^{9} + 168 \, a b d x \cosh\left(d x + c\right)^{6} - 44 \, b^{2} \cosh\left(d x + c\right)^{7} - 240 \, a b d x \cosh\left(d x + c\right)^{4} + 72 \, a b d x \cosh\left(d x + c\right)^{2} - 6 \, {\left(12 \, a^{2} - 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} - 4 \, {\left(12 \, a^{2} - 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - 11 \, b^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{24 \, {\left(d \cosh\left(d x + c\right)^{7} + 7 \, d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + d \sinh\left(d x + c\right)^{7} - 2 \, d \cosh\left(d x + c\right)^{5} + {\left(21 \, d \cosh\left(d x + c\right)^{2} - 2 \, d\right)} \sinh\left(d x + c\right)^{5} + 5 \, {\left(7 \, d \cosh\left(d x + c\right)^{3} - 2 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + d \cosh\left(d x + c\right)^{3} + {\left(35 \, d \cosh\left(d x + c\right)^{4} - 20 \, d \cosh\left(d x + c\right)^{2} + d\right)} \sinh\left(d x + c\right)^{3} + {\left(21 \, d \cosh\left(d x + c\right)^{5} - 20 \, d \cosh\left(d x + c\right)^{3} + 3 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(7 \, d \cosh\left(d x + c\right)^{6} - 10 \, d \cosh\left(d x + c\right)^{4} + 3 \, d \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"1/24*(b^2*cosh(d*x + c)^10 + 10*b^2*cosh(d*x + c)*sinh(d*x + c)^9 + b^2*sinh(d*x + c)^10 + 48*a*b*d*x*cosh(d*x + c)^7 - 11*b^2*cosh(d*x + c)^8 - 96*a*b*d*x*cosh(d*x + c)^5 + (45*b^2*cosh(d*x + c)^2 - 11*b^2)*sinh(d*x + c)^8 + 8*(15*b^2*cosh(d*x + c)^3 + 6*a*b*d*x - 11*b^2*cosh(d*x + c))*sinh(d*x + c)^7 + 48*a*b*d*x*cosh(d*x + c)^3 - 2*(12*a^2 - 5*b^2)*cosh(d*x + c)^6 + 2*(105*b^2*cosh(d*x + c)^4 + 168*a*b*d*x*cosh(d*x + c) - 154*b^2*cosh(d*x + c)^2 - 12*a^2 + 5*b^2)*sinh(d*x + c)^6 + 4*(63*b^2*cosh(d*x + c)^5 + 252*a*b*d*x*cosh(d*x + c)^2 - 154*b^2*cosh(d*x + c)^3 - 24*a*b*d*x - 3*(12*a^2 - 5*b^2)*cosh(d*x + c))*sinh(d*x + c)^5 - 2*(12*a^2 - 5*b^2)*cosh(d*x + c)^4 + 2*(105*b^2*cosh(d*x + c)^6 + 840*a*b*d*x*cosh(d*x + c)^3 - 385*b^2*cosh(d*x + c)^4 - 240*a*b*d*x*cosh(d*x + c) - 15*(12*a^2 - 5*b^2)*cosh(d*x + c)^2 - 12*a^2 + 5*b^2)*sinh(d*x + c)^4 - 11*b^2*cosh(d*x + c)^2 + 8*(15*b^2*cosh(d*x + c)^7 + 210*a*b*d*x*cosh(d*x + c)^4 - 77*b^2*cosh(d*x + c)^5 - 120*a*b*d*x*cosh(d*x + c)^2 + 6*a*b*d*x - 5*(12*a^2 - 5*b^2)*cosh(d*x + c)^3 - (12*a^2 - 5*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + (45*b^2*cosh(d*x + c)^8 + 1008*a*b*d*x*cosh(d*x + c)^5 - 308*b^2*cosh(d*x + c)^6 - 960*a*b*d*x*cosh(d*x + c)^3 + 144*a*b*d*x*cosh(d*x + c) - 30*(12*a^2 - 5*b^2)*cosh(d*x + c)^4 - 12*(12*a^2 - 5*b^2)*cosh(d*x + c)^2 - 11*b^2)*sinh(d*x + c)^2 + b^2 + 12*(a^2*cosh(d*x + c)^7 + 7*a^2*cosh(d*x + c)*sinh(d*x + c)^6 + a^2*sinh(d*x + c)^7 - 2*a^2*cosh(d*x + c)^5 + (21*a^2*cosh(d*x + c)^2 - 2*a^2)*sinh(d*x + c)^5 + a^2*cosh(d*x + c)^3 + 5*(7*a^2*cosh(d*x + c)^3 - 2*a^2*cosh(d*x + c))*sinh(d*x + c)^4 + (35*a^2*cosh(d*x + c)^4 - 20*a^2*cosh(d*x + c)^2 + a^2)*sinh(d*x + c)^3 + (21*a^2*cosh(d*x + c)^5 - 20*a^2*cosh(d*x + c)^3 + 3*a^2*cosh(d*x + c))*sinh(d*x + c)^2 + (7*a^2*cosh(d*x + c)^6 - 10*a^2*cosh(d*x + c)^4 + 3*a^2*cosh(d*x + c)^2)*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) + 1) - 12*(a^2*cosh(d*x + c)^7 + 7*a^2*cosh(d*x + c)*sinh(d*x + c)^6 + a^2*sinh(d*x + c)^7 - 2*a^2*cosh(d*x + c)^5 + (21*a^2*cosh(d*x + c)^2 - 2*a^2)*sinh(d*x + c)^5 + a^2*cosh(d*x + c)^3 + 5*(7*a^2*cosh(d*x + c)^3 - 2*a^2*cosh(d*x + c))*sinh(d*x + c)^4 + (35*a^2*cosh(d*x + c)^4 - 20*a^2*cosh(d*x + c)^2 + a^2)*sinh(d*x + c)^3 + (21*a^2*cosh(d*x + c)^5 - 20*a^2*cosh(d*x + c)^3 + 3*a^2*cosh(d*x + c))*sinh(d*x + c)^2 + (7*a^2*cosh(d*x + c)^6 - 10*a^2*cosh(d*x + c)^4 + 3*a^2*cosh(d*x + c)^2)*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) - 1) + 2*(5*b^2*cosh(d*x + c)^9 + 168*a*b*d*x*cosh(d*x + c)^6 - 44*b^2*cosh(d*x + c)^7 - 240*a*b*d*x*cosh(d*x + c)^4 + 72*a*b*d*x*cosh(d*x + c)^2 - 6*(12*a^2 - 5*b^2)*cosh(d*x + c)^5 - 4*(12*a^2 - 5*b^2)*cosh(d*x + c)^3 - 11*b^2*cosh(d*x + c))*sinh(d*x + c))/(d*cosh(d*x + c)^7 + 7*d*cosh(d*x + c)*sinh(d*x + c)^6 + d*sinh(d*x + c)^7 - 2*d*cosh(d*x + c)^5 + (21*d*cosh(d*x + c)^2 - 2*d)*sinh(d*x + c)^5 + 5*(7*d*cosh(d*x + c)^3 - 2*d*cosh(d*x + c))*sinh(d*x + c)^4 + d*cosh(d*x + c)^3 + (35*d*cosh(d*x + c)^4 - 20*d*cosh(d*x + c)^2 + d)*sinh(d*x + c)^3 + (21*d*cosh(d*x + c)^5 - 20*d*cosh(d*x + c)^3 + 3*d*cosh(d*x + c))*sinh(d*x + c)^2 + (7*d*cosh(d*x + c)^6 - 10*d*cosh(d*x + c)^4 + 3*d*cosh(d*x + c)^2)*sinh(d*x + c))","B",0
157,1,1748,0,0.565591," ","integrate(csch(d*x+c)^4*(a+b*sinh(d*x+c)^3)^2,x, algorithm=""fricas"")","\frac{3 \, b^{2} \cosh\left(d x + c\right)^{10} + 30 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + 3 \, b^{2} \sinh\left(d x + c\right)^{10} - 3 \, {\left(4 \, b^{2} d x + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{8} - 3 \, {\left(4 \, b^{2} d x - 45 \, b^{2} \cosh\left(d x + c\right)^{2} + 3 \, b^{2}\right)} \sinh\left(d x + c\right)^{8} + 24 \, {\left(15 \, b^{2} \cosh\left(d x + c\right)^{3} - {\left(4 \, b^{2} d x + 3 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 6 \, {\left(6 \, b^{2} d x + b^{2}\right)} \cosh\left(d x + c\right)^{6} + 6 \, {\left(105 \, b^{2} \cosh\left(d x + c\right)^{4} + 6 \, b^{2} d x - 14 \, {\left(4 \, b^{2} d x + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + b^{2}\right)} \sinh\left(d x + c\right)^{6} + 12 \, {\left(63 \, b^{2} \cosh\left(d x + c\right)^{5} - 14 \, {\left(4 \, b^{2} d x + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(6 \, b^{2} d x + b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 6 \, {\left(6 \, b^{2} d x + 16 \, a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{4} + 6 \, {\left(105 \, b^{2} \cosh\left(d x + c\right)^{6} - 35 \, {\left(4 \, b^{2} d x + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} - 6 \, b^{2} d x + 15 \, {\left(6 \, b^{2} d x + b^{2}\right)} \cosh\left(d x + c\right)^{2} - 16 \, a^{2} + b^{2}\right)} \sinh\left(d x + c\right)^{4} + 24 \, {\left(15 \, b^{2} \cosh\left(d x + c\right)^{7} - 7 \, {\left(4 \, b^{2} d x + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(6 \, b^{2} d x + b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(6 \, b^{2} d x + 16 \, a^{2} - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(12 \, b^{2} d x + 32 \, a^{2} - 9 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(135 \, b^{2} \cosh\left(d x + c\right)^{8} - 84 \, {\left(4 \, b^{2} d x + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 90 \, {\left(6 \, b^{2} d x + b^{2}\right)} \cosh\left(d x + c\right)^{4} + 12 \, b^{2} d x - 36 \, {\left(6 \, b^{2} d x + 16 \, a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 32 \, a^{2} - 9 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} + 3 \, b^{2} - 48 \, {\left(a b \cosh\left(d x + c\right)^{8} + 8 \, a b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + a b \sinh\left(d x + c\right)^{8} - 3 \, a b \cosh\left(d x + c\right)^{6} + {\left(28 \, a b \cosh\left(d x + c\right)^{2} - 3 \, a b\right)} \sinh\left(d x + c\right)^{6} + 3 \, a b \cosh\left(d x + c\right)^{4} + 2 \, {\left(28 \, a b \cosh\left(d x + c\right)^{3} - 9 \, a b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + {\left(70 \, a b \cosh\left(d x + c\right)^{4} - 45 \, a b \cosh\left(d x + c\right)^{2} + 3 \, a b\right)} \sinh\left(d x + c\right)^{4} - a b \cosh\left(d x + c\right)^{2} + 4 \, {\left(14 \, a b \cosh\left(d x + c\right)^{5} - 15 \, a b \cosh\left(d x + c\right)^{3} + 3 \, a b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(28 \, a b \cosh\left(d x + c\right)^{6} - 45 \, a b \cosh\left(d x + c\right)^{4} + 18 \, a b \cosh\left(d x + c\right)^{2} - a b\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(4 \, a b \cosh\left(d x + c\right)^{7} - 9 \, a b \cosh\left(d x + c\right)^{5} + 6 \, a b \cosh\left(d x + c\right)^{3} - a b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) + 48 \, {\left(a b \cosh\left(d x + c\right)^{8} + 8 \, a b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + a b \sinh\left(d x + c\right)^{8} - 3 \, a b \cosh\left(d x + c\right)^{6} + {\left(28 \, a b \cosh\left(d x + c\right)^{2} - 3 \, a b\right)} \sinh\left(d x + c\right)^{6} + 3 \, a b \cosh\left(d x + c\right)^{4} + 2 \, {\left(28 \, a b \cosh\left(d x + c\right)^{3} - 9 \, a b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + {\left(70 \, a b \cosh\left(d x + c\right)^{4} - 45 \, a b \cosh\left(d x + c\right)^{2} + 3 \, a b\right)} \sinh\left(d x + c\right)^{4} - a b \cosh\left(d x + c\right)^{2} + 4 \, {\left(14 \, a b \cosh\left(d x + c\right)^{5} - 15 \, a b \cosh\left(d x + c\right)^{3} + 3 \, a b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(28 \, a b \cosh\left(d x + c\right)^{6} - 45 \, a b \cosh\left(d x + c\right)^{4} + 18 \, a b \cosh\left(d x + c\right)^{2} - a b\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(4 \, a b \cosh\left(d x + c\right)^{7} - 9 \, a b \cosh\left(d x + c\right)^{5} + 6 \, a b \cosh\left(d x + c\right)^{3} - a b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) + 2 \, {\left(15 \, b^{2} \cosh\left(d x + c\right)^{9} - 12 \, {\left(4 \, b^{2} d x + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} + 18 \, {\left(6 \, b^{2} d x + b^{2}\right)} \cosh\left(d x + c\right)^{5} - 12 \, {\left(6 \, b^{2} d x + 16 \, a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(12 \, b^{2} d x + 32 \, a^{2} - 9 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{24 \, {\left(d \cosh\left(d x + c\right)^{8} + 8 \, d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + d \sinh\left(d x + c\right)^{8} - 3 \, d \cosh\left(d x + c\right)^{6} + {\left(28 \, d \cosh\left(d x + c\right)^{2} - 3 \, d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(28 \, d \cosh\left(d x + c\right)^{3} - 9 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 3 \, d \cosh\left(d x + c\right)^{4} + {\left(70 \, d \cosh\left(d x + c\right)^{4} - 45 \, d \cosh\left(d x + c\right)^{2} + 3 \, d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(14 \, d \cosh\left(d x + c\right)^{5} - 15 \, d \cosh\left(d x + c\right)^{3} + 3 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - d \cosh\left(d x + c\right)^{2} + {\left(28 \, d \cosh\left(d x + c\right)^{6} - 45 \, d \cosh\left(d x + c\right)^{4} + 18 \, d \cosh\left(d x + c\right)^{2} - d\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(4 \, d \cosh\left(d x + c\right)^{7} - 9 \, d \cosh\left(d x + c\right)^{5} + 6 \, d \cosh\left(d x + c\right)^{3} - d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"1/24*(3*b^2*cosh(d*x + c)^10 + 30*b^2*cosh(d*x + c)*sinh(d*x + c)^9 + 3*b^2*sinh(d*x + c)^10 - 3*(4*b^2*d*x + 3*b^2)*cosh(d*x + c)^8 - 3*(4*b^2*d*x - 45*b^2*cosh(d*x + c)^2 + 3*b^2)*sinh(d*x + c)^8 + 24*(15*b^2*cosh(d*x + c)^3 - (4*b^2*d*x + 3*b^2)*cosh(d*x + c))*sinh(d*x + c)^7 + 6*(6*b^2*d*x + b^2)*cosh(d*x + c)^6 + 6*(105*b^2*cosh(d*x + c)^4 + 6*b^2*d*x - 14*(4*b^2*d*x + 3*b^2)*cosh(d*x + c)^2 + b^2)*sinh(d*x + c)^6 + 12*(63*b^2*cosh(d*x + c)^5 - 14*(4*b^2*d*x + 3*b^2)*cosh(d*x + c)^3 + 3*(6*b^2*d*x + b^2)*cosh(d*x + c))*sinh(d*x + c)^5 - 6*(6*b^2*d*x + 16*a^2 - b^2)*cosh(d*x + c)^4 + 6*(105*b^2*cosh(d*x + c)^6 - 35*(4*b^2*d*x + 3*b^2)*cosh(d*x + c)^4 - 6*b^2*d*x + 15*(6*b^2*d*x + b^2)*cosh(d*x + c)^2 - 16*a^2 + b^2)*sinh(d*x + c)^4 + 24*(15*b^2*cosh(d*x + c)^7 - 7*(4*b^2*d*x + 3*b^2)*cosh(d*x + c)^5 + 5*(6*b^2*d*x + b^2)*cosh(d*x + c)^3 - (6*b^2*d*x + 16*a^2 - b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + (12*b^2*d*x + 32*a^2 - 9*b^2)*cosh(d*x + c)^2 + (135*b^2*cosh(d*x + c)^8 - 84*(4*b^2*d*x + 3*b^2)*cosh(d*x + c)^6 + 90*(6*b^2*d*x + b^2)*cosh(d*x + c)^4 + 12*b^2*d*x - 36*(6*b^2*d*x + 16*a^2 - b^2)*cosh(d*x + c)^2 + 32*a^2 - 9*b^2)*sinh(d*x + c)^2 + 3*b^2 - 48*(a*b*cosh(d*x + c)^8 + 8*a*b*cosh(d*x + c)*sinh(d*x + c)^7 + a*b*sinh(d*x + c)^8 - 3*a*b*cosh(d*x + c)^6 + (28*a*b*cosh(d*x + c)^2 - 3*a*b)*sinh(d*x + c)^6 + 3*a*b*cosh(d*x + c)^4 + 2*(28*a*b*cosh(d*x + c)^3 - 9*a*b*cosh(d*x + c))*sinh(d*x + c)^5 + (70*a*b*cosh(d*x + c)^4 - 45*a*b*cosh(d*x + c)^2 + 3*a*b)*sinh(d*x + c)^4 - a*b*cosh(d*x + c)^2 + 4*(14*a*b*cosh(d*x + c)^5 - 15*a*b*cosh(d*x + c)^3 + 3*a*b*cosh(d*x + c))*sinh(d*x + c)^3 + (28*a*b*cosh(d*x + c)^6 - 45*a*b*cosh(d*x + c)^4 + 18*a*b*cosh(d*x + c)^2 - a*b)*sinh(d*x + c)^2 + 2*(4*a*b*cosh(d*x + c)^7 - 9*a*b*cosh(d*x + c)^5 + 6*a*b*cosh(d*x + c)^3 - a*b*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) + 1) + 48*(a*b*cosh(d*x + c)^8 + 8*a*b*cosh(d*x + c)*sinh(d*x + c)^7 + a*b*sinh(d*x + c)^8 - 3*a*b*cosh(d*x + c)^6 + (28*a*b*cosh(d*x + c)^2 - 3*a*b)*sinh(d*x + c)^6 + 3*a*b*cosh(d*x + c)^4 + 2*(28*a*b*cosh(d*x + c)^3 - 9*a*b*cosh(d*x + c))*sinh(d*x + c)^5 + (70*a*b*cosh(d*x + c)^4 - 45*a*b*cosh(d*x + c)^2 + 3*a*b)*sinh(d*x + c)^4 - a*b*cosh(d*x + c)^2 + 4*(14*a*b*cosh(d*x + c)^5 - 15*a*b*cosh(d*x + c)^3 + 3*a*b*cosh(d*x + c))*sinh(d*x + c)^3 + (28*a*b*cosh(d*x + c)^6 - 45*a*b*cosh(d*x + c)^4 + 18*a*b*cosh(d*x + c)^2 - a*b)*sinh(d*x + c)^2 + 2*(4*a*b*cosh(d*x + c)^7 - 9*a*b*cosh(d*x + c)^5 + 6*a*b*cosh(d*x + c)^3 - a*b*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) - 1) + 2*(15*b^2*cosh(d*x + c)^9 - 12*(4*b^2*d*x + 3*b^2)*cosh(d*x + c)^7 + 18*(6*b^2*d*x + b^2)*cosh(d*x + c)^5 - 12*(6*b^2*d*x + 16*a^2 - b^2)*cosh(d*x + c)^3 + (12*b^2*d*x + 32*a^2 - 9*b^2)*cosh(d*x + c))*sinh(d*x + c))/(d*cosh(d*x + c)^8 + 8*d*cosh(d*x + c)*sinh(d*x + c)^7 + d*sinh(d*x + c)^8 - 3*d*cosh(d*x + c)^6 + (28*d*cosh(d*x + c)^2 - 3*d)*sinh(d*x + c)^6 + 2*(28*d*cosh(d*x + c)^3 - 9*d*cosh(d*x + c))*sinh(d*x + c)^5 + 3*d*cosh(d*x + c)^4 + (70*d*cosh(d*x + c)^4 - 45*d*cosh(d*x + c)^2 + 3*d)*sinh(d*x + c)^4 + 4*(14*d*cosh(d*x + c)^5 - 15*d*cosh(d*x + c)^3 + 3*d*cosh(d*x + c))*sinh(d*x + c)^3 - d*cosh(d*x + c)^2 + (28*d*cosh(d*x + c)^6 - 45*d*cosh(d*x + c)^4 + 18*d*cosh(d*x + c)^2 - d)*sinh(d*x + c)^2 + 2*(4*d*cosh(d*x + c)^7 - 9*d*cosh(d*x + c)^5 + 6*d*cosh(d*x + c)^3 - d*cosh(d*x + c))*sinh(d*x + c))","B",0
158,1,2119,0,0.532544," ","integrate(csch(d*x+c)^5*(a+b*sinh(d*x+c)^3)^2,x, algorithm=""fricas"")","\frac{4 \, b^{2} \cosh\left(d x + c\right)^{10} + 40 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + 4 \, b^{2} \sinh\left(d x + c\right)^{10} - 32 \, a b \cosh\left(d x + c\right)^{7} + 6 \, {\left(a^{2} - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{8} + 6 \, {\left(30 \, b^{2} \cosh\left(d x + c\right)^{2} + a^{2} - 2 \, b^{2}\right)} \sinh\left(d x + c\right)^{8} + 16 \, {\left(30 \, b^{2} \cosh\left(d x + c\right)^{3} - 2 \, a b + 3 \, {\left(a^{2} - 2 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 96 \, a b \cosh\left(d x + c\right)^{5} - 2 \, {\left(11 \, a^{2} - 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(420 \, b^{2} \cosh\left(d x + c\right)^{4} - 112 \, a b \cosh\left(d x + c\right) + 84 \, {\left(a^{2} - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 11 \, a^{2} + 4 \, b^{2}\right)} \sinh\left(d x + c\right)^{6} + 12 \, {\left(84 \, b^{2} \cosh\left(d x + c\right)^{5} - 56 \, a b \cosh\left(d x + c\right)^{2} + 28 \, {\left(a^{2} - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 8 \, a b - {\left(11 \, a^{2} - 4 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 96 \, a b \cosh\left(d x + c\right)^{3} - 2 \, {\left(11 \, a^{2} - 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(420 \, b^{2} \cosh\left(d x + c\right)^{6} - 560 \, a b \cosh\left(d x + c\right)^{3} + 210 \, {\left(a^{2} - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 240 \, a b \cosh\left(d x + c\right) - 15 \, {\left(11 \, a^{2} - 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 11 \, a^{2} + 4 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(60 \, b^{2} \cosh\left(d x + c\right)^{7} - 140 \, a b \cosh\left(d x + c\right)^{4} + 42 \, {\left(a^{2} - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 120 \, a b \cosh\left(d x + c\right)^{2} - 5 \, {\left(11 \, a^{2} - 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - 12 \, a b - {\left(11 \, a^{2} - 4 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 32 \, a b \cosh\left(d x + c\right) + 6 \, {\left(a^{2} - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 6 \, {\left(30 \, b^{2} \cosh\left(d x + c\right)^{8} - 112 \, a b \cosh\left(d x + c\right)^{5} + 28 \, {\left(a^{2} - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 160 \, a b \cosh\left(d x + c\right)^{3} - 5 \, {\left(11 \, a^{2} - 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} - 48 \, a b \cosh\left(d x + c\right) - 2 \, {\left(11 \, a^{2} - 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} - 2 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, b^{2} - 3 \, {\left(a^{2} \cosh\left(d x + c\right)^{9} + 9 \, a^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{8} + a^{2} \sinh\left(d x + c\right)^{9} - 4 \, a^{2} \cosh\left(d x + c\right)^{7} + 4 \, {\left(9 \, a^{2} \cosh\left(d x + c\right)^{2} - a^{2}\right)} \sinh\left(d x + c\right)^{7} + 6 \, a^{2} \cosh\left(d x + c\right)^{5} + 28 \, {\left(3 \, a^{2} \cosh\left(d x + c\right)^{3} - a^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} + 6 \, {\left(21 \, a^{2} \cosh\left(d x + c\right)^{4} - 14 \, a^{2} \cosh\left(d x + c\right)^{2} + a^{2}\right)} \sinh\left(d x + c\right)^{5} - 4 \, a^{2} \cosh\left(d x + c\right)^{3} + 2 \, {\left(63 \, a^{2} \cosh\left(d x + c\right)^{5} - 70 \, a^{2} \cosh\left(d x + c\right)^{3} + 15 \, a^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(21 \, a^{2} \cosh\left(d x + c\right)^{6} - 35 \, a^{2} \cosh\left(d x + c\right)^{4} + 15 \, a^{2} \cosh\left(d x + c\right)^{2} - a^{2}\right)} \sinh\left(d x + c\right)^{3} + a^{2} \cosh\left(d x + c\right) + 12 \, {\left(3 \, a^{2} \cosh\left(d x + c\right)^{7} - 7 \, a^{2} \cosh\left(d x + c\right)^{5} + 5 \, a^{2} \cosh\left(d x + c\right)^{3} - a^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(9 \, a^{2} \cosh\left(d x + c\right)^{8} - 28 \, a^{2} \cosh\left(d x + c\right)^{6} + 30 \, a^{2} \cosh\left(d x + c\right)^{4} - 12 \, a^{2} \cosh\left(d x + c\right)^{2} + a^{2}\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) + 3 \, {\left(a^{2} \cosh\left(d x + c\right)^{9} + 9 \, a^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{8} + a^{2} \sinh\left(d x + c\right)^{9} - 4 \, a^{2} \cosh\left(d x + c\right)^{7} + 4 \, {\left(9 \, a^{2} \cosh\left(d x + c\right)^{2} - a^{2}\right)} \sinh\left(d x + c\right)^{7} + 6 \, a^{2} \cosh\left(d x + c\right)^{5} + 28 \, {\left(3 \, a^{2} \cosh\left(d x + c\right)^{3} - a^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} + 6 \, {\left(21 \, a^{2} \cosh\left(d x + c\right)^{4} - 14 \, a^{2} \cosh\left(d x + c\right)^{2} + a^{2}\right)} \sinh\left(d x + c\right)^{5} - 4 \, a^{2} \cosh\left(d x + c\right)^{3} + 2 \, {\left(63 \, a^{2} \cosh\left(d x + c\right)^{5} - 70 \, a^{2} \cosh\left(d x + c\right)^{3} + 15 \, a^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(21 \, a^{2} \cosh\left(d x + c\right)^{6} - 35 \, a^{2} \cosh\left(d x + c\right)^{4} + 15 \, a^{2} \cosh\left(d x + c\right)^{2} - a^{2}\right)} \sinh\left(d x + c\right)^{3} + a^{2} \cosh\left(d x + c\right) + 12 \, {\left(3 \, a^{2} \cosh\left(d x + c\right)^{7} - 7 \, a^{2} \cosh\left(d x + c\right)^{5} + 5 \, a^{2} \cosh\left(d x + c\right)^{3} - a^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(9 \, a^{2} \cosh\left(d x + c\right)^{8} - 28 \, a^{2} \cosh\left(d x + c\right)^{6} + 30 \, a^{2} \cosh\left(d x + c\right)^{4} - 12 \, a^{2} \cosh\left(d x + c\right)^{2} + a^{2}\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) + 4 \, {\left(10 \, b^{2} \cosh\left(d x + c\right)^{9} - 56 \, a b \cosh\left(d x + c\right)^{6} + 12 \, {\left(a^{2} - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} + 120 \, a b \cosh\left(d x + c\right)^{4} - 3 \, {\left(11 \, a^{2} - 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} - 72 \, a b \cosh\left(d x + c\right)^{2} - 2 \, {\left(11 \, a^{2} - 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 8 \, a b + 3 \, {\left(a^{2} - 2 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{8 \, {\left(d \cosh\left(d x + c\right)^{9} + 9 \, d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{8} + d \sinh\left(d x + c\right)^{9} - 4 \, d \cosh\left(d x + c\right)^{7} + 4 \, {\left(9 \, d \cosh\left(d x + c\right)^{2} - d\right)} \sinh\left(d x + c\right)^{7} + 28 \, {\left(3 \, d \cosh\left(d x + c\right)^{3} - d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} + 6 \, d \cosh\left(d x + c\right)^{5} + 6 \, {\left(21 \, d \cosh\left(d x + c\right)^{4} - 14 \, d \cosh\left(d x + c\right)^{2} + d\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(63 \, d \cosh\left(d x + c\right)^{5} - 70 \, d \cosh\left(d x + c\right)^{3} + 15 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} - 4 \, d \cosh\left(d x + c\right)^{3} + 4 \, {\left(21 \, d \cosh\left(d x + c\right)^{6} - 35 \, d \cosh\left(d x + c\right)^{4} + 15 \, d \cosh\left(d x + c\right)^{2} - d\right)} \sinh\left(d x + c\right)^{3} + 12 \, {\left(3 \, d \cosh\left(d x + c\right)^{7} - 7 \, d \cosh\left(d x + c\right)^{5} + 5 \, d \cosh\left(d x + c\right)^{3} - d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + d \cosh\left(d x + c\right) + {\left(9 \, d \cosh\left(d x + c\right)^{8} - 28 \, d \cosh\left(d x + c\right)^{6} + 30 \, d \cosh\left(d x + c\right)^{4} - 12 \, d \cosh\left(d x + c\right)^{2} + d\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"1/8*(4*b^2*cosh(d*x + c)^10 + 40*b^2*cosh(d*x + c)*sinh(d*x + c)^9 + 4*b^2*sinh(d*x + c)^10 - 32*a*b*cosh(d*x + c)^7 + 6*(a^2 - 2*b^2)*cosh(d*x + c)^8 + 6*(30*b^2*cosh(d*x + c)^2 + a^2 - 2*b^2)*sinh(d*x + c)^8 + 16*(30*b^2*cosh(d*x + c)^3 - 2*a*b + 3*(a^2 - 2*b^2)*cosh(d*x + c))*sinh(d*x + c)^7 + 96*a*b*cosh(d*x + c)^5 - 2*(11*a^2 - 4*b^2)*cosh(d*x + c)^6 + 2*(420*b^2*cosh(d*x + c)^4 - 112*a*b*cosh(d*x + c) + 84*(a^2 - 2*b^2)*cosh(d*x + c)^2 - 11*a^2 + 4*b^2)*sinh(d*x + c)^6 + 12*(84*b^2*cosh(d*x + c)^5 - 56*a*b*cosh(d*x + c)^2 + 28*(a^2 - 2*b^2)*cosh(d*x + c)^3 + 8*a*b - (11*a^2 - 4*b^2)*cosh(d*x + c))*sinh(d*x + c)^5 - 96*a*b*cosh(d*x + c)^3 - 2*(11*a^2 - 4*b^2)*cosh(d*x + c)^4 + 2*(420*b^2*cosh(d*x + c)^6 - 560*a*b*cosh(d*x + c)^3 + 210*(a^2 - 2*b^2)*cosh(d*x + c)^4 + 240*a*b*cosh(d*x + c) - 15*(11*a^2 - 4*b^2)*cosh(d*x + c)^2 - 11*a^2 + 4*b^2)*sinh(d*x + c)^4 + 8*(60*b^2*cosh(d*x + c)^7 - 140*a*b*cosh(d*x + c)^4 + 42*(a^2 - 2*b^2)*cosh(d*x + c)^5 + 120*a*b*cosh(d*x + c)^2 - 5*(11*a^2 - 4*b^2)*cosh(d*x + c)^3 - 12*a*b - (11*a^2 - 4*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 32*a*b*cosh(d*x + c) + 6*(a^2 - 2*b^2)*cosh(d*x + c)^2 + 6*(30*b^2*cosh(d*x + c)^8 - 112*a*b*cosh(d*x + c)^5 + 28*(a^2 - 2*b^2)*cosh(d*x + c)^6 + 160*a*b*cosh(d*x + c)^3 - 5*(11*a^2 - 4*b^2)*cosh(d*x + c)^4 - 48*a*b*cosh(d*x + c) - 2*(11*a^2 - 4*b^2)*cosh(d*x + c)^2 + a^2 - 2*b^2)*sinh(d*x + c)^2 + 4*b^2 - 3*(a^2*cosh(d*x + c)^9 + 9*a^2*cosh(d*x + c)*sinh(d*x + c)^8 + a^2*sinh(d*x + c)^9 - 4*a^2*cosh(d*x + c)^7 + 4*(9*a^2*cosh(d*x + c)^2 - a^2)*sinh(d*x + c)^7 + 6*a^2*cosh(d*x + c)^5 + 28*(3*a^2*cosh(d*x + c)^3 - a^2*cosh(d*x + c))*sinh(d*x + c)^6 + 6*(21*a^2*cosh(d*x + c)^4 - 14*a^2*cosh(d*x + c)^2 + a^2)*sinh(d*x + c)^5 - 4*a^2*cosh(d*x + c)^3 + 2*(63*a^2*cosh(d*x + c)^5 - 70*a^2*cosh(d*x + c)^3 + 15*a^2*cosh(d*x + c))*sinh(d*x + c)^4 + 4*(21*a^2*cosh(d*x + c)^6 - 35*a^2*cosh(d*x + c)^4 + 15*a^2*cosh(d*x + c)^2 - a^2)*sinh(d*x + c)^3 + a^2*cosh(d*x + c) + 12*(3*a^2*cosh(d*x + c)^7 - 7*a^2*cosh(d*x + c)^5 + 5*a^2*cosh(d*x + c)^3 - a^2*cosh(d*x + c))*sinh(d*x + c)^2 + (9*a^2*cosh(d*x + c)^8 - 28*a^2*cosh(d*x + c)^6 + 30*a^2*cosh(d*x + c)^4 - 12*a^2*cosh(d*x + c)^2 + a^2)*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) + 1) + 3*(a^2*cosh(d*x + c)^9 + 9*a^2*cosh(d*x + c)*sinh(d*x + c)^8 + a^2*sinh(d*x + c)^9 - 4*a^2*cosh(d*x + c)^7 + 4*(9*a^2*cosh(d*x + c)^2 - a^2)*sinh(d*x + c)^7 + 6*a^2*cosh(d*x + c)^5 + 28*(3*a^2*cosh(d*x + c)^3 - a^2*cosh(d*x + c))*sinh(d*x + c)^6 + 6*(21*a^2*cosh(d*x + c)^4 - 14*a^2*cosh(d*x + c)^2 + a^2)*sinh(d*x + c)^5 - 4*a^2*cosh(d*x + c)^3 + 2*(63*a^2*cosh(d*x + c)^5 - 70*a^2*cosh(d*x + c)^3 + 15*a^2*cosh(d*x + c))*sinh(d*x + c)^4 + 4*(21*a^2*cosh(d*x + c)^6 - 35*a^2*cosh(d*x + c)^4 + 15*a^2*cosh(d*x + c)^2 - a^2)*sinh(d*x + c)^3 + a^2*cosh(d*x + c) + 12*(3*a^2*cosh(d*x + c)^7 - 7*a^2*cosh(d*x + c)^5 + 5*a^2*cosh(d*x + c)^3 - a^2*cosh(d*x + c))*sinh(d*x + c)^2 + (9*a^2*cosh(d*x + c)^8 - 28*a^2*cosh(d*x + c)^6 + 30*a^2*cosh(d*x + c)^4 - 12*a^2*cosh(d*x + c)^2 + a^2)*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) - 1) + 4*(10*b^2*cosh(d*x + c)^9 - 56*a*b*cosh(d*x + c)^6 + 12*(a^2 - 2*b^2)*cosh(d*x + c)^7 + 120*a*b*cosh(d*x + c)^4 - 3*(11*a^2 - 4*b^2)*cosh(d*x + c)^5 - 72*a*b*cosh(d*x + c)^2 - 2*(11*a^2 - 4*b^2)*cosh(d*x + c)^3 + 8*a*b + 3*(a^2 - 2*b^2)*cosh(d*x + c))*sinh(d*x + c))/(d*cosh(d*x + c)^9 + 9*d*cosh(d*x + c)*sinh(d*x + c)^8 + d*sinh(d*x + c)^9 - 4*d*cosh(d*x + c)^7 + 4*(9*d*cosh(d*x + c)^2 - d)*sinh(d*x + c)^7 + 28*(3*d*cosh(d*x + c)^3 - d*cosh(d*x + c))*sinh(d*x + c)^6 + 6*d*cosh(d*x + c)^5 + 6*(21*d*cosh(d*x + c)^4 - 14*d*cosh(d*x + c)^2 + d)*sinh(d*x + c)^5 + 2*(63*d*cosh(d*x + c)^5 - 70*d*cosh(d*x + c)^3 + 15*d*cosh(d*x + c))*sinh(d*x + c)^4 - 4*d*cosh(d*x + c)^3 + 4*(21*d*cosh(d*x + c)^6 - 35*d*cosh(d*x + c)^4 + 15*d*cosh(d*x + c)^2 - d)*sinh(d*x + c)^3 + 12*(3*d*cosh(d*x + c)^7 - 7*d*cosh(d*x + c)^5 + 5*d*cosh(d*x + c)^3 - d*cosh(d*x + c))*sinh(d*x + c)^2 + d*cosh(d*x + c) + (9*d*cosh(d*x + c)^8 - 28*d*cosh(d*x + c)^6 + 30*d*cosh(d*x + c)^4 - 12*d*cosh(d*x + c)^2 + d)*sinh(d*x + c))","B",0
159,1,2310,0,0.663128," ","integrate(csch(d*x+c)^6*(a+b*sinh(d*x+c)^3)^2,x, algorithm=""fricas"")","\frac{15 \, b^{2} d x \cosh\left(d x + c\right)^{10} + 15 \, b^{2} d x \sinh\left(d x + c\right)^{10} - 75 \, b^{2} d x \cosh\left(d x + c\right)^{8} - 30 \, a b \cosh\left(d x + c\right)^{9} + 150 \, b^{2} d x \cosh\left(d x + c\right)^{6} + 30 \, {\left(5 \, b^{2} d x \cosh\left(d x + c\right) - a b\right)} \sinh\left(d x + c\right)^{9} + 60 \, a b \cosh\left(d x + c\right)^{7} + 15 \, {\left(45 \, b^{2} d x \cosh\left(d x + c\right)^{2} - 5 \, b^{2} d x - 18 \, a b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{8} + 60 \, {\left(30 \, b^{2} d x \cosh\left(d x + c\right)^{3} - 10 \, b^{2} d x \cosh\left(d x + c\right) - 18 \, a b \cosh\left(d x + c\right)^{2} + a b\right)} \sinh\left(d x + c\right)^{7} + 30 \, {\left(105 \, b^{2} d x \cosh\left(d x + c\right)^{4} - 70 \, b^{2} d x \cosh\left(d x + c\right)^{2} - 84 \, a b \cosh\left(d x + c\right)^{3} + 5 \, b^{2} d x + 14 \, a b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} + 60 \, {\left(63 \, b^{2} d x \cosh\left(d x + c\right)^{5} - 70 \, b^{2} d x \cosh\left(d x + c\right)^{3} - 63 \, a b \cosh\left(d x + c\right)^{4} + 15 \, b^{2} d x \cosh\left(d x + c\right) + 21 \, a b \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{5} - 60 \, a b \cosh\left(d x + c\right)^{3} - 10 \, {\left(15 \, b^{2} d x + 16 \, a^{2}\right)} \cosh\left(d x + c\right)^{4} + 10 \, {\left(315 \, b^{2} d x \cosh\left(d x + c\right)^{6} - 525 \, b^{2} d x \cosh\left(d x + c\right)^{4} - 378 \, a b \cosh\left(d x + c\right)^{5} + 225 \, b^{2} d x \cosh\left(d x + c\right)^{2} + 210 \, a b \cosh\left(d x + c\right)^{3} - 15 \, b^{2} d x - 16 \, a^{2}\right)} \sinh\left(d x + c\right)^{4} - 15 \, b^{2} d x + 20 \, {\left(90 \, b^{2} d x \cosh\left(d x + c\right)^{7} - 210 \, b^{2} d x \cosh\left(d x + c\right)^{5} - 126 \, a b \cosh\left(d x + c\right)^{6} + 150 \, b^{2} d x \cosh\left(d x + c\right)^{3} + 105 \, a b \cosh\left(d x + c\right)^{4} - 3 \, a b - 2 \, {\left(15 \, b^{2} d x + 16 \, a^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 30 \, a b \cosh\left(d x + c\right) + 5 \, {\left(15 \, b^{2} d x + 16 \, a^{2}\right)} \cosh\left(d x + c\right)^{2} + 5 \, {\left(135 \, b^{2} d x \cosh\left(d x + c\right)^{8} - 420 \, b^{2} d x \cosh\left(d x + c\right)^{6} - 216 \, a b \cosh\left(d x + c\right)^{7} + 450 \, b^{2} d x \cosh\left(d x + c\right)^{4} + 252 \, a b \cosh\left(d x + c\right)^{5} + 15 \, b^{2} d x - 36 \, a b \cosh\left(d x + c\right) - 12 \, {\left(15 \, b^{2} d x + 16 \, a^{2}\right)} \cosh\left(d x + c\right)^{2} + 16 \, a^{2}\right)} \sinh\left(d x + c\right)^{2} - 16 \, a^{2} + 15 \, {\left(a b \cosh\left(d x + c\right)^{10} + 10 \, a b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + a b \sinh\left(d x + c\right)^{10} - 5 \, a b \cosh\left(d x + c\right)^{8} + 5 \, {\left(9 \, a b \cosh\left(d x + c\right)^{2} - a b\right)} \sinh\left(d x + c\right)^{8} + 10 \, a b \cosh\left(d x + c\right)^{6} + 40 \, {\left(3 \, a b \cosh\left(d x + c\right)^{3} - a b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 10 \, {\left(21 \, a b \cosh\left(d x + c\right)^{4} - 14 \, a b \cosh\left(d x + c\right)^{2} + a b\right)} \sinh\left(d x + c\right)^{6} - 10 \, a b \cosh\left(d x + c\right)^{4} + 4 \, {\left(63 \, a b \cosh\left(d x + c\right)^{5} - 70 \, a b \cosh\left(d x + c\right)^{3} + 15 \, a b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 10 \, {\left(21 \, a b \cosh\left(d x + c\right)^{6} - 35 \, a b \cosh\left(d x + c\right)^{4} + 15 \, a b \cosh\left(d x + c\right)^{2} - a b\right)} \sinh\left(d x + c\right)^{4} + 5 \, a b \cosh\left(d x + c\right)^{2} + 40 \, {\left(3 \, a b \cosh\left(d x + c\right)^{7} - 7 \, a b \cosh\left(d x + c\right)^{5} + 5 \, a b \cosh\left(d x + c\right)^{3} - a b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 5 \, {\left(9 \, a b \cosh\left(d x + c\right)^{8} - 28 \, a b \cosh\left(d x + c\right)^{6} + 30 \, a b \cosh\left(d x + c\right)^{4} - 12 \, a b \cosh\left(d x + c\right)^{2} + a b\right)} \sinh\left(d x + c\right)^{2} - a b + 10 \, {\left(a b \cosh\left(d x + c\right)^{9} - 4 \, a b \cosh\left(d x + c\right)^{7} + 6 \, a b \cosh\left(d x + c\right)^{5} - 4 \, a b \cosh\left(d x + c\right)^{3} + a b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) - 15 \, {\left(a b \cosh\left(d x + c\right)^{10} + 10 \, a b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + a b \sinh\left(d x + c\right)^{10} - 5 \, a b \cosh\left(d x + c\right)^{8} + 5 \, {\left(9 \, a b \cosh\left(d x + c\right)^{2} - a b\right)} \sinh\left(d x + c\right)^{8} + 10 \, a b \cosh\left(d x + c\right)^{6} + 40 \, {\left(3 \, a b \cosh\left(d x + c\right)^{3} - a b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 10 \, {\left(21 \, a b \cosh\left(d x + c\right)^{4} - 14 \, a b \cosh\left(d x + c\right)^{2} + a b\right)} \sinh\left(d x + c\right)^{6} - 10 \, a b \cosh\left(d x + c\right)^{4} + 4 \, {\left(63 \, a b \cosh\left(d x + c\right)^{5} - 70 \, a b \cosh\left(d x + c\right)^{3} + 15 \, a b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 10 \, {\left(21 \, a b \cosh\left(d x + c\right)^{6} - 35 \, a b \cosh\left(d x + c\right)^{4} + 15 \, a b \cosh\left(d x + c\right)^{2} - a b\right)} \sinh\left(d x + c\right)^{4} + 5 \, a b \cosh\left(d x + c\right)^{2} + 40 \, {\left(3 \, a b \cosh\left(d x + c\right)^{7} - 7 \, a b \cosh\left(d x + c\right)^{5} + 5 \, a b \cosh\left(d x + c\right)^{3} - a b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 5 \, {\left(9 \, a b \cosh\left(d x + c\right)^{8} - 28 \, a b \cosh\left(d x + c\right)^{6} + 30 \, a b \cosh\left(d x + c\right)^{4} - 12 \, a b \cosh\left(d x + c\right)^{2} + a b\right)} \sinh\left(d x + c\right)^{2} - a b + 10 \, {\left(a b \cosh\left(d x + c\right)^{9} - 4 \, a b \cosh\left(d x + c\right)^{7} + 6 \, a b \cosh\left(d x + c\right)^{5} - 4 \, a b \cosh\left(d x + c\right)^{3} + a b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) + 10 \, {\left(15 \, b^{2} d x \cosh\left(d x + c\right)^{9} - 60 \, b^{2} d x \cosh\left(d x + c\right)^{7} - 27 \, a b \cosh\left(d x + c\right)^{8} + 90 \, b^{2} d x \cosh\left(d x + c\right)^{5} + 42 \, a b \cosh\left(d x + c\right)^{6} - 18 \, a b \cosh\left(d x + c\right)^{2} - 4 \, {\left(15 \, b^{2} d x + 16 \, a^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, a b + {\left(15 \, b^{2} d x + 16 \, a^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{15 \, {\left(d \cosh\left(d x + c\right)^{10} + 10 \, d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + d \sinh\left(d x + c\right)^{10} - 5 \, d \cosh\left(d x + c\right)^{8} + 5 \, {\left(9 \, d \cosh\left(d x + c\right)^{2} - d\right)} \sinh\left(d x + c\right)^{8} + 40 \, {\left(3 \, d \cosh\left(d x + c\right)^{3} - d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 10 \, d \cosh\left(d x + c\right)^{6} + 10 \, {\left(21 \, d \cosh\left(d x + c\right)^{4} - 14 \, d \cosh\left(d x + c\right)^{2} + d\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(63 \, d \cosh\left(d x + c\right)^{5} - 70 \, d \cosh\left(d x + c\right)^{3} + 15 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 10 \, d \cosh\left(d x + c\right)^{4} + 10 \, {\left(21 \, d \cosh\left(d x + c\right)^{6} - 35 \, d \cosh\left(d x + c\right)^{4} + 15 \, d \cosh\left(d x + c\right)^{2} - d\right)} \sinh\left(d x + c\right)^{4} + 40 \, {\left(3 \, d \cosh\left(d x + c\right)^{7} - 7 \, d \cosh\left(d x + c\right)^{5} + 5 \, d \cosh\left(d x + c\right)^{3} - d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 5 \, d \cosh\left(d x + c\right)^{2} + 5 \, {\left(9 \, d \cosh\left(d x + c\right)^{8} - 28 \, d \cosh\left(d x + c\right)^{6} + 30 \, d \cosh\left(d x + c\right)^{4} - 12 \, d \cosh\left(d x + c\right)^{2} + d\right)} \sinh\left(d x + c\right)^{2} + 10 \, {\left(d \cosh\left(d x + c\right)^{9} - 4 \, d \cosh\left(d x + c\right)^{7} + 6 \, d \cosh\left(d x + c\right)^{5} - 4 \, d \cosh\left(d x + c\right)^{3} + d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) - d\right)}}"," ",0,"1/15*(15*b^2*d*x*cosh(d*x + c)^10 + 15*b^2*d*x*sinh(d*x + c)^10 - 75*b^2*d*x*cosh(d*x + c)^8 - 30*a*b*cosh(d*x + c)^9 + 150*b^2*d*x*cosh(d*x + c)^6 + 30*(5*b^2*d*x*cosh(d*x + c) - a*b)*sinh(d*x + c)^9 + 60*a*b*cosh(d*x + c)^7 + 15*(45*b^2*d*x*cosh(d*x + c)^2 - 5*b^2*d*x - 18*a*b*cosh(d*x + c))*sinh(d*x + c)^8 + 60*(30*b^2*d*x*cosh(d*x + c)^3 - 10*b^2*d*x*cosh(d*x + c) - 18*a*b*cosh(d*x + c)^2 + a*b)*sinh(d*x + c)^7 + 30*(105*b^2*d*x*cosh(d*x + c)^4 - 70*b^2*d*x*cosh(d*x + c)^2 - 84*a*b*cosh(d*x + c)^3 + 5*b^2*d*x + 14*a*b*cosh(d*x + c))*sinh(d*x + c)^6 + 60*(63*b^2*d*x*cosh(d*x + c)^5 - 70*b^2*d*x*cosh(d*x + c)^3 - 63*a*b*cosh(d*x + c)^4 + 15*b^2*d*x*cosh(d*x + c) + 21*a*b*cosh(d*x + c)^2)*sinh(d*x + c)^5 - 60*a*b*cosh(d*x + c)^3 - 10*(15*b^2*d*x + 16*a^2)*cosh(d*x + c)^4 + 10*(315*b^2*d*x*cosh(d*x + c)^6 - 525*b^2*d*x*cosh(d*x + c)^4 - 378*a*b*cosh(d*x + c)^5 + 225*b^2*d*x*cosh(d*x + c)^2 + 210*a*b*cosh(d*x + c)^3 - 15*b^2*d*x - 16*a^2)*sinh(d*x + c)^4 - 15*b^2*d*x + 20*(90*b^2*d*x*cosh(d*x + c)^7 - 210*b^2*d*x*cosh(d*x + c)^5 - 126*a*b*cosh(d*x + c)^6 + 150*b^2*d*x*cosh(d*x + c)^3 + 105*a*b*cosh(d*x + c)^4 - 3*a*b - 2*(15*b^2*d*x + 16*a^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 30*a*b*cosh(d*x + c) + 5*(15*b^2*d*x + 16*a^2)*cosh(d*x + c)^2 + 5*(135*b^2*d*x*cosh(d*x + c)^8 - 420*b^2*d*x*cosh(d*x + c)^6 - 216*a*b*cosh(d*x + c)^7 + 450*b^2*d*x*cosh(d*x + c)^4 + 252*a*b*cosh(d*x + c)^5 + 15*b^2*d*x - 36*a*b*cosh(d*x + c) - 12*(15*b^2*d*x + 16*a^2)*cosh(d*x + c)^2 + 16*a^2)*sinh(d*x + c)^2 - 16*a^2 + 15*(a*b*cosh(d*x + c)^10 + 10*a*b*cosh(d*x + c)*sinh(d*x + c)^9 + a*b*sinh(d*x + c)^10 - 5*a*b*cosh(d*x + c)^8 + 5*(9*a*b*cosh(d*x + c)^2 - a*b)*sinh(d*x + c)^8 + 10*a*b*cosh(d*x + c)^6 + 40*(3*a*b*cosh(d*x + c)^3 - a*b*cosh(d*x + c))*sinh(d*x + c)^7 + 10*(21*a*b*cosh(d*x + c)^4 - 14*a*b*cosh(d*x + c)^2 + a*b)*sinh(d*x + c)^6 - 10*a*b*cosh(d*x + c)^4 + 4*(63*a*b*cosh(d*x + c)^5 - 70*a*b*cosh(d*x + c)^3 + 15*a*b*cosh(d*x + c))*sinh(d*x + c)^5 + 10*(21*a*b*cosh(d*x + c)^6 - 35*a*b*cosh(d*x + c)^4 + 15*a*b*cosh(d*x + c)^2 - a*b)*sinh(d*x + c)^4 + 5*a*b*cosh(d*x + c)^2 + 40*(3*a*b*cosh(d*x + c)^7 - 7*a*b*cosh(d*x + c)^5 + 5*a*b*cosh(d*x + c)^3 - a*b*cosh(d*x + c))*sinh(d*x + c)^3 + 5*(9*a*b*cosh(d*x + c)^8 - 28*a*b*cosh(d*x + c)^6 + 30*a*b*cosh(d*x + c)^4 - 12*a*b*cosh(d*x + c)^2 + a*b)*sinh(d*x + c)^2 - a*b + 10*(a*b*cosh(d*x + c)^9 - 4*a*b*cosh(d*x + c)^7 + 6*a*b*cosh(d*x + c)^5 - 4*a*b*cosh(d*x + c)^3 + a*b*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) + 1) - 15*(a*b*cosh(d*x + c)^10 + 10*a*b*cosh(d*x + c)*sinh(d*x + c)^9 + a*b*sinh(d*x + c)^10 - 5*a*b*cosh(d*x + c)^8 + 5*(9*a*b*cosh(d*x + c)^2 - a*b)*sinh(d*x + c)^8 + 10*a*b*cosh(d*x + c)^6 + 40*(3*a*b*cosh(d*x + c)^3 - a*b*cosh(d*x + c))*sinh(d*x + c)^7 + 10*(21*a*b*cosh(d*x + c)^4 - 14*a*b*cosh(d*x + c)^2 + a*b)*sinh(d*x + c)^6 - 10*a*b*cosh(d*x + c)^4 + 4*(63*a*b*cosh(d*x + c)^5 - 70*a*b*cosh(d*x + c)^3 + 15*a*b*cosh(d*x + c))*sinh(d*x + c)^5 + 10*(21*a*b*cosh(d*x + c)^6 - 35*a*b*cosh(d*x + c)^4 + 15*a*b*cosh(d*x + c)^2 - a*b)*sinh(d*x + c)^4 + 5*a*b*cosh(d*x + c)^2 + 40*(3*a*b*cosh(d*x + c)^7 - 7*a*b*cosh(d*x + c)^5 + 5*a*b*cosh(d*x + c)^3 - a*b*cosh(d*x + c))*sinh(d*x + c)^3 + 5*(9*a*b*cosh(d*x + c)^8 - 28*a*b*cosh(d*x + c)^6 + 30*a*b*cosh(d*x + c)^4 - 12*a*b*cosh(d*x + c)^2 + a*b)*sinh(d*x + c)^2 - a*b + 10*(a*b*cosh(d*x + c)^9 - 4*a*b*cosh(d*x + c)^7 + 6*a*b*cosh(d*x + c)^5 - 4*a*b*cosh(d*x + c)^3 + a*b*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) - 1) + 10*(15*b^2*d*x*cosh(d*x + c)^9 - 60*b^2*d*x*cosh(d*x + c)^7 - 27*a*b*cosh(d*x + c)^8 + 90*b^2*d*x*cosh(d*x + c)^5 + 42*a*b*cosh(d*x + c)^6 - 18*a*b*cosh(d*x + c)^2 - 4*(15*b^2*d*x + 16*a^2)*cosh(d*x + c)^3 + 3*a*b + (15*b^2*d*x + 16*a^2)*cosh(d*x + c))*sinh(d*x + c))/(d*cosh(d*x + c)^10 + 10*d*cosh(d*x + c)*sinh(d*x + c)^9 + d*sinh(d*x + c)^10 - 5*d*cosh(d*x + c)^8 + 5*(9*d*cosh(d*x + c)^2 - d)*sinh(d*x + c)^8 + 40*(3*d*cosh(d*x + c)^3 - d*cosh(d*x + c))*sinh(d*x + c)^7 + 10*d*cosh(d*x + c)^6 + 10*(21*d*cosh(d*x + c)^4 - 14*d*cosh(d*x + c)^2 + d)*sinh(d*x + c)^6 + 4*(63*d*cosh(d*x + c)^5 - 70*d*cosh(d*x + c)^3 + 15*d*cosh(d*x + c))*sinh(d*x + c)^5 - 10*d*cosh(d*x + c)^4 + 10*(21*d*cosh(d*x + c)^6 - 35*d*cosh(d*x + c)^4 + 15*d*cosh(d*x + c)^2 - d)*sinh(d*x + c)^4 + 40*(3*d*cosh(d*x + c)^7 - 7*d*cosh(d*x + c)^5 + 5*d*cosh(d*x + c)^3 - d*cosh(d*x + c))*sinh(d*x + c)^3 + 5*d*cosh(d*x + c)^2 + 5*(9*d*cosh(d*x + c)^8 - 28*d*cosh(d*x + c)^6 + 30*d*cosh(d*x + c)^4 - 12*d*cosh(d*x + c)^2 + d)*sinh(d*x + c)^2 + 10*(d*cosh(d*x + c)^9 - 4*d*cosh(d*x + c)^7 + 6*d*cosh(d*x + c)^5 - 4*d*cosh(d*x + c)^3 + d*cosh(d*x + c))*sinh(d*x + c) - d)","B",0
160,1,3607,0,0.522930," ","integrate(csch(d*x+c)^7*(a+b*sinh(d*x+c)^3)^2,x, algorithm=""fricas"")","-\frac{30 \, a^{2} \cosh\left(d x + c\right)^{11} + 330 \, a^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{10} + 30 \, a^{2} \sinh\left(d x + c\right)^{11} - 170 \, a^{2} \cosh\left(d x + c\right)^{9} + 384 \, a b \cosh\left(d x + c\right)^{8} + 10 \, {\left(165 \, a^{2} \cosh\left(d x + c\right)^{2} - 17 \, a^{2}\right)} \sinh\left(d x + c\right)^{9} + 396 \, a^{2} \cosh\left(d x + c\right)^{7} + 6 \, {\left(825 \, a^{2} \cosh\left(d x + c\right)^{3} - 255 \, a^{2} \cosh\left(d x + c\right) + 64 \, a b\right)} \sinh\left(d x + c\right)^{8} - 1280 \, a b \cosh\left(d x + c\right)^{6} + 12 \, {\left(825 \, a^{2} \cosh\left(d x + c\right)^{4} - 510 \, a^{2} \cosh\left(d x + c\right)^{2} + 256 \, a b \cosh\left(d x + c\right) + 33 \, a^{2}\right)} \sinh\left(d x + c\right)^{7} + 396 \, a^{2} \cosh\left(d x + c\right)^{5} + 4 \, {\left(3465 \, a^{2} \cosh\left(d x + c\right)^{5} - 3570 \, a^{2} \cosh\left(d x + c\right)^{3} + 2688 \, a b \cosh\left(d x + c\right)^{2} + 693 \, a^{2} \cosh\left(d x + c\right) - 320 \, a b\right)} \sinh\left(d x + c\right)^{6} + 1536 \, a b \cosh\left(d x + c\right)^{4} + 12 \, {\left(1155 \, a^{2} \cosh\left(d x + c\right)^{6} - 1785 \, a^{2} \cosh\left(d x + c\right)^{4} + 1792 \, a b \cosh\left(d x + c\right)^{3} + 693 \, a^{2} \cosh\left(d x + c\right)^{2} - 640 \, a b \cosh\left(d x + c\right) + 33 \, a^{2}\right)} \sinh\left(d x + c\right)^{5} - 170 \, a^{2} \cosh\left(d x + c\right)^{3} + 12 \, {\left(825 \, a^{2} \cosh\left(d x + c\right)^{7} - 1785 \, a^{2} \cosh\left(d x + c\right)^{5} + 2240 \, a b \cosh\left(d x + c\right)^{4} + 1155 \, a^{2} \cosh\left(d x + c\right)^{3} - 1600 \, a b \cosh\left(d x + c\right)^{2} + 165 \, a^{2} \cosh\left(d x + c\right) + 128 \, a b\right)} \sinh\left(d x + c\right)^{4} - 768 \, a b \cosh\left(d x + c\right)^{2} + 2 \, {\left(2475 \, a^{2} \cosh\left(d x + c\right)^{8} - 7140 \, a^{2} \cosh\left(d x + c\right)^{6} + 10752 \, a b \cosh\left(d x + c\right)^{5} + 6930 \, a^{2} \cosh\left(d x + c\right)^{4} - 12800 \, a b \cosh\left(d x + c\right)^{3} + 1980 \, a^{2} \cosh\left(d x + c\right)^{2} + 3072 \, a b \cosh\left(d x + c\right) - 85 \, a^{2}\right)} \sinh\left(d x + c\right)^{3} + 30 \, a^{2} \cosh\left(d x + c\right) + 6 \, {\left(275 \, a^{2} \cosh\left(d x + c\right)^{9} - 1020 \, a^{2} \cosh\left(d x + c\right)^{7} + 1792 \, a b \cosh\left(d x + c\right)^{6} + 1386 \, a^{2} \cosh\left(d x + c\right)^{5} - 3200 \, a b \cosh\left(d x + c\right)^{4} + 660 \, a^{2} \cosh\left(d x + c\right)^{3} + 1536 \, a b \cosh\left(d x + c\right)^{2} - 85 \, a^{2} \cosh\left(d x + c\right) - 128 \, a b\right)} \sinh\left(d x + c\right)^{2} + 128 \, a b - 3 \, {\left({\left(5 \, a^{2} - 16 \, b^{2}\right)} \cosh\left(d x + c\right)^{12} + 12 \, {\left(5 \, a^{2} - 16 \, b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{11} + {\left(5 \, a^{2} - 16 \, b^{2}\right)} \sinh\left(d x + c\right)^{12} - 6 \, {\left(5 \, a^{2} - 16 \, b^{2}\right)} \cosh\left(d x + c\right)^{10} + 6 \, {\left(11 \, {\left(5 \, a^{2} - 16 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 5 \, a^{2} + 16 \, b^{2}\right)} \sinh\left(d x + c\right)^{10} + 20 \, {\left(11 \, {\left(5 \, a^{2} - 16 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(5 \, a^{2} - 16 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} + 15 \, {\left(5 \, a^{2} - 16 \, b^{2}\right)} \cosh\left(d x + c\right)^{8} + 15 \, {\left(33 \, {\left(5 \, a^{2} - 16 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} - 18 \, {\left(5 \, a^{2} - 16 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 5 \, a^{2} - 16 \, b^{2}\right)} \sinh\left(d x + c\right)^{8} + 24 \, {\left(33 \, {\left(5 \, a^{2} - 16 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} - 30 \, {\left(5 \, a^{2} - 16 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 5 \, {\left(5 \, a^{2} - 16 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} - 20 \, {\left(5 \, a^{2} - 16 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(231 \, {\left(5 \, a^{2} - 16 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} - 315 \, {\left(5 \, a^{2} - 16 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 105 \, {\left(5 \, a^{2} - 16 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 25 \, a^{2} + 80 \, b^{2}\right)} \sinh\left(d x + c\right)^{6} + 24 \, {\left(33 \, {\left(5 \, a^{2} - 16 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} - 63 \, {\left(5 \, a^{2} - 16 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 35 \, {\left(5 \, a^{2} - 16 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - 5 \, {\left(5 \, a^{2} - 16 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 15 \, {\left(5 \, a^{2} - 16 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 15 \, {\left(33 \, {\left(5 \, a^{2} - 16 \, b^{2}\right)} \cosh\left(d x + c\right)^{8} - 84 \, {\left(5 \, a^{2} - 16 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 70 \, {\left(5 \, a^{2} - 16 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} - 20 \, {\left(5 \, a^{2} - 16 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 5 \, a^{2} - 16 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 20 \, {\left(11 \, {\left(5 \, a^{2} - 16 \, b^{2}\right)} \cosh\left(d x + c\right)^{9} - 36 \, {\left(5 \, a^{2} - 16 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} + 42 \, {\left(5 \, a^{2} - 16 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} - 20 \, {\left(5 \, a^{2} - 16 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(5 \, a^{2} - 16 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 6 \, {\left(5 \, a^{2} - 16 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 6 \, {\left(11 \, {\left(5 \, a^{2} - 16 \, b^{2}\right)} \cosh\left(d x + c\right)^{10} - 45 \, {\left(5 \, a^{2} - 16 \, b^{2}\right)} \cosh\left(d x + c\right)^{8} + 70 \, {\left(5 \, a^{2} - 16 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} - 50 \, {\left(5 \, a^{2} - 16 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 15 \, {\left(5 \, a^{2} - 16 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 5 \, a^{2} + 16 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} + 5 \, a^{2} - 16 \, b^{2} + 12 \, {\left({\left(5 \, a^{2} - 16 \, b^{2}\right)} \cosh\left(d x + c\right)^{11} - 5 \, {\left(5 \, a^{2} - 16 \, b^{2}\right)} \cosh\left(d x + c\right)^{9} + 10 \, {\left(5 \, a^{2} - 16 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} - 10 \, {\left(5 \, a^{2} - 16 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(5 \, a^{2} - 16 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(5 \, a^{2} - 16 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) + 3 \, {\left({\left(5 \, a^{2} - 16 \, b^{2}\right)} \cosh\left(d x + c\right)^{12} + 12 \, {\left(5 \, a^{2} - 16 \, b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{11} + {\left(5 \, a^{2} - 16 \, b^{2}\right)} \sinh\left(d x + c\right)^{12} - 6 \, {\left(5 \, a^{2} - 16 \, b^{2}\right)} \cosh\left(d x + c\right)^{10} + 6 \, {\left(11 \, {\left(5 \, a^{2} - 16 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 5 \, a^{2} + 16 \, b^{2}\right)} \sinh\left(d x + c\right)^{10} + 20 \, {\left(11 \, {\left(5 \, a^{2} - 16 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(5 \, a^{2} - 16 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} + 15 \, {\left(5 \, a^{2} - 16 \, b^{2}\right)} \cosh\left(d x + c\right)^{8} + 15 \, {\left(33 \, {\left(5 \, a^{2} - 16 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} - 18 \, {\left(5 \, a^{2} - 16 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 5 \, a^{2} - 16 \, b^{2}\right)} \sinh\left(d x + c\right)^{8} + 24 \, {\left(33 \, {\left(5 \, a^{2} - 16 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} - 30 \, {\left(5 \, a^{2} - 16 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 5 \, {\left(5 \, a^{2} - 16 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} - 20 \, {\left(5 \, a^{2} - 16 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(231 \, {\left(5 \, a^{2} - 16 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} - 315 \, {\left(5 \, a^{2} - 16 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 105 \, {\left(5 \, a^{2} - 16 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 25 \, a^{2} + 80 \, b^{2}\right)} \sinh\left(d x + c\right)^{6} + 24 \, {\left(33 \, {\left(5 \, a^{2} - 16 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} - 63 \, {\left(5 \, a^{2} - 16 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 35 \, {\left(5 \, a^{2} - 16 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - 5 \, {\left(5 \, a^{2} - 16 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 15 \, {\left(5 \, a^{2} - 16 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 15 \, {\left(33 \, {\left(5 \, a^{2} - 16 \, b^{2}\right)} \cosh\left(d x + c\right)^{8} - 84 \, {\left(5 \, a^{2} - 16 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 70 \, {\left(5 \, a^{2} - 16 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} - 20 \, {\left(5 \, a^{2} - 16 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 5 \, a^{2} - 16 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 20 \, {\left(11 \, {\left(5 \, a^{2} - 16 \, b^{2}\right)} \cosh\left(d x + c\right)^{9} - 36 \, {\left(5 \, a^{2} - 16 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} + 42 \, {\left(5 \, a^{2} - 16 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} - 20 \, {\left(5 \, a^{2} - 16 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(5 \, a^{2} - 16 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 6 \, {\left(5 \, a^{2} - 16 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 6 \, {\left(11 \, {\left(5 \, a^{2} - 16 \, b^{2}\right)} \cosh\left(d x + c\right)^{10} - 45 \, {\left(5 \, a^{2} - 16 \, b^{2}\right)} \cosh\left(d x + c\right)^{8} + 70 \, {\left(5 \, a^{2} - 16 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} - 50 \, {\left(5 \, a^{2} - 16 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 15 \, {\left(5 \, a^{2} - 16 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 5 \, a^{2} + 16 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} + 5 \, a^{2} - 16 \, b^{2} + 12 \, {\left({\left(5 \, a^{2} - 16 \, b^{2}\right)} \cosh\left(d x + c\right)^{11} - 5 \, {\left(5 \, a^{2} - 16 \, b^{2}\right)} \cosh\left(d x + c\right)^{9} + 10 \, {\left(5 \, a^{2} - 16 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} - 10 \, {\left(5 \, a^{2} - 16 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(5 \, a^{2} - 16 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(5 \, a^{2} - 16 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) + 6 \, {\left(55 \, a^{2} \cosh\left(d x + c\right)^{10} - 255 \, a^{2} \cosh\left(d x + c\right)^{8} + 512 \, a b \cosh\left(d x + c\right)^{7} + 462 \, a^{2} \cosh\left(d x + c\right)^{6} - 1280 \, a b \cosh\left(d x + c\right)^{5} + 330 \, a^{2} \cosh\left(d x + c\right)^{4} + 1024 \, a b \cosh\left(d x + c\right)^{3} - 85 \, a^{2} \cosh\left(d x + c\right)^{2} - 256 \, a b \cosh\left(d x + c\right) + 5 \, a^{2}\right)} \sinh\left(d x + c\right)}{48 \, {\left(d \cosh\left(d x + c\right)^{12} + 12 \, d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{11} + d \sinh\left(d x + c\right)^{12} - 6 \, d \cosh\left(d x + c\right)^{10} + 6 \, {\left(11 \, d \cosh\left(d x + c\right)^{2} - d\right)} \sinh\left(d x + c\right)^{10} + 20 \, {\left(11 \, d \cosh\left(d x + c\right)^{3} - 3 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} + 15 \, d \cosh\left(d x + c\right)^{8} + 15 \, {\left(33 \, d \cosh\left(d x + c\right)^{4} - 18 \, d \cosh\left(d x + c\right)^{2} + d\right)} \sinh\left(d x + c\right)^{8} + 24 \, {\left(33 \, d \cosh\left(d x + c\right)^{5} - 30 \, d \cosh\left(d x + c\right)^{3} + 5 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} - 20 \, d \cosh\left(d x + c\right)^{6} + 4 \, {\left(231 \, d \cosh\left(d x + c\right)^{6} - 315 \, d \cosh\left(d x + c\right)^{4} + 105 \, d \cosh\left(d x + c\right)^{2} - 5 \, d\right)} \sinh\left(d x + c\right)^{6} + 24 \, {\left(33 \, d \cosh\left(d x + c\right)^{7} - 63 \, d \cosh\left(d x + c\right)^{5} + 35 \, d \cosh\left(d x + c\right)^{3} - 5 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 15 \, d \cosh\left(d x + c\right)^{4} + 15 \, {\left(33 \, d \cosh\left(d x + c\right)^{8} - 84 \, d \cosh\left(d x + c\right)^{6} + 70 \, d \cosh\left(d x + c\right)^{4} - 20 \, d \cosh\left(d x + c\right)^{2} + d\right)} \sinh\left(d x + c\right)^{4} + 20 \, {\left(11 \, d \cosh\left(d x + c\right)^{9} - 36 \, d \cosh\left(d x + c\right)^{7} + 42 \, d \cosh\left(d x + c\right)^{5} - 20 \, d \cosh\left(d x + c\right)^{3} + 3 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 6 \, d \cosh\left(d x + c\right)^{2} + 6 \, {\left(11 \, d \cosh\left(d x + c\right)^{10} - 45 \, d \cosh\left(d x + c\right)^{8} + 70 \, d \cosh\left(d x + c\right)^{6} - 50 \, d \cosh\left(d x + c\right)^{4} + 15 \, d \cosh\left(d x + c\right)^{2} - d\right)} \sinh\left(d x + c\right)^{2} + 12 \, {\left(d \cosh\left(d x + c\right)^{11} - 5 \, d \cosh\left(d x + c\right)^{9} + 10 \, d \cosh\left(d x + c\right)^{7} - 10 \, d \cosh\left(d x + c\right)^{5} + 5 \, d \cosh\left(d x + c\right)^{3} - d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + d\right)}}"," ",0,"-1/48*(30*a^2*cosh(d*x + c)^11 + 330*a^2*cosh(d*x + c)*sinh(d*x + c)^10 + 30*a^2*sinh(d*x + c)^11 - 170*a^2*cosh(d*x + c)^9 + 384*a*b*cosh(d*x + c)^8 + 10*(165*a^2*cosh(d*x + c)^2 - 17*a^2)*sinh(d*x + c)^9 + 396*a^2*cosh(d*x + c)^7 + 6*(825*a^2*cosh(d*x + c)^3 - 255*a^2*cosh(d*x + c) + 64*a*b)*sinh(d*x + c)^8 - 1280*a*b*cosh(d*x + c)^6 + 12*(825*a^2*cosh(d*x + c)^4 - 510*a^2*cosh(d*x + c)^2 + 256*a*b*cosh(d*x + c) + 33*a^2)*sinh(d*x + c)^7 + 396*a^2*cosh(d*x + c)^5 + 4*(3465*a^2*cosh(d*x + c)^5 - 3570*a^2*cosh(d*x + c)^3 + 2688*a*b*cosh(d*x + c)^2 + 693*a^2*cosh(d*x + c) - 320*a*b)*sinh(d*x + c)^6 + 1536*a*b*cosh(d*x + c)^4 + 12*(1155*a^2*cosh(d*x + c)^6 - 1785*a^2*cosh(d*x + c)^4 + 1792*a*b*cosh(d*x + c)^3 + 693*a^2*cosh(d*x + c)^2 - 640*a*b*cosh(d*x + c) + 33*a^2)*sinh(d*x + c)^5 - 170*a^2*cosh(d*x + c)^3 + 12*(825*a^2*cosh(d*x + c)^7 - 1785*a^2*cosh(d*x + c)^5 + 2240*a*b*cosh(d*x + c)^4 + 1155*a^2*cosh(d*x + c)^3 - 1600*a*b*cosh(d*x + c)^2 + 165*a^2*cosh(d*x + c) + 128*a*b)*sinh(d*x + c)^4 - 768*a*b*cosh(d*x + c)^2 + 2*(2475*a^2*cosh(d*x + c)^8 - 7140*a^2*cosh(d*x + c)^6 + 10752*a*b*cosh(d*x + c)^5 + 6930*a^2*cosh(d*x + c)^4 - 12800*a*b*cosh(d*x + c)^3 + 1980*a^2*cosh(d*x + c)^2 + 3072*a*b*cosh(d*x + c) - 85*a^2)*sinh(d*x + c)^3 + 30*a^2*cosh(d*x + c) + 6*(275*a^2*cosh(d*x + c)^9 - 1020*a^2*cosh(d*x + c)^7 + 1792*a*b*cosh(d*x + c)^6 + 1386*a^2*cosh(d*x + c)^5 - 3200*a*b*cosh(d*x + c)^4 + 660*a^2*cosh(d*x + c)^3 + 1536*a*b*cosh(d*x + c)^2 - 85*a^2*cosh(d*x + c) - 128*a*b)*sinh(d*x + c)^2 + 128*a*b - 3*((5*a^2 - 16*b^2)*cosh(d*x + c)^12 + 12*(5*a^2 - 16*b^2)*cosh(d*x + c)*sinh(d*x + c)^11 + (5*a^2 - 16*b^2)*sinh(d*x + c)^12 - 6*(5*a^2 - 16*b^2)*cosh(d*x + c)^10 + 6*(11*(5*a^2 - 16*b^2)*cosh(d*x + c)^2 - 5*a^2 + 16*b^2)*sinh(d*x + c)^10 + 20*(11*(5*a^2 - 16*b^2)*cosh(d*x + c)^3 - 3*(5*a^2 - 16*b^2)*cosh(d*x + c))*sinh(d*x + c)^9 + 15*(5*a^2 - 16*b^2)*cosh(d*x + c)^8 + 15*(33*(5*a^2 - 16*b^2)*cosh(d*x + c)^4 - 18*(5*a^2 - 16*b^2)*cosh(d*x + c)^2 + 5*a^2 - 16*b^2)*sinh(d*x + c)^8 + 24*(33*(5*a^2 - 16*b^2)*cosh(d*x + c)^5 - 30*(5*a^2 - 16*b^2)*cosh(d*x + c)^3 + 5*(5*a^2 - 16*b^2)*cosh(d*x + c))*sinh(d*x + c)^7 - 20*(5*a^2 - 16*b^2)*cosh(d*x + c)^6 + 4*(231*(5*a^2 - 16*b^2)*cosh(d*x + c)^6 - 315*(5*a^2 - 16*b^2)*cosh(d*x + c)^4 + 105*(5*a^2 - 16*b^2)*cosh(d*x + c)^2 - 25*a^2 + 80*b^2)*sinh(d*x + c)^6 + 24*(33*(5*a^2 - 16*b^2)*cosh(d*x + c)^7 - 63*(5*a^2 - 16*b^2)*cosh(d*x + c)^5 + 35*(5*a^2 - 16*b^2)*cosh(d*x + c)^3 - 5*(5*a^2 - 16*b^2)*cosh(d*x + c))*sinh(d*x + c)^5 + 15*(5*a^2 - 16*b^2)*cosh(d*x + c)^4 + 15*(33*(5*a^2 - 16*b^2)*cosh(d*x + c)^8 - 84*(5*a^2 - 16*b^2)*cosh(d*x + c)^6 + 70*(5*a^2 - 16*b^2)*cosh(d*x + c)^4 - 20*(5*a^2 - 16*b^2)*cosh(d*x + c)^2 + 5*a^2 - 16*b^2)*sinh(d*x + c)^4 + 20*(11*(5*a^2 - 16*b^2)*cosh(d*x + c)^9 - 36*(5*a^2 - 16*b^2)*cosh(d*x + c)^7 + 42*(5*a^2 - 16*b^2)*cosh(d*x + c)^5 - 20*(5*a^2 - 16*b^2)*cosh(d*x + c)^3 + 3*(5*a^2 - 16*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 - 6*(5*a^2 - 16*b^2)*cosh(d*x + c)^2 + 6*(11*(5*a^2 - 16*b^2)*cosh(d*x + c)^10 - 45*(5*a^2 - 16*b^2)*cosh(d*x + c)^8 + 70*(5*a^2 - 16*b^2)*cosh(d*x + c)^6 - 50*(5*a^2 - 16*b^2)*cosh(d*x + c)^4 + 15*(5*a^2 - 16*b^2)*cosh(d*x + c)^2 - 5*a^2 + 16*b^2)*sinh(d*x + c)^2 + 5*a^2 - 16*b^2 + 12*((5*a^2 - 16*b^2)*cosh(d*x + c)^11 - 5*(5*a^2 - 16*b^2)*cosh(d*x + c)^9 + 10*(5*a^2 - 16*b^2)*cosh(d*x + c)^7 - 10*(5*a^2 - 16*b^2)*cosh(d*x + c)^5 + 5*(5*a^2 - 16*b^2)*cosh(d*x + c)^3 - (5*a^2 - 16*b^2)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) + 1) + 3*((5*a^2 - 16*b^2)*cosh(d*x + c)^12 + 12*(5*a^2 - 16*b^2)*cosh(d*x + c)*sinh(d*x + c)^11 + (5*a^2 - 16*b^2)*sinh(d*x + c)^12 - 6*(5*a^2 - 16*b^2)*cosh(d*x + c)^10 + 6*(11*(5*a^2 - 16*b^2)*cosh(d*x + c)^2 - 5*a^2 + 16*b^2)*sinh(d*x + c)^10 + 20*(11*(5*a^2 - 16*b^2)*cosh(d*x + c)^3 - 3*(5*a^2 - 16*b^2)*cosh(d*x + c))*sinh(d*x + c)^9 + 15*(5*a^2 - 16*b^2)*cosh(d*x + c)^8 + 15*(33*(5*a^2 - 16*b^2)*cosh(d*x + c)^4 - 18*(5*a^2 - 16*b^2)*cosh(d*x + c)^2 + 5*a^2 - 16*b^2)*sinh(d*x + c)^8 + 24*(33*(5*a^2 - 16*b^2)*cosh(d*x + c)^5 - 30*(5*a^2 - 16*b^2)*cosh(d*x + c)^3 + 5*(5*a^2 - 16*b^2)*cosh(d*x + c))*sinh(d*x + c)^7 - 20*(5*a^2 - 16*b^2)*cosh(d*x + c)^6 + 4*(231*(5*a^2 - 16*b^2)*cosh(d*x + c)^6 - 315*(5*a^2 - 16*b^2)*cosh(d*x + c)^4 + 105*(5*a^2 - 16*b^2)*cosh(d*x + c)^2 - 25*a^2 + 80*b^2)*sinh(d*x + c)^6 + 24*(33*(5*a^2 - 16*b^2)*cosh(d*x + c)^7 - 63*(5*a^2 - 16*b^2)*cosh(d*x + c)^5 + 35*(5*a^2 - 16*b^2)*cosh(d*x + c)^3 - 5*(5*a^2 - 16*b^2)*cosh(d*x + c))*sinh(d*x + c)^5 + 15*(5*a^2 - 16*b^2)*cosh(d*x + c)^4 + 15*(33*(5*a^2 - 16*b^2)*cosh(d*x + c)^8 - 84*(5*a^2 - 16*b^2)*cosh(d*x + c)^6 + 70*(5*a^2 - 16*b^2)*cosh(d*x + c)^4 - 20*(5*a^2 - 16*b^2)*cosh(d*x + c)^2 + 5*a^2 - 16*b^2)*sinh(d*x + c)^4 + 20*(11*(5*a^2 - 16*b^2)*cosh(d*x + c)^9 - 36*(5*a^2 - 16*b^2)*cosh(d*x + c)^7 + 42*(5*a^2 - 16*b^2)*cosh(d*x + c)^5 - 20*(5*a^2 - 16*b^2)*cosh(d*x + c)^3 + 3*(5*a^2 - 16*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 - 6*(5*a^2 - 16*b^2)*cosh(d*x + c)^2 + 6*(11*(5*a^2 - 16*b^2)*cosh(d*x + c)^10 - 45*(5*a^2 - 16*b^2)*cosh(d*x + c)^8 + 70*(5*a^2 - 16*b^2)*cosh(d*x + c)^6 - 50*(5*a^2 - 16*b^2)*cosh(d*x + c)^4 + 15*(5*a^2 - 16*b^2)*cosh(d*x + c)^2 - 5*a^2 + 16*b^2)*sinh(d*x + c)^2 + 5*a^2 - 16*b^2 + 12*((5*a^2 - 16*b^2)*cosh(d*x + c)^11 - 5*(5*a^2 - 16*b^2)*cosh(d*x + c)^9 + 10*(5*a^2 - 16*b^2)*cosh(d*x + c)^7 - 10*(5*a^2 - 16*b^2)*cosh(d*x + c)^5 + 5*(5*a^2 - 16*b^2)*cosh(d*x + c)^3 - (5*a^2 - 16*b^2)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) - 1) + 6*(55*a^2*cosh(d*x + c)^10 - 255*a^2*cosh(d*x + c)^8 + 512*a*b*cosh(d*x + c)^7 + 462*a^2*cosh(d*x + c)^6 - 1280*a*b*cosh(d*x + c)^5 + 330*a^2*cosh(d*x + c)^4 + 1024*a*b*cosh(d*x + c)^3 - 85*a^2*cosh(d*x + c)^2 - 256*a*b*cosh(d*x + c) + 5*a^2)*sinh(d*x + c))/(d*cosh(d*x + c)^12 + 12*d*cosh(d*x + c)*sinh(d*x + c)^11 + d*sinh(d*x + c)^12 - 6*d*cosh(d*x + c)^10 + 6*(11*d*cosh(d*x + c)^2 - d)*sinh(d*x + c)^10 + 20*(11*d*cosh(d*x + c)^3 - 3*d*cosh(d*x + c))*sinh(d*x + c)^9 + 15*d*cosh(d*x + c)^8 + 15*(33*d*cosh(d*x + c)^4 - 18*d*cosh(d*x + c)^2 + d)*sinh(d*x + c)^8 + 24*(33*d*cosh(d*x + c)^5 - 30*d*cosh(d*x + c)^3 + 5*d*cosh(d*x + c))*sinh(d*x + c)^7 - 20*d*cosh(d*x + c)^6 + 4*(231*d*cosh(d*x + c)^6 - 315*d*cosh(d*x + c)^4 + 105*d*cosh(d*x + c)^2 - 5*d)*sinh(d*x + c)^6 + 24*(33*d*cosh(d*x + c)^7 - 63*d*cosh(d*x + c)^5 + 35*d*cosh(d*x + c)^3 - 5*d*cosh(d*x + c))*sinh(d*x + c)^5 + 15*d*cosh(d*x + c)^4 + 15*(33*d*cosh(d*x + c)^8 - 84*d*cosh(d*x + c)^6 + 70*d*cosh(d*x + c)^4 - 20*d*cosh(d*x + c)^2 + d)*sinh(d*x + c)^4 + 20*(11*d*cosh(d*x + c)^9 - 36*d*cosh(d*x + c)^7 + 42*d*cosh(d*x + c)^5 - 20*d*cosh(d*x + c)^3 + 3*d*cosh(d*x + c))*sinh(d*x + c)^3 - 6*d*cosh(d*x + c)^2 + 6*(11*d*cosh(d*x + c)^10 - 45*d*cosh(d*x + c)^8 + 70*d*cosh(d*x + c)^6 - 50*d*cosh(d*x + c)^4 + 15*d*cosh(d*x + c)^2 - d)*sinh(d*x + c)^2 + 12*(d*cosh(d*x + c)^11 - 5*d*cosh(d*x + c)^9 + 10*d*cosh(d*x + c)^7 - 10*d*cosh(d*x + c)^5 + 5*d*cosh(d*x + c)^3 - d*cosh(d*x + c))*sinh(d*x + c) + d)","B",0
161,1,568,0,0.524531," ","integrate(sinh(d*x+c)^2*(a+b*sinh(d*x+c)^3)^3,x, algorithm=""fricas"")","\frac{315 \, b^{3} \cosh\left(d x + c\right)^{11} + 3465 \, b^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{10} - 4235 \, b^{3} \cosh\left(d x + c\right)^{9} + 83160 \, a b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + 27225 \, b^{3} \cosh\left(d x + c\right)^{7} + 3465 \, {\left(15 \, b^{3} \cosh\left(d x + c\right)^{3} - 11 \, b^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{8} + 1155 \, {\left(126 \, b^{3} \cosh\left(d x + c\right)^{5} - 308 \, b^{3} \cosh\left(d x + c\right)^{3} + 165 \, b^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} + 2079 \, {\left(64 \, a^{2} b - 55 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 83160 \, {\left(7 \, a b^{2} \cosh\left(d x + c\right)^{3} - 8 \, a b^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 3465 \, {\left(30 \, b^{3} \cosh\left(d x + c\right)^{7} - 154 \, b^{3} \cosh\left(d x + c\right)^{5} + 275 \, b^{3} \cosh\left(d x + c\right)^{3} + 3 \, {\left(64 \, a^{2} b - 55 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} - 34650 \, {\left(32 \, a^{2} b - 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 27720 \, {\left(21 \, a b^{2} \cosh\left(d x + c\right)^{5} - 80 \, a b^{2} \cosh\left(d x + c\right)^{3} + 84 \, a b^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 27720 \, {\left(64 \, a^{3} - 105 \, a b^{2}\right)} d x + 3465 \, {\left(5 \, b^{3} \cosh\left(d x + c\right)^{9} - 44 \, b^{3} \cosh\left(d x + c\right)^{7} + 165 \, b^{3} \cosh\left(d x + c\right)^{5} + 6 \, {\left(64 \, a^{2} b - 55 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 30 \, {\left(32 \, a^{2} b - 11 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 20790 \, {\left(320 \, a^{2} b - 77 \, b^{3}\right)} \cosh\left(d x + c\right) + 27720 \, {\left(3 \, a b^{2} \cosh\left(d x + c\right)^{7} - 24 \, a b^{2} \cosh\left(d x + c\right)^{5} + 84 \, a b^{2} \cosh\left(d x + c\right)^{3} + 8 \, {\left(8 \, a^{3} - 21 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{3548160 \, d}"," ",0,"1/3548160*(315*b^3*cosh(d*x + c)^11 + 3465*b^3*cosh(d*x + c)*sinh(d*x + c)^10 - 4235*b^3*cosh(d*x + c)^9 + 83160*a*b^2*cosh(d*x + c)*sinh(d*x + c)^7 + 27225*b^3*cosh(d*x + c)^7 + 3465*(15*b^3*cosh(d*x + c)^3 - 11*b^3*cosh(d*x + c))*sinh(d*x + c)^8 + 1155*(126*b^3*cosh(d*x + c)^5 - 308*b^3*cosh(d*x + c)^3 + 165*b^3*cosh(d*x + c))*sinh(d*x + c)^6 + 2079*(64*a^2*b - 55*b^3)*cosh(d*x + c)^5 + 83160*(7*a*b^2*cosh(d*x + c)^3 - 8*a*b^2*cosh(d*x + c))*sinh(d*x + c)^5 + 3465*(30*b^3*cosh(d*x + c)^7 - 154*b^3*cosh(d*x + c)^5 + 275*b^3*cosh(d*x + c)^3 + 3*(64*a^2*b - 55*b^3)*cosh(d*x + c))*sinh(d*x + c)^4 - 34650*(32*a^2*b - 11*b^3)*cosh(d*x + c)^3 + 27720*(21*a*b^2*cosh(d*x + c)^5 - 80*a*b^2*cosh(d*x + c)^3 + 84*a*b^2*cosh(d*x + c))*sinh(d*x + c)^3 - 27720*(64*a^3 - 105*a*b^2)*d*x + 3465*(5*b^3*cosh(d*x + c)^9 - 44*b^3*cosh(d*x + c)^7 + 165*b^3*cosh(d*x + c)^5 + 6*(64*a^2*b - 55*b^3)*cosh(d*x + c)^3 - 30*(32*a^2*b - 11*b^3)*cosh(d*x + c))*sinh(d*x + c)^2 + 20790*(320*a^2*b - 77*b^3)*cosh(d*x + c) + 27720*(3*a*b^2*cosh(d*x + c)^7 - 24*a*b^2*cosh(d*x + c)^5 + 84*a*b^2*cosh(d*x + c)^3 + 8*(8*a^3 - 21*a*b^2)*cosh(d*x + c))*sinh(d*x + c))/d","B",0
162,1,453,0,0.555454," ","integrate(sinh(d*x+c)*(a+b*sinh(d*x+c)^3)^3,x, algorithm=""fricas"")","\frac{35 \, b^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + 120 \, a b^{2} \cosh\left(d x + c\right)^{7} + 840 \, a b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} - 1176 \, a b^{2} \cosh\left(d x + c\right)^{5} + 70 \, {\left(6 \, b^{3} \cosh\left(d x + c\right)^{3} - 5 \, b^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 5880 \, a b^{2} \cosh\left(d x + c\right)^{3} + 7 \, {\left(126 \, b^{3} \cosh\left(d x + c\right)^{5} - 350 \, b^{3} \cosh\left(d x + c\right)^{3} + 225 \, b^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 840 \, {\left(5 \, a b^{2} \cosh\left(d x + c\right)^{3} - 7 \, a b^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 70 \, {\left(6 \, b^{3} \cosh\left(d x + c\right)^{7} - 35 \, b^{3} \cosh\left(d x + c\right)^{5} + 75 \, b^{3} \cosh\left(d x + c\right)^{3} + 12 \, {\left(8 \, a^{2} b - 5 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 630 \, {\left(32 \, a^{2} b - 7 \, b^{3}\right)} d x + 840 \, {\left(3 \, a b^{2} \cosh\left(d x + c\right)^{5} - 14 \, a b^{2} \cosh\left(d x + c\right)^{3} + 21 \, a b^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 280 \, {\left(64 \, a^{3} - 105 \, a b^{2}\right)} \cosh\left(d x + c\right) + 35 \, {\left(b^{3} \cosh\left(d x + c\right)^{9} - 10 \, b^{3} \cosh\left(d x + c\right)^{7} + 45 \, b^{3} \cosh\left(d x + c\right)^{5} + 24 \, {\left(8 \, a^{2} b - 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 6 \, {\left(128 \, a^{2} b - 35 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{17920 \, d}"," ",0,"1/17920*(35*b^3*cosh(d*x + c)*sinh(d*x + c)^9 + 120*a*b^2*cosh(d*x + c)^7 + 840*a*b^2*cosh(d*x + c)*sinh(d*x + c)^6 - 1176*a*b^2*cosh(d*x + c)^5 + 70*(6*b^3*cosh(d*x + c)^3 - 5*b^3*cosh(d*x + c))*sinh(d*x + c)^7 + 5880*a*b^2*cosh(d*x + c)^3 + 7*(126*b^3*cosh(d*x + c)^5 - 350*b^3*cosh(d*x + c)^3 + 225*b^3*cosh(d*x + c))*sinh(d*x + c)^5 + 840*(5*a*b^2*cosh(d*x + c)^3 - 7*a*b^2*cosh(d*x + c))*sinh(d*x + c)^4 + 70*(6*b^3*cosh(d*x + c)^7 - 35*b^3*cosh(d*x + c)^5 + 75*b^3*cosh(d*x + c)^3 + 12*(8*a^2*b - 5*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 + 630*(32*a^2*b - 7*b^3)*d*x + 840*(3*a*b^2*cosh(d*x + c)^5 - 14*a*b^2*cosh(d*x + c)^3 + 21*a*b^2*cosh(d*x + c))*sinh(d*x + c)^2 + 280*(64*a^3 - 105*a*b^2)*cosh(d*x + c) + 35*(b^3*cosh(d*x + c)^9 - 10*b^3*cosh(d*x + c)^7 + 45*b^3*cosh(d*x + c)^5 + 24*(8*a^2*b - 5*b^3)*cosh(d*x + c)^3 - 6*(128*a^2*b - 35*b^3)*cosh(d*x + c))*sinh(d*x + c))/d","A",0
163,1,380,0,0.449228," ","integrate((a+b*sinh(d*x+c)^3)^3,x, algorithm=""fricas"")","\frac{35 \, b^{3} \cosh\left(d x + c\right)^{9} + 315 \, b^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{8} - 405 \, b^{3} \cosh\left(d x + c\right)^{7} + 7560 \, a b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + 2268 \, b^{3} \cosh\left(d x + c\right)^{5} + 105 \, {\left(28 \, b^{3} \cosh\left(d x + c\right)^{3} - 27 \, b^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} + 315 \, {\left(14 \, b^{3} \cosh\left(d x + c\right)^{5} - 45 \, b^{3} \cosh\left(d x + c\right)^{3} + 36 \, b^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 1260 \, {\left(16 \, a^{2} b - 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 5040 \, {\left(5 \, a b^{2} \cosh\left(d x + c\right)^{3} - 9 \, a b^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 5040 \, {\left(16 \, a^{3} - 15 \, a b^{2}\right)} d x + 315 \, {\left(4 \, b^{3} \cosh\left(d x + c\right)^{7} - 27 \, b^{3} \cosh\left(d x + c\right)^{5} + 72 \, b^{3} \cosh\left(d x + c\right)^{3} + 12 \, {\left(16 \, a^{2} b - 7 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 5670 \, {\left(32 \, a^{2} b - 7 \, b^{3}\right)} \cosh\left(d x + c\right) + 7560 \, {\left(a b^{2} \cosh\left(d x + c\right)^{5} - 6 \, a b^{2} \cosh\left(d x + c\right)^{3} + 15 \, a b^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{80640 \, d}"," ",0,"1/80640*(35*b^3*cosh(d*x + c)^9 + 315*b^3*cosh(d*x + c)*sinh(d*x + c)^8 - 405*b^3*cosh(d*x + c)^7 + 7560*a*b^2*cosh(d*x + c)*sinh(d*x + c)^5 + 2268*b^3*cosh(d*x + c)^5 + 105*(28*b^3*cosh(d*x + c)^3 - 27*b^3*cosh(d*x + c))*sinh(d*x + c)^6 + 315*(14*b^3*cosh(d*x + c)^5 - 45*b^3*cosh(d*x + c)^3 + 36*b^3*cosh(d*x + c))*sinh(d*x + c)^4 + 1260*(16*a^2*b - 7*b^3)*cosh(d*x + c)^3 + 5040*(5*a*b^2*cosh(d*x + c)^3 - 9*a*b^2*cosh(d*x + c))*sinh(d*x + c)^3 + 5040*(16*a^3 - 15*a*b^2)*d*x + 315*(4*b^3*cosh(d*x + c)^7 - 27*b^3*cosh(d*x + c)^5 + 72*b^3*cosh(d*x + c)^3 + 12*(16*a^2*b - 7*b^3)*cosh(d*x + c))*sinh(d*x + c)^2 - 5670*(32*a^2*b - 7*b^3)*cosh(d*x + c) + 7560*(a*b^2*cosh(d*x + c)^5 - 6*a*b^2*cosh(d*x + c)^3 + 15*a*b^2*cosh(d*x + c))*sinh(d*x + c))/d","B",0
164,1,2609,0,0.600166," ","integrate(csch(d*x+c)*(a+b*sinh(d*x+c)^3)^3,x, algorithm=""fricas"")","\frac{15 \, b^{3} \cosh\left(d x + c\right)^{16} + 240 \, b^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{15} + 15 \, b^{3} \sinh\left(d x + c\right)^{16} - 160 \, b^{3} \cosh\left(d x + c\right)^{14} + 576 \, a b^{2} \cosh\left(d x + c\right)^{13} + 840 \, b^{3} \cosh\left(d x + c\right)^{12} + 40 \, {\left(45 \, b^{3} \cosh\left(d x + c\right)^{2} - 4 \, b^{3}\right)} \sinh\left(d x + c\right)^{14} - 4800 \, a b^{2} \cosh\left(d x + c\right)^{11} + 16 \, {\left(525 \, b^{3} \cosh\left(d x + c\right)^{3} - 140 \, b^{3} \cosh\left(d x + c\right) + 36 \, a b^{2}\right)} \sinh\left(d x + c\right)^{13} + 4 \, {\left(6825 \, b^{3} \cosh\left(d x + c\right)^{4} - 3640 \, b^{3} \cosh\left(d x + c\right)^{2} + 1872 \, a b^{2} \cosh\left(d x + c\right) + 210 \, b^{3}\right)} \sinh\left(d x + c\right)^{12} + 28800 \, a b^{2} \cosh\left(d x + c\right)^{9} + 16 \, {\left(4095 \, b^{3} \cosh\left(d x + c\right)^{5} - 3640 \, b^{3} \cosh\left(d x + c\right)^{3} + 2808 \, a b^{2} \cosh\left(d x + c\right)^{2} + 630 \, b^{3} \cosh\left(d x + c\right) - 300 \, a b^{2}\right)} \sinh\left(d x + c\right)^{11} - 240 \, {\left(192 \, a^{2} b - 35 \, b^{3}\right)} d x \cosh\left(d x + c\right)^{8} + 480 \, {\left(24 \, a^{2} b - 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} + 8 \, {\left(15015 \, b^{3} \cosh\left(d x + c\right)^{6} - 20020 \, b^{3} \cosh\left(d x + c\right)^{4} + 20592 \, a b^{2} \cosh\left(d x + c\right)^{3} + 6930 \, b^{3} \cosh\left(d x + c\right)^{2} - 6600 \, a b^{2} \cosh\left(d x + c\right) + 1440 \, a^{2} b - 420 \, b^{3}\right)} \sinh\left(d x + c\right)^{10} + 28800 \, a b^{2} \cosh\left(d x + c\right)^{7} + 80 \, {\left(2145 \, b^{3} \cosh\left(d x + c\right)^{7} - 4004 \, b^{3} \cosh\left(d x + c\right)^{5} + 5148 \, a b^{2} \cosh\left(d x + c\right)^{4} + 2310 \, b^{3} \cosh\left(d x + c\right)^{3} - 3300 \, a b^{2} \cosh\left(d x + c\right)^{2} + 360 \, a b^{2} + 60 \, {\left(24 \, a^{2} b - 7 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} + 6 \, {\left(32175 \, b^{3} \cosh\left(d x + c\right)^{8} - 80080 \, b^{3} \cosh\left(d x + c\right)^{6} + 123552 \, a b^{2} \cosh\left(d x + c\right)^{5} + 69300 \, b^{3} \cosh\left(d x + c\right)^{4} - 132000 \, a b^{2} \cosh\left(d x + c\right)^{3} + 43200 \, a b^{2} \cosh\left(d x + c\right) - 40 \, {\left(192 \, a^{2} b - 35 \, b^{3}\right)} d x + 3600 \, {\left(24 \, a^{2} b - 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{8} - 4800 \, a b^{2} \cosh\left(d x + c\right)^{5} + 48 \, {\left(3575 \, b^{3} \cosh\left(d x + c\right)^{9} - 11440 \, b^{3} \cosh\left(d x + c\right)^{7} + 20592 \, a b^{2} \cosh\left(d x + c\right)^{6} + 13860 \, b^{3} \cosh\left(d x + c\right)^{5} - 33000 \, a b^{2} \cosh\left(d x + c\right)^{4} + 21600 \, a b^{2} \cosh\left(d x + c\right)^{2} - 40 \, {\left(192 \, a^{2} b - 35 \, b^{3}\right)} d x \cosh\left(d x + c\right) + 1200 \, {\left(24 \, a^{2} b - 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 600 \, a b^{2}\right)} \sinh\left(d x + c\right)^{7} - 840 \, b^{3} \cosh\left(d x + c\right)^{4} - 480 \, {\left(24 \, a^{2} b - 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 24 \, {\left(5005 \, b^{3} \cosh\left(d x + c\right)^{10} - 20020 \, b^{3} \cosh\left(d x + c\right)^{8} + 41184 \, a b^{2} \cosh\left(d x + c\right)^{7} + 32340 \, b^{3} \cosh\left(d x + c\right)^{6} - 92400 \, a b^{2} \cosh\left(d x + c\right)^{5} + 100800 \, a b^{2} \cosh\left(d x + c\right)^{3} - 280 \, {\left(192 \, a^{2} b - 35 \, b^{3}\right)} d x \cosh\left(d x + c\right)^{2} + 4200 \, {\left(24 \, a^{2} b - 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 8400 \, a b^{2} \cosh\left(d x + c\right) - 480 \, a^{2} b + 140 \, b^{3}\right)} \sinh\left(d x + c\right)^{6} + 576 \, a b^{2} \cosh\left(d x + c\right)^{3} + 16 \, {\left(4095 \, b^{3} \cosh\left(d x + c\right)^{11} - 20020 \, b^{3} \cosh\left(d x + c\right)^{9} + 46332 \, a b^{2} \cosh\left(d x + c\right)^{8} + 41580 \, b^{3} \cosh\left(d x + c\right)^{7} - 138600 \, a b^{2} \cosh\left(d x + c\right)^{6} + 226800 \, a b^{2} \cosh\left(d x + c\right)^{4} - 840 \, {\left(192 \, a^{2} b - 35 \, b^{3}\right)} d x \cosh\left(d x + c\right)^{3} + 7560 \, {\left(24 \, a^{2} b - 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 37800 \, a b^{2} \cosh\left(d x + c\right)^{2} - 300 \, a b^{2} - 180 \, {\left(24 \, a^{2} b - 7 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 160 \, b^{3} \cosh\left(d x + c\right)^{2} + 20 \, {\left(1365 \, b^{3} \cosh\left(d x + c\right)^{12} - 8008 \, b^{3} \cosh\left(d x + c\right)^{10} + 20592 \, a b^{2} \cosh\left(d x + c\right)^{9} + 20790 \, b^{3} \cosh\left(d x + c\right)^{8} - 79200 \, a b^{2} \cosh\left(d x + c\right)^{7} + 181440 \, a b^{2} \cosh\left(d x + c\right)^{5} - 840 \, {\left(192 \, a^{2} b - 35 \, b^{3}\right)} d x \cosh\left(d x + c\right)^{4} + 5040 \, {\left(24 \, a^{2} b - 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 50400 \, a b^{2} \cosh\left(d x + c\right)^{3} - 1200 \, a b^{2} \cosh\left(d x + c\right) - 42 \, b^{3} - 360 \, {\left(24 \, a^{2} b - 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 16 \, {\left(525 \, b^{3} \cosh\left(d x + c\right)^{13} - 3640 \, b^{3} \cosh\left(d x + c\right)^{11} + 10296 \, a b^{2} \cosh\left(d x + c\right)^{10} + 11550 \, b^{3} \cosh\left(d x + c\right)^{9} - 49500 \, a b^{2} \cosh\left(d x + c\right)^{8} + 151200 \, a b^{2} \cosh\left(d x + c\right)^{6} - 840 \, {\left(192 \, a^{2} b - 35 \, b^{3}\right)} d x \cosh\left(d x + c\right)^{5} + 3600 \, {\left(24 \, a^{2} b - 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 63000 \, a b^{2} \cosh\left(d x + c\right)^{4} - 3000 \, a b^{2} \cosh\left(d x + c\right)^{2} - 210 \, b^{3} \cosh\left(d x + c\right) - 600 \, {\left(24 \, a^{2} b - 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 36 \, a b^{2}\right)} \sinh\left(d x + c\right)^{3} - 15 \, b^{3} + 8 \, {\left(225 \, b^{3} \cosh\left(d x + c\right)^{14} - 1820 \, b^{3} \cosh\left(d x + c\right)^{12} + 5616 \, a b^{2} \cosh\left(d x + c\right)^{11} + 6930 \, b^{3} \cosh\left(d x + c\right)^{10} - 33000 \, a b^{2} \cosh\left(d x + c\right)^{9} + 129600 \, a b^{2} \cosh\left(d x + c\right)^{7} - 840 \, {\left(192 \, a^{2} b - 35 \, b^{3}\right)} d x \cosh\left(d x + c\right)^{6} + 2700 \, {\left(24 \, a^{2} b - 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 75600 \, a b^{2} \cosh\left(d x + c\right)^{5} - 6000 \, a b^{2} \cosh\left(d x + c\right)^{3} - 630 \, b^{3} \cosh\left(d x + c\right)^{2} - 900 \, {\left(24 \, a^{2} b - 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 216 \, a b^{2} \cosh\left(d x + c\right) + 20 \, b^{3}\right)} \sinh\left(d x + c\right)^{2} - 30720 \, {\left(a^{3} \cosh\left(d x + c\right)^{8} + 8 \, a^{3} \cosh\left(d x + c\right)^{7} \sinh\left(d x + c\right) + 28 \, a^{3} \cosh\left(d x + c\right)^{6} \sinh\left(d x + c\right)^{2} + 56 \, a^{3} \cosh\left(d x + c\right)^{5} \sinh\left(d x + c\right)^{3} + 70 \, a^{3} \cosh\left(d x + c\right)^{4} \sinh\left(d x + c\right)^{4} + 56 \, a^{3} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right)^{5} + 28 \, a^{3} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{6} + 8 \, a^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + a^{3} \sinh\left(d x + c\right)^{8}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) + 30720 \, {\left(a^{3} \cosh\left(d x + c\right)^{8} + 8 \, a^{3} \cosh\left(d x + c\right)^{7} \sinh\left(d x + c\right) + 28 \, a^{3} \cosh\left(d x + c\right)^{6} \sinh\left(d x + c\right)^{2} + 56 \, a^{3} \cosh\left(d x + c\right)^{5} \sinh\left(d x + c\right)^{3} + 70 \, a^{3} \cosh\left(d x + c\right)^{4} \sinh\left(d x + c\right)^{4} + 56 \, a^{3} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right)^{5} + 28 \, a^{3} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{6} + 8 \, a^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + a^{3} \sinh\left(d x + c\right)^{8}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) + 16 \, {\left(15 \, b^{3} \cosh\left(d x + c\right)^{15} - 140 \, b^{3} \cosh\left(d x + c\right)^{13} + 468 \, a b^{2} \cosh\left(d x + c\right)^{12} + 630 \, b^{3} \cosh\left(d x + c\right)^{11} - 3300 \, a b^{2} \cosh\left(d x + c\right)^{10} + 16200 \, a b^{2} \cosh\left(d x + c\right)^{8} - 120 \, {\left(192 \, a^{2} b - 35 \, b^{3}\right)} d x \cosh\left(d x + c\right)^{7} + 300 \, {\left(24 \, a^{2} b - 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + 12600 \, a b^{2} \cosh\left(d x + c\right)^{6} - 1500 \, a b^{2} \cosh\left(d x + c\right)^{4} - 210 \, b^{3} \cosh\left(d x + c\right)^{3} - 180 \, {\left(24 \, a^{2} b - 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 108 \, a b^{2} \cosh\left(d x + c\right)^{2} + 20 \, b^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{30720 \, {\left(d \cosh\left(d x + c\right)^{8} + 8 \, d \cosh\left(d x + c\right)^{7} \sinh\left(d x + c\right) + 28 \, d \cosh\left(d x + c\right)^{6} \sinh\left(d x + c\right)^{2} + 56 \, d \cosh\left(d x + c\right)^{5} \sinh\left(d x + c\right)^{3} + 70 \, d \cosh\left(d x + c\right)^{4} \sinh\left(d x + c\right)^{4} + 56 \, d \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right)^{5} + 28 \, d \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{6} + 8 \, d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + d \sinh\left(d x + c\right)^{8}\right)}}"," ",0,"1/30720*(15*b^3*cosh(d*x + c)^16 + 240*b^3*cosh(d*x + c)*sinh(d*x + c)^15 + 15*b^3*sinh(d*x + c)^16 - 160*b^3*cosh(d*x + c)^14 + 576*a*b^2*cosh(d*x + c)^13 + 840*b^3*cosh(d*x + c)^12 + 40*(45*b^3*cosh(d*x + c)^2 - 4*b^3)*sinh(d*x + c)^14 - 4800*a*b^2*cosh(d*x + c)^11 + 16*(525*b^3*cosh(d*x + c)^3 - 140*b^3*cosh(d*x + c) + 36*a*b^2)*sinh(d*x + c)^13 + 4*(6825*b^3*cosh(d*x + c)^4 - 3640*b^3*cosh(d*x + c)^2 + 1872*a*b^2*cosh(d*x + c) + 210*b^3)*sinh(d*x + c)^12 + 28800*a*b^2*cosh(d*x + c)^9 + 16*(4095*b^3*cosh(d*x + c)^5 - 3640*b^3*cosh(d*x + c)^3 + 2808*a*b^2*cosh(d*x + c)^2 + 630*b^3*cosh(d*x + c) - 300*a*b^2)*sinh(d*x + c)^11 - 240*(192*a^2*b - 35*b^3)*d*x*cosh(d*x + c)^8 + 480*(24*a^2*b - 7*b^3)*cosh(d*x + c)^10 + 8*(15015*b^3*cosh(d*x + c)^6 - 20020*b^3*cosh(d*x + c)^4 + 20592*a*b^2*cosh(d*x + c)^3 + 6930*b^3*cosh(d*x + c)^2 - 6600*a*b^2*cosh(d*x + c) + 1440*a^2*b - 420*b^3)*sinh(d*x + c)^10 + 28800*a*b^2*cosh(d*x + c)^7 + 80*(2145*b^3*cosh(d*x + c)^7 - 4004*b^3*cosh(d*x + c)^5 + 5148*a*b^2*cosh(d*x + c)^4 + 2310*b^3*cosh(d*x + c)^3 - 3300*a*b^2*cosh(d*x + c)^2 + 360*a*b^2 + 60*(24*a^2*b - 7*b^3)*cosh(d*x + c))*sinh(d*x + c)^9 + 6*(32175*b^3*cosh(d*x + c)^8 - 80080*b^3*cosh(d*x + c)^6 + 123552*a*b^2*cosh(d*x + c)^5 + 69300*b^3*cosh(d*x + c)^4 - 132000*a*b^2*cosh(d*x + c)^3 + 43200*a*b^2*cosh(d*x + c) - 40*(192*a^2*b - 35*b^3)*d*x + 3600*(24*a^2*b - 7*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^8 - 4800*a*b^2*cosh(d*x + c)^5 + 48*(3575*b^3*cosh(d*x + c)^9 - 11440*b^3*cosh(d*x + c)^7 + 20592*a*b^2*cosh(d*x + c)^6 + 13860*b^3*cosh(d*x + c)^5 - 33000*a*b^2*cosh(d*x + c)^4 + 21600*a*b^2*cosh(d*x + c)^2 - 40*(192*a^2*b - 35*b^3)*d*x*cosh(d*x + c) + 1200*(24*a^2*b - 7*b^3)*cosh(d*x + c)^3 + 600*a*b^2)*sinh(d*x + c)^7 - 840*b^3*cosh(d*x + c)^4 - 480*(24*a^2*b - 7*b^3)*cosh(d*x + c)^6 + 24*(5005*b^3*cosh(d*x + c)^10 - 20020*b^3*cosh(d*x + c)^8 + 41184*a*b^2*cosh(d*x + c)^7 + 32340*b^3*cosh(d*x + c)^6 - 92400*a*b^2*cosh(d*x + c)^5 + 100800*a*b^2*cosh(d*x + c)^3 - 280*(192*a^2*b - 35*b^3)*d*x*cosh(d*x + c)^2 + 4200*(24*a^2*b - 7*b^3)*cosh(d*x + c)^4 + 8400*a*b^2*cosh(d*x + c) - 480*a^2*b + 140*b^3)*sinh(d*x + c)^6 + 576*a*b^2*cosh(d*x + c)^3 + 16*(4095*b^3*cosh(d*x + c)^11 - 20020*b^3*cosh(d*x + c)^9 + 46332*a*b^2*cosh(d*x + c)^8 + 41580*b^3*cosh(d*x + c)^7 - 138600*a*b^2*cosh(d*x + c)^6 + 226800*a*b^2*cosh(d*x + c)^4 - 840*(192*a^2*b - 35*b^3)*d*x*cosh(d*x + c)^3 + 7560*(24*a^2*b - 7*b^3)*cosh(d*x + c)^5 + 37800*a*b^2*cosh(d*x + c)^2 - 300*a*b^2 - 180*(24*a^2*b - 7*b^3)*cosh(d*x + c))*sinh(d*x + c)^5 + 160*b^3*cosh(d*x + c)^2 + 20*(1365*b^3*cosh(d*x + c)^12 - 8008*b^3*cosh(d*x + c)^10 + 20592*a*b^2*cosh(d*x + c)^9 + 20790*b^3*cosh(d*x + c)^8 - 79200*a*b^2*cosh(d*x + c)^7 + 181440*a*b^2*cosh(d*x + c)^5 - 840*(192*a^2*b - 35*b^3)*d*x*cosh(d*x + c)^4 + 5040*(24*a^2*b - 7*b^3)*cosh(d*x + c)^6 + 50400*a*b^2*cosh(d*x + c)^3 - 1200*a*b^2*cosh(d*x + c) - 42*b^3 - 360*(24*a^2*b - 7*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 16*(525*b^3*cosh(d*x + c)^13 - 3640*b^3*cosh(d*x + c)^11 + 10296*a*b^2*cosh(d*x + c)^10 + 11550*b^3*cosh(d*x + c)^9 - 49500*a*b^2*cosh(d*x + c)^8 + 151200*a*b^2*cosh(d*x + c)^6 - 840*(192*a^2*b - 35*b^3)*d*x*cosh(d*x + c)^5 + 3600*(24*a^2*b - 7*b^3)*cosh(d*x + c)^7 + 63000*a*b^2*cosh(d*x + c)^4 - 3000*a*b^2*cosh(d*x + c)^2 - 210*b^3*cosh(d*x + c) - 600*(24*a^2*b - 7*b^3)*cosh(d*x + c)^3 + 36*a*b^2)*sinh(d*x + c)^3 - 15*b^3 + 8*(225*b^3*cosh(d*x + c)^14 - 1820*b^3*cosh(d*x + c)^12 + 5616*a*b^2*cosh(d*x + c)^11 + 6930*b^3*cosh(d*x + c)^10 - 33000*a*b^2*cosh(d*x + c)^9 + 129600*a*b^2*cosh(d*x + c)^7 - 840*(192*a^2*b - 35*b^3)*d*x*cosh(d*x + c)^6 + 2700*(24*a^2*b - 7*b^3)*cosh(d*x + c)^8 + 75600*a*b^2*cosh(d*x + c)^5 - 6000*a*b^2*cosh(d*x + c)^3 - 630*b^3*cosh(d*x + c)^2 - 900*(24*a^2*b - 7*b^3)*cosh(d*x + c)^4 + 216*a*b^2*cosh(d*x + c) + 20*b^3)*sinh(d*x + c)^2 - 30720*(a^3*cosh(d*x + c)^8 + 8*a^3*cosh(d*x + c)^7*sinh(d*x + c) + 28*a^3*cosh(d*x + c)^6*sinh(d*x + c)^2 + 56*a^3*cosh(d*x + c)^5*sinh(d*x + c)^3 + 70*a^3*cosh(d*x + c)^4*sinh(d*x + c)^4 + 56*a^3*cosh(d*x + c)^3*sinh(d*x + c)^5 + 28*a^3*cosh(d*x + c)^2*sinh(d*x + c)^6 + 8*a^3*cosh(d*x + c)*sinh(d*x + c)^7 + a^3*sinh(d*x + c)^8)*log(cosh(d*x + c) + sinh(d*x + c) + 1) + 30720*(a^3*cosh(d*x + c)^8 + 8*a^3*cosh(d*x + c)^7*sinh(d*x + c) + 28*a^3*cosh(d*x + c)^6*sinh(d*x + c)^2 + 56*a^3*cosh(d*x + c)^5*sinh(d*x + c)^3 + 70*a^3*cosh(d*x + c)^4*sinh(d*x + c)^4 + 56*a^3*cosh(d*x + c)^3*sinh(d*x + c)^5 + 28*a^3*cosh(d*x + c)^2*sinh(d*x + c)^6 + 8*a^3*cosh(d*x + c)*sinh(d*x + c)^7 + a^3*sinh(d*x + c)^8)*log(cosh(d*x + c) + sinh(d*x + c) - 1) + 16*(15*b^3*cosh(d*x + c)^15 - 140*b^3*cosh(d*x + c)^13 + 468*a*b^2*cosh(d*x + c)^12 + 630*b^3*cosh(d*x + c)^11 - 3300*a*b^2*cosh(d*x + c)^10 + 16200*a*b^2*cosh(d*x + c)^8 - 120*(192*a^2*b - 35*b^3)*d*x*cosh(d*x + c)^7 + 300*(24*a^2*b - 7*b^3)*cosh(d*x + c)^9 + 12600*a*b^2*cosh(d*x + c)^6 - 1500*a*b^2*cosh(d*x + c)^4 - 210*b^3*cosh(d*x + c)^3 - 180*(24*a^2*b - 7*b^3)*cosh(d*x + c)^5 + 108*a*b^2*cosh(d*x + c)^2 + 20*b^3*cosh(d*x + c))*sinh(d*x + c))/(d*cosh(d*x + c)^8 + 8*d*cosh(d*x + c)^7*sinh(d*x + c) + 28*d*cosh(d*x + c)^6*sinh(d*x + c)^2 + 56*d*cosh(d*x + c)^5*sinh(d*x + c)^3 + 70*d*cosh(d*x + c)^4*sinh(d*x + c)^4 + 56*d*cosh(d*x + c)^3*sinh(d*x + c)^5 + 28*d*cosh(d*x + c)^2*sinh(d*x + c)^6 + 8*d*cosh(d*x + c)*sinh(d*x + c)^7 + d*sinh(d*x + c)^8)","B",0
165,1,302,0,0.442490," ","integrate(csch(d*x+c)^2*(a+b*sinh(d*x+c)^3)^3,x, algorithm=""fricas"")","\frac{20 \, b^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + 105 \, a b^{2} \cosh\left(d x + c\right)^{5} + 525 \, a b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} - 945 \, a b^{2} \cosh\left(d x + c\right)^{3} + 2 \, {\left(70 \, b^{3} \cosh\left(d x + c\right)^{3} - 81 \, b^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 4 \, {\left(35 \, b^{3} \cosh\left(d x + c\right)^{5} - 135 \, b^{3} \cosh\left(d x + c\right)^{3} + 147 \, b^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 105 \, {\left(10 \, a b^{2} \cosh\left(d x + c\right)^{3} - 27 \, a b^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 280 \, {\left(8 \, a^{3} - 3 \, a b^{2}\right)} \cosh\left(d x + c\right) + 2 \, {\left(10 \, b^{3} \cosh\left(d x + c\right)^{7} - 81 \, b^{3} \cosh\left(d x + c\right)^{5} + 294 \, b^{3} \cosh\left(d x + c\right)^{3} + 1260 \, a b^{2} d x + 1120 \, a^{3} + 105 \, {\left(32 \, a^{2} b - 7 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{2240 \, d \sinh\left(d x + c\right)}"," ",0,"1/2240*(20*b^3*cosh(d*x + c)*sinh(d*x + c)^7 + 105*a*b^2*cosh(d*x + c)^5 + 525*a*b^2*cosh(d*x + c)*sinh(d*x + c)^4 - 945*a*b^2*cosh(d*x + c)^3 + 2*(70*b^3*cosh(d*x + c)^3 - 81*b^3*cosh(d*x + c))*sinh(d*x + c)^5 + 4*(35*b^3*cosh(d*x + c)^5 - 135*b^3*cosh(d*x + c)^3 + 147*b^3*cosh(d*x + c))*sinh(d*x + c)^3 + 105*(10*a*b^2*cosh(d*x + c)^3 - 27*a*b^2*cosh(d*x + c))*sinh(d*x + c)^2 - 280*(8*a^3 - 3*a*b^2)*cosh(d*x + c) + 2*(10*b^3*cosh(d*x + c)^7 - 81*b^3*cosh(d*x + c)^5 + 294*b^3*cosh(d*x + c)^3 + 1260*a*b^2*d*x + 1120*a^3 + 105*(32*a^2*b - 7*b^3)*cosh(d*x + c))*sinh(d*x + c))/(d*sinh(d*x + c))","B",0
166,1,3627,0,0.630076," ","integrate(csch(d*x+c)^3*(a+b*sinh(d*x+c)^3)^3,x, algorithm=""fricas"")","\frac{b^{3} \cosh\left(d x + c\right)^{16} + 16 \, b^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{15} + b^{3} \sinh\left(d x + c\right)^{16} - 11 \, b^{3} \cosh\left(d x + c\right)^{14} + 48 \, a b^{2} \cosh\left(d x + c\right)^{13} + 64 \, b^{3} \cosh\left(d x + c\right)^{12} + {\left(120 \, b^{3} \cosh\left(d x + c\right)^{2} - 11 \, b^{3}\right)} \sinh\left(d x + c\right)^{14} - 528 \, a b^{2} \cosh\left(d x + c\right)^{11} + 2 \, {\left(280 \, b^{3} \cosh\left(d x + c\right)^{3} - 77 \, b^{3} \cosh\left(d x + c\right) + 24 \, a b^{2}\right)} \sinh\left(d x + c\right)^{13} + {\left(1820 \, b^{3} \cosh\left(d x + c\right)^{4} - 1001 \, b^{3} \cosh\left(d x + c\right)^{2} + 624 \, a b^{2} \cosh\left(d x + c\right) + 64 \, b^{3}\right)} \sinh\left(d x + c\right)^{12} + 4 \, {\left(1092 \, b^{3} \cosh\left(d x + c\right)^{5} - 1001 \, b^{3} \cosh\left(d x + c\right)^{3} + 936 \, a b^{2} \cosh\left(d x + c\right)^{2} + 192 \, b^{3} \cosh\left(d x + c\right) - 132 \, a b^{2}\right)} \sinh\left(d x + c\right)^{11} - 48 \, {\left(48 \, a^{2} b - 5 \, b^{3}\right)} d x \cosh\left(d x + c\right)^{8} - 3 \, {\left(33 \, b^{3} - 8 \, {\left(48 \, a^{2} b - 5 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{10} + {\left(8008 \, b^{3} \cosh\left(d x + c\right)^{6} - 11011 \, b^{3} \cosh\left(d x + c\right)^{4} + 13728 \, a b^{2} \cosh\left(d x + c\right)^{3} + 4224 \, b^{3} \cosh\left(d x + c\right)^{2} - 5808 \, a b^{2} \cosh\left(d x + c\right) - 99 \, b^{3} + 24 \, {\left(48 \, a^{2} b - 5 \, b^{3}\right)} d x\right)} \sinh\left(d x + c\right)^{10} - 96 \, {\left(4 \, a^{3} - 5 \, a b^{2}\right)} \cosh\left(d x + c\right)^{9} + 2 \, {\left(5720 \, b^{3} \cosh\left(d x + c\right)^{7} - 11011 \, b^{3} \cosh\left(d x + c\right)^{5} + 17160 \, a b^{2} \cosh\left(d x + c\right)^{4} + 7040 \, b^{3} \cosh\left(d x + c\right)^{3} - 14520 \, a b^{2} \cosh\left(d x + c\right)^{2} - 192 \, a^{3} + 240 \, a b^{2} - 15 \, {\left(33 \, b^{3} - 8 \, {\left(48 \, a^{2} b - 5 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} + 3 \, {\left(4290 \, b^{3} \cosh\left(d x + c\right)^{8} - 11011 \, b^{3} \cosh\left(d x + c\right)^{6} + 20592 \, a b^{2} \cosh\left(d x + c\right)^{5} + 10560 \, b^{3} \cosh\left(d x + c\right)^{4} - 29040 \, a b^{2} \cosh\left(d x + c\right)^{3} - 16 \, {\left(48 \, a^{2} b - 5 \, b^{3}\right)} d x - 45 \, {\left(33 \, b^{3} - 8 \, {\left(48 \, a^{2} b - 5 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2} - 288 \, {\left(4 \, a^{3} - 5 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{8} - 528 \, a b^{2} \cosh\left(d x + c\right)^{5} - 96 \, {\left(4 \, a^{3} - 5 \, a b^{2}\right)} \cosh\left(d x + c\right)^{7} + 8 \, {\left(1430 \, b^{3} \cosh\left(d x + c\right)^{9} - 4719 \, b^{3} \cosh\left(d x + c\right)^{7} + 10296 \, a b^{2} \cosh\left(d x + c\right)^{6} + 6336 \, b^{3} \cosh\left(d x + c\right)^{5} - 21780 \, a b^{2} \cosh\left(d x + c\right)^{4} - 48 \, {\left(48 \, a^{2} b - 5 \, b^{3}\right)} d x \cosh\left(d x + c\right) - 45 \, {\left(33 \, b^{3} - 8 \, {\left(48 \, a^{2} b - 5 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - 48 \, a^{3} + 60 \, a b^{2} - 432 \, {\left(4 \, a^{3} - 5 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{7} - 64 \, b^{3} \cosh\left(d x + c\right)^{4} + 3 \, {\left(33 \, b^{3} + 8 \, {\left(48 \, a^{2} b - 5 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{6} + {\left(8008 \, b^{3} \cosh\left(d x + c\right)^{10} - 33033 \, b^{3} \cosh\left(d x + c\right)^{8} + 82368 \, a b^{2} \cosh\left(d x + c\right)^{7} + 59136 \, b^{3} \cosh\left(d x + c\right)^{6} - 243936 \, a b^{2} \cosh\left(d x + c\right)^{5} - 1344 \, {\left(48 \, a^{2} b - 5 \, b^{3}\right)} d x \cosh\left(d x + c\right)^{2} - 630 \, {\left(33 \, b^{3} - 8 \, {\left(48 \, a^{2} b - 5 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{4} - 8064 \, {\left(4 \, a^{3} - 5 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} + 99 \, b^{3} + 24 \, {\left(48 \, a^{2} b - 5 \, b^{3}\right)} d x - 672 \, {\left(4 \, a^{3} - 5 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} + 48 \, a b^{2} \cosh\left(d x + c\right)^{3} + 2 \, {\left(2184 \, b^{3} \cosh\left(d x + c\right)^{11} - 11011 \, b^{3} \cosh\left(d x + c\right)^{9} + 30888 \, a b^{2} \cosh\left(d x + c\right)^{8} + 25344 \, b^{3} \cosh\left(d x + c\right)^{7} - 121968 \, a b^{2} \cosh\left(d x + c\right)^{6} - 1344 \, {\left(48 \, a^{2} b - 5 \, b^{3}\right)} d x \cosh\left(d x + c\right)^{3} - 378 \, {\left(33 \, b^{3} - 8 \, {\left(48 \, a^{2} b - 5 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{5} - 6048 \, {\left(4 \, a^{3} - 5 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} - 264 \, a b^{2} - 1008 \, {\left(4 \, a^{3} - 5 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2} + 9 \, {\left(33 \, b^{3} + 8 \, {\left(48 \, a^{2} b - 5 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 11 \, b^{3} \cosh\left(d x + c\right)^{2} + {\left(1820 \, b^{3} \cosh\left(d x + c\right)^{12} - 11011 \, b^{3} \cosh\left(d x + c\right)^{10} + 34320 \, a b^{2} \cosh\left(d x + c\right)^{9} + 31680 \, b^{3} \cosh\left(d x + c\right)^{8} - 174240 \, a b^{2} \cosh\left(d x + c\right)^{7} - 3360 \, {\left(48 \, a^{2} b - 5 \, b^{3}\right)} d x \cosh\left(d x + c\right)^{4} - 630 \, {\left(33 \, b^{3} - 8 \, {\left(48 \, a^{2} b - 5 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{6} - 12096 \, {\left(4 \, a^{3} - 5 \, a b^{2}\right)} \cosh\left(d x + c\right)^{5} - 2640 \, a b^{2} \cosh\left(d x + c\right) - 3360 \, {\left(4 \, a^{3} - 5 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} - 64 \, b^{3} + 45 \, {\left(33 \, b^{3} + 8 \, {\left(48 \, a^{2} b - 5 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(140 \, b^{3} \cosh\left(d x + c\right)^{13} - 1001 \, b^{3} \cosh\left(d x + c\right)^{11} + 3432 \, a b^{2} \cosh\left(d x + c\right)^{10} + 3520 \, b^{3} \cosh\left(d x + c\right)^{9} - 21780 \, a b^{2} \cosh\left(d x + c\right)^{8} - 672 \, {\left(48 \, a^{2} b - 5 \, b^{3}\right)} d x \cosh\left(d x + c\right)^{5} - 90 \, {\left(33 \, b^{3} - 8 \, {\left(48 \, a^{2} b - 5 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{7} - 2016 \, {\left(4 \, a^{3} - 5 \, a b^{2}\right)} \cosh\left(d x + c\right)^{6} - 1320 \, a b^{2} \cosh\left(d x + c\right)^{2} - 840 \, {\left(4 \, a^{3} - 5 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} - 64 \, b^{3} \cosh\left(d x + c\right) + 15 \, {\left(33 \, b^{3} + 8 \, {\left(48 \, a^{2} b - 5 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + 12 \, a b^{2}\right)} \sinh\left(d x + c\right)^{3} - b^{3} + {\left(120 \, b^{3} \cosh\left(d x + c\right)^{14} - 1001 \, b^{3} \cosh\left(d x + c\right)^{12} + 3744 \, a b^{2} \cosh\left(d x + c\right)^{11} + 4224 \, b^{3} \cosh\left(d x + c\right)^{10} - 29040 \, a b^{2} \cosh\left(d x + c\right)^{9} - 1344 \, {\left(48 \, a^{2} b - 5 \, b^{3}\right)} d x \cosh\left(d x + c\right)^{6} - 135 \, {\left(33 \, b^{3} - 8 \, {\left(48 \, a^{2} b - 5 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{8} - 3456 \, {\left(4 \, a^{3} - 5 \, a b^{2}\right)} \cosh\left(d x + c\right)^{7} - 5280 \, a b^{2} \cosh\left(d x + c\right)^{3} - 2016 \, {\left(4 \, a^{3} - 5 \, a b^{2}\right)} \cosh\left(d x + c\right)^{5} - 384 \, b^{3} \cosh\left(d x + c\right)^{2} + 45 \, {\left(33 \, b^{3} + 8 \, {\left(48 \, a^{2} b - 5 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 144 \, a b^{2} \cosh\left(d x + c\right) + 11 \, b^{3}\right)} \sinh\left(d x + c\right)^{2} + 192 \, {\left(a^{3} \cosh\left(d x + c\right)^{10} + 10 \, a^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + a^{3} \sinh\left(d x + c\right)^{10} - 2 \, a^{3} \cosh\left(d x + c\right)^{8} + a^{3} \cosh\left(d x + c\right)^{6} + {\left(45 \, a^{3} \cosh\left(d x + c\right)^{2} - 2 \, a^{3}\right)} \sinh\left(d x + c\right)^{8} + 8 \, {\left(15 \, a^{3} \cosh\left(d x + c\right)^{3} - 2 \, a^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + {\left(210 \, a^{3} \cosh\left(d x + c\right)^{4} - 56 \, a^{3} \cosh\left(d x + c\right)^{2} + a^{3}\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(126 \, a^{3} \cosh\left(d x + c\right)^{5} - 56 \, a^{3} \cosh\left(d x + c\right)^{3} + 3 \, a^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 5 \, {\left(42 \, a^{3} \cosh\left(d x + c\right)^{6} - 28 \, a^{3} \cosh\left(d x + c\right)^{4} + 3 \, a^{3} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(30 \, a^{3} \cosh\left(d x + c\right)^{7} - 28 \, a^{3} \cosh\left(d x + c\right)^{5} + 5 \, a^{3} \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right)^{3} + {\left(45 \, a^{3} \cosh\left(d x + c\right)^{8} - 56 \, a^{3} \cosh\left(d x + c\right)^{6} + 15 \, a^{3} \cosh\left(d x + c\right)^{4}\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(5 \, a^{3} \cosh\left(d x + c\right)^{9} - 8 \, a^{3} \cosh\left(d x + c\right)^{7} + 3 \, a^{3} \cosh\left(d x + c\right)^{5}\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) - 192 \, {\left(a^{3} \cosh\left(d x + c\right)^{10} + 10 \, a^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + a^{3} \sinh\left(d x + c\right)^{10} - 2 \, a^{3} \cosh\left(d x + c\right)^{8} + a^{3} \cosh\left(d x + c\right)^{6} + {\left(45 \, a^{3} \cosh\left(d x + c\right)^{2} - 2 \, a^{3}\right)} \sinh\left(d x + c\right)^{8} + 8 \, {\left(15 \, a^{3} \cosh\left(d x + c\right)^{3} - 2 \, a^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + {\left(210 \, a^{3} \cosh\left(d x + c\right)^{4} - 56 \, a^{3} \cosh\left(d x + c\right)^{2} + a^{3}\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(126 \, a^{3} \cosh\left(d x + c\right)^{5} - 56 \, a^{3} \cosh\left(d x + c\right)^{3} + 3 \, a^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 5 \, {\left(42 \, a^{3} \cosh\left(d x + c\right)^{6} - 28 \, a^{3} \cosh\left(d x + c\right)^{4} + 3 \, a^{3} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(30 \, a^{3} \cosh\left(d x + c\right)^{7} - 28 \, a^{3} \cosh\left(d x + c\right)^{5} + 5 \, a^{3} \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right)^{3} + {\left(45 \, a^{3} \cosh\left(d x + c\right)^{8} - 56 \, a^{3} \cosh\left(d x + c\right)^{6} + 15 \, a^{3} \cosh\left(d x + c\right)^{4}\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(5 \, a^{3} \cosh\left(d x + c\right)^{9} - 8 \, a^{3} \cosh\left(d x + c\right)^{7} + 3 \, a^{3} \cosh\left(d x + c\right)^{5}\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) + 2 \, {\left(8 \, b^{3} \cosh\left(d x + c\right)^{15} - 77 \, b^{3} \cosh\left(d x + c\right)^{13} + 312 \, a b^{2} \cosh\left(d x + c\right)^{12} + 384 \, b^{3} \cosh\left(d x + c\right)^{11} - 2904 \, a b^{2} \cosh\left(d x + c\right)^{10} - 192 \, {\left(48 \, a^{2} b - 5 \, b^{3}\right)} d x \cosh\left(d x + c\right)^{7} - 15 \, {\left(33 \, b^{3} - 8 \, {\left(48 \, a^{2} b - 5 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{9} - 432 \, {\left(4 \, a^{3} - 5 \, a b^{2}\right)} \cosh\left(d x + c\right)^{8} - 1320 \, a b^{2} \cosh\left(d x + c\right)^{4} - 336 \, {\left(4 \, a^{3} - 5 \, a b^{2}\right)} \cosh\left(d x + c\right)^{6} - 128 \, b^{3} \cosh\left(d x + c\right)^{3} + 9 \, {\left(33 \, b^{3} + 8 \, {\left(48 \, a^{2} b - 5 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{5} + 72 \, a b^{2} \cosh\left(d x + c\right)^{2} + 11 \, b^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{384 \, {\left(d \cosh\left(d x + c\right)^{10} + 10 \, d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + d \sinh\left(d x + c\right)^{10} - 2 \, d \cosh\left(d x + c\right)^{8} + {\left(45 \, d \cosh\left(d x + c\right)^{2} - 2 \, d\right)} \sinh\left(d x + c\right)^{8} + 8 \, {\left(15 \, d \cosh\left(d x + c\right)^{3} - 2 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + d \cosh\left(d x + c\right)^{6} + {\left(210 \, d \cosh\left(d x + c\right)^{4} - 56 \, d \cosh\left(d x + c\right)^{2} + d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(126 \, d \cosh\left(d x + c\right)^{5} - 56 \, d \cosh\left(d x + c\right)^{3} + 3 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 5 \, {\left(42 \, d \cosh\left(d x + c\right)^{6} - 28 \, d \cosh\left(d x + c\right)^{4} + 3 \, d \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(30 \, d \cosh\left(d x + c\right)^{7} - 28 \, d \cosh\left(d x + c\right)^{5} + 5 \, d \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right)^{3} + {\left(45 \, d \cosh\left(d x + c\right)^{8} - 56 \, d \cosh\left(d x + c\right)^{6} + 15 \, d \cosh\left(d x + c\right)^{4}\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(5 \, d \cosh\left(d x + c\right)^{9} - 8 \, d \cosh\left(d x + c\right)^{7} + 3 \, d \cosh\left(d x + c\right)^{5}\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"1/384*(b^3*cosh(d*x + c)^16 + 16*b^3*cosh(d*x + c)*sinh(d*x + c)^15 + b^3*sinh(d*x + c)^16 - 11*b^3*cosh(d*x + c)^14 + 48*a*b^2*cosh(d*x + c)^13 + 64*b^3*cosh(d*x + c)^12 + (120*b^3*cosh(d*x + c)^2 - 11*b^3)*sinh(d*x + c)^14 - 528*a*b^2*cosh(d*x + c)^11 + 2*(280*b^3*cosh(d*x + c)^3 - 77*b^3*cosh(d*x + c) + 24*a*b^2)*sinh(d*x + c)^13 + (1820*b^3*cosh(d*x + c)^4 - 1001*b^3*cosh(d*x + c)^2 + 624*a*b^2*cosh(d*x + c) + 64*b^3)*sinh(d*x + c)^12 + 4*(1092*b^3*cosh(d*x + c)^5 - 1001*b^3*cosh(d*x + c)^3 + 936*a*b^2*cosh(d*x + c)^2 + 192*b^3*cosh(d*x + c) - 132*a*b^2)*sinh(d*x + c)^11 - 48*(48*a^2*b - 5*b^3)*d*x*cosh(d*x + c)^8 - 3*(33*b^3 - 8*(48*a^2*b - 5*b^3)*d*x)*cosh(d*x + c)^10 + (8008*b^3*cosh(d*x + c)^6 - 11011*b^3*cosh(d*x + c)^4 + 13728*a*b^2*cosh(d*x + c)^3 + 4224*b^3*cosh(d*x + c)^2 - 5808*a*b^2*cosh(d*x + c) - 99*b^3 + 24*(48*a^2*b - 5*b^3)*d*x)*sinh(d*x + c)^10 - 96*(4*a^3 - 5*a*b^2)*cosh(d*x + c)^9 + 2*(5720*b^3*cosh(d*x + c)^7 - 11011*b^3*cosh(d*x + c)^5 + 17160*a*b^2*cosh(d*x + c)^4 + 7040*b^3*cosh(d*x + c)^3 - 14520*a*b^2*cosh(d*x + c)^2 - 192*a^3 + 240*a*b^2 - 15*(33*b^3 - 8*(48*a^2*b - 5*b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c)^9 + 3*(4290*b^3*cosh(d*x + c)^8 - 11011*b^3*cosh(d*x + c)^6 + 20592*a*b^2*cosh(d*x + c)^5 + 10560*b^3*cosh(d*x + c)^4 - 29040*a*b^2*cosh(d*x + c)^3 - 16*(48*a^2*b - 5*b^3)*d*x - 45*(33*b^3 - 8*(48*a^2*b - 5*b^3)*d*x)*cosh(d*x + c)^2 - 288*(4*a^3 - 5*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^8 - 528*a*b^2*cosh(d*x + c)^5 - 96*(4*a^3 - 5*a*b^2)*cosh(d*x + c)^7 + 8*(1430*b^3*cosh(d*x + c)^9 - 4719*b^3*cosh(d*x + c)^7 + 10296*a*b^2*cosh(d*x + c)^6 + 6336*b^3*cosh(d*x + c)^5 - 21780*a*b^2*cosh(d*x + c)^4 - 48*(48*a^2*b - 5*b^3)*d*x*cosh(d*x + c) - 45*(33*b^3 - 8*(48*a^2*b - 5*b^3)*d*x)*cosh(d*x + c)^3 - 48*a^3 + 60*a*b^2 - 432*(4*a^3 - 5*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^7 - 64*b^3*cosh(d*x + c)^4 + 3*(33*b^3 + 8*(48*a^2*b - 5*b^3)*d*x)*cosh(d*x + c)^6 + (8008*b^3*cosh(d*x + c)^10 - 33033*b^3*cosh(d*x + c)^8 + 82368*a*b^2*cosh(d*x + c)^7 + 59136*b^3*cosh(d*x + c)^6 - 243936*a*b^2*cosh(d*x + c)^5 - 1344*(48*a^2*b - 5*b^3)*d*x*cosh(d*x + c)^2 - 630*(33*b^3 - 8*(48*a^2*b - 5*b^3)*d*x)*cosh(d*x + c)^4 - 8064*(4*a^3 - 5*a*b^2)*cosh(d*x + c)^3 + 99*b^3 + 24*(48*a^2*b - 5*b^3)*d*x - 672*(4*a^3 - 5*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^6 + 48*a*b^2*cosh(d*x + c)^3 + 2*(2184*b^3*cosh(d*x + c)^11 - 11011*b^3*cosh(d*x + c)^9 + 30888*a*b^2*cosh(d*x + c)^8 + 25344*b^3*cosh(d*x + c)^7 - 121968*a*b^2*cosh(d*x + c)^6 - 1344*(48*a^2*b - 5*b^3)*d*x*cosh(d*x + c)^3 - 378*(33*b^3 - 8*(48*a^2*b - 5*b^3)*d*x)*cosh(d*x + c)^5 - 6048*(4*a^3 - 5*a*b^2)*cosh(d*x + c)^4 - 264*a*b^2 - 1008*(4*a^3 - 5*a*b^2)*cosh(d*x + c)^2 + 9*(33*b^3 + 8*(48*a^2*b - 5*b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c)^5 + 11*b^3*cosh(d*x + c)^2 + (1820*b^3*cosh(d*x + c)^12 - 11011*b^3*cosh(d*x + c)^10 + 34320*a*b^2*cosh(d*x + c)^9 + 31680*b^3*cosh(d*x + c)^8 - 174240*a*b^2*cosh(d*x + c)^7 - 3360*(48*a^2*b - 5*b^3)*d*x*cosh(d*x + c)^4 - 630*(33*b^3 - 8*(48*a^2*b - 5*b^3)*d*x)*cosh(d*x + c)^6 - 12096*(4*a^3 - 5*a*b^2)*cosh(d*x + c)^5 - 2640*a*b^2*cosh(d*x + c) - 3360*(4*a^3 - 5*a*b^2)*cosh(d*x + c)^3 - 64*b^3 + 45*(33*b^3 + 8*(48*a^2*b - 5*b^3)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 4*(140*b^3*cosh(d*x + c)^13 - 1001*b^3*cosh(d*x + c)^11 + 3432*a*b^2*cosh(d*x + c)^10 + 3520*b^3*cosh(d*x + c)^9 - 21780*a*b^2*cosh(d*x + c)^8 - 672*(48*a^2*b - 5*b^3)*d*x*cosh(d*x + c)^5 - 90*(33*b^3 - 8*(48*a^2*b - 5*b^3)*d*x)*cosh(d*x + c)^7 - 2016*(4*a^3 - 5*a*b^2)*cosh(d*x + c)^6 - 1320*a*b^2*cosh(d*x + c)^2 - 840*(4*a^3 - 5*a*b^2)*cosh(d*x + c)^4 - 64*b^3*cosh(d*x + c) + 15*(33*b^3 + 8*(48*a^2*b - 5*b^3)*d*x)*cosh(d*x + c)^3 + 12*a*b^2)*sinh(d*x + c)^3 - b^3 + (120*b^3*cosh(d*x + c)^14 - 1001*b^3*cosh(d*x + c)^12 + 3744*a*b^2*cosh(d*x + c)^11 + 4224*b^3*cosh(d*x + c)^10 - 29040*a*b^2*cosh(d*x + c)^9 - 1344*(48*a^2*b - 5*b^3)*d*x*cosh(d*x + c)^6 - 135*(33*b^3 - 8*(48*a^2*b - 5*b^3)*d*x)*cosh(d*x + c)^8 - 3456*(4*a^3 - 5*a*b^2)*cosh(d*x + c)^7 - 5280*a*b^2*cosh(d*x + c)^3 - 2016*(4*a^3 - 5*a*b^2)*cosh(d*x + c)^5 - 384*b^3*cosh(d*x + c)^2 + 45*(33*b^3 + 8*(48*a^2*b - 5*b^3)*d*x)*cosh(d*x + c)^4 + 144*a*b^2*cosh(d*x + c) + 11*b^3)*sinh(d*x + c)^2 + 192*(a^3*cosh(d*x + c)^10 + 10*a^3*cosh(d*x + c)*sinh(d*x + c)^9 + a^3*sinh(d*x + c)^10 - 2*a^3*cosh(d*x + c)^8 + a^3*cosh(d*x + c)^6 + (45*a^3*cosh(d*x + c)^2 - 2*a^3)*sinh(d*x + c)^8 + 8*(15*a^3*cosh(d*x + c)^3 - 2*a^3*cosh(d*x + c))*sinh(d*x + c)^7 + (210*a^3*cosh(d*x + c)^4 - 56*a^3*cosh(d*x + c)^2 + a^3)*sinh(d*x + c)^6 + 2*(126*a^3*cosh(d*x + c)^5 - 56*a^3*cosh(d*x + c)^3 + 3*a^3*cosh(d*x + c))*sinh(d*x + c)^5 + 5*(42*a^3*cosh(d*x + c)^6 - 28*a^3*cosh(d*x + c)^4 + 3*a^3*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 4*(30*a^3*cosh(d*x + c)^7 - 28*a^3*cosh(d*x + c)^5 + 5*a^3*cosh(d*x + c)^3)*sinh(d*x + c)^3 + (45*a^3*cosh(d*x + c)^8 - 56*a^3*cosh(d*x + c)^6 + 15*a^3*cosh(d*x + c)^4)*sinh(d*x + c)^2 + 2*(5*a^3*cosh(d*x + c)^9 - 8*a^3*cosh(d*x + c)^7 + 3*a^3*cosh(d*x + c)^5)*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) + 1) - 192*(a^3*cosh(d*x + c)^10 + 10*a^3*cosh(d*x + c)*sinh(d*x + c)^9 + a^3*sinh(d*x + c)^10 - 2*a^3*cosh(d*x + c)^8 + a^3*cosh(d*x + c)^6 + (45*a^3*cosh(d*x + c)^2 - 2*a^3)*sinh(d*x + c)^8 + 8*(15*a^3*cosh(d*x + c)^3 - 2*a^3*cosh(d*x + c))*sinh(d*x + c)^7 + (210*a^3*cosh(d*x + c)^4 - 56*a^3*cosh(d*x + c)^2 + a^3)*sinh(d*x + c)^6 + 2*(126*a^3*cosh(d*x + c)^5 - 56*a^3*cosh(d*x + c)^3 + 3*a^3*cosh(d*x + c))*sinh(d*x + c)^5 + 5*(42*a^3*cosh(d*x + c)^6 - 28*a^3*cosh(d*x + c)^4 + 3*a^3*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 4*(30*a^3*cosh(d*x + c)^7 - 28*a^3*cosh(d*x + c)^5 + 5*a^3*cosh(d*x + c)^3)*sinh(d*x + c)^3 + (45*a^3*cosh(d*x + c)^8 - 56*a^3*cosh(d*x + c)^6 + 15*a^3*cosh(d*x + c)^4)*sinh(d*x + c)^2 + 2*(5*a^3*cosh(d*x + c)^9 - 8*a^3*cosh(d*x + c)^7 + 3*a^3*cosh(d*x + c)^5)*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) - 1) + 2*(8*b^3*cosh(d*x + c)^15 - 77*b^3*cosh(d*x + c)^13 + 312*a*b^2*cosh(d*x + c)^12 + 384*b^3*cosh(d*x + c)^11 - 2904*a*b^2*cosh(d*x + c)^10 - 192*(48*a^2*b - 5*b^3)*d*x*cosh(d*x + c)^7 - 15*(33*b^3 - 8*(48*a^2*b - 5*b^3)*d*x)*cosh(d*x + c)^9 - 432*(4*a^3 - 5*a*b^2)*cosh(d*x + c)^8 - 1320*a*b^2*cosh(d*x + c)^4 - 336*(4*a^3 - 5*a*b^2)*cosh(d*x + c)^6 - 128*b^3*cosh(d*x + c)^3 + 9*(33*b^3 + 8*(48*a^2*b - 5*b^3)*d*x)*cosh(d*x + c)^5 + 72*a*b^2*cosh(d*x + c)^2 + 11*b^3*cosh(d*x + c))*sinh(d*x + c))/(d*cosh(d*x + c)^10 + 10*d*cosh(d*x + c)*sinh(d*x + c)^9 + d*sinh(d*x + c)^10 - 2*d*cosh(d*x + c)^8 + (45*d*cosh(d*x + c)^2 - 2*d)*sinh(d*x + c)^8 + 8*(15*d*cosh(d*x + c)^3 - 2*d*cosh(d*x + c))*sinh(d*x + c)^7 + d*cosh(d*x + c)^6 + (210*d*cosh(d*x + c)^4 - 56*d*cosh(d*x + c)^2 + d)*sinh(d*x + c)^6 + 2*(126*d*cosh(d*x + c)^5 - 56*d*cosh(d*x + c)^3 + 3*d*cosh(d*x + c))*sinh(d*x + c)^5 + 5*(42*d*cosh(d*x + c)^6 - 28*d*cosh(d*x + c)^4 + 3*d*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 4*(30*d*cosh(d*x + c)^7 - 28*d*cosh(d*x + c)^5 + 5*d*cosh(d*x + c)^3)*sinh(d*x + c)^3 + (45*d*cosh(d*x + c)^8 - 56*d*cosh(d*x + c)^6 + 15*d*cosh(d*x + c)^4)*sinh(d*x + c)^2 + 2*(5*d*cosh(d*x + c)^9 - 8*d*cosh(d*x + c)^7 + 3*d*cosh(d*x + c)^5)*sinh(d*x + c))","B",0
167,1,3801,0,0.578505," ","integrate(csch(d*x+c)^4*(a+b*sinh(d*x+c)^3)^3,x, algorithm=""fricas"")","\frac{3 \, b^{3} \cosh\left(d x + c\right)^{16} + 48 \, b^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{15} + 3 \, b^{3} \sinh\left(d x + c\right)^{16} - 34 \, b^{3} \cosh\left(d x + c\right)^{14} + 180 \, a b^{2} \cosh\left(d x + c\right)^{13} + 234 \, b^{3} \cosh\left(d x + c\right)^{12} + 2 \, {\left(180 \, b^{3} \cosh\left(d x + c\right)^{2} - 17 \, b^{3}\right)} \sinh\left(d x + c\right)^{14} + 4 \, {\left(420 \, b^{3} \cosh\left(d x + c\right)^{3} - 119 \, b^{3} \cosh\left(d x + c\right) + 45 \, a b^{2}\right)} \sinh\left(d x + c\right)^{13} - 378 \, b^{3} \cosh\left(d x + c\right)^{10} + 26 \, {\left(210 \, b^{3} \cosh\left(d x + c\right)^{4} - 119 \, b^{3} \cosh\left(d x + c\right)^{2} + 90 \, a b^{2} \cosh\left(d x + c\right) + 9 \, b^{3}\right)} \sinh\left(d x + c\right)^{12} - 180 \, {\left(4 \, a b^{2} d x + 3 \, a b^{2}\right)} \cosh\left(d x + c\right)^{11} + 4 \, {\left(3276 \, b^{3} \cosh\left(d x + c\right)^{5} - 3094 \, b^{3} \cosh\left(d x + c\right)^{3} - 180 \, a b^{2} d x + 3510 \, a b^{2} \cosh\left(d x + c\right)^{2} + 702 \, b^{3} \cosh\left(d x + c\right) - 135 \, a b^{2}\right)} \sinh\left(d x + c\right)^{11} + 2 \, {\left(12012 \, b^{3} \cosh\left(d x + c\right)^{6} - 17017 \, b^{3} \cosh\left(d x + c\right)^{4} + 25740 \, a b^{2} \cosh\left(d x + c\right)^{3} + 7722 \, b^{3} \cosh\left(d x + c\right)^{2} - 189 \, b^{3} - 990 \, {\left(4 \, a b^{2} d x + 3 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{10} + 360 \, {\left(6 \, a b^{2} d x + a b^{2}\right)} \cosh\left(d x + c\right)^{9} + 4 \, {\left(8580 \, b^{3} \cosh\left(d x + c\right)^{7} - 17017 \, b^{3} \cosh\left(d x + c\right)^{5} + 32175 \, a b^{2} \cosh\left(d x + c\right)^{4} + 12870 \, b^{3} \cosh\left(d x + c\right)^{3} + 540 \, a b^{2} d x - 945 \, b^{3} \cosh\left(d x + c\right) + 90 \, a b^{2} - 2475 \, {\left(4 \, a b^{2} d x + 3 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{9} + 378 \, b^{3} \cosh\left(d x + c\right)^{6} + 6 \, {\left(6435 \, b^{3} \cosh\left(d x + c\right)^{8} - 17017 \, b^{3} \cosh\left(d x + c\right)^{6} + 38610 \, a b^{2} \cosh\left(d x + c\right)^{5} + 19305 \, b^{3} \cosh\left(d x + c\right)^{4} - 2835 \, b^{3} \cosh\left(d x + c\right)^{2} - 4950 \, {\left(4 \, a b^{2} d x + 3 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} + 540 \, {\left(6 \, a b^{2} d x + a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{8} - 120 \, {\left(18 \, a b^{2} d x + 16 \, a^{3} - 3 \, a b^{2}\right)} \cosh\left(d x + c\right)^{7} + 24 \, {\left(1430 \, b^{3} \cosh\left(d x + c\right)^{9} - 4862 \, b^{3} \cosh\left(d x + c\right)^{7} + 12870 \, a b^{2} \cosh\left(d x + c\right)^{6} + 7722 \, b^{3} \cosh\left(d x + c\right)^{5} - 1890 \, b^{3} \cosh\left(d x + c\right)^{3} - 90 \, a b^{2} d x - 2475 \, {\left(4 \, a b^{2} d x + 3 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} - 80 \, a^{3} + 15 \, a b^{2} + 540 \, {\left(6 \, a b^{2} d x + a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{7} - 234 \, b^{3} \cosh\left(d x + c\right)^{4} + 6 \, {\left(4004 \, b^{3} \cosh\left(d x + c\right)^{10} - 17017 \, b^{3} \cosh\left(d x + c\right)^{8} + 51480 \, a b^{2} \cosh\left(d x + c\right)^{7} + 36036 \, b^{3} \cosh\left(d x + c\right)^{6} - 13230 \, b^{3} \cosh\left(d x + c\right)^{4} - 13860 \, {\left(4 \, a b^{2} d x + 3 \, a b^{2}\right)} \cosh\left(d x + c\right)^{5} + 5040 \, {\left(6 \, a b^{2} d x + a b^{2}\right)} \cosh\left(d x + c\right)^{3} + 63 \, b^{3} - 140 \, {\left(18 \, a b^{2} d x + 16 \, a^{3} - 3 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} + 180 \, a b^{2} \cosh\left(d x + c\right)^{3} + 20 \, {\left(36 \, a b^{2} d x + 32 \, a^{3} - 27 \, a b^{2}\right)} \cosh\left(d x + c\right)^{5} + 4 \, {\left(3276 \, b^{3} \cosh\left(d x + c\right)^{11} - 17017 \, b^{3} \cosh\left(d x + c\right)^{9} + 57915 \, a b^{2} \cosh\left(d x + c\right)^{8} + 46332 \, b^{3} \cosh\left(d x + c\right)^{7} - 23814 \, b^{3} \cosh\left(d x + c\right)^{5} - 20790 \, {\left(4 \, a b^{2} d x + 3 \, a b^{2}\right)} \cosh\left(d x + c\right)^{6} + 180 \, a b^{2} d x + 11340 \, {\left(6 \, a b^{2} d x + a b^{2}\right)} \cosh\left(d x + c\right)^{4} + 567 \, b^{3} \cosh\left(d x + c\right) + 160 \, a^{3} - 135 \, a b^{2} - 630 \, {\left(18 \, a b^{2} d x + 16 \, a^{3} - 3 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{5} + 34 \, b^{3} \cosh\left(d x + c\right)^{2} + 2 \, {\left(2730 \, b^{3} \cosh\left(d x + c\right)^{12} - 17017 \, b^{3} \cosh\left(d x + c\right)^{10} + 64350 \, a b^{2} \cosh\left(d x + c\right)^{9} + 57915 \, b^{3} \cosh\left(d x + c\right)^{8} - 39690 \, b^{3} \cosh\left(d x + c\right)^{6} - 29700 \, {\left(4 \, a b^{2} d x + 3 \, a b^{2}\right)} \cosh\left(d x + c\right)^{7} + 22680 \, {\left(6 \, a b^{2} d x + a b^{2}\right)} \cosh\left(d x + c\right)^{5} + 2835 \, b^{3} \cosh\left(d x + c\right)^{2} - 2100 \, {\left(18 \, a b^{2} d x + 16 \, a^{3} - 3 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} - 117 \, b^{3} + 50 \, {\left(36 \, a b^{2} d x + 32 \, a^{3} - 27 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(420 \, b^{3} \cosh\left(d x + c\right)^{13} - 3094 \, b^{3} \cosh\left(d x + c\right)^{11} + 12870 \, a b^{2} \cosh\left(d x + c\right)^{10} + 12870 \, b^{3} \cosh\left(d x + c\right)^{9} - 11340 \, b^{3} \cosh\left(d x + c\right)^{7} - 7425 \, {\left(4 \, a b^{2} d x + 3 \, a b^{2}\right)} \cosh\left(d x + c\right)^{8} + 7560 \, {\left(6 \, a b^{2} d x + a b^{2}\right)} \cosh\left(d x + c\right)^{6} + 1890 \, b^{3} \cosh\left(d x + c\right)^{3} - 1050 \, {\left(18 \, a b^{2} d x + 16 \, a^{3} - 3 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} - 234 \, b^{3} \cosh\left(d x + c\right) + 45 \, a b^{2} + 50 \, {\left(36 \, a b^{2} d x + 32 \, a^{3} - 27 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} - 3 \, b^{3} + 2 \, {\left(180 \, b^{3} \cosh\left(d x + c\right)^{14} - 1547 \, b^{3} \cosh\left(d x + c\right)^{12} + 7020 \, a b^{2} \cosh\left(d x + c\right)^{11} + 7722 \, b^{3} \cosh\left(d x + c\right)^{10} - 8505 \, b^{3} \cosh\left(d x + c\right)^{8} - 4950 \, {\left(4 \, a b^{2} d x + 3 \, a b^{2}\right)} \cosh\left(d x + c\right)^{9} + 6480 \, {\left(6 \, a b^{2} d x + a b^{2}\right)} \cosh\left(d x + c\right)^{7} + 2835 \, b^{3} \cosh\left(d x + c\right)^{4} - 1260 \, {\left(18 \, a b^{2} d x + 16 \, a^{3} - 3 \, a b^{2}\right)} \cosh\left(d x + c\right)^{5} - 702 \, b^{3} \cosh\left(d x + c\right)^{2} + 270 \, a b^{2} \cosh\left(d x + c\right) + 100 \, {\left(36 \, a b^{2} d x + 32 \, a^{3} - 27 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} + 17 \, b^{3}\right)} \sinh\left(d x + c\right)^{2} - 1440 \, {\left(a^{2} b \cosh\left(d x + c\right)^{11} + 11 \, a^{2} b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{10} + a^{2} b \sinh\left(d x + c\right)^{11} - 3 \, a^{2} b \cosh\left(d x + c\right)^{9} + 3 \, a^{2} b \cosh\left(d x + c\right)^{7} + {\left(55 \, a^{2} b \cosh\left(d x + c\right)^{2} - 3 \, a^{2} b\right)} \sinh\left(d x + c\right)^{9} + 3 \, {\left(55 \, a^{2} b \cosh\left(d x + c\right)^{3} - 9 \, a^{2} b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{8} - a^{2} b \cosh\left(d x + c\right)^{5} + 3 \, {\left(110 \, a^{2} b \cosh\left(d x + c\right)^{4} - 36 \, a^{2} b \cosh\left(d x + c\right)^{2} + a^{2} b\right)} \sinh\left(d x + c\right)^{7} + 21 \, {\left(22 \, a^{2} b \cosh\left(d x + c\right)^{5} - 12 \, a^{2} b \cosh\left(d x + c\right)^{3} + a^{2} b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} + {\left(462 \, a^{2} b \cosh\left(d x + c\right)^{6} - 378 \, a^{2} b \cosh\left(d x + c\right)^{4} + 63 \, a^{2} b \cosh\left(d x + c\right)^{2} - a^{2} b\right)} \sinh\left(d x + c\right)^{5} + {\left(330 \, a^{2} b \cosh\left(d x + c\right)^{7} - 378 \, a^{2} b \cosh\left(d x + c\right)^{5} + 105 \, a^{2} b \cosh\left(d x + c\right)^{3} - 5 \, a^{2} b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + {\left(165 \, a^{2} b \cosh\left(d x + c\right)^{8} - 252 \, a^{2} b \cosh\left(d x + c\right)^{6} + 105 \, a^{2} b \cosh\left(d x + c\right)^{4} - 10 \, a^{2} b \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + {\left(55 \, a^{2} b \cosh\left(d x + c\right)^{9} - 108 \, a^{2} b \cosh\left(d x + c\right)^{7} + 63 \, a^{2} b \cosh\left(d x + c\right)^{5} - 10 \, a^{2} b \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right)^{2} + {\left(11 \, a^{2} b \cosh\left(d x + c\right)^{10} - 27 \, a^{2} b \cosh\left(d x + c\right)^{8} + 21 \, a^{2} b \cosh\left(d x + c\right)^{6} - 5 \, a^{2} b \cosh\left(d x + c\right)^{4}\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) + 1440 \, {\left(a^{2} b \cosh\left(d x + c\right)^{11} + 11 \, a^{2} b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{10} + a^{2} b \sinh\left(d x + c\right)^{11} - 3 \, a^{2} b \cosh\left(d x + c\right)^{9} + 3 \, a^{2} b \cosh\left(d x + c\right)^{7} + {\left(55 \, a^{2} b \cosh\left(d x + c\right)^{2} - 3 \, a^{2} b\right)} \sinh\left(d x + c\right)^{9} + 3 \, {\left(55 \, a^{2} b \cosh\left(d x + c\right)^{3} - 9 \, a^{2} b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{8} - a^{2} b \cosh\left(d x + c\right)^{5} + 3 \, {\left(110 \, a^{2} b \cosh\left(d x + c\right)^{4} - 36 \, a^{2} b \cosh\left(d x + c\right)^{2} + a^{2} b\right)} \sinh\left(d x + c\right)^{7} + 21 \, {\left(22 \, a^{2} b \cosh\left(d x + c\right)^{5} - 12 \, a^{2} b \cosh\left(d x + c\right)^{3} + a^{2} b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} + {\left(462 \, a^{2} b \cosh\left(d x + c\right)^{6} - 378 \, a^{2} b \cosh\left(d x + c\right)^{4} + 63 \, a^{2} b \cosh\left(d x + c\right)^{2} - a^{2} b\right)} \sinh\left(d x + c\right)^{5} + {\left(330 \, a^{2} b \cosh\left(d x + c\right)^{7} - 378 \, a^{2} b \cosh\left(d x + c\right)^{5} + 105 \, a^{2} b \cosh\left(d x + c\right)^{3} - 5 \, a^{2} b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + {\left(165 \, a^{2} b \cosh\left(d x + c\right)^{8} - 252 \, a^{2} b \cosh\left(d x + c\right)^{6} + 105 \, a^{2} b \cosh\left(d x + c\right)^{4} - 10 \, a^{2} b \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + {\left(55 \, a^{2} b \cosh\left(d x + c\right)^{9} - 108 \, a^{2} b \cosh\left(d x + c\right)^{7} + 63 \, a^{2} b \cosh\left(d x + c\right)^{5} - 10 \, a^{2} b \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right)^{2} + {\left(11 \, a^{2} b \cosh\left(d x + c\right)^{10} - 27 \, a^{2} b \cosh\left(d x + c\right)^{8} + 21 \, a^{2} b \cosh\left(d x + c\right)^{6} - 5 \, a^{2} b \cosh\left(d x + c\right)^{4}\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) + 4 \, {\left(12 \, b^{3} \cosh\left(d x + c\right)^{15} - 119 \, b^{3} \cosh\left(d x + c\right)^{13} + 585 \, a b^{2} \cosh\left(d x + c\right)^{12} + 702 \, b^{3} \cosh\left(d x + c\right)^{11} - 945 \, b^{3} \cosh\left(d x + c\right)^{9} - 495 \, {\left(4 \, a b^{2} d x + 3 \, a b^{2}\right)} \cosh\left(d x + c\right)^{10} + 810 \, {\left(6 \, a b^{2} d x + a b^{2}\right)} \cosh\left(d x + c\right)^{8} + 567 \, b^{3} \cosh\left(d x + c\right)^{5} - 210 \, {\left(18 \, a b^{2} d x + 16 \, a^{3} - 3 \, a b^{2}\right)} \cosh\left(d x + c\right)^{6} - 234 \, b^{3} \cosh\left(d x + c\right)^{3} + 135 \, a b^{2} \cosh\left(d x + c\right)^{2} + 25 \, {\left(36 \, a b^{2} d x + 32 \, a^{3} - 27 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} + 17 \, b^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{480 \, {\left(d \cosh\left(d x + c\right)^{11} + 11 \, d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{10} + d \sinh\left(d x + c\right)^{11} - 3 \, d \cosh\left(d x + c\right)^{9} + {\left(55 \, d \cosh\left(d x + c\right)^{2} - 3 \, d\right)} \sinh\left(d x + c\right)^{9} + 3 \, {\left(55 \, d \cosh\left(d x + c\right)^{3} - 9 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{8} + 3 \, d \cosh\left(d x + c\right)^{7} + 3 \, {\left(110 \, d \cosh\left(d x + c\right)^{4} - 36 \, d \cosh\left(d x + c\right)^{2} + d\right)} \sinh\left(d x + c\right)^{7} + 21 \, {\left(22 \, d \cosh\left(d x + c\right)^{5} - 12 \, d \cosh\left(d x + c\right)^{3} + d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} - d \cosh\left(d x + c\right)^{5} + {\left(462 \, d \cosh\left(d x + c\right)^{6} - 378 \, d \cosh\left(d x + c\right)^{4} + 63 \, d \cosh\left(d x + c\right)^{2} - d\right)} \sinh\left(d x + c\right)^{5} + {\left(330 \, d \cosh\left(d x + c\right)^{7} - 378 \, d \cosh\left(d x + c\right)^{5} + 105 \, d \cosh\left(d x + c\right)^{3} - 5 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + {\left(165 \, d \cosh\left(d x + c\right)^{8} - 252 \, d \cosh\left(d x + c\right)^{6} + 105 \, d \cosh\left(d x + c\right)^{4} - 10 \, d \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + {\left(55 \, d \cosh\left(d x + c\right)^{9} - 108 \, d \cosh\left(d x + c\right)^{7} + 63 \, d \cosh\left(d x + c\right)^{5} - 10 \, d \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right)^{2} + {\left(11 \, d \cosh\left(d x + c\right)^{10} - 27 \, d \cosh\left(d x + c\right)^{8} + 21 \, d \cosh\left(d x + c\right)^{6} - 5 \, d \cosh\left(d x + c\right)^{4}\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"1/480*(3*b^3*cosh(d*x + c)^16 + 48*b^3*cosh(d*x + c)*sinh(d*x + c)^15 + 3*b^3*sinh(d*x + c)^16 - 34*b^3*cosh(d*x + c)^14 + 180*a*b^2*cosh(d*x + c)^13 + 234*b^3*cosh(d*x + c)^12 + 2*(180*b^3*cosh(d*x + c)^2 - 17*b^3)*sinh(d*x + c)^14 + 4*(420*b^3*cosh(d*x + c)^3 - 119*b^3*cosh(d*x + c) + 45*a*b^2)*sinh(d*x + c)^13 - 378*b^3*cosh(d*x + c)^10 + 26*(210*b^3*cosh(d*x + c)^4 - 119*b^3*cosh(d*x + c)^2 + 90*a*b^2*cosh(d*x + c) + 9*b^3)*sinh(d*x + c)^12 - 180*(4*a*b^2*d*x + 3*a*b^2)*cosh(d*x + c)^11 + 4*(3276*b^3*cosh(d*x + c)^5 - 3094*b^3*cosh(d*x + c)^3 - 180*a*b^2*d*x + 3510*a*b^2*cosh(d*x + c)^2 + 702*b^3*cosh(d*x + c) - 135*a*b^2)*sinh(d*x + c)^11 + 2*(12012*b^3*cosh(d*x + c)^6 - 17017*b^3*cosh(d*x + c)^4 + 25740*a*b^2*cosh(d*x + c)^3 + 7722*b^3*cosh(d*x + c)^2 - 189*b^3 - 990*(4*a*b^2*d*x + 3*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^10 + 360*(6*a*b^2*d*x + a*b^2)*cosh(d*x + c)^9 + 4*(8580*b^3*cosh(d*x + c)^7 - 17017*b^3*cosh(d*x + c)^5 + 32175*a*b^2*cosh(d*x + c)^4 + 12870*b^3*cosh(d*x + c)^3 + 540*a*b^2*d*x - 945*b^3*cosh(d*x + c) + 90*a*b^2 - 2475*(4*a*b^2*d*x + 3*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^9 + 378*b^3*cosh(d*x + c)^6 + 6*(6435*b^3*cosh(d*x + c)^8 - 17017*b^3*cosh(d*x + c)^6 + 38610*a*b^2*cosh(d*x + c)^5 + 19305*b^3*cosh(d*x + c)^4 - 2835*b^3*cosh(d*x + c)^2 - 4950*(4*a*b^2*d*x + 3*a*b^2)*cosh(d*x + c)^3 + 540*(6*a*b^2*d*x + a*b^2)*cosh(d*x + c))*sinh(d*x + c)^8 - 120*(18*a*b^2*d*x + 16*a^3 - 3*a*b^2)*cosh(d*x + c)^7 + 24*(1430*b^3*cosh(d*x + c)^9 - 4862*b^3*cosh(d*x + c)^7 + 12870*a*b^2*cosh(d*x + c)^6 + 7722*b^3*cosh(d*x + c)^5 - 1890*b^3*cosh(d*x + c)^3 - 90*a*b^2*d*x - 2475*(4*a*b^2*d*x + 3*a*b^2)*cosh(d*x + c)^4 - 80*a^3 + 15*a*b^2 + 540*(6*a*b^2*d*x + a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^7 - 234*b^3*cosh(d*x + c)^4 + 6*(4004*b^3*cosh(d*x + c)^10 - 17017*b^3*cosh(d*x + c)^8 + 51480*a*b^2*cosh(d*x + c)^7 + 36036*b^3*cosh(d*x + c)^6 - 13230*b^3*cosh(d*x + c)^4 - 13860*(4*a*b^2*d*x + 3*a*b^2)*cosh(d*x + c)^5 + 5040*(6*a*b^2*d*x + a*b^2)*cosh(d*x + c)^3 + 63*b^3 - 140*(18*a*b^2*d*x + 16*a^3 - 3*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^6 + 180*a*b^2*cosh(d*x + c)^3 + 20*(36*a*b^2*d*x + 32*a^3 - 27*a*b^2)*cosh(d*x + c)^5 + 4*(3276*b^3*cosh(d*x + c)^11 - 17017*b^3*cosh(d*x + c)^9 + 57915*a*b^2*cosh(d*x + c)^8 + 46332*b^3*cosh(d*x + c)^7 - 23814*b^3*cosh(d*x + c)^5 - 20790*(4*a*b^2*d*x + 3*a*b^2)*cosh(d*x + c)^6 + 180*a*b^2*d*x + 11340*(6*a*b^2*d*x + a*b^2)*cosh(d*x + c)^4 + 567*b^3*cosh(d*x + c) + 160*a^3 - 135*a*b^2 - 630*(18*a*b^2*d*x + 16*a^3 - 3*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 34*b^3*cosh(d*x + c)^2 + 2*(2730*b^3*cosh(d*x + c)^12 - 17017*b^3*cosh(d*x + c)^10 + 64350*a*b^2*cosh(d*x + c)^9 + 57915*b^3*cosh(d*x + c)^8 - 39690*b^3*cosh(d*x + c)^6 - 29700*(4*a*b^2*d*x + 3*a*b^2)*cosh(d*x + c)^7 + 22680*(6*a*b^2*d*x + a*b^2)*cosh(d*x + c)^5 + 2835*b^3*cosh(d*x + c)^2 - 2100*(18*a*b^2*d*x + 16*a^3 - 3*a*b^2)*cosh(d*x + c)^3 - 117*b^3 + 50*(36*a*b^2*d*x + 32*a^3 - 27*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^4 + 4*(420*b^3*cosh(d*x + c)^13 - 3094*b^3*cosh(d*x + c)^11 + 12870*a*b^2*cosh(d*x + c)^10 + 12870*b^3*cosh(d*x + c)^9 - 11340*b^3*cosh(d*x + c)^7 - 7425*(4*a*b^2*d*x + 3*a*b^2)*cosh(d*x + c)^8 + 7560*(6*a*b^2*d*x + a*b^2)*cosh(d*x + c)^6 + 1890*b^3*cosh(d*x + c)^3 - 1050*(18*a*b^2*d*x + 16*a^3 - 3*a*b^2)*cosh(d*x + c)^4 - 234*b^3*cosh(d*x + c) + 45*a*b^2 + 50*(36*a*b^2*d*x + 32*a^3 - 27*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^3 - 3*b^3 + 2*(180*b^3*cosh(d*x + c)^14 - 1547*b^3*cosh(d*x + c)^12 + 7020*a*b^2*cosh(d*x + c)^11 + 7722*b^3*cosh(d*x + c)^10 - 8505*b^3*cosh(d*x + c)^8 - 4950*(4*a*b^2*d*x + 3*a*b^2)*cosh(d*x + c)^9 + 6480*(6*a*b^2*d*x + a*b^2)*cosh(d*x + c)^7 + 2835*b^3*cosh(d*x + c)^4 - 1260*(18*a*b^2*d*x + 16*a^3 - 3*a*b^2)*cosh(d*x + c)^5 - 702*b^3*cosh(d*x + c)^2 + 270*a*b^2*cosh(d*x + c) + 100*(36*a*b^2*d*x + 32*a^3 - 27*a*b^2)*cosh(d*x + c)^3 + 17*b^3)*sinh(d*x + c)^2 - 1440*(a^2*b*cosh(d*x + c)^11 + 11*a^2*b*cosh(d*x + c)*sinh(d*x + c)^10 + a^2*b*sinh(d*x + c)^11 - 3*a^2*b*cosh(d*x + c)^9 + 3*a^2*b*cosh(d*x + c)^7 + (55*a^2*b*cosh(d*x + c)^2 - 3*a^2*b)*sinh(d*x + c)^9 + 3*(55*a^2*b*cosh(d*x + c)^3 - 9*a^2*b*cosh(d*x + c))*sinh(d*x + c)^8 - a^2*b*cosh(d*x + c)^5 + 3*(110*a^2*b*cosh(d*x + c)^4 - 36*a^2*b*cosh(d*x + c)^2 + a^2*b)*sinh(d*x + c)^7 + 21*(22*a^2*b*cosh(d*x + c)^5 - 12*a^2*b*cosh(d*x + c)^3 + a^2*b*cosh(d*x + c))*sinh(d*x + c)^6 + (462*a^2*b*cosh(d*x + c)^6 - 378*a^2*b*cosh(d*x + c)^4 + 63*a^2*b*cosh(d*x + c)^2 - a^2*b)*sinh(d*x + c)^5 + (330*a^2*b*cosh(d*x + c)^7 - 378*a^2*b*cosh(d*x + c)^5 + 105*a^2*b*cosh(d*x + c)^3 - 5*a^2*b*cosh(d*x + c))*sinh(d*x + c)^4 + (165*a^2*b*cosh(d*x + c)^8 - 252*a^2*b*cosh(d*x + c)^6 + 105*a^2*b*cosh(d*x + c)^4 - 10*a^2*b*cosh(d*x + c)^2)*sinh(d*x + c)^3 + (55*a^2*b*cosh(d*x + c)^9 - 108*a^2*b*cosh(d*x + c)^7 + 63*a^2*b*cosh(d*x + c)^5 - 10*a^2*b*cosh(d*x + c)^3)*sinh(d*x + c)^2 + (11*a^2*b*cosh(d*x + c)^10 - 27*a^2*b*cosh(d*x + c)^8 + 21*a^2*b*cosh(d*x + c)^6 - 5*a^2*b*cosh(d*x + c)^4)*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) + 1) + 1440*(a^2*b*cosh(d*x + c)^11 + 11*a^2*b*cosh(d*x + c)*sinh(d*x + c)^10 + a^2*b*sinh(d*x + c)^11 - 3*a^2*b*cosh(d*x + c)^9 + 3*a^2*b*cosh(d*x + c)^7 + (55*a^2*b*cosh(d*x + c)^2 - 3*a^2*b)*sinh(d*x + c)^9 + 3*(55*a^2*b*cosh(d*x + c)^3 - 9*a^2*b*cosh(d*x + c))*sinh(d*x + c)^8 - a^2*b*cosh(d*x + c)^5 + 3*(110*a^2*b*cosh(d*x + c)^4 - 36*a^2*b*cosh(d*x + c)^2 + a^2*b)*sinh(d*x + c)^7 + 21*(22*a^2*b*cosh(d*x + c)^5 - 12*a^2*b*cosh(d*x + c)^3 + a^2*b*cosh(d*x + c))*sinh(d*x + c)^6 + (462*a^2*b*cosh(d*x + c)^6 - 378*a^2*b*cosh(d*x + c)^4 + 63*a^2*b*cosh(d*x + c)^2 - a^2*b)*sinh(d*x + c)^5 + (330*a^2*b*cosh(d*x + c)^7 - 378*a^2*b*cosh(d*x + c)^5 + 105*a^2*b*cosh(d*x + c)^3 - 5*a^2*b*cosh(d*x + c))*sinh(d*x + c)^4 + (165*a^2*b*cosh(d*x + c)^8 - 252*a^2*b*cosh(d*x + c)^6 + 105*a^2*b*cosh(d*x + c)^4 - 10*a^2*b*cosh(d*x + c)^2)*sinh(d*x + c)^3 + (55*a^2*b*cosh(d*x + c)^9 - 108*a^2*b*cosh(d*x + c)^7 + 63*a^2*b*cosh(d*x + c)^5 - 10*a^2*b*cosh(d*x + c)^3)*sinh(d*x + c)^2 + (11*a^2*b*cosh(d*x + c)^10 - 27*a^2*b*cosh(d*x + c)^8 + 21*a^2*b*cosh(d*x + c)^6 - 5*a^2*b*cosh(d*x + c)^4)*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) - 1) + 4*(12*b^3*cosh(d*x + c)^15 - 119*b^3*cosh(d*x + c)^13 + 585*a*b^2*cosh(d*x + c)^12 + 702*b^3*cosh(d*x + c)^11 - 945*b^3*cosh(d*x + c)^9 - 495*(4*a*b^2*d*x + 3*a*b^2)*cosh(d*x + c)^10 + 810*(6*a*b^2*d*x + a*b^2)*cosh(d*x + c)^8 + 567*b^3*cosh(d*x + c)^5 - 210*(18*a*b^2*d*x + 16*a^3 - 3*a*b^2)*cosh(d*x + c)^6 - 234*b^3*cosh(d*x + c)^3 + 135*a*b^2*cosh(d*x + c)^2 + 25*(36*a*b^2*d*x + 32*a^3 - 27*a*b^2)*cosh(d*x + c)^4 + 17*b^3*cosh(d*x + c))*sinh(d*x + c))/(d*cosh(d*x + c)^11 + 11*d*cosh(d*x + c)*sinh(d*x + c)^10 + d*sinh(d*x + c)^11 - 3*d*cosh(d*x + c)^9 + (55*d*cosh(d*x + c)^2 - 3*d)*sinh(d*x + c)^9 + 3*(55*d*cosh(d*x + c)^3 - 9*d*cosh(d*x + c))*sinh(d*x + c)^8 + 3*d*cosh(d*x + c)^7 + 3*(110*d*cosh(d*x + c)^4 - 36*d*cosh(d*x + c)^2 + d)*sinh(d*x + c)^7 + 21*(22*d*cosh(d*x + c)^5 - 12*d*cosh(d*x + c)^3 + d*cosh(d*x + c))*sinh(d*x + c)^6 - d*cosh(d*x + c)^5 + (462*d*cosh(d*x + c)^6 - 378*d*cosh(d*x + c)^4 + 63*d*cosh(d*x + c)^2 - d)*sinh(d*x + c)^5 + (330*d*cosh(d*x + c)^7 - 378*d*cosh(d*x + c)^5 + 105*d*cosh(d*x + c)^3 - 5*d*cosh(d*x + c))*sinh(d*x + c)^4 + (165*d*cosh(d*x + c)^8 - 252*d*cosh(d*x + c)^6 + 105*d*cosh(d*x + c)^4 - 10*d*cosh(d*x + c)^2)*sinh(d*x + c)^3 + (55*d*cosh(d*x + c)^9 - 108*d*cosh(d*x + c)^7 + 63*d*cosh(d*x + c)^5 - 10*d*cosh(d*x + c)^3)*sinh(d*x + c)^2 + (11*d*cosh(d*x + c)^10 - 27*d*cosh(d*x + c)^8 + 21*d*cosh(d*x + c)^6 - 5*d*cosh(d*x + c)^4)*sinh(d*x + c))","B",0
168,1,4541,0,0.619084," ","integrate(csch(d*x+c)^5*(a+b*sinh(d*x+c)^3)^3,x, algorithm=""fricas"")","\frac{b^{3} \cosh\left(d x + c\right)^{16} + 16 \, b^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{15} + b^{3} \sinh\left(d x + c\right)^{16} - 12 \, b^{3} \cosh\left(d x + c\right)^{14} + 96 \, a b^{2} \cosh\left(d x + c\right)^{13} + 12 \, {\left(10 \, b^{3} \cosh\left(d x + c\right)^{2} - b^{3}\right)} \sinh\left(d x + c\right)^{14} + 8 \, {\left(70 \, b^{3} \cosh\left(d x + c\right)^{3} - 21 \, b^{3} \cosh\left(d x + c\right) + 12 \, a b^{2}\right)} \sinh\left(d x + c\right)^{13} + 2 \, {\left(12 \, b^{3} d x + 19 \, b^{3}\right)} \cosh\left(d x + c\right)^{12} + 2 \, {\left(910 \, b^{3} \cosh\left(d x + c\right)^{4} + 12 \, b^{3} d x - 546 \, b^{3} \cosh\left(d x + c\right)^{2} + 624 \, a b^{2} \cosh\left(d x + c\right) + 19 \, b^{3}\right)} \sinh\left(d x + c\right)^{12} + 48 \, {\left(a^{3} - 6 \, a b^{2}\right)} \cosh\left(d x + c\right)^{11} + 24 \, {\left(182 \, b^{3} \cosh\left(d x + c\right)^{5} - 182 \, b^{3} \cosh\left(d x + c\right)^{3} + 312 \, a b^{2} \cosh\left(d x + c\right)^{2} + 2 \, a^{3} - 12 \, a b^{2} + {\left(12 \, b^{3} d x + 19 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{11} - 4 \, {\left(24 \, b^{3} d x + 96 \, a^{2} b + 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} + 4 \, {\left(2002 \, b^{3} \cosh\left(d x + c\right)^{6} - 3003 \, b^{3} \cosh\left(d x + c\right)^{4} + 6864 \, a b^{2} \cosh\left(d x + c\right)^{3} - 24 \, b^{3} d x - 96 \, a^{2} b - 11 \, b^{3} + 33 \, {\left(12 \, b^{3} d x + 19 \, b^{3}\right)} \cosh\left(d x + c\right)^{2} + 132 \, {\left(a^{3} - 6 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{10} - 16 \, {\left(11 \, a^{3} - 12 \, a b^{2}\right)} \cosh\left(d x + c\right)^{9} + 8 \, {\left(1430 \, b^{3} \cosh\left(d x + c\right)^{7} - 3003 \, b^{3} \cosh\left(d x + c\right)^{5} + 8580 \, a b^{2} \cosh\left(d x + c\right)^{4} + 55 \, {\left(12 \, b^{3} d x + 19 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 22 \, a^{3} + 24 \, a b^{2} + 330 \, {\left(a^{3} - 6 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2} - 5 \, {\left(24 \, b^{3} d x + 96 \, a^{2} b + 11 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} + 144 \, {\left(b^{3} d x + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{8} + 18 \, {\left(715 \, b^{3} \cosh\left(d x + c\right)^{8} - 2002 \, b^{3} \cosh\left(d x + c\right)^{6} + 6864 \, a b^{2} \cosh\left(d x + c\right)^{5} + 8 \, b^{3} d x + 55 \, {\left(12 \, b^{3} d x + 19 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 440 \, {\left(a^{3} - 6 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} + 64 \, a^{2} b - 10 \, {\left(24 \, b^{3} d x + 96 \, a^{2} b + 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{2} - 8 \, {\left(11 \, a^{3} - 12 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{8} - 16 \, {\left(11 \, a^{3} - 12 \, a b^{2}\right)} \cosh\left(d x + c\right)^{7} + 16 \, {\left(715 \, b^{3} \cosh\left(d x + c\right)^{9} - 2574 \, b^{3} \cosh\left(d x + c\right)^{7} + 10296 \, a b^{2} \cosh\left(d x + c\right)^{6} + 99 \, {\left(12 \, b^{3} d x + 19 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 990 \, {\left(a^{3} - 6 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} - 30 \, {\left(24 \, b^{3} d x + 96 \, a^{2} b + 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 11 \, a^{3} + 12 \, a b^{2} - 36 \, {\left(11 \, a^{3} - 12 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2} + 72 \, {\left(b^{3} d x + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} - 4 \, {\left(24 \, b^{3} d x + 288 \, a^{2} b - 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(2002 \, b^{3} \cosh\left(d x + c\right)^{10} - 9009 \, b^{3} \cosh\left(d x + c\right)^{8} + 41184 \, a b^{2} \cosh\left(d x + c\right)^{7} + 462 \, {\left(12 \, b^{3} d x + 19 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 5544 \, {\left(a^{3} - 6 \, a b^{2}\right)} \cosh\left(d x + c\right)^{5} - 24 \, b^{3} d x - 210 \, {\left(24 \, b^{3} d x + 96 \, a^{2} b + 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 336 \, {\left(11 \, a^{3} - 12 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} - 288 \, a^{2} b + 11 \, b^{3} + 1008 \, {\left(b^{3} d x + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{2} - 28 \, {\left(11 \, a^{3} - 12 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} + 96 \, a b^{2} \cosh\left(d x + c\right)^{3} + 48 \, {\left(a^{3} - 6 \, a b^{2}\right)} \cosh\left(d x + c\right)^{5} + 24 \, {\left(182 \, b^{3} \cosh\left(d x + c\right)^{11} - 1001 \, b^{3} \cosh\left(d x + c\right)^{9} + 5148 \, a b^{2} \cosh\left(d x + c\right)^{8} + 66 \, {\left(12 \, b^{3} d x + 19 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 924 \, {\left(a^{3} - 6 \, a b^{2}\right)} \cosh\left(d x + c\right)^{6} - 42 \, {\left(24 \, b^{3} d x + 96 \, a^{2} b + 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 84 \, {\left(11 \, a^{3} - 12 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} + 336 \, {\left(b^{3} d x + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{3} + 2 \, a^{3} - 12 \, a b^{2} - 14 \, {\left(11 \, a^{3} - 12 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2} - {\left(24 \, b^{3} d x + 288 \, a^{2} b - 11 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 12 \, b^{3} \cosh\left(d x + c\right)^{2} + 2 \, {\left(12 \, b^{3} d x + 192 \, a^{2} b - 19 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(910 \, b^{3} \cosh\left(d x + c\right)^{12} - 6006 \, b^{3} \cosh\left(d x + c\right)^{10} + 34320 \, a b^{2} \cosh\left(d x + c\right)^{9} + 495 \, {\left(12 \, b^{3} d x + 19 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 7920 \, {\left(a^{3} - 6 \, a b^{2}\right)} \cosh\left(d x + c\right)^{7} - 420 \, {\left(24 \, b^{3} d x + 96 \, a^{2} b + 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} - 1008 \, {\left(11 \, a^{3} - 12 \, a b^{2}\right)} \cosh\left(d x + c\right)^{5} + 12 \, b^{3} d x + 5040 \, {\left(b^{3} d x + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{4} - 280 \, {\left(11 \, a^{3} - 12 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} + 192 \, a^{2} b - 19 \, b^{3} - 30 \, {\left(24 \, b^{3} d x + 288 \, a^{2} b - 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{2} + 120 \, {\left(a^{3} - 6 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(70 \, b^{3} \cosh\left(d x + c\right)^{13} - 546 \, b^{3} \cosh\left(d x + c\right)^{11} + 3432 \, a b^{2} \cosh\left(d x + c\right)^{10} + 55 \, {\left(12 \, b^{3} d x + 19 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + 990 \, {\left(a^{3} - 6 \, a b^{2}\right)} \cosh\left(d x + c\right)^{8} - 60 \, {\left(24 \, b^{3} d x + 96 \, a^{2} b + 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} - 168 \, {\left(11 \, a^{3} - 12 \, a b^{2}\right)} \cosh\left(d x + c\right)^{6} + 1008 \, {\left(b^{3} d x + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{5} - 70 \, {\left(11 \, a^{3} - 12 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} - 10 \, {\left(24 \, b^{3} d x + 288 \, a^{2} b - 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 12 \, a b^{2} + 60 \, {\left(a^{3} - 6 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(12 \, b^{3} d x + 192 \, a^{2} b - 19 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - b^{3} + 12 \, {\left(10 \, b^{3} \cosh\left(d x + c\right)^{14} - 91 \, b^{3} \cosh\left(d x + c\right)^{12} + 624 \, a b^{2} \cosh\left(d x + c\right)^{11} + 11 \, {\left(12 \, b^{3} d x + 19 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} + 220 \, {\left(a^{3} - 6 \, a b^{2}\right)} \cosh\left(d x + c\right)^{9} - 15 \, {\left(24 \, b^{3} d x + 96 \, a^{2} b + 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} - 48 \, {\left(11 \, a^{3} - 12 \, a b^{2}\right)} \cosh\left(d x + c\right)^{7} + 336 \, {\left(b^{3} d x + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{6} - 28 \, {\left(11 \, a^{3} - 12 \, a b^{2}\right)} \cosh\left(d x + c\right)^{5} - 5 \, {\left(24 \, b^{3} d x + 288 \, a^{2} b - 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 24 \, a b^{2} \cosh\left(d x + c\right) + 40 \, {\left(a^{3} - 6 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} + b^{3} + {\left(12 \, b^{3} d x + 192 \, a^{2} b - 19 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} - 24 \, {\left(a^{3} \cosh\left(d x + c\right)^{12} + 12 \, a^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{11} + a^{3} \sinh\left(d x + c\right)^{12} - 4 \, a^{3} \cosh\left(d x + c\right)^{10} + 6 \, a^{3} \cosh\left(d x + c\right)^{8} + 2 \, {\left(33 \, a^{3} \cosh\left(d x + c\right)^{2} - 2 \, a^{3}\right)} \sinh\left(d x + c\right)^{10} + 20 \, {\left(11 \, a^{3} \cosh\left(d x + c\right)^{3} - 2 \, a^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} - 4 \, a^{3} \cosh\left(d x + c\right)^{6} + 3 \, {\left(165 \, a^{3} \cosh\left(d x + c\right)^{4} - 60 \, a^{3} \cosh\left(d x + c\right)^{2} + 2 \, a^{3}\right)} \sinh\left(d x + c\right)^{8} + 24 \, {\left(33 \, a^{3} \cosh\left(d x + c\right)^{5} - 20 \, a^{3} \cosh\left(d x + c\right)^{3} + 2 \, a^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + a^{3} \cosh\left(d x + c\right)^{4} + 4 \, {\left(231 \, a^{3} \cosh\left(d x + c\right)^{6} - 210 \, a^{3} \cosh\left(d x + c\right)^{4} + 42 \, a^{3} \cosh\left(d x + c\right)^{2} - a^{3}\right)} \sinh\left(d x + c\right)^{6} + 24 \, {\left(33 \, a^{3} \cosh\left(d x + c\right)^{7} - 42 \, a^{3} \cosh\left(d x + c\right)^{5} + 14 \, a^{3} \cosh\left(d x + c\right)^{3} - a^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + {\left(495 \, a^{3} \cosh\left(d x + c\right)^{8} - 840 \, a^{3} \cosh\left(d x + c\right)^{6} + 420 \, a^{3} \cosh\left(d x + c\right)^{4} - 60 \, a^{3} \cosh\left(d x + c\right)^{2} + a^{3}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(55 \, a^{3} \cosh\left(d x + c\right)^{9} - 120 \, a^{3} \cosh\left(d x + c\right)^{7} + 84 \, a^{3} \cosh\left(d x + c\right)^{5} - 20 \, a^{3} \cosh\left(d x + c\right)^{3} + a^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 6 \, {\left(11 \, a^{3} \cosh\left(d x + c\right)^{10} - 30 \, a^{3} \cosh\left(d x + c\right)^{8} + 28 \, a^{3} \cosh\left(d x + c\right)^{6} - 10 \, a^{3} \cosh\left(d x + c\right)^{4} + a^{3} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(3 \, a^{3} \cosh\left(d x + c\right)^{11} - 10 \, a^{3} \cosh\left(d x + c\right)^{9} + 12 \, a^{3} \cosh\left(d x + c\right)^{7} - 6 \, a^{3} \cosh\left(d x + c\right)^{5} + a^{3} \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) + 24 \, {\left(a^{3} \cosh\left(d x + c\right)^{12} + 12 \, a^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{11} + a^{3} \sinh\left(d x + c\right)^{12} - 4 \, a^{3} \cosh\left(d x + c\right)^{10} + 6 \, a^{3} \cosh\left(d x + c\right)^{8} + 2 \, {\left(33 \, a^{3} \cosh\left(d x + c\right)^{2} - 2 \, a^{3}\right)} \sinh\left(d x + c\right)^{10} + 20 \, {\left(11 \, a^{3} \cosh\left(d x + c\right)^{3} - 2 \, a^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} - 4 \, a^{3} \cosh\left(d x + c\right)^{6} + 3 \, {\left(165 \, a^{3} \cosh\left(d x + c\right)^{4} - 60 \, a^{3} \cosh\left(d x + c\right)^{2} + 2 \, a^{3}\right)} \sinh\left(d x + c\right)^{8} + 24 \, {\left(33 \, a^{3} \cosh\left(d x + c\right)^{5} - 20 \, a^{3} \cosh\left(d x + c\right)^{3} + 2 \, a^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + a^{3} \cosh\left(d x + c\right)^{4} + 4 \, {\left(231 \, a^{3} \cosh\left(d x + c\right)^{6} - 210 \, a^{3} \cosh\left(d x + c\right)^{4} + 42 \, a^{3} \cosh\left(d x + c\right)^{2} - a^{3}\right)} \sinh\left(d x + c\right)^{6} + 24 \, {\left(33 \, a^{3} \cosh\left(d x + c\right)^{7} - 42 \, a^{3} \cosh\left(d x + c\right)^{5} + 14 \, a^{3} \cosh\left(d x + c\right)^{3} - a^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + {\left(495 \, a^{3} \cosh\left(d x + c\right)^{8} - 840 \, a^{3} \cosh\left(d x + c\right)^{6} + 420 \, a^{3} \cosh\left(d x + c\right)^{4} - 60 \, a^{3} \cosh\left(d x + c\right)^{2} + a^{3}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(55 \, a^{3} \cosh\left(d x + c\right)^{9} - 120 \, a^{3} \cosh\left(d x + c\right)^{7} + 84 \, a^{3} \cosh\left(d x + c\right)^{5} - 20 \, a^{3} \cosh\left(d x + c\right)^{3} + a^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 6 \, {\left(11 \, a^{3} \cosh\left(d x + c\right)^{10} - 30 \, a^{3} \cosh\left(d x + c\right)^{8} + 28 \, a^{3} \cosh\left(d x + c\right)^{6} - 10 \, a^{3} \cosh\left(d x + c\right)^{4} + a^{3} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(3 \, a^{3} \cosh\left(d x + c\right)^{11} - 10 \, a^{3} \cosh\left(d x + c\right)^{9} + 12 \, a^{3} \cosh\left(d x + c\right)^{7} - 6 \, a^{3} \cosh\left(d x + c\right)^{5} + a^{3} \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) + 8 \, {\left(2 \, b^{3} \cosh\left(d x + c\right)^{15} - 21 \, b^{3} \cosh\left(d x + c\right)^{13} + 156 \, a b^{2} \cosh\left(d x + c\right)^{12} + 3 \, {\left(12 \, b^{3} d x + 19 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} + 66 \, {\left(a^{3} - 6 \, a b^{2}\right)} \cosh\left(d x + c\right)^{10} - 5 \, {\left(24 \, b^{3} d x + 96 \, a^{2} b + 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} - 18 \, {\left(11 \, a^{3} - 12 \, a b^{2}\right)} \cosh\left(d x + c\right)^{8} + 144 \, {\left(b^{3} d x + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{7} - 14 \, {\left(11 \, a^{3} - 12 \, a b^{2}\right)} \cosh\left(d x + c\right)^{6} - 3 \, {\left(24 \, b^{3} d x + 288 \, a^{2} b - 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 36 \, a b^{2} \cosh\left(d x + c\right)^{2} + 30 \, {\left(a^{3} - 6 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} + 3 \, b^{3} \cosh\left(d x + c\right) + {\left(12 \, b^{3} d x + 192 \, a^{2} b - 19 \, b^{3}\right)} \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right)}{64 \, {\left(d \cosh\left(d x + c\right)^{12} + 12 \, d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{11} + d \sinh\left(d x + c\right)^{12} - 4 \, d \cosh\left(d x + c\right)^{10} + 2 \, {\left(33 \, d \cosh\left(d x + c\right)^{2} - 2 \, d\right)} \sinh\left(d x + c\right)^{10} + 20 \, {\left(11 \, d \cosh\left(d x + c\right)^{3} - 2 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} + 6 \, d \cosh\left(d x + c\right)^{8} + 3 \, {\left(165 \, d \cosh\left(d x + c\right)^{4} - 60 \, d \cosh\left(d x + c\right)^{2} + 2 \, d\right)} \sinh\left(d x + c\right)^{8} + 24 \, {\left(33 \, d \cosh\left(d x + c\right)^{5} - 20 \, d \cosh\left(d x + c\right)^{3} + 2 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} - 4 \, d \cosh\left(d x + c\right)^{6} + 4 \, {\left(231 \, d \cosh\left(d x + c\right)^{6} - 210 \, d \cosh\left(d x + c\right)^{4} + 42 \, d \cosh\left(d x + c\right)^{2} - d\right)} \sinh\left(d x + c\right)^{6} + 24 \, {\left(33 \, d \cosh\left(d x + c\right)^{7} - 42 \, d \cosh\left(d x + c\right)^{5} + 14 \, d \cosh\left(d x + c\right)^{3} - d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + d \cosh\left(d x + c\right)^{4} + {\left(495 \, d \cosh\left(d x + c\right)^{8} - 840 \, d \cosh\left(d x + c\right)^{6} + 420 \, d \cosh\left(d x + c\right)^{4} - 60 \, d \cosh\left(d x + c\right)^{2} + d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(55 \, d \cosh\left(d x + c\right)^{9} - 120 \, d \cosh\left(d x + c\right)^{7} + 84 \, d \cosh\left(d x + c\right)^{5} - 20 \, d \cosh\left(d x + c\right)^{3} + d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 6 \, {\left(11 \, d \cosh\left(d x + c\right)^{10} - 30 \, d \cosh\left(d x + c\right)^{8} + 28 \, d \cosh\left(d x + c\right)^{6} - 10 \, d \cosh\left(d x + c\right)^{4} + d \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(3 \, d \cosh\left(d x + c\right)^{11} - 10 \, d \cosh\left(d x + c\right)^{9} + 12 \, d \cosh\left(d x + c\right)^{7} - 6 \, d \cosh\left(d x + c\right)^{5} + d \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"1/64*(b^3*cosh(d*x + c)^16 + 16*b^3*cosh(d*x + c)*sinh(d*x + c)^15 + b^3*sinh(d*x + c)^16 - 12*b^3*cosh(d*x + c)^14 + 96*a*b^2*cosh(d*x + c)^13 + 12*(10*b^3*cosh(d*x + c)^2 - b^3)*sinh(d*x + c)^14 + 8*(70*b^3*cosh(d*x + c)^3 - 21*b^3*cosh(d*x + c) + 12*a*b^2)*sinh(d*x + c)^13 + 2*(12*b^3*d*x + 19*b^3)*cosh(d*x + c)^12 + 2*(910*b^3*cosh(d*x + c)^4 + 12*b^3*d*x - 546*b^3*cosh(d*x + c)^2 + 624*a*b^2*cosh(d*x + c) + 19*b^3)*sinh(d*x + c)^12 + 48*(a^3 - 6*a*b^2)*cosh(d*x + c)^11 + 24*(182*b^3*cosh(d*x + c)^5 - 182*b^3*cosh(d*x + c)^3 + 312*a*b^2*cosh(d*x + c)^2 + 2*a^3 - 12*a*b^2 + (12*b^3*d*x + 19*b^3)*cosh(d*x + c))*sinh(d*x + c)^11 - 4*(24*b^3*d*x + 96*a^2*b + 11*b^3)*cosh(d*x + c)^10 + 4*(2002*b^3*cosh(d*x + c)^6 - 3003*b^3*cosh(d*x + c)^4 + 6864*a*b^2*cosh(d*x + c)^3 - 24*b^3*d*x - 96*a^2*b - 11*b^3 + 33*(12*b^3*d*x + 19*b^3)*cosh(d*x + c)^2 + 132*(a^3 - 6*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^10 - 16*(11*a^3 - 12*a*b^2)*cosh(d*x + c)^9 + 8*(1430*b^3*cosh(d*x + c)^7 - 3003*b^3*cosh(d*x + c)^5 + 8580*a*b^2*cosh(d*x + c)^4 + 55*(12*b^3*d*x + 19*b^3)*cosh(d*x + c)^3 - 22*a^3 + 24*a*b^2 + 330*(a^3 - 6*a*b^2)*cosh(d*x + c)^2 - 5*(24*b^3*d*x + 96*a^2*b + 11*b^3)*cosh(d*x + c))*sinh(d*x + c)^9 + 144*(b^3*d*x + 8*a^2*b)*cosh(d*x + c)^8 + 18*(715*b^3*cosh(d*x + c)^8 - 2002*b^3*cosh(d*x + c)^6 + 6864*a*b^2*cosh(d*x + c)^5 + 8*b^3*d*x + 55*(12*b^3*d*x + 19*b^3)*cosh(d*x + c)^4 + 440*(a^3 - 6*a*b^2)*cosh(d*x + c)^3 + 64*a^2*b - 10*(24*b^3*d*x + 96*a^2*b + 11*b^3)*cosh(d*x + c)^2 - 8*(11*a^3 - 12*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^8 - 16*(11*a^3 - 12*a*b^2)*cosh(d*x + c)^7 + 16*(715*b^3*cosh(d*x + c)^9 - 2574*b^3*cosh(d*x + c)^7 + 10296*a*b^2*cosh(d*x + c)^6 + 99*(12*b^3*d*x + 19*b^3)*cosh(d*x + c)^5 + 990*(a^3 - 6*a*b^2)*cosh(d*x + c)^4 - 30*(24*b^3*d*x + 96*a^2*b + 11*b^3)*cosh(d*x + c)^3 - 11*a^3 + 12*a*b^2 - 36*(11*a^3 - 12*a*b^2)*cosh(d*x + c)^2 + 72*(b^3*d*x + 8*a^2*b)*cosh(d*x + c))*sinh(d*x + c)^7 - 4*(24*b^3*d*x + 288*a^2*b - 11*b^3)*cosh(d*x + c)^6 + 4*(2002*b^3*cosh(d*x + c)^10 - 9009*b^3*cosh(d*x + c)^8 + 41184*a*b^2*cosh(d*x + c)^7 + 462*(12*b^3*d*x + 19*b^3)*cosh(d*x + c)^6 + 5544*(a^3 - 6*a*b^2)*cosh(d*x + c)^5 - 24*b^3*d*x - 210*(24*b^3*d*x + 96*a^2*b + 11*b^3)*cosh(d*x + c)^4 - 336*(11*a^3 - 12*a*b^2)*cosh(d*x + c)^3 - 288*a^2*b + 11*b^3 + 1008*(b^3*d*x + 8*a^2*b)*cosh(d*x + c)^2 - 28*(11*a^3 - 12*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^6 + 96*a*b^2*cosh(d*x + c)^3 + 48*(a^3 - 6*a*b^2)*cosh(d*x + c)^5 + 24*(182*b^3*cosh(d*x + c)^11 - 1001*b^3*cosh(d*x + c)^9 + 5148*a*b^2*cosh(d*x + c)^8 + 66*(12*b^3*d*x + 19*b^3)*cosh(d*x + c)^7 + 924*(a^3 - 6*a*b^2)*cosh(d*x + c)^6 - 42*(24*b^3*d*x + 96*a^2*b + 11*b^3)*cosh(d*x + c)^5 - 84*(11*a^3 - 12*a*b^2)*cosh(d*x + c)^4 + 336*(b^3*d*x + 8*a^2*b)*cosh(d*x + c)^3 + 2*a^3 - 12*a*b^2 - 14*(11*a^3 - 12*a*b^2)*cosh(d*x + c)^2 - (24*b^3*d*x + 288*a^2*b - 11*b^3)*cosh(d*x + c))*sinh(d*x + c)^5 + 12*b^3*cosh(d*x + c)^2 + 2*(12*b^3*d*x + 192*a^2*b - 19*b^3)*cosh(d*x + c)^4 + 2*(910*b^3*cosh(d*x + c)^12 - 6006*b^3*cosh(d*x + c)^10 + 34320*a*b^2*cosh(d*x + c)^9 + 495*(12*b^3*d*x + 19*b^3)*cosh(d*x + c)^8 + 7920*(a^3 - 6*a*b^2)*cosh(d*x + c)^7 - 420*(24*b^3*d*x + 96*a^2*b + 11*b^3)*cosh(d*x + c)^6 - 1008*(11*a^3 - 12*a*b^2)*cosh(d*x + c)^5 + 12*b^3*d*x + 5040*(b^3*d*x + 8*a^2*b)*cosh(d*x + c)^4 - 280*(11*a^3 - 12*a*b^2)*cosh(d*x + c)^3 + 192*a^2*b - 19*b^3 - 30*(24*b^3*d*x + 288*a^2*b - 11*b^3)*cosh(d*x + c)^2 + 120*(a^3 - 6*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^4 + 8*(70*b^3*cosh(d*x + c)^13 - 546*b^3*cosh(d*x + c)^11 + 3432*a*b^2*cosh(d*x + c)^10 + 55*(12*b^3*d*x + 19*b^3)*cosh(d*x + c)^9 + 990*(a^3 - 6*a*b^2)*cosh(d*x + c)^8 - 60*(24*b^3*d*x + 96*a^2*b + 11*b^3)*cosh(d*x + c)^7 - 168*(11*a^3 - 12*a*b^2)*cosh(d*x + c)^6 + 1008*(b^3*d*x + 8*a^2*b)*cosh(d*x + c)^5 - 70*(11*a^3 - 12*a*b^2)*cosh(d*x + c)^4 - 10*(24*b^3*d*x + 288*a^2*b - 11*b^3)*cosh(d*x + c)^3 + 12*a*b^2 + 60*(a^3 - 6*a*b^2)*cosh(d*x + c)^2 + (12*b^3*d*x + 192*a^2*b - 19*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 - b^3 + 12*(10*b^3*cosh(d*x + c)^14 - 91*b^3*cosh(d*x + c)^12 + 624*a*b^2*cosh(d*x + c)^11 + 11*(12*b^3*d*x + 19*b^3)*cosh(d*x + c)^10 + 220*(a^3 - 6*a*b^2)*cosh(d*x + c)^9 - 15*(24*b^3*d*x + 96*a^2*b + 11*b^3)*cosh(d*x + c)^8 - 48*(11*a^3 - 12*a*b^2)*cosh(d*x + c)^7 + 336*(b^3*d*x + 8*a^2*b)*cosh(d*x + c)^6 - 28*(11*a^3 - 12*a*b^2)*cosh(d*x + c)^5 - 5*(24*b^3*d*x + 288*a^2*b - 11*b^3)*cosh(d*x + c)^4 + 24*a*b^2*cosh(d*x + c) + 40*(a^3 - 6*a*b^2)*cosh(d*x + c)^3 + b^3 + (12*b^3*d*x + 192*a^2*b - 19*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - 24*(a^3*cosh(d*x + c)^12 + 12*a^3*cosh(d*x + c)*sinh(d*x + c)^11 + a^3*sinh(d*x + c)^12 - 4*a^3*cosh(d*x + c)^10 + 6*a^3*cosh(d*x + c)^8 + 2*(33*a^3*cosh(d*x + c)^2 - 2*a^3)*sinh(d*x + c)^10 + 20*(11*a^3*cosh(d*x + c)^3 - 2*a^3*cosh(d*x + c))*sinh(d*x + c)^9 - 4*a^3*cosh(d*x + c)^6 + 3*(165*a^3*cosh(d*x + c)^4 - 60*a^3*cosh(d*x + c)^2 + 2*a^3)*sinh(d*x + c)^8 + 24*(33*a^3*cosh(d*x + c)^5 - 20*a^3*cosh(d*x + c)^3 + 2*a^3*cosh(d*x + c))*sinh(d*x + c)^7 + a^3*cosh(d*x + c)^4 + 4*(231*a^3*cosh(d*x + c)^6 - 210*a^3*cosh(d*x + c)^4 + 42*a^3*cosh(d*x + c)^2 - a^3)*sinh(d*x + c)^6 + 24*(33*a^3*cosh(d*x + c)^7 - 42*a^3*cosh(d*x + c)^5 + 14*a^3*cosh(d*x + c)^3 - a^3*cosh(d*x + c))*sinh(d*x + c)^5 + (495*a^3*cosh(d*x + c)^8 - 840*a^3*cosh(d*x + c)^6 + 420*a^3*cosh(d*x + c)^4 - 60*a^3*cosh(d*x + c)^2 + a^3)*sinh(d*x + c)^4 + 4*(55*a^3*cosh(d*x + c)^9 - 120*a^3*cosh(d*x + c)^7 + 84*a^3*cosh(d*x + c)^5 - 20*a^3*cosh(d*x + c)^3 + a^3*cosh(d*x + c))*sinh(d*x + c)^3 + 6*(11*a^3*cosh(d*x + c)^10 - 30*a^3*cosh(d*x + c)^8 + 28*a^3*cosh(d*x + c)^6 - 10*a^3*cosh(d*x + c)^4 + a^3*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*(3*a^3*cosh(d*x + c)^11 - 10*a^3*cosh(d*x + c)^9 + 12*a^3*cosh(d*x + c)^7 - 6*a^3*cosh(d*x + c)^5 + a^3*cosh(d*x + c)^3)*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) + 1) + 24*(a^3*cosh(d*x + c)^12 + 12*a^3*cosh(d*x + c)*sinh(d*x + c)^11 + a^3*sinh(d*x + c)^12 - 4*a^3*cosh(d*x + c)^10 + 6*a^3*cosh(d*x + c)^8 + 2*(33*a^3*cosh(d*x + c)^2 - 2*a^3)*sinh(d*x + c)^10 + 20*(11*a^3*cosh(d*x + c)^3 - 2*a^3*cosh(d*x + c))*sinh(d*x + c)^9 - 4*a^3*cosh(d*x + c)^6 + 3*(165*a^3*cosh(d*x + c)^4 - 60*a^3*cosh(d*x + c)^2 + 2*a^3)*sinh(d*x + c)^8 + 24*(33*a^3*cosh(d*x + c)^5 - 20*a^3*cosh(d*x + c)^3 + 2*a^3*cosh(d*x + c))*sinh(d*x + c)^7 + a^3*cosh(d*x + c)^4 + 4*(231*a^3*cosh(d*x + c)^6 - 210*a^3*cosh(d*x + c)^4 + 42*a^3*cosh(d*x + c)^2 - a^3)*sinh(d*x + c)^6 + 24*(33*a^3*cosh(d*x + c)^7 - 42*a^3*cosh(d*x + c)^5 + 14*a^3*cosh(d*x + c)^3 - a^3*cosh(d*x + c))*sinh(d*x + c)^5 + (495*a^3*cosh(d*x + c)^8 - 840*a^3*cosh(d*x + c)^6 + 420*a^3*cosh(d*x + c)^4 - 60*a^3*cosh(d*x + c)^2 + a^3)*sinh(d*x + c)^4 + 4*(55*a^3*cosh(d*x + c)^9 - 120*a^3*cosh(d*x + c)^7 + 84*a^3*cosh(d*x + c)^5 - 20*a^3*cosh(d*x + c)^3 + a^3*cosh(d*x + c))*sinh(d*x + c)^3 + 6*(11*a^3*cosh(d*x + c)^10 - 30*a^3*cosh(d*x + c)^8 + 28*a^3*cosh(d*x + c)^6 - 10*a^3*cosh(d*x + c)^4 + a^3*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*(3*a^3*cosh(d*x + c)^11 - 10*a^3*cosh(d*x + c)^9 + 12*a^3*cosh(d*x + c)^7 - 6*a^3*cosh(d*x + c)^5 + a^3*cosh(d*x + c)^3)*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) - 1) + 8*(2*b^3*cosh(d*x + c)^15 - 21*b^3*cosh(d*x + c)^13 + 156*a*b^2*cosh(d*x + c)^12 + 3*(12*b^3*d*x + 19*b^3)*cosh(d*x + c)^11 + 66*(a^3 - 6*a*b^2)*cosh(d*x + c)^10 - 5*(24*b^3*d*x + 96*a^2*b + 11*b^3)*cosh(d*x + c)^9 - 18*(11*a^3 - 12*a*b^2)*cosh(d*x + c)^8 + 144*(b^3*d*x + 8*a^2*b)*cosh(d*x + c)^7 - 14*(11*a^3 - 12*a*b^2)*cosh(d*x + c)^6 - 3*(24*b^3*d*x + 288*a^2*b - 11*b^3)*cosh(d*x + c)^5 + 36*a*b^2*cosh(d*x + c)^2 + 30*(a^3 - 6*a*b^2)*cosh(d*x + c)^4 + 3*b^3*cosh(d*x + c) + (12*b^3*d*x + 192*a^2*b - 19*b^3)*cosh(d*x + c)^3)*sinh(d*x + c))/(d*cosh(d*x + c)^12 + 12*d*cosh(d*x + c)*sinh(d*x + c)^11 + d*sinh(d*x + c)^12 - 4*d*cosh(d*x + c)^10 + 2*(33*d*cosh(d*x + c)^2 - 2*d)*sinh(d*x + c)^10 + 20*(11*d*cosh(d*x + c)^3 - 2*d*cosh(d*x + c))*sinh(d*x + c)^9 + 6*d*cosh(d*x + c)^8 + 3*(165*d*cosh(d*x + c)^4 - 60*d*cosh(d*x + c)^2 + 2*d)*sinh(d*x + c)^8 + 24*(33*d*cosh(d*x + c)^5 - 20*d*cosh(d*x + c)^3 + 2*d*cosh(d*x + c))*sinh(d*x + c)^7 - 4*d*cosh(d*x + c)^6 + 4*(231*d*cosh(d*x + c)^6 - 210*d*cosh(d*x + c)^4 + 42*d*cosh(d*x + c)^2 - d)*sinh(d*x + c)^6 + 24*(33*d*cosh(d*x + c)^7 - 42*d*cosh(d*x + c)^5 + 14*d*cosh(d*x + c)^3 - d*cosh(d*x + c))*sinh(d*x + c)^5 + d*cosh(d*x + c)^4 + (495*d*cosh(d*x + c)^8 - 840*d*cosh(d*x + c)^6 + 420*d*cosh(d*x + c)^4 - 60*d*cosh(d*x + c)^2 + d)*sinh(d*x + c)^4 + 4*(55*d*cosh(d*x + c)^9 - 120*d*cosh(d*x + c)^7 + 84*d*cosh(d*x + c)^5 - 20*d*cosh(d*x + c)^3 + d*cosh(d*x + c))*sinh(d*x + c)^3 + 6*(11*d*cosh(d*x + c)^10 - 30*d*cosh(d*x + c)^8 + 28*d*cosh(d*x + c)^6 - 10*d*cosh(d*x + c)^4 + d*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*(3*d*cosh(d*x + c)^11 - 10*d*cosh(d*x + c)^9 + 12*d*cosh(d*x + c)^7 - 6*d*cosh(d*x + c)^5 + d*cosh(d*x + c)^3)*sinh(d*x + c))","B",0
169,1,4629,0,0.795905," ","integrate(csch(d*x+c)^6*(a+b*sinh(d*x+c)^3)^3,x, algorithm=""fricas"")","\frac{5 \, b^{3} \cosh\left(d x + c\right)^{16} + 80 \, b^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{15} + 5 \, b^{3} \sinh\left(d x + c\right)^{16} + 360 \, a b^{2} d x \cosh\left(d x + c\right)^{13} - 70 \, b^{3} \cosh\left(d x + c\right)^{14} - 1800 \, a b^{2} d x \cosh\left(d x + c\right)^{11} + 10 \, {\left(60 \, b^{3} \cosh\left(d x + c\right)^{2} - 7 \, b^{3}\right)} \sinh\left(d x + c\right)^{14} + 3600 \, a b^{2} d x \cosh\left(d x + c\right)^{9} + 20 \, {\left(140 \, b^{3} \cosh\left(d x + c\right)^{3} + 18 \, a b^{2} d x - 49 \, b^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{13} - 10 \, {\left(36 \, a^{2} b - 23 \, b^{3}\right)} \cosh\left(d x + c\right)^{12} + 10 \, {\left(910 \, b^{3} \cosh\left(d x + c\right)^{4} + 468 \, a b^{2} d x \cosh\left(d x + c\right) - 637 \, b^{3} \cosh\left(d x + c\right)^{2} - 36 \, a^{2} b + 23 \, b^{3}\right)} \sinh\left(d x + c\right)^{12} + 40 \, {\left(546 \, b^{3} \cosh\left(d x + c\right)^{5} + 702 \, a b^{2} d x \cosh\left(d x + c\right)^{2} - 637 \, b^{3} \cosh\left(d x + c\right)^{3} - 45 \, a b^{2} d x - 3 \, {\left(36 \, a^{2} b - 23 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{11} + 90 \, {\left(8 \, a^{2} b - 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} + 10 \, {\left(4004 \, b^{3} \cosh\left(d x + c\right)^{6} + 10296 \, a b^{2} d x \cosh\left(d x + c\right)^{3} - 7007 \, b^{3} \cosh\left(d x + c\right)^{4} - 1980 \, a b^{2} d x \cosh\left(d x + c\right) + 72 \, a^{2} b - 27 \, b^{3} - 66 \, {\left(36 \, a^{2} b - 23 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{10} + 20 \, {\left(2860 \, b^{3} \cosh\left(d x + c\right)^{7} + 12870 \, a b^{2} d x \cosh\left(d x + c\right)^{4} - 7007 \, b^{3} \cosh\left(d x + c\right)^{5} - 4950 \, a b^{2} d x \cosh\left(d x + c\right)^{2} + 180 \, a b^{2} d x - 110 \, {\left(36 \, a^{2} b - 23 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 45 \, {\left(8 \, a^{2} b - 3 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} + 30 \, {\left(2145 \, b^{3} \cosh\left(d x + c\right)^{8} + 15444 \, a b^{2} d x \cosh\left(d x + c\right)^{5} - 7007 \, b^{3} \cosh\left(d x + c\right)^{6} - 9900 \, a b^{2} d x \cosh\left(d x + c\right)^{3} + 1080 \, a b^{2} d x \cosh\left(d x + c\right) - 165 \, {\left(36 \, a^{2} b - 23 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 135 \, {\left(8 \, a^{2} b - 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{8} - 80 \, {\left(45 \, a b^{2} d x + 16 \, a^{3}\right)} \cosh\left(d x + c\right)^{7} + 80 \, {\left(715 \, b^{3} \cosh\left(d x + c\right)^{9} + 7722 \, a b^{2} d x \cosh\left(d x + c\right)^{6} - 3003 \, b^{3} \cosh\left(d x + c\right)^{7} - 7425 \, a b^{2} d x \cosh\left(d x + c\right)^{4} + 1620 \, a b^{2} d x \cosh\left(d x + c\right)^{2} - 99 \, {\left(36 \, a^{2} b - 23 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 45 \, a b^{2} d x + 135 \, {\left(8 \, a^{2} b - 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 16 \, a^{3}\right)} \sinh\left(d x + c\right)^{7} - 90 \, {\left(8 \, a^{2} b - 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 10 \, {\left(4004 \, b^{3} \cosh\left(d x + c\right)^{10} + 61776 \, a b^{2} d x \cosh\left(d x + c\right)^{7} - 21021 \, b^{3} \cosh\left(d x + c\right)^{8} - 83160 \, a b^{2} d x \cosh\left(d x + c\right)^{5} + 30240 \, a b^{2} d x \cosh\left(d x + c\right)^{3} - 924 \, {\left(36 \, a^{2} b - 23 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 1890 \, {\left(8 \, a^{2} b - 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 72 \, a^{2} b + 27 \, b^{3} - 56 \, {\left(45 \, a b^{2} d x + 16 \, a^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} + 40 \, {\left(45 \, a b^{2} d x + 16 \, a^{3}\right)} \cosh\left(d x + c\right)^{5} + 20 \, {\left(1092 \, b^{3} \cosh\left(d x + c\right)^{11} + 23166 \, a b^{2} d x \cosh\left(d x + c\right)^{8} - 7007 \, b^{3} \cosh\left(d x + c\right)^{9} - 41580 \, a b^{2} d x \cosh\left(d x + c\right)^{6} + 22680 \, a b^{2} d x \cosh\left(d x + c\right)^{4} - 396 \, {\left(36 \, a^{2} b - 23 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 1134 \, {\left(8 \, a^{2} b - 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 90 \, a b^{2} d x + 32 \, a^{3} - 84 \, {\left(45 \, a b^{2} d x + 16 \, a^{3}\right)} \cosh\left(d x + c\right)^{2} - 27 \, {\left(8 \, a^{2} b - 3 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 70 \, b^{3} \cosh\left(d x + c\right)^{2} + 10 \, {\left(36 \, a^{2} b - 23 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 10 \, {\left(910 \, b^{3} \cosh\left(d x + c\right)^{12} + 25740 \, a b^{2} d x \cosh\left(d x + c\right)^{9} - 7007 \, b^{3} \cosh\left(d x + c\right)^{10} - 59400 \, a b^{2} d x \cosh\left(d x + c\right)^{7} + 45360 \, a b^{2} d x \cosh\left(d x + c\right)^{5} - 495 \, {\left(36 \, a^{2} b - 23 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 1890 \, {\left(8 \, a^{2} b - 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} - 280 \, {\left(45 \, a b^{2} d x + 16 \, a^{3}\right)} \cosh\left(d x + c\right)^{3} + 36 \, a^{2} b - 23 \, b^{3} - 135 \, {\left(8 \, a^{2} b - 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{2} + 20 \, {\left(45 \, a b^{2} d x + 16 \, a^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} - 8 \, {\left(45 \, a b^{2} d x + 16 \, a^{3}\right)} \cosh\left(d x + c\right)^{3} + 8 \, {\left(350 \, b^{3} \cosh\left(d x + c\right)^{13} + 12870 \, a b^{2} d x \cosh\left(d x + c\right)^{10} - 3185 \, b^{3} \cosh\left(d x + c\right)^{11} - 37125 \, a b^{2} d x \cosh\left(d x + c\right)^{8} + 37800 \, a b^{2} d x \cosh\left(d x + c\right)^{6} - 275 \, {\left(36 \, a^{2} b - 23 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + 1350 \, {\left(8 \, a^{2} b - 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} - 45 \, a b^{2} d x - 350 \, {\left(45 \, a b^{2} d x + 16 \, a^{3}\right)} \cosh\left(d x + c\right)^{4} - 225 \, {\left(8 \, a^{2} b - 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 16 \, a^{3} + 50 \, {\left(45 \, a b^{2} d x + 16 \, a^{3}\right)} \cosh\left(d x + c\right)^{2} + 5 \, {\left(36 \, a^{2} b - 23 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 5 \, b^{3} + 2 \, {\left(300 \, b^{3} \cosh\left(d x + c\right)^{14} + 14040 \, a b^{2} d x \cosh\left(d x + c\right)^{11} - 3185 \, b^{3} \cosh\left(d x + c\right)^{12} - 49500 \, a b^{2} d x \cosh\left(d x + c\right)^{9} + 64800 \, a b^{2} d x \cosh\left(d x + c\right)^{7} - 330 \, {\left(36 \, a^{2} b - 23 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} + 2025 \, {\left(8 \, a^{2} b - 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} - 840 \, {\left(45 \, a b^{2} d x + 16 \, a^{3}\right)} \cosh\left(d x + c\right)^{5} - 675 \, {\left(8 \, a^{2} b - 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 200 \, {\left(45 \, a b^{2} d x + 16 \, a^{3}\right)} \cosh\left(d x + c\right)^{3} + 35 \, b^{3} + 30 \, {\left(36 \, a^{2} b - 23 \, b^{3}\right)} \cosh\left(d x + c\right)^{2} - 12 \, {\left(45 \, a b^{2} d x + 16 \, a^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 180 \, {\left(a^{2} b \cosh\left(d x + c\right)^{13} + 13 \, a^{2} b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{12} + a^{2} b \sinh\left(d x + c\right)^{13} - 5 \, a^{2} b \cosh\left(d x + c\right)^{11} + 10 \, a^{2} b \cosh\left(d x + c\right)^{9} + {\left(78 \, a^{2} b \cosh\left(d x + c\right)^{2} - 5 \, a^{2} b\right)} \sinh\left(d x + c\right)^{11} + 11 \, {\left(26 \, a^{2} b \cosh\left(d x + c\right)^{3} - 5 \, a^{2} b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{10} - 10 \, a^{2} b \cosh\left(d x + c\right)^{7} + 5 \, {\left(143 \, a^{2} b \cosh\left(d x + c\right)^{4} - 55 \, a^{2} b \cosh\left(d x + c\right)^{2} + 2 \, a^{2} b\right)} \sinh\left(d x + c\right)^{9} + 3 \, {\left(429 \, a^{2} b \cosh\left(d x + c\right)^{5} - 275 \, a^{2} b \cosh\left(d x + c\right)^{3} + 30 \, a^{2} b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{8} + 5 \, a^{2} b \cosh\left(d x + c\right)^{5} + 2 \, {\left(858 \, a^{2} b \cosh\left(d x + c\right)^{6} - 825 \, a^{2} b \cosh\left(d x + c\right)^{4} + 180 \, a^{2} b \cosh\left(d x + c\right)^{2} - 5 \, a^{2} b\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(858 \, a^{2} b \cosh\left(d x + c\right)^{7} - 1155 \, a^{2} b \cosh\left(d x + c\right)^{5} + 420 \, a^{2} b \cosh\left(d x + c\right)^{3} - 35 \, a^{2} b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} - a^{2} b \cosh\left(d x + c\right)^{3} + {\left(1287 \, a^{2} b \cosh\left(d x + c\right)^{8} - 2310 \, a^{2} b \cosh\left(d x + c\right)^{6} + 1260 \, a^{2} b \cosh\left(d x + c\right)^{4} - 210 \, a^{2} b \cosh\left(d x + c\right)^{2} + 5 \, a^{2} b\right)} \sinh\left(d x + c\right)^{5} + 5 \, {\left(143 \, a^{2} b \cosh\left(d x + c\right)^{9} - 330 \, a^{2} b \cosh\left(d x + c\right)^{7} + 252 \, a^{2} b \cosh\left(d x + c\right)^{5} - 70 \, a^{2} b \cosh\left(d x + c\right)^{3} + 5 \, a^{2} b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + {\left(286 \, a^{2} b \cosh\left(d x + c\right)^{10} - 825 \, a^{2} b \cosh\left(d x + c\right)^{8} + 840 \, a^{2} b \cosh\left(d x + c\right)^{6} - 350 \, a^{2} b \cosh\left(d x + c\right)^{4} + 50 \, a^{2} b \cosh\left(d x + c\right)^{2} - a^{2} b\right)} \sinh\left(d x + c\right)^{3} + {\left(78 \, a^{2} b \cosh\left(d x + c\right)^{11} - 275 \, a^{2} b \cosh\left(d x + c\right)^{9} + 360 \, a^{2} b \cosh\left(d x + c\right)^{7} - 210 \, a^{2} b \cosh\left(d x + c\right)^{5} + 50 \, a^{2} b \cosh\left(d x + c\right)^{3} - 3 \, a^{2} b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(13 \, a^{2} b \cosh\left(d x + c\right)^{12} - 55 \, a^{2} b \cosh\left(d x + c\right)^{10} + 90 \, a^{2} b \cosh\left(d x + c\right)^{8} - 70 \, a^{2} b \cosh\left(d x + c\right)^{6} + 25 \, a^{2} b \cosh\left(d x + c\right)^{4} - 3 \, a^{2} b \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) - 180 \, {\left(a^{2} b \cosh\left(d x + c\right)^{13} + 13 \, a^{2} b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{12} + a^{2} b \sinh\left(d x + c\right)^{13} - 5 \, a^{2} b \cosh\left(d x + c\right)^{11} + 10 \, a^{2} b \cosh\left(d x + c\right)^{9} + {\left(78 \, a^{2} b \cosh\left(d x + c\right)^{2} - 5 \, a^{2} b\right)} \sinh\left(d x + c\right)^{11} + 11 \, {\left(26 \, a^{2} b \cosh\left(d x + c\right)^{3} - 5 \, a^{2} b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{10} - 10 \, a^{2} b \cosh\left(d x + c\right)^{7} + 5 \, {\left(143 \, a^{2} b \cosh\left(d x + c\right)^{4} - 55 \, a^{2} b \cosh\left(d x + c\right)^{2} + 2 \, a^{2} b\right)} \sinh\left(d x + c\right)^{9} + 3 \, {\left(429 \, a^{2} b \cosh\left(d x + c\right)^{5} - 275 \, a^{2} b \cosh\left(d x + c\right)^{3} + 30 \, a^{2} b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{8} + 5 \, a^{2} b \cosh\left(d x + c\right)^{5} + 2 \, {\left(858 \, a^{2} b \cosh\left(d x + c\right)^{6} - 825 \, a^{2} b \cosh\left(d x + c\right)^{4} + 180 \, a^{2} b \cosh\left(d x + c\right)^{2} - 5 \, a^{2} b\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(858 \, a^{2} b \cosh\left(d x + c\right)^{7} - 1155 \, a^{2} b \cosh\left(d x + c\right)^{5} + 420 \, a^{2} b \cosh\left(d x + c\right)^{3} - 35 \, a^{2} b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} - a^{2} b \cosh\left(d x + c\right)^{3} + {\left(1287 \, a^{2} b \cosh\left(d x + c\right)^{8} - 2310 \, a^{2} b \cosh\left(d x + c\right)^{6} + 1260 \, a^{2} b \cosh\left(d x + c\right)^{4} - 210 \, a^{2} b \cosh\left(d x + c\right)^{2} + 5 \, a^{2} b\right)} \sinh\left(d x + c\right)^{5} + 5 \, {\left(143 \, a^{2} b \cosh\left(d x + c\right)^{9} - 330 \, a^{2} b \cosh\left(d x + c\right)^{7} + 252 \, a^{2} b \cosh\left(d x + c\right)^{5} - 70 \, a^{2} b \cosh\left(d x + c\right)^{3} + 5 \, a^{2} b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + {\left(286 \, a^{2} b \cosh\left(d x + c\right)^{10} - 825 \, a^{2} b \cosh\left(d x + c\right)^{8} + 840 \, a^{2} b \cosh\left(d x + c\right)^{6} - 350 \, a^{2} b \cosh\left(d x + c\right)^{4} + 50 \, a^{2} b \cosh\left(d x + c\right)^{2} - a^{2} b\right)} \sinh\left(d x + c\right)^{3} + {\left(78 \, a^{2} b \cosh\left(d x + c\right)^{11} - 275 \, a^{2} b \cosh\left(d x + c\right)^{9} + 360 \, a^{2} b \cosh\left(d x + c\right)^{7} - 210 \, a^{2} b \cosh\left(d x + c\right)^{5} + 50 \, a^{2} b \cosh\left(d x + c\right)^{3} - 3 \, a^{2} b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(13 \, a^{2} b \cosh\left(d x + c\right)^{12} - 55 \, a^{2} b \cosh\left(d x + c\right)^{10} + 90 \, a^{2} b \cosh\left(d x + c\right)^{8} - 70 \, a^{2} b \cosh\left(d x + c\right)^{6} + 25 \, a^{2} b \cosh\left(d x + c\right)^{4} - 3 \, a^{2} b \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) + 4 \, {\left(20 \, b^{3} \cosh\left(d x + c\right)^{15} + 1170 \, a b^{2} d x \cosh\left(d x + c\right)^{12} - 245 \, b^{3} \cosh\left(d x + c\right)^{13} - 4950 \, a b^{2} d x \cosh\left(d x + c\right)^{10} + 8100 \, a b^{2} d x \cosh\left(d x + c\right)^{8} - 30 \, {\left(36 \, a^{2} b - 23 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} + 225 \, {\left(8 \, a^{2} b - 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} - 140 \, {\left(45 \, a b^{2} d x + 16 \, a^{3}\right)} \cosh\left(d x + c\right)^{6} - 135 \, {\left(8 \, a^{2} b - 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 50 \, {\left(45 \, a b^{2} d x + 16 \, a^{3}\right)} \cosh\left(d x + c\right)^{4} + 35 \, b^{3} \cosh\left(d x + c\right) + 10 \, {\left(36 \, a^{2} b - 23 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 6 \, {\left(45 \, a b^{2} d x + 16 \, a^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)}{120 \, {\left(d \cosh\left(d x + c\right)^{13} + 13 \, d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{12} + d \sinh\left(d x + c\right)^{13} - 5 \, d \cosh\left(d x + c\right)^{11} + {\left(78 \, d \cosh\left(d x + c\right)^{2} - 5 \, d\right)} \sinh\left(d x + c\right)^{11} + 11 \, {\left(26 \, d \cosh\left(d x + c\right)^{3} - 5 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{10} + 10 \, d \cosh\left(d x + c\right)^{9} + 5 \, {\left(143 \, d \cosh\left(d x + c\right)^{4} - 55 \, d \cosh\left(d x + c\right)^{2} + 2 \, d\right)} \sinh\left(d x + c\right)^{9} + 3 \, {\left(429 \, d \cosh\left(d x + c\right)^{5} - 275 \, d \cosh\left(d x + c\right)^{3} + 30 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{8} - 10 \, d \cosh\left(d x + c\right)^{7} + 2 \, {\left(858 \, d \cosh\left(d x + c\right)^{6} - 825 \, d \cosh\left(d x + c\right)^{4} + 180 \, d \cosh\left(d x + c\right)^{2} - 5 \, d\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(858 \, d \cosh\left(d x + c\right)^{7} - 1155 \, d \cosh\left(d x + c\right)^{5} + 420 \, d \cosh\left(d x + c\right)^{3} - 35 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} + 5 \, d \cosh\left(d x + c\right)^{5} + {\left(1287 \, d \cosh\left(d x + c\right)^{8} - 2310 \, d \cosh\left(d x + c\right)^{6} + 1260 \, d \cosh\left(d x + c\right)^{4} - 210 \, d \cosh\left(d x + c\right)^{2} + 5 \, d\right)} \sinh\left(d x + c\right)^{5} + 5 \, {\left(143 \, d \cosh\left(d x + c\right)^{9} - 330 \, d \cosh\left(d x + c\right)^{7} + 252 \, d \cosh\left(d x + c\right)^{5} - 70 \, d \cosh\left(d x + c\right)^{3} + 5 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} - d \cosh\left(d x + c\right)^{3} + {\left(286 \, d \cosh\left(d x + c\right)^{10} - 825 \, d \cosh\left(d x + c\right)^{8} + 840 \, d \cosh\left(d x + c\right)^{6} - 350 \, d \cosh\left(d x + c\right)^{4} + 50 \, d \cosh\left(d x + c\right)^{2} - d\right)} \sinh\left(d x + c\right)^{3} + {\left(78 \, d \cosh\left(d x + c\right)^{11} - 275 \, d \cosh\left(d x + c\right)^{9} + 360 \, d \cosh\left(d x + c\right)^{7} - 210 \, d \cosh\left(d x + c\right)^{5} + 50 \, d \cosh\left(d x + c\right)^{3} - 3 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(13 \, d \cosh\left(d x + c\right)^{12} - 55 \, d \cosh\left(d x + c\right)^{10} + 90 \, d \cosh\left(d x + c\right)^{8} - 70 \, d \cosh\left(d x + c\right)^{6} + 25 \, d \cosh\left(d x + c\right)^{4} - 3 \, d \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"1/120*(5*b^3*cosh(d*x + c)^16 + 80*b^3*cosh(d*x + c)*sinh(d*x + c)^15 + 5*b^3*sinh(d*x + c)^16 + 360*a*b^2*d*x*cosh(d*x + c)^13 - 70*b^3*cosh(d*x + c)^14 - 1800*a*b^2*d*x*cosh(d*x + c)^11 + 10*(60*b^3*cosh(d*x + c)^2 - 7*b^3)*sinh(d*x + c)^14 + 3600*a*b^2*d*x*cosh(d*x + c)^9 + 20*(140*b^3*cosh(d*x + c)^3 + 18*a*b^2*d*x - 49*b^3*cosh(d*x + c))*sinh(d*x + c)^13 - 10*(36*a^2*b - 23*b^3)*cosh(d*x + c)^12 + 10*(910*b^3*cosh(d*x + c)^4 + 468*a*b^2*d*x*cosh(d*x + c) - 637*b^3*cosh(d*x + c)^2 - 36*a^2*b + 23*b^3)*sinh(d*x + c)^12 + 40*(546*b^3*cosh(d*x + c)^5 + 702*a*b^2*d*x*cosh(d*x + c)^2 - 637*b^3*cosh(d*x + c)^3 - 45*a*b^2*d*x - 3*(36*a^2*b - 23*b^3)*cosh(d*x + c))*sinh(d*x + c)^11 + 90*(8*a^2*b - 3*b^3)*cosh(d*x + c)^10 + 10*(4004*b^3*cosh(d*x + c)^6 + 10296*a*b^2*d*x*cosh(d*x + c)^3 - 7007*b^3*cosh(d*x + c)^4 - 1980*a*b^2*d*x*cosh(d*x + c) + 72*a^2*b - 27*b^3 - 66*(36*a^2*b - 23*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^10 + 20*(2860*b^3*cosh(d*x + c)^7 + 12870*a*b^2*d*x*cosh(d*x + c)^4 - 7007*b^3*cosh(d*x + c)^5 - 4950*a*b^2*d*x*cosh(d*x + c)^2 + 180*a*b^2*d*x - 110*(36*a^2*b - 23*b^3)*cosh(d*x + c)^3 + 45*(8*a^2*b - 3*b^3)*cosh(d*x + c))*sinh(d*x + c)^9 + 30*(2145*b^3*cosh(d*x + c)^8 + 15444*a*b^2*d*x*cosh(d*x + c)^5 - 7007*b^3*cosh(d*x + c)^6 - 9900*a*b^2*d*x*cosh(d*x + c)^3 + 1080*a*b^2*d*x*cosh(d*x + c) - 165*(36*a^2*b - 23*b^3)*cosh(d*x + c)^4 + 135*(8*a^2*b - 3*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^8 - 80*(45*a*b^2*d*x + 16*a^3)*cosh(d*x + c)^7 + 80*(715*b^3*cosh(d*x + c)^9 + 7722*a*b^2*d*x*cosh(d*x + c)^6 - 3003*b^3*cosh(d*x + c)^7 - 7425*a*b^2*d*x*cosh(d*x + c)^4 + 1620*a*b^2*d*x*cosh(d*x + c)^2 - 99*(36*a^2*b - 23*b^3)*cosh(d*x + c)^5 - 45*a*b^2*d*x + 135*(8*a^2*b - 3*b^3)*cosh(d*x + c)^3 - 16*a^3)*sinh(d*x + c)^7 - 90*(8*a^2*b - 3*b^3)*cosh(d*x + c)^6 + 10*(4004*b^3*cosh(d*x + c)^10 + 61776*a*b^2*d*x*cosh(d*x + c)^7 - 21021*b^3*cosh(d*x + c)^8 - 83160*a*b^2*d*x*cosh(d*x + c)^5 + 30240*a*b^2*d*x*cosh(d*x + c)^3 - 924*(36*a^2*b - 23*b^3)*cosh(d*x + c)^6 + 1890*(8*a^2*b - 3*b^3)*cosh(d*x + c)^4 - 72*a^2*b + 27*b^3 - 56*(45*a*b^2*d*x + 16*a^3)*cosh(d*x + c))*sinh(d*x + c)^6 + 40*(45*a*b^2*d*x + 16*a^3)*cosh(d*x + c)^5 + 20*(1092*b^3*cosh(d*x + c)^11 + 23166*a*b^2*d*x*cosh(d*x + c)^8 - 7007*b^3*cosh(d*x + c)^9 - 41580*a*b^2*d*x*cosh(d*x + c)^6 + 22680*a*b^2*d*x*cosh(d*x + c)^4 - 396*(36*a^2*b - 23*b^3)*cosh(d*x + c)^7 + 1134*(8*a^2*b - 3*b^3)*cosh(d*x + c)^5 + 90*a*b^2*d*x + 32*a^3 - 84*(45*a*b^2*d*x + 16*a^3)*cosh(d*x + c)^2 - 27*(8*a^2*b - 3*b^3)*cosh(d*x + c))*sinh(d*x + c)^5 + 70*b^3*cosh(d*x + c)^2 + 10*(36*a^2*b - 23*b^3)*cosh(d*x + c)^4 + 10*(910*b^3*cosh(d*x + c)^12 + 25740*a*b^2*d*x*cosh(d*x + c)^9 - 7007*b^3*cosh(d*x + c)^10 - 59400*a*b^2*d*x*cosh(d*x + c)^7 + 45360*a*b^2*d*x*cosh(d*x + c)^5 - 495*(36*a^2*b - 23*b^3)*cosh(d*x + c)^8 + 1890*(8*a^2*b - 3*b^3)*cosh(d*x + c)^6 - 280*(45*a*b^2*d*x + 16*a^3)*cosh(d*x + c)^3 + 36*a^2*b - 23*b^3 - 135*(8*a^2*b - 3*b^3)*cosh(d*x + c)^2 + 20*(45*a*b^2*d*x + 16*a^3)*cosh(d*x + c))*sinh(d*x + c)^4 - 8*(45*a*b^2*d*x + 16*a^3)*cosh(d*x + c)^3 + 8*(350*b^3*cosh(d*x + c)^13 + 12870*a*b^2*d*x*cosh(d*x + c)^10 - 3185*b^3*cosh(d*x + c)^11 - 37125*a*b^2*d*x*cosh(d*x + c)^8 + 37800*a*b^2*d*x*cosh(d*x + c)^6 - 275*(36*a^2*b - 23*b^3)*cosh(d*x + c)^9 + 1350*(8*a^2*b - 3*b^3)*cosh(d*x + c)^7 - 45*a*b^2*d*x - 350*(45*a*b^2*d*x + 16*a^3)*cosh(d*x + c)^4 - 225*(8*a^2*b - 3*b^3)*cosh(d*x + c)^3 - 16*a^3 + 50*(45*a*b^2*d*x + 16*a^3)*cosh(d*x + c)^2 + 5*(36*a^2*b - 23*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 - 5*b^3 + 2*(300*b^3*cosh(d*x + c)^14 + 14040*a*b^2*d*x*cosh(d*x + c)^11 - 3185*b^3*cosh(d*x + c)^12 - 49500*a*b^2*d*x*cosh(d*x + c)^9 + 64800*a*b^2*d*x*cosh(d*x + c)^7 - 330*(36*a^2*b - 23*b^3)*cosh(d*x + c)^10 + 2025*(8*a^2*b - 3*b^3)*cosh(d*x + c)^8 - 840*(45*a*b^2*d*x + 16*a^3)*cosh(d*x + c)^5 - 675*(8*a^2*b - 3*b^3)*cosh(d*x + c)^4 + 200*(45*a*b^2*d*x + 16*a^3)*cosh(d*x + c)^3 + 35*b^3 + 30*(36*a^2*b - 23*b^3)*cosh(d*x + c)^2 - 12*(45*a*b^2*d*x + 16*a^3)*cosh(d*x + c))*sinh(d*x + c)^2 + 180*(a^2*b*cosh(d*x + c)^13 + 13*a^2*b*cosh(d*x + c)*sinh(d*x + c)^12 + a^2*b*sinh(d*x + c)^13 - 5*a^2*b*cosh(d*x + c)^11 + 10*a^2*b*cosh(d*x + c)^9 + (78*a^2*b*cosh(d*x + c)^2 - 5*a^2*b)*sinh(d*x + c)^11 + 11*(26*a^2*b*cosh(d*x + c)^3 - 5*a^2*b*cosh(d*x + c))*sinh(d*x + c)^10 - 10*a^2*b*cosh(d*x + c)^7 + 5*(143*a^2*b*cosh(d*x + c)^4 - 55*a^2*b*cosh(d*x + c)^2 + 2*a^2*b)*sinh(d*x + c)^9 + 3*(429*a^2*b*cosh(d*x + c)^5 - 275*a^2*b*cosh(d*x + c)^3 + 30*a^2*b*cosh(d*x + c))*sinh(d*x + c)^8 + 5*a^2*b*cosh(d*x + c)^5 + 2*(858*a^2*b*cosh(d*x + c)^6 - 825*a^2*b*cosh(d*x + c)^4 + 180*a^2*b*cosh(d*x + c)^2 - 5*a^2*b)*sinh(d*x + c)^7 + 2*(858*a^2*b*cosh(d*x + c)^7 - 1155*a^2*b*cosh(d*x + c)^5 + 420*a^2*b*cosh(d*x + c)^3 - 35*a^2*b*cosh(d*x + c))*sinh(d*x + c)^6 - a^2*b*cosh(d*x + c)^3 + (1287*a^2*b*cosh(d*x + c)^8 - 2310*a^2*b*cosh(d*x + c)^6 + 1260*a^2*b*cosh(d*x + c)^4 - 210*a^2*b*cosh(d*x + c)^2 + 5*a^2*b)*sinh(d*x + c)^5 + 5*(143*a^2*b*cosh(d*x + c)^9 - 330*a^2*b*cosh(d*x + c)^7 + 252*a^2*b*cosh(d*x + c)^5 - 70*a^2*b*cosh(d*x + c)^3 + 5*a^2*b*cosh(d*x + c))*sinh(d*x + c)^4 + (286*a^2*b*cosh(d*x + c)^10 - 825*a^2*b*cosh(d*x + c)^8 + 840*a^2*b*cosh(d*x + c)^6 - 350*a^2*b*cosh(d*x + c)^4 + 50*a^2*b*cosh(d*x + c)^2 - a^2*b)*sinh(d*x + c)^3 + (78*a^2*b*cosh(d*x + c)^11 - 275*a^2*b*cosh(d*x + c)^9 + 360*a^2*b*cosh(d*x + c)^7 - 210*a^2*b*cosh(d*x + c)^5 + 50*a^2*b*cosh(d*x + c)^3 - 3*a^2*b*cosh(d*x + c))*sinh(d*x + c)^2 + (13*a^2*b*cosh(d*x + c)^12 - 55*a^2*b*cosh(d*x + c)^10 + 90*a^2*b*cosh(d*x + c)^8 - 70*a^2*b*cosh(d*x + c)^6 + 25*a^2*b*cosh(d*x + c)^4 - 3*a^2*b*cosh(d*x + c)^2)*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) + 1) - 180*(a^2*b*cosh(d*x + c)^13 + 13*a^2*b*cosh(d*x + c)*sinh(d*x + c)^12 + a^2*b*sinh(d*x + c)^13 - 5*a^2*b*cosh(d*x + c)^11 + 10*a^2*b*cosh(d*x + c)^9 + (78*a^2*b*cosh(d*x + c)^2 - 5*a^2*b)*sinh(d*x + c)^11 + 11*(26*a^2*b*cosh(d*x + c)^3 - 5*a^2*b*cosh(d*x + c))*sinh(d*x + c)^10 - 10*a^2*b*cosh(d*x + c)^7 + 5*(143*a^2*b*cosh(d*x + c)^4 - 55*a^2*b*cosh(d*x + c)^2 + 2*a^2*b)*sinh(d*x + c)^9 + 3*(429*a^2*b*cosh(d*x + c)^5 - 275*a^2*b*cosh(d*x + c)^3 + 30*a^2*b*cosh(d*x + c))*sinh(d*x + c)^8 + 5*a^2*b*cosh(d*x + c)^5 + 2*(858*a^2*b*cosh(d*x + c)^6 - 825*a^2*b*cosh(d*x + c)^4 + 180*a^2*b*cosh(d*x + c)^2 - 5*a^2*b)*sinh(d*x + c)^7 + 2*(858*a^2*b*cosh(d*x + c)^7 - 1155*a^2*b*cosh(d*x + c)^5 + 420*a^2*b*cosh(d*x + c)^3 - 35*a^2*b*cosh(d*x + c))*sinh(d*x + c)^6 - a^2*b*cosh(d*x + c)^3 + (1287*a^2*b*cosh(d*x + c)^8 - 2310*a^2*b*cosh(d*x + c)^6 + 1260*a^2*b*cosh(d*x + c)^4 - 210*a^2*b*cosh(d*x + c)^2 + 5*a^2*b)*sinh(d*x + c)^5 + 5*(143*a^2*b*cosh(d*x + c)^9 - 330*a^2*b*cosh(d*x + c)^7 + 252*a^2*b*cosh(d*x + c)^5 - 70*a^2*b*cosh(d*x + c)^3 + 5*a^2*b*cosh(d*x + c))*sinh(d*x + c)^4 + (286*a^2*b*cosh(d*x + c)^10 - 825*a^2*b*cosh(d*x + c)^8 + 840*a^2*b*cosh(d*x + c)^6 - 350*a^2*b*cosh(d*x + c)^4 + 50*a^2*b*cosh(d*x + c)^2 - a^2*b)*sinh(d*x + c)^3 + (78*a^2*b*cosh(d*x + c)^11 - 275*a^2*b*cosh(d*x + c)^9 + 360*a^2*b*cosh(d*x + c)^7 - 210*a^2*b*cosh(d*x + c)^5 + 50*a^2*b*cosh(d*x + c)^3 - 3*a^2*b*cosh(d*x + c))*sinh(d*x + c)^2 + (13*a^2*b*cosh(d*x + c)^12 - 55*a^2*b*cosh(d*x + c)^10 + 90*a^2*b*cosh(d*x + c)^8 - 70*a^2*b*cosh(d*x + c)^6 + 25*a^2*b*cosh(d*x + c)^4 - 3*a^2*b*cosh(d*x + c)^2)*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) - 1) + 4*(20*b^3*cosh(d*x + c)^15 + 1170*a*b^2*d*x*cosh(d*x + c)^12 - 245*b^3*cosh(d*x + c)^13 - 4950*a*b^2*d*x*cosh(d*x + c)^10 + 8100*a*b^2*d*x*cosh(d*x + c)^8 - 30*(36*a^2*b - 23*b^3)*cosh(d*x + c)^11 + 225*(8*a^2*b - 3*b^3)*cosh(d*x + c)^9 - 140*(45*a*b^2*d*x + 16*a^3)*cosh(d*x + c)^6 - 135*(8*a^2*b - 3*b^3)*cosh(d*x + c)^5 + 50*(45*a*b^2*d*x + 16*a^3)*cosh(d*x + c)^4 + 35*b^3*cosh(d*x + c) + 10*(36*a^2*b - 23*b^3)*cosh(d*x + c)^3 - 6*(45*a*b^2*d*x + 16*a^3)*cosh(d*x + c)^2)*sinh(d*x + c))/(d*cosh(d*x + c)^13 + 13*d*cosh(d*x + c)*sinh(d*x + c)^12 + d*sinh(d*x + c)^13 - 5*d*cosh(d*x + c)^11 + (78*d*cosh(d*x + c)^2 - 5*d)*sinh(d*x + c)^11 + 11*(26*d*cosh(d*x + c)^3 - 5*d*cosh(d*x + c))*sinh(d*x + c)^10 + 10*d*cosh(d*x + c)^9 + 5*(143*d*cosh(d*x + c)^4 - 55*d*cosh(d*x + c)^2 + 2*d)*sinh(d*x + c)^9 + 3*(429*d*cosh(d*x + c)^5 - 275*d*cosh(d*x + c)^3 + 30*d*cosh(d*x + c))*sinh(d*x + c)^8 - 10*d*cosh(d*x + c)^7 + 2*(858*d*cosh(d*x + c)^6 - 825*d*cosh(d*x + c)^4 + 180*d*cosh(d*x + c)^2 - 5*d)*sinh(d*x + c)^7 + 2*(858*d*cosh(d*x + c)^7 - 1155*d*cosh(d*x + c)^5 + 420*d*cosh(d*x + c)^3 - 35*d*cosh(d*x + c))*sinh(d*x + c)^6 + 5*d*cosh(d*x + c)^5 + (1287*d*cosh(d*x + c)^8 - 2310*d*cosh(d*x + c)^6 + 1260*d*cosh(d*x + c)^4 - 210*d*cosh(d*x + c)^2 + 5*d)*sinh(d*x + c)^5 + 5*(143*d*cosh(d*x + c)^9 - 330*d*cosh(d*x + c)^7 + 252*d*cosh(d*x + c)^5 - 70*d*cosh(d*x + c)^3 + 5*d*cosh(d*x + c))*sinh(d*x + c)^4 - d*cosh(d*x + c)^3 + (286*d*cosh(d*x + c)^10 - 825*d*cosh(d*x + c)^8 + 840*d*cosh(d*x + c)^6 - 350*d*cosh(d*x + c)^4 + 50*d*cosh(d*x + c)^2 - d)*sinh(d*x + c)^3 + (78*d*cosh(d*x + c)^11 - 275*d*cosh(d*x + c)^9 + 360*d*cosh(d*x + c)^7 - 210*d*cosh(d*x + c)^5 + 50*d*cosh(d*x + c)^3 - 3*d*cosh(d*x + c))*sinh(d*x + c)^2 + (13*d*cosh(d*x + c)^12 - 55*d*cosh(d*x + c)^10 + 90*d*cosh(d*x + c)^8 - 70*d*cosh(d*x + c)^6 + 25*d*cosh(d*x + c)^4 - 3*d*cosh(d*x + c)^2)*sinh(d*x + c))","B",0
170,1,6210,0,0.668137," ","integrate(csch(d*x+c)^7*(a+b*sinh(d*x+c)^3)^3,x, algorithm=""fricas"")","\frac{6 \, b^{3} \cosh\left(d x + c\right)^{16} + 96 \, b^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{15} + 6 \, b^{3} \sinh\left(d x + c\right)^{16} - 30 \, a^{3} \cosh\left(d x + c\right)^{13} - 12 \, {\left(2 \, b^{3} d x + 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{14} - 12 \, {\left(2 \, b^{3} d x - 60 \, b^{3} \cosh\left(d x + c\right)^{2} + 3 \, b^{3}\right)} \sinh\left(d x + c\right)^{14} + 170 \, a^{3} \cosh\left(d x + c\right)^{11} + 6 \, {\left(560 \, b^{3} \cosh\left(d x + c\right)^{3} - 5 \, a^{3} - 28 \, {\left(2 \, b^{3} d x + 3 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{13} + 12 \, {\left(12 \, b^{3} d x + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{12} + 6 \, {\left(1820 \, b^{3} \cosh\left(d x + c\right)^{4} + 24 \, b^{3} d x - 65 \, a^{3} \cosh\left(d x + c\right) + 14 \, b^{3} - 182 \, {\left(2 \, b^{3} d x + 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{12} - 396 \, a^{3} \cosh\left(d x + c\right)^{9} + 2 \, {\left(13104 \, b^{3} \cosh\left(d x + c\right)^{5} - 1170 \, a^{3} \cosh\left(d x + c\right)^{2} - 2184 \, {\left(2 \, b^{3} d x + 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 85 \, a^{3} + 72 \, {\left(12 \, b^{3} d x + 7 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{11} - 12 \, {\left(30 \, b^{3} d x + 48 \, a^{2} b + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} + 2 \, {\left(24024 \, b^{3} \cosh\left(d x + c\right)^{6} - 4290 \, a^{3} \cosh\left(d x + c\right)^{3} - 180 \, b^{3} d x - 6006 \, {\left(2 \, b^{3} d x + 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 935 \, a^{3} \cosh\left(d x + c\right) - 288 \, a^{2} b - 42 \, b^{3} + 396 \, {\left(12 \, b^{3} d x + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{10} - 396 \, a^{3} \cosh\left(d x + c\right)^{7} + 2 \, {\left(34320 \, b^{3} \cosh\left(d x + c\right)^{7} - 10725 \, a^{3} \cosh\left(d x + c\right)^{4} - 12012 \, {\left(2 \, b^{3} d x + 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 4675 \, a^{3} \cosh\left(d x + c\right)^{2} + 1320 \, {\left(12 \, b^{3} d x + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 198 \, a^{3} - 60 \, {\left(30 \, b^{3} d x + 48 \, a^{2} b + 7 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} + 480 \, {\left(b^{3} d x + 4 \, a^{2} b\right)} \cosh\left(d x + c\right)^{8} + 6 \, {\left(12870 \, b^{3} \cosh\left(d x + c\right)^{8} - 6435 \, a^{3} \cosh\left(d x + c\right)^{5} - 6006 \, {\left(2 \, b^{3} d x + 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 4675 \, a^{3} \cosh\left(d x + c\right)^{3} + 80 \, b^{3} d x + 990 \, {\left(12 \, b^{3} d x + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 594 \, a^{3} \cosh\left(d x + c\right) + 320 \, a^{2} b - 90 \, {\left(30 \, b^{3} d x + 48 \, a^{2} b + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{8} + 170 \, a^{3} \cosh\left(d x + c\right)^{5} + 12 \, {\left(5720 \, b^{3} \cosh\left(d x + c\right)^{9} - 4290 \, a^{3} \cosh\left(d x + c\right)^{6} - 3432 \, {\left(2 \, b^{3} d x + 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 4675 \, a^{3} \cosh\left(d x + c\right)^{4} + 792 \, {\left(12 \, b^{3} d x + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 1188 \, a^{3} \cosh\left(d x + c\right)^{2} - 120 \, {\left(30 \, b^{3} d x + 48 \, a^{2} b + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 33 \, a^{3} + 320 \, {\left(b^{3} d x + 4 \, a^{2} b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} - 12 \, {\left(30 \, b^{3} d x + 192 \, a^{2} b - 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 12 \, {\left(4004 \, b^{3} \cosh\left(d x + c\right)^{10} - 4290 \, a^{3} \cosh\left(d x + c\right)^{7} - 3003 \, {\left(2 \, b^{3} d x + 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 6545 \, a^{3} \cosh\left(d x + c\right)^{5} + 924 \, {\left(12 \, b^{3} d x + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} - 2772 \, a^{3} \cosh\left(d x + c\right)^{3} - 30 \, b^{3} d x - 210 \, {\left(30 \, b^{3} d x + 48 \, a^{2} b + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 231 \, a^{3} \cosh\left(d x + c\right) - 192 \, a^{2} b + 7 \, b^{3} + 1120 \, {\left(b^{3} d x + 4 \, a^{2} b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} - 30 \, a^{3} \cosh\left(d x + c\right)^{3} + 2 \, {\left(13104 \, b^{3} \cosh\left(d x + c\right)^{11} - 19305 \, a^{3} \cosh\left(d x + c\right)^{8} - 12012 \, {\left(2 \, b^{3} d x + 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + 39270 \, a^{3} \cosh\left(d x + c\right)^{6} + 4752 \, {\left(12 \, b^{3} d x + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} - 24948 \, a^{3} \cosh\left(d x + c\right)^{4} - 1512 \, {\left(30 \, b^{3} d x + 48 \, a^{2} b + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 4158 \, a^{3} \cosh\left(d x + c\right)^{2} + 13440 \, {\left(b^{3} d x + 4 \, a^{2} b\right)} \cosh\left(d x + c\right)^{3} + 85 \, a^{3} - 36 \, {\left(30 \, b^{3} d x + 192 \, a^{2} b - 7 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 12 \, {\left(12 \, b^{3} d x + 96 \, a^{2} b - 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(5460 \, b^{3} \cosh\left(d x + c\right)^{12} - 10725 \, a^{3} \cosh\left(d x + c\right)^{9} - 6006 \, {\left(2 \, b^{3} d x + 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} + 28050 \, a^{3} \cosh\left(d x + c\right)^{7} + 2970 \, {\left(12 \, b^{3} d x + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} - 24948 \, a^{3} \cosh\left(d x + c\right)^{5} - 1260 \, {\left(30 \, b^{3} d x + 48 \, a^{2} b + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} - 6930 \, a^{3} \cosh\left(d x + c\right)^{3} + 72 \, b^{3} d x + 16800 \, {\left(b^{3} d x + 4 \, a^{2} b\right)} \cosh\left(d x + c\right)^{4} + 425 \, a^{3} \cosh\left(d x + c\right) + 576 \, a^{2} b - 42 \, b^{3} - 90 \, {\left(30 \, b^{3} d x + 192 \, a^{2} b - 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(1680 \, b^{3} \cosh\left(d x + c\right)^{13} - 4290 \, a^{3} \cosh\left(d x + c\right)^{10} - 2184 \, {\left(2 \, b^{3} d x + 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} + 14025 \, a^{3} \cosh\left(d x + c\right)^{8} + 1320 \, {\left(12 \, b^{3} d x + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} - 16632 \, a^{3} \cosh\left(d x + c\right)^{6} - 720 \, {\left(30 \, b^{3} d x + 48 \, a^{2} b + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} - 6930 \, a^{3} \cosh\left(d x + c\right)^{4} + 13440 \, {\left(b^{3} d x + 4 \, a^{2} b\right)} \cosh\left(d x + c\right)^{5} + 850 \, a^{3} \cosh\left(d x + c\right)^{2} - 120 \, {\left(30 \, b^{3} d x + 192 \, a^{2} b - 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 15 \, a^{3} + 24 \, {\left(12 \, b^{3} d x + 96 \, a^{2} b - 7 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 6 \, b^{3} - 12 \, {\left(2 \, b^{3} d x + 16 \, a^{2} b - 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(360 \, b^{3} \cosh\left(d x + c\right)^{14} - 1170 \, a^{3} \cosh\left(d x + c\right)^{11} - 546 \, {\left(2 \, b^{3} d x + 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{12} + 4675 \, a^{3} \cosh\left(d x + c\right)^{9} + 396 \, {\left(12 \, b^{3} d x + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} - 7128 \, a^{3} \cosh\left(d x + c\right)^{7} - 270 \, {\left(30 \, b^{3} d x + 48 \, a^{2} b + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} - 4158 \, a^{3} \cosh\left(d x + c\right)^{5} + 6720 \, {\left(b^{3} d x + 4 \, a^{2} b\right)} \cosh\left(d x + c\right)^{6} + 850 \, a^{3} \cosh\left(d x + c\right)^{3} - 12 \, b^{3} d x - 90 \, {\left(30 \, b^{3} d x + 192 \, a^{2} b - 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 45 \, a^{3} \cosh\left(d x + c\right) - 96 \, a^{2} b + 18 \, b^{3} + 36 \, {\left(12 \, b^{3} d x + 96 \, a^{2} b - 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 3 \, {\left({\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{14} + 14 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{13} + {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \sinh\left(d x + c\right)^{14} - 6 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{12} - {\left(30 \, a^{3} - 288 \, a b^{2} - 91 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{12} + 4 \, {\left(91 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} - 18 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{11} + 15 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{10} + {\left(1001 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} + 75 \, a^{3} - 720 \, a b^{2} - 396 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{10} + 2 \, {\left(1001 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{5} - 660 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} + 75 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} - 20 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{8} + {\left(3003 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{6} - 2970 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} - 100 \, a^{3} + 960 \, a b^{2} + 675 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{8} + 8 \, {\left(429 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{7} - 594 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{5} + 225 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} - 20 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 15 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{6} + {\left(3003 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{8} - 5544 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{6} + 3150 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} + 75 \, a^{3} - 720 \, a b^{2} - 560 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(1001 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{9} - 2376 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{7} + 1890 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{5} - 560 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} + 45 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 6 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(1001 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{10} - 2970 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{8} + 3150 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{6} - 1400 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} - 30 \, a^{3} + 288 \, a b^{2} + 225 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(91 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{11} - 330 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{9} + 450 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{7} - 280 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{5} + 75 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} - 6 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(91 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{12} - 396 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{10} + 675 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{8} - 560 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{6} + 225 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} + 5 \, a^{3} - 48 \, a b^{2} - 36 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(7 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{13} - 36 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{11} + 75 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{9} - 80 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{7} + 45 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{5} - 12 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) - 3 \, {\left({\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{14} + 14 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{13} + {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \sinh\left(d x + c\right)^{14} - 6 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{12} - {\left(30 \, a^{3} - 288 \, a b^{2} - 91 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{12} + 4 \, {\left(91 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} - 18 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{11} + 15 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{10} + {\left(1001 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} + 75 \, a^{3} - 720 \, a b^{2} - 396 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{10} + 2 \, {\left(1001 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{5} - 660 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} + 75 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} - 20 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{8} + {\left(3003 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{6} - 2970 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} - 100 \, a^{3} + 960 \, a b^{2} + 675 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{8} + 8 \, {\left(429 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{7} - 594 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{5} + 225 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} - 20 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 15 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{6} + {\left(3003 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{8} - 5544 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{6} + 3150 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} + 75 \, a^{3} - 720 \, a b^{2} - 560 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(1001 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{9} - 2376 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{7} + 1890 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{5} - 560 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} + 45 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 6 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(1001 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{10} - 2970 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{8} + 3150 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{6} - 1400 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} - 30 \, a^{3} + 288 \, a b^{2} + 225 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(91 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{11} - 330 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{9} + 450 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{7} - 280 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{5} + 75 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} - 6 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(91 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{12} - 396 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{10} + 675 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{8} - 560 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{6} + 225 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} + 5 \, a^{3} - 48 \, a b^{2} - 36 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(7 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{13} - 36 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{11} + 75 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{9} - 80 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{7} + 45 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{5} - 12 \, {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(5 \, a^{3} - 48 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) + 2 \, {\left(48 \, b^{3} \cosh\left(d x + c\right)^{15} - 195 \, a^{3} \cosh\left(d x + c\right)^{12} - 84 \, {\left(2 \, b^{3} d x + 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{13} + 935 \, a^{3} \cosh\left(d x + c\right)^{10} + 72 \, {\left(12 \, b^{3} d x + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} - 1782 \, a^{3} \cosh\left(d x + c\right)^{8} - 60 \, {\left(30 \, b^{3} d x + 48 \, a^{2} b + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} - 1386 \, a^{3} \cosh\left(d x + c\right)^{6} + 1920 \, {\left(b^{3} d x + 4 \, a^{2} b\right)} \cosh\left(d x + c\right)^{7} + 425 \, a^{3} \cosh\left(d x + c\right)^{4} - 36 \, {\left(30 \, b^{3} d x + 192 \, a^{2} b - 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 45 \, a^{3} \cosh\left(d x + c\right)^{2} + 24 \, {\left(12 \, b^{3} d x + 96 \, a^{2} b - 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 12 \, {\left(2 \, b^{3} d x + 16 \, a^{2} b - 3 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{48 \, {\left(d \cosh\left(d x + c\right)^{14} + 14 \, d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{13} + d \sinh\left(d x + c\right)^{14} - 6 \, d \cosh\left(d x + c\right)^{12} + {\left(91 \, d \cosh\left(d x + c\right)^{2} - 6 \, d\right)} \sinh\left(d x + c\right)^{12} + 4 \, {\left(91 \, d \cosh\left(d x + c\right)^{3} - 18 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{11} + 15 \, d \cosh\left(d x + c\right)^{10} + {\left(1001 \, d \cosh\left(d x + c\right)^{4} - 396 \, d \cosh\left(d x + c\right)^{2} + 15 \, d\right)} \sinh\left(d x + c\right)^{10} + 2 \, {\left(1001 \, d \cosh\left(d x + c\right)^{5} - 660 \, d \cosh\left(d x + c\right)^{3} + 75 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} - 20 \, d \cosh\left(d x + c\right)^{8} + {\left(3003 \, d \cosh\left(d x + c\right)^{6} - 2970 \, d \cosh\left(d x + c\right)^{4} + 675 \, d \cosh\left(d x + c\right)^{2} - 20 \, d\right)} \sinh\left(d x + c\right)^{8} + 8 \, {\left(429 \, d \cosh\left(d x + c\right)^{7} - 594 \, d \cosh\left(d x + c\right)^{5} + 225 \, d \cosh\left(d x + c\right)^{3} - 20 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 15 \, d \cosh\left(d x + c\right)^{6} + {\left(3003 \, d \cosh\left(d x + c\right)^{8} - 5544 \, d \cosh\left(d x + c\right)^{6} + 3150 \, d \cosh\left(d x + c\right)^{4} - 560 \, d \cosh\left(d x + c\right)^{2} + 15 \, d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(1001 \, d \cosh\left(d x + c\right)^{9} - 2376 \, d \cosh\left(d x + c\right)^{7} + 1890 \, d \cosh\left(d x + c\right)^{5} - 560 \, d \cosh\left(d x + c\right)^{3} + 45 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 6 \, d \cosh\left(d x + c\right)^{4} + {\left(1001 \, d \cosh\left(d x + c\right)^{10} - 2970 \, d \cosh\left(d x + c\right)^{8} + 3150 \, d \cosh\left(d x + c\right)^{6} - 1400 \, d \cosh\left(d x + c\right)^{4} + 225 \, d \cosh\left(d x + c\right)^{2} - 6 \, d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(91 \, d \cosh\left(d x + c\right)^{11} - 330 \, d \cosh\left(d x + c\right)^{9} + 450 \, d \cosh\left(d x + c\right)^{7} - 280 \, d \cosh\left(d x + c\right)^{5} + 75 \, d \cosh\left(d x + c\right)^{3} - 6 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + d \cosh\left(d x + c\right)^{2} + {\left(91 \, d \cosh\left(d x + c\right)^{12} - 396 \, d \cosh\left(d x + c\right)^{10} + 675 \, d \cosh\left(d x + c\right)^{8} - 560 \, d \cosh\left(d x + c\right)^{6} + 225 \, d \cosh\left(d x + c\right)^{4} - 36 \, d \cosh\left(d x + c\right)^{2} + d\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(7 \, d \cosh\left(d x + c\right)^{13} - 36 \, d \cosh\left(d x + c\right)^{11} + 75 \, d \cosh\left(d x + c\right)^{9} - 80 \, d \cosh\left(d x + c\right)^{7} + 45 \, d \cosh\left(d x + c\right)^{5} - 12 \, d \cosh\left(d x + c\right)^{3} + d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"1/48*(6*b^3*cosh(d*x + c)^16 + 96*b^3*cosh(d*x + c)*sinh(d*x + c)^15 + 6*b^3*sinh(d*x + c)^16 - 30*a^3*cosh(d*x + c)^13 - 12*(2*b^3*d*x + 3*b^3)*cosh(d*x + c)^14 - 12*(2*b^3*d*x - 60*b^3*cosh(d*x + c)^2 + 3*b^3)*sinh(d*x + c)^14 + 170*a^3*cosh(d*x + c)^11 + 6*(560*b^3*cosh(d*x + c)^3 - 5*a^3 - 28*(2*b^3*d*x + 3*b^3)*cosh(d*x + c))*sinh(d*x + c)^13 + 12*(12*b^3*d*x + 7*b^3)*cosh(d*x + c)^12 + 6*(1820*b^3*cosh(d*x + c)^4 + 24*b^3*d*x - 65*a^3*cosh(d*x + c) + 14*b^3 - 182*(2*b^3*d*x + 3*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^12 - 396*a^3*cosh(d*x + c)^9 + 2*(13104*b^3*cosh(d*x + c)^5 - 1170*a^3*cosh(d*x + c)^2 - 2184*(2*b^3*d*x + 3*b^3)*cosh(d*x + c)^3 + 85*a^3 + 72*(12*b^3*d*x + 7*b^3)*cosh(d*x + c))*sinh(d*x + c)^11 - 12*(30*b^3*d*x + 48*a^2*b + 7*b^3)*cosh(d*x + c)^10 + 2*(24024*b^3*cosh(d*x + c)^6 - 4290*a^3*cosh(d*x + c)^3 - 180*b^3*d*x - 6006*(2*b^3*d*x + 3*b^3)*cosh(d*x + c)^4 + 935*a^3*cosh(d*x + c) - 288*a^2*b - 42*b^3 + 396*(12*b^3*d*x + 7*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^10 - 396*a^3*cosh(d*x + c)^7 + 2*(34320*b^3*cosh(d*x + c)^7 - 10725*a^3*cosh(d*x + c)^4 - 12012*(2*b^3*d*x + 3*b^3)*cosh(d*x + c)^5 + 4675*a^3*cosh(d*x + c)^2 + 1320*(12*b^3*d*x + 7*b^3)*cosh(d*x + c)^3 - 198*a^3 - 60*(30*b^3*d*x + 48*a^2*b + 7*b^3)*cosh(d*x + c))*sinh(d*x + c)^9 + 480*(b^3*d*x + 4*a^2*b)*cosh(d*x + c)^8 + 6*(12870*b^3*cosh(d*x + c)^8 - 6435*a^3*cosh(d*x + c)^5 - 6006*(2*b^3*d*x + 3*b^3)*cosh(d*x + c)^6 + 4675*a^3*cosh(d*x + c)^3 + 80*b^3*d*x + 990*(12*b^3*d*x + 7*b^3)*cosh(d*x + c)^4 - 594*a^3*cosh(d*x + c) + 320*a^2*b - 90*(30*b^3*d*x + 48*a^2*b + 7*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 170*a^3*cosh(d*x + c)^5 + 12*(5720*b^3*cosh(d*x + c)^9 - 4290*a^3*cosh(d*x + c)^6 - 3432*(2*b^3*d*x + 3*b^3)*cosh(d*x + c)^7 + 4675*a^3*cosh(d*x + c)^4 + 792*(12*b^3*d*x + 7*b^3)*cosh(d*x + c)^5 - 1188*a^3*cosh(d*x + c)^2 - 120*(30*b^3*d*x + 48*a^2*b + 7*b^3)*cosh(d*x + c)^3 - 33*a^3 + 320*(b^3*d*x + 4*a^2*b)*cosh(d*x + c))*sinh(d*x + c)^7 - 12*(30*b^3*d*x + 192*a^2*b - 7*b^3)*cosh(d*x + c)^6 + 12*(4004*b^3*cosh(d*x + c)^10 - 4290*a^3*cosh(d*x + c)^7 - 3003*(2*b^3*d*x + 3*b^3)*cosh(d*x + c)^8 + 6545*a^3*cosh(d*x + c)^5 + 924*(12*b^3*d*x + 7*b^3)*cosh(d*x + c)^6 - 2772*a^3*cosh(d*x + c)^3 - 30*b^3*d*x - 210*(30*b^3*d*x + 48*a^2*b + 7*b^3)*cosh(d*x + c)^4 - 231*a^3*cosh(d*x + c) - 192*a^2*b + 7*b^3 + 1120*(b^3*d*x + 4*a^2*b)*cosh(d*x + c)^2)*sinh(d*x + c)^6 - 30*a^3*cosh(d*x + c)^3 + 2*(13104*b^3*cosh(d*x + c)^11 - 19305*a^3*cosh(d*x + c)^8 - 12012*(2*b^3*d*x + 3*b^3)*cosh(d*x + c)^9 + 39270*a^3*cosh(d*x + c)^6 + 4752*(12*b^3*d*x + 7*b^3)*cosh(d*x + c)^7 - 24948*a^3*cosh(d*x + c)^4 - 1512*(30*b^3*d*x + 48*a^2*b + 7*b^3)*cosh(d*x + c)^5 - 4158*a^3*cosh(d*x + c)^2 + 13440*(b^3*d*x + 4*a^2*b)*cosh(d*x + c)^3 + 85*a^3 - 36*(30*b^3*d*x + 192*a^2*b - 7*b^3)*cosh(d*x + c))*sinh(d*x + c)^5 + 12*(12*b^3*d*x + 96*a^2*b - 7*b^3)*cosh(d*x + c)^4 + 2*(5460*b^3*cosh(d*x + c)^12 - 10725*a^3*cosh(d*x + c)^9 - 6006*(2*b^3*d*x + 3*b^3)*cosh(d*x + c)^10 + 28050*a^3*cosh(d*x + c)^7 + 2970*(12*b^3*d*x + 7*b^3)*cosh(d*x + c)^8 - 24948*a^3*cosh(d*x + c)^5 - 1260*(30*b^3*d*x + 48*a^2*b + 7*b^3)*cosh(d*x + c)^6 - 6930*a^3*cosh(d*x + c)^3 + 72*b^3*d*x + 16800*(b^3*d*x + 4*a^2*b)*cosh(d*x + c)^4 + 425*a^3*cosh(d*x + c) + 576*a^2*b - 42*b^3 - 90*(30*b^3*d*x + 192*a^2*b - 7*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 2*(1680*b^3*cosh(d*x + c)^13 - 4290*a^3*cosh(d*x + c)^10 - 2184*(2*b^3*d*x + 3*b^3)*cosh(d*x + c)^11 + 14025*a^3*cosh(d*x + c)^8 + 1320*(12*b^3*d*x + 7*b^3)*cosh(d*x + c)^9 - 16632*a^3*cosh(d*x + c)^6 - 720*(30*b^3*d*x + 48*a^2*b + 7*b^3)*cosh(d*x + c)^7 - 6930*a^3*cosh(d*x + c)^4 + 13440*(b^3*d*x + 4*a^2*b)*cosh(d*x + c)^5 + 850*a^3*cosh(d*x + c)^2 - 120*(30*b^3*d*x + 192*a^2*b - 7*b^3)*cosh(d*x + c)^3 - 15*a^3 + 24*(12*b^3*d*x + 96*a^2*b - 7*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 - 6*b^3 - 12*(2*b^3*d*x + 16*a^2*b - 3*b^3)*cosh(d*x + c)^2 + 2*(360*b^3*cosh(d*x + c)^14 - 1170*a^3*cosh(d*x + c)^11 - 546*(2*b^3*d*x + 3*b^3)*cosh(d*x + c)^12 + 4675*a^3*cosh(d*x + c)^9 + 396*(12*b^3*d*x + 7*b^3)*cosh(d*x + c)^10 - 7128*a^3*cosh(d*x + c)^7 - 270*(30*b^3*d*x + 48*a^2*b + 7*b^3)*cosh(d*x + c)^8 - 4158*a^3*cosh(d*x + c)^5 + 6720*(b^3*d*x + 4*a^2*b)*cosh(d*x + c)^6 + 850*a^3*cosh(d*x + c)^3 - 12*b^3*d*x - 90*(30*b^3*d*x + 192*a^2*b - 7*b^3)*cosh(d*x + c)^4 - 45*a^3*cosh(d*x + c) - 96*a^2*b + 18*b^3 + 36*(12*b^3*d*x + 96*a^2*b - 7*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 3*((5*a^3 - 48*a*b^2)*cosh(d*x + c)^14 + 14*(5*a^3 - 48*a*b^2)*cosh(d*x + c)*sinh(d*x + c)^13 + (5*a^3 - 48*a*b^2)*sinh(d*x + c)^14 - 6*(5*a^3 - 48*a*b^2)*cosh(d*x + c)^12 - (30*a^3 - 288*a*b^2 - 91*(5*a^3 - 48*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^12 + 4*(91*(5*a^3 - 48*a*b^2)*cosh(d*x + c)^3 - 18*(5*a^3 - 48*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^11 + 15*(5*a^3 - 48*a*b^2)*cosh(d*x + c)^10 + (1001*(5*a^3 - 48*a*b^2)*cosh(d*x + c)^4 + 75*a^3 - 720*a*b^2 - 396*(5*a^3 - 48*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^10 + 2*(1001*(5*a^3 - 48*a*b^2)*cosh(d*x + c)^5 - 660*(5*a^3 - 48*a*b^2)*cosh(d*x + c)^3 + 75*(5*a^3 - 48*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^9 - 20*(5*a^3 - 48*a*b^2)*cosh(d*x + c)^8 + (3003*(5*a^3 - 48*a*b^2)*cosh(d*x + c)^6 - 2970*(5*a^3 - 48*a*b^2)*cosh(d*x + c)^4 - 100*a^3 + 960*a*b^2 + 675*(5*a^3 - 48*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 8*(429*(5*a^3 - 48*a*b^2)*cosh(d*x + c)^7 - 594*(5*a^3 - 48*a*b^2)*cosh(d*x + c)^5 + 225*(5*a^3 - 48*a*b^2)*cosh(d*x + c)^3 - 20*(5*a^3 - 48*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^7 + 15*(5*a^3 - 48*a*b^2)*cosh(d*x + c)^6 + (3003*(5*a^3 - 48*a*b^2)*cosh(d*x + c)^8 - 5544*(5*a^3 - 48*a*b^2)*cosh(d*x + c)^6 + 3150*(5*a^3 - 48*a*b^2)*cosh(d*x + c)^4 + 75*a^3 - 720*a*b^2 - 560*(5*a^3 - 48*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 2*(1001*(5*a^3 - 48*a*b^2)*cosh(d*x + c)^9 - 2376*(5*a^3 - 48*a*b^2)*cosh(d*x + c)^7 + 1890*(5*a^3 - 48*a*b^2)*cosh(d*x + c)^5 - 560*(5*a^3 - 48*a*b^2)*cosh(d*x + c)^3 + 45*(5*a^3 - 48*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^5 - 6*(5*a^3 - 48*a*b^2)*cosh(d*x + c)^4 + (1001*(5*a^3 - 48*a*b^2)*cosh(d*x + c)^10 - 2970*(5*a^3 - 48*a*b^2)*cosh(d*x + c)^8 + 3150*(5*a^3 - 48*a*b^2)*cosh(d*x + c)^6 - 1400*(5*a^3 - 48*a*b^2)*cosh(d*x + c)^4 - 30*a^3 + 288*a*b^2 + 225*(5*a^3 - 48*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 4*(91*(5*a^3 - 48*a*b^2)*cosh(d*x + c)^11 - 330*(5*a^3 - 48*a*b^2)*cosh(d*x + c)^9 + 450*(5*a^3 - 48*a*b^2)*cosh(d*x + c)^7 - 280*(5*a^3 - 48*a*b^2)*cosh(d*x + c)^5 + 75*(5*a^3 - 48*a*b^2)*cosh(d*x + c)^3 - 6*(5*a^3 - 48*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + (5*a^3 - 48*a*b^2)*cosh(d*x + c)^2 + (91*(5*a^3 - 48*a*b^2)*cosh(d*x + c)^12 - 396*(5*a^3 - 48*a*b^2)*cosh(d*x + c)^10 + 675*(5*a^3 - 48*a*b^2)*cosh(d*x + c)^8 - 560*(5*a^3 - 48*a*b^2)*cosh(d*x + c)^6 + 225*(5*a^3 - 48*a*b^2)*cosh(d*x + c)^4 + 5*a^3 - 48*a*b^2 - 36*(5*a^3 - 48*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 2*(7*(5*a^3 - 48*a*b^2)*cosh(d*x + c)^13 - 36*(5*a^3 - 48*a*b^2)*cosh(d*x + c)^11 + 75*(5*a^3 - 48*a*b^2)*cosh(d*x + c)^9 - 80*(5*a^3 - 48*a*b^2)*cosh(d*x + c)^7 + 45*(5*a^3 - 48*a*b^2)*cosh(d*x + c)^5 - 12*(5*a^3 - 48*a*b^2)*cosh(d*x + c)^3 + (5*a^3 - 48*a*b^2)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) + 1) - 3*((5*a^3 - 48*a*b^2)*cosh(d*x + c)^14 + 14*(5*a^3 - 48*a*b^2)*cosh(d*x + c)*sinh(d*x + c)^13 + (5*a^3 - 48*a*b^2)*sinh(d*x + c)^14 - 6*(5*a^3 - 48*a*b^2)*cosh(d*x + c)^12 - (30*a^3 - 288*a*b^2 - 91*(5*a^3 - 48*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^12 + 4*(91*(5*a^3 - 48*a*b^2)*cosh(d*x + c)^3 - 18*(5*a^3 - 48*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^11 + 15*(5*a^3 - 48*a*b^2)*cosh(d*x + c)^10 + (1001*(5*a^3 - 48*a*b^2)*cosh(d*x + c)^4 + 75*a^3 - 720*a*b^2 - 396*(5*a^3 - 48*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^10 + 2*(1001*(5*a^3 - 48*a*b^2)*cosh(d*x + c)^5 - 660*(5*a^3 - 48*a*b^2)*cosh(d*x + c)^3 + 75*(5*a^3 - 48*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^9 - 20*(5*a^3 - 48*a*b^2)*cosh(d*x + c)^8 + (3003*(5*a^3 - 48*a*b^2)*cosh(d*x + c)^6 - 2970*(5*a^3 - 48*a*b^2)*cosh(d*x + c)^4 - 100*a^3 + 960*a*b^2 + 675*(5*a^3 - 48*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 8*(429*(5*a^3 - 48*a*b^2)*cosh(d*x + c)^7 - 594*(5*a^3 - 48*a*b^2)*cosh(d*x + c)^5 + 225*(5*a^3 - 48*a*b^2)*cosh(d*x + c)^3 - 20*(5*a^3 - 48*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^7 + 15*(5*a^3 - 48*a*b^2)*cosh(d*x + c)^6 + (3003*(5*a^3 - 48*a*b^2)*cosh(d*x + c)^8 - 5544*(5*a^3 - 48*a*b^2)*cosh(d*x + c)^6 + 3150*(5*a^3 - 48*a*b^2)*cosh(d*x + c)^4 + 75*a^3 - 720*a*b^2 - 560*(5*a^3 - 48*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 2*(1001*(5*a^3 - 48*a*b^2)*cosh(d*x + c)^9 - 2376*(5*a^3 - 48*a*b^2)*cosh(d*x + c)^7 + 1890*(5*a^3 - 48*a*b^2)*cosh(d*x + c)^5 - 560*(5*a^3 - 48*a*b^2)*cosh(d*x + c)^3 + 45*(5*a^3 - 48*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^5 - 6*(5*a^3 - 48*a*b^2)*cosh(d*x + c)^4 + (1001*(5*a^3 - 48*a*b^2)*cosh(d*x + c)^10 - 2970*(5*a^3 - 48*a*b^2)*cosh(d*x + c)^8 + 3150*(5*a^3 - 48*a*b^2)*cosh(d*x + c)^6 - 1400*(5*a^3 - 48*a*b^2)*cosh(d*x + c)^4 - 30*a^3 + 288*a*b^2 + 225*(5*a^3 - 48*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 4*(91*(5*a^3 - 48*a*b^2)*cosh(d*x + c)^11 - 330*(5*a^3 - 48*a*b^2)*cosh(d*x + c)^9 + 450*(5*a^3 - 48*a*b^2)*cosh(d*x + c)^7 - 280*(5*a^3 - 48*a*b^2)*cosh(d*x + c)^5 + 75*(5*a^3 - 48*a*b^2)*cosh(d*x + c)^3 - 6*(5*a^3 - 48*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + (5*a^3 - 48*a*b^2)*cosh(d*x + c)^2 + (91*(5*a^3 - 48*a*b^2)*cosh(d*x + c)^12 - 396*(5*a^3 - 48*a*b^2)*cosh(d*x + c)^10 + 675*(5*a^3 - 48*a*b^2)*cosh(d*x + c)^8 - 560*(5*a^3 - 48*a*b^2)*cosh(d*x + c)^6 + 225*(5*a^3 - 48*a*b^2)*cosh(d*x + c)^4 + 5*a^3 - 48*a*b^2 - 36*(5*a^3 - 48*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 2*(7*(5*a^3 - 48*a*b^2)*cosh(d*x + c)^13 - 36*(5*a^3 - 48*a*b^2)*cosh(d*x + c)^11 + 75*(5*a^3 - 48*a*b^2)*cosh(d*x + c)^9 - 80*(5*a^3 - 48*a*b^2)*cosh(d*x + c)^7 + 45*(5*a^3 - 48*a*b^2)*cosh(d*x + c)^5 - 12*(5*a^3 - 48*a*b^2)*cosh(d*x + c)^3 + (5*a^3 - 48*a*b^2)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) - 1) + 2*(48*b^3*cosh(d*x + c)^15 - 195*a^3*cosh(d*x + c)^12 - 84*(2*b^3*d*x + 3*b^3)*cosh(d*x + c)^13 + 935*a^3*cosh(d*x + c)^10 + 72*(12*b^3*d*x + 7*b^3)*cosh(d*x + c)^11 - 1782*a^3*cosh(d*x + c)^8 - 60*(30*b^3*d*x + 48*a^2*b + 7*b^3)*cosh(d*x + c)^9 - 1386*a^3*cosh(d*x + c)^6 + 1920*(b^3*d*x + 4*a^2*b)*cosh(d*x + c)^7 + 425*a^3*cosh(d*x + c)^4 - 36*(30*b^3*d*x + 192*a^2*b - 7*b^3)*cosh(d*x + c)^5 - 45*a^3*cosh(d*x + c)^2 + 24*(12*b^3*d*x + 96*a^2*b - 7*b^3)*cosh(d*x + c)^3 - 12*(2*b^3*d*x + 16*a^2*b - 3*b^3)*cosh(d*x + c))*sinh(d*x + c))/(d*cosh(d*x + c)^14 + 14*d*cosh(d*x + c)*sinh(d*x + c)^13 + d*sinh(d*x + c)^14 - 6*d*cosh(d*x + c)^12 + (91*d*cosh(d*x + c)^2 - 6*d)*sinh(d*x + c)^12 + 4*(91*d*cosh(d*x + c)^3 - 18*d*cosh(d*x + c))*sinh(d*x + c)^11 + 15*d*cosh(d*x + c)^10 + (1001*d*cosh(d*x + c)^4 - 396*d*cosh(d*x + c)^2 + 15*d)*sinh(d*x + c)^10 + 2*(1001*d*cosh(d*x + c)^5 - 660*d*cosh(d*x + c)^3 + 75*d*cosh(d*x + c))*sinh(d*x + c)^9 - 20*d*cosh(d*x + c)^8 + (3003*d*cosh(d*x + c)^6 - 2970*d*cosh(d*x + c)^4 + 675*d*cosh(d*x + c)^2 - 20*d)*sinh(d*x + c)^8 + 8*(429*d*cosh(d*x + c)^7 - 594*d*cosh(d*x + c)^5 + 225*d*cosh(d*x + c)^3 - 20*d*cosh(d*x + c))*sinh(d*x + c)^7 + 15*d*cosh(d*x + c)^6 + (3003*d*cosh(d*x + c)^8 - 5544*d*cosh(d*x + c)^6 + 3150*d*cosh(d*x + c)^4 - 560*d*cosh(d*x + c)^2 + 15*d)*sinh(d*x + c)^6 + 2*(1001*d*cosh(d*x + c)^9 - 2376*d*cosh(d*x + c)^7 + 1890*d*cosh(d*x + c)^5 - 560*d*cosh(d*x + c)^3 + 45*d*cosh(d*x + c))*sinh(d*x + c)^5 - 6*d*cosh(d*x + c)^4 + (1001*d*cosh(d*x + c)^10 - 2970*d*cosh(d*x + c)^8 + 3150*d*cosh(d*x + c)^6 - 1400*d*cosh(d*x + c)^4 + 225*d*cosh(d*x + c)^2 - 6*d)*sinh(d*x + c)^4 + 4*(91*d*cosh(d*x + c)^11 - 330*d*cosh(d*x + c)^9 + 450*d*cosh(d*x + c)^7 - 280*d*cosh(d*x + c)^5 + 75*d*cosh(d*x + c)^3 - 6*d*cosh(d*x + c))*sinh(d*x + c)^3 + d*cosh(d*x + c)^2 + (91*d*cosh(d*x + c)^12 - 396*d*cosh(d*x + c)^10 + 675*d*cosh(d*x + c)^8 - 560*d*cosh(d*x + c)^6 + 225*d*cosh(d*x + c)^4 - 36*d*cosh(d*x + c)^2 + d)*sinh(d*x + c)^2 + 2*(7*d*cosh(d*x + c)^13 - 36*d*cosh(d*x + c)^11 + 75*d*cosh(d*x + c)^9 - 80*d*cosh(d*x + c)^7 + 45*d*cosh(d*x + c)^5 - 12*d*cosh(d*x + c)^3 + d*cosh(d*x + c))*sinh(d*x + c))","B",0
171,-1,0,0,0.000000," ","integrate(sinh(d*x+c)^6/(a+b*sinh(d*x+c)^3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
172,-1,0,0,0.000000," ","integrate(sinh(d*x+c)^5/(a+b*sinh(d*x+c)^3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
173,-1,0,0,0.000000," ","integrate(sinh(d*x+c)^4/(a+b*sinh(d*x+c)^3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
174,-1,0,0,0.000000," ","integrate(sinh(d*x+c)^3/(a+b*sinh(d*x+c)^3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
175,-1,0,0,0.000000," ","integrate(sinh(d*x+c)^2/(a+b*sinh(d*x+c)^3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
176,-1,0,0,0.000000," ","integrate(sinh(d*x+c)/(a+b*sinh(d*x+c)^3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
177,-1,0,0,0.000000," ","integrate(1/(a+b*sinh(d*x+c)^3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
178,-1,0,0,0.000000," ","integrate(csch(d*x+c)/(a+b*sinh(d*x+c)^3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
179,-1,0,0,0.000000," ","integrate(csch(d*x+c)^2/(a+b*sinh(d*x+c)^3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
180,-1,0,0,0.000000," ","integrate(csch(d*x+c)^3/(a+b*sinh(d*x+c)^3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
181,-1,0,0,0.000000," ","integrate(csch(d*x+c)^4/(a+b*sinh(d*x+c)^3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
182,1,185,0,0.900107," ","integrate(1/(1+sinh(x)^3),x, algorithm=""fricas"")","-\frac{1}{6} \, \sqrt{3} \log\left(-4 \, {\left(\sqrt{3} + 1\right)} e^{x} + 4 \, \sqrt{3} + 4 \, e^{\left(2 \, x\right)} + 8\right) + \frac{1}{6} \, \sqrt{3} \log\left(4 \, {\left(\sqrt{3} - 1\right)} e^{x} - 4 \, \sqrt{3} + 4 \, e^{\left(2 \, x\right)} + 8\right) + \frac{1}{6} \, \sqrt{2} \log\left(-\frac{2 \, {\left(\sqrt{2} - 1\right)} e^{x} + 2 \, \sqrt{2} - e^{\left(2 \, x\right)} - 3}{e^{\left(2 \, x\right)} + 2 \, e^{x} - 1}\right) + \frac{2}{3} \, \arctan\left(-{\left(\sqrt{3} + 1\right)} e^{x} + \sqrt{{\left(\sqrt{3} - 1\right)} e^{x} - \sqrt{3} + e^{\left(2 \, x\right)} + 2} {\left(\sqrt{3} + 1\right)} - 1\right) - \frac{2}{3} \, \arctan\left(-{\left(\sqrt{3} - 1\right)} e^{x} + \frac{1}{2} \, \sqrt{-4 \, {\left(\sqrt{3} + 1\right)} e^{x} + 4 \, \sqrt{3} + 4 \, e^{\left(2 \, x\right)} + 8} {\left(\sqrt{3} - 1\right)} + 1\right)"," ",0,"-1/6*sqrt(3)*log(-4*(sqrt(3) + 1)*e^x + 4*sqrt(3) + 4*e^(2*x) + 8) + 1/6*sqrt(3)*log(4*(sqrt(3) - 1)*e^x - 4*sqrt(3) + 4*e^(2*x) + 8) + 1/6*sqrt(2)*log(-(2*(sqrt(2) - 1)*e^x + 2*sqrt(2) - e^(2*x) - 3)/(e^(2*x) + 2*e^x - 1)) + 2/3*arctan(-(sqrt(3) + 1)*e^x + sqrt((sqrt(3) - 1)*e^x - sqrt(3) + e^(2*x) + 2)*(sqrt(3) + 1) - 1) - 2/3*arctan(-(sqrt(3) - 1)*e^x + 1/2*sqrt(-4*(sqrt(3) + 1)*e^x + 4*sqrt(3) + 4*e^(2*x) + 8)*(sqrt(3) - 1) + 1)","B",0
183,1,180,0,1.480596," ","integrate(1/(1-sinh(x)^3),x, algorithm=""fricas"")","-\frac{1}{6} \, \sqrt{3} \log\left(4 \, {\left(\sqrt{3} + 1\right)} e^{x} + 4 \, \sqrt{3} + 4 \, e^{\left(2 \, x\right)} + 8\right) + \frac{1}{6} \, \sqrt{3} \log\left(-4 \, {\left(\sqrt{3} - 1\right)} e^{x} - 4 \, \sqrt{3} + 4 \, e^{\left(2 \, x\right)} + 8\right) + \frac{1}{6} \, \sqrt{2} \log\left(\frac{2 \, {\left(\sqrt{2} - 1\right)} e^{x} - 2 \, \sqrt{2} + e^{\left(2 \, x\right)} + 3}{e^{\left(2 \, x\right)} - 2 \, e^{x} - 1}\right) - \frac{2}{3} \, \arctan\left(-{\left(\sqrt{3} + 1\right)} e^{x} + \frac{1}{2} \, \sqrt{-4 \, {\left(\sqrt{3} - 1\right)} e^{x} - 4 \, \sqrt{3} + 4 \, e^{\left(2 \, x\right)} + 8} {\left(\sqrt{3} + 1\right)} + 1\right) + \frac{2}{3} \, \arctan\left(-{\left(\sqrt{3} - 1\right)} e^{x} + \sqrt{{\left(\sqrt{3} + 1\right)} e^{x} + \sqrt{3} + e^{\left(2 \, x\right)} + 2} {\left(\sqrt{3} - 1\right)} - 1\right)"," ",0,"-1/6*sqrt(3)*log(4*(sqrt(3) + 1)*e^x + 4*sqrt(3) + 4*e^(2*x) + 8) + 1/6*sqrt(3)*log(-4*(sqrt(3) - 1)*e^x - 4*sqrt(3) + 4*e^(2*x) + 8) + 1/6*sqrt(2)*log((2*(sqrt(2) - 1)*e^x - 2*sqrt(2) + e^(2*x) + 3)/(e^(2*x) - 2*e^x - 1)) - 2/3*arctan(-(sqrt(3) + 1)*e^x + 1/2*sqrt(-4*(sqrt(3) - 1)*e^x - 4*sqrt(3) + 4*e^(2*x) + 8)*(sqrt(3) + 1) + 1) + 2/3*arctan(-(sqrt(3) - 1)*e^x + sqrt((sqrt(3) + 1)*e^x + sqrt(3) + e^(2*x) + 2)*(sqrt(3) - 1) - 1)","B",0
184,1,174,0,1.074599," ","integrate(sinh(d*x+c)^4*(a+b*sinh(d*x+c)^4),x, algorithm=""fricas"")","\frac{3 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + 3 \, {\left(7 \, b \cosh\left(d x + c\right)^{3} - 8 \, b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + {\left(21 \, b \cosh\left(d x + c\right)^{5} - 80 \, b \cosh\left(d x + c\right)^{3} + 12 \, {\left(4 \, a + 7 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 3 \, {\left(48 \, a + 35 \, b\right)} d x + 3 \, {\left(b \cosh\left(d x + c\right)^{7} - 8 \, b \cosh\left(d x + c\right)^{5} + 4 \, {\left(4 \, a + 7 \, b\right)} \cosh\left(d x + c\right)^{3} - 8 \, {\left(8 \, a + 7 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{384 \, d}"," ",0,"1/384*(3*b*cosh(d*x + c)*sinh(d*x + c)^7 + 3*(7*b*cosh(d*x + c)^3 - 8*b*cosh(d*x + c))*sinh(d*x + c)^5 + (21*b*cosh(d*x + c)^5 - 80*b*cosh(d*x + c)^3 + 12*(4*a + 7*b)*cosh(d*x + c))*sinh(d*x + c)^3 + 3*(48*a + 35*b)*d*x + 3*(b*cosh(d*x + c)^7 - 8*b*cosh(d*x + c)^5 + 4*(4*a + 7*b)*cosh(d*x + c)^3 - 8*(8*a + 7*b)*cosh(d*x + c))*sinh(d*x + c))/d","A",0
185,1,155,0,1.813499," ","integrate(sinh(d*x+c)^3*(a+b*sinh(d*x+c)^4),x, algorithm=""fricas"")","\frac{15 \, b \cosh\left(d x + c\right)^{7} + 105 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} - 147 \, b \cosh\left(d x + c\right)^{5} + 105 \, {\left(5 \, b \cosh\left(d x + c\right)^{3} - 7 \, b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 35 \, {\left(16 \, a + 21 \, b\right)} \cosh\left(d x + c\right)^{3} + 105 \, {\left(3 \, b \cosh\left(d x + c\right)^{5} - 14 \, b \cosh\left(d x + c\right)^{3} + {\left(16 \, a + 21 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 105 \, {\left(48 \, a + 35 \, b\right)} \cosh\left(d x + c\right)}{6720 \, d}"," ",0,"1/6720*(15*b*cosh(d*x + c)^7 + 105*b*cosh(d*x + c)*sinh(d*x + c)^6 - 147*b*cosh(d*x + c)^5 + 105*(5*b*cosh(d*x + c)^3 - 7*b*cosh(d*x + c))*sinh(d*x + c)^4 + 35*(16*a + 21*b)*cosh(d*x + c)^3 + 105*(3*b*cosh(d*x + c)^5 - 14*b*cosh(d*x + c)^3 + (16*a + 21*b)*cosh(d*x + c))*sinh(d*x + c)^2 - 105*(48*a + 35*b)*cosh(d*x + c))/d","B",0
186,1,109,0,3.299822," ","integrate(sinh(d*x+c)^2*(a+b*sinh(d*x+c)^4),x, algorithm=""fricas"")","\frac{3 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + 2 \, {\left(5 \, b \cosh\left(d x + c\right)^{3} - 9 \, b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 6 \, {\left(8 \, a + 5 \, b\right)} d x + 3 \, {\left(b \cosh\left(d x + c\right)^{5} - 6 \, b \cosh\left(d x + c\right)^{3} + {\left(16 \, a + 15 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{96 \, d}"," ",0,"1/96*(3*b*cosh(d*x + c)*sinh(d*x + c)^5 + 2*(5*b*cosh(d*x + c)^3 - 9*b*cosh(d*x + c))*sinh(d*x + c)^3 - 6*(8*a + 5*b)*d*x + 3*(b*cosh(d*x + c)^5 - 6*b*cosh(d*x + c)^3 + (16*a + 15*b)*cosh(d*x + c))*sinh(d*x + c))/d","A",0
187,1,91,0,0.796503," ","integrate(sinh(d*x+c)*(a+b*sinh(d*x+c)^4),x, algorithm=""fricas"")","\frac{3 \, b \cosh\left(d x + c\right)^{5} + 15 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} - 25 \, b \cosh\left(d x + c\right)^{3} + 15 \, {\left(2 \, b \cosh\left(d x + c\right)^{3} - 5 \, b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 30 \, {\left(8 \, a + 5 \, b\right)} \cosh\left(d x + c\right)}{240 \, d}"," ",0,"1/240*(3*b*cosh(d*x + c)^5 + 15*b*cosh(d*x + c)*sinh(d*x + c)^4 - 25*b*cosh(d*x + c)^3 + 15*(2*b*cosh(d*x + c)^3 - 5*b*cosh(d*x + c))*sinh(d*x + c)^2 + 30*(8*a + 5*b)*cosh(d*x + c))/d","B",0
188,1,59,0,0.652020," ","integrate(a+b*sinh(d*x+c)^4,x, algorithm=""fricas"")","\frac{b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(8 \, a + 3 \, b\right)} d x + {\left(b \cosh\left(d x + c\right)^{3} - 4 \, b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{8 \, d}"," ",0,"1/8*(b*cosh(d*x + c)*sinh(d*x + c)^3 + (8*a + 3*b)*d*x + (b*cosh(d*x + c)^3 - 4*b*cosh(d*x + c))*sinh(d*x + c))/d","A",0
189,1,395,0,3.137632," ","integrate(csch(d*x+c)*(a+b*sinh(d*x+c)^4),x, algorithm=""fricas"")","\frac{b \cosh\left(d x + c\right)^{6} + 6 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + b \sinh\left(d x + c\right)^{6} - 9 \, b \cosh\left(d x + c\right)^{4} + 3 \, {\left(5 \, b \cosh\left(d x + c\right)^{2} - 3 \, b\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, b \cosh\left(d x + c\right)^{3} - 9 \, b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 9 \, b \cosh\left(d x + c\right)^{2} + 3 \, {\left(5 \, b \cosh\left(d x + c\right)^{4} - 18 \, b \cosh\left(d x + c\right)^{2} - 3 \, b\right)} \sinh\left(d x + c\right)^{2} - 24 \, {\left(a \cosh\left(d x + c\right)^{3} + 3 \, a \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{3}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) + 24 \, {\left(a \cosh\left(d x + c\right)^{3} + 3 \, a \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{3}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) + 6 \, {\left(b \cosh\left(d x + c\right)^{5} - 6 \, b \cosh\left(d x + c\right)^{3} - 3 \, b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b}{24 \, {\left(d \cosh\left(d x + c\right)^{3} + 3 \, d \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + d \sinh\left(d x + c\right)^{3}\right)}}"," ",0,"1/24*(b*cosh(d*x + c)^6 + 6*b*cosh(d*x + c)*sinh(d*x + c)^5 + b*sinh(d*x + c)^6 - 9*b*cosh(d*x + c)^4 + 3*(5*b*cosh(d*x + c)^2 - 3*b)*sinh(d*x + c)^4 + 4*(5*b*cosh(d*x + c)^3 - 9*b*cosh(d*x + c))*sinh(d*x + c)^3 - 9*b*cosh(d*x + c)^2 + 3*(5*b*cosh(d*x + c)^4 - 18*b*cosh(d*x + c)^2 - 3*b)*sinh(d*x + c)^2 - 24*(a*cosh(d*x + c)^3 + 3*a*cosh(d*x + c)^2*sinh(d*x + c) + 3*a*cosh(d*x + c)*sinh(d*x + c)^2 + a*sinh(d*x + c)^3)*log(cosh(d*x + c) + sinh(d*x + c) + 1) + 24*(a*cosh(d*x + c)^3 + 3*a*cosh(d*x + c)^2*sinh(d*x + c) + 3*a*cosh(d*x + c)*sinh(d*x + c)^2 + a*sinh(d*x + c)^3)*log(cosh(d*x + c) + sinh(d*x + c) - 1) + 6*(b*cosh(d*x + c)^5 - 6*b*cosh(d*x + c)^3 - 3*b*cosh(d*x + c))*sinh(d*x + c) + b)/(d*cosh(d*x + c)^3 + 3*d*cosh(d*x + c)^2*sinh(d*x + c) + 3*d*cosh(d*x + c)*sinh(d*x + c)^2 + d*sinh(d*x + c)^3)","B",0
190,1,70,0,0.803119," ","integrate(csch(d*x+c)^2*(a+b*sinh(d*x+c)^4),x, algorithm=""fricas"")","\frac{b \cosh\left(d x + c\right)^{3} + 3 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} - {\left(8 \, a + b\right)} \cosh\left(d x + c\right) - 4 \, {\left(b d x - 2 \, a\right)} \sinh\left(d x + c\right)}{8 \, d \sinh\left(d x + c\right)}"," ",0,"1/8*(b*cosh(d*x + c)^3 + 3*b*cosh(d*x + c)*sinh(d*x + c)^2 - (8*a + b)*cosh(d*x + c) - 4*(b*d*x - 2*a)*sinh(d*x + c))/(d*sinh(d*x + c))","A",0
191,1,690,0,1.584626," ","integrate(csch(d*x+c)^3*(a+b*sinh(d*x+c)^4),x, algorithm=""fricas"")","\frac{b \cosh\left(d x + c\right)^{6} + 6 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + b \sinh\left(d x + c\right)^{6} - {\left(2 \, a + b\right)} \cosh\left(d x + c\right)^{4} + {\left(15 \, b \cosh\left(d x + c\right)^{2} - 2 \, a - b\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, b \cosh\left(d x + c\right)^{3} - {\left(2 \, a + b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - {\left(2 \, a + b\right)} \cosh\left(d x + c\right)^{2} + {\left(15 \, b \cosh\left(d x + c\right)^{4} - 6 \, {\left(2 \, a + b\right)} \cosh\left(d x + c\right)^{2} - 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + {\left(a \cosh\left(d x + c\right)^{5} + 5 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} + a \sinh\left(d x + c\right)^{5} - 2 \, a \cosh\left(d x + c\right)^{3} + 2 \, {\left(5 \, a \cosh\left(d x + c\right)^{2} - a\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(5 \, a \cosh\left(d x + c\right)^{3} - 3 \, a \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + a \cosh\left(d x + c\right) + {\left(5 \, a \cosh\left(d x + c\right)^{4} - 6 \, a \cosh\left(d x + c\right)^{2} + a\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) - {\left(a \cosh\left(d x + c\right)^{5} + 5 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} + a \sinh\left(d x + c\right)^{5} - 2 \, a \cosh\left(d x + c\right)^{3} + 2 \, {\left(5 \, a \cosh\left(d x + c\right)^{2} - a\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(5 \, a \cosh\left(d x + c\right)^{3} - 3 \, a \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + a \cosh\left(d x + c\right) + {\left(5 \, a \cosh\left(d x + c\right)^{4} - 6 \, a \cosh\left(d x + c\right)^{2} + a\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{5} - 2 \, {\left(2 \, a + b\right)} \cosh\left(d x + c\right)^{3} - {\left(2 \, a + b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b}{2 \, {\left(d \cosh\left(d x + c\right)^{5} + 5 \, d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} + d \sinh\left(d x + c\right)^{5} - 2 \, d \cosh\left(d x + c\right)^{3} + 2 \, {\left(5 \, d \cosh\left(d x + c\right)^{2} - d\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(5 \, d \cosh\left(d x + c\right)^{3} - 3 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + d \cosh\left(d x + c\right) + {\left(5 \, d \cosh\left(d x + c\right)^{4} - 6 \, d \cosh\left(d x + c\right)^{2} + d\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"1/2*(b*cosh(d*x + c)^6 + 6*b*cosh(d*x + c)*sinh(d*x + c)^5 + b*sinh(d*x + c)^6 - (2*a + b)*cosh(d*x + c)^4 + (15*b*cosh(d*x + c)^2 - 2*a - b)*sinh(d*x + c)^4 + 4*(5*b*cosh(d*x + c)^3 - (2*a + b)*cosh(d*x + c))*sinh(d*x + c)^3 - (2*a + b)*cosh(d*x + c)^2 + (15*b*cosh(d*x + c)^4 - 6*(2*a + b)*cosh(d*x + c)^2 - 2*a - b)*sinh(d*x + c)^2 + (a*cosh(d*x + c)^5 + 5*a*cosh(d*x + c)*sinh(d*x + c)^4 + a*sinh(d*x + c)^5 - 2*a*cosh(d*x + c)^3 + 2*(5*a*cosh(d*x + c)^2 - a)*sinh(d*x + c)^3 + 2*(5*a*cosh(d*x + c)^3 - 3*a*cosh(d*x + c))*sinh(d*x + c)^2 + a*cosh(d*x + c) + (5*a*cosh(d*x + c)^4 - 6*a*cosh(d*x + c)^2 + a)*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) + 1) - (a*cosh(d*x + c)^5 + 5*a*cosh(d*x + c)*sinh(d*x + c)^4 + a*sinh(d*x + c)^5 - 2*a*cosh(d*x + c)^3 + 2*(5*a*cosh(d*x + c)^2 - a)*sinh(d*x + c)^3 + 2*(5*a*cosh(d*x + c)^3 - 3*a*cosh(d*x + c))*sinh(d*x + c)^2 + a*cosh(d*x + c) + (5*a*cosh(d*x + c)^4 - 6*a*cosh(d*x + c)^2 + a)*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) - 1) + 2*(3*b*cosh(d*x + c)^5 - 2*(2*a + b)*cosh(d*x + c)^3 - (2*a + b)*cosh(d*x + c))*sinh(d*x + c) + b)/(d*cosh(d*x + c)^5 + 5*d*cosh(d*x + c)*sinh(d*x + c)^4 + d*sinh(d*x + c)^5 - 2*d*cosh(d*x + c)^3 + 2*(5*d*cosh(d*x + c)^2 - d)*sinh(d*x + c)^3 + 2*(5*d*cosh(d*x + c)^3 - 3*d*cosh(d*x + c))*sinh(d*x + c)^2 + d*cosh(d*x + c) + (5*d*cosh(d*x + c)^4 - 6*d*cosh(d*x + c)^2 + d)*sinh(d*x + c))","B",0
192,1,129,0,0.732825," ","integrate(csch(d*x+c)^4*(a+b*sinh(d*x+c)^4),x, algorithm=""fricas"")","\frac{2 \, a \cosh\left(d x + c\right)^{3} + 6 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + {\left(3 \, b d x - 2 \, a\right)} \sinh\left(d x + c\right)^{3} - 6 \, a \cosh\left(d x + c\right) - 3 \, {\left(3 \, b d x - {\left(3 \, b d x - 2 \, a\right)} \cosh\left(d x + c\right)^{2} - 2 \, a\right)} \sinh\left(d x + c\right)}{3 \, {\left(d \sinh\left(d x + c\right)^{3} + 3 \, {\left(d \cosh\left(d x + c\right)^{2} - d\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"1/3*(2*a*cosh(d*x + c)^3 + 6*a*cosh(d*x + c)*sinh(d*x + c)^2 + (3*b*d*x - 2*a)*sinh(d*x + c)^3 - 6*a*cosh(d*x + c) - 3*(3*b*d*x - (3*b*d*x - 2*a)*cosh(d*x + c)^2 - 2*a)*sinh(d*x + c))/(d*sinh(d*x + c)^3 + 3*(d*cosh(d*x + c)^2 - d)*sinh(d*x + c))","B",0
193,1,1476,0,0.579308," ","integrate(csch(d*x+c)^5*(a+b*sinh(d*x+c)^4),x, algorithm=""fricas"")","\frac{6 \, a \cosh\left(d x + c\right)^{7} + 42 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + 6 \, a \sinh\left(d x + c\right)^{7} - 22 \, a \cosh\left(d x + c\right)^{5} + 2 \, {\left(63 \, a \cosh\left(d x + c\right)^{2} - 11 \, a\right)} \sinh\left(d x + c\right)^{5} + 10 \, {\left(21 \, a \cosh\left(d x + c\right)^{3} - 11 \, a \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} - 22 \, a \cosh\left(d x + c\right)^{3} + 2 \, {\left(105 \, a \cosh\left(d x + c\right)^{4} - 110 \, a \cosh\left(d x + c\right)^{2} - 11 \, a\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(63 \, a \cosh\left(d x + c\right)^{5} - 110 \, a \cosh\left(d x + c\right)^{3} - 33 \, a \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 6 \, a \cosh\left(d x + c\right) - {\left({\left(3 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(3 \, a + 8 \, b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(3 \, a + 8 \, b\right)} \sinh\left(d x + c\right)^{8} - 4 \, {\left(3 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(3 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{2} - 3 \, a - 8 \, b\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(3 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(3 \, a + 8 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 6 \, {\left(3 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(3 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{4} - 30 \, {\left(3 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{2} + 9 \, a + 24 \, b\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(3 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{5} - 10 \, {\left(3 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(3 \, a + 8 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 4 \, {\left(3 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(3 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{6} - 15 \, {\left(3 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{4} + 9 \, {\left(3 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{2} - 3 \, a - 8 \, b\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left({\left(3 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{7} - 3 \, {\left(3 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{5} + 3 \, {\left(3 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{3} - {\left(3 \, a + 8 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + 3 \, a + 8 \, b\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) + {\left({\left(3 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(3 \, a + 8 \, b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(3 \, a + 8 \, b\right)} \sinh\left(d x + c\right)^{8} - 4 \, {\left(3 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(3 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{2} - 3 \, a - 8 \, b\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(3 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(3 \, a + 8 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 6 \, {\left(3 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(3 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{4} - 30 \, {\left(3 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{2} + 9 \, a + 24 \, b\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(3 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{5} - 10 \, {\left(3 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(3 \, a + 8 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 4 \, {\left(3 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(3 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{6} - 15 \, {\left(3 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{4} + 9 \, {\left(3 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{2} - 3 \, a - 8 \, b\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left({\left(3 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{7} - 3 \, {\left(3 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{5} + 3 \, {\left(3 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{3} - {\left(3 \, a + 8 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + 3 \, a + 8 \, b\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) + 2 \, {\left(21 \, a \cosh\left(d x + c\right)^{6} - 55 \, a \cosh\left(d x + c\right)^{4} - 33 \, a \cosh\left(d x + c\right)^{2} + 3 \, a\right)} \sinh\left(d x + c\right)}{8 \, {\left(d \cosh\left(d x + c\right)^{8} + 8 \, d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + d \sinh\left(d x + c\right)^{8} - 4 \, d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, d \cosh\left(d x + c\right)^{2} - d\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, d \cosh\left(d x + c\right)^{3} - 3 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 6 \, d \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, d \cosh\left(d x + c\right)^{4} - 30 \, d \cosh\left(d x + c\right)^{2} + 3 \, d\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, d \cosh\left(d x + c\right)^{5} - 10 \, d \cosh\left(d x + c\right)^{3} + 3 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 4 \, d \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, d \cosh\left(d x + c\right)^{6} - 15 \, d \cosh\left(d x + c\right)^{4} + 9 \, d \cosh\left(d x + c\right)^{2} - d\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left(d \cosh\left(d x + c\right)^{7} - 3 \, d \cosh\left(d x + c\right)^{5} + 3 \, d \cosh\left(d x + c\right)^{3} - d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + d\right)}}"," ",0,"1/8*(6*a*cosh(d*x + c)^7 + 42*a*cosh(d*x + c)*sinh(d*x + c)^6 + 6*a*sinh(d*x + c)^7 - 22*a*cosh(d*x + c)^5 + 2*(63*a*cosh(d*x + c)^2 - 11*a)*sinh(d*x + c)^5 + 10*(21*a*cosh(d*x + c)^3 - 11*a*cosh(d*x + c))*sinh(d*x + c)^4 - 22*a*cosh(d*x + c)^3 + 2*(105*a*cosh(d*x + c)^4 - 110*a*cosh(d*x + c)^2 - 11*a)*sinh(d*x + c)^3 + 2*(63*a*cosh(d*x + c)^5 - 110*a*cosh(d*x + c)^3 - 33*a*cosh(d*x + c))*sinh(d*x + c)^2 + 6*a*cosh(d*x + c) - ((3*a + 8*b)*cosh(d*x + c)^8 + 8*(3*a + 8*b)*cosh(d*x + c)*sinh(d*x + c)^7 + (3*a + 8*b)*sinh(d*x + c)^8 - 4*(3*a + 8*b)*cosh(d*x + c)^6 + 4*(7*(3*a + 8*b)*cosh(d*x + c)^2 - 3*a - 8*b)*sinh(d*x + c)^6 + 8*(7*(3*a + 8*b)*cosh(d*x + c)^3 - 3*(3*a + 8*b)*cosh(d*x + c))*sinh(d*x + c)^5 + 6*(3*a + 8*b)*cosh(d*x + c)^4 + 2*(35*(3*a + 8*b)*cosh(d*x + c)^4 - 30*(3*a + 8*b)*cosh(d*x + c)^2 + 9*a + 24*b)*sinh(d*x + c)^4 + 8*(7*(3*a + 8*b)*cosh(d*x + c)^5 - 10*(3*a + 8*b)*cosh(d*x + c)^3 + 3*(3*a + 8*b)*cosh(d*x + c))*sinh(d*x + c)^3 - 4*(3*a + 8*b)*cosh(d*x + c)^2 + 4*(7*(3*a + 8*b)*cosh(d*x + c)^6 - 15*(3*a + 8*b)*cosh(d*x + c)^4 + 9*(3*a + 8*b)*cosh(d*x + c)^2 - 3*a - 8*b)*sinh(d*x + c)^2 + 8*((3*a + 8*b)*cosh(d*x + c)^7 - 3*(3*a + 8*b)*cosh(d*x + c)^5 + 3*(3*a + 8*b)*cosh(d*x + c)^3 - (3*a + 8*b)*cosh(d*x + c))*sinh(d*x + c) + 3*a + 8*b)*log(cosh(d*x + c) + sinh(d*x + c) + 1) + ((3*a + 8*b)*cosh(d*x + c)^8 + 8*(3*a + 8*b)*cosh(d*x + c)*sinh(d*x + c)^7 + (3*a + 8*b)*sinh(d*x + c)^8 - 4*(3*a + 8*b)*cosh(d*x + c)^6 + 4*(7*(3*a + 8*b)*cosh(d*x + c)^2 - 3*a - 8*b)*sinh(d*x + c)^6 + 8*(7*(3*a + 8*b)*cosh(d*x + c)^3 - 3*(3*a + 8*b)*cosh(d*x + c))*sinh(d*x + c)^5 + 6*(3*a + 8*b)*cosh(d*x + c)^4 + 2*(35*(3*a + 8*b)*cosh(d*x + c)^4 - 30*(3*a + 8*b)*cosh(d*x + c)^2 + 9*a + 24*b)*sinh(d*x + c)^4 + 8*(7*(3*a + 8*b)*cosh(d*x + c)^5 - 10*(3*a + 8*b)*cosh(d*x + c)^3 + 3*(3*a + 8*b)*cosh(d*x + c))*sinh(d*x + c)^3 - 4*(3*a + 8*b)*cosh(d*x + c)^2 + 4*(7*(3*a + 8*b)*cosh(d*x + c)^6 - 15*(3*a + 8*b)*cosh(d*x + c)^4 + 9*(3*a + 8*b)*cosh(d*x + c)^2 - 3*a - 8*b)*sinh(d*x + c)^2 + 8*((3*a + 8*b)*cosh(d*x + c)^7 - 3*(3*a + 8*b)*cosh(d*x + c)^5 + 3*(3*a + 8*b)*cosh(d*x + c)^3 - (3*a + 8*b)*cosh(d*x + c))*sinh(d*x + c) + 3*a + 8*b)*log(cosh(d*x + c) + sinh(d*x + c) - 1) + 2*(21*a*cosh(d*x + c)^6 - 55*a*cosh(d*x + c)^4 - 33*a*cosh(d*x + c)^2 + 3*a)*sinh(d*x + c))/(d*cosh(d*x + c)^8 + 8*d*cosh(d*x + c)*sinh(d*x + c)^7 + d*sinh(d*x + c)^8 - 4*d*cosh(d*x + c)^6 + 4*(7*d*cosh(d*x + c)^2 - d)*sinh(d*x + c)^6 + 8*(7*d*cosh(d*x + c)^3 - 3*d*cosh(d*x + c))*sinh(d*x + c)^5 + 6*d*cosh(d*x + c)^4 + 2*(35*d*cosh(d*x + c)^4 - 30*d*cosh(d*x + c)^2 + 3*d)*sinh(d*x + c)^4 + 8*(7*d*cosh(d*x + c)^5 - 10*d*cosh(d*x + c)^3 + 3*d*cosh(d*x + c))*sinh(d*x + c)^3 - 4*d*cosh(d*x + c)^2 + 4*(7*d*cosh(d*x + c)^6 - 15*d*cosh(d*x + c)^4 + 9*d*cosh(d*x + c)^2 - d)*sinh(d*x + c)^2 + 8*(d*cosh(d*x + c)^7 - 3*d*cosh(d*x + c)^5 + 3*d*cosh(d*x + c)^3 - d*cosh(d*x + c))*sinh(d*x + c) + d)","B",0
194,1,333,0,0.794380," ","integrate(csch(d*x+c)^6*(a+b*sinh(d*x+c)^4),x, algorithm=""fricas"")","-\frac{4 \, {\left({\left(4 \, a + 15 \, b\right)} \cosh\left(d x + c\right)^{4} - 16 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(4 \, a + 15 \, b\right)} \sinh\left(d x + c\right)^{4} - 20 \, {\left(a + 3 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(4 \, a + 15 \, b\right)} \cosh\left(d x + c\right)^{2} - 10 \, a - 30 \, b\right)} \sinh\left(d x + c\right)^{2} - 8 \, {\left(2 \, a \cosh\left(d x + c\right)^{3} - 5 \, a \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + 40 \, a + 45 \, b\right)}}{15 \, {\left(d \cosh\left(d x + c\right)^{6} + 6 \, d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + d \sinh\left(d x + c\right)^{6} - 6 \, d \cosh\left(d x + c\right)^{4} + 3 \, {\left(5 \, d \cosh\left(d x + c\right)^{2} - 2 \, d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, d \cosh\left(d x + c\right)^{3} - 4 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 15 \, d \cosh\left(d x + c\right)^{2} + 3 \, {\left(5 \, d \cosh\left(d x + c\right)^{4} - 12 \, d \cosh\left(d x + c\right)^{2} + 5 \, d\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(3 \, d \cosh\left(d x + c\right)^{5} - 8 \, d \cosh\left(d x + c\right)^{3} + 5 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) - 10 \, d\right)}}"," ",0,"-4/15*((4*a + 15*b)*cosh(d*x + c)^4 - 16*a*cosh(d*x + c)*sinh(d*x + c)^3 + (4*a + 15*b)*sinh(d*x + c)^4 - 20*(a + 3*b)*cosh(d*x + c)^2 + 2*(3*(4*a + 15*b)*cosh(d*x + c)^2 - 10*a - 30*b)*sinh(d*x + c)^2 - 8*(2*a*cosh(d*x + c)^3 - 5*a*cosh(d*x + c))*sinh(d*x + c) + 40*a + 45*b)/(d*cosh(d*x + c)^6 + 6*d*cosh(d*x + c)*sinh(d*x + c)^5 + d*sinh(d*x + c)^6 - 6*d*cosh(d*x + c)^4 + 3*(5*d*cosh(d*x + c)^2 - 2*d)*sinh(d*x + c)^4 + 4*(5*d*cosh(d*x + c)^3 - 4*d*cosh(d*x + c))*sinh(d*x + c)^3 + 15*d*cosh(d*x + c)^2 + 3*(5*d*cosh(d*x + c)^4 - 12*d*cosh(d*x + c)^2 + 5*d)*sinh(d*x + c)^2 + 2*(3*d*cosh(d*x + c)^5 - 8*d*cosh(d*x + c)^3 + 5*d*cosh(d*x + c))*sinh(d*x + c) - 10*d)","B",0
195,1,3115,0,2.013681," ","integrate(csch(d*x+c)^7*(a+b*sinh(d*x+c)^4),x, algorithm=""fricas"")","-\frac{6 \, {\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{11} + 66 \, {\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{10} + 6 \, {\left(5 \, a + 8 \, b\right)} \sinh\left(d x + c\right)^{11} - 2 \, {\left(85 \, a + 72 \, b\right)} \cosh\left(d x + c\right)^{9} + 2 \, {\left(165 \, {\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{2} - 85 \, a - 72 \, b\right)} \sinh\left(d x + c\right)^{9} + 18 \, {\left(55 \, {\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{3} - {\left(85 \, a + 72 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{8} + 12 \, {\left(33 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{7} + 12 \, {\left(165 \, {\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{4} - 6 \, {\left(85 \, a + 72 \, b\right)} \cosh\left(d x + c\right)^{2} + 33 \, a + 8 \, b\right)} \sinh\left(d x + c\right)^{7} + 84 \, {\left(33 \, {\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{5} - 2 \, {\left(85 \, a + 72 \, b\right)} \cosh\left(d x + c\right)^{3} + {\left(33 \, a + 8 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} + 12 \, {\left(33 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{5} + 12 \, {\left(231 \, {\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{6} - 21 \, {\left(85 \, a + 72 \, b\right)} \cosh\left(d x + c\right)^{4} + 21 \, {\left(33 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{2} + 33 \, a + 8 \, b\right)} \sinh\left(d x + c\right)^{5} + 12 \, {\left(165 \, {\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{7} - 21 \, {\left(85 \, a + 72 \, b\right)} \cosh\left(d x + c\right)^{5} + 35 \, {\left(33 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{3} + 5 \, {\left(33 \, a + 8 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(85 \, a + 72 \, b\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(495 \, {\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{8} - 84 \, {\left(85 \, a + 72 \, b\right)} \cosh\left(d x + c\right)^{6} + 210 \, {\left(33 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{4} + 60 \, {\left(33 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{2} - 85 \, a - 72 \, b\right)} \sinh\left(d x + c\right)^{3} + 6 \, {\left(55 \, {\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{9} - 12 \, {\left(85 \, a + 72 \, b\right)} \cosh\left(d x + c\right)^{7} + 42 \, {\left(33 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{5} + 20 \, {\left(33 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{3} - {\left(85 \, a + 72 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 6 \, {\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right) - 3 \, {\left({\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{12} + 12 \, {\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{11} + {\left(5 \, a + 8 \, b\right)} \sinh\left(d x + c\right)^{12} - 6 \, {\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{10} + 6 \, {\left(11 \, {\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{2} - 5 \, a - 8 \, b\right)} \sinh\left(d x + c\right)^{10} + 20 \, {\left(11 \, {\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} + 15 \, {\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{8} + 15 \, {\left(33 \, {\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{4} - 18 \, {\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{2} + 5 \, a + 8 \, b\right)} \sinh\left(d x + c\right)^{8} + 24 \, {\left(33 \, {\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{5} - 30 \, {\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{3} + 5 \, {\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} - 20 \, {\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(231 \, {\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{6} - 315 \, {\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{4} + 105 \, {\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{2} - 25 \, a - 40 \, b\right)} \sinh\left(d x + c\right)^{6} + 24 \, {\left(33 \, {\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{7} - 63 \, {\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{5} + 35 \, {\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{3} - 5 \, {\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 15 \, {\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{4} + 15 \, {\left(33 \, {\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{8} - 84 \, {\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{6} + 70 \, {\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{4} - 20 \, {\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{2} + 5 \, a + 8 \, b\right)} \sinh\left(d x + c\right)^{4} + 20 \, {\left(11 \, {\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{9} - 36 \, {\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{7} + 42 \, {\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{5} - 20 \, {\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 6 \, {\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{2} + 6 \, {\left(11 \, {\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{10} - 45 \, {\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{8} + 70 \, {\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{6} - 50 \, {\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{4} + 15 \, {\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{2} - 5 \, a - 8 \, b\right)} \sinh\left(d x + c\right)^{2} + 12 \, {\left({\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{11} - 5 \, {\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{9} + 10 \, {\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{7} - 10 \, {\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{3} - {\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + 5 \, a + 8 \, b\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) + 3 \, {\left({\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{12} + 12 \, {\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{11} + {\left(5 \, a + 8 \, b\right)} \sinh\left(d x + c\right)^{12} - 6 \, {\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{10} + 6 \, {\left(11 \, {\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{2} - 5 \, a - 8 \, b\right)} \sinh\left(d x + c\right)^{10} + 20 \, {\left(11 \, {\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} + 15 \, {\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{8} + 15 \, {\left(33 \, {\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{4} - 18 \, {\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{2} + 5 \, a + 8 \, b\right)} \sinh\left(d x + c\right)^{8} + 24 \, {\left(33 \, {\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{5} - 30 \, {\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{3} + 5 \, {\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} - 20 \, {\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(231 \, {\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{6} - 315 \, {\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{4} + 105 \, {\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{2} - 25 \, a - 40 \, b\right)} \sinh\left(d x + c\right)^{6} + 24 \, {\left(33 \, {\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{7} - 63 \, {\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{5} + 35 \, {\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{3} - 5 \, {\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 15 \, {\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{4} + 15 \, {\left(33 \, {\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{8} - 84 \, {\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{6} + 70 \, {\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{4} - 20 \, {\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{2} + 5 \, a + 8 \, b\right)} \sinh\left(d x + c\right)^{4} + 20 \, {\left(11 \, {\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{9} - 36 \, {\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{7} + 42 \, {\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{5} - 20 \, {\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 6 \, {\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{2} + 6 \, {\left(11 \, {\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{10} - 45 \, {\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{8} + 70 \, {\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{6} - 50 \, {\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{4} + 15 \, {\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{2} - 5 \, a - 8 \, b\right)} \sinh\left(d x + c\right)^{2} + 12 \, {\left({\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{11} - 5 \, {\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{9} + 10 \, {\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{7} - 10 \, {\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{3} - {\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + 5 \, a + 8 \, b\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) + 6 \, {\left(11 \, {\left(5 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{10} - 3 \, {\left(85 \, a + 72 \, b\right)} \cosh\left(d x + c\right)^{8} + 14 \, {\left(33 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{6} + 10 \, {\left(33 \, a + 8 \, b\right)} \cosh\left(d x + c\right)^{4} - {\left(85 \, a + 72 \, b\right)} \cosh\left(d x + c\right)^{2} + 5 \, a + 8 \, b\right)} \sinh\left(d x + c\right)}{48 \, {\left(d \cosh\left(d x + c\right)^{12} + 12 \, d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{11} + d \sinh\left(d x + c\right)^{12} - 6 \, d \cosh\left(d x + c\right)^{10} + 6 \, {\left(11 \, d \cosh\left(d x + c\right)^{2} - d\right)} \sinh\left(d x + c\right)^{10} + 20 \, {\left(11 \, d \cosh\left(d x + c\right)^{3} - 3 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} + 15 \, d \cosh\left(d x + c\right)^{8} + 15 \, {\left(33 \, d \cosh\left(d x + c\right)^{4} - 18 \, d \cosh\left(d x + c\right)^{2} + d\right)} \sinh\left(d x + c\right)^{8} + 24 \, {\left(33 \, d \cosh\left(d x + c\right)^{5} - 30 \, d \cosh\left(d x + c\right)^{3} + 5 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} - 20 \, d \cosh\left(d x + c\right)^{6} + 4 \, {\left(231 \, d \cosh\left(d x + c\right)^{6} - 315 \, d \cosh\left(d x + c\right)^{4} + 105 \, d \cosh\left(d x + c\right)^{2} - 5 \, d\right)} \sinh\left(d x + c\right)^{6} + 24 \, {\left(33 \, d \cosh\left(d x + c\right)^{7} - 63 \, d \cosh\left(d x + c\right)^{5} + 35 \, d \cosh\left(d x + c\right)^{3} - 5 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 15 \, d \cosh\left(d x + c\right)^{4} + 15 \, {\left(33 \, d \cosh\left(d x + c\right)^{8} - 84 \, d \cosh\left(d x + c\right)^{6} + 70 \, d \cosh\left(d x + c\right)^{4} - 20 \, d \cosh\left(d x + c\right)^{2} + d\right)} \sinh\left(d x + c\right)^{4} + 20 \, {\left(11 \, d \cosh\left(d x + c\right)^{9} - 36 \, d \cosh\left(d x + c\right)^{7} + 42 \, d \cosh\left(d x + c\right)^{5} - 20 \, d \cosh\left(d x + c\right)^{3} + 3 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 6 \, d \cosh\left(d x + c\right)^{2} + 6 \, {\left(11 \, d \cosh\left(d x + c\right)^{10} - 45 \, d \cosh\left(d x + c\right)^{8} + 70 \, d \cosh\left(d x + c\right)^{6} - 50 \, d \cosh\left(d x + c\right)^{4} + 15 \, d \cosh\left(d x + c\right)^{2} - d\right)} \sinh\left(d x + c\right)^{2} + 12 \, {\left(d \cosh\left(d x + c\right)^{11} - 5 \, d \cosh\left(d x + c\right)^{9} + 10 \, d \cosh\left(d x + c\right)^{7} - 10 \, d \cosh\left(d x + c\right)^{5} + 5 \, d \cosh\left(d x + c\right)^{3} - d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + d\right)}}"," ",0,"-1/48*(6*(5*a + 8*b)*cosh(d*x + c)^11 + 66*(5*a + 8*b)*cosh(d*x + c)*sinh(d*x + c)^10 + 6*(5*a + 8*b)*sinh(d*x + c)^11 - 2*(85*a + 72*b)*cosh(d*x + c)^9 + 2*(165*(5*a + 8*b)*cosh(d*x + c)^2 - 85*a - 72*b)*sinh(d*x + c)^9 + 18*(55*(5*a + 8*b)*cosh(d*x + c)^3 - (85*a + 72*b)*cosh(d*x + c))*sinh(d*x + c)^8 + 12*(33*a + 8*b)*cosh(d*x + c)^7 + 12*(165*(5*a + 8*b)*cosh(d*x + c)^4 - 6*(85*a + 72*b)*cosh(d*x + c)^2 + 33*a + 8*b)*sinh(d*x + c)^7 + 84*(33*(5*a + 8*b)*cosh(d*x + c)^5 - 2*(85*a + 72*b)*cosh(d*x + c)^3 + (33*a + 8*b)*cosh(d*x + c))*sinh(d*x + c)^6 + 12*(33*a + 8*b)*cosh(d*x + c)^5 + 12*(231*(5*a + 8*b)*cosh(d*x + c)^6 - 21*(85*a + 72*b)*cosh(d*x + c)^4 + 21*(33*a + 8*b)*cosh(d*x + c)^2 + 33*a + 8*b)*sinh(d*x + c)^5 + 12*(165*(5*a + 8*b)*cosh(d*x + c)^7 - 21*(85*a + 72*b)*cosh(d*x + c)^5 + 35*(33*a + 8*b)*cosh(d*x + c)^3 + 5*(33*a + 8*b)*cosh(d*x + c))*sinh(d*x + c)^4 - 2*(85*a + 72*b)*cosh(d*x + c)^3 + 2*(495*(5*a + 8*b)*cosh(d*x + c)^8 - 84*(85*a + 72*b)*cosh(d*x + c)^6 + 210*(33*a + 8*b)*cosh(d*x + c)^4 + 60*(33*a + 8*b)*cosh(d*x + c)^2 - 85*a - 72*b)*sinh(d*x + c)^3 + 6*(55*(5*a + 8*b)*cosh(d*x + c)^9 - 12*(85*a + 72*b)*cosh(d*x + c)^7 + 42*(33*a + 8*b)*cosh(d*x + c)^5 + 20*(33*a + 8*b)*cosh(d*x + c)^3 - (85*a + 72*b)*cosh(d*x + c))*sinh(d*x + c)^2 + 6*(5*a + 8*b)*cosh(d*x + c) - 3*((5*a + 8*b)*cosh(d*x + c)^12 + 12*(5*a + 8*b)*cosh(d*x + c)*sinh(d*x + c)^11 + (5*a + 8*b)*sinh(d*x + c)^12 - 6*(5*a + 8*b)*cosh(d*x + c)^10 + 6*(11*(5*a + 8*b)*cosh(d*x + c)^2 - 5*a - 8*b)*sinh(d*x + c)^10 + 20*(11*(5*a + 8*b)*cosh(d*x + c)^3 - 3*(5*a + 8*b)*cosh(d*x + c))*sinh(d*x + c)^9 + 15*(5*a + 8*b)*cosh(d*x + c)^8 + 15*(33*(5*a + 8*b)*cosh(d*x + c)^4 - 18*(5*a + 8*b)*cosh(d*x + c)^2 + 5*a + 8*b)*sinh(d*x + c)^8 + 24*(33*(5*a + 8*b)*cosh(d*x + c)^5 - 30*(5*a + 8*b)*cosh(d*x + c)^3 + 5*(5*a + 8*b)*cosh(d*x + c))*sinh(d*x + c)^7 - 20*(5*a + 8*b)*cosh(d*x + c)^6 + 4*(231*(5*a + 8*b)*cosh(d*x + c)^6 - 315*(5*a + 8*b)*cosh(d*x + c)^4 + 105*(5*a + 8*b)*cosh(d*x + c)^2 - 25*a - 40*b)*sinh(d*x + c)^6 + 24*(33*(5*a + 8*b)*cosh(d*x + c)^7 - 63*(5*a + 8*b)*cosh(d*x + c)^5 + 35*(5*a + 8*b)*cosh(d*x + c)^3 - 5*(5*a + 8*b)*cosh(d*x + c))*sinh(d*x + c)^5 + 15*(5*a + 8*b)*cosh(d*x + c)^4 + 15*(33*(5*a + 8*b)*cosh(d*x + c)^8 - 84*(5*a + 8*b)*cosh(d*x + c)^6 + 70*(5*a + 8*b)*cosh(d*x + c)^4 - 20*(5*a + 8*b)*cosh(d*x + c)^2 + 5*a + 8*b)*sinh(d*x + c)^4 + 20*(11*(5*a + 8*b)*cosh(d*x + c)^9 - 36*(5*a + 8*b)*cosh(d*x + c)^7 + 42*(5*a + 8*b)*cosh(d*x + c)^5 - 20*(5*a + 8*b)*cosh(d*x + c)^3 + 3*(5*a + 8*b)*cosh(d*x + c))*sinh(d*x + c)^3 - 6*(5*a + 8*b)*cosh(d*x + c)^2 + 6*(11*(5*a + 8*b)*cosh(d*x + c)^10 - 45*(5*a + 8*b)*cosh(d*x + c)^8 + 70*(5*a + 8*b)*cosh(d*x + c)^6 - 50*(5*a + 8*b)*cosh(d*x + c)^4 + 15*(5*a + 8*b)*cosh(d*x + c)^2 - 5*a - 8*b)*sinh(d*x + c)^2 + 12*((5*a + 8*b)*cosh(d*x + c)^11 - 5*(5*a + 8*b)*cosh(d*x + c)^9 + 10*(5*a + 8*b)*cosh(d*x + c)^7 - 10*(5*a + 8*b)*cosh(d*x + c)^5 + 5*(5*a + 8*b)*cosh(d*x + c)^3 - (5*a + 8*b)*cosh(d*x + c))*sinh(d*x + c) + 5*a + 8*b)*log(cosh(d*x + c) + sinh(d*x + c) + 1) + 3*((5*a + 8*b)*cosh(d*x + c)^12 + 12*(5*a + 8*b)*cosh(d*x + c)*sinh(d*x + c)^11 + (5*a + 8*b)*sinh(d*x + c)^12 - 6*(5*a + 8*b)*cosh(d*x + c)^10 + 6*(11*(5*a + 8*b)*cosh(d*x + c)^2 - 5*a - 8*b)*sinh(d*x + c)^10 + 20*(11*(5*a + 8*b)*cosh(d*x + c)^3 - 3*(5*a + 8*b)*cosh(d*x + c))*sinh(d*x + c)^9 + 15*(5*a + 8*b)*cosh(d*x + c)^8 + 15*(33*(5*a + 8*b)*cosh(d*x + c)^4 - 18*(5*a + 8*b)*cosh(d*x + c)^2 + 5*a + 8*b)*sinh(d*x + c)^8 + 24*(33*(5*a + 8*b)*cosh(d*x + c)^5 - 30*(5*a + 8*b)*cosh(d*x + c)^3 + 5*(5*a + 8*b)*cosh(d*x + c))*sinh(d*x + c)^7 - 20*(5*a + 8*b)*cosh(d*x + c)^6 + 4*(231*(5*a + 8*b)*cosh(d*x + c)^6 - 315*(5*a + 8*b)*cosh(d*x + c)^4 + 105*(5*a + 8*b)*cosh(d*x + c)^2 - 25*a - 40*b)*sinh(d*x + c)^6 + 24*(33*(5*a + 8*b)*cosh(d*x + c)^7 - 63*(5*a + 8*b)*cosh(d*x + c)^5 + 35*(5*a + 8*b)*cosh(d*x + c)^3 - 5*(5*a + 8*b)*cosh(d*x + c))*sinh(d*x + c)^5 + 15*(5*a + 8*b)*cosh(d*x + c)^4 + 15*(33*(5*a + 8*b)*cosh(d*x + c)^8 - 84*(5*a + 8*b)*cosh(d*x + c)^6 + 70*(5*a + 8*b)*cosh(d*x + c)^4 - 20*(5*a + 8*b)*cosh(d*x + c)^2 + 5*a + 8*b)*sinh(d*x + c)^4 + 20*(11*(5*a + 8*b)*cosh(d*x + c)^9 - 36*(5*a + 8*b)*cosh(d*x + c)^7 + 42*(5*a + 8*b)*cosh(d*x + c)^5 - 20*(5*a + 8*b)*cosh(d*x + c)^3 + 3*(5*a + 8*b)*cosh(d*x + c))*sinh(d*x + c)^3 - 6*(5*a + 8*b)*cosh(d*x + c)^2 + 6*(11*(5*a + 8*b)*cosh(d*x + c)^10 - 45*(5*a + 8*b)*cosh(d*x + c)^8 + 70*(5*a + 8*b)*cosh(d*x + c)^6 - 50*(5*a + 8*b)*cosh(d*x + c)^4 + 15*(5*a + 8*b)*cosh(d*x + c)^2 - 5*a - 8*b)*sinh(d*x + c)^2 + 12*((5*a + 8*b)*cosh(d*x + c)^11 - 5*(5*a + 8*b)*cosh(d*x + c)^9 + 10*(5*a + 8*b)*cosh(d*x + c)^7 - 10*(5*a + 8*b)*cosh(d*x + c)^5 + 5*(5*a + 8*b)*cosh(d*x + c)^3 - (5*a + 8*b)*cosh(d*x + c))*sinh(d*x + c) + 5*a + 8*b)*log(cosh(d*x + c) + sinh(d*x + c) - 1) + 6*(11*(5*a + 8*b)*cosh(d*x + c)^10 - 3*(85*a + 72*b)*cosh(d*x + c)^8 + 14*(33*a + 8*b)*cosh(d*x + c)^6 + 10*(33*a + 8*b)*cosh(d*x + c)^4 - (85*a + 72*b)*cosh(d*x + c)^2 + 5*a + 8*b)*sinh(d*x + c))/(d*cosh(d*x + c)^12 + 12*d*cosh(d*x + c)*sinh(d*x + c)^11 + d*sinh(d*x + c)^12 - 6*d*cosh(d*x + c)^10 + 6*(11*d*cosh(d*x + c)^2 - d)*sinh(d*x + c)^10 + 20*(11*d*cosh(d*x + c)^3 - 3*d*cosh(d*x + c))*sinh(d*x + c)^9 + 15*d*cosh(d*x + c)^8 + 15*(33*d*cosh(d*x + c)^4 - 18*d*cosh(d*x + c)^2 + d)*sinh(d*x + c)^8 + 24*(33*d*cosh(d*x + c)^5 - 30*d*cosh(d*x + c)^3 + 5*d*cosh(d*x + c))*sinh(d*x + c)^7 - 20*d*cosh(d*x + c)^6 + 4*(231*d*cosh(d*x + c)^6 - 315*d*cosh(d*x + c)^4 + 105*d*cosh(d*x + c)^2 - 5*d)*sinh(d*x + c)^6 + 24*(33*d*cosh(d*x + c)^7 - 63*d*cosh(d*x + c)^5 + 35*d*cosh(d*x + c)^3 - 5*d*cosh(d*x + c))*sinh(d*x + c)^5 + 15*d*cosh(d*x + c)^4 + 15*(33*d*cosh(d*x + c)^8 - 84*d*cosh(d*x + c)^6 + 70*d*cosh(d*x + c)^4 - 20*d*cosh(d*x + c)^2 + d)*sinh(d*x + c)^4 + 20*(11*d*cosh(d*x + c)^9 - 36*d*cosh(d*x + c)^7 + 42*d*cosh(d*x + c)^5 - 20*d*cosh(d*x + c)^3 + 3*d*cosh(d*x + c))*sinh(d*x + c)^3 - 6*d*cosh(d*x + c)^2 + 6*(11*d*cosh(d*x + c)^10 - 45*d*cosh(d*x + c)^8 + 70*d*cosh(d*x + c)^6 - 50*d*cosh(d*x + c)^4 + 15*d*cosh(d*x + c)^2 - d)*sinh(d*x + c)^2 + 12*(d*cosh(d*x + c)^11 - 5*d*cosh(d*x + c)^9 + 10*d*cosh(d*x + c)^7 - 10*d*cosh(d*x + c)^5 + 5*d*cosh(d*x + c)^3 - d*cosh(d*x + c))*sinh(d*x + c) + d)","B",0
196,1,404,0,0.405100," ","integrate(sinh(d*x+c)^3*(a+b*sinh(d*x+c)^4)^2,x, algorithm=""fricas"")","\frac{315 \, b^{2} \cosh\left(d x + c\right)^{11} + 3465 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{10} - 4235 \, b^{2} \cosh\left(d x + c\right)^{9} + 3465 \, {\left(15 \, b^{2} \cosh\left(d x + c\right)^{3} - 11 \, b^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{8} + 495 \, {\left(32 \, a b + 55 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} + 1155 \, {\left(126 \, b^{2} \cosh\left(d x + c\right)^{5} - 308 \, b^{2} \cosh\left(d x + c\right)^{3} + 3 \, {\left(32 \, a b + 55 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} - 693 \, {\left(224 \, a b + 165 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 3465 \, {\left(30 \, b^{2} \cosh\left(d x + c\right)^{7} - 154 \, b^{2} \cosh\left(d x + c\right)^{5} + 5 \, {\left(32 \, a b + 55 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(224 \, a b + 165 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 2310 \, {\left(128 \, a^{2} + 336 \, a b + 165 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3465 \, {\left(5 \, b^{2} \cosh\left(d x + c\right)^{9} - 44 \, b^{2} \cosh\left(d x + c\right)^{7} + 3 \, {\left(32 \, a b + 55 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} - 2 \, {\left(224 \, a b + 165 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(128 \, a^{2} + 336 \, a b + 165 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 6930 \, {\left(384 \, a^{2} + 560 \, a b + 231 \, b^{2}\right)} \cosh\left(d x + c\right)}{3548160 \, d}"," ",0,"1/3548160*(315*b^2*cosh(d*x + c)^11 + 3465*b^2*cosh(d*x + c)*sinh(d*x + c)^10 - 4235*b^2*cosh(d*x + c)^9 + 3465*(15*b^2*cosh(d*x + c)^3 - 11*b^2*cosh(d*x + c))*sinh(d*x + c)^8 + 495*(32*a*b + 55*b^2)*cosh(d*x + c)^7 + 1155*(126*b^2*cosh(d*x + c)^5 - 308*b^2*cosh(d*x + c)^3 + 3*(32*a*b + 55*b^2)*cosh(d*x + c))*sinh(d*x + c)^6 - 693*(224*a*b + 165*b^2)*cosh(d*x + c)^5 + 3465*(30*b^2*cosh(d*x + c)^7 - 154*b^2*cosh(d*x + c)^5 + 5*(32*a*b + 55*b^2)*cosh(d*x + c)^3 - (224*a*b + 165*b^2)*cosh(d*x + c))*sinh(d*x + c)^4 + 2310*(128*a^2 + 336*a*b + 165*b^2)*cosh(d*x + c)^3 + 3465*(5*b^2*cosh(d*x + c)^9 - 44*b^2*cosh(d*x + c)^7 + 3*(32*a*b + 55*b^2)*cosh(d*x + c)^5 - 2*(224*a*b + 165*b^2)*cosh(d*x + c)^3 + 2*(128*a^2 + 336*a*b + 165*b^2)*cosh(d*x + c))*sinh(d*x + c)^2 - 6930*(384*a^2 + 560*a*b + 231*b^2)*cosh(d*x + c))/d","B",0
197,1,305,0,0.606835," ","integrate(sinh(d*x+c)^2*(a+b*sinh(d*x+c)^4)^2,x, algorithm=""fricas"")","\frac{15 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + 30 \, {\left(6 \, b^{2} \cosh\left(d x + c\right)^{3} - 5 \, b^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 3 \, {\left(126 \, b^{2} \cosh\left(d x + c\right)^{5} - 350 \, b^{2} \cosh\left(d x + c\right)^{3} + 5 \, {\left(32 \, a b + 45 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 10 \, {\left(18 \, b^{2} \cosh\left(d x + c\right)^{7} - 105 \, b^{2} \cosh\left(d x + c\right)^{5} + 5 \, {\left(32 \, a b + 45 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - 36 \, {\left(8 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 30 \, {\left(128 \, a^{2} + 160 \, a b + 63 \, b^{2}\right)} d x + 15 \, {\left(b^{2} \cosh\left(d x + c\right)^{9} - 10 \, b^{2} \cosh\left(d x + c\right)^{7} + {\left(32 \, a b + 45 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} - 24 \, {\left(8 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(128 \, a^{2} + 240 \, a b + 105 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{7680 \, d}"," ",0,"1/7680*(15*b^2*cosh(d*x + c)*sinh(d*x + c)^9 + 30*(6*b^2*cosh(d*x + c)^3 - 5*b^2*cosh(d*x + c))*sinh(d*x + c)^7 + 3*(126*b^2*cosh(d*x + c)^5 - 350*b^2*cosh(d*x + c)^3 + 5*(32*a*b + 45*b^2)*cosh(d*x + c))*sinh(d*x + c)^5 + 10*(18*b^2*cosh(d*x + c)^7 - 105*b^2*cosh(d*x + c)^5 + 5*(32*a*b + 45*b^2)*cosh(d*x + c)^3 - 36*(8*a*b + 5*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 - 30*(128*a^2 + 160*a*b + 63*b^2)*d*x + 15*(b^2*cosh(d*x + c)^9 - 10*b^2*cosh(d*x + c)^7 + (32*a*b + 45*b^2)*cosh(d*x + c)^5 - 24*(8*a*b + 5*b^2)*cosh(d*x + c)^3 + 2*(128*a^2 + 240*a*b + 105*b^2)*cosh(d*x + c))*sinh(d*x + c))/d","B",0
198,1,279,0,1.667367," ","integrate(sinh(d*x+c)*(a+b*sinh(d*x+c)^4)^2,x, algorithm=""fricas"")","\frac{35 \, b^{2} \cosh\left(d x + c\right)^{9} + 315 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{8} - 405 \, b^{2} \cosh\left(d x + c\right)^{7} + 105 \, {\left(28 \, b^{2} \cosh\left(d x + c\right)^{3} - 27 \, b^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} + 252 \, {\left(8 \, a b + 9 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 315 \, {\left(14 \, b^{2} \cosh\left(d x + c\right)^{5} - 45 \, b^{2} \cosh\left(d x + c\right)^{3} + 4 \, {\left(8 \, a b + 9 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} - 420 \, {\left(40 \, a b + 21 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 315 \, {\left(4 \, b^{2} \cosh\left(d x + c\right)^{7} - 27 \, b^{2} \cosh\left(d x + c\right)^{5} + 8 \, {\left(8 \, a b + 9 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - 4 \, {\left(40 \, a b + 21 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 630 \, {\left(128 \, a^{2} + 160 \, a b + 63 \, b^{2}\right)} \cosh\left(d x + c\right)}{80640 \, d}"," ",0,"1/80640*(35*b^2*cosh(d*x + c)^9 + 315*b^2*cosh(d*x + c)*sinh(d*x + c)^8 - 405*b^2*cosh(d*x + c)^7 + 105*(28*b^2*cosh(d*x + c)^3 - 27*b^2*cosh(d*x + c))*sinh(d*x + c)^6 + 252*(8*a*b + 9*b^2)*cosh(d*x + c)^5 + 315*(14*b^2*cosh(d*x + c)^5 - 45*b^2*cosh(d*x + c)^3 + 4*(8*a*b + 9*b^2)*cosh(d*x + c))*sinh(d*x + c)^4 - 420*(40*a*b + 21*b^2)*cosh(d*x + c)^3 + 315*(4*b^2*cosh(d*x + c)^7 - 27*b^2*cosh(d*x + c)^5 + 8*(8*a*b + 9*b^2)*cosh(d*x + c)^3 - 4*(40*a*b + 21*b^2)*cosh(d*x + c))*sinh(d*x + c)^2 + 630*(128*a^2 + 160*a*b + 63*b^2)*cosh(d*x + c))/d","B",0
199,1,205,0,0.987427," ","integrate((a+b*sinh(d*x+c)^4)^2,x, algorithm=""fricas"")","\frac{3 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + 3 \, {\left(7 \, b^{2} \cosh\left(d x + c\right)^{3} - 8 \, b^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + {\left(21 \, b^{2} \cosh\left(d x + c\right)^{5} - 80 \, b^{2} \cosh\left(d x + c\right)^{3} + 12 \, {\left(8 \, a b + 7 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 3 \, {\left(128 \, a^{2} + 96 \, a b + 35 \, b^{2}\right)} d x + 3 \, {\left(b^{2} \cosh\left(d x + c\right)^{7} - 8 \, b^{2} \cosh\left(d x + c\right)^{5} + 4 \, {\left(8 \, a b + 7 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - 8 \, {\left(16 \, a b + 7 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{384 \, d}"," ",0,"1/384*(3*b^2*cosh(d*x + c)*sinh(d*x + c)^7 + 3*(7*b^2*cosh(d*x + c)^3 - 8*b^2*cosh(d*x + c))*sinh(d*x + c)^5 + (21*b^2*cosh(d*x + c)^5 - 80*b^2*cosh(d*x + c)^3 + 12*(8*a*b + 7*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 3*(128*a^2 + 96*a*b + 35*b^2)*d*x + 3*(b^2*cosh(d*x + c)^7 - 8*b^2*cosh(d*x + c)^5 + 4*(8*a*b + 7*b^2)*cosh(d*x + c)^3 - 8*(16*a*b + 7*b^2)*cosh(d*x + c))*sinh(d*x + c))/d","A",0
200,1,1575,0,0.854663," ","integrate(csch(d*x+c)*(a+b*sinh(d*x+c)^4)^2,x, algorithm=""fricas"")","\frac{15 \, b^{2} \cosh\left(d x + c\right)^{14} + 210 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{13} + 15 \, b^{2} \sinh\left(d x + c\right)^{14} - 147 \, b^{2} \cosh\left(d x + c\right)^{12} + 21 \, {\left(65 \, b^{2} \cosh\left(d x + c\right)^{2} - 7 \, b^{2}\right)} \sinh\left(d x + c\right)^{12} + 84 \, {\left(65 \, b^{2} \cosh\left(d x + c\right)^{3} - 21 \, b^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{11} + 35 \, {\left(32 \, a b + 21 \, b^{2}\right)} \cosh\left(d x + c\right)^{10} + 7 \, {\left(2145 \, b^{2} \cosh\left(d x + c\right)^{4} - 1386 \, b^{2} \cosh\left(d x + c\right)^{2} + 160 \, a b + 105 \, b^{2}\right)} \sinh\left(d x + c\right)^{10} + 70 \, {\left(429 \, b^{2} \cosh\left(d x + c\right)^{5} - 462 \, b^{2} \cosh\left(d x + c\right)^{3} + 5 \, {\left(32 \, a b + 21 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} - 105 \, {\left(96 \, a b + 35 \, b^{2}\right)} \cosh\left(d x + c\right)^{8} + 105 \, {\left(429 \, b^{2} \cosh\left(d x + c\right)^{6} - 693 \, b^{2} \cosh\left(d x + c\right)^{4} + 15 \, {\left(32 \, a b + 21 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 96 \, a b - 35 \, b^{2}\right)} \sinh\left(d x + c\right)^{8} + 24 \, {\left(2145 \, b^{2} \cosh\left(d x + c\right)^{7} - 4851 \, b^{2} \cosh\left(d x + c\right)^{5} + 175 \, {\left(32 \, a b + 21 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - 35 \, {\left(96 \, a b + 35 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} - 105 \, {\left(96 \, a b + 35 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 21 \, {\left(2145 \, b^{2} \cosh\left(d x + c\right)^{8} - 6468 \, b^{2} \cosh\left(d x + c\right)^{6} + 350 \, {\left(32 \, a b + 21 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} - 140 \, {\left(96 \, a b + 35 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 480 \, a b - 175 \, b^{2}\right)} \sinh\left(d x + c\right)^{6} + 42 \, {\left(715 \, b^{2} \cosh\left(d x + c\right)^{9} - 2772 \, b^{2} \cosh\left(d x + c\right)^{7} + 210 \, {\left(32 \, a b + 21 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} - 140 \, {\left(96 \, a b + 35 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - 15 \, {\left(96 \, a b + 35 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 35 \, {\left(32 \, a b + 21 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 35 \, {\left(429 \, b^{2} \cosh\left(d x + c\right)^{10} - 2079 \, b^{2} \cosh\left(d x + c\right)^{8} + 210 \, {\left(32 \, a b + 21 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} - 210 \, {\left(96 \, a b + 35 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} - 45 \, {\left(96 \, a b + 35 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 32 \, a b + 21 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} - 147 \, b^{2} \cosh\left(d x + c\right)^{2} + 140 \, {\left(39 \, b^{2} \cosh\left(d x + c\right)^{11} - 231 \, b^{2} \cosh\left(d x + c\right)^{9} + 30 \, {\left(32 \, a b + 21 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} - 42 \, {\left(96 \, a b + 35 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} - 15 \, {\left(96 \, a b + 35 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(32 \, a b + 21 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 21 \, {\left(65 \, b^{2} \cosh\left(d x + c\right)^{12} - 462 \, b^{2} \cosh\left(d x + c\right)^{10} + 75 \, {\left(32 \, a b + 21 \, b^{2}\right)} \cosh\left(d x + c\right)^{8} - 140 \, {\left(96 \, a b + 35 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} - 75 \, {\left(96 \, a b + 35 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 10 \, {\left(32 \, a b + 21 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 7 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} + 15 \, b^{2} - 13440 \, {\left(a^{2} \cosh\left(d x + c\right)^{7} + 7 \, a^{2} \cosh\left(d x + c\right)^{6} \sinh\left(d x + c\right) + 21 \, a^{2} \cosh\left(d x + c\right)^{5} \sinh\left(d x + c\right)^{2} + 35 \, a^{2} \cosh\left(d x + c\right)^{4} \sinh\left(d x + c\right)^{3} + 35 \, a^{2} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right)^{4} + 21 \, a^{2} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{5} + 7 \, a^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + a^{2} \sinh\left(d x + c\right)^{7}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) + 13440 \, {\left(a^{2} \cosh\left(d x + c\right)^{7} + 7 \, a^{2} \cosh\left(d x + c\right)^{6} \sinh\left(d x + c\right) + 21 \, a^{2} \cosh\left(d x + c\right)^{5} \sinh\left(d x + c\right)^{2} + 35 \, a^{2} \cosh\left(d x + c\right)^{4} \sinh\left(d x + c\right)^{3} + 35 \, a^{2} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right)^{4} + 21 \, a^{2} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{5} + 7 \, a^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + a^{2} \sinh\left(d x + c\right)^{7}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) + 14 \, {\left(15 \, b^{2} \cosh\left(d x + c\right)^{13} - 126 \, b^{2} \cosh\left(d x + c\right)^{11} + 25 \, {\left(32 \, a b + 21 \, b^{2}\right)} \cosh\left(d x + c\right)^{9} - 60 \, {\left(96 \, a b + 35 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} - 45 \, {\left(96 \, a b + 35 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(32 \, a b + 21 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - 21 \, b^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{13440 \, {\left(d \cosh\left(d x + c\right)^{7} + 7 \, d \cosh\left(d x + c\right)^{6} \sinh\left(d x + c\right) + 21 \, d \cosh\left(d x + c\right)^{5} \sinh\left(d x + c\right)^{2} + 35 \, d \cosh\left(d x + c\right)^{4} \sinh\left(d x + c\right)^{3} + 35 \, d \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right)^{4} + 21 \, d \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{5} + 7 \, d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + d \sinh\left(d x + c\right)^{7}\right)}}"," ",0,"1/13440*(15*b^2*cosh(d*x + c)^14 + 210*b^2*cosh(d*x + c)*sinh(d*x + c)^13 + 15*b^2*sinh(d*x + c)^14 - 147*b^2*cosh(d*x + c)^12 + 21*(65*b^2*cosh(d*x + c)^2 - 7*b^2)*sinh(d*x + c)^12 + 84*(65*b^2*cosh(d*x + c)^3 - 21*b^2*cosh(d*x + c))*sinh(d*x + c)^11 + 35*(32*a*b + 21*b^2)*cosh(d*x + c)^10 + 7*(2145*b^2*cosh(d*x + c)^4 - 1386*b^2*cosh(d*x + c)^2 + 160*a*b + 105*b^2)*sinh(d*x + c)^10 + 70*(429*b^2*cosh(d*x + c)^5 - 462*b^2*cosh(d*x + c)^3 + 5*(32*a*b + 21*b^2)*cosh(d*x + c))*sinh(d*x + c)^9 - 105*(96*a*b + 35*b^2)*cosh(d*x + c)^8 + 105*(429*b^2*cosh(d*x + c)^6 - 693*b^2*cosh(d*x + c)^4 + 15*(32*a*b + 21*b^2)*cosh(d*x + c)^2 - 96*a*b - 35*b^2)*sinh(d*x + c)^8 + 24*(2145*b^2*cosh(d*x + c)^7 - 4851*b^2*cosh(d*x + c)^5 + 175*(32*a*b + 21*b^2)*cosh(d*x + c)^3 - 35*(96*a*b + 35*b^2)*cosh(d*x + c))*sinh(d*x + c)^7 - 105*(96*a*b + 35*b^2)*cosh(d*x + c)^6 + 21*(2145*b^2*cosh(d*x + c)^8 - 6468*b^2*cosh(d*x + c)^6 + 350*(32*a*b + 21*b^2)*cosh(d*x + c)^4 - 140*(96*a*b + 35*b^2)*cosh(d*x + c)^2 - 480*a*b - 175*b^2)*sinh(d*x + c)^6 + 42*(715*b^2*cosh(d*x + c)^9 - 2772*b^2*cosh(d*x + c)^7 + 210*(32*a*b + 21*b^2)*cosh(d*x + c)^5 - 140*(96*a*b + 35*b^2)*cosh(d*x + c)^3 - 15*(96*a*b + 35*b^2)*cosh(d*x + c))*sinh(d*x + c)^5 + 35*(32*a*b + 21*b^2)*cosh(d*x + c)^4 + 35*(429*b^2*cosh(d*x + c)^10 - 2079*b^2*cosh(d*x + c)^8 + 210*(32*a*b + 21*b^2)*cosh(d*x + c)^6 - 210*(96*a*b + 35*b^2)*cosh(d*x + c)^4 - 45*(96*a*b + 35*b^2)*cosh(d*x + c)^2 + 32*a*b + 21*b^2)*sinh(d*x + c)^4 - 147*b^2*cosh(d*x + c)^2 + 140*(39*b^2*cosh(d*x + c)^11 - 231*b^2*cosh(d*x + c)^9 + 30*(32*a*b + 21*b^2)*cosh(d*x + c)^7 - 42*(96*a*b + 35*b^2)*cosh(d*x + c)^5 - 15*(96*a*b + 35*b^2)*cosh(d*x + c)^3 + (32*a*b + 21*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 21*(65*b^2*cosh(d*x + c)^12 - 462*b^2*cosh(d*x + c)^10 + 75*(32*a*b + 21*b^2)*cosh(d*x + c)^8 - 140*(96*a*b + 35*b^2)*cosh(d*x + c)^6 - 75*(96*a*b + 35*b^2)*cosh(d*x + c)^4 + 10*(32*a*b + 21*b^2)*cosh(d*x + c)^2 - 7*b^2)*sinh(d*x + c)^2 + 15*b^2 - 13440*(a^2*cosh(d*x + c)^7 + 7*a^2*cosh(d*x + c)^6*sinh(d*x + c) + 21*a^2*cosh(d*x + c)^5*sinh(d*x + c)^2 + 35*a^2*cosh(d*x + c)^4*sinh(d*x + c)^3 + 35*a^2*cosh(d*x + c)^3*sinh(d*x + c)^4 + 21*a^2*cosh(d*x + c)^2*sinh(d*x + c)^5 + 7*a^2*cosh(d*x + c)*sinh(d*x + c)^6 + a^2*sinh(d*x + c)^7)*log(cosh(d*x + c) + sinh(d*x + c) + 1) + 13440*(a^2*cosh(d*x + c)^7 + 7*a^2*cosh(d*x + c)^6*sinh(d*x + c) + 21*a^2*cosh(d*x + c)^5*sinh(d*x + c)^2 + 35*a^2*cosh(d*x + c)^4*sinh(d*x + c)^3 + 35*a^2*cosh(d*x + c)^3*sinh(d*x + c)^4 + 21*a^2*cosh(d*x + c)^2*sinh(d*x + c)^5 + 7*a^2*cosh(d*x + c)*sinh(d*x + c)^6 + a^2*sinh(d*x + c)^7)*log(cosh(d*x + c) + sinh(d*x + c) - 1) + 14*(15*b^2*cosh(d*x + c)^13 - 126*b^2*cosh(d*x + c)^11 + 25*(32*a*b + 21*b^2)*cosh(d*x + c)^9 - 60*(96*a*b + 35*b^2)*cosh(d*x + c)^7 - 45*(96*a*b + 35*b^2)*cosh(d*x + c)^5 + 10*(32*a*b + 21*b^2)*cosh(d*x + c)^3 - 21*b^2*cosh(d*x + c))*sinh(d*x + c))/(d*cosh(d*x + c)^7 + 7*d*cosh(d*x + c)^6*sinh(d*x + c) + 21*d*cosh(d*x + c)^5*sinh(d*x + c)^2 + 35*d*cosh(d*x + c)^4*sinh(d*x + c)^3 + 35*d*cosh(d*x + c)^3*sinh(d*x + c)^4 + 21*d*cosh(d*x + c)^2*sinh(d*x + c)^5 + 7*d*cosh(d*x + c)*sinh(d*x + c)^6 + d*sinh(d*x + c)^7)","B",0
201,1,217,0,0.994450," ","integrate(csch(d*x+c)^2*(a+b*sinh(d*x+c)^4)^2,x, algorithm=""fricas"")","\frac{b^{2} \cosh\left(d x + c\right)^{7} + 7 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} - 10 \, b^{2} \cosh\left(d x + c\right)^{5} + 5 \, {\left(7 \, b^{2} \cosh\left(d x + c\right)^{3} - 10 \, b^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 6 \, {\left(16 \, a b + 9 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(21 \, b^{2} \cosh\left(d x + c\right)^{5} - 100 \, b^{2} \cosh\left(d x + c\right)^{3} + 18 \, {\left(16 \, a b + 9 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 3 \, {\left(128 \, a^{2} + 32 \, a b + 15 \, b^{2}\right)} \cosh\left(d x + c\right) - 24 \, {\left({\left(16 \, a b + 5 \, b^{2}\right)} d x - 16 \, a^{2}\right)} \sinh\left(d x + c\right)}{384 \, d \sinh\left(d x + c\right)}"," ",0,"1/384*(b^2*cosh(d*x + c)^7 + 7*b^2*cosh(d*x + c)*sinh(d*x + c)^6 - 10*b^2*cosh(d*x + c)^5 + 5*(7*b^2*cosh(d*x + c)^3 - 10*b^2*cosh(d*x + c))*sinh(d*x + c)^4 + 6*(16*a*b + 9*b^2)*cosh(d*x + c)^3 + (21*b^2*cosh(d*x + c)^5 - 100*b^2*cosh(d*x + c)^3 + 18*(16*a*b + 9*b^2)*cosh(d*x + c))*sinh(d*x + c)^2 - 3*(128*a^2 + 32*a*b + 15*b^2)*cosh(d*x + c) - 24*((16*a*b + 5*b^2)*d*x - 16*a^2)*sinh(d*x + c))/(d*sinh(d*x + c))","B",0
202,1,2272,0,3.951415," ","integrate(csch(d*x+c)^3*(a+b*sinh(d*x+c)^4)^2,x, algorithm=""fricas"")","\frac{3 \, b^{2} \cosh\left(d x + c\right)^{14} + 42 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{13} + 3 \, b^{2} \sinh\left(d x + c\right)^{14} - 31 \, b^{2} \cosh\left(d x + c\right)^{12} + {\left(273 \, b^{2} \cosh\left(d x + c\right)^{2} - 31 \, b^{2}\right)} \sinh\left(d x + c\right)^{12} + 12 \, {\left(91 \, b^{2} \cosh\left(d x + c\right)^{3} - 31 \, b^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{11} + {\left(480 \, a b + 203 \, b^{2}\right)} \cosh\left(d x + c\right)^{10} + {\left(3003 \, b^{2} \cosh\left(d x + c\right)^{4} - 2046 \, b^{2} \cosh\left(d x + c\right)^{2} + 480 \, a b + 203 \, b^{2}\right)} \sinh\left(d x + c\right)^{10} + 2 \, {\left(3003 \, b^{2} \cosh\left(d x + c\right)^{5} - 3410 \, b^{2} \cosh\left(d x + c\right)^{3} + 5 \, {\left(480 \, a b + 203 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} - 5 \, {\left(96 \, a^{2} + 96 \, a b + 35 \, b^{2}\right)} \cosh\left(d x + c\right)^{8} + {\left(9009 \, b^{2} \cosh\left(d x + c\right)^{6} - 15345 \, b^{2} \cosh\left(d x + c\right)^{4} + 45 \, {\left(480 \, a b + 203 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 480 \, a^{2} - 480 \, a b - 175 \, b^{2}\right)} \sinh\left(d x + c\right)^{8} + 8 \, {\left(1287 \, b^{2} \cosh\left(d x + c\right)^{7} - 3069 \, b^{2} \cosh\left(d x + c\right)^{5} + 15 \, {\left(480 \, a b + 203 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - 5 \, {\left(96 \, a^{2} + 96 \, a b + 35 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} - 5 \, {\left(96 \, a^{2} + 96 \, a b + 35 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + {\left(9009 \, b^{2} \cosh\left(d x + c\right)^{8} - 28644 \, b^{2} \cosh\left(d x + c\right)^{6} + 210 \, {\left(480 \, a b + 203 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} - 140 \, {\left(96 \, a^{2} + 96 \, a b + 35 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 480 \, a^{2} - 480 \, a b - 175 \, b^{2}\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(3003 \, b^{2} \cosh\left(d x + c\right)^{9} - 12276 \, b^{2} \cosh\left(d x + c\right)^{7} + 126 \, {\left(480 \, a b + 203 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} - 140 \, {\left(96 \, a^{2} + 96 \, a b + 35 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - 15 \, {\left(96 \, a^{2} + 96 \, a b + 35 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + {\left(480 \, a b + 203 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(3003 \, b^{2} \cosh\left(d x + c\right)^{10} - 15345 \, b^{2} \cosh\left(d x + c\right)^{8} + 210 \, {\left(480 \, a b + 203 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} - 350 \, {\left(96 \, a^{2} + 96 \, a b + 35 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} - 75 \, {\left(96 \, a^{2} + 96 \, a b + 35 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 480 \, a b + 203 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} - 31 \, b^{2} \cosh\left(d x + c\right)^{2} + 4 \, {\left(273 \, b^{2} \cosh\left(d x + c\right)^{11} - 1705 \, b^{2} \cosh\left(d x + c\right)^{9} + 30 \, {\left(480 \, a b + 203 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} - 70 \, {\left(96 \, a^{2} + 96 \, a b + 35 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} - 25 \, {\left(96 \, a^{2} + 96 \, a b + 35 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(480 \, a b + 203 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(273 \, b^{2} \cosh\left(d x + c\right)^{12} - 2046 \, b^{2} \cosh\left(d x + c\right)^{10} + 45 \, {\left(480 \, a b + 203 \, b^{2}\right)} \cosh\left(d x + c\right)^{8} - 140 \, {\left(96 \, a^{2} + 96 \, a b + 35 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} - 75 \, {\left(96 \, a^{2} + 96 \, a b + 35 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 6 \, {\left(480 \, a b + 203 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 31 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} + 3 \, b^{2} + 240 \, {\left(a^{2} \cosh\left(d x + c\right)^{9} + 9 \, a^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{8} + a^{2} \sinh\left(d x + c\right)^{9} - 2 \, a^{2} \cosh\left(d x + c\right)^{7} + 2 \, {\left(18 \, a^{2} \cosh\left(d x + c\right)^{2} - a^{2}\right)} \sinh\left(d x + c\right)^{7} + a^{2} \cosh\left(d x + c\right)^{5} + 14 \, {\left(6 \, a^{2} \cosh\left(d x + c\right)^{3} - a^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} + {\left(126 \, a^{2} \cosh\left(d x + c\right)^{4} - 42 \, a^{2} \cosh\left(d x + c\right)^{2} + a^{2}\right)} \sinh\left(d x + c\right)^{5} + {\left(126 \, a^{2} \cosh\left(d x + c\right)^{5} - 70 \, a^{2} \cosh\left(d x + c\right)^{3} + 5 \, a^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(42 \, a^{2} \cosh\left(d x + c\right)^{6} - 35 \, a^{2} \cosh\left(d x + c\right)^{4} + 5 \, a^{2} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(18 \, a^{2} \cosh\left(d x + c\right)^{7} - 21 \, a^{2} \cosh\left(d x + c\right)^{5} + 5 \, a^{2} \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right)^{2} + {\left(9 \, a^{2} \cosh\left(d x + c\right)^{8} - 14 \, a^{2} \cosh\left(d x + c\right)^{6} + 5 \, a^{2} \cosh\left(d x + c\right)^{4}\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) - 240 \, {\left(a^{2} \cosh\left(d x + c\right)^{9} + 9 \, a^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{8} + a^{2} \sinh\left(d x + c\right)^{9} - 2 \, a^{2} \cosh\left(d x + c\right)^{7} + 2 \, {\left(18 \, a^{2} \cosh\left(d x + c\right)^{2} - a^{2}\right)} \sinh\left(d x + c\right)^{7} + a^{2} \cosh\left(d x + c\right)^{5} + 14 \, {\left(6 \, a^{2} \cosh\left(d x + c\right)^{3} - a^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} + {\left(126 \, a^{2} \cosh\left(d x + c\right)^{4} - 42 \, a^{2} \cosh\left(d x + c\right)^{2} + a^{2}\right)} \sinh\left(d x + c\right)^{5} + {\left(126 \, a^{2} \cosh\left(d x + c\right)^{5} - 70 \, a^{2} \cosh\left(d x + c\right)^{3} + 5 \, a^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(42 \, a^{2} \cosh\left(d x + c\right)^{6} - 35 \, a^{2} \cosh\left(d x + c\right)^{4} + 5 \, a^{2} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(18 \, a^{2} \cosh\left(d x + c\right)^{7} - 21 \, a^{2} \cosh\left(d x + c\right)^{5} + 5 \, a^{2} \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right)^{2} + {\left(9 \, a^{2} \cosh\left(d x + c\right)^{8} - 14 \, a^{2} \cosh\left(d x + c\right)^{6} + 5 \, a^{2} \cosh\left(d x + c\right)^{4}\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) + 2 \, {\left(21 \, b^{2} \cosh\left(d x + c\right)^{13} - 186 \, b^{2} \cosh\left(d x + c\right)^{11} + 5 \, {\left(480 \, a b + 203 \, b^{2}\right)} \cosh\left(d x + c\right)^{9} - 20 \, {\left(96 \, a^{2} + 96 \, a b + 35 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} - 15 \, {\left(96 \, a^{2} + 96 \, a b + 35 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(480 \, a b + 203 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - 31 \, b^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{480 \, {\left(d \cosh\left(d x + c\right)^{9} + 9 \, d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{8} + d \sinh\left(d x + c\right)^{9} - 2 \, d \cosh\left(d x + c\right)^{7} + 2 \, {\left(18 \, d \cosh\left(d x + c\right)^{2} - d\right)} \sinh\left(d x + c\right)^{7} + 14 \, {\left(6 \, d \cosh\left(d x + c\right)^{3} - d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} + d \cosh\left(d x + c\right)^{5} + {\left(126 \, d \cosh\left(d x + c\right)^{4} - 42 \, d \cosh\left(d x + c\right)^{2} + d\right)} \sinh\left(d x + c\right)^{5} + {\left(126 \, d \cosh\left(d x + c\right)^{5} - 70 \, d \cosh\left(d x + c\right)^{3} + 5 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(42 \, d \cosh\left(d x + c\right)^{6} - 35 \, d \cosh\left(d x + c\right)^{4} + 5 \, d \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(18 \, d \cosh\left(d x + c\right)^{7} - 21 \, d \cosh\left(d x + c\right)^{5} + 5 \, d \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right)^{2} + {\left(9 \, d \cosh\left(d x + c\right)^{8} - 14 \, d \cosh\left(d x + c\right)^{6} + 5 \, d \cosh\left(d x + c\right)^{4}\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"1/480*(3*b^2*cosh(d*x + c)^14 + 42*b^2*cosh(d*x + c)*sinh(d*x + c)^13 + 3*b^2*sinh(d*x + c)^14 - 31*b^2*cosh(d*x + c)^12 + (273*b^2*cosh(d*x + c)^2 - 31*b^2)*sinh(d*x + c)^12 + 12*(91*b^2*cosh(d*x + c)^3 - 31*b^2*cosh(d*x + c))*sinh(d*x + c)^11 + (480*a*b + 203*b^2)*cosh(d*x + c)^10 + (3003*b^2*cosh(d*x + c)^4 - 2046*b^2*cosh(d*x + c)^2 + 480*a*b + 203*b^2)*sinh(d*x + c)^10 + 2*(3003*b^2*cosh(d*x + c)^5 - 3410*b^2*cosh(d*x + c)^3 + 5*(480*a*b + 203*b^2)*cosh(d*x + c))*sinh(d*x + c)^9 - 5*(96*a^2 + 96*a*b + 35*b^2)*cosh(d*x + c)^8 + (9009*b^2*cosh(d*x + c)^6 - 15345*b^2*cosh(d*x + c)^4 + 45*(480*a*b + 203*b^2)*cosh(d*x + c)^2 - 480*a^2 - 480*a*b - 175*b^2)*sinh(d*x + c)^8 + 8*(1287*b^2*cosh(d*x + c)^7 - 3069*b^2*cosh(d*x + c)^5 + 15*(480*a*b + 203*b^2)*cosh(d*x + c)^3 - 5*(96*a^2 + 96*a*b + 35*b^2)*cosh(d*x + c))*sinh(d*x + c)^7 - 5*(96*a^2 + 96*a*b + 35*b^2)*cosh(d*x + c)^6 + (9009*b^2*cosh(d*x + c)^8 - 28644*b^2*cosh(d*x + c)^6 + 210*(480*a*b + 203*b^2)*cosh(d*x + c)^4 - 140*(96*a^2 + 96*a*b + 35*b^2)*cosh(d*x + c)^2 - 480*a^2 - 480*a*b - 175*b^2)*sinh(d*x + c)^6 + 2*(3003*b^2*cosh(d*x + c)^9 - 12276*b^2*cosh(d*x + c)^7 + 126*(480*a*b + 203*b^2)*cosh(d*x + c)^5 - 140*(96*a^2 + 96*a*b + 35*b^2)*cosh(d*x + c)^3 - 15*(96*a^2 + 96*a*b + 35*b^2)*cosh(d*x + c))*sinh(d*x + c)^5 + (480*a*b + 203*b^2)*cosh(d*x + c)^4 + (3003*b^2*cosh(d*x + c)^10 - 15345*b^2*cosh(d*x + c)^8 + 210*(480*a*b + 203*b^2)*cosh(d*x + c)^6 - 350*(96*a^2 + 96*a*b + 35*b^2)*cosh(d*x + c)^4 - 75*(96*a^2 + 96*a*b + 35*b^2)*cosh(d*x + c)^2 + 480*a*b + 203*b^2)*sinh(d*x + c)^4 - 31*b^2*cosh(d*x + c)^2 + 4*(273*b^2*cosh(d*x + c)^11 - 1705*b^2*cosh(d*x + c)^9 + 30*(480*a*b + 203*b^2)*cosh(d*x + c)^7 - 70*(96*a^2 + 96*a*b + 35*b^2)*cosh(d*x + c)^5 - 25*(96*a^2 + 96*a*b + 35*b^2)*cosh(d*x + c)^3 + (480*a*b + 203*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + (273*b^2*cosh(d*x + c)^12 - 2046*b^2*cosh(d*x + c)^10 + 45*(480*a*b + 203*b^2)*cosh(d*x + c)^8 - 140*(96*a^2 + 96*a*b + 35*b^2)*cosh(d*x + c)^6 - 75*(96*a^2 + 96*a*b + 35*b^2)*cosh(d*x + c)^4 + 6*(480*a*b + 203*b^2)*cosh(d*x + c)^2 - 31*b^2)*sinh(d*x + c)^2 + 3*b^2 + 240*(a^2*cosh(d*x + c)^9 + 9*a^2*cosh(d*x + c)*sinh(d*x + c)^8 + a^2*sinh(d*x + c)^9 - 2*a^2*cosh(d*x + c)^7 + 2*(18*a^2*cosh(d*x + c)^2 - a^2)*sinh(d*x + c)^7 + a^2*cosh(d*x + c)^5 + 14*(6*a^2*cosh(d*x + c)^3 - a^2*cosh(d*x + c))*sinh(d*x + c)^6 + (126*a^2*cosh(d*x + c)^4 - 42*a^2*cosh(d*x + c)^2 + a^2)*sinh(d*x + c)^5 + (126*a^2*cosh(d*x + c)^5 - 70*a^2*cosh(d*x + c)^3 + 5*a^2*cosh(d*x + c))*sinh(d*x + c)^4 + 2*(42*a^2*cosh(d*x + c)^6 - 35*a^2*cosh(d*x + c)^4 + 5*a^2*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 2*(18*a^2*cosh(d*x + c)^7 - 21*a^2*cosh(d*x + c)^5 + 5*a^2*cosh(d*x + c)^3)*sinh(d*x + c)^2 + (9*a^2*cosh(d*x + c)^8 - 14*a^2*cosh(d*x + c)^6 + 5*a^2*cosh(d*x + c)^4)*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) + 1) - 240*(a^2*cosh(d*x + c)^9 + 9*a^2*cosh(d*x + c)*sinh(d*x + c)^8 + a^2*sinh(d*x + c)^9 - 2*a^2*cosh(d*x + c)^7 + 2*(18*a^2*cosh(d*x + c)^2 - a^2)*sinh(d*x + c)^7 + a^2*cosh(d*x + c)^5 + 14*(6*a^2*cosh(d*x + c)^3 - a^2*cosh(d*x + c))*sinh(d*x + c)^6 + (126*a^2*cosh(d*x + c)^4 - 42*a^2*cosh(d*x + c)^2 + a^2)*sinh(d*x + c)^5 + (126*a^2*cosh(d*x + c)^5 - 70*a^2*cosh(d*x + c)^3 + 5*a^2*cosh(d*x + c))*sinh(d*x + c)^4 + 2*(42*a^2*cosh(d*x + c)^6 - 35*a^2*cosh(d*x + c)^4 + 5*a^2*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 2*(18*a^2*cosh(d*x + c)^7 - 21*a^2*cosh(d*x + c)^5 + 5*a^2*cosh(d*x + c)^3)*sinh(d*x + c)^2 + (9*a^2*cosh(d*x + c)^8 - 14*a^2*cosh(d*x + c)^6 + 5*a^2*cosh(d*x + c)^4)*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) - 1) + 2*(21*b^2*cosh(d*x + c)^13 - 186*b^2*cosh(d*x + c)^11 + 5*(480*a*b + 203*b^2)*cosh(d*x + c)^9 - 20*(96*a^2 + 96*a*b + 35*b^2)*cosh(d*x + c)^7 - 15*(96*a^2 + 96*a*b + 35*b^2)*cosh(d*x + c)^5 + 2*(480*a*b + 203*b^2)*cosh(d*x + c)^3 - 31*b^2*cosh(d*x + c))*sinh(d*x + c))/(d*cosh(d*x + c)^9 + 9*d*cosh(d*x + c)*sinh(d*x + c)^8 + d*sinh(d*x + c)^9 - 2*d*cosh(d*x + c)^7 + 2*(18*d*cosh(d*x + c)^2 - d)*sinh(d*x + c)^7 + 14*(6*d*cosh(d*x + c)^3 - d*cosh(d*x + c))*sinh(d*x + c)^6 + d*cosh(d*x + c)^5 + (126*d*cosh(d*x + c)^4 - 42*d*cosh(d*x + c)^2 + d)*sinh(d*x + c)^5 + (126*d*cosh(d*x + c)^5 - 70*d*cosh(d*x + c)^3 + 5*d*cosh(d*x + c))*sinh(d*x + c)^4 + 2*(42*d*cosh(d*x + c)^6 - 35*d*cosh(d*x + c)^4 + 5*d*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 2*(18*d*cosh(d*x + c)^7 - 21*d*cosh(d*x + c)^5 + 5*d*cosh(d*x + c)^3)*sinh(d*x + c)^2 + (9*d*cosh(d*x + c)^8 - 14*d*cosh(d*x + c)^6 + 5*d*cosh(d*x + c)^4)*sinh(d*x + c))","B",0
203,1,300,0,2.058195," ","integrate(csch(d*x+c)^4*(a+b*sinh(d*x+c)^4)^2,x, algorithm=""fricas"")","\frac{3 \, b^{2} \cosh\left(d x + c\right)^{7} + 21 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} - 33 \, b^{2} \cosh\left(d x + c\right)^{5} + 15 \, {\left(7 \, b^{2} \cosh\left(d x + c\right)^{3} - 11 \, b^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + {\left(128 \, a^{2} + 81 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 8 \, {\left(3 \, {\left(16 \, a b + 3 \, b^{2}\right)} d x - 16 \, a^{2}\right)} \sinh\left(d x + c\right)^{3} + 3 \, {\left(21 \, b^{2} \cosh\left(d x + c\right)^{5} - 110 \, b^{2} \cosh\left(d x + c\right)^{3} + {\left(128 \, a^{2} + 81 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 3 \, {\left(128 \, a^{2} + 17 \, b^{2}\right)} \cosh\left(d x + c\right) - 24 \, {\left(3 \, {\left(16 \, a b + 3 \, b^{2}\right)} d x - {\left(3 \, {\left(16 \, a b + 3 \, b^{2}\right)} d x - 16 \, a^{2}\right)} \cosh\left(d x + c\right)^{2} - 16 \, a^{2}\right)} \sinh\left(d x + c\right)}{192 \, {\left(d \sinh\left(d x + c\right)^{3} + 3 \, {\left(d \cosh\left(d x + c\right)^{2} - d\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"1/192*(3*b^2*cosh(d*x + c)^7 + 21*b^2*cosh(d*x + c)*sinh(d*x + c)^6 - 33*b^2*cosh(d*x + c)^5 + 15*(7*b^2*cosh(d*x + c)^3 - 11*b^2*cosh(d*x + c))*sinh(d*x + c)^4 + (128*a^2 + 81*b^2)*cosh(d*x + c)^3 + 8*(3*(16*a*b + 3*b^2)*d*x - 16*a^2)*sinh(d*x + c)^3 + 3*(21*b^2*cosh(d*x + c)^5 - 110*b^2*cosh(d*x + c)^3 + (128*a^2 + 81*b^2)*cosh(d*x + c))*sinh(d*x + c)^2 - 3*(128*a^2 + 17*b^2)*cosh(d*x + c) - 24*(3*(16*a*b + 3*b^2)*d*x - (3*(16*a*b + 3*b^2)*d*x - 16*a^2)*cosh(d*x + c)^2 - 16*a^2)*sinh(d*x + c))/(d*sinh(d*x + c)^3 + 3*(d*cosh(d*x + c)^2 - d)*sinh(d*x + c))","B",0
204,1,3356,0,1.068425," ","integrate(csch(d*x+c)^5*(a+b*sinh(d*x+c)^4)^2,x, algorithm=""fricas"")","\frac{b^{2} \cosh\left(d x + c\right)^{14} + 14 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{13} + b^{2} \sinh\left(d x + c\right)^{14} - 13 \, b^{2} \cosh\left(d x + c\right)^{12} + 13 \, {\left(7 \, b^{2} \cosh\left(d x + c\right)^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{12} + 52 \, {\left(7 \, b^{2} \cosh\left(d x + c\right)^{3} - 3 \, b^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{11} + 3 \, {\left(6 \, a^{2} + 11 \, b^{2}\right)} \cosh\left(d x + c\right)^{10} + {\left(1001 \, b^{2} \cosh\left(d x + c\right)^{4} - 858 \, b^{2} \cosh\left(d x + c\right)^{2} + 18 \, a^{2} + 33 \, b^{2}\right)} \sinh\left(d x + c\right)^{10} + 2 \, {\left(1001 \, b^{2} \cosh\left(d x + c\right)^{5} - 1430 \, b^{2} \cosh\left(d x + c\right)^{3} + 15 \, {\left(6 \, a^{2} + 11 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} - 3 \, {\left(22 \, a^{2} + 7 \, b^{2}\right)} \cosh\left(d x + c\right)^{8} + 3 \, {\left(1001 \, b^{2} \cosh\left(d x + c\right)^{6} - 2145 \, b^{2} \cosh\left(d x + c\right)^{4} + 45 \, {\left(6 \, a^{2} + 11 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 22 \, a^{2} - 7 \, b^{2}\right)} \sinh\left(d x + c\right)^{8} + 24 \, {\left(143 \, b^{2} \cosh\left(d x + c\right)^{7} - 429 \, b^{2} \cosh\left(d x + c\right)^{5} + 15 \, {\left(6 \, a^{2} + 11 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(22 \, a^{2} + 7 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} - 3 \, {\left(22 \, a^{2} + 7 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 3 \, {\left(1001 \, b^{2} \cosh\left(d x + c\right)^{8} - 4004 \, b^{2} \cosh\left(d x + c\right)^{6} + 210 \, {\left(6 \, a^{2} + 11 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} - 28 \, {\left(22 \, a^{2} + 7 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 22 \, a^{2} - 7 \, b^{2}\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(1001 \, b^{2} \cosh\left(d x + c\right)^{9} - 5148 \, b^{2} \cosh\left(d x + c\right)^{7} + 378 \, {\left(6 \, a^{2} + 11 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} - 84 \, {\left(22 \, a^{2} + 7 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - 9 \, {\left(22 \, a^{2} + 7 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 3 \, {\left(6 \, a^{2} + 11 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(1001 \, b^{2} \cosh\left(d x + c\right)^{10} - 6435 \, b^{2} \cosh\left(d x + c\right)^{8} + 630 \, {\left(6 \, a^{2} + 11 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} - 210 \, {\left(22 \, a^{2} + 7 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} - 45 \, {\left(22 \, a^{2} + 7 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 18 \, a^{2} + 33 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} - 13 \, b^{2} \cosh\left(d x + c\right)^{2} + 4 \, {\left(91 \, b^{2} \cosh\left(d x + c\right)^{11} - 715 \, b^{2} \cosh\left(d x + c\right)^{9} + 90 \, {\left(6 \, a^{2} + 11 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} - 42 \, {\left(22 \, a^{2} + 7 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} - 15 \, {\left(22 \, a^{2} + 7 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(6 \, a^{2} + 11 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(91 \, b^{2} \cosh\left(d x + c\right)^{12} - 858 \, b^{2} \cosh\left(d x + c\right)^{10} + 135 \, {\left(6 \, a^{2} + 11 \, b^{2}\right)} \cosh\left(d x + c\right)^{8} - 84 \, {\left(22 \, a^{2} + 7 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} - 45 \, {\left(22 \, a^{2} + 7 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 18 \, {\left(6 \, a^{2} + 11 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 13 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} + b^{2} - 3 \, {\left({\left(3 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{11} + 11 \, {\left(3 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{10} + {\left(3 \, a^{2} + 16 \, a b\right)} \sinh\left(d x + c\right)^{11} - 4 \, {\left(3 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{9} + {\left(55 \, {\left(3 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{2} - 12 \, a^{2} - 64 \, a b\right)} \sinh\left(d x + c\right)^{9} + 3 \, {\left(55 \, {\left(3 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{3} - 12 \, {\left(3 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{8} + 6 \, {\left(3 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{7} + 6 \, {\left(55 \, {\left(3 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{4} - 24 \, {\left(3 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{2} + 3 \, a^{2} + 16 \, a b\right)} \sinh\left(d x + c\right)^{7} + 42 \, {\left(11 \, {\left(3 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{5} - 8 \, {\left(3 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} - 4 \, {\left(3 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(231 \, {\left(3 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{6} - 252 \, {\left(3 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{4} + 63 \, {\left(3 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{2} - 6 \, a^{2} - 32 \, a b\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(165 \, {\left(3 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{7} - 252 \, {\left(3 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{5} + 105 \, {\left(3 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{3} - 10 \, {\left(3 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + {\left(3 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{3} + {\left(165 \, {\left(3 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{8} - 336 \, {\left(3 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{6} + 210 \, {\left(3 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{4} - 40 \, {\left(3 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{2} + 3 \, a^{2} + 16 \, a b\right)} \sinh\left(d x + c\right)^{3} + {\left(55 \, {\left(3 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{9} - 144 \, {\left(3 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{7} + 126 \, {\left(3 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{5} - 40 \, {\left(3 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(3 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(11 \, {\left(3 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{10} - 36 \, {\left(3 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{8} + 42 \, {\left(3 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{6} - 20 \, {\left(3 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) + 3 \, {\left({\left(3 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{11} + 11 \, {\left(3 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{10} + {\left(3 \, a^{2} + 16 \, a b\right)} \sinh\left(d x + c\right)^{11} - 4 \, {\left(3 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{9} + {\left(55 \, {\left(3 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{2} - 12 \, a^{2} - 64 \, a b\right)} \sinh\left(d x + c\right)^{9} + 3 \, {\left(55 \, {\left(3 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{3} - 12 \, {\left(3 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{8} + 6 \, {\left(3 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{7} + 6 \, {\left(55 \, {\left(3 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{4} - 24 \, {\left(3 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{2} + 3 \, a^{2} + 16 \, a b\right)} \sinh\left(d x + c\right)^{7} + 42 \, {\left(11 \, {\left(3 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{5} - 8 \, {\left(3 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} - 4 \, {\left(3 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(231 \, {\left(3 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{6} - 252 \, {\left(3 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{4} + 63 \, {\left(3 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{2} - 6 \, a^{2} - 32 \, a b\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(165 \, {\left(3 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{7} - 252 \, {\left(3 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{5} + 105 \, {\left(3 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{3} - 10 \, {\left(3 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + {\left(3 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{3} + {\left(165 \, {\left(3 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{8} - 336 \, {\left(3 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{6} + 210 \, {\left(3 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{4} - 40 \, {\left(3 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{2} + 3 \, a^{2} + 16 \, a b\right)} \sinh\left(d x + c\right)^{3} + {\left(55 \, {\left(3 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{9} - 144 \, {\left(3 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{7} + 126 \, {\left(3 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{5} - 40 \, {\left(3 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(3 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(11 \, {\left(3 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{10} - 36 \, {\left(3 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{8} + 42 \, {\left(3 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{6} - 20 \, {\left(3 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) + 2 \, {\left(7 \, b^{2} \cosh\left(d x + c\right)^{13} - 78 \, b^{2} \cosh\left(d x + c\right)^{11} + 15 \, {\left(6 \, a^{2} + 11 \, b^{2}\right)} \cosh\left(d x + c\right)^{9} - 12 \, {\left(22 \, a^{2} + 7 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} - 9 \, {\left(22 \, a^{2} + 7 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 6 \, {\left(6 \, a^{2} + 11 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - 13 \, b^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{24 \, {\left(d \cosh\left(d x + c\right)^{11} + 11 \, d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{10} + d \sinh\left(d x + c\right)^{11} - 4 \, d \cosh\left(d x + c\right)^{9} + {\left(55 \, d \cosh\left(d x + c\right)^{2} - 4 \, d\right)} \sinh\left(d x + c\right)^{9} + 3 \, {\left(55 \, d \cosh\left(d x + c\right)^{3} - 12 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{8} + 6 \, d \cosh\left(d x + c\right)^{7} + 6 \, {\left(55 \, d \cosh\left(d x + c\right)^{4} - 24 \, d \cosh\left(d x + c\right)^{2} + d\right)} \sinh\left(d x + c\right)^{7} + 42 \, {\left(11 \, d \cosh\left(d x + c\right)^{5} - 8 \, d \cosh\left(d x + c\right)^{3} + d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} - 4 \, d \cosh\left(d x + c\right)^{5} + 2 \, {\left(231 \, d \cosh\left(d x + c\right)^{6} - 252 \, d \cosh\left(d x + c\right)^{4} + 63 \, d \cosh\left(d x + c\right)^{2} - 2 \, d\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(165 \, d \cosh\left(d x + c\right)^{7} - 252 \, d \cosh\left(d x + c\right)^{5} + 105 \, d \cosh\left(d x + c\right)^{3} - 10 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + d \cosh\left(d x + c\right)^{3} + {\left(165 \, d \cosh\left(d x + c\right)^{8} - 336 \, d \cosh\left(d x + c\right)^{6} + 210 \, d \cosh\left(d x + c\right)^{4} - 40 \, d \cosh\left(d x + c\right)^{2} + d\right)} \sinh\left(d x + c\right)^{3} + {\left(55 \, d \cosh\left(d x + c\right)^{9} - 144 \, d \cosh\left(d x + c\right)^{7} + 126 \, d \cosh\left(d x + c\right)^{5} - 40 \, d \cosh\left(d x + c\right)^{3} + 3 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(11 \, d \cosh\left(d x + c\right)^{10} - 36 \, d \cosh\left(d x + c\right)^{8} + 42 \, d \cosh\left(d x + c\right)^{6} - 20 \, d \cosh\left(d x + c\right)^{4} + 3 \, d \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"1/24*(b^2*cosh(d*x + c)^14 + 14*b^2*cosh(d*x + c)*sinh(d*x + c)^13 + b^2*sinh(d*x + c)^14 - 13*b^2*cosh(d*x + c)^12 + 13*(7*b^2*cosh(d*x + c)^2 - b^2)*sinh(d*x + c)^12 + 52*(7*b^2*cosh(d*x + c)^3 - 3*b^2*cosh(d*x + c))*sinh(d*x + c)^11 + 3*(6*a^2 + 11*b^2)*cosh(d*x + c)^10 + (1001*b^2*cosh(d*x + c)^4 - 858*b^2*cosh(d*x + c)^2 + 18*a^2 + 33*b^2)*sinh(d*x + c)^10 + 2*(1001*b^2*cosh(d*x + c)^5 - 1430*b^2*cosh(d*x + c)^3 + 15*(6*a^2 + 11*b^2)*cosh(d*x + c))*sinh(d*x + c)^9 - 3*(22*a^2 + 7*b^2)*cosh(d*x + c)^8 + 3*(1001*b^2*cosh(d*x + c)^6 - 2145*b^2*cosh(d*x + c)^4 + 45*(6*a^2 + 11*b^2)*cosh(d*x + c)^2 - 22*a^2 - 7*b^2)*sinh(d*x + c)^8 + 24*(143*b^2*cosh(d*x + c)^7 - 429*b^2*cosh(d*x + c)^5 + 15*(6*a^2 + 11*b^2)*cosh(d*x + c)^3 - (22*a^2 + 7*b^2)*cosh(d*x + c))*sinh(d*x + c)^7 - 3*(22*a^2 + 7*b^2)*cosh(d*x + c)^6 + 3*(1001*b^2*cosh(d*x + c)^8 - 4004*b^2*cosh(d*x + c)^6 + 210*(6*a^2 + 11*b^2)*cosh(d*x + c)^4 - 28*(22*a^2 + 7*b^2)*cosh(d*x + c)^2 - 22*a^2 - 7*b^2)*sinh(d*x + c)^6 + 2*(1001*b^2*cosh(d*x + c)^9 - 5148*b^2*cosh(d*x + c)^7 + 378*(6*a^2 + 11*b^2)*cosh(d*x + c)^5 - 84*(22*a^2 + 7*b^2)*cosh(d*x + c)^3 - 9*(22*a^2 + 7*b^2)*cosh(d*x + c))*sinh(d*x + c)^5 + 3*(6*a^2 + 11*b^2)*cosh(d*x + c)^4 + (1001*b^2*cosh(d*x + c)^10 - 6435*b^2*cosh(d*x + c)^8 + 630*(6*a^2 + 11*b^2)*cosh(d*x + c)^6 - 210*(22*a^2 + 7*b^2)*cosh(d*x + c)^4 - 45*(22*a^2 + 7*b^2)*cosh(d*x + c)^2 + 18*a^2 + 33*b^2)*sinh(d*x + c)^4 - 13*b^2*cosh(d*x + c)^2 + 4*(91*b^2*cosh(d*x + c)^11 - 715*b^2*cosh(d*x + c)^9 + 90*(6*a^2 + 11*b^2)*cosh(d*x + c)^7 - 42*(22*a^2 + 7*b^2)*cosh(d*x + c)^5 - 15*(22*a^2 + 7*b^2)*cosh(d*x + c)^3 + 3*(6*a^2 + 11*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + (91*b^2*cosh(d*x + c)^12 - 858*b^2*cosh(d*x + c)^10 + 135*(6*a^2 + 11*b^2)*cosh(d*x + c)^8 - 84*(22*a^2 + 7*b^2)*cosh(d*x + c)^6 - 45*(22*a^2 + 7*b^2)*cosh(d*x + c)^4 + 18*(6*a^2 + 11*b^2)*cosh(d*x + c)^2 - 13*b^2)*sinh(d*x + c)^2 + b^2 - 3*((3*a^2 + 16*a*b)*cosh(d*x + c)^11 + 11*(3*a^2 + 16*a*b)*cosh(d*x + c)*sinh(d*x + c)^10 + (3*a^2 + 16*a*b)*sinh(d*x + c)^11 - 4*(3*a^2 + 16*a*b)*cosh(d*x + c)^9 + (55*(3*a^2 + 16*a*b)*cosh(d*x + c)^2 - 12*a^2 - 64*a*b)*sinh(d*x + c)^9 + 3*(55*(3*a^2 + 16*a*b)*cosh(d*x + c)^3 - 12*(3*a^2 + 16*a*b)*cosh(d*x + c))*sinh(d*x + c)^8 + 6*(3*a^2 + 16*a*b)*cosh(d*x + c)^7 + 6*(55*(3*a^2 + 16*a*b)*cosh(d*x + c)^4 - 24*(3*a^2 + 16*a*b)*cosh(d*x + c)^2 + 3*a^2 + 16*a*b)*sinh(d*x + c)^7 + 42*(11*(3*a^2 + 16*a*b)*cosh(d*x + c)^5 - 8*(3*a^2 + 16*a*b)*cosh(d*x + c)^3 + (3*a^2 + 16*a*b)*cosh(d*x + c))*sinh(d*x + c)^6 - 4*(3*a^2 + 16*a*b)*cosh(d*x + c)^5 + 2*(231*(3*a^2 + 16*a*b)*cosh(d*x + c)^6 - 252*(3*a^2 + 16*a*b)*cosh(d*x + c)^4 + 63*(3*a^2 + 16*a*b)*cosh(d*x + c)^2 - 6*a^2 - 32*a*b)*sinh(d*x + c)^5 + 2*(165*(3*a^2 + 16*a*b)*cosh(d*x + c)^7 - 252*(3*a^2 + 16*a*b)*cosh(d*x + c)^5 + 105*(3*a^2 + 16*a*b)*cosh(d*x + c)^3 - 10*(3*a^2 + 16*a*b)*cosh(d*x + c))*sinh(d*x + c)^4 + (3*a^2 + 16*a*b)*cosh(d*x + c)^3 + (165*(3*a^2 + 16*a*b)*cosh(d*x + c)^8 - 336*(3*a^2 + 16*a*b)*cosh(d*x + c)^6 + 210*(3*a^2 + 16*a*b)*cosh(d*x + c)^4 - 40*(3*a^2 + 16*a*b)*cosh(d*x + c)^2 + 3*a^2 + 16*a*b)*sinh(d*x + c)^3 + (55*(3*a^2 + 16*a*b)*cosh(d*x + c)^9 - 144*(3*a^2 + 16*a*b)*cosh(d*x + c)^7 + 126*(3*a^2 + 16*a*b)*cosh(d*x + c)^5 - 40*(3*a^2 + 16*a*b)*cosh(d*x + c)^3 + 3*(3*a^2 + 16*a*b)*cosh(d*x + c))*sinh(d*x + c)^2 + (11*(3*a^2 + 16*a*b)*cosh(d*x + c)^10 - 36*(3*a^2 + 16*a*b)*cosh(d*x + c)^8 + 42*(3*a^2 + 16*a*b)*cosh(d*x + c)^6 - 20*(3*a^2 + 16*a*b)*cosh(d*x + c)^4 + 3*(3*a^2 + 16*a*b)*cosh(d*x + c)^2)*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) + 1) + 3*((3*a^2 + 16*a*b)*cosh(d*x + c)^11 + 11*(3*a^2 + 16*a*b)*cosh(d*x + c)*sinh(d*x + c)^10 + (3*a^2 + 16*a*b)*sinh(d*x + c)^11 - 4*(3*a^2 + 16*a*b)*cosh(d*x + c)^9 + (55*(3*a^2 + 16*a*b)*cosh(d*x + c)^2 - 12*a^2 - 64*a*b)*sinh(d*x + c)^9 + 3*(55*(3*a^2 + 16*a*b)*cosh(d*x + c)^3 - 12*(3*a^2 + 16*a*b)*cosh(d*x + c))*sinh(d*x + c)^8 + 6*(3*a^2 + 16*a*b)*cosh(d*x + c)^7 + 6*(55*(3*a^2 + 16*a*b)*cosh(d*x + c)^4 - 24*(3*a^2 + 16*a*b)*cosh(d*x + c)^2 + 3*a^2 + 16*a*b)*sinh(d*x + c)^7 + 42*(11*(3*a^2 + 16*a*b)*cosh(d*x + c)^5 - 8*(3*a^2 + 16*a*b)*cosh(d*x + c)^3 + (3*a^2 + 16*a*b)*cosh(d*x + c))*sinh(d*x + c)^6 - 4*(3*a^2 + 16*a*b)*cosh(d*x + c)^5 + 2*(231*(3*a^2 + 16*a*b)*cosh(d*x + c)^6 - 252*(3*a^2 + 16*a*b)*cosh(d*x + c)^4 + 63*(3*a^2 + 16*a*b)*cosh(d*x + c)^2 - 6*a^2 - 32*a*b)*sinh(d*x + c)^5 + 2*(165*(3*a^2 + 16*a*b)*cosh(d*x + c)^7 - 252*(3*a^2 + 16*a*b)*cosh(d*x + c)^5 + 105*(3*a^2 + 16*a*b)*cosh(d*x + c)^3 - 10*(3*a^2 + 16*a*b)*cosh(d*x + c))*sinh(d*x + c)^4 + (3*a^2 + 16*a*b)*cosh(d*x + c)^3 + (165*(3*a^2 + 16*a*b)*cosh(d*x + c)^8 - 336*(3*a^2 + 16*a*b)*cosh(d*x + c)^6 + 210*(3*a^2 + 16*a*b)*cosh(d*x + c)^4 - 40*(3*a^2 + 16*a*b)*cosh(d*x + c)^2 + 3*a^2 + 16*a*b)*sinh(d*x + c)^3 + (55*(3*a^2 + 16*a*b)*cosh(d*x + c)^9 - 144*(3*a^2 + 16*a*b)*cosh(d*x + c)^7 + 126*(3*a^2 + 16*a*b)*cosh(d*x + c)^5 - 40*(3*a^2 + 16*a*b)*cosh(d*x + c)^3 + 3*(3*a^2 + 16*a*b)*cosh(d*x + c))*sinh(d*x + c)^2 + (11*(3*a^2 + 16*a*b)*cosh(d*x + c)^10 - 36*(3*a^2 + 16*a*b)*cosh(d*x + c)^8 + 42*(3*a^2 + 16*a*b)*cosh(d*x + c)^6 - 20*(3*a^2 + 16*a*b)*cosh(d*x + c)^4 + 3*(3*a^2 + 16*a*b)*cosh(d*x + c)^2)*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) - 1) + 2*(7*b^2*cosh(d*x + c)^13 - 78*b^2*cosh(d*x + c)^11 + 15*(6*a^2 + 11*b^2)*cosh(d*x + c)^9 - 12*(22*a^2 + 7*b^2)*cosh(d*x + c)^7 - 9*(22*a^2 + 7*b^2)*cosh(d*x + c)^5 + 6*(6*a^2 + 11*b^2)*cosh(d*x + c)^3 - 13*b^2*cosh(d*x + c))*sinh(d*x + c))/(d*cosh(d*x + c)^11 + 11*d*cosh(d*x + c)*sinh(d*x + c)^10 + d*sinh(d*x + c)^11 - 4*d*cosh(d*x + c)^9 + (55*d*cosh(d*x + c)^2 - 4*d)*sinh(d*x + c)^9 + 3*(55*d*cosh(d*x + c)^3 - 12*d*cosh(d*x + c))*sinh(d*x + c)^8 + 6*d*cosh(d*x + c)^7 + 6*(55*d*cosh(d*x + c)^4 - 24*d*cosh(d*x + c)^2 + d)*sinh(d*x + c)^7 + 42*(11*d*cosh(d*x + c)^5 - 8*d*cosh(d*x + c)^3 + d*cosh(d*x + c))*sinh(d*x + c)^6 - 4*d*cosh(d*x + c)^5 + 2*(231*d*cosh(d*x + c)^6 - 252*d*cosh(d*x + c)^4 + 63*d*cosh(d*x + c)^2 - 2*d)*sinh(d*x + c)^5 + 2*(165*d*cosh(d*x + c)^7 - 252*d*cosh(d*x + c)^5 + 105*d*cosh(d*x + c)^3 - 10*d*cosh(d*x + c))*sinh(d*x + c)^4 + d*cosh(d*x + c)^3 + (165*d*cosh(d*x + c)^8 - 336*d*cosh(d*x + c)^6 + 210*d*cosh(d*x + c)^4 - 40*d*cosh(d*x + c)^2 + d)*sinh(d*x + c)^3 + (55*d*cosh(d*x + c)^9 - 144*d*cosh(d*x + c)^7 + 126*d*cosh(d*x + c)^5 - 40*d*cosh(d*x + c)^3 + 3*d*cosh(d*x + c))*sinh(d*x + c)^2 + (11*d*cosh(d*x + c)^10 - 36*d*cosh(d*x + c)^8 + 42*d*cosh(d*x + c)^6 - 20*d*cosh(d*x + c)^4 + 3*d*cosh(d*x + c)^2)*sinh(d*x + c))","B",0
205,1,457,0,1.313942," ","integrate(csch(d*x+c)^6*(a+b*sinh(d*x+c)^4)^2,x, algorithm=""fricas"")","\frac{15 \, b^{2} \cosh\left(d x + c\right)^{7} + 105 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} - {\left(64 \, a^{2} + 240 \, a b + 75 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} - 4 \, {\left(15 \, b^{2} d x - 16 \, a^{2} - 60 \, a b\right)} \sinh\left(d x + c\right)^{5} + 5 \, {\left(105 \, b^{2} \cosh\left(d x + c\right)^{3} - {\left(64 \, a^{2} + 240 \, a b + 75 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 5 \, {\left(64 \, a^{2} + 144 \, a b + 27 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 20 \, {\left(15 \, b^{2} d x - 2 \, {\left(15 \, b^{2} d x - 16 \, a^{2} - 60 \, a b\right)} \cosh\left(d x + c\right)^{2} - 16 \, a^{2} - 60 \, a b\right)} \sinh\left(d x + c\right)^{3} + 5 \, {\left(63 \, b^{2} \cosh\left(d x + c\right)^{5} - 2 \, {\left(64 \, a^{2} + 240 \, a b + 75 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(64 \, a^{2} + 144 \, a b + 27 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 5 \, {\left(128 \, a^{2} + 96 \, a b + 15 \, b^{2}\right)} \cosh\left(d x + c\right) - 20 \, {\left({\left(15 \, b^{2} d x - 16 \, a^{2} - 60 \, a b\right)} \cosh\left(d x + c\right)^{4} + 30 \, b^{2} d x - 3 \, {\left(15 \, b^{2} d x - 16 \, a^{2} - 60 \, a b\right)} \cosh\left(d x + c\right)^{2} - 32 \, a^{2} - 120 \, a b\right)} \sinh\left(d x + c\right)}{120 \, {\left(d \sinh\left(d x + c\right)^{5} + 5 \, {\left(2 \, d \cosh\left(d x + c\right)^{2} - d\right)} \sinh\left(d x + c\right)^{3} + 5 \, {\left(d \cosh\left(d x + c\right)^{4} - 3 \, d \cosh\left(d x + c\right)^{2} + 2 \, d\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"1/120*(15*b^2*cosh(d*x + c)^7 + 105*b^2*cosh(d*x + c)*sinh(d*x + c)^6 - (64*a^2 + 240*a*b + 75*b^2)*cosh(d*x + c)^5 - 4*(15*b^2*d*x - 16*a^2 - 60*a*b)*sinh(d*x + c)^5 + 5*(105*b^2*cosh(d*x + c)^3 - (64*a^2 + 240*a*b + 75*b^2)*cosh(d*x + c))*sinh(d*x + c)^4 + 5*(64*a^2 + 144*a*b + 27*b^2)*cosh(d*x + c)^3 + 20*(15*b^2*d*x - 2*(15*b^2*d*x - 16*a^2 - 60*a*b)*cosh(d*x + c)^2 - 16*a^2 - 60*a*b)*sinh(d*x + c)^3 + 5*(63*b^2*cosh(d*x + c)^5 - 2*(64*a^2 + 240*a*b + 75*b^2)*cosh(d*x + c)^3 + 3*(64*a^2 + 144*a*b + 27*b^2)*cosh(d*x + c))*sinh(d*x + c)^2 - 5*(128*a^2 + 96*a*b + 15*b^2)*cosh(d*x + c) - 20*((15*b^2*d*x - 16*a^2 - 60*a*b)*cosh(d*x + c)^4 + 30*b^2*d*x - 3*(15*b^2*d*x - 16*a^2 - 60*a*b)*cosh(d*x + c)^2 - 32*a^2 - 120*a*b)*sinh(d*x + c))/(d*sinh(d*x + c)^5 + 5*(2*d*cosh(d*x + c)^2 - d)*sinh(d*x + c)^3 + 5*(d*cosh(d*x + c)^4 - 3*d*cosh(d*x + c)^2 + 2*d)*sinh(d*x + c))","B",0
206,1,4500,0,1.067751," ","integrate(csch(d*x+c)^7*(a+b*sinh(d*x+c)^4)^2,x, algorithm=""fricas"")","\frac{24 \, b^{2} \cosh\left(d x + c\right)^{14} + 336 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{13} + 24 \, b^{2} \sinh\left(d x + c\right)^{14} - 6 \, {\left(5 \, a^{2} + 16 \, a b + 20 \, b^{2}\right)} \cosh\left(d x + c\right)^{12} + 6 \, {\left(364 \, b^{2} \cosh\left(d x + c\right)^{2} - 5 \, a^{2} - 16 \, a b - 20 \, b^{2}\right)} \sinh\left(d x + c\right)^{12} + 24 \, {\left(364 \, b^{2} \cosh\left(d x + c\right)^{3} - 3 \, {\left(5 \, a^{2} + 16 \, a b + 20 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{11} + 2 \, {\left(85 \, a^{2} + 144 \, a b + 108 \, b^{2}\right)} \cosh\left(d x + c\right)^{10} + 2 \, {\left(12012 \, b^{2} \cosh\left(d x + c\right)^{4} - 198 \, {\left(5 \, a^{2} + 16 \, a b + 20 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 85 \, a^{2} + 144 \, a b + 108 \, b^{2}\right)} \sinh\left(d x + c\right)^{10} + 4 \, {\left(12012 \, b^{2} \cosh\left(d x + c\right)^{5} - 330 \, {\left(5 \, a^{2} + 16 \, a b + 20 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 5 \, {\left(85 \, a^{2} + 144 \, a b + 108 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} - 12 \, {\left(33 \, a^{2} + 16 \, a b + 10 \, b^{2}\right)} \cosh\left(d x + c\right)^{8} + 6 \, {\left(12012 \, b^{2} \cosh\left(d x + c\right)^{6} - 495 \, {\left(5 \, a^{2} + 16 \, a b + 20 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 15 \, {\left(85 \, a^{2} + 144 \, a b + 108 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 66 \, a^{2} - 32 \, a b - 20 \, b^{2}\right)} \sinh\left(d x + c\right)^{8} + 48 \, {\left(1716 \, b^{2} \cosh\left(d x + c\right)^{7} - 99 \, {\left(5 \, a^{2} + 16 \, a b + 20 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(85 \, a^{2} + 144 \, a b + 108 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - 2 \, {\left(33 \, a^{2} + 16 \, a b + 10 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} - 12 \, {\left(33 \, a^{2} + 16 \, a b + 10 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 12 \, {\left(6006 \, b^{2} \cosh\left(d x + c\right)^{8} - 462 \, {\left(5 \, a^{2} + 16 \, a b + 20 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 35 \, {\left(85 \, a^{2} + 144 \, a b + 108 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} - 28 \, {\left(33 \, a^{2} + 16 \, a b + 10 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 33 \, a^{2} - 16 \, a b - 10 \, b^{2}\right)} \sinh\left(d x + c\right)^{6} + 24 \, {\left(2002 \, b^{2} \cosh\left(d x + c\right)^{9} - 198 \, {\left(5 \, a^{2} + 16 \, a b + 20 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} + 21 \, {\left(85 \, a^{2} + 144 \, a b + 108 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} - 28 \, {\left(33 \, a^{2} + 16 \, a b + 10 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(33 \, a^{2} + 16 \, a b + 10 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(85 \, a^{2} + 144 \, a b + 108 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(12012 \, b^{2} \cosh\left(d x + c\right)^{10} - 1485 \, {\left(5 \, a^{2} + 16 \, a b + 20 \, b^{2}\right)} \cosh\left(d x + c\right)^{8} + 210 \, {\left(85 \, a^{2} + 144 \, a b + 108 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} - 420 \, {\left(33 \, a^{2} + 16 \, a b + 10 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} - 90 \, {\left(33 \, a^{2} + 16 \, a b + 10 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 85 \, a^{2} + 144 \, a b + 108 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(1092 \, b^{2} \cosh\left(d x + c\right)^{11} - 165 \, {\left(5 \, a^{2} + 16 \, a b + 20 \, b^{2}\right)} \cosh\left(d x + c\right)^{9} + 30 \, {\left(85 \, a^{2} + 144 \, a b + 108 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} - 84 \, {\left(33 \, a^{2} + 16 \, a b + 10 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} - 30 \, {\left(33 \, a^{2} + 16 \, a b + 10 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(85 \, a^{2} + 144 \, a b + 108 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 6 \, {\left(5 \, a^{2} + 16 \, a b + 20 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 6 \, {\left(364 \, b^{2} \cosh\left(d x + c\right)^{12} - 66 \, {\left(5 \, a^{2} + 16 \, a b + 20 \, b^{2}\right)} \cosh\left(d x + c\right)^{10} + 15 \, {\left(85 \, a^{2} + 144 \, a b + 108 \, b^{2}\right)} \cosh\left(d x + c\right)^{8} - 56 \, {\left(33 \, a^{2} + 16 \, a b + 10 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} - 30 \, {\left(33 \, a^{2} + 16 \, a b + 10 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(85 \, a^{2} + 144 \, a b + 108 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 5 \, a^{2} - 16 \, a b - 20 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} + 24 \, b^{2} + 3 \, {\left({\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{13} + 13 \, {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{12} + {\left(5 \, a^{2} + 16 \, a b\right)} \sinh\left(d x + c\right)^{13} - 6 \, {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{11} + 6 \, {\left(13 \, {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{2} - 5 \, a^{2} - 16 \, a b\right)} \sinh\left(d x + c\right)^{11} + 22 \, {\left(13 \, {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{10} + 15 \, {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{9} + 5 \, {\left(143 \, {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{4} - 66 \, {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{2} + 15 \, a^{2} + 48 \, a b\right)} \sinh\left(d x + c\right)^{9} + 9 \, {\left(143 \, {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{5} - 110 \, {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{3} + 15 \, {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{8} - 20 \, {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{7} + 4 \, {\left(429 \, {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{6} - 495 \, {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{4} + 135 \, {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{2} - 25 \, a^{2} - 80 \, a b\right)} \sinh\left(d x + c\right)^{7} + 4 \, {\left(429 \, {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{7} - 693 \, {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{5} + 315 \, {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{3} - 35 \, {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} + 15 \, {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{5} + 3 \, {\left(429 \, {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{8} - 924 \, {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{6} + 630 \, {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{4} - 140 \, {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{2} + 25 \, a^{2} + 80 \, a b\right)} \sinh\left(d x + c\right)^{5} + 5 \, {\left(143 \, {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{9} - 396 \, {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{7} + 378 \, {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{5} - 140 \, {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{3} + 15 \, {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} - 6 \, {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(143 \, {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{10} - 495 \, {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{8} + 630 \, {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{6} - 350 \, {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{4} + 75 \, {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{2} - 15 \, a^{2} - 48 \, a b\right)} \sinh\left(d x + c\right)^{3} + 6 \, {\left(13 \, {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{11} - 55 \, {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{9} + 90 \, {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{7} - 70 \, {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{5} + 25 \, {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right) + {\left(13 \, {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{12} - 66 \, {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{10} + 135 \, {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{8} - 140 \, {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{6} + 75 \, {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{4} - 18 \, {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{2} + 5 \, a^{2} + 16 \, a b\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) - 3 \, {\left({\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{13} + 13 \, {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{12} + {\left(5 \, a^{2} + 16 \, a b\right)} \sinh\left(d x + c\right)^{13} - 6 \, {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{11} + 6 \, {\left(13 \, {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{2} - 5 \, a^{2} - 16 \, a b\right)} \sinh\left(d x + c\right)^{11} + 22 \, {\left(13 \, {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{10} + 15 \, {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{9} + 5 \, {\left(143 \, {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{4} - 66 \, {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{2} + 15 \, a^{2} + 48 \, a b\right)} \sinh\left(d x + c\right)^{9} + 9 \, {\left(143 \, {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{5} - 110 \, {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{3} + 15 \, {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{8} - 20 \, {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{7} + 4 \, {\left(429 \, {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{6} - 495 \, {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{4} + 135 \, {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{2} - 25 \, a^{2} - 80 \, a b\right)} \sinh\left(d x + c\right)^{7} + 4 \, {\left(429 \, {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{7} - 693 \, {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{5} + 315 \, {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{3} - 35 \, {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} + 15 \, {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{5} + 3 \, {\left(429 \, {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{8} - 924 \, {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{6} + 630 \, {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{4} - 140 \, {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{2} + 25 \, a^{2} + 80 \, a b\right)} \sinh\left(d x + c\right)^{5} + 5 \, {\left(143 \, {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{9} - 396 \, {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{7} + 378 \, {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{5} - 140 \, {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{3} + 15 \, {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} - 6 \, {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(143 \, {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{10} - 495 \, {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{8} + 630 \, {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{6} - 350 \, {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{4} + 75 \, {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{2} - 15 \, a^{2} - 48 \, a b\right)} \sinh\left(d x + c\right)^{3} + 6 \, {\left(13 \, {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{11} - 55 \, {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{9} + 90 \, {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{7} - 70 \, {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{5} + 25 \, {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right) + {\left(13 \, {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{12} - 66 \, {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{10} + 135 \, {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{8} - 140 \, {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{6} + 75 \, {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{4} - 18 \, {\left(5 \, a^{2} + 16 \, a b\right)} \cosh\left(d x + c\right)^{2} + 5 \, a^{2} + 16 \, a b\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) + 4 \, {\left(84 \, b^{2} \cosh\left(d x + c\right)^{13} - 18 \, {\left(5 \, a^{2} + 16 \, a b + 20 \, b^{2}\right)} \cosh\left(d x + c\right)^{11} + 5 \, {\left(85 \, a^{2} + 144 \, a b + 108 \, b^{2}\right)} \cosh\left(d x + c\right)^{9} - 24 \, {\left(33 \, a^{2} + 16 \, a b + 10 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} - 18 \, {\left(33 \, a^{2} + 16 \, a b + 10 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(85 \, a^{2} + 144 \, a b + 108 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(5 \, a^{2} + 16 \, a b + 20 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{48 \, {\left(d \cosh\left(d x + c\right)^{13} + 13 \, d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{12} + d \sinh\left(d x + c\right)^{13} - 6 \, d \cosh\left(d x + c\right)^{11} + 6 \, {\left(13 \, d \cosh\left(d x + c\right)^{2} - d\right)} \sinh\left(d x + c\right)^{11} + 22 \, {\left(13 \, d \cosh\left(d x + c\right)^{3} - 3 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{10} + 15 \, d \cosh\left(d x + c\right)^{9} + 5 \, {\left(143 \, d \cosh\left(d x + c\right)^{4} - 66 \, d \cosh\left(d x + c\right)^{2} + 3 \, d\right)} \sinh\left(d x + c\right)^{9} + 9 \, {\left(143 \, d \cosh\left(d x + c\right)^{5} - 110 \, d \cosh\left(d x + c\right)^{3} + 15 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{8} - 20 \, d \cosh\left(d x + c\right)^{7} + 4 \, {\left(429 \, d \cosh\left(d x + c\right)^{6} - 495 \, d \cosh\left(d x + c\right)^{4} + 135 \, d \cosh\left(d x + c\right)^{2} - 5 \, d\right)} \sinh\left(d x + c\right)^{7} + 4 \, {\left(429 \, d \cosh\left(d x + c\right)^{7} - 693 \, d \cosh\left(d x + c\right)^{5} + 315 \, d \cosh\left(d x + c\right)^{3} - 35 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} + 15 \, d \cosh\left(d x + c\right)^{5} + 3 \, {\left(429 \, d \cosh\left(d x + c\right)^{8} - 924 \, d \cosh\left(d x + c\right)^{6} + 630 \, d \cosh\left(d x + c\right)^{4} - 140 \, d \cosh\left(d x + c\right)^{2} + 5 \, d\right)} \sinh\left(d x + c\right)^{5} + 5 \, {\left(143 \, d \cosh\left(d x + c\right)^{9} - 396 \, d \cosh\left(d x + c\right)^{7} + 378 \, d \cosh\left(d x + c\right)^{5} - 140 \, d \cosh\left(d x + c\right)^{3} + 15 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} - 6 \, d \cosh\left(d x + c\right)^{3} + 2 \, {\left(143 \, d \cosh\left(d x + c\right)^{10} - 495 \, d \cosh\left(d x + c\right)^{8} + 630 \, d \cosh\left(d x + c\right)^{6} - 350 \, d \cosh\left(d x + c\right)^{4} + 75 \, d \cosh\left(d x + c\right)^{2} - 3 \, d\right)} \sinh\left(d x + c\right)^{3} + 6 \, {\left(13 \, d \cosh\left(d x + c\right)^{11} - 55 \, d \cosh\left(d x + c\right)^{9} + 90 \, d \cosh\left(d x + c\right)^{7} - 70 \, d \cosh\left(d x + c\right)^{5} + 25 \, d \cosh\left(d x + c\right)^{3} - 3 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + d \cosh\left(d x + c\right) + {\left(13 \, d \cosh\left(d x + c\right)^{12} - 66 \, d \cosh\left(d x + c\right)^{10} + 135 \, d \cosh\left(d x + c\right)^{8} - 140 \, d \cosh\left(d x + c\right)^{6} + 75 \, d \cosh\left(d x + c\right)^{4} - 18 \, d \cosh\left(d x + c\right)^{2} + d\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"1/48*(24*b^2*cosh(d*x + c)^14 + 336*b^2*cosh(d*x + c)*sinh(d*x + c)^13 + 24*b^2*sinh(d*x + c)^14 - 6*(5*a^2 + 16*a*b + 20*b^2)*cosh(d*x + c)^12 + 6*(364*b^2*cosh(d*x + c)^2 - 5*a^2 - 16*a*b - 20*b^2)*sinh(d*x + c)^12 + 24*(364*b^2*cosh(d*x + c)^3 - 3*(5*a^2 + 16*a*b + 20*b^2)*cosh(d*x + c))*sinh(d*x + c)^11 + 2*(85*a^2 + 144*a*b + 108*b^2)*cosh(d*x + c)^10 + 2*(12012*b^2*cosh(d*x + c)^4 - 198*(5*a^2 + 16*a*b + 20*b^2)*cosh(d*x + c)^2 + 85*a^2 + 144*a*b + 108*b^2)*sinh(d*x + c)^10 + 4*(12012*b^2*cosh(d*x + c)^5 - 330*(5*a^2 + 16*a*b + 20*b^2)*cosh(d*x + c)^3 + 5*(85*a^2 + 144*a*b + 108*b^2)*cosh(d*x + c))*sinh(d*x + c)^9 - 12*(33*a^2 + 16*a*b + 10*b^2)*cosh(d*x + c)^8 + 6*(12012*b^2*cosh(d*x + c)^6 - 495*(5*a^2 + 16*a*b + 20*b^2)*cosh(d*x + c)^4 + 15*(85*a^2 + 144*a*b + 108*b^2)*cosh(d*x + c)^2 - 66*a^2 - 32*a*b - 20*b^2)*sinh(d*x + c)^8 + 48*(1716*b^2*cosh(d*x + c)^7 - 99*(5*a^2 + 16*a*b + 20*b^2)*cosh(d*x + c)^5 + 5*(85*a^2 + 144*a*b + 108*b^2)*cosh(d*x + c)^3 - 2*(33*a^2 + 16*a*b + 10*b^2)*cosh(d*x + c))*sinh(d*x + c)^7 - 12*(33*a^2 + 16*a*b + 10*b^2)*cosh(d*x + c)^6 + 12*(6006*b^2*cosh(d*x + c)^8 - 462*(5*a^2 + 16*a*b + 20*b^2)*cosh(d*x + c)^6 + 35*(85*a^2 + 144*a*b + 108*b^2)*cosh(d*x + c)^4 - 28*(33*a^2 + 16*a*b + 10*b^2)*cosh(d*x + c)^2 - 33*a^2 - 16*a*b - 10*b^2)*sinh(d*x + c)^6 + 24*(2002*b^2*cosh(d*x + c)^9 - 198*(5*a^2 + 16*a*b + 20*b^2)*cosh(d*x + c)^7 + 21*(85*a^2 + 144*a*b + 108*b^2)*cosh(d*x + c)^5 - 28*(33*a^2 + 16*a*b + 10*b^2)*cosh(d*x + c)^3 - 3*(33*a^2 + 16*a*b + 10*b^2)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(85*a^2 + 144*a*b + 108*b^2)*cosh(d*x + c)^4 + 2*(12012*b^2*cosh(d*x + c)^10 - 1485*(5*a^2 + 16*a*b + 20*b^2)*cosh(d*x + c)^8 + 210*(85*a^2 + 144*a*b + 108*b^2)*cosh(d*x + c)^6 - 420*(33*a^2 + 16*a*b + 10*b^2)*cosh(d*x + c)^4 - 90*(33*a^2 + 16*a*b + 10*b^2)*cosh(d*x + c)^2 + 85*a^2 + 144*a*b + 108*b^2)*sinh(d*x + c)^4 + 8*(1092*b^2*cosh(d*x + c)^11 - 165*(5*a^2 + 16*a*b + 20*b^2)*cosh(d*x + c)^9 + 30*(85*a^2 + 144*a*b + 108*b^2)*cosh(d*x + c)^7 - 84*(33*a^2 + 16*a*b + 10*b^2)*cosh(d*x + c)^5 - 30*(33*a^2 + 16*a*b + 10*b^2)*cosh(d*x + c)^3 + (85*a^2 + 144*a*b + 108*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 - 6*(5*a^2 + 16*a*b + 20*b^2)*cosh(d*x + c)^2 + 6*(364*b^2*cosh(d*x + c)^12 - 66*(5*a^2 + 16*a*b + 20*b^2)*cosh(d*x + c)^10 + 15*(85*a^2 + 144*a*b + 108*b^2)*cosh(d*x + c)^8 - 56*(33*a^2 + 16*a*b + 10*b^2)*cosh(d*x + c)^6 - 30*(33*a^2 + 16*a*b + 10*b^2)*cosh(d*x + c)^4 + 2*(85*a^2 + 144*a*b + 108*b^2)*cosh(d*x + c)^2 - 5*a^2 - 16*a*b - 20*b^2)*sinh(d*x + c)^2 + 24*b^2 + 3*((5*a^2 + 16*a*b)*cosh(d*x + c)^13 + 13*(5*a^2 + 16*a*b)*cosh(d*x + c)*sinh(d*x + c)^12 + (5*a^2 + 16*a*b)*sinh(d*x + c)^13 - 6*(5*a^2 + 16*a*b)*cosh(d*x + c)^11 + 6*(13*(5*a^2 + 16*a*b)*cosh(d*x + c)^2 - 5*a^2 - 16*a*b)*sinh(d*x + c)^11 + 22*(13*(5*a^2 + 16*a*b)*cosh(d*x + c)^3 - 3*(5*a^2 + 16*a*b)*cosh(d*x + c))*sinh(d*x + c)^10 + 15*(5*a^2 + 16*a*b)*cosh(d*x + c)^9 + 5*(143*(5*a^2 + 16*a*b)*cosh(d*x + c)^4 - 66*(5*a^2 + 16*a*b)*cosh(d*x + c)^2 + 15*a^2 + 48*a*b)*sinh(d*x + c)^9 + 9*(143*(5*a^2 + 16*a*b)*cosh(d*x + c)^5 - 110*(5*a^2 + 16*a*b)*cosh(d*x + c)^3 + 15*(5*a^2 + 16*a*b)*cosh(d*x + c))*sinh(d*x + c)^8 - 20*(5*a^2 + 16*a*b)*cosh(d*x + c)^7 + 4*(429*(5*a^2 + 16*a*b)*cosh(d*x + c)^6 - 495*(5*a^2 + 16*a*b)*cosh(d*x + c)^4 + 135*(5*a^2 + 16*a*b)*cosh(d*x + c)^2 - 25*a^2 - 80*a*b)*sinh(d*x + c)^7 + 4*(429*(5*a^2 + 16*a*b)*cosh(d*x + c)^7 - 693*(5*a^2 + 16*a*b)*cosh(d*x + c)^5 + 315*(5*a^2 + 16*a*b)*cosh(d*x + c)^3 - 35*(5*a^2 + 16*a*b)*cosh(d*x + c))*sinh(d*x + c)^6 + 15*(5*a^2 + 16*a*b)*cosh(d*x + c)^5 + 3*(429*(5*a^2 + 16*a*b)*cosh(d*x + c)^8 - 924*(5*a^2 + 16*a*b)*cosh(d*x + c)^6 + 630*(5*a^2 + 16*a*b)*cosh(d*x + c)^4 - 140*(5*a^2 + 16*a*b)*cosh(d*x + c)^2 + 25*a^2 + 80*a*b)*sinh(d*x + c)^5 + 5*(143*(5*a^2 + 16*a*b)*cosh(d*x + c)^9 - 396*(5*a^2 + 16*a*b)*cosh(d*x + c)^7 + 378*(5*a^2 + 16*a*b)*cosh(d*x + c)^5 - 140*(5*a^2 + 16*a*b)*cosh(d*x + c)^3 + 15*(5*a^2 + 16*a*b)*cosh(d*x + c))*sinh(d*x + c)^4 - 6*(5*a^2 + 16*a*b)*cosh(d*x + c)^3 + 2*(143*(5*a^2 + 16*a*b)*cosh(d*x + c)^10 - 495*(5*a^2 + 16*a*b)*cosh(d*x + c)^8 + 630*(5*a^2 + 16*a*b)*cosh(d*x + c)^6 - 350*(5*a^2 + 16*a*b)*cosh(d*x + c)^4 + 75*(5*a^2 + 16*a*b)*cosh(d*x + c)^2 - 15*a^2 - 48*a*b)*sinh(d*x + c)^3 + 6*(13*(5*a^2 + 16*a*b)*cosh(d*x + c)^11 - 55*(5*a^2 + 16*a*b)*cosh(d*x + c)^9 + 90*(5*a^2 + 16*a*b)*cosh(d*x + c)^7 - 70*(5*a^2 + 16*a*b)*cosh(d*x + c)^5 + 25*(5*a^2 + 16*a*b)*cosh(d*x + c)^3 - 3*(5*a^2 + 16*a*b)*cosh(d*x + c))*sinh(d*x + c)^2 + (5*a^2 + 16*a*b)*cosh(d*x + c) + (13*(5*a^2 + 16*a*b)*cosh(d*x + c)^12 - 66*(5*a^2 + 16*a*b)*cosh(d*x + c)^10 + 135*(5*a^2 + 16*a*b)*cosh(d*x + c)^8 - 140*(5*a^2 + 16*a*b)*cosh(d*x + c)^6 + 75*(5*a^2 + 16*a*b)*cosh(d*x + c)^4 - 18*(5*a^2 + 16*a*b)*cosh(d*x + c)^2 + 5*a^2 + 16*a*b)*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) + 1) - 3*((5*a^2 + 16*a*b)*cosh(d*x + c)^13 + 13*(5*a^2 + 16*a*b)*cosh(d*x + c)*sinh(d*x + c)^12 + (5*a^2 + 16*a*b)*sinh(d*x + c)^13 - 6*(5*a^2 + 16*a*b)*cosh(d*x + c)^11 + 6*(13*(5*a^2 + 16*a*b)*cosh(d*x + c)^2 - 5*a^2 - 16*a*b)*sinh(d*x + c)^11 + 22*(13*(5*a^2 + 16*a*b)*cosh(d*x + c)^3 - 3*(5*a^2 + 16*a*b)*cosh(d*x + c))*sinh(d*x + c)^10 + 15*(5*a^2 + 16*a*b)*cosh(d*x + c)^9 + 5*(143*(5*a^2 + 16*a*b)*cosh(d*x + c)^4 - 66*(5*a^2 + 16*a*b)*cosh(d*x + c)^2 + 15*a^2 + 48*a*b)*sinh(d*x + c)^9 + 9*(143*(5*a^2 + 16*a*b)*cosh(d*x + c)^5 - 110*(5*a^2 + 16*a*b)*cosh(d*x + c)^3 + 15*(5*a^2 + 16*a*b)*cosh(d*x + c))*sinh(d*x + c)^8 - 20*(5*a^2 + 16*a*b)*cosh(d*x + c)^7 + 4*(429*(5*a^2 + 16*a*b)*cosh(d*x + c)^6 - 495*(5*a^2 + 16*a*b)*cosh(d*x + c)^4 + 135*(5*a^2 + 16*a*b)*cosh(d*x + c)^2 - 25*a^2 - 80*a*b)*sinh(d*x + c)^7 + 4*(429*(5*a^2 + 16*a*b)*cosh(d*x + c)^7 - 693*(5*a^2 + 16*a*b)*cosh(d*x + c)^5 + 315*(5*a^2 + 16*a*b)*cosh(d*x + c)^3 - 35*(5*a^2 + 16*a*b)*cosh(d*x + c))*sinh(d*x + c)^6 + 15*(5*a^2 + 16*a*b)*cosh(d*x + c)^5 + 3*(429*(5*a^2 + 16*a*b)*cosh(d*x + c)^8 - 924*(5*a^2 + 16*a*b)*cosh(d*x + c)^6 + 630*(5*a^2 + 16*a*b)*cosh(d*x + c)^4 - 140*(5*a^2 + 16*a*b)*cosh(d*x + c)^2 + 25*a^2 + 80*a*b)*sinh(d*x + c)^5 + 5*(143*(5*a^2 + 16*a*b)*cosh(d*x + c)^9 - 396*(5*a^2 + 16*a*b)*cosh(d*x + c)^7 + 378*(5*a^2 + 16*a*b)*cosh(d*x + c)^5 - 140*(5*a^2 + 16*a*b)*cosh(d*x + c)^3 + 15*(5*a^2 + 16*a*b)*cosh(d*x + c))*sinh(d*x + c)^4 - 6*(5*a^2 + 16*a*b)*cosh(d*x + c)^3 + 2*(143*(5*a^2 + 16*a*b)*cosh(d*x + c)^10 - 495*(5*a^2 + 16*a*b)*cosh(d*x + c)^8 + 630*(5*a^2 + 16*a*b)*cosh(d*x + c)^6 - 350*(5*a^2 + 16*a*b)*cosh(d*x + c)^4 + 75*(5*a^2 + 16*a*b)*cosh(d*x + c)^2 - 15*a^2 - 48*a*b)*sinh(d*x + c)^3 + 6*(13*(5*a^2 + 16*a*b)*cosh(d*x + c)^11 - 55*(5*a^2 + 16*a*b)*cosh(d*x + c)^9 + 90*(5*a^2 + 16*a*b)*cosh(d*x + c)^7 - 70*(5*a^2 + 16*a*b)*cosh(d*x + c)^5 + 25*(5*a^2 + 16*a*b)*cosh(d*x + c)^3 - 3*(5*a^2 + 16*a*b)*cosh(d*x + c))*sinh(d*x + c)^2 + (5*a^2 + 16*a*b)*cosh(d*x + c) + (13*(5*a^2 + 16*a*b)*cosh(d*x + c)^12 - 66*(5*a^2 + 16*a*b)*cosh(d*x + c)^10 + 135*(5*a^2 + 16*a*b)*cosh(d*x + c)^8 - 140*(5*a^2 + 16*a*b)*cosh(d*x + c)^6 + 75*(5*a^2 + 16*a*b)*cosh(d*x + c)^4 - 18*(5*a^2 + 16*a*b)*cosh(d*x + c)^2 + 5*a^2 + 16*a*b)*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) - 1) + 4*(84*b^2*cosh(d*x + c)^13 - 18*(5*a^2 + 16*a*b + 20*b^2)*cosh(d*x + c)^11 + 5*(85*a^2 + 144*a*b + 108*b^2)*cosh(d*x + c)^9 - 24*(33*a^2 + 16*a*b + 10*b^2)*cosh(d*x + c)^7 - 18*(33*a^2 + 16*a*b + 10*b^2)*cosh(d*x + c)^5 + 2*(85*a^2 + 144*a*b + 108*b^2)*cosh(d*x + c)^3 - 3*(5*a^2 + 16*a*b + 20*b^2)*cosh(d*x + c))*sinh(d*x + c))/(d*cosh(d*x + c)^13 + 13*d*cosh(d*x + c)*sinh(d*x + c)^12 + d*sinh(d*x + c)^13 - 6*d*cosh(d*x + c)^11 + 6*(13*d*cosh(d*x + c)^2 - d)*sinh(d*x + c)^11 + 22*(13*d*cosh(d*x + c)^3 - 3*d*cosh(d*x + c))*sinh(d*x + c)^10 + 15*d*cosh(d*x + c)^9 + 5*(143*d*cosh(d*x + c)^4 - 66*d*cosh(d*x + c)^2 + 3*d)*sinh(d*x + c)^9 + 9*(143*d*cosh(d*x + c)^5 - 110*d*cosh(d*x + c)^3 + 15*d*cosh(d*x + c))*sinh(d*x + c)^8 - 20*d*cosh(d*x + c)^7 + 4*(429*d*cosh(d*x + c)^6 - 495*d*cosh(d*x + c)^4 + 135*d*cosh(d*x + c)^2 - 5*d)*sinh(d*x + c)^7 + 4*(429*d*cosh(d*x + c)^7 - 693*d*cosh(d*x + c)^5 + 315*d*cosh(d*x + c)^3 - 35*d*cosh(d*x + c))*sinh(d*x + c)^6 + 15*d*cosh(d*x + c)^5 + 3*(429*d*cosh(d*x + c)^8 - 924*d*cosh(d*x + c)^6 + 630*d*cosh(d*x + c)^4 - 140*d*cosh(d*x + c)^2 + 5*d)*sinh(d*x + c)^5 + 5*(143*d*cosh(d*x + c)^9 - 396*d*cosh(d*x + c)^7 + 378*d*cosh(d*x + c)^5 - 140*d*cosh(d*x + c)^3 + 15*d*cosh(d*x + c))*sinh(d*x + c)^4 - 6*d*cosh(d*x + c)^3 + 2*(143*d*cosh(d*x + c)^10 - 495*d*cosh(d*x + c)^8 + 630*d*cosh(d*x + c)^6 - 350*d*cosh(d*x + c)^4 + 75*d*cosh(d*x + c)^2 - 3*d)*sinh(d*x + c)^3 + 6*(13*d*cosh(d*x + c)^11 - 55*d*cosh(d*x + c)^9 + 90*d*cosh(d*x + c)^7 - 70*d*cosh(d*x + c)^5 + 25*d*cosh(d*x + c)^3 - 3*d*cosh(d*x + c))*sinh(d*x + c)^2 + d*cosh(d*x + c) + (13*d*cosh(d*x + c)^12 - 66*d*cosh(d*x + c)^10 + 135*d*cosh(d*x + c)^8 - 140*d*cosh(d*x + c)^6 + 75*d*cosh(d*x + c)^4 - 18*d*cosh(d*x + c)^2 + d)*sinh(d*x + c))","B",0
207,1,1030,0,0.853042," ","integrate(sinh(d*x+c)^5*(a+b*sinh(d*x+c)^4)^3,x, algorithm=""fricas"")","\frac{45045 \, b^{3} \cosh\left(d x + c\right)^{17} + 765765 \, b^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{16} - 867867 \, b^{3} \cosh\left(d x + c\right)^{15} + 765765 \, {\left(40 \, b^{3} \cosh\left(d x + c\right)^{3} - 17 \, b^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{14} + 471240 \, {\left(6 \, a b^{2} + 17 \, b^{3}\right)} \cosh\left(d x + c\right)^{13} + 255255 \, {\left(1092 \, b^{3} \cosh\left(d x + c\right)^{5} - 1547 \, b^{3} \cosh\left(d x + c\right)^{3} + 24 \, {\left(6 \, a b^{2} + 17 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{12} - 556920 \, {\left(78 \, a b^{2} + 85 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} + 153153 \, {\left(5720 \, b^{3} \cosh\left(d x + c\right)^{7} - 17017 \, b^{3} \cosh\left(d x + c\right)^{5} + 880 \, {\left(6 \, a b^{2} + 17 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 40 \, {\left(78 \, a b^{2} + 85 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{10} + 340340 \, {\left(192 \, a^{2} b + 936 \, a b^{2} + 595 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + 765765 \, {\left(1430 \, b^{3} \cosh\left(d x + c\right)^{9} - 7293 \, b^{3} \cosh\left(d x + c\right)^{7} + 792 \, {\left(6 \, a b^{2} + 17 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 120 \, {\left(78 \, a b^{2} + 85 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(192 \, a^{2} b + 936 \, a b^{2} + 595 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{8} - 437580 \, {\left(1728 \, a^{2} b + 3432 \, a b^{2} + 1547 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 255255 \, {\left(2184 \, b^{3} \cosh\left(d x + c\right)^{11} - 17017 \, b^{3} \cosh\left(d x + c\right)^{9} + 3168 \, {\left(6 \, a b^{2} + 17 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} - 1008 \, {\left(78 \, a b^{2} + 85 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 112 \, {\left(192 \, a^{2} b + 936 \, a b^{2} + 595 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 12 \, {\left(1728 \, a^{2} b + 3432 \, a b^{2} + 1547 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} + 1225224 \, {\left(512 \, a^{3} + 3456 \, a^{2} b + 4290 \, a b^{2} + 1547 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 765765 \, {\left(140 \, b^{3} \cosh\left(d x + c\right)^{13} - 1547 \, b^{3} \cosh\left(d x + c\right)^{11} + 440 \, {\left(6 \, a b^{2} + 17 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} - 240 \, {\left(78 \, a b^{2} + 85 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 56 \, {\left(192 \, a^{2} b + 936 \, a b^{2} + 595 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 20 \, {\left(1728 \, a^{2} b + 3432 \, a b^{2} + 1547 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 8 \, {\left(512 \, a^{3} + 3456 \, a^{2} b + 4290 \, a b^{2} + 1547 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} - 2042040 \, {\left(2560 \, a^{3} + 8064 \, a^{2} b + 7722 \, a b^{2} + 2431 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 765765 \, {\left(8 \, b^{3} \cosh\left(d x + c\right)^{15} - 119 \, b^{3} \cosh\left(d x + c\right)^{13} + 48 \, {\left(6 \, a b^{2} + 17 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} - 40 \, {\left(78 \, a b^{2} + 85 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + 16 \, {\left(192 \, a^{2} b + 936 \, a b^{2} + 595 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} - 12 \, {\left(1728 \, a^{2} b + 3432 \, a b^{2} + 1547 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 16 \, {\left(512 \, a^{3} + 3456 \, a^{2} b + 4290 \, a b^{2} + 1547 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 8 \, {\left(2560 \, a^{3} + 8064 \, a^{2} b + 7722 \, a b^{2} + 2431 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 1531530 \, {\left(20480 \, a^{3} + 48384 \, a^{2} b + 41184 \, a b^{2} + 12155 \, b^{3}\right)} \cosh\left(d x + c\right)}{50185175040 \, d}"," ",0,"1/50185175040*(45045*b^3*cosh(d*x + c)^17 + 765765*b^3*cosh(d*x + c)*sinh(d*x + c)^16 - 867867*b^3*cosh(d*x + c)^15 + 765765*(40*b^3*cosh(d*x + c)^3 - 17*b^3*cosh(d*x + c))*sinh(d*x + c)^14 + 471240*(6*a*b^2 + 17*b^3)*cosh(d*x + c)^13 + 255255*(1092*b^3*cosh(d*x + c)^5 - 1547*b^3*cosh(d*x + c)^3 + 24*(6*a*b^2 + 17*b^3)*cosh(d*x + c))*sinh(d*x + c)^12 - 556920*(78*a*b^2 + 85*b^3)*cosh(d*x + c)^11 + 153153*(5720*b^3*cosh(d*x + c)^7 - 17017*b^3*cosh(d*x + c)^5 + 880*(6*a*b^2 + 17*b^3)*cosh(d*x + c)^3 - 40*(78*a*b^2 + 85*b^3)*cosh(d*x + c))*sinh(d*x + c)^10 + 340340*(192*a^2*b + 936*a*b^2 + 595*b^3)*cosh(d*x + c)^9 + 765765*(1430*b^3*cosh(d*x + c)^9 - 7293*b^3*cosh(d*x + c)^7 + 792*(6*a*b^2 + 17*b^3)*cosh(d*x + c)^5 - 120*(78*a*b^2 + 85*b^3)*cosh(d*x + c)^3 + 4*(192*a^2*b + 936*a*b^2 + 595*b^3)*cosh(d*x + c))*sinh(d*x + c)^8 - 437580*(1728*a^2*b + 3432*a*b^2 + 1547*b^3)*cosh(d*x + c)^7 + 255255*(2184*b^3*cosh(d*x + c)^11 - 17017*b^3*cosh(d*x + c)^9 + 3168*(6*a*b^2 + 17*b^3)*cosh(d*x + c)^7 - 1008*(78*a*b^2 + 85*b^3)*cosh(d*x + c)^5 + 112*(192*a^2*b + 936*a*b^2 + 595*b^3)*cosh(d*x + c)^3 - 12*(1728*a^2*b + 3432*a*b^2 + 1547*b^3)*cosh(d*x + c))*sinh(d*x + c)^6 + 1225224*(512*a^3 + 3456*a^2*b + 4290*a*b^2 + 1547*b^3)*cosh(d*x + c)^5 + 765765*(140*b^3*cosh(d*x + c)^13 - 1547*b^3*cosh(d*x + c)^11 + 440*(6*a*b^2 + 17*b^3)*cosh(d*x + c)^9 - 240*(78*a*b^2 + 85*b^3)*cosh(d*x + c)^7 + 56*(192*a^2*b + 936*a*b^2 + 595*b^3)*cosh(d*x + c)^5 - 20*(1728*a^2*b + 3432*a*b^2 + 1547*b^3)*cosh(d*x + c)^3 + 8*(512*a^3 + 3456*a^2*b + 4290*a*b^2 + 1547*b^3)*cosh(d*x + c))*sinh(d*x + c)^4 - 2042040*(2560*a^3 + 8064*a^2*b + 7722*a*b^2 + 2431*b^3)*cosh(d*x + c)^3 + 765765*(8*b^3*cosh(d*x + c)^15 - 119*b^3*cosh(d*x + c)^13 + 48*(6*a*b^2 + 17*b^3)*cosh(d*x + c)^11 - 40*(78*a*b^2 + 85*b^3)*cosh(d*x + c)^9 + 16*(192*a^2*b + 936*a*b^2 + 595*b^3)*cosh(d*x + c)^7 - 12*(1728*a^2*b + 3432*a*b^2 + 1547*b^3)*cosh(d*x + c)^5 + 16*(512*a^3 + 3456*a^2*b + 4290*a*b^2 + 1547*b^3)*cosh(d*x + c)^3 - 8*(2560*a^3 + 8064*a^2*b + 7722*a*b^2 + 2431*b^3)*cosh(d*x + c))*sinh(d*x + c)^2 + 1531530*(20480*a^3 + 48384*a^2*b + 41184*a*b^2 + 12155*b^3)*cosh(d*x + c))/d","B",0
208,1,795,0,1.208810," ","integrate(sinh(d*x+c)^3*(a+b*sinh(d*x+c)^4)^3,x, algorithm=""fricas"")","\frac{3003 \, b^{3} \cosh\left(d x + c\right)^{15} + 45045 \, b^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{14} - 51975 \, b^{3} \cosh\left(d x + c\right)^{13} + 15015 \, {\left(91 \, b^{3} \cosh\left(d x + c\right)^{3} - 45 \, b^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{12} + 12285 \, {\left(16 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} + 9009 \, {\left(1001 \, b^{3} \cosh\left(d x + c\right)^{5} - 1650 \, b^{3} \cosh\left(d x + c\right)^{3} + 15 \, {\left(16 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{10} - 5005 \, {\left(528 \, a b^{2} + 455 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + 45045 \, {\left(429 \, b^{3} \cosh\left(d x + c\right)^{7} - 1485 \, b^{3} \cosh\left(d x + c\right)^{5} + 45 \, {\left(16 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - {\left(528 \, a b^{2} + 455 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{8} + 19305 \, {\left(256 \, a^{2} b + 880 \, a b^{2} + 455 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 15015 \, {\left(1001 \, b^{3} \cosh\left(d x + c\right)^{9} - 5940 \, b^{3} \cosh\left(d x + c\right)^{7} + 378 \, {\left(16 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 28 \, {\left(528 \, a b^{2} + 455 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 9 \, {\left(256 \, a^{2} b + 880 \, a b^{2} + 455 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} - 27027 \, {\left(1792 \, a^{2} b + 2640 \, a b^{2} + 1001 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 45045 \, {\left(91 \, b^{3} \cosh\left(d x + c\right)^{11} - 825 \, b^{3} \cosh\left(d x + c\right)^{9} + 90 \, {\left(16 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} - 14 \, {\left(528 \, a b^{2} + 455 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 15 \, {\left(256 \, a^{2} b + 880 \, a b^{2} + 455 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(1792 \, a^{2} b + 2640 \, a b^{2} + 1001 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 15015 \, {\left(4096 \, a^{3} + 16128 \, a^{2} b + 15840 \, a b^{2} + 5005 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 45045 \, {\left(7 \, b^{3} \cosh\left(d x + c\right)^{13} - 90 \, b^{3} \cosh\left(d x + c\right)^{11} + 15 \, {\left(16 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} - 4 \, {\left(528 \, a b^{2} + 455 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 9 \, {\left(256 \, a^{2} b + 880 \, a b^{2} + 455 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 6 \, {\left(1792 \, a^{2} b + 2640 \, a b^{2} + 1001 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(4096 \, a^{3} + 16128 \, a^{2} b + 15840 \, a b^{2} + 5005 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 135135 \, {\left(4096 \, a^{3} + 8960 \, a^{2} b + 7392 \, a b^{2} + 2145 \, b^{3}\right)} \cosh\left(d x + c\right)}{738017280 \, d}"," ",0,"1/738017280*(3003*b^3*cosh(d*x + c)^15 + 45045*b^3*cosh(d*x + c)*sinh(d*x + c)^14 - 51975*b^3*cosh(d*x + c)^13 + 15015*(91*b^3*cosh(d*x + c)^3 - 45*b^3*cosh(d*x + c))*sinh(d*x + c)^12 + 12285*(16*a*b^2 + 35*b^3)*cosh(d*x + c)^11 + 9009*(1001*b^3*cosh(d*x + c)^5 - 1650*b^3*cosh(d*x + c)^3 + 15*(16*a*b^2 + 35*b^3)*cosh(d*x + c))*sinh(d*x + c)^10 - 5005*(528*a*b^2 + 455*b^3)*cosh(d*x + c)^9 + 45045*(429*b^3*cosh(d*x + c)^7 - 1485*b^3*cosh(d*x + c)^5 + 45*(16*a*b^2 + 35*b^3)*cosh(d*x + c)^3 - (528*a*b^2 + 455*b^3)*cosh(d*x + c))*sinh(d*x + c)^8 + 19305*(256*a^2*b + 880*a*b^2 + 455*b^3)*cosh(d*x + c)^7 + 15015*(1001*b^3*cosh(d*x + c)^9 - 5940*b^3*cosh(d*x + c)^7 + 378*(16*a*b^2 + 35*b^3)*cosh(d*x + c)^5 - 28*(528*a*b^2 + 455*b^3)*cosh(d*x + c)^3 + 9*(256*a^2*b + 880*a*b^2 + 455*b^3)*cosh(d*x + c))*sinh(d*x + c)^6 - 27027*(1792*a^2*b + 2640*a*b^2 + 1001*b^3)*cosh(d*x + c)^5 + 45045*(91*b^3*cosh(d*x + c)^11 - 825*b^3*cosh(d*x + c)^9 + 90*(16*a*b^2 + 35*b^3)*cosh(d*x + c)^7 - 14*(528*a*b^2 + 455*b^3)*cosh(d*x + c)^5 + 15*(256*a^2*b + 880*a*b^2 + 455*b^3)*cosh(d*x + c)^3 - 3*(1792*a^2*b + 2640*a*b^2 + 1001*b^3)*cosh(d*x + c))*sinh(d*x + c)^4 + 15015*(4096*a^3 + 16128*a^2*b + 15840*a*b^2 + 5005*b^3)*cosh(d*x + c)^3 + 45045*(7*b^3*cosh(d*x + c)^13 - 90*b^3*cosh(d*x + c)^11 + 15*(16*a*b^2 + 35*b^3)*cosh(d*x + c)^9 - 4*(528*a*b^2 + 455*b^3)*cosh(d*x + c)^7 + 9*(256*a^2*b + 880*a*b^2 + 455*b^3)*cosh(d*x + c)^5 - 6*(1792*a^2*b + 2640*a*b^2 + 1001*b^3)*cosh(d*x + c)^3 + (4096*a^3 + 16128*a^2*b + 15840*a*b^2 + 5005*b^3)*cosh(d*x + c))*sinh(d*x + c)^2 - 135135*(4096*a^3 + 8960*a^2*b + 7392*a*b^2 + 2145*b^3)*cosh(d*x + c))/d","B",0
209,1,594,0,1.371935," ","integrate(sinh(d*x+c)*(a+b*sinh(d*x+c)^4)^3,x, algorithm=""fricas"")","\frac{1155 \, b^{3} \cosh\left(d x + c\right)^{13} + 15015 \, b^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{12} - 17745 \, b^{3} \cosh\left(d x + c\right)^{11} + 15015 \, {\left(22 \, b^{3} \cosh\left(d x + c\right)^{3} - 13 \, b^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{10} + 10010 \, {\left(8 \, a b^{2} + 13 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + 45045 \, {\left(33 \, b^{3} \cosh\left(d x + c\right)^{5} - 65 \, b^{3} \cosh\left(d x + c\right)^{3} + 2 \, {\left(8 \, a b^{2} + 13 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{8} - 4290 \, {\left(216 \, a b^{2} + 143 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 30030 \, {\left(66 \, b^{3} \cosh\left(d x + c\right)^{7} - 273 \, b^{3} \cosh\left(d x + c\right)^{5} + 28 \, {\left(8 \, a b^{2} + 13 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - {\left(216 \, a b^{2} + 143 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} + 3003 \, {\left(768 \, a^{2} b + 1728 \, a b^{2} + 715 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 15015 \, {\left(55 \, b^{3} \cosh\left(d x + c\right)^{9} - 390 \, b^{3} \cosh\left(d x + c\right)^{7} + 84 \, {\left(8 \, a b^{2} + 13 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 10 \, {\left(216 \, a b^{2} + 143 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(768 \, a^{2} b + 1728 \, a b^{2} + 715 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} - 15015 \, {\left(1280 \, a^{2} b + 1344 \, a b^{2} + 429 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 15015 \, {\left(6 \, b^{3} \cosh\left(d x + c\right)^{11} - 65 \, b^{3} \cosh\left(d x + c\right)^{9} + 24 \, {\left(8 \, a b^{2} + 13 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} - 6 \, {\left(216 \, a b^{2} + 143 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(768 \, a^{2} b + 1728 \, a b^{2} + 715 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(1280 \, a^{2} b + 1344 \, a b^{2} + 429 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 60060 \, {\left(1024 \, a^{3} + 1920 \, a^{2} b + 1512 \, a b^{2} + 429 \, b^{3}\right)} \cosh\left(d x + c\right)}{61501440 \, d}"," ",0,"1/61501440*(1155*b^3*cosh(d*x + c)^13 + 15015*b^3*cosh(d*x + c)*sinh(d*x + c)^12 - 17745*b^3*cosh(d*x + c)^11 + 15015*(22*b^3*cosh(d*x + c)^3 - 13*b^3*cosh(d*x + c))*sinh(d*x + c)^10 + 10010*(8*a*b^2 + 13*b^3)*cosh(d*x + c)^9 + 45045*(33*b^3*cosh(d*x + c)^5 - 65*b^3*cosh(d*x + c)^3 + 2*(8*a*b^2 + 13*b^3)*cosh(d*x + c))*sinh(d*x + c)^8 - 4290*(216*a*b^2 + 143*b^3)*cosh(d*x + c)^7 + 30030*(66*b^3*cosh(d*x + c)^7 - 273*b^3*cosh(d*x + c)^5 + 28*(8*a*b^2 + 13*b^3)*cosh(d*x + c)^3 - (216*a*b^2 + 143*b^3)*cosh(d*x + c))*sinh(d*x + c)^6 + 3003*(768*a^2*b + 1728*a*b^2 + 715*b^3)*cosh(d*x + c)^5 + 15015*(55*b^3*cosh(d*x + c)^9 - 390*b^3*cosh(d*x + c)^7 + 84*(8*a*b^2 + 13*b^3)*cosh(d*x + c)^5 - 10*(216*a*b^2 + 143*b^3)*cosh(d*x + c)^3 + (768*a^2*b + 1728*a*b^2 + 715*b^3)*cosh(d*x + c))*sinh(d*x + c)^4 - 15015*(1280*a^2*b + 1344*a*b^2 + 429*b^3)*cosh(d*x + c)^3 + 15015*(6*b^3*cosh(d*x + c)^11 - 65*b^3*cosh(d*x + c)^9 + 24*(8*a*b^2 + 13*b^3)*cosh(d*x + c)^7 - 6*(216*a*b^2 + 143*b^3)*cosh(d*x + c)^5 + 2*(768*a^2*b + 1728*a*b^2 + 715*b^3)*cosh(d*x + c)^3 - 3*(1280*a^2*b + 1344*a*b^2 + 429*b^3)*cosh(d*x + c))*sinh(d*x + c)^2 + 60060*(1024*a^3 + 1920*a^2*b + 1512*a*b^2 + 429*b^3)*cosh(d*x + c))/d","B",0
210,1,3824,0,0.973781," ","integrate(csch(d*x+c)*(a+b*sinh(d*x+c)^4)^3,x, algorithm=""fricas"")","\frac{315 \, b^{3} \cosh\left(d x + c\right)^{22} + 6930 \, b^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{21} + 315 \, b^{3} \sinh\left(d x + c\right)^{22} - 4235 \, b^{3} \cosh\left(d x + c\right)^{20} + 385 \, {\left(189 \, b^{3} \cosh\left(d x + c\right)^{2} - 11 \, b^{3}\right)} \sinh\left(d x + c\right)^{20} + 7700 \, {\left(63 \, b^{3} \cosh\left(d x + c\right)^{3} - 11 \, b^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{19} + 495 \, {\left(48 \, a b^{2} + 55 \, b^{3}\right)} \cosh\left(d x + c\right)^{18} + 55 \, {\left(41895 \, b^{3} \cosh\left(d x + c\right)^{4} - 14630 \, b^{3} \cosh\left(d x + c\right)^{2} + 432 \, a b^{2} + 495 \, b^{3}\right)} \sinh\left(d x + c\right)^{18} + 330 \, {\left(25137 \, b^{3} \cosh\left(d x + c\right)^{5} - 14630 \, b^{3} \cosh\left(d x + c\right)^{3} + 27 \, {\left(48 \, a b^{2} + 55 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{17} - 2079 \, {\left(112 \, a b^{2} + 55 \, b^{3}\right)} \cosh\left(d x + c\right)^{16} + 33 \, {\left(712215 \, b^{3} \cosh\left(d x + c\right)^{6} - 621775 \, b^{3} \cosh\left(d x + c\right)^{4} - 7056 \, a b^{2} - 3465 \, b^{3} + 2295 \, {\left(48 \, a b^{2} + 55 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{16} + 528 \, {\left(101745 \, b^{3} \cosh\left(d x + c\right)^{7} - 124355 \, b^{3} \cosh\left(d x + c\right)^{5} + 765 \, {\left(48 \, a b^{2} + 55 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 63 \, {\left(112 \, a b^{2} + 55 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{15} + 6930 \, {\left(128 \, a^{2} b + 168 \, a b^{2} + 55 \, b^{3}\right)} \cosh\left(d x + c\right)^{14} + 330 \, {\left(305235 \, b^{3} \cosh\left(d x + c\right)^{8} - 497420 \, b^{3} \cosh\left(d x + c\right)^{6} + 4590 \, {\left(48 \, a b^{2} + 55 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 2688 \, a^{2} b + 3528 \, a b^{2} + 1155 \, b^{3} - 756 \, {\left(112 \, a b^{2} + 55 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{14} + 4620 \, {\left(33915 \, b^{3} \cosh\left(d x + c\right)^{9} - 71060 \, b^{3} \cosh\left(d x + c\right)^{7} + 918 \, {\left(48 \, a b^{2} + 55 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 252 \, {\left(112 \, a b^{2} + 55 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 21 \, {\left(128 \, a^{2} b + 168 \, a b^{2} + 55 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{13} - 20790 \, {\left(384 \, a^{2} b + 280 \, a b^{2} + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{12} + 2310 \, {\left(88179 \, b^{3} \cosh\left(d x + c\right)^{10} - 230945 \, b^{3} \cosh\left(d x + c\right)^{8} + 3978 \, {\left(48 \, a b^{2} + 55 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} - 1638 \, {\left(112 \, a b^{2} + 55 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 3456 \, a^{2} b - 2520 \, a b^{2} - 693 \, b^{3} + 273 \, {\left(128 \, a^{2} b + 168 \, a b^{2} + 55 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{12} + 8 \, {\left(27776385 \, b^{3} \cosh\left(d x + c\right)^{11} - 88913825 \, b^{3} \cosh\left(d x + c\right)^{9} + 1969110 \, {\left(48 \, a b^{2} + 55 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} - 1135134 \, {\left(112 \, a b^{2} + 55 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 315315 \, {\left(128 \, a^{2} b + 168 \, a b^{2} + 55 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 31185 \, {\left(384 \, a^{2} b + 280 \, a b^{2} + 77 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{11} - 20790 \, {\left(384 \, a^{2} b + 280 \, a b^{2} + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} + 22 \, {\left(9258795 \, b^{3} \cosh\left(d x + c\right)^{12} - 35565530 \, b^{3} \cosh\left(d x + c\right)^{10} + 984555 \, {\left(48 \, a b^{2} + 55 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} - 756756 \, {\left(112 \, a b^{2} + 55 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 315315 \, {\left(128 \, a^{2} b + 168 \, a b^{2} + 55 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 362880 \, a^{2} b - 264600 \, a b^{2} - 72765 \, b^{3} - 62370 \, {\left(384 \, a^{2} b + 280 \, a b^{2} + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{10} + 220 \, {\left(712215 \, b^{3} \cosh\left(d x + c\right)^{13} - 3233230 \, b^{3} \cosh\left(d x + c\right)^{11} + 109395 \, {\left(48 \, a b^{2} + 55 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} - 108108 \, {\left(112 \, a b^{2} + 55 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 63063 \, {\left(128 \, a^{2} b + 168 \, a b^{2} + 55 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 20790 \, {\left(384 \, a^{2} b + 280 \, a b^{2} + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 945 \, {\left(384 \, a^{2} b + 280 \, a b^{2} + 77 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} + 6930 \, {\left(128 \, a^{2} b + 168 \, a b^{2} + 55 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 330 \, {\left(305235 \, b^{3} \cosh\left(d x + c\right)^{14} - 1616615 \, b^{3} \cosh\left(d x + c\right)^{12} + 65637 \, {\left(48 \, a b^{2} + 55 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} - 81081 \, {\left(112 \, a b^{2} + 55 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 63063 \, {\left(128 \, a^{2} b + 168 \, a b^{2} + 55 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} - 31185 \, {\left(384 \, a^{2} b + 280 \, a b^{2} + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 2688 \, a^{2} b + 3528 \, a b^{2} + 1155 \, b^{3} - 2835 \, {\left(384 \, a^{2} b + 280 \, a b^{2} + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{8} + 2640 \, {\left(20349 \, b^{3} \cosh\left(d x + c\right)^{15} - 124355 \, b^{3} \cosh\left(d x + c\right)^{13} + 5967 \, {\left(48 \, a b^{2} + 55 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} - 9009 \, {\left(112 \, a b^{2} + 55 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + 9009 \, {\left(128 \, a^{2} b + 168 \, a b^{2} + 55 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} - 6237 \, {\left(384 \, a^{2} b + 280 \, a b^{2} + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 945 \, {\left(384 \, a^{2} b + 280 \, a b^{2} + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 21 \, {\left(128 \, a^{2} b + 168 \, a b^{2} + 55 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} - 2079 \, {\left(112 \, a b^{2} + 55 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 231 \, {\left(101745 \, b^{3} \cosh\left(d x + c\right)^{16} - 710600 \, b^{3} \cosh\left(d x + c\right)^{14} + 39780 \, {\left(48 \, a b^{2} + 55 \, b^{3}\right)} \cosh\left(d x + c\right)^{12} - 72072 \, {\left(112 \, a b^{2} + 55 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} + 90090 \, {\left(128 \, a^{2} b + 168 \, a b^{2} + 55 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} - 83160 \, {\left(384 \, a^{2} b + 280 \, a b^{2} + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} - 18900 \, {\left(384 \, a^{2} b + 280 \, a b^{2} + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 1008 \, a b^{2} - 495 \, b^{3} + 840 \, {\left(128 \, a^{2} b + 168 \, a b^{2} + 55 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 462 \, {\left(17955 \, b^{3} \cosh\left(d x + c\right)^{17} - 142120 \, b^{3} \cosh\left(d x + c\right)^{15} + 9180 \, {\left(48 \, a b^{2} + 55 \, b^{3}\right)} \cosh\left(d x + c\right)^{13} - 19656 \, {\left(112 \, a b^{2} + 55 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} + 30030 \, {\left(128 \, a^{2} b + 168 \, a b^{2} + 55 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} - 35640 \, {\left(384 \, a^{2} b + 280 \, a b^{2} + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} - 11340 \, {\left(384 \, a^{2} b + 280 \, a b^{2} + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 840 \, {\left(128 \, a^{2} b + 168 \, a b^{2} + 55 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 27 \, {\left(112 \, a b^{2} + 55 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 4235 \, b^{3} \cosh\left(d x + c\right)^{2} + 495 \, {\left(48 \, a b^{2} + 55 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 165 \, {\left(13965 \, b^{3} \cosh\left(d x + c\right)^{18} - 124355 \, b^{3} \cosh\left(d x + c\right)^{16} + 9180 \, {\left(48 \, a b^{2} + 55 \, b^{3}\right)} \cosh\left(d x + c\right)^{14} - 22932 \, {\left(112 \, a b^{2} + 55 \, b^{3}\right)} \cosh\left(d x + c\right)^{12} + 42042 \, {\left(128 \, a^{2} b + 168 \, a b^{2} + 55 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} - 62370 \, {\left(384 \, a^{2} b + 280 \, a b^{2} + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} - 26460 \, {\left(384 \, a^{2} b + 280 \, a b^{2} + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 2940 \, {\left(128 \, a^{2} b + 168 \, a b^{2} + 55 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 144 \, a b^{2} + 165 \, b^{3} - 189 \, {\left(112 \, a b^{2} + 55 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 660 \, {\left(735 \, b^{3} \cosh\left(d x + c\right)^{19} - 7315 \, b^{3} \cosh\left(d x + c\right)^{17} + 612 \, {\left(48 \, a b^{2} + 55 \, b^{3}\right)} \cosh\left(d x + c\right)^{15} - 1764 \, {\left(112 \, a b^{2} + 55 \, b^{3}\right)} \cosh\left(d x + c\right)^{13} + 3822 \, {\left(128 \, a^{2} b + 168 \, a b^{2} + 55 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} - 6930 \, {\left(384 \, a^{2} b + 280 \, a b^{2} + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} - 3780 \, {\left(384 \, a^{2} b + 280 \, a b^{2} + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 588 \, {\left(128 \, a^{2} b + 168 \, a b^{2} + 55 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 63 \, {\left(112 \, a b^{2} + 55 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(48 \, a b^{2} + 55 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 315 \, b^{3} + 55 \, {\left(1323 \, b^{3} \cosh\left(d x + c\right)^{20} - 14630 \, b^{3} \cosh\left(d x + c\right)^{18} + 1377 \, {\left(48 \, a b^{2} + 55 \, b^{3}\right)} \cosh\left(d x + c\right)^{16} - 4536 \, {\left(112 \, a b^{2} + 55 \, b^{3}\right)} \cosh\left(d x + c\right)^{14} + 11466 \, {\left(128 \, a^{2} b + 168 \, a b^{2} + 55 \, b^{3}\right)} \cosh\left(d x + c\right)^{12} - 24948 \, {\left(384 \, a^{2} b + 280 \, a b^{2} + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} - 17010 \, {\left(384 \, a^{2} b + 280 \, a b^{2} + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 3528 \, {\left(128 \, a^{2} b + 168 \, a b^{2} + 55 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} - 567 \, {\left(112 \, a b^{2} + 55 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 77 \, b^{3} + 54 \, {\left(48 \, a b^{2} + 55 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} - 7096320 \, {\left(a^{3} \cosh\left(d x + c\right)^{11} + 11 \, a^{3} \cosh\left(d x + c\right)^{10} \sinh\left(d x + c\right) + 55 \, a^{3} \cosh\left(d x + c\right)^{9} \sinh\left(d x + c\right)^{2} + 165 \, a^{3} \cosh\left(d x + c\right)^{8} \sinh\left(d x + c\right)^{3} + 330 \, a^{3} \cosh\left(d x + c\right)^{7} \sinh\left(d x + c\right)^{4} + 462 \, a^{3} \cosh\left(d x + c\right)^{6} \sinh\left(d x + c\right)^{5} + 462 \, a^{3} \cosh\left(d x + c\right)^{5} \sinh\left(d x + c\right)^{6} + 330 \, a^{3} \cosh\left(d x + c\right)^{4} \sinh\left(d x + c\right)^{7} + 165 \, a^{3} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right)^{8} + 55 \, a^{3} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{9} + 11 \, a^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{10} + a^{3} \sinh\left(d x + c\right)^{11}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) + 7096320 \, {\left(a^{3} \cosh\left(d x + c\right)^{11} + 11 \, a^{3} \cosh\left(d x + c\right)^{10} \sinh\left(d x + c\right) + 55 \, a^{3} \cosh\left(d x + c\right)^{9} \sinh\left(d x + c\right)^{2} + 165 \, a^{3} \cosh\left(d x + c\right)^{8} \sinh\left(d x + c\right)^{3} + 330 \, a^{3} \cosh\left(d x + c\right)^{7} \sinh\left(d x + c\right)^{4} + 462 \, a^{3} \cosh\left(d x + c\right)^{6} \sinh\left(d x + c\right)^{5} + 462 \, a^{3} \cosh\left(d x + c\right)^{5} \sinh\left(d x + c\right)^{6} + 330 \, a^{3} \cosh\left(d x + c\right)^{4} \sinh\left(d x + c\right)^{7} + 165 \, a^{3} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right)^{8} + 55 \, a^{3} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{9} + 11 \, a^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{10} + a^{3} \sinh\left(d x + c\right)^{11}\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) + 22 \, {\left(315 \, b^{3} \cosh\left(d x + c\right)^{21} - 3850 \, b^{3} \cosh\left(d x + c\right)^{19} + 405 \, {\left(48 \, a b^{2} + 55 \, b^{3}\right)} \cosh\left(d x + c\right)^{17} - 1512 \, {\left(112 \, a b^{2} + 55 \, b^{3}\right)} \cosh\left(d x + c\right)^{15} + 4410 \, {\left(128 \, a^{2} b + 168 \, a b^{2} + 55 \, b^{3}\right)} \cosh\left(d x + c\right)^{13} - 11340 \, {\left(384 \, a^{2} b + 280 \, a b^{2} + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} - 9450 \, {\left(384 \, a^{2} b + 280 \, a b^{2} + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + 2520 \, {\left(128 \, a^{2} b + 168 \, a b^{2} + 55 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} - 567 \, {\left(112 \, a b^{2} + 55 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 385 \, b^{3} \cosh\left(d x + c\right) + 90 \, {\left(48 \, a b^{2} + 55 \, b^{3}\right)} \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right)}{7096320 \, {\left(d \cosh\left(d x + c\right)^{11} + 11 \, d \cosh\left(d x + c\right)^{10} \sinh\left(d x + c\right) + 55 \, d \cosh\left(d x + c\right)^{9} \sinh\left(d x + c\right)^{2} + 165 \, d \cosh\left(d x + c\right)^{8} \sinh\left(d x + c\right)^{3} + 330 \, d \cosh\left(d x + c\right)^{7} \sinh\left(d x + c\right)^{4} + 462 \, d \cosh\left(d x + c\right)^{6} \sinh\left(d x + c\right)^{5} + 462 \, d \cosh\left(d x + c\right)^{5} \sinh\left(d x + c\right)^{6} + 330 \, d \cosh\left(d x + c\right)^{4} \sinh\left(d x + c\right)^{7} + 165 \, d \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right)^{8} + 55 \, d \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{9} + 11 \, d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{10} + d \sinh\left(d x + c\right)^{11}\right)}}"," ",0,"1/7096320*(315*b^3*cosh(d*x + c)^22 + 6930*b^3*cosh(d*x + c)*sinh(d*x + c)^21 + 315*b^3*sinh(d*x + c)^22 - 4235*b^3*cosh(d*x + c)^20 + 385*(189*b^3*cosh(d*x + c)^2 - 11*b^3)*sinh(d*x + c)^20 + 7700*(63*b^3*cosh(d*x + c)^3 - 11*b^3*cosh(d*x + c))*sinh(d*x + c)^19 + 495*(48*a*b^2 + 55*b^3)*cosh(d*x + c)^18 + 55*(41895*b^3*cosh(d*x + c)^4 - 14630*b^3*cosh(d*x + c)^2 + 432*a*b^2 + 495*b^3)*sinh(d*x + c)^18 + 330*(25137*b^3*cosh(d*x + c)^5 - 14630*b^3*cosh(d*x + c)^3 + 27*(48*a*b^2 + 55*b^3)*cosh(d*x + c))*sinh(d*x + c)^17 - 2079*(112*a*b^2 + 55*b^3)*cosh(d*x + c)^16 + 33*(712215*b^3*cosh(d*x + c)^6 - 621775*b^3*cosh(d*x + c)^4 - 7056*a*b^2 - 3465*b^3 + 2295*(48*a*b^2 + 55*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^16 + 528*(101745*b^3*cosh(d*x + c)^7 - 124355*b^3*cosh(d*x + c)^5 + 765*(48*a*b^2 + 55*b^3)*cosh(d*x + c)^3 - 63*(112*a*b^2 + 55*b^3)*cosh(d*x + c))*sinh(d*x + c)^15 + 6930*(128*a^2*b + 168*a*b^2 + 55*b^3)*cosh(d*x + c)^14 + 330*(305235*b^3*cosh(d*x + c)^8 - 497420*b^3*cosh(d*x + c)^6 + 4590*(48*a*b^2 + 55*b^3)*cosh(d*x + c)^4 + 2688*a^2*b + 3528*a*b^2 + 1155*b^3 - 756*(112*a*b^2 + 55*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^14 + 4620*(33915*b^3*cosh(d*x + c)^9 - 71060*b^3*cosh(d*x + c)^7 + 918*(48*a*b^2 + 55*b^3)*cosh(d*x + c)^5 - 252*(112*a*b^2 + 55*b^3)*cosh(d*x + c)^3 + 21*(128*a^2*b + 168*a*b^2 + 55*b^3)*cosh(d*x + c))*sinh(d*x + c)^13 - 20790*(384*a^2*b + 280*a*b^2 + 77*b^3)*cosh(d*x + c)^12 + 2310*(88179*b^3*cosh(d*x + c)^10 - 230945*b^3*cosh(d*x + c)^8 + 3978*(48*a*b^2 + 55*b^3)*cosh(d*x + c)^6 - 1638*(112*a*b^2 + 55*b^3)*cosh(d*x + c)^4 - 3456*a^2*b - 2520*a*b^2 - 693*b^3 + 273*(128*a^2*b + 168*a*b^2 + 55*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^12 + 8*(27776385*b^3*cosh(d*x + c)^11 - 88913825*b^3*cosh(d*x + c)^9 + 1969110*(48*a*b^2 + 55*b^3)*cosh(d*x + c)^7 - 1135134*(112*a*b^2 + 55*b^3)*cosh(d*x + c)^5 + 315315*(128*a^2*b + 168*a*b^2 + 55*b^3)*cosh(d*x + c)^3 - 31185*(384*a^2*b + 280*a*b^2 + 77*b^3)*cosh(d*x + c))*sinh(d*x + c)^11 - 20790*(384*a^2*b + 280*a*b^2 + 77*b^3)*cosh(d*x + c)^10 + 22*(9258795*b^3*cosh(d*x + c)^12 - 35565530*b^3*cosh(d*x + c)^10 + 984555*(48*a*b^2 + 55*b^3)*cosh(d*x + c)^8 - 756756*(112*a*b^2 + 55*b^3)*cosh(d*x + c)^6 + 315315*(128*a^2*b + 168*a*b^2 + 55*b^3)*cosh(d*x + c)^4 - 362880*a^2*b - 264600*a*b^2 - 72765*b^3 - 62370*(384*a^2*b + 280*a*b^2 + 77*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^10 + 220*(712215*b^3*cosh(d*x + c)^13 - 3233230*b^3*cosh(d*x + c)^11 + 109395*(48*a*b^2 + 55*b^3)*cosh(d*x + c)^9 - 108108*(112*a*b^2 + 55*b^3)*cosh(d*x + c)^7 + 63063*(128*a^2*b + 168*a*b^2 + 55*b^3)*cosh(d*x + c)^5 - 20790*(384*a^2*b + 280*a*b^2 + 77*b^3)*cosh(d*x + c)^3 - 945*(384*a^2*b + 280*a*b^2 + 77*b^3)*cosh(d*x + c))*sinh(d*x + c)^9 + 6930*(128*a^2*b + 168*a*b^2 + 55*b^3)*cosh(d*x + c)^8 + 330*(305235*b^3*cosh(d*x + c)^14 - 1616615*b^3*cosh(d*x + c)^12 + 65637*(48*a*b^2 + 55*b^3)*cosh(d*x + c)^10 - 81081*(112*a*b^2 + 55*b^3)*cosh(d*x + c)^8 + 63063*(128*a^2*b + 168*a*b^2 + 55*b^3)*cosh(d*x + c)^6 - 31185*(384*a^2*b + 280*a*b^2 + 77*b^3)*cosh(d*x + c)^4 + 2688*a^2*b + 3528*a*b^2 + 1155*b^3 - 2835*(384*a^2*b + 280*a*b^2 + 77*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 2640*(20349*b^3*cosh(d*x + c)^15 - 124355*b^3*cosh(d*x + c)^13 + 5967*(48*a*b^2 + 55*b^3)*cosh(d*x + c)^11 - 9009*(112*a*b^2 + 55*b^3)*cosh(d*x + c)^9 + 9009*(128*a^2*b + 168*a*b^2 + 55*b^3)*cosh(d*x + c)^7 - 6237*(384*a^2*b + 280*a*b^2 + 77*b^3)*cosh(d*x + c)^5 - 945*(384*a^2*b + 280*a*b^2 + 77*b^3)*cosh(d*x + c)^3 + 21*(128*a^2*b + 168*a*b^2 + 55*b^3)*cosh(d*x + c))*sinh(d*x + c)^7 - 2079*(112*a*b^2 + 55*b^3)*cosh(d*x + c)^6 + 231*(101745*b^3*cosh(d*x + c)^16 - 710600*b^3*cosh(d*x + c)^14 + 39780*(48*a*b^2 + 55*b^3)*cosh(d*x + c)^12 - 72072*(112*a*b^2 + 55*b^3)*cosh(d*x + c)^10 + 90090*(128*a^2*b + 168*a*b^2 + 55*b^3)*cosh(d*x + c)^8 - 83160*(384*a^2*b + 280*a*b^2 + 77*b^3)*cosh(d*x + c)^6 - 18900*(384*a^2*b + 280*a*b^2 + 77*b^3)*cosh(d*x + c)^4 - 1008*a*b^2 - 495*b^3 + 840*(128*a^2*b + 168*a*b^2 + 55*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 462*(17955*b^3*cosh(d*x + c)^17 - 142120*b^3*cosh(d*x + c)^15 + 9180*(48*a*b^2 + 55*b^3)*cosh(d*x + c)^13 - 19656*(112*a*b^2 + 55*b^3)*cosh(d*x + c)^11 + 30030*(128*a^2*b + 168*a*b^2 + 55*b^3)*cosh(d*x + c)^9 - 35640*(384*a^2*b + 280*a*b^2 + 77*b^3)*cosh(d*x + c)^7 - 11340*(384*a^2*b + 280*a*b^2 + 77*b^3)*cosh(d*x + c)^5 + 840*(128*a^2*b + 168*a*b^2 + 55*b^3)*cosh(d*x + c)^3 - 27*(112*a*b^2 + 55*b^3)*cosh(d*x + c))*sinh(d*x + c)^5 - 4235*b^3*cosh(d*x + c)^2 + 495*(48*a*b^2 + 55*b^3)*cosh(d*x + c)^4 + 165*(13965*b^3*cosh(d*x + c)^18 - 124355*b^3*cosh(d*x + c)^16 + 9180*(48*a*b^2 + 55*b^3)*cosh(d*x + c)^14 - 22932*(112*a*b^2 + 55*b^3)*cosh(d*x + c)^12 + 42042*(128*a^2*b + 168*a*b^2 + 55*b^3)*cosh(d*x + c)^10 - 62370*(384*a^2*b + 280*a*b^2 + 77*b^3)*cosh(d*x + c)^8 - 26460*(384*a^2*b + 280*a*b^2 + 77*b^3)*cosh(d*x + c)^6 + 2940*(128*a^2*b + 168*a*b^2 + 55*b^3)*cosh(d*x + c)^4 + 144*a*b^2 + 165*b^3 - 189*(112*a*b^2 + 55*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 660*(735*b^3*cosh(d*x + c)^19 - 7315*b^3*cosh(d*x + c)^17 + 612*(48*a*b^2 + 55*b^3)*cosh(d*x + c)^15 - 1764*(112*a*b^2 + 55*b^3)*cosh(d*x + c)^13 + 3822*(128*a^2*b + 168*a*b^2 + 55*b^3)*cosh(d*x + c)^11 - 6930*(384*a^2*b + 280*a*b^2 + 77*b^3)*cosh(d*x + c)^9 - 3780*(384*a^2*b + 280*a*b^2 + 77*b^3)*cosh(d*x + c)^7 + 588*(128*a^2*b + 168*a*b^2 + 55*b^3)*cosh(d*x + c)^5 - 63*(112*a*b^2 + 55*b^3)*cosh(d*x + c)^3 + 3*(48*a*b^2 + 55*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 + 315*b^3 + 55*(1323*b^3*cosh(d*x + c)^20 - 14630*b^3*cosh(d*x + c)^18 + 1377*(48*a*b^2 + 55*b^3)*cosh(d*x + c)^16 - 4536*(112*a*b^2 + 55*b^3)*cosh(d*x + c)^14 + 11466*(128*a^2*b + 168*a*b^2 + 55*b^3)*cosh(d*x + c)^12 - 24948*(384*a^2*b + 280*a*b^2 + 77*b^3)*cosh(d*x + c)^10 - 17010*(384*a^2*b + 280*a*b^2 + 77*b^3)*cosh(d*x + c)^8 + 3528*(128*a^2*b + 168*a*b^2 + 55*b^3)*cosh(d*x + c)^6 - 567*(112*a*b^2 + 55*b^3)*cosh(d*x + c)^4 - 77*b^3 + 54*(48*a*b^2 + 55*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - 7096320*(a^3*cosh(d*x + c)^11 + 11*a^3*cosh(d*x + c)^10*sinh(d*x + c) + 55*a^3*cosh(d*x + c)^9*sinh(d*x + c)^2 + 165*a^3*cosh(d*x + c)^8*sinh(d*x + c)^3 + 330*a^3*cosh(d*x + c)^7*sinh(d*x + c)^4 + 462*a^3*cosh(d*x + c)^6*sinh(d*x + c)^5 + 462*a^3*cosh(d*x + c)^5*sinh(d*x + c)^6 + 330*a^3*cosh(d*x + c)^4*sinh(d*x + c)^7 + 165*a^3*cosh(d*x + c)^3*sinh(d*x + c)^8 + 55*a^3*cosh(d*x + c)^2*sinh(d*x + c)^9 + 11*a^3*cosh(d*x + c)*sinh(d*x + c)^10 + a^3*sinh(d*x + c)^11)*log(cosh(d*x + c) + sinh(d*x + c) + 1) + 7096320*(a^3*cosh(d*x + c)^11 + 11*a^3*cosh(d*x + c)^10*sinh(d*x + c) + 55*a^3*cosh(d*x + c)^9*sinh(d*x + c)^2 + 165*a^3*cosh(d*x + c)^8*sinh(d*x + c)^3 + 330*a^3*cosh(d*x + c)^7*sinh(d*x + c)^4 + 462*a^3*cosh(d*x + c)^6*sinh(d*x + c)^5 + 462*a^3*cosh(d*x + c)^5*sinh(d*x + c)^6 + 330*a^3*cosh(d*x + c)^4*sinh(d*x + c)^7 + 165*a^3*cosh(d*x + c)^3*sinh(d*x + c)^8 + 55*a^3*cosh(d*x + c)^2*sinh(d*x + c)^9 + 11*a^3*cosh(d*x + c)*sinh(d*x + c)^10 + a^3*sinh(d*x + c)^11)*log(cosh(d*x + c) + sinh(d*x + c) - 1) + 22*(315*b^3*cosh(d*x + c)^21 - 3850*b^3*cosh(d*x + c)^19 + 405*(48*a*b^2 + 55*b^3)*cosh(d*x + c)^17 - 1512*(112*a*b^2 + 55*b^3)*cosh(d*x + c)^15 + 4410*(128*a^2*b + 168*a*b^2 + 55*b^3)*cosh(d*x + c)^13 - 11340*(384*a^2*b + 280*a*b^2 + 77*b^3)*cosh(d*x + c)^11 - 9450*(384*a^2*b + 280*a*b^2 + 77*b^3)*cosh(d*x + c)^9 + 2520*(128*a^2*b + 168*a*b^2 + 55*b^3)*cosh(d*x + c)^7 - 567*(112*a*b^2 + 55*b^3)*cosh(d*x + c)^5 - 385*b^3*cosh(d*x + c) + 90*(48*a*b^2 + 55*b^3)*cosh(d*x + c)^3)*sinh(d*x + c))/(d*cosh(d*x + c)^11 + 11*d*cosh(d*x + c)^10*sinh(d*x + c) + 55*d*cosh(d*x + c)^9*sinh(d*x + c)^2 + 165*d*cosh(d*x + c)^8*sinh(d*x + c)^3 + 330*d*cosh(d*x + c)^7*sinh(d*x + c)^4 + 462*d*cosh(d*x + c)^6*sinh(d*x + c)^5 + 462*d*cosh(d*x + c)^5*sinh(d*x + c)^6 + 330*d*cosh(d*x + c)^4*sinh(d*x + c)^7 + 165*d*cosh(d*x + c)^3*sinh(d*x + c)^8 + 55*d*cosh(d*x + c)^2*sinh(d*x + c)^9 + 11*d*cosh(d*x + c)*sinh(d*x + c)^10 + d*sinh(d*x + c)^11)","B",0
211,1,4895,0,1.940518," ","integrate(csch(d*x+c)^3*(a+b*sinh(d*x+c)^4)^3,x, algorithm=""fricas"")","\frac{35 \, b^{3} \cosh\left(d x + c\right)^{22} + 770 \, b^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{21} + 35 \, b^{3} \sinh\left(d x + c\right)^{22} - 475 \, b^{3} \cosh\left(d x + c\right)^{20} + 5 \, {\left(1617 \, b^{3} \cosh\left(d x + c\right)^{2} - 95 \, b^{3}\right)} \sinh\left(d x + c\right)^{20} + 100 \, {\left(539 \, b^{3} \cosh\left(d x + c\right)^{3} - 95 \, b^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{19} + {\left(3024 \, a b^{2} + 3113 \, b^{3}\right)} \cosh\left(d x + c\right)^{18} + {\left(256025 \, b^{3} \cosh\left(d x + c\right)^{4} - 90250 \, b^{3} \cosh\left(d x + c\right)^{2} + 3024 \, a b^{2} + 3113 \, b^{3}\right)} \sinh\left(d x + c\right)^{18} + 6 \, {\left(153615 \, b^{3} \cosh\left(d x + c\right)^{5} - 90250 \, b^{3} \cosh\left(d x + c\right)^{3} + 3 \, {\left(3024 \, a b^{2} + 3113 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{17} - 9 \, {\left(3472 \, a b^{2} + 1529 \, b^{3}\right)} \cosh\left(d x + c\right)^{16} + 3 \, {\left(870485 \, b^{3} \cosh\left(d x + c\right)^{6} - 767125 \, b^{3} \cosh\left(d x + c\right)^{4} - 10416 \, a b^{2} - 4587 \, b^{3} + 51 \, {\left(3024 \, a b^{2} + 3113 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{16} + 48 \, {\left(124355 \, b^{3} \cosh\left(d x + c\right)^{7} - 153425 \, b^{3} \cosh\left(d x + c\right)^{5} + 17 \, {\left(3024 \, a b^{2} + 3113 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(3472 \, a b^{2} + 1529 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{15} + 126 \, {\left(1920 \, a^{2} b + 1624 \, a b^{2} + 473 \, b^{3}\right)} \cosh\left(d x + c\right)^{14} + 6 \, {\left(1865325 \, b^{3} \cosh\left(d x + c\right)^{8} - 3068500 \, b^{3} \cosh\left(d x + c\right)^{6} + 510 \, {\left(3024 \, a b^{2} + 3113 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 40320 \, a^{2} b + 34104 \, a b^{2} + 9933 \, b^{3} - 180 \, {\left(3472 \, a b^{2} + 1529 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{14} + 4 \, {\left(4352425 \, b^{3} \cosh\left(d x + c\right)^{9} - 9205500 \, b^{3} \cosh\left(d x + c\right)^{7} + 2142 \, {\left(3024 \, a b^{2} + 3113 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 1260 \, {\left(3472 \, a b^{2} + 1529 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 441 \, {\left(1920 \, a^{2} b + 1624 \, a b^{2} + 473 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{13} - 630 \, {\left(256 \, a^{3} + 384 \, a^{2} b + 280 \, a b^{2} + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{12} + 2 \, {\left(11316305 \, b^{3} \cosh\left(d x + c\right)^{10} - 29917875 \, b^{3} \cosh\left(d x + c\right)^{8} + 9282 \, {\left(3024 \, a b^{2} + 3113 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} - 8190 \, {\left(3472 \, a b^{2} + 1529 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 80640 \, a^{3} - 120960 \, a^{2} b - 88200 \, a b^{2} - 24255 \, b^{3} + 5733 \, {\left(1920 \, a^{2} b + 1624 \, a b^{2} + 473 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{12} + 8 \, {\left(3086265 \, b^{3} \cosh\left(d x + c\right)^{11} - 9972625 \, b^{3} \cosh\left(d x + c\right)^{9} + 3978 \, {\left(3024 \, a b^{2} + 3113 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} - 4914 \, {\left(3472 \, a b^{2} + 1529 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 5733 \, {\left(1920 \, a^{2} b + 1624 \, a b^{2} + 473 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 945 \, {\left(256 \, a^{3} + 384 \, a^{2} b + 280 \, a b^{2} + 77 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{11} - 630 \, {\left(256 \, a^{3} + 384 \, a^{2} b + 280 \, a b^{2} + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} + 2 \, {\left(11316305 \, b^{3} \cosh\left(d x + c\right)^{12} - 43879550 \, b^{3} \cosh\left(d x + c\right)^{10} + 21879 \, {\left(3024 \, a b^{2} + 3113 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} - 36036 \, {\left(3472 \, a b^{2} + 1529 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 63063 \, {\left(1920 \, a^{2} b + 1624 \, a b^{2} + 473 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 80640 \, a^{3} - 120960 \, a^{2} b - 88200 \, a b^{2} - 24255 \, b^{3} - 20790 \, {\left(256 \, a^{3} + 384 \, a^{2} b + 280 \, a b^{2} + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{10} + 4 \, {\left(4352425 \, b^{3} \cosh\left(d x + c\right)^{13} - 19945250 \, b^{3} \cosh\left(d x + c\right)^{11} + 12155 \, {\left(3024 \, a b^{2} + 3113 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} - 25740 \, {\left(3472 \, a b^{2} + 1529 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 63063 \, {\left(1920 \, a^{2} b + 1624 \, a b^{2} + 473 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 34650 \, {\left(256 \, a^{3} + 384 \, a^{2} b + 280 \, a b^{2} + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 1575 \, {\left(256 \, a^{3} + 384 \, a^{2} b + 280 \, a b^{2} + 77 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} + 126 \, {\left(1920 \, a^{2} b + 1624 \, a b^{2} + 473 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 6 \, {\left(1865325 \, b^{3} \cosh\left(d x + c\right)^{14} - 9972625 \, b^{3} \cosh\left(d x + c\right)^{12} + 7293 \, {\left(3024 \, a b^{2} + 3113 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} - 19305 \, {\left(3472 \, a b^{2} + 1529 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 63063 \, {\left(1920 \, a^{2} b + 1624 \, a b^{2} + 473 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} - 51975 \, {\left(256 \, a^{3} + 384 \, a^{2} b + 280 \, a b^{2} + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 40320 \, a^{2} b + 34104 \, a b^{2} + 9933 \, b^{3} - 4725 \, {\left(256 \, a^{3} + 384 \, a^{2} b + 280 \, a b^{2} + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{8} + 48 \, {\left(124355 \, b^{3} \cosh\left(d x + c\right)^{15} - 767125 \, b^{3} \cosh\left(d x + c\right)^{13} + 663 \, {\left(3024 \, a b^{2} + 3113 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} - 2145 \, {\left(3472 \, a b^{2} + 1529 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + 9009 \, {\left(1920 \, a^{2} b + 1624 \, a b^{2} + 473 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} - 10395 \, {\left(256 \, a^{3} + 384 \, a^{2} b + 280 \, a b^{2} + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 1575 \, {\left(256 \, a^{3} + 384 \, a^{2} b + 280 \, a b^{2} + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 21 \, {\left(1920 \, a^{2} b + 1624 \, a b^{2} + 473 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} - 9 \, {\left(3472 \, a b^{2} + 1529 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 3 \, {\left(870485 \, b^{3} \cosh\left(d x + c\right)^{16} - 6137000 \, b^{3} \cosh\left(d x + c\right)^{14} + 6188 \, {\left(3024 \, a b^{2} + 3113 \, b^{3}\right)} \cosh\left(d x + c\right)^{12} - 24024 \, {\left(3472 \, a b^{2} + 1529 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} + 126126 \, {\left(1920 \, a^{2} b + 1624 \, a b^{2} + 473 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} - 194040 \, {\left(256 \, a^{3} + 384 \, a^{2} b + 280 \, a b^{2} + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} - 44100 \, {\left(256 \, a^{3} + 384 \, a^{2} b + 280 \, a b^{2} + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 10416 \, a b^{2} - 4587 \, b^{3} + 1176 \, {\left(1920 \, a^{2} b + 1624 \, a b^{2} + 473 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 6 \, {\left(153615 \, b^{3} \cosh\left(d x + c\right)^{17} - 1227400 \, b^{3} \cosh\left(d x + c\right)^{15} + 1428 \, {\left(3024 \, a b^{2} + 3113 \, b^{3}\right)} \cosh\left(d x + c\right)^{13} - 6552 \, {\left(3472 \, a b^{2} + 1529 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} + 42042 \, {\left(1920 \, a^{2} b + 1624 \, a b^{2} + 473 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} - 83160 \, {\left(256 \, a^{3} + 384 \, a^{2} b + 280 \, a b^{2} + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} - 26460 \, {\left(256 \, a^{3} + 384 \, a^{2} b + 280 \, a b^{2} + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 1176 \, {\left(1920 \, a^{2} b + 1624 \, a b^{2} + 473 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 9 \, {\left(3472 \, a b^{2} + 1529 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 475 \, b^{3} \cosh\left(d x + c\right)^{2} + {\left(3024 \, a b^{2} + 3113 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + {\left(256025 \, b^{3} \cosh\left(d x + c\right)^{18} - 2301375 \, b^{3} \cosh\left(d x + c\right)^{16} + 3060 \, {\left(3024 \, a b^{2} + 3113 \, b^{3}\right)} \cosh\left(d x + c\right)^{14} - 16380 \, {\left(3472 \, a b^{2} + 1529 \, b^{3}\right)} \cosh\left(d x + c\right)^{12} + 126126 \, {\left(1920 \, a^{2} b + 1624 \, a b^{2} + 473 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} - 311850 \, {\left(256 \, a^{3} + 384 \, a^{2} b + 280 \, a b^{2} + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} - 132300 \, {\left(256 \, a^{3} + 384 \, a^{2} b + 280 \, a b^{2} + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 8820 \, {\left(1920 \, a^{2} b + 1624 \, a b^{2} + 473 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 3024 \, a b^{2} + 3113 \, b^{3} - 135 \, {\left(3472 \, a b^{2} + 1529 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(13475 \, b^{3} \cosh\left(d x + c\right)^{19} - 135375 \, b^{3} \cosh\left(d x + c\right)^{17} + 204 \, {\left(3024 \, a b^{2} + 3113 \, b^{3}\right)} \cosh\left(d x + c\right)^{15} - 1260 \, {\left(3472 \, a b^{2} + 1529 \, b^{3}\right)} \cosh\left(d x + c\right)^{13} + 11466 \, {\left(1920 \, a^{2} b + 1624 \, a b^{2} + 473 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} - 34650 \, {\left(256 \, a^{3} + 384 \, a^{2} b + 280 \, a b^{2} + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} - 18900 \, {\left(256 \, a^{3} + 384 \, a^{2} b + 280 \, a b^{2} + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 1764 \, {\left(1920 \, a^{2} b + 1624 \, a b^{2} + 473 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 45 \, {\left(3472 \, a b^{2} + 1529 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(3024 \, a b^{2} + 3113 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 35 \, b^{3} + {\left(8085 \, b^{3} \cosh\left(d x + c\right)^{20} - 90250 \, b^{3} \cosh\left(d x + c\right)^{18} + 153 \, {\left(3024 \, a b^{2} + 3113 \, b^{3}\right)} \cosh\left(d x + c\right)^{16} - 1080 \, {\left(3472 \, a b^{2} + 1529 \, b^{3}\right)} \cosh\left(d x + c\right)^{14} + 11466 \, {\left(1920 \, a^{2} b + 1624 \, a b^{2} + 473 \, b^{3}\right)} \cosh\left(d x + c\right)^{12} - 41580 \, {\left(256 \, a^{3} + 384 \, a^{2} b + 280 \, a b^{2} + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} - 28350 \, {\left(256 \, a^{3} + 384 \, a^{2} b + 280 \, a b^{2} + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 3528 \, {\left(1920 \, a^{2} b + 1624 \, a b^{2} + 473 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} - 135 \, {\left(3472 \, a b^{2} + 1529 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 475 \, b^{3} + 6 \, {\left(3024 \, a b^{2} + 3113 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 80640 \, {\left(a^{3} \cosh\left(d x + c\right)^{13} + 13 \, a^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{12} + a^{3} \sinh\left(d x + c\right)^{13} - 2 \, a^{3} \cosh\left(d x + c\right)^{11} + a^{3} \cosh\left(d x + c\right)^{9} + 2 \, {\left(39 \, a^{3} \cosh\left(d x + c\right)^{2} - a^{3}\right)} \sinh\left(d x + c\right)^{11} + 22 \, {\left(13 \, a^{3} \cosh\left(d x + c\right)^{3} - a^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{10} + {\left(715 \, a^{3} \cosh\left(d x + c\right)^{4} - 110 \, a^{3} \cosh\left(d x + c\right)^{2} + a^{3}\right)} \sinh\left(d x + c\right)^{9} + 3 \, {\left(429 \, a^{3} \cosh\left(d x + c\right)^{5} - 110 \, a^{3} \cosh\left(d x + c\right)^{3} + 3 \, a^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{8} + 12 \, {\left(143 \, a^{3} \cosh\left(d x + c\right)^{6} - 55 \, a^{3} \cosh\left(d x + c\right)^{4} + 3 \, a^{3} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{7} + 12 \, {\left(143 \, a^{3} \cosh\left(d x + c\right)^{7} - 77 \, a^{3} \cosh\left(d x + c\right)^{5} + 7 \, a^{3} \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right)^{6} + 3 \, {\left(429 \, a^{3} \cosh\left(d x + c\right)^{8} - 308 \, a^{3} \cosh\left(d x + c\right)^{6} + 42 \, a^{3} \cosh\left(d x + c\right)^{4}\right)} \sinh\left(d x + c\right)^{5} + {\left(715 \, a^{3} \cosh\left(d x + c\right)^{9} - 660 \, a^{3} \cosh\left(d x + c\right)^{7} + 126 \, a^{3} \cosh\left(d x + c\right)^{5}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(143 \, a^{3} \cosh\left(d x + c\right)^{10} - 165 \, a^{3} \cosh\left(d x + c\right)^{8} + 42 \, a^{3} \cosh\left(d x + c\right)^{6}\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(39 \, a^{3} \cosh\left(d x + c\right)^{11} - 55 \, a^{3} \cosh\left(d x + c\right)^{9} + 18 \, a^{3} \cosh\left(d x + c\right)^{7}\right)} \sinh\left(d x + c\right)^{2} + {\left(13 \, a^{3} \cosh\left(d x + c\right)^{12} - 22 \, a^{3} \cosh\left(d x + c\right)^{10} + 9 \, a^{3} \cosh\left(d x + c\right)^{8}\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) - 80640 \, {\left(a^{3} \cosh\left(d x + c\right)^{13} + 13 \, a^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{12} + a^{3} \sinh\left(d x + c\right)^{13} - 2 \, a^{3} \cosh\left(d x + c\right)^{11} + a^{3} \cosh\left(d x + c\right)^{9} + 2 \, {\left(39 \, a^{3} \cosh\left(d x + c\right)^{2} - a^{3}\right)} \sinh\left(d x + c\right)^{11} + 22 \, {\left(13 \, a^{3} \cosh\left(d x + c\right)^{3} - a^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{10} + {\left(715 \, a^{3} \cosh\left(d x + c\right)^{4} - 110 \, a^{3} \cosh\left(d x + c\right)^{2} + a^{3}\right)} \sinh\left(d x + c\right)^{9} + 3 \, {\left(429 \, a^{3} \cosh\left(d x + c\right)^{5} - 110 \, a^{3} \cosh\left(d x + c\right)^{3} + 3 \, a^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{8} + 12 \, {\left(143 \, a^{3} \cosh\left(d x + c\right)^{6} - 55 \, a^{3} \cosh\left(d x + c\right)^{4} + 3 \, a^{3} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{7} + 12 \, {\left(143 \, a^{3} \cosh\left(d x + c\right)^{7} - 77 \, a^{3} \cosh\left(d x + c\right)^{5} + 7 \, a^{3} \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right)^{6} + 3 \, {\left(429 \, a^{3} \cosh\left(d x + c\right)^{8} - 308 \, a^{3} \cosh\left(d x + c\right)^{6} + 42 \, a^{3} \cosh\left(d x + c\right)^{4}\right)} \sinh\left(d x + c\right)^{5} + {\left(715 \, a^{3} \cosh\left(d x + c\right)^{9} - 660 \, a^{3} \cosh\left(d x + c\right)^{7} + 126 \, a^{3} \cosh\left(d x + c\right)^{5}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(143 \, a^{3} \cosh\left(d x + c\right)^{10} - 165 \, a^{3} \cosh\left(d x + c\right)^{8} + 42 \, a^{3} \cosh\left(d x + c\right)^{6}\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(39 \, a^{3} \cosh\left(d x + c\right)^{11} - 55 \, a^{3} \cosh\left(d x + c\right)^{9} + 18 \, a^{3} \cosh\left(d x + c\right)^{7}\right)} \sinh\left(d x + c\right)^{2} + {\left(13 \, a^{3} \cosh\left(d x + c\right)^{12} - 22 \, a^{3} \cosh\left(d x + c\right)^{10} + 9 \, a^{3} \cosh\left(d x + c\right)^{8}\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) + 2 \, {\left(385 \, b^{3} \cosh\left(d x + c\right)^{21} - 4750 \, b^{3} \cosh\left(d x + c\right)^{19} + 9 \, {\left(3024 \, a b^{2} + 3113 \, b^{3}\right)} \cosh\left(d x + c\right)^{17} - 72 \, {\left(3472 \, a b^{2} + 1529 \, b^{3}\right)} \cosh\left(d x + c\right)^{15} + 882 \, {\left(1920 \, a^{2} b + 1624 \, a b^{2} + 473 \, b^{3}\right)} \cosh\left(d x + c\right)^{13} - 3780 \, {\left(256 \, a^{3} + 384 \, a^{2} b + 280 \, a b^{2} + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} - 3150 \, {\left(256 \, a^{3} + 384 \, a^{2} b + 280 \, a b^{2} + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + 504 \, {\left(1920 \, a^{2} b + 1624 \, a b^{2} + 473 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} - 27 \, {\left(3472 \, a b^{2} + 1529 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 475 \, b^{3} \cosh\left(d x + c\right) + 2 \, {\left(3024 \, a b^{2} + 3113 \, b^{3}\right)} \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right)}{161280 \, {\left(d \cosh\left(d x + c\right)^{13} + 13 \, d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{12} + d \sinh\left(d x + c\right)^{13} - 2 \, d \cosh\left(d x + c\right)^{11} + 2 \, {\left(39 \, d \cosh\left(d x + c\right)^{2} - d\right)} \sinh\left(d x + c\right)^{11} + 22 \, {\left(13 \, d \cosh\left(d x + c\right)^{3} - d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{10} + d \cosh\left(d x + c\right)^{9} + {\left(715 \, d \cosh\left(d x + c\right)^{4} - 110 \, d \cosh\left(d x + c\right)^{2} + d\right)} \sinh\left(d x + c\right)^{9} + 3 \, {\left(429 \, d \cosh\left(d x + c\right)^{5} - 110 \, d \cosh\left(d x + c\right)^{3} + 3 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{8} + 12 \, {\left(143 \, d \cosh\left(d x + c\right)^{6} - 55 \, d \cosh\left(d x + c\right)^{4} + 3 \, d \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{7} + 12 \, {\left(143 \, d \cosh\left(d x + c\right)^{7} - 77 \, d \cosh\left(d x + c\right)^{5} + 7 \, d \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right)^{6} + 3 \, {\left(429 \, d \cosh\left(d x + c\right)^{8} - 308 \, d \cosh\left(d x + c\right)^{6} + 42 \, d \cosh\left(d x + c\right)^{4}\right)} \sinh\left(d x + c\right)^{5} + {\left(715 \, d \cosh\left(d x + c\right)^{9} - 660 \, d \cosh\left(d x + c\right)^{7} + 126 \, d \cosh\left(d x + c\right)^{5}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(143 \, d \cosh\left(d x + c\right)^{10} - 165 \, d \cosh\left(d x + c\right)^{8} + 42 \, d \cosh\left(d x + c\right)^{6}\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(39 \, d \cosh\left(d x + c\right)^{11} - 55 \, d \cosh\left(d x + c\right)^{9} + 18 \, d \cosh\left(d x + c\right)^{7}\right)} \sinh\left(d x + c\right)^{2} + {\left(13 \, d \cosh\left(d x + c\right)^{12} - 22 \, d \cosh\left(d x + c\right)^{10} + 9 \, d \cosh\left(d x + c\right)^{8}\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"1/161280*(35*b^3*cosh(d*x + c)^22 + 770*b^3*cosh(d*x + c)*sinh(d*x + c)^21 + 35*b^3*sinh(d*x + c)^22 - 475*b^3*cosh(d*x + c)^20 + 5*(1617*b^3*cosh(d*x + c)^2 - 95*b^3)*sinh(d*x + c)^20 + 100*(539*b^3*cosh(d*x + c)^3 - 95*b^3*cosh(d*x + c))*sinh(d*x + c)^19 + (3024*a*b^2 + 3113*b^3)*cosh(d*x + c)^18 + (256025*b^3*cosh(d*x + c)^4 - 90250*b^3*cosh(d*x + c)^2 + 3024*a*b^2 + 3113*b^3)*sinh(d*x + c)^18 + 6*(153615*b^3*cosh(d*x + c)^5 - 90250*b^3*cosh(d*x + c)^3 + 3*(3024*a*b^2 + 3113*b^3)*cosh(d*x + c))*sinh(d*x + c)^17 - 9*(3472*a*b^2 + 1529*b^3)*cosh(d*x + c)^16 + 3*(870485*b^3*cosh(d*x + c)^6 - 767125*b^3*cosh(d*x + c)^4 - 10416*a*b^2 - 4587*b^3 + 51*(3024*a*b^2 + 3113*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^16 + 48*(124355*b^3*cosh(d*x + c)^7 - 153425*b^3*cosh(d*x + c)^5 + 17*(3024*a*b^2 + 3113*b^3)*cosh(d*x + c)^3 - 3*(3472*a*b^2 + 1529*b^3)*cosh(d*x + c))*sinh(d*x + c)^15 + 126*(1920*a^2*b + 1624*a*b^2 + 473*b^3)*cosh(d*x + c)^14 + 6*(1865325*b^3*cosh(d*x + c)^8 - 3068500*b^3*cosh(d*x + c)^6 + 510*(3024*a*b^2 + 3113*b^3)*cosh(d*x + c)^4 + 40320*a^2*b + 34104*a*b^2 + 9933*b^3 - 180*(3472*a*b^2 + 1529*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^14 + 4*(4352425*b^3*cosh(d*x + c)^9 - 9205500*b^3*cosh(d*x + c)^7 + 2142*(3024*a*b^2 + 3113*b^3)*cosh(d*x + c)^5 - 1260*(3472*a*b^2 + 1529*b^3)*cosh(d*x + c)^3 + 441*(1920*a^2*b + 1624*a*b^2 + 473*b^3)*cosh(d*x + c))*sinh(d*x + c)^13 - 630*(256*a^3 + 384*a^2*b + 280*a*b^2 + 77*b^3)*cosh(d*x + c)^12 + 2*(11316305*b^3*cosh(d*x + c)^10 - 29917875*b^3*cosh(d*x + c)^8 + 9282*(3024*a*b^2 + 3113*b^3)*cosh(d*x + c)^6 - 8190*(3472*a*b^2 + 1529*b^3)*cosh(d*x + c)^4 - 80640*a^3 - 120960*a^2*b - 88200*a*b^2 - 24255*b^3 + 5733*(1920*a^2*b + 1624*a*b^2 + 473*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^12 + 8*(3086265*b^3*cosh(d*x + c)^11 - 9972625*b^3*cosh(d*x + c)^9 + 3978*(3024*a*b^2 + 3113*b^3)*cosh(d*x + c)^7 - 4914*(3472*a*b^2 + 1529*b^3)*cosh(d*x + c)^5 + 5733*(1920*a^2*b + 1624*a*b^2 + 473*b^3)*cosh(d*x + c)^3 - 945*(256*a^3 + 384*a^2*b + 280*a*b^2 + 77*b^3)*cosh(d*x + c))*sinh(d*x + c)^11 - 630*(256*a^3 + 384*a^2*b + 280*a*b^2 + 77*b^3)*cosh(d*x + c)^10 + 2*(11316305*b^3*cosh(d*x + c)^12 - 43879550*b^3*cosh(d*x + c)^10 + 21879*(3024*a*b^2 + 3113*b^3)*cosh(d*x + c)^8 - 36036*(3472*a*b^2 + 1529*b^3)*cosh(d*x + c)^6 + 63063*(1920*a^2*b + 1624*a*b^2 + 473*b^3)*cosh(d*x + c)^4 - 80640*a^3 - 120960*a^2*b - 88200*a*b^2 - 24255*b^3 - 20790*(256*a^3 + 384*a^2*b + 280*a*b^2 + 77*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^10 + 4*(4352425*b^3*cosh(d*x + c)^13 - 19945250*b^3*cosh(d*x + c)^11 + 12155*(3024*a*b^2 + 3113*b^3)*cosh(d*x + c)^9 - 25740*(3472*a*b^2 + 1529*b^3)*cosh(d*x + c)^7 + 63063*(1920*a^2*b + 1624*a*b^2 + 473*b^3)*cosh(d*x + c)^5 - 34650*(256*a^3 + 384*a^2*b + 280*a*b^2 + 77*b^3)*cosh(d*x + c)^3 - 1575*(256*a^3 + 384*a^2*b + 280*a*b^2 + 77*b^3)*cosh(d*x + c))*sinh(d*x + c)^9 + 126*(1920*a^2*b + 1624*a*b^2 + 473*b^3)*cosh(d*x + c)^8 + 6*(1865325*b^3*cosh(d*x + c)^14 - 9972625*b^3*cosh(d*x + c)^12 + 7293*(3024*a*b^2 + 3113*b^3)*cosh(d*x + c)^10 - 19305*(3472*a*b^2 + 1529*b^3)*cosh(d*x + c)^8 + 63063*(1920*a^2*b + 1624*a*b^2 + 473*b^3)*cosh(d*x + c)^6 - 51975*(256*a^3 + 384*a^2*b + 280*a*b^2 + 77*b^3)*cosh(d*x + c)^4 + 40320*a^2*b + 34104*a*b^2 + 9933*b^3 - 4725*(256*a^3 + 384*a^2*b + 280*a*b^2 + 77*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 48*(124355*b^3*cosh(d*x + c)^15 - 767125*b^3*cosh(d*x + c)^13 + 663*(3024*a*b^2 + 3113*b^3)*cosh(d*x + c)^11 - 2145*(3472*a*b^2 + 1529*b^3)*cosh(d*x + c)^9 + 9009*(1920*a^2*b + 1624*a*b^2 + 473*b^3)*cosh(d*x + c)^7 - 10395*(256*a^3 + 384*a^2*b + 280*a*b^2 + 77*b^3)*cosh(d*x + c)^5 - 1575*(256*a^3 + 384*a^2*b + 280*a*b^2 + 77*b^3)*cosh(d*x + c)^3 + 21*(1920*a^2*b + 1624*a*b^2 + 473*b^3)*cosh(d*x + c))*sinh(d*x + c)^7 - 9*(3472*a*b^2 + 1529*b^3)*cosh(d*x + c)^6 + 3*(870485*b^3*cosh(d*x + c)^16 - 6137000*b^3*cosh(d*x + c)^14 + 6188*(3024*a*b^2 + 3113*b^3)*cosh(d*x + c)^12 - 24024*(3472*a*b^2 + 1529*b^3)*cosh(d*x + c)^10 + 126126*(1920*a^2*b + 1624*a*b^2 + 473*b^3)*cosh(d*x + c)^8 - 194040*(256*a^3 + 384*a^2*b + 280*a*b^2 + 77*b^3)*cosh(d*x + c)^6 - 44100*(256*a^3 + 384*a^2*b + 280*a*b^2 + 77*b^3)*cosh(d*x + c)^4 - 10416*a*b^2 - 4587*b^3 + 1176*(1920*a^2*b + 1624*a*b^2 + 473*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 6*(153615*b^3*cosh(d*x + c)^17 - 1227400*b^3*cosh(d*x + c)^15 + 1428*(3024*a*b^2 + 3113*b^3)*cosh(d*x + c)^13 - 6552*(3472*a*b^2 + 1529*b^3)*cosh(d*x + c)^11 + 42042*(1920*a^2*b + 1624*a*b^2 + 473*b^3)*cosh(d*x + c)^9 - 83160*(256*a^3 + 384*a^2*b + 280*a*b^2 + 77*b^3)*cosh(d*x + c)^7 - 26460*(256*a^3 + 384*a^2*b + 280*a*b^2 + 77*b^3)*cosh(d*x + c)^5 + 1176*(1920*a^2*b + 1624*a*b^2 + 473*b^3)*cosh(d*x + c)^3 - 9*(3472*a*b^2 + 1529*b^3)*cosh(d*x + c))*sinh(d*x + c)^5 - 475*b^3*cosh(d*x + c)^2 + (3024*a*b^2 + 3113*b^3)*cosh(d*x + c)^4 + (256025*b^3*cosh(d*x + c)^18 - 2301375*b^3*cosh(d*x + c)^16 + 3060*(3024*a*b^2 + 3113*b^3)*cosh(d*x + c)^14 - 16380*(3472*a*b^2 + 1529*b^3)*cosh(d*x + c)^12 + 126126*(1920*a^2*b + 1624*a*b^2 + 473*b^3)*cosh(d*x + c)^10 - 311850*(256*a^3 + 384*a^2*b + 280*a*b^2 + 77*b^3)*cosh(d*x + c)^8 - 132300*(256*a^3 + 384*a^2*b + 280*a*b^2 + 77*b^3)*cosh(d*x + c)^6 + 8820*(1920*a^2*b + 1624*a*b^2 + 473*b^3)*cosh(d*x + c)^4 + 3024*a*b^2 + 3113*b^3 - 135*(3472*a*b^2 + 1529*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 4*(13475*b^3*cosh(d*x + c)^19 - 135375*b^3*cosh(d*x + c)^17 + 204*(3024*a*b^2 + 3113*b^3)*cosh(d*x + c)^15 - 1260*(3472*a*b^2 + 1529*b^3)*cosh(d*x + c)^13 + 11466*(1920*a^2*b + 1624*a*b^2 + 473*b^3)*cosh(d*x + c)^11 - 34650*(256*a^3 + 384*a^2*b + 280*a*b^2 + 77*b^3)*cosh(d*x + c)^9 - 18900*(256*a^3 + 384*a^2*b + 280*a*b^2 + 77*b^3)*cosh(d*x + c)^7 + 1764*(1920*a^2*b + 1624*a*b^2 + 473*b^3)*cosh(d*x + c)^5 - 45*(3472*a*b^2 + 1529*b^3)*cosh(d*x + c)^3 + (3024*a*b^2 + 3113*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 + 35*b^3 + (8085*b^3*cosh(d*x + c)^20 - 90250*b^3*cosh(d*x + c)^18 + 153*(3024*a*b^2 + 3113*b^3)*cosh(d*x + c)^16 - 1080*(3472*a*b^2 + 1529*b^3)*cosh(d*x + c)^14 + 11466*(1920*a^2*b + 1624*a*b^2 + 473*b^3)*cosh(d*x + c)^12 - 41580*(256*a^3 + 384*a^2*b + 280*a*b^2 + 77*b^3)*cosh(d*x + c)^10 - 28350*(256*a^3 + 384*a^2*b + 280*a*b^2 + 77*b^3)*cosh(d*x + c)^8 + 3528*(1920*a^2*b + 1624*a*b^2 + 473*b^3)*cosh(d*x + c)^6 - 135*(3472*a*b^2 + 1529*b^3)*cosh(d*x + c)^4 - 475*b^3 + 6*(3024*a*b^2 + 3113*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 80640*(a^3*cosh(d*x + c)^13 + 13*a^3*cosh(d*x + c)*sinh(d*x + c)^12 + a^3*sinh(d*x + c)^13 - 2*a^3*cosh(d*x + c)^11 + a^3*cosh(d*x + c)^9 + 2*(39*a^3*cosh(d*x + c)^2 - a^3)*sinh(d*x + c)^11 + 22*(13*a^3*cosh(d*x + c)^3 - a^3*cosh(d*x + c))*sinh(d*x + c)^10 + (715*a^3*cosh(d*x + c)^4 - 110*a^3*cosh(d*x + c)^2 + a^3)*sinh(d*x + c)^9 + 3*(429*a^3*cosh(d*x + c)^5 - 110*a^3*cosh(d*x + c)^3 + 3*a^3*cosh(d*x + c))*sinh(d*x + c)^8 + 12*(143*a^3*cosh(d*x + c)^6 - 55*a^3*cosh(d*x + c)^4 + 3*a^3*cosh(d*x + c)^2)*sinh(d*x + c)^7 + 12*(143*a^3*cosh(d*x + c)^7 - 77*a^3*cosh(d*x + c)^5 + 7*a^3*cosh(d*x + c)^3)*sinh(d*x + c)^6 + 3*(429*a^3*cosh(d*x + c)^8 - 308*a^3*cosh(d*x + c)^6 + 42*a^3*cosh(d*x + c)^4)*sinh(d*x + c)^5 + (715*a^3*cosh(d*x + c)^9 - 660*a^3*cosh(d*x + c)^7 + 126*a^3*cosh(d*x + c)^5)*sinh(d*x + c)^4 + 2*(143*a^3*cosh(d*x + c)^10 - 165*a^3*cosh(d*x + c)^8 + 42*a^3*cosh(d*x + c)^6)*sinh(d*x + c)^3 + 2*(39*a^3*cosh(d*x + c)^11 - 55*a^3*cosh(d*x + c)^9 + 18*a^3*cosh(d*x + c)^7)*sinh(d*x + c)^2 + (13*a^3*cosh(d*x + c)^12 - 22*a^3*cosh(d*x + c)^10 + 9*a^3*cosh(d*x + c)^8)*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) + 1) - 80640*(a^3*cosh(d*x + c)^13 + 13*a^3*cosh(d*x + c)*sinh(d*x + c)^12 + a^3*sinh(d*x + c)^13 - 2*a^3*cosh(d*x + c)^11 + a^3*cosh(d*x + c)^9 + 2*(39*a^3*cosh(d*x + c)^2 - a^3)*sinh(d*x + c)^11 + 22*(13*a^3*cosh(d*x + c)^3 - a^3*cosh(d*x + c))*sinh(d*x + c)^10 + (715*a^3*cosh(d*x + c)^4 - 110*a^3*cosh(d*x + c)^2 + a^3)*sinh(d*x + c)^9 + 3*(429*a^3*cosh(d*x + c)^5 - 110*a^3*cosh(d*x + c)^3 + 3*a^3*cosh(d*x + c))*sinh(d*x + c)^8 + 12*(143*a^3*cosh(d*x + c)^6 - 55*a^3*cosh(d*x + c)^4 + 3*a^3*cosh(d*x + c)^2)*sinh(d*x + c)^7 + 12*(143*a^3*cosh(d*x + c)^7 - 77*a^3*cosh(d*x + c)^5 + 7*a^3*cosh(d*x + c)^3)*sinh(d*x + c)^6 + 3*(429*a^3*cosh(d*x + c)^8 - 308*a^3*cosh(d*x + c)^6 + 42*a^3*cosh(d*x + c)^4)*sinh(d*x + c)^5 + (715*a^3*cosh(d*x + c)^9 - 660*a^3*cosh(d*x + c)^7 + 126*a^3*cosh(d*x + c)^5)*sinh(d*x + c)^4 + 2*(143*a^3*cosh(d*x + c)^10 - 165*a^3*cosh(d*x + c)^8 + 42*a^3*cosh(d*x + c)^6)*sinh(d*x + c)^3 + 2*(39*a^3*cosh(d*x + c)^11 - 55*a^3*cosh(d*x + c)^9 + 18*a^3*cosh(d*x + c)^7)*sinh(d*x + c)^2 + (13*a^3*cosh(d*x + c)^12 - 22*a^3*cosh(d*x + c)^10 + 9*a^3*cosh(d*x + c)^8)*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) - 1) + 2*(385*b^3*cosh(d*x + c)^21 - 4750*b^3*cosh(d*x + c)^19 + 9*(3024*a*b^2 + 3113*b^3)*cosh(d*x + c)^17 - 72*(3472*a*b^2 + 1529*b^3)*cosh(d*x + c)^15 + 882*(1920*a^2*b + 1624*a*b^2 + 473*b^3)*cosh(d*x + c)^13 - 3780*(256*a^3 + 384*a^2*b + 280*a*b^2 + 77*b^3)*cosh(d*x + c)^11 - 3150*(256*a^3 + 384*a^2*b + 280*a*b^2 + 77*b^3)*cosh(d*x + c)^9 + 504*(1920*a^2*b + 1624*a*b^2 + 473*b^3)*cosh(d*x + c)^7 - 27*(3472*a*b^2 + 1529*b^3)*cosh(d*x + c)^5 - 475*b^3*cosh(d*x + c) + 2*(3024*a*b^2 + 3113*b^3)*cosh(d*x + c)^3)*sinh(d*x + c))/(d*cosh(d*x + c)^13 + 13*d*cosh(d*x + c)*sinh(d*x + c)^12 + d*sinh(d*x + c)^13 - 2*d*cosh(d*x + c)^11 + 2*(39*d*cosh(d*x + c)^2 - d)*sinh(d*x + c)^11 + 22*(13*d*cosh(d*x + c)^3 - d*cosh(d*x + c))*sinh(d*x + c)^10 + d*cosh(d*x + c)^9 + (715*d*cosh(d*x + c)^4 - 110*d*cosh(d*x + c)^2 + d)*sinh(d*x + c)^9 + 3*(429*d*cosh(d*x + c)^5 - 110*d*cosh(d*x + c)^3 + 3*d*cosh(d*x + c))*sinh(d*x + c)^8 + 12*(143*d*cosh(d*x + c)^6 - 55*d*cosh(d*x + c)^4 + 3*d*cosh(d*x + c)^2)*sinh(d*x + c)^7 + 12*(143*d*cosh(d*x + c)^7 - 77*d*cosh(d*x + c)^5 + 7*d*cosh(d*x + c)^3)*sinh(d*x + c)^6 + 3*(429*d*cosh(d*x + c)^8 - 308*d*cosh(d*x + c)^6 + 42*d*cosh(d*x + c)^4)*sinh(d*x + c)^5 + (715*d*cosh(d*x + c)^9 - 660*d*cosh(d*x + c)^7 + 126*d*cosh(d*x + c)^5)*sinh(d*x + c)^4 + 2*(143*d*cosh(d*x + c)^10 - 165*d*cosh(d*x + c)^8 + 42*d*cosh(d*x + c)^6)*sinh(d*x + c)^3 + 2*(39*d*cosh(d*x + c)^11 - 55*d*cosh(d*x + c)^9 + 18*d*cosh(d*x + c)^7)*sinh(d*x + c)^2 + (13*d*cosh(d*x + c)^12 - 22*d*cosh(d*x + c)^10 + 9*d*cosh(d*x + c)^8)*sinh(d*x + c))","B",0
212,1,6441,0,1.711347," ","integrate(csch(d*x+c)^5*(a+b*sinh(d*x+c)^4)^3,x, algorithm=""fricas"")","\frac{5 \, b^{3} \cosh\left(d x + c\right)^{22} + 110 \, b^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{21} + 5 \, b^{3} \sinh\left(d x + c\right)^{22} - 69 \, b^{3} \cosh\left(d x + c\right)^{20} + 3 \, {\left(385 \, b^{3} \cosh\left(d x + c\right)^{2} - 23 \, b^{3}\right)} \sinh\left(d x + c\right)^{20} + 20 \, {\left(385 \, b^{3} \cosh\left(d x + c\right)^{3} - 69 \, b^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{19} + {\left(560 \, a b^{2} + 471 \, b^{3}\right)} \cosh\left(d x + c\right)^{18} + {\left(36575 \, b^{3} \cosh\left(d x + c\right)^{4} - 13110 \, b^{3} \cosh\left(d x + c\right)^{2} + 560 \, a b^{2} + 471 \, b^{3}\right)} \sinh\left(d x + c\right)^{18} + 18 \, {\left(7315 \, b^{3} \cosh\left(d x + c\right)^{5} - 4370 \, b^{3} \cosh\left(d x + c\right)^{3} + {\left(560 \, a b^{2} + 471 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{17} - {\left(7280 \, a b^{2} + 2519 \, b^{3}\right)} \cosh\left(d x + c\right)^{16} + {\left(373065 \, b^{3} \cosh\left(d x + c\right)^{6} - 334305 \, b^{3} \cosh\left(d x + c\right)^{4} - 7280 \, a b^{2} - 2519 \, b^{3} + 153 \, {\left(560 \, a b^{2} + 471 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{16} + 16 \, {\left(53295 \, b^{3} \cosh\left(d x + c\right)^{7} - 66861 \, b^{3} \cosh\left(d x + c\right)^{5} + 51 \, {\left(560 \, a b^{2} + 471 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - {\left(7280 \, a b^{2} + 2519 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{15} + 6 \, {\left(560 \, a^{3} + 3080 \, a b^{2} + 891 \, b^{3}\right)} \cosh\left(d x + c\right)^{14} + 6 \, {\left(266475 \, b^{3} \cosh\left(d x + c\right)^{8} - 445740 \, b^{3} \cosh\left(d x + c\right)^{6} + 510 \, {\left(560 \, a b^{2} + 471 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 560 \, a^{3} + 3080 \, a b^{2} + 891 \, b^{3} - 20 \, {\left(7280 \, a b^{2} + 2519 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{14} + 4 \, {\left(621775 \, b^{3} \cosh\left(d x + c\right)^{9} - 1337220 \, b^{3} \cosh\left(d x + c\right)^{7} + 2142 \, {\left(560 \, a b^{2} + 471 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 140 \, {\left(7280 \, a b^{2} + 2519 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 21 \, {\left(560 \, a^{3} + 3080 \, a b^{2} + 891 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{13} - 14 \, {\left(880 \, a^{3} + 840 \, a b^{2} + 231 \, b^{3}\right)} \cosh\left(d x + c\right)^{12} + 2 \, {\left(1616615 \, b^{3} \cosh\left(d x + c\right)^{10} - 4345965 \, b^{3} \cosh\left(d x + c\right)^{8} + 9282 \, {\left(560 \, a b^{2} + 471 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} - 910 \, {\left(7280 \, a b^{2} + 2519 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 6160 \, a^{3} - 5880 \, a b^{2} - 1617 \, b^{3} + 273 \, {\left(560 \, a^{3} + 3080 \, a b^{2} + 891 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{12} + 24 \, {\left(146965 \, b^{3} \cosh\left(d x + c\right)^{11} - 482885 \, b^{3} \cosh\left(d x + c\right)^{9} + 1326 \, {\left(560 \, a b^{2} + 471 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} - 182 \, {\left(7280 \, a b^{2} + 2519 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 91 \, {\left(560 \, a^{3} + 3080 \, a b^{2} + 891 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 7 \, {\left(880 \, a^{3} + 840 \, a b^{2} + 231 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{11} - 14 \, {\left(880 \, a^{3} + 840 \, a b^{2} + 231 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} + 2 \, {\left(1616615 \, b^{3} \cosh\left(d x + c\right)^{12} - 6374082 \, b^{3} \cosh\left(d x + c\right)^{10} + 21879 \, {\left(560 \, a b^{2} + 471 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} - 4004 \, {\left(7280 \, a b^{2} + 2519 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 3003 \, {\left(560 \, a^{3} + 3080 \, a b^{2} + 891 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 6160 \, a^{3} - 5880 \, a b^{2} - 1617 \, b^{3} - 462 \, {\left(880 \, a^{3} + 840 \, a b^{2} + 231 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{10} + 4 \, {\left(621775 \, b^{3} \cosh\left(d x + c\right)^{13} - 2897310 \, b^{3} \cosh\left(d x + c\right)^{11} + 12155 \, {\left(560 \, a b^{2} + 471 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} - 2860 \, {\left(7280 \, a b^{2} + 2519 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 3003 \, {\left(560 \, a^{3} + 3080 \, a b^{2} + 891 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 770 \, {\left(880 \, a^{3} + 840 \, a b^{2} + 231 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 35 \, {\left(880 \, a^{3} + 840 \, a b^{2} + 231 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} + 6 \, {\left(560 \, a^{3} + 3080 \, a b^{2} + 891 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 6 \, {\left(266475 \, b^{3} \cosh\left(d x + c\right)^{14} - 1448655 \, b^{3} \cosh\left(d x + c\right)^{12} + 7293 \, {\left(560 \, a b^{2} + 471 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} - 2145 \, {\left(7280 \, a b^{2} + 2519 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 3003 \, {\left(560 \, a^{3} + 3080 \, a b^{2} + 891 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} - 1155 \, {\left(880 \, a^{3} + 840 \, a b^{2} + 231 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 560 \, a^{3} + 3080 \, a b^{2} + 891 \, b^{3} - 105 \, {\left(880 \, a^{3} + 840 \, a b^{2} + 231 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{8} + 16 \, {\left(53295 \, b^{3} \cosh\left(d x + c\right)^{15} - 334305 \, b^{3} \cosh\left(d x + c\right)^{13} + 1989 \, {\left(560 \, a b^{2} + 471 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} - 715 \, {\left(7280 \, a b^{2} + 2519 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + 1287 \, {\left(560 \, a^{3} + 3080 \, a b^{2} + 891 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} - 693 \, {\left(880 \, a^{3} + 840 \, a b^{2} + 231 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 105 \, {\left(880 \, a^{3} + 840 \, a b^{2} + 231 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(560 \, a^{3} + 3080 \, a b^{2} + 891 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} - {\left(7280 \, a b^{2} + 2519 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + {\left(373065 \, b^{3} \cosh\left(d x + c\right)^{16} - 2674440 \, b^{3} \cosh\left(d x + c\right)^{14} + 18564 \, {\left(560 \, a b^{2} + 471 \, b^{3}\right)} \cosh\left(d x + c\right)^{12} - 8008 \, {\left(7280 \, a b^{2} + 2519 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} + 18018 \, {\left(560 \, a^{3} + 3080 \, a b^{2} + 891 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} - 12936 \, {\left(880 \, a^{3} + 840 \, a b^{2} + 231 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} - 2940 \, {\left(880 \, a^{3} + 840 \, a b^{2} + 231 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 7280 \, a b^{2} - 2519 \, b^{3} + 168 \, {\left(560 \, a^{3} + 3080 \, a b^{2} + 891 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 6 \, {\left(21945 \, b^{3} \cosh\left(d x + c\right)^{17} - 178296 \, b^{3} \cosh\left(d x + c\right)^{15} + 1428 \, {\left(560 \, a b^{2} + 471 \, b^{3}\right)} \cosh\left(d x + c\right)^{13} - 728 \, {\left(7280 \, a b^{2} + 2519 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} + 2002 \, {\left(560 \, a^{3} + 3080 \, a b^{2} + 891 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} - 1848 \, {\left(880 \, a^{3} + 840 \, a b^{2} + 231 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} - 588 \, {\left(880 \, a^{3} + 840 \, a b^{2} + 231 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 56 \, {\left(560 \, a^{3} + 3080 \, a b^{2} + 891 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - {\left(7280 \, a b^{2} + 2519 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 69 \, b^{3} \cosh\left(d x + c\right)^{2} + {\left(560 \, a b^{2} + 471 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + {\left(36575 \, b^{3} \cosh\left(d x + c\right)^{18} - 334305 \, b^{3} \cosh\left(d x + c\right)^{16} + 3060 \, {\left(560 \, a b^{2} + 471 \, b^{3}\right)} \cosh\left(d x + c\right)^{14} - 1820 \, {\left(7280 \, a b^{2} + 2519 \, b^{3}\right)} \cosh\left(d x + c\right)^{12} + 6006 \, {\left(560 \, a^{3} + 3080 \, a b^{2} + 891 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} - 6930 \, {\left(880 \, a^{3} + 840 \, a b^{2} + 231 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} - 2940 \, {\left(880 \, a^{3} + 840 \, a b^{2} + 231 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 420 \, {\left(560 \, a^{3} + 3080 \, a b^{2} + 891 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 560 \, a b^{2} + 471 \, b^{3} - 15 \, {\left(7280 \, a b^{2} + 2519 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(1925 \, b^{3} \cosh\left(d x + c\right)^{19} - 19665 \, b^{3} \cosh\left(d x + c\right)^{17} + 204 \, {\left(560 \, a b^{2} + 471 \, b^{3}\right)} \cosh\left(d x + c\right)^{15} - 140 \, {\left(7280 \, a b^{2} + 2519 \, b^{3}\right)} \cosh\left(d x + c\right)^{13} + 546 \, {\left(560 \, a^{3} + 3080 \, a b^{2} + 891 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} - 770 \, {\left(880 \, a^{3} + 840 \, a b^{2} + 231 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} - 420 \, {\left(880 \, a^{3} + 840 \, a b^{2} + 231 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 84 \, {\left(560 \, a^{3} + 3080 \, a b^{2} + 891 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 5 \, {\left(7280 \, a b^{2} + 2519 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(560 \, a b^{2} + 471 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 5 \, b^{3} + 3 \, {\left(385 \, b^{3} \cosh\left(d x + c\right)^{20} - 4370 \, b^{3} \cosh\left(d x + c\right)^{18} + 51 \, {\left(560 \, a b^{2} + 471 \, b^{3}\right)} \cosh\left(d x + c\right)^{16} - 40 \, {\left(7280 \, a b^{2} + 2519 \, b^{3}\right)} \cosh\left(d x + c\right)^{14} + 182 \, {\left(560 \, a^{3} + 3080 \, a b^{2} + 891 \, b^{3}\right)} \cosh\left(d x + c\right)^{12} - 308 \, {\left(880 \, a^{3} + 840 \, a b^{2} + 231 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} - 210 \, {\left(880 \, a^{3} + 840 \, a b^{2} + 231 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 56 \, {\left(560 \, a^{3} + 3080 \, a b^{2} + 891 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} - 5 \, {\left(7280 \, a b^{2} + 2519 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 23 \, b^{3} + 2 \, {\left(560 \, a b^{2} + 471 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} - 1680 \, {\left({\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{15} + 15 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{14} + {\left(a^{3} + 8 \, a^{2} b\right)} \sinh\left(d x + c\right)^{15} - 4 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{13} - {\left(4 \, a^{3} + 32 \, a^{2} b - 105 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{13} + 13 \, {\left(35 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{3} - 4 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{12} + 6 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{11} + 3 \, {\left(455 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{4} + 2 \, a^{3} + 16 \, a^{2} b - 104 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{11} + 11 \, {\left(273 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{5} - 104 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{3} + 6 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{10} - 4 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{9} + {\left(5005 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{6} - 2860 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{4} - 4 \, a^{3} - 32 \, a^{2} b + 330 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{9} + 9 \, {\left(715 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{7} - 572 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{5} + 110 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{3} - 4 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{8} + {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{7} + {\left(6435 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{8} - 6864 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{6} + 1980 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{4} + a^{3} + 8 \, a^{2} b - 144 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{7} + {\left(5005 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{9} - 6864 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{7} + 2772 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{5} - 336 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{3} + 7 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} + 3 \, {\left(1001 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{10} - 1716 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{8} + 924 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{6} - 168 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{4} + 7 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{5} + {\left(1365 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{11} - 2860 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{9} + 1980 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{7} - 504 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{5} + 35 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right)^{4} + {\left(455 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{12} - 1144 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{10} + 990 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{8} - 336 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{6} + 35 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{4}\right)} \sinh\left(d x + c\right)^{3} + 3 \, {\left(35 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{13} - 104 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{11} + 110 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{9} - 48 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{7} + 7 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{5}\right)} \sinh\left(d x + c\right)^{2} + {\left(15 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{14} - 52 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{12} + 66 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{10} - 36 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{8} + 7 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{6}\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) + 1680 \, {\left({\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{15} + 15 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{14} + {\left(a^{3} + 8 \, a^{2} b\right)} \sinh\left(d x + c\right)^{15} - 4 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{13} - {\left(4 \, a^{3} + 32 \, a^{2} b - 105 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{13} + 13 \, {\left(35 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{3} - 4 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{12} + 6 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{11} + 3 \, {\left(455 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{4} + 2 \, a^{3} + 16 \, a^{2} b - 104 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{11} + 11 \, {\left(273 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{5} - 104 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{3} + 6 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{10} - 4 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{9} + {\left(5005 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{6} - 2860 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{4} - 4 \, a^{3} - 32 \, a^{2} b + 330 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{9} + 9 \, {\left(715 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{7} - 572 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{5} + 110 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{3} - 4 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{8} + {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{7} + {\left(6435 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{8} - 6864 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{6} + 1980 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{4} + a^{3} + 8 \, a^{2} b - 144 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{7} + {\left(5005 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{9} - 6864 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{7} + 2772 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{5} - 336 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{3} + 7 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} + 3 \, {\left(1001 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{10} - 1716 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{8} + 924 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{6} - 168 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{4} + 7 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{5} + {\left(1365 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{11} - 2860 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{9} + 1980 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{7} - 504 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{5} + 35 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right)^{4} + {\left(455 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{12} - 1144 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{10} + 990 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{8} - 336 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{6} + 35 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{4}\right)} \sinh\left(d x + c\right)^{3} + 3 \, {\left(35 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{13} - 104 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{11} + 110 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{9} - 48 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{7} + 7 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{5}\right)} \sinh\left(d x + c\right)^{2} + {\left(15 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{14} - 52 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{12} + 66 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{10} - 36 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{8} + 7 \, {\left(a^{3} + 8 \, a^{2} b\right)} \cosh\left(d x + c\right)^{6}\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) + 2 \, {\left(55 \, b^{3} \cosh\left(d x + c\right)^{21} - 690 \, b^{3} \cosh\left(d x + c\right)^{19} + 9 \, {\left(560 \, a b^{2} + 471 \, b^{3}\right)} \cosh\left(d x + c\right)^{17} - 8 \, {\left(7280 \, a b^{2} + 2519 \, b^{3}\right)} \cosh\left(d x + c\right)^{15} + 42 \, {\left(560 \, a^{3} + 3080 \, a b^{2} + 891 \, b^{3}\right)} \cosh\left(d x + c\right)^{13} - 84 \, {\left(880 \, a^{3} + 840 \, a b^{2} + 231 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} - 70 \, {\left(880 \, a^{3} + 840 \, a b^{2} + 231 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + 24 \, {\left(560 \, a^{3} + 3080 \, a b^{2} + 891 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} - 3 \, {\left(7280 \, a b^{2} + 2519 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 69 \, b^{3} \cosh\left(d x + c\right) + 2 \, {\left(560 \, a b^{2} + 471 \, b^{3}\right)} \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right)}{4480 \, {\left(d \cosh\left(d x + c\right)^{15} + 15 \, d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{14} + d \sinh\left(d x + c\right)^{15} - 4 \, d \cosh\left(d x + c\right)^{13} + {\left(105 \, d \cosh\left(d x + c\right)^{2} - 4 \, d\right)} \sinh\left(d x + c\right)^{13} + 13 \, {\left(35 \, d \cosh\left(d x + c\right)^{3} - 4 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{12} + 6 \, d \cosh\left(d x + c\right)^{11} + 3 \, {\left(455 \, d \cosh\left(d x + c\right)^{4} - 104 \, d \cosh\left(d x + c\right)^{2} + 2 \, d\right)} \sinh\left(d x + c\right)^{11} + 11 \, {\left(273 \, d \cosh\left(d x + c\right)^{5} - 104 \, d \cosh\left(d x + c\right)^{3} + 6 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{10} - 4 \, d \cosh\left(d x + c\right)^{9} + {\left(5005 \, d \cosh\left(d x + c\right)^{6} - 2860 \, d \cosh\left(d x + c\right)^{4} + 330 \, d \cosh\left(d x + c\right)^{2} - 4 \, d\right)} \sinh\left(d x + c\right)^{9} + 9 \, {\left(715 \, d \cosh\left(d x + c\right)^{7} - 572 \, d \cosh\left(d x + c\right)^{5} + 110 \, d \cosh\left(d x + c\right)^{3} - 4 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{8} + d \cosh\left(d x + c\right)^{7} + {\left(6435 \, d \cosh\left(d x + c\right)^{8} - 6864 \, d \cosh\left(d x + c\right)^{6} + 1980 \, d \cosh\left(d x + c\right)^{4} - 144 \, d \cosh\left(d x + c\right)^{2} + d\right)} \sinh\left(d x + c\right)^{7} + {\left(5005 \, d \cosh\left(d x + c\right)^{9} - 6864 \, d \cosh\left(d x + c\right)^{7} + 2772 \, d \cosh\left(d x + c\right)^{5} - 336 \, d \cosh\left(d x + c\right)^{3} + 7 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} + 3 \, {\left(1001 \, d \cosh\left(d x + c\right)^{10} - 1716 \, d \cosh\left(d x + c\right)^{8} + 924 \, d \cosh\left(d x + c\right)^{6} - 168 \, d \cosh\left(d x + c\right)^{4} + 7 \, d \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{5} + {\left(1365 \, d \cosh\left(d x + c\right)^{11} - 2860 \, d \cosh\left(d x + c\right)^{9} + 1980 \, d \cosh\left(d x + c\right)^{7} - 504 \, d \cosh\left(d x + c\right)^{5} + 35 \, d \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right)^{4} + {\left(455 \, d \cosh\left(d x + c\right)^{12} - 1144 \, d \cosh\left(d x + c\right)^{10} + 990 \, d \cosh\left(d x + c\right)^{8} - 336 \, d \cosh\left(d x + c\right)^{6} + 35 \, d \cosh\left(d x + c\right)^{4}\right)} \sinh\left(d x + c\right)^{3} + 3 \, {\left(35 \, d \cosh\left(d x + c\right)^{13} - 104 \, d \cosh\left(d x + c\right)^{11} + 110 \, d \cosh\left(d x + c\right)^{9} - 48 \, d \cosh\left(d x + c\right)^{7} + 7 \, d \cosh\left(d x + c\right)^{5}\right)} \sinh\left(d x + c\right)^{2} + {\left(15 \, d \cosh\left(d x + c\right)^{14} - 52 \, d \cosh\left(d x + c\right)^{12} + 66 \, d \cosh\left(d x + c\right)^{10} - 36 \, d \cosh\left(d x + c\right)^{8} + 7 \, d \cosh\left(d x + c\right)^{6}\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"1/4480*(5*b^3*cosh(d*x + c)^22 + 110*b^3*cosh(d*x + c)*sinh(d*x + c)^21 + 5*b^3*sinh(d*x + c)^22 - 69*b^3*cosh(d*x + c)^20 + 3*(385*b^3*cosh(d*x + c)^2 - 23*b^3)*sinh(d*x + c)^20 + 20*(385*b^3*cosh(d*x + c)^3 - 69*b^3*cosh(d*x + c))*sinh(d*x + c)^19 + (560*a*b^2 + 471*b^3)*cosh(d*x + c)^18 + (36575*b^3*cosh(d*x + c)^4 - 13110*b^3*cosh(d*x + c)^2 + 560*a*b^2 + 471*b^3)*sinh(d*x + c)^18 + 18*(7315*b^3*cosh(d*x + c)^5 - 4370*b^3*cosh(d*x + c)^3 + (560*a*b^2 + 471*b^3)*cosh(d*x + c))*sinh(d*x + c)^17 - (7280*a*b^2 + 2519*b^3)*cosh(d*x + c)^16 + (373065*b^3*cosh(d*x + c)^6 - 334305*b^3*cosh(d*x + c)^4 - 7280*a*b^2 - 2519*b^3 + 153*(560*a*b^2 + 471*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^16 + 16*(53295*b^3*cosh(d*x + c)^7 - 66861*b^3*cosh(d*x + c)^5 + 51*(560*a*b^2 + 471*b^3)*cosh(d*x + c)^3 - (7280*a*b^2 + 2519*b^3)*cosh(d*x + c))*sinh(d*x + c)^15 + 6*(560*a^3 + 3080*a*b^2 + 891*b^3)*cosh(d*x + c)^14 + 6*(266475*b^3*cosh(d*x + c)^8 - 445740*b^3*cosh(d*x + c)^6 + 510*(560*a*b^2 + 471*b^3)*cosh(d*x + c)^4 + 560*a^3 + 3080*a*b^2 + 891*b^3 - 20*(7280*a*b^2 + 2519*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^14 + 4*(621775*b^3*cosh(d*x + c)^9 - 1337220*b^3*cosh(d*x + c)^7 + 2142*(560*a*b^2 + 471*b^3)*cosh(d*x + c)^5 - 140*(7280*a*b^2 + 2519*b^3)*cosh(d*x + c)^3 + 21*(560*a^3 + 3080*a*b^2 + 891*b^3)*cosh(d*x + c))*sinh(d*x + c)^13 - 14*(880*a^3 + 840*a*b^2 + 231*b^3)*cosh(d*x + c)^12 + 2*(1616615*b^3*cosh(d*x + c)^10 - 4345965*b^3*cosh(d*x + c)^8 + 9282*(560*a*b^2 + 471*b^3)*cosh(d*x + c)^6 - 910*(7280*a*b^2 + 2519*b^3)*cosh(d*x + c)^4 - 6160*a^3 - 5880*a*b^2 - 1617*b^3 + 273*(560*a^3 + 3080*a*b^2 + 891*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^12 + 24*(146965*b^3*cosh(d*x + c)^11 - 482885*b^3*cosh(d*x + c)^9 + 1326*(560*a*b^2 + 471*b^3)*cosh(d*x + c)^7 - 182*(7280*a*b^2 + 2519*b^3)*cosh(d*x + c)^5 + 91*(560*a^3 + 3080*a*b^2 + 891*b^3)*cosh(d*x + c)^3 - 7*(880*a^3 + 840*a*b^2 + 231*b^3)*cosh(d*x + c))*sinh(d*x + c)^11 - 14*(880*a^3 + 840*a*b^2 + 231*b^3)*cosh(d*x + c)^10 + 2*(1616615*b^3*cosh(d*x + c)^12 - 6374082*b^3*cosh(d*x + c)^10 + 21879*(560*a*b^2 + 471*b^3)*cosh(d*x + c)^8 - 4004*(7280*a*b^2 + 2519*b^3)*cosh(d*x + c)^6 + 3003*(560*a^3 + 3080*a*b^2 + 891*b^3)*cosh(d*x + c)^4 - 6160*a^3 - 5880*a*b^2 - 1617*b^3 - 462*(880*a^3 + 840*a*b^2 + 231*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^10 + 4*(621775*b^3*cosh(d*x + c)^13 - 2897310*b^3*cosh(d*x + c)^11 + 12155*(560*a*b^2 + 471*b^3)*cosh(d*x + c)^9 - 2860*(7280*a*b^2 + 2519*b^3)*cosh(d*x + c)^7 + 3003*(560*a^3 + 3080*a*b^2 + 891*b^3)*cosh(d*x + c)^5 - 770*(880*a^3 + 840*a*b^2 + 231*b^3)*cosh(d*x + c)^3 - 35*(880*a^3 + 840*a*b^2 + 231*b^3)*cosh(d*x + c))*sinh(d*x + c)^9 + 6*(560*a^3 + 3080*a*b^2 + 891*b^3)*cosh(d*x + c)^8 + 6*(266475*b^3*cosh(d*x + c)^14 - 1448655*b^3*cosh(d*x + c)^12 + 7293*(560*a*b^2 + 471*b^3)*cosh(d*x + c)^10 - 2145*(7280*a*b^2 + 2519*b^3)*cosh(d*x + c)^8 + 3003*(560*a^3 + 3080*a*b^2 + 891*b^3)*cosh(d*x + c)^6 - 1155*(880*a^3 + 840*a*b^2 + 231*b^3)*cosh(d*x + c)^4 + 560*a^3 + 3080*a*b^2 + 891*b^3 - 105*(880*a^3 + 840*a*b^2 + 231*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 16*(53295*b^3*cosh(d*x + c)^15 - 334305*b^3*cosh(d*x + c)^13 + 1989*(560*a*b^2 + 471*b^3)*cosh(d*x + c)^11 - 715*(7280*a*b^2 + 2519*b^3)*cosh(d*x + c)^9 + 1287*(560*a^3 + 3080*a*b^2 + 891*b^3)*cosh(d*x + c)^7 - 693*(880*a^3 + 840*a*b^2 + 231*b^3)*cosh(d*x + c)^5 - 105*(880*a^3 + 840*a*b^2 + 231*b^3)*cosh(d*x + c)^3 + 3*(560*a^3 + 3080*a*b^2 + 891*b^3)*cosh(d*x + c))*sinh(d*x + c)^7 - (7280*a*b^2 + 2519*b^3)*cosh(d*x + c)^6 + (373065*b^3*cosh(d*x + c)^16 - 2674440*b^3*cosh(d*x + c)^14 + 18564*(560*a*b^2 + 471*b^3)*cosh(d*x + c)^12 - 8008*(7280*a*b^2 + 2519*b^3)*cosh(d*x + c)^10 + 18018*(560*a^3 + 3080*a*b^2 + 891*b^3)*cosh(d*x + c)^8 - 12936*(880*a^3 + 840*a*b^2 + 231*b^3)*cosh(d*x + c)^6 - 2940*(880*a^3 + 840*a*b^2 + 231*b^3)*cosh(d*x + c)^4 - 7280*a*b^2 - 2519*b^3 + 168*(560*a^3 + 3080*a*b^2 + 891*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 6*(21945*b^3*cosh(d*x + c)^17 - 178296*b^3*cosh(d*x + c)^15 + 1428*(560*a*b^2 + 471*b^3)*cosh(d*x + c)^13 - 728*(7280*a*b^2 + 2519*b^3)*cosh(d*x + c)^11 + 2002*(560*a^3 + 3080*a*b^2 + 891*b^3)*cosh(d*x + c)^9 - 1848*(880*a^3 + 840*a*b^2 + 231*b^3)*cosh(d*x + c)^7 - 588*(880*a^3 + 840*a*b^2 + 231*b^3)*cosh(d*x + c)^5 + 56*(560*a^3 + 3080*a*b^2 + 891*b^3)*cosh(d*x + c)^3 - (7280*a*b^2 + 2519*b^3)*cosh(d*x + c))*sinh(d*x + c)^5 - 69*b^3*cosh(d*x + c)^2 + (560*a*b^2 + 471*b^3)*cosh(d*x + c)^4 + (36575*b^3*cosh(d*x + c)^18 - 334305*b^3*cosh(d*x + c)^16 + 3060*(560*a*b^2 + 471*b^3)*cosh(d*x + c)^14 - 1820*(7280*a*b^2 + 2519*b^3)*cosh(d*x + c)^12 + 6006*(560*a^3 + 3080*a*b^2 + 891*b^3)*cosh(d*x + c)^10 - 6930*(880*a^3 + 840*a*b^2 + 231*b^3)*cosh(d*x + c)^8 - 2940*(880*a^3 + 840*a*b^2 + 231*b^3)*cosh(d*x + c)^6 + 420*(560*a^3 + 3080*a*b^2 + 891*b^3)*cosh(d*x + c)^4 + 560*a*b^2 + 471*b^3 - 15*(7280*a*b^2 + 2519*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 4*(1925*b^3*cosh(d*x + c)^19 - 19665*b^3*cosh(d*x + c)^17 + 204*(560*a*b^2 + 471*b^3)*cosh(d*x + c)^15 - 140*(7280*a*b^2 + 2519*b^3)*cosh(d*x + c)^13 + 546*(560*a^3 + 3080*a*b^2 + 891*b^3)*cosh(d*x + c)^11 - 770*(880*a^3 + 840*a*b^2 + 231*b^3)*cosh(d*x + c)^9 - 420*(880*a^3 + 840*a*b^2 + 231*b^3)*cosh(d*x + c)^7 + 84*(560*a^3 + 3080*a*b^2 + 891*b^3)*cosh(d*x + c)^5 - 5*(7280*a*b^2 + 2519*b^3)*cosh(d*x + c)^3 + (560*a*b^2 + 471*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 + 5*b^3 + 3*(385*b^3*cosh(d*x + c)^20 - 4370*b^3*cosh(d*x + c)^18 + 51*(560*a*b^2 + 471*b^3)*cosh(d*x + c)^16 - 40*(7280*a*b^2 + 2519*b^3)*cosh(d*x + c)^14 + 182*(560*a^3 + 3080*a*b^2 + 891*b^3)*cosh(d*x + c)^12 - 308*(880*a^3 + 840*a*b^2 + 231*b^3)*cosh(d*x + c)^10 - 210*(880*a^3 + 840*a*b^2 + 231*b^3)*cosh(d*x + c)^8 + 56*(560*a^3 + 3080*a*b^2 + 891*b^3)*cosh(d*x + c)^6 - 5*(7280*a*b^2 + 2519*b^3)*cosh(d*x + c)^4 - 23*b^3 + 2*(560*a*b^2 + 471*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - 1680*((a^3 + 8*a^2*b)*cosh(d*x + c)^15 + 15*(a^3 + 8*a^2*b)*cosh(d*x + c)*sinh(d*x + c)^14 + (a^3 + 8*a^2*b)*sinh(d*x + c)^15 - 4*(a^3 + 8*a^2*b)*cosh(d*x + c)^13 - (4*a^3 + 32*a^2*b - 105*(a^3 + 8*a^2*b)*cosh(d*x + c)^2)*sinh(d*x + c)^13 + 13*(35*(a^3 + 8*a^2*b)*cosh(d*x + c)^3 - 4*(a^3 + 8*a^2*b)*cosh(d*x + c))*sinh(d*x + c)^12 + 6*(a^3 + 8*a^2*b)*cosh(d*x + c)^11 + 3*(455*(a^3 + 8*a^2*b)*cosh(d*x + c)^4 + 2*a^3 + 16*a^2*b - 104*(a^3 + 8*a^2*b)*cosh(d*x + c)^2)*sinh(d*x + c)^11 + 11*(273*(a^3 + 8*a^2*b)*cosh(d*x + c)^5 - 104*(a^3 + 8*a^2*b)*cosh(d*x + c)^3 + 6*(a^3 + 8*a^2*b)*cosh(d*x + c))*sinh(d*x + c)^10 - 4*(a^3 + 8*a^2*b)*cosh(d*x + c)^9 + (5005*(a^3 + 8*a^2*b)*cosh(d*x + c)^6 - 2860*(a^3 + 8*a^2*b)*cosh(d*x + c)^4 - 4*a^3 - 32*a^2*b + 330*(a^3 + 8*a^2*b)*cosh(d*x + c)^2)*sinh(d*x + c)^9 + 9*(715*(a^3 + 8*a^2*b)*cosh(d*x + c)^7 - 572*(a^3 + 8*a^2*b)*cosh(d*x + c)^5 + 110*(a^3 + 8*a^2*b)*cosh(d*x + c)^3 - 4*(a^3 + 8*a^2*b)*cosh(d*x + c))*sinh(d*x + c)^8 + (a^3 + 8*a^2*b)*cosh(d*x + c)^7 + (6435*(a^3 + 8*a^2*b)*cosh(d*x + c)^8 - 6864*(a^3 + 8*a^2*b)*cosh(d*x + c)^6 + 1980*(a^3 + 8*a^2*b)*cosh(d*x + c)^4 + a^3 + 8*a^2*b - 144*(a^3 + 8*a^2*b)*cosh(d*x + c)^2)*sinh(d*x + c)^7 + (5005*(a^3 + 8*a^2*b)*cosh(d*x + c)^9 - 6864*(a^3 + 8*a^2*b)*cosh(d*x + c)^7 + 2772*(a^3 + 8*a^2*b)*cosh(d*x + c)^5 - 336*(a^3 + 8*a^2*b)*cosh(d*x + c)^3 + 7*(a^3 + 8*a^2*b)*cosh(d*x + c))*sinh(d*x + c)^6 + 3*(1001*(a^3 + 8*a^2*b)*cosh(d*x + c)^10 - 1716*(a^3 + 8*a^2*b)*cosh(d*x + c)^8 + 924*(a^3 + 8*a^2*b)*cosh(d*x + c)^6 - 168*(a^3 + 8*a^2*b)*cosh(d*x + c)^4 + 7*(a^3 + 8*a^2*b)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + (1365*(a^3 + 8*a^2*b)*cosh(d*x + c)^11 - 2860*(a^3 + 8*a^2*b)*cosh(d*x + c)^9 + 1980*(a^3 + 8*a^2*b)*cosh(d*x + c)^7 - 504*(a^3 + 8*a^2*b)*cosh(d*x + c)^5 + 35*(a^3 + 8*a^2*b)*cosh(d*x + c)^3)*sinh(d*x + c)^4 + (455*(a^3 + 8*a^2*b)*cosh(d*x + c)^12 - 1144*(a^3 + 8*a^2*b)*cosh(d*x + c)^10 + 990*(a^3 + 8*a^2*b)*cosh(d*x + c)^8 - 336*(a^3 + 8*a^2*b)*cosh(d*x + c)^6 + 35*(a^3 + 8*a^2*b)*cosh(d*x + c)^4)*sinh(d*x + c)^3 + 3*(35*(a^3 + 8*a^2*b)*cosh(d*x + c)^13 - 104*(a^3 + 8*a^2*b)*cosh(d*x + c)^11 + 110*(a^3 + 8*a^2*b)*cosh(d*x + c)^9 - 48*(a^3 + 8*a^2*b)*cosh(d*x + c)^7 + 7*(a^3 + 8*a^2*b)*cosh(d*x + c)^5)*sinh(d*x + c)^2 + (15*(a^3 + 8*a^2*b)*cosh(d*x + c)^14 - 52*(a^3 + 8*a^2*b)*cosh(d*x + c)^12 + 66*(a^3 + 8*a^2*b)*cosh(d*x + c)^10 - 36*(a^3 + 8*a^2*b)*cosh(d*x + c)^8 + 7*(a^3 + 8*a^2*b)*cosh(d*x + c)^6)*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) + 1) + 1680*((a^3 + 8*a^2*b)*cosh(d*x + c)^15 + 15*(a^3 + 8*a^2*b)*cosh(d*x + c)*sinh(d*x + c)^14 + (a^3 + 8*a^2*b)*sinh(d*x + c)^15 - 4*(a^3 + 8*a^2*b)*cosh(d*x + c)^13 - (4*a^3 + 32*a^2*b - 105*(a^3 + 8*a^2*b)*cosh(d*x + c)^2)*sinh(d*x + c)^13 + 13*(35*(a^3 + 8*a^2*b)*cosh(d*x + c)^3 - 4*(a^3 + 8*a^2*b)*cosh(d*x + c))*sinh(d*x + c)^12 + 6*(a^3 + 8*a^2*b)*cosh(d*x + c)^11 + 3*(455*(a^3 + 8*a^2*b)*cosh(d*x + c)^4 + 2*a^3 + 16*a^2*b - 104*(a^3 + 8*a^2*b)*cosh(d*x + c)^2)*sinh(d*x + c)^11 + 11*(273*(a^3 + 8*a^2*b)*cosh(d*x + c)^5 - 104*(a^3 + 8*a^2*b)*cosh(d*x + c)^3 + 6*(a^3 + 8*a^2*b)*cosh(d*x + c))*sinh(d*x + c)^10 - 4*(a^3 + 8*a^2*b)*cosh(d*x + c)^9 + (5005*(a^3 + 8*a^2*b)*cosh(d*x + c)^6 - 2860*(a^3 + 8*a^2*b)*cosh(d*x + c)^4 - 4*a^3 - 32*a^2*b + 330*(a^3 + 8*a^2*b)*cosh(d*x + c)^2)*sinh(d*x + c)^9 + 9*(715*(a^3 + 8*a^2*b)*cosh(d*x + c)^7 - 572*(a^3 + 8*a^2*b)*cosh(d*x + c)^5 + 110*(a^3 + 8*a^2*b)*cosh(d*x + c)^3 - 4*(a^3 + 8*a^2*b)*cosh(d*x + c))*sinh(d*x + c)^8 + (a^3 + 8*a^2*b)*cosh(d*x + c)^7 + (6435*(a^3 + 8*a^2*b)*cosh(d*x + c)^8 - 6864*(a^3 + 8*a^2*b)*cosh(d*x + c)^6 + 1980*(a^3 + 8*a^2*b)*cosh(d*x + c)^4 + a^3 + 8*a^2*b - 144*(a^3 + 8*a^2*b)*cosh(d*x + c)^2)*sinh(d*x + c)^7 + (5005*(a^3 + 8*a^2*b)*cosh(d*x + c)^9 - 6864*(a^3 + 8*a^2*b)*cosh(d*x + c)^7 + 2772*(a^3 + 8*a^2*b)*cosh(d*x + c)^5 - 336*(a^3 + 8*a^2*b)*cosh(d*x + c)^3 + 7*(a^3 + 8*a^2*b)*cosh(d*x + c))*sinh(d*x + c)^6 + 3*(1001*(a^3 + 8*a^2*b)*cosh(d*x + c)^10 - 1716*(a^3 + 8*a^2*b)*cosh(d*x + c)^8 + 924*(a^3 + 8*a^2*b)*cosh(d*x + c)^6 - 168*(a^3 + 8*a^2*b)*cosh(d*x + c)^4 + 7*(a^3 + 8*a^2*b)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + (1365*(a^3 + 8*a^2*b)*cosh(d*x + c)^11 - 2860*(a^3 + 8*a^2*b)*cosh(d*x + c)^9 + 1980*(a^3 + 8*a^2*b)*cosh(d*x + c)^7 - 504*(a^3 + 8*a^2*b)*cosh(d*x + c)^5 + 35*(a^3 + 8*a^2*b)*cosh(d*x + c)^3)*sinh(d*x + c)^4 + (455*(a^3 + 8*a^2*b)*cosh(d*x + c)^12 - 1144*(a^3 + 8*a^2*b)*cosh(d*x + c)^10 + 990*(a^3 + 8*a^2*b)*cosh(d*x + c)^8 - 336*(a^3 + 8*a^2*b)*cosh(d*x + c)^6 + 35*(a^3 + 8*a^2*b)*cosh(d*x + c)^4)*sinh(d*x + c)^3 + 3*(35*(a^3 + 8*a^2*b)*cosh(d*x + c)^13 - 104*(a^3 + 8*a^2*b)*cosh(d*x + c)^11 + 110*(a^3 + 8*a^2*b)*cosh(d*x + c)^9 - 48*(a^3 + 8*a^2*b)*cosh(d*x + c)^7 + 7*(a^3 + 8*a^2*b)*cosh(d*x + c)^5)*sinh(d*x + c)^2 + (15*(a^3 + 8*a^2*b)*cosh(d*x + c)^14 - 52*(a^3 + 8*a^2*b)*cosh(d*x + c)^12 + 66*(a^3 + 8*a^2*b)*cosh(d*x + c)^10 - 36*(a^3 + 8*a^2*b)*cosh(d*x + c)^8 + 7*(a^3 + 8*a^2*b)*cosh(d*x + c)^6)*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) - 1) + 2*(55*b^3*cosh(d*x + c)^21 - 690*b^3*cosh(d*x + c)^19 + 9*(560*a*b^2 + 471*b^3)*cosh(d*x + c)^17 - 8*(7280*a*b^2 + 2519*b^3)*cosh(d*x + c)^15 + 42*(560*a^3 + 3080*a*b^2 + 891*b^3)*cosh(d*x + c)^13 - 84*(880*a^3 + 840*a*b^2 + 231*b^3)*cosh(d*x + c)^11 - 70*(880*a^3 + 840*a*b^2 + 231*b^3)*cosh(d*x + c)^9 + 24*(560*a^3 + 3080*a*b^2 + 891*b^3)*cosh(d*x + c)^7 - 3*(7280*a*b^2 + 2519*b^3)*cosh(d*x + c)^5 - 69*b^3*cosh(d*x + c) + 2*(560*a*b^2 + 471*b^3)*cosh(d*x + c)^3)*sinh(d*x + c))/(d*cosh(d*x + c)^15 + 15*d*cosh(d*x + c)*sinh(d*x + c)^14 + d*sinh(d*x + c)^15 - 4*d*cosh(d*x + c)^13 + (105*d*cosh(d*x + c)^2 - 4*d)*sinh(d*x + c)^13 + 13*(35*d*cosh(d*x + c)^3 - 4*d*cosh(d*x + c))*sinh(d*x + c)^12 + 6*d*cosh(d*x + c)^11 + 3*(455*d*cosh(d*x + c)^4 - 104*d*cosh(d*x + c)^2 + 2*d)*sinh(d*x + c)^11 + 11*(273*d*cosh(d*x + c)^5 - 104*d*cosh(d*x + c)^3 + 6*d*cosh(d*x + c))*sinh(d*x + c)^10 - 4*d*cosh(d*x + c)^9 + (5005*d*cosh(d*x + c)^6 - 2860*d*cosh(d*x + c)^4 + 330*d*cosh(d*x + c)^2 - 4*d)*sinh(d*x + c)^9 + 9*(715*d*cosh(d*x + c)^7 - 572*d*cosh(d*x + c)^5 + 110*d*cosh(d*x + c)^3 - 4*d*cosh(d*x + c))*sinh(d*x + c)^8 + d*cosh(d*x + c)^7 + (6435*d*cosh(d*x + c)^8 - 6864*d*cosh(d*x + c)^6 + 1980*d*cosh(d*x + c)^4 - 144*d*cosh(d*x + c)^2 + d)*sinh(d*x + c)^7 + (5005*d*cosh(d*x + c)^9 - 6864*d*cosh(d*x + c)^7 + 2772*d*cosh(d*x + c)^5 - 336*d*cosh(d*x + c)^3 + 7*d*cosh(d*x + c))*sinh(d*x + c)^6 + 3*(1001*d*cosh(d*x + c)^10 - 1716*d*cosh(d*x + c)^8 + 924*d*cosh(d*x + c)^6 - 168*d*cosh(d*x + c)^4 + 7*d*cosh(d*x + c)^2)*sinh(d*x + c)^5 + (1365*d*cosh(d*x + c)^11 - 2860*d*cosh(d*x + c)^9 + 1980*d*cosh(d*x + c)^7 - 504*d*cosh(d*x + c)^5 + 35*d*cosh(d*x + c)^3)*sinh(d*x + c)^4 + (455*d*cosh(d*x + c)^12 - 1144*d*cosh(d*x + c)^10 + 990*d*cosh(d*x + c)^8 - 336*d*cosh(d*x + c)^6 + 35*d*cosh(d*x + c)^4)*sinh(d*x + c)^3 + 3*(35*d*cosh(d*x + c)^13 - 104*d*cosh(d*x + c)^11 + 110*d*cosh(d*x + c)^9 - 48*d*cosh(d*x + c)^7 + 7*d*cosh(d*x + c)^5)*sinh(d*x + c)^2 + (15*d*cosh(d*x + c)^14 - 52*d*cosh(d*x + c)^12 + 66*d*cosh(d*x + c)^10 - 36*d*cosh(d*x + c)^8 + 7*d*cosh(d*x + c)^6)*sinh(d*x + c))","B",0
213,1,8547,0,2.520785," ","integrate(csch(d*x+c)^7*(a+b*sinh(d*x+c)^4)^3,x, algorithm=""fricas"")","\frac{3 \, b^{3} \cosh\left(d x + c\right)^{22} + 66 \, b^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{21} + 3 \, b^{3} \sinh\left(d x + c\right)^{22} - 43 \, b^{3} \cosh\left(d x + c\right)^{20} + {\left(693 \, b^{3} \cosh\left(d x + c\right)^{2} - 43 \, b^{3}\right)} \sinh\left(d x + c\right)^{20} + 20 \, {\left(231 \, b^{3} \cosh\left(d x + c\right)^{3} - 43 \, b^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{19} + 15 \, {\left(48 \, a b^{2} + 23 \, b^{3}\right)} \cosh\left(d x + c\right)^{18} + 5 \, {\left(4389 \, b^{3} \cosh\left(d x + c\right)^{4} - 1634 \, b^{3} \cosh\left(d x + c\right)^{2} + 144 \, a b^{2} + 69 \, b^{3}\right)} \sinh\left(d x + c\right)^{18} + 6 \, {\left(13167 \, b^{3} \cosh\left(d x + c\right)^{5} - 8170 \, b^{3} \cosh\left(d x + c\right)^{3} + 45 \, {\left(48 \, a b^{2} + 23 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{17} - 15 \, {\left(20 \, a^{3} + 96 \, a^{2} b + 240 \, a b^{2} + 79 \, b^{3}\right)} \cosh\left(d x + c\right)^{16} + 3 \, {\left(74613 \, b^{3} \cosh\left(d x + c\right)^{6} - 69445 \, b^{3} \cosh\left(d x + c\right)^{4} - 100 \, a^{3} - 480 \, a^{2} b - 1200 \, a b^{2} - 395 \, b^{3} + 765 \, {\left(48 \, a b^{2} + 23 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{16} + 48 \, {\left(10659 \, b^{3} \cosh\left(d x + c\right)^{7} - 13889 \, b^{3} \cosh\left(d x + c\right)^{5} + 255 \, {\left(48 \, a b^{2} + 23 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 5 \, {\left(20 \, a^{3} + 96 \, a^{2} b + 240 \, a b^{2} + 79 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{15} + 10 \, {\left(170 \, a^{3} + 432 \, a^{2} b + 648 \, a b^{2} + 187 \, b^{3}\right)} \cosh\left(d x + c\right)^{14} + 10 \, {\left(95931 \, b^{3} \cosh\left(d x + c\right)^{8} - 166668 \, b^{3} \cosh\left(d x + c\right)^{6} + 4590 \, {\left(48 \, a b^{2} + 23 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 170 \, a^{3} + 432 \, a^{2} b + 648 \, a b^{2} + 187 \, b^{3} - 180 \, {\left(20 \, a^{3} + 96 \, a^{2} b + 240 \, a b^{2} + 79 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{14} + 20 \, {\left(74613 \, b^{3} \cosh\left(d x + c\right)^{9} - 166668 \, b^{3} \cosh\left(d x + c\right)^{7} + 6426 \, {\left(48 \, a b^{2} + 23 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 420 \, {\left(20 \, a^{3} + 96 \, a^{2} b + 240 \, a b^{2} + 79 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 7 \, {\left(170 \, a^{3} + 432 \, a^{2} b + 648 \, a b^{2} + 187 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{13} - 90 \, {\left(44 \, a^{3} + 32 \, a^{2} b + 40 \, a b^{2} + 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{12} + 2 \, {\left(969969 \, b^{3} \cosh\left(d x + c\right)^{10} - 2708355 \, b^{3} \cosh\left(d x + c\right)^{8} + 139230 \, {\left(48 \, a b^{2} + 23 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} - 13650 \, {\left(20 \, a^{3} + 96 \, a^{2} b + 240 \, a b^{2} + 79 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 1980 \, a^{3} - 1440 \, a^{2} b - 1800 \, a b^{2} - 495 \, b^{3} + 455 \, {\left(170 \, a^{3} + 432 \, a^{2} b + 648 \, a b^{2} + 187 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{12} + 8 \, {\left(264537 \, b^{3} \cosh\left(d x + c\right)^{11} - 902785 \, b^{3} \cosh\left(d x + c\right)^{9} + 59670 \, {\left(48 \, a b^{2} + 23 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} - 8190 \, {\left(20 \, a^{3} + 96 \, a^{2} b + 240 \, a b^{2} + 79 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 455 \, {\left(170 \, a^{3} + 432 \, a^{2} b + 648 \, a b^{2} + 187 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 135 \, {\left(44 \, a^{3} + 32 \, a^{2} b + 40 \, a b^{2} + 11 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{11} - 90 \, {\left(44 \, a^{3} + 32 \, a^{2} b + 40 \, a b^{2} + 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} + 2 \, {\left(969969 \, b^{3} \cosh\left(d x + c\right)^{12} - 3972254 \, b^{3} \cosh\left(d x + c\right)^{10} + 328185 \, {\left(48 \, a b^{2} + 23 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} - 60060 \, {\left(20 \, a^{3} + 96 \, a^{2} b + 240 \, a b^{2} + 79 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 5005 \, {\left(170 \, a^{3} + 432 \, a^{2} b + 648 \, a b^{2} + 187 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 1980 \, a^{3} - 1440 \, a^{2} b - 1800 \, a b^{2} - 495 \, b^{3} - 2970 \, {\left(44 \, a^{3} + 32 \, a^{2} b + 40 \, a b^{2} + 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{10} + 20 \, {\left(74613 \, b^{3} \cosh\left(d x + c\right)^{13} - 361114 \, b^{3} \cosh\left(d x + c\right)^{11} + 36465 \, {\left(48 \, a b^{2} + 23 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} - 8580 \, {\left(20 \, a^{3} + 96 \, a^{2} b + 240 \, a b^{2} + 79 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 1001 \, {\left(170 \, a^{3} + 432 \, a^{2} b + 648 \, a b^{2} + 187 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 990 \, {\left(44 \, a^{3} + 32 \, a^{2} b + 40 \, a b^{2} + 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 45 \, {\left(44 \, a^{3} + 32 \, a^{2} b + 40 \, a b^{2} + 11 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} + 10 \, {\left(170 \, a^{3} + 432 \, a^{2} b + 648 \, a b^{2} + 187 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 10 \, {\left(95931 \, b^{3} \cosh\left(d x + c\right)^{14} - 541671 \, b^{3} \cosh\left(d x + c\right)^{12} + 65637 \, {\left(48 \, a b^{2} + 23 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} - 19305 \, {\left(20 \, a^{3} + 96 \, a^{2} b + 240 \, a b^{2} + 79 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 3003 \, {\left(170 \, a^{3} + 432 \, a^{2} b + 648 \, a b^{2} + 187 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} - 4455 \, {\left(44 \, a^{3} + 32 \, a^{2} b + 40 \, a b^{2} + 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 170 \, a^{3} + 432 \, a^{2} b + 648 \, a b^{2} + 187 \, b^{3} - 405 \, {\left(44 \, a^{3} + 32 \, a^{2} b + 40 \, a b^{2} + 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{8} + 16 \, {\left(31977 \, b^{3} \cosh\left(d x + c\right)^{15} - 208335 \, b^{3} \cosh\left(d x + c\right)^{13} + 29835 \, {\left(48 \, a b^{2} + 23 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} - 10725 \, {\left(20 \, a^{3} + 96 \, a^{2} b + 240 \, a b^{2} + 79 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + 2145 \, {\left(170 \, a^{3} + 432 \, a^{2} b + 648 \, a b^{2} + 187 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} - 4455 \, {\left(44 \, a^{3} + 32 \, a^{2} b + 40 \, a b^{2} + 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 675 \, {\left(44 \, a^{3} + 32 \, a^{2} b + 40 \, a b^{2} + 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 5 \, {\left(170 \, a^{3} + 432 \, a^{2} b + 648 \, a b^{2} + 187 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} - 15 \, {\left(20 \, a^{3} + 96 \, a^{2} b + 240 \, a b^{2} + 79 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + {\left(223839 \, b^{3} \cosh\left(d x + c\right)^{16} - 1666680 \, b^{3} \cosh\left(d x + c\right)^{14} + 278460 \, {\left(48 \, a b^{2} + 23 \, b^{3}\right)} \cosh\left(d x + c\right)^{12} - 120120 \, {\left(20 \, a^{3} + 96 \, a^{2} b + 240 \, a b^{2} + 79 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} + 30030 \, {\left(170 \, a^{3} + 432 \, a^{2} b + 648 \, a b^{2} + 187 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} - 83160 \, {\left(44 \, a^{3} + 32 \, a^{2} b + 40 \, a b^{2} + 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} - 18900 \, {\left(44 \, a^{3} + 32 \, a^{2} b + 40 \, a b^{2} + 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 300 \, a^{3} - 1440 \, a^{2} b - 3600 \, a b^{2} - 1185 \, b^{3} + 280 \, {\left(170 \, a^{3} + 432 \, a^{2} b + 648 \, a b^{2} + 187 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(39501 \, b^{3} \cosh\left(d x + c\right)^{17} - 333336 \, b^{3} \cosh\left(d x + c\right)^{15} + 64260 \, {\left(48 \, a b^{2} + 23 \, b^{3}\right)} \cosh\left(d x + c\right)^{13} - 32760 \, {\left(20 \, a^{3} + 96 \, a^{2} b + 240 \, a b^{2} + 79 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} + 10010 \, {\left(170 \, a^{3} + 432 \, a^{2} b + 648 \, a b^{2} + 187 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} - 35640 \, {\left(44 \, a^{3} + 32 \, a^{2} b + 40 \, a b^{2} + 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} - 11340 \, {\left(44 \, a^{3} + 32 \, a^{2} b + 40 \, a b^{2} + 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 280 \, {\left(170 \, a^{3} + 432 \, a^{2} b + 648 \, a b^{2} + 187 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 45 \, {\left(20 \, a^{3} + 96 \, a^{2} b + 240 \, a b^{2} + 79 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 43 \, b^{3} \cosh\left(d x + c\right)^{2} + 15 \, {\left(48 \, a b^{2} + 23 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 5 \, {\left(4389 \, b^{3} \cosh\left(d x + c\right)^{18} - 41667 \, b^{3} \cosh\left(d x + c\right)^{16} + 9180 \, {\left(48 \, a b^{2} + 23 \, b^{3}\right)} \cosh\left(d x + c\right)^{14} - 5460 \, {\left(20 \, a^{3} + 96 \, a^{2} b + 240 \, a b^{2} + 79 \, b^{3}\right)} \cosh\left(d x + c\right)^{12} + 2002 \, {\left(170 \, a^{3} + 432 \, a^{2} b + 648 \, a b^{2} + 187 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} - 8910 \, {\left(44 \, a^{3} + 32 \, a^{2} b + 40 \, a b^{2} + 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} - 3780 \, {\left(44 \, a^{3} + 32 \, a^{2} b + 40 \, a b^{2} + 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 140 \, {\left(170 \, a^{3} + 432 \, a^{2} b + 648 \, a b^{2} + 187 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 144 \, a b^{2} + 69 \, b^{3} - 45 \, {\left(20 \, a^{3} + 96 \, a^{2} b + 240 \, a b^{2} + 79 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 20 \, {\left(231 \, b^{3} \cosh\left(d x + c\right)^{19} - 2451 \, b^{3} \cosh\left(d x + c\right)^{17} + 612 \, {\left(48 \, a b^{2} + 23 \, b^{3}\right)} \cosh\left(d x + c\right)^{15} - 420 \, {\left(20 \, a^{3} + 96 \, a^{2} b + 240 \, a b^{2} + 79 \, b^{3}\right)} \cosh\left(d x + c\right)^{13} + 182 \, {\left(170 \, a^{3} + 432 \, a^{2} b + 648 \, a b^{2} + 187 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} - 990 \, {\left(44 \, a^{3} + 32 \, a^{2} b + 40 \, a b^{2} + 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} - 540 \, {\left(44 \, a^{3} + 32 \, a^{2} b + 40 \, a b^{2} + 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 28 \, {\left(170 \, a^{3} + 432 \, a^{2} b + 648 \, a b^{2} + 187 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 15 \, {\left(20 \, a^{3} + 96 \, a^{2} b + 240 \, a b^{2} + 79 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(48 \, a b^{2} + 23 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 3 \, b^{3} + {\left(693 \, b^{3} \cosh\left(d x + c\right)^{20} - 8170 \, b^{3} \cosh\left(d x + c\right)^{18} + 2295 \, {\left(48 \, a b^{2} + 23 \, b^{3}\right)} \cosh\left(d x + c\right)^{16} - 1800 \, {\left(20 \, a^{3} + 96 \, a^{2} b + 240 \, a b^{2} + 79 \, b^{3}\right)} \cosh\left(d x + c\right)^{14} + 910 \, {\left(170 \, a^{3} + 432 \, a^{2} b + 648 \, a b^{2} + 187 \, b^{3}\right)} \cosh\left(d x + c\right)^{12} - 5940 \, {\left(44 \, a^{3} + 32 \, a^{2} b + 40 \, a b^{2} + 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} - 4050 \, {\left(44 \, a^{3} + 32 \, a^{2} b + 40 \, a b^{2} + 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 280 \, {\left(170 \, a^{3} + 432 \, a^{2} b + 648 \, a b^{2} + 187 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} - 225 \, {\left(20 \, a^{3} + 96 \, a^{2} b + 240 \, a b^{2} + 79 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 43 \, b^{3} + 90 \, {\left(48 \, a b^{2} + 23 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 30 \, {\left({\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{17} + 17 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{16} + {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \sinh\left(d x + c\right)^{17} - 6 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{15} - 2 \, {\left(15 \, a^{3} + 72 \, a^{2} b - 68 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{15} + 10 \, {\left(68 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{3} - 9 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{14} + 15 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{13} + 5 \, {\left(476 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{4} + 15 \, a^{3} + 72 \, a^{2} b - 126 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{13} + 13 \, {\left(476 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{5} - 210 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{3} + 15 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{12} - 20 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{11} + 2 \, {\left(6188 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{6} - 4095 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{4} - 50 \, a^{3} - 240 \, a^{2} b + 585 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{11} + 22 \, {\left(884 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{7} - 819 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{5} + 195 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{3} - 10 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{10} + 15 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{9} + 5 \, {\left(4862 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{8} - 6006 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{6} + 2145 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{4} + 15 \, a^{3} + 72 \, a^{2} b - 220 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{9} + 5 \, {\left(4862 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{9} - 7722 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{7} + 3861 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{5} - 660 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{3} + 27 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{8} - 6 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{7} + 2 \, {\left(9724 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{10} - 19305 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{8} + 12870 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{6} - 3300 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{4} - 15 \, a^{3} - 72 \, a^{2} b + 270 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(6188 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{11} - 15015 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{9} + 12870 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{7} - 4620 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{5} + 630 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{3} - 21 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} + {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{5} + {\left(6188 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{12} - 18018 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{10} + 19305 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{8} - 9240 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{6} + 1890 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{4} + 5 \, a^{3} + 24 \, a^{2} b - 126 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{5} + 5 \, {\left(476 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{13} - 1638 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{11} + 2145 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{9} - 1320 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{7} + 378 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{5} - 42 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{3} + {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 10 \, {\left(68 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{14} - 273 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{12} + 429 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{10} - 330 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{8} + 126 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{6} - 21 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{4} + {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(68 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{15} - 315 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{13} + 585 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{11} - 550 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{9} + 270 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{7} - 63 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right)^{2} + {\left(17 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{16} - 90 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{14} + 195 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{12} - 220 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{10} + 135 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{8} - 42 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{6} + 5 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{4}\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) - 30 \, {\left({\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{17} + 17 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{16} + {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \sinh\left(d x + c\right)^{17} - 6 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{15} - 2 \, {\left(15 \, a^{3} + 72 \, a^{2} b - 68 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{15} + 10 \, {\left(68 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{3} - 9 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{14} + 15 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{13} + 5 \, {\left(476 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{4} + 15 \, a^{3} + 72 \, a^{2} b - 126 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{13} + 13 \, {\left(476 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{5} - 210 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{3} + 15 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{12} - 20 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{11} + 2 \, {\left(6188 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{6} - 4095 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{4} - 50 \, a^{3} - 240 \, a^{2} b + 585 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{11} + 22 \, {\left(884 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{7} - 819 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{5} + 195 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{3} - 10 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{10} + 15 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{9} + 5 \, {\left(4862 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{8} - 6006 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{6} + 2145 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{4} + 15 \, a^{3} + 72 \, a^{2} b - 220 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{9} + 5 \, {\left(4862 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{9} - 7722 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{7} + 3861 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{5} - 660 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{3} + 27 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{8} - 6 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{7} + 2 \, {\left(9724 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{10} - 19305 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{8} + 12870 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{6} - 3300 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{4} - 15 \, a^{3} - 72 \, a^{2} b + 270 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(6188 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{11} - 15015 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{9} + 12870 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{7} - 4620 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{5} + 630 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{3} - 21 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} + {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{5} + {\left(6188 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{12} - 18018 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{10} + 19305 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{8} - 9240 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{6} + 1890 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{4} + 5 \, a^{3} + 24 \, a^{2} b - 126 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{5} + 5 \, {\left(476 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{13} - 1638 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{11} + 2145 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{9} - 1320 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{7} + 378 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{5} - 42 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{3} + {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 10 \, {\left(68 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{14} - 273 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{12} + 429 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{10} - 330 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{8} + 126 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{6} - 21 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{4} + {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(68 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{15} - 315 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{13} + 585 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{11} - 550 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{9} + 270 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{7} - 63 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right)^{2} + {\left(17 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{16} - 90 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{14} + 195 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{12} - 220 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{10} + 135 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{8} - 42 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{6} + 5 \, {\left(5 \, a^{3} + 24 \, a^{2} b\right)} \cosh\left(d x + c\right)^{4}\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) + 2 \, {\left(33 \, b^{3} \cosh\left(d x + c\right)^{21} - 430 \, b^{3} \cosh\left(d x + c\right)^{19} + 135 \, {\left(48 \, a b^{2} + 23 \, b^{3}\right)} \cosh\left(d x + c\right)^{17} - 120 \, {\left(20 \, a^{3} + 96 \, a^{2} b + 240 \, a b^{2} + 79 \, b^{3}\right)} \cosh\left(d x + c\right)^{15} + 70 \, {\left(170 \, a^{3} + 432 \, a^{2} b + 648 \, a b^{2} + 187 \, b^{3}\right)} \cosh\left(d x + c\right)^{13} - 540 \, {\left(44 \, a^{3} + 32 \, a^{2} b + 40 \, a b^{2} + 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} - 450 \, {\left(44 \, a^{3} + 32 \, a^{2} b + 40 \, a b^{2} + 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + 40 \, {\left(170 \, a^{3} + 432 \, a^{2} b + 648 \, a b^{2} + 187 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} - 45 \, {\left(20 \, a^{3} + 96 \, a^{2} b + 240 \, a b^{2} + 79 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 43 \, b^{3} \cosh\left(d x + c\right) + 30 \, {\left(48 \, a b^{2} + 23 \, b^{3}\right)} \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right)}{480 \, {\left(d \cosh\left(d x + c\right)^{17} + 17 \, d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{16} + d \sinh\left(d x + c\right)^{17} - 6 \, d \cosh\left(d x + c\right)^{15} + 2 \, {\left(68 \, d \cosh\left(d x + c\right)^{2} - 3 \, d\right)} \sinh\left(d x + c\right)^{15} + 10 \, {\left(68 \, d \cosh\left(d x + c\right)^{3} - 9 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{14} + 15 \, d \cosh\left(d x + c\right)^{13} + 5 \, {\left(476 \, d \cosh\left(d x + c\right)^{4} - 126 \, d \cosh\left(d x + c\right)^{2} + 3 \, d\right)} \sinh\left(d x + c\right)^{13} + 13 \, {\left(476 \, d \cosh\left(d x + c\right)^{5} - 210 \, d \cosh\left(d x + c\right)^{3} + 15 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{12} - 20 \, d \cosh\left(d x + c\right)^{11} + 2 \, {\left(6188 \, d \cosh\left(d x + c\right)^{6} - 4095 \, d \cosh\left(d x + c\right)^{4} + 585 \, d \cosh\left(d x + c\right)^{2} - 10 \, d\right)} \sinh\left(d x + c\right)^{11} + 22 \, {\left(884 \, d \cosh\left(d x + c\right)^{7} - 819 \, d \cosh\left(d x + c\right)^{5} + 195 \, d \cosh\left(d x + c\right)^{3} - 10 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{10} + 15 \, d \cosh\left(d x + c\right)^{9} + 5 \, {\left(4862 \, d \cosh\left(d x + c\right)^{8} - 6006 \, d \cosh\left(d x + c\right)^{6} + 2145 \, d \cosh\left(d x + c\right)^{4} - 220 \, d \cosh\left(d x + c\right)^{2} + 3 \, d\right)} \sinh\left(d x + c\right)^{9} + 5 \, {\left(4862 \, d \cosh\left(d x + c\right)^{9} - 7722 \, d \cosh\left(d x + c\right)^{7} + 3861 \, d \cosh\left(d x + c\right)^{5} - 660 \, d \cosh\left(d x + c\right)^{3} + 27 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{8} - 6 \, d \cosh\left(d x + c\right)^{7} + 2 \, {\left(9724 \, d \cosh\left(d x + c\right)^{10} - 19305 \, d \cosh\left(d x + c\right)^{8} + 12870 \, d \cosh\left(d x + c\right)^{6} - 3300 \, d \cosh\left(d x + c\right)^{4} + 270 \, d \cosh\left(d x + c\right)^{2} - 3 \, d\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(6188 \, d \cosh\left(d x + c\right)^{11} - 15015 \, d \cosh\left(d x + c\right)^{9} + 12870 \, d \cosh\left(d x + c\right)^{7} - 4620 \, d \cosh\left(d x + c\right)^{5} + 630 \, d \cosh\left(d x + c\right)^{3} - 21 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} + d \cosh\left(d x + c\right)^{5} + {\left(6188 \, d \cosh\left(d x + c\right)^{12} - 18018 \, d \cosh\left(d x + c\right)^{10} + 19305 \, d \cosh\left(d x + c\right)^{8} - 9240 \, d \cosh\left(d x + c\right)^{6} + 1890 \, d \cosh\left(d x + c\right)^{4} - 126 \, d \cosh\left(d x + c\right)^{2} + d\right)} \sinh\left(d x + c\right)^{5} + 5 \, {\left(476 \, d \cosh\left(d x + c\right)^{13} - 1638 \, d \cosh\left(d x + c\right)^{11} + 2145 \, d \cosh\left(d x + c\right)^{9} - 1320 \, d \cosh\left(d x + c\right)^{7} + 378 \, d \cosh\left(d x + c\right)^{5} - 42 \, d \cosh\left(d x + c\right)^{3} + d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 10 \, {\left(68 \, d \cosh\left(d x + c\right)^{14} - 273 \, d \cosh\left(d x + c\right)^{12} + 429 \, d \cosh\left(d x + c\right)^{10} - 330 \, d \cosh\left(d x + c\right)^{8} + 126 \, d \cosh\left(d x + c\right)^{6} - 21 \, d \cosh\left(d x + c\right)^{4} + d \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(68 \, d \cosh\left(d x + c\right)^{15} - 315 \, d \cosh\left(d x + c\right)^{13} + 585 \, d \cosh\left(d x + c\right)^{11} - 550 \, d \cosh\left(d x + c\right)^{9} + 270 \, d \cosh\left(d x + c\right)^{7} - 63 \, d \cosh\left(d x + c\right)^{5} + 5 \, d \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right)^{2} + {\left(17 \, d \cosh\left(d x + c\right)^{16} - 90 \, d \cosh\left(d x + c\right)^{14} + 195 \, d \cosh\left(d x + c\right)^{12} - 220 \, d \cosh\left(d x + c\right)^{10} + 135 \, d \cosh\left(d x + c\right)^{8} - 42 \, d \cosh\left(d x + c\right)^{6} + 5 \, d \cosh\left(d x + c\right)^{4}\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"1/480*(3*b^3*cosh(d*x + c)^22 + 66*b^3*cosh(d*x + c)*sinh(d*x + c)^21 + 3*b^3*sinh(d*x + c)^22 - 43*b^3*cosh(d*x + c)^20 + (693*b^3*cosh(d*x + c)^2 - 43*b^3)*sinh(d*x + c)^20 + 20*(231*b^3*cosh(d*x + c)^3 - 43*b^3*cosh(d*x + c))*sinh(d*x + c)^19 + 15*(48*a*b^2 + 23*b^3)*cosh(d*x + c)^18 + 5*(4389*b^3*cosh(d*x + c)^4 - 1634*b^3*cosh(d*x + c)^2 + 144*a*b^2 + 69*b^3)*sinh(d*x + c)^18 + 6*(13167*b^3*cosh(d*x + c)^5 - 8170*b^3*cosh(d*x + c)^3 + 45*(48*a*b^2 + 23*b^3)*cosh(d*x + c))*sinh(d*x + c)^17 - 15*(20*a^3 + 96*a^2*b + 240*a*b^2 + 79*b^3)*cosh(d*x + c)^16 + 3*(74613*b^3*cosh(d*x + c)^6 - 69445*b^3*cosh(d*x + c)^4 - 100*a^3 - 480*a^2*b - 1200*a*b^2 - 395*b^3 + 765*(48*a*b^2 + 23*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^16 + 48*(10659*b^3*cosh(d*x + c)^7 - 13889*b^3*cosh(d*x + c)^5 + 255*(48*a*b^2 + 23*b^3)*cosh(d*x + c)^3 - 5*(20*a^3 + 96*a^2*b + 240*a*b^2 + 79*b^3)*cosh(d*x + c))*sinh(d*x + c)^15 + 10*(170*a^3 + 432*a^2*b + 648*a*b^2 + 187*b^3)*cosh(d*x + c)^14 + 10*(95931*b^3*cosh(d*x + c)^8 - 166668*b^3*cosh(d*x + c)^6 + 4590*(48*a*b^2 + 23*b^3)*cosh(d*x + c)^4 + 170*a^3 + 432*a^2*b + 648*a*b^2 + 187*b^3 - 180*(20*a^3 + 96*a^2*b + 240*a*b^2 + 79*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^14 + 20*(74613*b^3*cosh(d*x + c)^9 - 166668*b^3*cosh(d*x + c)^7 + 6426*(48*a*b^2 + 23*b^3)*cosh(d*x + c)^5 - 420*(20*a^3 + 96*a^2*b + 240*a*b^2 + 79*b^3)*cosh(d*x + c)^3 + 7*(170*a^3 + 432*a^2*b + 648*a*b^2 + 187*b^3)*cosh(d*x + c))*sinh(d*x + c)^13 - 90*(44*a^3 + 32*a^2*b + 40*a*b^2 + 11*b^3)*cosh(d*x + c)^12 + 2*(969969*b^3*cosh(d*x + c)^10 - 2708355*b^3*cosh(d*x + c)^8 + 139230*(48*a*b^2 + 23*b^3)*cosh(d*x + c)^6 - 13650*(20*a^3 + 96*a^2*b + 240*a*b^2 + 79*b^3)*cosh(d*x + c)^4 - 1980*a^3 - 1440*a^2*b - 1800*a*b^2 - 495*b^3 + 455*(170*a^3 + 432*a^2*b + 648*a*b^2 + 187*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^12 + 8*(264537*b^3*cosh(d*x + c)^11 - 902785*b^3*cosh(d*x + c)^9 + 59670*(48*a*b^2 + 23*b^3)*cosh(d*x + c)^7 - 8190*(20*a^3 + 96*a^2*b + 240*a*b^2 + 79*b^3)*cosh(d*x + c)^5 + 455*(170*a^3 + 432*a^2*b + 648*a*b^2 + 187*b^3)*cosh(d*x + c)^3 - 135*(44*a^3 + 32*a^2*b + 40*a*b^2 + 11*b^3)*cosh(d*x + c))*sinh(d*x + c)^11 - 90*(44*a^3 + 32*a^2*b + 40*a*b^2 + 11*b^3)*cosh(d*x + c)^10 + 2*(969969*b^3*cosh(d*x + c)^12 - 3972254*b^3*cosh(d*x + c)^10 + 328185*(48*a*b^2 + 23*b^3)*cosh(d*x + c)^8 - 60060*(20*a^3 + 96*a^2*b + 240*a*b^2 + 79*b^3)*cosh(d*x + c)^6 + 5005*(170*a^3 + 432*a^2*b + 648*a*b^2 + 187*b^3)*cosh(d*x + c)^4 - 1980*a^3 - 1440*a^2*b - 1800*a*b^2 - 495*b^3 - 2970*(44*a^3 + 32*a^2*b + 40*a*b^2 + 11*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^10 + 20*(74613*b^3*cosh(d*x + c)^13 - 361114*b^3*cosh(d*x + c)^11 + 36465*(48*a*b^2 + 23*b^3)*cosh(d*x + c)^9 - 8580*(20*a^3 + 96*a^2*b + 240*a*b^2 + 79*b^3)*cosh(d*x + c)^7 + 1001*(170*a^3 + 432*a^2*b + 648*a*b^2 + 187*b^3)*cosh(d*x + c)^5 - 990*(44*a^3 + 32*a^2*b + 40*a*b^2 + 11*b^3)*cosh(d*x + c)^3 - 45*(44*a^3 + 32*a^2*b + 40*a*b^2 + 11*b^3)*cosh(d*x + c))*sinh(d*x + c)^9 + 10*(170*a^3 + 432*a^2*b + 648*a*b^2 + 187*b^3)*cosh(d*x + c)^8 + 10*(95931*b^3*cosh(d*x + c)^14 - 541671*b^3*cosh(d*x + c)^12 + 65637*(48*a*b^2 + 23*b^3)*cosh(d*x + c)^10 - 19305*(20*a^3 + 96*a^2*b + 240*a*b^2 + 79*b^3)*cosh(d*x + c)^8 + 3003*(170*a^3 + 432*a^2*b + 648*a*b^2 + 187*b^3)*cosh(d*x + c)^6 - 4455*(44*a^3 + 32*a^2*b + 40*a*b^2 + 11*b^3)*cosh(d*x + c)^4 + 170*a^3 + 432*a^2*b + 648*a*b^2 + 187*b^3 - 405*(44*a^3 + 32*a^2*b + 40*a*b^2 + 11*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 16*(31977*b^3*cosh(d*x + c)^15 - 208335*b^3*cosh(d*x + c)^13 + 29835*(48*a*b^2 + 23*b^3)*cosh(d*x + c)^11 - 10725*(20*a^3 + 96*a^2*b + 240*a*b^2 + 79*b^3)*cosh(d*x + c)^9 + 2145*(170*a^3 + 432*a^2*b + 648*a*b^2 + 187*b^3)*cosh(d*x + c)^7 - 4455*(44*a^3 + 32*a^2*b + 40*a*b^2 + 11*b^3)*cosh(d*x + c)^5 - 675*(44*a^3 + 32*a^2*b + 40*a*b^2 + 11*b^3)*cosh(d*x + c)^3 + 5*(170*a^3 + 432*a^2*b + 648*a*b^2 + 187*b^3)*cosh(d*x + c))*sinh(d*x + c)^7 - 15*(20*a^3 + 96*a^2*b + 240*a*b^2 + 79*b^3)*cosh(d*x + c)^6 + (223839*b^3*cosh(d*x + c)^16 - 1666680*b^3*cosh(d*x + c)^14 + 278460*(48*a*b^2 + 23*b^3)*cosh(d*x + c)^12 - 120120*(20*a^3 + 96*a^2*b + 240*a*b^2 + 79*b^3)*cosh(d*x + c)^10 + 30030*(170*a^3 + 432*a^2*b + 648*a*b^2 + 187*b^3)*cosh(d*x + c)^8 - 83160*(44*a^3 + 32*a^2*b + 40*a*b^2 + 11*b^3)*cosh(d*x + c)^6 - 18900*(44*a^3 + 32*a^2*b + 40*a*b^2 + 11*b^3)*cosh(d*x + c)^4 - 300*a^3 - 1440*a^2*b - 3600*a*b^2 - 1185*b^3 + 280*(170*a^3 + 432*a^2*b + 648*a*b^2 + 187*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 2*(39501*b^3*cosh(d*x + c)^17 - 333336*b^3*cosh(d*x + c)^15 + 64260*(48*a*b^2 + 23*b^3)*cosh(d*x + c)^13 - 32760*(20*a^3 + 96*a^2*b + 240*a*b^2 + 79*b^3)*cosh(d*x + c)^11 + 10010*(170*a^3 + 432*a^2*b + 648*a*b^2 + 187*b^3)*cosh(d*x + c)^9 - 35640*(44*a^3 + 32*a^2*b + 40*a*b^2 + 11*b^3)*cosh(d*x + c)^7 - 11340*(44*a^3 + 32*a^2*b + 40*a*b^2 + 11*b^3)*cosh(d*x + c)^5 + 280*(170*a^3 + 432*a^2*b + 648*a*b^2 + 187*b^3)*cosh(d*x + c)^3 - 45*(20*a^3 + 96*a^2*b + 240*a*b^2 + 79*b^3)*cosh(d*x + c))*sinh(d*x + c)^5 - 43*b^3*cosh(d*x + c)^2 + 15*(48*a*b^2 + 23*b^3)*cosh(d*x + c)^4 + 5*(4389*b^3*cosh(d*x + c)^18 - 41667*b^3*cosh(d*x + c)^16 + 9180*(48*a*b^2 + 23*b^3)*cosh(d*x + c)^14 - 5460*(20*a^3 + 96*a^2*b + 240*a*b^2 + 79*b^3)*cosh(d*x + c)^12 + 2002*(170*a^3 + 432*a^2*b + 648*a*b^2 + 187*b^3)*cosh(d*x + c)^10 - 8910*(44*a^3 + 32*a^2*b + 40*a*b^2 + 11*b^3)*cosh(d*x + c)^8 - 3780*(44*a^3 + 32*a^2*b + 40*a*b^2 + 11*b^3)*cosh(d*x + c)^6 + 140*(170*a^3 + 432*a^2*b + 648*a*b^2 + 187*b^3)*cosh(d*x + c)^4 + 144*a*b^2 + 69*b^3 - 45*(20*a^3 + 96*a^2*b + 240*a*b^2 + 79*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 20*(231*b^3*cosh(d*x + c)^19 - 2451*b^3*cosh(d*x + c)^17 + 612*(48*a*b^2 + 23*b^3)*cosh(d*x + c)^15 - 420*(20*a^3 + 96*a^2*b + 240*a*b^2 + 79*b^3)*cosh(d*x + c)^13 + 182*(170*a^3 + 432*a^2*b + 648*a*b^2 + 187*b^3)*cosh(d*x + c)^11 - 990*(44*a^3 + 32*a^2*b + 40*a*b^2 + 11*b^3)*cosh(d*x + c)^9 - 540*(44*a^3 + 32*a^2*b + 40*a*b^2 + 11*b^3)*cosh(d*x + c)^7 + 28*(170*a^3 + 432*a^2*b + 648*a*b^2 + 187*b^3)*cosh(d*x + c)^5 - 15*(20*a^3 + 96*a^2*b + 240*a*b^2 + 79*b^3)*cosh(d*x + c)^3 + 3*(48*a*b^2 + 23*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 + 3*b^3 + (693*b^3*cosh(d*x + c)^20 - 8170*b^3*cosh(d*x + c)^18 + 2295*(48*a*b^2 + 23*b^3)*cosh(d*x + c)^16 - 1800*(20*a^3 + 96*a^2*b + 240*a*b^2 + 79*b^3)*cosh(d*x + c)^14 + 910*(170*a^3 + 432*a^2*b + 648*a*b^2 + 187*b^3)*cosh(d*x + c)^12 - 5940*(44*a^3 + 32*a^2*b + 40*a*b^2 + 11*b^3)*cosh(d*x + c)^10 - 4050*(44*a^3 + 32*a^2*b + 40*a*b^2 + 11*b^3)*cosh(d*x + c)^8 + 280*(170*a^3 + 432*a^2*b + 648*a*b^2 + 187*b^3)*cosh(d*x + c)^6 - 225*(20*a^3 + 96*a^2*b + 240*a*b^2 + 79*b^3)*cosh(d*x + c)^4 - 43*b^3 + 90*(48*a*b^2 + 23*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 30*((5*a^3 + 24*a^2*b)*cosh(d*x + c)^17 + 17*(5*a^3 + 24*a^2*b)*cosh(d*x + c)*sinh(d*x + c)^16 + (5*a^3 + 24*a^2*b)*sinh(d*x + c)^17 - 6*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^15 - 2*(15*a^3 + 72*a^2*b - 68*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^2)*sinh(d*x + c)^15 + 10*(68*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^3 - 9*(5*a^3 + 24*a^2*b)*cosh(d*x + c))*sinh(d*x + c)^14 + 15*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^13 + 5*(476*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^4 + 15*a^3 + 72*a^2*b - 126*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^2)*sinh(d*x + c)^13 + 13*(476*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^5 - 210*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^3 + 15*(5*a^3 + 24*a^2*b)*cosh(d*x + c))*sinh(d*x + c)^12 - 20*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^11 + 2*(6188*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^6 - 4095*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^4 - 50*a^3 - 240*a^2*b + 585*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^2)*sinh(d*x + c)^11 + 22*(884*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^7 - 819*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^5 + 195*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^3 - 10*(5*a^3 + 24*a^2*b)*cosh(d*x + c))*sinh(d*x + c)^10 + 15*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^9 + 5*(4862*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^8 - 6006*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^6 + 2145*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^4 + 15*a^3 + 72*a^2*b - 220*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^2)*sinh(d*x + c)^9 + 5*(4862*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^9 - 7722*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^7 + 3861*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^5 - 660*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^3 + 27*(5*a^3 + 24*a^2*b)*cosh(d*x + c))*sinh(d*x + c)^8 - 6*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^7 + 2*(9724*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^10 - 19305*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^8 + 12870*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^6 - 3300*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^4 - 15*a^3 - 72*a^2*b + 270*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^2)*sinh(d*x + c)^7 + 2*(6188*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^11 - 15015*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^9 + 12870*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^7 - 4620*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^5 + 630*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^3 - 21*(5*a^3 + 24*a^2*b)*cosh(d*x + c))*sinh(d*x + c)^6 + (5*a^3 + 24*a^2*b)*cosh(d*x + c)^5 + (6188*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^12 - 18018*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^10 + 19305*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^8 - 9240*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^6 + 1890*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^4 + 5*a^3 + 24*a^2*b - 126*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 5*(476*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^13 - 1638*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^11 + 2145*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^9 - 1320*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^7 + 378*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^5 - 42*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^3 + (5*a^3 + 24*a^2*b)*cosh(d*x + c))*sinh(d*x + c)^4 + 10*(68*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^14 - 273*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^12 + 429*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^10 - 330*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^8 + 126*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^6 - 21*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^4 + (5*a^3 + 24*a^2*b)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 2*(68*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^15 - 315*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^13 + 585*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^11 - 550*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^9 + 270*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^7 - 63*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^5 + 5*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^3)*sinh(d*x + c)^2 + (17*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^16 - 90*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^14 + 195*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^12 - 220*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^10 + 135*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^8 - 42*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^6 + 5*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^4)*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) + 1) - 30*((5*a^3 + 24*a^2*b)*cosh(d*x + c)^17 + 17*(5*a^3 + 24*a^2*b)*cosh(d*x + c)*sinh(d*x + c)^16 + (5*a^3 + 24*a^2*b)*sinh(d*x + c)^17 - 6*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^15 - 2*(15*a^3 + 72*a^2*b - 68*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^2)*sinh(d*x + c)^15 + 10*(68*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^3 - 9*(5*a^3 + 24*a^2*b)*cosh(d*x + c))*sinh(d*x + c)^14 + 15*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^13 + 5*(476*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^4 + 15*a^3 + 72*a^2*b - 126*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^2)*sinh(d*x + c)^13 + 13*(476*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^5 - 210*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^3 + 15*(5*a^3 + 24*a^2*b)*cosh(d*x + c))*sinh(d*x + c)^12 - 20*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^11 + 2*(6188*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^6 - 4095*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^4 - 50*a^3 - 240*a^2*b + 585*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^2)*sinh(d*x + c)^11 + 22*(884*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^7 - 819*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^5 + 195*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^3 - 10*(5*a^3 + 24*a^2*b)*cosh(d*x + c))*sinh(d*x + c)^10 + 15*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^9 + 5*(4862*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^8 - 6006*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^6 + 2145*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^4 + 15*a^3 + 72*a^2*b - 220*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^2)*sinh(d*x + c)^9 + 5*(4862*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^9 - 7722*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^7 + 3861*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^5 - 660*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^3 + 27*(5*a^3 + 24*a^2*b)*cosh(d*x + c))*sinh(d*x + c)^8 - 6*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^7 + 2*(9724*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^10 - 19305*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^8 + 12870*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^6 - 3300*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^4 - 15*a^3 - 72*a^2*b + 270*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^2)*sinh(d*x + c)^7 + 2*(6188*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^11 - 15015*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^9 + 12870*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^7 - 4620*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^5 + 630*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^3 - 21*(5*a^3 + 24*a^2*b)*cosh(d*x + c))*sinh(d*x + c)^6 + (5*a^3 + 24*a^2*b)*cosh(d*x + c)^5 + (6188*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^12 - 18018*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^10 + 19305*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^8 - 9240*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^6 + 1890*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^4 + 5*a^3 + 24*a^2*b - 126*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 5*(476*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^13 - 1638*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^11 + 2145*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^9 - 1320*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^7 + 378*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^5 - 42*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^3 + (5*a^3 + 24*a^2*b)*cosh(d*x + c))*sinh(d*x + c)^4 + 10*(68*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^14 - 273*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^12 + 429*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^10 - 330*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^8 + 126*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^6 - 21*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^4 + (5*a^3 + 24*a^2*b)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 2*(68*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^15 - 315*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^13 + 585*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^11 - 550*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^9 + 270*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^7 - 63*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^5 + 5*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^3)*sinh(d*x + c)^2 + (17*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^16 - 90*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^14 + 195*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^12 - 220*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^10 + 135*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^8 - 42*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^6 + 5*(5*a^3 + 24*a^2*b)*cosh(d*x + c)^4)*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) - 1) + 2*(33*b^3*cosh(d*x + c)^21 - 430*b^3*cosh(d*x + c)^19 + 135*(48*a*b^2 + 23*b^3)*cosh(d*x + c)^17 - 120*(20*a^3 + 96*a^2*b + 240*a*b^2 + 79*b^3)*cosh(d*x + c)^15 + 70*(170*a^3 + 432*a^2*b + 648*a*b^2 + 187*b^3)*cosh(d*x + c)^13 - 540*(44*a^3 + 32*a^2*b + 40*a*b^2 + 11*b^3)*cosh(d*x + c)^11 - 450*(44*a^3 + 32*a^2*b + 40*a*b^2 + 11*b^3)*cosh(d*x + c)^9 + 40*(170*a^3 + 432*a^2*b + 648*a*b^2 + 187*b^3)*cosh(d*x + c)^7 - 45*(20*a^3 + 96*a^2*b + 240*a*b^2 + 79*b^3)*cosh(d*x + c)^5 - 43*b^3*cosh(d*x + c) + 30*(48*a*b^2 + 23*b^3)*cosh(d*x + c)^3)*sinh(d*x + c))/(d*cosh(d*x + c)^17 + 17*d*cosh(d*x + c)*sinh(d*x + c)^16 + d*sinh(d*x + c)^17 - 6*d*cosh(d*x + c)^15 + 2*(68*d*cosh(d*x + c)^2 - 3*d)*sinh(d*x + c)^15 + 10*(68*d*cosh(d*x + c)^3 - 9*d*cosh(d*x + c))*sinh(d*x + c)^14 + 15*d*cosh(d*x + c)^13 + 5*(476*d*cosh(d*x + c)^4 - 126*d*cosh(d*x + c)^2 + 3*d)*sinh(d*x + c)^13 + 13*(476*d*cosh(d*x + c)^5 - 210*d*cosh(d*x + c)^3 + 15*d*cosh(d*x + c))*sinh(d*x + c)^12 - 20*d*cosh(d*x + c)^11 + 2*(6188*d*cosh(d*x + c)^6 - 4095*d*cosh(d*x + c)^4 + 585*d*cosh(d*x + c)^2 - 10*d)*sinh(d*x + c)^11 + 22*(884*d*cosh(d*x + c)^7 - 819*d*cosh(d*x + c)^5 + 195*d*cosh(d*x + c)^3 - 10*d*cosh(d*x + c))*sinh(d*x + c)^10 + 15*d*cosh(d*x + c)^9 + 5*(4862*d*cosh(d*x + c)^8 - 6006*d*cosh(d*x + c)^6 + 2145*d*cosh(d*x + c)^4 - 220*d*cosh(d*x + c)^2 + 3*d)*sinh(d*x + c)^9 + 5*(4862*d*cosh(d*x + c)^9 - 7722*d*cosh(d*x + c)^7 + 3861*d*cosh(d*x + c)^5 - 660*d*cosh(d*x + c)^3 + 27*d*cosh(d*x + c))*sinh(d*x + c)^8 - 6*d*cosh(d*x + c)^7 + 2*(9724*d*cosh(d*x + c)^10 - 19305*d*cosh(d*x + c)^8 + 12870*d*cosh(d*x + c)^6 - 3300*d*cosh(d*x + c)^4 + 270*d*cosh(d*x + c)^2 - 3*d)*sinh(d*x + c)^7 + 2*(6188*d*cosh(d*x + c)^11 - 15015*d*cosh(d*x + c)^9 + 12870*d*cosh(d*x + c)^7 - 4620*d*cosh(d*x + c)^5 + 630*d*cosh(d*x + c)^3 - 21*d*cosh(d*x + c))*sinh(d*x + c)^6 + d*cosh(d*x + c)^5 + (6188*d*cosh(d*x + c)^12 - 18018*d*cosh(d*x + c)^10 + 19305*d*cosh(d*x + c)^8 - 9240*d*cosh(d*x + c)^6 + 1890*d*cosh(d*x + c)^4 - 126*d*cosh(d*x + c)^2 + d)*sinh(d*x + c)^5 + 5*(476*d*cosh(d*x + c)^13 - 1638*d*cosh(d*x + c)^11 + 2145*d*cosh(d*x + c)^9 - 1320*d*cosh(d*x + c)^7 + 378*d*cosh(d*x + c)^5 - 42*d*cosh(d*x + c)^3 + d*cosh(d*x + c))*sinh(d*x + c)^4 + 10*(68*d*cosh(d*x + c)^14 - 273*d*cosh(d*x + c)^12 + 429*d*cosh(d*x + c)^10 - 330*d*cosh(d*x + c)^8 + 126*d*cosh(d*x + c)^6 - 21*d*cosh(d*x + c)^4 + d*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 2*(68*d*cosh(d*x + c)^15 - 315*d*cosh(d*x + c)^13 + 585*d*cosh(d*x + c)^11 - 550*d*cosh(d*x + c)^9 + 270*d*cosh(d*x + c)^7 - 63*d*cosh(d*x + c)^5 + 5*d*cosh(d*x + c)^3)*sinh(d*x + c)^2 + (17*d*cosh(d*x + c)^16 - 90*d*cosh(d*x + c)^14 + 195*d*cosh(d*x + c)^12 - 220*d*cosh(d*x + c)^10 + 135*d*cosh(d*x + c)^8 - 42*d*cosh(d*x + c)^6 + 5*d*cosh(d*x + c)^4)*sinh(d*x + c))","B",0
214,1,10848,0,1.998943," ","integrate(csch(d*x+c)^9*(a+b*sinh(d*x+c)^4)^3,x, algorithm=""fricas"")","\frac{16 \, b^{3} \cosh\left(d x + c\right)^{22} + 352 \, b^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{21} + 16 \, b^{3} \sinh\left(d x + c\right)^{22} - 272 \, b^{3} \cosh\left(d x + c\right)^{20} + 16 \, {\left(231 \, b^{3} \cosh\left(d x + c\right)^{2} - 17 \, b^{3}\right)} \sinh\left(d x + c\right)^{20} + 320 \, {\left(77 \, b^{3} \cosh\left(d x + c\right)^{3} - 17 \, b^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{19} + 2 \, {\left(105 \, a^{3} + 432 \, a^{2} b + 728 \, b^{3}\right)} \cosh\left(d x + c\right)^{18} + 2 \, {\left(58520 \, b^{3} \cosh\left(d x + c\right)^{4} - 25840 \, b^{3} \cosh\left(d x + c\right)^{2} + 105 \, a^{3} + 432 \, a^{2} b + 728 \, b^{3}\right)} \sinh\left(d x + c\right)^{18} + 12 \, {\left(35112 \, b^{3} \cosh\left(d x + c\right)^{5} - 25840 \, b^{3} \cosh\left(d x + c\right)^{3} + 3 \, {\left(105 \, a^{3} + 432 \, a^{2} b + 728 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{17} - 2 \, {\left(805 \, a^{3} + 3312 \, a^{2} b + 1880 \, b^{3}\right)} \cosh\left(d x + c\right)^{16} + 2 \, {\left(596904 \, b^{3} \cosh\left(d x + c\right)^{6} - 658920 \, b^{3} \cosh\left(d x + c\right)^{4} - 805 \, a^{3} - 3312 \, a^{2} b - 1880 \, b^{3} + 153 \, {\left(105 \, a^{3} + 432 \, a^{2} b + 728 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{16} + 32 \, {\left(85272 \, b^{3} \cosh\left(d x + c\right)^{7} - 131784 \, b^{3} \cosh\left(d x + c\right)^{5} + 51 \, {\left(105 \, a^{3} + 432 \, a^{2} b + 728 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - {\left(805 \, a^{3} + 3312 \, a^{2} b + 1880 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{15} + 2 \, {\left(2681 \, a^{3} + 7344 \, a^{2} b + 2512 \, b^{3}\right)} \cosh\left(d x + c\right)^{14} + 2 \, {\left(2558160 \, b^{3} \cosh\left(d x + c\right)^{8} - 5271360 \, b^{3} \cosh\left(d x + c\right)^{6} + 3060 \, {\left(105 \, a^{3} + 432 \, a^{2} b + 728 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 2681 \, a^{3} + 7344 \, a^{2} b + 2512 \, b^{3} - 120 \, {\left(805 \, a^{3} + 3312 \, a^{2} b + 1880 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{14} + 4 \, {\left(1989680 \, b^{3} \cosh\left(d x + c\right)^{9} - 5271360 \, b^{3} \cosh\left(d x + c\right)^{7} + 4284 \, {\left(105 \, a^{3} + 432 \, a^{2} b + 728 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 280 \, {\left(805 \, a^{3} + 3312 \, a^{2} b + 1880 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 7 \, {\left(2681 \, a^{3} + 7344 \, a^{2} b + 2512 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{13} - 2 \, {\left(5053 \, a^{3} + 4464 \, a^{2} b + 1232 \, b^{3}\right)} \cosh\left(d x + c\right)^{12} + 2 \, {\left(5173168 \, b^{3} \cosh\left(d x + c\right)^{10} - 17131920 \, b^{3} \cosh\left(d x + c\right)^{8} + 18564 \, {\left(105 \, a^{3} + 432 \, a^{2} b + 728 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} - 1820 \, {\left(805 \, a^{3} + 3312 \, a^{2} b + 1880 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 5053 \, a^{3} - 4464 \, a^{2} b - 1232 \, b^{3} + 91 \, {\left(2681 \, a^{3} + 7344 \, a^{2} b + 2512 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{12} + 8 \, {\left(1410864 \, b^{3} \cosh\left(d x + c\right)^{11} - 5710640 \, b^{3} \cosh\left(d x + c\right)^{9} + 7956 \, {\left(105 \, a^{3} + 432 \, a^{2} b + 728 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} - 1092 \, {\left(805 \, a^{3} + 3312 \, a^{2} b + 1880 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 91 \, {\left(2681 \, a^{3} + 7344 \, a^{2} b + 2512 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(5053 \, a^{3} + 4464 \, a^{2} b + 1232 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{11} - 2 \, {\left(5053 \, a^{3} + 4464 \, a^{2} b + 1232 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} + 2 \, {\left(5173168 \, b^{3} \cosh\left(d x + c\right)^{12} - 25126816 \, b^{3} \cosh\left(d x + c\right)^{10} + 43758 \, {\left(105 \, a^{3} + 432 \, a^{2} b + 728 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} - 8008 \, {\left(805 \, a^{3} + 3312 \, a^{2} b + 1880 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 1001 \, {\left(2681 \, a^{3} + 7344 \, a^{2} b + 2512 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 5053 \, a^{3} - 4464 \, a^{2} b - 1232 \, b^{3} - 66 \, {\left(5053 \, a^{3} + 4464 \, a^{2} b + 1232 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{10} + 4 \, {\left(1989680 \, b^{3} \cosh\left(d x + c\right)^{13} - 11421280 \, b^{3} \cosh\left(d x + c\right)^{11} + 24310 \, {\left(105 \, a^{3} + 432 \, a^{2} b + 728 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} - 5720 \, {\left(805 \, a^{3} + 3312 \, a^{2} b + 1880 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 1001 \, {\left(2681 \, a^{3} + 7344 \, a^{2} b + 2512 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 110 \, {\left(5053 \, a^{3} + 4464 \, a^{2} b + 1232 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 5 \, {\left(5053 \, a^{3} + 4464 \, a^{2} b + 1232 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} + 2 \, {\left(2681 \, a^{3} + 7344 \, a^{2} b + 2512 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 2 \, {\left(2558160 \, b^{3} \cosh\left(d x + c\right)^{14} - 17131920 \, b^{3} \cosh\left(d x + c\right)^{12} + 43758 \, {\left(105 \, a^{3} + 432 \, a^{2} b + 728 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} - 12870 \, {\left(805 \, a^{3} + 3312 \, a^{2} b + 1880 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 3003 \, {\left(2681 \, a^{3} + 7344 \, a^{2} b + 2512 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} - 495 \, {\left(5053 \, a^{3} + 4464 \, a^{2} b + 1232 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 2681 \, a^{3} + 7344 \, a^{2} b + 2512 \, b^{3} - 45 \, {\left(5053 \, a^{3} + 4464 \, a^{2} b + 1232 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{8} + 16 \, {\left(170544 \, b^{3} \cosh\left(d x + c\right)^{15} - 1317840 \, b^{3} \cosh\left(d x + c\right)^{13} + 3978 \, {\left(105 \, a^{3} + 432 \, a^{2} b + 728 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} - 1430 \, {\left(805 \, a^{3} + 3312 \, a^{2} b + 1880 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + 429 \, {\left(2681 \, a^{3} + 7344 \, a^{2} b + 2512 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} - 99 \, {\left(5053 \, a^{3} + 4464 \, a^{2} b + 1232 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 15 \, {\left(5053 \, a^{3} + 4464 \, a^{2} b + 1232 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(2681 \, a^{3} + 7344 \, a^{2} b + 2512 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} - 2 \, {\left(805 \, a^{3} + 3312 \, a^{2} b + 1880 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(596904 \, b^{3} \cosh\left(d x + c\right)^{16} - 5271360 \, b^{3} \cosh\left(d x + c\right)^{14} + 18564 \, {\left(105 \, a^{3} + 432 \, a^{2} b + 728 \, b^{3}\right)} \cosh\left(d x + c\right)^{12} - 8008 \, {\left(805 \, a^{3} + 3312 \, a^{2} b + 1880 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} + 3003 \, {\left(2681 \, a^{3} + 7344 \, a^{2} b + 2512 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} - 924 \, {\left(5053 \, a^{3} + 4464 \, a^{2} b + 1232 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} - 210 \, {\left(5053 \, a^{3} + 4464 \, a^{2} b + 1232 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 805 \, a^{3} - 3312 \, a^{2} b - 1880 \, b^{3} + 28 \, {\left(2681 \, a^{3} + 7344 \, a^{2} b + 2512 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(105336 \, b^{3} \cosh\left(d x + c\right)^{17} - 1054272 \, b^{3} \cosh\left(d x + c\right)^{15} + 4284 \, {\left(105 \, a^{3} + 432 \, a^{2} b + 728 \, b^{3}\right)} \cosh\left(d x + c\right)^{13} - 2184 \, {\left(805 \, a^{3} + 3312 \, a^{2} b + 1880 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} + 1001 \, {\left(2681 \, a^{3} + 7344 \, a^{2} b + 2512 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} - 396 \, {\left(5053 \, a^{3} + 4464 \, a^{2} b + 1232 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} - 126 \, {\left(5053 \, a^{3} + 4464 \, a^{2} b + 1232 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 28 \, {\left(2681 \, a^{3} + 7344 \, a^{2} b + 2512 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(805 \, a^{3} + 3312 \, a^{2} b + 1880 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 272 \, b^{3} \cosh\left(d x + c\right)^{2} + 2 \, {\left(105 \, a^{3} + 432 \, a^{2} b + 728 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(58520 \, b^{3} \cosh\left(d x + c\right)^{18} - 658920 \, b^{3} \cosh\left(d x + c\right)^{16} + 3060 \, {\left(105 \, a^{3} + 432 \, a^{2} b + 728 \, b^{3}\right)} \cosh\left(d x + c\right)^{14} - 1820 \, {\left(805 \, a^{3} + 3312 \, a^{2} b + 1880 \, b^{3}\right)} \cosh\left(d x + c\right)^{12} + 1001 \, {\left(2681 \, a^{3} + 7344 \, a^{2} b + 2512 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} - 495 \, {\left(5053 \, a^{3} + 4464 \, a^{2} b + 1232 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} - 210 \, {\left(5053 \, a^{3} + 4464 \, a^{2} b + 1232 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 70 \, {\left(2681 \, a^{3} + 7344 \, a^{2} b + 2512 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 105 \, a^{3} + 432 \, a^{2} b + 728 \, b^{3} - 15 \, {\left(805 \, a^{3} + 3312 \, a^{2} b + 1880 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(3080 \, b^{3} \cosh\left(d x + c\right)^{19} - 38760 \, b^{3} \cosh\left(d x + c\right)^{17} + 204 \, {\left(105 \, a^{3} + 432 \, a^{2} b + 728 \, b^{3}\right)} \cosh\left(d x + c\right)^{15} - 140 \, {\left(805 \, a^{3} + 3312 \, a^{2} b + 1880 \, b^{3}\right)} \cosh\left(d x + c\right)^{13} + 91 \, {\left(2681 \, a^{3} + 7344 \, a^{2} b + 2512 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} - 55 \, {\left(5053 \, a^{3} + 4464 \, a^{2} b + 1232 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} - 30 \, {\left(5053 \, a^{3} + 4464 \, a^{2} b + 1232 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 14 \, {\left(2681 \, a^{3} + 7344 \, a^{2} b + 2512 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 5 \, {\left(805 \, a^{3} + 3312 \, a^{2} b + 1880 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(105 \, a^{3} + 432 \, a^{2} b + 728 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 16 \, b^{3} + 2 \, {\left(1848 \, b^{3} \cosh\left(d x + c\right)^{20} - 25840 \, b^{3} \cosh\left(d x + c\right)^{18} + 153 \, {\left(105 \, a^{3} + 432 \, a^{2} b + 728 \, b^{3}\right)} \cosh\left(d x + c\right)^{16} - 120 \, {\left(805 \, a^{3} + 3312 \, a^{2} b + 1880 \, b^{3}\right)} \cosh\left(d x + c\right)^{14} + 91 \, {\left(2681 \, a^{3} + 7344 \, a^{2} b + 2512 \, b^{3}\right)} \cosh\left(d x + c\right)^{12} - 66 \, {\left(5053 \, a^{3} + 4464 \, a^{2} b + 1232 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} - 45 \, {\left(5053 \, a^{3} + 4464 \, a^{2} b + 1232 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 28 \, {\left(2681 \, a^{3} + 7344 \, a^{2} b + 2512 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} - 15 \, {\left(805 \, a^{3} + 3312 \, a^{2} b + 1880 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 136 \, b^{3} + 6 \, {\left(105 \, a^{3} + 432 \, a^{2} b + 728 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} - 3 \, {\left({\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{19} + 19 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{18} + {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \sinh\left(d x + c\right)^{19} - 8 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{17} - {\left(280 \, a^{3} + 1152 \, a^{2} b + 3072 \, a b^{2} - 171 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{17} + 17 \, {\left(57 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} - 8 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{16} + 28 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{15} + 4 \, {\left(969 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} + 245 \, a^{3} + 1008 \, a^{2} b + 2688 \, a b^{2} - 272 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{15} + 4 \, {\left(2907 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{5} - 1360 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} + 105 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{14} - 56 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{13} + 28 \, {\left(969 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{6} - 680 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} - 70 \, a^{3} - 288 \, a^{2} b - 768 \, a b^{2} + 105 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{13} + 52 \, {\left(969 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{7} - 952 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{5} + 245 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} - 14 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{12} + 70 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{11} + 2 \, {\left(37791 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{8} - 49504 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{6} + 19110 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} + 1225 \, a^{3} + 5040 \, a^{2} b + 13440 \, a b^{2} - 2184 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{11} + 22 \, {\left(4199 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{9} - 7072 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{7} + 3822 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{5} - 728 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} + 35 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{10} - 56 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{9} + 2 \, {\left(46189 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{10} - 97240 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{8} + 70070 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{6} - 20020 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} - 980 \, a^{3} - 4032 \, a^{2} b - 10752 \, a b^{2} + 1925 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{9} + 2 \, {\left(37791 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{11} - 97240 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{9} + 90090 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{7} - 36036 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{5} + 5775 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} - 252 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{8} + 28 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{7} + 4 \, {\left(12597 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{12} - 38896 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{10} + 45045 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{8} - 24024 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{6} + 5775 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} + 245 \, a^{3} + 1008 \, a^{2} b + 2688 \, a b^{2} - 504 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{7} + 28 \, {\left(969 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{13} - 3536 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{11} + 5005 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{9} - 3432 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{7} + 1155 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{5} - 168 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} + 7 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} - 8 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{5} + 4 \, {\left(2907 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{14} - 12376 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{12} + 21021 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{10} - 18018 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{8} + 8085 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{6} - 1764 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} - 70 \, a^{3} - 288 \, a^{2} b - 768 \, a b^{2} + 147 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{5} + 4 \, {\left(969 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{15} - 4760 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{13} + 9555 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{11} - 10010 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{9} + 5775 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{7} - 1764 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{5} + 245 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} - 10 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(969 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{16} - 5440 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{14} + 12740 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{12} - 16016 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{10} + 11550 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{8} - 4704 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{6} + 980 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} + 35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2} - 80 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + {\left(171 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{17} - 1088 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{15} + 2940 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{13} - 4368 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{11} + 3850 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{9} - 2016 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{7} + 588 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{5} - 80 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(19 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{18} - 136 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{16} + 420 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{14} - 728 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{12} + 770 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{10} - 504 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{8} + 196 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{6} - 40 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) + 3 \, {\left({\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{19} + 19 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{18} + {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \sinh\left(d x + c\right)^{19} - 8 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{17} - {\left(280 \, a^{3} + 1152 \, a^{2} b + 3072 \, a b^{2} - 171 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{17} + 17 \, {\left(57 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} - 8 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{16} + 28 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{15} + 4 \, {\left(969 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} + 245 \, a^{3} + 1008 \, a^{2} b + 2688 \, a b^{2} - 272 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{15} + 4 \, {\left(2907 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{5} - 1360 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} + 105 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{14} - 56 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{13} + 28 \, {\left(969 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{6} - 680 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} - 70 \, a^{3} - 288 \, a^{2} b - 768 \, a b^{2} + 105 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{13} + 52 \, {\left(969 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{7} - 952 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{5} + 245 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} - 14 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{12} + 70 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{11} + 2 \, {\left(37791 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{8} - 49504 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{6} + 19110 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} + 1225 \, a^{3} + 5040 \, a^{2} b + 13440 \, a b^{2} - 2184 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{11} + 22 \, {\left(4199 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{9} - 7072 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{7} + 3822 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{5} - 728 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} + 35 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{10} - 56 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{9} + 2 \, {\left(46189 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{10} - 97240 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{8} + 70070 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{6} - 20020 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} - 980 \, a^{3} - 4032 \, a^{2} b - 10752 \, a b^{2} + 1925 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{9} + 2 \, {\left(37791 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{11} - 97240 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{9} + 90090 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{7} - 36036 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{5} + 5775 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} - 252 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{8} + 28 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{7} + 4 \, {\left(12597 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{12} - 38896 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{10} + 45045 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{8} - 24024 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{6} + 5775 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} + 245 \, a^{3} + 1008 \, a^{2} b + 2688 \, a b^{2} - 504 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{7} + 28 \, {\left(969 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{13} - 3536 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{11} + 5005 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{9} - 3432 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{7} + 1155 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{5} - 168 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} + 7 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} - 8 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{5} + 4 \, {\left(2907 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{14} - 12376 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{12} + 21021 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{10} - 18018 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{8} + 8085 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{6} - 1764 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} - 70 \, a^{3} - 288 \, a^{2} b - 768 \, a b^{2} + 147 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{5} + 4 \, {\left(969 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{15} - 4760 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{13} + 9555 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{11} - 10010 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{9} + 5775 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{7} - 1764 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{5} + 245 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} - 10 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(969 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{16} - 5440 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{14} + 12740 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{12} - 16016 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{10} + 11550 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{8} - 4704 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{6} + 980 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} + 35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2} - 80 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + {\left(171 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{17} - 1088 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{15} + 2940 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{13} - 4368 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{11} + 3850 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{9} - 2016 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{7} + 588 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{5} - 80 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(19 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{18} - 136 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{16} + 420 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{14} - 728 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{12} + 770 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{10} - 504 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{8} + 196 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{6} - 40 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(35 \, a^{3} + 144 \, a^{2} b + 384 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) + 4 \, {\left(88 \, b^{3} \cosh\left(d x + c\right)^{21} - 1360 \, b^{3} \cosh\left(d x + c\right)^{19} + 9 \, {\left(105 \, a^{3} + 432 \, a^{2} b + 728 \, b^{3}\right)} \cosh\left(d x + c\right)^{17} - 8 \, {\left(805 \, a^{3} + 3312 \, a^{2} b + 1880 \, b^{3}\right)} \cosh\left(d x + c\right)^{15} + 7 \, {\left(2681 \, a^{3} + 7344 \, a^{2} b + 2512 \, b^{3}\right)} \cosh\left(d x + c\right)^{13} - 6 \, {\left(5053 \, a^{3} + 4464 \, a^{2} b + 1232 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} - 5 \, {\left(5053 \, a^{3} + 4464 \, a^{2} b + 1232 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + 4 \, {\left(2681 \, a^{3} + 7344 \, a^{2} b + 2512 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} - 3 \, {\left(805 \, a^{3} + 3312 \, a^{2} b + 1880 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 136 \, b^{3} \cosh\left(d x + c\right) + 2 \, {\left(105 \, a^{3} + 432 \, a^{2} b + 728 \, b^{3}\right)} \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right)}{384 \, {\left(d \cosh\left(d x + c\right)^{19} + 19 \, d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{18} + d \sinh\left(d x + c\right)^{19} - 8 \, d \cosh\left(d x + c\right)^{17} + {\left(171 \, d \cosh\left(d x + c\right)^{2} - 8 \, d\right)} \sinh\left(d x + c\right)^{17} + 17 \, {\left(57 \, d \cosh\left(d x + c\right)^{3} - 8 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{16} + 28 \, d \cosh\left(d x + c\right)^{15} + 4 \, {\left(969 \, d \cosh\left(d x + c\right)^{4} - 272 \, d \cosh\left(d x + c\right)^{2} + 7 \, d\right)} \sinh\left(d x + c\right)^{15} + 4 \, {\left(2907 \, d \cosh\left(d x + c\right)^{5} - 1360 \, d \cosh\left(d x + c\right)^{3} + 105 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{14} - 56 \, d \cosh\left(d x + c\right)^{13} + 28 \, {\left(969 \, d \cosh\left(d x + c\right)^{6} - 680 \, d \cosh\left(d x + c\right)^{4} + 105 \, d \cosh\left(d x + c\right)^{2} - 2 \, d\right)} \sinh\left(d x + c\right)^{13} + 52 \, {\left(969 \, d \cosh\left(d x + c\right)^{7} - 952 \, d \cosh\left(d x + c\right)^{5} + 245 \, d \cosh\left(d x + c\right)^{3} - 14 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{12} + 70 \, d \cosh\left(d x + c\right)^{11} + 2 \, {\left(37791 \, d \cosh\left(d x + c\right)^{8} - 49504 \, d \cosh\left(d x + c\right)^{6} + 19110 \, d \cosh\left(d x + c\right)^{4} - 2184 \, d \cosh\left(d x + c\right)^{2} + 35 \, d\right)} \sinh\left(d x + c\right)^{11} + 22 \, {\left(4199 \, d \cosh\left(d x + c\right)^{9} - 7072 \, d \cosh\left(d x + c\right)^{7} + 3822 \, d \cosh\left(d x + c\right)^{5} - 728 \, d \cosh\left(d x + c\right)^{3} + 35 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{10} - 56 \, d \cosh\left(d x + c\right)^{9} + 2 \, {\left(46189 \, d \cosh\left(d x + c\right)^{10} - 97240 \, d \cosh\left(d x + c\right)^{8} + 70070 \, d \cosh\left(d x + c\right)^{6} - 20020 \, d \cosh\left(d x + c\right)^{4} + 1925 \, d \cosh\left(d x + c\right)^{2} - 28 \, d\right)} \sinh\left(d x + c\right)^{9} + 2 \, {\left(37791 \, d \cosh\left(d x + c\right)^{11} - 97240 \, d \cosh\left(d x + c\right)^{9} + 90090 \, d \cosh\left(d x + c\right)^{7} - 36036 \, d \cosh\left(d x + c\right)^{5} + 5775 \, d \cosh\left(d x + c\right)^{3} - 252 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{8} + 28 \, d \cosh\left(d x + c\right)^{7} + 4 \, {\left(12597 \, d \cosh\left(d x + c\right)^{12} - 38896 \, d \cosh\left(d x + c\right)^{10} + 45045 \, d \cosh\left(d x + c\right)^{8} - 24024 \, d \cosh\left(d x + c\right)^{6} + 5775 \, d \cosh\left(d x + c\right)^{4} - 504 \, d \cosh\left(d x + c\right)^{2} + 7 \, d\right)} \sinh\left(d x + c\right)^{7} + 28 \, {\left(969 \, d \cosh\left(d x + c\right)^{13} - 3536 \, d \cosh\left(d x + c\right)^{11} + 5005 \, d \cosh\left(d x + c\right)^{9} - 3432 \, d \cosh\left(d x + c\right)^{7} + 1155 \, d \cosh\left(d x + c\right)^{5} - 168 \, d \cosh\left(d x + c\right)^{3} + 7 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} - 8 \, d \cosh\left(d x + c\right)^{5} + 4 \, {\left(2907 \, d \cosh\left(d x + c\right)^{14} - 12376 \, d \cosh\left(d x + c\right)^{12} + 21021 \, d \cosh\left(d x + c\right)^{10} - 18018 \, d \cosh\left(d x + c\right)^{8} + 8085 \, d \cosh\left(d x + c\right)^{6} - 1764 \, d \cosh\left(d x + c\right)^{4} + 147 \, d \cosh\left(d x + c\right)^{2} - 2 \, d\right)} \sinh\left(d x + c\right)^{5} + 4 \, {\left(969 \, d \cosh\left(d x + c\right)^{15} - 4760 \, d \cosh\left(d x + c\right)^{13} + 9555 \, d \cosh\left(d x + c\right)^{11} - 10010 \, d \cosh\left(d x + c\right)^{9} + 5775 \, d \cosh\left(d x + c\right)^{7} - 1764 \, d \cosh\left(d x + c\right)^{5} + 245 \, d \cosh\left(d x + c\right)^{3} - 10 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + d \cosh\left(d x + c\right)^{3} + {\left(969 \, d \cosh\left(d x + c\right)^{16} - 5440 \, d \cosh\left(d x + c\right)^{14} + 12740 \, d \cosh\left(d x + c\right)^{12} - 16016 \, d \cosh\left(d x + c\right)^{10} + 11550 \, d \cosh\left(d x + c\right)^{8} - 4704 \, d \cosh\left(d x + c\right)^{6} + 980 \, d \cosh\left(d x + c\right)^{4} - 80 \, d \cosh\left(d x + c\right)^{2} + d\right)} \sinh\left(d x + c\right)^{3} + {\left(171 \, d \cosh\left(d x + c\right)^{17} - 1088 \, d \cosh\left(d x + c\right)^{15} + 2940 \, d \cosh\left(d x + c\right)^{13} - 4368 \, d \cosh\left(d x + c\right)^{11} + 3850 \, d \cosh\left(d x + c\right)^{9} - 2016 \, d \cosh\left(d x + c\right)^{7} + 588 \, d \cosh\left(d x + c\right)^{5} - 80 \, d \cosh\left(d x + c\right)^{3} + 3 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(19 \, d \cosh\left(d x + c\right)^{18} - 136 \, d \cosh\left(d x + c\right)^{16} + 420 \, d \cosh\left(d x + c\right)^{14} - 728 \, d \cosh\left(d x + c\right)^{12} + 770 \, d \cosh\left(d x + c\right)^{10} - 504 \, d \cosh\left(d x + c\right)^{8} + 196 \, d \cosh\left(d x + c\right)^{6} - 40 \, d \cosh\left(d x + c\right)^{4} + 3 \, d \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"1/384*(16*b^3*cosh(d*x + c)^22 + 352*b^3*cosh(d*x + c)*sinh(d*x + c)^21 + 16*b^3*sinh(d*x + c)^22 - 272*b^3*cosh(d*x + c)^20 + 16*(231*b^3*cosh(d*x + c)^2 - 17*b^3)*sinh(d*x + c)^20 + 320*(77*b^3*cosh(d*x + c)^3 - 17*b^3*cosh(d*x + c))*sinh(d*x + c)^19 + 2*(105*a^3 + 432*a^2*b + 728*b^3)*cosh(d*x + c)^18 + 2*(58520*b^3*cosh(d*x + c)^4 - 25840*b^3*cosh(d*x + c)^2 + 105*a^3 + 432*a^2*b + 728*b^3)*sinh(d*x + c)^18 + 12*(35112*b^3*cosh(d*x + c)^5 - 25840*b^3*cosh(d*x + c)^3 + 3*(105*a^3 + 432*a^2*b + 728*b^3)*cosh(d*x + c))*sinh(d*x + c)^17 - 2*(805*a^3 + 3312*a^2*b + 1880*b^3)*cosh(d*x + c)^16 + 2*(596904*b^3*cosh(d*x + c)^6 - 658920*b^3*cosh(d*x + c)^4 - 805*a^3 - 3312*a^2*b - 1880*b^3 + 153*(105*a^3 + 432*a^2*b + 728*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^16 + 32*(85272*b^3*cosh(d*x + c)^7 - 131784*b^3*cosh(d*x + c)^5 + 51*(105*a^3 + 432*a^2*b + 728*b^3)*cosh(d*x + c)^3 - (805*a^3 + 3312*a^2*b + 1880*b^3)*cosh(d*x + c))*sinh(d*x + c)^15 + 2*(2681*a^3 + 7344*a^2*b + 2512*b^3)*cosh(d*x + c)^14 + 2*(2558160*b^3*cosh(d*x + c)^8 - 5271360*b^3*cosh(d*x + c)^6 + 3060*(105*a^3 + 432*a^2*b + 728*b^3)*cosh(d*x + c)^4 + 2681*a^3 + 7344*a^2*b + 2512*b^3 - 120*(805*a^3 + 3312*a^2*b + 1880*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^14 + 4*(1989680*b^3*cosh(d*x + c)^9 - 5271360*b^3*cosh(d*x + c)^7 + 4284*(105*a^3 + 432*a^2*b + 728*b^3)*cosh(d*x + c)^5 - 280*(805*a^3 + 3312*a^2*b + 1880*b^3)*cosh(d*x + c)^3 + 7*(2681*a^3 + 7344*a^2*b + 2512*b^3)*cosh(d*x + c))*sinh(d*x + c)^13 - 2*(5053*a^3 + 4464*a^2*b + 1232*b^3)*cosh(d*x + c)^12 + 2*(5173168*b^3*cosh(d*x + c)^10 - 17131920*b^3*cosh(d*x + c)^8 + 18564*(105*a^3 + 432*a^2*b + 728*b^3)*cosh(d*x + c)^6 - 1820*(805*a^3 + 3312*a^2*b + 1880*b^3)*cosh(d*x + c)^4 - 5053*a^3 - 4464*a^2*b - 1232*b^3 + 91*(2681*a^3 + 7344*a^2*b + 2512*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^12 + 8*(1410864*b^3*cosh(d*x + c)^11 - 5710640*b^3*cosh(d*x + c)^9 + 7956*(105*a^3 + 432*a^2*b + 728*b^3)*cosh(d*x + c)^7 - 1092*(805*a^3 + 3312*a^2*b + 1880*b^3)*cosh(d*x + c)^5 + 91*(2681*a^3 + 7344*a^2*b + 2512*b^3)*cosh(d*x + c)^3 - 3*(5053*a^3 + 4464*a^2*b + 1232*b^3)*cosh(d*x + c))*sinh(d*x + c)^11 - 2*(5053*a^3 + 4464*a^2*b + 1232*b^3)*cosh(d*x + c)^10 + 2*(5173168*b^3*cosh(d*x + c)^12 - 25126816*b^3*cosh(d*x + c)^10 + 43758*(105*a^3 + 432*a^2*b + 728*b^3)*cosh(d*x + c)^8 - 8008*(805*a^3 + 3312*a^2*b + 1880*b^3)*cosh(d*x + c)^6 + 1001*(2681*a^3 + 7344*a^2*b + 2512*b^3)*cosh(d*x + c)^4 - 5053*a^3 - 4464*a^2*b - 1232*b^3 - 66*(5053*a^3 + 4464*a^2*b + 1232*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^10 + 4*(1989680*b^3*cosh(d*x + c)^13 - 11421280*b^3*cosh(d*x + c)^11 + 24310*(105*a^3 + 432*a^2*b + 728*b^3)*cosh(d*x + c)^9 - 5720*(805*a^3 + 3312*a^2*b + 1880*b^3)*cosh(d*x + c)^7 + 1001*(2681*a^3 + 7344*a^2*b + 2512*b^3)*cosh(d*x + c)^5 - 110*(5053*a^3 + 4464*a^2*b + 1232*b^3)*cosh(d*x + c)^3 - 5*(5053*a^3 + 4464*a^2*b + 1232*b^3)*cosh(d*x + c))*sinh(d*x + c)^9 + 2*(2681*a^3 + 7344*a^2*b + 2512*b^3)*cosh(d*x + c)^8 + 2*(2558160*b^3*cosh(d*x + c)^14 - 17131920*b^3*cosh(d*x + c)^12 + 43758*(105*a^3 + 432*a^2*b + 728*b^3)*cosh(d*x + c)^10 - 12870*(805*a^3 + 3312*a^2*b + 1880*b^3)*cosh(d*x + c)^8 + 3003*(2681*a^3 + 7344*a^2*b + 2512*b^3)*cosh(d*x + c)^6 - 495*(5053*a^3 + 4464*a^2*b + 1232*b^3)*cosh(d*x + c)^4 + 2681*a^3 + 7344*a^2*b + 2512*b^3 - 45*(5053*a^3 + 4464*a^2*b + 1232*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 16*(170544*b^3*cosh(d*x + c)^15 - 1317840*b^3*cosh(d*x + c)^13 + 3978*(105*a^3 + 432*a^2*b + 728*b^3)*cosh(d*x + c)^11 - 1430*(805*a^3 + 3312*a^2*b + 1880*b^3)*cosh(d*x + c)^9 + 429*(2681*a^3 + 7344*a^2*b + 2512*b^3)*cosh(d*x + c)^7 - 99*(5053*a^3 + 4464*a^2*b + 1232*b^3)*cosh(d*x + c)^5 - 15*(5053*a^3 + 4464*a^2*b + 1232*b^3)*cosh(d*x + c)^3 + (2681*a^3 + 7344*a^2*b + 2512*b^3)*cosh(d*x + c))*sinh(d*x + c)^7 - 2*(805*a^3 + 3312*a^2*b + 1880*b^3)*cosh(d*x + c)^6 + 2*(596904*b^3*cosh(d*x + c)^16 - 5271360*b^3*cosh(d*x + c)^14 + 18564*(105*a^3 + 432*a^2*b + 728*b^3)*cosh(d*x + c)^12 - 8008*(805*a^3 + 3312*a^2*b + 1880*b^3)*cosh(d*x + c)^10 + 3003*(2681*a^3 + 7344*a^2*b + 2512*b^3)*cosh(d*x + c)^8 - 924*(5053*a^3 + 4464*a^2*b + 1232*b^3)*cosh(d*x + c)^6 - 210*(5053*a^3 + 4464*a^2*b + 1232*b^3)*cosh(d*x + c)^4 - 805*a^3 - 3312*a^2*b - 1880*b^3 + 28*(2681*a^3 + 7344*a^2*b + 2512*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 4*(105336*b^3*cosh(d*x + c)^17 - 1054272*b^3*cosh(d*x + c)^15 + 4284*(105*a^3 + 432*a^2*b + 728*b^3)*cosh(d*x + c)^13 - 2184*(805*a^3 + 3312*a^2*b + 1880*b^3)*cosh(d*x + c)^11 + 1001*(2681*a^3 + 7344*a^2*b + 2512*b^3)*cosh(d*x + c)^9 - 396*(5053*a^3 + 4464*a^2*b + 1232*b^3)*cosh(d*x + c)^7 - 126*(5053*a^3 + 4464*a^2*b + 1232*b^3)*cosh(d*x + c)^5 + 28*(2681*a^3 + 7344*a^2*b + 2512*b^3)*cosh(d*x + c)^3 - 3*(805*a^3 + 3312*a^2*b + 1880*b^3)*cosh(d*x + c))*sinh(d*x + c)^5 - 272*b^3*cosh(d*x + c)^2 + 2*(105*a^3 + 432*a^2*b + 728*b^3)*cosh(d*x + c)^4 + 2*(58520*b^3*cosh(d*x + c)^18 - 658920*b^3*cosh(d*x + c)^16 + 3060*(105*a^3 + 432*a^2*b + 728*b^3)*cosh(d*x + c)^14 - 1820*(805*a^3 + 3312*a^2*b + 1880*b^3)*cosh(d*x + c)^12 + 1001*(2681*a^3 + 7344*a^2*b + 2512*b^3)*cosh(d*x + c)^10 - 495*(5053*a^3 + 4464*a^2*b + 1232*b^3)*cosh(d*x + c)^8 - 210*(5053*a^3 + 4464*a^2*b + 1232*b^3)*cosh(d*x + c)^6 + 70*(2681*a^3 + 7344*a^2*b + 2512*b^3)*cosh(d*x + c)^4 + 105*a^3 + 432*a^2*b + 728*b^3 - 15*(805*a^3 + 3312*a^2*b + 1880*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(3080*b^3*cosh(d*x + c)^19 - 38760*b^3*cosh(d*x + c)^17 + 204*(105*a^3 + 432*a^2*b + 728*b^3)*cosh(d*x + c)^15 - 140*(805*a^3 + 3312*a^2*b + 1880*b^3)*cosh(d*x + c)^13 + 91*(2681*a^3 + 7344*a^2*b + 2512*b^3)*cosh(d*x + c)^11 - 55*(5053*a^3 + 4464*a^2*b + 1232*b^3)*cosh(d*x + c)^9 - 30*(5053*a^3 + 4464*a^2*b + 1232*b^3)*cosh(d*x + c)^7 + 14*(2681*a^3 + 7344*a^2*b + 2512*b^3)*cosh(d*x + c)^5 - 5*(805*a^3 + 3312*a^2*b + 1880*b^3)*cosh(d*x + c)^3 + (105*a^3 + 432*a^2*b + 728*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 + 16*b^3 + 2*(1848*b^3*cosh(d*x + c)^20 - 25840*b^3*cosh(d*x + c)^18 + 153*(105*a^3 + 432*a^2*b + 728*b^3)*cosh(d*x + c)^16 - 120*(805*a^3 + 3312*a^2*b + 1880*b^3)*cosh(d*x + c)^14 + 91*(2681*a^3 + 7344*a^2*b + 2512*b^3)*cosh(d*x + c)^12 - 66*(5053*a^3 + 4464*a^2*b + 1232*b^3)*cosh(d*x + c)^10 - 45*(5053*a^3 + 4464*a^2*b + 1232*b^3)*cosh(d*x + c)^8 + 28*(2681*a^3 + 7344*a^2*b + 2512*b^3)*cosh(d*x + c)^6 - 15*(805*a^3 + 3312*a^2*b + 1880*b^3)*cosh(d*x + c)^4 - 136*b^3 + 6*(105*a^3 + 432*a^2*b + 728*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - 3*((35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^19 + 19*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)*sinh(d*x + c)^18 + (35*a^3 + 144*a^2*b + 384*a*b^2)*sinh(d*x + c)^19 - 8*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^17 - (280*a^3 + 1152*a^2*b + 3072*a*b^2 - 171*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^17 + 17*(57*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^3 - 8*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^16 + 28*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^15 + 4*(969*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^4 + 245*a^3 + 1008*a^2*b + 2688*a*b^2 - 272*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^15 + 4*(2907*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^5 - 1360*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^3 + 105*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^14 - 56*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^13 + 28*(969*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^6 - 680*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^4 - 70*a^3 - 288*a^2*b - 768*a*b^2 + 105*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^13 + 52*(969*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^7 - 952*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^5 + 245*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^3 - 14*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^12 + 70*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^11 + 2*(37791*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^8 - 49504*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^6 + 19110*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^4 + 1225*a^3 + 5040*a^2*b + 13440*a*b^2 - 2184*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^11 + 22*(4199*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^9 - 7072*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^7 + 3822*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^5 - 728*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^3 + 35*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^10 - 56*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^9 + 2*(46189*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^10 - 97240*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^8 + 70070*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^6 - 20020*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^4 - 980*a^3 - 4032*a^2*b - 10752*a*b^2 + 1925*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^9 + 2*(37791*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^11 - 97240*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^9 + 90090*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^7 - 36036*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^5 + 5775*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^3 - 252*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^8 + 28*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^7 + 4*(12597*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^12 - 38896*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^10 + 45045*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^8 - 24024*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^6 + 5775*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^4 + 245*a^3 + 1008*a^2*b + 2688*a*b^2 - 504*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^7 + 28*(969*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^13 - 3536*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^11 + 5005*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^9 - 3432*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^7 + 1155*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^5 - 168*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^3 + 7*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^6 - 8*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^5 + 4*(2907*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^14 - 12376*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^12 + 21021*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^10 - 18018*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^8 + 8085*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^6 - 1764*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^4 - 70*a^3 - 288*a^2*b - 768*a*b^2 + 147*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 4*(969*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^15 - 4760*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^13 + 9555*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^11 - 10010*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^9 + 5775*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^7 - 1764*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^5 + 245*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^3 - 10*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^4 + (35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^3 + (969*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^16 - 5440*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^14 + 12740*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^12 - 16016*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^10 + 11550*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^8 - 4704*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^6 + 980*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^4 + 35*a^3 + 144*a^2*b + 384*a*b^2 - 80*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + (171*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^17 - 1088*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^15 + 2940*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^13 - 4368*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^11 + 3850*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^9 - 2016*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^7 + 588*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^5 - 80*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^3 + 3*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^2 + (19*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^18 - 136*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^16 + 420*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^14 - 728*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^12 + 770*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^10 - 504*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^8 + 196*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^6 - 40*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^4 + 3*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) + 1) + 3*((35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^19 + 19*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)*sinh(d*x + c)^18 + (35*a^3 + 144*a^2*b + 384*a*b^2)*sinh(d*x + c)^19 - 8*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^17 - (280*a^3 + 1152*a^2*b + 3072*a*b^2 - 171*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^17 + 17*(57*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^3 - 8*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^16 + 28*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^15 + 4*(969*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^4 + 245*a^3 + 1008*a^2*b + 2688*a*b^2 - 272*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^15 + 4*(2907*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^5 - 1360*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^3 + 105*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^14 - 56*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^13 + 28*(969*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^6 - 680*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^4 - 70*a^3 - 288*a^2*b - 768*a*b^2 + 105*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^13 + 52*(969*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^7 - 952*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^5 + 245*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^3 - 14*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^12 + 70*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^11 + 2*(37791*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^8 - 49504*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^6 + 19110*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^4 + 1225*a^3 + 5040*a^2*b + 13440*a*b^2 - 2184*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^11 + 22*(4199*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^9 - 7072*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^7 + 3822*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^5 - 728*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^3 + 35*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^10 - 56*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^9 + 2*(46189*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^10 - 97240*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^8 + 70070*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^6 - 20020*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^4 - 980*a^3 - 4032*a^2*b - 10752*a*b^2 + 1925*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^9 + 2*(37791*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^11 - 97240*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^9 + 90090*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^7 - 36036*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^5 + 5775*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^3 - 252*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^8 + 28*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^7 + 4*(12597*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^12 - 38896*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^10 + 45045*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^8 - 24024*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^6 + 5775*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^4 + 245*a^3 + 1008*a^2*b + 2688*a*b^2 - 504*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^7 + 28*(969*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^13 - 3536*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^11 + 5005*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^9 - 3432*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^7 + 1155*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^5 - 168*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^3 + 7*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^6 - 8*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^5 + 4*(2907*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^14 - 12376*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^12 + 21021*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^10 - 18018*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^8 + 8085*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^6 - 1764*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^4 - 70*a^3 - 288*a^2*b - 768*a*b^2 + 147*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 4*(969*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^15 - 4760*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^13 + 9555*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^11 - 10010*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^9 + 5775*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^7 - 1764*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^5 + 245*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^3 - 10*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^4 + (35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^3 + (969*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^16 - 5440*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^14 + 12740*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^12 - 16016*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^10 + 11550*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^8 - 4704*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^6 + 980*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^4 + 35*a^3 + 144*a^2*b + 384*a*b^2 - 80*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + (171*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^17 - 1088*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^15 + 2940*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^13 - 4368*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^11 + 3850*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^9 - 2016*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^7 + 588*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^5 - 80*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^3 + 3*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^2 + (19*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^18 - 136*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^16 + 420*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^14 - 728*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^12 + 770*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^10 - 504*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^8 + 196*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^6 - 40*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^4 + 3*(35*a^3 + 144*a^2*b + 384*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) - 1) + 4*(88*b^3*cosh(d*x + c)^21 - 1360*b^3*cosh(d*x + c)^19 + 9*(105*a^3 + 432*a^2*b + 728*b^3)*cosh(d*x + c)^17 - 8*(805*a^3 + 3312*a^2*b + 1880*b^3)*cosh(d*x + c)^15 + 7*(2681*a^3 + 7344*a^2*b + 2512*b^3)*cosh(d*x + c)^13 - 6*(5053*a^3 + 4464*a^2*b + 1232*b^3)*cosh(d*x + c)^11 - 5*(5053*a^3 + 4464*a^2*b + 1232*b^3)*cosh(d*x + c)^9 + 4*(2681*a^3 + 7344*a^2*b + 2512*b^3)*cosh(d*x + c)^7 - 3*(805*a^3 + 3312*a^2*b + 1880*b^3)*cosh(d*x + c)^5 - 136*b^3*cosh(d*x + c) + 2*(105*a^3 + 432*a^2*b + 728*b^3)*cosh(d*x + c)^3)*sinh(d*x + c))/(d*cosh(d*x + c)^19 + 19*d*cosh(d*x + c)*sinh(d*x + c)^18 + d*sinh(d*x + c)^19 - 8*d*cosh(d*x + c)^17 + (171*d*cosh(d*x + c)^2 - 8*d)*sinh(d*x + c)^17 + 17*(57*d*cosh(d*x + c)^3 - 8*d*cosh(d*x + c))*sinh(d*x + c)^16 + 28*d*cosh(d*x + c)^15 + 4*(969*d*cosh(d*x + c)^4 - 272*d*cosh(d*x + c)^2 + 7*d)*sinh(d*x + c)^15 + 4*(2907*d*cosh(d*x + c)^5 - 1360*d*cosh(d*x + c)^3 + 105*d*cosh(d*x + c))*sinh(d*x + c)^14 - 56*d*cosh(d*x + c)^13 + 28*(969*d*cosh(d*x + c)^6 - 680*d*cosh(d*x + c)^4 + 105*d*cosh(d*x + c)^2 - 2*d)*sinh(d*x + c)^13 + 52*(969*d*cosh(d*x + c)^7 - 952*d*cosh(d*x + c)^5 + 245*d*cosh(d*x + c)^3 - 14*d*cosh(d*x + c))*sinh(d*x + c)^12 + 70*d*cosh(d*x + c)^11 + 2*(37791*d*cosh(d*x + c)^8 - 49504*d*cosh(d*x + c)^6 + 19110*d*cosh(d*x + c)^4 - 2184*d*cosh(d*x + c)^2 + 35*d)*sinh(d*x + c)^11 + 22*(4199*d*cosh(d*x + c)^9 - 7072*d*cosh(d*x + c)^7 + 3822*d*cosh(d*x + c)^5 - 728*d*cosh(d*x + c)^3 + 35*d*cosh(d*x + c))*sinh(d*x + c)^10 - 56*d*cosh(d*x + c)^9 + 2*(46189*d*cosh(d*x + c)^10 - 97240*d*cosh(d*x + c)^8 + 70070*d*cosh(d*x + c)^6 - 20020*d*cosh(d*x + c)^4 + 1925*d*cosh(d*x + c)^2 - 28*d)*sinh(d*x + c)^9 + 2*(37791*d*cosh(d*x + c)^11 - 97240*d*cosh(d*x + c)^9 + 90090*d*cosh(d*x + c)^7 - 36036*d*cosh(d*x + c)^5 + 5775*d*cosh(d*x + c)^3 - 252*d*cosh(d*x + c))*sinh(d*x + c)^8 + 28*d*cosh(d*x + c)^7 + 4*(12597*d*cosh(d*x + c)^12 - 38896*d*cosh(d*x + c)^10 + 45045*d*cosh(d*x + c)^8 - 24024*d*cosh(d*x + c)^6 + 5775*d*cosh(d*x + c)^4 - 504*d*cosh(d*x + c)^2 + 7*d)*sinh(d*x + c)^7 + 28*(969*d*cosh(d*x + c)^13 - 3536*d*cosh(d*x + c)^11 + 5005*d*cosh(d*x + c)^9 - 3432*d*cosh(d*x + c)^7 + 1155*d*cosh(d*x + c)^5 - 168*d*cosh(d*x + c)^3 + 7*d*cosh(d*x + c))*sinh(d*x + c)^6 - 8*d*cosh(d*x + c)^5 + 4*(2907*d*cosh(d*x + c)^14 - 12376*d*cosh(d*x + c)^12 + 21021*d*cosh(d*x + c)^10 - 18018*d*cosh(d*x + c)^8 + 8085*d*cosh(d*x + c)^6 - 1764*d*cosh(d*x + c)^4 + 147*d*cosh(d*x + c)^2 - 2*d)*sinh(d*x + c)^5 + 4*(969*d*cosh(d*x + c)^15 - 4760*d*cosh(d*x + c)^13 + 9555*d*cosh(d*x + c)^11 - 10010*d*cosh(d*x + c)^9 + 5775*d*cosh(d*x + c)^7 - 1764*d*cosh(d*x + c)^5 + 245*d*cosh(d*x + c)^3 - 10*d*cosh(d*x + c))*sinh(d*x + c)^4 + d*cosh(d*x + c)^3 + (969*d*cosh(d*x + c)^16 - 5440*d*cosh(d*x + c)^14 + 12740*d*cosh(d*x + c)^12 - 16016*d*cosh(d*x + c)^10 + 11550*d*cosh(d*x + c)^8 - 4704*d*cosh(d*x + c)^6 + 980*d*cosh(d*x + c)^4 - 80*d*cosh(d*x + c)^2 + d)*sinh(d*x + c)^3 + (171*d*cosh(d*x + c)^17 - 1088*d*cosh(d*x + c)^15 + 2940*d*cosh(d*x + c)^13 - 4368*d*cosh(d*x + c)^11 + 3850*d*cosh(d*x + c)^9 - 2016*d*cosh(d*x + c)^7 + 588*d*cosh(d*x + c)^5 - 80*d*cosh(d*x + c)^3 + 3*d*cosh(d*x + c))*sinh(d*x + c)^2 + (19*d*cosh(d*x + c)^18 - 136*d*cosh(d*x + c)^16 + 420*d*cosh(d*x + c)^14 - 728*d*cosh(d*x + c)^12 + 770*d*cosh(d*x + c)^10 - 504*d*cosh(d*x + c)^8 + 196*d*cosh(d*x + c)^6 - 40*d*cosh(d*x + c)^4 + 3*d*cosh(d*x + c)^2)*sinh(d*x + c))","B",0
215,-1,0,0,0.000000," ","integrate(csch(d*x+c)^11*(a+b*sinh(d*x+c)^4)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
216,-1,0,0,0.000000," ","integrate(csch(d*x+c)^13*(a+b*sinh(d*x+c)^4)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
217,1,627,0,0.735316," ","integrate(sinh(d*x+c)^2*(a+b*sinh(d*x+c)^4)^3,x, algorithm=""fricas"")","\frac{105 \, b^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{13} + 210 \, {\left(13 \, b^{3} \cosh\left(d x + c\right)^{3} - 7 \, b^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{11} + 35 \, {\left(429 \, b^{3} \cosh\left(d x + c\right)^{5} - 770 \, b^{3} \cosh\left(d x + c\right)^{3} + 3 \, {\left(48 \, a b^{2} + 91 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} + 60 \, {\left(429 \, b^{3} \cosh\left(d x + c\right)^{7} - 1617 \, b^{3} \cosh\left(d x + c\right)^{5} + 21 \, {\left(48 \, a b^{2} + 91 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 7 \, {\left(120 \, a b^{2} + 91 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 21 \, {\left(715 \, b^{3} \cosh\left(d x + c\right)^{9} - 4620 \, b^{3} \cosh\left(d x + c\right)^{7} + 126 \, {\left(48 \, a b^{2} + 91 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 140 \, {\left(120 \, a b^{2} + 91 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 5 \, {\left(768 \, a^{2} b + 2160 \, a b^{2} + 1001 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 70 \, {\left(39 \, b^{3} \cosh\left(d x + c\right)^{11} - 385 \, b^{3} \cosh\left(d x + c\right)^{9} + 18 \, {\left(48 \, a b^{2} + 91 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} - 42 \, {\left(120 \, a b^{2} + 91 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(768 \, a^{2} b + 2160 \, a b^{2} + 1001 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(2304 \, a^{2} b + 2880 \, a b^{2} + 1001 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 420 \, {\left(1024 \, a^{3} + 1920 \, a^{2} b + 1512 \, a b^{2} + 429 \, b^{3}\right)} d x + 105 \, {\left(b^{3} \cosh\left(d x + c\right)^{13} - 14 \, b^{3} \cosh\left(d x + c\right)^{11} + {\left(48 \, a b^{2} + 91 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} - 4 \, {\left(120 \, a b^{2} + 91 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + {\left(768 \, a^{2} b + 2160 \, a b^{2} + 1001 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 2 \, {\left(2304 \, a^{2} b + 2880 \, a b^{2} + 1001 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(4096 \, a^{3} + 11520 \, a^{2} b + 10080 \, a b^{2} + 3003 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{860160 \, d}"," ",0,"1/860160*(105*b^3*cosh(d*x + c)*sinh(d*x + c)^13 + 210*(13*b^3*cosh(d*x + c)^3 - 7*b^3*cosh(d*x + c))*sinh(d*x + c)^11 + 35*(429*b^3*cosh(d*x + c)^5 - 770*b^3*cosh(d*x + c)^3 + 3*(48*a*b^2 + 91*b^3)*cosh(d*x + c))*sinh(d*x + c)^9 + 60*(429*b^3*cosh(d*x + c)^7 - 1617*b^3*cosh(d*x + c)^5 + 21*(48*a*b^2 + 91*b^3)*cosh(d*x + c)^3 - 7*(120*a*b^2 + 91*b^3)*cosh(d*x + c))*sinh(d*x + c)^7 + 21*(715*b^3*cosh(d*x + c)^9 - 4620*b^3*cosh(d*x + c)^7 + 126*(48*a*b^2 + 91*b^3)*cosh(d*x + c)^5 - 140*(120*a*b^2 + 91*b^3)*cosh(d*x + c)^3 + 5*(768*a^2*b + 2160*a*b^2 + 1001*b^3)*cosh(d*x + c))*sinh(d*x + c)^5 + 70*(39*b^3*cosh(d*x + c)^11 - 385*b^3*cosh(d*x + c)^9 + 18*(48*a*b^2 + 91*b^3)*cosh(d*x + c)^7 - 42*(120*a*b^2 + 91*b^3)*cosh(d*x + c)^5 + 5*(768*a^2*b + 2160*a*b^2 + 1001*b^3)*cosh(d*x + c)^3 - 3*(2304*a^2*b + 2880*a*b^2 + 1001*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 - 420*(1024*a^3 + 1920*a^2*b + 1512*a*b^2 + 429*b^3)*d*x + 105*(b^3*cosh(d*x + c)^13 - 14*b^3*cosh(d*x + c)^11 + (48*a*b^2 + 91*b^3)*cosh(d*x + c)^9 - 4*(120*a*b^2 + 91*b^3)*cosh(d*x + c)^7 + (768*a^2*b + 2160*a*b^2 + 1001*b^3)*cosh(d*x + c)^5 - 2*(2304*a^2*b + 2880*a*b^2 + 1001*b^3)*cosh(d*x + c)^3 + (4096*a^3 + 11520*a^2*b + 10080*a*b^2 + 3003*b^3)*cosh(d*x + c))*sinh(d*x + c))/d","B",0
218,1,461,0,1.054156," ","integrate((a+b*sinh(d*x+c)^4)^3,x, algorithm=""fricas"")","\frac{15 \, b^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{11} + 5 \, {\left(55 \, b^{3} \cosh\left(d x + c\right)^{3} - 36 \, b^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} + 90 \, {\left(11 \, b^{3} \cosh\left(d x + c\right)^{5} - 24 \, b^{3} \cosh\left(d x + c\right)^{3} + {\left(8 \, a b^{2} + 11 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 6 \, {\left(165 \, b^{3} \cosh\left(d x + c\right)^{7} - 756 \, b^{3} \cosh\left(d x + c\right)^{5} + 105 \, {\left(8 \, a b^{2} + 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 10 \, {\left(96 \, a b^{2} + 55 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 5 \, {\left(55 \, b^{3} \cosh\left(d x + c\right)^{9} - 432 \, b^{3} \cosh\left(d x + c\right)^{7} + 126 \, {\left(8 \, a b^{2} + 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 40 \, {\left(96 \, a b^{2} + 55 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 9 \, {\left(256 \, a^{2} b + 448 \, a b^{2} + 165 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 30 \, {\left(1024 \, a^{3} + 1152 \, a^{2} b + 840 \, a b^{2} + 231 \, b^{3}\right)} d x + 15 \, {\left(b^{3} \cosh\left(d x + c\right)^{11} - 12 \, b^{3} \cosh\left(d x + c\right)^{9} + 6 \, {\left(8 \, a b^{2} + 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} - 4 \, {\left(96 \, a b^{2} + 55 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 3 \, {\left(256 \, a^{2} b + 448 \, a b^{2} + 165 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 24 \, {\left(128 \, a^{2} b + 112 \, a b^{2} + 33 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{30720 \, d}"," ",0,"1/30720*(15*b^3*cosh(d*x + c)*sinh(d*x + c)^11 + 5*(55*b^3*cosh(d*x + c)^3 - 36*b^3*cosh(d*x + c))*sinh(d*x + c)^9 + 90*(11*b^3*cosh(d*x + c)^5 - 24*b^3*cosh(d*x + c)^3 + (8*a*b^2 + 11*b^3)*cosh(d*x + c))*sinh(d*x + c)^7 + 6*(165*b^3*cosh(d*x + c)^7 - 756*b^3*cosh(d*x + c)^5 + 105*(8*a*b^2 + 11*b^3)*cosh(d*x + c)^3 - 10*(96*a*b^2 + 55*b^3)*cosh(d*x + c))*sinh(d*x + c)^5 + 5*(55*b^3*cosh(d*x + c)^9 - 432*b^3*cosh(d*x + c)^7 + 126*(8*a*b^2 + 11*b^3)*cosh(d*x + c)^5 - 40*(96*a*b^2 + 55*b^3)*cosh(d*x + c)^3 + 9*(256*a^2*b + 448*a*b^2 + 165*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 + 30*(1024*a^3 + 1152*a^2*b + 840*a*b^2 + 231*b^3)*d*x + 15*(b^3*cosh(d*x + c)^11 - 12*b^3*cosh(d*x + c)^9 + 6*(8*a*b^2 + 11*b^3)*cosh(d*x + c)^7 - 4*(96*a*b^2 + 55*b^3)*cosh(d*x + c)^5 + 3*(256*a^2*b + 448*a*b^2 + 165*b^3)*cosh(d*x + c)^3 - 24*(128*a^2*b + 112*a*b^2 + 33*b^3)*cosh(d*x + c))*sinh(d*x + c))/d","B",0
219,1,474,0,0.459252," ","integrate(csch(d*x+c)^2*(a+b*sinh(d*x+c)^4)^3,x, algorithm=""fricas"")","\frac{2 \, b^{3} \cosh\left(d x + c\right)^{11} + 22 \, b^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{10} - 27 \, b^{3} \cosh\left(d x + c\right)^{9} + 3 \, {\left(110 \, b^{3} \cosh\left(d x + c\right)^{3} - 81 \, b^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{8} + 5 \, {\left(32 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 7 \, {\left(132 \, b^{3} \cosh\left(d x + c\right)^{5} - 324 \, b^{3} \cosh\left(d x + c\right)^{3} + 5 \, {\left(32 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} - 50 \, {\left(32 \, a b^{2} + 15 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + {\left(660 \, b^{3} \cosh\left(d x + c\right)^{7} - 3402 \, b^{3} \cosh\left(d x + c\right)^{5} + 175 \, {\left(32 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 250 \, {\left(32 \, a b^{2} + 15 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 60 \, {\left(128 \, a^{2} b + 144 \, a b^{2} + 45 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(110 \, b^{3} \cosh\left(d x + c\right)^{9} - 972 \, b^{3} \cosh\left(d x + c\right)^{7} + 105 \, {\left(32 \, a b^{2} + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 500 \, {\left(32 \, a b^{2} + 15 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 180 \, {\left(128 \, a^{2} b + 144 \, a b^{2} + 45 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 20 \, {\left(1024 \, a^{3} + 384 \, a^{2} b + 360 \, a b^{2} + 105 \, b^{3}\right)} \cosh\left(d x + c\right) + 80 \, {\left(256 \, a^{3} - 3 \, {\left(128 \, a^{2} b + 80 \, a b^{2} + 21 \, b^{3}\right)} d x\right)} \sinh\left(d x + c\right)}{20480 \, d \sinh\left(d x + c\right)}"," ",0,"1/20480*(2*b^3*cosh(d*x + c)^11 + 22*b^3*cosh(d*x + c)*sinh(d*x + c)^10 - 27*b^3*cosh(d*x + c)^9 + 3*(110*b^3*cosh(d*x + c)^3 - 81*b^3*cosh(d*x + c))*sinh(d*x + c)^8 + 5*(32*a*b^2 + 35*b^3)*cosh(d*x + c)^7 + 7*(132*b^3*cosh(d*x + c)^5 - 324*b^3*cosh(d*x + c)^3 + 5*(32*a*b^2 + 35*b^3)*cosh(d*x + c))*sinh(d*x + c)^6 - 50*(32*a*b^2 + 15*b^3)*cosh(d*x + c)^5 + (660*b^3*cosh(d*x + c)^7 - 3402*b^3*cosh(d*x + c)^5 + 175*(32*a*b^2 + 35*b^3)*cosh(d*x + c)^3 - 250*(32*a*b^2 + 15*b^3)*cosh(d*x + c))*sinh(d*x + c)^4 + 60*(128*a^2*b + 144*a*b^2 + 45*b^3)*cosh(d*x + c)^3 + (110*b^3*cosh(d*x + c)^9 - 972*b^3*cosh(d*x + c)^7 + 105*(32*a*b^2 + 35*b^3)*cosh(d*x + c)^5 - 500*(32*a*b^2 + 15*b^3)*cosh(d*x + c)^3 + 180*(128*a^2*b + 144*a*b^2 + 45*b^3)*cosh(d*x + c))*sinh(d*x + c)^2 - 20*(1024*a^3 + 384*a^2*b + 360*a*b^2 + 105*b^3)*cosh(d*x + c) + 80*(256*a^3 - 3*(128*a^2*b + 80*a*b^2 + 21*b^3)*d*x)*sinh(d*x + c))/(d*sinh(d*x + c))","B",0
220,1,567,0,0.993245," ","integrate(csch(d*x+c)^4*(a+b*sinh(d*x+c)^4)^3,x, algorithm=""fricas"")","\frac{3 \, b^{3} \cosh\left(d x + c\right)^{11} + 33 \, b^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{10} - 41 \, b^{3} \cosh\left(d x + c\right)^{9} + 9 \, {\left(55 \, b^{3} \cosh\left(d x + c\right)^{3} - 41 \, b^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{8} + 3 \, {\left(96 \, a b^{2} + 91 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 21 \, {\left(66 \, b^{3} \cosh\left(d x + c\right)^{5} - 164 \, b^{3} \cosh\left(d x + c\right)^{3} + {\left(96 \, a b^{2} + 91 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} - 3 \, {\left(1056 \, a b^{2} + 425 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 3 \, {\left(330 \, b^{3} \cosh\left(d x + c\right)^{7} - 1722 \, b^{3} \cosh\left(d x + c\right)^{5} + 35 \, {\left(96 \, a b^{2} + 91 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 5 \, {\left(1056 \, a b^{2} + 425 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(512 \, a^{3} + 972 \, a b^{2} + 319 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 16 \, {\left(256 \, a^{3} - 3 \, {\left(384 \, a^{2} b + 144 \, a b^{2} + 35 \, b^{3}\right)} d x\right)} \sinh\left(d x + c\right)^{3} + 3 \, {\left(55 \, b^{3} \cosh\left(d x + c\right)^{9} - 492 \, b^{3} \cosh\left(d x + c\right)^{7} + 21 \, {\left(96 \, a b^{2} + 91 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 10 \, {\left(1056 \, a b^{2} + 425 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 8 \, {\left(512 \, a^{3} + 972 \, a b^{2} + 319 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 24 \, {\left(512 \, a^{3} + 204 \, a b^{2} + 63 \, b^{3}\right)} \cosh\left(d x + c\right) + 48 \, {\left(256 \, a^{3} - 3 \, {\left(384 \, a^{2} b + 144 \, a b^{2} + 35 \, b^{3}\right)} d x - {\left(256 \, a^{3} - 3 \, {\left(384 \, a^{2} b + 144 \, a b^{2} + 35 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)}{6144 \, {\left(d \sinh\left(d x + c\right)^{3} + 3 \, {\left(d \cosh\left(d x + c\right)^{2} - d\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"1/6144*(3*b^3*cosh(d*x + c)^11 + 33*b^3*cosh(d*x + c)*sinh(d*x + c)^10 - 41*b^3*cosh(d*x + c)^9 + 9*(55*b^3*cosh(d*x + c)^3 - 41*b^3*cosh(d*x + c))*sinh(d*x + c)^8 + 3*(96*a*b^2 + 91*b^3)*cosh(d*x + c)^7 + 21*(66*b^3*cosh(d*x + c)^5 - 164*b^3*cosh(d*x + c)^3 + (96*a*b^2 + 91*b^3)*cosh(d*x + c))*sinh(d*x + c)^6 - 3*(1056*a*b^2 + 425*b^3)*cosh(d*x + c)^5 + 3*(330*b^3*cosh(d*x + c)^7 - 1722*b^3*cosh(d*x + c)^5 + 35*(96*a*b^2 + 91*b^3)*cosh(d*x + c)^3 - 5*(1056*a*b^2 + 425*b^3)*cosh(d*x + c))*sinh(d*x + c)^4 + 8*(512*a^3 + 972*a*b^2 + 319*b^3)*cosh(d*x + c)^3 - 16*(256*a^3 - 3*(384*a^2*b + 144*a*b^2 + 35*b^3)*d*x)*sinh(d*x + c)^3 + 3*(55*b^3*cosh(d*x + c)^9 - 492*b^3*cosh(d*x + c)^7 + 21*(96*a*b^2 + 91*b^3)*cosh(d*x + c)^5 - 10*(1056*a*b^2 + 425*b^3)*cosh(d*x + c)^3 + 8*(512*a^3 + 972*a*b^2 + 319*b^3)*cosh(d*x + c))*sinh(d*x + c)^2 - 24*(512*a^3 + 204*a*b^2 + 63*b^3)*cosh(d*x + c) + 48*(256*a^3 - 3*(384*a^2*b + 144*a*b^2 + 35*b^3)*d*x - (256*a^3 - 3*(384*a^2*b + 144*a*b^2 + 35*b^3)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c))/(d*sinh(d*x + c)^3 + 3*(d*cosh(d*x + c)^2 - d)*sinh(d*x + c))","B",0
221,1,768,0,0.883372," ","integrate(csch(d*x+c)^6*(a+b*sinh(d*x+c)^4)^3,x, algorithm=""fricas"")","\frac{5 \, b^{3} \cosh\left(d x + c\right)^{11} + 55 \, b^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{10} - 70 \, b^{3} \cosh\left(d x + c\right)^{9} + 15 \, {\left(55 \, b^{3} \cosh\left(d x + c\right)^{3} - 42 \, b^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{8} + 20 \, {\left(36 \, a b^{2} + 25 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 70 \, {\left(33 \, b^{3} \cosh\left(d x + c\right)^{5} - 84 \, b^{3} \cosh\left(d x + c\right)^{3} + 2 \, {\left(36 \, a b^{2} + 25 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} - {\left(1024 \, a^{3} + 5760 \, a^{2} b + 3600 \, a b^{2} + 1625 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 8 \, {\left(128 \, a^{3} + 720 \, a^{2} b - 15 \, {\left(24 \, a b^{2} + 5 \, b^{3}\right)} d x\right)} \sinh\left(d x + c\right)^{5} + 5 \, {\left(330 \, b^{3} \cosh\left(d x + c\right)^{7} - 1764 \, b^{3} \cosh\left(d x + c\right)^{5} + 140 \, {\left(36 \, a b^{2} + 25 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - {\left(1024 \, a^{3} + 5760 \, a^{2} b + 3600 \, a b^{2} + 1625 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 20 \, {\left(256 \, a^{3} + 864 \, a^{2} b + 324 \, a b^{2} + 125 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 40 \, {\left(128 \, a^{3} + 720 \, a^{2} b - 15 \, {\left(24 \, a b^{2} + 5 \, b^{3}\right)} d x - 2 \, {\left(128 \, a^{3} + 720 \, a^{2} b - 15 \, {\left(24 \, a b^{2} + 5 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + 5 \, {\left(55 \, b^{3} \cosh\left(d x + c\right)^{9} - 504 \, b^{3} \cosh\left(d x + c\right)^{7} + 84 \, {\left(36 \, a b^{2} + 25 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 2 \, {\left(1024 \, a^{3} + 5760 \, a^{2} b + 3600 \, a b^{2} + 1625 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 12 \, {\left(256 \, a^{3} + 864 \, a^{2} b + 324 \, a b^{2} + 125 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 10 \, {\left(1024 \, a^{3} + 1152 \, a^{2} b + 360 \, a b^{2} + 131 \, b^{3}\right)} \cosh\left(d x + c\right) + 40 \, {\left({\left(128 \, a^{3} + 720 \, a^{2} b - 15 \, {\left(24 \, a b^{2} + 5 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 256 \, a^{3} + 1440 \, a^{2} b - 30 \, {\left(24 \, a b^{2} + 5 \, b^{3}\right)} d x - 3 \, {\left(128 \, a^{3} + 720 \, a^{2} b - 15 \, {\left(24 \, a b^{2} + 5 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)}{1920 \, {\left(d \sinh\left(d x + c\right)^{5} + 5 \, {\left(2 \, d \cosh\left(d x + c\right)^{2} - d\right)} \sinh\left(d x + c\right)^{3} + 5 \, {\left(d \cosh\left(d x + c\right)^{4} - 3 \, d \cosh\left(d x + c\right)^{2} + 2 \, d\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"1/1920*(5*b^3*cosh(d*x + c)^11 + 55*b^3*cosh(d*x + c)*sinh(d*x + c)^10 - 70*b^3*cosh(d*x + c)^9 + 15*(55*b^3*cosh(d*x + c)^3 - 42*b^3*cosh(d*x + c))*sinh(d*x + c)^8 + 20*(36*a*b^2 + 25*b^3)*cosh(d*x + c)^7 + 70*(33*b^3*cosh(d*x + c)^5 - 84*b^3*cosh(d*x + c)^3 + 2*(36*a*b^2 + 25*b^3)*cosh(d*x + c))*sinh(d*x + c)^6 - (1024*a^3 + 5760*a^2*b + 3600*a*b^2 + 1625*b^3)*cosh(d*x + c)^5 + 8*(128*a^3 + 720*a^2*b - 15*(24*a*b^2 + 5*b^3)*d*x)*sinh(d*x + c)^5 + 5*(330*b^3*cosh(d*x + c)^7 - 1764*b^3*cosh(d*x + c)^5 + 140*(36*a*b^2 + 25*b^3)*cosh(d*x + c)^3 - (1024*a^3 + 5760*a^2*b + 3600*a*b^2 + 1625*b^3)*cosh(d*x + c))*sinh(d*x + c)^4 + 20*(256*a^3 + 864*a^2*b + 324*a*b^2 + 125*b^3)*cosh(d*x + c)^3 - 40*(128*a^3 + 720*a^2*b - 15*(24*a*b^2 + 5*b^3)*d*x - 2*(128*a^3 + 720*a^2*b - 15*(24*a*b^2 + 5*b^3)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 5*(55*b^3*cosh(d*x + c)^9 - 504*b^3*cosh(d*x + c)^7 + 84*(36*a*b^2 + 25*b^3)*cosh(d*x + c)^5 - 2*(1024*a^3 + 5760*a^2*b + 3600*a*b^2 + 1625*b^3)*cosh(d*x + c)^3 + 12*(256*a^3 + 864*a^2*b + 324*a*b^2 + 125*b^3)*cosh(d*x + c))*sinh(d*x + c)^2 - 10*(1024*a^3 + 1152*a^2*b + 360*a*b^2 + 131*b^3)*cosh(d*x + c) + 40*((128*a^3 + 720*a^2*b - 15*(24*a*b^2 + 5*b^3)*d*x)*cosh(d*x + c)^4 + 256*a^3 + 1440*a^2*b - 30*(24*a*b^2 + 5*b^3)*d*x - 3*(128*a^3 + 720*a^2*b - 15*(24*a*b^2 + 5*b^3)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c))/(d*sinh(d*x + c)^5 + 5*(2*d*cosh(d*x + c)^2 - d)*sinh(d*x + c)^3 + 5*(d*cosh(d*x + c)^4 - 3*d*cosh(d*x + c)^2 + 2*d)*sinh(d*x + c))","B",0
222,1,928,0,0.734103," ","integrate(csch(d*x+c)^8*(a+b*sinh(d*x+c)^4)^3,x, algorithm=""fricas"")","\frac{35 \, b^{3} \cosh\left(d x + c\right)^{11} + 385 \, b^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{10} - 525 \, b^{3} \cosh\left(d x + c\right)^{9} + 525 \, {\left(11 \, b^{3} \cosh\left(d x + c\right)^{3} - 9 \, b^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{8} + {\left(1024 \, a^{3} + 4480 \, a^{2} b + 2695 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} - 8 \, {\left(128 \, a^{3} + 560 \, a^{2} b - 105 \, {\left(8 \, a b^{2} + b^{3}\right)} d x\right)} \sinh\left(d x + c\right)^{7} + 7 \, {\left(2310 \, b^{3} \cosh\left(d x + c\right)^{5} - 6300 \, b^{3} \cosh\left(d x + c\right)^{3} + {\left(1024 \, a^{3} + 4480 \, a^{2} b + 2695 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} - 7 \, {\left(1024 \, a^{3} + 4480 \, a^{2} b + 975 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 56 \, {\left(128 \, a^{3} + 560 \, a^{2} b - 105 \, {\left(8 \, a b^{2} + b^{3}\right)} d x - 3 \, {\left(128 \, a^{3} + 560 \, a^{2} b - 105 \, {\left(8 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{5} + 35 \, {\left(330 \, b^{3} \cosh\left(d x + c\right)^{7} - 1890 \, b^{3} \cosh\left(d x + c\right)^{5} + {\left(1024 \, a^{3} + 4480 \, a^{2} b + 2695 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - {\left(1024 \, a^{3} + 4480 \, a^{2} b + 975 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 42 \, {\left(512 \, a^{3} + 1600 \, a^{2} b + 215 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 56 \, {\left(5 \, {\left(128 \, a^{3} + 560 \, a^{2} b - 105 \, {\left(8 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 384 \, a^{3} + 1680 \, a^{2} b - 315 \, {\left(8 \, a b^{2} + b^{3}\right)} d x - 10 \, {\left(128 \, a^{3} + 560 \, a^{2} b - 105 \, {\left(8 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + 7 \, {\left(275 \, b^{3} \cosh\left(d x + c\right)^{9} - 2700 \, b^{3} \cosh\left(d x + c\right)^{7} + 3 \, {\left(1024 \, a^{3} + 4480 \, a^{2} b + 2695 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 10 \, {\left(1024 \, a^{3} + 4480 \, a^{2} b + 975 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 18 \, {\left(512 \, a^{3} + 1600 \, a^{2} b + 215 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 70 \, {\left(512 \, a^{3} + 576 \, a^{2} b + 63 \, b^{3}\right)} \cosh\left(d x + c\right) - 56 \, {\left({\left(128 \, a^{3} + 560 \, a^{2} b - 105 \, {\left(8 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{6} - 5 \, {\left(128 \, a^{3} + 560 \, a^{2} b - 105 \, {\left(8 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{4} - 640 \, a^{3} - 2800 \, a^{2} b + 525 \, {\left(8 \, a b^{2} + b^{3}\right)} d x + 9 \, {\left(128 \, a^{3} + 560 \, a^{2} b - 105 \, {\left(8 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)}{2240 \, {\left(d \sinh\left(d x + c\right)^{7} + 7 \, {\left(3 \, d \cosh\left(d x + c\right)^{2} - d\right)} \sinh\left(d x + c\right)^{5} + 7 \, {\left(5 \, d \cosh\left(d x + c\right)^{4} - 10 \, d \cosh\left(d x + c\right)^{2} + 3 \, d\right)} \sinh\left(d x + c\right)^{3} + 7 \, {\left(d \cosh\left(d x + c\right)^{6} - 5 \, d \cosh\left(d x + c\right)^{4} + 9 \, d \cosh\left(d x + c\right)^{2} - 5 \, d\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"1/2240*(35*b^3*cosh(d*x + c)^11 + 385*b^3*cosh(d*x + c)*sinh(d*x + c)^10 - 525*b^3*cosh(d*x + c)^9 + 525*(11*b^3*cosh(d*x + c)^3 - 9*b^3*cosh(d*x + c))*sinh(d*x + c)^8 + (1024*a^3 + 4480*a^2*b + 2695*b^3)*cosh(d*x + c)^7 - 8*(128*a^3 + 560*a^2*b - 105*(8*a*b^2 + b^3)*d*x)*sinh(d*x + c)^7 + 7*(2310*b^3*cosh(d*x + c)^5 - 6300*b^3*cosh(d*x + c)^3 + (1024*a^3 + 4480*a^2*b + 2695*b^3)*cosh(d*x + c))*sinh(d*x + c)^6 - 7*(1024*a^3 + 4480*a^2*b + 975*b^3)*cosh(d*x + c)^5 + 56*(128*a^3 + 560*a^2*b - 105*(8*a*b^2 + b^3)*d*x - 3*(128*a^3 + 560*a^2*b - 105*(8*a*b^2 + b^3)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 35*(330*b^3*cosh(d*x + c)^7 - 1890*b^3*cosh(d*x + c)^5 + (1024*a^3 + 4480*a^2*b + 2695*b^3)*cosh(d*x + c)^3 - (1024*a^3 + 4480*a^2*b + 975*b^3)*cosh(d*x + c))*sinh(d*x + c)^4 + 42*(512*a^3 + 1600*a^2*b + 215*b^3)*cosh(d*x + c)^3 - 56*(5*(128*a^3 + 560*a^2*b - 105*(8*a*b^2 + b^3)*d*x)*cosh(d*x + c)^4 + 384*a^3 + 1680*a^2*b - 315*(8*a*b^2 + b^3)*d*x - 10*(128*a^3 + 560*a^2*b - 105*(8*a*b^2 + b^3)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 7*(275*b^3*cosh(d*x + c)^9 - 2700*b^3*cosh(d*x + c)^7 + 3*(1024*a^3 + 4480*a^2*b + 2695*b^3)*cosh(d*x + c)^5 - 10*(1024*a^3 + 4480*a^2*b + 975*b^3)*cosh(d*x + c)^3 + 18*(512*a^3 + 1600*a^2*b + 215*b^3)*cosh(d*x + c))*sinh(d*x + c)^2 - 70*(512*a^3 + 576*a^2*b + 63*b^3)*cosh(d*x + c) - 56*((128*a^3 + 560*a^2*b - 105*(8*a*b^2 + b^3)*d*x)*cosh(d*x + c)^6 - 5*(128*a^3 + 560*a^2*b - 105*(8*a*b^2 + b^3)*d*x)*cosh(d*x + c)^4 - 640*a^3 - 2800*a^2*b + 525*(8*a*b^2 + b^3)*d*x + 9*(128*a^3 + 560*a^2*b - 105*(8*a*b^2 + b^3)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c))/(d*sinh(d*x + c)^7 + 7*(3*d*cosh(d*x + c)^2 - d)*sinh(d*x + c)^5 + 7*(5*d*cosh(d*x + c)^4 - 10*d*cosh(d*x + c)^2 + 3*d)*sinh(d*x + c)^3 + 7*(d*cosh(d*x + c)^6 - 5*d*cosh(d*x + c)^4 + 9*d*cosh(d*x + c)^2 - 5*d)*sinh(d*x + c))","B",0
223,1,1314,0,0.909343," ","integrate(csch(d*x+c)^10*(a+b*sinh(d*x+c)^4)^3,x, algorithm=""fricas"")","\frac{315 \, b^{3} \cosh\left(d x + c\right)^{11} + 3465 \, b^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{10} - {\left(1024 \, a^{3} + 4032 \, a^{2} b + 7560 \, a b^{2} + 2835 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} - 4 \, {\left(315 \, b^{3} d x - 256 \, a^{3} - 1008 \, a^{2} b - 1890 \, a b^{2}\right)} \sinh\left(d x + c\right)^{9} + 9 \, {\left(5775 \, b^{3} \cosh\left(d x + c\right)^{3} - {\left(1024 \, a^{3} + 4032 \, a^{2} b + 7560 \, a b^{2} + 2835 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{8} + 9 \, {\left(1024 \, a^{3} + 4032 \, a^{2} b + 5880 \, a b^{2} + 1225 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 36 \, {\left(315 \, b^{3} d x - 256 \, a^{3} - 1008 \, a^{2} b - 1890 \, a b^{2} - 4 \, {\left(315 \, b^{3} d x - 256 \, a^{3} - 1008 \, a^{2} b - 1890 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{7} + 21 \, {\left(6930 \, b^{3} \cosh\left(d x + c\right)^{5} - 4 \, {\left(1024 \, a^{3} + 4032 \, a^{2} b + 7560 \, a b^{2} + 2835 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(1024 \, a^{3} + 4032 \, a^{2} b + 5880 \, a b^{2} + 1225 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} - 9 \, {\left(4096 \, a^{3} + 16128 \, a^{2} b + 16800 \, a b^{2} + 2625 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 36 \, {\left(1260 \, b^{3} d x + 14 \, {\left(315 \, b^{3} d x - 256 \, a^{3} - 1008 \, a^{2} b - 1890 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} - 1024 \, a^{3} - 4032 \, a^{2} b - 7560 \, a b^{2} - 21 \, {\left(315 \, b^{3} d x - 256 \, a^{3} - 1008 \, a^{2} b - 1890 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{5} + 9 \, {\left(11550 \, b^{3} \cosh\left(d x + c\right)^{7} - 14 \, {\left(1024 \, a^{3} + 4032 \, a^{2} b + 7560 \, a b^{2} + 2835 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 35 \, {\left(1024 \, a^{3} + 4032 \, a^{2} b + 5880 \, a b^{2} + 1225 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 5 \, {\left(4096 \, a^{3} + 16128 \, a^{2} b + 16800 \, a b^{2} + 2625 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 42 \, {\left(2048 \, a^{3} + 6144 \, a^{2} b + 5040 \, a b^{2} + 675 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 12 \, {\left(28 \, {\left(315 \, b^{3} d x - 256 \, a^{3} - 1008 \, a^{2} b - 1890 \, a b^{2}\right)} \cosh\left(d x + c\right)^{6} - 8820 \, b^{3} d x - 105 \, {\left(315 \, b^{3} d x - 256 \, a^{3} - 1008 \, a^{2} b - 1890 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} + 7168 \, a^{3} + 28224 \, a^{2} b + 52920 \, a b^{2} + 120 \, {\left(315 \, b^{3} d x - 256 \, a^{3} - 1008 \, a^{2} b - 1890 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + 9 \, {\left(1925 \, b^{3} \cosh\left(d x + c\right)^{9} - 4 \, {\left(1024 \, a^{3} + 4032 \, a^{2} b + 7560 \, a b^{2} + 2835 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 21 \, {\left(1024 \, a^{3} + 4032 \, a^{2} b + 5880 \, a b^{2} + 1225 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 10 \, {\left(4096 \, a^{3} + 16128 \, a^{2} b + 16800 \, a b^{2} + 2625 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 14 \, {\left(2048 \, a^{3} + 6144 \, a^{2} b + 5040 \, a b^{2} + 675 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 126 \, {\left(1024 \, a^{3} + 1152 \, a^{2} b + 840 \, a b^{2} + 105 \, b^{3}\right)} \cosh\left(d x + c\right) - 36 \, {\left({\left(315 \, b^{3} d x - 256 \, a^{3} - 1008 \, a^{2} b - 1890 \, a b^{2}\right)} \cosh\left(d x + c\right)^{8} - 7 \, {\left(315 \, b^{3} d x - 256 \, a^{3} - 1008 \, a^{2} b - 1890 \, a b^{2}\right)} \cosh\left(d x + c\right)^{6} + 4410 \, b^{3} d x + 20 \, {\left(315 \, b^{3} d x - 256 \, a^{3} - 1008 \, a^{2} b - 1890 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} - 3584 \, a^{3} - 14112 \, a^{2} b - 26460 \, a b^{2} - 28 \, {\left(315 \, b^{3} d x - 256 \, a^{3} - 1008 \, a^{2} b - 1890 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)}{2520 \, {\left(d \sinh\left(d x + c\right)^{9} + 9 \, {\left(4 \, d \cosh\left(d x + c\right)^{2} - d\right)} \sinh\left(d x + c\right)^{7} + 9 \, {\left(14 \, d \cosh\left(d x + c\right)^{4} - 21 \, d \cosh\left(d x + c\right)^{2} + 4 \, d\right)} \sinh\left(d x + c\right)^{5} + 3 \, {\left(28 \, d \cosh\left(d x + c\right)^{6} - 105 \, d \cosh\left(d x + c\right)^{4} + 120 \, d \cosh\left(d x + c\right)^{2} - 28 \, d\right)} \sinh\left(d x + c\right)^{3} + 9 \, {\left(d \cosh\left(d x + c\right)^{8} - 7 \, d \cosh\left(d x + c\right)^{6} + 20 \, d \cosh\left(d x + c\right)^{4} - 28 \, d \cosh\left(d x + c\right)^{2} + 14 \, d\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"1/2520*(315*b^3*cosh(d*x + c)^11 + 3465*b^3*cosh(d*x + c)*sinh(d*x + c)^10 - (1024*a^3 + 4032*a^2*b + 7560*a*b^2 + 2835*b^3)*cosh(d*x + c)^9 - 4*(315*b^3*d*x - 256*a^3 - 1008*a^2*b - 1890*a*b^2)*sinh(d*x + c)^9 + 9*(5775*b^3*cosh(d*x + c)^3 - (1024*a^3 + 4032*a^2*b + 7560*a*b^2 + 2835*b^3)*cosh(d*x + c))*sinh(d*x + c)^8 + 9*(1024*a^3 + 4032*a^2*b + 5880*a*b^2 + 1225*b^3)*cosh(d*x + c)^7 + 36*(315*b^3*d*x - 256*a^3 - 1008*a^2*b - 1890*a*b^2 - 4*(315*b^3*d*x - 256*a^3 - 1008*a^2*b - 1890*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^7 + 21*(6930*b^3*cosh(d*x + c)^5 - 4*(1024*a^3 + 4032*a^2*b + 7560*a*b^2 + 2835*b^3)*cosh(d*x + c)^3 + 3*(1024*a^3 + 4032*a^2*b + 5880*a*b^2 + 1225*b^3)*cosh(d*x + c))*sinh(d*x + c)^6 - 9*(4096*a^3 + 16128*a^2*b + 16800*a*b^2 + 2625*b^3)*cosh(d*x + c)^5 - 36*(1260*b^3*d*x + 14*(315*b^3*d*x - 256*a^3 - 1008*a^2*b - 1890*a*b^2)*cosh(d*x + c)^4 - 1024*a^3 - 4032*a^2*b - 7560*a*b^2 - 21*(315*b^3*d*x - 256*a^3 - 1008*a^2*b - 1890*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 9*(11550*b^3*cosh(d*x + c)^7 - 14*(1024*a^3 + 4032*a^2*b + 7560*a*b^2 + 2835*b^3)*cosh(d*x + c)^5 + 35*(1024*a^3 + 4032*a^2*b + 5880*a*b^2 + 1225*b^3)*cosh(d*x + c)^3 - 5*(4096*a^3 + 16128*a^2*b + 16800*a*b^2 + 2625*b^3)*cosh(d*x + c))*sinh(d*x + c)^4 + 42*(2048*a^3 + 6144*a^2*b + 5040*a*b^2 + 675*b^3)*cosh(d*x + c)^3 - 12*(28*(315*b^3*d*x - 256*a^3 - 1008*a^2*b - 1890*a*b^2)*cosh(d*x + c)^6 - 8820*b^3*d*x - 105*(315*b^3*d*x - 256*a^3 - 1008*a^2*b - 1890*a*b^2)*cosh(d*x + c)^4 + 7168*a^3 + 28224*a^2*b + 52920*a*b^2 + 120*(315*b^3*d*x - 256*a^3 - 1008*a^2*b - 1890*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 9*(1925*b^3*cosh(d*x + c)^9 - 4*(1024*a^3 + 4032*a^2*b + 7560*a*b^2 + 2835*b^3)*cosh(d*x + c)^7 + 21*(1024*a^3 + 4032*a^2*b + 5880*a*b^2 + 1225*b^3)*cosh(d*x + c)^5 - 10*(4096*a^3 + 16128*a^2*b + 16800*a*b^2 + 2625*b^3)*cosh(d*x + c)^3 + 14*(2048*a^3 + 6144*a^2*b + 5040*a*b^2 + 675*b^3)*cosh(d*x + c))*sinh(d*x + c)^2 - 126*(1024*a^3 + 1152*a^2*b + 840*a*b^2 + 105*b^3)*cosh(d*x + c) - 36*((315*b^3*d*x - 256*a^3 - 1008*a^2*b - 1890*a*b^2)*cosh(d*x + c)^8 - 7*(315*b^3*d*x - 256*a^3 - 1008*a^2*b - 1890*a*b^2)*cosh(d*x + c)^6 + 4410*b^3*d*x + 20*(315*b^3*d*x - 256*a^3 - 1008*a^2*b - 1890*a*b^2)*cosh(d*x + c)^4 - 3584*a^3 - 14112*a^2*b - 26460*a*b^2 - 28*(315*b^3*d*x - 256*a^3 - 1008*a^2*b - 1890*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c))/(d*sinh(d*x + c)^9 + 9*(4*d*cosh(d*x + c)^2 - d)*sinh(d*x + c)^7 + 9*(14*d*cosh(d*x + c)^4 - 21*d*cosh(d*x + c)^2 + 4*d)*sinh(d*x + c)^5 + 3*(28*d*cosh(d*x + c)^6 - 105*d*cosh(d*x + c)^4 + 120*d*cosh(d*x + c)^2 - 28*d)*sinh(d*x + c)^3 + 9*(d*cosh(d*x + c)^8 - 7*d*cosh(d*x + c)^6 + 20*d*cosh(d*x + c)^4 - 28*d*cosh(d*x + c)^2 + 14*d)*sinh(d*x + c))","B",0
224,1,1607,0,0.536132," ","integrate(csch(d*x+c)^12*(a+b*sinh(d*x+c)^4)^3,x, algorithm=""fricas"")","\frac{2 \, {\left(640 \, a^{3} + 2376 \, a^{2} b + 3465 \, a b^{2}\right)} \cosh\left(d x + c\right)^{11} + 22 \, {\left(640 \, a^{3} + 2376 \, a^{2} b + 3465 \, a b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{10} + {\left(3465 \, b^{3} d x - 1280 \, a^{3} - 4752 \, a^{2} b - 6930 \, a b^{2}\right)} \sinh\left(d x + c\right)^{11} - 22 \, {\left(640 \, a^{3} + 2376 \, a^{2} b + 3465 \, a b^{2}\right)} \cosh\left(d x + c\right)^{9} - 11 \, {\left(3465 \, b^{3} d x - 1280 \, a^{3} - 4752 \, a^{2} b - 6930 \, a b^{2} - 5 \, {\left(3465 \, b^{3} d x - 1280 \, a^{3} - 4752 \, a^{2} b - 6930 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{9} + 66 \, {\left(5 \, {\left(640 \, a^{3} + 2376 \, a^{2} b + 3465 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(640 \, a^{3} + 2376 \, a^{2} b + 3465 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{8} + 110 \, {\left(640 \, a^{3} + 2376 \, a^{2} b + 3087 \, a b^{2}\right)} \cosh\left(d x + c\right)^{7} + 11 \, {\left(17325 \, b^{3} d x + 30 \, {\left(3465 \, b^{3} d x - 1280 \, a^{3} - 4752 \, a^{2} b - 6930 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} - 6400 \, a^{3} - 23760 \, a^{2} b - 34650 \, a b^{2} - 36 \, {\left(3465 \, b^{3} d x - 1280 \, a^{3} - 4752 \, a^{2} b - 6930 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{7} + 154 \, {\left(6 \, {\left(640 \, a^{3} + 2376 \, a^{2} b + 3465 \, a b^{2}\right)} \cosh\left(d x + c\right)^{5} - 12 \, {\left(640 \, a^{3} + 2376 \, a^{2} b + 3465 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} + 5 \, {\left(640 \, a^{3} + 2376 \, a^{2} b + 3087 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} - 330 \, {\left(640 \, a^{3} + 2376 \, a^{2} b + 2415 \, a b^{2}\right)} \cosh\left(d x + c\right)^{5} + 33 \, {\left(14 \, {\left(3465 \, b^{3} d x - 1280 \, a^{3} - 4752 \, a^{2} b - 6930 \, a b^{2}\right)} \cosh\left(d x + c\right)^{6} - 17325 \, b^{3} d x - 42 \, {\left(3465 \, b^{3} d x - 1280 \, a^{3} - 4752 \, a^{2} b - 6930 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} + 6400 \, a^{3} + 23760 \, a^{2} b + 34650 \, a b^{2} + 35 \, {\left(3465 \, b^{3} d x - 1280 \, a^{3} - 4752 \, a^{2} b - 6930 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{5} + 22 \, {\left(30 \, {\left(640 \, a^{3} + 2376 \, a^{2} b + 3465 \, a b^{2}\right)} \cosh\left(d x + c\right)^{7} - 126 \, {\left(640 \, a^{3} + 2376 \, a^{2} b + 3465 \, a b^{2}\right)} \cosh\left(d x + c\right)^{5} + 175 \, {\left(640 \, a^{3} + 2376 \, a^{2} b + 3087 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} - 75 \, {\left(640 \, a^{3} + 2376 \, a^{2} b + 2415 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 660 \, {\left(640 \, a^{3} + 1872 \, a^{2} b + 1533 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} + 11 \, {\left(15 \, {\left(3465 \, b^{3} d x - 1280 \, a^{3} - 4752 \, a^{2} b - 6930 \, a b^{2}\right)} \cosh\left(d x + c\right)^{8} - 84 \, {\left(3465 \, b^{3} d x - 1280 \, a^{3} - 4752 \, a^{2} b - 6930 \, a b^{2}\right)} \cosh\left(d x + c\right)^{6} + 103950 \, b^{3} d x + 175 \, {\left(3465 \, b^{3} d x - 1280 \, a^{3} - 4752 \, a^{2} b - 6930 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} - 38400 \, a^{3} - 142560 \, a^{2} b - 207900 \, a b^{2} - 150 \, {\left(3465 \, b^{3} d x - 1280 \, a^{3} - 4752 \, a^{2} b - 6930 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + 22 \, {\left(5 \, {\left(640 \, a^{3} + 2376 \, a^{2} b + 3465 \, a b^{2}\right)} \cosh\left(d x + c\right)^{9} - 36 \, {\left(640 \, a^{3} + 2376 \, a^{2} b + 3465 \, a b^{2}\right)} \cosh\left(d x + c\right)^{7} + 105 \, {\left(640 \, a^{3} + 2376 \, a^{2} b + 3087 \, a b^{2}\right)} \cosh\left(d x + c\right)^{5} - 150 \, {\left(640 \, a^{3} + 2376 \, a^{2} b + 2415 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} + 90 \, {\left(640 \, a^{3} + 1872 \, a^{2} b + 1533 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 4620 \, {\left(128 \, a^{3} + 144 \, a^{2} b + 105 \, a b^{2}\right)} \cosh\left(d x + c\right) + 11 \, {\left({\left(3465 \, b^{3} d x - 1280 \, a^{3} - 4752 \, a^{2} b - 6930 \, a b^{2}\right)} \cosh\left(d x + c\right)^{10} - 9 \, {\left(3465 \, b^{3} d x - 1280 \, a^{3} - 4752 \, a^{2} b - 6930 \, a b^{2}\right)} \cosh\left(d x + c\right)^{8} + 35 \, {\left(3465 \, b^{3} d x - 1280 \, a^{3} - 4752 \, a^{2} b - 6930 \, a b^{2}\right)} \cosh\left(d x + c\right)^{6} - 145530 \, b^{3} d x - 75 \, {\left(3465 \, b^{3} d x - 1280 \, a^{3} - 4752 \, a^{2} b - 6930 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} + 53760 \, a^{3} + 199584 \, a^{2} b + 291060 \, a b^{2} + 90 \, {\left(3465 \, b^{3} d x - 1280 \, a^{3} - 4752 \, a^{2} b - 6930 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)}{3465 \, {\left(d \sinh\left(d x + c\right)^{11} + 11 \, {\left(5 \, d \cosh\left(d x + c\right)^{2} - d\right)} \sinh\left(d x + c\right)^{9} + 11 \, {\left(30 \, d \cosh\left(d x + c\right)^{4} - 36 \, d \cosh\left(d x + c\right)^{2} + 5 \, d\right)} \sinh\left(d x + c\right)^{7} + 33 \, {\left(14 \, d \cosh\left(d x + c\right)^{6} - 42 \, d \cosh\left(d x + c\right)^{4} + 35 \, d \cosh\left(d x + c\right)^{2} - 5 \, d\right)} \sinh\left(d x + c\right)^{5} + 11 \, {\left(15 \, d \cosh\left(d x + c\right)^{8} - 84 \, d \cosh\left(d x + c\right)^{6} + 175 \, d \cosh\left(d x + c\right)^{4} - 150 \, d \cosh\left(d x + c\right)^{2} + 30 \, d\right)} \sinh\left(d x + c\right)^{3} + 11 \, {\left(d \cosh\left(d x + c\right)^{10} - 9 \, d \cosh\left(d x + c\right)^{8} + 35 \, d \cosh\left(d x + c\right)^{6} - 75 \, d \cosh\left(d x + c\right)^{4} + 90 \, d \cosh\left(d x + c\right)^{2} - 42 \, d\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"1/3465*(2*(640*a^3 + 2376*a^2*b + 3465*a*b^2)*cosh(d*x + c)^11 + 22*(640*a^3 + 2376*a^2*b + 3465*a*b^2)*cosh(d*x + c)*sinh(d*x + c)^10 + (3465*b^3*d*x - 1280*a^3 - 4752*a^2*b - 6930*a*b^2)*sinh(d*x + c)^11 - 22*(640*a^3 + 2376*a^2*b + 3465*a*b^2)*cosh(d*x + c)^9 - 11*(3465*b^3*d*x - 1280*a^3 - 4752*a^2*b - 6930*a*b^2 - 5*(3465*b^3*d*x - 1280*a^3 - 4752*a^2*b - 6930*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^9 + 66*(5*(640*a^3 + 2376*a^2*b + 3465*a*b^2)*cosh(d*x + c)^3 - 3*(640*a^3 + 2376*a^2*b + 3465*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^8 + 110*(640*a^3 + 2376*a^2*b + 3087*a*b^2)*cosh(d*x + c)^7 + 11*(17325*b^3*d*x + 30*(3465*b^3*d*x - 1280*a^3 - 4752*a^2*b - 6930*a*b^2)*cosh(d*x + c)^4 - 6400*a^3 - 23760*a^2*b - 34650*a*b^2 - 36*(3465*b^3*d*x - 1280*a^3 - 4752*a^2*b - 6930*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^7 + 154*(6*(640*a^3 + 2376*a^2*b + 3465*a*b^2)*cosh(d*x + c)^5 - 12*(640*a^3 + 2376*a^2*b + 3465*a*b^2)*cosh(d*x + c)^3 + 5*(640*a^3 + 2376*a^2*b + 3087*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^6 - 330*(640*a^3 + 2376*a^2*b + 2415*a*b^2)*cosh(d*x + c)^5 + 33*(14*(3465*b^3*d*x - 1280*a^3 - 4752*a^2*b - 6930*a*b^2)*cosh(d*x + c)^6 - 17325*b^3*d*x - 42*(3465*b^3*d*x - 1280*a^3 - 4752*a^2*b - 6930*a*b^2)*cosh(d*x + c)^4 + 6400*a^3 + 23760*a^2*b + 34650*a*b^2 + 35*(3465*b^3*d*x - 1280*a^3 - 4752*a^2*b - 6930*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 22*(30*(640*a^3 + 2376*a^2*b + 3465*a*b^2)*cosh(d*x + c)^7 - 126*(640*a^3 + 2376*a^2*b + 3465*a*b^2)*cosh(d*x + c)^5 + 175*(640*a^3 + 2376*a^2*b + 3087*a*b^2)*cosh(d*x + c)^3 - 75*(640*a^3 + 2376*a^2*b + 2415*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^4 + 660*(640*a^3 + 1872*a^2*b + 1533*a*b^2)*cosh(d*x + c)^3 + 11*(15*(3465*b^3*d*x - 1280*a^3 - 4752*a^2*b - 6930*a*b^2)*cosh(d*x + c)^8 - 84*(3465*b^3*d*x - 1280*a^3 - 4752*a^2*b - 6930*a*b^2)*cosh(d*x + c)^6 + 103950*b^3*d*x + 175*(3465*b^3*d*x - 1280*a^3 - 4752*a^2*b - 6930*a*b^2)*cosh(d*x + c)^4 - 38400*a^3 - 142560*a^2*b - 207900*a*b^2 - 150*(3465*b^3*d*x - 1280*a^3 - 4752*a^2*b - 6930*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 22*(5*(640*a^3 + 2376*a^2*b + 3465*a*b^2)*cosh(d*x + c)^9 - 36*(640*a^3 + 2376*a^2*b + 3465*a*b^2)*cosh(d*x + c)^7 + 105*(640*a^3 + 2376*a^2*b + 3087*a*b^2)*cosh(d*x + c)^5 - 150*(640*a^3 + 2376*a^2*b + 2415*a*b^2)*cosh(d*x + c)^3 + 90*(640*a^3 + 1872*a^2*b + 1533*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^2 - 4620*(128*a^3 + 144*a^2*b + 105*a*b^2)*cosh(d*x + c) + 11*((3465*b^3*d*x - 1280*a^3 - 4752*a^2*b - 6930*a*b^2)*cosh(d*x + c)^10 - 9*(3465*b^3*d*x - 1280*a^3 - 4752*a^2*b - 6930*a*b^2)*cosh(d*x + c)^8 + 35*(3465*b^3*d*x - 1280*a^3 - 4752*a^2*b - 6930*a*b^2)*cosh(d*x + c)^6 - 145530*b^3*d*x - 75*(3465*b^3*d*x - 1280*a^3 - 4752*a^2*b - 6930*a*b^2)*cosh(d*x + c)^4 + 53760*a^3 + 199584*a^2*b + 291060*a*b^2 + 90*(3465*b^3*d*x - 1280*a^3 - 4752*a^2*b - 6930*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c))/(d*sinh(d*x + c)^11 + 11*(5*d*cosh(d*x + c)^2 - d)*sinh(d*x + c)^9 + 11*(30*d*cosh(d*x + c)^4 - 36*d*cosh(d*x + c)^2 + 5*d)*sinh(d*x + c)^7 + 33*(14*d*cosh(d*x + c)^6 - 42*d*cosh(d*x + c)^4 + 35*d*cosh(d*x + c)^2 - 5*d)*sinh(d*x + c)^5 + 11*(15*d*cosh(d*x + c)^8 - 84*d*cosh(d*x + c)^6 + 175*d*cosh(d*x + c)^4 - 150*d*cosh(d*x + c)^2 + 30*d)*sinh(d*x + c)^3 + 11*(d*cosh(d*x + c)^10 - 9*d*cosh(d*x + c)^8 + 35*d*cosh(d*x + c)^6 - 75*d*cosh(d*x + c)^4 + 90*d*cosh(d*x + c)^2 - 42*d)*sinh(d*x + c))","B",0
225,1,2323,0,0.649297," ","integrate(csch(d*x+c)^14*(a+b*sinh(d*x+c)^4)^3,x, algorithm=""fricas"")","-\frac{4 \, {\left({\left(2560 \, a^{3} + 9152 \, a^{2} b + 12012 \, a b^{2} + 15015 \, b^{3}\right)} \cosh\left(d x + c\right)^{12} - 48 \, {\left(640 \, a^{3} + 2288 \, a^{2} b + 3003 \, a b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{11} + {\left(2560 \, a^{3} + 9152 \, a^{2} b + 12012 \, a b^{2} + 15015 \, b^{3}\right)} \sinh\left(d x + c\right)^{12} - 52 \, {\left(640 \, a^{3} + 2288 \, a^{2} b + 3003 \, a b^{2} + 3465 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} - 2 \, {\left(16640 \, a^{3} + 59488 \, a^{2} b + 78078 \, a b^{2} + 90090 \, b^{3} - 33 \, {\left(2560 \, a^{3} + 9152 \, a^{2} b + 12012 \, a b^{2} + 15015 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{10} - 40 \, {\left(22 \, {\left(640 \, a^{3} + 2288 \, a^{2} b + 3003 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} - 13 \, {\left(640 \, a^{3} + 2288 \, a^{2} b + 3003 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} + 78 \, {\left(2560 \, a^{3} + 9152 \, a^{2} b + 13552 \, a b^{2} + 12705 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 3 \, {\left(165 \, {\left(2560 \, a^{3} + 9152 \, a^{2} b + 12012 \, a b^{2} + 15015 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 66560 \, a^{3} + 237952 \, a^{2} b + 352352 \, a b^{2} + 330330 \, b^{3} - 780 \, {\left(640 \, a^{3} + 2288 \, a^{2} b + 3003 \, a b^{2} + 3465 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{8} - 96 \, {\left(33 \, {\left(640 \, a^{3} + 2288 \, a^{2} b + 3003 \, a b^{2}\right)} \cosh\left(d x + c\right)^{5} - 65 \, {\left(640 \, a^{3} + 2288 \, a^{2} b + 3003 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} + 52 \, {\left(320 \, a^{3} + 1144 \, a^{2} b + 1309 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} - 572 \, {\left(1280 \, a^{3} + 4576 \, a^{2} b + 7581 \, a b^{2} + 5775 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(231 \, {\left(2560 \, a^{3} + 9152 \, a^{2} b + 12012 \, a b^{2} + 15015 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} - 2730 \, {\left(640 \, a^{3} + 2288 \, a^{2} b + 3003 \, a b^{2} + 3465 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 183040 \, a^{3} - 654368 \, a^{2} b - 1084083 \, a b^{2} - 825825 \, b^{3} + 546 \, {\left(2560 \, a^{3} + 9152 \, a^{2} b + 13552 \, a b^{2} + 12705 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} - 24 \, {\left(132 \, {\left(640 \, a^{3} + 2288 \, a^{2} b + 3003 \, a b^{2}\right)} \cosh\left(d x + c\right)^{7} - 546 \, {\left(640 \, a^{3} + 2288 \, a^{2} b + 3003 \, a b^{2}\right)} \cosh\left(d x + c\right)^{5} + 1456 \, {\left(320 \, a^{3} + 1144 \, a^{2} b + 1309 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} - 143 \, {\left(1280 \, a^{3} + 4576 \, a^{2} b + 4011 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 143 \, {\left(12800 \, a^{3} + 53824 \, a^{2} b + 79884 \, a b^{2} + 51975 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + {\left(495 \, {\left(2560 \, a^{3} + 9152 \, a^{2} b + 12012 \, a b^{2} + 15015 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} - 10920 \, {\left(640 \, a^{3} + 2288 \, a^{2} b + 3003 \, a b^{2} + 3465 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 5460 \, {\left(2560 \, a^{3} + 9152 \, a^{2} b + 13552 \, a b^{2} + 12705 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 1830400 \, a^{3} + 7696832 \, a^{2} b + 11423412 \, a b^{2} + 7432425 \, b^{3} - 8580 \, {\left(1280 \, a^{3} + 4576 \, a^{2} b + 7581 \, a b^{2} + 5775 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} - 16 \, {\left(55 \, {\left(640 \, a^{3} + 2288 \, a^{2} b + 3003 \, a b^{2}\right)} \cosh\left(d x + c\right)^{9} - 390 \, {\left(640 \, a^{3} + 2288 \, a^{2} b + 3003 \, a b^{2}\right)} \cosh\left(d x + c\right)^{7} + 2184 \, {\left(320 \, a^{3} + 1144 \, a^{2} b + 1309 \, a b^{2}\right)} \cosh\left(d x + c\right)^{5} - 715 \, {\left(1280 \, a^{3} + 4576 \, a^{2} b + 4011 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} + 143 \, {\left(3200 \, a^{3} + 9424 \, a^{2} b + 6489 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4392960 \, a^{3} + 10323456 \, a^{2} b + 12108096 \, a b^{2} + 6936930 \, b^{3} - 3432 \, {\left(960 \, a^{3} + 4664 \, a^{2} b + 5859 \, a b^{2} + 3465 \, b^{3}\right)} \cosh\left(d x + c\right)^{2} + 6 \, {\left(11 \, {\left(2560 \, a^{3} + 9152 \, a^{2} b + 12012 \, a b^{2} + 15015 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} - 390 \, {\left(640 \, a^{3} + 2288 \, a^{2} b + 3003 \, a b^{2} + 3465 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 364 \, {\left(2560 \, a^{3} + 9152 \, a^{2} b + 13552 \, a b^{2} + 12705 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} - 1430 \, {\left(1280 \, a^{3} + 4576 \, a^{2} b + 7581 \, a b^{2} + 5775 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 549120 \, a^{3} - 2667808 \, a^{2} b - 3351348 \, a b^{2} - 1981980 \, b^{3} + 143 \, {\left(12800 \, a^{3} + 53824 \, a^{2} b + 79884 \, a b^{2} + 51975 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} - 8 \, {\left(6 \, {\left(640 \, a^{3} + 2288 \, a^{2} b + 3003 \, a b^{2}\right)} \cosh\left(d x + c\right)^{11} - 65 \, {\left(640 \, a^{3} + 2288 \, a^{2} b + 3003 \, a b^{2}\right)} \cosh\left(d x + c\right)^{9} + 624 \, {\left(320 \, a^{3} + 1144 \, a^{2} b + 1309 \, a b^{2}\right)} \cosh\left(d x + c\right)^{7} - 429 \, {\left(1280 \, a^{3} + 4576 \, a^{2} b + 4011 \, a b^{2}\right)} \cosh\left(d x + c\right)^{5} + 286 \, {\left(3200 \, a^{3} + 9424 \, a^{2} b + 6489 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} - 858 \, {\left(960 \, a^{3} + 1528 \, a^{2} b + 903 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}{15015 \, {\left(d \cosh\left(d x + c\right)^{14} + 14 \, d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{13} + d \sinh\left(d x + c\right)^{14} - 14 \, d \cosh\left(d x + c\right)^{12} + 7 \, {\left(13 \, d \cosh\left(d x + c\right)^{2} - 2 \, d\right)} \sinh\left(d x + c\right)^{12} + 4 \, {\left(91 \, d \cosh\left(d x + c\right)^{3} - 36 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{11} + 91 \, d \cosh\left(d x + c\right)^{10} + 7 \, {\left(143 \, d \cosh\left(d x + c\right)^{4} - 132 \, d \cosh\left(d x + c\right)^{2} + 13 \, d\right)} \sinh\left(d x + c\right)^{10} + 2 \, {\left(1001 \, d \cosh\left(d x + c\right)^{5} - 1320 \, d \cosh\left(d x + c\right)^{3} + 325 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} - 364 \, d \cosh\left(d x + c\right)^{8} + 7 \, {\left(429 \, d \cosh\left(d x + c\right)^{6} - 990 \, d \cosh\left(d x + c\right)^{4} + 585 \, d \cosh\left(d x + c\right)^{2} - 52 \, d\right)} \sinh\left(d x + c\right)^{8} + 8 \, {\left(429 \, d \cosh\left(d x + c\right)^{7} - 1188 \, d \cosh\left(d x + c\right)^{5} + 975 \, d \cosh\left(d x + c\right)^{3} - 208 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 1001 \, d \cosh\left(d x + c\right)^{6} + 7 \, {\left(429 \, d \cosh\left(d x + c\right)^{8} - 1848 \, d \cosh\left(d x + c\right)^{6} + 2730 \, d \cosh\left(d x + c\right)^{4} - 1456 \, d \cosh\left(d x + c\right)^{2} + 143 \, d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(1001 \, d \cosh\left(d x + c\right)^{9} - 4752 \, d \cosh\left(d x + c\right)^{7} + 8190 \, d \cosh\left(d x + c\right)^{5} - 5824 \, d \cosh\left(d x + c\right)^{3} + 1287 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 2002 \, d \cosh\left(d x + c\right)^{4} + 7 \, {\left(143 \, d \cosh\left(d x + c\right)^{10} - 990 \, d \cosh\left(d x + c\right)^{8} + 2730 \, d \cosh\left(d x + c\right)^{6} - 3640 \, d \cosh\left(d x + c\right)^{4} + 2145 \, d \cosh\left(d x + c\right)^{2} - 286 \, d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(91 \, d \cosh\left(d x + c\right)^{11} - 660 \, d \cosh\left(d x + c\right)^{9} + 1950 \, d \cosh\left(d x + c\right)^{7} - 2912 \, d \cosh\left(d x + c\right)^{5} + 2145 \, d \cosh\left(d x + c\right)^{3} - 572 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 3003 \, d \cosh\left(d x + c\right)^{2} + 7 \, {\left(13 \, d \cosh\left(d x + c\right)^{12} - 132 \, d \cosh\left(d x + c\right)^{10} + 585 \, d \cosh\left(d x + c\right)^{8} - 1456 \, d \cosh\left(d x + c\right)^{6} + 2145 \, d \cosh\left(d x + c\right)^{4} - 1716 \, d \cosh\left(d x + c\right)^{2} + 429 \, d\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(7 \, d \cosh\left(d x + c\right)^{13} - 72 \, d \cosh\left(d x + c\right)^{11} + 325 \, d \cosh\left(d x + c\right)^{9} - 832 \, d \cosh\left(d x + c\right)^{7} + 1287 \, d \cosh\left(d x + c\right)^{5} - 1144 \, d \cosh\left(d x + c\right)^{3} + 429 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) - 1716 \, d\right)}}"," ",0,"-4/15015*((2560*a^3 + 9152*a^2*b + 12012*a*b^2 + 15015*b^3)*cosh(d*x + c)^12 - 48*(640*a^3 + 2288*a^2*b + 3003*a*b^2)*cosh(d*x + c)*sinh(d*x + c)^11 + (2560*a^3 + 9152*a^2*b + 12012*a*b^2 + 15015*b^3)*sinh(d*x + c)^12 - 52*(640*a^3 + 2288*a^2*b + 3003*a*b^2 + 3465*b^3)*cosh(d*x + c)^10 - 2*(16640*a^3 + 59488*a^2*b + 78078*a*b^2 + 90090*b^3 - 33*(2560*a^3 + 9152*a^2*b + 12012*a*b^2 + 15015*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^10 - 40*(22*(640*a^3 + 2288*a^2*b + 3003*a*b^2)*cosh(d*x + c)^3 - 13*(640*a^3 + 2288*a^2*b + 3003*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^9 + 78*(2560*a^3 + 9152*a^2*b + 13552*a*b^2 + 12705*b^3)*cosh(d*x + c)^8 + 3*(165*(2560*a^3 + 9152*a^2*b + 12012*a*b^2 + 15015*b^3)*cosh(d*x + c)^4 + 66560*a^3 + 237952*a^2*b + 352352*a*b^2 + 330330*b^3 - 780*(640*a^3 + 2288*a^2*b + 3003*a*b^2 + 3465*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^8 - 96*(33*(640*a^3 + 2288*a^2*b + 3003*a*b^2)*cosh(d*x + c)^5 - 65*(640*a^3 + 2288*a^2*b + 3003*a*b^2)*cosh(d*x + c)^3 + 52*(320*a^3 + 1144*a^2*b + 1309*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^7 - 572*(1280*a^3 + 4576*a^2*b + 7581*a*b^2 + 5775*b^3)*cosh(d*x + c)^6 + 4*(231*(2560*a^3 + 9152*a^2*b + 12012*a*b^2 + 15015*b^3)*cosh(d*x + c)^6 - 2730*(640*a^3 + 2288*a^2*b + 3003*a*b^2 + 3465*b^3)*cosh(d*x + c)^4 - 183040*a^3 - 654368*a^2*b - 1084083*a*b^2 - 825825*b^3 + 546*(2560*a^3 + 9152*a^2*b + 13552*a*b^2 + 12705*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^6 - 24*(132*(640*a^3 + 2288*a^2*b + 3003*a*b^2)*cosh(d*x + c)^7 - 546*(640*a^3 + 2288*a^2*b + 3003*a*b^2)*cosh(d*x + c)^5 + 1456*(320*a^3 + 1144*a^2*b + 1309*a*b^2)*cosh(d*x + c)^3 - 143*(1280*a^3 + 4576*a^2*b + 4011*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^5 + 143*(12800*a^3 + 53824*a^2*b + 79884*a*b^2 + 51975*b^3)*cosh(d*x + c)^4 + (495*(2560*a^3 + 9152*a^2*b + 12012*a*b^2 + 15015*b^3)*cosh(d*x + c)^8 - 10920*(640*a^3 + 2288*a^2*b + 3003*a*b^2 + 3465*b^3)*cosh(d*x + c)^6 + 5460*(2560*a^3 + 9152*a^2*b + 13552*a*b^2 + 12705*b^3)*cosh(d*x + c)^4 + 1830400*a^3 + 7696832*a^2*b + 11423412*a*b^2 + 7432425*b^3 - 8580*(1280*a^3 + 4576*a^2*b + 7581*a*b^2 + 5775*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 - 16*(55*(640*a^3 + 2288*a^2*b + 3003*a*b^2)*cosh(d*x + c)^9 - 390*(640*a^3 + 2288*a^2*b + 3003*a*b^2)*cosh(d*x + c)^7 + 2184*(320*a^3 + 1144*a^2*b + 1309*a*b^2)*cosh(d*x + c)^5 - 715*(1280*a^3 + 4576*a^2*b + 4011*a*b^2)*cosh(d*x + c)^3 + 143*(3200*a^3 + 9424*a^2*b + 6489*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 4392960*a^3 + 10323456*a^2*b + 12108096*a*b^2 + 6936930*b^3 - 3432*(960*a^3 + 4664*a^2*b + 5859*a*b^2 + 3465*b^3)*cosh(d*x + c)^2 + 6*(11*(2560*a^3 + 9152*a^2*b + 12012*a*b^2 + 15015*b^3)*cosh(d*x + c)^10 - 390*(640*a^3 + 2288*a^2*b + 3003*a*b^2 + 3465*b^3)*cosh(d*x + c)^8 + 364*(2560*a^3 + 9152*a^2*b + 13552*a*b^2 + 12705*b^3)*cosh(d*x + c)^6 - 1430*(1280*a^3 + 4576*a^2*b + 7581*a*b^2 + 5775*b^3)*cosh(d*x + c)^4 - 549120*a^3 - 2667808*a^2*b - 3351348*a*b^2 - 1981980*b^3 + 143*(12800*a^3 + 53824*a^2*b + 79884*a*b^2 + 51975*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - 8*(6*(640*a^3 + 2288*a^2*b + 3003*a*b^2)*cosh(d*x + c)^11 - 65*(640*a^3 + 2288*a^2*b + 3003*a*b^2)*cosh(d*x + c)^9 + 624*(320*a^3 + 1144*a^2*b + 1309*a*b^2)*cosh(d*x + c)^7 - 429*(1280*a^3 + 4576*a^2*b + 4011*a*b^2)*cosh(d*x + c)^5 + 286*(3200*a^3 + 9424*a^2*b + 6489*a*b^2)*cosh(d*x + c)^3 - 858*(960*a^3 + 1528*a^2*b + 903*a*b^2)*cosh(d*x + c))*sinh(d*x + c))/(d*cosh(d*x + c)^14 + 14*d*cosh(d*x + c)*sinh(d*x + c)^13 + d*sinh(d*x + c)^14 - 14*d*cosh(d*x + c)^12 + 7*(13*d*cosh(d*x + c)^2 - 2*d)*sinh(d*x + c)^12 + 4*(91*d*cosh(d*x + c)^3 - 36*d*cosh(d*x + c))*sinh(d*x + c)^11 + 91*d*cosh(d*x + c)^10 + 7*(143*d*cosh(d*x + c)^4 - 132*d*cosh(d*x + c)^2 + 13*d)*sinh(d*x + c)^10 + 2*(1001*d*cosh(d*x + c)^5 - 1320*d*cosh(d*x + c)^3 + 325*d*cosh(d*x + c))*sinh(d*x + c)^9 - 364*d*cosh(d*x + c)^8 + 7*(429*d*cosh(d*x + c)^6 - 990*d*cosh(d*x + c)^4 + 585*d*cosh(d*x + c)^2 - 52*d)*sinh(d*x + c)^8 + 8*(429*d*cosh(d*x + c)^7 - 1188*d*cosh(d*x + c)^5 + 975*d*cosh(d*x + c)^3 - 208*d*cosh(d*x + c))*sinh(d*x + c)^7 + 1001*d*cosh(d*x + c)^6 + 7*(429*d*cosh(d*x + c)^8 - 1848*d*cosh(d*x + c)^6 + 2730*d*cosh(d*x + c)^4 - 1456*d*cosh(d*x + c)^2 + 143*d)*sinh(d*x + c)^6 + 2*(1001*d*cosh(d*x + c)^9 - 4752*d*cosh(d*x + c)^7 + 8190*d*cosh(d*x + c)^5 - 5824*d*cosh(d*x + c)^3 + 1287*d*cosh(d*x + c))*sinh(d*x + c)^5 - 2002*d*cosh(d*x + c)^4 + 7*(143*d*cosh(d*x + c)^10 - 990*d*cosh(d*x + c)^8 + 2730*d*cosh(d*x + c)^6 - 3640*d*cosh(d*x + c)^4 + 2145*d*cosh(d*x + c)^2 - 286*d)*sinh(d*x + c)^4 + 4*(91*d*cosh(d*x + c)^11 - 660*d*cosh(d*x + c)^9 + 1950*d*cosh(d*x + c)^7 - 2912*d*cosh(d*x + c)^5 + 2145*d*cosh(d*x + c)^3 - 572*d*cosh(d*x + c))*sinh(d*x + c)^3 + 3003*d*cosh(d*x + c)^2 + 7*(13*d*cosh(d*x + c)^12 - 132*d*cosh(d*x + c)^10 + 585*d*cosh(d*x + c)^8 - 1456*d*cosh(d*x + c)^6 + 2145*d*cosh(d*x + c)^4 - 1716*d*cosh(d*x + c)^2 + 429*d)*sinh(d*x + c)^2 + 2*(7*d*cosh(d*x + c)^13 - 72*d*cosh(d*x + c)^11 + 325*d*cosh(d*x + c)^9 - 832*d*cosh(d*x + c)^7 + 1287*d*cosh(d*x + c)^5 - 1144*d*cosh(d*x + c)^3 + 429*d*cosh(d*x + c))*sinh(d*x + c) - 1716*d)","B",0
226,1,2967,0,0.872309," ","integrate(csch(d*x+c)^16*(a+b*sinh(d*x+c)^4)^3,x, algorithm=""fricas"")","\frac{8 \, {\left({\left(3584 \, a^{3} + 12480 \, a^{2} b + 15444 \, a b^{2} - 15015 \, b^{3}\right)} \cosh\left(d x + c\right)^{13} + 13 \, {\left(3584 \, a^{3} + 12480 \, a^{2} b + 15444 \, a b^{2} - 15015 \, b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{12} - 2 \, {\left(1792 \, a^{3} + 6240 \, a^{2} b + 7722 \, a b^{2} + 15015 \, b^{3}\right)} \sinh\left(d x + c\right)^{13} - 15 \, {\left(3584 \, a^{3} + 12480 \, a^{2} b + 15444 \, a b^{2} - 11011 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} + 6 \, {\left(8960 \, a^{3} + 31200 \, a^{2} b + 38610 \, a b^{2} + 65065 \, b^{3} - 26 \, {\left(1792 \, a^{3} + 6240 \, a^{2} b + 7722 \, a b^{2} + 15015 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{11} + 11 \, {\left(26 \, {\left(3584 \, a^{3} + 12480 \, a^{2} b + 15444 \, a b^{2} - 15015 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 15 \, {\left(3584 \, a^{3} + 12480 \, a^{2} b + 15444 \, a b^{2} - 11011 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{10} + 210 \, {\left(1792 \, a^{3} + 6240 \, a^{2} b + 5148 \, a b^{2} - 3861 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} - 10 \, {\left(143 \, {\left(1792 \, a^{3} + 6240 \, a^{2} b + 7722 \, a b^{2} + 15015 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 37632 \, a^{3} + 131040 \, a^{2} b + 216216 \, a b^{2} + 234234 \, b^{3} - 165 \, {\left(1792 \, a^{3} + 6240 \, a^{2} b + 7722 \, a b^{2} + 13013 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{9} + 9 \, {\left(143 \, {\left(3584 \, a^{3} + 12480 \, a^{2} b + 15444 \, a b^{2} - 15015 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 275 \, {\left(3584 \, a^{3} + 12480 \, a^{2} b + 15444 \, a b^{2} - 11011 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 210 \, {\left(1792 \, a^{3} + 6240 \, a^{2} b + 5148 \, a b^{2} - 3861 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{8} - 182 \, {\left(8960 \, a^{3} + 31200 \, a^{2} b + 13068 \, a b^{2} - 12705 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} - 4 \, {\left(858 \, {\left(1792 \, a^{3} + 6240 \, a^{2} b + 7722 \, a b^{2} + 15015 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} - 2475 \, {\left(1792 \, a^{3} + 6240 \, a^{2} b + 7722 \, a b^{2} + 13013 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 407680 \, a^{3} - 1419600 \, a^{2} b - 2918916 \, a b^{2} - 2147145 \, b^{3} + 3780 \, {\left(896 \, a^{3} + 3120 \, a^{2} b + 5148 \, a b^{2} + 5577 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(858 \, {\left(3584 \, a^{3} + 12480 \, a^{2} b + 15444 \, a b^{2} - 15015 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} - 3465 \, {\left(3584 \, a^{3} + 12480 \, a^{2} b + 15444 \, a b^{2} - 11011 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 8820 \, {\left(1792 \, a^{3} + 6240 \, a^{2} b + 5148 \, a b^{2} - 3861 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 637 \, {\left(8960 \, a^{3} + 31200 \, a^{2} b + 13068 \, a b^{2} - 12705 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} + 1365 \, {\left(3584 \, a^{3} + 8256 \, a^{2} b + 1980 \, a b^{2} - 3025 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 6 \, {\left(429 \, {\left(1792 \, a^{3} + 6240 \, a^{2} b + 7722 \, a b^{2} + 15015 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} - 2310 \, {\left(1792 \, a^{3} + 6240 \, a^{2} b + 7722 \, a b^{2} + 13013 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 8820 \, {\left(896 \, a^{3} + 3120 \, a^{2} b + 5148 \, a b^{2} + 5577 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 815360 \, a^{3} + 3800160 \, a^{2} b + 6396390 \, a b^{2} + 3578575 \, b^{3} - 1274 \, {\left(4480 \, a^{3} + 15600 \, a^{2} b + 32076 \, a b^{2} + 23595 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{5} + 5 \, {\left(143 \, {\left(3584 \, a^{3} + 12480 \, a^{2} b + 15444 \, a b^{2} - 15015 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} - 990 \, {\left(3584 \, a^{3} + 12480 \, a^{2} b + 15444 \, a b^{2} - 11011 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 5292 \, {\left(1792 \, a^{3} + 6240 \, a^{2} b + 5148 \, a b^{2} - 3861 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 1274 \, {\left(8960 \, a^{3} + 31200 \, a^{2} b + 13068 \, a b^{2} - 12705 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 1365 \, {\left(3584 \, a^{3} + 8256 \, a^{2} b + 1980 \, a b^{2} - 3025 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} - 429 \, {\left(25088 \, a^{3} + 24000 \, a^{2} b + 3492 \, a b^{2} - 10395 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 2 \, {\left(286 \, {\left(1792 \, a^{3} + 6240 \, a^{2} b + 7722 \, a b^{2} + 15015 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} - 2475 \, {\left(1792 \, a^{3} + 6240 \, a^{2} b + 7722 \, a b^{2} + 13013 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 17640 \, {\left(896 \, a^{3} + 3120 \, a^{2} b + 5148 \, a b^{2} + 5577 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} - 6370 \, {\left(4480 \, a^{3} + 15600 \, a^{2} b + 32076 \, a b^{2} + 23595 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 5381376 \, a^{3} - 32329440 \, a^{2} b - 40980654 \, a b^{2} - 19324305 \, b^{3} + 13650 \, {\left(1792 \, a^{3} + 8352 \, a^{2} b + 14058 \, a b^{2} + 7865 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + 3 \, {\left(26 \, {\left(3584 \, a^{3} + 12480 \, a^{2} b + 15444 \, a b^{2} - 15015 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} - 275 \, {\left(3584 \, a^{3} + 12480 \, a^{2} b + 15444 \, a b^{2} - 11011 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + 2520 \, {\left(1792 \, a^{3} + 6240 \, a^{2} b + 5148 \, a b^{2} - 3861 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} - 1274 \, {\left(8960 \, a^{3} + 31200 \, a^{2} b + 13068 \, a b^{2} - 12705 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 4550 \, {\left(3584 \, a^{3} + 8256 \, a^{2} b + 1980 \, a b^{2} - 3025 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 429 \, {\left(25088 \, a^{3} + 24000 \, a^{2} b + 3492 \, a b^{2} - 10395 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 2860 \, {\left(1792 \, a^{3} - 1248 \, a^{2} b - 108 \, a b^{2} + 693 \, b^{3}\right)} \cosh\left(d x + c\right) - 2 \, {\left(13 \, {\left(1792 \, a^{3} + 6240 \, a^{2} b + 7722 \, a b^{2} + 15015 \, b^{3}\right)} \cosh\left(d x + c\right)^{12} - 165 \, {\left(1792 \, a^{3} + 6240 \, a^{2} b + 7722 \, a b^{2} + 13013 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} + 1890 \, {\left(896 \, a^{3} + 3120 \, a^{2} b + 5148 \, a b^{2} + 5577 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} - 1274 \, {\left(4480 \, a^{3} + 15600 \, a^{2} b + 32076 \, a b^{2} + 23595 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 6825 \, {\left(1792 \, a^{3} + 8352 \, a^{2} b + 14058 \, a b^{2} + 7865 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 20500480 \, a^{3} + 54912000 \, a^{2} b + 59304960 \, a b^{2} + 25765740 \, b^{3} - 1287 \, {\left(12544 \, a^{3} + 75360 \, a^{2} b + 95526 \, a b^{2} + 45045 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)\right)}}{45045 \, {\left(d \cosh\left(d x + c\right)^{17} + 17 \, d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{16} + d \sinh\left(d x + c\right)^{17} - 15 \, d \cosh\left(d x + c\right)^{15} + {\left(136 \, d \cosh\left(d x + c\right)^{2} - 15 \, d\right)} \sinh\left(d x + c\right)^{15} + 5 \, {\left(136 \, d \cosh\left(d x + c\right)^{3} - 45 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{14} + 104 \, d \cosh\left(d x + c\right)^{13} + {\left(2380 \, d \cosh\left(d x + c\right)^{4} - 1575 \, d \cosh\left(d x + c\right)^{2} + 106 \, d\right)} \sinh\left(d x + c\right)^{13} + 13 \, {\left(476 \, d \cosh\left(d x + c\right)^{5} - 525 \, d \cosh\left(d x + c\right)^{3} + 104 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{12} - 440 \, d \cosh\left(d x + c\right)^{11} + {\left(12376 \, d \cosh\left(d x + c\right)^{6} - 20475 \, d \cosh\left(d x + c\right)^{4} + 8268 \, d \cosh\left(d x + c\right)^{2} - 470 \, d\right)} \sinh\left(d x + c\right)^{11} + 11 \, {\left(1768 \, d \cosh\left(d x + c\right)^{7} - 4095 \, d \cosh\left(d x + c\right)^{5} + 2704 \, d \cosh\left(d x + c\right)^{3} - 440 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{10} + 1260 \, d \cosh\left(d x + c\right)^{9} + 5 \, {\left(4862 \, d \cosh\left(d x + c\right)^{8} - 15015 \, d \cosh\left(d x + c\right)^{6} + 15158 \, d \cosh\left(d x + c\right)^{4} - 5170 \, d \cosh\left(d x + c\right)^{2} + 294 \, d\right)} \sinh\left(d x + c\right)^{9} + {\left(24310 \, d \cosh\left(d x + c\right)^{9} - 96525 \, d \cosh\left(d x + c\right)^{7} + 133848 \, d \cosh\left(d x + c\right)^{5} - 72600 \, d \cosh\left(d x + c\right)^{3} + 11340 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{8} - 2548 \, d \cosh\left(d x + c\right)^{7} + {\left(19448 \, d \cosh\left(d x + c\right)^{10} - 96525 \, d \cosh\left(d x + c\right)^{8} + 181896 \, d \cosh\left(d x + c\right)^{6} - 155100 \, d \cosh\left(d x + c\right)^{4} + 52920 \, d \cosh\left(d x + c\right)^{2} - 3458 \, d\right)} \sinh\left(d x + c\right)^{7} + {\left(12376 \, d \cosh\left(d x + c\right)^{11} - 75075 \, d \cosh\left(d x + c\right)^{9} + 178464 \, d \cosh\left(d x + c\right)^{7} - 203280 \, d \cosh\left(d x + c\right)^{5} + 105840 \, d \cosh\left(d x + c\right)^{3} - 17836 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} + 3640 \, d \cosh\left(d x + c\right)^{5} + {\left(6188 \, d \cosh\left(d x + c\right)^{12} - 45045 \, d \cosh\left(d x + c\right)^{10} + 136422 \, d \cosh\left(d x + c\right)^{8} - 217140 \, d \cosh\left(d x + c\right)^{6} + 185220 \, d \cosh\left(d x + c\right)^{4} - 72618 \, d \cosh\left(d x + c\right)^{2} + 6370 \, d\right)} \sinh\left(d x + c\right)^{5} + 5 \, {\left(476 \, d \cosh\left(d x + c\right)^{13} - 4095 \, d \cosh\left(d x + c\right)^{11} + 14872 \, d \cosh\left(d x + c\right)^{9} - 29040 \, d \cosh\left(d x + c\right)^{7} + 31752 \, d \cosh\left(d x + c\right)^{5} - 17836 \, d \cosh\left(d x + c\right)^{3} + 3640 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} - 3432 \, d \cosh\left(d x + c\right)^{3} + {\left(680 \, d \cosh\left(d x + c\right)^{14} - 6825 \, d \cosh\left(d x + c\right)^{12} + 30316 \, d \cosh\left(d x + c\right)^{10} - 77550 \, d \cosh\left(d x + c\right)^{8} + 123480 \, d \cosh\left(d x + c\right)^{6} - 121030 \, d \cosh\left(d x + c\right)^{4} + 63700 \, d \cosh\left(d x + c\right)^{2} - 9438 \, d\right)} \sinh\left(d x + c\right)^{3} + {\left(136 \, d \cosh\left(d x + c\right)^{15} - 1575 \, d \cosh\left(d x + c\right)^{13} + 8112 \, d \cosh\left(d x + c\right)^{11} - 24200 \, d \cosh\left(d x + c\right)^{9} + 45360 \, d \cosh\left(d x + c\right)^{7} - 53508 \, d \cosh\left(d x + c\right)^{5} + 36400 \, d \cosh\left(d x + c\right)^{3} - 10296 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 1430 \, d \cosh\left(d x + c\right) + {\left(17 \, d \cosh\left(d x + c\right)^{16} - 225 \, d \cosh\left(d x + c\right)^{14} + 1378 \, d \cosh\left(d x + c\right)^{12} - 5170 \, d \cosh\left(d x + c\right)^{10} + 13230 \, d \cosh\left(d x + c\right)^{8} - 24206 \, d \cosh\left(d x + c\right)^{6} + 31850 \, d \cosh\left(d x + c\right)^{4} - 28314 \, d \cosh\left(d x + c\right)^{2} + 11440 \, d\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"8/45045*((3584*a^3 + 12480*a^2*b + 15444*a*b^2 - 15015*b^3)*cosh(d*x + c)^13 + 13*(3584*a^3 + 12480*a^2*b + 15444*a*b^2 - 15015*b^3)*cosh(d*x + c)*sinh(d*x + c)^12 - 2*(1792*a^3 + 6240*a^2*b + 7722*a*b^2 + 15015*b^3)*sinh(d*x + c)^13 - 15*(3584*a^3 + 12480*a^2*b + 15444*a*b^2 - 11011*b^3)*cosh(d*x + c)^11 + 6*(8960*a^3 + 31200*a^2*b + 38610*a*b^2 + 65065*b^3 - 26*(1792*a^3 + 6240*a^2*b + 7722*a*b^2 + 15015*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^11 + 11*(26*(3584*a^3 + 12480*a^2*b + 15444*a*b^2 - 15015*b^3)*cosh(d*x + c)^3 - 15*(3584*a^3 + 12480*a^2*b + 15444*a*b^2 - 11011*b^3)*cosh(d*x + c))*sinh(d*x + c)^10 + 210*(1792*a^3 + 6240*a^2*b + 5148*a*b^2 - 3861*b^3)*cosh(d*x + c)^9 - 10*(143*(1792*a^3 + 6240*a^2*b + 7722*a*b^2 + 15015*b^3)*cosh(d*x + c)^4 + 37632*a^3 + 131040*a^2*b + 216216*a*b^2 + 234234*b^3 - 165*(1792*a^3 + 6240*a^2*b + 7722*a*b^2 + 13013*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^9 + 9*(143*(3584*a^3 + 12480*a^2*b + 15444*a*b^2 - 15015*b^3)*cosh(d*x + c)^5 - 275*(3584*a^3 + 12480*a^2*b + 15444*a*b^2 - 11011*b^3)*cosh(d*x + c)^3 + 210*(1792*a^3 + 6240*a^2*b + 5148*a*b^2 - 3861*b^3)*cosh(d*x + c))*sinh(d*x + c)^8 - 182*(8960*a^3 + 31200*a^2*b + 13068*a*b^2 - 12705*b^3)*cosh(d*x + c)^7 - 4*(858*(1792*a^3 + 6240*a^2*b + 7722*a*b^2 + 15015*b^3)*cosh(d*x + c)^6 - 2475*(1792*a^3 + 6240*a^2*b + 7722*a*b^2 + 13013*b^3)*cosh(d*x + c)^4 - 407680*a^3 - 1419600*a^2*b - 2918916*a*b^2 - 2147145*b^3 + 3780*(896*a^3 + 3120*a^2*b + 5148*a*b^2 + 5577*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^7 + 2*(858*(3584*a^3 + 12480*a^2*b + 15444*a*b^2 - 15015*b^3)*cosh(d*x + c)^7 - 3465*(3584*a^3 + 12480*a^2*b + 15444*a*b^2 - 11011*b^3)*cosh(d*x + c)^5 + 8820*(1792*a^3 + 6240*a^2*b + 5148*a*b^2 - 3861*b^3)*cosh(d*x + c)^3 - 637*(8960*a^3 + 31200*a^2*b + 13068*a*b^2 - 12705*b^3)*cosh(d*x + c))*sinh(d*x + c)^6 + 1365*(3584*a^3 + 8256*a^2*b + 1980*a*b^2 - 3025*b^3)*cosh(d*x + c)^5 - 6*(429*(1792*a^3 + 6240*a^2*b + 7722*a*b^2 + 15015*b^3)*cosh(d*x + c)^8 - 2310*(1792*a^3 + 6240*a^2*b + 7722*a*b^2 + 13013*b^3)*cosh(d*x + c)^6 + 8820*(896*a^3 + 3120*a^2*b + 5148*a*b^2 + 5577*b^3)*cosh(d*x + c)^4 + 815360*a^3 + 3800160*a^2*b + 6396390*a*b^2 + 3578575*b^3 - 1274*(4480*a^3 + 15600*a^2*b + 32076*a*b^2 + 23595*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 5*(143*(3584*a^3 + 12480*a^2*b + 15444*a*b^2 - 15015*b^3)*cosh(d*x + c)^9 - 990*(3584*a^3 + 12480*a^2*b + 15444*a*b^2 - 11011*b^3)*cosh(d*x + c)^7 + 5292*(1792*a^3 + 6240*a^2*b + 5148*a*b^2 - 3861*b^3)*cosh(d*x + c)^5 - 1274*(8960*a^3 + 31200*a^2*b + 13068*a*b^2 - 12705*b^3)*cosh(d*x + c)^3 + 1365*(3584*a^3 + 8256*a^2*b + 1980*a*b^2 - 3025*b^3)*cosh(d*x + c))*sinh(d*x + c)^4 - 429*(25088*a^3 + 24000*a^2*b + 3492*a*b^2 - 10395*b^3)*cosh(d*x + c)^3 - 2*(286*(1792*a^3 + 6240*a^2*b + 7722*a*b^2 + 15015*b^3)*cosh(d*x + c)^10 - 2475*(1792*a^3 + 6240*a^2*b + 7722*a*b^2 + 13013*b^3)*cosh(d*x + c)^8 + 17640*(896*a^3 + 3120*a^2*b + 5148*a*b^2 + 5577*b^3)*cosh(d*x + c)^6 - 6370*(4480*a^3 + 15600*a^2*b + 32076*a*b^2 + 23595*b^3)*cosh(d*x + c)^4 - 5381376*a^3 - 32329440*a^2*b - 40980654*a*b^2 - 19324305*b^3 + 13650*(1792*a^3 + 8352*a^2*b + 14058*a*b^2 + 7865*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 3*(26*(3584*a^3 + 12480*a^2*b + 15444*a*b^2 - 15015*b^3)*cosh(d*x + c)^11 - 275*(3584*a^3 + 12480*a^2*b + 15444*a*b^2 - 11011*b^3)*cosh(d*x + c)^9 + 2520*(1792*a^3 + 6240*a^2*b + 5148*a*b^2 - 3861*b^3)*cosh(d*x + c)^7 - 1274*(8960*a^3 + 31200*a^2*b + 13068*a*b^2 - 12705*b^3)*cosh(d*x + c)^5 + 4550*(3584*a^3 + 8256*a^2*b + 1980*a*b^2 - 3025*b^3)*cosh(d*x + c)^3 - 429*(25088*a^3 + 24000*a^2*b + 3492*a*b^2 - 10395*b^3)*cosh(d*x + c))*sinh(d*x + c)^2 - 2860*(1792*a^3 - 1248*a^2*b - 108*a*b^2 + 693*b^3)*cosh(d*x + c) - 2*(13*(1792*a^3 + 6240*a^2*b + 7722*a*b^2 + 15015*b^3)*cosh(d*x + c)^12 - 165*(1792*a^3 + 6240*a^2*b + 7722*a*b^2 + 13013*b^3)*cosh(d*x + c)^10 + 1890*(896*a^3 + 3120*a^2*b + 5148*a*b^2 + 5577*b^3)*cosh(d*x + c)^8 - 1274*(4480*a^3 + 15600*a^2*b + 32076*a*b^2 + 23595*b^3)*cosh(d*x + c)^6 + 6825*(1792*a^3 + 8352*a^2*b + 14058*a*b^2 + 7865*b^3)*cosh(d*x + c)^4 + 20500480*a^3 + 54912000*a^2*b + 59304960*a*b^2 + 25765740*b^3 - 1287*(12544*a^3 + 75360*a^2*b + 95526*a*b^2 + 45045*b^3)*cosh(d*x + c)^2)*sinh(d*x + c))/(d*cosh(d*x + c)^17 + 17*d*cosh(d*x + c)*sinh(d*x + c)^16 + d*sinh(d*x + c)^17 - 15*d*cosh(d*x + c)^15 + (136*d*cosh(d*x + c)^2 - 15*d)*sinh(d*x + c)^15 + 5*(136*d*cosh(d*x + c)^3 - 45*d*cosh(d*x + c))*sinh(d*x + c)^14 + 104*d*cosh(d*x + c)^13 + (2380*d*cosh(d*x + c)^4 - 1575*d*cosh(d*x + c)^2 + 106*d)*sinh(d*x + c)^13 + 13*(476*d*cosh(d*x + c)^5 - 525*d*cosh(d*x + c)^3 + 104*d*cosh(d*x + c))*sinh(d*x + c)^12 - 440*d*cosh(d*x + c)^11 + (12376*d*cosh(d*x + c)^6 - 20475*d*cosh(d*x + c)^4 + 8268*d*cosh(d*x + c)^2 - 470*d)*sinh(d*x + c)^11 + 11*(1768*d*cosh(d*x + c)^7 - 4095*d*cosh(d*x + c)^5 + 2704*d*cosh(d*x + c)^3 - 440*d*cosh(d*x + c))*sinh(d*x + c)^10 + 1260*d*cosh(d*x + c)^9 + 5*(4862*d*cosh(d*x + c)^8 - 15015*d*cosh(d*x + c)^6 + 15158*d*cosh(d*x + c)^4 - 5170*d*cosh(d*x + c)^2 + 294*d)*sinh(d*x + c)^9 + (24310*d*cosh(d*x + c)^9 - 96525*d*cosh(d*x + c)^7 + 133848*d*cosh(d*x + c)^5 - 72600*d*cosh(d*x + c)^3 + 11340*d*cosh(d*x + c))*sinh(d*x + c)^8 - 2548*d*cosh(d*x + c)^7 + (19448*d*cosh(d*x + c)^10 - 96525*d*cosh(d*x + c)^8 + 181896*d*cosh(d*x + c)^6 - 155100*d*cosh(d*x + c)^4 + 52920*d*cosh(d*x + c)^2 - 3458*d)*sinh(d*x + c)^7 + (12376*d*cosh(d*x + c)^11 - 75075*d*cosh(d*x + c)^9 + 178464*d*cosh(d*x + c)^7 - 203280*d*cosh(d*x + c)^5 + 105840*d*cosh(d*x + c)^3 - 17836*d*cosh(d*x + c))*sinh(d*x + c)^6 + 3640*d*cosh(d*x + c)^5 + (6188*d*cosh(d*x + c)^12 - 45045*d*cosh(d*x + c)^10 + 136422*d*cosh(d*x + c)^8 - 217140*d*cosh(d*x + c)^6 + 185220*d*cosh(d*x + c)^4 - 72618*d*cosh(d*x + c)^2 + 6370*d)*sinh(d*x + c)^5 + 5*(476*d*cosh(d*x + c)^13 - 4095*d*cosh(d*x + c)^11 + 14872*d*cosh(d*x + c)^9 - 29040*d*cosh(d*x + c)^7 + 31752*d*cosh(d*x + c)^5 - 17836*d*cosh(d*x + c)^3 + 3640*d*cosh(d*x + c))*sinh(d*x + c)^4 - 3432*d*cosh(d*x + c)^3 + (680*d*cosh(d*x + c)^14 - 6825*d*cosh(d*x + c)^12 + 30316*d*cosh(d*x + c)^10 - 77550*d*cosh(d*x + c)^8 + 123480*d*cosh(d*x + c)^6 - 121030*d*cosh(d*x + c)^4 + 63700*d*cosh(d*x + c)^2 - 9438*d)*sinh(d*x + c)^3 + (136*d*cosh(d*x + c)^15 - 1575*d*cosh(d*x + c)^13 + 8112*d*cosh(d*x + c)^11 - 24200*d*cosh(d*x + c)^9 + 45360*d*cosh(d*x + c)^7 - 53508*d*cosh(d*x + c)^5 + 36400*d*cosh(d*x + c)^3 - 10296*d*cosh(d*x + c))*sinh(d*x + c)^2 + 1430*d*cosh(d*x + c) + (17*d*cosh(d*x + c)^16 - 225*d*cosh(d*x + c)^14 + 1378*d*cosh(d*x + c)^12 - 5170*d*cosh(d*x + c)^10 + 13230*d*cosh(d*x + c)^8 - 24206*d*cosh(d*x + c)^6 + 31850*d*cosh(d*x + c)^4 - 28314*d*cosh(d*x + c)^2 + 11440*d)*sinh(d*x + c))","B",0
227,1,3585,0,0.783180," ","integrate(csch(d*x+c)^18*(a+b*sinh(d*x+c)^4)^3,x, algorithm=""fricas"")","-\frac{16 \, {\left({\left(28672 \, a^{3} + 97920 \, a^{2} b + 116688 \, a b^{2} + 561561 \, b^{3}\right)} \cosh\left(d x + c\right)^{14} - 14 \, {\left(28672 \, a^{3} + 97920 \, a^{2} b + 116688 \, a b^{2} - 459459 \, b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{13} + {\left(28672 \, a^{3} + 97920 \, a^{2} b + 116688 \, a b^{2} + 561561 \, b^{3}\right)} \sinh\left(d x + c\right)^{14} - 34 \, {\left(14336 \, a^{3} + 48960 \, a^{2} b + 58344 \, a b^{2} + 213213 \, b^{3}\right)} \cosh\left(d x + c\right)^{12} - {\left(487424 \, a^{3} + 1664640 \, a^{2} b + 1983696 \, a b^{2} + 7249242 \, b^{3} - 91 \, {\left(28672 \, a^{3} + 97920 \, a^{2} b + 116688 \, a b^{2} + 561561 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{12} - 4 \, {\left(91 \, {\left(28672 \, a^{3} + 97920 \, a^{2} b + 116688 \, a b^{2} - 459459 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 204 \, {\left(7168 \, a^{3} + 24480 \, a^{2} b + 29172 \, a b^{2} - 81081 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{11} + 17 \, {\left(229376 \, a^{3} + 783360 \, a^{2} b + 1798368 \, a b^{2} + 2573571 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} + {\left(1001 \, {\left(28672 \, a^{3} + 97920 \, a^{2} b + 116688 \, a b^{2} + 561561 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 3899392 \, a^{3} + 13317120 \, a^{2} b + 30572256 \, a b^{2} + 43750707 \, b^{3} - 2244 \, {\left(14336 \, a^{3} + 48960 \, a^{2} b + 58344 \, a b^{2} + 213213 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{10} - 2 \, {\left(1001 \, {\left(28672 \, a^{3} + 97920 \, a^{2} b + 116688 \, a b^{2} - 459459 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 7480 \, {\left(7168 \, a^{3} + 24480 \, a^{2} b + 29172 \, a b^{2} - 81081 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 85 \, {\left(229376 \, a^{3} + 783360 \, a^{2} b + 68640 \, a b^{2} - 1756755 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} - 68 \, {\left(286720 \, a^{3} + 979200 \, a^{2} b + 3040752 \, a b^{2} + 2411409 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + {\left(3003 \, {\left(28672 \, a^{3} + 97920 \, a^{2} b + 116688 \, a b^{2} + 561561 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} - 16830 \, {\left(14336 \, a^{3} + 48960 \, a^{2} b + 58344 \, a b^{2} + 213213 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 19496960 \, a^{3} - 66585600 \, a^{2} b - 206771136 \, a b^{2} - 163975812 \, b^{3} + 765 \, {\left(229376 \, a^{3} + 783360 \, a^{2} b + 1798368 \, a b^{2} + 2573571 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{8} - 8 \, {\left(429 \, {\left(28672 \, a^{3} + 97920 \, a^{2} b + 116688 \, a b^{2} - 459459 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} - 6732 \, {\left(7168 \, a^{3} + 24480 \, a^{2} b + 29172 \, a b^{2} - 81081 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 255 \, {\left(229376 \, a^{3} + 783360 \, a^{2} b + 68640 \, a b^{2} - 1756755 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 272 \, {\left(71680 \, a^{3} + 244800 \, a^{2} b - 176748 \, a b^{2} - 351351 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 17 \, {\left(4014080 \, a^{3} + 23592960 \, a^{2} b + 45412224 \, a b^{2} + 25138113 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + {\left(3003 \, {\left(28672 \, a^{3} + 97920 \, a^{2} b + 116688 \, a b^{2} + 561561 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} - 31416 \, {\left(14336 \, a^{3} + 48960 \, a^{2} b + 58344 \, a b^{2} + 213213 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 3570 \, {\left(229376 \, a^{3} + 783360 \, a^{2} b + 1798368 \, a b^{2} + 2573571 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 68239360 \, a^{3} + 401080320 \, a^{2} b + 772007808 \, a b^{2} + 427347921 \, b^{3} - 1904 \, {\left(286720 \, a^{3} + 979200 \, a^{2} b + 3040752 \, a b^{2} + 2411409 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} - 2 \, {\left(1001 \, {\left(28672 \, a^{3} + 97920 \, a^{2} b + 116688 \, a b^{2} - 459459 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} - 26928 \, {\left(7168 \, a^{3} + 24480 \, a^{2} b + 29172 \, a b^{2} - 81081 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 2142 \, {\left(229376 \, a^{3} + 783360 \, a^{2} b + 68640 \, a b^{2} - 1756755 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 7616 \, {\left(71680 \, a^{3} + 244800 \, a^{2} b - 176748 \, a b^{2} - 351351 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 51 \, {\left(4014080 \, a^{3} + 3824640 \, a^{2} b - 12739584 \, a b^{2} - 11594583 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 442 \, {\left(401408 \, a^{3} + 3176640 \, a^{2} b + 4162488 \, a b^{2} + 1857471 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + {\left(1001 \, {\left(28672 \, a^{3} + 97920 \, a^{2} b + 116688 \, a b^{2} + 561561 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} - 16830 \, {\left(14336 \, a^{3} + 48960 \, a^{2} b + 58344 \, a b^{2} + 213213 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 3570 \, {\left(229376 \, a^{3} + 783360 \, a^{2} b + 1798368 \, a b^{2} + 2573571 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} - 4760 \, {\left(286720 \, a^{3} + 979200 \, a^{2} b + 3040752 \, a b^{2} + 2411409 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 177422336 \, a^{3} - 1404074880 \, a^{2} b - 1839819696 \, a b^{2} - 821002182 \, b^{3} + 255 \, {\left(4014080 \, a^{3} + 23592960 \, a^{2} b + 45412224 \, a b^{2} + 25138113 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} - 4 \, {\left(91 \, {\left(28672 \, a^{3} + 97920 \, a^{2} b + 116688 \, a b^{2} - 459459 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} - 3740 \, {\left(7168 \, a^{3} + 24480 \, a^{2} b + 29172 \, a b^{2} - 81081 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + 510 \, {\left(229376 \, a^{3} + 783360 \, a^{2} b + 68640 \, a b^{2} - 1756755 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} - 3808 \, {\left(71680 \, a^{3} + 244800 \, a^{2} b - 176748 \, a b^{2} - 351351 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 85 \, {\left(4014080 \, a^{3} + 3824640 \, a^{2} b - 12739584 \, a b^{2} - 11594583 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 884 \, {\left(200704 \, a^{3} - 217440 \, a^{2} b - 480876 \, a b^{2} - 297297 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 557613056 \, a^{3} - 1736317440 \, a^{2} b - 1775057856 \, a b^{2} - 680611932 \, b^{3} + 221 \, {\left(4759552 \, a^{3} + 12643200 \, a^{2} b + 13669392 \, a b^{2} + 5435199 \, b^{3}\right)} \cosh\left(d x + c\right)^{2} + {\left(91 \, {\left(28672 \, a^{3} + 97920 \, a^{2} b + 116688 \, a b^{2} + 561561 \, b^{3}\right)} \cosh\left(d x + c\right)^{12} - 2244 \, {\left(14336 \, a^{3} + 48960 \, a^{2} b + 58344 \, a b^{2} + 213213 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} + 765 \, {\left(229376 \, a^{3} + 783360 \, a^{2} b + 1798368 \, a b^{2} + 2573571 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} - 1904 \, {\left(286720 \, a^{3} + 979200 \, a^{2} b + 3040752 \, a b^{2} + 2411409 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 255 \, {\left(4014080 \, a^{3} + 23592960 \, a^{2} b + 45412224 \, a b^{2} + 25138113 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 1051860992 \, a^{3} + 2794147200 \, a^{2} b + 3020935632 \, a b^{2} + 1201178979 \, b^{3} - 2652 \, {\left(401408 \, a^{3} + 3176640 \, a^{2} b + 4162488 \, a b^{2} + 1857471 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} - 2 \, {\left(7 \, {\left(28672 \, a^{3} + 97920 \, a^{2} b + 116688 \, a b^{2} - 459459 \, b^{3}\right)} \cosh\left(d x + c\right)^{13} - 408 \, {\left(7168 \, a^{3} + 24480 \, a^{2} b + 29172 \, a b^{2} - 81081 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} + 85 \, {\left(229376 \, a^{3} + 783360 \, a^{2} b + 68640 \, a b^{2} - 1756755 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} - 1088 \, {\left(71680 \, a^{3} + 244800 \, a^{2} b - 176748 \, a b^{2} - 351351 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 51 \, {\left(4014080 \, a^{3} + 3824640 \, a^{2} b - 12739584 \, a b^{2} - 11594583 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 1768 \, {\left(200704 \, a^{3} - 217440 \, a^{2} b - 480876 \, a b^{2} - 297297 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 5967 \, {\left(57344 \, a^{3} + 62080 \, a^{2} b + 64944 \, a b^{2} + 33033 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}{765765 \, {\left(d \cosh\left(d x + c\right)^{20} + 20 \, d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{19} + d \sinh\left(d x + c\right)^{20} - 17 \, d \cosh\left(d x + c\right)^{18} + {\left(190 \, d \cosh\left(d x + c\right)^{2} - 17 \, d\right)} \sinh\left(d x + c\right)^{18} + 6 \, {\left(190 \, d \cosh\left(d x + c\right)^{3} - 51 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{17} + 136 \, d \cosh\left(d x + c\right)^{16} + 17 \, {\left(285 \, d \cosh\left(d x + c\right)^{4} - 153 \, d \cosh\left(d x + c\right)^{2} + 8 \, d\right)} \sinh\left(d x + c\right)^{16} + 272 \, {\left(57 \, d \cosh\left(d x + c\right)^{5} - 51 \, d \cosh\left(d x + c\right)^{3} + 8 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{15} - 681 \, d \cosh\left(d x + c\right)^{14} + 3 \, {\left(12920 \, d \cosh\left(d x + c\right)^{6} - 17340 \, d \cosh\left(d x + c\right)^{4} + 5440 \, d \cosh\left(d x + c\right)^{2} - 227 \, d\right)} \sinh\left(d x + c\right)^{14} + 2 \, {\left(38760 \, d \cosh\left(d x + c\right)^{7} - 72828 \, d \cosh\left(d x + c\right)^{5} + 38080 \, d \cosh\left(d x + c\right)^{3} - 4753 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{13} + 2397 \, d \cosh\left(d x + c\right)^{12} + {\left(125970 \, d \cosh\left(d x + c\right)^{8} - 315588 \, d \cosh\left(d x + c\right)^{6} + 247520 \, d \cosh\left(d x + c\right)^{4} - 61971 \, d \cosh\left(d x + c\right)^{2} + 2397 \, d\right)} \sinh\left(d x + c\right)^{12} + 4 \, {\left(41990 \, d \cosh\left(d x + c\right)^{9} - 135252 \, d \cosh\left(d x + c\right)^{7} + 148512 \, d \cosh\left(d x + c\right)^{5} - 61789 \, d \cosh\left(d x + c\right)^{3} + 7089 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{11} - 6324 \, d \cosh\left(d x + c\right)^{10} + {\left(184756 \, d \cosh\left(d x + c\right)^{10} - 743886 \, d \cosh\left(d x + c\right)^{8} + 1089088 \, d \cosh\left(d x + c\right)^{6} - 681681 \, d \cosh\left(d x + c\right)^{4} + 158202 \, d \cosh\left(d x + c\right)^{2} - 6324 \, d\right)} \sinh\left(d x + c\right)^{10} + 2 \, {\left(83980 \, d \cosh\left(d x + c\right)^{11} - 413270 \, d \cosh\left(d x + c\right)^{9} + 777920 \, d \cosh\left(d x + c\right)^{7} - 679679 \, d \cosh\left(d x + c\right)^{5} + 259930 \, d \cosh\left(d x + c\right)^{3} - 30260 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} + 13056 \, d \cosh\left(d x + c\right)^{8} + 3 \, {\left(41990 \, d \cosh\left(d x + c\right)^{12} - 247962 \, d \cosh\left(d x + c\right)^{10} + 583440 \, d \cosh\left(d x + c\right)^{8} - 681681 \, d \cosh\left(d x + c\right)^{6} + 395505 \, d \cosh\left(d x + c\right)^{4} - 94860 \, d \cosh\left(d x + c\right)^{2} + 4352 \, d\right)} \sinh\left(d x + c\right)^{8} + 8 \, {\left(9690 \, d \cosh\left(d x + c\right)^{13} - 67626 \, d \cosh\left(d x + c\right)^{11} + 194480 \, d \cosh\left(d x + c\right)^{9} - 291291 \, d \cosh\left(d x + c\right)^{7} + 233937 \, d \cosh\left(d x + c\right)^{5} - 90780 \, d \cosh\left(d x + c\right)^{3} + 11696 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} - 21828 \, d \cosh\left(d x + c\right)^{6} + {\left(38760 \, d \cosh\left(d x + c\right)^{14} - 315588 \, d \cosh\left(d x + c\right)^{12} + 1089088 \, d \cosh\left(d x + c\right)^{10} - 2045043 \, d \cosh\left(d x + c\right)^{8} + 2214828 \, d \cosh\left(d x + c\right)^{6} - 1328040 \, d \cosh\left(d x + c\right)^{4} + 365568 \, d \cosh\left(d x + c\right)^{2} - 21828 \, d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(7752 \, d \cosh\left(d x + c\right)^{15} - 72828 \, d \cosh\left(d x + c\right)^{13} + 297024 \, d \cosh\left(d x + c\right)^{11} - 679679 \, d \cosh\left(d x + c\right)^{9} + 935748 \, d \cosh\left(d x + c\right)^{7} - 762552 \, d \cosh\left(d x + c\right)^{5} + 327488 \, d \cosh\left(d x + c\right)^{3} - 51204 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 30498 \, d \cosh\left(d x + c\right)^{4} + {\left(4845 \, d \cosh\left(d x + c\right)^{16} - 52020 \, d \cosh\left(d x + c\right)^{14} + 247520 \, d \cosh\left(d x + c\right)^{12} - 681681 \, d \cosh\left(d x + c\right)^{10} + 1186515 \, d \cosh\left(d x + c\right)^{8} - 1328040 \, d \cosh\left(d x + c\right)^{6} + 913920 \, d \cosh\left(d x + c\right)^{4} - 327420 \, d \cosh\left(d x + c\right)^{2} + 30498 \, d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(285 \, d \cosh\left(d x + c\right)^{17} - 3468 \, d \cosh\left(d x + c\right)^{15} + 19040 \, d \cosh\left(d x + c\right)^{13} - 61789 \, d \cosh\left(d x + c\right)^{11} + 129965 \, d \cosh\left(d x + c\right)^{9} - 181560 \, d \cosh\left(d x + c\right)^{7} + 163744 \, d \cosh\left(d x + c\right)^{5} - 85340 \, d \cosh\left(d x + c\right)^{3} + 18122 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 36686 \, d \cosh\left(d x + c\right)^{2} + {\left(190 \, d \cosh\left(d x + c\right)^{18} - 2601 \, d \cosh\left(d x + c\right)^{16} + 16320 \, d \cosh\left(d x + c\right)^{14} - 61971 \, d \cosh\left(d x + c\right)^{12} + 158202 \, d \cosh\left(d x + c\right)^{10} - 284580 \, d \cosh\left(d x + c\right)^{8} + 365568 \, d \cosh\left(d x + c\right)^{6} - 327420 \, d \cosh\left(d x + c\right)^{4} + 182988 \, d \cosh\left(d x + c\right)^{2} - 36686 \, d\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(10 \, d \cosh\left(d x + c\right)^{19} - 153 \, d \cosh\left(d x + c\right)^{17} + 1088 \, d \cosh\left(d x + c\right)^{15} - 4753 \, d \cosh\left(d x + c\right)^{13} + 14178 \, d \cosh\left(d x + c\right)^{11} - 30260 \, d \cosh\left(d x + c\right)^{9} + 46784 \, d \cosh\left(d x + c\right)^{7} - 51204 \, d \cosh\left(d x + c\right)^{5} + 36244 \, d \cosh\left(d x + c\right)^{3} - 11934 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + 19448 \, d\right)}}"," ",0,"-16/765765*((28672*a^3 + 97920*a^2*b + 116688*a*b^2 + 561561*b^3)*cosh(d*x + c)^14 - 14*(28672*a^3 + 97920*a^2*b + 116688*a*b^2 - 459459*b^3)*cosh(d*x + c)*sinh(d*x + c)^13 + (28672*a^3 + 97920*a^2*b + 116688*a*b^2 + 561561*b^3)*sinh(d*x + c)^14 - 34*(14336*a^3 + 48960*a^2*b + 58344*a*b^2 + 213213*b^3)*cosh(d*x + c)^12 - (487424*a^3 + 1664640*a^2*b + 1983696*a*b^2 + 7249242*b^3 - 91*(28672*a^3 + 97920*a^2*b + 116688*a*b^2 + 561561*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^12 - 4*(91*(28672*a^3 + 97920*a^2*b + 116688*a*b^2 - 459459*b^3)*cosh(d*x + c)^3 - 204*(7168*a^3 + 24480*a^2*b + 29172*a*b^2 - 81081*b^3)*cosh(d*x + c))*sinh(d*x + c)^11 + 17*(229376*a^3 + 783360*a^2*b + 1798368*a*b^2 + 2573571*b^3)*cosh(d*x + c)^10 + (1001*(28672*a^3 + 97920*a^2*b + 116688*a*b^2 + 561561*b^3)*cosh(d*x + c)^4 + 3899392*a^3 + 13317120*a^2*b + 30572256*a*b^2 + 43750707*b^3 - 2244*(14336*a^3 + 48960*a^2*b + 58344*a*b^2 + 213213*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^10 - 2*(1001*(28672*a^3 + 97920*a^2*b + 116688*a*b^2 - 459459*b^3)*cosh(d*x + c)^5 - 7480*(7168*a^3 + 24480*a^2*b + 29172*a*b^2 - 81081*b^3)*cosh(d*x + c)^3 + 85*(229376*a^3 + 783360*a^2*b + 68640*a*b^2 - 1756755*b^3)*cosh(d*x + c))*sinh(d*x + c)^9 - 68*(286720*a^3 + 979200*a^2*b + 3040752*a*b^2 + 2411409*b^3)*cosh(d*x + c)^8 + (3003*(28672*a^3 + 97920*a^2*b + 116688*a*b^2 + 561561*b^3)*cosh(d*x + c)^6 - 16830*(14336*a^3 + 48960*a^2*b + 58344*a*b^2 + 213213*b^3)*cosh(d*x + c)^4 - 19496960*a^3 - 66585600*a^2*b - 206771136*a*b^2 - 163975812*b^3 + 765*(229376*a^3 + 783360*a^2*b + 1798368*a*b^2 + 2573571*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^8 - 8*(429*(28672*a^3 + 97920*a^2*b + 116688*a*b^2 - 459459*b^3)*cosh(d*x + c)^7 - 6732*(7168*a^3 + 24480*a^2*b + 29172*a*b^2 - 81081*b^3)*cosh(d*x + c)^5 + 255*(229376*a^3 + 783360*a^2*b + 68640*a*b^2 - 1756755*b^3)*cosh(d*x + c)^3 - 272*(71680*a^3 + 244800*a^2*b - 176748*a*b^2 - 351351*b^3)*cosh(d*x + c))*sinh(d*x + c)^7 + 17*(4014080*a^3 + 23592960*a^2*b + 45412224*a*b^2 + 25138113*b^3)*cosh(d*x + c)^6 + (3003*(28672*a^3 + 97920*a^2*b + 116688*a*b^2 + 561561*b^3)*cosh(d*x + c)^8 - 31416*(14336*a^3 + 48960*a^2*b + 58344*a*b^2 + 213213*b^3)*cosh(d*x + c)^6 + 3570*(229376*a^3 + 783360*a^2*b + 1798368*a*b^2 + 2573571*b^3)*cosh(d*x + c)^4 + 68239360*a^3 + 401080320*a^2*b + 772007808*a*b^2 + 427347921*b^3 - 1904*(286720*a^3 + 979200*a^2*b + 3040752*a*b^2 + 2411409*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^6 - 2*(1001*(28672*a^3 + 97920*a^2*b + 116688*a*b^2 - 459459*b^3)*cosh(d*x + c)^9 - 26928*(7168*a^3 + 24480*a^2*b + 29172*a*b^2 - 81081*b^3)*cosh(d*x + c)^7 + 2142*(229376*a^3 + 783360*a^2*b + 68640*a*b^2 - 1756755*b^3)*cosh(d*x + c)^5 - 7616*(71680*a^3 + 244800*a^2*b - 176748*a*b^2 - 351351*b^3)*cosh(d*x + c)^3 + 51*(4014080*a^3 + 3824640*a^2*b - 12739584*a*b^2 - 11594583*b^3)*cosh(d*x + c))*sinh(d*x + c)^5 - 442*(401408*a^3 + 3176640*a^2*b + 4162488*a*b^2 + 1857471*b^3)*cosh(d*x + c)^4 + (1001*(28672*a^3 + 97920*a^2*b + 116688*a*b^2 + 561561*b^3)*cosh(d*x + c)^10 - 16830*(14336*a^3 + 48960*a^2*b + 58344*a*b^2 + 213213*b^3)*cosh(d*x + c)^8 + 3570*(229376*a^3 + 783360*a^2*b + 1798368*a*b^2 + 2573571*b^3)*cosh(d*x + c)^6 - 4760*(286720*a^3 + 979200*a^2*b + 3040752*a*b^2 + 2411409*b^3)*cosh(d*x + c)^4 - 177422336*a^3 - 1404074880*a^2*b - 1839819696*a*b^2 - 821002182*b^3 + 255*(4014080*a^3 + 23592960*a^2*b + 45412224*a*b^2 + 25138113*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 - 4*(91*(28672*a^3 + 97920*a^2*b + 116688*a*b^2 - 459459*b^3)*cosh(d*x + c)^11 - 3740*(7168*a^3 + 24480*a^2*b + 29172*a*b^2 - 81081*b^3)*cosh(d*x + c)^9 + 510*(229376*a^3 + 783360*a^2*b + 68640*a*b^2 - 1756755*b^3)*cosh(d*x + c)^7 - 3808*(71680*a^3 + 244800*a^2*b - 176748*a*b^2 - 351351*b^3)*cosh(d*x + c)^5 + 85*(4014080*a^3 + 3824640*a^2*b - 12739584*a*b^2 - 11594583*b^3)*cosh(d*x + c)^3 - 884*(200704*a^3 - 217440*a^2*b - 480876*a*b^2 - 297297*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 - 557613056*a^3 - 1736317440*a^2*b - 1775057856*a*b^2 - 680611932*b^3 + 221*(4759552*a^3 + 12643200*a^2*b + 13669392*a*b^2 + 5435199*b^3)*cosh(d*x + c)^2 + (91*(28672*a^3 + 97920*a^2*b + 116688*a*b^2 + 561561*b^3)*cosh(d*x + c)^12 - 2244*(14336*a^3 + 48960*a^2*b + 58344*a*b^2 + 213213*b^3)*cosh(d*x + c)^10 + 765*(229376*a^3 + 783360*a^2*b + 1798368*a*b^2 + 2573571*b^3)*cosh(d*x + c)^8 - 1904*(286720*a^3 + 979200*a^2*b + 3040752*a*b^2 + 2411409*b^3)*cosh(d*x + c)^6 + 255*(4014080*a^3 + 23592960*a^2*b + 45412224*a*b^2 + 25138113*b^3)*cosh(d*x + c)^4 + 1051860992*a^3 + 2794147200*a^2*b + 3020935632*a*b^2 + 1201178979*b^3 - 2652*(401408*a^3 + 3176640*a^2*b + 4162488*a*b^2 + 1857471*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - 2*(7*(28672*a^3 + 97920*a^2*b + 116688*a*b^2 - 459459*b^3)*cosh(d*x + c)^13 - 408*(7168*a^3 + 24480*a^2*b + 29172*a*b^2 - 81081*b^3)*cosh(d*x + c)^11 + 85*(229376*a^3 + 783360*a^2*b + 68640*a*b^2 - 1756755*b^3)*cosh(d*x + c)^9 - 1088*(71680*a^3 + 244800*a^2*b - 176748*a*b^2 - 351351*b^3)*cosh(d*x + c)^7 + 51*(4014080*a^3 + 3824640*a^2*b - 12739584*a*b^2 - 11594583*b^3)*cosh(d*x + c)^5 - 1768*(200704*a^3 - 217440*a^2*b - 480876*a*b^2 - 297297*b^3)*cosh(d*x + c)^3 - 5967*(57344*a^3 + 62080*a^2*b + 64944*a*b^2 + 33033*b^3)*cosh(d*x + c))*sinh(d*x + c))/(d*cosh(d*x + c)^20 + 20*d*cosh(d*x + c)*sinh(d*x + c)^19 + d*sinh(d*x + c)^20 - 17*d*cosh(d*x + c)^18 + (190*d*cosh(d*x + c)^2 - 17*d)*sinh(d*x + c)^18 + 6*(190*d*cosh(d*x + c)^3 - 51*d*cosh(d*x + c))*sinh(d*x + c)^17 + 136*d*cosh(d*x + c)^16 + 17*(285*d*cosh(d*x + c)^4 - 153*d*cosh(d*x + c)^2 + 8*d)*sinh(d*x + c)^16 + 272*(57*d*cosh(d*x + c)^5 - 51*d*cosh(d*x + c)^3 + 8*d*cosh(d*x + c))*sinh(d*x + c)^15 - 681*d*cosh(d*x + c)^14 + 3*(12920*d*cosh(d*x + c)^6 - 17340*d*cosh(d*x + c)^4 + 5440*d*cosh(d*x + c)^2 - 227*d)*sinh(d*x + c)^14 + 2*(38760*d*cosh(d*x + c)^7 - 72828*d*cosh(d*x + c)^5 + 38080*d*cosh(d*x + c)^3 - 4753*d*cosh(d*x + c))*sinh(d*x + c)^13 + 2397*d*cosh(d*x + c)^12 + (125970*d*cosh(d*x + c)^8 - 315588*d*cosh(d*x + c)^6 + 247520*d*cosh(d*x + c)^4 - 61971*d*cosh(d*x + c)^2 + 2397*d)*sinh(d*x + c)^12 + 4*(41990*d*cosh(d*x + c)^9 - 135252*d*cosh(d*x + c)^7 + 148512*d*cosh(d*x + c)^5 - 61789*d*cosh(d*x + c)^3 + 7089*d*cosh(d*x + c))*sinh(d*x + c)^11 - 6324*d*cosh(d*x + c)^10 + (184756*d*cosh(d*x + c)^10 - 743886*d*cosh(d*x + c)^8 + 1089088*d*cosh(d*x + c)^6 - 681681*d*cosh(d*x + c)^4 + 158202*d*cosh(d*x + c)^2 - 6324*d)*sinh(d*x + c)^10 + 2*(83980*d*cosh(d*x + c)^11 - 413270*d*cosh(d*x + c)^9 + 777920*d*cosh(d*x + c)^7 - 679679*d*cosh(d*x + c)^5 + 259930*d*cosh(d*x + c)^3 - 30260*d*cosh(d*x + c))*sinh(d*x + c)^9 + 13056*d*cosh(d*x + c)^8 + 3*(41990*d*cosh(d*x + c)^12 - 247962*d*cosh(d*x + c)^10 + 583440*d*cosh(d*x + c)^8 - 681681*d*cosh(d*x + c)^6 + 395505*d*cosh(d*x + c)^4 - 94860*d*cosh(d*x + c)^2 + 4352*d)*sinh(d*x + c)^8 + 8*(9690*d*cosh(d*x + c)^13 - 67626*d*cosh(d*x + c)^11 + 194480*d*cosh(d*x + c)^9 - 291291*d*cosh(d*x + c)^7 + 233937*d*cosh(d*x + c)^5 - 90780*d*cosh(d*x + c)^3 + 11696*d*cosh(d*x + c))*sinh(d*x + c)^7 - 21828*d*cosh(d*x + c)^6 + (38760*d*cosh(d*x + c)^14 - 315588*d*cosh(d*x + c)^12 + 1089088*d*cosh(d*x + c)^10 - 2045043*d*cosh(d*x + c)^8 + 2214828*d*cosh(d*x + c)^6 - 1328040*d*cosh(d*x + c)^4 + 365568*d*cosh(d*x + c)^2 - 21828*d)*sinh(d*x + c)^6 + 2*(7752*d*cosh(d*x + c)^15 - 72828*d*cosh(d*x + c)^13 + 297024*d*cosh(d*x + c)^11 - 679679*d*cosh(d*x + c)^9 + 935748*d*cosh(d*x + c)^7 - 762552*d*cosh(d*x + c)^5 + 327488*d*cosh(d*x + c)^3 - 51204*d*cosh(d*x + c))*sinh(d*x + c)^5 + 30498*d*cosh(d*x + c)^4 + (4845*d*cosh(d*x + c)^16 - 52020*d*cosh(d*x + c)^14 + 247520*d*cosh(d*x + c)^12 - 681681*d*cosh(d*x + c)^10 + 1186515*d*cosh(d*x + c)^8 - 1328040*d*cosh(d*x + c)^6 + 913920*d*cosh(d*x + c)^4 - 327420*d*cosh(d*x + c)^2 + 30498*d)*sinh(d*x + c)^4 + 4*(285*d*cosh(d*x + c)^17 - 3468*d*cosh(d*x + c)^15 + 19040*d*cosh(d*x + c)^13 - 61789*d*cosh(d*x + c)^11 + 129965*d*cosh(d*x + c)^9 - 181560*d*cosh(d*x + c)^7 + 163744*d*cosh(d*x + c)^5 - 85340*d*cosh(d*x + c)^3 + 18122*d*cosh(d*x + c))*sinh(d*x + c)^3 - 36686*d*cosh(d*x + c)^2 + (190*d*cosh(d*x + c)^18 - 2601*d*cosh(d*x + c)^16 + 16320*d*cosh(d*x + c)^14 - 61971*d*cosh(d*x + c)^12 + 158202*d*cosh(d*x + c)^10 - 284580*d*cosh(d*x + c)^8 + 365568*d*cosh(d*x + c)^6 - 327420*d*cosh(d*x + c)^4 + 182988*d*cosh(d*x + c)^2 - 36686*d)*sinh(d*x + c)^2 + 2*(10*d*cosh(d*x + c)^19 - 153*d*cosh(d*x + c)^17 + 1088*d*cosh(d*x + c)^15 - 4753*d*cosh(d*x + c)^13 + 14178*d*cosh(d*x + c)^11 - 30260*d*cosh(d*x + c)^9 + 46784*d*cosh(d*x + c)^7 - 51204*d*cosh(d*x + c)^5 + 36244*d*cosh(d*x + c)^3 - 11934*d*cosh(d*x + c))*sinh(d*x + c) + 19448*d)","B",0
228,1,4259,0,0.548771," ","integrate(csch(d*x+c)^20*(a+b*sinh(d*x+c)^4)^3,x, algorithm=""fricas"")","\frac{64 \, {\left({\left(43008 \, a^{3} + 144704 \, a^{2} b + 167960 \, a b^{2} - 2355639 \, b^{3}\right)} \cosh\left(d x + c\right)^{15} + 15 \, {\left(43008 \, a^{3} + 144704 \, a^{2} b + 167960 \, a b^{2} - 2355639 \, b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{14} - 2 \, {\left(21504 \, a^{3} + 72352 \, a^{2} b + 83980 \, a b^{2} + 1247103 \, b^{3}\right)} \sinh\left(d x + c\right)^{15} - 19 \, {\left(43008 \, a^{3} + 144704 \, a^{2} b + 167960 \, a b^{2} - 1538823 \, b^{3}\right)} \cosh\left(d x + c\right)^{13} + 2 \, {\left(408576 \, a^{3} + 1374688 \, a^{2} b + 1595620 \, a b^{2} + 15935205 \, b^{3} - 105 \, {\left(21504 \, a^{3} + 72352 \, a^{2} b + 83980 \, a b^{2} + 1247103 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{13} + 13 \, {\left(35 \, {\left(43008 \, a^{3} + 144704 \, a^{2} b + 167960 \, a b^{2} - 2355639 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 19 \, {\left(43008 \, a^{3} + 144704 \, a^{2} b + 167960 \, a b^{2} - 1538823 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{12} + 57 \, {\left(129024 \, a^{3} + 434112 \, a^{2} b - 857480 \, a b^{2} - 2914769 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} - 6 \, {\left(455 \, {\left(21504 \, a^{3} + 72352 \, a^{2} b + 83980 \, a b^{2} + 1247103 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 1225728 \, a^{3} + 4124064 \, a^{2} b + 17719780 \, a b^{2} + 31639465 \, b^{3} - 494 \, {\left(21504 \, a^{3} + 72352 \, a^{2} b + 83980 \, a b^{2} + 838695 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{11} + 11 \, {\left(273 \, {\left(43008 \, a^{3} + 144704 \, a^{2} b + 167960 \, a b^{2} - 2355639 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 494 \, {\left(43008 \, a^{3} + 144704 \, a^{2} b + 167960 \, a b^{2} - 1538823 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 57 \, {\left(129024 \, a^{3} + 434112 \, a^{2} b - 857480 \, a b^{2} - 2914769 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{10} - 969 \, {\left(43008 \, a^{3} + 144704 \, a^{2} b - 529880 \, a b^{2} - 586443 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} - 2 \, {\left(5005 \, {\left(21504 \, a^{3} + 72352 \, a^{2} b + 83980 \, a b^{2} + 1247103 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} - 13585 \, {\left(21504 \, a^{3} + 72352 \, a^{2} b + 83980 \, a b^{2} + 838695 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 20837376 \, a^{3} - 70109088 \, a^{2} b - 419480100 \, a b^{2} - 351267345 \, b^{3} + 3135 \, {\left(64512 \, a^{3} + 217056 \, a^{2} b + 932620 \, a b^{2} + 1665235 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{9} + 9 \, {\left(715 \, {\left(43008 \, a^{3} + 144704 \, a^{2} b + 167960 \, a b^{2} - 2355639 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} - 2717 \, {\left(43008 \, a^{3} + 144704 \, a^{2} b + 167960 \, a b^{2} - 1538823 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 1045 \, {\left(129024 \, a^{3} + 434112 \, a^{2} b - 857480 \, a b^{2} - 2914769 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 969 \, {\left(43008 \, a^{3} + 144704 \, a^{2} b - 529880 \, a b^{2} - 586443 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{8} + 6783 \, {\left(24576 \, a^{3} - 54592 \, a^{2} b - 293800 \, a b^{2} - 189761 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} - 6 \, {\left(2145 \, {\left(21504 \, a^{3} + 72352 \, a^{2} b + 83980 \, a b^{2} + 1247103 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} - 10868 \, {\left(21504 \, a^{3} + 72352 \, a^{2} b + 83980 \, a b^{2} + 838695 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 6270 \, {\left(64512 \, a^{3} + 217056 \, a^{2} b + 932620 \, a b^{2} + 1665235 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 27783168 \, a^{3} + 248673824 \, a^{2} b + 549145220 \, a b^{2} + 303230785 \, b^{3} - 11628 \, {\left(21504 \, a^{3} + 72352 \, a^{2} b + 432900 \, a b^{2} + 362505 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{7} + {\left(5005 \, {\left(43008 \, a^{3} + 144704 \, a^{2} b + 167960 \, a b^{2} - 2355639 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} - 32604 \, {\left(43008 \, a^{3} + 144704 \, a^{2} b + 167960 \, a b^{2} - 1538823 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 26334 \, {\left(129024 \, a^{3} + 434112 \, a^{2} b - 857480 \, a b^{2} - 2914769 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 81396 \, {\left(43008 \, a^{3} + 144704 \, a^{2} b - 529880 \, a b^{2} - 586443 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 47481 \, {\left(24576 \, a^{3} - 54592 \, a^{2} b - 293800 \, a b^{2} - 189761 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} - 323 \, {\left(1548288 \, a^{3} - 8564416 \, a^{2} b - 12926680 \, a b^{2} - 6120543 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 2 \, {\left(3003 \, {\left(21504 \, a^{3} + 72352 \, a^{2} b + 83980 \, a b^{2} + 1247103 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} - 24453 \, {\left(21504 \, a^{3} + 72352 \, a^{2} b + 83980 \, a b^{2} + 838695 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 26334 \, {\left(64512 \, a^{3} + 217056 \, a^{2} b + 932620 \, a b^{2} + 1665235 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} - 122094 \, {\left(21504 \, a^{3} + 72352 \, a^{2} b + 432900 \, a b^{2} + 362505 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 250048512 \, a^{3} - 3065771296 \, a^{2} b - 4040697700 \, a b^{2} - 1763542209 \, b^{3} + 20349 \, {\left(86016 \, a^{3} + 769888 \, a^{2} b + 1700140 \, a b^{2} + 938795 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{5} + {\left(1365 \, {\left(43008 \, a^{3} + 144704 \, a^{2} b + 167960 \, a b^{2} - 2355639 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} - 13585 \, {\left(43008 \, a^{3} + 144704 \, a^{2} b + 167960 \, a b^{2} - 1538823 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + 18810 \, {\left(129024 \, a^{3} + 434112 \, a^{2} b - 857480 \, a b^{2} - 2914769 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} - 122094 \, {\left(43008 \, a^{3} + 144704 \, a^{2} b - 529880 \, a b^{2} - 586443 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 237405 \, {\left(24576 \, a^{3} - 54592 \, a^{2} b - 293800 \, a b^{2} - 189761 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 1615 \, {\left(1548288 \, a^{3} - 8564416 \, a^{2} b - 12926680 \, a b^{2} - 6120543 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} - 323 \, {\left(8687616 \, a^{3} + 15456448 \, a^{2} b + 15194920 \, a b^{2} + 6026163 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 2 \, {\left(455 \, {\left(21504 \, a^{3} + 72352 \, a^{2} b + 83980 \, a b^{2} + 1247103 \, b^{3}\right)} \cosh\left(d x + c\right)^{12} - 5434 \, {\left(21504 \, a^{3} + 72352 \, a^{2} b + 83980 \, a b^{2} + 838695 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} + 9405 \, {\left(64512 \, a^{3} + 217056 \, a^{2} b + 932620 \, a b^{2} + 1665235 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} - 81396 \, {\left(21504 \, a^{3} + 72352 \, a^{2} b + 432900 \, a b^{2} + 362505 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 33915 \, {\left(86016 \, a^{3} + 769888 \, a^{2} b + 1700140 \, a b^{2} + 938795 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 2569943040 \, a^{3} + 6422325280 \, a^{2} b + 6933472780 \, a b^{2} + 2675035935 \, b^{3} - 3230 \, {\left(774144 \, a^{3} + 9491552 \, a^{2} b + 12509900 \, a b^{2} + 5459883 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + {\left(105 \, {\left(43008 \, a^{3} + 144704 \, a^{2} b + 167960 \, a b^{2} - 2355639 \, b^{3}\right)} \cosh\left(d x + c\right)^{13} - 1482 \, {\left(43008 \, a^{3} + 144704 \, a^{2} b + 167960 \, a b^{2} - 1538823 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} + 3135 \, {\left(129024 \, a^{3} + 434112 \, a^{2} b - 857480 \, a b^{2} - 2914769 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} - 34884 \, {\left(43008 \, a^{3} + 144704 \, a^{2} b - 529880 \, a b^{2} - 586443 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 142443 \, {\left(24576 \, a^{3} - 54592 \, a^{2} b - 293800 \, a b^{2} - 189761 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 3230 \, {\left(1548288 \, a^{3} - 8564416 \, a^{2} b - 12926680 \, a b^{2} - 6120543 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 969 \, {\left(8687616 \, a^{3} + 15456448 \, a^{2} b + 15194920 \, a b^{2} + 6026163 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 12597 \, {\left(86016 \, a^{3} + 215488 \, a^{2} b + 179720 \, a b^{2} + 65703 \, b^{3}\right)} \cosh\left(d x + c\right) - 2 \, {\left(15 \, {\left(21504 \, a^{3} + 72352 \, a^{2} b + 83980 \, a b^{2} + 1247103 \, b^{3}\right)} \cosh\left(d x + c\right)^{14} - 247 \, {\left(21504 \, a^{3} + 72352 \, a^{2} b + 83980 \, a b^{2} + 838695 \, b^{3}\right)} \cosh\left(d x + c\right)^{12} + 627 \, {\left(64512 \, a^{3} + 217056 \, a^{2} b + 932620 \, a b^{2} + 1665235 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} - 8721 \, {\left(21504 \, a^{3} + 72352 \, a^{2} b + 432900 \, a b^{2} + 362505 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 6783 \, {\left(86016 \, a^{3} + 769888 \, a^{2} b + 1700140 \, a b^{2} + 938795 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} - 1615 \, {\left(774144 \, a^{3} + 9491552 \, a^{2} b + 12509900 \, a b^{2} + 5459883 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 2708858880 \, a^{3} - 8648596320 \, a^{2} b - 8918927940 \, a b^{2} - 3269488365 \, b^{3} + 4845 \, {\left(1591296 \, a^{3} + 3976672 \, a^{2} b + 4293172 \, a b^{2} + 1656369 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)\right)}}{4849845 \, {\left(d \cosh\left(d x + c\right)^{23} + 23 \, d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{22} + d \sinh\left(d x + c\right)^{23} - 19 \, d \cosh\left(d x + c\right)^{21} + {\left(253 \, d \cosh\left(d x + c\right)^{2} - 19 \, d\right)} \sinh\left(d x + c\right)^{21} + 7 \, {\left(253 \, d \cosh\left(d x + c\right)^{3} - 57 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{20} + 171 \, d \cosh\left(d x + c\right)^{19} + {\left(8855 \, d \cosh\left(d x + c\right)^{4} - 3990 \, d \cosh\left(d x + c\right)^{2} + 171 \, d\right)} \sinh\left(d x + c\right)^{19} + 19 \, {\left(1771 \, d \cosh\left(d x + c\right)^{5} - 1330 \, d \cosh\left(d x + c\right)^{3} + 171 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{18} - 969 \, d \cosh\left(d x + c\right)^{17} + 57 \, {\left(1771 \, d \cosh\left(d x + c\right)^{6} - 1995 \, d \cosh\left(d x + c\right)^{4} + 513 \, d \cosh\left(d x + c\right)^{2} - 17 \, d\right)} \sinh\left(d x + c\right)^{17} + 969 \, {\left(253 \, d \cosh\left(d x + c\right)^{7} - 399 \, d \cosh\left(d x + c\right)^{5} + 171 \, d \cosh\left(d x + c\right)^{3} - 17 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{16} + 3875 \, d \cosh\left(d x + c\right)^{15} + {\left(490314 \, d \cosh\left(d x + c\right)^{8} - 1031016 \, d \cosh\left(d x + c\right)^{6} + 662796 \, d \cosh\left(d x + c\right)^{4} - 131784 \, d \cosh\left(d x + c\right)^{2} + 3877 \, d\right)} \sinh\left(d x + c\right)^{15} + {\left(817190 \, d \cosh\left(d x + c\right)^{9} - 2209320 \, d \cosh\left(d x + c\right)^{7} + 1988388 \, d \cosh\left(d x + c\right)^{5} - 658920 \, d \cosh\left(d x + c\right)^{3} + 58125 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{14} - 11609 \, d \cosh\left(d x + c\right)^{13} + {\left(1144066 \, d \cosh\left(d x + c\right)^{10} - 3866310 \, d \cosh\left(d x + c\right)^{8} + 4639572 \, d \cosh\left(d x + c\right)^{6} - 2306220 \, d \cosh\left(d x + c\right)^{4} + 407085 \, d \cosh\left(d x + c\right)^{2} - 11647 \, d\right)} \sinh\left(d x + c\right)^{13} + 13 \, {\left(104006 \, d \cosh\left(d x + c\right)^{11} - 429590 \, d \cosh\left(d x + c\right)^{9} + 662796 \, d \cosh\left(d x + c\right)^{7} - 461244 \, d \cosh\left(d x + c\right)^{5} + 135625 \, d \cosh\left(d x + c\right)^{3} - 11609 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{12} + 26961 \, d \cosh\left(d x + c\right)^{11} + {\left(1352078 \, d \cosh\left(d x + c\right)^{12} - 6701604 \, d \cosh\left(d x + c\right)^{10} + 12924522 \, d \cosh\left(d x + c\right)^{8} - 11992344 \, d \cosh\left(d x + c\right)^{6} + 5292105 \, d \cosh\left(d x + c\right)^{4} - 908466 \, d \cosh\left(d x + c\right)^{2} + 27303 \, d\right)} \sinh\left(d x + c\right)^{11} + {\left(1144066 \, d \cosh\left(d x + c\right)^{13} - 6701604 \, d \cosh\left(d x + c\right)^{11} + 15796638 \, d \cosh\left(d x + c\right)^{9} - 18845112 \, d \cosh\left(d x + c\right)^{7} + 11636625 \, d \cosh\left(d x + c\right)^{5} - 3320174 \, d \cosh\left(d x + c\right)^{3} + 296571 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{10} - 49419 \, d \cosh\left(d x + c\right)^{9} + {\left(817190 \, d \cosh\left(d x + c\right)^{14} - 5584670 \, d \cosh\left(d x + c\right)^{12} + 15796638 \, d \cosh\left(d x + c\right)^{10} - 23556390 \, d \cosh\left(d x + c\right)^{8} + 19404385 \, d \cosh\left(d x + c\right)^{6} - 8327605 \, d \cosh\left(d x + c\right)^{4} + 1501665 \, d \cosh\left(d x + c\right)^{2} - 51357 \, d\right)} \sinh\left(d x + c\right)^{9} + 3 \, {\left(163438 \, d \cosh\left(d x + c\right)^{15} - 1288770 \, d \cosh\left(d x + c\right)^{13} + 4308174 \, d \cosh\left(d x + c\right)^{11} - 7852130 \, d \cosh\left(d x + c\right)^{9} + 8311875 \, d \cosh\left(d x + c\right)^{7} - 4980261 \, d \cosh\left(d x + c\right)^{5} + 1482855 \, d \cosh\left(d x + c\right)^{3} - 148257 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{8} + 71706 \, d \cosh\left(d x + c\right)^{7} + 3 \, {\left(81719 \, d \cosh\left(d x + c\right)^{16} - 736440 \, d \cosh\left(d x + c\right)^{14} + 2872116 \, d \cosh\left(d x + c\right)^{12} - 6281704 \, d \cosh\left(d x + c\right)^{10} + 8316165 \, d \cosh\left(d x + c\right)^{8} - 6662084 \, d \cosh\left(d x + c\right)^{6} + 3003330 \, d \cosh\left(d x + c\right)^{4} - 616284 \, d \cosh\left(d x + c\right)^{2} + 26486 \, d\right)} \sinh\left(d x + c\right)^{7} + {\left(100947 \, d \cosh\left(d x + c\right)^{17} - 1031016 \, d \cosh\left(d x + c\right)^{15} + 4639572 \, d \cosh\left(d x + c\right)^{13} - 11992344 \, d \cosh\left(d x + c\right)^{11} + 19394375 \, d \cosh\left(d x + c\right)^{9} - 19921044 \, d \cosh\left(d x + c\right)^{7} + 12455982 \, d \cosh\left(d x + c\right)^{5} - 4151196 \, d \cosh\left(d x + c\right)^{3} + 501942 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} - 80750 \, d \cosh\left(d x + c\right)^{5} + {\left(33649 \, d \cosh\left(d x + c\right)^{18} - 386631 \, d \cosh\left(d x + c\right)^{16} + 1988388 \, d \cosh\left(d x + c\right)^{14} - 5996172 \, d \cosh\left(d x + c\right)^{12} + 11642631 \, d \cosh\left(d x + c\right)^{10} - 14989689 \, d \cosh\left(d x + c\right)^{8} + 12613986 \, d \cosh\left(d x + c\right)^{6} - 6470982 \, d \cosh\left(d x + c\right)^{4} + 1668618 \, d \cosh\left(d x + c\right)^{2} - 104006 \, d\right)} \sinh\left(d x + c\right)^{5} + {\left(8855 \, d \cosh\left(d x + c\right)^{19} - 113715 \, d \cosh\left(d x + c\right)^{17} + 662796 \, d \cosh\left(d x + c\right)^{15} - 2306220 \, d \cosh\left(d x + c\right)^{13} + 5289375 \, d \cosh\left(d x + c\right)^{11} - 8300435 \, d \cosh\left(d x + c\right)^{9} + 8897130 \, d \cosh\left(d x + c\right)^{7} - 6226794 \, d \cosh\left(d x + c\right)^{5} + 2509710 \, d \cosh\left(d x + c\right)^{3} - 403750 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 65246 \, d \cosh\left(d x + c\right)^{3} + {\left(1771 \, d \cosh\left(d x + c\right)^{20} - 25270 \, d \cosh\left(d x + c\right)^{18} + 165699 \, d \cosh\left(d x + c\right)^{16} - 658920 \, d \cosh\left(d x + c\right)^{14} + 1764035 \, d \cosh\left(d x + c\right)^{12} - 3331042 \, d \cosh\left(d x + c\right)^{10} + 4504995 \, d \cosh\left(d x + c\right)^{8} - 4313988 \, d \cosh\left(d x + c\right)^{6} + 2781030 \, d \cosh\left(d x + c\right)^{4} - 1040060 \, d \cosh\left(d x + c\right)^{2} + 119510 \, d\right)} \sinh\left(d x + c\right)^{3} + {\left(253 \, d \cosh\left(d x + c\right)^{21} - 3990 \, d \cosh\left(d x + c\right)^{19} + 29241 \, d \cosh\left(d x + c\right)^{17} - 131784 \, d \cosh\left(d x + c\right)^{15} + 406875 \, d \cosh\left(d x + c\right)^{13} - 905502 \, d \cosh\left(d x + c\right)^{11} + 1482855 \, d \cosh\left(d x + c\right)^{9} - 1779084 \, d \cosh\left(d x + c\right)^{7} + 1505826 \, d \cosh\left(d x + c\right)^{5} - 807500 \, d \cosh\left(d x + c\right)^{3} + 195738 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 25194 \, d \cosh\left(d x + c\right) + {\left(23 \, d \cosh\left(d x + c\right)^{22} - 399 \, d \cosh\left(d x + c\right)^{20} + 3249 \, d \cosh\left(d x + c\right)^{18} - 16473 \, d \cosh\left(d x + c\right)^{16} + 58155 \, d \cosh\left(d x + c\right)^{14} - 151411 \, d \cosh\left(d x + c\right)^{12} + 300333 \, d \cosh\left(d x + c\right)^{10} - 462213 \, d \cosh\left(d x + c\right)^{8} + 556206 \, d \cosh\left(d x + c\right)^{6} - 520030 \, d \cosh\left(d x + c\right)^{4} + 358530 \, d \cosh\left(d x + c\right)^{2} - 125970 \, d\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"64/4849845*((43008*a^3 + 144704*a^2*b + 167960*a*b^2 - 2355639*b^3)*cosh(d*x + c)^15 + 15*(43008*a^3 + 144704*a^2*b + 167960*a*b^2 - 2355639*b^3)*cosh(d*x + c)*sinh(d*x + c)^14 - 2*(21504*a^3 + 72352*a^2*b + 83980*a*b^2 + 1247103*b^3)*sinh(d*x + c)^15 - 19*(43008*a^3 + 144704*a^2*b + 167960*a*b^2 - 1538823*b^3)*cosh(d*x + c)^13 + 2*(408576*a^3 + 1374688*a^2*b + 1595620*a*b^2 + 15935205*b^3 - 105*(21504*a^3 + 72352*a^2*b + 83980*a*b^2 + 1247103*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^13 + 13*(35*(43008*a^3 + 144704*a^2*b + 167960*a*b^2 - 2355639*b^3)*cosh(d*x + c)^3 - 19*(43008*a^3 + 144704*a^2*b + 167960*a*b^2 - 1538823*b^3)*cosh(d*x + c))*sinh(d*x + c)^12 + 57*(129024*a^3 + 434112*a^2*b - 857480*a*b^2 - 2914769*b^3)*cosh(d*x + c)^11 - 6*(455*(21504*a^3 + 72352*a^2*b + 83980*a*b^2 + 1247103*b^3)*cosh(d*x + c)^4 + 1225728*a^3 + 4124064*a^2*b + 17719780*a*b^2 + 31639465*b^3 - 494*(21504*a^3 + 72352*a^2*b + 83980*a*b^2 + 838695*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^11 + 11*(273*(43008*a^3 + 144704*a^2*b + 167960*a*b^2 - 2355639*b^3)*cosh(d*x + c)^5 - 494*(43008*a^3 + 144704*a^2*b + 167960*a*b^2 - 1538823*b^3)*cosh(d*x + c)^3 + 57*(129024*a^3 + 434112*a^2*b - 857480*a*b^2 - 2914769*b^3)*cosh(d*x + c))*sinh(d*x + c)^10 - 969*(43008*a^3 + 144704*a^2*b - 529880*a*b^2 - 586443*b^3)*cosh(d*x + c)^9 - 2*(5005*(21504*a^3 + 72352*a^2*b + 83980*a*b^2 + 1247103*b^3)*cosh(d*x + c)^6 - 13585*(21504*a^3 + 72352*a^2*b + 83980*a*b^2 + 838695*b^3)*cosh(d*x + c)^4 - 20837376*a^3 - 70109088*a^2*b - 419480100*a*b^2 - 351267345*b^3 + 3135*(64512*a^3 + 217056*a^2*b + 932620*a*b^2 + 1665235*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^9 + 9*(715*(43008*a^3 + 144704*a^2*b + 167960*a*b^2 - 2355639*b^3)*cosh(d*x + c)^7 - 2717*(43008*a^3 + 144704*a^2*b + 167960*a*b^2 - 1538823*b^3)*cosh(d*x + c)^5 + 1045*(129024*a^3 + 434112*a^2*b - 857480*a*b^2 - 2914769*b^3)*cosh(d*x + c)^3 - 969*(43008*a^3 + 144704*a^2*b - 529880*a*b^2 - 586443*b^3)*cosh(d*x + c))*sinh(d*x + c)^8 + 6783*(24576*a^3 - 54592*a^2*b - 293800*a*b^2 - 189761*b^3)*cosh(d*x + c)^7 - 6*(2145*(21504*a^3 + 72352*a^2*b + 83980*a*b^2 + 1247103*b^3)*cosh(d*x + c)^8 - 10868*(21504*a^3 + 72352*a^2*b + 83980*a*b^2 + 838695*b^3)*cosh(d*x + c)^6 + 6270*(64512*a^3 + 217056*a^2*b + 932620*a*b^2 + 1665235*b^3)*cosh(d*x + c)^4 + 27783168*a^3 + 248673824*a^2*b + 549145220*a*b^2 + 303230785*b^3 - 11628*(21504*a^3 + 72352*a^2*b + 432900*a*b^2 + 362505*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^7 + (5005*(43008*a^3 + 144704*a^2*b + 167960*a*b^2 - 2355639*b^3)*cosh(d*x + c)^9 - 32604*(43008*a^3 + 144704*a^2*b + 167960*a*b^2 - 1538823*b^3)*cosh(d*x + c)^7 + 26334*(129024*a^3 + 434112*a^2*b - 857480*a*b^2 - 2914769*b^3)*cosh(d*x + c)^5 - 81396*(43008*a^3 + 144704*a^2*b - 529880*a*b^2 - 586443*b^3)*cosh(d*x + c)^3 + 47481*(24576*a^3 - 54592*a^2*b - 293800*a*b^2 - 189761*b^3)*cosh(d*x + c))*sinh(d*x + c)^6 - 323*(1548288*a^3 - 8564416*a^2*b - 12926680*a*b^2 - 6120543*b^3)*cosh(d*x + c)^5 - 2*(3003*(21504*a^3 + 72352*a^2*b + 83980*a*b^2 + 1247103*b^3)*cosh(d*x + c)^10 - 24453*(21504*a^3 + 72352*a^2*b + 83980*a*b^2 + 838695*b^3)*cosh(d*x + c)^8 + 26334*(64512*a^3 + 217056*a^2*b + 932620*a*b^2 + 1665235*b^3)*cosh(d*x + c)^6 - 122094*(21504*a^3 + 72352*a^2*b + 432900*a*b^2 + 362505*b^3)*cosh(d*x + c)^4 - 250048512*a^3 - 3065771296*a^2*b - 4040697700*a*b^2 - 1763542209*b^3 + 20349*(86016*a^3 + 769888*a^2*b + 1700140*a*b^2 + 938795*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + (1365*(43008*a^3 + 144704*a^2*b + 167960*a*b^2 - 2355639*b^3)*cosh(d*x + c)^11 - 13585*(43008*a^3 + 144704*a^2*b + 167960*a*b^2 - 1538823*b^3)*cosh(d*x + c)^9 + 18810*(129024*a^3 + 434112*a^2*b - 857480*a*b^2 - 2914769*b^3)*cosh(d*x + c)^7 - 122094*(43008*a^3 + 144704*a^2*b - 529880*a*b^2 - 586443*b^3)*cosh(d*x + c)^5 + 237405*(24576*a^3 - 54592*a^2*b - 293800*a*b^2 - 189761*b^3)*cosh(d*x + c)^3 - 1615*(1548288*a^3 - 8564416*a^2*b - 12926680*a*b^2 - 6120543*b^3)*cosh(d*x + c))*sinh(d*x + c)^4 - 323*(8687616*a^3 + 15456448*a^2*b + 15194920*a*b^2 + 6026163*b^3)*cosh(d*x + c)^3 - 2*(455*(21504*a^3 + 72352*a^2*b + 83980*a*b^2 + 1247103*b^3)*cosh(d*x + c)^12 - 5434*(21504*a^3 + 72352*a^2*b + 83980*a*b^2 + 838695*b^3)*cosh(d*x + c)^10 + 9405*(64512*a^3 + 217056*a^2*b + 932620*a*b^2 + 1665235*b^3)*cosh(d*x + c)^8 - 81396*(21504*a^3 + 72352*a^2*b + 432900*a*b^2 + 362505*b^3)*cosh(d*x + c)^6 + 33915*(86016*a^3 + 769888*a^2*b + 1700140*a*b^2 + 938795*b^3)*cosh(d*x + c)^4 + 2569943040*a^3 + 6422325280*a^2*b + 6933472780*a*b^2 + 2675035935*b^3 - 3230*(774144*a^3 + 9491552*a^2*b + 12509900*a*b^2 + 5459883*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + (105*(43008*a^3 + 144704*a^2*b + 167960*a*b^2 - 2355639*b^3)*cosh(d*x + c)^13 - 1482*(43008*a^3 + 144704*a^2*b + 167960*a*b^2 - 1538823*b^3)*cosh(d*x + c)^11 + 3135*(129024*a^3 + 434112*a^2*b - 857480*a*b^2 - 2914769*b^3)*cosh(d*x + c)^9 - 34884*(43008*a^3 + 144704*a^2*b - 529880*a*b^2 - 586443*b^3)*cosh(d*x + c)^7 + 142443*(24576*a^3 - 54592*a^2*b - 293800*a*b^2 - 189761*b^3)*cosh(d*x + c)^5 - 3230*(1548288*a^3 - 8564416*a^2*b - 12926680*a*b^2 - 6120543*b^3)*cosh(d*x + c)^3 - 969*(8687616*a^3 + 15456448*a^2*b + 15194920*a*b^2 + 6026163*b^3)*cosh(d*x + c))*sinh(d*x + c)^2 + 12597*(86016*a^3 + 215488*a^2*b + 179720*a*b^2 + 65703*b^3)*cosh(d*x + c) - 2*(15*(21504*a^3 + 72352*a^2*b + 83980*a*b^2 + 1247103*b^3)*cosh(d*x + c)^14 - 247*(21504*a^3 + 72352*a^2*b + 83980*a*b^2 + 838695*b^3)*cosh(d*x + c)^12 + 627*(64512*a^3 + 217056*a^2*b + 932620*a*b^2 + 1665235*b^3)*cosh(d*x + c)^10 - 8721*(21504*a^3 + 72352*a^2*b + 432900*a*b^2 + 362505*b^3)*cosh(d*x + c)^8 + 6783*(86016*a^3 + 769888*a^2*b + 1700140*a*b^2 + 938795*b^3)*cosh(d*x + c)^6 - 1615*(774144*a^3 + 9491552*a^2*b + 12509900*a*b^2 + 5459883*b^3)*cosh(d*x + c)^4 - 2708858880*a^3 - 8648596320*a^2*b - 8918927940*a*b^2 - 3269488365*b^3 + 4845*(1591296*a^3 + 3976672*a^2*b + 4293172*a*b^2 + 1656369*b^3)*cosh(d*x + c)^2)*sinh(d*x + c))/(d*cosh(d*x + c)^23 + 23*d*cosh(d*x + c)*sinh(d*x + c)^22 + d*sinh(d*x + c)^23 - 19*d*cosh(d*x + c)^21 + (253*d*cosh(d*x + c)^2 - 19*d)*sinh(d*x + c)^21 + 7*(253*d*cosh(d*x + c)^3 - 57*d*cosh(d*x + c))*sinh(d*x + c)^20 + 171*d*cosh(d*x + c)^19 + (8855*d*cosh(d*x + c)^4 - 3990*d*cosh(d*x + c)^2 + 171*d)*sinh(d*x + c)^19 + 19*(1771*d*cosh(d*x + c)^5 - 1330*d*cosh(d*x + c)^3 + 171*d*cosh(d*x + c))*sinh(d*x + c)^18 - 969*d*cosh(d*x + c)^17 + 57*(1771*d*cosh(d*x + c)^6 - 1995*d*cosh(d*x + c)^4 + 513*d*cosh(d*x + c)^2 - 17*d)*sinh(d*x + c)^17 + 969*(253*d*cosh(d*x + c)^7 - 399*d*cosh(d*x + c)^5 + 171*d*cosh(d*x + c)^3 - 17*d*cosh(d*x + c))*sinh(d*x + c)^16 + 3875*d*cosh(d*x + c)^15 + (490314*d*cosh(d*x + c)^8 - 1031016*d*cosh(d*x + c)^6 + 662796*d*cosh(d*x + c)^4 - 131784*d*cosh(d*x + c)^2 + 3877*d)*sinh(d*x + c)^15 + (817190*d*cosh(d*x + c)^9 - 2209320*d*cosh(d*x + c)^7 + 1988388*d*cosh(d*x + c)^5 - 658920*d*cosh(d*x + c)^3 + 58125*d*cosh(d*x + c))*sinh(d*x + c)^14 - 11609*d*cosh(d*x + c)^13 + (1144066*d*cosh(d*x + c)^10 - 3866310*d*cosh(d*x + c)^8 + 4639572*d*cosh(d*x + c)^6 - 2306220*d*cosh(d*x + c)^4 + 407085*d*cosh(d*x + c)^2 - 11647*d)*sinh(d*x + c)^13 + 13*(104006*d*cosh(d*x + c)^11 - 429590*d*cosh(d*x + c)^9 + 662796*d*cosh(d*x + c)^7 - 461244*d*cosh(d*x + c)^5 + 135625*d*cosh(d*x + c)^3 - 11609*d*cosh(d*x + c))*sinh(d*x + c)^12 + 26961*d*cosh(d*x + c)^11 + (1352078*d*cosh(d*x + c)^12 - 6701604*d*cosh(d*x + c)^10 + 12924522*d*cosh(d*x + c)^8 - 11992344*d*cosh(d*x + c)^6 + 5292105*d*cosh(d*x + c)^4 - 908466*d*cosh(d*x + c)^2 + 27303*d)*sinh(d*x + c)^11 + (1144066*d*cosh(d*x + c)^13 - 6701604*d*cosh(d*x + c)^11 + 15796638*d*cosh(d*x + c)^9 - 18845112*d*cosh(d*x + c)^7 + 11636625*d*cosh(d*x + c)^5 - 3320174*d*cosh(d*x + c)^3 + 296571*d*cosh(d*x + c))*sinh(d*x + c)^10 - 49419*d*cosh(d*x + c)^9 + (817190*d*cosh(d*x + c)^14 - 5584670*d*cosh(d*x + c)^12 + 15796638*d*cosh(d*x + c)^10 - 23556390*d*cosh(d*x + c)^8 + 19404385*d*cosh(d*x + c)^6 - 8327605*d*cosh(d*x + c)^4 + 1501665*d*cosh(d*x + c)^2 - 51357*d)*sinh(d*x + c)^9 + 3*(163438*d*cosh(d*x + c)^15 - 1288770*d*cosh(d*x + c)^13 + 4308174*d*cosh(d*x + c)^11 - 7852130*d*cosh(d*x + c)^9 + 8311875*d*cosh(d*x + c)^7 - 4980261*d*cosh(d*x + c)^5 + 1482855*d*cosh(d*x + c)^3 - 148257*d*cosh(d*x + c))*sinh(d*x + c)^8 + 71706*d*cosh(d*x + c)^7 + 3*(81719*d*cosh(d*x + c)^16 - 736440*d*cosh(d*x + c)^14 + 2872116*d*cosh(d*x + c)^12 - 6281704*d*cosh(d*x + c)^10 + 8316165*d*cosh(d*x + c)^8 - 6662084*d*cosh(d*x + c)^6 + 3003330*d*cosh(d*x + c)^4 - 616284*d*cosh(d*x + c)^2 + 26486*d)*sinh(d*x + c)^7 + (100947*d*cosh(d*x + c)^17 - 1031016*d*cosh(d*x + c)^15 + 4639572*d*cosh(d*x + c)^13 - 11992344*d*cosh(d*x + c)^11 + 19394375*d*cosh(d*x + c)^9 - 19921044*d*cosh(d*x + c)^7 + 12455982*d*cosh(d*x + c)^5 - 4151196*d*cosh(d*x + c)^3 + 501942*d*cosh(d*x + c))*sinh(d*x + c)^6 - 80750*d*cosh(d*x + c)^5 + (33649*d*cosh(d*x + c)^18 - 386631*d*cosh(d*x + c)^16 + 1988388*d*cosh(d*x + c)^14 - 5996172*d*cosh(d*x + c)^12 + 11642631*d*cosh(d*x + c)^10 - 14989689*d*cosh(d*x + c)^8 + 12613986*d*cosh(d*x + c)^6 - 6470982*d*cosh(d*x + c)^4 + 1668618*d*cosh(d*x + c)^2 - 104006*d)*sinh(d*x + c)^5 + (8855*d*cosh(d*x + c)^19 - 113715*d*cosh(d*x + c)^17 + 662796*d*cosh(d*x + c)^15 - 2306220*d*cosh(d*x + c)^13 + 5289375*d*cosh(d*x + c)^11 - 8300435*d*cosh(d*x + c)^9 + 8897130*d*cosh(d*x + c)^7 - 6226794*d*cosh(d*x + c)^5 + 2509710*d*cosh(d*x + c)^3 - 403750*d*cosh(d*x + c))*sinh(d*x + c)^4 + 65246*d*cosh(d*x + c)^3 + (1771*d*cosh(d*x + c)^20 - 25270*d*cosh(d*x + c)^18 + 165699*d*cosh(d*x + c)^16 - 658920*d*cosh(d*x + c)^14 + 1764035*d*cosh(d*x + c)^12 - 3331042*d*cosh(d*x + c)^10 + 4504995*d*cosh(d*x + c)^8 - 4313988*d*cosh(d*x + c)^6 + 2781030*d*cosh(d*x + c)^4 - 1040060*d*cosh(d*x + c)^2 + 119510*d)*sinh(d*x + c)^3 + (253*d*cosh(d*x + c)^21 - 3990*d*cosh(d*x + c)^19 + 29241*d*cosh(d*x + c)^17 - 131784*d*cosh(d*x + c)^15 + 406875*d*cosh(d*x + c)^13 - 905502*d*cosh(d*x + c)^11 + 1482855*d*cosh(d*x + c)^9 - 1779084*d*cosh(d*x + c)^7 + 1505826*d*cosh(d*x + c)^5 - 807500*d*cosh(d*x + c)^3 + 195738*d*cosh(d*x + c))*sinh(d*x + c)^2 - 25194*d*cosh(d*x + c) + (23*d*cosh(d*x + c)^22 - 399*d*cosh(d*x + c)^20 + 3249*d*cosh(d*x + c)^18 - 16473*d*cosh(d*x + c)^16 + 58155*d*cosh(d*x + c)^14 - 151411*d*cosh(d*x + c)^12 + 300333*d*cosh(d*x + c)^10 - 462213*d*cosh(d*x + c)^8 + 556206*d*cosh(d*x + c)^6 - 520030*d*cosh(d*x + c)^4 + 358530*d*cosh(d*x + c)^2 - 125970*d)*sinh(d*x + c))","B",0
229,1,1617,0,0.745163," ","integrate(sinh(d*x+c)^7/(a-b*sinh(d*x+c)^4),x, algorithm=""fricas"")","-\frac{\cosh\left(d x + c\right)^{6} + 6 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + \sinh\left(d x + c\right)^{6} + 3 \, {\left(5 \, \cosh\left(d x + c\right)^{2} - 3\right)} \sinh\left(d x + c\right)^{4} - 9 \, \cosh\left(d x + c\right)^{4} + 4 \, {\left(5 \, \cosh\left(d x + c\right)^{3} - 9 \, \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 3 \, {\left(5 \, \cosh\left(d x + c\right)^{4} - 18 \, \cosh\left(d x + c\right)^{2} - 3\right)} \sinh\left(d x + c\right)^{2} - 6 \, {\left(b d \cosh\left(d x + c\right)^{3} + 3 \, b d \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, b d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + b d \sinh\left(d x + c\right)^{3}\right)} \sqrt{-\frac{{\left(a b^{3} - b^{4}\right)} d^{2} \sqrt{\frac{a^{5}}{{\left(a^{2} b^{7} - 2 \, a b^{8} + b^{9}\right)} d^{4}}} + a^{2}}{{\left(a b^{3} - b^{4}\right)} d^{2}}} \log\left(a^{3} \cosh\left(d x + c\right)^{2} + 2 \, a^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a^{3} \sinh\left(d x + c\right)^{2} + a^{3} + 2 \, {\left(a^{2} b^{2} d \cosh\left(d x + c\right) + a^{2} b^{2} d \sinh\left(d x + c\right) - {\left({\left(a b^{5} - b^{6}\right)} d^{3} \cosh\left(d x + c\right) + {\left(a b^{5} - b^{6}\right)} d^{3} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{5}}{{\left(a^{2} b^{7} - 2 \, a b^{8} + b^{9}\right)} d^{4}}}\right)} \sqrt{-\frac{{\left(a b^{3} - b^{4}\right)} d^{2} \sqrt{\frac{a^{5}}{{\left(a^{2} b^{7} - 2 \, a b^{8} + b^{9}\right)} d^{4}}} + a^{2}}{{\left(a b^{3} - b^{4}\right)} d^{2}}}\right) + 6 \, {\left(b d \cosh\left(d x + c\right)^{3} + 3 \, b d \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, b d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + b d \sinh\left(d x + c\right)^{3}\right)} \sqrt{-\frac{{\left(a b^{3} - b^{4}\right)} d^{2} \sqrt{\frac{a^{5}}{{\left(a^{2} b^{7} - 2 \, a b^{8} + b^{9}\right)} d^{4}}} + a^{2}}{{\left(a b^{3} - b^{4}\right)} d^{2}}} \log\left(a^{3} \cosh\left(d x + c\right)^{2} + 2 \, a^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a^{3} \sinh\left(d x + c\right)^{2} + a^{3} - 2 \, {\left(a^{2} b^{2} d \cosh\left(d x + c\right) + a^{2} b^{2} d \sinh\left(d x + c\right) - {\left({\left(a b^{5} - b^{6}\right)} d^{3} \cosh\left(d x + c\right) + {\left(a b^{5} - b^{6}\right)} d^{3} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{5}}{{\left(a^{2} b^{7} - 2 \, a b^{8} + b^{9}\right)} d^{4}}}\right)} \sqrt{-\frac{{\left(a b^{3} - b^{4}\right)} d^{2} \sqrt{\frac{a^{5}}{{\left(a^{2} b^{7} - 2 \, a b^{8} + b^{9}\right)} d^{4}}} + a^{2}}{{\left(a b^{3} - b^{4}\right)} d^{2}}}\right) - 6 \, {\left(b d \cosh\left(d x + c\right)^{3} + 3 \, b d \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, b d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + b d \sinh\left(d x + c\right)^{3}\right)} \sqrt{\frac{{\left(a b^{3} - b^{4}\right)} d^{2} \sqrt{\frac{a^{5}}{{\left(a^{2} b^{7} - 2 \, a b^{8} + b^{9}\right)} d^{4}}} - a^{2}}{{\left(a b^{3} - b^{4}\right)} d^{2}}} \log\left(a^{3} \cosh\left(d x + c\right)^{2} + 2 \, a^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a^{3} \sinh\left(d x + c\right)^{2} + a^{3} + 2 \, {\left(a^{2} b^{2} d \cosh\left(d x + c\right) + a^{2} b^{2} d \sinh\left(d x + c\right) + {\left({\left(a b^{5} - b^{6}\right)} d^{3} \cosh\left(d x + c\right) + {\left(a b^{5} - b^{6}\right)} d^{3} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{5}}{{\left(a^{2} b^{7} - 2 \, a b^{8} + b^{9}\right)} d^{4}}}\right)} \sqrt{\frac{{\left(a b^{3} - b^{4}\right)} d^{2} \sqrt{\frac{a^{5}}{{\left(a^{2} b^{7} - 2 \, a b^{8} + b^{9}\right)} d^{4}}} - a^{2}}{{\left(a b^{3} - b^{4}\right)} d^{2}}}\right) + 6 \, {\left(b d \cosh\left(d x + c\right)^{3} + 3 \, b d \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, b d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + b d \sinh\left(d x + c\right)^{3}\right)} \sqrt{\frac{{\left(a b^{3} - b^{4}\right)} d^{2} \sqrt{\frac{a^{5}}{{\left(a^{2} b^{7} - 2 \, a b^{8} + b^{9}\right)} d^{4}}} - a^{2}}{{\left(a b^{3} - b^{4}\right)} d^{2}}} \log\left(a^{3} \cosh\left(d x + c\right)^{2} + 2 \, a^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a^{3} \sinh\left(d x + c\right)^{2} + a^{3} - 2 \, {\left(a^{2} b^{2} d \cosh\left(d x + c\right) + a^{2} b^{2} d \sinh\left(d x + c\right) + {\left({\left(a b^{5} - b^{6}\right)} d^{3} \cosh\left(d x + c\right) + {\left(a b^{5} - b^{6}\right)} d^{3} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{5}}{{\left(a^{2} b^{7} - 2 \, a b^{8} + b^{9}\right)} d^{4}}}\right)} \sqrt{\frac{{\left(a b^{3} - b^{4}\right)} d^{2} \sqrt{\frac{a^{5}}{{\left(a^{2} b^{7} - 2 \, a b^{8} + b^{9}\right)} d^{4}}} - a^{2}}{{\left(a b^{3} - b^{4}\right)} d^{2}}}\right) - 9 \, \cosh\left(d x + c\right)^{2} + 6 \, {\left(\cosh\left(d x + c\right)^{5} - 6 \, \cosh\left(d x + c\right)^{3} - 3 \, \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + 1}{24 \, {\left(b d \cosh\left(d x + c\right)^{3} + 3 \, b d \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, b d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + b d \sinh\left(d x + c\right)^{3}\right)}}"," ",0,"-1/24*(cosh(d*x + c)^6 + 6*cosh(d*x + c)*sinh(d*x + c)^5 + sinh(d*x + c)^6 + 3*(5*cosh(d*x + c)^2 - 3)*sinh(d*x + c)^4 - 9*cosh(d*x + c)^4 + 4*(5*cosh(d*x + c)^3 - 9*cosh(d*x + c))*sinh(d*x + c)^3 + 3*(5*cosh(d*x + c)^4 - 18*cosh(d*x + c)^2 - 3)*sinh(d*x + c)^2 - 6*(b*d*cosh(d*x + c)^3 + 3*b*d*cosh(d*x + c)^2*sinh(d*x + c) + 3*b*d*cosh(d*x + c)*sinh(d*x + c)^2 + b*d*sinh(d*x + c)^3)*sqrt(-((a*b^3 - b^4)*d^2*sqrt(a^5/((a^2*b^7 - 2*a*b^8 + b^9)*d^4)) + a^2)/((a*b^3 - b^4)*d^2))*log(a^3*cosh(d*x + c)^2 + 2*a^3*cosh(d*x + c)*sinh(d*x + c) + a^3*sinh(d*x + c)^2 + a^3 + 2*(a^2*b^2*d*cosh(d*x + c) + a^2*b^2*d*sinh(d*x + c) - ((a*b^5 - b^6)*d^3*cosh(d*x + c) + (a*b^5 - b^6)*d^3*sinh(d*x + c))*sqrt(a^5/((a^2*b^7 - 2*a*b^8 + b^9)*d^4)))*sqrt(-((a*b^3 - b^4)*d^2*sqrt(a^5/((a^2*b^7 - 2*a*b^8 + b^9)*d^4)) + a^2)/((a*b^3 - b^4)*d^2))) + 6*(b*d*cosh(d*x + c)^3 + 3*b*d*cosh(d*x + c)^2*sinh(d*x + c) + 3*b*d*cosh(d*x + c)*sinh(d*x + c)^2 + b*d*sinh(d*x + c)^3)*sqrt(-((a*b^3 - b^4)*d^2*sqrt(a^5/((a^2*b^7 - 2*a*b^8 + b^9)*d^4)) + a^2)/((a*b^3 - b^4)*d^2))*log(a^3*cosh(d*x + c)^2 + 2*a^3*cosh(d*x + c)*sinh(d*x + c) + a^3*sinh(d*x + c)^2 + a^3 - 2*(a^2*b^2*d*cosh(d*x + c) + a^2*b^2*d*sinh(d*x + c) - ((a*b^5 - b^6)*d^3*cosh(d*x + c) + (a*b^5 - b^6)*d^3*sinh(d*x + c))*sqrt(a^5/((a^2*b^7 - 2*a*b^8 + b^9)*d^4)))*sqrt(-((a*b^3 - b^4)*d^2*sqrt(a^5/((a^2*b^7 - 2*a*b^8 + b^9)*d^4)) + a^2)/((a*b^3 - b^4)*d^2))) - 6*(b*d*cosh(d*x + c)^3 + 3*b*d*cosh(d*x + c)^2*sinh(d*x + c) + 3*b*d*cosh(d*x + c)*sinh(d*x + c)^2 + b*d*sinh(d*x + c)^3)*sqrt(((a*b^3 - b^4)*d^2*sqrt(a^5/((a^2*b^7 - 2*a*b^8 + b^9)*d^4)) - a^2)/((a*b^3 - b^4)*d^2))*log(a^3*cosh(d*x + c)^2 + 2*a^3*cosh(d*x + c)*sinh(d*x + c) + a^3*sinh(d*x + c)^2 + a^3 + 2*(a^2*b^2*d*cosh(d*x + c) + a^2*b^2*d*sinh(d*x + c) + ((a*b^5 - b^6)*d^3*cosh(d*x + c) + (a*b^5 - b^6)*d^3*sinh(d*x + c))*sqrt(a^5/((a^2*b^7 - 2*a*b^8 + b^9)*d^4)))*sqrt(((a*b^3 - b^4)*d^2*sqrt(a^5/((a^2*b^7 - 2*a*b^8 + b^9)*d^4)) - a^2)/((a*b^3 - b^4)*d^2))) + 6*(b*d*cosh(d*x + c)^3 + 3*b*d*cosh(d*x + c)^2*sinh(d*x + c) + 3*b*d*cosh(d*x + c)*sinh(d*x + c)^2 + b*d*sinh(d*x + c)^3)*sqrt(((a*b^3 - b^4)*d^2*sqrt(a^5/((a^2*b^7 - 2*a*b^8 + b^9)*d^4)) - a^2)/((a*b^3 - b^4)*d^2))*log(a^3*cosh(d*x + c)^2 + 2*a^3*cosh(d*x + c)*sinh(d*x + c) + a^3*sinh(d*x + c)^2 + a^3 - 2*(a^2*b^2*d*cosh(d*x + c) + a^2*b^2*d*sinh(d*x + c) + ((a*b^5 - b^6)*d^3*cosh(d*x + c) + (a*b^5 - b^6)*d^3*sinh(d*x + c))*sqrt(a^5/((a^2*b^7 - 2*a*b^8 + b^9)*d^4)))*sqrt(((a*b^3 - b^4)*d^2*sqrt(a^5/((a^2*b^7 - 2*a*b^8 + b^9)*d^4)) - a^2)/((a*b^3 - b^4)*d^2))) - 9*cosh(d*x + c)^2 + 6*(cosh(d*x + c)^5 - 6*cosh(d*x + c)^3 - 3*cosh(d*x + c))*sinh(d*x + c) + 1)/(b*d*cosh(d*x + c)^3 + 3*b*d*cosh(d*x + c)^2*sinh(d*x + c) + 3*b*d*cosh(d*x + c)*sinh(d*x + c)^2 + b*d*sinh(d*x + c)^3)","B",0
230,1,1247,0,0.559970," ","integrate(sinh(d*x+c)^5/(a-b*sinh(d*x+c)^4),x, algorithm=""fricas"")","\frac{{\left(b d \cosh\left(d x + c\right) + b d \sinh\left(d x + c\right)\right)} \sqrt{-\frac{{\left(a b^{2} - b^{3}\right)} d^{2} \sqrt{\frac{a^{3}}{{\left(a^{2} b^{5} - 2 \, a b^{6} + b^{7}\right)} d^{4}}} + a}{{\left(a b^{2} - b^{3}\right)} d^{2}}} \log\left(a^{2} \cosh\left(d x + c\right)^{2} + 2 \, a^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a^{2} \sinh\left(d x + c\right)^{2} + a^{2} + 2 \, {\left(a^{2} b d \cosh\left(d x + c\right) + a^{2} b d \sinh\left(d x + c\right) - {\left({\left(a b^{4} - b^{5}\right)} d^{3} \cosh\left(d x + c\right) + {\left(a b^{4} - b^{5}\right)} d^{3} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{3}}{{\left(a^{2} b^{5} - 2 \, a b^{6} + b^{7}\right)} d^{4}}}\right)} \sqrt{-\frac{{\left(a b^{2} - b^{3}\right)} d^{2} \sqrt{\frac{a^{3}}{{\left(a^{2} b^{5} - 2 \, a b^{6} + b^{7}\right)} d^{4}}} + a}{{\left(a b^{2} - b^{3}\right)} d^{2}}}\right) - {\left(b d \cosh\left(d x + c\right) + b d \sinh\left(d x + c\right)\right)} \sqrt{-\frac{{\left(a b^{2} - b^{3}\right)} d^{2} \sqrt{\frac{a^{3}}{{\left(a^{2} b^{5} - 2 \, a b^{6} + b^{7}\right)} d^{4}}} + a}{{\left(a b^{2} - b^{3}\right)} d^{2}}} \log\left(a^{2} \cosh\left(d x + c\right)^{2} + 2 \, a^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a^{2} \sinh\left(d x + c\right)^{2} + a^{2} - 2 \, {\left(a^{2} b d \cosh\left(d x + c\right) + a^{2} b d \sinh\left(d x + c\right) - {\left({\left(a b^{4} - b^{5}\right)} d^{3} \cosh\left(d x + c\right) + {\left(a b^{4} - b^{5}\right)} d^{3} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{3}}{{\left(a^{2} b^{5} - 2 \, a b^{6} + b^{7}\right)} d^{4}}}\right)} \sqrt{-\frac{{\left(a b^{2} - b^{3}\right)} d^{2} \sqrt{\frac{a^{3}}{{\left(a^{2} b^{5} - 2 \, a b^{6} + b^{7}\right)} d^{4}}} + a}{{\left(a b^{2} - b^{3}\right)} d^{2}}}\right) + {\left(b d \cosh\left(d x + c\right) + b d \sinh\left(d x + c\right)\right)} \sqrt{\frac{{\left(a b^{2} - b^{3}\right)} d^{2} \sqrt{\frac{a^{3}}{{\left(a^{2} b^{5} - 2 \, a b^{6} + b^{7}\right)} d^{4}}} - a}{{\left(a b^{2} - b^{3}\right)} d^{2}}} \log\left(a^{2} \cosh\left(d x + c\right)^{2} + 2 \, a^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a^{2} \sinh\left(d x + c\right)^{2} + a^{2} + 2 \, {\left(a^{2} b d \cosh\left(d x + c\right) + a^{2} b d \sinh\left(d x + c\right) + {\left({\left(a b^{4} - b^{5}\right)} d^{3} \cosh\left(d x + c\right) + {\left(a b^{4} - b^{5}\right)} d^{3} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{3}}{{\left(a^{2} b^{5} - 2 \, a b^{6} + b^{7}\right)} d^{4}}}\right)} \sqrt{\frac{{\left(a b^{2} - b^{3}\right)} d^{2} \sqrt{\frac{a^{3}}{{\left(a^{2} b^{5} - 2 \, a b^{6} + b^{7}\right)} d^{4}}} - a}{{\left(a b^{2} - b^{3}\right)} d^{2}}}\right) - {\left(b d \cosh\left(d x + c\right) + b d \sinh\left(d x + c\right)\right)} \sqrt{\frac{{\left(a b^{2} - b^{3}\right)} d^{2} \sqrt{\frac{a^{3}}{{\left(a^{2} b^{5} - 2 \, a b^{6} + b^{7}\right)} d^{4}}} - a}{{\left(a b^{2} - b^{3}\right)} d^{2}}} \log\left(a^{2} \cosh\left(d x + c\right)^{2} + 2 \, a^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a^{2} \sinh\left(d x + c\right)^{2} + a^{2} - 2 \, {\left(a^{2} b d \cosh\left(d x + c\right) + a^{2} b d \sinh\left(d x + c\right) + {\left({\left(a b^{4} - b^{5}\right)} d^{3} \cosh\left(d x + c\right) + {\left(a b^{4} - b^{5}\right)} d^{3} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{3}}{{\left(a^{2} b^{5} - 2 \, a b^{6} + b^{7}\right)} d^{4}}}\right)} \sqrt{\frac{{\left(a b^{2} - b^{3}\right)} d^{2} \sqrt{\frac{a^{3}}{{\left(a^{2} b^{5} - 2 \, a b^{6} + b^{7}\right)} d^{4}}} - a}{{\left(a b^{2} - b^{3}\right)} d^{2}}}\right) - 2 \, \cosh\left(d x + c\right)^{2} - 4 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) - 2 \, \sinh\left(d x + c\right)^{2} - 2}{4 \, {\left(b d \cosh\left(d x + c\right) + b d \sinh\left(d x + c\right)\right)}}"," ",0,"1/4*((b*d*cosh(d*x + c) + b*d*sinh(d*x + c))*sqrt(-((a*b^2 - b^3)*d^2*sqrt(a^3/((a^2*b^5 - 2*a*b^6 + b^7)*d^4)) + a)/((a*b^2 - b^3)*d^2))*log(a^2*cosh(d*x + c)^2 + 2*a^2*cosh(d*x + c)*sinh(d*x + c) + a^2*sinh(d*x + c)^2 + a^2 + 2*(a^2*b*d*cosh(d*x + c) + a^2*b*d*sinh(d*x + c) - ((a*b^4 - b^5)*d^3*cosh(d*x + c) + (a*b^4 - b^5)*d^3*sinh(d*x + c))*sqrt(a^3/((a^2*b^5 - 2*a*b^6 + b^7)*d^4)))*sqrt(-((a*b^2 - b^3)*d^2*sqrt(a^3/((a^2*b^5 - 2*a*b^6 + b^7)*d^4)) + a)/((a*b^2 - b^3)*d^2))) - (b*d*cosh(d*x + c) + b*d*sinh(d*x + c))*sqrt(-((a*b^2 - b^3)*d^2*sqrt(a^3/((a^2*b^5 - 2*a*b^6 + b^7)*d^4)) + a)/((a*b^2 - b^3)*d^2))*log(a^2*cosh(d*x + c)^2 + 2*a^2*cosh(d*x + c)*sinh(d*x + c) + a^2*sinh(d*x + c)^2 + a^2 - 2*(a^2*b*d*cosh(d*x + c) + a^2*b*d*sinh(d*x + c) - ((a*b^4 - b^5)*d^3*cosh(d*x + c) + (a*b^4 - b^5)*d^3*sinh(d*x + c))*sqrt(a^3/((a^2*b^5 - 2*a*b^6 + b^7)*d^4)))*sqrt(-((a*b^2 - b^3)*d^2*sqrt(a^3/((a^2*b^5 - 2*a*b^6 + b^7)*d^4)) + a)/((a*b^2 - b^3)*d^2))) + (b*d*cosh(d*x + c) + b*d*sinh(d*x + c))*sqrt(((a*b^2 - b^3)*d^2*sqrt(a^3/((a^2*b^5 - 2*a*b^6 + b^7)*d^4)) - a)/((a*b^2 - b^3)*d^2))*log(a^2*cosh(d*x + c)^2 + 2*a^2*cosh(d*x + c)*sinh(d*x + c) + a^2*sinh(d*x + c)^2 + a^2 + 2*(a^2*b*d*cosh(d*x + c) + a^2*b*d*sinh(d*x + c) + ((a*b^4 - b^5)*d^3*cosh(d*x + c) + (a*b^4 - b^5)*d^3*sinh(d*x + c))*sqrt(a^3/((a^2*b^5 - 2*a*b^6 + b^7)*d^4)))*sqrt(((a*b^2 - b^3)*d^2*sqrt(a^3/((a^2*b^5 - 2*a*b^6 + b^7)*d^4)) - a)/((a*b^2 - b^3)*d^2))) - (b*d*cosh(d*x + c) + b*d*sinh(d*x + c))*sqrt(((a*b^2 - b^3)*d^2*sqrt(a^3/((a^2*b^5 - 2*a*b^6 + b^7)*d^4)) - a)/((a*b^2 - b^3)*d^2))*log(a^2*cosh(d*x + c)^2 + 2*a^2*cosh(d*x + c)*sinh(d*x + c) + a^2*sinh(d*x + c)^2 + a^2 - 2*(a^2*b*d*cosh(d*x + c) + a^2*b*d*sinh(d*x + c) + ((a*b^4 - b^5)*d^3*cosh(d*x + c) + (a*b^4 - b^5)*d^3*sinh(d*x + c))*sqrt(a^3/((a^2*b^5 - 2*a*b^6 + b^7)*d^4)))*sqrt(((a*b^2 - b^3)*d^2*sqrt(a^3/((a^2*b^5 - 2*a*b^6 + b^7)*d^4)) - a)/((a*b^2 - b^3)*d^2))) - 2*cosh(d*x + c)^2 - 4*cosh(d*x + c)*sinh(d*x + c) - 2*sinh(d*x + c)^2 - 2)/(b*d*cosh(d*x + c) + b*d*sinh(d*x + c))","B",0
231,1,975,0,1.137694," ","integrate(sinh(d*x+c)^3/(a-b*sinh(d*x+c)^4),x, algorithm=""fricas"")","\frac{1}{4} \, \sqrt{-\frac{{\left(a b - b^{2}\right)} d^{2} \sqrt{\frac{a}{{\left(a^{2} b^{3} - 2 \, a b^{4} + b^{5}\right)} d^{4}}} + 1}{{\left(a b - b^{2}\right)} d^{2}}} \log\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} + 2 \, {\left(b d \cosh\left(d x + c\right) + b d \sinh\left(d x + c\right) - {\left({\left(a b^{2} - b^{3}\right)} d^{3} \cosh\left(d x + c\right) + {\left(a b^{2} - b^{3}\right)} d^{3} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a}{{\left(a^{2} b^{3} - 2 \, a b^{4} + b^{5}\right)} d^{4}}}\right)} \sqrt{-\frac{{\left(a b - b^{2}\right)} d^{2} \sqrt{\frac{a}{{\left(a^{2} b^{3} - 2 \, a b^{4} + b^{5}\right)} d^{4}}} + 1}{{\left(a b - b^{2}\right)} d^{2}}} + 1\right) - \frac{1}{4} \, \sqrt{-\frac{{\left(a b - b^{2}\right)} d^{2} \sqrt{\frac{a}{{\left(a^{2} b^{3} - 2 \, a b^{4} + b^{5}\right)} d^{4}}} + 1}{{\left(a b - b^{2}\right)} d^{2}}} \log\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} - 2 \, {\left(b d \cosh\left(d x + c\right) + b d \sinh\left(d x + c\right) - {\left({\left(a b^{2} - b^{3}\right)} d^{3} \cosh\left(d x + c\right) + {\left(a b^{2} - b^{3}\right)} d^{3} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a}{{\left(a^{2} b^{3} - 2 \, a b^{4} + b^{5}\right)} d^{4}}}\right)} \sqrt{-\frac{{\left(a b - b^{2}\right)} d^{2} \sqrt{\frac{a}{{\left(a^{2} b^{3} - 2 \, a b^{4} + b^{5}\right)} d^{4}}} + 1}{{\left(a b - b^{2}\right)} d^{2}}} + 1\right) + \frac{1}{4} \, \sqrt{\frac{{\left(a b - b^{2}\right)} d^{2} \sqrt{\frac{a}{{\left(a^{2} b^{3} - 2 \, a b^{4} + b^{5}\right)} d^{4}}} - 1}{{\left(a b - b^{2}\right)} d^{2}}} \log\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} + 2 \, {\left(b d \cosh\left(d x + c\right) + b d \sinh\left(d x + c\right) + {\left({\left(a b^{2} - b^{3}\right)} d^{3} \cosh\left(d x + c\right) + {\left(a b^{2} - b^{3}\right)} d^{3} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a}{{\left(a^{2} b^{3} - 2 \, a b^{4} + b^{5}\right)} d^{4}}}\right)} \sqrt{\frac{{\left(a b - b^{2}\right)} d^{2} \sqrt{\frac{a}{{\left(a^{2} b^{3} - 2 \, a b^{4} + b^{5}\right)} d^{4}}} - 1}{{\left(a b - b^{2}\right)} d^{2}}} + 1\right) - \frac{1}{4} \, \sqrt{\frac{{\left(a b - b^{2}\right)} d^{2} \sqrt{\frac{a}{{\left(a^{2} b^{3} - 2 \, a b^{4} + b^{5}\right)} d^{4}}} - 1}{{\left(a b - b^{2}\right)} d^{2}}} \log\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} - 2 \, {\left(b d \cosh\left(d x + c\right) + b d \sinh\left(d x + c\right) + {\left({\left(a b^{2} - b^{3}\right)} d^{3} \cosh\left(d x + c\right) + {\left(a b^{2} - b^{3}\right)} d^{3} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a}{{\left(a^{2} b^{3} - 2 \, a b^{4} + b^{5}\right)} d^{4}}}\right)} \sqrt{\frac{{\left(a b - b^{2}\right)} d^{2} \sqrt{\frac{a}{{\left(a^{2} b^{3} - 2 \, a b^{4} + b^{5}\right)} d^{4}}} - 1}{{\left(a b - b^{2}\right)} d^{2}}} + 1\right)"," ",0,"1/4*sqrt(-((a*b - b^2)*d^2*sqrt(a/((a^2*b^3 - 2*a*b^4 + b^5)*d^4)) + 1)/((a*b - b^2)*d^2))*log(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 2*(b*d*cosh(d*x + c) + b*d*sinh(d*x + c) - ((a*b^2 - b^3)*d^3*cosh(d*x + c) + (a*b^2 - b^3)*d^3*sinh(d*x + c))*sqrt(a/((a^2*b^3 - 2*a*b^4 + b^5)*d^4)))*sqrt(-((a*b - b^2)*d^2*sqrt(a/((a^2*b^3 - 2*a*b^4 + b^5)*d^4)) + 1)/((a*b - b^2)*d^2)) + 1) - 1/4*sqrt(-((a*b - b^2)*d^2*sqrt(a/((a^2*b^3 - 2*a*b^4 + b^5)*d^4)) + 1)/((a*b - b^2)*d^2))*log(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 2*(b*d*cosh(d*x + c) + b*d*sinh(d*x + c) - ((a*b^2 - b^3)*d^3*cosh(d*x + c) + (a*b^2 - b^3)*d^3*sinh(d*x + c))*sqrt(a/((a^2*b^3 - 2*a*b^4 + b^5)*d^4)))*sqrt(-((a*b - b^2)*d^2*sqrt(a/((a^2*b^3 - 2*a*b^4 + b^5)*d^4)) + 1)/((a*b - b^2)*d^2)) + 1) + 1/4*sqrt(((a*b - b^2)*d^2*sqrt(a/((a^2*b^3 - 2*a*b^4 + b^5)*d^4)) - 1)/((a*b - b^2)*d^2))*log(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 2*(b*d*cosh(d*x + c) + b*d*sinh(d*x + c) + ((a*b^2 - b^3)*d^3*cosh(d*x + c) + (a*b^2 - b^3)*d^3*sinh(d*x + c))*sqrt(a/((a^2*b^3 - 2*a*b^4 + b^5)*d^4)))*sqrt(((a*b - b^2)*d^2*sqrt(a/((a^2*b^3 - 2*a*b^4 + b^5)*d^4)) - 1)/((a*b - b^2)*d^2)) + 1) - 1/4*sqrt(((a*b - b^2)*d^2*sqrt(a/((a^2*b^3 - 2*a*b^4 + b^5)*d^4)) - 1)/((a*b - b^2)*d^2))*log(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 2*(b*d*cosh(d*x + c) + b*d*sinh(d*x + c) + ((a*b^2 - b^3)*d^3*cosh(d*x + c) + (a*b^2 - b^3)*d^3*sinh(d*x + c))*sqrt(a/((a^2*b^3 - 2*a*b^4 + b^5)*d^4)))*sqrt(((a*b - b^2)*d^2*sqrt(a/((a^2*b^3 - 2*a*b^4 + b^5)*d^4)) - 1)/((a*b - b^2)*d^2)) + 1)","B",0
232,1,979,0,0.935698," ","integrate(sinh(d*x+c)/(a-b*sinh(d*x+c)^4),x, algorithm=""fricas"")","\frac{1}{4} \, \sqrt{-\frac{{\left(a^{2} - a b\right)} d^{2} \sqrt{\frac{1}{{\left(a^{3} b - 2 \, a^{2} b^{2} + a b^{3}\right)} d^{4}}} + 1}{{\left(a^{2} - a b\right)} d^{2}}} \log\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} + 2 \, {\left(a d \cosh\left(d x + c\right) + a d \sinh\left(d x + c\right) - {\left({\left(a^{2} b - a b^{2}\right)} d^{3} \cosh\left(d x + c\right) + {\left(a^{2} b - a b^{2}\right)} d^{3} \sinh\left(d x + c\right)\right)} \sqrt{\frac{1}{{\left(a^{3} b - 2 \, a^{2} b^{2} + a b^{3}\right)} d^{4}}}\right)} \sqrt{-\frac{{\left(a^{2} - a b\right)} d^{2} \sqrt{\frac{1}{{\left(a^{3} b - 2 \, a^{2} b^{2} + a b^{3}\right)} d^{4}}} + 1}{{\left(a^{2} - a b\right)} d^{2}}} + 1\right) - \frac{1}{4} \, \sqrt{-\frac{{\left(a^{2} - a b\right)} d^{2} \sqrt{\frac{1}{{\left(a^{3} b - 2 \, a^{2} b^{2} + a b^{3}\right)} d^{4}}} + 1}{{\left(a^{2} - a b\right)} d^{2}}} \log\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} - 2 \, {\left(a d \cosh\left(d x + c\right) + a d \sinh\left(d x + c\right) - {\left({\left(a^{2} b - a b^{2}\right)} d^{3} \cosh\left(d x + c\right) + {\left(a^{2} b - a b^{2}\right)} d^{3} \sinh\left(d x + c\right)\right)} \sqrt{\frac{1}{{\left(a^{3} b - 2 \, a^{2} b^{2} + a b^{3}\right)} d^{4}}}\right)} \sqrt{-\frac{{\left(a^{2} - a b\right)} d^{2} \sqrt{\frac{1}{{\left(a^{3} b - 2 \, a^{2} b^{2} + a b^{3}\right)} d^{4}}} + 1}{{\left(a^{2} - a b\right)} d^{2}}} + 1\right) + \frac{1}{4} \, \sqrt{\frac{{\left(a^{2} - a b\right)} d^{2} \sqrt{\frac{1}{{\left(a^{3} b - 2 \, a^{2} b^{2} + a b^{3}\right)} d^{4}}} - 1}{{\left(a^{2} - a b\right)} d^{2}}} \log\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} + 2 \, {\left(a d \cosh\left(d x + c\right) + a d \sinh\left(d x + c\right) + {\left({\left(a^{2} b - a b^{2}\right)} d^{3} \cosh\left(d x + c\right) + {\left(a^{2} b - a b^{2}\right)} d^{3} \sinh\left(d x + c\right)\right)} \sqrt{\frac{1}{{\left(a^{3} b - 2 \, a^{2} b^{2} + a b^{3}\right)} d^{4}}}\right)} \sqrt{\frac{{\left(a^{2} - a b\right)} d^{2} \sqrt{\frac{1}{{\left(a^{3} b - 2 \, a^{2} b^{2} + a b^{3}\right)} d^{4}}} - 1}{{\left(a^{2} - a b\right)} d^{2}}} + 1\right) - \frac{1}{4} \, \sqrt{\frac{{\left(a^{2} - a b\right)} d^{2} \sqrt{\frac{1}{{\left(a^{3} b - 2 \, a^{2} b^{2} + a b^{3}\right)} d^{4}}} - 1}{{\left(a^{2} - a b\right)} d^{2}}} \log\left(\cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} - 2 \, {\left(a d \cosh\left(d x + c\right) + a d \sinh\left(d x + c\right) + {\left({\left(a^{2} b - a b^{2}\right)} d^{3} \cosh\left(d x + c\right) + {\left(a^{2} b - a b^{2}\right)} d^{3} \sinh\left(d x + c\right)\right)} \sqrt{\frac{1}{{\left(a^{3} b - 2 \, a^{2} b^{2} + a b^{3}\right)} d^{4}}}\right)} \sqrt{\frac{{\left(a^{2} - a b\right)} d^{2} \sqrt{\frac{1}{{\left(a^{3} b - 2 \, a^{2} b^{2} + a b^{3}\right)} d^{4}}} - 1}{{\left(a^{2} - a b\right)} d^{2}}} + 1\right)"," ",0,"1/4*sqrt(-((a^2 - a*b)*d^2*sqrt(1/((a^3*b - 2*a^2*b^2 + a*b^3)*d^4)) + 1)/((a^2 - a*b)*d^2))*log(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 2*(a*d*cosh(d*x + c) + a*d*sinh(d*x + c) - ((a^2*b - a*b^2)*d^3*cosh(d*x + c) + (a^2*b - a*b^2)*d^3*sinh(d*x + c))*sqrt(1/((a^3*b - 2*a^2*b^2 + a*b^3)*d^4)))*sqrt(-((a^2 - a*b)*d^2*sqrt(1/((a^3*b - 2*a^2*b^2 + a*b^3)*d^4)) + 1)/((a^2 - a*b)*d^2)) + 1) - 1/4*sqrt(-((a^2 - a*b)*d^2*sqrt(1/((a^3*b - 2*a^2*b^2 + a*b^3)*d^4)) + 1)/((a^2 - a*b)*d^2))*log(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 2*(a*d*cosh(d*x + c) + a*d*sinh(d*x + c) - ((a^2*b - a*b^2)*d^3*cosh(d*x + c) + (a^2*b - a*b^2)*d^3*sinh(d*x + c))*sqrt(1/((a^3*b - 2*a^2*b^2 + a*b^3)*d^4)))*sqrt(-((a^2 - a*b)*d^2*sqrt(1/((a^3*b - 2*a^2*b^2 + a*b^3)*d^4)) + 1)/((a^2 - a*b)*d^2)) + 1) + 1/4*sqrt(((a^2 - a*b)*d^2*sqrt(1/((a^3*b - 2*a^2*b^2 + a*b^3)*d^4)) - 1)/((a^2 - a*b)*d^2))*log(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 2*(a*d*cosh(d*x + c) + a*d*sinh(d*x + c) + ((a^2*b - a*b^2)*d^3*cosh(d*x + c) + (a^2*b - a*b^2)*d^3*sinh(d*x + c))*sqrt(1/((a^3*b - 2*a^2*b^2 + a*b^3)*d^4)))*sqrt(((a^2 - a*b)*d^2*sqrt(1/((a^3*b - 2*a^2*b^2 + a*b^3)*d^4)) - 1)/((a^2 - a*b)*d^2)) + 1) - 1/4*sqrt(((a^2 - a*b)*d^2*sqrt(1/((a^3*b - 2*a^2*b^2 + a*b^3)*d^4)) - 1)/((a^2 - a*b)*d^2))*log(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 2*(a*d*cosh(d*x + c) + a*d*sinh(d*x + c) + ((a^2*b - a*b^2)*d^3*cosh(d*x + c) + (a^2*b - a*b^2)*d^3*sinh(d*x + c))*sqrt(1/((a^3*b - 2*a^2*b^2 + a*b^3)*d^4)))*sqrt(((a^2 - a*b)*d^2*sqrt(1/((a^3*b - 2*a^2*b^2 + a*b^3)*d^4)) - 1)/((a^2 - a*b)*d^2)) + 1)","B",0
233,1,1067,0,2.215209," ","integrate(csch(d*x+c)/(a-b*sinh(d*x+c)^4),x, algorithm=""fricas"")","\frac{a d \sqrt{-\frac{{\left(a^{3} - a^{2} b\right)} d^{2} \sqrt{\frac{b}{{\left(a^{5} - 2 \, a^{4} b + a^{3} b^{2}\right)} d^{4}}} + b}{{\left(a^{3} - a^{2} b\right)} d^{2}}} \log\left(b \cosh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b \sinh\left(d x + c\right)^{2} + 2 \, {\left(a b d \cosh\left(d x + c\right) + a b d \sinh\left(d x + c\right) - {\left({\left(a^{4} - a^{3} b\right)} d^{3} \cosh\left(d x + c\right) + {\left(a^{4} - a^{3} b\right)} d^{3} \sinh\left(d x + c\right)\right)} \sqrt{\frac{b}{{\left(a^{5} - 2 \, a^{4} b + a^{3} b^{2}\right)} d^{4}}}\right)} \sqrt{-\frac{{\left(a^{3} - a^{2} b\right)} d^{2} \sqrt{\frac{b}{{\left(a^{5} - 2 \, a^{4} b + a^{3} b^{2}\right)} d^{4}}} + b}{{\left(a^{3} - a^{2} b\right)} d^{2}}} + b\right) - a d \sqrt{-\frac{{\left(a^{3} - a^{2} b\right)} d^{2} \sqrt{\frac{b}{{\left(a^{5} - 2 \, a^{4} b + a^{3} b^{2}\right)} d^{4}}} + b}{{\left(a^{3} - a^{2} b\right)} d^{2}}} \log\left(b \cosh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b \sinh\left(d x + c\right)^{2} - 2 \, {\left(a b d \cosh\left(d x + c\right) + a b d \sinh\left(d x + c\right) - {\left({\left(a^{4} - a^{3} b\right)} d^{3} \cosh\left(d x + c\right) + {\left(a^{4} - a^{3} b\right)} d^{3} \sinh\left(d x + c\right)\right)} \sqrt{\frac{b}{{\left(a^{5} - 2 \, a^{4} b + a^{3} b^{2}\right)} d^{4}}}\right)} \sqrt{-\frac{{\left(a^{3} - a^{2} b\right)} d^{2} \sqrt{\frac{b}{{\left(a^{5} - 2 \, a^{4} b + a^{3} b^{2}\right)} d^{4}}} + b}{{\left(a^{3} - a^{2} b\right)} d^{2}}} + b\right) + a d \sqrt{\frac{{\left(a^{3} - a^{2} b\right)} d^{2} \sqrt{\frac{b}{{\left(a^{5} - 2 \, a^{4} b + a^{3} b^{2}\right)} d^{4}}} - b}{{\left(a^{3} - a^{2} b\right)} d^{2}}} \log\left(b \cosh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b \sinh\left(d x + c\right)^{2} + 2 \, {\left(a b d \cosh\left(d x + c\right) + a b d \sinh\left(d x + c\right) + {\left({\left(a^{4} - a^{3} b\right)} d^{3} \cosh\left(d x + c\right) + {\left(a^{4} - a^{3} b\right)} d^{3} \sinh\left(d x + c\right)\right)} \sqrt{\frac{b}{{\left(a^{5} - 2 \, a^{4} b + a^{3} b^{2}\right)} d^{4}}}\right)} \sqrt{\frac{{\left(a^{3} - a^{2} b\right)} d^{2} \sqrt{\frac{b}{{\left(a^{5} - 2 \, a^{4} b + a^{3} b^{2}\right)} d^{4}}} - b}{{\left(a^{3} - a^{2} b\right)} d^{2}}} + b\right) - a d \sqrt{\frac{{\left(a^{3} - a^{2} b\right)} d^{2} \sqrt{\frac{b}{{\left(a^{5} - 2 \, a^{4} b + a^{3} b^{2}\right)} d^{4}}} - b}{{\left(a^{3} - a^{2} b\right)} d^{2}}} \log\left(b \cosh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b \sinh\left(d x + c\right)^{2} - 2 \, {\left(a b d \cosh\left(d x + c\right) + a b d \sinh\left(d x + c\right) + {\left({\left(a^{4} - a^{3} b\right)} d^{3} \cosh\left(d x + c\right) + {\left(a^{4} - a^{3} b\right)} d^{3} \sinh\left(d x + c\right)\right)} \sqrt{\frac{b}{{\left(a^{5} - 2 \, a^{4} b + a^{3} b^{2}\right)} d^{4}}}\right)} \sqrt{\frac{{\left(a^{3} - a^{2} b\right)} d^{2} \sqrt{\frac{b}{{\left(a^{5} - 2 \, a^{4} b + a^{3} b^{2}\right)} d^{4}}} - b}{{\left(a^{3} - a^{2} b\right)} d^{2}}} + b\right) - 4 \, \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) + 4 \, \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right)}{4 \, a d}"," ",0,"1/4*(a*d*sqrt(-((a^3 - a^2*b)*d^2*sqrt(b/((a^5 - 2*a^4*b + a^3*b^2)*d^4)) + b)/((a^3 - a^2*b)*d^2))*log(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + 2*(a*b*d*cosh(d*x + c) + a*b*d*sinh(d*x + c) - ((a^4 - a^3*b)*d^3*cosh(d*x + c) + (a^4 - a^3*b)*d^3*sinh(d*x + c))*sqrt(b/((a^5 - 2*a^4*b + a^3*b^2)*d^4)))*sqrt(-((a^3 - a^2*b)*d^2*sqrt(b/((a^5 - 2*a^4*b + a^3*b^2)*d^4)) + b)/((a^3 - a^2*b)*d^2)) + b) - a*d*sqrt(-((a^3 - a^2*b)*d^2*sqrt(b/((a^5 - 2*a^4*b + a^3*b^2)*d^4)) + b)/((a^3 - a^2*b)*d^2))*log(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 - 2*(a*b*d*cosh(d*x + c) + a*b*d*sinh(d*x + c) - ((a^4 - a^3*b)*d^3*cosh(d*x + c) + (a^4 - a^3*b)*d^3*sinh(d*x + c))*sqrt(b/((a^5 - 2*a^4*b + a^3*b^2)*d^4)))*sqrt(-((a^3 - a^2*b)*d^2*sqrt(b/((a^5 - 2*a^4*b + a^3*b^2)*d^4)) + b)/((a^3 - a^2*b)*d^2)) + b) + a*d*sqrt(((a^3 - a^2*b)*d^2*sqrt(b/((a^5 - 2*a^4*b + a^3*b^2)*d^4)) - b)/((a^3 - a^2*b)*d^2))*log(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + 2*(a*b*d*cosh(d*x + c) + a*b*d*sinh(d*x + c) + ((a^4 - a^3*b)*d^3*cosh(d*x + c) + (a^4 - a^3*b)*d^3*sinh(d*x + c))*sqrt(b/((a^5 - 2*a^4*b + a^3*b^2)*d^4)))*sqrt(((a^3 - a^2*b)*d^2*sqrt(b/((a^5 - 2*a^4*b + a^3*b^2)*d^4)) - b)/((a^3 - a^2*b)*d^2)) + b) - a*d*sqrt(((a^3 - a^2*b)*d^2*sqrt(b/((a^5 - 2*a^4*b + a^3*b^2)*d^4)) - b)/((a^3 - a^2*b)*d^2))*log(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 - 2*(a*b*d*cosh(d*x + c) + a*b*d*sinh(d*x + c) + ((a^4 - a^3*b)*d^3*cosh(d*x + c) + (a^4 - a^3*b)*d^3*sinh(d*x + c))*sqrt(b/((a^5 - 2*a^4*b + a^3*b^2)*d^4)))*sqrt(((a^3 - a^2*b)*d^2*sqrt(b/((a^5 - 2*a^4*b + a^3*b^2)*d^4)) - b)/((a^3 - a^2*b)*d^2)) + b) - 4*log(cosh(d*x + c) + sinh(d*x + c) + 1) + 4*log(cosh(d*x + c) + sinh(d*x + c) - 1))/(a*d)","B",0
234,1,1954,0,1.022971," ","integrate(csch(d*x+c)^3/(a-b*sinh(d*x+c)^4),x, algorithm=""fricas"")","-\frac{4 \, \cosh\left(d x + c\right)^{3} + 12 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + 4 \, \sinh\left(d x + c\right)^{3} - {\left(a d \cosh\left(d x + c\right)^{4} + 4 \, a d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a d \sinh\left(d x + c\right)^{4} - 2 \, a d \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a d \cosh\left(d x + c\right)^{2} - a d\right)} \sinh\left(d x + c\right)^{2} + a d + 4 \, {\left(a d \cosh\left(d x + c\right)^{3} - a d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{{\left(a^{4} - a^{3} b\right)} d^{2} \sqrt{\frac{b^{3}}{{\left(a^{7} - 2 \, a^{6} b + a^{5} b^{2}\right)} d^{4}}} + b^{2}}{{\left(a^{4} - a^{3} b\right)} d^{2}}} \log\left(b^{2} \cosh\left(d x + c\right)^{2} + 2 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b^{2} \sinh\left(d x + c\right)^{2} + b^{2} + 2 \, {\left(a^{2} b d \cosh\left(d x + c\right) + a^{2} b d \sinh\left(d x + c\right) - {\left({\left(a^{5} - a^{4} b\right)} d^{3} \cosh\left(d x + c\right) + {\left(a^{5} - a^{4} b\right)} d^{3} \sinh\left(d x + c\right)\right)} \sqrt{\frac{b^{3}}{{\left(a^{7} - 2 \, a^{6} b + a^{5} b^{2}\right)} d^{4}}}\right)} \sqrt{-\frac{{\left(a^{4} - a^{3} b\right)} d^{2} \sqrt{\frac{b^{3}}{{\left(a^{7} - 2 \, a^{6} b + a^{5} b^{2}\right)} d^{4}}} + b^{2}}{{\left(a^{4} - a^{3} b\right)} d^{2}}}\right) + {\left(a d \cosh\left(d x + c\right)^{4} + 4 \, a d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a d \sinh\left(d x + c\right)^{4} - 2 \, a d \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a d \cosh\left(d x + c\right)^{2} - a d\right)} \sinh\left(d x + c\right)^{2} + a d + 4 \, {\left(a d \cosh\left(d x + c\right)^{3} - a d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{{\left(a^{4} - a^{3} b\right)} d^{2} \sqrt{\frac{b^{3}}{{\left(a^{7} - 2 \, a^{6} b + a^{5} b^{2}\right)} d^{4}}} + b^{2}}{{\left(a^{4} - a^{3} b\right)} d^{2}}} \log\left(b^{2} \cosh\left(d x + c\right)^{2} + 2 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b^{2} \sinh\left(d x + c\right)^{2} + b^{2} - 2 \, {\left(a^{2} b d \cosh\left(d x + c\right) + a^{2} b d \sinh\left(d x + c\right) - {\left({\left(a^{5} - a^{4} b\right)} d^{3} \cosh\left(d x + c\right) + {\left(a^{5} - a^{4} b\right)} d^{3} \sinh\left(d x + c\right)\right)} \sqrt{\frac{b^{3}}{{\left(a^{7} - 2 \, a^{6} b + a^{5} b^{2}\right)} d^{4}}}\right)} \sqrt{-\frac{{\left(a^{4} - a^{3} b\right)} d^{2} \sqrt{\frac{b^{3}}{{\left(a^{7} - 2 \, a^{6} b + a^{5} b^{2}\right)} d^{4}}} + b^{2}}{{\left(a^{4} - a^{3} b\right)} d^{2}}}\right) - {\left(a d \cosh\left(d x + c\right)^{4} + 4 \, a d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a d \sinh\left(d x + c\right)^{4} - 2 \, a d \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a d \cosh\left(d x + c\right)^{2} - a d\right)} \sinh\left(d x + c\right)^{2} + a d + 4 \, {\left(a d \cosh\left(d x + c\right)^{3} - a d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{{\left(a^{4} - a^{3} b\right)} d^{2} \sqrt{\frac{b^{3}}{{\left(a^{7} - 2 \, a^{6} b + a^{5} b^{2}\right)} d^{4}}} - b^{2}}{{\left(a^{4} - a^{3} b\right)} d^{2}}} \log\left(b^{2} \cosh\left(d x + c\right)^{2} + 2 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b^{2} \sinh\left(d x + c\right)^{2} + b^{2} + 2 \, {\left(a^{2} b d \cosh\left(d x + c\right) + a^{2} b d \sinh\left(d x + c\right) + {\left({\left(a^{5} - a^{4} b\right)} d^{3} \cosh\left(d x + c\right) + {\left(a^{5} - a^{4} b\right)} d^{3} \sinh\left(d x + c\right)\right)} \sqrt{\frac{b^{3}}{{\left(a^{7} - 2 \, a^{6} b + a^{5} b^{2}\right)} d^{4}}}\right)} \sqrt{\frac{{\left(a^{4} - a^{3} b\right)} d^{2} \sqrt{\frac{b^{3}}{{\left(a^{7} - 2 \, a^{6} b + a^{5} b^{2}\right)} d^{4}}} - b^{2}}{{\left(a^{4} - a^{3} b\right)} d^{2}}}\right) + {\left(a d \cosh\left(d x + c\right)^{4} + 4 \, a d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a d \sinh\left(d x + c\right)^{4} - 2 \, a d \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a d \cosh\left(d x + c\right)^{2} - a d\right)} \sinh\left(d x + c\right)^{2} + a d + 4 \, {\left(a d \cosh\left(d x + c\right)^{3} - a d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{{\left(a^{4} - a^{3} b\right)} d^{2} \sqrt{\frac{b^{3}}{{\left(a^{7} - 2 \, a^{6} b + a^{5} b^{2}\right)} d^{4}}} - b^{2}}{{\left(a^{4} - a^{3} b\right)} d^{2}}} \log\left(b^{2} \cosh\left(d x + c\right)^{2} + 2 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b^{2} \sinh\left(d x + c\right)^{2} + b^{2} - 2 \, {\left(a^{2} b d \cosh\left(d x + c\right) + a^{2} b d \sinh\left(d x + c\right) + {\left({\left(a^{5} - a^{4} b\right)} d^{3} \cosh\left(d x + c\right) + {\left(a^{5} - a^{4} b\right)} d^{3} \sinh\left(d x + c\right)\right)} \sqrt{\frac{b^{3}}{{\left(a^{7} - 2 \, a^{6} b + a^{5} b^{2}\right)} d^{4}}}\right)} \sqrt{\frac{{\left(a^{4} - a^{3} b\right)} d^{2} \sqrt{\frac{b^{3}}{{\left(a^{7} - 2 \, a^{6} b + a^{5} b^{2}\right)} d^{4}}} - b^{2}}{{\left(a^{4} - a^{3} b\right)} d^{2}}}\right) - 2 \, {\left(\cosh\left(d x + c\right)^{4} + 4 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + \sinh\left(d x + c\right)^{4} + 2 \, {\left(3 \, \cosh\left(d x + c\right)^{2} - 1\right)} \sinh\left(d x + c\right)^{2} - 2 \, \cosh\left(d x + c\right)^{2} + 4 \, {\left(\cosh\left(d x + c\right)^{3} - \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + 1\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) + 2 \, {\left(\cosh\left(d x + c\right)^{4} + 4 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + \sinh\left(d x + c\right)^{4} + 2 \, {\left(3 \, \cosh\left(d x + c\right)^{2} - 1\right)} \sinh\left(d x + c\right)^{2} - 2 \, \cosh\left(d x + c\right)^{2} + 4 \, {\left(\cosh\left(d x + c\right)^{3} - \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + 1\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) + 4 \, {\left(3 \, \cosh\left(d x + c\right)^{2} + 1\right)} \sinh\left(d x + c\right) + 4 \, \cosh\left(d x + c\right)}{4 \, {\left(a d \cosh\left(d x + c\right)^{4} + 4 \, a d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a d \sinh\left(d x + c\right)^{4} - 2 \, a d \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a d \cosh\left(d x + c\right)^{2} - a d\right)} \sinh\left(d x + c\right)^{2} + a d + 4 \, {\left(a d \cosh\left(d x + c\right)^{3} - a d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"-1/4*(4*cosh(d*x + c)^3 + 12*cosh(d*x + c)*sinh(d*x + c)^2 + 4*sinh(d*x + c)^3 - (a*d*cosh(d*x + c)^4 + 4*a*d*cosh(d*x + c)*sinh(d*x + c)^3 + a*d*sinh(d*x + c)^4 - 2*a*d*cosh(d*x + c)^2 + 2*(3*a*d*cosh(d*x + c)^2 - a*d)*sinh(d*x + c)^2 + a*d + 4*(a*d*cosh(d*x + c)^3 - a*d*cosh(d*x + c))*sinh(d*x + c))*sqrt(-((a^4 - a^3*b)*d^2*sqrt(b^3/((a^7 - 2*a^6*b + a^5*b^2)*d^4)) + b^2)/((a^4 - a^3*b)*d^2))*log(b^2*cosh(d*x + c)^2 + 2*b^2*cosh(d*x + c)*sinh(d*x + c) + b^2*sinh(d*x + c)^2 + b^2 + 2*(a^2*b*d*cosh(d*x + c) + a^2*b*d*sinh(d*x + c) - ((a^5 - a^4*b)*d^3*cosh(d*x + c) + (a^5 - a^4*b)*d^3*sinh(d*x + c))*sqrt(b^3/((a^7 - 2*a^6*b + a^5*b^2)*d^4)))*sqrt(-((a^4 - a^3*b)*d^2*sqrt(b^3/((a^7 - 2*a^6*b + a^5*b^2)*d^4)) + b^2)/((a^4 - a^3*b)*d^2))) + (a*d*cosh(d*x + c)^4 + 4*a*d*cosh(d*x + c)*sinh(d*x + c)^3 + a*d*sinh(d*x + c)^4 - 2*a*d*cosh(d*x + c)^2 + 2*(3*a*d*cosh(d*x + c)^2 - a*d)*sinh(d*x + c)^2 + a*d + 4*(a*d*cosh(d*x + c)^3 - a*d*cosh(d*x + c))*sinh(d*x + c))*sqrt(-((a^4 - a^3*b)*d^2*sqrt(b^3/((a^7 - 2*a^6*b + a^5*b^2)*d^4)) + b^2)/((a^4 - a^3*b)*d^2))*log(b^2*cosh(d*x + c)^2 + 2*b^2*cosh(d*x + c)*sinh(d*x + c) + b^2*sinh(d*x + c)^2 + b^2 - 2*(a^2*b*d*cosh(d*x + c) + a^2*b*d*sinh(d*x + c) - ((a^5 - a^4*b)*d^3*cosh(d*x + c) + (a^5 - a^4*b)*d^3*sinh(d*x + c))*sqrt(b^3/((a^7 - 2*a^6*b + a^5*b^2)*d^4)))*sqrt(-((a^4 - a^3*b)*d^2*sqrt(b^3/((a^7 - 2*a^6*b + a^5*b^2)*d^4)) + b^2)/((a^4 - a^3*b)*d^2))) - (a*d*cosh(d*x + c)^4 + 4*a*d*cosh(d*x + c)*sinh(d*x + c)^3 + a*d*sinh(d*x + c)^4 - 2*a*d*cosh(d*x + c)^2 + 2*(3*a*d*cosh(d*x + c)^2 - a*d)*sinh(d*x + c)^2 + a*d + 4*(a*d*cosh(d*x + c)^3 - a*d*cosh(d*x + c))*sinh(d*x + c))*sqrt(((a^4 - a^3*b)*d^2*sqrt(b^3/((a^7 - 2*a^6*b + a^5*b^2)*d^4)) - b^2)/((a^4 - a^3*b)*d^2))*log(b^2*cosh(d*x + c)^2 + 2*b^2*cosh(d*x + c)*sinh(d*x + c) + b^2*sinh(d*x + c)^2 + b^2 + 2*(a^2*b*d*cosh(d*x + c) + a^2*b*d*sinh(d*x + c) + ((a^5 - a^4*b)*d^3*cosh(d*x + c) + (a^5 - a^4*b)*d^3*sinh(d*x + c))*sqrt(b^3/((a^7 - 2*a^6*b + a^5*b^2)*d^4)))*sqrt(((a^4 - a^3*b)*d^2*sqrt(b^3/((a^7 - 2*a^6*b + a^5*b^2)*d^4)) - b^2)/((a^4 - a^3*b)*d^2))) + (a*d*cosh(d*x + c)^4 + 4*a*d*cosh(d*x + c)*sinh(d*x + c)^3 + a*d*sinh(d*x + c)^4 - 2*a*d*cosh(d*x + c)^2 + 2*(3*a*d*cosh(d*x + c)^2 - a*d)*sinh(d*x + c)^2 + a*d + 4*(a*d*cosh(d*x + c)^3 - a*d*cosh(d*x + c))*sinh(d*x + c))*sqrt(((a^4 - a^3*b)*d^2*sqrt(b^3/((a^7 - 2*a^6*b + a^5*b^2)*d^4)) - b^2)/((a^4 - a^3*b)*d^2))*log(b^2*cosh(d*x + c)^2 + 2*b^2*cosh(d*x + c)*sinh(d*x + c) + b^2*sinh(d*x + c)^2 + b^2 - 2*(a^2*b*d*cosh(d*x + c) + a^2*b*d*sinh(d*x + c) + ((a^5 - a^4*b)*d^3*cosh(d*x + c) + (a^5 - a^4*b)*d^3*sinh(d*x + c))*sqrt(b^3/((a^7 - 2*a^6*b + a^5*b^2)*d^4)))*sqrt(((a^4 - a^3*b)*d^2*sqrt(b^3/((a^7 - 2*a^6*b + a^5*b^2)*d^4)) - b^2)/((a^4 - a^3*b)*d^2))) - 2*(cosh(d*x + c)^4 + 4*cosh(d*x + c)*sinh(d*x + c)^3 + sinh(d*x + c)^4 + 2*(3*cosh(d*x + c)^2 - 1)*sinh(d*x + c)^2 - 2*cosh(d*x + c)^2 + 4*(cosh(d*x + c)^3 - cosh(d*x + c))*sinh(d*x + c) + 1)*log(cosh(d*x + c) + sinh(d*x + c) + 1) + 2*(cosh(d*x + c)^4 + 4*cosh(d*x + c)*sinh(d*x + c)^3 + sinh(d*x + c)^4 + 2*(3*cosh(d*x + c)^2 - 1)*sinh(d*x + c)^2 - 2*cosh(d*x + c)^2 + 4*(cosh(d*x + c)^3 - cosh(d*x + c))*sinh(d*x + c) + 1)*log(cosh(d*x + c) + sinh(d*x + c) - 1) + 4*(3*cosh(d*x + c)^2 + 1)*sinh(d*x + c) + 4*cosh(d*x + c))/(a*d*cosh(d*x + c)^4 + 4*a*d*cosh(d*x + c)*sinh(d*x + c)^3 + a*d*sinh(d*x + c)^4 - 2*a*d*cosh(d*x + c)^2 + 2*(3*a*d*cosh(d*x + c)^2 - a*d)*sinh(d*x + c)^2 + a*d + 4*(a*d*cosh(d*x + c)^3 - a*d*cosh(d*x + c))*sinh(d*x + c))","B",0
235,1,1441,0,1.469580," ","integrate(sinh(d*x+c)^6/(a-b*sinh(d*x+c)^4),x, algorithm=""fricas"")","\frac{4 \, d x \cosh\left(d x + c\right)^{2} - \cosh\left(d x + c\right)^{4} - 4 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} - \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, d x - 3 \, \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} - 2 \, {\left(b d \cosh\left(d x + c\right)^{2} + 2 \, b d \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b d \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{{\left(a b^{3} - b^{4}\right)} d^{2} \sqrt{\frac{a^{3}}{{\left(a^{2} b^{5} - 2 \, a b^{6} + b^{7}\right)} d^{4}}} + a^{2}}{{\left(a b^{3} - b^{4}\right)} d^{2}}} \log\left(a^{2} \cosh\left(d x + c\right)^{2} + 2 \, a^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a^{2} \sinh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b^{2} - a b^{3}\right)} d^{2} \sqrt{\frac{a^{3}}{{\left(a^{2} b^{5} - 2 \, a b^{6} + b^{7}\right)} d^{4}}} - a^{2} + 2 \, {\left({\left(a b^{4} - b^{5}\right)} d^{3} \sqrt{\frac{a^{3}}{{\left(a^{2} b^{5} - 2 \, a b^{6} + b^{7}\right)} d^{4}}} - a^{2} b d\right)} \sqrt{\frac{{\left(a b^{3} - b^{4}\right)} d^{2} \sqrt{\frac{a^{3}}{{\left(a^{2} b^{5} - 2 \, a b^{6} + b^{7}\right)} d^{4}}} + a^{2}}{{\left(a b^{3} - b^{4}\right)} d^{2}}}\right) + 2 \, {\left(b d \cosh\left(d x + c\right)^{2} + 2 \, b d \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b d \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{{\left(a b^{3} - b^{4}\right)} d^{2} \sqrt{\frac{a^{3}}{{\left(a^{2} b^{5} - 2 \, a b^{6} + b^{7}\right)} d^{4}}} + a^{2}}{{\left(a b^{3} - b^{4}\right)} d^{2}}} \log\left(a^{2} \cosh\left(d x + c\right)^{2} + 2 \, a^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a^{2} \sinh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b^{2} - a b^{3}\right)} d^{2} \sqrt{\frac{a^{3}}{{\left(a^{2} b^{5} - 2 \, a b^{6} + b^{7}\right)} d^{4}}} - a^{2} - 2 \, {\left({\left(a b^{4} - b^{5}\right)} d^{3} \sqrt{\frac{a^{3}}{{\left(a^{2} b^{5} - 2 \, a b^{6} + b^{7}\right)} d^{4}}} - a^{2} b d\right)} \sqrt{\frac{{\left(a b^{3} - b^{4}\right)} d^{2} \sqrt{\frac{a^{3}}{{\left(a^{2} b^{5} - 2 \, a b^{6} + b^{7}\right)} d^{4}}} + a^{2}}{{\left(a b^{3} - b^{4}\right)} d^{2}}}\right) + 2 \, {\left(b d \cosh\left(d x + c\right)^{2} + 2 \, b d \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b d \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{{\left(a b^{3} - b^{4}\right)} d^{2} \sqrt{\frac{a^{3}}{{\left(a^{2} b^{5} - 2 \, a b^{6} + b^{7}\right)} d^{4}}} - a^{2}}{{\left(a b^{3} - b^{4}\right)} d^{2}}} \log\left(a^{2} \cosh\left(d x + c\right)^{2} + 2 \, a^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a^{2} \sinh\left(d x + c\right)^{2} - 2 \, {\left(a^{2} b^{2} - a b^{3}\right)} d^{2} \sqrt{\frac{a^{3}}{{\left(a^{2} b^{5} - 2 \, a b^{6} + b^{7}\right)} d^{4}}} - a^{2} + 2 \, {\left({\left(a b^{4} - b^{5}\right)} d^{3} \sqrt{\frac{a^{3}}{{\left(a^{2} b^{5} - 2 \, a b^{6} + b^{7}\right)} d^{4}}} + a^{2} b d\right)} \sqrt{-\frac{{\left(a b^{3} - b^{4}\right)} d^{2} \sqrt{\frac{a^{3}}{{\left(a^{2} b^{5} - 2 \, a b^{6} + b^{7}\right)} d^{4}}} - a^{2}}{{\left(a b^{3} - b^{4}\right)} d^{2}}}\right) - 2 \, {\left(b d \cosh\left(d x + c\right)^{2} + 2 \, b d \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b d \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{{\left(a b^{3} - b^{4}\right)} d^{2} \sqrt{\frac{a^{3}}{{\left(a^{2} b^{5} - 2 \, a b^{6} + b^{7}\right)} d^{4}}} - a^{2}}{{\left(a b^{3} - b^{4}\right)} d^{2}}} \log\left(a^{2} \cosh\left(d x + c\right)^{2} + 2 \, a^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a^{2} \sinh\left(d x + c\right)^{2} - 2 \, {\left(a^{2} b^{2} - a b^{3}\right)} d^{2} \sqrt{\frac{a^{3}}{{\left(a^{2} b^{5} - 2 \, a b^{6} + b^{7}\right)} d^{4}}} - a^{2} - 2 \, {\left({\left(a b^{4} - b^{5}\right)} d^{3} \sqrt{\frac{a^{3}}{{\left(a^{2} b^{5} - 2 \, a b^{6} + b^{7}\right)} d^{4}}} + a^{2} b d\right)} \sqrt{-\frac{{\left(a b^{3} - b^{4}\right)} d^{2} \sqrt{\frac{a^{3}}{{\left(a^{2} b^{5} - 2 \, a b^{6} + b^{7}\right)} d^{4}}} - a^{2}}{{\left(a b^{3} - b^{4}\right)} d^{2}}}\right) + 4 \, {\left(2 \, d x \cosh\left(d x + c\right) - \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right) + 1}{8 \, {\left(b d \cosh\left(d x + c\right)^{2} + 2 \, b d \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b d \sinh\left(d x + c\right)^{2}\right)}}"," ",0,"1/8*(4*d*x*cosh(d*x + c)^2 - cosh(d*x + c)^4 - 4*cosh(d*x + c)*sinh(d*x + c)^3 - sinh(d*x + c)^4 + 2*(2*d*x - 3*cosh(d*x + c)^2)*sinh(d*x + c)^2 - 2*(b*d*cosh(d*x + c)^2 + 2*b*d*cosh(d*x + c)*sinh(d*x + c) + b*d*sinh(d*x + c)^2)*sqrt(((a*b^3 - b^4)*d^2*sqrt(a^3/((a^2*b^5 - 2*a*b^6 + b^7)*d^4)) + a^2)/((a*b^3 - b^4)*d^2))*log(a^2*cosh(d*x + c)^2 + 2*a^2*cosh(d*x + c)*sinh(d*x + c) + a^2*sinh(d*x + c)^2 + 2*(a^2*b^2 - a*b^3)*d^2*sqrt(a^3/((a^2*b^5 - 2*a*b^6 + b^7)*d^4)) - a^2 + 2*((a*b^4 - b^5)*d^3*sqrt(a^3/((a^2*b^5 - 2*a*b^6 + b^7)*d^4)) - a^2*b*d)*sqrt(((a*b^3 - b^4)*d^2*sqrt(a^3/((a^2*b^5 - 2*a*b^6 + b^7)*d^4)) + a^2)/((a*b^3 - b^4)*d^2))) + 2*(b*d*cosh(d*x + c)^2 + 2*b*d*cosh(d*x + c)*sinh(d*x + c) + b*d*sinh(d*x + c)^2)*sqrt(((a*b^3 - b^4)*d^2*sqrt(a^3/((a^2*b^5 - 2*a*b^6 + b^7)*d^4)) + a^2)/((a*b^3 - b^4)*d^2))*log(a^2*cosh(d*x + c)^2 + 2*a^2*cosh(d*x + c)*sinh(d*x + c) + a^2*sinh(d*x + c)^2 + 2*(a^2*b^2 - a*b^3)*d^2*sqrt(a^3/((a^2*b^5 - 2*a*b^6 + b^7)*d^4)) - a^2 - 2*((a*b^4 - b^5)*d^3*sqrt(a^3/((a^2*b^5 - 2*a*b^6 + b^7)*d^4)) - a^2*b*d)*sqrt(((a*b^3 - b^4)*d^2*sqrt(a^3/((a^2*b^5 - 2*a*b^6 + b^7)*d^4)) + a^2)/((a*b^3 - b^4)*d^2))) + 2*(b*d*cosh(d*x + c)^2 + 2*b*d*cosh(d*x + c)*sinh(d*x + c) + b*d*sinh(d*x + c)^2)*sqrt(-((a*b^3 - b^4)*d^2*sqrt(a^3/((a^2*b^5 - 2*a*b^6 + b^7)*d^4)) - a^2)/((a*b^3 - b^4)*d^2))*log(a^2*cosh(d*x + c)^2 + 2*a^2*cosh(d*x + c)*sinh(d*x + c) + a^2*sinh(d*x + c)^2 - 2*(a^2*b^2 - a*b^3)*d^2*sqrt(a^3/((a^2*b^5 - 2*a*b^6 + b^7)*d^4)) - a^2 + 2*((a*b^4 - b^5)*d^3*sqrt(a^3/((a^2*b^5 - 2*a*b^6 + b^7)*d^4)) + a^2*b*d)*sqrt(-((a*b^3 - b^4)*d^2*sqrt(a^3/((a^2*b^5 - 2*a*b^6 + b^7)*d^4)) - a^2)/((a*b^3 - b^4)*d^2))) - 2*(b*d*cosh(d*x + c)^2 + 2*b*d*cosh(d*x + c)*sinh(d*x + c) + b*d*sinh(d*x + c)^2)*sqrt(-((a*b^3 - b^4)*d^2*sqrt(a^3/((a^2*b^5 - 2*a*b^6 + b^7)*d^4)) - a^2)/((a*b^3 - b^4)*d^2))*log(a^2*cosh(d*x + c)^2 + 2*a^2*cosh(d*x + c)*sinh(d*x + c) + a^2*sinh(d*x + c)^2 - 2*(a^2*b^2 - a*b^3)*d^2*sqrt(a^3/((a^2*b^5 - 2*a*b^6 + b^7)*d^4)) - a^2 - 2*((a*b^4 - b^5)*d^3*sqrt(a^3/((a^2*b^5 - 2*a*b^6 + b^7)*d^4)) + a^2*b*d)*sqrt(-((a*b^3 - b^4)*d^2*sqrt(a^3/((a^2*b^5 - 2*a*b^6 + b^7)*d^4)) - a^2)/((a*b^3 - b^4)*d^2))) + 4*(2*d*x*cosh(d*x + c) - cosh(d*x + c)^3)*sinh(d*x + c) + 1)/(b*d*cosh(d*x + c)^2 + 2*b*d*cosh(d*x + c)*sinh(d*x + c) + b*d*sinh(d*x + c)^2)","B",0
236,1,1009,0,1.172286," ","integrate(sinh(d*x+c)^4/(a-b*sinh(d*x+c)^4),x, algorithm=""fricas"")","-\frac{b \sqrt{\frac{{\left(a b^{2} - b^{3}\right)} d^{2} \sqrt{\frac{a}{{\left(a^{2} b^{3} - 2 \, a b^{4} + b^{5}\right)} d^{4}}} + a}{{\left(a b^{2} - b^{3}\right)} d^{2}}} \log\left(2 \, {\left(a b - b^{2}\right)} d^{2} \sqrt{\frac{a}{{\left(a^{2} b^{3} - 2 \, a b^{4} + b^{5}\right)} d^{4}}} + \cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} + 2 \, {\left({\left(a b^{2} - b^{3}\right)} d^{3} \sqrt{\frac{a}{{\left(a^{2} b^{3} - 2 \, a b^{4} + b^{5}\right)} d^{4}}} - b d\right)} \sqrt{\frac{{\left(a b^{2} - b^{3}\right)} d^{2} \sqrt{\frac{a}{{\left(a^{2} b^{3} - 2 \, a b^{4} + b^{5}\right)} d^{4}}} + a}{{\left(a b^{2} - b^{3}\right)} d^{2}}} - 1\right) - b \sqrt{\frac{{\left(a b^{2} - b^{3}\right)} d^{2} \sqrt{\frac{a}{{\left(a^{2} b^{3} - 2 \, a b^{4} + b^{5}\right)} d^{4}}} + a}{{\left(a b^{2} - b^{3}\right)} d^{2}}} \log\left(2 \, {\left(a b - b^{2}\right)} d^{2} \sqrt{\frac{a}{{\left(a^{2} b^{3} - 2 \, a b^{4} + b^{5}\right)} d^{4}}} + \cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} - 2 \, {\left({\left(a b^{2} - b^{3}\right)} d^{3} \sqrt{\frac{a}{{\left(a^{2} b^{3} - 2 \, a b^{4} + b^{5}\right)} d^{4}}} - b d\right)} \sqrt{\frac{{\left(a b^{2} - b^{3}\right)} d^{2} \sqrt{\frac{a}{{\left(a^{2} b^{3} - 2 \, a b^{4} + b^{5}\right)} d^{4}}} + a}{{\left(a b^{2} - b^{3}\right)} d^{2}}} - 1\right) - b \sqrt{-\frac{{\left(a b^{2} - b^{3}\right)} d^{2} \sqrt{\frac{a}{{\left(a^{2} b^{3} - 2 \, a b^{4} + b^{5}\right)} d^{4}}} - a}{{\left(a b^{2} - b^{3}\right)} d^{2}}} \log\left(-2 \, {\left(a b - b^{2}\right)} d^{2} \sqrt{\frac{a}{{\left(a^{2} b^{3} - 2 \, a b^{4} + b^{5}\right)} d^{4}}} + \cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} + 2 \, {\left({\left(a b^{2} - b^{3}\right)} d^{3} \sqrt{\frac{a}{{\left(a^{2} b^{3} - 2 \, a b^{4} + b^{5}\right)} d^{4}}} + b d\right)} \sqrt{-\frac{{\left(a b^{2} - b^{3}\right)} d^{2} \sqrt{\frac{a}{{\left(a^{2} b^{3} - 2 \, a b^{4} + b^{5}\right)} d^{4}}} - a}{{\left(a b^{2} - b^{3}\right)} d^{2}}} - 1\right) + b \sqrt{-\frac{{\left(a b^{2} - b^{3}\right)} d^{2} \sqrt{\frac{a}{{\left(a^{2} b^{3} - 2 \, a b^{4} + b^{5}\right)} d^{4}}} - a}{{\left(a b^{2} - b^{3}\right)} d^{2}}} \log\left(-2 \, {\left(a b - b^{2}\right)} d^{2} \sqrt{\frac{a}{{\left(a^{2} b^{3} - 2 \, a b^{4} + b^{5}\right)} d^{4}}} + \cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} - 2 \, {\left({\left(a b^{2} - b^{3}\right)} d^{3} \sqrt{\frac{a}{{\left(a^{2} b^{3} - 2 \, a b^{4} + b^{5}\right)} d^{4}}} + b d\right)} \sqrt{-\frac{{\left(a b^{2} - b^{3}\right)} d^{2} \sqrt{\frac{a}{{\left(a^{2} b^{3} - 2 \, a b^{4} + b^{5}\right)} d^{4}}} - a}{{\left(a b^{2} - b^{3}\right)} d^{2}}} - 1\right) + 4 \, x}{4 \, b}"," ",0,"-1/4*(b*sqrt(((a*b^2 - b^3)*d^2*sqrt(a/((a^2*b^3 - 2*a*b^4 + b^5)*d^4)) + a)/((a*b^2 - b^3)*d^2))*log(2*(a*b - b^2)*d^2*sqrt(a/((a^2*b^3 - 2*a*b^4 + b^5)*d^4)) + cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 2*((a*b^2 - b^3)*d^3*sqrt(a/((a^2*b^3 - 2*a*b^4 + b^5)*d^4)) - b*d)*sqrt(((a*b^2 - b^3)*d^2*sqrt(a/((a^2*b^3 - 2*a*b^4 + b^5)*d^4)) + a)/((a*b^2 - b^3)*d^2)) - 1) - b*sqrt(((a*b^2 - b^3)*d^2*sqrt(a/((a^2*b^3 - 2*a*b^4 + b^5)*d^4)) + a)/((a*b^2 - b^3)*d^2))*log(2*(a*b - b^2)*d^2*sqrt(a/((a^2*b^3 - 2*a*b^4 + b^5)*d^4)) + cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 2*((a*b^2 - b^3)*d^3*sqrt(a/((a^2*b^3 - 2*a*b^4 + b^5)*d^4)) - b*d)*sqrt(((a*b^2 - b^3)*d^2*sqrt(a/((a^2*b^3 - 2*a*b^4 + b^5)*d^4)) + a)/((a*b^2 - b^3)*d^2)) - 1) - b*sqrt(-((a*b^2 - b^3)*d^2*sqrt(a/((a^2*b^3 - 2*a*b^4 + b^5)*d^4)) - a)/((a*b^2 - b^3)*d^2))*log(-2*(a*b - b^2)*d^2*sqrt(a/((a^2*b^3 - 2*a*b^4 + b^5)*d^4)) + cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 2*((a*b^2 - b^3)*d^3*sqrt(a/((a^2*b^3 - 2*a*b^4 + b^5)*d^4)) + b*d)*sqrt(-((a*b^2 - b^3)*d^2*sqrt(a/((a^2*b^3 - 2*a*b^4 + b^5)*d^4)) - a)/((a*b^2 - b^3)*d^2)) - 1) + b*sqrt(-((a*b^2 - b^3)*d^2*sqrt(a/((a^2*b^3 - 2*a*b^4 + b^5)*d^4)) - a)/((a*b^2 - b^3)*d^2))*log(-2*(a*b - b^2)*d^2*sqrt(a/((a^2*b^3 - 2*a*b^4 + b^5)*d^4)) + cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 2*((a*b^2 - b^3)*d^3*sqrt(a/((a^2*b^3 - 2*a*b^4 + b^5)*d^4)) + b*d)*sqrt(-((a*b^2 - b^3)*d^2*sqrt(a/((a^2*b^3 - 2*a*b^4 + b^5)*d^4)) - a)/((a*b^2 - b^3)*d^2)) - 1) + 4*x)/b","B",0
237,1,975,0,1.020270," ","integrate(sinh(d*x+c)^2/(a-b*sinh(d*x+c)^4),x, algorithm=""fricas"")","-\frac{1}{4} \, \sqrt{\frac{{\left(a b - b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{3} b - 2 \, a^{2} b^{2} + a b^{3}\right)} d^{4}}} + 1}{{\left(a b - b^{2}\right)} d^{2}}} \log\left(2 \, {\left(a^{2} - a b\right)} d^{2} \sqrt{\frac{1}{{\left(a^{3} b - 2 \, a^{2} b^{2} + a b^{3}\right)} d^{4}}} + \cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{2} b - a b^{2}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{3} b - 2 \, a^{2} b^{2} + a b^{3}\right)} d^{4}}} - a d\right)} \sqrt{\frac{{\left(a b - b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{3} b - 2 \, a^{2} b^{2} + a b^{3}\right)} d^{4}}} + 1}{{\left(a b - b^{2}\right)} d^{2}}} - 1\right) + \frac{1}{4} \, \sqrt{\frac{{\left(a b - b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{3} b - 2 \, a^{2} b^{2} + a b^{3}\right)} d^{4}}} + 1}{{\left(a b - b^{2}\right)} d^{2}}} \log\left(2 \, {\left(a^{2} - a b\right)} d^{2} \sqrt{\frac{1}{{\left(a^{3} b - 2 \, a^{2} b^{2} + a b^{3}\right)} d^{4}}} + \cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{2} b - a b^{2}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{3} b - 2 \, a^{2} b^{2} + a b^{3}\right)} d^{4}}} - a d\right)} \sqrt{\frac{{\left(a b - b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{3} b - 2 \, a^{2} b^{2} + a b^{3}\right)} d^{4}}} + 1}{{\left(a b - b^{2}\right)} d^{2}}} - 1\right) + \frac{1}{4} \, \sqrt{-\frac{{\left(a b - b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{3} b - 2 \, a^{2} b^{2} + a b^{3}\right)} d^{4}}} - 1}{{\left(a b - b^{2}\right)} d^{2}}} \log\left(-2 \, {\left(a^{2} - a b\right)} d^{2} \sqrt{\frac{1}{{\left(a^{3} b - 2 \, a^{2} b^{2} + a b^{3}\right)} d^{4}}} + \cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{2} b - a b^{2}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{3} b - 2 \, a^{2} b^{2} + a b^{3}\right)} d^{4}}} + a d\right)} \sqrt{-\frac{{\left(a b - b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{3} b - 2 \, a^{2} b^{2} + a b^{3}\right)} d^{4}}} - 1}{{\left(a b - b^{2}\right)} d^{2}}} - 1\right) - \frac{1}{4} \, \sqrt{-\frac{{\left(a b - b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{3} b - 2 \, a^{2} b^{2} + a b^{3}\right)} d^{4}}} - 1}{{\left(a b - b^{2}\right)} d^{2}}} \log\left(-2 \, {\left(a^{2} - a b\right)} d^{2} \sqrt{\frac{1}{{\left(a^{3} b - 2 \, a^{2} b^{2} + a b^{3}\right)} d^{4}}} + \cosh\left(d x + c\right)^{2} + 2 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sinh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{2} b - a b^{2}\right)} d^{3} \sqrt{\frac{1}{{\left(a^{3} b - 2 \, a^{2} b^{2} + a b^{3}\right)} d^{4}}} + a d\right)} \sqrt{-\frac{{\left(a b - b^{2}\right)} d^{2} \sqrt{\frac{1}{{\left(a^{3} b - 2 \, a^{2} b^{2} + a b^{3}\right)} d^{4}}} - 1}{{\left(a b - b^{2}\right)} d^{2}}} - 1\right)"," ",0,"-1/4*sqrt(((a*b - b^2)*d^2*sqrt(1/((a^3*b - 2*a^2*b^2 + a*b^3)*d^4)) + 1)/((a*b - b^2)*d^2))*log(2*(a^2 - a*b)*d^2*sqrt(1/((a^3*b - 2*a^2*b^2 + a*b^3)*d^4)) + cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 2*((a^2*b - a*b^2)*d^3*sqrt(1/((a^3*b - 2*a^2*b^2 + a*b^3)*d^4)) - a*d)*sqrt(((a*b - b^2)*d^2*sqrt(1/((a^3*b - 2*a^2*b^2 + a*b^3)*d^4)) + 1)/((a*b - b^2)*d^2)) - 1) + 1/4*sqrt(((a*b - b^2)*d^2*sqrt(1/((a^3*b - 2*a^2*b^2 + a*b^3)*d^4)) + 1)/((a*b - b^2)*d^2))*log(2*(a^2 - a*b)*d^2*sqrt(1/((a^3*b - 2*a^2*b^2 + a*b^3)*d^4)) + cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 2*((a^2*b - a*b^2)*d^3*sqrt(1/((a^3*b - 2*a^2*b^2 + a*b^3)*d^4)) - a*d)*sqrt(((a*b - b^2)*d^2*sqrt(1/((a^3*b - 2*a^2*b^2 + a*b^3)*d^4)) + 1)/((a*b - b^2)*d^2)) - 1) + 1/4*sqrt(-((a*b - b^2)*d^2*sqrt(1/((a^3*b - 2*a^2*b^2 + a*b^3)*d^4)) - 1)/((a*b - b^2)*d^2))*log(-2*(a^2 - a*b)*d^2*sqrt(1/((a^3*b - 2*a^2*b^2 + a*b^3)*d^4)) + cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 2*((a^2*b - a*b^2)*d^3*sqrt(1/((a^3*b - 2*a^2*b^2 + a*b^3)*d^4)) + a*d)*sqrt(-((a*b - b^2)*d^2*sqrt(1/((a^3*b - 2*a^2*b^2 + a*b^3)*d^4)) - 1)/((a*b - b^2)*d^2)) - 1) - 1/4*sqrt(-((a*b - b^2)*d^2*sqrt(1/((a^3*b - 2*a^2*b^2 + a*b^3)*d^4)) - 1)/((a*b - b^2)*d^2))*log(-2*(a^2 - a*b)*d^2*sqrt(1/((a^3*b - 2*a^2*b^2 + a*b^3)*d^4)) + cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 2*((a^2*b - a*b^2)*d^3*sqrt(1/((a^3*b - 2*a^2*b^2 + a*b^3)*d^4)) + a*d)*sqrt(-((a*b - b^2)*d^2*sqrt(1/((a^3*b - 2*a^2*b^2 + a*b^3)*d^4)) - 1)/((a*b - b^2)*d^2)) - 1)","B",0
238,1,975,0,3.680551," ","integrate(1/(a-b*sinh(d*x+c)^4),x, algorithm=""fricas"")","-\frac{1}{4} \, \sqrt{\frac{{\left(a^{2} - a b\right)} d^{2} \sqrt{\frac{b}{{\left(a^{5} - 2 \, a^{4} b + a^{3} b^{2}\right)} d^{4}}} + 1}{{\left(a^{2} - a b\right)} d^{2}}} \log\left(2 \, {\left(a^{3} - a^{2} b\right)} d^{2} \sqrt{\frac{b}{{\left(a^{5} - 2 \, a^{4} b + a^{3} b^{2}\right)} d^{4}}} + b \cosh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b \sinh\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{4} - a^{3} b\right)} d^{3} \sqrt{\frac{b}{{\left(a^{5} - 2 \, a^{4} b + a^{3} b^{2}\right)} d^{4}}} - a b d\right)} \sqrt{\frac{{\left(a^{2} - a b\right)} d^{2} \sqrt{\frac{b}{{\left(a^{5} - 2 \, a^{4} b + a^{3} b^{2}\right)} d^{4}}} + 1}{{\left(a^{2} - a b\right)} d^{2}}} - b\right) + \frac{1}{4} \, \sqrt{\frac{{\left(a^{2} - a b\right)} d^{2} \sqrt{\frac{b}{{\left(a^{5} - 2 \, a^{4} b + a^{3} b^{2}\right)} d^{4}}} + 1}{{\left(a^{2} - a b\right)} d^{2}}} \log\left(2 \, {\left(a^{3} - a^{2} b\right)} d^{2} \sqrt{\frac{b}{{\left(a^{5} - 2 \, a^{4} b + a^{3} b^{2}\right)} d^{4}}} + b \cosh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b \sinh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{4} - a^{3} b\right)} d^{3} \sqrt{\frac{b}{{\left(a^{5} - 2 \, a^{4} b + a^{3} b^{2}\right)} d^{4}}} - a b d\right)} \sqrt{\frac{{\left(a^{2} - a b\right)} d^{2} \sqrt{\frac{b}{{\left(a^{5} - 2 \, a^{4} b + a^{3} b^{2}\right)} d^{4}}} + 1}{{\left(a^{2} - a b\right)} d^{2}}} - b\right) + \frac{1}{4} \, \sqrt{-\frac{{\left(a^{2} - a b\right)} d^{2} \sqrt{\frac{b}{{\left(a^{5} - 2 \, a^{4} b + a^{3} b^{2}\right)} d^{4}}} - 1}{{\left(a^{2} - a b\right)} d^{2}}} \log\left(-2 \, {\left(a^{3} - a^{2} b\right)} d^{2} \sqrt{\frac{b}{{\left(a^{5} - 2 \, a^{4} b + a^{3} b^{2}\right)} d^{4}}} + b \cosh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b \sinh\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{4} - a^{3} b\right)} d^{3} \sqrt{\frac{b}{{\left(a^{5} - 2 \, a^{4} b + a^{3} b^{2}\right)} d^{4}}} + a b d\right)} \sqrt{-\frac{{\left(a^{2} - a b\right)} d^{2} \sqrt{\frac{b}{{\left(a^{5} - 2 \, a^{4} b + a^{3} b^{2}\right)} d^{4}}} - 1}{{\left(a^{2} - a b\right)} d^{2}}} - b\right) - \frac{1}{4} \, \sqrt{-\frac{{\left(a^{2} - a b\right)} d^{2} \sqrt{\frac{b}{{\left(a^{5} - 2 \, a^{4} b + a^{3} b^{2}\right)} d^{4}}} - 1}{{\left(a^{2} - a b\right)} d^{2}}} \log\left(-2 \, {\left(a^{3} - a^{2} b\right)} d^{2} \sqrt{\frac{b}{{\left(a^{5} - 2 \, a^{4} b + a^{3} b^{2}\right)} d^{4}}} + b \cosh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b \sinh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{4} - a^{3} b\right)} d^{3} \sqrt{\frac{b}{{\left(a^{5} - 2 \, a^{4} b + a^{3} b^{2}\right)} d^{4}}} + a b d\right)} \sqrt{-\frac{{\left(a^{2} - a b\right)} d^{2} \sqrt{\frac{b}{{\left(a^{5} - 2 \, a^{4} b + a^{3} b^{2}\right)} d^{4}}} - 1}{{\left(a^{2} - a b\right)} d^{2}}} - b\right)"," ",0,"-1/4*sqrt(((a^2 - a*b)*d^2*sqrt(b/((a^5 - 2*a^4*b + a^3*b^2)*d^4)) + 1)/((a^2 - a*b)*d^2))*log(2*(a^3 - a^2*b)*d^2*sqrt(b/((a^5 - 2*a^4*b + a^3*b^2)*d^4)) + b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + 2*((a^4 - a^3*b)*d^3*sqrt(b/((a^5 - 2*a^4*b + a^3*b^2)*d^4)) - a*b*d)*sqrt(((a^2 - a*b)*d^2*sqrt(b/((a^5 - 2*a^4*b + a^3*b^2)*d^4)) + 1)/((a^2 - a*b)*d^2)) - b) + 1/4*sqrt(((a^2 - a*b)*d^2*sqrt(b/((a^5 - 2*a^4*b + a^3*b^2)*d^4)) + 1)/((a^2 - a*b)*d^2))*log(2*(a^3 - a^2*b)*d^2*sqrt(b/((a^5 - 2*a^4*b + a^3*b^2)*d^4)) + b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 - 2*((a^4 - a^3*b)*d^3*sqrt(b/((a^5 - 2*a^4*b + a^3*b^2)*d^4)) - a*b*d)*sqrt(((a^2 - a*b)*d^2*sqrt(b/((a^5 - 2*a^4*b + a^3*b^2)*d^4)) + 1)/((a^2 - a*b)*d^2)) - b) + 1/4*sqrt(-((a^2 - a*b)*d^2*sqrt(b/((a^5 - 2*a^4*b + a^3*b^2)*d^4)) - 1)/((a^2 - a*b)*d^2))*log(-2*(a^3 - a^2*b)*d^2*sqrt(b/((a^5 - 2*a^4*b + a^3*b^2)*d^4)) + b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + 2*((a^4 - a^3*b)*d^3*sqrt(b/((a^5 - 2*a^4*b + a^3*b^2)*d^4)) + a*b*d)*sqrt(-((a^2 - a*b)*d^2*sqrt(b/((a^5 - 2*a^4*b + a^3*b^2)*d^4)) - 1)/((a^2 - a*b)*d^2)) - b) - 1/4*sqrt(-((a^2 - a*b)*d^2*sqrt(b/((a^5 - 2*a^4*b + a^3*b^2)*d^4)) - 1)/((a^2 - a*b)*d^2))*log(-2*(a^3 - a^2*b)*d^2*sqrt(b/((a^5 - 2*a^4*b + a^3*b^2)*d^4)) + b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 - 2*((a^4 - a^3*b)*d^3*sqrt(b/((a^5 - 2*a^4*b + a^3*b^2)*d^4)) + a*b*d)*sqrt(-((a^2 - a*b)*d^2*sqrt(b/((a^5 - 2*a^4*b + a^3*b^2)*d^4)) - 1)/((a^2 - a*b)*d^2)) - b)","B",0
239,1,1305,0,1.135086," ","integrate(csch(d*x+c)^2/(a-b*sinh(d*x+c)^4),x, algorithm=""fricas"")","-\frac{{\left(a d \cosh\left(d x + c\right)^{2} + 2 \, a d \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a d \sinh\left(d x + c\right)^{2} - a d\right)} \sqrt{\frac{{\left(a^{3} - a^{2} b\right)} d^{2} \sqrt{\frac{b^{3}}{{\left(a^{7} - 2 \, a^{6} b + a^{5} b^{2}\right)} d^{4}}} + b}{{\left(a^{3} - a^{2} b\right)} d^{2}}} \log\left(b^{2} \cosh\left(d x + c\right)^{2} + 2 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b^{2} \sinh\left(d x + c\right)^{2} + 2 \, {\left(a^{4} - a^{3} b\right)} d^{2} \sqrt{\frac{b^{3}}{{\left(a^{7} - 2 \, a^{6} b + a^{5} b^{2}\right)} d^{4}}} - b^{2} + 2 \, {\left({\left(a^{5} - a^{4} b\right)} d^{3} \sqrt{\frac{b^{3}}{{\left(a^{7} - 2 \, a^{6} b + a^{5} b^{2}\right)} d^{4}}} - a^{2} b d\right)} \sqrt{\frac{{\left(a^{3} - a^{2} b\right)} d^{2} \sqrt{\frac{b^{3}}{{\left(a^{7} - 2 \, a^{6} b + a^{5} b^{2}\right)} d^{4}}} + b}{{\left(a^{3} - a^{2} b\right)} d^{2}}}\right) - {\left(a d \cosh\left(d x + c\right)^{2} + 2 \, a d \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a d \sinh\left(d x + c\right)^{2} - a d\right)} \sqrt{\frac{{\left(a^{3} - a^{2} b\right)} d^{2} \sqrt{\frac{b^{3}}{{\left(a^{7} - 2 \, a^{6} b + a^{5} b^{2}\right)} d^{4}}} + b}{{\left(a^{3} - a^{2} b\right)} d^{2}}} \log\left(b^{2} \cosh\left(d x + c\right)^{2} + 2 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b^{2} \sinh\left(d x + c\right)^{2} + 2 \, {\left(a^{4} - a^{3} b\right)} d^{2} \sqrt{\frac{b^{3}}{{\left(a^{7} - 2 \, a^{6} b + a^{5} b^{2}\right)} d^{4}}} - b^{2} - 2 \, {\left({\left(a^{5} - a^{4} b\right)} d^{3} \sqrt{\frac{b^{3}}{{\left(a^{7} - 2 \, a^{6} b + a^{5} b^{2}\right)} d^{4}}} - a^{2} b d\right)} \sqrt{\frac{{\left(a^{3} - a^{2} b\right)} d^{2} \sqrt{\frac{b^{3}}{{\left(a^{7} - 2 \, a^{6} b + a^{5} b^{2}\right)} d^{4}}} + b}{{\left(a^{3} - a^{2} b\right)} d^{2}}}\right) - {\left(a d \cosh\left(d x + c\right)^{2} + 2 \, a d \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a d \sinh\left(d x + c\right)^{2} - a d\right)} \sqrt{-\frac{{\left(a^{3} - a^{2} b\right)} d^{2} \sqrt{\frac{b^{3}}{{\left(a^{7} - 2 \, a^{6} b + a^{5} b^{2}\right)} d^{4}}} - b}{{\left(a^{3} - a^{2} b\right)} d^{2}}} \log\left(b^{2} \cosh\left(d x + c\right)^{2} + 2 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b^{2} \sinh\left(d x + c\right)^{2} - 2 \, {\left(a^{4} - a^{3} b\right)} d^{2} \sqrt{\frac{b^{3}}{{\left(a^{7} - 2 \, a^{6} b + a^{5} b^{2}\right)} d^{4}}} - b^{2} + 2 \, {\left({\left(a^{5} - a^{4} b\right)} d^{3} \sqrt{\frac{b^{3}}{{\left(a^{7} - 2 \, a^{6} b + a^{5} b^{2}\right)} d^{4}}} + a^{2} b d\right)} \sqrt{-\frac{{\left(a^{3} - a^{2} b\right)} d^{2} \sqrt{\frac{b^{3}}{{\left(a^{7} - 2 \, a^{6} b + a^{5} b^{2}\right)} d^{4}}} - b}{{\left(a^{3} - a^{2} b\right)} d^{2}}}\right) + {\left(a d \cosh\left(d x + c\right)^{2} + 2 \, a d \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a d \sinh\left(d x + c\right)^{2} - a d\right)} \sqrt{-\frac{{\left(a^{3} - a^{2} b\right)} d^{2} \sqrt{\frac{b^{3}}{{\left(a^{7} - 2 \, a^{6} b + a^{5} b^{2}\right)} d^{4}}} - b}{{\left(a^{3} - a^{2} b\right)} d^{2}}} \log\left(b^{2} \cosh\left(d x + c\right)^{2} + 2 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b^{2} \sinh\left(d x + c\right)^{2} - 2 \, {\left(a^{4} - a^{3} b\right)} d^{2} \sqrt{\frac{b^{3}}{{\left(a^{7} - 2 \, a^{6} b + a^{5} b^{2}\right)} d^{4}}} - b^{2} - 2 \, {\left({\left(a^{5} - a^{4} b\right)} d^{3} \sqrt{\frac{b^{3}}{{\left(a^{7} - 2 \, a^{6} b + a^{5} b^{2}\right)} d^{4}}} + a^{2} b d\right)} \sqrt{-\frac{{\left(a^{3} - a^{2} b\right)} d^{2} \sqrt{\frac{b^{3}}{{\left(a^{7} - 2 \, a^{6} b + a^{5} b^{2}\right)} d^{4}}} - b}{{\left(a^{3} - a^{2} b\right)} d^{2}}}\right) + 8}{4 \, {\left(a d \cosh\left(d x + c\right)^{2} + 2 \, a d \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a d \sinh\left(d x + c\right)^{2} - a d\right)}}"," ",0,"-1/4*((a*d*cosh(d*x + c)^2 + 2*a*d*cosh(d*x + c)*sinh(d*x + c) + a*d*sinh(d*x + c)^2 - a*d)*sqrt(((a^3 - a^2*b)*d^2*sqrt(b^3/((a^7 - 2*a^6*b + a^5*b^2)*d^4)) + b)/((a^3 - a^2*b)*d^2))*log(b^2*cosh(d*x + c)^2 + 2*b^2*cosh(d*x + c)*sinh(d*x + c) + b^2*sinh(d*x + c)^2 + 2*(a^4 - a^3*b)*d^2*sqrt(b^3/((a^7 - 2*a^6*b + a^5*b^2)*d^4)) - b^2 + 2*((a^5 - a^4*b)*d^3*sqrt(b^3/((a^7 - 2*a^6*b + a^5*b^2)*d^4)) - a^2*b*d)*sqrt(((a^3 - a^2*b)*d^2*sqrt(b^3/((a^7 - 2*a^6*b + a^5*b^2)*d^4)) + b)/((a^3 - a^2*b)*d^2))) - (a*d*cosh(d*x + c)^2 + 2*a*d*cosh(d*x + c)*sinh(d*x + c) + a*d*sinh(d*x + c)^2 - a*d)*sqrt(((a^3 - a^2*b)*d^2*sqrt(b^3/((a^7 - 2*a^6*b + a^5*b^2)*d^4)) + b)/((a^3 - a^2*b)*d^2))*log(b^2*cosh(d*x + c)^2 + 2*b^2*cosh(d*x + c)*sinh(d*x + c) + b^2*sinh(d*x + c)^2 + 2*(a^4 - a^3*b)*d^2*sqrt(b^3/((a^7 - 2*a^6*b + a^5*b^2)*d^4)) - b^2 - 2*((a^5 - a^4*b)*d^3*sqrt(b^3/((a^7 - 2*a^6*b + a^5*b^2)*d^4)) - a^2*b*d)*sqrt(((a^3 - a^2*b)*d^2*sqrt(b^3/((a^7 - 2*a^6*b + a^5*b^2)*d^4)) + b)/((a^3 - a^2*b)*d^2))) - (a*d*cosh(d*x + c)^2 + 2*a*d*cosh(d*x + c)*sinh(d*x + c) + a*d*sinh(d*x + c)^2 - a*d)*sqrt(-((a^3 - a^2*b)*d^2*sqrt(b^3/((a^7 - 2*a^6*b + a^5*b^2)*d^4)) - b)/((a^3 - a^2*b)*d^2))*log(b^2*cosh(d*x + c)^2 + 2*b^2*cosh(d*x + c)*sinh(d*x + c) + b^2*sinh(d*x + c)^2 - 2*(a^4 - a^3*b)*d^2*sqrt(b^3/((a^7 - 2*a^6*b + a^5*b^2)*d^4)) - b^2 + 2*((a^5 - a^4*b)*d^3*sqrt(b^3/((a^7 - 2*a^6*b + a^5*b^2)*d^4)) + a^2*b*d)*sqrt(-((a^3 - a^2*b)*d^2*sqrt(b^3/((a^7 - 2*a^6*b + a^5*b^2)*d^4)) - b)/((a^3 - a^2*b)*d^2))) + (a*d*cosh(d*x + c)^2 + 2*a*d*cosh(d*x + c)*sinh(d*x + c) + a*d*sinh(d*x + c)^2 - a*d)*sqrt(-((a^3 - a^2*b)*d^2*sqrt(b^3/((a^7 - 2*a^6*b + a^5*b^2)*d^4)) - b)/((a^3 - a^2*b)*d^2))*log(b^2*cosh(d*x + c)^2 + 2*b^2*cosh(d*x + c)*sinh(d*x + c) + b^2*sinh(d*x + c)^2 - 2*(a^4 - a^3*b)*d^2*sqrt(b^3/((a^7 - 2*a^6*b + a^5*b^2)*d^4)) - b^2 - 2*((a^5 - a^4*b)*d^3*sqrt(b^3/((a^7 - 2*a^6*b + a^5*b^2)*d^4)) + a^2*b*d)*sqrt(-((a^3 - a^2*b)*d^2*sqrt(b^3/((a^7 - 2*a^6*b + a^5*b^2)*d^4)) - b)/((a^3 - a^2*b)*d^2))) + 8)/(a*d*cosh(d*x + c)^2 + 2*a*d*cosh(d*x + c)*sinh(d*x + c) + a*d*sinh(d*x + c)^2 - a*d)","B",0
240,1,2206,0,3.493675," ","integrate(csch(d*x+c)^4/(a-b*sinh(d*x+c)^4),x, algorithm=""fricas"")","\frac{3 \, {\left(a d \cosh\left(d x + c\right)^{6} + 6 \, a d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + a d \sinh\left(d x + c\right)^{6} - 3 \, a d \cosh\left(d x + c\right)^{4} + 3 \, {\left(5 \, a d \cosh\left(d x + c\right)^{2} - a d\right)} \sinh\left(d x + c\right)^{4} + 3 \, a d \cosh\left(d x + c\right)^{2} + 4 \, {\left(5 \, a d \cosh\left(d x + c\right)^{3} - 3 \, a d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 3 \, {\left(5 \, a d \cosh\left(d x + c\right)^{4} - 6 \, a d \cosh\left(d x + c\right)^{2} + a d\right)} \sinh\left(d x + c\right)^{2} - a d + 6 \, {\left(a d \cosh\left(d x + c\right)^{5} - 2 \, a d \cosh\left(d x + c\right)^{3} + a d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{{\left(a^{4} - a^{3} b\right)} d^{2} \sqrt{\frac{b^{5}}{{\left(a^{9} - 2 \, a^{8} b + a^{7} b^{2}\right)} d^{4}}} + b^{2}}{{\left(a^{4} - a^{3} b\right)} d^{2}}} \log\left(b^{4} \cosh\left(d x + c\right)^{2} + 2 \, b^{4} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b^{4} \sinh\left(d x + c\right)^{2} - b^{4} + 2 \, {\left(a^{5} b - a^{4} b^{2}\right)} d^{2} \sqrt{\frac{b^{5}}{{\left(a^{9} - 2 \, a^{8} b + a^{7} b^{2}\right)} d^{4}}} + 2 \, {\left(a^{2} b^{3} d - {\left(a^{7} - a^{6} b\right)} d^{3} \sqrt{\frac{b^{5}}{{\left(a^{9} - 2 \, a^{8} b + a^{7} b^{2}\right)} d^{4}}}\right)} \sqrt{\frac{{\left(a^{4} - a^{3} b\right)} d^{2} \sqrt{\frac{b^{5}}{{\left(a^{9} - 2 \, a^{8} b + a^{7} b^{2}\right)} d^{4}}} + b^{2}}{{\left(a^{4} - a^{3} b\right)} d^{2}}}\right) - 3 \, {\left(a d \cosh\left(d x + c\right)^{6} + 6 \, a d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + a d \sinh\left(d x + c\right)^{6} - 3 \, a d \cosh\left(d x + c\right)^{4} + 3 \, {\left(5 \, a d \cosh\left(d x + c\right)^{2} - a d\right)} \sinh\left(d x + c\right)^{4} + 3 \, a d \cosh\left(d x + c\right)^{2} + 4 \, {\left(5 \, a d \cosh\left(d x + c\right)^{3} - 3 \, a d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 3 \, {\left(5 \, a d \cosh\left(d x + c\right)^{4} - 6 \, a d \cosh\left(d x + c\right)^{2} + a d\right)} \sinh\left(d x + c\right)^{2} - a d + 6 \, {\left(a d \cosh\left(d x + c\right)^{5} - 2 \, a d \cosh\left(d x + c\right)^{3} + a d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{{\left(a^{4} - a^{3} b\right)} d^{2} \sqrt{\frac{b^{5}}{{\left(a^{9} - 2 \, a^{8} b + a^{7} b^{2}\right)} d^{4}}} + b^{2}}{{\left(a^{4} - a^{3} b\right)} d^{2}}} \log\left(b^{4} \cosh\left(d x + c\right)^{2} + 2 \, b^{4} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b^{4} \sinh\left(d x + c\right)^{2} - b^{4} + 2 \, {\left(a^{5} b - a^{4} b^{2}\right)} d^{2} \sqrt{\frac{b^{5}}{{\left(a^{9} - 2 \, a^{8} b + a^{7} b^{2}\right)} d^{4}}} - 2 \, {\left(a^{2} b^{3} d - {\left(a^{7} - a^{6} b\right)} d^{3} \sqrt{\frac{b^{5}}{{\left(a^{9} - 2 \, a^{8} b + a^{7} b^{2}\right)} d^{4}}}\right)} \sqrt{\frac{{\left(a^{4} - a^{3} b\right)} d^{2} \sqrt{\frac{b^{5}}{{\left(a^{9} - 2 \, a^{8} b + a^{7} b^{2}\right)} d^{4}}} + b^{2}}{{\left(a^{4} - a^{3} b\right)} d^{2}}}\right) + 3 \, {\left(a d \cosh\left(d x + c\right)^{6} + 6 \, a d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + a d \sinh\left(d x + c\right)^{6} - 3 \, a d \cosh\left(d x + c\right)^{4} + 3 \, {\left(5 \, a d \cosh\left(d x + c\right)^{2} - a d\right)} \sinh\left(d x + c\right)^{4} + 3 \, a d \cosh\left(d x + c\right)^{2} + 4 \, {\left(5 \, a d \cosh\left(d x + c\right)^{3} - 3 \, a d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 3 \, {\left(5 \, a d \cosh\left(d x + c\right)^{4} - 6 \, a d \cosh\left(d x + c\right)^{2} + a d\right)} \sinh\left(d x + c\right)^{2} - a d + 6 \, {\left(a d \cosh\left(d x + c\right)^{5} - 2 \, a d \cosh\left(d x + c\right)^{3} + a d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{{\left(a^{4} - a^{3} b\right)} d^{2} \sqrt{\frac{b^{5}}{{\left(a^{9} - 2 \, a^{8} b + a^{7} b^{2}\right)} d^{4}}} - b^{2}}{{\left(a^{4} - a^{3} b\right)} d^{2}}} \log\left(b^{4} \cosh\left(d x + c\right)^{2} + 2 \, b^{4} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b^{4} \sinh\left(d x + c\right)^{2} - b^{4} - 2 \, {\left(a^{5} b - a^{4} b^{2}\right)} d^{2} \sqrt{\frac{b^{5}}{{\left(a^{9} - 2 \, a^{8} b + a^{7} b^{2}\right)} d^{4}}} + 2 \, {\left(a^{2} b^{3} d + {\left(a^{7} - a^{6} b\right)} d^{3} \sqrt{\frac{b^{5}}{{\left(a^{9} - 2 \, a^{8} b + a^{7} b^{2}\right)} d^{4}}}\right)} \sqrt{-\frac{{\left(a^{4} - a^{3} b\right)} d^{2} \sqrt{\frac{b^{5}}{{\left(a^{9} - 2 \, a^{8} b + a^{7} b^{2}\right)} d^{4}}} - b^{2}}{{\left(a^{4} - a^{3} b\right)} d^{2}}}\right) - 3 \, {\left(a d \cosh\left(d x + c\right)^{6} + 6 \, a d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + a d \sinh\left(d x + c\right)^{6} - 3 \, a d \cosh\left(d x + c\right)^{4} + 3 \, {\left(5 \, a d \cosh\left(d x + c\right)^{2} - a d\right)} \sinh\left(d x + c\right)^{4} + 3 \, a d \cosh\left(d x + c\right)^{2} + 4 \, {\left(5 \, a d \cosh\left(d x + c\right)^{3} - 3 \, a d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 3 \, {\left(5 \, a d \cosh\left(d x + c\right)^{4} - 6 \, a d \cosh\left(d x + c\right)^{2} + a d\right)} \sinh\left(d x + c\right)^{2} - a d + 6 \, {\left(a d \cosh\left(d x + c\right)^{5} - 2 \, a d \cosh\left(d x + c\right)^{3} + a d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{{\left(a^{4} - a^{3} b\right)} d^{2} \sqrt{\frac{b^{5}}{{\left(a^{9} - 2 \, a^{8} b + a^{7} b^{2}\right)} d^{4}}} - b^{2}}{{\left(a^{4} - a^{3} b\right)} d^{2}}} \log\left(b^{4} \cosh\left(d x + c\right)^{2} + 2 \, b^{4} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b^{4} \sinh\left(d x + c\right)^{2} - b^{4} - 2 \, {\left(a^{5} b - a^{4} b^{2}\right)} d^{2} \sqrt{\frac{b^{5}}{{\left(a^{9} - 2 \, a^{8} b + a^{7} b^{2}\right)} d^{4}}} - 2 \, {\left(a^{2} b^{3} d + {\left(a^{7} - a^{6} b\right)} d^{3} \sqrt{\frac{b^{5}}{{\left(a^{9} - 2 \, a^{8} b + a^{7} b^{2}\right)} d^{4}}}\right)} \sqrt{-\frac{{\left(a^{4} - a^{3} b\right)} d^{2} \sqrt{\frac{b^{5}}{{\left(a^{9} - 2 \, a^{8} b + a^{7} b^{2}\right)} d^{4}}} - b^{2}}{{\left(a^{4} - a^{3} b\right)} d^{2}}}\right) - 48 \, \cosh\left(d x + c\right)^{2} - 96 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right) - 48 \, \sinh\left(d x + c\right)^{2} + 16}{12 \, {\left(a d \cosh\left(d x + c\right)^{6} + 6 \, a d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + a d \sinh\left(d x + c\right)^{6} - 3 \, a d \cosh\left(d x + c\right)^{4} + 3 \, {\left(5 \, a d \cosh\left(d x + c\right)^{2} - a d\right)} \sinh\left(d x + c\right)^{4} + 3 \, a d \cosh\left(d x + c\right)^{2} + 4 \, {\left(5 \, a d \cosh\left(d x + c\right)^{3} - 3 \, a d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 3 \, {\left(5 \, a d \cosh\left(d x + c\right)^{4} - 6 \, a d \cosh\left(d x + c\right)^{2} + a d\right)} \sinh\left(d x + c\right)^{2} - a d + 6 \, {\left(a d \cosh\left(d x + c\right)^{5} - 2 \, a d \cosh\left(d x + c\right)^{3} + a d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"1/12*(3*(a*d*cosh(d*x + c)^6 + 6*a*d*cosh(d*x + c)*sinh(d*x + c)^5 + a*d*sinh(d*x + c)^6 - 3*a*d*cosh(d*x + c)^4 + 3*(5*a*d*cosh(d*x + c)^2 - a*d)*sinh(d*x + c)^4 + 3*a*d*cosh(d*x + c)^2 + 4*(5*a*d*cosh(d*x + c)^3 - 3*a*d*cosh(d*x + c))*sinh(d*x + c)^3 + 3*(5*a*d*cosh(d*x + c)^4 - 6*a*d*cosh(d*x + c)^2 + a*d)*sinh(d*x + c)^2 - a*d + 6*(a*d*cosh(d*x + c)^5 - 2*a*d*cosh(d*x + c)^3 + a*d*cosh(d*x + c))*sinh(d*x + c))*sqrt(((a^4 - a^3*b)*d^2*sqrt(b^5/((a^9 - 2*a^8*b + a^7*b^2)*d^4)) + b^2)/((a^4 - a^3*b)*d^2))*log(b^4*cosh(d*x + c)^2 + 2*b^4*cosh(d*x + c)*sinh(d*x + c) + b^4*sinh(d*x + c)^2 - b^4 + 2*(a^5*b - a^4*b^2)*d^2*sqrt(b^5/((a^9 - 2*a^8*b + a^7*b^2)*d^4)) + 2*(a^2*b^3*d - (a^7 - a^6*b)*d^3*sqrt(b^5/((a^9 - 2*a^8*b + a^7*b^2)*d^4)))*sqrt(((a^4 - a^3*b)*d^2*sqrt(b^5/((a^9 - 2*a^8*b + a^7*b^2)*d^4)) + b^2)/((a^4 - a^3*b)*d^2))) - 3*(a*d*cosh(d*x + c)^6 + 6*a*d*cosh(d*x + c)*sinh(d*x + c)^5 + a*d*sinh(d*x + c)^6 - 3*a*d*cosh(d*x + c)^4 + 3*(5*a*d*cosh(d*x + c)^2 - a*d)*sinh(d*x + c)^4 + 3*a*d*cosh(d*x + c)^2 + 4*(5*a*d*cosh(d*x + c)^3 - 3*a*d*cosh(d*x + c))*sinh(d*x + c)^3 + 3*(5*a*d*cosh(d*x + c)^4 - 6*a*d*cosh(d*x + c)^2 + a*d)*sinh(d*x + c)^2 - a*d + 6*(a*d*cosh(d*x + c)^5 - 2*a*d*cosh(d*x + c)^3 + a*d*cosh(d*x + c))*sinh(d*x + c))*sqrt(((a^4 - a^3*b)*d^2*sqrt(b^5/((a^9 - 2*a^8*b + a^7*b^2)*d^4)) + b^2)/((a^4 - a^3*b)*d^2))*log(b^4*cosh(d*x + c)^2 + 2*b^4*cosh(d*x + c)*sinh(d*x + c) + b^4*sinh(d*x + c)^2 - b^4 + 2*(a^5*b - a^4*b^2)*d^2*sqrt(b^5/((a^9 - 2*a^8*b + a^7*b^2)*d^4)) - 2*(a^2*b^3*d - (a^7 - a^6*b)*d^3*sqrt(b^5/((a^9 - 2*a^8*b + a^7*b^2)*d^4)))*sqrt(((a^4 - a^3*b)*d^2*sqrt(b^5/((a^9 - 2*a^8*b + a^7*b^2)*d^4)) + b^2)/((a^4 - a^3*b)*d^2))) + 3*(a*d*cosh(d*x + c)^6 + 6*a*d*cosh(d*x + c)*sinh(d*x + c)^5 + a*d*sinh(d*x + c)^6 - 3*a*d*cosh(d*x + c)^4 + 3*(5*a*d*cosh(d*x + c)^2 - a*d)*sinh(d*x + c)^4 + 3*a*d*cosh(d*x + c)^2 + 4*(5*a*d*cosh(d*x + c)^3 - 3*a*d*cosh(d*x + c))*sinh(d*x + c)^3 + 3*(5*a*d*cosh(d*x + c)^4 - 6*a*d*cosh(d*x + c)^2 + a*d)*sinh(d*x + c)^2 - a*d + 6*(a*d*cosh(d*x + c)^5 - 2*a*d*cosh(d*x + c)^3 + a*d*cosh(d*x + c))*sinh(d*x + c))*sqrt(-((a^4 - a^3*b)*d^2*sqrt(b^5/((a^9 - 2*a^8*b + a^7*b^2)*d^4)) - b^2)/((a^4 - a^3*b)*d^2))*log(b^4*cosh(d*x + c)^2 + 2*b^4*cosh(d*x + c)*sinh(d*x + c) + b^4*sinh(d*x + c)^2 - b^4 - 2*(a^5*b - a^4*b^2)*d^2*sqrt(b^5/((a^9 - 2*a^8*b + a^7*b^2)*d^4)) + 2*(a^2*b^3*d + (a^7 - a^6*b)*d^3*sqrt(b^5/((a^9 - 2*a^8*b + a^7*b^2)*d^4)))*sqrt(-((a^4 - a^3*b)*d^2*sqrt(b^5/((a^9 - 2*a^8*b + a^7*b^2)*d^4)) - b^2)/((a^4 - a^3*b)*d^2))) - 3*(a*d*cosh(d*x + c)^6 + 6*a*d*cosh(d*x + c)*sinh(d*x + c)^5 + a*d*sinh(d*x + c)^6 - 3*a*d*cosh(d*x + c)^4 + 3*(5*a*d*cosh(d*x + c)^2 - a*d)*sinh(d*x + c)^4 + 3*a*d*cosh(d*x + c)^2 + 4*(5*a*d*cosh(d*x + c)^3 - 3*a*d*cosh(d*x + c))*sinh(d*x + c)^3 + 3*(5*a*d*cosh(d*x + c)^4 - 6*a*d*cosh(d*x + c)^2 + a*d)*sinh(d*x + c)^2 - a*d + 6*(a*d*cosh(d*x + c)^5 - 2*a*d*cosh(d*x + c)^3 + a*d*cosh(d*x + c))*sinh(d*x + c))*sqrt(-((a^4 - a^3*b)*d^2*sqrt(b^5/((a^9 - 2*a^8*b + a^7*b^2)*d^4)) - b^2)/((a^4 - a^3*b)*d^2))*log(b^4*cosh(d*x + c)^2 + 2*b^4*cosh(d*x + c)*sinh(d*x + c) + b^4*sinh(d*x + c)^2 - b^4 - 2*(a^5*b - a^4*b^2)*d^2*sqrt(b^5/((a^9 - 2*a^8*b + a^7*b^2)*d^4)) - 2*(a^2*b^3*d + (a^7 - a^6*b)*d^3*sqrt(b^5/((a^9 - 2*a^8*b + a^7*b^2)*d^4)))*sqrt(-((a^4 - a^3*b)*d^2*sqrt(b^5/((a^9 - 2*a^8*b + a^7*b^2)*d^4)) - b^2)/((a^4 - a^3*b)*d^2))) - 48*cosh(d*x + c)^2 - 96*cosh(d*x + c)*sinh(d*x + c) - 48*sinh(d*x + c)^2 + 16)/(a*d*cosh(d*x + c)^6 + 6*a*d*cosh(d*x + c)*sinh(d*x + c)^5 + a*d*sinh(d*x + c)^6 - 3*a*d*cosh(d*x + c)^4 + 3*(5*a*d*cosh(d*x + c)^2 - a*d)*sinh(d*x + c)^4 + 3*a*d*cosh(d*x + c)^2 + 4*(5*a*d*cosh(d*x + c)^3 - 3*a*d*cosh(d*x + c))*sinh(d*x + c)^3 + 3*(5*a*d*cosh(d*x + c)^4 - 6*a*d*cosh(d*x + c)^2 + a*d)*sinh(d*x + c)^2 - a*d + 6*(a*d*cosh(d*x + c)^5 - 2*a*d*cosh(d*x + c)^3 + a*d*cosh(d*x + c))*sinh(d*x + c))","B",0
241,1,7664,0,0.931498," ","integrate(sinh(d*x+c)^9/(a-b*sinh(d*x+c)^4)^2,x, algorithm=""fricas"")","\frac{8 \, {\left(a b - b^{2}\right)} \cosh\left(d x + c\right)^{10} + 80 \, {\left(a b - b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + 8 \, {\left(a b - b^{2}\right)} \sinh\left(d x + c\right)^{10} - 8 \, {\left(2 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(45 \, {\left(a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, a b + 3 \, b^{2}\right)} \sinh\left(d x + c\right)^{8} + 64 \, {\left(15 \, {\left(a b - b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(2 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} - 8 \, {\left(20 \, a^{2} - 17 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 8 \, {\left(210 \, {\left(a b - b^{2}\right)} \cosh\left(d x + c\right)^{4} - 28 \, {\left(2 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 20 \, a^{2} + 17 \, a b - 2 \, b^{2}\right)} \sinh\left(d x + c\right)^{6} + 16 \, {\left(126 \, {\left(a b - b^{2}\right)} \cosh\left(d x + c\right)^{5} - 28 \, {\left(2 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(20 \, a^{2} - 17 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 8 \, {\left(20 \, a^{2} - 17 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 8 \, {\left(210 \, {\left(a b - b^{2}\right)} \cosh\left(d x + c\right)^{6} - 70 \, {\left(2 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} - 15 \, {\left(20 \, a^{2} - 17 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 20 \, a^{2} + 17 \, a b - 2 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 32 \, {\left(30 \, {\left(a b - b^{2}\right)} \cosh\left(d x + c\right)^{7} - 14 \, {\left(2 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} - 5 \, {\left(20 \, a^{2} - 17 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(20 \, a^{2} - 17 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 8 \, {\left(2 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 8 \, {\left(45 \, {\left(a b - b^{2}\right)} \cosh\left(d x + c\right)^{8} - 28 \, {\left(2 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} - 15 \, {\left(20 \, a^{2} - 17 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} - 6 \, {\left(20 \, a^{2} - 17 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, a b + 3 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{9} + 9 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{8} + {\left(a b^{3} - b^{4}\right)} d \sinh\left(d x + c\right)^{9} - 4 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{7} + 4 \, {\left(9 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a b^{3} - b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{7} - 2 \, {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d \cosh\left(d x + c\right)^{5} + 28 \, {\left(3 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(63 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{4} - 42 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{2} - {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{5} - 4 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{3} + 2 \, {\left(63 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{5} - 70 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{3} - 5 \, {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(21 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{6} - 35 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{4} - 5 \, {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a b^{3} - b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{3} + {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right) + 4 \, {\left(9 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{7} - 21 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{5} - 5 \, {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d \cosh\left(d x + c\right)^{3} - 3 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(9 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{8} - 28 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{6} - 10 \, {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d \cosh\left(d x + c\right)^{4} - 12 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a b^{3} - b^{4}\right)} d\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{{\left(a^{3} b^{4} - 3 \, a^{2} b^{5} + 3 \, a b^{6} - b^{7}\right)} d^{2} \sqrt{\frac{625 \, a^{7} - 3450 \, a^{6} b + 7161 \, a^{5} b^{2} - 6624 \, a^{4} b^{3} + 2304 \, a^{3} b^{4}}{{\left(a^{6} b^{9} - 6 \, a^{5} b^{10} + 15 \, a^{4} b^{11} - 20 \, a^{3} b^{12} + 15 \, a^{2} b^{13} - 6 \, a b^{14} + b^{15}\right)} d^{4}}} + 15 \, a^{3} - 47 \, a^{2} b + 36 \, a b^{2}}{{\left(a^{3} b^{4} - 3 \, a^{2} b^{5} + 3 \, a b^{6} - b^{7}\right)} d^{2}}} \log\left(-625 \, a^{5} + 2625 \, a^{4} b - 3684 \, a^{3} b^{2} + 1728 \, a^{2} b^{3} - {\left(625 \, a^{5} - 2625 \, a^{4} b + 3684 \, a^{3} b^{2} - 1728 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(625 \, a^{5} - 2625 \, a^{4} b + 3684 \, a^{3} b^{2} - 1728 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(625 \, a^{5} - 2625 \, a^{4} b + 3684 \, a^{3} b^{2} - 1728 \, a^{2} b^{3}\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left({\left(125 \, a^{5} b^{2} - 520 \, a^{4} b^{3} + 723 \, a^{3} b^{4} - 336 \, a^{2} b^{5}\right)} d \cosh\left(d x + c\right) + {\left(125 \, a^{5} b^{2} - 520 \, a^{4} b^{3} + 723 \, a^{3} b^{4} - 336 \, a^{2} b^{5}\right)} d \sinh\left(d x + c\right) - 2 \, {\left({\left(2 \, a^{4} b^{7} - 9 \, a^{3} b^{8} + 15 \, a^{2} b^{9} - 11 \, a b^{10} + 3 \, b^{11}\right)} d^{3} \cosh\left(d x + c\right) + {\left(2 \, a^{4} b^{7} - 9 \, a^{3} b^{8} + 15 \, a^{2} b^{9} - 11 \, a b^{10} + 3 \, b^{11}\right)} d^{3} \sinh\left(d x + c\right)\right)} \sqrt{\frac{625 \, a^{7} - 3450 \, a^{6} b + 7161 \, a^{5} b^{2} - 6624 \, a^{4} b^{3} + 2304 \, a^{3} b^{4}}{{\left(a^{6} b^{9} - 6 \, a^{5} b^{10} + 15 \, a^{4} b^{11} - 20 \, a^{3} b^{12} + 15 \, a^{2} b^{13} - 6 \, a b^{14} + b^{15}\right)} d^{4}}}\right)} \sqrt{-\frac{{\left(a^{3} b^{4} - 3 \, a^{2} b^{5} + 3 \, a b^{6} - b^{7}\right)} d^{2} \sqrt{\frac{625 \, a^{7} - 3450 \, a^{6} b + 7161 \, a^{5} b^{2} - 6624 \, a^{4} b^{3} + 2304 \, a^{3} b^{4}}{{\left(a^{6} b^{9} - 6 \, a^{5} b^{10} + 15 \, a^{4} b^{11} - 20 \, a^{3} b^{12} + 15 \, a^{2} b^{13} - 6 \, a b^{14} + b^{15}\right)} d^{4}}} + 15 \, a^{3} - 47 \, a^{2} b + 36 \, a b^{2}}{{\left(a^{3} b^{4} - 3 \, a^{2} b^{5} + 3 \, a b^{6} - b^{7}\right)} d^{2}}}\right) - {\left({\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{9} + 9 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{8} + {\left(a b^{3} - b^{4}\right)} d \sinh\left(d x + c\right)^{9} - 4 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{7} + 4 \, {\left(9 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a b^{3} - b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{7} - 2 \, {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d \cosh\left(d x + c\right)^{5} + 28 \, {\left(3 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(63 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{4} - 42 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{2} - {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{5} - 4 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{3} + 2 \, {\left(63 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{5} - 70 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{3} - 5 \, {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(21 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{6} - 35 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{4} - 5 \, {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a b^{3} - b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{3} + {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right) + 4 \, {\left(9 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{7} - 21 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{5} - 5 \, {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d \cosh\left(d x + c\right)^{3} - 3 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(9 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{8} - 28 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{6} - 10 \, {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d \cosh\left(d x + c\right)^{4} - 12 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a b^{3} - b^{4}\right)} d\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{{\left(a^{3} b^{4} - 3 \, a^{2} b^{5} + 3 \, a b^{6} - b^{7}\right)} d^{2} \sqrt{\frac{625 \, a^{7} - 3450 \, a^{6} b + 7161 \, a^{5} b^{2} - 6624 \, a^{4} b^{3} + 2304 \, a^{3} b^{4}}{{\left(a^{6} b^{9} - 6 \, a^{5} b^{10} + 15 \, a^{4} b^{11} - 20 \, a^{3} b^{12} + 15 \, a^{2} b^{13} - 6 \, a b^{14} + b^{15}\right)} d^{4}}} + 15 \, a^{3} - 47 \, a^{2} b + 36 \, a b^{2}}{{\left(a^{3} b^{4} - 3 \, a^{2} b^{5} + 3 \, a b^{6} - b^{7}\right)} d^{2}}} \log\left(-625 \, a^{5} + 2625 \, a^{4} b - 3684 \, a^{3} b^{2} + 1728 \, a^{2} b^{3} - {\left(625 \, a^{5} - 2625 \, a^{4} b + 3684 \, a^{3} b^{2} - 1728 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(625 \, a^{5} - 2625 \, a^{4} b + 3684 \, a^{3} b^{2} - 1728 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(625 \, a^{5} - 2625 \, a^{4} b + 3684 \, a^{3} b^{2} - 1728 \, a^{2} b^{3}\right)} \sinh\left(d x + c\right)^{2} - 2 \, {\left({\left(125 \, a^{5} b^{2} - 520 \, a^{4} b^{3} + 723 \, a^{3} b^{4} - 336 \, a^{2} b^{5}\right)} d \cosh\left(d x + c\right) + {\left(125 \, a^{5} b^{2} - 520 \, a^{4} b^{3} + 723 \, a^{3} b^{4} - 336 \, a^{2} b^{5}\right)} d \sinh\left(d x + c\right) - 2 \, {\left({\left(2 \, a^{4} b^{7} - 9 \, a^{3} b^{8} + 15 \, a^{2} b^{9} - 11 \, a b^{10} + 3 \, b^{11}\right)} d^{3} \cosh\left(d x + c\right) + {\left(2 \, a^{4} b^{7} - 9 \, a^{3} b^{8} + 15 \, a^{2} b^{9} - 11 \, a b^{10} + 3 \, b^{11}\right)} d^{3} \sinh\left(d x + c\right)\right)} \sqrt{\frac{625 \, a^{7} - 3450 \, a^{6} b + 7161 \, a^{5} b^{2} - 6624 \, a^{4} b^{3} + 2304 \, a^{3} b^{4}}{{\left(a^{6} b^{9} - 6 \, a^{5} b^{10} + 15 \, a^{4} b^{11} - 20 \, a^{3} b^{12} + 15 \, a^{2} b^{13} - 6 \, a b^{14} + b^{15}\right)} d^{4}}}\right)} \sqrt{-\frac{{\left(a^{3} b^{4} - 3 \, a^{2} b^{5} + 3 \, a b^{6} - b^{7}\right)} d^{2} \sqrt{\frac{625 \, a^{7} - 3450 \, a^{6} b + 7161 \, a^{5} b^{2} - 6624 \, a^{4} b^{3} + 2304 \, a^{3} b^{4}}{{\left(a^{6} b^{9} - 6 \, a^{5} b^{10} + 15 \, a^{4} b^{11} - 20 \, a^{3} b^{12} + 15 \, a^{2} b^{13} - 6 \, a b^{14} + b^{15}\right)} d^{4}}} + 15 \, a^{3} - 47 \, a^{2} b + 36 \, a b^{2}}{{\left(a^{3} b^{4} - 3 \, a^{2} b^{5} + 3 \, a b^{6} - b^{7}\right)} d^{2}}}\right) + {\left({\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{9} + 9 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{8} + {\left(a b^{3} - b^{4}\right)} d \sinh\left(d x + c\right)^{9} - 4 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{7} + 4 \, {\left(9 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a b^{3} - b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{7} - 2 \, {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d \cosh\left(d x + c\right)^{5} + 28 \, {\left(3 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(63 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{4} - 42 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{2} - {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{5} - 4 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{3} + 2 \, {\left(63 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{5} - 70 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{3} - 5 \, {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(21 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{6} - 35 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{4} - 5 \, {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a b^{3} - b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{3} + {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right) + 4 \, {\left(9 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{7} - 21 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{5} - 5 \, {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d \cosh\left(d x + c\right)^{3} - 3 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(9 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{8} - 28 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{6} - 10 \, {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d \cosh\left(d x + c\right)^{4} - 12 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a b^{3} - b^{4}\right)} d\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{{\left(a^{3} b^{4} - 3 \, a^{2} b^{5} + 3 \, a b^{6} - b^{7}\right)} d^{2} \sqrt{\frac{625 \, a^{7} - 3450 \, a^{6} b + 7161 \, a^{5} b^{2} - 6624 \, a^{4} b^{3} + 2304 \, a^{3} b^{4}}{{\left(a^{6} b^{9} - 6 \, a^{5} b^{10} + 15 \, a^{4} b^{11} - 20 \, a^{3} b^{12} + 15 \, a^{2} b^{13} - 6 \, a b^{14} + b^{15}\right)} d^{4}}} - 15 \, a^{3} + 47 \, a^{2} b - 36 \, a b^{2}}{{\left(a^{3} b^{4} - 3 \, a^{2} b^{5} + 3 \, a b^{6} - b^{7}\right)} d^{2}}} \log\left(-625 \, a^{5} + 2625 \, a^{4} b - 3684 \, a^{3} b^{2} + 1728 \, a^{2} b^{3} - {\left(625 \, a^{5} - 2625 \, a^{4} b + 3684 \, a^{3} b^{2} - 1728 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(625 \, a^{5} - 2625 \, a^{4} b + 3684 \, a^{3} b^{2} - 1728 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(625 \, a^{5} - 2625 \, a^{4} b + 3684 \, a^{3} b^{2} - 1728 \, a^{2} b^{3}\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left({\left(125 \, a^{5} b^{2} - 520 \, a^{4} b^{3} + 723 \, a^{3} b^{4} - 336 \, a^{2} b^{5}\right)} d \cosh\left(d x + c\right) + {\left(125 \, a^{5} b^{2} - 520 \, a^{4} b^{3} + 723 \, a^{3} b^{4} - 336 \, a^{2} b^{5}\right)} d \sinh\left(d x + c\right) + 2 \, {\left({\left(2 \, a^{4} b^{7} - 9 \, a^{3} b^{8} + 15 \, a^{2} b^{9} - 11 \, a b^{10} + 3 \, b^{11}\right)} d^{3} \cosh\left(d x + c\right) + {\left(2 \, a^{4} b^{7} - 9 \, a^{3} b^{8} + 15 \, a^{2} b^{9} - 11 \, a b^{10} + 3 \, b^{11}\right)} d^{3} \sinh\left(d x + c\right)\right)} \sqrt{\frac{625 \, a^{7} - 3450 \, a^{6} b + 7161 \, a^{5} b^{2} - 6624 \, a^{4} b^{3} + 2304 \, a^{3} b^{4}}{{\left(a^{6} b^{9} - 6 \, a^{5} b^{10} + 15 \, a^{4} b^{11} - 20 \, a^{3} b^{12} + 15 \, a^{2} b^{13} - 6 \, a b^{14} + b^{15}\right)} d^{4}}}\right)} \sqrt{\frac{{\left(a^{3} b^{4} - 3 \, a^{2} b^{5} + 3 \, a b^{6} - b^{7}\right)} d^{2} \sqrt{\frac{625 \, a^{7} - 3450 \, a^{6} b + 7161 \, a^{5} b^{2} - 6624 \, a^{4} b^{3} + 2304 \, a^{3} b^{4}}{{\left(a^{6} b^{9} - 6 \, a^{5} b^{10} + 15 \, a^{4} b^{11} - 20 \, a^{3} b^{12} + 15 \, a^{2} b^{13} - 6 \, a b^{14} + b^{15}\right)} d^{4}}} - 15 \, a^{3} + 47 \, a^{2} b - 36 \, a b^{2}}{{\left(a^{3} b^{4} - 3 \, a^{2} b^{5} + 3 \, a b^{6} - b^{7}\right)} d^{2}}}\right) - {\left({\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{9} + 9 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{8} + {\left(a b^{3} - b^{4}\right)} d \sinh\left(d x + c\right)^{9} - 4 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{7} + 4 \, {\left(9 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a b^{3} - b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{7} - 2 \, {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d \cosh\left(d x + c\right)^{5} + 28 \, {\left(3 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(63 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{4} - 42 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{2} - {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{5} - 4 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{3} + 2 \, {\left(63 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{5} - 70 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{3} - 5 \, {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(21 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{6} - 35 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{4} - 5 \, {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a b^{3} - b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{3} + {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right) + 4 \, {\left(9 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{7} - 21 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{5} - 5 \, {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d \cosh\left(d x + c\right)^{3} - 3 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(9 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{8} - 28 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{6} - 10 \, {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d \cosh\left(d x + c\right)^{4} - 12 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a b^{3} - b^{4}\right)} d\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{{\left(a^{3} b^{4} - 3 \, a^{2} b^{5} + 3 \, a b^{6} - b^{7}\right)} d^{2} \sqrt{\frac{625 \, a^{7} - 3450 \, a^{6} b + 7161 \, a^{5} b^{2} - 6624 \, a^{4} b^{3} + 2304 \, a^{3} b^{4}}{{\left(a^{6} b^{9} - 6 \, a^{5} b^{10} + 15 \, a^{4} b^{11} - 20 \, a^{3} b^{12} + 15 \, a^{2} b^{13} - 6 \, a b^{14} + b^{15}\right)} d^{4}}} - 15 \, a^{3} + 47 \, a^{2} b - 36 \, a b^{2}}{{\left(a^{3} b^{4} - 3 \, a^{2} b^{5} + 3 \, a b^{6} - b^{7}\right)} d^{2}}} \log\left(-625 \, a^{5} + 2625 \, a^{4} b - 3684 \, a^{3} b^{2} + 1728 \, a^{2} b^{3} - {\left(625 \, a^{5} - 2625 \, a^{4} b + 3684 \, a^{3} b^{2} - 1728 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(625 \, a^{5} - 2625 \, a^{4} b + 3684 \, a^{3} b^{2} - 1728 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(625 \, a^{5} - 2625 \, a^{4} b + 3684 \, a^{3} b^{2} - 1728 \, a^{2} b^{3}\right)} \sinh\left(d x + c\right)^{2} - 2 \, {\left({\left(125 \, a^{5} b^{2} - 520 \, a^{4} b^{3} + 723 \, a^{3} b^{4} - 336 \, a^{2} b^{5}\right)} d \cosh\left(d x + c\right) + {\left(125 \, a^{5} b^{2} - 520 \, a^{4} b^{3} + 723 \, a^{3} b^{4} - 336 \, a^{2} b^{5}\right)} d \sinh\left(d x + c\right) + 2 \, {\left({\left(2 \, a^{4} b^{7} - 9 \, a^{3} b^{8} + 15 \, a^{2} b^{9} - 11 \, a b^{10} + 3 \, b^{11}\right)} d^{3} \cosh\left(d x + c\right) + {\left(2 \, a^{4} b^{7} - 9 \, a^{3} b^{8} + 15 \, a^{2} b^{9} - 11 \, a b^{10} + 3 \, b^{11}\right)} d^{3} \sinh\left(d x + c\right)\right)} \sqrt{\frac{625 \, a^{7} - 3450 \, a^{6} b + 7161 \, a^{5} b^{2} - 6624 \, a^{4} b^{3} + 2304 \, a^{3} b^{4}}{{\left(a^{6} b^{9} - 6 \, a^{5} b^{10} + 15 \, a^{4} b^{11} - 20 \, a^{3} b^{12} + 15 \, a^{2} b^{13} - 6 \, a b^{14} + b^{15}\right)} d^{4}}}\right)} \sqrt{\frac{{\left(a^{3} b^{4} - 3 \, a^{2} b^{5} + 3 \, a b^{6} - b^{7}\right)} d^{2} \sqrt{\frac{625 \, a^{7} - 3450 \, a^{6} b + 7161 \, a^{5} b^{2} - 6624 \, a^{4} b^{3} + 2304 \, a^{3} b^{4}}{{\left(a^{6} b^{9} - 6 \, a^{5} b^{10} + 15 \, a^{4} b^{11} - 20 \, a^{3} b^{12} + 15 \, a^{2} b^{13} - 6 \, a b^{14} + b^{15}\right)} d^{4}}} - 15 \, a^{3} + 47 \, a^{2} b - 36 \, a b^{2}}{{\left(a^{3} b^{4} - 3 \, a^{2} b^{5} + 3 \, a b^{6} - b^{7}\right)} d^{2}}}\right) + 8 \, a b - 8 \, b^{2} + 16 \, {\left(5 \, {\left(a b - b^{2}\right)} \cosh\left(d x + c\right)^{9} - 4 \, {\left(2 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} - 3 \, {\left(20 \, a^{2} - 17 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} - 2 \, {\left(20 \, a^{2} - 17 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(2 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{16 \, {\left({\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{9} + 9 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{8} + {\left(a b^{3} - b^{4}\right)} d \sinh\left(d x + c\right)^{9} - 4 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{7} + 4 \, {\left(9 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a b^{3} - b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{7} - 2 \, {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d \cosh\left(d x + c\right)^{5} + 28 \, {\left(3 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(63 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{4} - 42 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{2} - {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{5} - 4 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{3} + 2 \, {\left(63 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{5} - 70 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{3} - 5 \, {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(21 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{6} - 35 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{4} - 5 \, {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a b^{3} - b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{3} + {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right) + 4 \, {\left(9 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{7} - 21 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{5} - 5 \, {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d \cosh\left(d x + c\right)^{3} - 3 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(9 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{8} - 28 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{6} - 10 \, {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d \cosh\left(d x + c\right)^{4} - 12 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a b^{3} - b^{4}\right)} d\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"1/16*(8*(a*b - b^2)*cosh(d*x + c)^10 + 80*(a*b - b^2)*cosh(d*x + c)*sinh(d*x + c)^9 + 8*(a*b - b^2)*sinh(d*x + c)^10 - 8*(2*a*b - 3*b^2)*cosh(d*x + c)^8 + 8*(45*(a*b - b^2)*cosh(d*x + c)^2 - 2*a*b + 3*b^2)*sinh(d*x + c)^8 + 64*(15*(a*b - b^2)*cosh(d*x + c)^3 - (2*a*b - 3*b^2)*cosh(d*x + c))*sinh(d*x + c)^7 - 8*(20*a^2 - 17*a*b + 2*b^2)*cosh(d*x + c)^6 + 8*(210*(a*b - b^2)*cosh(d*x + c)^4 - 28*(2*a*b - 3*b^2)*cosh(d*x + c)^2 - 20*a^2 + 17*a*b - 2*b^2)*sinh(d*x + c)^6 + 16*(126*(a*b - b^2)*cosh(d*x + c)^5 - 28*(2*a*b - 3*b^2)*cosh(d*x + c)^3 - 3*(20*a^2 - 17*a*b + 2*b^2)*cosh(d*x + c))*sinh(d*x + c)^5 - 8*(20*a^2 - 17*a*b + 2*b^2)*cosh(d*x + c)^4 + 8*(210*(a*b - b^2)*cosh(d*x + c)^6 - 70*(2*a*b - 3*b^2)*cosh(d*x + c)^4 - 15*(20*a^2 - 17*a*b + 2*b^2)*cosh(d*x + c)^2 - 20*a^2 + 17*a*b - 2*b^2)*sinh(d*x + c)^4 + 32*(30*(a*b - b^2)*cosh(d*x + c)^7 - 14*(2*a*b - 3*b^2)*cosh(d*x + c)^5 - 5*(20*a^2 - 17*a*b + 2*b^2)*cosh(d*x + c)^3 - (20*a^2 - 17*a*b + 2*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 - 8*(2*a*b - 3*b^2)*cosh(d*x + c)^2 + 8*(45*(a*b - b^2)*cosh(d*x + c)^8 - 28*(2*a*b - 3*b^2)*cosh(d*x + c)^6 - 15*(20*a^2 - 17*a*b + 2*b^2)*cosh(d*x + c)^4 - 6*(20*a^2 - 17*a*b + 2*b^2)*cosh(d*x + c)^2 - 2*a*b + 3*b^2)*sinh(d*x + c)^2 + ((a*b^3 - b^4)*d*cosh(d*x + c)^9 + 9*(a*b^3 - b^4)*d*cosh(d*x + c)*sinh(d*x + c)^8 + (a*b^3 - b^4)*d*sinh(d*x + c)^9 - 4*(a*b^3 - b^4)*d*cosh(d*x + c)^7 + 4*(9*(a*b^3 - b^4)*d*cosh(d*x + c)^2 - (a*b^3 - b^4)*d)*sinh(d*x + c)^7 - 2*(8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d*cosh(d*x + c)^5 + 28*(3*(a*b^3 - b^4)*d*cosh(d*x + c)^3 - (a*b^3 - b^4)*d*cosh(d*x + c))*sinh(d*x + c)^6 + 2*(63*(a*b^3 - b^4)*d*cosh(d*x + c)^4 - 42*(a*b^3 - b^4)*d*cosh(d*x + c)^2 - (8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d)*sinh(d*x + c)^5 - 4*(a*b^3 - b^4)*d*cosh(d*x + c)^3 + 2*(63*(a*b^3 - b^4)*d*cosh(d*x + c)^5 - 70*(a*b^3 - b^4)*d*cosh(d*x + c)^3 - 5*(8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d*cosh(d*x + c))*sinh(d*x + c)^4 + 4*(21*(a*b^3 - b^4)*d*cosh(d*x + c)^6 - 35*(a*b^3 - b^4)*d*cosh(d*x + c)^4 - 5*(8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d*cosh(d*x + c)^2 - (a*b^3 - b^4)*d)*sinh(d*x + c)^3 + (a*b^3 - b^4)*d*cosh(d*x + c) + 4*(9*(a*b^3 - b^4)*d*cosh(d*x + c)^7 - 21*(a*b^3 - b^4)*d*cosh(d*x + c)^5 - 5*(8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d*cosh(d*x + c)^3 - 3*(a*b^3 - b^4)*d*cosh(d*x + c))*sinh(d*x + c)^2 + (9*(a*b^3 - b^4)*d*cosh(d*x + c)^8 - 28*(a*b^3 - b^4)*d*cosh(d*x + c)^6 - 10*(8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d*cosh(d*x + c)^4 - 12*(a*b^3 - b^4)*d*cosh(d*x + c)^2 + (a*b^3 - b^4)*d)*sinh(d*x + c))*sqrt(-((a^3*b^4 - 3*a^2*b^5 + 3*a*b^6 - b^7)*d^2*sqrt((625*a^7 - 3450*a^6*b + 7161*a^5*b^2 - 6624*a^4*b^3 + 2304*a^3*b^4)/((a^6*b^9 - 6*a^5*b^10 + 15*a^4*b^11 - 20*a^3*b^12 + 15*a^2*b^13 - 6*a*b^14 + b^15)*d^4)) + 15*a^3 - 47*a^2*b + 36*a*b^2)/((a^3*b^4 - 3*a^2*b^5 + 3*a*b^6 - b^7)*d^2))*log(-625*a^5 + 2625*a^4*b - 3684*a^3*b^2 + 1728*a^2*b^3 - (625*a^5 - 2625*a^4*b + 3684*a^3*b^2 - 1728*a^2*b^3)*cosh(d*x + c)^2 - 2*(625*a^5 - 2625*a^4*b + 3684*a^3*b^2 - 1728*a^2*b^3)*cosh(d*x + c)*sinh(d*x + c) - (625*a^5 - 2625*a^4*b + 3684*a^3*b^2 - 1728*a^2*b^3)*sinh(d*x + c)^2 + 2*((125*a^5*b^2 - 520*a^4*b^3 + 723*a^3*b^4 - 336*a^2*b^5)*d*cosh(d*x + c) + (125*a^5*b^2 - 520*a^4*b^3 + 723*a^3*b^4 - 336*a^2*b^5)*d*sinh(d*x + c) - 2*((2*a^4*b^7 - 9*a^3*b^8 + 15*a^2*b^9 - 11*a*b^10 + 3*b^11)*d^3*cosh(d*x + c) + (2*a^4*b^7 - 9*a^3*b^8 + 15*a^2*b^9 - 11*a*b^10 + 3*b^11)*d^3*sinh(d*x + c))*sqrt((625*a^7 - 3450*a^6*b + 7161*a^5*b^2 - 6624*a^4*b^3 + 2304*a^3*b^4)/((a^6*b^9 - 6*a^5*b^10 + 15*a^4*b^11 - 20*a^3*b^12 + 15*a^2*b^13 - 6*a*b^14 + b^15)*d^4)))*sqrt(-((a^3*b^4 - 3*a^2*b^5 + 3*a*b^6 - b^7)*d^2*sqrt((625*a^7 - 3450*a^6*b + 7161*a^5*b^2 - 6624*a^4*b^3 + 2304*a^3*b^4)/((a^6*b^9 - 6*a^5*b^10 + 15*a^4*b^11 - 20*a^3*b^12 + 15*a^2*b^13 - 6*a*b^14 + b^15)*d^4)) + 15*a^3 - 47*a^2*b + 36*a*b^2)/((a^3*b^4 - 3*a^2*b^5 + 3*a*b^6 - b^7)*d^2))) - ((a*b^3 - b^4)*d*cosh(d*x + c)^9 + 9*(a*b^3 - b^4)*d*cosh(d*x + c)*sinh(d*x + c)^8 + (a*b^3 - b^4)*d*sinh(d*x + c)^9 - 4*(a*b^3 - b^4)*d*cosh(d*x + c)^7 + 4*(9*(a*b^3 - b^4)*d*cosh(d*x + c)^2 - (a*b^3 - b^4)*d)*sinh(d*x + c)^7 - 2*(8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d*cosh(d*x + c)^5 + 28*(3*(a*b^3 - b^4)*d*cosh(d*x + c)^3 - (a*b^3 - b^4)*d*cosh(d*x + c))*sinh(d*x + c)^6 + 2*(63*(a*b^3 - b^4)*d*cosh(d*x + c)^4 - 42*(a*b^3 - b^4)*d*cosh(d*x + c)^2 - (8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d)*sinh(d*x + c)^5 - 4*(a*b^3 - b^4)*d*cosh(d*x + c)^3 + 2*(63*(a*b^3 - b^4)*d*cosh(d*x + c)^5 - 70*(a*b^3 - b^4)*d*cosh(d*x + c)^3 - 5*(8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d*cosh(d*x + c))*sinh(d*x + c)^4 + 4*(21*(a*b^3 - b^4)*d*cosh(d*x + c)^6 - 35*(a*b^3 - b^4)*d*cosh(d*x + c)^4 - 5*(8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d*cosh(d*x + c)^2 - (a*b^3 - b^4)*d)*sinh(d*x + c)^3 + (a*b^3 - b^4)*d*cosh(d*x + c) + 4*(9*(a*b^3 - b^4)*d*cosh(d*x + c)^7 - 21*(a*b^3 - b^4)*d*cosh(d*x + c)^5 - 5*(8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d*cosh(d*x + c)^3 - 3*(a*b^3 - b^4)*d*cosh(d*x + c))*sinh(d*x + c)^2 + (9*(a*b^3 - b^4)*d*cosh(d*x + c)^8 - 28*(a*b^3 - b^4)*d*cosh(d*x + c)^6 - 10*(8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d*cosh(d*x + c)^4 - 12*(a*b^3 - b^4)*d*cosh(d*x + c)^2 + (a*b^3 - b^4)*d)*sinh(d*x + c))*sqrt(-((a^3*b^4 - 3*a^2*b^5 + 3*a*b^6 - b^7)*d^2*sqrt((625*a^7 - 3450*a^6*b + 7161*a^5*b^2 - 6624*a^4*b^3 + 2304*a^3*b^4)/((a^6*b^9 - 6*a^5*b^10 + 15*a^4*b^11 - 20*a^3*b^12 + 15*a^2*b^13 - 6*a*b^14 + b^15)*d^4)) + 15*a^3 - 47*a^2*b + 36*a*b^2)/((a^3*b^4 - 3*a^2*b^5 + 3*a*b^6 - b^7)*d^2))*log(-625*a^5 + 2625*a^4*b - 3684*a^3*b^2 + 1728*a^2*b^3 - (625*a^5 - 2625*a^4*b + 3684*a^3*b^2 - 1728*a^2*b^3)*cosh(d*x + c)^2 - 2*(625*a^5 - 2625*a^4*b + 3684*a^3*b^2 - 1728*a^2*b^3)*cosh(d*x + c)*sinh(d*x + c) - (625*a^5 - 2625*a^4*b + 3684*a^3*b^2 - 1728*a^2*b^3)*sinh(d*x + c)^2 - 2*((125*a^5*b^2 - 520*a^4*b^3 + 723*a^3*b^4 - 336*a^2*b^5)*d*cosh(d*x + c) + (125*a^5*b^2 - 520*a^4*b^3 + 723*a^3*b^4 - 336*a^2*b^5)*d*sinh(d*x + c) - 2*((2*a^4*b^7 - 9*a^3*b^8 + 15*a^2*b^9 - 11*a*b^10 + 3*b^11)*d^3*cosh(d*x + c) + (2*a^4*b^7 - 9*a^3*b^8 + 15*a^2*b^9 - 11*a*b^10 + 3*b^11)*d^3*sinh(d*x + c))*sqrt((625*a^7 - 3450*a^6*b + 7161*a^5*b^2 - 6624*a^4*b^3 + 2304*a^3*b^4)/((a^6*b^9 - 6*a^5*b^10 + 15*a^4*b^11 - 20*a^3*b^12 + 15*a^2*b^13 - 6*a*b^14 + b^15)*d^4)))*sqrt(-((a^3*b^4 - 3*a^2*b^5 + 3*a*b^6 - b^7)*d^2*sqrt((625*a^7 - 3450*a^6*b + 7161*a^5*b^2 - 6624*a^4*b^3 + 2304*a^3*b^4)/((a^6*b^9 - 6*a^5*b^10 + 15*a^4*b^11 - 20*a^3*b^12 + 15*a^2*b^13 - 6*a*b^14 + b^15)*d^4)) + 15*a^3 - 47*a^2*b + 36*a*b^2)/((a^3*b^4 - 3*a^2*b^5 + 3*a*b^6 - b^7)*d^2))) + ((a*b^3 - b^4)*d*cosh(d*x + c)^9 + 9*(a*b^3 - b^4)*d*cosh(d*x + c)*sinh(d*x + c)^8 + (a*b^3 - b^4)*d*sinh(d*x + c)^9 - 4*(a*b^3 - b^4)*d*cosh(d*x + c)^7 + 4*(9*(a*b^3 - b^4)*d*cosh(d*x + c)^2 - (a*b^3 - b^4)*d)*sinh(d*x + c)^7 - 2*(8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d*cosh(d*x + c)^5 + 28*(3*(a*b^3 - b^4)*d*cosh(d*x + c)^3 - (a*b^3 - b^4)*d*cosh(d*x + c))*sinh(d*x + c)^6 + 2*(63*(a*b^3 - b^4)*d*cosh(d*x + c)^4 - 42*(a*b^3 - b^4)*d*cosh(d*x + c)^2 - (8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d)*sinh(d*x + c)^5 - 4*(a*b^3 - b^4)*d*cosh(d*x + c)^3 + 2*(63*(a*b^3 - b^4)*d*cosh(d*x + c)^5 - 70*(a*b^3 - b^4)*d*cosh(d*x + c)^3 - 5*(8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d*cosh(d*x + c))*sinh(d*x + c)^4 + 4*(21*(a*b^3 - b^4)*d*cosh(d*x + c)^6 - 35*(a*b^3 - b^4)*d*cosh(d*x + c)^4 - 5*(8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d*cosh(d*x + c)^2 - (a*b^3 - b^4)*d)*sinh(d*x + c)^3 + (a*b^3 - b^4)*d*cosh(d*x + c) + 4*(9*(a*b^3 - b^4)*d*cosh(d*x + c)^7 - 21*(a*b^3 - b^4)*d*cosh(d*x + c)^5 - 5*(8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d*cosh(d*x + c)^3 - 3*(a*b^3 - b^4)*d*cosh(d*x + c))*sinh(d*x + c)^2 + (9*(a*b^3 - b^4)*d*cosh(d*x + c)^8 - 28*(a*b^3 - b^4)*d*cosh(d*x + c)^6 - 10*(8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d*cosh(d*x + c)^4 - 12*(a*b^3 - b^4)*d*cosh(d*x + c)^2 + (a*b^3 - b^4)*d)*sinh(d*x + c))*sqrt(((a^3*b^4 - 3*a^2*b^5 + 3*a*b^6 - b^7)*d^2*sqrt((625*a^7 - 3450*a^6*b + 7161*a^5*b^2 - 6624*a^4*b^3 + 2304*a^3*b^4)/((a^6*b^9 - 6*a^5*b^10 + 15*a^4*b^11 - 20*a^3*b^12 + 15*a^2*b^13 - 6*a*b^14 + b^15)*d^4)) - 15*a^3 + 47*a^2*b - 36*a*b^2)/((a^3*b^4 - 3*a^2*b^5 + 3*a*b^6 - b^7)*d^2))*log(-625*a^5 + 2625*a^4*b - 3684*a^3*b^2 + 1728*a^2*b^3 - (625*a^5 - 2625*a^4*b + 3684*a^3*b^2 - 1728*a^2*b^3)*cosh(d*x + c)^2 - 2*(625*a^5 - 2625*a^4*b + 3684*a^3*b^2 - 1728*a^2*b^3)*cosh(d*x + c)*sinh(d*x + c) - (625*a^5 - 2625*a^4*b + 3684*a^3*b^2 - 1728*a^2*b^3)*sinh(d*x + c)^2 + 2*((125*a^5*b^2 - 520*a^4*b^3 + 723*a^3*b^4 - 336*a^2*b^5)*d*cosh(d*x + c) + (125*a^5*b^2 - 520*a^4*b^3 + 723*a^3*b^4 - 336*a^2*b^5)*d*sinh(d*x + c) + 2*((2*a^4*b^7 - 9*a^3*b^8 + 15*a^2*b^9 - 11*a*b^10 + 3*b^11)*d^3*cosh(d*x + c) + (2*a^4*b^7 - 9*a^3*b^8 + 15*a^2*b^9 - 11*a*b^10 + 3*b^11)*d^3*sinh(d*x + c))*sqrt((625*a^7 - 3450*a^6*b + 7161*a^5*b^2 - 6624*a^4*b^3 + 2304*a^3*b^4)/((a^6*b^9 - 6*a^5*b^10 + 15*a^4*b^11 - 20*a^3*b^12 + 15*a^2*b^13 - 6*a*b^14 + b^15)*d^4)))*sqrt(((a^3*b^4 - 3*a^2*b^5 + 3*a*b^6 - b^7)*d^2*sqrt((625*a^7 - 3450*a^6*b + 7161*a^5*b^2 - 6624*a^4*b^3 + 2304*a^3*b^4)/((a^6*b^9 - 6*a^5*b^10 + 15*a^4*b^11 - 20*a^3*b^12 + 15*a^2*b^13 - 6*a*b^14 + b^15)*d^4)) - 15*a^3 + 47*a^2*b - 36*a*b^2)/((a^3*b^4 - 3*a^2*b^5 + 3*a*b^6 - b^7)*d^2))) - ((a*b^3 - b^4)*d*cosh(d*x + c)^9 + 9*(a*b^3 - b^4)*d*cosh(d*x + c)*sinh(d*x + c)^8 + (a*b^3 - b^4)*d*sinh(d*x + c)^9 - 4*(a*b^3 - b^4)*d*cosh(d*x + c)^7 + 4*(9*(a*b^3 - b^4)*d*cosh(d*x + c)^2 - (a*b^3 - b^4)*d)*sinh(d*x + c)^7 - 2*(8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d*cosh(d*x + c)^5 + 28*(3*(a*b^3 - b^4)*d*cosh(d*x + c)^3 - (a*b^3 - b^4)*d*cosh(d*x + c))*sinh(d*x + c)^6 + 2*(63*(a*b^3 - b^4)*d*cosh(d*x + c)^4 - 42*(a*b^3 - b^4)*d*cosh(d*x + c)^2 - (8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d)*sinh(d*x + c)^5 - 4*(a*b^3 - b^4)*d*cosh(d*x + c)^3 + 2*(63*(a*b^3 - b^4)*d*cosh(d*x + c)^5 - 70*(a*b^3 - b^4)*d*cosh(d*x + c)^3 - 5*(8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d*cosh(d*x + c))*sinh(d*x + c)^4 + 4*(21*(a*b^3 - b^4)*d*cosh(d*x + c)^6 - 35*(a*b^3 - b^4)*d*cosh(d*x + c)^4 - 5*(8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d*cosh(d*x + c)^2 - (a*b^3 - b^4)*d)*sinh(d*x + c)^3 + (a*b^3 - b^4)*d*cosh(d*x + c) + 4*(9*(a*b^3 - b^4)*d*cosh(d*x + c)^7 - 21*(a*b^3 - b^4)*d*cosh(d*x + c)^5 - 5*(8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d*cosh(d*x + c)^3 - 3*(a*b^3 - b^4)*d*cosh(d*x + c))*sinh(d*x + c)^2 + (9*(a*b^3 - b^4)*d*cosh(d*x + c)^8 - 28*(a*b^3 - b^4)*d*cosh(d*x + c)^6 - 10*(8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d*cosh(d*x + c)^4 - 12*(a*b^3 - b^4)*d*cosh(d*x + c)^2 + (a*b^3 - b^4)*d)*sinh(d*x + c))*sqrt(((a^3*b^4 - 3*a^2*b^5 + 3*a*b^6 - b^7)*d^2*sqrt((625*a^7 - 3450*a^6*b + 7161*a^5*b^2 - 6624*a^4*b^3 + 2304*a^3*b^4)/((a^6*b^9 - 6*a^5*b^10 + 15*a^4*b^11 - 20*a^3*b^12 + 15*a^2*b^13 - 6*a*b^14 + b^15)*d^4)) - 15*a^3 + 47*a^2*b - 36*a*b^2)/((a^3*b^4 - 3*a^2*b^5 + 3*a*b^6 - b^7)*d^2))*log(-625*a^5 + 2625*a^4*b - 3684*a^3*b^2 + 1728*a^2*b^3 - (625*a^5 - 2625*a^4*b + 3684*a^3*b^2 - 1728*a^2*b^3)*cosh(d*x + c)^2 - 2*(625*a^5 - 2625*a^4*b + 3684*a^3*b^2 - 1728*a^2*b^3)*cosh(d*x + c)*sinh(d*x + c) - (625*a^5 - 2625*a^4*b + 3684*a^3*b^2 - 1728*a^2*b^3)*sinh(d*x + c)^2 - 2*((125*a^5*b^2 - 520*a^4*b^3 + 723*a^3*b^4 - 336*a^2*b^5)*d*cosh(d*x + c) + (125*a^5*b^2 - 520*a^4*b^3 + 723*a^3*b^4 - 336*a^2*b^5)*d*sinh(d*x + c) + 2*((2*a^4*b^7 - 9*a^3*b^8 + 15*a^2*b^9 - 11*a*b^10 + 3*b^11)*d^3*cosh(d*x + c) + (2*a^4*b^7 - 9*a^3*b^8 + 15*a^2*b^9 - 11*a*b^10 + 3*b^11)*d^3*sinh(d*x + c))*sqrt((625*a^7 - 3450*a^6*b + 7161*a^5*b^2 - 6624*a^4*b^3 + 2304*a^3*b^4)/((a^6*b^9 - 6*a^5*b^10 + 15*a^4*b^11 - 20*a^3*b^12 + 15*a^2*b^13 - 6*a*b^14 + b^15)*d^4)))*sqrt(((a^3*b^4 - 3*a^2*b^5 + 3*a*b^6 - b^7)*d^2*sqrt((625*a^7 - 3450*a^6*b + 7161*a^5*b^2 - 6624*a^4*b^3 + 2304*a^3*b^4)/((a^6*b^9 - 6*a^5*b^10 + 15*a^4*b^11 - 20*a^3*b^12 + 15*a^2*b^13 - 6*a*b^14 + b^15)*d^4)) - 15*a^3 + 47*a^2*b - 36*a*b^2)/((a^3*b^4 - 3*a^2*b^5 + 3*a*b^6 - b^7)*d^2))) + 8*a*b - 8*b^2 + 16*(5*(a*b - b^2)*cosh(d*x + c)^9 - 4*(2*a*b - 3*b^2)*cosh(d*x + c)^7 - 3*(20*a^2 - 17*a*b + 2*b^2)*cosh(d*x + c)^5 - 2*(20*a^2 - 17*a*b + 2*b^2)*cosh(d*x + c)^3 - (2*a*b - 3*b^2)*cosh(d*x + c))*sinh(d*x + c))/((a*b^3 - b^4)*d*cosh(d*x + c)^9 + 9*(a*b^3 - b^4)*d*cosh(d*x + c)*sinh(d*x + c)^8 + (a*b^3 - b^4)*d*sinh(d*x + c)^9 - 4*(a*b^3 - b^4)*d*cosh(d*x + c)^7 + 4*(9*(a*b^3 - b^4)*d*cosh(d*x + c)^2 - (a*b^3 - b^4)*d)*sinh(d*x + c)^7 - 2*(8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d*cosh(d*x + c)^5 + 28*(3*(a*b^3 - b^4)*d*cosh(d*x + c)^3 - (a*b^3 - b^4)*d*cosh(d*x + c))*sinh(d*x + c)^6 + 2*(63*(a*b^3 - b^4)*d*cosh(d*x + c)^4 - 42*(a*b^3 - b^4)*d*cosh(d*x + c)^2 - (8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d)*sinh(d*x + c)^5 - 4*(a*b^3 - b^4)*d*cosh(d*x + c)^3 + 2*(63*(a*b^3 - b^4)*d*cosh(d*x + c)^5 - 70*(a*b^3 - b^4)*d*cosh(d*x + c)^3 - 5*(8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d*cosh(d*x + c))*sinh(d*x + c)^4 + 4*(21*(a*b^3 - b^4)*d*cosh(d*x + c)^6 - 35*(a*b^3 - b^4)*d*cosh(d*x + c)^4 - 5*(8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d*cosh(d*x + c)^2 - (a*b^3 - b^4)*d)*sinh(d*x + c)^3 + (a*b^3 - b^4)*d*cosh(d*x + c) + 4*(9*(a*b^3 - b^4)*d*cosh(d*x + c)^7 - 21*(a*b^3 - b^4)*d*cosh(d*x + c)^5 - 5*(8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d*cosh(d*x + c)^3 - 3*(a*b^3 - b^4)*d*cosh(d*x + c))*sinh(d*x + c)^2 + (9*(a*b^3 - b^4)*d*cosh(d*x + c)^8 - 28*(a*b^3 - b^4)*d*cosh(d*x + c)^6 - 10*(8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d*cosh(d*x + c)^4 - 12*(a*b^3 - b^4)*d*cosh(d*x + c)^2 + (a*b^3 - b^4)*d)*sinh(d*x + c))","B",0
242,1,6266,0,0.913088," ","integrate(sinh(d*x+c)^7/(a-b*sinh(d*x+c)^4)^2,x, algorithm=""fricas"")","-\frac{8 \, a \cosh\left(d x + c\right)^{7} + 56 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + 8 \, a \sinh\left(d x + c\right)^{7} - 40 \, a \cosh\left(d x + c\right)^{5} + 8 \, {\left(21 \, a \cosh\left(d x + c\right)^{2} - 5 \, a\right)} \sinh\left(d x + c\right)^{5} + 40 \, {\left(7 \, a \cosh\left(d x + c\right)^{3} - 5 \, a \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} - 40 \, a \cosh\left(d x + c\right)^{3} + 40 \, {\left(7 \, a \cosh\left(d x + c\right)^{4} - 10 \, a \cosh\left(d x + c\right)^{2} - a\right)} \sinh\left(d x + c\right)^{3} + 8 \, {\left(21 \, a \cosh\left(d x + c\right)^{5} - 50 \, a \cosh\left(d x + c\right)^{3} - 15 \, a \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - {\left({\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a b^{2} - b^{3}\right)} d \sinh\left(d x + c\right)^{8} - 4 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a b^{2} - b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{6} - 2 \, {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{3} - 3 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{4} - 30 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{2} - {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{4} - 4 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{5} - 10 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{3} - {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{6} - 15 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{4} - 3 \, {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a b^{2} - b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a b^{2} - b^{3}\right)} d + 8 \, {\left({\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{7} - 3 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{5} - {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{{\left(a^{3} b^{3} - 3 \, a^{2} b^{4} + 3 \, a b^{5} - b^{6}\right)} d^{2} \sqrt{\frac{81 \, a^{5} - 522 \, a^{4} b + 1273 \, a^{3} b^{2} - 1392 \, a^{2} b^{3} + 576 \, a b^{4}}{{\left(a^{6} b^{7} - 6 \, a^{5} b^{8} + 15 \, a^{4} b^{9} - 20 \, a^{3} b^{10} + 15 \, a^{2} b^{11} - 6 \, a b^{12} + b^{13}\right)} d^{4}}} + 3 \, a^{2} - 15 \, a b + 16 \, b^{2}}{{\left(a^{3} b^{3} - 3 \, a^{2} b^{4} + 3 \, a b^{5} - b^{6}\right)} d^{2}}} \log\left(-81 \, a^{3} + 405 \, a^{2} b - 680 \, a b^{2} + 384 \, b^{3} - {\left(81 \, a^{3} - 405 \, a^{2} b + 680 \, a b^{2} - 384 \, b^{3}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(81 \, a^{3} - 405 \, a^{2} b + 680 \, a b^{2} - 384 \, b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(81 \, a^{3} - 405 \, a^{2} b + 680 \, a b^{2} - 384 \, b^{3}\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(2 \, {\left(9 \, a^{3} b^{2} - 47 \, a^{2} b^{3} + 82 \, a b^{4} - 48 \, b^{5}\right)} d \cosh\left(d x + c\right) + 2 \, {\left(9 \, a^{3} b^{2} - 47 \, a^{2} b^{3} + 82 \, a b^{4} - 48 \, b^{5}\right)} d \sinh\left(d x + c\right) - {\left({\left(3 \, a^{4} b^{5} - 14 \, a^{3} b^{6} + 24 \, a^{2} b^{7} - 18 \, a b^{8} + 5 \, b^{9}\right)} d^{3} \cosh\left(d x + c\right) + {\left(3 \, a^{4} b^{5} - 14 \, a^{3} b^{6} + 24 \, a^{2} b^{7} - 18 \, a b^{8} + 5 \, b^{9}\right)} d^{3} \sinh\left(d x + c\right)\right)} \sqrt{\frac{81 \, a^{5} - 522 \, a^{4} b + 1273 \, a^{3} b^{2} - 1392 \, a^{2} b^{3} + 576 \, a b^{4}}{{\left(a^{6} b^{7} - 6 \, a^{5} b^{8} + 15 \, a^{4} b^{9} - 20 \, a^{3} b^{10} + 15 \, a^{2} b^{11} - 6 \, a b^{12} + b^{13}\right)} d^{4}}}\right)} \sqrt{-\frac{{\left(a^{3} b^{3} - 3 \, a^{2} b^{4} + 3 \, a b^{5} - b^{6}\right)} d^{2} \sqrt{\frac{81 \, a^{5} - 522 \, a^{4} b + 1273 \, a^{3} b^{2} - 1392 \, a^{2} b^{3} + 576 \, a b^{4}}{{\left(a^{6} b^{7} - 6 \, a^{5} b^{8} + 15 \, a^{4} b^{9} - 20 \, a^{3} b^{10} + 15 \, a^{2} b^{11} - 6 \, a b^{12} + b^{13}\right)} d^{4}}} + 3 \, a^{2} - 15 \, a b + 16 \, b^{2}}{{\left(a^{3} b^{3} - 3 \, a^{2} b^{4} + 3 \, a b^{5} - b^{6}\right)} d^{2}}}\right) + {\left({\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a b^{2} - b^{3}\right)} d \sinh\left(d x + c\right)^{8} - 4 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a b^{2} - b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{6} - 2 \, {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{3} - 3 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{4} - 30 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{2} - {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{4} - 4 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{5} - 10 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{3} - {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{6} - 15 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{4} - 3 \, {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a b^{2} - b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a b^{2} - b^{3}\right)} d + 8 \, {\left({\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{7} - 3 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{5} - {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{{\left(a^{3} b^{3} - 3 \, a^{2} b^{4} + 3 \, a b^{5} - b^{6}\right)} d^{2} \sqrt{\frac{81 \, a^{5} - 522 \, a^{4} b + 1273 \, a^{3} b^{2} - 1392 \, a^{2} b^{3} + 576 \, a b^{4}}{{\left(a^{6} b^{7} - 6 \, a^{5} b^{8} + 15 \, a^{4} b^{9} - 20 \, a^{3} b^{10} + 15 \, a^{2} b^{11} - 6 \, a b^{12} + b^{13}\right)} d^{4}}} + 3 \, a^{2} - 15 \, a b + 16 \, b^{2}}{{\left(a^{3} b^{3} - 3 \, a^{2} b^{4} + 3 \, a b^{5} - b^{6}\right)} d^{2}}} \log\left(-81 \, a^{3} + 405 \, a^{2} b - 680 \, a b^{2} + 384 \, b^{3} - {\left(81 \, a^{3} - 405 \, a^{2} b + 680 \, a b^{2} - 384 \, b^{3}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(81 \, a^{3} - 405 \, a^{2} b + 680 \, a b^{2} - 384 \, b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(81 \, a^{3} - 405 \, a^{2} b + 680 \, a b^{2} - 384 \, b^{3}\right)} \sinh\left(d x + c\right)^{2} - 2 \, {\left(2 \, {\left(9 \, a^{3} b^{2} - 47 \, a^{2} b^{3} + 82 \, a b^{4} - 48 \, b^{5}\right)} d \cosh\left(d x + c\right) + 2 \, {\left(9 \, a^{3} b^{2} - 47 \, a^{2} b^{3} + 82 \, a b^{4} - 48 \, b^{5}\right)} d \sinh\left(d x + c\right) - {\left({\left(3 \, a^{4} b^{5} - 14 \, a^{3} b^{6} + 24 \, a^{2} b^{7} - 18 \, a b^{8} + 5 \, b^{9}\right)} d^{3} \cosh\left(d x + c\right) + {\left(3 \, a^{4} b^{5} - 14 \, a^{3} b^{6} + 24 \, a^{2} b^{7} - 18 \, a b^{8} + 5 \, b^{9}\right)} d^{3} \sinh\left(d x + c\right)\right)} \sqrt{\frac{81 \, a^{5} - 522 \, a^{4} b + 1273 \, a^{3} b^{2} - 1392 \, a^{2} b^{3} + 576 \, a b^{4}}{{\left(a^{6} b^{7} - 6 \, a^{5} b^{8} + 15 \, a^{4} b^{9} - 20 \, a^{3} b^{10} + 15 \, a^{2} b^{11} - 6 \, a b^{12} + b^{13}\right)} d^{4}}}\right)} \sqrt{-\frac{{\left(a^{3} b^{3} - 3 \, a^{2} b^{4} + 3 \, a b^{5} - b^{6}\right)} d^{2} \sqrt{\frac{81 \, a^{5} - 522 \, a^{4} b + 1273 \, a^{3} b^{2} - 1392 \, a^{2} b^{3} + 576 \, a b^{4}}{{\left(a^{6} b^{7} - 6 \, a^{5} b^{8} + 15 \, a^{4} b^{9} - 20 \, a^{3} b^{10} + 15 \, a^{2} b^{11} - 6 \, a b^{12} + b^{13}\right)} d^{4}}} + 3 \, a^{2} - 15 \, a b + 16 \, b^{2}}{{\left(a^{3} b^{3} - 3 \, a^{2} b^{4} + 3 \, a b^{5} - b^{6}\right)} d^{2}}}\right) - {\left({\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a b^{2} - b^{3}\right)} d \sinh\left(d x + c\right)^{8} - 4 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a b^{2} - b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{6} - 2 \, {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{3} - 3 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{4} - 30 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{2} - {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{4} - 4 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{5} - 10 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{3} - {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{6} - 15 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{4} - 3 \, {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a b^{2} - b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a b^{2} - b^{3}\right)} d + 8 \, {\left({\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{7} - 3 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{5} - {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{{\left(a^{3} b^{3} - 3 \, a^{2} b^{4} + 3 \, a b^{5} - b^{6}\right)} d^{2} \sqrt{\frac{81 \, a^{5} - 522 \, a^{4} b + 1273 \, a^{3} b^{2} - 1392 \, a^{2} b^{3} + 576 \, a b^{4}}{{\left(a^{6} b^{7} - 6 \, a^{5} b^{8} + 15 \, a^{4} b^{9} - 20 \, a^{3} b^{10} + 15 \, a^{2} b^{11} - 6 \, a b^{12} + b^{13}\right)} d^{4}}} - 3 \, a^{2} + 15 \, a b - 16 \, b^{2}}{{\left(a^{3} b^{3} - 3 \, a^{2} b^{4} + 3 \, a b^{5} - b^{6}\right)} d^{2}}} \log\left(-81 \, a^{3} + 405 \, a^{2} b - 680 \, a b^{2} + 384 \, b^{3} - {\left(81 \, a^{3} - 405 \, a^{2} b + 680 \, a b^{2} - 384 \, b^{3}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(81 \, a^{3} - 405 \, a^{2} b + 680 \, a b^{2} - 384 \, b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(81 \, a^{3} - 405 \, a^{2} b + 680 \, a b^{2} - 384 \, b^{3}\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(2 \, {\left(9 \, a^{3} b^{2} - 47 \, a^{2} b^{3} + 82 \, a b^{4} - 48 \, b^{5}\right)} d \cosh\left(d x + c\right) + 2 \, {\left(9 \, a^{3} b^{2} - 47 \, a^{2} b^{3} + 82 \, a b^{4} - 48 \, b^{5}\right)} d \sinh\left(d x + c\right) + {\left({\left(3 \, a^{4} b^{5} - 14 \, a^{3} b^{6} + 24 \, a^{2} b^{7} - 18 \, a b^{8} + 5 \, b^{9}\right)} d^{3} \cosh\left(d x + c\right) + {\left(3 \, a^{4} b^{5} - 14 \, a^{3} b^{6} + 24 \, a^{2} b^{7} - 18 \, a b^{8} + 5 \, b^{9}\right)} d^{3} \sinh\left(d x + c\right)\right)} \sqrt{\frac{81 \, a^{5} - 522 \, a^{4} b + 1273 \, a^{3} b^{2} - 1392 \, a^{2} b^{3} + 576 \, a b^{4}}{{\left(a^{6} b^{7} - 6 \, a^{5} b^{8} + 15 \, a^{4} b^{9} - 20 \, a^{3} b^{10} + 15 \, a^{2} b^{11} - 6 \, a b^{12} + b^{13}\right)} d^{4}}}\right)} \sqrt{\frac{{\left(a^{3} b^{3} - 3 \, a^{2} b^{4} + 3 \, a b^{5} - b^{6}\right)} d^{2} \sqrt{\frac{81 \, a^{5} - 522 \, a^{4} b + 1273 \, a^{3} b^{2} - 1392 \, a^{2} b^{3} + 576 \, a b^{4}}{{\left(a^{6} b^{7} - 6 \, a^{5} b^{8} + 15 \, a^{4} b^{9} - 20 \, a^{3} b^{10} + 15 \, a^{2} b^{11} - 6 \, a b^{12} + b^{13}\right)} d^{4}}} - 3 \, a^{2} + 15 \, a b - 16 \, b^{2}}{{\left(a^{3} b^{3} - 3 \, a^{2} b^{4} + 3 \, a b^{5} - b^{6}\right)} d^{2}}}\right) + {\left({\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a b^{2} - b^{3}\right)} d \sinh\left(d x + c\right)^{8} - 4 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a b^{2} - b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{6} - 2 \, {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{3} - 3 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{4} - 30 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{2} - {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{4} - 4 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{5} - 10 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{3} - {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{6} - 15 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{4} - 3 \, {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a b^{2} - b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a b^{2} - b^{3}\right)} d + 8 \, {\left({\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{7} - 3 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{5} - {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{{\left(a^{3} b^{3} - 3 \, a^{2} b^{4} + 3 \, a b^{5} - b^{6}\right)} d^{2} \sqrt{\frac{81 \, a^{5} - 522 \, a^{4} b + 1273 \, a^{3} b^{2} - 1392 \, a^{2} b^{3} + 576 \, a b^{4}}{{\left(a^{6} b^{7} - 6 \, a^{5} b^{8} + 15 \, a^{4} b^{9} - 20 \, a^{3} b^{10} + 15 \, a^{2} b^{11} - 6 \, a b^{12} + b^{13}\right)} d^{4}}} - 3 \, a^{2} + 15 \, a b - 16 \, b^{2}}{{\left(a^{3} b^{3} - 3 \, a^{2} b^{4} + 3 \, a b^{5} - b^{6}\right)} d^{2}}} \log\left(-81 \, a^{3} + 405 \, a^{2} b - 680 \, a b^{2} + 384 \, b^{3} - {\left(81 \, a^{3} - 405 \, a^{2} b + 680 \, a b^{2} - 384 \, b^{3}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(81 \, a^{3} - 405 \, a^{2} b + 680 \, a b^{2} - 384 \, b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(81 \, a^{3} - 405 \, a^{2} b + 680 \, a b^{2} - 384 \, b^{3}\right)} \sinh\left(d x + c\right)^{2} - 2 \, {\left(2 \, {\left(9 \, a^{3} b^{2} - 47 \, a^{2} b^{3} + 82 \, a b^{4} - 48 \, b^{5}\right)} d \cosh\left(d x + c\right) + 2 \, {\left(9 \, a^{3} b^{2} - 47 \, a^{2} b^{3} + 82 \, a b^{4} - 48 \, b^{5}\right)} d \sinh\left(d x + c\right) + {\left({\left(3 \, a^{4} b^{5} - 14 \, a^{3} b^{6} + 24 \, a^{2} b^{7} - 18 \, a b^{8} + 5 \, b^{9}\right)} d^{3} \cosh\left(d x + c\right) + {\left(3 \, a^{4} b^{5} - 14 \, a^{3} b^{6} + 24 \, a^{2} b^{7} - 18 \, a b^{8} + 5 \, b^{9}\right)} d^{3} \sinh\left(d x + c\right)\right)} \sqrt{\frac{81 \, a^{5} - 522 \, a^{4} b + 1273 \, a^{3} b^{2} - 1392 \, a^{2} b^{3} + 576 \, a b^{4}}{{\left(a^{6} b^{7} - 6 \, a^{5} b^{8} + 15 \, a^{4} b^{9} - 20 \, a^{3} b^{10} + 15 \, a^{2} b^{11} - 6 \, a b^{12} + b^{13}\right)} d^{4}}}\right)} \sqrt{\frac{{\left(a^{3} b^{3} - 3 \, a^{2} b^{4} + 3 \, a b^{5} - b^{6}\right)} d^{2} \sqrt{\frac{81 \, a^{5} - 522 \, a^{4} b + 1273 \, a^{3} b^{2} - 1392 \, a^{2} b^{3} + 576 \, a b^{4}}{{\left(a^{6} b^{7} - 6 \, a^{5} b^{8} + 15 \, a^{4} b^{9} - 20 \, a^{3} b^{10} + 15 \, a^{2} b^{11} - 6 \, a b^{12} + b^{13}\right)} d^{4}}} - 3 \, a^{2} + 15 \, a b - 16 \, b^{2}}{{\left(a^{3} b^{3} - 3 \, a^{2} b^{4} + 3 \, a b^{5} - b^{6}\right)} d^{2}}}\right) + 8 \, a \cosh\left(d x + c\right) + 8 \, {\left(7 \, a \cosh\left(d x + c\right)^{6} - 25 \, a \cosh\left(d x + c\right)^{4} - 15 \, a \cosh\left(d x + c\right)^{2} + a\right)} \sinh\left(d x + c\right)}{16 \, {\left({\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a b^{2} - b^{3}\right)} d \sinh\left(d x + c\right)^{8} - 4 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a b^{2} - b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{6} - 2 \, {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{3} - 3 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{4} - 30 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{2} - {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{4} - 4 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{5} - 10 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{3} - {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{6} - 15 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{4} - 3 \, {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a b^{2} - b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a b^{2} - b^{3}\right)} d + 8 \, {\left({\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{7} - 3 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{5} - {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"-1/16*(8*a*cosh(d*x + c)^7 + 56*a*cosh(d*x + c)*sinh(d*x + c)^6 + 8*a*sinh(d*x + c)^7 - 40*a*cosh(d*x + c)^5 + 8*(21*a*cosh(d*x + c)^2 - 5*a)*sinh(d*x + c)^5 + 40*(7*a*cosh(d*x + c)^3 - 5*a*cosh(d*x + c))*sinh(d*x + c)^4 - 40*a*cosh(d*x + c)^3 + 40*(7*a*cosh(d*x + c)^4 - 10*a*cosh(d*x + c)^2 - a)*sinh(d*x + c)^3 + 8*(21*a*cosh(d*x + c)^5 - 50*a*cosh(d*x + c)^3 - 15*a*cosh(d*x + c))*sinh(d*x + c)^2 - ((a*b^2 - b^3)*d*cosh(d*x + c)^8 + 8*(a*b^2 - b^3)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a*b^2 - b^3)*d*sinh(d*x + c)^8 - 4*(a*b^2 - b^3)*d*cosh(d*x + c)^6 + 4*(7*(a*b^2 - b^3)*d*cosh(d*x + c)^2 - (a*b^2 - b^3)*d)*sinh(d*x + c)^6 - 2*(8*a^2*b - 11*a*b^2 + 3*b^3)*d*cosh(d*x + c)^4 + 8*(7*(a*b^2 - b^3)*d*cosh(d*x + c)^3 - 3*(a*b^2 - b^3)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a*b^2 - b^3)*d*cosh(d*x + c)^4 - 30*(a*b^2 - b^3)*d*cosh(d*x + c)^2 - (8*a^2*b - 11*a*b^2 + 3*b^3)*d)*sinh(d*x + c)^4 - 4*(a*b^2 - b^3)*d*cosh(d*x + c)^2 + 8*(7*(a*b^2 - b^3)*d*cosh(d*x + c)^5 - 10*(a*b^2 - b^3)*d*cosh(d*x + c)^3 - (8*a^2*b - 11*a*b^2 + 3*b^3)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a*b^2 - b^3)*d*cosh(d*x + c)^6 - 15*(a*b^2 - b^3)*d*cosh(d*x + c)^4 - 3*(8*a^2*b - 11*a*b^2 + 3*b^3)*d*cosh(d*x + c)^2 - (a*b^2 - b^3)*d)*sinh(d*x + c)^2 + (a*b^2 - b^3)*d + 8*((a*b^2 - b^3)*d*cosh(d*x + c)^7 - 3*(a*b^2 - b^3)*d*cosh(d*x + c)^5 - (8*a^2*b - 11*a*b^2 + 3*b^3)*d*cosh(d*x + c)^3 - (a*b^2 - b^3)*d*cosh(d*x + c))*sinh(d*x + c))*sqrt(-((a^3*b^3 - 3*a^2*b^4 + 3*a*b^5 - b^6)*d^2*sqrt((81*a^5 - 522*a^4*b + 1273*a^3*b^2 - 1392*a^2*b^3 + 576*a*b^4)/((a^6*b^7 - 6*a^5*b^8 + 15*a^4*b^9 - 20*a^3*b^10 + 15*a^2*b^11 - 6*a*b^12 + b^13)*d^4)) + 3*a^2 - 15*a*b + 16*b^2)/((a^3*b^3 - 3*a^2*b^4 + 3*a*b^5 - b^6)*d^2))*log(-81*a^3 + 405*a^2*b - 680*a*b^2 + 384*b^3 - (81*a^3 - 405*a^2*b + 680*a*b^2 - 384*b^3)*cosh(d*x + c)^2 - 2*(81*a^3 - 405*a^2*b + 680*a*b^2 - 384*b^3)*cosh(d*x + c)*sinh(d*x + c) - (81*a^3 - 405*a^2*b + 680*a*b^2 - 384*b^3)*sinh(d*x + c)^2 + 2*(2*(9*a^3*b^2 - 47*a^2*b^3 + 82*a*b^4 - 48*b^5)*d*cosh(d*x + c) + 2*(9*a^3*b^2 - 47*a^2*b^3 + 82*a*b^4 - 48*b^5)*d*sinh(d*x + c) - ((3*a^4*b^5 - 14*a^3*b^6 + 24*a^2*b^7 - 18*a*b^8 + 5*b^9)*d^3*cosh(d*x + c) + (3*a^4*b^5 - 14*a^3*b^6 + 24*a^2*b^7 - 18*a*b^8 + 5*b^9)*d^3*sinh(d*x + c))*sqrt((81*a^5 - 522*a^4*b + 1273*a^3*b^2 - 1392*a^2*b^3 + 576*a*b^4)/((a^6*b^7 - 6*a^5*b^8 + 15*a^4*b^9 - 20*a^3*b^10 + 15*a^2*b^11 - 6*a*b^12 + b^13)*d^4)))*sqrt(-((a^3*b^3 - 3*a^2*b^4 + 3*a*b^5 - b^6)*d^2*sqrt((81*a^5 - 522*a^4*b + 1273*a^3*b^2 - 1392*a^2*b^3 + 576*a*b^4)/((a^6*b^7 - 6*a^5*b^8 + 15*a^4*b^9 - 20*a^3*b^10 + 15*a^2*b^11 - 6*a*b^12 + b^13)*d^4)) + 3*a^2 - 15*a*b + 16*b^2)/((a^3*b^3 - 3*a^2*b^4 + 3*a*b^5 - b^6)*d^2))) + ((a*b^2 - b^3)*d*cosh(d*x + c)^8 + 8*(a*b^2 - b^3)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a*b^2 - b^3)*d*sinh(d*x + c)^8 - 4*(a*b^2 - b^3)*d*cosh(d*x + c)^6 + 4*(7*(a*b^2 - b^3)*d*cosh(d*x + c)^2 - (a*b^2 - b^3)*d)*sinh(d*x + c)^6 - 2*(8*a^2*b - 11*a*b^2 + 3*b^3)*d*cosh(d*x + c)^4 + 8*(7*(a*b^2 - b^3)*d*cosh(d*x + c)^3 - 3*(a*b^2 - b^3)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a*b^2 - b^3)*d*cosh(d*x + c)^4 - 30*(a*b^2 - b^3)*d*cosh(d*x + c)^2 - (8*a^2*b - 11*a*b^2 + 3*b^3)*d)*sinh(d*x + c)^4 - 4*(a*b^2 - b^3)*d*cosh(d*x + c)^2 + 8*(7*(a*b^2 - b^3)*d*cosh(d*x + c)^5 - 10*(a*b^2 - b^3)*d*cosh(d*x + c)^3 - (8*a^2*b - 11*a*b^2 + 3*b^3)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a*b^2 - b^3)*d*cosh(d*x + c)^6 - 15*(a*b^2 - b^3)*d*cosh(d*x + c)^4 - 3*(8*a^2*b - 11*a*b^2 + 3*b^3)*d*cosh(d*x + c)^2 - (a*b^2 - b^3)*d)*sinh(d*x + c)^2 + (a*b^2 - b^3)*d + 8*((a*b^2 - b^3)*d*cosh(d*x + c)^7 - 3*(a*b^2 - b^3)*d*cosh(d*x + c)^5 - (8*a^2*b - 11*a*b^2 + 3*b^3)*d*cosh(d*x + c)^3 - (a*b^2 - b^3)*d*cosh(d*x + c))*sinh(d*x + c))*sqrt(-((a^3*b^3 - 3*a^2*b^4 + 3*a*b^5 - b^6)*d^2*sqrt((81*a^5 - 522*a^4*b + 1273*a^3*b^2 - 1392*a^2*b^3 + 576*a*b^4)/((a^6*b^7 - 6*a^5*b^8 + 15*a^4*b^9 - 20*a^3*b^10 + 15*a^2*b^11 - 6*a*b^12 + b^13)*d^4)) + 3*a^2 - 15*a*b + 16*b^2)/((a^3*b^3 - 3*a^2*b^4 + 3*a*b^5 - b^6)*d^2))*log(-81*a^3 + 405*a^2*b - 680*a*b^2 + 384*b^3 - (81*a^3 - 405*a^2*b + 680*a*b^2 - 384*b^3)*cosh(d*x + c)^2 - 2*(81*a^3 - 405*a^2*b + 680*a*b^2 - 384*b^3)*cosh(d*x + c)*sinh(d*x + c) - (81*a^3 - 405*a^2*b + 680*a*b^2 - 384*b^3)*sinh(d*x + c)^2 - 2*(2*(9*a^3*b^2 - 47*a^2*b^3 + 82*a*b^4 - 48*b^5)*d*cosh(d*x + c) + 2*(9*a^3*b^2 - 47*a^2*b^3 + 82*a*b^4 - 48*b^5)*d*sinh(d*x + c) - ((3*a^4*b^5 - 14*a^3*b^6 + 24*a^2*b^7 - 18*a*b^8 + 5*b^9)*d^3*cosh(d*x + c) + (3*a^4*b^5 - 14*a^3*b^6 + 24*a^2*b^7 - 18*a*b^8 + 5*b^9)*d^3*sinh(d*x + c))*sqrt((81*a^5 - 522*a^4*b + 1273*a^3*b^2 - 1392*a^2*b^3 + 576*a*b^4)/((a^6*b^7 - 6*a^5*b^8 + 15*a^4*b^9 - 20*a^3*b^10 + 15*a^2*b^11 - 6*a*b^12 + b^13)*d^4)))*sqrt(-((a^3*b^3 - 3*a^2*b^4 + 3*a*b^5 - b^6)*d^2*sqrt((81*a^5 - 522*a^4*b + 1273*a^3*b^2 - 1392*a^2*b^3 + 576*a*b^4)/((a^6*b^7 - 6*a^5*b^8 + 15*a^4*b^9 - 20*a^3*b^10 + 15*a^2*b^11 - 6*a*b^12 + b^13)*d^4)) + 3*a^2 - 15*a*b + 16*b^2)/((a^3*b^3 - 3*a^2*b^4 + 3*a*b^5 - b^6)*d^2))) - ((a*b^2 - b^3)*d*cosh(d*x + c)^8 + 8*(a*b^2 - b^3)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a*b^2 - b^3)*d*sinh(d*x + c)^8 - 4*(a*b^2 - b^3)*d*cosh(d*x + c)^6 + 4*(7*(a*b^2 - b^3)*d*cosh(d*x + c)^2 - (a*b^2 - b^3)*d)*sinh(d*x + c)^6 - 2*(8*a^2*b - 11*a*b^2 + 3*b^3)*d*cosh(d*x + c)^4 + 8*(7*(a*b^2 - b^3)*d*cosh(d*x + c)^3 - 3*(a*b^2 - b^3)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a*b^2 - b^3)*d*cosh(d*x + c)^4 - 30*(a*b^2 - b^3)*d*cosh(d*x + c)^2 - (8*a^2*b - 11*a*b^2 + 3*b^3)*d)*sinh(d*x + c)^4 - 4*(a*b^2 - b^3)*d*cosh(d*x + c)^2 + 8*(7*(a*b^2 - b^3)*d*cosh(d*x + c)^5 - 10*(a*b^2 - b^3)*d*cosh(d*x + c)^3 - (8*a^2*b - 11*a*b^2 + 3*b^3)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a*b^2 - b^3)*d*cosh(d*x + c)^6 - 15*(a*b^2 - b^3)*d*cosh(d*x + c)^4 - 3*(8*a^2*b - 11*a*b^2 + 3*b^3)*d*cosh(d*x + c)^2 - (a*b^2 - b^3)*d)*sinh(d*x + c)^2 + (a*b^2 - b^3)*d + 8*((a*b^2 - b^3)*d*cosh(d*x + c)^7 - 3*(a*b^2 - b^3)*d*cosh(d*x + c)^5 - (8*a^2*b - 11*a*b^2 + 3*b^3)*d*cosh(d*x + c)^3 - (a*b^2 - b^3)*d*cosh(d*x + c))*sinh(d*x + c))*sqrt(((a^3*b^3 - 3*a^2*b^4 + 3*a*b^5 - b^6)*d^2*sqrt((81*a^5 - 522*a^4*b + 1273*a^3*b^2 - 1392*a^2*b^3 + 576*a*b^4)/((a^6*b^7 - 6*a^5*b^8 + 15*a^4*b^9 - 20*a^3*b^10 + 15*a^2*b^11 - 6*a*b^12 + b^13)*d^4)) - 3*a^2 + 15*a*b - 16*b^2)/((a^3*b^3 - 3*a^2*b^4 + 3*a*b^5 - b^6)*d^2))*log(-81*a^3 + 405*a^2*b - 680*a*b^2 + 384*b^3 - (81*a^3 - 405*a^2*b + 680*a*b^2 - 384*b^3)*cosh(d*x + c)^2 - 2*(81*a^3 - 405*a^2*b + 680*a*b^2 - 384*b^3)*cosh(d*x + c)*sinh(d*x + c) - (81*a^3 - 405*a^2*b + 680*a*b^2 - 384*b^3)*sinh(d*x + c)^2 + 2*(2*(9*a^3*b^2 - 47*a^2*b^3 + 82*a*b^4 - 48*b^5)*d*cosh(d*x + c) + 2*(9*a^3*b^2 - 47*a^2*b^3 + 82*a*b^4 - 48*b^5)*d*sinh(d*x + c) + ((3*a^4*b^5 - 14*a^3*b^6 + 24*a^2*b^7 - 18*a*b^8 + 5*b^9)*d^3*cosh(d*x + c) + (3*a^4*b^5 - 14*a^3*b^6 + 24*a^2*b^7 - 18*a*b^8 + 5*b^9)*d^3*sinh(d*x + c))*sqrt((81*a^5 - 522*a^4*b + 1273*a^3*b^2 - 1392*a^2*b^3 + 576*a*b^4)/((a^6*b^7 - 6*a^5*b^8 + 15*a^4*b^9 - 20*a^3*b^10 + 15*a^2*b^11 - 6*a*b^12 + b^13)*d^4)))*sqrt(((a^3*b^3 - 3*a^2*b^4 + 3*a*b^5 - b^6)*d^2*sqrt((81*a^5 - 522*a^4*b + 1273*a^3*b^2 - 1392*a^2*b^3 + 576*a*b^4)/((a^6*b^7 - 6*a^5*b^8 + 15*a^4*b^9 - 20*a^3*b^10 + 15*a^2*b^11 - 6*a*b^12 + b^13)*d^4)) - 3*a^2 + 15*a*b - 16*b^2)/((a^3*b^3 - 3*a^2*b^4 + 3*a*b^5 - b^6)*d^2))) + ((a*b^2 - b^3)*d*cosh(d*x + c)^8 + 8*(a*b^2 - b^3)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a*b^2 - b^3)*d*sinh(d*x + c)^8 - 4*(a*b^2 - b^3)*d*cosh(d*x + c)^6 + 4*(7*(a*b^2 - b^3)*d*cosh(d*x + c)^2 - (a*b^2 - b^3)*d)*sinh(d*x + c)^6 - 2*(8*a^2*b - 11*a*b^2 + 3*b^3)*d*cosh(d*x + c)^4 + 8*(7*(a*b^2 - b^3)*d*cosh(d*x + c)^3 - 3*(a*b^2 - b^3)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a*b^2 - b^3)*d*cosh(d*x + c)^4 - 30*(a*b^2 - b^3)*d*cosh(d*x + c)^2 - (8*a^2*b - 11*a*b^2 + 3*b^3)*d)*sinh(d*x + c)^4 - 4*(a*b^2 - b^3)*d*cosh(d*x + c)^2 + 8*(7*(a*b^2 - b^3)*d*cosh(d*x + c)^5 - 10*(a*b^2 - b^3)*d*cosh(d*x + c)^3 - (8*a^2*b - 11*a*b^2 + 3*b^3)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a*b^2 - b^3)*d*cosh(d*x + c)^6 - 15*(a*b^2 - b^3)*d*cosh(d*x + c)^4 - 3*(8*a^2*b - 11*a*b^2 + 3*b^3)*d*cosh(d*x + c)^2 - (a*b^2 - b^3)*d)*sinh(d*x + c)^2 + (a*b^2 - b^3)*d + 8*((a*b^2 - b^3)*d*cosh(d*x + c)^7 - 3*(a*b^2 - b^3)*d*cosh(d*x + c)^5 - (8*a^2*b - 11*a*b^2 + 3*b^3)*d*cosh(d*x + c)^3 - (a*b^2 - b^3)*d*cosh(d*x + c))*sinh(d*x + c))*sqrt(((a^3*b^3 - 3*a^2*b^4 + 3*a*b^5 - b^6)*d^2*sqrt((81*a^5 - 522*a^4*b + 1273*a^3*b^2 - 1392*a^2*b^3 + 576*a*b^4)/((a^6*b^7 - 6*a^5*b^8 + 15*a^4*b^9 - 20*a^3*b^10 + 15*a^2*b^11 - 6*a*b^12 + b^13)*d^4)) - 3*a^2 + 15*a*b - 16*b^2)/((a^3*b^3 - 3*a^2*b^4 + 3*a*b^5 - b^6)*d^2))*log(-81*a^3 + 405*a^2*b - 680*a*b^2 + 384*b^3 - (81*a^3 - 405*a^2*b + 680*a*b^2 - 384*b^3)*cosh(d*x + c)^2 - 2*(81*a^3 - 405*a^2*b + 680*a*b^2 - 384*b^3)*cosh(d*x + c)*sinh(d*x + c) - (81*a^3 - 405*a^2*b + 680*a*b^2 - 384*b^3)*sinh(d*x + c)^2 - 2*(2*(9*a^3*b^2 - 47*a^2*b^3 + 82*a*b^4 - 48*b^5)*d*cosh(d*x + c) + 2*(9*a^3*b^2 - 47*a^2*b^3 + 82*a*b^4 - 48*b^5)*d*sinh(d*x + c) + ((3*a^4*b^5 - 14*a^3*b^6 + 24*a^2*b^7 - 18*a*b^8 + 5*b^9)*d^3*cosh(d*x + c) + (3*a^4*b^5 - 14*a^3*b^6 + 24*a^2*b^7 - 18*a*b^8 + 5*b^9)*d^3*sinh(d*x + c))*sqrt((81*a^5 - 522*a^4*b + 1273*a^3*b^2 - 1392*a^2*b^3 + 576*a*b^4)/((a^6*b^7 - 6*a^5*b^8 + 15*a^4*b^9 - 20*a^3*b^10 + 15*a^2*b^11 - 6*a*b^12 + b^13)*d^4)))*sqrt(((a^3*b^3 - 3*a^2*b^4 + 3*a*b^5 - b^6)*d^2*sqrt((81*a^5 - 522*a^4*b + 1273*a^3*b^2 - 1392*a^2*b^3 + 576*a*b^4)/((a^6*b^7 - 6*a^5*b^8 + 15*a^4*b^9 - 20*a^3*b^10 + 15*a^2*b^11 - 6*a*b^12 + b^13)*d^4)) - 3*a^2 + 15*a*b - 16*b^2)/((a^3*b^3 - 3*a^2*b^4 + 3*a*b^5 - b^6)*d^2))) + 8*a*cosh(d*x + c) + 8*(7*a*cosh(d*x + c)^6 - 25*a*cosh(d*x + c)^4 - 15*a*cosh(d*x + c)^2 + a)*sinh(d*x + c))/((a*b^2 - b^3)*d*cosh(d*x + c)^8 + 8*(a*b^2 - b^3)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a*b^2 - b^3)*d*sinh(d*x + c)^8 - 4*(a*b^2 - b^3)*d*cosh(d*x + c)^6 + 4*(7*(a*b^2 - b^3)*d*cosh(d*x + c)^2 - (a*b^2 - b^3)*d)*sinh(d*x + c)^6 - 2*(8*a^2*b - 11*a*b^2 + 3*b^3)*d*cosh(d*x + c)^4 + 8*(7*(a*b^2 - b^3)*d*cosh(d*x + c)^3 - 3*(a*b^2 - b^3)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a*b^2 - b^3)*d*cosh(d*x + c)^4 - 30*(a*b^2 - b^3)*d*cosh(d*x + c)^2 - (8*a^2*b - 11*a*b^2 + 3*b^3)*d)*sinh(d*x + c)^4 - 4*(a*b^2 - b^3)*d*cosh(d*x + c)^2 + 8*(7*(a*b^2 - b^3)*d*cosh(d*x + c)^5 - 10*(a*b^2 - b^3)*d*cosh(d*x + c)^3 - (8*a^2*b - 11*a*b^2 + 3*b^3)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a*b^2 - b^3)*d*cosh(d*x + c)^6 - 15*(a*b^2 - b^3)*d*cosh(d*x + c)^4 - 3*(8*a^2*b - 11*a*b^2 + 3*b^3)*d*cosh(d*x + c)^2 - (a*b^2 - b^3)*d)*sinh(d*x + c)^2 + (a*b^2 - b^3)*d + 8*((a*b^2 - b^3)*d*cosh(d*x + c)^7 - 3*(a*b^2 - b^3)*d*cosh(d*x + c)^5 - (8*a^2*b - 11*a*b^2 + 3*b^3)*d*cosh(d*x + c)^3 - (a*b^2 - b^3)*d*cosh(d*x + c))*sinh(d*x + c))","B",0
243,1,6250,0,0.837618," ","integrate(sinh(d*x+c)^5/(a-b*sinh(d*x+c)^4)^2,x, algorithm=""fricas"")","\frac{8 \, b \cosh\left(d x + c\right)^{7} + 56 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + 8 \, b \sinh\left(d x + c\right)^{7} - 8 \, {\left(4 \, a + b\right)} \cosh\left(d x + c\right)^{5} + 8 \, {\left(21 \, b \cosh\left(d x + c\right)^{2} - 4 \, a - b\right)} \sinh\left(d x + c\right)^{5} + 40 \, {\left(7 \, b \cosh\left(d x + c\right)^{3} - {\left(4 \, a + b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} - 8 \, {\left(4 \, a + b\right)} \cosh\left(d x + c\right)^{3} + 8 \, {\left(35 \, b \cosh\left(d x + c\right)^{4} - 10 \, {\left(4 \, a + b\right)} \cosh\left(d x + c\right)^{2} - 4 \, a - b\right)} \sinh\left(d x + c\right)^{3} + 8 \, {\left(21 \, b \cosh\left(d x + c\right)^{5} - 10 \, {\left(4 \, a + b\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(4 \, a + b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a b^{2} - b^{3}\right)} d \sinh\left(d x + c\right)^{8} - 4 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a b^{2} - b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{6} - 2 \, {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{3} - 3 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{4} - 30 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{2} - {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{4} - 4 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{5} - 10 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{3} - {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{6} - 15 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{4} - 3 \, {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a b^{2} - b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a b^{2} - b^{3}\right)} d + 8 \, {\left({\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{7} - 3 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{5} - {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{{\left(a^{4} b^{2} - 3 \, a^{3} b^{3} + 3 \, a^{2} b^{4} - a b^{5}\right)} d^{2} \sqrt{\frac{a^{4} - 10 \, a^{3} b + 41 \, a^{2} b^{2} - 80 \, a b^{3} + 64 \, b^{4}}{{\left(a^{7} b^{5} - 6 \, a^{6} b^{6} + 15 \, a^{5} b^{7} - 20 \, a^{4} b^{8} + 15 \, a^{3} b^{9} - 6 \, a^{2} b^{10} + a b^{11}\right)} d^{4}}} + a^{2} - a b - 4 \, b^{2}}{{\left(a^{4} b^{2} - 3 \, a^{3} b^{3} + 3 \, a^{2} b^{4} - a b^{5}\right)} d^{2}}} \log\left(-a^{3} + 9 \, a^{2} b - 28 \, a b^{2} + 32 \, b^{3} - {\left(a^{3} - 9 \, a^{2} b + 28 \, a b^{2} - 32 \, b^{3}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(a^{3} - 9 \, a^{2} b + 28 \, a b^{2} - 32 \, b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(a^{3} - 9 \, a^{2} b + 28 \, a b^{2} - 32 \, b^{3}\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{4} b - 8 \, a^{3} b^{2} + 23 \, a^{2} b^{3} - 24 \, a b^{4}\right)} d \cosh\left(d x + c\right) + {\left(a^{4} b - 8 \, a^{3} b^{2} + 23 \, a^{2} b^{3} - 24 \, a b^{4}\right)} d \sinh\left(d x + c\right) - 2 \, {\left({\left(a^{4} b^{5} - 3 \, a^{3} b^{6} + 3 \, a^{2} b^{7} - a b^{8}\right)} d^{3} \cosh\left(d x + c\right) + {\left(a^{4} b^{5} - 3 \, a^{3} b^{6} + 3 \, a^{2} b^{7} - a b^{8}\right)} d^{3} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{4} - 10 \, a^{3} b + 41 \, a^{2} b^{2} - 80 \, a b^{3} + 64 \, b^{4}}{{\left(a^{7} b^{5} - 6 \, a^{6} b^{6} + 15 \, a^{5} b^{7} - 20 \, a^{4} b^{8} + 15 \, a^{3} b^{9} - 6 \, a^{2} b^{10} + a b^{11}\right)} d^{4}}}\right)} \sqrt{\frac{{\left(a^{4} b^{2} - 3 \, a^{3} b^{3} + 3 \, a^{2} b^{4} - a b^{5}\right)} d^{2} \sqrt{\frac{a^{4} - 10 \, a^{3} b + 41 \, a^{2} b^{2} - 80 \, a b^{3} + 64 \, b^{4}}{{\left(a^{7} b^{5} - 6 \, a^{6} b^{6} + 15 \, a^{5} b^{7} - 20 \, a^{4} b^{8} + 15 \, a^{3} b^{9} - 6 \, a^{2} b^{10} + a b^{11}\right)} d^{4}}} + a^{2} - a b - 4 \, b^{2}}{{\left(a^{4} b^{2} - 3 \, a^{3} b^{3} + 3 \, a^{2} b^{4} - a b^{5}\right)} d^{2}}}\right) - {\left({\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a b^{2} - b^{3}\right)} d \sinh\left(d x + c\right)^{8} - 4 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a b^{2} - b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{6} - 2 \, {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{3} - 3 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{4} - 30 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{2} - {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{4} - 4 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{5} - 10 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{3} - {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{6} - 15 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{4} - 3 \, {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a b^{2} - b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a b^{2} - b^{3}\right)} d + 8 \, {\left({\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{7} - 3 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{5} - {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{{\left(a^{4} b^{2} - 3 \, a^{3} b^{3} + 3 \, a^{2} b^{4} - a b^{5}\right)} d^{2} \sqrt{\frac{a^{4} - 10 \, a^{3} b + 41 \, a^{2} b^{2} - 80 \, a b^{3} + 64 \, b^{4}}{{\left(a^{7} b^{5} - 6 \, a^{6} b^{6} + 15 \, a^{5} b^{7} - 20 \, a^{4} b^{8} + 15 \, a^{3} b^{9} - 6 \, a^{2} b^{10} + a b^{11}\right)} d^{4}}} + a^{2} - a b - 4 \, b^{2}}{{\left(a^{4} b^{2} - 3 \, a^{3} b^{3} + 3 \, a^{2} b^{4} - a b^{5}\right)} d^{2}}} \log\left(-a^{3} + 9 \, a^{2} b - 28 \, a b^{2} + 32 \, b^{3} - {\left(a^{3} - 9 \, a^{2} b + 28 \, a b^{2} - 32 \, b^{3}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(a^{3} - 9 \, a^{2} b + 28 \, a b^{2} - 32 \, b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(a^{3} - 9 \, a^{2} b + 28 \, a b^{2} - 32 \, b^{3}\right)} \sinh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{4} b - 8 \, a^{3} b^{2} + 23 \, a^{2} b^{3} - 24 \, a b^{4}\right)} d \cosh\left(d x + c\right) + {\left(a^{4} b - 8 \, a^{3} b^{2} + 23 \, a^{2} b^{3} - 24 \, a b^{4}\right)} d \sinh\left(d x + c\right) - 2 \, {\left({\left(a^{4} b^{5} - 3 \, a^{3} b^{6} + 3 \, a^{2} b^{7} - a b^{8}\right)} d^{3} \cosh\left(d x + c\right) + {\left(a^{4} b^{5} - 3 \, a^{3} b^{6} + 3 \, a^{2} b^{7} - a b^{8}\right)} d^{3} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{4} - 10 \, a^{3} b + 41 \, a^{2} b^{2} - 80 \, a b^{3} + 64 \, b^{4}}{{\left(a^{7} b^{5} - 6 \, a^{6} b^{6} + 15 \, a^{5} b^{7} - 20 \, a^{4} b^{8} + 15 \, a^{3} b^{9} - 6 \, a^{2} b^{10} + a b^{11}\right)} d^{4}}}\right)} \sqrt{\frac{{\left(a^{4} b^{2} - 3 \, a^{3} b^{3} + 3 \, a^{2} b^{4} - a b^{5}\right)} d^{2} \sqrt{\frac{a^{4} - 10 \, a^{3} b + 41 \, a^{2} b^{2} - 80 \, a b^{3} + 64 \, b^{4}}{{\left(a^{7} b^{5} - 6 \, a^{6} b^{6} + 15 \, a^{5} b^{7} - 20 \, a^{4} b^{8} + 15 \, a^{3} b^{9} - 6 \, a^{2} b^{10} + a b^{11}\right)} d^{4}}} + a^{2} - a b - 4 \, b^{2}}{{\left(a^{4} b^{2} - 3 \, a^{3} b^{3} + 3 \, a^{2} b^{4} - a b^{5}\right)} d^{2}}}\right) + {\left({\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a b^{2} - b^{3}\right)} d \sinh\left(d x + c\right)^{8} - 4 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a b^{2} - b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{6} - 2 \, {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{3} - 3 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{4} - 30 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{2} - {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{4} - 4 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{5} - 10 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{3} - {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{6} - 15 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{4} - 3 \, {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a b^{2} - b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a b^{2} - b^{3}\right)} d + 8 \, {\left({\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{7} - 3 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{5} - {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{{\left(a^{4} b^{2} - 3 \, a^{3} b^{3} + 3 \, a^{2} b^{4} - a b^{5}\right)} d^{2} \sqrt{\frac{a^{4} - 10 \, a^{3} b + 41 \, a^{2} b^{2} - 80 \, a b^{3} + 64 \, b^{4}}{{\left(a^{7} b^{5} - 6 \, a^{6} b^{6} + 15 \, a^{5} b^{7} - 20 \, a^{4} b^{8} + 15 \, a^{3} b^{9} - 6 \, a^{2} b^{10} + a b^{11}\right)} d^{4}}} - a^{2} + a b + 4 \, b^{2}}{{\left(a^{4} b^{2} - 3 \, a^{3} b^{3} + 3 \, a^{2} b^{4} - a b^{5}\right)} d^{2}}} \log\left(-a^{3} + 9 \, a^{2} b - 28 \, a b^{2} + 32 \, b^{3} - {\left(a^{3} - 9 \, a^{2} b + 28 \, a b^{2} - 32 \, b^{3}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(a^{3} - 9 \, a^{2} b + 28 \, a b^{2} - 32 \, b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(a^{3} - 9 \, a^{2} b + 28 \, a b^{2} - 32 \, b^{3}\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left({\left(a^{4} b - 8 \, a^{3} b^{2} + 23 \, a^{2} b^{3} - 24 \, a b^{4}\right)} d \cosh\left(d x + c\right) + {\left(a^{4} b - 8 \, a^{3} b^{2} + 23 \, a^{2} b^{3} - 24 \, a b^{4}\right)} d \sinh\left(d x + c\right) + 2 \, {\left({\left(a^{4} b^{5} - 3 \, a^{3} b^{6} + 3 \, a^{2} b^{7} - a b^{8}\right)} d^{3} \cosh\left(d x + c\right) + {\left(a^{4} b^{5} - 3 \, a^{3} b^{6} + 3 \, a^{2} b^{7} - a b^{8}\right)} d^{3} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{4} - 10 \, a^{3} b + 41 \, a^{2} b^{2} - 80 \, a b^{3} + 64 \, b^{4}}{{\left(a^{7} b^{5} - 6 \, a^{6} b^{6} + 15 \, a^{5} b^{7} - 20 \, a^{4} b^{8} + 15 \, a^{3} b^{9} - 6 \, a^{2} b^{10} + a b^{11}\right)} d^{4}}}\right)} \sqrt{-\frac{{\left(a^{4} b^{2} - 3 \, a^{3} b^{3} + 3 \, a^{2} b^{4} - a b^{5}\right)} d^{2} \sqrt{\frac{a^{4} - 10 \, a^{3} b + 41 \, a^{2} b^{2} - 80 \, a b^{3} + 64 \, b^{4}}{{\left(a^{7} b^{5} - 6 \, a^{6} b^{6} + 15 \, a^{5} b^{7} - 20 \, a^{4} b^{8} + 15 \, a^{3} b^{9} - 6 \, a^{2} b^{10} + a b^{11}\right)} d^{4}}} - a^{2} + a b + 4 \, b^{2}}{{\left(a^{4} b^{2} - 3 \, a^{3} b^{3} + 3 \, a^{2} b^{4} - a b^{5}\right)} d^{2}}}\right) - {\left({\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a b^{2} - b^{3}\right)} d \sinh\left(d x + c\right)^{8} - 4 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a b^{2} - b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{6} - 2 \, {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{3} - 3 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{4} - 30 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{2} - {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{4} - 4 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{5} - 10 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{3} - {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{6} - 15 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{4} - 3 \, {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a b^{2} - b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a b^{2} - b^{3}\right)} d + 8 \, {\left({\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{7} - 3 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{5} - {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{{\left(a^{4} b^{2} - 3 \, a^{3} b^{3} + 3 \, a^{2} b^{4} - a b^{5}\right)} d^{2} \sqrt{\frac{a^{4} - 10 \, a^{3} b + 41 \, a^{2} b^{2} - 80 \, a b^{3} + 64 \, b^{4}}{{\left(a^{7} b^{5} - 6 \, a^{6} b^{6} + 15 \, a^{5} b^{7} - 20 \, a^{4} b^{8} + 15 \, a^{3} b^{9} - 6 \, a^{2} b^{10} + a b^{11}\right)} d^{4}}} - a^{2} + a b + 4 \, b^{2}}{{\left(a^{4} b^{2} - 3 \, a^{3} b^{3} + 3 \, a^{2} b^{4} - a b^{5}\right)} d^{2}}} \log\left(-a^{3} + 9 \, a^{2} b - 28 \, a b^{2} + 32 \, b^{3} - {\left(a^{3} - 9 \, a^{2} b + 28 \, a b^{2} - 32 \, b^{3}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(a^{3} - 9 \, a^{2} b + 28 \, a b^{2} - 32 \, b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(a^{3} - 9 \, a^{2} b + 28 \, a b^{2} - 32 \, b^{3}\right)} \sinh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{4} b - 8 \, a^{3} b^{2} + 23 \, a^{2} b^{3} - 24 \, a b^{4}\right)} d \cosh\left(d x + c\right) + {\left(a^{4} b - 8 \, a^{3} b^{2} + 23 \, a^{2} b^{3} - 24 \, a b^{4}\right)} d \sinh\left(d x + c\right) + 2 \, {\left({\left(a^{4} b^{5} - 3 \, a^{3} b^{6} + 3 \, a^{2} b^{7} - a b^{8}\right)} d^{3} \cosh\left(d x + c\right) + {\left(a^{4} b^{5} - 3 \, a^{3} b^{6} + 3 \, a^{2} b^{7} - a b^{8}\right)} d^{3} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{4} - 10 \, a^{3} b + 41 \, a^{2} b^{2} - 80 \, a b^{3} + 64 \, b^{4}}{{\left(a^{7} b^{5} - 6 \, a^{6} b^{6} + 15 \, a^{5} b^{7} - 20 \, a^{4} b^{8} + 15 \, a^{3} b^{9} - 6 \, a^{2} b^{10} + a b^{11}\right)} d^{4}}}\right)} \sqrt{-\frac{{\left(a^{4} b^{2} - 3 \, a^{3} b^{3} + 3 \, a^{2} b^{4} - a b^{5}\right)} d^{2} \sqrt{\frac{a^{4} - 10 \, a^{3} b + 41 \, a^{2} b^{2} - 80 \, a b^{3} + 64 \, b^{4}}{{\left(a^{7} b^{5} - 6 \, a^{6} b^{6} + 15 \, a^{5} b^{7} - 20 \, a^{4} b^{8} + 15 \, a^{3} b^{9} - 6 \, a^{2} b^{10} + a b^{11}\right)} d^{4}}} - a^{2} + a b + 4 \, b^{2}}{{\left(a^{4} b^{2} - 3 \, a^{3} b^{3} + 3 \, a^{2} b^{4} - a b^{5}\right)} d^{2}}}\right) + 8 \, b \cosh\left(d x + c\right) + 8 \, {\left(7 \, b \cosh\left(d x + c\right)^{6} - 5 \, {\left(4 \, a + b\right)} \cosh\left(d x + c\right)^{4} - 3 \, {\left(4 \, a + b\right)} \cosh\left(d x + c\right)^{2} + b\right)} \sinh\left(d x + c\right)}{16 \, {\left({\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a b^{2} - b^{3}\right)} d \sinh\left(d x + c\right)^{8} - 4 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a b^{2} - b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{6} - 2 \, {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{3} - 3 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{4} - 30 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{2} - {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{4} - 4 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{5} - 10 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{3} - {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{6} - 15 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{4} - 3 \, {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a b^{2} - b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a b^{2} - b^{3}\right)} d + 8 \, {\left({\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{7} - 3 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{5} - {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"1/16*(8*b*cosh(d*x + c)^7 + 56*b*cosh(d*x + c)*sinh(d*x + c)^6 + 8*b*sinh(d*x + c)^7 - 8*(4*a + b)*cosh(d*x + c)^5 + 8*(21*b*cosh(d*x + c)^2 - 4*a - b)*sinh(d*x + c)^5 + 40*(7*b*cosh(d*x + c)^3 - (4*a + b)*cosh(d*x + c))*sinh(d*x + c)^4 - 8*(4*a + b)*cosh(d*x + c)^3 + 8*(35*b*cosh(d*x + c)^4 - 10*(4*a + b)*cosh(d*x + c)^2 - 4*a - b)*sinh(d*x + c)^3 + 8*(21*b*cosh(d*x + c)^5 - 10*(4*a + b)*cosh(d*x + c)^3 - 3*(4*a + b)*cosh(d*x + c))*sinh(d*x + c)^2 + ((a*b^2 - b^3)*d*cosh(d*x + c)^8 + 8*(a*b^2 - b^3)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a*b^2 - b^3)*d*sinh(d*x + c)^8 - 4*(a*b^2 - b^3)*d*cosh(d*x + c)^6 + 4*(7*(a*b^2 - b^3)*d*cosh(d*x + c)^2 - (a*b^2 - b^3)*d)*sinh(d*x + c)^6 - 2*(8*a^2*b - 11*a*b^2 + 3*b^3)*d*cosh(d*x + c)^4 + 8*(7*(a*b^2 - b^3)*d*cosh(d*x + c)^3 - 3*(a*b^2 - b^3)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a*b^2 - b^3)*d*cosh(d*x + c)^4 - 30*(a*b^2 - b^3)*d*cosh(d*x + c)^2 - (8*a^2*b - 11*a*b^2 + 3*b^3)*d)*sinh(d*x + c)^4 - 4*(a*b^2 - b^3)*d*cosh(d*x + c)^2 + 8*(7*(a*b^2 - b^3)*d*cosh(d*x + c)^5 - 10*(a*b^2 - b^3)*d*cosh(d*x + c)^3 - (8*a^2*b - 11*a*b^2 + 3*b^3)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a*b^2 - b^3)*d*cosh(d*x + c)^6 - 15*(a*b^2 - b^3)*d*cosh(d*x + c)^4 - 3*(8*a^2*b - 11*a*b^2 + 3*b^3)*d*cosh(d*x + c)^2 - (a*b^2 - b^3)*d)*sinh(d*x + c)^2 + (a*b^2 - b^3)*d + 8*((a*b^2 - b^3)*d*cosh(d*x + c)^7 - 3*(a*b^2 - b^3)*d*cosh(d*x + c)^5 - (8*a^2*b - 11*a*b^2 + 3*b^3)*d*cosh(d*x + c)^3 - (a*b^2 - b^3)*d*cosh(d*x + c))*sinh(d*x + c))*sqrt(((a^4*b^2 - 3*a^3*b^3 + 3*a^2*b^4 - a*b^5)*d^2*sqrt((a^4 - 10*a^3*b + 41*a^2*b^2 - 80*a*b^3 + 64*b^4)/((a^7*b^5 - 6*a^6*b^6 + 15*a^5*b^7 - 20*a^4*b^8 + 15*a^3*b^9 - 6*a^2*b^10 + a*b^11)*d^4)) + a^2 - a*b - 4*b^2)/((a^4*b^2 - 3*a^3*b^3 + 3*a^2*b^4 - a*b^5)*d^2))*log(-a^3 + 9*a^2*b - 28*a*b^2 + 32*b^3 - (a^3 - 9*a^2*b + 28*a*b^2 - 32*b^3)*cosh(d*x + c)^2 - 2*(a^3 - 9*a^2*b + 28*a*b^2 - 32*b^3)*cosh(d*x + c)*sinh(d*x + c) - (a^3 - 9*a^2*b + 28*a*b^2 - 32*b^3)*sinh(d*x + c)^2 + 2*((a^4*b - 8*a^3*b^2 + 23*a^2*b^3 - 24*a*b^4)*d*cosh(d*x + c) + (a^4*b - 8*a^3*b^2 + 23*a^2*b^3 - 24*a*b^4)*d*sinh(d*x + c) - 2*((a^4*b^5 - 3*a^3*b^6 + 3*a^2*b^7 - a*b^8)*d^3*cosh(d*x + c) + (a^4*b^5 - 3*a^3*b^6 + 3*a^2*b^7 - a*b^8)*d^3*sinh(d*x + c))*sqrt((a^4 - 10*a^3*b + 41*a^2*b^2 - 80*a*b^3 + 64*b^4)/((a^7*b^5 - 6*a^6*b^6 + 15*a^5*b^7 - 20*a^4*b^8 + 15*a^3*b^9 - 6*a^2*b^10 + a*b^11)*d^4)))*sqrt(((a^4*b^2 - 3*a^3*b^3 + 3*a^2*b^4 - a*b^5)*d^2*sqrt((a^4 - 10*a^3*b + 41*a^2*b^2 - 80*a*b^3 + 64*b^4)/((a^7*b^5 - 6*a^6*b^6 + 15*a^5*b^7 - 20*a^4*b^8 + 15*a^3*b^9 - 6*a^2*b^10 + a*b^11)*d^4)) + a^2 - a*b - 4*b^2)/((a^4*b^2 - 3*a^3*b^3 + 3*a^2*b^4 - a*b^5)*d^2))) - ((a*b^2 - b^3)*d*cosh(d*x + c)^8 + 8*(a*b^2 - b^3)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a*b^2 - b^3)*d*sinh(d*x + c)^8 - 4*(a*b^2 - b^3)*d*cosh(d*x + c)^6 + 4*(7*(a*b^2 - b^3)*d*cosh(d*x + c)^2 - (a*b^2 - b^3)*d)*sinh(d*x + c)^6 - 2*(8*a^2*b - 11*a*b^2 + 3*b^3)*d*cosh(d*x + c)^4 + 8*(7*(a*b^2 - b^3)*d*cosh(d*x + c)^3 - 3*(a*b^2 - b^3)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a*b^2 - b^3)*d*cosh(d*x + c)^4 - 30*(a*b^2 - b^3)*d*cosh(d*x + c)^2 - (8*a^2*b - 11*a*b^2 + 3*b^3)*d)*sinh(d*x + c)^4 - 4*(a*b^2 - b^3)*d*cosh(d*x + c)^2 + 8*(7*(a*b^2 - b^3)*d*cosh(d*x + c)^5 - 10*(a*b^2 - b^3)*d*cosh(d*x + c)^3 - (8*a^2*b - 11*a*b^2 + 3*b^3)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a*b^2 - b^3)*d*cosh(d*x + c)^6 - 15*(a*b^2 - b^3)*d*cosh(d*x + c)^4 - 3*(8*a^2*b - 11*a*b^2 + 3*b^3)*d*cosh(d*x + c)^2 - (a*b^2 - b^3)*d)*sinh(d*x + c)^2 + (a*b^2 - b^3)*d + 8*((a*b^2 - b^3)*d*cosh(d*x + c)^7 - 3*(a*b^2 - b^3)*d*cosh(d*x + c)^5 - (8*a^2*b - 11*a*b^2 + 3*b^3)*d*cosh(d*x + c)^3 - (a*b^2 - b^3)*d*cosh(d*x + c))*sinh(d*x + c))*sqrt(((a^4*b^2 - 3*a^3*b^3 + 3*a^2*b^4 - a*b^5)*d^2*sqrt((a^4 - 10*a^3*b + 41*a^2*b^2 - 80*a*b^3 + 64*b^4)/((a^7*b^5 - 6*a^6*b^6 + 15*a^5*b^7 - 20*a^4*b^8 + 15*a^3*b^9 - 6*a^2*b^10 + a*b^11)*d^4)) + a^2 - a*b - 4*b^2)/((a^4*b^2 - 3*a^3*b^3 + 3*a^2*b^4 - a*b^5)*d^2))*log(-a^3 + 9*a^2*b - 28*a*b^2 + 32*b^3 - (a^3 - 9*a^2*b + 28*a*b^2 - 32*b^3)*cosh(d*x + c)^2 - 2*(a^3 - 9*a^2*b + 28*a*b^2 - 32*b^3)*cosh(d*x + c)*sinh(d*x + c) - (a^3 - 9*a^2*b + 28*a*b^2 - 32*b^3)*sinh(d*x + c)^2 - 2*((a^4*b - 8*a^3*b^2 + 23*a^2*b^3 - 24*a*b^4)*d*cosh(d*x + c) + (a^4*b - 8*a^3*b^2 + 23*a^2*b^3 - 24*a*b^4)*d*sinh(d*x + c) - 2*((a^4*b^5 - 3*a^3*b^6 + 3*a^2*b^7 - a*b^8)*d^3*cosh(d*x + c) + (a^4*b^5 - 3*a^3*b^6 + 3*a^2*b^7 - a*b^8)*d^3*sinh(d*x + c))*sqrt((a^4 - 10*a^3*b + 41*a^2*b^2 - 80*a*b^3 + 64*b^4)/((a^7*b^5 - 6*a^6*b^6 + 15*a^5*b^7 - 20*a^4*b^8 + 15*a^3*b^9 - 6*a^2*b^10 + a*b^11)*d^4)))*sqrt(((a^4*b^2 - 3*a^3*b^3 + 3*a^2*b^4 - a*b^5)*d^2*sqrt((a^4 - 10*a^3*b + 41*a^2*b^2 - 80*a*b^3 + 64*b^4)/((a^7*b^5 - 6*a^6*b^6 + 15*a^5*b^7 - 20*a^4*b^8 + 15*a^3*b^9 - 6*a^2*b^10 + a*b^11)*d^4)) + a^2 - a*b - 4*b^2)/((a^4*b^2 - 3*a^3*b^3 + 3*a^2*b^4 - a*b^5)*d^2))) + ((a*b^2 - b^3)*d*cosh(d*x + c)^8 + 8*(a*b^2 - b^3)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a*b^2 - b^3)*d*sinh(d*x + c)^8 - 4*(a*b^2 - b^3)*d*cosh(d*x + c)^6 + 4*(7*(a*b^2 - b^3)*d*cosh(d*x + c)^2 - (a*b^2 - b^3)*d)*sinh(d*x + c)^6 - 2*(8*a^2*b - 11*a*b^2 + 3*b^3)*d*cosh(d*x + c)^4 + 8*(7*(a*b^2 - b^3)*d*cosh(d*x + c)^3 - 3*(a*b^2 - b^3)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a*b^2 - b^3)*d*cosh(d*x + c)^4 - 30*(a*b^2 - b^3)*d*cosh(d*x + c)^2 - (8*a^2*b - 11*a*b^2 + 3*b^3)*d)*sinh(d*x + c)^4 - 4*(a*b^2 - b^3)*d*cosh(d*x + c)^2 + 8*(7*(a*b^2 - b^3)*d*cosh(d*x + c)^5 - 10*(a*b^2 - b^3)*d*cosh(d*x + c)^3 - (8*a^2*b - 11*a*b^2 + 3*b^3)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a*b^2 - b^3)*d*cosh(d*x + c)^6 - 15*(a*b^2 - b^3)*d*cosh(d*x + c)^4 - 3*(8*a^2*b - 11*a*b^2 + 3*b^3)*d*cosh(d*x + c)^2 - (a*b^2 - b^3)*d)*sinh(d*x + c)^2 + (a*b^2 - b^3)*d + 8*((a*b^2 - b^3)*d*cosh(d*x + c)^7 - 3*(a*b^2 - b^3)*d*cosh(d*x + c)^5 - (8*a^2*b - 11*a*b^2 + 3*b^3)*d*cosh(d*x + c)^3 - (a*b^2 - b^3)*d*cosh(d*x + c))*sinh(d*x + c))*sqrt(-((a^4*b^2 - 3*a^3*b^3 + 3*a^2*b^4 - a*b^5)*d^2*sqrt((a^4 - 10*a^3*b + 41*a^2*b^2 - 80*a*b^3 + 64*b^4)/((a^7*b^5 - 6*a^6*b^6 + 15*a^5*b^7 - 20*a^4*b^8 + 15*a^3*b^9 - 6*a^2*b^10 + a*b^11)*d^4)) - a^2 + a*b + 4*b^2)/((a^4*b^2 - 3*a^3*b^3 + 3*a^2*b^4 - a*b^5)*d^2))*log(-a^3 + 9*a^2*b - 28*a*b^2 + 32*b^3 - (a^3 - 9*a^2*b + 28*a*b^2 - 32*b^3)*cosh(d*x + c)^2 - 2*(a^3 - 9*a^2*b + 28*a*b^2 - 32*b^3)*cosh(d*x + c)*sinh(d*x + c) - (a^3 - 9*a^2*b + 28*a*b^2 - 32*b^3)*sinh(d*x + c)^2 + 2*((a^4*b - 8*a^3*b^2 + 23*a^2*b^3 - 24*a*b^4)*d*cosh(d*x + c) + (a^4*b - 8*a^3*b^2 + 23*a^2*b^3 - 24*a*b^4)*d*sinh(d*x + c) + 2*((a^4*b^5 - 3*a^3*b^6 + 3*a^2*b^7 - a*b^8)*d^3*cosh(d*x + c) + (a^4*b^5 - 3*a^3*b^6 + 3*a^2*b^7 - a*b^8)*d^3*sinh(d*x + c))*sqrt((a^4 - 10*a^3*b + 41*a^2*b^2 - 80*a*b^3 + 64*b^4)/((a^7*b^5 - 6*a^6*b^6 + 15*a^5*b^7 - 20*a^4*b^8 + 15*a^3*b^9 - 6*a^2*b^10 + a*b^11)*d^4)))*sqrt(-((a^4*b^2 - 3*a^3*b^3 + 3*a^2*b^4 - a*b^5)*d^2*sqrt((a^4 - 10*a^3*b + 41*a^2*b^2 - 80*a*b^3 + 64*b^4)/((a^7*b^5 - 6*a^6*b^6 + 15*a^5*b^7 - 20*a^4*b^8 + 15*a^3*b^9 - 6*a^2*b^10 + a*b^11)*d^4)) - a^2 + a*b + 4*b^2)/((a^4*b^2 - 3*a^3*b^3 + 3*a^2*b^4 - a*b^5)*d^2))) - ((a*b^2 - b^3)*d*cosh(d*x + c)^8 + 8*(a*b^2 - b^3)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a*b^2 - b^3)*d*sinh(d*x + c)^8 - 4*(a*b^2 - b^3)*d*cosh(d*x + c)^6 + 4*(7*(a*b^2 - b^3)*d*cosh(d*x + c)^2 - (a*b^2 - b^3)*d)*sinh(d*x + c)^6 - 2*(8*a^2*b - 11*a*b^2 + 3*b^3)*d*cosh(d*x + c)^4 + 8*(7*(a*b^2 - b^3)*d*cosh(d*x + c)^3 - 3*(a*b^2 - b^3)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a*b^2 - b^3)*d*cosh(d*x + c)^4 - 30*(a*b^2 - b^3)*d*cosh(d*x + c)^2 - (8*a^2*b - 11*a*b^2 + 3*b^3)*d)*sinh(d*x + c)^4 - 4*(a*b^2 - b^3)*d*cosh(d*x + c)^2 + 8*(7*(a*b^2 - b^3)*d*cosh(d*x + c)^5 - 10*(a*b^2 - b^3)*d*cosh(d*x + c)^3 - (8*a^2*b - 11*a*b^2 + 3*b^3)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a*b^2 - b^3)*d*cosh(d*x + c)^6 - 15*(a*b^2 - b^3)*d*cosh(d*x + c)^4 - 3*(8*a^2*b - 11*a*b^2 + 3*b^3)*d*cosh(d*x + c)^2 - (a*b^2 - b^3)*d)*sinh(d*x + c)^2 + (a*b^2 - b^3)*d + 8*((a*b^2 - b^3)*d*cosh(d*x + c)^7 - 3*(a*b^2 - b^3)*d*cosh(d*x + c)^5 - (8*a^2*b - 11*a*b^2 + 3*b^3)*d*cosh(d*x + c)^3 - (a*b^2 - b^3)*d*cosh(d*x + c))*sinh(d*x + c))*sqrt(-((a^4*b^2 - 3*a^3*b^3 + 3*a^2*b^4 - a*b^5)*d^2*sqrt((a^4 - 10*a^3*b + 41*a^2*b^2 - 80*a*b^3 + 64*b^4)/((a^7*b^5 - 6*a^6*b^6 + 15*a^5*b^7 - 20*a^4*b^8 + 15*a^3*b^9 - 6*a^2*b^10 + a*b^11)*d^4)) - a^2 + a*b + 4*b^2)/((a^4*b^2 - 3*a^3*b^3 + 3*a^2*b^4 - a*b^5)*d^2))*log(-a^3 + 9*a^2*b - 28*a*b^2 + 32*b^3 - (a^3 - 9*a^2*b + 28*a*b^2 - 32*b^3)*cosh(d*x + c)^2 - 2*(a^3 - 9*a^2*b + 28*a*b^2 - 32*b^3)*cosh(d*x + c)*sinh(d*x + c) - (a^3 - 9*a^2*b + 28*a*b^2 - 32*b^3)*sinh(d*x + c)^2 - 2*((a^4*b - 8*a^3*b^2 + 23*a^2*b^3 - 24*a*b^4)*d*cosh(d*x + c) + (a^4*b - 8*a^3*b^2 + 23*a^2*b^3 - 24*a*b^4)*d*sinh(d*x + c) + 2*((a^4*b^5 - 3*a^3*b^6 + 3*a^2*b^7 - a*b^8)*d^3*cosh(d*x + c) + (a^4*b^5 - 3*a^3*b^6 + 3*a^2*b^7 - a*b^8)*d^3*sinh(d*x + c))*sqrt((a^4 - 10*a^3*b + 41*a^2*b^2 - 80*a*b^3 + 64*b^4)/((a^7*b^5 - 6*a^6*b^6 + 15*a^5*b^7 - 20*a^4*b^8 + 15*a^3*b^9 - 6*a^2*b^10 + a*b^11)*d^4)))*sqrt(-((a^4*b^2 - 3*a^3*b^3 + 3*a^2*b^4 - a*b^5)*d^2*sqrt((a^4 - 10*a^3*b + 41*a^2*b^2 - 80*a*b^3 + 64*b^4)/((a^7*b^5 - 6*a^6*b^6 + 15*a^5*b^7 - 20*a^4*b^8 + 15*a^3*b^9 - 6*a^2*b^10 + a*b^11)*d^4)) - a^2 + a*b + 4*b^2)/((a^4*b^2 - 3*a^3*b^3 + 3*a^2*b^4 - a*b^5)*d^2))) + 8*b*cosh(d*x + c) + 8*(7*b*cosh(d*x + c)^6 - 5*(4*a + b)*cosh(d*x + c)^4 - 3*(4*a + b)*cosh(d*x + c)^2 + b)*sinh(d*x + c))/((a*b^2 - b^3)*d*cosh(d*x + c)^8 + 8*(a*b^2 - b^3)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a*b^2 - b^3)*d*sinh(d*x + c)^8 - 4*(a*b^2 - b^3)*d*cosh(d*x + c)^6 + 4*(7*(a*b^2 - b^3)*d*cosh(d*x + c)^2 - (a*b^2 - b^3)*d)*sinh(d*x + c)^6 - 2*(8*a^2*b - 11*a*b^2 + 3*b^3)*d*cosh(d*x + c)^4 + 8*(7*(a*b^2 - b^3)*d*cosh(d*x + c)^3 - 3*(a*b^2 - b^3)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a*b^2 - b^3)*d*cosh(d*x + c)^4 - 30*(a*b^2 - b^3)*d*cosh(d*x + c)^2 - (8*a^2*b - 11*a*b^2 + 3*b^3)*d)*sinh(d*x + c)^4 - 4*(a*b^2 - b^3)*d*cosh(d*x + c)^2 + 8*(7*(a*b^2 - b^3)*d*cosh(d*x + c)^5 - 10*(a*b^2 - b^3)*d*cosh(d*x + c)^3 - (8*a^2*b - 11*a*b^2 + 3*b^3)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a*b^2 - b^3)*d*cosh(d*x + c)^6 - 15*(a*b^2 - b^3)*d*cosh(d*x + c)^4 - 3*(8*a^2*b - 11*a*b^2 + 3*b^3)*d*cosh(d*x + c)^2 - (a*b^2 - b^3)*d)*sinh(d*x + c)^2 + (a*b^2 - b^3)*d + 8*((a*b^2 - b^3)*d*cosh(d*x + c)^7 - 3*(a*b^2 - b^3)*d*cosh(d*x + c)^5 - (8*a^2*b - 11*a*b^2 + 3*b^3)*d*cosh(d*x + c)^3 - (a*b^2 - b^3)*d*cosh(d*x + c))*sinh(d*x + c))","B",0
244,1,5238,0,0.637608," ","integrate(sinh(d*x+c)^3/(a-b*sinh(d*x+c)^4)^2,x, algorithm=""fricas"")","-\frac{8 \, \cosh\left(d x + c\right)^{7} + 56 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + 8 \, \sinh\left(d x + c\right)^{7} + 8 \, {\left(21 \, \cosh\left(d x + c\right)^{2} - 5\right)} \sinh\left(d x + c\right)^{5} - 40 \, \cosh\left(d x + c\right)^{5} + 40 \, {\left(7 \, \cosh\left(d x + c\right)^{3} - 5 \, \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 40 \, {\left(7 \, \cosh\left(d x + c\right)^{4} - 10 \, \cosh\left(d x + c\right)^{2} - 1\right)} \sinh\left(d x + c\right)^{3} - 40 \, \cosh\left(d x + c\right)^{3} + 8 \, {\left(21 \, \cosh\left(d x + c\right)^{5} - 50 \, \cosh\left(d x + c\right)^{3} - 15 \, \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - {\left({\left(a b - b^{2}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a b - b^{2}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a b - b^{2}\right)} d \sinh\left(d x + c\right)^{8} - 4 \, {\left(a b - b^{2}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a b - b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a b - b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{6} - 2 \, {\left(8 \, a^{2} - 11 \, a b + 3 \, b^{2}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a b - b^{2}\right)} d \cosh\left(d x + c\right)^{3} - 3 \, {\left(a b - b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a b - b^{2}\right)} d \cosh\left(d x + c\right)^{4} - 30 \, {\left(a b - b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(8 \, a^{2} - 11 \, a b + 3 \, b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{4} - 4 \, {\left(a b - b^{2}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a b - b^{2}\right)} d \cosh\left(d x + c\right)^{5} - 10 \, {\left(a b - b^{2}\right)} d \cosh\left(d x + c\right)^{3} - {\left(8 \, a^{2} - 11 \, a b + 3 \, b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a b - b^{2}\right)} d \cosh\left(d x + c\right)^{6} - 15 \, {\left(a b - b^{2}\right)} d \cosh\left(d x + c\right)^{4} - 3 \, {\left(8 \, a^{2} - 11 \, a b + 3 \, b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a b - b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a b - b^{2}\right)} d + 8 \, {\left({\left(a b - b^{2}\right)} d \cosh\left(d x + c\right)^{7} - 3 \, {\left(a b - b^{2}\right)} d \cosh\left(d x + c\right)^{5} - {\left(8 \, a^{2} - 11 \, a b + 3 \, b^{2}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a b - b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{{\left(a^{4} b - 3 \, a^{3} b^{2} + 3 \, a^{2} b^{3} - a b^{4}\right)} d^{2} \sqrt{\frac{a^{2} + 6 \, a b + 9 \, b^{2}}{{\left(a^{7} b^{3} - 6 \, a^{6} b^{4} + 15 \, a^{5} b^{5} - 20 \, a^{4} b^{6} + 15 \, a^{3} b^{7} - 6 \, a^{2} b^{8} + a b^{9}\right)} d^{4}}} + 3 \, a + b}{{\left(a^{4} b - 3 \, a^{3} b^{2} + 3 \, a^{2} b^{3} - a b^{4}\right)} d^{2}}} \log\left({\left(a + 3 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a + 3 \, b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a + 3 \, b\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(2 \, {\left(a^{2} b + 3 \, a b^{2}\right)} d \cosh\left(d x + c\right) + 2 \, {\left(a^{2} b + 3 \, a b^{2}\right)} d \sinh\left(d x + c\right) - {\left({\left(a^{5} b^{2} - 2 \, a^{4} b^{3} + 2 \, a^{2} b^{5} - a b^{6}\right)} d^{3} \cosh\left(d x + c\right) + {\left(a^{5} b^{2} - 2 \, a^{4} b^{3} + 2 \, a^{2} b^{5} - a b^{6}\right)} d^{3} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + 6 \, a b + 9 \, b^{2}}{{\left(a^{7} b^{3} - 6 \, a^{6} b^{4} + 15 \, a^{5} b^{5} - 20 \, a^{4} b^{6} + 15 \, a^{3} b^{7} - 6 \, a^{2} b^{8} + a b^{9}\right)} d^{4}}}\right)} \sqrt{-\frac{{\left(a^{4} b - 3 \, a^{3} b^{2} + 3 \, a^{2} b^{3} - a b^{4}\right)} d^{2} \sqrt{\frac{a^{2} + 6 \, a b + 9 \, b^{2}}{{\left(a^{7} b^{3} - 6 \, a^{6} b^{4} + 15 \, a^{5} b^{5} - 20 \, a^{4} b^{6} + 15 \, a^{3} b^{7} - 6 \, a^{2} b^{8} + a b^{9}\right)} d^{4}}} + 3 \, a + b}{{\left(a^{4} b - 3 \, a^{3} b^{2} + 3 \, a^{2} b^{3} - a b^{4}\right)} d^{2}}} + a + 3 \, b\right) + {\left({\left(a b - b^{2}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a b - b^{2}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a b - b^{2}\right)} d \sinh\left(d x + c\right)^{8} - 4 \, {\left(a b - b^{2}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a b - b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a b - b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{6} - 2 \, {\left(8 \, a^{2} - 11 \, a b + 3 \, b^{2}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a b - b^{2}\right)} d \cosh\left(d x + c\right)^{3} - 3 \, {\left(a b - b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a b - b^{2}\right)} d \cosh\left(d x + c\right)^{4} - 30 \, {\left(a b - b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(8 \, a^{2} - 11 \, a b + 3 \, b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{4} - 4 \, {\left(a b - b^{2}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a b - b^{2}\right)} d \cosh\left(d x + c\right)^{5} - 10 \, {\left(a b - b^{2}\right)} d \cosh\left(d x + c\right)^{3} - {\left(8 \, a^{2} - 11 \, a b + 3 \, b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a b - b^{2}\right)} d \cosh\left(d x + c\right)^{6} - 15 \, {\left(a b - b^{2}\right)} d \cosh\left(d x + c\right)^{4} - 3 \, {\left(8 \, a^{2} - 11 \, a b + 3 \, b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a b - b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a b - b^{2}\right)} d + 8 \, {\left({\left(a b - b^{2}\right)} d \cosh\left(d x + c\right)^{7} - 3 \, {\left(a b - b^{2}\right)} d \cosh\left(d x + c\right)^{5} - {\left(8 \, a^{2} - 11 \, a b + 3 \, b^{2}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a b - b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{{\left(a^{4} b - 3 \, a^{3} b^{2} + 3 \, a^{2} b^{3} - a b^{4}\right)} d^{2} \sqrt{\frac{a^{2} + 6 \, a b + 9 \, b^{2}}{{\left(a^{7} b^{3} - 6 \, a^{6} b^{4} + 15 \, a^{5} b^{5} - 20 \, a^{4} b^{6} + 15 \, a^{3} b^{7} - 6 \, a^{2} b^{8} + a b^{9}\right)} d^{4}}} + 3 \, a + b}{{\left(a^{4} b - 3 \, a^{3} b^{2} + 3 \, a^{2} b^{3} - a b^{4}\right)} d^{2}}} \log\left({\left(a + 3 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a + 3 \, b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a + 3 \, b\right)} \sinh\left(d x + c\right)^{2} - 2 \, {\left(2 \, {\left(a^{2} b + 3 \, a b^{2}\right)} d \cosh\left(d x + c\right) + 2 \, {\left(a^{2} b + 3 \, a b^{2}\right)} d \sinh\left(d x + c\right) - {\left({\left(a^{5} b^{2} - 2 \, a^{4} b^{3} + 2 \, a^{2} b^{5} - a b^{6}\right)} d^{3} \cosh\left(d x + c\right) + {\left(a^{5} b^{2} - 2 \, a^{4} b^{3} + 2 \, a^{2} b^{5} - a b^{6}\right)} d^{3} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + 6 \, a b + 9 \, b^{2}}{{\left(a^{7} b^{3} - 6 \, a^{6} b^{4} + 15 \, a^{5} b^{5} - 20 \, a^{4} b^{6} + 15 \, a^{3} b^{7} - 6 \, a^{2} b^{8} + a b^{9}\right)} d^{4}}}\right)} \sqrt{-\frac{{\left(a^{4} b - 3 \, a^{3} b^{2} + 3 \, a^{2} b^{3} - a b^{4}\right)} d^{2} \sqrt{\frac{a^{2} + 6 \, a b + 9 \, b^{2}}{{\left(a^{7} b^{3} - 6 \, a^{6} b^{4} + 15 \, a^{5} b^{5} - 20 \, a^{4} b^{6} + 15 \, a^{3} b^{7} - 6 \, a^{2} b^{8} + a b^{9}\right)} d^{4}}} + 3 \, a + b}{{\left(a^{4} b - 3 \, a^{3} b^{2} + 3 \, a^{2} b^{3} - a b^{4}\right)} d^{2}}} + a + 3 \, b\right) - {\left({\left(a b - b^{2}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a b - b^{2}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a b - b^{2}\right)} d \sinh\left(d x + c\right)^{8} - 4 \, {\left(a b - b^{2}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a b - b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a b - b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{6} - 2 \, {\left(8 \, a^{2} - 11 \, a b + 3 \, b^{2}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a b - b^{2}\right)} d \cosh\left(d x + c\right)^{3} - 3 \, {\left(a b - b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a b - b^{2}\right)} d \cosh\left(d x + c\right)^{4} - 30 \, {\left(a b - b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(8 \, a^{2} - 11 \, a b + 3 \, b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{4} - 4 \, {\left(a b - b^{2}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a b - b^{2}\right)} d \cosh\left(d x + c\right)^{5} - 10 \, {\left(a b - b^{2}\right)} d \cosh\left(d x + c\right)^{3} - {\left(8 \, a^{2} - 11 \, a b + 3 \, b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a b - b^{2}\right)} d \cosh\left(d x + c\right)^{6} - 15 \, {\left(a b - b^{2}\right)} d \cosh\left(d x + c\right)^{4} - 3 \, {\left(8 \, a^{2} - 11 \, a b + 3 \, b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a b - b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a b - b^{2}\right)} d + 8 \, {\left({\left(a b - b^{2}\right)} d \cosh\left(d x + c\right)^{7} - 3 \, {\left(a b - b^{2}\right)} d \cosh\left(d x + c\right)^{5} - {\left(8 \, a^{2} - 11 \, a b + 3 \, b^{2}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a b - b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{{\left(a^{4} b - 3 \, a^{3} b^{2} + 3 \, a^{2} b^{3} - a b^{4}\right)} d^{2} \sqrt{\frac{a^{2} + 6 \, a b + 9 \, b^{2}}{{\left(a^{7} b^{3} - 6 \, a^{6} b^{4} + 15 \, a^{5} b^{5} - 20 \, a^{4} b^{6} + 15 \, a^{3} b^{7} - 6 \, a^{2} b^{8} + a b^{9}\right)} d^{4}}} - 3 \, a - b}{{\left(a^{4} b - 3 \, a^{3} b^{2} + 3 \, a^{2} b^{3} - a b^{4}\right)} d^{2}}} \log\left({\left(a + 3 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a + 3 \, b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a + 3 \, b\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(2 \, {\left(a^{2} b + 3 \, a b^{2}\right)} d \cosh\left(d x + c\right) + 2 \, {\left(a^{2} b + 3 \, a b^{2}\right)} d \sinh\left(d x + c\right) + {\left({\left(a^{5} b^{2} - 2 \, a^{4} b^{3} + 2 \, a^{2} b^{5} - a b^{6}\right)} d^{3} \cosh\left(d x + c\right) + {\left(a^{5} b^{2} - 2 \, a^{4} b^{3} + 2 \, a^{2} b^{5} - a b^{6}\right)} d^{3} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + 6 \, a b + 9 \, b^{2}}{{\left(a^{7} b^{3} - 6 \, a^{6} b^{4} + 15 \, a^{5} b^{5} - 20 \, a^{4} b^{6} + 15 \, a^{3} b^{7} - 6 \, a^{2} b^{8} + a b^{9}\right)} d^{4}}}\right)} \sqrt{\frac{{\left(a^{4} b - 3 \, a^{3} b^{2} + 3 \, a^{2} b^{3} - a b^{4}\right)} d^{2} \sqrt{\frac{a^{2} + 6 \, a b + 9 \, b^{2}}{{\left(a^{7} b^{3} - 6 \, a^{6} b^{4} + 15 \, a^{5} b^{5} - 20 \, a^{4} b^{6} + 15 \, a^{3} b^{7} - 6 \, a^{2} b^{8} + a b^{9}\right)} d^{4}}} - 3 \, a - b}{{\left(a^{4} b - 3 \, a^{3} b^{2} + 3 \, a^{2} b^{3} - a b^{4}\right)} d^{2}}} + a + 3 \, b\right) + {\left({\left(a b - b^{2}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a b - b^{2}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a b - b^{2}\right)} d \sinh\left(d x + c\right)^{8} - 4 \, {\left(a b - b^{2}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a b - b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a b - b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{6} - 2 \, {\left(8 \, a^{2} - 11 \, a b + 3 \, b^{2}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a b - b^{2}\right)} d \cosh\left(d x + c\right)^{3} - 3 \, {\left(a b - b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a b - b^{2}\right)} d \cosh\left(d x + c\right)^{4} - 30 \, {\left(a b - b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(8 \, a^{2} - 11 \, a b + 3 \, b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{4} - 4 \, {\left(a b - b^{2}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a b - b^{2}\right)} d \cosh\left(d x + c\right)^{5} - 10 \, {\left(a b - b^{2}\right)} d \cosh\left(d x + c\right)^{3} - {\left(8 \, a^{2} - 11 \, a b + 3 \, b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a b - b^{2}\right)} d \cosh\left(d x + c\right)^{6} - 15 \, {\left(a b - b^{2}\right)} d \cosh\left(d x + c\right)^{4} - 3 \, {\left(8 \, a^{2} - 11 \, a b + 3 \, b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a b - b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a b - b^{2}\right)} d + 8 \, {\left({\left(a b - b^{2}\right)} d \cosh\left(d x + c\right)^{7} - 3 \, {\left(a b - b^{2}\right)} d \cosh\left(d x + c\right)^{5} - {\left(8 \, a^{2} - 11 \, a b + 3 \, b^{2}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a b - b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{{\left(a^{4} b - 3 \, a^{3} b^{2} + 3 \, a^{2} b^{3} - a b^{4}\right)} d^{2} \sqrt{\frac{a^{2} + 6 \, a b + 9 \, b^{2}}{{\left(a^{7} b^{3} - 6 \, a^{6} b^{4} + 15 \, a^{5} b^{5} - 20 \, a^{4} b^{6} + 15 \, a^{3} b^{7} - 6 \, a^{2} b^{8} + a b^{9}\right)} d^{4}}} - 3 \, a - b}{{\left(a^{4} b - 3 \, a^{3} b^{2} + 3 \, a^{2} b^{3} - a b^{4}\right)} d^{2}}} \log\left({\left(a + 3 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a + 3 \, b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a + 3 \, b\right)} \sinh\left(d x + c\right)^{2} - 2 \, {\left(2 \, {\left(a^{2} b + 3 \, a b^{2}\right)} d \cosh\left(d x + c\right) + 2 \, {\left(a^{2} b + 3 \, a b^{2}\right)} d \sinh\left(d x + c\right) + {\left({\left(a^{5} b^{2} - 2 \, a^{4} b^{3} + 2 \, a^{2} b^{5} - a b^{6}\right)} d^{3} \cosh\left(d x + c\right) + {\left(a^{5} b^{2} - 2 \, a^{4} b^{3} + 2 \, a^{2} b^{5} - a b^{6}\right)} d^{3} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a^{2} + 6 \, a b + 9 \, b^{2}}{{\left(a^{7} b^{3} - 6 \, a^{6} b^{4} + 15 \, a^{5} b^{5} - 20 \, a^{4} b^{6} + 15 \, a^{3} b^{7} - 6 \, a^{2} b^{8} + a b^{9}\right)} d^{4}}}\right)} \sqrt{\frac{{\left(a^{4} b - 3 \, a^{3} b^{2} + 3 \, a^{2} b^{3} - a b^{4}\right)} d^{2} \sqrt{\frac{a^{2} + 6 \, a b + 9 \, b^{2}}{{\left(a^{7} b^{3} - 6 \, a^{6} b^{4} + 15 \, a^{5} b^{5} - 20 \, a^{4} b^{6} + 15 \, a^{3} b^{7} - 6 \, a^{2} b^{8} + a b^{9}\right)} d^{4}}} - 3 \, a - b}{{\left(a^{4} b - 3 \, a^{3} b^{2} + 3 \, a^{2} b^{3} - a b^{4}\right)} d^{2}}} + a + 3 \, b\right) + 8 \, {\left(7 \, \cosh\left(d x + c\right)^{6} - 25 \, \cosh\left(d x + c\right)^{4} - 15 \, \cosh\left(d x + c\right)^{2} + 1\right)} \sinh\left(d x + c\right) + 8 \, \cosh\left(d x + c\right)}{16 \, {\left({\left(a b - b^{2}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a b - b^{2}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a b - b^{2}\right)} d \sinh\left(d x + c\right)^{8} - 4 \, {\left(a b - b^{2}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a b - b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a b - b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{6} - 2 \, {\left(8 \, a^{2} - 11 \, a b + 3 \, b^{2}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a b - b^{2}\right)} d \cosh\left(d x + c\right)^{3} - 3 \, {\left(a b - b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a b - b^{2}\right)} d \cosh\left(d x + c\right)^{4} - 30 \, {\left(a b - b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(8 \, a^{2} - 11 \, a b + 3 \, b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{4} - 4 \, {\left(a b - b^{2}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a b - b^{2}\right)} d \cosh\left(d x + c\right)^{5} - 10 \, {\left(a b - b^{2}\right)} d \cosh\left(d x + c\right)^{3} - {\left(8 \, a^{2} - 11 \, a b + 3 \, b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a b - b^{2}\right)} d \cosh\left(d x + c\right)^{6} - 15 \, {\left(a b - b^{2}\right)} d \cosh\left(d x + c\right)^{4} - 3 \, {\left(8 \, a^{2} - 11 \, a b + 3 \, b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a b - b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a b - b^{2}\right)} d + 8 \, {\left({\left(a b - b^{2}\right)} d \cosh\left(d x + c\right)^{7} - 3 \, {\left(a b - b^{2}\right)} d \cosh\left(d x + c\right)^{5} - {\left(8 \, a^{2} - 11 \, a b + 3 \, b^{2}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a b - b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"-1/16*(8*cosh(d*x + c)^7 + 56*cosh(d*x + c)*sinh(d*x + c)^6 + 8*sinh(d*x + c)^7 + 8*(21*cosh(d*x + c)^2 - 5)*sinh(d*x + c)^5 - 40*cosh(d*x + c)^5 + 40*(7*cosh(d*x + c)^3 - 5*cosh(d*x + c))*sinh(d*x + c)^4 + 40*(7*cosh(d*x + c)^4 - 10*cosh(d*x + c)^2 - 1)*sinh(d*x + c)^3 - 40*cosh(d*x + c)^3 + 8*(21*cosh(d*x + c)^5 - 50*cosh(d*x + c)^3 - 15*cosh(d*x + c))*sinh(d*x + c)^2 - ((a*b - b^2)*d*cosh(d*x + c)^8 + 8*(a*b - b^2)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a*b - b^2)*d*sinh(d*x + c)^8 - 4*(a*b - b^2)*d*cosh(d*x + c)^6 + 4*(7*(a*b - b^2)*d*cosh(d*x + c)^2 - (a*b - b^2)*d)*sinh(d*x + c)^6 - 2*(8*a^2 - 11*a*b + 3*b^2)*d*cosh(d*x + c)^4 + 8*(7*(a*b - b^2)*d*cosh(d*x + c)^3 - 3*(a*b - b^2)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a*b - b^2)*d*cosh(d*x + c)^4 - 30*(a*b - b^2)*d*cosh(d*x + c)^2 - (8*a^2 - 11*a*b + 3*b^2)*d)*sinh(d*x + c)^4 - 4*(a*b - b^2)*d*cosh(d*x + c)^2 + 8*(7*(a*b - b^2)*d*cosh(d*x + c)^5 - 10*(a*b - b^2)*d*cosh(d*x + c)^3 - (8*a^2 - 11*a*b + 3*b^2)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a*b - b^2)*d*cosh(d*x + c)^6 - 15*(a*b - b^2)*d*cosh(d*x + c)^4 - 3*(8*a^2 - 11*a*b + 3*b^2)*d*cosh(d*x + c)^2 - (a*b - b^2)*d)*sinh(d*x + c)^2 + (a*b - b^2)*d + 8*((a*b - b^2)*d*cosh(d*x + c)^7 - 3*(a*b - b^2)*d*cosh(d*x + c)^5 - (8*a^2 - 11*a*b + 3*b^2)*d*cosh(d*x + c)^3 - (a*b - b^2)*d*cosh(d*x + c))*sinh(d*x + c))*sqrt(-((a^4*b - 3*a^3*b^2 + 3*a^2*b^3 - a*b^4)*d^2*sqrt((a^2 + 6*a*b + 9*b^2)/((a^7*b^3 - 6*a^6*b^4 + 15*a^5*b^5 - 20*a^4*b^6 + 15*a^3*b^7 - 6*a^2*b^8 + a*b^9)*d^4)) + 3*a + b)/((a^4*b - 3*a^3*b^2 + 3*a^2*b^3 - a*b^4)*d^2))*log((a + 3*b)*cosh(d*x + c)^2 + 2*(a + 3*b)*cosh(d*x + c)*sinh(d*x + c) + (a + 3*b)*sinh(d*x + c)^2 + 2*(2*(a^2*b + 3*a*b^2)*d*cosh(d*x + c) + 2*(a^2*b + 3*a*b^2)*d*sinh(d*x + c) - ((a^5*b^2 - 2*a^4*b^3 + 2*a^2*b^5 - a*b^6)*d^3*cosh(d*x + c) + (a^5*b^2 - 2*a^4*b^3 + 2*a^2*b^5 - a*b^6)*d^3*sinh(d*x + c))*sqrt((a^2 + 6*a*b + 9*b^2)/((a^7*b^3 - 6*a^6*b^4 + 15*a^5*b^5 - 20*a^4*b^6 + 15*a^3*b^7 - 6*a^2*b^8 + a*b^9)*d^4)))*sqrt(-((a^4*b - 3*a^3*b^2 + 3*a^2*b^3 - a*b^4)*d^2*sqrt((a^2 + 6*a*b + 9*b^2)/((a^7*b^3 - 6*a^6*b^4 + 15*a^5*b^5 - 20*a^4*b^6 + 15*a^3*b^7 - 6*a^2*b^8 + a*b^9)*d^4)) + 3*a + b)/((a^4*b - 3*a^3*b^2 + 3*a^2*b^3 - a*b^4)*d^2)) + a + 3*b) + ((a*b - b^2)*d*cosh(d*x + c)^8 + 8*(a*b - b^2)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a*b - b^2)*d*sinh(d*x + c)^8 - 4*(a*b - b^2)*d*cosh(d*x + c)^6 + 4*(7*(a*b - b^2)*d*cosh(d*x + c)^2 - (a*b - b^2)*d)*sinh(d*x + c)^6 - 2*(8*a^2 - 11*a*b + 3*b^2)*d*cosh(d*x + c)^4 + 8*(7*(a*b - b^2)*d*cosh(d*x + c)^3 - 3*(a*b - b^2)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a*b - b^2)*d*cosh(d*x + c)^4 - 30*(a*b - b^2)*d*cosh(d*x + c)^2 - (8*a^2 - 11*a*b + 3*b^2)*d)*sinh(d*x + c)^4 - 4*(a*b - b^2)*d*cosh(d*x + c)^2 + 8*(7*(a*b - b^2)*d*cosh(d*x + c)^5 - 10*(a*b - b^2)*d*cosh(d*x + c)^3 - (8*a^2 - 11*a*b + 3*b^2)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a*b - b^2)*d*cosh(d*x + c)^6 - 15*(a*b - b^2)*d*cosh(d*x + c)^4 - 3*(8*a^2 - 11*a*b + 3*b^2)*d*cosh(d*x + c)^2 - (a*b - b^2)*d)*sinh(d*x + c)^2 + (a*b - b^2)*d + 8*((a*b - b^2)*d*cosh(d*x + c)^7 - 3*(a*b - b^2)*d*cosh(d*x + c)^5 - (8*a^2 - 11*a*b + 3*b^2)*d*cosh(d*x + c)^3 - (a*b - b^2)*d*cosh(d*x + c))*sinh(d*x + c))*sqrt(-((a^4*b - 3*a^3*b^2 + 3*a^2*b^3 - a*b^4)*d^2*sqrt((a^2 + 6*a*b + 9*b^2)/((a^7*b^3 - 6*a^6*b^4 + 15*a^5*b^5 - 20*a^4*b^6 + 15*a^3*b^7 - 6*a^2*b^8 + a*b^9)*d^4)) + 3*a + b)/((a^4*b - 3*a^3*b^2 + 3*a^2*b^3 - a*b^4)*d^2))*log((a + 3*b)*cosh(d*x + c)^2 + 2*(a + 3*b)*cosh(d*x + c)*sinh(d*x + c) + (a + 3*b)*sinh(d*x + c)^2 - 2*(2*(a^2*b + 3*a*b^2)*d*cosh(d*x + c) + 2*(a^2*b + 3*a*b^2)*d*sinh(d*x + c) - ((a^5*b^2 - 2*a^4*b^3 + 2*a^2*b^5 - a*b^6)*d^3*cosh(d*x + c) + (a^5*b^2 - 2*a^4*b^3 + 2*a^2*b^5 - a*b^6)*d^3*sinh(d*x + c))*sqrt((a^2 + 6*a*b + 9*b^2)/((a^7*b^3 - 6*a^6*b^4 + 15*a^5*b^5 - 20*a^4*b^6 + 15*a^3*b^7 - 6*a^2*b^8 + a*b^9)*d^4)))*sqrt(-((a^4*b - 3*a^3*b^2 + 3*a^2*b^3 - a*b^4)*d^2*sqrt((a^2 + 6*a*b + 9*b^2)/((a^7*b^3 - 6*a^6*b^4 + 15*a^5*b^5 - 20*a^4*b^6 + 15*a^3*b^7 - 6*a^2*b^8 + a*b^9)*d^4)) + 3*a + b)/((a^4*b - 3*a^3*b^2 + 3*a^2*b^3 - a*b^4)*d^2)) + a + 3*b) - ((a*b - b^2)*d*cosh(d*x + c)^8 + 8*(a*b - b^2)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a*b - b^2)*d*sinh(d*x + c)^8 - 4*(a*b - b^2)*d*cosh(d*x + c)^6 + 4*(7*(a*b - b^2)*d*cosh(d*x + c)^2 - (a*b - b^2)*d)*sinh(d*x + c)^6 - 2*(8*a^2 - 11*a*b + 3*b^2)*d*cosh(d*x + c)^4 + 8*(7*(a*b - b^2)*d*cosh(d*x + c)^3 - 3*(a*b - b^2)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a*b - b^2)*d*cosh(d*x + c)^4 - 30*(a*b - b^2)*d*cosh(d*x + c)^2 - (8*a^2 - 11*a*b + 3*b^2)*d)*sinh(d*x + c)^4 - 4*(a*b - b^2)*d*cosh(d*x + c)^2 + 8*(7*(a*b - b^2)*d*cosh(d*x + c)^5 - 10*(a*b - b^2)*d*cosh(d*x + c)^3 - (8*a^2 - 11*a*b + 3*b^2)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a*b - b^2)*d*cosh(d*x + c)^6 - 15*(a*b - b^2)*d*cosh(d*x + c)^4 - 3*(8*a^2 - 11*a*b + 3*b^2)*d*cosh(d*x + c)^2 - (a*b - b^2)*d)*sinh(d*x + c)^2 + (a*b - b^2)*d + 8*((a*b - b^2)*d*cosh(d*x + c)^7 - 3*(a*b - b^2)*d*cosh(d*x + c)^5 - (8*a^2 - 11*a*b + 3*b^2)*d*cosh(d*x + c)^3 - (a*b - b^2)*d*cosh(d*x + c))*sinh(d*x + c))*sqrt(((a^4*b - 3*a^3*b^2 + 3*a^2*b^3 - a*b^4)*d^2*sqrt((a^2 + 6*a*b + 9*b^2)/((a^7*b^3 - 6*a^6*b^4 + 15*a^5*b^5 - 20*a^4*b^6 + 15*a^3*b^7 - 6*a^2*b^8 + a*b^9)*d^4)) - 3*a - b)/((a^4*b - 3*a^3*b^2 + 3*a^2*b^3 - a*b^4)*d^2))*log((a + 3*b)*cosh(d*x + c)^2 + 2*(a + 3*b)*cosh(d*x + c)*sinh(d*x + c) + (a + 3*b)*sinh(d*x + c)^2 + 2*(2*(a^2*b + 3*a*b^2)*d*cosh(d*x + c) + 2*(a^2*b + 3*a*b^2)*d*sinh(d*x + c) + ((a^5*b^2 - 2*a^4*b^3 + 2*a^2*b^5 - a*b^6)*d^3*cosh(d*x + c) + (a^5*b^2 - 2*a^4*b^3 + 2*a^2*b^5 - a*b^6)*d^3*sinh(d*x + c))*sqrt((a^2 + 6*a*b + 9*b^2)/((a^7*b^3 - 6*a^6*b^4 + 15*a^5*b^5 - 20*a^4*b^6 + 15*a^3*b^7 - 6*a^2*b^8 + a*b^9)*d^4)))*sqrt(((a^4*b - 3*a^3*b^2 + 3*a^2*b^3 - a*b^4)*d^2*sqrt((a^2 + 6*a*b + 9*b^2)/((a^7*b^3 - 6*a^6*b^4 + 15*a^5*b^5 - 20*a^4*b^6 + 15*a^3*b^7 - 6*a^2*b^8 + a*b^9)*d^4)) - 3*a - b)/((a^4*b - 3*a^3*b^2 + 3*a^2*b^3 - a*b^4)*d^2)) + a + 3*b) + ((a*b - b^2)*d*cosh(d*x + c)^8 + 8*(a*b - b^2)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a*b - b^2)*d*sinh(d*x + c)^8 - 4*(a*b - b^2)*d*cosh(d*x + c)^6 + 4*(7*(a*b - b^2)*d*cosh(d*x + c)^2 - (a*b - b^2)*d)*sinh(d*x + c)^6 - 2*(8*a^2 - 11*a*b + 3*b^2)*d*cosh(d*x + c)^4 + 8*(7*(a*b - b^2)*d*cosh(d*x + c)^3 - 3*(a*b - b^2)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a*b - b^2)*d*cosh(d*x + c)^4 - 30*(a*b - b^2)*d*cosh(d*x + c)^2 - (8*a^2 - 11*a*b + 3*b^2)*d)*sinh(d*x + c)^4 - 4*(a*b - b^2)*d*cosh(d*x + c)^2 + 8*(7*(a*b - b^2)*d*cosh(d*x + c)^5 - 10*(a*b - b^2)*d*cosh(d*x + c)^3 - (8*a^2 - 11*a*b + 3*b^2)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a*b - b^2)*d*cosh(d*x + c)^6 - 15*(a*b - b^2)*d*cosh(d*x + c)^4 - 3*(8*a^2 - 11*a*b + 3*b^2)*d*cosh(d*x + c)^2 - (a*b - b^2)*d)*sinh(d*x + c)^2 + (a*b - b^2)*d + 8*((a*b - b^2)*d*cosh(d*x + c)^7 - 3*(a*b - b^2)*d*cosh(d*x + c)^5 - (8*a^2 - 11*a*b + 3*b^2)*d*cosh(d*x + c)^3 - (a*b - b^2)*d*cosh(d*x + c))*sinh(d*x + c))*sqrt(((a^4*b - 3*a^3*b^2 + 3*a^2*b^3 - a*b^4)*d^2*sqrt((a^2 + 6*a*b + 9*b^2)/((a^7*b^3 - 6*a^6*b^4 + 15*a^5*b^5 - 20*a^4*b^6 + 15*a^3*b^7 - 6*a^2*b^8 + a*b^9)*d^4)) - 3*a - b)/((a^4*b - 3*a^3*b^2 + 3*a^2*b^3 - a*b^4)*d^2))*log((a + 3*b)*cosh(d*x + c)^2 + 2*(a + 3*b)*cosh(d*x + c)*sinh(d*x + c) + (a + 3*b)*sinh(d*x + c)^2 - 2*(2*(a^2*b + 3*a*b^2)*d*cosh(d*x + c) + 2*(a^2*b + 3*a*b^2)*d*sinh(d*x + c) + ((a^5*b^2 - 2*a^4*b^3 + 2*a^2*b^5 - a*b^6)*d^3*cosh(d*x + c) + (a^5*b^2 - 2*a^4*b^3 + 2*a^2*b^5 - a*b^6)*d^3*sinh(d*x + c))*sqrt((a^2 + 6*a*b + 9*b^2)/((a^7*b^3 - 6*a^6*b^4 + 15*a^5*b^5 - 20*a^4*b^6 + 15*a^3*b^7 - 6*a^2*b^8 + a*b^9)*d^4)))*sqrt(((a^4*b - 3*a^3*b^2 + 3*a^2*b^3 - a*b^4)*d^2*sqrt((a^2 + 6*a*b + 9*b^2)/((a^7*b^3 - 6*a^6*b^4 + 15*a^5*b^5 - 20*a^4*b^6 + 15*a^3*b^7 - 6*a^2*b^8 + a*b^9)*d^4)) - 3*a - b)/((a^4*b - 3*a^3*b^2 + 3*a^2*b^3 - a*b^4)*d^2)) + a + 3*b) + 8*(7*cosh(d*x + c)^6 - 25*cosh(d*x + c)^4 - 15*cosh(d*x + c)^2 + 1)*sinh(d*x + c) + 8*cosh(d*x + c))/((a*b - b^2)*d*cosh(d*x + c)^8 + 8*(a*b - b^2)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a*b - b^2)*d*sinh(d*x + c)^8 - 4*(a*b - b^2)*d*cosh(d*x + c)^6 + 4*(7*(a*b - b^2)*d*cosh(d*x + c)^2 - (a*b - b^2)*d)*sinh(d*x + c)^6 - 2*(8*a^2 - 11*a*b + 3*b^2)*d*cosh(d*x + c)^4 + 8*(7*(a*b - b^2)*d*cosh(d*x + c)^3 - 3*(a*b - b^2)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a*b - b^2)*d*cosh(d*x + c)^4 - 30*(a*b - b^2)*d*cosh(d*x + c)^2 - (8*a^2 - 11*a*b + 3*b^2)*d)*sinh(d*x + c)^4 - 4*(a*b - b^2)*d*cosh(d*x + c)^2 + 8*(7*(a*b - b^2)*d*cosh(d*x + c)^5 - 10*(a*b - b^2)*d*cosh(d*x + c)^3 - (8*a^2 - 11*a*b + 3*b^2)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a*b - b^2)*d*cosh(d*x + c)^6 - 15*(a*b - b^2)*d*cosh(d*x + c)^4 - 3*(8*a^2 - 11*a*b + 3*b^2)*d*cosh(d*x + c)^2 - (a*b - b^2)*d)*sinh(d*x + c)^2 + (a*b - b^2)*d + 8*((a*b - b^2)*d*cosh(d*x + c)^7 - 3*(a*b - b^2)*d*cosh(d*x + c)^5 - (8*a^2 - 11*a*b + 3*b^2)*d*cosh(d*x + c)^3 - (a*b - b^2)*d*cosh(d*x + c))*sinh(d*x + c))","B",0
245,1,6018,0,0.877248," ","integrate(sinh(d*x+c)/(a-b*sinh(d*x+c)^4)^2,x, algorithm=""fricas"")","\frac{8 \, b \cosh\left(d x + c\right)^{7} + 56 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + 8 \, b \sinh\left(d x + c\right)^{7} - 8 \, {\left(4 \, a + b\right)} \cosh\left(d x + c\right)^{5} + 8 \, {\left(21 \, b \cosh\left(d x + c\right)^{2} - 4 \, a - b\right)} \sinh\left(d x + c\right)^{5} + 40 \, {\left(7 \, b \cosh\left(d x + c\right)^{3} - {\left(4 \, a + b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} - 8 \, {\left(4 \, a + b\right)} \cosh\left(d x + c\right)^{3} + 8 \, {\left(35 \, b \cosh\left(d x + c\right)^{4} - 10 \, {\left(4 \, a + b\right)} \cosh\left(d x + c\right)^{2} - 4 \, a - b\right)} \sinh\left(d x + c\right)^{3} + 8 \, {\left(21 \, b \cosh\left(d x + c\right)^{5} - 10 \, {\left(4 \, a + b\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(4 \, a + b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{2} b - a b^{2}\right)} d \sinh\left(d x + c\right)^{8} - 4 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{2} b - a b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{6} - 2 \, {\left(8 \, a^{3} - 11 \, a^{2} b + 3 \, a b^{2}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{4} - 30 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(8 \, a^{3} - 11 \, a^{2} b + 3 \, a b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{4} - 4 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{5} - 10 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{3} - {\left(8 \, a^{3} - 11 \, a^{2} b + 3 \, a b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{6} - 15 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{4} - 3 \, {\left(8 \, a^{3} - 11 \, a^{2} b + 3 \, a b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{2} b - a b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{2} b - a b^{2}\right)} d + 8 \, {\left({\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{7} - 3 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{5} - {\left(8 \, a^{3} - 11 \, a^{2} b + 3 \, a b^{2}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{{\left(a^{6} - 3 \, a^{5} b + 3 \, a^{4} b^{2} - a^{3} b^{3}\right)} d^{2} \sqrt{\frac{81 \, a^{2} - 90 \, a b + 25 \, b^{2}}{{\left(a^{9} b - 6 \, a^{8} b^{2} + 15 \, a^{7} b^{3} - 20 \, a^{6} b^{4} + 15 \, a^{5} b^{5} - 6 \, a^{4} b^{6} + a^{3} b^{7}\right)} d^{4}}} + 15 \, a^{2} - 15 \, a b + 4 \, b^{2}}{{\left(a^{6} - 3 \, a^{5} b + 3 \, a^{4} b^{2} - a^{3} b^{3}\right)} d^{2}}} \log\left({\left(81 \, a^{2} - 81 \, a b + 20 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(81 \, a^{2} - 81 \, a b + 20 \, b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(81 \, a^{2} - 81 \, a b + 20 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} + 81 \, a^{2} - 81 \, a b + 20 \, b^{2} + 2 \, {\left({\left(27 \, a^{4} - 24 \, a^{3} b + 5 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right) + {\left(27 \, a^{4} - 24 \, a^{3} b + 5 \, a^{2} b^{2}\right)} d \sinh\left(d x + c\right) - 2 \, {\left({\left(2 \, a^{7} b - 7 \, a^{6} b^{2} + 9 \, a^{5} b^{3} - 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} d^{3} \cosh\left(d x + c\right) + {\left(2 \, a^{7} b - 7 \, a^{6} b^{2} + 9 \, a^{5} b^{3} - 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} d^{3} \sinh\left(d x + c\right)\right)} \sqrt{\frac{81 \, a^{2} - 90 \, a b + 25 \, b^{2}}{{\left(a^{9} b - 6 \, a^{8} b^{2} + 15 \, a^{7} b^{3} - 20 \, a^{6} b^{4} + 15 \, a^{5} b^{5} - 6 \, a^{4} b^{6} + a^{3} b^{7}\right)} d^{4}}}\right)} \sqrt{-\frac{{\left(a^{6} - 3 \, a^{5} b + 3 \, a^{4} b^{2} - a^{3} b^{3}\right)} d^{2} \sqrt{\frac{81 \, a^{2} - 90 \, a b + 25 \, b^{2}}{{\left(a^{9} b - 6 \, a^{8} b^{2} + 15 \, a^{7} b^{3} - 20 \, a^{6} b^{4} + 15 \, a^{5} b^{5} - 6 \, a^{4} b^{6} + a^{3} b^{7}\right)} d^{4}}} + 15 \, a^{2} - 15 \, a b + 4 \, b^{2}}{{\left(a^{6} - 3 \, a^{5} b + 3 \, a^{4} b^{2} - a^{3} b^{3}\right)} d^{2}}}\right) - {\left({\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{2} b - a b^{2}\right)} d \sinh\left(d x + c\right)^{8} - 4 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{2} b - a b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{6} - 2 \, {\left(8 \, a^{3} - 11 \, a^{2} b + 3 \, a b^{2}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{4} - 30 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(8 \, a^{3} - 11 \, a^{2} b + 3 \, a b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{4} - 4 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{5} - 10 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{3} - {\left(8 \, a^{3} - 11 \, a^{2} b + 3 \, a b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{6} - 15 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{4} - 3 \, {\left(8 \, a^{3} - 11 \, a^{2} b + 3 \, a b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{2} b - a b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{2} b - a b^{2}\right)} d + 8 \, {\left({\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{7} - 3 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{5} - {\left(8 \, a^{3} - 11 \, a^{2} b + 3 \, a b^{2}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{{\left(a^{6} - 3 \, a^{5} b + 3 \, a^{4} b^{2} - a^{3} b^{3}\right)} d^{2} \sqrt{\frac{81 \, a^{2} - 90 \, a b + 25 \, b^{2}}{{\left(a^{9} b - 6 \, a^{8} b^{2} + 15 \, a^{7} b^{3} - 20 \, a^{6} b^{4} + 15 \, a^{5} b^{5} - 6 \, a^{4} b^{6} + a^{3} b^{7}\right)} d^{4}}} + 15 \, a^{2} - 15 \, a b + 4 \, b^{2}}{{\left(a^{6} - 3 \, a^{5} b + 3 \, a^{4} b^{2} - a^{3} b^{3}\right)} d^{2}}} \log\left({\left(81 \, a^{2} - 81 \, a b + 20 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(81 \, a^{2} - 81 \, a b + 20 \, b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(81 \, a^{2} - 81 \, a b + 20 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} + 81 \, a^{2} - 81 \, a b + 20 \, b^{2} - 2 \, {\left({\left(27 \, a^{4} - 24 \, a^{3} b + 5 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right) + {\left(27 \, a^{4} - 24 \, a^{3} b + 5 \, a^{2} b^{2}\right)} d \sinh\left(d x + c\right) - 2 \, {\left({\left(2 \, a^{7} b - 7 \, a^{6} b^{2} + 9 \, a^{5} b^{3} - 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} d^{3} \cosh\left(d x + c\right) + {\left(2 \, a^{7} b - 7 \, a^{6} b^{2} + 9 \, a^{5} b^{3} - 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} d^{3} \sinh\left(d x + c\right)\right)} \sqrt{\frac{81 \, a^{2} - 90 \, a b + 25 \, b^{2}}{{\left(a^{9} b - 6 \, a^{8} b^{2} + 15 \, a^{7} b^{3} - 20 \, a^{6} b^{4} + 15 \, a^{5} b^{5} - 6 \, a^{4} b^{6} + a^{3} b^{7}\right)} d^{4}}}\right)} \sqrt{-\frac{{\left(a^{6} - 3 \, a^{5} b + 3 \, a^{4} b^{2} - a^{3} b^{3}\right)} d^{2} \sqrt{\frac{81 \, a^{2} - 90 \, a b + 25 \, b^{2}}{{\left(a^{9} b - 6 \, a^{8} b^{2} + 15 \, a^{7} b^{3} - 20 \, a^{6} b^{4} + 15 \, a^{5} b^{5} - 6 \, a^{4} b^{6} + a^{3} b^{7}\right)} d^{4}}} + 15 \, a^{2} - 15 \, a b + 4 \, b^{2}}{{\left(a^{6} - 3 \, a^{5} b + 3 \, a^{4} b^{2} - a^{3} b^{3}\right)} d^{2}}}\right) + {\left({\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{2} b - a b^{2}\right)} d \sinh\left(d x + c\right)^{8} - 4 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{2} b - a b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{6} - 2 \, {\left(8 \, a^{3} - 11 \, a^{2} b + 3 \, a b^{2}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{4} - 30 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(8 \, a^{3} - 11 \, a^{2} b + 3 \, a b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{4} - 4 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{5} - 10 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{3} - {\left(8 \, a^{3} - 11 \, a^{2} b + 3 \, a b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{6} - 15 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{4} - 3 \, {\left(8 \, a^{3} - 11 \, a^{2} b + 3 \, a b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{2} b - a b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{2} b - a b^{2}\right)} d + 8 \, {\left({\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{7} - 3 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{5} - {\left(8 \, a^{3} - 11 \, a^{2} b + 3 \, a b^{2}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{{\left(a^{6} - 3 \, a^{5} b + 3 \, a^{4} b^{2} - a^{3} b^{3}\right)} d^{2} \sqrt{\frac{81 \, a^{2} - 90 \, a b + 25 \, b^{2}}{{\left(a^{9} b - 6 \, a^{8} b^{2} + 15 \, a^{7} b^{3} - 20 \, a^{6} b^{4} + 15 \, a^{5} b^{5} - 6 \, a^{4} b^{6} + a^{3} b^{7}\right)} d^{4}}} - 15 \, a^{2} + 15 \, a b - 4 \, b^{2}}{{\left(a^{6} - 3 \, a^{5} b + 3 \, a^{4} b^{2} - a^{3} b^{3}\right)} d^{2}}} \log\left({\left(81 \, a^{2} - 81 \, a b + 20 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(81 \, a^{2} - 81 \, a b + 20 \, b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(81 \, a^{2} - 81 \, a b + 20 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} + 81 \, a^{2} - 81 \, a b + 20 \, b^{2} + 2 \, {\left({\left(27 \, a^{4} - 24 \, a^{3} b + 5 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right) + {\left(27 \, a^{4} - 24 \, a^{3} b + 5 \, a^{2} b^{2}\right)} d \sinh\left(d x + c\right) + 2 \, {\left({\left(2 \, a^{7} b - 7 \, a^{6} b^{2} + 9 \, a^{5} b^{3} - 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} d^{3} \cosh\left(d x + c\right) + {\left(2 \, a^{7} b - 7 \, a^{6} b^{2} + 9 \, a^{5} b^{3} - 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} d^{3} \sinh\left(d x + c\right)\right)} \sqrt{\frac{81 \, a^{2} - 90 \, a b + 25 \, b^{2}}{{\left(a^{9} b - 6 \, a^{8} b^{2} + 15 \, a^{7} b^{3} - 20 \, a^{6} b^{4} + 15 \, a^{5} b^{5} - 6 \, a^{4} b^{6} + a^{3} b^{7}\right)} d^{4}}}\right)} \sqrt{\frac{{\left(a^{6} - 3 \, a^{5} b + 3 \, a^{4} b^{2} - a^{3} b^{3}\right)} d^{2} \sqrt{\frac{81 \, a^{2} - 90 \, a b + 25 \, b^{2}}{{\left(a^{9} b - 6 \, a^{8} b^{2} + 15 \, a^{7} b^{3} - 20 \, a^{6} b^{4} + 15 \, a^{5} b^{5} - 6 \, a^{4} b^{6} + a^{3} b^{7}\right)} d^{4}}} - 15 \, a^{2} + 15 \, a b - 4 \, b^{2}}{{\left(a^{6} - 3 \, a^{5} b + 3 \, a^{4} b^{2} - a^{3} b^{3}\right)} d^{2}}}\right) - {\left({\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{2} b - a b^{2}\right)} d \sinh\left(d x + c\right)^{8} - 4 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{2} b - a b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{6} - 2 \, {\left(8 \, a^{3} - 11 \, a^{2} b + 3 \, a b^{2}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{4} - 30 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(8 \, a^{3} - 11 \, a^{2} b + 3 \, a b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{4} - 4 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{5} - 10 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{3} - {\left(8 \, a^{3} - 11 \, a^{2} b + 3 \, a b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{6} - 15 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{4} - 3 \, {\left(8 \, a^{3} - 11 \, a^{2} b + 3 \, a b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{2} b - a b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{2} b - a b^{2}\right)} d + 8 \, {\left({\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{7} - 3 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{5} - {\left(8 \, a^{3} - 11 \, a^{2} b + 3 \, a b^{2}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{{\left(a^{6} - 3 \, a^{5} b + 3 \, a^{4} b^{2} - a^{3} b^{3}\right)} d^{2} \sqrt{\frac{81 \, a^{2} - 90 \, a b + 25 \, b^{2}}{{\left(a^{9} b - 6 \, a^{8} b^{2} + 15 \, a^{7} b^{3} - 20 \, a^{6} b^{4} + 15 \, a^{5} b^{5} - 6 \, a^{4} b^{6} + a^{3} b^{7}\right)} d^{4}}} - 15 \, a^{2} + 15 \, a b - 4 \, b^{2}}{{\left(a^{6} - 3 \, a^{5} b + 3 \, a^{4} b^{2} - a^{3} b^{3}\right)} d^{2}}} \log\left({\left(81 \, a^{2} - 81 \, a b + 20 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(81 \, a^{2} - 81 \, a b + 20 \, b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(81 \, a^{2} - 81 \, a b + 20 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} + 81 \, a^{2} - 81 \, a b + 20 \, b^{2} - 2 \, {\left({\left(27 \, a^{4} - 24 \, a^{3} b + 5 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right) + {\left(27 \, a^{4} - 24 \, a^{3} b + 5 \, a^{2} b^{2}\right)} d \sinh\left(d x + c\right) + 2 \, {\left({\left(2 \, a^{7} b - 7 \, a^{6} b^{2} + 9 \, a^{5} b^{3} - 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} d^{3} \cosh\left(d x + c\right) + {\left(2 \, a^{7} b - 7 \, a^{6} b^{2} + 9 \, a^{5} b^{3} - 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} d^{3} \sinh\left(d x + c\right)\right)} \sqrt{\frac{81 \, a^{2} - 90 \, a b + 25 \, b^{2}}{{\left(a^{9} b - 6 \, a^{8} b^{2} + 15 \, a^{7} b^{3} - 20 \, a^{6} b^{4} + 15 \, a^{5} b^{5} - 6 \, a^{4} b^{6} + a^{3} b^{7}\right)} d^{4}}}\right)} \sqrt{\frac{{\left(a^{6} - 3 \, a^{5} b + 3 \, a^{4} b^{2} - a^{3} b^{3}\right)} d^{2} \sqrt{\frac{81 \, a^{2} - 90 \, a b + 25 \, b^{2}}{{\left(a^{9} b - 6 \, a^{8} b^{2} + 15 \, a^{7} b^{3} - 20 \, a^{6} b^{4} + 15 \, a^{5} b^{5} - 6 \, a^{4} b^{6} + a^{3} b^{7}\right)} d^{4}}} - 15 \, a^{2} + 15 \, a b - 4 \, b^{2}}{{\left(a^{6} - 3 \, a^{5} b + 3 \, a^{4} b^{2} - a^{3} b^{3}\right)} d^{2}}}\right) + 8 \, b \cosh\left(d x + c\right) + 8 \, {\left(7 \, b \cosh\left(d x + c\right)^{6} - 5 \, {\left(4 \, a + b\right)} \cosh\left(d x + c\right)^{4} - 3 \, {\left(4 \, a + b\right)} \cosh\left(d x + c\right)^{2} + b\right)} \sinh\left(d x + c\right)}{16 \, {\left({\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{2} b - a b^{2}\right)} d \sinh\left(d x + c\right)^{8} - 4 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{2} b - a b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{6} - 2 \, {\left(8 \, a^{3} - 11 \, a^{2} b + 3 \, a b^{2}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{4} - 30 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(8 \, a^{3} - 11 \, a^{2} b + 3 \, a b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{4} - 4 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{5} - 10 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{3} - {\left(8 \, a^{3} - 11 \, a^{2} b + 3 \, a b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{6} - 15 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{4} - 3 \, {\left(8 \, a^{3} - 11 \, a^{2} b + 3 \, a b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{2} b - a b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{2} b - a b^{2}\right)} d + 8 \, {\left({\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{7} - 3 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{5} - {\left(8 \, a^{3} - 11 \, a^{2} b + 3 \, a b^{2}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"1/16*(8*b*cosh(d*x + c)^7 + 56*b*cosh(d*x + c)*sinh(d*x + c)^6 + 8*b*sinh(d*x + c)^7 - 8*(4*a + b)*cosh(d*x + c)^5 + 8*(21*b*cosh(d*x + c)^2 - 4*a - b)*sinh(d*x + c)^5 + 40*(7*b*cosh(d*x + c)^3 - (4*a + b)*cosh(d*x + c))*sinh(d*x + c)^4 - 8*(4*a + b)*cosh(d*x + c)^3 + 8*(35*b*cosh(d*x + c)^4 - 10*(4*a + b)*cosh(d*x + c)^2 - 4*a - b)*sinh(d*x + c)^3 + 8*(21*b*cosh(d*x + c)^5 - 10*(4*a + b)*cosh(d*x + c)^3 - 3*(4*a + b)*cosh(d*x + c))*sinh(d*x + c)^2 + ((a^2*b - a*b^2)*d*cosh(d*x + c)^8 + 8*(a^2*b - a*b^2)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^2*b - a*b^2)*d*sinh(d*x + c)^8 - 4*(a^2*b - a*b^2)*d*cosh(d*x + c)^6 + 4*(7*(a^2*b - a*b^2)*d*cosh(d*x + c)^2 - (a^2*b - a*b^2)*d)*sinh(d*x + c)^6 - 2*(8*a^3 - 11*a^2*b + 3*a*b^2)*d*cosh(d*x + c)^4 + 8*(7*(a^2*b - a*b^2)*d*cosh(d*x + c)^3 - 3*(a^2*b - a*b^2)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^2*b - a*b^2)*d*cosh(d*x + c)^4 - 30*(a^2*b - a*b^2)*d*cosh(d*x + c)^2 - (8*a^3 - 11*a^2*b + 3*a*b^2)*d)*sinh(d*x + c)^4 - 4*(a^2*b - a*b^2)*d*cosh(d*x + c)^2 + 8*(7*(a^2*b - a*b^2)*d*cosh(d*x + c)^5 - 10*(a^2*b - a*b^2)*d*cosh(d*x + c)^3 - (8*a^3 - 11*a^2*b + 3*a*b^2)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^2*b - a*b^2)*d*cosh(d*x + c)^6 - 15*(a^2*b - a*b^2)*d*cosh(d*x + c)^4 - 3*(8*a^3 - 11*a^2*b + 3*a*b^2)*d*cosh(d*x + c)^2 - (a^2*b - a*b^2)*d)*sinh(d*x + c)^2 + (a^2*b - a*b^2)*d + 8*((a^2*b - a*b^2)*d*cosh(d*x + c)^7 - 3*(a^2*b - a*b^2)*d*cosh(d*x + c)^5 - (8*a^3 - 11*a^2*b + 3*a*b^2)*d*cosh(d*x + c)^3 - (a^2*b - a*b^2)*d*cosh(d*x + c))*sinh(d*x + c))*sqrt(-((a^6 - 3*a^5*b + 3*a^4*b^2 - a^3*b^3)*d^2*sqrt((81*a^2 - 90*a*b + 25*b^2)/((a^9*b - 6*a^8*b^2 + 15*a^7*b^3 - 20*a^6*b^4 + 15*a^5*b^5 - 6*a^4*b^6 + a^3*b^7)*d^4)) + 15*a^2 - 15*a*b + 4*b^2)/((a^6 - 3*a^5*b + 3*a^4*b^2 - a^3*b^3)*d^2))*log((81*a^2 - 81*a*b + 20*b^2)*cosh(d*x + c)^2 + 2*(81*a^2 - 81*a*b + 20*b^2)*cosh(d*x + c)*sinh(d*x + c) + (81*a^2 - 81*a*b + 20*b^2)*sinh(d*x + c)^2 + 81*a^2 - 81*a*b + 20*b^2 + 2*((27*a^4 - 24*a^3*b + 5*a^2*b^2)*d*cosh(d*x + c) + (27*a^4 - 24*a^3*b + 5*a^2*b^2)*d*sinh(d*x + c) - 2*((2*a^7*b - 7*a^6*b^2 + 9*a^5*b^3 - 5*a^4*b^4 + a^3*b^5)*d^3*cosh(d*x + c) + (2*a^7*b - 7*a^6*b^2 + 9*a^5*b^3 - 5*a^4*b^4 + a^3*b^5)*d^3*sinh(d*x + c))*sqrt((81*a^2 - 90*a*b + 25*b^2)/((a^9*b - 6*a^8*b^2 + 15*a^7*b^3 - 20*a^6*b^4 + 15*a^5*b^5 - 6*a^4*b^6 + a^3*b^7)*d^4)))*sqrt(-((a^6 - 3*a^5*b + 3*a^4*b^2 - a^3*b^3)*d^2*sqrt((81*a^2 - 90*a*b + 25*b^2)/((a^9*b - 6*a^8*b^2 + 15*a^7*b^3 - 20*a^6*b^4 + 15*a^5*b^5 - 6*a^4*b^6 + a^3*b^7)*d^4)) + 15*a^2 - 15*a*b + 4*b^2)/((a^6 - 3*a^5*b + 3*a^4*b^2 - a^3*b^3)*d^2))) - ((a^2*b - a*b^2)*d*cosh(d*x + c)^8 + 8*(a^2*b - a*b^2)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^2*b - a*b^2)*d*sinh(d*x + c)^8 - 4*(a^2*b - a*b^2)*d*cosh(d*x + c)^6 + 4*(7*(a^2*b - a*b^2)*d*cosh(d*x + c)^2 - (a^2*b - a*b^2)*d)*sinh(d*x + c)^6 - 2*(8*a^3 - 11*a^2*b + 3*a*b^2)*d*cosh(d*x + c)^4 + 8*(7*(a^2*b - a*b^2)*d*cosh(d*x + c)^3 - 3*(a^2*b - a*b^2)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^2*b - a*b^2)*d*cosh(d*x + c)^4 - 30*(a^2*b - a*b^2)*d*cosh(d*x + c)^2 - (8*a^3 - 11*a^2*b + 3*a*b^2)*d)*sinh(d*x + c)^4 - 4*(a^2*b - a*b^2)*d*cosh(d*x + c)^2 + 8*(7*(a^2*b - a*b^2)*d*cosh(d*x + c)^5 - 10*(a^2*b - a*b^2)*d*cosh(d*x + c)^3 - (8*a^3 - 11*a^2*b + 3*a*b^2)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^2*b - a*b^2)*d*cosh(d*x + c)^6 - 15*(a^2*b - a*b^2)*d*cosh(d*x + c)^4 - 3*(8*a^3 - 11*a^2*b + 3*a*b^2)*d*cosh(d*x + c)^2 - (a^2*b - a*b^2)*d)*sinh(d*x + c)^2 + (a^2*b - a*b^2)*d + 8*((a^2*b - a*b^2)*d*cosh(d*x + c)^7 - 3*(a^2*b - a*b^2)*d*cosh(d*x + c)^5 - (8*a^3 - 11*a^2*b + 3*a*b^2)*d*cosh(d*x + c)^3 - (a^2*b - a*b^2)*d*cosh(d*x + c))*sinh(d*x + c))*sqrt(-((a^6 - 3*a^5*b + 3*a^4*b^2 - a^3*b^3)*d^2*sqrt((81*a^2 - 90*a*b + 25*b^2)/((a^9*b - 6*a^8*b^2 + 15*a^7*b^3 - 20*a^6*b^4 + 15*a^5*b^5 - 6*a^4*b^6 + a^3*b^7)*d^4)) + 15*a^2 - 15*a*b + 4*b^2)/((a^6 - 3*a^5*b + 3*a^4*b^2 - a^3*b^3)*d^2))*log((81*a^2 - 81*a*b + 20*b^2)*cosh(d*x + c)^2 + 2*(81*a^2 - 81*a*b + 20*b^2)*cosh(d*x + c)*sinh(d*x + c) + (81*a^2 - 81*a*b + 20*b^2)*sinh(d*x + c)^2 + 81*a^2 - 81*a*b + 20*b^2 - 2*((27*a^4 - 24*a^3*b + 5*a^2*b^2)*d*cosh(d*x + c) + (27*a^4 - 24*a^3*b + 5*a^2*b^2)*d*sinh(d*x + c) - 2*((2*a^7*b - 7*a^6*b^2 + 9*a^5*b^3 - 5*a^4*b^4 + a^3*b^5)*d^3*cosh(d*x + c) + (2*a^7*b - 7*a^6*b^2 + 9*a^5*b^3 - 5*a^4*b^4 + a^3*b^5)*d^3*sinh(d*x + c))*sqrt((81*a^2 - 90*a*b + 25*b^2)/((a^9*b - 6*a^8*b^2 + 15*a^7*b^3 - 20*a^6*b^4 + 15*a^5*b^5 - 6*a^4*b^6 + a^3*b^7)*d^4)))*sqrt(-((a^6 - 3*a^5*b + 3*a^4*b^2 - a^3*b^3)*d^2*sqrt((81*a^2 - 90*a*b + 25*b^2)/((a^9*b - 6*a^8*b^2 + 15*a^7*b^3 - 20*a^6*b^4 + 15*a^5*b^5 - 6*a^4*b^6 + a^3*b^7)*d^4)) + 15*a^2 - 15*a*b + 4*b^2)/((a^6 - 3*a^5*b + 3*a^4*b^2 - a^3*b^3)*d^2))) + ((a^2*b - a*b^2)*d*cosh(d*x + c)^8 + 8*(a^2*b - a*b^2)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^2*b - a*b^2)*d*sinh(d*x + c)^8 - 4*(a^2*b - a*b^2)*d*cosh(d*x + c)^6 + 4*(7*(a^2*b - a*b^2)*d*cosh(d*x + c)^2 - (a^2*b - a*b^2)*d)*sinh(d*x + c)^6 - 2*(8*a^3 - 11*a^2*b + 3*a*b^2)*d*cosh(d*x + c)^4 + 8*(7*(a^2*b - a*b^2)*d*cosh(d*x + c)^3 - 3*(a^2*b - a*b^2)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^2*b - a*b^2)*d*cosh(d*x + c)^4 - 30*(a^2*b - a*b^2)*d*cosh(d*x + c)^2 - (8*a^3 - 11*a^2*b + 3*a*b^2)*d)*sinh(d*x + c)^4 - 4*(a^2*b - a*b^2)*d*cosh(d*x + c)^2 + 8*(7*(a^2*b - a*b^2)*d*cosh(d*x + c)^5 - 10*(a^2*b - a*b^2)*d*cosh(d*x + c)^3 - (8*a^3 - 11*a^2*b + 3*a*b^2)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^2*b - a*b^2)*d*cosh(d*x + c)^6 - 15*(a^2*b - a*b^2)*d*cosh(d*x + c)^4 - 3*(8*a^3 - 11*a^2*b + 3*a*b^2)*d*cosh(d*x + c)^2 - (a^2*b - a*b^2)*d)*sinh(d*x + c)^2 + (a^2*b - a*b^2)*d + 8*((a^2*b - a*b^2)*d*cosh(d*x + c)^7 - 3*(a^2*b - a*b^2)*d*cosh(d*x + c)^5 - (8*a^3 - 11*a^2*b + 3*a*b^2)*d*cosh(d*x + c)^3 - (a^2*b - a*b^2)*d*cosh(d*x + c))*sinh(d*x + c))*sqrt(((a^6 - 3*a^5*b + 3*a^4*b^2 - a^3*b^3)*d^2*sqrt((81*a^2 - 90*a*b + 25*b^2)/((a^9*b - 6*a^8*b^2 + 15*a^7*b^3 - 20*a^6*b^4 + 15*a^5*b^5 - 6*a^4*b^6 + a^3*b^7)*d^4)) - 15*a^2 + 15*a*b - 4*b^2)/((a^6 - 3*a^5*b + 3*a^4*b^2 - a^3*b^3)*d^2))*log((81*a^2 - 81*a*b + 20*b^2)*cosh(d*x + c)^2 + 2*(81*a^2 - 81*a*b + 20*b^2)*cosh(d*x + c)*sinh(d*x + c) + (81*a^2 - 81*a*b + 20*b^2)*sinh(d*x + c)^2 + 81*a^2 - 81*a*b + 20*b^2 + 2*((27*a^4 - 24*a^3*b + 5*a^2*b^2)*d*cosh(d*x + c) + (27*a^4 - 24*a^3*b + 5*a^2*b^2)*d*sinh(d*x + c) + 2*((2*a^7*b - 7*a^6*b^2 + 9*a^5*b^3 - 5*a^4*b^4 + a^3*b^5)*d^3*cosh(d*x + c) + (2*a^7*b - 7*a^6*b^2 + 9*a^5*b^3 - 5*a^4*b^4 + a^3*b^5)*d^3*sinh(d*x + c))*sqrt((81*a^2 - 90*a*b + 25*b^2)/((a^9*b - 6*a^8*b^2 + 15*a^7*b^3 - 20*a^6*b^4 + 15*a^5*b^5 - 6*a^4*b^6 + a^3*b^7)*d^4)))*sqrt(((a^6 - 3*a^5*b + 3*a^4*b^2 - a^3*b^3)*d^2*sqrt((81*a^2 - 90*a*b + 25*b^2)/((a^9*b - 6*a^8*b^2 + 15*a^7*b^3 - 20*a^6*b^4 + 15*a^5*b^5 - 6*a^4*b^6 + a^3*b^7)*d^4)) - 15*a^2 + 15*a*b - 4*b^2)/((a^6 - 3*a^5*b + 3*a^4*b^2 - a^3*b^3)*d^2))) - ((a^2*b - a*b^2)*d*cosh(d*x + c)^8 + 8*(a^2*b - a*b^2)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^2*b - a*b^2)*d*sinh(d*x + c)^8 - 4*(a^2*b - a*b^2)*d*cosh(d*x + c)^6 + 4*(7*(a^2*b - a*b^2)*d*cosh(d*x + c)^2 - (a^2*b - a*b^2)*d)*sinh(d*x + c)^6 - 2*(8*a^3 - 11*a^2*b + 3*a*b^2)*d*cosh(d*x + c)^4 + 8*(7*(a^2*b - a*b^2)*d*cosh(d*x + c)^3 - 3*(a^2*b - a*b^2)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^2*b - a*b^2)*d*cosh(d*x + c)^4 - 30*(a^2*b - a*b^2)*d*cosh(d*x + c)^2 - (8*a^3 - 11*a^2*b + 3*a*b^2)*d)*sinh(d*x + c)^4 - 4*(a^2*b - a*b^2)*d*cosh(d*x + c)^2 + 8*(7*(a^2*b - a*b^2)*d*cosh(d*x + c)^5 - 10*(a^2*b - a*b^2)*d*cosh(d*x + c)^3 - (8*a^3 - 11*a^2*b + 3*a*b^2)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^2*b - a*b^2)*d*cosh(d*x + c)^6 - 15*(a^2*b - a*b^2)*d*cosh(d*x + c)^4 - 3*(8*a^3 - 11*a^2*b + 3*a*b^2)*d*cosh(d*x + c)^2 - (a^2*b - a*b^2)*d)*sinh(d*x + c)^2 + (a^2*b - a*b^2)*d + 8*((a^2*b - a*b^2)*d*cosh(d*x + c)^7 - 3*(a^2*b - a*b^2)*d*cosh(d*x + c)^5 - (8*a^3 - 11*a^2*b + 3*a*b^2)*d*cosh(d*x + c)^3 - (a^2*b - a*b^2)*d*cosh(d*x + c))*sinh(d*x + c))*sqrt(((a^6 - 3*a^5*b + 3*a^4*b^2 - a^3*b^3)*d^2*sqrt((81*a^2 - 90*a*b + 25*b^2)/((a^9*b - 6*a^8*b^2 + 15*a^7*b^3 - 20*a^6*b^4 + 15*a^5*b^5 - 6*a^4*b^6 + a^3*b^7)*d^4)) - 15*a^2 + 15*a*b - 4*b^2)/((a^6 - 3*a^5*b + 3*a^4*b^2 - a^3*b^3)*d^2))*log((81*a^2 - 81*a*b + 20*b^2)*cosh(d*x + c)^2 + 2*(81*a^2 - 81*a*b + 20*b^2)*cosh(d*x + c)*sinh(d*x + c) + (81*a^2 - 81*a*b + 20*b^2)*sinh(d*x + c)^2 + 81*a^2 - 81*a*b + 20*b^2 - 2*((27*a^4 - 24*a^3*b + 5*a^2*b^2)*d*cosh(d*x + c) + (27*a^4 - 24*a^3*b + 5*a^2*b^2)*d*sinh(d*x + c) + 2*((2*a^7*b - 7*a^6*b^2 + 9*a^5*b^3 - 5*a^4*b^4 + a^3*b^5)*d^3*cosh(d*x + c) + (2*a^7*b - 7*a^6*b^2 + 9*a^5*b^3 - 5*a^4*b^4 + a^3*b^5)*d^3*sinh(d*x + c))*sqrt((81*a^2 - 90*a*b + 25*b^2)/((a^9*b - 6*a^8*b^2 + 15*a^7*b^3 - 20*a^6*b^4 + 15*a^5*b^5 - 6*a^4*b^6 + a^3*b^7)*d^4)))*sqrt(((a^6 - 3*a^5*b + 3*a^4*b^2 - a^3*b^3)*d^2*sqrt((81*a^2 - 90*a*b + 25*b^2)/((a^9*b - 6*a^8*b^2 + 15*a^7*b^3 - 20*a^6*b^4 + 15*a^5*b^5 - 6*a^4*b^6 + a^3*b^7)*d^4)) - 15*a^2 + 15*a*b - 4*b^2)/((a^6 - 3*a^5*b + 3*a^4*b^2 - a^3*b^3)*d^2))) + 8*b*cosh(d*x + c) + 8*(7*b*cosh(d*x + c)^6 - 5*(4*a + b)*cosh(d*x + c)^4 - 3*(4*a + b)*cosh(d*x + c)^2 + b)*sinh(d*x + c))/((a^2*b - a*b^2)*d*cosh(d*x + c)^8 + 8*(a^2*b - a*b^2)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^2*b - a*b^2)*d*sinh(d*x + c)^8 - 4*(a^2*b - a*b^2)*d*cosh(d*x + c)^6 + 4*(7*(a^2*b - a*b^2)*d*cosh(d*x + c)^2 - (a^2*b - a*b^2)*d)*sinh(d*x + c)^6 - 2*(8*a^3 - 11*a^2*b + 3*a*b^2)*d*cosh(d*x + c)^4 + 8*(7*(a^2*b - a*b^2)*d*cosh(d*x + c)^3 - 3*(a^2*b - a*b^2)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^2*b - a*b^2)*d*cosh(d*x + c)^4 - 30*(a^2*b - a*b^2)*d*cosh(d*x + c)^2 - (8*a^3 - 11*a^2*b + 3*a*b^2)*d)*sinh(d*x + c)^4 - 4*(a^2*b - a*b^2)*d*cosh(d*x + c)^2 + 8*(7*(a^2*b - a*b^2)*d*cosh(d*x + c)^5 - 10*(a^2*b - a*b^2)*d*cosh(d*x + c)^3 - (8*a^3 - 11*a^2*b + 3*a*b^2)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^2*b - a*b^2)*d*cosh(d*x + c)^6 - 15*(a^2*b - a*b^2)*d*cosh(d*x + c)^4 - 3*(8*a^3 - 11*a^2*b + 3*a*b^2)*d*cosh(d*x + c)^2 - (a^2*b - a*b^2)*d)*sinh(d*x + c)^2 + (a^2*b - a*b^2)*d + 8*((a^2*b - a*b^2)*d*cosh(d*x + c)^7 - 3*(a^2*b - a*b^2)*d*cosh(d*x + c)^5 - (8*a^3 - 11*a^2*b + 3*a*b^2)*d*cosh(d*x + c)^3 - (a^2*b - a*b^2)*d*cosh(d*x + c))*sinh(d*x + c))","B",0
246,1,7793,0,1.557532," ","integrate(csch(d*x+c)/(a-b*sinh(d*x+c)^4)^2,x, algorithm=""fricas"")","-\frac{8 \, a b \cosh\left(d x + c\right)^{7} + 56 \, a b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + 8 \, a b \sinh\left(d x + c\right)^{7} - 40 \, a b \cosh\left(d x + c\right)^{5} + 8 \, {\left(21 \, a b \cosh\left(d x + c\right)^{2} - 5 \, a b\right)} \sinh\left(d x + c\right)^{5} - 40 \, a b \cosh\left(d x + c\right)^{3} + 40 \, {\left(7 \, a b \cosh\left(d x + c\right)^{3} - 5 \, a b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 40 \, {\left(7 \, a b \cosh\left(d x + c\right)^{4} - 10 \, a b \cosh\left(d x + c\right)^{2} - a b\right)} \sinh\left(d x + c\right)^{3} + 8 \, a b \cosh\left(d x + c\right) + 8 \, {\left(21 \, a b \cosh\left(d x + c\right)^{5} - 50 \, a b \cosh\left(d x + c\right)^{3} - 15 \, a b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{3} b - a^{2} b^{2}\right)} d \sinh\left(d x + c\right)^{8} - 4 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{3} b - a^{2} b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{6} - 2 \, {\left(8 \, a^{4} - 11 \, a^{3} b + 3 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{4} - 30 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(8 \, a^{4} - 11 \, a^{3} b + 3 \, a^{2} b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{4} - 4 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{5} - 10 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{3} - {\left(8 \, a^{4} - 11 \, a^{3} b + 3 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{6} - 15 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{4} - 3 \, {\left(8 \, a^{4} - 11 \, a^{3} b + 3 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{3} b - a^{2} b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{3} b - a^{2} b^{2}\right)} d + 8 \, {\left({\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{7} - 3 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{5} - {\left(8 \, a^{4} - 11 \, a^{3} b + 3 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{{\left(a^{7} - 3 \, a^{6} b + 3 \, a^{5} b^{2} - a^{4} b^{3}\right)} d^{2} \sqrt{\frac{625 \, a^{4} b - 1450 \, a^{3} b^{2} + 1241 \, a^{2} b^{3} - 464 \, a b^{4} + 64 \, b^{5}}{{\left(a^{13} - 6 \, a^{12} b + 15 \, a^{11} b^{2} - 20 \, a^{10} b^{3} + 15 \, a^{9} b^{4} - 6 \, a^{8} b^{5} + a^{7} b^{6}\right)} d^{4}}} + 35 \, a^{2} b - 47 \, a b^{2} + 16 \, b^{3}}{{\left(a^{7} - 3 \, a^{6} b + 3 \, a^{5} b^{2} - a^{4} b^{3}\right)} d^{2}}} \log\left(-625 \, a^{3} b + 1125 \, a^{2} b^{2} - 664 \, a b^{3} + 128 \, b^{4} - {\left(625 \, a^{3} b - 1125 \, a^{2} b^{2} + 664 \, a b^{3} - 128 \, b^{4}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(625 \, a^{3} b - 1125 \, a^{2} b^{2} + 664 \, a b^{3} - 128 \, b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(625 \, a^{3} b - 1125 \, a^{2} b^{2} + 664 \, a b^{3} - 128 \, b^{4}\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(2 \, {\left(75 \, a^{5} b - 137 \, a^{4} b^{2} + 82 \, a^{3} b^{3} - 16 \, a^{2} b^{4}\right)} d \cosh\left(d x + c\right) + 2 \, {\left(75 \, a^{5} b - 137 \, a^{4} b^{2} + 82 \, a^{3} b^{3} - 16 \, a^{2} b^{4}\right)} d \sinh\left(d x + c\right) - {\left({\left(5 \, a^{10} - 18 \, a^{9} b + 24 \, a^{8} b^{2} - 14 \, a^{7} b^{3} + 3 \, a^{6} b^{4}\right)} d^{3} \cosh\left(d x + c\right) + {\left(5 \, a^{10} - 18 \, a^{9} b + 24 \, a^{8} b^{2} - 14 \, a^{7} b^{3} + 3 \, a^{6} b^{4}\right)} d^{3} \sinh\left(d x + c\right)\right)} \sqrt{\frac{625 \, a^{4} b - 1450 \, a^{3} b^{2} + 1241 \, a^{2} b^{3} - 464 \, a b^{4} + 64 \, b^{5}}{{\left(a^{13} - 6 \, a^{12} b + 15 \, a^{11} b^{2} - 20 \, a^{10} b^{3} + 15 \, a^{9} b^{4} - 6 \, a^{8} b^{5} + a^{7} b^{6}\right)} d^{4}}}\right)} \sqrt{-\frac{{\left(a^{7} - 3 \, a^{6} b + 3 \, a^{5} b^{2} - a^{4} b^{3}\right)} d^{2} \sqrt{\frac{625 \, a^{4} b - 1450 \, a^{3} b^{2} + 1241 \, a^{2} b^{3} - 464 \, a b^{4} + 64 \, b^{5}}{{\left(a^{13} - 6 \, a^{12} b + 15 \, a^{11} b^{2} - 20 \, a^{10} b^{3} + 15 \, a^{9} b^{4} - 6 \, a^{8} b^{5} + a^{7} b^{6}\right)} d^{4}}} + 35 \, a^{2} b - 47 \, a b^{2} + 16 \, b^{3}}{{\left(a^{7} - 3 \, a^{6} b + 3 \, a^{5} b^{2} - a^{4} b^{3}\right)} d^{2}}}\right) - {\left({\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{3} b - a^{2} b^{2}\right)} d \sinh\left(d x + c\right)^{8} - 4 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{3} b - a^{2} b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{6} - 2 \, {\left(8 \, a^{4} - 11 \, a^{3} b + 3 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{4} - 30 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(8 \, a^{4} - 11 \, a^{3} b + 3 \, a^{2} b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{4} - 4 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{5} - 10 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{3} - {\left(8 \, a^{4} - 11 \, a^{3} b + 3 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{6} - 15 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{4} - 3 \, {\left(8 \, a^{4} - 11 \, a^{3} b + 3 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{3} b - a^{2} b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{3} b - a^{2} b^{2}\right)} d + 8 \, {\left({\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{7} - 3 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{5} - {\left(8 \, a^{4} - 11 \, a^{3} b + 3 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{{\left(a^{7} - 3 \, a^{6} b + 3 \, a^{5} b^{2} - a^{4} b^{3}\right)} d^{2} \sqrt{\frac{625 \, a^{4} b - 1450 \, a^{3} b^{2} + 1241 \, a^{2} b^{3} - 464 \, a b^{4} + 64 \, b^{5}}{{\left(a^{13} - 6 \, a^{12} b + 15 \, a^{11} b^{2} - 20 \, a^{10} b^{3} + 15 \, a^{9} b^{4} - 6 \, a^{8} b^{5} + a^{7} b^{6}\right)} d^{4}}} + 35 \, a^{2} b - 47 \, a b^{2} + 16 \, b^{3}}{{\left(a^{7} - 3 \, a^{6} b + 3 \, a^{5} b^{2} - a^{4} b^{3}\right)} d^{2}}} \log\left(-625 \, a^{3} b + 1125 \, a^{2} b^{2} - 664 \, a b^{3} + 128 \, b^{4} - {\left(625 \, a^{3} b - 1125 \, a^{2} b^{2} + 664 \, a b^{3} - 128 \, b^{4}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(625 \, a^{3} b - 1125 \, a^{2} b^{2} + 664 \, a b^{3} - 128 \, b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(625 \, a^{3} b - 1125 \, a^{2} b^{2} + 664 \, a b^{3} - 128 \, b^{4}\right)} \sinh\left(d x + c\right)^{2} - 2 \, {\left(2 \, {\left(75 \, a^{5} b - 137 \, a^{4} b^{2} + 82 \, a^{3} b^{3} - 16 \, a^{2} b^{4}\right)} d \cosh\left(d x + c\right) + 2 \, {\left(75 \, a^{5} b - 137 \, a^{4} b^{2} + 82 \, a^{3} b^{3} - 16 \, a^{2} b^{4}\right)} d \sinh\left(d x + c\right) - {\left({\left(5 \, a^{10} - 18 \, a^{9} b + 24 \, a^{8} b^{2} - 14 \, a^{7} b^{3} + 3 \, a^{6} b^{4}\right)} d^{3} \cosh\left(d x + c\right) + {\left(5 \, a^{10} - 18 \, a^{9} b + 24 \, a^{8} b^{2} - 14 \, a^{7} b^{3} + 3 \, a^{6} b^{4}\right)} d^{3} \sinh\left(d x + c\right)\right)} \sqrt{\frac{625 \, a^{4} b - 1450 \, a^{3} b^{2} + 1241 \, a^{2} b^{3} - 464 \, a b^{4} + 64 \, b^{5}}{{\left(a^{13} - 6 \, a^{12} b + 15 \, a^{11} b^{2} - 20 \, a^{10} b^{3} + 15 \, a^{9} b^{4} - 6 \, a^{8} b^{5} + a^{7} b^{6}\right)} d^{4}}}\right)} \sqrt{-\frac{{\left(a^{7} - 3 \, a^{6} b + 3 \, a^{5} b^{2} - a^{4} b^{3}\right)} d^{2} \sqrt{\frac{625 \, a^{4} b - 1450 \, a^{3} b^{2} + 1241 \, a^{2} b^{3} - 464 \, a b^{4} + 64 \, b^{5}}{{\left(a^{13} - 6 \, a^{12} b + 15 \, a^{11} b^{2} - 20 \, a^{10} b^{3} + 15 \, a^{9} b^{4} - 6 \, a^{8} b^{5} + a^{7} b^{6}\right)} d^{4}}} + 35 \, a^{2} b - 47 \, a b^{2} + 16 \, b^{3}}{{\left(a^{7} - 3 \, a^{6} b + 3 \, a^{5} b^{2} - a^{4} b^{3}\right)} d^{2}}}\right) + {\left({\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{3} b - a^{2} b^{2}\right)} d \sinh\left(d x + c\right)^{8} - 4 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{3} b - a^{2} b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{6} - 2 \, {\left(8 \, a^{4} - 11 \, a^{3} b + 3 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{4} - 30 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(8 \, a^{4} - 11 \, a^{3} b + 3 \, a^{2} b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{4} - 4 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{5} - 10 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{3} - {\left(8 \, a^{4} - 11 \, a^{3} b + 3 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{6} - 15 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{4} - 3 \, {\left(8 \, a^{4} - 11 \, a^{3} b + 3 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{3} b - a^{2} b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{3} b - a^{2} b^{2}\right)} d + 8 \, {\left({\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{7} - 3 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{5} - {\left(8 \, a^{4} - 11 \, a^{3} b + 3 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{{\left(a^{7} - 3 \, a^{6} b + 3 \, a^{5} b^{2} - a^{4} b^{3}\right)} d^{2} \sqrt{\frac{625 \, a^{4} b - 1450 \, a^{3} b^{2} + 1241 \, a^{2} b^{3} - 464 \, a b^{4} + 64 \, b^{5}}{{\left(a^{13} - 6 \, a^{12} b + 15 \, a^{11} b^{2} - 20 \, a^{10} b^{3} + 15 \, a^{9} b^{4} - 6 \, a^{8} b^{5} + a^{7} b^{6}\right)} d^{4}}} - 35 \, a^{2} b + 47 \, a b^{2} - 16 \, b^{3}}{{\left(a^{7} - 3 \, a^{6} b + 3 \, a^{5} b^{2} - a^{4} b^{3}\right)} d^{2}}} \log\left(-625 \, a^{3} b + 1125 \, a^{2} b^{2} - 664 \, a b^{3} + 128 \, b^{4} - {\left(625 \, a^{3} b - 1125 \, a^{2} b^{2} + 664 \, a b^{3} - 128 \, b^{4}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(625 \, a^{3} b - 1125 \, a^{2} b^{2} + 664 \, a b^{3} - 128 \, b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(625 \, a^{3} b - 1125 \, a^{2} b^{2} + 664 \, a b^{3} - 128 \, b^{4}\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(2 \, {\left(75 \, a^{5} b - 137 \, a^{4} b^{2} + 82 \, a^{3} b^{3} - 16 \, a^{2} b^{4}\right)} d \cosh\left(d x + c\right) + 2 \, {\left(75 \, a^{5} b - 137 \, a^{4} b^{2} + 82 \, a^{3} b^{3} - 16 \, a^{2} b^{4}\right)} d \sinh\left(d x + c\right) + {\left({\left(5 \, a^{10} - 18 \, a^{9} b + 24 \, a^{8} b^{2} - 14 \, a^{7} b^{3} + 3 \, a^{6} b^{4}\right)} d^{3} \cosh\left(d x + c\right) + {\left(5 \, a^{10} - 18 \, a^{9} b + 24 \, a^{8} b^{2} - 14 \, a^{7} b^{3} + 3 \, a^{6} b^{4}\right)} d^{3} \sinh\left(d x + c\right)\right)} \sqrt{\frac{625 \, a^{4} b - 1450 \, a^{3} b^{2} + 1241 \, a^{2} b^{3} - 464 \, a b^{4} + 64 \, b^{5}}{{\left(a^{13} - 6 \, a^{12} b + 15 \, a^{11} b^{2} - 20 \, a^{10} b^{3} + 15 \, a^{9} b^{4} - 6 \, a^{8} b^{5} + a^{7} b^{6}\right)} d^{4}}}\right)} \sqrt{\frac{{\left(a^{7} - 3 \, a^{6} b + 3 \, a^{5} b^{2} - a^{4} b^{3}\right)} d^{2} \sqrt{\frac{625 \, a^{4} b - 1450 \, a^{3} b^{2} + 1241 \, a^{2} b^{3} - 464 \, a b^{4} + 64 \, b^{5}}{{\left(a^{13} - 6 \, a^{12} b + 15 \, a^{11} b^{2} - 20 \, a^{10} b^{3} + 15 \, a^{9} b^{4} - 6 \, a^{8} b^{5} + a^{7} b^{6}\right)} d^{4}}} - 35 \, a^{2} b + 47 \, a b^{2} - 16 \, b^{3}}{{\left(a^{7} - 3 \, a^{6} b + 3 \, a^{5} b^{2} - a^{4} b^{3}\right)} d^{2}}}\right) - {\left({\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{3} b - a^{2} b^{2}\right)} d \sinh\left(d x + c\right)^{8} - 4 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{3} b - a^{2} b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{6} - 2 \, {\left(8 \, a^{4} - 11 \, a^{3} b + 3 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{4} - 30 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(8 \, a^{4} - 11 \, a^{3} b + 3 \, a^{2} b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{4} - 4 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{5} - 10 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{3} - {\left(8 \, a^{4} - 11 \, a^{3} b + 3 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{6} - 15 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{4} - 3 \, {\left(8 \, a^{4} - 11 \, a^{3} b + 3 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{3} b - a^{2} b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{3} b - a^{2} b^{2}\right)} d + 8 \, {\left({\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{7} - 3 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{5} - {\left(8 \, a^{4} - 11 \, a^{3} b + 3 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{{\left(a^{7} - 3 \, a^{6} b + 3 \, a^{5} b^{2} - a^{4} b^{3}\right)} d^{2} \sqrt{\frac{625 \, a^{4} b - 1450 \, a^{3} b^{2} + 1241 \, a^{2} b^{3} - 464 \, a b^{4} + 64 \, b^{5}}{{\left(a^{13} - 6 \, a^{12} b + 15 \, a^{11} b^{2} - 20 \, a^{10} b^{3} + 15 \, a^{9} b^{4} - 6 \, a^{8} b^{5} + a^{7} b^{6}\right)} d^{4}}} - 35 \, a^{2} b + 47 \, a b^{2} - 16 \, b^{3}}{{\left(a^{7} - 3 \, a^{6} b + 3 \, a^{5} b^{2} - a^{4} b^{3}\right)} d^{2}}} \log\left(-625 \, a^{3} b + 1125 \, a^{2} b^{2} - 664 \, a b^{3} + 128 \, b^{4} - {\left(625 \, a^{3} b - 1125 \, a^{2} b^{2} + 664 \, a b^{3} - 128 \, b^{4}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(625 \, a^{3} b - 1125 \, a^{2} b^{2} + 664 \, a b^{3} - 128 \, b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(625 \, a^{3} b - 1125 \, a^{2} b^{2} + 664 \, a b^{3} - 128 \, b^{4}\right)} \sinh\left(d x + c\right)^{2} - 2 \, {\left(2 \, {\left(75 \, a^{5} b - 137 \, a^{4} b^{2} + 82 \, a^{3} b^{3} - 16 \, a^{2} b^{4}\right)} d \cosh\left(d x + c\right) + 2 \, {\left(75 \, a^{5} b - 137 \, a^{4} b^{2} + 82 \, a^{3} b^{3} - 16 \, a^{2} b^{4}\right)} d \sinh\left(d x + c\right) + {\left({\left(5 \, a^{10} - 18 \, a^{9} b + 24 \, a^{8} b^{2} - 14 \, a^{7} b^{3} + 3 \, a^{6} b^{4}\right)} d^{3} \cosh\left(d x + c\right) + {\left(5 \, a^{10} - 18 \, a^{9} b + 24 \, a^{8} b^{2} - 14 \, a^{7} b^{3} + 3 \, a^{6} b^{4}\right)} d^{3} \sinh\left(d x + c\right)\right)} \sqrt{\frac{625 \, a^{4} b - 1450 \, a^{3} b^{2} + 1241 \, a^{2} b^{3} - 464 \, a b^{4} + 64 \, b^{5}}{{\left(a^{13} - 6 \, a^{12} b + 15 \, a^{11} b^{2} - 20 \, a^{10} b^{3} + 15 \, a^{9} b^{4} - 6 \, a^{8} b^{5} + a^{7} b^{6}\right)} d^{4}}}\right)} \sqrt{\frac{{\left(a^{7} - 3 \, a^{6} b + 3 \, a^{5} b^{2} - a^{4} b^{3}\right)} d^{2} \sqrt{\frac{625 \, a^{4} b - 1450 \, a^{3} b^{2} + 1241 \, a^{2} b^{3} - 464 \, a b^{4} + 64 \, b^{5}}{{\left(a^{13} - 6 \, a^{12} b + 15 \, a^{11} b^{2} - 20 \, a^{10} b^{3} + 15 \, a^{9} b^{4} - 6 \, a^{8} b^{5} + a^{7} b^{6}\right)} d^{4}}} - 35 \, a^{2} b + 47 \, a b^{2} - 16 \, b^{3}}{{\left(a^{7} - 3 \, a^{6} b + 3 \, a^{5} b^{2} - a^{4} b^{3}\right)} d^{2}}}\right) + 16 \, {\left({\left(a b - b^{2}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(a b - b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a b - b^{2}\right)} \sinh\left(d x + c\right)^{8} - 4 \, {\left(a b - b^{2}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} - a b + b^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(a b - b^{2}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(a b - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 2 \, {\left(8 \, a^{2} - 11 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(a b - b^{2}\right)} \cosh\left(d x + c\right)^{4} - 30 \, {\left(a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} - 8 \, a^{2} + 11 \, a b - 3 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a b - b^{2}\right)} \cosh\left(d x + c\right)^{5} - 10 \, {\left(a b - b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(8 \, a^{2} - 11 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 4 \, {\left(a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(a b - b^{2}\right)} \cosh\left(d x + c\right)^{6} - 15 \, {\left(a b - b^{2}\right)} \cosh\left(d x + c\right)^{4} - 3 \, {\left(8 \, a^{2} - 11 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - a b + b^{2}\right)} \sinh\left(d x + c\right)^{2} + a b - b^{2} + 8 \, {\left({\left(a b - b^{2}\right)} \cosh\left(d x + c\right)^{7} - 3 \, {\left(a b - b^{2}\right)} \cosh\left(d x + c\right)^{5} - {\left(8 \, a^{2} - 11 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(a b - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) - 16 \, {\left({\left(a b - b^{2}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(a b - b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a b - b^{2}\right)} \sinh\left(d x + c\right)^{8} - 4 \, {\left(a b - b^{2}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} - a b + b^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(a b - b^{2}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(a b - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 2 \, {\left(8 \, a^{2} - 11 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(a b - b^{2}\right)} \cosh\left(d x + c\right)^{4} - 30 \, {\left(a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} - 8 \, a^{2} + 11 \, a b - 3 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a b - b^{2}\right)} \cosh\left(d x + c\right)^{5} - 10 \, {\left(a b - b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(8 \, a^{2} - 11 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 4 \, {\left(a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(a b - b^{2}\right)} \cosh\left(d x + c\right)^{6} - 15 \, {\left(a b - b^{2}\right)} \cosh\left(d x + c\right)^{4} - 3 \, {\left(8 \, a^{2} - 11 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - a b + b^{2}\right)} \sinh\left(d x + c\right)^{2} + a b - b^{2} + 8 \, {\left({\left(a b - b^{2}\right)} \cosh\left(d x + c\right)^{7} - 3 \, {\left(a b - b^{2}\right)} \cosh\left(d x + c\right)^{5} - {\left(8 \, a^{2} - 11 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(a b - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) + 8 \, {\left(7 \, a b \cosh\left(d x + c\right)^{6} - 25 \, a b \cosh\left(d x + c\right)^{4} - 15 \, a b \cosh\left(d x + c\right)^{2} + a b\right)} \sinh\left(d x + c\right)}{16 \, {\left({\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{3} b - a^{2} b^{2}\right)} d \sinh\left(d x + c\right)^{8} - 4 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{3} b - a^{2} b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{6} - 2 \, {\left(8 \, a^{4} - 11 \, a^{3} b + 3 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{4} - 30 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(8 \, a^{4} - 11 \, a^{3} b + 3 \, a^{2} b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{4} - 4 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{5} - 10 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{3} - {\left(8 \, a^{4} - 11 \, a^{3} b + 3 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{6} - 15 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{4} - 3 \, {\left(8 \, a^{4} - 11 \, a^{3} b + 3 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{3} b - a^{2} b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{3} b - a^{2} b^{2}\right)} d + 8 \, {\left({\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{7} - 3 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{5} - {\left(8 \, a^{4} - 11 \, a^{3} b + 3 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"-1/16*(8*a*b*cosh(d*x + c)^7 + 56*a*b*cosh(d*x + c)*sinh(d*x + c)^6 + 8*a*b*sinh(d*x + c)^7 - 40*a*b*cosh(d*x + c)^5 + 8*(21*a*b*cosh(d*x + c)^2 - 5*a*b)*sinh(d*x + c)^5 - 40*a*b*cosh(d*x + c)^3 + 40*(7*a*b*cosh(d*x + c)^3 - 5*a*b*cosh(d*x + c))*sinh(d*x + c)^4 + 40*(7*a*b*cosh(d*x + c)^4 - 10*a*b*cosh(d*x + c)^2 - a*b)*sinh(d*x + c)^3 + 8*a*b*cosh(d*x + c) + 8*(21*a*b*cosh(d*x + c)^5 - 50*a*b*cosh(d*x + c)^3 - 15*a*b*cosh(d*x + c))*sinh(d*x + c)^2 + ((a^3*b - a^2*b^2)*d*cosh(d*x + c)^8 + 8*(a^3*b - a^2*b^2)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^3*b - a^2*b^2)*d*sinh(d*x + c)^8 - 4*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^6 + 4*(7*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^2 - (a^3*b - a^2*b^2)*d)*sinh(d*x + c)^6 - 2*(8*a^4 - 11*a^3*b + 3*a^2*b^2)*d*cosh(d*x + c)^4 + 8*(7*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^3 - 3*(a^3*b - a^2*b^2)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^4 - 30*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^2 - (8*a^4 - 11*a^3*b + 3*a^2*b^2)*d)*sinh(d*x + c)^4 - 4*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^2 + 8*(7*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^5 - 10*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^3 - (8*a^4 - 11*a^3*b + 3*a^2*b^2)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^6 - 15*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^4 - 3*(8*a^4 - 11*a^3*b + 3*a^2*b^2)*d*cosh(d*x + c)^2 - (a^3*b - a^2*b^2)*d)*sinh(d*x + c)^2 + (a^3*b - a^2*b^2)*d + 8*((a^3*b - a^2*b^2)*d*cosh(d*x + c)^7 - 3*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^5 - (8*a^4 - 11*a^3*b + 3*a^2*b^2)*d*cosh(d*x + c)^3 - (a^3*b - a^2*b^2)*d*cosh(d*x + c))*sinh(d*x + c))*sqrt(-((a^7 - 3*a^6*b + 3*a^5*b^2 - a^4*b^3)*d^2*sqrt((625*a^4*b - 1450*a^3*b^2 + 1241*a^2*b^3 - 464*a*b^4 + 64*b^5)/((a^13 - 6*a^12*b + 15*a^11*b^2 - 20*a^10*b^3 + 15*a^9*b^4 - 6*a^8*b^5 + a^7*b^6)*d^4)) + 35*a^2*b - 47*a*b^2 + 16*b^3)/((a^7 - 3*a^6*b + 3*a^5*b^2 - a^4*b^3)*d^2))*log(-625*a^3*b + 1125*a^2*b^2 - 664*a*b^3 + 128*b^4 - (625*a^3*b - 1125*a^2*b^2 + 664*a*b^3 - 128*b^4)*cosh(d*x + c)^2 - 2*(625*a^3*b - 1125*a^2*b^2 + 664*a*b^3 - 128*b^4)*cosh(d*x + c)*sinh(d*x + c) - (625*a^3*b - 1125*a^2*b^2 + 664*a*b^3 - 128*b^4)*sinh(d*x + c)^2 + 2*(2*(75*a^5*b - 137*a^4*b^2 + 82*a^3*b^3 - 16*a^2*b^4)*d*cosh(d*x + c) + 2*(75*a^5*b - 137*a^4*b^2 + 82*a^3*b^3 - 16*a^2*b^4)*d*sinh(d*x + c) - ((5*a^10 - 18*a^9*b + 24*a^8*b^2 - 14*a^7*b^3 + 3*a^6*b^4)*d^3*cosh(d*x + c) + (5*a^10 - 18*a^9*b + 24*a^8*b^2 - 14*a^7*b^3 + 3*a^6*b^4)*d^3*sinh(d*x + c))*sqrt((625*a^4*b - 1450*a^3*b^2 + 1241*a^2*b^3 - 464*a*b^4 + 64*b^5)/((a^13 - 6*a^12*b + 15*a^11*b^2 - 20*a^10*b^3 + 15*a^9*b^4 - 6*a^8*b^5 + a^7*b^6)*d^4)))*sqrt(-((a^7 - 3*a^6*b + 3*a^5*b^2 - a^4*b^3)*d^2*sqrt((625*a^4*b - 1450*a^3*b^2 + 1241*a^2*b^3 - 464*a*b^4 + 64*b^5)/((a^13 - 6*a^12*b + 15*a^11*b^2 - 20*a^10*b^3 + 15*a^9*b^4 - 6*a^8*b^5 + a^7*b^6)*d^4)) + 35*a^2*b - 47*a*b^2 + 16*b^3)/((a^7 - 3*a^6*b + 3*a^5*b^2 - a^4*b^3)*d^2))) - ((a^3*b - a^2*b^2)*d*cosh(d*x + c)^8 + 8*(a^3*b - a^2*b^2)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^3*b - a^2*b^2)*d*sinh(d*x + c)^8 - 4*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^6 + 4*(7*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^2 - (a^3*b - a^2*b^2)*d)*sinh(d*x + c)^6 - 2*(8*a^4 - 11*a^3*b + 3*a^2*b^2)*d*cosh(d*x + c)^4 + 8*(7*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^3 - 3*(a^3*b - a^2*b^2)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^4 - 30*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^2 - (8*a^4 - 11*a^3*b + 3*a^2*b^2)*d)*sinh(d*x + c)^4 - 4*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^2 + 8*(7*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^5 - 10*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^3 - (8*a^4 - 11*a^3*b + 3*a^2*b^2)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^6 - 15*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^4 - 3*(8*a^4 - 11*a^3*b + 3*a^2*b^2)*d*cosh(d*x + c)^2 - (a^3*b - a^2*b^2)*d)*sinh(d*x + c)^2 + (a^3*b - a^2*b^2)*d + 8*((a^3*b - a^2*b^2)*d*cosh(d*x + c)^7 - 3*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^5 - (8*a^4 - 11*a^3*b + 3*a^2*b^2)*d*cosh(d*x + c)^3 - (a^3*b - a^2*b^2)*d*cosh(d*x + c))*sinh(d*x + c))*sqrt(-((a^7 - 3*a^6*b + 3*a^5*b^2 - a^4*b^3)*d^2*sqrt((625*a^4*b - 1450*a^3*b^2 + 1241*a^2*b^3 - 464*a*b^4 + 64*b^5)/((a^13 - 6*a^12*b + 15*a^11*b^2 - 20*a^10*b^3 + 15*a^9*b^4 - 6*a^8*b^5 + a^7*b^6)*d^4)) + 35*a^2*b - 47*a*b^2 + 16*b^3)/((a^7 - 3*a^6*b + 3*a^5*b^2 - a^4*b^3)*d^2))*log(-625*a^3*b + 1125*a^2*b^2 - 664*a*b^3 + 128*b^4 - (625*a^3*b - 1125*a^2*b^2 + 664*a*b^3 - 128*b^4)*cosh(d*x + c)^2 - 2*(625*a^3*b - 1125*a^2*b^2 + 664*a*b^3 - 128*b^4)*cosh(d*x + c)*sinh(d*x + c) - (625*a^3*b - 1125*a^2*b^2 + 664*a*b^3 - 128*b^4)*sinh(d*x + c)^2 - 2*(2*(75*a^5*b - 137*a^4*b^2 + 82*a^3*b^3 - 16*a^2*b^4)*d*cosh(d*x + c) + 2*(75*a^5*b - 137*a^4*b^2 + 82*a^3*b^3 - 16*a^2*b^4)*d*sinh(d*x + c) - ((5*a^10 - 18*a^9*b + 24*a^8*b^2 - 14*a^7*b^3 + 3*a^6*b^4)*d^3*cosh(d*x + c) + (5*a^10 - 18*a^9*b + 24*a^8*b^2 - 14*a^7*b^3 + 3*a^6*b^4)*d^3*sinh(d*x + c))*sqrt((625*a^4*b - 1450*a^3*b^2 + 1241*a^2*b^3 - 464*a*b^4 + 64*b^5)/((a^13 - 6*a^12*b + 15*a^11*b^2 - 20*a^10*b^3 + 15*a^9*b^4 - 6*a^8*b^5 + a^7*b^6)*d^4)))*sqrt(-((a^7 - 3*a^6*b + 3*a^5*b^2 - a^4*b^3)*d^2*sqrt((625*a^4*b - 1450*a^3*b^2 + 1241*a^2*b^3 - 464*a*b^4 + 64*b^5)/((a^13 - 6*a^12*b + 15*a^11*b^2 - 20*a^10*b^3 + 15*a^9*b^4 - 6*a^8*b^5 + a^7*b^6)*d^4)) + 35*a^2*b - 47*a*b^2 + 16*b^3)/((a^7 - 3*a^6*b + 3*a^5*b^2 - a^4*b^3)*d^2))) + ((a^3*b - a^2*b^2)*d*cosh(d*x + c)^8 + 8*(a^3*b - a^2*b^2)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^3*b - a^2*b^2)*d*sinh(d*x + c)^8 - 4*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^6 + 4*(7*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^2 - (a^3*b - a^2*b^2)*d)*sinh(d*x + c)^6 - 2*(8*a^4 - 11*a^3*b + 3*a^2*b^2)*d*cosh(d*x + c)^4 + 8*(7*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^3 - 3*(a^3*b - a^2*b^2)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^4 - 30*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^2 - (8*a^4 - 11*a^3*b + 3*a^2*b^2)*d)*sinh(d*x + c)^4 - 4*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^2 + 8*(7*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^5 - 10*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^3 - (8*a^4 - 11*a^3*b + 3*a^2*b^2)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^6 - 15*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^4 - 3*(8*a^4 - 11*a^3*b + 3*a^2*b^2)*d*cosh(d*x + c)^2 - (a^3*b - a^2*b^2)*d)*sinh(d*x + c)^2 + (a^3*b - a^2*b^2)*d + 8*((a^3*b - a^2*b^2)*d*cosh(d*x + c)^7 - 3*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^5 - (8*a^4 - 11*a^3*b + 3*a^2*b^2)*d*cosh(d*x + c)^3 - (a^3*b - a^2*b^2)*d*cosh(d*x + c))*sinh(d*x + c))*sqrt(((a^7 - 3*a^6*b + 3*a^5*b^2 - a^4*b^3)*d^2*sqrt((625*a^4*b - 1450*a^3*b^2 + 1241*a^2*b^3 - 464*a*b^4 + 64*b^5)/((a^13 - 6*a^12*b + 15*a^11*b^2 - 20*a^10*b^3 + 15*a^9*b^4 - 6*a^8*b^5 + a^7*b^6)*d^4)) - 35*a^2*b + 47*a*b^2 - 16*b^3)/((a^7 - 3*a^6*b + 3*a^5*b^2 - a^4*b^3)*d^2))*log(-625*a^3*b + 1125*a^2*b^2 - 664*a*b^3 + 128*b^4 - (625*a^3*b - 1125*a^2*b^2 + 664*a*b^3 - 128*b^4)*cosh(d*x + c)^2 - 2*(625*a^3*b - 1125*a^2*b^2 + 664*a*b^3 - 128*b^4)*cosh(d*x + c)*sinh(d*x + c) - (625*a^3*b - 1125*a^2*b^2 + 664*a*b^3 - 128*b^4)*sinh(d*x + c)^2 + 2*(2*(75*a^5*b - 137*a^4*b^2 + 82*a^3*b^3 - 16*a^2*b^4)*d*cosh(d*x + c) + 2*(75*a^5*b - 137*a^4*b^2 + 82*a^3*b^3 - 16*a^2*b^4)*d*sinh(d*x + c) + ((5*a^10 - 18*a^9*b + 24*a^8*b^2 - 14*a^7*b^3 + 3*a^6*b^4)*d^3*cosh(d*x + c) + (5*a^10 - 18*a^9*b + 24*a^8*b^2 - 14*a^7*b^3 + 3*a^6*b^4)*d^3*sinh(d*x + c))*sqrt((625*a^4*b - 1450*a^3*b^2 + 1241*a^2*b^3 - 464*a*b^4 + 64*b^5)/((a^13 - 6*a^12*b + 15*a^11*b^2 - 20*a^10*b^3 + 15*a^9*b^4 - 6*a^8*b^5 + a^7*b^6)*d^4)))*sqrt(((a^7 - 3*a^6*b + 3*a^5*b^2 - a^4*b^3)*d^2*sqrt((625*a^4*b - 1450*a^3*b^2 + 1241*a^2*b^3 - 464*a*b^4 + 64*b^5)/((a^13 - 6*a^12*b + 15*a^11*b^2 - 20*a^10*b^3 + 15*a^9*b^4 - 6*a^8*b^5 + a^7*b^6)*d^4)) - 35*a^2*b + 47*a*b^2 - 16*b^3)/((a^7 - 3*a^6*b + 3*a^5*b^2 - a^4*b^3)*d^2))) - ((a^3*b - a^2*b^2)*d*cosh(d*x + c)^8 + 8*(a^3*b - a^2*b^2)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^3*b - a^2*b^2)*d*sinh(d*x + c)^8 - 4*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^6 + 4*(7*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^2 - (a^3*b - a^2*b^2)*d)*sinh(d*x + c)^6 - 2*(8*a^4 - 11*a^3*b + 3*a^2*b^2)*d*cosh(d*x + c)^4 + 8*(7*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^3 - 3*(a^3*b - a^2*b^2)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^4 - 30*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^2 - (8*a^4 - 11*a^3*b + 3*a^2*b^2)*d)*sinh(d*x + c)^4 - 4*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^2 + 8*(7*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^5 - 10*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^3 - (8*a^4 - 11*a^3*b + 3*a^2*b^2)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^6 - 15*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^4 - 3*(8*a^4 - 11*a^3*b + 3*a^2*b^2)*d*cosh(d*x + c)^2 - (a^3*b - a^2*b^2)*d)*sinh(d*x + c)^2 + (a^3*b - a^2*b^2)*d + 8*((a^3*b - a^2*b^2)*d*cosh(d*x + c)^7 - 3*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^5 - (8*a^4 - 11*a^3*b + 3*a^2*b^2)*d*cosh(d*x + c)^3 - (a^3*b - a^2*b^2)*d*cosh(d*x + c))*sinh(d*x + c))*sqrt(((a^7 - 3*a^6*b + 3*a^5*b^2 - a^4*b^3)*d^2*sqrt((625*a^4*b - 1450*a^3*b^2 + 1241*a^2*b^3 - 464*a*b^4 + 64*b^5)/((a^13 - 6*a^12*b + 15*a^11*b^2 - 20*a^10*b^3 + 15*a^9*b^4 - 6*a^8*b^5 + a^7*b^6)*d^4)) - 35*a^2*b + 47*a*b^2 - 16*b^3)/((a^7 - 3*a^6*b + 3*a^5*b^2 - a^4*b^3)*d^2))*log(-625*a^3*b + 1125*a^2*b^2 - 664*a*b^3 + 128*b^4 - (625*a^3*b - 1125*a^2*b^2 + 664*a*b^3 - 128*b^4)*cosh(d*x + c)^2 - 2*(625*a^3*b - 1125*a^2*b^2 + 664*a*b^3 - 128*b^4)*cosh(d*x + c)*sinh(d*x + c) - (625*a^3*b - 1125*a^2*b^2 + 664*a*b^3 - 128*b^4)*sinh(d*x + c)^2 - 2*(2*(75*a^5*b - 137*a^4*b^2 + 82*a^3*b^3 - 16*a^2*b^4)*d*cosh(d*x + c) + 2*(75*a^5*b - 137*a^4*b^2 + 82*a^3*b^3 - 16*a^2*b^4)*d*sinh(d*x + c) + ((5*a^10 - 18*a^9*b + 24*a^8*b^2 - 14*a^7*b^3 + 3*a^6*b^4)*d^3*cosh(d*x + c) + (5*a^10 - 18*a^9*b + 24*a^8*b^2 - 14*a^7*b^3 + 3*a^6*b^4)*d^3*sinh(d*x + c))*sqrt((625*a^4*b - 1450*a^3*b^2 + 1241*a^2*b^3 - 464*a*b^4 + 64*b^5)/((a^13 - 6*a^12*b + 15*a^11*b^2 - 20*a^10*b^3 + 15*a^9*b^4 - 6*a^8*b^5 + a^7*b^6)*d^4)))*sqrt(((a^7 - 3*a^6*b + 3*a^5*b^2 - a^4*b^3)*d^2*sqrt((625*a^4*b - 1450*a^3*b^2 + 1241*a^2*b^3 - 464*a*b^4 + 64*b^5)/((a^13 - 6*a^12*b + 15*a^11*b^2 - 20*a^10*b^3 + 15*a^9*b^4 - 6*a^8*b^5 + a^7*b^6)*d^4)) - 35*a^2*b + 47*a*b^2 - 16*b^3)/((a^7 - 3*a^6*b + 3*a^5*b^2 - a^4*b^3)*d^2))) + 16*((a*b - b^2)*cosh(d*x + c)^8 + 8*(a*b - b^2)*cosh(d*x + c)*sinh(d*x + c)^7 + (a*b - b^2)*sinh(d*x + c)^8 - 4*(a*b - b^2)*cosh(d*x + c)^6 + 4*(7*(a*b - b^2)*cosh(d*x + c)^2 - a*b + b^2)*sinh(d*x + c)^6 + 8*(7*(a*b - b^2)*cosh(d*x + c)^3 - 3*(a*b - b^2)*cosh(d*x + c))*sinh(d*x + c)^5 - 2*(8*a^2 - 11*a*b + 3*b^2)*cosh(d*x + c)^4 + 2*(35*(a*b - b^2)*cosh(d*x + c)^4 - 30*(a*b - b^2)*cosh(d*x + c)^2 - 8*a^2 + 11*a*b - 3*b^2)*sinh(d*x + c)^4 + 8*(7*(a*b - b^2)*cosh(d*x + c)^5 - 10*(a*b - b^2)*cosh(d*x + c)^3 - (8*a^2 - 11*a*b + 3*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 - 4*(a*b - b^2)*cosh(d*x + c)^2 + 4*(7*(a*b - b^2)*cosh(d*x + c)^6 - 15*(a*b - b^2)*cosh(d*x + c)^4 - 3*(8*a^2 - 11*a*b + 3*b^2)*cosh(d*x + c)^2 - a*b + b^2)*sinh(d*x + c)^2 + a*b - b^2 + 8*((a*b - b^2)*cosh(d*x + c)^7 - 3*(a*b - b^2)*cosh(d*x + c)^5 - (8*a^2 - 11*a*b + 3*b^2)*cosh(d*x + c)^3 - (a*b - b^2)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) + 1) - 16*((a*b - b^2)*cosh(d*x + c)^8 + 8*(a*b - b^2)*cosh(d*x + c)*sinh(d*x + c)^7 + (a*b - b^2)*sinh(d*x + c)^8 - 4*(a*b - b^2)*cosh(d*x + c)^6 + 4*(7*(a*b - b^2)*cosh(d*x + c)^2 - a*b + b^2)*sinh(d*x + c)^6 + 8*(7*(a*b - b^2)*cosh(d*x + c)^3 - 3*(a*b - b^2)*cosh(d*x + c))*sinh(d*x + c)^5 - 2*(8*a^2 - 11*a*b + 3*b^2)*cosh(d*x + c)^4 + 2*(35*(a*b - b^2)*cosh(d*x + c)^4 - 30*(a*b - b^2)*cosh(d*x + c)^2 - 8*a^2 + 11*a*b - 3*b^2)*sinh(d*x + c)^4 + 8*(7*(a*b - b^2)*cosh(d*x + c)^5 - 10*(a*b - b^2)*cosh(d*x + c)^3 - (8*a^2 - 11*a*b + 3*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 - 4*(a*b - b^2)*cosh(d*x + c)^2 + 4*(7*(a*b - b^2)*cosh(d*x + c)^6 - 15*(a*b - b^2)*cosh(d*x + c)^4 - 3*(8*a^2 - 11*a*b + 3*b^2)*cosh(d*x + c)^2 - a*b + b^2)*sinh(d*x + c)^2 + a*b - b^2 + 8*((a*b - b^2)*cosh(d*x + c)^7 - 3*(a*b - b^2)*cosh(d*x + c)^5 - (8*a^2 - 11*a*b + 3*b^2)*cosh(d*x + c)^3 - (a*b - b^2)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) - 1) + 8*(7*a*b*cosh(d*x + c)^6 - 25*a*b*cosh(d*x + c)^4 - 15*a*b*cosh(d*x + c)^2 + a*b)*sinh(d*x + c))/((a^3*b - a^2*b^2)*d*cosh(d*x + c)^8 + 8*(a^3*b - a^2*b^2)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^3*b - a^2*b^2)*d*sinh(d*x + c)^8 - 4*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^6 + 4*(7*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^2 - (a^3*b - a^2*b^2)*d)*sinh(d*x + c)^6 - 2*(8*a^4 - 11*a^3*b + 3*a^2*b^2)*d*cosh(d*x + c)^4 + 8*(7*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^3 - 3*(a^3*b - a^2*b^2)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^4 - 30*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^2 - (8*a^4 - 11*a^3*b + 3*a^2*b^2)*d)*sinh(d*x + c)^4 - 4*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^2 + 8*(7*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^5 - 10*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^3 - (8*a^4 - 11*a^3*b + 3*a^2*b^2)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^6 - 15*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^4 - 3*(8*a^4 - 11*a^3*b + 3*a^2*b^2)*d*cosh(d*x + c)^2 - (a^3*b - a^2*b^2)*d)*sinh(d*x + c)^2 + (a^3*b - a^2*b^2)*d + 8*((a^3*b - a^2*b^2)*d*cosh(d*x + c)^7 - 3*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^5 - (8*a^4 - 11*a^3*b + 3*a^2*b^2)*d*cosh(d*x + c)^3 - (a^3*b - a^2*b^2)*d*cosh(d*x + c))*sinh(d*x + c))","B",0
247,1,6944,0,1.406894," ","integrate(sinh(d*x+c)^8/(a-b*sinh(d*x+c)^4)^2,x, algorithm=""fricas"")","\frac{16 \, {\left(a b - b^{2}\right)} d x \cosh\left(d x + c\right)^{8} + 128 \, {\left(a b - b^{2}\right)} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + 16 \, {\left(a b - b^{2}\right)} d x \sinh\left(d x + c\right)^{8} - 8 \, {\left(8 \, {\left(a b - b^{2}\right)} d x - a b\right)} \cosh\left(d x + c\right)^{6} + 8 \, {\left(56 \, {\left(a b - b^{2}\right)} d x \cosh\left(d x + c\right)^{2} - 8 \, {\left(a b - b^{2}\right)} d x + a b\right)} \sinh\left(d x + c\right)^{6} + 16 \, {\left(56 \, {\left(a b - b^{2}\right)} d x \cosh\left(d x + c\right)^{3} - 3 \, {\left(8 \, {\left(a b - b^{2}\right)} d x - a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 8 \, {\left(4 \, {\left(8 \, a^{2} - 11 \, a b + 3 \, b^{2}\right)} d x + 8 \, a^{2} - 3 \, a b\right)} \cosh\left(d x + c\right)^{4} + 8 \, {\left(140 \, {\left(a b - b^{2}\right)} d x \cosh\left(d x + c\right)^{4} - 4 \, {\left(8 \, a^{2} - 11 \, a b + 3 \, b^{2}\right)} d x - 15 \, {\left(8 \, {\left(a b - b^{2}\right)} d x - a b\right)} \cosh\left(d x + c\right)^{2} - 8 \, a^{2} + 3 \, a b\right)} \sinh\left(d x + c\right)^{4} + 32 \, {\left(28 \, {\left(a b - b^{2}\right)} d x \cosh\left(d x + c\right)^{5} - 5 \, {\left(8 \, {\left(a b - b^{2}\right)} d x - a b\right)} \cosh\left(d x + c\right)^{3} - {\left(4 \, {\left(8 \, a^{2} - 11 \, a b + 3 \, b^{2}\right)} d x + 8 \, a^{2} - 3 \, a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 16 \, {\left(a b - b^{2}\right)} d x - 8 \, {\left(8 \, {\left(a b - b^{2}\right)} d x + 5 \, a b\right)} \cosh\left(d x + c\right)^{2} + 8 \, {\left(56 \, {\left(a b - b^{2}\right)} d x \cosh\left(d x + c\right)^{6} - 15 \, {\left(8 \, {\left(a b - b^{2}\right)} d x - a b\right)} \cosh\left(d x + c\right)^{4} - 8 \, {\left(a b - b^{2}\right)} d x - 6 \, {\left(4 \, {\left(8 \, a^{2} - 11 \, a b + 3 \, b^{2}\right)} d x + 8 \, a^{2} - 3 \, a b\right)} \cosh\left(d x + c\right)^{2} - 5 \, a b\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a b^{3} - b^{4}\right)} d \sinh\left(d x + c\right)^{8} - 4 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a b^{3} - b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{6} - 2 \, {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{3} - 3 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{4} - 30 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{2} - {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{4} - 4 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{5} - 10 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{3} - {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{6} - 15 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{4} - 3 \, {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a b^{3} - b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a b^{3} - b^{4}\right)} d + 8 \, {\left({\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{7} - 3 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{5} - {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{{\left(a^{3} b^{4} - 3 \, a^{2} b^{5} + 3 \, a b^{6} - b^{7}\right)} d^{2} \sqrt{\frac{64 \, a^{5} - 464 \, a^{4} b + 1241 \, a^{3} b^{2} - 1450 \, a^{2} b^{3} + 625 \, a b^{4}}{{\left(a^{6} b^{7} - 6 \, a^{5} b^{8} + 15 \, a^{4} b^{9} - 20 \, a^{3} b^{10} + 15 \, a^{2} b^{11} - 6 \, a b^{12} + b^{13}\right)} d^{4}}} - 16 \, a^{3} + 47 \, a^{2} b - 35 \, a b^{2}}{{\left(a^{3} b^{4} - 3 \, a^{2} b^{5} + 3 \, a b^{6} - b^{7}\right)} d^{2}}} \log\left(2 \, {\left(16 \, a^{4} b^{3} - 73 \, a^{3} b^{4} + 123 \, a^{2} b^{5} - 91 \, a b^{6} + 25 \, b^{7}\right)} d^{2} \sqrt{\frac{64 \, a^{5} - 464 \, a^{4} b + 1241 \, a^{3} b^{2} - 1450 \, a^{2} b^{3} + 625 \, a b^{4}}{{\left(a^{6} b^{7} - 6 \, a^{5} b^{8} + 15 \, a^{4} b^{9} - 20 \, a^{3} b^{10} + 15 \, a^{2} b^{11} - 6 \, a b^{12} + b^{13}\right)} d^{4}}} + 128 \, a^{3} - 664 \, a^{2} b + 1125 \, a b^{2} - 625 \, b^{3} - {\left(128 \, a^{3} - 664 \, a^{2} b + 1125 \, a b^{2} - 625 \, b^{3}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(128 \, a^{3} - 664 \, a^{2} b + 1125 \, a b^{2} - 625 \, b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(128 \, a^{3} - 664 \, a^{2} b + 1125 \, a b^{2} - 625 \, b^{3}\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(2 \, {\left(2 \, a^{4} b^{5} - 9 \, a^{3} b^{6} + 15 \, a^{2} b^{7} - 11 \, a b^{8} + 3 \, b^{9}\right)} d^{3} \sqrt{\frac{64 \, a^{5} - 464 \, a^{4} b + 1241 \, a^{3} b^{2} - 1450 \, a^{2} b^{3} + 625 \, a b^{4}}{{\left(a^{6} b^{7} - 6 \, a^{5} b^{8} + 15 \, a^{4} b^{9} - 20 \, a^{3} b^{10} + 15 \, a^{2} b^{11} - 6 \, a b^{12} + b^{13}\right)} d^{4}}} + {\left(24 \, a^{3} b^{2} - 127 \, a^{2} b^{3} + 220 \, a b^{4} - 125 \, b^{5}\right)} d\right)} \sqrt{-\frac{{\left(a^{3} b^{4} - 3 \, a^{2} b^{5} + 3 \, a b^{6} - b^{7}\right)} d^{2} \sqrt{\frac{64 \, a^{5} - 464 \, a^{4} b + 1241 \, a^{3} b^{2} - 1450 \, a^{2} b^{3} + 625 \, a b^{4}}{{\left(a^{6} b^{7} - 6 \, a^{5} b^{8} + 15 \, a^{4} b^{9} - 20 \, a^{3} b^{10} + 15 \, a^{2} b^{11} - 6 \, a b^{12} + b^{13}\right)} d^{4}}} - 16 \, a^{3} + 47 \, a^{2} b - 35 \, a b^{2}}{{\left(a^{3} b^{4} - 3 \, a^{2} b^{5} + 3 \, a b^{6} - b^{7}\right)} d^{2}}}\right) - {\left({\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a b^{3} - b^{4}\right)} d \sinh\left(d x + c\right)^{8} - 4 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a b^{3} - b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{6} - 2 \, {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{3} - 3 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{4} - 30 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{2} - {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{4} - 4 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{5} - 10 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{3} - {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{6} - 15 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{4} - 3 \, {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a b^{3} - b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a b^{3} - b^{4}\right)} d + 8 \, {\left({\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{7} - 3 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{5} - {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{{\left(a^{3} b^{4} - 3 \, a^{2} b^{5} + 3 \, a b^{6} - b^{7}\right)} d^{2} \sqrt{\frac{64 \, a^{5} - 464 \, a^{4} b + 1241 \, a^{3} b^{2} - 1450 \, a^{2} b^{3} + 625 \, a b^{4}}{{\left(a^{6} b^{7} - 6 \, a^{5} b^{8} + 15 \, a^{4} b^{9} - 20 \, a^{3} b^{10} + 15 \, a^{2} b^{11} - 6 \, a b^{12} + b^{13}\right)} d^{4}}} - 16 \, a^{3} + 47 \, a^{2} b - 35 \, a b^{2}}{{\left(a^{3} b^{4} - 3 \, a^{2} b^{5} + 3 \, a b^{6} - b^{7}\right)} d^{2}}} \log\left(2 \, {\left(16 \, a^{4} b^{3} - 73 \, a^{3} b^{4} + 123 \, a^{2} b^{5} - 91 \, a b^{6} + 25 \, b^{7}\right)} d^{2} \sqrt{\frac{64 \, a^{5} - 464 \, a^{4} b + 1241 \, a^{3} b^{2} - 1450 \, a^{2} b^{3} + 625 \, a b^{4}}{{\left(a^{6} b^{7} - 6 \, a^{5} b^{8} + 15 \, a^{4} b^{9} - 20 \, a^{3} b^{10} + 15 \, a^{2} b^{11} - 6 \, a b^{12} + b^{13}\right)} d^{4}}} + 128 \, a^{3} - 664 \, a^{2} b + 1125 \, a b^{2} - 625 \, b^{3} - {\left(128 \, a^{3} - 664 \, a^{2} b + 1125 \, a b^{2} - 625 \, b^{3}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(128 \, a^{3} - 664 \, a^{2} b + 1125 \, a b^{2} - 625 \, b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(128 \, a^{3} - 664 \, a^{2} b + 1125 \, a b^{2} - 625 \, b^{3}\right)} \sinh\left(d x + c\right)^{2} - 2 \, {\left(2 \, {\left(2 \, a^{4} b^{5} - 9 \, a^{3} b^{6} + 15 \, a^{2} b^{7} - 11 \, a b^{8} + 3 \, b^{9}\right)} d^{3} \sqrt{\frac{64 \, a^{5} - 464 \, a^{4} b + 1241 \, a^{3} b^{2} - 1450 \, a^{2} b^{3} + 625 \, a b^{4}}{{\left(a^{6} b^{7} - 6 \, a^{5} b^{8} + 15 \, a^{4} b^{9} - 20 \, a^{3} b^{10} + 15 \, a^{2} b^{11} - 6 \, a b^{12} + b^{13}\right)} d^{4}}} + {\left(24 \, a^{3} b^{2} - 127 \, a^{2} b^{3} + 220 \, a b^{4} - 125 \, b^{5}\right)} d\right)} \sqrt{-\frac{{\left(a^{3} b^{4} - 3 \, a^{2} b^{5} + 3 \, a b^{6} - b^{7}\right)} d^{2} \sqrt{\frac{64 \, a^{5} - 464 \, a^{4} b + 1241 \, a^{3} b^{2} - 1450 \, a^{2} b^{3} + 625 \, a b^{4}}{{\left(a^{6} b^{7} - 6 \, a^{5} b^{8} + 15 \, a^{4} b^{9} - 20 \, a^{3} b^{10} + 15 \, a^{2} b^{11} - 6 \, a b^{12} + b^{13}\right)} d^{4}}} - 16 \, a^{3} + 47 \, a^{2} b - 35 \, a b^{2}}{{\left(a^{3} b^{4} - 3 \, a^{2} b^{5} + 3 \, a b^{6} - b^{7}\right)} d^{2}}}\right) - {\left({\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a b^{3} - b^{4}\right)} d \sinh\left(d x + c\right)^{8} - 4 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a b^{3} - b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{6} - 2 \, {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{3} - 3 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{4} - 30 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{2} - {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{4} - 4 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{5} - 10 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{3} - {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{6} - 15 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{4} - 3 \, {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a b^{3} - b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a b^{3} - b^{4}\right)} d + 8 \, {\left({\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{7} - 3 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{5} - {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{{\left(a^{3} b^{4} - 3 \, a^{2} b^{5} + 3 \, a b^{6} - b^{7}\right)} d^{2} \sqrt{\frac{64 \, a^{5} - 464 \, a^{4} b + 1241 \, a^{3} b^{2} - 1450 \, a^{2} b^{3} + 625 \, a b^{4}}{{\left(a^{6} b^{7} - 6 \, a^{5} b^{8} + 15 \, a^{4} b^{9} - 20 \, a^{3} b^{10} + 15 \, a^{2} b^{11} - 6 \, a b^{12} + b^{13}\right)} d^{4}}} + 16 \, a^{3} - 47 \, a^{2} b + 35 \, a b^{2}}{{\left(a^{3} b^{4} - 3 \, a^{2} b^{5} + 3 \, a b^{6} - b^{7}\right)} d^{2}}} \log\left(-2 \, {\left(16 \, a^{4} b^{3} - 73 \, a^{3} b^{4} + 123 \, a^{2} b^{5} - 91 \, a b^{6} + 25 \, b^{7}\right)} d^{2} \sqrt{\frac{64 \, a^{5} - 464 \, a^{4} b + 1241 \, a^{3} b^{2} - 1450 \, a^{2} b^{3} + 625 \, a b^{4}}{{\left(a^{6} b^{7} - 6 \, a^{5} b^{8} + 15 \, a^{4} b^{9} - 20 \, a^{3} b^{10} + 15 \, a^{2} b^{11} - 6 \, a b^{12} + b^{13}\right)} d^{4}}} + 128 \, a^{3} - 664 \, a^{2} b + 1125 \, a b^{2} - 625 \, b^{3} - {\left(128 \, a^{3} - 664 \, a^{2} b + 1125 \, a b^{2} - 625 \, b^{3}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(128 \, a^{3} - 664 \, a^{2} b + 1125 \, a b^{2} - 625 \, b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(128 \, a^{3} - 664 \, a^{2} b + 1125 \, a b^{2} - 625 \, b^{3}\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(2 \, {\left(2 \, a^{4} b^{5} - 9 \, a^{3} b^{6} + 15 \, a^{2} b^{7} - 11 \, a b^{8} + 3 \, b^{9}\right)} d^{3} \sqrt{\frac{64 \, a^{5} - 464 \, a^{4} b + 1241 \, a^{3} b^{2} - 1450 \, a^{2} b^{3} + 625 \, a b^{4}}{{\left(a^{6} b^{7} - 6 \, a^{5} b^{8} + 15 \, a^{4} b^{9} - 20 \, a^{3} b^{10} + 15 \, a^{2} b^{11} - 6 \, a b^{12} + b^{13}\right)} d^{4}}} - {\left(24 \, a^{3} b^{2} - 127 \, a^{2} b^{3} + 220 \, a b^{4} - 125 \, b^{5}\right)} d\right)} \sqrt{\frac{{\left(a^{3} b^{4} - 3 \, a^{2} b^{5} + 3 \, a b^{6} - b^{7}\right)} d^{2} \sqrt{\frac{64 \, a^{5} - 464 \, a^{4} b + 1241 \, a^{3} b^{2} - 1450 \, a^{2} b^{3} + 625 \, a b^{4}}{{\left(a^{6} b^{7} - 6 \, a^{5} b^{8} + 15 \, a^{4} b^{9} - 20 \, a^{3} b^{10} + 15 \, a^{2} b^{11} - 6 \, a b^{12} + b^{13}\right)} d^{4}}} + 16 \, a^{3} - 47 \, a^{2} b + 35 \, a b^{2}}{{\left(a^{3} b^{4} - 3 \, a^{2} b^{5} + 3 \, a b^{6} - b^{7}\right)} d^{2}}}\right) + {\left({\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a b^{3} - b^{4}\right)} d \sinh\left(d x + c\right)^{8} - 4 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a b^{3} - b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{6} - 2 \, {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{3} - 3 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{4} - 30 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{2} - {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{4} - 4 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{5} - 10 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{3} - {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{6} - 15 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{4} - 3 \, {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a b^{3} - b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a b^{3} - b^{4}\right)} d + 8 \, {\left({\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{7} - 3 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{5} - {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{{\left(a^{3} b^{4} - 3 \, a^{2} b^{5} + 3 \, a b^{6} - b^{7}\right)} d^{2} \sqrt{\frac{64 \, a^{5} - 464 \, a^{4} b + 1241 \, a^{3} b^{2} - 1450 \, a^{2} b^{3} + 625 \, a b^{4}}{{\left(a^{6} b^{7} - 6 \, a^{5} b^{8} + 15 \, a^{4} b^{9} - 20 \, a^{3} b^{10} + 15 \, a^{2} b^{11} - 6 \, a b^{12} + b^{13}\right)} d^{4}}} + 16 \, a^{3} - 47 \, a^{2} b + 35 \, a b^{2}}{{\left(a^{3} b^{4} - 3 \, a^{2} b^{5} + 3 \, a b^{6} - b^{7}\right)} d^{2}}} \log\left(-2 \, {\left(16 \, a^{4} b^{3} - 73 \, a^{3} b^{4} + 123 \, a^{2} b^{5} - 91 \, a b^{6} + 25 \, b^{7}\right)} d^{2} \sqrt{\frac{64 \, a^{5} - 464 \, a^{4} b + 1241 \, a^{3} b^{2} - 1450 \, a^{2} b^{3} + 625 \, a b^{4}}{{\left(a^{6} b^{7} - 6 \, a^{5} b^{8} + 15 \, a^{4} b^{9} - 20 \, a^{3} b^{10} + 15 \, a^{2} b^{11} - 6 \, a b^{12} + b^{13}\right)} d^{4}}} + 128 \, a^{3} - 664 \, a^{2} b + 1125 \, a b^{2} - 625 \, b^{3} - {\left(128 \, a^{3} - 664 \, a^{2} b + 1125 \, a b^{2} - 625 \, b^{3}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(128 \, a^{3} - 664 \, a^{2} b + 1125 \, a b^{2} - 625 \, b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(128 \, a^{3} - 664 \, a^{2} b + 1125 \, a b^{2} - 625 \, b^{3}\right)} \sinh\left(d x + c\right)^{2} - 2 \, {\left(2 \, {\left(2 \, a^{4} b^{5} - 9 \, a^{3} b^{6} + 15 \, a^{2} b^{7} - 11 \, a b^{8} + 3 \, b^{9}\right)} d^{3} \sqrt{\frac{64 \, a^{5} - 464 \, a^{4} b + 1241 \, a^{3} b^{2} - 1450 \, a^{2} b^{3} + 625 \, a b^{4}}{{\left(a^{6} b^{7} - 6 \, a^{5} b^{8} + 15 \, a^{4} b^{9} - 20 \, a^{3} b^{10} + 15 \, a^{2} b^{11} - 6 \, a b^{12} + b^{13}\right)} d^{4}}} - {\left(24 \, a^{3} b^{2} - 127 \, a^{2} b^{3} + 220 \, a b^{4} - 125 \, b^{5}\right)} d\right)} \sqrt{\frac{{\left(a^{3} b^{4} - 3 \, a^{2} b^{5} + 3 \, a b^{6} - b^{7}\right)} d^{2} \sqrt{\frac{64 \, a^{5} - 464 \, a^{4} b + 1241 \, a^{3} b^{2} - 1450 \, a^{2} b^{3} + 625 \, a b^{4}}{{\left(a^{6} b^{7} - 6 \, a^{5} b^{8} + 15 \, a^{4} b^{9} - 20 \, a^{3} b^{10} + 15 \, a^{2} b^{11} - 6 \, a b^{12} + b^{13}\right)} d^{4}}} + 16 \, a^{3} - 47 \, a^{2} b + 35 \, a b^{2}}{{\left(a^{3} b^{4} - 3 \, a^{2} b^{5} + 3 \, a b^{6} - b^{7}\right)} d^{2}}}\right) + 8 \, a b + 16 \, {\left(8 \, {\left(a b - b^{2}\right)} d x \cosh\left(d x + c\right)^{7} - 3 \, {\left(8 \, {\left(a b - b^{2}\right)} d x - a b\right)} \cosh\left(d x + c\right)^{5} - 2 \, {\left(4 \, {\left(8 \, a^{2} - 11 \, a b + 3 \, b^{2}\right)} d x + 8 \, a^{2} - 3 \, a b\right)} \cosh\left(d x + c\right)^{3} - {\left(8 \, {\left(a b - b^{2}\right)} d x + 5 \, a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{16 \, {\left({\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a b^{3} - b^{4}\right)} d \sinh\left(d x + c\right)^{8} - 4 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a b^{3} - b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{6} - 2 \, {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{3} - 3 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{4} - 30 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{2} - {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{4} - 4 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{5} - 10 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{3} - {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{6} - 15 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{4} - 3 \, {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a b^{3} - b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a b^{3} - b^{4}\right)} d + 8 \, {\left({\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{7} - 3 \, {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{5} - {\left(8 \, a^{2} b^{2} - 11 \, a b^{3} + 3 \, b^{4}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"1/16*(16*(a*b - b^2)*d*x*cosh(d*x + c)^8 + 128*(a*b - b^2)*d*x*cosh(d*x + c)*sinh(d*x + c)^7 + 16*(a*b - b^2)*d*x*sinh(d*x + c)^8 - 8*(8*(a*b - b^2)*d*x - a*b)*cosh(d*x + c)^6 + 8*(56*(a*b - b^2)*d*x*cosh(d*x + c)^2 - 8*(a*b - b^2)*d*x + a*b)*sinh(d*x + c)^6 + 16*(56*(a*b - b^2)*d*x*cosh(d*x + c)^3 - 3*(8*(a*b - b^2)*d*x - a*b)*cosh(d*x + c))*sinh(d*x + c)^5 - 8*(4*(8*a^2 - 11*a*b + 3*b^2)*d*x + 8*a^2 - 3*a*b)*cosh(d*x + c)^4 + 8*(140*(a*b - b^2)*d*x*cosh(d*x + c)^4 - 4*(8*a^2 - 11*a*b + 3*b^2)*d*x - 15*(8*(a*b - b^2)*d*x - a*b)*cosh(d*x + c)^2 - 8*a^2 + 3*a*b)*sinh(d*x + c)^4 + 32*(28*(a*b - b^2)*d*x*cosh(d*x + c)^5 - 5*(8*(a*b - b^2)*d*x - a*b)*cosh(d*x + c)^3 - (4*(8*a^2 - 11*a*b + 3*b^2)*d*x + 8*a^2 - 3*a*b)*cosh(d*x + c))*sinh(d*x + c)^3 + 16*(a*b - b^2)*d*x - 8*(8*(a*b - b^2)*d*x + 5*a*b)*cosh(d*x + c)^2 + 8*(56*(a*b - b^2)*d*x*cosh(d*x + c)^6 - 15*(8*(a*b - b^2)*d*x - a*b)*cosh(d*x + c)^4 - 8*(a*b - b^2)*d*x - 6*(4*(8*a^2 - 11*a*b + 3*b^2)*d*x + 8*a^2 - 3*a*b)*cosh(d*x + c)^2 - 5*a*b)*sinh(d*x + c)^2 + ((a*b^3 - b^4)*d*cosh(d*x + c)^8 + 8*(a*b^3 - b^4)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a*b^3 - b^4)*d*sinh(d*x + c)^8 - 4*(a*b^3 - b^4)*d*cosh(d*x + c)^6 + 4*(7*(a*b^3 - b^4)*d*cosh(d*x + c)^2 - (a*b^3 - b^4)*d)*sinh(d*x + c)^6 - 2*(8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d*cosh(d*x + c)^4 + 8*(7*(a*b^3 - b^4)*d*cosh(d*x + c)^3 - 3*(a*b^3 - b^4)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a*b^3 - b^4)*d*cosh(d*x + c)^4 - 30*(a*b^3 - b^4)*d*cosh(d*x + c)^2 - (8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d)*sinh(d*x + c)^4 - 4*(a*b^3 - b^4)*d*cosh(d*x + c)^2 + 8*(7*(a*b^3 - b^4)*d*cosh(d*x + c)^5 - 10*(a*b^3 - b^4)*d*cosh(d*x + c)^3 - (8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a*b^3 - b^4)*d*cosh(d*x + c)^6 - 15*(a*b^3 - b^4)*d*cosh(d*x + c)^4 - 3*(8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d*cosh(d*x + c)^2 - (a*b^3 - b^4)*d)*sinh(d*x + c)^2 + (a*b^3 - b^4)*d + 8*((a*b^3 - b^4)*d*cosh(d*x + c)^7 - 3*(a*b^3 - b^4)*d*cosh(d*x + c)^5 - (8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d*cosh(d*x + c)^3 - (a*b^3 - b^4)*d*cosh(d*x + c))*sinh(d*x + c))*sqrt(-((a^3*b^4 - 3*a^2*b^5 + 3*a*b^6 - b^7)*d^2*sqrt((64*a^5 - 464*a^4*b + 1241*a^3*b^2 - 1450*a^2*b^3 + 625*a*b^4)/((a^6*b^7 - 6*a^5*b^8 + 15*a^4*b^9 - 20*a^3*b^10 + 15*a^2*b^11 - 6*a*b^12 + b^13)*d^4)) - 16*a^3 + 47*a^2*b - 35*a*b^2)/((a^3*b^4 - 3*a^2*b^5 + 3*a*b^6 - b^7)*d^2))*log(2*(16*a^4*b^3 - 73*a^3*b^4 + 123*a^2*b^5 - 91*a*b^6 + 25*b^7)*d^2*sqrt((64*a^5 - 464*a^4*b + 1241*a^3*b^2 - 1450*a^2*b^3 + 625*a*b^4)/((a^6*b^7 - 6*a^5*b^8 + 15*a^4*b^9 - 20*a^3*b^10 + 15*a^2*b^11 - 6*a*b^12 + b^13)*d^4)) + 128*a^3 - 664*a^2*b + 1125*a*b^2 - 625*b^3 - (128*a^3 - 664*a^2*b + 1125*a*b^2 - 625*b^3)*cosh(d*x + c)^2 - 2*(128*a^3 - 664*a^2*b + 1125*a*b^2 - 625*b^3)*cosh(d*x + c)*sinh(d*x + c) - (128*a^3 - 664*a^2*b + 1125*a*b^2 - 625*b^3)*sinh(d*x + c)^2 + 2*(2*(2*a^4*b^5 - 9*a^3*b^6 + 15*a^2*b^7 - 11*a*b^8 + 3*b^9)*d^3*sqrt((64*a^5 - 464*a^4*b + 1241*a^3*b^2 - 1450*a^2*b^3 + 625*a*b^4)/((a^6*b^7 - 6*a^5*b^8 + 15*a^4*b^9 - 20*a^3*b^10 + 15*a^2*b^11 - 6*a*b^12 + b^13)*d^4)) + (24*a^3*b^2 - 127*a^2*b^3 + 220*a*b^4 - 125*b^5)*d)*sqrt(-((a^3*b^4 - 3*a^2*b^5 + 3*a*b^6 - b^7)*d^2*sqrt((64*a^5 - 464*a^4*b + 1241*a^3*b^2 - 1450*a^2*b^3 + 625*a*b^4)/((a^6*b^7 - 6*a^5*b^8 + 15*a^4*b^9 - 20*a^3*b^10 + 15*a^2*b^11 - 6*a*b^12 + b^13)*d^4)) - 16*a^3 + 47*a^2*b - 35*a*b^2)/((a^3*b^4 - 3*a^2*b^5 + 3*a*b^6 - b^7)*d^2))) - ((a*b^3 - b^4)*d*cosh(d*x + c)^8 + 8*(a*b^3 - b^4)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a*b^3 - b^4)*d*sinh(d*x + c)^8 - 4*(a*b^3 - b^4)*d*cosh(d*x + c)^6 + 4*(7*(a*b^3 - b^4)*d*cosh(d*x + c)^2 - (a*b^3 - b^4)*d)*sinh(d*x + c)^6 - 2*(8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d*cosh(d*x + c)^4 + 8*(7*(a*b^3 - b^4)*d*cosh(d*x + c)^3 - 3*(a*b^3 - b^4)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a*b^3 - b^4)*d*cosh(d*x + c)^4 - 30*(a*b^3 - b^4)*d*cosh(d*x + c)^2 - (8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d)*sinh(d*x + c)^4 - 4*(a*b^3 - b^4)*d*cosh(d*x + c)^2 + 8*(7*(a*b^3 - b^4)*d*cosh(d*x + c)^5 - 10*(a*b^3 - b^4)*d*cosh(d*x + c)^3 - (8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a*b^3 - b^4)*d*cosh(d*x + c)^6 - 15*(a*b^3 - b^4)*d*cosh(d*x + c)^4 - 3*(8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d*cosh(d*x + c)^2 - (a*b^3 - b^4)*d)*sinh(d*x + c)^2 + (a*b^3 - b^4)*d + 8*((a*b^3 - b^4)*d*cosh(d*x + c)^7 - 3*(a*b^3 - b^4)*d*cosh(d*x + c)^5 - (8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d*cosh(d*x + c)^3 - (a*b^3 - b^4)*d*cosh(d*x + c))*sinh(d*x + c))*sqrt(-((a^3*b^4 - 3*a^2*b^5 + 3*a*b^6 - b^7)*d^2*sqrt((64*a^5 - 464*a^4*b + 1241*a^3*b^2 - 1450*a^2*b^3 + 625*a*b^4)/((a^6*b^7 - 6*a^5*b^8 + 15*a^4*b^9 - 20*a^3*b^10 + 15*a^2*b^11 - 6*a*b^12 + b^13)*d^4)) - 16*a^3 + 47*a^2*b - 35*a*b^2)/((a^3*b^4 - 3*a^2*b^5 + 3*a*b^6 - b^7)*d^2))*log(2*(16*a^4*b^3 - 73*a^3*b^4 + 123*a^2*b^5 - 91*a*b^6 + 25*b^7)*d^2*sqrt((64*a^5 - 464*a^4*b + 1241*a^3*b^2 - 1450*a^2*b^3 + 625*a*b^4)/((a^6*b^7 - 6*a^5*b^8 + 15*a^4*b^9 - 20*a^3*b^10 + 15*a^2*b^11 - 6*a*b^12 + b^13)*d^4)) + 128*a^3 - 664*a^2*b + 1125*a*b^2 - 625*b^3 - (128*a^3 - 664*a^2*b + 1125*a*b^2 - 625*b^3)*cosh(d*x + c)^2 - 2*(128*a^3 - 664*a^2*b + 1125*a*b^2 - 625*b^3)*cosh(d*x + c)*sinh(d*x + c) - (128*a^3 - 664*a^2*b + 1125*a*b^2 - 625*b^3)*sinh(d*x + c)^2 - 2*(2*(2*a^4*b^5 - 9*a^3*b^6 + 15*a^2*b^7 - 11*a*b^8 + 3*b^9)*d^3*sqrt((64*a^5 - 464*a^4*b + 1241*a^3*b^2 - 1450*a^2*b^3 + 625*a*b^4)/((a^6*b^7 - 6*a^5*b^8 + 15*a^4*b^9 - 20*a^3*b^10 + 15*a^2*b^11 - 6*a*b^12 + b^13)*d^4)) + (24*a^3*b^2 - 127*a^2*b^3 + 220*a*b^4 - 125*b^5)*d)*sqrt(-((a^3*b^4 - 3*a^2*b^5 + 3*a*b^6 - b^7)*d^2*sqrt((64*a^5 - 464*a^4*b + 1241*a^3*b^2 - 1450*a^2*b^3 + 625*a*b^4)/((a^6*b^7 - 6*a^5*b^8 + 15*a^4*b^9 - 20*a^3*b^10 + 15*a^2*b^11 - 6*a*b^12 + b^13)*d^4)) - 16*a^3 + 47*a^2*b - 35*a*b^2)/((a^3*b^4 - 3*a^2*b^5 + 3*a*b^6 - b^7)*d^2))) - ((a*b^3 - b^4)*d*cosh(d*x + c)^8 + 8*(a*b^3 - b^4)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a*b^3 - b^4)*d*sinh(d*x + c)^8 - 4*(a*b^3 - b^4)*d*cosh(d*x + c)^6 + 4*(7*(a*b^3 - b^4)*d*cosh(d*x + c)^2 - (a*b^3 - b^4)*d)*sinh(d*x + c)^6 - 2*(8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d*cosh(d*x + c)^4 + 8*(7*(a*b^3 - b^4)*d*cosh(d*x + c)^3 - 3*(a*b^3 - b^4)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a*b^3 - b^4)*d*cosh(d*x + c)^4 - 30*(a*b^3 - b^4)*d*cosh(d*x + c)^2 - (8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d)*sinh(d*x + c)^4 - 4*(a*b^3 - b^4)*d*cosh(d*x + c)^2 + 8*(7*(a*b^3 - b^4)*d*cosh(d*x + c)^5 - 10*(a*b^3 - b^4)*d*cosh(d*x + c)^3 - (8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a*b^3 - b^4)*d*cosh(d*x + c)^6 - 15*(a*b^3 - b^4)*d*cosh(d*x + c)^4 - 3*(8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d*cosh(d*x + c)^2 - (a*b^3 - b^4)*d)*sinh(d*x + c)^2 + (a*b^3 - b^4)*d + 8*((a*b^3 - b^4)*d*cosh(d*x + c)^7 - 3*(a*b^3 - b^4)*d*cosh(d*x + c)^5 - (8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d*cosh(d*x + c)^3 - (a*b^3 - b^4)*d*cosh(d*x + c))*sinh(d*x + c))*sqrt(((a^3*b^4 - 3*a^2*b^5 + 3*a*b^6 - b^7)*d^2*sqrt((64*a^5 - 464*a^4*b + 1241*a^3*b^2 - 1450*a^2*b^3 + 625*a*b^4)/((a^6*b^7 - 6*a^5*b^8 + 15*a^4*b^9 - 20*a^3*b^10 + 15*a^2*b^11 - 6*a*b^12 + b^13)*d^4)) + 16*a^3 - 47*a^2*b + 35*a*b^2)/((a^3*b^4 - 3*a^2*b^5 + 3*a*b^6 - b^7)*d^2))*log(-2*(16*a^4*b^3 - 73*a^3*b^4 + 123*a^2*b^5 - 91*a*b^6 + 25*b^7)*d^2*sqrt((64*a^5 - 464*a^4*b + 1241*a^3*b^2 - 1450*a^2*b^3 + 625*a*b^4)/((a^6*b^7 - 6*a^5*b^8 + 15*a^4*b^9 - 20*a^3*b^10 + 15*a^2*b^11 - 6*a*b^12 + b^13)*d^4)) + 128*a^3 - 664*a^2*b + 1125*a*b^2 - 625*b^3 - (128*a^3 - 664*a^2*b + 1125*a*b^2 - 625*b^3)*cosh(d*x + c)^2 - 2*(128*a^3 - 664*a^2*b + 1125*a*b^2 - 625*b^3)*cosh(d*x + c)*sinh(d*x + c) - (128*a^3 - 664*a^2*b + 1125*a*b^2 - 625*b^3)*sinh(d*x + c)^2 + 2*(2*(2*a^4*b^5 - 9*a^3*b^6 + 15*a^2*b^7 - 11*a*b^8 + 3*b^9)*d^3*sqrt((64*a^5 - 464*a^4*b + 1241*a^3*b^2 - 1450*a^2*b^3 + 625*a*b^4)/((a^6*b^7 - 6*a^5*b^8 + 15*a^4*b^9 - 20*a^3*b^10 + 15*a^2*b^11 - 6*a*b^12 + b^13)*d^4)) - (24*a^3*b^2 - 127*a^2*b^3 + 220*a*b^4 - 125*b^5)*d)*sqrt(((a^3*b^4 - 3*a^2*b^5 + 3*a*b^6 - b^7)*d^2*sqrt((64*a^5 - 464*a^4*b + 1241*a^3*b^2 - 1450*a^2*b^3 + 625*a*b^4)/((a^6*b^7 - 6*a^5*b^8 + 15*a^4*b^9 - 20*a^3*b^10 + 15*a^2*b^11 - 6*a*b^12 + b^13)*d^4)) + 16*a^3 - 47*a^2*b + 35*a*b^2)/((a^3*b^4 - 3*a^2*b^5 + 3*a*b^6 - b^7)*d^2))) + ((a*b^3 - b^4)*d*cosh(d*x + c)^8 + 8*(a*b^3 - b^4)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a*b^3 - b^4)*d*sinh(d*x + c)^8 - 4*(a*b^3 - b^4)*d*cosh(d*x + c)^6 + 4*(7*(a*b^3 - b^4)*d*cosh(d*x + c)^2 - (a*b^3 - b^4)*d)*sinh(d*x + c)^6 - 2*(8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d*cosh(d*x + c)^4 + 8*(7*(a*b^3 - b^4)*d*cosh(d*x + c)^3 - 3*(a*b^3 - b^4)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a*b^3 - b^4)*d*cosh(d*x + c)^4 - 30*(a*b^3 - b^4)*d*cosh(d*x + c)^2 - (8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d)*sinh(d*x + c)^4 - 4*(a*b^3 - b^4)*d*cosh(d*x + c)^2 + 8*(7*(a*b^3 - b^4)*d*cosh(d*x + c)^5 - 10*(a*b^3 - b^4)*d*cosh(d*x + c)^3 - (8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a*b^3 - b^4)*d*cosh(d*x + c)^6 - 15*(a*b^3 - b^4)*d*cosh(d*x + c)^4 - 3*(8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d*cosh(d*x + c)^2 - (a*b^3 - b^4)*d)*sinh(d*x + c)^2 + (a*b^3 - b^4)*d + 8*((a*b^3 - b^4)*d*cosh(d*x + c)^7 - 3*(a*b^3 - b^4)*d*cosh(d*x + c)^5 - (8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d*cosh(d*x + c)^3 - (a*b^3 - b^4)*d*cosh(d*x + c))*sinh(d*x + c))*sqrt(((a^3*b^4 - 3*a^2*b^5 + 3*a*b^6 - b^7)*d^2*sqrt((64*a^5 - 464*a^4*b + 1241*a^3*b^2 - 1450*a^2*b^3 + 625*a*b^4)/((a^6*b^7 - 6*a^5*b^8 + 15*a^4*b^9 - 20*a^3*b^10 + 15*a^2*b^11 - 6*a*b^12 + b^13)*d^4)) + 16*a^3 - 47*a^2*b + 35*a*b^2)/((a^3*b^4 - 3*a^2*b^5 + 3*a*b^6 - b^7)*d^2))*log(-2*(16*a^4*b^3 - 73*a^3*b^4 + 123*a^2*b^5 - 91*a*b^6 + 25*b^7)*d^2*sqrt((64*a^5 - 464*a^4*b + 1241*a^3*b^2 - 1450*a^2*b^3 + 625*a*b^4)/((a^6*b^7 - 6*a^5*b^8 + 15*a^4*b^9 - 20*a^3*b^10 + 15*a^2*b^11 - 6*a*b^12 + b^13)*d^4)) + 128*a^3 - 664*a^2*b + 1125*a*b^2 - 625*b^3 - (128*a^3 - 664*a^2*b + 1125*a*b^2 - 625*b^3)*cosh(d*x + c)^2 - 2*(128*a^3 - 664*a^2*b + 1125*a*b^2 - 625*b^3)*cosh(d*x + c)*sinh(d*x + c) - (128*a^3 - 664*a^2*b + 1125*a*b^2 - 625*b^3)*sinh(d*x + c)^2 - 2*(2*(2*a^4*b^5 - 9*a^3*b^6 + 15*a^2*b^7 - 11*a*b^8 + 3*b^9)*d^3*sqrt((64*a^5 - 464*a^4*b + 1241*a^3*b^2 - 1450*a^2*b^3 + 625*a*b^4)/((a^6*b^7 - 6*a^5*b^8 + 15*a^4*b^9 - 20*a^3*b^10 + 15*a^2*b^11 - 6*a*b^12 + b^13)*d^4)) - (24*a^3*b^2 - 127*a^2*b^3 + 220*a*b^4 - 125*b^5)*d)*sqrt(((a^3*b^4 - 3*a^2*b^5 + 3*a*b^6 - b^7)*d^2*sqrt((64*a^5 - 464*a^4*b + 1241*a^3*b^2 - 1450*a^2*b^3 + 625*a*b^4)/((a^6*b^7 - 6*a^5*b^8 + 15*a^4*b^9 - 20*a^3*b^10 + 15*a^2*b^11 - 6*a*b^12 + b^13)*d^4)) + 16*a^3 - 47*a^2*b + 35*a*b^2)/((a^3*b^4 - 3*a^2*b^5 + 3*a*b^6 - b^7)*d^2))) + 8*a*b + 16*(8*(a*b - b^2)*d*x*cosh(d*x + c)^7 - 3*(8*(a*b - b^2)*d*x - a*b)*cosh(d*x + c)^5 - 2*(4*(8*a^2 - 11*a*b + 3*b^2)*d*x + 8*a^2 - 3*a*b)*cosh(d*x + c)^3 - (8*(a*b - b^2)*d*x + 5*a*b)*cosh(d*x + c))*sinh(d*x + c))/((a*b^3 - b^4)*d*cosh(d*x + c)^8 + 8*(a*b^3 - b^4)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a*b^3 - b^4)*d*sinh(d*x + c)^8 - 4*(a*b^3 - b^4)*d*cosh(d*x + c)^6 + 4*(7*(a*b^3 - b^4)*d*cosh(d*x + c)^2 - (a*b^3 - b^4)*d)*sinh(d*x + c)^6 - 2*(8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d*cosh(d*x + c)^4 + 8*(7*(a*b^3 - b^4)*d*cosh(d*x + c)^3 - 3*(a*b^3 - b^4)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a*b^3 - b^4)*d*cosh(d*x + c)^4 - 30*(a*b^3 - b^4)*d*cosh(d*x + c)^2 - (8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d)*sinh(d*x + c)^4 - 4*(a*b^3 - b^4)*d*cosh(d*x + c)^2 + 8*(7*(a*b^3 - b^4)*d*cosh(d*x + c)^5 - 10*(a*b^3 - b^4)*d*cosh(d*x + c)^3 - (8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a*b^3 - b^4)*d*cosh(d*x + c)^6 - 15*(a*b^3 - b^4)*d*cosh(d*x + c)^4 - 3*(8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d*cosh(d*x + c)^2 - (a*b^3 - b^4)*d)*sinh(d*x + c)^2 + (a*b^3 - b^4)*d + 8*((a*b^3 - b^4)*d*cosh(d*x + c)^7 - 3*(a*b^3 - b^4)*d*cosh(d*x + c)^5 - (8*a^2*b^2 - 11*a*b^3 + 3*b^4)*d*cosh(d*x + c)^3 - (a*b^3 - b^4)*d*cosh(d*x + c))*sinh(d*x + c))","B",0
248,1,6045,0,1.364463," ","integrate(sinh(d*x+c)^6/(a-b*sinh(d*x+c)^4)^2,x, algorithm=""fricas"")","-\frac{8 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{6} + 48 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + 8 \, {\left(2 \, a - b\right)} \sinh\left(d x + c\right)^{6} - 8 \, {\left(8 \, a - 3 \, b\right)} \cosh\left(d x + c\right)^{4} + 8 \, {\left(15 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} - 8 \, a + 3 \, b\right)} \sinh\left(d x + c\right)^{4} + 32 \, {\left(5 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{3} - {\left(8 \, a - 3 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 8 \, {\left(2 \, a + 3 \, b\right)} \cosh\left(d x + c\right)^{2} + 8 \, {\left(15 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{4} - 6 \, {\left(8 \, a - 3 \, b\right)} \cosh\left(d x + c\right)^{2} - 2 \, a - 3 \, b\right)} \sinh\left(d x + c\right)^{2} - {\left({\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a b^{2} - b^{3}\right)} d \sinh\left(d x + c\right)^{8} - 4 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a b^{2} - b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{6} - 2 \, {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{3} - 3 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{4} - 30 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{2} - {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{4} - 4 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{5} - 10 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{3} - {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{6} - 15 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{4} - 3 \, {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a b^{2} - b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a b^{2} - b^{3}\right)} d + 8 \, {\left({\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{7} - 3 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{5} - {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{{\left(a^{3} b^{3} - 3 \, a^{2} b^{4} + 3 \, a b^{5} - b^{6}\right)} d^{2} \sqrt{\frac{25 \, a^{2} - 90 \, a b + 81 \, b^{2}}{{\left(a^{7} b^{3} - 6 \, a^{6} b^{4} + 15 \, a^{5} b^{5} - 20 \, a^{4} b^{6} + 15 \, a^{3} b^{7} - 6 \, a^{2} b^{8} + a b^{9}\right)} d^{4}}} - 4 \, a^{2} + 15 \, a b - 15 \, b^{2}}{{\left(a^{3} b^{3} - 3 \, a^{2} b^{4} + 3 \, a b^{5} - b^{6}\right)} d^{2}}} \log\left(2 \, {\left(4 \, a^{5} b - 21 \, a^{4} b^{2} + 39 \, a^{3} b^{3} - 31 \, a^{2} b^{4} + 9 \, a b^{5}\right)} d^{2} \sqrt{\frac{25 \, a^{2} - 90 \, a b + 81 \, b^{2}}{{\left(a^{7} b^{3} - 6 \, a^{6} b^{4} + 15 \, a^{5} b^{5} - 20 \, a^{4} b^{6} + 15 \, a^{3} b^{7} - 6 \, a^{2} b^{8} + a b^{9}\right)} d^{4}}} + {\left(20 \, a^{2} - 81 \, a b + 81 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(20 \, a^{2} - 81 \, a b + 81 \, b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(20 \, a^{2} - 81 \, a b + 81 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} - 20 \, a^{2} + 81 \, a b - 81 \, b^{2} + 2 \, {\left({\left(a^{5} b^{3} - 6 \, a^{4} b^{4} + 12 \, a^{3} b^{5} - 10 \, a^{2} b^{6} + 3 \, a b^{7}\right)} d^{3} \sqrt{\frac{25 \, a^{2} - 90 \, a b + 81 \, b^{2}}{{\left(a^{7} b^{3} - 6 \, a^{6} b^{4} + 15 \, a^{5} b^{5} - 20 \, a^{4} b^{6} + 15 \, a^{3} b^{7} - 6 \, a^{2} b^{8} + a b^{9}\right)} d^{4}}} - 2 \, {\left(5 \, a^{3} b - 19 \, a^{2} b^{2} + 18 \, a b^{3}\right)} d\right)} \sqrt{-\frac{{\left(a^{3} b^{3} - 3 \, a^{2} b^{4} + 3 \, a b^{5} - b^{6}\right)} d^{2} \sqrt{\frac{25 \, a^{2} - 90 \, a b + 81 \, b^{2}}{{\left(a^{7} b^{3} - 6 \, a^{6} b^{4} + 15 \, a^{5} b^{5} - 20 \, a^{4} b^{6} + 15 \, a^{3} b^{7} - 6 \, a^{2} b^{8} + a b^{9}\right)} d^{4}}} - 4 \, a^{2} + 15 \, a b - 15 \, b^{2}}{{\left(a^{3} b^{3} - 3 \, a^{2} b^{4} + 3 \, a b^{5} - b^{6}\right)} d^{2}}}\right) + {\left({\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a b^{2} - b^{3}\right)} d \sinh\left(d x + c\right)^{8} - 4 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a b^{2} - b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{6} - 2 \, {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{3} - 3 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{4} - 30 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{2} - {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{4} - 4 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{5} - 10 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{3} - {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{6} - 15 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{4} - 3 \, {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a b^{2} - b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a b^{2} - b^{3}\right)} d + 8 \, {\left({\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{7} - 3 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{5} - {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{{\left(a^{3} b^{3} - 3 \, a^{2} b^{4} + 3 \, a b^{5} - b^{6}\right)} d^{2} \sqrt{\frac{25 \, a^{2} - 90 \, a b + 81 \, b^{2}}{{\left(a^{7} b^{3} - 6 \, a^{6} b^{4} + 15 \, a^{5} b^{5} - 20 \, a^{4} b^{6} + 15 \, a^{3} b^{7} - 6 \, a^{2} b^{8} + a b^{9}\right)} d^{4}}} - 4 \, a^{2} + 15 \, a b - 15 \, b^{2}}{{\left(a^{3} b^{3} - 3 \, a^{2} b^{4} + 3 \, a b^{5} - b^{6}\right)} d^{2}}} \log\left(2 \, {\left(4 \, a^{5} b - 21 \, a^{4} b^{2} + 39 \, a^{3} b^{3} - 31 \, a^{2} b^{4} + 9 \, a b^{5}\right)} d^{2} \sqrt{\frac{25 \, a^{2} - 90 \, a b + 81 \, b^{2}}{{\left(a^{7} b^{3} - 6 \, a^{6} b^{4} + 15 \, a^{5} b^{5} - 20 \, a^{4} b^{6} + 15 \, a^{3} b^{7} - 6 \, a^{2} b^{8} + a b^{9}\right)} d^{4}}} + {\left(20 \, a^{2} - 81 \, a b + 81 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(20 \, a^{2} - 81 \, a b + 81 \, b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(20 \, a^{2} - 81 \, a b + 81 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} - 20 \, a^{2} + 81 \, a b - 81 \, b^{2} - 2 \, {\left({\left(a^{5} b^{3} - 6 \, a^{4} b^{4} + 12 \, a^{3} b^{5} - 10 \, a^{2} b^{6} + 3 \, a b^{7}\right)} d^{3} \sqrt{\frac{25 \, a^{2} - 90 \, a b + 81 \, b^{2}}{{\left(a^{7} b^{3} - 6 \, a^{6} b^{4} + 15 \, a^{5} b^{5} - 20 \, a^{4} b^{6} + 15 \, a^{3} b^{7} - 6 \, a^{2} b^{8} + a b^{9}\right)} d^{4}}} - 2 \, {\left(5 \, a^{3} b - 19 \, a^{2} b^{2} + 18 \, a b^{3}\right)} d\right)} \sqrt{-\frac{{\left(a^{3} b^{3} - 3 \, a^{2} b^{4} + 3 \, a b^{5} - b^{6}\right)} d^{2} \sqrt{\frac{25 \, a^{2} - 90 \, a b + 81 \, b^{2}}{{\left(a^{7} b^{3} - 6 \, a^{6} b^{4} + 15 \, a^{5} b^{5} - 20 \, a^{4} b^{6} + 15 \, a^{3} b^{7} - 6 \, a^{2} b^{8} + a b^{9}\right)} d^{4}}} - 4 \, a^{2} + 15 \, a b - 15 \, b^{2}}{{\left(a^{3} b^{3} - 3 \, a^{2} b^{4} + 3 \, a b^{5} - b^{6}\right)} d^{2}}}\right) + {\left({\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a b^{2} - b^{3}\right)} d \sinh\left(d x + c\right)^{8} - 4 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a b^{2} - b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{6} - 2 \, {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{3} - 3 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{4} - 30 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{2} - {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{4} - 4 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{5} - 10 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{3} - {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{6} - 15 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{4} - 3 \, {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a b^{2} - b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a b^{2} - b^{3}\right)} d + 8 \, {\left({\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{7} - 3 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{5} - {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{{\left(a^{3} b^{3} - 3 \, a^{2} b^{4} + 3 \, a b^{5} - b^{6}\right)} d^{2} \sqrt{\frac{25 \, a^{2} - 90 \, a b + 81 \, b^{2}}{{\left(a^{7} b^{3} - 6 \, a^{6} b^{4} + 15 \, a^{5} b^{5} - 20 \, a^{4} b^{6} + 15 \, a^{3} b^{7} - 6 \, a^{2} b^{8} + a b^{9}\right)} d^{4}}} + 4 \, a^{2} - 15 \, a b + 15 \, b^{2}}{{\left(a^{3} b^{3} - 3 \, a^{2} b^{4} + 3 \, a b^{5} - b^{6}\right)} d^{2}}} \log\left(-2 \, {\left(4 \, a^{5} b - 21 \, a^{4} b^{2} + 39 \, a^{3} b^{3} - 31 \, a^{2} b^{4} + 9 \, a b^{5}\right)} d^{2} \sqrt{\frac{25 \, a^{2} - 90 \, a b + 81 \, b^{2}}{{\left(a^{7} b^{3} - 6 \, a^{6} b^{4} + 15 \, a^{5} b^{5} - 20 \, a^{4} b^{6} + 15 \, a^{3} b^{7} - 6 \, a^{2} b^{8} + a b^{9}\right)} d^{4}}} + {\left(20 \, a^{2} - 81 \, a b + 81 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(20 \, a^{2} - 81 \, a b + 81 \, b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(20 \, a^{2} - 81 \, a b + 81 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} - 20 \, a^{2} + 81 \, a b - 81 \, b^{2} + 2 \, {\left({\left(a^{5} b^{3} - 6 \, a^{4} b^{4} + 12 \, a^{3} b^{5} - 10 \, a^{2} b^{6} + 3 \, a b^{7}\right)} d^{3} \sqrt{\frac{25 \, a^{2} - 90 \, a b + 81 \, b^{2}}{{\left(a^{7} b^{3} - 6 \, a^{6} b^{4} + 15 \, a^{5} b^{5} - 20 \, a^{4} b^{6} + 15 \, a^{3} b^{7} - 6 \, a^{2} b^{8} + a b^{9}\right)} d^{4}}} + 2 \, {\left(5 \, a^{3} b - 19 \, a^{2} b^{2} + 18 \, a b^{3}\right)} d\right)} \sqrt{\frac{{\left(a^{3} b^{3} - 3 \, a^{2} b^{4} + 3 \, a b^{5} - b^{6}\right)} d^{2} \sqrt{\frac{25 \, a^{2} - 90 \, a b + 81 \, b^{2}}{{\left(a^{7} b^{3} - 6 \, a^{6} b^{4} + 15 \, a^{5} b^{5} - 20 \, a^{4} b^{6} + 15 \, a^{3} b^{7} - 6 \, a^{2} b^{8} + a b^{9}\right)} d^{4}}} + 4 \, a^{2} - 15 \, a b + 15 \, b^{2}}{{\left(a^{3} b^{3} - 3 \, a^{2} b^{4} + 3 \, a b^{5} - b^{6}\right)} d^{2}}}\right) - {\left({\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a b^{2} - b^{3}\right)} d \sinh\left(d x + c\right)^{8} - 4 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a b^{2} - b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{6} - 2 \, {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{3} - 3 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{4} - 30 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{2} - {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{4} - 4 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{5} - 10 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{3} - {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{6} - 15 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{4} - 3 \, {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a b^{2} - b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a b^{2} - b^{3}\right)} d + 8 \, {\left({\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{7} - 3 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{5} - {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{{\left(a^{3} b^{3} - 3 \, a^{2} b^{4} + 3 \, a b^{5} - b^{6}\right)} d^{2} \sqrt{\frac{25 \, a^{2} - 90 \, a b + 81 \, b^{2}}{{\left(a^{7} b^{3} - 6 \, a^{6} b^{4} + 15 \, a^{5} b^{5} - 20 \, a^{4} b^{6} + 15 \, a^{3} b^{7} - 6 \, a^{2} b^{8} + a b^{9}\right)} d^{4}}} + 4 \, a^{2} - 15 \, a b + 15 \, b^{2}}{{\left(a^{3} b^{3} - 3 \, a^{2} b^{4} + 3 \, a b^{5} - b^{6}\right)} d^{2}}} \log\left(-2 \, {\left(4 \, a^{5} b - 21 \, a^{4} b^{2} + 39 \, a^{3} b^{3} - 31 \, a^{2} b^{4} + 9 \, a b^{5}\right)} d^{2} \sqrt{\frac{25 \, a^{2} - 90 \, a b + 81 \, b^{2}}{{\left(a^{7} b^{3} - 6 \, a^{6} b^{4} + 15 \, a^{5} b^{5} - 20 \, a^{4} b^{6} + 15 \, a^{3} b^{7} - 6 \, a^{2} b^{8} + a b^{9}\right)} d^{4}}} + {\left(20 \, a^{2} - 81 \, a b + 81 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(20 \, a^{2} - 81 \, a b + 81 \, b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(20 \, a^{2} - 81 \, a b + 81 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} - 20 \, a^{2} + 81 \, a b - 81 \, b^{2} - 2 \, {\left({\left(a^{5} b^{3} - 6 \, a^{4} b^{4} + 12 \, a^{3} b^{5} - 10 \, a^{2} b^{6} + 3 \, a b^{7}\right)} d^{3} \sqrt{\frac{25 \, a^{2} - 90 \, a b + 81 \, b^{2}}{{\left(a^{7} b^{3} - 6 \, a^{6} b^{4} + 15 \, a^{5} b^{5} - 20 \, a^{4} b^{6} + 15 \, a^{3} b^{7} - 6 \, a^{2} b^{8} + a b^{9}\right)} d^{4}}} + 2 \, {\left(5 \, a^{3} b - 19 \, a^{2} b^{2} + 18 \, a b^{3}\right)} d\right)} \sqrt{\frac{{\left(a^{3} b^{3} - 3 \, a^{2} b^{4} + 3 \, a b^{5} - b^{6}\right)} d^{2} \sqrt{\frac{25 \, a^{2} - 90 \, a b + 81 \, b^{2}}{{\left(a^{7} b^{3} - 6 \, a^{6} b^{4} + 15 \, a^{5} b^{5} - 20 \, a^{4} b^{6} + 15 \, a^{3} b^{7} - 6 \, a^{2} b^{8} + a b^{9}\right)} d^{4}}} + 4 \, a^{2} - 15 \, a b + 15 \, b^{2}}{{\left(a^{3} b^{3} - 3 \, a^{2} b^{4} + 3 \, a b^{5} - b^{6}\right)} d^{2}}}\right) + 16 \, {\left(3 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{5} - 2 \, {\left(8 \, a - 3 \, b\right)} \cosh\left(d x + c\right)^{3} - {\left(2 \, a + 3 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + 8 \, b}{16 \, {\left({\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a b^{2} - b^{3}\right)} d \sinh\left(d x + c\right)^{8} - 4 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a b^{2} - b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{6} - 2 \, {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{3} - 3 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{4} - 30 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{2} - {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{4} - 4 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{5} - 10 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{3} - {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{6} - 15 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{4} - 3 \, {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a b^{2} - b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a b^{2} - b^{3}\right)} d + 8 \, {\left({\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{7} - 3 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{5} - {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"-1/16*(8*(2*a - b)*cosh(d*x + c)^6 + 48*(2*a - b)*cosh(d*x + c)*sinh(d*x + c)^5 + 8*(2*a - b)*sinh(d*x + c)^6 - 8*(8*a - 3*b)*cosh(d*x + c)^4 + 8*(15*(2*a - b)*cosh(d*x + c)^2 - 8*a + 3*b)*sinh(d*x + c)^4 + 32*(5*(2*a - b)*cosh(d*x + c)^3 - (8*a - 3*b)*cosh(d*x + c))*sinh(d*x + c)^3 - 8*(2*a + 3*b)*cosh(d*x + c)^2 + 8*(15*(2*a - b)*cosh(d*x + c)^4 - 6*(8*a - 3*b)*cosh(d*x + c)^2 - 2*a - 3*b)*sinh(d*x + c)^2 - ((a*b^2 - b^3)*d*cosh(d*x + c)^8 + 8*(a*b^2 - b^3)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a*b^2 - b^3)*d*sinh(d*x + c)^8 - 4*(a*b^2 - b^3)*d*cosh(d*x + c)^6 + 4*(7*(a*b^2 - b^3)*d*cosh(d*x + c)^2 - (a*b^2 - b^3)*d)*sinh(d*x + c)^6 - 2*(8*a^2*b - 11*a*b^2 + 3*b^3)*d*cosh(d*x + c)^4 + 8*(7*(a*b^2 - b^3)*d*cosh(d*x + c)^3 - 3*(a*b^2 - b^3)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a*b^2 - b^3)*d*cosh(d*x + c)^4 - 30*(a*b^2 - b^3)*d*cosh(d*x + c)^2 - (8*a^2*b - 11*a*b^2 + 3*b^3)*d)*sinh(d*x + c)^4 - 4*(a*b^2 - b^3)*d*cosh(d*x + c)^2 + 8*(7*(a*b^2 - b^3)*d*cosh(d*x + c)^5 - 10*(a*b^2 - b^3)*d*cosh(d*x + c)^3 - (8*a^2*b - 11*a*b^2 + 3*b^3)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a*b^2 - b^3)*d*cosh(d*x + c)^6 - 15*(a*b^2 - b^3)*d*cosh(d*x + c)^4 - 3*(8*a^2*b - 11*a*b^2 + 3*b^3)*d*cosh(d*x + c)^2 - (a*b^2 - b^3)*d)*sinh(d*x + c)^2 + (a*b^2 - b^3)*d + 8*((a*b^2 - b^3)*d*cosh(d*x + c)^7 - 3*(a*b^2 - b^3)*d*cosh(d*x + c)^5 - (8*a^2*b - 11*a*b^2 + 3*b^3)*d*cosh(d*x + c)^3 - (a*b^2 - b^3)*d*cosh(d*x + c))*sinh(d*x + c))*sqrt(-((a^3*b^3 - 3*a^2*b^4 + 3*a*b^5 - b^6)*d^2*sqrt((25*a^2 - 90*a*b + 81*b^2)/((a^7*b^3 - 6*a^6*b^4 + 15*a^5*b^5 - 20*a^4*b^6 + 15*a^3*b^7 - 6*a^2*b^8 + a*b^9)*d^4)) - 4*a^2 + 15*a*b - 15*b^2)/((a^3*b^3 - 3*a^2*b^4 + 3*a*b^5 - b^6)*d^2))*log(2*(4*a^5*b - 21*a^4*b^2 + 39*a^3*b^3 - 31*a^2*b^4 + 9*a*b^5)*d^2*sqrt((25*a^2 - 90*a*b + 81*b^2)/((a^7*b^3 - 6*a^6*b^4 + 15*a^5*b^5 - 20*a^4*b^6 + 15*a^3*b^7 - 6*a^2*b^8 + a*b^9)*d^4)) + (20*a^2 - 81*a*b + 81*b^2)*cosh(d*x + c)^2 + 2*(20*a^2 - 81*a*b + 81*b^2)*cosh(d*x + c)*sinh(d*x + c) + (20*a^2 - 81*a*b + 81*b^2)*sinh(d*x + c)^2 - 20*a^2 + 81*a*b - 81*b^2 + 2*((a^5*b^3 - 6*a^4*b^4 + 12*a^3*b^5 - 10*a^2*b^6 + 3*a*b^7)*d^3*sqrt((25*a^2 - 90*a*b + 81*b^2)/((a^7*b^3 - 6*a^6*b^4 + 15*a^5*b^5 - 20*a^4*b^6 + 15*a^3*b^7 - 6*a^2*b^8 + a*b^9)*d^4)) - 2*(5*a^3*b - 19*a^2*b^2 + 18*a*b^3)*d)*sqrt(-((a^3*b^3 - 3*a^2*b^4 + 3*a*b^5 - b^6)*d^2*sqrt((25*a^2 - 90*a*b + 81*b^2)/((a^7*b^3 - 6*a^6*b^4 + 15*a^5*b^5 - 20*a^4*b^6 + 15*a^3*b^7 - 6*a^2*b^8 + a*b^9)*d^4)) - 4*a^2 + 15*a*b - 15*b^2)/((a^3*b^3 - 3*a^2*b^4 + 3*a*b^5 - b^6)*d^2))) + ((a*b^2 - b^3)*d*cosh(d*x + c)^8 + 8*(a*b^2 - b^3)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a*b^2 - b^3)*d*sinh(d*x + c)^8 - 4*(a*b^2 - b^3)*d*cosh(d*x + c)^6 + 4*(7*(a*b^2 - b^3)*d*cosh(d*x + c)^2 - (a*b^2 - b^3)*d)*sinh(d*x + c)^6 - 2*(8*a^2*b - 11*a*b^2 + 3*b^3)*d*cosh(d*x + c)^4 + 8*(7*(a*b^2 - b^3)*d*cosh(d*x + c)^3 - 3*(a*b^2 - b^3)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a*b^2 - b^3)*d*cosh(d*x + c)^4 - 30*(a*b^2 - b^3)*d*cosh(d*x + c)^2 - (8*a^2*b - 11*a*b^2 + 3*b^3)*d)*sinh(d*x + c)^4 - 4*(a*b^2 - b^3)*d*cosh(d*x + c)^2 + 8*(7*(a*b^2 - b^3)*d*cosh(d*x + c)^5 - 10*(a*b^2 - b^3)*d*cosh(d*x + c)^3 - (8*a^2*b - 11*a*b^2 + 3*b^3)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a*b^2 - b^3)*d*cosh(d*x + c)^6 - 15*(a*b^2 - b^3)*d*cosh(d*x + c)^4 - 3*(8*a^2*b - 11*a*b^2 + 3*b^3)*d*cosh(d*x + c)^2 - (a*b^2 - b^3)*d)*sinh(d*x + c)^2 + (a*b^2 - b^3)*d + 8*((a*b^2 - b^3)*d*cosh(d*x + c)^7 - 3*(a*b^2 - b^3)*d*cosh(d*x + c)^5 - (8*a^2*b - 11*a*b^2 + 3*b^3)*d*cosh(d*x + c)^3 - (a*b^2 - b^3)*d*cosh(d*x + c))*sinh(d*x + c))*sqrt(-((a^3*b^3 - 3*a^2*b^4 + 3*a*b^5 - b^6)*d^2*sqrt((25*a^2 - 90*a*b + 81*b^2)/((a^7*b^3 - 6*a^6*b^4 + 15*a^5*b^5 - 20*a^4*b^6 + 15*a^3*b^7 - 6*a^2*b^8 + a*b^9)*d^4)) - 4*a^2 + 15*a*b - 15*b^2)/((a^3*b^3 - 3*a^2*b^4 + 3*a*b^5 - b^6)*d^2))*log(2*(4*a^5*b - 21*a^4*b^2 + 39*a^3*b^3 - 31*a^2*b^4 + 9*a*b^5)*d^2*sqrt((25*a^2 - 90*a*b + 81*b^2)/((a^7*b^3 - 6*a^6*b^4 + 15*a^5*b^5 - 20*a^4*b^6 + 15*a^3*b^7 - 6*a^2*b^8 + a*b^9)*d^4)) + (20*a^2 - 81*a*b + 81*b^2)*cosh(d*x + c)^2 + 2*(20*a^2 - 81*a*b + 81*b^2)*cosh(d*x + c)*sinh(d*x + c) + (20*a^2 - 81*a*b + 81*b^2)*sinh(d*x + c)^2 - 20*a^2 + 81*a*b - 81*b^2 - 2*((a^5*b^3 - 6*a^4*b^4 + 12*a^3*b^5 - 10*a^2*b^6 + 3*a*b^7)*d^3*sqrt((25*a^2 - 90*a*b + 81*b^2)/((a^7*b^3 - 6*a^6*b^4 + 15*a^5*b^5 - 20*a^4*b^6 + 15*a^3*b^7 - 6*a^2*b^8 + a*b^9)*d^4)) - 2*(5*a^3*b - 19*a^2*b^2 + 18*a*b^3)*d)*sqrt(-((a^3*b^3 - 3*a^2*b^4 + 3*a*b^5 - b^6)*d^2*sqrt((25*a^2 - 90*a*b + 81*b^2)/((a^7*b^3 - 6*a^6*b^4 + 15*a^5*b^5 - 20*a^4*b^6 + 15*a^3*b^7 - 6*a^2*b^8 + a*b^9)*d^4)) - 4*a^2 + 15*a*b - 15*b^2)/((a^3*b^3 - 3*a^2*b^4 + 3*a*b^5 - b^6)*d^2))) + ((a*b^2 - b^3)*d*cosh(d*x + c)^8 + 8*(a*b^2 - b^3)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a*b^2 - b^3)*d*sinh(d*x + c)^8 - 4*(a*b^2 - b^3)*d*cosh(d*x + c)^6 + 4*(7*(a*b^2 - b^3)*d*cosh(d*x + c)^2 - (a*b^2 - b^3)*d)*sinh(d*x + c)^6 - 2*(8*a^2*b - 11*a*b^2 + 3*b^3)*d*cosh(d*x + c)^4 + 8*(7*(a*b^2 - b^3)*d*cosh(d*x + c)^3 - 3*(a*b^2 - b^3)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a*b^2 - b^3)*d*cosh(d*x + c)^4 - 30*(a*b^2 - b^3)*d*cosh(d*x + c)^2 - (8*a^2*b - 11*a*b^2 + 3*b^3)*d)*sinh(d*x + c)^4 - 4*(a*b^2 - b^3)*d*cosh(d*x + c)^2 + 8*(7*(a*b^2 - b^3)*d*cosh(d*x + c)^5 - 10*(a*b^2 - b^3)*d*cosh(d*x + c)^3 - (8*a^2*b - 11*a*b^2 + 3*b^3)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a*b^2 - b^3)*d*cosh(d*x + c)^6 - 15*(a*b^2 - b^3)*d*cosh(d*x + c)^4 - 3*(8*a^2*b - 11*a*b^2 + 3*b^3)*d*cosh(d*x + c)^2 - (a*b^2 - b^3)*d)*sinh(d*x + c)^2 + (a*b^2 - b^3)*d + 8*((a*b^2 - b^3)*d*cosh(d*x + c)^7 - 3*(a*b^2 - b^3)*d*cosh(d*x + c)^5 - (8*a^2*b - 11*a*b^2 + 3*b^3)*d*cosh(d*x + c)^3 - (a*b^2 - b^3)*d*cosh(d*x + c))*sinh(d*x + c))*sqrt(((a^3*b^3 - 3*a^2*b^4 + 3*a*b^5 - b^6)*d^2*sqrt((25*a^2 - 90*a*b + 81*b^2)/((a^7*b^3 - 6*a^6*b^4 + 15*a^5*b^5 - 20*a^4*b^6 + 15*a^3*b^7 - 6*a^2*b^8 + a*b^9)*d^4)) + 4*a^2 - 15*a*b + 15*b^2)/((a^3*b^3 - 3*a^2*b^4 + 3*a*b^5 - b^6)*d^2))*log(-2*(4*a^5*b - 21*a^4*b^2 + 39*a^3*b^3 - 31*a^2*b^4 + 9*a*b^5)*d^2*sqrt((25*a^2 - 90*a*b + 81*b^2)/((a^7*b^3 - 6*a^6*b^4 + 15*a^5*b^5 - 20*a^4*b^6 + 15*a^3*b^7 - 6*a^2*b^8 + a*b^9)*d^4)) + (20*a^2 - 81*a*b + 81*b^2)*cosh(d*x + c)^2 + 2*(20*a^2 - 81*a*b + 81*b^2)*cosh(d*x + c)*sinh(d*x + c) + (20*a^2 - 81*a*b + 81*b^2)*sinh(d*x + c)^2 - 20*a^2 + 81*a*b - 81*b^2 + 2*((a^5*b^3 - 6*a^4*b^4 + 12*a^3*b^5 - 10*a^2*b^6 + 3*a*b^7)*d^3*sqrt((25*a^2 - 90*a*b + 81*b^2)/((a^7*b^3 - 6*a^6*b^4 + 15*a^5*b^5 - 20*a^4*b^6 + 15*a^3*b^7 - 6*a^2*b^8 + a*b^9)*d^4)) + 2*(5*a^3*b - 19*a^2*b^2 + 18*a*b^3)*d)*sqrt(((a^3*b^3 - 3*a^2*b^4 + 3*a*b^5 - b^6)*d^2*sqrt((25*a^2 - 90*a*b + 81*b^2)/((a^7*b^3 - 6*a^6*b^4 + 15*a^5*b^5 - 20*a^4*b^6 + 15*a^3*b^7 - 6*a^2*b^8 + a*b^9)*d^4)) + 4*a^2 - 15*a*b + 15*b^2)/((a^3*b^3 - 3*a^2*b^4 + 3*a*b^5 - b^6)*d^2))) - ((a*b^2 - b^3)*d*cosh(d*x + c)^8 + 8*(a*b^2 - b^3)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a*b^2 - b^3)*d*sinh(d*x + c)^8 - 4*(a*b^2 - b^3)*d*cosh(d*x + c)^6 + 4*(7*(a*b^2 - b^3)*d*cosh(d*x + c)^2 - (a*b^2 - b^3)*d)*sinh(d*x + c)^6 - 2*(8*a^2*b - 11*a*b^2 + 3*b^3)*d*cosh(d*x + c)^4 + 8*(7*(a*b^2 - b^3)*d*cosh(d*x + c)^3 - 3*(a*b^2 - b^3)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a*b^2 - b^3)*d*cosh(d*x + c)^4 - 30*(a*b^2 - b^3)*d*cosh(d*x + c)^2 - (8*a^2*b - 11*a*b^2 + 3*b^3)*d)*sinh(d*x + c)^4 - 4*(a*b^2 - b^3)*d*cosh(d*x + c)^2 + 8*(7*(a*b^2 - b^3)*d*cosh(d*x + c)^5 - 10*(a*b^2 - b^3)*d*cosh(d*x + c)^3 - (8*a^2*b - 11*a*b^2 + 3*b^3)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a*b^2 - b^3)*d*cosh(d*x + c)^6 - 15*(a*b^2 - b^3)*d*cosh(d*x + c)^4 - 3*(8*a^2*b - 11*a*b^2 + 3*b^3)*d*cosh(d*x + c)^2 - (a*b^2 - b^3)*d)*sinh(d*x + c)^2 + (a*b^2 - b^3)*d + 8*((a*b^2 - b^3)*d*cosh(d*x + c)^7 - 3*(a*b^2 - b^3)*d*cosh(d*x + c)^5 - (8*a^2*b - 11*a*b^2 + 3*b^3)*d*cosh(d*x + c)^3 - (a*b^2 - b^3)*d*cosh(d*x + c))*sinh(d*x + c))*sqrt(((a^3*b^3 - 3*a^2*b^4 + 3*a*b^5 - b^6)*d^2*sqrt((25*a^2 - 90*a*b + 81*b^2)/((a^7*b^3 - 6*a^6*b^4 + 15*a^5*b^5 - 20*a^4*b^6 + 15*a^3*b^7 - 6*a^2*b^8 + a*b^9)*d^4)) + 4*a^2 - 15*a*b + 15*b^2)/((a^3*b^3 - 3*a^2*b^4 + 3*a*b^5 - b^6)*d^2))*log(-2*(4*a^5*b - 21*a^4*b^2 + 39*a^3*b^3 - 31*a^2*b^4 + 9*a*b^5)*d^2*sqrt((25*a^2 - 90*a*b + 81*b^2)/((a^7*b^3 - 6*a^6*b^4 + 15*a^5*b^5 - 20*a^4*b^6 + 15*a^3*b^7 - 6*a^2*b^8 + a*b^9)*d^4)) + (20*a^2 - 81*a*b + 81*b^2)*cosh(d*x + c)^2 + 2*(20*a^2 - 81*a*b + 81*b^2)*cosh(d*x + c)*sinh(d*x + c) + (20*a^2 - 81*a*b + 81*b^2)*sinh(d*x + c)^2 - 20*a^2 + 81*a*b - 81*b^2 - 2*((a^5*b^3 - 6*a^4*b^4 + 12*a^3*b^5 - 10*a^2*b^6 + 3*a*b^7)*d^3*sqrt((25*a^2 - 90*a*b + 81*b^2)/((a^7*b^3 - 6*a^6*b^4 + 15*a^5*b^5 - 20*a^4*b^6 + 15*a^3*b^7 - 6*a^2*b^8 + a*b^9)*d^4)) + 2*(5*a^3*b - 19*a^2*b^2 + 18*a*b^3)*d)*sqrt(((a^3*b^3 - 3*a^2*b^4 + 3*a*b^5 - b^6)*d^2*sqrt((25*a^2 - 90*a*b + 81*b^2)/((a^7*b^3 - 6*a^6*b^4 + 15*a^5*b^5 - 20*a^4*b^6 + 15*a^3*b^7 - 6*a^2*b^8 + a*b^9)*d^4)) + 4*a^2 - 15*a*b + 15*b^2)/((a^3*b^3 - 3*a^2*b^4 + 3*a*b^5 - b^6)*d^2))) + 16*(3*(2*a - b)*cosh(d*x + c)^5 - 2*(8*a - 3*b)*cosh(d*x + c)^3 - (2*a + 3*b)*cosh(d*x + c))*sinh(d*x + c) + 8*b)/((a*b^2 - b^3)*d*cosh(d*x + c)^8 + 8*(a*b^2 - b^3)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a*b^2 - b^3)*d*sinh(d*x + c)^8 - 4*(a*b^2 - b^3)*d*cosh(d*x + c)^6 + 4*(7*(a*b^2 - b^3)*d*cosh(d*x + c)^2 - (a*b^2 - b^3)*d)*sinh(d*x + c)^6 - 2*(8*a^2*b - 11*a*b^2 + 3*b^3)*d*cosh(d*x + c)^4 + 8*(7*(a*b^2 - b^3)*d*cosh(d*x + c)^3 - 3*(a*b^2 - b^3)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a*b^2 - b^3)*d*cosh(d*x + c)^4 - 30*(a*b^2 - b^3)*d*cosh(d*x + c)^2 - (8*a^2*b - 11*a*b^2 + 3*b^3)*d)*sinh(d*x + c)^4 - 4*(a*b^2 - b^3)*d*cosh(d*x + c)^2 + 8*(7*(a*b^2 - b^3)*d*cosh(d*x + c)^5 - 10*(a*b^2 - b^3)*d*cosh(d*x + c)^3 - (8*a^2*b - 11*a*b^2 + 3*b^3)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a*b^2 - b^3)*d*cosh(d*x + c)^6 - 15*(a*b^2 - b^3)*d*cosh(d*x + c)^4 - 3*(8*a^2*b - 11*a*b^2 + 3*b^3)*d*cosh(d*x + c)^2 - (a*b^2 - b^3)*d)*sinh(d*x + c)^2 + (a*b^2 - b^3)*d + 8*((a*b^2 - b^3)*d*cosh(d*x + c)^7 - 3*(a*b^2 - b^3)*d*cosh(d*x + c)^5 - (8*a^2*b - 11*a*b^2 + 3*b^3)*d*cosh(d*x + c)^3 - (a*b^2 - b^3)*d*cosh(d*x + c))*sinh(d*x + c))","B",0
249,1,5658,0,0.704120," ","integrate(sinh(d*x+c)^4/(a-b*sinh(d*x+c)^4)^2,x, algorithm=""fricas"")","\frac{8 \, b \cosh\left(d x + c\right)^{6} + 48 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + 8 \, b \sinh\left(d x + c\right)^{6} - 8 \, {\left(8 \, a - 3 \, b\right)} \cosh\left(d x + c\right)^{4} + 8 \, {\left(15 \, b \cosh\left(d x + c\right)^{2} - 8 \, a + 3 \, b\right)} \sinh\left(d x + c\right)^{4} + 32 \, {\left(5 \, b \cosh\left(d x + c\right)^{3} - {\left(8 \, a - 3 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 40 \, b \cosh\left(d x + c\right)^{2} + 8 \, {\left(15 \, b \cosh\left(d x + c\right)^{4} - 6 \, {\left(8 \, a - 3 \, b\right)} \cosh\left(d x + c\right)^{2} - 5 \, b\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a b^{2} - b^{3}\right)} d \sinh\left(d x + c\right)^{8} - 4 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a b^{2} - b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{6} - 2 \, {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{3} - 3 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{4} - 30 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{2} - {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{4} - 4 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{5} - 10 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{3} - {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{6} - 15 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{4} - 3 \, {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a b^{2} - b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a b^{2} - b^{3}\right)} d + 8 \, {\left({\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{7} - 3 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{5} - {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{{\left(a^{4} b - 3 \, a^{3} b^{2} + 3 \, a^{2} b^{3} - a b^{4}\right)} d^{2} \sqrt{\frac{9 \, a^{2} + 6 \, a b + b^{2}}{{\left(a^{9} b - 6 \, a^{8} b^{2} + 15 \, a^{7} b^{3} - 20 \, a^{6} b^{4} + 15 \, a^{5} b^{5} - 6 \, a^{4} b^{6} + a^{3} b^{7}\right)} d^{4}}} + a + 3 \, b}{{\left(a^{4} b - 3 \, a^{3} b^{2} + 3 \, a^{2} b^{3} - a b^{4}\right)} d^{2}}} \log\left(2 \, {\left(a^{5} - 3 \, a^{4} b + 3 \, a^{3} b^{2} - a^{2} b^{3}\right)} d^{2} \sqrt{\frac{9 \, a^{2} + 6 \, a b + b^{2}}{{\left(a^{9} b - 6 \, a^{8} b^{2} + 15 \, a^{7} b^{3} - 20 \, a^{6} b^{4} + 15 \, a^{5} b^{5} - 6 \, a^{4} b^{6} + a^{3} b^{7}\right)} d^{4}}} + {\left(3 \, a + b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a + b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(3 \, a + b\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(2 \, {\left(a^{6} b - 3 \, a^{5} b^{2} + 3 \, a^{4} b^{3} - a^{3} b^{4}\right)} d^{3} \sqrt{\frac{9 \, a^{2} + 6 \, a b + b^{2}}{{\left(a^{9} b - 6 \, a^{8} b^{2} + 15 \, a^{7} b^{3} - 20 \, a^{6} b^{4} + 15 \, a^{5} b^{5} - 6 \, a^{4} b^{6} + a^{3} b^{7}\right)} d^{4}}} - {\left(3 \, a^{3} + 4 \, a^{2} b + a b^{2}\right)} d\right)} \sqrt{\frac{{\left(a^{4} b - 3 \, a^{3} b^{2} + 3 \, a^{2} b^{3} - a b^{4}\right)} d^{2} \sqrt{\frac{9 \, a^{2} + 6 \, a b + b^{2}}{{\left(a^{9} b - 6 \, a^{8} b^{2} + 15 \, a^{7} b^{3} - 20 \, a^{6} b^{4} + 15 \, a^{5} b^{5} - 6 \, a^{4} b^{6} + a^{3} b^{7}\right)} d^{4}}} + a + 3 \, b}{{\left(a^{4} b - 3 \, a^{3} b^{2} + 3 \, a^{2} b^{3} - a b^{4}\right)} d^{2}}} - 3 \, a - b\right) - {\left({\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a b^{2} - b^{3}\right)} d \sinh\left(d x + c\right)^{8} - 4 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a b^{2} - b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{6} - 2 \, {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{3} - 3 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{4} - 30 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{2} - {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{4} - 4 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{5} - 10 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{3} - {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{6} - 15 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{4} - 3 \, {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a b^{2} - b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a b^{2} - b^{3}\right)} d + 8 \, {\left({\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{7} - 3 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{5} - {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{{\left(a^{4} b - 3 \, a^{3} b^{2} + 3 \, a^{2} b^{3} - a b^{4}\right)} d^{2} \sqrt{\frac{9 \, a^{2} + 6 \, a b + b^{2}}{{\left(a^{9} b - 6 \, a^{8} b^{2} + 15 \, a^{7} b^{3} - 20 \, a^{6} b^{4} + 15 \, a^{5} b^{5} - 6 \, a^{4} b^{6} + a^{3} b^{7}\right)} d^{4}}} + a + 3 \, b}{{\left(a^{4} b - 3 \, a^{3} b^{2} + 3 \, a^{2} b^{3} - a b^{4}\right)} d^{2}}} \log\left(2 \, {\left(a^{5} - 3 \, a^{4} b + 3 \, a^{3} b^{2} - a^{2} b^{3}\right)} d^{2} \sqrt{\frac{9 \, a^{2} + 6 \, a b + b^{2}}{{\left(a^{9} b - 6 \, a^{8} b^{2} + 15 \, a^{7} b^{3} - 20 \, a^{6} b^{4} + 15 \, a^{5} b^{5} - 6 \, a^{4} b^{6} + a^{3} b^{7}\right)} d^{4}}} + {\left(3 \, a + b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a + b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(3 \, a + b\right)} \sinh\left(d x + c\right)^{2} - 2 \, {\left(2 \, {\left(a^{6} b - 3 \, a^{5} b^{2} + 3 \, a^{4} b^{3} - a^{3} b^{4}\right)} d^{3} \sqrt{\frac{9 \, a^{2} + 6 \, a b + b^{2}}{{\left(a^{9} b - 6 \, a^{8} b^{2} + 15 \, a^{7} b^{3} - 20 \, a^{6} b^{4} + 15 \, a^{5} b^{5} - 6 \, a^{4} b^{6} + a^{3} b^{7}\right)} d^{4}}} - {\left(3 \, a^{3} + 4 \, a^{2} b + a b^{2}\right)} d\right)} \sqrt{\frac{{\left(a^{4} b - 3 \, a^{3} b^{2} + 3 \, a^{2} b^{3} - a b^{4}\right)} d^{2} \sqrt{\frac{9 \, a^{2} + 6 \, a b + b^{2}}{{\left(a^{9} b - 6 \, a^{8} b^{2} + 15 \, a^{7} b^{3} - 20 \, a^{6} b^{4} + 15 \, a^{5} b^{5} - 6 \, a^{4} b^{6} + a^{3} b^{7}\right)} d^{4}}} + a + 3 \, b}{{\left(a^{4} b - 3 \, a^{3} b^{2} + 3 \, a^{2} b^{3} - a b^{4}\right)} d^{2}}} - 3 \, a - b\right) - {\left({\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a b^{2} - b^{3}\right)} d \sinh\left(d x + c\right)^{8} - 4 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a b^{2} - b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{6} - 2 \, {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{3} - 3 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{4} - 30 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{2} - {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{4} - 4 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{5} - 10 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{3} - {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{6} - 15 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{4} - 3 \, {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a b^{2} - b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a b^{2} - b^{3}\right)} d + 8 \, {\left({\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{7} - 3 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{5} - {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{{\left(a^{4} b - 3 \, a^{3} b^{2} + 3 \, a^{2} b^{3} - a b^{4}\right)} d^{2} \sqrt{\frac{9 \, a^{2} + 6 \, a b + b^{2}}{{\left(a^{9} b - 6 \, a^{8} b^{2} + 15 \, a^{7} b^{3} - 20 \, a^{6} b^{4} + 15 \, a^{5} b^{5} - 6 \, a^{4} b^{6} + a^{3} b^{7}\right)} d^{4}}} - a - 3 \, b}{{\left(a^{4} b - 3 \, a^{3} b^{2} + 3 \, a^{2} b^{3} - a b^{4}\right)} d^{2}}} \log\left(-2 \, {\left(a^{5} - 3 \, a^{4} b + 3 \, a^{3} b^{2} - a^{2} b^{3}\right)} d^{2} \sqrt{\frac{9 \, a^{2} + 6 \, a b + b^{2}}{{\left(a^{9} b - 6 \, a^{8} b^{2} + 15 \, a^{7} b^{3} - 20 \, a^{6} b^{4} + 15 \, a^{5} b^{5} - 6 \, a^{4} b^{6} + a^{3} b^{7}\right)} d^{4}}} + {\left(3 \, a + b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a + b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(3 \, a + b\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(2 \, {\left(a^{6} b - 3 \, a^{5} b^{2} + 3 \, a^{4} b^{3} - a^{3} b^{4}\right)} d^{3} \sqrt{\frac{9 \, a^{2} + 6 \, a b + b^{2}}{{\left(a^{9} b - 6 \, a^{8} b^{2} + 15 \, a^{7} b^{3} - 20 \, a^{6} b^{4} + 15 \, a^{5} b^{5} - 6 \, a^{4} b^{6} + a^{3} b^{7}\right)} d^{4}}} + {\left(3 \, a^{3} + 4 \, a^{2} b + a b^{2}\right)} d\right)} \sqrt{-\frac{{\left(a^{4} b - 3 \, a^{3} b^{2} + 3 \, a^{2} b^{3} - a b^{4}\right)} d^{2} \sqrt{\frac{9 \, a^{2} + 6 \, a b + b^{2}}{{\left(a^{9} b - 6 \, a^{8} b^{2} + 15 \, a^{7} b^{3} - 20 \, a^{6} b^{4} + 15 \, a^{5} b^{5} - 6 \, a^{4} b^{6} + a^{3} b^{7}\right)} d^{4}}} - a - 3 \, b}{{\left(a^{4} b - 3 \, a^{3} b^{2} + 3 \, a^{2} b^{3} - a b^{4}\right)} d^{2}}} - 3 \, a - b\right) + {\left({\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a b^{2} - b^{3}\right)} d \sinh\left(d x + c\right)^{8} - 4 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a b^{2} - b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{6} - 2 \, {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{3} - 3 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{4} - 30 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{2} - {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{4} - 4 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{5} - 10 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{3} - {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{6} - 15 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{4} - 3 \, {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a b^{2} - b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a b^{2} - b^{3}\right)} d + 8 \, {\left({\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{7} - 3 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{5} - {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{{\left(a^{4} b - 3 \, a^{3} b^{2} + 3 \, a^{2} b^{3} - a b^{4}\right)} d^{2} \sqrt{\frac{9 \, a^{2} + 6 \, a b + b^{2}}{{\left(a^{9} b - 6 \, a^{8} b^{2} + 15 \, a^{7} b^{3} - 20 \, a^{6} b^{4} + 15 \, a^{5} b^{5} - 6 \, a^{4} b^{6} + a^{3} b^{7}\right)} d^{4}}} - a - 3 \, b}{{\left(a^{4} b - 3 \, a^{3} b^{2} + 3 \, a^{2} b^{3} - a b^{4}\right)} d^{2}}} \log\left(-2 \, {\left(a^{5} - 3 \, a^{4} b + 3 \, a^{3} b^{2} - a^{2} b^{3}\right)} d^{2} \sqrt{\frac{9 \, a^{2} + 6 \, a b + b^{2}}{{\left(a^{9} b - 6 \, a^{8} b^{2} + 15 \, a^{7} b^{3} - 20 \, a^{6} b^{4} + 15 \, a^{5} b^{5} - 6 \, a^{4} b^{6} + a^{3} b^{7}\right)} d^{4}}} + {\left(3 \, a + b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a + b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(3 \, a + b\right)} \sinh\left(d x + c\right)^{2} - 2 \, {\left(2 \, {\left(a^{6} b - 3 \, a^{5} b^{2} + 3 \, a^{4} b^{3} - a^{3} b^{4}\right)} d^{3} \sqrt{\frac{9 \, a^{2} + 6 \, a b + b^{2}}{{\left(a^{9} b - 6 \, a^{8} b^{2} + 15 \, a^{7} b^{3} - 20 \, a^{6} b^{4} + 15 \, a^{5} b^{5} - 6 \, a^{4} b^{6} + a^{3} b^{7}\right)} d^{4}}} + {\left(3 \, a^{3} + 4 \, a^{2} b + a b^{2}\right)} d\right)} \sqrt{-\frac{{\left(a^{4} b - 3 \, a^{3} b^{2} + 3 \, a^{2} b^{3} - a b^{4}\right)} d^{2} \sqrt{\frac{9 \, a^{2} + 6 \, a b + b^{2}}{{\left(a^{9} b - 6 \, a^{8} b^{2} + 15 \, a^{7} b^{3} - 20 \, a^{6} b^{4} + 15 \, a^{5} b^{5} - 6 \, a^{4} b^{6} + a^{3} b^{7}\right)} d^{4}}} - a - 3 \, b}{{\left(a^{4} b - 3 \, a^{3} b^{2} + 3 \, a^{2} b^{3} - a b^{4}\right)} d^{2}}} - 3 \, a - b\right) + 16 \, {\left(3 \, b \cosh\left(d x + c\right)^{5} - 2 \, {\left(8 \, a - 3 \, b\right)} \cosh\left(d x + c\right)^{3} - 5 \, b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + 8 \, b}{16 \, {\left({\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a b^{2} - b^{3}\right)} d \sinh\left(d x + c\right)^{8} - 4 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a b^{2} - b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{6} - 2 \, {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{3} - 3 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{4} - 30 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{2} - {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{4} - 4 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{5} - 10 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{3} - {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{6} - 15 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{4} - 3 \, {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a b^{2} - b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a b^{2} - b^{3}\right)} d + 8 \, {\left({\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{7} - 3 \, {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{5} - {\left(8 \, a^{2} b - 11 \, a b^{2} + 3 \, b^{3}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"1/16*(8*b*cosh(d*x + c)^6 + 48*b*cosh(d*x + c)*sinh(d*x + c)^5 + 8*b*sinh(d*x + c)^6 - 8*(8*a - 3*b)*cosh(d*x + c)^4 + 8*(15*b*cosh(d*x + c)^2 - 8*a + 3*b)*sinh(d*x + c)^4 + 32*(5*b*cosh(d*x + c)^3 - (8*a - 3*b)*cosh(d*x + c))*sinh(d*x + c)^3 - 40*b*cosh(d*x + c)^2 + 8*(15*b*cosh(d*x + c)^4 - 6*(8*a - 3*b)*cosh(d*x + c)^2 - 5*b)*sinh(d*x + c)^2 + ((a*b^2 - b^3)*d*cosh(d*x + c)^8 + 8*(a*b^2 - b^3)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a*b^2 - b^3)*d*sinh(d*x + c)^8 - 4*(a*b^2 - b^3)*d*cosh(d*x + c)^6 + 4*(7*(a*b^2 - b^3)*d*cosh(d*x + c)^2 - (a*b^2 - b^3)*d)*sinh(d*x + c)^6 - 2*(8*a^2*b - 11*a*b^2 + 3*b^3)*d*cosh(d*x + c)^4 + 8*(7*(a*b^2 - b^3)*d*cosh(d*x + c)^3 - 3*(a*b^2 - b^3)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a*b^2 - b^3)*d*cosh(d*x + c)^4 - 30*(a*b^2 - b^3)*d*cosh(d*x + c)^2 - (8*a^2*b - 11*a*b^2 + 3*b^3)*d)*sinh(d*x + c)^4 - 4*(a*b^2 - b^3)*d*cosh(d*x + c)^2 + 8*(7*(a*b^2 - b^3)*d*cosh(d*x + c)^5 - 10*(a*b^2 - b^3)*d*cosh(d*x + c)^3 - (8*a^2*b - 11*a*b^2 + 3*b^3)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a*b^2 - b^3)*d*cosh(d*x + c)^6 - 15*(a*b^2 - b^3)*d*cosh(d*x + c)^4 - 3*(8*a^2*b - 11*a*b^2 + 3*b^3)*d*cosh(d*x + c)^2 - (a*b^2 - b^3)*d)*sinh(d*x + c)^2 + (a*b^2 - b^3)*d + 8*((a*b^2 - b^3)*d*cosh(d*x + c)^7 - 3*(a*b^2 - b^3)*d*cosh(d*x + c)^5 - (8*a^2*b - 11*a*b^2 + 3*b^3)*d*cosh(d*x + c)^3 - (a*b^2 - b^3)*d*cosh(d*x + c))*sinh(d*x + c))*sqrt(((a^4*b - 3*a^3*b^2 + 3*a^2*b^3 - a*b^4)*d^2*sqrt((9*a^2 + 6*a*b + b^2)/((a^9*b - 6*a^8*b^2 + 15*a^7*b^3 - 20*a^6*b^4 + 15*a^5*b^5 - 6*a^4*b^6 + a^3*b^7)*d^4)) + a + 3*b)/((a^4*b - 3*a^3*b^2 + 3*a^2*b^3 - a*b^4)*d^2))*log(2*(a^5 - 3*a^4*b + 3*a^3*b^2 - a^2*b^3)*d^2*sqrt((9*a^2 + 6*a*b + b^2)/((a^9*b - 6*a^8*b^2 + 15*a^7*b^3 - 20*a^6*b^4 + 15*a^5*b^5 - 6*a^4*b^6 + a^3*b^7)*d^4)) + (3*a + b)*cosh(d*x + c)^2 + 2*(3*a + b)*cosh(d*x + c)*sinh(d*x + c) + (3*a + b)*sinh(d*x + c)^2 + 2*(2*(a^6*b - 3*a^5*b^2 + 3*a^4*b^3 - a^3*b^4)*d^3*sqrt((9*a^2 + 6*a*b + b^2)/((a^9*b - 6*a^8*b^2 + 15*a^7*b^3 - 20*a^6*b^4 + 15*a^5*b^5 - 6*a^4*b^6 + a^3*b^7)*d^4)) - (3*a^3 + 4*a^2*b + a*b^2)*d)*sqrt(((a^4*b - 3*a^3*b^2 + 3*a^2*b^3 - a*b^4)*d^2*sqrt((9*a^2 + 6*a*b + b^2)/((a^9*b - 6*a^8*b^2 + 15*a^7*b^3 - 20*a^6*b^4 + 15*a^5*b^5 - 6*a^4*b^6 + a^3*b^7)*d^4)) + a + 3*b)/((a^4*b - 3*a^3*b^2 + 3*a^2*b^3 - a*b^4)*d^2)) - 3*a - b) - ((a*b^2 - b^3)*d*cosh(d*x + c)^8 + 8*(a*b^2 - b^3)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a*b^2 - b^3)*d*sinh(d*x + c)^8 - 4*(a*b^2 - b^3)*d*cosh(d*x + c)^6 + 4*(7*(a*b^2 - b^3)*d*cosh(d*x + c)^2 - (a*b^2 - b^3)*d)*sinh(d*x + c)^6 - 2*(8*a^2*b - 11*a*b^2 + 3*b^3)*d*cosh(d*x + c)^4 + 8*(7*(a*b^2 - b^3)*d*cosh(d*x + c)^3 - 3*(a*b^2 - b^3)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a*b^2 - b^3)*d*cosh(d*x + c)^4 - 30*(a*b^2 - b^3)*d*cosh(d*x + c)^2 - (8*a^2*b - 11*a*b^2 + 3*b^3)*d)*sinh(d*x + c)^4 - 4*(a*b^2 - b^3)*d*cosh(d*x + c)^2 + 8*(7*(a*b^2 - b^3)*d*cosh(d*x + c)^5 - 10*(a*b^2 - b^3)*d*cosh(d*x + c)^3 - (8*a^2*b - 11*a*b^2 + 3*b^3)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a*b^2 - b^3)*d*cosh(d*x + c)^6 - 15*(a*b^2 - b^3)*d*cosh(d*x + c)^4 - 3*(8*a^2*b - 11*a*b^2 + 3*b^3)*d*cosh(d*x + c)^2 - (a*b^2 - b^3)*d)*sinh(d*x + c)^2 + (a*b^2 - b^3)*d + 8*((a*b^2 - b^3)*d*cosh(d*x + c)^7 - 3*(a*b^2 - b^3)*d*cosh(d*x + c)^5 - (8*a^2*b - 11*a*b^2 + 3*b^3)*d*cosh(d*x + c)^3 - (a*b^2 - b^3)*d*cosh(d*x + c))*sinh(d*x + c))*sqrt(((a^4*b - 3*a^3*b^2 + 3*a^2*b^3 - a*b^4)*d^2*sqrt((9*a^2 + 6*a*b + b^2)/((a^9*b - 6*a^8*b^2 + 15*a^7*b^3 - 20*a^6*b^4 + 15*a^5*b^5 - 6*a^4*b^6 + a^3*b^7)*d^4)) + a + 3*b)/((a^4*b - 3*a^3*b^2 + 3*a^2*b^3 - a*b^4)*d^2))*log(2*(a^5 - 3*a^4*b + 3*a^3*b^2 - a^2*b^3)*d^2*sqrt((9*a^2 + 6*a*b + b^2)/((a^9*b - 6*a^8*b^2 + 15*a^7*b^3 - 20*a^6*b^4 + 15*a^5*b^5 - 6*a^4*b^6 + a^3*b^7)*d^4)) + (3*a + b)*cosh(d*x + c)^2 + 2*(3*a + b)*cosh(d*x + c)*sinh(d*x + c) + (3*a + b)*sinh(d*x + c)^2 - 2*(2*(a^6*b - 3*a^5*b^2 + 3*a^4*b^3 - a^3*b^4)*d^3*sqrt((9*a^2 + 6*a*b + b^2)/((a^9*b - 6*a^8*b^2 + 15*a^7*b^3 - 20*a^6*b^4 + 15*a^5*b^5 - 6*a^4*b^6 + a^3*b^7)*d^4)) - (3*a^3 + 4*a^2*b + a*b^2)*d)*sqrt(((a^4*b - 3*a^3*b^2 + 3*a^2*b^3 - a*b^4)*d^2*sqrt((9*a^2 + 6*a*b + b^2)/((a^9*b - 6*a^8*b^2 + 15*a^7*b^3 - 20*a^6*b^4 + 15*a^5*b^5 - 6*a^4*b^6 + a^3*b^7)*d^4)) + a + 3*b)/((a^4*b - 3*a^3*b^2 + 3*a^2*b^3 - a*b^4)*d^2)) - 3*a - b) - ((a*b^2 - b^3)*d*cosh(d*x + c)^8 + 8*(a*b^2 - b^3)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a*b^2 - b^3)*d*sinh(d*x + c)^8 - 4*(a*b^2 - b^3)*d*cosh(d*x + c)^6 + 4*(7*(a*b^2 - b^3)*d*cosh(d*x + c)^2 - (a*b^2 - b^3)*d)*sinh(d*x + c)^6 - 2*(8*a^2*b - 11*a*b^2 + 3*b^3)*d*cosh(d*x + c)^4 + 8*(7*(a*b^2 - b^3)*d*cosh(d*x + c)^3 - 3*(a*b^2 - b^3)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a*b^2 - b^3)*d*cosh(d*x + c)^4 - 30*(a*b^2 - b^3)*d*cosh(d*x + c)^2 - (8*a^2*b - 11*a*b^2 + 3*b^3)*d)*sinh(d*x + c)^4 - 4*(a*b^2 - b^3)*d*cosh(d*x + c)^2 + 8*(7*(a*b^2 - b^3)*d*cosh(d*x + c)^5 - 10*(a*b^2 - b^3)*d*cosh(d*x + c)^3 - (8*a^2*b - 11*a*b^2 + 3*b^3)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a*b^2 - b^3)*d*cosh(d*x + c)^6 - 15*(a*b^2 - b^3)*d*cosh(d*x + c)^4 - 3*(8*a^2*b - 11*a*b^2 + 3*b^3)*d*cosh(d*x + c)^2 - (a*b^2 - b^3)*d)*sinh(d*x + c)^2 + (a*b^2 - b^3)*d + 8*((a*b^2 - b^3)*d*cosh(d*x + c)^7 - 3*(a*b^2 - b^3)*d*cosh(d*x + c)^5 - (8*a^2*b - 11*a*b^2 + 3*b^3)*d*cosh(d*x + c)^3 - (a*b^2 - b^3)*d*cosh(d*x + c))*sinh(d*x + c))*sqrt(-((a^4*b - 3*a^3*b^2 + 3*a^2*b^3 - a*b^4)*d^2*sqrt((9*a^2 + 6*a*b + b^2)/((a^9*b - 6*a^8*b^2 + 15*a^7*b^3 - 20*a^6*b^4 + 15*a^5*b^5 - 6*a^4*b^6 + a^3*b^7)*d^4)) - a - 3*b)/((a^4*b - 3*a^3*b^2 + 3*a^2*b^3 - a*b^4)*d^2))*log(-2*(a^5 - 3*a^4*b + 3*a^3*b^2 - a^2*b^3)*d^2*sqrt((9*a^2 + 6*a*b + b^2)/((a^9*b - 6*a^8*b^2 + 15*a^7*b^3 - 20*a^6*b^4 + 15*a^5*b^5 - 6*a^4*b^6 + a^3*b^7)*d^4)) + (3*a + b)*cosh(d*x + c)^2 + 2*(3*a + b)*cosh(d*x + c)*sinh(d*x + c) + (3*a + b)*sinh(d*x + c)^2 + 2*(2*(a^6*b - 3*a^5*b^2 + 3*a^4*b^3 - a^3*b^4)*d^3*sqrt((9*a^2 + 6*a*b + b^2)/((a^9*b - 6*a^8*b^2 + 15*a^7*b^3 - 20*a^6*b^4 + 15*a^5*b^5 - 6*a^4*b^6 + a^3*b^7)*d^4)) + (3*a^3 + 4*a^2*b + a*b^2)*d)*sqrt(-((a^4*b - 3*a^3*b^2 + 3*a^2*b^3 - a*b^4)*d^2*sqrt((9*a^2 + 6*a*b + b^2)/((a^9*b - 6*a^8*b^2 + 15*a^7*b^3 - 20*a^6*b^4 + 15*a^5*b^5 - 6*a^4*b^6 + a^3*b^7)*d^4)) - a - 3*b)/((a^4*b - 3*a^3*b^2 + 3*a^2*b^3 - a*b^4)*d^2)) - 3*a - b) + ((a*b^2 - b^3)*d*cosh(d*x + c)^8 + 8*(a*b^2 - b^3)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a*b^2 - b^3)*d*sinh(d*x + c)^8 - 4*(a*b^2 - b^3)*d*cosh(d*x + c)^6 + 4*(7*(a*b^2 - b^3)*d*cosh(d*x + c)^2 - (a*b^2 - b^3)*d)*sinh(d*x + c)^6 - 2*(8*a^2*b - 11*a*b^2 + 3*b^3)*d*cosh(d*x + c)^4 + 8*(7*(a*b^2 - b^3)*d*cosh(d*x + c)^3 - 3*(a*b^2 - b^3)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a*b^2 - b^3)*d*cosh(d*x + c)^4 - 30*(a*b^2 - b^3)*d*cosh(d*x + c)^2 - (8*a^2*b - 11*a*b^2 + 3*b^3)*d)*sinh(d*x + c)^4 - 4*(a*b^2 - b^3)*d*cosh(d*x + c)^2 + 8*(7*(a*b^2 - b^3)*d*cosh(d*x + c)^5 - 10*(a*b^2 - b^3)*d*cosh(d*x + c)^3 - (8*a^2*b - 11*a*b^2 + 3*b^3)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a*b^2 - b^3)*d*cosh(d*x + c)^6 - 15*(a*b^2 - b^3)*d*cosh(d*x + c)^4 - 3*(8*a^2*b - 11*a*b^2 + 3*b^3)*d*cosh(d*x + c)^2 - (a*b^2 - b^3)*d)*sinh(d*x + c)^2 + (a*b^2 - b^3)*d + 8*((a*b^2 - b^3)*d*cosh(d*x + c)^7 - 3*(a*b^2 - b^3)*d*cosh(d*x + c)^5 - (8*a^2*b - 11*a*b^2 + 3*b^3)*d*cosh(d*x + c)^3 - (a*b^2 - b^3)*d*cosh(d*x + c))*sinh(d*x + c))*sqrt(-((a^4*b - 3*a^3*b^2 + 3*a^2*b^3 - a*b^4)*d^2*sqrt((9*a^2 + 6*a*b + b^2)/((a^9*b - 6*a^8*b^2 + 15*a^7*b^3 - 20*a^6*b^4 + 15*a^5*b^5 - 6*a^4*b^6 + a^3*b^7)*d^4)) - a - 3*b)/((a^4*b - 3*a^3*b^2 + 3*a^2*b^3 - a*b^4)*d^2))*log(-2*(a^5 - 3*a^4*b + 3*a^3*b^2 - a^2*b^3)*d^2*sqrt((9*a^2 + 6*a*b + b^2)/((a^9*b - 6*a^8*b^2 + 15*a^7*b^3 - 20*a^6*b^4 + 15*a^5*b^5 - 6*a^4*b^6 + a^3*b^7)*d^4)) + (3*a + b)*cosh(d*x + c)^2 + 2*(3*a + b)*cosh(d*x + c)*sinh(d*x + c) + (3*a + b)*sinh(d*x + c)^2 - 2*(2*(a^6*b - 3*a^5*b^2 + 3*a^4*b^3 - a^3*b^4)*d^3*sqrt((9*a^2 + 6*a*b + b^2)/((a^9*b - 6*a^8*b^2 + 15*a^7*b^3 - 20*a^6*b^4 + 15*a^5*b^5 - 6*a^4*b^6 + a^3*b^7)*d^4)) + (3*a^3 + 4*a^2*b + a*b^2)*d)*sqrt(-((a^4*b - 3*a^3*b^2 + 3*a^2*b^3 - a*b^4)*d^2*sqrt((9*a^2 + 6*a*b + b^2)/((a^9*b - 6*a^8*b^2 + 15*a^7*b^3 - 20*a^6*b^4 + 15*a^5*b^5 - 6*a^4*b^6 + a^3*b^7)*d^4)) - a - 3*b)/((a^4*b - 3*a^3*b^2 + 3*a^2*b^3 - a*b^4)*d^2)) - 3*a - b) + 16*(3*b*cosh(d*x + c)^5 - 2*(8*a - 3*b)*cosh(d*x + c)^3 - 5*b*cosh(d*x + c))*sinh(d*x + c) + 8*b)/((a*b^2 - b^3)*d*cosh(d*x + c)^8 + 8*(a*b^2 - b^3)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a*b^2 - b^3)*d*sinh(d*x + c)^8 - 4*(a*b^2 - b^3)*d*cosh(d*x + c)^6 + 4*(7*(a*b^2 - b^3)*d*cosh(d*x + c)^2 - (a*b^2 - b^3)*d)*sinh(d*x + c)^6 - 2*(8*a^2*b - 11*a*b^2 + 3*b^3)*d*cosh(d*x + c)^4 + 8*(7*(a*b^2 - b^3)*d*cosh(d*x + c)^3 - 3*(a*b^2 - b^3)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a*b^2 - b^3)*d*cosh(d*x + c)^4 - 30*(a*b^2 - b^3)*d*cosh(d*x + c)^2 - (8*a^2*b - 11*a*b^2 + 3*b^3)*d)*sinh(d*x + c)^4 - 4*(a*b^2 - b^3)*d*cosh(d*x + c)^2 + 8*(7*(a*b^2 - b^3)*d*cosh(d*x + c)^5 - 10*(a*b^2 - b^3)*d*cosh(d*x + c)^3 - (8*a^2*b - 11*a*b^2 + 3*b^3)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a*b^2 - b^3)*d*cosh(d*x + c)^6 - 15*(a*b^2 - b^3)*d*cosh(d*x + c)^4 - 3*(8*a^2*b - 11*a*b^2 + 3*b^3)*d*cosh(d*x + c)^2 - (a*b^2 - b^3)*d)*sinh(d*x + c)^2 + (a*b^2 - b^3)*d + 8*((a*b^2 - b^3)*d*cosh(d*x + c)^7 - 3*(a*b^2 - b^3)*d*cosh(d*x + c)^5 - (8*a^2*b - 11*a*b^2 + 3*b^3)*d*cosh(d*x + c)^3 - (a*b^2 - b^3)*d*cosh(d*x + c))*sinh(d*x + c))","B",0
250,1,6525,0,1.367871," ","integrate(sinh(d*x+c)^2/(a-b*sinh(d*x+c)^4)^2,x, algorithm=""fricas"")","-\frac{8 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{6} + 48 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + 8 \, {\left(2 \, a - b\right)} \sinh\left(d x + c\right)^{6} - 8 \, {\left(8 \, a - 3 \, b\right)} \cosh\left(d x + c\right)^{4} + 8 \, {\left(15 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} - 8 \, a + 3 \, b\right)} \sinh\left(d x + c\right)^{4} + 32 \, {\left(5 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{3} - {\left(8 \, a - 3 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 8 \, {\left(2 \, a + 3 \, b\right)} \cosh\left(d x + c\right)^{2} + 8 \, {\left(15 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{4} - 6 \, {\left(8 \, a - 3 \, b\right)} \cosh\left(d x + c\right)^{2} - 2 \, a - 3 \, b\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{2} b - a b^{2}\right)} d \sinh\left(d x + c\right)^{8} - 4 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{2} b - a b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{6} - 2 \, {\left(8 \, a^{3} - 11 \, a^{2} b + 3 \, a b^{2}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{4} - 30 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(8 \, a^{3} - 11 \, a^{2} b + 3 \, a b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{4} - 4 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{5} - 10 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{3} - {\left(8 \, a^{3} - 11 \, a^{2} b + 3 \, a b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{6} - 15 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{4} - 3 \, {\left(8 \, a^{3} - 11 \, a^{2} b + 3 \, a b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{2} b - a b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{2} b - a b^{2}\right)} d + 8 \, {\left({\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{7} - 3 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{5} - {\left(8 \, a^{3} - 11 \, a^{2} b + 3 \, a b^{2}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{{\left(a^{5} b - 3 \, a^{4} b^{2} + 3 \, a^{3} b^{3} - a^{2} b^{4}\right)} d^{2} \sqrt{\frac{64 \, a^{4} - 80 \, a^{3} b + 41 \, a^{2} b^{2} - 10 \, a b^{3} + b^{4}}{{\left(a^{11} b - 6 \, a^{10} b^{2} + 15 \, a^{9} b^{3} - 20 \, a^{8} b^{4} + 15 \, a^{7} b^{5} - 6 \, a^{6} b^{6} + a^{5} b^{7}\right)} d^{4}}} - 4 \, a^{2} - a b + b^{2}}{{\left(a^{5} b - 3 \, a^{4} b^{2} + 3 \, a^{3} b^{3} - a^{2} b^{4}\right)} d^{2}}} \log\left(2 \, {\left(4 \, a^{7} - 13 \, a^{6} b + 15 \, a^{5} b^{2} - 7 \, a^{4} b^{3} + a^{3} b^{4}\right)} d^{2} \sqrt{\frac{64 \, a^{4} - 80 \, a^{3} b + 41 \, a^{2} b^{2} - 10 \, a b^{3} + b^{4}}{{\left(a^{11} b - 6 \, a^{10} b^{2} + 15 \, a^{9} b^{3} - 20 \, a^{8} b^{4} + 15 \, a^{7} b^{5} - 6 \, a^{6} b^{6} + a^{5} b^{7}\right)} d^{4}}} + 32 \, a^{3} - 28 \, a^{2} b + 9 \, a b^{2} - b^{3} - {\left(32 \, a^{3} - 28 \, a^{2} b + 9 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(32 \, a^{3} - 28 \, a^{2} b + 9 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(32 \, a^{3} - 28 \, a^{2} b + 9 \, a b^{2} - b^{3}\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left({\left(3 \, a^{8} b - 10 \, a^{7} b^{2} + 12 \, a^{6} b^{3} - 6 \, a^{5} b^{4} + a^{4} b^{5}\right)} d^{3} \sqrt{\frac{64 \, a^{4} - 80 \, a^{3} b + 41 \, a^{2} b^{2} - 10 \, a b^{3} + b^{4}}{{\left(a^{11} b - 6 \, a^{10} b^{2} + 15 \, a^{9} b^{3} - 20 \, a^{8} b^{4} + 15 \, a^{7} b^{5} - 6 \, a^{6} b^{6} + a^{5} b^{7}\right)} d^{4}}} + 2 \, {\left(8 \, a^{5} - 5 \, a^{4} b + a^{3} b^{2}\right)} d\right)} \sqrt{-\frac{{\left(a^{5} b - 3 \, a^{4} b^{2} + 3 \, a^{3} b^{3} - a^{2} b^{4}\right)} d^{2} \sqrt{\frac{64 \, a^{4} - 80 \, a^{3} b + 41 \, a^{2} b^{2} - 10 \, a b^{3} + b^{4}}{{\left(a^{11} b - 6 \, a^{10} b^{2} + 15 \, a^{9} b^{3} - 20 \, a^{8} b^{4} + 15 \, a^{7} b^{5} - 6 \, a^{6} b^{6} + a^{5} b^{7}\right)} d^{4}}} - 4 \, a^{2} - a b + b^{2}}{{\left(a^{5} b - 3 \, a^{4} b^{2} + 3 \, a^{3} b^{3} - a^{2} b^{4}\right)} d^{2}}}\right) - {\left({\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{2} b - a b^{2}\right)} d \sinh\left(d x + c\right)^{8} - 4 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{2} b - a b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{6} - 2 \, {\left(8 \, a^{3} - 11 \, a^{2} b + 3 \, a b^{2}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{4} - 30 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(8 \, a^{3} - 11 \, a^{2} b + 3 \, a b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{4} - 4 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{5} - 10 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{3} - {\left(8 \, a^{3} - 11 \, a^{2} b + 3 \, a b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{6} - 15 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{4} - 3 \, {\left(8 \, a^{3} - 11 \, a^{2} b + 3 \, a b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{2} b - a b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{2} b - a b^{2}\right)} d + 8 \, {\left({\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{7} - 3 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{5} - {\left(8 \, a^{3} - 11 \, a^{2} b + 3 \, a b^{2}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{{\left(a^{5} b - 3 \, a^{4} b^{2} + 3 \, a^{3} b^{3} - a^{2} b^{4}\right)} d^{2} \sqrt{\frac{64 \, a^{4} - 80 \, a^{3} b + 41 \, a^{2} b^{2} - 10 \, a b^{3} + b^{4}}{{\left(a^{11} b - 6 \, a^{10} b^{2} + 15 \, a^{9} b^{3} - 20 \, a^{8} b^{4} + 15 \, a^{7} b^{5} - 6 \, a^{6} b^{6} + a^{5} b^{7}\right)} d^{4}}} - 4 \, a^{2} - a b + b^{2}}{{\left(a^{5} b - 3 \, a^{4} b^{2} + 3 \, a^{3} b^{3} - a^{2} b^{4}\right)} d^{2}}} \log\left(2 \, {\left(4 \, a^{7} - 13 \, a^{6} b + 15 \, a^{5} b^{2} - 7 \, a^{4} b^{3} + a^{3} b^{4}\right)} d^{2} \sqrt{\frac{64 \, a^{4} - 80 \, a^{3} b + 41 \, a^{2} b^{2} - 10 \, a b^{3} + b^{4}}{{\left(a^{11} b - 6 \, a^{10} b^{2} + 15 \, a^{9} b^{3} - 20 \, a^{8} b^{4} + 15 \, a^{7} b^{5} - 6 \, a^{6} b^{6} + a^{5} b^{7}\right)} d^{4}}} + 32 \, a^{3} - 28 \, a^{2} b + 9 \, a b^{2} - b^{3} - {\left(32 \, a^{3} - 28 \, a^{2} b + 9 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(32 \, a^{3} - 28 \, a^{2} b + 9 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(32 \, a^{3} - 28 \, a^{2} b + 9 \, a b^{2} - b^{3}\right)} \sinh\left(d x + c\right)^{2} - 2 \, {\left({\left(3 \, a^{8} b - 10 \, a^{7} b^{2} + 12 \, a^{6} b^{3} - 6 \, a^{5} b^{4} + a^{4} b^{5}\right)} d^{3} \sqrt{\frac{64 \, a^{4} - 80 \, a^{3} b + 41 \, a^{2} b^{2} - 10 \, a b^{3} + b^{4}}{{\left(a^{11} b - 6 \, a^{10} b^{2} + 15 \, a^{9} b^{3} - 20 \, a^{8} b^{4} + 15 \, a^{7} b^{5} - 6 \, a^{6} b^{6} + a^{5} b^{7}\right)} d^{4}}} + 2 \, {\left(8 \, a^{5} - 5 \, a^{4} b + a^{3} b^{2}\right)} d\right)} \sqrt{-\frac{{\left(a^{5} b - 3 \, a^{4} b^{2} + 3 \, a^{3} b^{3} - a^{2} b^{4}\right)} d^{2} \sqrt{\frac{64 \, a^{4} - 80 \, a^{3} b + 41 \, a^{2} b^{2} - 10 \, a b^{3} + b^{4}}{{\left(a^{11} b - 6 \, a^{10} b^{2} + 15 \, a^{9} b^{3} - 20 \, a^{8} b^{4} + 15 \, a^{7} b^{5} - 6 \, a^{6} b^{6} + a^{5} b^{7}\right)} d^{4}}} - 4 \, a^{2} - a b + b^{2}}{{\left(a^{5} b - 3 \, a^{4} b^{2} + 3 \, a^{3} b^{3} - a^{2} b^{4}\right)} d^{2}}}\right) - {\left({\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{2} b - a b^{2}\right)} d \sinh\left(d x + c\right)^{8} - 4 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{2} b - a b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{6} - 2 \, {\left(8 \, a^{3} - 11 \, a^{2} b + 3 \, a b^{2}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{4} - 30 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(8 \, a^{3} - 11 \, a^{2} b + 3 \, a b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{4} - 4 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{5} - 10 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{3} - {\left(8 \, a^{3} - 11 \, a^{2} b + 3 \, a b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{6} - 15 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{4} - 3 \, {\left(8 \, a^{3} - 11 \, a^{2} b + 3 \, a b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{2} b - a b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{2} b - a b^{2}\right)} d + 8 \, {\left({\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{7} - 3 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{5} - {\left(8 \, a^{3} - 11 \, a^{2} b + 3 \, a b^{2}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{{\left(a^{5} b - 3 \, a^{4} b^{2} + 3 \, a^{3} b^{3} - a^{2} b^{4}\right)} d^{2} \sqrt{\frac{64 \, a^{4} - 80 \, a^{3} b + 41 \, a^{2} b^{2} - 10 \, a b^{3} + b^{4}}{{\left(a^{11} b - 6 \, a^{10} b^{2} + 15 \, a^{9} b^{3} - 20 \, a^{8} b^{4} + 15 \, a^{7} b^{5} - 6 \, a^{6} b^{6} + a^{5} b^{7}\right)} d^{4}}} + 4 \, a^{2} + a b - b^{2}}{{\left(a^{5} b - 3 \, a^{4} b^{2} + 3 \, a^{3} b^{3} - a^{2} b^{4}\right)} d^{2}}} \log\left(-2 \, {\left(4 \, a^{7} - 13 \, a^{6} b + 15 \, a^{5} b^{2} - 7 \, a^{4} b^{3} + a^{3} b^{4}\right)} d^{2} \sqrt{\frac{64 \, a^{4} - 80 \, a^{3} b + 41 \, a^{2} b^{2} - 10 \, a b^{3} + b^{4}}{{\left(a^{11} b - 6 \, a^{10} b^{2} + 15 \, a^{9} b^{3} - 20 \, a^{8} b^{4} + 15 \, a^{7} b^{5} - 6 \, a^{6} b^{6} + a^{5} b^{7}\right)} d^{4}}} + 32 \, a^{3} - 28 \, a^{2} b + 9 \, a b^{2} - b^{3} - {\left(32 \, a^{3} - 28 \, a^{2} b + 9 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(32 \, a^{3} - 28 \, a^{2} b + 9 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(32 \, a^{3} - 28 \, a^{2} b + 9 \, a b^{2} - b^{3}\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left({\left(3 \, a^{8} b - 10 \, a^{7} b^{2} + 12 \, a^{6} b^{3} - 6 \, a^{5} b^{4} + a^{4} b^{5}\right)} d^{3} \sqrt{\frac{64 \, a^{4} - 80 \, a^{3} b + 41 \, a^{2} b^{2} - 10 \, a b^{3} + b^{4}}{{\left(a^{11} b - 6 \, a^{10} b^{2} + 15 \, a^{9} b^{3} - 20 \, a^{8} b^{4} + 15 \, a^{7} b^{5} - 6 \, a^{6} b^{6} + a^{5} b^{7}\right)} d^{4}}} - 2 \, {\left(8 \, a^{5} - 5 \, a^{4} b + a^{3} b^{2}\right)} d\right)} \sqrt{\frac{{\left(a^{5} b - 3 \, a^{4} b^{2} + 3 \, a^{3} b^{3} - a^{2} b^{4}\right)} d^{2} \sqrt{\frac{64 \, a^{4} - 80 \, a^{3} b + 41 \, a^{2} b^{2} - 10 \, a b^{3} + b^{4}}{{\left(a^{11} b - 6 \, a^{10} b^{2} + 15 \, a^{9} b^{3} - 20 \, a^{8} b^{4} + 15 \, a^{7} b^{5} - 6 \, a^{6} b^{6} + a^{5} b^{7}\right)} d^{4}}} + 4 \, a^{2} + a b - b^{2}}{{\left(a^{5} b - 3 \, a^{4} b^{2} + 3 \, a^{3} b^{3} - a^{2} b^{4}\right)} d^{2}}}\right) + {\left({\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{2} b - a b^{2}\right)} d \sinh\left(d x + c\right)^{8} - 4 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{2} b - a b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{6} - 2 \, {\left(8 \, a^{3} - 11 \, a^{2} b + 3 \, a b^{2}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{4} - 30 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(8 \, a^{3} - 11 \, a^{2} b + 3 \, a b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{4} - 4 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{5} - 10 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{3} - {\left(8 \, a^{3} - 11 \, a^{2} b + 3 \, a b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{6} - 15 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{4} - 3 \, {\left(8 \, a^{3} - 11 \, a^{2} b + 3 \, a b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{2} b - a b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{2} b - a b^{2}\right)} d + 8 \, {\left({\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{7} - 3 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{5} - {\left(8 \, a^{3} - 11 \, a^{2} b + 3 \, a b^{2}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{{\left(a^{5} b - 3 \, a^{4} b^{2} + 3 \, a^{3} b^{3} - a^{2} b^{4}\right)} d^{2} \sqrt{\frac{64 \, a^{4} - 80 \, a^{3} b + 41 \, a^{2} b^{2} - 10 \, a b^{3} + b^{4}}{{\left(a^{11} b - 6 \, a^{10} b^{2} + 15 \, a^{9} b^{3} - 20 \, a^{8} b^{4} + 15 \, a^{7} b^{5} - 6 \, a^{6} b^{6} + a^{5} b^{7}\right)} d^{4}}} + 4 \, a^{2} + a b - b^{2}}{{\left(a^{5} b - 3 \, a^{4} b^{2} + 3 \, a^{3} b^{3} - a^{2} b^{4}\right)} d^{2}}} \log\left(-2 \, {\left(4 \, a^{7} - 13 \, a^{6} b + 15 \, a^{5} b^{2} - 7 \, a^{4} b^{3} + a^{3} b^{4}\right)} d^{2} \sqrt{\frac{64 \, a^{4} - 80 \, a^{3} b + 41 \, a^{2} b^{2} - 10 \, a b^{3} + b^{4}}{{\left(a^{11} b - 6 \, a^{10} b^{2} + 15 \, a^{9} b^{3} - 20 \, a^{8} b^{4} + 15 \, a^{7} b^{5} - 6 \, a^{6} b^{6} + a^{5} b^{7}\right)} d^{4}}} + 32 \, a^{3} - 28 \, a^{2} b + 9 \, a b^{2} - b^{3} - {\left(32 \, a^{3} - 28 \, a^{2} b + 9 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(32 \, a^{3} - 28 \, a^{2} b + 9 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(32 \, a^{3} - 28 \, a^{2} b + 9 \, a b^{2} - b^{3}\right)} \sinh\left(d x + c\right)^{2} - 2 \, {\left({\left(3 \, a^{8} b - 10 \, a^{7} b^{2} + 12 \, a^{6} b^{3} - 6 \, a^{5} b^{4} + a^{4} b^{5}\right)} d^{3} \sqrt{\frac{64 \, a^{4} - 80 \, a^{3} b + 41 \, a^{2} b^{2} - 10 \, a b^{3} + b^{4}}{{\left(a^{11} b - 6 \, a^{10} b^{2} + 15 \, a^{9} b^{3} - 20 \, a^{8} b^{4} + 15 \, a^{7} b^{5} - 6 \, a^{6} b^{6} + a^{5} b^{7}\right)} d^{4}}} - 2 \, {\left(8 \, a^{5} - 5 \, a^{4} b + a^{3} b^{2}\right)} d\right)} \sqrt{\frac{{\left(a^{5} b - 3 \, a^{4} b^{2} + 3 \, a^{3} b^{3} - a^{2} b^{4}\right)} d^{2} \sqrt{\frac{64 \, a^{4} - 80 \, a^{3} b + 41 \, a^{2} b^{2} - 10 \, a b^{3} + b^{4}}{{\left(a^{11} b - 6 \, a^{10} b^{2} + 15 \, a^{9} b^{3} - 20 \, a^{8} b^{4} + 15 \, a^{7} b^{5} - 6 \, a^{6} b^{6} + a^{5} b^{7}\right)} d^{4}}} + 4 \, a^{2} + a b - b^{2}}{{\left(a^{5} b - 3 \, a^{4} b^{2} + 3 \, a^{3} b^{3} - a^{2} b^{4}\right)} d^{2}}}\right) + 16 \, {\left(3 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{5} - 2 \, {\left(8 \, a - 3 \, b\right)} \cosh\left(d x + c\right)^{3} - {\left(2 \, a + 3 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + 8 \, b}{16 \, {\left({\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{2} b - a b^{2}\right)} d \sinh\left(d x + c\right)^{8} - 4 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{2} b - a b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{6} - 2 \, {\left(8 \, a^{3} - 11 \, a^{2} b + 3 \, a b^{2}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{4} - 30 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(8 \, a^{3} - 11 \, a^{2} b + 3 \, a b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{4} - 4 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{5} - 10 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{3} - {\left(8 \, a^{3} - 11 \, a^{2} b + 3 \, a b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{6} - 15 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{4} - 3 \, {\left(8 \, a^{3} - 11 \, a^{2} b + 3 \, a b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{2} b - a b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{2} b - a b^{2}\right)} d + 8 \, {\left({\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{7} - 3 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{5} - {\left(8 \, a^{3} - 11 \, a^{2} b + 3 \, a b^{2}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"-1/16*(8*(2*a - b)*cosh(d*x + c)^6 + 48*(2*a - b)*cosh(d*x + c)*sinh(d*x + c)^5 + 8*(2*a - b)*sinh(d*x + c)^6 - 8*(8*a - 3*b)*cosh(d*x + c)^4 + 8*(15*(2*a - b)*cosh(d*x + c)^2 - 8*a + 3*b)*sinh(d*x + c)^4 + 32*(5*(2*a - b)*cosh(d*x + c)^3 - (8*a - 3*b)*cosh(d*x + c))*sinh(d*x + c)^3 - 8*(2*a + 3*b)*cosh(d*x + c)^2 + 8*(15*(2*a - b)*cosh(d*x + c)^4 - 6*(8*a - 3*b)*cosh(d*x + c)^2 - 2*a - 3*b)*sinh(d*x + c)^2 + ((a^2*b - a*b^2)*d*cosh(d*x + c)^8 + 8*(a^2*b - a*b^2)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^2*b - a*b^2)*d*sinh(d*x + c)^8 - 4*(a^2*b - a*b^2)*d*cosh(d*x + c)^6 + 4*(7*(a^2*b - a*b^2)*d*cosh(d*x + c)^2 - (a^2*b - a*b^2)*d)*sinh(d*x + c)^6 - 2*(8*a^3 - 11*a^2*b + 3*a*b^2)*d*cosh(d*x + c)^4 + 8*(7*(a^2*b - a*b^2)*d*cosh(d*x + c)^3 - 3*(a^2*b - a*b^2)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^2*b - a*b^2)*d*cosh(d*x + c)^4 - 30*(a^2*b - a*b^2)*d*cosh(d*x + c)^2 - (8*a^3 - 11*a^2*b + 3*a*b^2)*d)*sinh(d*x + c)^4 - 4*(a^2*b - a*b^2)*d*cosh(d*x + c)^2 + 8*(7*(a^2*b - a*b^2)*d*cosh(d*x + c)^5 - 10*(a^2*b - a*b^2)*d*cosh(d*x + c)^3 - (8*a^3 - 11*a^2*b + 3*a*b^2)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^2*b - a*b^2)*d*cosh(d*x + c)^6 - 15*(a^2*b - a*b^2)*d*cosh(d*x + c)^4 - 3*(8*a^3 - 11*a^2*b + 3*a*b^2)*d*cosh(d*x + c)^2 - (a^2*b - a*b^2)*d)*sinh(d*x + c)^2 + (a^2*b - a*b^2)*d + 8*((a^2*b - a*b^2)*d*cosh(d*x + c)^7 - 3*(a^2*b - a*b^2)*d*cosh(d*x + c)^5 - (8*a^3 - 11*a^2*b + 3*a*b^2)*d*cosh(d*x + c)^3 - (a^2*b - a*b^2)*d*cosh(d*x + c))*sinh(d*x + c))*sqrt(-((a^5*b - 3*a^4*b^2 + 3*a^3*b^3 - a^2*b^4)*d^2*sqrt((64*a^4 - 80*a^3*b + 41*a^2*b^2 - 10*a*b^3 + b^4)/((a^11*b - 6*a^10*b^2 + 15*a^9*b^3 - 20*a^8*b^4 + 15*a^7*b^5 - 6*a^6*b^6 + a^5*b^7)*d^4)) - 4*a^2 - a*b + b^2)/((a^5*b - 3*a^4*b^2 + 3*a^3*b^3 - a^2*b^4)*d^2))*log(2*(4*a^7 - 13*a^6*b + 15*a^5*b^2 - 7*a^4*b^3 + a^3*b^4)*d^2*sqrt((64*a^4 - 80*a^3*b + 41*a^2*b^2 - 10*a*b^3 + b^4)/((a^11*b - 6*a^10*b^2 + 15*a^9*b^3 - 20*a^8*b^4 + 15*a^7*b^5 - 6*a^6*b^6 + a^5*b^7)*d^4)) + 32*a^3 - 28*a^2*b + 9*a*b^2 - b^3 - (32*a^3 - 28*a^2*b + 9*a*b^2 - b^3)*cosh(d*x + c)^2 - 2*(32*a^3 - 28*a^2*b + 9*a*b^2 - b^3)*cosh(d*x + c)*sinh(d*x + c) - (32*a^3 - 28*a^2*b + 9*a*b^2 - b^3)*sinh(d*x + c)^2 + 2*((3*a^8*b - 10*a^7*b^2 + 12*a^6*b^3 - 6*a^5*b^4 + a^4*b^5)*d^3*sqrt((64*a^4 - 80*a^3*b + 41*a^2*b^2 - 10*a*b^3 + b^4)/((a^11*b - 6*a^10*b^2 + 15*a^9*b^3 - 20*a^8*b^4 + 15*a^7*b^5 - 6*a^6*b^6 + a^5*b^7)*d^4)) + 2*(8*a^5 - 5*a^4*b + a^3*b^2)*d)*sqrt(-((a^5*b - 3*a^4*b^2 + 3*a^3*b^3 - a^2*b^4)*d^2*sqrt((64*a^4 - 80*a^3*b + 41*a^2*b^2 - 10*a*b^3 + b^4)/((a^11*b - 6*a^10*b^2 + 15*a^9*b^3 - 20*a^8*b^4 + 15*a^7*b^5 - 6*a^6*b^6 + a^5*b^7)*d^4)) - 4*a^2 - a*b + b^2)/((a^5*b - 3*a^4*b^2 + 3*a^3*b^3 - a^2*b^4)*d^2))) - ((a^2*b - a*b^2)*d*cosh(d*x + c)^8 + 8*(a^2*b - a*b^2)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^2*b - a*b^2)*d*sinh(d*x + c)^8 - 4*(a^2*b - a*b^2)*d*cosh(d*x + c)^6 + 4*(7*(a^2*b - a*b^2)*d*cosh(d*x + c)^2 - (a^2*b - a*b^2)*d)*sinh(d*x + c)^6 - 2*(8*a^3 - 11*a^2*b + 3*a*b^2)*d*cosh(d*x + c)^4 + 8*(7*(a^2*b - a*b^2)*d*cosh(d*x + c)^3 - 3*(a^2*b - a*b^2)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^2*b - a*b^2)*d*cosh(d*x + c)^4 - 30*(a^2*b - a*b^2)*d*cosh(d*x + c)^2 - (8*a^3 - 11*a^2*b + 3*a*b^2)*d)*sinh(d*x + c)^4 - 4*(a^2*b - a*b^2)*d*cosh(d*x + c)^2 + 8*(7*(a^2*b - a*b^2)*d*cosh(d*x + c)^5 - 10*(a^2*b - a*b^2)*d*cosh(d*x + c)^3 - (8*a^3 - 11*a^2*b + 3*a*b^2)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^2*b - a*b^2)*d*cosh(d*x + c)^6 - 15*(a^2*b - a*b^2)*d*cosh(d*x + c)^4 - 3*(8*a^3 - 11*a^2*b + 3*a*b^2)*d*cosh(d*x + c)^2 - (a^2*b - a*b^2)*d)*sinh(d*x + c)^2 + (a^2*b - a*b^2)*d + 8*((a^2*b - a*b^2)*d*cosh(d*x + c)^7 - 3*(a^2*b - a*b^2)*d*cosh(d*x + c)^5 - (8*a^3 - 11*a^2*b + 3*a*b^2)*d*cosh(d*x + c)^3 - (a^2*b - a*b^2)*d*cosh(d*x + c))*sinh(d*x + c))*sqrt(-((a^5*b - 3*a^4*b^2 + 3*a^3*b^3 - a^2*b^4)*d^2*sqrt((64*a^4 - 80*a^3*b + 41*a^2*b^2 - 10*a*b^3 + b^4)/((a^11*b - 6*a^10*b^2 + 15*a^9*b^3 - 20*a^8*b^4 + 15*a^7*b^5 - 6*a^6*b^6 + a^5*b^7)*d^4)) - 4*a^2 - a*b + b^2)/((a^5*b - 3*a^4*b^2 + 3*a^3*b^3 - a^2*b^4)*d^2))*log(2*(4*a^7 - 13*a^6*b + 15*a^5*b^2 - 7*a^4*b^3 + a^3*b^4)*d^2*sqrt((64*a^4 - 80*a^3*b + 41*a^2*b^2 - 10*a*b^3 + b^4)/((a^11*b - 6*a^10*b^2 + 15*a^9*b^3 - 20*a^8*b^4 + 15*a^7*b^5 - 6*a^6*b^6 + a^5*b^7)*d^4)) + 32*a^3 - 28*a^2*b + 9*a*b^2 - b^3 - (32*a^3 - 28*a^2*b + 9*a*b^2 - b^3)*cosh(d*x + c)^2 - 2*(32*a^3 - 28*a^2*b + 9*a*b^2 - b^3)*cosh(d*x + c)*sinh(d*x + c) - (32*a^3 - 28*a^2*b + 9*a*b^2 - b^3)*sinh(d*x + c)^2 - 2*((3*a^8*b - 10*a^7*b^2 + 12*a^6*b^3 - 6*a^5*b^4 + a^4*b^5)*d^3*sqrt((64*a^4 - 80*a^3*b + 41*a^2*b^2 - 10*a*b^3 + b^4)/((a^11*b - 6*a^10*b^2 + 15*a^9*b^3 - 20*a^8*b^4 + 15*a^7*b^5 - 6*a^6*b^6 + a^5*b^7)*d^4)) + 2*(8*a^5 - 5*a^4*b + a^3*b^2)*d)*sqrt(-((a^5*b - 3*a^4*b^2 + 3*a^3*b^3 - a^2*b^4)*d^2*sqrt((64*a^4 - 80*a^3*b + 41*a^2*b^2 - 10*a*b^3 + b^4)/((a^11*b - 6*a^10*b^2 + 15*a^9*b^3 - 20*a^8*b^4 + 15*a^7*b^5 - 6*a^6*b^6 + a^5*b^7)*d^4)) - 4*a^2 - a*b + b^2)/((a^5*b - 3*a^4*b^2 + 3*a^3*b^3 - a^2*b^4)*d^2))) - ((a^2*b - a*b^2)*d*cosh(d*x + c)^8 + 8*(a^2*b - a*b^2)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^2*b - a*b^2)*d*sinh(d*x + c)^8 - 4*(a^2*b - a*b^2)*d*cosh(d*x + c)^6 + 4*(7*(a^2*b - a*b^2)*d*cosh(d*x + c)^2 - (a^2*b - a*b^2)*d)*sinh(d*x + c)^6 - 2*(8*a^3 - 11*a^2*b + 3*a*b^2)*d*cosh(d*x + c)^4 + 8*(7*(a^2*b - a*b^2)*d*cosh(d*x + c)^3 - 3*(a^2*b - a*b^2)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^2*b - a*b^2)*d*cosh(d*x + c)^4 - 30*(a^2*b - a*b^2)*d*cosh(d*x + c)^2 - (8*a^3 - 11*a^2*b + 3*a*b^2)*d)*sinh(d*x + c)^4 - 4*(a^2*b - a*b^2)*d*cosh(d*x + c)^2 + 8*(7*(a^2*b - a*b^2)*d*cosh(d*x + c)^5 - 10*(a^2*b - a*b^2)*d*cosh(d*x + c)^3 - (8*a^3 - 11*a^2*b + 3*a*b^2)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^2*b - a*b^2)*d*cosh(d*x + c)^6 - 15*(a^2*b - a*b^2)*d*cosh(d*x + c)^4 - 3*(8*a^3 - 11*a^2*b + 3*a*b^2)*d*cosh(d*x + c)^2 - (a^2*b - a*b^2)*d)*sinh(d*x + c)^2 + (a^2*b - a*b^2)*d + 8*((a^2*b - a*b^2)*d*cosh(d*x + c)^7 - 3*(a^2*b - a*b^2)*d*cosh(d*x + c)^5 - (8*a^3 - 11*a^2*b + 3*a*b^2)*d*cosh(d*x + c)^3 - (a^2*b - a*b^2)*d*cosh(d*x + c))*sinh(d*x + c))*sqrt(((a^5*b - 3*a^4*b^2 + 3*a^3*b^3 - a^2*b^4)*d^2*sqrt((64*a^4 - 80*a^3*b + 41*a^2*b^2 - 10*a*b^3 + b^4)/((a^11*b - 6*a^10*b^2 + 15*a^9*b^3 - 20*a^8*b^4 + 15*a^7*b^5 - 6*a^6*b^6 + a^5*b^7)*d^4)) + 4*a^2 + a*b - b^2)/((a^5*b - 3*a^4*b^2 + 3*a^3*b^3 - a^2*b^4)*d^2))*log(-2*(4*a^7 - 13*a^6*b + 15*a^5*b^2 - 7*a^4*b^3 + a^3*b^4)*d^2*sqrt((64*a^4 - 80*a^3*b + 41*a^2*b^2 - 10*a*b^3 + b^4)/((a^11*b - 6*a^10*b^2 + 15*a^9*b^3 - 20*a^8*b^4 + 15*a^7*b^5 - 6*a^6*b^6 + a^5*b^7)*d^4)) + 32*a^3 - 28*a^2*b + 9*a*b^2 - b^3 - (32*a^3 - 28*a^2*b + 9*a*b^2 - b^3)*cosh(d*x + c)^2 - 2*(32*a^3 - 28*a^2*b + 9*a*b^2 - b^3)*cosh(d*x + c)*sinh(d*x + c) - (32*a^3 - 28*a^2*b + 9*a*b^2 - b^3)*sinh(d*x + c)^2 + 2*((3*a^8*b - 10*a^7*b^2 + 12*a^6*b^3 - 6*a^5*b^4 + a^4*b^5)*d^3*sqrt((64*a^4 - 80*a^3*b + 41*a^2*b^2 - 10*a*b^3 + b^4)/((a^11*b - 6*a^10*b^2 + 15*a^9*b^3 - 20*a^8*b^4 + 15*a^7*b^5 - 6*a^6*b^6 + a^5*b^7)*d^4)) - 2*(8*a^5 - 5*a^4*b + a^3*b^2)*d)*sqrt(((a^5*b - 3*a^4*b^2 + 3*a^3*b^3 - a^2*b^4)*d^2*sqrt((64*a^4 - 80*a^3*b + 41*a^2*b^2 - 10*a*b^3 + b^4)/((a^11*b - 6*a^10*b^2 + 15*a^9*b^3 - 20*a^8*b^4 + 15*a^7*b^5 - 6*a^6*b^6 + a^5*b^7)*d^4)) + 4*a^2 + a*b - b^2)/((a^5*b - 3*a^4*b^2 + 3*a^3*b^3 - a^2*b^4)*d^2))) + ((a^2*b - a*b^2)*d*cosh(d*x + c)^8 + 8*(a^2*b - a*b^2)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^2*b - a*b^2)*d*sinh(d*x + c)^8 - 4*(a^2*b - a*b^2)*d*cosh(d*x + c)^6 + 4*(7*(a^2*b - a*b^2)*d*cosh(d*x + c)^2 - (a^2*b - a*b^2)*d)*sinh(d*x + c)^6 - 2*(8*a^3 - 11*a^2*b + 3*a*b^2)*d*cosh(d*x + c)^4 + 8*(7*(a^2*b - a*b^2)*d*cosh(d*x + c)^3 - 3*(a^2*b - a*b^2)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^2*b - a*b^2)*d*cosh(d*x + c)^4 - 30*(a^2*b - a*b^2)*d*cosh(d*x + c)^2 - (8*a^3 - 11*a^2*b + 3*a*b^2)*d)*sinh(d*x + c)^4 - 4*(a^2*b - a*b^2)*d*cosh(d*x + c)^2 + 8*(7*(a^2*b - a*b^2)*d*cosh(d*x + c)^5 - 10*(a^2*b - a*b^2)*d*cosh(d*x + c)^3 - (8*a^3 - 11*a^2*b + 3*a*b^2)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^2*b - a*b^2)*d*cosh(d*x + c)^6 - 15*(a^2*b - a*b^2)*d*cosh(d*x + c)^4 - 3*(8*a^3 - 11*a^2*b + 3*a*b^2)*d*cosh(d*x + c)^2 - (a^2*b - a*b^2)*d)*sinh(d*x + c)^2 + (a^2*b - a*b^2)*d + 8*((a^2*b - a*b^2)*d*cosh(d*x + c)^7 - 3*(a^2*b - a*b^2)*d*cosh(d*x + c)^5 - (8*a^3 - 11*a^2*b + 3*a*b^2)*d*cosh(d*x + c)^3 - (a^2*b - a*b^2)*d*cosh(d*x + c))*sinh(d*x + c))*sqrt(((a^5*b - 3*a^4*b^2 + 3*a^3*b^3 - a^2*b^4)*d^2*sqrt((64*a^4 - 80*a^3*b + 41*a^2*b^2 - 10*a*b^3 + b^4)/((a^11*b - 6*a^10*b^2 + 15*a^9*b^3 - 20*a^8*b^4 + 15*a^7*b^5 - 6*a^6*b^6 + a^5*b^7)*d^4)) + 4*a^2 + a*b - b^2)/((a^5*b - 3*a^4*b^2 + 3*a^3*b^3 - a^2*b^4)*d^2))*log(-2*(4*a^7 - 13*a^6*b + 15*a^5*b^2 - 7*a^4*b^3 + a^3*b^4)*d^2*sqrt((64*a^4 - 80*a^3*b + 41*a^2*b^2 - 10*a*b^3 + b^4)/((a^11*b - 6*a^10*b^2 + 15*a^9*b^3 - 20*a^8*b^4 + 15*a^7*b^5 - 6*a^6*b^6 + a^5*b^7)*d^4)) + 32*a^3 - 28*a^2*b + 9*a*b^2 - b^3 - (32*a^3 - 28*a^2*b + 9*a*b^2 - b^3)*cosh(d*x + c)^2 - 2*(32*a^3 - 28*a^2*b + 9*a*b^2 - b^3)*cosh(d*x + c)*sinh(d*x + c) - (32*a^3 - 28*a^2*b + 9*a*b^2 - b^3)*sinh(d*x + c)^2 - 2*((3*a^8*b - 10*a^7*b^2 + 12*a^6*b^3 - 6*a^5*b^4 + a^4*b^5)*d^3*sqrt((64*a^4 - 80*a^3*b + 41*a^2*b^2 - 10*a*b^3 + b^4)/((a^11*b - 6*a^10*b^2 + 15*a^9*b^3 - 20*a^8*b^4 + 15*a^7*b^5 - 6*a^6*b^6 + a^5*b^7)*d^4)) - 2*(8*a^5 - 5*a^4*b + a^3*b^2)*d)*sqrt(((a^5*b - 3*a^4*b^2 + 3*a^3*b^3 - a^2*b^4)*d^2*sqrt((64*a^4 - 80*a^3*b + 41*a^2*b^2 - 10*a*b^3 + b^4)/((a^11*b - 6*a^10*b^2 + 15*a^9*b^3 - 20*a^8*b^4 + 15*a^7*b^5 - 6*a^6*b^6 + a^5*b^7)*d^4)) + 4*a^2 + a*b - b^2)/((a^5*b - 3*a^4*b^2 + 3*a^3*b^3 - a^2*b^4)*d^2))) + 16*(3*(2*a - b)*cosh(d*x + c)^5 - 2*(8*a - 3*b)*cosh(d*x + c)^3 - (2*a + 3*b)*cosh(d*x + c))*sinh(d*x + c) + 8*b)/((a^2*b - a*b^2)*d*cosh(d*x + c)^8 + 8*(a^2*b - a*b^2)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^2*b - a*b^2)*d*sinh(d*x + c)^8 - 4*(a^2*b - a*b^2)*d*cosh(d*x + c)^6 + 4*(7*(a^2*b - a*b^2)*d*cosh(d*x + c)^2 - (a^2*b - a*b^2)*d)*sinh(d*x + c)^6 - 2*(8*a^3 - 11*a^2*b + 3*a*b^2)*d*cosh(d*x + c)^4 + 8*(7*(a^2*b - a*b^2)*d*cosh(d*x + c)^3 - 3*(a^2*b - a*b^2)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^2*b - a*b^2)*d*cosh(d*x + c)^4 - 30*(a^2*b - a*b^2)*d*cosh(d*x + c)^2 - (8*a^3 - 11*a^2*b + 3*a*b^2)*d)*sinh(d*x + c)^4 - 4*(a^2*b - a*b^2)*d*cosh(d*x + c)^2 + 8*(7*(a^2*b - a*b^2)*d*cosh(d*x + c)^5 - 10*(a^2*b - a*b^2)*d*cosh(d*x + c)^3 - (8*a^3 - 11*a^2*b + 3*a*b^2)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^2*b - a*b^2)*d*cosh(d*x + c)^6 - 15*(a^2*b - a*b^2)*d*cosh(d*x + c)^4 - 3*(8*a^3 - 11*a^2*b + 3*a*b^2)*d*cosh(d*x + c)^2 - (a^2*b - a*b^2)*d)*sinh(d*x + c)^2 + (a^2*b - a*b^2)*d + 8*((a^2*b - a*b^2)*d*cosh(d*x + c)^7 - 3*(a^2*b - a*b^2)*d*cosh(d*x + c)^5 - (8*a^3 - 11*a^2*b + 3*a*b^2)*d*cosh(d*x + c)^3 - (a^2*b - a*b^2)*d*cosh(d*x + c))*sinh(d*x + c))","B",0
251,1,6522,0,1.258845," ","integrate(1/(a-b*sinh(d*x+c)^4)^2,x, algorithm=""fricas"")","\frac{8 \, b \cosh\left(d x + c\right)^{6} + 48 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + 8 \, b \sinh\left(d x + c\right)^{6} - 8 \, {\left(8 \, a - 3 \, b\right)} \cosh\left(d x + c\right)^{4} + 8 \, {\left(15 \, b \cosh\left(d x + c\right)^{2} - 8 \, a + 3 \, b\right)} \sinh\left(d x + c\right)^{4} + 32 \, {\left(5 \, b \cosh\left(d x + c\right)^{3} - {\left(8 \, a - 3 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 40 \, b \cosh\left(d x + c\right)^{2} + 8 \, {\left(15 \, b \cosh\left(d x + c\right)^{4} - 6 \, {\left(8 \, a - 3 \, b\right)} \cosh\left(d x + c\right)^{2} - 5 \, b\right)} \sinh\left(d x + c\right)^{2} - {\left({\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{2} b - a b^{2}\right)} d \sinh\left(d x + c\right)^{8} - 4 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{2} b - a b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{6} - 2 \, {\left(8 \, a^{3} - 11 \, a^{2} b + 3 \, a b^{2}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{4} - 30 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(8 \, a^{3} - 11 \, a^{2} b + 3 \, a b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{4} - 4 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{5} - 10 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{3} - {\left(8 \, a^{3} - 11 \, a^{2} b + 3 \, a b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{6} - 15 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{4} - 3 \, {\left(8 \, a^{3} - 11 \, a^{2} b + 3 \, a b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{2} b - a b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{2} b - a b^{2}\right)} d + 8 \, {\left({\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{7} - 3 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{5} - {\left(8 \, a^{3} - 11 \, a^{2} b + 3 \, a b^{2}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{{\left(a^{6} - 3 \, a^{5} b + 3 \, a^{4} b^{2} - a^{3} b^{3}\right)} d^{2} \sqrt{\frac{576 \, a^{4} b - 1392 \, a^{3} b^{2} + 1273 \, a^{2} b^{3} - 522 \, a b^{4} + 81 \, b^{5}}{{\left(a^{13} - 6 \, a^{12} b + 15 \, a^{11} b^{2} - 20 \, a^{10} b^{3} + 15 \, a^{9} b^{4} - 6 \, a^{8} b^{5} + a^{7} b^{6}\right)} d^{4}}} - 16 \, a^{2} + 15 \, a b - 3 \, b^{2}}{{\left(a^{6} - 3 \, a^{5} b + 3 \, a^{4} b^{2} - a^{3} b^{3}\right)} d^{2}}} \log\left(384 \, a^{3} b - 680 \, a^{2} b^{2} + 405 \, a b^{3} - 81 \, b^{4} + 2 \, {\left(16 \, a^{8} - 57 \, a^{7} b + 75 \, a^{6} b^{2} - 43 \, a^{5} b^{3} + 9 \, a^{4} b^{4}\right)} d^{2} \sqrt{\frac{576 \, a^{4} b - 1392 \, a^{3} b^{2} + 1273 \, a^{2} b^{3} - 522 \, a b^{4} + 81 \, b^{5}}{{\left(a^{13} - 6 \, a^{12} b + 15 \, a^{11} b^{2} - 20 \, a^{10} b^{3} + 15 \, a^{9} b^{4} - 6 \, a^{8} b^{5} + a^{7} b^{6}\right)} d^{4}}} - {\left(384 \, a^{3} b - 680 \, a^{2} b^{2} + 405 \, a b^{3} - 81 \, b^{4}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(384 \, a^{3} b - 680 \, a^{2} b^{2} + 405 \, a b^{3} - 81 \, b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(384 \, a^{3} b - 680 \, a^{2} b^{2} + 405 \, a b^{3} - 81 \, b^{4}\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(2 \, {\left(2 \, a^{10} - 7 \, a^{9} b + 9 \, a^{8} b^{2} - 5 \, a^{7} b^{3} + a^{6} b^{4}\right)} d^{3} \sqrt{\frac{576 \, a^{4} b - 1392 \, a^{3} b^{2} + 1273 \, a^{2} b^{3} - 522 \, a b^{4} + 81 \, b^{5}}{{\left(a^{13} - 6 \, a^{12} b + 15 \, a^{11} b^{2} - 20 \, a^{10} b^{3} + 15 \, a^{9} b^{4} - 6 \, a^{8} b^{5} + a^{7} b^{6}\right)} d^{4}}} + {\left(120 \, a^{5} b - 217 \, a^{4} b^{2} + 132 \, a^{3} b^{3} - 27 \, a^{2} b^{4}\right)} d\right)} \sqrt{-\frac{{\left(a^{6} - 3 \, a^{5} b + 3 \, a^{4} b^{2} - a^{3} b^{3}\right)} d^{2} \sqrt{\frac{576 \, a^{4} b - 1392 \, a^{3} b^{2} + 1273 \, a^{2} b^{3} - 522 \, a b^{4} + 81 \, b^{5}}{{\left(a^{13} - 6 \, a^{12} b + 15 \, a^{11} b^{2} - 20 \, a^{10} b^{3} + 15 \, a^{9} b^{4} - 6 \, a^{8} b^{5} + a^{7} b^{6}\right)} d^{4}}} - 16 \, a^{2} + 15 \, a b - 3 \, b^{2}}{{\left(a^{6} - 3 \, a^{5} b + 3 \, a^{4} b^{2} - a^{3} b^{3}\right)} d^{2}}}\right) + {\left({\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{2} b - a b^{2}\right)} d \sinh\left(d x + c\right)^{8} - 4 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{2} b - a b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{6} - 2 \, {\left(8 \, a^{3} - 11 \, a^{2} b + 3 \, a b^{2}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{4} - 30 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(8 \, a^{3} - 11 \, a^{2} b + 3 \, a b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{4} - 4 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{5} - 10 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{3} - {\left(8 \, a^{3} - 11 \, a^{2} b + 3 \, a b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{6} - 15 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{4} - 3 \, {\left(8 \, a^{3} - 11 \, a^{2} b + 3 \, a b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{2} b - a b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{2} b - a b^{2}\right)} d + 8 \, {\left({\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{7} - 3 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{5} - {\left(8 \, a^{3} - 11 \, a^{2} b + 3 \, a b^{2}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{{\left(a^{6} - 3 \, a^{5} b + 3 \, a^{4} b^{2} - a^{3} b^{3}\right)} d^{2} \sqrt{\frac{576 \, a^{4} b - 1392 \, a^{3} b^{2} + 1273 \, a^{2} b^{3} - 522 \, a b^{4} + 81 \, b^{5}}{{\left(a^{13} - 6 \, a^{12} b + 15 \, a^{11} b^{2} - 20 \, a^{10} b^{3} + 15 \, a^{9} b^{4} - 6 \, a^{8} b^{5} + a^{7} b^{6}\right)} d^{4}}} - 16 \, a^{2} + 15 \, a b - 3 \, b^{2}}{{\left(a^{6} - 3 \, a^{5} b + 3 \, a^{4} b^{2} - a^{3} b^{3}\right)} d^{2}}} \log\left(384 \, a^{3} b - 680 \, a^{2} b^{2} + 405 \, a b^{3} - 81 \, b^{4} + 2 \, {\left(16 \, a^{8} - 57 \, a^{7} b + 75 \, a^{6} b^{2} - 43 \, a^{5} b^{3} + 9 \, a^{4} b^{4}\right)} d^{2} \sqrt{\frac{576 \, a^{4} b - 1392 \, a^{3} b^{2} + 1273 \, a^{2} b^{3} - 522 \, a b^{4} + 81 \, b^{5}}{{\left(a^{13} - 6 \, a^{12} b + 15 \, a^{11} b^{2} - 20 \, a^{10} b^{3} + 15 \, a^{9} b^{4} - 6 \, a^{8} b^{5} + a^{7} b^{6}\right)} d^{4}}} - {\left(384 \, a^{3} b - 680 \, a^{2} b^{2} + 405 \, a b^{3} - 81 \, b^{4}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(384 \, a^{3} b - 680 \, a^{2} b^{2} + 405 \, a b^{3} - 81 \, b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(384 \, a^{3} b - 680 \, a^{2} b^{2} + 405 \, a b^{3} - 81 \, b^{4}\right)} \sinh\left(d x + c\right)^{2} - 2 \, {\left(2 \, {\left(2 \, a^{10} - 7 \, a^{9} b + 9 \, a^{8} b^{2} - 5 \, a^{7} b^{3} + a^{6} b^{4}\right)} d^{3} \sqrt{\frac{576 \, a^{4} b - 1392 \, a^{3} b^{2} + 1273 \, a^{2} b^{3} - 522 \, a b^{4} + 81 \, b^{5}}{{\left(a^{13} - 6 \, a^{12} b + 15 \, a^{11} b^{2} - 20 \, a^{10} b^{3} + 15 \, a^{9} b^{4} - 6 \, a^{8} b^{5} + a^{7} b^{6}\right)} d^{4}}} + {\left(120 \, a^{5} b - 217 \, a^{4} b^{2} + 132 \, a^{3} b^{3} - 27 \, a^{2} b^{4}\right)} d\right)} \sqrt{-\frac{{\left(a^{6} - 3 \, a^{5} b + 3 \, a^{4} b^{2} - a^{3} b^{3}\right)} d^{2} \sqrt{\frac{576 \, a^{4} b - 1392 \, a^{3} b^{2} + 1273 \, a^{2} b^{3} - 522 \, a b^{4} + 81 \, b^{5}}{{\left(a^{13} - 6 \, a^{12} b + 15 \, a^{11} b^{2} - 20 \, a^{10} b^{3} + 15 \, a^{9} b^{4} - 6 \, a^{8} b^{5} + a^{7} b^{6}\right)} d^{4}}} - 16 \, a^{2} + 15 \, a b - 3 \, b^{2}}{{\left(a^{6} - 3 \, a^{5} b + 3 \, a^{4} b^{2} - a^{3} b^{3}\right)} d^{2}}}\right) + {\left({\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{2} b - a b^{2}\right)} d \sinh\left(d x + c\right)^{8} - 4 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{2} b - a b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{6} - 2 \, {\left(8 \, a^{3} - 11 \, a^{2} b + 3 \, a b^{2}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{4} - 30 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(8 \, a^{3} - 11 \, a^{2} b + 3 \, a b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{4} - 4 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{5} - 10 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{3} - {\left(8 \, a^{3} - 11 \, a^{2} b + 3 \, a b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{6} - 15 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{4} - 3 \, {\left(8 \, a^{3} - 11 \, a^{2} b + 3 \, a b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{2} b - a b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{2} b - a b^{2}\right)} d + 8 \, {\left({\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{7} - 3 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{5} - {\left(8 \, a^{3} - 11 \, a^{2} b + 3 \, a b^{2}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{{\left(a^{6} - 3 \, a^{5} b + 3 \, a^{4} b^{2} - a^{3} b^{3}\right)} d^{2} \sqrt{\frac{576 \, a^{4} b - 1392 \, a^{3} b^{2} + 1273 \, a^{2} b^{3} - 522 \, a b^{4} + 81 \, b^{5}}{{\left(a^{13} - 6 \, a^{12} b + 15 \, a^{11} b^{2} - 20 \, a^{10} b^{3} + 15 \, a^{9} b^{4} - 6 \, a^{8} b^{5} + a^{7} b^{6}\right)} d^{4}}} + 16 \, a^{2} - 15 \, a b + 3 \, b^{2}}{{\left(a^{6} - 3 \, a^{5} b + 3 \, a^{4} b^{2} - a^{3} b^{3}\right)} d^{2}}} \log\left(384 \, a^{3} b - 680 \, a^{2} b^{2} + 405 \, a b^{3} - 81 \, b^{4} - 2 \, {\left(16 \, a^{8} - 57 \, a^{7} b + 75 \, a^{6} b^{2} - 43 \, a^{5} b^{3} + 9 \, a^{4} b^{4}\right)} d^{2} \sqrt{\frac{576 \, a^{4} b - 1392 \, a^{3} b^{2} + 1273 \, a^{2} b^{3} - 522 \, a b^{4} + 81 \, b^{5}}{{\left(a^{13} - 6 \, a^{12} b + 15 \, a^{11} b^{2} - 20 \, a^{10} b^{3} + 15 \, a^{9} b^{4} - 6 \, a^{8} b^{5} + a^{7} b^{6}\right)} d^{4}}} - {\left(384 \, a^{3} b - 680 \, a^{2} b^{2} + 405 \, a b^{3} - 81 \, b^{4}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(384 \, a^{3} b - 680 \, a^{2} b^{2} + 405 \, a b^{3} - 81 \, b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(384 \, a^{3} b - 680 \, a^{2} b^{2} + 405 \, a b^{3} - 81 \, b^{4}\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(2 \, {\left(2 \, a^{10} - 7 \, a^{9} b + 9 \, a^{8} b^{2} - 5 \, a^{7} b^{3} + a^{6} b^{4}\right)} d^{3} \sqrt{\frac{576 \, a^{4} b - 1392 \, a^{3} b^{2} + 1273 \, a^{2} b^{3} - 522 \, a b^{4} + 81 \, b^{5}}{{\left(a^{13} - 6 \, a^{12} b + 15 \, a^{11} b^{2} - 20 \, a^{10} b^{3} + 15 \, a^{9} b^{4} - 6 \, a^{8} b^{5} + a^{7} b^{6}\right)} d^{4}}} - {\left(120 \, a^{5} b - 217 \, a^{4} b^{2} + 132 \, a^{3} b^{3} - 27 \, a^{2} b^{4}\right)} d\right)} \sqrt{\frac{{\left(a^{6} - 3 \, a^{5} b + 3 \, a^{4} b^{2} - a^{3} b^{3}\right)} d^{2} \sqrt{\frac{576 \, a^{4} b - 1392 \, a^{3} b^{2} + 1273 \, a^{2} b^{3} - 522 \, a b^{4} + 81 \, b^{5}}{{\left(a^{13} - 6 \, a^{12} b + 15 \, a^{11} b^{2} - 20 \, a^{10} b^{3} + 15 \, a^{9} b^{4} - 6 \, a^{8} b^{5} + a^{7} b^{6}\right)} d^{4}}} + 16 \, a^{2} - 15 \, a b + 3 \, b^{2}}{{\left(a^{6} - 3 \, a^{5} b + 3 \, a^{4} b^{2} - a^{3} b^{3}\right)} d^{2}}}\right) - {\left({\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{2} b - a b^{2}\right)} d \sinh\left(d x + c\right)^{8} - 4 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{2} b - a b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{6} - 2 \, {\left(8 \, a^{3} - 11 \, a^{2} b + 3 \, a b^{2}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{4} - 30 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(8 \, a^{3} - 11 \, a^{2} b + 3 \, a b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{4} - 4 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{5} - 10 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{3} - {\left(8 \, a^{3} - 11 \, a^{2} b + 3 \, a b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{6} - 15 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{4} - 3 \, {\left(8 \, a^{3} - 11 \, a^{2} b + 3 \, a b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{2} b - a b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{2} b - a b^{2}\right)} d + 8 \, {\left({\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{7} - 3 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{5} - {\left(8 \, a^{3} - 11 \, a^{2} b + 3 \, a b^{2}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{{\left(a^{6} - 3 \, a^{5} b + 3 \, a^{4} b^{2} - a^{3} b^{3}\right)} d^{2} \sqrt{\frac{576 \, a^{4} b - 1392 \, a^{3} b^{2} + 1273 \, a^{2} b^{3} - 522 \, a b^{4} + 81 \, b^{5}}{{\left(a^{13} - 6 \, a^{12} b + 15 \, a^{11} b^{2} - 20 \, a^{10} b^{3} + 15 \, a^{9} b^{4} - 6 \, a^{8} b^{5} + a^{7} b^{6}\right)} d^{4}}} + 16 \, a^{2} - 15 \, a b + 3 \, b^{2}}{{\left(a^{6} - 3 \, a^{5} b + 3 \, a^{4} b^{2} - a^{3} b^{3}\right)} d^{2}}} \log\left(384 \, a^{3} b - 680 \, a^{2} b^{2} + 405 \, a b^{3} - 81 \, b^{4} - 2 \, {\left(16 \, a^{8} - 57 \, a^{7} b + 75 \, a^{6} b^{2} - 43 \, a^{5} b^{3} + 9 \, a^{4} b^{4}\right)} d^{2} \sqrt{\frac{576 \, a^{4} b - 1392 \, a^{3} b^{2} + 1273 \, a^{2} b^{3} - 522 \, a b^{4} + 81 \, b^{5}}{{\left(a^{13} - 6 \, a^{12} b + 15 \, a^{11} b^{2} - 20 \, a^{10} b^{3} + 15 \, a^{9} b^{4} - 6 \, a^{8} b^{5} + a^{7} b^{6}\right)} d^{4}}} - {\left(384 \, a^{3} b - 680 \, a^{2} b^{2} + 405 \, a b^{3} - 81 \, b^{4}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(384 \, a^{3} b - 680 \, a^{2} b^{2} + 405 \, a b^{3} - 81 \, b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(384 \, a^{3} b - 680 \, a^{2} b^{2} + 405 \, a b^{3} - 81 \, b^{4}\right)} \sinh\left(d x + c\right)^{2} - 2 \, {\left(2 \, {\left(2 \, a^{10} - 7 \, a^{9} b + 9 \, a^{8} b^{2} - 5 \, a^{7} b^{3} + a^{6} b^{4}\right)} d^{3} \sqrt{\frac{576 \, a^{4} b - 1392 \, a^{3} b^{2} + 1273 \, a^{2} b^{3} - 522 \, a b^{4} + 81 \, b^{5}}{{\left(a^{13} - 6 \, a^{12} b + 15 \, a^{11} b^{2} - 20 \, a^{10} b^{3} + 15 \, a^{9} b^{4} - 6 \, a^{8} b^{5} + a^{7} b^{6}\right)} d^{4}}} - {\left(120 \, a^{5} b - 217 \, a^{4} b^{2} + 132 \, a^{3} b^{3} - 27 \, a^{2} b^{4}\right)} d\right)} \sqrt{\frac{{\left(a^{6} - 3 \, a^{5} b + 3 \, a^{4} b^{2} - a^{3} b^{3}\right)} d^{2} \sqrt{\frac{576 \, a^{4} b - 1392 \, a^{3} b^{2} + 1273 \, a^{2} b^{3} - 522 \, a b^{4} + 81 \, b^{5}}{{\left(a^{13} - 6 \, a^{12} b + 15 \, a^{11} b^{2} - 20 \, a^{10} b^{3} + 15 \, a^{9} b^{4} - 6 \, a^{8} b^{5} + a^{7} b^{6}\right)} d^{4}}} + 16 \, a^{2} - 15 \, a b + 3 \, b^{2}}{{\left(a^{6} - 3 \, a^{5} b + 3 \, a^{4} b^{2} - a^{3} b^{3}\right)} d^{2}}}\right) + 16 \, {\left(3 \, b \cosh\left(d x + c\right)^{5} - 2 \, {\left(8 \, a - 3 \, b\right)} \cosh\left(d x + c\right)^{3} - 5 \, b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + 8 \, b}{16 \, {\left({\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{2} b - a b^{2}\right)} d \sinh\left(d x + c\right)^{8} - 4 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{2} b - a b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{6} - 2 \, {\left(8 \, a^{3} - 11 \, a^{2} b + 3 \, a b^{2}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{4} - 30 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(8 \, a^{3} - 11 \, a^{2} b + 3 \, a b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{4} - 4 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{5} - 10 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{3} - {\left(8 \, a^{3} - 11 \, a^{2} b + 3 \, a b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{6} - 15 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{4} - 3 \, {\left(8 \, a^{3} - 11 \, a^{2} b + 3 \, a b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{2} b - a b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{2} b - a b^{2}\right)} d + 8 \, {\left({\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{7} - 3 \, {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)^{5} - {\left(8 \, a^{3} - 11 \, a^{2} b + 3 \, a b^{2}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a^{2} b - a b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"1/16*(8*b*cosh(d*x + c)^6 + 48*b*cosh(d*x + c)*sinh(d*x + c)^5 + 8*b*sinh(d*x + c)^6 - 8*(8*a - 3*b)*cosh(d*x + c)^4 + 8*(15*b*cosh(d*x + c)^2 - 8*a + 3*b)*sinh(d*x + c)^4 + 32*(5*b*cosh(d*x + c)^3 - (8*a - 3*b)*cosh(d*x + c))*sinh(d*x + c)^3 - 40*b*cosh(d*x + c)^2 + 8*(15*b*cosh(d*x + c)^4 - 6*(8*a - 3*b)*cosh(d*x + c)^2 - 5*b)*sinh(d*x + c)^2 - ((a^2*b - a*b^2)*d*cosh(d*x + c)^8 + 8*(a^2*b - a*b^2)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^2*b - a*b^2)*d*sinh(d*x + c)^8 - 4*(a^2*b - a*b^2)*d*cosh(d*x + c)^6 + 4*(7*(a^2*b - a*b^2)*d*cosh(d*x + c)^2 - (a^2*b - a*b^2)*d)*sinh(d*x + c)^6 - 2*(8*a^3 - 11*a^2*b + 3*a*b^2)*d*cosh(d*x + c)^4 + 8*(7*(a^2*b - a*b^2)*d*cosh(d*x + c)^3 - 3*(a^2*b - a*b^2)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^2*b - a*b^2)*d*cosh(d*x + c)^4 - 30*(a^2*b - a*b^2)*d*cosh(d*x + c)^2 - (8*a^3 - 11*a^2*b + 3*a*b^2)*d)*sinh(d*x + c)^4 - 4*(a^2*b - a*b^2)*d*cosh(d*x + c)^2 + 8*(7*(a^2*b - a*b^2)*d*cosh(d*x + c)^5 - 10*(a^2*b - a*b^2)*d*cosh(d*x + c)^3 - (8*a^3 - 11*a^2*b + 3*a*b^2)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^2*b - a*b^2)*d*cosh(d*x + c)^6 - 15*(a^2*b - a*b^2)*d*cosh(d*x + c)^4 - 3*(8*a^3 - 11*a^2*b + 3*a*b^2)*d*cosh(d*x + c)^2 - (a^2*b - a*b^2)*d)*sinh(d*x + c)^2 + (a^2*b - a*b^2)*d + 8*((a^2*b - a*b^2)*d*cosh(d*x + c)^7 - 3*(a^2*b - a*b^2)*d*cosh(d*x + c)^5 - (8*a^3 - 11*a^2*b + 3*a*b^2)*d*cosh(d*x + c)^3 - (a^2*b - a*b^2)*d*cosh(d*x + c))*sinh(d*x + c))*sqrt(-((a^6 - 3*a^5*b + 3*a^4*b^2 - a^3*b^3)*d^2*sqrt((576*a^4*b - 1392*a^3*b^2 + 1273*a^2*b^3 - 522*a*b^4 + 81*b^5)/((a^13 - 6*a^12*b + 15*a^11*b^2 - 20*a^10*b^3 + 15*a^9*b^4 - 6*a^8*b^5 + a^7*b^6)*d^4)) - 16*a^2 + 15*a*b - 3*b^2)/((a^6 - 3*a^5*b + 3*a^4*b^2 - a^3*b^3)*d^2))*log(384*a^3*b - 680*a^2*b^2 + 405*a*b^3 - 81*b^4 + 2*(16*a^8 - 57*a^7*b + 75*a^6*b^2 - 43*a^5*b^3 + 9*a^4*b^4)*d^2*sqrt((576*a^4*b - 1392*a^3*b^2 + 1273*a^2*b^3 - 522*a*b^4 + 81*b^5)/((a^13 - 6*a^12*b + 15*a^11*b^2 - 20*a^10*b^3 + 15*a^9*b^4 - 6*a^8*b^5 + a^7*b^6)*d^4)) - (384*a^3*b - 680*a^2*b^2 + 405*a*b^3 - 81*b^4)*cosh(d*x + c)^2 - 2*(384*a^3*b - 680*a^2*b^2 + 405*a*b^3 - 81*b^4)*cosh(d*x + c)*sinh(d*x + c) - (384*a^3*b - 680*a^2*b^2 + 405*a*b^3 - 81*b^4)*sinh(d*x + c)^2 + 2*(2*(2*a^10 - 7*a^9*b + 9*a^8*b^2 - 5*a^7*b^3 + a^6*b^4)*d^3*sqrt((576*a^4*b - 1392*a^3*b^2 + 1273*a^2*b^3 - 522*a*b^4 + 81*b^5)/((a^13 - 6*a^12*b + 15*a^11*b^2 - 20*a^10*b^3 + 15*a^9*b^4 - 6*a^8*b^5 + a^7*b^6)*d^4)) + (120*a^5*b - 217*a^4*b^2 + 132*a^3*b^3 - 27*a^2*b^4)*d)*sqrt(-((a^6 - 3*a^5*b + 3*a^4*b^2 - a^3*b^3)*d^2*sqrt((576*a^4*b - 1392*a^3*b^2 + 1273*a^2*b^3 - 522*a*b^4 + 81*b^5)/((a^13 - 6*a^12*b + 15*a^11*b^2 - 20*a^10*b^3 + 15*a^9*b^4 - 6*a^8*b^5 + a^7*b^6)*d^4)) - 16*a^2 + 15*a*b - 3*b^2)/((a^6 - 3*a^5*b + 3*a^4*b^2 - a^3*b^3)*d^2))) + ((a^2*b - a*b^2)*d*cosh(d*x + c)^8 + 8*(a^2*b - a*b^2)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^2*b - a*b^2)*d*sinh(d*x + c)^8 - 4*(a^2*b - a*b^2)*d*cosh(d*x + c)^6 + 4*(7*(a^2*b - a*b^2)*d*cosh(d*x + c)^2 - (a^2*b - a*b^2)*d)*sinh(d*x + c)^6 - 2*(8*a^3 - 11*a^2*b + 3*a*b^2)*d*cosh(d*x + c)^4 + 8*(7*(a^2*b - a*b^2)*d*cosh(d*x + c)^3 - 3*(a^2*b - a*b^2)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^2*b - a*b^2)*d*cosh(d*x + c)^4 - 30*(a^2*b - a*b^2)*d*cosh(d*x + c)^2 - (8*a^3 - 11*a^2*b + 3*a*b^2)*d)*sinh(d*x + c)^4 - 4*(a^2*b - a*b^2)*d*cosh(d*x + c)^2 + 8*(7*(a^2*b - a*b^2)*d*cosh(d*x + c)^5 - 10*(a^2*b - a*b^2)*d*cosh(d*x + c)^3 - (8*a^3 - 11*a^2*b + 3*a*b^2)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^2*b - a*b^2)*d*cosh(d*x + c)^6 - 15*(a^2*b - a*b^2)*d*cosh(d*x + c)^4 - 3*(8*a^3 - 11*a^2*b + 3*a*b^2)*d*cosh(d*x + c)^2 - (a^2*b - a*b^2)*d)*sinh(d*x + c)^2 + (a^2*b - a*b^2)*d + 8*((a^2*b - a*b^2)*d*cosh(d*x + c)^7 - 3*(a^2*b - a*b^2)*d*cosh(d*x + c)^5 - (8*a^3 - 11*a^2*b + 3*a*b^2)*d*cosh(d*x + c)^3 - (a^2*b - a*b^2)*d*cosh(d*x + c))*sinh(d*x + c))*sqrt(-((a^6 - 3*a^5*b + 3*a^4*b^2 - a^3*b^3)*d^2*sqrt((576*a^4*b - 1392*a^3*b^2 + 1273*a^2*b^3 - 522*a*b^4 + 81*b^5)/((a^13 - 6*a^12*b + 15*a^11*b^2 - 20*a^10*b^3 + 15*a^9*b^4 - 6*a^8*b^5 + a^7*b^6)*d^4)) - 16*a^2 + 15*a*b - 3*b^2)/((a^6 - 3*a^5*b + 3*a^4*b^2 - a^3*b^3)*d^2))*log(384*a^3*b - 680*a^2*b^2 + 405*a*b^3 - 81*b^4 + 2*(16*a^8 - 57*a^7*b + 75*a^6*b^2 - 43*a^5*b^3 + 9*a^4*b^4)*d^2*sqrt((576*a^4*b - 1392*a^3*b^2 + 1273*a^2*b^3 - 522*a*b^4 + 81*b^5)/((a^13 - 6*a^12*b + 15*a^11*b^2 - 20*a^10*b^3 + 15*a^9*b^4 - 6*a^8*b^5 + a^7*b^6)*d^4)) - (384*a^3*b - 680*a^2*b^2 + 405*a*b^3 - 81*b^4)*cosh(d*x + c)^2 - 2*(384*a^3*b - 680*a^2*b^2 + 405*a*b^3 - 81*b^4)*cosh(d*x + c)*sinh(d*x + c) - (384*a^3*b - 680*a^2*b^2 + 405*a*b^3 - 81*b^4)*sinh(d*x + c)^2 - 2*(2*(2*a^10 - 7*a^9*b + 9*a^8*b^2 - 5*a^7*b^3 + a^6*b^4)*d^3*sqrt((576*a^4*b - 1392*a^3*b^2 + 1273*a^2*b^3 - 522*a*b^4 + 81*b^5)/((a^13 - 6*a^12*b + 15*a^11*b^2 - 20*a^10*b^3 + 15*a^9*b^4 - 6*a^8*b^5 + a^7*b^6)*d^4)) + (120*a^5*b - 217*a^4*b^2 + 132*a^3*b^3 - 27*a^2*b^4)*d)*sqrt(-((a^6 - 3*a^5*b + 3*a^4*b^2 - a^3*b^3)*d^2*sqrt((576*a^4*b - 1392*a^3*b^2 + 1273*a^2*b^3 - 522*a*b^4 + 81*b^5)/((a^13 - 6*a^12*b + 15*a^11*b^2 - 20*a^10*b^3 + 15*a^9*b^4 - 6*a^8*b^5 + a^7*b^6)*d^4)) - 16*a^2 + 15*a*b - 3*b^2)/((a^6 - 3*a^5*b + 3*a^4*b^2 - a^3*b^3)*d^2))) + ((a^2*b - a*b^2)*d*cosh(d*x + c)^8 + 8*(a^2*b - a*b^2)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^2*b - a*b^2)*d*sinh(d*x + c)^8 - 4*(a^2*b - a*b^2)*d*cosh(d*x + c)^6 + 4*(7*(a^2*b - a*b^2)*d*cosh(d*x + c)^2 - (a^2*b - a*b^2)*d)*sinh(d*x + c)^6 - 2*(8*a^3 - 11*a^2*b + 3*a*b^2)*d*cosh(d*x + c)^4 + 8*(7*(a^2*b - a*b^2)*d*cosh(d*x + c)^3 - 3*(a^2*b - a*b^2)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^2*b - a*b^2)*d*cosh(d*x + c)^4 - 30*(a^2*b - a*b^2)*d*cosh(d*x + c)^2 - (8*a^3 - 11*a^2*b + 3*a*b^2)*d)*sinh(d*x + c)^4 - 4*(a^2*b - a*b^2)*d*cosh(d*x + c)^2 + 8*(7*(a^2*b - a*b^2)*d*cosh(d*x + c)^5 - 10*(a^2*b - a*b^2)*d*cosh(d*x + c)^3 - (8*a^3 - 11*a^2*b + 3*a*b^2)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^2*b - a*b^2)*d*cosh(d*x + c)^6 - 15*(a^2*b - a*b^2)*d*cosh(d*x + c)^4 - 3*(8*a^3 - 11*a^2*b + 3*a*b^2)*d*cosh(d*x + c)^2 - (a^2*b - a*b^2)*d)*sinh(d*x + c)^2 + (a^2*b - a*b^2)*d + 8*((a^2*b - a*b^2)*d*cosh(d*x + c)^7 - 3*(a^2*b - a*b^2)*d*cosh(d*x + c)^5 - (8*a^3 - 11*a^2*b + 3*a*b^2)*d*cosh(d*x + c)^3 - (a^2*b - a*b^2)*d*cosh(d*x + c))*sinh(d*x + c))*sqrt(((a^6 - 3*a^5*b + 3*a^4*b^2 - a^3*b^3)*d^2*sqrt((576*a^4*b - 1392*a^3*b^2 + 1273*a^2*b^3 - 522*a*b^4 + 81*b^5)/((a^13 - 6*a^12*b + 15*a^11*b^2 - 20*a^10*b^3 + 15*a^9*b^4 - 6*a^8*b^5 + a^7*b^6)*d^4)) + 16*a^2 - 15*a*b + 3*b^2)/((a^6 - 3*a^5*b + 3*a^4*b^2 - a^3*b^3)*d^2))*log(384*a^3*b - 680*a^2*b^2 + 405*a*b^3 - 81*b^4 - 2*(16*a^8 - 57*a^7*b + 75*a^6*b^2 - 43*a^5*b^3 + 9*a^4*b^4)*d^2*sqrt((576*a^4*b - 1392*a^3*b^2 + 1273*a^2*b^3 - 522*a*b^4 + 81*b^5)/((a^13 - 6*a^12*b + 15*a^11*b^2 - 20*a^10*b^3 + 15*a^9*b^4 - 6*a^8*b^5 + a^7*b^6)*d^4)) - (384*a^3*b - 680*a^2*b^2 + 405*a*b^3 - 81*b^4)*cosh(d*x + c)^2 - 2*(384*a^3*b - 680*a^2*b^2 + 405*a*b^3 - 81*b^4)*cosh(d*x + c)*sinh(d*x + c) - (384*a^3*b - 680*a^2*b^2 + 405*a*b^3 - 81*b^4)*sinh(d*x + c)^2 + 2*(2*(2*a^10 - 7*a^9*b + 9*a^8*b^2 - 5*a^7*b^3 + a^6*b^4)*d^3*sqrt((576*a^4*b - 1392*a^3*b^2 + 1273*a^2*b^3 - 522*a*b^4 + 81*b^5)/((a^13 - 6*a^12*b + 15*a^11*b^2 - 20*a^10*b^3 + 15*a^9*b^4 - 6*a^8*b^5 + a^7*b^6)*d^4)) - (120*a^5*b - 217*a^4*b^2 + 132*a^3*b^3 - 27*a^2*b^4)*d)*sqrt(((a^6 - 3*a^5*b + 3*a^4*b^2 - a^3*b^3)*d^2*sqrt((576*a^4*b - 1392*a^3*b^2 + 1273*a^2*b^3 - 522*a*b^4 + 81*b^5)/((a^13 - 6*a^12*b + 15*a^11*b^2 - 20*a^10*b^3 + 15*a^9*b^4 - 6*a^8*b^5 + a^7*b^6)*d^4)) + 16*a^2 - 15*a*b + 3*b^2)/((a^6 - 3*a^5*b + 3*a^4*b^2 - a^3*b^3)*d^2))) - ((a^2*b - a*b^2)*d*cosh(d*x + c)^8 + 8*(a^2*b - a*b^2)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^2*b - a*b^2)*d*sinh(d*x + c)^8 - 4*(a^2*b - a*b^2)*d*cosh(d*x + c)^6 + 4*(7*(a^2*b - a*b^2)*d*cosh(d*x + c)^2 - (a^2*b - a*b^2)*d)*sinh(d*x + c)^6 - 2*(8*a^3 - 11*a^2*b + 3*a*b^2)*d*cosh(d*x + c)^4 + 8*(7*(a^2*b - a*b^2)*d*cosh(d*x + c)^3 - 3*(a^2*b - a*b^2)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^2*b - a*b^2)*d*cosh(d*x + c)^4 - 30*(a^2*b - a*b^2)*d*cosh(d*x + c)^2 - (8*a^3 - 11*a^2*b + 3*a*b^2)*d)*sinh(d*x + c)^4 - 4*(a^2*b - a*b^2)*d*cosh(d*x + c)^2 + 8*(7*(a^2*b - a*b^2)*d*cosh(d*x + c)^5 - 10*(a^2*b - a*b^2)*d*cosh(d*x + c)^3 - (8*a^3 - 11*a^2*b + 3*a*b^2)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^2*b - a*b^2)*d*cosh(d*x + c)^6 - 15*(a^2*b - a*b^2)*d*cosh(d*x + c)^4 - 3*(8*a^3 - 11*a^2*b + 3*a*b^2)*d*cosh(d*x + c)^2 - (a^2*b - a*b^2)*d)*sinh(d*x + c)^2 + (a^2*b - a*b^2)*d + 8*((a^2*b - a*b^2)*d*cosh(d*x + c)^7 - 3*(a^2*b - a*b^2)*d*cosh(d*x + c)^5 - (8*a^3 - 11*a^2*b + 3*a*b^2)*d*cosh(d*x + c)^3 - (a^2*b - a*b^2)*d*cosh(d*x + c))*sinh(d*x + c))*sqrt(((a^6 - 3*a^5*b + 3*a^4*b^2 - a^3*b^3)*d^2*sqrt((576*a^4*b - 1392*a^3*b^2 + 1273*a^2*b^3 - 522*a*b^4 + 81*b^5)/((a^13 - 6*a^12*b + 15*a^11*b^2 - 20*a^10*b^3 + 15*a^9*b^4 - 6*a^8*b^5 + a^7*b^6)*d^4)) + 16*a^2 - 15*a*b + 3*b^2)/((a^6 - 3*a^5*b + 3*a^4*b^2 - a^3*b^3)*d^2))*log(384*a^3*b - 680*a^2*b^2 + 405*a*b^3 - 81*b^4 - 2*(16*a^8 - 57*a^7*b + 75*a^6*b^2 - 43*a^5*b^3 + 9*a^4*b^4)*d^2*sqrt((576*a^4*b - 1392*a^3*b^2 + 1273*a^2*b^3 - 522*a*b^4 + 81*b^5)/((a^13 - 6*a^12*b + 15*a^11*b^2 - 20*a^10*b^3 + 15*a^9*b^4 - 6*a^8*b^5 + a^7*b^6)*d^4)) - (384*a^3*b - 680*a^2*b^2 + 405*a*b^3 - 81*b^4)*cosh(d*x + c)^2 - 2*(384*a^3*b - 680*a^2*b^2 + 405*a*b^3 - 81*b^4)*cosh(d*x + c)*sinh(d*x + c) - (384*a^3*b - 680*a^2*b^2 + 405*a*b^3 - 81*b^4)*sinh(d*x + c)^2 - 2*(2*(2*a^10 - 7*a^9*b + 9*a^8*b^2 - 5*a^7*b^3 + a^6*b^4)*d^3*sqrt((576*a^4*b - 1392*a^3*b^2 + 1273*a^2*b^3 - 522*a*b^4 + 81*b^5)/((a^13 - 6*a^12*b + 15*a^11*b^2 - 20*a^10*b^3 + 15*a^9*b^4 - 6*a^8*b^5 + a^7*b^6)*d^4)) - (120*a^5*b - 217*a^4*b^2 + 132*a^3*b^3 - 27*a^2*b^4)*d)*sqrt(((a^6 - 3*a^5*b + 3*a^4*b^2 - a^3*b^3)*d^2*sqrt((576*a^4*b - 1392*a^3*b^2 + 1273*a^2*b^3 - 522*a*b^4 + 81*b^5)/((a^13 - 6*a^12*b + 15*a^11*b^2 - 20*a^10*b^3 + 15*a^9*b^4 - 6*a^8*b^5 + a^7*b^6)*d^4)) + 16*a^2 - 15*a*b + 3*b^2)/((a^6 - 3*a^5*b + 3*a^4*b^2 - a^3*b^3)*d^2))) + 16*(3*b*cosh(d*x + c)^5 - 2*(8*a - 3*b)*cosh(d*x + c)^3 - 5*b*cosh(d*x + c))*sinh(d*x + c) + 8*b)/((a^2*b - a*b^2)*d*cosh(d*x + c)^8 + 8*(a^2*b - a*b^2)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^2*b - a*b^2)*d*sinh(d*x + c)^8 - 4*(a^2*b - a*b^2)*d*cosh(d*x + c)^6 + 4*(7*(a^2*b - a*b^2)*d*cosh(d*x + c)^2 - (a^2*b - a*b^2)*d)*sinh(d*x + c)^6 - 2*(8*a^3 - 11*a^2*b + 3*a*b^2)*d*cosh(d*x + c)^4 + 8*(7*(a^2*b - a*b^2)*d*cosh(d*x + c)^3 - 3*(a^2*b - a*b^2)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^2*b - a*b^2)*d*cosh(d*x + c)^4 - 30*(a^2*b - a*b^2)*d*cosh(d*x + c)^2 - (8*a^3 - 11*a^2*b + 3*a*b^2)*d)*sinh(d*x + c)^4 - 4*(a^2*b - a*b^2)*d*cosh(d*x + c)^2 + 8*(7*(a^2*b - a*b^2)*d*cosh(d*x + c)^5 - 10*(a^2*b - a*b^2)*d*cosh(d*x + c)^3 - (8*a^3 - 11*a^2*b + 3*a*b^2)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^2*b - a*b^2)*d*cosh(d*x + c)^6 - 15*(a^2*b - a*b^2)*d*cosh(d*x + c)^4 - 3*(8*a^3 - 11*a^2*b + 3*a*b^2)*d*cosh(d*x + c)^2 - (a^2*b - a*b^2)*d)*sinh(d*x + c)^2 + (a^2*b - a*b^2)*d + 8*((a^2*b - a*b^2)*d*cosh(d*x + c)^7 - 3*(a^2*b - a*b^2)*d*cosh(d*x + c)^5 - (8*a^3 - 11*a^2*b + 3*a*b^2)*d*cosh(d*x + c)^3 - (a^2*b - a*b^2)*d*cosh(d*x + c))*sinh(d*x + c))","B",0
252,1,8824,0,1.077407," ","integrate(csch(d*x+c)^2/(a-b*sinh(d*x+c)^4)^2,x, algorithm=""fricas"")","-\frac{8 \, {\left(6 \, a b - 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{8} + 64 \, {\left(6 \, a b - 5 \, b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + 8 \, {\left(6 \, a b - 5 \, b^{2}\right)} \sinh\left(d x + c\right)^{8} - 16 \, {\left(13 \, a b - 10 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 16 \, {\left(14 \, {\left(6 \, a b - 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 13 \, a b + 10 \, b^{2}\right)} \sinh\left(d x + c\right)^{6} + 32 \, {\left(14 \, {\left(6 \, a b - 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(13 \, a b - 10 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 16 \, {\left(32 \, a^{2} - 47 \, a b + 15 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 16 \, {\left(35 \, {\left(6 \, a b - 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} - 15 \, {\left(13 \, a b - 10 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 32 \, a^{2} + 47 \, a b - 15 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 64 \, {\left(7 \, {\left(6 \, a b - 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} - 5 \, {\left(13 \, a b - 10 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(32 \, a^{2} - 47 \, a b + 15 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 16 \, {\left(7 \, a b - 10 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 16 \, {\left(14 \, {\left(6 \, a b - 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} - 15 \, {\left(13 \, a b - 10 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} - 6 \, {\left(32 \, a^{2} - 47 \, a b + 15 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 7 \, a b + 10 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{10} + 10 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + {\left(a^{3} b - a^{2} b^{2}\right)} d \sinh\left(d x + c\right)^{10} - 5 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{8} + 5 \, {\left(9 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{3} b - a^{2} b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{8} - 2 \, {\left(8 \, a^{4} - 13 \, a^{3} b + 5 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{6} + 40 \, {\left(3 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(105 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{4} - 70 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(8 \, a^{4} - 13 \, a^{3} b + 5 \, a^{2} b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(8 \, a^{4} - 13 \, a^{3} b + 5 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(63 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{5} - 70 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{3} - 3 \, {\left(8 \, a^{4} - 13 \, a^{3} b + 5 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(105 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{6} - 175 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{4} - 15 \, {\left(8 \, a^{4} - 13 \, a^{3} b + 5 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{2} + {\left(8 \, a^{4} - 13 \, a^{3} b + 5 \, a^{2} b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 5 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(15 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{7} - 35 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{5} - 5 \, {\left(8 \, a^{4} - 13 \, a^{3} b + 5 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{4} - 13 \, a^{3} b + 5 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(45 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{8} - 140 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{6} - 30 \, {\left(8 \, a^{4} - 13 \, a^{3} b + 5 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{4} + 12 \, {\left(8 \, a^{4} - 13 \, a^{3} b + 5 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{2} + 5 \, {\left(a^{3} b - a^{2} b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{2} - {\left(a^{3} b - a^{2} b^{2}\right)} d + 2 \, {\left(5 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{9} - 20 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{7} - 6 \, {\left(8 \, a^{4} - 13 \, a^{3} b + 5 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{5} + 4 \, {\left(8 \, a^{4} - 13 \, a^{3} b + 5 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{3} + 5 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{{\left(a^{7} - 3 \, a^{6} b + 3 \, a^{5} b^{2} - a^{4} b^{3}\right)} d^{2} \sqrt{\frac{2304 \, a^{4} b^{3} - 6624 \, a^{3} b^{4} + 7161 \, a^{2} b^{5} - 3450 \, a b^{6} + 625 \, b^{7}}{{\left(a^{15} - 6 \, a^{14} b + 15 \, a^{13} b^{2} - 20 \, a^{12} b^{3} + 15 \, a^{11} b^{4} - 6 \, a^{10} b^{5} + a^{9} b^{6}\right)} d^{4}}} - 36 \, a^{2} b + 47 \, a b^{2} - 15 \, b^{3}}{{\left(a^{7} - 3 \, a^{6} b + 3 \, a^{5} b^{2} - a^{4} b^{3}\right)} d^{2}}} \log\left(1728 \, a^{3} b^{2} - 3684 \, a^{2} b^{3} + 2625 \, a b^{4} - 625 \, b^{5} + 2 \, {\left(36 \, a^{9} - 133 \, a^{8} b + 183 \, a^{7} b^{2} - 111 \, a^{6} b^{3} + 25 \, a^{5} b^{4}\right)} d^{2} \sqrt{\frac{2304 \, a^{4} b^{3} - 6624 \, a^{3} b^{4} + 7161 \, a^{2} b^{5} - 3450 \, a b^{6} + 625 \, b^{7}}{{\left(a^{15} - 6 \, a^{14} b + 15 \, a^{13} b^{2} - 20 \, a^{12} b^{3} + 15 \, a^{11} b^{4} - 6 \, a^{10} b^{5} + a^{9} b^{6}\right)} d^{4}}} - {\left(1728 \, a^{3} b^{2} - 3684 \, a^{2} b^{3} + 2625 \, a b^{4} - 625 \, b^{5}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(1728 \, a^{3} b^{2} - 3684 \, a^{2} b^{3} + 2625 \, a b^{4} - 625 \, b^{5}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(1728 \, a^{3} b^{2} - 3684 \, a^{2} b^{3} + 2625 \, a b^{4} - 625 \, b^{5}\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left({\left(7 \, a^{11} - 26 \, a^{10} b + 36 \, a^{9} b^{2} - 22 \, a^{8} b^{3} + 5 \, a^{7} b^{4}\right)} d^{3} \sqrt{\frac{2304 \, a^{4} b^{3} - 6624 \, a^{3} b^{4} + 7161 \, a^{2} b^{5} - 3450 \, a b^{6} + 625 \, b^{7}}{{\left(a^{15} - 6 \, a^{14} b + 15 \, a^{13} b^{2} - 20 \, a^{12} b^{3} + 15 \, a^{11} b^{4} - 6 \, a^{10} b^{5} + a^{9} b^{6}\right)} d^{4}}} + 2 \, {\left(144 \, a^{6} b - 303 \, a^{5} b^{2} + 213 \, a^{4} b^{3} - 50 \, a^{3} b^{4}\right)} d\right)} \sqrt{-\frac{{\left(a^{7} - 3 \, a^{6} b + 3 \, a^{5} b^{2} - a^{4} b^{3}\right)} d^{2} \sqrt{\frac{2304 \, a^{4} b^{3} - 6624 \, a^{3} b^{4} + 7161 \, a^{2} b^{5} - 3450 \, a b^{6} + 625 \, b^{7}}{{\left(a^{15} - 6 \, a^{14} b + 15 \, a^{13} b^{2} - 20 \, a^{12} b^{3} + 15 \, a^{11} b^{4} - 6 \, a^{10} b^{5} + a^{9} b^{6}\right)} d^{4}}} - 36 \, a^{2} b + 47 \, a b^{2} - 15 \, b^{3}}{{\left(a^{7} - 3 \, a^{6} b + 3 \, a^{5} b^{2} - a^{4} b^{3}\right)} d^{2}}}\right) - {\left({\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{10} + 10 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + {\left(a^{3} b - a^{2} b^{2}\right)} d \sinh\left(d x + c\right)^{10} - 5 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{8} + 5 \, {\left(9 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{3} b - a^{2} b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{8} - 2 \, {\left(8 \, a^{4} - 13 \, a^{3} b + 5 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{6} + 40 \, {\left(3 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(105 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{4} - 70 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(8 \, a^{4} - 13 \, a^{3} b + 5 \, a^{2} b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(8 \, a^{4} - 13 \, a^{3} b + 5 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(63 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{5} - 70 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{3} - 3 \, {\left(8 \, a^{4} - 13 \, a^{3} b + 5 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(105 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{6} - 175 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{4} - 15 \, {\left(8 \, a^{4} - 13 \, a^{3} b + 5 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{2} + {\left(8 \, a^{4} - 13 \, a^{3} b + 5 \, a^{2} b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 5 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(15 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{7} - 35 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{5} - 5 \, {\left(8 \, a^{4} - 13 \, a^{3} b + 5 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{4} - 13 \, a^{3} b + 5 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(45 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{8} - 140 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{6} - 30 \, {\left(8 \, a^{4} - 13 \, a^{3} b + 5 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{4} + 12 \, {\left(8 \, a^{4} - 13 \, a^{3} b + 5 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{2} + 5 \, {\left(a^{3} b - a^{2} b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{2} - {\left(a^{3} b - a^{2} b^{2}\right)} d + 2 \, {\left(5 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{9} - 20 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{7} - 6 \, {\left(8 \, a^{4} - 13 \, a^{3} b + 5 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{5} + 4 \, {\left(8 \, a^{4} - 13 \, a^{3} b + 5 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{3} + 5 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{{\left(a^{7} - 3 \, a^{6} b + 3 \, a^{5} b^{2} - a^{4} b^{3}\right)} d^{2} \sqrt{\frac{2304 \, a^{4} b^{3} - 6624 \, a^{3} b^{4} + 7161 \, a^{2} b^{5} - 3450 \, a b^{6} + 625 \, b^{7}}{{\left(a^{15} - 6 \, a^{14} b + 15 \, a^{13} b^{2} - 20 \, a^{12} b^{3} + 15 \, a^{11} b^{4} - 6 \, a^{10} b^{5} + a^{9} b^{6}\right)} d^{4}}} - 36 \, a^{2} b + 47 \, a b^{2} - 15 \, b^{3}}{{\left(a^{7} - 3 \, a^{6} b + 3 \, a^{5} b^{2} - a^{4} b^{3}\right)} d^{2}}} \log\left(1728 \, a^{3} b^{2} - 3684 \, a^{2} b^{3} + 2625 \, a b^{4} - 625 \, b^{5} + 2 \, {\left(36 \, a^{9} - 133 \, a^{8} b + 183 \, a^{7} b^{2} - 111 \, a^{6} b^{3} + 25 \, a^{5} b^{4}\right)} d^{2} \sqrt{\frac{2304 \, a^{4} b^{3} - 6624 \, a^{3} b^{4} + 7161 \, a^{2} b^{5} - 3450 \, a b^{6} + 625 \, b^{7}}{{\left(a^{15} - 6 \, a^{14} b + 15 \, a^{13} b^{2} - 20 \, a^{12} b^{3} + 15 \, a^{11} b^{4} - 6 \, a^{10} b^{5} + a^{9} b^{6}\right)} d^{4}}} - {\left(1728 \, a^{3} b^{2} - 3684 \, a^{2} b^{3} + 2625 \, a b^{4} - 625 \, b^{5}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(1728 \, a^{3} b^{2} - 3684 \, a^{2} b^{3} + 2625 \, a b^{4} - 625 \, b^{5}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(1728 \, a^{3} b^{2} - 3684 \, a^{2} b^{3} + 2625 \, a b^{4} - 625 \, b^{5}\right)} \sinh\left(d x + c\right)^{2} - 2 \, {\left({\left(7 \, a^{11} - 26 \, a^{10} b + 36 \, a^{9} b^{2} - 22 \, a^{8} b^{3} + 5 \, a^{7} b^{4}\right)} d^{3} \sqrt{\frac{2304 \, a^{4} b^{3} - 6624 \, a^{3} b^{4} + 7161 \, a^{2} b^{5} - 3450 \, a b^{6} + 625 \, b^{7}}{{\left(a^{15} - 6 \, a^{14} b + 15 \, a^{13} b^{2} - 20 \, a^{12} b^{3} + 15 \, a^{11} b^{4} - 6 \, a^{10} b^{5} + a^{9} b^{6}\right)} d^{4}}} + 2 \, {\left(144 \, a^{6} b - 303 \, a^{5} b^{2} + 213 \, a^{4} b^{3} - 50 \, a^{3} b^{4}\right)} d\right)} \sqrt{-\frac{{\left(a^{7} - 3 \, a^{6} b + 3 \, a^{5} b^{2} - a^{4} b^{3}\right)} d^{2} \sqrt{\frac{2304 \, a^{4} b^{3} - 6624 \, a^{3} b^{4} + 7161 \, a^{2} b^{5} - 3450 \, a b^{6} + 625 \, b^{7}}{{\left(a^{15} - 6 \, a^{14} b + 15 \, a^{13} b^{2} - 20 \, a^{12} b^{3} + 15 \, a^{11} b^{4} - 6 \, a^{10} b^{5} + a^{9} b^{6}\right)} d^{4}}} - 36 \, a^{2} b + 47 \, a b^{2} - 15 \, b^{3}}{{\left(a^{7} - 3 \, a^{6} b + 3 \, a^{5} b^{2} - a^{4} b^{3}\right)} d^{2}}}\right) - {\left({\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{10} + 10 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + {\left(a^{3} b - a^{2} b^{2}\right)} d \sinh\left(d x + c\right)^{10} - 5 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{8} + 5 \, {\left(9 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{3} b - a^{2} b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{8} - 2 \, {\left(8 \, a^{4} - 13 \, a^{3} b + 5 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{6} + 40 \, {\left(3 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(105 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{4} - 70 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(8 \, a^{4} - 13 \, a^{3} b + 5 \, a^{2} b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(8 \, a^{4} - 13 \, a^{3} b + 5 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(63 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{5} - 70 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{3} - 3 \, {\left(8 \, a^{4} - 13 \, a^{3} b + 5 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(105 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{6} - 175 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{4} - 15 \, {\left(8 \, a^{4} - 13 \, a^{3} b + 5 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{2} + {\left(8 \, a^{4} - 13 \, a^{3} b + 5 \, a^{2} b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 5 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(15 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{7} - 35 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{5} - 5 \, {\left(8 \, a^{4} - 13 \, a^{3} b + 5 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{4} - 13 \, a^{3} b + 5 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(45 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{8} - 140 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{6} - 30 \, {\left(8 \, a^{4} - 13 \, a^{3} b + 5 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{4} + 12 \, {\left(8 \, a^{4} - 13 \, a^{3} b + 5 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{2} + 5 \, {\left(a^{3} b - a^{2} b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{2} - {\left(a^{3} b - a^{2} b^{2}\right)} d + 2 \, {\left(5 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{9} - 20 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{7} - 6 \, {\left(8 \, a^{4} - 13 \, a^{3} b + 5 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{5} + 4 \, {\left(8 \, a^{4} - 13 \, a^{3} b + 5 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{3} + 5 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{{\left(a^{7} - 3 \, a^{6} b + 3 \, a^{5} b^{2} - a^{4} b^{3}\right)} d^{2} \sqrt{\frac{2304 \, a^{4} b^{3} - 6624 \, a^{3} b^{4} + 7161 \, a^{2} b^{5} - 3450 \, a b^{6} + 625 \, b^{7}}{{\left(a^{15} - 6 \, a^{14} b + 15 \, a^{13} b^{2} - 20 \, a^{12} b^{3} + 15 \, a^{11} b^{4} - 6 \, a^{10} b^{5} + a^{9} b^{6}\right)} d^{4}}} + 36 \, a^{2} b - 47 \, a b^{2} + 15 \, b^{3}}{{\left(a^{7} - 3 \, a^{6} b + 3 \, a^{5} b^{2} - a^{4} b^{3}\right)} d^{2}}} \log\left(1728 \, a^{3} b^{2} - 3684 \, a^{2} b^{3} + 2625 \, a b^{4} - 625 \, b^{5} - 2 \, {\left(36 \, a^{9} - 133 \, a^{8} b + 183 \, a^{7} b^{2} - 111 \, a^{6} b^{3} + 25 \, a^{5} b^{4}\right)} d^{2} \sqrt{\frac{2304 \, a^{4} b^{3} - 6624 \, a^{3} b^{4} + 7161 \, a^{2} b^{5} - 3450 \, a b^{6} + 625 \, b^{7}}{{\left(a^{15} - 6 \, a^{14} b + 15 \, a^{13} b^{2} - 20 \, a^{12} b^{3} + 15 \, a^{11} b^{4} - 6 \, a^{10} b^{5} + a^{9} b^{6}\right)} d^{4}}} - {\left(1728 \, a^{3} b^{2} - 3684 \, a^{2} b^{3} + 2625 \, a b^{4} - 625 \, b^{5}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(1728 \, a^{3} b^{2} - 3684 \, a^{2} b^{3} + 2625 \, a b^{4} - 625 \, b^{5}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(1728 \, a^{3} b^{2} - 3684 \, a^{2} b^{3} + 2625 \, a b^{4} - 625 \, b^{5}\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left({\left(7 \, a^{11} - 26 \, a^{10} b + 36 \, a^{9} b^{2} - 22 \, a^{8} b^{3} + 5 \, a^{7} b^{4}\right)} d^{3} \sqrt{\frac{2304 \, a^{4} b^{3} - 6624 \, a^{3} b^{4} + 7161 \, a^{2} b^{5} - 3450 \, a b^{6} + 625 \, b^{7}}{{\left(a^{15} - 6 \, a^{14} b + 15 \, a^{13} b^{2} - 20 \, a^{12} b^{3} + 15 \, a^{11} b^{4} - 6 \, a^{10} b^{5} + a^{9} b^{6}\right)} d^{4}}} - 2 \, {\left(144 \, a^{6} b - 303 \, a^{5} b^{2} + 213 \, a^{4} b^{3} - 50 \, a^{3} b^{4}\right)} d\right)} \sqrt{\frac{{\left(a^{7} - 3 \, a^{6} b + 3 \, a^{5} b^{2} - a^{4} b^{3}\right)} d^{2} \sqrt{\frac{2304 \, a^{4} b^{3} - 6624 \, a^{3} b^{4} + 7161 \, a^{2} b^{5} - 3450 \, a b^{6} + 625 \, b^{7}}{{\left(a^{15} - 6 \, a^{14} b + 15 \, a^{13} b^{2} - 20 \, a^{12} b^{3} + 15 \, a^{11} b^{4} - 6 \, a^{10} b^{5} + a^{9} b^{6}\right)} d^{4}}} + 36 \, a^{2} b - 47 \, a b^{2} + 15 \, b^{3}}{{\left(a^{7} - 3 \, a^{6} b + 3 \, a^{5} b^{2} - a^{4} b^{3}\right)} d^{2}}}\right) + {\left({\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{10} + 10 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + {\left(a^{3} b - a^{2} b^{2}\right)} d \sinh\left(d x + c\right)^{10} - 5 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{8} + 5 \, {\left(9 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{3} b - a^{2} b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{8} - 2 \, {\left(8 \, a^{4} - 13 \, a^{3} b + 5 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{6} + 40 \, {\left(3 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(105 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{4} - 70 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(8 \, a^{4} - 13 \, a^{3} b + 5 \, a^{2} b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(8 \, a^{4} - 13 \, a^{3} b + 5 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(63 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{5} - 70 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{3} - 3 \, {\left(8 \, a^{4} - 13 \, a^{3} b + 5 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(105 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{6} - 175 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{4} - 15 \, {\left(8 \, a^{4} - 13 \, a^{3} b + 5 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{2} + {\left(8 \, a^{4} - 13 \, a^{3} b + 5 \, a^{2} b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 5 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(15 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{7} - 35 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{5} - 5 \, {\left(8 \, a^{4} - 13 \, a^{3} b + 5 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{4} - 13 \, a^{3} b + 5 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(45 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{8} - 140 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{6} - 30 \, {\left(8 \, a^{4} - 13 \, a^{3} b + 5 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{4} + 12 \, {\left(8 \, a^{4} - 13 \, a^{3} b + 5 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{2} + 5 \, {\left(a^{3} b - a^{2} b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{2} - {\left(a^{3} b - a^{2} b^{2}\right)} d + 2 \, {\left(5 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{9} - 20 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{7} - 6 \, {\left(8 \, a^{4} - 13 \, a^{3} b + 5 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{5} + 4 \, {\left(8 \, a^{4} - 13 \, a^{3} b + 5 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{3} + 5 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{{\left(a^{7} - 3 \, a^{6} b + 3 \, a^{5} b^{2} - a^{4} b^{3}\right)} d^{2} \sqrt{\frac{2304 \, a^{4} b^{3} - 6624 \, a^{3} b^{4} + 7161 \, a^{2} b^{5} - 3450 \, a b^{6} + 625 \, b^{7}}{{\left(a^{15} - 6 \, a^{14} b + 15 \, a^{13} b^{2} - 20 \, a^{12} b^{3} + 15 \, a^{11} b^{4} - 6 \, a^{10} b^{5} + a^{9} b^{6}\right)} d^{4}}} + 36 \, a^{2} b - 47 \, a b^{2} + 15 \, b^{3}}{{\left(a^{7} - 3 \, a^{6} b + 3 \, a^{5} b^{2} - a^{4} b^{3}\right)} d^{2}}} \log\left(1728 \, a^{3} b^{2} - 3684 \, a^{2} b^{3} + 2625 \, a b^{4} - 625 \, b^{5} - 2 \, {\left(36 \, a^{9} - 133 \, a^{8} b + 183 \, a^{7} b^{2} - 111 \, a^{6} b^{3} + 25 \, a^{5} b^{4}\right)} d^{2} \sqrt{\frac{2304 \, a^{4} b^{3} - 6624 \, a^{3} b^{4} + 7161 \, a^{2} b^{5} - 3450 \, a b^{6} + 625 \, b^{7}}{{\left(a^{15} - 6 \, a^{14} b + 15 \, a^{13} b^{2} - 20 \, a^{12} b^{3} + 15 \, a^{11} b^{4} - 6 \, a^{10} b^{5} + a^{9} b^{6}\right)} d^{4}}} - {\left(1728 \, a^{3} b^{2} - 3684 \, a^{2} b^{3} + 2625 \, a b^{4} - 625 \, b^{5}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(1728 \, a^{3} b^{2} - 3684 \, a^{2} b^{3} + 2625 \, a b^{4} - 625 \, b^{5}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) - {\left(1728 \, a^{3} b^{2} - 3684 \, a^{2} b^{3} + 2625 \, a b^{4} - 625 \, b^{5}\right)} \sinh\left(d x + c\right)^{2} - 2 \, {\left({\left(7 \, a^{11} - 26 \, a^{10} b + 36 \, a^{9} b^{2} - 22 \, a^{8} b^{3} + 5 \, a^{7} b^{4}\right)} d^{3} \sqrt{\frac{2304 \, a^{4} b^{3} - 6624 \, a^{3} b^{4} + 7161 \, a^{2} b^{5} - 3450 \, a b^{6} + 625 \, b^{7}}{{\left(a^{15} - 6 \, a^{14} b + 15 \, a^{13} b^{2} - 20 \, a^{12} b^{3} + 15 \, a^{11} b^{4} - 6 \, a^{10} b^{5} + a^{9} b^{6}\right)} d^{4}}} - 2 \, {\left(144 \, a^{6} b - 303 \, a^{5} b^{2} + 213 \, a^{4} b^{3} - 50 \, a^{3} b^{4}\right)} d\right)} \sqrt{\frac{{\left(a^{7} - 3 \, a^{6} b + 3 \, a^{5} b^{2} - a^{4} b^{3}\right)} d^{2} \sqrt{\frac{2304 \, a^{4} b^{3} - 6624 \, a^{3} b^{4} + 7161 \, a^{2} b^{5} - 3450 \, a b^{6} + 625 \, b^{7}}{{\left(a^{15} - 6 \, a^{14} b + 15 \, a^{13} b^{2} - 20 \, a^{12} b^{3} + 15 \, a^{11} b^{4} - 6 \, a^{10} b^{5} + a^{9} b^{6}\right)} d^{4}}} + 36 \, a^{2} b - 47 \, a b^{2} + 15 \, b^{3}}{{\left(a^{7} - 3 \, a^{6} b + 3 \, a^{5} b^{2} - a^{4} b^{3}\right)} d^{2}}}\right) + 32 \, a b - 40 \, b^{2} + 32 \, {\left(2 \, {\left(6 \, a b - 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} - 3 \, {\left(13 \, a b - 10 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} - 2 \, {\left(32 \, a^{2} - 47 \, a b + 15 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(7 \, a b - 10 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{16 \, {\left({\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{10} + 10 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + {\left(a^{3} b - a^{2} b^{2}\right)} d \sinh\left(d x + c\right)^{10} - 5 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{8} + 5 \, {\left(9 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{3} b - a^{2} b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{8} - 2 \, {\left(8 \, a^{4} - 13 \, a^{3} b + 5 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{6} + 40 \, {\left(3 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(105 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{4} - 70 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(8 \, a^{4} - 13 \, a^{3} b + 5 \, a^{2} b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(8 \, a^{4} - 13 \, a^{3} b + 5 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(63 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{5} - 70 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{3} - 3 \, {\left(8 \, a^{4} - 13 \, a^{3} b + 5 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(105 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{6} - 175 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{4} - 15 \, {\left(8 \, a^{4} - 13 \, a^{3} b + 5 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{2} + {\left(8 \, a^{4} - 13 \, a^{3} b + 5 \, a^{2} b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 5 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(15 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{7} - 35 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{5} - 5 \, {\left(8 \, a^{4} - 13 \, a^{3} b + 5 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{4} - 13 \, a^{3} b + 5 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(45 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{8} - 140 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{6} - 30 \, {\left(8 \, a^{4} - 13 \, a^{3} b + 5 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{4} + 12 \, {\left(8 \, a^{4} - 13 \, a^{3} b + 5 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{2} + 5 \, {\left(a^{3} b - a^{2} b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{2} - {\left(a^{3} b - a^{2} b^{2}\right)} d + 2 \, {\left(5 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{9} - 20 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{7} - 6 \, {\left(8 \, a^{4} - 13 \, a^{3} b + 5 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{5} + 4 \, {\left(8 \, a^{4} - 13 \, a^{3} b + 5 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{3} + 5 \, {\left(a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"-1/16*(8*(6*a*b - 5*b^2)*cosh(d*x + c)^8 + 64*(6*a*b - 5*b^2)*cosh(d*x + c)*sinh(d*x + c)^7 + 8*(6*a*b - 5*b^2)*sinh(d*x + c)^8 - 16*(13*a*b - 10*b^2)*cosh(d*x + c)^6 + 16*(14*(6*a*b - 5*b^2)*cosh(d*x + c)^2 - 13*a*b + 10*b^2)*sinh(d*x + c)^6 + 32*(14*(6*a*b - 5*b^2)*cosh(d*x + c)^3 - 3*(13*a*b - 10*b^2)*cosh(d*x + c))*sinh(d*x + c)^5 - 16*(32*a^2 - 47*a*b + 15*b^2)*cosh(d*x + c)^4 + 16*(35*(6*a*b - 5*b^2)*cosh(d*x + c)^4 - 15*(13*a*b - 10*b^2)*cosh(d*x + c)^2 - 32*a^2 + 47*a*b - 15*b^2)*sinh(d*x + c)^4 + 64*(7*(6*a*b - 5*b^2)*cosh(d*x + c)^5 - 5*(13*a*b - 10*b^2)*cosh(d*x + c)^3 - (32*a^2 - 47*a*b + 15*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 - 16*(7*a*b - 10*b^2)*cosh(d*x + c)^2 + 16*(14*(6*a*b - 5*b^2)*cosh(d*x + c)^6 - 15*(13*a*b - 10*b^2)*cosh(d*x + c)^4 - 6*(32*a^2 - 47*a*b + 15*b^2)*cosh(d*x + c)^2 - 7*a*b + 10*b^2)*sinh(d*x + c)^2 + ((a^3*b - a^2*b^2)*d*cosh(d*x + c)^10 + 10*(a^3*b - a^2*b^2)*d*cosh(d*x + c)*sinh(d*x + c)^9 + (a^3*b - a^2*b^2)*d*sinh(d*x + c)^10 - 5*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^8 + 5*(9*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^2 - (a^3*b - a^2*b^2)*d)*sinh(d*x + c)^8 - 2*(8*a^4 - 13*a^3*b + 5*a^2*b^2)*d*cosh(d*x + c)^6 + 40*(3*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^3 - (a^3*b - a^2*b^2)*d*cosh(d*x + c))*sinh(d*x + c)^7 + 2*(105*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^4 - 70*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^2 - (8*a^4 - 13*a^3*b + 5*a^2*b^2)*d)*sinh(d*x + c)^6 + 2*(8*a^4 - 13*a^3*b + 5*a^2*b^2)*d*cosh(d*x + c)^4 + 4*(63*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^5 - 70*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^3 - 3*(8*a^4 - 13*a^3*b + 5*a^2*b^2)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(105*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^6 - 175*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^4 - 15*(8*a^4 - 13*a^3*b + 5*a^2*b^2)*d*cosh(d*x + c)^2 + (8*a^4 - 13*a^3*b + 5*a^2*b^2)*d)*sinh(d*x + c)^4 + 5*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^2 + 8*(15*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^7 - 35*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^5 - 5*(8*a^4 - 13*a^3*b + 5*a^2*b^2)*d*cosh(d*x + c)^3 + (8*a^4 - 13*a^3*b + 5*a^2*b^2)*d*cosh(d*x + c))*sinh(d*x + c)^3 + (45*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^8 - 140*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^6 - 30*(8*a^4 - 13*a^3*b + 5*a^2*b^2)*d*cosh(d*x + c)^4 + 12*(8*a^4 - 13*a^3*b + 5*a^2*b^2)*d*cosh(d*x + c)^2 + 5*(a^3*b - a^2*b^2)*d)*sinh(d*x + c)^2 - (a^3*b - a^2*b^2)*d + 2*(5*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^9 - 20*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^7 - 6*(8*a^4 - 13*a^3*b + 5*a^2*b^2)*d*cosh(d*x + c)^5 + 4*(8*a^4 - 13*a^3*b + 5*a^2*b^2)*d*cosh(d*x + c)^3 + 5*(a^3*b - a^2*b^2)*d*cosh(d*x + c))*sinh(d*x + c))*sqrt(-((a^7 - 3*a^6*b + 3*a^5*b^2 - a^4*b^3)*d^2*sqrt((2304*a^4*b^3 - 6624*a^3*b^4 + 7161*a^2*b^5 - 3450*a*b^6 + 625*b^7)/((a^15 - 6*a^14*b + 15*a^13*b^2 - 20*a^12*b^3 + 15*a^11*b^4 - 6*a^10*b^5 + a^9*b^6)*d^4)) - 36*a^2*b + 47*a*b^2 - 15*b^3)/((a^7 - 3*a^6*b + 3*a^5*b^2 - a^4*b^3)*d^2))*log(1728*a^3*b^2 - 3684*a^2*b^3 + 2625*a*b^4 - 625*b^5 + 2*(36*a^9 - 133*a^8*b + 183*a^7*b^2 - 111*a^6*b^3 + 25*a^5*b^4)*d^2*sqrt((2304*a^4*b^3 - 6624*a^3*b^4 + 7161*a^2*b^5 - 3450*a*b^6 + 625*b^7)/((a^15 - 6*a^14*b + 15*a^13*b^2 - 20*a^12*b^3 + 15*a^11*b^4 - 6*a^10*b^5 + a^9*b^6)*d^4)) - (1728*a^3*b^2 - 3684*a^2*b^3 + 2625*a*b^4 - 625*b^5)*cosh(d*x + c)^2 - 2*(1728*a^3*b^2 - 3684*a^2*b^3 + 2625*a*b^4 - 625*b^5)*cosh(d*x + c)*sinh(d*x + c) - (1728*a^3*b^2 - 3684*a^2*b^3 + 2625*a*b^4 - 625*b^5)*sinh(d*x + c)^2 + 2*((7*a^11 - 26*a^10*b + 36*a^9*b^2 - 22*a^8*b^3 + 5*a^7*b^4)*d^3*sqrt((2304*a^4*b^3 - 6624*a^3*b^4 + 7161*a^2*b^5 - 3450*a*b^6 + 625*b^7)/((a^15 - 6*a^14*b + 15*a^13*b^2 - 20*a^12*b^3 + 15*a^11*b^4 - 6*a^10*b^5 + a^9*b^6)*d^4)) + 2*(144*a^6*b - 303*a^5*b^2 + 213*a^4*b^3 - 50*a^3*b^4)*d)*sqrt(-((a^7 - 3*a^6*b + 3*a^5*b^2 - a^4*b^3)*d^2*sqrt((2304*a^4*b^3 - 6624*a^3*b^4 + 7161*a^2*b^5 - 3450*a*b^6 + 625*b^7)/((a^15 - 6*a^14*b + 15*a^13*b^2 - 20*a^12*b^3 + 15*a^11*b^4 - 6*a^10*b^5 + a^9*b^6)*d^4)) - 36*a^2*b + 47*a*b^2 - 15*b^3)/((a^7 - 3*a^6*b + 3*a^5*b^2 - a^4*b^3)*d^2))) - ((a^3*b - a^2*b^2)*d*cosh(d*x + c)^10 + 10*(a^3*b - a^2*b^2)*d*cosh(d*x + c)*sinh(d*x + c)^9 + (a^3*b - a^2*b^2)*d*sinh(d*x + c)^10 - 5*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^8 + 5*(9*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^2 - (a^3*b - a^2*b^2)*d)*sinh(d*x + c)^8 - 2*(8*a^4 - 13*a^3*b + 5*a^2*b^2)*d*cosh(d*x + c)^6 + 40*(3*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^3 - (a^3*b - a^2*b^2)*d*cosh(d*x + c))*sinh(d*x + c)^7 + 2*(105*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^4 - 70*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^2 - (8*a^4 - 13*a^3*b + 5*a^2*b^2)*d)*sinh(d*x + c)^6 + 2*(8*a^4 - 13*a^3*b + 5*a^2*b^2)*d*cosh(d*x + c)^4 + 4*(63*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^5 - 70*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^3 - 3*(8*a^4 - 13*a^3*b + 5*a^2*b^2)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(105*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^6 - 175*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^4 - 15*(8*a^4 - 13*a^3*b + 5*a^2*b^2)*d*cosh(d*x + c)^2 + (8*a^4 - 13*a^3*b + 5*a^2*b^2)*d)*sinh(d*x + c)^4 + 5*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^2 + 8*(15*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^7 - 35*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^5 - 5*(8*a^4 - 13*a^3*b + 5*a^2*b^2)*d*cosh(d*x + c)^3 + (8*a^4 - 13*a^3*b + 5*a^2*b^2)*d*cosh(d*x + c))*sinh(d*x + c)^3 + (45*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^8 - 140*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^6 - 30*(8*a^4 - 13*a^3*b + 5*a^2*b^2)*d*cosh(d*x + c)^4 + 12*(8*a^4 - 13*a^3*b + 5*a^2*b^2)*d*cosh(d*x + c)^2 + 5*(a^3*b - a^2*b^2)*d)*sinh(d*x + c)^2 - (a^3*b - a^2*b^2)*d + 2*(5*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^9 - 20*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^7 - 6*(8*a^4 - 13*a^3*b + 5*a^2*b^2)*d*cosh(d*x + c)^5 + 4*(8*a^4 - 13*a^3*b + 5*a^2*b^2)*d*cosh(d*x + c)^3 + 5*(a^3*b - a^2*b^2)*d*cosh(d*x + c))*sinh(d*x + c))*sqrt(-((a^7 - 3*a^6*b + 3*a^5*b^2 - a^4*b^3)*d^2*sqrt((2304*a^4*b^3 - 6624*a^3*b^4 + 7161*a^2*b^5 - 3450*a*b^6 + 625*b^7)/((a^15 - 6*a^14*b + 15*a^13*b^2 - 20*a^12*b^3 + 15*a^11*b^4 - 6*a^10*b^5 + a^9*b^6)*d^4)) - 36*a^2*b + 47*a*b^2 - 15*b^3)/((a^7 - 3*a^6*b + 3*a^5*b^2 - a^4*b^3)*d^2))*log(1728*a^3*b^2 - 3684*a^2*b^3 + 2625*a*b^4 - 625*b^5 + 2*(36*a^9 - 133*a^8*b + 183*a^7*b^2 - 111*a^6*b^3 + 25*a^5*b^4)*d^2*sqrt((2304*a^4*b^3 - 6624*a^3*b^4 + 7161*a^2*b^5 - 3450*a*b^6 + 625*b^7)/((a^15 - 6*a^14*b + 15*a^13*b^2 - 20*a^12*b^3 + 15*a^11*b^4 - 6*a^10*b^5 + a^9*b^6)*d^4)) - (1728*a^3*b^2 - 3684*a^2*b^3 + 2625*a*b^4 - 625*b^5)*cosh(d*x + c)^2 - 2*(1728*a^3*b^2 - 3684*a^2*b^3 + 2625*a*b^4 - 625*b^5)*cosh(d*x + c)*sinh(d*x + c) - (1728*a^3*b^2 - 3684*a^2*b^3 + 2625*a*b^4 - 625*b^5)*sinh(d*x + c)^2 - 2*((7*a^11 - 26*a^10*b + 36*a^9*b^2 - 22*a^8*b^3 + 5*a^7*b^4)*d^3*sqrt((2304*a^4*b^3 - 6624*a^3*b^4 + 7161*a^2*b^5 - 3450*a*b^6 + 625*b^7)/((a^15 - 6*a^14*b + 15*a^13*b^2 - 20*a^12*b^3 + 15*a^11*b^4 - 6*a^10*b^5 + a^9*b^6)*d^4)) + 2*(144*a^6*b - 303*a^5*b^2 + 213*a^4*b^3 - 50*a^3*b^4)*d)*sqrt(-((a^7 - 3*a^6*b + 3*a^5*b^2 - a^4*b^3)*d^2*sqrt((2304*a^4*b^3 - 6624*a^3*b^4 + 7161*a^2*b^5 - 3450*a*b^6 + 625*b^7)/((a^15 - 6*a^14*b + 15*a^13*b^2 - 20*a^12*b^3 + 15*a^11*b^4 - 6*a^10*b^5 + a^9*b^6)*d^4)) - 36*a^2*b + 47*a*b^2 - 15*b^3)/((a^7 - 3*a^6*b + 3*a^5*b^2 - a^4*b^3)*d^2))) - ((a^3*b - a^2*b^2)*d*cosh(d*x + c)^10 + 10*(a^3*b - a^2*b^2)*d*cosh(d*x + c)*sinh(d*x + c)^9 + (a^3*b - a^2*b^2)*d*sinh(d*x + c)^10 - 5*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^8 + 5*(9*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^2 - (a^3*b - a^2*b^2)*d)*sinh(d*x + c)^8 - 2*(8*a^4 - 13*a^3*b + 5*a^2*b^2)*d*cosh(d*x + c)^6 + 40*(3*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^3 - (a^3*b - a^2*b^2)*d*cosh(d*x + c))*sinh(d*x + c)^7 + 2*(105*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^4 - 70*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^2 - (8*a^4 - 13*a^3*b + 5*a^2*b^2)*d)*sinh(d*x + c)^6 + 2*(8*a^4 - 13*a^3*b + 5*a^2*b^2)*d*cosh(d*x + c)^4 + 4*(63*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^5 - 70*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^3 - 3*(8*a^4 - 13*a^3*b + 5*a^2*b^2)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(105*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^6 - 175*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^4 - 15*(8*a^4 - 13*a^3*b + 5*a^2*b^2)*d*cosh(d*x + c)^2 + (8*a^4 - 13*a^3*b + 5*a^2*b^2)*d)*sinh(d*x + c)^4 + 5*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^2 + 8*(15*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^7 - 35*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^5 - 5*(8*a^4 - 13*a^3*b + 5*a^2*b^2)*d*cosh(d*x + c)^3 + (8*a^4 - 13*a^3*b + 5*a^2*b^2)*d*cosh(d*x + c))*sinh(d*x + c)^3 + (45*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^8 - 140*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^6 - 30*(8*a^4 - 13*a^3*b + 5*a^2*b^2)*d*cosh(d*x + c)^4 + 12*(8*a^4 - 13*a^3*b + 5*a^2*b^2)*d*cosh(d*x + c)^2 + 5*(a^3*b - a^2*b^2)*d)*sinh(d*x + c)^2 - (a^3*b - a^2*b^2)*d + 2*(5*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^9 - 20*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^7 - 6*(8*a^4 - 13*a^3*b + 5*a^2*b^2)*d*cosh(d*x + c)^5 + 4*(8*a^4 - 13*a^3*b + 5*a^2*b^2)*d*cosh(d*x + c)^3 + 5*(a^3*b - a^2*b^2)*d*cosh(d*x + c))*sinh(d*x + c))*sqrt(((a^7 - 3*a^6*b + 3*a^5*b^2 - a^4*b^3)*d^2*sqrt((2304*a^4*b^3 - 6624*a^3*b^4 + 7161*a^2*b^5 - 3450*a*b^6 + 625*b^7)/((a^15 - 6*a^14*b + 15*a^13*b^2 - 20*a^12*b^3 + 15*a^11*b^4 - 6*a^10*b^5 + a^9*b^6)*d^4)) + 36*a^2*b - 47*a*b^2 + 15*b^3)/((a^7 - 3*a^6*b + 3*a^5*b^2 - a^4*b^3)*d^2))*log(1728*a^3*b^2 - 3684*a^2*b^3 + 2625*a*b^4 - 625*b^5 - 2*(36*a^9 - 133*a^8*b + 183*a^7*b^2 - 111*a^6*b^3 + 25*a^5*b^4)*d^2*sqrt((2304*a^4*b^3 - 6624*a^3*b^4 + 7161*a^2*b^5 - 3450*a*b^6 + 625*b^7)/((a^15 - 6*a^14*b + 15*a^13*b^2 - 20*a^12*b^3 + 15*a^11*b^4 - 6*a^10*b^5 + a^9*b^6)*d^4)) - (1728*a^3*b^2 - 3684*a^2*b^3 + 2625*a*b^4 - 625*b^5)*cosh(d*x + c)^2 - 2*(1728*a^3*b^2 - 3684*a^2*b^3 + 2625*a*b^4 - 625*b^5)*cosh(d*x + c)*sinh(d*x + c) - (1728*a^3*b^2 - 3684*a^2*b^3 + 2625*a*b^4 - 625*b^5)*sinh(d*x + c)^2 + 2*((7*a^11 - 26*a^10*b + 36*a^9*b^2 - 22*a^8*b^3 + 5*a^7*b^4)*d^3*sqrt((2304*a^4*b^3 - 6624*a^3*b^4 + 7161*a^2*b^5 - 3450*a*b^6 + 625*b^7)/((a^15 - 6*a^14*b + 15*a^13*b^2 - 20*a^12*b^3 + 15*a^11*b^4 - 6*a^10*b^5 + a^9*b^6)*d^4)) - 2*(144*a^6*b - 303*a^5*b^2 + 213*a^4*b^3 - 50*a^3*b^4)*d)*sqrt(((a^7 - 3*a^6*b + 3*a^5*b^2 - a^4*b^3)*d^2*sqrt((2304*a^4*b^3 - 6624*a^3*b^4 + 7161*a^2*b^5 - 3450*a*b^6 + 625*b^7)/((a^15 - 6*a^14*b + 15*a^13*b^2 - 20*a^12*b^3 + 15*a^11*b^4 - 6*a^10*b^5 + a^9*b^6)*d^4)) + 36*a^2*b - 47*a*b^2 + 15*b^3)/((a^7 - 3*a^6*b + 3*a^5*b^2 - a^4*b^3)*d^2))) + ((a^3*b - a^2*b^2)*d*cosh(d*x + c)^10 + 10*(a^3*b - a^2*b^2)*d*cosh(d*x + c)*sinh(d*x + c)^9 + (a^3*b - a^2*b^2)*d*sinh(d*x + c)^10 - 5*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^8 + 5*(9*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^2 - (a^3*b - a^2*b^2)*d)*sinh(d*x + c)^8 - 2*(8*a^4 - 13*a^3*b + 5*a^2*b^2)*d*cosh(d*x + c)^6 + 40*(3*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^3 - (a^3*b - a^2*b^2)*d*cosh(d*x + c))*sinh(d*x + c)^7 + 2*(105*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^4 - 70*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^2 - (8*a^4 - 13*a^3*b + 5*a^2*b^2)*d)*sinh(d*x + c)^6 + 2*(8*a^4 - 13*a^3*b + 5*a^2*b^2)*d*cosh(d*x + c)^4 + 4*(63*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^5 - 70*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^3 - 3*(8*a^4 - 13*a^3*b + 5*a^2*b^2)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(105*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^6 - 175*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^4 - 15*(8*a^4 - 13*a^3*b + 5*a^2*b^2)*d*cosh(d*x + c)^2 + (8*a^4 - 13*a^3*b + 5*a^2*b^2)*d)*sinh(d*x + c)^4 + 5*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^2 + 8*(15*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^7 - 35*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^5 - 5*(8*a^4 - 13*a^3*b + 5*a^2*b^2)*d*cosh(d*x + c)^3 + (8*a^4 - 13*a^3*b + 5*a^2*b^2)*d*cosh(d*x + c))*sinh(d*x + c)^3 + (45*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^8 - 140*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^6 - 30*(8*a^4 - 13*a^3*b + 5*a^2*b^2)*d*cosh(d*x + c)^4 + 12*(8*a^4 - 13*a^3*b + 5*a^2*b^2)*d*cosh(d*x + c)^2 + 5*(a^3*b - a^2*b^2)*d)*sinh(d*x + c)^2 - (a^3*b - a^2*b^2)*d + 2*(5*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^9 - 20*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^7 - 6*(8*a^4 - 13*a^3*b + 5*a^2*b^2)*d*cosh(d*x + c)^5 + 4*(8*a^4 - 13*a^3*b + 5*a^2*b^2)*d*cosh(d*x + c)^3 + 5*(a^3*b - a^2*b^2)*d*cosh(d*x + c))*sinh(d*x + c))*sqrt(((a^7 - 3*a^6*b + 3*a^5*b^2 - a^4*b^3)*d^2*sqrt((2304*a^4*b^3 - 6624*a^3*b^4 + 7161*a^2*b^5 - 3450*a*b^6 + 625*b^7)/((a^15 - 6*a^14*b + 15*a^13*b^2 - 20*a^12*b^3 + 15*a^11*b^4 - 6*a^10*b^5 + a^9*b^6)*d^4)) + 36*a^2*b - 47*a*b^2 + 15*b^3)/((a^7 - 3*a^6*b + 3*a^5*b^2 - a^4*b^3)*d^2))*log(1728*a^3*b^2 - 3684*a^2*b^3 + 2625*a*b^4 - 625*b^5 - 2*(36*a^9 - 133*a^8*b + 183*a^7*b^2 - 111*a^6*b^3 + 25*a^5*b^4)*d^2*sqrt((2304*a^4*b^3 - 6624*a^3*b^4 + 7161*a^2*b^5 - 3450*a*b^6 + 625*b^7)/((a^15 - 6*a^14*b + 15*a^13*b^2 - 20*a^12*b^3 + 15*a^11*b^4 - 6*a^10*b^5 + a^9*b^6)*d^4)) - (1728*a^3*b^2 - 3684*a^2*b^3 + 2625*a*b^4 - 625*b^5)*cosh(d*x + c)^2 - 2*(1728*a^3*b^2 - 3684*a^2*b^3 + 2625*a*b^4 - 625*b^5)*cosh(d*x + c)*sinh(d*x + c) - (1728*a^3*b^2 - 3684*a^2*b^3 + 2625*a*b^4 - 625*b^5)*sinh(d*x + c)^2 - 2*((7*a^11 - 26*a^10*b + 36*a^9*b^2 - 22*a^8*b^3 + 5*a^7*b^4)*d^3*sqrt((2304*a^4*b^3 - 6624*a^3*b^4 + 7161*a^2*b^5 - 3450*a*b^6 + 625*b^7)/((a^15 - 6*a^14*b + 15*a^13*b^2 - 20*a^12*b^3 + 15*a^11*b^4 - 6*a^10*b^5 + a^9*b^6)*d^4)) - 2*(144*a^6*b - 303*a^5*b^2 + 213*a^4*b^3 - 50*a^3*b^4)*d)*sqrt(((a^7 - 3*a^6*b + 3*a^5*b^2 - a^4*b^3)*d^2*sqrt((2304*a^4*b^3 - 6624*a^3*b^4 + 7161*a^2*b^5 - 3450*a*b^6 + 625*b^7)/((a^15 - 6*a^14*b + 15*a^13*b^2 - 20*a^12*b^3 + 15*a^11*b^4 - 6*a^10*b^5 + a^9*b^6)*d^4)) + 36*a^2*b - 47*a*b^2 + 15*b^3)/((a^7 - 3*a^6*b + 3*a^5*b^2 - a^4*b^3)*d^2))) + 32*a*b - 40*b^2 + 32*(2*(6*a*b - 5*b^2)*cosh(d*x + c)^7 - 3*(13*a*b - 10*b^2)*cosh(d*x + c)^5 - 2*(32*a^2 - 47*a*b + 15*b^2)*cosh(d*x + c)^3 - (7*a*b - 10*b^2)*cosh(d*x + c))*sinh(d*x + c))/((a^3*b - a^2*b^2)*d*cosh(d*x + c)^10 + 10*(a^3*b - a^2*b^2)*d*cosh(d*x + c)*sinh(d*x + c)^9 + (a^3*b - a^2*b^2)*d*sinh(d*x + c)^10 - 5*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^8 + 5*(9*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^2 - (a^3*b - a^2*b^2)*d)*sinh(d*x + c)^8 - 2*(8*a^4 - 13*a^3*b + 5*a^2*b^2)*d*cosh(d*x + c)^6 + 40*(3*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^3 - (a^3*b - a^2*b^2)*d*cosh(d*x + c))*sinh(d*x + c)^7 + 2*(105*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^4 - 70*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^2 - (8*a^4 - 13*a^3*b + 5*a^2*b^2)*d)*sinh(d*x + c)^6 + 2*(8*a^4 - 13*a^3*b + 5*a^2*b^2)*d*cosh(d*x + c)^4 + 4*(63*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^5 - 70*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^3 - 3*(8*a^4 - 13*a^3*b + 5*a^2*b^2)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(105*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^6 - 175*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^4 - 15*(8*a^4 - 13*a^3*b + 5*a^2*b^2)*d*cosh(d*x + c)^2 + (8*a^4 - 13*a^3*b + 5*a^2*b^2)*d)*sinh(d*x + c)^4 + 5*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^2 + 8*(15*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^7 - 35*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^5 - 5*(8*a^4 - 13*a^3*b + 5*a^2*b^2)*d*cosh(d*x + c)^3 + (8*a^4 - 13*a^3*b + 5*a^2*b^2)*d*cosh(d*x + c))*sinh(d*x + c)^3 + (45*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^8 - 140*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^6 - 30*(8*a^4 - 13*a^3*b + 5*a^2*b^2)*d*cosh(d*x + c)^4 + 12*(8*a^4 - 13*a^3*b + 5*a^2*b^2)*d*cosh(d*x + c)^2 + 5*(a^3*b - a^2*b^2)*d)*sinh(d*x + c)^2 - (a^3*b - a^2*b^2)*d + 2*(5*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^9 - 20*(a^3*b - a^2*b^2)*d*cosh(d*x + c)^7 - 6*(8*a^4 - 13*a^3*b + 5*a^2*b^2)*d*cosh(d*x + c)^5 + 4*(8*a^4 - 13*a^3*b + 5*a^2*b^2)*d*cosh(d*x + c)^3 + 5*(a^3*b - a^2*b^2)*d*cosh(d*x + c))*sinh(d*x + c))","B",0
253,-1,0,0,0.000000," ","integrate(sinh(d*x+c)^9/(a-b*sinh(d*x+c)^4)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
254,-1,0,0,0.000000," ","integrate(sinh(d*x+c)^7/(a-b*sinh(d*x+c)^4)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
255,-1,0,0,0.000000," ","integrate(sinh(d*x+c)^5/(a-b*sinh(d*x+c)^4)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
256,-1,0,0,0.000000," ","integrate(sinh(d*x+c)^3/(a-b*sinh(d*x+c)^4)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
257,-1,0,0,0.000000," ","integrate(sinh(d*x+c)/(a-b*sinh(d*x+c)^4)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
258,-1,0,0,0.000000," ","integrate(csch(d*x+c)/(a-b*sinh(d*x+c)^4)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
259,-1,0,0,0.000000," ","integrate(sinh(d*x+c)^8/(a-b*sinh(d*x+c)^4)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
260,-1,0,0,0.000000," ","integrate(sinh(d*x+c)^6/(a-b*sinh(d*x+c)^4)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
261,-1,0,0,0.000000," ","integrate(sinh(d*x+c)^4/(a-b*sinh(d*x+c)^4)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
262,-1,0,0,0.000000," ","integrate(sinh(d*x+c)^2/(a-b*sinh(d*x+c)^4)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
263,-1,0,0,0.000000," ","integrate(1/(a-b*sinh(d*x+c)^4)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
264,-1,0,0,0.000000," ","integrate(csch(d*x+c)^2/(a-b*sinh(d*x+c)^4)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
265,1,113,0,0.608145," ","integrate(1/(1-sinh(x)^4),x, algorithm=""fricas"")","\frac{{\left(\sqrt{2} \cosh\left(x\right)^{2} + 2 \, \sqrt{2} \cosh\left(x\right) \sinh\left(x\right) + \sqrt{2} \sinh\left(x\right)^{2} + \sqrt{2}\right)} \log\left(-\frac{3 \, {\left(2 \, \sqrt{2} - 3\right)} \cosh\left(x\right)^{2} - 4 \, {\left(3 \, \sqrt{2} - 4\right)} \cosh\left(x\right) \sinh\left(x\right) + 3 \, {\left(2 \, \sqrt{2} - 3\right)} \sinh\left(x\right)^{2} - 2 \, \sqrt{2} + 3}{\cosh\left(x\right)^{2} + \sinh\left(x\right)^{2} - 3}\right) - 8}{8 \, {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)}}"," ",0,"1/8*((sqrt(2)*cosh(x)^2 + 2*sqrt(2)*cosh(x)*sinh(x) + sqrt(2)*sinh(x)^2 + sqrt(2))*log(-(3*(2*sqrt(2) - 3)*cosh(x)^2 - 4*(3*sqrt(2) - 4)*cosh(x)*sinh(x) + 3*(2*sqrt(2) - 3)*sinh(x)^2 - 2*sqrt(2) + 3)/(cosh(x)^2 + sinh(x)^2 - 3)) - 8)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)","B",0
266,1,596,0,1.233501," ","integrate(1/(1+sinh(x)^4),x, algorithm=""fricas"")","\frac{1}{16} \cdot 2^{\frac{1}{4}} {\left(\sqrt{2} + 1\right)} \sqrt{-2 \, \sqrt{2} + 4} \log\left({\left(2^{\frac{3}{4}} e^{\left(2 \, x\right)} - 2^{\frac{1}{4}} {\left(3 \, \sqrt{2} + 4\right)}\right)} \sqrt{-2 \, \sqrt{2} + 4} + 4 \, \sqrt{2} + e^{\left(4 \, x\right)} - 2 \, e^{\left(2 \, x\right)} + 5\right) - \frac{1}{16} \cdot 2^{\frac{1}{4}} {\left(\sqrt{2} + 1\right)} \sqrt{-2 \, \sqrt{2} + 4} \log\left(-{\left(2^{\frac{3}{4}} e^{\left(2 \, x\right)} - 2^{\frac{1}{4}} {\left(3 \, \sqrt{2} + 4\right)}\right)} \sqrt{-2 \, \sqrt{2} + 4} + 4 \, \sqrt{2} + e^{\left(4 \, x\right)} - 2 \, e^{\left(2 \, x\right)} + 5\right) - \frac{1}{4} \cdot 2^{\frac{1}{4}} \sqrt{-2 \, \sqrt{2} + 4} \arctan\left(\frac{1}{14} \, {\left(\sqrt{2} {\left(5 \, \sqrt{2} + 6\right)} + 8 \, \sqrt{2} + 4\right)} e^{\left(2 \, x\right)} - \frac{1}{28} \, {\left(2 \, \sqrt{2} {\left(5 \, \sqrt{2} + 6\right)} - {\left(2^{\frac{3}{4}} {\left(8 \, \sqrt{2} + 11\right)} + 2 \cdot 2^{\frac{1}{4}} {\left(5 \, \sqrt{2} + 6\right)}\right)} \sqrt{-2 \, \sqrt{2} + 4} + 16 \, \sqrt{2} + 8\right)} \sqrt{-{\left(2^{\frac{3}{4}} e^{\left(2 \, x\right)} - 2^{\frac{1}{4}} {\left(3 \, \sqrt{2} + 4\right)}\right)} \sqrt{-2 \, \sqrt{2} + 4} + 4 \, \sqrt{2} + e^{\left(4 \, x\right)} - 2 \, e^{\left(2 \, x\right)} + 5} - \frac{1}{14} \, \sqrt{2} {\left(3 \, \sqrt{2} - 2\right)} - \frac{1}{28} \, {\left({\left(2^{\frac{3}{4}} {\left(8 \, \sqrt{2} + 11\right)} + 2 \cdot 2^{\frac{1}{4}} {\left(5 \, \sqrt{2} + 6\right)}\right)} e^{\left(2 \, x\right)} - 2^{\frac{3}{4}} {\left(2 \, \sqrt{2} + 1\right)} - 2 \cdot 2^{\frac{1}{4}} {\left(3 \, \sqrt{2} - 2\right)}\right)} \sqrt{-2 \, \sqrt{2} + 4} - \frac{1}{7} \, \sqrt{2} + \frac{3}{7}\right) - \frac{1}{4} \cdot 2^{\frac{1}{4}} \sqrt{-2 \, \sqrt{2} + 4} \arctan\left(-\frac{1}{14} \, {\left(\sqrt{2} {\left(5 \, \sqrt{2} + 6\right)} + 8 \, \sqrt{2} + 4\right)} e^{\left(2 \, x\right)} + \frac{1}{28} \, {\left(2 \, \sqrt{2} {\left(5 \, \sqrt{2} + 6\right)} + {\left(2^{\frac{3}{4}} {\left(8 \, \sqrt{2} + 11\right)} + 2 \cdot 2^{\frac{1}{4}} {\left(5 \, \sqrt{2} + 6\right)}\right)} \sqrt{-2 \, \sqrt{2} + 4} + 16 \, \sqrt{2} + 8\right)} \sqrt{{\left(2^{\frac{3}{4}} e^{\left(2 \, x\right)} - 2^{\frac{1}{4}} {\left(3 \, \sqrt{2} + 4\right)}\right)} \sqrt{-2 \, \sqrt{2} + 4} + 4 \, \sqrt{2} + e^{\left(4 \, x\right)} - 2 \, e^{\left(2 \, x\right)} + 5} + \frac{1}{14} \, \sqrt{2} {\left(3 \, \sqrt{2} - 2\right)} - \frac{1}{28} \, {\left({\left(2^{\frac{3}{4}} {\left(8 \, \sqrt{2} + 11\right)} + 2 \cdot 2^{\frac{1}{4}} {\left(5 \, \sqrt{2} + 6\right)}\right)} e^{\left(2 \, x\right)} - 2^{\frac{3}{4}} {\left(2 \, \sqrt{2} + 1\right)} - 2 \cdot 2^{\frac{1}{4}} {\left(3 \, \sqrt{2} - 2\right)}\right)} \sqrt{-2 \, \sqrt{2} + 4} + \frac{1}{7} \, \sqrt{2} - \frac{3}{7}\right)"," ",0,"1/16*2^(1/4)*(sqrt(2) + 1)*sqrt(-2*sqrt(2) + 4)*log((2^(3/4)*e^(2*x) - 2^(1/4)*(3*sqrt(2) + 4))*sqrt(-2*sqrt(2) + 4) + 4*sqrt(2) + e^(4*x) - 2*e^(2*x) + 5) - 1/16*2^(1/4)*(sqrt(2) + 1)*sqrt(-2*sqrt(2) + 4)*log(-(2^(3/4)*e^(2*x) - 2^(1/4)*(3*sqrt(2) + 4))*sqrt(-2*sqrt(2) + 4) + 4*sqrt(2) + e^(4*x) - 2*e^(2*x) + 5) - 1/4*2^(1/4)*sqrt(-2*sqrt(2) + 4)*arctan(1/14*(sqrt(2)*(5*sqrt(2) + 6) + 8*sqrt(2) + 4)*e^(2*x) - 1/28*(2*sqrt(2)*(5*sqrt(2) + 6) - (2^(3/4)*(8*sqrt(2) + 11) + 2*2^(1/4)*(5*sqrt(2) + 6))*sqrt(-2*sqrt(2) + 4) + 16*sqrt(2) + 8)*sqrt(-(2^(3/4)*e^(2*x) - 2^(1/4)*(3*sqrt(2) + 4))*sqrt(-2*sqrt(2) + 4) + 4*sqrt(2) + e^(4*x) - 2*e^(2*x) + 5) - 1/14*sqrt(2)*(3*sqrt(2) - 2) - 1/28*((2^(3/4)*(8*sqrt(2) + 11) + 2*2^(1/4)*(5*sqrt(2) + 6))*e^(2*x) - 2^(3/4)*(2*sqrt(2) + 1) - 2*2^(1/4)*(3*sqrt(2) - 2))*sqrt(-2*sqrt(2) + 4) - 1/7*sqrt(2) + 3/7) - 1/4*2^(1/4)*sqrt(-2*sqrt(2) + 4)*arctan(-1/14*(sqrt(2)*(5*sqrt(2) + 6) + 8*sqrt(2) + 4)*e^(2*x) + 1/28*(2*sqrt(2)*(5*sqrt(2) + 6) + (2^(3/4)*(8*sqrt(2) + 11) + 2*2^(1/4)*(5*sqrt(2) + 6))*sqrt(-2*sqrt(2) + 4) + 16*sqrt(2) + 8)*sqrt((2^(3/4)*e^(2*x) - 2^(1/4)*(3*sqrt(2) + 4))*sqrt(-2*sqrt(2) + 4) + 4*sqrt(2) + e^(4*x) - 2*e^(2*x) + 5) + 1/14*sqrt(2)*(3*sqrt(2) - 2) - 1/28*((2^(3/4)*(8*sqrt(2) + 11) + 2*2^(1/4)*(5*sqrt(2) + 6))*e^(2*x) - 2^(3/4)*(2*sqrt(2) + 1) - 2*2^(1/4)*(3*sqrt(2) - 2))*sqrt(-2*sqrt(2) + 4) + 1/7*sqrt(2) - 3/7)","B",0
267,-2,0,0,0.000000," ","integrate(1/(a+b*sinh(x)^5),x, algorithm=""fricas"")","\text{Exception raised: RuntimeError}"," ",0,"Exception raised: RuntimeError >> no explicit roots found","F(-2)",0
268,-1,0,0,0.000000," ","integrate(1/(a+b*sinh(x)^6),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
269,-1,0,0,0.000000," ","integrate(1/(a+b*sinh(x)^8),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
270,1,3507,0,1.242106," ","integrate(1/(1+sinh(x)^5),x, algorithm=""fricas"")","-\frac{1}{200} \, \sqrt{2} \sqrt{2 \, \sqrt{2} {\left(2 \, \sqrt{5} - 5\right)} \sqrt{\sqrt{5} + 3} - 4 \, \sqrt{5} + 20} {\left(8 \, \sqrt{5} + 24\right)}^{\frac{1}{4}} {\left(3 \, \sqrt{5} - 5\right)} \sqrt{2 \, \sqrt{5} + 5} \sqrt{\sqrt{5} + 3} \arctan\left(\frac{1}{40} \, \sqrt{2} {\left({\left(11 \, \sqrt{5} - 25\right)} e^{x} - 7 \, \sqrt{5} + 15\right)} \sqrt{2 \, \sqrt{5} + 5} \sqrt{\sqrt{5} + 3} + \frac{1}{80} \, \sqrt{2} {\left(\sqrt{2} {\left({\left(11 \, \sqrt{5} - 25\right)} e^{x} + 4 \, \sqrt{5} - 10\right)} \sqrt{2 \, \sqrt{5} + 5} \sqrt{\sqrt{5} + 3} + 2 \, {\left({\left(3 \, \sqrt{5} - 5\right)} e^{x} + 7 \, \sqrt{5} - 15\right)} \sqrt{2 \, \sqrt{5} + 5}\right)} \sqrt{\sqrt{5} + 3} + \frac{1}{12800} \, {\left(80 \, \sqrt{2} {\left(5 \, \sqrt{5} - 11\right)} \sqrt{2 \, \sqrt{5} + 5} \sqrt{\sqrt{5} + 3} + 40 \, \sqrt{2} {\left(\sqrt{2} {\left(5 \, \sqrt{5} - 11\right)} \sqrt{2 \, \sqrt{5} + 5} \sqrt{\sqrt{5} + 3} + 2 \, \sqrt{2 \, \sqrt{5} + 5} {\left(\sqrt{5} - 3\right)}\right)} \sqrt{\sqrt{5} + 3} + \sqrt{2 \, \sqrt{2} {\left(2 \, \sqrt{5} - 5\right)} \sqrt{\sqrt{5} + 3} - 4 \, \sqrt{5} + 20} {\left({\left(\sqrt{2} {\left(7 \, \sqrt{5} - 15\right)} \sqrt{2 \, \sqrt{5} + 5} \sqrt{\sqrt{5} + 3} + 2 \, {\left(11 \, \sqrt{5} - 25\right)} \sqrt{2 \, \sqrt{5} + 5}\right)} {\left(8 \, \sqrt{5} + 24\right)}^{\frac{3}{4}} + 4 \, {\left(\sqrt{2} {\left(17 \, \sqrt{5} - 35\right)} \sqrt{2 \, \sqrt{5} + 5} \sqrt{\sqrt{5} + 3} + 2 \, {\left(11 \, \sqrt{5} - 25\right)} \sqrt{2 \, \sqrt{5} + 5}\right)} {\left(8 \, \sqrt{5} + 24\right)}^{\frac{1}{4}}\right)} + 320 \, \sqrt{2 \, \sqrt{5} + 5} {\left(\sqrt{5} - 4\right)}\right)} \sqrt{-20 \, \sqrt{2} \sqrt{\sqrt{5} + 3} {\left(\sqrt{5} - 3\right)} + 40 \, {\left(\sqrt{5} - 1\right)} e^{x} - 2 \, {\left(\sqrt{2} {\left({\left(2 \, \sqrt{5} - 5\right)} e^{x} - 3 \, \sqrt{5} + 5\right)} \sqrt{\sqrt{5} + 3} + 2 \, {\left(\sqrt{5} - 5\right)} e^{x} - 3 \, \sqrt{5} + 5\right)} \sqrt{2 \, \sqrt{2} {\left(2 \, \sqrt{5} - 5\right)} \sqrt{\sqrt{5} + 3} - 4 \, \sqrt{5} + 20} {\left(8 \, \sqrt{5} + 24\right)}^{\frac{1}{4}} + 80 \, e^{\left(2 \, x\right)} + 80} + \frac{1}{640} \, \sqrt{2 \, \sqrt{2} {\left(2 \, \sqrt{5} - 5\right)} \sqrt{\sqrt{5} + 3} - 4 \, \sqrt{5} + 20} {\left({\left(\sqrt{2} {\left({\left(3 \, \sqrt{5} - 7\right)} e^{x} + 8 \, \sqrt{5} - 18\right)} \sqrt{2 \, \sqrt{5} + 5} \sqrt{\sqrt{5} + 3} + 2 \, {\left({\left(5 \, \sqrt{5} - 11\right)} e^{x} + 2 \, \sqrt{5} - 4\right)} \sqrt{2 \, \sqrt{5} + 5}\right)} {\left(8 \, \sqrt{5} + 24\right)}^{\frac{3}{4}} + 4 \, {\left(\sqrt{2} {\left({\left(7 \, \sqrt{5} - 17\right)} e^{x} + 8 \, \sqrt{5} - 18\right)} \sqrt{2 \, \sqrt{5} + 5} \sqrt{\sqrt{5} + 3} + 2 \, {\left({\left(5 \, \sqrt{5} - 11\right)} e^{x} + 5 \, \sqrt{5} - 9\right)} \sqrt{2 \, \sqrt{5} + 5}\right)} {\left(8 \, \sqrt{5} + 24\right)}^{\frac{1}{4}}\right)} + \frac{1}{20} \, {\left(2 \, {\left(4 \, \sqrt{5} - 5\right)} e^{x} - \sqrt{5} + 5\right)} \sqrt{2 \, \sqrt{5} + 5}\right) - \frac{1}{200} \, \sqrt{2} \sqrt{2 \, \sqrt{2} {\left(2 \, \sqrt{5} - 5\right)} \sqrt{\sqrt{5} + 3} - 4 \, \sqrt{5} + 20} {\left(8 \, \sqrt{5} + 24\right)}^{\frac{1}{4}} {\left(3 \, \sqrt{5} - 5\right)} \sqrt{2 \, \sqrt{5} + 5} \sqrt{\sqrt{5} + 3} \arctan\left(-\frac{1}{40} \, \sqrt{2} {\left({\left(11 \, \sqrt{5} - 25\right)} e^{x} - 7 \, \sqrt{5} + 15\right)} \sqrt{2 \, \sqrt{5} + 5} \sqrt{\sqrt{5} + 3} - \frac{1}{80} \, \sqrt{2} {\left(\sqrt{2} {\left({\left(11 \, \sqrt{5} - 25\right)} e^{x} + 4 \, \sqrt{5} - 10\right)} \sqrt{2 \, \sqrt{5} + 5} \sqrt{\sqrt{5} + 3} + 2 \, {\left({\left(3 \, \sqrt{5} - 5\right)} e^{x} + 7 \, \sqrt{5} - 15\right)} \sqrt{2 \, \sqrt{5} + 5}\right)} \sqrt{\sqrt{5} + 3} - \frac{1}{12800} \, {\left(80 \, \sqrt{2} {\left(5 \, \sqrt{5} - 11\right)} \sqrt{2 \, \sqrt{5} + 5} \sqrt{\sqrt{5} + 3} + 40 \, \sqrt{2} {\left(\sqrt{2} {\left(5 \, \sqrt{5} - 11\right)} \sqrt{2 \, \sqrt{5} + 5} \sqrt{\sqrt{5} + 3} + 2 \, \sqrt{2 \, \sqrt{5} + 5} {\left(\sqrt{5} - 3\right)}\right)} \sqrt{\sqrt{5} + 3} - \sqrt{2 \, \sqrt{2} {\left(2 \, \sqrt{5} - 5\right)} \sqrt{\sqrt{5} + 3} - 4 \, \sqrt{5} + 20} {\left({\left(\sqrt{2} {\left(7 \, \sqrt{5} - 15\right)} \sqrt{2 \, \sqrt{5} + 5} \sqrt{\sqrt{5} + 3} + 2 \, {\left(11 \, \sqrt{5} - 25\right)} \sqrt{2 \, \sqrt{5} + 5}\right)} {\left(8 \, \sqrt{5} + 24\right)}^{\frac{3}{4}} + 4 \, {\left(\sqrt{2} {\left(17 \, \sqrt{5} - 35\right)} \sqrt{2 \, \sqrt{5} + 5} \sqrt{\sqrt{5} + 3} + 2 \, {\left(11 \, \sqrt{5} - 25\right)} \sqrt{2 \, \sqrt{5} + 5}\right)} {\left(8 \, \sqrt{5} + 24\right)}^{\frac{1}{4}}\right)} + 320 \, \sqrt{2 \, \sqrt{5} + 5} {\left(\sqrt{5} - 4\right)}\right)} \sqrt{-20 \, \sqrt{2} \sqrt{\sqrt{5} + 3} {\left(\sqrt{5} - 3\right)} + 40 \, {\left(\sqrt{5} - 1\right)} e^{x} + 2 \, {\left(\sqrt{2} {\left({\left(2 \, \sqrt{5} - 5\right)} e^{x} - 3 \, \sqrt{5} + 5\right)} \sqrt{\sqrt{5} + 3} + 2 \, {\left(\sqrt{5} - 5\right)} e^{x} - 3 \, \sqrt{5} + 5\right)} \sqrt{2 \, \sqrt{2} {\left(2 \, \sqrt{5} - 5\right)} \sqrt{\sqrt{5} + 3} - 4 \, \sqrt{5} + 20} {\left(8 \, \sqrt{5} + 24\right)}^{\frac{1}{4}} + 80 \, e^{\left(2 \, x\right)} + 80} + \frac{1}{640} \, \sqrt{2 \, \sqrt{2} {\left(2 \, \sqrt{5} - 5\right)} \sqrt{\sqrt{5} + 3} - 4 \, \sqrt{5} + 20} {\left({\left(\sqrt{2} {\left({\left(3 \, \sqrt{5} - 7\right)} e^{x} + 8 \, \sqrt{5} - 18\right)} \sqrt{2 \, \sqrt{5} + 5} \sqrt{\sqrt{5} + 3} + 2 \, {\left({\left(5 \, \sqrt{5} - 11\right)} e^{x} + 2 \, \sqrt{5} - 4\right)} \sqrt{2 \, \sqrt{5} + 5}\right)} {\left(8 \, \sqrt{5} + 24\right)}^{\frac{3}{4}} + 4 \, {\left(\sqrt{2} {\left({\left(7 \, \sqrt{5} - 17\right)} e^{x} + 8 \, \sqrt{5} - 18\right)} \sqrt{2 \, \sqrt{5} + 5} \sqrt{\sqrt{5} + 3} + 2 \, {\left({\left(5 \, \sqrt{5} - 11\right)} e^{x} + 5 \, \sqrt{5} - 9\right)} \sqrt{2 \, \sqrt{5} + 5}\right)} {\left(8 \, \sqrt{5} + 24\right)}^{\frac{1}{4}}\right)} - \frac{1}{20} \, {\left(2 \, {\left(4 \, \sqrt{5} - 5\right)} e^{x} - \sqrt{5} + 5\right)} \sqrt{2 \, \sqrt{5} + 5}\right) + \frac{1}{400} \, \sqrt{-{\left(2 \, \sqrt{5} + 5\right)} \sqrt{-8 \, \sqrt{5} + 24} + 4 \, \sqrt{5} + 20} {\left(3 \, \sqrt{5} + 5\right)} \sqrt{-2 \, \sqrt{5} + 5} {\left(-8 \, \sqrt{5} + 24\right)}^{\frac{3}{4}} \arctan\left(-\frac{1}{1280} \, {\left({\left(4 \, {\left(5 \, \sqrt{5} + 11\right)} e^{x} + {\left({\left(3 \, \sqrt{5} + 7\right)} e^{x} + 8 \, \sqrt{5} + 18\right)} \sqrt{-8 \, \sqrt{5} + 24} + 8 \, \sqrt{5} + 16\right)} {\left(-8 \, \sqrt{5} + 24\right)}^{\frac{3}{4}} + 4 \, {\left(4 \, {\left(5 \, \sqrt{5} + 11\right)} e^{x} + {\left({\left(7 \, \sqrt{5} + 17\right)} e^{x} + 8 \, \sqrt{5} + 18\right)} \sqrt{-8 \, \sqrt{5} + 24} + 20 \, \sqrt{5} + 36\right)} {\left(-8 \, \sqrt{5} + 24\right)}^{\frac{1}{4}}\right)} \sqrt{-{\left(2 \, \sqrt{5} + 5\right)} \sqrt{-8 \, \sqrt{5} + 24} + 4 \, \sqrt{5} + 20} \sqrt{-2 \, \sqrt{5} + 5} + \frac{1}{25600} \, {\left({\left({\left({\left(7 \, \sqrt{5} + 15\right)} \sqrt{-8 \, \sqrt{5} + 24} + 44 \, \sqrt{5} + 100\right)} {\left(-8 \, \sqrt{5} + 24\right)}^{\frac{3}{4}} + 4 \, {\left({\left(17 \, \sqrt{5} + 35\right)} \sqrt{-8 \, \sqrt{5} + 24} + 44 \, \sqrt{5} + 100\right)} {\left(-8 \, \sqrt{5} + 24\right)}^{\frac{1}{4}}\right)} \sqrt{-{\left(2 \, \sqrt{5} + 5\right)} \sqrt{-8 \, \sqrt{5} + 24} + 4 \, \sqrt{5} + 20} \sqrt{-2 \, \sqrt{5} + 5} + 20 \, {\left({\left({\left(5 \, \sqrt{5} + 11\right)} \sqrt{-8 \, \sqrt{5} + 24} + 4 \, \sqrt{5} + 12\right)} \sqrt{-8 \, \sqrt{5} + 24} + 4 \, {\left(5 \, \sqrt{5} + 11\right)} \sqrt{-8 \, \sqrt{5} + 24} + 32 \, \sqrt{5} + 128\right)} \sqrt{-2 \, \sqrt{5} + 5}\right)} \sqrt{-40 \, {\left(\sqrt{5} + 1\right)} e^{x} + {\left(4 \, {\left(\sqrt{5} + 5\right)} e^{x} + {\left({\left(2 \, \sqrt{5} + 5\right)} e^{x} - 3 \, \sqrt{5} - 5\right)} \sqrt{-8 \, \sqrt{5} + 24} - 6 \, \sqrt{5} - 10\right)} \sqrt{-{\left(2 \, \sqrt{5} + 5\right)} \sqrt{-8 \, \sqrt{5} + 24} + 4 \, \sqrt{5} + 20} {\left(-8 \, \sqrt{5} + 24\right)}^{\frac{1}{4}} + 10 \, {\left(\sqrt{5} + 3\right)} \sqrt{-8 \, \sqrt{5} + 24} + 80 \, e^{\left(2 \, x\right)} + 80} - \frac{1}{320} \, {\left(32 \, {\left(4 \, \sqrt{5} + 5\right)} e^{x} + 4 \, {\left({\left(11 \, \sqrt{5} + 25\right)} e^{x} - 7 \, \sqrt{5} - 15\right)} \sqrt{-8 \, \sqrt{5} + 24} + {\left(4 \, {\left(3 \, \sqrt{5} + 5\right)} e^{x} + {\left({\left(11 \, \sqrt{5} + 25\right)} e^{x} + 4 \, \sqrt{5} + 10\right)} \sqrt{-8 \, \sqrt{5} + 24} + 28 \, \sqrt{5} + 60\right)} \sqrt{-8 \, \sqrt{5} + 24} - 16 \, \sqrt{5} - 80\right)} \sqrt{-2 \, \sqrt{5} + 5}\right) + \frac{1}{400} \, \sqrt{-{\left(2 \, \sqrt{5} + 5\right)} \sqrt{-8 \, \sqrt{5} + 24} + 4 \, \sqrt{5} + 20} {\left(3 \, \sqrt{5} + 5\right)} \sqrt{-2 \, \sqrt{5} + 5} {\left(-8 \, \sqrt{5} + 24\right)}^{\frac{3}{4}} \arctan\left(-\frac{1}{1280} \, {\left({\left(4 \, {\left(5 \, \sqrt{5} + 11\right)} e^{x} + {\left({\left(3 \, \sqrt{5} + 7\right)} e^{x} + 8 \, \sqrt{5} + 18\right)} \sqrt{-8 \, \sqrt{5} + 24} + 8 \, \sqrt{5} + 16\right)} {\left(-8 \, \sqrt{5} + 24\right)}^{\frac{3}{4}} + 4 \, {\left(4 \, {\left(5 \, \sqrt{5} + 11\right)} e^{x} + {\left({\left(7 \, \sqrt{5} + 17\right)} e^{x} + 8 \, \sqrt{5} + 18\right)} \sqrt{-8 \, \sqrt{5} + 24} + 20 \, \sqrt{5} + 36\right)} {\left(-8 \, \sqrt{5} + 24\right)}^{\frac{1}{4}}\right)} \sqrt{-{\left(2 \, \sqrt{5} + 5\right)} \sqrt{-8 \, \sqrt{5} + 24} + 4 \, \sqrt{5} + 20} \sqrt{-2 \, \sqrt{5} + 5} + \frac{1}{25600} \, {\left({\left({\left({\left(7 \, \sqrt{5} + 15\right)} \sqrt{-8 \, \sqrt{5} + 24} + 44 \, \sqrt{5} + 100\right)} {\left(-8 \, \sqrt{5} + 24\right)}^{\frac{3}{4}} + 4 \, {\left({\left(17 \, \sqrt{5} + 35\right)} \sqrt{-8 \, \sqrt{5} + 24} + 44 \, \sqrt{5} + 100\right)} {\left(-8 \, \sqrt{5} + 24\right)}^{\frac{1}{4}}\right)} \sqrt{-{\left(2 \, \sqrt{5} + 5\right)} \sqrt{-8 \, \sqrt{5} + 24} + 4 \, \sqrt{5} + 20} \sqrt{-2 \, \sqrt{5} + 5} - 20 \, {\left({\left({\left(5 \, \sqrt{5} + 11\right)} \sqrt{-8 \, \sqrt{5} + 24} + 4 \, \sqrt{5} + 12\right)} \sqrt{-8 \, \sqrt{5} + 24} + 4 \, {\left(5 \, \sqrt{5} + 11\right)} \sqrt{-8 \, \sqrt{5} + 24} + 32 \, \sqrt{5} + 128\right)} \sqrt{-2 \, \sqrt{5} + 5}\right)} \sqrt{-40 \, {\left(\sqrt{5} + 1\right)} e^{x} - {\left(4 \, {\left(\sqrt{5} + 5\right)} e^{x} + {\left({\left(2 \, \sqrt{5} + 5\right)} e^{x} - 3 \, \sqrt{5} - 5\right)} \sqrt{-8 \, \sqrt{5} + 24} - 6 \, \sqrt{5} - 10\right)} \sqrt{-{\left(2 \, \sqrt{5} + 5\right)} \sqrt{-8 \, \sqrt{5} + 24} + 4 \, \sqrt{5} + 20} {\left(-8 \, \sqrt{5} + 24\right)}^{\frac{1}{4}} + 10 \, {\left(\sqrt{5} + 3\right)} \sqrt{-8 \, \sqrt{5} + 24} + 80 \, e^{\left(2 \, x\right)} + 80} + \frac{1}{320} \, {\left(32 \, {\left(4 \, \sqrt{5} + 5\right)} e^{x} + 4 \, {\left({\left(11 \, \sqrt{5} + 25\right)} e^{x} - 7 \, \sqrt{5} - 15\right)} \sqrt{-8 \, \sqrt{5} + 24} + {\left(4 \, {\left(3 \, \sqrt{5} + 5\right)} e^{x} + {\left({\left(11 \, \sqrt{5} + 25\right)} e^{x} + 4 \, \sqrt{5} + 10\right)} \sqrt{-8 \, \sqrt{5} + 24} + 28 \, \sqrt{5} + 60\right)} \sqrt{-8 \, \sqrt{5} + 24} - 16 \, \sqrt{5} - 80\right)} \sqrt{-2 \, \sqrt{5} + 5}\right) + \frac{1}{800} \, {\left(\sqrt{2} {\left(3 \, \sqrt{5} - 5\right)} \sqrt{\sqrt{5} + 3} + 8 \, \sqrt{5}\right)} \sqrt{2 \, \sqrt{2} {\left(2 \, \sqrt{5} - 5\right)} \sqrt{\sqrt{5} + 3} - 4 \, \sqrt{5} + 20} {\left(8 \, \sqrt{5} + 24\right)}^{\frac{1}{4}} \log\left(-4 \, \sqrt{2} \sqrt{\sqrt{5} + 3} {\left(\sqrt{5} - 3\right)} + 8 \, {\left(\sqrt{5} - 1\right)} e^{x} + \frac{2}{5} \, {\left(\sqrt{2} {\left({\left(2 \, \sqrt{5} - 5\right)} e^{x} - 3 \, \sqrt{5} + 5\right)} \sqrt{\sqrt{5} + 3} + 2 \, {\left(\sqrt{5} - 5\right)} e^{x} - 3 \, \sqrt{5} + 5\right)} \sqrt{2 \, \sqrt{2} {\left(2 \, \sqrt{5} - 5\right)} \sqrt{\sqrt{5} + 3} - 4 \, \sqrt{5} + 20} {\left(8 \, \sqrt{5} + 24\right)}^{\frac{1}{4}} + 16 \, e^{\left(2 \, x\right)} + 16\right) - \frac{1}{800} \, {\left(\sqrt{2} {\left(3 \, \sqrt{5} - 5\right)} \sqrt{\sqrt{5} + 3} + 8 \, \sqrt{5}\right)} \sqrt{2 \, \sqrt{2} {\left(2 \, \sqrt{5} - 5\right)} \sqrt{\sqrt{5} + 3} - 4 \, \sqrt{5} + 20} {\left(8 \, \sqrt{5} + 24\right)}^{\frac{1}{4}} \log\left(-4 \, \sqrt{2} \sqrt{\sqrt{5} + 3} {\left(\sqrt{5} - 3\right)} + 8 \, {\left(\sqrt{5} - 1\right)} e^{x} - \frac{2}{5} \, {\left(\sqrt{2} {\left({\left(2 \, \sqrt{5} - 5\right)} e^{x} - 3 \, \sqrt{5} + 5\right)} \sqrt{\sqrt{5} + 3} + 2 \, {\left(\sqrt{5} - 5\right)} e^{x} - 3 \, \sqrt{5} + 5\right)} \sqrt{2 \, \sqrt{2} {\left(2 \, \sqrt{5} - 5\right)} \sqrt{\sqrt{5} + 3} - 4 \, \sqrt{5} + 20} {\left(8 \, \sqrt{5} + 24\right)}^{\frac{1}{4}} + 16 \, e^{\left(2 \, x\right)} + 16\right) + \frac{1}{1600} \, {\left({\left(3 \, \sqrt{5} + 5\right)} \sqrt{-8 \, \sqrt{5} + 24} + 16 \, \sqrt{5}\right)} \sqrt{-{\left(2 \, \sqrt{5} + 5\right)} \sqrt{-8 \, \sqrt{5} + 24} + 4 \, \sqrt{5} + 20} {\left(-8 \, \sqrt{5} + 24\right)}^{\frac{1}{4}} \log\left(-8 \, {\left(\sqrt{5} + 1\right)} e^{x} + \frac{1}{5} \, {\left(4 \, {\left(\sqrt{5} + 5\right)} e^{x} + {\left({\left(2 \, \sqrt{5} + 5\right)} e^{x} - 3 \, \sqrt{5} - 5\right)} \sqrt{-8 \, \sqrt{5} + 24} - 6 \, \sqrt{5} - 10\right)} \sqrt{-{\left(2 \, \sqrt{5} + 5\right)} \sqrt{-8 \, \sqrt{5} + 24} + 4 \, \sqrt{5} + 20} {\left(-8 \, \sqrt{5} + 24\right)}^{\frac{1}{4}} + 2 \, {\left(\sqrt{5} + 3\right)} \sqrt{-8 \, \sqrt{5} + 24} + 16 \, e^{\left(2 \, x\right)} + 16\right) - \frac{1}{1600} \, {\left({\left(3 \, \sqrt{5} + 5\right)} \sqrt{-8 \, \sqrt{5} + 24} + 16 \, \sqrt{5}\right)} \sqrt{-{\left(2 \, \sqrt{5} + 5\right)} \sqrt{-8 \, \sqrt{5} + 24} + 4 \, \sqrt{5} + 20} {\left(-8 \, \sqrt{5} + 24\right)}^{\frac{1}{4}} \log\left(-8 \, {\left(\sqrt{5} + 1\right)} e^{x} - \frac{1}{5} \, {\left(4 \, {\left(\sqrt{5} + 5\right)} e^{x} + {\left({\left(2 \, \sqrt{5} + 5\right)} e^{x} - 3 \, \sqrt{5} - 5\right)} \sqrt{-8 \, \sqrt{5} + 24} - 6 \, \sqrt{5} - 10\right)} \sqrt{-{\left(2 \, \sqrt{5} + 5\right)} \sqrt{-8 \, \sqrt{5} + 24} + 4 \, \sqrt{5} + 20} {\left(-8 \, \sqrt{5} + 24\right)}^{\frac{1}{4}} + 2 \, {\left(\sqrt{5} + 3\right)} \sqrt{-8 \, \sqrt{5} + 24} + 16 \, e^{\left(2 \, x\right)} + 16\right) + \frac{1}{10} \, \sqrt{2} \log\left(-\frac{2 \, {\left(\sqrt{2} - 1\right)} e^{x} + 2 \, \sqrt{2} - e^{\left(2 \, x\right)} - 3}{e^{\left(2 \, x\right)} + 2 \, e^{x} - 1}\right)"," ",0,"-1/200*sqrt(2)*sqrt(2*sqrt(2)*(2*sqrt(5) - 5)*sqrt(sqrt(5) + 3) - 4*sqrt(5) + 20)*(8*sqrt(5) + 24)^(1/4)*(3*sqrt(5) - 5)*sqrt(2*sqrt(5) + 5)*sqrt(sqrt(5) + 3)*arctan(1/40*sqrt(2)*((11*sqrt(5) - 25)*e^x - 7*sqrt(5) + 15)*sqrt(2*sqrt(5) + 5)*sqrt(sqrt(5) + 3) + 1/80*sqrt(2)*(sqrt(2)*((11*sqrt(5) - 25)*e^x + 4*sqrt(5) - 10)*sqrt(2*sqrt(5) + 5)*sqrt(sqrt(5) + 3) + 2*((3*sqrt(5) - 5)*e^x + 7*sqrt(5) - 15)*sqrt(2*sqrt(5) + 5))*sqrt(sqrt(5) + 3) + 1/12800*(80*sqrt(2)*(5*sqrt(5) - 11)*sqrt(2*sqrt(5) + 5)*sqrt(sqrt(5) + 3) + 40*sqrt(2)*(sqrt(2)*(5*sqrt(5) - 11)*sqrt(2*sqrt(5) + 5)*sqrt(sqrt(5) + 3) + 2*sqrt(2*sqrt(5) + 5)*(sqrt(5) - 3))*sqrt(sqrt(5) + 3) + sqrt(2*sqrt(2)*(2*sqrt(5) - 5)*sqrt(sqrt(5) + 3) - 4*sqrt(5) + 20)*((sqrt(2)*(7*sqrt(5) - 15)*sqrt(2*sqrt(5) + 5)*sqrt(sqrt(5) + 3) + 2*(11*sqrt(5) - 25)*sqrt(2*sqrt(5) + 5))*(8*sqrt(5) + 24)^(3/4) + 4*(sqrt(2)*(17*sqrt(5) - 35)*sqrt(2*sqrt(5) + 5)*sqrt(sqrt(5) + 3) + 2*(11*sqrt(5) - 25)*sqrt(2*sqrt(5) + 5))*(8*sqrt(5) + 24)^(1/4)) + 320*sqrt(2*sqrt(5) + 5)*(sqrt(5) - 4))*sqrt(-20*sqrt(2)*sqrt(sqrt(5) + 3)*(sqrt(5) - 3) + 40*(sqrt(5) - 1)*e^x - 2*(sqrt(2)*((2*sqrt(5) - 5)*e^x - 3*sqrt(5) + 5)*sqrt(sqrt(5) + 3) + 2*(sqrt(5) - 5)*e^x - 3*sqrt(5) + 5)*sqrt(2*sqrt(2)*(2*sqrt(5) - 5)*sqrt(sqrt(5) + 3) - 4*sqrt(5) + 20)*(8*sqrt(5) + 24)^(1/4) + 80*e^(2*x) + 80) + 1/640*sqrt(2*sqrt(2)*(2*sqrt(5) - 5)*sqrt(sqrt(5) + 3) - 4*sqrt(5) + 20)*((sqrt(2)*((3*sqrt(5) - 7)*e^x + 8*sqrt(5) - 18)*sqrt(2*sqrt(5) + 5)*sqrt(sqrt(5) + 3) + 2*((5*sqrt(5) - 11)*e^x + 2*sqrt(5) - 4)*sqrt(2*sqrt(5) + 5))*(8*sqrt(5) + 24)^(3/4) + 4*(sqrt(2)*((7*sqrt(5) - 17)*e^x + 8*sqrt(5) - 18)*sqrt(2*sqrt(5) + 5)*sqrt(sqrt(5) + 3) + 2*((5*sqrt(5) - 11)*e^x + 5*sqrt(5) - 9)*sqrt(2*sqrt(5) + 5))*(8*sqrt(5) + 24)^(1/4)) + 1/20*(2*(4*sqrt(5) - 5)*e^x - sqrt(5) + 5)*sqrt(2*sqrt(5) + 5)) - 1/200*sqrt(2)*sqrt(2*sqrt(2)*(2*sqrt(5) - 5)*sqrt(sqrt(5) + 3) - 4*sqrt(5) + 20)*(8*sqrt(5) + 24)^(1/4)*(3*sqrt(5) - 5)*sqrt(2*sqrt(5) + 5)*sqrt(sqrt(5) + 3)*arctan(-1/40*sqrt(2)*((11*sqrt(5) - 25)*e^x - 7*sqrt(5) + 15)*sqrt(2*sqrt(5) + 5)*sqrt(sqrt(5) + 3) - 1/80*sqrt(2)*(sqrt(2)*((11*sqrt(5) - 25)*e^x + 4*sqrt(5) - 10)*sqrt(2*sqrt(5) + 5)*sqrt(sqrt(5) + 3) + 2*((3*sqrt(5) - 5)*e^x + 7*sqrt(5) - 15)*sqrt(2*sqrt(5) + 5))*sqrt(sqrt(5) + 3) - 1/12800*(80*sqrt(2)*(5*sqrt(5) - 11)*sqrt(2*sqrt(5) + 5)*sqrt(sqrt(5) + 3) + 40*sqrt(2)*(sqrt(2)*(5*sqrt(5) - 11)*sqrt(2*sqrt(5) + 5)*sqrt(sqrt(5) + 3) + 2*sqrt(2*sqrt(5) + 5)*(sqrt(5) - 3))*sqrt(sqrt(5) + 3) - sqrt(2*sqrt(2)*(2*sqrt(5) - 5)*sqrt(sqrt(5) + 3) - 4*sqrt(5) + 20)*((sqrt(2)*(7*sqrt(5) - 15)*sqrt(2*sqrt(5) + 5)*sqrt(sqrt(5) + 3) + 2*(11*sqrt(5) - 25)*sqrt(2*sqrt(5) + 5))*(8*sqrt(5) + 24)^(3/4) + 4*(sqrt(2)*(17*sqrt(5) - 35)*sqrt(2*sqrt(5) + 5)*sqrt(sqrt(5) + 3) + 2*(11*sqrt(5) - 25)*sqrt(2*sqrt(5) + 5))*(8*sqrt(5) + 24)^(1/4)) + 320*sqrt(2*sqrt(5) + 5)*(sqrt(5) - 4))*sqrt(-20*sqrt(2)*sqrt(sqrt(5) + 3)*(sqrt(5) - 3) + 40*(sqrt(5) - 1)*e^x + 2*(sqrt(2)*((2*sqrt(5) - 5)*e^x - 3*sqrt(5) + 5)*sqrt(sqrt(5) + 3) + 2*(sqrt(5) - 5)*e^x - 3*sqrt(5) + 5)*sqrt(2*sqrt(2)*(2*sqrt(5) - 5)*sqrt(sqrt(5) + 3) - 4*sqrt(5) + 20)*(8*sqrt(5) + 24)^(1/4) + 80*e^(2*x) + 80) + 1/640*sqrt(2*sqrt(2)*(2*sqrt(5) - 5)*sqrt(sqrt(5) + 3) - 4*sqrt(5) + 20)*((sqrt(2)*((3*sqrt(5) - 7)*e^x + 8*sqrt(5) - 18)*sqrt(2*sqrt(5) + 5)*sqrt(sqrt(5) + 3) + 2*((5*sqrt(5) - 11)*e^x + 2*sqrt(5) - 4)*sqrt(2*sqrt(5) + 5))*(8*sqrt(5) + 24)^(3/4) + 4*(sqrt(2)*((7*sqrt(5) - 17)*e^x + 8*sqrt(5) - 18)*sqrt(2*sqrt(5) + 5)*sqrt(sqrt(5) + 3) + 2*((5*sqrt(5) - 11)*e^x + 5*sqrt(5) - 9)*sqrt(2*sqrt(5) + 5))*(8*sqrt(5) + 24)^(1/4)) - 1/20*(2*(4*sqrt(5) - 5)*e^x - sqrt(5) + 5)*sqrt(2*sqrt(5) + 5)) + 1/400*sqrt(-(2*sqrt(5) + 5)*sqrt(-8*sqrt(5) + 24) + 4*sqrt(5) + 20)*(3*sqrt(5) + 5)*sqrt(-2*sqrt(5) + 5)*(-8*sqrt(5) + 24)^(3/4)*arctan(-1/1280*((4*(5*sqrt(5) + 11)*e^x + ((3*sqrt(5) + 7)*e^x + 8*sqrt(5) + 18)*sqrt(-8*sqrt(5) + 24) + 8*sqrt(5) + 16)*(-8*sqrt(5) + 24)^(3/4) + 4*(4*(5*sqrt(5) + 11)*e^x + ((7*sqrt(5) + 17)*e^x + 8*sqrt(5) + 18)*sqrt(-8*sqrt(5) + 24) + 20*sqrt(5) + 36)*(-8*sqrt(5) + 24)^(1/4))*sqrt(-(2*sqrt(5) + 5)*sqrt(-8*sqrt(5) + 24) + 4*sqrt(5) + 20)*sqrt(-2*sqrt(5) + 5) + 1/25600*((((7*sqrt(5) + 15)*sqrt(-8*sqrt(5) + 24) + 44*sqrt(5) + 100)*(-8*sqrt(5) + 24)^(3/4) + 4*((17*sqrt(5) + 35)*sqrt(-8*sqrt(5) + 24) + 44*sqrt(5) + 100)*(-8*sqrt(5) + 24)^(1/4))*sqrt(-(2*sqrt(5) + 5)*sqrt(-8*sqrt(5) + 24) + 4*sqrt(5) + 20)*sqrt(-2*sqrt(5) + 5) + 20*(((5*sqrt(5) + 11)*sqrt(-8*sqrt(5) + 24) + 4*sqrt(5) + 12)*sqrt(-8*sqrt(5) + 24) + 4*(5*sqrt(5) + 11)*sqrt(-8*sqrt(5) + 24) + 32*sqrt(5) + 128)*sqrt(-2*sqrt(5) + 5))*sqrt(-40*(sqrt(5) + 1)*e^x + (4*(sqrt(5) + 5)*e^x + ((2*sqrt(5) + 5)*e^x - 3*sqrt(5) - 5)*sqrt(-8*sqrt(5) + 24) - 6*sqrt(5) - 10)*sqrt(-(2*sqrt(5) + 5)*sqrt(-8*sqrt(5) + 24) + 4*sqrt(5) + 20)*(-8*sqrt(5) + 24)^(1/4) + 10*(sqrt(5) + 3)*sqrt(-8*sqrt(5) + 24) + 80*e^(2*x) + 80) - 1/320*(32*(4*sqrt(5) + 5)*e^x + 4*((11*sqrt(5) + 25)*e^x - 7*sqrt(5) - 15)*sqrt(-8*sqrt(5) + 24) + (4*(3*sqrt(5) + 5)*e^x + ((11*sqrt(5) + 25)*e^x + 4*sqrt(5) + 10)*sqrt(-8*sqrt(5) + 24) + 28*sqrt(5) + 60)*sqrt(-8*sqrt(5) + 24) - 16*sqrt(5) - 80)*sqrt(-2*sqrt(5) + 5)) + 1/400*sqrt(-(2*sqrt(5) + 5)*sqrt(-8*sqrt(5) + 24) + 4*sqrt(5) + 20)*(3*sqrt(5) + 5)*sqrt(-2*sqrt(5) + 5)*(-8*sqrt(5) + 24)^(3/4)*arctan(-1/1280*((4*(5*sqrt(5) + 11)*e^x + ((3*sqrt(5) + 7)*e^x + 8*sqrt(5) + 18)*sqrt(-8*sqrt(5) + 24) + 8*sqrt(5) + 16)*(-8*sqrt(5) + 24)^(3/4) + 4*(4*(5*sqrt(5) + 11)*e^x + ((7*sqrt(5) + 17)*e^x + 8*sqrt(5) + 18)*sqrt(-8*sqrt(5) + 24) + 20*sqrt(5) + 36)*(-8*sqrt(5) + 24)^(1/4))*sqrt(-(2*sqrt(5) + 5)*sqrt(-8*sqrt(5) + 24) + 4*sqrt(5) + 20)*sqrt(-2*sqrt(5) + 5) + 1/25600*((((7*sqrt(5) + 15)*sqrt(-8*sqrt(5) + 24) + 44*sqrt(5) + 100)*(-8*sqrt(5) + 24)^(3/4) + 4*((17*sqrt(5) + 35)*sqrt(-8*sqrt(5) + 24) + 44*sqrt(5) + 100)*(-8*sqrt(5) + 24)^(1/4))*sqrt(-(2*sqrt(5) + 5)*sqrt(-8*sqrt(5) + 24) + 4*sqrt(5) + 20)*sqrt(-2*sqrt(5) + 5) - 20*(((5*sqrt(5) + 11)*sqrt(-8*sqrt(5) + 24) + 4*sqrt(5) + 12)*sqrt(-8*sqrt(5) + 24) + 4*(5*sqrt(5) + 11)*sqrt(-8*sqrt(5) + 24) + 32*sqrt(5) + 128)*sqrt(-2*sqrt(5) + 5))*sqrt(-40*(sqrt(5) + 1)*e^x - (4*(sqrt(5) + 5)*e^x + ((2*sqrt(5) + 5)*e^x - 3*sqrt(5) - 5)*sqrt(-8*sqrt(5) + 24) - 6*sqrt(5) - 10)*sqrt(-(2*sqrt(5) + 5)*sqrt(-8*sqrt(5) + 24) + 4*sqrt(5) + 20)*(-8*sqrt(5) + 24)^(1/4) + 10*(sqrt(5) + 3)*sqrt(-8*sqrt(5) + 24) + 80*e^(2*x) + 80) + 1/320*(32*(4*sqrt(5) + 5)*e^x + 4*((11*sqrt(5) + 25)*e^x - 7*sqrt(5) - 15)*sqrt(-8*sqrt(5) + 24) + (4*(3*sqrt(5) + 5)*e^x + ((11*sqrt(5) + 25)*e^x + 4*sqrt(5) + 10)*sqrt(-8*sqrt(5) + 24) + 28*sqrt(5) + 60)*sqrt(-8*sqrt(5) + 24) - 16*sqrt(5) - 80)*sqrt(-2*sqrt(5) + 5)) + 1/800*(sqrt(2)*(3*sqrt(5) - 5)*sqrt(sqrt(5) + 3) + 8*sqrt(5))*sqrt(2*sqrt(2)*(2*sqrt(5) - 5)*sqrt(sqrt(5) + 3) - 4*sqrt(5) + 20)*(8*sqrt(5) + 24)^(1/4)*log(-4*sqrt(2)*sqrt(sqrt(5) + 3)*(sqrt(5) - 3) + 8*(sqrt(5) - 1)*e^x + 2/5*(sqrt(2)*((2*sqrt(5) - 5)*e^x - 3*sqrt(5) + 5)*sqrt(sqrt(5) + 3) + 2*(sqrt(5) - 5)*e^x - 3*sqrt(5) + 5)*sqrt(2*sqrt(2)*(2*sqrt(5) - 5)*sqrt(sqrt(5) + 3) - 4*sqrt(5) + 20)*(8*sqrt(5) + 24)^(1/4) + 16*e^(2*x) + 16) - 1/800*(sqrt(2)*(3*sqrt(5) - 5)*sqrt(sqrt(5) + 3) + 8*sqrt(5))*sqrt(2*sqrt(2)*(2*sqrt(5) - 5)*sqrt(sqrt(5) + 3) - 4*sqrt(5) + 20)*(8*sqrt(5) + 24)^(1/4)*log(-4*sqrt(2)*sqrt(sqrt(5) + 3)*(sqrt(5) - 3) + 8*(sqrt(5) - 1)*e^x - 2/5*(sqrt(2)*((2*sqrt(5) - 5)*e^x - 3*sqrt(5) + 5)*sqrt(sqrt(5) + 3) + 2*(sqrt(5) - 5)*e^x - 3*sqrt(5) + 5)*sqrt(2*sqrt(2)*(2*sqrt(5) - 5)*sqrt(sqrt(5) + 3) - 4*sqrt(5) + 20)*(8*sqrt(5) + 24)^(1/4) + 16*e^(2*x) + 16) + 1/1600*((3*sqrt(5) + 5)*sqrt(-8*sqrt(5) + 24) + 16*sqrt(5))*sqrt(-(2*sqrt(5) + 5)*sqrt(-8*sqrt(5) + 24) + 4*sqrt(5) + 20)*(-8*sqrt(5) + 24)^(1/4)*log(-8*(sqrt(5) + 1)*e^x + 1/5*(4*(sqrt(5) + 5)*e^x + ((2*sqrt(5) + 5)*e^x - 3*sqrt(5) - 5)*sqrt(-8*sqrt(5) + 24) - 6*sqrt(5) - 10)*sqrt(-(2*sqrt(5) + 5)*sqrt(-8*sqrt(5) + 24) + 4*sqrt(5) + 20)*(-8*sqrt(5) + 24)^(1/4) + 2*(sqrt(5) + 3)*sqrt(-8*sqrt(5) + 24) + 16*e^(2*x) + 16) - 1/1600*((3*sqrt(5) + 5)*sqrt(-8*sqrt(5) + 24) + 16*sqrt(5))*sqrt(-(2*sqrt(5) + 5)*sqrt(-8*sqrt(5) + 24) + 4*sqrt(5) + 20)*(-8*sqrt(5) + 24)^(1/4)*log(-8*(sqrt(5) + 1)*e^x - 1/5*(4*(sqrt(5) + 5)*e^x + ((2*sqrt(5) + 5)*e^x - 3*sqrt(5) - 5)*sqrt(-8*sqrt(5) + 24) - 6*sqrt(5) - 10)*sqrt(-(2*sqrt(5) + 5)*sqrt(-8*sqrt(5) + 24) + 4*sqrt(5) + 20)*(-8*sqrt(5) + 24)^(1/4) + 2*(sqrt(5) + 3)*sqrt(-8*sqrt(5) + 24) + 16*e^(2*x) + 16) + 1/10*sqrt(2)*log(-(2*(sqrt(2) - 1)*e^x + 2*sqrt(2) - e^(2*x) - 3)/(e^(2*x) + 2*e^x - 1))","B",0
271,1,692,0,1.079938," ","integrate(1/(1+sinh(x)^6),x, algorithm=""fricas"")","-\frac{4 \, {\left(12^{\frac{1}{4}} \sqrt{6} e^{\left(2 \, x\right)} + 12^{\frac{1}{4}} \sqrt{6}\right)} \sqrt{-4 \, \sqrt{3} + 8} \arctan\left({\left(\sqrt{3} + 2\right)} e^{\left(2 \, x\right)} + \frac{1}{216} \, \sqrt{-6 \, {\left(12^{\frac{1}{4}} \sqrt{6} {\left(\sqrt{3} + 3\right)} e^{\left(2 \, x\right)} - 12^{\frac{1}{4}} \sqrt{6} {\left(5 \, \sqrt{3} + 9\right)}\right)} \sqrt{-4 \, \sqrt{3} + 8} + 144 \, \sqrt{3} + 36 \, e^{\left(4 \, x\right)} - 144 \, e^{\left(2 \, x\right)} + 252} {\left({\left(12^{\frac{3}{4}} \sqrt{6} {\left(\sqrt{3} + 3\right)} + 3 \cdot 12^{\frac{1}{4}} \sqrt{6} {\left(\sqrt{3} + 3\right)}\right)} \sqrt{-4 \, \sqrt{3} + 8} - 36 \, \sqrt{3} - 72\right)} - \frac{2}{3} \, \sqrt{3} {\left(2 \, \sqrt{3} - 3\right)} - \frac{1}{36} \, {\left(12^{\frac{3}{4}} \sqrt{6} {\left(\sqrt{3} - 3\right)} + {\left(12^{\frac{3}{4}} \sqrt{6} {\left(\sqrt{3} + 3\right)} + 3 \cdot 12^{\frac{1}{4}} \sqrt{6} {\left(\sqrt{3} + 3\right)}\right)} e^{\left(2 \, x\right)} + 3 \cdot 12^{\frac{1}{4}} \sqrt{6} {\left(\sqrt{3} - 3\right)}\right)} \sqrt{-4 \, \sqrt{3} + 8} - 2 \, \sqrt{3} + 4\right) + 4 \, {\left(12^{\frac{1}{4}} \sqrt{6} e^{\left(2 \, x\right)} + 12^{\frac{1}{4}} \sqrt{6}\right)} \sqrt{-4 \, \sqrt{3} + 8} \arctan\left(-{\left(\sqrt{3} + 2\right)} e^{\left(2 \, x\right)} + \frac{1}{216} \, \sqrt{6 \, {\left(12^{\frac{1}{4}} \sqrt{6} {\left(\sqrt{3} + 3\right)} e^{\left(2 \, x\right)} - 12^{\frac{1}{4}} \sqrt{6} {\left(5 \, \sqrt{3} + 9\right)}\right)} \sqrt{-4 \, \sqrt{3} + 8} + 144 \, \sqrt{3} + 36 \, e^{\left(4 \, x\right)} - 144 \, e^{\left(2 \, x\right)} + 252} {\left({\left(12^{\frac{3}{4}} \sqrt{6} {\left(\sqrt{3} + 3\right)} + 3 \cdot 12^{\frac{1}{4}} \sqrt{6} {\left(\sqrt{3} + 3\right)}\right)} \sqrt{-4 \, \sqrt{3} + 8} + 36 \, \sqrt{3} + 72\right)} + \frac{2}{3} \, \sqrt{3} {\left(2 \, \sqrt{3} - 3\right)} - \frac{1}{36} \, {\left(12^{\frac{3}{4}} \sqrt{6} {\left(\sqrt{3} - 3\right)} + {\left(12^{\frac{3}{4}} \sqrt{6} {\left(\sqrt{3} + 3\right)} + 3 \cdot 12^{\frac{1}{4}} \sqrt{6} {\left(\sqrt{3} + 3\right)}\right)} e^{\left(2 \, x\right)} + 3 \cdot 12^{\frac{1}{4}} \sqrt{6} {\left(\sqrt{3} - 3\right)}\right)} \sqrt{-4 \, \sqrt{3} + 8} + 2 \, \sqrt{3} - 4\right) - {\left(12^{\frac{1}{4}} \sqrt{6} {\left(\sqrt{3} + 2\right)} e^{\left(2 \, x\right)} + 12^{\frac{1}{4}} \sqrt{6} {\left(\sqrt{3} + 2\right)}\right)} \sqrt{-4 \, \sqrt{3} + 8} \log\left(6 \, {\left(12^{\frac{1}{4}} \sqrt{6} {\left(\sqrt{3} + 3\right)} e^{\left(2 \, x\right)} - 12^{\frac{1}{4}} \sqrt{6} {\left(5 \, \sqrt{3} + 9\right)}\right)} \sqrt{-4 \, \sqrt{3} + 8} + 144 \, \sqrt{3} + 36 \, e^{\left(4 \, x\right)} - 144 \, e^{\left(2 \, x\right)} + 252\right) + {\left(12^{\frac{1}{4}} \sqrt{6} {\left(\sqrt{3} + 2\right)} e^{\left(2 \, x\right)} + 12^{\frac{1}{4}} \sqrt{6} {\left(\sqrt{3} + 2\right)}\right)} \sqrt{-4 \, \sqrt{3} + 8} \log\left(-6 \, {\left(12^{\frac{1}{4}} \sqrt{6} {\left(\sqrt{3} + 3\right)} e^{\left(2 \, x\right)} - 12^{\frac{1}{4}} \sqrt{6} {\left(5 \, \sqrt{3} + 9\right)}\right)} \sqrt{-4 \, \sqrt{3} + 8} + 144 \, \sqrt{3} + 36 \, e^{\left(4 \, x\right)} - 144 \, e^{\left(2 \, x\right)} + 252\right) + 96}{144 \, {\left(e^{\left(2 \, x\right)} + 1\right)}}"," ",0,"-1/144*(4*(12^(1/4)*sqrt(6)*e^(2*x) + 12^(1/4)*sqrt(6))*sqrt(-4*sqrt(3) + 8)*arctan((sqrt(3) + 2)*e^(2*x) + 1/216*sqrt(-6*(12^(1/4)*sqrt(6)*(sqrt(3) + 3)*e^(2*x) - 12^(1/4)*sqrt(6)*(5*sqrt(3) + 9))*sqrt(-4*sqrt(3) + 8) + 144*sqrt(3) + 36*e^(4*x) - 144*e^(2*x) + 252)*((12^(3/4)*sqrt(6)*(sqrt(3) + 3) + 3*12^(1/4)*sqrt(6)*(sqrt(3) + 3))*sqrt(-4*sqrt(3) + 8) - 36*sqrt(3) - 72) - 2/3*sqrt(3)*(2*sqrt(3) - 3) - 1/36*(12^(3/4)*sqrt(6)*(sqrt(3) - 3) + (12^(3/4)*sqrt(6)*(sqrt(3) + 3) + 3*12^(1/4)*sqrt(6)*(sqrt(3) + 3))*e^(2*x) + 3*12^(1/4)*sqrt(6)*(sqrt(3) - 3))*sqrt(-4*sqrt(3) + 8) - 2*sqrt(3) + 4) + 4*(12^(1/4)*sqrt(6)*e^(2*x) + 12^(1/4)*sqrt(6))*sqrt(-4*sqrt(3) + 8)*arctan(-(sqrt(3) + 2)*e^(2*x) + 1/216*sqrt(6*(12^(1/4)*sqrt(6)*(sqrt(3) + 3)*e^(2*x) - 12^(1/4)*sqrt(6)*(5*sqrt(3) + 9))*sqrt(-4*sqrt(3) + 8) + 144*sqrt(3) + 36*e^(4*x) - 144*e^(2*x) + 252)*((12^(3/4)*sqrt(6)*(sqrt(3) + 3) + 3*12^(1/4)*sqrt(6)*(sqrt(3) + 3))*sqrt(-4*sqrt(3) + 8) + 36*sqrt(3) + 72) + 2/3*sqrt(3)*(2*sqrt(3) - 3) - 1/36*(12^(3/4)*sqrt(6)*(sqrt(3) - 3) + (12^(3/4)*sqrt(6)*(sqrt(3) + 3) + 3*12^(1/4)*sqrt(6)*(sqrt(3) + 3))*e^(2*x) + 3*12^(1/4)*sqrt(6)*(sqrt(3) - 3))*sqrt(-4*sqrt(3) + 8) + 2*sqrt(3) - 4) - (12^(1/4)*sqrt(6)*(sqrt(3) + 2)*e^(2*x) + 12^(1/4)*sqrt(6)*(sqrt(3) + 2))*sqrt(-4*sqrt(3) + 8)*log(6*(12^(1/4)*sqrt(6)*(sqrt(3) + 3)*e^(2*x) - 12^(1/4)*sqrt(6)*(5*sqrt(3) + 9))*sqrt(-4*sqrt(3) + 8) + 144*sqrt(3) + 36*e^(4*x) - 144*e^(2*x) + 252) + (12^(1/4)*sqrt(6)*(sqrt(3) + 2)*e^(2*x) + 12^(1/4)*sqrt(6)*(sqrt(3) + 2))*sqrt(-4*sqrt(3) + 8)*log(-6*(12^(1/4)*sqrt(6)*(sqrt(3) + 3)*e^(2*x) - 12^(1/4)*sqrt(6)*(5*sqrt(3) + 9))*sqrt(-4*sqrt(3) + 8) + 144*sqrt(3) + 36*e^(4*x) - 144*e^(2*x) + 252) + 96)/(e^(2*x) + 1)","B",0
272,1,3773,0,2.760463," ","integrate(1/(1+sinh(x)^8),x, algorithm=""fricas"")","\frac{1}{16} \, \sqrt{2 \, \sqrt{2 \, \sqrt{2} + 4} {\left(2 \, \sqrt{2} - 3\right)} - 4 \, \sqrt{2} + 8} {\left(2 \, \sqrt{2} + 4\right)}^{\frac{3}{4}} \sqrt{2 \, \sqrt{2} + 3} {\left(\sqrt{2} - 1\right)} \arctan\left(\frac{1}{31} \, {\left(2 \, {\left(13 \, \sqrt{2} - 20\right)} e^{\left(2 \, x\right)} + 23 \, \sqrt{2} - 33\right)} \sqrt{2 \, \sqrt{2} + 4} \sqrt{2 \, \sqrt{2} + 3} + \frac{1}{496} \, {\left(32 \, {\left(10 \, \sqrt{2} - 13\right)} \sqrt{2 \, \sqrt{2} + 4} \sqrt{2 \, \sqrt{2} + 3} + {\left({\left({\left(355 \, \sqrt{2} - 508\right)} \sqrt{2 \, \sqrt{2} + 4} \sqrt{2 \, \sqrt{2} + 3} + 6 \, {\left(59 \, \sqrt{2} - 86\right)} \sqrt{2 \, \sqrt{2} + 3}\right)} {\left(2 \, \sqrt{2} + 4\right)}^{\frac{3}{4}} + 4 \, {\left({\left(82 \, \sqrt{2} - 119\right)} \sqrt{2 \, \sqrt{2} + 4} \sqrt{2 \, \sqrt{2} + 3} + {\left(85 \, \sqrt{2} - 126\right)} \sqrt{2 \, \sqrt{2} + 3}\right)} {\left(2 \, \sqrt{2} + 4\right)}^{\frac{1}{4}}\right)} \sqrt{2 \, \sqrt{2 \, \sqrt{2} + 4} {\left(2 \, \sqrt{2} - 3\right)} - 4 \, \sqrt{2} + 8} + 4 \, {\left({\left(76 \, \sqrt{2} - 105\right)} \sqrt{2 \, \sqrt{2} + 4} \sqrt{2 \, \sqrt{2} + 3} + 2 \, {\left(53 \, \sqrt{2} - 72\right)} \sqrt{2 \, \sqrt{2} + 3}\right)} \sqrt{2 \, \sqrt{2} + 4} + 16 \, {\left(23 \, \sqrt{2} - 33\right)} \sqrt{2 \, \sqrt{2} + 3}\right)} \sqrt{4 \, {\left(\sqrt{2} - 1\right)} e^{\left(2 \, x\right)} - {\left(2 \, {\left(\sqrt{2} - 1\right)} e^{\left(2 \, x\right)} + {\left({\left(\sqrt{2} - 2\right)} e^{\left(2 \, x\right)} - 5 \, \sqrt{2} + 6\right)} \sqrt{2 \, \sqrt{2} + 4} - 6 \, \sqrt{2} + 6\right)} \sqrt{2 \, \sqrt{2 \, \sqrt{2} + 4} {\left(2 \, \sqrt{2} - 3\right)} - 4 \, \sqrt{2} + 8} {\left(2 \, \sqrt{2} + 4\right)}^{\frac{1}{4}} - 4 \, \sqrt{2 \, \sqrt{2} + 4} {\left(\sqrt{2} - 2\right)} - 4 \, \sqrt{2} + 2 \, e^{\left(4 \, x\right)} + 10} + \frac{1}{248} \, {\left({\left({\left({\left(254 \, \sqrt{2} - 355\right)} e^{\left(2 \, x\right)} - 102 \, \sqrt{2} + 145\right)} \sqrt{2 \, \sqrt{2} + 4} \sqrt{2 \, \sqrt{2} + 3} + 2 \, {\left(3 \, {\left(43 \, \sqrt{2} - 59\right)} e^{\left(2 \, x\right)} - 23 \, \sqrt{2} + 33\right)} \sqrt{2 \, \sqrt{2} + 3}\right)} {\left(2 \, \sqrt{2} + 4\right)}^{\frac{3}{4}} + 2 \, {\left({\left({\left(119 \, \sqrt{2} - 164\right)} e^{\left(2 \, x\right)} - 39 \, \sqrt{2} + 60\right)} \sqrt{2 \, \sqrt{2} + 4} \sqrt{2 \, \sqrt{2} + 3} + 2 \, {\left({\left(63 \, \sqrt{2} - 85\right)} e^{\left(2 \, x\right)} - 17 \, \sqrt{2} + 19\right)} \sqrt{2 \, \sqrt{2} + 3}\right)} {\left(2 \, \sqrt{2} + 4\right)}^{\frac{1}{4}}\right)} \sqrt{2 \, \sqrt{2 \, \sqrt{2} + 4} {\left(2 \, \sqrt{2} - 3\right)} - 4 \, \sqrt{2} + 8} + \frac{1}{124} \, {\left({\left({\left(105 \, \sqrt{2} - 152\right)} e^{\left(2 \, x\right)} + 13 \, \sqrt{2} - 20\right)} \sqrt{2 \, \sqrt{2} + 4} \sqrt{2 \, \sqrt{2} + 3} + 4 \, {\left({\left(36 \, \sqrt{2} - 53\right)} e^{\left(2 \, x\right)} - 23 \, \sqrt{2} + 33\right)} \sqrt{2 \, \sqrt{2} + 3}\right)} \sqrt{2 \, \sqrt{2} + 4} + \frac{1}{31} \, {\left({\left(33 \, \sqrt{2} - 46\right)} e^{\left(2 \, x\right)} - 3 \, \sqrt{2} + 7\right)} \sqrt{2 \, \sqrt{2} + 3}\right) + \frac{1}{16} \, \sqrt{2 \, \sqrt{2 \, \sqrt{2} + 4} {\left(2 \, \sqrt{2} - 3\right)} - 4 \, \sqrt{2} + 8} {\left(2 \, \sqrt{2} + 4\right)}^{\frac{3}{4}} \sqrt{2 \, \sqrt{2} + 3} {\left(\sqrt{2} - 1\right)} \arctan\left(-\frac{1}{31} \, {\left(2 \, {\left(13 \, \sqrt{2} - 20\right)} e^{\left(2 \, x\right)} + 23 \, \sqrt{2} - 33\right)} \sqrt{2 \, \sqrt{2} + 4} \sqrt{2 \, \sqrt{2} + 3} - \frac{1}{496} \, {\left(32 \, {\left(10 \, \sqrt{2} - 13\right)} \sqrt{2 \, \sqrt{2} + 4} \sqrt{2 \, \sqrt{2} + 3} - {\left({\left({\left(355 \, \sqrt{2} - 508\right)} \sqrt{2 \, \sqrt{2} + 4} \sqrt{2 \, \sqrt{2} + 3} + 6 \, {\left(59 \, \sqrt{2} - 86\right)} \sqrt{2 \, \sqrt{2} + 3}\right)} {\left(2 \, \sqrt{2} + 4\right)}^{\frac{3}{4}} + 4 \, {\left({\left(82 \, \sqrt{2} - 119\right)} \sqrt{2 \, \sqrt{2} + 4} \sqrt{2 \, \sqrt{2} + 3} + {\left(85 \, \sqrt{2} - 126\right)} \sqrt{2 \, \sqrt{2} + 3}\right)} {\left(2 \, \sqrt{2} + 4\right)}^{\frac{1}{4}}\right)} \sqrt{2 \, \sqrt{2 \, \sqrt{2} + 4} {\left(2 \, \sqrt{2} - 3\right)} - 4 \, \sqrt{2} + 8} + 4 \, {\left({\left(76 \, \sqrt{2} - 105\right)} \sqrt{2 \, \sqrt{2} + 4} \sqrt{2 \, \sqrt{2} + 3} + 2 \, {\left(53 \, \sqrt{2} - 72\right)} \sqrt{2 \, \sqrt{2} + 3}\right)} \sqrt{2 \, \sqrt{2} + 4} + 16 \, {\left(23 \, \sqrt{2} - 33\right)} \sqrt{2 \, \sqrt{2} + 3}\right)} \sqrt{4 \, {\left(\sqrt{2} - 1\right)} e^{\left(2 \, x\right)} + {\left(2 \, {\left(\sqrt{2} - 1\right)} e^{\left(2 \, x\right)} + {\left({\left(\sqrt{2} - 2\right)} e^{\left(2 \, x\right)} - 5 \, \sqrt{2} + 6\right)} \sqrt{2 \, \sqrt{2} + 4} - 6 \, \sqrt{2} + 6\right)} \sqrt{2 \, \sqrt{2 \, \sqrt{2} + 4} {\left(2 \, \sqrt{2} - 3\right)} - 4 \, \sqrt{2} + 8} {\left(2 \, \sqrt{2} + 4\right)}^{\frac{1}{4}} - 4 \, \sqrt{2 \, \sqrt{2} + 4} {\left(\sqrt{2} - 2\right)} - 4 \, \sqrt{2} + 2 \, e^{\left(4 \, x\right)} + 10} + \frac{1}{248} \, {\left({\left({\left({\left(254 \, \sqrt{2} - 355\right)} e^{\left(2 \, x\right)} - 102 \, \sqrt{2} + 145\right)} \sqrt{2 \, \sqrt{2} + 4} \sqrt{2 \, \sqrt{2} + 3} + 2 \, {\left(3 \, {\left(43 \, \sqrt{2} - 59\right)} e^{\left(2 \, x\right)} - 23 \, \sqrt{2} + 33\right)} \sqrt{2 \, \sqrt{2} + 3}\right)} {\left(2 \, \sqrt{2} + 4\right)}^{\frac{3}{4}} + 2 \, {\left({\left({\left(119 \, \sqrt{2} - 164\right)} e^{\left(2 \, x\right)} - 39 \, \sqrt{2} + 60\right)} \sqrt{2 \, \sqrt{2} + 4} \sqrt{2 \, \sqrt{2} + 3} + 2 \, {\left({\left(63 \, \sqrt{2} - 85\right)} e^{\left(2 \, x\right)} - 17 \, \sqrt{2} + 19\right)} \sqrt{2 \, \sqrt{2} + 3}\right)} {\left(2 \, \sqrt{2} + 4\right)}^{\frac{1}{4}}\right)} \sqrt{2 \, \sqrt{2 \, \sqrt{2} + 4} {\left(2 \, \sqrt{2} - 3\right)} - 4 \, \sqrt{2} + 8} - \frac{1}{124} \, {\left({\left({\left(105 \, \sqrt{2} - 152\right)} e^{\left(2 \, x\right)} + 13 \, \sqrt{2} - 20\right)} \sqrt{2 \, \sqrt{2} + 4} \sqrt{2 \, \sqrt{2} + 3} + 4 \, {\left({\left(36 \, \sqrt{2} - 53\right)} e^{\left(2 \, x\right)} - 23 \, \sqrt{2} + 33\right)} \sqrt{2 \, \sqrt{2} + 3}\right)} \sqrt{2 \, \sqrt{2} + 4} - \frac{1}{31} \, {\left({\left(33 \, \sqrt{2} - 46\right)} e^{\left(2 \, x\right)} - 3 \, \sqrt{2} + 7\right)} \sqrt{2 \, \sqrt{2} + 3}\right) - \frac{1}{16} \, \sqrt{-2 \, {\left(2 \, \sqrt{2} + 3\right)} \sqrt{-2 \, \sqrt{2} + 4} + 4 \, \sqrt{2} + 8} {\left(\sqrt{2} + 1\right)} {\left(-2 \, \sqrt{2} + 4\right)}^{\frac{3}{4}} \sqrt{-2 \, \sqrt{2} + 3} \arctan\left(\frac{1}{31} \, {\left(2 \, {\left(13 \, \sqrt{2} + 20\right)} e^{\left(2 \, x\right)} + 23 \, \sqrt{2} + 33\right)} \sqrt{-2 \, \sqrt{2} + 4} \sqrt{-2 \, \sqrt{2} + 3} - \frac{1}{496} \, {\left(32 \, {\left(10 \, \sqrt{2} + 13\right)} \sqrt{-2 \, \sqrt{2} + 4} \sqrt{-2 \, \sqrt{2} + 3} - {\left({\left({\left(355 \, \sqrt{2} + 508\right)} \sqrt{-2 \, \sqrt{2} + 4} \sqrt{-2 \, \sqrt{2} + 3} + 6 \, {\left(59 \, \sqrt{2} + 86\right)} \sqrt{-2 \, \sqrt{2} + 3}\right)} {\left(-2 \, \sqrt{2} + 4\right)}^{\frac{3}{4}} + 4 \, {\left({\left(82 \, \sqrt{2} + 119\right)} \sqrt{-2 \, \sqrt{2} + 4} \sqrt{-2 \, \sqrt{2} + 3} + {\left(85 \, \sqrt{2} + 126\right)} \sqrt{-2 \, \sqrt{2} + 3}\right)} {\left(-2 \, \sqrt{2} + 4\right)}^{\frac{1}{4}}\right)} \sqrt{-2 \, {\left(2 \, \sqrt{2} + 3\right)} \sqrt{-2 \, \sqrt{2} + 4} + 4 \, \sqrt{2} + 8} + 4 \, {\left({\left(76 \, \sqrt{2} + 105\right)} \sqrt{-2 \, \sqrt{2} + 4} \sqrt{-2 \, \sqrt{2} + 3} + 2 \, {\left(53 \, \sqrt{2} + 72\right)} \sqrt{-2 \, \sqrt{2} + 3}\right)} \sqrt{-2 \, \sqrt{2} + 4} + 16 \, {\left(23 \, \sqrt{2} + 33\right)} \sqrt{-2 \, \sqrt{2} + 3}\right)} \sqrt{-4 \, {\left(\sqrt{2} + 1\right)} e^{\left(2 \, x\right)} - {\left(2 \, {\left(\sqrt{2} + 1\right)} e^{\left(2 \, x\right)} + {\left({\left(\sqrt{2} + 2\right)} e^{\left(2 \, x\right)} - 5 \, \sqrt{2} - 6\right)} \sqrt{-2 \, \sqrt{2} + 4} - 6 \, \sqrt{2} - 6\right)} \sqrt{-2 \, {\left(2 \, \sqrt{2} + 3\right)} \sqrt{-2 \, \sqrt{2} + 4} + 4 \, \sqrt{2} + 8} {\left(-2 \, \sqrt{2} + 4\right)}^{\frac{1}{4}} + 4 \, {\left(\sqrt{2} + 2\right)} \sqrt{-2 \, \sqrt{2} + 4} + 4 \, \sqrt{2} + 2 \, e^{\left(4 \, x\right)} + 10} - \frac{1}{248} \, {\left({\left({\left({\left(254 \, \sqrt{2} + 355\right)} e^{\left(2 \, x\right)} - 102 \, \sqrt{2} - 145\right)} \sqrt{-2 \, \sqrt{2} + 4} \sqrt{-2 \, \sqrt{2} + 3} + 2 \, {\left(3 \, {\left(43 \, \sqrt{2} + 59\right)} e^{\left(2 \, x\right)} - 23 \, \sqrt{2} - 33\right)} \sqrt{-2 \, \sqrt{2} + 3}\right)} {\left(-2 \, \sqrt{2} + 4\right)}^{\frac{3}{4}} + 2 \, {\left({\left({\left(119 \, \sqrt{2} + 164\right)} e^{\left(2 \, x\right)} - 39 \, \sqrt{2} - 60\right)} \sqrt{-2 \, \sqrt{2} + 4} \sqrt{-2 \, \sqrt{2} + 3} + 2 \, {\left({\left(63 \, \sqrt{2} + 85\right)} e^{\left(2 \, x\right)} - 17 \, \sqrt{2} - 19\right)} \sqrt{-2 \, \sqrt{2} + 3}\right)} {\left(-2 \, \sqrt{2} + 4\right)}^{\frac{1}{4}}\right)} \sqrt{-2 \, {\left(2 \, \sqrt{2} + 3\right)} \sqrt{-2 \, \sqrt{2} + 4} + 4 \, \sqrt{2} + 8} + \frac{1}{124} \, {\left({\left({\left(105 \, \sqrt{2} + 152\right)} e^{\left(2 \, x\right)} + 13 \, \sqrt{2} + 20\right)} \sqrt{-2 \, \sqrt{2} + 4} \sqrt{-2 \, \sqrt{2} + 3} + 4 \, {\left({\left(36 \, \sqrt{2} + 53\right)} e^{\left(2 \, x\right)} - 23 \, \sqrt{2} - 33\right)} \sqrt{-2 \, \sqrt{2} + 3}\right)} \sqrt{-2 \, \sqrt{2} + 4} + \frac{1}{31} \, {\left({\left(33 \, \sqrt{2} + 46\right)} e^{\left(2 \, x\right)} - 3 \, \sqrt{2} - 7\right)} \sqrt{-2 \, \sqrt{2} + 3}\right) - \frac{1}{16} \, \sqrt{-2 \, {\left(2 \, \sqrt{2} + 3\right)} \sqrt{-2 \, \sqrt{2} + 4} + 4 \, \sqrt{2} + 8} {\left(\sqrt{2} + 1\right)} {\left(-2 \, \sqrt{2} + 4\right)}^{\frac{3}{4}} \sqrt{-2 \, \sqrt{2} + 3} \arctan\left(-\frac{1}{31} \, {\left(2 \, {\left(13 \, \sqrt{2} + 20\right)} e^{\left(2 \, x\right)} + 23 \, \sqrt{2} + 33\right)} \sqrt{-2 \, \sqrt{2} + 4} \sqrt{-2 \, \sqrt{2} + 3} + \frac{1}{496} \, {\left(32 \, {\left(10 \, \sqrt{2} + 13\right)} \sqrt{-2 \, \sqrt{2} + 4} \sqrt{-2 \, \sqrt{2} + 3} + {\left({\left({\left(355 \, \sqrt{2} + 508\right)} \sqrt{-2 \, \sqrt{2} + 4} \sqrt{-2 \, \sqrt{2} + 3} + 6 \, {\left(59 \, \sqrt{2} + 86\right)} \sqrt{-2 \, \sqrt{2} + 3}\right)} {\left(-2 \, \sqrt{2} + 4\right)}^{\frac{3}{4}} + 4 \, {\left({\left(82 \, \sqrt{2} + 119\right)} \sqrt{-2 \, \sqrt{2} + 4} \sqrt{-2 \, \sqrt{2} + 3} + {\left(85 \, \sqrt{2} + 126\right)} \sqrt{-2 \, \sqrt{2} + 3}\right)} {\left(-2 \, \sqrt{2} + 4\right)}^{\frac{1}{4}}\right)} \sqrt{-2 \, {\left(2 \, \sqrt{2} + 3\right)} \sqrt{-2 \, \sqrt{2} + 4} + 4 \, \sqrt{2} + 8} + 4 \, {\left({\left(76 \, \sqrt{2} + 105\right)} \sqrt{-2 \, \sqrt{2} + 4} \sqrt{-2 \, \sqrt{2} + 3} + 2 \, {\left(53 \, \sqrt{2} + 72\right)} \sqrt{-2 \, \sqrt{2} + 3}\right)} \sqrt{-2 \, \sqrt{2} + 4} + 16 \, {\left(23 \, \sqrt{2} + 33\right)} \sqrt{-2 \, \sqrt{2} + 3}\right)} \sqrt{-4 \, {\left(\sqrt{2} + 1\right)} e^{\left(2 \, x\right)} + {\left(2 \, {\left(\sqrt{2} + 1\right)} e^{\left(2 \, x\right)} + {\left({\left(\sqrt{2} + 2\right)} e^{\left(2 \, x\right)} - 5 \, \sqrt{2} - 6\right)} \sqrt{-2 \, \sqrt{2} + 4} - 6 \, \sqrt{2} - 6\right)} \sqrt{-2 \, {\left(2 \, \sqrt{2} + 3\right)} \sqrt{-2 \, \sqrt{2} + 4} + 4 \, \sqrt{2} + 8} {\left(-2 \, \sqrt{2} + 4\right)}^{\frac{1}{4}} + 4 \, {\left(\sqrt{2} + 2\right)} \sqrt{-2 \, \sqrt{2} + 4} + 4 \, \sqrt{2} + 2 \, e^{\left(4 \, x\right)} + 10} - \frac{1}{248} \, {\left({\left({\left({\left(254 \, \sqrt{2} + 355\right)} e^{\left(2 \, x\right)} - 102 \, \sqrt{2} - 145\right)} \sqrt{-2 \, \sqrt{2} + 4} \sqrt{-2 \, \sqrt{2} + 3} + 2 \, {\left(3 \, {\left(43 \, \sqrt{2} + 59\right)} e^{\left(2 \, x\right)} - 23 \, \sqrt{2} - 33\right)} \sqrt{-2 \, \sqrt{2} + 3}\right)} {\left(-2 \, \sqrt{2} + 4\right)}^{\frac{3}{4}} + 2 \, {\left({\left({\left(119 \, \sqrt{2} + 164\right)} e^{\left(2 \, x\right)} - 39 \, \sqrt{2} - 60\right)} \sqrt{-2 \, \sqrt{2} + 4} \sqrt{-2 \, \sqrt{2} + 3} + 2 \, {\left({\left(63 \, \sqrt{2} + 85\right)} e^{\left(2 \, x\right)} - 17 \, \sqrt{2} - 19\right)} \sqrt{-2 \, \sqrt{2} + 3}\right)} {\left(-2 \, \sqrt{2} + 4\right)}^{\frac{1}{4}}\right)} \sqrt{-2 \, {\left(2 \, \sqrt{2} + 3\right)} \sqrt{-2 \, \sqrt{2} + 4} + 4 \, \sqrt{2} + 8} - \frac{1}{124} \, {\left({\left({\left(105 \, \sqrt{2} + 152\right)} e^{\left(2 \, x\right)} + 13 \, \sqrt{2} + 20\right)} \sqrt{-2 \, \sqrt{2} + 4} \sqrt{-2 \, \sqrt{2} + 3} + 4 \, {\left({\left(36 \, \sqrt{2} + 53\right)} e^{\left(2 \, x\right)} - 23 \, \sqrt{2} - 33\right)} \sqrt{-2 \, \sqrt{2} + 3}\right)} \sqrt{-2 \, \sqrt{2} + 4} - \frac{1}{31} \, {\left({\left(33 \, \sqrt{2} + 46\right)} e^{\left(2 \, x\right)} - 3 \, \sqrt{2} - 7\right)} \sqrt{-2 \, \sqrt{2} + 3}\right) + \frac{1}{64} \, \sqrt{-2 \, {\left(2 \, \sqrt{2} + 3\right)} \sqrt{-2 \, \sqrt{2} + 4} + 4 \, \sqrt{2} + 8} {\left({\left(\sqrt{2} + 1\right)} \sqrt{-2 \, \sqrt{2} + 4} + 2 \, \sqrt{2}\right)} {\left(-2 \, \sqrt{2} + 4\right)}^{\frac{1}{4}} \log\left(-2 \, {\left(\sqrt{2} + 1\right)} e^{\left(2 \, x\right)} + \frac{1}{2} \, {\left(2 \, {\left(\sqrt{2} + 1\right)} e^{\left(2 \, x\right)} + {\left({\left(\sqrt{2} + 2\right)} e^{\left(2 \, x\right)} - 5 \, \sqrt{2} - 6\right)} \sqrt{-2 \, \sqrt{2} + 4} - 6 \, \sqrt{2} - 6\right)} \sqrt{-2 \, {\left(2 \, \sqrt{2} + 3\right)} \sqrt{-2 \, \sqrt{2} + 4} + 4 \, \sqrt{2} + 8} {\left(-2 \, \sqrt{2} + 4\right)}^{\frac{1}{4}} + 2 \, {\left(\sqrt{2} + 2\right)} \sqrt{-2 \, \sqrt{2} + 4} + 2 \, \sqrt{2} + e^{\left(4 \, x\right)} + 5\right) - \frac{1}{64} \, \sqrt{-2 \, {\left(2 \, \sqrt{2} + 3\right)} \sqrt{-2 \, \sqrt{2} + 4} + 4 \, \sqrt{2} + 8} {\left({\left(\sqrt{2} + 1\right)} \sqrt{-2 \, \sqrt{2} + 4} + 2 \, \sqrt{2}\right)} {\left(-2 \, \sqrt{2} + 4\right)}^{\frac{1}{4}} \log\left(-2 \, {\left(\sqrt{2} + 1\right)} e^{\left(2 \, x\right)} - \frac{1}{2} \, {\left(2 \, {\left(\sqrt{2} + 1\right)} e^{\left(2 \, x\right)} + {\left({\left(\sqrt{2} + 2\right)} e^{\left(2 \, x\right)} - 5 \, \sqrt{2} - 6\right)} \sqrt{-2 \, \sqrt{2} + 4} - 6 \, \sqrt{2} - 6\right)} \sqrt{-2 \, {\left(2 \, \sqrt{2} + 3\right)} \sqrt{-2 \, \sqrt{2} + 4} + 4 \, \sqrt{2} + 8} {\left(-2 \, \sqrt{2} + 4\right)}^{\frac{1}{4}} + 2 \, {\left(\sqrt{2} + 2\right)} \sqrt{-2 \, \sqrt{2} + 4} + 2 \, \sqrt{2} + e^{\left(4 \, x\right)} + 5\right) + \frac{1}{64} \, \sqrt{2 \, \sqrt{2 \, \sqrt{2} + 4} {\left(2 \, \sqrt{2} - 3\right)} - 4 \, \sqrt{2} + 8} {\left(\sqrt{2 \, \sqrt{2} + 4} {\left(\sqrt{2} - 1\right)} + 2 \, \sqrt{2}\right)} {\left(2 \, \sqrt{2} + 4\right)}^{\frac{1}{4}} \log\left(2 \, {\left(\sqrt{2} - 1\right)} e^{\left(2 \, x\right)} + \frac{1}{2} \, {\left(2 \, {\left(\sqrt{2} - 1\right)} e^{\left(2 \, x\right)} + {\left({\left(\sqrt{2} - 2\right)} e^{\left(2 \, x\right)} - 5 \, \sqrt{2} + 6\right)} \sqrt{2 \, \sqrt{2} + 4} - 6 \, \sqrt{2} + 6\right)} \sqrt{2 \, \sqrt{2 \, \sqrt{2} + 4} {\left(2 \, \sqrt{2} - 3\right)} - 4 \, \sqrt{2} + 8} {\left(2 \, \sqrt{2} + 4\right)}^{\frac{1}{4}} - 2 \, \sqrt{2 \, \sqrt{2} + 4} {\left(\sqrt{2} - 2\right)} - 2 \, \sqrt{2} + e^{\left(4 \, x\right)} + 5\right) - \frac{1}{64} \, \sqrt{2 \, \sqrt{2 \, \sqrt{2} + 4} {\left(2 \, \sqrt{2} - 3\right)} - 4 \, \sqrt{2} + 8} {\left(\sqrt{2 \, \sqrt{2} + 4} {\left(\sqrt{2} - 1\right)} + 2 \, \sqrt{2}\right)} {\left(2 \, \sqrt{2} + 4\right)}^{\frac{1}{4}} \log\left(2 \, {\left(\sqrt{2} - 1\right)} e^{\left(2 \, x\right)} - \frac{1}{2} \, {\left(2 \, {\left(\sqrt{2} - 1\right)} e^{\left(2 \, x\right)} + {\left({\left(\sqrt{2} - 2\right)} e^{\left(2 \, x\right)} - 5 \, \sqrt{2} + 6\right)} \sqrt{2 \, \sqrt{2} + 4} - 6 \, \sqrt{2} + 6\right)} \sqrt{2 \, \sqrt{2 \, \sqrt{2} + 4} {\left(2 \, \sqrt{2} - 3\right)} - 4 \, \sqrt{2} + 8} {\left(2 \, \sqrt{2} + 4\right)}^{\frac{1}{4}} - 2 \, \sqrt{2 \, \sqrt{2} + 4} {\left(\sqrt{2} - 2\right)} - 2 \, \sqrt{2} + e^{\left(4 \, x\right)} + 5\right)"," ",0,"1/16*sqrt(2*sqrt(2*sqrt(2) + 4)*(2*sqrt(2) - 3) - 4*sqrt(2) + 8)*(2*sqrt(2) + 4)^(3/4)*sqrt(2*sqrt(2) + 3)*(sqrt(2) - 1)*arctan(1/31*(2*(13*sqrt(2) - 20)*e^(2*x) + 23*sqrt(2) - 33)*sqrt(2*sqrt(2) + 4)*sqrt(2*sqrt(2) + 3) + 1/496*(32*(10*sqrt(2) - 13)*sqrt(2*sqrt(2) + 4)*sqrt(2*sqrt(2) + 3) + (((355*sqrt(2) - 508)*sqrt(2*sqrt(2) + 4)*sqrt(2*sqrt(2) + 3) + 6*(59*sqrt(2) - 86)*sqrt(2*sqrt(2) + 3))*(2*sqrt(2) + 4)^(3/4) + 4*((82*sqrt(2) - 119)*sqrt(2*sqrt(2) + 4)*sqrt(2*sqrt(2) + 3) + (85*sqrt(2) - 126)*sqrt(2*sqrt(2) + 3))*(2*sqrt(2) + 4)^(1/4))*sqrt(2*sqrt(2*sqrt(2) + 4)*(2*sqrt(2) - 3) - 4*sqrt(2) + 8) + 4*((76*sqrt(2) - 105)*sqrt(2*sqrt(2) + 4)*sqrt(2*sqrt(2) + 3) + 2*(53*sqrt(2) - 72)*sqrt(2*sqrt(2) + 3))*sqrt(2*sqrt(2) + 4) + 16*(23*sqrt(2) - 33)*sqrt(2*sqrt(2) + 3))*sqrt(4*(sqrt(2) - 1)*e^(2*x) - (2*(sqrt(2) - 1)*e^(2*x) + ((sqrt(2) - 2)*e^(2*x) - 5*sqrt(2) + 6)*sqrt(2*sqrt(2) + 4) - 6*sqrt(2) + 6)*sqrt(2*sqrt(2*sqrt(2) + 4)*(2*sqrt(2) - 3) - 4*sqrt(2) + 8)*(2*sqrt(2) + 4)^(1/4) - 4*sqrt(2*sqrt(2) + 4)*(sqrt(2) - 2) - 4*sqrt(2) + 2*e^(4*x) + 10) + 1/248*((((254*sqrt(2) - 355)*e^(2*x) - 102*sqrt(2) + 145)*sqrt(2*sqrt(2) + 4)*sqrt(2*sqrt(2) + 3) + 2*(3*(43*sqrt(2) - 59)*e^(2*x) - 23*sqrt(2) + 33)*sqrt(2*sqrt(2) + 3))*(2*sqrt(2) + 4)^(3/4) + 2*(((119*sqrt(2) - 164)*e^(2*x) - 39*sqrt(2) + 60)*sqrt(2*sqrt(2) + 4)*sqrt(2*sqrt(2) + 3) + 2*((63*sqrt(2) - 85)*e^(2*x) - 17*sqrt(2) + 19)*sqrt(2*sqrt(2) + 3))*(2*sqrt(2) + 4)^(1/4))*sqrt(2*sqrt(2*sqrt(2) + 4)*(2*sqrt(2) - 3) - 4*sqrt(2) + 8) + 1/124*(((105*sqrt(2) - 152)*e^(2*x) + 13*sqrt(2) - 20)*sqrt(2*sqrt(2) + 4)*sqrt(2*sqrt(2) + 3) + 4*((36*sqrt(2) - 53)*e^(2*x) - 23*sqrt(2) + 33)*sqrt(2*sqrt(2) + 3))*sqrt(2*sqrt(2) + 4) + 1/31*((33*sqrt(2) - 46)*e^(2*x) - 3*sqrt(2) + 7)*sqrt(2*sqrt(2) + 3)) + 1/16*sqrt(2*sqrt(2*sqrt(2) + 4)*(2*sqrt(2) - 3) - 4*sqrt(2) + 8)*(2*sqrt(2) + 4)^(3/4)*sqrt(2*sqrt(2) + 3)*(sqrt(2) - 1)*arctan(-1/31*(2*(13*sqrt(2) - 20)*e^(2*x) + 23*sqrt(2) - 33)*sqrt(2*sqrt(2) + 4)*sqrt(2*sqrt(2) + 3) - 1/496*(32*(10*sqrt(2) - 13)*sqrt(2*sqrt(2) + 4)*sqrt(2*sqrt(2) + 3) - (((355*sqrt(2) - 508)*sqrt(2*sqrt(2) + 4)*sqrt(2*sqrt(2) + 3) + 6*(59*sqrt(2) - 86)*sqrt(2*sqrt(2) + 3))*(2*sqrt(2) + 4)^(3/4) + 4*((82*sqrt(2) - 119)*sqrt(2*sqrt(2) + 4)*sqrt(2*sqrt(2) + 3) + (85*sqrt(2) - 126)*sqrt(2*sqrt(2) + 3))*(2*sqrt(2) + 4)^(1/4))*sqrt(2*sqrt(2*sqrt(2) + 4)*(2*sqrt(2) - 3) - 4*sqrt(2) + 8) + 4*((76*sqrt(2) - 105)*sqrt(2*sqrt(2) + 4)*sqrt(2*sqrt(2) + 3) + 2*(53*sqrt(2) - 72)*sqrt(2*sqrt(2) + 3))*sqrt(2*sqrt(2) + 4) + 16*(23*sqrt(2) - 33)*sqrt(2*sqrt(2) + 3))*sqrt(4*(sqrt(2) - 1)*e^(2*x) + (2*(sqrt(2) - 1)*e^(2*x) + ((sqrt(2) - 2)*e^(2*x) - 5*sqrt(2) + 6)*sqrt(2*sqrt(2) + 4) - 6*sqrt(2) + 6)*sqrt(2*sqrt(2*sqrt(2) + 4)*(2*sqrt(2) - 3) - 4*sqrt(2) + 8)*(2*sqrt(2) + 4)^(1/4) - 4*sqrt(2*sqrt(2) + 4)*(sqrt(2) - 2) - 4*sqrt(2) + 2*e^(4*x) + 10) + 1/248*((((254*sqrt(2) - 355)*e^(2*x) - 102*sqrt(2) + 145)*sqrt(2*sqrt(2) + 4)*sqrt(2*sqrt(2) + 3) + 2*(3*(43*sqrt(2) - 59)*e^(2*x) - 23*sqrt(2) + 33)*sqrt(2*sqrt(2) + 3))*(2*sqrt(2) + 4)^(3/4) + 2*(((119*sqrt(2) - 164)*e^(2*x) - 39*sqrt(2) + 60)*sqrt(2*sqrt(2) + 4)*sqrt(2*sqrt(2) + 3) + 2*((63*sqrt(2) - 85)*e^(2*x) - 17*sqrt(2) + 19)*sqrt(2*sqrt(2) + 3))*(2*sqrt(2) + 4)^(1/4))*sqrt(2*sqrt(2*sqrt(2) + 4)*(2*sqrt(2) - 3) - 4*sqrt(2) + 8) - 1/124*(((105*sqrt(2) - 152)*e^(2*x) + 13*sqrt(2) - 20)*sqrt(2*sqrt(2) + 4)*sqrt(2*sqrt(2) + 3) + 4*((36*sqrt(2) - 53)*e^(2*x) - 23*sqrt(2) + 33)*sqrt(2*sqrt(2) + 3))*sqrt(2*sqrt(2) + 4) - 1/31*((33*sqrt(2) - 46)*e^(2*x) - 3*sqrt(2) + 7)*sqrt(2*sqrt(2) + 3)) - 1/16*sqrt(-2*(2*sqrt(2) + 3)*sqrt(-2*sqrt(2) + 4) + 4*sqrt(2) + 8)*(sqrt(2) + 1)*(-2*sqrt(2) + 4)^(3/4)*sqrt(-2*sqrt(2) + 3)*arctan(1/31*(2*(13*sqrt(2) + 20)*e^(2*x) + 23*sqrt(2) + 33)*sqrt(-2*sqrt(2) + 4)*sqrt(-2*sqrt(2) + 3) - 1/496*(32*(10*sqrt(2) + 13)*sqrt(-2*sqrt(2) + 4)*sqrt(-2*sqrt(2) + 3) - (((355*sqrt(2) + 508)*sqrt(-2*sqrt(2) + 4)*sqrt(-2*sqrt(2) + 3) + 6*(59*sqrt(2) + 86)*sqrt(-2*sqrt(2) + 3))*(-2*sqrt(2) + 4)^(3/4) + 4*((82*sqrt(2) + 119)*sqrt(-2*sqrt(2) + 4)*sqrt(-2*sqrt(2) + 3) + (85*sqrt(2) + 126)*sqrt(-2*sqrt(2) + 3))*(-2*sqrt(2) + 4)^(1/4))*sqrt(-2*(2*sqrt(2) + 3)*sqrt(-2*sqrt(2) + 4) + 4*sqrt(2) + 8) + 4*((76*sqrt(2) + 105)*sqrt(-2*sqrt(2) + 4)*sqrt(-2*sqrt(2) + 3) + 2*(53*sqrt(2) + 72)*sqrt(-2*sqrt(2) + 3))*sqrt(-2*sqrt(2) + 4) + 16*(23*sqrt(2) + 33)*sqrt(-2*sqrt(2) + 3))*sqrt(-4*(sqrt(2) + 1)*e^(2*x) - (2*(sqrt(2) + 1)*e^(2*x) + ((sqrt(2) + 2)*e^(2*x) - 5*sqrt(2) - 6)*sqrt(-2*sqrt(2) + 4) - 6*sqrt(2) - 6)*sqrt(-2*(2*sqrt(2) + 3)*sqrt(-2*sqrt(2) + 4) + 4*sqrt(2) + 8)*(-2*sqrt(2) + 4)^(1/4) + 4*(sqrt(2) + 2)*sqrt(-2*sqrt(2) + 4) + 4*sqrt(2) + 2*e^(4*x) + 10) - 1/248*((((254*sqrt(2) + 355)*e^(2*x) - 102*sqrt(2) - 145)*sqrt(-2*sqrt(2) + 4)*sqrt(-2*sqrt(2) + 3) + 2*(3*(43*sqrt(2) + 59)*e^(2*x) - 23*sqrt(2) - 33)*sqrt(-2*sqrt(2) + 3))*(-2*sqrt(2) + 4)^(3/4) + 2*(((119*sqrt(2) + 164)*e^(2*x) - 39*sqrt(2) - 60)*sqrt(-2*sqrt(2) + 4)*sqrt(-2*sqrt(2) + 3) + 2*((63*sqrt(2) + 85)*e^(2*x) - 17*sqrt(2) - 19)*sqrt(-2*sqrt(2) + 3))*(-2*sqrt(2) + 4)^(1/4))*sqrt(-2*(2*sqrt(2) + 3)*sqrt(-2*sqrt(2) + 4) + 4*sqrt(2) + 8) + 1/124*(((105*sqrt(2) + 152)*e^(2*x) + 13*sqrt(2) + 20)*sqrt(-2*sqrt(2) + 4)*sqrt(-2*sqrt(2) + 3) + 4*((36*sqrt(2) + 53)*e^(2*x) - 23*sqrt(2) - 33)*sqrt(-2*sqrt(2) + 3))*sqrt(-2*sqrt(2) + 4) + 1/31*((33*sqrt(2) + 46)*e^(2*x) - 3*sqrt(2) - 7)*sqrt(-2*sqrt(2) + 3)) - 1/16*sqrt(-2*(2*sqrt(2) + 3)*sqrt(-2*sqrt(2) + 4) + 4*sqrt(2) + 8)*(sqrt(2) + 1)*(-2*sqrt(2) + 4)^(3/4)*sqrt(-2*sqrt(2) + 3)*arctan(-1/31*(2*(13*sqrt(2) + 20)*e^(2*x) + 23*sqrt(2) + 33)*sqrt(-2*sqrt(2) + 4)*sqrt(-2*sqrt(2) + 3) + 1/496*(32*(10*sqrt(2) + 13)*sqrt(-2*sqrt(2) + 4)*sqrt(-2*sqrt(2) + 3) + (((355*sqrt(2) + 508)*sqrt(-2*sqrt(2) + 4)*sqrt(-2*sqrt(2) + 3) + 6*(59*sqrt(2) + 86)*sqrt(-2*sqrt(2) + 3))*(-2*sqrt(2) + 4)^(3/4) + 4*((82*sqrt(2) + 119)*sqrt(-2*sqrt(2) + 4)*sqrt(-2*sqrt(2) + 3) + (85*sqrt(2) + 126)*sqrt(-2*sqrt(2) + 3))*(-2*sqrt(2) + 4)^(1/4))*sqrt(-2*(2*sqrt(2) + 3)*sqrt(-2*sqrt(2) + 4) + 4*sqrt(2) + 8) + 4*((76*sqrt(2) + 105)*sqrt(-2*sqrt(2) + 4)*sqrt(-2*sqrt(2) + 3) + 2*(53*sqrt(2) + 72)*sqrt(-2*sqrt(2) + 3))*sqrt(-2*sqrt(2) + 4) + 16*(23*sqrt(2) + 33)*sqrt(-2*sqrt(2) + 3))*sqrt(-4*(sqrt(2) + 1)*e^(2*x) + (2*(sqrt(2) + 1)*e^(2*x) + ((sqrt(2) + 2)*e^(2*x) - 5*sqrt(2) - 6)*sqrt(-2*sqrt(2) + 4) - 6*sqrt(2) - 6)*sqrt(-2*(2*sqrt(2) + 3)*sqrt(-2*sqrt(2) + 4) + 4*sqrt(2) + 8)*(-2*sqrt(2) + 4)^(1/4) + 4*(sqrt(2) + 2)*sqrt(-2*sqrt(2) + 4) + 4*sqrt(2) + 2*e^(4*x) + 10) - 1/248*((((254*sqrt(2) + 355)*e^(2*x) - 102*sqrt(2) - 145)*sqrt(-2*sqrt(2) + 4)*sqrt(-2*sqrt(2) + 3) + 2*(3*(43*sqrt(2) + 59)*e^(2*x) - 23*sqrt(2) - 33)*sqrt(-2*sqrt(2) + 3))*(-2*sqrt(2) + 4)^(3/4) + 2*(((119*sqrt(2) + 164)*e^(2*x) - 39*sqrt(2) - 60)*sqrt(-2*sqrt(2) + 4)*sqrt(-2*sqrt(2) + 3) + 2*((63*sqrt(2) + 85)*e^(2*x) - 17*sqrt(2) - 19)*sqrt(-2*sqrt(2) + 3))*(-2*sqrt(2) + 4)^(1/4))*sqrt(-2*(2*sqrt(2) + 3)*sqrt(-2*sqrt(2) + 4) + 4*sqrt(2) + 8) - 1/124*(((105*sqrt(2) + 152)*e^(2*x) + 13*sqrt(2) + 20)*sqrt(-2*sqrt(2) + 4)*sqrt(-2*sqrt(2) + 3) + 4*((36*sqrt(2) + 53)*e^(2*x) - 23*sqrt(2) - 33)*sqrt(-2*sqrt(2) + 3))*sqrt(-2*sqrt(2) + 4) - 1/31*((33*sqrt(2) + 46)*e^(2*x) - 3*sqrt(2) - 7)*sqrt(-2*sqrt(2) + 3)) + 1/64*sqrt(-2*(2*sqrt(2) + 3)*sqrt(-2*sqrt(2) + 4) + 4*sqrt(2) + 8)*((sqrt(2) + 1)*sqrt(-2*sqrt(2) + 4) + 2*sqrt(2))*(-2*sqrt(2) + 4)^(1/4)*log(-2*(sqrt(2) + 1)*e^(2*x) + 1/2*(2*(sqrt(2) + 1)*e^(2*x) + ((sqrt(2) + 2)*e^(2*x) - 5*sqrt(2) - 6)*sqrt(-2*sqrt(2) + 4) - 6*sqrt(2) - 6)*sqrt(-2*(2*sqrt(2) + 3)*sqrt(-2*sqrt(2) + 4) + 4*sqrt(2) + 8)*(-2*sqrt(2) + 4)^(1/4) + 2*(sqrt(2) + 2)*sqrt(-2*sqrt(2) + 4) + 2*sqrt(2) + e^(4*x) + 5) - 1/64*sqrt(-2*(2*sqrt(2) + 3)*sqrt(-2*sqrt(2) + 4) + 4*sqrt(2) + 8)*((sqrt(2) + 1)*sqrt(-2*sqrt(2) + 4) + 2*sqrt(2))*(-2*sqrt(2) + 4)^(1/4)*log(-2*(sqrt(2) + 1)*e^(2*x) - 1/2*(2*(sqrt(2) + 1)*e^(2*x) + ((sqrt(2) + 2)*e^(2*x) - 5*sqrt(2) - 6)*sqrt(-2*sqrt(2) + 4) - 6*sqrt(2) - 6)*sqrt(-2*(2*sqrt(2) + 3)*sqrt(-2*sqrt(2) + 4) + 4*sqrt(2) + 8)*(-2*sqrt(2) + 4)^(1/4) + 2*(sqrt(2) + 2)*sqrt(-2*sqrt(2) + 4) + 2*sqrt(2) + e^(4*x) + 5) + 1/64*sqrt(2*sqrt(2*sqrt(2) + 4)*(2*sqrt(2) - 3) - 4*sqrt(2) + 8)*(sqrt(2*sqrt(2) + 4)*(sqrt(2) - 1) + 2*sqrt(2))*(2*sqrt(2) + 4)^(1/4)*log(2*(sqrt(2) - 1)*e^(2*x) + 1/2*(2*(sqrt(2) - 1)*e^(2*x) + ((sqrt(2) - 2)*e^(2*x) - 5*sqrt(2) + 6)*sqrt(2*sqrt(2) + 4) - 6*sqrt(2) + 6)*sqrt(2*sqrt(2*sqrt(2) + 4)*(2*sqrt(2) - 3) - 4*sqrt(2) + 8)*(2*sqrt(2) + 4)^(1/4) - 2*sqrt(2*sqrt(2) + 4)*(sqrt(2) - 2) - 2*sqrt(2) + e^(4*x) + 5) - 1/64*sqrt(2*sqrt(2*sqrt(2) + 4)*(2*sqrt(2) - 3) - 4*sqrt(2) + 8)*(sqrt(2*sqrt(2) + 4)*(sqrt(2) - 1) + 2*sqrt(2))*(2*sqrt(2) + 4)^(1/4)*log(2*(sqrt(2) - 1)*e^(2*x) - 1/2*(2*(sqrt(2) - 1)*e^(2*x) + ((sqrt(2) - 2)*e^(2*x) - 5*sqrt(2) + 6)*sqrt(2*sqrt(2) + 4) - 6*sqrt(2) + 6)*sqrt(2*sqrt(2*sqrt(2) + 4)*(2*sqrt(2) - 3) - 4*sqrt(2) + 8)*(2*sqrt(2) + 4)^(1/4) - 2*sqrt(2*sqrt(2) + 4)*(sqrt(2) - 2) - 2*sqrt(2) + e^(4*x) + 5)","B",0
273,1,3500,0,2.646232," ","integrate(1/(1-sinh(x)^5),x, algorithm=""fricas"")","\frac{1}{200} \, \sqrt{2} \sqrt{2 \, \sqrt{2} {\left(2 \, \sqrt{5} - 5\right)} \sqrt{\sqrt{5} + 3} - 4 \, \sqrt{5} + 20} {\left(8 \, \sqrt{5} + 24\right)}^{\frac{1}{4}} {\left(3 \, \sqrt{5} - 5\right)} \sqrt{2 \, \sqrt{5} + 5} \sqrt{\sqrt{5} + 3} \arctan\left(\frac{1}{40} \, \sqrt{2} {\left({\left(11 \, \sqrt{5} - 25\right)} e^{x} + 7 \, \sqrt{5} - 15\right)} \sqrt{2 \, \sqrt{5} + 5} \sqrt{\sqrt{5} + 3} + \frac{1}{80} \, \sqrt{2} {\left(\sqrt{2} {\left({\left(11 \, \sqrt{5} - 25\right)} e^{x} - 4 \, \sqrt{5} + 10\right)} \sqrt{2 \, \sqrt{5} + 5} \sqrt{\sqrt{5} + 3} + 2 \, {\left({\left(3 \, \sqrt{5} - 5\right)} e^{x} - 7 \, \sqrt{5} + 15\right)} \sqrt{2 \, \sqrt{5} + 5}\right)} \sqrt{\sqrt{5} + 3} + \frac{1}{12800} \, {\left(80 \, \sqrt{2} {\left(5 \, \sqrt{5} - 11\right)} \sqrt{2 \, \sqrt{5} + 5} \sqrt{\sqrt{5} + 3} + 40 \, \sqrt{2} {\left(\sqrt{2} {\left(5 \, \sqrt{5} - 11\right)} \sqrt{2 \, \sqrt{5} + 5} \sqrt{\sqrt{5} + 3} + 2 \, \sqrt{2 \, \sqrt{5} + 5} {\left(\sqrt{5} - 3\right)}\right)} \sqrt{\sqrt{5} + 3} + \sqrt{2 \, \sqrt{2} {\left(2 \, \sqrt{5} - 5\right)} \sqrt{\sqrt{5} + 3} - 4 \, \sqrt{5} + 20} {\left({\left(\sqrt{2} {\left(7 \, \sqrt{5} - 15\right)} \sqrt{2 \, \sqrt{5} + 5} \sqrt{\sqrt{5} + 3} + 2 \, {\left(11 \, \sqrt{5} - 25\right)} \sqrt{2 \, \sqrt{5} + 5}\right)} {\left(8 \, \sqrt{5} + 24\right)}^{\frac{3}{4}} + 4 \, {\left(\sqrt{2} {\left(17 \, \sqrt{5} - 35\right)} \sqrt{2 \, \sqrt{5} + 5} \sqrt{\sqrt{5} + 3} + 2 \, {\left(11 \, \sqrt{5} - 25\right)} \sqrt{2 \, \sqrt{5} + 5}\right)} {\left(8 \, \sqrt{5} + 24\right)}^{\frac{1}{4}}\right)} + 320 \, \sqrt{2 \, \sqrt{5} + 5} {\left(\sqrt{5} - 4\right)}\right)} \sqrt{-20 \, \sqrt{2} \sqrt{\sqrt{5} + 3} {\left(\sqrt{5} - 3\right)} - 40 \, {\left(\sqrt{5} - 1\right)} e^{x} + 2 \, {\left(\sqrt{2} {\left({\left(2 \, \sqrt{5} - 5\right)} e^{x} + 3 \, \sqrt{5} - 5\right)} \sqrt{\sqrt{5} + 3} + 2 \, {\left(\sqrt{5} - 5\right)} e^{x} + 3 \, \sqrt{5} - 5\right)} \sqrt{2 \, \sqrt{2} {\left(2 \, \sqrt{5} - 5\right)} \sqrt{\sqrt{5} + 3} - 4 \, \sqrt{5} + 20} {\left(8 \, \sqrt{5} + 24\right)}^{\frac{1}{4}} + 80 \, e^{\left(2 \, x\right)} + 80} + \frac{1}{640} \, \sqrt{2 \, \sqrt{2} {\left(2 \, \sqrt{5} - 5\right)} \sqrt{\sqrt{5} + 3} - 4 \, \sqrt{5} + 20} {\left({\left(\sqrt{2} {\left({\left(3 \, \sqrt{5} - 7\right)} e^{x} - 8 \, \sqrt{5} + 18\right)} \sqrt{2 \, \sqrt{5} + 5} \sqrt{\sqrt{5} + 3} + 2 \, {\left({\left(5 \, \sqrt{5} - 11\right)} e^{x} - 2 \, \sqrt{5} + 4\right)} \sqrt{2 \, \sqrt{5} + 5}\right)} {\left(8 \, \sqrt{5} + 24\right)}^{\frac{3}{4}} + 4 \, {\left(\sqrt{2} {\left({\left(7 \, \sqrt{5} - 17\right)} e^{x} - 8 \, \sqrt{5} + 18\right)} \sqrt{2 \, \sqrt{5} + 5} \sqrt{\sqrt{5} + 3} + 2 \, {\left({\left(5 \, \sqrt{5} - 11\right)} e^{x} - 5 \, \sqrt{5} + 9\right)} \sqrt{2 \, \sqrt{5} + 5}\right)} {\left(8 \, \sqrt{5} + 24\right)}^{\frac{1}{4}}\right)} + \frac{1}{20} \, {\left(2 \, {\left(4 \, \sqrt{5} - 5\right)} e^{x} + \sqrt{5} - 5\right)} \sqrt{2 \, \sqrt{5} + 5}\right) + \frac{1}{200} \, \sqrt{2} \sqrt{2 \, \sqrt{2} {\left(2 \, \sqrt{5} - 5\right)} \sqrt{\sqrt{5} + 3} - 4 \, \sqrt{5} + 20} {\left(8 \, \sqrt{5} + 24\right)}^{\frac{1}{4}} {\left(3 \, \sqrt{5} - 5\right)} \sqrt{2 \, \sqrt{5} + 5} \sqrt{\sqrt{5} + 3} \arctan\left(-\frac{1}{40} \, \sqrt{2} {\left({\left(11 \, \sqrt{5} - 25\right)} e^{x} + 7 \, \sqrt{5} - 15\right)} \sqrt{2 \, \sqrt{5} + 5} \sqrt{\sqrt{5} + 3} - \frac{1}{80} \, \sqrt{2} {\left(\sqrt{2} {\left({\left(11 \, \sqrt{5} - 25\right)} e^{x} - 4 \, \sqrt{5} + 10\right)} \sqrt{2 \, \sqrt{5} + 5} \sqrt{\sqrt{5} + 3} + 2 \, {\left({\left(3 \, \sqrt{5} - 5\right)} e^{x} - 7 \, \sqrt{5} + 15\right)} \sqrt{2 \, \sqrt{5} + 5}\right)} \sqrt{\sqrt{5} + 3} - \frac{1}{12800} \, {\left(80 \, \sqrt{2} {\left(5 \, \sqrt{5} - 11\right)} \sqrt{2 \, \sqrt{5} + 5} \sqrt{\sqrt{5} + 3} + 40 \, \sqrt{2} {\left(\sqrt{2} {\left(5 \, \sqrt{5} - 11\right)} \sqrt{2 \, \sqrt{5} + 5} \sqrt{\sqrt{5} + 3} + 2 \, \sqrt{2 \, \sqrt{5} + 5} {\left(\sqrt{5} - 3\right)}\right)} \sqrt{\sqrt{5} + 3} - \sqrt{2 \, \sqrt{2} {\left(2 \, \sqrt{5} - 5\right)} \sqrt{\sqrt{5} + 3} - 4 \, \sqrt{5} + 20} {\left({\left(\sqrt{2} {\left(7 \, \sqrt{5} - 15\right)} \sqrt{2 \, \sqrt{5} + 5} \sqrt{\sqrt{5} + 3} + 2 \, {\left(11 \, \sqrt{5} - 25\right)} \sqrt{2 \, \sqrt{5} + 5}\right)} {\left(8 \, \sqrt{5} + 24\right)}^{\frac{3}{4}} + 4 \, {\left(\sqrt{2} {\left(17 \, \sqrt{5} - 35\right)} \sqrt{2 \, \sqrt{5} + 5} \sqrt{\sqrt{5} + 3} + 2 \, {\left(11 \, \sqrt{5} - 25\right)} \sqrt{2 \, \sqrt{5} + 5}\right)} {\left(8 \, \sqrt{5} + 24\right)}^{\frac{1}{4}}\right)} + 320 \, \sqrt{2 \, \sqrt{5} + 5} {\left(\sqrt{5} - 4\right)}\right)} \sqrt{-20 \, \sqrt{2} \sqrt{\sqrt{5} + 3} {\left(\sqrt{5} - 3\right)} - 40 \, {\left(\sqrt{5} - 1\right)} e^{x} - 2 \, {\left(\sqrt{2} {\left({\left(2 \, \sqrt{5} - 5\right)} e^{x} + 3 \, \sqrt{5} - 5\right)} \sqrt{\sqrt{5} + 3} + 2 \, {\left(\sqrt{5} - 5\right)} e^{x} + 3 \, \sqrt{5} - 5\right)} \sqrt{2 \, \sqrt{2} {\left(2 \, \sqrt{5} - 5\right)} \sqrt{\sqrt{5} + 3} - 4 \, \sqrt{5} + 20} {\left(8 \, \sqrt{5} + 24\right)}^{\frac{1}{4}} + 80 \, e^{\left(2 \, x\right)} + 80} + \frac{1}{640} \, \sqrt{2 \, \sqrt{2} {\left(2 \, \sqrt{5} - 5\right)} \sqrt{\sqrt{5} + 3} - 4 \, \sqrt{5} + 20} {\left({\left(\sqrt{2} {\left({\left(3 \, \sqrt{5} - 7\right)} e^{x} - 8 \, \sqrt{5} + 18\right)} \sqrt{2 \, \sqrt{5} + 5} \sqrt{\sqrt{5} + 3} + 2 \, {\left({\left(5 \, \sqrt{5} - 11\right)} e^{x} - 2 \, \sqrt{5} + 4\right)} \sqrt{2 \, \sqrt{5} + 5}\right)} {\left(8 \, \sqrt{5} + 24\right)}^{\frac{3}{4}} + 4 \, {\left(\sqrt{2} {\left({\left(7 \, \sqrt{5} - 17\right)} e^{x} - 8 \, \sqrt{5} + 18\right)} \sqrt{2 \, \sqrt{5} + 5} \sqrt{\sqrt{5} + 3} + 2 \, {\left({\left(5 \, \sqrt{5} - 11\right)} e^{x} - 5 \, \sqrt{5} + 9\right)} \sqrt{2 \, \sqrt{5} + 5}\right)} {\left(8 \, \sqrt{5} + 24\right)}^{\frac{1}{4}}\right)} - \frac{1}{20} \, {\left(2 \, {\left(4 \, \sqrt{5} - 5\right)} e^{x} + \sqrt{5} - 5\right)} \sqrt{2 \, \sqrt{5} + 5}\right) - \frac{1}{400} \, \sqrt{-{\left(2 \, \sqrt{5} + 5\right)} \sqrt{-8 \, \sqrt{5} + 24} + 4 \, \sqrt{5} + 20} {\left(3 \, \sqrt{5} + 5\right)} \sqrt{-2 \, \sqrt{5} + 5} {\left(-8 \, \sqrt{5} + 24\right)}^{\frac{3}{4}} \arctan\left(-\frac{1}{1280} \, {\left({\left(4 \, {\left(5 \, \sqrt{5} + 11\right)} e^{x} + {\left({\left(3 \, \sqrt{5} + 7\right)} e^{x} - 8 \, \sqrt{5} - 18\right)} \sqrt{-8 \, \sqrt{5} + 24} - 8 \, \sqrt{5} - 16\right)} {\left(-8 \, \sqrt{5} + 24\right)}^{\frac{3}{4}} + 4 \, {\left(4 \, {\left(5 \, \sqrt{5} + 11\right)} e^{x} + {\left({\left(7 \, \sqrt{5} + 17\right)} e^{x} - 8 \, \sqrt{5} - 18\right)} \sqrt{-8 \, \sqrt{5} + 24} - 20 \, \sqrt{5} - 36\right)} {\left(-8 \, \sqrt{5} + 24\right)}^{\frac{1}{4}}\right)} \sqrt{-{\left(2 \, \sqrt{5} + 5\right)} \sqrt{-8 \, \sqrt{5} + 24} + 4 \, \sqrt{5} + 20} \sqrt{-2 \, \sqrt{5} + 5} + \frac{1}{25600} \, {\left({\left({\left({\left(7 \, \sqrt{5} + 15\right)} \sqrt{-8 \, \sqrt{5} + 24} + 44 \, \sqrt{5} + 100\right)} {\left(-8 \, \sqrt{5} + 24\right)}^{\frac{3}{4}} + 4 \, {\left({\left(17 \, \sqrt{5} + 35\right)} \sqrt{-8 \, \sqrt{5} + 24} + 44 \, \sqrt{5} + 100\right)} {\left(-8 \, \sqrt{5} + 24\right)}^{\frac{1}{4}}\right)} \sqrt{-{\left(2 \, \sqrt{5} + 5\right)} \sqrt{-8 \, \sqrt{5} + 24} + 4 \, \sqrt{5} + 20} \sqrt{-2 \, \sqrt{5} + 5} - 20 \, {\left({\left({\left(5 \, \sqrt{5} + 11\right)} \sqrt{-8 \, \sqrt{5} + 24} + 4 \, \sqrt{5} + 12\right)} \sqrt{-8 \, \sqrt{5} + 24} + 4 \, {\left(5 \, \sqrt{5} + 11\right)} \sqrt{-8 \, \sqrt{5} + 24} + 32 \, \sqrt{5} + 128\right)} \sqrt{-2 \, \sqrt{5} + 5}\right)} \sqrt{40 \, {\left(\sqrt{5} + 1\right)} e^{x} + {\left(4 \, {\left(\sqrt{5} + 5\right)} e^{x} + {\left({\left(2 \, \sqrt{5} + 5\right)} e^{x} + 3 \, \sqrt{5} + 5\right)} \sqrt{-8 \, \sqrt{5} + 24} + 6 \, \sqrt{5} + 10\right)} \sqrt{-{\left(2 \, \sqrt{5} + 5\right)} \sqrt{-8 \, \sqrt{5} + 24} + 4 \, \sqrt{5} + 20} {\left(-8 \, \sqrt{5} + 24\right)}^{\frac{1}{4}} + 10 \, {\left(\sqrt{5} + 3\right)} \sqrt{-8 \, \sqrt{5} + 24} + 80 \, e^{\left(2 \, x\right)} + 80} + \frac{1}{320} \, {\left(32 \, {\left(4 \, \sqrt{5} + 5\right)} e^{x} + 4 \, {\left({\left(11 \, \sqrt{5} + 25\right)} e^{x} + 7 \, \sqrt{5} + 15\right)} \sqrt{-8 \, \sqrt{5} + 24} + {\left(4 \, {\left(3 \, \sqrt{5} + 5\right)} e^{x} + {\left({\left(11 \, \sqrt{5} + 25\right)} e^{x} - 4 \, \sqrt{5} - 10\right)} \sqrt{-8 \, \sqrt{5} + 24} - 28 \, \sqrt{5} - 60\right)} \sqrt{-8 \, \sqrt{5} + 24} + 16 \, \sqrt{5} + 80\right)} \sqrt{-2 \, \sqrt{5} + 5}\right) - \frac{1}{400} \, \sqrt{-{\left(2 \, \sqrt{5} + 5\right)} \sqrt{-8 \, \sqrt{5} + 24} + 4 \, \sqrt{5} + 20} {\left(3 \, \sqrt{5} + 5\right)} \sqrt{-2 \, \sqrt{5} + 5} {\left(-8 \, \sqrt{5} + 24\right)}^{\frac{3}{4}} \arctan\left(-\frac{1}{1280} \, {\left({\left(4 \, {\left(5 \, \sqrt{5} + 11\right)} e^{x} + {\left({\left(3 \, \sqrt{5} + 7\right)} e^{x} - 8 \, \sqrt{5} - 18\right)} \sqrt{-8 \, \sqrt{5} + 24} - 8 \, \sqrt{5} - 16\right)} {\left(-8 \, \sqrt{5} + 24\right)}^{\frac{3}{4}} + 4 \, {\left(4 \, {\left(5 \, \sqrt{5} + 11\right)} e^{x} + {\left({\left(7 \, \sqrt{5} + 17\right)} e^{x} - 8 \, \sqrt{5} - 18\right)} \sqrt{-8 \, \sqrt{5} + 24} - 20 \, \sqrt{5} - 36\right)} {\left(-8 \, \sqrt{5} + 24\right)}^{\frac{1}{4}}\right)} \sqrt{-{\left(2 \, \sqrt{5} + 5\right)} \sqrt{-8 \, \sqrt{5} + 24} + 4 \, \sqrt{5} + 20} \sqrt{-2 \, \sqrt{5} + 5} + \frac{1}{25600} \, {\left({\left({\left({\left(7 \, \sqrt{5} + 15\right)} \sqrt{-8 \, \sqrt{5} + 24} + 44 \, \sqrt{5} + 100\right)} {\left(-8 \, \sqrt{5} + 24\right)}^{\frac{3}{4}} + 4 \, {\left({\left(17 \, \sqrt{5} + 35\right)} \sqrt{-8 \, \sqrt{5} + 24} + 44 \, \sqrt{5} + 100\right)} {\left(-8 \, \sqrt{5} + 24\right)}^{\frac{1}{4}}\right)} \sqrt{-{\left(2 \, \sqrt{5} + 5\right)} \sqrt{-8 \, \sqrt{5} + 24} + 4 \, \sqrt{5} + 20} \sqrt{-2 \, \sqrt{5} + 5} + 20 \, {\left({\left({\left(5 \, \sqrt{5} + 11\right)} \sqrt{-8 \, \sqrt{5} + 24} + 4 \, \sqrt{5} + 12\right)} \sqrt{-8 \, \sqrt{5} + 24} + 4 \, {\left(5 \, \sqrt{5} + 11\right)} \sqrt{-8 \, \sqrt{5} + 24} + 32 \, \sqrt{5} + 128\right)} \sqrt{-2 \, \sqrt{5} + 5}\right)} \sqrt{40 \, {\left(\sqrt{5} + 1\right)} e^{x} - {\left(4 \, {\left(\sqrt{5} + 5\right)} e^{x} + {\left({\left(2 \, \sqrt{5} + 5\right)} e^{x} + 3 \, \sqrt{5} + 5\right)} \sqrt{-8 \, \sqrt{5} + 24} + 6 \, \sqrt{5} + 10\right)} \sqrt{-{\left(2 \, \sqrt{5} + 5\right)} \sqrt{-8 \, \sqrt{5} + 24} + 4 \, \sqrt{5} + 20} {\left(-8 \, \sqrt{5} + 24\right)}^{\frac{1}{4}} + 10 \, {\left(\sqrt{5} + 3\right)} \sqrt{-8 \, \sqrt{5} + 24} + 80 \, e^{\left(2 \, x\right)} + 80} - \frac{1}{320} \, {\left(32 \, {\left(4 \, \sqrt{5} + 5\right)} e^{x} + 4 \, {\left({\left(11 \, \sqrt{5} + 25\right)} e^{x} + 7 \, \sqrt{5} + 15\right)} \sqrt{-8 \, \sqrt{5} + 24} + {\left(4 \, {\left(3 \, \sqrt{5} + 5\right)} e^{x} + {\left({\left(11 \, \sqrt{5} + 25\right)} e^{x} - 4 \, \sqrt{5} - 10\right)} \sqrt{-8 \, \sqrt{5} + 24} - 28 \, \sqrt{5} - 60\right)} \sqrt{-8 \, \sqrt{5} + 24} + 16 \, \sqrt{5} + 80\right)} \sqrt{-2 \, \sqrt{5} + 5}\right) - \frac{1}{800} \, {\left(\sqrt{2} {\left(3 \, \sqrt{5} - 5\right)} \sqrt{\sqrt{5} + 3} + 8 \, \sqrt{5}\right)} \sqrt{2 \, \sqrt{2} {\left(2 \, \sqrt{5} - 5\right)} \sqrt{\sqrt{5} + 3} - 4 \, \sqrt{5} + 20} {\left(8 \, \sqrt{5} + 24\right)}^{\frac{1}{4}} \log\left(-4 \, \sqrt{2} \sqrt{\sqrt{5} + 3} {\left(\sqrt{5} - 3\right)} - 8 \, {\left(\sqrt{5} - 1\right)} e^{x} + \frac{2}{5} \, {\left(\sqrt{2} {\left({\left(2 \, \sqrt{5} - 5\right)} e^{x} + 3 \, \sqrt{5} - 5\right)} \sqrt{\sqrt{5} + 3} + 2 \, {\left(\sqrt{5} - 5\right)} e^{x} + 3 \, \sqrt{5} - 5\right)} \sqrt{2 \, \sqrt{2} {\left(2 \, \sqrt{5} - 5\right)} \sqrt{\sqrt{5} + 3} - 4 \, \sqrt{5} + 20} {\left(8 \, \sqrt{5} + 24\right)}^{\frac{1}{4}} + 16 \, e^{\left(2 \, x\right)} + 16\right) + \frac{1}{800} \, {\left(\sqrt{2} {\left(3 \, \sqrt{5} - 5\right)} \sqrt{\sqrt{5} + 3} + 8 \, \sqrt{5}\right)} \sqrt{2 \, \sqrt{2} {\left(2 \, \sqrt{5} - 5\right)} \sqrt{\sqrt{5} + 3} - 4 \, \sqrt{5} + 20} {\left(8 \, \sqrt{5} + 24\right)}^{\frac{1}{4}} \log\left(-4 \, \sqrt{2} \sqrt{\sqrt{5} + 3} {\left(\sqrt{5} - 3\right)} - 8 \, {\left(\sqrt{5} - 1\right)} e^{x} - \frac{2}{5} \, {\left(\sqrt{2} {\left({\left(2 \, \sqrt{5} - 5\right)} e^{x} + 3 \, \sqrt{5} - 5\right)} \sqrt{\sqrt{5} + 3} + 2 \, {\left(\sqrt{5} - 5\right)} e^{x} + 3 \, \sqrt{5} - 5\right)} \sqrt{2 \, \sqrt{2} {\left(2 \, \sqrt{5} - 5\right)} \sqrt{\sqrt{5} + 3} - 4 \, \sqrt{5} + 20} {\left(8 \, \sqrt{5} + 24\right)}^{\frac{1}{4}} + 16 \, e^{\left(2 \, x\right)} + 16\right) - \frac{1}{1600} \, {\left({\left(3 \, \sqrt{5} + 5\right)} \sqrt{-8 \, \sqrt{5} + 24} + 16 \, \sqrt{5}\right)} \sqrt{-{\left(2 \, \sqrt{5} + 5\right)} \sqrt{-8 \, \sqrt{5} + 24} + 4 \, \sqrt{5} + 20} {\left(-8 \, \sqrt{5} + 24\right)}^{\frac{1}{4}} \log\left(8 \, {\left(\sqrt{5} + 1\right)} e^{x} + \frac{1}{5} \, {\left(4 \, {\left(\sqrt{5} + 5\right)} e^{x} + {\left({\left(2 \, \sqrt{5} + 5\right)} e^{x} + 3 \, \sqrt{5} + 5\right)} \sqrt{-8 \, \sqrt{5} + 24} + 6 \, \sqrt{5} + 10\right)} \sqrt{-{\left(2 \, \sqrt{5} + 5\right)} \sqrt{-8 \, \sqrt{5} + 24} + 4 \, \sqrt{5} + 20} {\left(-8 \, \sqrt{5} + 24\right)}^{\frac{1}{4}} + 2 \, {\left(\sqrt{5} + 3\right)} \sqrt{-8 \, \sqrt{5} + 24} + 16 \, e^{\left(2 \, x\right)} + 16\right) + \frac{1}{1600} \, {\left({\left(3 \, \sqrt{5} + 5\right)} \sqrt{-8 \, \sqrt{5} + 24} + 16 \, \sqrt{5}\right)} \sqrt{-{\left(2 \, \sqrt{5} + 5\right)} \sqrt{-8 \, \sqrt{5} + 24} + 4 \, \sqrt{5} + 20} {\left(-8 \, \sqrt{5} + 24\right)}^{\frac{1}{4}} \log\left(8 \, {\left(\sqrt{5} + 1\right)} e^{x} - \frac{1}{5} \, {\left(4 \, {\left(\sqrt{5} + 5\right)} e^{x} + {\left({\left(2 \, \sqrt{5} + 5\right)} e^{x} + 3 \, \sqrt{5} + 5\right)} \sqrt{-8 \, \sqrt{5} + 24} + 6 \, \sqrt{5} + 10\right)} \sqrt{-{\left(2 \, \sqrt{5} + 5\right)} \sqrt{-8 \, \sqrt{5} + 24} + 4 \, \sqrt{5} + 20} {\left(-8 \, \sqrt{5} + 24\right)}^{\frac{1}{4}} + 2 \, {\left(\sqrt{5} + 3\right)} \sqrt{-8 \, \sqrt{5} + 24} + 16 \, e^{\left(2 \, x\right)} + 16\right) + \frac{1}{10} \, \sqrt{2} \log\left(\frac{2 \, {\left(\sqrt{2} - 1\right)} e^{x} - 2 \, \sqrt{2} + e^{\left(2 \, x\right)} + 3}{e^{\left(2 \, x\right)} - 2 \, e^{x} - 1}\right)"," ",0,"1/200*sqrt(2)*sqrt(2*sqrt(2)*(2*sqrt(5) - 5)*sqrt(sqrt(5) + 3) - 4*sqrt(5) + 20)*(8*sqrt(5) + 24)^(1/4)*(3*sqrt(5) - 5)*sqrt(2*sqrt(5) + 5)*sqrt(sqrt(5) + 3)*arctan(1/40*sqrt(2)*((11*sqrt(5) - 25)*e^x + 7*sqrt(5) - 15)*sqrt(2*sqrt(5) + 5)*sqrt(sqrt(5) + 3) + 1/80*sqrt(2)*(sqrt(2)*((11*sqrt(5) - 25)*e^x - 4*sqrt(5) + 10)*sqrt(2*sqrt(5) + 5)*sqrt(sqrt(5) + 3) + 2*((3*sqrt(5) - 5)*e^x - 7*sqrt(5) + 15)*sqrt(2*sqrt(5) + 5))*sqrt(sqrt(5) + 3) + 1/12800*(80*sqrt(2)*(5*sqrt(5) - 11)*sqrt(2*sqrt(5) + 5)*sqrt(sqrt(5) + 3) + 40*sqrt(2)*(sqrt(2)*(5*sqrt(5) - 11)*sqrt(2*sqrt(5) + 5)*sqrt(sqrt(5) + 3) + 2*sqrt(2*sqrt(5) + 5)*(sqrt(5) - 3))*sqrt(sqrt(5) + 3) + sqrt(2*sqrt(2)*(2*sqrt(5) - 5)*sqrt(sqrt(5) + 3) - 4*sqrt(5) + 20)*((sqrt(2)*(7*sqrt(5) - 15)*sqrt(2*sqrt(5) + 5)*sqrt(sqrt(5) + 3) + 2*(11*sqrt(5) - 25)*sqrt(2*sqrt(5) + 5))*(8*sqrt(5) + 24)^(3/4) + 4*(sqrt(2)*(17*sqrt(5) - 35)*sqrt(2*sqrt(5) + 5)*sqrt(sqrt(5) + 3) + 2*(11*sqrt(5) - 25)*sqrt(2*sqrt(5) + 5))*(8*sqrt(5) + 24)^(1/4)) + 320*sqrt(2*sqrt(5) + 5)*(sqrt(5) - 4))*sqrt(-20*sqrt(2)*sqrt(sqrt(5) + 3)*(sqrt(5) - 3) - 40*(sqrt(5) - 1)*e^x + 2*(sqrt(2)*((2*sqrt(5) - 5)*e^x + 3*sqrt(5) - 5)*sqrt(sqrt(5) + 3) + 2*(sqrt(5) - 5)*e^x + 3*sqrt(5) - 5)*sqrt(2*sqrt(2)*(2*sqrt(5) - 5)*sqrt(sqrt(5) + 3) - 4*sqrt(5) + 20)*(8*sqrt(5) + 24)^(1/4) + 80*e^(2*x) + 80) + 1/640*sqrt(2*sqrt(2)*(2*sqrt(5) - 5)*sqrt(sqrt(5) + 3) - 4*sqrt(5) + 20)*((sqrt(2)*((3*sqrt(5) - 7)*e^x - 8*sqrt(5) + 18)*sqrt(2*sqrt(5) + 5)*sqrt(sqrt(5) + 3) + 2*((5*sqrt(5) - 11)*e^x - 2*sqrt(5) + 4)*sqrt(2*sqrt(5) + 5))*(8*sqrt(5) + 24)^(3/4) + 4*(sqrt(2)*((7*sqrt(5) - 17)*e^x - 8*sqrt(5) + 18)*sqrt(2*sqrt(5) + 5)*sqrt(sqrt(5) + 3) + 2*((5*sqrt(5) - 11)*e^x - 5*sqrt(5) + 9)*sqrt(2*sqrt(5) + 5))*(8*sqrt(5) + 24)^(1/4)) + 1/20*(2*(4*sqrt(5) - 5)*e^x + sqrt(5) - 5)*sqrt(2*sqrt(5) + 5)) + 1/200*sqrt(2)*sqrt(2*sqrt(2)*(2*sqrt(5) - 5)*sqrt(sqrt(5) + 3) - 4*sqrt(5) + 20)*(8*sqrt(5) + 24)^(1/4)*(3*sqrt(5) - 5)*sqrt(2*sqrt(5) + 5)*sqrt(sqrt(5) + 3)*arctan(-1/40*sqrt(2)*((11*sqrt(5) - 25)*e^x + 7*sqrt(5) - 15)*sqrt(2*sqrt(5) + 5)*sqrt(sqrt(5) + 3) - 1/80*sqrt(2)*(sqrt(2)*((11*sqrt(5) - 25)*e^x - 4*sqrt(5) + 10)*sqrt(2*sqrt(5) + 5)*sqrt(sqrt(5) + 3) + 2*((3*sqrt(5) - 5)*e^x - 7*sqrt(5) + 15)*sqrt(2*sqrt(5) + 5))*sqrt(sqrt(5) + 3) - 1/12800*(80*sqrt(2)*(5*sqrt(5) - 11)*sqrt(2*sqrt(5) + 5)*sqrt(sqrt(5) + 3) + 40*sqrt(2)*(sqrt(2)*(5*sqrt(5) - 11)*sqrt(2*sqrt(5) + 5)*sqrt(sqrt(5) + 3) + 2*sqrt(2*sqrt(5) + 5)*(sqrt(5) - 3))*sqrt(sqrt(5) + 3) - sqrt(2*sqrt(2)*(2*sqrt(5) - 5)*sqrt(sqrt(5) + 3) - 4*sqrt(5) + 20)*((sqrt(2)*(7*sqrt(5) - 15)*sqrt(2*sqrt(5) + 5)*sqrt(sqrt(5) + 3) + 2*(11*sqrt(5) - 25)*sqrt(2*sqrt(5) + 5))*(8*sqrt(5) + 24)^(3/4) + 4*(sqrt(2)*(17*sqrt(5) - 35)*sqrt(2*sqrt(5) + 5)*sqrt(sqrt(5) + 3) + 2*(11*sqrt(5) - 25)*sqrt(2*sqrt(5) + 5))*(8*sqrt(5) + 24)^(1/4)) + 320*sqrt(2*sqrt(5) + 5)*(sqrt(5) - 4))*sqrt(-20*sqrt(2)*sqrt(sqrt(5) + 3)*(sqrt(5) - 3) - 40*(sqrt(5) - 1)*e^x - 2*(sqrt(2)*((2*sqrt(5) - 5)*e^x + 3*sqrt(5) - 5)*sqrt(sqrt(5) + 3) + 2*(sqrt(5) - 5)*e^x + 3*sqrt(5) - 5)*sqrt(2*sqrt(2)*(2*sqrt(5) - 5)*sqrt(sqrt(5) + 3) - 4*sqrt(5) + 20)*(8*sqrt(5) + 24)^(1/4) + 80*e^(2*x) + 80) + 1/640*sqrt(2*sqrt(2)*(2*sqrt(5) - 5)*sqrt(sqrt(5) + 3) - 4*sqrt(5) + 20)*((sqrt(2)*((3*sqrt(5) - 7)*e^x - 8*sqrt(5) + 18)*sqrt(2*sqrt(5) + 5)*sqrt(sqrt(5) + 3) + 2*((5*sqrt(5) - 11)*e^x - 2*sqrt(5) + 4)*sqrt(2*sqrt(5) + 5))*(8*sqrt(5) + 24)^(3/4) + 4*(sqrt(2)*((7*sqrt(5) - 17)*e^x - 8*sqrt(5) + 18)*sqrt(2*sqrt(5) + 5)*sqrt(sqrt(5) + 3) + 2*((5*sqrt(5) - 11)*e^x - 5*sqrt(5) + 9)*sqrt(2*sqrt(5) + 5))*(8*sqrt(5) + 24)^(1/4)) - 1/20*(2*(4*sqrt(5) - 5)*e^x + sqrt(5) - 5)*sqrt(2*sqrt(5) + 5)) - 1/400*sqrt(-(2*sqrt(5) + 5)*sqrt(-8*sqrt(5) + 24) + 4*sqrt(5) + 20)*(3*sqrt(5) + 5)*sqrt(-2*sqrt(5) + 5)*(-8*sqrt(5) + 24)^(3/4)*arctan(-1/1280*((4*(5*sqrt(5) + 11)*e^x + ((3*sqrt(5) + 7)*e^x - 8*sqrt(5) - 18)*sqrt(-8*sqrt(5) + 24) - 8*sqrt(5) - 16)*(-8*sqrt(5) + 24)^(3/4) + 4*(4*(5*sqrt(5) + 11)*e^x + ((7*sqrt(5) + 17)*e^x - 8*sqrt(5) - 18)*sqrt(-8*sqrt(5) + 24) - 20*sqrt(5) - 36)*(-8*sqrt(5) + 24)^(1/4))*sqrt(-(2*sqrt(5) + 5)*sqrt(-8*sqrt(5) + 24) + 4*sqrt(5) + 20)*sqrt(-2*sqrt(5) + 5) + 1/25600*((((7*sqrt(5) + 15)*sqrt(-8*sqrt(5) + 24) + 44*sqrt(5) + 100)*(-8*sqrt(5) + 24)^(3/4) + 4*((17*sqrt(5) + 35)*sqrt(-8*sqrt(5) + 24) + 44*sqrt(5) + 100)*(-8*sqrt(5) + 24)^(1/4))*sqrt(-(2*sqrt(5) + 5)*sqrt(-8*sqrt(5) + 24) + 4*sqrt(5) + 20)*sqrt(-2*sqrt(5) + 5) - 20*(((5*sqrt(5) + 11)*sqrt(-8*sqrt(5) + 24) + 4*sqrt(5) + 12)*sqrt(-8*sqrt(5) + 24) + 4*(5*sqrt(5) + 11)*sqrt(-8*sqrt(5) + 24) + 32*sqrt(5) + 128)*sqrt(-2*sqrt(5) + 5))*sqrt(40*(sqrt(5) + 1)*e^x + (4*(sqrt(5) + 5)*e^x + ((2*sqrt(5) + 5)*e^x + 3*sqrt(5) + 5)*sqrt(-8*sqrt(5) + 24) + 6*sqrt(5) + 10)*sqrt(-(2*sqrt(5) + 5)*sqrt(-8*sqrt(5) + 24) + 4*sqrt(5) + 20)*(-8*sqrt(5) + 24)^(1/4) + 10*(sqrt(5) + 3)*sqrt(-8*sqrt(5) + 24) + 80*e^(2*x) + 80) + 1/320*(32*(4*sqrt(5) + 5)*e^x + 4*((11*sqrt(5) + 25)*e^x + 7*sqrt(5) + 15)*sqrt(-8*sqrt(5) + 24) + (4*(3*sqrt(5) + 5)*e^x + ((11*sqrt(5) + 25)*e^x - 4*sqrt(5) - 10)*sqrt(-8*sqrt(5) + 24) - 28*sqrt(5) - 60)*sqrt(-8*sqrt(5) + 24) + 16*sqrt(5) + 80)*sqrt(-2*sqrt(5) + 5)) - 1/400*sqrt(-(2*sqrt(5) + 5)*sqrt(-8*sqrt(5) + 24) + 4*sqrt(5) + 20)*(3*sqrt(5) + 5)*sqrt(-2*sqrt(5) + 5)*(-8*sqrt(5) + 24)^(3/4)*arctan(-1/1280*((4*(5*sqrt(5) + 11)*e^x + ((3*sqrt(5) + 7)*e^x - 8*sqrt(5) - 18)*sqrt(-8*sqrt(5) + 24) - 8*sqrt(5) - 16)*(-8*sqrt(5) + 24)^(3/4) + 4*(4*(5*sqrt(5) + 11)*e^x + ((7*sqrt(5) + 17)*e^x - 8*sqrt(5) - 18)*sqrt(-8*sqrt(5) + 24) - 20*sqrt(5) - 36)*(-8*sqrt(5) + 24)^(1/4))*sqrt(-(2*sqrt(5) + 5)*sqrt(-8*sqrt(5) + 24) + 4*sqrt(5) + 20)*sqrt(-2*sqrt(5) + 5) + 1/25600*((((7*sqrt(5) + 15)*sqrt(-8*sqrt(5) + 24) + 44*sqrt(5) + 100)*(-8*sqrt(5) + 24)^(3/4) + 4*((17*sqrt(5) + 35)*sqrt(-8*sqrt(5) + 24) + 44*sqrt(5) + 100)*(-8*sqrt(5) + 24)^(1/4))*sqrt(-(2*sqrt(5) + 5)*sqrt(-8*sqrt(5) + 24) + 4*sqrt(5) + 20)*sqrt(-2*sqrt(5) + 5) + 20*(((5*sqrt(5) + 11)*sqrt(-8*sqrt(5) + 24) + 4*sqrt(5) + 12)*sqrt(-8*sqrt(5) + 24) + 4*(5*sqrt(5) + 11)*sqrt(-8*sqrt(5) + 24) + 32*sqrt(5) + 128)*sqrt(-2*sqrt(5) + 5))*sqrt(40*(sqrt(5) + 1)*e^x - (4*(sqrt(5) + 5)*e^x + ((2*sqrt(5) + 5)*e^x + 3*sqrt(5) + 5)*sqrt(-8*sqrt(5) + 24) + 6*sqrt(5) + 10)*sqrt(-(2*sqrt(5) + 5)*sqrt(-8*sqrt(5) + 24) + 4*sqrt(5) + 20)*(-8*sqrt(5) + 24)^(1/4) + 10*(sqrt(5) + 3)*sqrt(-8*sqrt(5) + 24) + 80*e^(2*x) + 80) - 1/320*(32*(4*sqrt(5) + 5)*e^x + 4*((11*sqrt(5) + 25)*e^x + 7*sqrt(5) + 15)*sqrt(-8*sqrt(5) + 24) + (4*(3*sqrt(5) + 5)*e^x + ((11*sqrt(5) + 25)*e^x - 4*sqrt(5) - 10)*sqrt(-8*sqrt(5) + 24) - 28*sqrt(5) - 60)*sqrt(-8*sqrt(5) + 24) + 16*sqrt(5) + 80)*sqrt(-2*sqrt(5) + 5)) - 1/800*(sqrt(2)*(3*sqrt(5) - 5)*sqrt(sqrt(5) + 3) + 8*sqrt(5))*sqrt(2*sqrt(2)*(2*sqrt(5) - 5)*sqrt(sqrt(5) + 3) - 4*sqrt(5) + 20)*(8*sqrt(5) + 24)^(1/4)*log(-4*sqrt(2)*sqrt(sqrt(5) + 3)*(sqrt(5) - 3) - 8*(sqrt(5) - 1)*e^x + 2/5*(sqrt(2)*((2*sqrt(5) - 5)*e^x + 3*sqrt(5) - 5)*sqrt(sqrt(5) + 3) + 2*(sqrt(5) - 5)*e^x + 3*sqrt(5) - 5)*sqrt(2*sqrt(2)*(2*sqrt(5) - 5)*sqrt(sqrt(5) + 3) - 4*sqrt(5) + 20)*(8*sqrt(5) + 24)^(1/4) + 16*e^(2*x) + 16) + 1/800*(sqrt(2)*(3*sqrt(5) - 5)*sqrt(sqrt(5) + 3) + 8*sqrt(5))*sqrt(2*sqrt(2)*(2*sqrt(5) - 5)*sqrt(sqrt(5) + 3) - 4*sqrt(5) + 20)*(8*sqrt(5) + 24)^(1/4)*log(-4*sqrt(2)*sqrt(sqrt(5) + 3)*(sqrt(5) - 3) - 8*(sqrt(5) - 1)*e^x - 2/5*(sqrt(2)*((2*sqrt(5) - 5)*e^x + 3*sqrt(5) - 5)*sqrt(sqrt(5) + 3) + 2*(sqrt(5) - 5)*e^x + 3*sqrt(5) - 5)*sqrt(2*sqrt(2)*(2*sqrt(5) - 5)*sqrt(sqrt(5) + 3) - 4*sqrt(5) + 20)*(8*sqrt(5) + 24)^(1/4) + 16*e^(2*x) + 16) - 1/1600*((3*sqrt(5) + 5)*sqrt(-8*sqrt(5) + 24) + 16*sqrt(5))*sqrt(-(2*sqrt(5) + 5)*sqrt(-8*sqrt(5) + 24) + 4*sqrt(5) + 20)*(-8*sqrt(5) + 24)^(1/4)*log(8*(sqrt(5) + 1)*e^x + 1/5*(4*(sqrt(5) + 5)*e^x + ((2*sqrt(5) + 5)*e^x + 3*sqrt(5) + 5)*sqrt(-8*sqrt(5) + 24) + 6*sqrt(5) + 10)*sqrt(-(2*sqrt(5) + 5)*sqrt(-8*sqrt(5) + 24) + 4*sqrt(5) + 20)*(-8*sqrt(5) + 24)^(1/4) + 2*(sqrt(5) + 3)*sqrt(-8*sqrt(5) + 24) + 16*e^(2*x) + 16) + 1/1600*((3*sqrt(5) + 5)*sqrt(-8*sqrt(5) + 24) + 16*sqrt(5))*sqrt(-(2*sqrt(5) + 5)*sqrt(-8*sqrt(5) + 24) + 4*sqrt(5) + 20)*(-8*sqrt(5) + 24)^(1/4)*log(8*(sqrt(5) + 1)*e^x - 1/5*(4*(sqrt(5) + 5)*e^x + ((2*sqrt(5) + 5)*e^x + 3*sqrt(5) + 5)*sqrt(-8*sqrt(5) + 24) + 6*sqrt(5) + 10)*sqrt(-(2*sqrt(5) + 5)*sqrt(-8*sqrt(5) + 24) + 4*sqrt(5) + 20)*(-8*sqrt(5) + 24)^(1/4) + 2*(sqrt(5) + 3)*sqrt(-8*sqrt(5) + 24) + 16*e^(2*x) + 16) + 1/10*sqrt(2)*log((2*(sqrt(2) - 1)*e^x - 2*sqrt(2) + e^(2*x) + 3)/(e^(2*x) - 2*e^x - 1))","B",0
274,1,155,0,0.946518," ","integrate(1/(1-sinh(x)^6),x, algorithm=""fricas"")","-\frac{1}{12} \, \sqrt{3} \log\left(16 \, \sqrt{3} + 4 \, e^{\left(4 \, x\right)} + 28\right) + \frac{1}{12} \, \sqrt{3} \log\left(-16 \, \sqrt{3} + 4 \, e^{\left(4 \, x\right)} + 28\right) + \frac{1}{12} \, \sqrt{2} \log\left(\frac{2 \, {\left(2 \, \sqrt{2} - 3\right)} e^{\left(2 \, x\right)} - 12 \, \sqrt{2} + e^{\left(4 \, x\right)} + 17}{e^{\left(4 \, x\right)} - 6 \, e^{\left(2 \, x\right)} + 1}\right) - \frac{1}{3} \, \arctan\left(-{\left(\sqrt{3} + 2\right)} e^{\left(2 \, x\right)} + \frac{1}{2} \, {\left(\sqrt{3} + 2\right)} \sqrt{-16 \, \sqrt{3} + 4 \, e^{\left(4 \, x\right)} + 28}\right) + \frac{1}{3} \, \arctan\left(-{\left(\sqrt{3} - 2\right)} e^{\left(2 \, x\right)} + \sqrt{4 \, \sqrt{3} + e^{\left(4 \, x\right)} + 7} {\left(\sqrt{3} - 2\right)}\right)"," ",0,"-1/12*sqrt(3)*log(16*sqrt(3) + 4*e^(4*x) + 28) + 1/12*sqrt(3)*log(-16*sqrt(3) + 4*e^(4*x) + 28) + 1/12*sqrt(2)*log((2*(2*sqrt(2) - 3)*e^(2*x) - 12*sqrt(2) + e^(4*x) + 17)/(e^(4*x) - 6*e^(2*x) + 1)) - 1/3*arctan(-(sqrt(3) + 2)*e^(2*x) + 1/2*(sqrt(3) + 2)*sqrt(-16*sqrt(3) + 4*e^(4*x) + 28)) + 1/3*arctan(-(sqrt(3) - 2)*e^(2*x) + sqrt(4*sqrt(3) + e^(4*x) + 7)*(sqrt(3) - 2))","B",0
275,1,708,0,1.554287," ","integrate(1/(1-sinh(x)^8),x, algorithm=""fricas"")","-\frac{4 \, {\left(2^{\frac{1}{4}} e^{\left(2 \, x\right)} + 2^{\frac{1}{4}}\right)} \sqrt{-2 \, \sqrt{2} + 4} \arctan\left(\frac{1}{14} \, {\left(\sqrt{2} {\left(5 \, \sqrt{2} + 6\right)} + 8 \, \sqrt{2} + 4\right)} e^{\left(2 \, x\right)} - \frac{1}{28} \, {\left(2 \, \sqrt{2} {\left(5 \, \sqrt{2} + 6\right)} - {\left(2^{\frac{3}{4}} {\left(8 \, \sqrt{2} + 11\right)} + 2 \cdot 2^{\frac{1}{4}} {\left(5 \, \sqrt{2} + 6\right)}\right)} \sqrt{-2 \, \sqrt{2} + 4} + 16 \, \sqrt{2} + 8\right)} \sqrt{-{\left(2^{\frac{3}{4}} e^{\left(2 \, x\right)} - 2^{\frac{1}{4}} {\left(3 \, \sqrt{2} + 4\right)}\right)} \sqrt{-2 \, \sqrt{2} + 4} + 4 \, \sqrt{2} + e^{\left(4 \, x\right)} - 2 \, e^{\left(2 \, x\right)} + 5} - \frac{1}{14} \, \sqrt{2} {\left(3 \, \sqrt{2} - 2\right)} - \frac{1}{28} \, {\left({\left(2^{\frac{3}{4}} {\left(8 \, \sqrt{2} + 11\right)} + 2 \cdot 2^{\frac{1}{4}} {\left(5 \, \sqrt{2} + 6\right)}\right)} e^{\left(2 \, x\right)} - 2^{\frac{3}{4}} {\left(2 \, \sqrt{2} + 1\right)} - 2 \cdot 2^{\frac{1}{4}} {\left(3 \, \sqrt{2} - 2\right)}\right)} \sqrt{-2 \, \sqrt{2} + 4} - \frac{1}{7} \, \sqrt{2} + \frac{3}{7}\right) + 4 \, {\left(2^{\frac{1}{4}} e^{\left(2 \, x\right)} + 2^{\frac{1}{4}}\right)} \sqrt{-2 \, \sqrt{2} + 4} \arctan\left(-\frac{1}{14} \, {\left(\sqrt{2} {\left(5 \, \sqrt{2} + 6\right)} + 8 \, \sqrt{2} + 4\right)} e^{\left(2 \, x\right)} + \frac{1}{28} \, {\left(2 \, \sqrt{2} {\left(5 \, \sqrt{2} + 6\right)} + {\left(2^{\frac{3}{4}} {\left(8 \, \sqrt{2} + 11\right)} + 2 \cdot 2^{\frac{1}{4}} {\left(5 \, \sqrt{2} + 6\right)}\right)} \sqrt{-2 \, \sqrt{2} + 4} + 16 \, \sqrt{2} + 8\right)} \sqrt{{\left(2^{\frac{3}{4}} e^{\left(2 \, x\right)} - 2^{\frac{1}{4}} {\left(3 \, \sqrt{2} + 4\right)}\right)} \sqrt{-2 \, \sqrt{2} + 4} + 4 \, \sqrt{2} + e^{\left(4 \, x\right)} - 2 \, e^{\left(2 \, x\right)} + 5} + \frac{1}{14} \, \sqrt{2} {\left(3 \, \sqrt{2} - 2\right)} - \frac{1}{28} \, {\left({\left(2^{\frac{3}{4}} {\left(8 \, \sqrt{2} + 11\right)} + 2 \cdot 2^{\frac{1}{4}} {\left(5 \, \sqrt{2} + 6\right)}\right)} e^{\left(2 \, x\right)} - 2^{\frac{3}{4}} {\left(2 \, \sqrt{2} + 1\right)} - 2 \cdot 2^{\frac{1}{4}} {\left(3 \, \sqrt{2} - 2\right)}\right)} \sqrt{-2 \, \sqrt{2} + 4} + \frac{1}{7} \, \sqrt{2} - \frac{3}{7}\right) - {\left(2^{\frac{1}{4}} {\left(\sqrt{2} + 1\right)} e^{\left(2 \, x\right)} + 2^{\frac{1}{4}} {\left(\sqrt{2} + 1\right)}\right)} \sqrt{-2 \, \sqrt{2} + 4} \log\left({\left(2^{\frac{3}{4}} e^{\left(2 \, x\right)} - 2^{\frac{1}{4}} {\left(3 \, \sqrt{2} + 4\right)}\right)} \sqrt{-2 \, \sqrt{2} + 4} + 4 \, \sqrt{2} + e^{\left(4 \, x\right)} - 2 \, e^{\left(2 \, x\right)} + 5\right) + {\left(2^{\frac{1}{4}} {\left(\sqrt{2} + 1\right)} e^{\left(2 \, x\right)} + 2^{\frac{1}{4}} {\left(\sqrt{2} + 1\right)}\right)} \sqrt{-2 \, \sqrt{2} + 4} \log\left(-{\left(2^{\frac{3}{4}} e^{\left(2 \, x\right)} - 2^{\frac{1}{4}} {\left(3 \, \sqrt{2} + 4\right)}\right)} \sqrt{-2 \, \sqrt{2} + 4} + 4 \, \sqrt{2} + e^{\left(4 \, x\right)} - 2 \, e^{\left(2 \, x\right)} + 5\right) - 2 \, {\left(\sqrt{2} e^{\left(2 \, x\right)} + \sqrt{2}\right)} \log\left(\frac{2 \, {\left(2 \, \sqrt{2} - 3\right)} e^{\left(2 \, x\right)} - 12 \, \sqrt{2} + e^{\left(4 \, x\right)} + 17}{e^{\left(4 \, x\right)} - 6 \, e^{\left(2 \, x\right)} + 1}\right) + 16}{32 \, {\left(e^{\left(2 \, x\right)} + 1\right)}}"," ",0,"-1/32*(4*(2^(1/4)*e^(2*x) + 2^(1/4))*sqrt(-2*sqrt(2) + 4)*arctan(1/14*(sqrt(2)*(5*sqrt(2) + 6) + 8*sqrt(2) + 4)*e^(2*x) - 1/28*(2*sqrt(2)*(5*sqrt(2) + 6) - (2^(3/4)*(8*sqrt(2) + 11) + 2*2^(1/4)*(5*sqrt(2) + 6))*sqrt(-2*sqrt(2) + 4) + 16*sqrt(2) + 8)*sqrt(-(2^(3/4)*e^(2*x) - 2^(1/4)*(3*sqrt(2) + 4))*sqrt(-2*sqrt(2) + 4) + 4*sqrt(2) + e^(4*x) - 2*e^(2*x) + 5) - 1/14*sqrt(2)*(3*sqrt(2) - 2) - 1/28*((2^(3/4)*(8*sqrt(2) + 11) + 2*2^(1/4)*(5*sqrt(2) + 6))*e^(2*x) - 2^(3/4)*(2*sqrt(2) + 1) - 2*2^(1/4)*(3*sqrt(2) - 2))*sqrt(-2*sqrt(2) + 4) - 1/7*sqrt(2) + 3/7) + 4*(2^(1/4)*e^(2*x) + 2^(1/4))*sqrt(-2*sqrt(2) + 4)*arctan(-1/14*(sqrt(2)*(5*sqrt(2) + 6) + 8*sqrt(2) + 4)*e^(2*x) + 1/28*(2*sqrt(2)*(5*sqrt(2) + 6) + (2^(3/4)*(8*sqrt(2) + 11) + 2*2^(1/4)*(5*sqrt(2) + 6))*sqrt(-2*sqrt(2) + 4) + 16*sqrt(2) + 8)*sqrt((2^(3/4)*e^(2*x) - 2^(1/4)*(3*sqrt(2) + 4))*sqrt(-2*sqrt(2) + 4) + 4*sqrt(2) + e^(4*x) - 2*e^(2*x) + 5) + 1/14*sqrt(2)*(3*sqrt(2) - 2) - 1/28*((2^(3/4)*(8*sqrt(2) + 11) + 2*2^(1/4)*(5*sqrt(2) + 6))*e^(2*x) - 2^(3/4)*(2*sqrt(2) + 1) - 2*2^(1/4)*(3*sqrt(2) - 2))*sqrt(-2*sqrt(2) + 4) + 1/7*sqrt(2) - 3/7) - (2^(1/4)*(sqrt(2) + 1)*e^(2*x) + 2^(1/4)*(sqrt(2) + 1))*sqrt(-2*sqrt(2) + 4)*log((2^(3/4)*e^(2*x) - 2^(1/4)*(3*sqrt(2) + 4))*sqrt(-2*sqrt(2) + 4) + 4*sqrt(2) + e^(4*x) - 2*e^(2*x) + 5) + (2^(1/4)*(sqrt(2) + 1)*e^(2*x) + 2^(1/4)*(sqrt(2) + 1))*sqrt(-2*sqrt(2) + 4)*log(-(2^(3/4)*e^(2*x) - 2^(1/4)*(3*sqrt(2) + 4))*sqrt(-2*sqrt(2) + 4) + 4*sqrt(2) + e^(4*x) - 2*e^(2*x) + 5) - 2*(sqrt(2)*e^(2*x) + sqrt(2))*log((2*(2*sqrt(2) - 3)*e^(2*x) - 12*sqrt(2) + e^(4*x) + 17)/(e^(4*x) - 6*e^(2*x) + 1)) + 16)/(e^(2*x) + 1)","B",0
276,1,20,0,2.569219," ","integrate(cosh(x)^5/(a+a*sinh(x)^2),x, algorithm=""fricas"")","\frac{\sinh\left(x\right)^{3} + 3 \, {\left(\cosh\left(x\right)^{2} + 3\right)} \sinh\left(x\right)}{12 \, a}"," ",0,"1/12*(sinh(x)^3 + 3*(cosh(x)^2 + 3)*sinh(x))/a","A",0
277,1,12,0,0.738898," ","integrate(cosh(x)^4/(a+a*sinh(x)^2),x, algorithm=""fricas"")","\frac{\cosh\left(x\right) \sinh\left(x\right) + x}{2 \, a}"," ",0,"1/2*(cosh(x)*sinh(x) + x)/a","A",0
278,1,6,0,1.505343," ","integrate(cosh(x)^3/(a+a*sinh(x)^2),x, algorithm=""fricas"")","\frac{\sinh\left(x\right)}{a}"," ",0,"sinh(x)/a","A",0
279,1,5,0,0.811371," ","integrate(cosh(x)^2/(a+a*sinh(x)^2),x, algorithm=""fricas"")","\frac{x}{a}"," ",0,"x/a","A",0
280,1,11,0,0.780838," ","integrate(cosh(x)/(a+a*sinh(x)^2),x, algorithm=""fricas"")","\frac{2 \, \arctan\left(\cosh\left(x\right) + \sinh\left(x\right)\right)}{a}"," ",0,"2*arctan(cosh(x) + sinh(x))/a","A",0
281,1,151,0,1.357176," ","integrate(sech(x)/(a+a*sinh(x)^2),x, algorithm=""fricas"")","\frac{\cosh\left(x\right)^{3} + 3 \, \cosh\left(x\right) \sinh\left(x\right)^{2} + \sinh\left(x\right)^{3} + {\left(\cosh\left(x\right)^{4} + 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4} + 2 \, {\left(3 \, \cosh\left(x\right)^{2} + 1\right)} \sinh\left(x\right)^{2} + 2 \, \cosh\left(x\right)^{2} + 4 \, {\left(\cosh\left(x\right)^{3} + \cosh\left(x\right)\right)} \sinh\left(x\right) + 1\right)} \arctan\left(\cosh\left(x\right) + \sinh\left(x\right)\right) + {\left(3 \, \cosh\left(x\right)^{2} - 1\right)} \sinh\left(x\right) - \cosh\left(x\right)}{a \cosh\left(x\right)^{4} + 4 \, a \cosh\left(x\right) \sinh\left(x\right)^{3} + a \sinh\left(x\right)^{4} + 2 \, a \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a \cosh\left(x\right)^{2} + a\right)} \sinh\left(x\right)^{2} + 4 \, {\left(a \cosh\left(x\right)^{3} + a \cosh\left(x\right)\right)} \sinh\left(x\right) + a}"," ",0,"(cosh(x)^3 + 3*cosh(x)*sinh(x)^2 + sinh(x)^3 + (cosh(x)^4 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4 + 2*(3*cosh(x)^2 + 1)*sinh(x)^2 + 2*cosh(x)^2 + 4*(cosh(x)^3 + cosh(x))*sinh(x) + 1)*arctan(cosh(x) + sinh(x)) + (3*cosh(x)^2 - 1)*sinh(x) - cosh(x))/(a*cosh(x)^4 + 4*a*cosh(x)*sinh(x)^3 + a*sinh(x)^4 + 2*a*cosh(x)^2 + 2*(3*a*cosh(x)^2 + a)*sinh(x)^2 + 4*(a*cosh(x)^3 + a*cosh(x))*sinh(x) + a)","B",0
282,1,488,0,1.549761," ","integrate(sech(x)^3/(a+a*sinh(x)^2),x, algorithm=""fricas"")","\frac{3 \, \cosh\left(x\right)^{7} + 21 \, \cosh\left(x\right) \sinh\left(x\right)^{6} + 3 \, \sinh\left(x\right)^{7} + {\left(63 \, \cosh\left(x\right)^{2} + 11\right)} \sinh\left(x\right)^{5} + 11 \, \cosh\left(x\right)^{5} + 5 \, {\left(21 \, \cosh\left(x\right)^{3} + 11 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{4} + {\left(105 \, \cosh\left(x\right)^{4} + 110 \, \cosh\left(x\right)^{2} - 11\right)} \sinh\left(x\right)^{3} - 11 \, \cosh\left(x\right)^{3} + {\left(63 \, \cosh\left(x\right)^{5} + 110 \, \cosh\left(x\right)^{3} - 33 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{2} + 3 \, {\left(\cosh\left(x\right)^{8} + 8 \, \cosh\left(x\right) \sinh\left(x\right)^{7} + \sinh\left(x\right)^{8} + 4 \, {\left(7 \, \cosh\left(x\right)^{2} + 1\right)} \sinh\left(x\right)^{6} + 4 \, \cosh\left(x\right)^{6} + 8 \, {\left(7 \, \cosh\left(x\right)^{3} + 3 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(35 \, \cosh\left(x\right)^{4} + 30 \, \cosh\left(x\right)^{2} + 3\right)} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right)^{4} + 8 \, {\left(7 \, \cosh\left(x\right)^{5} + 10 \, \cosh\left(x\right)^{3} + 3 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(7 \, \cosh\left(x\right)^{6} + 15 \, \cosh\left(x\right)^{4} + 9 \, \cosh\left(x\right)^{2} + 1\right)} \sinh\left(x\right)^{2} + 4 \, \cosh\left(x\right)^{2} + 8 \, {\left(\cosh\left(x\right)^{7} + 3 \, \cosh\left(x\right)^{5} + 3 \, \cosh\left(x\right)^{3} + \cosh\left(x\right)\right)} \sinh\left(x\right) + 1\right)} \arctan\left(\cosh\left(x\right) + \sinh\left(x\right)\right) + {\left(21 \, \cosh\left(x\right)^{6} + 55 \, \cosh\left(x\right)^{4} - 33 \, \cosh\left(x\right)^{2} - 3\right)} \sinh\left(x\right) - 3 \, \cosh\left(x\right)}{4 \, {\left(a \cosh\left(x\right)^{8} + 8 \, a \cosh\left(x\right) \sinh\left(x\right)^{7} + a \sinh\left(x\right)^{8} + 4 \, a \cosh\left(x\right)^{6} + 4 \, {\left(7 \, a \cosh\left(x\right)^{2} + a\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, a \cosh\left(x\right)^{3} + 3 \, a \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 6 \, a \cosh\left(x\right)^{4} + 2 \, {\left(35 \, a \cosh\left(x\right)^{4} + 30 \, a \cosh\left(x\right)^{2} + 3 \, a\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, a \cosh\left(x\right)^{5} + 10 \, a \cosh\left(x\right)^{3} + 3 \, a \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, a \cosh\left(x\right)^{2} + 4 \, {\left(7 \, a \cosh\left(x\right)^{6} + 15 \, a \cosh\left(x\right)^{4} + 9 \, a \cosh\left(x\right)^{2} + a\right)} \sinh\left(x\right)^{2} + 8 \, {\left(a \cosh\left(x\right)^{7} + 3 \, a \cosh\left(x\right)^{5} + 3 \, a \cosh\left(x\right)^{3} + a \cosh\left(x\right)\right)} \sinh\left(x\right) + a\right)}}"," ",0,"1/4*(3*cosh(x)^7 + 21*cosh(x)*sinh(x)^6 + 3*sinh(x)^7 + (63*cosh(x)^2 + 11)*sinh(x)^5 + 11*cosh(x)^5 + 5*(21*cosh(x)^3 + 11*cosh(x))*sinh(x)^4 + (105*cosh(x)^4 + 110*cosh(x)^2 - 11)*sinh(x)^3 - 11*cosh(x)^3 + (63*cosh(x)^5 + 110*cosh(x)^3 - 33*cosh(x))*sinh(x)^2 + 3*(cosh(x)^8 + 8*cosh(x)*sinh(x)^7 + sinh(x)^8 + 4*(7*cosh(x)^2 + 1)*sinh(x)^6 + 4*cosh(x)^6 + 8*(7*cosh(x)^3 + 3*cosh(x))*sinh(x)^5 + 2*(35*cosh(x)^4 + 30*cosh(x)^2 + 3)*sinh(x)^4 + 6*cosh(x)^4 + 8*(7*cosh(x)^5 + 10*cosh(x)^3 + 3*cosh(x))*sinh(x)^3 + 4*(7*cosh(x)^6 + 15*cosh(x)^4 + 9*cosh(x)^2 + 1)*sinh(x)^2 + 4*cosh(x)^2 + 8*(cosh(x)^7 + 3*cosh(x)^5 + 3*cosh(x)^3 + cosh(x))*sinh(x) + 1)*arctan(cosh(x) + sinh(x)) + (21*cosh(x)^6 + 55*cosh(x)^4 - 33*cosh(x)^2 - 3)*sinh(x) - 3*cosh(x))/(a*cosh(x)^8 + 8*a*cosh(x)*sinh(x)^7 + a*sinh(x)^8 + 4*a*cosh(x)^6 + 4*(7*a*cosh(x)^2 + a)*sinh(x)^6 + 8*(7*a*cosh(x)^3 + 3*a*cosh(x))*sinh(x)^5 + 6*a*cosh(x)^4 + 2*(35*a*cosh(x)^4 + 30*a*cosh(x)^2 + 3*a)*sinh(x)^4 + 8*(7*a*cosh(x)^5 + 10*a*cosh(x)^3 + 3*a*cosh(x))*sinh(x)^3 + 4*a*cosh(x)^2 + 4*(7*a*cosh(x)^6 + 15*a*cosh(x)^4 + 9*a*cosh(x)^2 + a)*sinh(x)^2 + 8*(a*cosh(x)^7 + 3*a*cosh(x)^5 + 3*a*cosh(x)^3 + a*cosh(x))*sinh(x) + a)","B",0
283,1,117,0,0.701684," ","integrate(cosh(d*x+c)^4*(a+b*sinh(d*x+c)^2),x, algorithm=""fricas"")","\frac{3 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + 2 \, {\left(5 \, b \cosh\left(d x + c\right)^{3} + 3 \, {\left(2 \, a + b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 6 \, {\left(6 \, a - b\right)} d x + 3 \, {\left(b \cosh\left(d x + c\right)^{5} + 2 \, {\left(2 \, a + b\right)} \cosh\left(d x + c\right)^{3} + {\left(16 \, a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{96 \, d}"," ",0,"1/96*(3*b*cosh(d*x + c)*sinh(d*x + c)^5 + 2*(5*b*cosh(d*x + c)^3 + 3*(2*a + b)*cosh(d*x + c))*sinh(d*x + c)^3 + 6*(6*a - b)*d*x + 3*(b*cosh(d*x + c)^5 + 2*(2*a + b)*cosh(d*x + c)^3 + (16*a - b)*cosh(d*x + c))*sinh(d*x + c))/d","A",0
284,1,82,0,2.506898," ","integrate(cosh(d*x+c)^3*(a+b*sinh(d*x+c)^2),x, algorithm=""fricas"")","\frac{3 \, b \sinh\left(d x + c\right)^{5} + 5 \, {\left(6 \, b \cosh\left(d x + c\right)^{2} + 4 \, a + b\right)} \sinh\left(d x + c\right)^{3} + 15 \, {\left(b \cosh\left(d x + c\right)^{4} + {\left(4 \, a + b\right)} \cosh\left(d x + c\right)^{2} + 12 \, a - 2 \, b\right)} \sinh\left(d x + c\right)}{240 \, d}"," ",0,"1/240*(3*b*sinh(d*x + c)^5 + 5*(6*b*cosh(d*x + c)^2 + 4*a + b)*sinh(d*x + c)^3 + 15*(b*cosh(d*x + c)^4 + (4*a + b)*cosh(d*x + c)^2 + 12*a - 2*b)*sinh(d*x + c))/d","A",0
285,1,59,0,1.061186," ","integrate(cosh(d*x+c)^2*(a+b*sinh(d*x+c)^2),x, algorithm=""fricas"")","\frac{b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(4 \, a - b\right)} d x + {\left(b \cosh\left(d x + c\right)^{3} + 4 \, a \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{8 \, d}"," ",0,"1/8*(b*cosh(d*x + c)*sinh(d*x + c)^3 + (4*a - b)*d*x + (b*cosh(d*x + c)^3 + 4*a*cosh(d*x + c))*sinh(d*x + c))/d","A",0
286,1,41,0,2.024658," ","integrate(cosh(d*x+c)*(a+b*sinh(d*x+c)^2),x, algorithm=""fricas"")","\frac{b \sinh\left(d x + c\right)^{3} + 3 \, {\left(b \cosh\left(d x + c\right)^{2} + 4 \, a - b\right)} \sinh\left(d x + c\right)}{12 \, d}"," ",0,"1/12*(b*sinh(d*x + c)^3 + 3*(b*cosh(d*x + c)^2 + 4*a - b)*sinh(d*x + c))/d","A",0
287,1,101,0,0.584349," ","integrate(sech(d*x+c)*(a+b*sinh(d*x+c)^2),x, algorithm=""fricas"")","\frac{b \cosh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a - b\right)} \cosh\left(d x + c\right) + {\left(a - b\right)} \sinh\left(d x + c\right)\right)} \arctan\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) - b}{2 \, {\left(d \cosh\left(d x + c\right) + d \sinh\left(d x + c\right)\right)}}"," ",0,"1/2*(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + 4*((a - b)*cosh(d*x + c) + (a - b)*sinh(d*x + c))*arctan(cosh(d*x + c) + sinh(d*x + c)) - b)/(d*cosh(d*x + c) + d*sinh(d*x + c))","B",0
288,1,41,0,0.893447," ","integrate(sech(d*x+c)^2*(a+b*sinh(d*x+c)^2),x, algorithm=""fricas"")","\frac{{\left(b d x - a + b\right)} \cosh\left(d x + c\right) + {\left(a - b\right)} \sinh\left(d x + c\right)}{d \cosh\left(d x + c\right)}"," ",0,"((b*d*x - a + b)*cosh(d*x + c) + (a - b)*sinh(d*x + c))/(d*cosh(d*x + c))","B",0
289,1,324,0,1.664789," ","integrate(sech(d*x+c)^3*(a+b*sinh(d*x+c)^2),x, algorithm=""fricas"")","\frac{{\left(a - b\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a - b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + {\left(a - b\right)} \sinh\left(d x + c\right)^{3} + {\left({\left(a + b\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a + b\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} + a + b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(d x + c\right)^{3} + {\left(a + b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + a + b\right)} \arctan\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) - {\left(a - b\right)} \cosh\left(d x + c\right) + {\left(3 \, {\left(a - b\right)} \cosh\left(d x + c\right)^{2} - a + b\right)} \sinh\left(d x + c\right)}{d \cosh\left(d x + c\right)^{4} + 4 \, d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + d \sinh\left(d x + c\right)^{4} + 2 \, d \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, d \cosh\left(d x + c\right)^{2} + d\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(d \cosh\left(d x + c\right)^{3} + d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + d}"," ",0,"((a - b)*cosh(d*x + c)^3 + 3*(a - b)*cosh(d*x + c)*sinh(d*x + c)^2 + (a - b)*sinh(d*x + c)^3 + ((a + b)*cosh(d*x + c)^4 + 4*(a + b)*cosh(d*x + c)*sinh(d*x + c)^3 + (a + b)*sinh(d*x + c)^4 + 2*(a + b)*cosh(d*x + c)^2 + 2*(3*(a + b)*cosh(d*x + c)^2 + a + b)*sinh(d*x + c)^2 + 4*((a + b)*cosh(d*x + c)^3 + (a + b)*cosh(d*x + c))*sinh(d*x + c) + a + b)*arctan(cosh(d*x + c) + sinh(d*x + c)) - (a - b)*cosh(d*x + c) + (3*(a - b)*cosh(d*x + c)^2 - a + b)*sinh(d*x + c))/(d*cosh(d*x + c)^4 + 4*d*cosh(d*x + c)*sinh(d*x + c)^3 + d*sinh(d*x + c)^4 + 2*d*cosh(d*x + c)^2 + 2*(3*d*cosh(d*x + c)^2 + d)*sinh(d*x + c)^2 + 4*(d*cosh(d*x + c)^3 + d*cosh(d*x + c))*sinh(d*x + c) + d)","B",0
290,1,159,0,1.460286," ","integrate(sech(d*x+c)^4*(a+b*sinh(d*x+c)^2),x, algorithm=""fricas"")","-\frac{4 \, {\left({\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(a - b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a + 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 3 \, a\right)}}{3 \, {\left(d \cosh\left(d x + c\right)^{4} + 4 \, d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + d \sinh\left(d x + c\right)^{4} + 4 \, d \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, d \cosh\left(d x + c\right)^{2} + 2 \, d\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(d \cosh\left(d x + c\right)^{3} + d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + 3 \, d\right)}}"," ",0,"-4/3*((a + 2*b)*cosh(d*x + c)^2 - 2*(a - b)*cosh(d*x + c)*sinh(d*x + c) + (a + 2*b)*sinh(d*x + c)^2 + 3*a)/(d*cosh(d*x + c)^4 + 4*d*cosh(d*x + c)*sinh(d*x + c)^3 + d*sinh(d*x + c)^4 + 4*d*cosh(d*x + c)^2 + 2*(3*d*cosh(d*x + c)^2 + 2*d)*sinh(d*x + c)^2 + 4*(d*cosh(d*x + c)^3 + d*cosh(d*x + c))*sinh(d*x + c) + 3*d)","B",0
291,1,1046,0,1.368130," ","integrate(sech(d*x+c)^5*(a+b*sinh(d*x+c)^2),x, algorithm=""fricas"")","\frac{{\left(3 \, a + b\right)} \cosh\left(d x + c\right)^{7} + 7 \, {\left(3 \, a + b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + {\left(3 \, a + b\right)} \sinh\left(d x + c\right)^{7} + {\left(11 \, a - 7 \, b\right)} \cosh\left(d x + c\right)^{5} + {\left(21 \, {\left(3 \, a + b\right)} \cosh\left(d x + c\right)^{2} + 11 \, a - 7 \, b\right)} \sinh\left(d x + c\right)^{5} + 5 \, {\left(7 \, {\left(3 \, a + b\right)} \cosh\left(d x + c\right)^{3} + {\left(11 \, a - 7 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} - {\left(11 \, a - 7 \, b\right)} \cosh\left(d x + c\right)^{3} + {\left(35 \, {\left(3 \, a + b\right)} \cosh\left(d x + c\right)^{4} + 10 \, {\left(11 \, a - 7 \, b\right)} \cosh\left(d x + c\right)^{2} - 11 \, a + 7 \, b\right)} \sinh\left(d x + c\right)^{3} + {\left(21 \, {\left(3 \, a + b\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(11 \, a - 7 \, b\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(11 \, a - 7 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(3 \, a + b\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(3 \, a + b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(3 \, a + b\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(3 \, a + b\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(3 \, a + b\right)} \cosh\left(d x + c\right)^{2} + 3 \, a + b\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(3 \, a + b\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(3 \, a + b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 6 \, {\left(3 \, a + b\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(3 \, a + b\right)} \cosh\left(d x + c\right)^{4} + 30 \, {\left(3 \, a + b\right)} \cosh\left(d x + c\right)^{2} + 9 \, a + 3 \, b\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(3 \, a + b\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(3 \, a + b\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(3 \, a + b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(3 \, a + b\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(3 \, a + b\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(3 \, a + b\right)} \cosh\left(d x + c\right)^{4} + 9 \, {\left(3 \, a + b\right)} \cosh\left(d x + c\right)^{2} + 3 \, a + b\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left({\left(3 \, a + b\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(3 \, a + b\right)} \cosh\left(d x + c\right)^{5} + 3 \, {\left(3 \, a + b\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a + b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + 3 \, a + b\right)} \arctan\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) - {\left(3 \, a + b\right)} \cosh\left(d x + c\right) + {\left(7 \, {\left(3 \, a + b\right)} \cosh\left(d x + c\right)^{6} + 5 \, {\left(11 \, a - 7 \, b\right)} \cosh\left(d x + c\right)^{4} - 3 \, {\left(11 \, a - 7 \, b\right)} \cosh\left(d x + c\right)^{2} - 3 \, a - b\right)} \sinh\left(d x + c\right)}{4 \, {\left(d \cosh\left(d x + c\right)^{8} + 8 \, d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + d \sinh\left(d x + c\right)^{8} + 4 \, d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, d \cosh\left(d x + c\right)^{2} + d\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, d \cosh\left(d x + c\right)^{3} + 3 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 6 \, d \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, d \cosh\left(d x + c\right)^{4} + 30 \, d \cosh\left(d x + c\right)^{2} + 3 \, d\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, d \cosh\left(d x + c\right)^{5} + 10 \, d \cosh\left(d x + c\right)^{3} + 3 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, d \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, d \cosh\left(d x + c\right)^{6} + 15 \, d \cosh\left(d x + c\right)^{4} + 9 \, d \cosh\left(d x + c\right)^{2} + d\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left(d \cosh\left(d x + c\right)^{7} + 3 \, d \cosh\left(d x + c\right)^{5} + 3 \, d \cosh\left(d x + c\right)^{3} + d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + d\right)}}"," ",0,"1/4*((3*a + b)*cosh(d*x + c)^7 + 7*(3*a + b)*cosh(d*x + c)*sinh(d*x + c)^6 + (3*a + b)*sinh(d*x + c)^7 + (11*a - 7*b)*cosh(d*x + c)^5 + (21*(3*a + b)*cosh(d*x + c)^2 + 11*a - 7*b)*sinh(d*x + c)^5 + 5*(7*(3*a + b)*cosh(d*x + c)^3 + (11*a - 7*b)*cosh(d*x + c))*sinh(d*x + c)^4 - (11*a - 7*b)*cosh(d*x + c)^3 + (35*(3*a + b)*cosh(d*x + c)^4 + 10*(11*a - 7*b)*cosh(d*x + c)^2 - 11*a + 7*b)*sinh(d*x + c)^3 + (21*(3*a + b)*cosh(d*x + c)^5 + 10*(11*a - 7*b)*cosh(d*x + c)^3 - 3*(11*a - 7*b)*cosh(d*x + c))*sinh(d*x + c)^2 + ((3*a + b)*cosh(d*x + c)^8 + 8*(3*a + b)*cosh(d*x + c)*sinh(d*x + c)^7 + (3*a + b)*sinh(d*x + c)^8 + 4*(3*a + b)*cosh(d*x + c)^6 + 4*(7*(3*a + b)*cosh(d*x + c)^2 + 3*a + b)*sinh(d*x + c)^6 + 8*(7*(3*a + b)*cosh(d*x + c)^3 + 3*(3*a + b)*cosh(d*x + c))*sinh(d*x + c)^5 + 6*(3*a + b)*cosh(d*x + c)^4 + 2*(35*(3*a + b)*cosh(d*x + c)^4 + 30*(3*a + b)*cosh(d*x + c)^2 + 9*a + 3*b)*sinh(d*x + c)^4 + 8*(7*(3*a + b)*cosh(d*x + c)^5 + 10*(3*a + b)*cosh(d*x + c)^3 + 3*(3*a + b)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(3*a + b)*cosh(d*x + c)^2 + 4*(7*(3*a + b)*cosh(d*x + c)^6 + 15*(3*a + b)*cosh(d*x + c)^4 + 9*(3*a + b)*cosh(d*x + c)^2 + 3*a + b)*sinh(d*x + c)^2 + 8*((3*a + b)*cosh(d*x + c)^7 + 3*(3*a + b)*cosh(d*x + c)^5 + 3*(3*a + b)*cosh(d*x + c)^3 + (3*a + b)*cosh(d*x + c))*sinh(d*x + c) + 3*a + b)*arctan(cosh(d*x + c) + sinh(d*x + c)) - (3*a + b)*cosh(d*x + c) + (7*(3*a + b)*cosh(d*x + c)^6 + 5*(11*a - 7*b)*cosh(d*x + c)^4 - 3*(11*a - 7*b)*cosh(d*x + c)^2 - 3*a - b)*sinh(d*x + c))/(d*cosh(d*x + c)^8 + 8*d*cosh(d*x + c)*sinh(d*x + c)^7 + d*sinh(d*x + c)^8 + 4*d*cosh(d*x + c)^6 + 4*(7*d*cosh(d*x + c)^2 + d)*sinh(d*x + c)^6 + 8*(7*d*cosh(d*x + c)^3 + 3*d*cosh(d*x + c))*sinh(d*x + c)^5 + 6*d*cosh(d*x + c)^4 + 2*(35*d*cosh(d*x + c)^4 + 30*d*cosh(d*x + c)^2 + 3*d)*sinh(d*x + c)^4 + 8*(7*d*cosh(d*x + c)^5 + 10*d*cosh(d*x + c)^3 + 3*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*d*cosh(d*x + c)^2 + 4*(7*d*cosh(d*x + c)^6 + 15*d*cosh(d*x + c)^4 + 9*d*cosh(d*x + c)^2 + d)*sinh(d*x + c)^2 + 8*(d*cosh(d*x + c)^7 + 3*d*cosh(d*x + c)^5 + 3*d*cosh(d*x + c)^3 + d*cosh(d*x + c))*sinh(d*x + c) + d)","B",0
292,1,343,0,2.096205," ","integrate(sech(d*x+c)^6*(a+b*sinh(d*x+c)^2),x, algorithm=""fricas"")","-\frac{8 \, {\left(2 \, {\left(a + 4 \, b\right)} \cosh\left(d x + c\right)^{3} + 6 \, {\left(a + 4 \, b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} - {\left(2 \, a - 7 \, b\right)} \sinh\left(d x + c\right)^{3} + 30 \, a \cosh\left(d x + c\right) - {\left(3 \, {\left(2 \, a - 7 \, b\right)} \cosh\left(d x + c\right)^{2} - 10 \, a + 5 \, b\right)} \sinh\left(d x + c\right)\right)}}{15 \, {\left(d \cosh\left(d x + c\right)^{7} + 7 \, d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + d \sinh\left(d x + c\right)^{7} + 5 \, d \cosh\left(d x + c\right)^{5} + {\left(21 \, d \cosh\left(d x + c\right)^{2} + 5 \, d\right)} \sinh\left(d x + c\right)^{5} + 5 \, {\left(7 \, d \cosh\left(d x + c\right)^{3} + 5 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 11 \, d \cosh\left(d x + c\right)^{3} + {\left(35 \, d \cosh\left(d x + c\right)^{4} + 50 \, d \cosh\left(d x + c\right)^{2} + 9 \, d\right)} \sinh\left(d x + c\right)^{3} + {\left(21 \, d \cosh\left(d x + c\right)^{5} + 50 \, d \cosh\left(d x + c\right)^{3} + 33 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 15 \, d \cosh\left(d x + c\right) + {\left(7 \, d \cosh\left(d x + c\right)^{6} + 25 \, d \cosh\left(d x + c\right)^{4} + 27 \, d \cosh\left(d x + c\right)^{2} + 5 \, d\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"-8/15*(2*(a + 4*b)*cosh(d*x + c)^3 + 6*(a + 4*b)*cosh(d*x + c)*sinh(d*x + c)^2 - (2*a - 7*b)*sinh(d*x + c)^3 + 30*a*cosh(d*x + c) - (3*(2*a - 7*b)*cosh(d*x + c)^2 - 10*a + 5*b)*sinh(d*x + c))/(d*cosh(d*x + c)^7 + 7*d*cosh(d*x + c)*sinh(d*x + c)^6 + d*sinh(d*x + c)^7 + 5*d*cosh(d*x + c)^5 + (21*d*cosh(d*x + c)^2 + 5*d)*sinh(d*x + c)^5 + 5*(7*d*cosh(d*x + c)^3 + 5*d*cosh(d*x + c))*sinh(d*x + c)^4 + 11*d*cosh(d*x + c)^3 + (35*d*cosh(d*x + c)^4 + 50*d*cosh(d*x + c)^2 + 9*d)*sinh(d*x + c)^3 + (21*d*cosh(d*x + c)^5 + 50*d*cosh(d*x + c)^3 + 33*d*cosh(d*x + c))*sinh(d*x + c)^2 + 15*d*cosh(d*x + c) + (7*d*cosh(d*x + c)^6 + 25*d*cosh(d*x + c)^4 + 27*d*cosh(d*x + c)^2 + 5*d)*sinh(d*x + c))","B",0
293,1,212,0,0.523751," ","integrate(cosh(d*x+c)^4*(a+b*sinh(d*x+c)^2)^2,x, algorithm=""fricas"")","\frac{3 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + 3 \, {\left(7 \, b^{2} \cosh\left(d x + c\right)^{3} + 8 \, a b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + {\left(21 \, b^{2} \cosh\left(d x + c\right)^{5} + 80 \, a b \cosh\left(d x + c\right)^{3} + 12 \, {\left(4 \, a^{2} + 4 \, a b - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 3 \, {\left(48 \, a^{2} - 16 \, a b + 3 \, b^{2}\right)} d x + 3 \, {\left(b^{2} \cosh\left(d x + c\right)^{7} + 8 \, a b \cosh\left(d x + c\right)^{5} + 4 \, {\left(4 \, a^{2} + 4 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{3} + 8 \, {\left(8 \, a^{2} - a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{384 \, d}"," ",0,"1/384*(3*b^2*cosh(d*x + c)*sinh(d*x + c)^7 + 3*(7*b^2*cosh(d*x + c)^3 + 8*a*b*cosh(d*x + c))*sinh(d*x + c)^5 + (21*b^2*cosh(d*x + c)^5 + 80*a*b*cosh(d*x + c)^3 + 12*(4*a^2 + 4*a*b - b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 3*(48*a^2 - 16*a*b + 3*b^2)*d*x + 3*(b^2*cosh(d*x + c)^7 + 8*a*b*cosh(d*x + c)^5 + 4*(4*a^2 + 4*a*b - b^2)*cosh(d*x + c)^3 + 8*(8*a^2 - a*b)*cosh(d*x + c))*sinh(d*x + c))/d","A",0
294,1,188,0,1.554833," ","integrate(cosh(d*x+c)^3*(a+b*sinh(d*x+c)^2)^2,x, algorithm=""fricas"")","\frac{15 \, b^{2} \sinh\left(d x + c\right)^{7} + 21 \, {\left(15 \, b^{2} \cosh\left(d x + c\right)^{2} + 8 \, a b - b^{2}\right)} \sinh\left(d x + c\right)^{5} + 35 \, {\left(15 \, b^{2} \cosh\left(d x + c\right)^{4} + 6 \, {\left(8 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 16 \, a^{2} + 8 \, a b - 3 \, b^{2}\right)} \sinh\left(d x + c\right)^{3} + 105 \, {\left(b^{2} \cosh\left(d x + c\right)^{6} + {\left(8 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(16 \, a^{2} + 8 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 48 \, a^{2} - 16 \, a b + 3 \, b^{2}\right)} \sinh\left(d x + c\right)}{6720 \, d}"," ",0,"1/6720*(15*b^2*sinh(d*x + c)^7 + 21*(15*b^2*cosh(d*x + c)^2 + 8*a*b - b^2)*sinh(d*x + c)^5 + 35*(15*b^2*cosh(d*x + c)^4 + 6*(8*a*b - b^2)*cosh(d*x + c)^2 + 16*a^2 + 8*a*b - 3*b^2)*sinh(d*x + c)^3 + 105*(b^2*cosh(d*x + c)^6 + (8*a*b - b^2)*cosh(d*x + c)^4 + (16*a^2 + 8*a*b - 3*b^2)*cosh(d*x + c)^2 + 48*a^2 - 16*a*b + 3*b^2)*sinh(d*x + c))/d","B",0
295,1,143,0,2.222692," ","integrate(cosh(d*x+c)^2*(a+b*sinh(d*x+c)^2)^2,x, algorithm=""fricas"")","\frac{3 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + 2 \, {\left(5 \, b^{2} \cosh\left(d x + c\right)^{3} + 3 \, {\left(4 \, a b - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 6 \, {\left(8 \, a^{2} - 4 \, a b + b^{2}\right)} d x + 3 \, {\left(b^{2} \cosh\left(d x + c\right)^{5} + 2 \, {\left(4 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(16 \, a^{2} - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{96 \, d}"," ",0,"1/96*(3*b^2*cosh(d*x + c)*sinh(d*x + c)^5 + 2*(5*b^2*cosh(d*x + c)^3 + 3*(4*a*b - b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 6*(8*a^2 - 4*a*b + b^2)*d*x + 3*(b^2*cosh(d*x + c)^5 + 2*(4*a*b - b^2)*cosh(d*x + c)^3 + (16*a^2 - b^2)*cosh(d*x + c))*sinh(d*x + c))/d","A",0
296,1,106,0,0.955323," ","integrate(cosh(d*x+c)*(a+b*sinh(d*x+c)^2)^2,x, algorithm=""fricas"")","\frac{3 \, b^{2} \sinh\left(d x + c\right)^{5} + 5 \, {\left(6 \, b^{2} \cosh\left(d x + c\right)^{2} + 8 \, a b - 3 \, b^{2}\right)} \sinh\left(d x + c\right)^{3} + 15 \, {\left(b^{2} \cosh\left(d x + c\right)^{4} + {\left(8 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 16 \, a^{2} - 8 \, a b + 2 \, b^{2}\right)} \sinh\left(d x + c\right)}{240 \, d}"," ",0,"1/240*(3*b^2*sinh(d*x + c)^5 + 5*(6*b^2*cosh(d*x + c)^2 + 8*a*b - 3*b^2)*sinh(d*x + c)^3 + 15*(b^2*cosh(d*x + c)^4 + (8*a*b - 3*b^2)*cosh(d*x + c)^2 + 16*a^2 - 8*a*b + 2*b^2)*sinh(d*x + c))/d","B",0
297,1,446,0,0.905742," ","integrate(sech(d*x+c)*(a+b*sinh(d*x+c)^2)^2,x, algorithm=""fricas"")","\frac{b^{2} \cosh\left(d x + c\right)^{6} + 6 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + b^{2} \sinh\left(d x + c\right)^{6} + 3 \, {\left(8 \, a b - 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(5 \, b^{2} \cosh\left(d x + c\right)^{2} + 8 \, a b - 5 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, b^{2} \cosh\left(d x + c\right)^{3} + 3 \, {\left(8 \, a b - 5 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 3 \, {\left(8 \, a b - 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 3 \, {\left(5 \, b^{2} \cosh\left(d x + c\right)^{4} + 6 \, {\left(8 \, a b - 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 8 \, a b + 5 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} - b^{2} + 48 \, {\left({\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + {\left(a^{2} - 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{3}\right)} \arctan\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) + 6 \, {\left(b^{2} \cosh\left(d x + c\right)^{5} + 2 \, {\left(8 \, a b - 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(8 \, a b - 5 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{24 \, {\left(d \cosh\left(d x + c\right)^{3} + 3 \, d \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + d \sinh\left(d x + c\right)^{3}\right)}}"," ",0,"1/24*(b^2*cosh(d*x + c)^6 + 6*b^2*cosh(d*x + c)*sinh(d*x + c)^5 + b^2*sinh(d*x + c)^6 + 3*(8*a*b - 5*b^2)*cosh(d*x + c)^4 + 3*(5*b^2*cosh(d*x + c)^2 + 8*a*b - 5*b^2)*sinh(d*x + c)^4 + 4*(5*b^2*cosh(d*x + c)^3 + 3*(8*a*b - 5*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 - 3*(8*a*b - 5*b^2)*cosh(d*x + c)^2 + 3*(5*b^2*cosh(d*x + c)^4 + 6*(8*a*b - 5*b^2)*cosh(d*x + c)^2 - 8*a*b + 5*b^2)*sinh(d*x + c)^2 - b^2 + 48*((a^2 - 2*a*b + b^2)*cosh(d*x + c)^3 + 3*(a^2 - 2*a*b + b^2)*cosh(d*x + c)^2*sinh(d*x + c) + 3*(a^2 - 2*a*b + b^2)*cosh(d*x + c)*sinh(d*x + c)^2 + (a^2 - 2*a*b + b^2)*sinh(d*x + c)^3)*arctan(cosh(d*x + c) + sinh(d*x + c)) + 6*(b^2*cosh(d*x + c)^5 + 2*(8*a*b - 5*b^2)*cosh(d*x + c)^3 - (8*a*b - 5*b^2)*cosh(d*x + c))*sinh(d*x + c))/(d*cosh(d*x + c)^3 + 3*d*cosh(d*x + c)^2*sinh(d*x + c) + 3*d*cosh(d*x + c)*sinh(d*x + c)^2 + d*sinh(d*x + c)^3)","B",0
298,1,97,0,1.420952," ","integrate(sech(d*x+c)^2*(a+b*sinh(d*x+c)^2)^2,x, algorithm=""fricas"")","\frac{b^{2} \sinh\left(d x + c\right)^{3} + 4 \, {\left({\left(4 \, a b - 3 \, b^{2}\right)} d x - 2 \, a^{2} + 4 \, a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right) + {\left(3 \, b^{2} \cosh\left(d x + c\right)^{2} + 8 \, a^{2} - 16 \, a b + 9 \, b^{2}\right)} \sinh\left(d x + c\right)}{8 \, d \cosh\left(d x + c\right)}"," ",0,"1/8*(b^2*sinh(d*x + c)^3 + 4*((4*a*b - 3*b^2)*d*x - 2*a^2 + 4*a*b - 2*b^2)*cosh(d*x + c) + (3*b^2*cosh(d*x + c)^2 + 8*a^2 - 16*a*b + 9*b^2)*sinh(d*x + c))/(d*cosh(d*x + c))","A",0
299,1,759,0,1.914724," ","integrate(sech(d*x+c)^3*(a+b*sinh(d*x+c)^2)^2,x, algorithm=""fricas"")","\frac{b^{2} \cosh\left(d x + c\right)^{6} + 6 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + b^{2} \sinh\left(d x + c\right)^{6} + {\left(2 \, a^{2} - 4 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(15 \, b^{2} \cosh\left(d x + c\right)^{2} + 2 \, a^{2} - 4 \, a b + 3 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, b^{2} \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{2} - 4 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - {\left(2 \, a^{2} - 4 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(15 \, b^{2} \cosh\left(d x + c\right)^{4} + 6 \, {\left(2 \, a^{2} - 4 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, a^{2} + 4 \, a b - 3 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} - b^{2} + 2 \, {\left({\left(a^{2} + 2 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(a^{2} + 2 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} + {\left(a^{2} + 2 \, a b - 3 \, b^{2}\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(a^{2} + 2 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(5 \, {\left(a^{2} + 2 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} + 2 \, a b - 3 \, b^{2}\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(5 \, {\left(a^{2} + 2 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{2} + 2 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{2} + 2 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right) + {\left(5 \, {\left(a^{2} + 2 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 6 \, {\left(a^{2} + 2 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} + 2 \, a b - 3 \, b^{2}\right)} \sinh\left(d x + c\right)\right)} \arctan\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) + 2 \, {\left(3 \, b^{2} \cosh\left(d x + c\right)^{5} + 2 \, {\left(2 \, a^{2} - 4 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(2 \, a^{2} - 4 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{2 \, {\left(d \cosh\left(d x + c\right)^{5} + 5 \, d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} + d \sinh\left(d x + c\right)^{5} + 2 \, d \cosh\left(d x + c\right)^{3} + 2 \, {\left(5 \, d \cosh\left(d x + c\right)^{2} + d\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(5 \, d \cosh\left(d x + c\right)^{3} + 3 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + d \cosh\left(d x + c\right) + {\left(5 \, d \cosh\left(d x + c\right)^{4} + 6 \, d \cosh\left(d x + c\right)^{2} + d\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"1/2*(b^2*cosh(d*x + c)^6 + 6*b^2*cosh(d*x + c)*sinh(d*x + c)^5 + b^2*sinh(d*x + c)^6 + (2*a^2 - 4*a*b + 3*b^2)*cosh(d*x + c)^4 + (15*b^2*cosh(d*x + c)^2 + 2*a^2 - 4*a*b + 3*b^2)*sinh(d*x + c)^4 + 4*(5*b^2*cosh(d*x + c)^3 + (2*a^2 - 4*a*b + 3*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 - (2*a^2 - 4*a*b + 3*b^2)*cosh(d*x + c)^2 + (15*b^2*cosh(d*x + c)^4 + 6*(2*a^2 - 4*a*b + 3*b^2)*cosh(d*x + c)^2 - 2*a^2 + 4*a*b - 3*b^2)*sinh(d*x + c)^2 - b^2 + 2*((a^2 + 2*a*b - 3*b^2)*cosh(d*x + c)^5 + 5*(a^2 + 2*a*b - 3*b^2)*cosh(d*x + c)*sinh(d*x + c)^4 + (a^2 + 2*a*b - 3*b^2)*sinh(d*x + c)^5 + 2*(a^2 + 2*a*b - 3*b^2)*cosh(d*x + c)^3 + 2*(5*(a^2 + 2*a*b - 3*b^2)*cosh(d*x + c)^2 + a^2 + 2*a*b - 3*b^2)*sinh(d*x + c)^3 + 2*(5*(a^2 + 2*a*b - 3*b^2)*cosh(d*x + c)^3 + 3*(a^2 + 2*a*b - 3*b^2)*cosh(d*x + c))*sinh(d*x + c)^2 + (a^2 + 2*a*b - 3*b^2)*cosh(d*x + c) + (5*(a^2 + 2*a*b - 3*b^2)*cosh(d*x + c)^4 + 6*(a^2 + 2*a*b - 3*b^2)*cosh(d*x + c)^2 + a^2 + 2*a*b - 3*b^2)*sinh(d*x + c))*arctan(cosh(d*x + c) + sinh(d*x + c)) + 2*(3*b^2*cosh(d*x + c)^5 + 2*(2*a^2 - 4*a*b + 3*b^2)*cosh(d*x + c)^3 - (2*a^2 - 4*a*b + 3*b^2)*cosh(d*x + c))*sinh(d*x + c))/(d*cosh(d*x + c)^5 + 5*d*cosh(d*x + c)*sinh(d*x + c)^4 + d*sinh(d*x + c)^5 + 2*d*cosh(d*x + c)^3 + 2*(5*d*cosh(d*x + c)^2 + d)*sinh(d*x + c)^3 + 2*(5*d*cosh(d*x + c)^3 + 3*d*cosh(d*x + c))*sinh(d*x + c)^2 + d*cosh(d*x + c) + (5*d*cosh(d*x + c)^4 + 6*d*cosh(d*x + c)^2 + d)*sinh(d*x + c))","B",0
300,1,200,0,1.744570," ","integrate(sech(d*x+c)^4*(a+b*sinh(d*x+c)^2)^2,x, algorithm=""fricas"")","\frac{{\left(3 \, b^{2} d x - 2 \, a^{2} - 2 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(3 \, b^{2} d x - 2 \, a^{2} - 2 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} + a b - 2 \, b^{2}\right)} \sinh\left(d x + c\right)^{3} + 3 \, {\left(3 \, b^{2} d x - 2 \, a^{2} - 2 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right) + 6 \, {\left({\left(a^{2} + a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} - a b\right)} \sinh\left(d x + c\right)}{3 \, {\left(d \cosh\left(d x + c\right)^{3} + 3 \, d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + 3 \, d \cosh\left(d x + c\right)\right)}}"," ",0,"1/3*((3*b^2*d*x - 2*a^2 - 2*a*b + 4*b^2)*cosh(d*x + c)^3 + 3*(3*b^2*d*x - 2*a^2 - 2*a*b + 4*b^2)*cosh(d*x + c)*sinh(d*x + c)^2 + 2*(a^2 + a*b - 2*b^2)*sinh(d*x + c)^3 + 3*(3*b^2*d*x - 2*a^2 - 2*a*b + 4*b^2)*cosh(d*x + c) + 6*((a^2 + a*b - 2*b^2)*cosh(d*x + c)^2 + a^2 - a*b)*sinh(d*x + c))/(d*cosh(d*x + c)^3 + 3*d*cosh(d*x + c)*sinh(d*x + c)^2 + 3*d*cosh(d*x + c))","B",0
301,1,1472,0,0.747705," ","integrate(sech(d*x+c)^5*(a+b*sinh(d*x+c)^2)^2,x, algorithm=""fricas"")","\frac{{\left(3 \, a^{2} + 2 \, a b - 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} + 7 \, {\left(3 \, a^{2} + 2 \, a b - 5 \, b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + {\left(3 \, a^{2} + 2 \, a b - 5 \, b^{2}\right)} \sinh\left(d x + c\right)^{7} + {\left(11 \, a^{2} - 14 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + {\left(21 \, {\left(3 \, a^{2} + 2 \, a b - 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 11 \, a^{2} - 14 \, a b + 3 \, b^{2}\right)} \sinh\left(d x + c\right)^{5} + 5 \, {\left(7 \, {\left(3 \, a^{2} + 2 \, a b - 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(11 \, a^{2} - 14 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} - {\left(11 \, a^{2} - 14 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(35 \, {\left(3 \, a^{2} + 2 \, a b - 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 10 \, {\left(11 \, a^{2} - 14 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 11 \, a^{2} + 14 \, a b - 3 \, b^{2}\right)} \sinh\left(d x + c\right)^{3} + {\left(21 \, {\left(3 \, a^{2} + 2 \, a b - 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(11 \, a^{2} - 14 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(11 \, a^{2} - 14 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(3 \, a^{2} + 2 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(3 \, a^{2} + 2 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(3 \, a^{2} + 2 \, a b + 3 \, b^{2}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(3 \, a^{2} + 2 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(3 \, a^{2} + 2 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 3 \, a^{2} + 2 \, a b + 3 \, b^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(3 \, a^{2} + 2 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(3 \, a^{2} + 2 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 6 \, {\left(3 \, a^{2} + 2 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(3 \, a^{2} + 2 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 30 \, {\left(3 \, a^{2} + 2 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 9 \, a^{2} + 6 \, a b + 9 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(3 \, a^{2} + 2 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(3 \, a^{2} + 2 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(3 \, a^{2} + 2 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(3 \, a^{2} + 2 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(3 \, a^{2} + 2 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(3 \, a^{2} + 2 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 9 \, {\left(3 \, a^{2} + 2 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 3 \, a^{2} + 2 \, a b + 3 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} + 3 \, a^{2} + 2 \, a b + 3 \, b^{2} + 8 \, {\left({\left(3 \, a^{2} + 2 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(3 \, a^{2} + 2 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 3 \, {\left(3 \, a^{2} + 2 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{2} + 2 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \arctan\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) - {\left(3 \, a^{2} + 2 \, a b - 5 \, b^{2}\right)} \cosh\left(d x + c\right) + {\left(7 \, {\left(3 \, a^{2} + 2 \, a b - 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 5 \, {\left(11 \, a^{2} - 14 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} - 3 \, {\left(11 \, a^{2} - 14 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 3 \, a^{2} - 2 \, a b + 5 \, b^{2}\right)} \sinh\left(d x + c\right)}{4 \, {\left(d \cosh\left(d x + c\right)^{8} + 8 \, d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + d \sinh\left(d x + c\right)^{8} + 4 \, d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, d \cosh\left(d x + c\right)^{2} + d\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, d \cosh\left(d x + c\right)^{3} + 3 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 6 \, d \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, d \cosh\left(d x + c\right)^{4} + 30 \, d \cosh\left(d x + c\right)^{2} + 3 \, d\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, d \cosh\left(d x + c\right)^{5} + 10 \, d \cosh\left(d x + c\right)^{3} + 3 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, d \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, d \cosh\left(d x + c\right)^{6} + 15 \, d \cosh\left(d x + c\right)^{4} + 9 \, d \cosh\left(d x + c\right)^{2} + d\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left(d \cosh\left(d x + c\right)^{7} + 3 \, d \cosh\left(d x + c\right)^{5} + 3 \, d \cosh\left(d x + c\right)^{3} + d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + d\right)}}"," ",0,"1/4*((3*a^2 + 2*a*b - 5*b^2)*cosh(d*x + c)^7 + 7*(3*a^2 + 2*a*b - 5*b^2)*cosh(d*x + c)*sinh(d*x + c)^6 + (3*a^2 + 2*a*b - 5*b^2)*sinh(d*x + c)^7 + (11*a^2 - 14*a*b + 3*b^2)*cosh(d*x + c)^5 + (21*(3*a^2 + 2*a*b - 5*b^2)*cosh(d*x + c)^2 + 11*a^2 - 14*a*b + 3*b^2)*sinh(d*x + c)^5 + 5*(7*(3*a^2 + 2*a*b - 5*b^2)*cosh(d*x + c)^3 + (11*a^2 - 14*a*b + 3*b^2)*cosh(d*x + c))*sinh(d*x + c)^4 - (11*a^2 - 14*a*b + 3*b^2)*cosh(d*x + c)^3 + (35*(3*a^2 + 2*a*b - 5*b^2)*cosh(d*x + c)^4 + 10*(11*a^2 - 14*a*b + 3*b^2)*cosh(d*x + c)^2 - 11*a^2 + 14*a*b - 3*b^2)*sinh(d*x + c)^3 + (21*(3*a^2 + 2*a*b - 5*b^2)*cosh(d*x + c)^5 + 10*(11*a^2 - 14*a*b + 3*b^2)*cosh(d*x + c)^3 - 3*(11*a^2 - 14*a*b + 3*b^2)*cosh(d*x + c))*sinh(d*x + c)^2 + ((3*a^2 + 2*a*b + 3*b^2)*cosh(d*x + c)^8 + 8*(3*a^2 + 2*a*b + 3*b^2)*cosh(d*x + c)*sinh(d*x + c)^7 + (3*a^2 + 2*a*b + 3*b^2)*sinh(d*x + c)^8 + 4*(3*a^2 + 2*a*b + 3*b^2)*cosh(d*x + c)^6 + 4*(7*(3*a^2 + 2*a*b + 3*b^2)*cosh(d*x + c)^2 + 3*a^2 + 2*a*b + 3*b^2)*sinh(d*x + c)^6 + 8*(7*(3*a^2 + 2*a*b + 3*b^2)*cosh(d*x + c)^3 + 3*(3*a^2 + 2*a*b + 3*b^2)*cosh(d*x + c))*sinh(d*x + c)^5 + 6*(3*a^2 + 2*a*b + 3*b^2)*cosh(d*x + c)^4 + 2*(35*(3*a^2 + 2*a*b + 3*b^2)*cosh(d*x + c)^4 + 30*(3*a^2 + 2*a*b + 3*b^2)*cosh(d*x + c)^2 + 9*a^2 + 6*a*b + 9*b^2)*sinh(d*x + c)^4 + 8*(7*(3*a^2 + 2*a*b + 3*b^2)*cosh(d*x + c)^5 + 10*(3*a^2 + 2*a*b + 3*b^2)*cosh(d*x + c)^3 + 3*(3*a^2 + 2*a*b + 3*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(3*a^2 + 2*a*b + 3*b^2)*cosh(d*x + c)^2 + 4*(7*(3*a^2 + 2*a*b + 3*b^2)*cosh(d*x + c)^6 + 15*(3*a^2 + 2*a*b + 3*b^2)*cosh(d*x + c)^4 + 9*(3*a^2 + 2*a*b + 3*b^2)*cosh(d*x + c)^2 + 3*a^2 + 2*a*b + 3*b^2)*sinh(d*x + c)^2 + 3*a^2 + 2*a*b + 3*b^2 + 8*((3*a^2 + 2*a*b + 3*b^2)*cosh(d*x + c)^7 + 3*(3*a^2 + 2*a*b + 3*b^2)*cosh(d*x + c)^5 + 3*(3*a^2 + 2*a*b + 3*b^2)*cosh(d*x + c)^3 + (3*a^2 + 2*a*b + 3*b^2)*cosh(d*x + c))*sinh(d*x + c))*arctan(cosh(d*x + c) + sinh(d*x + c)) - (3*a^2 + 2*a*b - 5*b^2)*cosh(d*x + c) + (7*(3*a^2 + 2*a*b - 5*b^2)*cosh(d*x + c)^6 + 5*(11*a^2 - 14*a*b + 3*b^2)*cosh(d*x + c)^4 - 3*(11*a^2 - 14*a*b + 3*b^2)*cosh(d*x + c)^2 - 3*a^2 - 2*a*b + 5*b^2)*sinh(d*x + c))/(d*cosh(d*x + c)^8 + 8*d*cosh(d*x + c)*sinh(d*x + c)^7 + d*sinh(d*x + c)^8 + 4*d*cosh(d*x + c)^6 + 4*(7*d*cosh(d*x + c)^2 + d)*sinh(d*x + c)^6 + 8*(7*d*cosh(d*x + c)^3 + 3*d*cosh(d*x + c))*sinh(d*x + c)^5 + 6*d*cosh(d*x + c)^4 + 2*(35*d*cosh(d*x + c)^4 + 30*d*cosh(d*x + c)^2 + 3*d)*sinh(d*x + c)^4 + 8*(7*d*cosh(d*x + c)^5 + 10*d*cosh(d*x + c)^3 + 3*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*d*cosh(d*x + c)^2 + 4*(7*d*cosh(d*x + c)^6 + 15*d*cosh(d*x + c)^4 + 9*d*cosh(d*x + c)^2 + d)*sinh(d*x + c)^2 + 8*(d*cosh(d*x + c)^7 + 3*d*cosh(d*x + c)^5 + 3*d*cosh(d*x + c)^3 + d*cosh(d*x + c))*sinh(d*x + c) + d)","B",0
302,1,403,0,0.593222," ","integrate(sech(d*x+c)^6*(a+b*sinh(d*x+c)^2)^2,x, algorithm=""fricas"")","-\frac{4 \, {\left({\left(4 \, a^{2} + 2 \, a b + 9 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} - 8 \, {\left(2 \, a^{2} + a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(4 \, a^{2} + 2 \, a b + 9 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 20 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(4 \, a^{2} + 2 \, a b + 9 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 10 \, a^{2} + 20 \, a b\right)} \sinh\left(d x + c\right)^{2} + 40 \, a^{2} - 10 \, a b + 15 \, b^{2} - 8 \, {\left({\left(2 \, a^{2} + a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 5 \, {\left(a^{2} - a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}{15 \, {\left(d \cosh\left(d x + c\right)^{6} + 6 \, d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + d \sinh\left(d x + c\right)^{6} + 6 \, d \cosh\left(d x + c\right)^{4} + 3 \, {\left(5 \, d \cosh\left(d x + c\right)^{2} + 2 \, d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, d \cosh\left(d x + c\right)^{3} + 4 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 15 \, d \cosh\left(d x + c\right)^{2} + 3 \, {\left(5 \, d \cosh\left(d x + c\right)^{4} + 12 \, d \cosh\left(d x + c\right)^{2} + 5 \, d\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(3 \, d \cosh\left(d x + c\right)^{5} + 8 \, d \cosh\left(d x + c\right)^{3} + 5 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + 10 \, d\right)}}"," ",0,"-4/15*((4*a^2 + 2*a*b + 9*b^2)*cosh(d*x + c)^4 - 8*(2*a^2 + a*b - 3*b^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (4*a^2 + 2*a*b + 9*b^2)*sinh(d*x + c)^4 + 20*(a^2 + 2*a*b)*cosh(d*x + c)^2 + 2*(3*(4*a^2 + 2*a*b + 9*b^2)*cosh(d*x + c)^2 + 10*a^2 + 20*a*b)*sinh(d*x + c)^2 + 40*a^2 - 10*a*b + 15*b^2 - 8*((2*a^2 + a*b - 3*b^2)*cosh(d*x + c)^3 + 5*(a^2 - a*b)*cosh(d*x + c))*sinh(d*x + c))/(d*cosh(d*x + c)^6 + 6*d*cosh(d*x + c)*sinh(d*x + c)^5 + d*sinh(d*x + c)^6 + 6*d*cosh(d*x + c)^4 + 3*(5*d*cosh(d*x + c)^2 + 2*d)*sinh(d*x + c)^4 + 4*(5*d*cosh(d*x + c)^3 + 4*d*cosh(d*x + c))*sinh(d*x + c)^3 + 15*d*cosh(d*x + c)^2 + 3*(5*d*cosh(d*x + c)^4 + 12*d*cosh(d*x + c)^2 + 5*d)*sinh(d*x + c)^2 + 2*(3*d*cosh(d*x + c)^5 + 8*d*cosh(d*x + c)^3 + 5*d*cosh(d*x + c))*sinh(d*x + c) + 10*d)","B",0
303,1,2824,0,2.176380," ","integrate(sech(d*x+c)^7*(a+b*sinh(d*x+c)^2)^2,x, algorithm=""fricas"")","\frac{3 \, {\left(5 \, a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{11} + 33 \, {\left(5 \, a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{10} + 3 \, {\left(5 \, a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{11} + {\left(85 \, a^{2} + 34 \, a b - 47 \, b^{2}\right)} \cosh\left(d x + c\right)^{9} + {\left(165 \, {\left(5 \, a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 85 \, a^{2} + 34 \, a b - 47 \, b^{2}\right)} \sinh\left(d x + c\right)^{9} + 9 \, {\left(55 \, {\left(5 \, a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(85 \, a^{2} + 34 \, a b - 47 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{8} + 6 \, {\left(33 \, a^{2} - 38 \, a b + 13 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} + 6 \, {\left(165 \, {\left(5 \, a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + 6 \, {\left(85 \, a^{2} + 34 \, a b - 47 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 33 \, a^{2} - 38 \, a b + 13 \, b^{2}\right)} \sinh\left(d x + c\right)^{7} + 42 \, {\left(33 \, {\left(5 \, a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(85 \, a^{2} + 34 \, a b - 47 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(33 \, a^{2} - 38 \, a b + 13 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} - 6 \, {\left(33 \, a^{2} - 38 \, a b + 13 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 6 \, {\left(231 \, {\left(5 \, a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{6} + 21 \, {\left(85 \, a^{2} + 34 \, a b - 47 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 21 \, {\left(33 \, a^{2} - 38 \, a b + 13 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 33 \, a^{2} + 38 \, a b - 13 \, b^{2}\right)} \sinh\left(d x + c\right)^{5} + 6 \, {\left(165 \, {\left(5 \, a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{7} + 21 \, {\left(85 \, a^{2} + 34 \, a b - 47 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 35 \, {\left(33 \, a^{2} - 38 \, a b + 13 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - 5 \, {\left(33 \, a^{2} - 38 \, a b + 13 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} - {\left(85 \, a^{2} + 34 \, a b - 47 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(495 \, {\left(5 \, a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{8} + 84 \, {\left(85 \, a^{2} + 34 \, a b - 47 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 210 \, {\left(33 \, a^{2} - 38 \, a b + 13 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} - 60 \, {\left(33 \, a^{2} - 38 \, a b + 13 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 85 \, a^{2} - 34 \, a b + 47 \, b^{2}\right)} \sinh\left(d x + c\right)^{3} + 3 \, {\left(55 \, {\left(5 \, a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{9} + 12 \, {\left(85 \, a^{2} + 34 \, a b - 47 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} + 42 \, {\left(33 \, a^{2} - 38 \, a b + 13 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} - 20 \, {\left(33 \, a^{2} - 38 \, a b + 13 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(85 \, a^{2} + 34 \, a b - 47 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 3 \, {\left({\left(5 \, a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{12} + 12 \, {\left(5 \, a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{11} + {\left(5 \, a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{12} + 6 \, {\left(5 \, a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{10} + 6 \, {\left(11 \, {\left(5 \, a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 5 \, a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{10} + 20 \, {\left(11 \, {\left(5 \, a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(5 \, a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} + 15 \, {\left(5 \, a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{8} + 15 \, {\left(33 \, {\left(5 \, a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + 18 \, {\left(5 \, a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 5 \, a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{8} + 24 \, {\left(33 \, {\left(5 \, a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{5} + 30 \, {\left(5 \, a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + 5 \, {\left(5 \, a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 20 \, {\left(5 \, a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(231 \, {\left(5 \, a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{6} + 315 \, {\left(5 \, a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + 105 \, {\left(5 \, a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 25 \, a^{2} + 10 \, a b + 5 \, b^{2}\right)} \sinh\left(d x + c\right)^{6} + 24 \, {\left(33 \, {\left(5 \, a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{7} + 63 \, {\left(5 \, a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{5} + 35 \, {\left(5 \, a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + 5 \, {\left(5 \, a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 15 \, {\left(5 \, a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + 15 \, {\left(33 \, {\left(5 \, a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{8} + 84 \, {\left(5 \, a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{6} + 70 \, {\left(5 \, a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + 20 \, {\left(5 \, a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 5 \, a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{4} + 20 \, {\left(11 \, {\left(5 \, a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{9} + 36 \, {\left(5 \, a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{7} + 42 \, {\left(5 \, a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{5} + 20 \, {\left(5 \, a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(5 \, a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 6 \, {\left(5 \, a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 6 \, {\left(11 \, {\left(5 \, a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{10} + 45 \, {\left(5 \, a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{8} + 70 \, {\left(5 \, a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{6} + 50 \, {\left(5 \, a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + 15 \, {\left(5 \, a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 5 \, a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{2} + 5 \, a^{2} + 2 \, a b + b^{2} + 12 \, {\left({\left(5 \, a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{11} + 5 \, {\left(5 \, a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{9} + 10 \, {\left(5 \, a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{7} + 10 \, {\left(5 \, a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(5 \, a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(5 \, a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \arctan\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) - 3 \, {\left(5 \, a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right) + 3 \, {\left(11 \, {\left(5 \, a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{10} + 3 \, {\left(85 \, a^{2} + 34 \, a b - 47 \, b^{2}\right)} \cosh\left(d x + c\right)^{8} + 14 \, {\left(33 \, a^{2} - 38 \, a b + 13 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} - 10 \, {\left(33 \, a^{2} - 38 \, a b + 13 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} - {\left(85 \, a^{2} + 34 \, a b - 47 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 5 \, a^{2} - 2 \, a b - b^{2}\right)} \sinh\left(d x + c\right)}{24 \, {\left(d \cosh\left(d x + c\right)^{12} + 12 \, d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{11} + d \sinh\left(d x + c\right)^{12} + 6 \, d \cosh\left(d x + c\right)^{10} + 6 \, {\left(11 \, d \cosh\left(d x + c\right)^{2} + d\right)} \sinh\left(d x + c\right)^{10} + 20 \, {\left(11 \, d \cosh\left(d x + c\right)^{3} + 3 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} + 15 \, d \cosh\left(d x + c\right)^{8} + 15 \, {\left(33 \, d \cosh\left(d x + c\right)^{4} + 18 \, d \cosh\left(d x + c\right)^{2} + d\right)} \sinh\left(d x + c\right)^{8} + 24 \, {\left(33 \, d \cosh\left(d x + c\right)^{5} + 30 \, d \cosh\left(d x + c\right)^{3} + 5 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 20 \, d \cosh\left(d x + c\right)^{6} + 4 \, {\left(231 \, d \cosh\left(d x + c\right)^{6} + 315 \, d \cosh\left(d x + c\right)^{4} + 105 \, d \cosh\left(d x + c\right)^{2} + 5 \, d\right)} \sinh\left(d x + c\right)^{6} + 24 \, {\left(33 \, d \cosh\left(d x + c\right)^{7} + 63 \, d \cosh\left(d x + c\right)^{5} + 35 \, d \cosh\left(d x + c\right)^{3} + 5 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 15 \, d \cosh\left(d x + c\right)^{4} + 15 \, {\left(33 \, d \cosh\left(d x + c\right)^{8} + 84 \, d \cosh\left(d x + c\right)^{6} + 70 \, d \cosh\left(d x + c\right)^{4} + 20 \, d \cosh\left(d x + c\right)^{2} + d\right)} \sinh\left(d x + c\right)^{4} + 20 \, {\left(11 \, d \cosh\left(d x + c\right)^{9} + 36 \, d \cosh\left(d x + c\right)^{7} + 42 \, d \cosh\left(d x + c\right)^{5} + 20 \, d \cosh\left(d x + c\right)^{3} + 3 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 6 \, d \cosh\left(d x + c\right)^{2} + 6 \, {\left(11 \, d \cosh\left(d x + c\right)^{10} + 45 \, d \cosh\left(d x + c\right)^{8} + 70 \, d \cosh\left(d x + c\right)^{6} + 50 \, d \cosh\left(d x + c\right)^{4} + 15 \, d \cosh\left(d x + c\right)^{2} + d\right)} \sinh\left(d x + c\right)^{2} + 12 \, {\left(d \cosh\left(d x + c\right)^{11} + 5 \, d \cosh\left(d x + c\right)^{9} + 10 \, d \cosh\left(d x + c\right)^{7} + 10 \, d \cosh\left(d x + c\right)^{5} + 5 \, d \cosh\left(d x + c\right)^{3} + d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + d\right)}}"," ",0,"1/24*(3*(5*a^2 + 2*a*b + b^2)*cosh(d*x + c)^11 + 33*(5*a^2 + 2*a*b + b^2)*cosh(d*x + c)*sinh(d*x + c)^10 + 3*(5*a^2 + 2*a*b + b^2)*sinh(d*x + c)^11 + (85*a^2 + 34*a*b - 47*b^2)*cosh(d*x + c)^9 + (165*(5*a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + 85*a^2 + 34*a*b - 47*b^2)*sinh(d*x + c)^9 + 9*(55*(5*a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 + (85*a^2 + 34*a*b - 47*b^2)*cosh(d*x + c))*sinh(d*x + c)^8 + 6*(33*a^2 - 38*a*b + 13*b^2)*cosh(d*x + c)^7 + 6*(165*(5*a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 + 6*(85*a^2 + 34*a*b - 47*b^2)*cosh(d*x + c)^2 + 33*a^2 - 38*a*b + 13*b^2)*sinh(d*x + c)^7 + 42*(33*(5*a^2 + 2*a*b + b^2)*cosh(d*x + c)^5 + 2*(85*a^2 + 34*a*b - 47*b^2)*cosh(d*x + c)^3 + (33*a^2 - 38*a*b + 13*b^2)*cosh(d*x + c))*sinh(d*x + c)^6 - 6*(33*a^2 - 38*a*b + 13*b^2)*cosh(d*x + c)^5 + 6*(231*(5*a^2 + 2*a*b + b^2)*cosh(d*x + c)^6 + 21*(85*a^2 + 34*a*b - 47*b^2)*cosh(d*x + c)^4 + 21*(33*a^2 - 38*a*b + 13*b^2)*cosh(d*x + c)^2 - 33*a^2 + 38*a*b - 13*b^2)*sinh(d*x + c)^5 + 6*(165*(5*a^2 + 2*a*b + b^2)*cosh(d*x + c)^7 + 21*(85*a^2 + 34*a*b - 47*b^2)*cosh(d*x + c)^5 + 35*(33*a^2 - 38*a*b + 13*b^2)*cosh(d*x + c)^3 - 5*(33*a^2 - 38*a*b + 13*b^2)*cosh(d*x + c))*sinh(d*x + c)^4 - (85*a^2 + 34*a*b - 47*b^2)*cosh(d*x + c)^3 + (495*(5*a^2 + 2*a*b + b^2)*cosh(d*x + c)^8 + 84*(85*a^2 + 34*a*b - 47*b^2)*cosh(d*x + c)^6 + 210*(33*a^2 - 38*a*b + 13*b^2)*cosh(d*x + c)^4 - 60*(33*a^2 - 38*a*b + 13*b^2)*cosh(d*x + c)^2 - 85*a^2 - 34*a*b + 47*b^2)*sinh(d*x + c)^3 + 3*(55*(5*a^2 + 2*a*b + b^2)*cosh(d*x + c)^9 + 12*(85*a^2 + 34*a*b - 47*b^2)*cosh(d*x + c)^7 + 42*(33*a^2 - 38*a*b + 13*b^2)*cosh(d*x + c)^5 - 20*(33*a^2 - 38*a*b + 13*b^2)*cosh(d*x + c)^3 - (85*a^2 + 34*a*b - 47*b^2)*cosh(d*x + c))*sinh(d*x + c)^2 + 3*((5*a^2 + 2*a*b + b^2)*cosh(d*x + c)^12 + 12*(5*a^2 + 2*a*b + b^2)*cosh(d*x + c)*sinh(d*x + c)^11 + (5*a^2 + 2*a*b + b^2)*sinh(d*x + c)^12 + 6*(5*a^2 + 2*a*b + b^2)*cosh(d*x + c)^10 + 6*(11*(5*a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + 5*a^2 + 2*a*b + b^2)*sinh(d*x + c)^10 + 20*(11*(5*a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 + 3*(5*a^2 + 2*a*b + b^2)*cosh(d*x + c))*sinh(d*x + c)^9 + 15*(5*a^2 + 2*a*b + b^2)*cosh(d*x + c)^8 + 15*(33*(5*a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 + 18*(5*a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + 5*a^2 + 2*a*b + b^2)*sinh(d*x + c)^8 + 24*(33*(5*a^2 + 2*a*b + b^2)*cosh(d*x + c)^5 + 30*(5*a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 + 5*(5*a^2 + 2*a*b + b^2)*cosh(d*x + c))*sinh(d*x + c)^7 + 20*(5*a^2 + 2*a*b + b^2)*cosh(d*x + c)^6 + 4*(231*(5*a^2 + 2*a*b + b^2)*cosh(d*x + c)^6 + 315*(5*a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 + 105*(5*a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + 25*a^2 + 10*a*b + 5*b^2)*sinh(d*x + c)^6 + 24*(33*(5*a^2 + 2*a*b + b^2)*cosh(d*x + c)^7 + 63*(5*a^2 + 2*a*b + b^2)*cosh(d*x + c)^5 + 35*(5*a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 + 5*(5*a^2 + 2*a*b + b^2)*cosh(d*x + c))*sinh(d*x + c)^5 + 15*(5*a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 + 15*(33*(5*a^2 + 2*a*b + b^2)*cosh(d*x + c)^8 + 84*(5*a^2 + 2*a*b + b^2)*cosh(d*x + c)^6 + 70*(5*a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 + 20*(5*a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + 5*a^2 + 2*a*b + b^2)*sinh(d*x + c)^4 + 20*(11*(5*a^2 + 2*a*b + b^2)*cosh(d*x + c)^9 + 36*(5*a^2 + 2*a*b + b^2)*cosh(d*x + c)^7 + 42*(5*a^2 + 2*a*b + b^2)*cosh(d*x + c)^5 + 20*(5*a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 + 3*(5*a^2 + 2*a*b + b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 6*(5*a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + 6*(11*(5*a^2 + 2*a*b + b^2)*cosh(d*x + c)^10 + 45*(5*a^2 + 2*a*b + b^2)*cosh(d*x + c)^8 + 70*(5*a^2 + 2*a*b + b^2)*cosh(d*x + c)^6 + 50*(5*a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 + 15*(5*a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + 5*a^2 + 2*a*b + b^2)*sinh(d*x + c)^2 + 5*a^2 + 2*a*b + b^2 + 12*((5*a^2 + 2*a*b + b^2)*cosh(d*x + c)^11 + 5*(5*a^2 + 2*a*b + b^2)*cosh(d*x + c)^9 + 10*(5*a^2 + 2*a*b + b^2)*cosh(d*x + c)^7 + 10*(5*a^2 + 2*a*b + b^2)*cosh(d*x + c)^5 + 5*(5*a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 + (5*a^2 + 2*a*b + b^2)*cosh(d*x + c))*sinh(d*x + c))*arctan(cosh(d*x + c) + sinh(d*x + c)) - 3*(5*a^2 + 2*a*b + b^2)*cosh(d*x + c) + 3*(11*(5*a^2 + 2*a*b + b^2)*cosh(d*x + c)^10 + 3*(85*a^2 + 34*a*b - 47*b^2)*cosh(d*x + c)^8 + 14*(33*a^2 - 38*a*b + 13*b^2)*cosh(d*x + c)^6 - 10*(33*a^2 - 38*a*b + 13*b^2)*cosh(d*x + c)^4 - (85*a^2 + 34*a*b - 47*b^2)*cosh(d*x + c)^2 - 5*a^2 - 2*a*b - b^2)*sinh(d*x + c))/(d*cosh(d*x + c)^12 + 12*d*cosh(d*x + c)*sinh(d*x + c)^11 + d*sinh(d*x + c)^12 + 6*d*cosh(d*x + c)^10 + 6*(11*d*cosh(d*x + c)^2 + d)*sinh(d*x + c)^10 + 20*(11*d*cosh(d*x + c)^3 + 3*d*cosh(d*x + c))*sinh(d*x + c)^9 + 15*d*cosh(d*x + c)^8 + 15*(33*d*cosh(d*x + c)^4 + 18*d*cosh(d*x + c)^2 + d)*sinh(d*x + c)^8 + 24*(33*d*cosh(d*x + c)^5 + 30*d*cosh(d*x + c)^3 + 5*d*cosh(d*x + c))*sinh(d*x + c)^7 + 20*d*cosh(d*x + c)^6 + 4*(231*d*cosh(d*x + c)^6 + 315*d*cosh(d*x + c)^4 + 105*d*cosh(d*x + c)^2 + 5*d)*sinh(d*x + c)^6 + 24*(33*d*cosh(d*x + c)^7 + 63*d*cosh(d*x + c)^5 + 35*d*cosh(d*x + c)^3 + 5*d*cosh(d*x + c))*sinh(d*x + c)^5 + 15*d*cosh(d*x + c)^4 + 15*(33*d*cosh(d*x + c)^8 + 84*d*cosh(d*x + c)^6 + 70*d*cosh(d*x + c)^4 + 20*d*cosh(d*x + c)^2 + d)*sinh(d*x + c)^4 + 20*(11*d*cosh(d*x + c)^9 + 36*d*cosh(d*x + c)^7 + 42*d*cosh(d*x + c)^5 + 20*d*cosh(d*x + c)^3 + 3*d*cosh(d*x + c))*sinh(d*x + c)^3 + 6*d*cosh(d*x + c)^2 + 6*(11*d*cosh(d*x + c)^10 + 45*d*cosh(d*x + c)^8 + 70*d*cosh(d*x + c)^6 + 50*d*cosh(d*x + c)^4 + 15*d*cosh(d*x + c)^2 + d)*sinh(d*x + c)^2 + 12*(d*cosh(d*x + c)^11 + 5*d*cosh(d*x + c)^9 + 10*d*cosh(d*x + c)^7 + 10*d*cosh(d*x + c)^5 + 5*d*cosh(d*x + c)^3 + d*cosh(d*x + c))*sinh(d*x + c) + d)","B",0
304,1,376,0,0.727877," ","integrate(cosh(d*x+c)^4*(a+b*sinh(d*x+c)^2)^3,x, algorithm=""fricas"")","\frac{5 \, b^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + 10 \, {\left(6 \, b^{3} \cosh\left(d x + c\right)^{3} + {\left(6 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + {\left(126 \, b^{3} \cosh\left(d x + c\right)^{5} + 70 \, {\left(6 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{3} + 15 \, {\left(16 \, a^{2} b - b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 10 \, {\left(6 \, b^{3} \cosh\left(d x + c\right)^{7} + 7 \, {\left(6 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(16 \, a^{2} b - b^{3}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(8 \, a^{3} + 12 \, a^{2} b - 6 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 30 \, {\left(32 \, a^{3} - 16 \, a^{2} b + 6 \, a b^{2} - b^{3}\right)} d x + 5 \, {\left(b^{3} \cosh\left(d x + c\right)^{9} + 2 \, {\left(6 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(16 \, a^{2} b - b^{3}\right)} \cosh\left(d x + c\right)^{5} + 8 \, {\left(8 \, a^{3} + 12 \, a^{2} b - 6 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(128 \, a^{3} - 24 \, a^{2} b + b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{2560 \, d}"," ",0,"1/2560*(5*b^3*cosh(d*x + c)*sinh(d*x + c)^9 + 10*(6*b^3*cosh(d*x + c)^3 + (6*a*b^2 - b^3)*cosh(d*x + c))*sinh(d*x + c)^7 + (126*b^3*cosh(d*x + c)^5 + 70*(6*a*b^2 - b^3)*cosh(d*x + c)^3 + 15*(16*a^2*b - b^3)*cosh(d*x + c))*sinh(d*x + c)^5 + 10*(6*b^3*cosh(d*x + c)^7 + 7*(6*a*b^2 - b^3)*cosh(d*x + c)^5 + 5*(16*a^2*b - b^3)*cosh(d*x + c)^3 + 4*(8*a^3 + 12*a^2*b - 6*a*b^2 + b^3)*cosh(d*x + c))*sinh(d*x + c)^3 + 30*(32*a^3 - 16*a^2*b + 6*a*b^2 - b^3)*d*x + 5*(b^3*cosh(d*x + c)^9 + 2*(6*a*b^2 - b^3)*cosh(d*x + c)^7 + 3*(16*a^2*b - b^3)*cosh(d*x + c)^5 + 8*(8*a^3 + 12*a^2*b - 6*a*b^2 + b^3)*cosh(d*x + c)^3 + 2*(128*a^3 - 24*a^2*b + b^3)*cosh(d*x + c))*sinh(d*x + c))/d","A",0
305,1,324,0,0.578229," ","integrate(cosh(d*x+c)^3*(a+b*sinh(d*x+c)^2)^3,x, algorithm=""fricas"")","\frac{35 \, b^{3} \sinh\left(d x + c\right)^{9} + 45 \, {\left(28 \, b^{3} \cosh\left(d x + c\right)^{2} + 12 \, a b^{2} - 3 \, b^{3}\right)} \sinh\left(d x + c\right)^{7} + 63 \, {\left(70 \, b^{3} \cosh\left(d x + c\right)^{4} + 48 \, a^{2} b - 12 \, a b^{2} + 45 \, {\left(4 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{5} + 105 \, {\left(28 \, b^{3} \cosh\left(d x + c\right)^{6} + 45 \, {\left(4 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{4} + 64 \, a^{3} + 48 \, a^{2} b - 36 \, a b^{2} + 8 \, b^{3} + 72 \, {\left(4 \, a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + 315 \, {\left(b^{3} \cosh\left(d x + c\right)^{8} + 3 \, {\left(4 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{6} + 12 \, {\left(4 \, a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right)^{4} + 192 \, a^{3} - 96 \, a^{2} b + 36 \, a b^{2} - 6 \, b^{3} + 4 \, {\left(16 \, a^{3} + 12 \, a^{2} b - 9 \, a b^{2} + 2 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)}{80640 \, d}"," ",0,"1/80640*(35*b^3*sinh(d*x + c)^9 + 45*(28*b^3*cosh(d*x + c)^2 + 12*a*b^2 - 3*b^3)*sinh(d*x + c)^7 + 63*(70*b^3*cosh(d*x + c)^4 + 48*a^2*b - 12*a*b^2 + 45*(4*a*b^2 - b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 105*(28*b^3*cosh(d*x + c)^6 + 45*(4*a*b^2 - b^3)*cosh(d*x + c)^4 + 64*a^3 + 48*a^2*b - 36*a*b^2 + 8*b^3 + 72*(4*a^2*b - a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 315*(b^3*cosh(d*x + c)^8 + 3*(4*a*b^2 - b^3)*cosh(d*x + c)^6 + 12*(4*a^2*b - a*b^2)*cosh(d*x + c)^4 + 192*a^3 - 96*a^2*b + 36*a*b^2 - 6*b^3 + 4*(16*a^3 + 12*a^2*b - 9*a*b^2 + 2*b^3)*cosh(d*x + c)^2)*sinh(d*x + c))/d","B",0
306,1,257,0,0.547912," ","integrate(cosh(d*x+c)^2*(a+b*sinh(d*x+c)^2)^3,x, algorithm=""fricas"")","\frac{3 \, b^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + 3 \, {\left(7 \, b^{3} \cosh\left(d x + c\right)^{3} + 4 \, {\left(3 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + {\left(21 \, b^{3} \cosh\left(d x + c\right)^{5} + 40 \, {\left(3 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{3} + 12 \, {\left(12 \, a^{2} b - 6 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 3 \, {\left(64 \, a^{3} - 48 \, a^{2} b + 24 \, a b^{2} - 5 \, b^{3}\right)} d x + 3 \, {\left(b^{3} \cosh\left(d x + c\right)^{7} + 4 \, {\left(3 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{5} + 4 \, {\left(12 \, a^{2} b - 6 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(16 \, a^{3} - 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{384 \, d}"," ",0,"1/384*(3*b^3*cosh(d*x + c)*sinh(d*x + c)^7 + 3*(7*b^3*cosh(d*x + c)^3 + 4*(3*a*b^2 - b^3)*cosh(d*x + c))*sinh(d*x + c)^5 + (21*b^3*cosh(d*x + c)^5 + 40*(3*a*b^2 - b^3)*cosh(d*x + c)^3 + 12*(12*a^2*b - 6*a*b^2 + b^3)*cosh(d*x + c))*sinh(d*x + c)^3 + 3*(64*a^3 - 48*a^2*b + 24*a*b^2 - 5*b^3)*d*x + 3*(b^3*cosh(d*x + c)^7 + 4*(3*a*b^2 - b^3)*cosh(d*x + c)^5 + 4*(12*a^2*b - 6*a*b^2 + b^3)*cosh(d*x + c)^3 + 4*(16*a^3 - 3*a*b^2 + b^3)*cosh(d*x + c))*sinh(d*x + c))/d","A",0
307,1,209,0,1.397058," ","integrate(cosh(d*x+c)*(a+b*sinh(d*x+c)^2)^3,x, algorithm=""fricas"")","\frac{5 \, b^{3} \sinh\left(d x + c\right)^{7} + 7 \, {\left(15 \, b^{3} \cosh\left(d x + c\right)^{2} + 12 \, a b^{2} - 5 \, b^{3}\right)} \sinh\left(d x + c\right)^{5} + 35 \, {\left(5 \, b^{3} \cosh\left(d x + c\right)^{4} + 16 \, a^{2} b - 12 \, a b^{2} + 3 \, b^{3} + 2 \, {\left(12 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + 35 \, {\left(b^{3} \cosh\left(d x + c\right)^{6} + {\left(12 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 64 \, a^{3} - 48 \, a^{2} b + 24 \, a b^{2} - 5 \, b^{3} + 3 \, {\left(16 \, a^{2} b - 12 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)}{2240 \, d}"," ",0,"1/2240*(5*b^3*sinh(d*x + c)^7 + 7*(15*b^3*cosh(d*x + c)^2 + 12*a*b^2 - 5*b^3)*sinh(d*x + c)^5 + 35*(5*b^3*cosh(d*x + c)^4 + 16*a^2*b - 12*a*b^2 + 3*b^3 + 2*(12*a*b^2 - 5*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 35*(b^3*cosh(d*x + c)^6 + (12*a*b^2 - 5*b^3)*cosh(d*x + c)^4 + 64*a^3 - 48*a^2*b + 24*a*b^2 - 5*b^3 + 3*(16*a^2*b - 12*a*b^2 + 3*b^3)*cosh(d*x + c)^2)*sinh(d*x + c))/d","B",0
308,1,1114,0,1.469170," ","integrate(sech(d*x+c)*(a+b*sinh(d*x+c)^2)^3,x, algorithm=""fricas"")","\frac{3 \, b^{3} \cosh\left(d x + c\right)^{10} + 30 \, b^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + 3 \, b^{3} \sinh\left(d x + c\right)^{10} + 5 \, {\left(12 \, a b^{2} - 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 5 \, {\left(27 \, b^{3} \cosh\left(d x + c\right)^{2} + 12 \, a b^{2} - 7 \, b^{3}\right)} \sinh\left(d x + c\right)^{8} + 40 \, {\left(9 \, b^{3} \cosh\left(d x + c\right)^{3} + {\left(12 \, a b^{2} - 7 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 30 \, {\left(24 \, a^{2} b - 30 \, a b^{2} + 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 10 \, {\left(63 \, b^{3} \cosh\left(d x + c\right)^{4} + 72 \, a^{2} b - 90 \, a b^{2} + 33 \, b^{3} + 14 \, {\left(12 \, a b^{2} - 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(189 \, b^{3} \cosh\left(d x + c\right)^{5} + 70 \, {\left(12 \, a b^{2} - 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 45 \, {\left(24 \, a^{2} b - 30 \, a b^{2} + 11 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 30 \, {\left(24 \, a^{2} b - 30 \, a b^{2} + 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 10 \, {\left(63 \, b^{3} \cosh\left(d x + c\right)^{6} + 35 \, {\left(12 \, a b^{2} - 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 72 \, a^{2} b + 90 \, a b^{2} - 33 \, b^{3} + 45 \, {\left(24 \, a^{2} b - 30 \, a b^{2} + 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 40 \, {\left(9 \, b^{3} \cosh\left(d x + c\right)^{7} + 7 \, {\left(12 \, a b^{2} - 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 15 \, {\left(24 \, a^{2} b - 30 \, a b^{2} + 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(24 \, a^{2} b - 30 \, a b^{2} + 11 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 3 \, b^{3} - 5 \, {\left(12 \, a b^{2} - 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{2} + 5 \, {\left(27 \, b^{3} \cosh\left(d x + c\right)^{8} + 28 \, {\left(12 \, a b^{2} - 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 90 \, {\left(24 \, a^{2} b - 30 \, a b^{2} + 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 12 \, a b^{2} + 7 \, b^{3} - 36 \, {\left(24 \, a^{2} b - 30 \, a b^{2} + 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 960 \, {\left({\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{4} \sinh\left(d x + c\right) + 10 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right)^{2} + 10 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{3} + 5 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} + {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} \sinh\left(d x + c\right)^{5}\right)} \arctan\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) + 10 \, {\left(3 \, b^{3} \cosh\left(d x + c\right)^{9} + 4 \, {\left(12 \, a b^{2} - 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 18 \, {\left(24 \, a^{2} b - 30 \, a b^{2} + 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 12 \, {\left(24 \, a^{2} b - 30 \, a b^{2} + 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - {\left(12 \, a b^{2} - 7 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{480 \, {\left(d \cosh\left(d x + c\right)^{5} + 5 \, d \cosh\left(d x + c\right)^{4} \sinh\left(d x + c\right) + 10 \, d \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right)^{2} + 10 \, d \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{3} + 5 \, d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} + d \sinh\left(d x + c\right)^{5}\right)}}"," ",0,"1/480*(3*b^3*cosh(d*x + c)^10 + 30*b^3*cosh(d*x + c)*sinh(d*x + c)^9 + 3*b^3*sinh(d*x + c)^10 + 5*(12*a*b^2 - 7*b^3)*cosh(d*x + c)^8 + 5*(27*b^3*cosh(d*x + c)^2 + 12*a*b^2 - 7*b^3)*sinh(d*x + c)^8 + 40*(9*b^3*cosh(d*x + c)^3 + (12*a*b^2 - 7*b^3)*cosh(d*x + c))*sinh(d*x + c)^7 + 30*(24*a^2*b - 30*a*b^2 + 11*b^3)*cosh(d*x + c)^6 + 10*(63*b^3*cosh(d*x + c)^4 + 72*a^2*b - 90*a*b^2 + 33*b^3 + 14*(12*a*b^2 - 7*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 4*(189*b^3*cosh(d*x + c)^5 + 70*(12*a*b^2 - 7*b^3)*cosh(d*x + c)^3 + 45*(24*a^2*b - 30*a*b^2 + 11*b^3)*cosh(d*x + c))*sinh(d*x + c)^5 - 30*(24*a^2*b - 30*a*b^2 + 11*b^3)*cosh(d*x + c)^4 + 10*(63*b^3*cosh(d*x + c)^6 + 35*(12*a*b^2 - 7*b^3)*cosh(d*x + c)^4 - 72*a^2*b + 90*a*b^2 - 33*b^3 + 45*(24*a^2*b - 30*a*b^2 + 11*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 40*(9*b^3*cosh(d*x + c)^7 + 7*(12*a*b^2 - 7*b^3)*cosh(d*x + c)^5 + 15*(24*a^2*b - 30*a*b^2 + 11*b^3)*cosh(d*x + c)^3 - 3*(24*a^2*b - 30*a*b^2 + 11*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 - 3*b^3 - 5*(12*a*b^2 - 7*b^3)*cosh(d*x + c)^2 + 5*(27*b^3*cosh(d*x + c)^8 + 28*(12*a*b^2 - 7*b^3)*cosh(d*x + c)^6 + 90*(24*a^2*b - 30*a*b^2 + 11*b^3)*cosh(d*x + c)^4 - 12*a*b^2 + 7*b^3 - 36*(24*a^2*b - 30*a*b^2 + 11*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 960*((a^3 - 3*a^2*b + 3*a*b^2 - b^3)*cosh(d*x + c)^5 + 5*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*cosh(d*x + c)^4*sinh(d*x + c) + 10*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*cosh(d*x + c)^3*sinh(d*x + c)^2 + 10*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*cosh(d*x + c)^2*sinh(d*x + c)^3 + 5*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*cosh(d*x + c)*sinh(d*x + c)^4 + (a^3 - 3*a^2*b + 3*a*b^2 - b^3)*sinh(d*x + c)^5)*arctan(cosh(d*x + c) + sinh(d*x + c)) + 10*(3*b^3*cosh(d*x + c)^9 + 4*(12*a*b^2 - 7*b^3)*cosh(d*x + c)^7 + 18*(24*a^2*b - 30*a*b^2 + 11*b^3)*cosh(d*x + c)^5 - 12*(24*a^2*b - 30*a*b^2 + 11*b^3)*cosh(d*x + c)^3 - (12*a*b^2 - 7*b^3)*cosh(d*x + c))*sinh(d*x + c))/(d*cosh(d*x + c)^5 + 5*d*cosh(d*x + c)^4*sinh(d*x + c) + 10*d*cosh(d*x + c)^3*sinh(d*x + c)^2 + 10*d*cosh(d*x + c)^2*sinh(d*x + c)^3 + 5*d*cosh(d*x + c)*sinh(d*x + c)^4 + d*sinh(d*x + c)^5)","B",0
309,1,178,0,1.182425," ","integrate(sech(d*x+c)^2*(a+b*sinh(d*x+c)^2)^3,x, algorithm=""fricas"")","\frac{b^{3} \sinh\left(d x + c\right)^{5} + {\left(10 \, b^{3} \cosh\left(d x + c\right)^{2} + 24 \, a b^{2} - 15 \, b^{3}\right)} \sinh\left(d x + c\right)^{3} - 8 \, {\left(8 \, a^{3} - 24 \, a^{2} b + 24 \, a b^{2} - 8 \, b^{3} - 3 \, {\left(8 \, a^{2} b - 12 \, a b^{2} + 5 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right) + {\left(5 \, b^{3} \cosh\left(d x + c\right)^{4} + 64 \, a^{3} - 192 \, a^{2} b + 216 \, a b^{2} - 80 \, b^{3} + 9 \, {\left(8 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)}{64 \, d \cosh\left(d x + c\right)}"," ",0,"1/64*(b^3*sinh(d*x + c)^5 + (10*b^3*cosh(d*x + c)^2 + 24*a*b^2 - 15*b^3)*sinh(d*x + c)^3 - 8*(8*a^3 - 24*a^2*b + 24*a*b^2 - 8*b^3 - 3*(8*a^2*b - 12*a*b^2 + 5*b^3)*d*x)*cosh(d*x + c) + (5*b^3*cosh(d*x + c)^4 + 64*a^3 - 192*a^2*b + 216*a*b^2 - 80*b^3 + 9*(8*a*b^2 - 5*b^3)*cosh(d*x + c)^2)*sinh(d*x + c))/(d*cosh(d*x + c))","B",0
310,1,1679,0,0.666200," ","integrate(sech(d*x+c)^3*(a+b*sinh(d*x+c)^2)^3,x, algorithm=""fricas"")","\frac{b^{3} \cosh\left(d x + c\right)^{10} + 10 \, b^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + b^{3} \sinh\left(d x + c\right)^{10} + {\left(36 \, a b^{2} - 25 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + {\left(45 \, b^{3} \cosh\left(d x + c\right)^{2} + 36 \, a b^{2} - 25 \, b^{3}\right)} \sinh\left(d x + c\right)^{8} + 8 \, {\left(15 \, b^{3} \cosh\left(d x + c\right)^{3} + {\left(36 \, a b^{2} - 25 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(12 \, a^{3} - 36 \, a^{2} b + 54 \, a b^{2} - 25 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(105 \, b^{3} \cosh\left(d x + c\right)^{4} + 12 \, a^{3} - 36 \, a^{2} b + 54 \, a b^{2} - 25 \, b^{3} + 14 \, {\left(36 \, a b^{2} - 25 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(63 \, b^{3} \cosh\left(d x + c\right)^{5} + 14 \, {\left(36 \, a b^{2} - 25 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(12 \, a^{3} - 36 \, a^{2} b + 54 \, a b^{2} - 25 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 2 \, {\left(12 \, a^{3} - 36 \, a^{2} b + 54 \, a b^{2} - 25 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(105 \, b^{3} \cosh\left(d x + c\right)^{6} + 35 \, {\left(36 \, a b^{2} - 25 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 12 \, a^{3} + 36 \, a^{2} b - 54 \, a b^{2} + 25 \, b^{3} + 15 \, {\left(12 \, a^{3} - 36 \, a^{2} b + 54 \, a b^{2} - 25 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(15 \, b^{3} \cosh\left(d x + c\right)^{7} + 7 \, {\left(36 \, a b^{2} - 25 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(12 \, a^{3} - 36 \, a^{2} b + 54 \, a b^{2} - 25 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - {\left(12 \, a^{3} - 36 \, a^{2} b + 54 \, a b^{2} - 25 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - b^{3} - {\left(36 \, a b^{2} - 25 \, b^{3}\right)} \cosh\left(d x + c\right)^{2} + {\left(45 \, b^{3} \cosh\left(d x + c\right)^{8} + 28 \, {\left(36 \, a b^{2} - 25 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 30 \, {\left(12 \, a^{3} - 36 \, a^{2} b + 54 \, a b^{2} - 25 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 36 \, a b^{2} + 25 \, b^{3} - 12 \, {\left(12 \, a^{3} - 36 \, a^{2} b + 54 \, a b^{2} - 25 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 24 \, {\left({\left(a^{3} + 3 \, a^{2} b - 9 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 7 \, {\left(a^{3} + 3 \, a^{2} b - 9 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + {\left(a^{3} + 3 \, a^{2} b - 9 \, a b^{2} + 5 \, b^{3}\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(a^{3} + 3 \, a^{2} b - 9 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + {\left(2 \, a^{3} + 6 \, a^{2} b - 18 \, a b^{2} + 10 \, b^{3} + 21 \, {\left(a^{3} + 3 \, a^{2} b - 9 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{5} + 5 \, {\left(7 \, {\left(a^{3} + 3 \, a^{2} b - 9 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(a^{3} + 3 \, a^{2} b - 9 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + {\left(a^{3} + 3 \, a^{2} b - 9 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(35 \, {\left(a^{3} + 3 \, a^{2} b - 9 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + a^{3} + 3 \, a^{2} b - 9 \, a b^{2} + 5 \, b^{3} + 20 \, {\left(a^{3} + 3 \, a^{2} b - 9 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + {\left(21 \, {\left(a^{3} + 3 \, a^{2} b - 9 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 20 \, {\left(a^{3} + 3 \, a^{2} b - 9 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{3} + 3 \, a^{2} b - 9 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(7 \, {\left(a^{3} + 3 \, a^{2} b - 9 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 10 \, {\left(a^{3} + 3 \, a^{2} b - 9 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(a^{3} + 3 \, a^{2} b - 9 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)\right)} \arctan\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) + 2 \, {\left(5 \, b^{3} \cosh\left(d x + c\right)^{9} + 4 \, {\left(36 \, a b^{2} - 25 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 6 \, {\left(12 \, a^{3} - 36 \, a^{2} b + 54 \, a b^{2} - 25 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 4 \, {\left(12 \, a^{3} - 36 \, a^{2} b + 54 \, a b^{2} - 25 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - {\left(36 \, a b^{2} - 25 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{24 \, {\left(d \cosh\left(d x + c\right)^{7} + 7 \, d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + d \sinh\left(d x + c\right)^{7} + 2 \, d \cosh\left(d x + c\right)^{5} + {\left(21 \, d \cosh\left(d x + c\right)^{2} + 2 \, d\right)} \sinh\left(d x + c\right)^{5} + 5 \, {\left(7 \, d \cosh\left(d x + c\right)^{3} + 2 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + d \cosh\left(d x + c\right)^{3} + {\left(35 \, d \cosh\left(d x + c\right)^{4} + 20 \, d \cosh\left(d x + c\right)^{2} + d\right)} \sinh\left(d x + c\right)^{3} + {\left(21 \, d \cosh\left(d x + c\right)^{5} + 20 \, d \cosh\left(d x + c\right)^{3} + 3 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(7 \, d \cosh\left(d x + c\right)^{6} + 10 \, d \cosh\left(d x + c\right)^{4} + 3 \, d \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"1/24*(b^3*cosh(d*x + c)^10 + 10*b^3*cosh(d*x + c)*sinh(d*x + c)^9 + b^3*sinh(d*x + c)^10 + (36*a*b^2 - 25*b^3)*cosh(d*x + c)^8 + (45*b^3*cosh(d*x + c)^2 + 36*a*b^2 - 25*b^3)*sinh(d*x + c)^8 + 8*(15*b^3*cosh(d*x + c)^3 + (36*a*b^2 - 25*b^3)*cosh(d*x + c))*sinh(d*x + c)^7 + 2*(12*a^3 - 36*a^2*b + 54*a*b^2 - 25*b^3)*cosh(d*x + c)^6 + 2*(105*b^3*cosh(d*x + c)^4 + 12*a^3 - 36*a^2*b + 54*a*b^2 - 25*b^3 + 14*(36*a*b^2 - 25*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 4*(63*b^3*cosh(d*x + c)^5 + 14*(36*a*b^2 - 25*b^3)*cosh(d*x + c)^3 + 3*(12*a^3 - 36*a^2*b + 54*a*b^2 - 25*b^3)*cosh(d*x + c))*sinh(d*x + c)^5 - 2*(12*a^3 - 36*a^2*b + 54*a*b^2 - 25*b^3)*cosh(d*x + c)^4 + 2*(105*b^3*cosh(d*x + c)^6 + 35*(36*a*b^2 - 25*b^3)*cosh(d*x + c)^4 - 12*a^3 + 36*a^2*b - 54*a*b^2 + 25*b^3 + 15*(12*a^3 - 36*a^2*b + 54*a*b^2 - 25*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(15*b^3*cosh(d*x + c)^7 + 7*(36*a*b^2 - 25*b^3)*cosh(d*x + c)^5 + 5*(12*a^3 - 36*a^2*b + 54*a*b^2 - 25*b^3)*cosh(d*x + c)^3 - (12*a^3 - 36*a^2*b + 54*a*b^2 - 25*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 - b^3 - (36*a*b^2 - 25*b^3)*cosh(d*x + c)^2 + (45*b^3*cosh(d*x + c)^8 + 28*(36*a*b^2 - 25*b^3)*cosh(d*x + c)^6 + 30*(12*a^3 - 36*a^2*b + 54*a*b^2 - 25*b^3)*cosh(d*x + c)^4 - 36*a*b^2 + 25*b^3 - 12*(12*a^3 - 36*a^2*b + 54*a*b^2 - 25*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 24*((a^3 + 3*a^2*b - 9*a*b^2 + 5*b^3)*cosh(d*x + c)^7 + 7*(a^3 + 3*a^2*b - 9*a*b^2 + 5*b^3)*cosh(d*x + c)*sinh(d*x + c)^6 + (a^3 + 3*a^2*b - 9*a*b^2 + 5*b^3)*sinh(d*x + c)^7 + 2*(a^3 + 3*a^2*b - 9*a*b^2 + 5*b^3)*cosh(d*x + c)^5 + (2*a^3 + 6*a^2*b - 18*a*b^2 + 10*b^3 + 21*(a^3 + 3*a^2*b - 9*a*b^2 + 5*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 5*(7*(a^3 + 3*a^2*b - 9*a*b^2 + 5*b^3)*cosh(d*x + c)^3 + 2*(a^3 + 3*a^2*b - 9*a*b^2 + 5*b^3)*cosh(d*x + c))*sinh(d*x + c)^4 + (a^3 + 3*a^2*b - 9*a*b^2 + 5*b^3)*cosh(d*x + c)^3 + (35*(a^3 + 3*a^2*b - 9*a*b^2 + 5*b^3)*cosh(d*x + c)^4 + a^3 + 3*a^2*b - 9*a*b^2 + 5*b^3 + 20*(a^3 + 3*a^2*b - 9*a*b^2 + 5*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + (21*(a^3 + 3*a^2*b - 9*a*b^2 + 5*b^3)*cosh(d*x + c)^5 + 20*(a^3 + 3*a^2*b - 9*a*b^2 + 5*b^3)*cosh(d*x + c)^3 + 3*(a^3 + 3*a^2*b - 9*a*b^2 + 5*b^3)*cosh(d*x + c))*sinh(d*x + c)^2 + (7*(a^3 + 3*a^2*b - 9*a*b^2 + 5*b^3)*cosh(d*x + c)^6 + 10*(a^3 + 3*a^2*b - 9*a*b^2 + 5*b^3)*cosh(d*x + c)^4 + 3*(a^3 + 3*a^2*b - 9*a*b^2 + 5*b^3)*cosh(d*x + c)^2)*sinh(d*x + c))*arctan(cosh(d*x + c) + sinh(d*x + c)) + 2*(5*b^3*cosh(d*x + c)^9 + 4*(36*a*b^2 - 25*b^3)*cosh(d*x + c)^7 + 6*(12*a^3 - 36*a^2*b + 54*a*b^2 - 25*b^3)*cosh(d*x + c)^5 - 4*(12*a^3 - 36*a^2*b + 54*a*b^2 - 25*b^3)*cosh(d*x + c)^3 - (36*a*b^2 - 25*b^3)*cosh(d*x + c))*sinh(d*x + c))/(d*cosh(d*x + c)^7 + 7*d*cosh(d*x + c)*sinh(d*x + c)^6 + d*sinh(d*x + c)^7 + 2*d*cosh(d*x + c)^5 + (21*d*cosh(d*x + c)^2 + 2*d)*sinh(d*x + c)^5 + 5*(7*d*cosh(d*x + c)^3 + 2*d*cosh(d*x + c))*sinh(d*x + c)^4 + d*cosh(d*x + c)^3 + (35*d*cosh(d*x + c)^4 + 20*d*cosh(d*x + c)^2 + d)*sinh(d*x + c)^3 + (21*d*cosh(d*x + c)^5 + 20*d*cosh(d*x + c)^3 + 3*d*cosh(d*x + c))*sinh(d*x + c)^2 + (7*d*cosh(d*x + c)^6 + 10*d*cosh(d*x + c)^4 + 3*d*cosh(d*x + c)^2)*sinh(d*x + c))","B",0
311,1,321,0,0.737991," ","integrate(sech(d*x+c)^4*(a+b*sinh(d*x+c)^2)^3,x, algorithm=""fricas"")","\frac{3 \, b^{3} \sinh\left(d x + c\right)^{5} - 4 \, {\left(4 \, a^{3} + 6 \, a^{2} b - 24 \, a b^{2} + 14 \, b^{3} - 3 \, {\left(6 \, a b^{2} - 5 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - 12 \, {\left(4 \, a^{3} + 6 \, a^{2} b - 24 \, a b^{2} + 14 \, b^{3} - 3 \, {\left(6 \, a b^{2} - 5 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + {\left(30 \, b^{3} \cosh\left(d x + c\right)^{2} + 16 \, a^{3} + 24 \, a^{2} b - 96 \, a b^{2} + 65 \, b^{3}\right)} \sinh\left(d x + c\right)^{3} - 12 \, {\left(4 \, a^{3} + 6 \, a^{2} b - 24 \, a b^{2} + 14 \, b^{3} - 3 \, {\left(6 \, a b^{2} - 5 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right) + 3 \, {\left(5 \, b^{3} \cosh\left(d x + c\right)^{4} + 16 \, a^{3} - 24 \, a^{2} b + 10 \, b^{3} + {\left(16 \, a^{3} + 24 \, a^{2} b - 96 \, a b^{2} + 65 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)}{24 \, {\left(d \cosh\left(d x + c\right)^{3} + 3 \, d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + 3 \, d \cosh\left(d x + c\right)\right)}}"," ",0,"1/24*(3*b^3*sinh(d*x + c)^5 - 4*(4*a^3 + 6*a^2*b - 24*a*b^2 + 14*b^3 - 3*(6*a*b^2 - 5*b^3)*d*x)*cosh(d*x + c)^3 - 12*(4*a^3 + 6*a^2*b - 24*a*b^2 + 14*b^3 - 3*(6*a*b^2 - 5*b^3)*d*x)*cosh(d*x + c)*sinh(d*x + c)^2 + (30*b^3*cosh(d*x + c)^2 + 16*a^3 + 24*a^2*b - 96*a*b^2 + 65*b^3)*sinh(d*x + c)^3 - 12*(4*a^3 + 6*a^2*b - 24*a*b^2 + 14*b^3 - 3*(6*a*b^2 - 5*b^3)*d*x)*cosh(d*x + c) + 3*(5*b^3*cosh(d*x + c)^4 + 16*a^3 - 24*a^2*b + 10*b^3 + (16*a^3 + 24*a^2*b - 96*a*b^2 + 65*b^3)*cosh(d*x + c)^2)*sinh(d*x + c))/(d*cosh(d*x + c)^3 + 3*d*cosh(d*x + c)*sinh(d*x + c)^2 + 3*d*cosh(d*x + c))","B",0
312,1,2245,0,1.033890," ","integrate(sech(d*x+c)^5*(a+b*sinh(d*x+c)^2)^3,x, algorithm=""fricas"")","\frac{2 \, b^{3} \cosh\left(d x + c\right)^{10} + 20 \, b^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + 2 \, b^{3} \sinh\left(d x + c\right)^{10} + 3 \, {\left(a^{3} + a^{2} b - 5 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 3 \, {\left(30 \, b^{3} \cosh\left(d x + c\right)^{2} + a^{3} + a^{2} b - 5 \, a b^{2} + 5 \, b^{3}\right)} \sinh\left(d x + c\right)^{8} + 24 \, {\left(10 \, b^{3} \cosh\left(d x + c\right)^{3} + {\left(a^{3} + a^{2} b - 5 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + {\left(11 \, a^{3} - 21 \, a^{2} b + 9 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + {\left(420 \, b^{3} \cosh\left(d x + c\right)^{4} + 11 \, a^{3} - 21 \, a^{2} b + 9 \, a b^{2} + 5 \, b^{3} + 84 \, {\left(a^{3} + a^{2} b - 5 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 6 \, {\left(84 \, b^{3} \cosh\left(d x + c\right)^{5} + 28 \, {\left(a^{3} + a^{2} b - 5 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(11 \, a^{3} - 21 \, a^{2} b + 9 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - {\left(11 \, a^{3} - 21 \, a^{2} b + 9 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + {\left(420 \, b^{3} \cosh\left(d x + c\right)^{6} + 210 \, {\left(a^{3} + a^{2} b - 5 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 11 \, a^{3} + 21 \, a^{2} b - 9 \, a b^{2} - 5 \, b^{3} + 15 \, {\left(11 \, a^{3} - 21 \, a^{2} b + 9 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(60 \, b^{3} \cosh\left(d x + c\right)^{7} + 42 \, {\left(a^{3} + a^{2} b - 5 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(11 \, a^{3} - 21 \, a^{2} b + 9 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - {\left(11 \, a^{3} - 21 \, a^{2} b + 9 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 2 \, b^{3} - 3 \, {\left(a^{3} + a^{2} b - 5 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{2} + 3 \, {\left(30 \, b^{3} \cosh\left(d x + c\right)^{8} + 28 \, {\left(a^{3} + a^{2} b - 5 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 5 \, {\left(11 \, a^{3} - 21 \, a^{2} b + 9 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - a^{3} - a^{2} b + 5 \, a b^{2} - 5 \, b^{3} - 2 \, {\left(11 \, a^{3} - 21 \, a^{2} b + 9 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 3 \, {\left({\left(a^{3} + a^{2} b + 3 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + 9 \, {\left(a^{3} + a^{2} b + 3 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{8} + {\left(a^{3} + a^{2} b + 3 \, a b^{2} - 5 \, b^{3}\right)} \sinh\left(d x + c\right)^{9} + 4 \, {\left(a^{3} + a^{2} b + 3 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 4 \, {\left(a^{3} + a^{2} b + 3 \, a b^{2} - 5 \, b^{3} + 9 \, {\left(a^{3} + a^{2} b + 3 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{7} + 28 \, {\left(3 \, {\left(a^{3} + a^{2} b + 3 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{3} + a^{2} b + 3 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} + 6 \, {\left(a^{3} + a^{2} b + 3 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 6 \, {\left(21 \, {\left(a^{3} + a^{2} b + 3 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + a^{3} + a^{2} b + 3 \, a b^{2} - 5 \, b^{3} + 14 \, {\left(a^{3} + a^{2} b + 3 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(63 \, {\left(a^{3} + a^{2} b + 3 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 70 \, {\left(a^{3} + a^{2} b + 3 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 15 \, {\left(a^{3} + a^{2} b + 3 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{3} + a^{2} b + 3 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(21 \, {\left(a^{3} + a^{2} b + 3 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 35 \, {\left(a^{3} + a^{2} b + 3 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + a^{3} + a^{2} b + 3 \, a b^{2} - 5 \, b^{3} + 15 \, {\left(a^{3} + a^{2} b + 3 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + 12 \, {\left(3 \, {\left(a^{3} + a^{2} b + 3 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 7 \, {\left(a^{3} + a^{2} b + 3 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(a^{3} + a^{2} b + 3 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{3} + a^{2} b + 3 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{3} + a^{2} b + 3 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(d x + c\right) + {\left(9 \, {\left(a^{3} + a^{2} b + 3 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 28 \, {\left(a^{3} + a^{2} b + 3 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 30 \, {\left(a^{3} + a^{2} b + 3 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + a^{3} + a^{2} b + 3 \, a b^{2} - 5 \, b^{3} + 12 \, {\left(a^{3} + a^{2} b + 3 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)\right)} \arctan\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) + 2 \, {\left(10 \, b^{3} \cosh\left(d x + c\right)^{9} + 12 \, {\left(a^{3} + a^{2} b - 5 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(11 \, a^{3} - 21 \, a^{2} b + 9 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 2 \, {\left(11 \, a^{3} - 21 \, a^{2} b + 9 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{3} + a^{2} b - 5 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{4 \, {\left(d \cosh\left(d x + c\right)^{9} + 9 \, d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{8} + d \sinh\left(d x + c\right)^{9} + 4 \, d \cosh\left(d x + c\right)^{7} + 4 \, {\left(9 \, d \cosh\left(d x + c\right)^{2} + d\right)} \sinh\left(d x + c\right)^{7} + 28 \, {\left(3 \, d \cosh\left(d x + c\right)^{3} + d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} + 6 \, d \cosh\left(d x + c\right)^{5} + 6 \, {\left(21 \, d \cosh\left(d x + c\right)^{4} + 14 \, d \cosh\left(d x + c\right)^{2} + d\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(63 \, d \cosh\left(d x + c\right)^{5} + 70 \, d \cosh\left(d x + c\right)^{3} + 15 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 4 \, d \cosh\left(d x + c\right)^{3} + 4 \, {\left(21 \, d \cosh\left(d x + c\right)^{6} + 35 \, d \cosh\left(d x + c\right)^{4} + 15 \, d \cosh\left(d x + c\right)^{2} + d\right)} \sinh\left(d x + c\right)^{3} + 12 \, {\left(3 \, d \cosh\left(d x + c\right)^{7} + 7 \, d \cosh\left(d x + c\right)^{5} + 5 \, d \cosh\left(d x + c\right)^{3} + d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + d \cosh\left(d x + c\right) + {\left(9 \, d \cosh\left(d x + c\right)^{8} + 28 \, d \cosh\left(d x + c\right)^{6} + 30 \, d \cosh\left(d x + c\right)^{4} + 12 \, d \cosh\left(d x + c\right)^{2} + d\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"1/4*(2*b^3*cosh(d*x + c)^10 + 20*b^3*cosh(d*x + c)*sinh(d*x + c)^9 + 2*b^3*sinh(d*x + c)^10 + 3*(a^3 + a^2*b - 5*a*b^2 + 5*b^3)*cosh(d*x + c)^8 + 3*(30*b^3*cosh(d*x + c)^2 + a^3 + a^2*b - 5*a*b^2 + 5*b^3)*sinh(d*x + c)^8 + 24*(10*b^3*cosh(d*x + c)^3 + (a^3 + a^2*b - 5*a*b^2 + 5*b^3)*cosh(d*x + c))*sinh(d*x + c)^7 + (11*a^3 - 21*a^2*b + 9*a*b^2 + 5*b^3)*cosh(d*x + c)^6 + (420*b^3*cosh(d*x + c)^4 + 11*a^3 - 21*a^2*b + 9*a*b^2 + 5*b^3 + 84*(a^3 + a^2*b - 5*a*b^2 + 5*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 6*(84*b^3*cosh(d*x + c)^5 + 28*(a^3 + a^2*b - 5*a*b^2 + 5*b^3)*cosh(d*x + c)^3 + (11*a^3 - 21*a^2*b + 9*a*b^2 + 5*b^3)*cosh(d*x + c))*sinh(d*x + c)^5 - (11*a^3 - 21*a^2*b + 9*a*b^2 + 5*b^3)*cosh(d*x + c)^4 + (420*b^3*cosh(d*x + c)^6 + 210*(a^3 + a^2*b - 5*a*b^2 + 5*b^3)*cosh(d*x + c)^4 - 11*a^3 + 21*a^2*b - 9*a*b^2 - 5*b^3 + 15*(11*a^3 - 21*a^2*b + 9*a*b^2 + 5*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 4*(60*b^3*cosh(d*x + c)^7 + 42*(a^3 + a^2*b - 5*a*b^2 + 5*b^3)*cosh(d*x + c)^5 + 5*(11*a^3 - 21*a^2*b + 9*a*b^2 + 5*b^3)*cosh(d*x + c)^3 - (11*a^3 - 21*a^2*b + 9*a*b^2 + 5*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 - 2*b^3 - 3*(a^3 + a^2*b - 5*a*b^2 + 5*b^3)*cosh(d*x + c)^2 + 3*(30*b^3*cosh(d*x + c)^8 + 28*(a^3 + a^2*b - 5*a*b^2 + 5*b^3)*cosh(d*x + c)^6 + 5*(11*a^3 - 21*a^2*b + 9*a*b^2 + 5*b^3)*cosh(d*x + c)^4 - a^3 - a^2*b + 5*a*b^2 - 5*b^3 - 2*(11*a^3 - 21*a^2*b + 9*a*b^2 + 5*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 3*((a^3 + a^2*b + 3*a*b^2 - 5*b^3)*cosh(d*x + c)^9 + 9*(a^3 + a^2*b + 3*a*b^2 - 5*b^3)*cosh(d*x + c)*sinh(d*x + c)^8 + (a^3 + a^2*b + 3*a*b^2 - 5*b^3)*sinh(d*x + c)^9 + 4*(a^3 + a^2*b + 3*a*b^2 - 5*b^3)*cosh(d*x + c)^7 + 4*(a^3 + a^2*b + 3*a*b^2 - 5*b^3 + 9*(a^3 + a^2*b + 3*a*b^2 - 5*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^7 + 28*(3*(a^3 + a^2*b + 3*a*b^2 - 5*b^3)*cosh(d*x + c)^3 + (a^3 + a^2*b + 3*a*b^2 - 5*b^3)*cosh(d*x + c))*sinh(d*x + c)^6 + 6*(a^3 + a^2*b + 3*a*b^2 - 5*b^3)*cosh(d*x + c)^5 + 6*(21*(a^3 + a^2*b + 3*a*b^2 - 5*b^3)*cosh(d*x + c)^4 + a^3 + a^2*b + 3*a*b^2 - 5*b^3 + 14*(a^3 + a^2*b + 3*a*b^2 - 5*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 2*(63*(a^3 + a^2*b + 3*a*b^2 - 5*b^3)*cosh(d*x + c)^5 + 70*(a^3 + a^2*b + 3*a*b^2 - 5*b^3)*cosh(d*x + c)^3 + 15*(a^3 + a^2*b + 3*a*b^2 - 5*b^3)*cosh(d*x + c))*sinh(d*x + c)^4 + 4*(a^3 + a^2*b + 3*a*b^2 - 5*b^3)*cosh(d*x + c)^3 + 4*(21*(a^3 + a^2*b + 3*a*b^2 - 5*b^3)*cosh(d*x + c)^6 + 35*(a^3 + a^2*b + 3*a*b^2 - 5*b^3)*cosh(d*x + c)^4 + a^3 + a^2*b + 3*a*b^2 - 5*b^3 + 15*(a^3 + a^2*b + 3*a*b^2 - 5*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 12*(3*(a^3 + a^2*b + 3*a*b^2 - 5*b^3)*cosh(d*x + c)^7 + 7*(a^3 + a^2*b + 3*a*b^2 - 5*b^3)*cosh(d*x + c)^5 + 5*(a^3 + a^2*b + 3*a*b^2 - 5*b^3)*cosh(d*x + c)^3 + (a^3 + a^2*b + 3*a*b^2 - 5*b^3)*cosh(d*x + c))*sinh(d*x + c)^2 + (a^3 + a^2*b + 3*a*b^2 - 5*b^3)*cosh(d*x + c) + (9*(a^3 + a^2*b + 3*a*b^2 - 5*b^3)*cosh(d*x + c)^8 + 28*(a^3 + a^2*b + 3*a*b^2 - 5*b^3)*cosh(d*x + c)^6 + 30*(a^3 + a^2*b + 3*a*b^2 - 5*b^3)*cosh(d*x + c)^4 + a^3 + a^2*b + 3*a*b^2 - 5*b^3 + 12*(a^3 + a^2*b + 3*a*b^2 - 5*b^3)*cosh(d*x + c)^2)*sinh(d*x + c))*arctan(cosh(d*x + c) + sinh(d*x + c)) + 2*(10*b^3*cosh(d*x + c)^9 + 12*(a^3 + a^2*b - 5*a*b^2 + 5*b^3)*cosh(d*x + c)^7 + 3*(11*a^3 - 21*a^2*b + 9*a*b^2 + 5*b^3)*cosh(d*x + c)^5 - 2*(11*a^3 - 21*a^2*b + 9*a*b^2 + 5*b^3)*cosh(d*x + c)^3 - 3*(a^3 + a^2*b - 5*a*b^2 + 5*b^3)*cosh(d*x + c))*sinh(d*x + c))/(d*cosh(d*x + c)^9 + 9*d*cosh(d*x + c)*sinh(d*x + c)^8 + d*sinh(d*x + c)^9 + 4*d*cosh(d*x + c)^7 + 4*(9*d*cosh(d*x + c)^2 + d)*sinh(d*x + c)^7 + 28*(3*d*cosh(d*x + c)^3 + d*cosh(d*x + c))*sinh(d*x + c)^6 + 6*d*cosh(d*x + c)^5 + 6*(21*d*cosh(d*x + c)^4 + 14*d*cosh(d*x + c)^2 + d)*sinh(d*x + c)^5 + 2*(63*d*cosh(d*x + c)^5 + 70*d*cosh(d*x + c)^3 + 15*d*cosh(d*x + c))*sinh(d*x + c)^4 + 4*d*cosh(d*x + c)^3 + 4*(21*d*cosh(d*x + c)^6 + 35*d*cosh(d*x + c)^4 + 15*d*cosh(d*x + c)^2 + d)*sinh(d*x + c)^3 + 12*(3*d*cosh(d*x + c)^7 + 7*d*cosh(d*x + c)^5 + 5*d*cosh(d*x + c)^3 + d*cosh(d*x + c))*sinh(d*x + c)^2 + d*cosh(d*x + c) + (9*d*cosh(d*x + c)^8 + 28*d*cosh(d*x + c)^6 + 30*d*cosh(d*x + c)^4 + 12*d*cosh(d*x + c)^2 + d)*sinh(d*x + c))","B",0
313,1,530,0,0.583749," ","integrate(sech(d*x+c)^6*(a+b*sinh(d*x+c)^2)^3,x, algorithm=""fricas"")","\frac{{\left(15 \, b^{3} d x - 8 \, a^{3} - 6 \, a^{2} b - 9 \, a b^{2} + 23 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(15 \, b^{3} d x - 8 \, a^{3} - 6 \, a^{2} b - 9 \, a b^{2} + 23 \, b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} + {\left(8 \, a^{3} + 6 \, a^{2} b + 9 \, a b^{2} - 23 \, b^{3}\right)} \sinh\left(d x + c\right)^{5} + 5 \, {\left(15 \, b^{3} d x - 8 \, a^{3} - 6 \, a^{2} b - 9 \, a b^{2} + 23 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 5 \, {\left(8 \, a^{3} + 6 \, a^{2} b - 9 \, a b^{2} - 5 \, b^{3} + 2 \, {\left(8 \, a^{3} + 6 \, a^{2} b + 9 \, a b^{2} - 23 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + 5 \, {\left(2 \, {\left(15 \, b^{3} d x - 8 \, a^{3} - 6 \, a^{2} b - 9 \, a b^{2} + 23 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(15 \, b^{3} d x - 8 \, a^{3} - 6 \, a^{2} b - 9 \, a b^{2} + 23 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 10 \, {\left(15 \, b^{3} d x - 8 \, a^{3} - 6 \, a^{2} b - 9 \, a b^{2} + 23 \, b^{3}\right)} \cosh\left(d x + c\right) + 5 \, {\left({\left(8 \, a^{3} + 6 \, a^{2} b + 9 \, a b^{2} - 23 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 16 \, a^{3} - 24 \, a^{2} b + 18 \, a b^{2} - 10 \, b^{3} + 3 \, {\left(8 \, a^{3} + 6 \, a^{2} b - 9 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)}{15 \, {\left(d \cosh\left(d x + c\right)^{5} + 5 \, d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} + 5 \, d \cosh\left(d x + c\right)^{3} + 5 \, {\left(2 \, d \cosh\left(d x + c\right)^{3} + 3 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 10 \, d \cosh\left(d x + c\right)\right)}}"," ",0,"1/15*((15*b^3*d*x - 8*a^3 - 6*a^2*b - 9*a*b^2 + 23*b^3)*cosh(d*x + c)^5 + 5*(15*b^3*d*x - 8*a^3 - 6*a^2*b - 9*a*b^2 + 23*b^3)*cosh(d*x + c)*sinh(d*x + c)^4 + (8*a^3 + 6*a^2*b + 9*a*b^2 - 23*b^3)*sinh(d*x + c)^5 + 5*(15*b^3*d*x - 8*a^3 - 6*a^2*b - 9*a*b^2 + 23*b^3)*cosh(d*x + c)^3 + 5*(8*a^3 + 6*a^2*b - 9*a*b^2 - 5*b^3 + 2*(8*a^3 + 6*a^2*b + 9*a*b^2 - 23*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 5*(2*(15*b^3*d*x - 8*a^3 - 6*a^2*b - 9*a*b^2 + 23*b^3)*cosh(d*x + c)^3 + 3*(15*b^3*d*x - 8*a^3 - 6*a^2*b - 9*a*b^2 + 23*b^3)*cosh(d*x + c))*sinh(d*x + c)^2 + 10*(15*b^3*d*x - 8*a^3 - 6*a^2*b - 9*a*b^2 + 23*b^3)*cosh(d*x + c) + 5*((8*a^3 + 6*a^2*b + 9*a*b^2 - 23*b^3)*cosh(d*x + c)^4 + 16*a^3 - 24*a^2*b + 18*a*b^2 - 10*b^3 + 3*(8*a^3 + 6*a^2*b - 9*a*b^2 - 5*b^3)*cosh(d*x + c)^2)*sinh(d*x + c))/(d*cosh(d*x + c)^5 + 5*d*cosh(d*x + c)*sinh(d*x + c)^4 + 5*d*cosh(d*x + c)^3 + 5*(2*d*cosh(d*x + c)^3 + 3*d*cosh(d*x + c))*sinh(d*x + c)^2 + 10*d*cosh(d*x + c))","B",0
314,1,3675,0,0.712462," ","integrate(sech(d*x+c)^7*(a+b*sinh(d*x+c)^2)^3,x, algorithm=""fricas"")","\frac{3 \, {\left(5 \, a^{3} + 3 \, a^{2} b + 3 \, a b^{2} - 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} + 33 \, {\left(5 \, a^{3} + 3 \, a^{2} b + 3 \, a b^{2} - 11 \, b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{10} + 3 \, {\left(5 \, a^{3} + 3 \, a^{2} b + 3 \, a b^{2} - 11 \, b^{3}\right)} \sinh\left(d x + c\right)^{11} + {\left(85 \, a^{3} + 51 \, a^{2} b - 141 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + {\left(85 \, a^{3} + 51 \, a^{2} b - 141 \, a b^{2} + 5 \, b^{3} + 165 \, {\left(5 \, a^{3} + 3 \, a^{2} b + 3 \, a b^{2} - 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{9} + 9 \, {\left(55 \, {\left(5 \, a^{3} + 3 \, a^{2} b + 3 \, a b^{2} - 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(85 \, a^{3} + 51 \, a^{2} b - 141 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{8} + 18 \, {\left(11 \, a^{3} - 19 \, a^{2} b + 13 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 18 \, {\left(55 \, {\left(5 \, a^{3} + 3 \, a^{2} b + 3 \, a b^{2} - 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 11 \, a^{3} - 19 \, a^{2} b + 13 \, a b^{2} - 5 \, b^{3} + 2 \, {\left(85 \, a^{3} + 51 \, a^{2} b - 141 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{7} + 42 \, {\left(33 \, {\left(5 \, a^{3} + 3 \, a^{2} b + 3 \, a b^{2} - 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(85 \, a^{3} + 51 \, a^{2} b - 141 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(11 \, a^{3} - 19 \, a^{2} b + 13 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} - 18 \, {\left(11 \, a^{3} - 19 \, a^{2} b + 13 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 18 \, {\left(77 \, {\left(5 \, a^{3} + 3 \, a^{2} b + 3 \, a b^{2} - 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 7 \, {\left(85 \, a^{3} + 51 \, a^{2} b - 141 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 11 \, a^{3} + 19 \, a^{2} b - 13 \, a b^{2} + 5 \, b^{3} + 21 \, {\left(11 \, a^{3} - 19 \, a^{2} b + 13 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{5} + 18 \, {\left(55 \, {\left(5 \, a^{3} + 3 \, a^{2} b + 3 \, a b^{2} - 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 7 \, {\left(85 \, a^{3} + 51 \, a^{2} b - 141 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 35 \, {\left(11 \, a^{3} - 19 \, a^{2} b + 13 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 5 \, {\left(11 \, a^{3} - 19 \, a^{2} b + 13 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} - {\left(85 \, a^{3} + 51 \, a^{2} b - 141 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(495 \, {\left(5 \, a^{3} + 3 \, a^{2} b + 3 \, a b^{2} - 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 84 \, {\left(85 \, a^{3} + 51 \, a^{2} b - 141 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 630 \, {\left(11 \, a^{3} - 19 \, a^{2} b + 13 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 85 \, a^{3} - 51 \, a^{2} b + 141 \, a b^{2} - 5 \, b^{3} - 180 \, {\left(11 \, a^{3} - 19 \, a^{2} b + 13 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + 3 \, {\left(55 \, {\left(5 \, a^{3} + 3 \, a^{2} b + 3 \, a b^{2} - 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + 12 \, {\left(85 \, a^{3} + 51 \, a^{2} b - 141 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 126 \, {\left(11 \, a^{3} - 19 \, a^{2} b + 13 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 60 \, {\left(11 \, a^{3} - 19 \, a^{2} b + 13 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - {\left(85 \, a^{3} + 51 \, a^{2} b - 141 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 3 \, {\left({\left(5 \, a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{12} + 12 \, {\left(5 \, a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{11} + {\left(5 \, a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + 5 \, b^{3}\right)} \sinh\left(d x + c\right)^{12} + 6 \, {\left(5 \, a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} + 6 \, {\left(5 \, a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + 5 \, b^{3} + 11 \, {\left(5 \, a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{10} + 20 \, {\left(11 \, {\left(5 \, a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(5 \, a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} + 15 \, {\left(5 \, a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 15 \, {\left(33 \, {\left(5 \, a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 5 \, a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + 5 \, b^{3} + 18 \, {\left(5 \, a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{8} + 24 \, {\left(33 \, {\left(5 \, a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 30 \, {\left(5 \, a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 5 \, {\left(5 \, a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 20 \, {\left(5 \, a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(231 \, {\left(5 \, a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 315 \, {\left(5 \, a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 25 \, a^{3} + 15 \, a^{2} b + 15 \, a b^{2} + 25 \, b^{3} + 105 \, {\left(5 \, a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 24 \, {\left(33 \, {\left(5 \, a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 63 \, {\left(5 \, a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 35 \, {\left(5 \, a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 5 \, {\left(5 \, a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 15 \, {\left(5 \, a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 15 \, {\left(33 \, {\left(5 \, a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 84 \, {\left(5 \, a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 70 \, {\left(5 \, a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 5 \, a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + 5 \, b^{3} + 20 \, {\left(5 \, a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 20 \, {\left(11 \, {\left(5 \, a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + 36 \, {\left(5 \, a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 42 \, {\left(5 \, a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 20 \, {\left(5 \, a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(5 \, a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 5 \, a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + 5 \, b^{3} + 6 \, {\left(5 \, a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{2} + 6 \, {\left(11 \, {\left(5 \, a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} + 45 \, {\left(5 \, a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 70 \, {\left(5 \, a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 50 \, {\left(5 \, a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 5 \, a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + 5 \, b^{3} + 15 \, {\left(5 \, a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 12 \, {\left({\left(5 \, a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} + 5 \, {\left(5 \, a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + 10 \, {\left(5 \, a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 10 \, {\left(5 \, a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(5 \, a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(5 \, a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \arctan\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) - 3 \, {\left(5 \, a^{3} + 3 \, a^{2} b + 3 \, a b^{2} - 11 \, b^{3}\right)} \cosh\left(d x + c\right) + 3 \, {\left(11 \, {\left(5 \, a^{3} + 3 \, a^{2} b + 3 \, a b^{2} - 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} + 3 \, {\left(85 \, a^{3} + 51 \, a^{2} b - 141 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 42 \, {\left(11 \, a^{3} - 19 \, a^{2} b + 13 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} - 30 \, {\left(11 \, a^{3} - 19 \, a^{2} b + 13 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 5 \, a^{3} - 3 \, a^{2} b - 3 \, a b^{2} + 11 \, b^{3} - {\left(85 \, a^{3} + 51 \, a^{2} b - 141 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)}{24 \, {\left(d \cosh\left(d x + c\right)^{12} + 12 \, d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{11} + d \sinh\left(d x + c\right)^{12} + 6 \, d \cosh\left(d x + c\right)^{10} + 6 \, {\left(11 \, d \cosh\left(d x + c\right)^{2} + d\right)} \sinh\left(d x + c\right)^{10} + 20 \, {\left(11 \, d \cosh\left(d x + c\right)^{3} + 3 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} + 15 \, d \cosh\left(d x + c\right)^{8} + 15 \, {\left(33 \, d \cosh\left(d x + c\right)^{4} + 18 \, d \cosh\left(d x + c\right)^{2} + d\right)} \sinh\left(d x + c\right)^{8} + 24 \, {\left(33 \, d \cosh\left(d x + c\right)^{5} + 30 \, d \cosh\left(d x + c\right)^{3} + 5 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 20 \, d \cosh\left(d x + c\right)^{6} + 4 \, {\left(231 \, d \cosh\left(d x + c\right)^{6} + 315 \, d \cosh\left(d x + c\right)^{4} + 105 \, d \cosh\left(d x + c\right)^{2} + 5 \, d\right)} \sinh\left(d x + c\right)^{6} + 24 \, {\left(33 \, d \cosh\left(d x + c\right)^{7} + 63 \, d \cosh\left(d x + c\right)^{5} + 35 \, d \cosh\left(d x + c\right)^{3} + 5 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 15 \, d \cosh\left(d x + c\right)^{4} + 15 \, {\left(33 \, d \cosh\left(d x + c\right)^{8} + 84 \, d \cosh\left(d x + c\right)^{6} + 70 \, d \cosh\left(d x + c\right)^{4} + 20 \, d \cosh\left(d x + c\right)^{2} + d\right)} \sinh\left(d x + c\right)^{4} + 20 \, {\left(11 \, d \cosh\left(d x + c\right)^{9} + 36 \, d \cosh\left(d x + c\right)^{7} + 42 \, d \cosh\left(d x + c\right)^{5} + 20 \, d \cosh\left(d x + c\right)^{3} + 3 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 6 \, d \cosh\left(d x + c\right)^{2} + 6 \, {\left(11 \, d \cosh\left(d x + c\right)^{10} + 45 \, d \cosh\left(d x + c\right)^{8} + 70 \, d \cosh\left(d x + c\right)^{6} + 50 \, d \cosh\left(d x + c\right)^{4} + 15 \, d \cosh\left(d x + c\right)^{2} + d\right)} \sinh\left(d x + c\right)^{2} + 12 \, {\left(d \cosh\left(d x + c\right)^{11} + 5 \, d \cosh\left(d x + c\right)^{9} + 10 \, d \cosh\left(d x + c\right)^{7} + 10 \, d \cosh\left(d x + c\right)^{5} + 5 \, d \cosh\left(d x + c\right)^{3} + d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + d\right)}}"," ",0,"1/24*(3*(5*a^3 + 3*a^2*b + 3*a*b^2 - 11*b^3)*cosh(d*x + c)^11 + 33*(5*a^3 + 3*a^2*b + 3*a*b^2 - 11*b^3)*cosh(d*x + c)*sinh(d*x + c)^10 + 3*(5*a^3 + 3*a^2*b + 3*a*b^2 - 11*b^3)*sinh(d*x + c)^11 + (85*a^3 + 51*a^2*b - 141*a*b^2 + 5*b^3)*cosh(d*x + c)^9 + (85*a^3 + 51*a^2*b - 141*a*b^2 + 5*b^3 + 165*(5*a^3 + 3*a^2*b + 3*a*b^2 - 11*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^9 + 9*(55*(5*a^3 + 3*a^2*b + 3*a*b^2 - 11*b^3)*cosh(d*x + c)^3 + (85*a^3 + 51*a^2*b - 141*a*b^2 + 5*b^3)*cosh(d*x + c))*sinh(d*x + c)^8 + 18*(11*a^3 - 19*a^2*b + 13*a*b^2 - 5*b^3)*cosh(d*x + c)^7 + 18*(55*(5*a^3 + 3*a^2*b + 3*a*b^2 - 11*b^3)*cosh(d*x + c)^4 + 11*a^3 - 19*a^2*b + 13*a*b^2 - 5*b^3 + 2*(85*a^3 + 51*a^2*b - 141*a*b^2 + 5*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^7 + 42*(33*(5*a^3 + 3*a^2*b + 3*a*b^2 - 11*b^3)*cosh(d*x + c)^5 + 2*(85*a^3 + 51*a^2*b - 141*a*b^2 + 5*b^3)*cosh(d*x + c)^3 + 3*(11*a^3 - 19*a^2*b + 13*a*b^2 - 5*b^3)*cosh(d*x + c))*sinh(d*x + c)^6 - 18*(11*a^3 - 19*a^2*b + 13*a*b^2 - 5*b^3)*cosh(d*x + c)^5 + 18*(77*(5*a^3 + 3*a^2*b + 3*a*b^2 - 11*b^3)*cosh(d*x + c)^6 + 7*(85*a^3 + 51*a^2*b - 141*a*b^2 + 5*b^3)*cosh(d*x + c)^4 - 11*a^3 + 19*a^2*b - 13*a*b^2 + 5*b^3 + 21*(11*a^3 - 19*a^2*b + 13*a*b^2 - 5*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 18*(55*(5*a^3 + 3*a^2*b + 3*a*b^2 - 11*b^3)*cosh(d*x + c)^7 + 7*(85*a^3 + 51*a^2*b - 141*a*b^2 + 5*b^3)*cosh(d*x + c)^5 + 35*(11*a^3 - 19*a^2*b + 13*a*b^2 - 5*b^3)*cosh(d*x + c)^3 - 5*(11*a^3 - 19*a^2*b + 13*a*b^2 - 5*b^3)*cosh(d*x + c))*sinh(d*x + c)^4 - (85*a^3 + 51*a^2*b - 141*a*b^2 + 5*b^3)*cosh(d*x + c)^3 + (495*(5*a^3 + 3*a^2*b + 3*a*b^2 - 11*b^3)*cosh(d*x + c)^8 + 84*(85*a^3 + 51*a^2*b - 141*a*b^2 + 5*b^3)*cosh(d*x + c)^6 + 630*(11*a^3 - 19*a^2*b + 13*a*b^2 - 5*b^3)*cosh(d*x + c)^4 - 85*a^3 - 51*a^2*b + 141*a*b^2 - 5*b^3 - 180*(11*a^3 - 19*a^2*b + 13*a*b^2 - 5*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 3*(55*(5*a^3 + 3*a^2*b + 3*a*b^2 - 11*b^3)*cosh(d*x + c)^9 + 12*(85*a^3 + 51*a^2*b - 141*a*b^2 + 5*b^3)*cosh(d*x + c)^7 + 126*(11*a^3 - 19*a^2*b + 13*a*b^2 - 5*b^3)*cosh(d*x + c)^5 - 60*(11*a^3 - 19*a^2*b + 13*a*b^2 - 5*b^3)*cosh(d*x + c)^3 - (85*a^3 + 51*a^2*b - 141*a*b^2 + 5*b^3)*cosh(d*x + c))*sinh(d*x + c)^2 + 3*((5*a^3 + 3*a^2*b + 3*a*b^2 + 5*b^3)*cosh(d*x + c)^12 + 12*(5*a^3 + 3*a^2*b + 3*a*b^2 + 5*b^3)*cosh(d*x + c)*sinh(d*x + c)^11 + (5*a^3 + 3*a^2*b + 3*a*b^2 + 5*b^3)*sinh(d*x + c)^12 + 6*(5*a^3 + 3*a^2*b + 3*a*b^2 + 5*b^3)*cosh(d*x + c)^10 + 6*(5*a^3 + 3*a^2*b + 3*a*b^2 + 5*b^3 + 11*(5*a^3 + 3*a^2*b + 3*a*b^2 + 5*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^10 + 20*(11*(5*a^3 + 3*a^2*b + 3*a*b^2 + 5*b^3)*cosh(d*x + c)^3 + 3*(5*a^3 + 3*a^2*b + 3*a*b^2 + 5*b^3)*cosh(d*x + c))*sinh(d*x + c)^9 + 15*(5*a^3 + 3*a^2*b + 3*a*b^2 + 5*b^3)*cosh(d*x + c)^8 + 15*(33*(5*a^3 + 3*a^2*b + 3*a*b^2 + 5*b^3)*cosh(d*x + c)^4 + 5*a^3 + 3*a^2*b + 3*a*b^2 + 5*b^3 + 18*(5*a^3 + 3*a^2*b + 3*a*b^2 + 5*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 24*(33*(5*a^3 + 3*a^2*b + 3*a*b^2 + 5*b^3)*cosh(d*x + c)^5 + 30*(5*a^3 + 3*a^2*b + 3*a*b^2 + 5*b^3)*cosh(d*x + c)^3 + 5*(5*a^3 + 3*a^2*b + 3*a*b^2 + 5*b^3)*cosh(d*x + c))*sinh(d*x + c)^7 + 20*(5*a^3 + 3*a^2*b + 3*a*b^2 + 5*b^3)*cosh(d*x + c)^6 + 4*(231*(5*a^3 + 3*a^2*b + 3*a*b^2 + 5*b^3)*cosh(d*x + c)^6 + 315*(5*a^3 + 3*a^2*b + 3*a*b^2 + 5*b^3)*cosh(d*x + c)^4 + 25*a^3 + 15*a^2*b + 15*a*b^2 + 25*b^3 + 105*(5*a^3 + 3*a^2*b + 3*a*b^2 + 5*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 24*(33*(5*a^3 + 3*a^2*b + 3*a*b^2 + 5*b^3)*cosh(d*x + c)^7 + 63*(5*a^3 + 3*a^2*b + 3*a*b^2 + 5*b^3)*cosh(d*x + c)^5 + 35*(5*a^3 + 3*a^2*b + 3*a*b^2 + 5*b^3)*cosh(d*x + c)^3 + 5*(5*a^3 + 3*a^2*b + 3*a*b^2 + 5*b^3)*cosh(d*x + c))*sinh(d*x + c)^5 + 15*(5*a^3 + 3*a^2*b + 3*a*b^2 + 5*b^3)*cosh(d*x + c)^4 + 15*(33*(5*a^3 + 3*a^2*b + 3*a*b^2 + 5*b^3)*cosh(d*x + c)^8 + 84*(5*a^3 + 3*a^2*b + 3*a*b^2 + 5*b^3)*cosh(d*x + c)^6 + 70*(5*a^3 + 3*a^2*b + 3*a*b^2 + 5*b^3)*cosh(d*x + c)^4 + 5*a^3 + 3*a^2*b + 3*a*b^2 + 5*b^3 + 20*(5*a^3 + 3*a^2*b + 3*a*b^2 + 5*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 20*(11*(5*a^3 + 3*a^2*b + 3*a*b^2 + 5*b^3)*cosh(d*x + c)^9 + 36*(5*a^3 + 3*a^2*b + 3*a*b^2 + 5*b^3)*cosh(d*x + c)^7 + 42*(5*a^3 + 3*a^2*b + 3*a*b^2 + 5*b^3)*cosh(d*x + c)^5 + 20*(5*a^3 + 3*a^2*b + 3*a*b^2 + 5*b^3)*cosh(d*x + c)^3 + 3*(5*a^3 + 3*a^2*b + 3*a*b^2 + 5*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 + 5*a^3 + 3*a^2*b + 3*a*b^2 + 5*b^3 + 6*(5*a^3 + 3*a^2*b + 3*a*b^2 + 5*b^3)*cosh(d*x + c)^2 + 6*(11*(5*a^3 + 3*a^2*b + 3*a*b^2 + 5*b^3)*cosh(d*x + c)^10 + 45*(5*a^3 + 3*a^2*b + 3*a*b^2 + 5*b^3)*cosh(d*x + c)^8 + 70*(5*a^3 + 3*a^2*b + 3*a*b^2 + 5*b^3)*cosh(d*x + c)^6 + 50*(5*a^3 + 3*a^2*b + 3*a*b^2 + 5*b^3)*cosh(d*x + c)^4 + 5*a^3 + 3*a^2*b + 3*a*b^2 + 5*b^3 + 15*(5*a^3 + 3*a^2*b + 3*a*b^2 + 5*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 12*((5*a^3 + 3*a^2*b + 3*a*b^2 + 5*b^3)*cosh(d*x + c)^11 + 5*(5*a^3 + 3*a^2*b + 3*a*b^2 + 5*b^3)*cosh(d*x + c)^9 + 10*(5*a^3 + 3*a^2*b + 3*a*b^2 + 5*b^3)*cosh(d*x + c)^7 + 10*(5*a^3 + 3*a^2*b + 3*a*b^2 + 5*b^3)*cosh(d*x + c)^5 + 5*(5*a^3 + 3*a^2*b + 3*a*b^2 + 5*b^3)*cosh(d*x + c)^3 + (5*a^3 + 3*a^2*b + 3*a*b^2 + 5*b^3)*cosh(d*x + c))*sinh(d*x + c))*arctan(cosh(d*x + c) + sinh(d*x + c)) - 3*(5*a^3 + 3*a^2*b + 3*a*b^2 - 11*b^3)*cosh(d*x + c) + 3*(11*(5*a^3 + 3*a^2*b + 3*a*b^2 - 11*b^3)*cosh(d*x + c)^10 + 3*(85*a^3 + 51*a^2*b - 141*a*b^2 + 5*b^3)*cosh(d*x + c)^8 + 42*(11*a^3 - 19*a^2*b + 13*a*b^2 - 5*b^3)*cosh(d*x + c)^6 - 30*(11*a^3 - 19*a^2*b + 13*a*b^2 - 5*b^3)*cosh(d*x + c)^4 - 5*a^3 - 3*a^2*b - 3*a*b^2 + 11*b^3 - (85*a^3 + 51*a^2*b - 141*a*b^2 + 5*b^3)*cosh(d*x + c)^2)*sinh(d*x + c))/(d*cosh(d*x + c)^12 + 12*d*cosh(d*x + c)*sinh(d*x + c)^11 + d*sinh(d*x + c)^12 + 6*d*cosh(d*x + c)^10 + 6*(11*d*cosh(d*x + c)^2 + d)*sinh(d*x + c)^10 + 20*(11*d*cosh(d*x + c)^3 + 3*d*cosh(d*x + c))*sinh(d*x + c)^9 + 15*d*cosh(d*x + c)^8 + 15*(33*d*cosh(d*x + c)^4 + 18*d*cosh(d*x + c)^2 + d)*sinh(d*x + c)^8 + 24*(33*d*cosh(d*x + c)^5 + 30*d*cosh(d*x + c)^3 + 5*d*cosh(d*x + c))*sinh(d*x + c)^7 + 20*d*cosh(d*x + c)^6 + 4*(231*d*cosh(d*x + c)^6 + 315*d*cosh(d*x + c)^4 + 105*d*cosh(d*x + c)^2 + 5*d)*sinh(d*x + c)^6 + 24*(33*d*cosh(d*x + c)^7 + 63*d*cosh(d*x + c)^5 + 35*d*cosh(d*x + c)^3 + 5*d*cosh(d*x + c))*sinh(d*x + c)^5 + 15*d*cosh(d*x + c)^4 + 15*(33*d*cosh(d*x + c)^8 + 84*d*cosh(d*x + c)^6 + 70*d*cosh(d*x + c)^4 + 20*d*cosh(d*x + c)^2 + d)*sinh(d*x + c)^4 + 20*(11*d*cosh(d*x + c)^9 + 36*d*cosh(d*x + c)^7 + 42*d*cosh(d*x + c)^5 + 20*d*cosh(d*x + c)^3 + 3*d*cosh(d*x + c))*sinh(d*x + c)^3 + 6*d*cosh(d*x + c)^2 + 6*(11*d*cosh(d*x + c)^10 + 45*d*cosh(d*x + c)^8 + 70*d*cosh(d*x + c)^6 + 50*d*cosh(d*x + c)^4 + 15*d*cosh(d*x + c)^2 + d)*sinh(d*x + c)^2 + 12*(d*cosh(d*x + c)^11 + 5*d*cosh(d*x + c)^9 + 10*d*cosh(d*x + c)^7 + 10*d*cosh(d*x + c)^5 + 5*d*cosh(d*x + c)^3 + d*cosh(d*x + c))*sinh(d*x + c) + d)","B",0
315,1,814,0,0.637905," ","integrate(sech(d*x+c)^8*(a+b*sinh(d*x+c)^2)^3,x, algorithm=""fricas"")","-\frac{4 \, {\left({\left(8 \, a^{3} + 4 \, a^{2} b + 3 \, a b^{2} + 20 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} - 6 \, {\left(8 \, a^{3} + 4 \, a^{2} b + 3 \, a b^{2} - 15 \, b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(8 \, a^{3} + 4 \, a^{2} b + 3 \, a b^{2} + 20 \, b^{3}\right)} \sinh\left(d x + c\right)^{6} + 14 \, {\left(4 \, a^{3} + 2 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(56 \, a^{3} + 28 \, a^{2} b + 126 \, a b^{2} + 15 \, {\left(8 \, a^{3} + 4 \, a^{2} b + 3 \, a b^{2} + 20 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} - 4 \, {\left(5 \, {\left(8 \, a^{3} + 4 \, a^{2} b + 3 \, a b^{2} - 15 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 28 \, {\left(2 \, a^{3} + a^{2} b - 3 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 280 \, a^{3} - 140 \, a^{2} b + 210 \, a b^{2} + 7 \, {\left(24 \, a^{3} + 52 \, a^{2} b - 21 \, a b^{2} + 20 \, b^{3}\right)} \cosh\left(d x + c\right)^{2} + {\left(15 \, {\left(8 \, a^{3} + 4 \, a^{2} b + 3 \, a b^{2} + 20 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 168 \, a^{3} + 364 \, a^{2} b - 147 \, a b^{2} + 140 \, b^{3} + 84 \, {\left(4 \, a^{3} + 2 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} - 2 \, {\left(3 \, {\left(8 \, a^{3} + 4 \, a^{2} b + 3 \, a b^{2} - 15 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 56 \, {\left(2 \, a^{3} + a^{2} b - 3 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} + 7 \, {\left(24 \, a^{3} - 28 \, a^{2} b + 9 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}{35 \, {\left(d \cosh\left(d x + c\right)^{8} + 8 \, d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + d \sinh\left(d x + c\right)^{8} + 8 \, d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, d \cosh\left(d x + c\right)^{2} + 2 \, d\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(14 \, d \cosh\left(d x + c\right)^{3} + 9 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 28 \, d \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, d \cosh\left(d x + c\right)^{4} + 60 \, d \cosh\left(d x + c\right)^{2} + 14 \, d\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, d \cosh\left(d x + c\right)^{5} + 15 \, d \cosh\left(d x + c\right)^{3} + 7 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 56 \, d \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, d \cosh\left(d x + c\right)^{6} + 30 \, d \cosh\left(d x + c\right)^{4} + 42 \, d \cosh\left(d x + c\right)^{2} + 14 \, d\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(2 \, d \cosh\left(d x + c\right)^{7} + 9 \, d \cosh\left(d x + c\right)^{5} + 14 \, d \cosh\left(d x + c\right)^{3} + 7 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + 35 \, d\right)}}"," ",0,"-4/35*((8*a^3 + 4*a^2*b + 3*a*b^2 + 20*b^3)*cosh(d*x + c)^6 - 6*(8*a^3 + 4*a^2*b + 3*a*b^2 - 15*b^3)*cosh(d*x + c)*sinh(d*x + c)^5 + (8*a^3 + 4*a^2*b + 3*a*b^2 + 20*b^3)*sinh(d*x + c)^6 + 14*(4*a^3 + 2*a^2*b + 9*a*b^2)*cosh(d*x + c)^4 + (56*a^3 + 28*a^2*b + 126*a*b^2 + 15*(8*a^3 + 4*a^2*b + 3*a*b^2 + 20*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 - 4*(5*(8*a^3 + 4*a^2*b + 3*a*b^2 - 15*b^3)*cosh(d*x + c)^3 + 28*(2*a^3 + a^2*b - 3*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 280*a^3 - 140*a^2*b + 210*a*b^2 + 7*(24*a^3 + 52*a^2*b - 21*a*b^2 + 20*b^3)*cosh(d*x + c)^2 + (15*(8*a^3 + 4*a^2*b + 3*a*b^2 + 20*b^3)*cosh(d*x + c)^4 + 168*a^3 + 364*a^2*b - 147*a*b^2 + 140*b^3 + 84*(4*a^3 + 2*a^2*b + 9*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - 2*(3*(8*a^3 + 4*a^2*b + 3*a*b^2 - 15*b^3)*cosh(d*x + c)^5 + 56*(2*a^3 + a^2*b - 3*a*b^2)*cosh(d*x + c)^3 + 7*(24*a^3 - 28*a^2*b + 9*a*b^2 - 5*b^3)*cosh(d*x + c))*sinh(d*x + c))/(d*cosh(d*x + c)^8 + 8*d*cosh(d*x + c)*sinh(d*x + c)^7 + d*sinh(d*x + c)^8 + 8*d*cosh(d*x + c)^6 + 4*(7*d*cosh(d*x + c)^2 + 2*d)*sinh(d*x + c)^6 + 4*(14*d*cosh(d*x + c)^3 + 9*d*cosh(d*x + c))*sinh(d*x + c)^5 + 28*d*cosh(d*x + c)^4 + 2*(35*d*cosh(d*x + c)^4 + 60*d*cosh(d*x + c)^2 + 14*d)*sinh(d*x + c)^4 + 8*(7*d*cosh(d*x + c)^5 + 15*d*cosh(d*x + c)^3 + 7*d*cosh(d*x + c))*sinh(d*x + c)^3 + 56*d*cosh(d*x + c)^2 + 4*(7*d*cosh(d*x + c)^6 + 30*d*cosh(d*x + c)^4 + 42*d*cosh(d*x + c)^2 + 14*d)*sinh(d*x + c)^2 + 4*(2*d*cosh(d*x + c)^7 + 9*d*cosh(d*x + c)^5 + 14*d*cosh(d*x + c)^3 + 7*d*cosh(d*x + c))*sinh(d*x + c) + 35*d)","B",0
316,1,3066,0,0.983211," ","integrate(cosh(d*x+c)^7/(a+b*sinh(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{3 \, a b^{3} \cosh\left(d x + c\right)^{10} + 30 \, a b^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + 3 \, a b^{3} \sinh\left(d x + c\right)^{10} - 5 \, {\left(4 \, a^{2} b^{2} - 9 \, a b^{3}\right)} \cosh\left(d x + c\right)^{8} + 5 \, {\left(27 \, a b^{3} \cosh\left(d x + c\right)^{2} - 4 \, a^{2} b^{2} + 9 \, a b^{3}\right)} \sinh\left(d x + c\right)^{8} + 40 \, {\left(9 \, a b^{3} \cosh\left(d x + c\right)^{3} - {\left(4 \, a^{2} b^{2} - 9 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 30 \, {\left(8 \, a^{3} b - 22 \, a^{2} b^{2} + 19 \, a b^{3}\right)} \cosh\left(d x + c\right)^{6} + 10 \, {\left(63 \, a b^{3} \cosh\left(d x + c\right)^{4} + 24 \, a^{3} b - 66 \, a^{2} b^{2} + 57 \, a b^{3} - 14 \, {\left(4 \, a^{2} b^{2} - 9 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(189 \, a b^{3} \cosh\left(d x + c\right)^{5} - 70 \, {\left(4 \, a^{2} b^{2} - 9 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + 45 \, {\left(8 \, a^{3} b - 22 \, a^{2} b^{2} + 19 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 30 \, {\left(8 \, a^{3} b - 22 \, a^{2} b^{2} + 19 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} + 10 \, {\left(63 \, a b^{3} \cosh\left(d x + c\right)^{6} - 35 \, {\left(4 \, a^{2} b^{2} - 9 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} - 24 \, a^{3} b + 66 \, a^{2} b^{2} - 57 \, a b^{3} + 45 \, {\left(8 \, a^{3} b - 22 \, a^{2} b^{2} + 19 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} - 3 \, a b^{3} + 40 \, {\left(9 \, a b^{3} \cosh\left(d x + c\right)^{7} - 7 \, {\left(4 \, a^{2} b^{2} - 9 \, a b^{3}\right)} \cosh\left(d x + c\right)^{5} + 15 \, {\left(8 \, a^{3} b - 22 \, a^{2} b^{2} + 19 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(8 \, a^{3} b - 22 \, a^{2} b^{2} + 19 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 5 \, {\left(4 \, a^{2} b^{2} - 9 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2} + 5 \, {\left(27 \, a b^{3} \cosh\left(d x + c\right)^{8} - 28 \, {\left(4 \, a^{2} b^{2} - 9 \, a b^{3}\right)} \cosh\left(d x + c\right)^{6} + 90 \, {\left(8 \, a^{3} b - 22 \, a^{2} b^{2} + 19 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} + 4 \, a^{2} b^{2} - 9 \, a b^{3} - 36 \, {\left(8 \, a^{3} b - 22 \, a^{2} b^{2} + 19 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 240 \, {\left({\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{4} \sinh\left(d x + c\right) + 10 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right)^{2} + 10 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{3} + 5 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} + {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} \sinh\left(d x + c\right)^{5}\right)} \sqrt{-a b} \log\left(\frac{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} - 2 \, {\left(2 \, a + b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} - 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} - {\left(2 \, a + b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) - 4 \, {\left(\cosh\left(d x + c\right)^{3} + 3 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{3} + {\left(3 \, \cosh\left(d x + c\right)^{2} - 1\right)} \sinh\left(d x + c\right) - \cosh\left(d x + c\right)\right)} \sqrt{-a b} + b}{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b}\right) + 10 \, {\left(3 \, a b^{3} \cosh\left(d x + c\right)^{9} - 4 \, {\left(4 \, a^{2} b^{2} - 9 \, a b^{3}\right)} \cosh\left(d x + c\right)^{7} + 18 \, {\left(8 \, a^{3} b - 22 \, a^{2} b^{2} + 19 \, a b^{3}\right)} \cosh\left(d x + c\right)^{5} - 12 \, {\left(8 \, a^{3} b - 22 \, a^{2} b^{2} + 19 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(4 \, a^{2} b^{2} - 9 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{480 \, {\left(a b^{4} d \cosh\left(d x + c\right)^{5} + 5 \, a b^{4} d \cosh\left(d x + c\right)^{4} \sinh\left(d x + c\right) + 10 \, a b^{4} d \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right)^{2} + 10 \, a b^{4} d \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{3} + 5 \, a b^{4} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} + a b^{4} d \sinh\left(d x + c\right)^{5}\right)}}, \frac{3 \, a b^{3} \cosh\left(d x + c\right)^{10} + 30 \, a b^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + 3 \, a b^{3} \sinh\left(d x + c\right)^{10} - 5 \, {\left(4 \, a^{2} b^{2} - 9 \, a b^{3}\right)} \cosh\left(d x + c\right)^{8} + 5 \, {\left(27 \, a b^{3} \cosh\left(d x + c\right)^{2} - 4 \, a^{2} b^{2} + 9 \, a b^{3}\right)} \sinh\left(d x + c\right)^{8} + 40 \, {\left(9 \, a b^{3} \cosh\left(d x + c\right)^{3} - {\left(4 \, a^{2} b^{2} - 9 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 30 \, {\left(8 \, a^{3} b - 22 \, a^{2} b^{2} + 19 \, a b^{3}\right)} \cosh\left(d x + c\right)^{6} + 10 \, {\left(63 \, a b^{3} \cosh\left(d x + c\right)^{4} + 24 \, a^{3} b - 66 \, a^{2} b^{2} + 57 \, a b^{3} - 14 \, {\left(4 \, a^{2} b^{2} - 9 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(189 \, a b^{3} \cosh\left(d x + c\right)^{5} - 70 \, {\left(4 \, a^{2} b^{2} - 9 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + 45 \, {\left(8 \, a^{3} b - 22 \, a^{2} b^{2} + 19 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 30 \, {\left(8 \, a^{3} b - 22 \, a^{2} b^{2} + 19 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} + 10 \, {\left(63 \, a b^{3} \cosh\left(d x + c\right)^{6} - 35 \, {\left(4 \, a^{2} b^{2} - 9 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} - 24 \, a^{3} b + 66 \, a^{2} b^{2} - 57 \, a b^{3} + 45 \, {\left(8 \, a^{3} b - 22 \, a^{2} b^{2} + 19 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} - 3 \, a b^{3} + 40 \, {\left(9 \, a b^{3} \cosh\left(d x + c\right)^{7} - 7 \, {\left(4 \, a^{2} b^{2} - 9 \, a b^{3}\right)} \cosh\left(d x + c\right)^{5} + 15 \, {\left(8 \, a^{3} b - 22 \, a^{2} b^{2} + 19 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(8 \, a^{3} b - 22 \, a^{2} b^{2} + 19 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 5 \, {\left(4 \, a^{2} b^{2} - 9 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2} + 5 \, {\left(27 \, a b^{3} \cosh\left(d x + c\right)^{8} - 28 \, {\left(4 \, a^{2} b^{2} - 9 \, a b^{3}\right)} \cosh\left(d x + c\right)^{6} + 90 \, {\left(8 \, a^{3} b - 22 \, a^{2} b^{2} + 19 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} + 4 \, a^{2} b^{2} - 9 \, a b^{3} - 36 \, {\left(8 \, a^{3} b - 22 \, a^{2} b^{2} + 19 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} - 480 \, {\left({\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{4} \sinh\left(d x + c\right) + 10 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right)^{2} + 10 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{3} + 5 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} + {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} \sinh\left(d x + c\right)^{5}\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} {\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right)}}{2 \, a}\right) - 480 \, {\left({\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{4} \sinh\left(d x + c\right) + 10 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right)^{2} + 10 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{3} + 5 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} + {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} \sinh\left(d x + c\right)^{5}\right)} \sqrt{a b} \arctan\left(\frac{{\left(b \cosh\left(d x + c\right)^{3} + 3 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{3} + {\left(4 \, a - b\right)} \cosh\left(d x + c\right) + {\left(3 \, b \cosh\left(d x + c\right)^{2} + 4 \, a - b\right)} \sinh\left(d x + c\right)\right)} \sqrt{a b}}{2 \, a b}\right) + 10 \, {\left(3 \, a b^{3} \cosh\left(d x + c\right)^{9} - 4 \, {\left(4 \, a^{2} b^{2} - 9 \, a b^{3}\right)} \cosh\left(d x + c\right)^{7} + 18 \, {\left(8 \, a^{3} b - 22 \, a^{2} b^{2} + 19 \, a b^{3}\right)} \cosh\left(d x + c\right)^{5} - 12 \, {\left(8 \, a^{3} b - 22 \, a^{2} b^{2} + 19 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(4 \, a^{2} b^{2} - 9 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{480 \, {\left(a b^{4} d \cosh\left(d x + c\right)^{5} + 5 \, a b^{4} d \cosh\left(d x + c\right)^{4} \sinh\left(d x + c\right) + 10 \, a b^{4} d \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right)^{2} + 10 \, a b^{4} d \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{3} + 5 \, a b^{4} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} + a b^{4} d \sinh\left(d x + c\right)^{5}\right)}}\right]"," ",0,"[1/480*(3*a*b^3*cosh(d*x + c)^10 + 30*a*b^3*cosh(d*x + c)*sinh(d*x + c)^9 + 3*a*b^3*sinh(d*x + c)^10 - 5*(4*a^2*b^2 - 9*a*b^3)*cosh(d*x + c)^8 + 5*(27*a*b^3*cosh(d*x + c)^2 - 4*a^2*b^2 + 9*a*b^3)*sinh(d*x + c)^8 + 40*(9*a*b^3*cosh(d*x + c)^3 - (4*a^2*b^2 - 9*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^7 + 30*(8*a^3*b - 22*a^2*b^2 + 19*a*b^3)*cosh(d*x + c)^6 + 10*(63*a*b^3*cosh(d*x + c)^4 + 24*a^3*b - 66*a^2*b^2 + 57*a*b^3 - 14*(4*a^2*b^2 - 9*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 4*(189*a*b^3*cosh(d*x + c)^5 - 70*(4*a^2*b^2 - 9*a*b^3)*cosh(d*x + c)^3 + 45*(8*a^3*b - 22*a^2*b^2 + 19*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^5 - 30*(8*a^3*b - 22*a^2*b^2 + 19*a*b^3)*cosh(d*x + c)^4 + 10*(63*a*b^3*cosh(d*x + c)^6 - 35*(4*a^2*b^2 - 9*a*b^3)*cosh(d*x + c)^4 - 24*a^3*b + 66*a^2*b^2 - 57*a*b^3 + 45*(8*a^3*b - 22*a^2*b^2 + 19*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 - 3*a*b^3 + 40*(9*a*b^3*cosh(d*x + c)^7 - 7*(4*a^2*b^2 - 9*a*b^3)*cosh(d*x + c)^5 + 15*(8*a^3*b - 22*a^2*b^2 + 19*a*b^3)*cosh(d*x + c)^3 - 3*(8*a^3*b - 22*a^2*b^2 + 19*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 + 5*(4*a^2*b^2 - 9*a*b^3)*cosh(d*x + c)^2 + 5*(27*a*b^3*cosh(d*x + c)^8 - 28*(4*a^2*b^2 - 9*a*b^3)*cosh(d*x + c)^6 + 90*(8*a^3*b - 22*a^2*b^2 + 19*a*b^3)*cosh(d*x + c)^4 + 4*a^2*b^2 - 9*a*b^3 - 36*(8*a^3*b - 22*a^2*b^2 + 19*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 240*((a^3 - 3*a^2*b + 3*a*b^2 - b^3)*cosh(d*x + c)^5 + 5*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*cosh(d*x + c)^4*sinh(d*x + c) + 10*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*cosh(d*x + c)^3*sinh(d*x + c)^2 + 10*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*cosh(d*x + c)^2*sinh(d*x + c)^3 + 5*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*cosh(d*x + c)*sinh(d*x + c)^4 + (a^3 - 3*a^2*b + 3*a*b^2 - b^3)*sinh(d*x + c)^5)*sqrt(-a*b)*log((b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 - 2*(2*a + b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 - 2*a - b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 - (2*a + b)*cosh(d*x + c))*sinh(d*x + c) - 4*(cosh(d*x + c)^3 + 3*cosh(d*x + c)*sinh(d*x + c)^2 + sinh(d*x + c)^3 + (3*cosh(d*x + c)^2 - 1)*sinh(d*x + c) - cosh(d*x + c))*sqrt(-a*b) + b)/(b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 + 2*(2*a - b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 + 2*a - b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 + (2*a - b)*cosh(d*x + c))*sinh(d*x + c) + b)) + 10*(3*a*b^3*cosh(d*x + c)^9 - 4*(4*a^2*b^2 - 9*a*b^3)*cosh(d*x + c)^7 + 18*(8*a^3*b - 22*a^2*b^2 + 19*a*b^3)*cosh(d*x + c)^5 - 12*(8*a^3*b - 22*a^2*b^2 + 19*a*b^3)*cosh(d*x + c)^3 + (4*a^2*b^2 - 9*a*b^3)*cosh(d*x + c))*sinh(d*x + c))/(a*b^4*d*cosh(d*x + c)^5 + 5*a*b^4*d*cosh(d*x + c)^4*sinh(d*x + c) + 10*a*b^4*d*cosh(d*x + c)^3*sinh(d*x + c)^2 + 10*a*b^4*d*cosh(d*x + c)^2*sinh(d*x + c)^3 + 5*a*b^4*d*cosh(d*x + c)*sinh(d*x + c)^4 + a*b^4*d*sinh(d*x + c)^5), 1/480*(3*a*b^3*cosh(d*x + c)^10 + 30*a*b^3*cosh(d*x + c)*sinh(d*x + c)^9 + 3*a*b^3*sinh(d*x + c)^10 - 5*(4*a^2*b^2 - 9*a*b^3)*cosh(d*x + c)^8 + 5*(27*a*b^3*cosh(d*x + c)^2 - 4*a^2*b^2 + 9*a*b^3)*sinh(d*x + c)^8 + 40*(9*a*b^3*cosh(d*x + c)^3 - (4*a^2*b^2 - 9*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^7 + 30*(8*a^3*b - 22*a^2*b^2 + 19*a*b^3)*cosh(d*x + c)^6 + 10*(63*a*b^3*cosh(d*x + c)^4 + 24*a^3*b - 66*a^2*b^2 + 57*a*b^3 - 14*(4*a^2*b^2 - 9*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 4*(189*a*b^3*cosh(d*x + c)^5 - 70*(4*a^2*b^2 - 9*a*b^3)*cosh(d*x + c)^3 + 45*(8*a^3*b - 22*a^2*b^2 + 19*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^5 - 30*(8*a^3*b - 22*a^2*b^2 + 19*a*b^3)*cosh(d*x + c)^4 + 10*(63*a*b^3*cosh(d*x + c)^6 - 35*(4*a^2*b^2 - 9*a*b^3)*cosh(d*x + c)^4 - 24*a^3*b + 66*a^2*b^2 - 57*a*b^3 + 45*(8*a^3*b - 22*a^2*b^2 + 19*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 - 3*a*b^3 + 40*(9*a*b^3*cosh(d*x + c)^7 - 7*(4*a^2*b^2 - 9*a*b^3)*cosh(d*x + c)^5 + 15*(8*a^3*b - 22*a^2*b^2 + 19*a*b^3)*cosh(d*x + c)^3 - 3*(8*a^3*b - 22*a^2*b^2 + 19*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 + 5*(4*a^2*b^2 - 9*a*b^3)*cosh(d*x + c)^2 + 5*(27*a*b^3*cosh(d*x + c)^8 - 28*(4*a^2*b^2 - 9*a*b^3)*cosh(d*x + c)^6 + 90*(8*a^3*b - 22*a^2*b^2 + 19*a*b^3)*cosh(d*x + c)^4 + 4*a^2*b^2 - 9*a*b^3 - 36*(8*a^3*b - 22*a^2*b^2 + 19*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - 480*((a^3 - 3*a^2*b + 3*a*b^2 - b^3)*cosh(d*x + c)^5 + 5*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*cosh(d*x + c)^4*sinh(d*x + c) + 10*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*cosh(d*x + c)^3*sinh(d*x + c)^2 + 10*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*cosh(d*x + c)^2*sinh(d*x + c)^3 + 5*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*cosh(d*x + c)*sinh(d*x + c)^4 + (a^3 - 3*a^2*b + 3*a*b^2 - b^3)*sinh(d*x + c)^5)*sqrt(a*b)*arctan(1/2*sqrt(a*b)*(cosh(d*x + c) + sinh(d*x + c))/a) - 480*((a^3 - 3*a^2*b + 3*a*b^2 - b^3)*cosh(d*x + c)^5 + 5*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*cosh(d*x + c)^4*sinh(d*x + c) + 10*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*cosh(d*x + c)^3*sinh(d*x + c)^2 + 10*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*cosh(d*x + c)^2*sinh(d*x + c)^3 + 5*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*cosh(d*x + c)*sinh(d*x + c)^4 + (a^3 - 3*a^2*b + 3*a*b^2 - b^3)*sinh(d*x + c)^5)*sqrt(a*b)*arctan(1/2*(b*cosh(d*x + c)^3 + 3*b*cosh(d*x + c)*sinh(d*x + c)^2 + b*sinh(d*x + c)^3 + (4*a - b)*cosh(d*x + c) + (3*b*cosh(d*x + c)^2 + 4*a - b)*sinh(d*x + c))*sqrt(a*b)/(a*b)) + 10*(3*a*b^3*cosh(d*x + c)^9 - 4*(4*a^2*b^2 - 9*a*b^3)*cosh(d*x + c)^7 + 18*(8*a^3*b - 22*a^2*b^2 + 19*a*b^3)*cosh(d*x + c)^5 - 12*(8*a^3*b - 22*a^2*b^2 + 19*a*b^3)*cosh(d*x + c)^3 + (4*a^2*b^2 - 9*a*b^3)*cosh(d*x + c))*sinh(d*x + c))/(a*b^4*d*cosh(d*x + c)^5 + 5*a*b^4*d*cosh(d*x + c)^4*sinh(d*x + c) + 10*a*b^4*d*cosh(d*x + c)^3*sinh(d*x + c)^2 + 10*a*b^4*d*cosh(d*x + c)^2*sinh(d*x + c)^3 + 5*a*b^4*d*cosh(d*x + c)*sinh(d*x + c)^4 + a*b^4*d*sinh(d*x + c)^5)]","B",0
317,1,1817,0,1.077575," ","integrate(cosh(d*x+c)^6/(a+b*sinh(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{b^{2} \cosh\left(d x + c\right)^{8} + 8 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + b^{2} \sinh\left(d x + c\right)^{8} + 8 \, {\left(8 \, a^{2} - 20 \, a b + 15 \, b^{2}\right)} d x \cosh\left(d x + c\right)^{4} - 8 \, {\left(a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, b^{2} \cosh\left(d x + c\right)^{2} - 2 \, a b + 4 \, b^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, b^{2} \cosh\left(d x + c\right)^{3} - 6 \, {\left(a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, b^{2} \cosh\left(d x + c\right)^{4} + 4 \, {\left(8 \, a^{2} - 20 \, a b + 15 \, b^{2}\right)} d x - 60 \, {\left(a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, b^{2} \cosh\left(d x + c\right)^{5} + 4 \, {\left(8 \, a^{2} - 20 \, a b + 15 \, b^{2}\right)} d x \cosh\left(d x + c\right) - 20 \, {\left(a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right)^{3} + 8 \, {\left(a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, b^{2} \cosh\left(d x + c\right)^{6} + 12 \, {\left(8 \, a^{2} - 20 \, a b + 15 \, b^{2}\right)} d x \cosh\left(d x + c\right)^{2} - 30 \, {\left(a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, a b - 4 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} + 32 \, {\left({\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{2} - 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{4}\right)} \sqrt{\frac{a - b}{a}} \log\left(\frac{b^{2} \cosh\left(d x + c\right)^{4} + 4 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{2} \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(d x + c\right)^{2} + 2 \, a b - b^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, a^{2} - 8 \, a b + b^{2} + 4 \, {\left(b^{2} \cosh\left(d x + c\right)^{3} + {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + 4 \, {\left(a b \cosh\left(d x + c\right)^{2} + 2 \, a b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a b \sinh\left(d x + c\right)^{2} + 2 \, a^{2} - a b\right)} \sqrt{\frac{a - b}{a}}}{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b}\right) - b^{2} + 8 \, {\left(b^{2} \cosh\left(d x + c\right)^{7} + 4 \, {\left(8 \, a^{2} - 20 \, a b + 15 \, b^{2}\right)} d x \cosh\left(d x + c\right)^{3} - 6 \, {\left(a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{64 \, {\left(b^{3} d \cosh\left(d x + c\right)^{4} + 4 \, b^{3} d \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, b^{3} d \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, b^{3} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{3} d \sinh\left(d x + c\right)^{4}\right)}}, \frac{b^{2} \cosh\left(d x + c\right)^{8} + 8 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + b^{2} \sinh\left(d x + c\right)^{8} + 8 \, {\left(8 \, a^{2} - 20 \, a b + 15 \, b^{2}\right)} d x \cosh\left(d x + c\right)^{4} - 8 \, {\left(a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, b^{2} \cosh\left(d x + c\right)^{2} - 2 \, a b + 4 \, b^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, b^{2} \cosh\left(d x + c\right)^{3} - 6 \, {\left(a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, b^{2} \cosh\left(d x + c\right)^{4} + 4 \, {\left(8 \, a^{2} - 20 \, a b + 15 \, b^{2}\right)} d x - 60 \, {\left(a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, b^{2} \cosh\left(d x + c\right)^{5} + 4 \, {\left(8 \, a^{2} - 20 \, a b + 15 \, b^{2}\right)} d x \cosh\left(d x + c\right) - 20 \, {\left(a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right)^{3} + 8 \, {\left(a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, b^{2} \cosh\left(d x + c\right)^{6} + 12 \, {\left(8 \, a^{2} - 20 \, a b + 15 \, b^{2}\right)} d x \cosh\left(d x + c\right)^{2} - 30 \, {\left(a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, a b - 4 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} + 64 \, {\left({\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{2} - 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{4}\right)} \sqrt{-\frac{a - b}{a}} \arctan\left(-\frac{{\left(b \cosh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b \sinh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sqrt{-\frac{a - b}{a}}}{2 \, {\left(a - b\right)}}\right) - b^{2} + 8 \, {\left(b^{2} \cosh\left(d x + c\right)^{7} + 4 \, {\left(8 \, a^{2} - 20 \, a b + 15 \, b^{2}\right)} d x \cosh\left(d x + c\right)^{3} - 6 \, {\left(a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{64 \, {\left(b^{3} d \cosh\left(d x + c\right)^{4} + 4 \, b^{3} d \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, b^{3} d \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, b^{3} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{3} d \sinh\left(d x + c\right)^{4}\right)}}\right]"," ",0,"[1/64*(b^2*cosh(d*x + c)^8 + 8*b^2*cosh(d*x + c)*sinh(d*x + c)^7 + b^2*sinh(d*x + c)^8 + 8*(8*a^2 - 20*a*b + 15*b^2)*d*x*cosh(d*x + c)^4 - 8*(a*b - 2*b^2)*cosh(d*x + c)^6 + 4*(7*b^2*cosh(d*x + c)^2 - 2*a*b + 4*b^2)*sinh(d*x + c)^6 + 8*(7*b^2*cosh(d*x + c)^3 - 6*(a*b - 2*b^2)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*b^2*cosh(d*x + c)^4 + 4*(8*a^2 - 20*a*b + 15*b^2)*d*x - 60*(a*b - 2*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(7*b^2*cosh(d*x + c)^5 + 4*(8*a^2 - 20*a*b + 15*b^2)*d*x*cosh(d*x + c) - 20*(a*b - 2*b^2)*cosh(d*x + c)^3)*sinh(d*x + c)^3 + 8*(a*b - 2*b^2)*cosh(d*x + c)^2 + 4*(7*b^2*cosh(d*x + c)^6 + 12*(8*a^2 - 20*a*b + 15*b^2)*d*x*cosh(d*x + c)^2 - 30*(a*b - 2*b^2)*cosh(d*x + c)^4 + 2*a*b - 4*b^2)*sinh(d*x + c)^2 + 32*((a^2 - 2*a*b + b^2)*cosh(d*x + c)^4 + 4*(a^2 - 2*a*b + b^2)*cosh(d*x + c)^3*sinh(d*x + c) + 6*(a^2 - 2*a*b + b^2)*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*(a^2 - 2*a*b + b^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (a^2 - 2*a*b + b^2)*sinh(d*x + c)^4)*sqrt((a - b)/a)*log((b^2*cosh(d*x + c)^4 + 4*b^2*cosh(d*x + c)*sinh(d*x + c)^3 + b^2*sinh(d*x + c)^4 + 2*(2*a*b - b^2)*cosh(d*x + c)^2 + 2*(3*b^2*cosh(d*x + c)^2 + 2*a*b - b^2)*sinh(d*x + c)^2 + 8*a^2 - 8*a*b + b^2 + 4*(b^2*cosh(d*x + c)^3 + (2*a*b - b^2)*cosh(d*x + c))*sinh(d*x + c) + 4*(a*b*cosh(d*x + c)^2 + 2*a*b*cosh(d*x + c)*sinh(d*x + c) + a*b*sinh(d*x + c)^2 + 2*a^2 - a*b)*sqrt((a - b)/a))/(b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 + 2*(2*a - b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 + 2*a - b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 + (2*a - b)*cosh(d*x + c))*sinh(d*x + c) + b)) - b^2 + 8*(b^2*cosh(d*x + c)^7 + 4*(8*a^2 - 20*a*b + 15*b^2)*d*x*cosh(d*x + c)^3 - 6*(a*b - 2*b^2)*cosh(d*x + c)^5 + 2*(a*b - 2*b^2)*cosh(d*x + c))*sinh(d*x + c))/(b^3*d*cosh(d*x + c)^4 + 4*b^3*d*cosh(d*x + c)^3*sinh(d*x + c) + 6*b^3*d*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*b^3*d*cosh(d*x + c)*sinh(d*x + c)^3 + b^3*d*sinh(d*x + c)^4), 1/64*(b^2*cosh(d*x + c)^8 + 8*b^2*cosh(d*x + c)*sinh(d*x + c)^7 + b^2*sinh(d*x + c)^8 + 8*(8*a^2 - 20*a*b + 15*b^2)*d*x*cosh(d*x + c)^4 - 8*(a*b - 2*b^2)*cosh(d*x + c)^6 + 4*(7*b^2*cosh(d*x + c)^2 - 2*a*b + 4*b^2)*sinh(d*x + c)^6 + 8*(7*b^2*cosh(d*x + c)^3 - 6*(a*b - 2*b^2)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*b^2*cosh(d*x + c)^4 + 4*(8*a^2 - 20*a*b + 15*b^2)*d*x - 60*(a*b - 2*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(7*b^2*cosh(d*x + c)^5 + 4*(8*a^2 - 20*a*b + 15*b^2)*d*x*cosh(d*x + c) - 20*(a*b - 2*b^2)*cosh(d*x + c)^3)*sinh(d*x + c)^3 + 8*(a*b - 2*b^2)*cosh(d*x + c)^2 + 4*(7*b^2*cosh(d*x + c)^6 + 12*(8*a^2 - 20*a*b + 15*b^2)*d*x*cosh(d*x + c)^2 - 30*(a*b - 2*b^2)*cosh(d*x + c)^4 + 2*a*b - 4*b^2)*sinh(d*x + c)^2 + 64*((a^2 - 2*a*b + b^2)*cosh(d*x + c)^4 + 4*(a^2 - 2*a*b + b^2)*cosh(d*x + c)^3*sinh(d*x + c) + 6*(a^2 - 2*a*b + b^2)*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*(a^2 - 2*a*b + b^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (a^2 - 2*a*b + b^2)*sinh(d*x + c)^4)*sqrt(-(a - b)/a)*arctan(-1/2*(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + 2*a - b)*sqrt(-(a - b)/a)/(a - b)) - b^2 + 8*(b^2*cosh(d*x + c)^7 + 4*(8*a^2 - 20*a*b + 15*b^2)*d*x*cosh(d*x + c)^3 - 6*(a*b - 2*b^2)*cosh(d*x + c)^5 + 2*(a*b - 2*b^2)*cosh(d*x + c))*sinh(d*x + c))/(b^3*d*cosh(d*x + c)^4 + 4*b^3*d*cosh(d*x + c)^3*sinh(d*x + c) + 6*b^3*d*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*b^3*d*cosh(d*x + c)*sinh(d*x + c)^3 + b^3*d*sinh(d*x + c)^4)]","B",0
318,1,1490,0,0.538237," ","integrate(cosh(d*x+c)^5/(a+b*sinh(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{a b^{2} \cosh\left(d x + c\right)^{6} + 6 \, a b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + a b^{2} \sinh\left(d x + c\right)^{6} - 3 \, {\left(4 \, a^{2} b - 7 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(5 \, a b^{2} \cosh\left(d x + c\right)^{2} - 4 \, a^{2} b + 7 \, a b^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, a b^{2} \cosh\left(d x + c\right)^{3} - 3 \, {\left(4 \, a^{2} b - 7 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - a b^{2} + 3 \, {\left(4 \, a^{2} b - 7 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2} + 3 \, {\left(5 \, a b^{2} \cosh\left(d x + c\right)^{4} + 4 \, a^{2} b - 7 \, a b^{2} - 6 \, {\left(4 \, a^{2} b - 7 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} - 12 \, {\left({\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + {\left(a^{2} - 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{3}\right)} \sqrt{-a b} \log\left(\frac{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} - 2 \, {\left(2 \, a + b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} - 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} - {\left(2 \, a + b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) - 4 \, {\left(\cosh\left(d x + c\right)^{3} + 3 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{3} + {\left(3 \, \cosh\left(d x + c\right)^{2} - 1\right)} \sinh\left(d x + c\right) - \cosh\left(d x + c\right)\right)} \sqrt{-a b} + b}{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b}\right) + 6 \, {\left(a b^{2} \cosh\left(d x + c\right)^{5} - 2 \, {\left(4 \, a^{2} b - 7 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(4 \, a^{2} b - 7 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{24 \, {\left(a b^{3} d \cosh\left(d x + c\right)^{3} + 3 \, a b^{3} d \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, a b^{3} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + a b^{3} d \sinh\left(d x + c\right)^{3}\right)}}, \frac{a b^{2} \cosh\left(d x + c\right)^{6} + 6 \, a b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + a b^{2} \sinh\left(d x + c\right)^{6} - 3 \, {\left(4 \, a^{2} b - 7 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(5 \, a b^{2} \cosh\left(d x + c\right)^{2} - 4 \, a^{2} b + 7 \, a b^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, a b^{2} \cosh\left(d x + c\right)^{3} - 3 \, {\left(4 \, a^{2} b - 7 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - a b^{2} + 3 \, {\left(4 \, a^{2} b - 7 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2} + 3 \, {\left(5 \, a b^{2} \cosh\left(d x + c\right)^{4} + 4 \, a^{2} b - 7 \, a b^{2} - 6 \, {\left(4 \, a^{2} b - 7 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 24 \, {\left({\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + {\left(a^{2} - 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{3}\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} {\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right)}}{2 \, a}\right) + 24 \, {\left({\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + {\left(a^{2} - 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{3}\right)} \sqrt{a b} \arctan\left(\frac{{\left(b \cosh\left(d x + c\right)^{3} + 3 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{3} + {\left(4 \, a - b\right)} \cosh\left(d x + c\right) + {\left(3 \, b \cosh\left(d x + c\right)^{2} + 4 \, a - b\right)} \sinh\left(d x + c\right)\right)} \sqrt{a b}}{2 \, a b}\right) + 6 \, {\left(a b^{2} \cosh\left(d x + c\right)^{5} - 2 \, {\left(4 \, a^{2} b - 7 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(4 \, a^{2} b - 7 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{24 \, {\left(a b^{3} d \cosh\left(d x + c\right)^{3} + 3 \, a b^{3} d \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, a b^{3} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + a b^{3} d \sinh\left(d x + c\right)^{3}\right)}}\right]"," ",0,"[1/24*(a*b^2*cosh(d*x + c)^6 + 6*a*b^2*cosh(d*x + c)*sinh(d*x + c)^5 + a*b^2*sinh(d*x + c)^6 - 3*(4*a^2*b - 7*a*b^2)*cosh(d*x + c)^4 + 3*(5*a*b^2*cosh(d*x + c)^2 - 4*a^2*b + 7*a*b^2)*sinh(d*x + c)^4 + 4*(5*a*b^2*cosh(d*x + c)^3 - 3*(4*a^2*b - 7*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 - a*b^2 + 3*(4*a^2*b - 7*a*b^2)*cosh(d*x + c)^2 + 3*(5*a*b^2*cosh(d*x + c)^4 + 4*a^2*b - 7*a*b^2 - 6*(4*a^2*b - 7*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - 12*((a^2 - 2*a*b + b^2)*cosh(d*x + c)^3 + 3*(a^2 - 2*a*b + b^2)*cosh(d*x + c)^2*sinh(d*x + c) + 3*(a^2 - 2*a*b + b^2)*cosh(d*x + c)*sinh(d*x + c)^2 + (a^2 - 2*a*b + b^2)*sinh(d*x + c)^3)*sqrt(-a*b)*log((b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 - 2*(2*a + b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 - 2*a - b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 - (2*a + b)*cosh(d*x + c))*sinh(d*x + c) - 4*(cosh(d*x + c)^3 + 3*cosh(d*x + c)*sinh(d*x + c)^2 + sinh(d*x + c)^3 + (3*cosh(d*x + c)^2 - 1)*sinh(d*x + c) - cosh(d*x + c))*sqrt(-a*b) + b)/(b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 + 2*(2*a - b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 + 2*a - b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 + (2*a - b)*cosh(d*x + c))*sinh(d*x + c) + b)) + 6*(a*b^2*cosh(d*x + c)^5 - 2*(4*a^2*b - 7*a*b^2)*cosh(d*x + c)^3 + (4*a^2*b - 7*a*b^2)*cosh(d*x + c))*sinh(d*x + c))/(a*b^3*d*cosh(d*x + c)^3 + 3*a*b^3*d*cosh(d*x + c)^2*sinh(d*x + c) + 3*a*b^3*d*cosh(d*x + c)*sinh(d*x + c)^2 + a*b^3*d*sinh(d*x + c)^3), 1/24*(a*b^2*cosh(d*x + c)^6 + 6*a*b^2*cosh(d*x + c)*sinh(d*x + c)^5 + a*b^2*sinh(d*x + c)^6 - 3*(4*a^2*b - 7*a*b^2)*cosh(d*x + c)^4 + 3*(5*a*b^2*cosh(d*x + c)^2 - 4*a^2*b + 7*a*b^2)*sinh(d*x + c)^4 + 4*(5*a*b^2*cosh(d*x + c)^3 - 3*(4*a^2*b - 7*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 - a*b^2 + 3*(4*a^2*b - 7*a*b^2)*cosh(d*x + c)^2 + 3*(5*a*b^2*cosh(d*x + c)^4 + 4*a^2*b - 7*a*b^2 - 6*(4*a^2*b - 7*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 24*((a^2 - 2*a*b + b^2)*cosh(d*x + c)^3 + 3*(a^2 - 2*a*b + b^2)*cosh(d*x + c)^2*sinh(d*x + c) + 3*(a^2 - 2*a*b + b^2)*cosh(d*x + c)*sinh(d*x + c)^2 + (a^2 - 2*a*b + b^2)*sinh(d*x + c)^3)*sqrt(a*b)*arctan(1/2*sqrt(a*b)*(cosh(d*x + c) + sinh(d*x + c))/a) + 24*((a^2 - 2*a*b + b^2)*cosh(d*x + c)^3 + 3*(a^2 - 2*a*b + b^2)*cosh(d*x + c)^2*sinh(d*x + c) + 3*(a^2 - 2*a*b + b^2)*cosh(d*x + c)*sinh(d*x + c)^2 + (a^2 - 2*a*b + b^2)*sinh(d*x + c)^3)*sqrt(a*b)*arctan(1/2*(b*cosh(d*x + c)^3 + 3*b*cosh(d*x + c)*sinh(d*x + c)^2 + b*sinh(d*x + c)^3 + (4*a - b)*cosh(d*x + c) + (3*b*cosh(d*x + c)^2 + 4*a - b)*sinh(d*x + c))*sqrt(a*b)/(a*b)) + 6*(a*b^2*cosh(d*x + c)^5 - 2*(4*a^2*b - 7*a*b^2)*cosh(d*x + c)^3 + (4*a^2*b - 7*a*b^2)*cosh(d*x + c))*sinh(d*x + c))/(a*b^3*d*cosh(d*x + c)^3 + 3*a*b^3*d*cosh(d*x + c)^2*sinh(d*x + c) + 3*a*b^3*d*cosh(d*x + c)*sinh(d*x + c)^2 + a*b^3*d*sinh(d*x + c)^3)]","B",0
319,1,875,0,0.579117," ","integrate(cosh(d*x+c)^4/(a+b*sinh(d*x+c)^2),x, algorithm=""fricas"")","\left[-\frac{4 \, {\left(2 \, a - 3 \, b\right)} d x \cosh\left(d x + c\right)^{2} - b \cosh\left(d x + c\right)^{4} - 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} - b \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, {\left(2 \, a - 3 \, b\right)} d x - 3 \, b \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a - b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a - b\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{a - b}{a}} \log\left(\frac{b^{2} \cosh\left(d x + c\right)^{4} + 4 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{2} \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(d x + c\right)^{2} + 2 \, a b - b^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, a^{2} - 8 \, a b + b^{2} + 4 \, {\left(b^{2} \cosh\left(d x + c\right)^{3} + {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + 4 \, {\left(a b \cosh\left(d x + c\right)^{2} + 2 \, a b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a b \sinh\left(d x + c\right)^{2} + 2 \, a^{2} - a b\right)} \sqrt{\frac{a - b}{a}}}{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b}\right) + 4 \, {\left(2 \, {\left(2 \, a - 3 \, b\right)} d x \cosh\left(d x + c\right) - b \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right) + b}{8 \, {\left(b^{2} d \cosh\left(d x + c\right)^{2} + 2 \, b^{2} d \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b^{2} d \sinh\left(d x + c\right)^{2}\right)}}, -\frac{4 \, {\left(2 \, a - 3 \, b\right)} d x \cosh\left(d x + c\right)^{2} - b \cosh\left(d x + c\right)^{4} - 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} - b \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, {\left(2 \, a - 3 \, b\right)} d x - 3 \, b \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left({\left(a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a - b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a - b\right)} \sinh\left(d x + c\right)^{2}\right)} \sqrt{-\frac{a - b}{a}} \arctan\left(-\frac{{\left(b \cosh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b \sinh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sqrt{-\frac{a - b}{a}}}{2 \, {\left(a - b\right)}}\right) + 4 \, {\left(2 \, {\left(2 \, a - 3 \, b\right)} d x \cosh\left(d x + c\right) - b \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right) + b}{8 \, {\left(b^{2} d \cosh\left(d x + c\right)^{2} + 2 \, b^{2} d \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b^{2} d \sinh\left(d x + c\right)^{2}\right)}}\right]"," ",0,"[-1/8*(4*(2*a - 3*b)*d*x*cosh(d*x + c)^2 - b*cosh(d*x + c)^4 - 4*b*cosh(d*x + c)*sinh(d*x + c)^3 - b*sinh(d*x + c)^4 + 2*(2*(2*a - 3*b)*d*x - 3*b*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((a - b)*cosh(d*x + c)^2 + 2*(a - b)*cosh(d*x + c)*sinh(d*x + c) + (a - b)*sinh(d*x + c)^2)*sqrt((a - b)/a)*log((b^2*cosh(d*x + c)^4 + 4*b^2*cosh(d*x + c)*sinh(d*x + c)^3 + b^2*sinh(d*x + c)^4 + 2*(2*a*b - b^2)*cosh(d*x + c)^2 + 2*(3*b^2*cosh(d*x + c)^2 + 2*a*b - b^2)*sinh(d*x + c)^2 + 8*a^2 - 8*a*b + b^2 + 4*(b^2*cosh(d*x + c)^3 + (2*a*b - b^2)*cosh(d*x + c))*sinh(d*x + c) + 4*(a*b*cosh(d*x + c)^2 + 2*a*b*cosh(d*x + c)*sinh(d*x + c) + a*b*sinh(d*x + c)^2 + 2*a^2 - a*b)*sqrt((a - b)/a))/(b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 + 2*(2*a - b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 + 2*a - b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 + (2*a - b)*cosh(d*x + c))*sinh(d*x + c) + b)) + 4*(2*(2*a - 3*b)*d*x*cosh(d*x + c) - b*cosh(d*x + c)^3)*sinh(d*x + c) + b)/(b^2*d*cosh(d*x + c)^2 + 2*b^2*d*cosh(d*x + c)*sinh(d*x + c) + b^2*d*sinh(d*x + c)^2), -1/8*(4*(2*a - 3*b)*d*x*cosh(d*x + c)^2 - b*cosh(d*x + c)^4 - 4*b*cosh(d*x + c)*sinh(d*x + c)^3 - b*sinh(d*x + c)^4 + 2*(2*(2*a - 3*b)*d*x - 3*b*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((a - b)*cosh(d*x + c)^2 + 2*(a - b)*cosh(d*x + c)*sinh(d*x + c) + (a - b)*sinh(d*x + c)^2)*sqrt(-(a - b)/a)*arctan(-1/2*(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + 2*a - b)*sqrt(-(a - b)/a)/(a - b)) + 4*(2*(2*a - 3*b)*d*x*cosh(d*x + c) - b*cosh(d*x + c)^3)*sinh(d*x + c) + b)/(b^2*d*cosh(d*x + c)^2 + 2*b^2*d*cosh(d*x + c)*sinh(d*x + c) + b^2*d*sinh(d*x + c)^2)]","B",0
320,1,659,0,0.591865," ","integrate(cosh(d*x+c)^3/(a+b*sinh(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{a b \cosh\left(d x + c\right)^{2} + 2 \, a b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a b \sinh\left(d x + c\right)^{2} + \sqrt{-a b} {\left({\left(a - b\right)} \cosh\left(d x + c\right) + {\left(a - b\right)} \sinh\left(d x + c\right)\right)} \log\left(\frac{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} - 2 \, {\left(2 \, a + b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} - 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} - {\left(2 \, a + b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) - 4 \, {\left(\cosh\left(d x + c\right)^{3} + 3 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{3} + {\left(3 \, \cosh\left(d x + c\right)^{2} - 1\right)} \sinh\left(d x + c\right) - \cosh\left(d x + c\right)\right)} \sqrt{-a b} + b}{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b}\right) - a b}{2 \, {\left(a b^{2} d \cosh\left(d x + c\right) + a b^{2} d \sinh\left(d x + c\right)\right)}}, \frac{a b \cosh\left(d x + c\right)^{2} + 2 \, a b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a b \sinh\left(d x + c\right)^{2} - 2 \, \sqrt{a b} {\left({\left(a - b\right)} \cosh\left(d x + c\right) + {\left(a - b\right)} \sinh\left(d x + c\right)\right)} \arctan\left(\frac{\sqrt{a b} {\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right)}}{2 \, a}\right) - 2 \, \sqrt{a b} {\left({\left(a - b\right)} \cosh\left(d x + c\right) + {\left(a - b\right)} \sinh\left(d x + c\right)\right)} \arctan\left(\frac{{\left(b \cosh\left(d x + c\right)^{3} + 3 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{3} + {\left(4 \, a - b\right)} \cosh\left(d x + c\right) + {\left(3 \, b \cosh\left(d x + c\right)^{2} + 4 \, a - b\right)} \sinh\left(d x + c\right)\right)} \sqrt{a b}}{2 \, a b}\right) - a b}{2 \, {\left(a b^{2} d \cosh\left(d x + c\right) + a b^{2} d \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[1/2*(a*b*cosh(d*x + c)^2 + 2*a*b*cosh(d*x + c)*sinh(d*x + c) + a*b*sinh(d*x + c)^2 + sqrt(-a*b)*((a - b)*cosh(d*x + c) + (a - b)*sinh(d*x + c))*log((b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 - 2*(2*a + b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 - 2*a - b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 - (2*a + b)*cosh(d*x + c))*sinh(d*x + c) - 4*(cosh(d*x + c)^3 + 3*cosh(d*x + c)*sinh(d*x + c)^2 + sinh(d*x + c)^3 + (3*cosh(d*x + c)^2 - 1)*sinh(d*x + c) - cosh(d*x + c))*sqrt(-a*b) + b)/(b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 + 2*(2*a - b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 + 2*a - b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 + (2*a - b)*cosh(d*x + c))*sinh(d*x + c) + b)) - a*b)/(a*b^2*d*cosh(d*x + c) + a*b^2*d*sinh(d*x + c)), 1/2*(a*b*cosh(d*x + c)^2 + 2*a*b*cosh(d*x + c)*sinh(d*x + c) + a*b*sinh(d*x + c)^2 - 2*sqrt(a*b)*((a - b)*cosh(d*x + c) + (a - b)*sinh(d*x + c))*arctan(1/2*sqrt(a*b)*(cosh(d*x + c) + sinh(d*x + c))/a) - 2*sqrt(a*b)*((a - b)*cosh(d*x + c) + (a - b)*sinh(d*x + c))*arctan(1/2*(b*cosh(d*x + c)^3 + 3*b*cosh(d*x + c)*sinh(d*x + c)^2 + b*sinh(d*x + c)^3 + (4*a - b)*cosh(d*x + c) + (3*b*cosh(d*x + c)^2 + 4*a - b)*sinh(d*x + c))*sqrt(a*b)/(a*b)) - a*b)/(a*b^2*d*cosh(d*x + c) + a*b^2*d*sinh(d*x + c))]","B",0
321,1,443,0,0.491669," ","integrate(cosh(d*x+c)^2/(a+b*sinh(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{2 \, d x + \sqrt{\frac{a - b}{a}} \log\left(\frac{b^{2} \cosh\left(d x + c\right)^{4} + 4 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{2} \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(d x + c\right)^{2} + 2 \, a b - b^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, a^{2} - 8 \, a b + b^{2} + 4 \, {\left(b^{2} \cosh\left(d x + c\right)^{3} + {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + 4 \, {\left(a b \cosh\left(d x + c\right)^{2} + 2 \, a b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a b \sinh\left(d x + c\right)^{2} + 2 \, a^{2} - a b\right)} \sqrt{\frac{a - b}{a}}}{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b}\right)}{2 \, b d}, \frac{d x + \sqrt{-\frac{a - b}{a}} \arctan\left(-\frac{{\left(b \cosh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b \sinh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sqrt{-\frac{a - b}{a}}}{2 \, {\left(a - b\right)}}\right)}{b d}\right]"," ",0,"[1/2*(2*d*x + sqrt((a - b)/a)*log((b^2*cosh(d*x + c)^4 + 4*b^2*cosh(d*x + c)*sinh(d*x + c)^3 + b^2*sinh(d*x + c)^4 + 2*(2*a*b - b^2)*cosh(d*x + c)^2 + 2*(3*b^2*cosh(d*x + c)^2 + 2*a*b - b^2)*sinh(d*x + c)^2 + 8*a^2 - 8*a*b + b^2 + 4*(b^2*cosh(d*x + c)^3 + (2*a*b - b^2)*cosh(d*x + c))*sinh(d*x + c) + 4*(a*b*cosh(d*x + c)^2 + 2*a*b*cosh(d*x + c)*sinh(d*x + c) + a*b*sinh(d*x + c)^2 + 2*a^2 - a*b)*sqrt((a - b)/a))/(b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 + 2*(2*a - b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 + 2*a - b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 + (2*a - b)*cosh(d*x + c))*sinh(d*x + c) + b)))/(b*d), (d*x + sqrt(-(a - b)/a)*arctan(-1/2*(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + 2*a - b)*sqrt(-(a - b)/a)/(a - b)))/(b*d)]","B",0
322,1,459,0,0.588267," ","integrate(cosh(d*x+c)/(a+b*sinh(d*x+c)^2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-a b} \log\left(\frac{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} - 2 \, {\left(2 \, a + b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} - 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} - {\left(2 \, a + b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) - 4 \, {\left(\cosh\left(d x + c\right)^{3} + 3 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{3} + {\left(3 \, \cosh\left(d x + c\right)^{2} - 1\right)} \sinh\left(d x + c\right) - \cosh\left(d x + c\right)\right)} \sqrt{-a b} + b}{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b}\right)}{2 \, a b d}, \frac{\sqrt{a b} \arctan\left(\frac{\sqrt{a b} {\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right)}}{2 \, a}\right) + \sqrt{a b} \arctan\left(\frac{{\left(b \cosh\left(d x + c\right)^{3} + 3 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{3} + {\left(4 \, a - b\right)} \cosh\left(d x + c\right) + {\left(3 \, b \cosh\left(d x + c\right)^{2} + 4 \, a - b\right)} \sinh\left(d x + c\right)\right)} \sqrt{a b}}{2 \, a b}\right)}{a b d}\right]"," ",0,"[-1/2*sqrt(-a*b)*log((b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 - 2*(2*a + b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 - 2*a - b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 - (2*a + b)*cosh(d*x + c))*sinh(d*x + c) - 4*(cosh(d*x + c)^3 + 3*cosh(d*x + c)*sinh(d*x + c)^2 + sinh(d*x + c)^3 + (3*cosh(d*x + c)^2 - 1)*sinh(d*x + c) - cosh(d*x + c))*sqrt(-a*b) + b)/(b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 + 2*(2*a - b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 + 2*a - b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 + (2*a - b)*cosh(d*x + c))*sinh(d*x + c) + b))/(a*b*d), (sqrt(a*b)*arctan(1/2*sqrt(a*b)*(cosh(d*x + c) + sinh(d*x + c))/a) + sqrt(a*b)*arctan(1/2*(b*cosh(d*x + c)^3 + 3*b*cosh(d*x + c)*sinh(d*x + c)^2 + b*sinh(d*x + c)^3 + (4*a - b)*cosh(d*x + c) + (3*b*cosh(d*x + c)^2 + 4*a - b)*sinh(d*x + c))*sqrt(a*b)/(a*b)))/(a*b*d)]","B",0
323,1,511,0,0.891657," ","integrate(sech(d*x+c)/(a+b*sinh(d*x+c)^2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-\frac{b}{a}} \log\left(\frac{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} - 2 \, {\left(2 \, a + b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} - 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} - {\left(2 \, a + b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + 4 \, {\left(a \cosh\left(d x + c\right)^{3} + 3 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{3} - a \cosh\left(d x + c\right) + {\left(3 \, a \cosh\left(d x + c\right)^{2} - a\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{b}{a}} + b}{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b}\right) - 4 \, \arctan\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right)}{2 \, {\left(a - b\right)} d}, -\frac{\sqrt{\frac{b}{a}} \arctan\left(\frac{1}{2} \, \sqrt{\frac{b}{a}} {\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right)}\right) + \sqrt{\frac{b}{a}} \arctan\left(\frac{{\left(b \cosh\left(d x + c\right)^{3} + 3 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{3} + {\left(4 \, a - b\right)} \cosh\left(d x + c\right) + {\left(3 \, b \cosh\left(d x + c\right)^{2} + 4 \, a - b\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{b}{a}}}{2 \, b}\right) - 2 \, \arctan\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right)}{{\left(a - b\right)} d}\right]"," ",0,"[-1/2*(sqrt(-b/a)*log((b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 - 2*(2*a + b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 - 2*a - b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 - (2*a + b)*cosh(d*x + c))*sinh(d*x + c) + 4*(a*cosh(d*x + c)^3 + 3*a*cosh(d*x + c)*sinh(d*x + c)^2 + a*sinh(d*x + c)^3 - a*cosh(d*x + c) + (3*a*cosh(d*x + c)^2 - a)*sinh(d*x + c))*sqrt(-b/a) + b)/(b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 + 2*(2*a - b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 + 2*a - b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 + (2*a - b)*cosh(d*x + c))*sinh(d*x + c) + b)) - 4*arctan(cosh(d*x + c) + sinh(d*x + c)))/((a - b)*d), -(sqrt(b/a)*arctan(1/2*sqrt(b/a)*(cosh(d*x + c) + sinh(d*x + c))) + sqrt(b/a)*arctan(1/2*(b*cosh(d*x + c)^3 + 3*b*cosh(d*x + c)*sinh(d*x + c)^2 + b*sinh(d*x + c)^3 + (4*a - b)*cosh(d*x + c) + (3*b*cosh(d*x + c)^2 + 4*a - b)*sinh(d*x + c))*sqrt(b/a)/b) - 2*arctan(cosh(d*x + c) + sinh(d*x + c)))/((a - b)*d)]","B",0
324,1,709,0,0.590018," ","integrate(sech(d*x+c)^2/(a+b*sinh(d*x+c)^2),x, algorithm=""fricas"")","\left[-\frac{{\left(b \cosh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b \sinh\left(d x + c\right)^{2} + b\right)} \sqrt{a^{2} - a b} \log\left(\frac{b^{2} \cosh\left(d x + c\right)^{4} + 4 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{2} \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(d x + c\right)^{2} + 2 \, a b - b^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, a^{2} - 8 \, a b + b^{2} + 4 \, {\left(b^{2} \cosh\left(d x + c\right)^{3} + {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) - 4 \, {\left(b \cosh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b \sinh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sqrt{a^{2} - a b}}{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b}\right) + 4 \, a^{2} - 4 \, a b}{2 \, {\left({\left(a^{3} - 2 \, a^{2} b + a b^{2}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{3} - 2 \, a^{2} b + a b^{2}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{3} - 2 \, a^{2} b + a b^{2}\right)} d \sinh\left(d x + c\right)^{2} + {\left(a^{3} - 2 \, a^{2} b + a b^{2}\right)} d\right)}}, \frac{{\left(b \cosh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b \sinh\left(d x + c\right)^{2} + b\right)} \sqrt{-a^{2} + a b} \arctan\left(-\frac{{\left(b \cosh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b \sinh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sqrt{-a^{2} + a b}}{2 \, {\left(a^{2} - a b\right)}}\right) - 2 \, a^{2} + 2 \, a b}{{\left(a^{3} - 2 \, a^{2} b + a b^{2}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{3} - 2 \, a^{2} b + a b^{2}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{3} - 2 \, a^{2} b + a b^{2}\right)} d \sinh\left(d x + c\right)^{2} + {\left(a^{3} - 2 \, a^{2} b + a b^{2}\right)} d}\right]"," ",0,"[-1/2*((b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + b)*sqrt(a^2 - a*b)*log((b^2*cosh(d*x + c)^4 + 4*b^2*cosh(d*x + c)*sinh(d*x + c)^3 + b^2*sinh(d*x + c)^4 + 2*(2*a*b - b^2)*cosh(d*x + c)^2 + 2*(3*b^2*cosh(d*x + c)^2 + 2*a*b - b^2)*sinh(d*x + c)^2 + 8*a^2 - 8*a*b + b^2 + 4*(b^2*cosh(d*x + c)^3 + (2*a*b - b^2)*cosh(d*x + c))*sinh(d*x + c) - 4*(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + 2*a - b)*sqrt(a^2 - a*b))/(b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 + 2*(2*a - b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 + 2*a - b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 + (2*a - b)*cosh(d*x + c))*sinh(d*x + c) + b)) + 4*a^2 - 4*a*b)/((a^3 - 2*a^2*b + a*b^2)*d*cosh(d*x + c)^2 + 2*(a^3 - 2*a^2*b + a*b^2)*d*cosh(d*x + c)*sinh(d*x + c) + (a^3 - 2*a^2*b + a*b^2)*d*sinh(d*x + c)^2 + (a^3 - 2*a^2*b + a*b^2)*d), ((b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + b)*sqrt(-a^2 + a*b)*arctan(-1/2*(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + 2*a - b)*sqrt(-a^2 + a*b)/(a^2 - a*b)) - 2*a^2 + 2*a*b)/((a^3 - 2*a^2*b + a*b^2)*d*cosh(d*x + c)^2 + 2*(a^3 - 2*a^2*b + a*b^2)*d*cosh(d*x + c)*sinh(d*x + c) + (a^3 - 2*a^2*b + a*b^2)*d*sinh(d*x + c)^2 + (a^3 - 2*a^2*b + a*b^2)*d)]","B",0
325,1,1644,0,0.713840," ","integrate(sech(d*x+c)^3/(a+b*sinh(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{2 \, {\left(a - b\right)} \cosh\left(d x + c\right)^{3} + 6 \, {\left(a - b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + 2 \, {\left(a - b\right)} \sinh\left(d x + c\right)^{3} + {\left(b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} + 2 \, b \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} + b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} + b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} - 2 \, {\left(2 \, a + b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} - 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} - {\left(2 \, a + b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + 4 \, {\left(a \cosh\left(d x + c\right)^{3} + 3 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{3} - a \cosh\left(d x + c\right) + {\left(3 \, a \cosh\left(d x + c\right)^{2} - a\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{b}{a}} + b}{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b}\right) + 2 \, {\left({\left(a - 3 \, b\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a - 3 \, b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a - 3 \, b\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a - 3 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a - 3 \, b\right)} \cosh\left(d x + c\right)^{2} + a - 3 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a - 3 \, b\right)} \cosh\left(d x + c\right)^{3} + {\left(a - 3 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + a - 3 \, b\right)} \arctan\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) - 2 \, {\left(a - b\right)} \cosh\left(d x + c\right) + 2 \, {\left(3 \, {\left(a - b\right)} \cosh\left(d x + c\right)^{2} - a + b\right)} \sinh\left(d x + c\right)}{2 \, {\left({\left(a^{2} - 2 \, a b + b^{2}\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{2} - 2 \, a b + b^{2}\right)} d \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{2} - 2 \, a b + b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{2} - 2 \, a b + b^{2}\right)} d + 4 \, {\left({\left(a^{2} - 2 \, a b + b^{2}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{2} - 2 \, a b + b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}, \frac{{\left(a - b\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a - b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + {\left(a - b\right)} \sinh\left(d x + c\right)^{3} + {\left(b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} + 2 \, b \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} + b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} + b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b\right)} \sqrt{\frac{b}{a}} \arctan\left(\frac{1}{2} \, \sqrt{\frac{b}{a}} {\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right)}\right) + {\left(b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} + 2 \, b \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} + b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} + b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b\right)} \sqrt{\frac{b}{a}} \arctan\left(\frac{{\left(b \cosh\left(d x + c\right)^{3} + 3 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{3} + {\left(4 \, a - b\right)} \cosh\left(d x + c\right) + {\left(3 \, b \cosh\left(d x + c\right)^{2} + 4 \, a - b\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{b}{a}}}{2 \, b}\right) + {\left({\left(a - 3 \, b\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a - 3 \, b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a - 3 \, b\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a - 3 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a - 3 \, b\right)} \cosh\left(d x + c\right)^{2} + a - 3 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a - 3 \, b\right)} \cosh\left(d x + c\right)^{3} + {\left(a - 3 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + a - 3 \, b\right)} \arctan\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) - {\left(a - b\right)} \cosh\left(d x + c\right) + {\left(3 \, {\left(a - b\right)} \cosh\left(d x + c\right)^{2} - a + b\right)} \sinh\left(d x + c\right)}{{\left(a^{2} - 2 \, a b + b^{2}\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{2} - 2 \, a b + b^{2}\right)} d \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{2} - 2 \, a b + b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{2} - 2 \, a b + b^{2}\right)} d + 4 \, {\left({\left(a^{2} - 2 \, a b + b^{2}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{2} - 2 \, a b + b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}\right]"," ",0,"[1/2*(2*(a - b)*cosh(d*x + c)^3 + 6*(a - b)*cosh(d*x + c)*sinh(d*x + c)^2 + 2*(a - b)*sinh(d*x + c)^3 + (b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 + 2*b*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 + b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 + b*cosh(d*x + c))*sinh(d*x + c) + b)*sqrt(-b/a)*log((b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 - 2*(2*a + b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 - 2*a - b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 - (2*a + b)*cosh(d*x + c))*sinh(d*x + c) + 4*(a*cosh(d*x + c)^3 + 3*a*cosh(d*x + c)*sinh(d*x + c)^2 + a*sinh(d*x + c)^3 - a*cosh(d*x + c) + (3*a*cosh(d*x + c)^2 - a)*sinh(d*x + c))*sqrt(-b/a) + b)/(b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 + 2*(2*a - b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 + 2*a - b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 + (2*a - b)*cosh(d*x + c))*sinh(d*x + c) + b)) + 2*((a - 3*b)*cosh(d*x + c)^4 + 4*(a - 3*b)*cosh(d*x + c)*sinh(d*x + c)^3 + (a - 3*b)*sinh(d*x + c)^4 + 2*(a - 3*b)*cosh(d*x + c)^2 + 2*(3*(a - 3*b)*cosh(d*x + c)^2 + a - 3*b)*sinh(d*x + c)^2 + 4*((a - 3*b)*cosh(d*x + c)^3 + (a - 3*b)*cosh(d*x + c))*sinh(d*x + c) + a - 3*b)*arctan(cosh(d*x + c) + sinh(d*x + c)) - 2*(a - b)*cosh(d*x + c) + 2*(3*(a - b)*cosh(d*x + c)^2 - a + b)*sinh(d*x + c))/((a^2 - 2*a*b + b^2)*d*cosh(d*x + c)^4 + 4*(a^2 - 2*a*b + b^2)*d*cosh(d*x + c)*sinh(d*x + c)^3 + (a^2 - 2*a*b + b^2)*d*sinh(d*x + c)^4 + 2*(a^2 - 2*a*b + b^2)*d*cosh(d*x + c)^2 + 2*(3*(a^2 - 2*a*b + b^2)*d*cosh(d*x + c)^2 + (a^2 - 2*a*b + b^2)*d)*sinh(d*x + c)^2 + (a^2 - 2*a*b + b^2)*d + 4*((a^2 - 2*a*b + b^2)*d*cosh(d*x + c)^3 + (a^2 - 2*a*b + b^2)*d*cosh(d*x + c))*sinh(d*x + c)), ((a - b)*cosh(d*x + c)^3 + 3*(a - b)*cosh(d*x + c)*sinh(d*x + c)^2 + (a - b)*sinh(d*x + c)^3 + (b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 + 2*b*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 + b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 + b*cosh(d*x + c))*sinh(d*x + c) + b)*sqrt(b/a)*arctan(1/2*sqrt(b/a)*(cosh(d*x + c) + sinh(d*x + c))) + (b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 + 2*b*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 + b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 + b*cosh(d*x + c))*sinh(d*x + c) + b)*sqrt(b/a)*arctan(1/2*(b*cosh(d*x + c)^3 + 3*b*cosh(d*x + c)*sinh(d*x + c)^2 + b*sinh(d*x + c)^3 + (4*a - b)*cosh(d*x + c) + (3*b*cosh(d*x + c)^2 + 4*a - b)*sinh(d*x + c))*sqrt(b/a)/b) + ((a - 3*b)*cosh(d*x + c)^4 + 4*(a - 3*b)*cosh(d*x + c)*sinh(d*x + c)^3 + (a - 3*b)*sinh(d*x + c)^4 + 2*(a - 3*b)*cosh(d*x + c)^2 + 2*(3*(a - 3*b)*cosh(d*x + c)^2 + a - 3*b)*sinh(d*x + c)^2 + 4*((a - 3*b)*cosh(d*x + c)^3 + (a - 3*b)*cosh(d*x + c))*sinh(d*x + c) + a - 3*b)*arctan(cosh(d*x + c) + sinh(d*x + c)) - (a - b)*cosh(d*x + c) + (3*(a - b)*cosh(d*x + c)^2 - a + b)*sinh(d*x + c))/((a^2 - 2*a*b + b^2)*d*cosh(d*x + c)^4 + 4*(a^2 - 2*a*b + b^2)*d*cosh(d*x + c)*sinh(d*x + c)^3 + (a^2 - 2*a*b + b^2)*d*sinh(d*x + c)^4 + 2*(a^2 - 2*a*b + b^2)*d*cosh(d*x + c)^2 + 2*(3*(a^2 - 2*a*b + b^2)*d*cosh(d*x + c)^2 + (a^2 - 2*a*b + b^2)*d)*sinh(d*x + c)^2 + (a^2 - 2*a*b + b^2)*d + 4*((a^2 - 2*a*b + b^2)*d*cosh(d*x + c)^3 + (a^2 - 2*a*b + b^2)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
326,1,2444,0,0.572294," ","integrate(sech(d*x+c)^4/(a+b*sinh(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{12 \, {\left(a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right)^{4} + 48 \, {\left(a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + 12 \, {\left(a^{2} b - a b^{2}\right)} \sinh\left(d x + c\right)^{4} - 8 \, a^{3} + 28 \, a^{2} b - 20 \, a b^{2} - 24 \, {\left(a^{3} - 3 \, a^{2} b + 2 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2} - 24 \, {\left(a^{3} - 3 \, a^{2} b + 2 \, a b^{2} - 3 \, {\left(a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 3 \, {\left(b^{2} \cosh\left(d x + c\right)^{6} + 6 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + b^{2} \sinh\left(d x + c\right)^{6} + 3 \, b^{2} \cosh\left(d x + c\right)^{4} + 3 \, {\left(5 \, b^{2} \cosh\left(d x + c\right)^{2} + b^{2}\right)} \sinh\left(d x + c\right)^{4} + 3 \, b^{2} \cosh\left(d x + c\right)^{2} + 4 \, {\left(5 \, b^{2} \cosh\left(d x + c\right)^{3} + 3 \, b^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 3 \, {\left(5 \, b^{2} \cosh\left(d x + c\right)^{4} + 6 \, b^{2} \cosh\left(d x + c\right)^{2} + b^{2}\right)} \sinh\left(d x + c\right)^{2} + b^{2} + 6 \, {\left(b^{2} \cosh\left(d x + c\right)^{5} + 2 \, b^{2} \cosh\left(d x + c\right)^{3} + b^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{a^{2} - a b} \log\left(\frac{b^{2} \cosh\left(d x + c\right)^{4} + 4 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{2} \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(d x + c\right)^{2} + 2 \, a b - b^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, a^{2} - 8 \, a b + b^{2} + 4 \, {\left(b^{2} \cosh\left(d x + c\right)^{3} + {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) - 4 \, {\left(b \cosh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b \sinh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sqrt{a^{2} - a b}}{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b}\right) + 48 \, {\left({\left(a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(a^{3} - 3 \, a^{2} b + 2 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{6 \, {\left({\left(a^{4} - 3 \, a^{3} b + 3 \, a^{2} b^{2} - a b^{3}\right)} d \cosh\left(d x + c\right)^{6} + 6 \, {\left(a^{4} - 3 \, a^{3} b + 3 \, a^{2} b^{2} - a b^{3}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(a^{4} - 3 \, a^{3} b + 3 \, a^{2} b^{2} - a b^{3}\right)} d \sinh\left(d x + c\right)^{6} + 3 \, {\left(a^{4} - 3 \, a^{3} b + 3 \, a^{2} b^{2} - a b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(5 \, {\left(a^{4} - 3 \, a^{3} b + 3 \, a^{2} b^{2} - a b^{3}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{4} - 3 \, a^{3} b + 3 \, a^{2} b^{2} - a b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 3 \, {\left(a^{4} - 3 \, a^{3} b + 3 \, a^{2} b^{2} - a b^{3}\right)} d \cosh\left(d x + c\right)^{2} + 4 \, {\left(5 \, {\left(a^{4} - 3 \, a^{3} b + 3 \, a^{2} b^{2} - a b^{3}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{4} - 3 \, a^{3} b + 3 \, a^{2} b^{2} - a b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 3 \, {\left(5 \, {\left(a^{4} - 3 \, a^{3} b + 3 \, a^{2} b^{2} - a b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 6 \, {\left(a^{4} - 3 \, a^{3} b + 3 \, a^{2} b^{2} - a b^{3}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{4} - 3 \, a^{3} b + 3 \, a^{2} b^{2} - a b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{4} - 3 \, a^{3} b + 3 \, a^{2} b^{2} - a b^{3}\right)} d + 6 \, {\left({\left(a^{4} - 3 \, a^{3} b + 3 \, a^{2} b^{2} - a b^{3}\right)} d \cosh\left(d x + c\right)^{5} + 2 \, {\left(a^{4} - 3 \, a^{3} b + 3 \, a^{2} b^{2} - a b^{3}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{4} - 3 \, a^{3} b + 3 \, a^{2} b^{2} - a b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}, \frac{6 \, {\left(a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right)^{4} + 24 \, {\left(a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + 6 \, {\left(a^{2} b - a b^{2}\right)} \sinh\left(d x + c\right)^{4} - 4 \, a^{3} + 14 \, a^{2} b - 10 \, a b^{2} - 12 \, {\left(a^{3} - 3 \, a^{2} b + 2 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2} - 12 \, {\left(a^{3} - 3 \, a^{2} b + 2 \, a b^{2} - 3 \, {\left(a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} - 3 \, {\left(b^{2} \cosh\left(d x + c\right)^{6} + 6 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + b^{2} \sinh\left(d x + c\right)^{6} + 3 \, b^{2} \cosh\left(d x + c\right)^{4} + 3 \, {\left(5 \, b^{2} \cosh\left(d x + c\right)^{2} + b^{2}\right)} \sinh\left(d x + c\right)^{4} + 3 \, b^{2} \cosh\left(d x + c\right)^{2} + 4 \, {\left(5 \, b^{2} \cosh\left(d x + c\right)^{3} + 3 \, b^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 3 \, {\left(5 \, b^{2} \cosh\left(d x + c\right)^{4} + 6 \, b^{2} \cosh\left(d x + c\right)^{2} + b^{2}\right)} \sinh\left(d x + c\right)^{2} + b^{2} + 6 \, {\left(b^{2} \cosh\left(d x + c\right)^{5} + 2 \, b^{2} \cosh\left(d x + c\right)^{3} + b^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-a^{2} + a b} \arctan\left(-\frac{{\left(b \cosh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b \sinh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sqrt{-a^{2} + a b}}{2 \, {\left(a^{2} - a b\right)}}\right) + 24 \, {\left({\left(a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(a^{3} - 3 \, a^{2} b + 2 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{3 \, {\left({\left(a^{4} - 3 \, a^{3} b + 3 \, a^{2} b^{2} - a b^{3}\right)} d \cosh\left(d x + c\right)^{6} + 6 \, {\left(a^{4} - 3 \, a^{3} b + 3 \, a^{2} b^{2} - a b^{3}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(a^{4} - 3 \, a^{3} b + 3 \, a^{2} b^{2} - a b^{3}\right)} d \sinh\left(d x + c\right)^{6} + 3 \, {\left(a^{4} - 3 \, a^{3} b + 3 \, a^{2} b^{2} - a b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(5 \, {\left(a^{4} - 3 \, a^{3} b + 3 \, a^{2} b^{2} - a b^{3}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{4} - 3 \, a^{3} b + 3 \, a^{2} b^{2} - a b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 3 \, {\left(a^{4} - 3 \, a^{3} b + 3 \, a^{2} b^{2} - a b^{3}\right)} d \cosh\left(d x + c\right)^{2} + 4 \, {\left(5 \, {\left(a^{4} - 3 \, a^{3} b + 3 \, a^{2} b^{2} - a b^{3}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{4} - 3 \, a^{3} b + 3 \, a^{2} b^{2} - a b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 3 \, {\left(5 \, {\left(a^{4} - 3 \, a^{3} b + 3 \, a^{2} b^{2} - a b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 6 \, {\left(a^{4} - 3 \, a^{3} b + 3 \, a^{2} b^{2} - a b^{3}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{4} - 3 \, a^{3} b + 3 \, a^{2} b^{2} - a b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{4} - 3 \, a^{3} b + 3 \, a^{2} b^{2} - a b^{3}\right)} d + 6 \, {\left({\left(a^{4} - 3 \, a^{3} b + 3 \, a^{2} b^{2} - a b^{3}\right)} d \cosh\left(d x + c\right)^{5} + 2 \, {\left(a^{4} - 3 \, a^{3} b + 3 \, a^{2} b^{2} - a b^{3}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{4} - 3 \, a^{3} b + 3 \, a^{2} b^{2} - a b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[1/6*(12*(a^2*b - a*b^2)*cosh(d*x + c)^4 + 48*(a^2*b - a*b^2)*cosh(d*x + c)*sinh(d*x + c)^3 + 12*(a^2*b - a*b^2)*sinh(d*x + c)^4 - 8*a^3 + 28*a^2*b - 20*a*b^2 - 24*(a^3 - 3*a^2*b + 2*a*b^2)*cosh(d*x + c)^2 - 24*(a^3 - 3*a^2*b + 2*a*b^2 - 3*(a^2*b - a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 3*(b^2*cosh(d*x + c)^6 + 6*b^2*cosh(d*x + c)*sinh(d*x + c)^5 + b^2*sinh(d*x + c)^6 + 3*b^2*cosh(d*x + c)^4 + 3*(5*b^2*cosh(d*x + c)^2 + b^2)*sinh(d*x + c)^4 + 3*b^2*cosh(d*x + c)^2 + 4*(5*b^2*cosh(d*x + c)^3 + 3*b^2*cosh(d*x + c))*sinh(d*x + c)^3 + 3*(5*b^2*cosh(d*x + c)^4 + 6*b^2*cosh(d*x + c)^2 + b^2)*sinh(d*x + c)^2 + b^2 + 6*(b^2*cosh(d*x + c)^5 + 2*b^2*cosh(d*x + c)^3 + b^2*cosh(d*x + c))*sinh(d*x + c))*sqrt(a^2 - a*b)*log((b^2*cosh(d*x + c)^4 + 4*b^2*cosh(d*x + c)*sinh(d*x + c)^3 + b^2*sinh(d*x + c)^4 + 2*(2*a*b - b^2)*cosh(d*x + c)^2 + 2*(3*b^2*cosh(d*x + c)^2 + 2*a*b - b^2)*sinh(d*x + c)^2 + 8*a^2 - 8*a*b + b^2 + 4*(b^2*cosh(d*x + c)^3 + (2*a*b - b^2)*cosh(d*x + c))*sinh(d*x + c) - 4*(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + 2*a - b)*sqrt(a^2 - a*b))/(b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 + 2*(2*a - b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 + 2*a - b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 + (2*a - b)*cosh(d*x + c))*sinh(d*x + c) + b)) + 48*((a^2*b - a*b^2)*cosh(d*x + c)^3 - (a^3 - 3*a^2*b + 2*a*b^2)*cosh(d*x + c))*sinh(d*x + c))/((a^4 - 3*a^3*b + 3*a^2*b^2 - a*b^3)*d*cosh(d*x + c)^6 + 6*(a^4 - 3*a^3*b + 3*a^2*b^2 - a*b^3)*d*cosh(d*x + c)*sinh(d*x + c)^5 + (a^4 - 3*a^3*b + 3*a^2*b^2 - a*b^3)*d*sinh(d*x + c)^6 + 3*(a^4 - 3*a^3*b + 3*a^2*b^2 - a*b^3)*d*cosh(d*x + c)^4 + 3*(5*(a^4 - 3*a^3*b + 3*a^2*b^2 - a*b^3)*d*cosh(d*x + c)^2 + (a^4 - 3*a^3*b + 3*a^2*b^2 - a*b^3)*d)*sinh(d*x + c)^4 + 3*(a^4 - 3*a^3*b + 3*a^2*b^2 - a*b^3)*d*cosh(d*x + c)^2 + 4*(5*(a^4 - 3*a^3*b + 3*a^2*b^2 - a*b^3)*d*cosh(d*x + c)^3 + 3*(a^4 - 3*a^3*b + 3*a^2*b^2 - a*b^3)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 3*(5*(a^4 - 3*a^3*b + 3*a^2*b^2 - a*b^3)*d*cosh(d*x + c)^4 + 6*(a^4 - 3*a^3*b + 3*a^2*b^2 - a*b^3)*d*cosh(d*x + c)^2 + (a^4 - 3*a^3*b + 3*a^2*b^2 - a*b^3)*d)*sinh(d*x + c)^2 + (a^4 - 3*a^3*b + 3*a^2*b^2 - a*b^3)*d + 6*((a^4 - 3*a^3*b + 3*a^2*b^2 - a*b^3)*d*cosh(d*x + c)^5 + 2*(a^4 - 3*a^3*b + 3*a^2*b^2 - a*b^3)*d*cosh(d*x + c)^3 + (a^4 - 3*a^3*b + 3*a^2*b^2 - a*b^3)*d*cosh(d*x + c))*sinh(d*x + c)), 1/3*(6*(a^2*b - a*b^2)*cosh(d*x + c)^4 + 24*(a^2*b - a*b^2)*cosh(d*x + c)*sinh(d*x + c)^3 + 6*(a^2*b - a*b^2)*sinh(d*x + c)^4 - 4*a^3 + 14*a^2*b - 10*a*b^2 - 12*(a^3 - 3*a^2*b + 2*a*b^2)*cosh(d*x + c)^2 - 12*(a^3 - 3*a^2*b + 2*a*b^2 - 3*(a^2*b - a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - 3*(b^2*cosh(d*x + c)^6 + 6*b^2*cosh(d*x + c)*sinh(d*x + c)^5 + b^2*sinh(d*x + c)^6 + 3*b^2*cosh(d*x + c)^4 + 3*(5*b^2*cosh(d*x + c)^2 + b^2)*sinh(d*x + c)^4 + 3*b^2*cosh(d*x + c)^2 + 4*(5*b^2*cosh(d*x + c)^3 + 3*b^2*cosh(d*x + c))*sinh(d*x + c)^3 + 3*(5*b^2*cosh(d*x + c)^4 + 6*b^2*cosh(d*x + c)^2 + b^2)*sinh(d*x + c)^2 + b^2 + 6*(b^2*cosh(d*x + c)^5 + 2*b^2*cosh(d*x + c)^3 + b^2*cosh(d*x + c))*sinh(d*x + c))*sqrt(-a^2 + a*b)*arctan(-1/2*(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + 2*a - b)*sqrt(-a^2 + a*b)/(a^2 - a*b)) + 24*((a^2*b - a*b^2)*cosh(d*x + c)^3 - (a^3 - 3*a^2*b + 2*a*b^2)*cosh(d*x + c))*sinh(d*x + c))/((a^4 - 3*a^3*b + 3*a^2*b^2 - a*b^3)*d*cosh(d*x + c)^6 + 6*(a^4 - 3*a^3*b + 3*a^2*b^2 - a*b^3)*d*cosh(d*x + c)*sinh(d*x + c)^5 + (a^4 - 3*a^3*b + 3*a^2*b^2 - a*b^3)*d*sinh(d*x + c)^6 + 3*(a^4 - 3*a^3*b + 3*a^2*b^2 - a*b^3)*d*cosh(d*x + c)^4 + 3*(5*(a^4 - 3*a^3*b + 3*a^2*b^2 - a*b^3)*d*cosh(d*x + c)^2 + (a^4 - 3*a^3*b + 3*a^2*b^2 - a*b^3)*d)*sinh(d*x + c)^4 + 3*(a^4 - 3*a^3*b + 3*a^2*b^2 - a*b^3)*d*cosh(d*x + c)^2 + 4*(5*(a^4 - 3*a^3*b + 3*a^2*b^2 - a*b^3)*d*cosh(d*x + c)^3 + 3*(a^4 - 3*a^3*b + 3*a^2*b^2 - a*b^3)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 3*(5*(a^4 - 3*a^3*b + 3*a^2*b^2 - a*b^3)*d*cosh(d*x + c)^4 + 6*(a^4 - 3*a^3*b + 3*a^2*b^2 - a*b^3)*d*cosh(d*x + c)^2 + (a^4 - 3*a^3*b + 3*a^2*b^2 - a*b^3)*d)*sinh(d*x + c)^2 + (a^4 - 3*a^3*b + 3*a^2*b^2 - a*b^3)*d + 6*((a^4 - 3*a^3*b + 3*a^2*b^2 - a*b^3)*d*cosh(d*x + c)^5 + 2*(a^4 - 3*a^3*b + 3*a^2*b^2 - a*b^3)*d*cosh(d*x + c)^3 + (a^4 - 3*a^3*b + 3*a^2*b^2 - a*b^3)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
327,1,5500,0,0.643086," ","integrate(sech(d*x+c)^5/(a+b*sinh(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{{\left(3 \, a^{2} - 10 \, a b + 7 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} + 7 \, {\left(3 \, a^{2} - 10 \, a b + 7 \, b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + {\left(3 \, a^{2} - 10 \, a b + 7 \, b^{2}\right)} \sinh\left(d x + c\right)^{7} + {\left(11 \, a^{2} - 26 \, a b + 15 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + {\left(21 \, {\left(3 \, a^{2} - 10 \, a b + 7 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 11 \, a^{2} - 26 \, a b + 15 \, b^{2}\right)} \sinh\left(d x + c\right)^{5} + 5 \, {\left(7 \, {\left(3 \, a^{2} - 10 \, a b + 7 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(11 \, a^{2} - 26 \, a b + 15 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} - {\left(11 \, a^{2} - 26 \, a b + 15 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(35 \, {\left(3 \, a^{2} - 10 \, a b + 7 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 10 \, {\left(11 \, a^{2} - 26 \, a b + 15 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 11 \, a^{2} + 26 \, a b - 15 \, b^{2}\right)} \sinh\left(d x + c\right)^{3} + {\left(21 \, {\left(3 \, a^{2} - 10 \, a b + 7 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(11 \, a^{2} - 26 \, a b + 15 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(11 \, a^{2} - 26 \, a b + 15 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 2 \, {\left(b^{2} \cosh\left(d x + c\right)^{8} + 8 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + b^{2} \sinh\left(d x + c\right)^{8} + 4 \, b^{2} \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, b^{2} \cosh\left(d x + c\right)^{2} + b^{2}\right)} \sinh\left(d x + c\right)^{6} + 6 \, b^{2} \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, b^{2} \cosh\left(d x + c\right)^{3} + 3 \, b^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, b^{2} \cosh\left(d x + c\right)^{4} + 30 \, b^{2} \cosh\left(d x + c\right)^{2} + 3 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, b^{2} \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, b^{2} \cosh\left(d x + c\right)^{5} + 10 \, b^{2} \cosh\left(d x + c\right)^{3} + 3 \, b^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, b^{2} \cosh\left(d x + c\right)^{6} + 15 \, b^{2} \cosh\left(d x + c\right)^{4} + 9 \, b^{2} \cosh\left(d x + c\right)^{2} + b^{2}\right)} \sinh\left(d x + c\right)^{2} + b^{2} + 8 \, {\left(b^{2} \cosh\left(d x + c\right)^{7} + 3 \, b^{2} \cosh\left(d x + c\right)^{5} + 3 \, b^{2} \cosh\left(d x + c\right)^{3} + b^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} - 2 \, {\left(2 \, a + b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} - 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} - {\left(2 \, a + b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + 4 \, {\left(a \cosh\left(d x + c\right)^{3} + 3 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{3} - a \cosh\left(d x + c\right) + {\left(3 \, a \cosh\left(d x + c\right)^{2} - a\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{b}{a}} + b}{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b}\right) + {\left({\left(3 \, a^{2} - 10 \, a b + 15 \, b^{2}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(3 \, a^{2} - 10 \, a b + 15 \, b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(3 \, a^{2} - 10 \, a b + 15 \, b^{2}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(3 \, a^{2} - 10 \, a b + 15 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(3 \, a^{2} - 10 \, a b + 15 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 3 \, a^{2} - 10 \, a b + 15 \, b^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(3 \, a^{2} - 10 \, a b + 15 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(3 \, a^{2} - 10 \, a b + 15 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 6 \, {\left(3 \, a^{2} - 10 \, a b + 15 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(3 \, a^{2} - 10 \, a b + 15 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 30 \, {\left(3 \, a^{2} - 10 \, a b + 15 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 9 \, a^{2} - 30 \, a b + 45 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(3 \, a^{2} - 10 \, a b + 15 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(3 \, a^{2} - 10 \, a b + 15 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(3 \, a^{2} - 10 \, a b + 15 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(3 \, a^{2} - 10 \, a b + 15 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(3 \, a^{2} - 10 \, a b + 15 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(3 \, a^{2} - 10 \, a b + 15 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 9 \, {\left(3 \, a^{2} - 10 \, a b + 15 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 3 \, a^{2} - 10 \, a b + 15 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} + 3 \, a^{2} - 10 \, a b + 15 \, b^{2} + 8 \, {\left({\left(3 \, a^{2} - 10 \, a b + 15 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(3 \, a^{2} - 10 \, a b + 15 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 3 \, {\left(3 \, a^{2} - 10 \, a b + 15 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{2} - 10 \, a b + 15 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \arctan\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) - {\left(3 \, a^{2} - 10 \, a b + 7 \, b^{2}\right)} \cosh\left(d x + c\right) + {\left(7 \, {\left(3 \, a^{2} - 10 \, a b + 7 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 5 \, {\left(11 \, a^{2} - 26 \, a b + 15 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} - 3 \, {\left(11 \, a^{2} - 26 \, a b + 15 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 3 \, a^{2} + 10 \, a b - 7 \, b^{2}\right)} \sinh\left(d x + c\right)}{4 \, {\left({\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 6 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 30 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{2} + 3 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 9 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d + 8 \, {\left({\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{5} + 3 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}, \frac{{\left(3 \, a^{2} - 10 \, a b + 7 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} + 7 \, {\left(3 \, a^{2} - 10 \, a b + 7 \, b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + {\left(3 \, a^{2} - 10 \, a b + 7 \, b^{2}\right)} \sinh\left(d x + c\right)^{7} + {\left(11 \, a^{2} - 26 \, a b + 15 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + {\left(21 \, {\left(3 \, a^{2} - 10 \, a b + 7 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 11 \, a^{2} - 26 \, a b + 15 \, b^{2}\right)} \sinh\left(d x + c\right)^{5} + 5 \, {\left(7 \, {\left(3 \, a^{2} - 10 \, a b + 7 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(11 \, a^{2} - 26 \, a b + 15 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} - {\left(11 \, a^{2} - 26 \, a b + 15 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(35 \, {\left(3 \, a^{2} - 10 \, a b + 7 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 10 \, {\left(11 \, a^{2} - 26 \, a b + 15 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 11 \, a^{2} + 26 \, a b - 15 \, b^{2}\right)} \sinh\left(d x + c\right)^{3} + {\left(21 \, {\left(3 \, a^{2} - 10 \, a b + 7 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(11 \, a^{2} - 26 \, a b + 15 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(11 \, a^{2} - 26 \, a b + 15 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 4 \, {\left(b^{2} \cosh\left(d x + c\right)^{8} + 8 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + b^{2} \sinh\left(d x + c\right)^{8} + 4 \, b^{2} \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, b^{2} \cosh\left(d x + c\right)^{2} + b^{2}\right)} \sinh\left(d x + c\right)^{6} + 6 \, b^{2} \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, b^{2} \cosh\left(d x + c\right)^{3} + 3 \, b^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, b^{2} \cosh\left(d x + c\right)^{4} + 30 \, b^{2} \cosh\left(d x + c\right)^{2} + 3 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, b^{2} \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, b^{2} \cosh\left(d x + c\right)^{5} + 10 \, b^{2} \cosh\left(d x + c\right)^{3} + 3 \, b^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, b^{2} \cosh\left(d x + c\right)^{6} + 15 \, b^{2} \cosh\left(d x + c\right)^{4} + 9 \, b^{2} \cosh\left(d x + c\right)^{2} + b^{2}\right)} \sinh\left(d x + c\right)^{2} + b^{2} + 8 \, {\left(b^{2} \cosh\left(d x + c\right)^{7} + 3 \, b^{2} \cosh\left(d x + c\right)^{5} + 3 \, b^{2} \cosh\left(d x + c\right)^{3} + b^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{b}{a}} \arctan\left(\frac{1}{2} \, \sqrt{\frac{b}{a}} {\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right)}\right) - 4 \, {\left(b^{2} \cosh\left(d x + c\right)^{8} + 8 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + b^{2} \sinh\left(d x + c\right)^{8} + 4 \, b^{2} \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, b^{2} \cosh\left(d x + c\right)^{2} + b^{2}\right)} \sinh\left(d x + c\right)^{6} + 6 \, b^{2} \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, b^{2} \cosh\left(d x + c\right)^{3} + 3 \, b^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, b^{2} \cosh\left(d x + c\right)^{4} + 30 \, b^{2} \cosh\left(d x + c\right)^{2} + 3 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, b^{2} \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, b^{2} \cosh\left(d x + c\right)^{5} + 10 \, b^{2} \cosh\left(d x + c\right)^{3} + 3 \, b^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, b^{2} \cosh\left(d x + c\right)^{6} + 15 \, b^{2} \cosh\left(d x + c\right)^{4} + 9 \, b^{2} \cosh\left(d x + c\right)^{2} + b^{2}\right)} \sinh\left(d x + c\right)^{2} + b^{2} + 8 \, {\left(b^{2} \cosh\left(d x + c\right)^{7} + 3 \, b^{2} \cosh\left(d x + c\right)^{5} + 3 \, b^{2} \cosh\left(d x + c\right)^{3} + b^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{b}{a}} \arctan\left(\frac{{\left(b \cosh\left(d x + c\right)^{3} + 3 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{3} + {\left(4 \, a - b\right)} \cosh\left(d x + c\right) + {\left(3 \, b \cosh\left(d x + c\right)^{2} + 4 \, a - b\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{b}{a}}}{2 \, b}\right) + {\left({\left(3 \, a^{2} - 10 \, a b + 15 \, b^{2}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(3 \, a^{2} - 10 \, a b + 15 \, b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(3 \, a^{2} - 10 \, a b + 15 \, b^{2}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(3 \, a^{2} - 10 \, a b + 15 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(3 \, a^{2} - 10 \, a b + 15 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 3 \, a^{2} - 10 \, a b + 15 \, b^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(3 \, a^{2} - 10 \, a b + 15 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(3 \, a^{2} - 10 \, a b + 15 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 6 \, {\left(3 \, a^{2} - 10 \, a b + 15 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(3 \, a^{2} - 10 \, a b + 15 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 30 \, {\left(3 \, a^{2} - 10 \, a b + 15 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 9 \, a^{2} - 30 \, a b + 45 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(3 \, a^{2} - 10 \, a b + 15 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(3 \, a^{2} - 10 \, a b + 15 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(3 \, a^{2} - 10 \, a b + 15 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(3 \, a^{2} - 10 \, a b + 15 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(3 \, a^{2} - 10 \, a b + 15 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(3 \, a^{2} - 10 \, a b + 15 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 9 \, {\left(3 \, a^{2} - 10 \, a b + 15 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 3 \, a^{2} - 10 \, a b + 15 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} + 3 \, a^{2} - 10 \, a b + 15 \, b^{2} + 8 \, {\left({\left(3 \, a^{2} - 10 \, a b + 15 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(3 \, a^{2} - 10 \, a b + 15 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 3 \, {\left(3 \, a^{2} - 10 \, a b + 15 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{2} - 10 \, a b + 15 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \arctan\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) - {\left(3 \, a^{2} - 10 \, a b + 7 \, b^{2}\right)} \cosh\left(d x + c\right) + {\left(7 \, {\left(3 \, a^{2} - 10 \, a b + 7 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 5 \, {\left(11 \, a^{2} - 26 \, a b + 15 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} - 3 \, {\left(11 \, a^{2} - 26 \, a b + 15 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 3 \, a^{2} + 10 \, a b - 7 \, b^{2}\right)} \sinh\left(d x + c\right)}{4 \, {\left({\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 6 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 30 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{2} + 3 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 9 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d + 8 \, {\left({\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{5} + 3 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[1/4*((3*a^2 - 10*a*b + 7*b^2)*cosh(d*x + c)^7 + 7*(3*a^2 - 10*a*b + 7*b^2)*cosh(d*x + c)*sinh(d*x + c)^6 + (3*a^2 - 10*a*b + 7*b^2)*sinh(d*x + c)^7 + (11*a^2 - 26*a*b + 15*b^2)*cosh(d*x + c)^5 + (21*(3*a^2 - 10*a*b + 7*b^2)*cosh(d*x + c)^2 + 11*a^2 - 26*a*b + 15*b^2)*sinh(d*x + c)^5 + 5*(7*(3*a^2 - 10*a*b + 7*b^2)*cosh(d*x + c)^3 + (11*a^2 - 26*a*b + 15*b^2)*cosh(d*x + c))*sinh(d*x + c)^4 - (11*a^2 - 26*a*b + 15*b^2)*cosh(d*x + c)^3 + (35*(3*a^2 - 10*a*b + 7*b^2)*cosh(d*x + c)^4 + 10*(11*a^2 - 26*a*b + 15*b^2)*cosh(d*x + c)^2 - 11*a^2 + 26*a*b - 15*b^2)*sinh(d*x + c)^3 + (21*(3*a^2 - 10*a*b + 7*b^2)*cosh(d*x + c)^5 + 10*(11*a^2 - 26*a*b + 15*b^2)*cosh(d*x + c)^3 - 3*(11*a^2 - 26*a*b + 15*b^2)*cosh(d*x + c))*sinh(d*x + c)^2 - 2*(b^2*cosh(d*x + c)^8 + 8*b^2*cosh(d*x + c)*sinh(d*x + c)^7 + b^2*sinh(d*x + c)^8 + 4*b^2*cosh(d*x + c)^6 + 4*(7*b^2*cosh(d*x + c)^2 + b^2)*sinh(d*x + c)^6 + 6*b^2*cosh(d*x + c)^4 + 8*(7*b^2*cosh(d*x + c)^3 + 3*b^2*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*b^2*cosh(d*x + c)^4 + 30*b^2*cosh(d*x + c)^2 + 3*b^2)*sinh(d*x + c)^4 + 4*b^2*cosh(d*x + c)^2 + 8*(7*b^2*cosh(d*x + c)^5 + 10*b^2*cosh(d*x + c)^3 + 3*b^2*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*b^2*cosh(d*x + c)^6 + 15*b^2*cosh(d*x + c)^4 + 9*b^2*cosh(d*x + c)^2 + b^2)*sinh(d*x + c)^2 + b^2 + 8*(b^2*cosh(d*x + c)^7 + 3*b^2*cosh(d*x + c)^5 + 3*b^2*cosh(d*x + c)^3 + b^2*cosh(d*x + c))*sinh(d*x + c))*sqrt(-b/a)*log((b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 - 2*(2*a + b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 - 2*a - b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 - (2*a + b)*cosh(d*x + c))*sinh(d*x + c) + 4*(a*cosh(d*x + c)^3 + 3*a*cosh(d*x + c)*sinh(d*x + c)^2 + a*sinh(d*x + c)^3 - a*cosh(d*x + c) + (3*a*cosh(d*x + c)^2 - a)*sinh(d*x + c))*sqrt(-b/a) + b)/(b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 + 2*(2*a - b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 + 2*a - b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 + (2*a - b)*cosh(d*x + c))*sinh(d*x + c) + b)) + ((3*a^2 - 10*a*b + 15*b^2)*cosh(d*x + c)^8 + 8*(3*a^2 - 10*a*b + 15*b^2)*cosh(d*x + c)*sinh(d*x + c)^7 + (3*a^2 - 10*a*b + 15*b^2)*sinh(d*x + c)^8 + 4*(3*a^2 - 10*a*b + 15*b^2)*cosh(d*x + c)^6 + 4*(7*(3*a^2 - 10*a*b + 15*b^2)*cosh(d*x + c)^2 + 3*a^2 - 10*a*b + 15*b^2)*sinh(d*x + c)^6 + 8*(7*(3*a^2 - 10*a*b + 15*b^2)*cosh(d*x + c)^3 + 3*(3*a^2 - 10*a*b + 15*b^2)*cosh(d*x + c))*sinh(d*x + c)^5 + 6*(3*a^2 - 10*a*b + 15*b^2)*cosh(d*x + c)^4 + 2*(35*(3*a^2 - 10*a*b + 15*b^2)*cosh(d*x + c)^4 + 30*(3*a^2 - 10*a*b + 15*b^2)*cosh(d*x + c)^2 + 9*a^2 - 30*a*b + 45*b^2)*sinh(d*x + c)^4 + 8*(7*(3*a^2 - 10*a*b + 15*b^2)*cosh(d*x + c)^5 + 10*(3*a^2 - 10*a*b + 15*b^2)*cosh(d*x + c)^3 + 3*(3*a^2 - 10*a*b + 15*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(3*a^2 - 10*a*b + 15*b^2)*cosh(d*x + c)^2 + 4*(7*(3*a^2 - 10*a*b + 15*b^2)*cosh(d*x + c)^6 + 15*(3*a^2 - 10*a*b + 15*b^2)*cosh(d*x + c)^4 + 9*(3*a^2 - 10*a*b + 15*b^2)*cosh(d*x + c)^2 + 3*a^2 - 10*a*b + 15*b^2)*sinh(d*x + c)^2 + 3*a^2 - 10*a*b + 15*b^2 + 8*((3*a^2 - 10*a*b + 15*b^2)*cosh(d*x + c)^7 + 3*(3*a^2 - 10*a*b + 15*b^2)*cosh(d*x + c)^5 + 3*(3*a^2 - 10*a*b + 15*b^2)*cosh(d*x + c)^3 + (3*a^2 - 10*a*b + 15*b^2)*cosh(d*x + c))*sinh(d*x + c))*arctan(cosh(d*x + c) + sinh(d*x + c)) - (3*a^2 - 10*a*b + 7*b^2)*cosh(d*x + c) + (7*(3*a^2 - 10*a*b + 7*b^2)*cosh(d*x + c)^6 + 5*(11*a^2 - 26*a*b + 15*b^2)*cosh(d*x + c)^4 - 3*(11*a^2 - 26*a*b + 15*b^2)*cosh(d*x + c)^2 - 3*a^2 + 10*a*b - 7*b^2)*sinh(d*x + c))/((a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*cosh(d*x + c)^8 + 8*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*sinh(d*x + c)^8 + 4*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*cosh(d*x + c)^6 + 4*(7*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*cosh(d*x + c)^2 + (a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d)*sinh(d*x + c)^6 + 6*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*cosh(d*x + c)^4 + 8*(7*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*cosh(d*x + c)^3 + 3*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*cosh(d*x + c)^4 + 30*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*cosh(d*x + c)^2 + 3*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d)*sinh(d*x + c)^4 + 4*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*cosh(d*x + c)^2 + 8*(7*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*cosh(d*x + c)^5 + 10*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*cosh(d*x + c)^3 + 3*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*cosh(d*x + c)^6 + 15*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*cosh(d*x + c)^4 + 9*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*cosh(d*x + c)^2 + (a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d)*sinh(d*x + c)^2 + (a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d + 8*((a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*cosh(d*x + c)^7 + 3*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*cosh(d*x + c)^5 + 3*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*cosh(d*x + c)^3 + (a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*cosh(d*x + c))*sinh(d*x + c)), 1/4*((3*a^2 - 10*a*b + 7*b^2)*cosh(d*x + c)^7 + 7*(3*a^2 - 10*a*b + 7*b^2)*cosh(d*x + c)*sinh(d*x + c)^6 + (3*a^2 - 10*a*b + 7*b^2)*sinh(d*x + c)^7 + (11*a^2 - 26*a*b + 15*b^2)*cosh(d*x + c)^5 + (21*(3*a^2 - 10*a*b + 7*b^2)*cosh(d*x + c)^2 + 11*a^2 - 26*a*b + 15*b^2)*sinh(d*x + c)^5 + 5*(7*(3*a^2 - 10*a*b + 7*b^2)*cosh(d*x + c)^3 + (11*a^2 - 26*a*b + 15*b^2)*cosh(d*x + c))*sinh(d*x + c)^4 - (11*a^2 - 26*a*b + 15*b^2)*cosh(d*x + c)^3 + (35*(3*a^2 - 10*a*b + 7*b^2)*cosh(d*x + c)^4 + 10*(11*a^2 - 26*a*b + 15*b^2)*cosh(d*x + c)^2 - 11*a^2 + 26*a*b - 15*b^2)*sinh(d*x + c)^3 + (21*(3*a^2 - 10*a*b + 7*b^2)*cosh(d*x + c)^5 + 10*(11*a^2 - 26*a*b + 15*b^2)*cosh(d*x + c)^3 - 3*(11*a^2 - 26*a*b + 15*b^2)*cosh(d*x + c))*sinh(d*x + c)^2 - 4*(b^2*cosh(d*x + c)^8 + 8*b^2*cosh(d*x + c)*sinh(d*x + c)^7 + b^2*sinh(d*x + c)^8 + 4*b^2*cosh(d*x + c)^6 + 4*(7*b^2*cosh(d*x + c)^2 + b^2)*sinh(d*x + c)^6 + 6*b^2*cosh(d*x + c)^4 + 8*(7*b^2*cosh(d*x + c)^3 + 3*b^2*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*b^2*cosh(d*x + c)^4 + 30*b^2*cosh(d*x + c)^2 + 3*b^2)*sinh(d*x + c)^4 + 4*b^2*cosh(d*x + c)^2 + 8*(7*b^2*cosh(d*x + c)^5 + 10*b^2*cosh(d*x + c)^3 + 3*b^2*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*b^2*cosh(d*x + c)^6 + 15*b^2*cosh(d*x + c)^4 + 9*b^2*cosh(d*x + c)^2 + b^2)*sinh(d*x + c)^2 + b^2 + 8*(b^2*cosh(d*x + c)^7 + 3*b^2*cosh(d*x + c)^5 + 3*b^2*cosh(d*x + c)^3 + b^2*cosh(d*x + c))*sinh(d*x + c))*sqrt(b/a)*arctan(1/2*sqrt(b/a)*(cosh(d*x + c) + sinh(d*x + c))) - 4*(b^2*cosh(d*x + c)^8 + 8*b^2*cosh(d*x + c)*sinh(d*x + c)^7 + b^2*sinh(d*x + c)^8 + 4*b^2*cosh(d*x + c)^6 + 4*(7*b^2*cosh(d*x + c)^2 + b^2)*sinh(d*x + c)^6 + 6*b^2*cosh(d*x + c)^4 + 8*(7*b^2*cosh(d*x + c)^3 + 3*b^2*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*b^2*cosh(d*x + c)^4 + 30*b^2*cosh(d*x + c)^2 + 3*b^2)*sinh(d*x + c)^4 + 4*b^2*cosh(d*x + c)^2 + 8*(7*b^2*cosh(d*x + c)^5 + 10*b^2*cosh(d*x + c)^3 + 3*b^2*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*b^2*cosh(d*x + c)^6 + 15*b^2*cosh(d*x + c)^4 + 9*b^2*cosh(d*x + c)^2 + b^2)*sinh(d*x + c)^2 + b^2 + 8*(b^2*cosh(d*x + c)^7 + 3*b^2*cosh(d*x + c)^5 + 3*b^2*cosh(d*x + c)^3 + b^2*cosh(d*x + c))*sinh(d*x + c))*sqrt(b/a)*arctan(1/2*(b*cosh(d*x + c)^3 + 3*b*cosh(d*x + c)*sinh(d*x + c)^2 + b*sinh(d*x + c)^3 + (4*a - b)*cosh(d*x + c) + (3*b*cosh(d*x + c)^2 + 4*a - b)*sinh(d*x + c))*sqrt(b/a)/b) + ((3*a^2 - 10*a*b + 15*b^2)*cosh(d*x + c)^8 + 8*(3*a^2 - 10*a*b + 15*b^2)*cosh(d*x + c)*sinh(d*x + c)^7 + (3*a^2 - 10*a*b + 15*b^2)*sinh(d*x + c)^8 + 4*(3*a^2 - 10*a*b + 15*b^2)*cosh(d*x + c)^6 + 4*(7*(3*a^2 - 10*a*b + 15*b^2)*cosh(d*x + c)^2 + 3*a^2 - 10*a*b + 15*b^2)*sinh(d*x + c)^6 + 8*(7*(3*a^2 - 10*a*b + 15*b^2)*cosh(d*x + c)^3 + 3*(3*a^2 - 10*a*b + 15*b^2)*cosh(d*x + c))*sinh(d*x + c)^5 + 6*(3*a^2 - 10*a*b + 15*b^2)*cosh(d*x + c)^4 + 2*(35*(3*a^2 - 10*a*b + 15*b^2)*cosh(d*x + c)^4 + 30*(3*a^2 - 10*a*b + 15*b^2)*cosh(d*x + c)^2 + 9*a^2 - 30*a*b + 45*b^2)*sinh(d*x + c)^4 + 8*(7*(3*a^2 - 10*a*b + 15*b^2)*cosh(d*x + c)^5 + 10*(3*a^2 - 10*a*b + 15*b^2)*cosh(d*x + c)^3 + 3*(3*a^2 - 10*a*b + 15*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(3*a^2 - 10*a*b + 15*b^2)*cosh(d*x + c)^2 + 4*(7*(3*a^2 - 10*a*b + 15*b^2)*cosh(d*x + c)^6 + 15*(3*a^2 - 10*a*b + 15*b^2)*cosh(d*x + c)^4 + 9*(3*a^2 - 10*a*b + 15*b^2)*cosh(d*x + c)^2 + 3*a^2 - 10*a*b + 15*b^2)*sinh(d*x + c)^2 + 3*a^2 - 10*a*b + 15*b^2 + 8*((3*a^2 - 10*a*b + 15*b^2)*cosh(d*x + c)^7 + 3*(3*a^2 - 10*a*b + 15*b^2)*cosh(d*x + c)^5 + 3*(3*a^2 - 10*a*b + 15*b^2)*cosh(d*x + c)^3 + (3*a^2 - 10*a*b + 15*b^2)*cosh(d*x + c))*sinh(d*x + c))*arctan(cosh(d*x + c) + sinh(d*x + c)) - (3*a^2 - 10*a*b + 7*b^2)*cosh(d*x + c) + (7*(3*a^2 - 10*a*b + 7*b^2)*cosh(d*x + c)^6 + 5*(11*a^2 - 26*a*b + 15*b^2)*cosh(d*x + c)^4 - 3*(11*a^2 - 26*a*b + 15*b^2)*cosh(d*x + c)^2 - 3*a^2 + 10*a*b - 7*b^2)*sinh(d*x + c))/((a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*cosh(d*x + c)^8 + 8*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*sinh(d*x + c)^8 + 4*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*cosh(d*x + c)^6 + 4*(7*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*cosh(d*x + c)^2 + (a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d)*sinh(d*x + c)^6 + 6*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*cosh(d*x + c)^4 + 8*(7*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*cosh(d*x + c)^3 + 3*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*cosh(d*x + c)^4 + 30*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*cosh(d*x + c)^2 + 3*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d)*sinh(d*x + c)^4 + 4*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*cosh(d*x + c)^2 + 8*(7*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*cosh(d*x + c)^5 + 10*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*cosh(d*x + c)^3 + 3*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*cosh(d*x + c)^6 + 15*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*cosh(d*x + c)^4 + 9*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*cosh(d*x + c)^2 + (a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d)*sinh(d*x + c)^2 + (a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d + 8*((a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*cosh(d*x + c)^7 + 3*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*cosh(d*x + c)^5 + 3*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*cosh(d*x + c)^3 + (a^3 - 3*a^2*b + 3*a*b^2 - b^3)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
328,1,6046,0,0.827040," ","integrate(sech(d*x+c)^6/(a+b*sinh(d*x+c)^2),x, algorithm=""fricas"")","\left[-\frac{60 \, {\left(a^{2} b^{2} - a b^{3}\right)} \cosh\left(d x + c\right)^{8} + 480 \, {\left(a^{2} b^{2} - a b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + 60 \, {\left(a^{2} b^{2} - a b^{3}\right)} \sinh\left(d x + c\right)^{8} - 120 \, {\left(a^{3} b - 4 \, a^{2} b^{2} + 3 \, a b^{3}\right)} \cosh\left(d x + c\right)^{6} - 120 \, {\left(a^{3} b - 4 \, a^{2} b^{2} + 3 \, a b^{3} - 14 \, {\left(a^{2} b^{2} - a b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 240 \, {\left(14 \, {\left(a^{2} b^{2} - a b^{3}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{3} b - 4 \, a^{2} b^{2} + 3 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 40 \, {\left(8 \, a^{4} - 31 \, a^{3} b + 47 \, a^{2} b^{2} - 24 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} + 40 \, {\left(105 \, {\left(a^{2} b^{2} - a b^{3}\right)} \cosh\left(d x + c\right)^{4} + 8 \, a^{4} - 31 \, a^{3} b + 47 \, a^{2} b^{2} - 24 \, a b^{3} - 45 \, {\left(a^{3} b - 4 \, a^{2} b^{2} + 3 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 32 \, a^{4} - 136 \, a^{3} b + 236 \, a^{2} b^{2} - 132 \, a b^{3} + 160 \, {\left(21 \, {\left(a^{2} b^{2} - a b^{3}\right)} \cosh\left(d x + c\right)^{5} - 15 \, {\left(a^{3} b - 4 \, a^{2} b^{2} + 3 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{4} - 31 \, a^{3} b + 47 \, a^{2} b^{2} - 24 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 40 \, {\left(4 \, a^{4} - 17 \, a^{3} b + 28 \, a^{2} b^{2} - 15 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2} + 40 \, {\left(42 \, {\left(a^{2} b^{2} - a b^{3}\right)} \cosh\left(d x + c\right)^{6} - 45 \, {\left(a^{3} b - 4 \, a^{2} b^{2} + 3 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} + 4 \, a^{4} - 17 \, a^{3} b + 28 \, a^{2} b^{2} - 15 \, a b^{3} + 6 \, {\left(8 \, a^{4} - 31 \, a^{3} b + 47 \, a^{2} b^{2} - 24 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 15 \, {\left(b^{3} \cosh\left(d x + c\right)^{10} + 10 \, b^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + b^{3} \sinh\left(d x + c\right)^{10} + 5 \, b^{3} \cosh\left(d x + c\right)^{8} + 10 \, b^{3} \cosh\left(d x + c\right)^{6} + 5 \, {\left(9 \, b^{3} \cosh\left(d x + c\right)^{2} + b^{3}\right)} \sinh\left(d x + c\right)^{8} + 40 \, {\left(3 \, b^{3} \cosh\left(d x + c\right)^{3} + b^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 10 \, b^{3} \cosh\left(d x + c\right)^{4} + 10 \, {\left(21 \, b^{3} \cosh\left(d x + c\right)^{4} + 14 \, b^{3} \cosh\left(d x + c\right)^{2} + b^{3}\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(63 \, b^{3} \cosh\left(d x + c\right)^{5} + 70 \, b^{3} \cosh\left(d x + c\right)^{3} + 15 \, b^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 5 \, b^{3} \cosh\left(d x + c\right)^{2} + 10 \, {\left(21 \, b^{3} \cosh\left(d x + c\right)^{6} + 35 \, b^{3} \cosh\left(d x + c\right)^{4} + 15 \, b^{3} \cosh\left(d x + c\right)^{2} + b^{3}\right)} \sinh\left(d x + c\right)^{4} + 40 \, {\left(3 \, b^{3} \cosh\left(d x + c\right)^{7} + 7 \, b^{3} \cosh\left(d x + c\right)^{5} + 5 \, b^{3} \cosh\left(d x + c\right)^{3} + b^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + b^{3} + 5 \, {\left(9 \, b^{3} \cosh\left(d x + c\right)^{8} + 28 \, b^{3} \cosh\left(d x + c\right)^{6} + 30 \, b^{3} \cosh\left(d x + c\right)^{4} + 12 \, b^{3} \cosh\left(d x + c\right)^{2} + b^{3}\right)} \sinh\left(d x + c\right)^{2} + 10 \, {\left(b^{3} \cosh\left(d x + c\right)^{9} + 4 \, b^{3} \cosh\left(d x + c\right)^{7} + 6 \, b^{3} \cosh\left(d x + c\right)^{5} + 4 \, b^{3} \cosh\left(d x + c\right)^{3} + b^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{a^{2} - a b} \log\left(\frac{b^{2} \cosh\left(d x + c\right)^{4} + 4 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{2} \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(d x + c\right)^{2} + 2 \, a b - b^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, a^{2} - 8 \, a b + b^{2} + 4 \, {\left(b^{2} \cosh\left(d x + c\right)^{3} + {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) - 4 \, {\left(b \cosh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b \sinh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sqrt{a^{2} - a b}}{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b}\right) + 80 \, {\left(6 \, {\left(a^{2} b^{2} - a b^{3}\right)} \cosh\left(d x + c\right)^{7} - 9 \, {\left(a^{3} b - 4 \, a^{2} b^{2} + 3 \, a b^{3}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(8 \, a^{4} - 31 \, a^{3} b + 47 \, a^{2} b^{2} - 24 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(4 \, a^{4} - 17 \, a^{3} b + 28 \, a^{2} b^{2} - 15 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{30 \, {\left({\left(a^{5} - 4 \, a^{4} b + 6 \, a^{3} b^{2} - 4 \, a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)^{10} + 10 \, {\left(a^{5} - 4 \, a^{4} b + 6 \, a^{3} b^{2} - 4 \, a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + {\left(a^{5} - 4 \, a^{4} b + 6 \, a^{3} b^{2} - 4 \, a^{2} b^{3} + a b^{4}\right)} d \sinh\left(d x + c\right)^{10} + 5 \, {\left(a^{5} - 4 \, a^{4} b + 6 \, a^{3} b^{2} - 4 \, a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)^{8} + 5 \, {\left(9 \, {\left(a^{5} - 4 \, a^{4} b + 6 \, a^{3} b^{2} - 4 \, a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{5} - 4 \, a^{4} b + 6 \, a^{3} b^{2} - 4 \, a^{2} b^{3} + a b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{8} + 10 \, {\left(a^{5} - 4 \, a^{4} b + 6 \, a^{3} b^{2} - 4 \, a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)^{6} + 40 \, {\left(3 \, {\left(a^{5} - 4 \, a^{4} b + 6 \, a^{3} b^{2} - 4 \, a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{5} - 4 \, a^{4} b + 6 \, a^{3} b^{2} - 4 \, a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 10 \, {\left(21 \, {\left(a^{5} - 4 \, a^{4} b + 6 \, a^{3} b^{2} - 4 \, a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 14 \, {\left(a^{5} - 4 \, a^{4} b + 6 \, a^{3} b^{2} - 4 \, a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{5} - 4 \, a^{4} b + 6 \, a^{3} b^{2} - 4 \, a^{2} b^{3} + a b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 10 \, {\left(a^{5} - 4 \, a^{4} b + 6 \, a^{3} b^{2} - 4 \, a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(63 \, {\left(a^{5} - 4 \, a^{4} b + 6 \, a^{3} b^{2} - 4 \, a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)^{5} + 70 \, {\left(a^{5} - 4 \, a^{4} b + 6 \, a^{3} b^{2} - 4 \, a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)^{3} + 15 \, {\left(a^{5} - 4 \, a^{4} b + 6 \, a^{3} b^{2} - 4 \, a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 10 \, {\left(21 \, {\left(a^{5} - 4 \, a^{4} b + 6 \, a^{3} b^{2} - 4 \, a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)^{6} + 35 \, {\left(a^{5} - 4 \, a^{4} b + 6 \, a^{3} b^{2} - 4 \, a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 15 \, {\left(a^{5} - 4 \, a^{4} b + 6 \, a^{3} b^{2} - 4 \, a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{5} - 4 \, a^{4} b + 6 \, a^{3} b^{2} - 4 \, a^{2} b^{3} + a b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 5 \, {\left(a^{5} - 4 \, a^{4} b + 6 \, a^{3} b^{2} - 4 \, a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)^{2} + 40 \, {\left(3 \, {\left(a^{5} - 4 \, a^{4} b + 6 \, a^{3} b^{2} - 4 \, a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)^{7} + 7 \, {\left(a^{5} - 4 \, a^{4} b + 6 \, a^{3} b^{2} - 4 \, a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)^{5} + 5 \, {\left(a^{5} - 4 \, a^{4} b + 6 \, a^{3} b^{2} - 4 \, a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{5} - 4 \, a^{4} b + 6 \, a^{3} b^{2} - 4 \, a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 5 \, {\left(9 \, {\left(a^{5} - 4 \, a^{4} b + 6 \, a^{3} b^{2} - 4 \, a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)^{8} + 28 \, {\left(a^{5} - 4 \, a^{4} b + 6 \, a^{3} b^{2} - 4 \, a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)^{6} + 30 \, {\left(a^{5} - 4 \, a^{4} b + 6 \, a^{3} b^{2} - 4 \, a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 12 \, {\left(a^{5} - 4 \, a^{4} b + 6 \, a^{3} b^{2} - 4 \, a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{5} - 4 \, a^{4} b + 6 \, a^{3} b^{2} - 4 \, a^{2} b^{3} + a b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{5} - 4 \, a^{4} b + 6 \, a^{3} b^{2} - 4 \, a^{2} b^{3} + a b^{4}\right)} d + 10 \, {\left({\left(a^{5} - 4 \, a^{4} b + 6 \, a^{3} b^{2} - 4 \, a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)^{9} + 4 \, {\left(a^{5} - 4 \, a^{4} b + 6 \, a^{3} b^{2} - 4 \, a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)^{7} + 6 \, {\left(a^{5} - 4 \, a^{4} b + 6 \, a^{3} b^{2} - 4 \, a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)^{5} + 4 \, {\left(a^{5} - 4 \, a^{4} b + 6 \, a^{3} b^{2} - 4 \, a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{5} - 4 \, a^{4} b + 6 \, a^{3} b^{2} - 4 \, a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}, -\frac{30 \, {\left(a^{2} b^{2} - a b^{3}\right)} \cosh\left(d x + c\right)^{8} + 240 \, {\left(a^{2} b^{2} - a b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + 30 \, {\left(a^{2} b^{2} - a b^{3}\right)} \sinh\left(d x + c\right)^{8} - 60 \, {\left(a^{3} b - 4 \, a^{2} b^{2} + 3 \, a b^{3}\right)} \cosh\left(d x + c\right)^{6} - 60 \, {\left(a^{3} b - 4 \, a^{2} b^{2} + 3 \, a b^{3} - 14 \, {\left(a^{2} b^{2} - a b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 120 \, {\left(14 \, {\left(a^{2} b^{2} - a b^{3}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{3} b - 4 \, a^{2} b^{2} + 3 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 20 \, {\left(8 \, a^{4} - 31 \, a^{3} b + 47 \, a^{2} b^{2} - 24 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} + 20 \, {\left(105 \, {\left(a^{2} b^{2} - a b^{3}\right)} \cosh\left(d x + c\right)^{4} + 8 \, a^{4} - 31 \, a^{3} b + 47 \, a^{2} b^{2} - 24 \, a b^{3} - 45 \, {\left(a^{3} b - 4 \, a^{2} b^{2} + 3 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 16 \, a^{4} - 68 \, a^{3} b + 118 \, a^{2} b^{2} - 66 \, a b^{3} + 80 \, {\left(21 \, {\left(a^{2} b^{2} - a b^{3}\right)} \cosh\left(d x + c\right)^{5} - 15 \, {\left(a^{3} b - 4 \, a^{2} b^{2} + 3 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{4} - 31 \, a^{3} b + 47 \, a^{2} b^{2} - 24 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 20 \, {\left(4 \, a^{4} - 17 \, a^{3} b + 28 \, a^{2} b^{2} - 15 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2} + 20 \, {\left(42 \, {\left(a^{2} b^{2} - a b^{3}\right)} \cosh\left(d x + c\right)^{6} - 45 \, {\left(a^{3} b - 4 \, a^{2} b^{2} + 3 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} + 4 \, a^{4} - 17 \, a^{3} b + 28 \, a^{2} b^{2} - 15 \, a b^{3} + 6 \, {\left(8 \, a^{4} - 31 \, a^{3} b + 47 \, a^{2} b^{2} - 24 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} - 15 \, {\left(b^{3} \cosh\left(d x + c\right)^{10} + 10 \, b^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + b^{3} \sinh\left(d x + c\right)^{10} + 5 \, b^{3} \cosh\left(d x + c\right)^{8} + 10 \, b^{3} \cosh\left(d x + c\right)^{6} + 5 \, {\left(9 \, b^{3} \cosh\left(d x + c\right)^{2} + b^{3}\right)} \sinh\left(d x + c\right)^{8} + 40 \, {\left(3 \, b^{3} \cosh\left(d x + c\right)^{3} + b^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 10 \, b^{3} \cosh\left(d x + c\right)^{4} + 10 \, {\left(21 \, b^{3} \cosh\left(d x + c\right)^{4} + 14 \, b^{3} \cosh\left(d x + c\right)^{2} + b^{3}\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(63 \, b^{3} \cosh\left(d x + c\right)^{5} + 70 \, b^{3} \cosh\left(d x + c\right)^{3} + 15 \, b^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 5 \, b^{3} \cosh\left(d x + c\right)^{2} + 10 \, {\left(21 \, b^{3} \cosh\left(d x + c\right)^{6} + 35 \, b^{3} \cosh\left(d x + c\right)^{4} + 15 \, b^{3} \cosh\left(d x + c\right)^{2} + b^{3}\right)} \sinh\left(d x + c\right)^{4} + 40 \, {\left(3 \, b^{3} \cosh\left(d x + c\right)^{7} + 7 \, b^{3} \cosh\left(d x + c\right)^{5} + 5 \, b^{3} \cosh\left(d x + c\right)^{3} + b^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + b^{3} + 5 \, {\left(9 \, b^{3} \cosh\left(d x + c\right)^{8} + 28 \, b^{3} \cosh\left(d x + c\right)^{6} + 30 \, b^{3} \cosh\left(d x + c\right)^{4} + 12 \, b^{3} \cosh\left(d x + c\right)^{2} + b^{3}\right)} \sinh\left(d x + c\right)^{2} + 10 \, {\left(b^{3} \cosh\left(d x + c\right)^{9} + 4 \, b^{3} \cosh\left(d x + c\right)^{7} + 6 \, b^{3} \cosh\left(d x + c\right)^{5} + 4 \, b^{3} \cosh\left(d x + c\right)^{3} + b^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-a^{2} + a b} \arctan\left(-\frac{{\left(b \cosh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b \sinh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sqrt{-a^{2} + a b}}{2 \, {\left(a^{2} - a b\right)}}\right) + 40 \, {\left(6 \, {\left(a^{2} b^{2} - a b^{3}\right)} \cosh\left(d x + c\right)^{7} - 9 \, {\left(a^{3} b - 4 \, a^{2} b^{2} + 3 \, a b^{3}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(8 \, a^{4} - 31 \, a^{3} b + 47 \, a^{2} b^{2} - 24 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(4 \, a^{4} - 17 \, a^{3} b + 28 \, a^{2} b^{2} - 15 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{15 \, {\left({\left(a^{5} - 4 \, a^{4} b + 6 \, a^{3} b^{2} - 4 \, a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)^{10} + 10 \, {\left(a^{5} - 4 \, a^{4} b + 6 \, a^{3} b^{2} - 4 \, a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + {\left(a^{5} - 4 \, a^{4} b + 6 \, a^{3} b^{2} - 4 \, a^{2} b^{3} + a b^{4}\right)} d \sinh\left(d x + c\right)^{10} + 5 \, {\left(a^{5} - 4 \, a^{4} b + 6 \, a^{3} b^{2} - 4 \, a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)^{8} + 5 \, {\left(9 \, {\left(a^{5} - 4 \, a^{4} b + 6 \, a^{3} b^{2} - 4 \, a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{5} - 4 \, a^{4} b + 6 \, a^{3} b^{2} - 4 \, a^{2} b^{3} + a b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{8} + 10 \, {\left(a^{5} - 4 \, a^{4} b + 6 \, a^{3} b^{2} - 4 \, a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)^{6} + 40 \, {\left(3 \, {\left(a^{5} - 4 \, a^{4} b + 6 \, a^{3} b^{2} - 4 \, a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{5} - 4 \, a^{4} b + 6 \, a^{3} b^{2} - 4 \, a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 10 \, {\left(21 \, {\left(a^{5} - 4 \, a^{4} b + 6 \, a^{3} b^{2} - 4 \, a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 14 \, {\left(a^{5} - 4 \, a^{4} b + 6 \, a^{3} b^{2} - 4 \, a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{5} - 4 \, a^{4} b + 6 \, a^{3} b^{2} - 4 \, a^{2} b^{3} + a b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 10 \, {\left(a^{5} - 4 \, a^{4} b + 6 \, a^{3} b^{2} - 4 \, a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(63 \, {\left(a^{5} - 4 \, a^{4} b + 6 \, a^{3} b^{2} - 4 \, a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)^{5} + 70 \, {\left(a^{5} - 4 \, a^{4} b + 6 \, a^{3} b^{2} - 4 \, a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)^{3} + 15 \, {\left(a^{5} - 4 \, a^{4} b + 6 \, a^{3} b^{2} - 4 \, a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 10 \, {\left(21 \, {\left(a^{5} - 4 \, a^{4} b + 6 \, a^{3} b^{2} - 4 \, a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)^{6} + 35 \, {\left(a^{5} - 4 \, a^{4} b + 6 \, a^{3} b^{2} - 4 \, a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 15 \, {\left(a^{5} - 4 \, a^{4} b + 6 \, a^{3} b^{2} - 4 \, a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{5} - 4 \, a^{4} b + 6 \, a^{3} b^{2} - 4 \, a^{2} b^{3} + a b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 5 \, {\left(a^{5} - 4 \, a^{4} b + 6 \, a^{3} b^{2} - 4 \, a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)^{2} + 40 \, {\left(3 \, {\left(a^{5} - 4 \, a^{4} b + 6 \, a^{3} b^{2} - 4 \, a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)^{7} + 7 \, {\left(a^{5} - 4 \, a^{4} b + 6 \, a^{3} b^{2} - 4 \, a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)^{5} + 5 \, {\left(a^{5} - 4 \, a^{4} b + 6 \, a^{3} b^{2} - 4 \, a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{5} - 4 \, a^{4} b + 6 \, a^{3} b^{2} - 4 \, a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 5 \, {\left(9 \, {\left(a^{5} - 4 \, a^{4} b + 6 \, a^{3} b^{2} - 4 \, a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)^{8} + 28 \, {\left(a^{5} - 4 \, a^{4} b + 6 \, a^{3} b^{2} - 4 \, a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)^{6} + 30 \, {\left(a^{5} - 4 \, a^{4} b + 6 \, a^{3} b^{2} - 4 \, a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 12 \, {\left(a^{5} - 4 \, a^{4} b + 6 \, a^{3} b^{2} - 4 \, a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{5} - 4 \, a^{4} b + 6 \, a^{3} b^{2} - 4 \, a^{2} b^{3} + a b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{5} - 4 \, a^{4} b + 6 \, a^{3} b^{2} - 4 \, a^{2} b^{3} + a b^{4}\right)} d + 10 \, {\left({\left(a^{5} - 4 \, a^{4} b + 6 \, a^{3} b^{2} - 4 \, a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)^{9} + 4 \, {\left(a^{5} - 4 \, a^{4} b + 6 \, a^{3} b^{2} - 4 \, a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)^{7} + 6 \, {\left(a^{5} - 4 \, a^{4} b + 6 \, a^{3} b^{2} - 4 \, a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)^{5} + 4 \, {\left(a^{5} - 4 \, a^{4} b + 6 \, a^{3} b^{2} - 4 \, a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{5} - 4 \, a^{4} b + 6 \, a^{3} b^{2} - 4 \, a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[-1/30*(60*(a^2*b^2 - a*b^3)*cosh(d*x + c)^8 + 480*(a^2*b^2 - a*b^3)*cosh(d*x + c)*sinh(d*x + c)^7 + 60*(a^2*b^2 - a*b^3)*sinh(d*x + c)^8 - 120*(a^3*b - 4*a^2*b^2 + 3*a*b^3)*cosh(d*x + c)^6 - 120*(a^3*b - 4*a^2*b^2 + 3*a*b^3 - 14*(a^2*b^2 - a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 240*(14*(a^2*b^2 - a*b^3)*cosh(d*x + c)^3 - 3*(a^3*b - 4*a^2*b^2 + 3*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^5 + 40*(8*a^4 - 31*a^3*b + 47*a^2*b^2 - 24*a*b^3)*cosh(d*x + c)^4 + 40*(105*(a^2*b^2 - a*b^3)*cosh(d*x + c)^4 + 8*a^4 - 31*a^3*b + 47*a^2*b^2 - 24*a*b^3 - 45*(a^3*b - 4*a^2*b^2 + 3*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 32*a^4 - 136*a^3*b + 236*a^2*b^2 - 132*a*b^3 + 160*(21*(a^2*b^2 - a*b^3)*cosh(d*x + c)^5 - 15*(a^3*b - 4*a^2*b^2 + 3*a*b^3)*cosh(d*x + c)^3 + (8*a^4 - 31*a^3*b + 47*a^2*b^2 - 24*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 + 40*(4*a^4 - 17*a^3*b + 28*a^2*b^2 - 15*a*b^3)*cosh(d*x + c)^2 + 40*(42*(a^2*b^2 - a*b^3)*cosh(d*x + c)^6 - 45*(a^3*b - 4*a^2*b^2 + 3*a*b^3)*cosh(d*x + c)^4 + 4*a^4 - 17*a^3*b + 28*a^2*b^2 - 15*a*b^3 + 6*(8*a^4 - 31*a^3*b + 47*a^2*b^2 - 24*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 15*(b^3*cosh(d*x + c)^10 + 10*b^3*cosh(d*x + c)*sinh(d*x + c)^9 + b^3*sinh(d*x + c)^10 + 5*b^3*cosh(d*x + c)^8 + 10*b^3*cosh(d*x + c)^6 + 5*(9*b^3*cosh(d*x + c)^2 + b^3)*sinh(d*x + c)^8 + 40*(3*b^3*cosh(d*x + c)^3 + b^3*cosh(d*x + c))*sinh(d*x + c)^7 + 10*b^3*cosh(d*x + c)^4 + 10*(21*b^3*cosh(d*x + c)^4 + 14*b^3*cosh(d*x + c)^2 + b^3)*sinh(d*x + c)^6 + 4*(63*b^3*cosh(d*x + c)^5 + 70*b^3*cosh(d*x + c)^3 + 15*b^3*cosh(d*x + c))*sinh(d*x + c)^5 + 5*b^3*cosh(d*x + c)^2 + 10*(21*b^3*cosh(d*x + c)^6 + 35*b^3*cosh(d*x + c)^4 + 15*b^3*cosh(d*x + c)^2 + b^3)*sinh(d*x + c)^4 + 40*(3*b^3*cosh(d*x + c)^7 + 7*b^3*cosh(d*x + c)^5 + 5*b^3*cosh(d*x + c)^3 + b^3*cosh(d*x + c))*sinh(d*x + c)^3 + b^3 + 5*(9*b^3*cosh(d*x + c)^8 + 28*b^3*cosh(d*x + c)^6 + 30*b^3*cosh(d*x + c)^4 + 12*b^3*cosh(d*x + c)^2 + b^3)*sinh(d*x + c)^2 + 10*(b^3*cosh(d*x + c)^9 + 4*b^3*cosh(d*x + c)^7 + 6*b^3*cosh(d*x + c)^5 + 4*b^3*cosh(d*x + c)^3 + b^3*cosh(d*x + c))*sinh(d*x + c))*sqrt(a^2 - a*b)*log((b^2*cosh(d*x + c)^4 + 4*b^2*cosh(d*x + c)*sinh(d*x + c)^3 + b^2*sinh(d*x + c)^4 + 2*(2*a*b - b^2)*cosh(d*x + c)^2 + 2*(3*b^2*cosh(d*x + c)^2 + 2*a*b - b^2)*sinh(d*x + c)^2 + 8*a^2 - 8*a*b + b^2 + 4*(b^2*cosh(d*x + c)^3 + (2*a*b - b^2)*cosh(d*x + c))*sinh(d*x + c) - 4*(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + 2*a - b)*sqrt(a^2 - a*b))/(b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 + 2*(2*a - b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 + 2*a - b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 + (2*a - b)*cosh(d*x + c))*sinh(d*x + c) + b)) + 80*(6*(a^2*b^2 - a*b^3)*cosh(d*x + c)^7 - 9*(a^3*b - 4*a^2*b^2 + 3*a*b^3)*cosh(d*x + c)^5 + 2*(8*a^4 - 31*a^3*b + 47*a^2*b^2 - 24*a*b^3)*cosh(d*x + c)^3 + (4*a^4 - 17*a^3*b + 28*a^2*b^2 - 15*a*b^3)*cosh(d*x + c))*sinh(d*x + c))/((a^5 - 4*a^4*b + 6*a^3*b^2 - 4*a^2*b^3 + a*b^4)*d*cosh(d*x + c)^10 + 10*(a^5 - 4*a^4*b + 6*a^3*b^2 - 4*a^2*b^3 + a*b^4)*d*cosh(d*x + c)*sinh(d*x + c)^9 + (a^5 - 4*a^4*b + 6*a^3*b^2 - 4*a^2*b^3 + a*b^4)*d*sinh(d*x + c)^10 + 5*(a^5 - 4*a^4*b + 6*a^3*b^2 - 4*a^2*b^3 + a*b^4)*d*cosh(d*x + c)^8 + 5*(9*(a^5 - 4*a^4*b + 6*a^3*b^2 - 4*a^2*b^3 + a*b^4)*d*cosh(d*x + c)^2 + (a^5 - 4*a^4*b + 6*a^3*b^2 - 4*a^2*b^3 + a*b^4)*d)*sinh(d*x + c)^8 + 10*(a^5 - 4*a^4*b + 6*a^3*b^2 - 4*a^2*b^3 + a*b^4)*d*cosh(d*x + c)^6 + 40*(3*(a^5 - 4*a^4*b + 6*a^3*b^2 - 4*a^2*b^3 + a*b^4)*d*cosh(d*x + c)^3 + (a^5 - 4*a^4*b + 6*a^3*b^2 - 4*a^2*b^3 + a*b^4)*d*cosh(d*x + c))*sinh(d*x + c)^7 + 10*(21*(a^5 - 4*a^4*b + 6*a^3*b^2 - 4*a^2*b^3 + a*b^4)*d*cosh(d*x + c)^4 + 14*(a^5 - 4*a^4*b + 6*a^3*b^2 - 4*a^2*b^3 + a*b^4)*d*cosh(d*x + c)^2 + (a^5 - 4*a^4*b + 6*a^3*b^2 - 4*a^2*b^3 + a*b^4)*d)*sinh(d*x + c)^6 + 10*(a^5 - 4*a^4*b + 6*a^3*b^2 - 4*a^2*b^3 + a*b^4)*d*cosh(d*x + c)^4 + 4*(63*(a^5 - 4*a^4*b + 6*a^3*b^2 - 4*a^2*b^3 + a*b^4)*d*cosh(d*x + c)^5 + 70*(a^5 - 4*a^4*b + 6*a^3*b^2 - 4*a^2*b^3 + a*b^4)*d*cosh(d*x + c)^3 + 15*(a^5 - 4*a^4*b + 6*a^3*b^2 - 4*a^2*b^3 + a*b^4)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 10*(21*(a^5 - 4*a^4*b + 6*a^3*b^2 - 4*a^2*b^3 + a*b^4)*d*cosh(d*x + c)^6 + 35*(a^5 - 4*a^4*b + 6*a^3*b^2 - 4*a^2*b^3 + a*b^4)*d*cosh(d*x + c)^4 + 15*(a^5 - 4*a^4*b + 6*a^3*b^2 - 4*a^2*b^3 + a*b^4)*d*cosh(d*x + c)^2 + (a^5 - 4*a^4*b + 6*a^3*b^2 - 4*a^2*b^3 + a*b^4)*d)*sinh(d*x + c)^4 + 5*(a^5 - 4*a^4*b + 6*a^3*b^2 - 4*a^2*b^3 + a*b^4)*d*cosh(d*x + c)^2 + 40*(3*(a^5 - 4*a^4*b + 6*a^3*b^2 - 4*a^2*b^3 + a*b^4)*d*cosh(d*x + c)^7 + 7*(a^5 - 4*a^4*b + 6*a^3*b^2 - 4*a^2*b^3 + a*b^4)*d*cosh(d*x + c)^5 + 5*(a^5 - 4*a^4*b + 6*a^3*b^2 - 4*a^2*b^3 + a*b^4)*d*cosh(d*x + c)^3 + (a^5 - 4*a^4*b + 6*a^3*b^2 - 4*a^2*b^3 + a*b^4)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 5*(9*(a^5 - 4*a^4*b + 6*a^3*b^2 - 4*a^2*b^3 + a*b^4)*d*cosh(d*x + c)^8 + 28*(a^5 - 4*a^4*b + 6*a^3*b^2 - 4*a^2*b^3 + a*b^4)*d*cosh(d*x + c)^6 + 30*(a^5 - 4*a^4*b + 6*a^3*b^2 - 4*a^2*b^3 + a*b^4)*d*cosh(d*x + c)^4 + 12*(a^5 - 4*a^4*b + 6*a^3*b^2 - 4*a^2*b^3 + a*b^4)*d*cosh(d*x + c)^2 + (a^5 - 4*a^4*b + 6*a^3*b^2 - 4*a^2*b^3 + a*b^4)*d)*sinh(d*x + c)^2 + (a^5 - 4*a^4*b + 6*a^3*b^2 - 4*a^2*b^3 + a*b^4)*d + 10*((a^5 - 4*a^4*b + 6*a^3*b^2 - 4*a^2*b^3 + a*b^4)*d*cosh(d*x + c)^9 + 4*(a^5 - 4*a^4*b + 6*a^3*b^2 - 4*a^2*b^3 + a*b^4)*d*cosh(d*x + c)^7 + 6*(a^5 - 4*a^4*b + 6*a^3*b^2 - 4*a^2*b^3 + a*b^4)*d*cosh(d*x + c)^5 + 4*(a^5 - 4*a^4*b + 6*a^3*b^2 - 4*a^2*b^3 + a*b^4)*d*cosh(d*x + c)^3 + (a^5 - 4*a^4*b + 6*a^3*b^2 - 4*a^2*b^3 + a*b^4)*d*cosh(d*x + c))*sinh(d*x + c)), -1/15*(30*(a^2*b^2 - a*b^3)*cosh(d*x + c)^8 + 240*(a^2*b^2 - a*b^3)*cosh(d*x + c)*sinh(d*x + c)^7 + 30*(a^2*b^2 - a*b^3)*sinh(d*x + c)^8 - 60*(a^3*b - 4*a^2*b^2 + 3*a*b^3)*cosh(d*x + c)^6 - 60*(a^3*b - 4*a^2*b^2 + 3*a*b^3 - 14*(a^2*b^2 - a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 120*(14*(a^2*b^2 - a*b^3)*cosh(d*x + c)^3 - 3*(a^3*b - 4*a^2*b^2 + 3*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^5 + 20*(8*a^4 - 31*a^3*b + 47*a^2*b^2 - 24*a*b^3)*cosh(d*x + c)^4 + 20*(105*(a^2*b^2 - a*b^3)*cosh(d*x + c)^4 + 8*a^4 - 31*a^3*b + 47*a^2*b^2 - 24*a*b^3 - 45*(a^3*b - 4*a^2*b^2 + 3*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 16*a^4 - 68*a^3*b + 118*a^2*b^2 - 66*a*b^3 + 80*(21*(a^2*b^2 - a*b^3)*cosh(d*x + c)^5 - 15*(a^3*b - 4*a^2*b^2 + 3*a*b^3)*cosh(d*x + c)^3 + (8*a^4 - 31*a^3*b + 47*a^2*b^2 - 24*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 + 20*(4*a^4 - 17*a^3*b + 28*a^2*b^2 - 15*a*b^3)*cosh(d*x + c)^2 + 20*(42*(a^2*b^2 - a*b^3)*cosh(d*x + c)^6 - 45*(a^3*b - 4*a^2*b^2 + 3*a*b^3)*cosh(d*x + c)^4 + 4*a^4 - 17*a^3*b + 28*a^2*b^2 - 15*a*b^3 + 6*(8*a^4 - 31*a^3*b + 47*a^2*b^2 - 24*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - 15*(b^3*cosh(d*x + c)^10 + 10*b^3*cosh(d*x + c)*sinh(d*x + c)^9 + b^3*sinh(d*x + c)^10 + 5*b^3*cosh(d*x + c)^8 + 10*b^3*cosh(d*x + c)^6 + 5*(9*b^3*cosh(d*x + c)^2 + b^3)*sinh(d*x + c)^8 + 40*(3*b^3*cosh(d*x + c)^3 + b^3*cosh(d*x + c))*sinh(d*x + c)^7 + 10*b^3*cosh(d*x + c)^4 + 10*(21*b^3*cosh(d*x + c)^4 + 14*b^3*cosh(d*x + c)^2 + b^3)*sinh(d*x + c)^6 + 4*(63*b^3*cosh(d*x + c)^5 + 70*b^3*cosh(d*x + c)^3 + 15*b^3*cosh(d*x + c))*sinh(d*x + c)^5 + 5*b^3*cosh(d*x + c)^2 + 10*(21*b^3*cosh(d*x + c)^6 + 35*b^3*cosh(d*x + c)^4 + 15*b^3*cosh(d*x + c)^2 + b^3)*sinh(d*x + c)^4 + 40*(3*b^3*cosh(d*x + c)^7 + 7*b^3*cosh(d*x + c)^5 + 5*b^3*cosh(d*x + c)^3 + b^3*cosh(d*x + c))*sinh(d*x + c)^3 + b^3 + 5*(9*b^3*cosh(d*x + c)^8 + 28*b^3*cosh(d*x + c)^6 + 30*b^3*cosh(d*x + c)^4 + 12*b^3*cosh(d*x + c)^2 + b^3)*sinh(d*x + c)^2 + 10*(b^3*cosh(d*x + c)^9 + 4*b^3*cosh(d*x + c)^7 + 6*b^3*cosh(d*x + c)^5 + 4*b^3*cosh(d*x + c)^3 + b^3*cosh(d*x + c))*sinh(d*x + c))*sqrt(-a^2 + a*b)*arctan(-1/2*(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + 2*a - b)*sqrt(-a^2 + a*b)/(a^2 - a*b)) + 40*(6*(a^2*b^2 - a*b^3)*cosh(d*x + c)^7 - 9*(a^3*b - 4*a^2*b^2 + 3*a*b^3)*cosh(d*x + c)^5 + 2*(8*a^4 - 31*a^3*b + 47*a^2*b^2 - 24*a*b^3)*cosh(d*x + c)^3 + (4*a^4 - 17*a^3*b + 28*a^2*b^2 - 15*a*b^3)*cosh(d*x + c))*sinh(d*x + c))/((a^5 - 4*a^4*b + 6*a^3*b^2 - 4*a^2*b^3 + a*b^4)*d*cosh(d*x + c)^10 + 10*(a^5 - 4*a^4*b + 6*a^3*b^2 - 4*a^2*b^3 + a*b^4)*d*cosh(d*x + c)*sinh(d*x + c)^9 + (a^5 - 4*a^4*b + 6*a^3*b^2 - 4*a^2*b^3 + a*b^4)*d*sinh(d*x + c)^10 + 5*(a^5 - 4*a^4*b + 6*a^3*b^2 - 4*a^2*b^3 + a*b^4)*d*cosh(d*x + c)^8 + 5*(9*(a^5 - 4*a^4*b + 6*a^3*b^2 - 4*a^2*b^3 + a*b^4)*d*cosh(d*x + c)^2 + (a^5 - 4*a^4*b + 6*a^3*b^2 - 4*a^2*b^3 + a*b^4)*d)*sinh(d*x + c)^8 + 10*(a^5 - 4*a^4*b + 6*a^3*b^2 - 4*a^2*b^3 + a*b^4)*d*cosh(d*x + c)^6 + 40*(3*(a^5 - 4*a^4*b + 6*a^3*b^2 - 4*a^2*b^3 + a*b^4)*d*cosh(d*x + c)^3 + (a^5 - 4*a^4*b + 6*a^3*b^2 - 4*a^2*b^3 + a*b^4)*d*cosh(d*x + c))*sinh(d*x + c)^7 + 10*(21*(a^5 - 4*a^4*b + 6*a^3*b^2 - 4*a^2*b^3 + a*b^4)*d*cosh(d*x + c)^4 + 14*(a^5 - 4*a^4*b + 6*a^3*b^2 - 4*a^2*b^3 + a*b^4)*d*cosh(d*x + c)^2 + (a^5 - 4*a^4*b + 6*a^3*b^2 - 4*a^2*b^3 + a*b^4)*d)*sinh(d*x + c)^6 + 10*(a^5 - 4*a^4*b + 6*a^3*b^2 - 4*a^2*b^3 + a*b^4)*d*cosh(d*x + c)^4 + 4*(63*(a^5 - 4*a^4*b + 6*a^3*b^2 - 4*a^2*b^3 + a*b^4)*d*cosh(d*x + c)^5 + 70*(a^5 - 4*a^4*b + 6*a^3*b^2 - 4*a^2*b^3 + a*b^4)*d*cosh(d*x + c)^3 + 15*(a^5 - 4*a^4*b + 6*a^3*b^2 - 4*a^2*b^3 + a*b^4)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 10*(21*(a^5 - 4*a^4*b + 6*a^3*b^2 - 4*a^2*b^3 + a*b^4)*d*cosh(d*x + c)^6 + 35*(a^5 - 4*a^4*b + 6*a^3*b^2 - 4*a^2*b^3 + a*b^4)*d*cosh(d*x + c)^4 + 15*(a^5 - 4*a^4*b + 6*a^3*b^2 - 4*a^2*b^3 + a*b^4)*d*cosh(d*x + c)^2 + (a^5 - 4*a^4*b + 6*a^3*b^2 - 4*a^2*b^3 + a*b^4)*d)*sinh(d*x + c)^4 + 5*(a^5 - 4*a^4*b + 6*a^3*b^2 - 4*a^2*b^3 + a*b^4)*d*cosh(d*x + c)^2 + 40*(3*(a^5 - 4*a^4*b + 6*a^3*b^2 - 4*a^2*b^3 + a*b^4)*d*cosh(d*x + c)^7 + 7*(a^5 - 4*a^4*b + 6*a^3*b^2 - 4*a^2*b^3 + a*b^4)*d*cosh(d*x + c)^5 + 5*(a^5 - 4*a^4*b + 6*a^3*b^2 - 4*a^2*b^3 + a*b^4)*d*cosh(d*x + c)^3 + (a^5 - 4*a^4*b + 6*a^3*b^2 - 4*a^2*b^3 + a*b^4)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 5*(9*(a^5 - 4*a^4*b + 6*a^3*b^2 - 4*a^2*b^3 + a*b^4)*d*cosh(d*x + c)^8 + 28*(a^5 - 4*a^4*b + 6*a^3*b^2 - 4*a^2*b^3 + a*b^4)*d*cosh(d*x + c)^6 + 30*(a^5 - 4*a^4*b + 6*a^3*b^2 - 4*a^2*b^3 + a*b^4)*d*cosh(d*x + c)^4 + 12*(a^5 - 4*a^4*b + 6*a^3*b^2 - 4*a^2*b^3 + a*b^4)*d*cosh(d*x + c)^2 + (a^5 - 4*a^4*b + 6*a^3*b^2 - 4*a^2*b^3 + a*b^4)*d)*sinh(d*x + c)^2 + (a^5 - 4*a^4*b + 6*a^3*b^2 - 4*a^2*b^3 + a*b^4)*d + 10*((a^5 - 4*a^4*b + 6*a^3*b^2 - 4*a^2*b^3 + a*b^4)*d*cosh(d*x + c)^9 + 4*(a^5 - 4*a^4*b + 6*a^3*b^2 - 4*a^2*b^3 + a*b^4)*d*cosh(d*x + c)^7 + 6*(a^5 - 4*a^4*b + 6*a^3*b^2 - 4*a^2*b^3 + a*b^4)*d*cosh(d*x + c)^5 + 4*(a^5 - 4*a^4*b + 6*a^3*b^2 - 4*a^2*b^3 + a*b^4)*d*cosh(d*x + c)^3 + (a^5 - 4*a^4*b + 6*a^3*b^2 - 4*a^2*b^3 + a*b^4)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
329,1,3629,0,0.555311," ","integrate(cosh(d*x+c)^6/(a+b*sinh(d*x+c)^2)^2,x, algorithm=""fricas"")","\left[\frac{a b^{2} \cosh\left(d x + c\right)^{8} + 8 \, a b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + a b^{2} \sinh\left(d x + c\right)^{8} + 2 \, {\left(2 \, a^{2} b - a b^{2} - 2 \, {\left(4 \, a^{2} b - 5 \, a b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(14 \, a b^{2} \cosh\left(d x + c\right)^{2} + 2 \, a^{2} b - a b^{2} - 2 \, {\left(4 \, a^{2} b - 5 \, a b^{2}\right)} d x\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(14 \, a b^{2} \cosh\left(d x + c\right)^{3} + 3 \, {\left(2 \, a^{2} b - a b^{2} - 2 \, {\left(4 \, a^{2} b - 5 \, a b^{2}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 8 \, {\left(2 \, a^{3} - 5 \, a^{2} b + 4 \, a b^{2} - b^{3} + {\left(8 \, a^{3} - 14 \, a^{2} b + 5 \, a b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, a b^{2} \cosh\left(d x + c\right)^{4} - 8 \, a^{3} + 20 \, a^{2} b - 16 \, a b^{2} + 4 \, b^{3} - 4 \, {\left(8 \, a^{3} - 14 \, a^{2} b + 5 \, a b^{2}\right)} d x + 15 \, {\left(2 \, a^{2} b - a b^{2} - 2 \, {\left(4 \, a^{2} b - 5 \, a b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, a b^{2} \cosh\left(d x + c\right)^{5} + 5 \, {\left(2 \, a^{2} b - a b^{2} - 2 \, {\left(4 \, a^{2} b - 5 \, a b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - 4 \, {\left(2 \, a^{3} - 5 \, a^{2} b + 4 \, a b^{2} - b^{3} + {\left(8 \, a^{3} - 14 \, a^{2} b + 5 \, a b^{2}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - a b^{2} - 2 \, {\left(6 \, a^{2} b - 9 \, a b^{2} + 4 \, b^{3} + 2 \, {\left(4 \, a^{2} b - 5 \, a b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(14 \, a b^{2} \cosh\left(d x + c\right)^{6} + 15 \, {\left(2 \, a^{2} b - a b^{2} - 2 \, {\left(4 \, a^{2} b - 5 \, a b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{4} - 6 \, a^{2} b + 9 \, a b^{2} - 4 \, b^{3} - 2 \, {\left(4 \, a^{2} b - 5 \, a b^{2}\right)} d x - 24 \, {\left(2 \, a^{3} - 5 \, a^{2} b + 4 \, a b^{2} - b^{3} + {\left(8 \, a^{3} - 14 \, a^{2} b + 5 \, a b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} - 2 \, {\left({\left(4 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{6} + 6 \, {\left(4 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(4 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(8 \, a^{3} - 10 \, a^{2} b + a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{4} + {\left(16 \, a^{3} - 20 \, a^{2} b + 2 \, a b^{2} + 2 \, b^{3} + 15 \, {\left(4 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, {\left(4 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(8 \, a^{3} - 10 \, a^{2} b + a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(4 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{2} + {\left(15 \, {\left(4 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{4} + 4 \, a^{2} b - 3 \, a b^{2} - b^{3} + 12 \, {\left(8 \, a^{3} - 10 \, a^{2} b + a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(4 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{5} + 4 \, {\left(8 \, a^{3} - 10 \, a^{2} b + a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(4 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a - b}{a}} \log\left(\frac{b^{2} \cosh\left(d x + c\right)^{4} + 4 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{2} \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(d x + c\right)^{2} + 2 \, a b - b^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, a^{2} - 8 \, a b + b^{2} + 4 \, {\left(b^{2} \cosh\left(d x + c\right)^{3} + {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + 4 \, {\left(a b \cosh\left(d x + c\right)^{2} + 2 \, a b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a b \sinh\left(d x + c\right)^{2} + 2 \, a^{2} - a b\right)} \sqrt{\frac{a - b}{a}}}{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b}\right) + 4 \, {\left(2 \, a b^{2} \cosh\left(d x + c\right)^{7} + 3 \, {\left(2 \, a^{2} b - a b^{2} - 2 \, {\left(4 \, a^{2} b - 5 \, a b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{5} - 8 \, {\left(2 \, a^{3} - 5 \, a^{2} b + 4 \, a b^{2} - b^{3} + {\left(8 \, a^{3} - 14 \, a^{2} b + 5 \, a b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - {\left(6 \, a^{2} b - 9 \, a b^{2} + 4 \, b^{3} + 2 \, {\left(4 \, a^{2} b - 5 \, a b^{2}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{8 \, {\left(a b^{4} d \cosh\left(d x + c\right)^{6} + 6 \, a b^{4} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + a b^{4} d \sinh\left(d x + c\right)^{6} + a b^{4} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(2 \, a^{2} b^{3} - a b^{4}\right)} d \cosh\left(d x + c\right)^{4} + {\left(15 \, a b^{4} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(2 \, a^{2} b^{3} - a b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, a b^{4} d \cosh\left(d x + c\right)^{3} + 2 \, {\left(2 \, a^{2} b^{3} - a b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(15 \, a b^{4} d \cosh\left(d x + c\right)^{4} + a b^{4} d + 12 \, {\left(2 \, a^{2} b^{3} - a b^{4}\right)} d \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a b^{4} d \cosh\left(d x + c\right)^{5} + a b^{4} d \cosh\left(d x + c\right) + 4 \, {\left(2 \, a^{2} b^{3} - a b^{4}\right)} d \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right)\right)}}, \frac{a b^{2} \cosh\left(d x + c\right)^{8} + 8 \, a b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + a b^{2} \sinh\left(d x + c\right)^{8} + 2 \, {\left(2 \, a^{2} b - a b^{2} - 2 \, {\left(4 \, a^{2} b - 5 \, a b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(14 \, a b^{2} \cosh\left(d x + c\right)^{2} + 2 \, a^{2} b - a b^{2} - 2 \, {\left(4 \, a^{2} b - 5 \, a b^{2}\right)} d x\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(14 \, a b^{2} \cosh\left(d x + c\right)^{3} + 3 \, {\left(2 \, a^{2} b - a b^{2} - 2 \, {\left(4 \, a^{2} b - 5 \, a b^{2}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 8 \, {\left(2 \, a^{3} - 5 \, a^{2} b + 4 \, a b^{2} - b^{3} + {\left(8 \, a^{3} - 14 \, a^{2} b + 5 \, a b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, a b^{2} \cosh\left(d x + c\right)^{4} - 8 \, a^{3} + 20 \, a^{2} b - 16 \, a b^{2} + 4 \, b^{3} - 4 \, {\left(8 \, a^{3} - 14 \, a^{2} b + 5 \, a b^{2}\right)} d x + 15 \, {\left(2 \, a^{2} b - a b^{2} - 2 \, {\left(4 \, a^{2} b - 5 \, a b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, a b^{2} \cosh\left(d x + c\right)^{5} + 5 \, {\left(2 \, a^{2} b - a b^{2} - 2 \, {\left(4 \, a^{2} b - 5 \, a b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - 4 \, {\left(2 \, a^{3} - 5 \, a^{2} b + 4 \, a b^{2} - b^{3} + {\left(8 \, a^{3} - 14 \, a^{2} b + 5 \, a b^{2}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - a b^{2} - 2 \, {\left(6 \, a^{2} b - 9 \, a b^{2} + 4 \, b^{3} + 2 \, {\left(4 \, a^{2} b - 5 \, a b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(14 \, a b^{2} \cosh\left(d x + c\right)^{6} + 15 \, {\left(2 \, a^{2} b - a b^{2} - 2 \, {\left(4 \, a^{2} b - 5 \, a b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{4} - 6 \, a^{2} b + 9 \, a b^{2} - 4 \, b^{3} - 2 \, {\left(4 \, a^{2} b - 5 \, a b^{2}\right)} d x - 24 \, {\left(2 \, a^{3} - 5 \, a^{2} b + 4 \, a b^{2} - b^{3} + {\left(8 \, a^{3} - 14 \, a^{2} b + 5 \, a b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} - 4 \, {\left({\left(4 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{6} + 6 \, {\left(4 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(4 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(8 \, a^{3} - 10 \, a^{2} b + a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{4} + {\left(16 \, a^{3} - 20 \, a^{2} b + 2 \, a b^{2} + 2 \, b^{3} + 15 \, {\left(4 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, {\left(4 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(8 \, a^{3} - 10 \, a^{2} b + a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(4 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{2} + {\left(15 \, {\left(4 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{4} + 4 \, a^{2} b - 3 \, a b^{2} - b^{3} + 12 \, {\left(8 \, a^{3} - 10 \, a^{2} b + a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(4 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{5} + 4 \, {\left(8 \, a^{3} - 10 \, a^{2} b + a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(4 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{a - b}{a}} \arctan\left(-\frac{{\left(b \cosh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b \sinh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sqrt{-\frac{a - b}{a}}}{2 \, {\left(a - b\right)}}\right) + 4 \, {\left(2 \, a b^{2} \cosh\left(d x + c\right)^{7} + 3 \, {\left(2 \, a^{2} b - a b^{2} - 2 \, {\left(4 \, a^{2} b - 5 \, a b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{5} - 8 \, {\left(2 \, a^{3} - 5 \, a^{2} b + 4 \, a b^{2} - b^{3} + {\left(8 \, a^{3} - 14 \, a^{2} b + 5 \, a b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - {\left(6 \, a^{2} b - 9 \, a b^{2} + 4 \, b^{3} + 2 \, {\left(4 \, a^{2} b - 5 \, a b^{2}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{8 \, {\left(a b^{4} d \cosh\left(d x + c\right)^{6} + 6 \, a b^{4} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + a b^{4} d \sinh\left(d x + c\right)^{6} + a b^{4} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(2 \, a^{2} b^{3} - a b^{4}\right)} d \cosh\left(d x + c\right)^{4} + {\left(15 \, a b^{4} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(2 \, a^{2} b^{3} - a b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, a b^{4} d \cosh\left(d x + c\right)^{3} + 2 \, {\left(2 \, a^{2} b^{3} - a b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(15 \, a b^{4} d \cosh\left(d x + c\right)^{4} + a b^{4} d + 12 \, {\left(2 \, a^{2} b^{3} - a b^{4}\right)} d \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a b^{4} d \cosh\left(d x + c\right)^{5} + a b^{4} d \cosh\left(d x + c\right) + 4 \, {\left(2 \, a^{2} b^{3} - a b^{4}\right)} d \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[1/8*(a*b^2*cosh(d*x + c)^8 + 8*a*b^2*cosh(d*x + c)*sinh(d*x + c)^7 + a*b^2*sinh(d*x + c)^8 + 2*(2*a^2*b - a*b^2 - 2*(4*a^2*b - 5*a*b^2)*d*x)*cosh(d*x + c)^6 + 2*(14*a*b^2*cosh(d*x + c)^2 + 2*a^2*b - a*b^2 - 2*(4*a^2*b - 5*a*b^2)*d*x)*sinh(d*x + c)^6 + 4*(14*a*b^2*cosh(d*x + c)^3 + 3*(2*a^2*b - a*b^2 - 2*(4*a^2*b - 5*a*b^2)*d*x)*cosh(d*x + c))*sinh(d*x + c)^5 - 8*(2*a^3 - 5*a^2*b + 4*a*b^2 - b^3 + (8*a^3 - 14*a^2*b + 5*a*b^2)*d*x)*cosh(d*x + c)^4 + 2*(35*a*b^2*cosh(d*x + c)^4 - 8*a^3 + 20*a^2*b - 16*a*b^2 + 4*b^3 - 4*(8*a^3 - 14*a^2*b + 5*a*b^2)*d*x + 15*(2*a^2*b - a*b^2 - 2*(4*a^2*b - 5*a*b^2)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(7*a*b^2*cosh(d*x + c)^5 + 5*(2*a^2*b - a*b^2 - 2*(4*a^2*b - 5*a*b^2)*d*x)*cosh(d*x + c)^3 - 4*(2*a^3 - 5*a^2*b + 4*a*b^2 - b^3 + (8*a^3 - 14*a^2*b + 5*a*b^2)*d*x)*cosh(d*x + c))*sinh(d*x + c)^3 - a*b^2 - 2*(6*a^2*b - 9*a*b^2 + 4*b^3 + 2*(4*a^2*b - 5*a*b^2)*d*x)*cosh(d*x + c)^2 + 2*(14*a*b^2*cosh(d*x + c)^6 + 15*(2*a^2*b - a*b^2 - 2*(4*a^2*b - 5*a*b^2)*d*x)*cosh(d*x + c)^4 - 6*a^2*b + 9*a*b^2 - 4*b^3 - 2*(4*a^2*b - 5*a*b^2)*d*x - 24*(2*a^3 - 5*a^2*b + 4*a*b^2 - b^3 + (8*a^3 - 14*a^2*b + 5*a*b^2)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - 2*((4*a^2*b - 3*a*b^2 - b^3)*cosh(d*x + c)^6 + 6*(4*a^2*b - 3*a*b^2 - b^3)*cosh(d*x + c)*sinh(d*x + c)^5 + (4*a^2*b - 3*a*b^2 - b^3)*sinh(d*x + c)^6 + 2*(8*a^3 - 10*a^2*b + a*b^2 + b^3)*cosh(d*x + c)^4 + (16*a^3 - 20*a^2*b + 2*a*b^2 + 2*b^3 + 15*(4*a^2*b - 3*a*b^2 - b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 4*(5*(4*a^2*b - 3*a*b^2 - b^3)*cosh(d*x + c)^3 + 2*(8*a^3 - 10*a^2*b + a*b^2 + b^3)*cosh(d*x + c))*sinh(d*x + c)^3 + (4*a^2*b - 3*a*b^2 - b^3)*cosh(d*x + c)^2 + (15*(4*a^2*b - 3*a*b^2 - b^3)*cosh(d*x + c)^4 + 4*a^2*b - 3*a*b^2 - b^3 + 12*(8*a^3 - 10*a^2*b + a*b^2 + b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 2*(3*(4*a^2*b - 3*a*b^2 - b^3)*cosh(d*x + c)^5 + 4*(8*a^3 - 10*a^2*b + a*b^2 + b^3)*cosh(d*x + c)^3 + (4*a^2*b - 3*a*b^2 - b^3)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a - b)/a)*log((b^2*cosh(d*x + c)^4 + 4*b^2*cosh(d*x + c)*sinh(d*x + c)^3 + b^2*sinh(d*x + c)^4 + 2*(2*a*b - b^2)*cosh(d*x + c)^2 + 2*(3*b^2*cosh(d*x + c)^2 + 2*a*b - b^2)*sinh(d*x + c)^2 + 8*a^2 - 8*a*b + b^2 + 4*(b^2*cosh(d*x + c)^3 + (2*a*b - b^2)*cosh(d*x + c))*sinh(d*x + c) + 4*(a*b*cosh(d*x + c)^2 + 2*a*b*cosh(d*x + c)*sinh(d*x + c) + a*b*sinh(d*x + c)^2 + 2*a^2 - a*b)*sqrt((a - b)/a))/(b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 + 2*(2*a - b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 + 2*a - b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 + (2*a - b)*cosh(d*x + c))*sinh(d*x + c) + b)) + 4*(2*a*b^2*cosh(d*x + c)^7 + 3*(2*a^2*b - a*b^2 - 2*(4*a^2*b - 5*a*b^2)*d*x)*cosh(d*x + c)^5 - 8*(2*a^3 - 5*a^2*b + 4*a*b^2 - b^3 + (8*a^3 - 14*a^2*b + 5*a*b^2)*d*x)*cosh(d*x + c)^3 - (6*a^2*b - 9*a*b^2 + 4*b^3 + 2*(4*a^2*b - 5*a*b^2)*d*x)*cosh(d*x + c))*sinh(d*x + c))/(a*b^4*d*cosh(d*x + c)^6 + 6*a*b^4*d*cosh(d*x + c)*sinh(d*x + c)^5 + a*b^4*d*sinh(d*x + c)^6 + a*b^4*d*cosh(d*x + c)^2 + 2*(2*a^2*b^3 - a*b^4)*d*cosh(d*x + c)^4 + (15*a*b^4*d*cosh(d*x + c)^2 + 2*(2*a^2*b^3 - a*b^4)*d)*sinh(d*x + c)^4 + 4*(5*a*b^4*d*cosh(d*x + c)^3 + 2*(2*a^2*b^3 - a*b^4)*d*cosh(d*x + c))*sinh(d*x + c)^3 + (15*a*b^4*d*cosh(d*x + c)^4 + a*b^4*d + 12*(2*a^2*b^3 - a*b^4)*d*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 2*(3*a*b^4*d*cosh(d*x + c)^5 + a*b^4*d*cosh(d*x + c) + 4*(2*a^2*b^3 - a*b^4)*d*cosh(d*x + c)^3)*sinh(d*x + c)), 1/8*(a*b^2*cosh(d*x + c)^8 + 8*a*b^2*cosh(d*x + c)*sinh(d*x + c)^7 + a*b^2*sinh(d*x + c)^8 + 2*(2*a^2*b - a*b^2 - 2*(4*a^2*b - 5*a*b^2)*d*x)*cosh(d*x + c)^6 + 2*(14*a*b^2*cosh(d*x + c)^2 + 2*a^2*b - a*b^2 - 2*(4*a^2*b - 5*a*b^2)*d*x)*sinh(d*x + c)^6 + 4*(14*a*b^2*cosh(d*x + c)^3 + 3*(2*a^2*b - a*b^2 - 2*(4*a^2*b - 5*a*b^2)*d*x)*cosh(d*x + c))*sinh(d*x + c)^5 - 8*(2*a^3 - 5*a^2*b + 4*a*b^2 - b^3 + (8*a^3 - 14*a^2*b + 5*a*b^2)*d*x)*cosh(d*x + c)^4 + 2*(35*a*b^2*cosh(d*x + c)^4 - 8*a^3 + 20*a^2*b - 16*a*b^2 + 4*b^3 - 4*(8*a^3 - 14*a^2*b + 5*a*b^2)*d*x + 15*(2*a^2*b - a*b^2 - 2*(4*a^2*b - 5*a*b^2)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(7*a*b^2*cosh(d*x + c)^5 + 5*(2*a^2*b - a*b^2 - 2*(4*a^2*b - 5*a*b^2)*d*x)*cosh(d*x + c)^3 - 4*(2*a^3 - 5*a^2*b + 4*a*b^2 - b^3 + (8*a^3 - 14*a^2*b + 5*a*b^2)*d*x)*cosh(d*x + c))*sinh(d*x + c)^3 - a*b^2 - 2*(6*a^2*b - 9*a*b^2 + 4*b^3 + 2*(4*a^2*b - 5*a*b^2)*d*x)*cosh(d*x + c)^2 + 2*(14*a*b^2*cosh(d*x + c)^6 + 15*(2*a^2*b - a*b^2 - 2*(4*a^2*b - 5*a*b^2)*d*x)*cosh(d*x + c)^4 - 6*a^2*b + 9*a*b^2 - 4*b^3 - 2*(4*a^2*b - 5*a*b^2)*d*x - 24*(2*a^3 - 5*a^2*b + 4*a*b^2 - b^3 + (8*a^3 - 14*a^2*b + 5*a*b^2)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - 4*((4*a^2*b - 3*a*b^2 - b^3)*cosh(d*x + c)^6 + 6*(4*a^2*b - 3*a*b^2 - b^3)*cosh(d*x + c)*sinh(d*x + c)^5 + (4*a^2*b - 3*a*b^2 - b^3)*sinh(d*x + c)^6 + 2*(8*a^3 - 10*a^2*b + a*b^2 + b^3)*cosh(d*x + c)^4 + (16*a^3 - 20*a^2*b + 2*a*b^2 + 2*b^3 + 15*(4*a^2*b - 3*a*b^2 - b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 4*(5*(4*a^2*b - 3*a*b^2 - b^3)*cosh(d*x + c)^3 + 2*(8*a^3 - 10*a^2*b + a*b^2 + b^3)*cosh(d*x + c))*sinh(d*x + c)^3 + (4*a^2*b - 3*a*b^2 - b^3)*cosh(d*x + c)^2 + (15*(4*a^2*b - 3*a*b^2 - b^3)*cosh(d*x + c)^4 + 4*a^2*b - 3*a*b^2 - b^3 + 12*(8*a^3 - 10*a^2*b + a*b^2 + b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 2*(3*(4*a^2*b - 3*a*b^2 - b^3)*cosh(d*x + c)^5 + 4*(8*a^3 - 10*a^2*b + a*b^2 + b^3)*cosh(d*x + c)^3 + (4*a^2*b - 3*a*b^2 - b^3)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-(a - b)/a)*arctan(-1/2*(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + 2*a - b)*sqrt(-(a - b)/a)/(a - b)) + 4*(2*a*b^2*cosh(d*x + c)^7 + 3*(2*a^2*b - a*b^2 - 2*(4*a^2*b - 5*a*b^2)*d*x)*cosh(d*x + c)^5 - 8*(2*a^3 - 5*a^2*b + 4*a*b^2 - b^3 + (8*a^3 - 14*a^2*b + 5*a*b^2)*d*x)*cosh(d*x + c)^3 - (6*a^2*b - 9*a*b^2 + 4*b^3 + 2*(4*a^2*b - 5*a*b^2)*d*x)*cosh(d*x + c))*sinh(d*x + c))/(a*b^4*d*cosh(d*x + c)^6 + 6*a*b^4*d*cosh(d*x + c)*sinh(d*x + c)^5 + a*b^4*d*sinh(d*x + c)^6 + a*b^4*d*cosh(d*x + c)^2 + 2*(2*a^2*b^3 - a*b^4)*d*cosh(d*x + c)^4 + (15*a*b^4*d*cosh(d*x + c)^2 + 2*(2*a^2*b^3 - a*b^4)*d)*sinh(d*x + c)^4 + 4*(5*a*b^4*d*cosh(d*x + c)^3 + 2*(2*a^2*b^3 - a*b^4)*d*cosh(d*x + c))*sinh(d*x + c)^3 + (15*a*b^4*d*cosh(d*x + c)^4 + a*b^4*d + 12*(2*a^2*b^3 - a*b^4)*d*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 2*(3*a*b^4*d*cosh(d*x + c)^5 + a*b^4*d*cosh(d*x + c) + 4*(2*a^2*b^3 - a*b^4)*d*cosh(d*x + c)^3)*sinh(d*x + c))]","B",0
330,1,2739,0,0.747256," ","integrate(cosh(d*x+c)^5/(a+b*sinh(d*x+c)^2)^2,x, algorithm=""fricas"")","\left[\frac{2 \, a^{2} b^{2} \cosh\left(d x + c\right)^{6} + 12 \, a^{2} b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + 2 \, a^{2} b^{2} \sinh\left(d x + c\right)^{6} + 2 \, {\left(6 \, a^{3} b - 7 \, a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(15 \, a^{2} b^{2} \cosh\left(d x + c\right)^{2} + 6 \, a^{3} b - 7 \, a^{2} b^{2} + 2 \, a b^{3}\right)} \sinh\left(d x + c\right)^{4} - 2 \, a^{2} b^{2} + 8 \, {\left(5 \, a^{2} b^{2} \cosh\left(d x + c\right)^{3} + {\left(6 \, a^{3} b - 7 \, a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 2 \, {\left(6 \, a^{3} b - 7 \, a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(15 \, a^{2} b^{2} \cosh\left(d x + c\right)^{4} - 6 \, a^{3} b + 7 \, a^{2} b^{2} - 2 \, a b^{3} + 6 \, {\left(6 \, a^{3} b - 7 \, a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(3 \, a^{2} b - 2 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(3 \, a^{2} b - 2 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} + {\left(3 \, a^{2} b - 2 \, a b^{2} - b^{3}\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(6 \, a^{3} - 7 \, a^{2} b + b^{3}\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(6 \, a^{3} - 7 \, a^{2} b + b^{3} + 5 \, {\left(3 \, a^{2} b - 2 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(5 \, {\left(3 \, a^{2} b - 2 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(6 \, a^{3} - 7 \, a^{2} b + b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(3 \, a^{2} b - 2 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right) + {\left(5 \, {\left(3 \, a^{2} b - 2 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{4} + 3 \, a^{2} b - 2 \, a b^{2} - b^{3} + 6 \, {\left(6 \, a^{3} - 7 \, a^{2} b + b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)\right)} \sqrt{-a b} \log\left(\frac{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} - 2 \, {\left(2 \, a + b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} - 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} - {\left(2 \, a + b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) - 4 \, {\left(\cosh\left(d x + c\right)^{3} + 3 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{3} + {\left(3 \, \cosh\left(d x + c\right)^{2} - 1\right)} \sinh\left(d x + c\right) - \cosh\left(d x + c\right)\right)} \sqrt{-a b} + b}{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b}\right) + 4 \, {\left(3 \, a^{2} b^{2} \cosh\left(d x + c\right)^{5} + 2 \, {\left(6 \, a^{3} b - 7 \, a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} - {\left(6 \, a^{3} b - 7 \, a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{4 \, {\left(a^{2} b^{4} d \cosh\left(d x + c\right)^{5} + 5 \, a^{2} b^{4} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} + a^{2} b^{4} d \sinh\left(d x + c\right)^{5} + a^{2} b^{4} d \cosh\left(d x + c\right) + 2 \, {\left(2 \, a^{3} b^{3} - a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{3} + 2 \, {\left(5 \, a^{2} b^{4} d \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{3} b^{3} - a^{2} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(5 \, a^{2} b^{4} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(2 \, a^{3} b^{3} - a^{2} b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(5 \, a^{2} b^{4} d \cosh\left(d x + c\right)^{4} + a^{2} b^{4} d + 6 \, {\left(2 \, a^{3} b^{3} - a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)\right)}}, \frac{a^{2} b^{2} \cosh\left(d x + c\right)^{6} + 6 \, a^{2} b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + a^{2} b^{2} \sinh\left(d x + c\right)^{6} + {\left(6 \, a^{3} b - 7 \, a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} + {\left(15 \, a^{2} b^{2} \cosh\left(d x + c\right)^{2} + 6 \, a^{3} b - 7 \, a^{2} b^{2} + 2 \, a b^{3}\right)} \sinh\left(d x + c\right)^{4} - a^{2} b^{2} + 4 \, {\left(5 \, a^{2} b^{2} \cosh\left(d x + c\right)^{3} + {\left(6 \, a^{3} b - 7 \, a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - {\left(6 \, a^{3} b - 7 \, a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2} + {\left(15 \, a^{2} b^{2} \cosh\left(d x + c\right)^{4} - 6 \, a^{3} b + 7 \, a^{2} b^{2} - 2 \, a b^{3} + 6 \, {\left(6 \, a^{3} b - 7 \, a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} - {\left({\left(3 \, a^{2} b - 2 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(3 \, a^{2} b - 2 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} + {\left(3 \, a^{2} b - 2 \, a b^{2} - b^{3}\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(6 \, a^{3} - 7 \, a^{2} b + b^{3}\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(6 \, a^{3} - 7 \, a^{2} b + b^{3} + 5 \, {\left(3 \, a^{2} b - 2 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(5 \, {\left(3 \, a^{2} b - 2 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(6 \, a^{3} - 7 \, a^{2} b + b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(3 \, a^{2} b - 2 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right) + {\left(5 \, {\left(3 \, a^{2} b - 2 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{4} + 3 \, a^{2} b - 2 \, a b^{2} - b^{3} + 6 \, {\left(6 \, a^{3} - 7 \, a^{2} b + b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} {\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right)}}{2 \, a}\right) - {\left({\left(3 \, a^{2} b - 2 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(3 \, a^{2} b - 2 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} + {\left(3 \, a^{2} b - 2 \, a b^{2} - b^{3}\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(6 \, a^{3} - 7 \, a^{2} b + b^{3}\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(6 \, a^{3} - 7 \, a^{2} b + b^{3} + 5 \, {\left(3 \, a^{2} b - 2 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(5 \, {\left(3 \, a^{2} b - 2 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(6 \, a^{3} - 7 \, a^{2} b + b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(3 \, a^{2} b - 2 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right) + {\left(5 \, {\left(3 \, a^{2} b - 2 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{4} + 3 \, a^{2} b - 2 \, a b^{2} - b^{3} + 6 \, {\left(6 \, a^{3} - 7 \, a^{2} b + b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)\right)} \sqrt{a b} \arctan\left(\frac{{\left(b \cosh\left(d x + c\right)^{3} + 3 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{3} + {\left(4 \, a - b\right)} \cosh\left(d x + c\right) + {\left(3 \, b \cosh\left(d x + c\right)^{2} + 4 \, a - b\right)} \sinh\left(d x + c\right)\right)} \sqrt{a b}}{2 \, a b}\right) + 2 \, {\left(3 \, a^{2} b^{2} \cosh\left(d x + c\right)^{5} + 2 \, {\left(6 \, a^{3} b - 7 \, a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} - {\left(6 \, a^{3} b - 7 \, a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{2 \, {\left(a^{2} b^{4} d \cosh\left(d x + c\right)^{5} + 5 \, a^{2} b^{4} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} + a^{2} b^{4} d \sinh\left(d x + c\right)^{5} + a^{2} b^{4} d \cosh\left(d x + c\right) + 2 \, {\left(2 \, a^{3} b^{3} - a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{3} + 2 \, {\left(5 \, a^{2} b^{4} d \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{3} b^{3} - a^{2} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(5 \, a^{2} b^{4} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(2 \, a^{3} b^{3} - a^{2} b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(5 \, a^{2} b^{4} d \cosh\left(d x + c\right)^{4} + a^{2} b^{4} d + 6 \, {\left(2 \, a^{3} b^{3} - a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[1/4*(2*a^2*b^2*cosh(d*x + c)^6 + 12*a^2*b^2*cosh(d*x + c)*sinh(d*x + c)^5 + 2*a^2*b^2*sinh(d*x + c)^6 + 2*(6*a^3*b - 7*a^2*b^2 + 2*a*b^3)*cosh(d*x + c)^4 + 2*(15*a^2*b^2*cosh(d*x + c)^2 + 6*a^3*b - 7*a^2*b^2 + 2*a*b^3)*sinh(d*x + c)^4 - 2*a^2*b^2 + 8*(5*a^2*b^2*cosh(d*x + c)^3 + (6*a^3*b - 7*a^2*b^2 + 2*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 - 2*(6*a^3*b - 7*a^2*b^2 + 2*a*b^3)*cosh(d*x + c)^2 + 2*(15*a^2*b^2*cosh(d*x + c)^4 - 6*a^3*b + 7*a^2*b^2 - 2*a*b^3 + 6*(6*a^3*b - 7*a^2*b^2 + 2*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((3*a^2*b - 2*a*b^2 - b^3)*cosh(d*x + c)^5 + 5*(3*a^2*b - 2*a*b^2 - b^3)*cosh(d*x + c)*sinh(d*x + c)^4 + (3*a^2*b - 2*a*b^2 - b^3)*sinh(d*x + c)^5 + 2*(6*a^3 - 7*a^2*b + b^3)*cosh(d*x + c)^3 + 2*(6*a^3 - 7*a^2*b + b^3 + 5*(3*a^2*b - 2*a*b^2 - b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 2*(5*(3*a^2*b - 2*a*b^2 - b^3)*cosh(d*x + c)^3 + 3*(6*a^3 - 7*a^2*b + b^3)*cosh(d*x + c))*sinh(d*x + c)^2 + (3*a^2*b - 2*a*b^2 - b^3)*cosh(d*x + c) + (5*(3*a^2*b - 2*a*b^2 - b^3)*cosh(d*x + c)^4 + 3*a^2*b - 2*a*b^2 - b^3 + 6*(6*a^3 - 7*a^2*b + b^3)*cosh(d*x + c)^2)*sinh(d*x + c))*sqrt(-a*b)*log((b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 - 2*(2*a + b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 - 2*a - b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 - (2*a + b)*cosh(d*x + c))*sinh(d*x + c) - 4*(cosh(d*x + c)^3 + 3*cosh(d*x + c)*sinh(d*x + c)^2 + sinh(d*x + c)^3 + (3*cosh(d*x + c)^2 - 1)*sinh(d*x + c) - cosh(d*x + c))*sqrt(-a*b) + b)/(b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 + 2*(2*a - b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 + 2*a - b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 + (2*a - b)*cosh(d*x + c))*sinh(d*x + c) + b)) + 4*(3*a^2*b^2*cosh(d*x + c)^5 + 2*(6*a^3*b - 7*a^2*b^2 + 2*a*b^3)*cosh(d*x + c)^3 - (6*a^3*b - 7*a^2*b^2 + 2*a*b^3)*cosh(d*x + c))*sinh(d*x + c))/(a^2*b^4*d*cosh(d*x + c)^5 + 5*a^2*b^4*d*cosh(d*x + c)*sinh(d*x + c)^4 + a^2*b^4*d*sinh(d*x + c)^5 + a^2*b^4*d*cosh(d*x + c) + 2*(2*a^3*b^3 - a^2*b^4)*d*cosh(d*x + c)^3 + 2*(5*a^2*b^4*d*cosh(d*x + c)^2 + (2*a^3*b^3 - a^2*b^4)*d)*sinh(d*x + c)^3 + 2*(5*a^2*b^4*d*cosh(d*x + c)^3 + 3*(2*a^3*b^3 - a^2*b^4)*d*cosh(d*x + c))*sinh(d*x + c)^2 + (5*a^2*b^4*d*cosh(d*x + c)^4 + a^2*b^4*d + 6*(2*a^3*b^3 - a^2*b^4)*d*cosh(d*x + c)^2)*sinh(d*x + c)), 1/2*(a^2*b^2*cosh(d*x + c)^6 + 6*a^2*b^2*cosh(d*x + c)*sinh(d*x + c)^5 + a^2*b^2*sinh(d*x + c)^6 + (6*a^3*b - 7*a^2*b^2 + 2*a*b^3)*cosh(d*x + c)^4 + (15*a^2*b^2*cosh(d*x + c)^2 + 6*a^3*b - 7*a^2*b^2 + 2*a*b^3)*sinh(d*x + c)^4 - a^2*b^2 + 4*(5*a^2*b^2*cosh(d*x + c)^3 + (6*a^3*b - 7*a^2*b^2 + 2*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 - (6*a^3*b - 7*a^2*b^2 + 2*a*b^3)*cosh(d*x + c)^2 + (15*a^2*b^2*cosh(d*x + c)^4 - 6*a^3*b + 7*a^2*b^2 - 2*a*b^3 + 6*(6*a^3*b - 7*a^2*b^2 + 2*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - ((3*a^2*b - 2*a*b^2 - b^3)*cosh(d*x + c)^5 + 5*(3*a^2*b - 2*a*b^2 - b^3)*cosh(d*x + c)*sinh(d*x + c)^4 + (3*a^2*b - 2*a*b^2 - b^3)*sinh(d*x + c)^5 + 2*(6*a^3 - 7*a^2*b + b^3)*cosh(d*x + c)^3 + 2*(6*a^3 - 7*a^2*b + b^3 + 5*(3*a^2*b - 2*a*b^2 - b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 2*(5*(3*a^2*b - 2*a*b^2 - b^3)*cosh(d*x + c)^3 + 3*(6*a^3 - 7*a^2*b + b^3)*cosh(d*x + c))*sinh(d*x + c)^2 + (3*a^2*b - 2*a*b^2 - b^3)*cosh(d*x + c) + (5*(3*a^2*b - 2*a*b^2 - b^3)*cosh(d*x + c)^4 + 3*a^2*b - 2*a*b^2 - b^3 + 6*(6*a^3 - 7*a^2*b + b^3)*cosh(d*x + c)^2)*sinh(d*x + c))*sqrt(a*b)*arctan(1/2*sqrt(a*b)*(cosh(d*x + c) + sinh(d*x + c))/a) - ((3*a^2*b - 2*a*b^2 - b^3)*cosh(d*x + c)^5 + 5*(3*a^2*b - 2*a*b^2 - b^3)*cosh(d*x + c)*sinh(d*x + c)^4 + (3*a^2*b - 2*a*b^2 - b^3)*sinh(d*x + c)^5 + 2*(6*a^3 - 7*a^2*b + b^3)*cosh(d*x + c)^3 + 2*(6*a^3 - 7*a^2*b + b^3 + 5*(3*a^2*b - 2*a*b^2 - b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 2*(5*(3*a^2*b - 2*a*b^2 - b^3)*cosh(d*x + c)^3 + 3*(6*a^3 - 7*a^2*b + b^3)*cosh(d*x + c))*sinh(d*x + c)^2 + (3*a^2*b - 2*a*b^2 - b^3)*cosh(d*x + c) + (5*(3*a^2*b - 2*a*b^2 - b^3)*cosh(d*x + c)^4 + 3*a^2*b - 2*a*b^2 - b^3 + 6*(6*a^3 - 7*a^2*b + b^3)*cosh(d*x + c)^2)*sinh(d*x + c))*sqrt(a*b)*arctan(1/2*(b*cosh(d*x + c)^3 + 3*b*cosh(d*x + c)*sinh(d*x + c)^2 + b*sinh(d*x + c)^3 + (4*a - b)*cosh(d*x + c) + (3*b*cosh(d*x + c)^2 + 4*a - b)*sinh(d*x + c))*sqrt(a*b)/(a*b)) + 2*(3*a^2*b^2*cosh(d*x + c)^5 + 2*(6*a^3*b - 7*a^2*b^2 + 2*a*b^3)*cosh(d*x + c)^3 - (6*a^3*b - 7*a^2*b^2 + 2*a*b^3)*cosh(d*x + c))*sinh(d*x + c))/(a^2*b^4*d*cosh(d*x + c)^5 + 5*a^2*b^4*d*cosh(d*x + c)*sinh(d*x + c)^4 + a^2*b^4*d*sinh(d*x + c)^5 + a^2*b^4*d*cosh(d*x + c) + 2*(2*a^3*b^3 - a^2*b^4)*d*cosh(d*x + c)^3 + 2*(5*a^2*b^4*d*cosh(d*x + c)^2 + (2*a^3*b^3 - a^2*b^4)*d)*sinh(d*x + c)^3 + 2*(5*a^2*b^4*d*cosh(d*x + c)^3 + 3*(2*a^3*b^3 - a^2*b^4)*d*cosh(d*x + c))*sinh(d*x + c)^2 + (5*a^2*b^4*d*cosh(d*x + c)^4 + a^2*b^4*d + 6*(2*a^3*b^3 - a^2*b^4)*d*cosh(d*x + c)^2)*sinh(d*x + c))]","B",0
331,1,1527,0,0.499076," ","integrate(cosh(d*x+c)^4/(a+b*sinh(d*x+c)^2)^2,x, algorithm=""fricas"")","\left[\frac{4 \, a b d x \cosh\left(d x + c\right)^{4} + 16 \, a b d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + 4 \, a b d x \sinh\left(d x + c\right)^{4} + 4 \, a b d x + 4 \, {\left(2 \, {\left(2 \, a^{2} - a b\right)} d x + 2 \, a^{2} - 3 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(6 \, a b d x \cosh\left(d x + c\right)^{2} + 2 \, {\left(2 \, a^{2} - a b\right)} d x + 2 \, a^{2} - 3 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(2 \, a b + b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(4 \, a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, a^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{2} + 2 \, a b + b^{2} + 4 \, {\left({\left(2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(4 \, a^{2} - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a - b}{a}} \log\left(\frac{b^{2} \cosh\left(d x + c\right)^{4} + 4 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{2} \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(d x + c\right)^{2} + 2 \, a b - b^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, a^{2} - 8 \, a b + b^{2} + 4 \, {\left(b^{2} \cosh\left(d x + c\right)^{3} + {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + 4 \, {\left(a b \cosh\left(d x + c\right)^{2} + 2 \, a b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a b \sinh\left(d x + c\right)^{2} + 2 \, a^{2} - a b\right)} \sqrt{\frac{a - b}{a}}}{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b}\right) + 4 \, a b - 4 \, b^{2} + 8 \, {\left(2 \, a b d x \cosh\left(d x + c\right)^{3} + {\left(2 \, {\left(2 \, a^{2} - a b\right)} d x + 2 \, a^{2} - 3 \, a b + b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{4 \, {\left(a b^{3} d \cosh\left(d x + c\right)^{4} + 4 \, a b^{3} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a b^{3} d \sinh\left(d x + c\right)^{4} + a b^{3} d + 2 \, {\left(2 \, a^{2} b^{2} - a b^{3}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a b^{3} d \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{2} b^{2} - a b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a b^{3} d \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{2} b^{2} - a b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}, \frac{2 \, a b d x \cosh\left(d x + c\right)^{4} + 8 \, a b d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + 2 \, a b d x \sinh\left(d x + c\right)^{4} + 2 \, a b d x + 2 \, {\left(2 \, {\left(2 \, a^{2} - a b\right)} d x + 2 \, a^{2} - 3 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(6 \, a b d x \cosh\left(d x + c\right)^{2} + 2 \, {\left(2 \, a^{2} - a b\right)} d x + 2 \, a^{2} - 3 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(2 \, a b + b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(4 \, a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, a^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{2} + 2 \, a b + b^{2} + 4 \, {\left({\left(2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(4 \, a^{2} - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{a - b}{a}} \arctan\left(-\frac{{\left(b \cosh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b \sinh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sqrt{-\frac{a - b}{a}}}{2 \, {\left(a - b\right)}}\right) + 2 \, a b - 2 \, b^{2} + 4 \, {\left(2 \, a b d x \cosh\left(d x + c\right)^{3} + {\left(2 \, {\left(2 \, a^{2} - a b\right)} d x + 2 \, a^{2} - 3 \, a b + b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{2 \, {\left(a b^{3} d \cosh\left(d x + c\right)^{4} + 4 \, a b^{3} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a b^{3} d \sinh\left(d x + c\right)^{4} + a b^{3} d + 2 \, {\left(2 \, a^{2} b^{2} - a b^{3}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a b^{3} d \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{2} b^{2} - a b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a b^{3} d \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{2} b^{2} - a b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[1/4*(4*a*b*d*x*cosh(d*x + c)^4 + 16*a*b*d*x*cosh(d*x + c)*sinh(d*x + c)^3 + 4*a*b*d*x*sinh(d*x + c)^4 + 4*a*b*d*x + 4*(2*(2*a^2 - a*b)*d*x + 2*a^2 - 3*a*b + b^2)*cosh(d*x + c)^2 + 4*(6*a*b*d*x*cosh(d*x + c)^2 + 2*(2*a^2 - a*b)*d*x + 2*a^2 - 3*a*b + b^2)*sinh(d*x + c)^2 + ((2*a*b + b^2)*cosh(d*x + c)^4 + 4*(2*a*b + b^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (2*a*b + b^2)*sinh(d*x + c)^4 + 2*(4*a^2 - b^2)*cosh(d*x + c)^2 + 2*(3*(2*a*b + b^2)*cosh(d*x + c)^2 + 4*a^2 - b^2)*sinh(d*x + c)^2 + 2*a*b + b^2 + 4*((2*a*b + b^2)*cosh(d*x + c)^3 + (4*a^2 - b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a - b)/a)*log((b^2*cosh(d*x + c)^4 + 4*b^2*cosh(d*x + c)*sinh(d*x + c)^3 + b^2*sinh(d*x + c)^4 + 2*(2*a*b - b^2)*cosh(d*x + c)^2 + 2*(3*b^2*cosh(d*x + c)^2 + 2*a*b - b^2)*sinh(d*x + c)^2 + 8*a^2 - 8*a*b + b^2 + 4*(b^2*cosh(d*x + c)^3 + (2*a*b - b^2)*cosh(d*x + c))*sinh(d*x + c) + 4*(a*b*cosh(d*x + c)^2 + 2*a*b*cosh(d*x + c)*sinh(d*x + c) + a*b*sinh(d*x + c)^2 + 2*a^2 - a*b)*sqrt((a - b)/a))/(b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 + 2*(2*a - b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 + 2*a - b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 + (2*a - b)*cosh(d*x + c))*sinh(d*x + c) + b)) + 4*a*b - 4*b^2 + 8*(2*a*b*d*x*cosh(d*x + c)^3 + (2*(2*a^2 - a*b)*d*x + 2*a^2 - 3*a*b + b^2)*cosh(d*x + c))*sinh(d*x + c))/(a*b^3*d*cosh(d*x + c)^4 + 4*a*b^3*d*cosh(d*x + c)*sinh(d*x + c)^3 + a*b^3*d*sinh(d*x + c)^4 + a*b^3*d + 2*(2*a^2*b^2 - a*b^3)*d*cosh(d*x + c)^2 + 2*(3*a*b^3*d*cosh(d*x + c)^2 + (2*a^2*b^2 - a*b^3)*d)*sinh(d*x + c)^2 + 4*(a*b^3*d*cosh(d*x + c)^3 + (2*a^2*b^2 - a*b^3)*d*cosh(d*x + c))*sinh(d*x + c)), 1/2*(2*a*b*d*x*cosh(d*x + c)^4 + 8*a*b*d*x*cosh(d*x + c)*sinh(d*x + c)^3 + 2*a*b*d*x*sinh(d*x + c)^4 + 2*a*b*d*x + 2*(2*(2*a^2 - a*b)*d*x + 2*a^2 - 3*a*b + b^2)*cosh(d*x + c)^2 + 2*(6*a*b*d*x*cosh(d*x + c)^2 + 2*(2*a^2 - a*b)*d*x + 2*a^2 - 3*a*b + b^2)*sinh(d*x + c)^2 + ((2*a*b + b^2)*cosh(d*x + c)^4 + 4*(2*a*b + b^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (2*a*b + b^2)*sinh(d*x + c)^4 + 2*(4*a^2 - b^2)*cosh(d*x + c)^2 + 2*(3*(2*a*b + b^2)*cosh(d*x + c)^2 + 4*a^2 - b^2)*sinh(d*x + c)^2 + 2*a*b + b^2 + 4*((2*a*b + b^2)*cosh(d*x + c)^3 + (4*a^2 - b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-(a - b)/a)*arctan(-1/2*(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + 2*a - b)*sqrt(-(a - b)/a)/(a - b)) + 2*a*b - 2*b^2 + 4*(2*a*b*d*x*cosh(d*x + c)^3 + (2*(2*a^2 - a*b)*d*x + 2*a^2 - 3*a*b + b^2)*cosh(d*x + c))*sinh(d*x + c))/(a*b^3*d*cosh(d*x + c)^4 + 4*a*b^3*d*cosh(d*x + c)*sinh(d*x + c)^3 + a*b^3*d*sinh(d*x + c)^4 + a*b^3*d + 2*(2*a^2*b^2 - a*b^3)*d*cosh(d*x + c)^2 + 2*(3*a*b^3*d*cosh(d*x + c)^2 + (2*a^2*b^2 - a*b^3)*d)*sinh(d*x + c)^2 + 4*(a*b^3*d*cosh(d*x + c)^3 + (2*a^2*b^2 - a*b^3)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
332,1,1615,0,0.561189," ","integrate(cosh(d*x+c)^3/(a+b*sinh(d*x+c)^2)^2,x, algorithm=""fricas"")","\left[-\frac{4 \, {\left(a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right)^{3} + 12 \, {\left(a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + 4 \, {\left(a^{2} b - a b^{2}\right)} \sinh\left(d x + c\right)^{3} + {\left({\left(a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a b + b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a b + b^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, a^{2} + a b - b^{2}\right)} \sinh\left(d x + c\right)^{2} + a b + b^{2} + 4 \, {\left({\left(a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-a b} \log\left(\frac{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} - 2 \, {\left(2 \, a + b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} - 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} - {\left(2 \, a + b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) - 4 \, {\left(\cosh\left(d x + c\right)^{3} + 3 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{3} + {\left(3 \, \cosh\left(d x + c\right)^{2} - 1\right)} \sinh\left(d x + c\right) - \cosh\left(d x + c\right)\right)} \sqrt{-a b} + b}{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b}\right) - 4 \, {\left(a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right) - 4 \, {\left(a^{2} b - a b^{2} - 3 \, {\left(a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)}{4 \, {\left(a^{2} b^{3} d \cosh\left(d x + c\right)^{4} + 4 \, a^{2} b^{3} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a^{2} b^{3} d \sinh\left(d x + c\right)^{4} + a^{2} b^{3} d + 2 \, {\left(2 \, a^{3} b^{2} - a^{2} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{2} b^{3} d \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{3} b^{2} - a^{2} b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a^{2} b^{3} d \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{3} b^{2} - a^{2} b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}, -\frac{2 \, {\left(a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right)^{3} + 6 \, {\left(a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} b - a b^{2}\right)} \sinh\left(d x + c\right)^{3} - {\left({\left(a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a b + b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a b + b^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, a^{2} + a b - b^{2}\right)} \sinh\left(d x + c\right)^{2} + a b + b^{2} + 4 \, {\left({\left(a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} {\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right)}}{2 \, a}\right) - {\left({\left(a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a b + b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a b + b^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, a^{2} + a b - b^{2}\right)} \sinh\left(d x + c\right)^{2} + a b + b^{2} + 4 \, {\left({\left(a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{a b} \arctan\left(\frac{{\left(b \cosh\left(d x + c\right)^{3} + 3 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{3} + {\left(4 \, a - b\right)} \cosh\left(d x + c\right) + {\left(3 \, b \cosh\left(d x + c\right)^{2} + 4 \, a - b\right)} \sinh\left(d x + c\right)\right)} \sqrt{a b}}{2 \, a b}\right) - 2 \, {\left(a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right) - 2 \, {\left(a^{2} b - a b^{2} - 3 \, {\left(a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)}{2 \, {\left(a^{2} b^{3} d \cosh\left(d x + c\right)^{4} + 4 \, a^{2} b^{3} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a^{2} b^{3} d \sinh\left(d x + c\right)^{4} + a^{2} b^{3} d + 2 \, {\left(2 \, a^{3} b^{2} - a^{2} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{2} b^{3} d \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{3} b^{2} - a^{2} b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a^{2} b^{3} d \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{3} b^{2} - a^{2} b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[-1/4*(4*(a^2*b - a*b^2)*cosh(d*x + c)^3 + 12*(a^2*b - a*b^2)*cosh(d*x + c)*sinh(d*x + c)^2 + 4*(a^2*b - a*b^2)*sinh(d*x + c)^3 + ((a*b + b^2)*cosh(d*x + c)^4 + 4*(a*b + b^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (a*b + b^2)*sinh(d*x + c)^4 + 2*(2*a^2 + a*b - b^2)*cosh(d*x + c)^2 + 2*(3*(a*b + b^2)*cosh(d*x + c)^2 + 2*a^2 + a*b - b^2)*sinh(d*x + c)^2 + a*b + b^2 + 4*((a*b + b^2)*cosh(d*x + c)^3 + (2*a^2 + a*b - b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-a*b)*log((b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 - 2*(2*a + b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 - 2*a - b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 - (2*a + b)*cosh(d*x + c))*sinh(d*x + c) - 4*(cosh(d*x + c)^3 + 3*cosh(d*x + c)*sinh(d*x + c)^2 + sinh(d*x + c)^3 + (3*cosh(d*x + c)^2 - 1)*sinh(d*x + c) - cosh(d*x + c))*sqrt(-a*b) + b)/(b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 + 2*(2*a - b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 + 2*a - b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 + (2*a - b)*cosh(d*x + c))*sinh(d*x + c) + b)) - 4*(a^2*b - a*b^2)*cosh(d*x + c) - 4*(a^2*b - a*b^2 - 3*(a^2*b - a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c))/(a^2*b^3*d*cosh(d*x + c)^4 + 4*a^2*b^3*d*cosh(d*x + c)*sinh(d*x + c)^3 + a^2*b^3*d*sinh(d*x + c)^4 + a^2*b^3*d + 2*(2*a^3*b^2 - a^2*b^3)*d*cosh(d*x + c)^2 + 2*(3*a^2*b^3*d*cosh(d*x + c)^2 + (2*a^3*b^2 - a^2*b^3)*d)*sinh(d*x + c)^2 + 4*(a^2*b^3*d*cosh(d*x + c)^3 + (2*a^3*b^2 - a^2*b^3)*d*cosh(d*x + c))*sinh(d*x + c)), -1/2*(2*(a^2*b - a*b^2)*cosh(d*x + c)^3 + 6*(a^2*b - a*b^2)*cosh(d*x + c)*sinh(d*x + c)^2 + 2*(a^2*b - a*b^2)*sinh(d*x + c)^3 - ((a*b + b^2)*cosh(d*x + c)^4 + 4*(a*b + b^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (a*b + b^2)*sinh(d*x + c)^4 + 2*(2*a^2 + a*b - b^2)*cosh(d*x + c)^2 + 2*(3*(a*b + b^2)*cosh(d*x + c)^2 + 2*a^2 + a*b - b^2)*sinh(d*x + c)^2 + a*b + b^2 + 4*((a*b + b^2)*cosh(d*x + c)^3 + (2*a^2 + a*b - b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(a*b)*arctan(1/2*sqrt(a*b)*(cosh(d*x + c) + sinh(d*x + c))/a) - ((a*b + b^2)*cosh(d*x + c)^4 + 4*(a*b + b^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (a*b + b^2)*sinh(d*x + c)^4 + 2*(2*a^2 + a*b - b^2)*cosh(d*x + c)^2 + 2*(3*(a*b + b^2)*cosh(d*x + c)^2 + 2*a^2 + a*b - b^2)*sinh(d*x + c)^2 + a*b + b^2 + 4*((a*b + b^2)*cosh(d*x + c)^3 + (2*a^2 + a*b - b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(a*b)*arctan(1/2*(b*cosh(d*x + c)^3 + 3*b*cosh(d*x + c)*sinh(d*x + c)^2 + b*sinh(d*x + c)^3 + (4*a - b)*cosh(d*x + c) + (3*b*cosh(d*x + c)^2 + 4*a - b)*sinh(d*x + c))*sqrt(a*b)/(a*b)) - 2*(a^2*b - a*b^2)*cosh(d*x + c) - 2*(a^2*b - a*b^2 - 3*(a^2*b - a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c))/(a^2*b^3*d*cosh(d*x + c)^4 + 4*a^2*b^3*d*cosh(d*x + c)*sinh(d*x + c)^3 + a^2*b^3*d*sinh(d*x + c)^4 + a^2*b^3*d + 2*(2*a^3*b^2 - a^2*b^3)*d*cosh(d*x + c)^2 + 2*(3*a^2*b^3*d*cosh(d*x + c)^2 + (2*a^3*b^2 - a^2*b^3)*d)*sinh(d*x + c)^2 + 4*(a^2*b^3*d*cosh(d*x + c)^3 + (2*a^3*b^2 - a^2*b^3)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
333,1,1421,0,0.684122," ","integrate(cosh(d*x+c)^2/(a+b*sinh(d*x+c)^2)^2,x, algorithm=""fricas"")","\left[-\frac{4 \, a^{2} b - 4 \, a b^{2} + 4 \, {\left(2 \, a^{3} - 3 \, a^{2} b + a b^{2}\right)} \cosh\left(d x + c\right)^{2} + 8 \, {\left(2 \, a^{3} - 3 \, a^{2} b + a b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + 4 \, {\left(2 \, a^{3} - 3 \, a^{2} b + a b^{2}\right)} \sinh\left(d x + c\right)^{2} - {\left(b^{2} \cosh\left(d x + c\right)^{4} + 4 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{2} \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(d x + c\right)^{2} + 2 \, a b - b^{2}\right)} \sinh\left(d x + c\right)^{2} + b^{2} + 4 \, {\left(b^{2} \cosh\left(d x + c\right)^{3} + {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{a^{2} - a b} \log\left(\frac{b^{2} \cosh\left(d x + c\right)^{4} + 4 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{2} \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(d x + c\right)^{2} + 2 \, a b - b^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, a^{2} - 8 \, a b + b^{2} + 4 \, {\left(b^{2} \cosh\left(d x + c\right)^{3} + {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) - 4 \, {\left(b \cosh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b \sinh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sqrt{a^{2} - a b}}{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b}\right)}{4 \, {\left({\left(a^{3} b^{2} - a^{2} b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{3} b^{2} - a^{2} b^{3}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{3} b^{2} - a^{2} b^{3}\right)} d \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a^{4} b - 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{3} b^{2} - a^{2} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{4} b - 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{3} b^{2} - a^{2} b^{3}\right)} d + 4 \, {\left({\left(a^{3} b^{2} - a^{2} b^{3}\right)} d \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{4} b - 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}, -\frac{2 \, a^{2} b - 2 \, a b^{2} + 2 \, {\left(2 \, a^{3} - 3 \, a^{2} b + a b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(2 \, a^{3} - 3 \, a^{2} b + a b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + 2 \, {\left(2 \, a^{3} - 3 \, a^{2} b + a b^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left(b^{2} \cosh\left(d x + c\right)^{4} + 4 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{2} \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(d x + c\right)^{2} + 2 \, a b - b^{2}\right)} \sinh\left(d x + c\right)^{2} + b^{2} + 4 \, {\left(b^{2} \cosh\left(d x + c\right)^{3} + {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-a^{2} + a b} \arctan\left(-\frac{{\left(b \cosh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b \sinh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sqrt{-a^{2} + a b}}{2 \, {\left(a^{2} - a b\right)}}\right)}{2 \, {\left({\left(a^{3} b^{2} - a^{2} b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{3} b^{2} - a^{2} b^{3}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{3} b^{2} - a^{2} b^{3}\right)} d \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a^{4} b - 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{3} b^{2} - a^{2} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{4} b - 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{3} b^{2} - a^{2} b^{3}\right)} d + 4 \, {\left({\left(a^{3} b^{2} - a^{2} b^{3}\right)} d \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{4} b - 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[-1/4*(4*a^2*b - 4*a*b^2 + 4*(2*a^3 - 3*a^2*b + a*b^2)*cosh(d*x + c)^2 + 8*(2*a^3 - 3*a^2*b + a*b^2)*cosh(d*x + c)*sinh(d*x + c) + 4*(2*a^3 - 3*a^2*b + a*b^2)*sinh(d*x + c)^2 - (b^2*cosh(d*x + c)^4 + 4*b^2*cosh(d*x + c)*sinh(d*x + c)^3 + b^2*sinh(d*x + c)^4 + 2*(2*a*b - b^2)*cosh(d*x + c)^2 + 2*(3*b^2*cosh(d*x + c)^2 + 2*a*b - b^2)*sinh(d*x + c)^2 + b^2 + 4*(b^2*cosh(d*x + c)^3 + (2*a*b - b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(a^2 - a*b)*log((b^2*cosh(d*x + c)^4 + 4*b^2*cosh(d*x + c)*sinh(d*x + c)^3 + b^2*sinh(d*x + c)^4 + 2*(2*a*b - b^2)*cosh(d*x + c)^2 + 2*(3*b^2*cosh(d*x + c)^2 + 2*a*b - b^2)*sinh(d*x + c)^2 + 8*a^2 - 8*a*b + b^2 + 4*(b^2*cosh(d*x + c)^3 + (2*a*b - b^2)*cosh(d*x + c))*sinh(d*x + c) - 4*(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + 2*a - b)*sqrt(a^2 - a*b))/(b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 + 2*(2*a - b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 + 2*a - b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 + (2*a - b)*cosh(d*x + c))*sinh(d*x + c) + b)))/((a^3*b^2 - a^2*b^3)*d*cosh(d*x + c)^4 + 4*(a^3*b^2 - a^2*b^3)*d*cosh(d*x + c)*sinh(d*x + c)^3 + (a^3*b^2 - a^2*b^3)*d*sinh(d*x + c)^4 + 2*(2*a^4*b - 3*a^3*b^2 + a^2*b^3)*d*cosh(d*x + c)^2 + 2*(3*(a^3*b^2 - a^2*b^3)*d*cosh(d*x + c)^2 + (2*a^4*b - 3*a^3*b^2 + a^2*b^3)*d)*sinh(d*x + c)^2 + (a^3*b^2 - a^2*b^3)*d + 4*((a^3*b^2 - a^2*b^3)*d*cosh(d*x + c)^3 + (2*a^4*b - 3*a^3*b^2 + a^2*b^3)*d*cosh(d*x + c))*sinh(d*x + c)), -1/2*(2*a^2*b - 2*a*b^2 + 2*(2*a^3 - 3*a^2*b + a*b^2)*cosh(d*x + c)^2 + 4*(2*a^3 - 3*a^2*b + a*b^2)*cosh(d*x + c)*sinh(d*x + c) + 2*(2*a^3 - 3*a^2*b + a*b^2)*sinh(d*x + c)^2 + (b^2*cosh(d*x + c)^4 + 4*b^2*cosh(d*x + c)*sinh(d*x + c)^3 + b^2*sinh(d*x + c)^4 + 2*(2*a*b - b^2)*cosh(d*x + c)^2 + 2*(3*b^2*cosh(d*x + c)^2 + 2*a*b - b^2)*sinh(d*x + c)^2 + b^2 + 4*(b^2*cosh(d*x + c)^3 + (2*a*b - b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-a^2 + a*b)*arctan(-1/2*(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + 2*a - b)*sqrt(-a^2 + a*b)/(a^2 - a*b)))/((a^3*b^2 - a^2*b^3)*d*cosh(d*x + c)^4 + 4*(a^3*b^2 - a^2*b^3)*d*cosh(d*x + c)*sinh(d*x + c)^3 + (a^3*b^2 - a^2*b^3)*d*sinh(d*x + c)^4 + 2*(2*a^4*b - 3*a^3*b^2 + a^2*b^3)*d*cosh(d*x + c)^2 + 2*(3*(a^3*b^2 - a^2*b^3)*d*cosh(d*x + c)^2 + (2*a^4*b - 3*a^3*b^2 + a^2*b^3)*d)*sinh(d*x + c)^2 + (a^3*b^2 - a^2*b^3)*d + 4*((a^3*b^2 - a^2*b^3)*d*cosh(d*x + c)^3 + (2*a^4*b - 3*a^3*b^2 + a^2*b^3)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
334,1,1320,0,0.710709," ","integrate(cosh(d*x+c)/(a+b*sinh(d*x+c)^2)^2,x, algorithm=""fricas"")","\left[\frac{4 \, a b \cosh\left(d x + c\right)^{3} + 12 \, a b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + 4 \, a b \sinh\left(d x + c\right)^{3} - 4 \, a b \cosh\left(d x + c\right) - {\left(b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b\right)} \sqrt{-a b} \log\left(\frac{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} - 2 \, {\left(2 \, a + b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} - 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} - {\left(2 \, a + b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) - 4 \, {\left(\cosh\left(d x + c\right)^{3} + 3 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{3} + {\left(3 \, \cosh\left(d x + c\right)^{2} - 1\right)} \sinh\left(d x + c\right) - \cosh\left(d x + c\right)\right)} \sqrt{-a b} + b}{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b}\right) + 4 \, {\left(3 \, a b \cosh\left(d x + c\right)^{2} - a b\right)} \sinh\left(d x + c\right)}{4 \, {\left(a^{2} b^{2} d \cosh\left(d x + c\right)^{4} + 4 \, a^{2} b^{2} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a^{2} b^{2} d \sinh\left(d x + c\right)^{4} + a^{2} b^{2} d + 2 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{2} b^{2} d \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{3} b - a^{2} b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a^{2} b^{2} d \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}, \frac{2 \, a b \cosh\left(d x + c\right)^{3} + 6 \, a b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + 2 \, a b \sinh\left(d x + c\right)^{3} - 2 \, a b \cosh\left(d x + c\right) + {\left(b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} {\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right)}}{2 \, a}\right) + {\left(b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b\right)} \sqrt{a b} \arctan\left(\frac{{\left(b \cosh\left(d x + c\right)^{3} + 3 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{3} + {\left(4 \, a - b\right)} \cosh\left(d x + c\right) + {\left(3 \, b \cosh\left(d x + c\right)^{2} + 4 \, a - b\right)} \sinh\left(d x + c\right)\right)} \sqrt{a b}}{2 \, a b}\right) + 2 \, {\left(3 \, a b \cosh\left(d x + c\right)^{2} - a b\right)} \sinh\left(d x + c\right)}{2 \, {\left(a^{2} b^{2} d \cosh\left(d x + c\right)^{4} + 4 \, a^{2} b^{2} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a^{2} b^{2} d \sinh\left(d x + c\right)^{4} + a^{2} b^{2} d + 2 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{2} b^{2} d \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{3} b - a^{2} b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a^{2} b^{2} d \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{3} b - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[1/4*(4*a*b*cosh(d*x + c)^3 + 12*a*b*cosh(d*x + c)*sinh(d*x + c)^2 + 4*a*b*sinh(d*x + c)^3 - 4*a*b*cosh(d*x + c) - (b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 + 2*(2*a - b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 + 2*a - b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 + (2*a - b)*cosh(d*x + c))*sinh(d*x + c) + b)*sqrt(-a*b)*log((b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 - 2*(2*a + b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 - 2*a - b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 - (2*a + b)*cosh(d*x + c))*sinh(d*x + c) - 4*(cosh(d*x + c)^3 + 3*cosh(d*x + c)*sinh(d*x + c)^2 + sinh(d*x + c)^3 + (3*cosh(d*x + c)^2 - 1)*sinh(d*x + c) - cosh(d*x + c))*sqrt(-a*b) + b)/(b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 + 2*(2*a - b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 + 2*a - b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 + (2*a - b)*cosh(d*x + c))*sinh(d*x + c) + b)) + 4*(3*a*b*cosh(d*x + c)^2 - a*b)*sinh(d*x + c))/(a^2*b^2*d*cosh(d*x + c)^4 + 4*a^2*b^2*d*cosh(d*x + c)*sinh(d*x + c)^3 + a^2*b^2*d*sinh(d*x + c)^4 + a^2*b^2*d + 2*(2*a^3*b - a^2*b^2)*d*cosh(d*x + c)^2 + 2*(3*a^2*b^2*d*cosh(d*x + c)^2 + (2*a^3*b - a^2*b^2)*d)*sinh(d*x + c)^2 + 4*(a^2*b^2*d*cosh(d*x + c)^3 + (2*a^3*b - a^2*b^2)*d*cosh(d*x + c))*sinh(d*x + c)), 1/2*(2*a*b*cosh(d*x + c)^3 + 6*a*b*cosh(d*x + c)*sinh(d*x + c)^2 + 2*a*b*sinh(d*x + c)^3 - 2*a*b*cosh(d*x + c) + (b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 + 2*(2*a - b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 + 2*a - b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 + (2*a - b)*cosh(d*x + c))*sinh(d*x + c) + b)*sqrt(a*b)*arctan(1/2*sqrt(a*b)*(cosh(d*x + c) + sinh(d*x + c))/a) + (b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 + 2*(2*a - b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 + 2*a - b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 + (2*a - b)*cosh(d*x + c))*sinh(d*x + c) + b)*sqrt(a*b)*arctan(1/2*(b*cosh(d*x + c)^3 + 3*b*cosh(d*x + c)*sinh(d*x + c)^2 + b*sinh(d*x + c)^3 + (4*a - b)*cosh(d*x + c) + (3*b*cosh(d*x + c)^2 + 4*a - b)*sinh(d*x + c))*sqrt(a*b)/(a*b)) + 2*(3*a*b*cosh(d*x + c)^2 - a*b)*sinh(d*x + c))/(a^2*b^2*d*cosh(d*x + c)^4 + 4*a^2*b^2*d*cosh(d*x + c)*sinh(d*x + c)^3 + a^2*b^2*d*sinh(d*x + c)^4 + a^2*b^2*d + 2*(2*a^3*b - a^2*b^2)*d*cosh(d*x + c)^2 + 2*(3*a^2*b^2*d*cosh(d*x + c)^2 + (2*a^3*b - a^2*b^2)*d)*sinh(d*x + c)^2 + 4*(a^2*b^2*d*cosh(d*x + c)^3 + (2*a^3*b - a^2*b^2)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
335,1,2143,0,0.650896," ","integrate(sech(d*x+c)/(a+b*sinh(d*x+c)^2)^2,x, algorithm=""fricas"")","\left[-\frac{4 \, {\left(a b - b^{2}\right)} \cosh\left(d x + c\right)^{3} + 12 \, {\left(a b - b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + 4 \, {\left(a b - b^{2}\right)} \sinh\left(d x + c\right)^{3} + {\left({\left(3 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(3 \, a b - b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(3 \, a b - b^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(6 \, a^{2} - 5 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(3 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 6 \, a^{2} - 5 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{2} + 3 \, a b - b^{2} + 4 \, {\left({\left(3 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(6 \, a^{2} - 5 \, a b + b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} - 2 \, {\left(2 \, a + b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} - 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} - {\left(2 \, a + b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + 4 \, {\left(a \cosh\left(d x + c\right)^{3} + 3 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{3} - a \cosh\left(d x + c\right) + {\left(3 \, a \cosh\left(d x + c\right)^{2} - a\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{b}{a}} + b}{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b}\right) - 8 \, {\left(a b \cosh\left(d x + c\right)^{4} + 4 \, a b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a b \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a^{2} - a b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a b \cosh\left(d x + c\right)^{2} + 2 \, a^{2} - a b\right)} \sinh\left(d x + c\right)^{2} + a b + 4 \, {\left(a b \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{2} - a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \arctan\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) - 4 \, {\left(a b - b^{2}\right)} \cosh\left(d x + c\right) + 4 \, {\left(3 \, {\left(a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} - a b + b^{2}\right)} \sinh\left(d x + c\right)}{4 \, {\left({\left(a^{3} b - 2 \, a^{2} b^{2} + a b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{3} b - 2 \, a^{2} b^{2} + a b^{3}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{3} b - 2 \, a^{2} b^{2} + a b^{3}\right)} d \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a^{4} - 5 \, a^{3} b + 4 \, a^{2} b^{2} - a b^{3}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{3} b - 2 \, a^{2} b^{2} + a b^{3}\right)} d \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{4} - 5 \, a^{3} b + 4 \, a^{2} b^{2} - a b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{3} b - 2 \, a^{2} b^{2} + a b^{3}\right)} d + 4 \, {\left({\left(a^{3} b - 2 \, a^{2} b^{2} + a b^{3}\right)} d \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{4} - 5 \, a^{3} b + 4 \, a^{2} b^{2} - a b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}, -\frac{2 \, {\left(a b - b^{2}\right)} \cosh\left(d x + c\right)^{3} + 6 \, {\left(a b - b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + 2 \, {\left(a b - b^{2}\right)} \sinh\left(d x + c\right)^{3} + {\left({\left(3 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(3 \, a b - b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(3 \, a b - b^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(6 \, a^{2} - 5 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(3 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 6 \, a^{2} - 5 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{2} + 3 \, a b - b^{2} + 4 \, {\left({\left(3 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(6 \, a^{2} - 5 \, a b + b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{b}{a}} \arctan\left(\frac{1}{2} \, \sqrt{\frac{b}{a}} {\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right)}\right) + {\left({\left(3 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(3 \, a b - b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(3 \, a b - b^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(6 \, a^{2} - 5 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(3 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 6 \, a^{2} - 5 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{2} + 3 \, a b - b^{2} + 4 \, {\left({\left(3 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(6 \, a^{2} - 5 \, a b + b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{b}{a}} \arctan\left(\frac{{\left(b \cosh\left(d x + c\right)^{3} + 3 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{3} + {\left(4 \, a - b\right)} \cosh\left(d x + c\right) + {\left(3 \, b \cosh\left(d x + c\right)^{2} + 4 \, a - b\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{b}{a}}}{2 \, b}\right) - 4 \, {\left(a b \cosh\left(d x + c\right)^{4} + 4 \, a b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a b \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a^{2} - a b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a b \cosh\left(d x + c\right)^{2} + 2 \, a^{2} - a b\right)} \sinh\left(d x + c\right)^{2} + a b + 4 \, {\left(a b \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{2} - a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \arctan\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) - 2 \, {\left(a b - b^{2}\right)} \cosh\left(d x + c\right) + 2 \, {\left(3 \, {\left(a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} - a b + b^{2}\right)} \sinh\left(d x + c\right)}{2 \, {\left({\left(a^{3} b - 2 \, a^{2} b^{2} + a b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{3} b - 2 \, a^{2} b^{2} + a b^{3}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{3} b - 2 \, a^{2} b^{2} + a b^{3}\right)} d \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a^{4} - 5 \, a^{3} b + 4 \, a^{2} b^{2} - a b^{3}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{3} b - 2 \, a^{2} b^{2} + a b^{3}\right)} d \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{4} - 5 \, a^{3} b + 4 \, a^{2} b^{2} - a b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{3} b - 2 \, a^{2} b^{2} + a b^{3}\right)} d + 4 \, {\left({\left(a^{3} b - 2 \, a^{2} b^{2} + a b^{3}\right)} d \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{4} - 5 \, a^{3} b + 4 \, a^{2} b^{2} - a b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[-1/4*(4*(a*b - b^2)*cosh(d*x + c)^3 + 12*(a*b - b^2)*cosh(d*x + c)*sinh(d*x + c)^2 + 4*(a*b - b^2)*sinh(d*x + c)^3 + ((3*a*b - b^2)*cosh(d*x + c)^4 + 4*(3*a*b - b^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (3*a*b - b^2)*sinh(d*x + c)^4 + 2*(6*a^2 - 5*a*b + b^2)*cosh(d*x + c)^2 + 2*(3*(3*a*b - b^2)*cosh(d*x + c)^2 + 6*a^2 - 5*a*b + b^2)*sinh(d*x + c)^2 + 3*a*b - b^2 + 4*((3*a*b - b^2)*cosh(d*x + c)^3 + (6*a^2 - 5*a*b + b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-b/a)*log((b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 - 2*(2*a + b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 - 2*a - b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 - (2*a + b)*cosh(d*x + c))*sinh(d*x + c) + 4*(a*cosh(d*x + c)^3 + 3*a*cosh(d*x + c)*sinh(d*x + c)^2 + a*sinh(d*x + c)^3 - a*cosh(d*x + c) + (3*a*cosh(d*x + c)^2 - a)*sinh(d*x + c))*sqrt(-b/a) + b)/(b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 + 2*(2*a - b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 + 2*a - b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 + (2*a - b)*cosh(d*x + c))*sinh(d*x + c) + b)) - 8*(a*b*cosh(d*x + c)^4 + 4*a*b*cosh(d*x + c)*sinh(d*x + c)^3 + a*b*sinh(d*x + c)^4 + 2*(2*a^2 - a*b)*cosh(d*x + c)^2 + 2*(3*a*b*cosh(d*x + c)^2 + 2*a^2 - a*b)*sinh(d*x + c)^2 + a*b + 4*(a*b*cosh(d*x + c)^3 + (2*a^2 - a*b)*cosh(d*x + c))*sinh(d*x + c))*arctan(cosh(d*x + c) + sinh(d*x + c)) - 4*(a*b - b^2)*cosh(d*x + c) + 4*(3*(a*b - b^2)*cosh(d*x + c)^2 - a*b + b^2)*sinh(d*x + c))/((a^3*b - 2*a^2*b^2 + a*b^3)*d*cosh(d*x + c)^4 + 4*(a^3*b - 2*a^2*b^2 + a*b^3)*d*cosh(d*x + c)*sinh(d*x + c)^3 + (a^3*b - 2*a^2*b^2 + a*b^3)*d*sinh(d*x + c)^4 + 2*(2*a^4 - 5*a^3*b + 4*a^2*b^2 - a*b^3)*d*cosh(d*x + c)^2 + 2*(3*(a^3*b - 2*a^2*b^2 + a*b^3)*d*cosh(d*x + c)^2 + (2*a^4 - 5*a^3*b + 4*a^2*b^2 - a*b^3)*d)*sinh(d*x + c)^2 + (a^3*b - 2*a^2*b^2 + a*b^3)*d + 4*((a^3*b - 2*a^2*b^2 + a*b^3)*d*cosh(d*x + c)^3 + (2*a^4 - 5*a^3*b + 4*a^2*b^2 - a*b^3)*d*cosh(d*x + c))*sinh(d*x + c)), -1/2*(2*(a*b - b^2)*cosh(d*x + c)^3 + 6*(a*b - b^2)*cosh(d*x + c)*sinh(d*x + c)^2 + 2*(a*b - b^2)*sinh(d*x + c)^3 + ((3*a*b - b^2)*cosh(d*x + c)^4 + 4*(3*a*b - b^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (3*a*b - b^2)*sinh(d*x + c)^4 + 2*(6*a^2 - 5*a*b + b^2)*cosh(d*x + c)^2 + 2*(3*(3*a*b - b^2)*cosh(d*x + c)^2 + 6*a^2 - 5*a*b + b^2)*sinh(d*x + c)^2 + 3*a*b - b^2 + 4*((3*a*b - b^2)*cosh(d*x + c)^3 + (6*a^2 - 5*a*b + b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(b/a)*arctan(1/2*sqrt(b/a)*(cosh(d*x + c) + sinh(d*x + c))) + ((3*a*b - b^2)*cosh(d*x + c)^4 + 4*(3*a*b - b^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (3*a*b - b^2)*sinh(d*x + c)^4 + 2*(6*a^2 - 5*a*b + b^2)*cosh(d*x + c)^2 + 2*(3*(3*a*b - b^2)*cosh(d*x + c)^2 + 6*a^2 - 5*a*b + b^2)*sinh(d*x + c)^2 + 3*a*b - b^2 + 4*((3*a*b - b^2)*cosh(d*x + c)^3 + (6*a^2 - 5*a*b + b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(b/a)*arctan(1/2*(b*cosh(d*x + c)^3 + 3*b*cosh(d*x + c)*sinh(d*x + c)^2 + b*sinh(d*x + c)^3 + (4*a - b)*cosh(d*x + c) + (3*b*cosh(d*x + c)^2 + 4*a - b)*sinh(d*x + c))*sqrt(b/a)/b) - 4*(a*b*cosh(d*x + c)^4 + 4*a*b*cosh(d*x + c)*sinh(d*x + c)^3 + a*b*sinh(d*x + c)^4 + 2*(2*a^2 - a*b)*cosh(d*x + c)^2 + 2*(3*a*b*cosh(d*x + c)^2 + 2*a^2 - a*b)*sinh(d*x + c)^2 + a*b + 4*(a*b*cosh(d*x + c)^3 + (2*a^2 - a*b)*cosh(d*x + c))*sinh(d*x + c))*arctan(cosh(d*x + c) + sinh(d*x + c)) - 2*(a*b - b^2)*cosh(d*x + c) + 2*(3*(a*b - b^2)*cosh(d*x + c)^2 - a*b + b^2)*sinh(d*x + c))/((a^3*b - 2*a^2*b^2 + a*b^3)*d*cosh(d*x + c)^4 + 4*(a^3*b - 2*a^2*b^2 + a*b^3)*d*cosh(d*x + c)*sinh(d*x + c)^3 + (a^3*b - 2*a^2*b^2 + a*b^3)*d*sinh(d*x + c)^4 + 2*(2*a^4 - 5*a^3*b + 4*a^2*b^2 - a*b^3)*d*cosh(d*x + c)^2 + 2*(3*(a^3*b - 2*a^2*b^2 + a*b^3)*d*cosh(d*x + c)^2 + (2*a^4 - 5*a^3*b + 4*a^2*b^2 - a*b^3)*d)*sinh(d*x + c)^2 + (a^3*b - 2*a^2*b^2 + a*b^3)*d + 4*((a^3*b - 2*a^2*b^2 + a*b^3)*d*cosh(d*x + c)^3 + (2*a^4 - 5*a^3*b + 4*a^2*b^2 - a*b^3)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
336,1,3147,0,0.612338," ","integrate(sech(d*x+c)^2/(a+b*sinh(d*x+c)^2)^2,x, algorithm=""fricas"")","\left[-\frac{4 \, {\left(4 \, a^{3} b - 5 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(d x + c\right)^{4} + 16 \, {\left(4 \, a^{3} b - 5 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + 4 \, {\left(4 \, a^{3} b - 5 \, a^{2} b^{2} + a b^{3}\right)} \sinh\left(d x + c\right)^{4} + 8 \, a^{3} b - 4 \, a^{2} b^{2} - 4 \, a b^{3} + 8 \, {\left(4 \, a^{4} - 5 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{2} + 8 \, {\left(4 \, a^{4} - 5 \, a^{3} b + a^{2} b^{2} + 3 \, {\left(4 \, a^{3} b - 5 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(4 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{6} + 6 \, {\left(4 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(4 \, a b^{2} - b^{3}\right)} \sinh\left(d x + c\right)^{6} + {\left(16 \, a^{2} b - 8 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{4} + {\left(16 \, a^{2} b - 8 \, a b^{2} + b^{3} + 15 \, {\left(4 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, {\left(4 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(16 \, a^{2} b - 8 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, a b^{2} - b^{3} + {\left(16 \, a^{2} b - 8 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{2} + {\left(15 \, {\left(4 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{4} + 16 \, a^{2} b - 8 \, a b^{2} + b^{3} + 6 \, {\left(16 \, a^{2} b - 8 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(4 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(16 \, a^{2} b - 8 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(16 \, a^{2} b - 8 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{a^{2} - a b} \log\left(\frac{b^{2} \cosh\left(d x + c\right)^{4} + 4 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{2} \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(d x + c\right)^{2} + 2 \, a b - b^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, a^{2} - 8 \, a b + b^{2} + 4 \, {\left(b^{2} \cosh\left(d x + c\right)^{3} + {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) - 4 \, {\left(b \cosh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b \sinh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sqrt{a^{2} - a b}}{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b}\right) + 16 \, {\left({\left(4 \, a^{3} b - 5 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(4 \, a^{4} - 5 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{4 \, {\left({\left(a^{5} b - 3 \, a^{4} b^{2} + 3 \, a^{3} b^{3} - a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{6} + 6 \, {\left(a^{5} b - 3 \, a^{4} b^{2} + 3 \, a^{3} b^{3} - a^{2} b^{4}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(a^{5} b - 3 \, a^{4} b^{2} + 3 \, a^{3} b^{3} - a^{2} b^{4}\right)} d \sinh\left(d x + c\right)^{6} + {\left(4 \, a^{6} - 13 \, a^{5} b + 15 \, a^{4} b^{2} - 7 \, a^{3} b^{3} + a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{4} + {\left(15 \, {\left(a^{5} b - 3 \, a^{4} b^{2} + 3 \, a^{3} b^{3} - a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(4 \, a^{6} - 13 \, a^{5} b + 15 \, a^{4} b^{2} - 7 \, a^{3} b^{3} + a^{2} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{4} + {\left(4 \, a^{6} - 13 \, a^{5} b + 15 \, a^{4} b^{2} - 7 \, a^{3} b^{3} + a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + 4 \, {\left(5 \, {\left(a^{5} b - 3 \, a^{4} b^{2} + 3 \, a^{3} b^{3} - a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{3} + {\left(4 \, a^{6} - 13 \, a^{5} b + 15 \, a^{4} b^{2} - 7 \, a^{3} b^{3} + a^{2} b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(15 \, {\left(a^{5} b - 3 \, a^{4} b^{2} + 3 \, a^{3} b^{3} - a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 6 \, {\left(4 \, a^{6} - 13 \, a^{5} b + 15 \, a^{4} b^{2} - 7 \, a^{3} b^{3} + a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(4 \, a^{6} - 13 \, a^{5} b + 15 \, a^{4} b^{2} - 7 \, a^{3} b^{3} + a^{2} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{5} b - 3 \, a^{4} b^{2} + 3 \, a^{3} b^{3} - a^{2} b^{4}\right)} d + 2 \, {\left(3 \, {\left(a^{5} b - 3 \, a^{4} b^{2} + 3 \, a^{3} b^{3} - a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{5} + 2 \, {\left(4 \, a^{6} - 13 \, a^{5} b + 15 \, a^{4} b^{2} - 7 \, a^{3} b^{3} + a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{3} + {\left(4 \, a^{6} - 13 \, a^{5} b + 15 \, a^{4} b^{2} - 7 \, a^{3} b^{3} + a^{2} b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}, -\frac{2 \, {\left(4 \, a^{3} b - 5 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(d x + c\right)^{4} + 8 \, {\left(4 \, a^{3} b - 5 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + 2 \, {\left(4 \, a^{3} b - 5 \, a^{2} b^{2} + a b^{3}\right)} \sinh\left(d x + c\right)^{4} + 4 \, a^{3} b - 2 \, a^{2} b^{2} - 2 \, a b^{3} + 4 \, {\left(4 \, a^{4} - 5 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(4 \, a^{4} - 5 \, a^{3} b + a^{2} b^{2} + 3 \, {\left(4 \, a^{3} b - 5 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} - {\left({\left(4 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{6} + 6 \, {\left(4 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(4 \, a b^{2} - b^{3}\right)} \sinh\left(d x + c\right)^{6} + {\left(16 \, a^{2} b - 8 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{4} + {\left(16 \, a^{2} b - 8 \, a b^{2} + b^{3} + 15 \, {\left(4 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, {\left(4 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(16 \, a^{2} b - 8 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, a b^{2} - b^{3} + {\left(16 \, a^{2} b - 8 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{2} + {\left(15 \, {\left(4 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{4} + 16 \, a^{2} b - 8 \, a b^{2} + b^{3} + 6 \, {\left(16 \, a^{2} b - 8 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(4 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(16 \, a^{2} b - 8 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(16 \, a^{2} b - 8 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-a^{2} + a b} \arctan\left(-\frac{{\left(b \cosh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b \sinh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sqrt{-a^{2} + a b}}{2 \, {\left(a^{2} - a b\right)}}\right) + 8 \, {\left({\left(4 \, a^{3} b - 5 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(4 \, a^{4} - 5 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{2 \, {\left({\left(a^{5} b - 3 \, a^{4} b^{2} + 3 \, a^{3} b^{3} - a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{6} + 6 \, {\left(a^{5} b - 3 \, a^{4} b^{2} + 3 \, a^{3} b^{3} - a^{2} b^{4}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(a^{5} b - 3 \, a^{4} b^{2} + 3 \, a^{3} b^{3} - a^{2} b^{4}\right)} d \sinh\left(d x + c\right)^{6} + {\left(4 \, a^{6} - 13 \, a^{5} b + 15 \, a^{4} b^{2} - 7 \, a^{3} b^{3} + a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{4} + {\left(15 \, {\left(a^{5} b - 3 \, a^{4} b^{2} + 3 \, a^{3} b^{3} - a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(4 \, a^{6} - 13 \, a^{5} b + 15 \, a^{4} b^{2} - 7 \, a^{3} b^{3} + a^{2} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{4} + {\left(4 \, a^{6} - 13 \, a^{5} b + 15 \, a^{4} b^{2} - 7 \, a^{3} b^{3} + a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + 4 \, {\left(5 \, {\left(a^{5} b - 3 \, a^{4} b^{2} + 3 \, a^{3} b^{3} - a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{3} + {\left(4 \, a^{6} - 13 \, a^{5} b + 15 \, a^{4} b^{2} - 7 \, a^{3} b^{3} + a^{2} b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(15 \, {\left(a^{5} b - 3 \, a^{4} b^{2} + 3 \, a^{3} b^{3} - a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 6 \, {\left(4 \, a^{6} - 13 \, a^{5} b + 15 \, a^{4} b^{2} - 7 \, a^{3} b^{3} + a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(4 \, a^{6} - 13 \, a^{5} b + 15 \, a^{4} b^{2} - 7 \, a^{3} b^{3} + a^{2} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{5} b - 3 \, a^{4} b^{2} + 3 \, a^{3} b^{3} - a^{2} b^{4}\right)} d + 2 \, {\left(3 \, {\left(a^{5} b - 3 \, a^{4} b^{2} + 3 \, a^{3} b^{3} - a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{5} + 2 \, {\left(4 \, a^{6} - 13 \, a^{5} b + 15 \, a^{4} b^{2} - 7 \, a^{3} b^{3} + a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{3} + {\left(4 \, a^{6} - 13 \, a^{5} b + 15 \, a^{4} b^{2} - 7 \, a^{3} b^{3} + a^{2} b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[-1/4*(4*(4*a^3*b - 5*a^2*b^2 + a*b^3)*cosh(d*x + c)^4 + 16*(4*a^3*b - 5*a^2*b^2 + a*b^3)*cosh(d*x + c)*sinh(d*x + c)^3 + 4*(4*a^3*b - 5*a^2*b^2 + a*b^3)*sinh(d*x + c)^4 + 8*a^3*b - 4*a^2*b^2 - 4*a*b^3 + 8*(4*a^4 - 5*a^3*b + a^2*b^2)*cosh(d*x + c)^2 + 8*(4*a^4 - 5*a^3*b + a^2*b^2 + 3*(4*a^3*b - 5*a^2*b^2 + a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((4*a*b^2 - b^3)*cosh(d*x + c)^6 + 6*(4*a*b^2 - b^3)*cosh(d*x + c)*sinh(d*x + c)^5 + (4*a*b^2 - b^3)*sinh(d*x + c)^6 + (16*a^2*b - 8*a*b^2 + b^3)*cosh(d*x + c)^4 + (16*a^2*b - 8*a*b^2 + b^3 + 15*(4*a*b^2 - b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 4*(5*(4*a*b^2 - b^3)*cosh(d*x + c)^3 + (16*a^2*b - 8*a*b^2 + b^3)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*a*b^2 - b^3 + (16*a^2*b - 8*a*b^2 + b^3)*cosh(d*x + c)^2 + (15*(4*a*b^2 - b^3)*cosh(d*x + c)^4 + 16*a^2*b - 8*a*b^2 + b^3 + 6*(16*a^2*b - 8*a*b^2 + b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 2*(3*(4*a*b^2 - b^3)*cosh(d*x + c)^5 + 2*(16*a^2*b - 8*a*b^2 + b^3)*cosh(d*x + c)^3 + (16*a^2*b - 8*a*b^2 + b^3)*cosh(d*x + c))*sinh(d*x + c))*sqrt(a^2 - a*b)*log((b^2*cosh(d*x + c)^4 + 4*b^2*cosh(d*x + c)*sinh(d*x + c)^3 + b^2*sinh(d*x + c)^4 + 2*(2*a*b - b^2)*cosh(d*x + c)^2 + 2*(3*b^2*cosh(d*x + c)^2 + 2*a*b - b^2)*sinh(d*x + c)^2 + 8*a^2 - 8*a*b + b^2 + 4*(b^2*cosh(d*x + c)^3 + (2*a*b - b^2)*cosh(d*x + c))*sinh(d*x + c) - 4*(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + 2*a - b)*sqrt(a^2 - a*b))/(b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 + 2*(2*a - b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 + 2*a - b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 + (2*a - b)*cosh(d*x + c))*sinh(d*x + c) + b)) + 16*((4*a^3*b - 5*a^2*b^2 + a*b^3)*cosh(d*x + c)^3 + (4*a^4 - 5*a^3*b + a^2*b^2)*cosh(d*x + c))*sinh(d*x + c))/((a^5*b - 3*a^4*b^2 + 3*a^3*b^3 - a^2*b^4)*d*cosh(d*x + c)^6 + 6*(a^5*b - 3*a^4*b^2 + 3*a^3*b^3 - a^2*b^4)*d*cosh(d*x + c)*sinh(d*x + c)^5 + (a^5*b - 3*a^4*b^2 + 3*a^3*b^3 - a^2*b^4)*d*sinh(d*x + c)^6 + (4*a^6 - 13*a^5*b + 15*a^4*b^2 - 7*a^3*b^3 + a^2*b^4)*d*cosh(d*x + c)^4 + (15*(a^5*b - 3*a^4*b^2 + 3*a^3*b^3 - a^2*b^4)*d*cosh(d*x + c)^2 + (4*a^6 - 13*a^5*b + 15*a^4*b^2 - 7*a^3*b^3 + a^2*b^4)*d)*sinh(d*x + c)^4 + (4*a^6 - 13*a^5*b + 15*a^4*b^2 - 7*a^3*b^3 + a^2*b^4)*d*cosh(d*x + c)^2 + 4*(5*(a^5*b - 3*a^4*b^2 + 3*a^3*b^3 - a^2*b^4)*d*cosh(d*x + c)^3 + (4*a^6 - 13*a^5*b + 15*a^4*b^2 - 7*a^3*b^3 + a^2*b^4)*d*cosh(d*x + c))*sinh(d*x + c)^3 + (15*(a^5*b - 3*a^4*b^2 + 3*a^3*b^3 - a^2*b^4)*d*cosh(d*x + c)^4 + 6*(4*a^6 - 13*a^5*b + 15*a^4*b^2 - 7*a^3*b^3 + a^2*b^4)*d*cosh(d*x + c)^2 + (4*a^6 - 13*a^5*b + 15*a^4*b^2 - 7*a^3*b^3 + a^2*b^4)*d)*sinh(d*x + c)^2 + (a^5*b - 3*a^4*b^2 + 3*a^3*b^3 - a^2*b^4)*d + 2*(3*(a^5*b - 3*a^4*b^2 + 3*a^3*b^3 - a^2*b^4)*d*cosh(d*x + c)^5 + 2*(4*a^6 - 13*a^5*b + 15*a^4*b^2 - 7*a^3*b^3 + a^2*b^4)*d*cosh(d*x + c)^3 + (4*a^6 - 13*a^5*b + 15*a^4*b^2 - 7*a^3*b^3 + a^2*b^4)*d*cosh(d*x + c))*sinh(d*x + c)), -1/2*(2*(4*a^3*b - 5*a^2*b^2 + a*b^3)*cosh(d*x + c)^4 + 8*(4*a^3*b - 5*a^2*b^2 + a*b^3)*cosh(d*x + c)*sinh(d*x + c)^3 + 2*(4*a^3*b - 5*a^2*b^2 + a*b^3)*sinh(d*x + c)^4 + 4*a^3*b - 2*a^2*b^2 - 2*a*b^3 + 4*(4*a^4 - 5*a^3*b + a^2*b^2)*cosh(d*x + c)^2 + 4*(4*a^4 - 5*a^3*b + a^2*b^2 + 3*(4*a^3*b - 5*a^2*b^2 + a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - ((4*a*b^2 - b^3)*cosh(d*x + c)^6 + 6*(4*a*b^2 - b^3)*cosh(d*x + c)*sinh(d*x + c)^5 + (4*a*b^2 - b^3)*sinh(d*x + c)^6 + (16*a^2*b - 8*a*b^2 + b^3)*cosh(d*x + c)^4 + (16*a^2*b - 8*a*b^2 + b^3 + 15*(4*a*b^2 - b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 4*(5*(4*a*b^2 - b^3)*cosh(d*x + c)^3 + (16*a^2*b - 8*a*b^2 + b^3)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*a*b^2 - b^3 + (16*a^2*b - 8*a*b^2 + b^3)*cosh(d*x + c)^2 + (15*(4*a*b^2 - b^3)*cosh(d*x + c)^4 + 16*a^2*b - 8*a*b^2 + b^3 + 6*(16*a^2*b - 8*a*b^2 + b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 2*(3*(4*a*b^2 - b^3)*cosh(d*x + c)^5 + 2*(16*a^2*b - 8*a*b^2 + b^3)*cosh(d*x + c)^3 + (16*a^2*b - 8*a*b^2 + b^3)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-a^2 + a*b)*arctan(-1/2*(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + 2*a - b)*sqrt(-a^2 + a*b)/(a^2 - a*b)) + 8*((4*a^3*b - 5*a^2*b^2 + a*b^3)*cosh(d*x + c)^3 + (4*a^4 - 5*a^3*b + a^2*b^2)*cosh(d*x + c))*sinh(d*x + c))/((a^5*b - 3*a^4*b^2 + 3*a^3*b^3 - a^2*b^4)*d*cosh(d*x + c)^6 + 6*(a^5*b - 3*a^4*b^2 + 3*a^3*b^3 - a^2*b^4)*d*cosh(d*x + c)*sinh(d*x + c)^5 + (a^5*b - 3*a^4*b^2 + 3*a^3*b^3 - a^2*b^4)*d*sinh(d*x + c)^6 + (4*a^6 - 13*a^5*b + 15*a^4*b^2 - 7*a^3*b^3 + a^2*b^4)*d*cosh(d*x + c)^4 + (15*(a^5*b - 3*a^4*b^2 + 3*a^3*b^3 - a^2*b^4)*d*cosh(d*x + c)^2 + (4*a^6 - 13*a^5*b + 15*a^4*b^2 - 7*a^3*b^3 + a^2*b^4)*d)*sinh(d*x + c)^4 + (4*a^6 - 13*a^5*b + 15*a^4*b^2 - 7*a^3*b^3 + a^2*b^4)*d*cosh(d*x + c)^2 + 4*(5*(a^5*b - 3*a^4*b^2 + 3*a^3*b^3 - a^2*b^4)*d*cosh(d*x + c)^3 + (4*a^6 - 13*a^5*b + 15*a^4*b^2 - 7*a^3*b^3 + a^2*b^4)*d*cosh(d*x + c))*sinh(d*x + c)^3 + (15*(a^5*b - 3*a^4*b^2 + 3*a^3*b^3 - a^2*b^4)*d*cosh(d*x + c)^4 + 6*(4*a^6 - 13*a^5*b + 15*a^4*b^2 - 7*a^3*b^3 + a^2*b^4)*d*cosh(d*x + c)^2 + (4*a^6 - 13*a^5*b + 15*a^4*b^2 - 7*a^3*b^3 + a^2*b^4)*d)*sinh(d*x + c)^2 + (a^5*b - 3*a^4*b^2 + 3*a^3*b^3 - a^2*b^4)*d + 2*(3*(a^5*b - 3*a^4*b^2 + 3*a^3*b^3 - a^2*b^4)*d*cosh(d*x + c)^5 + 2*(4*a^6 - 13*a^5*b + 15*a^4*b^2 - 7*a^3*b^3 + a^2*b^4)*d*cosh(d*x + c)^3 + (4*a^6 - 13*a^5*b + 15*a^4*b^2 - 7*a^3*b^3 + a^2*b^4)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
337,1,6548,0,0.774004," ","integrate(sech(d*x+c)^3/(a+b*sinh(d*x+c)^2)^2,x, algorithm=""fricas"")","\left[\frac{4 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(d x + c\right)^{7} + 28 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + 4 \, {\left(a^{2} b - b^{3}\right)} \sinh\left(d x + c\right)^{7} + 4 \, {\left(4 \, a^{3} - 7 \, a^{2} b + 4 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{5} + 4 \, {\left(4 \, a^{3} - 7 \, a^{2} b + 4 \, a b^{2} - b^{3} + 21 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{5} + 20 \, {\left(7 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(4 \, a^{3} - 7 \, a^{2} b + 4 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} - 4 \, {\left(4 \, a^{3} - 7 \, a^{2} b + 4 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(35 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(d x + c\right)^{4} - 4 \, a^{3} + 7 \, a^{2} b - 4 \, a b^{2} + b^{3} + 10 \, {\left(4 \, a^{3} - 7 \, a^{2} b + 4 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(21 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(4 \, a^{3} - 7 \, a^{2} b + 4 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(4 \, a^{3} - 7 \, a^{2} b + 4 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(5 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(5 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(5 \, a b^{2} - b^{3}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(5 \, a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(5 \, a^{2} b - a b^{2} + 7 \, {\left(5 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(5 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(5 \, a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(20 \, a^{2} b - 9 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(5 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{4} + 20 \, a^{2} b - 9 \, a b^{2} + b^{3} + 30 \, {\left(5 \, a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(5 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(5 \, a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(20 \, a^{2} b - 9 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 5 \, a b^{2} - b^{3} + 4 \, {\left(5 \, a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(5 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(5 \, a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right)^{4} + 5 \, a^{2} b - a b^{2} + 3 \, {\left(20 \, a^{2} b - 9 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left({\left(5 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(5 \, a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right)^{5} + {\left(20 \, a^{2} b - 9 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(5 \, a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} - 2 \, {\left(2 \, a + b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} - 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} - {\left(2 \, a + b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + 4 \, {\left(a \cosh\left(d x + c\right)^{3} + 3 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{3} - a \cosh\left(d x + c\right) + {\left(3 \, a \cosh\left(d x + c\right)^{2} - a\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{b}{a}} + b}{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b}\right) + 4 \, {\left({\left(a^{2} b - 5 \, a b^{2}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{2} b - 5 \, a b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{2} b - 5 \, a b^{2}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{3} - 5 \, a^{2} b\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(a^{3} - 5 \, a^{2} b + 7 \, {\left(a^{2} b - 5 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} b - 5 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{3} - 5 \, a^{2} b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(4 \, a^{3} - 21 \, a^{2} b + 5 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} b - 5 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, a^{3} - 21 \, a^{2} b + 5 \, a b^{2} + 30 \, {\left(a^{3} - 5 \, a^{2} b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} b - 5 \, a b^{2}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{3} - 5 \, a^{2} b\right)} \cosh\left(d x + c\right)^{3} + {\left(4 \, a^{3} - 21 \, a^{2} b + 5 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + a^{2} b - 5 \, a b^{2} + 4 \, {\left(a^{3} - 5 \, a^{2} b\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} b - 5 \, a b^{2}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{3} - 5 \, a^{2} b\right)} \cosh\left(d x + c\right)^{4} + a^{3} - 5 \, a^{2} b + 3 \, {\left(4 \, a^{3} - 21 \, a^{2} b + 5 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left({\left(a^{2} b - 5 \, a b^{2}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{3} - 5 \, a^{2} b\right)} \cosh\left(d x + c\right)^{5} + {\left(4 \, a^{3} - 21 \, a^{2} b + 5 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{3} - 5 \, a^{2} b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \arctan\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) - 4 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(d x + c\right) + 4 \, {\left(7 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(d x + c\right)^{6} + 5 \, {\left(4 \, a^{3} - 7 \, a^{2} b + 4 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{4} - a^{2} b + b^{3} - 3 \, {\left(4 \, a^{3} - 7 \, a^{2} b + 4 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)}{4 \, {\left({\left(a^{4} b - 3 \, a^{3} b^{2} + 3 \, a^{2} b^{3} - a b^{4}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{4} b - 3 \, a^{3} b^{2} + 3 \, a^{2} b^{3} - a b^{4}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{4} b - 3 \, a^{3} b^{2} + 3 \, a^{2} b^{3} - a b^{4}\right)} d \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{5} - 3 \, a^{4} b + 3 \, a^{3} b^{2} - a^{2} b^{3}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{4} b - 3 \, a^{3} b^{2} + 3 \, a^{2} b^{3} - a b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{5} - 3 \, a^{4} b + 3 \, a^{3} b^{2} - a^{2} b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(4 \, a^{5} - 13 \, a^{4} b + 15 \, a^{3} b^{2} - 7 \, a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{4} b - 3 \, a^{3} b^{2} + 3 \, a^{2} b^{3} - a b^{4}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{5} - 3 \, a^{4} b + 3 \, a^{3} b^{2} - a^{2} b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a^{4} b - 3 \, a^{3} b^{2} + 3 \, a^{2} b^{3} - a b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 30 \, {\left(a^{5} - 3 \, a^{4} b + 3 \, a^{3} b^{2} - a^{2} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + {\left(4 \, a^{5} - 13 \, a^{4} b + 15 \, a^{3} b^{2} - 7 \, a^{2} b^{3} + a b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{5} - 3 \, a^{4} b + 3 \, a^{3} b^{2} - a^{2} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a^{4} b - 3 \, a^{3} b^{2} + 3 \, a^{2} b^{3} - a b^{4}\right)} d \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{5} - 3 \, a^{4} b + 3 \, a^{3} b^{2} - a^{2} b^{3}\right)} d \cosh\left(d x + c\right)^{3} + {\left(4 \, a^{5} - 13 \, a^{4} b + 15 \, a^{3} b^{2} - 7 \, a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a^{4} b - 3 \, a^{3} b^{2} + 3 \, a^{2} b^{3} - a b^{4}\right)} d \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{5} - 3 \, a^{4} b + 3 \, a^{3} b^{2} - a^{2} b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(4 \, a^{5} - 13 \, a^{4} b + 15 \, a^{3} b^{2} - 7 \, a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{5} - 3 \, a^{4} b + 3 \, a^{3} b^{2} - a^{2} b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{4} b - 3 \, a^{3} b^{2} + 3 \, a^{2} b^{3} - a b^{4}\right)} d + 8 \, {\left({\left(a^{4} b - 3 \, a^{3} b^{2} + 3 \, a^{2} b^{3} - a b^{4}\right)} d \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{5} - 3 \, a^{4} b + 3 \, a^{3} b^{2} - a^{2} b^{3}\right)} d \cosh\left(d x + c\right)^{5} + {\left(4 \, a^{5} - 13 \, a^{4} b + 15 \, a^{3} b^{2} - 7 \, a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{5} - 3 \, a^{4} b + 3 \, a^{3} b^{2} - a^{2} b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}, \frac{2 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(d x + c\right)^{7} + 14 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + 2 \, {\left(a^{2} b - b^{3}\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(4 \, a^{3} - 7 \, a^{2} b + 4 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(4 \, a^{3} - 7 \, a^{2} b + 4 \, a b^{2} - b^{3} + 21 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{5} + 10 \, {\left(7 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(4 \, a^{3} - 7 \, a^{2} b + 4 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(4 \, a^{3} - 7 \, a^{2} b + 4 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(35 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(d x + c\right)^{4} - 4 \, a^{3} + 7 \, a^{2} b - 4 \, a b^{2} + b^{3} + 10 \, {\left(4 \, a^{3} - 7 \, a^{2} b + 4 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(21 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(4 \, a^{3} - 7 \, a^{2} b + 4 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(4 \, a^{3} - 7 \, a^{2} b + 4 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(5 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(5 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(5 \, a b^{2} - b^{3}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(5 \, a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(5 \, a^{2} b - a b^{2} + 7 \, {\left(5 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(5 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(5 \, a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(20 \, a^{2} b - 9 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(5 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{4} + 20 \, a^{2} b - 9 \, a b^{2} + b^{3} + 30 \, {\left(5 \, a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(5 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(5 \, a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(20 \, a^{2} b - 9 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 5 \, a b^{2} - b^{3} + 4 \, {\left(5 \, a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(5 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(5 \, a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right)^{4} + 5 \, a^{2} b - a b^{2} + 3 \, {\left(20 \, a^{2} b - 9 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left({\left(5 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(5 \, a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right)^{5} + {\left(20 \, a^{2} b - 9 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(5 \, a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{b}{a}} \arctan\left(\frac{1}{2} \, \sqrt{\frac{b}{a}} {\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right)}\right) + {\left({\left(5 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(5 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(5 \, a b^{2} - b^{3}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(5 \, a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(5 \, a^{2} b - a b^{2} + 7 \, {\left(5 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(5 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(5 \, a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(20 \, a^{2} b - 9 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(5 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{4} + 20 \, a^{2} b - 9 \, a b^{2} + b^{3} + 30 \, {\left(5 \, a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(5 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(5 \, a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(20 \, a^{2} b - 9 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 5 \, a b^{2} - b^{3} + 4 \, {\left(5 \, a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(5 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(5 \, a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right)^{4} + 5 \, a^{2} b - a b^{2} + 3 \, {\left(20 \, a^{2} b - 9 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left({\left(5 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(5 \, a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right)^{5} + {\left(20 \, a^{2} b - 9 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(5 \, a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{b}{a}} \arctan\left(\frac{{\left(b \cosh\left(d x + c\right)^{3} + 3 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{3} + {\left(4 \, a - b\right)} \cosh\left(d x + c\right) + {\left(3 \, b \cosh\left(d x + c\right)^{2} + 4 \, a - b\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{b}{a}}}{2 \, b}\right) + 2 \, {\left({\left(a^{2} b - 5 \, a b^{2}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{2} b - 5 \, a b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{2} b - 5 \, a b^{2}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{3} - 5 \, a^{2} b\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(a^{3} - 5 \, a^{2} b + 7 \, {\left(a^{2} b - 5 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} b - 5 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{3} - 5 \, a^{2} b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(4 \, a^{3} - 21 \, a^{2} b + 5 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} b - 5 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, a^{3} - 21 \, a^{2} b + 5 \, a b^{2} + 30 \, {\left(a^{3} - 5 \, a^{2} b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} b - 5 \, a b^{2}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{3} - 5 \, a^{2} b\right)} \cosh\left(d x + c\right)^{3} + {\left(4 \, a^{3} - 21 \, a^{2} b + 5 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + a^{2} b - 5 \, a b^{2} + 4 \, {\left(a^{3} - 5 \, a^{2} b\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} b - 5 \, a b^{2}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{3} - 5 \, a^{2} b\right)} \cosh\left(d x + c\right)^{4} + a^{3} - 5 \, a^{2} b + 3 \, {\left(4 \, a^{3} - 21 \, a^{2} b + 5 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left({\left(a^{2} b - 5 \, a b^{2}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{3} - 5 \, a^{2} b\right)} \cosh\left(d x + c\right)^{5} + {\left(4 \, a^{3} - 21 \, a^{2} b + 5 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{3} - 5 \, a^{2} b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \arctan\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) - 2 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(d x + c\right) + 2 \, {\left(7 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(d x + c\right)^{6} + 5 \, {\left(4 \, a^{3} - 7 \, a^{2} b + 4 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{4} - a^{2} b + b^{3} - 3 \, {\left(4 \, a^{3} - 7 \, a^{2} b + 4 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)}{2 \, {\left({\left(a^{4} b - 3 \, a^{3} b^{2} + 3 \, a^{2} b^{3} - a b^{4}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{4} b - 3 \, a^{3} b^{2} + 3 \, a^{2} b^{3} - a b^{4}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{4} b - 3 \, a^{3} b^{2} + 3 \, a^{2} b^{3} - a b^{4}\right)} d \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{5} - 3 \, a^{4} b + 3 \, a^{3} b^{2} - a^{2} b^{3}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{4} b - 3 \, a^{3} b^{2} + 3 \, a^{2} b^{3} - a b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{5} - 3 \, a^{4} b + 3 \, a^{3} b^{2} - a^{2} b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(4 \, a^{5} - 13 \, a^{4} b + 15 \, a^{3} b^{2} - 7 \, a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{4} b - 3 \, a^{3} b^{2} + 3 \, a^{2} b^{3} - a b^{4}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{5} - 3 \, a^{4} b + 3 \, a^{3} b^{2} - a^{2} b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a^{4} b - 3 \, a^{3} b^{2} + 3 \, a^{2} b^{3} - a b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 30 \, {\left(a^{5} - 3 \, a^{4} b + 3 \, a^{3} b^{2} - a^{2} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + {\left(4 \, a^{5} - 13 \, a^{4} b + 15 \, a^{3} b^{2} - 7 \, a^{2} b^{3} + a b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{5} - 3 \, a^{4} b + 3 \, a^{3} b^{2} - a^{2} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a^{4} b - 3 \, a^{3} b^{2} + 3 \, a^{2} b^{3} - a b^{4}\right)} d \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{5} - 3 \, a^{4} b + 3 \, a^{3} b^{2} - a^{2} b^{3}\right)} d \cosh\left(d x + c\right)^{3} + {\left(4 \, a^{5} - 13 \, a^{4} b + 15 \, a^{3} b^{2} - 7 \, a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a^{4} b - 3 \, a^{3} b^{2} + 3 \, a^{2} b^{3} - a b^{4}\right)} d \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{5} - 3 \, a^{4} b + 3 \, a^{3} b^{2} - a^{2} b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(4 \, a^{5} - 13 \, a^{4} b + 15 \, a^{3} b^{2} - 7 \, a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{5} - 3 \, a^{4} b + 3 \, a^{3} b^{2} - a^{2} b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{4} b - 3 \, a^{3} b^{2} + 3 \, a^{2} b^{3} - a b^{4}\right)} d + 8 \, {\left({\left(a^{4} b - 3 \, a^{3} b^{2} + 3 \, a^{2} b^{3} - a b^{4}\right)} d \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{5} - 3 \, a^{4} b + 3 \, a^{3} b^{2} - a^{2} b^{3}\right)} d \cosh\left(d x + c\right)^{5} + {\left(4 \, a^{5} - 13 \, a^{4} b + 15 \, a^{3} b^{2} - 7 \, a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{5} - 3 \, a^{4} b + 3 \, a^{3} b^{2} - a^{2} b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[1/4*(4*(a^2*b - b^3)*cosh(d*x + c)^7 + 28*(a^2*b - b^3)*cosh(d*x + c)*sinh(d*x + c)^6 + 4*(a^2*b - b^3)*sinh(d*x + c)^7 + 4*(4*a^3 - 7*a^2*b + 4*a*b^2 - b^3)*cosh(d*x + c)^5 + 4*(4*a^3 - 7*a^2*b + 4*a*b^2 - b^3 + 21*(a^2*b - b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 20*(7*(a^2*b - b^3)*cosh(d*x + c)^3 + (4*a^3 - 7*a^2*b + 4*a*b^2 - b^3)*cosh(d*x + c))*sinh(d*x + c)^4 - 4*(4*a^3 - 7*a^2*b + 4*a*b^2 - b^3)*cosh(d*x + c)^3 + 4*(35*(a^2*b - b^3)*cosh(d*x + c)^4 - 4*a^3 + 7*a^2*b - 4*a*b^2 + b^3 + 10*(4*a^3 - 7*a^2*b + 4*a*b^2 - b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 4*(21*(a^2*b - b^3)*cosh(d*x + c)^5 + 10*(4*a^3 - 7*a^2*b + 4*a*b^2 - b^3)*cosh(d*x + c)^3 - 3*(4*a^3 - 7*a^2*b + 4*a*b^2 - b^3)*cosh(d*x + c))*sinh(d*x + c)^2 + ((5*a*b^2 - b^3)*cosh(d*x + c)^8 + 8*(5*a*b^2 - b^3)*cosh(d*x + c)*sinh(d*x + c)^7 + (5*a*b^2 - b^3)*sinh(d*x + c)^8 + 4*(5*a^2*b - a*b^2)*cosh(d*x + c)^6 + 4*(5*a^2*b - a*b^2 + 7*(5*a*b^2 - b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(5*a*b^2 - b^3)*cosh(d*x + c)^3 + 3*(5*a^2*b - a*b^2)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(20*a^2*b - 9*a*b^2 + b^3)*cosh(d*x + c)^4 + 2*(35*(5*a*b^2 - b^3)*cosh(d*x + c)^4 + 20*a^2*b - 9*a*b^2 + b^3 + 30*(5*a^2*b - a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(7*(5*a*b^2 - b^3)*cosh(d*x + c)^5 + 10*(5*a^2*b - a*b^2)*cosh(d*x + c)^3 + (20*a^2*b - 9*a*b^2 + b^3)*cosh(d*x + c))*sinh(d*x + c)^3 + 5*a*b^2 - b^3 + 4*(5*a^2*b - a*b^2)*cosh(d*x + c)^2 + 4*(7*(5*a*b^2 - b^3)*cosh(d*x + c)^6 + 15*(5*a^2*b - a*b^2)*cosh(d*x + c)^4 + 5*a^2*b - a*b^2 + 3*(20*a^2*b - 9*a*b^2 + b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((5*a*b^2 - b^3)*cosh(d*x + c)^7 + 3*(5*a^2*b - a*b^2)*cosh(d*x + c)^5 + (20*a^2*b - 9*a*b^2 + b^3)*cosh(d*x + c)^3 + (5*a^2*b - a*b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-b/a)*log((b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 - 2*(2*a + b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 - 2*a - b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 - (2*a + b)*cosh(d*x + c))*sinh(d*x + c) + 4*(a*cosh(d*x + c)^3 + 3*a*cosh(d*x + c)*sinh(d*x + c)^2 + a*sinh(d*x + c)^3 - a*cosh(d*x + c) + (3*a*cosh(d*x + c)^2 - a)*sinh(d*x + c))*sqrt(-b/a) + b)/(b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 + 2*(2*a - b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 + 2*a - b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 + (2*a - b)*cosh(d*x + c))*sinh(d*x + c) + b)) + 4*((a^2*b - 5*a*b^2)*cosh(d*x + c)^8 + 8*(a^2*b - 5*a*b^2)*cosh(d*x + c)*sinh(d*x + c)^7 + (a^2*b - 5*a*b^2)*sinh(d*x + c)^8 + 4*(a^3 - 5*a^2*b)*cosh(d*x + c)^6 + 4*(a^3 - 5*a^2*b + 7*(a^2*b - 5*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(a^2*b - 5*a*b^2)*cosh(d*x + c)^3 + 3*(a^3 - 5*a^2*b)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(4*a^3 - 21*a^2*b + 5*a*b^2)*cosh(d*x + c)^4 + 2*(35*(a^2*b - 5*a*b^2)*cosh(d*x + c)^4 + 4*a^3 - 21*a^2*b + 5*a*b^2 + 30*(a^3 - 5*a^2*b)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(7*(a^2*b - 5*a*b^2)*cosh(d*x + c)^5 + 10*(a^3 - 5*a^2*b)*cosh(d*x + c)^3 + (4*a^3 - 21*a^2*b + 5*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + a^2*b - 5*a*b^2 + 4*(a^3 - 5*a^2*b)*cosh(d*x + c)^2 + 4*(7*(a^2*b - 5*a*b^2)*cosh(d*x + c)^6 + 15*(a^3 - 5*a^2*b)*cosh(d*x + c)^4 + a^3 - 5*a^2*b + 3*(4*a^3 - 21*a^2*b + 5*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((a^2*b - 5*a*b^2)*cosh(d*x + c)^7 + 3*(a^3 - 5*a^2*b)*cosh(d*x + c)^5 + (4*a^3 - 21*a^2*b + 5*a*b^2)*cosh(d*x + c)^3 + (a^3 - 5*a^2*b)*cosh(d*x + c))*sinh(d*x + c))*arctan(cosh(d*x + c) + sinh(d*x + c)) - 4*(a^2*b - b^3)*cosh(d*x + c) + 4*(7*(a^2*b - b^3)*cosh(d*x + c)^6 + 5*(4*a^3 - 7*a^2*b + 4*a*b^2 - b^3)*cosh(d*x + c)^4 - a^2*b + b^3 - 3*(4*a^3 - 7*a^2*b + 4*a*b^2 - b^3)*cosh(d*x + c)^2)*sinh(d*x + c))/((a^4*b - 3*a^3*b^2 + 3*a^2*b^3 - a*b^4)*d*cosh(d*x + c)^8 + 8*(a^4*b - 3*a^3*b^2 + 3*a^2*b^3 - a*b^4)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^4*b - 3*a^3*b^2 + 3*a^2*b^3 - a*b^4)*d*sinh(d*x + c)^8 + 4*(a^5 - 3*a^4*b + 3*a^3*b^2 - a^2*b^3)*d*cosh(d*x + c)^6 + 4*(7*(a^4*b - 3*a^3*b^2 + 3*a^2*b^3 - a*b^4)*d*cosh(d*x + c)^2 + (a^5 - 3*a^4*b + 3*a^3*b^2 - a^2*b^3)*d)*sinh(d*x + c)^6 + 2*(4*a^5 - 13*a^4*b + 15*a^3*b^2 - 7*a^2*b^3 + a*b^4)*d*cosh(d*x + c)^4 + 8*(7*(a^4*b - 3*a^3*b^2 + 3*a^2*b^3 - a*b^4)*d*cosh(d*x + c)^3 + 3*(a^5 - 3*a^4*b + 3*a^3*b^2 - a^2*b^3)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^4*b - 3*a^3*b^2 + 3*a^2*b^3 - a*b^4)*d*cosh(d*x + c)^4 + 30*(a^5 - 3*a^4*b + 3*a^3*b^2 - a^2*b^3)*d*cosh(d*x + c)^2 + (4*a^5 - 13*a^4*b + 15*a^3*b^2 - 7*a^2*b^3 + a*b^4)*d)*sinh(d*x + c)^4 + 4*(a^5 - 3*a^4*b + 3*a^3*b^2 - a^2*b^3)*d*cosh(d*x + c)^2 + 8*(7*(a^4*b - 3*a^3*b^2 + 3*a^2*b^3 - a*b^4)*d*cosh(d*x + c)^5 + 10*(a^5 - 3*a^4*b + 3*a^3*b^2 - a^2*b^3)*d*cosh(d*x + c)^3 + (4*a^5 - 13*a^4*b + 15*a^3*b^2 - 7*a^2*b^3 + a*b^4)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^4*b - 3*a^3*b^2 + 3*a^2*b^3 - a*b^4)*d*cosh(d*x + c)^6 + 15*(a^5 - 3*a^4*b + 3*a^3*b^2 - a^2*b^3)*d*cosh(d*x + c)^4 + 3*(4*a^5 - 13*a^4*b + 15*a^3*b^2 - 7*a^2*b^3 + a*b^4)*d*cosh(d*x + c)^2 + (a^5 - 3*a^4*b + 3*a^3*b^2 - a^2*b^3)*d)*sinh(d*x + c)^2 + (a^4*b - 3*a^3*b^2 + 3*a^2*b^3 - a*b^4)*d + 8*((a^4*b - 3*a^3*b^2 + 3*a^2*b^3 - a*b^4)*d*cosh(d*x + c)^7 + 3*(a^5 - 3*a^4*b + 3*a^3*b^2 - a^2*b^3)*d*cosh(d*x + c)^5 + (4*a^5 - 13*a^4*b + 15*a^3*b^2 - 7*a^2*b^3 + a*b^4)*d*cosh(d*x + c)^3 + (a^5 - 3*a^4*b + 3*a^3*b^2 - a^2*b^3)*d*cosh(d*x + c))*sinh(d*x + c)), 1/2*(2*(a^2*b - b^3)*cosh(d*x + c)^7 + 14*(a^2*b - b^3)*cosh(d*x + c)*sinh(d*x + c)^6 + 2*(a^2*b - b^3)*sinh(d*x + c)^7 + 2*(4*a^3 - 7*a^2*b + 4*a*b^2 - b^3)*cosh(d*x + c)^5 + 2*(4*a^3 - 7*a^2*b + 4*a*b^2 - b^3 + 21*(a^2*b - b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 10*(7*(a^2*b - b^3)*cosh(d*x + c)^3 + (4*a^3 - 7*a^2*b + 4*a*b^2 - b^3)*cosh(d*x + c))*sinh(d*x + c)^4 - 2*(4*a^3 - 7*a^2*b + 4*a*b^2 - b^3)*cosh(d*x + c)^3 + 2*(35*(a^2*b - b^3)*cosh(d*x + c)^4 - 4*a^3 + 7*a^2*b - 4*a*b^2 + b^3 + 10*(4*a^3 - 7*a^2*b + 4*a*b^2 - b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 2*(21*(a^2*b - b^3)*cosh(d*x + c)^5 + 10*(4*a^3 - 7*a^2*b + 4*a*b^2 - b^3)*cosh(d*x + c)^3 - 3*(4*a^3 - 7*a^2*b + 4*a*b^2 - b^3)*cosh(d*x + c))*sinh(d*x + c)^2 + ((5*a*b^2 - b^3)*cosh(d*x + c)^8 + 8*(5*a*b^2 - b^3)*cosh(d*x + c)*sinh(d*x + c)^7 + (5*a*b^2 - b^3)*sinh(d*x + c)^8 + 4*(5*a^2*b - a*b^2)*cosh(d*x + c)^6 + 4*(5*a^2*b - a*b^2 + 7*(5*a*b^2 - b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(5*a*b^2 - b^3)*cosh(d*x + c)^3 + 3*(5*a^2*b - a*b^2)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(20*a^2*b - 9*a*b^2 + b^3)*cosh(d*x + c)^4 + 2*(35*(5*a*b^2 - b^3)*cosh(d*x + c)^4 + 20*a^2*b - 9*a*b^2 + b^3 + 30*(5*a^2*b - a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(7*(5*a*b^2 - b^3)*cosh(d*x + c)^5 + 10*(5*a^2*b - a*b^2)*cosh(d*x + c)^3 + (20*a^2*b - 9*a*b^2 + b^3)*cosh(d*x + c))*sinh(d*x + c)^3 + 5*a*b^2 - b^3 + 4*(5*a^2*b - a*b^2)*cosh(d*x + c)^2 + 4*(7*(5*a*b^2 - b^3)*cosh(d*x + c)^6 + 15*(5*a^2*b - a*b^2)*cosh(d*x + c)^4 + 5*a^2*b - a*b^2 + 3*(20*a^2*b - 9*a*b^2 + b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((5*a*b^2 - b^3)*cosh(d*x + c)^7 + 3*(5*a^2*b - a*b^2)*cosh(d*x + c)^5 + (20*a^2*b - 9*a*b^2 + b^3)*cosh(d*x + c)^3 + (5*a^2*b - a*b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(b/a)*arctan(1/2*sqrt(b/a)*(cosh(d*x + c) + sinh(d*x + c))) + ((5*a*b^2 - b^3)*cosh(d*x + c)^8 + 8*(5*a*b^2 - b^3)*cosh(d*x + c)*sinh(d*x + c)^7 + (5*a*b^2 - b^3)*sinh(d*x + c)^8 + 4*(5*a^2*b - a*b^2)*cosh(d*x + c)^6 + 4*(5*a^2*b - a*b^2 + 7*(5*a*b^2 - b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(5*a*b^2 - b^3)*cosh(d*x + c)^3 + 3*(5*a^2*b - a*b^2)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(20*a^2*b - 9*a*b^2 + b^3)*cosh(d*x + c)^4 + 2*(35*(5*a*b^2 - b^3)*cosh(d*x + c)^4 + 20*a^2*b - 9*a*b^2 + b^3 + 30*(5*a^2*b - a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(7*(5*a*b^2 - b^3)*cosh(d*x + c)^5 + 10*(5*a^2*b - a*b^2)*cosh(d*x + c)^3 + (20*a^2*b - 9*a*b^2 + b^3)*cosh(d*x + c))*sinh(d*x + c)^3 + 5*a*b^2 - b^3 + 4*(5*a^2*b - a*b^2)*cosh(d*x + c)^2 + 4*(7*(5*a*b^2 - b^3)*cosh(d*x + c)^6 + 15*(5*a^2*b - a*b^2)*cosh(d*x + c)^4 + 5*a^2*b - a*b^2 + 3*(20*a^2*b - 9*a*b^2 + b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((5*a*b^2 - b^3)*cosh(d*x + c)^7 + 3*(5*a^2*b - a*b^2)*cosh(d*x + c)^5 + (20*a^2*b - 9*a*b^2 + b^3)*cosh(d*x + c)^3 + (5*a^2*b - a*b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(b/a)*arctan(1/2*(b*cosh(d*x + c)^3 + 3*b*cosh(d*x + c)*sinh(d*x + c)^2 + b*sinh(d*x + c)^3 + (4*a - b)*cosh(d*x + c) + (3*b*cosh(d*x + c)^2 + 4*a - b)*sinh(d*x + c))*sqrt(b/a)/b) + 2*((a^2*b - 5*a*b^2)*cosh(d*x + c)^8 + 8*(a^2*b - 5*a*b^2)*cosh(d*x + c)*sinh(d*x + c)^7 + (a^2*b - 5*a*b^2)*sinh(d*x + c)^8 + 4*(a^3 - 5*a^2*b)*cosh(d*x + c)^6 + 4*(a^3 - 5*a^2*b + 7*(a^2*b - 5*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(a^2*b - 5*a*b^2)*cosh(d*x + c)^3 + 3*(a^3 - 5*a^2*b)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(4*a^3 - 21*a^2*b + 5*a*b^2)*cosh(d*x + c)^4 + 2*(35*(a^2*b - 5*a*b^2)*cosh(d*x + c)^4 + 4*a^3 - 21*a^2*b + 5*a*b^2 + 30*(a^3 - 5*a^2*b)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(7*(a^2*b - 5*a*b^2)*cosh(d*x + c)^5 + 10*(a^3 - 5*a^2*b)*cosh(d*x + c)^3 + (4*a^3 - 21*a^2*b + 5*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + a^2*b - 5*a*b^2 + 4*(a^3 - 5*a^2*b)*cosh(d*x + c)^2 + 4*(7*(a^2*b - 5*a*b^2)*cosh(d*x + c)^6 + 15*(a^3 - 5*a^2*b)*cosh(d*x + c)^4 + a^3 - 5*a^2*b + 3*(4*a^3 - 21*a^2*b + 5*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((a^2*b - 5*a*b^2)*cosh(d*x + c)^7 + 3*(a^3 - 5*a^2*b)*cosh(d*x + c)^5 + (4*a^3 - 21*a^2*b + 5*a*b^2)*cosh(d*x + c)^3 + (a^3 - 5*a^2*b)*cosh(d*x + c))*sinh(d*x + c))*arctan(cosh(d*x + c) + sinh(d*x + c)) - 2*(a^2*b - b^3)*cosh(d*x + c) + 2*(7*(a^2*b - b^3)*cosh(d*x + c)^6 + 5*(4*a^3 - 7*a^2*b + 4*a*b^2 - b^3)*cosh(d*x + c)^4 - a^2*b + b^3 - 3*(4*a^3 - 7*a^2*b + 4*a*b^2 - b^3)*cosh(d*x + c)^2)*sinh(d*x + c))/((a^4*b - 3*a^3*b^2 + 3*a^2*b^3 - a*b^4)*d*cosh(d*x + c)^8 + 8*(a^4*b - 3*a^3*b^2 + 3*a^2*b^3 - a*b^4)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^4*b - 3*a^3*b^2 + 3*a^2*b^3 - a*b^4)*d*sinh(d*x + c)^8 + 4*(a^5 - 3*a^4*b + 3*a^3*b^2 - a^2*b^3)*d*cosh(d*x + c)^6 + 4*(7*(a^4*b - 3*a^3*b^2 + 3*a^2*b^3 - a*b^4)*d*cosh(d*x + c)^2 + (a^5 - 3*a^4*b + 3*a^3*b^2 - a^2*b^3)*d)*sinh(d*x + c)^6 + 2*(4*a^5 - 13*a^4*b + 15*a^3*b^2 - 7*a^2*b^3 + a*b^4)*d*cosh(d*x + c)^4 + 8*(7*(a^4*b - 3*a^3*b^2 + 3*a^2*b^3 - a*b^4)*d*cosh(d*x + c)^3 + 3*(a^5 - 3*a^4*b + 3*a^3*b^2 - a^2*b^3)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^4*b - 3*a^3*b^2 + 3*a^2*b^3 - a*b^4)*d*cosh(d*x + c)^4 + 30*(a^5 - 3*a^4*b + 3*a^3*b^2 - a^2*b^3)*d*cosh(d*x + c)^2 + (4*a^5 - 13*a^4*b + 15*a^3*b^2 - 7*a^2*b^3 + a*b^4)*d)*sinh(d*x + c)^4 + 4*(a^5 - 3*a^4*b + 3*a^3*b^2 - a^2*b^3)*d*cosh(d*x + c)^2 + 8*(7*(a^4*b - 3*a^3*b^2 + 3*a^2*b^3 - a*b^4)*d*cosh(d*x + c)^5 + 10*(a^5 - 3*a^4*b + 3*a^3*b^2 - a^2*b^3)*d*cosh(d*x + c)^3 + (4*a^5 - 13*a^4*b + 15*a^3*b^2 - 7*a^2*b^3 + a*b^4)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^4*b - 3*a^3*b^2 + 3*a^2*b^3 - a*b^4)*d*cosh(d*x + c)^6 + 15*(a^5 - 3*a^4*b + 3*a^3*b^2 - a^2*b^3)*d*cosh(d*x + c)^4 + 3*(4*a^5 - 13*a^4*b + 15*a^3*b^2 - 7*a^2*b^3 + a*b^4)*d*cosh(d*x + c)^2 + (a^5 - 3*a^4*b + 3*a^3*b^2 - a^2*b^3)*d)*sinh(d*x + c)^2 + (a^4*b - 3*a^3*b^2 + 3*a^2*b^3 - a*b^4)*d + 8*((a^4*b - 3*a^3*b^2 + 3*a^2*b^3 - a*b^4)*d*cosh(d*x + c)^7 + 3*(a^5 - 3*a^4*b + 3*a^3*b^2 - a^2*b^3)*d*cosh(d*x + c)^5 + (4*a^5 - 13*a^4*b + 15*a^3*b^2 - 7*a^2*b^3 + a*b^4)*d*cosh(d*x + c)^3 + (a^5 - 3*a^4*b + 3*a^3*b^2 - a^2*b^3)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
338,1,7894,0,0.749254," ","integrate(sech(d*x+c)^4/(a+b*sinh(d*x+c)^2)^2,x, algorithm=""fricas"")","\left[\frac{12 \, {\left(6 \, a^{3} b^{2} - 7 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(d x + c\right)^{8} + 96 \, {\left(6 \, a^{3} b^{2} - 7 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + 12 \, {\left(6 \, a^{3} b^{2} - 7 \, a^{2} b^{3} + a b^{4}\right)} \sinh\left(d x + c\right)^{8} + 24 \, {\left(6 \, a^{4} b - a^{3} b^{2} - 6 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(d x + c\right)^{6} + 24 \, {\left(6 \, a^{4} b - a^{3} b^{2} - 6 \, a^{2} b^{3} + a b^{4} + 14 \, {\left(6 \, a^{3} b^{2} - 7 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 48 \, {\left(14 \, {\left(6 \, a^{3} b^{2} - 7 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(6 \, a^{4} b - a^{3} b^{2} - 6 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 16 \, a^{4} b + 80 \, a^{3} b^{2} - 52 \, a^{2} b^{3} - 12 \, a b^{4} - 8 \, {\left(24 \, a^{5} - 106 \, a^{4} b + 95 \, a^{3} b^{2} - 13 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{4} - 8 \, {\left(24 \, a^{5} - 106 \, a^{4} b + 95 \, a^{3} b^{2} - 13 \, a^{2} b^{3} - 105 \, {\left(6 \, a^{3} b^{2} - 7 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(d x + c\right)^{4} - 45 \, {\left(6 \, a^{4} b - a^{3} b^{2} - 6 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 32 \, {\left(21 \, {\left(6 \, a^{3} b^{2} - 7 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(d x + c\right)^{5} + 15 \, {\left(6 \, a^{4} b - a^{3} b^{2} - 6 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(d x + c\right)^{3} - {\left(24 \, a^{5} - 106 \, a^{4} b + 95 \, a^{3} b^{2} - 13 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 8 \, {\left(8 \, a^{5} - 38 \, a^{4} b + 25 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{2} + 8 \, {\left(42 \, {\left(6 \, a^{3} b^{2} - 7 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(d x + c\right)^{6} - 8 \, a^{5} + 38 \, a^{4} b - 25 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} + 45 \, {\left(6 \, a^{4} b - a^{3} b^{2} - 6 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(d x + c\right)^{4} - 6 \, {\left(24 \, a^{5} - 106 \, a^{4} b + 95 \, a^{3} b^{2} - 13 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 3 \, {\left({\left(6 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{10} + 10 \, {\left(6 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + {\left(6 \, a b^{3} - b^{4}\right)} \sinh\left(d x + c\right)^{10} + {\left(24 \, a^{2} b^{2} + 2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{8} + {\left(24 \, a^{2} b^{2} + 2 \, a b^{3} - b^{4} + 45 \, {\left(6 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{8} + 8 \, {\left(15 \, {\left(6 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(24 \, a^{2} b^{2} + 2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(36 \, a^{2} b^{2} - 12 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(105 \, {\left(6 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{4} + 36 \, a^{2} b^{2} - 12 \, a b^{3} + b^{4} + 14 \, {\left(24 \, a^{2} b^{2} + 2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(63 \, {\left(6 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{5} + 14 \, {\left(24 \, a^{2} b^{2} + 2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(36 \, a^{2} b^{2} - 12 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(36 \, a^{2} b^{2} - 12 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(105 \, {\left(6 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{6} + 35 \, {\left(24 \, a^{2} b^{2} + 2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{4} + 36 \, a^{2} b^{2} - 12 \, a b^{3} + b^{4} + 15 \, {\left(36 \, a^{2} b^{2} - 12 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 6 \, a b^{3} - b^{4} + 8 \, {\left(15 \, {\left(6 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{7} + 7 \, {\left(24 \, a^{2} b^{2} + 2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(36 \, a^{2} b^{2} - 12 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(36 \, a^{2} b^{2} - 12 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(24 \, a^{2} b^{2} + 2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{2} + {\left(45 \, {\left(6 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{8} + 28 \, {\left(24 \, a^{2} b^{2} + 2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{6} + 30 \, {\left(36 \, a^{2} b^{2} - 12 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{4} + 24 \, a^{2} b^{2} + 2 \, a b^{3} - b^{4} + 12 \, {\left(36 \, a^{2} b^{2} - 12 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(5 \, {\left(6 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{9} + 4 \, {\left(24 \, a^{2} b^{2} + 2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{7} + 6 \, {\left(36 \, a^{2} b^{2} - 12 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{5} + 4 \, {\left(36 \, a^{2} b^{2} - 12 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(24 \, a^{2} b^{2} + 2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{a^{2} - a b} \log\left(\frac{b^{2} \cosh\left(d x + c\right)^{4} + 4 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{2} \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(d x + c\right)^{2} + 2 \, a b - b^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, a^{2} - 8 \, a b + b^{2} + 4 \, {\left(b^{2} \cosh\left(d x + c\right)^{3} + {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) - 4 \, {\left(b \cosh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b \sinh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sqrt{a^{2} - a b}}{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b}\right) + 16 \, {\left(6 \, {\left(6 \, a^{3} b^{2} - 7 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(d x + c\right)^{7} + 9 \, {\left(6 \, a^{4} b - a^{3} b^{2} - 6 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(d x + c\right)^{5} - 2 \, {\left(24 \, a^{5} - 106 \, a^{4} b + 95 \, a^{3} b^{2} - 13 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{3} - {\left(8 \, a^{5} - 38 \, a^{4} b + 25 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{12 \, {\left({\left(a^{6} b - 4 \, a^{5} b^{2} + 6 \, a^{4} b^{3} - 4 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{10} + 10 \, {\left(a^{6} b - 4 \, a^{5} b^{2} + 6 \, a^{4} b^{3} - 4 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + {\left(a^{6} b - 4 \, a^{5} b^{2} + 6 \, a^{4} b^{3} - 4 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \sinh\left(d x + c\right)^{10} + {\left(4 \, a^{7} - 15 \, a^{6} b + 20 \, a^{5} b^{2} - 10 \, a^{4} b^{3} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{8} + {\left(45 \, {\left(a^{6} b - 4 \, a^{5} b^{2} + 6 \, a^{4} b^{3} - 4 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(4 \, a^{7} - 15 \, a^{6} b + 20 \, a^{5} b^{2} - 10 \, a^{4} b^{3} + a^{2} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{8} + 2 \, {\left(6 \, a^{7} - 25 \, a^{6} b + 40 \, a^{5} b^{2} - 30 \, a^{4} b^{3} + 10 \, a^{3} b^{4} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{6} + 8 \, {\left(15 \, {\left(a^{6} b - 4 \, a^{5} b^{2} + 6 \, a^{4} b^{3} - 4 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(4 \, a^{7} - 15 \, a^{6} b + 20 \, a^{5} b^{2} - 10 \, a^{4} b^{3} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(105 \, {\left(a^{6} b - 4 \, a^{5} b^{2} + 6 \, a^{4} b^{3} - 4 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 14 \, {\left(4 \, a^{7} - 15 \, a^{6} b + 20 \, a^{5} b^{2} - 10 \, a^{4} b^{3} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(6 \, a^{7} - 25 \, a^{6} b + 40 \, a^{5} b^{2} - 30 \, a^{4} b^{3} + 10 \, a^{3} b^{4} - a^{2} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(6 \, a^{7} - 25 \, a^{6} b + 40 \, a^{5} b^{2} - 30 \, a^{4} b^{3} + 10 \, a^{3} b^{4} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(63 \, {\left(a^{6} b - 4 \, a^{5} b^{2} + 6 \, a^{4} b^{3} - 4 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{5} + 14 \, {\left(4 \, a^{7} - 15 \, a^{6} b + 20 \, a^{5} b^{2} - 10 \, a^{4} b^{3} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(6 \, a^{7} - 25 \, a^{6} b + 40 \, a^{5} b^{2} - 30 \, a^{4} b^{3} + 10 \, a^{3} b^{4} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(105 \, {\left(a^{6} b - 4 \, a^{5} b^{2} + 6 \, a^{4} b^{3} - 4 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{6} + 35 \, {\left(4 \, a^{7} - 15 \, a^{6} b + 20 \, a^{5} b^{2} - 10 \, a^{4} b^{3} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 15 \, {\left(6 \, a^{7} - 25 \, a^{6} b + 40 \, a^{5} b^{2} - 30 \, a^{4} b^{3} + 10 \, a^{3} b^{4} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(6 \, a^{7} - 25 \, a^{6} b + 40 \, a^{5} b^{2} - 30 \, a^{4} b^{3} + 10 \, a^{3} b^{4} - a^{2} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{4} + {\left(4 \, a^{7} - 15 \, a^{6} b + 20 \, a^{5} b^{2} - 10 \, a^{4} b^{3} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(15 \, {\left(a^{6} b - 4 \, a^{5} b^{2} + 6 \, a^{4} b^{3} - 4 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{7} + 7 \, {\left(4 \, a^{7} - 15 \, a^{6} b + 20 \, a^{5} b^{2} - 10 \, a^{4} b^{3} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{5} + 5 \, {\left(6 \, a^{7} - 25 \, a^{6} b + 40 \, a^{5} b^{2} - 30 \, a^{4} b^{3} + 10 \, a^{3} b^{4} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(6 \, a^{7} - 25 \, a^{6} b + 40 \, a^{5} b^{2} - 30 \, a^{4} b^{3} + 10 \, a^{3} b^{4} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(45 \, {\left(a^{6} b - 4 \, a^{5} b^{2} + 6 \, a^{4} b^{3} - 4 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{8} + 28 \, {\left(4 \, a^{7} - 15 \, a^{6} b + 20 \, a^{5} b^{2} - 10 \, a^{4} b^{3} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{6} + 30 \, {\left(6 \, a^{7} - 25 \, a^{6} b + 40 \, a^{5} b^{2} - 30 \, a^{4} b^{3} + 10 \, a^{3} b^{4} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 12 \, {\left(6 \, a^{7} - 25 \, a^{6} b + 40 \, a^{5} b^{2} - 30 \, a^{4} b^{3} + 10 \, a^{3} b^{4} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(4 \, a^{7} - 15 \, a^{6} b + 20 \, a^{5} b^{2} - 10 \, a^{4} b^{3} + a^{2} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{6} b - 4 \, a^{5} b^{2} + 6 \, a^{4} b^{3} - 4 \, a^{3} b^{4} + a^{2} b^{5}\right)} d + 2 \, {\left(5 \, {\left(a^{6} b - 4 \, a^{5} b^{2} + 6 \, a^{4} b^{3} - 4 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{9} + 4 \, {\left(4 \, a^{7} - 15 \, a^{6} b + 20 \, a^{5} b^{2} - 10 \, a^{4} b^{3} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{7} + 6 \, {\left(6 \, a^{7} - 25 \, a^{6} b + 40 \, a^{5} b^{2} - 30 \, a^{4} b^{3} + 10 \, a^{3} b^{4} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{5} + 4 \, {\left(6 \, a^{7} - 25 \, a^{6} b + 40 \, a^{5} b^{2} - 30 \, a^{4} b^{3} + 10 \, a^{3} b^{4} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(4 \, a^{7} - 15 \, a^{6} b + 20 \, a^{5} b^{2} - 10 \, a^{4} b^{3} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}, \frac{6 \, {\left(6 \, a^{3} b^{2} - 7 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(d x + c\right)^{8} + 48 \, {\left(6 \, a^{3} b^{2} - 7 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + 6 \, {\left(6 \, a^{3} b^{2} - 7 \, a^{2} b^{3} + a b^{4}\right)} \sinh\left(d x + c\right)^{8} + 12 \, {\left(6 \, a^{4} b - a^{3} b^{2} - 6 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(d x + c\right)^{6} + 12 \, {\left(6 \, a^{4} b - a^{3} b^{2} - 6 \, a^{2} b^{3} + a b^{4} + 14 \, {\left(6 \, a^{3} b^{2} - 7 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 24 \, {\left(14 \, {\left(6 \, a^{3} b^{2} - 7 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(6 \, a^{4} b - a^{3} b^{2} - 6 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 8 \, a^{4} b + 40 \, a^{3} b^{2} - 26 \, a^{2} b^{3} - 6 \, a b^{4} - 4 \, {\left(24 \, a^{5} - 106 \, a^{4} b + 95 \, a^{3} b^{2} - 13 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{4} - 4 \, {\left(24 \, a^{5} - 106 \, a^{4} b + 95 \, a^{3} b^{2} - 13 \, a^{2} b^{3} - 105 \, {\left(6 \, a^{3} b^{2} - 7 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(d x + c\right)^{4} - 45 \, {\left(6 \, a^{4} b - a^{3} b^{2} - 6 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 16 \, {\left(21 \, {\left(6 \, a^{3} b^{2} - 7 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(d x + c\right)^{5} + 15 \, {\left(6 \, a^{4} b - a^{3} b^{2} - 6 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(d x + c\right)^{3} - {\left(24 \, a^{5} - 106 \, a^{4} b + 95 \, a^{3} b^{2} - 13 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 4 \, {\left(8 \, a^{5} - 38 \, a^{4} b + 25 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(42 \, {\left(6 \, a^{3} b^{2} - 7 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(d x + c\right)^{6} - 8 \, a^{5} + 38 \, a^{4} b - 25 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} + 45 \, {\left(6 \, a^{4} b - a^{3} b^{2} - 6 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(d x + c\right)^{4} - 6 \, {\left(24 \, a^{5} - 106 \, a^{4} b + 95 \, a^{3} b^{2} - 13 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} - 3 \, {\left({\left(6 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{10} + 10 \, {\left(6 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + {\left(6 \, a b^{3} - b^{4}\right)} \sinh\left(d x + c\right)^{10} + {\left(24 \, a^{2} b^{2} + 2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{8} + {\left(24 \, a^{2} b^{2} + 2 \, a b^{3} - b^{4} + 45 \, {\left(6 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{8} + 8 \, {\left(15 \, {\left(6 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(24 \, a^{2} b^{2} + 2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(36 \, a^{2} b^{2} - 12 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(105 \, {\left(6 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{4} + 36 \, a^{2} b^{2} - 12 \, a b^{3} + b^{4} + 14 \, {\left(24 \, a^{2} b^{2} + 2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(63 \, {\left(6 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{5} + 14 \, {\left(24 \, a^{2} b^{2} + 2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(36 \, a^{2} b^{2} - 12 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(36 \, a^{2} b^{2} - 12 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(105 \, {\left(6 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{6} + 35 \, {\left(24 \, a^{2} b^{2} + 2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{4} + 36 \, a^{2} b^{2} - 12 \, a b^{3} + b^{4} + 15 \, {\left(36 \, a^{2} b^{2} - 12 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 6 \, a b^{3} - b^{4} + 8 \, {\left(15 \, {\left(6 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{7} + 7 \, {\left(24 \, a^{2} b^{2} + 2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(36 \, a^{2} b^{2} - 12 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(36 \, a^{2} b^{2} - 12 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(24 \, a^{2} b^{2} + 2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{2} + {\left(45 \, {\left(6 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{8} + 28 \, {\left(24 \, a^{2} b^{2} + 2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{6} + 30 \, {\left(36 \, a^{2} b^{2} - 12 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{4} + 24 \, a^{2} b^{2} + 2 \, a b^{3} - b^{4} + 12 \, {\left(36 \, a^{2} b^{2} - 12 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(5 \, {\left(6 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{9} + 4 \, {\left(24 \, a^{2} b^{2} + 2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{7} + 6 \, {\left(36 \, a^{2} b^{2} - 12 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{5} + 4 \, {\left(36 \, a^{2} b^{2} - 12 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(24 \, a^{2} b^{2} + 2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-a^{2} + a b} \arctan\left(-\frac{{\left(b \cosh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b \sinh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sqrt{-a^{2} + a b}}{2 \, {\left(a^{2} - a b\right)}}\right) + 8 \, {\left(6 \, {\left(6 \, a^{3} b^{2} - 7 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(d x + c\right)^{7} + 9 \, {\left(6 \, a^{4} b - a^{3} b^{2} - 6 \, a^{2} b^{3} + a b^{4}\right)} \cosh\left(d x + c\right)^{5} - 2 \, {\left(24 \, a^{5} - 106 \, a^{4} b + 95 \, a^{3} b^{2} - 13 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{3} - {\left(8 \, a^{5} - 38 \, a^{4} b + 25 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{6 \, {\left({\left(a^{6} b - 4 \, a^{5} b^{2} + 6 \, a^{4} b^{3} - 4 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{10} + 10 \, {\left(a^{6} b - 4 \, a^{5} b^{2} + 6 \, a^{4} b^{3} - 4 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + {\left(a^{6} b - 4 \, a^{5} b^{2} + 6 \, a^{4} b^{3} - 4 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \sinh\left(d x + c\right)^{10} + {\left(4 \, a^{7} - 15 \, a^{6} b + 20 \, a^{5} b^{2} - 10 \, a^{4} b^{3} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{8} + {\left(45 \, {\left(a^{6} b - 4 \, a^{5} b^{2} + 6 \, a^{4} b^{3} - 4 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(4 \, a^{7} - 15 \, a^{6} b + 20 \, a^{5} b^{2} - 10 \, a^{4} b^{3} + a^{2} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{8} + 2 \, {\left(6 \, a^{7} - 25 \, a^{6} b + 40 \, a^{5} b^{2} - 30 \, a^{4} b^{3} + 10 \, a^{3} b^{4} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{6} + 8 \, {\left(15 \, {\left(a^{6} b - 4 \, a^{5} b^{2} + 6 \, a^{4} b^{3} - 4 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(4 \, a^{7} - 15 \, a^{6} b + 20 \, a^{5} b^{2} - 10 \, a^{4} b^{3} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(105 \, {\left(a^{6} b - 4 \, a^{5} b^{2} + 6 \, a^{4} b^{3} - 4 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 14 \, {\left(4 \, a^{7} - 15 \, a^{6} b + 20 \, a^{5} b^{2} - 10 \, a^{4} b^{3} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(6 \, a^{7} - 25 \, a^{6} b + 40 \, a^{5} b^{2} - 30 \, a^{4} b^{3} + 10 \, a^{3} b^{4} - a^{2} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(6 \, a^{7} - 25 \, a^{6} b + 40 \, a^{5} b^{2} - 30 \, a^{4} b^{3} + 10 \, a^{3} b^{4} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(63 \, {\left(a^{6} b - 4 \, a^{5} b^{2} + 6 \, a^{4} b^{3} - 4 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{5} + 14 \, {\left(4 \, a^{7} - 15 \, a^{6} b + 20 \, a^{5} b^{2} - 10 \, a^{4} b^{3} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(6 \, a^{7} - 25 \, a^{6} b + 40 \, a^{5} b^{2} - 30 \, a^{4} b^{3} + 10 \, a^{3} b^{4} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(105 \, {\left(a^{6} b - 4 \, a^{5} b^{2} + 6 \, a^{4} b^{3} - 4 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{6} + 35 \, {\left(4 \, a^{7} - 15 \, a^{6} b + 20 \, a^{5} b^{2} - 10 \, a^{4} b^{3} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 15 \, {\left(6 \, a^{7} - 25 \, a^{6} b + 40 \, a^{5} b^{2} - 30 \, a^{4} b^{3} + 10 \, a^{3} b^{4} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(6 \, a^{7} - 25 \, a^{6} b + 40 \, a^{5} b^{2} - 30 \, a^{4} b^{3} + 10 \, a^{3} b^{4} - a^{2} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{4} + {\left(4 \, a^{7} - 15 \, a^{6} b + 20 \, a^{5} b^{2} - 10 \, a^{4} b^{3} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(15 \, {\left(a^{6} b - 4 \, a^{5} b^{2} + 6 \, a^{4} b^{3} - 4 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{7} + 7 \, {\left(4 \, a^{7} - 15 \, a^{6} b + 20 \, a^{5} b^{2} - 10 \, a^{4} b^{3} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{5} + 5 \, {\left(6 \, a^{7} - 25 \, a^{6} b + 40 \, a^{5} b^{2} - 30 \, a^{4} b^{3} + 10 \, a^{3} b^{4} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(6 \, a^{7} - 25 \, a^{6} b + 40 \, a^{5} b^{2} - 30 \, a^{4} b^{3} + 10 \, a^{3} b^{4} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(45 \, {\left(a^{6} b - 4 \, a^{5} b^{2} + 6 \, a^{4} b^{3} - 4 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{8} + 28 \, {\left(4 \, a^{7} - 15 \, a^{6} b + 20 \, a^{5} b^{2} - 10 \, a^{4} b^{3} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{6} + 30 \, {\left(6 \, a^{7} - 25 \, a^{6} b + 40 \, a^{5} b^{2} - 30 \, a^{4} b^{3} + 10 \, a^{3} b^{4} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 12 \, {\left(6 \, a^{7} - 25 \, a^{6} b + 40 \, a^{5} b^{2} - 30 \, a^{4} b^{3} + 10 \, a^{3} b^{4} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(4 \, a^{7} - 15 \, a^{6} b + 20 \, a^{5} b^{2} - 10 \, a^{4} b^{3} + a^{2} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{6} b - 4 \, a^{5} b^{2} + 6 \, a^{4} b^{3} - 4 \, a^{3} b^{4} + a^{2} b^{5}\right)} d + 2 \, {\left(5 \, {\left(a^{6} b - 4 \, a^{5} b^{2} + 6 \, a^{4} b^{3} - 4 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{9} + 4 \, {\left(4 \, a^{7} - 15 \, a^{6} b + 20 \, a^{5} b^{2} - 10 \, a^{4} b^{3} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{7} + 6 \, {\left(6 \, a^{7} - 25 \, a^{6} b + 40 \, a^{5} b^{2} - 30 \, a^{4} b^{3} + 10 \, a^{3} b^{4} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{5} + 4 \, {\left(6 \, a^{7} - 25 \, a^{6} b + 40 \, a^{5} b^{2} - 30 \, a^{4} b^{3} + 10 \, a^{3} b^{4} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(4 \, a^{7} - 15 \, a^{6} b + 20 \, a^{5} b^{2} - 10 \, a^{4} b^{3} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[1/12*(12*(6*a^3*b^2 - 7*a^2*b^3 + a*b^4)*cosh(d*x + c)^8 + 96*(6*a^3*b^2 - 7*a^2*b^3 + a*b^4)*cosh(d*x + c)*sinh(d*x + c)^7 + 12*(6*a^3*b^2 - 7*a^2*b^3 + a*b^4)*sinh(d*x + c)^8 + 24*(6*a^4*b - a^3*b^2 - 6*a^2*b^3 + a*b^4)*cosh(d*x + c)^6 + 24*(6*a^4*b - a^3*b^2 - 6*a^2*b^3 + a*b^4 + 14*(6*a^3*b^2 - 7*a^2*b^3 + a*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 48*(14*(6*a^3*b^2 - 7*a^2*b^3 + a*b^4)*cosh(d*x + c)^3 + 3*(6*a^4*b - a^3*b^2 - 6*a^2*b^3 + a*b^4)*cosh(d*x + c))*sinh(d*x + c)^5 - 16*a^4*b + 80*a^3*b^2 - 52*a^2*b^3 - 12*a*b^4 - 8*(24*a^5 - 106*a^4*b + 95*a^3*b^2 - 13*a^2*b^3)*cosh(d*x + c)^4 - 8*(24*a^5 - 106*a^4*b + 95*a^3*b^2 - 13*a^2*b^3 - 105*(6*a^3*b^2 - 7*a^2*b^3 + a*b^4)*cosh(d*x + c)^4 - 45*(6*a^4*b - a^3*b^2 - 6*a^2*b^3 + a*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 32*(21*(6*a^3*b^2 - 7*a^2*b^3 + a*b^4)*cosh(d*x + c)^5 + 15*(6*a^4*b - a^3*b^2 - 6*a^2*b^3 + a*b^4)*cosh(d*x + c)^3 - (24*a^5 - 106*a^4*b + 95*a^3*b^2 - 13*a^2*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 - 8*(8*a^5 - 38*a^4*b + 25*a^3*b^2 + 2*a^2*b^3 + 3*a*b^4)*cosh(d*x + c)^2 + 8*(42*(6*a^3*b^2 - 7*a^2*b^3 + a*b^4)*cosh(d*x + c)^6 - 8*a^5 + 38*a^4*b - 25*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 + 45*(6*a^4*b - a^3*b^2 - 6*a^2*b^3 + a*b^4)*cosh(d*x + c)^4 - 6*(24*a^5 - 106*a^4*b + 95*a^3*b^2 - 13*a^2*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 3*((6*a*b^3 - b^4)*cosh(d*x + c)^10 + 10*(6*a*b^3 - b^4)*cosh(d*x + c)*sinh(d*x + c)^9 + (6*a*b^3 - b^4)*sinh(d*x + c)^10 + (24*a^2*b^2 + 2*a*b^3 - b^4)*cosh(d*x + c)^8 + (24*a^2*b^2 + 2*a*b^3 - b^4 + 45*(6*a*b^3 - b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 8*(15*(6*a*b^3 - b^4)*cosh(d*x + c)^3 + (24*a^2*b^2 + 2*a*b^3 - b^4)*cosh(d*x + c))*sinh(d*x + c)^7 + 2*(36*a^2*b^2 - 12*a*b^3 + b^4)*cosh(d*x + c)^6 + 2*(105*(6*a*b^3 - b^4)*cosh(d*x + c)^4 + 36*a^2*b^2 - 12*a*b^3 + b^4 + 14*(24*a^2*b^2 + 2*a*b^3 - b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 4*(63*(6*a*b^3 - b^4)*cosh(d*x + c)^5 + 14*(24*a^2*b^2 + 2*a*b^3 - b^4)*cosh(d*x + c)^3 + 3*(36*a^2*b^2 - 12*a*b^3 + b^4)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(36*a^2*b^2 - 12*a*b^3 + b^4)*cosh(d*x + c)^4 + 2*(105*(6*a*b^3 - b^4)*cosh(d*x + c)^6 + 35*(24*a^2*b^2 + 2*a*b^3 - b^4)*cosh(d*x + c)^4 + 36*a^2*b^2 - 12*a*b^3 + b^4 + 15*(36*a^2*b^2 - 12*a*b^3 + b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 6*a*b^3 - b^4 + 8*(15*(6*a*b^3 - b^4)*cosh(d*x + c)^7 + 7*(24*a^2*b^2 + 2*a*b^3 - b^4)*cosh(d*x + c)^5 + 5*(36*a^2*b^2 - 12*a*b^3 + b^4)*cosh(d*x + c)^3 + (36*a^2*b^2 - 12*a*b^3 + b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + (24*a^2*b^2 + 2*a*b^3 - b^4)*cosh(d*x + c)^2 + (45*(6*a*b^3 - b^4)*cosh(d*x + c)^8 + 28*(24*a^2*b^2 + 2*a*b^3 - b^4)*cosh(d*x + c)^6 + 30*(36*a^2*b^2 - 12*a*b^3 + b^4)*cosh(d*x + c)^4 + 24*a^2*b^2 + 2*a*b^3 - b^4 + 12*(36*a^2*b^2 - 12*a*b^3 + b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 2*(5*(6*a*b^3 - b^4)*cosh(d*x + c)^9 + 4*(24*a^2*b^2 + 2*a*b^3 - b^4)*cosh(d*x + c)^7 + 6*(36*a^2*b^2 - 12*a*b^3 + b^4)*cosh(d*x + c)^5 + 4*(36*a^2*b^2 - 12*a*b^3 + b^4)*cosh(d*x + c)^3 + (24*a^2*b^2 + 2*a*b^3 - b^4)*cosh(d*x + c))*sinh(d*x + c))*sqrt(a^2 - a*b)*log((b^2*cosh(d*x + c)^4 + 4*b^2*cosh(d*x + c)*sinh(d*x + c)^3 + b^2*sinh(d*x + c)^4 + 2*(2*a*b - b^2)*cosh(d*x + c)^2 + 2*(3*b^2*cosh(d*x + c)^2 + 2*a*b - b^2)*sinh(d*x + c)^2 + 8*a^2 - 8*a*b + b^2 + 4*(b^2*cosh(d*x + c)^3 + (2*a*b - b^2)*cosh(d*x + c))*sinh(d*x + c) - 4*(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + 2*a - b)*sqrt(a^2 - a*b))/(b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 + 2*(2*a - b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 + 2*a - b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 + (2*a - b)*cosh(d*x + c))*sinh(d*x + c) + b)) + 16*(6*(6*a^3*b^2 - 7*a^2*b^3 + a*b^4)*cosh(d*x + c)^7 + 9*(6*a^4*b - a^3*b^2 - 6*a^2*b^3 + a*b^4)*cosh(d*x + c)^5 - 2*(24*a^5 - 106*a^4*b + 95*a^3*b^2 - 13*a^2*b^3)*cosh(d*x + c)^3 - (8*a^5 - 38*a^4*b + 25*a^3*b^2 + 2*a^2*b^3 + 3*a*b^4)*cosh(d*x + c))*sinh(d*x + c))/((a^6*b - 4*a^5*b^2 + 6*a^4*b^3 - 4*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)^10 + 10*(a^6*b - 4*a^5*b^2 + 6*a^4*b^3 - 4*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)*sinh(d*x + c)^9 + (a^6*b - 4*a^5*b^2 + 6*a^4*b^3 - 4*a^3*b^4 + a^2*b^5)*d*sinh(d*x + c)^10 + (4*a^7 - 15*a^6*b + 20*a^5*b^2 - 10*a^4*b^3 + a^2*b^5)*d*cosh(d*x + c)^8 + (45*(a^6*b - 4*a^5*b^2 + 6*a^4*b^3 - 4*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)^2 + (4*a^7 - 15*a^6*b + 20*a^5*b^2 - 10*a^4*b^3 + a^2*b^5)*d)*sinh(d*x + c)^8 + 2*(6*a^7 - 25*a^6*b + 40*a^5*b^2 - 30*a^4*b^3 + 10*a^3*b^4 - a^2*b^5)*d*cosh(d*x + c)^6 + 8*(15*(a^6*b - 4*a^5*b^2 + 6*a^4*b^3 - 4*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)^3 + (4*a^7 - 15*a^6*b + 20*a^5*b^2 - 10*a^4*b^3 + a^2*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^7 + 2*(105*(a^6*b - 4*a^5*b^2 + 6*a^4*b^3 - 4*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)^4 + 14*(4*a^7 - 15*a^6*b + 20*a^5*b^2 - 10*a^4*b^3 + a^2*b^5)*d*cosh(d*x + c)^2 + (6*a^7 - 25*a^6*b + 40*a^5*b^2 - 30*a^4*b^3 + 10*a^3*b^4 - a^2*b^5)*d)*sinh(d*x + c)^6 + 2*(6*a^7 - 25*a^6*b + 40*a^5*b^2 - 30*a^4*b^3 + 10*a^3*b^4 - a^2*b^5)*d*cosh(d*x + c)^4 + 4*(63*(a^6*b - 4*a^5*b^2 + 6*a^4*b^3 - 4*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)^5 + 14*(4*a^7 - 15*a^6*b + 20*a^5*b^2 - 10*a^4*b^3 + a^2*b^5)*d*cosh(d*x + c)^3 + 3*(6*a^7 - 25*a^6*b + 40*a^5*b^2 - 30*a^4*b^3 + 10*a^3*b^4 - a^2*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(105*(a^6*b - 4*a^5*b^2 + 6*a^4*b^3 - 4*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)^6 + 35*(4*a^7 - 15*a^6*b + 20*a^5*b^2 - 10*a^4*b^3 + a^2*b^5)*d*cosh(d*x + c)^4 + 15*(6*a^7 - 25*a^6*b + 40*a^5*b^2 - 30*a^4*b^3 + 10*a^3*b^4 - a^2*b^5)*d*cosh(d*x + c)^2 + (6*a^7 - 25*a^6*b + 40*a^5*b^2 - 30*a^4*b^3 + 10*a^3*b^4 - a^2*b^5)*d)*sinh(d*x + c)^4 + (4*a^7 - 15*a^6*b + 20*a^5*b^2 - 10*a^4*b^3 + a^2*b^5)*d*cosh(d*x + c)^2 + 8*(15*(a^6*b - 4*a^5*b^2 + 6*a^4*b^3 - 4*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)^7 + 7*(4*a^7 - 15*a^6*b + 20*a^5*b^2 - 10*a^4*b^3 + a^2*b^5)*d*cosh(d*x + c)^5 + 5*(6*a^7 - 25*a^6*b + 40*a^5*b^2 - 30*a^4*b^3 + 10*a^3*b^4 - a^2*b^5)*d*cosh(d*x + c)^3 + (6*a^7 - 25*a^6*b + 40*a^5*b^2 - 30*a^4*b^3 + 10*a^3*b^4 - a^2*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^3 + (45*(a^6*b - 4*a^5*b^2 + 6*a^4*b^3 - 4*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)^8 + 28*(4*a^7 - 15*a^6*b + 20*a^5*b^2 - 10*a^4*b^3 + a^2*b^5)*d*cosh(d*x + c)^6 + 30*(6*a^7 - 25*a^6*b + 40*a^5*b^2 - 30*a^4*b^3 + 10*a^3*b^4 - a^2*b^5)*d*cosh(d*x + c)^4 + 12*(6*a^7 - 25*a^6*b + 40*a^5*b^2 - 30*a^4*b^3 + 10*a^3*b^4 - a^2*b^5)*d*cosh(d*x + c)^2 + (4*a^7 - 15*a^6*b + 20*a^5*b^2 - 10*a^4*b^3 + a^2*b^5)*d)*sinh(d*x + c)^2 + (a^6*b - 4*a^5*b^2 + 6*a^4*b^3 - 4*a^3*b^4 + a^2*b^5)*d + 2*(5*(a^6*b - 4*a^5*b^2 + 6*a^4*b^3 - 4*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)^9 + 4*(4*a^7 - 15*a^6*b + 20*a^5*b^2 - 10*a^4*b^3 + a^2*b^5)*d*cosh(d*x + c)^7 + 6*(6*a^7 - 25*a^6*b + 40*a^5*b^2 - 30*a^4*b^3 + 10*a^3*b^4 - a^2*b^5)*d*cosh(d*x + c)^5 + 4*(6*a^7 - 25*a^6*b + 40*a^5*b^2 - 30*a^4*b^3 + 10*a^3*b^4 - a^2*b^5)*d*cosh(d*x + c)^3 + (4*a^7 - 15*a^6*b + 20*a^5*b^2 - 10*a^4*b^3 + a^2*b^5)*d*cosh(d*x + c))*sinh(d*x + c)), 1/6*(6*(6*a^3*b^2 - 7*a^2*b^3 + a*b^4)*cosh(d*x + c)^8 + 48*(6*a^3*b^2 - 7*a^2*b^3 + a*b^4)*cosh(d*x + c)*sinh(d*x + c)^7 + 6*(6*a^3*b^2 - 7*a^2*b^3 + a*b^4)*sinh(d*x + c)^8 + 12*(6*a^4*b - a^3*b^2 - 6*a^2*b^3 + a*b^4)*cosh(d*x + c)^6 + 12*(6*a^4*b - a^3*b^2 - 6*a^2*b^3 + a*b^4 + 14*(6*a^3*b^2 - 7*a^2*b^3 + a*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 24*(14*(6*a^3*b^2 - 7*a^2*b^3 + a*b^4)*cosh(d*x + c)^3 + 3*(6*a^4*b - a^3*b^2 - 6*a^2*b^3 + a*b^4)*cosh(d*x + c))*sinh(d*x + c)^5 - 8*a^4*b + 40*a^3*b^2 - 26*a^2*b^3 - 6*a*b^4 - 4*(24*a^5 - 106*a^4*b + 95*a^3*b^2 - 13*a^2*b^3)*cosh(d*x + c)^4 - 4*(24*a^5 - 106*a^4*b + 95*a^3*b^2 - 13*a^2*b^3 - 105*(6*a^3*b^2 - 7*a^2*b^3 + a*b^4)*cosh(d*x + c)^4 - 45*(6*a^4*b - a^3*b^2 - 6*a^2*b^3 + a*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 16*(21*(6*a^3*b^2 - 7*a^2*b^3 + a*b^4)*cosh(d*x + c)^5 + 15*(6*a^4*b - a^3*b^2 - 6*a^2*b^3 + a*b^4)*cosh(d*x + c)^3 - (24*a^5 - 106*a^4*b + 95*a^3*b^2 - 13*a^2*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 - 4*(8*a^5 - 38*a^4*b + 25*a^3*b^2 + 2*a^2*b^3 + 3*a*b^4)*cosh(d*x + c)^2 + 4*(42*(6*a^3*b^2 - 7*a^2*b^3 + a*b^4)*cosh(d*x + c)^6 - 8*a^5 + 38*a^4*b - 25*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 + 45*(6*a^4*b - a^3*b^2 - 6*a^2*b^3 + a*b^4)*cosh(d*x + c)^4 - 6*(24*a^5 - 106*a^4*b + 95*a^3*b^2 - 13*a^2*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - 3*((6*a*b^3 - b^4)*cosh(d*x + c)^10 + 10*(6*a*b^3 - b^4)*cosh(d*x + c)*sinh(d*x + c)^9 + (6*a*b^3 - b^4)*sinh(d*x + c)^10 + (24*a^2*b^2 + 2*a*b^3 - b^4)*cosh(d*x + c)^8 + (24*a^2*b^2 + 2*a*b^3 - b^4 + 45*(6*a*b^3 - b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 8*(15*(6*a*b^3 - b^4)*cosh(d*x + c)^3 + (24*a^2*b^2 + 2*a*b^3 - b^4)*cosh(d*x + c))*sinh(d*x + c)^7 + 2*(36*a^2*b^2 - 12*a*b^3 + b^4)*cosh(d*x + c)^6 + 2*(105*(6*a*b^3 - b^4)*cosh(d*x + c)^4 + 36*a^2*b^2 - 12*a*b^3 + b^4 + 14*(24*a^2*b^2 + 2*a*b^3 - b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 4*(63*(6*a*b^3 - b^4)*cosh(d*x + c)^5 + 14*(24*a^2*b^2 + 2*a*b^3 - b^4)*cosh(d*x + c)^3 + 3*(36*a^2*b^2 - 12*a*b^3 + b^4)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(36*a^2*b^2 - 12*a*b^3 + b^4)*cosh(d*x + c)^4 + 2*(105*(6*a*b^3 - b^4)*cosh(d*x + c)^6 + 35*(24*a^2*b^2 + 2*a*b^3 - b^4)*cosh(d*x + c)^4 + 36*a^2*b^2 - 12*a*b^3 + b^4 + 15*(36*a^2*b^2 - 12*a*b^3 + b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 6*a*b^3 - b^4 + 8*(15*(6*a*b^3 - b^4)*cosh(d*x + c)^7 + 7*(24*a^2*b^2 + 2*a*b^3 - b^4)*cosh(d*x + c)^5 + 5*(36*a^2*b^2 - 12*a*b^3 + b^4)*cosh(d*x + c)^3 + (36*a^2*b^2 - 12*a*b^3 + b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + (24*a^2*b^2 + 2*a*b^3 - b^4)*cosh(d*x + c)^2 + (45*(6*a*b^3 - b^4)*cosh(d*x + c)^8 + 28*(24*a^2*b^2 + 2*a*b^3 - b^4)*cosh(d*x + c)^6 + 30*(36*a^2*b^2 - 12*a*b^3 + b^4)*cosh(d*x + c)^4 + 24*a^2*b^2 + 2*a*b^3 - b^4 + 12*(36*a^2*b^2 - 12*a*b^3 + b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 2*(5*(6*a*b^3 - b^4)*cosh(d*x + c)^9 + 4*(24*a^2*b^2 + 2*a*b^3 - b^4)*cosh(d*x + c)^7 + 6*(36*a^2*b^2 - 12*a*b^3 + b^4)*cosh(d*x + c)^5 + 4*(36*a^2*b^2 - 12*a*b^3 + b^4)*cosh(d*x + c)^3 + (24*a^2*b^2 + 2*a*b^3 - b^4)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-a^2 + a*b)*arctan(-1/2*(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + 2*a - b)*sqrt(-a^2 + a*b)/(a^2 - a*b)) + 8*(6*(6*a^3*b^2 - 7*a^2*b^3 + a*b^4)*cosh(d*x + c)^7 + 9*(6*a^4*b - a^3*b^2 - 6*a^2*b^3 + a*b^4)*cosh(d*x + c)^5 - 2*(24*a^5 - 106*a^4*b + 95*a^3*b^2 - 13*a^2*b^3)*cosh(d*x + c)^3 - (8*a^5 - 38*a^4*b + 25*a^3*b^2 + 2*a^2*b^3 + 3*a*b^4)*cosh(d*x + c))*sinh(d*x + c))/((a^6*b - 4*a^5*b^2 + 6*a^4*b^3 - 4*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)^10 + 10*(a^6*b - 4*a^5*b^2 + 6*a^4*b^3 - 4*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)*sinh(d*x + c)^9 + (a^6*b - 4*a^5*b^2 + 6*a^4*b^3 - 4*a^3*b^4 + a^2*b^5)*d*sinh(d*x + c)^10 + (4*a^7 - 15*a^6*b + 20*a^5*b^2 - 10*a^4*b^3 + a^2*b^5)*d*cosh(d*x + c)^8 + (45*(a^6*b - 4*a^5*b^2 + 6*a^4*b^3 - 4*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)^2 + (4*a^7 - 15*a^6*b + 20*a^5*b^2 - 10*a^4*b^3 + a^2*b^5)*d)*sinh(d*x + c)^8 + 2*(6*a^7 - 25*a^6*b + 40*a^5*b^2 - 30*a^4*b^3 + 10*a^3*b^4 - a^2*b^5)*d*cosh(d*x + c)^6 + 8*(15*(a^6*b - 4*a^5*b^2 + 6*a^4*b^3 - 4*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)^3 + (4*a^7 - 15*a^6*b + 20*a^5*b^2 - 10*a^4*b^3 + a^2*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^7 + 2*(105*(a^6*b - 4*a^5*b^2 + 6*a^4*b^3 - 4*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)^4 + 14*(4*a^7 - 15*a^6*b + 20*a^5*b^2 - 10*a^4*b^3 + a^2*b^5)*d*cosh(d*x + c)^2 + (6*a^7 - 25*a^6*b + 40*a^5*b^2 - 30*a^4*b^3 + 10*a^3*b^4 - a^2*b^5)*d)*sinh(d*x + c)^6 + 2*(6*a^7 - 25*a^6*b + 40*a^5*b^2 - 30*a^4*b^3 + 10*a^3*b^4 - a^2*b^5)*d*cosh(d*x + c)^4 + 4*(63*(a^6*b - 4*a^5*b^2 + 6*a^4*b^3 - 4*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)^5 + 14*(4*a^7 - 15*a^6*b + 20*a^5*b^2 - 10*a^4*b^3 + a^2*b^5)*d*cosh(d*x + c)^3 + 3*(6*a^7 - 25*a^6*b + 40*a^5*b^2 - 30*a^4*b^3 + 10*a^3*b^4 - a^2*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(105*(a^6*b - 4*a^5*b^2 + 6*a^4*b^3 - 4*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)^6 + 35*(4*a^7 - 15*a^6*b + 20*a^5*b^2 - 10*a^4*b^3 + a^2*b^5)*d*cosh(d*x + c)^4 + 15*(6*a^7 - 25*a^6*b + 40*a^5*b^2 - 30*a^4*b^3 + 10*a^3*b^4 - a^2*b^5)*d*cosh(d*x + c)^2 + (6*a^7 - 25*a^6*b + 40*a^5*b^2 - 30*a^4*b^3 + 10*a^3*b^4 - a^2*b^5)*d)*sinh(d*x + c)^4 + (4*a^7 - 15*a^6*b + 20*a^5*b^2 - 10*a^4*b^3 + a^2*b^5)*d*cosh(d*x + c)^2 + 8*(15*(a^6*b - 4*a^5*b^2 + 6*a^4*b^3 - 4*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)^7 + 7*(4*a^7 - 15*a^6*b + 20*a^5*b^2 - 10*a^4*b^3 + a^2*b^5)*d*cosh(d*x + c)^5 + 5*(6*a^7 - 25*a^6*b + 40*a^5*b^2 - 30*a^4*b^3 + 10*a^3*b^4 - a^2*b^5)*d*cosh(d*x + c)^3 + (6*a^7 - 25*a^6*b + 40*a^5*b^2 - 30*a^4*b^3 + 10*a^3*b^4 - a^2*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^3 + (45*(a^6*b - 4*a^5*b^2 + 6*a^4*b^3 - 4*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)^8 + 28*(4*a^7 - 15*a^6*b + 20*a^5*b^2 - 10*a^4*b^3 + a^2*b^5)*d*cosh(d*x + c)^6 + 30*(6*a^7 - 25*a^6*b + 40*a^5*b^2 - 30*a^4*b^3 + 10*a^3*b^4 - a^2*b^5)*d*cosh(d*x + c)^4 + 12*(6*a^7 - 25*a^6*b + 40*a^5*b^2 - 30*a^4*b^3 + 10*a^3*b^4 - a^2*b^5)*d*cosh(d*x + c)^2 + (4*a^7 - 15*a^6*b + 20*a^5*b^2 - 10*a^4*b^3 + a^2*b^5)*d)*sinh(d*x + c)^2 + (a^6*b - 4*a^5*b^2 + 6*a^4*b^3 - 4*a^3*b^4 + a^2*b^5)*d + 2*(5*(a^6*b - 4*a^5*b^2 + 6*a^4*b^3 - 4*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)^9 + 4*(4*a^7 - 15*a^6*b + 20*a^5*b^2 - 10*a^4*b^3 + a^2*b^5)*d*cosh(d*x + c)^7 + 6*(6*a^7 - 25*a^6*b + 40*a^5*b^2 - 30*a^4*b^3 + 10*a^3*b^4 - a^2*b^5)*d*cosh(d*x + c)^5 + 4*(6*a^7 - 25*a^6*b + 40*a^5*b^2 - 30*a^4*b^3 + 10*a^3*b^4 - a^2*b^5)*d*cosh(d*x + c)^3 + (4*a^7 - 15*a^6*b + 20*a^5*b^2 - 10*a^4*b^3 + a^2*b^5)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
339,1,5511,0,0.573165," ","integrate(cosh(d*x+c)^6/(a+b*sinh(d*x+c)^2)^3,x, algorithm=""fricas"")","\left[\frac{16 \, a^{2} b^{2} d x \cosh\left(d x + c\right)^{8} + 128 \, a^{2} b^{2} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + 16 \, a^{2} b^{2} d x \sinh\left(d x + c\right)^{8} + 4 \, {\left(16 \, a^{3} b - 20 \, a^{2} b^{2} + a b^{3} + 3 \, b^{4} + 16 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(112 \, a^{2} b^{2} d x \cosh\left(d x + c\right)^{2} + 16 \, a^{3} b - 20 \, a^{2} b^{2} + a b^{3} + 3 \, b^{4} + 16 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} d x\right)} \sinh\left(d x + c\right)^{6} + 16 \, a^{2} b^{2} d x + 8 \, {\left(112 \, a^{2} b^{2} d x \cosh\left(d x + c\right)^{3} + 3 \, {\left(16 \, a^{3} b - 20 \, a^{2} b^{2} + a b^{3} + 3 \, b^{4} + 16 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 4 \, {\left(48 \, a^{4} - 72 \, a^{3} b + 18 \, a^{2} b^{2} + 15 \, a b^{3} - 9 \, b^{4} + 8 \, {\left(8 \, a^{4} - 8 \, a^{3} b + 3 \, a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(280 \, a^{2} b^{2} d x \cosh\left(d x + c\right)^{4} + 48 \, a^{4} - 72 \, a^{3} b + 18 \, a^{2} b^{2} + 15 \, a b^{3} - 9 \, b^{4} + 8 \, {\left(8 \, a^{4} - 8 \, a^{3} b + 3 \, a^{2} b^{2}\right)} d x + 15 \, {\left(16 \, a^{3} b - 20 \, a^{2} b^{2} + a b^{3} + 3 \, b^{4} + 16 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 24 \, a^{2} b^{2} - 12 \, a b^{3} - 12 \, b^{4} + 16 \, {\left(56 \, a^{2} b^{2} d x \cosh\left(d x + c\right)^{5} + 5 \, {\left(16 \, a^{3} b - 20 \, a^{2} b^{2} + a b^{3} + 3 \, b^{4} + 16 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + {\left(48 \, a^{4} - 72 \, a^{3} b + 18 \, a^{2} b^{2} + 15 \, a b^{3} - 9 \, b^{4} + 8 \, {\left(8 \, a^{4} - 8 \, a^{3} b + 3 \, a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(32 \, a^{3} b - 28 \, a^{2} b^{2} - 13 \, a b^{3} + 9 \, b^{4} + 16 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(112 \, a^{2} b^{2} d x \cosh\left(d x + c\right)^{6} + 15 \, {\left(16 \, a^{3} b - 20 \, a^{2} b^{2} + a b^{3} + 3 \, b^{4} + 16 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 32 \, a^{3} b - 28 \, a^{2} b^{2} - 13 \, a b^{3} + 9 \, b^{4} + 16 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} d x + 6 \, {\left(48 \, a^{4} - 72 \, a^{3} b + 18 \, a^{2} b^{2} + 15 \, a b^{3} - 9 \, b^{4} + 8 \, {\left(8 \, a^{4} - 8 \, a^{3} b + 3 \, a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(8 \, a^{2} b^{2} + 4 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(8 \, a^{2} b^{2} + 4 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(8 \, a^{2} b^{2} + 4 \, a b^{3} + 3 \, b^{4}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(16 \, a^{3} b + 2 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(16 \, a^{3} b + 2 \, a b^{3} - 3 \, b^{4} + 7 \, {\left(8 \, a^{2} b^{2} + 4 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(8 \, a^{2} b^{2} + 4 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(16 \, a^{3} b + 2 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(64 \, a^{4} - 32 \, a^{3} b + 16 \, a^{2} b^{2} - 12 \, a b^{3} + 9 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(8 \, a^{2} b^{2} + 4 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 64 \, a^{4} - 32 \, a^{3} b + 16 \, a^{2} b^{2} - 12 \, a b^{3} + 9 \, b^{4} + 30 \, {\left(16 \, a^{3} b + 2 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, a^{2} b^{2} + 4 \, a b^{3} + 3 \, b^{4} + 8 \, {\left(7 \, {\left(8 \, a^{2} b^{2} + 4 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(16 \, a^{3} b + 2 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(64 \, a^{4} - 32 \, a^{3} b + 16 \, a^{2} b^{2} - 12 \, a b^{3} + 9 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(16 \, a^{3} b + 2 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(8 \, a^{2} b^{2} + 4 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(16 \, a^{3} b + 2 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 16 \, a^{3} b + 2 \, a b^{3} - 3 \, b^{4} + 3 \, {\left(64 \, a^{4} - 32 \, a^{3} b + 16 \, a^{2} b^{2} - 12 \, a b^{3} + 9 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left({\left(8 \, a^{2} b^{2} + 4 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(16 \, a^{3} b + 2 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + {\left(64 \, a^{4} - 32 \, a^{3} b + 16 \, a^{2} b^{2} - 12 \, a b^{3} + 9 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(16 \, a^{3} b + 2 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a - b}{a}} \log\left(\frac{b^{2} \cosh\left(d x + c\right)^{4} + 4 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{2} \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(d x + c\right)^{2} + 2 \, a b - b^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, a^{2} - 8 \, a b + b^{2} + 4 \, {\left(b^{2} \cosh\left(d x + c\right)^{3} + {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + 4 \, {\left(a b \cosh\left(d x + c\right)^{2} + 2 \, a b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a b \sinh\left(d x + c\right)^{2} + 2 \, a^{2} - a b\right)} \sqrt{\frac{a - b}{a}}}{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b}\right) + 8 \, {\left(16 \, a^{2} b^{2} d x \cosh\left(d x + c\right)^{7} + 3 \, {\left(16 \, a^{3} b - 20 \, a^{2} b^{2} + a b^{3} + 3 \, b^{4} + 16 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(48 \, a^{4} - 72 \, a^{3} b + 18 \, a^{2} b^{2} + 15 \, a b^{3} - 9 \, b^{4} + 8 \, {\left(8 \, a^{4} - 8 \, a^{3} b + 3 \, a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + {\left(32 \, a^{3} b - 28 \, a^{2} b^{2} - 13 \, a b^{3} + 9 \, b^{4} + 16 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{16 \, {\left(a^{2} b^{5} d \cosh\left(d x + c\right)^{8} + 8 \, a^{2} b^{5} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + a^{2} b^{5} d \sinh\left(d x + c\right)^{8} + a^{2} b^{5} d + 4 \, {\left(2 \, a^{3} b^{4} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, a^{2} b^{5} d \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{3} b^{4} - a^{2} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(8 \, a^{4} b^{3} - 8 \, a^{3} b^{4} + 3 \, a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, a^{2} b^{5} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(2 \, a^{3} b^{4} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, a^{2} b^{5} d \cosh\left(d x + c\right)^{4} + 30 \, {\left(2 \, a^{3} b^{4} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(8 \, a^{4} b^{3} - 8 \, a^{3} b^{4} + 3 \, a^{2} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(2 \, a^{3} b^{4} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, a^{2} b^{5} d \cosh\left(d x + c\right)^{5} + 10 \, {\left(2 \, a^{3} b^{4} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{4} b^{3} - 8 \, a^{3} b^{4} + 3 \, a^{2} b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, a^{2} b^{5} d \cosh\left(d x + c\right)^{6} + 15 \, {\left(2 \, a^{3} b^{4} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(8 \, a^{4} b^{3} - 8 \, a^{3} b^{4} + 3 \, a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{3} b^{4} - a^{2} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left(a^{2} b^{5} d \cosh\left(d x + c\right)^{7} + 3 \, {\left(2 \, a^{3} b^{4} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{5} + {\left(8 \, a^{4} b^{3} - 8 \, a^{3} b^{4} + 3 \, a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{3} b^{4} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}, \frac{8 \, a^{2} b^{2} d x \cosh\left(d x + c\right)^{8} + 64 \, a^{2} b^{2} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + 8 \, a^{2} b^{2} d x \sinh\left(d x + c\right)^{8} + 2 \, {\left(16 \, a^{3} b - 20 \, a^{2} b^{2} + a b^{3} + 3 \, b^{4} + 16 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(112 \, a^{2} b^{2} d x \cosh\left(d x + c\right)^{2} + 16 \, a^{3} b - 20 \, a^{2} b^{2} + a b^{3} + 3 \, b^{4} + 16 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} d x\right)} \sinh\left(d x + c\right)^{6} + 8 \, a^{2} b^{2} d x + 4 \, {\left(112 \, a^{2} b^{2} d x \cosh\left(d x + c\right)^{3} + 3 \, {\left(16 \, a^{3} b - 20 \, a^{2} b^{2} + a b^{3} + 3 \, b^{4} + 16 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(48 \, a^{4} - 72 \, a^{3} b + 18 \, a^{2} b^{2} + 15 \, a b^{3} - 9 \, b^{4} + 8 \, {\left(8 \, a^{4} - 8 \, a^{3} b + 3 \, a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(280 \, a^{2} b^{2} d x \cosh\left(d x + c\right)^{4} + 48 \, a^{4} - 72 \, a^{3} b + 18 \, a^{2} b^{2} + 15 \, a b^{3} - 9 \, b^{4} + 8 \, {\left(8 \, a^{4} - 8 \, a^{3} b + 3 \, a^{2} b^{2}\right)} d x + 15 \, {\left(16 \, a^{3} b - 20 \, a^{2} b^{2} + a b^{3} + 3 \, b^{4} + 16 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 12 \, a^{2} b^{2} - 6 \, a b^{3} - 6 \, b^{4} + 8 \, {\left(56 \, a^{2} b^{2} d x \cosh\left(d x + c\right)^{5} + 5 \, {\left(16 \, a^{3} b - 20 \, a^{2} b^{2} + a b^{3} + 3 \, b^{4} + 16 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + {\left(48 \, a^{4} - 72 \, a^{3} b + 18 \, a^{2} b^{2} + 15 \, a b^{3} - 9 \, b^{4} + 8 \, {\left(8 \, a^{4} - 8 \, a^{3} b + 3 \, a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(32 \, a^{3} b - 28 \, a^{2} b^{2} - 13 \, a b^{3} + 9 \, b^{4} + 16 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(112 \, a^{2} b^{2} d x \cosh\left(d x + c\right)^{6} + 15 \, {\left(16 \, a^{3} b - 20 \, a^{2} b^{2} + a b^{3} + 3 \, b^{4} + 16 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 32 \, a^{3} b - 28 \, a^{2} b^{2} - 13 \, a b^{3} + 9 \, b^{4} + 16 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} d x + 6 \, {\left(48 \, a^{4} - 72 \, a^{3} b + 18 \, a^{2} b^{2} + 15 \, a b^{3} - 9 \, b^{4} + 8 \, {\left(8 \, a^{4} - 8 \, a^{3} b + 3 \, a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(8 \, a^{2} b^{2} + 4 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(8 \, a^{2} b^{2} + 4 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(8 \, a^{2} b^{2} + 4 \, a b^{3} + 3 \, b^{4}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(16 \, a^{3} b + 2 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(16 \, a^{3} b + 2 \, a b^{3} - 3 \, b^{4} + 7 \, {\left(8 \, a^{2} b^{2} + 4 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(8 \, a^{2} b^{2} + 4 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(16 \, a^{3} b + 2 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(64 \, a^{4} - 32 \, a^{3} b + 16 \, a^{2} b^{2} - 12 \, a b^{3} + 9 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(8 \, a^{2} b^{2} + 4 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 64 \, a^{4} - 32 \, a^{3} b + 16 \, a^{2} b^{2} - 12 \, a b^{3} + 9 \, b^{4} + 30 \, {\left(16 \, a^{3} b + 2 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, a^{2} b^{2} + 4 \, a b^{3} + 3 \, b^{4} + 8 \, {\left(7 \, {\left(8 \, a^{2} b^{2} + 4 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(16 \, a^{3} b + 2 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(64 \, a^{4} - 32 \, a^{3} b + 16 \, a^{2} b^{2} - 12 \, a b^{3} + 9 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(16 \, a^{3} b + 2 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(8 \, a^{2} b^{2} + 4 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(16 \, a^{3} b + 2 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 16 \, a^{3} b + 2 \, a b^{3} - 3 \, b^{4} + 3 \, {\left(64 \, a^{4} - 32 \, a^{3} b + 16 \, a^{2} b^{2} - 12 \, a b^{3} + 9 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left({\left(8 \, a^{2} b^{2} + 4 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(16 \, a^{3} b + 2 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + {\left(64 \, a^{4} - 32 \, a^{3} b + 16 \, a^{2} b^{2} - 12 \, a b^{3} + 9 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(16 \, a^{3} b + 2 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{a - b}{a}} \arctan\left(-\frac{{\left(b \cosh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b \sinh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sqrt{-\frac{a - b}{a}}}{2 \, {\left(a - b\right)}}\right) + 4 \, {\left(16 \, a^{2} b^{2} d x \cosh\left(d x + c\right)^{7} + 3 \, {\left(16 \, a^{3} b - 20 \, a^{2} b^{2} + a b^{3} + 3 \, b^{4} + 16 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(48 \, a^{4} - 72 \, a^{3} b + 18 \, a^{2} b^{2} + 15 \, a b^{3} - 9 \, b^{4} + 8 \, {\left(8 \, a^{4} - 8 \, a^{3} b + 3 \, a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + {\left(32 \, a^{3} b - 28 \, a^{2} b^{2} - 13 \, a b^{3} + 9 \, b^{4} + 16 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{8 \, {\left(a^{2} b^{5} d \cosh\left(d x + c\right)^{8} + 8 \, a^{2} b^{5} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + a^{2} b^{5} d \sinh\left(d x + c\right)^{8} + a^{2} b^{5} d + 4 \, {\left(2 \, a^{3} b^{4} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, a^{2} b^{5} d \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{3} b^{4} - a^{2} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(8 \, a^{4} b^{3} - 8 \, a^{3} b^{4} + 3 \, a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, a^{2} b^{5} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(2 \, a^{3} b^{4} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, a^{2} b^{5} d \cosh\left(d x + c\right)^{4} + 30 \, {\left(2 \, a^{3} b^{4} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(8 \, a^{4} b^{3} - 8 \, a^{3} b^{4} + 3 \, a^{2} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(2 \, a^{3} b^{4} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, a^{2} b^{5} d \cosh\left(d x + c\right)^{5} + 10 \, {\left(2 \, a^{3} b^{4} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{4} b^{3} - 8 \, a^{3} b^{4} + 3 \, a^{2} b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, a^{2} b^{5} d \cosh\left(d x + c\right)^{6} + 15 \, {\left(2 \, a^{3} b^{4} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(8 \, a^{4} b^{3} - 8 \, a^{3} b^{4} + 3 \, a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{3} b^{4} - a^{2} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left(a^{2} b^{5} d \cosh\left(d x + c\right)^{7} + 3 \, {\left(2 \, a^{3} b^{4} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{5} + {\left(8 \, a^{4} b^{3} - 8 \, a^{3} b^{4} + 3 \, a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{3} b^{4} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[1/16*(16*a^2*b^2*d*x*cosh(d*x + c)^8 + 128*a^2*b^2*d*x*cosh(d*x + c)*sinh(d*x + c)^7 + 16*a^2*b^2*d*x*sinh(d*x + c)^8 + 4*(16*a^3*b - 20*a^2*b^2 + a*b^3 + 3*b^4 + 16*(2*a^3*b - a^2*b^2)*d*x)*cosh(d*x + c)^6 + 4*(112*a^2*b^2*d*x*cosh(d*x + c)^2 + 16*a^3*b - 20*a^2*b^2 + a*b^3 + 3*b^4 + 16*(2*a^3*b - a^2*b^2)*d*x)*sinh(d*x + c)^6 + 16*a^2*b^2*d*x + 8*(112*a^2*b^2*d*x*cosh(d*x + c)^3 + 3*(16*a^3*b - 20*a^2*b^2 + a*b^3 + 3*b^4 + 16*(2*a^3*b - a^2*b^2)*d*x)*cosh(d*x + c))*sinh(d*x + c)^5 + 4*(48*a^4 - 72*a^3*b + 18*a^2*b^2 + 15*a*b^3 - 9*b^4 + 8*(8*a^4 - 8*a^3*b + 3*a^2*b^2)*d*x)*cosh(d*x + c)^4 + 4*(280*a^2*b^2*d*x*cosh(d*x + c)^4 + 48*a^4 - 72*a^3*b + 18*a^2*b^2 + 15*a*b^3 - 9*b^4 + 8*(8*a^4 - 8*a^3*b + 3*a^2*b^2)*d*x + 15*(16*a^3*b - 20*a^2*b^2 + a*b^3 + 3*b^4 + 16*(2*a^3*b - a^2*b^2)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 24*a^2*b^2 - 12*a*b^3 - 12*b^4 + 16*(56*a^2*b^2*d*x*cosh(d*x + c)^5 + 5*(16*a^3*b - 20*a^2*b^2 + a*b^3 + 3*b^4 + 16*(2*a^3*b - a^2*b^2)*d*x)*cosh(d*x + c)^3 + (48*a^4 - 72*a^3*b + 18*a^2*b^2 + 15*a*b^3 - 9*b^4 + 8*(8*a^4 - 8*a^3*b + 3*a^2*b^2)*d*x)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(32*a^3*b - 28*a^2*b^2 - 13*a*b^3 + 9*b^4 + 16*(2*a^3*b - a^2*b^2)*d*x)*cosh(d*x + c)^2 + 4*(112*a^2*b^2*d*x*cosh(d*x + c)^6 + 15*(16*a^3*b - 20*a^2*b^2 + a*b^3 + 3*b^4 + 16*(2*a^3*b - a^2*b^2)*d*x)*cosh(d*x + c)^4 + 32*a^3*b - 28*a^2*b^2 - 13*a*b^3 + 9*b^4 + 16*(2*a^3*b - a^2*b^2)*d*x + 6*(48*a^4 - 72*a^3*b + 18*a^2*b^2 + 15*a*b^3 - 9*b^4 + 8*(8*a^4 - 8*a^3*b + 3*a^2*b^2)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((8*a^2*b^2 + 4*a*b^3 + 3*b^4)*cosh(d*x + c)^8 + 8*(8*a^2*b^2 + 4*a*b^3 + 3*b^4)*cosh(d*x + c)*sinh(d*x + c)^7 + (8*a^2*b^2 + 4*a*b^3 + 3*b^4)*sinh(d*x + c)^8 + 4*(16*a^3*b + 2*a*b^3 - 3*b^4)*cosh(d*x + c)^6 + 4*(16*a^3*b + 2*a*b^3 - 3*b^4 + 7*(8*a^2*b^2 + 4*a*b^3 + 3*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(8*a^2*b^2 + 4*a*b^3 + 3*b^4)*cosh(d*x + c)^3 + 3*(16*a^3*b + 2*a*b^3 - 3*b^4)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(64*a^4 - 32*a^3*b + 16*a^2*b^2 - 12*a*b^3 + 9*b^4)*cosh(d*x + c)^4 + 2*(35*(8*a^2*b^2 + 4*a*b^3 + 3*b^4)*cosh(d*x + c)^4 + 64*a^4 - 32*a^3*b + 16*a^2*b^2 - 12*a*b^3 + 9*b^4 + 30*(16*a^3*b + 2*a*b^3 - 3*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*a^2*b^2 + 4*a*b^3 + 3*b^4 + 8*(7*(8*a^2*b^2 + 4*a*b^3 + 3*b^4)*cosh(d*x + c)^5 + 10*(16*a^3*b + 2*a*b^3 - 3*b^4)*cosh(d*x + c)^3 + (64*a^4 - 32*a^3*b + 16*a^2*b^2 - 12*a*b^3 + 9*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(16*a^3*b + 2*a*b^3 - 3*b^4)*cosh(d*x + c)^2 + 4*(7*(8*a^2*b^2 + 4*a*b^3 + 3*b^4)*cosh(d*x + c)^6 + 15*(16*a^3*b + 2*a*b^3 - 3*b^4)*cosh(d*x + c)^4 + 16*a^3*b + 2*a*b^3 - 3*b^4 + 3*(64*a^4 - 32*a^3*b + 16*a^2*b^2 - 12*a*b^3 + 9*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((8*a^2*b^2 + 4*a*b^3 + 3*b^4)*cosh(d*x + c)^7 + 3*(16*a^3*b + 2*a*b^3 - 3*b^4)*cosh(d*x + c)^5 + (64*a^4 - 32*a^3*b + 16*a^2*b^2 - 12*a*b^3 + 9*b^4)*cosh(d*x + c)^3 + (16*a^3*b + 2*a*b^3 - 3*b^4)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a - b)/a)*log((b^2*cosh(d*x + c)^4 + 4*b^2*cosh(d*x + c)*sinh(d*x + c)^3 + b^2*sinh(d*x + c)^4 + 2*(2*a*b - b^2)*cosh(d*x + c)^2 + 2*(3*b^2*cosh(d*x + c)^2 + 2*a*b - b^2)*sinh(d*x + c)^2 + 8*a^2 - 8*a*b + b^2 + 4*(b^2*cosh(d*x + c)^3 + (2*a*b - b^2)*cosh(d*x + c))*sinh(d*x + c) + 4*(a*b*cosh(d*x + c)^2 + 2*a*b*cosh(d*x + c)*sinh(d*x + c) + a*b*sinh(d*x + c)^2 + 2*a^2 - a*b)*sqrt((a - b)/a))/(b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 + 2*(2*a - b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 + 2*a - b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 + (2*a - b)*cosh(d*x + c))*sinh(d*x + c) + b)) + 8*(16*a^2*b^2*d*x*cosh(d*x + c)^7 + 3*(16*a^3*b - 20*a^2*b^2 + a*b^3 + 3*b^4 + 16*(2*a^3*b - a^2*b^2)*d*x)*cosh(d*x + c)^5 + 2*(48*a^4 - 72*a^3*b + 18*a^2*b^2 + 15*a*b^3 - 9*b^4 + 8*(8*a^4 - 8*a^3*b + 3*a^2*b^2)*d*x)*cosh(d*x + c)^3 + (32*a^3*b - 28*a^2*b^2 - 13*a*b^3 + 9*b^4 + 16*(2*a^3*b - a^2*b^2)*d*x)*cosh(d*x + c))*sinh(d*x + c))/(a^2*b^5*d*cosh(d*x + c)^8 + 8*a^2*b^5*d*cosh(d*x + c)*sinh(d*x + c)^7 + a^2*b^5*d*sinh(d*x + c)^8 + a^2*b^5*d + 4*(2*a^3*b^4 - a^2*b^5)*d*cosh(d*x + c)^6 + 4*(7*a^2*b^5*d*cosh(d*x + c)^2 + (2*a^3*b^4 - a^2*b^5)*d)*sinh(d*x + c)^6 + 2*(8*a^4*b^3 - 8*a^3*b^4 + 3*a^2*b^5)*d*cosh(d*x + c)^4 + 8*(7*a^2*b^5*d*cosh(d*x + c)^3 + 3*(2*a^3*b^4 - a^2*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*a^2*b^5*d*cosh(d*x + c)^4 + 30*(2*a^3*b^4 - a^2*b^5)*d*cosh(d*x + c)^2 + (8*a^4*b^3 - 8*a^3*b^4 + 3*a^2*b^5)*d)*sinh(d*x + c)^4 + 4*(2*a^3*b^4 - a^2*b^5)*d*cosh(d*x + c)^2 + 8*(7*a^2*b^5*d*cosh(d*x + c)^5 + 10*(2*a^3*b^4 - a^2*b^5)*d*cosh(d*x + c)^3 + (8*a^4*b^3 - 8*a^3*b^4 + 3*a^2*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*a^2*b^5*d*cosh(d*x + c)^6 + 15*(2*a^3*b^4 - a^2*b^5)*d*cosh(d*x + c)^4 + 3*(8*a^4*b^3 - 8*a^3*b^4 + 3*a^2*b^5)*d*cosh(d*x + c)^2 + (2*a^3*b^4 - a^2*b^5)*d)*sinh(d*x + c)^2 + 8*(a^2*b^5*d*cosh(d*x + c)^7 + 3*(2*a^3*b^4 - a^2*b^5)*d*cosh(d*x + c)^5 + (8*a^4*b^3 - 8*a^3*b^4 + 3*a^2*b^5)*d*cosh(d*x + c)^3 + (2*a^3*b^4 - a^2*b^5)*d*cosh(d*x + c))*sinh(d*x + c)), 1/8*(8*a^2*b^2*d*x*cosh(d*x + c)^8 + 64*a^2*b^2*d*x*cosh(d*x + c)*sinh(d*x + c)^7 + 8*a^2*b^2*d*x*sinh(d*x + c)^8 + 2*(16*a^3*b - 20*a^2*b^2 + a*b^3 + 3*b^4 + 16*(2*a^3*b - a^2*b^2)*d*x)*cosh(d*x + c)^6 + 2*(112*a^2*b^2*d*x*cosh(d*x + c)^2 + 16*a^3*b - 20*a^2*b^2 + a*b^3 + 3*b^4 + 16*(2*a^3*b - a^2*b^2)*d*x)*sinh(d*x + c)^6 + 8*a^2*b^2*d*x + 4*(112*a^2*b^2*d*x*cosh(d*x + c)^3 + 3*(16*a^3*b - 20*a^2*b^2 + a*b^3 + 3*b^4 + 16*(2*a^3*b - a^2*b^2)*d*x)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(48*a^4 - 72*a^3*b + 18*a^2*b^2 + 15*a*b^3 - 9*b^4 + 8*(8*a^4 - 8*a^3*b + 3*a^2*b^2)*d*x)*cosh(d*x + c)^4 + 2*(280*a^2*b^2*d*x*cosh(d*x + c)^4 + 48*a^4 - 72*a^3*b + 18*a^2*b^2 + 15*a*b^3 - 9*b^4 + 8*(8*a^4 - 8*a^3*b + 3*a^2*b^2)*d*x + 15*(16*a^3*b - 20*a^2*b^2 + a*b^3 + 3*b^4 + 16*(2*a^3*b - a^2*b^2)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 12*a^2*b^2 - 6*a*b^3 - 6*b^4 + 8*(56*a^2*b^2*d*x*cosh(d*x + c)^5 + 5*(16*a^3*b - 20*a^2*b^2 + a*b^3 + 3*b^4 + 16*(2*a^3*b - a^2*b^2)*d*x)*cosh(d*x + c)^3 + (48*a^4 - 72*a^3*b + 18*a^2*b^2 + 15*a*b^3 - 9*b^4 + 8*(8*a^4 - 8*a^3*b + 3*a^2*b^2)*d*x)*cosh(d*x + c))*sinh(d*x + c)^3 + 2*(32*a^3*b - 28*a^2*b^2 - 13*a*b^3 + 9*b^4 + 16*(2*a^3*b - a^2*b^2)*d*x)*cosh(d*x + c)^2 + 2*(112*a^2*b^2*d*x*cosh(d*x + c)^6 + 15*(16*a^3*b - 20*a^2*b^2 + a*b^3 + 3*b^4 + 16*(2*a^3*b - a^2*b^2)*d*x)*cosh(d*x + c)^4 + 32*a^3*b - 28*a^2*b^2 - 13*a*b^3 + 9*b^4 + 16*(2*a^3*b - a^2*b^2)*d*x + 6*(48*a^4 - 72*a^3*b + 18*a^2*b^2 + 15*a*b^3 - 9*b^4 + 8*(8*a^4 - 8*a^3*b + 3*a^2*b^2)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((8*a^2*b^2 + 4*a*b^3 + 3*b^4)*cosh(d*x + c)^8 + 8*(8*a^2*b^2 + 4*a*b^3 + 3*b^4)*cosh(d*x + c)*sinh(d*x + c)^7 + (8*a^2*b^2 + 4*a*b^3 + 3*b^4)*sinh(d*x + c)^8 + 4*(16*a^3*b + 2*a*b^3 - 3*b^4)*cosh(d*x + c)^6 + 4*(16*a^3*b + 2*a*b^3 - 3*b^4 + 7*(8*a^2*b^2 + 4*a*b^3 + 3*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(8*a^2*b^2 + 4*a*b^3 + 3*b^4)*cosh(d*x + c)^3 + 3*(16*a^3*b + 2*a*b^3 - 3*b^4)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(64*a^4 - 32*a^3*b + 16*a^2*b^2 - 12*a*b^3 + 9*b^4)*cosh(d*x + c)^4 + 2*(35*(8*a^2*b^2 + 4*a*b^3 + 3*b^4)*cosh(d*x + c)^4 + 64*a^4 - 32*a^3*b + 16*a^2*b^2 - 12*a*b^3 + 9*b^4 + 30*(16*a^3*b + 2*a*b^3 - 3*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*a^2*b^2 + 4*a*b^3 + 3*b^4 + 8*(7*(8*a^2*b^2 + 4*a*b^3 + 3*b^4)*cosh(d*x + c)^5 + 10*(16*a^3*b + 2*a*b^3 - 3*b^4)*cosh(d*x + c)^3 + (64*a^4 - 32*a^3*b + 16*a^2*b^2 - 12*a*b^3 + 9*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(16*a^3*b + 2*a*b^3 - 3*b^4)*cosh(d*x + c)^2 + 4*(7*(8*a^2*b^2 + 4*a*b^3 + 3*b^4)*cosh(d*x + c)^6 + 15*(16*a^3*b + 2*a*b^3 - 3*b^4)*cosh(d*x + c)^4 + 16*a^3*b + 2*a*b^3 - 3*b^4 + 3*(64*a^4 - 32*a^3*b + 16*a^2*b^2 - 12*a*b^3 + 9*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((8*a^2*b^2 + 4*a*b^3 + 3*b^4)*cosh(d*x + c)^7 + 3*(16*a^3*b + 2*a*b^3 - 3*b^4)*cosh(d*x + c)^5 + (64*a^4 - 32*a^3*b + 16*a^2*b^2 - 12*a*b^3 + 9*b^4)*cosh(d*x + c)^3 + (16*a^3*b + 2*a*b^3 - 3*b^4)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-(a - b)/a)*arctan(-1/2*(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + 2*a - b)*sqrt(-(a - b)/a)/(a - b)) + 4*(16*a^2*b^2*d*x*cosh(d*x + c)^7 + 3*(16*a^3*b - 20*a^2*b^2 + a*b^3 + 3*b^4 + 16*(2*a^3*b - a^2*b^2)*d*x)*cosh(d*x + c)^5 + 2*(48*a^4 - 72*a^3*b + 18*a^2*b^2 + 15*a*b^3 - 9*b^4 + 8*(8*a^4 - 8*a^3*b + 3*a^2*b^2)*d*x)*cosh(d*x + c)^3 + (32*a^3*b - 28*a^2*b^2 - 13*a*b^3 + 9*b^4 + 16*(2*a^3*b - a^2*b^2)*d*x)*cosh(d*x + c))*sinh(d*x + c))/(a^2*b^5*d*cosh(d*x + c)^8 + 8*a^2*b^5*d*cosh(d*x + c)*sinh(d*x + c)^7 + a^2*b^5*d*sinh(d*x + c)^8 + a^2*b^5*d + 4*(2*a^3*b^4 - a^2*b^5)*d*cosh(d*x + c)^6 + 4*(7*a^2*b^5*d*cosh(d*x + c)^2 + (2*a^3*b^4 - a^2*b^5)*d)*sinh(d*x + c)^6 + 2*(8*a^4*b^3 - 8*a^3*b^4 + 3*a^2*b^5)*d*cosh(d*x + c)^4 + 8*(7*a^2*b^5*d*cosh(d*x + c)^3 + 3*(2*a^3*b^4 - a^2*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*a^2*b^5*d*cosh(d*x + c)^4 + 30*(2*a^3*b^4 - a^2*b^5)*d*cosh(d*x + c)^2 + (8*a^4*b^3 - 8*a^3*b^4 + 3*a^2*b^5)*d)*sinh(d*x + c)^4 + 4*(2*a^3*b^4 - a^2*b^5)*d*cosh(d*x + c)^2 + 8*(7*a^2*b^5*d*cosh(d*x + c)^5 + 10*(2*a^3*b^4 - a^2*b^5)*d*cosh(d*x + c)^3 + (8*a^4*b^3 - 8*a^3*b^4 + 3*a^2*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*a^2*b^5*d*cosh(d*x + c)^6 + 15*(2*a^3*b^4 - a^2*b^5)*d*cosh(d*x + c)^4 + 3*(8*a^4*b^3 - 8*a^3*b^4 + 3*a^2*b^5)*d*cosh(d*x + c)^2 + (2*a^3*b^4 - a^2*b^5)*d)*sinh(d*x + c)^2 + 8*(a^2*b^5*d*cosh(d*x + c)^7 + 3*(2*a^3*b^4 - a^2*b^5)*d*cosh(d*x + c)^5 + (8*a^4*b^3 - 8*a^3*b^4 + 3*a^2*b^5)*d*cosh(d*x + c)^3 + (2*a^3*b^4 - a^2*b^5)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
340,1,5844,0,0.687111," ","integrate(cosh(d*x+c)^5/(a+b*sinh(d*x+c)^2)^3,x, algorithm=""fricas"")","\left[-\frac{4 \, {\left(5 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{7} + 28 \, {\left(5 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + 4 \, {\left(5 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4}\right)} \sinh\left(d x + c\right)^{7} + 4 \, {\left(12 \, a^{4} b - 7 \, a^{3} b^{2} - 14 \, a^{2} b^{3} + 9 \, a b^{4}\right)} \cosh\left(d x + c\right)^{5} + 4 \, {\left(12 \, a^{4} b - 7 \, a^{3} b^{2} - 14 \, a^{2} b^{3} + 9 \, a b^{4} + 21 \, {\left(5 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{5} + 20 \, {\left(7 \, {\left(5 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(12 \, a^{4} b - 7 \, a^{3} b^{2} - 14 \, a^{2} b^{3} + 9 \, a b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} - 4 \, {\left(12 \, a^{4} b - 7 \, a^{3} b^{2} - 14 \, a^{2} b^{3} + 9 \, a b^{4}\right)} \cosh\left(d x + c\right)^{3} - 4 \, {\left(12 \, a^{4} b - 7 \, a^{3} b^{2} - 14 \, a^{2} b^{3} + 9 \, a b^{4} - 35 \, {\left(5 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{4} - 10 \, {\left(12 \, a^{4} b - 7 \, a^{3} b^{2} - 14 \, a^{2} b^{3} + 9 \, a b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(21 \, {\left(5 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(12 \, a^{4} b - 7 \, a^{3} b^{2} - 14 \, a^{2} b^{3} + 9 \, a b^{4}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(12 \, a^{4} b - 7 \, a^{3} b^{2} - 14 \, a^{2} b^{3} + 9 \, a b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(3 \, a^{2} b^{2} + 2 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(3 \, a^{2} b^{2} + 2 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(3 \, a^{2} b^{2} + 2 \, a b^{3} + 3 \, b^{4}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(6 \, a^{3} b + a^{2} b^{2} + 4 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(6 \, a^{3} b + a^{2} b^{2} + 4 \, a b^{3} - 3 \, b^{4} + 7 \, {\left(3 \, a^{2} b^{2} + 2 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(3 \, a^{2} b^{2} + 2 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(6 \, a^{3} b + a^{2} b^{2} + 4 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(24 \, a^{4} - 8 \, a^{3} b + 17 \, a^{2} b^{2} - 18 \, a b^{3} + 9 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(3 \, a^{2} b^{2} + 2 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 24 \, a^{4} - 8 \, a^{3} b + 17 \, a^{2} b^{2} - 18 \, a b^{3} + 9 \, b^{4} + 30 \, {\left(6 \, a^{3} b + a^{2} b^{2} + 4 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 3 \, a^{2} b^{2} + 2 \, a b^{3} + 3 \, b^{4} + 8 \, {\left(7 \, {\left(3 \, a^{2} b^{2} + 2 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(6 \, a^{3} b + a^{2} b^{2} + 4 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(24 \, a^{4} - 8 \, a^{3} b + 17 \, a^{2} b^{2} - 18 \, a b^{3} + 9 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(6 \, a^{3} b + a^{2} b^{2} + 4 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(3 \, a^{2} b^{2} + 2 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(6 \, a^{3} b + a^{2} b^{2} + 4 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 6 \, a^{3} b + a^{2} b^{2} + 4 \, a b^{3} - 3 \, b^{4} + 3 \, {\left(24 \, a^{4} - 8 \, a^{3} b + 17 \, a^{2} b^{2} - 18 \, a b^{3} + 9 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left({\left(3 \, a^{2} b^{2} + 2 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(6 \, a^{3} b + a^{2} b^{2} + 4 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + {\left(24 \, a^{4} - 8 \, a^{3} b + 17 \, a^{2} b^{2} - 18 \, a b^{3} + 9 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(6 \, a^{3} b + a^{2} b^{2} + 4 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-a b} \log\left(\frac{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} - 2 \, {\left(2 \, a + b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} - 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} - {\left(2 \, a + b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) - 4 \, {\left(\cosh\left(d x + c\right)^{3} + 3 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{3} + {\left(3 \, \cosh\left(d x + c\right)^{2} - 1\right)} \sinh\left(d x + c\right) - \cosh\left(d x + c\right)\right)} \sqrt{-a b} + b}{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b}\right) - 4 \, {\left(5 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4}\right)} \cosh\left(d x + c\right) + 4 \, {\left(7 \, {\left(5 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{6} - 5 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + 3 \, a b^{4} + 5 \, {\left(12 \, a^{4} b - 7 \, a^{3} b^{2} - 14 \, a^{2} b^{3} + 9 \, a b^{4}\right)} \cosh\left(d x + c\right)^{4} - 3 \, {\left(12 \, a^{4} b - 7 \, a^{3} b^{2} - 14 \, a^{2} b^{3} + 9 \, a b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)}{16 \, {\left(a^{3} b^{5} d \cosh\left(d x + c\right)^{8} + 8 \, a^{3} b^{5} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + a^{3} b^{5} d \sinh\left(d x + c\right)^{8} + a^{3} b^{5} d + 4 \, {\left(2 \, a^{4} b^{4} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, a^{3} b^{5} d \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{4} b^{4} - a^{3} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(8 \, a^{5} b^{3} - 8 \, a^{4} b^{4} + 3 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, a^{3} b^{5} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(2 \, a^{4} b^{4} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, a^{3} b^{5} d \cosh\left(d x + c\right)^{4} + 30 \, {\left(2 \, a^{4} b^{4} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(8 \, a^{5} b^{3} - 8 \, a^{4} b^{4} + 3 \, a^{3} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(2 \, a^{4} b^{4} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, a^{3} b^{5} d \cosh\left(d x + c\right)^{5} + 10 \, {\left(2 \, a^{4} b^{4} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{5} b^{3} - 8 \, a^{4} b^{4} + 3 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, a^{3} b^{5} d \cosh\left(d x + c\right)^{6} + 15 \, {\left(2 \, a^{4} b^{4} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(8 \, a^{5} b^{3} - 8 \, a^{4} b^{4} + 3 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{4} b^{4} - a^{3} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left(a^{3} b^{5} d \cosh\left(d x + c\right)^{7} + 3 \, {\left(2 \, a^{4} b^{4} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{5} + {\left(8 \, a^{5} b^{3} - 8 \, a^{4} b^{4} + 3 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{4} b^{4} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}, -\frac{2 \, {\left(5 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{7} + 14 \, {\left(5 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + 2 \, {\left(5 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4}\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(12 \, a^{4} b - 7 \, a^{3} b^{2} - 14 \, a^{2} b^{3} + 9 \, a b^{4}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(12 \, a^{4} b - 7 \, a^{3} b^{2} - 14 \, a^{2} b^{3} + 9 \, a b^{4} + 21 \, {\left(5 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{5} + 10 \, {\left(7 \, {\left(5 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(12 \, a^{4} b - 7 \, a^{3} b^{2} - 14 \, a^{2} b^{3} + 9 \, a b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(12 \, a^{4} b - 7 \, a^{3} b^{2} - 14 \, a^{2} b^{3} + 9 \, a b^{4}\right)} \cosh\left(d x + c\right)^{3} - 2 \, {\left(12 \, a^{4} b - 7 \, a^{3} b^{2} - 14 \, a^{2} b^{3} + 9 \, a b^{4} - 35 \, {\left(5 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{4} - 10 \, {\left(12 \, a^{4} b - 7 \, a^{3} b^{2} - 14 \, a^{2} b^{3} + 9 \, a b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(21 \, {\left(5 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(12 \, a^{4} b - 7 \, a^{3} b^{2} - 14 \, a^{2} b^{3} + 9 \, a b^{4}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(12 \, a^{4} b - 7 \, a^{3} b^{2} - 14 \, a^{2} b^{3} + 9 \, a b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - {\left({\left(3 \, a^{2} b^{2} + 2 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(3 \, a^{2} b^{2} + 2 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(3 \, a^{2} b^{2} + 2 \, a b^{3} + 3 \, b^{4}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(6 \, a^{3} b + a^{2} b^{2} + 4 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(6 \, a^{3} b + a^{2} b^{2} + 4 \, a b^{3} - 3 \, b^{4} + 7 \, {\left(3 \, a^{2} b^{2} + 2 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(3 \, a^{2} b^{2} + 2 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(6 \, a^{3} b + a^{2} b^{2} + 4 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(24 \, a^{4} - 8 \, a^{3} b + 17 \, a^{2} b^{2} - 18 \, a b^{3} + 9 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(3 \, a^{2} b^{2} + 2 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 24 \, a^{4} - 8 \, a^{3} b + 17 \, a^{2} b^{2} - 18 \, a b^{3} + 9 \, b^{4} + 30 \, {\left(6 \, a^{3} b + a^{2} b^{2} + 4 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 3 \, a^{2} b^{2} + 2 \, a b^{3} + 3 \, b^{4} + 8 \, {\left(7 \, {\left(3 \, a^{2} b^{2} + 2 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(6 \, a^{3} b + a^{2} b^{2} + 4 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(24 \, a^{4} - 8 \, a^{3} b + 17 \, a^{2} b^{2} - 18 \, a b^{3} + 9 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(6 \, a^{3} b + a^{2} b^{2} + 4 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(3 \, a^{2} b^{2} + 2 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(6 \, a^{3} b + a^{2} b^{2} + 4 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 6 \, a^{3} b + a^{2} b^{2} + 4 \, a b^{3} - 3 \, b^{4} + 3 \, {\left(24 \, a^{4} - 8 \, a^{3} b + 17 \, a^{2} b^{2} - 18 \, a b^{3} + 9 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left({\left(3 \, a^{2} b^{2} + 2 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(6 \, a^{3} b + a^{2} b^{2} + 4 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + {\left(24 \, a^{4} - 8 \, a^{3} b + 17 \, a^{2} b^{2} - 18 \, a b^{3} + 9 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(6 \, a^{3} b + a^{2} b^{2} + 4 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} {\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right)}}{2 \, a}\right) - {\left({\left(3 \, a^{2} b^{2} + 2 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(3 \, a^{2} b^{2} + 2 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(3 \, a^{2} b^{2} + 2 \, a b^{3} + 3 \, b^{4}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(6 \, a^{3} b + a^{2} b^{2} + 4 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(6 \, a^{3} b + a^{2} b^{2} + 4 \, a b^{3} - 3 \, b^{4} + 7 \, {\left(3 \, a^{2} b^{2} + 2 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(3 \, a^{2} b^{2} + 2 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(6 \, a^{3} b + a^{2} b^{2} + 4 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(24 \, a^{4} - 8 \, a^{3} b + 17 \, a^{2} b^{2} - 18 \, a b^{3} + 9 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(3 \, a^{2} b^{2} + 2 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 24 \, a^{4} - 8 \, a^{3} b + 17 \, a^{2} b^{2} - 18 \, a b^{3} + 9 \, b^{4} + 30 \, {\left(6 \, a^{3} b + a^{2} b^{2} + 4 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 3 \, a^{2} b^{2} + 2 \, a b^{3} + 3 \, b^{4} + 8 \, {\left(7 \, {\left(3 \, a^{2} b^{2} + 2 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(6 \, a^{3} b + a^{2} b^{2} + 4 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(24 \, a^{4} - 8 \, a^{3} b + 17 \, a^{2} b^{2} - 18 \, a b^{3} + 9 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(6 \, a^{3} b + a^{2} b^{2} + 4 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(3 \, a^{2} b^{2} + 2 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(6 \, a^{3} b + a^{2} b^{2} + 4 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 6 \, a^{3} b + a^{2} b^{2} + 4 \, a b^{3} - 3 \, b^{4} + 3 \, {\left(24 \, a^{4} - 8 \, a^{3} b + 17 \, a^{2} b^{2} - 18 \, a b^{3} + 9 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left({\left(3 \, a^{2} b^{2} + 2 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(6 \, a^{3} b + a^{2} b^{2} + 4 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + {\left(24 \, a^{4} - 8 \, a^{3} b + 17 \, a^{2} b^{2} - 18 \, a b^{3} + 9 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(6 \, a^{3} b + a^{2} b^{2} + 4 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{a b} \arctan\left(\frac{{\left(b \cosh\left(d x + c\right)^{3} + 3 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{3} + {\left(4 \, a - b\right)} \cosh\left(d x + c\right) + {\left(3 \, b \cosh\left(d x + c\right)^{2} + 4 \, a - b\right)} \sinh\left(d x + c\right)\right)} \sqrt{a b}}{2 \, a b}\right) - 2 \, {\left(5 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4}\right)} \cosh\left(d x + c\right) + 2 \, {\left(7 \, {\left(5 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{6} - 5 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + 3 \, a b^{4} + 5 \, {\left(12 \, a^{4} b - 7 \, a^{3} b^{2} - 14 \, a^{2} b^{3} + 9 \, a b^{4}\right)} \cosh\left(d x + c\right)^{4} - 3 \, {\left(12 \, a^{4} b - 7 \, a^{3} b^{2} - 14 \, a^{2} b^{3} + 9 \, a b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)}{8 \, {\left(a^{3} b^{5} d \cosh\left(d x + c\right)^{8} + 8 \, a^{3} b^{5} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + a^{3} b^{5} d \sinh\left(d x + c\right)^{8} + a^{3} b^{5} d + 4 \, {\left(2 \, a^{4} b^{4} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, a^{3} b^{5} d \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{4} b^{4} - a^{3} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(8 \, a^{5} b^{3} - 8 \, a^{4} b^{4} + 3 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, a^{3} b^{5} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(2 \, a^{4} b^{4} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, a^{3} b^{5} d \cosh\left(d x + c\right)^{4} + 30 \, {\left(2 \, a^{4} b^{4} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(8 \, a^{5} b^{3} - 8 \, a^{4} b^{4} + 3 \, a^{3} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(2 \, a^{4} b^{4} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, a^{3} b^{5} d \cosh\left(d x + c\right)^{5} + 10 \, {\left(2 \, a^{4} b^{4} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{5} b^{3} - 8 \, a^{4} b^{4} + 3 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, a^{3} b^{5} d \cosh\left(d x + c\right)^{6} + 15 \, {\left(2 \, a^{4} b^{4} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(8 \, a^{5} b^{3} - 8 \, a^{4} b^{4} + 3 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{4} b^{4} - a^{3} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left(a^{3} b^{5} d \cosh\left(d x + c\right)^{7} + 3 \, {\left(2 \, a^{4} b^{4} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{5} + {\left(8 \, a^{5} b^{3} - 8 \, a^{4} b^{4} + 3 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{4} b^{4} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[-1/16*(4*(5*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4)*cosh(d*x + c)^7 + 28*(5*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4)*cosh(d*x + c)*sinh(d*x + c)^6 + 4*(5*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4)*sinh(d*x + c)^7 + 4*(12*a^4*b - 7*a^3*b^2 - 14*a^2*b^3 + 9*a*b^4)*cosh(d*x + c)^5 + 4*(12*a^4*b - 7*a^3*b^2 - 14*a^2*b^3 + 9*a*b^4 + 21*(5*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 20*(7*(5*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4)*cosh(d*x + c)^3 + (12*a^4*b - 7*a^3*b^2 - 14*a^2*b^3 + 9*a*b^4)*cosh(d*x + c))*sinh(d*x + c)^4 - 4*(12*a^4*b - 7*a^3*b^2 - 14*a^2*b^3 + 9*a*b^4)*cosh(d*x + c)^3 - 4*(12*a^4*b - 7*a^3*b^2 - 14*a^2*b^3 + 9*a*b^4 - 35*(5*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4)*cosh(d*x + c)^4 - 10*(12*a^4*b - 7*a^3*b^2 - 14*a^2*b^3 + 9*a*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 4*(21*(5*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4)*cosh(d*x + c)^5 + 10*(12*a^4*b - 7*a^3*b^2 - 14*a^2*b^3 + 9*a*b^4)*cosh(d*x + c)^3 - 3*(12*a^4*b - 7*a^3*b^2 - 14*a^2*b^3 + 9*a*b^4)*cosh(d*x + c))*sinh(d*x + c)^2 + ((3*a^2*b^2 + 2*a*b^3 + 3*b^4)*cosh(d*x + c)^8 + 8*(3*a^2*b^2 + 2*a*b^3 + 3*b^4)*cosh(d*x + c)*sinh(d*x + c)^7 + (3*a^2*b^2 + 2*a*b^3 + 3*b^4)*sinh(d*x + c)^8 + 4*(6*a^3*b + a^2*b^2 + 4*a*b^3 - 3*b^4)*cosh(d*x + c)^6 + 4*(6*a^3*b + a^2*b^2 + 4*a*b^3 - 3*b^4 + 7*(3*a^2*b^2 + 2*a*b^3 + 3*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(3*a^2*b^2 + 2*a*b^3 + 3*b^4)*cosh(d*x + c)^3 + 3*(6*a^3*b + a^2*b^2 + 4*a*b^3 - 3*b^4)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(24*a^4 - 8*a^3*b + 17*a^2*b^2 - 18*a*b^3 + 9*b^4)*cosh(d*x + c)^4 + 2*(35*(3*a^2*b^2 + 2*a*b^3 + 3*b^4)*cosh(d*x + c)^4 + 24*a^4 - 8*a^3*b + 17*a^2*b^2 - 18*a*b^3 + 9*b^4 + 30*(6*a^3*b + a^2*b^2 + 4*a*b^3 - 3*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 3*a^2*b^2 + 2*a*b^3 + 3*b^4 + 8*(7*(3*a^2*b^2 + 2*a*b^3 + 3*b^4)*cosh(d*x + c)^5 + 10*(6*a^3*b + a^2*b^2 + 4*a*b^3 - 3*b^4)*cosh(d*x + c)^3 + (24*a^4 - 8*a^3*b + 17*a^2*b^2 - 18*a*b^3 + 9*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(6*a^3*b + a^2*b^2 + 4*a*b^3 - 3*b^4)*cosh(d*x + c)^2 + 4*(7*(3*a^2*b^2 + 2*a*b^3 + 3*b^4)*cosh(d*x + c)^6 + 15*(6*a^3*b + a^2*b^2 + 4*a*b^3 - 3*b^4)*cosh(d*x + c)^4 + 6*a^3*b + a^2*b^2 + 4*a*b^3 - 3*b^4 + 3*(24*a^4 - 8*a^3*b + 17*a^2*b^2 - 18*a*b^3 + 9*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((3*a^2*b^2 + 2*a*b^3 + 3*b^4)*cosh(d*x + c)^7 + 3*(6*a^3*b + a^2*b^2 + 4*a*b^3 - 3*b^4)*cosh(d*x + c)^5 + (24*a^4 - 8*a^3*b + 17*a^2*b^2 - 18*a*b^3 + 9*b^4)*cosh(d*x + c)^3 + (6*a^3*b + a^2*b^2 + 4*a*b^3 - 3*b^4)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-a*b)*log((b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 - 2*(2*a + b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 - 2*a - b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 - (2*a + b)*cosh(d*x + c))*sinh(d*x + c) - 4*(cosh(d*x + c)^3 + 3*cosh(d*x + c)*sinh(d*x + c)^2 + sinh(d*x + c)^3 + (3*cosh(d*x + c)^2 - 1)*sinh(d*x + c) - cosh(d*x + c))*sqrt(-a*b) + b)/(b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 + 2*(2*a - b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 + 2*a - b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 + (2*a - b)*cosh(d*x + c))*sinh(d*x + c) + b)) - 4*(5*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4)*cosh(d*x + c) + 4*(7*(5*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4)*cosh(d*x + c)^6 - 5*a^3*b^2 + 2*a^2*b^3 + 3*a*b^4 + 5*(12*a^4*b - 7*a^3*b^2 - 14*a^2*b^3 + 9*a*b^4)*cosh(d*x + c)^4 - 3*(12*a^4*b - 7*a^3*b^2 - 14*a^2*b^3 + 9*a*b^4)*cosh(d*x + c)^2)*sinh(d*x + c))/(a^3*b^5*d*cosh(d*x + c)^8 + 8*a^3*b^5*d*cosh(d*x + c)*sinh(d*x + c)^7 + a^3*b^5*d*sinh(d*x + c)^8 + a^3*b^5*d + 4*(2*a^4*b^4 - a^3*b^5)*d*cosh(d*x + c)^6 + 4*(7*a^3*b^5*d*cosh(d*x + c)^2 + (2*a^4*b^4 - a^3*b^5)*d)*sinh(d*x + c)^6 + 2*(8*a^5*b^3 - 8*a^4*b^4 + 3*a^3*b^5)*d*cosh(d*x + c)^4 + 8*(7*a^3*b^5*d*cosh(d*x + c)^3 + 3*(2*a^4*b^4 - a^3*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*a^3*b^5*d*cosh(d*x + c)^4 + 30*(2*a^4*b^4 - a^3*b^5)*d*cosh(d*x + c)^2 + (8*a^5*b^3 - 8*a^4*b^4 + 3*a^3*b^5)*d)*sinh(d*x + c)^4 + 4*(2*a^4*b^4 - a^3*b^5)*d*cosh(d*x + c)^2 + 8*(7*a^3*b^5*d*cosh(d*x + c)^5 + 10*(2*a^4*b^4 - a^3*b^5)*d*cosh(d*x + c)^3 + (8*a^5*b^3 - 8*a^4*b^4 + 3*a^3*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*a^3*b^5*d*cosh(d*x + c)^6 + 15*(2*a^4*b^4 - a^3*b^5)*d*cosh(d*x + c)^4 + 3*(8*a^5*b^3 - 8*a^4*b^4 + 3*a^3*b^5)*d*cosh(d*x + c)^2 + (2*a^4*b^4 - a^3*b^5)*d)*sinh(d*x + c)^2 + 8*(a^3*b^5*d*cosh(d*x + c)^7 + 3*(2*a^4*b^4 - a^3*b^5)*d*cosh(d*x + c)^5 + (8*a^5*b^3 - 8*a^4*b^4 + 3*a^3*b^5)*d*cosh(d*x + c)^3 + (2*a^4*b^4 - a^3*b^5)*d*cosh(d*x + c))*sinh(d*x + c)), -1/8*(2*(5*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4)*cosh(d*x + c)^7 + 14*(5*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4)*cosh(d*x + c)*sinh(d*x + c)^6 + 2*(5*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4)*sinh(d*x + c)^7 + 2*(12*a^4*b - 7*a^3*b^2 - 14*a^2*b^3 + 9*a*b^4)*cosh(d*x + c)^5 + 2*(12*a^4*b - 7*a^3*b^2 - 14*a^2*b^3 + 9*a*b^4 + 21*(5*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 10*(7*(5*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4)*cosh(d*x + c)^3 + (12*a^4*b - 7*a^3*b^2 - 14*a^2*b^3 + 9*a*b^4)*cosh(d*x + c))*sinh(d*x + c)^4 - 2*(12*a^4*b - 7*a^3*b^2 - 14*a^2*b^3 + 9*a*b^4)*cosh(d*x + c)^3 - 2*(12*a^4*b - 7*a^3*b^2 - 14*a^2*b^3 + 9*a*b^4 - 35*(5*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4)*cosh(d*x + c)^4 - 10*(12*a^4*b - 7*a^3*b^2 - 14*a^2*b^3 + 9*a*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 2*(21*(5*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4)*cosh(d*x + c)^5 + 10*(12*a^4*b - 7*a^3*b^2 - 14*a^2*b^3 + 9*a*b^4)*cosh(d*x + c)^3 - 3*(12*a^4*b - 7*a^3*b^2 - 14*a^2*b^3 + 9*a*b^4)*cosh(d*x + c))*sinh(d*x + c)^2 - ((3*a^2*b^2 + 2*a*b^3 + 3*b^4)*cosh(d*x + c)^8 + 8*(3*a^2*b^2 + 2*a*b^3 + 3*b^4)*cosh(d*x + c)*sinh(d*x + c)^7 + (3*a^2*b^2 + 2*a*b^3 + 3*b^4)*sinh(d*x + c)^8 + 4*(6*a^3*b + a^2*b^2 + 4*a*b^3 - 3*b^4)*cosh(d*x + c)^6 + 4*(6*a^3*b + a^2*b^2 + 4*a*b^3 - 3*b^4 + 7*(3*a^2*b^2 + 2*a*b^3 + 3*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(3*a^2*b^2 + 2*a*b^3 + 3*b^4)*cosh(d*x + c)^3 + 3*(6*a^3*b + a^2*b^2 + 4*a*b^3 - 3*b^4)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(24*a^4 - 8*a^3*b + 17*a^2*b^2 - 18*a*b^3 + 9*b^4)*cosh(d*x + c)^4 + 2*(35*(3*a^2*b^2 + 2*a*b^3 + 3*b^4)*cosh(d*x + c)^4 + 24*a^4 - 8*a^3*b + 17*a^2*b^2 - 18*a*b^3 + 9*b^4 + 30*(6*a^3*b + a^2*b^2 + 4*a*b^3 - 3*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 3*a^2*b^2 + 2*a*b^3 + 3*b^4 + 8*(7*(3*a^2*b^2 + 2*a*b^3 + 3*b^4)*cosh(d*x + c)^5 + 10*(6*a^3*b + a^2*b^2 + 4*a*b^3 - 3*b^4)*cosh(d*x + c)^3 + (24*a^4 - 8*a^3*b + 17*a^2*b^2 - 18*a*b^3 + 9*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(6*a^3*b + a^2*b^2 + 4*a*b^3 - 3*b^4)*cosh(d*x + c)^2 + 4*(7*(3*a^2*b^2 + 2*a*b^3 + 3*b^4)*cosh(d*x + c)^6 + 15*(6*a^3*b + a^2*b^2 + 4*a*b^3 - 3*b^4)*cosh(d*x + c)^4 + 6*a^3*b + a^2*b^2 + 4*a*b^3 - 3*b^4 + 3*(24*a^4 - 8*a^3*b + 17*a^2*b^2 - 18*a*b^3 + 9*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((3*a^2*b^2 + 2*a*b^3 + 3*b^4)*cosh(d*x + c)^7 + 3*(6*a^3*b + a^2*b^2 + 4*a*b^3 - 3*b^4)*cosh(d*x + c)^5 + (24*a^4 - 8*a^3*b + 17*a^2*b^2 - 18*a*b^3 + 9*b^4)*cosh(d*x + c)^3 + (6*a^3*b + a^2*b^2 + 4*a*b^3 - 3*b^4)*cosh(d*x + c))*sinh(d*x + c))*sqrt(a*b)*arctan(1/2*sqrt(a*b)*(cosh(d*x + c) + sinh(d*x + c))/a) - ((3*a^2*b^2 + 2*a*b^3 + 3*b^4)*cosh(d*x + c)^8 + 8*(3*a^2*b^2 + 2*a*b^3 + 3*b^4)*cosh(d*x + c)*sinh(d*x + c)^7 + (3*a^2*b^2 + 2*a*b^3 + 3*b^4)*sinh(d*x + c)^8 + 4*(6*a^3*b + a^2*b^2 + 4*a*b^3 - 3*b^4)*cosh(d*x + c)^6 + 4*(6*a^3*b + a^2*b^2 + 4*a*b^3 - 3*b^4 + 7*(3*a^2*b^2 + 2*a*b^3 + 3*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(3*a^2*b^2 + 2*a*b^3 + 3*b^4)*cosh(d*x + c)^3 + 3*(6*a^3*b + a^2*b^2 + 4*a*b^3 - 3*b^4)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(24*a^4 - 8*a^3*b + 17*a^2*b^2 - 18*a*b^3 + 9*b^4)*cosh(d*x + c)^4 + 2*(35*(3*a^2*b^2 + 2*a*b^3 + 3*b^4)*cosh(d*x + c)^4 + 24*a^4 - 8*a^3*b + 17*a^2*b^2 - 18*a*b^3 + 9*b^4 + 30*(6*a^3*b + a^2*b^2 + 4*a*b^3 - 3*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 3*a^2*b^2 + 2*a*b^3 + 3*b^4 + 8*(7*(3*a^2*b^2 + 2*a*b^3 + 3*b^4)*cosh(d*x + c)^5 + 10*(6*a^3*b + a^2*b^2 + 4*a*b^3 - 3*b^4)*cosh(d*x + c)^3 + (24*a^4 - 8*a^3*b + 17*a^2*b^2 - 18*a*b^3 + 9*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(6*a^3*b + a^2*b^2 + 4*a*b^3 - 3*b^4)*cosh(d*x + c)^2 + 4*(7*(3*a^2*b^2 + 2*a*b^3 + 3*b^4)*cosh(d*x + c)^6 + 15*(6*a^3*b + a^2*b^2 + 4*a*b^3 - 3*b^4)*cosh(d*x + c)^4 + 6*a^3*b + a^2*b^2 + 4*a*b^3 - 3*b^4 + 3*(24*a^4 - 8*a^3*b + 17*a^2*b^2 - 18*a*b^3 + 9*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((3*a^2*b^2 + 2*a*b^3 + 3*b^4)*cosh(d*x + c)^7 + 3*(6*a^3*b + a^2*b^2 + 4*a*b^3 - 3*b^4)*cosh(d*x + c)^5 + (24*a^4 - 8*a^3*b + 17*a^2*b^2 - 18*a*b^3 + 9*b^4)*cosh(d*x + c)^3 + (6*a^3*b + a^2*b^2 + 4*a*b^3 - 3*b^4)*cosh(d*x + c))*sinh(d*x + c))*sqrt(a*b)*arctan(1/2*(b*cosh(d*x + c)^3 + 3*b*cosh(d*x + c)*sinh(d*x + c)^2 + b*sinh(d*x + c)^3 + (4*a - b)*cosh(d*x + c) + (3*b*cosh(d*x + c)^2 + 4*a - b)*sinh(d*x + c))*sqrt(a*b)/(a*b)) - 2*(5*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4)*cosh(d*x + c) + 2*(7*(5*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4)*cosh(d*x + c)^6 - 5*a^3*b^2 + 2*a^2*b^3 + 3*a*b^4 + 5*(12*a^4*b - 7*a^3*b^2 - 14*a^2*b^3 + 9*a*b^4)*cosh(d*x + c)^4 - 3*(12*a^4*b - 7*a^3*b^2 - 14*a^2*b^3 + 9*a*b^4)*cosh(d*x + c)^2)*sinh(d*x + c))/(a^3*b^5*d*cosh(d*x + c)^8 + 8*a^3*b^5*d*cosh(d*x + c)*sinh(d*x + c)^7 + a^3*b^5*d*sinh(d*x + c)^8 + a^3*b^5*d + 4*(2*a^4*b^4 - a^3*b^5)*d*cosh(d*x + c)^6 + 4*(7*a^3*b^5*d*cosh(d*x + c)^2 + (2*a^4*b^4 - a^3*b^5)*d)*sinh(d*x + c)^6 + 2*(8*a^5*b^3 - 8*a^4*b^4 + 3*a^3*b^5)*d*cosh(d*x + c)^4 + 8*(7*a^3*b^5*d*cosh(d*x + c)^3 + 3*(2*a^4*b^4 - a^3*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*a^3*b^5*d*cosh(d*x + c)^4 + 30*(2*a^4*b^4 - a^3*b^5)*d*cosh(d*x + c)^2 + (8*a^5*b^3 - 8*a^4*b^4 + 3*a^3*b^5)*d)*sinh(d*x + c)^4 + 4*(2*a^4*b^4 - a^3*b^5)*d*cosh(d*x + c)^2 + 8*(7*a^3*b^5*d*cosh(d*x + c)^5 + 10*(2*a^4*b^4 - a^3*b^5)*d*cosh(d*x + c)^3 + (8*a^5*b^3 - 8*a^4*b^4 + 3*a^3*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*a^3*b^5*d*cosh(d*x + c)^6 + 15*(2*a^4*b^4 - a^3*b^5)*d*cosh(d*x + c)^4 + 3*(8*a^5*b^3 - 8*a^4*b^4 + 3*a^3*b^5)*d*cosh(d*x + c)^2 + (2*a^4*b^4 - a^3*b^5)*d)*sinh(d*x + c)^2 + 8*(a^3*b^5*d*cosh(d*x + c)^7 + 3*(2*a^4*b^4 - a^3*b^5)*d*cosh(d*x + c)^5 + (8*a^5*b^3 - 8*a^4*b^4 + 3*a^3*b^5)*d*cosh(d*x + c)^3 + (2*a^4*b^4 - a^3*b^5)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
341,1,4486,0,0.588689," ","integrate(cosh(d*x+c)^4/(a+b*sinh(d*x+c)^2)^3,x, algorithm=""fricas"")","\left[-\frac{4 \, {\left(8 \, a^{4} b - 8 \, a^{3} b^{2} - 3 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{6} + 24 \, {\left(8 \, a^{4} b - 8 \, a^{3} b^{2} - 3 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + 4 \, {\left(8 \, a^{4} b - 8 \, a^{3} b^{2} - 3 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \sinh\left(d x + c\right)^{6} + 8 \, a^{3} b^{2} + 4 \, a^{2} b^{3} - 12 \, a b^{4} + 4 \, {\left(16 \, a^{5} - 8 \, a^{4} b - 26 \, a^{3} b^{2} + 27 \, a^{2} b^{3} - 9 \, a b^{4}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(16 \, a^{5} - 8 \, a^{4} b - 26 \, a^{3} b^{2} + 27 \, a^{2} b^{3} - 9 \, a b^{4} + 15 \, {\left(8 \, a^{4} b - 8 \, a^{3} b^{2} - 3 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 16 \, {\left(5 \, {\left(8 \, a^{4} b - 8 \, a^{3} b^{2} - 3 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(16 \, a^{5} - 8 \, a^{4} b - 26 \, a^{3} b^{2} + 27 \, a^{2} b^{3} - 9 \, a b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(8 \, a^{4} b + 8 \, a^{3} b^{2} - 25 \, a^{2} b^{3} + 9 \, a b^{4}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(8 \, a^{4} b + 8 \, a^{3} b^{2} - 25 \, a^{2} b^{3} + 9 \, a b^{4} + 15 \, {\left(8 \, a^{4} b - 8 \, a^{3} b^{2} - 3 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{4} + 6 \, {\left(16 \, a^{5} - 8 \, a^{4} b - 26 \, a^{3} b^{2} + 27 \, a^{2} b^{3} - 9 \, a b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} - 3 \, {\left(b^{4} \cosh\left(d x + c\right)^{8} + 8 \, b^{4} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + b^{4} \sinh\left(d x + c\right)^{8} + 4 \, {\left(2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, b^{4} \cosh\left(d x + c\right)^{2} + 2 \, a b^{3} - b^{4}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, b^{4} \cosh\left(d x + c\right)^{3} + 3 \, {\left(2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(8 \, a^{2} b^{2} - 8 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, b^{4} \cosh\left(d x + c\right)^{4} + 8 \, a^{2} b^{2} - 8 \, a b^{3} + 3 \, b^{4} + 30 \, {\left(2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + b^{4} + 8 \, {\left(7 \, b^{4} \cosh\left(d x + c\right)^{5} + 10 \, {\left(2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{2} b^{2} - 8 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, b^{4} \cosh\left(d x + c\right)^{6} + 15 \, {\left(2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, a b^{3} - b^{4} + 3 \, {\left(8 \, a^{2} b^{2} - 8 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left(b^{4} \cosh\left(d x + c\right)^{7} + 3 \, {\left(2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{5} + {\left(8 \, a^{2} b^{2} - 8 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{a^{2} - a b} \log\left(\frac{b^{2} \cosh\left(d x + c\right)^{4} + 4 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{2} \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(d x + c\right)^{2} + 2 \, a b - b^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, a^{2} - 8 \, a b + b^{2} + 4 \, {\left(b^{2} \cosh\left(d x + c\right)^{3} + {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) - 4 \, {\left(b \cosh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b \sinh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sqrt{a^{2} - a b}}{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b}\right) + 8 \, {\left(3 \, {\left(8 \, a^{4} b - 8 \, a^{3} b^{2} - 3 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(16 \, a^{5} - 8 \, a^{4} b - 26 \, a^{3} b^{2} + 27 \, a^{2} b^{3} - 9 \, a b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{4} b + 8 \, a^{3} b^{2} - 25 \, a^{2} b^{3} + 9 \, a b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{16 \, {\left({\left(a^{4} b^{4} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{4} b^{4} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{4} b^{4} - a^{3} b^{5}\right)} d \sinh\left(d x + c\right)^{8} + 4 \, {\left(2 \, a^{5} b^{3} - 3 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{4} b^{4} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{5} b^{3} - 3 \, a^{4} b^{4} + a^{3} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(8 \, a^{6} b^{2} - 16 \, a^{5} b^{3} + 11 \, a^{4} b^{4} - 3 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{4} b^{4} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(2 \, a^{5} b^{3} - 3 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a^{4} b^{4} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 30 \, {\left(2 \, a^{5} b^{3} - 3 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(8 \, a^{6} b^{2} - 16 \, a^{5} b^{3} + 11 \, a^{4} b^{4} - 3 \, a^{3} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(2 \, a^{5} b^{3} - 3 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a^{4} b^{4} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{5} + 10 \, {\left(2 \, a^{5} b^{3} - 3 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{6} b^{2} - 16 \, a^{5} b^{3} + 11 \, a^{4} b^{4} - 3 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a^{4} b^{4} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{6} + 15 \, {\left(2 \, a^{5} b^{3} - 3 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(8 \, a^{6} b^{2} - 16 \, a^{5} b^{3} + 11 \, a^{4} b^{4} - 3 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{5} b^{3} - 3 \, a^{4} b^{4} + a^{3} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{4} b^{4} - a^{3} b^{5}\right)} d + 8 \, {\left({\left(a^{4} b^{4} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{7} + 3 \, {\left(2 \, a^{5} b^{3} - 3 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{5} + {\left(8 \, a^{6} b^{2} - 16 \, a^{5} b^{3} + 11 \, a^{4} b^{4} - 3 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{5} b^{3} - 3 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}, -\frac{2 \, {\left(8 \, a^{4} b - 8 \, a^{3} b^{2} - 3 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{6} + 12 \, {\left(8 \, a^{4} b - 8 \, a^{3} b^{2} - 3 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + 2 \, {\left(8 \, a^{4} b - 8 \, a^{3} b^{2} - 3 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \sinh\left(d x + c\right)^{6} + 4 \, a^{3} b^{2} + 2 \, a^{2} b^{3} - 6 \, a b^{4} + 2 \, {\left(16 \, a^{5} - 8 \, a^{4} b - 26 \, a^{3} b^{2} + 27 \, a^{2} b^{3} - 9 \, a b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(16 \, a^{5} - 8 \, a^{4} b - 26 \, a^{3} b^{2} + 27 \, a^{2} b^{3} - 9 \, a b^{4} + 15 \, {\left(8 \, a^{4} b - 8 \, a^{3} b^{2} - 3 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(5 \, {\left(8 \, a^{4} b - 8 \, a^{3} b^{2} - 3 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(16 \, a^{5} - 8 \, a^{4} b - 26 \, a^{3} b^{2} + 27 \, a^{2} b^{3} - 9 \, a b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(8 \, a^{4} b + 8 \, a^{3} b^{2} - 25 \, a^{2} b^{3} + 9 \, a b^{4}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(8 \, a^{4} b + 8 \, a^{3} b^{2} - 25 \, a^{2} b^{3} + 9 \, a b^{4} + 15 \, {\left(8 \, a^{4} b - 8 \, a^{3} b^{2} - 3 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{4} + 6 \, {\left(16 \, a^{5} - 8 \, a^{4} b - 26 \, a^{3} b^{2} + 27 \, a^{2} b^{3} - 9 \, a b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 3 \, {\left(b^{4} \cosh\left(d x + c\right)^{8} + 8 \, b^{4} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + b^{4} \sinh\left(d x + c\right)^{8} + 4 \, {\left(2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, b^{4} \cosh\left(d x + c\right)^{2} + 2 \, a b^{3} - b^{4}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, b^{4} \cosh\left(d x + c\right)^{3} + 3 \, {\left(2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(8 \, a^{2} b^{2} - 8 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, b^{4} \cosh\left(d x + c\right)^{4} + 8 \, a^{2} b^{2} - 8 \, a b^{3} + 3 \, b^{4} + 30 \, {\left(2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + b^{4} + 8 \, {\left(7 \, b^{4} \cosh\left(d x + c\right)^{5} + 10 \, {\left(2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{2} b^{2} - 8 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, b^{4} \cosh\left(d x + c\right)^{6} + 15 \, {\left(2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, a b^{3} - b^{4} + 3 \, {\left(8 \, a^{2} b^{2} - 8 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left(b^{4} \cosh\left(d x + c\right)^{7} + 3 \, {\left(2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{5} + {\left(8 \, a^{2} b^{2} - 8 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-a^{2} + a b} \arctan\left(-\frac{{\left(b \cosh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b \sinh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sqrt{-a^{2} + a b}}{2 \, {\left(a^{2} - a b\right)}}\right) + 4 \, {\left(3 \, {\left(8 \, a^{4} b - 8 \, a^{3} b^{2} - 3 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(16 \, a^{5} - 8 \, a^{4} b - 26 \, a^{3} b^{2} + 27 \, a^{2} b^{3} - 9 \, a b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{4} b + 8 \, a^{3} b^{2} - 25 \, a^{2} b^{3} + 9 \, a b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{8 \, {\left({\left(a^{4} b^{4} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{4} b^{4} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{4} b^{4} - a^{3} b^{5}\right)} d \sinh\left(d x + c\right)^{8} + 4 \, {\left(2 \, a^{5} b^{3} - 3 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{4} b^{4} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{5} b^{3} - 3 \, a^{4} b^{4} + a^{3} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(8 \, a^{6} b^{2} - 16 \, a^{5} b^{3} + 11 \, a^{4} b^{4} - 3 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{4} b^{4} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(2 \, a^{5} b^{3} - 3 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a^{4} b^{4} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 30 \, {\left(2 \, a^{5} b^{3} - 3 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(8 \, a^{6} b^{2} - 16 \, a^{5} b^{3} + 11 \, a^{4} b^{4} - 3 \, a^{3} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(2 \, a^{5} b^{3} - 3 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a^{4} b^{4} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{5} + 10 \, {\left(2 \, a^{5} b^{3} - 3 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{6} b^{2} - 16 \, a^{5} b^{3} + 11 \, a^{4} b^{4} - 3 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a^{4} b^{4} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{6} + 15 \, {\left(2 \, a^{5} b^{3} - 3 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(8 \, a^{6} b^{2} - 16 \, a^{5} b^{3} + 11 \, a^{4} b^{4} - 3 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{5} b^{3} - 3 \, a^{4} b^{4} + a^{3} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{4} b^{4} - a^{3} b^{5}\right)} d + 8 \, {\left({\left(a^{4} b^{4} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{7} + 3 \, {\left(2 \, a^{5} b^{3} - 3 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{5} + {\left(8 \, a^{6} b^{2} - 16 \, a^{5} b^{3} + 11 \, a^{4} b^{4} - 3 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{5} b^{3} - 3 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[-1/16*(4*(8*a^4*b - 8*a^3*b^2 - 3*a^2*b^3 + 3*a*b^4)*cosh(d*x + c)^6 + 24*(8*a^4*b - 8*a^3*b^2 - 3*a^2*b^3 + 3*a*b^4)*cosh(d*x + c)*sinh(d*x + c)^5 + 4*(8*a^4*b - 8*a^3*b^2 - 3*a^2*b^3 + 3*a*b^4)*sinh(d*x + c)^6 + 8*a^3*b^2 + 4*a^2*b^3 - 12*a*b^4 + 4*(16*a^5 - 8*a^4*b - 26*a^3*b^2 + 27*a^2*b^3 - 9*a*b^4)*cosh(d*x + c)^4 + 4*(16*a^5 - 8*a^4*b - 26*a^3*b^2 + 27*a^2*b^3 - 9*a*b^4 + 15*(8*a^4*b - 8*a^3*b^2 - 3*a^2*b^3 + 3*a*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 16*(5*(8*a^4*b - 8*a^3*b^2 - 3*a^2*b^3 + 3*a*b^4)*cosh(d*x + c)^3 + (16*a^5 - 8*a^4*b - 26*a^3*b^2 + 27*a^2*b^3 - 9*a*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(8*a^4*b + 8*a^3*b^2 - 25*a^2*b^3 + 9*a*b^4)*cosh(d*x + c)^2 + 4*(8*a^4*b + 8*a^3*b^2 - 25*a^2*b^3 + 9*a*b^4 + 15*(8*a^4*b - 8*a^3*b^2 - 3*a^2*b^3 + 3*a*b^4)*cosh(d*x + c)^4 + 6*(16*a^5 - 8*a^4*b - 26*a^3*b^2 + 27*a^2*b^3 - 9*a*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - 3*(b^4*cosh(d*x + c)^8 + 8*b^4*cosh(d*x + c)*sinh(d*x + c)^7 + b^4*sinh(d*x + c)^8 + 4*(2*a*b^3 - b^4)*cosh(d*x + c)^6 + 4*(7*b^4*cosh(d*x + c)^2 + 2*a*b^3 - b^4)*sinh(d*x + c)^6 + 8*(7*b^4*cosh(d*x + c)^3 + 3*(2*a*b^3 - b^4)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(8*a^2*b^2 - 8*a*b^3 + 3*b^4)*cosh(d*x + c)^4 + 2*(35*b^4*cosh(d*x + c)^4 + 8*a^2*b^2 - 8*a*b^3 + 3*b^4 + 30*(2*a*b^3 - b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + b^4 + 8*(7*b^4*cosh(d*x + c)^5 + 10*(2*a*b^3 - b^4)*cosh(d*x + c)^3 + (8*a^2*b^2 - 8*a*b^3 + 3*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(2*a*b^3 - b^4)*cosh(d*x + c)^2 + 4*(7*b^4*cosh(d*x + c)^6 + 15*(2*a*b^3 - b^4)*cosh(d*x + c)^4 + 2*a*b^3 - b^4 + 3*(8*a^2*b^2 - 8*a*b^3 + 3*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*(b^4*cosh(d*x + c)^7 + 3*(2*a*b^3 - b^4)*cosh(d*x + c)^5 + (8*a^2*b^2 - 8*a*b^3 + 3*b^4)*cosh(d*x + c)^3 + (2*a*b^3 - b^4)*cosh(d*x + c))*sinh(d*x + c))*sqrt(a^2 - a*b)*log((b^2*cosh(d*x + c)^4 + 4*b^2*cosh(d*x + c)*sinh(d*x + c)^3 + b^2*sinh(d*x + c)^4 + 2*(2*a*b - b^2)*cosh(d*x + c)^2 + 2*(3*b^2*cosh(d*x + c)^2 + 2*a*b - b^2)*sinh(d*x + c)^2 + 8*a^2 - 8*a*b + b^2 + 4*(b^2*cosh(d*x + c)^3 + (2*a*b - b^2)*cosh(d*x + c))*sinh(d*x + c) - 4*(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + 2*a - b)*sqrt(a^2 - a*b))/(b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 + 2*(2*a - b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 + 2*a - b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 + (2*a - b)*cosh(d*x + c))*sinh(d*x + c) + b)) + 8*(3*(8*a^4*b - 8*a^3*b^2 - 3*a^2*b^3 + 3*a*b^4)*cosh(d*x + c)^5 + 2*(16*a^5 - 8*a^4*b - 26*a^3*b^2 + 27*a^2*b^3 - 9*a*b^4)*cosh(d*x + c)^3 + (8*a^4*b + 8*a^3*b^2 - 25*a^2*b^3 + 9*a*b^4)*cosh(d*x + c))*sinh(d*x + c))/((a^4*b^4 - a^3*b^5)*d*cosh(d*x + c)^8 + 8*(a^4*b^4 - a^3*b^5)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^4*b^4 - a^3*b^5)*d*sinh(d*x + c)^8 + 4*(2*a^5*b^3 - 3*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)^6 + 4*(7*(a^4*b^4 - a^3*b^5)*d*cosh(d*x + c)^2 + (2*a^5*b^3 - 3*a^4*b^4 + a^3*b^5)*d)*sinh(d*x + c)^6 + 2*(8*a^6*b^2 - 16*a^5*b^3 + 11*a^4*b^4 - 3*a^3*b^5)*d*cosh(d*x + c)^4 + 8*(7*(a^4*b^4 - a^3*b^5)*d*cosh(d*x + c)^3 + 3*(2*a^5*b^3 - 3*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^4*b^4 - a^3*b^5)*d*cosh(d*x + c)^4 + 30*(2*a^5*b^3 - 3*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)^2 + (8*a^6*b^2 - 16*a^5*b^3 + 11*a^4*b^4 - 3*a^3*b^5)*d)*sinh(d*x + c)^4 + 4*(2*a^5*b^3 - 3*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)^2 + 8*(7*(a^4*b^4 - a^3*b^5)*d*cosh(d*x + c)^5 + 10*(2*a^5*b^3 - 3*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)^3 + (8*a^6*b^2 - 16*a^5*b^3 + 11*a^4*b^4 - 3*a^3*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^4*b^4 - a^3*b^5)*d*cosh(d*x + c)^6 + 15*(2*a^5*b^3 - 3*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)^4 + 3*(8*a^6*b^2 - 16*a^5*b^3 + 11*a^4*b^4 - 3*a^3*b^5)*d*cosh(d*x + c)^2 + (2*a^5*b^3 - 3*a^4*b^4 + a^3*b^5)*d)*sinh(d*x + c)^2 + (a^4*b^4 - a^3*b^5)*d + 8*((a^4*b^4 - a^3*b^5)*d*cosh(d*x + c)^7 + 3*(2*a^5*b^3 - 3*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)^5 + (8*a^6*b^2 - 16*a^5*b^3 + 11*a^4*b^4 - 3*a^3*b^5)*d*cosh(d*x + c)^3 + (2*a^5*b^3 - 3*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c))*sinh(d*x + c)), -1/8*(2*(8*a^4*b - 8*a^3*b^2 - 3*a^2*b^3 + 3*a*b^4)*cosh(d*x + c)^6 + 12*(8*a^4*b - 8*a^3*b^2 - 3*a^2*b^3 + 3*a*b^4)*cosh(d*x + c)*sinh(d*x + c)^5 + 2*(8*a^4*b - 8*a^3*b^2 - 3*a^2*b^3 + 3*a*b^4)*sinh(d*x + c)^6 + 4*a^3*b^2 + 2*a^2*b^3 - 6*a*b^4 + 2*(16*a^5 - 8*a^4*b - 26*a^3*b^2 + 27*a^2*b^3 - 9*a*b^4)*cosh(d*x + c)^4 + 2*(16*a^5 - 8*a^4*b - 26*a^3*b^2 + 27*a^2*b^3 - 9*a*b^4 + 15*(8*a^4*b - 8*a^3*b^2 - 3*a^2*b^3 + 3*a*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(5*(8*a^4*b - 8*a^3*b^2 - 3*a^2*b^3 + 3*a*b^4)*cosh(d*x + c)^3 + (16*a^5 - 8*a^4*b - 26*a^3*b^2 + 27*a^2*b^3 - 9*a*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 2*(8*a^4*b + 8*a^3*b^2 - 25*a^2*b^3 + 9*a*b^4)*cosh(d*x + c)^2 + 2*(8*a^4*b + 8*a^3*b^2 - 25*a^2*b^3 + 9*a*b^4 + 15*(8*a^4*b - 8*a^3*b^2 - 3*a^2*b^3 + 3*a*b^4)*cosh(d*x + c)^4 + 6*(16*a^5 - 8*a^4*b - 26*a^3*b^2 + 27*a^2*b^3 - 9*a*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 3*(b^4*cosh(d*x + c)^8 + 8*b^4*cosh(d*x + c)*sinh(d*x + c)^7 + b^4*sinh(d*x + c)^8 + 4*(2*a*b^3 - b^4)*cosh(d*x + c)^6 + 4*(7*b^4*cosh(d*x + c)^2 + 2*a*b^3 - b^4)*sinh(d*x + c)^6 + 8*(7*b^4*cosh(d*x + c)^3 + 3*(2*a*b^3 - b^4)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(8*a^2*b^2 - 8*a*b^3 + 3*b^4)*cosh(d*x + c)^4 + 2*(35*b^4*cosh(d*x + c)^4 + 8*a^2*b^2 - 8*a*b^3 + 3*b^4 + 30*(2*a*b^3 - b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + b^4 + 8*(7*b^4*cosh(d*x + c)^5 + 10*(2*a*b^3 - b^4)*cosh(d*x + c)^3 + (8*a^2*b^2 - 8*a*b^3 + 3*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(2*a*b^3 - b^4)*cosh(d*x + c)^2 + 4*(7*b^4*cosh(d*x + c)^6 + 15*(2*a*b^3 - b^4)*cosh(d*x + c)^4 + 2*a*b^3 - b^4 + 3*(8*a^2*b^2 - 8*a*b^3 + 3*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*(b^4*cosh(d*x + c)^7 + 3*(2*a*b^3 - b^4)*cosh(d*x + c)^5 + (8*a^2*b^2 - 8*a*b^3 + 3*b^4)*cosh(d*x + c)^3 + (2*a*b^3 - b^4)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-a^2 + a*b)*arctan(-1/2*(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + 2*a - b)*sqrt(-a^2 + a*b)/(a^2 - a*b)) + 4*(3*(8*a^4*b - 8*a^3*b^2 - 3*a^2*b^3 + 3*a*b^4)*cosh(d*x + c)^5 + 2*(16*a^5 - 8*a^4*b - 26*a^3*b^2 + 27*a^2*b^3 - 9*a*b^4)*cosh(d*x + c)^3 + (8*a^4*b + 8*a^3*b^2 - 25*a^2*b^3 + 9*a*b^4)*cosh(d*x + c))*sinh(d*x + c))/((a^4*b^4 - a^3*b^5)*d*cosh(d*x + c)^8 + 8*(a^4*b^4 - a^3*b^5)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^4*b^4 - a^3*b^5)*d*sinh(d*x + c)^8 + 4*(2*a^5*b^3 - 3*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)^6 + 4*(7*(a^4*b^4 - a^3*b^5)*d*cosh(d*x + c)^2 + (2*a^5*b^3 - 3*a^4*b^4 + a^3*b^5)*d)*sinh(d*x + c)^6 + 2*(8*a^6*b^2 - 16*a^5*b^3 + 11*a^4*b^4 - 3*a^3*b^5)*d*cosh(d*x + c)^4 + 8*(7*(a^4*b^4 - a^3*b^5)*d*cosh(d*x + c)^3 + 3*(2*a^5*b^3 - 3*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^4*b^4 - a^3*b^5)*d*cosh(d*x + c)^4 + 30*(2*a^5*b^3 - 3*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)^2 + (8*a^6*b^2 - 16*a^5*b^3 + 11*a^4*b^4 - 3*a^3*b^5)*d)*sinh(d*x + c)^4 + 4*(2*a^5*b^3 - 3*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)^2 + 8*(7*(a^4*b^4 - a^3*b^5)*d*cosh(d*x + c)^5 + 10*(2*a^5*b^3 - 3*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)^3 + (8*a^6*b^2 - 16*a^5*b^3 + 11*a^4*b^4 - 3*a^3*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^4*b^4 - a^3*b^5)*d*cosh(d*x + c)^6 + 15*(2*a^5*b^3 - 3*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)^4 + 3*(8*a^6*b^2 - 16*a^5*b^3 + 11*a^4*b^4 - 3*a^3*b^5)*d*cosh(d*x + c)^2 + (2*a^5*b^3 - 3*a^4*b^4 + a^3*b^5)*d)*sinh(d*x + c)^2 + (a^4*b^4 - a^3*b^5)*d + 8*((a^4*b^4 - a^3*b^5)*d*cosh(d*x + c)^7 + 3*(2*a^5*b^3 - 3*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)^5 + (8*a^6*b^2 - 16*a^5*b^3 + 11*a^4*b^4 - 3*a^3*b^5)*d*cosh(d*x + c)^3 + (2*a^5*b^3 - 3*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
342,1,4907,0,0.786114," ","integrate(cosh(d*x+c)^3/(a+b*sinh(d*x+c)^2)^3,x, algorithm=""fricas"")","\left[\frac{4 \, {\left(a^{2} b^{2} + 3 \, a b^{3}\right)} \cosh\left(d x + c\right)^{7} + 28 \, {\left(a^{2} b^{2} + 3 \, a b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + 4 \, {\left(a^{2} b^{2} + 3 \, a b^{3}\right)} \sinh\left(d x + c\right)^{7} - 4 \, {\left(4 \, a^{3} b - 17 \, a^{2} b^{2} + 9 \, a b^{3}\right)} \cosh\left(d x + c\right)^{5} - 4 \, {\left(4 \, a^{3} b - 17 \, a^{2} b^{2} + 9 \, a b^{3} - 21 \, {\left(a^{2} b^{2} + 3 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{5} + 20 \, {\left(7 \, {\left(a^{2} b^{2} + 3 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} - {\left(4 \, a^{3} b - 17 \, a^{2} b^{2} + 9 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(4 \, a^{3} b - 17 \, a^{2} b^{2} + 9 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(35 \, {\left(a^{2} b^{2} + 3 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} + 4 \, a^{3} b - 17 \, a^{2} b^{2} + 9 \, a b^{3} - 10 \, {\left(4 \, a^{3} b - 17 \, a^{2} b^{2} + 9 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(21 \, {\left(a^{2} b^{2} + 3 \, a b^{3}\right)} \cosh\left(d x + c\right)^{5} - 10 \, {\left(4 \, a^{3} b - 17 \, a^{2} b^{2} + 9 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(4 \, a^{3} b - 17 \, a^{2} b^{2} + 9 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - {\left({\left(a b^{2} + 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(a b^{2} + 3 \, b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a b^{2} + 3 \, b^{3}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(2 \, a^{2} b + 5 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(2 \, a^{2} b + 5 \, a b^{2} - 3 \, b^{3} + 7 \, {\left(a b^{2} + 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(a b^{2} + 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(2 \, a^{2} b + 5 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(8 \, a^{3} + 16 \, a^{2} b - 21 \, a b^{2} + 9 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(a b^{2} + 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 8 \, a^{3} + 16 \, a^{2} b - 21 \, a b^{2} + 9 \, b^{3} + 30 \, {\left(2 \, a^{2} b + 5 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a b^{2} + 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(2 \, a^{2} b + 5 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{3} + 16 \, a^{2} b - 21 \, a b^{2} + 9 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + a b^{2} + 3 \, b^{3} + 4 \, {\left(2 \, a^{2} b + 5 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(a b^{2} + 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(2 \, a^{2} b + 5 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 2 \, a^{2} b + 5 \, a b^{2} - 3 \, b^{3} + 3 \, {\left(8 \, a^{3} + 16 \, a^{2} b - 21 \, a b^{2} + 9 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left({\left(a b^{2} + 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(2 \, a^{2} b + 5 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + {\left(8 \, a^{3} + 16 \, a^{2} b - 21 \, a b^{2} + 9 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{2} b + 5 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-a b} \log\left(\frac{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} - 2 \, {\left(2 \, a + b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} - 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} - {\left(2 \, a + b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) - 4 \, {\left(\cosh\left(d x + c\right)^{3} + 3 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{3} + {\left(3 \, \cosh\left(d x + c\right)^{2} - 1\right)} \sinh\left(d x + c\right) - \cosh\left(d x + c\right)\right)} \sqrt{-a b} + b}{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b}\right) - 4 \, {\left(a^{2} b^{2} + 3 \, a b^{3}\right)} \cosh\left(d x + c\right) + 4 \, {\left(7 \, {\left(a^{2} b^{2} + 3 \, a b^{3}\right)} \cosh\left(d x + c\right)^{6} - 5 \, {\left(4 \, a^{3} b - 17 \, a^{2} b^{2} + 9 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} - a^{2} b^{2} - 3 \, a b^{3} + 3 \, {\left(4 \, a^{3} b - 17 \, a^{2} b^{2} + 9 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)}{16 \, {\left(a^{3} b^{4} d \cosh\left(d x + c\right)^{8} + 8 \, a^{3} b^{4} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + a^{3} b^{4} d \sinh\left(d x + c\right)^{8} + a^{3} b^{4} d + 4 \, {\left(2 \, a^{4} b^{3} - a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, a^{3} b^{4} d \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{4} b^{3} - a^{3} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(8 \, a^{5} b^{2} - 8 \, a^{4} b^{3} + 3 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, a^{3} b^{4} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(2 \, a^{4} b^{3} - a^{3} b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, a^{3} b^{4} d \cosh\left(d x + c\right)^{4} + 30 \, {\left(2 \, a^{4} b^{3} - a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(8 \, a^{5} b^{2} - 8 \, a^{4} b^{3} + 3 \, a^{3} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(2 \, a^{4} b^{3} - a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, a^{3} b^{4} d \cosh\left(d x + c\right)^{5} + 10 \, {\left(2 \, a^{4} b^{3} - a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{5} b^{2} - 8 \, a^{4} b^{3} + 3 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, a^{3} b^{4} d \cosh\left(d x + c\right)^{6} + 15 \, {\left(2 \, a^{4} b^{3} - a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(8 \, a^{5} b^{2} - 8 \, a^{4} b^{3} + 3 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{4} b^{3} - a^{3} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left(a^{3} b^{4} d \cosh\left(d x + c\right)^{7} + 3 \, {\left(2 \, a^{4} b^{3} - a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{5} + {\left(8 \, a^{5} b^{2} - 8 \, a^{4} b^{3} + 3 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{4} b^{3} - a^{3} b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}, \frac{2 \, {\left(a^{2} b^{2} + 3 \, a b^{3}\right)} \cosh\left(d x + c\right)^{7} + 14 \, {\left(a^{2} b^{2} + 3 \, a b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + 2 \, {\left(a^{2} b^{2} + 3 \, a b^{3}\right)} \sinh\left(d x + c\right)^{7} - 2 \, {\left(4 \, a^{3} b - 17 \, a^{2} b^{2} + 9 \, a b^{3}\right)} \cosh\left(d x + c\right)^{5} - 2 \, {\left(4 \, a^{3} b - 17 \, a^{2} b^{2} + 9 \, a b^{3} - 21 \, {\left(a^{2} b^{2} + 3 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{5} + 10 \, {\left(7 \, {\left(a^{2} b^{2} + 3 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} - {\left(4 \, a^{3} b - 17 \, a^{2} b^{2} + 9 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(4 \, a^{3} b - 17 \, a^{2} b^{2} + 9 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(35 \, {\left(a^{2} b^{2} + 3 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} + 4 \, a^{3} b - 17 \, a^{2} b^{2} + 9 \, a b^{3} - 10 \, {\left(4 \, a^{3} b - 17 \, a^{2} b^{2} + 9 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(21 \, {\left(a^{2} b^{2} + 3 \, a b^{3}\right)} \cosh\left(d x + c\right)^{5} - 10 \, {\left(4 \, a^{3} b - 17 \, a^{2} b^{2} + 9 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(4 \, a^{3} b - 17 \, a^{2} b^{2} + 9 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(a b^{2} + 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(a b^{2} + 3 \, b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a b^{2} + 3 \, b^{3}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(2 \, a^{2} b + 5 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(2 \, a^{2} b + 5 \, a b^{2} - 3 \, b^{3} + 7 \, {\left(a b^{2} + 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(a b^{2} + 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(2 \, a^{2} b + 5 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(8 \, a^{3} + 16 \, a^{2} b - 21 \, a b^{2} + 9 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(a b^{2} + 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 8 \, a^{3} + 16 \, a^{2} b - 21 \, a b^{2} + 9 \, b^{3} + 30 \, {\left(2 \, a^{2} b + 5 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a b^{2} + 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(2 \, a^{2} b + 5 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{3} + 16 \, a^{2} b - 21 \, a b^{2} + 9 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + a b^{2} + 3 \, b^{3} + 4 \, {\left(2 \, a^{2} b + 5 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(a b^{2} + 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(2 \, a^{2} b + 5 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 2 \, a^{2} b + 5 \, a b^{2} - 3 \, b^{3} + 3 \, {\left(8 \, a^{3} + 16 \, a^{2} b - 21 \, a b^{2} + 9 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left({\left(a b^{2} + 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(2 \, a^{2} b + 5 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + {\left(8 \, a^{3} + 16 \, a^{2} b - 21 \, a b^{2} + 9 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{2} b + 5 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} {\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right)}}{2 \, a}\right) + {\left({\left(a b^{2} + 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(a b^{2} + 3 \, b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a b^{2} + 3 \, b^{3}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(2 \, a^{2} b + 5 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(2 \, a^{2} b + 5 \, a b^{2} - 3 \, b^{3} + 7 \, {\left(a b^{2} + 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(a b^{2} + 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(2 \, a^{2} b + 5 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(8 \, a^{3} + 16 \, a^{2} b - 21 \, a b^{2} + 9 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(a b^{2} + 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 8 \, a^{3} + 16 \, a^{2} b - 21 \, a b^{2} + 9 \, b^{3} + 30 \, {\left(2 \, a^{2} b + 5 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a b^{2} + 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(2 \, a^{2} b + 5 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{3} + 16 \, a^{2} b - 21 \, a b^{2} + 9 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + a b^{2} + 3 \, b^{3} + 4 \, {\left(2 \, a^{2} b + 5 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(a b^{2} + 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(2 \, a^{2} b + 5 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 2 \, a^{2} b + 5 \, a b^{2} - 3 \, b^{3} + 3 \, {\left(8 \, a^{3} + 16 \, a^{2} b - 21 \, a b^{2} + 9 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left({\left(a b^{2} + 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(2 \, a^{2} b + 5 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + {\left(8 \, a^{3} + 16 \, a^{2} b - 21 \, a b^{2} + 9 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{2} b + 5 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{a b} \arctan\left(\frac{{\left(b \cosh\left(d x + c\right)^{3} + 3 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{3} + {\left(4 \, a - b\right)} \cosh\left(d x + c\right) + {\left(3 \, b \cosh\left(d x + c\right)^{2} + 4 \, a - b\right)} \sinh\left(d x + c\right)\right)} \sqrt{a b}}{2 \, a b}\right) - 2 \, {\left(a^{2} b^{2} + 3 \, a b^{3}\right)} \cosh\left(d x + c\right) + 2 \, {\left(7 \, {\left(a^{2} b^{2} + 3 \, a b^{3}\right)} \cosh\left(d x + c\right)^{6} - 5 \, {\left(4 \, a^{3} b - 17 \, a^{2} b^{2} + 9 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} - a^{2} b^{2} - 3 \, a b^{3} + 3 \, {\left(4 \, a^{3} b - 17 \, a^{2} b^{2} + 9 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)}{8 \, {\left(a^{3} b^{4} d \cosh\left(d x + c\right)^{8} + 8 \, a^{3} b^{4} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + a^{3} b^{4} d \sinh\left(d x + c\right)^{8} + a^{3} b^{4} d + 4 \, {\left(2 \, a^{4} b^{3} - a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, a^{3} b^{4} d \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{4} b^{3} - a^{3} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(8 \, a^{5} b^{2} - 8 \, a^{4} b^{3} + 3 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, a^{3} b^{4} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(2 \, a^{4} b^{3} - a^{3} b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, a^{3} b^{4} d \cosh\left(d x + c\right)^{4} + 30 \, {\left(2 \, a^{4} b^{3} - a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(8 \, a^{5} b^{2} - 8 \, a^{4} b^{3} + 3 \, a^{3} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(2 \, a^{4} b^{3} - a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, a^{3} b^{4} d \cosh\left(d x + c\right)^{5} + 10 \, {\left(2 \, a^{4} b^{3} - a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{5} b^{2} - 8 \, a^{4} b^{3} + 3 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, a^{3} b^{4} d \cosh\left(d x + c\right)^{6} + 15 \, {\left(2 \, a^{4} b^{3} - a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(8 \, a^{5} b^{2} - 8 \, a^{4} b^{3} + 3 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{4} b^{3} - a^{3} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left(a^{3} b^{4} d \cosh\left(d x + c\right)^{7} + 3 \, {\left(2 \, a^{4} b^{3} - a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{5} + {\left(8 \, a^{5} b^{2} - 8 \, a^{4} b^{3} + 3 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{4} b^{3} - a^{3} b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[1/16*(4*(a^2*b^2 + 3*a*b^3)*cosh(d*x + c)^7 + 28*(a^2*b^2 + 3*a*b^3)*cosh(d*x + c)*sinh(d*x + c)^6 + 4*(a^2*b^2 + 3*a*b^3)*sinh(d*x + c)^7 - 4*(4*a^3*b - 17*a^2*b^2 + 9*a*b^3)*cosh(d*x + c)^5 - 4*(4*a^3*b - 17*a^2*b^2 + 9*a*b^3 - 21*(a^2*b^2 + 3*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 20*(7*(a^2*b^2 + 3*a*b^3)*cosh(d*x + c)^3 - (4*a^3*b - 17*a^2*b^2 + 9*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^4 + 4*(4*a^3*b - 17*a^2*b^2 + 9*a*b^3)*cosh(d*x + c)^3 + 4*(35*(a^2*b^2 + 3*a*b^3)*cosh(d*x + c)^4 + 4*a^3*b - 17*a^2*b^2 + 9*a*b^3 - 10*(4*a^3*b - 17*a^2*b^2 + 9*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 4*(21*(a^2*b^2 + 3*a*b^3)*cosh(d*x + c)^5 - 10*(4*a^3*b - 17*a^2*b^2 + 9*a*b^3)*cosh(d*x + c)^3 + 3*(4*a^3*b - 17*a^2*b^2 + 9*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^2 - ((a*b^2 + 3*b^3)*cosh(d*x + c)^8 + 8*(a*b^2 + 3*b^3)*cosh(d*x + c)*sinh(d*x + c)^7 + (a*b^2 + 3*b^3)*sinh(d*x + c)^8 + 4*(2*a^2*b + 5*a*b^2 - 3*b^3)*cosh(d*x + c)^6 + 4*(2*a^2*b + 5*a*b^2 - 3*b^3 + 7*(a*b^2 + 3*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(a*b^2 + 3*b^3)*cosh(d*x + c)^3 + 3*(2*a^2*b + 5*a*b^2 - 3*b^3)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(8*a^3 + 16*a^2*b - 21*a*b^2 + 9*b^3)*cosh(d*x + c)^4 + 2*(35*(a*b^2 + 3*b^3)*cosh(d*x + c)^4 + 8*a^3 + 16*a^2*b - 21*a*b^2 + 9*b^3 + 30*(2*a^2*b + 5*a*b^2 - 3*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(7*(a*b^2 + 3*b^3)*cosh(d*x + c)^5 + 10*(2*a^2*b + 5*a*b^2 - 3*b^3)*cosh(d*x + c)^3 + (8*a^3 + 16*a^2*b - 21*a*b^2 + 9*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 + a*b^2 + 3*b^3 + 4*(2*a^2*b + 5*a*b^2 - 3*b^3)*cosh(d*x + c)^2 + 4*(7*(a*b^2 + 3*b^3)*cosh(d*x + c)^6 + 15*(2*a^2*b + 5*a*b^2 - 3*b^3)*cosh(d*x + c)^4 + 2*a^2*b + 5*a*b^2 - 3*b^3 + 3*(8*a^3 + 16*a^2*b - 21*a*b^2 + 9*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((a*b^2 + 3*b^3)*cosh(d*x + c)^7 + 3*(2*a^2*b + 5*a*b^2 - 3*b^3)*cosh(d*x + c)^5 + (8*a^3 + 16*a^2*b - 21*a*b^2 + 9*b^3)*cosh(d*x + c)^3 + (2*a^2*b + 5*a*b^2 - 3*b^3)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-a*b)*log((b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 - 2*(2*a + b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 - 2*a - b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 - (2*a + b)*cosh(d*x + c))*sinh(d*x + c) - 4*(cosh(d*x + c)^3 + 3*cosh(d*x + c)*sinh(d*x + c)^2 + sinh(d*x + c)^3 + (3*cosh(d*x + c)^2 - 1)*sinh(d*x + c) - cosh(d*x + c))*sqrt(-a*b) + b)/(b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 + 2*(2*a - b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 + 2*a - b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 + (2*a - b)*cosh(d*x + c))*sinh(d*x + c) + b)) - 4*(a^2*b^2 + 3*a*b^3)*cosh(d*x + c) + 4*(7*(a^2*b^2 + 3*a*b^3)*cosh(d*x + c)^6 - 5*(4*a^3*b - 17*a^2*b^2 + 9*a*b^3)*cosh(d*x + c)^4 - a^2*b^2 - 3*a*b^3 + 3*(4*a^3*b - 17*a^2*b^2 + 9*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c))/(a^3*b^4*d*cosh(d*x + c)^8 + 8*a^3*b^4*d*cosh(d*x + c)*sinh(d*x + c)^7 + a^3*b^4*d*sinh(d*x + c)^8 + a^3*b^4*d + 4*(2*a^4*b^3 - a^3*b^4)*d*cosh(d*x + c)^6 + 4*(7*a^3*b^4*d*cosh(d*x + c)^2 + (2*a^4*b^3 - a^3*b^4)*d)*sinh(d*x + c)^6 + 2*(8*a^5*b^2 - 8*a^4*b^3 + 3*a^3*b^4)*d*cosh(d*x + c)^4 + 8*(7*a^3*b^4*d*cosh(d*x + c)^3 + 3*(2*a^4*b^3 - a^3*b^4)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*a^3*b^4*d*cosh(d*x + c)^4 + 30*(2*a^4*b^3 - a^3*b^4)*d*cosh(d*x + c)^2 + (8*a^5*b^2 - 8*a^4*b^3 + 3*a^3*b^4)*d)*sinh(d*x + c)^4 + 4*(2*a^4*b^3 - a^3*b^4)*d*cosh(d*x + c)^2 + 8*(7*a^3*b^4*d*cosh(d*x + c)^5 + 10*(2*a^4*b^3 - a^3*b^4)*d*cosh(d*x + c)^3 + (8*a^5*b^2 - 8*a^4*b^3 + 3*a^3*b^4)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*a^3*b^4*d*cosh(d*x + c)^6 + 15*(2*a^4*b^3 - a^3*b^4)*d*cosh(d*x + c)^4 + 3*(8*a^5*b^2 - 8*a^4*b^3 + 3*a^3*b^4)*d*cosh(d*x + c)^2 + (2*a^4*b^3 - a^3*b^4)*d)*sinh(d*x + c)^2 + 8*(a^3*b^4*d*cosh(d*x + c)^7 + 3*(2*a^4*b^3 - a^3*b^4)*d*cosh(d*x + c)^5 + (8*a^5*b^2 - 8*a^4*b^3 + 3*a^3*b^4)*d*cosh(d*x + c)^3 + (2*a^4*b^3 - a^3*b^4)*d*cosh(d*x + c))*sinh(d*x + c)), 1/8*(2*(a^2*b^2 + 3*a*b^3)*cosh(d*x + c)^7 + 14*(a^2*b^2 + 3*a*b^3)*cosh(d*x + c)*sinh(d*x + c)^6 + 2*(a^2*b^2 + 3*a*b^3)*sinh(d*x + c)^7 - 2*(4*a^3*b - 17*a^2*b^2 + 9*a*b^3)*cosh(d*x + c)^5 - 2*(4*a^3*b - 17*a^2*b^2 + 9*a*b^3 - 21*(a^2*b^2 + 3*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 10*(7*(a^2*b^2 + 3*a*b^3)*cosh(d*x + c)^3 - (4*a^3*b - 17*a^2*b^2 + 9*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^4 + 2*(4*a^3*b - 17*a^2*b^2 + 9*a*b^3)*cosh(d*x + c)^3 + 2*(35*(a^2*b^2 + 3*a*b^3)*cosh(d*x + c)^4 + 4*a^3*b - 17*a^2*b^2 + 9*a*b^3 - 10*(4*a^3*b - 17*a^2*b^2 + 9*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 2*(21*(a^2*b^2 + 3*a*b^3)*cosh(d*x + c)^5 - 10*(4*a^3*b - 17*a^2*b^2 + 9*a*b^3)*cosh(d*x + c)^3 + 3*(4*a^3*b - 17*a^2*b^2 + 9*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^2 + ((a*b^2 + 3*b^3)*cosh(d*x + c)^8 + 8*(a*b^2 + 3*b^3)*cosh(d*x + c)*sinh(d*x + c)^7 + (a*b^2 + 3*b^3)*sinh(d*x + c)^8 + 4*(2*a^2*b + 5*a*b^2 - 3*b^3)*cosh(d*x + c)^6 + 4*(2*a^2*b + 5*a*b^2 - 3*b^3 + 7*(a*b^2 + 3*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(a*b^2 + 3*b^3)*cosh(d*x + c)^3 + 3*(2*a^2*b + 5*a*b^2 - 3*b^3)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(8*a^3 + 16*a^2*b - 21*a*b^2 + 9*b^3)*cosh(d*x + c)^4 + 2*(35*(a*b^2 + 3*b^3)*cosh(d*x + c)^4 + 8*a^3 + 16*a^2*b - 21*a*b^2 + 9*b^3 + 30*(2*a^2*b + 5*a*b^2 - 3*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(7*(a*b^2 + 3*b^3)*cosh(d*x + c)^5 + 10*(2*a^2*b + 5*a*b^2 - 3*b^3)*cosh(d*x + c)^3 + (8*a^3 + 16*a^2*b - 21*a*b^2 + 9*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 + a*b^2 + 3*b^3 + 4*(2*a^2*b + 5*a*b^2 - 3*b^3)*cosh(d*x + c)^2 + 4*(7*(a*b^2 + 3*b^3)*cosh(d*x + c)^6 + 15*(2*a^2*b + 5*a*b^2 - 3*b^3)*cosh(d*x + c)^4 + 2*a^2*b + 5*a*b^2 - 3*b^3 + 3*(8*a^3 + 16*a^2*b - 21*a*b^2 + 9*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((a*b^2 + 3*b^3)*cosh(d*x + c)^7 + 3*(2*a^2*b + 5*a*b^2 - 3*b^3)*cosh(d*x + c)^5 + (8*a^3 + 16*a^2*b - 21*a*b^2 + 9*b^3)*cosh(d*x + c)^3 + (2*a^2*b + 5*a*b^2 - 3*b^3)*cosh(d*x + c))*sinh(d*x + c))*sqrt(a*b)*arctan(1/2*sqrt(a*b)*(cosh(d*x + c) + sinh(d*x + c))/a) + ((a*b^2 + 3*b^3)*cosh(d*x + c)^8 + 8*(a*b^2 + 3*b^3)*cosh(d*x + c)*sinh(d*x + c)^7 + (a*b^2 + 3*b^3)*sinh(d*x + c)^8 + 4*(2*a^2*b + 5*a*b^2 - 3*b^3)*cosh(d*x + c)^6 + 4*(2*a^2*b + 5*a*b^2 - 3*b^3 + 7*(a*b^2 + 3*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(a*b^2 + 3*b^3)*cosh(d*x + c)^3 + 3*(2*a^2*b + 5*a*b^2 - 3*b^3)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(8*a^3 + 16*a^2*b - 21*a*b^2 + 9*b^3)*cosh(d*x + c)^4 + 2*(35*(a*b^2 + 3*b^3)*cosh(d*x + c)^4 + 8*a^3 + 16*a^2*b - 21*a*b^2 + 9*b^3 + 30*(2*a^2*b + 5*a*b^2 - 3*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(7*(a*b^2 + 3*b^3)*cosh(d*x + c)^5 + 10*(2*a^2*b + 5*a*b^2 - 3*b^3)*cosh(d*x + c)^3 + (8*a^3 + 16*a^2*b - 21*a*b^2 + 9*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 + a*b^2 + 3*b^3 + 4*(2*a^2*b + 5*a*b^2 - 3*b^3)*cosh(d*x + c)^2 + 4*(7*(a*b^2 + 3*b^3)*cosh(d*x + c)^6 + 15*(2*a^2*b + 5*a*b^2 - 3*b^3)*cosh(d*x + c)^4 + 2*a^2*b + 5*a*b^2 - 3*b^3 + 3*(8*a^3 + 16*a^2*b - 21*a*b^2 + 9*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((a*b^2 + 3*b^3)*cosh(d*x + c)^7 + 3*(2*a^2*b + 5*a*b^2 - 3*b^3)*cosh(d*x + c)^5 + (8*a^3 + 16*a^2*b - 21*a*b^2 + 9*b^3)*cosh(d*x + c)^3 + (2*a^2*b + 5*a*b^2 - 3*b^3)*cosh(d*x + c))*sinh(d*x + c))*sqrt(a*b)*arctan(1/2*(b*cosh(d*x + c)^3 + 3*b*cosh(d*x + c)*sinh(d*x + c)^2 + b*sinh(d*x + c)^3 + (4*a - b)*cosh(d*x + c) + (3*b*cosh(d*x + c)^2 + 4*a - b)*sinh(d*x + c))*sqrt(a*b)/(a*b)) - 2*(a^2*b^2 + 3*a*b^3)*cosh(d*x + c) + 2*(7*(a^2*b^2 + 3*a*b^3)*cosh(d*x + c)^6 - 5*(4*a^3*b - 17*a^2*b^2 + 9*a*b^3)*cosh(d*x + c)^4 - a^2*b^2 - 3*a*b^3 + 3*(4*a^3*b - 17*a^2*b^2 + 9*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c))/(a^3*b^4*d*cosh(d*x + c)^8 + 8*a^3*b^4*d*cosh(d*x + c)*sinh(d*x + c)^7 + a^3*b^4*d*sinh(d*x + c)^8 + a^3*b^4*d + 4*(2*a^4*b^3 - a^3*b^4)*d*cosh(d*x + c)^6 + 4*(7*a^3*b^4*d*cosh(d*x + c)^2 + (2*a^4*b^3 - a^3*b^4)*d)*sinh(d*x + c)^6 + 2*(8*a^5*b^2 - 8*a^4*b^3 + 3*a^3*b^4)*d*cosh(d*x + c)^4 + 8*(7*a^3*b^4*d*cosh(d*x + c)^3 + 3*(2*a^4*b^3 - a^3*b^4)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*a^3*b^4*d*cosh(d*x + c)^4 + 30*(2*a^4*b^3 - a^3*b^4)*d*cosh(d*x + c)^2 + (8*a^5*b^2 - 8*a^4*b^3 + 3*a^3*b^4)*d)*sinh(d*x + c)^4 + 4*(2*a^4*b^3 - a^3*b^4)*d*cosh(d*x + c)^2 + 8*(7*a^3*b^4*d*cosh(d*x + c)^5 + 10*(2*a^4*b^3 - a^3*b^4)*d*cosh(d*x + c)^3 + (8*a^5*b^2 - 8*a^4*b^3 + 3*a^3*b^4)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*a^3*b^4*d*cosh(d*x + c)^6 + 15*(2*a^4*b^3 - a^3*b^4)*d*cosh(d*x + c)^4 + 3*(8*a^5*b^2 - 8*a^4*b^3 + 3*a^3*b^4)*d*cosh(d*x + c)^2 + (2*a^4*b^3 - a^3*b^4)*d)*sinh(d*x + c)^2 + 8*(a^3*b^4*d*cosh(d*x + c)^7 + 3*(2*a^4*b^3 - a^3*b^4)*d*cosh(d*x + c)^5 + (8*a^5*b^2 - 8*a^4*b^3 + 3*a^3*b^4)*d*cosh(d*x + c)^3 + (2*a^4*b^3 - a^3*b^4)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
343,1,5183,0,0.839654," ","integrate(cosh(d*x+c)^2/(a+b*sinh(d*x+c)^2)^3,x, algorithm=""fricas"")","\left[\frac{4 \, {\left(4 \, a^{3} b^{2} - 7 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{6} + 24 \, {\left(4 \, a^{3} b^{2} - 7 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + 4 \, {\left(4 \, a^{3} b^{2} - 7 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \sinh\left(d x + c\right)^{6} - 8 \, a^{3} b^{2} + 20 \, a^{2} b^{3} - 12 \, a b^{4} - 4 \, {\left(16 \, a^{5} - 56 \, a^{4} b + 70 \, a^{3} b^{2} - 39 \, a^{2} b^{3} + 9 \, a b^{4}\right)} \cosh\left(d x + c\right)^{4} - 4 \, {\left(16 \, a^{5} - 56 \, a^{4} b + 70 \, a^{3} b^{2} - 39 \, a^{2} b^{3} + 9 \, a b^{4} - 15 \, {\left(4 \, a^{3} b^{2} - 7 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 16 \, {\left(5 \, {\left(4 \, a^{3} b^{2} - 7 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{3} - {\left(16 \, a^{5} - 56 \, a^{4} b + 70 \, a^{3} b^{2} - 39 \, a^{2} b^{3} + 9 \, a b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 4 \, {\left(16 \, a^{4} b - 44 \, a^{3} b^{2} + 37 \, a^{2} b^{3} - 9 \, a b^{4}\right)} \cosh\left(d x + c\right)^{2} - 4 \, {\left(16 \, a^{4} b - 44 \, a^{3} b^{2} + 37 \, a^{2} b^{3} - 9 \, a b^{4} - 15 \, {\left(4 \, a^{3} b^{2} - 7 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{4} + 6 \, {\left(16 \, a^{5} - 56 \, a^{4} b + 70 \, a^{3} b^{2} - 39 \, a^{2} b^{3} + 9 \, a b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(4 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(4 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(4 \, a b^{3} - 3 \, b^{4}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(8 \, a^{2} b^{2} - 10 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(8 \, a^{2} b^{2} - 10 \, a b^{3} + 3 \, b^{4} + 7 \, {\left(4 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(4 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(8 \, a^{2} b^{2} - 10 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(32 \, a^{3} b - 56 \, a^{2} b^{2} + 36 \, a b^{3} - 9 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(4 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 32 \, a^{3} b - 56 \, a^{2} b^{2} + 36 \, a b^{3} - 9 \, b^{4} + 30 \, {\left(8 \, a^{2} b^{2} - 10 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, a b^{3} - 3 \, b^{4} + 8 \, {\left(7 \, {\left(4 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(8 \, a^{2} b^{2} - 10 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(32 \, a^{3} b - 56 \, a^{2} b^{2} + 36 \, a b^{3} - 9 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(8 \, a^{2} b^{2} - 10 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(4 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(8 \, a^{2} b^{2} - 10 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 8 \, a^{2} b^{2} - 10 \, a b^{3} + 3 \, b^{4} + 3 \, {\left(32 \, a^{3} b - 56 \, a^{2} b^{2} + 36 \, a b^{3} - 9 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left({\left(4 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(8 \, a^{2} b^{2} - 10 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + {\left(32 \, a^{3} b - 56 \, a^{2} b^{2} + 36 \, a b^{3} - 9 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{2} b^{2} - 10 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{a^{2} - a b} \log\left(\frac{b^{2} \cosh\left(d x + c\right)^{4} + 4 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{2} \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(d x + c\right)^{2} + 2 \, a b - b^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, a^{2} - 8 \, a b + b^{2} + 4 \, {\left(b^{2} \cosh\left(d x + c\right)^{3} + {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) - 4 \, {\left(b \cosh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b \sinh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sqrt{a^{2} - a b}}{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b}\right) + 8 \, {\left(3 \, {\left(4 \, a^{3} b^{2} - 7 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{5} - 2 \, {\left(16 \, a^{5} - 56 \, a^{4} b + 70 \, a^{3} b^{2} - 39 \, a^{2} b^{3} + 9 \, a b^{4}\right)} \cosh\left(d x + c\right)^{3} - {\left(16 \, a^{4} b - 44 \, a^{3} b^{2} + 37 \, a^{2} b^{3} - 9 \, a b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{16 \, {\left({\left(a^{5} b^{3} - 2 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{5} b^{3} - 2 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{5} b^{3} - 2 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \sinh\left(d x + c\right)^{8} + 4 \, {\left(2 \, a^{6} b^{2} - 5 \, a^{5} b^{3} + 4 \, a^{4} b^{4} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{5} b^{3} - 2 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{6} b^{2} - 5 \, a^{5} b^{3} + 4 \, a^{4} b^{4} - a^{3} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(8 \, a^{7} b - 24 \, a^{6} b^{2} + 27 \, a^{5} b^{3} - 14 \, a^{4} b^{4} + 3 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{5} b^{3} - 2 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(2 \, a^{6} b^{2} - 5 \, a^{5} b^{3} + 4 \, a^{4} b^{4} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a^{5} b^{3} - 2 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 30 \, {\left(2 \, a^{6} b^{2} - 5 \, a^{5} b^{3} + 4 \, a^{4} b^{4} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(8 \, a^{7} b - 24 \, a^{6} b^{2} + 27 \, a^{5} b^{3} - 14 \, a^{4} b^{4} + 3 \, a^{3} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(2 \, a^{6} b^{2} - 5 \, a^{5} b^{3} + 4 \, a^{4} b^{4} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a^{5} b^{3} - 2 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{5} + 10 \, {\left(2 \, a^{6} b^{2} - 5 \, a^{5} b^{3} + 4 \, a^{4} b^{4} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{7} b - 24 \, a^{6} b^{2} + 27 \, a^{5} b^{3} - 14 \, a^{4} b^{4} + 3 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a^{5} b^{3} - 2 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{6} + 15 \, {\left(2 \, a^{6} b^{2} - 5 \, a^{5} b^{3} + 4 \, a^{4} b^{4} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(8 \, a^{7} b - 24 \, a^{6} b^{2} + 27 \, a^{5} b^{3} - 14 \, a^{4} b^{4} + 3 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{6} b^{2} - 5 \, a^{5} b^{3} + 4 \, a^{4} b^{4} - a^{3} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{5} b^{3} - 2 \, a^{4} b^{4} + a^{3} b^{5}\right)} d + 8 \, {\left({\left(a^{5} b^{3} - 2 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{7} + 3 \, {\left(2 \, a^{6} b^{2} - 5 \, a^{5} b^{3} + 4 \, a^{4} b^{4} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{5} + {\left(8 \, a^{7} b - 24 \, a^{6} b^{2} + 27 \, a^{5} b^{3} - 14 \, a^{4} b^{4} + 3 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{6} b^{2} - 5 \, a^{5} b^{3} + 4 \, a^{4} b^{4} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}, \frac{2 \, {\left(4 \, a^{3} b^{2} - 7 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{6} + 12 \, {\left(4 \, a^{3} b^{2} - 7 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + 2 \, {\left(4 \, a^{3} b^{2} - 7 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \sinh\left(d x + c\right)^{6} - 4 \, a^{3} b^{2} + 10 \, a^{2} b^{3} - 6 \, a b^{4} - 2 \, {\left(16 \, a^{5} - 56 \, a^{4} b + 70 \, a^{3} b^{2} - 39 \, a^{2} b^{3} + 9 \, a b^{4}\right)} \cosh\left(d x + c\right)^{4} - 2 \, {\left(16 \, a^{5} - 56 \, a^{4} b + 70 \, a^{3} b^{2} - 39 \, a^{2} b^{3} + 9 \, a b^{4} - 15 \, {\left(4 \, a^{3} b^{2} - 7 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(5 \, {\left(4 \, a^{3} b^{2} - 7 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{3} - {\left(16 \, a^{5} - 56 \, a^{4} b + 70 \, a^{3} b^{2} - 39 \, a^{2} b^{3} + 9 \, a b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 2 \, {\left(16 \, a^{4} b - 44 \, a^{3} b^{2} + 37 \, a^{2} b^{3} - 9 \, a b^{4}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(16 \, a^{4} b - 44 \, a^{3} b^{2} + 37 \, a^{2} b^{3} - 9 \, a b^{4} - 15 \, {\left(4 \, a^{3} b^{2} - 7 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{4} + 6 \, {\left(16 \, a^{5} - 56 \, a^{4} b + 70 \, a^{3} b^{2} - 39 \, a^{2} b^{3} + 9 \, a b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} - {\left({\left(4 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(4 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(4 \, a b^{3} - 3 \, b^{4}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(8 \, a^{2} b^{2} - 10 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(8 \, a^{2} b^{2} - 10 \, a b^{3} + 3 \, b^{4} + 7 \, {\left(4 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(4 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(8 \, a^{2} b^{2} - 10 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(32 \, a^{3} b - 56 \, a^{2} b^{2} + 36 \, a b^{3} - 9 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(4 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 32 \, a^{3} b - 56 \, a^{2} b^{2} + 36 \, a b^{3} - 9 \, b^{4} + 30 \, {\left(8 \, a^{2} b^{2} - 10 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, a b^{3} - 3 \, b^{4} + 8 \, {\left(7 \, {\left(4 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(8 \, a^{2} b^{2} - 10 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(32 \, a^{3} b - 56 \, a^{2} b^{2} + 36 \, a b^{3} - 9 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(8 \, a^{2} b^{2} - 10 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(4 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(8 \, a^{2} b^{2} - 10 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 8 \, a^{2} b^{2} - 10 \, a b^{3} + 3 \, b^{4} + 3 \, {\left(32 \, a^{3} b - 56 \, a^{2} b^{2} + 36 \, a b^{3} - 9 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left({\left(4 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(8 \, a^{2} b^{2} - 10 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + {\left(32 \, a^{3} b - 56 \, a^{2} b^{2} + 36 \, a b^{3} - 9 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{2} b^{2} - 10 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-a^{2} + a b} \arctan\left(-\frac{{\left(b \cosh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b \sinh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sqrt{-a^{2} + a b}}{2 \, {\left(a^{2} - a b\right)}}\right) + 4 \, {\left(3 \, {\left(4 \, a^{3} b^{2} - 7 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{5} - 2 \, {\left(16 \, a^{5} - 56 \, a^{4} b + 70 \, a^{3} b^{2} - 39 \, a^{2} b^{3} + 9 \, a b^{4}\right)} \cosh\left(d x + c\right)^{3} - {\left(16 \, a^{4} b - 44 \, a^{3} b^{2} + 37 \, a^{2} b^{3} - 9 \, a b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{8 \, {\left({\left(a^{5} b^{3} - 2 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{5} b^{3} - 2 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{5} b^{3} - 2 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \sinh\left(d x + c\right)^{8} + 4 \, {\left(2 \, a^{6} b^{2} - 5 \, a^{5} b^{3} + 4 \, a^{4} b^{4} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{5} b^{3} - 2 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{6} b^{2} - 5 \, a^{5} b^{3} + 4 \, a^{4} b^{4} - a^{3} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(8 \, a^{7} b - 24 \, a^{6} b^{2} + 27 \, a^{5} b^{3} - 14 \, a^{4} b^{4} + 3 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{5} b^{3} - 2 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(2 \, a^{6} b^{2} - 5 \, a^{5} b^{3} + 4 \, a^{4} b^{4} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a^{5} b^{3} - 2 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 30 \, {\left(2 \, a^{6} b^{2} - 5 \, a^{5} b^{3} + 4 \, a^{4} b^{4} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(8 \, a^{7} b - 24 \, a^{6} b^{2} + 27 \, a^{5} b^{3} - 14 \, a^{4} b^{4} + 3 \, a^{3} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(2 \, a^{6} b^{2} - 5 \, a^{5} b^{3} + 4 \, a^{4} b^{4} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a^{5} b^{3} - 2 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{5} + 10 \, {\left(2 \, a^{6} b^{2} - 5 \, a^{5} b^{3} + 4 \, a^{4} b^{4} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{7} b - 24 \, a^{6} b^{2} + 27 \, a^{5} b^{3} - 14 \, a^{4} b^{4} + 3 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a^{5} b^{3} - 2 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{6} + 15 \, {\left(2 \, a^{6} b^{2} - 5 \, a^{5} b^{3} + 4 \, a^{4} b^{4} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(8 \, a^{7} b - 24 \, a^{6} b^{2} + 27 \, a^{5} b^{3} - 14 \, a^{4} b^{4} + 3 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{6} b^{2} - 5 \, a^{5} b^{3} + 4 \, a^{4} b^{4} - a^{3} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{5} b^{3} - 2 \, a^{4} b^{4} + a^{3} b^{5}\right)} d + 8 \, {\left({\left(a^{5} b^{3} - 2 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{7} + 3 \, {\left(2 \, a^{6} b^{2} - 5 \, a^{5} b^{3} + 4 \, a^{4} b^{4} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{5} + {\left(8 \, a^{7} b - 24 \, a^{6} b^{2} + 27 \, a^{5} b^{3} - 14 \, a^{4} b^{4} + 3 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{6} b^{2} - 5 \, a^{5} b^{3} + 4 \, a^{4} b^{4} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[1/16*(4*(4*a^3*b^2 - 7*a^2*b^3 + 3*a*b^4)*cosh(d*x + c)^6 + 24*(4*a^3*b^2 - 7*a^2*b^3 + 3*a*b^4)*cosh(d*x + c)*sinh(d*x + c)^5 + 4*(4*a^3*b^2 - 7*a^2*b^3 + 3*a*b^4)*sinh(d*x + c)^6 - 8*a^3*b^2 + 20*a^2*b^3 - 12*a*b^4 - 4*(16*a^5 - 56*a^4*b + 70*a^3*b^2 - 39*a^2*b^3 + 9*a*b^4)*cosh(d*x + c)^4 - 4*(16*a^5 - 56*a^4*b + 70*a^3*b^2 - 39*a^2*b^3 + 9*a*b^4 - 15*(4*a^3*b^2 - 7*a^2*b^3 + 3*a*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 16*(5*(4*a^3*b^2 - 7*a^2*b^3 + 3*a*b^4)*cosh(d*x + c)^3 - (16*a^5 - 56*a^4*b + 70*a^3*b^2 - 39*a^2*b^3 + 9*a*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 - 4*(16*a^4*b - 44*a^3*b^2 + 37*a^2*b^3 - 9*a*b^4)*cosh(d*x + c)^2 - 4*(16*a^4*b - 44*a^3*b^2 + 37*a^2*b^3 - 9*a*b^4 - 15*(4*a^3*b^2 - 7*a^2*b^3 + 3*a*b^4)*cosh(d*x + c)^4 + 6*(16*a^5 - 56*a^4*b + 70*a^3*b^2 - 39*a^2*b^3 + 9*a*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((4*a*b^3 - 3*b^4)*cosh(d*x + c)^8 + 8*(4*a*b^3 - 3*b^4)*cosh(d*x + c)*sinh(d*x + c)^7 + (4*a*b^3 - 3*b^4)*sinh(d*x + c)^8 + 4*(8*a^2*b^2 - 10*a*b^3 + 3*b^4)*cosh(d*x + c)^6 + 4*(8*a^2*b^2 - 10*a*b^3 + 3*b^4 + 7*(4*a*b^3 - 3*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(4*a*b^3 - 3*b^4)*cosh(d*x + c)^3 + 3*(8*a^2*b^2 - 10*a*b^3 + 3*b^4)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(32*a^3*b - 56*a^2*b^2 + 36*a*b^3 - 9*b^4)*cosh(d*x + c)^4 + 2*(35*(4*a*b^3 - 3*b^4)*cosh(d*x + c)^4 + 32*a^3*b - 56*a^2*b^2 + 36*a*b^3 - 9*b^4 + 30*(8*a^2*b^2 - 10*a*b^3 + 3*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 4*a*b^3 - 3*b^4 + 8*(7*(4*a*b^3 - 3*b^4)*cosh(d*x + c)^5 + 10*(8*a^2*b^2 - 10*a*b^3 + 3*b^4)*cosh(d*x + c)^3 + (32*a^3*b - 56*a^2*b^2 + 36*a*b^3 - 9*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(8*a^2*b^2 - 10*a*b^3 + 3*b^4)*cosh(d*x + c)^2 + 4*(7*(4*a*b^3 - 3*b^4)*cosh(d*x + c)^6 + 15*(8*a^2*b^2 - 10*a*b^3 + 3*b^4)*cosh(d*x + c)^4 + 8*a^2*b^2 - 10*a*b^3 + 3*b^4 + 3*(32*a^3*b - 56*a^2*b^2 + 36*a*b^3 - 9*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((4*a*b^3 - 3*b^4)*cosh(d*x + c)^7 + 3*(8*a^2*b^2 - 10*a*b^3 + 3*b^4)*cosh(d*x + c)^5 + (32*a^3*b - 56*a^2*b^2 + 36*a*b^3 - 9*b^4)*cosh(d*x + c)^3 + (8*a^2*b^2 - 10*a*b^3 + 3*b^4)*cosh(d*x + c))*sinh(d*x + c))*sqrt(a^2 - a*b)*log((b^2*cosh(d*x + c)^4 + 4*b^2*cosh(d*x + c)*sinh(d*x + c)^3 + b^2*sinh(d*x + c)^4 + 2*(2*a*b - b^2)*cosh(d*x + c)^2 + 2*(3*b^2*cosh(d*x + c)^2 + 2*a*b - b^2)*sinh(d*x + c)^2 + 8*a^2 - 8*a*b + b^2 + 4*(b^2*cosh(d*x + c)^3 + (2*a*b - b^2)*cosh(d*x + c))*sinh(d*x + c) - 4*(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + 2*a - b)*sqrt(a^2 - a*b))/(b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 + 2*(2*a - b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 + 2*a - b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 + (2*a - b)*cosh(d*x + c))*sinh(d*x + c) + b)) + 8*(3*(4*a^3*b^2 - 7*a^2*b^3 + 3*a*b^4)*cosh(d*x + c)^5 - 2*(16*a^5 - 56*a^4*b + 70*a^3*b^2 - 39*a^2*b^3 + 9*a*b^4)*cosh(d*x + c)^3 - (16*a^4*b - 44*a^3*b^2 + 37*a^2*b^3 - 9*a*b^4)*cosh(d*x + c))*sinh(d*x + c))/((a^5*b^3 - 2*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)^8 + 8*(a^5*b^3 - 2*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^5*b^3 - 2*a^4*b^4 + a^3*b^5)*d*sinh(d*x + c)^8 + 4*(2*a^6*b^2 - 5*a^5*b^3 + 4*a^4*b^4 - a^3*b^5)*d*cosh(d*x + c)^6 + 4*(7*(a^5*b^3 - 2*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)^2 + (2*a^6*b^2 - 5*a^5*b^3 + 4*a^4*b^4 - a^3*b^5)*d)*sinh(d*x + c)^6 + 2*(8*a^7*b - 24*a^6*b^2 + 27*a^5*b^3 - 14*a^4*b^4 + 3*a^3*b^5)*d*cosh(d*x + c)^4 + 8*(7*(a^5*b^3 - 2*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)^3 + 3*(2*a^6*b^2 - 5*a^5*b^3 + 4*a^4*b^4 - a^3*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^5*b^3 - 2*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)^4 + 30*(2*a^6*b^2 - 5*a^5*b^3 + 4*a^4*b^4 - a^3*b^5)*d*cosh(d*x + c)^2 + (8*a^7*b - 24*a^6*b^2 + 27*a^5*b^3 - 14*a^4*b^4 + 3*a^3*b^5)*d)*sinh(d*x + c)^4 + 4*(2*a^6*b^2 - 5*a^5*b^3 + 4*a^4*b^4 - a^3*b^5)*d*cosh(d*x + c)^2 + 8*(7*(a^5*b^3 - 2*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)^5 + 10*(2*a^6*b^2 - 5*a^5*b^3 + 4*a^4*b^4 - a^3*b^5)*d*cosh(d*x + c)^3 + (8*a^7*b - 24*a^6*b^2 + 27*a^5*b^3 - 14*a^4*b^4 + 3*a^3*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^5*b^3 - 2*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)^6 + 15*(2*a^6*b^2 - 5*a^5*b^3 + 4*a^4*b^4 - a^3*b^5)*d*cosh(d*x + c)^4 + 3*(8*a^7*b - 24*a^6*b^2 + 27*a^5*b^3 - 14*a^4*b^4 + 3*a^3*b^5)*d*cosh(d*x + c)^2 + (2*a^6*b^2 - 5*a^5*b^3 + 4*a^4*b^4 - a^3*b^5)*d)*sinh(d*x + c)^2 + (a^5*b^3 - 2*a^4*b^4 + a^3*b^5)*d + 8*((a^5*b^3 - 2*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)^7 + 3*(2*a^6*b^2 - 5*a^5*b^3 + 4*a^4*b^4 - a^3*b^5)*d*cosh(d*x + c)^5 + (8*a^7*b - 24*a^6*b^2 + 27*a^5*b^3 - 14*a^4*b^4 + 3*a^3*b^5)*d*cosh(d*x + c)^3 + (2*a^6*b^2 - 5*a^5*b^3 + 4*a^4*b^4 - a^3*b^5)*d*cosh(d*x + c))*sinh(d*x + c)), 1/8*(2*(4*a^3*b^2 - 7*a^2*b^3 + 3*a*b^4)*cosh(d*x + c)^6 + 12*(4*a^3*b^2 - 7*a^2*b^3 + 3*a*b^4)*cosh(d*x + c)*sinh(d*x + c)^5 + 2*(4*a^3*b^2 - 7*a^2*b^3 + 3*a*b^4)*sinh(d*x + c)^6 - 4*a^3*b^2 + 10*a^2*b^3 - 6*a*b^4 - 2*(16*a^5 - 56*a^4*b + 70*a^3*b^2 - 39*a^2*b^3 + 9*a*b^4)*cosh(d*x + c)^4 - 2*(16*a^5 - 56*a^4*b + 70*a^3*b^2 - 39*a^2*b^3 + 9*a*b^4 - 15*(4*a^3*b^2 - 7*a^2*b^3 + 3*a*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(5*(4*a^3*b^2 - 7*a^2*b^3 + 3*a*b^4)*cosh(d*x + c)^3 - (16*a^5 - 56*a^4*b + 70*a^3*b^2 - 39*a^2*b^3 + 9*a*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 - 2*(16*a^4*b - 44*a^3*b^2 + 37*a^2*b^3 - 9*a*b^4)*cosh(d*x + c)^2 - 2*(16*a^4*b - 44*a^3*b^2 + 37*a^2*b^3 - 9*a*b^4 - 15*(4*a^3*b^2 - 7*a^2*b^3 + 3*a*b^4)*cosh(d*x + c)^4 + 6*(16*a^5 - 56*a^4*b + 70*a^3*b^2 - 39*a^2*b^3 + 9*a*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - ((4*a*b^3 - 3*b^4)*cosh(d*x + c)^8 + 8*(4*a*b^3 - 3*b^4)*cosh(d*x + c)*sinh(d*x + c)^7 + (4*a*b^3 - 3*b^4)*sinh(d*x + c)^8 + 4*(8*a^2*b^2 - 10*a*b^3 + 3*b^4)*cosh(d*x + c)^6 + 4*(8*a^2*b^2 - 10*a*b^3 + 3*b^4 + 7*(4*a*b^3 - 3*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(4*a*b^3 - 3*b^4)*cosh(d*x + c)^3 + 3*(8*a^2*b^2 - 10*a*b^3 + 3*b^4)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(32*a^3*b - 56*a^2*b^2 + 36*a*b^3 - 9*b^4)*cosh(d*x + c)^4 + 2*(35*(4*a*b^3 - 3*b^4)*cosh(d*x + c)^4 + 32*a^3*b - 56*a^2*b^2 + 36*a*b^3 - 9*b^4 + 30*(8*a^2*b^2 - 10*a*b^3 + 3*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 4*a*b^3 - 3*b^4 + 8*(7*(4*a*b^3 - 3*b^4)*cosh(d*x + c)^5 + 10*(8*a^2*b^2 - 10*a*b^3 + 3*b^4)*cosh(d*x + c)^3 + (32*a^3*b - 56*a^2*b^2 + 36*a*b^3 - 9*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(8*a^2*b^2 - 10*a*b^3 + 3*b^4)*cosh(d*x + c)^2 + 4*(7*(4*a*b^3 - 3*b^4)*cosh(d*x + c)^6 + 15*(8*a^2*b^2 - 10*a*b^3 + 3*b^4)*cosh(d*x + c)^4 + 8*a^2*b^2 - 10*a*b^3 + 3*b^4 + 3*(32*a^3*b - 56*a^2*b^2 + 36*a*b^3 - 9*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((4*a*b^3 - 3*b^4)*cosh(d*x + c)^7 + 3*(8*a^2*b^2 - 10*a*b^3 + 3*b^4)*cosh(d*x + c)^5 + (32*a^3*b - 56*a^2*b^2 + 36*a*b^3 - 9*b^4)*cosh(d*x + c)^3 + (8*a^2*b^2 - 10*a*b^3 + 3*b^4)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-a^2 + a*b)*arctan(-1/2*(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + 2*a - b)*sqrt(-a^2 + a*b)/(a^2 - a*b)) + 4*(3*(4*a^3*b^2 - 7*a^2*b^3 + 3*a*b^4)*cosh(d*x + c)^5 - 2*(16*a^5 - 56*a^4*b + 70*a^3*b^2 - 39*a^2*b^3 + 9*a*b^4)*cosh(d*x + c)^3 - (16*a^4*b - 44*a^3*b^2 + 37*a^2*b^3 - 9*a*b^4)*cosh(d*x + c))*sinh(d*x + c))/((a^5*b^3 - 2*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)^8 + 8*(a^5*b^3 - 2*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^5*b^3 - 2*a^4*b^4 + a^3*b^5)*d*sinh(d*x + c)^8 + 4*(2*a^6*b^2 - 5*a^5*b^3 + 4*a^4*b^4 - a^3*b^5)*d*cosh(d*x + c)^6 + 4*(7*(a^5*b^3 - 2*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)^2 + (2*a^6*b^2 - 5*a^5*b^3 + 4*a^4*b^4 - a^3*b^5)*d)*sinh(d*x + c)^6 + 2*(8*a^7*b - 24*a^6*b^2 + 27*a^5*b^3 - 14*a^4*b^4 + 3*a^3*b^5)*d*cosh(d*x + c)^4 + 8*(7*(a^5*b^3 - 2*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)^3 + 3*(2*a^6*b^2 - 5*a^5*b^3 + 4*a^4*b^4 - a^3*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^5*b^3 - 2*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)^4 + 30*(2*a^6*b^2 - 5*a^5*b^3 + 4*a^4*b^4 - a^3*b^5)*d*cosh(d*x + c)^2 + (8*a^7*b - 24*a^6*b^2 + 27*a^5*b^3 - 14*a^4*b^4 + 3*a^3*b^5)*d)*sinh(d*x + c)^4 + 4*(2*a^6*b^2 - 5*a^5*b^3 + 4*a^4*b^4 - a^3*b^5)*d*cosh(d*x + c)^2 + 8*(7*(a^5*b^3 - 2*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)^5 + 10*(2*a^6*b^2 - 5*a^5*b^3 + 4*a^4*b^4 - a^3*b^5)*d*cosh(d*x + c)^3 + (8*a^7*b - 24*a^6*b^2 + 27*a^5*b^3 - 14*a^4*b^4 + 3*a^3*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^5*b^3 - 2*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)^6 + 15*(2*a^6*b^2 - 5*a^5*b^3 + 4*a^4*b^4 - a^3*b^5)*d*cosh(d*x + c)^4 + 3*(8*a^7*b - 24*a^6*b^2 + 27*a^5*b^3 - 14*a^4*b^4 + 3*a^3*b^5)*d*cosh(d*x + c)^2 + (2*a^6*b^2 - 5*a^5*b^3 + 4*a^4*b^4 - a^3*b^5)*d)*sinh(d*x + c)^2 + (a^5*b^3 - 2*a^4*b^4 + a^3*b^5)*d + 8*((a^5*b^3 - 2*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)^7 + 3*(2*a^6*b^2 - 5*a^5*b^3 + 4*a^4*b^4 - a^3*b^5)*d*cosh(d*x + c)^5 + (8*a^7*b - 24*a^6*b^2 + 27*a^5*b^3 - 14*a^4*b^4 + 3*a^3*b^5)*d*cosh(d*x + c)^3 + (2*a^6*b^2 - 5*a^5*b^3 + 4*a^4*b^4 - a^3*b^5)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
344,1,3934,0,0.563611," ","integrate(cosh(d*x+c)/(a+b*sinh(d*x+c)^2)^3,x, algorithm=""fricas"")","\left[\frac{12 \, a b^{2} \cosh\left(d x + c\right)^{7} + 84 \, a b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + 12 \, a b^{2} \sinh\left(d x + c\right)^{7} + 4 \, {\left(20 \, a^{2} b - 9 \, a b^{2}\right)} \cosh\left(d x + c\right)^{5} + 4 \, {\left(63 \, a b^{2} \cosh\left(d x + c\right)^{2} + 20 \, a^{2} b - 9 \, a b^{2}\right)} \sinh\left(d x + c\right)^{5} + 20 \, {\left(21 \, a b^{2} \cosh\left(d x + c\right)^{3} + {\left(20 \, a^{2} b - 9 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} - 12 \, a b^{2} \cosh\left(d x + c\right) - 4 \, {\left(20 \, a^{2} b - 9 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(105 \, a b^{2} \cosh\left(d x + c\right)^{4} - 20 \, a^{2} b + 9 \, a b^{2} + 10 \, {\left(20 \, a^{2} b - 9 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(63 \, a b^{2} \cosh\left(d x + c\right)^{5} + 10 \, {\left(20 \, a^{2} b - 9 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(20 \, a^{2} b - 9 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 3 \, {\left(b^{2} \cosh\left(d x + c\right)^{8} + 8 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + b^{2} \sinh\left(d x + c\right)^{8} + 4 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, b^{2} \cosh\left(d x + c\right)^{2} + 2 \, a b - b^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, b^{2} \cosh\left(d x + c\right)^{3} + 3 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, b^{2} \cosh\left(d x + c\right)^{4} + 30 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, b^{2} \cosh\left(d x + c\right)^{5} + 10 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, b^{2} \cosh\left(d x + c\right)^{6} + 15 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, a b - b^{2}\right)} \sinh\left(d x + c\right)^{2} + b^{2} + 8 \, {\left(b^{2} \cosh\left(d x + c\right)^{7} + 3 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{5} + {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-a b} \log\left(\frac{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} - 2 \, {\left(2 \, a + b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} - 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} - {\left(2 \, a + b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) - 4 \, {\left(\cosh\left(d x + c\right)^{3} + 3 \, \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + \sinh\left(d x + c\right)^{3} + {\left(3 \, \cosh\left(d x + c\right)^{2} - 1\right)} \sinh\left(d x + c\right) - \cosh\left(d x + c\right)\right)} \sqrt{-a b} + b}{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b}\right) + 4 \, {\left(21 \, a b^{2} \cosh\left(d x + c\right)^{6} + 5 \, {\left(20 \, a^{2} b - 9 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} - 3 \, a b^{2} - 3 \, {\left(20 \, a^{2} b - 9 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)}{16 \, {\left(a^{3} b^{3} d \cosh\left(d x + c\right)^{8} + 8 \, a^{3} b^{3} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + a^{3} b^{3} d \sinh\left(d x + c\right)^{8} + 4 \, {\left(2 \, a^{4} b^{2} - a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{6} + a^{3} b^{3} d + 4 \, {\left(7 \, a^{3} b^{3} d \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{4} b^{2} - a^{3} b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(8 \, a^{5} b - 8 \, a^{4} b^{2} + 3 \, a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, a^{3} b^{3} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(2 \, a^{4} b^{2} - a^{3} b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, a^{3} b^{3} d \cosh\left(d x + c\right)^{4} + 30 \, {\left(2 \, a^{4} b^{2} - a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + {\left(8 \, a^{5} b - 8 \, a^{4} b^{2} + 3 \, a^{3} b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(2 \, a^{4} b^{2} - a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, a^{3} b^{3} d \cosh\left(d x + c\right)^{5} + 10 \, {\left(2 \, a^{4} b^{2} - a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{5} b - 8 \, a^{4} b^{2} + 3 \, a^{3} b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, a^{3} b^{3} d \cosh\left(d x + c\right)^{6} + 15 \, {\left(2 \, a^{4} b^{2} - a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(8 \, a^{5} b - 8 \, a^{4} b^{2} + 3 \, a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{4} b^{2} - a^{3} b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left(a^{3} b^{3} d \cosh\left(d x + c\right)^{7} + 3 \, {\left(2 \, a^{4} b^{2} - a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{5} + {\left(8 \, a^{5} b - 8 \, a^{4} b^{2} + 3 \, a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{4} b^{2} - a^{3} b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}, \frac{6 \, a b^{2} \cosh\left(d x + c\right)^{7} + 42 \, a b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + 6 \, a b^{2} \sinh\left(d x + c\right)^{7} + 2 \, {\left(20 \, a^{2} b - 9 \, a b^{2}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(63 \, a b^{2} \cosh\left(d x + c\right)^{2} + 20 \, a^{2} b - 9 \, a b^{2}\right)} \sinh\left(d x + c\right)^{5} + 10 \, {\left(21 \, a b^{2} \cosh\left(d x + c\right)^{3} + {\left(20 \, a^{2} b - 9 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} - 6 \, a b^{2} \cosh\left(d x + c\right) - 2 \, {\left(20 \, a^{2} b - 9 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(105 \, a b^{2} \cosh\left(d x + c\right)^{4} - 20 \, a^{2} b + 9 \, a b^{2} + 10 \, {\left(20 \, a^{2} b - 9 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(63 \, a b^{2} \cosh\left(d x + c\right)^{5} + 10 \, {\left(20 \, a^{2} b - 9 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(20 \, a^{2} b - 9 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 3 \, {\left(b^{2} \cosh\left(d x + c\right)^{8} + 8 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + b^{2} \sinh\left(d x + c\right)^{8} + 4 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, b^{2} \cosh\left(d x + c\right)^{2} + 2 \, a b - b^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, b^{2} \cosh\left(d x + c\right)^{3} + 3 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, b^{2} \cosh\left(d x + c\right)^{4} + 30 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, b^{2} \cosh\left(d x + c\right)^{5} + 10 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, b^{2} \cosh\left(d x + c\right)^{6} + 15 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, a b - b^{2}\right)} \sinh\left(d x + c\right)^{2} + b^{2} + 8 \, {\left(b^{2} \cosh\left(d x + c\right)^{7} + 3 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{5} + {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{a b} \arctan\left(\frac{\sqrt{a b} {\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right)}}{2 \, a}\right) + 3 \, {\left(b^{2} \cosh\left(d x + c\right)^{8} + 8 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + b^{2} \sinh\left(d x + c\right)^{8} + 4 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, b^{2} \cosh\left(d x + c\right)^{2} + 2 \, a b - b^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, b^{2} \cosh\left(d x + c\right)^{3} + 3 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, b^{2} \cosh\left(d x + c\right)^{4} + 30 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, b^{2} \cosh\left(d x + c\right)^{5} + 10 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, b^{2} \cosh\left(d x + c\right)^{6} + 15 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, a b - b^{2}\right)} \sinh\left(d x + c\right)^{2} + b^{2} + 8 \, {\left(b^{2} \cosh\left(d x + c\right)^{7} + 3 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{5} + {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{a b} \arctan\left(\frac{{\left(b \cosh\left(d x + c\right)^{3} + 3 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{3} + {\left(4 \, a - b\right)} \cosh\left(d x + c\right) + {\left(3 \, b \cosh\left(d x + c\right)^{2} + 4 \, a - b\right)} \sinh\left(d x + c\right)\right)} \sqrt{a b}}{2 \, a b}\right) + 2 \, {\left(21 \, a b^{2} \cosh\left(d x + c\right)^{6} + 5 \, {\left(20 \, a^{2} b - 9 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} - 3 \, a b^{2} - 3 \, {\left(20 \, a^{2} b - 9 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)}{8 \, {\left(a^{3} b^{3} d \cosh\left(d x + c\right)^{8} + 8 \, a^{3} b^{3} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + a^{3} b^{3} d \sinh\left(d x + c\right)^{8} + 4 \, {\left(2 \, a^{4} b^{2} - a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{6} + a^{3} b^{3} d + 4 \, {\left(7 \, a^{3} b^{3} d \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{4} b^{2} - a^{3} b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(8 \, a^{5} b - 8 \, a^{4} b^{2} + 3 \, a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, a^{3} b^{3} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(2 \, a^{4} b^{2} - a^{3} b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, a^{3} b^{3} d \cosh\left(d x + c\right)^{4} + 30 \, {\left(2 \, a^{4} b^{2} - a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + {\left(8 \, a^{5} b - 8 \, a^{4} b^{2} + 3 \, a^{3} b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(2 \, a^{4} b^{2} - a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, a^{3} b^{3} d \cosh\left(d x + c\right)^{5} + 10 \, {\left(2 \, a^{4} b^{2} - a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{5} b - 8 \, a^{4} b^{2} + 3 \, a^{3} b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, a^{3} b^{3} d \cosh\left(d x + c\right)^{6} + 15 \, {\left(2 \, a^{4} b^{2} - a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(8 \, a^{5} b - 8 \, a^{4} b^{2} + 3 \, a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{4} b^{2} - a^{3} b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left(a^{3} b^{3} d \cosh\left(d x + c\right)^{7} + 3 \, {\left(2 \, a^{4} b^{2} - a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{5} + {\left(8 \, a^{5} b - 8 \, a^{4} b^{2} + 3 \, a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{4} b^{2} - a^{3} b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[1/16*(12*a*b^2*cosh(d*x + c)^7 + 84*a*b^2*cosh(d*x + c)*sinh(d*x + c)^6 + 12*a*b^2*sinh(d*x + c)^7 + 4*(20*a^2*b - 9*a*b^2)*cosh(d*x + c)^5 + 4*(63*a*b^2*cosh(d*x + c)^2 + 20*a^2*b - 9*a*b^2)*sinh(d*x + c)^5 + 20*(21*a*b^2*cosh(d*x + c)^3 + (20*a^2*b - 9*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^4 - 12*a*b^2*cosh(d*x + c) - 4*(20*a^2*b - 9*a*b^2)*cosh(d*x + c)^3 + 4*(105*a*b^2*cosh(d*x + c)^4 - 20*a^2*b + 9*a*b^2 + 10*(20*a^2*b - 9*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 4*(63*a*b^2*cosh(d*x + c)^5 + 10*(20*a^2*b - 9*a*b^2)*cosh(d*x + c)^3 - 3*(20*a^2*b - 9*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^2 - 3*(b^2*cosh(d*x + c)^8 + 8*b^2*cosh(d*x + c)*sinh(d*x + c)^7 + b^2*sinh(d*x + c)^8 + 4*(2*a*b - b^2)*cosh(d*x + c)^6 + 4*(7*b^2*cosh(d*x + c)^2 + 2*a*b - b^2)*sinh(d*x + c)^6 + 8*(7*b^2*cosh(d*x + c)^3 + 3*(2*a*b - b^2)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(8*a^2 - 8*a*b + 3*b^2)*cosh(d*x + c)^4 + 2*(35*b^2*cosh(d*x + c)^4 + 30*(2*a*b - b^2)*cosh(d*x + c)^2 + 8*a^2 - 8*a*b + 3*b^2)*sinh(d*x + c)^4 + 8*(7*b^2*cosh(d*x + c)^5 + 10*(2*a*b - b^2)*cosh(d*x + c)^3 + (8*a^2 - 8*a*b + 3*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(2*a*b - b^2)*cosh(d*x + c)^2 + 4*(7*b^2*cosh(d*x + c)^6 + 15*(2*a*b - b^2)*cosh(d*x + c)^4 + 3*(8*a^2 - 8*a*b + 3*b^2)*cosh(d*x + c)^2 + 2*a*b - b^2)*sinh(d*x + c)^2 + b^2 + 8*(b^2*cosh(d*x + c)^7 + 3*(2*a*b - b^2)*cosh(d*x + c)^5 + (8*a^2 - 8*a*b + 3*b^2)*cosh(d*x + c)^3 + (2*a*b - b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-a*b)*log((b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 - 2*(2*a + b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 - 2*a - b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 - (2*a + b)*cosh(d*x + c))*sinh(d*x + c) - 4*(cosh(d*x + c)^3 + 3*cosh(d*x + c)*sinh(d*x + c)^2 + sinh(d*x + c)^3 + (3*cosh(d*x + c)^2 - 1)*sinh(d*x + c) - cosh(d*x + c))*sqrt(-a*b) + b)/(b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 + 2*(2*a - b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 + 2*a - b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 + (2*a - b)*cosh(d*x + c))*sinh(d*x + c) + b)) + 4*(21*a*b^2*cosh(d*x + c)^6 + 5*(20*a^2*b - 9*a*b^2)*cosh(d*x + c)^4 - 3*a*b^2 - 3*(20*a^2*b - 9*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c))/(a^3*b^3*d*cosh(d*x + c)^8 + 8*a^3*b^3*d*cosh(d*x + c)*sinh(d*x + c)^7 + a^3*b^3*d*sinh(d*x + c)^8 + 4*(2*a^4*b^2 - a^3*b^3)*d*cosh(d*x + c)^6 + a^3*b^3*d + 4*(7*a^3*b^3*d*cosh(d*x + c)^2 + (2*a^4*b^2 - a^3*b^3)*d)*sinh(d*x + c)^6 + 2*(8*a^5*b - 8*a^4*b^2 + 3*a^3*b^3)*d*cosh(d*x + c)^4 + 8*(7*a^3*b^3*d*cosh(d*x + c)^3 + 3*(2*a^4*b^2 - a^3*b^3)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*a^3*b^3*d*cosh(d*x + c)^4 + 30*(2*a^4*b^2 - a^3*b^3)*d*cosh(d*x + c)^2 + (8*a^5*b - 8*a^4*b^2 + 3*a^3*b^3)*d)*sinh(d*x + c)^4 + 4*(2*a^4*b^2 - a^3*b^3)*d*cosh(d*x + c)^2 + 8*(7*a^3*b^3*d*cosh(d*x + c)^5 + 10*(2*a^4*b^2 - a^3*b^3)*d*cosh(d*x + c)^3 + (8*a^5*b - 8*a^4*b^2 + 3*a^3*b^3)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*a^3*b^3*d*cosh(d*x + c)^6 + 15*(2*a^4*b^2 - a^3*b^3)*d*cosh(d*x + c)^4 + 3*(8*a^5*b - 8*a^4*b^2 + 3*a^3*b^3)*d*cosh(d*x + c)^2 + (2*a^4*b^2 - a^3*b^3)*d)*sinh(d*x + c)^2 + 8*(a^3*b^3*d*cosh(d*x + c)^7 + 3*(2*a^4*b^2 - a^3*b^3)*d*cosh(d*x + c)^5 + (8*a^5*b - 8*a^4*b^2 + 3*a^3*b^3)*d*cosh(d*x + c)^3 + (2*a^4*b^2 - a^3*b^3)*d*cosh(d*x + c))*sinh(d*x + c)), 1/8*(6*a*b^2*cosh(d*x + c)^7 + 42*a*b^2*cosh(d*x + c)*sinh(d*x + c)^6 + 6*a*b^2*sinh(d*x + c)^7 + 2*(20*a^2*b - 9*a*b^2)*cosh(d*x + c)^5 + 2*(63*a*b^2*cosh(d*x + c)^2 + 20*a^2*b - 9*a*b^2)*sinh(d*x + c)^5 + 10*(21*a*b^2*cosh(d*x + c)^3 + (20*a^2*b - 9*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^4 - 6*a*b^2*cosh(d*x + c) - 2*(20*a^2*b - 9*a*b^2)*cosh(d*x + c)^3 + 2*(105*a*b^2*cosh(d*x + c)^4 - 20*a^2*b + 9*a*b^2 + 10*(20*a^2*b - 9*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 2*(63*a*b^2*cosh(d*x + c)^5 + 10*(20*a^2*b - 9*a*b^2)*cosh(d*x + c)^3 - 3*(20*a^2*b - 9*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^2 + 3*(b^2*cosh(d*x + c)^8 + 8*b^2*cosh(d*x + c)*sinh(d*x + c)^7 + b^2*sinh(d*x + c)^8 + 4*(2*a*b - b^2)*cosh(d*x + c)^6 + 4*(7*b^2*cosh(d*x + c)^2 + 2*a*b - b^2)*sinh(d*x + c)^6 + 8*(7*b^2*cosh(d*x + c)^3 + 3*(2*a*b - b^2)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(8*a^2 - 8*a*b + 3*b^2)*cosh(d*x + c)^4 + 2*(35*b^2*cosh(d*x + c)^4 + 30*(2*a*b - b^2)*cosh(d*x + c)^2 + 8*a^2 - 8*a*b + 3*b^2)*sinh(d*x + c)^4 + 8*(7*b^2*cosh(d*x + c)^5 + 10*(2*a*b - b^2)*cosh(d*x + c)^3 + (8*a^2 - 8*a*b + 3*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(2*a*b - b^2)*cosh(d*x + c)^2 + 4*(7*b^2*cosh(d*x + c)^6 + 15*(2*a*b - b^2)*cosh(d*x + c)^4 + 3*(8*a^2 - 8*a*b + 3*b^2)*cosh(d*x + c)^2 + 2*a*b - b^2)*sinh(d*x + c)^2 + b^2 + 8*(b^2*cosh(d*x + c)^7 + 3*(2*a*b - b^2)*cosh(d*x + c)^5 + (8*a^2 - 8*a*b + 3*b^2)*cosh(d*x + c)^3 + (2*a*b - b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(a*b)*arctan(1/2*sqrt(a*b)*(cosh(d*x + c) + sinh(d*x + c))/a) + 3*(b^2*cosh(d*x + c)^8 + 8*b^2*cosh(d*x + c)*sinh(d*x + c)^7 + b^2*sinh(d*x + c)^8 + 4*(2*a*b - b^2)*cosh(d*x + c)^6 + 4*(7*b^2*cosh(d*x + c)^2 + 2*a*b - b^2)*sinh(d*x + c)^6 + 8*(7*b^2*cosh(d*x + c)^3 + 3*(2*a*b - b^2)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(8*a^2 - 8*a*b + 3*b^2)*cosh(d*x + c)^4 + 2*(35*b^2*cosh(d*x + c)^4 + 30*(2*a*b - b^2)*cosh(d*x + c)^2 + 8*a^2 - 8*a*b + 3*b^2)*sinh(d*x + c)^4 + 8*(7*b^2*cosh(d*x + c)^5 + 10*(2*a*b - b^2)*cosh(d*x + c)^3 + (8*a^2 - 8*a*b + 3*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(2*a*b - b^2)*cosh(d*x + c)^2 + 4*(7*b^2*cosh(d*x + c)^6 + 15*(2*a*b - b^2)*cosh(d*x + c)^4 + 3*(8*a^2 - 8*a*b + 3*b^2)*cosh(d*x + c)^2 + 2*a*b - b^2)*sinh(d*x + c)^2 + b^2 + 8*(b^2*cosh(d*x + c)^7 + 3*(2*a*b - b^2)*cosh(d*x + c)^5 + (8*a^2 - 8*a*b + 3*b^2)*cosh(d*x + c)^3 + (2*a*b - b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(a*b)*arctan(1/2*(b*cosh(d*x + c)^3 + 3*b*cosh(d*x + c)*sinh(d*x + c)^2 + b*sinh(d*x + c)^3 + (4*a - b)*cosh(d*x + c) + (3*b*cosh(d*x + c)^2 + 4*a - b)*sinh(d*x + c))*sqrt(a*b)/(a*b)) + 2*(21*a*b^2*cosh(d*x + c)^6 + 5*(20*a^2*b - 9*a*b^2)*cosh(d*x + c)^4 - 3*a*b^2 - 3*(20*a^2*b - 9*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c))/(a^3*b^3*d*cosh(d*x + c)^8 + 8*a^3*b^3*d*cosh(d*x + c)*sinh(d*x + c)^7 + a^3*b^3*d*sinh(d*x + c)^8 + 4*(2*a^4*b^2 - a^3*b^3)*d*cosh(d*x + c)^6 + a^3*b^3*d + 4*(7*a^3*b^3*d*cosh(d*x + c)^2 + (2*a^4*b^2 - a^3*b^3)*d)*sinh(d*x + c)^6 + 2*(8*a^5*b - 8*a^4*b^2 + 3*a^3*b^3)*d*cosh(d*x + c)^4 + 8*(7*a^3*b^3*d*cosh(d*x + c)^3 + 3*(2*a^4*b^2 - a^3*b^3)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*a^3*b^3*d*cosh(d*x + c)^4 + 30*(2*a^4*b^2 - a^3*b^3)*d*cosh(d*x + c)^2 + (8*a^5*b - 8*a^4*b^2 + 3*a^3*b^3)*d)*sinh(d*x + c)^4 + 4*(2*a^4*b^2 - a^3*b^3)*d*cosh(d*x + c)^2 + 8*(7*a^3*b^3*d*cosh(d*x + c)^5 + 10*(2*a^4*b^2 - a^3*b^3)*d*cosh(d*x + c)^3 + (8*a^5*b - 8*a^4*b^2 + 3*a^3*b^3)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*a^3*b^3*d*cosh(d*x + c)^6 + 15*(2*a^4*b^2 - a^3*b^3)*d*cosh(d*x + c)^4 + 3*(8*a^5*b - 8*a^4*b^2 + 3*a^3*b^3)*d*cosh(d*x + c)^2 + (2*a^4*b^2 - a^3*b^3)*d)*sinh(d*x + c)^2 + 8*(a^3*b^3*d*cosh(d*x + c)^7 + 3*(2*a^4*b^2 - a^3*b^3)*d*cosh(d*x + c)^5 + (8*a^5*b - 8*a^4*b^2 + 3*a^3*b^3)*d*cosh(d*x + c)^3 + (2*a^4*b^2 - a^3*b^3)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
345,1,8083,0,0.741898," ","integrate(sech(d*x+c)/(a+b*sinh(d*x+c)^2)^3,x, algorithm=""fricas"")","\left[-\frac{4 \, {\left(7 \, a^{2} b^{2} - 10 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{7} + 28 \, {\left(7 \, a^{2} b^{2} - 10 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + 4 \, {\left(7 \, a^{2} b^{2} - 10 \, a b^{3} + 3 \, b^{4}\right)} \sinh\left(d x + c\right)^{7} + 4 \, {\left(36 \, a^{3} b - 77 \, a^{2} b^{2} + 50 \, a b^{3} - 9 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + 4 \, {\left(36 \, a^{3} b - 77 \, a^{2} b^{2} + 50 \, a b^{3} - 9 \, b^{4} + 21 \, {\left(7 \, a^{2} b^{2} - 10 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{5} + 20 \, {\left(7 \, {\left(7 \, a^{2} b^{2} - 10 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(36 \, a^{3} b - 77 \, a^{2} b^{2} + 50 \, a b^{3} - 9 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} - 4 \, {\left(36 \, a^{3} b - 77 \, a^{2} b^{2} + 50 \, a b^{3} - 9 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(35 \, {\left(7 \, a^{2} b^{2} - 10 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} - 36 \, a^{3} b + 77 \, a^{2} b^{2} - 50 \, a b^{3} + 9 \, b^{4} + 10 \, {\left(36 \, a^{3} b - 77 \, a^{2} b^{2} + 50 \, a b^{3} - 9 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(21 \, {\left(7 \, a^{2} b^{2} - 10 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(36 \, a^{3} b - 77 \, a^{2} b^{2} + 50 \, a b^{3} - 9 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(36 \, a^{3} b - 77 \, a^{2} b^{2} + 50 \, a b^{3} - 9 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(15 \, a^{2} b^{2} - 10 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(15 \, a^{2} b^{2} - 10 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(15 \, a^{2} b^{2} - 10 \, a b^{3} + 3 \, b^{4}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(30 \, a^{3} b - 35 \, a^{2} b^{2} + 16 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(30 \, a^{3} b - 35 \, a^{2} b^{2} + 16 \, a b^{3} - 3 \, b^{4} + 7 \, {\left(15 \, a^{2} b^{2} - 10 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(15 \, a^{2} b^{2} - 10 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(30 \, a^{3} b - 35 \, a^{2} b^{2} + 16 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(120 \, a^{4} - 200 \, a^{3} b + 149 \, a^{2} b^{2} - 54 \, a b^{3} + 9 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(15 \, a^{2} b^{2} - 10 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 120 \, a^{4} - 200 \, a^{3} b + 149 \, a^{2} b^{2} - 54 \, a b^{3} + 9 \, b^{4} + 30 \, {\left(30 \, a^{3} b - 35 \, a^{2} b^{2} + 16 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 15 \, a^{2} b^{2} - 10 \, a b^{3} + 3 \, b^{4} + 8 \, {\left(7 \, {\left(15 \, a^{2} b^{2} - 10 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(30 \, a^{3} b - 35 \, a^{2} b^{2} + 16 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(120 \, a^{4} - 200 \, a^{3} b + 149 \, a^{2} b^{2} - 54 \, a b^{3} + 9 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(30 \, a^{3} b - 35 \, a^{2} b^{2} + 16 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(15 \, a^{2} b^{2} - 10 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(30 \, a^{3} b - 35 \, a^{2} b^{2} + 16 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 30 \, a^{3} b - 35 \, a^{2} b^{2} + 16 \, a b^{3} - 3 \, b^{4} + 3 \, {\left(120 \, a^{4} - 200 \, a^{3} b + 149 \, a^{2} b^{2} - 54 \, a b^{3} + 9 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left({\left(15 \, a^{2} b^{2} - 10 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(30 \, a^{3} b - 35 \, a^{2} b^{2} + 16 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + {\left(120 \, a^{4} - 200 \, a^{3} b + 149 \, a^{2} b^{2} - 54 \, a b^{3} + 9 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(30 \, a^{3} b - 35 \, a^{2} b^{2} + 16 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} - 2 \, {\left(2 \, a + b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} - 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} - {\left(2 \, a + b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + 4 \, {\left(a \cosh\left(d x + c\right)^{3} + 3 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + a \sinh\left(d x + c\right)^{3} - a \cosh\left(d x + c\right) + {\left(3 \, a \cosh\left(d x + c\right)^{2} - a\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{b}{a}} + b}{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b}\right) - 32 \, {\left(a^{2} b^{2} \cosh\left(d x + c\right)^{8} + 8 \, a^{2} b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + a^{2} b^{2} \sinh\left(d x + c\right)^{8} + 4 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, a^{2} b^{2} \cosh\left(d x + c\right)^{2} + 2 \, a^{3} b - a^{2} b^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, a^{2} b^{2} \cosh\left(d x + c\right)^{3} + 3 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(8 \, a^{4} - 8 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, a^{2} b^{2} \cosh\left(d x + c\right)^{4} + 8 \, a^{4} - 8 \, a^{3} b + 3 \, a^{2} b^{2} + 30 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + a^{2} b^{2} + 8 \, {\left(7 \, a^{2} b^{2} \cosh\left(d x + c\right)^{5} + 10 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{4} - 8 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, a^{2} b^{2} \cosh\left(d x + c\right)^{6} + 15 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, a^{3} b - a^{2} b^{2} + 3 \, {\left(8 \, a^{4} - 8 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left(a^{2} b^{2} \cosh\left(d x + c\right)^{7} + 3 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{5} + {\left(8 \, a^{4} - 8 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{3} b - a^{2} b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \arctan\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) - 4 \, {\left(7 \, a^{2} b^{2} - 10 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right) + 4 \, {\left(7 \, {\left(7 \, a^{2} b^{2} - 10 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 5 \, {\left(36 \, a^{3} b - 77 \, a^{2} b^{2} + 50 \, a b^{3} - 9 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} - 7 \, a^{2} b^{2} + 10 \, a b^{3} - 3 \, b^{4} - 3 \, {\left(36 \, a^{3} b - 77 \, a^{2} b^{2} + 50 \, a b^{3} - 9 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)}{16 \, {\left({\left(a^{5} b^{2} - 3 \, a^{4} b^{3} + 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{5} b^{2} - 3 \, a^{4} b^{3} + 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{5} b^{2} - 3 \, a^{4} b^{3} + 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} d \sinh\left(d x + c\right)^{8} + 4 \, {\left(2 \, a^{6} b - 7 \, a^{5} b^{2} + 9 \, a^{4} b^{3} - 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{5} b^{2} - 3 \, a^{4} b^{3} + 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{6} b - 7 \, a^{5} b^{2} + 9 \, a^{4} b^{3} - 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(8 \, a^{7} - 32 \, a^{6} b + 51 \, a^{5} b^{2} - 41 \, a^{4} b^{3} + 17 \, a^{3} b^{4} - 3 \, a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{5} b^{2} - 3 \, a^{4} b^{3} + 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(2 \, a^{6} b - 7 \, a^{5} b^{2} + 9 \, a^{4} b^{3} - 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a^{5} b^{2} - 3 \, a^{4} b^{3} + 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 30 \, {\left(2 \, a^{6} b - 7 \, a^{5} b^{2} + 9 \, a^{4} b^{3} - 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(8 \, a^{7} - 32 \, a^{6} b + 51 \, a^{5} b^{2} - 41 \, a^{4} b^{3} + 17 \, a^{3} b^{4} - 3 \, a^{2} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(2 \, a^{6} b - 7 \, a^{5} b^{2} + 9 \, a^{4} b^{3} - 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a^{5} b^{2} - 3 \, a^{4} b^{3} + 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{5} + 10 \, {\left(2 \, a^{6} b - 7 \, a^{5} b^{2} + 9 \, a^{4} b^{3} - 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{7} - 32 \, a^{6} b + 51 \, a^{5} b^{2} - 41 \, a^{4} b^{3} + 17 \, a^{3} b^{4} - 3 \, a^{2} b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a^{5} b^{2} - 3 \, a^{4} b^{3} + 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{6} + 15 \, {\left(2 \, a^{6} b - 7 \, a^{5} b^{2} + 9 \, a^{4} b^{3} - 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(8 \, a^{7} - 32 \, a^{6} b + 51 \, a^{5} b^{2} - 41 \, a^{4} b^{3} + 17 \, a^{3} b^{4} - 3 \, a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{6} b - 7 \, a^{5} b^{2} + 9 \, a^{4} b^{3} - 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{5} b^{2} - 3 \, a^{4} b^{3} + 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} d + 8 \, {\left({\left(a^{5} b^{2} - 3 \, a^{4} b^{3} + 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{7} + 3 \, {\left(2 \, a^{6} b - 7 \, a^{5} b^{2} + 9 \, a^{4} b^{3} - 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{5} + {\left(8 \, a^{7} - 32 \, a^{6} b + 51 \, a^{5} b^{2} - 41 \, a^{4} b^{3} + 17 \, a^{3} b^{4} - 3 \, a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{6} b - 7 \, a^{5} b^{2} + 9 \, a^{4} b^{3} - 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}, -\frac{2 \, {\left(7 \, a^{2} b^{2} - 10 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{7} + 14 \, {\left(7 \, a^{2} b^{2} - 10 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + 2 \, {\left(7 \, a^{2} b^{2} - 10 \, a b^{3} + 3 \, b^{4}\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(36 \, a^{3} b - 77 \, a^{2} b^{2} + 50 \, a b^{3} - 9 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(36 \, a^{3} b - 77 \, a^{2} b^{2} + 50 \, a b^{3} - 9 \, b^{4} + 21 \, {\left(7 \, a^{2} b^{2} - 10 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{5} + 10 \, {\left(7 \, {\left(7 \, a^{2} b^{2} - 10 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(36 \, a^{3} b - 77 \, a^{2} b^{2} + 50 \, a b^{3} - 9 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(36 \, a^{3} b - 77 \, a^{2} b^{2} + 50 \, a b^{3} - 9 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(35 \, {\left(7 \, a^{2} b^{2} - 10 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} - 36 \, a^{3} b + 77 \, a^{2} b^{2} - 50 \, a b^{3} + 9 \, b^{4} + 10 \, {\left(36 \, a^{3} b - 77 \, a^{2} b^{2} + 50 \, a b^{3} - 9 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(21 \, {\left(7 \, a^{2} b^{2} - 10 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(36 \, a^{3} b - 77 \, a^{2} b^{2} + 50 \, a b^{3} - 9 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(36 \, a^{3} b - 77 \, a^{2} b^{2} + 50 \, a b^{3} - 9 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(15 \, a^{2} b^{2} - 10 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(15 \, a^{2} b^{2} - 10 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(15 \, a^{2} b^{2} - 10 \, a b^{3} + 3 \, b^{4}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(30 \, a^{3} b - 35 \, a^{2} b^{2} + 16 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(30 \, a^{3} b - 35 \, a^{2} b^{2} + 16 \, a b^{3} - 3 \, b^{4} + 7 \, {\left(15 \, a^{2} b^{2} - 10 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(15 \, a^{2} b^{2} - 10 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(30 \, a^{3} b - 35 \, a^{2} b^{2} + 16 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(120 \, a^{4} - 200 \, a^{3} b + 149 \, a^{2} b^{2} - 54 \, a b^{3} + 9 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(15 \, a^{2} b^{2} - 10 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 120 \, a^{4} - 200 \, a^{3} b + 149 \, a^{2} b^{2} - 54 \, a b^{3} + 9 \, b^{4} + 30 \, {\left(30 \, a^{3} b - 35 \, a^{2} b^{2} + 16 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 15 \, a^{2} b^{2} - 10 \, a b^{3} + 3 \, b^{4} + 8 \, {\left(7 \, {\left(15 \, a^{2} b^{2} - 10 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(30 \, a^{3} b - 35 \, a^{2} b^{2} + 16 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(120 \, a^{4} - 200 \, a^{3} b + 149 \, a^{2} b^{2} - 54 \, a b^{3} + 9 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(30 \, a^{3} b - 35 \, a^{2} b^{2} + 16 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(15 \, a^{2} b^{2} - 10 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(30 \, a^{3} b - 35 \, a^{2} b^{2} + 16 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 30 \, a^{3} b - 35 \, a^{2} b^{2} + 16 \, a b^{3} - 3 \, b^{4} + 3 \, {\left(120 \, a^{4} - 200 \, a^{3} b + 149 \, a^{2} b^{2} - 54 \, a b^{3} + 9 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left({\left(15 \, a^{2} b^{2} - 10 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(30 \, a^{3} b - 35 \, a^{2} b^{2} + 16 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + {\left(120 \, a^{4} - 200 \, a^{3} b + 149 \, a^{2} b^{2} - 54 \, a b^{3} + 9 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(30 \, a^{3} b - 35 \, a^{2} b^{2} + 16 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{b}{a}} \arctan\left(\frac{1}{2} \, \sqrt{\frac{b}{a}} {\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right)}\right) + {\left({\left(15 \, a^{2} b^{2} - 10 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(15 \, a^{2} b^{2} - 10 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(15 \, a^{2} b^{2} - 10 \, a b^{3} + 3 \, b^{4}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(30 \, a^{3} b - 35 \, a^{2} b^{2} + 16 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(30 \, a^{3} b - 35 \, a^{2} b^{2} + 16 \, a b^{3} - 3 \, b^{4} + 7 \, {\left(15 \, a^{2} b^{2} - 10 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(15 \, a^{2} b^{2} - 10 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(30 \, a^{3} b - 35 \, a^{2} b^{2} + 16 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(120 \, a^{4} - 200 \, a^{3} b + 149 \, a^{2} b^{2} - 54 \, a b^{3} + 9 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(15 \, a^{2} b^{2} - 10 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 120 \, a^{4} - 200 \, a^{3} b + 149 \, a^{2} b^{2} - 54 \, a b^{3} + 9 \, b^{4} + 30 \, {\left(30 \, a^{3} b - 35 \, a^{2} b^{2} + 16 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 15 \, a^{2} b^{2} - 10 \, a b^{3} + 3 \, b^{4} + 8 \, {\left(7 \, {\left(15 \, a^{2} b^{2} - 10 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(30 \, a^{3} b - 35 \, a^{2} b^{2} + 16 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(120 \, a^{4} - 200 \, a^{3} b + 149 \, a^{2} b^{2} - 54 \, a b^{3} + 9 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(30 \, a^{3} b - 35 \, a^{2} b^{2} + 16 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(15 \, a^{2} b^{2} - 10 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(30 \, a^{3} b - 35 \, a^{2} b^{2} + 16 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 30 \, a^{3} b - 35 \, a^{2} b^{2} + 16 \, a b^{3} - 3 \, b^{4} + 3 \, {\left(120 \, a^{4} - 200 \, a^{3} b + 149 \, a^{2} b^{2} - 54 \, a b^{3} + 9 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left({\left(15 \, a^{2} b^{2} - 10 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(30 \, a^{3} b - 35 \, a^{2} b^{2} + 16 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + {\left(120 \, a^{4} - 200 \, a^{3} b + 149 \, a^{2} b^{2} - 54 \, a b^{3} + 9 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(30 \, a^{3} b - 35 \, a^{2} b^{2} + 16 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{b}{a}} \arctan\left(\frac{{\left(b \cosh\left(d x + c\right)^{3} + 3 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + b \sinh\left(d x + c\right)^{3} + {\left(4 \, a - b\right)} \cosh\left(d x + c\right) + {\left(3 \, b \cosh\left(d x + c\right)^{2} + 4 \, a - b\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{b}{a}}}{2 \, b}\right) - 16 \, {\left(a^{2} b^{2} \cosh\left(d x + c\right)^{8} + 8 \, a^{2} b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + a^{2} b^{2} \sinh\left(d x + c\right)^{8} + 4 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, a^{2} b^{2} \cosh\left(d x + c\right)^{2} + 2 \, a^{3} b - a^{2} b^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, a^{2} b^{2} \cosh\left(d x + c\right)^{3} + 3 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(8 \, a^{4} - 8 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, a^{2} b^{2} \cosh\left(d x + c\right)^{4} + 8 \, a^{4} - 8 \, a^{3} b + 3 \, a^{2} b^{2} + 30 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + a^{2} b^{2} + 8 \, {\left(7 \, a^{2} b^{2} \cosh\left(d x + c\right)^{5} + 10 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{4} - 8 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, a^{2} b^{2} \cosh\left(d x + c\right)^{6} + 15 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, a^{3} b - a^{2} b^{2} + 3 \, {\left(8 \, a^{4} - 8 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left(a^{2} b^{2} \cosh\left(d x + c\right)^{7} + 3 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{5} + {\left(8 \, a^{4} - 8 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{3} b - a^{2} b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \arctan\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) - 2 \, {\left(7 \, a^{2} b^{2} - 10 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right) + 2 \, {\left(7 \, {\left(7 \, a^{2} b^{2} - 10 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 5 \, {\left(36 \, a^{3} b - 77 \, a^{2} b^{2} + 50 \, a b^{3} - 9 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} - 7 \, a^{2} b^{2} + 10 \, a b^{3} - 3 \, b^{4} - 3 \, {\left(36 \, a^{3} b - 77 \, a^{2} b^{2} + 50 \, a b^{3} - 9 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)}{8 \, {\left({\left(a^{5} b^{2} - 3 \, a^{4} b^{3} + 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{5} b^{2} - 3 \, a^{4} b^{3} + 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{5} b^{2} - 3 \, a^{4} b^{3} + 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} d \sinh\left(d x + c\right)^{8} + 4 \, {\left(2 \, a^{6} b - 7 \, a^{5} b^{2} + 9 \, a^{4} b^{3} - 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{5} b^{2} - 3 \, a^{4} b^{3} + 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{6} b - 7 \, a^{5} b^{2} + 9 \, a^{4} b^{3} - 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(8 \, a^{7} - 32 \, a^{6} b + 51 \, a^{5} b^{2} - 41 \, a^{4} b^{3} + 17 \, a^{3} b^{4} - 3 \, a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{5} b^{2} - 3 \, a^{4} b^{3} + 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(2 \, a^{6} b - 7 \, a^{5} b^{2} + 9 \, a^{4} b^{3} - 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a^{5} b^{2} - 3 \, a^{4} b^{3} + 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 30 \, {\left(2 \, a^{6} b - 7 \, a^{5} b^{2} + 9 \, a^{4} b^{3} - 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(8 \, a^{7} - 32 \, a^{6} b + 51 \, a^{5} b^{2} - 41 \, a^{4} b^{3} + 17 \, a^{3} b^{4} - 3 \, a^{2} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(2 \, a^{6} b - 7 \, a^{5} b^{2} + 9 \, a^{4} b^{3} - 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a^{5} b^{2} - 3 \, a^{4} b^{3} + 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{5} + 10 \, {\left(2 \, a^{6} b - 7 \, a^{5} b^{2} + 9 \, a^{4} b^{3} - 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{7} - 32 \, a^{6} b + 51 \, a^{5} b^{2} - 41 \, a^{4} b^{3} + 17 \, a^{3} b^{4} - 3 \, a^{2} b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a^{5} b^{2} - 3 \, a^{4} b^{3} + 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{6} + 15 \, {\left(2 \, a^{6} b - 7 \, a^{5} b^{2} + 9 \, a^{4} b^{3} - 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(8 \, a^{7} - 32 \, a^{6} b + 51 \, a^{5} b^{2} - 41 \, a^{4} b^{3} + 17 \, a^{3} b^{4} - 3 \, a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(2 \, a^{6} b - 7 \, a^{5} b^{2} + 9 \, a^{4} b^{3} - 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{5} b^{2} - 3 \, a^{4} b^{3} + 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} d + 8 \, {\left({\left(a^{5} b^{2} - 3 \, a^{4} b^{3} + 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{7} + 3 \, {\left(2 \, a^{6} b - 7 \, a^{5} b^{2} + 9 \, a^{4} b^{3} - 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{5} + {\left(8 \, a^{7} - 32 \, a^{6} b + 51 \, a^{5} b^{2} - 41 \, a^{4} b^{3} + 17 \, a^{3} b^{4} - 3 \, a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{6} b - 7 \, a^{5} b^{2} + 9 \, a^{4} b^{3} - 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[-1/16*(4*(7*a^2*b^2 - 10*a*b^3 + 3*b^4)*cosh(d*x + c)^7 + 28*(7*a^2*b^2 - 10*a*b^3 + 3*b^4)*cosh(d*x + c)*sinh(d*x + c)^6 + 4*(7*a^2*b^2 - 10*a*b^3 + 3*b^4)*sinh(d*x + c)^7 + 4*(36*a^3*b - 77*a^2*b^2 + 50*a*b^3 - 9*b^4)*cosh(d*x + c)^5 + 4*(36*a^3*b - 77*a^2*b^2 + 50*a*b^3 - 9*b^4 + 21*(7*a^2*b^2 - 10*a*b^3 + 3*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 20*(7*(7*a^2*b^2 - 10*a*b^3 + 3*b^4)*cosh(d*x + c)^3 + (36*a^3*b - 77*a^2*b^2 + 50*a*b^3 - 9*b^4)*cosh(d*x + c))*sinh(d*x + c)^4 - 4*(36*a^3*b - 77*a^2*b^2 + 50*a*b^3 - 9*b^4)*cosh(d*x + c)^3 + 4*(35*(7*a^2*b^2 - 10*a*b^3 + 3*b^4)*cosh(d*x + c)^4 - 36*a^3*b + 77*a^2*b^2 - 50*a*b^3 + 9*b^4 + 10*(36*a^3*b - 77*a^2*b^2 + 50*a*b^3 - 9*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 4*(21*(7*a^2*b^2 - 10*a*b^3 + 3*b^4)*cosh(d*x + c)^5 + 10*(36*a^3*b - 77*a^2*b^2 + 50*a*b^3 - 9*b^4)*cosh(d*x + c)^3 - 3*(36*a^3*b - 77*a^2*b^2 + 50*a*b^3 - 9*b^4)*cosh(d*x + c))*sinh(d*x + c)^2 + ((15*a^2*b^2 - 10*a*b^3 + 3*b^4)*cosh(d*x + c)^8 + 8*(15*a^2*b^2 - 10*a*b^3 + 3*b^4)*cosh(d*x + c)*sinh(d*x + c)^7 + (15*a^2*b^2 - 10*a*b^3 + 3*b^4)*sinh(d*x + c)^8 + 4*(30*a^3*b - 35*a^2*b^2 + 16*a*b^3 - 3*b^4)*cosh(d*x + c)^6 + 4*(30*a^3*b - 35*a^2*b^2 + 16*a*b^3 - 3*b^4 + 7*(15*a^2*b^2 - 10*a*b^3 + 3*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(15*a^2*b^2 - 10*a*b^3 + 3*b^4)*cosh(d*x + c)^3 + 3*(30*a^3*b - 35*a^2*b^2 + 16*a*b^3 - 3*b^4)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(120*a^4 - 200*a^3*b + 149*a^2*b^2 - 54*a*b^3 + 9*b^4)*cosh(d*x + c)^4 + 2*(35*(15*a^2*b^2 - 10*a*b^3 + 3*b^4)*cosh(d*x + c)^4 + 120*a^4 - 200*a^3*b + 149*a^2*b^2 - 54*a*b^3 + 9*b^4 + 30*(30*a^3*b - 35*a^2*b^2 + 16*a*b^3 - 3*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 15*a^2*b^2 - 10*a*b^3 + 3*b^4 + 8*(7*(15*a^2*b^2 - 10*a*b^3 + 3*b^4)*cosh(d*x + c)^5 + 10*(30*a^3*b - 35*a^2*b^2 + 16*a*b^3 - 3*b^4)*cosh(d*x + c)^3 + (120*a^4 - 200*a^3*b + 149*a^2*b^2 - 54*a*b^3 + 9*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(30*a^3*b - 35*a^2*b^2 + 16*a*b^3 - 3*b^4)*cosh(d*x + c)^2 + 4*(7*(15*a^2*b^2 - 10*a*b^3 + 3*b^4)*cosh(d*x + c)^6 + 15*(30*a^3*b - 35*a^2*b^2 + 16*a*b^3 - 3*b^4)*cosh(d*x + c)^4 + 30*a^3*b - 35*a^2*b^2 + 16*a*b^3 - 3*b^4 + 3*(120*a^4 - 200*a^3*b + 149*a^2*b^2 - 54*a*b^3 + 9*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((15*a^2*b^2 - 10*a*b^3 + 3*b^4)*cosh(d*x + c)^7 + 3*(30*a^3*b - 35*a^2*b^2 + 16*a*b^3 - 3*b^4)*cosh(d*x + c)^5 + (120*a^4 - 200*a^3*b + 149*a^2*b^2 - 54*a*b^3 + 9*b^4)*cosh(d*x + c)^3 + (30*a^3*b - 35*a^2*b^2 + 16*a*b^3 - 3*b^4)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-b/a)*log((b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 - 2*(2*a + b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 - 2*a - b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 - (2*a + b)*cosh(d*x + c))*sinh(d*x + c) + 4*(a*cosh(d*x + c)^3 + 3*a*cosh(d*x + c)*sinh(d*x + c)^2 + a*sinh(d*x + c)^3 - a*cosh(d*x + c) + (3*a*cosh(d*x + c)^2 - a)*sinh(d*x + c))*sqrt(-b/a) + b)/(b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 + 2*(2*a - b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 + 2*a - b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 + (2*a - b)*cosh(d*x + c))*sinh(d*x + c) + b)) - 32*(a^2*b^2*cosh(d*x + c)^8 + 8*a^2*b^2*cosh(d*x + c)*sinh(d*x + c)^7 + a^2*b^2*sinh(d*x + c)^8 + 4*(2*a^3*b - a^2*b^2)*cosh(d*x + c)^6 + 4*(7*a^2*b^2*cosh(d*x + c)^2 + 2*a^3*b - a^2*b^2)*sinh(d*x + c)^6 + 8*(7*a^2*b^2*cosh(d*x + c)^3 + 3*(2*a^3*b - a^2*b^2)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(8*a^4 - 8*a^3*b + 3*a^2*b^2)*cosh(d*x + c)^4 + 2*(35*a^2*b^2*cosh(d*x + c)^4 + 8*a^4 - 8*a^3*b + 3*a^2*b^2 + 30*(2*a^3*b - a^2*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + a^2*b^2 + 8*(7*a^2*b^2*cosh(d*x + c)^5 + 10*(2*a^3*b - a^2*b^2)*cosh(d*x + c)^3 + (8*a^4 - 8*a^3*b + 3*a^2*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(2*a^3*b - a^2*b^2)*cosh(d*x + c)^2 + 4*(7*a^2*b^2*cosh(d*x + c)^6 + 15*(2*a^3*b - a^2*b^2)*cosh(d*x + c)^4 + 2*a^3*b - a^2*b^2 + 3*(8*a^4 - 8*a^3*b + 3*a^2*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*(a^2*b^2*cosh(d*x + c)^7 + 3*(2*a^3*b - a^2*b^2)*cosh(d*x + c)^5 + (8*a^4 - 8*a^3*b + 3*a^2*b^2)*cosh(d*x + c)^3 + (2*a^3*b - a^2*b^2)*cosh(d*x + c))*sinh(d*x + c))*arctan(cosh(d*x + c) + sinh(d*x + c)) - 4*(7*a^2*b^2 - 10*a*b^3 + 3*b^4)*cosh(d*x + c) + 4*(7*(7*a^2*b^2 - 10*a*b^3 + 3*b^4)*cosh(d*x + c)^6 + 5*(36*a^3*b - 77*a^2*b^2 + 50*a*b^3 - 9*b^4)*cosh(d*x + c)^4 - 7*a^2*b^2 + 10*a*b^3 - 3*b^4 - 3*(36*a^3*b - 77*a^2*b^2 + 50*a*b^3 - 9*b^4)*cosh(d*x + c)^2)*sinh(d*x + c))/((a^5*b^2 - 3*a^4*b^3 + 3*a^3*b^4 - a^2*b^5)*d*cosh(d*x + c)^8 + 8*(a^5*b^2 - 3*a^4*b^3 + 3*a^3*b^4 - a^2*b^5)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^5*b^2 - 3*a^4*b^3 + 3*a^3*b^4 - a^2*b^5)*d*sinh(d*x + c)^8 + 4*(2*a^6*b - 7*a^5*b^2 + 9*a^4*b^3 - 5*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)^6 + 4*(7*(a^5*b^2 - 3*a^4*b^3 + 3*a^3*b^4 - a^2*b^5)*d*cosh(d*x + c)^2 + (2*a^6*b - 7*a^5*b^2 + 9*a^4*b^3 - 5*a^3*b^4 + a^2*b^5)*d)*sinh(d*x + c)^6 + 2*(8*a^7 - 32*a^6*b + 51*a^5*b^2 - 41*a^4*b^3 + 17*a^3*b^4 - 3*a^2*b^5)*d*cosh(d*x + c)^4 + 8*(7*(a^5*b^2 - 3*a^4*b^3 + 3*a^3*b^4 - a^2*b^5)*d*cosh(d*x + c)^3 + 3*(2*a^6*b - 7*a^5*b^2 + 9*a^4*b^3 - 5*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^5*b^2 - 3*a^4*b^3 + 3*a^3*b^4 - a^2*b^5)*d*cosh(d*x + c)^4 + 30*(2*a^6*b - 7*a^5*b^2 + 9*a^4*b^3 - 5*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)^2 + (8*a^7 - 32*a^6*b + 51*a^5*b^2 - 41*a^4*b^3 + 17*a^3*b^4 - 3*a^2*b^5)*d)*sinh(d*x + c)^4 + 4*(2*a^6*b - 7*a^5*b^2 + 9*a^4*b^3 - 5*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)^2 + 8*(7*(a^5*b^2 - 3*a^4*b^3 + 3*a^3*b^4 - a^2*b^5)*d*cosh(d*x + c)^5 + 10*(2*a^6*b - 7*a^5*b^2 + 9*a^4*b^3 - 5*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)^3 + (8*a^7 - 32*a^6*b + 51*a^5*b^2 - 41*a^4*b^3 + 17*a^3*b^4 - 3*a^2*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^5*b^2 - 3*a^4*b^3 + 3*a^3*b^4 - a^2*b^5)*d*cosh(d*x + c)^6 + 15*(2*a^6*b - 7*a^5*b^2 + 9*a^4*b^3 - 5*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)^4 + 3*(8*a^7 - 32*a^6*b + 51*a^5*b^2 - 41*a^4*b^3 + 17*a^3*b^4 - 3*a^2*b^5)*d*cosh(d*x + c)^2 + (2*a^6*b - 7*a^5*b^2 + 9*a^4*b^3 - 5*a^3*b^4 + a^2*b^5)*d)*sinh(d*x + c)^2 + (a^5*b^2 - 3*a^4*b^3 + 3*a^3*b^4 - a^2*b^5)*d + 8*((a^5*b^2 - 3*a^4*b^3 + 3*a^3*b^4 - a^2*b^5)*d*cosh(d*x + c)^7 + 3*(2*a^6*b - 7*a^5*b^2 + 9*a^4*b^3 - 5*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)^5 + (8*a^7 - 32*a^6*b + 51*a^5*b^2 - 41*a^4*b^3 + 17*a^3*b^4 - 3*a^2*b^5)*d*cosh(d*x + c)^3 + (2*a^6*b - 7*a^5*b^2 + 9*a^4*b^3 - 5*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c))*sinh(d*x + c)), -1/8*(2*(7*a^2*b^2 - 10*a*b^3 + 3*b^4)*cosh(d*x + c)^7 + 14*(7*a^2*b^2 - 10*a*b^3 + 3*b^4)*cosh(d*x + c)*sinh(d*x + c)^6 + 2*(7*a^2*b^2 - 10*a*b^3 + 3*b^4)*sinh(d*x + c)^7 + 2*(36*a^3*b - 77*a^2*b^2 + 50*a*b^3 - 9*b^4)*cosh(d*x + c)^5 + 2*(36*a^3*b - 77*a^2*b^2 + 50*a*b^3 - 9*b^4 + 21*(7*a^2*b^2 - 10*a*b^3 + 3*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 10*(7*(7*a^2*b^2 - 10*a*b^3 + 3*b^4)*cosh(d*x + c)^3 + (36*a^3*b - 77*a^2*b^2 + 50*a*b^3 - 9*b^4)*cosh(d*x + c))*sinh(d*x + c)^4 - 2*(36*a^3*b - 77*a^2*b^2 + 50*a*b^3 - 9*b^4)*cosh(d*x + c)^3 + 2*(35*(7*a^2*b^2 - 10*a*b^3 + 3*b^4)*cosh(d*x + c)^4 - 36*a^3*b + 77*a^2*b^2 - 50*a*b^3 + 9*b^4 + 10*(36*a^3*b - 77*a^2*b^2 + 50*a*b^3 - 9*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 2*(21*(7*a^2*b^2 - 10*a*b^3 + 3*b^4)*cosh(d*x + c)^5 + 10*(36*a^3*b - 77*a^2*b^2 + 50*a*b^3 - 9*b^4)*cosh(d*x + c)^3 - 3*(36*a^3*b - 77*a^2*b^2 + 50*a*b^3 - 9*b^4)*cosh(d*x + c))*sinh(d*x + c)^2 + ((15*a^2*b^2 - 10*a*b^3 + 3*b^4)*cosh(d*x + c)^8 + 8*(15*a^2*b^2 - 10*a*b^3 + 3*b^4)*cosh(d*x + c)*sinh(d*x + c)^7 + (15*a^2*b^2 - 10*a*b^3 + 3*b^4)*sinh(d*x + c)^8 + 4*(30*a^3*b - 35*a^2*b^2 + 16*a*b^3 - 3*b^4)*cosh(d*x + c)^6 + 4*(30*a^3*b - 35*a^2*b^2 + 16*a*b^3 - 3*b^4 + 7*(15*a^2*b^2 - 10*a*b^3 + 3*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(15*a^2*b^2 - 10*a*b^3 + 3*b^4)*cosh(d*x + c)^3 + 3*(30*a^3*b - 35*a^2*b^2 + 16*a*b^3 - 3*b^4)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(120*a^4 - 200*a^3*b + 149*a^2*b^2 - 54*a*b^3 + 9*b^4)*cosh(d*x + c)^4 + 2*(35*(15*a^2*b^2 - 10*a*b^3 + 3*b^4)*cosh(d*x + c)^4 + 120*a^4 - 200*a^3*b + 149*a^2*b^2 - 54*a*b^3 + 9*b^4 + 30*(30*a^3*b - 35*a^2*b^2 + 16*a*b^3 - 3*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 15*a^2*b^2 - 10*a*b^3 + 3*b^4 + 8*(7*(15*a^2*b^2 - 10*a*b^3 + 3*b^4)*cosh(d*x + c)^5 + 10*(30*a^3*b - 35*a^2*b^2 + 16*a*b^3 - 3*b^4)*cosh(d*x + c)^3 + (120*a^4 - 200*a^3*b + 149*a^2*b^2 - 54*a*b^3 + 9*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(30*a^3*b - 35*a^2*b^2 + 16*a*b^3 - 3*b^4)*cosh(d*x + c)^2 + 4*(7*(15*a^2*b^2 - 10*a*b^3 + 3*b^4)*cosh(d*x + c)^6 + 15*(30*a^3*b - 35*a^2*b^2 + 16*a*b^3 - 3*b^4)*cosh(d*x + c)^4 + 30*a^3*b - 35*a^2*b^2 + 16*a*b^3 - 3*b^4 + 3*(120*a^4 - 200*a^3*b + 149*a^2*b^2 - 54*a*b^3 + 9*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((15*a^2*b^2 - 10*a*b^3 + 3*b^4)*cosh(d*x + c)^7 + 3*(30*a^3*b - 35*a^2*b^2 + 16*a*b^3 - 3*b^4)*cosh(d*x + c)^5 + (120*a^4 - 200*a^3*b + 149*a^2*b^2 - 54*a*b^3 + 9*b^4)*cosh(d*x + c)^3 + (30*a^3*b - 35*a^2*b^2 + 16*a*b^3 - 3*b^4)*cosh(d*x + c))*sinh(d*x + c))*sqrt(b/a)*arctan(1/2*sqrt(b/a)*(cosh(d*x + c) + sinh(d*x + c))) + ((15*a^2*b^2 - 10*a*b^3 + 3*b^4)*cosh(d*x + c)^8 + 8*(15*a^2*b^2 - 10*a*b^3 + 3*b^4)*cosh(d*x + c)*sinh(d*x + c)^7 + (15*a^2*b^2 - 10*a*b^3 + 3*b^4)*sinh(d*x + c)^8 + 4*(30*a^3*b - 35*a^2*b^2 + 16*a*b^3 - 3*b^4)*cosh(d*x + c)^6 + 4*(30*a^3*b - 35*a^2*b^2 + 16*a*b^3 - 3*b^4 + 7*(15*a^2*b^2 - 10*a*b^3 + 3*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(15*a^2*b^2 - 10*a*b^3 + 3*b^4)*cosh(d*x + c)^3 + 3*(30*a^3*b - 35*a^2*b^2 + 16*a*b^3 - 3*b^4)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(120*a^4 - 200*a^3*b + 149*a^2*b^2 - 54*a*b^3 + 9*b^4)*cosh(d*x + c)^4 + 2*(35*(15*a^2*b^2 - 10*a*b^3 + 3*b^4)*cosh(d*x + c)^4 + 120*a^4 - 200*a^3*b + 149*a^2*b^2 - 54*a*b^3 + 9*b^4 + 30*(30*a^3*b - 35*a^2*b^2 + 16*a*b^3 - 3*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 15*a^2*b^2 - 10*a*b^3 + 3*b^4 + 8*(7*(15*a^2*b^2 - 10*a*b^3 + 3*b^4)*cosh(d*x + c)^5 + 10*(30*a^3*b - 35*a^2*b^2 + 16*a*b^3 - 3*b^4)*cosh(d*x + c)^3 + (120*a^4 - 200*a^3*b + 149*a^2*b^2 - 54*a*b^3 + 9*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(30*a^3*b - 35*a^2*b^2 + 16*a*b^3 - 3*b^4)*cosh(d*x + c)^2 + 4*(7*(15*a^2*b^2 - 10*a*b^3 + 3*b^4)*cosh(d*x + c)^6 + 15*(30*a^3*b - 35*a^2*b^2 + 16*a*b^3 - 3*b^4)*cosh(d*x + c)^4 + 30*a^3*b - 35*a^2*b^2 + 16*a*b^3 - 3*b^4 + 3*(120*a^4 - 200*a^3*b + 149*a^2*b^2 - 54*a*b^3 + 9*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((15*a^2*b^2 - 10*a*b^3 + 3*b^4)*cosh(d*x + c)^7 + 3*(30*a^3*b - 35*a^2*b^2 + 16*a*b^3 - 3*b^4)*cosh(d*x + c)^5 + (120*a^4 - 200*a^3*b + 149*a^2*b^2 - 54*a*b^3 + 9*b^4)*cosh(d*x + c)^3 + (30*a^3*b - 35*a^2*b^2 + 16*a*b^3 - 3*b^4)*cosh(d*x + c))*sinh(d*x + c))*sqrt(b/a)*arctan(1/2*(b*cosh(d*x + c)^3 + 3*b*cosh(d*x + c)*sinh(d*x + c)^2 + b*sinh(d*x + c)^3 + (4*a - b)*cosh(d*x + c) + (3*b*cosh(d*x + c)^2 + 4*a - b)*sinh(d*x + c))*sqrt(b/a)/b) - 16*(a^2*b^2*cosh(d*x + c)^8 + 8*a^2*b^2*cosh(d*x + c)*sinh(d*x + c)^7 + a^2*b^2*sinh(d*x + c)^8 + 4*(2*a^3*b - a^2*b^2)*cosh(d*x + c)^6 + 4*(7*a^2*b^2*cosh(d*x + c)^2 + 2*a^3*b - a^2*b^2)*sinh(d*x + c)^6 + 8*(7*a^2*b^2*cosh(d*x + c)^3 + 3*(2*a^3*b - a^2*b^2)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(8*a^4 - 8*a^3*b + 3*a^2*b^2)*cosh(d*x + c)^4 + 2*(35*a^2*b^2*cosh(d*x + c)^4 + 8*a^4 - 8*a^3*b + 3*a^2*b^2 + 30*(2*a^3*b - a^2*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + a^2*b^2 + 8*(7*a^2*b^2*cosh(d*x + c)^5 + 10*(2*a^3*b - a^2*b^2)*cosh(d*x + c)^3 + (8*a^4 - 8*a^3*b + 3*a^2*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(2*a^3*b - a^2*b^2)*cosh(d*x + c)^2 + 4*(7*a^2*b^2*cosh(d*x + c)^6 + 15*(2*a^3*b - a^2*b^2)*cosh(d*x + c)^4 + 2*a^3*b - a^2*b^2 + 3*(8*a^4 - 8*a^3*b + 3*a^2*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*(a^2*b^2*cosh(d*x + c)^7 + 3*(2*a^3*b - a^2*b^2)*cosh(d*x + c)^5 + (8*a^4 - 8*a^3*b + 3*a^2*b^2)*cosh(d*x + c)^3 + (2*a^3*b - a^2*b^2)*cosh(d*x + c))*sinh(d*x + c))*arctan(cosh(d*x + c) + sinh(d*x + c)) - 2*(7*a^2*b^2 - 10*a*b^3 + 3*b^4)*cosh(d*x + c) + 2*(7*(7*a^2*b^2 - 10*a*b^3 + 3*b^4)*cosh(d*x + c)^6 + 5*(36*a^3*b - 77*a^2*b^2 + 50*a*b^3 - 9*b^4)*cosh(d*x + c)^4 - 7*a^2*b^2 + 10*a*b^3 - 3*b^4 - 3*(36*a^3*b - 77*a^2*b^2 + 50*a*b^3 - 9*b^4)*cosh(d*x + c)^2)*sinh(d*x + c))/((a^5*b^2 - 3*a^4*b^3 + 3*a^3*b^4 - a^2*b^5)*d*cosh(d*x + c)^8 + 8*(a^5*b^2 - 3*a^4*b^3 + 3*a^3*b^4 - a^2*b^5)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^5*b^2 - 3*a^4*b^3 + 3*a^3*b^4 - a^2*b^5)*d*sinh(d*x + c)^8 + 4*(2*a^6*b - 7*a^5*b^2 + 9*a^4*b^3 - 5*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)^6 + 4*(7*(a^5*b^2 - 3*a^4*b^3 + 3*a^3*b^4 - a^2*b^5)*d*cosh(d*x + c)^2 + (2*a^6*b - 7*a^5*b^2 + 9*a^4*b^3 - 5*a^3*b^4 + a^2*b^5)*d)*sinh(d*x + c)^6 + 2*(8*a^7 - 32*a^6*b + 51*a^5*b^2 - 41*a^4*b^3 + 17*a^3*b^4 - 3*a^2*b^5)*d*cosh(d*x + c)^4 + 8*(7*(a^5*b^2 - 3*a^4*b^3 + 3*a^3*b^4 - a^2*b^5)*d*cosh(d*x + c)^3 + 3*(2*a^6*b - 7*a^5*b^2 + 9*a^4*b^3 - 5*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^5*b^2 - 3*a^4*b^3 + 3*a^3*b^4 - a^2*b^5)*d*cosh(d*x + c)^4 + 30*(2*a^6*b - 7*a^5*b^2 + 9*a^4*b^3 - 5*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)^2 + (8*a^7 - 32*a^6*b + 51*a^5*b^2 - 41*a^4*b^3 + 17*a^3*b^4 - 3*a^2*b^5)*d)*sinh(d*x + c)^4 + 4*(2*a^6*b - 7*a^5*b^2 + 9*a^4*b^3 - 5*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)^2 + 8*(7*(a^5*b^2 - 3*a^4*b^3 + 3*a^3*b^4 - a^2*b^5)*d*cosh(d*x + c)^5 + 10*(2*a^6*b - 7*a^5*b^2 + 9*a^4*b^3 - 5*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)^3 + (8*a^7 - 32*a^6*b + 51*a^5*b^2 - 41*a^4*b^3 + 17*a^3*b^4 - 3*a^2*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^5*b^2 - 3*a^4*b^3 + 3*a^3*b^4 - a^2*b^5)*d*cosh(d*x + c)^6 + 15*(2*a^6*b - 7*a^5*b^2 + 9*a^4*b^3 - 5*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)^4 + 3*(8*a^7 - 32*a^6*b + 51*a^5*b^2 - 41*a^4*b^3 + 17*a^3*b^4 - 3*a^2*b^5)*d*cosh(d*x + c)^2 + (2*a^6*b - 7*a^5*b^2 + 9*a^4*b^3 - 5*a^3*b^4 + a^2*b^5)*d)*sinh(d*x + c)^2 + (a^5*b^2 - 3*a^4*b^3 + 3*a^3*b^4 - a^2*b^5)*d + 8*((a^5*b^2 - 3*a^4*b^3 + 3*a^3*b^4 - a^2*b^5)*d*cosh(d*x + c)^7 + 3*(2*a^6*b - 7*a^5*b^2 + 9*a^4*b^3 - 5*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)^5 + (8*a^7 - 32*a^6*b + 51*a^5*b^2 - 41*a^4*b^3 + 17*a^3*b^4 - 3*a^2*b^5)*d*cosh(d*x + c)^3 + (2*a^6*b - 7*a^5*b^2 + 9*a^4*b^3 - 5*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
346,1,9442,0,0.827947," ","integrate(sech(d*x+c)^2/(a+b*sinh(d*x+c)^2)^3,x, algorithm=""fricas"")","\left[-\frac{12 \, {\left(8 \, a^{4} b^{2} - 12 \, a^{3} b^{3} + 5 \, a^{2} b^{4} - a b^{5}\right)} \cosh\left(d x + c\right)^{8} + 96 \, {\left(8 \, a^{4} b^{2} - 12 \, a^{3} b^{3} + 5 \, a^{2} b^{4} - a b^{5}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + 12 \, {\left(8 \, a^{4} b^{2} - 12 \, a^{3} b^{3} + 5 \, a^{2} b^{4} - a b^{5}\right)} \sinh\left(d x + c\right)^{8} + 24 \, {\left(24 \, a^{5} b - 44 \, a^{4} b^{2} + 27 \, a^{3} b^{3} - 8 \, a^{2} b^{4} + a b^{5}\right)} \cosh\left(d x + c\right)^{6} + 24 \, {\left(24 \, a^{5} b - 44 \, a^{4} b^{2} + 27 \, a^{3} b^{3} - 8 \, a^{2} b^{4} + a b^{5} + 14 \, {\left(8 \, a^{4} b^{2} - 12 \, a^{3} b^{3} + 5 \, a^{2} b^{4} - a b^{5}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 32 \, a^{4} b^{2} + 8 \, a^{3} b^{3} - 52 \, a^{2} b^{4} + 12 \, a b^{5} + 48 \, {\left(14 \, {\left(8 \, a^{4} b^{2} - 12 \, a^{3} b^{3} + 5 \, a^{2} b^{4} - a b^{5}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(24 \, a^{5} b - 44 \, a^{4} b^{2} + 27 \, a^{3} b^{3} - 8 \, a^{2} b^{4} + a b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 8 \, {\left(64 \, a^{6} - 88 \, a^{5} b + 28 \, a^{4} b^{2} - 3 \, a^{3} b^{3} - a^{2} b^{4}\right)} \cosh\left(d x + c\right)^{4} + 8 \, {\left(64 \, a^{6} - 88 \, a^{5} b + 28 \, a^{4} b^{2} - 3 \, a^{3} b^{3} - a^{2} b^{4} + 105 \, {\left(8 \, a^{4} b^{2} - 12 \, a^{3} b^{3} + 5 \, a^{2} b^{4} - a b^{5}\right)} \cosh\left(d x + c\right)^{4} + 45 \, {\left(24 \, a^{5} b - 44 \, a^{4} b^{2} + 27 \, a^{3} b^{3} - 8 \, a^{2} b^{4} + a b^{5}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 32 \, {\left(21 \, {\left(8 \, a^{4} b^{2} - 12 \, a^{3} b^{3} + 5 \, a^{2} b^{4} - a b^{5}\right)} \cosh\left(d x + c\right)^{5} + 15 \, {\left(24 \, a^{5} b - 44 \, a^{4} b^{2} + 27 \, a^{3} b^{3} - 8 \, a^{2} b^{4} + a b^{5}\right)} \cosh\left(d x + c\right)^{3} + {\left(64 \, a^{6} - 88 \, a^{5} b + 28 \, a^{4} b^{2} - 3 \, a^{3} b^{3} - a^{2} b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 8 \, {\left(32 \, a^{5} b - 16 \, a^{4} b^{2} - 37 \, a^{3} b^{3} + 24 \, a^{2} b^{4} - 3 \, a b^{5}\right)} \cosh\left(d x + c\right)^{2} + 8 \, {\left(42 \, {\left(8 \, a^{4} b^{2} - 12 \, a^{3} b^{3} + 5 \, a^{2} b^{4} - a b^{5}\right)} \cosh\left(d x + c\right)^{6} + 32 \, a^{5} b - 16 \, a^{4} b^{2} - 37 \, a^{3} b^{3} + 24 \, a^{2} b^{4} - 3 \, a b^{5} + 45 \, {\left(24 \, a^{5} b - 44 \, a^{4} b^{2} + 27 \, a^{3} b^{3} - 8 \, a^{2} b^{4} + a b^{5}\right)} \cosh\left(d x + c\right)^{4} + 6 \, {\left(64 \, a^{6} - 88 \, a^{5} b + 28 \, a^{4} b^{2} - 3 \, a^{3} b^{3} - a^{2} b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 3 \, {\left({\left(8 \, a^{2} b^{3} - 4 \, a b^{4} + b^{5}\right)} \cosh\left(d x + c\right)^{10} + 10 \, {\left(8 \, a^{2} b^{3} - 4 \, a b^{4} + b^{5}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + {\left(8 \, a^{2} b^{3} - 4 \, a b^{4} + b^{5}\right)} \sinh\left(d x + c\right)^{10} + {\left(64 \, a^{3} b^{2} - 56 \, a^{2} b^{3} + 20 \, a b^{4} - 3 \, b^{5}\right)} \cosh\left(d x + c\right)^{8} + {\left(64 \, a^{3} b^{2} - 56 \, a^{2} b^{3} + 20 \, a b^{4} - 3 \, b^{5} + 45 \, {\left(8 \, a^{2} b^{3} - 4 \, a b^{4} + b^{5}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{8} + 8 \, {\left(15 \, {\left(8 \, a^{2} b^{3} - 4 \, a b^{4} + b^{5}\right)} \cosh\left(d x + c\right)^{3} + {\left(64 \, a^{3} b^{2} - 56 \, a^{2} b^{3} + 20 \, a b^{4} - 3 \, b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(64 \, a^{4} b - 64 \, a^{3} b^{2} + 32 \, a^{2} b^{3} - 8 \, a b^{4} + b^{5}\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(64 \, a^{4} b - 64 \, a^{3} b^{2} + 32 \, a^{2} b^{3} - 8 \, a b^{4} + b^{5} + 105 \, {\left(8 \, a^{2} b^{3} - 4 \, a b^{4} + b^{5}\right)} \cosh\left(d x + c\right)^{4} + 14 \, {\left(64 \, a^{3} b^{2} - 56 \, a^{2} b^{3} + 20 \, a b^{4} - 3 \, b^{5}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(63 \, {\left(8 \, a^{2} b^{3} - 4 \, a b^{4} + b^{5}\right)} \cosh\left(d x + c\right)^{5} + 14 \, {\left(64 \, a^{3} b^{2} - 56 \, a^{2} b^{3} + 20 \, a b^{4} - 3 \, b^{5}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(64 \, a^{4} b - 64 \, a^{3} b^{2} + 32 \, a^{2} b^{3} - 8 \, a b^{4} + b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 8 \, a^{2} b^{3} - 4 \, a b^{4} + b^{5} + 2 \, {\left(64 \, a^{4} b - 64 \, a^{3} b^{2} + 32 \, a^{2} b^{3} - 8 \, a b^{4} + b^{5}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(105 \, {\left(8 \, a^{2} b^{3} - 4 \, a b^{4} + b^{5}\right)} \cosh\left(d x + c\right)^{6} + 64 \, a^{4} b - 64 \, a^{3} b^{2} + 32 \, a^{2} b^{3} - 8 \, a b^{4} + b^{5} + 35 \, {\left(64 \, a^{3} b^{2} - 56 \, a^{2} b^{3} + 20 \, a b^{4} - 3 \, b^{5}\right)} \cosh\left(d x + c\right)^{4} + 15 \, {\left(64 \, a^{4} b - 64 \, a^{3} b^{2} + 32 \, a^{2} b^{3} - 8 \, a b^{4} + b^{5}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(15 \, {\left(8 \, a^{2} b^{3} - 4 \, a b^{4} + b^{5}\right)} \cosh\left(d x + c\right)^{7} + 7 \, {\left(64 \, a^{3} b^{2} - 56 \, a^{2} b^{3} + 20 \, a b^{4} - 3 \, b^{5}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(64 \, a^{4} b - 64 \, a^{3} b^{2} + 32 \, a^{2} b^{3} - 8 \, a b^{4} + b^{5}\right)} \cosh\left(d x + c\right)^{3} + {\left(64 \, a^{4} b - 64 \, a^{3} b^{2} + 32 \, a^{2} b^{3} - 8 \, a b^{4} + b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(64 \, a^{3} b^{2} - 56 \, a^{2} b^{3} + 20 \, a b^{4} - 3 \, b^{5}\right)} \cosh\left(d x + c\right)^{2} + {\left(45 \, {\left(8 \, a^{2} b^{3} - 4 \, a b^{4} + b^{5}\right)} \cosh\left(d x + c\right)^{8} + 28 \, {\left(64 \, a^{3} b^{2} - 56 \, a^{2} b^{3} + 20 \, a b^{4} - 3 \, b^{5}\right)} \cosh\left(d x + c\right)^{6} + 64 \, a^{3} b^{2} - 56 \, a^{2} b^{3} + 20 \, a b^{4} - 3 \, b^{5} + 30 \, {\left(64 \, a^{4} b - 64 \, a^{3} b^{2} + 32 \, a^{2} b^{3} - 8 \, a b^{4} + b^{5}\right)} \cosh\left(d x + c\right)^{4} + 12 \, {\left(64 \, a^{4} b - 64 \, a^{3} b^{2} + 32 \, a^{2} b^{3} - 8 \, a b^{4} + b^{5}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(5 \, {\left(8 \, a^{2} b^{3} - 4 \, a b^{4} + b^{5}\right)} \cosh\left(d x + c\right)^{9} + 4 \, {\left(64 \, a^{3} b^{2} - 56 \, a^{2} b^{3} + 20 \, a b^{4} - 3 \, b^{5}\right)} \cosh\left(d x + c\right)^{7} + 6 \, {\left(64 \, a^{4} b - 64 \, a^{3} b^{2} + 32 \, a^{2} b^{3} - 8 \, a b^{4} + b^{5}\right)} \cosh\left(d x + c\right)^{5} + 4 \, {\left(64 \, a^{4} b - 64 \, a^{3} b^{2} + 32 \, a^{2} b^{3} - 8 \, a b^{4} + b^{5}\right)} \cosh\left(d x + c\right)^{3} + {\left(64 \, a^{3} b^{2} - 56 \, a^{2} b^{3} + 20 \, a b^{4} - 3 \, b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{a^{2} - a b} \log\left(\frac{b^{2} \cosh\left(d x + c\right)^{4} + 4 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{2} \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(d x + c\right)^{2} + 2 \, a b - b^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, a^{2} - 8 \, a b + b^{2} + 4 \, {\left(b^{2} \cosh\left(d x + c\right)^{3} + {\left(2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) - 4 \, {\left(b \cosh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b \sinh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sqrt{a^{2} - a b}}{b \cosh\left(d x + c\right)^{4} + 4 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b \cosh\left(d x + c\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + b}\right) + 16 \, {\left(6 \, {\left(8 \, a^{4} b^{2} - 12 \, a^{3} b^{3} + 5 \, a^{2} b^{4} - a b^{5}\right)} \cosh\left(d x + c\right)^{7} + 9 \, {\left(24 \, a^{5} b - 44 \, a^{4} b^{2} + 27 \, a^{3} b^{3} - 8 \, a^{2} b^{4} + a b^{5}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(64 \, a^{6} - 88 \, a^{5} b + 28 \, a^{4} b^{2} - 3 \, a^{3} b^{3} - a^{2} b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(32 \, a^{5} b - 16 \, a^{4} b^{2} - 37 \, a^{3} b^{3} + 24 \, a^{2} b^{4} - 3 \, a b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{16 \, {\left({\left(a^{7} b^{2} - 4 \, a^{6} b^{3} + 6 \, a^{5} b^{4} - 4 \, a^{4} b^{5} + a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{10} + 10 \, {\left(a^{7} b^{2} - 4 \, a^{6} b^{3} + 6 \, a^{5} b^{4} - 4 \, a^{4} b^{5} + a^{3} b^{6}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + {\left(a^{7} b^{2} - 4 \, a^{6} b^{3} + 6 \, a^{5} b^{4} - 4 \, a^{4} b^{5} + a^{3} b^{6}\right)} d \sinh\left(d x + c\right)^{10} + {\left(8 \, a^{8} b - 35 \, a^{7} b^{2} + 60 \, a^{6} b^{3} - 50 \, a^{5} b^{4} + 20 \, a^{4} b^{5} - 3 \, a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{8} + {\left(45 \, {\left(a^{7} b^{2} - 4 \, a^{6} b^{3} + 6 \, a^{5} b^{4} - 4 \, a^{4} b^{5} + a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{2} + {\left(8 \, a^{8} b - 35 \, a^{7} b^{2} + 60 \, a^{6} b^{3} - 50 \, a^{5} b^{4} + 20 \, a^{4} b^{5} - 3 \, a^{3} b^{6}\right)} d\right)} \sinh\left(d x + c\right)^{8} + 2 \, {\left(8 \, a^{9} - 36 \, a^{8} b + 65 \, a^{7} b^{2} - 60 \, a^{6} b^{3} + 30 \, a^{5} b^{4} - 8 \, a^{4} b^{5} + a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{6} + 8 \, {\left(15 \, {\left(a^{7} b^{2} - 4 \, a^{6} b^{3} + 6 \, a^{5} b^{4} - 4 \, a^{4} b^{5} + a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{8} b - 35 \, a^{7} b^{2} + 60 \, a^{6} b^{3} - 50 \, a^{5} b^{4} + 20 \, a^{4} b^{5} - 3 \, a^{3} b^{6}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(105 \, {\left(a^{7} b^{2} - 4 \, a^{6} b^{3} + 6 \, a^{5} b^{4} - 4 \, a^{4} b^{5} + a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{4} + 14 \, {\left(8 \, a^{8} b - 35 \, a^{7} b^{2} + 60 \, a^{6} b^{3} - 50 \, a^{5} b^{4} + 20 \, a^{4} b^{5} - 3 \, a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{2} + {\left(8 \, a^{9} - 36 \, a^{8} b + 65 \, a^{7} b^{2} - 60 \, a^{6} b^{3} + 30 \, a^{5} b^{4} - 8 \, a^{4} b^{5} + a^{3} b^{6}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(8 \, a^{9} - 36 \, a^{8} b + 65 \, a^{7} b^{2} - 60 \, a^{6} b^{3} + 30 \, a^{5} b^{4} - 8 \, a^{4} b^{5} + a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(63 \, {\left(a^{7} b^{2} - 4 \, a^{6} b^{3} + 6 \, a^{5} b^{4} - 4 \, a^{4} b^{5} + a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{5} + 14 \, {\left(8 \, a^{8} b - 35 \, a^{7} b^{2} + 60 \, a^{6} b^{3} - 50 \, a^{5} b^{4} + 20 \, a^{4} b^{5} - 3 \, a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(8 \, a^{9} - 36 \, a^{8} b + 65 \, a^{7} b^{2} - 60 \, a^{6} b^{3} + 30 \, a^{5} b^{4} - 8 \, a^{4} b^{5} + a^{3} b^{6}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(105 \, {\left(a^{7} b^{2} - 4 \, a^{6} b^{3} + 6 \, a^{5} b^{4} - 4 \, a^{4} b^{5} + a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{6} + 35 \, {\left(8 \, a^{8} b - 35 \, a^{7} b^{2} + 60 \, a^{6} b^{3} - 50 \, a^{5} b^{4} + 20 \, a^{4} b^{5} - 3 \, a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{4} + 15 \, {\left(8 \, a^{9} - 36 \, a^{8} b + 65 \, a^{7} b^{2} - 60 \, a^{6} b^{3} + 30 \, a^{5} b^{4} - 8 \, a^{4} b^{5} + a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{2} + {\left(8 \, a^{9} - 36 \, a^{8} b + 65 \, a^{7} b^{2} - 60 \, a^{6} b^{3} + 30 \, a^{5} b^{4} - 8 \, a^{4} b^{5} + a^{3} b^{6}\right)} d\right)} \sinh\left(d x + c\right)^{4} + {\left(8 \, a^{8} b - 35 \, a^{7} b^{2} + 60 \, a^{6} b^{3} - 50 \, a^{5} b^{4} + 20 \, a^{4} b^{5} - 3 \, a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(15 \, {\left(a^{7} b^{2} - 4 \, a^{6} b^{3} + 6 \, a^{5} b^{4} - 4 \, a^{4} b^{5} + a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{7} + 7 \, {\left(8 \, a^{8} b - 35 \, a^{7} b^{2} + 60 \, a^{6} b^{3} - 50 \, a^{5} b^{4} + 20 \, a^{4} b^{5} - 3 \, a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{5} + 5 \, {\left(8 \, a^{9} - 36 \, a^{8} b + 65 \, a^{7} b^{2} - 60 \, a^{6} b^{3} + 30 \, a^{5} b^{4} - 8 \, a^{4} b^{5} + a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{9} - 36 \, a^{8} b + 65 \, a^{7} b^{2} - 60 \, a^{6} b^{3} + 30 \, a^{5} b^{4} - 8 \, a^{4} b^{5} + a^{3} b^{6}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(45 \, {\left(a^{7} b^{2} - 4 \, a^{6} b^{3} + 6 \, a^{5} b^{4} - 4 \, a^{4} b^{5} + a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{8} + 28 \, {\left(8 \, a^{8} b - 35 \, a^{7} b^{2} + 60 \, a^{6} b^{3} - 50 \, a^{5} b^{4} + 20 \, a^{4} b^{5} - 3 \, a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{6} + 30 \, {\left(8 \, a^{9} - 36 \, a^{8} b + 65 \, a^{7} b^{2} - 60 \, a^{6} b^{3} + 30 \, a^{5} b^{4} - 8 \, a^{4} b^{5} + a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{4} + 12 \, {\left(8 \, a^{9} - 36 \, a^{8} b + 65 \, a^{7} b^{2} - 60 \, a^{6} b^{3} + 30 \, a^{5} b^{4} - 8 \, a^{4} b^{5} + a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{2} + {\left(8 \, a^{8} b - 35 \, a^{7} b^{2} + 60 \, a^{6} b^{3} - 50 \, a^{5} b^{4} + 20 \, a^{4} b^{5} - 3 \, a^{3} b^{6}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{7} b^{2} - 4 \, a^{6} b^{3} + 6 \, a^{5} b^{4} - 4 \, a^{4} b^{5} + a^{3} b^{6}\right)} d + 2 \, {\left(5 \, {\left(a^{7} b^{2} - 4 \, a^{6} b^{3} + 6 \, a^{5} b^{4} - 4 \, a^{4} b^{5} + a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{9} + 4 \, {\left(8 \, a^{8} b - 35 \, a^{7} b^{2} + 60 \, a^{6} b^{3} - 50 \, a^{5} b^{4} + 20 \, a^{4} b^{5} - 3 \, a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{7} + 6 \, {\left(8 \, a^{9} - 36 \, a^{8} b + 65 \, a^{7} b^{2} - 60 \, a^{6} b^{3} + 30 \, a^{5} b^{4} - 8 \, a^{4} b^{5} + a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{5} + 4 \, {\left(8 \, a^{9} - 36 \, a^{8} b + 65 \, a^{7} b^{2} - 60 \, a^{6} b^{3} + 30 \, a^{5} b^{4} - 8 \, a^{4} b^{5} + a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{8} b - 35 \, a^{7} b^{2} + 60 \, a^{6} b^{3} - 50 \, a^{5} b^{4} + 20 \, a^{4} b^{5} - 3 \, a^{3} b^{6}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}, -\frac{6 \, {\left(8 \, a^{4} b^{2} - 12 \, a^{3} b^{3} + 5 \, a^{2} b^{4} - a b^{5}\right)} \cosh\left(d x + c\right)^{8} + 48 \, {\left(8 \, a^{4} b^{2} - 12 \, a^{3} b^{3} + 5 \, a^{2} b^{4} - a b^{5}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + 6 \, {\left(8 \, a^{4} b^{2} - 12 \, a^{3} b^{3} + 5 \, a^{2} b^{4} - a b^{5}\right)} \sinh\left(d x + c\right)^{8} + 12 \, {\left(24 \, a^{5} b - 44 \, a^{4} b^{2} + 27 \, a^{3} b^{3} - 8 \, a^{2} b^{4} + a b^{5}\right)} \cosh\left(d x + c\right)^{6} + 12 \, {\left(24 \, a^{5} b - 44 \, a^{4} b^{2} + 27 \, a^{3} b^{3} - 8 \, a^{2} b^{4} + a b^{5} + 14 \, {\left(8 \, a^{4} b^{2} - 12 \, a^{3} b^{3} + 5 \, a^{2} b^{4} - a b^{5}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 16 \, a^{4} b^{2} + 4 \, a^{3} b^{3} - 26 \, a^{2} b^{4} + 6 \, a b^{5} + 24 \, {\left(14 \, {\left(8 \, a^{4} b^{2} - 12 \, a^{3} b^{3} + 5 \, a^{2} b^{4} - a b^{5}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(24 \, a^{5} b - 44 \, a^{4} b^{2} + 27 \, a^{3} b^{3} - 8 \, a^{2} b^{4} + a b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 4 \, {\left(64 \, a^{6} - 88 \, a^{5} b + 28 \, a^{4} b^{2} - 3 \, a^{3} b^{3} - a^{2} b^{4}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(64 \, a^{6} - 88 \, a^{5} b + 28 \, a^{4} b^{2} - 3 \, a^{3} b^{3} - a^{2} b^{4} + 105 \, {\left(8 \, a^{4} b^{2} - 12 \, a^{3} b^{3} + 5 \, a^{2} b^{4} - a b^{5}\right)} \cosh\left(d x + c\right)^{4} + 45 \, {\left(24 \, a^{5} b - 44 \, a^{4} b^{2} + 27 \, a^{3} b^{3} - 8 \, a^{2} b^{4} + a b^{5}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 16 \, {\left(21 \, {\left(8 \, a^{4} b^{2} - 12 \, a^{3} b^{3} + 5 \, a^{2} b^{4} - a b^{5}\right)} \cosh\left(d x + c\right)^{5} + 15 \, {\left(24 \, a^{5} b - 44 \, a^{4} b^{2} + 27 \, a^{3} b^{3} - 8 \, a^{2} b^{4} + a b^{5}\right)} \cosh\left(d x + c\right)^{3} + {\left(64 \, a^{6} - 88 \, a^{5} b + 28 \, a^{4} b^{2} - 3 \, a^{3} b^{3} - a^{2} b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(32 \, a^{5} b - 16 \, a^{4} b^{2} - 37 \, a^{3} b^{3} + 24 \, a^{2} b^{4} - 3 \, a b^{5}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(42 \, {\left(8 \, a^{4} b^{2} - 12 \, a^{3} b^{3} + 5 \, a^{2} b^{4} - a b^{5}\right)} \cosh\left(d x + c\right)^{6} + 32 \, a^{5} b - 16 \, a^{4} b^{2} - 37 \, a^{3} b^{3} + 24 \, a^{2} b^{4} - 3 \, a b^{5} + 45 \, {\left(24 \, a^{5} b - 44 \, a^{4} b^{2} + 27 \, a^{3} b^{3} - 8 \, a^{2} b^{4} + a b^{5}\right)} \cosh\left(d x + c\right)^{4} + 6 \, {\left(64 \, a^{6} - 88 \, a^{5} b + 28 \, a^{4} b^{2} - 3 \, a^{3} b^{3} - a^{2} b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} - 3 \, {\left({\left(8 \, a^{2} b^{3} - 4 \, a b^{4} + b^{5}\right)} \cosh\left(d x + c\right)^{10} + 10 \, {\left(8 \, a^{2} b^{3} - 4 \, a b^{4} + b^{5}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + {\left(8 \, a^{2} b^{3} - 4 \, a b^{4} + b^{5}\right)} \sinh\left(d x + c\right)^{10} + {\left(64 \, a^{3} b^{2} - 56 \, a^{2} b^{3} + 20 \, a b^{4} - 3 \, b^{5}\right)} \cosh\left(d x + c\right)^{8} + {\left(64 \, a^{3} b^{2} - 56 \, a^{2} b^{3} + 20 \, a b^{4} - 3 \, b^{5} + 45 \, {\left(8 \, a^{2} b^{3} - 4 \, a b^{4} + b^{5}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{8} + 8 \, {\left(15 \, {\left(8 \, a^{2} b^{3} - 4 \, a b^{4} + b^{5}\right)} \cosh\left(d x + c\right)^{3} + {\left(64 \, a^{3} b^{2} - 56 \, a^{2} b^{3} + 20 \, a b^{4} - 3 \, b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(64 \, a^{4} b - 64 \, a^{3} b^{2} + 32 \, a^{2} b^{3} - 8 \, a b^{4} + b^{5}\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(64 \, a^{4} b - 64 \, a^{3} b^{2} + 32 \, a^{2} b^{3} - 8 \, a b^{4} + b^{5} + 105 \, {\left(8 \, a^{2} b^{3} - 4 \, a b^{4} + b^{5}\right)} \cosh\left(d x + c\right)^{4} + 14 \, {\left(64 \, a^{3} b^{2} - 56 \, a^{2} b^{3} + 20 \, a b^{4} - 3 \, b^{5}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(63 \, {\left(8 \, a^{2} b^{3} - 4 \, a b^{4} + b^{5}\right)} \cosh\left(d x + c\right)^{5} + 14 \, {\left(64 \, a^{3} b^{2} - 56 \, a^{2} b^{3} + 20 \, a b^{4} - 3 \, b^{5}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(64 \, a^{4} b - 64 \, a^{3} b^{2} + 32 \, a^{2} b^{3} - 8 \, a b^{4} + b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 8 \, a^{2} b^{3} - 4 \, a b^{4} + b^{5} + 2 \, {\left(64 \, a^{4} b - 64 \, a^{3} b^{2} + 32 \, a^{2} b^{3} - 8 \, a b^{4} + b^{5}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(105 \, {\left(8 \, a^{2} b^{3} - 4 \, a b^{4} + b^{5}\right)} \cosh\left(d x + c\right)^{6} + 64 \, a^{4} b - 64 \, a^{3} b^{2} + 32 \, a^{2} b^{3} - 8 \, a b^{4} + b^{5} + 35 \, {\left(64 \, a^{3} b^{2} - 56 \, a^{2} b^{3} + 20 \, a b^{4} - 3 \, b^{5}\right)} \cosh\left(d x + c\right)^{4} + 15 \, {\left(64 \, a^{4} b - 64 \, a^{3} b^{2} + 32 \, a^{2} b^{3} - 8 \, a b^{4} + b^{5}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(15 \, {\left(8 \, a^{2} b^{3} - 4 \, a b^{4} + b^{5}\right)} \cosh\left(d x + c\right)^{7} + 7 \, {\left(64 \, a^{3} b^{2} - 56 \, a^{2} b^{3} + 20 \, a b^{4} - 3 \, b^{5}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(64 \, a^{4} b - 64 \, a^{3} b^{2} + 32 \, a^{2} b^{3} - 8 \, a b^{4} + b^{5}\right)} \cosh\left(d x + c\right)^{3} + {\left(64 \, a^{4} b - 64 \, a^{3} b^{2} + 32 \, a^{2} b^{3} - 8 \, a b^{4} + b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(64 \, a^{3} b^{2} - 56 \, a^{2} b^{3} + 20 \, a b^{4} - 3 \, b^{5}\right)} \cosh\left(d x + c\right)^{2} + {\left(45 \, {\left(8 \, a^{2} b^{3} - 4 \, a b^{4} + b^{5}\right)} \cosh\left(d x + c\right)^{8} + 28 \, {\left(64 \, a^{3} b^{2} - 56 \, a^{2} b^{3} + 20 \, a b^{4} - 3 \, b^{5}\right)} \cosh\left(d x + c\right)^{6} + 64 \, a^{3} b^{2} - 56 \, a^{2} b^{3} + 20 \, a b^{4} - 3 \, b^{5} + 30 \, {\left(64 \, a^{4} b - 64 \, a^{3} b^{2} + 32 \, a^{2} b^{3} - 8 \, a b^{4} + b^{5}\right)} \cosh\left(d x + c\right)^{4} + 12 \, {\left(64 \, a^{4} b - 64 \, a^{3} b^{2} + 32 \, a^{2} b^{3} - 8 \, a b^{4} + b^{5}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(5 \, {\left(8 \, a^{2} b^{3} - 4 \, a b^{4} + b^{5}\right)} \cosh\left(d x + c\right)^{9} + 4 \, {\left(64 \, a^{3} b^{2} - 56 \, a^{2} b^{3} + 20 \, a b^{4} - 3 \, b^{5}\right)} \cosh\left(d x + c\right)^{7} + 6 \, {\left(64 \, a^{4} b - 64 \, a^{3} b^{2} + 32 \, a^{2} b^{3} - 8 \, a b^{4} + b^{5}\right)} \cosh\left(d x + c\right)^{5} + 4 \, {\left(64 \, a^{4} b - 64 \, a^{3} b^{2} + 32 \, a^{2} b^{3} - 8 \, a b^{4} + b^{5}\right)} \cosh\left(d x + c\right)^{3} + {\left(64 \, a^{3} b^{2} - 56 \, a^{2} b^{3} + 20 \, a b^{4} - 3 \, b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-a^{2} + a b} \arctan\left(-\frac{{\left(b \cosh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b \sinh\left(d x + c\right)^{2} + 2 \, a - b\right)} \sqrt{-a^{2} + a b}}{2 \, {\left(a^{2} - a b\right)}}\right) + 8 \, {\left(6 \, {\left(8 \, a^{4} b^{2} - 12 \, a^{3} b^{3} + 5 \, a^{2} b^{4} - a b^{5}\right)} \cosh\left(d x + c\right)^{7} + 9 \, {\left(24 \, a^{5} b - 44 \, a^{4} b^{2} + 27 \, a^{3} b^{3} - 8 \, a^{2} b^{4} + a b^{5}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(64 \, a^{6} - 88 \, a^{5} b + 28 \, a^{4} b^{2} - 3 \, a^{3} b^{3} - a^{2} b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(32 \, a^{5} b - 16 \, a^{4} b^{2} - 37 \, a^{3} b^{3} + 24 \, a^{2} b^{4} - 3 \, a b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{8 \, {\left({\left(a^{7} b^{2} - 4 \, a^{6} b^{3} + 6 \, a^{5} b^{4} - 4 \, a^{4} b^{5} + a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{10} + 10 \, {\left(a^{7} b^{2} - 4 \, a^{6} b^{3} + 6 \, a^{5} b^{4} - 4 \, a^{4} b^{5} + a^{3} b^{6}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + {\left(a^{7} b^{2} - 4 \, a^{6} b^{3} + 6 \, a^{5} b^{4} - 4 \, a^{4} b^{5} + a^{3} b^{6}\right)} d \sinh\left(d x + c\right)^{10} + {\left(8 \, a^{8} b - 35 \, a^{7} b^{2} + 60 \, a^{6} b^{3} - 50 \, a^{5} b^{4} + 20 \, a^{4} b^{5} - 3 \, a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{8} + {\left(45 \, {\left(a^{7} b^{2} - 4 \, a^{6} b^{3} + 6 \, a^{5} b^{4} - 4 \, a^{4} b^{5} + a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{2} + {\left(8 \, a^{8} b - 35 \, a^{7} b^{2} + 60 \, a^{6} b^{3} - 50 \, a^{5} b^{4} + 20 \, a^{4} b^{5} - 3 \, a^{3} b^{6}\right)} d\right)} \sinh\left(d x + c\right)^{8} + 2 \, {\left(8 \, a^{9} - 36 \, a^{8} b + 65 \, a^{7} b^{2} - 60 \, a^{6} b^{3} + 30 \, a^{5} b^{4} - 8 \, a^{4} b^{5} + a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{6} + 8 \, {\left(15 \, {\left(a^{7} b^{2} - 4 \, a^{6} b^{3} + 6 \, a^{5} b^{4} - 4 \, a^{4} b^{5} + a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{8} b - 35 \, a^{7} b^{2} + 60 \, a^{6} b^{3} - 50 \, a^{5} b^{4} + 20 \, a^{4} b^{5} - 3 \, a^{3} b^{6}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(105 \, {\left(a^{7} b^{2} - 4 \, a^{6} b^{3} + 6 \, a^{5} b^{4} - 4 \, a^{4} b^{5} + a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{4} + 14 \, {\left(8 \, a^{8} b - 35 \, a^{7} b^{2} + 60 \, a^{6} b^{3} - 50 \, a^{5} b^{4} + 20 \, a^{4} b^{5} - 3 \, a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{2} + {\left(8 \, a^{9} - 36 \, a^{8} b + 65 \, a^{7} b^{2} - 60 \, a^{6} b^{3} + 30 \, a^{5} b^{4} - 8 \, a^{4} b^{5} + a^{3} b^{6}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(8 \, a^{9} - 36 \, a^{8} b + 65 \, a^{7} b^{2} - 60 \, a^{6} b^{3} + 30 \, a^{5} b^{4} - 8 \, a^{4} b^{5} + a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(63 \, {\left(a^{7} b^{2} - 4 \, a^{6} b^{3} + 6 \, a^{5} b^{4} - 4 \, a^{4} b^{5} + a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{5} + 14 \, {\left(8 \, a^{8} b - 35 \, a^{7} b^{2} + 60 \, a^{6} b^{3} - 50 \, a^{5} b^{4} + 20 \, a^{4} b^{5} - 3 \, a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(8 \, a^{9} - 36 \, a^{8} b + 65 \, a^{7} b^{2} - 60 \, a^{6} b^{3} + 30 \, a^{5} b^{4} - 8 \, a^{4} b^{5} + a^{3} b^{6}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(105 \, {\left(a^{7} b^{2} - 4 \, a^{6} b^{3} + 6 \, a^{5} b^{4} - 4 \, a^{4} b^{5} + a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{6} + 35 \, {\left(8 \, a^{8} b - 35 \, a^{7} b^{2} + 60 \, a^{6} b^{3} - 50 \, a^{5} b^{4} + 20 \, a^{4} b^{5} - 3 \, a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{4} + 15 \, {\left(8 \, a^{9} - 36 \, a^{8} b + 65 \, a^{7} b^{2} - 60 \, a^{6} b^{3} + 30 \, a^{5} b^{4} - 8 \, a^{4} b^{5} + a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{2} + {\left(8 \, a^{9} - 36 \, a^{8} b + 65 \, a^{7} b^{2} - 60 \, a^{6} b^{3} + 30 \, a^{5} b^{4} - 8 \, a^{4} b^{5} + a^{3} b^{6}\right)} d\right)} \sinh\left(d x + c\right)^{4} + {\left(8 \, a^{8} b - 35 \, a^{7} b^{2} + 60 \, a^{6} b^{3} - 50 \, a^{5} b^{4} + 20 \, a^{4} b^{5} - 3 \, a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(15 \, {\left(a^{7} b^{2} - 4 \, a^{6} b^{3} + 6 \, a^{5} b^{4} - 4 \, a^{4} b^{5} + a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{7} + 7 \, {\left(8 \, a^{8} b - 35 \, a^{7} b^{2} + 60 \, a^{6} b^{3} - 50 \, a^{5} b^{4} + 20 \, a^{4} b^{5} - 3 \, a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{5} + 5 \, {\left(8 \, a^{9} - 36 \, a^{8} b + 65 \, a^{7} b^{2} - 60 \, a^{6} b^{3} + 30 \, a^{5} b^{4} - 8 \, a^{4} b^{5} + a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{9} - 36 \, a^{8} b + 65 \, a^{7} b^{2} - 60 \, a^{6} b^{3} + 30 \, a^{5} b^{4} - 8 \, a^{4} b^{5} + a^{3} b^{6}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(45 \, {\left(a^{7} b^{2} - 4 \, a^{6} b^{3} + 6 \, a^{5} b^{4} - 4 \, a^{4} b^{5} + a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{8} + 28 \, {\left(8 \, a^{8} b - 35 \, a^{7} b^{2} + 60 \, a^{6} b^{3} - 50 \, a^{5} b^{4} + 20 \, a^{4} b^{5} - 3 \, a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{6} + 30 \, {\left(8 \, a^{9} - 36 \, a^{8} b + 65 \, a^{7} b^{2} - 60 \, a^{6} b^{3} + 30 \, a^{5} b^{4} - 8 \, a^{4} b^{5} + a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{4} + 12 \, {\left(8 \, a^{9} - 36 \, a^{8} b + 65 \, a^{7} b^{2} - 60 \, a^{6} b^{3} + 30 \, a^{5} b^{4} - 8 \, a^{4} b^{5} + a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{2} + {\left(8 \, a^{8} b - 35 \, a^{7} b^{2} + 60 \, a^{6} b^{3} - 50 \, a^{5} b^{4} + 20 \, a^{4} b^{5} - 3 \, a^{3} b^{6}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{7} b^{2} - 4 \, a^{6} b^{3} + 6 \, a^{5} b^{4} - 4 \, a^{4} b^{5} + a^{3} b^{6}\right)} d + 2 \, {\left(5 \, {\left(a^{7} b^{2} - 4 \, a^{6} b^{3} + 6 \, a^{5} b^{4} - 4 \, a^{4} b^{5} + a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{9} + 4 \, {\left(8 \, a^{8} b - 35 \, a^{7} b^{2} + 60 \, a^{6} b^{3} - 50 \, a^{5} b^{4} + 20 \, a^{4} b^{5} - 3 \, a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{7} + 6 \, {\left(8 \, a^{9} - 36 \, a^{8} b + 65 \, a^{7} b^{2} - 60 \, a^{6} b^{3} + 30 \, a^{5} b^{4} - 8 \, a^{4} b^{5} + a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{5} + 4 \, {\left(8 \, a^{9} - 36 \, a^{8} b + 65 \, a^{7} b^{2} - 60 \, a^{6} b^{3} + 30 \, a^{5} b^{4} - 8 \, a^{4} b^{5} + a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{8} b - 35 \, a^{7} b^{2} + 60 \, a^{6} b^{3} - 50 \, a^{5} b^{4} + 20 \, a^{4} b^{5} - 3 \, a^{3} b^{6}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[-1/16*(12*(8*a^4*b^2 - 12*a^3*b^3 + 5*a^2*b^4 - a*b^5)*cosh(d*x + c)^8 + 96*(8*a^4*b^2 - 12*a^3*b^3 + 5*a^2*b^4 - a*b^5)*cosh(d*x + c)*sinh(d*x + c)^7 + 12*(8*a^4*b^2 - 12*a^3*b^3 + 5*a^2*b^4 - a*b^5)*sinh(d*x + c)^8 + 24*(24*a^5*b - 44*a^4*b^2 + 27*a^3*b^3 - 8*a^2*b^4 + a*b^5)*cosh(d*x + c)^6 + 24*(24*a^5*b - 44*a^4*b^2 + 27*a^3*b^3 - 8*a^2*b^4 + a*b^5 + 14*(8*a^4*b^2 - 12*a^3*b^3 + 5*a^2*b^4 - a*b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 32*a^4*b^2 + 8*a^3*b^3 - 52*a^2*b^4 + 12*a*b^5 + 48*(14*(8*a^4*b^2 - 12*a^3*b^3 + 5*a^2*b^4 - a*b^5)*cosh(d*x + c)^3 + 3*(24*a^5*b - 44*a^4*b^2 + 27*a^3*b^3 - 8*a^2*b^4 + a*b^5)*cosh(d*x + c))*sinh(d*x + c)^5 + 8*(64*a^6 - 88*a^5*b + 28*a^4*b^2 - 3*a^3*b^3 - a^2*b^4)*cosh(d*x + c)^4 + 8*(64*a^6 - 88*a^5*b + 28*a^4*b^2 - 3*a^3*b^3 - a^2*b^4 + 105*(8*a^4*b^2 - 12*a^3*b^3 + 5*a^2*b^4 - a*b^5)*cosh(d*x + c)^4 + 45*(24*a^5*b - 44*a^4*b^2 + 27*a^3*b^3 - 8*a^2*b^4 + a*b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 32*(21*(8*a^4*b^2 - 12*a^3*b^3 + 5*a^2*b^4 - a*b^5)*cosh(d*x + c)^5 + 15*(24*a^5*b - 44*a^4*b^2 + 27*a^3*b^3 - 8*a^2*b^4 + a*b^5)*cosh(d*x + c)^3 + (64*a^6 - 88*a^5*b + 28*a^4*b^2 - 3*a^3*b^3 - a^2*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 8*(32*a^5*b - 16*a^4*b^2 - 37*a^3*b^3 + 24*a^2*b^4 - 3*a*b^5)*cosh(d*x + c)^2 + 8*(42*(8*a^4*b^2 - 12*a^3*b^3 + 5*a^2*b^4 - a*b^5)*cosh(d*x + c)^6 + 32*a^5*b - 16*a^4*b^2 - 37*a^3*b^3 + 24*a^2*b^4 - 3*a*b^5 + 45*(24*a^5*b - 44*a^4*b^2 + 27*a^3*b^3 - 8*a^2*b^4 + a*b^5)*cosh(d*x + c)^4 + 6*(64*a^6 - 88*a^5*b + 28*a^4*b^2 - 3*a^3*b^3 - a^2*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 3*((8*a^2*b^3 - 4*a*b^4 + b^5)*cosh(d*x + c)^10 + 10*(8*a^2*b^3 - 4*a*b^4 + b^5)*cosh(d*x + c)*sinh(d*x + c)^9 + (8*a^2*b^3 - 4*a*b^4 + b^5)*sinh(d*x + c)^10 + (64*a^3*b^2 - 56*a^2*b^3 + 20*a*b^4 - 3*b^5)*cosh(d*x + c)^8 + (64*a^3*b^2 - 56*a^2*b^3 + 20*a*b^4 - 3*b^5 + 45*(8*a^2*b^3 - 4*a*b^4 + b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 8*(15*(8*a^2*b^3 - 4*a*b^4 + b^5)*cosh(d*x + c)^3 + (64*a^3*b^2 - 56*a^2*b^3 + 20*a*b^4 - 3*b^5)*cosh(d*x + c))*sinh(d*x + c)^7 + 2*(64*a^4*b - 64*a^3*b^2 + 32*a^2*b^3 - 8*a*b^4 + b^5)*cosh(d*x + c)^6 + 2*(64*a^4*b - 64*a^3*b^2 + 32*a^2*b^3 - 8*a*b^4 + b^5 + 105*(8*a^2*b^3 - 4*a*b^4 + b^5)*cosh(d*x + c)^4 + 14*(64*a^3*b^2 - 56*a^2*b^3 + 20*a*b^4 - 3*b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 4*(63*(8*a^2*b^3 - 4*a*b^4 + b^5)*cosh(d*x + c)^5 + 14*(64*a^3*b^2 - 56*a^2*b^3 + 20*a*b^4 - 3*b^5)*cosh(d*x + c)^3 + 3*(64*a^4*b - 64*a^3*b^2 + 32*a^2*b^3 - 8*a*b^4 + b^5)*cosh(d*x + c))*sinh(d*x + c)^5 + 8*a^2*b^3 - 4*a*b^4 + b^5 + 2*(64*a^4*b - 64*a^3*b^2 + 32*a^2*b^3 - 8*a*b^4 + b^5)*cosh(d*x + c)^4 + 2*(105*(8*a^2*b^3 - 4*a*b^4 + b^5)*cosh(d*x + c)^6 + 64*a^4*b - 64*a^3*b^2 + 32*a^2*b^3 - 8*a*b^4 + b^5 + 35*(64*a^3*b^2 - 56*a^2*b^3 + 20*a*b^4 - 3*b^5)*cosh(d*x + c)^4 + 15*(64*a^4*b - 64*a^3*b^2 + 32*a^2*b^3 - 8*a*b^4 + b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(15*(8*a^2*b^3 - 4*a*b^4 + b^5)*cosh(d*x + c)^7 + 7*(64*a^3*b^2 - 56*a^2*b^3 + 20*a*b^4 - 3*b^5)*cosh(d*x + c)^5 + 5*(64*a^4*b - 64*a^3*b^2 + 32*a^2*b^3 - 8*a*b^4 + b^5)*cosh(d*x + c)^3 + (64*a^4*b - 64*a^3*b^2 + 32*a^2*b^3 - 8*a*b^4 + b^5)*cosh(d*x + c))*sinh(d*x + c)^3 + (64*a^3*b^2 - 56*a^2*b^3 + 20*a*b^4 - 3*b^5)*cosh(d*x + c)^2 + (45*(8*a^2*b^3 - 4*a*b^4 + b^5)*cosh(d*x + c)^8 + 28*(64*a^3*b^2 - 56*a^2*b^3 + 20*a*b^4 - 3*b^5)*cosh(d*x + c)^6 + 64*a^3*b^2 - 56*a^2*b^3 + 20*a*b^4 - 3*b^5 + 30*(64*a^4*b - 64*a^3*b^2 + 32*a^2*b^3 - 8*a*b^4 + b^5)*cosh(d*x + c)^4 + 12*(64*a^4*b - 64*a^3*b^2 + 32*a^2*b^3 - 8*a*b^4 + b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 2*(5*(8*a^2*b^3 - 4*a*b^4 + b^5)*cosh(d*x + c)^9 + 4*(64*a^3*b^2 - 56*a^2*b^3 + 20*a*b^4 - 3*b^5)*cosh(d*x + c)^7 + 6*(64*a^4*b - 64*a^3*b^2 + 32*a^2*b^3 - 8*a*b^4 + b^5)*cosh(d*x + c)^5 + 4*(64*a^4*b - 64*a^3*b^2 + 32*a^2*b^3 - 8*a*b^4 + b^5)*cosh(d*x + c)^3 + (64*a^3*b^2 - 56*a^2*b^3 + 20*a*b^4 - 3*b^5)*cosh(d*x + c))*sinh(d*x + c))*sqrt(a^2 - a*b)*log((b^2*cosh(d*x + c)^4 + 4*b^2*cosh(d*x + c)*sinh(d*x + c)^3 + b^2*sinh(d*x + c)^4 + 2*(2*a*b - b^2)*cosh(d*x + c)^2 + 2*(3*b^2*cosh(d*x + c)^2 + 2*a*b - b^2)*sinh(d*x + c)^2 + 8*a^2 - 8*a*b + b^2 + 4*(b^2*cosh(d*x + c)^3 + (2*a*b - b^2)*cosh(d*x + c))*sinh(d*x + c) - 4*(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + 2*a - b)*sqrt(a^2 - a*b))/(b*cosh(d*x + c)^4 + 4*b*cosh(d*x + c)*sinh(d*x + c)^3 + b*sinh(d*x + c)^4 + 2*(2*a - b)*cosh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^2 + 2*a - b)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^3 + (2*a - b)*cosh(d*x + c))*sinh(d*x + c) + b)) + 16*(6*(8*a^4*b^2 - 12*a^3*b^3 + 5*a^2*b^4 - a*b^5)*cosh(d*x + c)^7 + 9*(24*a^5*b - 44*a^4*b^2 + 27*a^3*b^3 - 8*a^2*b^4 + a*b^5)*cosh(d*x + c)^5 + 2*(64*a^6 - 88*a^5*b + 28*a^4*b^2 - 3*a^3*b^3 - a^2*b^4)*cosh(d*x + c)^3 + (32*a^5*b - 16*a^4*b^2 - 37*a^3*b^3 + 24*a^2*b^4 - 3*a*b^5)*cosh(d*x + c))*sinh(d*x + c))/((a^7*b^2 - 4*a^6*b^3 + 6*a^5*b^4 - 4*a^4*b^5 + a^3*b^6)*d*cosh(d*x + c)^10 + 10*(a^7*b^2 - 4*a^6*b^3 + 6*a^5*b^4 - 4*a^4*b^5 + a^3*b^6)*d*cosh(d*x + c)*sinh(d*x + c)^9 + (a^7*b^2 - 4*a^6*b^3 + 6*a^5*b^4 - 4*a^4*b^5 + a^3*b^6)*d*sinh(d*x + c)^10 + (8*a^8*b - 35*a^7*b^2 + 60*a^6*b^3 - 50*a^5*b^4 + 20*a^4*b^5 - 3*a^3*b^6)*d*cosh(d*x + c)^8 + (45*(a^7*b^2 - 4*a^6*b^3 + 6*a^5*b^4 - 4*a^4*b^5 + a^3*b^6)*d*cosh(d*x + c)^2 + (8*a^8*b - 35*a^7*b^2 + 60*a^6*b^3 - 50*a^5*b^4 + 20*a^4*b^5 - 3*a^3*b^6)*d)*sinh(d*x + c)^8 + 2*(8*a^9 - 36*a^8*b + 65*a^7*b^2 - 60*a^6*b^3 + 30*a^5*b^4 - 8*a^4*b^5 + a^3*b^6)*d*cosh(d*x + c)^6 + 8*(15*(a^7*b^2 - 4*a^6*b^3 + 6*a^5*b^4 - 4*a^4*b^5 + a^3*b^6)*d*cosh(d*x + c)^3 + (8*a^8*b - 35*a^7*b^2 + 60*a^6*b^3 - 50*a^5*b^4 + 20*a^4*b^5 - 3*a^3*b^6)*d*cosh(d*x + c))*sinh(d*x + c)^7 + 2*(105*(a^7*b^2 - 4*a^6*b^3 + 6*a^5*b^4 - 4*a^4*b^5 + a^3*b^6)*d*cosh(d*x + c)^4 + 14*(8*a^8*b - 35*a^7*b^2 + 60*a^6*b^3 - 50*a^5*b^4 + 20*a^4*b^5 - 3*a^3*b^6)*d*cosh(d*x + c)^2 + (8*a^9 - 36*a^8*b + 65*a^7*b^2 - 60*a^6*b^3 + 30*a^5*b^4 - 8*a^4*b^5 + a^3*b^6)*d)*sinh(d*x + c)^6 + 2*(8*a^9 - 36*a^8*b + 65*a^7*b^2 - 60*a^6*b^3 + 30*a^5*b^4 - 8*a^4*b^5 + a^3*b^6)*d*cosh(d*x + c)^4 + 4*(63*(a^7*b^2 - 4*a^6*b^3 + 6*a^5*b^4 - 4*a^4*b^5 + a^3*b^6)*d*cosh(d*x + c)^5 + 14*(8*a^8*b - 35*a^7*b^2 + 60*a^6*b^3 - 50*a^5*b^4 + 20*a^4*b^5 - 3*a^3*b^6)*d*cosh(d*x + c)^3 + 3*(8*a^9 - 36*a^8*b + 65*a^7*b^2 - 60*a^6*b^3 + 30*a^5*b^4 - 8*a^4*b^5 + a^3*b^6)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(105*(a^7*b^2 - 4*a^6*b^3 + 6*a^5*b^4 - 4*a^4*b^5 + a^3*b^6)*d*cosh(d*x + c)^6 + 35*(8*a^8*b - 35*a^7*b^2 + 60*a^6*b^3 - 50*a^5*b^4 + 20*a^4*b^5 - 3*a^3*b^6)*d*cosh(d*x + c)^4 + 15*(8*a^9 - 36*a^8*b + 65*a^7*b^2 - 60*a^6*b^3 + 30*a^5*b^4 - 8*a^4*b^5 + a^3*b^6)*d*cosh(d*x + c)^2 + (8*a^9 - 36*a^8*b + 65*a^7*b^2 - 60*a^6*b^3 + 30*a^5*b^4 - 8*a^4*b^5 + a^3*b^6)*d)*sinh(d*x + c)^4 + (8*a^8*b - 35*a^7*b^2 + 60*a^6*b^3 - 50*a^5*b^4 + 20*a^4*b^5 - 3*a^3*b^6)*d*cosh(d*x + c)^2 + 8*(15*(a^7*b^2 - 4*a^6*b^3 + 6*a^5*b^4 - 4*a^4*b^5 + a^3*b^6)*d*cosh(d*x + c)^7 + 7*(8*a^8*b - 35*a^7*b^2 + 60*a^6*b^3 - 50*a^5*b^4 + 20*a^4*b^5 - 3*a^3*b^6)*d*cosh(d*x + c)^5 + 5*(8*a^9 - 36*a^8*b + 65*a^7*b^2 - 60*a^6*b^3 + 30*a^5*b^4 - 8*a^4*b^5 + a^3*b^6)*d*cosh(d*x + c)^3 + (8*a^9 - 36*a^8*b + 65*a^7*b^2 - 60*a^6*b^3 + 30*a^5*b^4 - 8*a^4*b^5 + a^3*b^6)*d*cosh(d*x + c))*sinh(d*x + c)^3 + (45*(a^7*b^2 - 4*a^6*b^3 + 6*a^5*b^4 - 4*a^4*b^5 + a^3*b^6)*d*cosh(d*x + c)^8 + 28*(8*a^8*b - 35*a^7*b^2 + 60*a^6*b^3 - 50*a^5*b^4 + 20*a^4*b^5 - 3*a^3*b^6)*d*cosh(d*x + c)^6 + 30*(8*a^9 - 36*a^8*b + 65*a^7*b^2 - 60*a^6*b^3 + 30*a^5*b^4 - 8*a^4*b^5 + a^3*b^6)*d*cosh(d*x + c)^4 + 12*(8*a^9 - 36*a^8*b + 65*a^7*b^2 - 60*a^6*b^3 + 30*a^5*b^4 - 8*a^4*b^5 + a^3*b^6)*d*cosh(d*x + c)^2 + (8*a^8*b - 35*a^7*b^2 + 60*a^6*b^3 - 50*a^5*b^4 + 20*a^4*b^5 - 3*a^3*b^6)*d)*sinh(d*x + c)^2 + (a^7*b^2 - 4*a^6*b^3 + 6*a^5*b^4 - 4*a^4*b^5 + a^3*b^6)*d + 2*(5*(a^7*b^2 - 4*a^6*b^3 + 6*a^5*b^4 - 4*a^4*b^5 + a^3*b^6)*d*cosh(d*x + c)^9 + 4*(8*a^8*b - 35*a^7*b^2 + 60*a^6*b^3 - 50*a^5*b^4 + 20*a^4*b^5 - 3*a^3*b^6)*d*cosh(d*x + c)^7 + 6*(8*a^9 - 36*a^8*b + 65*a^7*b^2 - 60*a^6*b^3 + 30*a^5*b^4 - 8*a^4*b^5 + a^3*b^6)*d*cosh(d*x + c)^5 + 4*(8*a^9 - 36*a^8*b + 65*a^7*b^2 - 60*a^6*b^3 + 30*a^5*b^4 - 8*a^4*b^5 + a^3*b^6)*d*cosh(d*x + c)^3 + (8*a^8*b - 35*a^7*b^2 + 60*a^6*b^3 - 50*a^5*b^4 + 20*a^4*b^5 - 3*a^3*b^6)*d*cosh(d*x + c))*sinh(d*x + c)), -1/8*(6*(8*a^4*b^2 - 12*a^3*b^3 + 5*a^2*b^4 - a*b^5)*cosh(d*x + c)^8 + 48*(8*a^4*b^2 - 12*a^3*b^3 + 5*a^2*b^4 - a*b^5)*cosh(d*x + c)*sinh(d*x + c)^7 + 6*(8*a^4*b^2 - 12*a^3*b^3 + 5*a^2*b^4 - a*b^5)*sinh(d*x + c)^8 + 12*(24*a^5*b - 44*a^4*b^2 + 27*a^3*b^3 - 8*a^2*b^4 + a*b^5)*cosh(d*x + c)^6 + 12*(24*a^5*b - 44*a^4*b^2 + 27*a^3*b^3 - 8*a^2*b^4 + a*b^5 + 14*(8*a^4*b^2 - 12*a^3*b^3 + 5*a^2*b^4 - a*b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 16*a^4*b^2 + 4*a^3*b^3 - 26*a^2*b^4 + 6*a*b^5 + 24*(14*(8*a^4*b^2 - 12*a^3*b^3 + 5*a^2*b^4 - a*b^5)*cosh(d*x + c)^3 + 3*(24*a^5*b - 44*a^4*b^2 + 27*a^3*b^3 - 8*a^2*b^4 + a*b^5)*cosh(d*x + c))*sinh(d*x + c)^5 + 4*(64*a^6 - 88*a^5*b + 28*a^4*b^2 - 3*a^3*b^3 - a^2*b^4)*cosh(d*x + c)^4 + 4*(64*a^6 - 88*a^5*b + 28*a^4*b^2 - 3*a^3*b^3 - a^2*b^4 + 105*(8*a^4*b^2 - 12*a^3*b^3 + 5*a^2*b^4 - a*b^5)*cosh(d*x + c)^4 + 45*(24*a^5*b - 44*a^4*b^2 + 27*a^3*b^3 - 8*a^2*b^4 + a*b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 16*(21*(8*a^4*b^2 - 12*a^3*b^3 + 5*a^2*b^4 - a*b^5)*cosh(d*x + c)^5 + 15*(24*a^5*b - 44*a^4*b^2 + 27*a^3*b^3 - 8*a^2*b^4 + a*b^5)*cosh(d*x + c)^3 + (64*a^6 - 88*a^5*b + 28*a^4*b^2 - 3*a^3*b^3 - a^2*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(32*a^5*b - 16*a^4*b^2 - 37*a^3*b^3 + 24*a^2*b^4 - 3*a*b^5)*cosh(d*x + c)^2 + 4*(42*(8*a^4*b^2 - 12*a^3*b^3 + 5*a^2*b^4 - a*b^5)*cosh(d*x + c)^6 + 32*a^5*b - 16*a^4*b^2 - 37*a^3*b^3 + 24*a^2*b^4 - 3*a*b^5 + 45*(24*a^5*b - 44*a^4*b^2 + 27*a^3*b^3 - 8*a^2*b^4 + a*b^5)*cosh(d*x + c)^4 + 6*(64*a^6 - 88*a^5*b + 28*a^4*b^2 - 3*a^3*b^3 - a^2*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - 3*((8*a^2*b^3 - 4*a*b^4 + b^5)*cosh(d*x + c)^10 + 10*(8*a^2*b^3 - 4*a*b^4 + b^5)*cosh(d*x + c)*sinh(d*x + c)^9 + (8*a^2*b^3 - 4*a*b^4 + b^5)*sinh(d*x + c)^10 + (64*a^3*b^2 - 56*a^2*b^3 + 20*a*b^4 - 3*b^5)*cosh(d*x + c)^8 + (64*a^3*b^2 - 56*a^2*b^3 + 20*a*b^4 - 3*b^5 + 45*(8*a^2*b^3 - 4*a*b^4 + b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 8*(15*(8*a^2*b^3 - 4*a*b^4 + b^5)*cosh(d*x + c)^3 + (64*a^3*b^2 - 56*a^2*b^3 + 20*a*b^4 - 3*b^5)*cosh(d*x + c))*sinh(d*x + c)^7 + 2*(64*a^4*b - 64*a^3*b^2 + 32*a^2*b^3 - 8*a*b^4 + b^5)*cosh(d*x + c)^6 + 2*(64*a^4*b - 64*a^3*b^2 + 32*a^2*b^3 - 8*a*b^4 + b^5 + 105*(8*a^2*b^3 - 4*a*b^4 + b^5)*cosh(d*x + c)^4 + 14*(64*a^3*b^2 - 56*a^2*b^3 + 20*a*b^4 - 3*b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 4*(63*(8*a^2*b^3 - 4*a*b^4 + b^5)*cosh(d*x + c)^5 + 14*(64*a^3*b^2 - 56*a^2*b^3 + 20*a*b^4 - 3*b^5)*cosh(d*x + c)^3 + 3*(64*a^4*b - 64*a^3*b^2 + 32*a^2*b^3 - 8*a*b^4 + b^5)*cosh(d*x + c))*sinh(d*x + c)^5 + 8*a^2*b^3 - 4*a*b^4 + b^5 + 2*(64*a^4*b - 64*a^3*b^2 + 32*a^2*b^3 - 8*a*b^4 + b^5)*cosh(d*x + c)^4 + 2*(105*(8*a^2*b^3 - 4*a*b^4 + b^5)*cosh(d*x + c)^6 + 64*a^4*b - 64*a^3*b^2 + 32*a^2*b^3 - 8*a*b^4 + b^5 + 35*(64*a^3*b^2 - 56*a^2*b^3 + 20*a*b^4 - 3*b^5)*cosh(d*x + c)^4 + 15*(64*a^4*b - 64*a^3*b^2 + 32*a^2*b^3 - 8*a*b^4 + b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(15*(8*a^2*b^3 - 4*a*b^4 + b^5)*cosh(d*x + c)^7 + 7*(64*a^3*b^2 - 56*a^2*b^3 + 20*a*b^4 - 3*b^5)*cosh(d*x + c)^5 + 5*(64*a^4*b - 64*a^3*b^2 + 32*a^2*b^3 - 8*a*b^4 + b^5)*cosh(d*x + c)^3 + (64*a^4*b - 64*a^3*b^2 + 32*a^2*b^3 - 8*a*b^4 + b^5)*cosh(d*x + c))*sinh(d*x + c)^3 + (64*a^3*b^2 - 56*a^2*b^3 + 20*a*b^4 - 3*b^5)*cosh(d*x + c)^2 + (45*(8*a^2*b^3 - 4*a*b^4 + b^5)*cosh(d*x + c)^8 + 28*(64*a^3*b^2 - 56*a^2*b^3 + 20*a*b^4 - 3*b^5)*cosh(d*x + c)^6 + 64*a^3*b^2 - 56*a^2*b^3 + 20*a*b^4 - 3*b^5 + 30*(64*a^4*b - 64*a^3*b^2 + 32*a^2*b^3 - 8*a*b^4 + b^5)*cosh(d*x + c)^4 + 12*(64*a^4*b - 64*a^3*b^2 + 32*a^2*b^3 - 8*a*b^4 + b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 2*(5*(8*a^2*b^3 - 4*a*b^4 + b^5)*cosh(d*x + c)^9 + 4*(64*a^3*b^2 - 56*a^2*b^3 + 20*a*b^4 - 3*b^5)*cosh(d*x + c)^7 + 6*(64*a^4*b - 64*a^3*b^2 + 32*a^2*b^3 - 8*a*b^4 + b^5)*cosh(d*x + c)^5 + 4*(64*a^4*b - 64*a^3*b^2 + 32*a^2*b^3 - 8*a*b^4 + b^5)*cosh(d*x + c)^3 + (64*a^3*b^2 - 56*a^2*b^3 + 20*a*b^4 - 3*b^5)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-a^2 + a*b)*arctan(-1/2*(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 + 2*a - b)*sqrt(-a^2 + a*b)/(a^2 - a*b)) + 8*(6*(8*a^4*b^2 - 12*a^3*b^3 + 5*a^2*b^4 - a*b^5)*cosh(d*x + c)^7 + 9*(24*a^5*b - 44*a^4*b^2 + 27*a^3*b^3 - 8*a^2*b^4 + a*b^5)*cosh(d*x + c)^5 + 2*(64*a^6 - 88*a^5*b + 28*a^4*b^2 - 3*a^3*b^3 - a^2*b^4)*cosh(d*x + c)^3 + (32*a^5*b - 16*a^4*b^2 - 37*a^3*b^3 + 24*a^2*b^4 - 3*a*b^5)*cosh(d*x + c))*sinh(d*x + c))/((a^7*b^2 - 4*a^6*b^3 + 6*a^5*b^4 - 4*a^4*b^5 + a^3*b^6)*d*cosh(d*x + c)^10 + 10*(a^7*b^2 - 4*a^6*b^3 + 6*a^5*b^4 - 4*a^4*b^5 + a^3*b^6)*d*cosh(d*x + c)*sinh(d*x + c)^9 + (a^7*b^2 - 4*a^6*b^3 + 6*a^5*b^4 - 4*a^4*b^5 + a^3*b^6)*d*sinh(d*x + c)^10 + (8*a^8*b - 35*a^7*b^2 + 60*a^6*b^3 - 50*a^5*b^4 + 20*a^4*b^5 - 3*a^3*b^6)*d*cosh(d*x + c)^8 + (45*(a^7*b^2 - 4*a^6*b^3 + 6*a^5*b^4 - 4*a^4*b^5 + a^3*b^6)*d*cosh(d*x + c)^2 + (8*a^8*b - 35*a^7*b^2 + 60*a^6*b^3 - 50*a^5*b^4 + 20*a^4*b^5 - 3*a^3*b^6)*d)*sinh(d*x + c)^8 + 2*(8*a^9 - 36*a^8*b + 65*a^7*b^2 - 60*a^6*b^3 + 30*a^5*b^4 - 8*a^4*b^5 + a^3*b^6)*d*cosh(d*x + c)^6 + 8*(15*(a^7*b^2 - 4*a^6*b^3 + 6*a^5*b^4 - 4*a^4*b^5 + a^3*b^6)*d*cosh(d*x + c)^3 + (8*a^8*b - 35*a^7*b^2 + 60*a^6*b^3 - 50*a^5*b^4 + 20*a^4*b^5 - 3*a^3*b^6)*d*cosh(d*x + c))*sinh(d*x + c)^7 + 2*(105*(a^7*b^2 - 4*a^6*b^3 + 6*a^5*b^4 - 4*a^4*b^5 + a^3*b^6)*d*cosh(d*x + c)^4 + 14*(8*a^8*b - 35*a^7*b^2 + 60*a^6*b^3 - 50*a^5*b^4 + 20*a^4*b^5 - 3*a^3*b^6)*d*cosh(d*x + c)^2 + (8*a^9 - 36*a^8*b + 65*a^7*b^2 - 60*a^6*b^3 + 30*a^5*b^4 - 8*a^4*b^5 + a^3*b^6)*d)*sinh(d*x + c)^6 + 2*(8*a^9 - 36*a^8*b + 65*a^7*b^2 - 60*a^6*b^3 + 30*a^5*b^4 - 8*a^4*b^5 + a^3*b^6)*d*cosh(d*x + c)^4 + 4*(63*(a^7*b^2 - 4*a^6*b^3 + 6*a^5*b^4 - 4*a^4*b^5 + a^3*b^6)*d*cosh(d*x + c)^5 + 14*(8*a^8*b - 35*a^7*b^2 + 60*a^6*b^3 - 50*a^5*b^4 + 20*a^4*b^5 - 3*a^3*b^6)*d*cosh(d*x + c)^3 + 3*(8*a^9 - 36*a^8*b + 65*a^7*b^2 - 60*a^6*b^3 + 30*a^5*b^4 - 8*a^4*b^5 + a^3*b^6)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(105*(a^7*b^2 - 4*a^6*b^3 + 6*a^5*b^4 - 4*a^4*b^5 + a^3*b^6)*d*cosh(d*x + c)^6 + 35*(8*a^8*b - 35*a^7*b^2 + 60*a^6*b^3 - 50*a^5*b^4 + 20*a^4*b^5 - 3*a^3*b^6)*d*cosh(d*x + c)^4 + 15*(8*a^9 - 36*a^8*b + 65*a^7*b^2 - 60*a^6*b^3 + 30*a^5*b^4 - 8*a^4*b^5 + a^3*b^6)*d*cosh(d*x + c)^2 + (8*a^9 - 36*a^8*b + 65*a^7*b^2 - 60*a^6*b^3 + 30*a^5*b^4 - 8*a^4*b^5 + a^3*b^6)*d)*sinh(d*x + c)^4 + (8*a^8*b - 35*a^7*b^2 + 60*a^6*b^3 - 50*a^5*b^4 + 20*a^4*b^5 - 3*a^3*b^6)*d*cosh(d*x + c)^2 + 8*(15*(a^7*b^2 - 4*a^6*b^3 + 6*a^5*b^4 - 4*a^4*b^5 + a^3*b^6)*d*cosh(d*x + c)^7 + 7*(8*a^8*b - 35*a^7*b^2 + 60*a^6*b^3 - 50*a^5*b^4 + 20*a^4*b^5 - 3*a^3*b^6)*d*cosh(d*x + c)^5 + 5*(8*a^9 - 36*a^8*b + 65*a^7*b^2 - 60*a^6*b^3 + 30*a^5*b^4 - 8*a^4*b^5 + a^3*b^6)*d*cosh(d*x + c)^3 + (8*a^9 - 36*a^8*b + 65*a^7*b^2 - 60*a^6*b^3 + 30*a^5*b^4 - 8*a^4*b^5 + a^3*b^6)*d*cosh(d*x + c))*sinh(d*x + c)^3 + (45*(a^7*b^2 - 4*a^6*b^3 + 6*a^5*b^4 - 4*a^4*b^5 + a^3*b^6)*d*cosh(d*x + c)^8 + 28*(8*a^8*b - 35*a^7*b^2 + 60*a^6*b^3 - 50*a^5*b^4 + 20*a^4*b^5 - 3*a^3*b^6)*d*cosh(d*x + c)^6 + 30*(8*a^9 - 36*a^8*b + 65*a^7*b^2 - 60*a^6*b^3 + 30*a^5*b^4 - 8*a^4*b^5 + a^3*b^6)*d*cosh(d*x + c)^4 + 12*(8*a^9 - 36*a^8*b + 65*a^7*b^2 - 60*a^6*b^3 + 30*a^5*b^4 - 8*a^4*b^5 + a^3*b^6)*d*cosh(d*x + c)^2 + (8*a^8*b - 35*a^7*b^2 + 60*a^6*b^3 - 50*a^5*b^4 + 20*a^4*b^5 - 3*a^3*b^6)*d)*sinh(d*x + c)^2 + (a^7*b^2 - 4*a^6*b^3 + 6*a^5*b^4 - 4*a^4*b^5 + a^3*b^6)*d + 2*(5*(a^7*b^2 - 4*a^6*b^3 + 6*a^5*b^4 - 4*a^4*b^5 + a^3*b^6)*d*cosh(d*x + c)^9 + 4*(8*a^8*b - 35*a^7*b^2 + 60*a^6*b^3 - 50*a^5*b^4 + 20*a^4*b^5 - 3*a^3*b^6)*d*cosh(d*x + c)^7 + 6*(8*a^9 - 36*a^8*b + 65*a^7*b^2 - 60*a^6*b^3 + 30*a^5*b^4 - 8*a^4*b^5 + a^3*b^6)*d*cosh(d*x + c)^5 + 4*(8*a^9 - 36*a^8*b + 65*a^7*b^2 - 60*a^6*b^3 + 30*a^5*b^4 - 8*a^4*b^5 + a^3*b^6)*d*cosh(d*x + c)^3 + (8*a^8*b - 35*a^7*b^2 + 60*a^6*b^3 - 50*a^5*b^4 + 20*a^4*b^5 - 3*a^3*b^6)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
347,-1,0,0,0.000000," ","integrate(sech(d*x+c)^3/(a+b*sinh(d*x+c)^2)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
348,-1,0,0,0.000000," ","integrate(sech(d*x+c)^4/(a+b*sinh(d*x+c)^2)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
349,1,70,0,0.628984," ","integrate(cosh(x)^2/(1-sinh(x)^2),x, algorithm=""fricas"")","\frac{1}{2} \, \sqrt{2} \log\left(-\frac{3 \, {\left(2 \, \sqrt{2} - 3\right)} \cosh\left(x\right)^{2} - 4 \, {\left(3 \, \sqrt{2} - 4\right)} \cosh\left(x\right) \sinh\left(x\right) + 3 \, {\left(2 \, \sqrt{2} - 3\right)} \sinh\left(x\right)^{2} - 2 \, \sqrt{2} + 3}{\cosh\left(x\right)^{2} + \sinh\left(x\right)^{2} - 3}\right) - x"," ",0,"1/2*sqrt(2)*log(-(3*(2*sqrt(2) - 3)*cosh(x)^2 - 4*(3*sqrt(2) - 4)*cosh(x)*sinh(x) + 3*(2*sqrt(2) - 3)*sinh(x)^2 - 2*sqrt(2) + 3)/(cosh(x)^2 + sinh(x)^2 - 3)) - x","B",0
350,1,71,0,1.008484," ","integrate(cosh(x)^3/(1-sinh(x)^2),x, algorithm=""fricas"")","-\frac{\cosh\left(x\right)^{2} - 2 \, {\left(\cosh\left(x\right) + \sinh\left(x\right)\right)} \log\left(\frac{2 \, {\left(\sinh\left(x\right) + 1\right)}}{\cosh\left(x\right) - \sinh\left(x\right)}\right) + 2 \, {\left(\cosh\left(x\right) + \sinh\left(x\right)\right)} \log\left(\frac{2 \, {\left(\sinh\left(x\right) - 1\right)}}{\cosh\left(x\right) - \sinh\left(x\right)}\right) + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1}{2 \, {\left(\cosh\left(x\right) + \sinh\left(x\right)\right)}}"," ",0,"-1/2*(cosh(x)^2 - 2*(cosh(x) + sinh(x))*log(2*(sinh(x) + 1)/(cosh(x) - sinh(x))) + 2*(cosh(x) + sinh(x))*log(2*(sinh(x) - 1)/(cosh(x) - sinh(x))) + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)/(cosh(x) + sinh(x))","B",0
351,1,163,0,0.600055," ","integrate(cosh(x)^4/(1-sinh(x)^2),x, algorithm=""fricas"")","-\frac{\cosh\left(x\right)^{4} + 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4} + 20 \, x \cosh\left(x\right)^{2} + 2 \, {\left(3 \, \cosh\left(x\right)^{2} + 10 \, x\right)} \sinh\left(x\right)^{2} - 8 \, {\left(\sqrt{2} \cosh\left(x\right)^{2} + 2 \, \sqrt{2} \cosh\left(x\right) \sinh\left(x\right) + \sqrt{2} \sinh\left(x\right)^{2}\right)} \log\left(-\frac{3 \, {\left(2 \, \sqrt{2} - 3\right)} \cosh\left(x\right)^{2} - 4 \, {\left(3 \, \sqrt{2} - 4\right)} \cosh\left(x\right) \sinh\left(x\right) + 3 \, {\left(2 \, \sqrt{2} - 3\right)} \sinh\left(x\right)^{2} - 2 \, \sqrt{2} + 3}{\cosh\left(x\right)^{2} + \sinh\left(x\right)^{2} - 3}\right) + 4 \, {\left(\cosh\left(x\right)^{3} + 10 \, x \cosh\left(x\right)\right)} \sinh\left(x\right) - 1}{8 \, {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}\right)}}"," ",0,"-1/8*(cosh(x)^4 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4 + 20*x*cosh(x)^2 + 2*(3*cosh(x)^2 + 10*x)*sinh(x)^2 - 8*(sqrt(2)*cosh(x)^2 + 2*sqrt(2)*cosh(x)*sinh(x) + sqrt(2)*sinh(x)^2)*log(-(3*(2*sqrt(2) - 3)*cosh(x)^2 - 4*(3*sqrt(2) - 4)*cosh(x)*sinh(x) + 3*(2*sqrt(2) - 3)*sinh(x)^2 - 2*sqrt(2) + 3)/(cosh(x)^2 + sinh(x)^2 - 3)) + 4*(cosh(x)^3 + 10*x*cosh(x))*sinh(x) - 1)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)","B",0
352,1,3281,0,0.813490," ","integrate(cosh(f*x+e)^3*(a+b*sinh(f*x+e)^2)^(1/2),x, algorithm=""fricas"")","\left[-\frac{2 \, {\left({\left(a^{2} - 4 \, a b\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left(a^{2} - 4 \, a b\right)} \cosh\left(f x + e\right)^{3} \sinh\left(f x + e\right) + 6 \, {\left(a^{2} - 4 \, a b\right)} \cosh\left(f x + e\right)^{2} \sinh\left(f x + e\right)^{2} + 4 \, {\left(a^{2} - 4 \, a b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(a^{2} - 4 \, a b\right)} \sinh\left(f x + e\right)^{4}\right)} \sqrt{b} \log\left(-\frac{{\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{8} + 8 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \sinh\left(f x + e\right)^{8} + 2 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{6} + 2 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3} + 14 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{6} + 4 \, {\left(14 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + {\left(9 \, a^{2} b - 14 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} + {\left(70 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{4} + 9 \, a^{2} b - 14 \, a b^{2} + 6 \, b^{3} + 30 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(14 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{5} + 10 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} + {\left(9 \, a^{2} b - 14 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + b^{3} + 2 \, {\left(3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(14 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{6} + 15 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} + 3 \, a b^{2} - 2 \, b^{3} + 3 \, {\left(9 \, a^{2} b - 14 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{2} + \sqrt{2} {\left({\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{6} + 6 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + {\left(a^{2} - 2 \, a b + b^{2}\right)} \sinh\left(f x + e\right)^{6} - 3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{4} + 3 \, {\left(5 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{2} - a^{2} + 2 \, a b - b^{2}\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(5 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{3} - 3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} - {\left(4 \, a b - 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + {\left(15 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{4} - 18 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{2} - 4 \, a b + 3 \, b^{2}\right)} \sinh\left(f x + e\right)^{2} - b^{2} + 2 \, {\left(3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{5} - 6 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{3} - {\left(4 \, a b - 3 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} + 4 \, {\left(2 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{7} + 3 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{5} + {\left(9 \, a^{2} b - 14 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} + {\left(3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)}{\cosh\left(f x + e\right)^{6} + 6 \, \cosh\left(f x + e\right)^{5} \sinh\left(f x + e\right) + 15 \, \cosh\left(f x + e\right)^{4} \sinh\left(f x + e\right)^{2} + 20 \, \cosh\left(f x + e\right)^{3} \sinh\left(f x + e\right)^{3} + 15 \, \cosh\left(f x + e\right)^{2} \sinh\left(f x + e\right)^{4} + 6 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + \sinh\left(f x + e\right)^{6}}\right) + 2 \, {\left({\left(a^{2} - 4 \, a b\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left(a^{2} - 4 \, a b\right)} \cosh\left(f x + e\right)^{3} \sinh\left(f x + e\right) + 6 \, {\left(a^{2} - 4 \, a b\right)} \cosh\left(f x + e\right)^{2} \sinh\left(f x + e\right)^{2} + 4 \, {\left(a^{2} - 4 \, a b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(a^{2} - 4 \, a b\right)} \sinh\left(f x + e\right)^{4}\right)} \sqrt{b} \log\left(\frac{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, a \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + a\right)} \sinh\left(f x + e\right)^{2} + \sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} + 1\right)} \sqrt{b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + a \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}{\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}\right) - \sqrt{2} {\left(b^{2} \cosh\left(f x + e\right)^{6} + 6 \, b^{2} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + b^{2} \sinh\left(f x + e\right)^{6} + {\left(2 \, a b + 5 \, b^{2}\right)} \cosh\left(f x + e\right)^{4} + {\left(15 \, b^{2} \cosh\left(f x + e\right)^{2} + 2 \, a b + 5 \, b^{2}\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(5 \, b^{2} \cosh\left(f x + e\right)^{3} + {\left(2 \, a b + 5 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} - {\left(2 \, a b + 5 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + {\left(15 \, b^{2} \cosh\left(f x + e\right)^{4} + 6 \, {\left(2 \, a b + 5 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} - 2 \, a b - 5 \, b^{2}\right)} \sinh\left(f x + e\right)^{2} - b^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(f x + e\right)^{5} + 2 \, {\left(2 \, a b + 5 \, b^{2}\right)} \cosh\left(f x + e\right)^{3} - {\left(2 \, a b + 5 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{64 \, {\left(b^{2} f \cosh\left(f x + e\right)^{4} + 4 \, b^{2} f \cosh\left(f x + e\right)^{3} \sinh\left(f x + e\right) + 6 \, b^{2} f \cosh\left(f x + e\right)^{2} \sinh\left(f x + e\right)^{2} + 4 \, b^{2} f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b^{2} f \sinh\left(f x + e\right)^{4}\right)}}, \frac{4 \, {\left({\left(a^{2} - 4 \, a b\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left(a^{2} - 4 \, a b\right)} \cosh\left(f x + e\right)^{3} \sinh\left(f x + e\right) + 6 \, {\left(a^{2} - 4 \, a b\right)} \cosh\left(f x + e\right)^{2} \sinh\left(f x + e\right)^{2} + 4 \, {\left(a^{2} - 4 \, a b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(a^{2} - 4 \, a b\right)} \sinh\left(f x + e\right)^{4}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{2} {\left({\left(a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(a - b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) + {\left(a - b\right)} \sinh\left(f x + e\right)^{2} + b\right)} \sqrt{-b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{{\left(a b - b^{2}\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left(a b - b^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(a b - b^{2}\right)} \sinh\left(f x + e\right)^{4} - {\left(3 \, a b - 2 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + {\left(6 \, {\left(a b - b^{2}\right)} \cosh\left(f x + e\right)^{2} - 3 \, a b + 2 \, b^{2}\right)} \sinh\left(f x + e\right)^{2} - b^{2} + 2 \, {\left(2 \, {\left(a b - b^{2}\right)} \cosh\left(f x + e\right)^{3} - {\left(3 \, a b - 2 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)}\right) + 4 \, {\left({\left(a^{2} - 4 \, a b\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left(a^{2} - 4 \, a b\right)} \cosh\left(f x + e\right)^{3} \sinh\left(f x + e\right) + 6 \, {\left(a^{2} - 4 \, a b\right)} \cosh\left(f x + e\right)^{2} \sinh\left(f x + e\right)^{2} + 4 \, {\left(a^{2} - 4 \, a b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(a^{2} - 4 \, a b\right)} \sinh\left(f x + e\right)^{4}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} + 1\right)} \sqrt{-b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + 2 \, a - b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}\right) + \sqrt{2} {\left(b^{2} \cosh\left(f x + e\right)^{6} + 6 \, b^{2} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + b^{2} \sinh\left(f x + e\right)^{6} + {\left(2 \, a b + 5 \, b^{2}\right)} \cosh\left(f x + e\right)^{4} + {\left(15 \, b^{2} \cosh\left(f x + e\right)^{2} + 2 \, a b + 5 \, b^{2}\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(5 \, b^{2} \cosh\left(f x + e\right)^{3} + {\left(2 \, a b + 5 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} - {\left(2 \, a b + 5 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + {\left(15 \, b^{2} \cosh\left(f x + e\right)^{4} + 6 \, {\left(2 \, a b + 5 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} - 2 \, a b - 5 \, b^{2}\right)} \sinh\left(f x + e\right)^{2} - b^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(f x + e\right)^{5} + 2 \, {\left(2 \, a b + 5 \, b^{2}\right)} \cosh\left(f x + e\right)^{3} - {\left(2 \, a b + 5 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{64 \, {\left(b^{2} f \cosh\left(f x + e\right)^{4} + 4 \, b^{2} f \cosh\left(f x + e\right)^{3} \sinh\left(f x + e\right) + 6 \, b^{2} f \cosh\left(f x + e\right)^{2} \sinh\left(f x + e\right)^{2} + 4 \, b^{2} f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b^{2} f \sinh\left(f x + e\right)^{4}\right)}}\right]"," ",0,"[-1/64*(2*((a^2 - 4*a*b)*cosh(f*x + e)^4 + 4*(a^2 - 4*a*b)*cosh(f*x + e)^3*sinh(f*x + e) + 6*(a^2 - 4*a*b)*cosh(f*x + e)^2*sinh(f*x + e)^2 + 4*(a^2 - 4*a*b)*cosh(f*x + e)*sinh(f*x + e)^3 + (a^2 - 4*a*b)*sinh(f*x + e)^4)*sqrt(b)*log(-((a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^8 + 8*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)*sinh(f*x + e)^7 + (a^2*b - 2*a*b^2 + b^3)*sinh(f*x + e)^8 + 2*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e)^6 + 2*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3 + 14*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^6 + 4*(14*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^3 + 3*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e))*sinh(f*x + e)^5 + (9*a^2*b - 14*a*b^2 + 6*b^3)*cosh(f*x + e)^4 + (70*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^4 + 9*a^2*b - 14*a*b^2 + 6*b^3 + 30*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^4 + 4*(14*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^5 + 10*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e)^3 + (9*a^2*b - 14*a*b^2 + 6*b^3)*cosh(f*x + e))*sinh(f*x + e)^3 + b^3 + 2*(3*a*b^2 - 2*b^3)*cosh(f*x + e)^2 + 2*(14*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^6 + 15*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e)^4 + 3*a*b^2 - 2*b^3 + 3*(9*a^2*b - 14*a*b^2 + 6*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^2 + sqrt(2)*((a^2 - 2*a*b + b^2)*cosh(f*x + e)^6 + 6*(a^2 - 2*a*b + b^2)*cosh(f*x + e)*sinh(f*x + e)^5 + (a^2 - 2*a*b + b^2)*sinh(f*x + e)^6 - 3*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^4 + 3*(5*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^2 - a^2 + 2*a*b - b^2)*sinh(f*x + e)^4 + 4*(5*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^3 - 3*(a^2 - 2*a*b + b^2)*cosh(f*x + e))*sinh(f*x + e)^3 - (4*a*b - 3*b^2)*cosh(f*x + e)^2 + (15*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^4 - 18*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^2 - 4*a*b + 3*b^2)*sinh(f*x + e)^2 - b^2 + 2*(3*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^5 - 6*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^3 - (4*a*b - 3*b^2)*cosh(f*x + e))*sinh(f*x + e))*sqrt(b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + 4*(2*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^7 + 3*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e)^5 + (9*a^2*b - 14*a*b^2 + 6*b^3)*cosh(f*x + e)^3 + (3*a*b^2 - 2*b^3)*cosh(f*x + e))*sinh(f*x + e))/(cosh(f*x + e)^6 + 6*cosh(f*x + e)^5*sinh(f*x + e) + 15*cosh(f*x + e)^4*sinh(f*x + e)^2 + 20*cosh(f*x + e)^3*sinh(f*x + e)^3 + 15*cosh(f*x + e)^2*sinh(f*x + e)^4 + 6*cosh(f*x + e)*sinh(f*x + e)^5 + sinh(f*x + e)^6)) + 2*((a^2 - 4*a*b)*cosh(f*x + e)^4 + 4*(a^2 - 4*a*b)*cosh(f*x + e)^3*sinh(f*x + e) + 6*(a^2 - 4*a*b)*cosh(f*x + e)^2*sinh(f*x + e)^2 + 4*(a^2 - 4*a*b)*cosh(f*x + e)*sinh(f*x + e)^3 + (a^2 - 4*a*b)*sinh(f*x + e)^4)*sqrt(b)*log((b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*a*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + a)*sinh(f*x + e)^2 + sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 + 1)*sqrt(b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + 4*(b*cosh(f*x + e)^3 + a*cosh(f*x + e))*sinh(f*x + e) + b)/(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) - sqrt(2)*(b^2*cosh(f*x + e)^6 + 6*b^2*cosh(f*x + e)*sinh(f*x + e)^5 + b^2*sinh(f*x + e)^6 + (2*a*b + 5*b^2)*cosh(f*x + e)^4 + (15*b^2*cosh(f*x + e)^2 + 2*a*b + 5*b^2)*sinh(f*x + e)^4 + 4*(5*b^2*cosh(f*x + e)^3 + (2*a*b + 5*b^2)*cosh(f*x + e))*sinh(f*x + e)^3 - (2*a*b + 5*b^2)*cosh(f*x + e)^2 + (15*b^2*cosh(f*x + e)^4 + 6*(2*a*b + 5*b^2)*cosh(f*x + e)^2 - 2*a*b - 5*b^2)*sinh(f*x + e)^2 - b^2 + 2*(3*b^2*cosh(f*x + e)^5 + 2*(2*a*b + 5*b^2)*cosh(f*x + e)^3 - (2*a*b + 5*b^2)*cosh(f*x + e))*sinh(f*x + e))*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/(b^2*f*cosh(f*x + e)^4 + 4*b^2*f*cosh(f*x + e)^3*sinh(f*x + e) + 6*b^2*f*cosh(f*x + e)^2*sinh(f*x + e)^2 + 4*b^2*f*cosh(f*x + e)*sinh(f*x + e)^3 + b^2*f*sinh(f*x + e)^4), 1/64*(4*((a^2 - 4*a*b)*cosh(f*x + e)^4 + 4*(a^2 - 4*a*b)*cosh(f*x + e)^3*sinh(f*x + e) + 6*(a^2 - 4*a*b)*cosh(f*x + e)^2*sinh(f*x + e)^2 + 4*(a^2 - 4*a*b)*cosh(f*x + e)*sinh(f*x + e)^3 + (a^2 - 4*a*b)*sinh(f*x + e)^4)*sqrt(-b)*arctan(sqrt(2)*((a - b)*cosh(f*x + e)^2 + 2*(a - b)*cosh(f*x + e)*sinh(f*x + e) + (a - b)*sinh(f*x + e)^2 + b)*sqrt(-b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/((a*b - b^2)*cosh(f*x + e)^4 + 4*(a*b - b^2)*cosh(f*x + e)*sinh(f*x + e)^3 + (a*b - b^2)*sinh(f*x + e)^4 - (3*a*b - 2*b^2)*cosh(f*x + e)^2 + (6*(a*b - b^2)*cosh(f*x + e)^2 - 3*a*b + 2*b^2)*sinh(f*x + e)^2 - b^2 + 2*(2*(a*b - b^2)*cosh(f*x + e)^3 - (3*a*b - 2*b^2)*cosh(f*x + e))*sinh(f*x + e))) + 4*((a^2 - 4*a*b)*cosh(f*x + e)^4 + 4*(a^2 - 4*a*b)*cosh(f*x + e)^3*sinh(f*x + e) + 6*(a^2 - 4*a*b)*cosh(f*x + e)^2*sinh(f*x + e)^2 + 4*(a^2 - 4*a*b)*cosh(f*x + e)*sinh(f*x + e)^3 + (a^2 - 4*a*b)*sinh(f*x + e)^4)*sqrt(-b)*arctan(sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 + 1)*sqrt(-b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/(b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(2*a - b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 2*a - b)*sinh(f*x + e)^2 + 4*(b*cosh(f*x + e)^3 + (2*a - b)*cosh(f*x + e))*sinh(f*x + e) + b)) + sqrt(2)*(b^2*cosh(f*x + e)^6 + 6*b^2*cosh(f*x + e)*sinh(f*x + e)^5 + b^2*sinh(f*x + e)^6 + (2*a*b + 5*b^2)*cosh(f*x + e)^4 + (15*b^2*cosh(f*x + e)^2 + 2*a*b + 5*b^2)*sinh(f*x + e)^4 + 4*(5*b^2*cosh(f*x + e)^3 + (2*a*b + 5*b^2)*cosh(f*x + e))*sinh(f*x + e)^3 - (2*a*b + 5*b^2)*cosh(f*x + e)^2 + (15*b^2*cosh(f*x + e)^4 + 6*(2*a*b + 5*b^2)*cosh(f*x + e)^2 - 2*a*b - 5*b^2)*sinh(f*x + e)^2 - b^2 + 2*(3*b^2*cosh(f*x + e)^5 + 2*(2*a*b + 5*b^2)*cosh(f*x + e)^3 - (2*a*b + 5*b^2)*cosh(f*x + e))*sinh(f*x + e))*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/(b^2*f*cosh(f*x + e)^4 + 4*b^2*f*cosh(f*x + e)^3*sinh(f*x + e) + 6*b^2*f*cosh(f*x + e)^2*sinh(f*x + e)^2 + 4*b^2*f*cosh(f*x + e)*sinh(f*x + e)^3 + b^2*f*sinh(f*x + e)^4)]","B",0
353,1,2419,0,0.686119," ","integrate(cosh(f*x+e)*(a+b*sinh(f*x+e)^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(a \cosh\left(f x + e\right)^{2} + 2 \, a \cosh\left(f x + e\right) \sinh\left(f x + e\right) + a \sinh\left(f x + e\right)^{2}\right)} \sqrt{b} \log\left(-\frac{{\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{8} + 8 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \sinh\left(f x + e\right)^{8} + 2 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{6} + 2 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3} + 14 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{6} + 4 \, {\left(14 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + {\left(9 \, a^{2} b - 14 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} + {\left(70 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{4} + 9 \, a^{2} b - 14 \, a b^{2} + 6 \, b^{3} + 30 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(14 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{5} + 10 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} + {\left(9 \, a^{2} b - 14 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + b^{3} + 2 \, {\left(3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(14 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{6} + 15 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} + 3 \, a b^{2} - 2 \, b^{3} + 3 \, {\left(9 \, a^{2} b - 14 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{2} + \sqrt{2} {\left({\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{6} + 6 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + {\left(a^{2} - 2 \, a b + b^{2}\right)} \sinh\left(f x + e\right)^{6} - 3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{4} + 3 \, {\left(5 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{2} - a^{2} + 2 \, a b - b^{2}\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(5 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{3} - 3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} - {\left(4 \, a b - 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + {\left(15 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{4} - 18 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{2} - 4 \, a b + 3 \, b^{2}\right)} \sinh\left(f x + e\right)^{2} - b^{2} + 2 \, {\left(3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{5} - 6 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{3} - {\left(4 \, a b - 3 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} + 4 \, {\left(2 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{7} + 3 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{5} + {\left(9 \, a^{2} b - 14 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} + {\left(3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)}{\cosh\left(f x + e\right)^{6} + 6 \, \cosh\left(f x + e\right)^{5} \sinh\left(f x + e\right) + 15 \, \cosh\left(f x + e\right)^{4} \sinh\left(f x + e\right)^{2} + 20 \, \cosh\left(f x + e\right)^{3} \sinh\left(f x + e\right)^{3} + 15 \, \cosh\left(f x + e\right)^{2} \sinh\left(f x + e\right)^{4} + 6 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + \sinh\left(f x + e\right)^{6}}\right) + {\left(a \cosh\left(f x + e\right)^{2} + 2 \, a \cosh\left(f x + e\right) \sinh\left(f x + e\right) + a \sinh\left(f x + e\right)^{2}\right)} \sqrt{b} \log\left(\frac{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, a \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + a\right)} \sinh\left(f x + e\right)^{2} + \sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} + 1\right)} \sqrt{b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + a \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}{\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}\right) + \sqrt{2} {\left(b \cosh\left(f x + e\right)^{2} + 2 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right) + b \sinh\left(f x + e\right)^{2} - b\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{8 \, {\left(b f \cosh\left(f x + e\right)^{2} + 2 \, b f \cosh\left(f x + e\right) \sinh\left(f x + e\right) + b f \sinh\left(f x + e\right)^{2}\right)}}, -\frac{2 \, {\left(a \cosh\left(f x + e\right)^{2} + 2 \, a \cosh\left(f x + e\right) \sinh\left(f x + e\right) + a \sinh\left(f x + e\right)^{2}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{2} {\left({\left(a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(a - b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) + {\left(a - b\right)} \sinh\left(f x + e\right)^{2} + b\right)} \sqrt{-b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{{\left(a b - b^{2}\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left(a b - b^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(a b - b^{2}\right)} \sinh\left(f x + e\right)^{4} - {\left(3 \, a b - 2 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + {\left(6 \, {\left(a b - b^{2}\right)} \cosh\left(f x + e\right)^{2} - 3 \, a b + 2 \, b^{2}\right)} \sinh\left(f x + e\right)^{2} - b^{2} + 2 \, {\left(2 \, {\left(a b - b^{2}\right)} \cosh\left(f x + e\right)^{3} - {\left(3 \, a b - 2 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)}\right) + 2 \, {\left(a \cosh\left(f x + e\right)^{2} + 2 \, a \cosh\left(f x + e\right) \sinh\left(f x + e\right) + a \sinh\left(f x + e\right)^{2}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} + 1\right)} \sqrt{-b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + 2 \, a - b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}\right) - \sqrt{2} {\left(b \cosh\left(f x + e\right)^{2} + 2 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right) + b \sinh\left(f x + e\right)^{2} - b\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{8 \, {\left(b f \cosh\left(f x + e\right)^{2} + 2 \, b f \cosh\left(f x + e\right) \sinh\left(f x + e\right) + b f \sinh\left(f x + e\right)^{2}\right)}}\right]"," ",0,"[1/8*((a*cosh(f*x + e)^2 + 2*a*cosh(f*x + e)*sinh(f*x + e) + a*sinh(f*x + e)^2)*sqrt(b)*log(-((a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^8 + 8*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)*sinh(f*x + e)^7 + (a^2*b - 2*a*b^2 + b^3)*sinh(f*x + e)^8 + 2*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e)^6 + 2*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3 + 14*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^6 + 4*(14*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^3 + 3*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e))*sinh(f*x + e)^5 + (9*a^2*b - 14*a*b^2 + 6*b^3)*cosh(f*x + e)^4 + (70*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^4 + 9*a^2*b - 14*a*b^2 + 6*b^3 + 30*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^4 + 4*(14*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^5 + 10*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e)^3 + (9*a^2*b - 14*a*b^2 + 6*b^3)*cosh(f*x + e))*sinh(f*x + e)^3 + b^3 + 2*(3*a*b^2 - 2*b^3)*cosh(f*x + e)^2 + 2*(14*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^6 + 15*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e)^4 + 3*a*b^2 - 2*b^3 + 3*(9*a^2*b - 14*a*b^2 + 6*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^2 + sqrt(2)*((a^2 - 2*a*b + b^2)*cosh(f*x + e)^6 + 6*(a^2 - 2*a*b + b^2)*cosh(f*x + e)*sinh(f*x + e)^5 + (a^2 - 2*a*b + b^2)*sinh(f*x + e)^6 - 3*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^4 + 3*(5*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^2 - a^2 + 2*a*b - b^2)*sinh(f*x + e)^4 + 4*(5*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^3 - 3*(a^2 - 2*a*b + b^2)*cosh(f*x + e))*sinh(f*x + e)^3 - (4*a*b - 3*b^2)*cosh(f*x + e)^2 + (15*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^4 - 18*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^2 - 4*a*b + 3*b^2)*sinh(f*x + e)^2 - b^2 + 2*(3*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^5 - 6*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^3 - (4*a*b - 3*b^2)*cosh(f*x + e))*sinh(f*x + e))*sqrt(b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + 4*(2*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^7 + 3*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e)^5 + (9*a^2*b - 14*a*b^2 + 6*b^3)*cosh(f*x + e)^3 + (3*a*b^2 - 2*b^3)*cosh(f*x + e))*sinh(f*x + e))/(cosh(f*x + e)^6 + 6*cosh(f*x + e)^5*sinh(f*x + e) + 15*cosh(f*x + e)^4*sinh(f*x + e)^2 + 20*cosh(f*x + e)^3*sinh(f*x + e)^3 + 15*cosh(f*x + e)^2*sinh(f*x + e)^4 + 6*cosh(f*x + e)*sinh(f*x + e)^5 + sinh(f*x + e)^6)) + (a*cosh(f*x + e)^2 + 2*a*cosh(f*x + e)*sinh(f*x + e) + a*sinh(f*x + e)^2)*sqrt(b)*log((b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*a*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + a)*sinh(f*x + e)^2 + sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 + 1)*sqrt(b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + 4*(b*cosh(f*x + e)^3 + a*cosh(f*x + e))*sinh(f*x + e) + b)/(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + sqrt(2)*(b*cosh(f*x + e)^2 + 2*b*cosh(f*x + e)*sinh(f*x + e) + b*sinh(f*x + e)^2 - b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/(b*f*cosh(f*x + e)^2 + 2*b*f*cosh(f*x + e)*sinh(f*x + e) + b*f*sinh(f*x + e)^2), -1/8*(2*(a*cosh(f*x + e)^2 + 2*a*cosh(f*x + e)*sinh(f*x + e) + a*sinh(f*x + e)^2)*sqrt(-b)*arctan(sqrt(2)*((a - b)*cosh(f*x + e)^2 + 2*(a - b)*cosh(f*x + e)*sinh(f*x + e) + (a - b)*sinh(f*x + e)^2 + b)*sqrt(-b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/((a*b - b^2)*cosh(f*x + e)^4 + 4*(a*b - b^2)*cosh(f*x + e)*sinh(f*x + e)^3 + (a*b - b^2)*sinh(f*x + e)^4 - (3*a*b - 2*b^2)*cosh(f*x + e)^2 + (6*(a*b - b^2)*cosh(f*x + e)^2 - 3*a*b + 2*b^2)*sinh(f*x + e)^2 - b^2 + 2*(2*(a*b - b^2)*cosh(f*x + e)^3 - (3*a*b - 2*b^2)*cosh(f*x + e))*sinh(f*x + e))) + 2*(a*cosh(f*x + e)^2 + 2*a*cosh(f*x + e)*sinh(f*x + e) + a*sinh(f*x + e)^2)*sqrt(-b)*arctan(sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 + 1)*sqrt(-b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/(b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(2*a - b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 2*a - b)*sinh(f*x + e)^2 + 4*(b*cosh(f*x + e)^3 + (2*a - b)*cosh(f*x + e))*sinh(f*x + e) + b)) - sqrt(2)*(b*cosh(f*x + e)^2 + 2*b*cosh(f*x + e)*sinh(f*x + e) + b*sinh(f*x + e)^2 - b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/(b*f*cosh(f*x + e)^2 + 2*b*f*cosh(f*x + e)*sinh(f*x + e) + b*f*sinh(f*x + e)^2)]","B",0
354,1,5139,0,0.808736," ","integrate(sech(f*x+e)*(a+b*sinh(f*x+e)^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{b} \log\left(-\frac{{\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{8} + 8 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \sinh\left(f x + e\right)^{8} + 2 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{6} + 2 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3} + 14 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{6} + 4 \, {\left(14 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + {\left(9 \, a^{2} b - 14 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} + {\left(70 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{4} + 9 \, a^{2} b - 14 \, a b^{2} + 6 \, b^{3} + 30 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(14 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{5} + 10 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} + {\left(9 \, a^{2} b - 14 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + b^{3} + 2 \, {\left(3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(14 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{6} + 15 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} + 3 \, a b^{2} - 2 \, b^{3} + 3 \, {\left(9 \, a^{2} b - 14 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{2} + \sqrt{2} {\left({\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{6} + 6 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + {\left(a^{2} - 2 \, a b + b^{2}\right)} \sinh\left(f x + e\right)^{6} - 3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{4} + 3 \, {\left(5 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{2} - a^{2} + 2 \, a b - b^{2}\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(5 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{3} - 3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} - {\left(4 \, a b - 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + {\left(15 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{4} - 18 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{2} - 4 \, a b + 3 \, b^{2}\right)} \sinh\left(f x + e\right)^{2} - b^{2} + 2 \, {\left(3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{5} - 6 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{3} - {\left(4 \, a b - 3 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} + 4 \, {\left(2 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{7} + 3 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{5} + {\left(9 \, a^{2} b - 14 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} + {\left(3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)}{\cosh\left(f x + e\right)^{6} + 6 \, \cosh\left(f x + e\right)^{5} \sinh\left(f x + e\right) + 15 \, \cosh\left(f x + e\right)^{4} \sinh\left(f x + e\right)^{2} + 20 \, \cosh\left(f x + e\right)^{3} \sinh\left(f x + e\right)^{3} + 15 \, \cosh\left(f x + e\right)^{2} \sinh\left(f x + e\right)^{4} + 6 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + \sinh\left(f x + e\right)^{6}}\right) + 2 \, \sqrt{-a + b} \log\left(\frac{{\left(a - 2 \, b\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left(a - 2 \, b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(a - 2 \, b\right)} \sinh\left(f x + e\right)^{4} - 2 \, {\left(3 \, a - 2 \, b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, {\left(a - 2 \, b\right)} \cosh\left(f x + e\right)^{2} - 3 \, a + 2 \, b\right)} \sinh\left(f x + e\right)^{2} + 2 \, \sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} - 1\right)} \sqrt{-a + b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} + 4 \, {\left({\left(a - 2 \, b\right)} \cosh\left(f x + e\right)^{3} - {\left(3 \, a - 2 \, b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + a - 2 \, b}{\cosh\left(f x + e\right)^{4} + 4 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + \sinh\left(f x + e\right)^{4} + 2 \, {\left(3 \, \cosh\left(f x + e\right)^{2} + 1\right)} \sinh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right)^{2} + 4 \, {\left(\cosh\left(f x + e\right)^{3} + \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + 1}\right) + \sqrt{b} \log\left(\frac{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, a \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + a\right)} \sinh\left(f x + e\right)^{2} + \sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} + 1\right)} \sqrt{b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + a \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}{\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}\right)}{4 \, f}, \frac{4 \, \sqrt{a - b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} - 1\right)} \sqrt{a - b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + 2 \, a - b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}\right) + \sqrt{b} \log\left(-\frac{{\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{8} + 8 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \sinh\left(f x + e\right)^{8} + 2 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{6} + 2 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3} + 14 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{6} + 4 \, {\left(14 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + {\left(9 \, a^{2} b - 14 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} + {\left(70 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{4} + 9 \, a^{2} b - 14 \, a b^{2} + 6 \, b^{3} + 30 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(14 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{5} + 10 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} + {\left(9 \, a^{2} b - 14 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + b^{3} + 2 \, {\left(3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(14 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{6} + 15 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} + 3 \, a b^{2} - 2 \, b^{3} + 3 \, {\left(9 \, a^{2} b - 14 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{2} + \sqrt{2} {\left({\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{6} + 6 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + {\left(a^{2} - 2 \, a b + b^{2}\right)} \sinh\left(f x + e\right)^{6} - 3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{4} + 3 \, {\left(5 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{2} - a^{2} + 2 \, a b - b^{2}\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(5 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{3} - 3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} - {\left(4 \, a b - 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + {\left(15 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{4} - 18 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{2} - 4 \, a b + 3 \, b^{2}\right)} \sinh\left(f x + e\right)^{2} - b^{2} + 2 \, {\left(3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{5} - 6 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{3} - {\left(4 \, a b - 3 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} + 4 \, {\left(2 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{7} + 3 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{5} + {\left(9 \, a^{2} b - 14 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} + {\left(3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)}{\cosh\left(f x + e\right)^{6} + 6 \, \cosh\left(f x + e\right)^{5} \sinh\left(f x + e\right) + 15 \, \cosh\left(f x + e\right)^{4} \sinh\left(f x + e\right)^{2} + 20 \, \cosh\left(f x + e\right)^{3} \sinh\left(f x + e\right)^{3} + 15 \, \cosh\left(f x + e\right)^{2} \sinh\left(f x + e\right)^{4} + 6 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + \sinh\left(f x + e\right)^{6}}\right) + \sqrt{b} \log\left(\frac{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, a \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + a\right)} \sinh\left(f x + e\right)^{2} + \sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} + 1\right)} \sqrt{b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + a \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}{\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}\right)}{4 \, f}, -\frac{\sqrt{-b} \arctan\left(\frac{\sqrt{2} {\left({\left(a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(a - b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) + {\left(a - b\right)} \sinh\left(f x + e\right)^{2} + b\right)} \sqrt{-b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{{\left(a b - b^{2}\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left(a b - b^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(a b - b^{2}\right)} \sinh\left(f x + e\right)^{4} - {\left(3 \, a b - 2 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + {\left(6 \, {\left(a b - b^{2}\right)} \cosh\left(f x + e\right)^{2} - 3 \, a b + 2 \, b^{2}\right)} \sinh\left(f x + e\right)^{2} - b^{2} + 2 \, {\left(2 \, {\left(a b - b^{2}\right)} \cosh\left(f x + e\right)^{3} - {\left(3 \, a b - 2 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)}\right) + \sqrt{-b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} + 1\right)} \sqrt{-b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + 2 \, a - b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}\right) - \sqrt{-a + b} \log\left(\frac{{\left(a - 2 \, b\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left(a - 2 \, b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(a - 2 \, b\right)} \sinh\left(f x + e\right)^{4} - 2 \, {\left(3 \, a - 2 \, b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, {\left(a - 2 \, b\right)} \cosh\left(f x + e\right)^{2} - 3 \, a + 2 \, b\right)} \sinh\left(f x + e\right)^{2} + 2 \, \sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} - 1\right)} \sqrt{-a + b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} + 4 \, {\left({\left(a - 2 \, b\right)} \cosh\left(f x + e\right)^{3} - {\left(3 \, a - 2 \, b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + a - 2 \, b}{\cosh\left(f x + e\right)^{4} + 4 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + \sinh\left(f x + e\right)^{4} + 2 \, {\left(3 \, \cosh\left(f x + e\right)^{2} + 1\right)} \sinh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right)^{2} + 4 \, {\left(\cosh\left(f x + e\right)^{3} + \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + 1}\right)}{2 \, f}, \frac{2 \, \sqrt{a - b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} - 1\right)} \sqrt{a - b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + 2 \, a - b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}\right) - \sqrt{-b} \arctan\left(\frac{\sqrt{2} {\left({\left(a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(a - b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) + {\left(a - b\right)} \sinh\left(f x + e\right)^{2} + b\right)} \sqrt{-b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{{\left(a b - b^{2}\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left(a b - b^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(a b - b^{2}\right)} \sinh\left(f x + e\right)^{4} - {\left(3 \, a b - 2 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + {\left(6 \, {\left(a b - b^{2}\right)} \cosh\left(f x + e\right)^{2} - 3 \, a b + 2 \, b^{2}\right)} \sinh\left(f x + e\right)^{2} - b^{2} + 2 \, {\left(2 \, {\left(a b - b^{2}\right)} \cosh\left(f x + e\right)^{3} - {\left(3 \, a b - 2 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)}\right) - \sqrt{-b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} + 1\right)} \sqrt{-b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + 2 \, a - b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}\right)}{2 \, f}\right]"," ",0,"[1/4*(sqrt(b)*log(-((a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^8 + 8*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)*sinh(f*x + e)^7 + (a^2*b - 2*a*b^2 + b^3)*sinh(f*x + e)^8 + 2*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e)^6 + 2*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3 + 14*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^6 + 4*(14*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^3 + 3*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e))*sinh(f*x + e)^5 + (9*a^2*b - 14*a*b^2 + 6*b^3)*cosh(f*x + e)^4 + (70*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^4 + 9*a^2*b - 14*a*b^2 + 6*b^3 + 30*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^4 + 4*(14*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^5 + 10*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e)^3 + (9*a^2*b - 14*a*b^2 + 6*b^3)*cosh(f*x + e))*sinh(f*x + e)^3 + b^3 + 2*(3*a*b^2 - 2*b^3)*cosh(f*x + e)^2 + 2*(14*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^6 + 15*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e)^4 + 3*a*b^2 - 2*b^3 + 3*(9*a^2*b - 14*a*b^2 + 6*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^2 + sqrt(2)*((a^2 - 2*a*b + b^2)*cosh(f*x + e)^6 + 6*(a^2 - 2*a*b + b^2)*cosh(f*x + e)*sinh(f*x + e)^5 + (a^2 - 2*a*b + b^2)*sinh(f*x + e)^6 - 3*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^4 + 3*(5*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^2 - a^2 + 2*a*b - b^2)*sinh(f*x + e)^4 + 4*(5*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^3 - 3*(a^2 - 2*a*b + b^2)*cosh(f*x + e))*sinh(f*x + e)^3 - (4*a*b - 3*b^2)*cosh(f*x + e)^2 + (15*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^4 - 18*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^2 - 4*a*b + 3*b^2)*sinh(f*x + e)^2 - b^2 + 2*(3*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^5 - 6*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^3 - (4*a*b - 3*b^2)*cosh(f*x + e))*sinh(f*x + e))*sqrt(b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + 4*(2*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^7 + 3*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e)^5 + (9*a^2*b - 14*a*b^2 + 6*b^3)*cosh(f*x + e)^3 + (3*a*b^2 - 2*b^3)*cosh(f*x + e))*sinh(f*x + e))/(cosh(f*x + e)^6 + 6*cosh(f*x + e)^5*sinh(f*x + e) + 15*cosh(f*x + e)^4*sinh(f*x + e)^2 + 20*cosh(f*x + e)^3*sinh(f*x + e)^3 + 15*cosh(f*x + e)^2*sinh(f*x + e)^4 + 6*cosh(f*x + e)*sinh(f*x + e)^5 + sinh(f*x + e)^6)) + 2*sqrt(-a + b)*log(((a - 2*b)*cosh(f*x + e)^4 + 4*(a - 2*b)*cosh(f*x + e)*sinh(f*x + e)^3 + (a - 2*b)*sinh(f*x + e)^4 - 2*(3*a - 2*b)*cosh(f*x + e)^2 + 2*(3*(a - 2*b)*cosh(f*x + e)^2 - 3*a + 2*b)*sinh(f*x + e)^2 + 2*sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 - 1)*sqrt(-a + b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + 4*((a - 2*b)*cosh(f*x + e)^3 - (3*a - 2*b)*cosh(f*x + e))*sinh(f*x + e) + a - 2*b)/(cosh(f*x + e)^4 + 4*cosh(f*x + e)*sinh(f*x + e)^3 + sinh(f*x + e)^4 + 2*(3*cosh(f*x + e)^2 + 1)*sinh(f*x + e)^2 + 2*cosh(f*x + e)^2 + 4*(cosh(f*x + e)^3 + cosh(f*x + e))*sinh(f*x + e) + 1)) + sqrt(b)*log((b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*a*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + a)*sinh(f*x + e)^2 + sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 + 1)*sqrt(b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + 4*(b*cosh(f*x + e)^3 + a*cosh(f*x + e))*sinh(f*x + e) + b)/(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/f, 1/4*(4*sqrt(a - b)*arctan(sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 - 1)*sqrt(a - b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/(b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(2*a - b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 2*a - b)*sinh(f*x + e)^2 + 4*(b*cosh(f*x + e)^3 + (2*a - b)*cosh(f*x + e))*sinh(f*x + e) + b)) + sqrt(b)*log(-((a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^8 + 8*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)*sinh(f*x + e)^7 + (a^2*b - 2*a*b^2 + b^3)*sinh(f*x + e)^8 + 2*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e)^6 + 2*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3 + 14*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^6 + 4*(14*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^3 + 3*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e))*sinh(f*x + e)^5 + (9*a^2*b - 14*a*b^2 + 6*b^3)*cosh(f*x + e)^4 + (70*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^4 + 9*a^2*b - 14*a*b^2 + 6*b^3 + 30*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^4 + 4*(14*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^5 + 10*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e)^3 + (9*a^2*b - 14*a*b^2 + 6*b^3)*cosh(f*x + e))*sinh(f*x + e)^3 + b^3 + 2*(3*a*b^2 - 2*b^3)*cosh(f*x + e)^2 + 2*(14*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^6 + 15*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e)^4 + 3*a*b^2 - 2*b^3 + 3*(9*a^2*b - 14*a*b^2 + 6*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^2 + sqrt(2)*((a^2 - 2*a*b + b^2)*cosh(f*x + e)^6 + 6*(a^2 - 2*a*b + b^2)*cosh(f*x + e)*sinh(f*x + e)^5 + (a^2 - 2*a*b + b^2)*sinh(f*x + e)^6 - 3*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^4 + 3*(5*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^2 - a^2 + 2*a*b - b^2)*sinh(f*x + e)^4 + 4*(5*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^3 - 3*(a^2 - 2*a*b + b^2)*cosh(f*x + e))*sinh(f*x + e)^3 - (4*a*b - 3*b^2)*cosh(f*x + e)^2 + (15*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^4 - 18*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^2 - 4*a*b + 3*b^2)*sinh(f*x + e)^2 - b^2 + 2*(3*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^5 - 6*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^3 - (4*a*b - 3*b^2)*cosh(f*x + e))*sinh(f*x + e))*sqrt(b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + 4*(2*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^7 + 3*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e)^5 + (9*a^2*b - 14*a*b^2 + 6*b^3)*cosh(f*x + e)^3 + (3*a*b^2 - 2*b^3)*cosh(f*x + e))*sinh(f*x + e))/(cosh(f*x + e)^6 + 6*cosh(f*x + e)^5*sinh(f*x + e) + 15*cosh(f*x + e)^4*sinh(f*x + e)^2 + 20*cosh(f*x + e)^3*sinh(f*x + e)^3 + 15*cosh(f*x + e)^2*sinh(f*x + e)^4 + 6*cosh(f*x + e)*sinh(f*x + e)^5 + sinh(f*x + e)^6)) + sqrt(b)*log((b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*a*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + a)*sinh(f*x + e)^2 + sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 + 1)*sqrt(b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + 4*(b*cosh(f*x + e)^3 + a*cosh(f*x + e))*sinh(f*x + e) + b)/(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/f, -1/2*(sqrt(-b)*arctan(sqrt(2)*((a - b)*cosh(f*x + e)^2 + 2*(a - b)*cosh(f*x + e)*sinh(f*x + e) + (a - b)*sinh(f*x + e)^2 + b)*sqrt(-b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/((a*b - b^2)*cosh(f*x + e)^4 + 4*(a*b - b^2)*cosh(f*x + e)*sinh(f*x + e)^3 + (a*b - b^2)*sinh(f*x + e)^4 - (3*a*b - 2*b^2)*cosh(f*x + e)^2 + (6*(a*b - b^2)*cosh(f*x + e)^2 - 3*a*b + 2*b^2)*sinh(f*x + e)^2 - b^2 + 2*(2*(a*b - b^2)*cosh(f*x + e)^3 - (3*a*b - 2*b^2)*cosh(f*x + e))*sinh(f*x + e))) + sqrt(-b)*arctan(sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 + 1)*sqrt(-b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/(b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(2*a - b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 2*a - b)*sinh(f*x + e)^2 + 4*(b*cosh(f*x + e)^3 + (2*a - b)*cosh(f*x + e))*sinh(f*x + e) + b)) - sqrt(-a + b)*log(((a - 2*b)*cosh(f*x + e)^4 + 4*(a - 2*b)*cosh(f*x + e)*sinh(f*x + e)^3 + (a - 2*b)*sinh(f*x + e)^4 - 2*(3*a - 2*b)*cosh(f*x + e)^2 + 2*(3*(a - 2*b)*cosh(f*x + e)^2 - 3*a + 2*b)*sinh(f*x + e)^2 + 2*sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 - 1)*sqrt(-a + b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + 4*((a - 2*b)*cosh(f*x + e)^3 - (3*a - 2*b)*cosh(f*x + e))*sinh(f*x + e) + a - 2*b)/(cosh(f*x + e)^4 + 4*cosh(f*x + e)*sinh(f*x + e)^3 + sinh(f*x + e)^4 + 2*(3*cosh(f*x + e)^2 + 1)*sinh(f*x + e)^2 + 2*cosh(f*x + e)^2 + 4*(cosh(f*x + e)^3 + cosh(f*x + e))*sinh(f*x + e) + 1)))/f, 1/2*(2*sqrt(a - b)*arctan(sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 - 1)*sqrt(a - b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/(b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(2*a - b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 2*a - b)*sinh(f*x + e)^2 + 4*(b*cosh(f*x + e)^3 + (2*a - b)*cosh(f*x + e))*sinh(f*x + e) + b)) - sqrt(-b)*arctan(sqrt(2)*((a - b)*cosh(f*x + e)^2 + 2*(a - b)*cosh(f*x + e)*sinh(f*x + e) + (a - b)*sinh(f*x + e)^2 + b)*sqrt(-b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/((a*b - b^2)*cosh(f*x + e)^4 + 4*(a*b - b^2)*cosh(f*x + e)*sinh(f*x + e)^3 + (a*b - b^2)*sinh(f*x + e)^4 - (3*a*b - 2*b^2)*cosh(f*x + e)^2 + (6*(a*b - b^2)*cosh(f*x + e)^2 - 3*a*b + 2*b^2)*sinh(f*x + e)^2 - b^2 + 2*(2*(a*b - b^2)*cosh(f*x + e)^3 - (3*a*b - 2*b^2)*cosh(f*x + e))*sinh(f*x + e))) - sqrt(-b)*arctan(sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 + 1)*sqrt(-b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/(b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(2*a - b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 2*a - b)*sinh(f*x + e)^2 + 4*(b*cosh(f*x + e)^3 + (2*a - b)*cosh(f*x + e))*sinh(f*x + e) + b)))/f]","B",0
355,1,1327,0,0.733580," ","integrate(sech(f*x+e)^3*(a+b*sinh(f*x+e)^2)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left(a \cosh\left(f x + e\right)^{4} + 4 \, a \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + a \sinh\left(f x + e\right)^{4} + 2 \, a \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, a \cosh\left(f x + e\right)^{2} + a\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(a \cosh\left(f x + e\right)^{3} + a \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + a\right)} \sqrt{-a + b} \log\left(\frac{{\left(a - 2 \, b\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left(a - 2 \, b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(a - 2 \, b\right)} \sinh\left(f x + e\right)^{4} - 2 \, {\left(3 \, a - 2 \, b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, {\left(a - 2 \, b\right)} \cosh\left(f x + e\right)^{2} - 3 \, a + 2 \, b\right)} \sinh\left(f x + e\right)^{2} - 2 \, \sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} - 1\right)} \sqrt{-a + b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} + 4 \, {\left({\left(a - 2 \, b\right)} \cosh\left(f x + e\right)^{3} - {\left(3 \, a - 2 \, b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + a - 2 \, b}{\cosh\left(f x + e\right)^{4} + 4 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + \sinh\left(f x + e\right)^{4} + 2 \, {\left(3 \, \cosh\left(f x + e\right)^{2} + 1\right)} \sinh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right)^{2} + 4 \, {\left(\cosh\left(f x + e\right)^{3} + \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + 1}\right) - 2 \, \sqrt{2} {\left({\left(a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(a - b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) + {\left(a - b\right)} \sinh\left(f x + e\right)^{2} - a + b\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{4 \, {\left({\left(a - b\right)} f \cosh\left(f x + e\right)^{4} + 4 \, {\left(a - b\right)} f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(a - b\right)} f \sinh\left(f x + e\right)^{4} + 2 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{2} + {\left(a - b\right)} f\right)} \sinh\left(f x + e\right)^{2} + {\left(a - b\right)} f + 4 \, {\left({\left(a - b\right)} f \cosh\left(f x + e\right)^{3} + {\left(a - b\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)}}, \frac{{\left(a \cosh\left(f x + e\right)^{4} + 4 \, a \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + a \sinh\left(f x + e\right)^{4} + 2 \, a \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, a \cosh\left(f x + e\right)^{2} + a\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(a \cosh\left(f x + e\right)^{3} + a \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + a\right)} \sqrt{a - b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} - 1\right)} \sqrt{a - b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + 2 \, a - b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}\right) + \sqrt{2} {\left({\left(a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(a - b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) + {\left(a - b\right)} \sinh\left(f x + e\right)^{2} - a + b\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{2 \, {\left({\left(a - b\right)} f \cosh\left(f x + e\right)^{4} + 4 \, {\left(a - b\right)} f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(a - b\right)} f \sinh\left(f x + e\right)^{4} + 2 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{2} + {\left(a - b\right)} f\right)} \sinh\left(f x + e\right)^{2} + {\left(a - b\right)} f + 4 \, {\left({\left(a - b\right)} f \cosh\left(f x + e\right)^{3} + {\left(a - b\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)}}\right]"," ",0,"[-1/4*((a*cosh(f*x + e)^4 + 4*a*cosh(f*x + e)*sinh(f*x + e)^3 + a*sinh(f*x + e)^4 + 2*a*cosh(f*x + e)^2 + 2*(3*a*cosh(f*x + e)^2 + a)*sinh(f*x + e)^2 + 4*(a*cosh(f*x + e)^3 + a*cosh(f*x + e))*sinh(f*x + e) + a)*sqrt(-a + b)*log(((a - 2*b)*cosh(f*x + e)^4 + 4*(a - 2*b)*cosh(f*x + e)*sinh(f*x + e)^3 + (a - 2*b)*sinh(f*x + e)^4 - 2*(3*a - 2*b)*cosh(f*x + e)^2 + 2*(3*(a - 2*b)*cosh(f*x + e)^2 - 3*a + 2*b)*sinh(f*x + e)^2 - 2*sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 - 1)*sqrt(-a + b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + 4*((a - 2*b)*cosh(f*x + e)^3 - (3*a - 2*b)*cosh(f*x + e))*sinh(f*x + e) + a - 2*b)/(cosh(f*x + e)^4 + 4*cosh(f*x + e)*sinh(f*x + e)^3 + sinh(f*x + e)^4 + 2*(3*cosh(f*x + e)^2 + 1)*sinh(f*x + e)^2 + 2*cosh(f*x + e)^2 + 4*(cosh(f*x + e)^3 + cosh(f*x + e))*sinh(f*x + e) + 1)) - 2*sqrt(2)*((a - b)*cosh(f*x + e)^2 + 2*(a - b)*cosh(f*x + e)*sinh(f*x + e) + (a - b)*sinh(f*x + e)^2 - a + b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/((a - b)*f*cosh(f*x + e)^4 + 4*(a - b)*f*cosh(f*x + e)*sinh(f*x + e)^3 + (a - b)*f*sinh(f*x + e)^4 + 2*(a - b)*f*cosh(f*x + e)^2 + 2*(3*(a - b)*f*cosh(f*x + e)^2 + (a - b)*f)*sinh(f*x + e)^2 + (a - b)*f + 4*((a - b)*f*cosh(f*x + e)^3 + (a - b)*f*cosh(f*x + e))*sinh(f*x + e)), 1/2*((a*cosh(f*x + e)^4 + 4*a*cosh(f*x + e)*sinh(f*x + e)^3 + a*sinh(f*x + e)^4 + 2*a*cosh(f*x + e)^2 + 2*(3*a*cosh(f*x + e)^2 + a)*sinh(f*x + e)^2 + 4*(a*cosh(f*x + e)^3 + a*cosh(f*x + e))*sinh(f*x + e) + a)*sqrt(a - b)*arctan(sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 - 1)*sqrt(a - b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/(b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(2*a - b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 2*a - b)*sinh(f*x + e)^2 + 4*(b*cosh(f*x + e)^3 + (2*a - b)*cosh(f*x + e))*sinh(f*x + e) + b)) + sqrt(2)*((a - b)*cosh(f*x + e)^2 + 2*(a - b)*cosh(f*x + e)*sinh(f*x + e) + (a - b)*sinh(f*x + e)^2 - a + b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/((a - b)*f*cosh(f*x + e)^4 + 4*(a - b)*f*cosh(f*x + e)*sinh(f*x + e)^3 + (a - b)*f*sinh(f*x + e)^4 + 2*(a - b)*f*cosh(f*x + e)^2 + 2*(3*(a - b)*f*cosh(f*x + e)^2 + (a - b)*f)*sinh(f*x + e)^2 + (a - b)*f + 4*((a - b)*f*cosh(f*x + e)^3 + (a - b)*f*cosh(f*x + e))*sinh(f*x + e))]","B",0
356,1,3727,0,0.983702," ","integrate(sech(f*x+e)^5*(a+b*sinh(f*x+e)^2)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left({\left(3 \, a^{2} - 4 \, a b\right)} \cosh\left(f x + e\right)^{8} + 8 \, {\left(3 \, a^{2} - 4 \, a b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + {\left(3 \, a^{2} - 4 \, a b\right)} \sinh\left(f x + e\right)^{8} + 4 \, {\left(3 \, a^{2} - 4 \, a b\right)} \cosh\left(f x + e\right)^{6} + 4 \, {\left(7 \, {\left(3 \, a^{2} - 4 \, a b\right)} \cosh\left(f x + e\right)^{2} + 3 \, a^{2} - 4 \, a b\right)} \sinh\left(f x + e\right)^{6} + 8 \, {\left(7 \, {\left(3 \, a^{2} - 4 \, a b\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(3 \, a^{2} - 4 \, a b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + 6 \, {\left(3 \, a^{2} - 4 \, a b\right)} \cosh\left(f x + e\right)^{4} + 2 \, {\left(35 \, {\left(3 \, a^{2} - 4 \, a b\right)} \cosh\left(f x + e\right)^{4} + 30 \, {\left(3 \, a^{2} - 4 \, a b\right)} \cosh\left(f x + e\right)^{2} + 9 \, a^{2} - 12 \, a b\right)} \sinh\left(f x + e\right)^{4} + 8 \, {\left(7 \, {\left(3 \, a^{2} - 4 \, a b\right)} \cosh\left(f x + e\right)^{5} + 10 \, {\left(3 \, a^{2} - 4 \, a b\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(3 \, a^{2} - 4 \, a b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 4 \, {\left(3 \, a^{2} - 4 \, a b\right)} \cosh\left(f x + e\right)^{2} + 4 \, {\left(7 \, {\left(3 \, a^{2} - 4 \, a b\right)} \cosh\left(f x + e\right)^{6} + 15 \, {\left(3 \, a^{2} - 4 \, a b\right)} \cosh\left(f x + e\right)^{4} + 9 \, {\left(3 \, a^{2} - 4 \, a b\right)} \cosh\left(f x + e\right)^{2} + 3 \, a^{2} - 4 \, a b\right)} \sinh\left(f x + e\right)^{2} + 3 \, a^{2} - 4 \, a b + 8 \, {\left({\left(3 \, a^{2} - 4 \, a b\right)} \cosh\left(f x + e\right)^{7} + 3 \, {\left(3 \, a^{2} - 4 \, a b\right)} \cosh\left(f x + e\right)^{5} + 3 \, {\left(3 \, a^{2} - 4 \, a b\right)} \cosh\left(f x + e\right)^{3} + {\left(3 \, a^{2} - 4 \, a b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{-a + b} \log\left(\frac{{\left(a - 2 \, b\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left(a - 2 \, b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(a - 2 \, b\right)} \sinh\left(f x + e\right)^{4} - 2 \, {\left(3 \, a - 2 \, b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, {\left(a - 2 \, b\right)} \cosh\left(f x + e\right)^{2} - 3 \, a + 2 \, b\right)} \sinh\left(f x + e\right)^{2} - 2 \, \sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} - 1\right)} \sqrt{-a + b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} + 4 \, {\left({\left(a - 2 \, b\right)} \cosh\left(f x + e\right)^{3} - {\left(3 \, a - 2 \, b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + a - 2 \, b}{\cosh\left(f x + e\right)^{4} + 4 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + \sinh\left(f x + e\right)^{4} + 2 \, {\left(3 \, \cosh\left(f x + e\right)^{2} + 1\right)} \sinh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right)^{2} + 4 \, {\left(\cosh\left(f x + e\right)^{3} + \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + 1}\right) - 2 \, \sqrt{2} {\left({\left(3 \, a^{2} - 5 \, a b + 2 \, b^{2}\right)} \cosh\left(f x + e\right)^{6} + 6 \, {\left(3 \, a^{2} - 5 \, a b + 2 \, b^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + {\left(3 \, a^{2} - 5 \, a b + 2 \, b^{2}\right)} \sinh\left(f x + e\right)^{6} + {\left(11 \, a^{2} - 21 \, a b + 10 \, b^{2}\right)} \cosh\left(f x + e\right)^{4} + {\left(15 \, {\left(3 \, a^{2} - 5 \, a b + 2 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + 11 \, a^{2} - 21 \, a b + 10 \, b^{2}\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(5 \, {\left(3 \, a^{2} - 5 \, a b + 2 \, b^{2}\right)} \cosh\left(f x + e\right)^{3} + {\left(11 \, a^{2} - 21 \, a b + 10 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} - {\left(11 \, a^{2} - 21 \, a b + 10 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + {\left(15 \, {\left(3 \, a^{2} - 5 \, a b + 2 \, b^{2}\right)} \cosh\left(f x + e\right)^{4} + 6 \, {\left(11 \, a^{2} - 21 \, a b + 10 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} - 11 \, a^{2} + 21 \, a b - 10 \, b^{2}\right)} \sinh\left(f x + e\right)^{2} - 3 \, a^{2} + 5 \, a b - 2 \, b^{2} + 2 \, {\left(3 \, {\left(3 \, a^{2} - 5 \, a b + 2 \, b^{2}\right)} \cosh\left(f x + e\right)^{5} + 2 \, {\left(11 \, a^{2} - 21 \, a b + 10 \, b^{2}\right)} \cosh\left(f x + e\right)^{3} - {\left(11 \, a^{2} - 21 \, a b + 10 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{16 \, {\left({\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{8} + 8 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + {\left(a^{2} - 2 \, a b + b^{2}\right)} f \sinh\left(f x + e\right)^{8} + 4 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{2} + {\left(a^{2} - 2 \, a b + b^{2}\right)} f\right)} \sinh\left(f x + e\right)^{6} + 6 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{3} + 3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(35 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{4} + 30 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{2} + 3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{2} + 8 \, {\left(7 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{5} + 10 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{3} + 3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 4 \, {\left(7 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{6} + 15 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{4} + 9 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{2} + {\left(a^{2} - 2 \, a b + b^{2}\right)} f\right)} \sinh\left(f x + e\right)^{2} + {\left(a^{2} - 2 \, a b + b^{2}\right)} f + 8 \, {\left({\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{7} + 3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{5} + 3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{3} + {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)}}, \frac{{\left({\left(3 \, a^{2} - 4 \, a b\right)} \cosh\left(f x + e\right)^{8} + 8 \, {\left(3 \, a^{2} - 4 \, a b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + {\left(3 \, a^{2} - 4 \, a b\right)} \sinh\left(f x + e\right)^{8} + 4 \, {\left(3 \, a^{2} - 4 \, a b\right)} \cosh\left(f x + e\right)^{6} + 4 \, {\left(7 \, {\left(3 \, a^{2} - 4 \, a b\right)} \cosh\left(f x + e\right)^{2} + 3 \, a^{2} - 4 \, a b\right)} \sinh\left(f x + e\right)^{6} + 8 \, {\left(7 \, {\left(3 \, a^{2} - 4 \, a b\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(3 \, a^{2} - 4 \, a b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + 6 \, {\left(3 \, a^{2} - 4 \, a b\right)} \cosh\left(f x + e\right)^{4} + 2 \, {\left(35 \, {\left(3 \, a^{2} - 4 \, a b\right)} \cosh\left(f x + e\right)^{4} + 30 \, {\left(3 \, a^{2} - 4 \, a b\right)} \cosh\left(f x + e\right)^{2} + 9 \, a^{2} - 12 \, a b\right)} \sinh\left(f x + e\right)^{4} + 8 \, {\left(7 \, {\left(3 \, a^{2} - 4 \, a b\right)} \cosh\left(f x + e\right)^{5} + 10 \, {\left(3 \, a^{2} - 4 \, a b\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(3 \, a^{2} - 4 \, a b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 4 \, {\left(3 \, a^{2} - 4 \, a b\right)} \cosh\left(f x + e\right)^{2} + 4 \, {\left(7 \, {\left(3 \, a^{2} - 4 \, a b\right)} \cosh\left(f x + e\right)^{6} + 15 \, {\left(3 \, a^{2} - 4 \, a b\right)} \cosh\left(f x + e\right)^{4} + 9 \, {\left(3 \, a^{2} - 4 \, a b\right)} \cosh\left(f x + e\right)^{2} + 3 \, a^{2} - 4 \, a b\right)} \sinh\left(f x + e\right)^{2} + 3 \, a^{2} - 4 \, a b + 8 \, {\left({\left(3 \, a^{2} - 4 \, a b\right)} \cosh\left(f x + e\right)^{7} + 3 \, {\left(3 \, a^{2} - 4 \, a b\right)} \cosh\left(f x + e\right)^{5} + 3 \, {\left(3 \, a^{2} - 4 \, a b\right)} \cosh\left(f x + e\right)^{3} + {\left(3 \, a^{2} - 4 \, a b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{a - b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} - 1\right)} \sqrt{a - b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + 2 \, a - b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}\right) + \sqrt{2} {\left({\left(3 \, a^{2} - 5 \, a b + 2 \, b^{2}\right)} \cosh\left(f x + e\right)^{6} + 6 \, {\left(3 \, a^{2} - 5 \, a b + 2 \, b^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + {\left(3 \, a^{2} - 5 \, a b + 2 \, b^{2}\right)} \sinh\left(f x + e\right)^{6} + {\left(11 \, a^{2} - 21 \, a b + 10 \, b^{2}\right)} \cosh\left(f x + e\right)^{4} + {\left(15 \, {\left(3 \, a^{2} - 5 \, a b + 2 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + 11 \, a^{2} - 21 \, a b + 10 \, b^{2}\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(5 \, {\left(3 \, a^{2} - 5 \, a b + 2 \, b^{2}\right)} \cosh\left(f x + e\right)^{3} + {\left(11 \, a^{2} - 21 \, a b + 10 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} - {\left(11 \, a^{2} - 21 \, a b + 10 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + {\left(15 \, {\left(3 \, a^{2} - 5 \, a b + 2 \, b^{2}\right)} \cosh\left(f x + e\right)^{4} + 6 \, {\left(11 \, a^{2} - 21 \, a b + 10 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} - 11 \, a^{2} + 21 \, a b - 10 \, b^{2}\right)} \sinh\left(f x + e\right)^{2} - 3 \, a^{2} + 5 \, a b - 2 \, b^{2} + 2 \, {\left(3 \, {\left(3 \, a^{2} - 5 \, a b + 2 \, b^{2}\right)} \cosh\left(f x + e\right)^{5} + 2 \, {\left(11 \, a^{2} - 21 \, a b + 10 \, b^{2}\right)} \cosh\left(f x + e\right)^{3} - {\left(11 \, a^{2} - 21 \, a b + 10 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{8 \, {\left({\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{8} + 8 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + {\left(a^{2} - 2 \, a b + b^{2}\right)} f \sinh\left(f x + e\right)^{8} + 4 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{2} + {\left(a^{2} - 2 \, a b + b^{2}\right)} f\right)} \sinh\left(f x + e\right)^{6} + 6 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{3} + 3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(35 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{4} + 30 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{2} + 3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{2} + 8 \, {\left(7 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{5} + 10 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{3} + 3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 4 \, {\left(7 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{6} + 15 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{4} + 9 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{2} + {\left(a^{2} - 2 \, a b + b^{2}\right)} f\right)} \sinh\left(f x + e\right)^{2} + {\left(a^{2} - 2 \, a b + b^{2}\right)} f + 8 \, {\left({\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{7} + 3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{5} + 3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{3} + {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)}}\right]"," ",0,"[-1/16*(((3*a^2 - 4*a*b)*cosh(f*x + e)^8 + 8*(3*a^2 - 4*a*b)*cosh(f*x + e)*sinh(f*x + e)^7 + (3*a^2 - 4*a*b)*sinh(f*x + e)^8 + 4*(3*a^2 - 4*a*b)*cosh(f*x + e)^6 + 4*(7*(3*a^2 - 4*a*b)*cosh(f*x + e)^2 + 3*a^2 - 4*a*b)*sinh(f*x + e)^6 + 8*(7*(3*a^2 - 4*a*b)*cosh(f*x + e)^3 + 3*(3*a^2 - 4*a*b)*cosh(f*x + e))*sinh(f*x + e)^5 + 6*(3*a^2 - 4*a*b)*cosh(f*x + e)^4 + 2*(35*(3*a^2 - 4*a*b)*cosh(f*x + e)^4 + 30*(3*a^2 - 4*a*b)*cosh(f*x + e)^2 + 9*a^2 - 12*a*b)*sinh(f*x + e)^4 + 8*(7*(3*a^2 - 4*a*b)*cosh(f*x + e)^5 + 10*(3*a^2 - 4*a*b)*cosh(f*x + e)^3 + 3*(3*a^2 - 4*a*b)*cosh(f*x + e))*sinh(f*x + e)^3 + 4*(3*a^2 - 4*a*b)*cosh(f*x + e)^2 + 4*(7*(3*a^2 - 4*a*b)*cosh(f*x + e)^6 + 15*(3*a^2 - 4*a*b)*cosh(f*x + e)^4 + 9*(3*a^2 - 4*a*b)*cosh(f*x + e)^2 + 3*a^2 - 4*a*b)*sinh(f*x + e)^2 + 3*a^2 - 4*a*b + 8*((3*a^2 - 4*a*b)*cosh(f*x + e)^7 + 3*(3*a^2 - 4*a*b)*cosh(f*x + e)^5 + 3*(3*a^2 - 4*a*b)*cosh(f*x + e)^3 + (3*a^2 - 4*a*b)*cosh(f*x + e))*sinh(f*x + e))*sqrt(-a + b)*log(((a - 2*b)*cosh(f*x + e)^4 + 4*(a - 2*b)*cosh(f*x + e)*sinh(f*x + e)^3 + (a - 2*b)*sinh(f*x + e)^4 - 2*(3*a - 2*b)*cosh(f*x + e)^2 + 2*(3*(a - 2*b)*cosh(f*x + e)^2 - 3*a + 2*b)*sinh(f*x + e)^2 - 2*sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 - 1)*sqrt(-a + b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + 4*((a - 2*b)*cosh(f*x + e)^3 - (3*a - 2*b)*cosh(f*x + e))*sinh(f*x + e) + a - 2*b)/(cosh(f*x + e)^4 + 4*cosh(f*x + e)*sinh(f*x + e)^3 + sinh(f*x + e)^4 + 2*(3*cosh(f*x + e)^2 + 1)*sinh(f*x + e)^2 + 2*cosh(f*x + e)^2 + 4*(cosh(f*x + e)^3 + cosh(f*x + e))*sinh(f*x + e) + 1)) - 2*sqrt(2)*((3*a^2 - 5*a*b + 2*b^2)*cosh(f*x + e)^6 + 6*(3*a^2 - 5*a*b + 2*b^2)*cosh(f*x + e)*sinh(f*x + e)^5 + (3*a^2 - 5*a*b + 2*b^2)*sinh(f*x + e)^6 + (11*a^2 - 21*a*b + 10*b^2)*cosh(f*x + e)^4 + (15*(3*a^2 - 5*a*b + 2*b^2)*cosh(f*x + e)^2 + 11*a^2 - 21*a*b + 10*b^2)*sinh(f*x + e)^4 + 4*(5*(3*a^2 - 5*a*b + 2*b^2)*cosh(f*x + e)^3 + (11*a^2 - 21*a*b + 10*b^2)*cosh(f*x + e))*sinh(f*x + e)^3 - (11*a^2 - 21*a*b + 10*b^2)*cosh(f*x + e)^2 + (15*(3*a^2 - 5*a*b + 2*b^2)*cosh(f*x + e)^4 + 6*(11*a^2 - 21*a*b + 10*b^2)*cosh(f*x + e)^2 - 11*a^2 + 21*a*b - 10*b^2)*sinh(f*x + e)^2 - 3*a^2 + 5*a*b - 2*b^2 + 2*(3*(3*a^2 - 5*a*b + 2*b^2)*cosh(f*x + e)^5 + 2*(11*a^2 - 21*a*b + 10*b^2)*cosh(f*x + e)^3 - (11*a^2 - 21*a*b + 10*b^2)*cosh(f*x + e))*sinh(f*x + e))*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/((a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^8 + 8*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)*sinh(f*x + e)^7 + (a^2 - 2*a*b + b^2)*f*sinh(f*x + e)^8 + 4*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^6 + 4*(7*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^2 + (a^2 - 2*a*b + b^2)*f)*sinh(f*x + e)^6 + 6*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^4 + 8*(7*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^3 + 3*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e))*sinh(f*x + e)^5 + 2*(35*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^4 + 30*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^2 + 3*(a^2 - 2*a*b + b^2)*f)*sinh(f*x + e)^4 + 4*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^2 + 8*(7*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^5 + 10*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^3 + 3*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e))*sinh(f*x + e)^3 + 4*(7*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^6 + 15*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^4 + 9*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^2 + (a^2 - 2*a*b + b^2)*f)*sinh(f*x + e)^2 + (a^2 - 2*a*b + b^2)*f + 8*((a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^7 + 3*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^5 + 3*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^3 + (a^2 - 2*a*b + b^2)*f*cosh(f*x + e))*sinh(f*x + e)), 1/8*(((3*a^2 - 4*a*b)*cosh(f*x + e)^8 + 8*(3*a^2 - 4*a*b)*cosh(f*x + e)*sinh(f*x + e)^7 + (3*a^2 - 4*a*b)*sinh(f*x + e)^8 + 4*(3*a^2 - 4*a*b)*cosh(f*x + e)^6 + 4*(7*(3*a^2 - 4*a*b)*cosh(f*x + e)^2 + 3*a^2 - 4*a*b)*sinh(f*x + e)^6 + 8*(7*(3*a^2 - 4*a*b)*cosh(f*x + e)^3 + 3*(3*a^2 - 4*a*b)*cosh(f*x + e))*sinh(f*x + e)^5 + 6*(3*a^2 - 4*a*b)*cosh(f*x + e)^4 + 2*(35*(3*a^2 - 4*a*b)*cosh(f*x + e)^4 + 30*(3*a^2 - 4*a*b)*cosh(f*x + e)^2 + 9*a^2 - 12*a*b)*sinh(f*x + e)^4 + 8*(7*(3*a^2 - 4*a*b)*cosh(f*x + e)^5 + 10*(3*a^2 - 4*a*b)*cosh(f*x + e)^3 + 3*(3*a^2 - 4*a*b)*cosh(f*x + e))*sinh(f*x + e)^3 + 4*(3*a^2 - 4*a*b)*cosh(f*x + e)^2 + 4*(7*(3*a^2 - 4*a*b)*cosh(f*x + e)^6 + 15*(3*a^2 - 4*a*b)*cosh(f*x + e)^4 + 9*(3*a^2 - 4*a*b)*cosh(f*x + e)^2 + 3*a^2 - 4*a*b)*sinh(f*x + e)^2 + 3*a^2 - 4*a*b + 8*((3*a^2 - 4*a*b)*cosh(f*x + e)^7 + 3*(3*a^2 - 4*a*b)*cosh(f*x + e)^5 + 3*(3*a^2 - 4*a*b)*cosh(f*x + e)^3 + (3*a^2 - 4*a*b)*cosh(f*x + e))*sinh(f*x + e))*sqrt(a - b)*arctan(sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 - 1)*sqrt(a - b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/(b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(2*a - b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 2*a - b)*sinh(f*x + e)^2 + 4*(b*cosh(f*x + e)^3 + (2*a - b)*cosh(f*x + e))*sinh(f*x + e) + b)) + sqrt(2)*((3*a^2 - 5*a*b + 2*b^2)*cosh(f*x + e)^6 + 6*(3*a^2 - 5*a*b + 2*b^2)*cosh(f*x + e)*sinh(f*x + e)^5 + (3*a^2 - 5*a*b + 2*b^2)*sinh(f*x + e)^6 + (11*a^2 - 21*a*b + 10*b^2)*cosh(f*x + e)^4 + (15*(3*a^2 - 5*a*b + 2*b^2)*cosh(f*x + e)^2 + 11*a^2 - 21*a*b + 10*b^2)*sinh(f*x + e)^4 + 4*(5*(3*a^2 - 5*a*b + 2*b^2)*cosh(f*x + e)^3 + (11*a^2 - 21*a*b + 10*b^2)*cosh(f*x + e))*sinh(f*x + e)^3 - (11*a^2 - 21*a*b + 10*b^2)*cosh(f*x + e)^2 + (15*(3*a^2 - 5*a*b + 2*b^2)*cosh(f*x + e)^4 + 6*(11*a^2 - 21*a*b + 10*b^2)*cosh(f*x + e)^2 - 11*a^2 + 21*a*b - 10*b^2)*sinh(f*x + e)^2 - 3*a^2 + 5*a*b - 2*b^2 + 2*(3*(3*a^2 - 5*a*b + 2*b^2)*cosh(f*x + e)^5 + 2*(11*a^2 - 21*a*b + 10*b^2)*cosh(f*x + e)^3 - (11*a^2 - 21*a*b + 10*b^2)*cosh(f*x + e))*sinh(f*x + e))*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/((a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^8 + 8*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)*sinh(f*x + e)^7 + (a^2 - 2*a*b + b^2)*f*sinh(f*x + e)^8 + 4*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^6 + 4*(7*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^2 + (a^2 - 2*a*b + b^2)*f)*sinh(f*x + e)^6 + 6*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^4 + 8*(7*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^3 + 3*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e))*sinh(f*x + e)^5 + 2*(35*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^4 + 30*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^2 + 3*(a^2 - 2*a*b + b^2)*f)*sinh(f*x + e)^4 + 4*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^2 + 8*(7*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^5 + 10*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^3 + 3*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e))*sinh(f*x + e)^3 + 4*(7*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^6 + 15*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^4 + 9*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^2 + (a^2 - 2*a*b + b^2)*f)*sinh(f*x + e)^2 + (a^2 - 2*a*b + b^2)*f + 8*((a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^7 + 3*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^5 + 3*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^3 + (a^2 - 2*a*b + b^2)*f*cosh(f*x + e))*sinh(f*x + e))]","B",0
357,0,0,0,0.570511," ","integrate(cosh(f*x+e)^4*(a+b*sinh(f*x+e)^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{b \sinh\left(f x + e\right)^{2} + a} \cosh\left(f x + e\right)^{4}, x\right)"," ",0,"integral(sqrt(b*sinh(f*x + e)^2 + a)*cosh(f*x + e)^4, x)","F",0
358,0,0,0,0.833958," ","integrate(cosh(f*x+e)^2*(a+b*sinh(f*x+e)^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{b \sinh\left(f x + e\right)^{2} + a} \cosh\left(f x + e\right)^{2}, x\right)"," ",0,"integral(sqrt(b*sinh(f*x + e)^2 + a)*cosh(f*x + e)^2, x)","F",0
359,0,0,0,0.654727," ","integrate((a+b*sinh(f*x+e)^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{b \sinh\left(f x + e\right)^{2} + a}, x\right)"," ",0,"integral(sqrt(b*sinh(f*x + e)^2 + a), x)","F",0
360,0,0,0,0.452646," ","integrate(sech(f*x+e)^2*(a+b*sinh(f*x+e)^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{b \sinh\left(f x + e\right)^{2} + a} \operatorname{sech}\left(f x + e\right)^{2}, x\right)"," ",0,"integral(sqrt(b*sinh(f*x + e)^2 + a)*sech(f*x + e)^2, x)","F",0
361,0,0,0,0.487423," ","integrate(sech(f*x+e)^4*(a+b*sinh(f*x+e)^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{b \sinh\left(f x + e\right)^{2} + a} \operatorname{sech}\left(f x + e\right)^{4}, x\right)"," ",0,"integral(sqrt(b*sinh(f*x + e)^2 + a)*sech(f*x + e)^4, x)","F",0
362,1,4603,0,1.028430," ","integrate(cosh(f*x+e)^3*(a+b*sinh(f*x+e)^2)^(3/2),x, algorithm=""fricas"")","\left[-\frac{6 \, {\left({\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)^{6} + 6 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)^{5} \sinh\left(f x + e\right) + 15 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)^{4} \sinh\left(f x + e\right)^{2} + 20 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)^{3} \sinh\left(f x + e\right)^{3} + 15 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)^{2} \sinh\left(f x + e\right)^{4} + 6 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + {\left(a^{3} - 6 \, a^{2} b\right)} \sinh\left(f x + e\right)^{6}\right)} \sqrt{b} \log\left(-\frac{{\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{8} + 8 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \sinh\left(f x + e\right)^{8} + 2 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{6} + 2 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3} + 14 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{6} + 4 \, {\left(14 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + {\left(9 \, a^{2} b - 14 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} + {\left(70 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{4} + 9 \, a^{2} b - 14 \, a b^{2} + 6 \, b^{3} + 30 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(14 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{5} + 10 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} + {\left(9 \, a^{2} b - 14 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + b^{3} + 2 \, {\left(3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(14 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{6} + 15 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} + 3 \, a b^{2} - 2 \, b^{3} + 3 \, {\left(9 \, a^{2} b - 14 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{2} + \sqrt{2} {\left({\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{6} + 6 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + {\left(a^{2} - 2 \, a b + b^{2}\right)} \sinh\left(f x + e\right)^{6} - 3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{4} + 3 \, {\left(5 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{2} - a^{2} + 2 \, a b - b^{2}\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(5 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{3} - 3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} - {\left(4 \, a b - 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + {\left(15 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{4} - 18 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{2} - 4 \, a b + 3 \, b^{2}\right)} \sinh\left(f x + e\right)^{2} - b^{2} + 2 \, {\left(3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{5} - 6 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{3} - {\left(4 \, a b - 3 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} + 4 \, {\left(2 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{7} + 3 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{5} + {\left(9 \, a^{2} b - 14 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} + {\left(3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)}{\cosh\left(f x + e\right)^{6} + 6 \, \cosh\left(f x + e\right)^{5} \sinh\left(f x + e\right) + 15 \, \cosh\left(f x + e\right)^{4} \sinh\left(f x + e\right)^{2} + 20 \, \cosh\left(f x + e\right)^{3} \sinh\left(f x + e\right)^{3} + 15 \, \cosh\left(f x + e\right)^{2} \sinh\left(f x + e\right)^{4} + 6 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + \sinh\left(f x + e\right)^{6}}\right) + 6 \, {\left({\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)^{6} + 6 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)^{5} \sinh\left(f x + e\right) + 15 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)^{4} \sinh\left(f x + e\right)^{2} + 20 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)^{3} \sinh\left(f x + e\right)^{3} + 15 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)^{2} \sinh\left(f x + e\right)^{4} + 6 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + {\left(a^{3} - 6 \, a^{2} b\right)} \sinh\left(f x + e\right)^{6}\right)} \sqrt{b} \log\left(\frac{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, a \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + a\right)} \sinh\left(f x + e\right)^{2} + \sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} + 1\right)} \sqrt{b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + a \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}{\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}\right) - \sqrt{2} {\left(b^{3} \cosh\left(f x + e\right)^{10} + 10 \, b^{3} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{9} + b^{3} \sinh\left(f x + e\right)^{10} + {\left(7 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{8} + {\left(45 \, b^{3} \cosh\left(f x + e\right)^{2} + 7 \, a b^{2} + b^{3}\right)} \sinh\left(f x + e\right)^{8} + 8 \, {\left(15 \, b^{3} \cosh\left(f x + e\right)^{3} + {\left(7 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{7} + {\left(6 \, a^{2} b + 39 \, a b^{2} - 8 \, b^{3}\right)} \cosh\left(f x + e\right)^{6} + {\left(210 \, b^{3} \cosh\left(f x + e\right)^{4} + 6 \, a^{2} b + 39 \, a b^{2} - 8 \, b^{3} + 28 \, {\left(7 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{6} + 2 \, {\left(126 \, b^{3} \cosh\left(f x + e\right)^{5} + 28 \, {\left(7 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(6 \, a^{2} b + 39 \, a b^{2} - 8 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} - {\left(6 \, a^{2} b + 39 \, a b^{2} - 8 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} + {\left(210 \, b^{3} \cosh\left(f x + e\right)^{6} + 70 \, {\left(7 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{4} - 6 \, a^{2} b - 39 \, a b^{2} + 8 \, b^{3} + 15 \, {\left(6 \, a^{2} b + 39 \, a b^{2} - 8 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(30 \, b^{3} \cosh\left(f x + e\right)^{7} + 14 \, {\left(7 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{5} + 5 \, {\left(6 \, a^{2} b + 39 \, a b^{2} - 8 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} - {\left(6 \, a^{2} b + 39 \, a b^{2} - 8 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} - b^{3} - {\left(7 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{2} + {\left(45 \, b^{3} \cosh\left(f x + e\right)^{8} + 28 \, {\left(7 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{6} + 15 \, {\left(6 \, a^{2} b + 39 \, a b^{2} - 8 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} - 7 \, a b^{2} - b^{3} - 6 \, {\left(6 \, a^{2} b + 39 \, a b^{2} - 8 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{2} + 2 \, {\left(5 \, b^{3} \cosh\left(f x + e\right)^{9} + 4 \, {\left(7 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{7} + 3 \, {\left(6 \, a^{2} b + 39 \, a b^{2} - 8 \, b^{3}\right)} \cosh\left(f x + e\right)^{5} - 2 \, {\left(6 \, a^{2} b + 39 \, a b^{2} - 8 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} - {\left(7 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{384 \, {\left(b^{2} f \cosh\left(f x + e\right)^{6} + 6 \, b^{2} f \cosh\left(f x + e\right)^{5} \sinh\left(f x + e\right) + 15 \, b^{2} f \cosh\left(f x + e\right)^{4} \sinh\left(f x + e\right)^{2} + 20 \, b^{2} f \cosh\left(f x + e\right)^{3} \sinh\left(f x + e\right)^{3} + 15 \, b^{2} f \cosh\left(f x + e\right)^{2} \sinh\left(f x + e\right)^{4} + 6 \, b^{2} f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + b^{2} f \sinh\left(f x + e\right)^{6}\right)}}, \frac{12 \, {\left({\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)^{6} + 6 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)^{5} \sinh\left(f x + e\right) + 15 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)^{4} \sinh\left(f x + e\right)^{2} + 20 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)^{3} \sinh\left(f x + e\right)^{3} + 15 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)^{2} \sinh\left(f x + e\right)^{4} + 6 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + {\left(a^{3} - 6 \, a^{2} b\right)} \sinh\left(f x + e\right)^{6}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{2} {\left({\left(a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(a - b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) + {\left(a - b\right)} \sinh\left(f x + e\right)^{2} + b\right)} \sqrt{-b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{{\left(a b - b^{2}\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left(a b - b^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(a b - b^{2}\right)} \sinh\left(f x + e\right)^{4} - {\left(3 \, a b - 2 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + {\left(6 \, {\left(a b - b^{2}\right)} \cosh\left(f x + e\right)^{2} - 3 \, a b + 2 \, b^{2}\right)} \sinh\left(f x + e\right)^{2} - b^{2} + 2 \, {\left(2 \, {\left(a b - b^{2}\right)} \cosh\left(f x + e\right)^{3} - {\left(3 \, a b - 2 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)}\right) + 12 \, {\left({\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)^{6} + 6 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)^{5} \sinh\left(f x + e\right) + 15 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)^{4} \sinh\left(f x + e\right)^{2} + 20 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)^{3} \sinh\left(f x + e\right)^{3} + 15 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)^{2} \sinh\left(f x + e\right)^{4} + 6 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + {\left(a^{3} - 6 \, a^{2} b\right)} \sinh\left(f x + e\right)^{6}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} + 1\right)} \sqrt{-b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + 2 \, a - b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}\right) + \sqrt{2} {\left(b^{3} \cosh\left(f x + e\right)^{10} + 10 \, b^{3} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{9} + b^{3} \sinh\left(f x + e\right)^{10} + {\left(7 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{8} + {\left(45 \, b^{3} \cosh\left(f x + e\right)^{2} + 7 \, a b^{2} + b^{3}\right)} \sinh\left(f x + e\right)^{8} + 8 \, {\left(15 \, b^{3} \cosh\left(f x + e\right)^{3} + {\left(7 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{7} + {\left(6 \, a^{2} b + 39 \, a b^{2} - 8 \, b^{3}\right)} \cosh\left(f x + e\right)^{6} + {\left(210 \, b^{3} \cosh\left(f x + e\right)^{4} + 6 \, a^{2} b + 39 \, a b^{2} - 8 \, b^{3} + 28 \, {\left(7 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{6} + 2 \, {\left(126 \, b^{3} \cosh\left(f x + e\right)^{5} + 28 \, {\left(7 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(6 \, a^{2} b + 39 \, a b^{2} - 8 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} - {\left(6 \, a^{2} b + 39 \, a b^{2} - 8 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} + {\left(210 \, b^{3} \cosh\left(f x + e\right)^{6} + 70 \, {\left(7 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{4} - 6 \, a^{2} b - 39 \, a b^{2} + 8 \, b^{3} + 15 \, {\left(6 \, a^{2} b + 39 \, a b^{2} - 8 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(30 \, b^{3} \cosh\left(f x + e\right)^{7} + 14 \, {\left(7 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{5} + 5 \, {\left(6 \, a^{2} b + 39 \, a b^{2} - 8 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} - {\left(6 \, a^{2} b + 39 \, a b^{2} - 8 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} - b^{3} - {\left(7 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{2} + {\left(45 \, b^{3} \cosh\left(f x + e\right)^{8} + 28 \, {\left(7 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{6} + 15 \, {\left(6 \, a^{2} b + 39 \, a b^{2} - 8 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} - 7 \, a b^{2} - b^{3} - 6 \, {\left(6 \, a^{2} b + 39 \, a b^{2} - 8 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{2} + 2 \, {\left(5 \, b^{3} \cosh\left(f x + e\right)^{9} + 4 \, {\left(7 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{7} + 3 \, {\left(6 \, a^{2} b + 39 \, a b^{2} - 8 \, b^{3}\right)} \cosh\left(f x + e\right)^{5} - 2 \, {\left(6 \, a^{2} b + 39 \, a b^{2} - 8 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} - {\left(7 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{384 \, {\left(b^{2} f \cosh\left(f x + e\right)^{6} + 6 \, b^{2} f \cosh\left(f x + e\right)^{5} \sinh\left(f x + e\right) + 15 \, b^{2} f \cosh\left(f x + e\right)^{4} \sinh\left(f x + e\right)^{2} + 20 \, b^{2} f \cosh\left(f x + e\right)^{3} \sinh\left(f x + e\right)^{3} + 15 \, b^{2} f \cosh\left(f x + e\right)^{2} \sinh\left(f x + e\right)^{4} + 6 \, b^{2} f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + b^{2} f \sinh\left(f x + e\right)^{6}\right)}}\right]"," ",0,"[-1/384*(6*((a^3 - 6*a^2*b)*cosh(f*x + e)^6 + 6*(a^3 - 6*a^2*b)*cosh(f*x + e)^5*sinh(f*x + e) + 15*(a^3 - 6*a^2*b)*cosh(f*x + e)^4*sinh(f*x + e)^2 + 20*(a^3 - 6*a^2*b)*cosh(f*x + e)^3*sinh(f*x + e)^3 + 15*(a^3 - 6*a^2*b)*cosh(f*x + e)^2*sinh(f*x + e)^4 + 6*(a^3 - 6*a^2*b)*cosh(f*x + e)*sinh(f*x + e)^5 + (a^3 - 6*a^2*b)*sinh(f*x + e)^6)*sqrt(b)*log(-((a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^8 + 8*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)*sinh(f*x + e)^7 + (a^2*b - 2*a*b^2 + b^3)*sinh(f*x + e)^8 + 2*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e)^6 + 2*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3 + 14*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^6 + 4*(14*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^3 + 3*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e))*sinh(f*x + e)^5 + (9*a^2*b - 14*a*b^2 + 6*b^3)*cosh(f*x + e)^4 + (70*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^4 + 9*a^2*b - 14*a*b^2 + 6*b^3 + 30*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^4 + 4*(14*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^5 + 10*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e)^3 + (9*a^2*b - 14*a*b^2 + 6*b^3)*cosh(f*x + e))*sinh(f*x + e)^3 + b^3 + 2*(3*a*b^2 - 2*b^3)*cosh(f*x + e)^2 + 2*(14*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^6 + 15*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e)^4 + 3*a*b^2 - 2*b^3 + 3*(9*a^2*b - 14*a*b^2 + 6*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^2 + sqrt(2)*((a^2 - 2*a*b + b^2)*cosh(f*x + e)^6 + 6*(a^2 - 2*a*b + b^2)*cosh(f*x + e)*sinh(f*x + e)^5 + (a^2 - 2*a*b + b^2)*sinh(f*x + e)^6 - 3*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^4 + 3*(5*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^2 - a^2 + 2*a*b - b^2)*sinh(f*x + e)^4 + 4*(5*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^3 - 3*(a^2 - 2*a*b + b^2)*cosh(f*x + e))*sinh(f*x + e)^3 - (4*a*b - 3*b^2)*cosh(f*x + e)^2 + (15*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^4 - 18*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^2 - 4*a*b + 3*b^2)*sinh(f*x + e)^2 - b^2 + 2*(3*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^5 - 6*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^3 - (4*a*b - 3*b^2)*cosh(f*x + e))*sinh(f*x + e))*sqrt(b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + 4*(2*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^7 + 3*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e)^5 + (9*a^2*b - 14*a*b^2 + 6*b^3)*cosh(f*x + e)^3 + (3*a*b^2 - 2*b^3)*cosh(f*x + e))*sinh(f*x + e))/(cosh(f*x + e)^6 + 6*cosh(f*x + e)^5*sinh(f*x + e) + 15*cosh(f*x + e)^4*sinh(f*x + e)^2 + 20*cosh(f*x + e)^3*sinh(f*x + e)^3 + 15*cosh(f*x + e)^2*sinh(f*x + e)^4 + 6*cosh(f*x + e)*sinh(f*x + e)^5 + sinh(f*x + e)^6)) + 6*((a^3 - 6*a^2*b)*cosh(f*x + e)^6 + 6*(a^3 - 6*a^2*b)*cosh(f*x + e)^5*sinh(f*x + e) + 15*(a^3 - 6*a^2*b)*cosh(f*x + e)^4*sinh(f*x + e)^2 + 20*(a^3 - 6*a^2*b)*cosh(f*x + e)^3*sinh(f*x + e)^3 + 15*(a^3 - 6*a^2*b)*cosh(f*x + e)^2*sinh(f*x + e)^4 + 6*(a^3 - 6*a^2*b)*cosh(f*x + e)*sinh(f*x + e)^5 + (a^3 - 6*a^2*b)*sinh(f*x + e)^6)*sqrt(b)*log((b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*a*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + a)*sinh(f*x + e)^2 + sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 + 1)*sqrt(b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + 4*(b*cosh(f*x + e)^3 + a*cosh(f*x + e))*sinh(f*x + e) + b)/(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) - sqrt(2)*(b^3*cosh(f*x + e)^10 + 10*b^3*cosh(f*x + e)*sinh(f*x + e)^9 + b^3*sinh(f*x + e)^10 + (7*a*b^2 + b^3)*cosh(f*x + e)^8 + (45*b^3*cosh(f*x + e)^2 + 7*a*b^2 + b^3)*sinh(f*x + e)^8 + 8*(15*b^3*cosh(f*x + e)^3 + (7*a*b^2 + b^3)*cosh(f*x + e))*sinh(f*x + e)^7 + (6*a^2*b + 39*a*b^2 - 8*b^3)*cosh(f*x + e)^6 + (210*b^3*cosh(f*x + e)^4 + 6*a^2*b + 39*a*b^2 - 8*b^3 + 28*(7*a*b^2 + b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^6 + 2*(126*b^3*cosh(f*x + e)^5 + 28*(7*a*b^2 + b^3)*cosh(f*x + e)^3 + 3*(6*a^2*b + 39*a*b^2 - 8*b^3)*cosh(f*x + e))*sinh(f*x + e)^5 - (6*a^2*b + 39*a*b^2 - 8*b^3)*cosh(f*x + e)^4 + (210*b^3*cosh(f*x + e)^6 + 70*(7*a*b^2 + b^3)*cosh(f*x + e)^4 - 6*a^2*b - 39*a*b^2 + 8*b^3 + 15*(6*a^2*b + 39*a*b^2 - 8*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^4 + 4*(30*b^3*cosh(f*x + e)^7 + 14*(7*a*b^2 + b^3)*cosh(f*x + e)^5 + 5*(6*a^2*b + 39*a*b^2 - 8*b^3)*cosh(f*x + e)^3 - (6*a^2*b + 39*a*b^2 - 8*b^3)*cosh(f*x + e))*sinh(f*x + e)^3 - b^3 - (7*a*b^2 + b^3)*cosh(f*x + e)^2 + (45*b^3*cosh(f*x + e)^8 + 28*(7*a*b^2 + b^3)*cosh(f*x + e)^6 + 15*(6*a^2*b + 39*a*b^2 - 8*b^3)*cosh(f*x + e)^4 - 7*a*b^2 - b^3 - 6*(6*a^2*b + 39*a*b^2 - 8*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^2 + 2*(5*b^3*cosh(f*x + e)^9 + 4*(7*a*b^2 + b^3)*cosh(f*x + e)^7 + 3*(6*a^2*b + 39*a*b^2 - 8*b^3)*cosh(f*x + e)^5 - 2*(6*a^2*b + 39*a*b^2 - 8*b^3)*cosh(f*x + e)^3 - (7*a*b^2 + b^3)*cosh(f*x + e))*sinh(f*x + e))*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/(b^2*f*cosh(f*x + e)^6 + 6*b^2*f*cosh(f*x + e)^5*sinh(f*x + e) + 15*b^2*f*cosh(f*x + e)^4*sinh(f*x + e)^2 + 20*b^2*f*cosh(f*x + e)^3*sinh(f*x + e)^3 + 15*b^2*f*cosh(f*x + e)^2*sinh(f*x + e)^4 + 6*b^2*f*cosh(f*x + e)*sinh(f*x + e)^5 + b^2*f*sinh(f*x + e)^6), 1/384*(12*((a^3 - 6*a^2*b)*cosh(f*x + e)^6 + 6*(a^3 - 6*a^2*b)*cosh(f*x + e)^5*sinh(f*x + e) + 15*(a^3 - 6*a^2*b)*cosh(f*x + e)^4*sinh(f*x + e)^2 + 20*(a^3 - 6*a^2*b)*cosh(f*x + e)^3*sinh(f*x + e)^3 + 15*(a^3 - 6*a^2*b)*cosh(f*x + e)^2*sinh(f*x + e)^4 + 6*(a^3 - 6*a^2*b)*cosh(f*x + e)*sinh(f*x + e)^5 + (a^3 - 6*a^2*b)*sinh(f*x + e)^6)*sqrt(-b)*arctan(sqrt(2)*((a - b)*cosh(f*x + e)^2 + 2*(a - b)*cosh(f*x + e)*sinh(f*x + e) + (a - b)*sinh(f*x + e)^2 + b)*sqrt(-b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/((a*b - b^2)*cosh(f*x + e)^4 + 4*(a*b - b^2)*cosh(f*x + e)*sinh(f*x + e)^3 + (a*b - b^2)*sinh(f*x + e)^4 - (3*a*b - 2*b^2)*cosh(f*x + e)^2 + (6*(a*b - b^2)*cosh(f*x + e)^2 - 3*a*b + 2*b^2)*sinh(f*x + e)^2 - b^2 + 2*(2*(a*b - b^2)*cosh(f*x + e)^3 - (3*a*b - 2*b^2)*cosh(f*x + e))*sinh(f*x + e))) + 12*((a^3 - 6*a^2*b)*cosh(f*x + e)^6 + 6*(a^3 - 6*a^2*b)*cosh(f*x + e)^5*sinh(f*x + e) + 15*(a^3 - 6*a^2*b)*cosh(f*x + e)^4*sinh(f*x + e)^2 + 20*(a^3 - 6*a^2*b)*cosh(f*x + e)^3*sinh(f*x + e)^3 + 15*(a^3 - 6*a^2*b)*cosh(f*x + e)^2*sinh(f*x + e)^4 + 6*(a^3 - 6*a^2*b)*cosh(f*x + e)*sinh(f*x + e)^5 + (a^3 - 6*a^2*b)*sinh(f*x + e)^6)*sqrt(-b)*arctan(sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 + 1)*sqrt(-b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/(b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(2*a - b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 2*a - b)*sinh(f*x + e)^2 + 4*(b*cosh(f*x + e)^3 + (2*a - b)*cosh(f*x + e))*sinh(f*x + e) + b)) + sqrt(2)*(b^3*cosh(f*x + e)^10 + 10*b^3*cosh(f*x + e)*sinh(f*x + e)^9 + b^3*sinh(f*x + e)^10 + (7*a*b^2 + b^3)*cosh(f*x + e)^8 + (45*b^3*cosh(f*x + e)^2 + 7*a*b^2 + b^3)*sinh(f*x + e)^8 + 8*(15*b^3*cosh(f*x + e)^3 + (7*a*b^2 + b^3)*cosh(f*x + e))*sinh(f*x + e)^7 + (6*a^2*b + 39*a*b^2 - 8*b^3)*cosh(f*x + e)^6 + (210*b^3*cosh(f*x + e)^4 + 6*a^2*b + 39*a*b^2 - 8*b^3 + 28*(7*a*b^2 + b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^6 + 2*(126*b^3*cosh(f*x + e)^5 + 28*(7*a*b^2 + b^3)*cosh(f*x + e)^3 + 3*(6*a^2*b + 39*a*b^2 - 8*b^3)*cosh(f*x + e))*sinh(f*x + e)^5 - (6*a^2*b + 39*a*b^2 - 8*b^3)*cosh(f*x + e)^4 + (210*b^3*cosh(f*x + e)^6 + 70*(7*a*b^2 + b^3)*cosh(f*x + e)^4 - 6*a^2*b - 39*a*b^2 + 8*b^3 + 15*(6*a^2*b + 39*a*b^2 - 8*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^4 + 4*(30*b^3*cosh(f*x + e)^7 + 14*(7*a*b^2 + b^3)*cosh(f*x + e)^5 + 5*(6*a^2*b + 39*a*b^2 - 8*b^3)*cosh(f*x + e)^3 - (6*a^2*b + 39*a*b^2 - 8*b^3)*cosh(f*x + e))*sinh(f*x + e)^3 - b^3 - (7*a*b^2 + b^3)*cosh(f*x + e)^2 + (45*b^3*cosh(f*x + e)^8 + 28*(7*a*b^2 + b^3)*cosh(f*x + e)^6 + 15*(6*a^2*b + 39*a*b^2 - 8*b^3)*cosh(f*x + e)^4 - 7*a*b^2 - b^3 - 6*(6*a^2*b + 39*a*b^2 - 8*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^2 + 2*(5*b^3*cosh(f*x + e)^9 + 4*(7*a*b^2 + b^3)*cosh(f*x + e)^7 + 3*(6*a^2*b + 39*a*b^2 - 8*b^3)*cosh(f*x + e)^5 - 2*(6*a^2*b + 39*a*b^2 - 8*b^3)*cosh(f*x + e)^3 - (7*a*b^2 + b^3)*cosh(f*x + e))*sinh(f*x + e))*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/(b^2*f*cosh(f*x + e)^6 + 6*b^2*f*cosh(f*x + e)^5*sinh(f*x + e) + 15*b^2*f*cosh(f*x + e)^4*sinh(f*x + e)^2 + 20*b^2*f*cosh(f*x + e)^3*sinh(f*x + e)^3 + 15*b^2*f*cosh(f*x + e)^2*sinh(f*x + e)^4 + 6*b^2*f*cosh(f*x + e)*sinh(f*x + e)^5 + b^2*f*sinh(f*x + e)^6)]","B",0
363,1,3161,0,1.038257," ","integrate(cosh(f*x+e)*(a+b*sinh(f*x+e)^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{6 \, {\left(a^{2} \cosh\left(f x + e\right)^{4} + 4 \, a^{2} \cosh\left(f x + e\right)^{3} \sinh\left(f x + e\right) + 6 \, a^{2} \cosh\left(f x + e\right)^{2} \sinh\left(f x + e\right)^{2} + 4 \, a^{2} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + a^{2} \sinh\left(f x + e\right)^{4}\right)} \sqrt{b} \log\left(-\frac{{\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{8} + 8 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \sinh\left(f x + e\right)^{8} + 2 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{6} + 2 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3} + 14 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{6} + 4 \, {\left(14 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + {\left(9 \, a^{2} b - 14 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} + {\left(70 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{4} + 9 \, a^{2} b - 14 \, a b^{2} + 6 \, b^{3} + 30 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(14 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{5} + 10 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} + {\left(9 \, a^{2} b - 14 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + b^{3} + 2 \, {\left(3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(14 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{6} + 15 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} + 3 \, a b^{2} - 2 \, b^{3} + 3 \, {\left(9 \, a^{2} b - 14 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{2} + \sqrt{2} {\left({\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{6} + 6 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + {\left(a^{2} - 2 \, a b + b^{2}\right)} \sinh\left(f x + e\right)^{6} - 3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{4} + 3 \, {\left(5 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{2} - a^{2} + 2 \, a b - b^{2}\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(5 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{3} - 3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} - {\left(4 \, a b - 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + {\left(15 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{4} - 18 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{2} - 4 \, a b + 3 \, b^{2}\right)} \sinh\left(f x + e\right)^{2} - b^{2} + 2 \, {\left(3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{5} - 6 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{3} - {\left(4 \, a b - 3 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} + 4 \, {\left(2 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{7} + 3 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{5} + {\left(9 \, a^{2} b - 14 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} + {\left(3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)}{\cosh\left(f x + e\right)^{6} + 6 \, \cosh\left(f x + e\right)^{5} \sinh\left(f x + e\right) + 15 \, \cosh\left(f x + e\right)^{4} \sinh\left(f x + e\right)^{2} + 20 \, \cosh\left(f x + e\right)^{3} \sinh\left(f x + e\right)^{3} + 15 \, \cosh\left(f x + e\right)^{2} \sinh\left(f x + e\right)^{4} + 6 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + \sinh\left(f x + e\right)^{6}}\right) + 6 \, {\left(a^{2} \cosh\left(f x + e\right)^{4} + 4 \, a^{2} \cosh\left(f x + e\right)^{3} \sinh\left(f x + e\right) + 6 \, a^{2} \cosh\left(f x + e\right)^{2} \sinh\left(f x + e\right)^{2} + 4 \, a^{2} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + a^{2} \sinh\left(f x + e\right)^{4}\right)} \sqrt{b} \log\left(\frac{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, a \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + a\right)} \sinh\left(f x + e\right)^{2} + \sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} + 1\right)} \sqrt{b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + a \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}{\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}\right) + \sqrt{2} {\left(b^{2} \cosh\left(f x + e\right)^{6} + 6 \, b^{2} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + b^{2} \sinh\left(f x + e\right)^{6} + {\left(10 \, a b - 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{4} + {\left(15 \, b^{2} \cosh\left(f x + e\right)^{2} + 10 \, a b - 3 \, b^{2}\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(5 \, b^{2} \cosh\left(f x + e\right)^{3} + {\left(10 \, a b - 3 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} - {\left(10 \, a b - 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + {\left(15 \, b^{2} \cosh\left(f x + e\right)^{4} + 6 \, {\left(10 \, a b - 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} - 10 \, a b + 3 \, b^{2}\right)} \sinh\left(f x + e\right)^{2} - b^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(f x + e\right)^{5} + 2 \, {\left(10 \, a b - 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{3} - {\left(10 \, a b - 3 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{64 \, {\left(b f \cosh\left(f x + e\right)^{4} + 4 \, b f \cosh\left(f x + e\right)^{3} \sinh\left(f x + e\right) + 6 \, b f \cosh\left(f x + e\right)^{2} \sinh\left(f x + e\right)^{2} + 4 \, b f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b f \sinh\left(f x + e\right)^{4}\right)}}, -\frac{12 \, {\left(a^{2} \cosh\left(f x + e\right)^{4} + 4 \, a^{2} \cosh\left(f x + e\right)^{3} \sinh\left(f x + e\right) + 6 \, a^{2} \cosh\left(f x + e\right)^{2} \sinh\left(f x + e\right)^{2} + 4 \, a^{2} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + a^{2} \sinh\left(f x + e\right)^{4}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{2} {\left({\left(a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(a - b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) + {\left(a - b\right)} \sinh\left(f x + e\right)^{2} + b\right)} \sqrt{-b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{{\left(a b - b^{2}\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left(a b - b^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(a b - b^{2}\right)} \sinh\left(f x + e\right)^{4} - {\left(3 \, a b - 2 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + {\left(6 \, {\left(a b - b^{2}\right)} \cosh\left(f x + e\right)^{2} - 3 \, a b + 2 \, b^{2}\right)} \sinh\left(f x + e\right)^{2} - b^{2} + 2 \, {\left(2 \, {\left(a b - b^{2}\right)} \cosh\left(f x + e\right)^{3} - {\left(3 \, a b - 2 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)}\right) + 12 \, {\left(a^{2} \cosh\left(f x + e\right)^{4} + 4 \, a^{2} \cosh\left(f x + e\right)^{3} \sinh\left(f x + e\right) + 6 \, a^{2} \cosh\left(f x + e\right)^{2} \sinh\left(f x + e\right)^{2} + 4 \, a^{2} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + a^{2} \sinh\left(f x + e\right)^{4}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} + 1\right)} \sqrt{-b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + 2 \, a - b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}\right) - \sqrt{2} {\left(b^{2} \cosh\left(f x + e\right)^{6} + 6 \, b^{2} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + b^{2} \sinh\left(f x + e\right)^{6} + {\left(10 \, a b - 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{4} + {\left(15 \, b^{2} \cosh\left(f x + e\right)^{2} + 10 \, a b - 3 \, b^{2}\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(5 \, b^{2} \cosh\left(f x + e\right)^{3} + {\left(10 \, a b - 3 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} - {\left(10 \, a b - 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + {\left(15 \, b^{2} \cosh\left(f x + e\right)^{4} + 6 \, {\left(10 \, a b - 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} - 10 \, a b + 3 \, b^{2}\right)} \sinh\left(f x + e\right)^{2} - b^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(f x + e\right)^{5} + 2 \, {\left(10 \, a b - 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{3} - {\left(10 \, a b - 3 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{64 \, {\left(b f \cosh\left(f x + e\right)^{4} + 4 \, b f \cosh\left(f x + e\right)^{3} \sinh\left(f x + e\right) + 6 \, b f \cosh\left(f x + e\right)^{2} \sinh\left(f x + e\right)^{2} + 4 \, b f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b f \sinh\left(f x + e\right)^{4}\right)}}\right]"," ",0,"[1/64*(6*(a^2*cosh(f*x + e)^4 + 4*a^2*cosh(f*x + e)^3*sinh(f*x + e) + 6*a^2*cosh(f*x + e)^2*sinh(f*x + e)^2 + 4*a^2*cosh(f*x + e)*sinh(f*x + e)^3 + a^2*sinh(f*x + e)^4)*sqrt(b)*log(-((a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^8 + 8*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)*sinh(f*x + e)^7 + (a^2*b - 2*a*b^2 + b^3)*sinh(f*x + e)^8 + 2*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e)^6 + 2*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3 + 14*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^6 + 4*(14*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^3 + 3*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e))*sinh(f*x + e)^5 + (9*a^2*b - 14*a*b^2 + 6*b^3)*cosh(f*x + e)^4 + (70*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^4 + 9*a^2*b - 14*a*b^2 + 6*b^3 + 30*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^4 + 4*(14*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^5 + 10*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e)^3 + (9*a^2*b - 14*a*b^2 + 6*b^3)*cosh(f*x + e))*sinh(f*x + e)^3 + b^3 + 2*(3*a*b^2 - 2*b^3)*cosh(f*x + e)^2 + 2*(14*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^6 + 15*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e)^4 + 3*a*b^2 - 2*b^3 + 3*(9*a^2*b - 14*a*b^2 + 6*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^2 + sqrt(2)*((a^2 - 2*a*b + b^2)*cosh(f*x + e)^6 + 6*(a^2 - 2*a*b + b^2)*cosh(f*x + e)*sinh(f*x + e)^5 + (a^2 - 2*a*b + b^2)*sinh(f*x + e)^6 - 3*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^4 + 3*(5*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^2 - a^2 + 2*a*b - b^2)*sinh(f*x + e)^4 + 4*(5*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^3 - 3*(a^2 - 2*a*b + b^2)*cosh(f*x + e))*sinh(f*x + e)^3 - (4*a*b - 3*b^2)*cosh(f*x + e)^2 + (15*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^4 - 18*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^2 - 4*a*b + 3*b^2)*sinh(f*x + e)^2 - b^2 + 2*(3*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^5 - 6*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^3 - (4*a*b - 3*b^2)*cosh(f*x + e))*sinh(f*x + e))*sqrt(b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + 4*(2*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^7 + 3*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e)^5 + (9*a^2*b - 14*a*b^2 + 6*b^3)*cosh(f*x + e)^3 + (3*a*b^2 - 2*b^3)*cosh(f*x + e))*sinh(f*x + e))/(cosh(f*x + e)^6 + 6*cosh(f*x + e)^5*sinh(f*x + e) + 15*cosh(f*x + e)^4*sinh(f*x + e)^2 + 20*cosh(f*x + e)^3*sinh(f*x + e)^3 + 15*cosh(f*x + e)^2*sinh(f*x + e)^4 + 6*cosh(f*x + e)*sinh(f*x + e)^5 + sinh(f*x + e)^6)) + 6*(a^2*cosh(f*x + e)^4 + 4*a^2*cosh(f*x + e)^3*sinh(f*x + e) + 6*a^2*cosh(f*x + e)^2*sinh(f*x + e)^2 + 4*a^2*cosh(f*x + e)*sinh(f*x + e)^3 + a^2*sinh(f*x + e)^4)*sqrt(b)*log((b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*a*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + a)*sinh(f*x + e)^2 + sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 + 1)*sqrt(b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + 4*(b*cosh(f*x + e)^3 + a*cosh(f*x + e))*sinh(f*x + e) + b)/(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + sqrt(2)*(b^2*cosh(f*x + e)^6 + 6*b^2*cosh(f*x + e)*sinh(f*x + e)^5 + b^2*sinh(f*x + e)^6 + (10*a*b - 3*b^2)*cosh(f*x + e)^4 + (15*b^2*cosh(f*x + e)^2 + 10*a*b - 3*b^2)*sinh(f*x + e)^4 + 4*(5*b^2*cosh(f*x + e)^3 + (10*a*b - 3*b^2)*cosh(f*x + e))*sinh(f*x + e)^3 - (10*a*b - 3*b^2)*cosh(f*x + e)^2 + (15*b^2*cosh(f*x + e)^4 + 6*(10*a*b - 3*b^2)*cosh(f*x + e)^2 - 10*a*b + 3*b^2)*sinh(f*x + e)^2 - b^2 + 2*(3*b^2*cosh(f*x + e)^5 + 2*(10*a*b - 3*b^2)*cosh(f*x + e)^3 - (10*a*b - 3*b^2)*cosh(f*x + e))*sinh(f*x + e))*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/(b*f*cosh(f*x + e)^4 + 4*b*f*cosh(f*x + e)^3*sinh(f*x + e) + 6*b*f*cosh(f*x + e)^2*sinh(f*x + e)^2 + 4*b*f*cosh(f*x + e)*sinh(f*x + e)^3 + b*f*sinh(f*x + e)^4), -1/64*(12*(a^2*cosh(f*x + e)^4 + 4*a^2*cosh(f*x + e)^3*sinh(f*x + e) + 6*a^2*cosh(f*x + e)^2*sinh(f*x + e)^2 + 4*a^2*cosh(f*x + e)*sinh(f*x + e)^3 + a^2*sinh(f*x + e)^4)*sqrt(-b)*arctan(sqrt(2)*((a - b)*cosh(f*x + e)^2 + 2*(a - b)*cosh(f*x + e)*sinh(f*x + e) + (a - b)*sinh(f*x + e)^2 + b)*sqrt(-b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/((a*b - b^2)*cosh(f*x + e)^4 + 4*(a*b - b^2)*cosh(f*x + e)*sinh(f*x + e)^3 + (a*b - b^2)*sinh(f*x + e)^4 - (3*a*b - 2*b^2)*cosh(f*x + e)^2 + (6*(a*b - b^2)*cosh(f*x + e)^2 - 3*a*b + 2*b^2)*sinh(f*x + e)^2 - b^2 + 2*(2*(a*b - b^2)*cosh(f*x + e)^3 - (3*a*b - 2*b^2)*cosh(f*x + e))*sinh(f*x + e))) + 12*(a^2*cosh(f*x + e)^4 + 4*a^2*cosh(f*x + e)^3*sinh(f*x + e) + 6*a^2*cosh(f*x + e)^2*sinh(f*x + e)^2 + 4*a^2*cosh(f*x + e)*sinh(f*x + e)^3 + a^2*sinh(f*x + e)^4)*sqrt(-b)*arctan(sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 + 1)*sqrt(-b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/(b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(2*a - b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 2*a - b)*sinh(f*x + e)^2 + 4*(b*cosh(f*x + e)^3 + (2*a - b)*cosh(f*x + e))*sinh(f*x + e) + b)) - sqrt(2)*(b^2*cosh(f*x + e)^6 + 6*b^2*cosh(f*x + e)*sinh(f*x + e)^5 + b^2*sinh(f*x + e)^6 + (10*a*b - 3*b^2)*cosh(f*x + e)^4 + (15*b^2*cosh(f*x + e)^2 + 10*a*b - 3*b^2)*sinh(f*x + e)^4 + 4*(5*b^2*cosh(f*x + e)^3 + (10*a*b - 3*b^2)*cosh(f*x + e))*sinh(f*x + e)^3 - (10*a*b - 3*b^2)*cosh(f*x + e)^2 + (15*b^2*cosh(f*x + e)^4 + 6*(10*a*b - 3*b^2)*cosh(f*x + e)^2 - 10*a*b + 3*b^2)*sinh(f*x + e)^2 - b^2 + 2*(3*b^2*cosh(f*x + e)^5 + 2*(10*a*b - 3*b^2)*cosh(f*x + e)^3 - (10*a*b - 3*b^2)*cosh(f*x + e))*sinh(f*x + e))*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/(b*f*cosh(f*x + e)^4 + 4*b*f*cosh(f*x + e)^3*sinh(f*x + e) + 6*b*f*cosh(f*x + e)^2*sinh(f*x + e)^2 + 4*b*f*cosh(f*x + e)*sinh(f*x + e)^3 + b*f*sinh(f*x + e)^4)]","B",0
364,1,6337,0,1.186980," ","integrate(sech(f*x+e)*(a+b*sinh(f*x+e)^2)^(3/2),x, algorithm=""fricas"")","\left[-\frac{{\left({\left(3 \, a - 2 \, b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, a - 2 \, b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) + {\left(3 \, a - 2 \, b\right)} \sinh\left(f x + e\right)^{2}\right)} \sqrt{b} \log\left(-\frac{{\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{8} + 8 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \sinh\left(f x + e\right)^{8} + 2 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{6} + 2 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3} + 14 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{6} + 4 \, {\left(14 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + {\left(9 \, a^{2} b - 14 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} + {\left(70 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{4} + 9 \, a^{2} b - 14 \, a b^{2} + 6 \, b^{3} + 30 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(14 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{5} + 10 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} + {\left(9 \, a^{2} b - 14 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + b^{3} + 2 \, {\left(3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(14 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{6} + 15 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} + 3 \, a b^{2} - 2 \, b^{3} + 3 \, {\left(9 \, a^{2} b - 14 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{2} - \sqrt{2} {\left({\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{6} + 6 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + {\left(a^{2} - 2 \, a b + b^{2}\right)} \sinh\left(f x + e\right)^{6} - 3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{4} + 3 \, {\left(5 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{2} - a^{2} + 2 \, a b - b^{2}\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(5 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{3} - 3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} - {\left(4 \, a b - 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + {\left(15 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{4} - 18 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{2} - 4 \, a b + 3 \, b^{2}\right)} \sinh\left(f x + e\right)^{2} - b^{2} + 2 \, {\left(3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{5} - 6 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{3} - {\left(4 \, a b - 3 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} + 4 \, {\left(2 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{7} + 3 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{5} + {\left(9 \, a^{2} b - 14 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} + {\left(3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)}{\cosh\left(f x + e\right)^{6} + 6 \, \cosh\left(f x + e\right)^{5} \sinh\left(f x + e\right) + 15 \, \cosh\left(f x + e\right)^{4} \sinh\left(f x + e\right)^{2} + 20 \, \cosh\left(f x + e\right)^{3} \sinh\left(f x + e\right)^{3} + 15 \, \cosh\left(f x + e\right)^{2} \sinh\left(f x + e\right)^{4} + 6 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + \sinh\left(f x + e\right)^{6}}\right) + 4 \, {\left({\left(a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(a - b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) + {\left(a - b\right)} \sinh\left(f x + e\right)^{2}\right)} \sqrt{-a + b} \log\left(\frac{{\left(a - 2 \, b\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left(a - 2 \, b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(a - 2 \, b\right)} \sinh\left(f x + e\right)^{4} - 2 \, {\left(3 \, a - 2 \, b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, {\left(a - 2 \, b\right)} \cosh\left(f x + e\right)^{2} - 3 \, a + 2 \, b\right)} \sinh\left(f x + e\right)^{2} - 2 \, \sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} - 1\right)} \sqrt{-a + b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} + 4 \, {\left({\left(a - 2 \, b\right)} \cosh\left(f x + e\right)^{3} - {\left(3 \, a - 2 \, b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + a - 2 \, b}{\cosh\left(f x + e\right)^{4} + 4 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + \sinh\left(f x + e\right)^{4} + 2 \, {\left(3 \, \cosh\left(f x + e\right)^{2} + 1\right)} \sinh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right)^{2} + 4 \, {\left(\cosh\left(f x + e\right)^{3} + \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + 1}\right) + {\left({\left(3 \, a - 2 \, b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, a - 2 \, b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) + {\left(3 \, a - 2 \, b\right)} \sinh\left(f x + e\right)^{2}\right)} \sqrt{b} \log\left(\frac{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, a \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + a\right)} \sinh\left(f x + e\right)^{2} - \sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} + 1\right)} \sqrt{b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + a \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}{\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}\right) - \sqrt{2} {\left(b \cosh\left(f x + e\right)^{2} + 2 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right) + b \sinh\left(f x + e\right)^{2} - b\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{8 \, {\left(f \cosh\left(f x + e\right)^{2} + 2 \, f \cosh\left(f x + e\right) \sinh\left(f x + e\right) + f \sinh\left(f x + e\right)^{2}\right)}}, \frac{8 \, {\left({\left(a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(a - b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) + {\left(a - b\right)} \sinh\left(f x + e\right)^{2}\right)} \sqrt{a - b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} - 1\right)} \sqrt{a - b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + 2 \, a - b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}\right) - {\left({\left(3 \, a - 2 \, b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, a - 2 \, b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) + {\left(3 \, a - 2 \, b\right)} \sinh\left(f x + e\right)^{2}\right)} \sqrt{b} \log\left(-\frac{{\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{8} + 8 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \sinh\left(f x + e\right)^{8} + 2 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{6} + 2 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3} + 14 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{6} + 4 \, {\left(14 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + {\left(9 \, a^{2} b - 14 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} + {\left(70 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{4} + 9 \, a^{2} b - 14 \, a b^{2} + 6 \, b^{3} + 30 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(14 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{5} + 10 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} + {\left(9 \, a^{2} b - 14 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + b^{3} + 2 \, {\left(3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(14 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{6} + 15 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} + 3 \, a b^{2} - 2 \, b^{3} + 3 \, {\left(9 \, a^{2} b - 14 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{2} - \sqrt{2} {\left({\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{6} + 6 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + {\left(a^{2} - 2 \, a b + b^{2}\right)} \sinh\left(f x + e\right)^{6} - 3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{4} + 3 \, {\left(5 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{2} - a^{2} + 2 \, a b - b^{2}\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(5 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{3} - 3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} - {\left(4 \, a b - 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + {\left(15 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{4} - 18 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{2} - 4 \, a b + 3 \, b^{2}\right)} \sinh\left(f x + e\right)^{2} - b^{2} + 2 \, {\left(3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{5} - 6 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{3} - {\left(4 \, a b - 3 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} + 4 \, {\left(2 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{7} + 3 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{5} + {\left(9 \, a^{2} b - 14 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} + {\left(3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)}{\cosh\left(f x + e\right)^{6} + 6 \, \cosh\left(f x + e\right)^{5} \sinh\left(f x + e\right) + 15 \, \cosh\left(f x + e\right)^{4} \sinh\left(f x + e\right)^{2} + 20 \, \cosh\left(f x + e\right)^{3} \sinh\left(f x + e\right)^{3} + 15 \, \cosh\left(f x + e\right)^{2} \sinh\left(f x + e\right)^{4} + 6 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + \sinh\left(f x + e\right)^{6}}\right) - {\left({\left(3 \, a - 2 \, b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, a - 2 \, b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) + {\left(3 \, a - 2 \, b\right)} \sinh\left(f x + e\right)^{2}\right)} \sqrt{b} \log\left(\frac{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, a \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + a\right)} \sinh\left(f x + e\right)^{2} - \sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} + 1\right)} \sqrt{b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + a \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}{\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}\right) + \sqrt{2} {\left(b \cosh\left(f x + e\right)^{2} + 2 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right) + b \sinh\left(f x + e\right)^{2} - b\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{8 \, {\left(f \cosh\left(f x + e\right)^{2} + 2 \, f \cosh\left(f x + e\right) \sinh\left(f x + e\right) + f \sinh\left(f x + e\right)^{2}\right)}}, -\frac{2 \, {\left({\left(3 \, a - 2 \, b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, a - 2 \, b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) + {\left(3 \, a - 2 \, b\right)} \sinh\left(f x + e\right)^{2}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{2} {\left({\left(a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(a - b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) + {\left(a - b\right)} \sinh\left(f x + e\right)^{2} + b\right)} \sqrt{-b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{{\left(a b - b^{2}\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left(a b - b^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(a b - b^{2}\right)} \sinh\left(f x + e\right)^{4} - {\left(3 \, a b - 2 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + {\left(6 \, {\left(a b - b^{2}\right)} \cosh\left(f x + e\right)^{2} - 3 \, a b + 2 \, b^{2}\right)} \sinh\left(f x + e\right)^{2} - b^{2} + 2 \, {\left(2 \, {\left(a b - b^{2}\right)} \cosh\left(f x + e\right)^{3} - {\left(3 \, a b - 2 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)}\right) + 2 \, {\left({\left(3 \, a - 2 \, b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, a - 2 \, b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) + {\left(3 \, a - 2 \, b\right)} \sinh\left(f x + e\right)^{2}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} + 1\right)} \sqrt{-b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + 2 \, a - b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}\right) + 4 \, {\left({\left(a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(a - b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) + {\left(a - b\right)} \sinh\left(f x + e\right)^{2}\right)} \sqrt{-a + b} \log\left(\frac{{\left(a - 2 \, b\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left(a - 2 \, b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(a - 2 \, b\right)} \sinh\left(f x + e\right)^{4} - 2 \, {\left(3 \, a - 2 \, b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, {\left(a - 2 \, b\right)} \cosh\left(f x + e\right)^{2} - 3 \, a + 2 \, b\right)} \sinh\left(f x + e\right)^{2} - 2 \, \sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} - 1\right)} \sqrt{-a + b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} + 4 \, {\left({\left(a - 2 \, b\right)} \cosh\left(f x + e\right)^{3} - {\left(3 \, a - 2 \, b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + a - 2 \, b}{\cosh\left(f x + e\right)^{4} + 4 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + \sinh\left(f x + e\right)^{4} + 2 \, {\left(3 \, \cosh\left(f x + e\right)^{2} + 1\right)} \sinh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right)^{2} + 4 \, {\left(\cosh\left(f x + e\right)^{3} + \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + 1}\right) - \sqrt{2} {\left(b \cosh\left(f x + e\right)^{2} + 2 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right) + b \sinh\left(f x + e\right)^{2} - b\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{8 \, {\left(f \cosh\left(f x + e\right)^{2} + 2 \, f \cosh\left(f x + e\right) \sinh\left(f x + e\right) + f \sinh\left(f x + e\right)^{2}\right)}}, \frac{8 \, {\left({\left(a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(a - b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) + {\left(a - b\right)} \sinh\left(f x + e\right)^{2}\right)} \sqrt{a - b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} - 1\right)} \sqrt{a - b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + 2 \, a - b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}\right) - 2 \, {\left({\left(3 \, a - 2 \, b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, a - 2 \, b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) + {\left(3 \, a - 2 \, b\right)} \sinh\left(f x + e\right)^{2}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{2} {\left({\left(a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(a - b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) + {\left(a - b\right)} \sinh\left(f x + e\right)^{2} + b\right)} \sqrt{-b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{{\left(a b - b^{2}\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left(a b - b^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(a b - b^{2}\right)} \sinh\left(f x + e\right)^{4} - {\left(3 \, a b - 2 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + {\left(6 \, {\left(a b - b^{2}\right)} \cosh\left(f x + e\right)^{2} - 3 \, a b + 2 \, b^{2}\right)} \sinh\left(f x + e\right)^{2} - b^{2} + 2 \, {\left(2 \, {\left(a b - b^{2}\right)} \cosh\left(f x + e\right)^{3} - {\left(3 \, a b - 2 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)}\right) - 2 \, {\left({\left(3 \, a - 2 \, b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, a - 2 \, b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) + {\left(3 \, a - 2 \, b\right)} \sinh\left(f x + e\right)^{2}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} + 1\right)} \sqrt{-b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + 2 \, a - b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}\right) + \sqrt{2} {\left(b \cosh\left(f x + e\right)^{2} + 2 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right) + b \sinh\left(f x + e\right)^{2} - b\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{8 \, {\left(f \cosh\left(f x + e\right)^{2} + 2 \, f \cosh\left(f x + e\right) \sinh\left(f x + e\right) + f \sinh\left(f x + e\right)^{2}\right)}}\right]"," ",0,"[-1/8*(((3*a - 2*b)*cosh(f*x + e)^2 + 2*(3*a - 2*b)*cosh(f*x + e)*sinh(f*x + e) + (3*a - 2*b)*sinh(f*x + e)^2)*sqrt(b)*log(-((a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^8 + 8*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)*sinh(f*x + e)^7 + (a^2*b - 2*a*b^2 + b^3)*sinh(f*x + e)^8 + 2*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e)^6 + 2*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3 + 14*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^6 + 4*(14*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^3 + 3*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e))*sinh(f*x + e)^5 + (9*a^2*b - 14*a*b^2 + 6*b^3)*cosh(f*x + e)^4 + (70*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^4 + 9*a^2*b - 14*a*b^2 + 6*b^3 + 30*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^4 + 4*(14*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^5 + 10*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e)^3 + (9*a^2*b - 14*a*b^2 + 6*b^3)*cosh(f*x + e))*sinh(f*x + e)^3 + b^3 + 2*(3*a*b^2 - 2*b^3)*cosh(f*x + e)^2 + 2*(14*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^6 + 15*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e)^4 + 3*a*b^2 - 2*b^3 + 3*(9*a^2*b - 14*a*b^2 + 6*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^2 - sqrt(2)*((a^2 - 2*a*b + b^2)*cosh(f*x + e)^6 + 6*(a^2 - 2*a*b + b^2)*cosh(f*x + e)*sinh(f*x + e)^5 + (a^2 - 2*a*b + b^2)*sinh(f*x + e)^6 - 3*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^4 + 3*(5*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^2 - a^2 + 2*a*b - b^2)*sinh(f*x + e)^4 + 4*(5*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^3 - 3*(a^2 - 2*a*b + b^2)*cosh(f*x + e))*sinh(f*x + e)^3 - (4*a*b - 3*b^2)*cosh(f*x + e)^2 + (15*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^4 - 18*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^2 - 4*a*b + 3*b^2)*sinh(f*x + e)^2 - b^2 + 2*(3*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^5 - 6*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^3 - (4*a*b - 3*b^2)*cosh(f*x + e))*sinh(f*x + e))*sqrt(b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + 4*(2*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^7 + 3*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e)^5 + (9*a^2*b - 14*a*b^2 + 6*b^3)*cosh(f*x + e)^3 + (3*a*b^2 - 2*b^3)*cosh(f*x + e))*sinh(f*x + e))/(cosh(f*x + e)^6 + 6*cosh(f*x + e)^5*sinh(f*x + e) + 15*cosh(f*x + e)^4*sinh(f*x + e)^2 + 20*cosh(f*x + e)^3*sinh(f*x + e)^3 + 15*cosh(f*x + e)^2*sinh(f*x + e)^4 + 6*cosh(f*x + e)*sinh(f*x + e)^5 + sinh(f*x + e)^6)) + 4*((a - b)*cosh(f*x + e)^2 + 2*(a - b)*cosh(f*x + e)*sinh(f*x + e) + (a - b)*sinh(f*x + e)^2)*sqrt(-a + b)*log(((a - 2*b)*cosh(f*x + e)^4 + 4*(a - 2*b)*cosh(f*x + e)*sinh(f*x + e)^3 + (a - 2*b)*sinh(f*x + e)^4 - 2*(3*a - 2*b)*cosh(f*x + e)^2 + 2*(3*(a - 2*b)*cosh(f*x + e)^2 - 3*a + 2*b)*sinh(f*x + e)^2 - 2*sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 - 1)*sqrt(-a + b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + 4*((a - 2*b)*cosh(f*x + e)^3 - (3*a - 2*b)*cosh(f*x + e))*sinh(f*x + e) + a - 2*b)/(cosh(f*x + e)^4 + 4*cosh(f*x + e)*sinh(f*x + e)^3 + sinh(f*x + e)^4 + 2*(3*cosh(f*x + e)^2 + 1)*sinh(f*x + e)^2 + 2*cosh(f*x + e)^2 + 4*(cosh(f*x + e)^3 + cosh(f*x + e))*sinh(f*x + e) + 1)) + ((3*a - 2*b)*cosh(f*x + e)^2 + 2*(3*a - 2*b)*cosh(f*x + e)*sinh(f*x + e) + (3*a - 2*b)*sinh(f*x + e)^2)*sqrt(b)*log((b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*a*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + a)*sinh(f*x + e)^2 - sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 + 1)*sqrt(b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + 4*(b*cosh(f*x + e)^3 + a*cosh(f*x + e))*sinh(f*x + e) + b)/(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) - sqrt(2)*(b*cosh(f*x + e)^2 + 2*b*cosh(f*x + e)*sinh(f*x + e) + b*sinh(f*x + e)^2 - b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/(f*cosh(f*x + e)^2 + 2*f*cosh(f*x + e)*sinh(f*x + e) + f*sinh(f*x + e)^2), 1/8*(8*((a - b)*cosh(f*x + e)^2 + 2*(a - b)*cosh(f*x + e)*sinh(f*x + e) + (a - b)*sinh(f*x + e)^2)*sqrt(a - b)*arctan(sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 - 1)*sqrt(a - b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/(b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(2*a - b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 2*a - b)*sinh(f*x + e)^2 + 4*(b*cosh(f*x + e)^3 + (2*a - b)*cosh(f*x + e))*sinh(f*x + e) + b)) - ((3*a - 2*b)*cosh(f*x + e)^2 + 2*(3*a - 2*b)*cosh(f*x + e)*sinh(f*x + e) + (3*a - 2*b)*sinh(f*x + e)^2)*sqrt(b)*log(-((a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^8 + 8*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)*sinh(f*x + e)^7 + (a^2*b - 2*a*b^2 + b^3)*sinh(f*x + e)^8 + 2*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e)^6 + 2*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3 + 14*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^6 + 4*(14*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^3 + 3*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e))*sinh(f*x + e)^5 + (9*a^2*b - 14*a*b^2 + 6*b^3)*cosh(f*x + e)^4 + (70*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^4 + 9*a^2*b - 14*a*b^2 + 6*b^3 + 30*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^4 + 4*(14*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^5 + 10*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e)^3 + (9*a^2*b - 14*a*b^2 + 6*b^3)*cosh(f*x + e))*sinh(f*x + e)^3 + b^3 + 2*(3*a*b^2 - 2*b^3)*cosh(f*x + e)^2 + 2*(14*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^6 + 15*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e)^4 + 3*a*b^2 - 2*b^3 + 3*(9*a^2*b - 14*a*b^2 + 6*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^2 - sqrt(2)*((a^2 - 2*a*b + b^2)*cosh(f*x + e)^6 + 6*(a^2 - 2*a*b + b^2)*cosh(f*x + e)*sinh(f*x + e)^5 + (a^2 - 2*a*b + b^2)*sinh(f*x + e)^6 - 3*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^4 + 3*(5*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^2 - a^2 + 2*a*b - b^2)*sinh(f*x + e)^4 + 4*(5*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^3 - 3*(a^2 - 2*a*b + b^2)*cosh(f*x + e))*sinh(f*x + e)^3 - (4*a*b - 3*b^2)*cosh(f*x + e)^2 + (15*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^4 - 18*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^2 - 4*a*b + 3*b^2)*sinh(f*x + e)^2 - b^2 + 2*(3*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^5 - 6*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^3 - (4*a*b - 3*b^2)*cosh(f*x + e))*sinh(f*x + e))*sqrt(b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + 4*(2*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^7 + 3*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e)^5 + (9*a^2*b - 14*a*b^2 + 6*b^3)*cosh(f*x + e)^3 + (3*a*b^2 - 2*b^3)*cosh(f*x + e))*sinh(f*x + e))/(cosh(f*x + e)^6 + 6*cosh(f*x + e)^5*sinh(f*x + e) + 15*cosh(f*x + e)^4*sinh(f*x + e)^2 + 20*cosh(f*x + e)^3*sinh(f*x + e)^3 + 15*cosh(f*x + e)^2*sinh(f*x + e)^4 + 6*cosh(f*x + e)*sinh(f*x + e)^5 + sinh(f*x + e)^6)) - ((3*a - 2*b)*cosh(f*x + e)^2 + 2*(3*a - 2*b)*cosh(f*x + e)*sinh(f*x + e) + (3*a - 2*b)*sinh(f*x + e)^2)*sqrt(b)*log((b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*a*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + a)*sinh(f*x + e)^2 - sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 + 1)*sqrt(b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + 4*(b*cosh(f*x + e)^3 + a*cosh(f*x + e))*sinh(f*x + e) + b)/(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + sqrt(2)*(b*cosh(f*x + e)^2 + 2*b*cosh(f*x + e)*sinh(f*x + e) + b*sinh(f*x + e)^2 - b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/(f*cosh(f*x + e)^2 + 2*f*cosh(f*x + e)*sinh(f*x + e) + f*sinh(f*x + e)^2), -1/8*(2*((3*a - 2*b)*cosh(f*x + e)^2 + 2*(3*a - 2*b)*cosh(f*x + e)*sinh(f*x + e) + (3*a - 2*b)*sinh(f*x + e)^2)*sqrt(-b)*arctan(sqrt(2)*((a - b)*cosh(f*x + e)^2 + 2*(a - b)*cosh(f*x + e)*sinh(f*x + e) + (a - b)*sinh(f*x + e)^2 + b)*sqrt(-b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/((a*b - b^2)*cosh(f*x + e)^4 + 4*(a*b - b^2)*cosh(f*x + e)*sinh(f*x + e)^3 + (a*b - b^2)*sinh(f*x + e)^4 - (3*a*b - 2*b^2)*cosh(f*x + e)^2 + (6*(a*b - b^2)*cosh(f*x + e)^2 - 3*a*b + 2*b^2)*sinh(f*x + e)^2 - b^2 + 2*(2*(a*b - b^2)*cosh(f*x + e)^3 - (3*a*b - 2*b^2)*cosh(f*x + e))*sinh(f*x + e))) + 2*((3*a - 2*b)*cosh(f*x + e)^2 + 2*(3*a - 2*b)*cosh(f*x + e)*sinh(f*x + e) + (3*a - 2*b)*sinh(f*x + e)^2)*sqrt(-b)*arctan(sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 + 1)*sqrt(-b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/(b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(2*a - b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 2*a - b)*sinh(f*x + e)^2 + 4*(b*cosh(f*x + e)^3 + (2*a - b)*cosh(f*x + e))*sinh(f*x + e) + b)) + 4*((a - b)*cosh(f*x + e)^2 + 2*(a - b)*cosh(f*x + e)*sinh(f*x + e) + (a - b)*sinh(f*x + e)^2)*sqrt(-a + b)*log(((a - 2*b)*cosh(f*x + e)^4 + 4*(a - 2*b)*cosh(f*x + e)*sinh(f*x + e)^3 + (a - 2*b)*sinh(f*x + e)^4 - 2*(3*a - 2*b)*cosh(f*x + e)^2 + 2*(3*(a - 2*b)*cosh(f*x + e)^2 - 3*a + 2*b)*sinh(f*x + e)^2 - 2*sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 - 1)*sqrt(-a + b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + 4*((a - 2*b)*cosh(f*x + e)^3 - (3*a - 2*b)*cosh(f*x + e))*sinh(f*x + e) + a - 2*b)/(cosh(f*x + e)^4 + 4*cosh(f*x + e)*sinh(f*x + e)^3 + sinh(f*x + e)^4 + 2*(3*cosh(f*x + e)^2 + 1)*sinh(f*x + e)^2 + 2*cosh(f*x + e)^2 + 4*(cosh(f*x + e)^3 + cosh(f*x + e))*sinh(f*x + e) + 1)) - sqrt(2)*(b*cosh(f*x + e)^2 + 2*b*cosh(f*x + e)*sinh(f*x + e) + b*sinh(f*x + e)^2 - b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/(f*cosh(f*x + e)^2 + 2*f*cosh(f*x + e)*sinh(f*x + e) + f*sinh(f*x + e)^2), 1/8*(8*((a - b)*cosh(f*x + e)^2 + 2*(a - b)*cosh(f*x + e)*sinh(f*x + e) + (a - b)*sinh(f*x + e)^2)*sqrt(a - b)*arctan(sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 - 1)*sqrt(a - b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/(b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(2*a - b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 2*a - b)*sinh(f*x + e)^2 + 4*(b*cosh(f*x + e)^3 + (2*a - b)*cosh(f*x + e))*sinh(f*x + e) + b)) - 2*((3*a - 2*b)*cosh(f*x + e)^2 + 2*(3*a - 2*b)*cosh(f*x + e)*sinh(f*x + e) + (3*a - 2*b)*sinh(f*x + e)^2)*sqrt(-b)*arctan(sqrt(2)*((a - b)*cosh(f*x + e)^2 + 2*(a - b)*cosh(f*x + e)*sinh(f*x + e) + (a - b)*sinh(f*x + e)^2 + b)*sqrt(-b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/((a*b - b^2)*cosh(f*x + e)^4 + 4*(a*b - b^2)*cosh(f*x + e)*sinh(f*x + e)^3 + (a*b - b^2)*sinh(f*x + e)^4 - (3*a*b - 2*b^2)*cosh(f*x + e)^2 + (6*(a*b - b^2)*cosh(f*x + e)^2 - 3*a*b + 2*b^2)*sinh(f*x + e)^2 - b^2 + 2*(2*(a*b - b^2)*cosh(f*x + e)^3 - (3*a*b - 2*b^2)*cosh(f*x + e))*sinh(f*x + e))) - 2*((3*a - 2*b)*cosh(f*x + e)^2 + 2*(3*a - 2*b)*cosh(f*x + e)*sinh(f*x + e) + (3*a - 2*b)*sinh(f*x + e)^2)*sqrt(-b)*arctan(sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 + 1)*sqrt(-b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/(b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(2*a - b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 2*a - b)*sinh(f*x + e)^2 + 4*(b*cosh(f*x + e)^3 + (2*a - b)*cosh(f*x + e))*sinh(f*x + e) + b)) + sqrt(2)*(b*cosh(f*x + e)^2 + 2*b*cosh(f*x + e)*sinh(f*x + e) + b*sinh(f*x + e)^2 - b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/(f*cosh(f*x + e)^2 + 2*f*cosh(f*x + e)*sinh(f*x + e) + f*sinh(f*x + e)^2)]","B",0
365,1,7350,0,1.111595," ","integrate(sech(f*x+e)^3*(a+b*sinh(f*x+e)^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, b \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + b \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b\right)} \sqrt{b} \log\left(-\frac{{\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{8} + 8 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \sinh\left(f x + e\right)^{8} + 2 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{6} + 2 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3} + 14 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{6} + 4 \, {\left(14 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + {\left(9 \, a^{2} b - 14 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} + {\left(70 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{4} + 9 \, a^{2} b - 14 \, a b^{2} + 6 \, b^{3} + 30 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(14 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{5} + 10 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} + {\left(9 \, a^{2} b - 14 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + b^{3} + 2 \, {\left(3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(14 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{6} + 15 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} + 3 \, a b^{2} - 2 \, b^{3} + 3 \, {\left(9 \, a^{2} b - 14 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{2} + \sqrt{2} {\left({\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{6} + 6 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + {\left(a^{2} - 2 \, a b + b^{2}\right)} \sinh\left(f x + e\right)^{6} - 3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{4} + 3 \, {\left(5 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{2} - a^{2} + 2 \, a b - b^{2}\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(5 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{3} - 3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} - {\left(4 \, a b - 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + {\left(15 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{4} - 18 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{2} - 4 \, a b + 3 \, b^{2}\right)} \sinh\left(f x + e\right)^{2} - b^{2} + 2 \, {\left(3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{5} - 6 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{3} - {\left(4 \, a b - 3 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} + 4 \, {\left(2 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{7} + 3 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{5} + {\left(9 \, a^{2} b - 14 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} + {\left(3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)}{\cosh\left(f x + e\right)^{6} + 6 \, \cosh\left(f x + e\right)^{5} \sinh\left(f x + e\right) + 15 \, \cosh\left(f x + e\right)^{4} \sinh\left(f x + e\right)^{2} + 20 \, \cosh\left(f x + e\right)^{3} \sinh\left(f x + e\right)^{3} + 15 \, \cosh\left(f x + e\right)^{2} \sinh\left(f x + e\right)^{4} + 6 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + \sinh\left(f x + e\right)^{6}}\right) + {\left({\left(a + 2 \, b\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left(a + 2 \, b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(a + 2 \, b\right)} \sinh\left(f x + e\right)^{4} + 2 \, {\left(a + 2 \, b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, {\left(a + 2 \, b\right)} \cosh\left(f x + e\right)^{2} + a + 2 \, b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left({\left(a + 2 \, b\right)} \cosh\left(f x + e\right)^{3} + {\left(a + 2 \, b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + a + 2 \, b\right)} \sqrt{-a + b} \log\left(\frac{{\left(a - 2 \, b\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left(a - 2 \, b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(a - 2 \, b\right)} \sinh\left(f x + e\right)^{4} - 2 \, {\left(3 \, a - 2 \, b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, {\left(a - 2 \, b\right)} \cosh\left(f x + e\right)^{2} - 3 \, a + 2 \, b\right)} \sinh\left(f x + e\right)^{2} + 2 \, \sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} - 1\right)} \sqrt{-a + b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} + 4 \, {\left({\left(a - 2 \, b\right)} \cosh\left(f x + e\right)^{3} - {\left(3 \, a - 2 \, b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + a - 2 \, b}{\cosh\left(f x + e\right)^{4} + 4 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + \sinh\left(f x + e\right)^{4} + 2 \, {\left(3 \, \cosh\left(f x + e\right)^{2} + 1\right)} \sinh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right)^{2} + 4 \, {\left(\cosh\left(f x + e\right)^{3} + \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + 1}\right) + {\left(b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, b \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + b \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b\right)} \sqrt{b} \log\left(\frac{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, a \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + a\right)} \sinh\left(f x + e\right)^{2} + \sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} + 1\right)} \sqrt{b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + a \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}{\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}\right) + 2 \, \sqrt{2} {\left({\left(a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(a - b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) + {\left(a - b\right)} \sinh\left(f x + e\right)^{2} - a + b\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{4 \, {\left(f \cosh\left(f x + e\right)^{4} + 4 \, f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + f \sinh\left(f x + e\right)^{4} + 2 \, f \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, f \cosh\left(f x + e\right)^{2} + f\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(f \cosh\left(f x + e\right)^{3} + f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + f\right)}}, \frac{2 \, {\left({\left(a + 2 \, b\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left(a + 2 \, b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(a + 2 \, b\right)} \sinh\left(f x + e\right)^{4} + 2 \, {\left(a + 2 \, b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, {\left(a + 2 \, b\right)} \cosh\left(f x + e\right)^{2} + a + 2 \, b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left({\left(a + 2 \, b\right)} \cosh\left(f x + e\right)^{3} + {\left(a + 2 \, b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + a + 2 \, b\right)} \sqrt{a - b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} - 1\right)} \sqrt{a - b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + 2 \, a - b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}\right) + {\left(b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, b \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + b \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b\right)} \sqrt{b} \log\left(-\frac{{\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{8} + 8 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \sinh\left(f x + e\right)^{8} + 2 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{6} + 2 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3} + 14 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{6} + 4 \, {\left(14 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + {\left(9 \, a^{2} b - 14 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} + {\left(70 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{4} + 9 \, a^{2} b - 14 \, a b^{2} + 6 \, b^{3} + 30 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(14 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{5} + 10 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} + {\left(9 \, a^{2} b - 14 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + b^{3} + 2 \, {\left(3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(14 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{6} + 15 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} + 3 \, a b^{2} - 2 \, b^{3} + 3 \, {\left(9 \, a^{2} b - 14 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{2} + \sqrt{2} {\left({\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{6} + 6 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + {\left(a^{2} - 2 \, a b + b^{2}\right)} \sinh\left(f x + e\right)^{6} - 3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{4} + 3 \, {\left(5 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{2} - a^{2} + 2 \, a b - b^{2}\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(5 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{3} - 3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} - {\left(4 \, a b - 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + {\left(15 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{4} - 18 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{2} - 4 \, a b + 3 \, b^{2}\right)} \sinh\left(f x + e\right)^{2} - b^{2} + 2 \, {\left(3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{5} - 6 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{3} - {\left(4 \, a b - 3 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} + 4 \, {\left(2 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{7} + 3 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{5} + {\left(9 \, a^{2} b - 14 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} + {\left(3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)}{\cosh\left(f x + e\right)^{6} + 6 \, \cosh\left(f x + e\right)^{5} \sinh\left(f x + e\right) + 15 \, \cosh\left(f x + e\right)^{4} \sinh\left(f x + e\right)^{2} + 20 \, \cosh\left(f x + e\right)^{3} \sinh\left(f x + e\right)^{3} + 15 \, \cosh\left(f x + e\right)^{2} \sinh\left(f x + e\right)^{4} + 6 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + \sinh\left(f x + e\right)^{6}}\right) + {\left(b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, b \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + b \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b\right)} \sqrt{b} \log\left(\frac{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, a \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + a\right)} \sinh\left(f x + e\right)^{2} + \sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} + 1\right)} \sqrt{b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + a \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}{\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}\right) + 2 \, \sqrt{2} {\left({\left(a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(a - b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) + {\left(a - b\right)} \sinh\left(f x + e\right)^{2} - a + b\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{4 \, {\left(f \cosh\left(f x + e\right)^{4} + 4 \, f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + f \sinh\left(f x + e\right)^{4} + 2 \, f \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, f \cosh\left(f x + e\right)^{2} + f\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(f \cosh\left(f x + e\right)^{3} + f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + f\right)}}, -\frac{2 \, {\left(b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, b \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + b \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{2} {\left({\left(a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(a - b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) + {\left(a - b\right)} \sinh\left(f x + e\right)^{2} + b\right)} \sqrt{-b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{{\left(a b - b^{2}\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left(a b - b^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(a b - b^{2}\right)} \sinh\left(f x + e\right)^{4} - {\left(3 \, a b - 2 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + {\left(6 \, {\left(a b - b^{2}\right)} \cosh\left(f x + e\right)^{2} - 3 \, a b + 2 \, b^{2}\right)} \sinh\left(f x + e\right)^{2} - b^{2} + 2 \, {\left(2 \, {\left(a b - b^{2}\right)} \cosh\left(f x + e\right)^{3} - {\left(3 \, a b - 2 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)}\right) + 2 \, {\left(b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, b \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + b \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} + 1\right)} \sqrt{-b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + 2 \, a - b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}\right) - {\left({\left(a + 2 \, b\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left(a + 2 \, b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(a + 2 \, b\right)} \sinh\left(f x + e\right)^{4} + 2 \, {\left(a + 2 \, b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, {\left(a + 2 \, b\right)} \cosh\left(f x + e\right)^{2} + a + 2 \, b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left({\left(a + 2 \, b\right)} \cosh\left(f x + e\right)^{3} + {\left(a + 2 \, b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + a + 2 \, b\right)} \sqrt{-a + b} \log\left(\frac{{\left(a - 2 \, b\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left(a - 2 \, b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(a - 2 \, b\right)} \sinh\left(f x + e\right)^{4} - 2 \, {\left(3 \, a - 2 \, b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, {\left(a - 2 \, b\right)} \cosh\left(f x + e\right)^{2} - 3 \, a + 2 \, b\right)} \sinh\left(f x + e\right)^{2} + 2 \, \sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} - 1\right)} \sqrt{-a + b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} + 4 \, {\left({\left(a - 2 \, b\right)} \cosh\left(f x + e\right)^{3} - {\left(3 \, a - 2 \, b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + a - 2 \, b}{\cosh\left(f x + e\right)^{4} + 4 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + \sinh\left(f x + e\right)^{4} + 2 \, {\left(3 \, \cosh\left(f x + e\right)^{2} + 1\right)} \sinh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right)^{2} + 4 \, {\left(\cosh\left(f x + e\right)^{3} + \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + 1}\right) - 2 \, \sqrt{2} {\left({\left(a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(a - b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) + {\left(a - b\right)} \sinh\left(f x + e\right)^{2} - a + b\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{4 \, {\left(f \cosh\left(f x + e\right)^{4} + 4 \, f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + f \sinh\left(f x + e\right)^{4} + 2 \, f \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, f \cosh\left(f x + e\right)^{2} + f\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(f \cosh\left(f x + e\right)^{3} + f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + f\right)}}, \frac{{\left({\left(a + 2 \, b\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left(a + 2 \, b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(a + 2 \, b\right)} \sinh\left(f x + e\right)^{4} + 2 \, {\left(a + 2 \, b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, {\left(a + 2 \, b\right)} \cosh\left(f x + e\right)^{2} + a + 2 \, b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left({\left(a + 2 \, b\right)} \cosh\left(f x + e\right)^{3} + {\left(a + 2 \, b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + a + 2 \, b\right)} \sqrt{a - b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} - 1\right)} \sqrt{a - b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + 2 \, a - b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}\right) - {\left(b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, b \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + b \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{2} {\left({\left(a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(a - b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) + {\left(a - b\right)} \sinh\left(f x + e\right)^{2} + b\right)} \sqrt{-b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{{\left(a b - b^{2}\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left(a b - b^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(a b - b^{2}\right)} \sinh\left(f x + e\right)^{4} - {\left(3 \, a b - 2 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + {\left(6 \, {\left(a b - b^{2}\right)} \cosh\left(f x + e\right)^{2} - 3 \, a b + 2 \, b^{2}\right)} \sinh\left(f x + e\right)^{2} - b^{2} + 2 \, {\left(2 \, {\left(a b - b^{2}\right)} \cosh\left(f x + e\right)^{3} - {\left(3 \, a b - 2 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)}\right) - {\left(b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, b \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + b \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} + 1\right)} \sqrt{-b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + 2 \, a - b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}\right) + \sqrt{2} {\left({\left(a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(a - b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) + {\left(a - b\right)} \sinh\left(f x + e\right)^{2} - a + b\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{2 \, {\left(f \cosh\left(f x + e\right)^{4} + 4 \, f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + f \sinh\left(f x + e\right)^{4} + 2 \, f \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, f \cosh\left(f x + e\right)^{2} + f\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(f \cosh\left(f x + e\right)^{3} + f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + f\right)}}\right]"," ",0,"[1/4*((b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*b*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + b)*sinh(f*x + e)^2 + 4*(b*cosh(f*x + e)^3 + b*cosh(f*x + e))*sinh(f*x + e) + b)*sqrt(b)*log(-((a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^8 + 8*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)*sinh(f*x + e)^7 + (a^2*b - 2*a*b^2 + b^3)*sinh(f*x + e)^8 + 2*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e)^6 + 2*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3 + 14*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^6 + 4*(14*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^3 + 3*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e))*sinh(f*x + e)^5 + (9*a^2*b - 14*a*b^2 + 6*b^3)*cosh(f*x + e)^4 + (70*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^4 + 9*a^2*b - 14*a*b^2 + 6*b^3 + 30*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^4 + 4*(14*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^5 + 10*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e)^3 + (9*a^2*b - 14*a*b^2 + 6*b^3)*cosh(f*x + e))*sinh(f*x + e)^3 + b^3 + 2*(3*a*b^2 - 2*b^3)*cosh(f*x + e)^2 + 2*(14*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^6 + 15*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e)^4 + 3*a*b^2 - 2*b^3 + 3*(9*a^2*b - 14*a*b^2 + 6*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^2 + sqrt(2)*((a^2 - 2*a*b + b^2)*cosh(f*x + e)^6 + 6*(a^2 - 2*a*b + b^2)*cosh(f*x + e)*sinh(f*x + e)^5 + (a^2 - 2*a*b + b^2)*sinh(f*x + e)^6 - 3*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^4 + 3*(5*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^2 - a^2 + 2*a*b - b^2)*sinh(f*x + e)^4 + 4*(5*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^3 - 3*(a^2 - 2*a*b + b^2)*cosh(f*x + e))*sinh(f*x + e)^3 - (4*a*b - 3*b^2)*cosh(f*x + e)^2 + (15*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^4 - 18*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^2 - 4*a*b + 3*b^2)*sinh(f*x + e)^2 - b^2 + 2*(3*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^5 - 6*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^3 - (4*a*b - 3*b^2)*cosh(f*x + e))*sinh(f*x + e))*sqrt(b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + 4*(2*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^7 + 3*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e)^5 + (9*a^2*b - 14*a*b^2 + 6*b^3)*cosh(f*x + e)^3 + (3*a*b^2 - 2*b^3)*cosh(f*x + e))*sinh(f*x + e))/(cosh(f*x + e)^6 + 6*cosh(f*x + e)^5*sinh(f*x + e) + 15*cosh(f*x + e)^4*sinh(f*x + e)^2 + 20*cosh(f*x + e)^3*sinh(f*x + e)^3 + 15*cosh(f*x + e)^2*sinh(f*x + e)^4 + 6*cosh(f*x + e)*sinh(f*x + e)^5 + sinh(f*x + e)^6)) + ((a + 2*b)*cosh(f*x + e)^4 + 4*(a + 2*b)*cosh(f*x + e)*sinh(f*x + e)^3 + (a + 2*b)*sinh(f*x + e)^4 + 2*(a + 2*b)*cosh(f*x + e)^2 + 2*(3*(a + 2*b)*cosh(f*x + e)^2 + a + 2*b)*sinh(f*x + e)^2 + 4*((a + 2*b)*cosh(f*x + e)^3 + (a + 2*b)*cosh(f*x + e))*sinh(f*x + e) + a + 2*b)*sqrt(-a + b)*log(((a - 2*b)*cosh(f*x + e)^4 + 4*(a - 2*b)*cosh(f*x + e)*sinh(f*x + e)^3 + (a - 2*b)*sinh(f*x + e)^4 - 2*(3*a - 2*b)*cosh(f*x + e)^2 + 2*(3*(a - 2*b)*cosh(f*x + e)^2 - 3*a + 2*b)*sinh(f*x + e)^2 + 2*sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 - 1)*sqrt(-a + b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + 4*((a - 2*b)*cosh(f*x + e)^3 - (3*a - 2*b)*cosh(f*x + e))*sinh(f*x + e) + a - 2*b)/(cosh(f*x + e)^4 + 4*cosh(f*x + e)*sinh(f*x + e)^3 + sinh(f*x + e)^4 + 2*(3*cosh(f*x + e)^2 + 1)*sinh(f*x + e)^2 + 2*cosh(f*x + e)^2 + 4*(cosh(f*x + e)^3 + cosh(f*x + e))*sinh(f*x + e) + 1)) + (b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*b*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + b)*sinh(f*x + e)^2 + 4*(b*cosh(f*x + e)^3 + b*cosh(f*x + e))*sinh(f*x + e) + b)*sqrt(b)*log((b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*a*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + a)*sinh(f*x + e)^2 + sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 + 1)*sqrt(b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + 4*(b*cosh(f*x + e)^3 + a*cosh(f*x + e))*sinh(f*x + e) + b)/(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + 2*sqrt(2)*((a - b)*cosh(f*x + e)^2 + 2*(a - b)*cosh(f*x + e)*sinh(f*x + e) + (a - b)*sinh(f*x + e)^2 - a + b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/(f*cosh(f*x + e)^4 + 4*f*cosh(f*x + e)*sinh(f*x + e)^3 + f*sinh(f*x + e)^4 + 2*f*cosh(f*x + e)^2 + 2*(3*f*cosh(f*x + e)^2 + f)*sinh(f*x + e)^2 + 4*(f*cosh(f*x + e)^3 + f*cosh(f*x + e))*sinh(f*x + e) + f), 1/4*(2*((a + 2*b)*cosh(f*x + e)^4 + 4*(a + 2*b)*cosh(f*x + e)*sinh(f*x + e)^3 + (a + 2*b)*sinh(f*x + e)^4 + 2*(a + 2*b)*cosh(f*x + e)^2 + 2*(3*(a + 2*b)*cosh(f*x + e)^2 + a + 2*b)*sinh(f*x + e)^2 + 4*((a + 2*b)*cosh(f*x + e)^3 + (a + 2*b)*cosh(f*x + e))*sinh(f*x + e) + a + 2*b)*sqrt(a - b)*arctan(sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 - 1)*sqrt(a - b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/(b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(2*a - b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 2*a - b)*sinh(f*x + e)^2 + 4*(b*cosh(f*x + e)^3 + (2*a - b)*cosh(f*x + e))*sinh(f*x + e) + b)) + (b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*b*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + b)*sinh(f*x + e)^2 + 4*(b*cosh(f*x + e)^3 + b*cosh(f*x + e))*sinh(f*x + e) + b)*sqrt(b)*log(-((a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^8 + 8*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)*sinh(f*x + e)^7 + (a^2*b - 2*a*b^2 + b^3)*sinh(f*x + e)^8 + 2*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e)^6 + 2*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3 + 14*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^6 + 4*(14*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^3 + 3*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e))*sinh(f*x + e)^5 + (9*a^2*b - 14*a*b^2 + 6*b^3)*cosh(f*x + e)^4 + (70*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^4 + 9*a^2*b - 14*a*b^2 + 6*b^3 + 30*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^4 + 4*(14*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^5 + 10*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e)^3 + (9*a^2*b - 14*a*b^2 + 6*b^3)*cosh(f*x + e))*sinh(f*x + e)^3 + b^3 + 2*(3*a*b^2 - 2*b^3)*cosh(f*x + e)^2 + 2*(14*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^6 + 15*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e)^4 + 3*a*b^2 - 2*b^3 + 3*(9*a^2*b - 14*a*b^2 + 6*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^2 + sqrt(2)*((a^2 - 2*a*b + b^2)*cosh(f*x + e)^6 + 6*(a^2 - 2*a*b + b^2)*cosh(f*x + e)*sinh(f*x + e)^5 + (a^2 - 2*a*b + b^2)*sinh(f*x + e)^6 - 3*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^4 + 3*(5*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^2 - a^2 + 2*a*b - b^2)*sinh(f*x + e)^4 + 4*(5*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^3 - 3*(a^2 - 2*a*b + b^2)*cosh(f*x + e))*sinh(f*x + e)^3 - (4*a*b - 3*b^2)*cosh(f*x + e)^2 + (15*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^4 - 18*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^2 - 4*a*b + 3*b^2)*sinh(f*x + e)^2 - b^2 + 2*(3*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^5 - 6*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^3 - (4*a*b - 3*b^2)*cosh(f*x + e))*sinh(f*x + e))*sqrt(b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + 4*(2*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^7 + 3*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e)^5 + (9*a^2*b - 14*a*b^2 + 6*b^3)*cosh(f*x + e)^3 + (3*a*b^2 - 2*b^3)*cosh(f*x + e))*sinh(f*x + e))/(cosh(f*x + e)^6 + 6*cosh(f*x + e)^5*sinh(f*x + e) + 15*cosh(f*x + e)^4*sinh(f*x + e)^2 + 20*cosh(f*x + e)^3*sinh(f*x + e)^3 + 15*cosh(f*x + e)^2*sinh(f*x + e)^4 + 6*cosh(f*x + e)*sinh(f*x + e)^5 + sinh(f*x + e)^6)) + (b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*b*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + b)*sinh(f*x + e)^2 + 4*(b*cosh(f*x + e)^3 + b*cosh(f*x + e))*sinh(f*x + e) + b)*sqrt(b)*log((b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*a*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + a)*sinh(f*x + e)^2 + sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 + 1)*sqrt(b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + 4*(b*cosh(f*x + e)^3 + a*cosh(f*x + e))*sinh(f*x + e) + b)/(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + 2*sqrt(2)*((a - b)*cosh(f*x + e)^2 + 2*(a - b)*cosh(f*x + e)*sinh(f*x + e) + (a - b)*sinh(f*x + e)^2 - a + b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/(f*cosh(f*x + e)^4 + 4*f*cosh(f*x + e)*sinh(f*x + e)^3 + f*sinh(f*x + e)^4 + 2*f*cosh(f*x + e)^2 + 2*(3*f*cosh(f*x + e)^2 + f)*sinh(f*x + e)^2 + 4*(f*cosh(f*x + e)^3 + f*cosh(f*x + e))*sinh(f*x + e) + f), -1/4*(2*(b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*b*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + b)*sinh(f*x + e)^2 + 4*(b*cosh(f*x + e)^3 + b*cosh(f*x + e))*sinh(f*x + e) + b)*sqrt(-b)*arctan(sqrt(2)*((a - b)*cosh(f*x + e)^2 + 2*(a - b)*cosh(f*x + e)*sinh(f*x + e) + (a - b)*sinh(f*x + e)^2 + b)*sqrt(-b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/((a*b - b^2)*cosh(f*x + e)^4 + 4*(a*b - b^2)*cosh(f*x + e)*sinh(f*x + e)^3 + (a*b - b^2)*sinh(f*x + e)^4 - (3*a*b - 2*b^2)*cosh(f*x + e)^2 + (6*(a*b - b^2)*cosh(f*x + e)^2 - 3*a*b + 2*b^2)*sinh(f*x + e)^2 - b^2 + 2*(2*(a*b - b^2)*cosh(f*x + e)^3 - (3*a*b - 2*b^2)*cosh(f*x + e))*sinh(f*x + e))) + 2*(b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*b*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + b)*sinh(f*x + e)^2 + 4*(b*cosh(f*x + e)^3 + b*cosh(f*x + e))*sinh(f*x + e) + b)*sqrt(-b)*arctan(sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 + 1)*sqrt(-b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/(b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(2*a - b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 2*a - b)*sinh(f*x + e)^2 + 4*(b*cosh(f*x + e)^3 + (2*a - b)*cosh(f*x + e))*sinh(f*x + e) + b)) - ((a + 2*b)*cosh(f*x + e)^4 + 4*(a + 2*b)*cosh(f*x + e)*sinh(f*x + e)^3 + (a + 2*b)*sinh(f*x + e)^4 + 2*(a + 2*b)*cosh(f*x + e)^2 + 2*(3*(a + 2*b)*cosh(f*x + e)^2 + a + 2*b)*sinh(f*x + e)^2 + 4*((a + 2*b)*cosh(f*x + e)^3 + (a + 2*b)*cosh(f*x + e))*sinh(f*x + e) + a + 2*b)*sqrt(-a + b)*log(((a - 2*b)*cosh(f*x + e)^4 + 4*(a - 2*b)*cosh(f*x + e)*sinh(f*x + e)^3 + (a - 2*b)*sinh(f*x + e)^4 - 2*(3*a - 2*b)*cosh(f*x + e)^2 + 2*(3*(a - 2*b)*cosh(f*x + e)^2 - 3*a + 2*b)*sinh(f*x + e)^2 + 2*sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 - 1)*sqrt(-a + b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + 4*((a - 2*b)*cosh(f*x + e)^3 - (3*a - 2*b)*cosh(f*x + e))*sinh(f*x + e) + a - 2*b)/(cosh(f*x + e)^4 + 4*cosh(f*x + e)*sinh(f*x + e)^3 + sinh(f*x + e)^4 + 2*(3*cosh(f*x + e)^2 + 1)*sinh(f*x + e)^2 + 2*cosh(f*x + e)^2 + 4*(cosh(f*x + e)^3 + cosh(f*x + e))*sinh(f*x + e) + 1)) - 2*sqrt(2)*((a - b)*cosh(f*x + e)^2 + 2*(a - b)*cosh(f*x + e)*sinh(f*x + e) + (a - b)*sinh(f*x + e)^2 - a + b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/(f*cosh(f*x + e)^4 + 4*f*cosh(f*x + e)*sinh(f*x + e)^3 + f*sinh(f*x + e)^4 + 2*f*cosh(f*x + e)^2 + 2*(3*f*cosh(f*x + e)^2 + f)*sinh(f*x + e)^2 + 4*(f*cosh(f*x + e)^3 + f*cosh(f*x + e))*sinh(f*x + e) + f), 1/2*(((a + 2*b)*cosh(f*x + e)^4 + 4*(a + 2*b)*cosh(f*x + e)*sinh(f*x + e)^3 + (a + 2*b)*sinh(f*x + e)^4 + 2*(a + 2*b)*cosh(f*x + e)^2 + 2*(3*(a + 2*b)*cosh(f*x + e)^2 + a + 2*b)*sinh(f*x + e)^2 + 4*((a + 2*b)*cosh(f*x + e)^3 + (a + 2*b)*cosh(f*x + e))*sinh(f*x + e) + a + 2*b)*sqrt(a - b)*arctan(sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 - 1)*sqrt(a - b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/(b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(2*a - b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 2*a - b)*sinh(f*x + e)^2 + 4*(b*cosh(f*x + e)^3 + (2*a - b)*cosh(f*x + e))*sinh(f*x + e) + b)) - (b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*b*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + b)*sinh(f*x + e)^2 + 4*(b*cosh(f*x + e)^3 + b*cosh(f*x + e))*sinh(f*x + e) + b)*sqrt(-b)*arctan(sqrt(2)*((a - b)*cosh(f*x + e)^2 + 2*(a - b)*cosh(f*x + e)*sinh(f*x + e) + (a - b)*sinh(f*x + e)^2 + b)*sqrt(-b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/((a*b - b^2)*cosh(f*x + e)^4 + 4*(a*b - b^2)*cosh(f*x + e)*sinh(f*x + e)^3 + (a*b - b^2)*sinh(f*x + e)^4 - (3*a*b - 2*b^2)*cosh(f*x + e)^2 + (6*(a*b - b^2)*cosh(f*x + e)^2 - 3*a*b + 2*b^2)*sinh(f*x + e)^2 - b^2 + 2*(2*(a*b - b^2)*cosh(f*x + e)^3 - (3*a*b - 2*b^2)*cosh(f*x + e))*sinh(f*x + e))) - (b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*b*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + b)*sinh(f*x + e)^2 + 4*(b*cosh(f*x + e)^3 + b*cosh(f*x + e))*sinh(f*x + e) + b)*sqrt(-b)*arctan(sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 + 1)*sqrt(-b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/(b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(2*a - b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 2*a - b)*sinh(f*x + e)^2 + 4*(b*cosh(f*x + e)^3 + (2*a - b)*cosh(f*x + e))*sinh(f*x + e) + b)) + sqrt(2)*((a - b)*cosh(f*x + e)^2 + 2*(a - b)*cosh(f*x + e)*sinh(f*x + e) + (a - b)*sinh(f*x + e)^2 - a + b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/(f*cosh(f*x + e)^4 + 4*f*cosh(f*x + e)*sinh(f*x + e)^3 + f*sinh(f*x + e)^4 + 2*f*cosh(f*x + e)^2 + 2*(3*f*cosh(f*x + e)^2 + f)*sinh(f*x + e)^2 + 4*(f*cosh(f*x + e)^3 + f*cosh(f*x + e))*sinh(f*x + e) + f)]","B",0
366,1,3089,0,1.020885," ","integrate(sech(f*x+e)^5*(a+b*sinh(f*x+e)^2)^(3/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(a^{2} \cosh\left(f x + e\right)^{8} + 8 \, a^{2} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + a^{2} \sinh\left(f x + e\right)^{8} + 4 \, a^{2} \cosh\left(f x + e\right)^{6} + 4 \, {\left(7 \, a^{2} \cosh\left(f x + e\right)^{2} + a^{2}\right)} \sinh\left(f x + e\right)^{6} + 6 \, a^{2} \cosh\left(f x + e\right)^{4} + 8 \, {\left(7 \, a^{2} \cosh\left(f x + e\right)^{3} + 3 \, a^{2} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(35 \, a^{2} \cosh\left(f x + e\right)^{4} + 30 \, a^{2} \cosh\left(f x + e\right)^{2} + 3 \, a^{2}\right)} \sinh\left(f x + e\right)^{4} + 4 \, a^{2} \cosh\left(f x + e\right)^{2} + 8 \, {\left(7 \, a^{2} \cosh\left(f x + e\right)^{5} + 10 \, a^{2} \cosh\left(f x + e\right)^{3} + 3 \, a^{2} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 4 \, {\left(7 \, a^{2} \cosh\left(f x + e\right)^{6} + 15 \, a^{2} \cosh\left(f x + e\right)^{4} + 9 \, a^{2} \cosh\left(f x + e\right)^{2} + a^{2}\right)} \sinh\left(f x + e\right)^{2} + a^{2} + 8 \, {\left(a^{2} \cosh\left(f x + e\right)^{7} + 3 \, a^{2} \cosh\left(f x + e\right)^{5} + 3 \, a^{2} \cosh\left(f x + e\right)^{3} + a^{2} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{-a + b} \log\left(\frac{{\left(a - 2 \, b\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left(a - 2 \, b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(a - 2 \, b\right)} \sinh\left(f x + e\right)^{4} - 2 \, {\left(3 \, a - 2 \, b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, {\left(a - 2 \, b\right)} \cosh\left(f x + e\right)^{2} - 3 \, a + 2 \, b\right)} \sinh\left(f x + e\right)^{2} - 2 \, \sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} - 1\right)} \sqrt{-a + b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} + 4 \, {\left({\left(a - 2 \, b\right)} \cosh\left(f x + e\right)^{3} - {\left(3 \, a - 2 \, b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + a - 2 \, b}{\cosh\left(f x + e\right)^{4} + 4 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + \sinh\left(f x + e\right)^{4} + 2 \, {\left(3 \, \cosh\left(f x + e\right)^{2} + 1\right)} \sinh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right)^{2} + 4 \, {\left(\cosh\left(f x + e\right)^{3} + \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + 1}\right) - 2 \, \sqrt{2} {\left({\left(3 \, a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(f x + e\right)^{6} + 6 \, {\left(3 \, a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + {\left(3 \, a^{2} - a b - 2 \, b^{2}\right)} \sinh\left(f x + e\right)^{6} + {\left(11 \, a^{2} - 17 \, a b + 6 \, b^{2}\right)} \cosh\left(f x + e\right)^{4} + {\left(15 \, {\left(3 \, a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + 11 \, a^{2} - 17 \, a b + 6 \, b^{2}\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(5 \, {\left(3 \, a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(f x + e\right)^{3} + {\left(11 \, a^{2} - 17 \, a b + 6 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} - {\left(11 \, a^{2} - 17 \, a b + 6 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + {\left(15 \, {\left(3 \, a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(f x + e\right)^{4} + 6 \, {\left(11 \, a^{2} - 17 \, a b + 6 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} - 11 \, a^{2} + 17 \, a b - 6 \, b^{2}\right)} \sinh\left(f x + e\right)^{2} - 3 \, a^{2} + a b + 2 \, b^{2} + 2 \, {\left(3 \, {\left(3 \, a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(f x + e\right)^{5} + 2 \, {\left(11 \, a^{2} - 17 \, a b + 6 \, b^{2}\right)} \cosh\left(f x + e\right)^{3} - {\left(11 \, a^{2} - 17 \, a b + 6 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{16 \, {\left({\left(a - b\right)} f \cosh\left(f x + e\right)^{8} + 8 \, {\left(a - b\right)} f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + {\left(a - b\right)} f \sinh\left(f x + e\right)^{8} + 4 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{6} + 4 \, {\left(7 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{2} + {\left(a - b\right)} f\right)} \sinh\left(f x + e\right)^{6} + 6 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{4} + 8 \, {\left(7 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{3} + 3 \, {\left(a - b\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(35 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{4} + 30 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{2} + 3 \, {\left(a - b\right)} f\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{2} + 8 \, {\left(7 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{5} + 10 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{3} + 3 \, {\left(a - b\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 4 \, {\left(7 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{6} + 15 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{4} + 9 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{2} + {\left(a - b\right)} f\right)} \sinh\left(f x + e\right)^{2} + {\left(a - b\right)} f + 8 \, {\left({\left(a - b\right)} f \cosh\left(f x + e\right)^{7} + 3 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{5} + 3 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{3} + {\left(a - b\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)}}, \frac{3 \, {\left(a^{2} \cosh\left(f x + e\right)^{8} + 8 \, a^{2} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + a^{2} \sinh\left(f x + e\right)^{8} + 4 \, a^{2} \cosh\left(f x + e\right)^{6} + 4 \, {\left(7 \, a^{2} \cosh\left(f x + e\right)^{2} + a^{2}\right)} \sinh\left(f x + e\right)^{6} + 6 \, a^{2} \cosh\left(f x + e\right)^{4} + 8 \, {\left(7 \, a^{2} \cosh\left(f x + e\right)^{3} + 3 \, a^{2} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(35 \, a^{2} \cosh\left(f x + e\right)^{4} + 30 \, a^{2} \cosh\left(f x + e\right)^{2} + 3 \, a^{2}\right)} \sinh\left(f x + e\right)^{4} + 4 \, a^{2} \cosh\left(f x + e\right)^{2} + 8 \, {\left(7 \, a^{2} \cosh\left(f x + e\right)^{5} + 10 \, a^{2} \cosh\left(f x + e\right)^{3} + 3 \, a^{2} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 4 \, {\left(7 \, a^{2} \cosh\left(f x + e\right)^{6} + 15 \, a^{2} \cosh\left(f x + e\right)^{4} + 9 \, a^{2} \cosh\left(f x + e\right)^{2} + a^{2}\right)} \sinh\left(f x + e\right)^{2} + a^{2} + 8 \, {\left(a^{2} \cosh\left(f x + e\right)^{7} + 3 \, a^{2} \cosh\left(f x + e\right)^{5} + 3 \, a^{2} \cosh\left(f x + e\right)^{3} + a^{2} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{a - b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} - 1\right)} \sqrt{a - b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + 2 \, a - b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}\right) + \sqrt{2} {\left({\left(3 \, a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(f x + e\right)^{6} + 6 \, {\left(3 \, a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + {\left(3 \, a^{2} - a b - 2 \, b^{2}\right)} \sinh\left(f x + e\right)^{6} + {\left(11 \, a^{2} - 17 \, a b + 6 \, b^{2}\right)} \cosh\left(f x + e\right)^{4} + {\left(15 \, {\left(3 \, a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + 11 \, a^{2} - 17 \, a b + 6 \, b^{2}\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(5 \, {\left(3 \, a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(f x + e\right)^{3} + {\left(11 \, a^{2} - 17 \, a b + 6 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} - {\left(11 \, a^{2} - 17 \, a b + 6 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + {\left(15 \, {\left(3 \, a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(f x + e\right)^{4} + 6 \, {\left(11 \, a^{2} - 17 \, a b + 6 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} - 11 \, a^{2} + 17 \, a b - 6 \, b^{2}\right)} \sinh\left(f x + e\right)^{2} - 3 \, a^{2} + a b + 2 \, b^{2} + 2 \, {\left(3 \, {\left(3 \, a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(f x + e\right)^{5} + 2 \, {\left(11 \, a^{2} - 17 \, a b + 6 \, b^{2}\right)} \cosh\left(f x + e\right)^{3} - {\left(11 \, a^{2} - 17 \, a b + 6 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{8 \, {\left({\left(a - b\right)} f \cosh\left(f x + e\right)^{8} + 8 \, {\left(a - b\right)} f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + {\left(a - b\right)} f \sinh\left(f x + e\right)^{8} + 4 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{6} + 4 \, {\left(7 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{2} + {\left(a - b\right)} f\right)} \sinh\left(f x + e\right)^{6} + 6 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{4} + 8 \, {\left(7 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{3} + 3 \, {\left(a - b\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(35 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{4} + 30 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{2} + 3 \, {\left(a - b\right)} f\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{2} + 8 \, {\left(7 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{5} + 10 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{3} + 3 \, {\left(a - b\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 4 \, {\left(7 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{6} + 15 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{4} + 9 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{2} + {\left(a - b\right)} f\right)} \sinh\left(f x + e\right)^{2} + {\left(a - b\right)} f + 8 \, {\left({\left(a - b\right)} f \cosh\left(f x + e\right)^{7} + 3 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{5} + 3 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{3} + {\left(a - b\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)}}\right]"," ",0,"[-1/16*(3*(a^2*cosh(f*x + e)^8 + 8*a^2*cosh(f*x + e)*sinh(f*x + e)^7 + a^2*sinh(f*x + e)^8 + 4*a^2*cosh(f*x + e)^6 + 4*(7*a^2*cosh(f*x + e)^2 + a^2)*sinh(f*x + e)^6 + 6*a^2*cosh(f*x + e)^4 + 8*(7*a^2*cosh(f*x + e)^3 + 3*a^2*cosh(f*x + e))*sinh(f*x + e)^5 + 2*(35*a^2*cosh(f*x + e)^4 + 30*a^2*cosh(f*x + e)^2 + 3*a^2)*sinh(f*x + e)^4 + 4*a^2*cosh(f*x + e)^2 + 8*(7*a^2*cosh(f*x + e)^5 + 10*a^2*cosh(f*x + e)^3 + 3*a^2*cosh(f*x + e))*sinh(f*x + e)^3 + 4*(7*a^2*cosh(f*x + e)^6 + 15*a^2*cosh(f*x + e)^4 + 9*a^2*cosh(f*x + e)^2 + a^2)*sinh(f*x + e)^2 + a^2 + 8*(a^2*cosh(f*x + e)^7 + 3*a^2*cosh(f*x + e)^5 + 3*a^2*cosh(f*x + e)^3 + a^2*cosh(f*x + e))*sinh(f*x + e))*sqrt(-a + b)*log(((a - 2*b)*cosh(f*x + e)^4 + 4*(a - 2*b)*cosh(f*x + e)*sinh(f*x + e)^3 + (a - 2*b)*sinh(f*x + e)^4 - 2*(3*a - 2*b)*cosh(f*x + e)^2 + 2*(3*(a - 2*b)*cosh(f*x + e)^2 - 3*a + 2*b)*sinh(f*x + e)^2 - 2*sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 - 1)*sqrt(-a + b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + 4*((a - 2*b)*cosh(f*x + e)^3 - (3*a - 2*b)*cosh(f*x + e))*sinh(f*x + e) + a - 2*b)/(cosh(f*x + e)^4 + 4*cosh(f*x + e)*sinh(f*x + e)^3 + sinh(f*x + e)^4 + 2*(3*cosh(f*x + e)^2 + 1)*sinh(f*x + e)^2 + 2*cosh(f*x + e)^2 + 4*(cosh(f*x + e)^3 + cosh(f*x + e))*sinh(f*x + e) + 1)) - 2*sqrt(2)*((3*a^2 - a*b - 2*b^2)*cosh(f*x + e)^6 + 6*(3*a^2 - a*b - 2*b^2)*cosh(f*x + e)*sinh(f*x + e)^5 + (3*a^2 - a*b - 2*b^2)*sinh(f*x + e)^6 + (11*a^2 - 17*a*b + 6*b^2)*cosh(f*x + e)^4 + (15*(3*a^2 - a*b - 2*b^2)*cosh(f*x + e)^2 + 11*a^2 - 17*a*b + 6*b^2)*sinh(f*x + e)^4 + 4*(5*(3*a^2 - a*b - 2*b^2)*cosh(f*x + e)^3 + (11*a^2 - 17*a*b + 6*b^2)*cosh(f*x + e))*sinh(f*x + e)^3 - (11*a^2 - 17*a*b + 6*b^2)*cosh(f*x + e)^2 + (15*(3*a^2 - a*b - 2*b^2)*cosh(f*x + e)^4 + 6*(11*a^2 - 17*a*b + 6*b^2)*cosh(f*x + e)^2 - 11*a^2 + 17*a*b - 6*b^2)*sinh(f*x + e)^2 - 3*a^2 + a*b + 2*b^2 + 2*(3*(3*a^2 - a*b - 2*b^2)*cosh(f*x + e)^5 + 2*(11*a^2 - 17*a*b + 6*b^2)*cosh(f*x + e)^3 - (11*a^2 - 17*a*b + 6*b^2)*cosh(f*x + e))*sinh(f*x + e))*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/((a - b)*f*cosh(f*x + e)^8 + 8*(a - b)*f*cosh(f*x + e)*sinh(f*x + e)^7 + (a - b)*f*sinh(f*x + e)^8 + 4*(a - b)*f*cosh(f*x + e)^6 + 4*(7*(a - b)*f*cosh(f*x + e)^2 + (a - b)*f)*sinh(f*x + e)^6 + 6*(a - b)*f*cosh(f*x + e)^4 + 8*(7*(a - b)*f*cosh(f*x + e)^3 + 3*(a - b)*f*cosh(f*x + e))*sinh(f*x + e)^5 + 2*(35*(a - b)*f*cosh(f*x + e)^4 + 30*(a - b)*f*cosh(f*x + e)^2 + 3*(a - b)*f)*sinh(f*x + e)^4 + 4*(a - b)*f*cosh(f*x + e)^2 + 8*(7*(a - b)*f*cosh(f*x + e)^5 + 10*(a - b)*f*cosh(f*x + e)^3 + 3*(a - b)*f*cosh(f*x + e))*sinh(f*x + e)^3 + 4*(7*(a - b)*f*cosh(f*x + e)^6 + 15*(a - b)*f*cosh(f*x + e)^4 + 9*(a - b)*f*cosh(f*x + e)^2 + (a - b)*f)*sinh(f*x + e)^2 + (a - b)*f + 8*((a - b)*f*cosh(f*x + e)^7 + 3*(a - b)*f*cosh(f*x + e)^5 + 3*(a - b)*f*cosh(f*x + e)^3 + (a - b)*f*cosh(f*x + e))*sinh(f*x + e)), 1/8*(3*(a^2*cosh(f*x + e)^8 + 8*a^2*cosh(f*x + e)*sinh(f*x + e)^7 + a^2*sinh(f*x + e)^8 + 4*a^2*cosh(f*x + e)^6 + 4*(7*a^2*cosh(f*x + e)^2 + a^2)*sinh(f*x + e)^6 + 6*a^2*cosh(f*x + e)^4 + 8*(7*a^2*cosh(f*x + e)^3 + 3*a^2*cosh(f*x + e))*sinh(f*x + e)^5 + 2*(35*a^2*cosh(f*x + e)^4 + 30*a^2*cosh(f*x + e)^2 + 3*a^2)*sinh(f*x + e)^4 + 4*a^2*cosh(f*x + e)^2 + 8*(7*a^2*cosh(f*x + e)^5 + 10*a^2*cosh(f*x + e)^3 + 3*a^2*cosh(f*x + e))*sinh(f*x + e)^3 + 4*(7*a^2*cosh(f*x + e)^6 + 15*a^2*cosh(f*x + e)^4 + 9*a^2*cosh(f*x + e)^2 + a^2)*sinh(f*x + e)^2 + a^2 + 8*(a^2*cosh(f*x + e)^7 + 3*a^2*cosh(f*x + e)^5 + 3*a^2*cosh(f*x + e)^3 + a^2*cosh(f*x + e))*sinh(f*x + e))*sqrt(a - b)*arctan(sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 - 1)*sqrt(a - b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/(b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(2*a - b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 2*a - b)*sinh(f*x + e)^2 + 4*(b*cosh(f*x + e)^3 + (2*a - b)*cosh(f*x + e))*sinh(f*x + e) + b)) + sqrt(2)*((3*a^2 - a*b - 2*b^2)*cosh(f*x + e)^6 + 6*(3*a^2 - a*b - 2*b^2)*cosh(f*x + e)*sinh(f*x + e)^5 + (3*a^2 - a*b - 2*b^2)*sinh(f*x + e)^6 + (11*a^2 - 17*a*b + 6*b^2)*cosh(f*x + e)^4 + (15*(3*a^2 - a*b - 2*b^2)*cosh(f*x + e)^2 + 11*a^2 - 17*a*b + 6*b^2)*sinh(f*x + e)^4 + 4*(5*(3*a^2 - a*b - 2*b^2)*cosh(f*x + e)^3 + (11*a^2 - 17*a*b + 6*b^2)*cosh(f*x + e))*sinh(f*x + e)^3 - (11*a^2 - 17*a*b + 6*b^2)*cosh(f*x + e)^2 + (15*(3*a^2 - a*b - 2*b^2)*cosh(f*x + e)^4 + 6*(11*a^2 - 17*a*b + 6*b^2)*cosh(f*x + e)^2 - 11*a^2 + 17*a*b - 6*b^2)*sinh(f*x + e)^2 - 3*a^2 + a*b + 2*b^2 + 2*(3*(3*a^2 - a*b - 2*b^2)*cosh(f*x + e)^5 + 2*(11*a^2 - 17*a*b + 6*b^2)*cosh(f*x + e)^3 - (11*a^2 - 17*a*b + 6*b^2)*cosh(f*x + e))*sinh(f*x + e))*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/((a - b)*f*cosh(f*x + e)^8 + 8*(a - b)*f*cosh(f*x + e)*sinh(f*x + e)^7 + (a - b)*f*sinh(f*x + e)^8 + 4*(a - b)*f*cosh(f*x + e)^6 + 4*(7*(a - b)*f*cosh(f*x + e)^2 + (a - b)*f)*sinh(f*x + e)^6 + 6*(a - b)*f*cosh(f*x + e)^4 + 8*(7*(a - b)*f*cosh(f*x + e)^3 + 3*(a - b)*f*cosh(f*x + e))*sinh(f*x + e)^5 + 2*(35*(a - b)*f*cosh(f*x + e)^4 + 30*(a - b)*f*cosh(f*x + e)^2 + 3*(a - b)*f)*sinh(f*x + e)^4 + 4*(a - b)*f*cosh(f*x + e)^2 + 8*(7*(a - b)*f*cosh(f*x + e)^5 + 10*(a - b)*f*cosh(f*x + e)^3 + 3*(a - b)*f*cosh(f*x + e))*sinh(f*x + e)^3 + 4*(7*(a - b)*f*cosh(f*x + e)^6 + 15*(a - b)*f*cosh(f*x + e)^4 + 9*(a - b)*f*cosh(f*x + e)^2 + (a - b)*f)*sinh(f*x + e)^2 + (a - b)*f + 8*((a - b)*f*cosh(f*x + e)^7 + 3*(a - b)*f*cosh(f*x + e)^5 + 3*(a - b)*f*cosh(f*x + e)^3 + (a - b)*f*cosh(f*x + e))*sinh(f*x + e))]","B",0
367,1,7633,0,2.706625," ","integrate(sech(f*x+e)^7*(a+b*sinh(f*x+e)^2)^(3/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left({\left(5 \, a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)^{12} + 12 \, {\left(5 \, a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{11} + {\left(5 \, a^{3} - 6 \, a^{2} b\right)} \sinh\left(f x + e\right)^{12} + 6 \, {\left(5 \, a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)^{10} + 6 \, {\left(5 \, a^{3} - 6 \, a^{2} b + 11 \, {\left(5 \, a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{10} + 20 \, {\left(11 \, {\left(5 \, a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(5 \, a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{9} + 15 \, {\left(5 \, a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)^{8} + 15 \, {\left(33 \, {\left(5 \, a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)^{4} + 5 \, a^{3} - 6 \, a^{2} b + 18 \, {\left(5 \, a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{8} + 24 \, {\left(33 \, {\left(5 \, a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)^{5} + 30 \, {\left(5 \, a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)^{3} + 5 \, {\left(5 \, a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{7} + 20 \, {\left(5 \, a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)^{6} + 4 \, {\left(231 \, {\left(5 \, a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)^{6} + 315 \, {\left(5 \, a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)^{4} + 25 \, a^{3} - 30 \, a^{2} b + 105 \, {\left(5 \, a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{6} + 24 \, {\left(33 \, {\left(5 \, a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)^{7} + 63 \, {\left(5 \, a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)^{5} + 35 \, {\left(5 \, a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)^{3} + 5 \, {\left(5 \, a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + 15 \, {\left(5 \, a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)^{4} + 15 \, {\left(33 \, {\left(5 \, a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)^{8} + 84 \, {\left(5 \, a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)^{6} + 70 \, {\left(5 \, a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)^{4} + 5 \, a^{3} - 6 \, a^{2} b + 20 \, {\left(5 \, a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{4} + 20 \, {\left(11 \, {\left(5 \, a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)^{9} + 36 \, {\left(5 \, a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)^{7} + 42 \, {\left(5 \, a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)^{5} + 20 \, {\left(5 \, a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(5 \, a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 5 \, a^{3} - 6 \, a^{2} b + 6 \, {\left(5 \, a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)^{2} + 6 \, {\left(11 \, {\left(5 \, a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)^{10} + 45 \, {\left(5 \, a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)^{8} + 70 \, {\left(5 \, a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)^{6} + 50 \, {\left(5 \, a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)^{4} + 5 \, a^{3} - 6 \, a^{2} b + 15 \, {\left(5 \, a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{2} + 12 \, {\left({\left(5 \, a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)^{11} + 5 \, {\left(5 \, a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)^{9} + 10 \, {\left(5 \, a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)^{7} + 10 \, {\left(5 \, a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)^{5} + 5 \, {\left(5 \, a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)^{3} + {\left(5 \, a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{-a + b} \log\left(\frac{{\left(a - 2 \, b\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left(a - 2 \, b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(a - 2 \, b\right)} \sinh\left(f x + e\right)^{4} - 2 \, {\left(3 \, a - 2 \, b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, {\left(a - 2 \, b\right)} \cosh\left(f x + e\right)^{2} - 3 \, a + 2 \, b\right)} \sinh\left(f x + e\right)^{2} - 2 \, \sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} - 1\right)} \sqrt{-a + b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} + 4 \, {\left({\left(a - 2 \, b\right)} \cosh\left(f x + e\right)^{3} - {\left(3 \, a - 2 \, b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + a - 2 \, b}{\cosh\left(f x + e\right)^{4} + 4 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + \sinh\left(f x + e\right)^{4} + 2 \, {\left(3 \, \cosh\left(f x + e\right)^{2} + 1\right)} \sinh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right)^{2} + 4 \, {\left(\cosh\left(f x + e\right)^{3} + \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + 1}\right) - 2 \, \sqrt{2} {\left({\left(15 \, a^{3} - 23 \, a^{2} b + 4 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(f x + e\right)^{10} + 10 \, {\left(15 \, a^{3} - 23 \, a^{2} b + 4 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{9} + {\left(15 \, a^{3} - 23 \, a^{2} b + 4 \, a b^{2} + 4 \, b^{3}\right)} \sinh\left(f x + e\right)^{10} + {\left(85 \, a^{3} - 133 \, a^{2} b + 20 \, a b^{2} + 28 \, b^{3}\right)} \cosh\left(f x + e\right)^{8} + {\left(85 \, a^{3} - 133 \, a^{2} b + 20 \, a b^{2} + 28 \, b^{3} + 45 \, {\left(15 \, a^{3} - 23 \, a^{2} b + 4 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{8} + 8 \, {\left(15 \, {\left(15 \, a^{3} - 23 \, a^{2} b + 4 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} + {\left(85 \, a^{3} - 133 \, a^{2} b + 20 \, a b^{2} + 28 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{7} + 2 \, {\left(99 \, a^{3} - 247 \, a^{2} b + 200 \, a b^{2} - 52 \, b^{3}\right)} \cosh\left(f x + e\right)^{6} + 2 \, {\left(105 \, {\left(15 \, a^{3} - 23 \, a^{2} b + 4 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} + 99 \, a^{3} - 247 \, a^{2} b + 200 \, a b^{2} - 52 \, b^{3} + 14 \, {\left(85 \, a^{3} - 133 \, a^{2} b + 20 \, a b^{2} + 28 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{6} + 4 \, {\left(63 \, {\left(15 \, a^{3} - 23 \, a^{2} b + 4 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(f x + e\right)^{5} + 14 \, {\left(85 \, a^{3} - 133 \, a^{2} b + 20 \, a b^{2} + 28 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(99 \, a^{3} - 247 \, a^{2} b + 200 \, a b^{2} - 52 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} - 2 \, {\left(99 \, a^{3} - 247 \, a^{2} b + 200 \, a b^{2} - 52 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} + 2 \, {\left(105 \, {\left(15 \, a^{3} - 23 \, a^{2} b + 4 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(f x + e\right)^{6} + 35 \, {\left(85 \, a^{3} - 133 \, a^{2} b + 20 \, a b^{2} + 28 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} - 99 \, a^{3} + 247 \, a^{2} b - 200 \, a b^{2} + 52 \, b^{3} + 15 \, {\left(99 \, a^{3} - 247 \, a^{2} b + 200 \, a b^{2} - 52 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{4} + 8 \, {\left(15 \, {\left(15 \, a^{3} - 23 \, a^{2} b + 4 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(f x + e\right)^{7} + 7 \, {\left(85 \, a^{3} - 133 \, a^{2} b + 20 \, a b^{2} + 28 \, b^{3}\right)} \cosh\left(f x + e\right)^{5} + 5 \, {\left(99 \, a^{3} - 247 \, a^{2} b + 200 \, a b^{2} - 52 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} - {\left(99 \, a^{3} - 247 \, a^{2} b + 200 \, a b^{2} - 52 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} - 15 \, a^{3} + 23 \, a^{2} b - 4 \, a b^{2} - 4 \, b^{3} - {\left(85 \, a^{3} - 133 \, a^{2} b + 20 \, a b^{2} + 28 \, b^{3}\right)} \cosh\left(f x + e\right)^{2} + {\left(45 \, {\left(15 \, a^{3} - 23 \, a^{2} b + 4 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(f x + e\right)^{8} + 28 \, {\left(85 \, a^{3} - 133 \, a^{2} b + 20 \, a b^{2} + 28 \, b^{3}\right)} \cosh\left(f x + e\right)^{6} + 30 \, {\left(99 \, a^{3} - 247 \, a^{2} b + 200 \, a b^{2} - 52 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} - 85 \, a^{3} + 133 \, a^{2} b - 20 \, a b^{2} - 28 \, b^{3} - 12 \, {\left(99 \, a^{3} - 247 \, a^{2} b + 200 \, a b^{2} - 52 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{2} + 2 \, {\left(5 \, {\left(15 \, a^{3} - 23 \, a^{2} b + 4 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(f x + e\right)^{9} + 4 \, {\left(85 \, a^{3} - 133 \, a^{2} b + 20 \, a b^{2} + 28 \, b^{3}\right)} \cosh\left(f x + e\right)^{7} + 6 \, {\left(99 \, a^{3} - 247 \, a^{2} b + 200 \, a b^{2} - 52 \, b^{3}\right)} \cosh\left(f x + e\right)^{5} - 4 \, {\left(99 \, a^{3} - 247 \, a^{2} b + 200 \, a b^{2} - 52 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} - {\left(85 \, a^{3} - 133 \, a^{2} b + 20 \, a b^{2} + 28 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{96 \, {\left({\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{12} + 12 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{11} + {\left(a^{2} - 2 \, a b + b^{2}\right)} f \sinh\left(f x + e\right)^{12} + 6 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{10} + 6 \, {\left(11 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{2} + {\left(a^{2} - 2 \, a b + b^{2}\right)} f\right)} \sinh\left(f x + e\right)^{10} + 15 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{8} + 20 \, {\left(11 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{3} + 3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{9} + 15 \, {\left(33 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{4} + 18 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{2} + {\left(a^{2} - 2 \, a b + b^{2}\right)} f\right)} \sinh\left(f x + e\right)^{8} + 20 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{6} + 24 \, {\left(33 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{5} + 30 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{3} + 5 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{7} + 4 \, {\left(231 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{6} + 315 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{4} + 105 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{2} + 5 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f\right)} \sinh\left(f x + e\right)^{6} + 15 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{4} + 24 \, {\left(33 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{7} + 63 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{5} + 35 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{3} + 5 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + 15 \, {\left(33 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{8} + 84 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{6} + 70 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{4} + 20 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{2} + {\left(a^{2} - 2 \, a b + b^{2}\right)} f\right)} \sinh\left(f x + e\right)^{4} + 6 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{2} + 20 \, {\left(11 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{9} + 36 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{7} + 42 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{5} + 20 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{3} + 3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 6 \, {\left(11 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{10} + 45 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{8} + 70 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{6} + 50 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{4} + 15 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{2} + {\left(a^{2} - 2 \, a b + b^{2}\right)} f\right)} \sinh\left(f x + e\right)^{2} + {\left(a^{2} - 2 \, a b + b^{2}\right)} f + 12 \, {\left({\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{11} + 5 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{9} + 10 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{7} + 10 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{5} + 5 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{3} + {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)}}, \frac{3 \, {\left({\left(5 \, a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)^{12} + 12 \, {\left(5 \, a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{11} + {\left(5 \, a^{3} - 6 \, a^{2} b\right)} \sinh\left(f x + e\right)^{12} + 6 \, {\left(5 \, a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)^{10} + 6 \, {\left(5 \, a^{3} - 6 \, a^{2} b + 11 \, {\left(5 \, a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{10} + 20 \, {\left(11 \, {\left(5 \, a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(5 \, a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{9} + 15 \, {\left(5 \, a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)^{8} + 15 \, {\left(33 \, {\left(5 \, a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)^{4} + 5 \, a^{3} - 6 \, a^{2} b + 18 \, {\left(5 \, a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{8} + 24 \, {\left(33 \, {\left(5 \, a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)^{5} + 30 \, {\left(5 \, a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)^{3} + 5 \, {\left(5 \, a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{7} + 20 \, {\left(5 \, a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)^{6} + 4 \, {\left(231 \, {\left(5 \, a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)^{6} + 315 \, {\left(5 \, a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)^{4} + 25 \, a^{3} - 30 \, a^{2} b + 105 \, {\left(5 \, a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{6} + 24 \, {\left(33 \, {\left(5 \, a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)^{7} + 63 \, {\left(5 \, a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)^{5} + 35 \, {\left(5 \, a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)^{3} + 5 \, {\left(5 \, a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + 15 \, {\left(5 \, a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)^{4} + 15 \, {\left(33 \, {\left(5 \, a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)^{8} + 84 \, {\left(5 \, a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)^{6} + 70 \, {\left(5 \, a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)^{4} + 5 \, a^{3} - 6 \, a^{2} b + 20 \, {\left(5 \, a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{4} + 20 \, {\left(11 \, {\left(5 \, a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)^{9} + 36 \, {\left(5 \, a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)^{7} + 42 \, {\left(5 \, a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)^{5} + 20 \, {\left(5 \, a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(5 \, a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 5 \, a^{3} - 6 \, a^{2} b + 6 \, {\left(5 \, a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)^{2} + 6 \, {\left(11 \, {\left(5 \, a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)^{10} + 45 \, {\left(5 \, a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)^{8} + 70 \, {\left(5 \, a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)^{6} + 50 \, {\left(5 \, a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)^{4} + 5 \, a^{3} - 6 \, a^{2} b + 15 \, {\left(5 \, a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{2} + 12 \, {\left({\left(5 \, a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)^{11} + 5 \, {\left(5 \, a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)^{9} + 10 \, {\left(5 \, a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)^{7} + 10 \, {\left(5 \, a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)^{5} + 5 \, {\left(5 \, a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)^{3} + {\left(5 \, a^{3} - 6 \, a^{2} b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{a - b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} - 1\right)} \sqrt{a - b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + 2 \, a - b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}\right) + \sqrt{2} {\left({\left(15 \, a^{3} - 23 \, a^{2} b + 4 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(f x + e\right)^{10} + 10 \, {\left(15 \, a^{3} - 23 \, a^{2} b + 4 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{9} + {\left(15 \, a^{3} - 23 \, a^{2} b + 4 \, a b^{2} + 4 \, b^{3}\right)} \sinh\left(f x + e\right)^{10} + {\left(85 \, a^{3} - 133 \, a^{2} b + 20 \, a b^{2} + 28 \, b^{3}\right)} \cosh\left(f x + e\right)^{8} + {\left(85 \, a^{3} - 133 \, a^{2} b + 20 \, a b^{2} + 28 \, b^{3} + 45 \, {\left(15 \, a^{3} - 23 \, a^{2} b + 4 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{8} + 8 \, {\left(15 \, {\left(15 \, a^{3} - 23 \, a^{2} b + 4 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} + {\left(85 \, a^{3} - 133 \, a^{2} b + 20 \, a b^{2} + 28 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{7} + 2 \, {\left(99 \, a^{3} - 247 \, a^{2} b + 200 \, a b^{2} - 52 \, b^{3}\right)} \cosh\left(f x + e\right)^{6} + 2 \, {\left(105 \, {\left(15 \, a^{3} - 23 \, a^{2} b + 4 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} + 99 \, a^{3} - 247 \, a^{2} b + 200 \, a b^{2} - 52 \, b^{3} + 14 \, {\left(85 \, a^{3} - 133 \, a^{2} b + 20 \, a b^{2} + 28 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{6} + 4 \, {\left(63 \, {\left(15 \, a^{3} - 23 \, a^{2} b + 4 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(f x + e\right)^{5} + 14 \, {\left(85 \, a^{3} - 133 \, a^{2} b + 20 \, a b^{2} + 28 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(99 \, a^{3} - 247 \, a^{2} b + 200 \, a b^{2} - 52 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} - 2 \, {\left(99 \, a^{3} - 247 \, a^{2} b + 200 \, a b^{2} - 52 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} + 2 \, {\left(105 \, {\left(15 \, a^{3} - 23 \, a^{2} b + 4 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(f x + e\right)^{6} + 35 \, {\left(85 \, a^{3} - 133 \, a^{2} b + 20 \, a b^{2} + 28 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} - 99 \, a^{3} + 247 \, a^{2} b - 200 \, a b^{2} + 52 \, b^{3} + 15 \, {\left(99 \, a^{3} - 247 \, a^{2} b + 200 \, a b^{2} - 52 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{4} + 8 \, {\left(15 \, {\left(15 \, a^{3} - 23 \, a^{2} b + 4 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(f x + e\right)^{7} + 7 \, {\left(85 \, a^{3} - 133 \, a^{2} b + 20 \, a b^{2} + 28 \, b^{3}\right)} \cosh\left(f x + e\right)^{5} + 5 \, {\left(99 \, a^{3} - 247 \, a^{2} b + 200 \, a b^{2} - 52 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} - {\left(99 \, a^{3} - 247 \, a^{2} b + 200 \, a b^{2} - 52 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} - 15 \, a^{3} + 23 \, a^{2} b - 4 \, a b^{2} - 4 \, b^{3} - {\left(85 \, a^{3} - 133 \, a^{2} b + 20 \, a b^{2} + 28 \, b^{3}\right)} \cosh\left(f x + e\right)^{2} + {\left(45 \, {\left(15 \, a^{3} - 23 \, a^{2} b + 4 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(f x + e\right)^{8} + 28 \, {\left(85 \, a^{3} - 133 \, a^{2} b + 20 \, a b^{2} + 28 \, b^{3}\right)} \cosh\left(f x + e\right)^{6} + 30 \, {\left(99 \, a^{3} - 247 \, a^{2} b + 200 \, a b^{2} - 52 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} - 85 \, a^{3} + 133 \, a^{2} b - 20 \, a b^{2} - 28 \, b^{3} - 12 \, {\left(99 \, a^{3} - 247 \, a^{2} b + 200 \, a b^{2} - 52 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{2} + 2 \, {\left(5 \, {\left(15 \, a^{3} - 23 \, a^{2} b + 4 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(f x + e\right)^{9} + 4 \, {\left(85 \, a^{3} - 133 \, a^{2} b + 20 \, a b^{2} + 28 \, b^{3}\right)} \cosh\left(f x + e\right)^{7} + 6 \, {\left(99 \, a^{3} - 247 \, a^{2} b + 200 \, a b^{2} - 52 \, b^{3}\right)} \cosh\left(f x + e\right)^{5} - 4 \, {\left(99 \, a^{3} - 247 \, a^{2} b + 200 \, a b^{2} - 52 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} - {\left(85 \, a^{3} - 133 \, a^{2} b + 20 \, a b^{2} + 28 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{48 \, {\left({\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{12} + 12 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{11} + {\left(a^{2} - 2 \, a b + b^{2}\right)} f \sinh\left(f x + e\right)^{12} + 6 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{10} + 6 \, {\left(11 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{2} + {\left(a^{2} - 2 \, a b + b^{2}\right)} f\right)} \sinh\left(f x + e\right)^{10} + 15 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{8} + 20 \, {\left(11 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{3} + 3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{9} + 15 \, {\left(33 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{4} + 18 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{2} + {\left(a^{2} - 2 \, a b + b^{2}\right)} f\right)} \sinh\left(f x + e\right)^{8} + 20 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{6} + 24 \, {\left(33 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{5} + 30 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{3} + 5 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{7} + 4 \, {\left(231 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{6} + 315 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{4} + 105 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{2} + 5 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f\right)} \sinh\left(f x + e\right)^{6} + 15 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{4} + 24 \, {\left(33 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{7} + 63 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{5} + 35 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{3} + 5 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + 15 \, {\left(33 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{8} + 84 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{6} + 70 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{4} + 20 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{2} + {\left(a^{2} - 2 \, a b + b^{2}\right)} f\right)} \sinh\left(f x + e\right)^{4} + 6 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{2} + 20 \, {\left(11 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{9} + 36 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{7} + 42 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{5} + 20 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{3} + 3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 6 \, {\left(11 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{10} + 45 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{8} + 70 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{6} + 50 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{4} + 15 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{2} + {\left(a^{2} - 2 \, a b + b^{2}\right)} f\right)} \sinh\left(f x + e\right)^{2} + {\left(a^{2} - 2 \, a b + b^{2}\right)} f + 12 \, {\left({\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{11} + 5 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{9} + 10 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{7} + 10 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{5} + 5 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{3} + {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)}}\right]"," ",0,"[-1/96*(3*((5*a^3 - 6*a^2*b)*cosh(f*x + e)^12 + 12*(5*a^3 - 6*a^2*b)*cosh(f*x + e)*sinh(f*x + e)^11 + (5*a^3 - 6*a^2*b)*sinh(f*x + e)^12 + 6*(5*a^3 - 6*a^2*b)*cosh(f*x + e)^10 + 6*(5*a^3 - 6*a^2*b + 11*(5*a^3 - 6*a^2*b)*cosh(f*x + e)^2)*sinh(f*x + e)^10 + 20*(11*(5*a^3 - 6*a^2*b)*cosh(f*x + e)^3 + 3*(5*a^3 - 6*a^2*b)*cosh(f*x + e))*sinh(f*x + e)^9 + 15*(5*a^3 - 6*a^2*b)*cosh(f*x + e)^8 + 15*(33*(5*a^3 - 6*a^2*b)*cosh(f*x + e)^4 + 5*a^3 - 6*a^2*b + 18*(5*a^3 - 6*a^2*b)*cosh(f*x + e)^2)*sinh(f*x + e)^8 + 24*(33*(5*a^3 - 6*a^2*b)*cosh(f*x + e)^5 + 30*(5*a^3 - 6*a^2*b)*cosh(f*x + e)^3 + 5*(5*a^3 - 6*a^2*b)*cosh(f*x + e))*sinh(f*x + e)^7 + 20*(5*a^3 - 6*a^2*b)*cosh(f*x + e)^6 + 4*(231*(5*a^3 - 6*a^2*b)*cosh(f*x + e)^6 + 315*(5*a^3 - 6*a^2*b)*cosh(f*x + e)^4 + 25*a^3 - 30*a^2*b + 105*(5*a^3 - 6*a^2*b)*cosh(f*x + e)^2)*sinh(f*x + e)^6 + 24*(33*(5*a^3 - 6*a^2*b)*cosh(f*x + e)^7 + 63*(5*a^3 - 6*a^2*b)*cosh(f*x + e)^5 + 35*(5*a^3 - 6*a^2*b)*cosh(f*x + e)^3 + 5*(5*a^3 - 6*a^2*b)*cosh(f*x + e))*sinh(f*x + e)^5 + 15*(5*a^3 - 6*a^2*b)*cosh(f*x + e)^4 + 15*(33*(5*a^3 - 6*a^2*b)*cosh(f*x + e)^8 + 84*(5*a^3 - 6*a^2*b)*cosh(f*x + e)^6 + 70*(5*a^3 - 6*a^2*b)*cosh(f*x + e)^4 + 5*a^3 - 6*a^2*b + 20*(5*a^3 - 6*a^2*b)*cosh(f*x + e)^2)*sinh(f*x + e)^4 + 20*(11*(5*a^3 - 6*a^2*b)*cosh(f*x + e)^9 + 36*(5*a^3 - 6*a^2*b)*cosh(f*x + e)^7 + 42*(5*a^3 - 6*a^2*b)*cosh(f*x + e)^5 + 20*(5*a^3 - 6*a^2*b)*cosh(f*x + e)^3 + 3*(5*a^3 - 6*a^2*b)*cosh(f*x + e))*sinh(f*x + e)^3 + 5*a^3 - 6*a^2*b + 6*(5*a^3 - 6*a^2*b)*cosh(f*x + e)^2 + 6*(11*(5*a^3 - 6*a^2*b)*cosh(f*x + e)^10 + 45*(5*a^3 - 6*a^2*b)*cosh(f*x + e)^8 + 70*(5*a^3 - 6*a^2*b)*cosh(f*x + e)^6 + 50*(5*a^3 - 6*a^2*b)*cosh(f*x + e)^4 + 5*a^3 - 6*a^2*b + 15*(5*a^3 - 6*a^2*b)*cosh(f*x + e)^2)*sinh(f*x + e)^2 + 12*((5*a^3 - 6*a^2*b)*cosh(f*x + e)^11 + 5*(5*a^3 - 6*a^2*b)*cosh(f*x + e)^9 + 10*(5*a^3 - 6*a^2*b)*cosh(f*x + e)^7 + 10*(5*a^3 - 6*a^2*b)*cosh(f*x + e)^5 + 5*(5*a^3 - 6*a^2*b)*cosh(f*x + e)^3 + (5*a^3 - 6*a^2*b)*cosh(f*x + e))*sinh(f*x + e))*sqrt(-a + b)*log(((a - 2*b)*cosh(f*x + e)^4 + 4*(a - 2*b)*cosh(f*x + e)*sinh(f*x + e)^3 + (a - 2*b)*sinh(f*x + e)^4 - 2*(3*a - 2*b)*cosh(f*x + e)^2 + 2*(3*(a - 2*b)*cosh(f*x + e)^2 - 3*a + 2*b)*sinh(f*x + e)^2 - 2*sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 - 1)*sqrt(-a + b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + 4*((a - 2*b)*cosh(f*x + e)^3 - (3*a - 2*b)*cosh(f*x + e))*sinh(f*x + e) + a - 2*b)/(cosh(f*x + e)^4 + 4*cosh(f*x + e)*sinh(f*x + e)^3 + sinh(f*x + e)^4 + 2*(3*cosh(f*x + e)^2 + 1)*sinh(f*x + e)^2 + 2*cosh(f*x + e)^2 + 4*(cosh(f*x + e)^3 + cosh(f*x + e))*sinh(f*x + e) + 1)) - 2*sqrt(2)*((15*a^3 - 23*a^2*b + 4*a*b^2 + 4*b^3)*cosh(f*x + e)^10 + 10*(15*a^3 - 23*a^2*b + 4*a*b^2 + 4*b^3)*cosh(f*x + e)*sinh(f*x + e)^9 + (15*a^3 - 23*a^2*b + 4*a*b^2 + 4*b^3)*sinh(f*x + e)^10 + (85*a^3 - 133*a^2*b + 20*a*b^2 + 28*b^3)*cosh(f*x + e)^8 + (85*a^3 - 133*a^2*b + 20*a*b^2 + 28*b^3 + 45*(15*a^3 - 23*a^2*b + 4*a*b^2 + 4*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^8 + 8*(15*(15*a^3 - 23*a^2*b + 4*a*b^2 + 4*b^3)*cosh(f*x + e)^3 + (85*a^3 - 133*a^2*b + 20*a*b^2 + 28*b^3)*cosh(f*x + e))*sinh(f*x + e)^7 + 2*(99*a^3 - 247*a^2*b + 200*a*b^2 - 52*b^3)*cosh(f*x + e)^6 + 2*(105*(15*a^3 - 23*a^2*b + 4*a*b^2 + 4*b^3)*cosh(f*x + e)^4 + 99*a^3 - 247*a^2*b + 200*a*b^2 - 52*b^3 + 14*(85*a^3 - 133*a^2*b + 20*a*b^2 + 28*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^6 + 4*(63*(15*a^3 - 23*a^2*b + 4*a*b^2 + 4*b^3)*cosh(f*x + e)^5 + 14*(85*a^3 - 133*a^2*b + 20*a*b^2 + 28*b^3)*cosh(f*x + e)^3 + 3*(99*a^3 - 247*a^2*b + 200*a*b^2 - 52*b^3)*cosh(f*x + e))*sinh(f*x + e)^5 - 2*(99*a^3 - 247*a^2*b + 200*a*b^2 - 52*b^3)*cosh(f*x + e)^4 + 2*(105*(15*a^3 - 23*a^2*b + 4*a*b^2 + 4*b^3)*cosh(f*x + e)^6 + 35*(85*a^3 - 133*a^2*b + 20*a*b^2 + 28*b^3)*cosh(f*x + e)^4 - 99*a^3 + 247*a^2*b - 200*a*b^2 + 52*b^3 + 15*(99*a^3 - 247*a^2*b + 200*a*b^2 - 52*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^4 + 8*(15*(15*a^3 - 23*a^2*b + 4*a*b^2 + 4*b^3)*cosh(f*x + e)^7 + 7*(85*a^3 - 133*a^2*b + 20*a*b^2 + 28*b^3)*cosh(f*x + e)^5 + 5*(99*a^3 - 247*a^2*b + 200*a*b^2 - 52*b^3)*cosh(f*x + e)^3 - (99*a^3 - 247*a^2*b + 200*a*b^2 - 52*b^3)*cosh(f*x + e))*sinh(f*x + e)^3 - 15*a^3 + 23*a^2*b - 4*a*b^2 - 4*b^3 - (85*a^3 - 133*a^2*b + 20*a*b^2 + 28*b^3)*cosh(f*x + e)^2 + (45*(15*a^3 - 23*a^2*b + 4*a*b^2 + 4*b^3)*cosh(f*x + e)^8 + 28*(85*a^3 - 133*a^2*b + 20*a*b^2 + 28*b^3)*cosh(f*x + e)^6 + 30*(99*a^3 - 247*a^2*b + 200*a*b^2 - 52*b^3)*cosh(f*x + e)^4 - 85*a^3 + 133*a^2*b - 20*a*b^2 - 28*b^3 - 12*(99*a^3 - 247*a^2*b + 200*a*b^2 - 52*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^2 + 2*(5*(15*a^3 - 23*a^2*b + 4*a*b^2 + 4*b^3)*cosh(f*x + e)^9 + 4*(85*a^3 - 133*a^2*b + 20*a*b^2 + 28*b^3)*cosh(f*x + e)^7 + 6*(99*a^3 - 247*a^2*b + 200*a*b^2 - 52*b^3)*cosh(f*x + e)^5 - 4*(99*a^3 - 247*a^2*b + 200*a*b^2 - 52*b^3)*cosh(f*x + e)^3 - (85*a^3 - 133*a^2*b + 20*a*b^2 + 28*b^3)*cosh(f*x + e))*sinh(f*x + e))*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/((a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^12 + 12*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)*sinh(f*x + e)^11 + (a^2 - 2*a*b + b^2)*f*sinh(f*x + e)^12 + 6*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^10 + 6*(11*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^2 + (a^2 - 2*a*b + b^2)*f)*sinh(f*x + e)^10 + 15*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^8 + 20*(11*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^3 + 3*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e))*sinh(f*x + e)^9 + 15*(33*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^4 + 18*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^2 + (a^2 - 2*a*b + b^2)*f)*sinh(f*x + e)^8 + 20*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^6 + 24*(33*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^5 + 30*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^3 + 5*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e))*sinh(f*x + e)^7 + 4*(231*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^6 + 315*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^4 + 105*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^2 + 5*(a^2 - 2*a*b + b^2)*f)*sinh(f*x + e)^6 + 15*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^4 + 24*(33*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^7 + 63*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^5 + 35*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^3 + 5*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e))*sinh(f*x + e)^5 + 15*(33*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^8 + 84*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^6 + 70*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^4 + 20*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^2 + (a^2 - 2*a*b + b^2)*f)*sinh(f*x + e)^4 + 6*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^2 + 20*(11*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^9 + 36*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^7 + 42*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^5 + 20*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^3 + 3*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e))*sinh(f*x + e)^3 + 6*(11*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^10 + 45*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^8 + 70*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^6 + 50*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^4 + 15*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^2 + (a^2 - 2*a*b + b^2)*f)*sinh(f*x + e)^2 + (a^2 - 2*a*b + b^2)*f + 12*((a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^11 + 5*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^9 + 10*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^7 + 10*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^5 + 5*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^3 + (a^2 - 2*a*b + b^2)*f*cosh(f*x + e))*sinh(f*x + e)), 1/48*(3*((5*a^3 - 6*a^2*b)*cosh(f*x + e)^12 + 12*(5*a^3 - 6*a^2*b)*cosh(f*x + e)*sinh(f*x + e)^11 + (5*a^3 - 6*a^2*b)*sinh(f*x + e)^12 + 6*(5*a^3 - 6*a^2*b)*cosh(f*x + e)^10 + 6*(5*a^3 - 6*a^2*b + 11*(5*a^3 - 6*a^2*b)*cosh(f*x + e)^2)*sinh(f*x + e)^10 + 20*(11*(5*a^3 - 6*a^2*b)*cosh(f*x + e)^3 + 3*(5*a^3 - 6*a^2*b)*cosh(f*x + e))*sinh(f*x + e)^9 + 15*(5*a^3 - 6*a^2*b)*cosh(f*x + e)^8 + 15*(33*(5*a^3 - 6*a^2*b)*cosh(f*x + e)^4 + 5*a^3 - 6*a^2*b + 18*(5*a^3 - 6*a^2*b)*cosh(f*x + e)^2)*sinh(f*x + e)^8 + 24*(33*(5*a^3 - 6*a^2*b)*cosh(f*x + e)^5 + 30*(5*a^3 - 6*a^2*b)*cosh(f*x + e)^3 + 5*(5*a^3 - 6*a^2*b)*cosh(f*x + e))*sinh(f*x + e)^7 + 20*(5*a^3 - 6*a^2*b)*cosh(f*x + e)^6 + 4*(231*(5*a^3 - 6*a^2*b)*cosh(f*x + e)^6 + 315*(5*a^3 - 6*a^2*b)*cosh(f*x + e)^4 + 25*a^3 - 30*a^2*b + 105*(5*a^3 - 6*a^2*b)*cosh(f*x + e)^2)*sinh(f*x + e)^6 + 24*(33*(5*a^3 - 6*a^2*b)*cosh(f*x + e)^7 + 63*(5*a^3 - 6*a^2*b)*cosh(f*x + e)^5 + 35*(5*a^3 - 6*a^2*b)*cosh(f*x + e)^3 + 5*(5*a^3 - 6*a^2*b)*cosh(f*x + e))*sinh(f*x + e)^5 + 15*(5*a^3 - 6*a^2*b)*cosh(f*x + e)^4 + 15*(33*(5*a^3 - 6*a^2*b)*cosh(f*x + e)^8 + 84*(5*a^3 - 6*a^2*b)*cosh(f*x + e)^6 + 70*(5*a^3 - 6*a^2*b)*cosh(f*x + e)^4 + 5*a^3 - 6*a^2*b + 20*(5*a^3 - 6*a^2*b)*cosh(f*x + e)^2)*sinh(f*x + e)^4 + 20*(11*(5*a^3 - 6*a^2*b)*cosh(f*x + e)^9 + 36*(5*a^3 - 6*a^2*b)*cosh(f*x + e)^7 + 42*(5*a^3 - 6*a^2*b)*cosh(f*x + e)^5 + 20*(5*a^3 - 6*a^2*b)*cosh(f*x + e)^3 + 3*(5*a^3 - 6*a^2*b)*cosh(f*x + e))*sinh(f*x + e)^3 + 5*a^3 - 6*a^2*b + 6*(5*a^3 - 6*a^2*b)*cosh(f*x + e)^2 + 6*(11*(5*a^3 - 6*a^2*b)*cosh(f*x + e)^10 + 45*(5*a^3 - 6*a^2*b)*cosh(f*x + e)^8 + 70*(5*a^3 - 6*a^2*b)*cosh(f*x + e)^6 + 50*(5*a^3 - 6*a^2*b)*cosh(f*x + e)^4 + 5*a^3 - 6*a^2*b + 15*(5*a^3 - 6*a^2*b)*cosh(f*x + e)^2)*sinh(f*x + e)^2 + 12*((5*a^3 - 6*a^2*b)*cosh(f*x + e)^11 + 5*(5*a^3 - 6*a^2*b)*cosh(f*x + e)^9 + 10*(5*a^3 - 6*a^2*b)*cosh(f*x + e)^7 + 10*(5*a^3 - 6*a^2*b)*cosh(f*x + e)^5 + 5*(5*a^3 - 6*a^2*b)*cosh(f*x + e)^3 + (5*a^3 - 6*a^2*b)*cosh(f*x + e))*sinh(f*x + e))*sqrt(a - b)*arctan(sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 - 1)*sqrt(a - b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/(b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(2*a - b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 2*a - b)*sinh(f*x + e)^2 + 4*(b*cosh(f*x + e)^3 + (2*a - b)*cosh(f*x + e))*sinh(f*x + e) + b)) + sqrt(2)*((15*a^3 - 23*a^2*b + 4*a*b^2 + 4*b^3)*cosh(f*x + e)^10 + 10*(15*a^3 - 23*a^2*b + 4*a*b^2 + 4*b^3)*cosh(f*x + e)*sinh(f*x + e)^9 + (15*a^3 - 23*a^2*b + 4*a*b^2 + 4*b^3)*sinh(f*x + e)^10 + (85*a^3 - 133*a^2*b + 20*a*b^2 + 28*b^3)*cosh(f*x + e)^8 + (85*a^3 - 133*a^2*b + 20*a*b^2 + 28*b^3 + 45*(15*a^3 - 23*a^2*b + 4*a*b^2 + 4*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^8 + 8*(15*(15*a^3 - 23*a^2*b + 4*a*b^2 + 4*b^3)*cosh(f*x + e)^3 + (85*a^3 - 133*a^2*b + 20*a*b^2 + 28*b^3)*cosh(f*x + e))*sinh(f*x + e)^7 + 2*(99*a^3 - 247*a^2*b + 200*a*b^2 - 52*b^3)*cosh(f*x + e)^6 + 2*(105*(15*a^3 - 23*a^2*b + 4*a*b^2 + 4*b^3)*cosh(f*x + e)^4 + 99*a^3 - 247*a^2*b + 200*a*b^2 - 52*b^3 + 14*(85*a^3 - 133*a^2*b + 20*a*b^2 + 28*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^6 + 4*(63*(15*a^3 - 23*a^2*b + 4*a*b^2 + 4*b^3)*cosh(f*x + e)^5 + 14*(85*a^3 - 133*a^2*b + 20*a*b^2 + 28*b^3)*cosh(f*x + e)^3 + 3*(99*a^3 - 247*a^2*b + 200*a*b^2 - 52*b^3)*cosh(f*x + e))*sinh(f*x + e)^5 - 2*(99*a^3 - 247*a^2*b + 200*a*b^2 - 52*b^3)*cosh(f*x + e)^4 + 2*(105*(15*a^3 - 23*a^2*b + 4*a*b^2 + 4*b^3)*cosh(f*x + e)^6 + 35*(85*a^3 - 133*a^2*b + 20*a*b^2 + 28*b^3)*cosh(f*x + e)^4 - 99*a^3 + 247*a^2*b - 200*a*b^2 + 52*b^3 + 15*(99*a^3 - 247*a^2*b + 200*a*b^2 - 52*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^4 + 8*(15*(15*a^3 - 23*a^2*b + 4*a*b^2 + 4*b^3)*cosh(f*x + e)^7 + 7*(85*a^3 - 133*a^2*b + 20*a*b^2 + 28*b^3)*cosh(f*x + e)^5 + 5*(99*a^3 - 247*a^2*b + 200*a*b^2 - 52*b^3)*cosh(f*x + e)^3 - (99*a^3 - 247*a^2*b + 200*a*b^2 - 52*b^3)*cosh(f*x + e))*sinh(f*x + e)^3 - 15*a^3 + 23*a^2*b - 4*a*b^2 - 4*b^3 - (85*a^3 - 133*a^2*b + 20*a*b^2 + 28*b^3)*cosh(f*x + e)^2 + (45*(15*a^3 - 23*a^2*b + 4*a*b^2 + 4*b^3)*cosh(f*x + e)^8 + 28*(85*a^3 - 133*a^2*b + 20*a*b^2 + 28*b^3)*cosh(f*x + e)^6 + 30*(99*a^3 - 247*a^2*b + 200*a*b^2 - 52*b^3)*cosh(f*x + e)^4 - 85*a^3 + 133*a^2*b - 20*a*b^2 - 28*b^3 - 12*(99*a^3 - 247*a^2*b + 200*a*b^2 - 52*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^2 + 2*(5*(15*a^3 - 23*a^2*b + 4*a*b^2 + 4*b^3)*cosh(f*x + e)^9 + 4*(85*a^3 - 133*a^2*b + 20*a*b^2 + 28*b^3)*cosh(f*x + e)^7 + 6*(99*a^3 - 247*a^2*b + 200*a*b^2 - 52*b^3)*cosh(f*x + e)^5 - 4*(99*a^3 - 247*a^2*b + 200*a*b^2 - 52*b^3)*cosh(f*x + e)^3 - (85*a^3 - 133*a^2*b + 20*a*b^2 + 28*b^3)*cosh(f*x + e))*sinh(f*x + e))*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/((a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^12 + 12*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)*sinh(f*x + e)^11 + (a^2 - 2*a*b + b^2)*f*sinh(f*x + e)^12 + 6*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^10 + 6*(11*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^2 + (a^2 - 2*a*b + b^2)*f)*sinh(f*x + e)^10 + 15*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^8 + 20*(11*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^3 + 3*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e))*sinh(f*x + e)^9 + 15*(33*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^4 + 18*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^2 + (a^2 - 2*a*b + b^2)*f)*sinh(f*x + e)^8 + 20*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^6 + 24*(33*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^5 + 30*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^3 + 5*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e))*sinh(f*x + e)^7 + 4*(231*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^6 + 315*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^4 + 105*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^2 + 5*(a^2 - 2*a*b + b^2)*f)*sinh(f*x + e)^6 + 15*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^4 + 24*(33*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^7 + 63*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^5 + 35*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^3 + 5*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e))*sinh(f*x + e)^5 + 15*(33*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^8 + 84*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^6 + 70*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^4 + 20*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^2 + (a^2 - 2*a*b + b^2)*f)*sinh(f*x + e)^4 + 6*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^2 + 20*(11*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^9 + 36*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^7 + 42*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^5 + 20*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^3 + 3*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e))*sinh(f*x + e)^3 + 6*(11*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^10 + 45*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^8 + 70*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^6 + 50*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^4 + 15*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^2 + (a^2 - 2*a*b + b^2)*f)*sinh(f*x + e)^2 + (a^2 - 2*a*b + b^2)*f + 12*((a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^11 + 5*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^9 + 10*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^7 + 10*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^5 + 5*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^3 + (a^2 - 2*a*b + b^2)*f*cosh(f*x + e))*sinh(f*x + e))]","B",0
368,0,0,0,0.693801," ","integrate(cosh(f*x+e)^4*(a+b*sinh(f*x+e)^2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \cosh\left(f x + e\right)^{4} \sinh\left(f x + e\right)^{2} + a \cosh\left(f x + e\right)^{4}\right)} \sqrt{b \sinh\left(f x + e\right)^{2} + a}, x\right)"," ",0,"integral((b*cosh(f*x + e)^4*sinh(f*x + e)^2 + a*cosh(f*x + e)^4)*sqrt(b*sinh(f*x + e)^2 + a), x)","F",0
369,0,0,0,0.624940," ","integrate(cosh(f*x+e)^2*(a+b*sinh(f*x+e)^2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \cosh\left(f x + e\right)^{2} \sinh\left(f x + e\right)^{2} + a \cosh\left(f x + e\right)^{2}\right)} \sqrt{b \sinh\left(f x + e\right)^{2} + a}, x\right)"," ",0,"integral((b*cosh(f*x + e)^2*sinh(f*x + e)^2 + a*cosh(f*x + e)^2)*sqrt(b*sinh(f*x + e)^2 + a), x)","F",0
370,0,0,0,0.743443," ","integrate((a+b*sinh(f*x+e)^2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sinh\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}}, x\right)"," ",0,"integral((b*sinh(f*x + e)^2 + a)^(3/2), x)","F",0
371,0,0,0,0.491614," ","integrate(sech(f*x+e)^2*(a+b*sinh(f*x+e)^2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \operatorname{sech}\left(f x + e\right)^{2} \sinh\left(f x + e\right)^{2} + a \operatorname{sech}\left(f x + e\right)^{2}\right)} \sqrt{b \sinh\left(f x + e\right)^{2} + a}, x\right)"," ",0,"integral((b*sech(f*x + e)^2*sinh(f*x + e)^2 + a*sech(f*x + e)^2)*sqrt(b*sinh(f*x + e)^2 + a), x)","F",0
372,0,0,0,0.720778," ","integrate(sech(f*x+e)^4*(a+b*sinh(f*x+e)^2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \operatorname{sech}\left(f x + e\right)^{4} \sinh\left(f x + e\right)^{2} + a \operatorname{sech}\left(f x + e\right)^{4}\right)} \sqrt{b \sinh\left(f x + e\right)^{2} + a}, x\right)"," ",0,"integral((b*sech(f*x + e)^4*sinh(f*x + e)^2 + a*sech(f*x + e)^4)*sqrt(b*sinh(f*x + e)^2 + a), x)","F",0
373,1,2479,0,1.003148," ","integrate(cosh(f*x+e)^3/(a+b*sinh(f*x+e)^2)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left({\left(a - 2 \, b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(a - 2 \, b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) + {\left(a - 2 \, b\right)} \sinh\left(f x + e\right)^{2}\right)} \sqrt{b} \log\left(-\frac{{\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{8} + 8 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \sinh\left(f x + e\right)^{8} + 2 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{6} + 2 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3} + 14 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{6} + 4 \, {\left(14 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + {\left(9 \, a^{2} b - 14 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} + {\left(70 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{4} + 9 \, a^{2} b - 14 \, a b^{2} + 6 \, b^{3} + 30 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(14 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{5} + 10 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} + {\left(9 \, a^{2} b - 14 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + b^{3} + 2 \, {\left(3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(14 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{6} + 15 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} + 3 \, a b^{2} - 2 \, b^{3} + 3 \, {\left(9 \, a^{2} b - 14 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{2} + \sqrt{2} {\left({\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{6} + 6 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + {\left(a^{2} - 2 \, a b + b^{2}\right)} \sinh\left(f x + e\right)^{6} - 3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{4} + 3 \, {\left(5 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{2} - a^{2} + 2 \, a b - b^{2}\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(5 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{3} - 3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} - {\left(4 \, a b - 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + {\left(15 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{4} - 18 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{2} - 4 \, a b + 3 \, b^{2}\right)} \sinh\left(f x + e\right)^{2} - b^{2} + 2 \, {\left(3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{5} - 6 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{3} - {\left(4 \, a b - 3 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} + 4 \, {\left(2 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{7} + 3 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{5} + {\left(9 \, a^{2} b - 14 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} + {\left(3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)}{\cosh\left(f x + e\right)^{6} + 6 \, \cosh\left(f x + e\right)^{5} \sinh\left(f x + e\right) + 15 \, \cosh\left(f x + e\right)^{4} \sinh\left(f x + e\right)^{2} + 20 \, \cosh\left(f x + e\right)^{3} \sinh\left(f x + e\right)^{3} + 15 \, \cosh\left(f x + e\right)^{2} \sinh\left(f x + e\right)^{4} + 6 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + \sinh\left(f x + e\right)^{6}}\right) + {\left({\left(a - 2 \, b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(a - 2 \, b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) + {\left(a - 2 \, b\right)} \sinh\left(f x + e\right)^{2}\right)} \sqrt{b} \log\left(\frac{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, a \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + a\right)} \sinh\left(f x + e\right)^{2} + \sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} + 1\right)} \sqrt{b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + a \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}{\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}\right) - \sqrt{2} {\left(b \cosh\left(f x + e\right)^{2} + 2 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right) + b \sinh\left(f x + e\right)^{2} - b\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{8 \, {\left(b^{2} f \cosh\left(f x + e\right)^{2} + 2 \, b^{2} f \cosh\left(f x + e\right) \sinh\left(f x + e\right) + b^{2} f \sinh\left(f x + e\right)^{2}\right)}}, \frac{2 \, {\left({\left(a - 2 \, b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(a - 2 \, b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) + {\left(a - 2 \, b\right)} \sinh\left(f x + e\right)^{2}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{2} {\left({\left(a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(a - b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) + {\left(a - b\right)} \sinh\left(f x + e\right)^{2} + b\right)} \sqrt{-b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{{\left(a b - b^{2}\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left(a b - b^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(a b - b^{2}\right)} \sinh\left(f x + e\right)^{4} - {\left(3 \, a b - 2 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + {\left(6 \, {\left(a b - b^{2}\right)} \cosh\left(f x + e\right)^{2} - 3 \, a b + 2 \, b^{2}\right)} \sinh\left(f x + e\right)^{2} - b^{2} + 2 \, {\left(2 \, {\left(a b - b^{2}\right)} \cosh\left(f x + e\right)^{3} - {\left(3 \, a b - 2 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)}\right) + 2 \, {\left({\left(a - 2 \, b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(a - 2 \, b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) + {\left(a - 2 \, b\right)} \sinh\left(f x + e\right)^{2}\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} + 1\right)} \sqrt{-b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + 2 \, a - b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}\right) + \sqrt{2} {\left(b \cosh\left(f x + e\right)^{2} + 2 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right) + b \sinh\left(f x + e\right)^{2} - b\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{8 \, {\left(b^{2} f \cosh\left(f x + e\right)^{2} + 2 \, b^{2} f \cosh\left(f x + e\right) \sinh\left(f x + e\right) + b^{2} f \sinh\left(f x + e\right)^{2}\right)}}\right]"," ",0,"[-1/8*(((a - 2*b)*cosh(f*x + e)^2 + 2*(a - 2*b)*cosh(f*x + e)*sinh(f*x + e) + (a - 2*b)*sinh(f*x + e)^2)*sqrt(b)*log(-((a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^8 + 8*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)*sinh(f*x + e)^7 + (a^2*b - 2*a*b^2 + b^3)*sinh(f*x + e)^8 + 2*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e)^6 + 2*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3 + 14*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^6 + 4*(14*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^3 + 3*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e))*sinh(f*x + e)^5 + (9*a^2*b - 14*a*b^2 + 6*b^3)*cosh(f*x + e)^4 + (70*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^4 + 9*a^2*b - 14*a*b^2 + 6*b^3 + 30*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^4 + 4*(14*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^5 + 10*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e)^3 + (9*a^2*b - 14*a*b^2 + 6*b^3)*cosh(f*x + e))*sinh(f*x + e)^3 + b^3 + 2*(3*a*b^2 - 2*b^3)*cosh(f*x + e)^2 + 2*(14*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^6 + 15*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e)^4 + 3*a*b^2 - 2*b^3 + 3*(9*a^2*b - 14*a*b^2 + 6*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^2 + sqrt(2)*((a^2 - 2*a*b + b^2)*cosh(f*x + e)^6 + 6*(a^2 - 2*a*b + b^2)*cosh(f*x + e)*sinh(f*x + e)^5 + (a^2 - 2*a*b + b^2)*sinh(f*x + e)^6 - 3*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^4 + 3*(5*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^2 - a^2 + 2*a*b - b^2)*sinh(f*x + e)^4 + 4*(5*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^3 - 3*(a^2 - 2*a*b + b^2)*cosh(f*x + e))*sinh(f*x + e)^3 - (4*a*b - 3*b^2)*cosh(f*x + e)^2 + (15*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^4 - 18*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^2 - 4*a*b + 3*b^2)*sinh(f*x + e)^2 - b^2 + 2*(3*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^5 - 6*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^3 - (4*a*b - 3*b^2)*cosh(f*x + e))*sinh(f*x + e))*sqrt(b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + 4*(2*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^7 + 3*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e)^5 + (9*a^2*b - 14*a*b^2 + 6*b^3)*cosh(f*x + e)^3 + (3*a*b^2 - 2*b^3)*cosh(f*x + e))*sinh(f*x + e))/(cosh(f*x + e)^6 + 6*cosh(f*x + e)^5*sinh(f*x + e) + 15*cosh(f*x + e)^4*sinh(f*x + e)^2 + 20*cosh(f*x + e)^3*sinh(f*x + e)^3 + 15*cosh(f*x + e)^2*sinh(f*x + e)^4 + 6*cosh(f*x + e)*sinh(f*x + e)^5 + sinh(f*x + e)^6)) + ((a - 2*b)*cosh(f*x + e)^2 + 2*(a - 2*b)*cosh(f*x + e)*sinh(f*x + e) + (a - 2*b)*sinh(f*x + e)^2)*sqrt(b)*log((b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*a*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + a)*sinh(f*x + e)^2 + sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 + 1)*sqrt(b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + 4*(b*cosh(f*x + e)^3 + a*cosh(f*x + e))*sinh(f*x + e) + b)/(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) - sqrt(2)*(b*cosh(f*x + e)^2 + 2*b*cosh(f*x + e)*sinh(f*x + e) + b*sinh(f*x + e)^2 - b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/(b^2*f*cosh(f*x + e)^2 + 2*b^2*f*cosh(f*x + e)*sinh(f*x + e) + b^2*f*sinh(f*x + e)^2), 1/8*(2*((a - 2*b)*cosh(f*x + e)^2 + 2*(a - 2*b)*cosh(f*x + e)*sinh(f*x + e) + (a - 2*b)*sinh(f*x + e)^2)*sqrt(-b)*arctan(sqrt(2)*((a - b)*cosh(f*x + e)^2 + 2*(a - b)*cosh(f*x + e)*sinh(f*x + e) + (a - b)*sinh(f*x + e)^2 + b)*sqrt(-b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/((a*b - b^2)*cosh(f*x + e)^4 + 4*(a*b - b^2)*cosh(f*x + e)*sinh(f*x + e)^3 + (a*b - b^2)*sinh(f*x + e)^4 - (3*a*b - 2*b^2)*cosh(f*x + e)^2 + (6*(a*b - b^2)*cosh(f*x + e)^2 - 3*a*b + 2*b^2)*sinh(f*x + e)^2 - b^2 + 2*(2*(a*b - b^2)*cosh(f*x + e)^3 - (3*a*b - 2*b^2)*cosh(f*x + e))*sinh(f*x + e))) + 2*((a - 2*b)*cosh(f*x + e)^2 + 2*(a - 2*b)*cosh(f*x + e)*sinh(f*x + e) + (a - 2*b)*sinh(f*x + e)^2)*sqrt(-b)*arctan(sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 + 1)*sqrt(-b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/(b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(2*a - b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 2*a - b)*sinh(f*x + e)^2 + 4*(b*cosh(f*x + e)^3 + (2*a - b)*cosh(f*x + e))*sinh(f*x + e) + b)) + sqrt(2)*(b*cosh(f*x + e)^2 + 2*b*cosh(f*x + e)*sinh(f*x + e) + b*sinh(f*x + e)^2 - b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/(b^2*f*cosh(f*x + e)^2 + 2*b^2*f*cosh(f*x + e)*sinh(f*x + e) + b^2*f*sinh(f*x + e)^2)]","B",0
374,1,1990,0,0.807433," ","integrate(cosh(f*x+e)/(a+b*sinh(f*x+e)^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{b} \log\left(-\frac{{\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{8} + 8 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \sinh\left(f x + e\right)^{8} + 2 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{6} + 2 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3} + 14 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{6} + 4 \, {\left(14 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + {\left(9 \, a^{2} b - 14 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} + {\left(70 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{4} + 9 \, a^{2} b - 14 \, a b^{2} + 6 \, b^{3} + 30 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(14 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{5} + 10 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} + {\left(9 \, a^{2} b - 14 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + b^{3} + 2 \, {\left(3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(14 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{6} + 15 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} + 3 \, a b^{2} - 2 \, b^{3} + 3 \, {\left(9 \, a^{2} b - 14 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{2} + \sqrt{2} {\left({\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{6} + 6 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + {\left(a^{2} - 2 \, a b + b^{2}\right)} \sinh\left(f x + e\right)^{6} - 3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{4} + 3 \, {\left(5 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{2} - a^{2} + 2 \, a b - b^{2}\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(5 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{3} - 3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} - {\left(4 \, a b - 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + {\left(15 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{4} - 18 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{2} - 4 \, a b + 3 \, b^{2}\right)} \sinh\left(f x + e\right)^{2} - b^{2} + 2 \, {\left(3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{5} - 6 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{3} - {\left(4 \, a b - 3 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} + 4 \, {\left(2 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{7} + 3 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{5} + {\left(9 \, a^{2} b - 14 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} + {\left(3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)}{\cosh\left(f x + e\right)^{6} + 6 \, \cosh\left(f x + e\right)^{5} \sinh\left(f x + e\right) + 15 \, \cosh\left(f x + e\right)^{4} \sinh\left(f x + e\right)^{2} + 20 \, \cosh\left(f x + e\right)^{3} \sinh\left(f x + e\right)^{3} + 15 \, \cosh\left(f x + e\right)^{2} \sinh\left(f x + e\right)^{4} + 6 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + \sinh\left(f x + e\right)^{6}}\right) + \sqrt{b} \log\left(\frac{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, a \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + a\right)} \sinh\left(f x + e\right)^{2} + \sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} + 1\right)} \sqrt{b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + a \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}{\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}\right)}{4 \, b f}, -\frac{\sqrt{-b} \arctan\left(\frac{\sqrt{2} {\left({\left(a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(a - b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) + {\left(a - b\right)} \sinh\left(f x + e\right)^{2} + b\right)} \sqrt{-b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{{\left(a b - b^{2}\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left(a b - b^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(a b - b^{2}\right)} \sinh\left(f x + e\right)^{4} - {\left(3 \, a b - 2 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + {\left(6 \, {\left(a b - b^{2}\right)} \cosh\left(f x + e\right)^{2} - 3 \, a b + 2 \, b^{2}\right)} \sinh\left(f x + e\right)^{2} - b^{2} + 2 \, {\left(2 \, {\left(a b - b^{2}\right)} \cosh\left(f x + e\right)^{3} - {\left(3 \, a b - 2 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)}\right) + \sqrt{-b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} + 1\right)} \sqrt{-b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + 2 \, a - b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}\right)}{2 \, b f}\right]"," ",0,"[1/4*(sqrt(b)*log(-((a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^8 + 8*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)*sinh(f*x + e)^7 + (a^2*b - 2*a*b^2 + b^3)*sinh(f*x + e)^8 + 2*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e)^6 + 2*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3 + 14*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^6 + 4*(14*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^3 + 3*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e))*sinh(f*x + e)^5 + (9*a^2*b - 14*a*b^2 + 6*b^3)*cosh(f*x + e)^4 + (70*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^4 + 9*a^2*b - 14*a*b^2 + 6*b^3 + 30*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^4 + 4*(14*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^5 + 10*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e)^3 + (9*a^2*b - 14*a*b^2 + 6*b^3)*cosh(f*x + e))*sinh(f*x + e)^3 + b^3 + 2*(3*a*b^2 - 2*b^3)*cosh(f*x + e)^2 + 2*(14*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^6 + 15*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e)^4 + 3*a*b^2 - 2*b^3 + 3*(9*a^2*b - 14*a*b^2 + 6*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^2 + sqrt(2)*((a^2 - 2*a*b + b^2)*cosh(f*x + e)^6 + 6*(a^2 - 2*a*b + b^2)*cosh(f*x + e)*sinh(f*x + e)^5 + (a^2 - 2*a*b + b^2)*sinh(f*x + e)^6 - 3*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^4 + 3*(5*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^2 - a^2 + 2*a*b - b^2)*sinh(f*x + e)^4 + 4*(5*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^3 - 3*(a^2 - 2*a*b + b^2)*cosh(f*x + e))*sinh(f*x + e)^3 - (4*a*b - 3*b^2)*cosh(f*x + e)^2 + (15*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^4 - 18*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^2 - 4*a*b + 3*b^2)*sinh(f*x + e)^2 - b^2 + 2*(3*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^5 - 6*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^3 - (4*a*b - 3*b^2)*cosh(f*x + e))*sinh(f*x + e))*sqrt(b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + 4*(2*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^7 + 3*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e)^5 + (9*a^2*b - 14*a*b^2 + 6*b^3)*cosh(f*x + e)^3 + (3*a*b^2 - 2*b^3)*cosh(f*x + e))*sinh(f*x + e))/(cosh(f*x + e)^6 + 6*cosh(f*x + e)^5*sinh(f*x + e) + 15*cosh(f*x + e)^4*sinh(f*x + e)^2 + 20*cosh(f*x + e)^3*sinh(f*x + e)^3 + 15*cosh(f*x + e)^2*sinh(f*x + e)^4 + 6*cosh(f*x + e)*sinh(f*x + e)^5 + sinh(f*x + e)^6)) + sqrt(b)*log((b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*a*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + a)*sinh(f*x + e)^2 + sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 + 1)*sqrt(b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + 4*(b*cosh(f*x + e)^3 + a*cosh(f*x + e))*sinh(f*x + e) + b)/(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/(b*f), -1/2*(sqrt(-b)*arctan(sqrt(2)*((a - b)*cosh(f*x + e)^2 + 2*(a - b)*cosh(f*x + e)*sinh(f*x + e) + (a - b)*sinh(f*x + e)^2 + b)*sqrt(-b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/((a*b - b^2)*cosh(f*x + e)^4 + 4*(a*b - b^2)*cosh(f*x + e)*sinh(f*x + e)^3 + (a*b - b^2)*sinh(f*x + e)^4 - (3*a*b - 2*b^2)*cosh(f*x + e)^2 + (6*(a*b - b^2)*cosh(f*x + e)^2 - 3*a*b + 2*b^2)*sinh(f*x + e)^2 - b^2 + 2*(2*(a*b - b^2)*cosh(f*x + e)^3 - (3*a*b - 2*b^2)*cosh(f*x + e))*sinh(f*x + e))) + sqrt(-b)*arctan(sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 + 1)*sqrt(-b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/(b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(2*a - b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 2*a - b)*sinh(f*x + e)^2 + 4*(b*cosh(f*x + e)^3 + (2*a - b)*cosh(f*x + e))*sinh(f*x + e) + b)))/(b*f)]","B",0
375,1,598,0,0.510221," ","integrate(sech(f*x+e)/(a+b*sinh(f*x+e)^2)^(1/2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-a + b} \log\left(\frac{{\left(a - 2 \, b\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left(a - 2 \, b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(a - 2 \, b\right)} \sinh\left(f x + e\right)^{4} - 2 \, {\left(3 \, a - 2 \, b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, {\left(a - 2 \, b\right)} \cosh\left(f x + e\right)^{2} - 3 \, a + 2 \, b\right)} \sinh\left(f x + e\right)^{2} - 2 \, \sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} - 1\right)} \sqrt{-a + b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} + 4 \, {\left({\left(a - 2 \, b\right)} \cosh\left(f x + e\right)^{3} - {\left(3 \, a - 2 \, b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + a - 2 \, b}{\cosh\left(f x + e\right)^{4} + 4 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + \sinh\left(f x + e\right)^{4} + 2 \, {\left(3 \, \cosh\left(f x + e\right)^{2} + 1\right)} \sinh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right)^{2} + 4 \, {\left(\cosh\left(f x + e\right)^{3} + \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + 1}\right)}{2 \, {\left(a - b\right)} f}, \frac{\arctan\left(\frac{\sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} - 1\right)} \sqrt{a - b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + 2 \, a - b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}\right)}{\sqrt{a - b} f}\right]"," ",0,"[-1/2*sqrt(-a + b)*log(((a - 2*b)*cosh(f*x + e)^4 + 4*(a - 2*b)*cosh(f*x + e)*sinh(f*x + e)^3 + (a - 2*b)*sinh(f*x + e)^4 - 2*(3*a - 2*b)*cosh(f*x + e)^2 + 2*(3*(a - 2*b)*cosh(f*x + e)^2 - 3*a + 2*b)*sinh(f*x + e)^2 - 2*sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 - 1)*sqrt(-a + b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + 4*((a - 2*b)*cosh(f*x + e)^3 - (3*a - 2*b)*cosh(f*x + e))*sinh(f*x + e) + a - 2*b)/(cosh(f*x + e)^4 + 4*cosh(f*x + e)*sinh(f*x + e)^3 + sinh(f*x + e)^4 + 2*(3*cosh(f*x + e)^2 + 1)*sinh(f*x + e)^2 + 2*cosh(f*x + e)^2 + 4*(cosh(f*x + e)^3 + cosh(f*x + e))*sinh(f*x + e) + 1))/((a - b)*f), arctan(sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 - 1)*sqrt(a - b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/(b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(2*a - b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 2*a - b)*sinh(f*x + e)^2 + 4*(b*cosh(f*x + e)^3 + (2*a - b)*cosh(f*x + e))*sinh(f*x + e) + b))/(sqrt(a - b)*f)]","B",0
376,1,1503,0,0.667940," ","integrate(sech(f*x+e)^3/(a+b*sinh(f*x+e)^2)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left({\left(a - 2 \, b\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left(a - 2 \, b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(a - 2 \, b\right)} \sinh\left(f x + e\right)^{4} + 2 \, {\left(a - 2 \, b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, {\left(a - 2 \, b\right)} \cosh\left(f x + e\right)^{2} + a - 2 \, b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left({\left(a - 2 \, b\right)} \cosh\left(f x + e\right)^{3} + {\left(a - 2 \, b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + a - 2 \, b\right)} \sqrt{-a + b} \log\left(\frac{{\left(a - 2 \, b\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left(a - 2 \, b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(a - 2 \, b\right)} \sinh\left(f x + e\right)^{4} - 2 \, {\left(3 \, a - 2 \, b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, {\left(a - 2 \, b\right)} \cosh\left(f x + e\right)^{2} - 3 \, a + 2 \, b\right)} \sinh\left(f x + e\right)^{2} - 2 \, \sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} - 1\right)} \sqrt{-a + b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} + 4 \, {\left({\left(a - 2 \, b\right)} \cosh\left(f x + e\right)^{3} - {\left(3 \, a - 2 \, b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + a - 2 \, b}{\cosh\left(f x + e\right)^{4} + 4 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + \sinh\left(f x + e\right)^{4} + 2 \, {\left(3 \, \cosh\left(f x + e\right)^{2} + 1\right)} \sinh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right)^{2} + 4 \, {\left(\cosh\left(f x + e\right)^{3} + \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + 1}\right) - 2 \, \sqrt{2} {\left({\left(a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(a - b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) + {\left(a - b\right)} \sinh\left(f x + e\right)^{2} - a + b\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{4 \, {\left({\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{4} + 4 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(a^{2} - 2 \, a b + b^{2}\right)} f \sinh\left(f x + e\right)^{4} + 2 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{2} + {\left(a^{2} - 2 \, a b + b^{2}\right)} f\right)} \sinh\left(f x + e\right)^{2} + {\left(a^{2} - 2 \, a b + b^{2}\right)} f + 4 \, {\left({\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{3} + {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)}}, \frac{{\left({\left(a - 2 \, b\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left(a - 2 \, b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(a - 2 \, b\right)} \sinh\left(f x + e\right)^{4} + 2 \, {\left(a - 2 \, b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, {\left(a - 2 \, b\right)} \cosh\left(f x + e\right)^{2} + a - 2 \, b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left({\left(a - 2 \, b\right)} \cosh\left(f x + e\right)^{3} + {\left(a - 2 \, b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + a - 2 \, b\right)} \sqrt{a - b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} - 1\right)} \sqrt{a - b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + 2 \, a - b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}\right) + \sqrt{2} {\left({\left(a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(a - b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) + {\left(a - b\right)} \sinh\left(f x + e\right)^{2} - a + b\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{2 \, {\left({\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{4} + 4 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(a^{2} - 2 \, a b + b^{2}\right)} f \sinh\left(f x + e\right)^{4} + 2 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{2} + {\left(a^{2} - 2 \, a b + b^{2}\right)} f\right)} \sinh\left(f x + e\right)^{2} + {\left(a^{2} - 2 \, a b + b^{2}\right)} f + 4 \, {\left({\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{3} + {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)}}\right]"," ",0,"[-1/4*(((a - 2*b)*cosh(f*x + e)^4 + 4*(a - 2*b)*cosh(f*x + e)*sinh(f*x + e)^3 + (a - 2*b)*sinh(f*x + e)^4 + 2*(a - 2*b)*cosh(f*x + e)^2 + 2*(3*(a - 2*b)*cosh(f*x + e)^2 + a - 2*b)*sinh(f*x + e)^2 + 4*((a - 2*b)*cosh(f*x + e)^3 + (a - 2*b)*cosh(f*x + e))*sinh(f*x + e) + a - 2*b)*sqrt(-a + b)*log(((a - 2*b)*cosh(f*x + e)^4 + 4*(a - 2*b)*cosh(f*x + e)*sinh(f*x + e)^3 + (a - 2*b)*sinh(f*x + e)^4 - 2*(3*a - 2*b)*cosh(f*x + e)^2 + 2*(3*(a - 2*b)*cosh(f*x + e)^2 - 3*a + 2*b)*sinh(f*x + e)^2 - 2*sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 - 1)*sqrt(-a + b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + 4*((a - 2*b)*cosh(f*x + e)^3 - (3*a - 2*b)*cosh(f*x + e))*sinh(f*x + e) + a - 2*b)/(cosh(f*x + e)^4 + 4*cosh(f*x + e)*sinh(f*x + e)^3 + sinh(f*x + e)^4 + 2*(3*cosh(f*x + e)^2 + 1)*sinh(f*x + e)^2 + 2*cosh(f*x + e)^2 + 4*(cosh(f*x + e)^3 + cosh(f*x + e))*sinh(f*x + e) + 1)) - 2*sqrt(2)*((a - b)*cosh(f*x + e)^2 + 2*(a - b)*cosh(f*x + e)*sinh(f*x + e) + (a - b)*sinh(f*x + e)^2 - a + b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/((a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^4 + 4*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)*sinh(f*x + e)^3 + (a^2 - 2*a*b + b^2)*f*sinh(f*x + e)^4 + 2*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^2 + 2*(3*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^2 + (a^2 - 2*a*b + b^2)*f)*sinh(f*x + e)^2 + (a^2 - 2*a*b + b^2)*f + 4*((a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^3 + (a^2 - 2*a*b + b^2)*f*cosh(f*x + e))*sinh(f*x + e)), 1/2*(((a - 2*b)*cosh(f*x + e)^4 + 4*(a - 2*b)*cosh(f*x + e)*sinh(f*x + e)^3 + (a - 2*b)*sinh(f*x + e)^4 + 2*(a - 2*b)*cosh(f*x + e)^2 + 2*(3*(a - 2*b)*cosh(f*x + e)^2 + a - 2*b)*sinh(f*x + e)^2 + 4*((a - 2*b)*cosh(f*x + e)^3 + (a - 2*b)*cosh(f*x + e))*sinh(f*x + e) + a - 2*b)*sqrt(a - b)*arctan(sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 - 1)*sqrt(a - b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/(b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(2*a - b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 2*a - b)*sinh(f*x + e)^2 + 4*(b*cosh(f*x + e)^3 + (2*a - b)*cosh(f*x + e))*sinh(f*x + e) + b)) + sqrt(2)*((a - b)*cosh(f*x + e)^2 + 2*(a - b)*cosh(f*x + e)*sinh(f*x + e) + (a - b)*sinh(f*x + e)^2 - a + b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/((a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^4 + 4*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)*sinh(f*x + e)^3 + (a^2 - 2*a*b + b^2)*f*sinh(f*x + e)^4 + 2*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^2 + 2*(3*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^2 + (a^2 - 2*a*b + b^2)*f)*sinh(f*x + e)^2 + (a^2 - 2*a*b + b^2)*f + 4*((a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^3 + (a^2 - 2*a*b + b^2)*f*cosh(f*x + e))*sinh(f*x + e))]","B",0
377,0,0,0,0.653900," ","integrate(cosh(f*x+e)^4/(a+b*sinh(f*x+e)^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cosh\left(f x + e\right)^{4}}{\sqrt{b \sinh\left(f x + e\right)^{2} + a}}, x\right)"," ",0,"integral(cosh(f*x + e)^4/sqrt(b*sinh(f*x + e)^2 + a), x)","F",0
378,0,0,0,0.447836," ","integrate(cosh(f*x+e)^2/(a+b*sinh(f*x+e)^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cosh\left(f x + e\right)^{2}}{\sqrt{b \sinh\left(f x + e\right)^{2} + a}}, x\right)"," ",0,"integral(cosh(f*x + e)^2/sqrt(b*sinh(f*x + e)^2 + a), x)","F",0
379,0,0,0,0.721358," ","integrate(1/(a+b*sinh(f*x+e)^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{b \sinh\left(f x + e\right)^{2} + a}}, x\right)"," ",0,"integral(1/sqrt(b*sinh(f*x + e)^2 + a), x)","F",0
380,0,0,0,0.735575," ","integrate(sech(f*x+e)^2/(a+b*sinh(f*x+e)^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{sech}\left(f x + e\right)^{2}}{\sqrt{b \sinh\left(f x + e\right)^{2} + a}}, x\right)"," ",0,"integral(sech(f*x + e)^2/sqrt(b*sinh(f*x + e)^2 + a), x)","F",0
381,0,0,0,0.492995," ","integrate(sech(f*x+e)^4/(a+b*sinh(f*x+e)^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\operatorname{sech}\left(f x + e\right)^{4}}{\sqrt{b \sinh\left(f x + e\right)^{2} + a}}, x\right)"," ",0,"integral(sech(f*x + e)^4/sqrt(b*sinh(f*x + e)^2 + a), x)","F",0
382,1,3126,0,1.175089," ","integrate(cosh(f*x+e)^3/(a+b*sinh(f*x+e)^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(a b \cosh\left(f x + e\right)^{4} + 4 \, a b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + a b \sinh\left(f x + e\right)^{4} + 2 \, {\left(2 \, a^{2} - a b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, a b \cosh\left(f x + e\right)^{2} + 2 \, a^{2} - a b\right)} \sinh\left(f x + e\right)^{2} + a b + 4 \, {\left(a b \cosh\left(f x + e\right)^{3} + {\left(2 \, a^{2} - a b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{b} \log\left(-\frac{{\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{8} + 8 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \sinh\left(f x + e\right)^{8} + 2 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{6} + 2 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3} + 14 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{6} + 4 \, {\left(14 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + {\left(9 \, a^{2} b - 14 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} + {\left(70 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{4} + 9 \, a^{2} b - 14 \, a b^{2} + 6 \, b^{3} + 30 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(14 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{5} + 10 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} + {\left(9 \, a^{2} b - 14 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + b^{3} + 2 \, {\left(3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(14 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{6} + 15 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} + 3 \, a b^{2} - 2 \, b^{3} + 3 \, {\left(9 \, a^{2} b - 14 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{2} + \sqrt{2} {\left({\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{6} + 6 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + {\left(a^{2} - 2 \, a b + b^{2}\right)} \sinh\left(f x + e\right)^{6} - 3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{4} + 3 \, {\left(5 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{2} - a^{2} + 2 \, a b - b^{2}\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(5 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{3} - 3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} - {\left(4 \, a b - 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + {\left(15 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{4} - 18 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{2} - 4 \, a b + 3 \, b^{2}\right)} \sinh\left(f x + e\right)^{2} - b^{2} + 2 \, {\left(3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{5} - 6 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{3} - {\left(4 \, a b - 3 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} + 4 \, {\left(2 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{7} + 3 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{5} + {\left(9 \, a^{2} b - 14 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} + {\left(3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)}{\cosh\left(f x + e\right)^{6} + 6 \, \cosh\left(f x + e\right)^{5} \sinh\left(f x + e\right) + 15 \, \cosh\left(f x + e\right)^{4} \sinh\left(f x + e\right)^{2} + 20 \, \cosh\left(f x + e\right)^{3} \sinh\left(f x + e\right)^{3} + 15 \, \cosh\left(f x + e\right)^{2} \sinh\left(f x + e\right)^{4} + 6 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + \sinh\left(f x + e\right)^{6}}\right) + {\left(a b \cosh\left(f x + e\right)^{4} + 4 \, a b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + a b \sinh\left(f x + e\right)^{4} + 2 \, {\left(2 \, a^{2} - a b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, a b \cosh\left(f x + e\right)^{2} + 2 \, a^{2} - a b\right)} \sinh\left(f x + e\right)^{2} + a b + 4 \, {\left(a b \cosh\left(f x + e\right)^{3} + {\left(2 \, a^{2} - a b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{b} \log\left(\frac{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, a \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + a\right)} \sinh\left(f x + e\right)^{2} + \sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} + 1\right)} \sqrt{b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + a \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}{\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}\right) - 4 \, \sqrt{2} {\left({\left(a b - b^{2}\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(a b - b^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) + {\left(a b - b^{2}\right)} \sinh\left(f x + e\right)^{2} - a b + b^{2}\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{4 \, {\left(a b^{3} f \cosh\left(f x + e\right)^{4} + 4 \, a b^{3} f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + a b^{3} f \sinh\left(f x + e\right)^{4} + a b^{3} f + 2 \, {\left(2 \, a^{2} b^{2} - a b^{3}\right)} f \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, a b^{3} f \cosh\left(f x + e\right)^{2} + {\left(2 \, a^{2} b^{2} - a b^{3}\right)} f\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(a b^{3} f \cosh\left(f x + e\right)^{3} + {\left(2 \, a^{2} b^{2} - a b^{3}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)}}, -\frac{{\left(a b \cosh\left(f x + e\right)^{4} + 4 \, a b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + a b \sinh\left(f x + e\right)^{4} + 2 \, {\left(2 \, a^{2} - a b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, a b \cosh\left(f x + e\right)^{2} + 2 \, a^{2} - a b\right)} \sinh\left(f x + e\right)^{2} + a b + 4 \, {\left(a b \cosh\left(f x + e\right)^{3} + {\left(2 \, a^{2} - a b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{2} {\left({\left(a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(a - b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) + {\left(a - b\right)} \sinh\left(f x + e\right)^{2} + b\right)} \sqrt{-b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{{\left(a b - b^{2}\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left(a b - b^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(a b - b^{2}\right)} \sinh\left(f x + e\right)^{4} - {\left(3 \, a b - 2 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + {\left(6 \, {\left(a b - b^{2}\right)} \cosh\left(f x + e\right)^{2} - 3 \, a b + 2 \, b^{2}\right)} \sinh\left(f x + e\right)^{2} - b^{2} + 2 \, {\left(2 \, {\left(a b - b^{2}\right)} \cosh\left(f x + e\right)^{3} - {\left(3 \, a b - 2 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)}\right) + {\left(a b \cosh\left(f x + e\right)^{4} + 4 \, a b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + a b \sinh\left(f x + e\right)^{4} + 2 \, {\left(2 \, a^{2} - a b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, a b \cosh\left(f x + e\right)^{2} + 2 \, a^{2} - a b\right)} \sinh\left(f x + e\right)^{2} + a b + 4 \, {\left(a b \cosh\left(f x + e\right)^{3} + {\left(2 \, a^{2} - a b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} + 1\right)} \sqrt{-b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + 2 \, a - b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}\right) + 2 \, \sqrt{2} {\left({\left(a b - b^{2}\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(a b - b^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) + {\left(a b - b^{2}\right)} \sinh\left(f x + e\right)^{2} - a b + b^{2}\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{2 \, {\left(a b^{3} f \cosh\left(f x + e\right)^{4} + 4 \, a b^{3} f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + a b^{3} f \sinh\left(f x + e\right)^{4} + a b^{3} f + 2 \, {\left(2 \, a^{2} b^{2} - a b^{3}\right)} f \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, a b^{3} f \cosh\left(f x + e\right)^{2} + {\left(2 \, a^{2} b^{2} - a b^{3}\right)} f\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(a b^{3} f \cosh\left(f x + e\right)^{3} + {\left(2 \, a^{2} b^{2} - a b^{3}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)}}\right]"," ",0,"[1/4*((a*b*cosh(f*x + e)^4 + 4*a*b*cosh(f*x + e)*sinh(f*x + e)^3 + a*b*sinh(f*x + e)^4 + 2*(2*a^2 - a*b)*cosh(f*x + e)^2 + 2*(3*a*b*cosh(f*x + e)^2 + 2*a^2 - a*b)*sinh(f*x + e)^2 + a*b + 4*(a*b*cosh(f*x + e)^3 + (2*a^2 - a*b)*cosh(f*x + e))*sinh(f*x + e))*sqrt(b)*log(-((a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^8 + 8*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)*sinh(f*x + e)^7 + (a^2*b - 2*a*b^2 + b^3)*sinh(f*x + e)^8 + 2*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e)^6 + 2*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3 + 14*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^6 + 4*(14*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^3 + 3*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e))*sinh(f*x + e)^5 + (9*a^2*b - 14*a*b^2 + 6*b^3)*cosh(f*x + e)^4 + (70*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^4 + 9*a^2*b - 14*a*b^2 + 6*b^3 + 30*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^4 + 4*(14*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^5 + 10*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e)^3 + (9*a^2*b - 14*a*b^2 + 6*b^3)*cosh(f*x + e))*sinh(f*x + e)^3 + b^3 + 2*(3*a*b^2 - 2*b^3)*cosh(f*x + e)^2 + 2*(14*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^6 + 15*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e)^4 + 3*a*b^2 - 2*b^3 + 3*(9*a^2*b - 14*a*b^2 + 6*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^2 + sqrt(2)*((a^2 - 2*a*b + b^2)*cosh(f*x + e)^6 + 6*(a^2 - 2*a*b + b^2)*cosh(f*x + e)*sinh(f*x + e)^5 + (a^2 - 2*a*b + b^2)*sinh(f*x + e)^6 - 3*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^4 + 3*(5*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^2 - a^2 + 2*a*b - b^2)*sinh(f*x + e)^4 + 4*(5*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^3 - 3*(a^2 - 2*a*b + b^2)*cosh(f*x + e))*sinh(f*x + e)^3 - (4*a*b - 3*b^2)*cosh(f*x + e)^2 + (15*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^4 - 18*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^2 - 4*a*b + 3*b^2)*sinh(f*x + e)^2 - b^2 + 2*(3*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^5 - 6*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^3 - (4*a*b - 3*b^2)*cosh(f*x + e))*sinh(f*x + e))*sqrt(b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + 4*(2*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^7 + 3*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e)^5 + (9*a^2*b - 14*a*b^2 + 6*b^3)*cosh(f*x + e)^3 + (3*a*b^2 - 2*b^3)*cosh(f*x + e))*sinh(f*x + e))/(cosh(f*x + e)^6 + 6*cosh(f*x + e)^5*sinh(f*x + e) + 15*cosh(f*x + e)^4*sinh(f*x + e)^2 + 20*cosh(f*x + e)^3*sinh(f*x + e)^3 + 15*cosh(f*x + e)^2*sinh(f*x + e)^4 + 6*cosh(f*x + e)*sinh(f*x + e)^5 + sinh(f*x + e)^6)) + (a*b*cosh(f*x + e)^4 + 4*a*b*cosh(f*x + e)*sinh(f*x + e)^3 + a*b*sinh(f*x + e)^4 + 2*(2*a^2 - a*b)*cosh(f*x + e)^2 + 2*(3*a*b*cosh(f*x + e)^2 + 2*a^2 - a*b)*sinh(f*x + e)^2 + a*b + 4*(a*b*cosh(f*x + e)^3 + (2*a^2 - a*b)*cosh(f*x + e))*sinh(f*x + e))*sqrt(b)*log((b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*a*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + a)*sinh(f*x + e)^2 + sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 + 1)*sqrt(b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + 4*(b*cosh(f*x + e)^3 + a*cosh(f*x + e))*sinh(f*x + e) + b)/(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) - 4*sqrt(2)*((a*b - b^2)*cosh(f*x + e)^2 + 2*(a*b - b^2)*cosh(f*x + e)*sinh(f*x + e) + (a*b - b^2)*sinh(f*x + e)^2 - a*b + b^2)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/(a*b^3*f*cosh(f*x + e)^4 + 4*a*b^3*f*cosh(f*x + e)*sinh(f*x + e)^3 + a*b^3*f*sinh(f*x + e)^4 + a*b^3*f + 2*(2*a^2*b^2 - a*b^3)*f*cosh(f*x + e)^2 + 2*(3*a*b^3*f*cosh(f*x + e)^2 + (2*a^2*b^2 - a*b^3)*f)*sinh(f*x + e)^2 + 4*(a*b^3*f*cosh(f*x + e)^3 + (2*a^2*b^2 - a*b^3)*f*cosh(f*x + e))*sinh(f*x + e)), -1/2*((a*b*cosh(f*x + e)^4 + 4*a*b*cosh(f*x + e)*sinh(f*x + e)^3 + a*b*sinh(f*x + e)^4 + 2*(2*a^2 - a*b)*cosh(f*x + e)^2 + 2*(3*a*b*cosh(f*x + e)^2 + 2*a^2 - a*b)*sinh(f*x + e)^2 + a*b + 4*(a*b*cosh(f*x + e)^3 + (2*a^2 - a*b)*cosh(f*x + e))*sinh(f*x + e))*sqrt(-b)*arctan(sqrt(2)*((a - b)*cosh(f*x + e)^2 + 2*(a - b)*cosh(f*x + e)*sinh(f*x + e) + (a - b)*sinh(f*x + e)^2 + b)*sqrt(-b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/((a*b - b^2)*cosh(f*x + e)^4 + 4*(a*b - b^2)*cosh(f*x + e)*sinh(f*x + e)^3 + (a*b - b^2)*sinh(f*x + e)^4 - (3*a*b - 2*b^2)*cosh(f*x + e)^2 + (6*(a*b - b^2)*cosh(f*x + e)^2 - 3*a*b + 2*b^2)*sinh(f*x + e)^2 - b^2 + 2*(2*(a*b - b^2)*cosh(f*x + e)^3 - (3*a*b - 2*b^2)*cosh(f*x + e))*sinh(f*x + e))) + (a*b*cosh(f*x + e)^4 + 4*a*b*cosh(f*x + e)*sinh(f*x + e)^3 + a*b*sinh(f*x + e)^4 + 2*(2*a^2 - a*b)*cosh(f*x + e)^2 + 2*(3*a*b*cosh(f*x + e)^2 + 2*a^2 - a*b)*sinh(f*x + e)^2 + a*b + 4*(a*b*cosh(f*x + e)^3 + (2*a^2 - a*b)*cosh(f*x + e))*sinh(f*x + e))*sqrt(-b)*arctan(sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 + 1)*sqrt(-b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/(b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(2*a - b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 2*a - b)*sinh(f*x + e)^2 + 4*(b*cosh(f*x + e)^3 + (2*a - b)*cosh(f*x + e))*sinh(f*x + e) + b)) + 2*sqrt(2)*((a*b - b^2)*cosh(f*x + e)^2 + 2*(a*b - b^2)*cosh(f*x + e)*sinh(f*x + e) + (a*b - b^2)*sinh(f*x + e)^2 - a*b + b^2)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/(a*b^3*f*cosh(f*x + e)^4 + 4*a*b^3*f*cosh(f*x + e)*sinh(f*x + e)^3 + a*b^3*f*sinh(f*x + e)^4 + a*b^3*f + 2*(2*a^2*b^2 - a*b^3)*f*cosh(f*x + e)^2 + 2*(3*a*b^3*f*cosh(f*x + e)^2 + (2*a^2*b^2 - a*b^3)*f)*sinh(f*x + e)^2 + 4*(a*b^3*f*cosh(f*x + e)^3 + (2*a^2*b^2 - a*b^3)*f*cosh(f*x + e))*sinh(f*x + e))]","B",0
383,1,245,0,0.622932," ","integrate(cosh(f*x+e)/(a+b*sinh(f*x+e)^2)^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} - 1\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{a b f \cosh\left(f x + e\right)^{4} + 4 \, a b f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + a b f \sinh\left(f x + e\right)^{4} + 2 \, {\left(2 \, a^{2} - a b\right)} f \cosh\left(f x + e\right)^{2} + a b f + 2 \, {\left(3 \, a b f \cosh\left(f x + e\right)^{2} + {\left(2 \, a^{2} - a b\right)} f\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(a b f \cosh\left(f x + e\right)^{3} + {\left(2 \, a^{2} - a b\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)}"," ",0,"sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 - 1)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/(a*b*f*cosh(f*x + e)^4 + 4*a*b*f*cosh(f*x + e)*sinh(f*x + e)^3 + a*b*f*sinh(f*x + e)^4 + 2*(2*a^2 - a*b)*f*cosh(f*x + e)^2 + a*b*f + 2*(3*a*b*f*cosh(f*x + e)^2 + (2*a^2 - a*b)*f)*sinh(f*x + e)^2 + 4*(a*b*f*cosh(f*x + e)^3 + (2*a^2 - a*b)*f*cosh(f*x + e))*sinh(f*x + e))","B",0
384,1,1717,0,0.768362," ","integrate(sech(f*x+e)/(a+b*sinh(f*x+e)^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(a b \cosh\left(f x + e\right)^{4} + 4 \, a b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + a b \sinh\left(f x + e\right)^{4} + 2 \, {\left(2 \, a^{2} - a b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, a b \cosh\left(f x + e\right)^{2} + 2 \, a^{2} - a b\right)} \sinh\left(f x + e\right)^{2} + a b + 4 \, {\left(a b \cosh\left(f x + e\right)^{3} + {\left(2 \, a^{2} - a b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{-a + b} \log\left(\frac{{\left(a - 2 \, b\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left(a - 2 \, b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(a - 2 \, b\right)} \sinh\left(f x + e\right)^{4} - 2 \, {\left(3 \, a - 2 \, b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, {\left(a - 2 \, b\right)} \cosh\left(f x + e\right)^{2} - 3 \, a + 2 \, b\right)} \sinh\left(f x + e\right)^{2} + 2 \, \sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} - 1\right)} \sqrt{-a + b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} + 4 \, {\left({\left(a - 2 \, b\right)} \cosh\left(f x + e\right)^{3} - {\left(3 \, a - 2 \, b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + a - 2 \, b}{\cosh\left(f x + e\right)^{4} + 4 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + \sinh\left(f x + e\right)^{4} + 2 \, {\left(3 \, \cosh\left(f x + e\right)^{2} + 1\right)} \sinh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right)^{2} + 4 \, {\left(\cosh\left(f x + e\right)^{3} + \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + 1}\right) - 2 \, \sqrt{2} {\left({\left(a b - b^{2}\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(a b - b^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) + {\left(a b - b^{2}\right)} \sinh\left(f x + e\right)^{2} - a b + b^{2}\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{2 \, {\left({\left(a^{3} b - 2 \, a^{2} b^{2} + a b^{3}\right)} f \cosh\left(f x + e\right)^{4} + 4 \, {\left(a^{3} b - 2 \, a^{2} b^{2} + a b^{3}\right)} f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(a^{3} b - 2 \, a^{2} b^{2} + a b^{3}\right)} f \sinh\left(f x + e\right)^{4} + 2 \, {\left(2 \, a^{4} - 5 \, a^{3} b + 4 \, a^{2} b^{2} - a b^{3}\right)} f \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, {\left(a^{3} b - 2 \, a^{2} b^{2} + a b^{3}\right)} f \cosh\left(f x + e\right)^{2} + {\left(2 \, a^{4} - 5 \, a^{3} b + 4 \, a^{2} b^{2} - a b^{3}\right)} f\right)} \sinh\left(f x + e\right)^{2} + {\left(a^{3} b - 2 \, a^{2} b^{2} + a b^{3}\right)} f + 4 \, {\left({\left(a^{3} b - 2 \, a^{2} b^{2} + a b^{3}\right)} f \cosh\left(f x + e\right)^{3} + {\left(2 \, a^{4} - 5 \, a^{3} b + 4 \, a^{2} b^{2} - a b^{3}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)}}, \frac{{\left(a b \cosh\left(f x + e\right)^{4} + 4 \, a b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + a b \sinh\left(f x + e\right)^{4} + 2 \, {\left(2 \, a^{2} - a b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, a b \cosh\left(f x + e\right)^{2} + 2 \, a^{2} - a b\right)} \sinh\left(f x + e\right)^{2} + a b + 4 \, {\left(a b \cosh\left(f x + e\right)^{3} + {\left(2 \, a^{2} - a b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{a - b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} - 1\right)} \sqrt{a - b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + 2 \, a - b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}\right) - \sqrt{2} {\left({\left(a b - b^{2}\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(a b - b^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) + {\left(a b - b^{2}\right)} \sinh\left(f x + e\right)^{2} - a b + b^{2}\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{{\left(a^{3} b - 2 \, a^{2} b^{2} + a b^{3}\right)} f \cosh\left(f x + e\right)^{4} + 4 \, {\left(a^{3} b - 2 \, a^{2} b^{2} + a b^{3}\right)} f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(a^{3} b - 2 \, a^{2} b^{2} + a b^{3}\right)} f \sinh\left(f x + e\right)^{4} + 2 \, {\left(2 \, a^{4} - 5 \, a^{3} b + 4 \, a^{2} b^{2} - a b^{3}\right)} f \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, {\left(a^{3} b - 2 \, a^{2} b^{2} + a b^{3}\right)} f \cosh\left(f x + e\right)^{2} + {\left(2 \, a^{4} - 5 \, a^{3} b + 4 \, a^{2} b^{2} - a b^{3}\right)} f\right)} \sinh\left(f x + e\right)^{2} + {\left(a^{3} b - 2 \, a^{2} b^{2} + a b^{3}\right)} f + 4 \, {\left({\left(a^{3} b - 2 \, a^{2} b^{2} + a b^{3}\right)} f \cosh\left(f x + e\right)^{3} + {\left(2 \, a^{4} - 5 \, a^{3} b + 4 \, a^{2} b^{2} - a b^{3}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)}\right]"," ",0,"[1/2*((a*b*cosh(f*x + e)^4 + 4*a*b*cosh(f*x + e)*sinh(f*x + e)^3 + a*b*sinh(f*x + e)^4 + 2*(2*a^2 - a*b)*cosh(f*x + e)^2 + 2*(3*a*b*cosh(f*x + e)^2 + 2*a^2 - a*b)*sinh(f*x + e)^2 + a*b + 4*(a*b*cosh(f*x + e)^3 + (2*a^2 - a*b)*cosh(f*x + e))*sinh(f*x + e))*sqrt(-a + b)*log(((a - 2*b)*cosh(f*x + e)^4 + 4*(a - 2*b)*cosh(f*x + e)*sinh(f*x + e)^3 + (a - 2*b)*sinh(f*x + e)^4 - 2*(3*a - 2*b)*cosh(f*x + e)^2 + 2*(3*(a - 2*b)*cosh(f*x + e)^2 - 3*a + 2*b)*sinh(f*x + e)^2 + 2*sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 - 1)*sqrt(-a + b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + 4*((a - 2*b)*cosh(f*x + e)^3 - (3*a - 2*b)*cosh(f*x + e))*sinh(f*x + e) + a - 2*b)/(cosh(f*x + e)^4 + 4*cosh(f*x + e)*sinh(f*x + e)^3 + sinh(f*x + e)^4 + 2*(3*cosh(f*x + e)^2 + 1)*sinh(f*x + e)^2 + 2*cosh(f*x + e)^2 + 4*(cosh(f*x + e)^3 + cosh(f*x + e))*sinh(f*x + e) + 1)) - 2*sqrt(2)*((a*b - b^2)*cosh(f*x + e)^2 + 2*(a*b - b^2)*cosh(f*x + e)*sinh(f*x + e) + (a*b - b^2)*sinh(f*x + e)^2 - a*b + b^2)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/((a^3*b - 2*a^2*b^2 + a*b^3)*f*cosh(f*x + e)^4 + 4*(a^3*b - 2*a^2*b^2 + a*b^3)*f*cosh(f*x + e)*sinh(f*x + e)^3 + (a^3*b - 2*a^2*b^2 + a*b^3)*f*sinh(f*x + e)^4 + 2*(2*a^4 - 5*a^3*b + 4*a^2*b^2 - a*b^3)*f*cosh(f*x + e)^2 + 2*(3*(a^3*b - 2*a^2*b^2 + a*b^3)*f*cosh(f*x + e)^2 + (2*a^4 - 5*a^3*b + 4*a^2*b^2 - a*b^3)*f)*sinh(f*x + e)^2 + (a^3*b - 2*a^2*b^2 + a*b^3)*f + 4*((a^3*b - 2*a^2*b^2 + a*b^3)*f*cosh(f*x + e)^3 + (2*a^4 - 5*a^3*b + 4*a^2*b^2 - a*b^3)*f*cosh(f*x + e))*sinh(f*x + e)), ((a*b*cosh(f*x + e)^4 + 4*a*b*cosh(f*x + e)*sinh(f*x + e)^3 + a*b*sinh(f*x + e)^4 + 2*(2*a^2 - a*b)*cosh(f*x + e)^2 + 2*(3*a*b*cosh(f*x + e)^2 + 2*a^2 - a*b)*sinh(f*x + e)^2 + a*b + 4*(a*b*cosh(f*x + e)^3 + (2*a^2 - a*b)*cosh(f*x + e))*sinh(f*x + e))*sqrt(a - b)*arctan(sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 - 1)*sqrt(a - b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/(b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(2*a - b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 2*a - b)*sinh(f*x + e)^2 + 4*(b*cosh(f*x + e)^3 + (2*a - b)*cosh(f*x + e))*sinh(f*x + e) + b)) - sqrt(2)*((a*b - b^2)*cosh(f*x + e)^2 + 2*(a*b - b^2)*cosh(f*x + e)*sinh(f*x + e) + (a*b - b^2)*sinh(f*x + e)^2 - a*b + b^2)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/((a^3*b - 2*a^2*b^2 + a*b^3)*f*cosh(f*x + e)^4 + 4*(a^3*b - 2*a^2*b^2 + a*b^3)*f*cosh(f*x + e)*sinh(f*x + e)^3 + (a^3*b - 2*a^2*b^2 + a*b^3)*f*sinh(f*x + e)^4 + 2*(2*a^4 - 5*a^3*b + 4*a^2*b^2 - a*b^3)*f*cosh(f*x + e)^2 + 2*(3*(a^3*b - 2*a^2*b^2 + a*b^3)*f*cosh(f*x + e)^2 + (2*a^4 - 5*a^3*b + 4*a^2*b^2 - a*b^3)*f)*sinh(f*x + e)^2 + (a^3*b - 2*a^2*b^2 + a*b^3)*f + 4*((a^3*b - 2*a^2*b^2 + a*b^3)*f*cosh(f*x + e)^3 + (2*a^4 - 5*a^3*b + 4*a^2*b^2 - a*b^3)*f*cosh(f*x + e))*sinh(f*x + e))]","B",0
385,1,4845,0,1.276918," ","integrate(sech(f*x+e)^3/(a+b*sinh(f*x+e)^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(a^{2} b - 4 \, a b^{2}\right)} \cosh\left(f x + e\right)^{8} + 8 \, {\left(a^{2} b - 4 \, a b^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + {\left(a^{2} b - 4 \, a b^{2}\right)} \sinh\left(f x + e\right)^{8} + 4 \, {\left(a^{3} - 4 \, a^{2} b\right)} \cosh\left(f x + e\right)^{6} + 4 \, {\left(a^{3} - 4 \, a^{2} b + 7 \, {\left(a^{2} b - 4 \, a b^{2}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} b - 4 \, a b^{2}\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(a^{3} - 4 \, a^{2} b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(4 \, a^{3} - 17 \, a^{2} b + 4 \, a b^{2}\right)} \cosh\left(f x + e\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} b - 4 \, a b^{2}\right)} \cosh\left(f x + e\right)^{4} + 4 \, a^{3} - 17 \, a^{2} b + 4 \, a b^{2} + 30 \, {\left(a^{3} - 4 \, a^{2} b\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} b - 4 \, a b^{2}\right)} \cosh\left(f x + e\right)^{5} + 10 \, {\left(a^{3} - 4 \, a^{2} b\right)} \cosh\left(f x + e\right)^{3} + {\left(4 \, a^{3} - 17 \, a^{2} b + 4 \, a b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + a^{2} b - 4 \, a b^{2} + 4 \, {\left(a^{3} - 4 \, a^{2} b\right)} \cosh\left(f x + e\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} b - 4 \, a b^{2}\right)} \cosh\left(f x + e\right)^{6} + 15 \, {\left(a^{3} - 4 \, a^{2} b\right)} \cosh\left(f x + e\right)^{4} + a^{3} - 4 \, a^{2} b + 3 \, {\left(4 \, a^{3} - 17 \, a^{2} b + 4 \, a b^{2}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{2} + 8 \, {\left({\left(a^{2} b - 4 \, a b^{2}\right)} \cosh\left(f x + e\right)^{7} + 3 \, {\left(a^{3} - 4 \, a^{2} b\right)} \cosh\left(f x + e\right)^{5} + {\left(4 \, a^{3} - 17 \, a^{2} b + 4 \, a b^{2}\right)} \cosh\left(f x + e\right)^{3} + {\left(a^{3} - 4 \, a^{2} b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{-a + b} \log\left(\frac{{\left(a - 2 \, b\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left(a - 2 \, b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(a - 2 \, b\right)} \sinh\left(f x + e\right)^{4} - 2 \, {\left(3 \, a - 2 \, b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, {\left(a - 2 \, b\right)} \cosh\left(f x + e\right)^{2} - 3 \, a + 2 \, b\right)} \sinh\left(f x + e\right)^{2} + 2 \, \sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} - 1\right)} \sqrt{-a + b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} + 4 \, {\left({\left(a - 2 \, b\right)} \cosh\left(f x + e\right)^{3} - {\left(3 \, a - 2 \, b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + a - 2 \, b}{\cosh\left(f x + e\right)^{4} + 4 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + \sinh\left(f x + e\right)^{4} + 2 \, {\left(3 \, \cosh\left(f x + e\right)^{2} + 1\right)} \sinh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right)^{2} + 4 \, {\left(\cosh\left(f x + e\right)^{3} + \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + 1}\right) + 2 \, \sqrt{2} {\left({\left(a^{2} b + a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{6} + 6 \, {\left(a^{2} b + a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + {\left(a^{2} b + a b^{2} - 2 \, b^{3}\right)} \sinh\left(f x + e\right)^{6} + {\left(4 \, a^{3} - 7 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} + {\left(4 \, a^{3} - 7 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3} + 15 \, {\left(a^{2} b + a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(5 \, {\left(a^{2} b + a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} + {\left(4 \, a^{3} - 7 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} - a^{2} b - a b^{2} + 2 \, b^{3} - {\left(4 \, a^{3} - 7 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{2} + {\left(15 \, {\left(a^{2} b + a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} - 4 \, a^{3} + 7 \, a^{2} b - 5 \, a b^{2} + 2 \, b^{3} + 6 \, {\left(4 \, a^{3} - 7 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} b + a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{5} + 2 \, {\left(4 \, a^{3} - 7 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} - {\left(4 \, a^{3} - 7 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{4 \, {\left({\left(a^{4} b - 3 \, a^{3} b^{2} + 3 \, a^{2} b^{3} - a b^{4}\right)} f \cosh\left(f x + e\right)^{8} + 8 \, {\left(a^{4} b - 3 \, a^{3} b^{2} + 3 \, a^{2} b^{3} - a b^{4}\right)} f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + {\left(a^{4} b - 3 \, a^{3} b^{2} + 3 \, a^{2} b^{3} - a b^{4}\right)} f \sinh\left(f x + e\right)^{8} + 4 \, {\left(a^{5} - 3 \, a^{4} b + 3 \, a^{3} b^{2} - a^{2} b^{3}\right)} f \cosh\left(f x + e\right)^{6} + 4 \, {\left(7 \, {\left(a^{4} b - 3 \, a^{3} b^{2} + 3 \, a^{2} b^{3} - a b^{4}\right)} f \cosh\left(f x + e\right)^{2} + {\left(a^{5} - 3 \, a^{4} b + 3 \, a^{3} b^{2} - a^{2} b^{3}\right)} f\right)} \sinh\left(f x + e\right)^{6} + 2 \, {\left(4 \, a^{5} - 13 \, a^{4} b + 15 \, a^{3} b^{2} - 7 \, a^{2} b^{3} + a b^{4}\right)} f \cosh\left(f x + e\right)^{4} + 8 \, {\left(7 \, {\left(a^{4} b - 3 \, a^{3} b^{2} + 3 \, a^{2} b^{3} - a b^{4}\right)} f \cosh\left(f x + e\right)^{3} + 3 \, {\left(a^{5} - 3 \, a^{4} b + 3 \, a^{3} b^{2} - a^{2} b^{3}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(35 \, {\left(a^{4} b - 3 \, a^{3} b^{2} + 3 \, a^{2} b^{3} - a b^{4}\right)} f \cosh\left(f x + e\right)^{4} + 30 \, {\left(a^{5} - 3 \, a^{4} b + 3 \, a^{3} b^{2} - a^{2} b^{3}\right)} f \cosh\left(f x + e\right)^{2} + {\left(4 \, a^{5} - 13 \, a^{4} b + 15 \, a^{3} b^{2} - 7 \, a^{2} b^{3} + a b^{4}\right)} f\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(a^{5} - 3 \, a^{4} b + 3 \, a^{3} b^{2} - a^{2} b^{3}\right)} f \cosh\left(f x + e\right)^{2} + 8 \, {\left(7 \, {\left(a^{4} b - 3 \, a^{3} b^{2} + 3 \, a^{2} b^{3} - a b^{4}\right)} f \cosh\left(f x + e\right)^{5} + 10 \, {\left(a^{5} - 3 \, a^{4} b + 3 \, a^{3} b^{2} - a^{2} b^{3}\right)} f \cosh\left(f x + e\right)^{3} + {\left(4 \, a^{5} - 13 \, a^{4} b + 15 \, a^{3} b^{2} - 7 \, a^{2} b^{3} + a b^{4}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 4 \, {\left(7 \, {\left(a^{4} b - 3 \, a^{3} b^{2} + 3 \, a^{2} b^{3} - a b^{4}\right)} f \cosh\left(f x + e\right)^{6} + 15 \, {\left(a^{5} - 3 \, a^{4} b + 3 \, a^{3} b^{2} - a^{2} b^{3}\right)} f \cosh\left(f x + e\right)^{4} + 3 \, {\left(4 \, a^{5} - 13 \, a^{4} b + 15 \, a^{3} b^{2} - 7 \, a^{2} b^{3} + a b^{4}\right)} f \cosh\left(f x + e\right)^{2} + {\left(a^{5} - 3 \, a^{4} b + 3 \, a^{3} b^{2} - a^{2} b^{3}\right)} f\right)} \sinh\left(f x + e\right)^{2} + {\left(a^{4} b - 3 \, a^{3} b^{2} + 3 \, a^{2} b^{3} - a b^{4}\right)} f + 8 \, {\left({\left(a^{4} b - 3 \, a^{3} b^{2} + 3 \, a^{2} b^{3} - a b^{4}\right)} f \cosh\left(f x + e\right)^{7} + 3 \, {\left(a^{5} - 3 \, a^{4} b + 3 \, a^{3} b^{2} - a^{2} b^{3}\right)} f \cosh\left(f x + e\right)^{5} + {\left(4 \, a^{5} - 13 \, a^{4} b + 15 \, a^{3} b^{2} - 7 \, a^{2} b^{3} + a b^{4}\right)} f \cosh\left(f x + e\right)^{3} + {\left(a^{5} - 3 \, a^{4} b + 3 \, a^{3} b^{2} - a^{2} b^{3}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)}}, \frac{{\left({\left(a^{2} b - 4 \, a b^{2}\right)} \cosh\left(f x + e\right)^{8} + 8 \, {\left(a^{2} b - 4 \, a b^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + {\left(a^{2} b - 4 \, a b^{2}\right)} \sinh\left(f x + e\right)^{8} + 4 \, {\left(a^{3} - 4 \, a^{2} b\right)} \cosh\left(f x + e\right)^{6} + 4 \, {\left(a^{3} - 4 \, a^{2} b + 7 \, {\left(a^{2} b - 4 \, a b^{2}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} b - 4 \, a b^{2}\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(a^{3} - 4 \, a^{2} b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(4 \, a^{3} - 17 \, a^{2} b + 4 \, a b^{2}\right)} \cosh\left(f x + e\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} b - 4 \, a b^{2}\right)} \cosh\left(f x + e\right)^{4} + 4 \, a^{3} - 17 \, a^{2} b + 4 \, a b^{2} + 30 \, {\left(a^{3} - 4 \, a^{2} b\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} b - 4 \, a b^{2}\right)} \cosh\left(f x + e\right)^{5} + 10 \, {\left(a^{3} - 4 \, a^{2} b\right)} \cosh\left(f x + e\right)^{3} + {\left(4 \, a^{3} - 17 \, a^{2} b + 4 \, a b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + a^{2} b - 4 \, a b^{2} + 4 \, {\left(a^{3} - 4 \, a^{2} b\right)} \cosh\left(f x + e\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} b - 4 \, a b^{2}\right)} \cosh\left(f x + e\right)^{6} + 15 \, {\left(a^{3} - 4 \, a^{2} b\right)} \cosh\left(f x + e\right)^{4} + a^{3} - 4 \, a^{2} b + 3 \, {\left(4 \, a^{3} - 17 \, a^{2} b + 4 \, a b^{2}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{2} + 8 \, {\left({\left(a^{2} b - 4 \, a b^{2}\right)} \cosh\left(f x + e\right)^{7} + 3 \, {\left(a^{3} - 4 \, a^{2} b\right)} \cosh\left(f x + e\right)^{5} + {\left(4 \, a^{3} - 17 \, a^{2} b + 4 \, a b^{2}\right)} \cosh\left(f x + e\right)^{3} + {\left(a^{3} - 4 \, a^{2} b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{a - b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} - 1\right)} \sqrt{a - b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + 2 \, a - b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}\right) + \sqrt{2} {\left({\left(a^{2} b + a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{6} + 6 \, {\left(a^{2} b + a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + {\left(a^{2} b + a b^{2} - 2 \, b^{3}\right)} \sinh\left(f x + e\right)^{6} + {\left(4 \, a^{3} - 7 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} + {\left(4 \, a^{3} - 7 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3} + 15 \, {\left(a^{2} b + a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(5 \, {\left(a^{2} b + a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} + {\left(4 \, a^{3} - 7 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} - a^{2} b - a b^{2} + 2 \, b^{3} - {\left(4 \, a^{3} - 7 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{2} + {\left(15 \, {\left(a^{2} b + a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} - 4 \, a^{3} + 7 \, a^{2} b - 5 \, a b^{2} + 2 \, b^{3} + 6 \, {\left(4 \, a^{3} - 7 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} b + a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{5} + 2 \, {\left(4 \, a^{3} - 7 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} - {\left(4 \, a^{3} - 7 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{2 \, {\left({\left(a^{4} b - 3 \, a^{3} b^{2} + 3 \, a^{2} b^{3} - a b^{4}\right)} f \cosh\left(f x + e\right)^{8} + 8 \, {\left(a^{4} b - 3 \, a^{3} b^{2} + 3 \, a^{2} b^{3} - a b^{4}\right)} f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + {\left(a^{4} b - 3 \, a^{3} b^{2} + 3 \, a^{2} b^{3} - a b^{4}\right)} f \sinh\left(f x + e\right)^{8} + 4 \, {\left(a^{5} - 3 \, a^{4} b + 3 \, a^{3} b^{2} - a^{2} b^{3}\right)} f \cosh\left(f x + e\right)^{6} + 4 \, {\left(7 \, {\left(a^{4} b - 3 \, a^{3} b^{2} + 3 \, a^{2} b^{3} - a b^{4}\right)} f \cosh\left(f x + e\right)^{2} + {\left(a^{5} - 3 \, a^{4} b + 3 \, a^{3} b^{2} - a^{2} b^{3}\right)} f\right)} \sinh\left(f x + e\right)^{6} + 2 \, {\left(4 \, a^{5} - 13 \, a^{4} b + 15 \, a^{3} b^{2} - 7 \, a^{2} b^{3} + a b^{4}\right)} f \cosh\left(f x + e\right)^{4} + 8 \, {\left(7 \, {\left(a^{4} b - 3 \, a^{3} b^{2} + 3 \, a^{2} b^{3} - a b^{4}\right)} f \cosh\left(f x + e\right)^{3} + 3 \, {\left(a^{5} - 3 \, a^{4} b + 3 \, a^{3} b^{2} - a^{2} b^{3}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(35 \, {\left(a^{4} b - 3 \, a^{3} b^{2} + 3 \, a^{2} b^{3} - a b^{4}\right)} f \cosh\left(f x + e\right)^{4} + 30 \, {\left(a^{5} - 3 \, a^{4} b + 3 \, a^{3} b^{2} - a^{2} b^{3}\right)} f \cosh\left(f x + e\right)^{2} + {\left(4 \, a^{5} - 13 \, a^{4} b + 15 \, a^{3} b^{2} - 7 \, a^{2} b^{3} + a b^{4}\right)} f\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(a^{5} - 3 \, a^{4} b + 3 \, a^{3} b^{2} - a^{2} b^{3}\right)} f \cosh\left(f x + e\right)^{2} + 8 \, {\left(7 \, {\left(a^{4} b - 3 \, a^{3} b^{2} + 3 \, a^{2} b^{3} - a b^{4}\right)} f \cosh\left(f x + e\right)^{5} + 10 \, {\left(a^{5} - 3 \, a^{4} b + 3 \, a^{3} b^{2} - a^{2} b^{3}\right)} f \cosh\left(f x + e\right)^{3} + {\left(4 \, a^{5} - 13 \, a^{4} b + 15 \, a^{3} b^{2} - 7 \, a^{2} b^{3} + a b^{4}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 4 \, {\left(7 \, {\left(a^{4} b - 3 \, a^{3} b^{2} + 3 \, a^{2} b^{3} - a b^{4}\right)} f \cosh\left(f x + e\right)^{6} + 15 \, {\left(a^{5} - 3 \, a^{4} b + 3 \, a^{3} b^{2} - a^{2} b^{3}\right)} f \cosh\left(f x + e\right)^{4} + 3 \, {\left(4 \, a^{5} - 13 \, a^{4} b + 15 \, a^{3} b^{2} - 7 \, a^{2} b^{3} + a b^{4}\right)} f \cosh\left(f x + e\right)^{2} + {\left(a^{5} - 3 \, a^{4} b + 3 \, a^{3} b^{2} - a^{2} b^{3}\right)} f\right)} \sinh\left(f x + e\right)^{2} + {\left(a^{4} b - 3 \, a^{3} b^{2} + 3 \, a^{2} b^{3} - a b^{4}\right)} f + 8 \, {\left({\left(a^{4} b - 3 \, a^{3} b^{2} + 3 \, a^{2} b^{3} - a b^{4}\right)} f \cosh\left(f x + e\right)^{7} + 3 \, {\left(a^{5} - 3 \, a^{4} b + 3 \, a^{3} b^{2} - a^{2} b^{3}\right)} f \cosh\left(f x + e\right)^{5} + {\left(4 \, a^{5} - 13 \, a^{4} b + 15 \, a^{3} b^{2} - 7 \, a^{2} b^{3} + a b^{4}\right)} f \cosh\left(f x + e\right)^{3} + {\left(a^{5} - 3 \, a^{4} b + 3 \, a^{3} b^{2} - a^{2} b^{3}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)}}\right]"," ",0,"[1/4*(((a^2*b - 4*a*b^2)*cosh(f*x + e)^8 + 8*(a^2*b - 4*a*b^2)*cosh(f*x + e)*sinh(f*x + e)^7 + (a^2*b - 4*a*b^2)*sinh(f*x + e)^8 + 4*(a^3 - 4*a^2*b)*cosh(f*x + e)^6 + 4*(a^3 - 4*a^2*b + 7*(a^2*b - 4*a*b^2)*cosh(f*x + e)^2)*sinh(f*x + e)^6 + 8*(7*(a^2*b - 4*a*b^2)*cosh(f*x + e)^3 + 3*(a^3 - 4*a^2*b)*cosh(f*x + e))*sinh(f*x + e)^5 + 2*(4*a^3 - 17*a^2*b + 4*a*b^2)*cosh(f*x + e)^4 + 2*(35*(a^2*b - 4*a*b^2)*cosh(f*x + e)^4 + 4*a^3 - 17*a^2*b + 4*a*b^2 + 30*(a^3 - 4*a^2*b)*cosh(f*x + e)^2)*sinh(f*x + e)^4 + 8*(7*(a^2*b - 4*a*b^2)*cosh(f*x + e)^5 + 10*(a^3 - 4*a^2*b)*cosh(f*x + e)^3 + (4*a^3 - 17*a^2*b + 4*a*b^2)*cosh(f*x + e))*sinh(f*x + e)^3 + a^2*b - 4*a*b^2 + 4*(a^3 - 4*a^2*b)*cosh(f*x + e)^2 + 4*(7*(a^2*b - 4*a*b^2)*cosh(f*x + e)^6 + 15*(a^3 - 4*a^2*b)*cosh(f*x + e)^4 + a^3 - 4*a^2*b + 3*(4*a^3 - 17*a^2*b + 4*a*b^2)*cosh(f*x + e)^2)*sinh(f*x + e)^2 + 8*((a^2*b - 4*a*b^2)*cosh(f*x + e)^7 + 3*(a^3 - 4*a^2*b)*cosh(f*x + e)^5 + (4*a^3 - 17*a^2*b + 4*a*b^2)*cosh(f*x + e)^3 + (a^3 - 4*a^2*b)*cosh(f*x + e))*sinh(f*x + e))*sqrt(-a + b)*log(((a - 2*b)*cosh(f*x + e)^4 + 4*(a - 2*b)*cosh(f*x + e)*sinh(f*x + e)^3 + (a - 2*b)*sinh(f*x + e)^4 - 2*(3*a - 2*b)*cosh(f*x + e)^2 + 2*(3*(a - 2*b)*cosh(f*x + e)^2 - 3*a + 2*b)*sinh(f*x + e)^2 + 2*sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 - 1)*sqrt(-a + b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + 4*((a - 2*b)*cosh(f*x + e)^3 - (3*a - 2*b)*cosh(f*x + e))*sinh(f*x + e) + a - 2*b)/(cosh(f*x + e)^4 + 4*cosh(f*x + e)*sinh(f*x + e)^3 + sinh(f*x + e)^4 + 2*(3*cosh(f*x + e)^2 + 1)*sinh(f*x + e)^2 + 2*cosh(f*x + e)^2 + 4*(cosh(f*x + e)^3 + cosh(f*x + e))*sinh(f*x + e) + 1)) + 2*sqrt(2)*((a^2*b + a*b^2 - 2*b^3)*cosh(f*x + e)^6 + 6*(a^2*b + a*b^2 - 2*b^3)*cosh(f*x + e)*sinh(f*x + e)^5 + (a^2*b + a*b^2 - 2*b^3)*sinh(f*x + e)^6 + (4*a^3 - 7*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e)^4 + (4*a^3 - 7*a^2*b + 5*a*b^2 - 2*b^3 + 15*(a^2*b + a*b^2 - 2*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^4 + 4*(5*(a^2*b + a*b^2 - 2*b^3)*cosh(f*x + e)^3 + (4*a^3 - 7*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e))*sinh(f*x + e)^3 - a^2*b - a*b^2 + 2*b^3 - (4*a^3 - 7*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e)^2 + (15*(a^2*b + a*b^2 - 2*b^3)*cosh(f*x + e)^4 - 4*a^3 + 7*a^2*b - 5*a*b^2 + 2*b^3 + 6*(4*a^3 - 7*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^2 + 2*(3*(a^2*b + a*b^2 - 2*b^3)*cosh(f*x + e)^5 + 2*(4*a^3 - 7*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e)^3 - (4*a^3 - 7*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e))*sinh(f*x + e))*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/((a^4*b - 3*a^3*b^2 + 3*a^2*b^3 - a*b^4)*f*cosh(f*x + e)^8 + 8*(a^4*b - 3*a^3*b^2 + 3*a^2*b^3 - a*b^4)*f*cosh(f*x + e)*sinh(f*x + e)^7 + (a^4*b - 3*a^3*b^2 + 3*a^2*b^3 - a*b^4)*f*sinh(f*x + e)^8 + 4*(a^5 - 3*a^4*b + 3*a^3*b^2 - a^2*b^3)*f*cosh(f*x + e)^6 + 4*(7*(a^4*b - 3*a^3*b^2 + 3*a^2*b^3 - a*b^4)*f*cosh(f*x + e)^2 + (a^5 - 3*a^4*b + 3*a^3*b^2 - a^2*b^3)*f)*sinh(f*x + e)^6 + 2*(4*a^5 - 13*a^4*b + 15*a^3*b^2 - 7*a^2*b^3 + a*b^4)*f*cosh(f*x + e)^4 + 8*(7*(a^4*b - 3*a^3*b^2 + 3*a^2*b^3 - a*b^4)*f*cosh(f*x + e)^3 + 3*(a^5 - 3*a^4*b + 3*a^3*b^2 - a^2*b^3)*f*cosh(f*x + e))*sinh(f*x + e)^5 + 2*(35*(a^4*b - 3*a^3*b^2 + 3*a^2*b^3 - a*b^4)*f*cosh(f*x + e)^4 + 30*(a^5 - 3*a^4*b + 3*a^3*b^2 - a^2*b^3)*f*cosh(f*x + e)^2 + (4*a^5 - 13*a^4*b + 15*a^3*b^2 - 7*a^2*b^3 + a*b^4)*f)*sinh(f*x + e)^4 + 4*(a^5 - 3*a^4*b + 3*a^3*b^2 - a^2*b^3)*f*cosh(f*x + e)^2 + 8*(7*(a^4*b - 3*a^3*b^2 + 3*a^2*b^3 - a*b^4)*f*cosh(f*x + e)^5 + 10*(a^5 - 3*a^4*b + 3*a^3*b^2 - a^2*b^3)*f*cosh(f*x + e)^3 + (4*a^5 - 13*a^4*b + 15*a^3*b^2 - 7*a^2*b^3 + a*b^4)*f*cosh(f*x + e))*sinh(f*x + e)^3 + 4*(7*(a^4*b - 3*a^3*b^2 + 3*a^2*b^3 - a*b^4)*f*cosh(f*x + e)^6 + 15*(a^5 - 3*a^4*b + 3*a^3*b^2 - a^2*b^3)*f*cosh(f*x + e)^4 + 3*(4*a^5 - 13*a^4*b + 15*a^3*b^2 - 7*a^2*b^3 + a*b^4)*f*cosh(f*x + e)^2 + (a^5 - 3*a^4*b + 3*a^3*b^2 - a^2*b^3)*f)*sinh(f*x + e)^2 + (a^4*b - 3*a^3*b^2 + 3*a^2*b^3 - a*b^4)*f + 8*((a^4*b - 3*a^3*b^2 + 3*a^2*b^3 - a*b^4)*f*cosh(f*x + e)^7 + 3*(a^5 - 3*a^4*b + 3*a^3*b^2 - a^2*b^3)*f*cosh(f*x + e)^5 + (4*a^5 - 13*a^4*b + 15*a^3*b^2 - 7*a^2*b^3 + a*b^4)*f*cosh(f*x + e)^3 + (a^5 - 3*a^4*b + 3*a^3*b^2 - a^2*b^3)*f*cosh(f*x + e))*sinh(f*x + e)), 1/2*(((a^2*b - 4*a*b^2)*cosh(f*x + e)^8 + 8*(a^2*b - 4*a*b^2)*cosh(f*x + e)*sinh(f*x + e)^7 + (a^2*b - 4*a*b^2)*sinh(f*x + e)^8 + 4*(a^3 - 4*a^2*b)*cosh(f*x + e)^6 + 4*(a^3 - 4*a^2*b + 7*(a^2*b - 4*a*b^2)*cosh(f*x + e)^2)*sinh(f*x + e)^6 + 8*(7*(a^2*b - 4*a*b^2)*cosh(f*x + e)^3 + 3*(a^3 - 4*a^2*b)*cosh(f*x + e))*sinh(f*x + e)^5 + 2*(4*a^3 - 17*a^2*b + 4*a*b^2)*cosh(f*x + e)^4 + 2*(35*(a^2*b - 4*a*b^2)*cosh(f*x + e)^4 + 4*a^3 - 17*a^2*b + 4*a*b^2 + 30*(a^3 - 4*a^2*b)*cosh(f*x + e)^2)*sinh(f*x + e)^4 + 8*(7*(a^2*b - 4*a*b^2)*cosh(f*x + e)^5 + 10*(a^3 - 4*a^2*b)*cosh(f*x + e)^3 + (4*a^3 - 17*a^2*b + 4*a*b^2)*cosh(f*x + e))*sinh(f*x + e)^3 + a^2*b - 4*a*b^2 + 4*(a^3 - 4*a^2*b)*cosh(f*x + e)^2 + 4*(7*(a^2*b - 4*a*b^2)*cosh(f*x + e)^6 + 15*(a^3 - 4*a^2*b)*cosh(f*x + e)^4 + a^3 - 4*a^2*b + 3*(4*a^3 - 17*a^2*b + 4*a*b^2)*cosh(f*x + e)^2)*sinh(f*x + e)^2 + 8*((a^2*b - 4*a*b^2)*cosh(f*x + e)^7 + 3*(a^3 - 4*a^2*b)*cosh(f*x + e)^5 + (4*a^3 - 17*a^2*b + 4*a*b^2)*cosh(f*x + e)^3 + (a^3 - 4*a^2*b)*cosh(f*x + e))*sinh(f*x + e))*sqrt(a - b)*arctan(sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 - 1)*sqrt(a - b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/(b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(2*a - b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 2*a - b)*sinh(f*x + e)^2 + 4*(b*cosh(f*x + e)^3 + (2*a - b)*cosh(f*x + e))*sinh(f*x + e) + b)) + sqrt(2)*((a^2*b + a*b^2 - 2*b^3)*cosh(f*x + e)^6 + 6*(a^2*b + a*b^2 - 2*b^3)*cosh(f*x + e)*sinh(f*x + e)^5 + (a^2*b + a*b^2 - 2*b^3)*sinh(f*x + e)^6 + (4*a^3 - 7*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e)^4 + (4*a^3 - 7*a^2*b + 5*a*b^2 - 2*b^3 + 15*(a^2*b + a*b^2 - 2*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^4 + 4*(5*(a^2*b + a*b^2 - 2*b^3)*cosh(f*x + e)^3 + (4*a^3 - 7*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e))*sinh(f*x + e)^3 - a^2*b - a*b^2 + 2*b^3 - (4*a^3 - 7*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e)^2 + (15*(a^2*b + a*b^2 - 2*b^3)*cosh(f*x + e)^4 - 4*a^3 + 7*a^2*b - 5*a*b^2 + 2*b^3 + 6*(4*a^3 - 7*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^2 + 2*(3*(a^2*b + a*b^2 - 2*b^3)*cosh(f*x + e)^5 + 2*(4*a^3 - 7*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e)^3 - (4*a^3 - 7*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e))*sinh(f*x + e))*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/((a^4*b - 3*a^3*b^2 + 3*a^2*b^3 - a*b^4)*f*cosh(f*x + e)^8 + 8*(a^4*b - 3*a^3*b^2 + 3*a^2*b^3 - a*b^4)*f*cosh(f*x + e)*sinh(f*x + e)^7 + (a^4*b - 3*a^3*b^2 + 3*a^2*b^3 - a*b^4)*f*sinh(f*x + e)^8 + 4*(a^5 - 3*a^4*b + 3*a^3*b^2 - a^2*b^3)*f*cosh(f*x + e)^6 + 4*(7*(a^4*b - 3*a^3*b^2 + 3*a^2*b^3 - a*b^4)*f*cosh(f*x + e)^2 + (a^5 - 3*a^4*b + 3*a^3*b^2 - a^2*b^3)*f)*sinh(f*x + e)^6 + 2*(4*a^5 - 13*a^4*b + 15*a^3*b^2 - 7*a^2*b^3 + a*b^4)*f*cosh(f*x + e)^4 + 8*(7*(a^4*b - 3*a^3*b^2 + 3*a^2*b^3 - a*b^4)*f*cosh(f*x + e)^3 + 3*(a^5 - 3*a^4*b + 3*a^3*b^2 - a^2*b^3)*f*cosh(f*x + e))*sinh(f*x + e)^5 + 2*(35*(a^4*b - 3*a^3*b^2 + 3*a^2*b^3 - a*b^4)*f*cosh(f*x + e)^4 + 30*(a^5 - 3*a^4*b + 3*a^3*b^2 - a^2*b^3)*f*cosh(f*x + e)^2 + (4*a^5 - 13*a^4*b + 15*a^3*b^2 - 7*a^2*b^3 + a*b^4)*f)*sinh(f*x + e)^4 + 4*(a^5 - 3*a^4*b + 3*a^3*b^2 - a^2*b^3)*f*cosh(f*x + e)^2 + 8*(7*(a^4*b - 3*a^3*b^2 + 3*a^2*b^3 - a*b^4)*f*cosh(f*x + e)^5 + 10*(a^5 - 3*a^4*b + 3*a^3*b^2 - a^2*b^3)*f*cosh(f*x + e)^3 + (4*a^5 - 13*a^4*b + 15*a^3*b^2 - 7*a^2*b^3 + a*b^4)*f*cosh(f*x + e))*sinh(f*x + e)^3 + 4*(7*(a^4*b - 3*a^3*b^2 + 3*a^2*b^3 - a*b^4)*f*cosh(f*x + e)^6 + 15*(a^5 - 3*a^4*b + 3*a^3*b^2 - a^2*b^3)*f*cosh(f*x + e)^4 + 3*(4*a^5 - 13*a^4*b + 15*a^3*b^2 - 7*a^2*b^3 + a*b^4)*f*cosh(f*x + e)^2 + (a^5 - 3*a^4*b + 3*a^3*b^2 - a^2*b^3)*f)*sinh(f*x + e)^2 + (a^4*b - 3*a^3*b^2 + 3*a^2*b^3 - a*b^4)*f + 8*((a^4*b - 3*a^3*b^2 + 3*a^2*b^3 - a*b^4)*f*cosh(f*x + e)^7 + 3*(a^5 - 3*a^4*b + 3*a^3*b^2 - a^2*b^3)*f*cosh(f*x + e)^5 + (4*a^5 - 13*a^4*b + 15*a^3*b^2 - 7*a^2*b^3 + a*b^4)*f*cosh(f*x + e)^3 + (a^5 - 3*a^4*b + 3*a^3*b^2 - a^2*b^3)*f*cosh(f*x + e))*sinh(f*x + e))]","B",0
386,0,0,0,0.517219," ","integrate(cosh(f*x+e)^6/(a+b*sinh(f*x+e)^2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sinh\left(f x + e\right)^{2} + a} \cosh\left(f x + e\right)^{6}}{b^{2} \sinh\left(f x + e\right)^{4} + 2 \, a b \sinh\left(f x + e\right)^{2} + a^{2}}, x\right)"," ",0,"integral(sqrt(b*sinh(f*x + e)^2 + a)*cosh(f*x + e)^6/(b^2*sinh(f*x + e)^4 + 2*a*b*sinh(f*x + e)^2 + a^2), x)","F",0
387,0,0,0,0.562747," ","integrate(cosh(f*x+e)^4/(a+b*sinh(f*x+e)^2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sinh\left(f x + e\right)^{2} + a} \cosh\left(f x + e\right)^{4}}{b^{2} \sinh\left(f x + e\right)^{4} + 2 \, a b \sinh\left(f x + e\right)^{2} + a^{2}}, x\right)"," ",0,"integral(sqrt(b*sinh(f*x + e)^2 + a)*cosh(f*x + e)^4/(b^2*sinh(f*x + e)^4 + 2*a*b*sinh(f*x + e)^2 + a^2), x)","F",0
388,0,0,0,0.608782," ","integrate(cosh(f*x+e)^2/(a+b*sinh(f*x+e)^2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sinh\left(f x + e\right)^{2} + a} \cosh\left(f x + e\right)^{2}}{b^{2} \sinh\left(f x + e\right)^{4} + 2 \, a b \sinh\left(f x + e\right)^{2} + a^{2}}, x\right)"," ",0,"integral(sqrt(b*sinh(f*x + e)^2 + a)*cosh(f*x + e)^2/(b^2*sinh(f*x + e)^4 + 2*a*b*sinh(f*x + e)^2 + a^2), x)","F",0
389,0,0,0,0.988357," ","integrate(1/(a+b*sinh(f*x+e)^2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sinh\left(f x + e\right)^{2} + a}}{b^{2} \sinh\left(f x + e\right)^{4} + 2 \, a b \sinh\left(f x + e\right)^{2} + a^{2}}, x\right)"," ",0,"integral(sqrt(b*sinh(f*x + e)^2 + a)/(b^2*sinh(f*x + e)^4 + 2*a*b*sinh(f*x + e)^2 + a^2), x)","F",0
390,0,0,0,0.724878," ","integrate(sech(f*x+e)^2/(a+b*sinh(f*x+e)^2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sinh\left(f x + e\right)^{2} + a} \operatorname{sech}\left(f x + e\right)^{2}}{b^{2} \sinh\left(f x + e\right)^{4} + 2 \, a b \sinh\left(f x + e\right)^{2} + a^{2}}, x\right)"," ",0,"integral(sqrt(b*sinh(f*x + e)^2 + a)*sech(f*x + e)^2/(b^2*sinh(f*x + e)^4 + 2*a*b*sinh(f*x + e)^2 + a^2), x)","F",0
391,1,6774,0,2.139844," ","integrate(cosh(f*x+e)^5/(a+b*sinh(f*x+e)^2)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(a^{2} b^{2} \cosh\left(f x + e\right)^{8} + 8 \, a^{2} b^{2} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + a^{2} b^{2} \sinh\left(f x + e\right)^{8} + 4 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} \cosh\left(f x + e\right)^{6} + 4 \, {\left(7 \, a^{2} b^{2} \cosh\left(f x + e\right)^{2} + 2 \, a^{3} b - a^{2} b^{2}\right)} \sinh\left(f x + e\right)^{6} + 8 \, {\left(7 \, a^{2} b^{2} \cosh\left(f x + e\right)^{3} + 3 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(8 \, a^{4} - 8 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(f x + e\right)^{4} + 2 \, {\left(35 \, a^{2} b^{2} \cosh\left(f x + e\right)^{4} + 8 \, a^{4} - 8 \, a^{3} b + 3 \, a^{2} b^{2} + 30 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{4} + a^{2} b^{2} + 8 \, {\left(7 \, a^{2} b^{2} \cosh\left(f x + e\right)^{5} + 10 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} \cosh\left(f x + e\right)^{3} + {\left(8 \, a^{4} - 8 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 4 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} \cosh\left(f x + e\right)^{2} + 4 \, {\left(7 \, a^{2} b^{2} \cosh\left(f x + e\right)^{6} + 15 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} \cosh\left(f x + e\right)^{4} + 2 \, a^{3} b - a^{2} b^{2} + 3 \, {\left(8 \, a^{4} - 8 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{2} + 8 \, {\left(a^{2} b^{2} \cosh\left(f x + e\right)^{7} + 3 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} \cosh\left(f x + e\right)^{5} + {\left(8 \, a^{4} - 8 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(f x + e\right)^{3} + {\left(2 \, a^{3} b - a^{2} b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{b} \log\left(-\frac{{\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{8} + 8 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \sinh\left(f x + e\right)^{8} + 2 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{6} + 2 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3} + 14 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{6} + 4 \, {\left(14 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + {\left(9 \, a^{2} b - 14 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} + {\left(70 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{4} + 9 \, a^{2} b - 14 \, a b^{2} + 6 \, b^{3} + 30 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(14 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{5} + 10 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} + {\left(9 \, a^{2} b - 14 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + b^{3} + 2 \, {\left(3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(14 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{6} + 15 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} + 3 \, a b^{2} - 2 \, b^{3} + 3 \, {\left(9 \, a^{2} b - 14 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{2} + \sqrt{2} {\left({\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{6} + 6 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + {\left(a^{2} - 2 \, a b + b^{2}\right)} \sinh\left(f x + e\right)^{6} - 3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{4} + 3 \, {\left(5 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{2} - a^{2} + 2 \, a b - b^{2}\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(5 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{3} - 3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} - {\left(4 \, a b - 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + {\left(15 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{4} - 18 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{2} - 4 \, a b + 3 \, b^{2}\right)} \sinh\left(f x + e\right)^{2} - b^{2} + 2 \, {\left(3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{5} - 6 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{3} - {\left(4 \, a b - 3 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} + 4 \, {\left(2 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{7} + 3 \, {\left(a^{3} - 4 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{5} + {\left(9 \, a^{2} b - 14 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} + {\left(3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)}{\cosh\left(f x + e\right)^{6} + 6 \, \cosh\left(f x + e\right)^{5} \sinh\left(f x + e\right) + 15 \, \cosh\left(f x + e\right)^{4} \sinh\left(f x + e\right)^{2} + 20 \, \cosh\left(f x + e\right)^{3} \sinh\left(f x + e\right)^{3} + 15 \, \cosh\left(f x + e\right)^{2} \sinh\left(f x + e\right)^{4} + 6 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + \sinh\left(f x + e\right)^{6}}\right) + 3 \, {\left(a^{2} b^{2} \cosh\left(f x + e\right)^{8} + 8 \, a^{2} b^{2} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + a^{2} b^{2} \sinh\left(f x + e\right)^{8} + 4 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} \cosh\left(f x + e\right)^{6} + 4 \, {\left(7 \, a^{2} b^{2} \cosh\left(f x + e\right)^{2} + 2 \, a^{3} b - a^{2} b^{2}\right)} \sinh\left(f x + e\right)^{6} + 8 \, {\left(7 \, a^{2} b^{2} \cosh\left(f x + e\right)^{3} + 3 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(8 \, a^{4} - 8 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(f x + e\right)^{4} + 2 \, {\left(35 \, a^{2} b^{2} \cosh\left(f x + e\right)^{4} + 8 \, a^{4} - 8 \, a^{3} b + 3 \, a^{2} b^{2} + 30 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{4} + a^{2} b^{2} + 8 \, {\left(7 \, a^{2} b^{2} \cosh\left(f x + e\right)^{5} + 10 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} \cosh\left(f x + e\right)^{3} + {\left(8 \, a^{4} - 8 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 4 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} \cosh\left(f x + e\right)^{2} + 4 \, {\left(7 \, a^{2} b^{2} \cosh\left(f x + e\right)^{6} + 15 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} \cosh\left(f x + e\right)^{4} + 2 \, a^{3} b - a^{2} b^{2} + 3 \, {\left(8 \, a^{4} - 8 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{2} + 8 \, {\left(a^{2} b^{2} \cosh\left(f x + e\right)^{7} + 3 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} \cosh\left(f x + e\right)^{5} + {\left(8 \, a^{4} - 8 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(f x + e\right)^{3} + {\left(2 \, a^{3} b - a^{2} b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{b} \log\left(\frac{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, a \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + a\right)} \sinh\left(f x + e\right)^{2} + \sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} + 1\right)} \sqrt{b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + a \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}{\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}\right) - 8 \, \sqrt{2} {\left({\left(2 \, a^{2} b^{2} - a b^{3} - b^{4}\right)} \cosh\left(f x + e\right)^{6} + 6 \, {\left(2 \, a^{2} b^{2} - a b^{3} - b^{4}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + {\left(2 \, a^{2} b^{2} - a b^{3} - b^{4}\right)} \sinh\left(f x + e\right)^{6} + 3 \, {\left(2 \, a^{3} b - 2 \, a^{2} b^{2} - a b^{3} + b^{4}\right)} \cosh\left(f x + e\right)^{4} + 3 \, {\left(2 \, a^{3} b - 2 \, a^{2} b^{2} - a b^{3} + b^{4} + 5 \, {\left(2 \, a^{2} b^{2} - a b^{3} - b^{4}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{4} - 2 \, a^{2} b^{2} + a b^{3} + b^{4} + 4 \, {\left(5 \, {\left(2 \, a^{2} b^{2} - a b^{3} - b^{4}\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(2 \, a^{3} b - 2 \, a^{2} b^{2} - a b^{3} + b^{4}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} - 3 \, {\left(2 \, a^{3} b - 2 \, a^{2} b^{2} - a b^{3} + b^{4}\right)} \cosh\left(f x + e\right)^{2} + 3 \, {\left(5 \, {\left(2 \, a^{2} b^{2} - a b^{3} - b^{4}\right)} \cosh\left(f x + e\right)^{4} - 2 \, a^{3} b + 2 \, a^{2} b^{2} + a b^{3} - b^{4} + 6 \, {\left(2 \, a^{3} b - 2 \, a^{2} b^{2} - a b^{3} + b^{4}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{2} + 6 \, {\left({\left(2 \, a^{2} b^{2} - a b^{3} - b^{4}\right)} \cosh\left(f x + e\right)^{5} + 2 \, {\left(2 \, a^{3} b - 2 \, a^{2} b^{2} - a b^{3} + b^{4}\right)} \cosh\left(f x + e\right)^{3} - {\left(2 \, a^{3} b - 2 \, a^{2} b^{2} - a b^{3} + b^{4}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{12 \, {\left(a^{2} b^{5} f \cosh\left(f x + e\right)^{8} + 8 \, a^{2} b^{5} f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + a^{2} b^{5} f \sinh\left(f x + e\right)^{8} + a^{2} b^{5} f + 4 \, {\left(2 \, a^{3} b^{4} - a^{2} b^{5}\right)} f \cosh\left(f x + e\right)^{6} + 4 \, {\left(7 \, a^{2} b^{5} f \cosh\left(f x + e\right)^{2} + {\left(2 \, a^{3} b^{4} - a^{2} b^{5}\right)} f\right)} \sinh\left(f x + e\right)^{6} + 2 \, {\left(8 \, a^{4} b^{3} - 8 \, a^{3} b^{4} + 3 \, a^{2} b^{5}\right)} f \cosh\left(f x + e\right)^{4} + 8 \, {\left(7 \, a^{2} b^{5} f \cosh\left(f x + e\right)^{3} + 3 \, {\left(2 \, a^{3} b^{4} - a^{2} b^{5}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(35 \, a^{2} b^{5} f \cosh\left(f x + e\right)^{4} + 30 \, {\left(2 \, a^{3} b^{4} - a^{2} b^{5}\right)} f \cosh\left(f x + e\right)^{2} + {\left(8 \, a^{4} b^{3} - 8 \, a^{3} b^{4} + 3 \, a^{2} b^{5}\right)} f\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(2 \, a^{3} b^{4} - a^{2} b^{5}\right)} f \cosh\left(f x + e\right)^{2} + 8 \, {\left(7 \, a^{2} b^{5} f \cosh\left(f x + e\right)^{5} + 10 \, {\left(2 \, a^{3} b^{4} - a^{2} b^{5}\right)} f \cosh\left(f x + e\right)^{3} + {\left(8 \, a^{4} b^{3} - 8 \, a^{3} b^{4} + 3 \, a^{2} b^{5}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 4 \, {\left(7 \, a^{2} b^{5} f \cosh\left(f x + e\right)^{6} + 15 \, {\left(2 \, a^{3} b^{4} - a^{2} b^{5}\right)} f \cosh\left(f x + e\right)^{4} + 3 \, {\left(8 \, a^{4} b^{3} - 8 \, a^{3} b^{4} + 3 \, a^{2} b^{5}\right)} f \cosh\left(f x + e\right)^{2} + {\left(2 \, a^{3} b^{4} - a^{2} b^{5}\right)} f\right)} \sinh\left(f x + e\right)^{2} + 8 \, {\left(a^{2} b^{5} f \cosh\left(f x + e\right)^{7} + 3 \, {\left(2 \, a^{3} b^{4} - a^{2} b^{5}\right)} f \cosh\left(f x + e\right)^{5} + {\left(8 \, a^{4} b^{3} - 8 \, a^{3} b^{4} + 3 \, a^{2} b^{5}\right)} f \cosh\left(f x + e\right)^{3} + {\left(2 \, a^{3} b^{4} - a^{2} b^{5}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)}}, -\frac{3 \, {\left(a^{2} b^{2} \cosh\left(f x + e\right)^{8} + 8 \, a^{2} b^{2} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + a^{2} b^{2} \sinh\left(f x + e\right)^{8} + 4 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} \cosh\left(f x + e\right)^{6} + 4 \, {\left(7 \, a^{2} b^{2} \cosh\left(f x + e\right)^{2} + 2 \, a^{3} b - a^{2} b^{2}\right)} \sinh\left(f x + e\right)^{6} + 8 \, {\left(7 \, a^{2} b^{2} \cosh\left(f x + e\right)^{3} + 3 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(8 \, a^{4} - 8 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(f x + e\right)^{4} + 2 \, {\left(35 \, a^{2} b^{2} \cosh\left(f x + e\right)^{4} + 8 \, a^{4} - 8 \, a^{3} b + 3 \, a^{2} b^{2} + 30 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{4} + a^{2} b^{2} + 8 \, {\left(7 \, a^{2} b^{2} \cosh\left(f x + e\right)^{5} + 10 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} \cosh\left(f x + e\right)^{3} + {\left(8 \, a^{4} - 8 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 4 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} \cosh\left(f x + e\right)^{2} + 4 \, {\left(7 \, a^{2} b^{2} \cosh\left(f x + e\right)^{6} + 15 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} \cosh\left(f x + e\right)^{4} + 2 \, a^{3} b - a^{2} b^{2} + 3 \, {\left(8 \, a^{4} - 8 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{2} + 8 \, {\left(a^{2} b^{2} \cosh\left(f x + e\right)^{7} + 3 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} \cosh\left(f x + e\right)^{5} + {\left(8 \, a^{4} - 8 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(f x + e\right)^{3} + {\left(2 \, a^{3} b - a^{2} b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{2} {\left({\left(a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(a - b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right) + {\left(a - b\right)} \sinh\left(f x + e\right)^{2} + b\right)} \sqrt{-b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{{\left(a b - b^{2}\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left(a b - b^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(a b - b^{2}\right)} \sinh\left(f x + e\right)^{4} - {\left(3 \, a b - 2 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + {\left(6 \, {\left(a b - b^{2}\right)} \cosh\left(f x + e\right)^{2} - 3 \, a b + 2 \, b^{2}\right)} \sinh\left(f x + e\right)^{2} - b^{2} + 2 \, {\left(2 \, {\left(a b - b^{2}\right)} \cosh\left(f x + e\right)^{3} - {\left(3 \, a b - 2 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)}\right) + 3 \, {\left(a^{2} b^{2} \cosh\left(f x + e\right)^{8} + 8 \, a^{2} b^{2} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + a^{2} b^{2} \sinh\left(f x + e\right)^{8} + 4 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} \cosh\left(f x + e\right)^{6} + 4 \, {\left(7 \, a^{2} b^{2} \cosh\left(f x + e\right)^{2} + 2 \, a^{3} b - a^{2} b^{2}\right)} \sinh\left(f x + e\right)^{6} + 8 \, {\left(7 \, a^{2} b^{2} \cosh\left(f x + e\right)^{3} + 3 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(8 \, a^{4} - 8 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(f x + e\right)^{4} + 2 \, {\left(35 \, a^{2} b^{2} \cosh\left(f x + e\right)^{4} + 8 \, a^{4} - 8 \, a^{3} b + 3 \, a^{2} b^{2} + 30 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{4} + a^{2} b^{2} + 8 \, {\left(7 \, a^{2} b^{2} \cosh\left(f x + e\right)^{5} + 10 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} \cosh\left(f x + e\right)^{3} + {\left(8 \, a^{4} - 8 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 4 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} \cosh\left(f x + e\right)^{2} + 4 \, {\left(7 \, a^{2} b^{2} \cosh\left(f x + e\right)^{6} + 15 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} \cosh\left(f x + e\right)^{4} + 2 \, a^{3} b - a^{2} b^{2} + 3 \, {\left(8 \, a^{4} - 8 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{2} + 8 \, {\left(a^{2} b^{2} \cosh\left(f x + e\right)^{7} + 3 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} \cosh\left(f x + e\right)^{5} + {\left(8 \, a^{4} - 8 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(f x + e\right)^{3} + {\left(2 \, a^{3} b - a^{2} b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} + 1\right)} \sqrt{-b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + 2 \, a - b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}\right) + 4 \, \sqrt{2} {\left({\left(2 \, a^{2} b^{2} - a b^{3} - b^{4}\right)} \cosh\left(f x + e\right)^{6} + 6 \, {\left(2 \, a^{2} b^{2} - a b^{3} - b^{4}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + {\left(2 \, a^{2} b^{2} - a b^{3} - b^{4}\right)} \sinh\left(f x + e\right)^{6} + 3 \, {\left(2 \, a^{3} b - 2 \, a^{2} b^{2} - a b^{3} + b^{4}\right)} \cosh\left(f x + e\right)^{4} + 3 \, {\left(2 \, a^{3} b - 2 \, a^{2} b^{2} - a b^{3} + b^{4} + 5 \, {\left(2 \, a^{2} b^{2} - a b^{3} - b^{4}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{4} - 2 \, a^{2} b^{2} + a b^{3} + b^{4} + 4 \, {\left(5 \, {\left(2 \, a^{2} b^{2} - a b^{3} - b^{4}\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(2 \, a^{3} b - 2 \, a^{2} b^{2} - a b^{3} + b^{4}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} - 3 \, {\left(2 \, a^{3} b - 2 \, a^{2} b^{2} - a b^{3} + b^{4}\right)} \cosh\left(f x + e\right)^{2} + 3 \, {\left(5 \, {\left(2 \, a^{2} b^{2} - a b^{3} - b^{4}\right)} \cosh\left(f x + e\right)^{4} - 2 \, a^{3} b + 2 \, a^{2} b^{2} + a b^{3} - b^{4} + 6 \, {\left(2 \, a^{3} b - 2 \, a^{2} b^{2} - a b^{3} + b^{4}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{2} + 6 \, {\left({\left(2 \, a^{2} b^{2} - a b^{3} - b^{4}\right)} \cosh\left(f x + e\right)^{5} + 2 \, {\left(2 \, a^{3} b - 2 \, a^{2} b^{2} - a b^{3} + b^{4}\right)} \cosh\left(f x + e\right)^{3} - {\left(2 \, a^{3} b - 2 \, a^{2} b^{2} - a b^{3} + b^{4}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{6 \, {\left(a^{2} b^{5} f \cosh\left(f x + e\right)^{8} + 8 \, a^{2} b^{5} f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + a^{2} b^{5} f \sinh\left(f x + e\right)^{8} + a^{2} b^{5} f + 4 \, {\left(2 \, a^{3} b^{4} - a^{2} b^{5}\right)} f \cosh\left(f x + e\right)^{6} + 4 \, {\left(7 \, a^{2} b^{5} f \cosh\left(f x + e\right)^{2} + {\left(2 \, a^{3} b^{4} - a^{2} b^{5}\right)} f\right)} \sinh\left(f x + e\right)^{6} + 2 \, {\left(8 \, a^{4} b^{3} - 8 \, a^{3} b^{4} + 3 \, a^{2} b^{5}\right)} f \cosh\left(f x + e\right)^{4} + 8 \, {\left(7 \, a^{2} b^{5} f \cosh\left(f x + e\right)^{3} + 3 \, {\left(2 \, a^{3} b^{4} - a^{2} b^{5}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(35 \, a^{2} b^{5} f \cosh\left(f x + e\right)^{4} + 30 \, {\left(2 \, a^{3} b^{4} - a^{2} b^{5}\right)} f \cosh\left(f x + e\right)^{2} + {\left(8 \, a^{4} b^{3} - 8 \, a^{3} b^{4} + 3 \, a^{2} b^{5}\right)} f\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(2 \, a^{3} b^{4} - a^{2} b^{5}\right)} f \cosh\left(f x + e\right)^{2} + 8 \, {\left(7 \, a^{2} b^{5} f \cosh\left(f x + e\right)^{5} + 10 \, {\left(2 \, a^{3} b^{4} - a^{2} b^{5}\right)} f \cosh\left(f x + e\right)^{3} + {\left(8 \, a^{4} b^{3} - 8 \, a^{3} b^{4} + 3 \, a^{2} b^{5}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 4 \, {\left(7 \, a^{2} b^{5} f \cosh\left(f x + e\right)^{6} + 15 \, {\left(2 \, a^{3} b^{4} - a^{2} b^{5}\right)} f \cosh\left(f x + e\right)^{4} + 3 \, {\left(8 \, a^{4} b^{3} - 8 \, a^{3} b^{4} + 3 \, a^{2} b^{5}\right)} f \cosh\left(f x + e\right)^{2} + {\left(2 \, a^{3} b^{4} - a^{2} b^{5}\right)} f\right)} \sinh\left(f x + e\right)^{2} + 8 \, {\left(a^{2} b^{5} f \cosh\left(f x + e\right)^{7} + 3 \, {\left(2 \, a^{3} b^{4} - a^{2} b^{5}\right)} f \cosh\left(f x + e\right)^{5} + {\left(8 \, a^{4} b^{3} - 8 \, a^{3} b^{4} + 3 \, a^{2} b^{5}\right)} f \cosh\left(f x + e\right)^{3} + {\left(2 \, a^{3} b^{4} - a^{2} b^{5}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)}}\right]"," ",0,"[1/12*(3*(a^2*b^2*cosh(f*x + e)^8 + 8*a^2*b^2*cosh(f*x + e)*sinh(f*x + e)^7 + a^2*b^2*sinh(f*x + e)^8 + 4*(2*a^3*b - a^2*b^2)*cosh(f*x + e)^6 + 4*(7*a^2*b^2*cosh(f*x + e)^2 + 2*a^3*b - a^2*b^2)*sinh(f*x + e)^6 + 8*(7*a^2*b^2*cosh(f*x + e)^3 + 3*(2*a^3*b - a^2*b^2)*cosh(f*x + e))*sinh(f*x + e)^5 + 2*(8*a^4 - 8*a^3*b + 3*a^2*b^2)*cosh(f*x + e)^4 + 2*(35*a^2*b^2*cosh(f*x + e)^4 + 8*a^4 - 8*a^3*b + 3*a^2*b^2 + 30*(2*a^3*b - a^2*b^2)*cosh(f*x + e)^2)*sinh(f*x + e)^4 + a^2*b^2 + 8*(7*a^2*b^2*cosh(f*x + e)^5 + 10*(2*a^3*b - a^2*b^2)*cosh(f*x + e)^3 + (8*a^4 - 8*a^3*b + 3*a^2*b^2)*cosh(f*x + e))*sinh(f*x + e)^3 + 4*(2*a^3*b - a^2*b^2)*cosh(f*x + e)^2 + 4*(7*a^2*b^2*cosh(f*x + e)^6 + 15*(2*a^3*b - a^2*b^2)*cosh(f*x + e)^4 + 2*a^3*b - a^2*b^2 + 3*(8*a^4 - 8*a^3*b + 3*a^2*b^2)*cosh(f*x + e)^2)*sinh(f*x + e)^2 + 8*(a^2*b^2*cosh(f*x + e)^7 + 3*(2*a^3*b - a^2*b^2)*cosh(f*x + e)^5 + (8*a^4 - 8*a^3*b + 3*a^2*b^2)*cosh(f*x + e)^3 + (2*a^3*b - a^2*b^2)*cosh(f*x + e))*sinh(f*x + e))*sqrt(b)*log(-((a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^8 + 8*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)*sinh(f*x + e)^7 + (a^2*b - 2*a*b^2 + b^3)*sinh(f*x + e)^8 + 2*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e)^6 + 2*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3 + 14*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^6 + 4*(14*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^3 + 3*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e))*sinh(f*x + e)^5 + (9*a^2*b - 14*a*b^2 + 6*b^3)*cosh(f*x + e)^4 + (70*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^4 + 9*a^2*b - 14*a*b^2 + 6*b^3 + 30*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^4 + 4*(14*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^5 + 10*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e)^3 + (9*a^2*b - 14*a*b^2 + 6*b^3)*cosh(f*x + e))*sinh(f*x + e)^3 + b^3 + 2*(3*a*b^2 - 2*b^3)*cosh(f*x + e)^2 + 2*(14*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^6 + 15*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e)^4 + 3*a*b^2 - 2*b^3 + 3*(9*a^2*b - 14*a*b^2 + 6*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^2 + sqrt(2)*((a^2 - 2*a*b + b^2)*cosh(f*x + e)^6 + 6*(a^2 - 2*a*b + b^2)*cosh(f*x + e)*sinh(f*x + e)^5 + (a^2 - 2*a*b + b^2)*sinh(f*x + e)^6 - 3*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^4 + 3*(5*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^2 - a^2 + 2*a*b - b^2)*sinh(f*x + e)^4 + 4*(5*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^3 - 3*(a^2 - 2*a*b + b^2)*cosh(f*x + e))*sinh(f*x + e)^3 - (4*a*b - 3*b^2)*cosh(f*x + e)^2 + (15*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^4 - 18*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^2 - 4*a*b + 3*b^2)*sinh(f*x + e)^2 - b^2 + 2*(3*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^5 - 6*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^3 - (4*a*b - 3*b^2)*cosh(f*x + e))*sinh(f*x + e))*sqrt(b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + 4*(2*(a^2*b - 2*a*b^2 + b^3)*cosh(f*x + e)^7 + 3*(a^3 - 4*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e)^5 + (9*a^2*b - 14*a*b^2 + 6*b^3)*cosh(f*x + e)^3 + (3*a*b^2 - 2*b^3)*cosh(f*x + e))*sinh(f*x + e))/(cosh(f*x + e)^6 + 6*cosh(f*x + e)^5*sinh(f*x + e) + 15*cosh(f*x + e)^4*sinh(f*x + e)^2 + 20*cosh(f*x + e)^3*sinh(f*x + e)^3 + 15*cosh(f*x + e)^2*sinh(f*x + e)^4 + 6*cosh(f*x + e)*sinh(f*x + e)^5 + sinh(f*x + e)^6)) + 3*(a^2*b^2*cosh(f*x + e)^8 + 8*a^2*b^2*cosh(f*x + e)*sinh(f*x + e)^7 + a^2*b^2*sinh(f*x + e)^8 + 4*(2*a^3*b - a^2*b^2)*cosh(f*x + e)^6 + 4*(7*a^2*b^2*cosh(f*x + e)^2 + 2*a^3*b - a^2*b^2)*sinh(f*x + e)^6 + 8*(7*a^2*b^2*cosh(f*x + e)^3 + 3*(2*a^3*b - a^2*b^2)*cosh(f*x + e))*sinh(f*x + e)^5 + 2*(8*a^4 - 8*a^3*b + 3*a^2*b^2)*cosh(f*x + e)^4 + 2*(35*a^2*b^2*cosh(f*x + e)^4 + 8*a^4 - 8*a^3*b + 3*a^2*b^2 + 30*(2*a^3*b - a^2*b^2)*cosh(f*x + e)^2)*sinh(f*x + e)^4 + a^2*b^2 + 8*(7*a^2*b^2*cosh(f*x + e)^5 + 10*(2*a^3*b - a^2*b^2)*cosh(f*x + e)^3 + (8*a^4 - 8*a^3*b + 3*a^2*b^2)*cosh(f*x + e))*sinh(f*x + e)^3 + 4*(2*a^3*b - a^2*b^2)*cosh(f*x + e)^2 + 4*(7*a^2*b^2*cosh(f*x + e)^6 + 15*(2*a^3*b - a^2*b^2)*cosh(f*x + e)^4 + 2*a^3*b - a^2*b^2 + 3*(8*a^4 - 8*a^3*b + 3*a^2*b^2)*cosh(f*x + e)^2)*sinh(f*x + e)^2 + 8*(a^2*b^2*cosh(f*x + e)^7 + 3*(2*a^3*b - a^2*b^2)*cosh(f*x + e)^5 + (8*a^4 - 8*a^3*b + 3*a^2*b^2)*cosh(f*x + e)^3 + (2*a^3*b - a^2*b^2)*cosh(f*x + e))*sinh(f*x + e))*sqrt(b)*log((b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*a*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + a)*sinh(f*x + e)^2 + sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 + 1)*sqrt(b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + 4*(b*cosh(f*x + e)^3 + a*cosh(f*x + e))*sinh(f*x + e) + b)/(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) - 8*sqrt(2)*((2*a^2*b^2 - a*b^3 - b^4)*cosh(f*x + e)^6 + 6*(2*a^2*b^2 - a*b^3 - b^4)*cosh(f*x + e)*sinh(f*x + e)^5 + (2*a^2*b^2 - a*b^3 - b^4)*sinh(f*x + e)^6 + 3*(2*a^3*b - 2*a^2*b^2 - a*b^3 + b^4)*cosh(f*x + e)^4 + 3*(2*a^3*b - 2*a^2*b^2 - a*b^3 + b^4 + 5*(2*a^2*b^2 - a*b^3 - b^4)*cosh(f*x + e)^2)*sinh(f*x + e)^4 - 2*a^2*b^2 + a*b^3 + b^4 + 4*(5*(2*a^2*b^2 - a*b^3 - b^4)*cosh(f*x + e)^3 + 3*(2*a^3*b - 2*a^2*b^2 - a*b^3 + b^4)*cosh(f*x + e))*sinh(f*x + e)^3 - 3*(2*a^3*b - 2*a^2*b^2 - a*b^3 + b^4)*cosh(f*x + e)^2 + 3*(5*(2*a^2*b^2 - a*b^3 - b^4)*cosh(f*x + e)^4 - 2*a^3*b + 2*a^2*b^2 + a*b^3 - b^4 + 6*(2*a^3*b - 2*a^2*b^2 - a*b^3 + b^4)*cosh(f*x + e)^2)*sinh(f*x + e)^2 + 6*((2*a^2*b^2 - a*b^3 - b^4)*cosh(f*x + e)^5 + 2*(2*a^3*b - 2*a^2*b^2 - a*b^3 + b^4)*cosh(f*x + e)^3 - (2*a^3*b - 2*a^2*b^2 - a*b^3 + b^4)*cosh(f*x + e))*sinh(f*x + e))*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/(a^2*b^5*f*cosh(f*x + e)^8 + 8*a^2*b^5*f*cosh(f*x + e)*sinh(f*x + e)^7 + a^2*b^5*f*sinh(f*x + e)^8 + a^2*b^5*f + 4*(2*a^3*b^4 - a^2*b^5)*f*cosh(f*x + e)^6 + 4*(7*a^2*b^5*f*cosh(f*x + e)^2 + (2*a^3*b^4 - a^2*b^5)*f)*sinh(f*x + e)^6 + 2*(8*a^4*b^3 - 8*a^3*b^4 + 3*a^2*b^5)*f*cosh(f*x + e)^4 + 8*(7*a^2*b^5*f*cosh(f*x + e)^3 + 3*(2*a^3*b^4 - a^2*b^5)*f*cosh(f*x + e))*sinh(f*x + e)^5 + 2*(35*a^2*b^5*f*cosh(f*x + e)^4 + 30*(2*a^3*b^4 - a^2*b^5)*f*cosh(f*x + e)^2 + (8*a^4*b^3 - 8*a^3*b^4 + 3*a^2*b^5)*f)*sinh(f*x + e)^4 + 4*(2*a^3*b^4 - a^2*b^5)*f*cosh(f*x + e)^2 + 8*(7*a^2*b^5*f*cosh(f*x + e)^5 + 10*(2*a^3*b^4 - a^2*b^5)*f*cosh(f*x + e)^3 + (8*a^4*b^3 - 8*a^3*b^4 + 3*a^2*b^5)*f*cosh(f*x + e))*sinh(f*x + e)^3 + 4*(7*a^2*b^5*f*cosh(f*x + e)^6 + 15*(2*a^3*b^4 - a^2*b^5)*f*cosh(f*x + e)^4 + 3*(8*a^4*b^3 - 8*a^3*b^4 + 3*a^2*b^5)*f*cosh(f*x + e)^2 + (2*a^3*b^4 - a^2*b^5)*f)*sinh(f*x + e)^2 + 8*(a^2*b^5*f*cosh(f*x + e)^7 + 3*(2*a^3*b^4 - a^2*b^5)*f*cosh(f*x + e)^5 + (8*a^4*b^3 - 8*a^3*b^4 + 3*a^2*b^5)*f*cosh(f*x + e)^3 + (2*a^3*b^4 - a^2*b^5)*f*cosh(f*x + e))*sinh(f*x + e)), -1/6*(3*(a^2*b^2*cosh(f*x + e)^8 + 8*a^2*b^2*cosh(f*x + e)*sinh(f*x + e)^7 + a^2*b^2*sinh(f*x + e)^8 + 4*(2*a^3*b - a^2*b^2)*cosh(f*x + e)^6 + 4*(7*a^2*b^2*cosh(f*x + e)^2 + 2*a^3*b - a^2*b^2)*sinh(f*x + e)^6 + 8*(7*a^2*b^2*cosh(f*x + e)^3 + 3*(2*a^3*b - a^2*b^2)*cosh(f*x + e))*sinh(f*x + e)^5 + 2*(8*a^4 - 8*a^3*b + 3*a^2*b^2)*cosh(f*x + e)^4 + 2*(35*a^2*b^2*cosh(f*x + e)^4 + 8*a^4 - 8*a^3*b + 3*a^2*b^2 + 30*(2*a^3*b - a^2*b^2)*cosh(f*x + e)^2)*sinh(f*x + e)^4 + a^2*b^2 + 8*(7*a^2*b^2*cosh(f*x + e)^5 + 10*(2*a^3*b - a^2*b^2)*cosh(f*x + e)^3 + (8*a^4 - 8*a^3*b + 3*a^2*b^2)*cosh(f*x + e))*sinh(f*x + e)^3 + 4*(2*a^3*b - a^2*b^2)*cosh(f*x + e)^2 + 4*(7*a^2*b^2*cosh(f*x + e)^6 + 15*(2*a^3*b - a^2*b^2)*cosh(f*x + e)^4 + 2*a^3*b - a^2*b^2 + 3*(8*a^4 - 8*a^3*b + 3*a^2*b^2)*cosh(f*x + e)^2)*sinh(f*x + e)^2 + 8*(a^2*b^2*cosh(f*x + e)^7 + 3*(2*a^3*b - a^2*b^2)*cosh(f*x + e)^5 + (8*a^4 - 8*a^3*b + 3*a^2*b^2)*cosh(f*x + e)^3 + (2*a^3*b - a^2*b^2)*cosh(f*x + e))*sinh(f*x + e))*sqrt(-b)*arctan(sqrt(2)*((a - b)*cosh(f*x + e)^2 + 2*(a - b)*cosh(f*x + e)*sinh(f*x + e) + (a - b)*sinh(f*x + e)^2 + b)*sqrt(-b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/((a*b - b^2)*cosh(f*x + e)^4 + 4*(a*b - b^2)*cosh(f*x + e)*sinh(f*x + e)^3 + (a*b - b^2)*sinh(f*x + e)^4 - (3*a*b - 2*b^2)*cosh(f*x + e)^2 + (6*(a*b - b^2)*cosh(f*x + e)^2 - 3*a*b + 2*b^2)*sinh(f*x + e)^2 - b^2 + 2*(2*(a*b - b^2)*cosh(f*x + e)^3 - (3*a*b - 2*b^2)*cosh(f*x + e))*sinh(f*x + e))) + 3*(a^2*b^2*cosh(f*x + e)^8 + 8*a^2*b^2*cosh(f*x + e)*sinh(f*x + e)^7 + a^2*b^2*sinh(f*x + e)^8 + 4*(2*a^3*b - a^2*b^2)*cosh(f*x + e)^6 + 4*(7*a^2*b^2*cosh(f*x + e)^2 + 2*a^3*b - a^2*b^2)*sinh(f*x + e)^6 + 8*(7*a^2*b^2*cosh(f*x + e)^3 + 3*(2*a^3*b - a^2*b^2)*cosh(f*x + e))*sinh(f*x + e)^5 + 2*(8*a^4 - 8*a^3*b + 3*a^2*b^2)*cosh(f*x + e)^4 + 2*(35*a^2*b^2*cosh(f*x + e)^4 + 8*a^4 - 8*a^3*b + 3*a^2*b^2 + 30*(2*a^3*b - a^2*b^2)*cosh(f*x + e)^2)*sinh(f*x + e)^4 + a^2*b^2 + 8*(7*a^2*b^2*cosh(f*x + e)^5 + 10*(2*a^3*b - a^2*b^2)*cosh(f*x + e)^3 + (8*a^4 - 8*a^3*b + 3*a^2*b^2)*cosh(f*x + e))*sinh(f*x + e)^3 + 4*(2*a^3*b - a^2*b^2)*cosh(f*x + e)^2 + 4*(7*a^2*b^2*cosh(f*x + e)^6 + 15*(2*a^3*b - a^2*b^2)*cosh(f*x + e)^4 + 2*a^3*b - a^2*b^2 + 3*(8*a^4 - 8*a^3*b + 3*a^2*b^2)*cosh(f*x + e)^2)*sinh(f*x + e)^2 + 8*(a^2*b^2*cosh(f*x + e)^7 + 3*(2*a^3*b - a^2*b^2)*cosh(f*x + e)^5 + (8*a^4 - 8*a^3*b + 3*a^2*b^2)*cosh(f*x + e)^3 + (2*a^3*b - a^2*b^2)*cosh(f*x + e))*sinh(f*x + e))*sqrt(-b)*arctan(sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 + 1)*sqrt(-b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/(b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(2*a - b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 2*a - b)*sinh(f*x + e)^2 + 4*(b*cosh(f*x + e)^3 + (2*a - b)*cosh(f*x + e))*sinh(f*x + e) + b)) + 4*sqrt(2)*((2*a^2*b^2 - a*b^3 - b^4)*cosh(f*x + e)^6 + 6*(2*a^2*b^2 - a*b^3 - b^4)*cosh(f*x + e)*sinh(f*x + e)^5 + (2*a^2*b^2 - a*b^3 - b^4)*sinh(f*x + e)^6 + 3*(2*a^3*b - 2*a^2*b^2 - a*b^3 + b^4)*cosh(f*x + e)^4 + 3*(2*a^3*b - 2*a^2*b^2 - a*b^3 + b^4 + 5*(2*a^2*b^2 - a*b^3 - b^4)*cosh(f*x + e)^2)*sinh(f*x + e)^4 - 2*a^2*b^2 + a*b^3 + b^4 + 4*(5*(2*a^2*b^2 - a*b^3 - b^4)*cosh(f*x + e)^3 + 3*(2*a^3*b - 2*a^2*b^2 - a*b^3 + b^4)*cosh(f*x + e))*sinh(f*x + e)^3 - 3*(2*a^3*b - 2*a^2*b^2 - a*b^3 + b^4)*cosh(f*x + e)^2 + 3*(5*(2*a^2*b^2 - a*b^3 - b^4)*cosh(f*x + e)^4 - 2*a^3*b + 2*a^2*b^2 + a*b^3 - b^4 + 6*(2*a^3*b - 2*a^2*b^2 - a*b^3 + b^4)*cosh(f*x + e)^2)*sinh(f*x + e)^2 + 6*((2*a^2*b^2 - a*b^3 - b^4)*cosh(f*x + e)^5 + 2*(2*a^3*b - 2*a^2*b^2 - a*b^3 + b^4)*cosh(f*x + e)^3 - (2*a^3*b - 2*a^2*b^2 - a*b^3 + b^4)*cosh(f*x + e))*sinh(f*x + e))*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/(a^2*b^5*f*cosh(f*x + e)^8 + 8*a^2*b^5*f*cosh(f*x + e)*sinh(f*x + e)^7 + a^2*b^5*f*sinh(f*x + e)^8 + a^2*b^5*f + 4*(2*a^3*b^4 - a^2*b^5)*f*cosh(f*x + e)^6 + 4*(7*a^2*b^5*f*cosh(f*x + e)^2 + (2*a^3*b^4 - a^2*b^5)*f)*sinh(f*x + e)^6 + 2*(8*a^4*b^3 - 8*a^3*b^4 + 3*a^2*b^5)*f*cosh(f*x + e)^4 + 8*(7*a^2*b^5*f*cosh(f*x + e)^3 + 3*(2*a^3*b^4 - a^2*b^5)*f*cosh(f*x + e))*sinh(f*x + e)^5 + 2*(35*a^2*b^5*f*cosh(f*x + e)^4 + 30*(2*a^3*b^4 - a^2*b^5)*f*cosh(f*x + e)^2 + (8*a^4*b^3 - 8*a^3*b^4 + 3*a^2*b^5)*f)*sinh(f*x + e)^4 + 4*(2*a^3*b^4 - a^2*b^5)*f*cosh(f*x + e)^2 + 8*(7*a^2*b^5*f*cosh(f*x + e)^5 + 10*(2*a^3*b^4 - a^2*b^5)*f*cosh(f*x + e)^3 + (8*a^4*b^3 - 8*a^3*b^4 + 3*a^2*b^5)*f*cosh(f*x + e))*sinh(f*x + e)^3 + 4*(7*a^2*b^5*f*cosh(f*x + e)^6 + 15*(2*a^3*b^4 - a^2*b^5)*f*cosh(f*x + e)^4 + 3*(8*a^4*b^3 - 8*a^3*b^4 + 3*a^2*b^5)*f*cosh(f*x + e)^2 + (2*a^3*b^4 - a^2*b^5)*f)*sinh(f*x + e)^2 + 8*(a^2*b^5*f*cosh(f*x + e)^7 + 3*(2*a^3*b^4 - a^2*b^5)*f*cosh(f*x + e)^5 + (8*a^4*b^3 - 8*a^3*b^4 + 3*a^2*b^5)*f*cosh(f*x + e)^3 + (2*a^3*b^4 - a^2*b^5)*f*cosh(f*x + e))*sinh(f*x + e))]","B",0
392,1,945,0,0.989960," ","integrate(cosh(f*x+e)^3/(a+b*sinh(f*x+e)^2)^(5/2),x, algorithm=""fricas"")","\frac{\sqrt{2} {\left({\left(a + 2 \, b\right)} \cosh\left(f x + e\right)^{6} + 6 \, {\left(a + 2 \, b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + {\left(a + 2 \, b\right)} \sinh\left(f x + e\right)^{6} + 3 \, {\left(3 \, a - 2 \, b\right)} \cosh\left(f x + e\right)^{4} + 3 \, {\left(5 \, {\left(a + 2 \, b\right)} \cosh\left(f x + e\right)^{2} + 3 \, a - 2 \, b\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(5 \, {\left(a + 2 \, b\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(3 \, a - 2 \, b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} - 3 \, {\left(3 \, a - 2 \, b\right)} \cosh\left(f x + e\right)^{2} + 3 \, {\left(5 \, {\left(a + 2 \, b\right)} \cosh\left(f x + e\right)^{4} + 6 \, {\left(3 \, a - 2 \, b\right)} \cosh\left(f x + e\right)^{2} - 3 \, a + 2 \, b\right)} \sinh\left(f x + e\right)^{2} + 6 \, {\left({\left(a + 2 \, b\right)} \cosh\left(f x + e\right)^{5} + 2 \, {\left(3 \, a - 2 \, b\right)} \cosh\left(f x + e\right)^{3} - {\left(3 \, a - 2 \, b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) - a - 2 \, b\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{3 \, {\left(a^{2} b^{2} f \cosh\left(f x + e\right)^{8} + 8 \, a^{2} b^{2} f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + a^{2} b^{2} f \sinh\left(f x + e\right)^{8} + 4 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} f \cosh\left(f x + e\right)^{6} + 4 \, {\left(7 \, a^{2} b^{2} f \cosh\left(f x + e\right)^{2} + {\left(2 \, a^{3} b - a^{2} b^{2}\right)} f\right)} \sinh\left(f x + e\right)^{6} + 2 \, {\left(8 \, a^{4} - 8 \, a^{3} b + 3 \, a^{2} b^{2}\right)} f \cosh\left(f x + e\right)^{4} + 8 \, {\left(7 \, a^{2} b^{2} f \cosh\left(f x + e\right)^{3} + 3 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + a^{2} b^{2} f + 2 \, {\left(35 \, a^{2} b^{2} f \cosh\left(f x + e\right)^{4} + 30 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} f \cosh\left(f x + e\right)^{2} + {\left(8 \, a^{4} - 8 \, a^{3} b + 3 \, a^{2} b^{2}\right)} f\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} f \cosh\left(f x + e\right)^{2} + 8 \, {\left(7 \, a^{2} b^{2} f \cosh\left(f x + e\right)^{5} + 10 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} f \cosh\left(f x + e\right)^{3} + {\left(8 \, a^{4} - 8 \, a^{3} b + 3 \, a^{2} b^{2}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 4 \, {\left(7 \, a^{2} b^{2} f \cosh\left(f x + e\right)^{6} + 15 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} f \cosh\left(f x + e\right)^{4} + 3 \, {\left(8 \, a^{4} - 8 \, a^{3} b + 3 \, a^{2} b^{2}\right)} f \cosh\left(f x + e\right)^{2} + {\left(2 \, a^{3} b - a^{2} b^{2}\right)} f\right)} \sinh\left(f x + e\right)^{2} + 8 \, {\left(a^{2} b^{2} f \cosh\left(f x + e\right)^{7} + 3 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} f \cosh\left(f x + e\right)^{5} + {\left(8 \, a^{4} - 8 \, a^{3} b + 3 \, a^{2} b^{2}\right)} f \cosh\left(f x + e\right)^{3} + {\left(2 \, a^{3} b - a^{2} b^{2}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)}}"," ",0,"1/3*sqrt(2)*((a + 2*b)*cosh(f*x + e)^6 + 6*(a + 2*b)*cosh(f*x + e)*sinh(f*x + e)^5 + (a + 2*b)*sinh(f*x + e)^6 + 3*(3*a - 2*b)*cosh(f*x + e)^4 + 3*(5*(a + 2*b)*cosh(f*x + e)^2 + 3*a - 2*b)*sinh(f*x + e)^4 + 4*(5*(a + 2*b)*cosh(f*x + e)^3 + 3*(3*a - 2*b)*cosh(f*x + e))*sinh(f*x + e)^3 - 3*(3*a - 2*b)*cosh(f*x + e)^2 + 3*(5*(a + 2*b)*cosh(f*x + e)^4 + 6*(3*a - 2*b)*cosh(f*x + e)^2 - 3*a + 2*b)*sinh(f*x + e)^2 + 6*((a + 2*b)*cosh(f*x + e)^5 + 2*(3*a - 2*b)*cosh(f*x + e)^3 - (3*a - 2*b)*cosh(f*x + e))*sinh(f*x + e) - a - 2*b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/(a^2*b^2*f*cosh(f*x + e)^8 + 8*a^2*b^2*f*cosh(f*x + e)*sinh(f*x + e)^7 + a^2*b^2*f*sinh(f*x + e)^8 + 4*(2*a^3*b - a^2*b^2)*f*cosh(f*x + e)^6 + 4*(7*a^2*b^2*f*cosh(f*x + e)^2 + (2*a^3*b - a^2*b^2)*f)*sinh(f*x + e)^6 + 2*(8*a^4 - 8*a^3*b + 3*a^2*b^2)*f*cosh(f*x + e)^4 + 8*(7*a^2*b^2*f*cosh(f*x + e)^3 + 3*(2*a^3*b - a^2*b^2)*f*cosh(f*x + e))*sinh(f*x + e)^5 + a^2*b^2*f + 2*(35*a^2*b^2*f*cosh(f*x + e)^4 + 30*(2*a^3*b - a^2*b^2)*f*cosh(f*x + e)^2 + (8*a^4 - 8*a^3*b + 3*a^2*b^2)*f)*sinh(f*x + e)^4 + 4*(2*a^3*b - a^2*b^2)*f*cosh(f*x + e)^2 + 8*(7*a^2*b^2*f*cosh(f*x + e)^5 + 10*(2*a^3*b - a^2*b^2)*f*cosh(f*x + e)^3 + (8*a^4 - 8*a^3*b + 3*a^2*b^2)*f*cosh(f*x + e))*sinh(f*x + e)^3 + 4*(7*a^2*b^2*f*cosh(f*x + e)^6 + 15*(2*a^3*b - a^2*b^2)*f*cosh(f*x + e)^4 + 3*(8*a^4 - 8*a^3*b + 3*a^2*b^2)*f*cosh(f*x + e)^2 + (2*a^3*b - a^2*b^2)*f)*sinh(f*x + e)^2 + 8*(a^2*b^2*f*cosh(f*x + e)^7 + 3*(2*a^3*b - a^2*b^2)*f*cosh(f*x + e)^5 + (8*a^4 - 8*a^3*b + 3*a^2*b^2)*f*cosh(f*x + e)^3 + (2*a^3*b - a^2*b^2)*f*cosh(f*x + e))*sinh(f*x + e))","B",0
393,1,912,0,2.052720," ","integrate(cosh(f*x+e)/(a+b*sinh(f*x+e)^2)^(5/2),x, algorithm=""fricas"")","\frac{2 \, \sqrt{2} {\left(b \cosh\left(f x + e\right)^{6} + 6 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + b \sinh\left(f x + e\right)^{6} + 3 \, {\left(2 \, a - b\right)} \cosh\left(f x + e\right)^{4} + 3 \, {\left(5 \, b \cosh\left(f x + e\right)^{2} + 2 \, a - b\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(5 \, b \cosh\left(f x + e\right)^{3} + 3 \, {\left(2 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} - 3 \, {\left(2 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 3 \, {\left(5 \, b \cosh\left(f x + e\right)^{4} + 6 \, {\left(2 \, a - b\right)} \cosh\left(f x + e\right)^{2} - 2 \, a + b\right)} \sinh\left(f x + e\right)^{2} + 6 \, {\left(b \cosh\left(f x + e\right)^{5} + 2 \, {\left(2 \, a - b\right)} \cosh\left(f x + e\right)^{3} - {\left(2 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) - b\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{3 \, {\left(a^{2} b^{2} f \cosh\left(f x + e\right)^{8} + 8 \, a^{2} b^{2} f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + a^{2} b^{2} f \sinh\left(f x + e\right)^{8} + 4 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} f \cosh\left(f x + e\right)^{6} + 4 \, {\left(7 \, a^{2} b^{2} f \cosh\left(f x + e\right)^{2} + {\left(2 \, a^{3} b - a^{2} b^{2}\right)} f\right)} \sinh\left(f x + e\right)^{6} + 2 \, {\left(8 \, a^{4} - 8 \, a^{3} b + 3 \, a^{2} b^{2}\right)} f \cosh\left(f x + e\right)^{4} + 8 \, {\left(7 \, a^{2} b^{2} f \cosh\left(f x + e\right)^{3} + 3 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + a^{2} b^{2} f + 2 \, {\left(35 \, a^{2} b^{2} f \cosh\left(f x + e\right)^{4} + 30 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} f \cosh\left(f x + e\right)^{2} + {\left(8 \, a^{4} - 8 \, a^{3} b + 3 \, a^{2} b^{2}\right)} f\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} f \cosh\left(f x + e\right)^{2} + 8 \, {\left(7 \, a^{2} b^{2} f \cosh\left(f x + e\right)^{5} + 10 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} f \cosh\left(f x + e\right)^{3} + {\left(8 \, a^{4} - 8 \, a^{3} b + 3 \, a^{2} b^{2}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 4 \, {\left(7 \, a^{2} b^{2} f \cosh\left(f x + e\right)^{6} + 15 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} f \cosh\left(f x + e\right)^{4} + 3 \, {\left(8 \, a^{4} - 8 \, a^{3} b + 3 \, a^{2} b^{2}\right)} f \cosh\left(f x + e\right)^{2} + {\left(2 \, a^{3} b - a^{2} b^{2}\right)} f\right)} \sinh\left(f x + e\right)^{2} + 8 \, {\left(a^{2} b^{2} f \cosh\left(f x + e\right)^{7} + 3 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} f \cosh\left(f x + e\right)^{5} + {\left(8 \, a^{4} - 8 \, a^{3} b + 3 \, a^{2} b^{2}\right)} f \cosh\left(f x + e\right)^{3} + {\left(2 \, a^{3} b - a^{2} b^{2}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)}}"," ",0,"2/3*sqrt(2)*(b*cosh(f*x + e)^6 + 6*b*cosh(f*x + e)*sinh(f*x + e)^5 + b*sinh(f*x + e)^6 + 3*(2*a - b)*cosh(f*x + e)^4 + 3*(5*b*cosh(f*x + e)^2 + 2*a - b)*sinh(f*x + e)^4 + 4*(5*b*cosh(f*x + e)^3 + 3*(2*a - b)*cosh(f*x + e))*sinh(f*x + e)^3 - 3*(2*a - b)*cosh(f*x + e)^2 + 3*(5*b*cosh(f*x + e)^4 + 6*(2*a - b)*cosh(f*x + e)^2 - 2*a + b)*sinh(f*x + e)^2 + 6*(b*cosh(f*x + e)^5 + 2*(2*a - b)*cosh(f*x + e)^3 - (2*a - b)*cosh(f*x + e))*sinh(f*x + e) - b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/(a^2*b^2*f*cosh(f*x + e)^8 + 8*a^2*b^2*f*cosh(f*x + e)*sinh(f*x + e)^7 + a^2*b^2*f*sinh(f*x + e)^8 + 4*(2*a^3*b - a^2*b^2)*f*cosh(f*x + e)^6 + 4*(7*a^2*b^2*f*cosh(f*x + e)^2 + (2*a^3*b - a^2*b^2)*f)*sinh(f*x + e)^6 + 2*(8*a^4 - 8*a^3*b + 3*a^2*b^2)*f*cosh(f*x + e)^4 + 8*(7*a^2*b^2*f*cosh(f*x + e)^3 + 3*(2*a^3*b - a^2*b^2)*f*cosh(f*x + e))*sinh(f*x + e)^5 + a^2*b^2*f + 2*(35*a^2*b^2*f*cosh(f*x + e)^4 + 30*(2*a^3*b - a^2*b^2)*f*cosh(f*x + e)^2 + (8*a^4 - 8*a^3*b + 3*a^2*b^2)*f)*sinh(f*x + e)^4 + 4*(2*a^3*b - a^2*b^2)*f*cosh(f*x + e)^2 + 8*(7*a^2*b^2*f*cosh(f*x + e)^5 + 10*(2*a^3*b - a^2*b^2)*f*cosh(f*x + e)^3 + (8*a^4 - 8*a^3*b + 3*a^2*b^2)*f*cosh(f*x + e))*sinh(f*x + e)^3 + 4*(7*a^2*b^2*f*cosh(f*x + e)^6 + 15*(2*a^3*b - a^2*b^2)*f*cosh(f*x + e)^4 + 3*(8*a^4 - 8*a^3*b + 3*a^2*b^2)*f*cosh(f*x + e)^2 + (2*a^3*b - a^2*b^2)*f)*sinh(f*x + e)^2 + 8*(a^2*b^2*f*cosh(f*x + e)^7 + 3*(2*a^3*b - a^2*b^2)*f*cosh(f*x + e)^5 + (8*a^4 - 8*a^3*b + 3*a^2*b^2)*f*cosh(f*x + e)^3 + (2*a^3*b - a^2*b^2)*f*cosh(f*x + e))*sinh(f*x + e))","B",0
394,1,5396,0,1.236583," ","integrate(sech(f*x+e)/(a+b*sinh(f*x+e)^2)^(5/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left(a^{2} b^{2} \cosh\left(f x + e\right)^{8} + 8 \, a^{2} b^{2} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + a^{2} b^{2} \sinh\left(f x + e\right)^{8} + 4 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} \cosh\left(f x + e\right)^{6} + 4 \, {\left(7 \, a^{2} b^{2} \cosh\left(f x + e\right)^{2} + 2 \, a^{3} b - a^{2} b^{2}\right)} \sinh\left(f x + e\right)^{6} + 8 \, {\left(7 \, a^{2} b^{2} \cosh\left(f x + e\right)^{3} + 3 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(8 \, a^{4} - 8 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(f x + e\right)^{4} + 2 \, {\left(35 \, a^{2} b^{2} \cosh\left(f x + e\right)^{4} + 8 \, a^{4} - 8 \, a^{3} b + 3 \, a^{2} b^{2} + 30 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{4} + a^{2} b^{2} + 8 \, {\left(7 \, a^{2} b^{2} \cosh\left(f x + e\right)^{5} + 10 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} \cosh\left(f x + e\right)^{3} + {\left(8 \, a^{4} - 8 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 4 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} \cosh\left(f x + e\right)^{2} + 4 \, {\left(7 \, a^{2} b^{2} \cosh\left(f x + e\right)^{6} + 15 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} \cosh\left(f x + e\right)^{4} + 2 \, a^{3} b - a^{2} b^{2} + 3 \, {\left(8 \, a^{4} - 8 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{2} + 8 \, {\left(a^{2} b^{2} \cosh\left(f x + e\right)^{7} + 3 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} \cosh\left(f x + e\right)^{5} + {\left(8 \, a^{4} - 8 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(f x + e\right)^{3} + {\left(2 \, a^{3} b - a^{2} b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{-a + b} \log\left(\frac{{\left(a - 2 \, b\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left(a - 2 \, b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(a - 2 \, b\right)} \sinh\left(f x + e\right)^{4} - 2 \, {\left(3 \, a - 2 \, b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, {\left(a - 2 \, b\right)} \cosh\left(f x + e\right)^{2} - 3 \, a + 2 \, b\right)} \sinh\left(f x + e\right)^{2} - 2 \, \sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} - 1\right)} \sqrt{-a + b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} + 4 \, {\left({\left(a - 2 \, b\right)} \cosh\left(f x + e\right)^{3} - {\left(3 \, a - 2 \, b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + a - 2 \, b}{\cosh\left(f x + e\right)^{4} + 4 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + \sinh\left(f x + e\right)^{4} + 2 \, {\left(3 \, \cosh\left(f x + e\right)^{2} + 1\right)} \sinh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right)^{2} + 4 \, {\left(\cosh\left(f x + e\right)^{3} + \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + 1}\right) + 2 \, \sqrt{2} {\left({\left(5 \, a^{2} b^{2} - 7 \, a b^{3} + 2 \, b^{4}\right)} \cosh\left(f x + e\right)^{6} + 6 \, {\left(5 \, a^{2} b^{2} - 7 \, a b^{3} + 2 \, b^{4}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + {\left(5 \, a^{2} b^{2} - 7 \, a b^{3} + 2 \, b^{4}\right)} \sinh\left(f x + e\right)^{6} + 3 \, {\left(8 \, a^{3} b - 17 \, a^{2} b^{2} + 11 \, a b^{3} - 2 \, b^{4}\right)} \cosh\left(f x + e\right)^{4} + 3 \, {\left(8 \, a^{3} b - 17 \, a^{2} b^{2} + 11 \, a b^{3} - 2 \, b^{4} + 5 \, {\left(5 \, a^{2} b^{2} - 7 \, a b^{3} + 2 \, b^{4}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{4} - 5 \, a^{2} b^{2} + 7 \, a b^{3} - 2 \, b^{4} + 4 \, {\left(5 \, {\left(5 \, a^{2} b^{2} - 7 \, a b^{3} + 2 \, b^{4}\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(8 \, a^{3} b - 17 \, a^{2} b^{2} + 11 \, a b^{3} - 2 \, b^{4}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} - 3 \, {\left(8 \, a^{3} b - 17 \, a^{2} b^{2} + 11 \, a b^{3} - 2 \, b^{4}\right)} \cosh\left(f x + e\right)^{2} + 3 \, {\left(5 \, {\left(5 \, a^{2} b^{2} - 7 \, a b^{3} + 2 \, b^{4}\right)} \cosh\left(f x + e\right)^{4} - 8 \, a^{3} b + 17 \, a^{2} b^{2} - 11 \, a b^{3} + 2 \, b^{4} + 6 \, {\left(8 \, a^{3} b - 17 \, a^{2} b^{2} + 11 \, a b^{3} - 2 \, b^{4}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{2} + 6 \, {\left({\left(5 \, a^{2} b^{2} - 7 \, a b^{3} + 2 \, b^{4}\right)} \cosh\left(f x + e\right)^{5} + 2 \, {\left(8 \, a^{3} b - 17 \, a^{2} b^{2} + 11 \, a b^{3} - 2 \, b^{4}\right)} \cosh\left(f x + e\right)^{3} - {\left(8 \, a^{3} b - 17 \, a^{2} b^{2} + 11 \, a b^{3} - 2 \, b^{4}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{6 \, {\left({\left(a^{5} b^{2} - 3 \, a^{4} b^{3} + 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} f \cosh\left(f x + e\right)^{8} + 8 \, {\left(a^{5} b^{2} - 3 \, a^{4} b^{3} + 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + {\left(a^{5} b^{2} - 3 \, a^{4} b^{3} + 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} f \sinh\left(f x + e\right)^{8} + 4 \, {\left(2 \, a^{6} b - 7 \, a^{5} b^{2} + 9 \, a^{4} b^{3} - 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} f \cosh\left(f x + e\right)^{6} + 4 \, {\left(7 \, {\left(a^{5} b^{2} - 3 \, a^{4} b^{3} + 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} f \cosh\left(f x + e\right)^{2} + {\left(2 \, a^{6} b - 7 \, a^{5} b^{2} + 9 \, a^{4} b^{3} - 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} f\right)} \sinh\left(f x + e\right)^{6} + 2 \, {\left(8 \, a^{7} - 32 \, a^{6} b + 51 \, a^{5} b^{2} - 41 \, a^{4} b^{3} + 17 \, a^{3} b^{4} - 3 \, a^{2} b^{5}\right)} f \cosh\left(f x + e\right)^{4} + 8 \, {\left(7 \, {\left(a^{5} b^{2} - 3 \, a^{4} b^{3} + 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} f \cosh\left(f x + e\right)^{3} + 3 \, {\left(2 \, a^{6} b - 7 \, a^{5} b^{2} + 9 \, a^{4} b^{3} - 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(35 \, {\left(a^{5} b^{2} - 3 \, a^{4} b^{3} + 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} f \cosh\left(f x + e\right)^{4} + 30 \, {\left(2 \, a^{6} b - 7 \, a^{5} b^{2} + 9 \, a^{4} b^{3} - 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} f \cosh\left(f x + e\right)^{2} + {\left(8 \, a^{7} - 32 \, a^{6} b + 51 \, a^{5} b^{2} - 41 \, a^{4} b^{3} + 17 \, a^{3} b^{4} - 3 \, a^{2} b^{5}\right)} f\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(2 \, a^{6} b - 7 \, a^{5} b^{2} + 9 \, a^{4} b^{3} - 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} f \cosh\left(f x + e\right)^{2} + 8 \, {\left(7 \, {\left(a^{5} b^{2} - 3 \, a^{4} b^{3} + 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} f \cosh\left(f x + e\right)^{5} + 10 \, {\left(2 \, a^{6} b - 7 \, a^{5} b^{2} + 9 \, a^{4} b^{3} - 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} f \cosh\left(f x + e\right)^{3} + {\left(8 \, a^{7} - 32 \, a^{6} b + 51 \, a^{5} b^{2} - 41 \, a^{4} b^{3} + 17 \, a^{3} b^{4} - 3 \, a^{2} b^{5}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 4 \, {\left(7 \, {\left(a^{5} b^{2} - 3 \, a^{4} b^{3} + 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} f \cosh\left(f x + e\right)^{6} + 15 \, {\left(2 \, a^{6} b - 7 \, a^{5} b^{2} + 9 \, a^{4} b^{3} - 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} f \cosh\left(f x + e\right)^{4} + 3 \, {\left(8 \, a^{7} - 32 \, a^{6} b + 51 \, a^{5} b^{2} - 41 \, a^{4} b^{3} + 17 \, a^{3} b^{4} - 3 \, a^{2} b^{5}\right)} f \cosh\left(f x + e\right)^{2} + {\left(2 \, a^{6} b - 7 \, a^{5} b^{2} + 9 \, a^{4} b^{3} - 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} f\right)} \sinh\left(f x + e\right)^{2} + {\left(a^{5} b^{2} - 3 \, a^{4} b^{3} + 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} f + 8 \, {\left({\left(a^{5} b^{2} - 3 \, a^{4} b^{3} + 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} f \cosh\left(f x + e\right)^{7} + 3 \, {\left(2 \, a^{6} b - 7 \, a^{5} b^{2} + 9 \, a^{4} b^{3} - 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} f \cosh\left(f x + e\right)^{5} + {\left(8 \, a^{7} - 32 \, a^{6} b + 51 \, a^{5} b^{2} - 41 \, a^{4} b^{3} + 17 \, a^{3} b^{4} - 3 \, a^{2} b^{5}\right)} f \cosh\left(f x + e\right)^{3} + {\left(2 \, a^{6} b - 7 \, a^{5} b^{2} + 9 \, a^{4} b^{3} - 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)}}, \frac{3 \, {\left(a^{2} b^{2} \cosh\left(f x + e\right)^{8} + 8 \, a^{2} b^{2} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + a^{2} b^{2} \sinh\left(f x + e\right)^{8} + 4 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} \cosh\left(f x + e\right)^{6} + 4 \, {\left(7 \, a^{2} b^{2} \cosh\left(f x + e\right)^{2} + 2 \, a^{3} b - a^{2} b^{2}\right)} \sinh\left(f x + e\right)^{6} + 8 \, {\left(7 \, a^{2} b^{2} \cosh\left(f x + e\right)^{3} + 3 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(8 \, a^{4} - 8 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(f x + e\right)^{4} + 2 \, {\left(35 \, a^{2} b^{2} \cosh\left(f x + e\right)^{4} + 8 \, a^{4} - 8 \, a^{3} b + 3 \, a^{2} b^{2} + 30 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{4} + a^{2} b^{2} + 8 \, {\left(7 \, a^{2} b^{2} \cosh\left(f x + e\right)^{5} + 10 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} \cosh\left(f x + e\right)^{3} + {\left(8 \, a^{4} - 8 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 4 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} \cosh\left(f x + e\right)^{2} + 4 \, {\left(7 \, a^{2} b^{2} \cosh\left(f x + e\right)^{6} + 15 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} \cosh\left(f x + e\right)^{4} + 2 \, a^{3} b - a^{2} b^{2} + 3 \, {\left(8 \, a^{4} - 8 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{2} + 8 \, {\left(a^{2} b^{2} \cosh\left(f x + e\right)^{7} + 3 \, {\left(2 \, a^{3} b - a^{2} b^{2}\right)} \cosh\left(f x + e\right)^{5} + {\left(8 \, a^{4} - 8 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(f x + e\right)^{3} + {\left(2 \, a^{3} b - a^{2} b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{a - b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2} - 1\right)} \sqrt{a - b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + 2 \, a - b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}\right) - \sqrt{2} {\left({\left(5 \, a^{2} b^{2} - 7 \, a b^{3} + 2 \, b^{4}\right)} \cosh\left(f x + e\right)^{6} + 6 \, {\left(5 \, a^{2} b^{2} - 7 \, a b^{3} + 2 \, b^{4}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{5} + {\left(5 \, a^{2} b^{2} - 7 \, a b^{3} + 2 \, b^{4}\right)} \sinh\left(f x + e\right)^{6} + 3 \, {\left(8 \, a^{3} b - 17 \, a^{2} b^{2} + 11 \, a b^{3} - 2 \, b^{4}\right)} \cosh\left(f x + e\right)^{4} + 3 \, {\left(8 \, a^{3} b - 17 \, a^{2} b^{2} + 11 \, a b^{3} - 2 \, b^{4} + 5 \, {\left(5 \, a^{2} b^{2} - 7 \, a b^{3} + 2 \, b^{4}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{4} - 5 \, a^{2} b^{2} + 7 \, a b^{3} - 2 \, b^{4} + 4 \, {\left(5 \, {\left(5 \, a^{2} b^{2} - 7 \, a b^{3} + 2 \, b^{4}\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(8 \, a^{3} b - 17 \, a^{2} b^{2} + 11 \, a b^{3} - 2 \, b^{4}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} - 3 \, {\left(8 \, a^{3} b - 17 \, a^{2} b^{2} + 11 \, a b^{3} - 2 \, b^{4}\right)} \cosh\left(f x + e\right)^{2} + 3 \, {\left(5 \, {\left(5 \, a^{2} b^{2} - 7 \, a b^{3} + 2 \, b^{4}\right)} \cosh\left(f x + e\right)^{4} - 8 \, a^{3} b + 17 \, a^{2} b^{2} - 11 \, a b^{3} + 2 \, b^{4} + 6 \, {\left(8 \, a^{3} b - 17 \, a^{2} b^{2} + 11 \, a b^{3} - 2 \, b^{4}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{2} + 6 \, {\left({\left(5 \, a^{2} b^{2} - 7 \, a b^{3} + 2 \, b^{4}\right)} \cosh\left(f x + e\right)^{5} + 2 \, {\left(8 \, a^{3} b - 17 \, a^{2} b^{2} + 11 \, a b^{3} - 2 \, b^{4}\right)} \cosh\left(f x + e\right)^{3} - {\left(8 \, a^{3} b - 17 \, a^{2} b^{2} + 11 \, a b^{3} - 2 \, b^{4}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{3 \, {\left({\left(a^{5} b^{2} - 3 \, a^{4} b^{3} + 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} f \cosh\left(f x + e\right)^{8} + 8 \, {\left(a^{5} b^{2} - 3 \, a^{4} b^{3} + 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + {\left(a^{5} b^{2} - 3 \, a^{4} b^{3} + 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} f \sinh\left(f x + e\right)^{8} + 4 \, {\left(2 \, a^{6} b - 7 \, a^{5} b^{2} + 9 \, a^{4} b^{3} - 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} f \cosh\left(f x + e\right)^{6} + 4 \, {\left(7 \, {\left(a^{5} b^{2} - 3 \, a^{4} b^{3} + 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} f \cosh\left(f x + e\right)^{2} + {\left(2 \, a^{6} b - 7 \, a^{5} b^{2} + 9 \, a^{4} b^{3} - 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} f\right)} \sinh\left(f x + e\right)^{6} + 2 \, {\left(8 \, a^{7} - 32 \, a^{6} b + 51 \, a^{5} b^{2} - 41 \, a^{4} b^{3} + 17 \, a^{3} b^{4} - 3 \, a^{2} b^{5}\right)} f \cosh\left(f x + e\right)^{4} + 8 \, {\left(7 \, {\left(a^{5} b^{2} - 3 \, a^{4} b^{3} + 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} f \cosh\left(f x + e\right)^{3} + 3 \, {\left(2 \, a^{6} b - 7 \, a^{5} b^{2} + 9 \, a^{4} b^{3} - 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(35 \, {\left(a^{5} b^{2} - 3 \, a^{4} b^{3} + 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} f \cosh\left(f x + e\right)^{4} + 30 \, {\left(2 \, a^{6} b - 7 \, a^{5} b^{2} + 9 \, a^{4} b^{3} - 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} f \cosh\left(f x + e\right)^{2} + {\left(8 \, a^{7} - 32 \, a^{6} b + 51 \, a^{5} b^{2} - 41 \, a^{4} b^{3} + 17 \, a^{3} b^{4} - 3 \, a^{2} b^{5}\right)} f\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(2 \, a^{6} b - 7 \, a^{5} b^{2} + 9 \, a^{4} b^{3} - 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} f \cosh\left(f x + e\right)^{2} + 8 \, {\left(7 \, {\left(a^{5} b^{2} - 3 \, a^{4} b^{3} + 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} f \cosh\left(f x + e\right)^{5} + 10 \, {\left(2 \, a^{6} b - 7 \, a^{5} b^{2} + 9 \, a^{4} b^{3} - 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} f \cosh\left(f x + e\right)^{3} + {\left(8 \, a^{7} - 32 \, a^{6} b + 51 \, a^{5} b^{2} - 41 \, a^{4} b^{3} + 17 \, a^{3} b^{4} - 3 \, a^{2} b^{5}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 4 \, {\left(7 \, {\left(a^{5} b^{2} - 3 \, a^{4} b^{3} + 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} f \cosh\left(f x + e\right)^{6} + 15 \, {\left(2 \, a^{6} b - 7 \, a^{5} b^{2} + 9 \, a^{4} b^{3} - 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} f \cosh\left(f x + e\right)^{4} + 3 \, {\left(8 \, a^{7} - 32 \, a^{6} b + 51 \, a^{5} b^{2} - 41 \, a^{4} b^{3} + 17 \, a^{3} b^{4} - 3 \, a^{2} b^{5}\right)} f \cosh\left(f x + e\right)^{2} + {\left(2 \, a^{6} b - 7 \, a^{5} b^{2} + 9 \, a^{4} b^{3} - 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} f\right)} \sinh\left(f x + e\right)^{2} + {\left(a^{5} b^{2} - 3 \, a^{4} b^{3} + 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} f + 8 \, {\left({\left(a^{5} b^{2} - 3 \, a^{4} b^{3} + 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} f \cosh\left(f x + e\right)^{7} + 3 \, {\left(2 \, a^{6} b - 7 \, a^{5} b^{2} + 9 \, a^{4} b^{3} - 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} f \cosh\left(f x + e\right)^{5} + {\left(8 \, a^{7} - 32 \, a^{6} b + 51 \, a^{5} b^{2} - 41 \, a^{4} b^{3} + 17 \, a^{3} b^{4} - 3 \, a^{2} b^{5}\right)} f \cosh\left(f x + e\right)^{3} + {\left(2 \, a^{6} b - 7 \, a^{5} b^{2} + 9 \, a^{4} b^{3} - 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)}}\right]"," ",0,"[-1/6*(3*(a^2*b^2*cosh(f*x + e)^8 + 8*a^2*b^2*cosh(f*x + e)*sinh(f*x + e)^7 + a^2*b^2*sinh(f*x + e)^8 + 4*(2*a^3*b - a^2*b^2)*cosh(f*x + e)^6 + 4*(7*a^2*b^2*cosh(f*x + e)^2 + 2*a^3*b - a^2*b^2)*sinh(f*x + e)^6 + 8*(7*a^2*b^2*cosh(f*x + e)^3 + 3*(2*a^3*b - a^2*b^2)*cosh(f*x + e))*sinh(f*x + e)^5 + 2*(8*a^4 - 8*a^3*b + 3*a^2*b^2)*cosh(f*x + e)^4 + 2*(35*a^2*b^2*cosh(f*x + e)^4 + 8*a^4 - 8*a^3*b + 3*a^2*b^2 + 30*(2*a^3*b - a^2*b^2)*cosh(f*x + e)^2)*sinh(f*x + e)^4 + a^2*b^2 + 8*(7*a^2*b^2*cosh(f*x + e)^5 + 10*(2*a^3*b - a^2*b^2)*cosh(f*x + e)^3 + (8*a^4 - 8*a^3*b + 3*a^2*b^2)*cosh(f*x + e))*sinh(f*x + e)^3 + 4*(2*a^3*b - a^2*b^2)*cosh(f*x + e)^2 + 4*(7*a^2*b^2*cosh(f*x + e)^6 + 15*(2*a^3*b - a^2*b^2)*cosh(f*x + e)^4 + 2*a^3*b - a^2*b^2 + 3*(8*a^4 - 8*a^3*b + 3*a^2*b^2)*cosh(f*x + e)^2)*sinh(f*x + e)^2 + 8*(a^2*b^2*cosh(f*x + e)^7 + 3*(2*a^3*b - a^2*b^2)*cosh(f*x + e)^5 + (8*a^4 - 8*a^3*b + 3*a^2*b^2)*cosh(f*x + e)^3 + (2*a^3*b - a^2*b^2)*cosh(f*x + e))*sinh(f*x + e))*sqrt(-a + b)*log(((a - 2*b)*cosh(f*x + e)^4 + 4*(a - 2*b)*cosh(f*x + e)*sinh(f*x + e)^3 + (a - 2*b)*sinh(f*x + e)^4 - 2*(3*a - 2*b)*cosh(f*x + e)^2 + 2*(3*(a - 2*b)*cosh(f*x + e)^2 - 3*a + 2*b)*sinh(f*x + e)^2 - 2*sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 - 1)*sqrt(-a + b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)) + 4*((a - 2*b)*cosh(f*x + e)^3 - (3*a - 2*b)*cosh(f*x + e))*sinh(f*x + e) + a - 2*b)/(cosh(f*x + e)^4 + 4*cosh(f*x + e)*sinh(f*x + e)^3 + sinh(f*x + e)^4 + 2*(3*cosh(f*x + e)^2 + 1)*sinh(f*x + e)^2 + 2*cosh(f*x + e)^2 + 4*(cosh(f*x + e)^3 + cosh(f*x + e))*sinh(f*x + e) + 1)) + 2*sqrt(2)*((5*a^2*b^2 - 7*a*b^3 + 2*b^4)*cosh(f*x + e)^6 + 6*(5*a^2*b^2 - 7*a*b^3 + 2*b^4)*cosh(f*x + e)*sinh(f*x + e)^5 + (5*a^2*b^2 - 7*a*b^3 + 2*b^4)*sinh(f*x + e)^6 + 3*(8*a^3*b - 17*a^2*b^2 + 11*a*b^3 - 2*b^4)*cosh(f*x + e)^4 + 3*(8*a^3*b - 17*a^2*b^2 + 11*a*b^3 - 2*b^4 + 5*(5*a^2*b^2 - 7*a*b^3 + 2*b^4)*cosh(f*x + e)^2)*sinh(f*x + e)^4 - 5*a^2*b^2 + 7*a*b^3 - 2*b^4 + 4*(5*(5*a^2*b^2 - 7*a*b^3 + 2*b^4)*cosh(f*x + e)^3 + 3*(8*a^3*b - 17*a^2*b^2 + 11*a*b^3 - 2*b^4)*cosh(f*x + e))*sinh(f*x + e)^3 - 3*(8*a^3*b - 17*a^2*b^2 + 11*a*b^3 - 2*b^4)*cosh(f*x + e)^2 + 3*(5*(5*a^2*b^2 - 7*a*b^3 + 2*b^4)*cosh(f*x + e)^4 - 8*a^3*b + 17*a^2*b^2 - 11*a*b^3 + 2*b^4 + 6*(8*a^3*b - 17*a^2*b^2 + 11*a*b^3 - 2*b^4)*cosh(f*x + e)^2)*sinh(f*x + e)^2 + 6*((5*a^2*b^2 - 7*a*b^3 + 2*b^4)*cosh(f*x + e)^5 + 2*(8*a^3*b - 17*a^2*b^2 + 11*a*b^3 - 2*b^4)*cosh(f*x + e)^3 - (8*a^3*b - 17*a^2*b^2 + 11*a*b^3 - 2*b^4)*cosh(f*x + e))*sinh(f*x + e))*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/((a^5*b^2 - 3*a^4*b^3 + 3*a^3*b^4 - a^2*b^5)*f*cosh(f*x + e)^8 + 8*(a^5*b^2 - 3*a^4*b^3 + 3*a^3*b^4 - a^2*b^5)*f*cosh(f*x + e)*sinh(f*x + e)^7 + (a^5*b^2 - 3*a^4*b^3 + 3*a^3*b^4 - a^2*b^5)*f*sinh(f*x + e)^8 + 4*(2*a^6*b - 7*a^5*b^2 + 9*a^4*b^3 - 5*a^3*b^4 + a^2*b^5)*f*cosh(f*x + e)^6 + 4*(7*(a^5*b^2 - 3*a^4*b^3 + 3*a^3*b^4 - a^2*b^5)*f*cosh(f*x + e)^2 + (2*a^6*b - 7*a^5*b^2 + 9*a^4*b^3 - 5*a^3*b^4 + a^2*b^5)*f)*sinh(f*x + e)^6 + 2*(8*a^7 - 32*a^6*b + 51*a^5*b^2 - 41*a^4*b^3 + 17*a^3*b^4 - 3*a^2*b^5)*f*cosh(f*x + e)^4 + 8*(7*(a^5*b^2 - 3*a^4*b^3 + 3*a^3*b^4 - a^2*b^5)*f*cosh(f*x + e)^3 + 3*(2*a^6*b - 7*a^5*b^2 + 9*a^4*b^3 - 5*a^3*b^4 + a^2*b^5)*f*cosh(f*x + e))*sinh(f*x + e)^5 + 2*(35*(a^5*b^2 - 3*a^4*b^3 + 3*a^3*b^4 - a^2*b^5)*f*cosh(f*x + e)^4 + 30*(2*a^6*b - 7*a^5*b^2 + 9*a^4*b^3 - 5*a^3*b^4 + a^2*b^5)*f*cosh(f*x + e)^2 + (8*a^7 - 32*a^6*b + 51*a^5*b^2 - 41*a^4*b^3 + 17*a^3*b^4 - 3*a^2*b^5)*f)*sinh(f*x + e)^4 + 4*(2*a^6*b - 7*a^5*b^2 + 9*a^4*b^3 - 5*a^3*b^4 + a^2*b^5)*f*cosh(f*x + e)^2 + 8*(7*(a^5*b^2 - 3*a^4*b^3 + 3*a^3*b^4 - a^2*b^5)*f*cosh(f*x + e)^5 + 10*(2*a^6*b - 7*a^5*b^2 + 9*a^4*b^3 - 5*a^3*b^4 + a^2*b^5)*f*cosh(f*x + e)^3 + (8*a^7 - 32*a^6*b + 51*a^5*b^2 - 41*a^4*b^3 + 17*a^3*b^4 - 3*a^2*b^5)*f*cosh(f*x + e))*sinh(f*x + e)^3 + 4*(7*(a^5*b^2 - 3*a^4*b^3 + 3*a^3*b^4 - a^2*b^5)*f*cosh(f*x + e)^6 + 15*(2*a^6*b - 7*a^5*b^2 + 9*a^4*b^3 - 5*a^3*b^4 + a^2*b^5)*f*cosh(f*x + e)^4 + 3*(8*a^7 - 32*a^6*b + 51*a^5*b^2 - 41*a^4*b^3 + 17*a^3*b^4 - 3*a^2*b^5)*f*cosh(f*x + e)^2 + (2*a^6*b - 7*a^5*b^2 + 9*a^4*b^3 - 5*a^3*b^4 + a^2*b^5)*f)*sinh(f*x + e)^2 + (a^5*b^2 - 3*a^4*b^3 + 3*a^3*b^4 - a^2*b^5)*f + 8*((a^5*b^2 - 3*a^4*b^3 + 3*a^3*b^4 - a^2*b^5)*f*cosh(f*x + e)^7 + 3*(2*a^6*b - 7*a^5*b^2 + 9*a^4*b^3 - 5*a^3*b^4 + a^2*b^5)*f*cosh(f*x + e)^5 + (8*a^7 - 32*a^6*b + 51*a^5*b^2 - 41*a^4*b^3 + 17*a^3*b^4 - 3*a^2*b^5)*f*cosh(f*x + e)^3 + (2*a^6*b - 7*a^5*b^2 + 9*a^4*b^3 - 5*a^3*b^4 + a^2*b^5)*f*cosh(f*x + e))*sinh(f*x + e)), 1/3*(3*(a^2*b^2*cosh(f*x + e)^8 + 8*a^2*b^2*cosh(f*x + e)*sinh(f*x + e)^7 + a^2*b^2*sinh(f*x + e)^8 + 4*(2*a^3*b - a^2*b^2)*cosh(f*x + e)^6 + 4*(7*a^2*b^2*cosh(f*x + e)^2 + 2*a^3*b - a^2*b^2)*sinh(f*x + e)^6 + 8*(7*a^2*b^2*cosh(f*x + e)^3 + 3*(2*a^3*b - a^2*b^2)*cosh(f*x + e))*sinh(f*x + e)^5 + 2*(8*a^4 - 8*a^3*b + 3*a^2*b^2)*cosh(f*x + e)^4 + 2*(35*a^2*b^2*cosh(f*x + e)^4 + 8*a^4 - 8*a^3*b + 3*a^2*b^2 + 30*(2*a^3*b - a^2*b^2)*cosh(f*x + e)^2)*sinh(f*x + e)^4 + a^2*b^2 + 8*(7*a^2*b^2*cosh(f*x + e)^5 + 10*(2*a^3*b - a^2*b^2)*cosh(f*x + e)^3 + (8*a^4 - 8*a^3*b + 3*a^2*b^2)*cosh(f*x + e))*sinh(f*x + e)^3 + 4*(2*a^3*b - a^2*b^2)*cosh(f*x + e)^2 + 4*(7*a^2*b^2*cosh(f*x + e)^6 + 15*(2*a^3*b - a^2*b^2)*cosh(f*x + e)^4 + 2*a^3*b - a^2*b^2 + 3*(8*a^4 - 8*a^3*b + 3*a^2*b^2)*cosh(f*x + e)^2)*sinh(f*x + e)^2 + 8*(a^2*b^2*cosh(f*x + e)^7 + 3*(2*a^3*b - a^2*b^2)*cosh(f*x + e)^5 + (8*a^4 - 8*a^3*b + 3*a^2*b^2)*cosh(f*x + e)^3 + (2*a^3*b - a^2*b^2)*cosh(f*x + e))*sinh(f*x + e))*sqrt(a - b)*arctan(sqrt(2)*(cosh(f*x + e)^2 + 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2 - 1)*sqrt(a - b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/(b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(2*a - b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 2*a - b)*sinh(f*x + e)^2 + 4*(b*cosh(f*x + e)^3 + (2*a - b)*cosh(f*x + e))*sinh(f*x + e) + b)) - sqrt(2)*((5*a^2*b^2 - 7*a*b^3 + 2*b^4)*cosh(f*x + e)^6 + 6*(5*a^2*b^2 - 7*a*b^3 + 2*b^4)*cosh(f*x + e)*sinh(f*x + e)^5 + (5*a^2*b^2 - 7*a*b^3 + 2*b^4)*sinh(f*x + e)^6 + 3*(8*a^3*b - 17*a^2*b^2 + 11*a*b^3 - 2*b^4)*cosh(f*x + e)^4 + 3*(8*a^3*b - 17*a^2*b^2 + 11*a*b^3 - 2*b^4 + 5*(5*a^2*b^2 - 7*a*b^3 + 2*b^4)*cosh(f*x + e)^2)*sinh(f*x + e)^4 - 5*a^2*b^2 + 7*a*b^3 - 2*b^4 + 4*(5*(5*a^2*b^2 - 7*a*b^3 + 2*b^4)*cosh(f*x + e)^3 + 3*(8*a^3*b - 17*a^2*b^2 + 11*a*b^3 - 2*b^4)*cosh(f*x + e))*sinh(f*x + e)^3 - 3*(8*a^3*b - 17*a^2*b^2 + 11*a*b^3 - 2*b^4)*cosh(f*x + e)^2 + 3*(5*(5*a^2*b^2 - 7*a*b^3 + 2*b^4)*cosh(f*x + e)^4 - 8*a^3*b + 17*a^2*b^2 - 11*a*b^3 + 2*b^4 + 6*(8*a^3*b - 17*a^2*b^2 + 11*a*b^3 - 2*b^4)*cosh(f*x + e)^2)*sinh(f*x + e)^2 + 6*((5*a^2*b^2 - 7*a*b^3 + 2*b^4)*cosh(f*x + e)^5 + 2*(8*a^3*b - 17*a^2*b^2 + 11*a*b^3 - 2*b^4)*cosh(f*x + e)^3 - (8*a^3*b - 17*a^2*b^2 + 11*a*b^3 - 2*b^4)*cosh(f*x + e))*sinh(f*x + e))*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/((a^5*b^2 - 3*a^4*b^3 + 3*a^3*b^4 - a^2*b^5)*f*cosh(f*x + e)^8 + 8*(a^5*b^2 - 3*a^4*b^3 + 3*a^3*b^4 - a^2*b^5)*f*cosh(f*x + e)*sinh(f*x + e)^7 + (a^5*b^2 - 3*a^4*b^3 + 3*a^3*b^4 - a^2*b^5)*f*sinh(f*x + e)^8 + 4*(2*a^6*b - 7*a^5*b^2 + 9*a^4*b^3 - 5*a^3*b^4 + a^2*b^5)*f*cosh(f*x + e)^6 + 4*(7*(a^5*b^2 - 3*a^4*b^3 + 3*a^3*b^4 - a^2*b^5)*f*cosh(f*x + e)^2 + (2*a^6*b - 7*a^5*b^2 + 9*a^4*b^3 - 5*a^3*b^4 + a^2*b^5)*f)*sinh(f*x + e)^6 + 2*(8*a^7 - 32*a^6*b + 51*a^5*b^2 - 41*a^4*b^3 + 17*a^3*b^4 - 3*a^2*b^5)*f*cosh(f*x + e)^4 + 8*(7*(a^5*b^2 - 3*a^4*b^3 + 3*a^3*b^4 - a^2*b^5)*f*cosh(f*x + e)^3 + 3*(2*a^6*b - 7*a^5*b^2 + 9*a^4*b^3 - 5*a^3*b^4 + a^2*b^5)*f*cosh(f*x + e))*sinh(f*x + e)^5 + 2*(35*(a^5*b^2 - 3*a^4*b^3 + 3*a^3*b^4 - a^2*b^5)*f*cosh(f*x + e)^4 + 30*(2*a^6*b - 7*a^5*b^2 + 9*a^4*b^3 - 5*a^3*b^4 + a^2*b^5)*f*cosh(f*x + e)^2 + (8*a^7 - 32*a^6*b + 51*a^5*b^2 - 41*a^4*b^3 + 17*a^3*b^4 - 3*a^2*b^5)*f)*sinh(f*x + e)^4 + 4*(2*a^6*b - 7*a^5*b^2 + 9*a^4*b^3 - 5*a^3*b^4 + a^2*b^5)*f*cosh(f*x + e)^2 + 8*(7*(a^5*b^2 - 3*a^4*b^3 + 3*a^3*b^4 - a^2*b^5)*f*cosh(f*x + e)^5 + 10*(2*a^6*b - 7*a^5*b^2 + 9*a^4*b^3 - 5*a^3*b^4 + a^2*b^5)*f*cosh(f*x + e)^3 + (8*a^7 - 32*a^6*b + 51*a^5*b^2 - 41*a^4*b^3 + 17*a^3*b^4 - 3*a^2*b^5)*f*cosh(f*x + e))*sinh(f*x + e)^3 + 4*(7*(a^5*b^2 - 3*a^4*b^3 + 3*a^3*b^4 - a^2*b^5)*f*cosh(f*x + e)^6 + 15*(2*a^6*b - 7*a^5*b^2 + 9*a^4*b^3 - 5*a^3*b^4 + a^2*b^5)*f*cosh(f*x + e)^4 + 3*(8*a^7 - 32*a^6*b + 51*a^5*b^2 - 41*a^4*b^3 + 17*a^3*b^4 - 3*a^2*b^5)*f*cosh(f*x + e)^2 + (2*a^6*b - 7*a^5*b^2 + 9*a^4*b^3 - 5*a^3*b^4 + a^2*b^5)*f)*sinh(f*x + e)^2 + (a^5*b^2 - 3*a^4*b^3 + 3*a^3*b^4 - a^2*b^5)*f + 8*((a^5*b^2 - 3*a^4*b^3 + 3*a^3*b^4 - a^2*b^5)*f*cosh(f*x + e)^7 + 3*(2*a^6*b - 7*a^5*b^2 + 9*a^4*b^3 - 5*a^3*b^4 + a^2*b^5)*f*cosh(f*x + e)^5 + (8*a^7 - 32*a^6*b + 51*a^5*b^2 - 41*a^4*b^3 + 17*a^3*b^4 - 3*a^2*b^5)*f*cosh(f*x + e)^3 + (2*a^6*b - 7*a^5*b^2 + 9*a^4*b^3 - 5*a^3*b^4 + a^2*b^5)*f*cosh(f*x + e))*sinh(f*x + e))]","B",0
395,0,0,0,0.474568," ","integrate(cosh(f*x+e)^6/(a+b*sinh(f*x+e)^2)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sinh\left(f x + e\right)^{2} + a} \cosh\left(f x + e\right)^{6}}{b^{3} \sinh\left(f x + e\right)^{6} + 3 \, a b^{2} \sinh\left(f x + e\right)^{4} + 3 \, a^{2} b \sinh\left(f x + e\right)^{2} + a^{3}}, x\right)"," ",0,"integral(sqrt(b*sinh(f*x + e)^2 + a)*cosh(f*x + e)^6/(b^3*sinh(f*x + e)^6 + 3*a*b^2*sinh(f*x + e)^4 + 3*a^2*b*sinh(f*x + e)^2 + a^3), x)","F",0
396,0,0,0,0.637115," ","integrate(cosh(f*x+e)^4/(a+b*sinh(f*x+e)^2)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sinh\left(f x + e\right)^{2} + a} \cosh\left(f x + e\right)^{4}}{b^{3} \sinh\left(f x + e\right)^{6} + 3 \, a b^{2} \sinh\left(f x + e\right)^{4} + 3 \, a^{2} b \sinh\left(f x + e\right)^{2} + a^{3}}, x\right)"," ",0,"integral(sqrt(b*sinh(f*x + e)^2 + a)*cosh(f*x + e)^4/(b^3*sinh(f*x + e)^6 + 3*a*b^2*sinh(f*x + e)^4 + 3*a^2*b*sinh(f*x + e)^2 + a^3), x)","F",0
397,0,0,0,2.880377," ","integrate(cosh(f*x+e)^2/(a+b*sinh(f*x+e)^2)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sinh\left(f x + e\right)^{2} + a} \cosh\left(f x + e\right)^{2}}{b^{3} \sinh\left(f x + e\right)^{6} + 3 \, a b^{2} \sinh\left(f x + e\right)^{4} + 3 \, a^{2} b \sinh\left(f x + e\right)^{2} + a^{3}}, x\right)"," ",0,"integral(sqrt(b*sinh(f*x + e)^2 + a)*cosh(f*x + e)^2/(b^3*sinh(f*x + e)^6 + 3*a*b^2*sinh(f*x + e)^4 + 3*a^2*b*sinh(f*x + e)^2 + a^3), x)","F",0
398,0,0,0,1.480217," ","integrate(1/(a+b*sinh(f*x+e)^2)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sinh\left(f x + e\right)^{2} + a}}{b^{3} \sinh\left(f x + e\right)^{6} + 3 \, a b^{2} \sinh\left(f x + e\right)^{4} + 3 \, a^{2} b \sinh\left(f x + e\right)^{2} + a^{3}}, x\right)"," ",0,"integral(sqrt(b*sinh(f*x + e)^2 + a)/(b^3*sinh(f*x + e)^6 + 3*a*b^2*sinh(f*x + e)^4 + 3*a^2*b*sinh(f*x + e)^2 + a^3), x)","F",0
399,0,0,0,1.943794," ","integrate(sech(f*x+e)^2/(a+b*sinh(f*x+e)^2)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sinh\left(f x + e\right)^{2} + a} \operatorname{sech}\left(f x + e\right)^{2}}{b^{3} \sinh\left(f x + e\right)^{6} + 3 \, a b^{2} \sinh\left(f x + e\right)^{4} + 3 \, a^{2} b \sinh\left(f x + e\right)^{2} + a^{3}}, x\right)"," ",0,"integral(sqrt(b*sinh(f*x + e)^2 + a)*sech(f*x + e)^2/(b^3*sinh(f*x + e)^6 + 3*a*b^2*sinh(f*x + e)^4 + 3*a^2*b*sinh(f*x + e)^2 + a^3), x)","F",0
400,0,0,0,2.829262," ","integrate((d*cosh(f*x+e))^m*(a+b*sinh(f*x+e)^2)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sinh\left(f x + e\right)^{2} + a\right)}^{p} \left(d \cosh\left(f x + e\right)\right)^{m}, x\right)"," ",0,"integral((b*sinh(f*x + e)^2 + a)^p*(d*cosh(f*x + e))^m, x)","F",0
401,0,0,0,0.758556," ","integrate(cosh(f*x+e)^5*(a+b*sinh(f*x+e)^2)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sinh\left(f x + e\right)^{2} + a\right)}^{p} \cosh\left(f x + e\right)^{5}, x\right)"," ",0,"integral((b*sinh(f*x + e)^2 + a)^p*cosh(f*x + e)^5, x)","F",0
402,0,0,0,0.485237," ","integrate(cosh(f*x+e)^3*(a+b*sinh(f*x+e)^2)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sinh\left(f x + e\right)^{2} + a\right)}^{p} \cosh\left(f x + e\right)^{3}, x\right)"," ",0,"integral((b*sinh(f*x + e)^2 + a)^p*cosh(f*x + e)^3, x)","F",0
403,0,0,0,1.495061," ","integrate(cosh(f*x+e)*(a+b*sinh(f*x+e)^2)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sinh\left(f x + e\right)^{2} + a\right)}^{p} \cosh\left(f x + e\right), x\right)"," ",0,"integral((b*sinh(f*x + e)^2 + a)^p*cosh(f*x + e), x)","F",0
404,0,0,0,0.579296," ","integrate(sech(f*x+e)*(a+b*sinh(f*x+e)^2)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sinh\left(f x + e\right)^{2} + a\right)}^{p} \operatorname{sech}\left(f x + e\right), x\right)"," ",0,"integral((b*sinh(f*x + e)^2 + a)^p*sech(f*x + e), x)","F",0
405,0,0,0,0.717188," ","integrate(sech(f*x+e)^3*(a+b*sinh(f*x+e)^2)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sinh\left(f x + e\right)^{2} + a\right)}^{p} \operatorname{sech}\left(f x + e\right)^{3}, x\right)"," ",0,"integral((b*sinh(f*x + e)^2 + a)^p*sech(f*x + e)^3, x)","F",0
406,0,0,0,0.646976," ","integrate(cosh(f*x+e)^4*(a+b*sinh(f*x+e)^2)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sinh\left(f x + e\right)^{2} + a\right)}^{p} \cosh\left(f x + e\right)^{4}, x\right)"," ",0,"integral((b*sinh(f*x + e)^2 + a)^p*cosh(f*x + e)^4, x)","F",0
407,0,0,0,0.829824," ","integrate(cosh(f*x+e)^2*(a+b*sinh(f*x+e)^2)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sinh\left(f x + e\right)^{2} + a\right)}^{p} \cosh\left(f x + e\right)^{2}, x\right)"," ",0,"integral((b*sinh(f*x + e)^2 + a)^p*cosh(f*x + e)^2, x)","F",0
408,0,0,0,1.686280," ","integrate((a+b*sinh(f*x+e)^2)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sinh\left(f x + e\right)^{2} + a\right)}^{p}, x\right)"," ",0,"integral((b*sinh(f*x + e)^2 + a)^p, x)","F",0
409,0,0,0,0.851255," ","integrate(sech(f*x+e)^2*(a+b*sinh(f*x+e)^2)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sinh\left(f x + e\right)^{2} + a\right)}^{p} \operatorname{sech}\left(f x + e\right)^{2}, x\right)"," ",0,"integral((b*sinh(f*x + e)^2 + a)^p*sech(f*x + e)^2, x)","F",0
410,0,0,0,0.858185," ","integrate(sech(f*x+e)^4*(a+b*sinh(f*x+e)^2)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sinh\left(f x + e\right)^{2} + a\right)}^{p} \operatorname{sech}\left(f x + e\right)^{4}, x\right)"," ",0,"integral((b*sinh(f*x + e)^2 + a)^p*sech(f*x + e)^4, x)","F",0
411,1,2595,0,3.911029," ","integrate(cosh(d*x+c)^5/(a+b*sinh(d*x+c)^(1/2)),x, algorithm=""fricas"")","-\frac{315 \, a b^{8} \cosh\left(d x + c\right)^{8} + 315 \, a b^{8} \sinh\left(d x + c\right)^{8} + 840 \, a^{3} b^{6} \cosh\left(d x + c\right)^{7} - 840 \, a^{3} b^{6} \cosh\left(d x + c\right) + 315 \, a b^{8} + 840 \, {\left(3 \, a b^{8} \cosh\left(d x + c\right) + a^{3} b^{6}\right)} \sinh\left(d x + c\right)^{7} + 1260 \, {\left(2 \, a^{5} b^{4} + 3 \, a b^{8}\right)} \cosh\left(d x + c\right)^{6} + 420 \, {\left(21 \, a b^{8} \cosh\left(d x + c\right)^{2} + 14 \, a^{3} b^{6} \cosh\left(d x + c\right) + 6 \, a^{5} b^{4} + 9 \, a b^{8}\right)} \sinh\left(d x + c\right)^{6} + 2520 \, {\left(4 \, a^{7} b^{2} + 7 \, a^{3} b^{6}\right)} \cosh\left(d x + c\right)^{5} + 2520 \, {\left(7 \, a b^{8} \cosh\left(d x + c\right)^{3} + 7 \, a^{3} b^{6} \cosh\left(d x + c\right)^{2} + 4 \, a^{7} b^{2} + 7 \, a^{3} b^{6} + 3 \, {\left(2 \, a^{5} b^{4} + 3 \, a b^{8}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 20160 \, {\left({\left(a^{9} + 2 \, a^{5} b^{4} + a b^{8}\right)} d x + {\left(a^{9} + 2 \, a^{5} b^{4} + a b^{8}\right)} c\right)} \cosh\left(d x + c\right)^{4} + 210 \, {\left(105 \, a b^{8} \cosh\left(d x + c\right)^{4} + 140 \, a^{3} b^{6} \cosh\left(d x + c\right)^{3} - 96 \, {\left(a^{9} + 2 \, a^{5} b^{4} + a b^{8}\right)} d x + 90 \, {\left(2 \, a^{5} b^{4} + 3 \, a b^{8}\right)} \cosh\left(d x + c\right)^{2} - 96 \, {\left(a^{9} + 2 \, a^{5} b^{4} + a b^{8}\right)} c + 60 \, {\left(4 \, a^{7} b^{2} + 7 \, a^{3} b^{6}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} - 2520 \, {\left(4 \, a^{7} b^{2} + 7 \, a^{3} b^{6}\right)} \cosh\left(d x + c\right)^{3} + 840 \, {\left(21 \, a b^{8} \cosh\left(d x + c\right)^{5} + 35 \, a^{3} b^{6} \cosh\left(d x + c\right)^{4} - 12 \, a^{7} b^{2} - 21 \, a^{3} b^{6} + 30 \, {\left(2 \, a^{5} b^{4} + 3 \, a b^{8}\right)} \cosh\left(d x + c\right)^{3} + 30 \, {\left(4 \, a^{7} b^{2} + 7 \, a^{3} b^{6}\right)} \cosh\left(d x + c\right)^{2} - 96 \, {\left({\left(a^{9} + 2 \, a^{5} b^{4} + a b^{8}\right)} d x + {\left(a^{9} + 2 \, a^{5} b^{4} + a b^{8}\right)} c\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 1260 \, {\left(2 \, a^{5} b^{4} + 3 \, a b^{8}\right)} \cosh\left(d x + c\right)^{2} + 1260 \, {\left(7 \, a b^{8} \cosh\left(d x + c\right)^{6} + 14 \, a^{3} b^{6} \cosh\left(d x + c\right)^{5} + 2 \, a^{5} b^{4} + 3 \, a b^{8} + 15 \, {\left(2 \, a^{5} b^{4} + 3 \, a b^{8}\right)} \cosh\left(d x + c\right)^{4} + 20 \, {\left(4 \, a^{7} b^{2} + 7 \, a^{3} b^{6}\right)} \cosh\left(d x + c\right)^{3} - 96 \, {\left({\left(a^{9} + 2 \, a^{5} b^{4} + a b^{8}\right)} d x + {\left(a^{9} + 2 \, a^{5} b^{4} + a b^{8}\right)} c\right)} \cosh\left(d x + c\right)^{2} - 6 \, {\left(4 \, a^{7} b^{2} + 7 \, a^{3} b^{6}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 20160 \, {\left({\left(a^{9} + 2 \, a^{5} b^{4} + a b^{8}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{9} + 2 \, a^{5} b^{4} + a b^{8}\right)} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, {\left(a^{9} + 2 \, a^{5} b^{4} + a b^{8}\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a^{9} + 2 \, a^{5} b^{4} + a b^{8}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{9} + 2 \, a^{5} b^{4} + a b^{8}\right)} \sinh\left(d x + c\right)^{4}\right)} \log\left(\frac{b^{2} \cosh\left(d x + c\right)^{2} + b^{2} \sinh\left(d x + c\right)^{2} + 2 \, a^{2} \cosh\left(d x + c\right) - b^{2} + 2 \, {\left(b^{2} \cosh\left(d x + c\right) + a^{2}\right)} \sinh\left(d x + c\right) - 4 \, {\left(a b \cosh\left(d x + c\right) + a b \sinh\left(d x + c\right)\right)} \sqrt{\sinh\left(d x + c\right)}}{b^{2} \cosh\left(d x + c\right)^{2} + b^{2} \sinh\left(d x + c\right)^{2} - 2 \, a^{2} \cosh\left(d x + c\right) - b^{2} + 2 \, {\left(b^{2} \cosh\left(d x + c\right) - a^{2}\right)} \sinh\left(d x + c\right)}\right) + 20160 \, {\left({\left(a^{9} + 2 \, a^{5} b^{4} + a b^{8}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{9} + 2 \, a^{5} b^{4} + a b^{8}\right)} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, {\left(a^{9} + 2 \, a^{5} b^{4} + a b^{8}\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, {\left(a^{9} + 2 \, a^{5} b^{4} + a b^{8}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{9} + 2 \, a^{5} b^{4} + a b^{8}\right)} \sinh\left(d x + c\right)^{4}\right)} \log\left(\frac{2 \, {\left(b^{2} \sinh\left(d x + c\right) - a^{2}\right)}}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) + 840 \, {\left(3 \, a b^{8} \cosh\left(d x + c\right)^{7} + 7 \, a^{3} b^{6} \cosh\left(d x + c\right)^{6} - a^{3} b^{6} + 9 \, {\left(2 \, a^{5} b^{4} + 3 \, a b^{8}\right)} \cosh\left(d x + c\right)^{5} + 15 \, {\left(4 \, a^{7} b^{2} + 7 \, a^{3} b^{6}\right)} \cosh\left(d x + c\right)^{4} - 96 \, {\left({\left(a^{9} + 2 \, a^{5} b^{4} + a b^{8}\right)} d x + {\left(a^{9} + 2 \, a^{5} b^{4} + a b^{8}\right)} c\right)} \cosh\left(d x + c\right)^{3} - 9 \, {\left(4 \, a^{7} b^{2} + 7 \, a^{3} b^{6}\right)} \cosh\left(d x + c\right)^{2} + 3 \, {\left(2 \, a^{5} b^{4} + 3 \, a b^{8}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) - 8 \, {\left(35 \, b^{9} \cosh\left(d x + c\right)^{8} + 35 \, b^{9} \sinh\left(d x + c\right)^{8} + 90 \, a^{2} b^{7} \cosh\left(d x + c\right)^{7} - 90 \, a^{2} b^{7} \cosh\left(d x + c\right) + 35 \, b^{9} + 10 \, {\left(28 \, b^{9} \cosh\left(d x + c\right) + 9 \, a^{2} b^{7}\right)} \sinh\left(d x + c\right)^{7} + 28 \, {\left(9 \, a^{4} b^{5} + 13 \, b^{9}\right)} \cosh\left(d x + c\right)^{6} + 14 \, {\left(70 \, b^{9} \cosh\left(d x + c\right)^{2} + 45 \, a^{2} b^{7} \cosh\left(d x + c\right) + 18 \, a^{4} b^{5} + 26 \, b^{9}\right)} \sinh\left(d x + c\right)^{6} + 30 \, {\left(28 \, a^{6} b^{3} + 47 \, a^{2} b^{7}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(980 \, b^{9} \cosh\left(d x + c\right)^{3} + 945 \, a^{2} b^{7} \cosh\left(d x + c\right)^{2} + 420 \, a^{6} b^{3} + 705 \, a^{2} b^{7} + 84 \, {\left(9 \, a^{4} b^{5} + 13 \, b^{9}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 42 \, {\left(120 \, a^{8} b + 228 \, a^{4} b^{5} + 101 \, b^{9}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(1225 \, b^{9} \cosh\left(d x + c\right)^{4} + 1575 \, a^{2} b^{7} \cosh\left(d x + c\right)^{3} + 2520 \, a^{8} b + 4788 \, a^{4} b^{5} + 2121 \, b^{9} + 210 \, {\left(9 \, a^{4} b^{5} + 13 \, b^{9}\right)} \cosh\left(d x + c\right)^{2} + 75 \, {\left(28 \, a^{6} b^{3} + 47 \, a^{2} b^{7}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} - 30 \, {\left(28 \, a^{6} b^{3} + 47 \, a^{2} b^{7}\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(980 \, b^{9} \cosh\left(d x + c\right)^{5} + 1575 \, a^{2} b^{7} \cosh\left(d x + c\right)^{4} - 420 \, a^{6} b^{3} - 705 \, a^{2} b^{7} + 280 \, {\left(9 \, a^{4} b^{5} + 13 \, b^{9}\right)} \cosh\left(d x + c\right)^{3} + 150 \, {\left(28 \, a^{6} b^{3} + 47 \, a^{2} b^{7}\right)} \cosh\left(d x + c\right)^{2} + 84 \, {\left(120 \, a^{8} b + 228 \, a^{4} b^{5} + 101 \, b^{9}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 28 \, {\left(9 \, a^{4} b^{5} + 13 \, b^{9}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(490 \, b^{9} \cosh\left(d x + c\right)^{6} + 945 \, a^{2} b^{7} \cosh\left(d x + c\right)^{5} + 126 \, a^{4} b^{5} + 182 \, b^{9} + 210 \, {\left(9 \, a^{4} b^{5} + 13 \, b^{9}\right)} \cosh\left(d x + c\right)^{4} + 150 \, {\left(28 \, a^{6} b^{3} + 47 \, a^{2} b^{7}\right)} \cosh\left(d x + c\right)^{3} + 126 \, {\left(120 \, a^{8} b + 228 \, a^{4} b^{5} + 101 \, b^{9}\right)} \cosh\left(d x + c\right)^{2} - 45 \, {\left(28 \, a^{6} b^{3} + 47 \, a^{2} b^{7}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(140 \, b^{9} \cosh\left(d x + c\right)^{7} + 315 \, a^{2} b^{7} \cosh\left(d x + c\right)^{6} - 45 \, a^{2} b^{7} + 84 \, {\left(9 \, a^{4} b^{5} + 13 \, b^{9}\right)} \cosh\left(d x + c\right)^{5} + 75 \, {\left(28 \, a^{6} b^{3} + 47 \, a^{2} b^{7}\right)} \cosh\left(d x + c\right)^{4} + 84 \, {\left(120 \, a^{8} b + 228 \, a^{4} b^{5} + 101 \, b^{9}\right)} \cosh\left(d x + c\right)^{3} - 45 \, {\left(28 \, a^{6} b^{3} + 47 \, a^{2} b^{7}\right)} \cosh\left(d x + c\right)^{2} + 28 \, {\left(9 \, a^{4} b^{5} + 13 \, b^{9}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\sinh\left(d x + c\right)}}{20160 \, {\left(b^{10} d \cosh\left(d x + c\right)^{4} + 4 \, b^{10} d \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, b^{10} d \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, b^{10} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{10} d \sinh\left(d x + c\right)^{4}\right)}}"," ",0,"-1/20160*(315*a*b^8*cosh(d*x + c)^8 + 315*a*b^8*sinh(d*x + c)^8 + 840*a^3*b^6*cosh(d*x + c)^7 - 840*a^3*b^6*cosh(d*x + c) + 315*a*b^8 + 840*(3*a*b^8*cosh(d*x + c) + a^3*b^6)*sinh(d*x + c)^7 + 1260*(2*a^5*b^4 + 3*a*b^8)*cosh(d*x + c)^6 + 420*(21*a*b^8*cosh(d*x + c)^2 + 14*a^3*b^6*cosh(d*x + c) + 6*a^5*b^4 + 9*a*b^8)*sinh(d*x + c)^6 + 2520*(4*a^7*b^2 + 7*a^3*b^6)*cosh(d*x + c)^5 + 2520*(7*a*b^8*cosh(d*x + c)^3 + 7*a^3*b^6*cosh(d*x + c)^2 + 4*a^7*b^2 + 7*a^3*b^6 + 3*(2*a^5*b^4 + 3*a*b^8)*cosh(d*x + c))*sinh(d*x + c)^5 - 20160*((a^9 + 2*a^5*b^4 + a*b^8)*d*x + (a^9 + 2*a^5*b^4 + a*b^8)*c)*cosh(d*x + c)^4 + 210*(105*a*b^8*cosh(d*x + c)^4 + 140*a^3*b^6*cosh(d*x + c)^3 - 96*(a^9 + 2*a^5*b^4 + a*b^8)*d*x + 90*(2*a^5*b^4 + 3*a*b^8)*cosh(d*x + c)^2 - 96*(a^9 + 2*a^5*b^4 + a*b^8)*c + 60*(4*a^7*b^2 + 7*a^3*b^6)*cosh(d*x + c))*sinh(d*x + c)^4 - 2520*(4*a^7*b^2 + 7*a^3*b^6)*cosh(d*x + c)^3 + 840*(21*a*b^8*cosh(d*x + c)^5 + 35*a^3*b^6*cosh(d*x + c)^4 - 12*a^7*b^2 - 21*a^3*b^6 + 30*(2*a^5*b^4 + 3*a*b^8)*cosh(d*x + c)^3 + 30*(4*a^7*b^2 + 7*a^3*b^6)*cosh(d*x + c)^2 - 96*((a^9 + 2*a^5*b^4 + a*b^8)*d*x + (a^9 + 2*a^5*b^4 + a*b^8)*c)*cosh(d*x + c))*sinh(d*x + c)^3 + 1260*(2*a^5*b^4 + 3*a*b^8)*cosh(d*x + c)^2 + 1260*(7*a*b^8*cosh(d*x + c)^6 + 14*a^3*b^6*cosh(d*x + c)^5 + 2*a^5*b^4 + 3*a*b^8 + 15*(2*a^5*b^4 + 3*a*b^8)*cosh(d*x + c)^4 + 20*(4*a^7*b^2 + 7*a^3*b^6)*cosh(d*x + c)^3 - 96*((a^9 + 2*a^5*b^4 + a*b^8)*d*x + (a^9 + 2*a^5*b^4 + a*b^8)*c)*cosh(d*x + c)^2 - 6*(4*a^7*b^2 + 7*a^3*b^6)*cosh(d*x + c))*sinh(d*x + c)^2 - 20160*((a^9 + 2*a^5*b^4 + a*b^8)*cosh(d*x + c)^4 + 4*(a^9 + 2*a^5*b^4 + a*b^8)*cosh(d*x + c)^3*sinh(d*x + c) + 6*(a^9 + 2*a^5*b^4 + a*b^8)*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*(a^9 + 2*a^5*b^4 + a*b^8)*cosh(d*x + c)*sinh(d*x + c)^3 + (a^9 + 2*a^5*b^4 + a*b^8)*sinh(d*x + c)^4)*log((b^2*cosh(d*x + c)^2 + b^2*sinh(d*x + c)^2 + 2*a^2*cosh(d*x + c) - b^2 + 2*(b^2*cosh(d*x + c) + a^2)*sinh(d*x + c) - 4*(a*b*cosh(d*x + c) + a*b*sinh(d*x + c))*sqrt(sinh(d*x + c)))/(b^2*cosh(d*x + c)^2 + b^2*sinh(d*x + c)^2 - 2*a^2*cosh(d*x + c) - b^2 + 2*(b^2*cosh(d*x + c) - a^2)*sinh(d*x + c))) + 20160*((a^9 + 2*a^5*b^4 + a*b^8)*cosh(d*x + c)^4 + 4*(a^9 + 2*a^5*b^4 + a*b^8)*cosh(d*x + c)^3*sinh(d*x + c) + 6*(a^9 + 2*a^5*b^4 + a*b^8)*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*(a^9 + 2*a^5*b^4 + a*b^8)*cosh(d*x + c)*sinh(d*x + c)^3 + (a^9 + 2*a^5*b^4 + a*b^8)*sinh(d*x + c)^4)*log(2*(b^2*sinh(d*x + c) - a^2)/(cosh(d*x + c) - sinh(d*x + c))) + 840*(3*a*b^8*cosh(d*x + c)^7 + 7*a^3*b^6*cosh(d*x + c)^6 - a^3*b^6 + 9*(2*a^5*b^4 + 3*a*b^8)*cosh(d*x + c)^5 + 15*(4*a^7*b^2 + 7*a^3*b^6)*cosh(d*x + c)^4 - 96*((a^9 + 2*a^5*b^4 + a*b^8)*d*x + (a^9 + 2*a^5*b^4 + a*b^8)*c)*cosh(d*x + c)^3 - 9*(4*a^7*b^2 + 7*a^3*b^6)*cosh(d*x + c)^2 + 3*(2*a^5*b^4 + 3*a*b^8)*cosh(d*x + c))*sinh(d*x + c) - 8*(35*b^9*cosh(d*x + c)^8 + 35*b^9*sinh(d*x + c)^8 + 90*a^2*b^7*cosh(d*x + c)^7 - 90*a^2*b^7*cosh(d*x + c) + 35*b^9 + 10*(28*b^9*cosh(d*x + c) + 9*a^2*b^7)*sinh(d*x + c)^7 + 28*(9*a^4*b^5 + 13*b^9)*cosh(d*x + c)^6 + 14*(70*b^9*cosh(d*x + c)^2 + 45*a^2*b^7*cosh(d*x + c) + 18*a^4*b^5 + 26*b^9)*sinh(d*x + c)^6 + 30*(28*a^6*b^3 + 47*a^2*b^7)*cosh(d*x + c)^5 + 2*(980*b^9*cosh(d*x + c)^3 + 945*a^2*b^7*cosh(d*x + c)^2 + 420*a^6*b^3 + 705*a^2*b^7 + 84*(9*a^4*b^5 + 13*b^9)*cosh(d*x + c))*sinh(d*x + c)^5 + 42*(120*a^8*b + 228*a^4*b^5 + 101*b^9)*cosh(d*x + c)^4 + 2*(1225*b^9*cosh(d*x + c)^4 + 1575*a^2*b^7*cosh(d*x + c)^3 + 2520*a^8*b + 4788*a^4*b^5 + 2121*b^9 + 210*(9*a^4*b^5 + 13*b^9)*cosh(d*x + c)^2 + 75*(28*a^6*b^3 + 47*a^2*b^7)*cosh(d*x + c))*sinh(d*x + c)^4 - 30*(28*a^6*b^3 + 47*a^2*b^7)*cosh(d*x + c)^3 + 2*(980*b^9*cosh(d*x + c)^5 + 1575*a^2*b^7*cosh(d*x + c)^4 - 420*a^6*b^3 - 705*a^2*b^7 + 280*(9*a^4*b^5 + 13*b^9)*cosh(d*x + c)^3 + 150*(28*a^6*b^3 + 47*a^2*b^7)*cosh(d*x + c)^2 + 84*(120*a^8*b + 228*a^4*b^5 + 101*b^9)*cosh(d*x + c))*sinh(d*x + c)^3 + 28*(9*a^4*b^5 + 13*b^9)*cosh(d*x + c)^2 + 2*(490*b^9*cosh(d*x + c)^6 + 945*a^2*b^7*cosh(d*x + c)^5 + 126*a^4*b^5 + 182*b^9 + 210*(9*a^4*b^5 + 13*b^9)*cosh(d*x + c)^4 + 150*(28*a^6*b^3 + 47*a^2*b^7)*cosh(d*x + c)^3 + 126*(120*a^8*b + 228*a^4*b^5 + 101*b^9)*cosh(d*x + c)^2 - 45*(28*a^6*b^3 + 47*a^2*b^7)*cosh(d*x + c))*sinh(d*x + c)^2 + 2*(140*b^9*cosh(d*x + c)^7 + 315*a^2*b^7*cosh(d*x + c)^6 - 45*a^2*b^7 + 84*(9*a^4*b^5 + 13*b^9)*cosh(d*x + c)^5 + 75*(28*a^6*b^3 + 47*a^2*b^7)*cosh(d*x + c)^4 + 84*(120*a^8*b + 228*a^4*b^5 + 101*b^9)*cosh(d*x + c)^3 - 45*(28*a^6*b^3 + 47*a^2*b^7)*cosh(d*x + c)^2 + 28*(9*a^4*b^5 + 13*b^9)*cosh(d*x + c))*sinh(d*x + c))*sqrt(sinh(d*x + c)))/(b^10*d*cosh(d*x + c)^4 + 4*b^10*d*cosh(d*x + c)^3*sinh(d*x + c) + 6*b^10*d*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*b^10*d*cosh(d*x + c)*sinh(d*x + c)^3 + b^10*d*sinh(d*x + c)^4)","B",0
412,1,879,0,2.073706," ","integrate(cosh(d*x+c)^3/(a+b*sinh(d*x+c)^(1/2)),x, algorithm=""fricas"")","-\frac{15 \, a b^{4} \cosh\left(d x + c\right)^{4} + 15 \, a b^{4} \sinh\left(d x + c\right)^{4} + 60 \, a^{3} b^{2} \cosh\left(d x + c\right)^{3} - 60 \, a^{3} b^{2} \cosh\left(d x + c\right) + 15 \, a b^{4} + 60 \, {\left(a b^{4} \cosh\left(d x + c\right) + a^{3} b^{2}\right)} \sinh\left(d x + c\right)^{3} - 120 \, {\left({\left(a^{5} + a b^{4}\right)} d x + {\left(a^{5} + a b^{4}\right)} c\right)} \cosh\left(d x + c\right)^{2} + 30 \, {\left(3 \, a b^{4} \cosh\left(d x + c\right)^{2} + 6 \, a^{3} b^{2} \cosh\left(d x + c\right) - 4 \, {\left(a^{5} + a b^{4}\right)} d x - 4 \, {\left(a^{5} + a b^{4}\right)} c\right)} \sinh\left(d x + c\right)^{2} - 120 \, {\left({\left(a^{5} + a b^{4}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{5} + a b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{5} + a b^{4}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(\frac{b^{2} \cosh\left(d x + c\right)^{2} + b^{2} \sinh\left(d x + c\right)^{2} + 2 \, a^{2} \cosh\left(d x + c\right) - b^{2} + 2 \, {\left(b^{2} \cosh\left(d x + c\right) + a^{2}\right)} \sinh\left(d x + c\right) - 4 \, {\left(a b \cosh\left(d x + c\right) + a b \sinh\left(d x + c\right)\right)} \sqrt{\sinh\left(d x + c\right)}}{b^{2} \cosh\left(d x + c\right)^{2} + b^{2} \sinh\left(d x + c\right)^{2} - 2 \, a^{2} \cosh\left(d x + c\right) - b^{2} + 2 \, {\left(b^{2} \cosh\left(d x + c\right) - a^{2}\right)} \sinh\left(d x + c\right)}\right) + 120 \, {\left({\left(a^{5} + a b^{4}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{5} + a b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{5} + a b^{4}\right)} \sinh\left(d x + c\right)^{2}\right)} \log\left(\frac{2 \, {\left(b^{2} \sinh\left(d x + c\right) - a^{2}\right)}}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) + 60 \, {\left(a b^{4} \cosh\left(d x + c\right)^{3} + 3 \, a^{3} b^{2} \cosh\left(d x + c\right)^{2} - a^{3} b^{2} - 4 \, {\left({\left(a^{5} + a b^{4}\right)} d x + {\left(a^{5} + a b^{4}\right)} c\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) - 4 \, {\left(3 \, b^{5} \cosh\left(d x + c\right)^{4} + 3 \, b^{5} \sinh\left(d x + c\right)^{4} + 10 \, a^{2} b^{3} \cosh\left(d x + c\right)^{3} - 10 \, a^{2} b^{3} \cosh\left(d x + c\right) + 3 \, b^{5} + 2 \, {\left(6 \, b^{5} \cosh\left(d x + c\right) + 5 \, a^{2} b^{3}\right)} \sinh\left(d x + c\right)^{3} + 6 \, {\left(10 \, a^{4} b + 9 \, b^{5}\right)} \cosh\left(d x + c\right)^{2} + 6 \, {\left(3 \, b^{5} \cosh\left(d x + c\right)^{2} + 5 \, a^{2} b^{3} \cosh\left(d x + c\right) + 10 \, a^{4} b + 9 \, b^{5}\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(6 \, b^{5} \cosh\left(d x + c\right)^{3} + 15 \, a^{2} b^{3} \cosh\left(d x + c\right)^{2} - 5 \, a^{2} b^{3} + 6 \, {\left(10 \, a^{4} b + 9 \, b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\sinh\left(d x + c\right)}}{120 \, {\left(b^{6} d \cosh\left(d x + c\right)^{2} + 2 \, b^{6} d \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b^{6} d \sinh\left(d x + c\right)^{2}\right)}}"," ",0,"-1/120*(15*a*b^4*cosh(d*x + c)^4 + 15*a*b^4*sinh(d*x + c)^4 + 60*a^3*b^2*cosh(d*x + c)^3 - 60*a^3*b^2*cosh(d*x + c) + 15*a*b^4 + 60*(a*b^4*cosh(d*x + c) + a^3*b^2)*sinh(d*x + c)^3 - 120*((a^5 + a*b^4)*d*x + (a^5 + a*b^4)*c)*cosh(d*x + c)^2 + 30*(3*a*b^4*cosh(d*x + c)^2 + 6*a^3*b^2*cosh(d*x + c) - 4*(a^5 + a*b^4)*d*x - 4*(a^5 + a*b^4)*c)*sinh(d*x + c)^2 - 120*((a^5 + a*b^4)*cosh(d*x + c)^2 + 2*(a^5 + a*b^4)*cosh(d*x + c)*sinh(d*x + c) + (a^5 + a*b^4)*sinh(d*x + c)^2)*log((b^2*cosh(d*x + c)^2 + b^2*sinh(d*x + c)^2 + 2*a^2*cosh(d*x + c) - b^2 + 2*(b^2*cosh(d*x + c) + a^2)*sinh(d*x + c) - 4*(a*b*cosh(d*x + c) + a*b*sinh(d*x + c))*sqrt(sinh(d*x + c)))/(b^2*cosh(d*x + c)^2 + b^2*sinh(d*x + c)^2 - 2*a^2*cosh(d*x + c) - b^2 + 2*(b^2*cosh(d*x + c) - a^2)*sinh(d*x + c))) + 120*((a^5 + a*b^4)*cosh(d*x + c)^2 + 2*(a^5 + a*b^4)*cosh(d*x + c)*sinh(d*x + c) + (a^5 + a*b^4)*sinh(d*x + c)^2)*log(2*(b^2*sinh(d*x + c) - a^2)/(cosh(d*x + c) - sinh(d*x + c))) + 60*(a*b^4*cosh(d*x + c)^3 + 3*a^3*b^2*cosh(d*x + c)^2 - a^3*b^2 - 4*((a^5 + a*b^4)*d*x + (a^5 + a*b^4)*c)*cosh(d*x + c))*sinh(d*x + c) - 4*(3*b^5*cosh(d*x + c)^4 + 3*b^5*sinh(d*x + c)^4 + 10*a^2*b^3*cosh(d*x + c)^3 - 10*a^2*b^3*cosh(d*x + c) + 3*b^5 + 2*(6*b^5*cosh(d*x + c) + 5*a^2*b^3)*sinh(d*x + c)^3 + 6*(10*a^4*b + 9*b^5)*cosh(d*x + c)^2 + 6*(3*b^5*cosh(d*x + c)^2 + 5*a^2*b^3*cosh(d*x + c) + 10*a^4*b + 9*b^5)*sinh(d*x + c)^2 + 2*(6*b^5*cosh(d*x + c)^3 + 15*a^2*b^3*cosh(d*x + c)^2 - 5*a^2*b^3 + 6*(10*a^4*b + 9*b^5)*cosh(d*x + c))*sinh(d*x + c))*sqrt(sinh(d*x + c)))/(b^6*d*cosh(d*x + c)^2 + 2*b^6*d*cosh(d*x + c)*sinh(d*x + c) + b^6*d*sinh(d*x + c)^2)","B",0
413,1,225,0,2.305898," ","integrate(cosh(d*x+c)/(a+b*sinh(d*x+c)^(1/2)),x, algorithm=""fricas"")","\frac{a d x + a \log\left(\frac{b^{2} \cosh\left(d x + c\right)^{2} + b^{2} \sinh\left(d x + c\right)^{2} + 2 \, a^{2} \cosh\left(d x + c\right) - b^{2} + 2 \, {\left(b^{2} \cosh\left(d x + c\right) + a^{2}\right)} \sinh\left(d x + c\right) - 4 \, {\left(a b \cosh\left(d x + c\right) + a b \sinh\left(d x + c\right)\right)} \sqrt{\sinh\left(d x + c\right)}}{b^{2} \cosh\left(d x + c\right)^{2} + b^{2} \sinh\left(d x + c\right)^{2} - 2 \, a^{2} \cosh\left(d x + c\right) - b^{2} + 2 \, {\left(b^{2} \cosh\left(d x + c\right) - a^{2}\right)} \sinh\left(d x + c\right)}\right) - a \log\left(\frac{2 \, {\left(b^{2} \sinh\left(d x + c\right) - a^{2}\right)}}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) + 2 \, b \sqrt{\sinh\left(d x + c\right)}}{b^{2} d}"," ",0,"(a*d*x + a*log((b^2*cosh(d*x + c)^2 + b^2*sinh(d*x + c)^2 + 2*a^2*cosh(d*x + c) - b^2 + 2*(b^2*cosh(d*x + c) + a^2)*sinh(d*x + c) - 4*(a*b*cosh(d*x + c) + a*b*sinh(d*x + c))*sqrt(sinh(d*x + c)))/(b^2*cosh(d*x + c)^2 + b^2*sinh(d*x + c)^2 - 2*a^2*cosh(d*x + c) - b^2 + 2*(b^2*cosh(d*x + c) - a^2)*sinh(d*x + c))) - a*log(2*(b^2*sinh(d*x + c) - a^2)/(cosh(d*x + c) - sinh(d*x + c))) + 2*b*sqrt(sinh(d*x + c)))/(b^2*d)","B",0
414,-1,0,0,0.000000," ","integrate(sech(d*x+c)/(a+b*sinh(d*x+c)^(1/2)),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
415,1,5181,0,2.134809," ","integrate(cosh(d*x+c)^5/(a+b*sinh(d*x+c)^(1/2))^2,x, algorithm=""fricas"")","\frac{105 \, b^{10} \cosh\left(d x + c\right)^{10} + 105 \, b^{10} \sinh\left(d x + c\right)^{10} + 630 \, a^{2} b^{8} \cosh\left(d x + c\right)^{9} + 630 \, a^{2} b^{8} \cosh\left(d x + c\right) - 105 \, b^{10} + 210 \, {\left(5 \, b^{10} \cosh\left(d x + c\right) + 3 \, a^{2} b^{8}\right)} \sinh\left(d x + c\right)^{9} + 105 \, {\left(24 \, a^{4} b^{6} + 11 \, b^{10}\right)} \cosh\left(d x + c\right)^{8} + 105 \, {\left(45 \, b^{10} \cosh\left(d x + c\right)^{2} + 54 \, a^{2} b^{8} \cosh\left(d x + c\right) + 24 \, a^{4} b^{6} + 11 \, b^{10}\right)} \sinh\left(d x + c\right)^{8} + 840 \, {\left(18 \, a^{6} b^{4} + 17 \, a^{2} b^{8}\right)} \cosh\left(d x + c\right)^{7} + 840 \, {\left(15 \, b^{10} \cosh\left(d x + c\right)^{3} + 27 \, a^{2} b^{8} \cosh\left(d x + c\right)^{2} + 18 \, a^{6} b^{4} + 17 \, a^{2} b^{8} + {\left(24 \, a^{4} b^{6} + 11 \, b^{10}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} - 420 \, {\left(112 \, a^{8} b^{2} + 94 \, a^{4} b^{6} + 3 \, b^{10} + 16 \, {\left(9 \, a^{8} b^{2} + 10 \, a^{4} b^{6} + b^{10}\right)} d x + 16 \, {\left(9 \, a^{8} b^{2} + 10 \, a^{4} b^{6} + b^{10}\right)} c\right)} \cosh\left(d x + c\right)^{6} + 210 \, {\left(105 \, b^{10} \cosh\left(d x + c\right)^{4} + 252 \, a^{2} b^{8} \cosh\left(d x + c\right)^{3} - 224 \, a^{8} b^{2} - 188 \, a^{4} b^{6} - 6 \, b^{10} - 32 \, {\left(9 \, a^{8} b^{2} + 10 \, a^{4} b^{6} + b^{10}\right)} d x + 14 \, {\left(24 \, a^{4} b^{6} + 11 \, b^{10}\right)} \cosh\left(d x + c\right)^{2} - 32 \, {\left(9 \, a^{8} b^{2} + 10 \, a^{4} b^{6} + b^{10}\right)} c + 28 \, {\left(18 \, a^{6} b^{4} + 17 \, a^{2} b^{8}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} - 1680 \, {\left(16 \, a^{10} + 60 \, a^{6} b^{4} + 37 \, a^{2} b^{8} - 8 \, {\left(9 \, a^{10} + 10 \, a^{6} b^{4} + a^{2} b^{8}\right)} d x - 8 \, {\left(9 \, a^{10} + 10 \, a^{6} b^{4} + a^{2} b^{8}\right)} c\right)} \cosh\left(d x + c\right)^{5} + 420 \, {\left(63 \, b^{10} \cosh\left(d x + c\right)^{5} + 189 \, a^{2} b^{8} \cosh\left(d x + c\right)^{4} - 64 \, a^{10} - 240 \, a^{6} b^{4} - 148 \, a^{2} b^{8} + 14 \, {\left(24 \, a^{4} b^{6} + 11 \, b^{10}\right)} \cosh\left(d x + c\right)^{3} + 32 \, {\left(9 \, a^{10} + 10 \, a^{6} b^{4} + a^{2} b^{8}\right)} d x + 42 \, {\left(18 \, a^{6} b^{4} + 17 \, a^{2} b^{8}\right)} \cosh\left(d x + c\right)^{2} + 32 \, {\left(9 \, a^{10} + 10 \, a^{6} b^{4} + a^{2} b^{8}\right)} c - 6 \, {\left(112 \, a^{8} b^{2} + 94 \, a^{4} b^{6} + 3 \, b^{10} + 16 \, {\left(9 \, a^{8} b^{2} + 10 \, a^{4} b^{6} + b^{10}\right)} d x + 16 \, {\left(9 \, a^{8} b^{2} + 10 \, a^{4} b^{6} + b^{10}\right)} c\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 420 \, {\left(112 \, a^{8} b^{2} + 94 \, a^{4} b^{6} + 3 \, b^{10} + 16 \, {\left(9 \, a^{8} b^{2} + 10 \, a^{4} b^{6} + b^{10}\right)} d x + 16 \, {\left(9 \, a^{8} b^{2} + 10 \, a^{4} b^{6} + b^{10}\right)} c\right)} \cosh\left(d x + c\right)^{4} + 210 \, {\left(105 \, b^{10} \cosh\left(d x + c\right)^{6} + 378 \, a^{2} b^{8} \cosh\left(d x + c\right)^{5} + 224 \, a^{8} b^{2} + 188 \, a^{4} b^{6} + 6 \, b^{10} + 35 \, {\left(24 \, a^{4} b^{6} + 11 \, b^{10}\right)} \cosh\left(d x + c\right)^{4} + 140 \, {\left(18 \, a^{6} b^{4} + 17 \, a^{2} b^{8}\right)} \cosh\left(d x + c\right)^{3} + 32 \, {\left(9 \, a^{8} b^{2} + 10 \, a^{4} b^{6} + b^{10}\right)} d x - 30 \, {\left(112 \, a^{8} b^{2} + 94 \, a^{4} b^{6} + 3 \, b^{10} + 16 \, {\left(9 \, a^{8} b^{2} + 10 \, a^{4} b^{6} + b^{10}\right)} d x + 16 \, {\left(9 \, a^{8} b^{2} + 10 \, a^{4} b^{6} + b^{10}\right)} c\right)} \cosh\left(d x + c\right)^{2} + 32 \, {\left(9 \, a^{8} b^{2} + 10 \, a^{4} b^{6} + b^{10}\right)} c - 40 \, {\left(16 \, a^{10} + 60 \, a^{6} b^{4} + 37 \, a^{2} b^{8} - 8 \, {\left(9 \, a^{10} + 10 \, a^{6} b^{4} + a^{2} b^{8}\right)} d x - 8 \, {\left(9 \, a^{10} + 10 \, a^{6} b^{4} + a^{2} b^{8}\right)} c\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 840 \, {\left(18 \, a^{6} b^{4} + 17 \, a^{2} b^{8}\right)} \cosh\left(d x + c\right)^{3} + 840 \, {\left(15 \, b^{10} \cosh\left(d x + c\right)^{7} + 63 \, a^{2} b^{8} \cosh\left(d x + c\right)^{6} + 18 \, a^{6} b^{4} + 17 \, a^{2} b^{8} + 7 \, {\left(24 \, a^{4} b^{6} + 11 \, b^{10}\right)} \cosh\left(d x + c\right)^{5} + 35 \, {\left(18 \, a^{6} b^{4} + 17 \, a^{2} b^{8}\right)} \cosh\left(d x + c\right)^{4} - 10 \, {\left(112 \, a^{8} b^{2} + 94 \, a^{4} b^{6} + 3 \, b^{10} + 16 \, {\left(9 \, a^{8} b^{2} + 10 \, a^{4} b^{6} + b^{10}\right)} d x + 16 \, {\left(9 \, a^{8} b^{2} + 10 \, a^{4} b^{6} + b^{10}\right)} c\right)} \cosh\left(d x + c\right)^{3} - 20 \, {\left(16 \, a^{10} + 60 \, a^{6} b^{4} + 37 \, a^{2} b^{8} - 8 \, {\left(9 \, a^{10} + 10 \, a^{6} b^{4} + a^{2} b^{8}\right)} d x - 8 \, {\left(9 \, a^{10} + 10 \, a^{6} b^{4} + a^{2} b^{8}\right)} c\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(112 \, a^{8} b^{2} + 94 \, a^{4} b^{6} + 3 \, b^{10} + 16 \, {\left(9 \, a^{8} b^{2} + 10 \, a^{4} b^{6} + b^{10}\right)} d x + 16 \, {\left(9 \, a^{8} b^{2} + 10 \, a^{4} b^{6} + b^{10}\right)} c\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 105 \, {\left(24 \, a^{4} b^{6} + 11 \, b^{10}\right)} \cosh\left(d x + c\right)^{2} + 105 \, {\left(45 \, b^{10} \cosh\left(d x + c\right)^{8} + 216 \, a^{2} b^{8} \cosh\left(d x + c\right)^{7} - 24 \, a^{4} b^{6} - 11 \, b^{10} + 28 \, {\left(24 \, a^{4} b^{6} + 11 \, b^{10}\right)} \cosh\left(d x + c\right)^{6} + 168 \, {\left(18 \, a^{6} b^{4} + 17 \, a^{2} b^{8}\right)} \cosh\left(d x + c\right)^{5} - 60 \, {\left(112 \, a^{8} b^{2} + 94 \, a^{4} b^{6} + 3 \, b^{10} + 16 \, {\left(9 \, a^{8} b^{2} + 10 \, a^{4} b^{6} + b^{10}\right)} d x + 16 \, {\left(9 \, a^{8} b^{2} + 10 \, a^{4} b^{6} + b^{10}\right)} c\right)} \cosh\left(d x + c\right)^{4} - 160 \, {\left(16 \, a^{10} + 60 \, a^{6} b^{4} + 37 \, a^{2} b^{8} - 8 \, {\left(9 \, a^{10} + 10 \, a^{6} b^{4} + a^{2} b^{8}\right)} d x - 8 \, {\left(9 \, a^{10} + 10 \, a^{6} b^{4} + a^{2} b^{8}\right)} c\right)} \cosh\left(d x + c\right)^{3} + 24 \, {\left(112 \, a^{8} b^{2} + 94 \, a^{4} b^{6} + 3 \, b^{10} + 16 \, {\left(9 \, a^{8} b^{2} + 10 \, a^{4} b^{6} + b^{10}\right)} d x + 16 \, {\left(9 \, a^{8} b^{2} + 10 \, a^{4} b^{6} + b^{10}\right)} c\right)} \cosh\left(d x + c\right)^{2} + 24 \, {\left(18 \, a^{6} b^{4} + 17 \, a^{2} b^{8}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 6720 \, {\left({\left(9 \, a^{8} b^{2} + 10 \, a^{4} b^{6} + b^{10}\right)} \cosh\left(d x + c\right)^{6} + {\left(9 \, a^{8} b^{2} + 10 \, a^{4} b^{6} + b^{10}\right)} \sinh\left(d x + c\right)^{6} - 2 \, {\left(9 \, a^{10} + 10 \, a^{6} b^{4} + a^{2} b^{8}\right)} \cosh\left(d x + c\right)^{5} - 2 \, {\left(9 \, a^{10} + 10 \, a^{6} b^{4} + a^{2} b^{8} - 3 \, {\left(9 \, a^{8} b^{2} + 10 \, a^{4} b^{6} + b^{10}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - {\left(9 \, a^{8} b^{2} + 10 \, a^{4} b^{6} + b^{10}\right)} \cosh\left(d x + c\right)^{4} - {\left(9 \, a^{8} b^{2} + 10 \, a^{4} b^{6} + b^{10} - 15 \, {\left(9 \, a^{8} b^{2} + 10 \, a^{4} b^{6} + b^{10}\right)} \cosh\left(d x + c\right)^{2} + 10 \, {\left(9 \, a^{10} + 10 \, a^{6} b^{4} + a^{2} b^{8}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, {\left(9 \, a^{8} b^{2} + 10 \, a^{4} b^{6} + b^{10}\right)} \cosh\left(d x + c\right)^{3} - 5 \, {\left(9 \, a^{10} + 10 \, a^{6} b^{4} + a^{2} b^{8}\right)} \cosh\left(d x + c\right)^{2} - {\left(9 \, a^{8} b^{2} + 10 \, a^{4} b^{6} + b^{10}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(15 \, {\left(9 \, a^{8} b^{2} + 10 \, a^{4} b^{6} + b^{10}\right)} \cosh\left(d x + c\right)^{4} - 20 \, {\left(9 \, a^{10} + 10 \, a^{6} b^{4} + a^{2} b^{8}\right)} \cosh\left(d x + c\right)^{3} - 6 \, {\left(9 \, a^{8} b^{2} + 10 \, a^{4} b^{6} + b^{10}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(9 \, a^{8} b^{2} + 10 \, a^{4} b^{6} + b^{10}\right)} \cosh\left(d x + c\right)^{5} - 5 \, {\left(9 \, a^{10} + 10 \, a^{6} b^{4} + a^{2} b^{8}\right)} \cosh\left(d x + c\right)^{4} - 2 \, {\left(9 \, a^{8} b^{2} + 10 \, a^{4} b^{6} + b^{10}\right)} \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right)\right)} \log\left(-\frac{b^{2} \cosh\left(d x + c\right)^{2} + b^{2} \sinh\left(d x + c\right)^{2} + 2 \, a^{2} \cosh\left(d x + c\right) - b^{2} + 2 \, {\left(b^{2} \cosh\left(d x + c\right) + a^{2}\right)} \sinh\left(d x + c\right) + 4 \, {\left(a b \cosh\left(d x + c\right) + a b \sinh\left(d x + c\right)\right)} \sqrt{\sinh\left(d x + c\right)}}{b^{2} \cosh\left(d x + c\right)^{2} + b^{2} \sinh\left(d x + c\right)^{2} - 2 \, a^{2} \cosh\left(d x + c\right) - b^{2} + 2 \, {\left(b^{2} \cosh\left(d x + c\right) - a^{2}\right)} \sinh\left(d x + c\right)}\right) + 6720 \, {\left({\left(9 \, a^{8} b^{2} + 10 \, a^{4} b^{6} + b^{10}\right)} \cosh\left(d x + c\right)^{6} + {\left(9 \, a^{8} b^{2} + 10 \, a^{4} b^{6} + b^{10}\right)} \sinh\left(d x + c\right)^{6} - 2 \, {\left(9 \, a^{10} + 10 \, a^{6} b^{4} + a^{2} b^{8}\right)} \cosh\left(d x + c\right)^{5} - 2 \, {\left(9 \, a^{10} + 10 \, a^{6} b^{4} + a^{2} b^{8} - 3 \, {\left(9 \, a^{8} b^{2} + 10 \, a^{4} b^{6} + b^{10}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - {\left(9 \, a^{8} b^{2} + 10 \, a^{4} b^{6} + b^{10}\right)} \cosh\left(d x + c\right)^{4} - {\left(9 \, a^{8} b^{2} + 10 \, a^{4} b^{6} + b^{10} - 15 \, {\left(9 \, a^{8} b^{2} + 10 \, a^{4} b^{6} + b^{10}\right)} \cosh\left(d x + c\right)^{2} + 10 \, {\left(9 \, a^{10} + 10 \, a^{6} b^{4} + a^{2} b^{8}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, {\left(9 \, a^{8} b^{2} + 10 \, a^{4} b^{6} + b^{10}\right)} \cosh\left(d x + c\right)^{3} - 5 \, {\left(9 \, a^{10} + 10 \, a^{6} b^{4} + a^{2} b^{8}\right)} \cosh\left(d x + c\right)^{2} - {\left(9 \, a^{8} b^{2} + 10 \, a^{4} b^{6} + b^{10}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(15 \, {\left(9 \, a^{8} b^{2} + 10 \, a^{4} b^{6} + b^{10}\right)} \cosh\left(d x + c\right)^{4} - 20 \, {\left(9 \, a^{10} + 10 \, a^{6} b^{4} + a^{2} b^{8}\right)} \cosh\left(d x + c\right)^{3} - 6 \, {\left(9 \, a^{8} b^{2} + 10 \, a^{4} b^{6} + b^{10}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(9 \, a^{8} b^{2} + 10 \, a^{4} b^{6} + b^{10}\right)} \cosh\left(d x + c\right)^{5} - 5 \, {\left(9 \, a^{10} + 10 \, a^{6} b^{4} + a^{2} b^{8}\right)} \cosh\left(d x + c\right)^{4} - 2 \, {\left(9 \, a^{8} b^{2} + 10 \, a^{4} b^{6} + b^{10}\right)} \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right)\right)} \log\left(\frac{2 \, {\left(b^{2} \sinh\left(d x + c\right) - a^{2}\right)}}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) + 210 \, {\left(5 \, b^{10} \cosh\left(d x + c\right)^{9} + 27 \, a^{2} b^{8} \cosh\left(d x + c\right)^{8} + 3 \, a^{2} b^{8} + 4 \, {\left(24 \, a^{4} b^{6} + 11 \, b^{10}\right)} \cosh\left(d x + c\right)^{7} + 28 \, {\left(18 \, a^{6} b^{4} + 17 \, a^{2} b^{8}\right)} \cosh\left(d x + c\right)^{6} - 12 \, {\left(112 \, a^{8} b^{2} + 94 \, a^{4} b^{6} + 3 \, b^{10} + 16 \, {\left(9 \, a^{8} b^{2} + 10 \, a^{4} b^{6} + b^{10}\right)} d x + 16 \, {\left(9 \, a^{8} b^{2} + 10 \, a^{4} b^{6} + b^{10}\right)} c\right)} \cosh\left(d x + c\right)^{5} - 40 \, {\left(16 \, a^{10} + 60 \, a^{6} b^{4} + 37 \, a^{2} b^{8} - 8 \, {\left(9 \, a^{10} + 10 \, a^{6} b^{4} + a^{2} b^{8}\right)} d x - 8 \, {\left(9 \, a^{10} + 10 \, a^{6} b^{4} + a^{2} b^{8}\right)} c\right)} \cosh\left(d x + c\right)^{4} + 8 \, {\left(112 \, a^{8} b^{2} + 94 \, a^{4} b^{6} + 3 \, b^{10} + 16 \, {\left(9 \, a^{8} b^{2} + 10 \, a^{4} b^{6} + b^{10}\right)} d x + 16 \, {\left(9 \, a^{8} b^{2} + 10 \, a^{4} b^{6} + b^{10}\right)} c\right)} \cosh\left(d x + c\right)^{3} + 12 \, {\left(18 \, a^{6} b^{4} + 17 \, a^{2} b^{8}\right)} \cosh\left(d x + c\right)^{2} - {\left(24 \, a^{4} b^{6} + 11 \, b^{10}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) - 32 \, {\left(15 \, a b^{9} \cosh\left(d x + c\right)^{9} + 15 \, a b^{9} \sinh\left(d x + c\right)^{9} + 54 \, a^{3} b^{7} \cosh\left(d x + c\right)^{8} - 54 \, a^{3} b^{7} \cosh\left(d x + c\right)^{2} + 15 \, a b^{9} \cosh\left(d x + c\right) + 27 \, {\left(5 \, a b^{9} \cosh\left(d x + c\right) + 2 \, a^{3} b^{7}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(63 \, a^{5} b^{5} + 55 \, a b^{9}\right)} \cosh\left(d x + c\right)^{7} + 4 \, {\left(135 \, a b^{9} \cosh\left(d x + c\right)^{2} + 108 \, a^{3} b^{7} \cosh\left(d x + c\right) + 63 \, a^{5} b^{5} + 55 \, a b^{9}\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(1260 \, a^{7} b^{3} + 1319 \, a^{3} b^{7}\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(630 \, a b^{9} \cosh\left(d x + c\right)^{3} + 756 \, a^{3} b^{7} \cosh\left(d x + c\right)^{2} + 1260 \, a^{7} b^{3} + 1319 \, a^{3} b^{7} + 14 \, {\left(63 \, a^{5} b^{5} + 55 \, a b^{9}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} - 2 \, {\left(3780 \, a^{9} b + 4452 \, a^{5} b^{5} + 655 \, a b^{9}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(945 \, a b^{9} \cosh\left(d x + c\right)^{4} + 1512 \, a^{3} b^{7} \cosh\left(d x + c\right)^{3} - 3780 \, a^{9} b - 4452 \, a^{5} b^{5} - 655 \, a b^{9} + 42 \, {\left(63 \, a^{5} b^{5} + 55 \, a b^{9}\right)} \cosh\left(d x + c\right)^{2} + 6 \, {\left(1260 \, a^{7} b^{3} + 1319 \, a^{3} b^{7}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 2 \, {\left(1260 \, a^{7} b^{3} + 1319 \, a^{3} b^{7}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(945 \, a b^{9} \cosh\left(d x + c\right)^{5} + 1890 \, a^{3} b^{7} \cosh\left(d x + c\right)^{4} - 1260 \, a^{7} b^{3} - 1319 \, a^{3} b^{7} + 70 \, {\left(63 \, a^{5} b^{5} + 55 \, a b^{9}\right)} \cosh\left(d x + c\right)^{3} + 15 \, {\left(1260 \, a^{7} b^{3} + 1319 \, a^{3} b^{7}\right)} \cosh\left(d x + c\right)^{2} - 5 \, {\left(3780 \, a^{9} b + 4452 \, a^{5} b^{5} + 655 \, a b^{9}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(63 \, a^{5} b^{5} + 55 \, a b^{9}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(315 \, a b^{9} \cosh\left(d x + c\right)^{6} + 756 \, a^{3} b^{7} \cosh\left(d x + c\right)^{5} + 63 \, a^{5} b^{5} + 55 \, a b^{9} + 35 \, {\left(63 \, a^{5} b^{5} + 55 \, a b^{9}\right)} \cosh\left(d x + c\right)^{4} + 10 \, {\left(1260 \, a^{7} b^{3} + 1319 \, a^{3} b^{7}\right)} \cosh\left(d x + c\right)^{3} - 5 \, {\left(3780 \, a^{9} b + 4452 \, a^{5} b^{5} + 655 \, a b^{9}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left(1260 \, a^{7} b^{3} + 1319 \, a^{3} b^{7}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(270 \, a b^{9} \cosh\left(d x + c\right)^{7} + 756 \, a^{3} b^{7} \cosh\left(d x + c\right)^{6} - 27 \, a^{3} b^{7} + 42 \, {\left(63 \, a^{5} b^{5} + 55 \, a b^{9}\right)} \cosh\left(d x + c\right)^{5} + 15 \, {\left(1260 \, a^{7} b^{3} + 1319 \, a^{3} b^{7}\right)} \cosh\left(d x + c\right)^{4} - 10 \, {\left(3780 \, a^{9} b + 4452 \, a^{5} b^{5} + 655 \, a b^{9}\right)} \cosh\left(d x + c\right)^{3} - 6 \, {\left(1260 \, a^{7} b^{3} + 1319 \, a^{3} b^{7}\right)} \cosh\left(d x + c\right)^{2} + 6 \, {\left(63 \, a^{5} b^{5} + 55 \, a b^{9}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(135 \, a b^{9} \cosh\left(d x + c\right)^{8} + 432 \, a^{3} b^{7} \cosh\left(d x + c\right)^{7} - 108 \, a^{3} b^{7} \cosh\left(d x + c\right) + 15 \, a b^{9} + 28 \, {\left(63 \, a^{5} b^{5} + 55 \, a b^{9}\right)} \cosh\left(d x + c\right)^{6} + 12 \, {\left(1260 \, a^{7} b^{3} + 1319 \, a^{3} b^{7}\right)} \cosh\left(d x + c\right)^{5} - 10 \, {\left(3780 \, a^{9} b + 4452 \, a^{5} b^{5} + 655 \, a b^{9}\right)} \cosh\left(d x + c\right)^{4} - 8 \, {\left(1260 \, a^{7} b^{3} + 1319 \, a^{3} b^{7}\right)} \cosh\left(d x + c\right)^{3} + 12 \, {\left(63 \, a^{5} b^{5} + 55 \, a b^{9}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)\right)} \sqrt{\sinh\left(d x + c\right)}}{6720 \, {\left(b^{12} d \cosh\left(d x + c\right)^{6} + b^{12} d \sinh\left(d x + c\right)^{6} - 2 \, a^{2} b^{10} d \cosh\left(d x + c\right)^{5} - b^{12} d \cosh\left(d x + c\right)^{4} + 2 \, {\left(3 \, b^{12} d \cosh\left(d x + c\right) - a^{2} b^{10} d\right)} \sinh\left(d x + c\right)^{5} + {\left(15 \, b^{12} d \cosh\left(d x + c\right)^{2} - 10 \, a^{2} b^{10} d \cosh\left(d x + c\right) - b^{12} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, b^{12} d \cosh\left(d x + c\right)^{3} - 5 \, a^{2} b^{10} d \cosh\left(d x + c\right)^{2} - b^{12} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(15 \, b^{12} d \cosh\left(d x + c\right)^{4} - 20 \, a^{2} b^{10} d \cosh\left(d x + c\right)^{3} - 6 \, b^{12} d \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b^{12} d \cosh\left(d x + c\right)^{5} - 5 \, a^{2} b^{10} d \cosh\left(d x + c\right)^{4} - 2 \, b^{12} d \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"1/6720*(105*b^10*cosh(d*x + c)^10 + 105*b^10*sinh(d*x + c)^10 + 630*a^2*b^8*cosh(d*x + c)^9 + 630*a^2*b^8*cosh(d*x + c) - 105*b^10 + 210*(5*b^10*cosh(d*x + c) + 3*a^2*b^8)*sinh(d*x + c)^9 + 105*(24*a^4*b^6 + 11*b^10)*cosh(d*x + c)^8 + 105*(45*b^10*cosh(d*x + c)^2 + 54*a^2*b^8*cosh(d*x + c) + 24*a^4*b^6 + 11*b^10)*sinh(d*x + c)^8 + 840*(18*a^6*b^4 + 17*a^2*b^8)*cosh(d*x + c)^7 + 840*(15*b^10*cosh(d*x + c)^3 + 27*a^2*b^8*cosh(d*x + c)^2 + 18*a^6*b^4 + 17*a^2*b^8 + (24*a^4*b^6 + 11*b^10)*cosh(d*x + c))*sinh(d*x + c)^7 - 420*(112*a^8*b^2 + 94*a^4*b^6 + 3*b^10 + 16*(9*a^8*b^2 + 10*a^4*b^6 + b^10)*d*x + 16*(9*a^8*b^2 + 10*a^4*b^6 + b^10)*c)*cosh(d*x + c)^6 + 210*(105*b^10*cosh(d*x + c)^4 + 252*a^2*b^8*cosh(d*x + c)^3 - 224*a^8*b^2 - 188*a^4*b^6 - 6*b^10 - 32*(9*a^8*b^2 + 10*a^4*b^6 + b^10)*d*x + 14*(24*a^4*b^6 + 11*b^10)*cosh(d*x + c)^2 - 32*(9*a^8*b^2 + 10*a^4*b^6 + b^10)*c + 28*(18*a^6*b^4 + 17*a^2*b^8)*cosh(d*x + c))*sinh(d*x + c)^6 - 1680*(16*a^10 + 60*a^6*b^4 + 37*a^2*b^8 - 8*(9*a^10 + 10*a^6*b^4 + a^2*b^8)*d*x - 8*(9*a^10 + 10*a^6*b^4 + a^2*b^8)*c)*cosh(d*x + c)^5 + 420*(63*b^10*cosh(d*x + c)^5 + 189*a^2*b^8*cosh(d*x + c)^4 - 64*a^10 - 240*a^6*b^4 - 148*a^2*b^8 + 14*(24*a^4*b^6 + 11*b^10)*cosh(d*x + c)^3 + 32*(9*a^10 + 10*a^6*b^4 + a^2*b^8)*d*x + 42*(18*a^6*b^4 + 17*a^2*b^8)*cosh(d*x + c)^2 + 32*(9*a^10 + 10*a^6*b^4 + a^2*b^8)*c - 6*(112*a^8*b^2 + 94*a^4*b^6 + 3*b^10 + 16*(9*a^8*b^2 + 10*a^4*b^6 + b^10)*d*x + 16*(9*a^8*b^2 + 10*a^4*b^6 + b^10)*c)*cosh(d*x + c))*sinh(d*x + c)^5 + 420*(112*a^8*b^2 + 94*a^4*b^6 + 3*b^10 + 16*(9*a^8*b^2 + 10*a^4*b^6 + b^10)*d*x + 16*(9*a^8*b^2 + 10*a^4*b^6 + b^10)*c)*cosh(d*x + c)^4 + 210*(105*b^10*cosh(d*x + c)^6 + 378*a^2*b^8*cosh(d*x + c)^5 + 224*a^8*b^2 + 188*a^4*b^6 + 6*b^10 + 35*(24*a^4*b^6 + 11*b^10)*cosh(d*x + c)^4 + 140*(18*a^6*b^4 + 17*a^2*b^8)*cosh(d*x + c)^3 + 32*(9*a^8*b^2 + 10*a^4*b^6 + b^10)*d*x - 30*(112*a^8*b^2 + 94*a^4*b^6 + 3*b^10 + 16*(9*a^8*b^2 + 10*a^4*b^6 + b^10)*d*x + 16*(9*a^8*b^2 + 10*a^4*b^6 + b^10)*c)*cosh(d*x + c)^2 + 32*(9*a^8*b^2 + 10*a^4*b^6 + b^10)*c - 40*(16*a^10 + 60*a^6*b^4 + 37*a^2*b^8 - 8*(9*a^10 + 10*a^6*b^4 + a^2*b^8)*d*x - 8*(9*a^10 + 10*a^6*b^4 + a^2*b^8)*c)*cosh(d*x + c))*sinh(d*x + c)^4 + 840*(18*a^6*b^4 + 17*a^2*b^8)*cosh(d*x + c)^3 + 840*(15*b^10*cosh(d*x + c)^7 + 63*a^2*b^8*cosh(d*x + c)^6 + 18*a^6*b^4 + 17*a^2*b^8 + 7*(24*a^4*b^6 + 11*b^10)*cosh(d*x + c)^5 + 35*(18*a^6*b^4 + 17*a^2*b^8)*cosh(d*x + c)^4 - 10*(112*a^8*b^2 + 94*a^4*b^6 + 3*b^10 + 16*(9*a^8*b^2 + 10*a^4*b^6 + b^10)*d*x + 16*(9*a^8*b^2 + 10*a^4*b^6 + b^10)*c)*cosh(d*x + c)^3 - 20*(16*a^10 + 60*a^6*b^4 + 37*a^2*b^8 - 8*(9*a^10 + 10*a^6*b^4 + a^2*b^8)*d*x - 8*(9*a^10 + 10*a^6*b^4 + a^2*b^8)*c)*cosh(d*x + c)^2 + 2*(112*a^8*b^2 + 94*a^4*b^6 + 3*b^10 + 16*(9*a^8*b^2 + 10*a^4*b^6 + b^10)*d*x + 16*(9*a^8*b^2 + 10*a^4*b^6 + b^10)*c)*cosh(d*x + c))*sinh(d*x + c)^3 - 105*(24*a^4*b^6 + 11*b^10)*cosh(d*x + c)^2 + 105*(45*b^10*cosh(d*x + c)^8 + 216*a^2*b^8*cosh(d*x + c)^7 - 24*a^4*b^6 - 11*b^10 + 28*(24*a^4*b^6 + 11*b^10)*cosh(d*x + c)^6 + 168*(18*a^6*b^4 + 17*a^2*b^8)*cosh(d*x + c)^5 - 60*(112*a^8*b^2 + 94*a^4*b^6 + 3*b^10 + 16*(9*a^8*b^2 + 10*a^4*b^6 + b^10)*d*x + 16*(9*a^8*b^2 + 10*a^4*b^6 + b^10)*c)*cosh(d*x + c)^4 - 160*(16*a^10 + 60*a^6*b^4 + 37*a^2*b^8 - 8*(9*a^10 + 10*a^6*b^4 + a^2*b^8)*d*x - 8*(9*a^10 + 10*a^6*b^4 + a^2*b^8)*c)*cosh(d*x + c)^3 + 24*(112*a^8*b^2 + 94*a^4*b^6 + 3*b^10 + 16*(9*a^8*b^2 + 10*a^4*b^6 + b^10)*d*x + 16*(9*a^8*b^2 + 10*a^4*b^6 + b^10)*c)*cosh(d*x + c)^2 + 24*(18*a^6*b^4 + 17*a^2*b^8)*cosh(d*x + c))*sinh(d*x + c)^2 + 6720*((9*a^8*b^2 + 10*a^4*b^6 + b^10)*cosh(d*x + c)^6 + (9*a^8*b^2 + 10*a^4*b^6 + b^10)*sinh(d*x + c)^6 - 2*(9*a^10 + 10*a^6*b^4 + a^2*b^8)*cosh(d*x + c)^5 - 2*(9*a^10 + 10*a^6*b^4 + a^2*b^8 - 3*(9*a^8*b^2 + 10*a^4*b^6 + b^10)*cosh(d*x + c))*sinh(d*x + c)^5 - (9*a^8*b^2 + 10*a^4*b^6 + b^10)*cosh(d*x + c)^4 - (9*a^8*b^2 + 10*a^4*b^6 + b^10 - 15*(9*a^8*b^2 + 10*a^4*b^6 + b^10)*cosh(d*x + c)^2 + 10*(9*a^10 + 10*a^6*b^4 + a^2*b^8)*cosh(d*x + c))*sinh(d*x + c)^4 + 4*(5*(9*a^8*b^2 + 10*a^4*b^6 + b^10)*cosh(d*x + c)^3 - 5*(9*a^10 + 10*a^6*b^4 + a^2*b^8)*cosh(d*x + c)^2 - (9*a^8*b^2 + 10*a^4*b^6 + b^10)*cosh(d*x + c))*sinh(d*x + c)^3 + (15*(9*a^8*b^2 + 10*a^4*b^6 + b^10)*cosh(d*x + c)^4 - 20*(9*a^10 + 10*a^6*b^4 + a^2*b^8)*cosh(d*x + c)^3 - 6*(9*a^8*b^2 + 10*a^4*b^6 + b^10)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 2*(3*(9*a^8*b^2 + 10*a^4*b^6 + b^10)*cosh(d*x + c)^5 - 5*(9*a^10 + 10*a^6*b^4 + a^2*b^8)*cosh(d*x + c)^4 - 2*(9*a^8*b^2 + 10*a^4*b^6 + b^10)*cosh(d*x + c)^3)*sinh(d*x + c))*log(-(b^2*cosh(d*x + c)^2 + b^2*sinh(d*x + c)^2 + 2*a^2*cosh(d*x + c) - b^2 + 2*(b^2*cosh(d*x + c) + a^2)*sinh(d*x + c) + 4*(a*b*cosh(d*x + c) + a*b*sinh(d*x + c))*sqrt(sinh(d*x + c)))/(b^2*cosh(d*x + c)^2 + b^2*sinh(d*x + c)^2 - 2*a^2*cosh(d*x + c) - b^2 + 2*(b^2*cosh(d*x + c) - a^2)*sinh(d*x + c))) + 6720*((9*a^8*b^2 + 10*a^4*b^6 + b^10)*cosh(d*x + c)^6 + (9*a^8*b^2 + 10*a^4*b^6 + b^10)*sinh(d*x + c)^6 - 2*(9*a^10 + 10*a^6*b^4 + a^2*b^8)*cosh(d*x + c)^5 - 2*(9*a^10 + 10*a^6*b^4 + a^2*b^8 - 3*(9*a^8*b^2 + 10*a^4*b^6 + b^10)*cosh(d*x + c))*sinh(d*x + c)^5 - (9*a^8*b^2 + 10*a^4*b^6 + b^10)*cosh(d*x + c)^4 - (9*a^8*b^2 + 10*a^4*b^6 + b^10 - 15*(9*a^8*b^2 + 10*a^4*b^6 + b^10)*cosh(d*x + c)^2 + 10*(9*a^10 + 10*a^6*b^4 + a^2*b^8)*cosh(d*x + c))*sinh(d*x + c)^4 + 4*(5*(9*a^8*b^2 + 10*a^4*b^6 + b^10)*cosh(d*x + c)^3 - 5*(9*a^10 + 10*a^6*b^4 + a^2*b^8)*cosh(d*x + c)^2 - (9*a^8*b^2 + 10*a^4*b^6 + b^10)*cosh(d*x + c))*sinh(d*x + c)^3 + (15*(9*a^8*b^2 + 10*a^4*b^6 + b^10)*cosh(d*x + c)^4 - 20*(9*a^10 + 10*a^6*b^4 + a^2*b^8)*cosh(d*x + c)^3 - 6*(9*a^8*b^2 + 10*a^4*b^6 + b^10)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 2*(3*(9*a^8*b^2 + 10*a^4*b^6 + b^10)*cosh(d*x + c)^5 - 5*(9*a^10 + 10*a^6*b^4 + a^2*b^8)*cosh(d*x + c)^4 - 2*(9*a^8*b^2 + 10*a^4*b^6 + b^10)*cosh(d*x + c)^3)*sinh(d*x + c))*log(2*(b^2*sinh(d*x + c) - a^2)/(cosh(d*x + c) - sinh(d*x + c))) + 210*(5*b^10*cosh(d*x + c)^9 + 27*a^2*b^8*cosh(d*x + c)^8 + 3*a^2*b^8 + 4*(24*a^4*b^6 + 11*b^10)*cosh(d*x + c)^7 + 28*(18*a^6*b^4 + 17*a^2*b^8)*cosh(d*x + c)^6 - 12*(112*a^8*b^2 + 94*a^4*b^6 + 3*b^10 + 16*(9*a^8*b^2 + 10*a^4*b^6 + b^10)*d*x + 16*(9*a^8*b^2 + 10*a^4*b^6 + b^10)*c)*cosh(d*x + c)^5 - 40*(16*a^10 + 60*a^6*b^4 + 37*a^2*b^8 - 8*(9*a^10 + 10*a^6*b^4 + a^2*b^8)*d*x - 8*(9*a^10 + 10*a^6*b^4 + a^2*b^8)*c)*cosh(d*x + c)^4 + 8*(112*a^8*b^2 + 94*a^4*b^6 + 3*b^10 + 16*(9*a^8*b^2 + 10*a^4*b^6 + b^10)*d*x + 16*(9*a^8*b^2 + 10*a^4*b^6 + b^10)*c)*cosh(d*x + c)^3 + 12*(18*a^6*b^4 + 17*a^2*b^8)*cosh(d*x + c)^2 - (24*a^4*b^6 + 11*b^10)*cosh(d*x + c))*sinh(d*x + c) - 32*(15*a*b^9*cosh(d*x + c)^9 + 15*a*b^9*sinh(d*x + c)^9 + 54*a^3*b^7*cosh(d*x + c)^8 - 54*a^3*b^7*cosh(d*x + c)^2 + 15*a*b^9*cosh(d*x + c) + 27*(5*a*b^9*cosh(d*x + c) + 2*a^3*b^7)*sinh(d*x + c)^8 + 4*(63*a^5*b^5 + 55*a*b^9)*cosh(d*x + c)^7 + 4*(135*a*b^9*cosh(d*x + c)^2 + 108*a^3*b^7*cosh(d*x + c) + 63*a^5*b^5 + 55*a*b^9)*sinh(d*x + c)^7 + 2*(1260*a^7*b^3 + 1319*a^3*b^7)*cosh(d*x + c)^6 + 2*(630*a*b^9*cosh(d*x + c)^3 + 756*a^3*b^7*cosh(d*x + c)^2 + 1260*a^7*b^3 + 1319*a^3*b^7 + 14*(63*a^5*b^5 + 55*a*b^9)*cosh(d*x + c))*sinh(d*x + c)^6 - 2*(3780*a^9*b + 4452*a^5*b^5 + 655*a*b^9)*cosh(d*x + c)^5 + 2*(945*a*b^9*cosh(d*x + c)^4 + 1512*a^3*b^7*cosh(d*x + c)^3 - 3780*a^9*b - 4452*a^5*b^5 - 655*a*b^9 + 42*(63*a^5*b^5 + 55*a*b^9)*cosh(d*x + c)^2 + 6*(1260*a^7*b^3 + 1319*a^3*b^7)*cosh(d*x + c))*sinh(d*x + c)^5 - 2*(1260*a^7*b^3 + 1319*a^3*b^7)*cosh(d*x + c)^4 + 2*(945*a*b^9*cosh(d*x + c)^5 + 1890*a^3*b^7*cosh(d*x + c)^4 - 1260*a^7*b^3 - 1319*a^3*b^7 + 70*(63*a^5*b^5 + 55*a*b^9)*cosh(d*x + c)^3 + 15*(1260*a^7*b^3 + 1319*a^3*b^7)*cosh(d*x + c)^2 - 5*(3780*a^9*b + 4452*a^5*b^5 + 655*a*b^9)*cosh(d*x + c))*sinh(d*x + c)^4 + 4*(63*a^5*b^5 + 55*a*b^9)*cosh(d*x + c)^3 + 4*(315*a*b^9*cosh(d*x + c)^6 + 756*a^3*b^7*cosh(d*x + c)^5 + 63*a^5*b^5 + 55*a*b^9 + 35*(63*a^5*b^5 + 55*a*b^9)*cosh(d*x + c)^4 + 10*(1260*a^7*b^3 + 1319*a^3*b^7)*cosh(d*x + c)^3 - 5*(3780*a^9*b + 4452*a^5*b^5 + 655*a*b^9)*cosh(d*x + c)^2 - 2*(1260*a^7*b^3 + 1319*a^3*b^7)*cosh(d*x + c))*sinh(d*x + c)^3 + 2*(270*a*b^9*cosh(d*x + c)^7 + 756*a^3*b^7*cosh(d*x + c)^6 - 27*a^3*b^7 + 42*(63*a^5*b^5 + 55*a*b^9)*cosh(d*x + c)^5 + 15*(1260*a^7*b^3 + 1319*a^3*b^7)*cosh(d*x + c)^4 - 10*(3780*a^9*b + 4452*a^5*b^5 + 655*a*b^9)*cosh(d*x + c)^3 - 6*(1260*a^7*b^3 + 1319*a^3*b^7)*cosh(d*x + c)^2 + 6*(63*a^5*b^5 + 55*a*b^9)*cosh(d*x + c))*sinh(d*x + c)^2 + (135*a*b^9*cosh(d*x + c)^8 + 432*a^3*b^7*cosh(d*x + c)^7 - 108*a^3*b^7*cosh(d*x + c) + 15*a*b^9 + 28*(63*a^5*b^5 + 55*a*b^9)*cosh(d*x + c)^6 + 12*(1260*a^7*b^3 + 1319*a^3*b^7)*cosh(d*x + c)^5 - 10*(3780*a^9*b + 4452*a^5*b^5 + 655*a*b^9)*cosh(d*x + c)^4 - 8*(1260*a^7*b^3 + 1319*a^3*b^7)*cosh(d*x + c)^3 + 12*(63*a^5*b^5 + 55*a*b^9)*cosh(d*x + c)^2)*sinh(d*x + c))*sqrt(sinh(d*x + c)))/(b^12*d*cosh(d*x + c)^6 + b^12*d*sinh(d*x + c)^6 - 2*a^2*b^10*d*cosh(d*x + c)^5 - b^12*d*cosh(d*x + c)^4 + 2*(3*b^12*d*cosh(d*x + c) - a^2*b^10*d)*sinh(d*x + c)^5 + (15*b^12*d*cosh(d*x + c)^2 - 10*a^2*b^10*d*cosh(d*x + c) - b^12*d)*sinh(d*x + c)^4 + 4*(5*b^12*d*cosh(d*x + c)^3 - 5*a^2*b^10*d*cosh(d*x + c)^2 - b^12*d*cosh(d*x + c))*sinh(d*x + c)^3 + (15*b^12*d*cosh(d*x + c)^4 - 20*a^2*b^10*d*cosh(d*x + c)^3 - 6*b^12*d*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 2*(3*b^12*d*cosh(d*x + c)^5 - 5*a^2*b^10*d*cosh(d*x + c)^4 - 2*b^12*d*cosh(d*x + c)^3)*sinh(d*x + c))","B",0
416,1,2137,0,1.974776," ","integrate(cosh(d*x+c)^3/(a+b*sinh(d*x+c)^(1/2))^2,x, algorithm=""fricas"")","\frac{3 \, b^{6} \cosh\left(d x + c\right)^{6} + 3 \, b^{6} \sinh\left(d x + c\right)^{6} + 30 \, a^{2} b^{4} \cosh\left(d x + c\right)^{5} + 30 \, a^{2} b^{4} \cosh\left(d x + c\right) - 3 \, b^{6} + 6 \, {\left(3 \, b^{6} \cosh\left(d x + c\right) + 5 \, a^{2} b^{4}\right)} \sinh\left(d x + c\right)^{5} - 3 \, {\left(24 \, a^{4} b^{2} + b^{6} + 8 \, {\left(5 \, a^{4} b^{2} + b^{6}\right)} d x + 8 \, {\left(5 \, a^{4} b^{2} + b^{6}\right)} c\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(15 \, b^{6} \cosh\left(d x + c\right)^{2} + 50 \, a^{2} b^{4} \cosh\left(d x + c\right) - 24 \, a^{4} b^{2} - b^{6} - 8 \, {\left(5 \, a^{4} b^{2} + b^{6}\right)} d x - 8 \, {\left(5 \, a^{4} b^{2} + b^{6}\right)} c\right)} \sinh\left(d x + c\right)^{4} - 24 \, {\left(4 \, a^{6} + 7 \, a^{2} b^{4} - 2 \, {\left(5 \, a^{6} + a^{2} b^{4}\right)} d x - 2 \, {\left(5 \, a^{6} + a^{2} b^{4}\right)} c\right)} \cosh\left(d x + c\right)^{3} + 12 \, {\left(5 \, b^{6} \cosh\left(d x + c\right)^{3} + 25 \, a^{2} b^{4} \cosh\left(d x + c\right)^{2} - 8 \, a^{6} - 14 \, a^{2} b^{4} + 4 \, {\left(5 \, a^{6} + a^{2} b^{4}\right)} d x + 4 \, {\left(5 \, a^{6} + a^{2} b^{4}\right)} c - {\left(24 \, a^{4} b^{2} + b^{6} + 8 \, {\left(5 \, a^{4} b^{2} + b^{6}\right)} d x + 8 \, {\left(5 \, a^{4} b^{2} + b^{6}\right)} c\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 3 \, {\left(24 \, a^{4} b^{2} + b^{6} + 8 \, {\left(5 \, a^{4} b^{2} + b^{6}\right)} d x + 8 \, {\left(5 \, a^{4} b^{2} + b^{6}\right)} c\right)} \cosh\left(d x + c\right)^{2} + 3 \, {\left(15 \, b^{6} \cosh\left(d x + c\right)^{4} + 100 \, a^{2} b^{4} \cosh\left(d x + c\right)^{3} + 24 \, a^{4} b^{2} + b^{6} + 8 \, {\left(5 \, a^{4} b^{2} + b^{6}\right)} d x - 6 \, {\left(24 \, a^{4} b^{2} + b^{6} + 8 \, {\left(5 \, a^{4} b^{2} + b^{6}\right)} d x + 8 \, {\left(5 \, a^{4} b^{2} + b^{6}\right)} c\right)} \cosh\left(d x + c\right)^{2} + 8 \, {\left(5 \, a^{4} b^{2} + b^{6}\right)} c - 24 \, {\left(4 \, a^{6} + 7 \, a^{2} b^{4} - 2 \, {\left(5 \, a^{6} + a^{2} b^{4}\right)} d x - 2 \, {\left(5 \, a^{6} + a^{2} b^{4}\right)} c\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 24 \, {\left({\left(5 \, a^{4} b^{2} + b^{6}\right)} \cosh\left(d x + c\right)^{4} + {\left(5 \, a^{4} b^{2} + b^{6}\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(5 \, a^{6} + a^{2} b^{4}\right)} \cosh\left(d x + c\right)^{3} - 2 \, {\left(5 \, a^{6} + a^{2} b^{4} - 2 \, {\left(5 \, a^{4} b^{2} + b^{6}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - {\left(5 \, a^{4} b^{2} + b^{6}\right)} \cosh\left(d x + c\right)^{2} - {\left(5 \, a^{4} b^{2} + b^{6} - 6 \, {\left(5 \, a^{4} b^{2} + b^{6}\right)} \cosh\left(d x + c\right)^{2} + 6 \, {\left(5 \, a^{6} + a^{2} b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(2 \, {\left(5 \, a^{4} b^{2} + b^{6}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(5 \, a^{6} + a^{2} b^{4}\right)} \cosh\left(d x + c\right)^{2} - {\left(5 \, a^{4} b^{2} + b^{6}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(-\frac{b^{2} \cosh\left(d x + c\right)^{2} + b^{2} \sinh\left(d x + c\right)^{2} + 2 \, a^{2} \cosh\left(d x + c\right) - b^{2} + 2 \, {\left(b^{2} \cosh\left(d x + c\right) + a^{2}\right)} \sinh\left(d x + c\right) + 4 \, {\left(a b \cosh\left(d x + c\right) + a b \sinh\left(d x + c\right)\right)} \sqrt{\sinh\left(d x + c\right)}}{b^{2} \cosh\left(d x + c\right)^{2} + b^{2} \sinh\left(d x + c\right)^{2} - 2 \, a^{2} \cosh\left(d x + c\right) - b^{2} + 2 \, {\left(b^{2} \cosh\left(d x + c\right) - a^{2}\right)} \sinh\left(d x + c\right)}\right) + 24 \, {\left({\left(5 \, a^{4} b^{2} + b^{6}\right)} \cosh\left(d x + c\right)^{4} + {\left(5 \, a^{4} b^{2} + b^{6}\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(5 \, a^{6} + a^{2} b^{4}\right)} \cosh\left(d x + c\right)^{3} - 2 \, {\left(5 \, a^{6} + a^{2} b^{4} - 2 \, {\left(5 \, a^{4} b^{2} + b^{6}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - {\left(5 \, a^{4} b^{2} + b^{6}\right)} \cosh\left(d x + c\right)^{2} - {\left(5 \, a^{4} b^{2} + b^{6} - 6 \, {\left(5 \, a^{4} b^{2} + b^{6}\right)} \cosh\left(d x + c\right)^{2} + 6 \, {\left(5 \, a^{6} + a^{2} b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(2 \, {\left(5 \, a^{4} b^{2} + b^{6}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(5 \, a^{6} + a^{2} b^{4}\right)} \cosh\left(d x + c\right)^{2} - {\left(5 \, a^{4} b^{2} + b^{6}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\frac{2 \, {\left(b^{2} \sinh\left(d x + c\right) - a^{2}\right)}}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) + 6 \, {\left(3 \, b^{6} \cosh\left(d x + c\right)^{5} + 25 \, a^{2} b^{4} \cosh\left(d x + c\right)^{4} + 5 \, a^{2} b^{4} - 2 \, {\left(24 \, a^{4} b^{2} + b^{6} + 8 \, {\left(5 \, a^{4} b^{2} + b^{6}\right)} d x + 8 \, {\left(5 \, a^{4} b^{2} + b^{6}\right)} c\right)} \cosh\left(d x + c\right)^{3} - 12 \, {\left(4 \, a^{6} + 7 \, a^{2} b^{4} - 2 \, {\left(5 \, a^{6} + a^{2} b^{4}\right)} d x - 2 \, {\left(5 \, a^{6} + a^{2} b^{4}\right)} c\right)} \cosh\left(d x + c\right)^{2} + {\left(24 \, a^{4} b^{2} + b^{6} + 8 \, {\left(5 \, a^{4} b^{2} + b^{6}\right)} d x + 8 \, {\left(5 \, a^{4} b^{2} + b^{6}\right)} c\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) - 16 \, {\left(a b^{5} \cosh\left(d x + c\right)^{5} + a b^{5} \sinh\left(d x + c\right)^{5} + 10 \, a^{3} b^{3} \cosh\left(d x + c\right)^{4} - 10 \, a^{3} b^{3} \cosh\left(d x + c\right)^{2} + a b^{5} \cosh\left(d x + c\right) + 5 \, {\left(a b^{5} \cosh\left(d x + c\right) + 2 \, a^{3} b^{3}\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(15 \, a^{5} b + 4 \, a b^{5}\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(5 \, a b^{5} \cosh\left(d x + c\right)^{2} + 20 \, a^{3} b^{3} \cosh\left(d x + c\right) - 15 \, a^{5} b - 4 \, a b^{5}\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(5 \, a b^{5} \cosh\left(d x + c\right)^{3} + 30 \, a^{3} b^{3} \cosh\left(d x + c\right)^{2} - 5 \, a^{3} b^{3} - 3 \, {\left(15 \, a^{5} b + 4 \, a b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(5 \, a b^{5} \cosh\left(d x + c\right)^{4} + 40 \, a^{3} b^{3} \cosh\left(d x + c\right)^{3} - 20 \, a^{3} b^{3} \cosh\left(d x + c\right) + a b^{5} - 6 \, {\left(15 \, a^{5} b + 4 \, a b^{5}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)\right)} \sqrt{\sinh\left(d x + c\right)}}{24 \, {\left(b^{8} d \cosh\left(d x + c\right)^{4} + b^{8} d \sinh\left(d x + c\right)^{4} - 2 \, a^{2} b^{6} d \cosh\left(d x + c\right)^{3} - b^{8} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(2 \, b^{8} d \cosh\left(d x + c\right) - a^{2} b^{6} d\right)} \sinh\left(d x + c\right)^{3} + {\left(6 \, b^{8} d \cosh\left(d x + c\right)^{2} - 6 \, a^{2} b^{6} d \cosh\left(d x + c\right) - b^{8} d\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(2 \, b^{8} d \cosh\left(d x + c\right)^{3} - 3 \, a^{2} b^{6} d \cosh\left(d x + c\right)^{2} - b^{8} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"1/24*(3*b^6*cosh(d*x + c)^6 + 3*b^6*sinh(d*x + c)^6 + 30*a^2*b^4*cosh(d*x + c)^5 + 30*a^2*b^4*cosh(d*x + c) - 3*b^6 + 6*(3*b^6*cosh(d*x + c) + 5*a^2*b^4)*sinh(d*x + c)^5 - 3*(24*a^4*b^2 + b^6 + 8*(5*a^4*b^2 + b^6)*d*x + 8*(5*a^4*b^2 + b^6)*c)*cosh(d*x + c)^4 + 3*(15*b^6*cosh(d*x + c)^2 + 50*a^2*b^4*cosh(d*x + c) - 24*a^4*b^2 - b^6 - 8*(5*a^4*b^2 + b^6)*d*x - 8*(5*a^4*b^2 + b^6)*c)*sinh(d*x + c)^4 - 24*(4*a^6 + 7*a^2*b^4 - 2*(5*a^6 + a^2*b^4)*d*x - 2*(5*a^6 + a^2*b^4)*c)*cosh(d*x + c)^3 + 12*(5*b^6*cosh(d*x + c)^3 + 25*a^2*b^4*cosh(d*x + c)^2 - 8*a^6 - 14*a^2*b^4 + 4*(5*a^6 + a^2*b^4)*d*x + 4*(5*a^6 + a^2*b^4)*c - (24*a^4*b^2 + b^6 + 8*(5*a^4*b^2 + b^6)*d*x + 8*(5*a^4*b^2 + b^6)*c)*cosh(d*x + c))*sinh(d*x + c)^3 + 3*(24*a^4*b^2 + b^6 + 8*(5*a^4*b^2 + b^6)*d*x + 8*(5*a^4*b^2 + b^6)*c)*cosh(d*x + c)^2 + 3*(15*b^6*cosh(d*x + c)^4 + 100*a^2*b^4*cosh(d*x + c)^3 + 24*a^4*b^2 + b^6 + 8*(5*a^4*b^2 + b^6)*d*x - 6*(24*a^4*b^2 + b^6 + 8*(5*a^4*b^2 + b^6)*d*x + 8*(5*a^4*b^2 + b^6)*c)*cosh(d*x + c)^2 + 8*(5*a^4*b^2 + b^6)*c - 24*(4*a^6 + 7*a^2*b^4 - 2*(5*a^6 + a^2*b^4)*d*x - 2*(5*a^6 + a^2*b^4)*c)*cosh(d*x + c))*sinh(d*x + c)^2 + 24*((5*a^4*b^2 + b^6)*cosh(d*x + c)^4 + (5*a^4*b^2 + b^6)*sinh(d*x + c)^4 - 2*(5*a^6 + a^2*b^4)*cosh(d*x + c)^3 - 2*(5*a^6 + a^2*b^4 - 2*(5*a^4*b^2 + b^6)*cosh(d*x + c))*sinh(d*x + c)^3 - (5*a^4*b^2 + b^6)*cosh(d*x + c)^2 - (5*a^4*b^2 + b^6 - 6*(5*a^4*b^2 + b^6)*cosh(d*x + c)^2 + 6*(5*a^6 + a^2*b^4)*cosh(d*x + c))*sinh(d*x + c)^2 + 2*(2*(5*a^4*b^2 + b^6)*cosh(d*x + c)^3 - 3*(5*a^6 + a^2*b^4)*cosh(d*x + c)^2 - (5*a^4*b^2 + b^6)*cosh(d*x + c))*sinh(d*x + c))*log(-(b^2*cosh(d*x + c)^2 + b^2*sinh(d*x + c)^2 + 2*a^2*cosh(d*x + c) - b^2 + 2*(b^2*cosh(d*x + c) + a^2)*sinh(d*x + c) + 4*(a*b*cosh(d*x + c) + a*b*sinh(d*x + c))*sqrt(sinh(d*x + c)))/(b^2*cosh(d*x + c)^2 + b^2*sinh(d*x + c)^2 - 2*a^2*cosh(d*x + c) - b^2 + 2*(b^2*cosh(d*x + c) - a^2)*sinh(d*x + c))) + 24*((5*a^4*b^2 + b^6)*cosh(d*x + c)^4 + (5*a^4*b^2 + b^6)*sinh(d*x + c)^4 - 2*(5*a^6 + a^2*b^4)*cosh(d*x + c)^3 - 2*(5*a^6 + a^2*b^4 - 2*(5*a^4*b^2 + b^6)*cosh(d*x + c))*sinh(d*x + c)^3 - (5*a^4*b^2 + b^6)*cosh(d*x + c)^2 - (5*a^4*b^2 + b^6 - 6*(5*a^4*b^2 + b^6)*cosh(d*x + c)^2 + 6*(5*a^6 + a^2*b^4)*cosh(d*x + c))*sinh(d*x + c)^2 + 2*(2*(5*a^4*b^2 + b^6)*cosh(d*x + c)^3 - 3*(5*a^6 + a^2*b^4)*cosh(d*x + c)^2 - (5*a^4*b^2 + b^6)*cosh(d*x + c))*sinh(d*x + c))*log(2*(b^2*sinh(d*x + c) - a^2)/(cosh(d*x + c) - sinh(d*x + c))) + 6*(3*b^6*cosh(d*x + c)^5 + 25*a^2*b^4*cosh(d*x + c)^4 + 5*a^2*b^4 - 2*(24*a^4*b^2 + b^6 + 8*(5*a^4*b^2 + b^6)*d*x + 8*(5*a^4*b^2 + b^6)*c)*cosh(d*x + c)^3 - 12*(4*a^6 + 7*a^2*b^4 - 2*(5*a^6 + a^2*b^4)*d*x - 2*(5*a^6 + a^2*b^4)*c)*cosh(d*x + c)^2 + (24*a^4*b^2 + b^6 + 8*(5*a^4*b^2 + b^6)*d*x + 8*(5*a^4*b^2 + b^6)*c)*cosh(d*x + c))*sinh(d*x + c) - 16*(a*b^5*cosh(d*x + c)^5 + a*b^5*sinh(d*x + c)^5 + 10*a^3*b^3*cosh(d*x + c)^4 - 10*a^3*b^3*cosh(d*x + c)^2 + a*b^5*cosh(d*x + c) + 5*(a*b^5*cosh(d*x + c) + 2*a^3*b^3)*sinh(d*x + c)^4 - 2*(15*a^5*b + 4*a*b^5)*cosh(d*x + c)^3 + 2*(5*a*b^5*cosh(d*x + c)^2 + 20*a^3*b^3*cosh(d*x + c) - 15*a^5*b - 4*a*b^5)*sinh(d*x + c)^3 + 2*(5*a*b^5*cosh(d*x + c)^3 + 30*a^3*b^3*cosh(d*x + c)^2 - 5*a^3*b^3 - 3*(15*a^5*b + 4*a*b^5)*cosh(d*x + c))*sinh(d*x + c)^2 + (5*a*b^5*cosh(d*x + c)^4 + 40*a^3*b^3*cosh(d*x + c)^3 - 20*a^3*b^3*cosh(d*x + c) + a*b^5 - 6*(15*a^5*b + 4*a*b^5)*cosh(d*x + c)^2)*sinh(d*x + c))*sqrt(sinh(d*x + c)))/(b^8*d*cosh(d*x + c)^4 + b^8*d*sinh(d*x + c)^4 - 2*a^2*b^6*d*cosh(d*x + c)^3 - b^8*d*cosh(d*x + c)^2 + 2*(2*b^8*d*cosh(d*x + c) - a^2*b^6*d)*sinh(d*x + c)^3 + (6*b^8*d*cosh(d*x + c)^2 - 6*a^2*b^6*d*cosh(d*x + c) - b^8*d)*sinh(d*x + c)^2 + 2*(2*b^8*d*cosh(d*x + c)^3 - 3*a^2*b^6*d*cosh(d*x + c)^2 - b^8*d*cosh(d*x + c))*sinh(d*x + c))","B",0
417,1,564,0,0.527601," ","integrate(cosh(d*x+c)/(a+b*sinh(d*x+c)^(1/2))^2,x, algorithm=""fricas"")","\frac{b^{2} d x + b^{2} c - {\left(b^{2} d x + b^{2} c\right)} \cosh\left(d x + c\right)^{2} - {\left(b^{2} d x + b^{2} c\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} d x + a^{2} c - 2 \, a^{2}\right)} \cosh\left(d x + c\right) + {\left(b^{2} \cosh\left(d x + c\right)^{2} + b^{2} \sinh\left(d x + c\right)^{2} - 2 \, a^{2} \cosh\left(d x + c\right) - b^{2} + 2 \, {\left(b^{2} \cosh\left(d x + c\right) - a^{2}\right)} \sinh\left(d x + c\right)\right)} \log\left(\frac{b^{2} \cosh\left(d x + c\right)^{2} + b^{2} \sinh\left(d x + c\right)^{2} + 2 \, a^{2} \cosh\left(d x + c\right) - b^{2} + 2 \, {\left(b^{2} \cosh\left(d x + c\right) + a^{2}\right)} \sinh\left(d x + c\right) + 4 \, {\left(a b \cosh\left(d x + c\right) + a b \sinh\left(d x + c\right)\right)} \sqrt{\sinh\left(d x + c\right)}}{b^{2} \cosh\left(d x + c\right)^{2} + b^{2} \sinh\left(d x + c\right)^{2} - 2 \, a^{2} \cosh\left(d x + c\right) - b^{2} + 2 \, {\left(b^{2} \cosh\left(d x + c\right) - a^{2}\right)} \sinh\left(d x + c\right)}\right) + {\left(b^{2} \cosh\left(d x + c\right)^{2} + b^{2} \sinh\left(d x + c\right)^{2} - 2 \, a^{2} \cosh\left(d x + c\right) - b^{2} + 2 \, {\left(b^{2} \cosh\left(d x + c\right) - a^{2}\right)} \sinh\left(d x + c\right)\right)} \log\left(\frac{2 \, {\left(b^{2} \sinh\left(d x + c\right) - a^{2}\right)}}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) + 2 \, {\left(a^{2} d x + a^{2} c - 2 \, a^{2} - {\left(b^{2} d x + b^{2} c\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + 4 \, {\left(a b \cosh\left(d x + c\right) + a b \sinh\left(d x + c\right)\right)} \sqrt{\sinh\left(d x + c\right)}}{b^{4} d \cosh\left(d x + c\right)^{2} + b^{4} d \sinh\left(d x + c\right)^{2} - 2 \, a^{2} b^{2} d \cosh\left(d x + c\right) - b^{4} d + 2 \, {\left(b^{4} d \cosh\left(d x + c\right) - a^{2} b^{2} d\right)} \sinh\left(d x + c\right)}"," ",0,"(b^2*d*x + b^2*c - (b^2*d*x + b^2*c)*cosh(d*x + c)^2 - (b^2*d*x + b^2*c)*sinh(d*x + c)^2 + 2*(a^2*d*x + a^2*c - 2*a^2)*cosh(d*x + c) + (b^2*cosh(d*x + c)^2 + b^2*sinh(d*x + c)^2 - 2*a^2*cosh(d*x + c) - b^2 + 2*(b^2*cosh(d*x + c) - a^2)*sinh(d*x + c))*log((b^2*cosh(d*x + c)^2 + b^2*sinh(d*x + c)^2 + 2*a^2*cosh(d*x + c) - b^2 + 2*(b^2*cosh(d*x + c) + a^2)*sinh(d*x + c) + 4*(a*b*cosh(d*x + c) + a*b*sinh(d*x + c))*sqrt(sinh(d*x + c)))/(b^2*cosh(d*x + c)^2 + b^2*sinh(d*x + c)^2 - 2*a^2*cosh(d*x + c) - b^2 + 2*(b^2*cosh(d*x + c) - a^2)*sinh(d*x + c))) + (b^2*cosh(d*x + c)^2 + b^2*sinh(d*x + c)^2 - 2*a^2*cosh(d*x + c) - b^2 + 2*(b^2*cosh(d*x + c) - a^2)*sinh(d*x + c))*log(2*(b^2*sinh(d*x + c) - a^2)/(cosh(d*x + c) - sinh(d*x + c))) + 2*(a^2*d*x + a^2*c - 2*a^2 - (b^2*d*x + b^2*c)*cosh(d*x + c))*sinh(d*x + c) + 4*(a*b*cosh(d*x + c) + a*b*sinh(d*x + c))*sqrt(sinh(d*x + c)))/(b^4*d*cosh(d*x + c)^2 + b^4*d*sinh(d*x + c)^2 - 2*a^2*b^2*d*cosh(d*x + c) - b^4*d + 2*(b^4*d*cosh(d*x + c) - a^2*b^2*d)*sinh(d*x + c))","B",0
418,-1,0,0,0.000000," ","integrate(sech(d*x+c)/(a+b*sinh(d*x+c)^(1/2))^2,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
419,0,0,0,0.710212," ","integrate(cosh(d*x+c)^5/(a+b*sinh(d*x+c)^n),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cosh\left(d x + c\right)^{5}}{b \sinh\left(d x + c\right)^{n} + a}, x\right)"," ",0,"integral(cosh(d*x + c)^5/(b*sinh(d*x + c)^n + a), x)","F",0
420,0,0,0,1.499895," ","integrate(cosh(d*x+c)^3/(a+b*sinh(d*x+c)^n),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cosh\left(d x + c\right)^{3}}{b \sinh\left(d x + c\right)^{n} + a}, x\right)"," ",0,"integral(cosh(d*x + c)^3/(b*sinh(d*x + c)^n + a), x)","F",0
421,0,0,0,2.385020," ","integrate(cosh(d*x+c)/(a+b*sinh(d*x+c)^n),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cosh\left(d x + c\right)}{b \sinh\left(d x + c\right)^{n} + a}, x\right)"," ",0,"integral(cosh(d*x + c)/(b*sinh(d*x + c)^n + a), x)","F",0
422,0,0,0,0.478652," ","integrate(cosh(d*x+c)^5/(a+b*sinh(d*x+c)^n)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cosh\left(d x + c\right)^{5}}{b^{2} \sinh\left(d x + c\right)^{2 \, n} + 2 \, a b \sinh\left(d x + c\right)^{n} + a^{2}}, x\right)"," ",0,"integral(cosh(d*x + c)^5/(b^2*sinh(d*x + c)^(2*n) + 2*a*b*sinh(d*x + c)^n + a^2), x)","F",0
423,0,0,0,2.913980," ","integrate(cosh(d*x+c)^3/(a+b*sinh(d*x+c)^n)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cosh\left(d x + c\right)^{3}}{b^{2} \sinh\left(d x + c\right)^{2 \, n} + 2 \, a b \sinh\left(d x + c\right)^{n} + a^{2}}, x\right)"," ",0,"integral(cosh(d*x + c)^3/(b^2*sinh(d*x + c)^(2*n) + 2*a*b*sinh(d*x + c)^n + a^2), x)","F",0
424,0,0,0,2.034724," ","integrate(cosh(d*x+c)/(a+b*sinh(d*x+c)^n)^2,x, algorithm=""fricas"")","{\rm integral}\left(\frac{\cosh\left(d x + c\right)}{b^{2} \sinh\left(d x + c\right)^{2 \, n} + 2 \, a b \sinh\left(d x + c\right)^{n} + a^{2}}, x\right)"," ",0,"integral(cosh(d*x + c)/(b^2*sinh(d*x + c)^(2*n) + 2*a*b*sinh(d*x + c)^n + a^2), x)","F",0
425,1,47,0,1.034696," ","integrate(coth(x)/(1-sinh(x)^2),x, algorithm=""fricas"")","-\frac{1}{2} \, \log\left(\frac{2 \, {\left(\cosh\left(x\right)^{2} + \sinh\left(x\right)^{2} - 3\right)}}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right) + \log\left(\frac{2 \, \sinh\left(x\right)}{\cosh\left(x\right) - \sinh\left(x\right)}\right)"," ",0,"-1/2*log(2*(cosh(x)^2 + sinh(x)^2 - 3)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + log(2*sinh(x)/(cosh(x) - sinh(x)))","B",0
426,1,875,0,2.952656," ","integrate((a+a*sinh(f*x+e)^2)^(1/2)*tanh(f*x+e)^5,x, algorithm=""fricas"")","\frac{{\left(24 \, \cosh\left(f x + e\right) e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{7} + 3 \, e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{8} + 12 \, {\left(7 \, \cosh\left(f x + e\right)^{2} + 3\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{6} + 24 \, {\left(7 \, \cosh\left(f x + e\right)^{3} + 9 \, \cosh\left(f x + e\right)\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{5} + 10 \, {\left(21 \, \cosh\left(f x + e\right)^{4} + 54 \, \cosh\left(f x + e\right)^{2} + 5\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{4} + 8 \, {\left(21 \, \cosh\left(f x + e\right)^{5} + 90 \, \cosh\left(f x + e\right)^{3} + 25 \, \cosh\left(f x + e\right)\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{3} + 12 \, {\left(7 \, \cosh\left(f x + e\right)^{6} + 45 \, \cosh\left(f x + e\right)^{4} + 25 \, \cosh\left(f x + e\right)^{2} + 3\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{2} + 8 \, {\left(3 \, \cosh\left(f x + e\right)^{7} + 27 \, \cosh\left(f x + e\right)^{5} + 25 \, \cosh\left(f x + e\right)^{3} + 9 \, \cosh\left(f x + e\right)\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right) + {\left(3 \, \cosh\left(f x + e\right)^{8} + 36 \, \cosh\left(f x + e\right)^{6} + 50 \, \cosh\left(f x + e\right)^{4} + 36 \, \cosh\left(f x + e\right)^{2} + 3\right)} e^{\left(f x + e\right)}\right)} \sqrt{a e^{\left(4 \, f x + 4 \, e\right)} + 2 \, a e^{\left(2 \, f x + 2 \, e\right)} + a} e^{\left(-f x - e\right)}}{6 \, {\left(f \cosh\left(f x + e\right)^{7} + {\left(f e^{\left(2 \, f x + 2 \, e\right)} + f\right)} \sinh\left(f x + e\right)^{7} + 7 \, {\left(f \cosh\left(f x + e\right) e^{\left(2 \, f x + 2 \, e\right)} + f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{6} + 3 \, f \cosh\left(f x + e\right)^{5} + 3 \, {\left(7 \, f \cosh\left(f x + e\right)^{2} + {\left(7 \, f \cosh\left(f x + e\right)^{2} + f\right)} e^{\left(2 \, f x + 2 \, e\right)} + f\right)} \sinh\left(f x + e\right)^{5} + 5 \, {\left(7 \, f \cosh\left(f x + e\right)^{3} + 3 \, f \cosh\left(f x + e\right) + {\left(7 \, f \cosh\left(f x + e\right)^{3} + 3 \, f \cosh\left(f x + e\right)\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)^{4} + 3 \, f \cosh\left(f x + e\right)^{3} + {\left(35 \, f \cosh\left(f x + e\right)^{4} + 30 \, f \cosh\left(f x + e\right)^{2} + {\left(35 \, f \cosh\left(f x + e\right)^{4} + 30 \, f \cosh\left(f x + e\right)^{2} + 3 \, f\right)} e^{\left(2 \, f x + 2 \, e\right)} + 3 \, f\right)} \sinh\left(f x + e\right)^{3} + 3 \, {\left(7 \, f \cosh\left(f x + e\right)^{5} + 10 \, f \cosh\left(f x + e\right)^{3} + 3 \, f \cosh\left(f x + e\right) + {\left(7 \, f \cosh\left(f x + e\right)^{5} + 10 \, f \cosh\left(f x + e\right)^{3} + 3 \, f \cosh\left(f x + e\right)\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)^{2} + f \cosh\left(f x + e\right) + {\left(f \cosh\left(f x + e\right)^{7} + 3 \, f \cosh\left(f x + e\right)^{5} + 3 \, f \cosh\left(f x + e\right)^{3} + f \cosh\left(f x + e\right)\right)} e^{\left(2 \, f x + 2 \, e\right)} + {\left(7 \, f \cosh\left(f x + e\right)^{6} + 15 \, f \cosh\left(f x + e\right)^{4} + 9 \, f \cosh\left(f x + e\right)^{2} + {\left(7 \, f \cosh\left(f x + e\right)^{6} + 15 \, f \cosh\left(f x + e\right)^{4} + 9 \, f \cosh\left(f x + e\right)^{2} + f\right)} e^{\left(2 \, f x + 2 \, e\right)} + f\right)} \sinh\left(f x + e\right)\right)}}"," ",0,"1/6*(24*cosh(f*x + e)*e^(f*x + e)*sinh(f*x + e)^7 + 3*e^(f*x + e)*sinh(f*x + e)^8 + 12*(7*cosh(f*x + e)^2 + 3)*e^(f*x + e)*sinh(f*x + e)^6 + 24*(7*cosh(f*x + e)^3 + 9*cosh(f*x + e))*e^(f*x + e)*sinh(f*x + e)^5 + 10*(21*cosh(f*x + e)^4 + 54*cosh(f*x + e)^2 + 5)*e^(f*x + e)*sinh(f*x + e)^4 + 8*(21*cosh(f*x + e)^5 + 90*cosh(f*x + e)^3 + 25*cosh(f*x + e))*e^(f*x + e)*sinh(f*x + e)^3 + 12*(7*cosh(f*x + e)^6 + 45*cosh(f*x + e)^4 + 25*cosh(f*x + e)^2 + 3)*e^(f*x + e)*sinh(f*x + e)^2 + 8*(3*cosh(f*x + e)^7 + 27*cosh(f*x + e)^5 + 25*cosh(f*x + e)^3 + 9*cosh(f*x + e))*e^(f*x + e)*sinh(f*x + e) + (3*cosh(f*x + e)^8 + 36*cosh(f*x + e)^6 + 50*cosh(f*x + e)^4 + 36*cosh(f*x + e)^2 + 3)*e^(f*x + e))*sqrt(a*e^(4*f*x + 4*e) + 2*a*e^(2*f*x + 2*e) + a)*e^(-f*x - e)/(f*cosh(f*x + e)^7 + (f*e^(2*f*x + 2*e) + f)*sinh(f*x + e)^7 + 7*(f*cosh(f*x + e)*e^(2*f*x + 2*e) + f*cosh(f*x + e))*sinh(f*x + e)^6 + 3*f*cosh(f*x + e)^5 + 3*(7*f*cosh(f*x + e)^2 + (7*f*cosh(f*x + e)^2 + f)*e^(2*f*x + 2*e) + f)*sinh(f*x + e)^5 + 5*(7*f*cosh(f*x + e)^3 + 3*f*cosh(f*x + e) + (7*f*cosh(f*x + e)^3 + 3*f*cosh(f*x + e))*e^(2*f*x + 2*e))*sinh(f*x + e)^4 + 3*f*cosh(f*x + e)^3 + (35*f*cosh(f*x + e)^4 + 30*f*cosh(f*x + e)^2 + (35*f*cosh(f*x + e)^4 + 30*f*cosh(f*x + e)^2 + 3*f)*e^(2*f*x + 2*e) + 3*f)*sinh(f*x + e)^3 + 3*(7*f*cosh(f*x + e)^5 + 10*f*cosh(f*x + e)^3 + 3*f*cosh(f*x + e) + (7*f*cosh(f*x + e)^5 + 10*f*cosh(f*x + e)^3 + 3*f*cosh(f*x + e))*e^(2*f*x + 2*e))*sinh(f*x + e)^2 + f*cosh(f*x + e) + (f*cosh(f*x + e)^7 + 3*f*cosh(f*x + e)^5 + 3*f*cosh(f*x + e)^3 + f*cosh(f*x + e))*e^(2*f*x + 2*e) + (7*f*cosh(f*x + e)^6 + 15*f*cosh(f*x + e)^4 + 9*f*cosh(f*x + e)^2 + (7*f*cosh(f*x + e)^6 + 15*f*cosh(f*x + e)^4 + 9*f*cosh(f*x + e)^2 + f)*e^(2*f*x + 2*e) + f)*sinh(f*x + e))","B",0
427,1,311,0,0.699590," ","integrate((a+a*sinh(f*x+e)^2)^(1/2)*tanh(f*x+e)^3,x, algorithm=""fricas"")","\frac{{\left(4 \, \cosh\left(f x + e\right) e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{3} + e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{4} + 6 \, {\left(\cosh\left(f x + e\right)^{2} + 1\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(\cosh\left(f x + e\right)^{3} + 3 \, \cosh\left(f x + e\right)\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right) + {\left(\cosh\left(f x + e\right)^{4} + 6 \, \cosh\left(f x + e\right)^{2} + 1\right)} e^{\left(f x + e\right)}\right)} \sqrt{a e^{\left(4 \, f x + 4 \, e\right)} + 2 \, a e^{\left(2 \, f x + 2 \, e\right)} + a} e^{\left(-f x - e\right)}}{2 \, {\left(f \cosh\left(f x + e\right)^{3} + {\left(f e^{\left(2 \, f x + 2 \, e\right)} + f\right)} \sinh\left(f x + e\right)^{3} + 3 \, {\left(f \cosh\left(f x + e\right) e^{\left(2 \, f x + 2 \, e\right)} + f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{2} + f \cosh\left(f x + e\right) + {\left(f \cosh\left(f x + e\right)^{3} + f \cosh\left(f x + e\right)\right)} e^{\left(2 \, f x + 2 \, e\right)} + {\left(3 \, f \cosh\left(f x + e\right)^{2} + {\left(3 \, f \cosh\left(f x + e\right)^{2} + f\right)} e^{\left(2 \, f x + 2 \, e\right)} + f\right)} \sinh\left(f x + e\right)\right)}}"," ",0,"1/2*(4*cosh(f*x + e)*e^(f*x + e)*sinh(f*x + e)^3 + e^(f*x + e)*sinh(f*x + e)^4 + 6*(cosh(f*x + e)^2 + 1)*e^(f*x + e)*sinh(f*x + e)^2 + 4*(cosh(f*x + e)^3 + 3*cosh(f*x + e))*e^(f*x + e)*sinh(f*x + e) + (cosh(f*x + e)^4 + 6*cosh(f*x + e)^2 + 1)*e^(f*x + e))*sqrt(a*e^(4*f*x + 4*e) + 2*a*e^(2*f*x + 2*e) + a)*e^(-f*x - e)/(f*cosh(f*x + e)^3 + (f*e^(2*f*x + 2*e) + f)*sinh(f*x + e)^3 + 3*(f*cosh(f*x + e)*e^(2*f*x + 2*e) + f*cosh(f*x + e))*sinh(f*x + e)^2 + f*cosh(f*x + e) + (f*cosh(f*x + e)^3 + f*cosh(f*x + e))*e^(2*f*x + 2*e) + (3*f*cosh(f*x + e)^2 + (3*f*cosh(f*x + e)^2 + f)*e^(2*f*x + 2*e) + f)*sinh(f*x + e))","B",0
428,1,139,0,1.021376," ","integrate((a+a*sinh(f*x+e)^2)^(1/2)*tanh(f*x+e),x, algorithm=""fricas"")","\frac{{\left(2 \, \cosh\left(f x + e\right) e^{\left(f x + e\right)} \sinh\left(f x + e\right) + e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{2} + {\left(\cosh\left(f x + e\right)^{2} + 1\right)} e^{\left(f x + e\right)}\right)} \sqrt{a e^{\left(4 \, f x + 4 \, e\right)} + 2 \, a e^{\left(2 \, f x + 2 \, e\right)} + a} e^{\left(-f x - e\right)}}{2 \, {\left(f \cosh\left(f x + e\right) e^{\left(2 \, f x + 2 \, e\right)} + f \cosh\left(f x + e\right) + {\left(f e^{\left(2 \, f x + 2 \, e\right)} + f\right)} \sinh\left(f x + e\right)\right)}}"," ",0,"1/2*(2*cosh(f*x + e)*e^(f*x + e)*sinh(f*x + e) + e^(f*x + e)*sinh(f*x + e)^2 + (cosh(f*x + e)^2 + 1)*e^(f*x + e))*sqrt(a*e^(4*f*x + 4*e) + 2*a*e^(2*f*x + 2*e) + a)*e^(-f*x - e)/(f*cosh(f*x + e)*e^(2*f*x + 2*e) + f*cosh(f*x + e) + (f*e^(2*f*x + 2*e) + f)*sinh(f*x + e))","B",0
429,1,200,0,2.386394," ","integrate(coth(f*x+e)*(a+a*sinh(f*x+e)^2)^(1/2),x, algorithm=""fricas"")","\frac{{\left(2 \, \cosh\left(f x + e\right) e^{\left(f x + e\right)} \sinh\left(f x + e\right) + e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{2} + {\left(\cosh\left(f x + e\right)^{2} + 1\right)} e^{\left(f x + e\right)} + 2 \, {\left(\cosh\left(f x + e\right) e^{\left(f x + e\right)} + e^{\left(f x + e\right)} \sinh\left(f x + e\right)\right)} \log\left(\frac{\cosh\left(f x + e\right) + \sinh\left(f x + e\right) - 1}{\cosh\left(f x + e\right) + \sinh\left(f x + e\right) + 1}\right)\right)} \sqrt{a e^{\left(4 \, f x + 4 \, e\right)} + 2 \, a e^{\left(2 \, f x + 2 \, e\right)} + a} e^{\left(-f x - e\right)}}{2 \, {\left(f \cosh\left(f x + e\right) e^{\left(2 \, f x + 2 \, e\right)} + f \cosh\left(f x + e\right) + {\left(f e^{\left(2 \, f x + 2 \, e\right)} + f\right)} \sinh\left(f x + e\right)\right)}}"," ",0,"1/2*(2*cosh(f*x + e)*e^(f*x + e)*sinh(f*x + e) + e^(f*x + e)*sinh(f*x + e)^2 + (cosh(f*x + e)^2 + 1)*e^(f*x + e) + 2*(cosh(f*x + e)*e^(f*x + e) + e^(f*x + e)*sinh(f*x + e))*log((cosh(f*x + e) + sinh(f*x + e) - 1)/(cosh(f*x + e) + sinh(f*x + e) + 1)))*sqrt(a*e^(4*f*x + 4*e) + 2*a*e^(2*f*x + 2*e) + a)*e^(-f*x - e)/(f*cosh(f*x + e)*e^(2*f*x + 2*e) + f*cosh(f*x + e) + (f*e^(2*f*x + 2*e) + f)*sinh(f*x + e))","B",0
430,1,764,0,1.386199," ","integrate(coth(f*x+e)^3*(a+a*sinh(f*x+e)^2)^(1/2),x, algorithm=""fricas"")","\frac{{\left(6 \, \cosh\left(f x + e\right) e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{5} + e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{6} + 3 \, {\left(5 \, \cosh\left(f x + e\right)^{2} - 1\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(5 \, \cosh\left(f x + e\right)^{3} - 3 \, \cosh\left(f x + e\right)\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{3} + 3 \, {\left(5 \, \cosh\left(f x + e\right)^{4} - 6 \, \cosh\left(f x + e\right)^{2} - 1\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{2} + 6 \, {\left(\cosh\left(f x + e\right)^{5} - 2 \, \cosh\left(f x + e\right)^{3} - \cosh\left(f x + e\right)\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right) + {\left(\cosh\left(f x + e\right)^{6} - 3 \, \cosh\left(f x + e\right)^{4} - 3 \, \cosh\left(f x + e\right)^{2} + 1\right)} e^{\left(f x + e\right)} + 3 \, {\left(5 \, \cosh\left(f x + e\right) e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{4} + e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(5 \, \cosh\left(f x + e\right)^{2} - 1\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{3} + 2 \, {\left(5 \, \cosh\left(f x + e\right)^{3} - 3 \, \cosh\left(f x + e\right)\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{2} + {\left(5 \, \cosh\left(f x + e\right)^{4} - 6 \, \cosh\left(f x + e\right)^{2} + 1\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right) + {\left(\cosh\left(f x + e\right)^{5} - 2 \, \cosh\left(f x + e\right)^{3} + \cosh\left(f x + e\right)\right)} e^{\left(f x + e\right)}\right)} \log\left(\frac{\cosh\left(f x + e\right) + \sinh\left(f x + e\right) - 1}{\cosh\left(f x + e\right) + \sinh\left(f x + e\right) + 1}\right)\right)} \sqrt{a e^{\left(4 \, f x + 4 \, e\right)} + 2 \, a e^{\left(2 \, f x + 2 \, e\right)} + a} e^{\left(-f x - e\right)}}{2 \, {\left(f \cosh\left(f x + e\right)^{5} + {\left(f e^{\left(2 \, f x + 2 \, e\right)} + f\right)} \sinh\left(f x + e\right)^{5} + 5 \, {\left(f \cosh\left(f x + e\right) e^{\left(2 \, f x + 2 \, e\right)} + f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{4} - 2 \, f \cosh\left(f x + e\right)^{3} + 2 \, {\left(5 \, f \cosh\left(f x + e\right)^{2} + {\left(5 \, f \cosh\left(f x + e\right)^{2} - f\right)} e^{\left(2 \, f x + 2 \, e\right)} - f\right)} \sinh\left(f x + e\right)^{3} + 2 \, {\left(5 \, f \cosh\left(f x + e\right)^{3} - 3 \, f \cosh\left(f x + e\right) + {\left(5 \, f \cosh\left(f x + e\right)^{3} - 3 \, f \cosh\left(f x + e\right)\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)^{2} + f \cosh\left(f x + e\right) + {\left(f \cosh\left(f x + e\right)^{5} - 2 \, f \cosh\left(f x + e\right)^{3} + f \cosh\left(f x + e\right)\right)} e^{\left(2 \, f x + 2 \, e\right)} + {\left(5 \, f \cosh\left(f x + e\right)^{4} - 6 \, f \cosh\left(f x + e\right)^{2} + {\left(5 \, f \cosh\left(f x + e\right)^{4} - 6 \, f \cosh\left(f x + e\right)^{2} + f\right)} e^{\left(2 \, f x + 2 \, e\right)} + f\right)} \sinh\left(f x + e\right)\right)}}"," ",0,"1/2*(6*cosh(f*x + e)*e^(f*x + e)*sinh(f*x + e)^5 + e^(f*x + e)*sinh(f*x + e)^6 + 3*(5*cosh(f*x + e)^2 - 1)*e^(f*x + e)*sinh(f*x + e)^4 + 4*(5*cosh(f*x + e)^3 - 3*cosh(f*x + e))*e^(f*x + e)*sinh(f*x + e)^3 + 3*(5*cosh(f*x + e)^4 - 6*cosh(f*x + e)^2 - 1)*e^(f*x + e)*sinh(f*x + e)^2 + 6*(cosh(f*x + e)^5 - 2*cosh(f*x + e)^3 - cosh(f*x + e))*e^(f*x + e)*sinh(f*x + e) + (cosh(f*x + e)^6 - 3*cosh(f*x + e)^4 - 3*cosh(f*x + e)^2 + 1)*e^(f*x + e) + 3*(5*cosh(f*x + e)*e^(f*x + e)*sinh(f*x + e)^4 + e^(f*x + e)*sinh(f*x + e)^5 + 2*(5*cosh(f*x + e)^2 - 1)*e^(f*x + e)*sinh(f*x + e)^3 + 2*(5*cosh(f*x + e)^3 - 3*cosh(f*x + e))*e^(f*x + e)*sinh(f*x + e)^2 + (5*cosh(f*x + e)^4 - 6*cosh(f*x + e)^2 + 1)*e^(f*x + e)*sinh(f*x + e) + (cosh(f*x + e)^5 - 2*cosh(f*x + e)^3 + cosh(f*x + e))*e^(f*x + e))*log((cosh(f*x + e) + sinh(f*x + e) - 1)/(cosh(f*x + e) + sinh(f*x + e) + 1)))*sqrt(a*e^(4*f*x + 4*e) + 2*a*e^(2*f*x + 2*e) + a)*e^(-f*x - e)/(f*cosh(f*x + e)^5 + (f*e^(2*f*x + 2*e) + f)*sinh(f*x + e)^5 + 5*(f*cosh(f*x + e)*e^(2*f*x + 2*e) + f*cosh(f*x + e))*sinh(f*x + e)^4 - 2*f*cosh(f*x + e)^3 + 2*(5*f*cosh(f*x + e)^2 + (5*f*cosh(f*x + e)^2 - f)*e^(2*f*x + 2*e) - f)*sinh(f*x + e)^3 + 2*(5*f*cosh(f*x + e)^3 - 3*f*cosh(f*x + e) + (5*f*cosh(f*x + e)^3 - 3*f*cosh(f*x + e))*e^(2*f*x + 2*e))*sinh(f*x + e)^2 + f*cosh(f*x + e) + (f*cosh(f*x + e)^5 - 2*f*cosh(f*x + e)^3 + f*cosh(f*x + e))*e^(2*f*x + 2*e) + (5*f*cosh(f*x + e)^4 - 6*f*cosh(f*x + e)^2 + (5*f*cosh(f*x + e)^4 - 6*f*cosh(f*x + e)^2 + f)*e^(2*f*x + 2*e) + f)*sinh(f*x + e))","B",0
431,1,1645,0,0.572763," ","integrate((a+a*sinh(f*x+e)^2)^(1/2)*tanh(f*x+e)^6,x, algorithm=""fricas"")","\frac{{\left(20 \, \cosh\left(f x + e\right) e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{9} + 2 \, e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{10} + 15 \, {\left(6 \, \cosh\left(f x + e\right)^{2} + 1\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{8} + 120 \, {\left(2 \, \cosh\left(f x + e\right)^{3} + \cosh\left(f x + e\right)\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{7} + 5 \, {\left(84 \, \cosh\left(f x + e\right)^{4} + 84 \, \cosh\left(f x + e\right)^{2} + 1\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{6} + 6 \, {\left(84 \, \cosh\left(f x + e\right)^{5} + 140 \, \cosh\left(f x + e\right)^{3} + 5 \, \cosh\left(f x + e\right)\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{5} + 5 \, {\left(84 \, \cosh\left(f x + e\right)^{6} + 210 \, \cosh\left(f x + e\right)^{4} + 15 \, \cosh\left(f x + e\right)^{2} - 1\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{4} + 20 \, {\left(12 \, \cosh\left(f x + e\right)^{7} + 42 \, \cosh\left(f x + e\right)^{5} + 5 \, \cosh\left(f x + e\right)^{3} - \cosh\left(f x + e\right)\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{3} + 15 \, {\left(6 \, \cosh\left(f x + e\right)^{8} + 28 \, \cosh\left(f x + e\right)^{6} + 5 \, \cosh\left(f x + e\right)^{4} - 2 \, \cosh\left(f x + e\right)^{2} - 1\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{2} + 10 \, {\left(2 \, \cosh\left(f x + e\right)^{9} + 12 \, \cosh\left(f x + e\right)^{7} + 3 \, \cosh\left(f x + e\right)^{5} - 2 \, \cosh\left(f x + e\right)^{3} - 3 \, \cosh\left(f x + e\right)\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right) - 15 \, {\left(9 \, \cosh\left(f x + e\right) e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{8} + e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{9} + 4 \, {\left(9 \, \cosh\left(f x + e\right)^{2} + 1\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{7} + 28 \, {\left(3 \, \cosh\left(f x + e\right)^{3} + \cosh\left(f x + e\right)\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{6} + 6 \, {\left(21 \, \cosh\left(f x + e\right)^{4} + 14 \, \cosh\left(f x + e\right)^{2} + 1\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(63 \, \cosh\left(f x + e\right)^{5} + 70 \, \cosh\left(f x + e\right)^{3} + 15 \, \cosh\left(f x + e\right)\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(21 \, \cosh\left(f x + e\right)^{6} + 35 \, \cosh\left(f x + e\right)^{4} + 15 \, \cosh\left(f x + e\right)^{2} + 1\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{3} + 12 \, {\left(3 \, \cosh\left(f x + e\right)^{7} + 7 \, \cosh\left(f x + e\right)^{5} + 5 \, \cosh\left(f x + e\right)^{3} + \cosh\left(f x + e\right)\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{2} + {\left(9 \, \cosh\left(f x + e\right)^{8} + 28 \, \cosh\left(f x + e\right)^{6} + 30 \, \cosh\left(f x + e\right)^{4} + 12 \, \cosh\left(f x + e\right)^{2} + 1\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right) + {\left(\cosh\left(f x + e\right)^{9} + 4 \, \cosh\left(f x + e\right)^{7} + 6 \, \cosh\left(f x + e\right)^{5} + 4 \, \cosh\left(f x + e\right)^{3} + \cosh\left(f x + e\right)\right)} e^{\left(f x + e\right)}\right)} \arctan\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right)\right) + {\left(2 \, \cosh\left(f x + e\right)^{10} + 15 \, \cosh\left(f x + e\right)^{8} + 5 \, \cosh\left(f x + e\right)^{6} - 5 \, \cosh\left(f x + e\right)^{4} - 15 \, \cosh\left(f x + e\right)^{2} - 2\right)} e^{\left(f x + e\right)}\right)} \sqrt{a e^{\left(4 \, f x + 4 \, e\right)} + 2 \, a e^{\left(2 \, f x + 2 \, e\right)} + a} e^{\left(-f x - e\right)}}{4 \, {\left(f \cosh\left(f x + e\right)^{9} + {\left(f e^{\left(2 \, f x + 2 \, e\right)} + f\right)} \sinh\left(f x + e\right)^{9} + 9 \, {\left(f \cosh\left(f x + e\right) e^{\left(2 \, f x + 2 \, e\right)} + f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{8} + 4 \, f \cosh\left(f x + e\right)^{7} + 4 \, {\left(9 \, f \cosh\left(f x + e\right)^{2} + {\left(9 \, f \cosh\left(f x + e\right)^{2} + f\right)} e^{\left(2 \, f x + 2 \, e\right)} + f\right)} \sinh\left(f x + e\right)^{7} + 28 \, {\left(3 \, f \cosh\left(f x + e\right)^{3} + f \cosh\left(f x + e\right) + {\left(3 \, f \cosh\left(f x + e\right)^{3} + f \cosh\left(f x + e\right)\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)^{6} + 6 \, f \cosh\left(f x + e\right)^{5} + 6 \, {\left(21 \, f \cosh\left(f x + e\right)^{4} + 14 \, f \cosh\left(f x + e\right)^{2} + {\left(21 \, f \cosh\left(f x + e\right)^{4} + 14 \, f \cosh\left(f x + e\right)^{2} + f\right)} e^{\left(2 \, f x + 2 \, e\right)} + f\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(63 \, f \cosh\left(f x + e\right)^{5} + 70 \, f \cosh\left(f x + e\right)^{3} + 15 \, f \cosh\left(f x + e\right) + {\left(63 \, f \cosh\left(f x + e\right)^{5} + 70 \, f \cosh\left(f x + e\right)^{3} + 15 \, f \cosh\left(f x + e\right)\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)^{4} + 4 \, f \cosh\left(f x + e\right)^{3} + 4 \, {\left(21 \, f \cosh\left(f x + e\right)^{6} + 35 \, f \cosh\left(f x + e\right)^{4} + 15 \, f \cosh\left(f x + e\right)^{2} + {\left(21 \, f \cosh\left(f x + e\right)^{6} + 35 \, f \cosh\left(f x + e\right)^{4} + 15 \, f \cosh\left(f x + e\right)^{2} + f\right)} e^{\left(2 \, f x + 2 \, e\right)} + f\right)} \sinh\left(f x + e\right)^{3} + 12 \, {\left(3 \, f \cosh\left(f x + e\right)^{7} + 7 \, f \cosh\left(f x + e\right)^{5} + 5 \, f \cosh\left(f x + e\right)^{3} + f \cosh\left(f x + e\right) + {\left(3 \, f \cosh\left(f x + e\right)^{7} + 7 \, f \cosh\left(f x + e\right)^{5} + 5 \, f \cosh\left(f x + e\right)^{3} + f \cosh\left(f x + e\right)\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)^{2} + f \cosh\left(f x + e\right) + {\left(f \cosh\left(f x + e\right)^{9} + 4 \, f \cosh\left(f x + e\right)^{7} + 6 \, f \cosh\left(f x + e\right)^{5} + 4 \, f \cosh\left(f x + e\right)^{3} + f \cosh\left(f x + e\right)\right)} e^{\left(2 \, f x + 2 \, e\right)} + {\left(9 \, f \cosh\left(f x + e\right)^{8} + 28 \, f \cosh\left(f x + e\right)^{6} + 30 \, f \cosh\left(f x + e\right)^{4} + 12 \, f \cosh\left(f x + e\right)^{2} + {\left(9 \, f \cosh\left(f x + e\right)^{8} + 28 \, f \cosh\left(f x + e\right)^{6} + 30 \, f \cosh\left(f x + e\right)^{4} + 12 \, f \cosh\left(f x + e\right)^{2} + f\right)} e^{\left(2 \, f x + 2 \, e\right)} + f\right)} \sinh\left(f x + e\right)\right)}}"," ",0,"1/4*(20*cosh(f*x + e)*e^(f*x + e)*sinh(f*x + e)^9 + 2*e^(f*x + e)*sinh(f*x + e)^10 + 15*(6*cosh(f*x + e)^2 + 1)*e^(f*x + e)*sinh(f*x + e)^8 + 120*(2*cosh(f*x + e)^3 + cosh(f*x + e))*e^(f*x + e)*sinh(f*x + e)^7 + 5*(84*cosh(f*x + e)^4 + 84*cosh(f*x + e)^2 + 1)*e^(f*x + e)*sinh(f*x + e)^6 + 6*(84*cosh(f*x + e)^5 + 140*cosh(f*x + e)^3 + 5*cosh(f*x + e))*e^(f*x + e)*sinh(f*x + e)^5 + 5*(84*cosh(f*x + e)^6 + 210*cosh(f*x + e)^4 + 15*cosh(f*x + e)^2 - 1)*e^(f*x + e)*sinh(f*x + e)^4 + 20*(12*cosh(f*x + e)^7 + 42*cosh(f*x + e)^5 + 5*cosh(f*x + e)^3 - cosh(f*x + e))*e^(f*x + e)*sinh(f*x + e)^3 + 15*(6*cosh(f*x + e)^8 + 28*cosh(f*x + e)^6 + 5*cosh(f*x + e)^4 - 2*cosh(f*x + e)^2 - 1)*e^(f*x + e)*sinh(f*x + e)^2 + 10*(2*cosh(f*x + e)^9 + 12*cosh(f*x + e)^7 + 3*cosh(f*x + e)^5 - 2*cosh(f*x + e)^3 - 3*cosh(f*x + e))*e^(f*x + e)*sinh(f*x + e) - 15*(9*cosh(f*x + e)*e^(f*x + e)*sinh(f*x + e)^8 + e^(f*x + e)*sinh(f*x + e)^9 + 4*(9*cosh(f*x + e)^2 + 1)*e^(f*x + e)*sinh(f*x + e)^7 + 28*(3*cosh(f*x + e)^3 + cosh(f*x + e))*e^(f*x + e)*sinh(f*x + e)^6 + 6*(21*cosh(f*x + e)^4 + 14*cosh(f*x + e)^2 + 1)*e^(f*x + e)*sinh(f*x + e)^5 + 2*(63*cosh(f*x + e)^5 + 70*cosh(f*x + e)^3 + 15*cosh(f*x + e))*e^(f*x + e)*sinh(f*x + e)^4 + 4*(21*cosh(f*x + e)^6 + 35*cosh(f*x + e)^4 + 15*cosh(f*x + e)^2 + 1)*e^(f*x + e)*sinh(f*x + e)^3 + 12*(3*cosh(f*x + e)^7 + 7*cosh(f*x + e)^5 + 5*cosh(f*x + e)^3 + cosh(f*x + e))*e^(f*x + e)*sinh(f*x + e)^2 + (9*cosh(f*x + e)^8 + 28*cosh(f*x + e)^6 + 30*cosh(f*x + e)^4 + 12*cosh(f*x + e)^2 + 1)*e^(f*x + e)*sinh(f*x + e) + (cosh(f*x + e)^9 + 4*cosh(f*x + e)^7 + 6*cosh(f*x + e)^5 + 4*cosh(f*x + e)^3 + cosh(f*x + e))*e^(f*x + e))*arctan(cosh(f*x + e) + sinh(f*x + e)) + (2*cosh(f*x + e)^10 + 15*cosh(f*x + e)^8 + 5*cosh(f*x + e)^6 - 5*cosh(f*x + e)^4 - 15*cosh(f*x + e)^2 - 2)*e^(f*x + e))*sqrt(a*e^(4*f*x + 4*e) + 2*a*e^(2*f*x + 2*e) + a)*e^(-f*x - e)/(f*cosh(f*x + e)^9 + (f*e^(2*f*x + 2*e) + f)*sinh(f*x + e)^9 + 9*(f*cosh(f*x + e)*e^(2*f*x + 2*e) + f*cosh(f*x + e))*sinh(f*x + e)^8 + 4*f*cosh(f*x + e)^7 + 4*(9*f*cosh(f*x + e)^2 + (9*f*cosh(f*x + e)^2 + f)*e^(2*f*x + 2*e) + f)*sinh(f*x + e)^7 + 28*(3*f*cosh(f*x + e)^3 + f*cosh(f*x + e) + (3*f*cosh(f*x + e)^3 + f*cosh(f*x + e))*e^(2*f*x + 2*e))*sinh(f*x + e)^6 + 6*f*cosh(f*x + e)^5 + 6*(21*f*cosh(f*x + e)^4 + 14*f*cosh(f*x + e)^2 + (21*f*cosh(f*x + e)^4 + 14*f*cosh(f*x + e)^2 + f)*e^(2*f*x + 2*e) + f)*sinh(f*x + e)^5 + 2*(63*f*cosh(f*x + e)^5 + 70*f*cosh(f*x + e)^3 + 15*f*cosh(f*x + e) + (63*f*cosh(f*x + e)^5 + 70*f*cosh(f*x + e)^3 + 15*f*cosh(f*x + e))*e^(2*f*x + 2*e))*sinh(f*x + e)^4 + 4*f*cosh(f*x + e)^3 + 4*(21*f*cosh(f*x + e)^6 + 35*f*cosh(f*x + e)^4 + 15*f*cosh(f*x + e)^2 + (21*f*cosh(f*x + e)^6 + 35*f*cosh(f*x + e)^4 + 15*f*cosh(f*x + e)^2 + f)*e^(2*f*x + 2*e) + f)*sinh(f*x + e)^3 + 12*(3*f*cosh(f*x + e)^7 + 7*f*cosh(f*x + e)^5 + 5*f*cosh(f*x + e)^3 + f*cosh(f*x + e) + (3*f*cosh(f*x + e)^7 + 7*f*cosh(f*x + e)^5 + 5*f*cosh(f*x + e)^3 + f*cosh(f*x + e))*e^(2*f*x + 2*e))*sinh(f*x + e)^2 + f*cosh(f*x + e) + (f*cosh(f*x + e)^9 + 4*f*cosh(f*x + e)^7 + 6*f*cosh(f*x + e)^5 + 4*f*cosh(f*x + e)^3 + f*cosh(f*x + e))*e^(2*f*x + 2*e) + (9*f*cosh(f*x + e)^8 + 28*f*cosh(f*x + e)^6 + 30*f*cosh(f*x + e)^4 + 12*f*cosh(f*x + e)^2 + (9*f*cosh(f*x + e)^8 + 28*f*cosh(f*x + e)^6 + 30*f*cosh(f*x + e)^4 + 12*f*cosh(f*x + e)^2 + f)*e^(2*f*x + 2*e) + f)*sinh(f*x + e))","B",0
432,1,742,0,2.118582," ","integrate((a+a*sinh(f*x+e)^2)^(1/2)*tanh(f*x+e)^4,x, algorithm=""fricas"")","\frac{{\left(6 \, \cosh\left(f x + e\right) e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{5} + e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{6} + 3 \, {\left(5 \, \cosh\left(f x + e\right)^{2} + 1\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(5 \, \cosh\left(f x + e\right)^{3} + 3 \, \cosh\left(f x + e\right)\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{3} + 3 \, {\left(5 \, \cosh\left(f x + e\right)^{4} + 6 \, \cosh\left(f x + e\right)^{2} - 1\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{2} + 6 \, {\left(\cosh\left(f x + e\right)^{5} + 2 \, \cosh\left(f x + e\right)^{3} - \cosh\left(f x + e\right)\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right) - 6 \, {\left(5 \, \cosh\left(f x + e\right) e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{4} + e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(5 \, \cosh\left(f x + e\right)^{2} + 1\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{3} + 2 \, {\left(5 \, \cosh\left(f x + e\right)^{3} + 3 \, \cosh\left(f x + e\right)\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{2} + {\left(5 \, \cosh\left(f x + e\right)^{4} + 6 \, \cosh\left(f x + e\right)^{2} + 1\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right) + {\left(\cosh\left(f x + e\right)^{5} + 2 \, \cosh\left(f x + e\right)^{3} + \cosh\left(f x + e\right)\right)} e^{\left(f x + e\right)}\right)} \arctan\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right)\right) + {\left(\cosh\left(f x + e\right)^{6} + 3 \, \cosh\left(f x + e\right)^{4} - 3 \, \cosh\left(f x + e\right)^{2} - 1\right)} e^{\left(f x + e\right)}\right)} \sqrt{a e^{\left(4 \, f x + 4 \, e\right)} + 2 \, a e^{\left(2 \, f x + 2 \, e\right)} + a} e^{\left(-f x - e\right)}}{2 \, {\left(f \cosh\left(f x + e\right)^{5} + {\left(f e^{\left(2 \, f x + 2 \, e\right)} + f\right)} \sinh\left(f x + e\right)^{5} + 5 \, {\left(f \cosh\left(f x + e\right) e^{\left(2 \, f x + 2 \, e\right)} + f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{4} + 2 \, f \cosh\left(f x + e\right)^{3} + 2 \, {\left(5 \, f \cosh\left(f x + e\right)^{2} + {\left(5 \, f \cosh\left(f x + e\right)^{2} + f\right)} e^{\left(2 \, f x + 2 \, e\right)} + f\right)} \sinh\left(f x + e\right)^{3} + 2 \, {\left(5 \, f \cosh\left(f x + e\right)^{3} + 3 \, f \cosh\left(f x + e\right) + {\left(5 \, f \cosh\left(f x + e\right)^{3} + 3 \, f \cosh\left(f x + e\right)\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)^{2} + f \cosh\left(f x + e\right) + {\left(f \cosh\left(f x + e\right)^{5} + 2 \, f \cosh\left(f x + e\right)^{3} + f \cosh\left(f x + e\right)\right)} e^{\left(2 \, f x + 2 \, e\right)} + {\left(5 \, f \cosh\left(f x + e\right)^{4} + 6 \, f \cosh\left(f x + e\right)^{2} + {\left(5 \, f \cosh\left(f x + e\right)^{4} + 6 \, f \cosh\left(f x + e\right)^{2} + f\right)} e^{\left(2 \, f x + 2 \, e\right)} + f\right)} \sinh\left(f x + e\right)\right)}}"," ",0,"1/2*(6*cosh(f*x + e)*e^(f*x + e)*sinh(f*x + e)^5 + e^(f*x + e)*sinh(f*x + e)^6 + 3*(5*cosh(f*x + e)^2 + 1)*e^(f*x + e)*sinh(f*x + e)^4 + 4*(5*cosh(f*x + e)^3 + 3*cosh(f*x + e))*e^(f*x + e)*sinh(f*x + e)^3 + 3*(5*cosh(f*x + e)^4 + 6*cosh(f*x + e)^2 - 1)*e^(f*x + e)*sinh(f*x + e)^2 + 6*(cosh(f*x + e)^5 + 2*cosh(f*x + e)^3 - cosh(f*x + e))*e^(f*x + e)*sinh(f*x + e) - 6*(5*cosh(f*x + e)*e^(f*x + e)*sinh(f*x + e)^4 + e^(f*x + e)*sinh(f*x + e)^5 + 2*(5*cosh(f*x + e)^2 + 1)*e^(f*x + e)*sinh(f*x + e)^3 + 2*(5*cosh(f*x + e)^3 + 3*cosh(f*x + e))*e^(f*x + e)*sinh(f*x + e)^2 + (5*cosh(f*x + e)^4 + 6*cosh(f*x + e)^2 + 1)*e^(f*x + e)*sinh(f*x + e) + (cosh(f*x + e)^5 + 2*cosh(f*x + e)^3 + cosh(f*x + e))*e^(f*x + e))*arctan(cosh(f*x + e) + sinh(f*x + e)) + (cosh(f*x + e)^6 + 3*cosh(f*x + e)^4 - 3*cosh(f*x + e)^2 - 1)*e^(f*x + e))*sqrt(a*e^(4*f*x + 4*e) + 2*a*e^(2*f*x + 2*e) + a)*e^(-f*x - e)/(f*cosh(f*x + e)^5 + (f*e^(2*f*x + 2*e) + f)*sinh(f*x + e)^5 + 5*(f*cosh(f*x + e)*e^(2*f*x + 2*e) + f*cosh(f*x + e))*sinh(f*x + e)^4 + 2*f*cosh(f*x + e)^3 + 2*(5*f*cosh(f*x + e)^2 + (5*f*cosh(f*x + e)^2 + f)*e^(2*f*x + 2*e) + f)*sinh(f*x + e)^3 + 2*(5*f*cosh(f*x + e)^3 + 3*f*cosh(f*x + e) + (5*f*cosh(f*x + e)^3 + 3*f*cosh(f*x + e))*e^(2*f*x + 2*e))*sinh(f*x + e)^2 + f*cosh(f*x + e) + (f*cosh(f*x + e)^5 + 2*f*cosh(f*x + e)^3 + f*cosh(f*x + e))*e^(2*f*x + 2*e) + (5*f*cosh(f*x + e)^4 + 6*f*cosh(f*x + e)^2 + (5*f*cosh(f*x + e)^4 + 6*f*cosh(f*x + e)^2 + f)*e^(2*f*x + 2*e) + f)*sinh(f*x + e))","B",0
433,1,182,0,0.919786," ","integrate((a+a*sinh(f*x+e)^2)^(1/2)*tanh(f*x+e)^2,x, algorithm=""fricas"")","\frac{{\left(2 \, \cosh\left(f x + e\right) e^{\left(f x + e\right)} \sinh\left(f x + e\right) + e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{2} - 4 \, {\left(\cosh\left(f x + e\right) e^{\left(f x + e\right)} + e^{\left(f x + e\right)} \sinh\left(f x + e\right)\right)} \arctan\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right)\right) + {\left(\cosh\left(f x + e\right)^{2} - 1\right)} e^{\left(f x + e\right)}\right)} \sqrt{a e^{\left(4 \, f x + 4 \, e\right)} + 2 \, a e^{\left(2 \, f x + 2 \, e\right)} + a} e^{\left(-f x - e\right)}}{2 \, {\left(f \cosh\left(f x + e\right) e^{\left(2 \, f x + 2 \, e\right)} + f \cosh\left(f x + e\right) + {\left(f e^{\left(2 \, f x + 2 \, e\right)} + f\right)} \sinh\left(f x + e\right)\right)}}"," ",0,"1/2*(2*cosh(f*x + e)*e^(f*x + e)*sinh(f*x + e) + e^(f*x + e)*sinh(f*x + e)^2 - 4*(cosh(f*x + e)*e^(f*x + e) + e^(f*x + e)*sinh(f*x + e))*arctan(cosh(f*x + e) + sinh(f*x + e)) + (cosh(f*x + e)^2 - 1)*e^(f*x + e))*sqrt(a*e^(4*f*x + 4*e) + 2*a*e^(2*f*x + 2*e) + a)*e^(-f*x - e)/(f*cosh(f*x + e)*e^(2*f*x + 2*e) + f*cosh(f*x + e) + (f*e^(2*f*x + 2*e) + f)*sinh(f*x + e))","B",0
434,1,317,0,1.125024," ","integrate(coth(f*x+e)^2*(a+a*sinh(f*x+e)^2)^(1/2),x, algorithm=""fricas"")","\frac{{\left(4 \, \cosh\left(f x + e\right) e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{3} + e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{4} + 6 \, {\left(\cosh\left(f x + e\right)^{2} - 1\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(\cosh\left(f x + e\right)^{3} - 3 \, \cosh\left(f x + e\right)\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right) + {\left(\cosh\left(f x + e\right)^{4} - 6 \, \cosh\left(f x + e\right)^{2} + 1\right)} e^{\left(f x + e\right)}\right)} \sqrt{a e^{\left(4 \, f x + 4 \, e\right)} + 2 \, a e^{\left(2 \, f x + 2 \, e\right)} + a} e^{\left(-f x - e\right)}}{2 \, {\left(f \cosh\left(f x + e\right)^{3} + {\left(f e^{\left(2 \, f x + 2 \, e\right)} + f\right)} \sinh\left(f x + e\right)^{3} + 3 \, {\left(f \cosh\left(f x + e\right) e^{\left(2 \, f x + 2 \, e\right)} + f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{2} - f \cosh\left(f x + e\right) + {\left(f \cosh\left(f x + e\right)^{3} - f \cosh\left(f x + e\right)\right)} e^{\left(2 \, f x + 2 \, e\right)} + {\left(3 \, f \cosh\left(f x + e\right)^{2} + {\left(3 \, f \cosh\left(f x + e\right)^{2} - f\right)} e^{\left(2 \, f x + 2 \, e\right)} - f\right)} \sinh\left(f x + e\right)\right)}}"," ",0,"1/2*(4*cosh(f*x + e)*e^(f*x + e)*sinh(f*x + e)^3 + e^(f*x + e)*sinh(f*x + e)^4 + 6*(cosh(f*x + e)^2 - 1)*e^(f*x + e)*sinh(f*x + e)^2 + 4*(cosh(f*x + e)^3 - 3*cosh(f*x + e))*e^(f*x + e)*sinh(f*x + e) + (cosh(f*x + e)^4 - 6*cosh(f*x + e)^2 + 1)*e^(f*x + e))*sqrt(a*e^(4*f*x + 4*e) + 2*a*e^(2*f*x + 2*e) + a)*e^(-f*x - e)/(f*cosh(f*x + e)^3 + (f*e^(2*f*x + 2*e) + f)*sinh(f*x + e)^3 + 3*(f*cosh(f*x + e)*e^(2*f*x + 2*e) + f*cosh(f*x + e))*sinh(f*x + e)^2 - f*cosh(f*x + e) + (f*cosh(f*x + e)^3 - f*cosh(f*x + e))*e^(2*f*x + 2*e) + (3*f*cosh(f*x + e)^2 + (3*f*cosh(f*x + e)^2 - f)*e^(2*f*x + 2*e) - f)*sinh(f*x + e))","B",0
435,1,885,0,0.680802," ","integrate(coth(f*x+e)^4*(a+a*sinh(f*x+e)^2)^(1/2),x, algorithm=""fricas"")","\frac{{\left(24 \, \cosh\left(f x + e\right) e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{7} + 3 \, e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{8} + 12 \, {\left(7 \, \cosh\left(f x + e\right)^{2} - 3\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{6} + 24 \, {\left(7 \, \cosh\left(f x + e\right)^{3} - 9 \, \cosh\left(f x + e\right)\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{5} + 10 \, {\left(21 \, \cosh\left(f x + e\right)^{4} - 54 \, \cosh\left(f x + e\right)^{2} + 5\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{4} + 8 \, {\left(21 \, \cosh\left(f x + e\right)^{5} - 90 \, \cosh\left(f x + e\right)^{3} + 25 \, \cosh\left(f x + e\right)\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{3} + 12 \, {\left(7 \, \cosh\left(f x + e\right)^{6} - 45 \, \cosh\left(f x + e\right)^{4} + 25 \, \cosh\left(f x + e\right)^{2} - 3\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{2} + 8 \, {\left(3 \, \cosh\left(f x + e\right)^{7} - 27 \, \cosh\left(f x + e\right)^{5} + 25 \, \cosh\left(f x + e\right)^{3} - 9 \, \cosh\left(f x + e\right)\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right) + {\left(3 \, \cosh\left(f x + e\right)^{8} - 36 \, \cosh\left(f x + e\right)^{6} + 50 \, \cosh\left(f x + e\right)^{4} - 36 \, \cosh\left(f x + e\right)^{2} + 3\right)} e^{\left(f x + e\right)}\right)} \sqrt{a e^{\left(4 \, f x + 4 \, e\right)} + 2 \, a e^{\left(2 \, f x + 2 \, e\right)} + a} e^{\left(-f x - e\right)}}{6 \, {\left(f \cosh\left(f x + e\right)^{7} + {\left(f e^{\left(2 \, f x + 2 \, e\right)} + f\right)} \sinh\left(f x + e\right)^{7} + 7 \, {\left(f \cosh\left(f x + e\right) e^{\left(2 \, f x + 2 \, e\right)} + f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{6} - 3 \, f \cosh\left(f x + e\right)^{5} + 3 \, {\left(7 \, f \cosh\left(f x + e\right)^{2} + {\left(7 \, f \cosh\left(f x + e\right)^{2} - f\right)} e^{\left(2 \, f x + 2 \, e\right)} - f\right)} \sinh\left(f x + e\right)^{5} + 5 \, {\left(7 \, f \cosh\left(f x + e\right)^{3} - 3 \, f \cosh\left(f x + e\right) + {\left(7 \, f \cosh\left(f x + e\right)^{3} - 3 \, f \cosh\left(f x + e\right)\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)^{4} + 3 \, f \cosh\left(f x + e\right)^{3} + {\left(35 \, f \cosh\left(f x + e\right)^{4} - 30 \, f \cosh\left(f x + e\right)^{2} + {\left(35 \, f \cosh\left(f x + e\right)^{4} - 30 \, f \cosh\left(f x + e\right)^{2} + 3 \, f\right)} e^{\left(2 \, f x + 2 \, e\right)} + 3 \, f\right)} \sinh\left(f x + e\right)^{3} + 3 \, {\left(7 \, f \cosh\left(f x + e\right)^{5} - 10 \, f \cosh\left(f x + e\right)^{3} + 3 \, f \cosh\left(f x + e\right) + {\left(7 \, f \cosh\left(f x + e\right)^{5} - 10 \, f \cosh\left(f x + e\right)^{3} + 3 \, f \cosh\left(f x + e\right)\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)^{2} - f \cosh\left(f x + e\right) + {\left(f \cosh\left(f x + e\right)^{7} - 3 \, f \cosh\left(f x + e\right)^{5} + 3 \, f \cosh\left(f x + e\right)^{3} - f \cosh\left(f x + e\right)\right)} e^{\left(2 \, f x + 2 \, e\right)} + {\left(7 \, f \cosh\left(f x + e\right)^{6} - 15 \, f \cosh\left(f x + e\right)^{4} + 9 \, f \cosh\left(f x + e\right)^{2} + {\left(7 \, f \cosh\left(f x + e\right)^{6} - 15 \, f \cosh\left(f x + e\right)^{4} + 9 \, f \cosh\left(f x + e\right)^{2} - f\right)} e^{\left(2 \, f x + 2 \, e\right)} - f\right)} \sinh\left(f x + e\right)\right)}}"," ",0,"1/6*(24*cosh(f*x + e)*e^(f*x + e)*sinh(f*x + e)^7 + 3*e^(f*x + e)*sinh(f*x + e)^8 + 12*(7*cosh(f*x + e)^2 - 3)*e^(f*x + e)*sinh(f*x + e)^6 + 24*(7*cosh(f*x + e)^3 - 9*cosh(f*x + e))*e^(f*x + e)*sinh(f*x + e)^5 + 10*(21*cosh(f*x + e)^4 - 54*cosh(f*x + e)^2 + 5)*e^(f*x + e)*sinh(f*x + e)^4 + 8*(21*cosh(f*x + e)^5 - 90*cosh(f*x + e)^3 + 25*cosh(f*x + e))*e^(f*x + e)*sinh(f*x + e)^3 + 12*(7*cosh(f*x + e)^6 - 45*cosh(f*x + e)^4 + 25*cosh(f*x + e)^2 - 3)*e^(f*x + e)*sinh(f*x + e)^2 + 8*(3*cosh(f*x + e)^7 - 27*cosh(f*x + e)^5 + 25*cosh(f*x + e)^3 - 9*cosh(f*x + e))*e^(f*x + e)*sinh(f*x + e) + (3*cosh(f*x + e)^8 - 36*cosh(f*x + e)^6 + 50*cosh(f*x + e)^4 - 36*cosh(f*x + e)^2 + 3)*e^(f*x + e))*sqrt(a*e^(4*f*x + 4*e) + 2*a*e^(2*f*x + 2*e) + a)*e^(-f*x - e)/(f*cosh(f*x + e)^7 + (f*e^(2*f*x + 2*e) + f)*sinh(f*x + e)^7 + 7*(f*cosh(f*x + e)*e^(2*f*x + 2*e) + f*cosh(f*x + e))*sinh(f*x + e)^6 - 3*f*cosh(f*x + e)^5 + 3*(7*f*cosh(f*x + e)^2 + (7*f*cosh(f*x + e)^2 - f)*e^(2*f*x + 2*e) - f)*sinh(f*x + e)^5 + 5*(7*f*cosh(f*x + e)^3 - 3*f*cosh(f*x + e) + (7*f*cosh(f*x + e)^3 - 3*f*cosh(f*x + e))*e^(2*f*x + 2*e))*sinh(f*x + e)^4 + 3*f*cosh(f*x + e)^3 + (35*f*cosh(f*x + e)^4 - 30*f*cosh(f*x + e)^2 + (35*f*cosh(f*x + e)^4 - 30*f*cosh(f*x + e)^2 + 3*f)*e^(2*f*x + 2*e) + 3*f)*sinh(f*x + e)^3 + 3*(7*f*cosh(f*x + e)^5 - 10*f*cosh(f*x + e)^3 + 3*f*cosh(f*x + e) + (7*f*cosh(f*x + e)^5 - 10*f*cosh(f*x + e)^3 + 3*f*cosh(f*x + e))*e^(2*f*x + 2*e))*sinh(f*x + e)^2 - f*cosh(f*x + e) + (f*cosh(f*x + e)^7 - 3*f*cosh(f*x + e)^5 + 3*f*cosh(f*x + e)^3 - f*cosh(f*x + e))*e^(2*f*x + 2*e) + (7*f*cosh(f*x + e)^6 - 15*f*cosh(f*x + e)^4 + 9*f*cosh(f*x + e)^2 + (7*f*cosh(f*x + e)^6 - 15*f*cosh(f*x + e)^4 + 9*f*cosh(f*x + e)^2 - f)*e^(2*f*x + 2*e) - f)*sinh(f*x + e))","B",0
436,1,1696,0,0.624348," ","integrate(coth(f*x+e)^6*(a+a*sinh(f*x+e)^2)^(1/2),x, algorithm=""fricas"")","\frac{{\left(60 \, \cosh\left(f x + e\right) e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{11} + 5 \, e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{12} + 30 \, {\left(11 \, \cosh\left(f x + e\right)^{2} - 3\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{10} + 100 \, {\left(11 \, \cosh\left(f x + e\right)^{3} - 9 \, \cosh\left(f x + e\right)\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{9} + 5 \, {\left(495 \, \cosh\left(f x + e\right)^{4} - 810 \, \cosh\left(f x + e\right)^{2} + 47\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{8} + 40 \, {\left(99 \, \cosh\left(f x + e\right)^{5} - 270 \, \cosh\left(f x + e\right)^{3} + 47 \, \cosh\left(f x + e\right)\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{7} + 28 \, {\left(165 \, \cosh\left(f x + e\right)^{6} - 675 \, \cosh\left(f x + e\right)^{4} + 235 \, \cosh\left(f x + e\right)^{2} - 13\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{6} + 8 \, {\left(495 \, \cosh\left(f x + e\right)^{7} - 2835 \, \cosh\left(f x + e\right)^{5} + 1645 \, \cosh\left(f x + e\right)^{3} - 273 \, \cosh\left(f x + e\right)\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{5} + 5 \, {\left(495 \, \cosh\left(f x + e\right)^{8} - 3780 \, \cosh\left(f x + e\right)^{6} + 3290 \, \cosh\left(f x + e\right)^{4} - 1092 \, \cosh\left(f x + e\right)^{2} + 47\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{4} + 20 \, {\left(55 \, \cosh\left(f x + e\right)^{9} - 540 \, \cosh\left(f x + e\right)^{7} + 658 \, \cosh\left(f x + e\right)^{5} - 364 \, \cosh\left(f x + e\right)^{3} + 47 \, \cosh\left(f x + e\right)\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{3} + 10 \, {\left(33 \, \cosh\left(f x + e\right)^{10} - 405 \, \cosh\left(f x + e\right)^{8} + 658 \, \cosh\left(f x + e\right)^{6} - 546 \, \cosh\left(f x + e\right)^{4} + 141 \, \cosh\left(f x + e\right)^{2} - 9\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(15 \, \cosh\left(f x + e\right)^{11} - 225 \, \cosh\left(f x + e\right)^{9} + 470 \, \cosh\left(f x + e\right)^{7} - 546 \, \cosh\left(f x + e\right)^{5} + 235 \, \cosh\left(f x + e\right)^{3} - 45 \, \cosh\left(f x + e\right)\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right) + {\left(5 \, \cosh\left(f x + e\right)^{12} - 90 \, \cosh\left(f x + e\right)^{10} + 235 \, \cosh\left(f x + e\right)^{8} - 364 \, \cosh\left(f x + e\right)^{6} + 235 \, \cosh\left(f x + e\right)^{4} - 90 \, \cosh\left(f x + e\right)^{2} + 5\right)} e^{\left(f x + e\right)}\right)} \sqrt{a e^{\left(4 \, f x + 4 \, e\right)} + 2 \, a e^{\left(2 \, f x + 2 \, e\right)} + a} e^{\left(-f x - e\right)}}{10 \, {\left(f \cosh\left(f x + e\right)^{11} + {\left(f e^{\left(2 \, f x + 2 \, e\right)} + f\right)} \sinh\left(f x + e\right)^{11} + 11 \, {\left(f \cosh\left(f x + e\right) e^{\left(2 \, f x + 2 \, e\right)} + f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{10} - 5 \, f \cosh\left(f x + e\right)^{9} + 5 \, {\left(11 \, f \cosh\left(f x + e\right)^{2} + {\left(11 \, f \cosh\left(f x + e\right)^{2} - f\right)} e^{\left(2 \, f x + 2 \, e\right)} - f\right)} \sinh\left(f x + e\right)^{9} + 15 \, {\left(11 \, f \cosh\left(f x + e\right)^{3} - 3 \, f \cosh\left(f x + e\right) + {\left(11 \, f \cosh\left(f x + e\right)^{3} - 3 \, f \cosh\left(f x + e\right)\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)^{8} + 10 \, f \cosh\left(f x + e\right)^{7} + 10 \, {\left(33 \, f \cosh\left(f x + e\right)^{4} - 18 \, f \cosh\left(f x + e\right)^{2} + {\left(33 \, f \cosh\left(f x + e\right)^{4} - 18 \, f \cosh\left(f x + e\right)^{2} + f\right)} e^{\left(2 \, f x + 2 \, e\right)} + f\right)} \sinh\left(f x + e\right)^{7} + 14 \, {\left(33 \, f \cosh\left(f x + e\right)^{5} - 30 \, f \cosh\left(f x + e\right)^{3} + 5 \, f \cosh\left(f x + e\right) + {\left(33 \, f \cosh\left(f x + e\right)^{5} - 30 \, f \cosh\left(f x + e\right)^{3} + 5 \, f \cosh\left(f x + e\right)\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)^{6} - 10 \, f \cosh\left(f x + e\right)^{5} + 2 \, {\left(231 \, f \cosh\left(f x + e\right)^{6} - 315 \, f \cosh\left(f x + e\right)^{4} + 105 \, f \cosh\left(f x + e\right)^{2} + {\left(231 \, f \cosh\left(f x + e\right)^{6} - 315 \, f \cosh\left(f x + e\right)^{4} + 105 \, f \cosh\left(f x + e\right)^{2} - 5 \, f\right)} e^{\left(2 \, f x + 2 \, e\right)} - 5 \, f\right)} \sinh\left(f x + e\right)^{5} + 10 \, {\left(33 \, f \cosh\left(f x + e\right)^{7} - 63 \, f \cosh\left(f x + e\right)^{5} + 35 \, f \cosh\left(f x + e\right)^{3} - 5 \, f \cosh\left(f x + e\right) + {\left(33 \, f \cosh\left(f x + e\right)^{7} - 63 \, f \cosh\left(f x + e\right)^{5} + 35 \, f \cosh\left(f x + e\right)^{3} - 5 \, f \cosh\left(f x + e\right)\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)^{4} + 5 \, f \cosh\left(f x + e\right)^{3} + 5 \, {\left(33 \, f \cosh\left(f x + e\right)^{8} - 84 \, f \cosh\left(f x + e\right)^{6} + 70 \, f \cosh\left(f x + e\right)^{4} - 20 \, f \cosh\left(f x + e\right)^{2} + {\left(33 \, f \cosh\left(f x + e\right)^{8} - 84 \, f \cosh\left(f x + e\right)^{6} + 70 \, f \cosh\left(f x + e\right)^{4} - 20 \, f \cosh\left(f x + e\right)^{2} + f\right)} e^{\left(2 \, f x + 2 \, e\right)} + f\right)} \sinh\left(f x + e\right)^{3} + 5 \, {\left(11 \, f \cosh\left(f x + e\right)^{9} - 36 \, f \cosh\left(f x + e\right)^{7} + 42 \, f \cosh\left(f x + e\right)^{5} - 20 \, f \cosh\left(f x + e\right)^{3} + 3 \, f \cosh\left(f x + e\right) + {\left(11 \, f \cosh\left(f x + e\right)^{9} - 36 \, f \cosh\left(f x + e\right)^{7} + 42 \, f \cosh\left(f x + e\right)^{5} - 20 \, f \cosh\left(f x + e\right)^{3} + 3 \, f \cosh\left(f x + e\right)\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)^{2} - f \cosh\left(f x + e\right) + {\left(f \cosh\left(f x + e\right)^{11} - 5 \, f \cosh\left(f x + e\right)^{9} + 10 \, f \cosh\left(f x + e\right)^{7} - 10 \, f \cosh\left(f x + e\right)^{5} + 5 \, f \cosh\left(f x + e\right)^{3} - f \cosh\left(f x + e\right)\right)} e^{\left(2 \, f x + 2 \, e\right)} + {\left(11 \, f \cosh\left(f x + e\right)^{10} - 45 \, f \cosh\left(f x + e\right)^{8} + 70 \, f \cosh\left(f x + e\right)^{6} - 50 \, f \cosh\left(f x + e\right)^{4} + 15 \, f \cosh\left(f x + e\right)^{2} + {\left(11 \, f \cosh\left(f x + e\right)^{10} - 45 \, f \cosh\left(f x + e\right)^{8} + 70 \, f \cosh\left(f x + e\right)^{6} - 50 \, f \cosh\left(f x + e\right)^{4} + 15 \, f \cosh\left(f x + e\right)^{2} - f\right)} e^{\left(2 \, f x + 2 \, e\right)} - f\right)} \sinh\left(f x + e\right)\right)}}"," ",0,"1/10*(60*cosh(f*x + e)*e^(f*x + e)*sinh(f*x + e)^11 + 5*e^(f*x + e)*sinh(f*x + e)^12 + 30*(11*cosh(f*x + e)^2 - 3)*e^(f*x + e)*sinh(f*x + e)^10 + 100*(11*cosh(f*x + e)^3 - 9*cosh(f*x + e))*e^(f*x + e)*sinh(f*x + e)^9 + 5*(495*cosh(f*x + e)^4 - 810*cosh(f*x + e)^2 + 47)*e^(f*x + e)*sinh(f*x + e)^8 + 40*(99*cosh(f*x + e)^5 - 270*cosh(f*x + e)^3 + 47*cosh(f*x + e))*e^(f*x + e)*sinh(f*x + e)^7 + 28*(165*cosh(f*x + e)^6 - 675*cosh(f*x + e)^4 + 235*cosh(f*x + e)^2 - 13)*e^(f*x + e)*sinh(f*x + e)^6 + 8*(495*cosh(f*x + e)^7 - 2835*cosh(f*x + e)^5 + 1645*cosh(f*x + e)^3 - 273*cosh(f*x + e))*e^(f*x + e)*sinh(f*x + e)^5 + 5*(495*cosh(f*x + e)^8 - 3780*cosh(f*x + e)^6 + 3290*cosh(f*x + e)^4 - 1092*cosh(f*x + e)^2 + 47)*e^(f*x + e)*sinh(f*x + e)^4 + 20*(55*cosh(f*x + e)^9 - 540*cosh(f*x + e)^7 + 658*cosh(f*x + e)^5 - 364*cosh(f*x + e)^3 + 47*cosh(f*x + e))*e^(f*x + e)*sinh(f*x + e)^3 + 10*(33*cosh(f*x + e)^10 - 405*cosh(f*x + e)^8 + 658*cosh(f*x + e)^6 - 546*cosh(f*x + e)^4 + 141*cosh(f*x + e)^2 - 9)*e^(f*x + e)*sinh(f*x + e)^2 + 4*(15*cosh(f*x + e)^11 - 225*cosh(f*x + e)^9 + 470*cosh(f*x + e)^7 - 546*cosh(f*x + e)^5 + 235*cosh(f*x + e)^3 - 45*cosh(f*x + e))*e^(f*x + e)*sinh(f*x + e) + (5*cosh(f*x + e)^12 - 90*cosh(f*x + e)^10 + 235*cosh(f*x + e)^8 - 364*cosh(f*x + e)^6 + 235*cosh(f*x + e)^4 - 90*cosh(f*x + e)^2 + 5)*e^(f*x + e))*sqrt(a*e^(4*f*x + 4*e) + 2*a*e^(2*f*x + 2*e) + a)*e^(-f*x - e)/(f*cosh(f*x + e)^11 + (f*e^(2*f*x + 2*e) + f)*sinh(f*x + e)^11 + 11*(f*cosh(f*x + e)*e^(2*f*x + 2*e) + f*cosh(f*x + e))*sinh(f*x + e)^10 - 5*f*cosh(f*x + e)^9 + 5*(11*f*cosh(f*x + e)^2 + (11*f*cosh(f*x + e)^2 - f)*e^(2*f*x + 2*e) - f)*sinh(f*x + e)^9 + 15*(11*f*cosh(f*x + e)^3 - 3*f*cosh(f*x + e) + (11*f*cosh(f*x + e)^3 - 3*f*cosh(f*x + e))*e^(2*f*x + 2*e))*sinh(f*x + e)^8 + 10*f*cosh(f*x + e)^7 + 10*(33*f*cosh(f*x + e)^4 - 18*f*cosh(f*x + e)^2 + (33*f*cosh(f*x + e)^4 - 18*f*cosh(f*x + e)^2 + f)*e^(2*f*x + 2*e) + f)*sinh(f*x + e)^7 + 14*(33*f*cosh(f*x + e)^5 - 30*f*cosh(f*x + e)^3 + 5*f*cosh(f*x + e) + (33*f*cosh(f*x + e)^5 - 30*f*cosh(f*x + e)^3 + 5*f*cosh(f*x + e))*e^(2*f*x + 2*e))*sinh(f*x + e)^6 - 10*f*cosh(f*x + e)^5 + 2*(231*f*cosh(f*x + e)^6 - 315*f*cosh(f*x + e)^4 + 105*f*cosh(f*x + e)^2 + (231*f*cosh(f*x + e)^6 - 315*f*cosh(f*x + e)^4 + 105*f*cosh(f*x + e)^2 - 5*f)*e^(2*f*x + 2*e) - 5*f)*sinh(f*x + e)^5 + 10*(33*f*cosh(f*x + e)^7 - 63*f*cosh(f*x + e)^5 + 35*f*cosh(f*x + e)^3 - 5*f*cosh(f*x + e) + (33*f*cosh(f*x + e)^7 - 63*f*cosh(f*x + e)^5 + 35*f*cosh(f*x + e)^3 - 5*f*cosh(f*x + e))*e^(2*f*x + 2*e))*sinh(f*x + e)^4 + 5*f*cosh(f*x + e)^3 + 5*(33*f*cosh(f*x + e)^8 - 84*f*cosh(f*x + e)^6 + 70*f*cosh(f*x + e)^4 - 20*f*cosh(f*x + e)^2 + (33*f*cosh(f*x + e)^8 - 84*f*cosh(f*x + e)^6 + 70*f*cosh(f*x + e)^4 - 20*f*cosh(f*x + e)^2 + f)*e^(2*f*x + 2*e) + f)*sinh(f*x + e)^3 + 5*(11*f*cosh(f*x + e)^9 - 36*f*cosh(f*x + e)^7 + 42*f*cosh(f*x + e)^5 - 20*f*cosh(f*x + e)^3 + 3*f*cosh(f*x + e) + (11*f*cosh(f*x + e)^9 - 36*f*cosh(f*x + e)^7 + 42*f*cosh(f*x + e)^5 - 20*f*cosh(f*x + e)^3 + 3*f*cosh(f*x + e))*e^(2*f*x + 2*e))*sinh(f*x + e)^2 - f*cosh(f*x + e) + (f*cosh(f*x + e)^11 - 5*f*cosh(f*x + e)^9 + 10*f*cosh(f*x + e)^7 - 10*f*cosh(f*x + e)^5 + 5*f*cosh(f*x + e)^3 - f*cosh(f*x + e))*e^(2*f*x + 2*e) + (11*f*cosh(f*x + e)^10 - 45*f*cosh(f*x + e)^8 + 70*f*cosh(f*x + e)^6 - 50*f*cosh(f*x + e)^4 + 15*f*cosh(f*x + e)^2 + (11*f*cosh(f*x + e)^10 - 45*f*cosh(f*x + e)^8 + 70*f*cosh(f*x + e)^6 - 50*f*cosh(f*x + e)^4 + 15*f*cosh(f*x + e)^2 - f)*e^(2*f*x + 2*e) - f)*sinh(f*x + e))","B",0
437,1,1387,0,0.494102," ","integrate(tanh(f*x+e)^5/(a+a*sinh(f*x+e)^2)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(135 \, \cosh\left(f x + e\right) e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{8} + 15 \, e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{9} + 20 \, {\left(27 \, \cosh\left(f x + e\right)^{2} + 1\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{7} + 140 \, {\left(9 \, \cosh\left(f x + e\right)^{3} + \cosh\left(f x + e\right)\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{6} + 2 \, {\left(945 \, \cosh\left(f x + e\right)^{4} + 210 \, \cosh\left(f x + e\right)^{2} + 29\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{5} + 10 \, {\left(189 \, \cosh\left(f x + e\right)^{5} + 70 \, \cosh\left(f x + e\right)^{3} + 29 \, \cosh\left(f x + e\right)\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{4} + 20 \, {\left(63 \, \cosh\left(f x + e\right)^{6} + 35 \, \cosh\left(f x + e\right)^{4} + 29 \, \cosh\left(f x + e\right)^{2} + 1\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{3} + 20 \, {\left(27 \, \cosh\left(f x + e\right)^{7} + 21 \, \cosh\left(f x + e\right)^{5} + 29 \, \cosh\left(f x + e\right)^{3} + 3 \, \cosh\left(f x + e\right)\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{2} + 5 \, {\left(27 \, \cosh\left(f x + e\right)^{8} + 28 \, \cosh\left(f x + e\right)^{6} + 58 \, \cosh\left(f x + e\right)^{4} + 12 \, \cosh\left(f x + e\right)^{2} + 3\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right) + {\left(15 \, \cosh\left(f x + e\right)^{9} + 20 \, \cosh\left(f x + e\right)^{7} + 58 \, \cosh\left(f x + e\right)^{5} + 20 \, \cosh\left(f x + e\right)^{3} + 15 \, \cosh\left(f x + e\right)\right)} e^{\left(f x + e\right)}\right)} \sqrt{a e^{\left(4 \, f x + 4 \, e\right)} + 2 \, a e^{\left(2 \, f x + 2 \, e\right)} + a} e^{\left(-f x - e\right)}}{15 \, {\left(a f \cosh\left(f x + e\right)^{10} + {\left(a f e^{\left(2 \, f x + 2 \, e\right)} + a f\right)} \sinh\left(f x + e\right)^{10} + 5 \, a f \cosh\left(f x + e\right)^{8} + 10 \, {\left(a f \cosh\left(f x + e\right) e^{\left(2 \, f x + 2 \, e\right)} + a f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{9} + 5 \, {\left(9 \, a f \cosh\left(f x + e\right)^{2} + a f + {\left(9 \, a f \cosh\left(f x + e\right)^{2} + a f\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)^{8} + 10 \, a f \cosh\left(f x + e\right)^{6} + 40 \, {\left(3 \, a f \cosh\left(f x + e\right)^{3} + a f \cosh\left(f x + e\right) + {\left(3 \, a f \cosh\left(f x + e\right)^{3} + a f \cosh\left(f x + e\right)\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)^{7} + 10 \, {\left(21 \, a f \cosh\left(f x + e\right)^{4} + 14 \, a f \cosh\left(f x + e\right)^{2} + a f + {\left(21 \, a f \cosh\left(f x + e\right)^{4} + 14 \, a f \cosh\left(f x + e\right)^{2} + a f\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)^{6} + 10 \, a f \cosh\left(f x + e\right)^{4} + 4 \, {\left(63 \, a f \cosh\left(f x + e\right)^{5} + 70 \, a f \cosh\left(f x + e\right)^{3} + 15 \, a f \cosh\left(f x + e\right) + {\left(63 \, a f \cosh\left(f x + e\right)^{5} + 70 \, a f \cosh\left(f x + e\right)^{3} + 15 \, a f \cosh\left(f x + e\right)\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)^{5} + 10 \, {\left(21 \, a f \cosh\left(f x + e\right)^{6} + 35 \, a f \cosh\left(f x + e\right)^{4} + 15 \, a f \cosh\left(f x + e\right)^{2} + a f + {\left(21 \, a f \cosh\left(f x + e\right)^{6} + 35 \, a f \cosh\left(f x + e\right)^{4} + 15 \, a f \cosh\left(f x + e\right)^{2} + a f\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)^{4} + 5 \, a f \cosh\left(f x + e\right)^{2} + 40 \, {\left(3 \, a f \cosh\left(f x + e\right)^{7} + 7 \, a f \cosh\left(f x + e\right)^{5} + 5 \, a f \cosh\left(f x + e\right)^{3} + a f \cosh\left(f x + e\right) + {\left(3 \, a f \cosh\left(f x + e\right)^{7} + 7 \, a f \cosh\left(f x + e\right)^{5} + 5 \, a f \cosh\left(f x + e\right)^{3} + a f \cosh\left(f x + e\right)\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)^{3} + 5 \, {\left(9 \, a f \cosh\left(f x + e\right)^{8} + 28 \, a f \cosh\left(f x + e\right)^{6} + 30 \, a f \cosh\left(f x + e\right)^{4} + 12 \, a f \cosh\left(f x + e\right)^{2} + a f + {\left(9 \, a f \cosh\left(f x + e\right)^{8} + 28 \, a f \cosh\left(f x + e\right)^{6} + 30 \, a f \cosh\left(f x + e\right)^{4} + 12 \, a f \cosh\left(f x + e\right)^{2} + a f\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)^{2} + a f + {\left(a f \cosh\left(f x + e\right)^{10} + 5 \, a f \cosh\left(f x + e\right)^{8} + 10 \, a f \cosh\left(f x + e\right)^{6} + 10 \, a f \cosh\left(f x + e\right)^{4} + 5 \, a f \cosh\left(f x + e\right)^{2} + a f\right)} e^{\left(2 \, f x + 2 \, e\right)} + 10 \, {\left(a f \cosh\left(f x + e\right)^{9} + 4 \, a f \cosh\left(f x + e\right)^{7} + 6 \, a f \cosh\left(f x + e\right)^{5} + 4 \, a f \cosh\left(f x + e\right)^{3} + a f \cosh\left(f x + e\right) + {\left(a f \cosh\left(f x + e\right)^{9} + 4 \, a f \cosh\left(f x + e\right)^{7} + 6 \, a f \cosh\left(f x + e\right)^{5} + 4 \, a f \cosh\left(f x + e\right)^{3} + a f \cosh\left(f x + e\right)\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)\right)}}"," ",0,"-2/15*(135*cosh(f*x + e)*e^(f*x + e)*sinh(f*x + e)^8 + 15*e^(f*x + e)*sinh(f*x + e)^9 + 20*(27*cosh(f*x + e)^2 + 1)*e^(f*x + e)*sinh(f*x + e)^7 + 140*(9*cosh(f*x + e)^3 + cosh(f*x + e))*e^(f*x + e)*sinh(f*x + e)^6 + 2*(945*cosh(f*x + e)^4 + 210*cosh(f*x + e)^2 + 29)*e^(f*x + e)*sinh(f*x + e)^5 + 10*(189*cosh(f*x + e)^5 + 70*cosh(f*x + e)^3 + 29*cosh(f*x + e))*e^(f*x + e)*sinh(f*x + e)^4 + 20*(63*cosh(f*x + e)^6 + 35*cosh(f*x + e)^4 + 29*cosh(f*x + e)^2 + 1)*e^(f*x + e)*sinh(f*x + e)^3 + 20*(27*cosh(f*x + e)^7 + 21*cosh(f*x + e)^5 + 29*cosh(f*x + e)^3 + 3*cosh(f*x + e))*e^(f*x + e)*sinh(f*x + e)^2 + 5*(27*cosh(f*x + e)^8 + 28*cosh(f*x + e)^6 + 58*cosh(f*x + e)^4 + 12*cosh(f*x + e)^2 + 3)*e^(f*x + e)*sinh(f*x + e) + (15*cosh(f*x + e)^9 + 20*cosh(f*x + e)^7 + 58*cosh(f*x + e)^5 + 20*cosh(f*x + e)^3 + 15*cosh(f*x + e))*e^(f*x + e))*sqrt(a*e^(4*f*x + 4*e) + 2*a*e^(2*f*x + 2*e) + a)*e^(-f*x - e)/(a*f*cosh(f*x + e)^10 + (a*f*e^(2*f*x + 2*e) + a*f)*sinh(f*x + e)^10 + 5*a*f*cosh(f*x + e)^8 + 10*(a*f*cosh(f*x + e)*e^(2*f*x + 2*e) + a*f*cosh(f*x + e))*sinh(f*x + e)^9 + 5*(9*a*f*cosh(f*x + e)^2 + a*f + (9*a*f*cosh(f*x + e)^2 + a*f)*e^(2*f*x + 2*e))*sinh(f*x + e)^8 + 10*a*f*cosh(f*x + e)^6 + 40*(3*a*f*cosh(f*x + e)^3 + a*f*cosh(f*x + e) + (3*a*f*cosh(f*x + e)^3 + a*f*cosh(f*x + e))*e^(2*f*x + 2*e))*sinh(f*x + e)^7 + 10*(21*a*f*cosh(f*x + e)^4 + 14*a*f*cosh(f*x + e)^2 + a*f + (21*a*f*cosh(f*x + e)^4 + 14*a*f*cosh(f*x + e)^2 + a*f)*e^(2*f*x + 2*e))*sinh(f*x + e)^6 + 10*a*f*cosh(f*x + e)^4 + 4*(63*a*f*cosh(f*x + e)^5 + 70*a*f*cosh(f*x + e)^3 + 15*a*f*cosh(f*x + e) + (63*a*f*cosh(f*x + e)^5 + 70*a*f*cosh(f*x + e)^3 + 15*a*f*cosh(f*x + e))*e^(2*f*x + 2*e))*sinh(f*x + e)^5 + 10*(21*a*f*cosh(f*x + e)^6 + 35*a*f*cosh(f*x + e)^4 + 15*a*f*cosh(f*x + e)^2 + a*f + (21*a*f*cosh(f*x + e)^6 + 35*a*f*cosh(f*x + e)^4 + 15*a*f*cosh(f*x + e)^2 + a*f)*e^(2*f*x + 2*e))*sinh(f*x + e)^4 + 5*a*f*cosh(f*x + e)^2 + 40*(3*a*f*cosh(f*x + e)^7 + 7*a*f*cosh(f*x + e)^5 + 5*a*f*cosh(f*x + e)^3 + a*f*cosh(f*x + e) + (3*a*f*cosh(f*x + e)^7 + 7*a*f*cosh(f*x + e)^5 + 5*a*f*cosh(f*x + e)^3 + a*f*cosh(f*x + e))*e^(2*f*x + 2*e))*sinh(f*x + e)^3 + 5*(9*a*f*cosh(f*x + e)^8 + 28*a*f*cosh(f*x + e)^6 + 30*a*f*cosh(f*x + e)^4 + 12*a*f*cosh(f*x + e)^2 + a*f + (9*a*f*cosh(f*x + e)^8 + 28*a*f*cosh(f*x + e)^6 + 30*a*f*cosh(f*x + e)^4 + 12*a*f*cosh(f*x + e)^2 + a*f)*e^(2*f*x + 2*e))*sinh(f*x + e)^2 + a*f + (a*f*cosh(f*x + e)^10 + 5*a*f*cosh(f*x + e)^8 + 10*a*f*cosh(f*x + e)^6 + 10*a*f*cosh(f*x + e)^4 + 5*a*f*cosh(f*x + e)^2 + a*f)*e^(2*f*x + 2*e) + 10*(a*f*cosh(f*x + e)^9 + 4*a*f*cosh(f*x + e)^7 + 6*a*f*cosh(f*x + e)^5 + 4*a*f*cosh(f*x + e)^3 + a*f*cosh(f*x + e) + (a*f*cosh(f*x + e)^9 + 4*a*f*cosh(f*x + e)^7 + 6*a*f*cosh(f*x + e)^5 + 4*a*f*cosh(f*x + e)^3 + a*f*cosh(f*x + e))*e^(2*f*x + 2*e))*sinh(f*x + e))","B",0
438,1,641,0,0.428145," ","integrate(tanh(f*x+e)^3/(a+a*sinh(f*x+e)^2)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(15 \, \cosh\left(f x + e\right) e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{4} + 3 \, e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(15 \, \cosh\left(f x + e\right)^{2} + 1\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{3} + 6 \, {\left(5 \, \cosh\left(f x + e\right)^{3} + \cosh\left(f x + e\right)\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{2} + 3 \, {\left(5 \, \cosh\left(f x + e\right)^{4} + 2 \, \cosh\left(f x + e\right)^{2} + 1\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right) + {\left(3 \, \cosh\left(f x + e\right)^{5} + 2 \, \cosh\left(f x + e\right)^{3} + 3 \, \cosh\left(f x + e\right)\right)} e^{\left(f x + e\right)}\right)} \sqrt{a e^{\left(4 \, f x + 4 \, e\right)} + 2 \, a e^{\left(2 \, f x + 2 \, e\right)} + a} e^{\left(-f x - e\right)}}{3 \, {\left(a f \cosh\left(f x + e\right)^{6} + {\left(a f e^{\left(2 \, f x + 2 \, e\right)} + a f\right)} \sinh\left(f x + e\right)^{6} + 3 \, a f \cosh\left(f x + e\right)^{4} + 6 \, {\left(a f \cosh\left(f x + e\right) e^{\left(2 \, f x + 2 \, e\right)} + a f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + 3 \, {\left(5 \, a f \cosh\left(f x + e\right)^{2} + a f + {\left(5 \, a f \cosh\left(f x + e\right)^{2} + a f\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)^{4} + 3 \, a f \cosh\left(f x + e\right)^{2} + 4 \, {\left(5 \, a f \cosh\left(f x + e\right)^{3} + 3 \, a f \cosh\left(f x + e\right) + {\left(5 \, a f \cosh\left(f x + e\right)^{3} + 3 \, a f \cosh\left(f x + e\right)\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)^{3} + 3 \, {\left(5 \, a f \cosh\left(f x + e\right)^{4} + 6 \, a f \cosh\left(f x + e\right)^{2} + a f + {\left(5 \, a f \cosh\left(f x + e\right)^{4} + 6 \, a f \cosh\left(f x + e\right)^{2} + a f\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)^{2} + a f + {\left(a f \cosh\left(f x + e\right)^{6} + 3 \, a f \cosh\left(f x + e\right)^{4} + 3 \, a f \cosh\left(f x + e\right)^{2} + a f\right)} e^{\left(2 \, f x + 2 \, e\right)} + 6 \, {\left(a f \cosh\left(f x + e\right)^{5} + 2 \, a f \cosh\left(f x + e\right)^{3} + a f \cosh\left(f x + e\right) + {\left(a f \cosh\left(f x + e\right)^{5} + 2 \, a f \cosh\left(f x + e\right)^{3} + a f \cosh\left(f x + e\right)\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)\right)}}"," ",0,"-2/3*(15*cosh(f*x + e)*e^(f*x + e)*sinh(f*x + e)^4 + 3*e^(f*x + e)*sinh(f*x + e)^5 + 2*(15*cosh(f*x + e)^2 + 1)*e^(f*x + e)*sinh(f*x + e)^3 + 6*(5*cosh(f*x + e)^3 + cosh(f*x + e))*e^(f*x + e)*sinh(f*x + e)^2 + 3*(5*cosh(f*x + e)^4 + 2*cosh(f*x + e)^2 + 1)*e^(f*x + e)*sinh(f*x + e) + (3*cosh(f*x + e)^5 + 2*cosh(f*x + e)^3 + 3*cosh(f*x + e))*e^(f*x + e))*sqrt(a*e^(4*f*x + 4*e) + 2*a*e^(2*f*x + 2*e) + a)*e^(-f*x - e)/(a*f*cosh(f*x + e)^6 + (a*f*e^(2*f*x + 2*e) + a*f)*sinh(f*x + e)^6 + 3*a*f*cosh(f*x + e)^4 + 6*(a*f*cosh(f*x + e)*e^(2*f*x + 2*e) + a*f*cosh(f*x + e))*sinh(f*x + e)^5 + 3*(5*a*f*cosh(f*x + e)^2 + a*f + (5*a*f*cosh(f*x + e)^2 + a*f)*e^(2*f*x + 2*e))*sinh(f*x + e)^4 + 3*a*f*cosh(f*x + e)^2 + 4*(5*a*f*cosh(f*x + e)^3 + 3*a*f*cosh(f*x + e) + (5*a*f*cosh(f*x + e)^3 + 3*a*f*cosh(f*x + e))*e^(2*f*x + 2*e))*sinh(f*x + e)^3 + 3*(5*a*f*cosh(f*x + e)^4 + 6*a*f*cosh(f*x + e)^2 + a*f + (5*a*f*cosh(f*x + e)^4 + 6*a*f*cosh(f*x + e)^2 + a*f)*e^(2*f*x + 2*e))*sinh(f*x + e)^2 + a*f + (a*f*cosh(f*x + e)^6 + 3*a*f*cosh(f*x + e)^4 + 3*a*f*cosh(f*x + e)^2 + a*f)*e^(2*f*x + 2*e) + 6*(a*f*cosh(f*x + e)^5 + 2*a*f*cosh(f*x + e)^3 + a*f*cosh(f*x + e) + (a*f*cosh(f*x + e)^5 + 2*a*f*cosh(f*x + e)^3 + a*f*cosh(f*x + e))*e^(2*f*x + 2*e))*sinh(f*x + e))","B",0
439,1,168,0,0.516269," ","integrate(tanh(f*x+e)/(a+a*sinh(f*x+e)^2)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{a e^{\left(4 \, f x + 4 \, e\right)} + 2 \, a e^{\left(2 \, f x + 2 \, e\right)} + a} {\left(\cosh\left(f x + e\right) e^{\left(f x + e\right)} + e^{\left(f x + e\right)} \sinh\left(f x + e\right)\right)} e^{\left(-f x - e\right)}}{a f \cosh\left(f x + e\right)^{2} + {\left(a f e^{\left(2 \, f x + 2 \, e\right)} + a f\right)} \sinh\left(f x + e\right)^{2} + a f + {\left(a f \cosh\left(f x + e\right)^{2} + a f\right)} e^{\left(2 \, f x + 2 \, e\right)} + 2 \, {\left(a f \cosh\left(f x + e\right) e^{\left(2 \, f x + 2 \, e\right)} + a f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)}"," ",0,"-2*sqrt(a*e^(4*f*x + 4*e) + 2*a*e^(2*f*x + 2*e) + a)*(cosh(f*x + e)*e^(f*x + e) + e^(f*x + e)*sinh(f*x + e))*e^(-f*x - e)/(a*f*cosh(f*x + e)^2 + (a*f*e^(2*f*x + 2*e) + a*f)*sinh(f*x + e)^2 + a*f + (a*f*cosh(f*x + e)^2 + a*f)*e^(2*f*x + 2*e) + 2*(a*f*cosh(f*x + e)*e^(2*f*x + 2*e) + a*f*cosh(f*x + e))*sinh(f*x + e))","B",0
440,1,174,0,0.533391," ","integrate(coth(f*x+e)/(a+a*sinh(f*x+e)^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{a e^{\left(4 \, f x + 4 \, e\right)} + 2 \, a e^{\left(2 \, f x + 2 \, e\right)} + a} \log\left(\frac{\cosh\left(f x + e\right) + \sinh\left(f x + e\right) - 1}{\cosh\left(f x + e\right) + \sinh\left(f x + e\right) + 1}\right)}{a f e^{\left(2 \, f x + 2 \, e\right)} + a f}, \frac{2 \, \sqrt{-a} \arctan\left(\frac{\sqrt{a e^{\left(4 \, f x + 4 \, e\right)} + 2 \, a e^{\left(2 \, f x + 2 \, e\right)} + a} \sqrt{-a}}{a \cosh\left(f x + e\right) e^{\left(2 \, f x + 2 \, e\right)} + a \cosh\left(f x + e\right) + {\left(a e^{\left(2 \, f x + 2 \, e\right)} + a\right)} \sinh\left(f x + e\right)}\right)}{a f}\right]"," ",0,"[sqrt(a*e^(4*f*x + 4*e) + 2*a*e^(2*f*x + 2*e) + a)*log((cosh(f*x + e) + sinh(f*x + e) - 1)/(cosh(f*x + e) + sinh(f*x + e) + 1))/(a*f*e^(2*f*x + 2*e) + a*f), 2*sqrt(-a)*arctan(sqrt(a*e^(4*f*x + 4*e) + 2*a*e^(2*f*x + 2*e) + a)*sqrt(-a)/(a*cosh(f*x + e)*e^(2*f*x + 2*e) + a*cosh(f*x + e) + (a*e^(2*f*x + 2*e) + a)*sinh(f*x + e)))/(a*f)]","B",0
441,1,529,0,0.920686," ","integrate(coth(f*x+e)^3/(a+a*sinh(f*x+e)^2)^(1/2),x, algorithm=""fricas"")","-\frac{{\left(6 \, \cosh\left(f x + e\right) e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{2} + 2 \, e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{3} + 2 \, {\left(3 \, \cosh\left(f x + e\right)^{2} + 1\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right) + 2 \, {\left(\cosh\left(f x + e\right)^{3} + \cosh\left(f x + e\right)\right)} e^{\left(f x + e\right)} - {\left(4 \, \cosh\left(f x + e\right) e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{3} + e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{4} + 2 \, {\left(3 \, \cosh\left(f x + e\right)^{2} - 1\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(\cosh\left(f x + e\right)^{3} - \cosh\left(f x + e\right)\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right) + {\left(\cosh\left(f x + e\right)^{4} - 2 \, \cosh\left(f x + e\right)^{2} + 1\right)} e^{\left(f x + e\right)}\right)} \log\left(\frac{\cosh\left(f x + e\right) + \sinh\left(f x + e\right) - 1}{\cosh\left(f x + e\right) + \sinh\left(f x + e\right) + 1}\right)\right)} \sqrt{a e^{\left(4 \, f x + 4 \, e\right)} + 2 \, a e^{\left(2 \, f x + 2 \, e\right)} + a} e^{\left(-f x - e\right)}}{2 \, {\left(a f \cosh\left(f x + e\right)^{4} + {\left(a f e^{\left(2 \, f x + 2 \, e\right)} + a f\right)} \sinh\left(f x + e\right)^{4} - 2 \, a f \cosh\left(f x + e\right)^{2} + 4 \, {\left(a f \cosh\left(f x + e\right) e^{\left(2 \, f x + 2 \, e\right)} + a f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 2 \, {\left(3 \, a f \cosh\left(f x + e\right)^{2} - a f + {\left(3 \, a f \cosh\left(f x + e\right)^{2} - a f\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)^{2} + a f + {\left(a f \cosh\left(f x + e\right)^{4} - 2 \, a f \cosh\left(f x + e\right)^{2} + a f\right)} e^{\left(2 \, f x + 2 \, e\right)} + 4 \, {\left(a f \cosh\left(f x + e\right)^{3} - a f \cosh\left(f x + e\right) + {\left(a f \cosh\left(f x + e\right)^{3} - a f \cosh\left(f x + e\right)\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)\right)}}"," ",0,"-1/2*(6*cosh(f*x + e)*e^(f*x + e)*sinh(f*x + e)^2 + 2*e^(f*x + e)*sinh(f*x + e)^3 + 2*(3*cosh(f*x + e)^2 + 1)*e^(f*x + e)*sinh(f*x + e) + 2*(cosh(f*x + e)^3 + cosh(f*x + e))*e^(f*x + e) - (4*cosh(f*x + e)*e^(f*x + e)*sinh(f*x + e)^3 + e^(f*x + e)*sinh(f*x + e)^4 + 2*(3*cosh(f*x + e)^2 - 1)*e^(f*x + e)*sinh(f*x + e)^2 + 4*(cosh(f*x + e)^3 - cosh(f*x + e))*e^(f*x + e)*sinh(f*x + e) + (cosh(f*x + e)^4 - 2*cosh(f*x + e)^2 + 1)*e^(f*x + e))*log((cosh(f*x + e) + sinh(f*x + e) - 1)/(cosh(f*x + e) + sinh(f*x + e) + 1)))*sqrt(a*e^(4*f*x + 4*e) + 2*a*e^(2*f*x + 2*e) + a)*e^(-f*x - e)/(a*f*cosh(f*x + e)^4 + (a*f*e^(2*f*x + 2*e) + a*f)*sinh(f*x + e)^4 - 2*a*f*cosh(f*x + e)^2 + 4*(a*f*cosh(f*x + e)*e^(2*f*x + 2*e) + a*f*cosh(f*x + e))*sinh(f*x + e)^3 + 2*(3*a*f*cosh(f*x + e)^2 - a*f + (3*a*f*cosh(f*x + e)^2 - a*f)*e^(2*f*x + 2*e))*sinh(f*x + e)^2 + a*f + (a*f*cosh(f*x + e)^4 - 2*a*f*cosh(f*x + e)^2 + a*f)*e^(2*f*x + 2*e) + 4*(a*f*cosh(f*x + e)^3 - a*f*cosh(f*x + e) + (a*f*cosh(f*x + e)^3 - a*f*cosh(f*x + e))*e^(2*f*x + 2*e))*sinh(f*x + e))","B",0
442,1,1328,0,0.467520," ","integrate(tanh(f*x+e)^4/(a+a*sinh(f*x+e)^2)^(1/2),x, algorithm=""fricas"")","-\frac{{\left(35 \, \cosh\left(f x + e\right) e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{6} + 5 \, e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{7} + 3 \, {\left(35 \, \cosh\left(f x + e\right)^{2} - 1\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{5} + 5 \, {\left(35 \, \cosh\left(f x + e\right)^{3} - 3 \, \cosh\left(f x + e\right)\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{4} + {\left(175 \, \cosh\left(f x + e\right)^{4} - 30 \, \cosh\left(f x + e\right)^{2} + 3\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{3} + 3 \, {\left(35 \, \cosh\left(f x + e\right)^{5} - 10 \, \cosh\left(f x + e\right)^{3} + 3 \, \cosh\left(f x + e\right)\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{2} + {\left(35 \, \cosh\left(f x + e\right)^{6} - 15 \, \cosh\left(f x + e\right)^{4} + 9 \, \cosh\left(f x + e\right)^{2} - 5\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right) - 3 \, {\left(8 \, \cosh\left(f x + e\right) e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{7} + e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{8} + 4 \, {\left(7 \, \cosh\left(f x + e\right)^{2} + 1\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{6} + 8 \, {\left(7 \, \cosh\left(f x + e\right)^{3} + 3 \, \cosh\left(f x + e\right)\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(35 \, \cosh\left(f x + e\right)^{4} + 30 \, \cosh\left(f x + e\right)^{2} + 3\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{4} + 8 \, {\left(7 \, \cosh\left(f x + e\right)^{5} + 10 \, \cosh\left(f x + e\right)^{3} + 3 \, \cosh\left(f x + e\right)\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{3} + 4 \, {\left(7 \, \cosh\left(f x + e\right)^{6} + 15 \, \cosh\left(f x + e\right)^{4} + 9 \, \cosh\left(f x + e\right)^{2} + 1\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{2} + 8 \, {\left(\cosh\left(f x + e\right)^{7} + 3 \, \cosh\left(f x + e\right)^{5} + 3 \, \cosh\left(f x + e\right)^{3} + \cosh\left(f x + e\right)\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right) + {\left(\cosh\left(f x + e\right)^{8} + 4 \, \cosh\left(f x + e\right)^{6} + 6 \, \cosh\left(f x + e\right)^{4} + 4 \, \cosh\left(f x + e\right)^{2} + 1\right)} e^{\left(f x + e\right)}\right)} \arctan\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right)\right) + {\left(5 \, \cosh\left(f x + e\right)^{7} - 3 \, \cosh\left(f x + e\right)^{5} + 3 \, \cosh\left(f x + e\right)^{3} - 5 \, \cosh\left(f x + e\right)\right)} e^{\left(f x + e\right)}\right)} \sqrt{a e^{\left(4 \, f x + 4 \, e\right)} + 2 \, a e^{\left(2 \, f x + 2 \, e\right)} + a} e^{\left(-f x - e\right)}}{4 \, {\left(a f \cosh\left(f x + e\right)^{8} + {\left(a f e^{\left(2 \, f x + 2 \, e\right)} + a f\right)} \sinh\left(f x + e\right)^{8} + 4 \, a f \cosh\left(f x + e\right)^{6} + 8 \, {\left(a f \cosh\left(f x + e\right) e^{\left(2 \, f x + 2 \, e\right)} + a f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{7} + 4 \, {\left(7 \, a f \cosh\left(f x + e\right)^{2} + a f + {\left(7 \, a f \cosh\left(f x + e\right)^{2} + a f\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)^{6} + 6 \, a f \cosh\left(f x + e\right)^{4} + 8 \, {\left(7 \, a f \cosh\left(f x + e\right)^{3} + 3 \, a f \cosh\left(f x + e\right) + {\left(7 \, a f \cosh\left(f x + e\right)^{3} + 3 \, a f \cosh\left(f x + e\right)\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(35 \, a f \cosh\left(f x + e\right)^{4} + 30 \, a f \cosh\left(f x + e\right)^{2} + 3 \, a f + {\left(35 \, a f \cosh\left(f x + e\right)^{4} + 30 \, a f \cosh\left(f x + e\right)^{2} + 3 \, a f\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)^{4} + 4 \, a f \cosh\left(f x + e\right)^{2} + 8 \, {\left(7 \, a f \cosh\left(f x + e\right)^{5} + 10 \, a f \cosh\left(f x + e\right)^{3} + 3 \, a f \cosh\left(f x + e\right) + {\left(7 \, a f \cosh\left(f x + e\right)^{5} + 10 \, a f \cosh\left(f x + e\right)^{3} + 3 \, a f \cosh\left(f x + e\right)\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)^{3} + 4 \, {\left(7 \, a f \cosh\left(f x + e\right)^{6} + 15 \, a f \cosh\left(f x + e\right)^{4} + 9 \, a f \cosh\left(f x + e\right)^{2} + a f + {\left(7 \, a f \cosh\left(f x + e\right)^{6} + 15 \, a f \cosh\left(f x + e\right)^{4} + 9 \, a f \cosh\left(f x + e\right)^{2} + a f\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)^{2} + a f + {\left(a f \cosh\left(f x + e\right)^{8} + 4 \, a f \cosh\left(f x + e\right)^{6} + 6 \, a f \cosh\left(f x + e\right)^{4} + 4 \, a f \cosh\left(f x + e\right)^{2} + a f\right)} e^{\left(2 \, f x + 2 \, e\right)} + 8 \, {\left(a f \cosh\left(f x + e\right)^{7} + 3 \, a f \cosh\left(f x + e\right)^{5} + 3 \, a f \cosh\left(f x + e\right)^{3} + a f \cosh\left(f x + e\right) + {\left(a f \cosh\left(f x + e\right)^{7} + 3 \, a f \cosh\left(f x + e\right)^{5} + 3 \, a f \cosh\left(f x + e\right)^{3} + a f \cosh\left(f x + e\right)\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)\right)}}"," ",0,"-1/4*(35*cosh(f*x + e)*e^(f*x + e)*sinh(f*x + e)^6 + 5*e^(f*x + e)*sinh(f*x + e)^7 + 3*(35*cosh(f*x + e)^2 - 1)*e^(f*x + e)*sinh(f*x + e)^5 + 5*(35*cosh(f*x + e)^3 - 3*cosh(f*x + e))*e^(f*x + e)*sinh(f*x + e)^4 + (175*cosh(f*x + e)^4 - 30*cosh(f*x + e)^2 + 3)*e^(f*x + e)*sinh(f*x + e)^3 + 3*(35*cosh(f*x + e)^5 - 10*cosh(f*x + e)^3 + 3*cosh(f*x + e))*e^(f*x + e)*sinh(f*x + e)^2 + (35*cosh(f*x + e)^6 - 15*cosh(f*x + e)^4 + 9*cosh(f*x + e)^2 - 5)*e^(f*x + e)*sinh(f*x + e) - 3*(8*cosh(f*x + e)*e^(f*x + e)*sinh(f*x + e)^7 + e^(f*x + e)*sinh(f*x + e)^8 + 4*(7*cosh(f*x + e)^2 + 1)*e^(f*x + e)*sinh(f*x + e)^6 + 8*(7*cosh(f*x + e)^3 + 3*cosh(f*x + e))*e^(f*x + e)*sinh(f*x + e)^5 + 2*(35*cosh(f*x + e)^4 + 30*cosh(f*x + e)^2 + 3)*e^(f*x + e)*sinh(f*x + e)^4 + 8*(7*cosh(f*x + e)^5 + 10*cosh(f*x + e)^3 + 3*cosh(f*x + e))*e^(f*x + e)*sinh(f*x + e)^3 + 4*(7*cosh(f*x + e)^6 + 15*cosh(f*x + e)^4 + 9*cosh(f*x + e)^2 + 1)*e^(f*x + e)*sinh(f*x + e)^2 + 8*(cosh(f*x + e)^7 + 3*cosh(f*x + e)^5 + 3*cosh(f*x + e)^3 + cosh(f*x + e))*e^(f*x + e)*sinh(f*x + e) + (cosh(f*x + e)^8 + 4*cosh(f*x + e)^6 + 6*cosh(f*x + e)^4 + 4*cosh(f*x + e)^2 + 1)*e^(f*x + e))*arctan(cosh(f*x + e) + sinh(f*x + e)) + (5*cosh(f*x + e)^7 - 3*cosh(f*x + e)^5 + 3*cosh(f*x + e)^3 - 5*cosh(f*x + e))*e^(f*x + e))*sqrt(a*e^(4*f*x + 4*e) + 2*a*e^(2*f*x + 2*e) + a)*e^(-f*x - e)/(a*f*cosh(f*x + e)^8 + (a*f*e^(2*f*x + 2*e) + a*f)*sinh(f*x + e)^8 + 4*a*f*cosh(f*x + e)^6 + 8*(a*f*cosh(f*x + e)*e^(2*f*x + 2*e) + a*f*cosh(f*x + e))*sinh(f*x + e)^7 + 4*(7*a*f*cosh(f*x + e)^2 + a*f + (7*a*f*cosh(f*x + e)^2 + a*f)*e^(2*f*x + 2*e))*sinh(f*x + e)^6 + 6*a*f*cosh(f*x + e)^4 + 8*(7*a*f*cosh(f*x + e)^3 + 3*a*f*cosh(f*x + e) + (7*a*f*cosh(f*x + e)^3 + 3*a*f*cosh(f*x + e))*e^(2*f*x + 2*e))*sinh(f*x + e)^5 + 2*(35*a*f*cosh(f*x + e)^4 + 30*a*f*cosh(f*x + e)^2 + 3*a*f + (35*a*f*cosh(f*x + e)^4 + 30*a*f*cosh(f*x + e)^2 + 3*a*f)*e^(2*f*x + 2*e))*sinh(f*x + e)^4 + 4*a*f*cosh(f*x + e)^2 + 8*(7*a*f*cosh(f*x + e)^5 + 10*a*f*cosh(f*x + e)^3 + 3*a*f*cosh(f*x + e) + (7*a*f*cosh(f*x + e)^5 + 10*a*f*cosh(f*x + e)^3 + 3*a*f*cosh(f*x + e))*e^(2*f*x + 2*e))*sinh(f*x + e)^3 + 4*(7*a*f*cosh(f*x + e)^6 + 15*a*f*cosh(f*x + e)^4 + 9*a*f*cosh(f*x + e)^2 + a*f + (7*a*f*cosh(f*x + e)^6 + 15*a*f*cosh(f*x + e)^4 + 9*a*f*cosh(f*x + e)^2 + a*f)*e^(2*f*x + 2*e))*sinh(f*x + e)^2 + a*f + (a*f*cosh(f*x + e)^8 + 4*a*f*cosh(f*x + e)^6 + 6*a*f*cosh(f*x + e)^4 + 4*a*f*cosh(f*x + e)^2 + a*f)*e^(2*f*x + 2*e) + 8*(a*f*cosh(f*x + e)^7 + 3*a*f*cosh(f*x + e)^5 + 3*a*f*cosh(f*x + e)^3 + a*f*cosh(f*x + e) + (a*f*cosh(f*x + e)^7 + 3*a*f*cosh(f*x + e)^5 + 3*a*f*cosh(f*x + e)^3 + a*f*cosh(f*x + e))*e^(2*f*x + 2*e))*sinh(f*x + e))","B",0
443,1,504,0,0.577257," ","integrate(tanh(f*x+e)^2/(a+a*sinh(f*x+e)^2)^(1/2),x, algorithm=""fricas"")","-\frac{{\left(3 \, \cosh\left(f x + e\right) e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{2} + e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{3} + {\left(3 \, \cosh\left(f x + e\right)^{2} - 1\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right) - {\left(4 \, \cosh\left(f x + e\right) e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{3} + e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{4} + 2 \, {\left(3 \, \cosh\left(f x + e\right)^{2} + 1\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(\cosh\left(f x + e\right)^{3} + \cosh\left(f x + e\right)\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right) + {\left(\cosh\left(f x + e\right)^{4} + 2 \, \cosh\left(f x + e\right)^{2} + 1\right)} e^{\left(f x + e\right)}\right)} \arctan\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right)\right) + {\left(\cosh\left(f x + e\right)^{3} - \cosh\left(f x + e\right)\right)} e^{\left(f x + e\right)}\right)} \sqrt{a e^{\left(4 \, f x + 4 \, e\right)} + 2 \, a e^{\left(2 \, f x + 2 \, e\right)} + a} e^{\left(-f x - e\right)}}{a f \cosh\left(f x + e\right)^{4} + {\left(a f e^{\left(2 \, f x + 2 \, e\right)} + a f\right)} \sinh\left(f x + e\right)^{4} + 2 \, a f \cosh\left(f x + e\right)^{2} + 4 \, {\left(a f \cosh\left(f x + e\right) e^{\left(2 \, f x + 2 \, e\right)} + a f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 2 \, {\left(3 \, a f \cosh\left(f x + e\right)^{2} + a f + {\left(3 \, a f \cosh\left(f x + e\right)^{2} + a f\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)^{2} + a f + {\left(a f \cosh\left(f x + e\right)^{4} + 2 \, a f \cosh\left(f x + e\right)^{2} + a f\right)} e^{\left(2 \, f x + 2 \, e\right)} + 4 \, {\left(a f \cosh\left(f x + e\right)^{3} + a f \cosh\left(f x + e\right) + {\left(a f \cosh\left(f x + e\right)^{3} + a f \cosh\left(f x + e\right)\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)}"," ",0,"-(3*cosh(f*x + e)*e^(f*x + e)*sinh(f*x + e)^2 + e^(f*x + e)*sinh(f*x + e)^3 + (3*cosh(f*x + e)^2 - 1)*e^(f*x + e)*sinh(f*x + e) - (4*cosh(f*x + e)*e^(f*x + e)*sinh(f*x + e)^3 + e^(f*x + e)*sinh(f*x + e)^4 + 2*(3*cosh(f*x + e)^2 + 1)*e^(f*x + e)*sinh(f*x + e)^2 + 4*(cosh(f*x + e)^3 + cosh(f*x + e))*e^(f*x + e)*sinh(f*x + e) + (cosh(f*x + e)^4 + 2*cosh(f*x + e)^2 + 1)*e^(f*x + e))*arctan(cosh(f*x + e) + sinh(f*x + e)) + (cosh(f*x + e)^3 - cosh(f*x + e))*e^(f*x + e))*sqrt(a*e^(4*f*x + 4*e) + 2*a*e^(2*f*x + 2*e) + a)*e^(-f*x - e)/(a*f*cosh(f*x + e)^4 + (a*f*e^(2*f*x + 2*e) + a*f)*sinh(f*x + e)^4 + 2*a*f*cosh(f*x + e)^2 + 4*(a*f*cosh(f*x + e)*e^(2*f*x + 2*e) + a*f*cosh(f*x + e))*sinh(f*x + e)^3 + 2*(3*a*f*cosh(f*x + e)^2 + a*f + (3*a*f*cosh(f*x + e)^2 + a*f)*e^(2*f*x + 2*e))*sinh(f*x + e)^2 + a*f + (a*f*cosh(f*x + e)^4 + 2*a*f*cosh(f*x + e)^2 + a*f)*e^(2*f*x + 2*e) + 4*(a*f*cosh(f*x + e)^3 + a*f*cosh(f*x + e) + (a*f*cosh(f*x + e)^3 + a*f*cosh(f*x + e))*e^(2*f*x + 2*e))*sinh(f*x + e))","B",0
444,1,170,0,0.510886," ","integrate(coth(f*x+e)^2/(a+a*sinh(f*x+e)^2)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, \sqrt{a e^{\left(4 \, f x + 4 \, e\right)} + 2 \, a e^{\left(2 \, f x + 2 \, e\right)} + a} {\left(\cosh\left(f x + e\right) e^{\left(f x + e\right)} + e^{\left(f x + e\right)} \sinh\left(f x + e\right)\right)} e^{\left(-f x - e\right)}}{a f \cosh\left(f x + e\right)^{2} + {\left(a f e^{\left(2 \, f x + 2 \, e\right)} + a f\right)} \sinh\left(f x + e\right)^{2} - a f + {\left(a f \cosh\left(f x + e\right)^{2} - a f\right)} e^{\left(2 \, f x + 2 \, e\right)} + 2 \, {\left(a f \cosh\left(f x + e\right) e^{\left(2 \, f x + 2 \, e\right)} + a f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)}"," ",0,"-2*sqrt(a*e^(4*f*x + 4*e) + 2*a*e^(2*f*x + 2*e) + a)*(cosh(f*x + e)*e^(f*x + e) + e^(f*x + e)*sinh(f*x + e))*e^(-f*x - e)/(a*f*cosh(f*x + e)^2 + (a*f*e^(2*f*x + 2*e) + a*f)*sinh(f*x + e)^2 - a*f + (a*f*cosh(f*x + e)^2 - a*f)*e^(2*f*x + 2*e) + 2*(a*f*cosh(f*x + e)*e^(2*f*x + 2*e) + a*f*cosh(f*x + e))*sinh(f*x + e))","B",0
445,1,647,0,0.432815," ","integrate(coth(f*x+e)^4/(a+a*sinh(f*x+e)^2)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(15 \, \cosh\left(f x + e\right) e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{4} + 3 \, e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(15 \, \cosh\left(f x + e\right)^{2} - 1\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{3} + 6 \, {\left(5 \, \cosh\left(f x + e\right)^{3} - \cosh\left(f x + e\right)\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{2} + 3 \, {\left(5 \, \cosh\left(f x + e\right)^{4} - 2 \, \cosh\left(f x + e\right)^{2} + 1\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right) + {\left(3 \, \cosh\left(f x + e\right)^{5} - 2 \, \cosh\left(f x + e\right)^{3} + 3 \, \cosh\left(f x + e\right)\right)} e^{\left(f x + e\right)}\right)} \sqrt{a e^{\left(4 \, f x + 4 \, e\right)} + 2 \, a e^{\left(2 \, f x + 2 \, e\right)} + a} e^{\left(-f x - e\right)}}{3 \, {\left(a f \cosh\left(f x + e\right)^{6} + {\left(a f e^{\left(2 \, f x + 2 \, e\right)} + a f\right)} \sinh\left(f x + e\right)^{6} - 3 \, a f \cosh\left(f x + e\right)^{4} + 6 \, {\left(a f \cosh\left(f x + e\right) e^{\left(2 \, f x + 2 \, e\right)} + a f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + 3 \, {\left(5 \, a f \cosh\left(f x + e\right)^{2} - a f + {\left(5 \, a f \cosh\left(f x + e\right)^{2} - a f\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)^{4} + 3 \, a f \cosh\left(f x + e\right)^{2} + 4 \, {\left(5 \, a f \cosh\left(f x + e\right)^{3} - 3 \, a f \cosh\left(f x + e\right) + {\left(5 \, a f \cosh\left(f x + e\right)^{3} - 3 \, a f \cosh\left(f x + e\right)\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)^{3} + 3 \, {\left(5 \, a f \cosh\left(f x + e\right)^{4} - 6 \, a f \cosh\left(f x + e\right)^{2} + a f + {\left(5 \, a f \cosh\left(f x + e\right)^{4} - 6 \, a f \cosh\left(f x + e\right)^{2} + a f\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)^{2} - a f + {\left(a f \cosh\left(f x + e\right)^{6} - 3 \, a f \cosh\left(f x + e\right)^{4} + 3 \, a f \cosh\left(f x + e\right)^{2} - a f\right)} e^{\left(2 \, f x + 2 \, e\right)} + 6 \, {\left(a f \cosh\left(f x + e\right)^{5} - 2 \, a f \cosh\left(f x + e\right)^{3} + a f \cosh\left(f x + e\right) + {\left(a f \cosh\left(f x + e\right)^{5} - 2 \, a f \cosh\left(f x + e\right)^{3} + a f \cosh\left(f x + e\right)\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)\right)}}"," ",0,"-2/3*(15*cosh(f*x + e)*e^(f*x + e)*sinh(f*x + e)^4 + 3*e^(f*x + e)*sinh(f*x + e)^5 + 2*(15*cosh(f*x + e)^2 - 1)*e^(f*x + e)*sinh(f*x + e)^3 + 6*(5*cosh(f*x + e)^3 - cosh(f*x + e))*e^(f*x + e)*sinh(f*x + e)^2 + 3*(5*cosh(f*x + e)^4 - 2*cosh(f*x + e)^2 + 1)*e^(f*x + e)*sinh(f*x + e) + (3*cosh(f*x + e)^5 - 2*cosh(f*x + e)^3 + 3*cosh(f*x + e))*e^(f*x + e))*sqrt(a*e^(4*f*x + 4*e) + 2*a*e^(2*f*x + 2*e) + a)*e^(-f*x - e)/(a*f*cosh(f*x + e)^6 + (a*f*e^(2*f*x + 2*e) + a*f)*sinh(f*x + e)^6 - 3*a*f*cosh(f*x + e)^4 + 6*(a*f*cosh(f*x + e)*e^(2*f*x + 2*e) + a*f*cosh(f*x + e))*sinh(f*x + e)^5 + 3*(5*a*f*cosh(f*x + e)^2 - a*f + (5*a*f*cosh(f*x + e)^2 - a*f)*e^(2*f*x + 2*e))*sinh(f*x + e)^4 + 3*a*f*cosh(f*x + e)^2 + 4*(5*a*f*cosh(f*x + e)^3 - 3*a*f*cosh(f*x + e) + (5*a*f*cosh(f*x + e)^3 - 3*a*f*cosh(f*x + e))*e^(2*f*x + 2*e))*sinh(f*x + e)^3 + 3*(5*a*f*cosh(f*x + e)^4 - 6*a*f*cosh(f*x + e)^2 + a*f + (5*a*f*cosh(f*x + e)^4 - 6*a*f*cosh(f*x + e)^2 + a*f)*e^(2*f*x + 2*e))*sinh(f*x + e)^2 - a*f + (a*f*cosh(f*x + e)^6 - 3*a*f*cosh(f*x + e)^4 + 3*a*f*cosh(f*x + e)^2 - a*f)*e^(2*f*x + 2*e) + 6*(a*f*cosh(f*x + e)^5 - 2*a*f*cosh(f*x + e)^3 + a*f*cosh(f*x + e) + (a*f*cosh(f*x + e)^5 - 2*a*f*cosh(f*x + e)^3 + a*f*cosh(f*x + e))*e^(2*f*x + 2*e))*sinh(f*x + e))","B",0
446,1,1399,0,0.531692," ","integrate(coth(f*x+e)^6/(a+a*sinh(f*x+e)^2)^(1/2),x, algorithm=""fricas"")","-\frac{2 \, {\left(135 \, \cosh\left(f x + e\right) e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{8} + 15 \, e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{9} + 20 \, {\left(27 \, \cosh\left(f x + e\right)^{2} - 1\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{7} + 140 \, {\left(9 \, \cosh\left(f x + e\right)^{3} - \cosh\left(f x + e\right)\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{6} + 2 \, {\left(945 \, \cosh\left(f x + e\right)^{4} - 210 \, \cosh\left(f x + e\right)^{2} + 29\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{5} + 10 \, {\left(189 \, \cosh\left(f x + e\right)^{5} - 70 \, \cosh\left(f x + e\right)^{3} + 29 \, \cosh\left(f x + e\right)\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{4} + 20 \, {\left(63 \, \cosh\left(f x + e\right)^{6} - 35 \, \cosh\left(f x + e\right)^{4} + 29 \, \cosh\left(f x + e\right)^{2} - 1\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{3} + 20 \, {\left(27 \, \cosh\left(f x + e\right)^{7} - 21 \, \cosh\left(f x + e\right)^{5} + 29 \, \cosh\left(f x + e\right)^{3} - 3 \, \cosh\left(f x + e\right)\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{2} + 5 \, {\left(27 \, \cosh\left(f x + e\right)^{8} - 28 \, \cosh\left(f x + e\right)^{6} + 58 \, \cosh\left(f x + e\right)^{4} - 12 \, \cosh\left(f x + e\right)^{2} + 3\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right) + {\left(15 \, \cosh\left(f x + e\right)^{9} - 20 \, \cosh\left(f x + e\right)^{7} + 58 \, \cosh\left(f x + e\right)^{5} - 20 \, \cosh\left(f x + e\right)^{3} + 15 \, \cosh\left(f x + e\right)\right)} e^{\left(f x + e\right)}\right)} \sqrt{a e^{\left(4 \, f x + 4 \, e\right)} + 2 \, a e^{\left(2 \, f x + 2 \, e\right)} + a} e^{\left(-f x - e\right)}}{15 \, {\left(a f \cosh\left(f x + e\right)^{10} + {\left(a f e^{\left(2 \, f x + 2 \, e\right)} + a f\right)} \sinh\left(f x + e\right)^{10} - 5 \, a f \cosh\left(f x + e\right)^{8} + 10 \, {\left(a f \cosh\left(f x + e\right) e^{\left(2 \, f x + 2 \, e\right)} + a f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{9} + 5 \, {\left(9 \, a f \cosh\left(f x + e\right)^{2} - a f + {\left(9 \, a f \cosh\left(f x + e\right)^{2} - a f\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)^{8} + 10 \, a f \cosh\left(f x + e\right)^{6} + 40 \, {\left(3 \, a f \cosh\left(f x + e\right)^{3} - a f \cosh\left(f x + e\right) + {\left(3 \, a f \cosh\left(f x + e\right)^{3} - a f \cosh\left(f x + e\right)\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)^{7} + 10 \, {\left(21 \, a f \cosh\left(f x + e\right)^{4} - 14 \, a f \cosh\left(f x + e\right)^{2} + a f + {\left(21 \, a f \cosh\left(f x + e\right)^{4} - 14 \, a f \cosh\left(f x + e\right)^{2} + a f\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)^{6} - 10 \, a f \cosh\left(f x + e\right)^{4} + 4 \, {\left(63 \, a f \cosh\left(f x + e\right)^{5} - 70 \, a f \cosh\left(f x + e\right)^{3} + 15 \, a f \cosh\left(f x + e\right) + {\left(63 \, a f \cosh\left(f x + e\right)^{5} - 70 \, a f \cosh\left(f x + e\right)^{3} + 15 \, a f \cosh\left(f x + e\right)\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)^{5} + 10 \, {\left(21 \, a f \cosh\left(f x + e\right)^{6} - 35 \, a f \cosh\left(f x + e\right)^{4} + 15 \, a f \cosh\left(f x + e\right)^{2} - a f + {\left(21 \, a f \cosh\left(f x + e\right)^{6} - 35 \, a f \cosh\left(f x + e\right)^{4} + 15 \, a f \cosh\left(f x + e\right)^{2} - a f\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)^{4} + 5 \, a f \cosh\left(f x + e\right)^{2} + 40 \, {\left(3 \, a f \cosh\left(f x + e\right)^{7} - 7 \, a f \cosh\left(f x + e\right)^{5} + 5 \, a f \cosh\left(f x + e\right)^{3} - a f \cosh\left(f x + e\right) + {\left(3 \, a f \cosh\left(f x + e\right)^{7} - 7 \, a f \cosh\left(f x + e\right)^{5} + 5 \, a f \cosh\left(f x + e\right)^{3} - a f \cosh\left(f x + e\right)\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)^{3} + 5 \, {\left(9 \, a f \cosh\left(f x + e\right)^{8} - 28 \, a f \cosh\left(f x + e\right)^{6} + 30 \, a f \cosh\left(f x + e\right)^{4} - 12 \, a f \cosh\left(f x + e\right)^{2} + a f + {\left(9 \, a f \cosh\left(f x + e\right)^{8} - 28 \, a f \cosh\left(f x + e\right)^{6} + 30 \, a f \cosh\left(f x + e\right)^{4} - 12 \, a f \cosh\left(f x + e\right)^{2} + a f\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)^{2} - a f + {\left(a f \cosh\left(f x + e\right)^{10} - 5 \, a f \cosh\left(f x + e\right)^{8} + 10 \, a f \cosh\left(f x + e\right)^{6} - 10 \, a f \cosh\left(f x + e\right)^{4} + 5 \, a f \cosh\left(f x + e\right)^{2} - a f\right)} e^{\left(2 \, f x + 2 \, e\right)} + 10 \, {\left(a f \cosh\left(f x + e\right)^{9} - 4 \, a f \cosh\left(f x + e\right)^{7} + 6 \, a f \cosh\left(f x + e\right)^{5} - 4 \, a f \cosh\left(f x + e\right)^{3} + a f \cosh\left(f x + e\right) + {\left(a f \cosh\left(f x + e\right)^{9} - 4 \, a f \cosh\left(f x + e\right)^{7} + 6 \, a f \cosh\left(f x + e\right)^{5} - 4 \, a f \cosh\left(f x + e\right)^{3} + a f \cosh\left(f x + e\right)\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)\right)}}"," ",0,"-2/15*(135*cosh(f*x + e)*e^(f*x + e)*sinh(f*x + e)^8 + 15*e^(f*x + e)*sinh(f*x + e)^9 + 20*(27*cosh(f*x + e)^2 - 1)*e^(f*x + e)*sinh(f*x + e)^7 + 140*(9*cosh(f*x + e)^3 - cosh(f*x + e))*e^(f*x + e)*sinh(f*x + e)^6 + 2*(945*cosh(f*x + e)^4 - 210*cosh(f*x + e)^2 + 29)*e^(f*x + e)*sinh(f*x + e)^5 + 10*(189*cosh(f*x + e)^5 - 70*cosh(f*x + e)^3 + 29*cosh(f*x + e))*e^(f*x + e)*sinh(f*x + e)^4 + 20*(63*cosh(f*x + e)^6 - 35*cosh(f*x + e)^4 + 29*cosh(f*x + e)^2 - 1)*e^(f*x + e)*sinh(f*x + e)^3 + 20*(27*cosh(f*x + e)^7 - 21*cosh(f*x + e)^5 + 29*cosh(f*x + e)^3 - 3*cosh(f*x + e))*e^(f*x + e)*sinh(f*x + e)^2 + 5*(27*cosh(f*x + e)^8 - 28*cosh(f*x + e)^6 + 58*cosh(f*x + e)^4 - 12*cosh(f*x + e)^2 + 3)*e^(f*x + e)*sinh(f*x + e) + (15*cosh(f*x + e)^9 - 20*cosh(f*x + e)^7 + 58*cosh(f*x + e)^5 - 20*cosh(f*x + e)^3 + 15*cosh(f*x + e))*e^(f*x + e))*sqrt(a*e^(4*f*x + 4*e) + 2*a*e^(2*f*x + 2*e) + a)*e^(-f*x - e)/(a*f*cosh(f*x + e)^10 + (a*f*e^(2*f*x + 2*e) + a*f)*sinh(f*x + e)^10 - 5*a*f*cosh(f*x + e)^8 + 10*(a*f*cosh(f*x + e)*e^(2*f*x + 2*e) + a*f*cosh(f*x + e))*sinh(f*x + e)^9 + 5*(9*a*f*cosh(f*x + e)^2 - a*f + (9*a*f*cosh(f*x + e)^2 - a*f)*e^(2*f*x + 2*e))*sinh(f*x + e)^8 + 10*a*f*cosh(f*x + e)^6 + 40*(3*a*f*cosh(f*x + e)^3 - a*f*cosh(f*x + e) + (3*a*f*cosh(f*x + e)^3 - a*f*cosh(f*x + e))*e^(2*f*x + 2*e))*sinh(f*x + e)^7 + 10*(21*a*f*cosh(f*x + e)^4 - 14*a*f*cosh(f*x + e)^2 + a*f + (21*a*f*cosh(f*x + e)^4 - 14*a*f*cosh(f*x + e)^2 + a*f)*e^(2*f*x + 2*e))*sinh(f*x + e)^6 - 10*a*f*cosh(f*x + e)^4 + 4*(63*a*f*cosh(f*x + e)^5 - 70*a*f*cosh(f*x + e)^3 + 15*a*f*cosh(f*x + e) + (63*a*f*cosh(f*x + e)^5 - 70*a*f*cosh(f*x + e)^3 + 15*a*f*cosh(f*x + e))*e^(2*f*x + 2*e))*sinh(f*x + e)^5 + 10*(21*a*f*cosh(f*x + e)^6 - 35*a*f*cosh(f*x + e)^4 + 15*a*f*cosh(f*x + e)^2 - a*f + (21*a*f*cosh(f*x + e)^6 - 35*a*f*cosh(f*x + e)^4 + 15*a*f*cosh(f*x + e)^2 - a*f)*e^(2*f*x + 2*e))*sinh(f*x + e)^4 + 5*a*f*cosh(f*x + e)^2 + 40*(3*a*f*cosh(f*x + e)^7 - 7*a*f*cosh(f*x + e)^5 + 5*a*f*cosh(f*x + e)^3 - a*f*cosh(f*x + e) + (3*a*f*cosh(f*x + e)^7 - 7*a*f*cosh(f*x + e)^5 + 5*a*f*cosh(f*x + e)^3 - a*f*cosh(f*x + e))*e^(2*f*x + 2*e))*sinh(f*x + e)^3 + 5*(9*a*f*cosh(f*x + e)^8 - 28*a*f*cosh(f*x + e)^6 + 30*a*f*cosh(f*x + e)^4 - 12*a*f*cosh(f*x + e)^2 + a*f + (9*a*f*cosh(f*x + e)^8 - 28*a*f*cosh(f*x + e)^6 + 30*a*f*cosh(f*x + e)^4 - 12*a*f*cosh(f*x + e)^2 + a*f)*e^(2*f*x + 2*e))*sinh(f*x + e)^2 - a*f + (a*f*cosh(f*x + e)^10 - 5*a*f*cosh(f*x + e)^8 + 10*a*f*cosh(f*x + e)^6 - 10*a*f*cosh(f*x + e)^4 + 5*a*f*cosh(f*x + e)^2 - a*f)*e^(2*f*x + 2*e) + 10*(a*f*cosh(f*x + e)^9 - 4*a*f*cosh(f*x + e)^7 + 6*a*f*cosh(f*x + e)^5 - 4*a*f*cosh(f*x + e)^3 + a*f*cosh(f*x + e) + (a*f*cosh(f*x + e)^9 - 4*a*f*cosh(f*x + e)^7 + 6*a*f*cosh(f*x + e)^5 - 4*a*f*cosh(f*x + e)^3 + a*f*cosh(f*x + e))*e^(2*f*x + 2*e))*sinh(f*x + e))","B",0
447,1,2507,0,0.560044," ","integrate(tanh(f*x+e)^5/(a+a*sinh(f*x+e)^2)^(3/2),x, algorithm=""fricas"")","-\frac{8 \, {\left(385 \, \cosh\left(f x + e\right) e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{10} + 35 \, e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{11} + 7 \, {\left(275 \, \cosh\left(f x + e\right)^{2} - 4\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{9} + 21 \, {\left(275 \, \cosh\left(f x + e\right)^{3} - 12 \, \cosh\left(f x + e\right)\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{8} + 6 \, {\left(1925 \, \cosh\left(f x + e\right)^{4} - 168 \, \cosh\left(f x + e\right)^{2} + 19\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{7} + 42 \, {\left(385 \, \cosh\left(f x + e\right)^{5} - 56 \, \cosh\left(f x + e\right)^{3} + 19 \, \cosh\left(f x + e\right)\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{6} + 14 \, {\left(1155 \, \cosh\left(f x + e\right)^{6} - 252 \, \cosh\left(f x + e\right)^{4} + 171 \, \cosh\left(f x + e\right)^{2} - 2\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{5} + 14 \, {\left(825 \, \cosh\left(f x + e\right)^{7} - 252 \, \cosh\left(f x + e\right)^{5} + 285 \, \cosh\left(f x + e\right)^{3} - 10 \, \cosh\left(f x + e\right)\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{4} + 7 \, {\left(825 \, \cosh\left(f x + e\right)^{8} - 336 \, \cosh\left(f x + e\right)^{6} + 570 \, \cosh\left(f x + e\right)^{4} - 40 \, \cosh\left(f x + e\right)^{2} + 5\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{3} + 7 \, {\left(275 \, \cosh\left(f x + e\right)^{9} - 144 \, \cosh\left(f x + e\right)^{7} + 342 \, \cosh\left(f x + e\right)^{5} - 40 \, \cosh\left(f x + e\right)^{3} + 15 \, \cosh\left(f x + e\right)\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{2} + 7 \, {\left(55 \, \cosh\left(f x + e\right)^{10} - 36 \, \cosh\left(f x + e\right)^{8} + 114 \, \cosh\left(f x + e\right)^{6} - 20 \, \cosh\left(f x + e\right)^{4} + 15 \, \cosh\left(f x + e\right)^{2}\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right) + {\left(35 \, \cosh\left(f x + e\right)^{11} - 28 \, \cosh\left(f x + e\right)^{9} + 114 \, \cosh\left(f x + e\right)^{7} - 28 \, \cosh\left(f x + e\right)^{5} + 35 \, \cosh\left(f x + e\right)^{3}\right)} e^{\left(f x + e\right)}\right)} \sqrt{a e^{\left(4 \, f x + 4 \, e\right)} + 2 \, a e^{\left(2 \, f x + 2 \, e\right)} + a} e^{\left(-f x - e\right)}}{105 \, {\left(a^{2} f \cosh\left(f x + e\right)^{14} + 7 \, a^{2} f \cosh\left(f x + e\right)^{12} + {\left(a^{2} f e^{\left(2 \, f x + 2 \, e\right)} + a^{2} f\right)} \sinh\left(f x + e\right)^{14} + 14 \, {\left(a^{2} f \cosh\left(f x + e\right) e^{\left(2 \, f x + 2 \, e\right)} + a^{2} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{13} + 21 \, a^{2} f \cosh\left(f x + e\right)^{10} + 7 \, {\left(13 \, a^{2} f \cosh\left(f x + e\right)^{2} + a^{2} f + {\left(13 \, a^{2} f \cosh\left(f x + e\right)^{2} + a^{2} f\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)^{12} + 28 \, {\left(13 \, a^{2} f \cosh\left(f x + e\right)^{3} + 3 \, a^{2} f \cosh\left(f x + e\right) + {\left(13 \, a^{2} f \cosh\left(f x + e\right)^{3} + 3 \, a^{2} f \cosh\left(f x + e\right)\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)^{11} + 35 \, a^{2} f \cosh\left(f x + e\right)^{8} + 7 \, {\left(143 \, a^{2} f \cosh\left(f x + e\right)^{4} + 66 \, a^{2} f \cosh\left(f x + e\right)^{2} + 3 \, a^{2} f + {\left(143 \, a^{2} f \cosh\left(f x + e\right)^{4} + 66 \, a^{2} f \cosh\left(f x + e\right)^{2} + 3 \, a^{2} f\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)^{10} + 14 \, {\left(143 \, a^{2} f \cosh\left(f x + e\right)^{5} + 110 \, a^{2} f \cosh\left(f x + e\right)^{3} + 15 \, a^{2} f \cosh\left(f x + e\right) + {\left(143 \, a^{2} f \cosh\left(f x + e\right)^{5} + 110 \, a^{2} f \cosh\left(f x + e\right)^{3} + 15 \, a^{2} f \cosh\left(f x + e\right)\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)^{9} + 35 \, a^{2} f \cosh\left(f x + e\right)^{6} + 7 \, {\left(429 \, a^{2} f \cosh\left(f x + e\right)^{6} + 495 \, a^{2} f \cosh\left(f x + e\right)^{4} + 135 \, a^{2} f \cosh\left(f x + e\right)^{2} + 5 \, a^{2} f + {\left(429 \, a^{2} f \cosh\left(f x + e\right)^{6} + 495 \, a^{2} f \cosh\left(f x + e\right)^{4} + 135 \, a^{2} f \cosh\left(f x + e\right)^{2} + 5 \, a^{2} f\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)^{8} + 8 \, {\left(429 \, a^{2} f \cosh\left(f x + e\right)^{7} + 693 \, a^{2} f \cosh\left(f x + e\right)^{5} + 315 \, a^{2} f \cosh\left(f x + e\right)^{3} + 35 \, a^{2} f \cosh\left(f x + e\right) + {\left(429 \, a^{2} f \cosh\left(f x + e\right)^{7} + 693 \, a^{2} f \cosh\left(f x + e\right)^{5} + 315 \, a^{2} f \cosh\left(f x + e\right)^{3} + 35 \, a^{2} f \cosh\left(f x + e\right)\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)^{7} + 21 \, a^{2} f \cosh\left(f x + e\right)^{4} + 7 \, {\left(429 \, a^{2} f \cosh\left(f x + e\right)^{8} + 924 \, a^{2} f \cosh\left(f x + e\right)^{6} + 630 \, a^{2} f \cosh\left(f x + e\right)^{4} + 140 \, a^{2} f \cosh\left(f x + e\right)^{2} + 5 \, a^{2} f + {\left(429 \, a^{2} f \cosh\left(f x + e\right)^{8} + 924 \, a^{2} f \cosh\left(f x + e\right)^{6} + 630 \, a^{2} f \cosh\left(f x + e\right)^{4} + 140 \, a^{2} f \cosh\left(f x + e\right)^{2} + 5 \, a^{2} f\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)^{6} + 14 \, {\left(143 \, a^{2} f \cosh\left(f x + e\right)^{9} + 396 \, a^{2} f \cosh\left(f x + e\right)^{7} + 378 \, a^{2} f \cosh\left(f x + e\right)^{5} + 140 \, a^{2} f \cosh\left(f x + e\right)^{3} + 15 \, a^{2} f \cosh\left(f x + e\right) + {\left(143 \, a^{2} f \cosh\left(f x + e\right)^{9} + 396 \, a^{2} f \cosh\left(f x + e\right)^{7} + 378 \, a^{2} f \cosh\left(f x + e\right)^{5} + 140 \, a^{2} f \cosh\left(f x + e\right)^{3} + 15 \, a^{2} f \cosh\left(f x + e\right)\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)^{5} + 7 \, a^{2} f \cosh\left(f x + e\right)^{2} + 7 \, {\left(143 \, a^{2} f \cosh\left(f x + e\right)^{10} + 495 \, a^{2} f \cosh\left(f x + e\right)^{8} + 630 \, a^{2} f \cosh\left(f x + e\right)^{6} + 350 \, a^{2} f \cosh\left(f x + e\right)^{4} + 75 \, a^{2} f \cosh\left(f x + e\right)^{2} + 3 \, a^{2} f + {\left(143 \, a^{2} f \cosh\left(f x + e\right)^{10} + 495 \, a^{2} f \cosh\left(f x + e\right)^{8} + 630 \, a^{2} f \cosh\left(f x + e\right)^{6} + 350 \, a^{2} f \cosh\left(f x + e\right)^{4} + 75 \, a^{2} f \cosh\left(f x + e\right)^{2} + 3 \, a^{2} f\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)^{4} + 28 \, {\left(13 \, a^{2} f \cosh\left(f x + e\right)^{11} + 55 \, a^{2} f \cosh\left(f x + e\right)^{9} + 90 \, a^{2} f \cosh\left(f x + e\right)^{7} + 70 \, a^{2} f \cosh\left(f x + e\right)^{5} + 25 \, a^{2} f \cosh\left(f x + e\right)^{3} + 3 \, a^{2} f \cosh\left(f x + e\right) + {\left(13 \, a^{2} f \cosh\left(f x + e\right)^{11} + 55 \, a^{2} f \cosh\left(f x + e\right)^{9} + 90 \, a^{2} f \cosh\left(f x + e\right)^{7} + 70 \, a^{2} f \cosh\left(f x + e\right)^{5} + 25 \, a^{2} f \cosh\left(f x + e\right)^{3} + 3 \, a^{2} f \cosh\left(f x + e\right)\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)^{3} + a^{2} f + 7 \, {\left(13 \, a^{2} f \cosh\left(f x + e\right)^{12} + 66 \, a^{2} f \cosh\left(f x + e\right)^{10} + 135 \, a^{2} f \cosh\left(f x + e\right)^{8} + 140 \, a^{2} f \cosh\left(f x + e\right)^{6} + 75 \, a^{2} f \cosh\left(f x + e\right)^{4} + 18 \, a^{2} f \cosh\left(f x + e\right)^{2} + a^{2} f + {\left(13 \, a^{2} f \cosh\left(f x + e\right)^{12} + 66 \, a^{2} f \cosh\left(f x + e\right)^{10} + 135 \, a^{2} f \cosh\left(f x + e\right)^{8} + 140 \, a^{2} f \cosh\left(f x + e\right)^{6} + 75 \, a^{2} f \cosh\left(f x + e\right)^{4} + 18 \, a^{2} f \cosh\left(f x + e\right)^{2} + a^{2} f\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)^{2} + {\left(a^{2} f \cosh\left(f x + e\right)^{14} + 7 \, a^{2} f \cosh\left(f x + e\right)^{12} + 21 \, a^{2} f \cosh\left(f x + e\right)^{10} + 35 \, a^{2} f \cosh\left(f x + e\right)^{8} + 35 \, a^{2} f \cosh\left(f x + e\right)^{6} + 21 \, a^{2} f \cosh\left(f x + e\right)^{4} + 7 \, a^{2} f \cosh\left(f x + e\right)^{2} + a^{2} f\right)} e^{\left(2 \, f x + 2 \, e\right)} + 14 \, {\left(a^{2} f \cosh\left(f x + e\right)^{13} + 6 \, a^{2} f \cosh\left(f x + e\right)^{11} + 15 \, a^{2} f \cosh\left(f x + e\right)^{9} + 20 \, a^{2} f \cosh\left(f x + e\right)^{7} + 15 \, a^{2} f \cosh\left(f x + e\right)^{5} + 6 \, a^{2} f \cosh\left(f x + e\right)^{3} + a^{2} f \cosh\left(f x + e\right) + {\left(a^{2} f \cosh\left(f x + e\right)^{13} + 6 \, a^{2} f \cosh\left(f x + e\right)^{11} + 15 \, a^{2} f \cosh\left(f x + e\right)^{9} + 20 \, a^{2} f \cosh\left(f x + e\right)^{7} + 15 \, a^{2} f \cosh\left(f x + e\right)^{5} + 6 \, a^{2} f \cosh\left(f x + e\right)^{3} + a^{2} f \cosh\left(f x + e\right)\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)\right)}}"," ",0,"-8/105*(385*cosh(f*x + e)*e^(f*x + e)*sinh(f*x + e)^10 + 35*e^(f*x + e)*sinh(f*x + e)^11 + 7*(275*cosh(f*x + e)^2 - 4)*e^(f*x + e)*sinh(f*x + e)^9 + 21*(275*cosh(f*x + e)^3 - 12*cosh(f*x + e))*e^(f*x + e)*sinh(f*x + e)^8 + 6*(1925*cosh(f*x + e)^4 - 168*cosh(f*x + e)^2 + 19)*e^(f*x + e)*sinh(f*x + e)^7 + 42*(385*cosh(f*x + e)^5 - 56*cosh(f*x + e)^3 + 19*cosh(f*x + e))*e^(f*x + e)*sinh(f*x + e)^6 + 14*(1155*cosh(f*x + e)^6 - 252*cosh(f*x + e)^4 + 171*cosh(f*x + e)^2 - 2)*e^(f*x + e)*sinh(f*x + e)^5 + 14*(825*cosh(f*x + e)^7 - 252*cosh(f*x + e)^5 + 285*cosh(f*x + e)^3 - 10*cosh(f*x + e))*e^(f*x + e)*sinh(f*x + e)^4 + 7*(825*cosh(f*x + e)^8 - 336*cosh(f*x + e)^6 + 570*cosh(f*x + e)^4 - 40*cosh(f*x + e)^2 + 5)*e^(f*x + e)*sinh(f*x + e)^3 + 7*(275*cosh(f*x + e)^9 - 144*cosh(f*x + e)^7 + 342*cosh(f*x + e)^5 - 40*cosh(f*x + e)^3 + 15*cosh(f*x + e))*e^(f*x + e)*sinh(f*x + e)^2 + 7*(55*cosh(f*x + e)^10 - 36*cosh(f*x + e)^8 + 114*cosh(f*x + e)^6 - 20*cosh(f*x + e)^4 + 15*cosh(f*x + e)^2)*e^(f*x + e)*sinh(f*x + e) + (35*cosh(f*x + e)^11 - 28*cosh(f*x + e)^9 + 114*cosh(f*x + e)^7 - 28*cosh(f*x + e)^5 + 35*cosh(f*x + e)^3)*e^(f*x + e))*sqrt(a*e^(4*f*x + 4*e) + 2*a*e^(2*f*x + 2*e) + a)*e^(-f*x - e)/(a^2*f*cosh(f*x + e)^14 + 7*a^2*f*cosh(f*x + e)^12 + (a^2*f*e^(2*f*x + 2*e) + a^2*f)*sinh(f*x + e)^14 + 14*(a^2*f*cosh(f*x + e)*e^(2*f*x + 2*e) + a^2*f*cosh(f*x + e))*sinh(f*x + e)^13 + 21*a^2*f*cosh(f*x + e)^10 + 7*(13*a^2*f*cosh(f*x + e)^2 + a^2*f + (13*a^2*f*cosh(f*x + e)^2 + a^2*f)*e^(2*f*x + 2*e))*sinh(f*x + e)^12 + 28*(13*a^2*f*cosh(f*x + e)^3 + 3*a^2*f*cosh(f*x + e) + (13*a^2*f*cosh(f*x + e)^3 + 3*a^2*f*cosh(f*x + e))*e^(2*f*x + 2*e))*sinh(f*x + e)^11 + 35*a^2*f*cosh(f*x + e)^8 + 7*(143*a^2*f*cosh(f*x + e)^4 + 66*a^2*f*cosh(f*x + e)^2 + 3*a^2*f + (143*a^2*f*cosh(f*x + e)^4 + 66*a^2*f*cosh(f*x + e)^2 + 3*a^2*f)*e^(2*f*x + 2*e))*sinh(f*x + e)^10 + 14*(143*a^2*f*cosh(f*x + e)^5 + 110*a^2*f*cosh(f*x + e)^3 + 15*a^2*f*cosh(f*x + e) + (143*a^2*f*cosh(f*x + e)^5 + 110*a^2*f*cosh(f*x + e)^3 + 15*a^2*f*cosh(f*x + e))*e^(2*f*x + 2*e))*sinh(f*x + e)^9 + 35*a^2*f*cosh(f*x + e)^6 + 7*(429*a^2*f*cosh(f*x + e)^6 + 495*a^2*f*cosh(f*x + e)^4 + 135*a^2*f*cosh(f*x + e)^2 + 5*a^2*f + (429*a^2*f*cosh(f*x + e)^6 + 495*a^2*f*cosh(f*x + e)^4 + 135*a^2*f*cosh(f*x + e)^2 + 5*a^2*f)*e^(2*f*x + 2*e))*sinh(f*x + e)^8 + 8*(429*a^2*f*cosh(f*x + e)^7 + 693*a^2*f*cosh(f*x + e)^5 + 315*a^2*f*cosh(f*x + e)^3 + 35*a^2*f*cosh(f*x + e) + (429*a^2*f*cosh(f*x + e)^7 + 693*a^2*f*cosh(f*x + e)^5 + 315*a^2*f*cosh(f*x + e)^3 + 35*a^2*f*cosh(f*x + e))*e^(2*f*x + 2*e))*sinh(f*x + e)^7 + 21*a^2*f*cosh(f*x + e)^4 + 7*(429*a^2*f*cosh(f*x + e)^8 + 924*a^2*f*cosh(f*x + e)^6 + 630*a^2*f*cosh(f*x + e)^4 + 140*a^2*f*cosh(f*x + e)^2 + 5*a^2*f + (429*a^2*f*cosh(f*x + e)^8 + 924*a^2*f*cosh(f*x + e)^6 + 630*a^2*f*cosh(f*x + e)^4 + 140*a^2*f*cosh(f*x + e)^2 + 5*a^2*f)*e^(2*f*x + 2*e))*sinh(f*x + e)^6 + 14*(143*a^2*f*cosh(f*x + e)^9 + 396*a^2*f*cosh(f*x + e)^7 + 378*a^2*f*cosh(f*x + e)^5 + 140*a^2*f*cosh(f*x + e)^3 + 15*a^2*f*cosh(f*x + e) + (143*a^2*f*cosh(f*x + e)^9 + 396*a^2*f*cosh(f*x + e)^7 + 378*a^2*f*cosh(f*x + e)^5 + 140*a^2*f*cosh(f*x + e)^3 + 15*a^2*f*cosh(f*x + e))*e^(2*f*x + 2*e))*sinh(f*x + e)^5 + 7*a^2*f*cosh(f*x + e)^2 + 7*(143*a^2*f*cosh(f*x + e)^10 + 495*a^2*f*cosh(f*x + e)^8 + 630*a^2*f*cosh(f*x + e)^6 + 350*a^2*f*cosh(f*x + e)^4 + 75*a^2*f*cosh(f*x + e)^2 + 3*a^2*f + (143*a^2*f*cosh(f*x + e)^10 + 495*a^2*f*cosh(f*x + e)^8 + 630*a^2*f*cosh(f*x + e)^6 + 350*a^2*f*cosh(f*x + e)^4 + 75*a^2*f*cosh(f*x + e)^2 + 3*a^2*f)*e^(2*f*x + 2*e))*sinh(f*x + e)^4 + 28*(13*a^2*f*cosh(f*x + e)^11 + 55*a^2*f*cosh(f*x + e)^9 + 90*a^2*f*cosh(f*x + e)^7 + 70*a^2*f*cosh(f*x + e)^5 + 25*a^2*f*cosh(f*x + e)^3 + 3*a^2*f*cosh(f*x + e) + (13*a^2*f*cosh(f*x + e)^11 + 55*a^2*f*cosh(f*x + e)^9 + 90*a^2*f*cosh(f*x + e)^7 + 70*a^2*f*cosh(f*x + e)^5 + 25*a^2*f*cosh(f*x + e)^3 + 3*a^2*f*cosh(f*x + e))*e^(2*f*x + 2*e))*sinh(f*x + e)^3 + a^2*f + 7*(13*a^2*f*cosh(f*x + e)^12 + 66*a^2*f*cosh(f*x + e)^10 + 135*a^2*f*cosh(f*x + e)^8 + 140*a^2*f*cosh(f*x + e)^6 + 75*a^2*f*cosh(f*x + e)^4 + 18*a^2*f*cosh(f*x + e)^2 + a^2*f + (13*a^2*f*cosh(f*x + e)^12 + 66*a^2*f*cosh(f*x + e)^10 + 135*a^2*f*cosh(f*x + e)^8 + 140*a^2*f*cosh(f*x + e)^6 + 75*a^2*f*cosh(f*x + e)^4 + 18*a^2*f*cosh(f*x + e)^2 + a^2*f)*e^(2*f*x + 2*e))*sinh(f*x + e)^2 + (a^2*f*cosh(f*x + e)^14 + 7*a^2*f*cosh(f*x + e)^12 + 21*a^2*f*cosh(f*x + e)^10 + 35*a^2*f*cosh(f*x + e)^8 + 35*a^2*f*cosh(f*x + e)^6 + 21*a^2*f*cosh(f*x + e)^4 + 7*a^2*f*cosh(f*x + e)^2 + a^2*f)*e^(2*f*x + 2*e) + 14*(a^2*f*cosh(f*x + e)^13 + 6*a^2*f*cosh(f*x + e)^11 + 15*a^2*f*cosh(f*x + e)^9 + 20*a^2*f*cosh(f*x + e)^7 + 15*a^2*f*cosh(f*x + e)^5 + 6*a^2*f*cosh(f*x + e)^3 + a^2*f*cosh(f*x + e) + (a^2*f*cosh(f*x + e)^13 + 6*a^2*f*cosh(f*x + e)^11 + 15*a^2*f*cosh(f*x + e)^9 + 20*a^2*f*cosh(f*x + e)^7 + 15*a^2*f*cosh(f*x + e)^5 + 6*a^2*f*cosh(f*x + e)^3 + a^2*f*cosh(f*x + e))*e^(2*f*x + 2*e))*sinh(f*x + e))","B",0
448,1,1400,0,0.451917," ","integrate(tanh(f*x+e)^3/(a+a*sinh(f*x+e)^2)^(3/2),x, algorithm=""fricas"")","-\frac{8 \, {\left(35 \, \cosh\left(f x + e\right) e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{6} + 5 \, e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{7} + {\left(105 \, \cosh\left(f x + e\right)^{2} - 2\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{5} + 5 \, {\left(35 \, \cosh\left(f x + e\right)^{3} - 2 \, \cosh\left(f x + e\right)\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{4} + 5 \, {\left(35 \, \cosh\left(f x + e\right)^{4} - 4 \, \cosh\left(f x + e\right)^{2} + 1\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{3} + 5 \, {\left(21 \, \cosh\left(f x + e\right)^{5} - 4 \, \cosh\left(f x + e\right)^{3} + 3 \, \cosh\left(f x + e\right)\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{2} + 5 \, {\left(7 \, \cosh\left(f x + e\right)^{6} - 2 \, \cosh\left(f x + e\right)^{4} + 3 \, \cosh\left(f x + e\right)^{2}\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right) + {\left(5 \, \cosh\left(f x + e\right)^{7} - 2 \, \cosh\left(f x + e\right)^{5} + 5 \, \cosh\left(f x + e\right)^{3}\right)} e^{\left(f x + e\right)}\right)} \sqrt{a e^{\left(4 \, f x + 4 \, e\right)} + 2 \, a e^{\left(2 \, f x + 2 \, e\right)} + a} e^{\left(-f x - e\right)}}{15 \, {\left(a^{2} f \cosh\left(f x + e\right)^{10} + 5 \, a^{2} f \cosh\left(f x + e\right)^{8} + {\left(a^{2} f e^{\left(2 \, f x + 2 \, e\right)} + a^{2} f\right)} \sinh\left(f x + e\right)^{10} + 10 \, {\left(a^{2} f \cosh\left(f x + e\right) e^{\left(2 \, f x + 2 \, e\right)} + a^{2} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{9} + 10 \, a^{2} f \cosh\left(f x + e\right)^{6} + 5 \, {\left(9 \, a^{2} f \cosh\left(f x + e\right)^{2} + a^{2} f + {\left(9 \, a^{2} f \cosh\left(f x + e\right)^{2} + a^{2} f\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)^{8} + 40 \, {\left(3 \, a^{2} f \cosh\left(f x + e\right)^{3} + a^{2} f \cosh\left(f x + e\right) + {\left(3 \, a^{2} f \cosh\left(f x + e\right)^{3} + a^{2} f \cosh\left(f x + e\right)\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)^{7} + 10 \, a^{2} f \cosh\left(f x + e\right)^{4} + 10 \, {\left(21 \, a^{2} f \cosh\left(f x + e\right)^{4} + 14 \, a^{2} f \cosh\left(f x + e\right)^{2} + a^{2} f + {\left(21 \, a^{2} f \cosh\left(f x + e\right)^{4} + 14 \, a^{2} f \cosh\left(f x + e\right)^{2} + a^{2} f\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)^{6} + 4 \, {\left(63 \, a^{2} f \cosh\left(f x + e\right)^{5} + 70 \, a^{2} f \cosh\left(f x + e\right)^{3} + 15 \, a^{2} f \cosh\left(f x + e\right) + {\left(63 \, a^{2} f \cosh\left(f x + e\right)^{5} + 70 \, a^{2} f \cosh\left(f x + e\right)^{3} + 15 \, a^{2} f \cosh\left(f x + e\right)\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)^{5} + 5 \, a^{2} f \cosh\left(f x + e\right)^{2} + 10 \, {\left(21 \, a^{2} f \cosh\left(f x + e\right)^{6} + 35 \, a^{2} f \cosh\left(f x + e\right)^{4} + 15 \, a^{2} f \cosh\left(f x + e\right)^{2} + a^{2} f + {\left(21 \, a^{2} f \cosh\left(f x + e\right)^{6} + 35 \, a^{2} f \cosh\left(f x + e\right)^{4} + 15 \, a^{2} f \cosh\left(f x + e\right)^{2} + a^{2} f\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)^{4} + 40 \, {\left(3 \, a^{2} f \cosh\left(f x + e\right)^{7} + 7 \, a^{2} f \cosh\left(f x + e\right)^{5} + 5 \, a^{2} f \cosh\left(f x + e\right)^{3} + a^{2} f \cosh\left(f x + e\right) + {\left(3 \, a^{2} f \cosh\left(f x + e\right)^{7} + 7 \, a^{2} f \cosh\left(f x + e\right)^{5} + 5 \, a^{2} f \cosh\left(f x + e\right)^{3} + a^{2} f \cosh\left(f x + e\right)\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)^{3} + a^{2} f + 5 \, {\left(9 \, a^{2} f \cosh\left(f x + e\right)^{8} + 28 \, a^{2} f \cosh\left(f x + e\right)^{6} + 30 \, a^{2} f \cosh\left(f x + e\right)^{4} + 12 \, a^{2} f \cosh\left(f x + e\right)^{2} + a^{2} f + {\left(9 \, a^{2} f \cosh\left(f x + e\right)^{8} + 28 \, a^{2} f \cosh\left(f x + e\right)^{6} + 30 \, a^{2} f \cosh\left(f x + e\right)^{4} + 12 \, a^{2} f \cosh\left(f x + e\right)^{2} + a^{2} f\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)^{2} + {\left(a^{2} f \cosh\left(f x + e\right)^{10} + 5 \, a^{2} f \cosh\left(f x + e\right)^{8} + 10 \, a^{2} f \cosh\left(f x + e\right)^{6} + 10 \, a^{2} f \cosh\left(f x + e\right)^{4} + 5 \, a^{2} f \cosh\left(f x + e\right)^{2} + a^{2} f\right)} e^{\left(2 \, f x + 2 \, e\right)} + 10 \, {\left(a^{2} f \cosh\left(f x + e\right)^{9} + 4 \, a^{2} f \cosh\left(f x + e\right)^{7} + 6 \, a^{2} f \cosh\left(f x + e\right)^{5} + 4 \, a^{2} f \cosh\left(f x + e\right)^{3} + a^{2} f \cosh\left(f x + e\right) + {\left(a^{2} f \cosh\left(f x + e\right)^{9} + 4 \, a^{2} f \cosh\left(f x + e\right)^{7} + 6 \, a^{2} f \cosh\left(f x + e\right)^{5} + 4 \, a^{2} f \cosh\left(f x + e\right)^{3} + a^{2} f \cosh\left(f x + e\right)\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)\right)}}"," ",0,"-8/15*(35*cosh(f*x + e)*e^(f*x + e)*sinh(f*x + e)^6 + 5*e^(f*x + e)*sinh(f*x + e)^7 + (105*cosh(f*x + e)^2 - 2)*e^(f*x + e)*sinh(f*x + e)^5 + 5*(35*cosh(f*x + e)^3 - 2*cosh(f*x + e))*e^(f*x + e)*sinh(f*x + e)^4 + 5*(35*cosh(f*x + e)^4 - 4*cosh(f*x + e)^2 + 1)*e^(f*x + e)*sinh(f*x + e)^3 + 5*(21*cosh(f*x + e)^5 - 4*cosh(f*x + e)^3 + 3*cosh(f*x + e))*e^(f*x + e)*sinh(f*x + e)^2 + 5*(7*cosh(f*x + e)^6 - 2*cosh(f*x + e)^4 + 3*cosh(f*x + e)^2)*e^(f*x + e)*sinh(f*x + e) + (5*cosh(f*x + e)^7 - 2*cosh(f*x + e)^5 + 5*cosh(f*x + e)^3)*e^(f*x + e))*sqrt(a*e^(4*f*x + 4*e) + 2*a*e^(2*f*x + 2*e) + a)*e^(-f*x - e)/(a^2*f*cosh(f*x + e)^10 + 5*a^2*f*cosh(f*x + e)^8 + (a^2*f*e^(2*f*x + 2*e) + a^2*f)*sinh(f*x + e)^10 + 10*(a^2*f*cosh(f*x + e)*e^(2*f*x + 2*e) + a^2*f*cosh(f*x + e))*sinh(f*x + e)^9 + 10*a^2*f*cosh(f*x + e)^6 + 5*(9*a^2*f*cosh(f*x + e)^2 + a^2*f + (9*a^2*f*cosh(f*x + e)^2 + a^2*f)*e^(2*f*x + 2*e))*sinh(f*x + e)^8 + 40*(3*a^2*f*cosh(f*x + e)^3 + a^2*f*cosh(f*x + e) + (3*a^2*f*cosh(f*x + e)^3 + a^2*f*cosh(f*x + e))*e^(2*f*x + 2*e))*sinh(f*x + e)^7 + 10*a^2*f*cosh(f*x + e)^4 + 10*(21*a^2*f*cosh(f*x + e)^4 + 14*a^2*f*cosh(f*x + e)^2 + a^2*f + (21*a^2*f*cosh(f*x + e)^4 + 14*a^2*f*cosh(f*x + e)^2 + a^2*f)*e^(2*f*x + 2*e))*sinh(f*x + e)^6 + 4*(63*a^2*f*cosh(f*x + e)^5 + 70*a^2*f*cosh(f*x + e)^3 + 15*a^2*f*cosh(f*x + e) + (63*a^2*f*cosh(f*x + e)^5 + 70*a^2*f*cosh(f*x + e)^3 + 15*a^2*f*cosh(f*x + e))*e^(2*f*x + 2*e))*sinh(f*x + e)^5 + 5*a^2*f*cosh(f*x + e)^2 + 10*(21*a^2*f*cosh(f*x + e)^6 + 35*a^2*f*cosh(f*x + e)^4 + 15*a^2*f*cosh(f*x + e)^2 + a^2*f + (21*a^2*f*cosh(f*x + e)^6 + 35*a^2*f*cosh(f*x + e)^4 + 15*a^2*f*cosh(f*x + e)^2 + a^2*f)*e^(2*f*x + 2*e))*sinh(f*x + e)^4 + 40*(3*a^2*f*cosh(f*x + e)^7 + 7*a^2*f*cosh(f*x + e)^5 + 5*a^2*f*cosh(f*x + e)^3 + a^2*f*cosh(f*x + e) + (3*a^2*f*cosh(f*x + e)^7 + 7*a^2*f*cosh(f*x + e)^5 + 5*a^2*f*cosh(f*x + e)^3 + a^2*f*cosh(f*x + e))*e^(2*f*x + 2*e))*sinh(f*x + e)^3 + a^2*f + 5*(9*a^2*f*cosh(f*x + e)^8 + 28*a^2*f*cosh(f*x + e)^6 + 30*a^2*f*cosh(f*x + e)^4 + 12*a^2*f*cosh(f*x + e)^2 + a^2*f + (9*a^2*f*cosh(f*x + e)^8 + 28*a^2*f*cosh(f*x + e)^6 + 30*a^2*f*cosh(f*x + e)^4 + 12*a^2*f*cosh(f*x + e)^2 + a^2*f)*e^(2*f*x + 2*e))*sinh(f*x + e)^2 + (a^2*f*cosh(f*x + e)^10 + 5*a^2*f*cosh(f*x + e)^8 + 10*a^2*f*cosh(f*x + e)^6 + 10*a^2*f*cosh(f*x + e)^4 + 5*a^2*f*cosh(f*x + e)^2 + a^2*f)*e^(2*f*x + 2*e) + 10*(a^2*f*cosh(f*x + e)^9 + 4*a^2*f*cosh(f*x + e)^7 + 6*a^2*f*cosh(f*x + e)^5 + 4*a^2*f*cosh(f*x + e)^3 + a^2*f*cosh(f*x + e) + (a^2*f*cosh(f*x + e)^9 + 4*a^2*f*cosh(f*x + e)^7 + 6*a^2*f*cosh(f*x + e)^5 + 4*a^2*f*cosh(f*x + e)^3 + a^2*f*cosh(f*x + e))*e^(2*f*x + 2*e))*sinh(f*x + e))","B",0
449,1,608,0,0.497782," ","integrate(tanh(f*x+e)/(a+a*sinh(f*x+e)^2)^(3/2),x, algorithm=""fricas"")","-\frac{8 \, {\left(\cosh\left(f x + e\right)^{3} e^{\left(f x + e\right)} + 3 \, \cosh\left(f x + e\right)^{2} e^{\left(f x + e\right)} \sinh\left(f x + e\right) + 3 \, \cosh\left(f x + e\right) e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{2} + e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{3}\right)} \sqrt{a e^{\left(4 \, f x + 4 \, e\right)} + 2 \, a e^{\left(2 \, f x + 2 \, e\right)} + a} e^{\left(-f x - e\right)}}{3 \, {\left(a^{2} f \cosh\left(f x + e\right)^{6} + 3 \, a^{2} f \cosh\left(f x + e\right)^{4} + {\left(a^{2} f e^{\left(2 \, f x + 2 \, e\right)} + a^{2} f\right)} \sinh\left(f x + e\right)^{6} + 6 \, {\left(a^{2} f \cosh\left(f x + e\right) e^{\left(2 \, f x + 2 \, e\right)} + a^{2} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + 3 \, a^{2} f \cosh\left(f x + e\right)^{2} + 3 \, {\left(5 \, a^{2} f \cosh\left(f x + e\right)^{2} + a^{2} f + {\left(5 \, a^{2} f \cosh\left(f x + e\right)^{2} + a^{2} f\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(5 \, a^{2} f \cosh\left(f x + e\right)^{3} + 3 \, a^{2} f \cosh\left(f x + e\right) + {\left(5 \, a^{2} f \cosh\left(f x + e\right)^{3} + 3 \, a^{2} f \cosh\left(f x + e\right)\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)^{3} + a^{2} f + 3 \, {\left(5 \, a^{2} f \cosh\left(f x + e\right)^{4} + 6 \, a^{2} f \cosh\left(f x + e\right)^{2} + a^{2} f + {\left(5 \, a^{2} f \cosh\left(f x + e\right)^{4} + 6 \, a^{2} f \cosh\left(f x + e\right)^{2} + a^{2} f\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)^{2} + {\left(a^{2} f \cosh\left(f x + e\right)^{6} + 3 \, a^{2} f \cosh\left(f x + e\right)^{4} + 3 \, a^{2} f \cosh\left(f x + e\right)^{2} + a^{2} f\right)} e^{\left(2 \, f x + 2 \, e\right)} + 6 \, {\left(a^{2} f \cosh\left(f x + e\right)^{5} + 2 \, a^{2} f \cosh\left(f x + e\right)^{3} + a^{2} f \cosh\left(f x + e\right) + {\left(a^{2} f \cosh\left(f x + e\right)^{5} + 2 \, a^{2} f \cosh\left(f x + e\right)^{3} + a^{2} f \cosh\left(f x + e\right)\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)\right)}}"," ",0,"-8/3*(cosh(f*x + e)^3*e^(f*x + e) + 3*cosh(f*x + e)^2*e^(f*x + e)*sinh(f*x + e) + 3*cosh(f*x + e)*e^(f*x + e)*sinh(f*x + e)^2 + e^(f*x + e)*sinh(f*x + e)^3)*sqrt(a*e^(4*f*x + 4*e) + 2*a*e^(2*f*x + 2*e) + a)*e^(-f*x - e)/(a^2*f*cosh(f*x + e)^6 + 3*a^2*f*cosh(f*x + e)^4 + (a^2*f*e^(2*f*x + 2*e) + a^2*f)*sinh(f*x + e)^6 + 6*(a^2*f*cosh(f*x + e)*e^(2*f*x + 2*e) + a^2*f*cosh(f*x + e))*sinh(f*x + e)^5 + 3*a^2*f*cosh(f*x + e)^2 + 3*(5*a^2*f*cosh(f*x + e)^2 + a^2*f + (5*a^2*f*cosh(f*x + e)^2 + a^2*f)*e^(2*f*x + 2*e))*sinh(f*x + e)^4 + 4*(5*a^2*f*cosh(f*x + e)^3 + 3*a^2*f*cosh(f*x + e) + (5*a^2*f*cosh(f*x + e)^3 + 3*a^2*f*cosh(f*x + e))*e^(2*f*x + 2*e))*sinh(f*x + e)^3 + a^2*f + 3*(5*a^2*f*cosh(f*x + e)^4 + 6*a^2*f*cosh(f*x + e)^2 + a^2*f + (5*a^2*f*cosh(f*x + e)^4 + 6*a^2*f*cosh(f*x + e)^2 + a^2*f)*e^(2*f*x + 2*e))*sinh(f*x + e)^2 + (a^2*f*cosh(f*x + e)^6 + 3*a^2*f*cosh(f*x + e)^4 + 3*a^2*f*cosh(f*x + e)^2 + a^2*f)*e^(2*f*x + 2*e) + 6*(a^2*f*cosh(f*x + e)^5 + 2*a^2*f*cosh(f*x + e)^3 + a^2*f*cosh(f*x + e) + (a^2*f*cosh(f*x + e)^5 + 2*a^2*f*cosh(f*x + e)^3 + a^2*f*cosh(f*x + e))*e^(2*f*x + 2*e))*sinh(f*x + e))","B",0
450,1,271,0,0.466318," ","integrate(coth(f*x+e)/(a+a*sinh(f*x+e)^2)^(3/2),x, algorithm=""fricas"")","\frac{\sqrt{a e^{\left(4 \, f x + 4 \, e\right)} + 2 \, a e^{\left(2 \, f x + 2 \, e\right)} + a} {\left(2 \, \cosh\left(f x + e\right) e^{\left(f x + e\right)} + {\left(2 \, \cosh\left(f x + e\right) e^{\left(f x + e\right)} \sinh\left(f x + e\right) + e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{2} + {\left(\cosh\left(f x + e\right)^{2} + 1\right)} e^{\left(f x + e\right)}\right)} \log\left(\frac{\cosh\left(f x + e\right) + \sinh\left(f x + e\right) - 1}{\cosh\left(f x + e\right) + \sinh\left(f x + e\right) + 1}\right) + 2 \, e^{\left(f x + e\right)} \sinh\left(f x + e\right)\right)} e^{\left(-f x - e\right)}}{a^{2} f \cosh\left(f x + e\right)^{2} + a^{2} f + {\left(a^{2} f e^{\left(2 \, f x + 2 \, e\right)} + a^{2} f\right)} \sinh\left(f x + e\right)^{2} + {\left(a^{2} f \cosh\left(f x + e\right)^{2} + a^{2} f\right)} e^{\left(2 \, f x + 2 \, e\right)} + 2 \, {\left(a^{2} f \cosh\left(f x + e\right) e^{\left(2 \, f x + 2 \, e\right)} + a^{2} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)}"," ",0,"sqrt(a*e^(4*f*x + 4*e) + 2*a*e^(2*f*x + 2*e) + a)*(2*cosh(f*x + e)*e^(f*x + e) + (2*cosh(f*x + e)*e^(f*x + e)*sinh(f*x + e) + e^(f*x + e)*sinh(f*x + e)^2 + (cosh(f*x + e)^2 + 1)*e^(f*x + e))*log((cosh(f*x + e) + sinh(f*x + e) - 1)/(cosh(f*x + e) + sinh(f*x + e) + 1)) + 2*e^(f*x + e)*sinh(f*x + e))*e^(-f*x - e)/(a^2*f*cosh(f*x + e)^2 + a^2*f + (a^2*f*e^(2*f*x + 2*e) + a^2*f)*sinh(f*x + e)^2 + (a^2*f*cosh(f*x + e)^2 + a^2*f)*e^(2*f*x + 2*e) + 2*(a^2*f*cosh(f*x + e)*e^(2*f*x + 2*e) + a^2*f*cosh(f*x + e))*sinh(f*x + e))","B",0
451,1,565,0,0.524063," ","integrate(coth(f*x+e)^3/(a+a*sinh(f*x+e)^2)^(3/2),x, algorithm=""fricas"")","-\frac{{\left(6 \, \cosh\left(f x + e\right) e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{2} + 2 \, e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{3} + 2 \, {\left(3 \, \cosh\left(f x + e\right)^{2} + 1\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right) + 2 \, {\left(\cosh\left(f x + e\right)^{3} + \cosh\left(f x + e\right)\right)} e^{\left(f x + e\right)} - {\left(4 \, \cosh\left(f x + e\right) e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{3} + e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{4} + 2 \, {\left(3 \, \cosh\left(f x + e\right)^{2} - 1\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(\cosh\left(f x + e\right)^{3} - \cosh\left(f x + e\right)\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right) + {\left(\cosh\left(f x + e\right)^{4} - 2 \, \cosh\left(f x + e\right)^{2} + 1\right)} e^{\left(f x + e\right)}\right)} \log\left(\frac{\cosh\left(f x + e\right) + \sinh\left(f x + e\right) + 1}{\cosh\left(f x + e\right) + \sinh\left(f x + e\right) - 1}\right)\right)} \sqrt{a e^{\left(4 \, f x + 4 \, e\right)} + 2 \, a e^{\left(2 \, f x + 2 \, e\right)} + a} e^{\left(-f x - e\right)}}{2 \, {\left(a^{2} f \cosh\left(f x + e\right)^{4} - 2 \, a^{2} f \cosh\left(f x + e\right)^{2} + {\left(a^{2} f e^{\left(2 \, f x + 2 \, e\right)} + a^{2} f\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(a^{2} f \cosh\left(f x + e\right) e^{\left(2 \, f x + 2 \, e\right)} + a^{2} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + a^{2} f + 2 \, {\left(3 \, a^{2} f \cosh\left(f x + e\right)^{2} - a^{2} f + {\left(3 \, a^{2} f \cosh\left(f x + e\right)^{2} - a^{2} f\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)^{2} + {\left(a^{2} f \cosh\left(f x + e\right)^{4} - 2 \, a^{2} f \cosh\left(f x + e\right)^{2} + a^{2} f\right)} e^{\left(2 \, f x + 2 \, e\right)} + 4 \, {\left(a^{2} f \cosh\left(f x + e\right)^{3} - a^{2} f \cosh\left(f x + e\right) + {\left(a^{2} f \cosh\left(f x + e\right)^{3} - a^{2} f \cosh\left(f x + e\right)\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)\right)}}"," ",0,"-1/2*(6*cosh(f*x + e)*e^(f*x + e)*sinh(f*x + e)^2 + 2*e^(f*x + e)*sinh(f*x + e)^3 + 2*(3*cosh(f*x + e)^2 + 1)*e^(f*x + e)*sinh(f*x + e) + 2*(cosh(f*x + e)^3 + cosh(f*x + e))*e^(f*x + e) - (4*cosh(f*x + e)*e^(f*x + e)*sinh(f*x + e)^3 + e^(f*x + e)*sinh(f*x + e)^4 + 2*(3*cosh(f*x + e)^2 - 1)*e^(f*x + e)*sinh(f*x + e)^2 + 4*(cosh(f*x + e)^3 - cosh(f*x + e))*e^(f*x + e)*sinh(f*x + e) + (cosh(f*x + e)^4 - 2*cosh(f*x + e)^2 + 1)*e^(f*x + e))*log((cosh(f*x + e) + sinh(f*x + e) + 1)/(cosh(f*x + e) + sinh(f*x + e) - 1)))*sqrt(a*e^(4*f*x + 4*e) + 2*a*e^(2*f*x + 2*e) + a)*e^(-f*x - e)/(a^2*f*cosh(f*x + e)^4 - 2*a^2*f*cosh(f*x + e)^2 + (a^2*f*e^(2*f*x + 2*e) + a^2*f)*sinh(f*x + e)^4 + 4*(a^2*f*cosh(f*x + e)*e^(2*f*x + 2*e) + a^2*f*cosh(f*x + e))*sinh(f*x + e)^3 + a^2*f + 2*(3*a^2*f*cosh(f*x + e)^2 - a^2*f + (3*a^2*f*cosh(f*x + e)^2 - a^2*f)*e^(2*f*x + 2*e))*sinh(f*x + e)^2 + (a^2*f*cosh(f*x + e)^4 - 2*a^2*f*cosh(f*x + e)^2 + a^2*f)*e^(2*f*x + 2*e) + 4*(a^2*f*cosh(f*x + e)^3 - a^2*f*cosh(f*x + e) + (a^2*f*cosh(f*x + e)^3 - a^2*f*cosh(f*x + e))*e^(2*f*x + 2*e))*sinh(f*x + e))","B",0
452,1,1423,0,0.528274," ","integrate(tanh(f*x+e)^2/(a+a*sinh(f*x+e)^2)^(3/2),x, algorithm=""fricas"")","\frac{{\left(7 \, \cosh\left(f x + e\right) e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{6} + e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{7} + 7 \, {\left(3 \, \cosh\left(f x + e\right)^{2} - 1\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{5} + 35 \, {\left(\cosh\left(f x + e\right)^{3} - \cosh\left(f x + e\right)\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{4} + 7 \, {\left(5 \, \cosh\left(f x + e\right)^{4} - 10 \, \cosh\left(f x + e\right)^{2} + 1\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{3} + 7 \, {\left(3 \, \cosh\left(f x + e\right)^{5} - 10 \, \cosh\left(f x + e\right)^{3} + 3 \, \cosh\left(f x + e\right)\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{2} + {\left(7 \, \cosh\left(f x + e\right)^{6} - 35 \, \cosh\left(f x + e\right)^{4} + 21 \, \cosh\left(f x + e\right)^{2} - 1\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right) + {\left(8 \, \cosh\left(f x + e\right) e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{7} + e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{8} + 4 \, {\left(7 \, \cosh\left(f x + e\right)^{2} + 1\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{6} + 8 \, {\left(7 \, \cosh\left(f x + e\right)^{3} + 3 \, \cosh\left(f x + e\right)\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(35 \, \cosh\left(f x + e\right)^{4} + 30 \, \cosh\left(f x + e\right)^{2} + 3\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{4} + 8 \, {\left(7 \, \cosh\left(f x + e\right)^{5} + 10 \, \cosh\left(f x + e\right)^{3} + 3 \, \cosh\left(f x + e\right)\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{3} + 4 \, {\left(7 \, \cosh\left(f x + e\right)^{6} + 15 \, \cosh\left(f x + e\right)^{4} + 9 \, \cosh\left(f x + e\right)^{2} + 1\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{2} + 8 \, {\left(\cosh\left(f x + e\right)^{7} + 3 \, \cosh\left(f x + e\right)^{5} + 3 \, \cosh\left(f x + e\right)^{3} + \cosh\left(f x + e\right)\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right) + {\left(\cosh\left(f x + e\right)^{8} + 4 \, \cosh\left(f x + e\right)^{6} + 6 \, \cosh\left(f x + e\right)^{4} + 4 \, \cosh\left(f x + e\right)^{2} + 1\right)} e^{\left(f x + e\right)}\right)} \arctan\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right)\right) + {\left(\cosh\left(f x + e\right)^{7} - 7 \, \cosh\left(f x + e\right)^{5} + 7 \, \cosh\left(f x + e\right)^{3} - \cosh\left(f x + e\right)\right)} e^{\left(f x + e\right)}\right)} \sqrt{a e^{\left(4 \, f x + 4 \, e\right)} + 2 \, a e^{\left(2 \, f x + 2 \, e\right)} + a} e^{\left(-f x - e\right)}}{4 \, {\left(a^{2} f \cosh\left(f x + e\right)^{8} + 4 \, a^{2} f \cosh\left(f x + e\right)^{6} + {\left(a^{2} f e^{\left(2 \, f x + 2 \, e\right)} + a^{2} f\right)} \sinh\left(f x + e\right)^{8} + 8 \, {\left(a^{2} f \cosh\left(f x + e\right) e^{\left(2 \, f x + 2 \, e\right)} + a^{2} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{7} + 6 \, a^{2} f \cosh\left(f x + e\right)^{4} + 4 \, {\left(7 \, a^{2} f \cosh\left(f x + e\right)^{2} + a^{2} f + {\left(7 \, a^{2} f \cosh\left(f x + e\right)^{2} + a^{2} f\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)^{6} + 8 \, {\left(7 \, a^{2} f \cosh\left(f x + e\right)^{3} + 3 \, a^{2} f \cosh\left(f x + e\right) + {\left(7 \, a^{2} f \cosh\left(f x + e\right)^{3} + 3 \, a^{2} f \cosh\left(f x + e\right)\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)^{5} + 4 \, a^{2} f \cosh\left(f x + e\right)^{2} + 2 \, {\left(35 \, a^{2} f \cosh\left(f x + e\right)^{4} + 30 \, a^{2} f \cosh\left(f x + e\right)^{2} + 3 \, a^{2} f + {\left(35 \, a^{2} f \cosh\left(f x + e\right)^{4} + 30 \, a^{2} f \cosh\left(f x + e\right)^{2} + 3 \, a^{2} f\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)^{4} + 8 \, {\left(7 \, a^{2} f \cosh\left(f x + e\right)^{5} + 10 \, a^{2} f \cosh\left(f x + e\right)^{3} + 3 \, a^{2} f \cosh\left(f x + e\right) + {\left(7 \, a^{2} f \cosh\left(f x + e\right)^{5} + 10 \, a^{2} f \cosh\left(f x + e\right)^{3} + 3 \, a^{2} f \cosh\left(f x + e\right)\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)^{3} + a^{2} f + 4 \, {\left(7 \, a^{2} f \cosh\left(f x + e\right)^{6} + 15 \, a^{2} f \cosh\left(f x + e\right)^{4} + 9 \, a^{2} f \cosh\left(f x + e\right)^{2} + a^{2} f + {\left(7 \, a^{2} f \cosh\left(f x + e\right)^{6} + 15 \, a^{2} f \cosh\left(f x + e\right)^{4} + 9 \, a^{2} f \cosh\left(f x + e\right)^{2} + a^{2} f\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)^{2} + {\left(a^{2} f \cosh\left(f x + e\right)^{8} + 4 \, a^{2} f \cosh\left(f x + e\right)^{6} + 6 \, a^{2} f \cosh\left(f x + e\right)^{4} + 4 \, a^{2} f \cosh\left(f x + e\right)^{2} + a^{2} f\right)} e^{\left(2 \, f x + 2 \, e\right)} + 8 \, {\left(a^{2} f \cosh\left(f x + e\right)^{7} + 3 \, a^{2} f \cosh\left(f x + e\right)^{5} + 3 \, a^{2} f \cosh\left(f x + e\right)^{3} + a^{2} f \cosh\left(f x + e\right) + {\left(a^{2} f \cosh\left(f x + e\right)^{7} + 3 \, a^{2} f \cosh\left(f x + e\right)^{5} + 3 \, a^{2} f \cosh\left(f x + e\right)^{3} + a^{2} f \cosh\left(f x + e\right)\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)\right)}}"," ",0,"1/4*(7*cosh(f*x + e)*e^(f*x + e)*sinh(f*x + e)^6 + e^(f*x + e)*sinh(f*x + e)^7 + 7*(3*cosh(f*x + e)^2 - 1)*e^(f*x + e)*sinh(f*x + e)^5 + 35*(cosh(f*x + e)^3 - cosh(f*x + e))*e^(f*x + e)*sinh(f*x + e)^4 + 7*(5*cosh(f*x + e)^4 - 10*cosh(f*x + e)^2 + 1)*e^(f*x + e)*sinh(f*x + e)^3 + 7*(3*cosh(f*x + e)^5 - 10*cosh(f*x + e)^3 + 3*cosh(f*x + e))*e^(f*x + e)*sinh(f*x + e)^2 + (7*cosh(f*x + e)^6 - 35*cosh(f*x + e)^4 + 21*cosh(f*x + e)^2 - 1)*e^(f*x + e)*sinh(f*x + e) + (8*cosh(f*x + e)*e^(f*x + e)*sinh(f*x + e)^7 + e^(f*x + e)*sinh(f*x + e)^8 + 4*(7*cosh(f*x + e)^2 + 1)*e^(f*x + e)*sinh(f*x + e)^6 + 8*(7*cosh(f*x + e)^3 + 3*cosh(f*x + e))*e^(f*x + e)*sinh(f*x + e)^5 + 2*(35*cosh(f*x + e)^4 + 30*cosh(f*x + e)^2 + 3)*e^(f*x + e)*sinh(f*x + e)^4 + 8*(7*cosh(f*x + e)^5 + 10*cosh(f*x + e)^3 + 3*cosh(f*x + e))*e^(f*x + e)*sinh(f*x + e)^3 + 4*(7*cosh(f*x + e)^6 + 15*cosh(f*x + e)^4 + 9*cosh(f*x + e)^2 + 1)*e^(f*x + e)*sinh(f*x + e)^2 + 8*(cosh(f*x + e)^7 + 3*cosh(f*x + e)^5 + 3*cosh(f*x + e)^3 + cosh(f*x + e))*e^(f*x + e)*sinh(f*x + e) + (cosh(f*x + e)^8 + 4*cosh(f*x + e)^6 + 6*cosh(f*x + e)^4 + 4*cosh(f*x + e)^2 + 1)*e^(f*x + e))*arctan(cosh(f*x + e) + sinh(f*x + e)) + (cosh(f*x + e)^7 - 7*cosh(f*x + e)^5 + 7*cosh(f*x + e)^3 - cosh(f*x + e))*e^(f*x + e))*sqrt(a*e^(4*f*x + 4*e) + 2*a*e^(2*f*x + 2*e) + a)*e^(-f*x - e)/(a^2*f*cosh(f*x + e)^8 + 4*a^2*f*cosh(f*x + e)^6 + (a^2*f*e^(2*f*x + 2*e) + a^2*f)*sinh(f*x + e)^8 + 8*(a^2*f*cosh(f*x + e)*e^(2*f*x + 2*e) + a^2*f*cosh(f*x + e))*sinh(f*x + e)^7 + 6*a^2*f*cosh(f*x + e)^4 + 4*(7*a^2*f*cosh(f*x + e)^2 + a^2*f + (7*a^2*f*cosh(f*x + e)^2 + a^2*f)*e^(2*f*x + 2*e))*sinh(f*x + e)^6 + 8*(7*a^2*f*cosh(f*x + e)^3 + 3*a^2*f*cosh(f*x + e) + (7*a^2*f*cosh(f*x + e)^3 + 3*a^2*f*cosh(f*x + e))*e^(2*f*x + 2*e))*sinh(f*x + e)^5 + 4*a^2*f*cosh(f*x + e)^2 + 2*(35*a^2*f*cosh(f*x + e)^4 + 30*a^2*f*cosh(f*x + e)^2 + 3*a^2*f + (35*a^2*f*cosh(f*x + e)^4 + 30*a^2*f*cosh(f*x + e)^2 + 3*a^2*f)*e^(2*f*x + 2*e))*sinh(f*x + e)^4 + 8*(7*a^2*f*cosh(f*x + e)^5 + 10*a^2*f*cosh(f*x + e)^3 + 3*a^2*f*cosh(f*x + e) + (7*a^2*f*cosh(f*x + e)^5 + 10*a^2*f*cosh(f*x + e)^3 + 3*a^2*f*cosh(f*x + e))*e^(2*f*x + 2*e))*sinh(f*x + e)^3 + a^2*f + 4*(7*a^2*f*cosh(f*x + e)^6 + 15*a^2*f*cosh(f*x + e)^4 + 9*a^2*f*cosh(f*x + e)^2 + a^2*f + (7*a^2*f*cosh(f*x + e)^6 + 15*a^2*f*cosh(f*x + e)^4 + 9*a^2*f*cosh(f*x + e)^2 + a^2*f)*e^(2*f*x + 2*e))*sinh(f*x + e)^2 + (a^2*f*cosh(f*x + e)^8 + 4*a^2*f*cosh(f*x + e)^6 + 6*a^2*f*cosh(f*x + e)^4 + 4*a^2*f*cosh(f*x + e)^2 + a^2*f)*e^(2*f*x + 2*e) + 8*(a^2*f*cosh(f*x + e)^7 + 3*a^2*f*cosh(f*x + e)^5 + 3*a^2*f*cosh(f*x + e)^3 + a^2*f*cosh(f*x + e) + (a^2*f*cosh(f*x + e)^7 + 3*a^2*f*cosh(f*x + e)^5 + 3*a^2*f*cosh(f*x + e)^3 + a^2*f*cosh(f*x + e))*e^(2*f*x + 2*e))*sinh(f*x + e))","B",0
453,1,254,0,0.559094," ","integrate(coth(f*x+e)^2/(a+a*sinh(f*x+e)^2)^(3/2),x, algorithm=""fricas"")","-\frac{2 \, {\left({\left(2 \, \cosh\left(f x + e\right) e^{\left(f x + e\right)} \sinh\left(f x + e\right) + e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{2} + {\left(\cosh\left(f x + e\right)^{2} - 1\right)} e^{\left(f x + e\right)}\right)} \arctan\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right)\right) + \cosh\left(f x + e\right) e^{\left(f x + e\right)} + e^{\left(f x + e\right)} \sinh\left(f x + e\right)\right)} \sqrt{a e^{\left(4 \, f x + 4 \, e\right)} + 2 \, a e^{\left(2 \, f x + 2 \, e\right)} + a} e^{\left(-f x - e\right)}}{a^{2} f \cosh\left(f x + e\right)^{2} - a^{2} f + {\left(a^{2} f e^{\left(2 \, f x + 2 \, e\right)} + a^{2} f\right)} \sinh\left(f x + e\right)^{2} + {\left(a^{2} f \cosh\left(f x + e\right)^{2} - a^{2} f\right)} e^{\left(2 \, f x + 2 \, e\right)} + 2 \, {\left(a^{2} f \cosh\left(f x + e\right) e^{\left(2 \, f x + 2 \, e\right)} + a^{2} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)}"," ",0,"-2*((2*cosh(f*x + e)*e^(f*x + e)*sinh(f*x + e) + e^(f*x + e)*sinh(f*x + e)^2 + (cosh(f*x + e)^2 - 1)*e^(f*x + e))*arctan(cosh(f*x + e) + sinh(f*x + e)) + cosh(f*x + e)*e^(f*x + e) + e^(f*x + e)*sinh(f*x + e))*sqrt(a*e^(4*f*x + 4*e) + 2*a*e^(2*f*x + 2*e) + a)*e^(-f*x - e)/(a^2*f*cosh(f*x + e)^2 - a^2*f + (a^2*f*e^(2*f*x + 2*e) + a^2*f)*sinh(f*x + e)^2 + (a^2*f*cosh(f*x + e)^2 - a^2*f)*e^(2*f*x + 2*e) + 2*(a^2*f*cosh(f*x + e)*e^(2*f*x + 2*e) + a^2*f*cosh(f*x + e))*sinh(f*x + e))","B",0
454,1,612,0,0.601293," ","integrate(coth(f*x+e)^4/(a+a*sinh(f*x+e)^2)^(3/2),x, algorithm=""fricas"")","-\frac{8 \, {\left(\cosh\left(f x + e\right)^{3} e^{\left(f x + e\right)} + 3 \, \cosh\left(f x + e\right)^{2} e^{\left(f x + e\right)} \sinh\left(f x + e\right) + 3 \, \cosh\left(f x + e\right) e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{2} + e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{3}\right)} \sqrt{a e^{\left(4 \, f x + 4 \, e\right)} + 2 \, a e^{\left(2 \, f x + 2 \, e\right)} + a} e^{\left(-f x - e\right)}}{3 \, {\left(a^{2} f \cosh\left(f x + e\right)^{6} - 3 \, a^{2} f \cosh\left(f x + e\right)^{4} + {\left(a^{2} f e^{\left(2 \, f x + 2 \, e\right)} + a^{2} f\right)} \sinh\left(f x + e\right)^{6} + 6 \, {\left(a^{2} f \cosh\left(f x + e\right) e^{\left(2 \, f x + 2 \, e\right)} + a^{2} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + 3 \, a^{2} f \cosh\left(f x + e\right)^{2} + 3 \, {\left(5 \, a^{2} f \cosh\left(f x + e\right)^{2} - a^{2} f + {\left(5 \, a^{2} f \cosh\left(f x + e\right)^{2} - a^{2} f\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(5 \, a^{2} f \cosh\left(f x + e\right)^{3} - 3 \, a^{2} f \cosh\left(f x + e\right) + {\left(5 \, a^{2} f \cosh\left(f x + e\right)^{3} - 3 \, a^{2} f \cosh\left(f x + e\right)\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)^{3} - a^{2} f + 3 \, {\left(5 \, a^{2} f \cosh\left(f x + e\right)^{4} - 6 \, a^{2} f \cosh\left(f x + e\right)^{2} + a^{2} f + {\left(5 \, a^{2} f \cosh\left(f x + e\right)^{4} - 6 \, a^{2} f \cosh\left(f x + e\right)^{2} + a^{2} f\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)^{2} + {\left(a^{2} f \cosh\left(f x + e\right)^{6} - 3 \, a^{2} f \cosh\left(f x + e\right)^{4} + 3 \, a^{2} f \cosh\left(f x + e\right)^{2} - a^{2} f\right)} e^{\left(2 \, f x + 2 \, e\right)} + 6 \, {\left(a^{2} f \cosh\left(f x + e\right)^{5} - 2 \, a^{2} f \cosh\left(f x + e\right)^{3} + a^{2} f \cosh\left(f x + e\right) + {\left(a^{2} f \cosh\left(f x + e\right)^{5} - 2 \, a^{2} f \cosh\left(f x + e\right)^{3} + a^{2} f \cosh\left(f x + e\right)\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)\right)}}"," ",0,"-8/3*(cosh(f*x + e)^3*e^(f*x + e) + 3*cosh(f*x + e)^2*e^(f*x + e)*sinh(f*x + e) + 3*cosh(f*x + e)*e^(f*x + e)*sinh(f*x + e)^2 + e^(f*x + e)*sinh(f*x + e)^3)*sqrt(a*e^(4*f*x + 4*e) + 2*a*e^(2*f*x + 2*e) + a)*e^(-f*x - e)/(a^2*f*cosh(f*x + e)^6 - 3*a^2*f*cosh(f*x + e)^4 + (a^2*f*e^(2*f*x + 2*e) + a^2*f)*sinh(f*x + e)^6 + 6*(a^2*f*cosh(f*x + e)*e^(2*f*x + 2*e) + a^2*f*cosh(f*x + e))*sinh(f*x + e)^5 + 3*a^2*f*cosh(f*x + e)^2 + 3*(5*a^2*f*cosh(f*x + e)^2 - a^2*f + (5*a^2*f*cosh(f*x + e)^2 - a^2*f)*e^(2*f*x + 2*e))*sinh(f*x + e)^4 + 4*(5*a^2*f*cosh(f*x + e)^3 - 3*a^2*f*cosh(f*x + e) + (5*a^2*f*cosh(f*x + e)^3 - 3*a^2*f*cosh(f*x + e))*e^(2*f*x + 2*e))*sinh(f*x + e)^3 - a^2*f + 3*(5*a^2*f*cosh(f*x + e)^4 - 6*a^2*f*cosh(f*x + e)^2 + a^2*f + (5*a^2*f*cosh(f*x + e)^4 - 6*a^2*f*cosh(f*x + e)^2 + a^2*f)*e^(2*f*x + 2*e))*sinh(f*x + e)^2 + (a^2*f*cosh(f*x + e)^6 - 3*a^2*f*cosh(f*x + e)^4 + 3*a^2*f*cosh(f*x + e)^2 - a^2*f)*e^(2*f*x + 2*e) + 6*(a^2*f*cosh(f*x + e)^5 - 2*a^2*f*cosh(f*x + e)^3 + a^2*f*cosh(f*x + e) + (a^2*f*cosh(f*x + e)^5 - 2*a^2*f*cosh(f*x + e)^3 + a^2*f*cosh(f*x + e))*e^(2*f*x + 2*e))*sinh(f*x + e))","B",0
455,1,1410,0,0.495947," ","integrate(coth(f*x+e)^6/(a+a*sinh(f*x+e)^2)^(3/2),x, algorithm=""fricas"")","-\frac{8 \, {\left(35 \, \cosh\left(f x + e\right) e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{6} + 5 \, e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{7} + {\left(105 \, \cosh\left(f x + e\right)^{2} + 2\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{5} + 5 \, {\left(35 \, \cosh\left(f x + e\right)^{3} + 2 \, \cosh\left(f x + e\right)\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{4} + 5 \, {\left(35 \, \cosh\left(f x + e\right)^{4} + 4 \, \cosh\left(f x + e\right)^{2} + 1\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{3} + 5 \, {\left(21 \, \cosh\left(f x + e\right)^{5} + 4 \, \cosh\left(f x + e\right)^{3} + 3 \, \cosh\left(f x + e\right)\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{2} + 5 \, {\left(7 \, \cosh\left(f x + e\right)^{6} + 2 \, \cosh\left(f x + e\right)^{4} + 3 \, \cosh\left(f x + e\right)^{2}\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right) + {\left(5 \, \cosh\left(f x + e\right)^{7} + 2 \, \cosh\left(f x + e\right)^{5} + 5 \, \cosh\left(f x + e\right)^{3}\right)} e^{\left(f x + e\right)}\right)} \sqrt{a e^{\left(4 \, f x + 4 \, e\right)} + 2 \, a e^{\left(2 \, f x + 2 \, e\right)} + a} e^{\left(-f x - e\right)}}{15 \, {\left(a^{2} f \cosh\left(f x + e\right)^{10} - 5 \, a^{2} f \cosh\left(f x + e\right)^{8} + {\left(a^{2} f e^{\left(2 \, f x + 2 \, e\right)} + a^{2} f\right)} \sinh\left(f x + e\right)^{10} + 10 \, {\left(a^{2} f \cosh\left(f x + e\right) e^{\left(2 \, f x + 2 \, e\right)} + a^{2} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{9} + 10 \, a^{2} f \cosh\left(f x + e\right)^{6} + 5 \, {\left(9 \, a^{2} f \cosh\left(f x + e\right)^{2} - a^{2} f + {\left(9 \, a^{2} f \cosh\left(f x + e\right)^{2} - a^{2} f\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)^{8} + 40 \, {\left(3 \, a^{2} f \cosh\left(f x + e\right)^{3} - a^{2} f \cosh\left(f x + e\right) + {\left(3 \, a^{2} f \cosh\left(f x + e\right)^{3} - a^{2} f \cosh\left(f x + e\right)\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)^{7} - 10 \, a^{2} f \cosh\left(f x + e\right)^{4} + 10 \, {\left(21 \, a^{2} f \cosh\left(f x + e\right)^{4} - 14 \, a^{2} f \cosh\left(f x + e\right)^{2} + a^{2} f + {\left(21 \, a^{2} f \cosh\left(f x + e\right)^{4} - 14 \, a^{2} f \cosh\left(f x + e\right)^{2} + a^{2} f\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)^{6} + 4 \, {\left(63 \, a^{2} f \cosh\left(f x + e\right)^{5} - 70 \, a^{2} f \cosh\left(f x + e\right)^{3} + 15 \, a^{2} f \cosh\left(f x + e\right) + {\left(63 \, a^{2} f \cosh\left(f x + e\right)^{5} - 70 \, a^{2} f \cosh\left(f x + e\right)^{3} + 15 \, a^{2} f \cosh\left(f x + e\right)\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)^{5} + 5 \, a^{2} f \cosh\left(f x + e\right)^{2} + 10 \, {\left(21 \, a^{2} f \cosh\left(f x + e\right)^{6} - 35 \, a^{2} f \cosh\left(f x + e\right)^{4} + 15 \, a^{2} f \cosh\left(f x + e\right)^{2} - a^{2} f + {\left(21 \, a^{2} f \cosh\left(f x + e\right)^{6} - 35 \, a^{2} f \cosh\left(f x + e\right)^{4} + 15 \, a^{2} f \cosh\left(f x + e\right)^{2} - a^{2} f\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)^{4} + 40 \, {\left(3 \, a^{2} f \cosh\left(f x + e\right)^{7} - 7 \, a^{2} f \cosh\left(f x + e\right)^{5} + 5 \, a^{2} f \cosh\left(f x + e\right)^{3} - a^{2} f \cosh\left(f x + e\right) + {\left(3 \, a^{2} f \cosh\left(f x + e\right)^{7} - 7 \, a^{2} f \cosh\left(f x + e\right)^{5} + 5 \, a^{2} f \cosh\left(f x + e\right)^{3} - a^{2} f \cosh\left(f x + e\right)\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)^{3} - a^{2} f + 5 \, {\left(9 \, a^{2} f \cosh\left(f x + e\right)^{8} - 28 \, a^{2} f \cosh\left(f x + e\right)^{6} + 30 \, a^{2} f \cosh\left(f x + e\right)^{4} - 12 \, a^{2} f \cosh\left(f x + e\right)^{2} + a^{2} f + {\left(9 \, a^{2} f \cosh\left(f x + e\right)^{8} - 28 \, a^{2} f \cosh\left(f x + e\right)^{6} + 30 \, a^{2} f \cosh\left(f x + e\right)^{4} - 12 \, a^{2} f \cosh\left(f x + e\right)^{2} + a^{2} f\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)^{2} + {\left(a^{2} f \cosh\left(f x + e\right)^{10} - 5 \, a^{2} f \cosh\left(f x + e\right)^{8} + 10 \, a^{2} f \cosh\left(f x + e\right)^{6} - 10 \, a^{2} f \cosh\left(f x + e\right)^{4} + 5 \, a^{2} f \cosh\left(f x + e\right)^{2} - a^{2} f\right)} e^{\left(2 \, f x + 2 \, e\right)} + 10 \, {\left(a^{2} f \cosh\left(f x + e\right)^{9} - 4 \, a^{2} f \cosh\left(f x + e\right)^{7} + 6 \, a^{2} f \cosh\left(f x + e\right)^{5} - 4 \, a^{2} f \cosh\left(f x + e\right)^{3} + a^{2} f \cosh\left(f x + e\right) + {\left(a^{2} f \cosh\left(f x + e\right)^{9} - 4 \, a^{2} f \cosh\left(f x + e\right)^{7} + 6 \, a^{2} f \cosh\left(f x + e\right)^{5} - 4 \, a^{2} f \cosh\left(f x + e\right)^{3} + a^{2} f \cosh\left(f x + e\right)\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)\right)}}"," ",0,"-8/15*(35*cosh(f*x + e)*e^(f*x + e)*sinh(f*x + e)^6 + 5*e^(f*x + e)*sinh(f*x + e)^7 + (105*cosh(f*x + e)^2 + 2)*e^(f*x + e)*sinh(f*x + e)^5 + 5*(35*cosh(f*x + e)^3 + 2*cosh(f*x + e))*e^(f*x + e)*sinh(f*x + e)^4 + 5*(35*cosh(f*x + e)^4 + 4*cosh(f*x + e)^2 + 1)*e^(f*x + e)*sinh(f*x + e)^3 + 5*(21*cosh(f*x + e)^5 + 4*cosh(f*x + e)^3 + 3*cosh(f*x + e))*e^(f*x + e)*sinh(f*x + e)^2 + 5*(7*cosh(f*x + e)^6 + 2*cosh(f*x + e)^4 + 3*cosh(f*x + e)^2)*e^(f*x + e)*sinh(f*x + e) + (5*cosh(f*x + e)^7 + 2*cosh(f*x + e)^5 + 5*cosh(f*x + e)^3)*e^(f*x + e))*sqrt(a*e^(4*f*x + 4*e) + 2*a*e^(2*f*x + 2*e) + a)*e^(-f*x - e)/(a^2*f*cosh(f*x + e)^10 - 5*a^2*f*cosh(f*x + e)^8 + (a^2*f*e^(2*f*x + 2*e) + a^2*f)*sinh(f*x + e)^10 + 10*(a^2*f*cosh(f*x + e)*e^(2*f*x + 2*e) + a^2*f*cosh(f*x + e))*sinh(f*x + e)^9 + 10*a^2*f*cosh(f*x + e)^6 + 5*(9*a^2*f*cosh(f*x + e)^2 - a^2*f + (9*a^2*f*cosh(f*x + e)^2 - a^2*f)*e^(2*f*x + 2*e))*sinh(f*x + e)^8 + 40*(3*a^2*f*cosh(f*x + e)^3 - a^2*f*cosh(f*x + e) + (3*a^2*f*cosh(f*x + e)^3 - a^2*f*cosh(f*x + e))*e^(2*f*x + 2*e))*sinh(f*x + e)^7 - 10*a^2*f*cosh(f*x + e)^4 + 10*(21*a^2*f*cosh(f*x + e)^4 - 14*a^2*f*cosh(f*x + e)^2 + a^2*f + (21*a^2*f*cosh(f*x + e)^4 - 14*a^2*f*cosh(f*x + e)^2 + a^2*f)*e^(2*f*x + 2*e))*sinh(f*x + e)^6 + 4*(63*a^2*f*cosh(f*x + e)^5 - 70*a^2*f*cosh(f*x + e)^3 + 15*a^2*f*cosh(f*x + e) + (63*a^2*f*cosh(f*x + e)^5 - 70*a^2*f*cosh(f*x + e)^3 + 15*a^2*f*cosh(f*x + e))*e^(2*f*x + 2*e))*sinh(f*x + e)^5 + 5*a^2*f*cosh(f*x + e)^2 + 10*(21*a^2*f*cosh(f*x + e)^6 - 35*a^2*f*cosh(f*x + e)^4 + 15*a^2*f*cosh(f*x + e)^2 - a^2*f + (21*a^2*f*cosh(f*x + e)^6 - 35*a^2*f*cosh(f*x + e)^4 + 15*a^2*f*cosh(f*x + e)^2 - a^2*f)*e^(2*f*x + 2*e))*sinh(f*x + e)^4 + 40*(3*a^2*f*cosh(f*x + e)^7 - 7*a^2*f*cosh(f*x + e)^5 + 5*a^2*f*cosh(f*x + e)^3 - a^2*f*cosh(f*x + e) + (3*a^2*f*cosh(f*x + e)^7 - 7*a^2*f*cosh(f*x + e)^5 + 5*a^2*f*cosh(f*x + e)^3 - a^2*f*cosh(f*x + e))*e^(2*f*x + 2*e))*sinh(f*x + e)^3 - a^2*f + 5*(9*a^2*f*cosh(f*x + e)^8 - 28*a^2*f*cosh(f*x + e)^6 + 30*a^2*f*cosh(f*x + e)^4 - 12*a^2*f*cosh(f*x + e)^2 + a^2*f + (9*a^2*f*cosh(f*x + e)^8 - 28*a^2*f*cosh(f*x + e)^6 + 30*a^2*f*cosh(f*x + e)^4 - 12*a^2*f*cosh(f*x + e)^2 + a^2*f)*e^(2*f*x + 2*e))*sinh(f*x + e)^2 + (a^2*f*cosh(f*x + e)^10 - 5*a^2*f*cosh(f*x + e)^8 + 10*a^2*f*cosh(f*x + e)^6 - 10*a^2*f*cosh(f*x + e)^4 + 5*a^2*f*cosh(f*x + e)^2 - a^2*f)*e^(2*f*x + 2*e) + 10*(a^2*f*cosh(f*x + e)^9 - 4*a^2*f*cosh(f*x + e)^7 + 6*a^2*f*cosh(f*x + e)^5 - 4*a^2*f*cosh(f*x + e)^3 + a^2*f*cosh(f*x + e) + (a^2*f*cosh(f*x + e)^9 - 4*a^2*f*cosh(f*x + e)^7 + 6*a^2*f*cosh(f*x + e)^5 - 4*a^2*f*cosh(f*x + e)^3 + a^2*f*cosh(f*x + e))*e^(2*f*x + 2*e))*sinh(f*x + e))","B",0
456,1,2511,0,0.565091," ","integrate(coth(f*x+e)^8/(a+a*sinh(f*x+e)^2)^(3/2),x, algorithm=""fricas"")","-\frac{8 \, {\left(385 \, \cosh\left(f x + e\right) e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{10} + 35 \, e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{11} + 7 \, {\left(275 \, \cosh\left(f x + e\right)^{2} + 4\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{9} + 21 \, {\left(275 \, \cosh\left(f x + e\right)^{3} + 12 \, \cosh\left(f x + e\right)\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{8} + 6 \, {\left(1925 \, \cosh\left(f x + e\right)^{4} + 168 \, \cosh\left(f x + e\right)^{2} + 19\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{7} + 42 \, {\left(385 \, \cosh\left(f x + e\right)^{5} + 56 \, \cosh\left(f x + e\right)^{3} + 19 \, \cosh\left(f x + e\right)\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{6} + 14 \, {\left(1155 \, \cosh\left(f x + e\right)^{6} + 252 \, \cosh\left(f x + e\right)^{4} + 171 \, \cosh\left(f x + e\right)^{2} + 2\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{5} + 14 \, {\left(825 \, \cosh\left(f x + e\right)^{7} + 252 \, \cosh\left(f x + e\right)^{5} + 285 \, \cosh\left(f x + e\right)^{3} + 10 \, \cosh\left(f x + e\right)\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{4} + 7 \, {\left(825 \, \cosh\left(f x + e\right)^{8} + 336 \, \cosh\left(f x + e\right)^{6} + 570 \, \cosh\left(f x + e\right)^{4} + 40 \, \cosh\left(f x + e\right)^{2} + 5\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{3} + 7 \, {\left(275 \, \cosh\left(f x + e\right)^{9} + 144 \, \cosh\left(f x + e\right)^{7} + 342 \, \cosh\left(f x + e\right)^{5} + 40 \, \cosh\left(f x + e\right)^{3} + 15 \, \cosh\left(f x + e\right)\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right)^{2} + 7 \, {\left(55 \, \cosh\left(f x + e\right)^{10} + 36 \, \cosh\left(f x + e\right)^{8} + 114 \, \cosh\left(f x + e\right)^{6} + 20 \, \cosh\left(f x + e\right)^{4} + 15 \, \cosh\left(f x + e\right)^{2}\right)} e^{\left(f x + e\right)} \sinh\left(f x + e\right) + {\left(35 \, \cosh\left(f x + e\right)^{11} + 28 \, \cosh\left(f x + e\right)^{9} + 114 \, \cosh\left(f x + e\right)^{7} + 28 \, \cosh\left(f x + e\right)^{5} + 35 \, \cosh\left(f x + e\right)^{3}\right)} e^{\left(f x + e\right)}\right)} \sqrt{a e^{\left(4 \, f x + 4 \, e\right)} + 2 \, a e^{\left(2 \, f x + 2 \, e\right)} + a} e^{\left(-f x - e\right)}}{105 \, {\left(a^{2} f \cosh\left(f x + e\right)^{14} - 7 \, a^{2} f \cosh\left(f x + e\right)^{12} + {\left(a^{2} f e^{\left(2 \, f x + 2 \, e\right)} + a^{2} f\right)} \sinh\left(f x + e\right)^{14} + 14 \, {\left(a^{2} f \cosh\left(f x + e\right) e^{\left(2 \, f x + 2 \, e\right)} + a^{2} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{13} + 21 \, a^{2} f \cosh\left(f x + e\right)^{10} + 7 \, {\left(13 \, a^{2} f \cosh\left(f x + e\right)^{2} - a^{2} f + {\left(13 \, a^{2} f \cosh\left(f x + e\right)^{2} - a^{2} f\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)^{12} + 28 \, {\left(13 \, a^{2} f \cosh\left(f x + e\right)^{3} - 3 \, a^{2} f \cosh\left(f x + e\right) + {\left(13 \, a^{2} f \cosh\left(f x + e\right)^{3} - 3 \, a^{2} f \cosh\left(f x + e\right)\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)^{11} - 35 \, a^{2} f \cosh\left(f x + e\right)^{8} + 7 \, {\left(143 \, a^{2} f \cosh\left(f x + e\right)^{4} - 66 \, a^{2} f \cosh\left(f x + e\right)^{2} + 3 \, a^{2} f + {\left(143 \, a^{2} f \cosh\left(f x + e\right)^{4} - 66 \, a^{2} f \cosh\left(f x + e\right)^{2} + 3 \, a^{2} f\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)^{10} + 14 \, {\left(143 \, a^{2} f \cosh\left(f x + e\right)^{5} - 110 \, a^{2} f \cosh\left(f x + e\right)^{3} + 15 \, a^{2} f \cosh\left(f x + e\right) + {\left(143 \, a^{2} f \cosh\left(f x + e\right)^{5} - 110 \, a^{2} f \cosh\left(f x + e\right)^{3} + 15 \, a^{2} f \cosh\left(f x + e\right)\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)^{9} + 35 \, a^{2} f \cosh\left(f x + e\right)^{6} + 7 \, {\left(429 \, a^{2} f \cosh\left(f x + e\right)^{6} - 495 \, a^{2} f \cosh\left(f x + e\right)^{4} + 135 \, a^{2} f \cosh\left(f x + e\right)^{2} - 5 \, a^{2} f + {\left(429 \, a^{2} f \cosh\left(f x + e\right)^{6} - 495 \, a^{2} f \cosh\left(f x + e\right)^{4} + 135 \, a^{2} f \cosh\left(f x + e\right)^{2} - 5 \, a^{2} f\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)^{8} + 8 \, {\left(429 \, a^{2} f \cosh\left(f x + e\right)^{7} - 693 \, a^{2} f \cosh\left(f x + e\right)^{5} + 315 \, a^{2} f \cosh\left(f x + e\right)^{3} - 35 \, a^{2} f \cosh\left(f x + e\right) + {\left(429 \, a^{2} f \cosh\left(f x + e\right)^{7} - 693 \, a^{2} f \cosh\left(f x + e\right)^{5} + 315 \, a^{2} f \cosh\left(f x + e\right)^{3} - 35 \, a^{2} f \cosh\left(f x + e\right)\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)^{7} - 21 \, a^{2} f \cosh\left(f x + e\right)^{4} + 7 \, {\left(429 \, a^{2} f \cosh\left(f x + e\right)^{8} - 924 \, a^{2} f \cosh\left(f x + e\right)^{6} + 630 \, a^{2} f \cosh\left(f x + e\right)^{4} - 140 \, a^{2} f \cosh\left(f x + e\right)^{2} + 5 \, a^{2} f + {\left(429 \, a^{2} f \cosh\left(f x + e\right)^{8} - 924 \, a^{2} f \cosh\left(f x + e\right)^{6} + 630 \, a^{2} f \cosh\left(f x + e\right)^{4} - 140 \, a^{2} f \cosh\left(f x + e\right)^{2} + 5 \, a^{2} f\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)^{6} + 14 \, {\left(143 \, a^{2} f \cosh\left(f x + e\right)^{9} - 396 \, a^{2} f \cosh\left(f x + e\right)^{7} + 378 \, a^{2} f \cosh\left(f x + e\right)^{5} - 140 \, a^{2} f \cosh\left(f x + e\right)^{3} + 15 \, a^{2} f \cosh\left(f x + e\right) + {\left(143 \, a^{2} f \cosh\left(f x + e\right)^{9} - 396 \, a^{2} f \cosh\left(f x + e\right)^{7} + 378 \, a^{2} f \cosh\left(f x + e\right)^{5} - 140 \, a^{2} f \cosh\left(f x + e\right)^{3} + 15 \, a^{2} f \cosh\left(f x + e\right)\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)^{5} + 7 \, a^{2} f \cosh\left(f x + e\right)^{2} + 7 \, {\left(143 \, a^{2} f \cosh\left(f x + e\right)^{10} - 495 \, a^{2} f \cosh\left(f x + e\right)^{8} + 630 \, a^{2} f \cosh\left(f x + e\right)^{6} - 350 \, a^{2} f \cosh\left(f x + e\right)^{4} + 75 \, a^{2} f \cosh\left(f x + e\right)^{2} - 3 \, a^{2} f + {\left(143 \, a^{2} f \cosh\left(f x + e\right)^{10} - 495 \, a^{2} f \cosh\left(f x + e\right)^{8} + 630 \, a^{2} f \cosh\left(f x + e\right)^{6} - 350 \, a^{2} f \cosh\left(f x + e\right)^{4} + 75 \, a^{2} f \cosh\left(f x + e\right)^{2} - 3 \, a^{2} f\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)^{4} + 28 \, {\left(13 \, a^{2} f \cosh\left(f x + e\right)^{11} - 55 \, a^{2} f \cosh\left(f x + e\right)^{9} + 90 \, a^{2} f \cosh\left(f x + e\right)^{7} - 70 \, a^{2} f \cosh\left(f x + e\right)^{5} + 25 \, a^{2} f \cosh\left(f x + e\right)^{3} - 3 \, a^{2} f \cosh\left(f x + e\right) + {\left(13 \, a^{2} f \cosh\left(f x + e\right)^{11} - 55 \, a^{2} f \cosh\left(f x + e\right)^{9} + 90 \, a^{2} f \cosh\left(f x + e\right)^{7} - 70 \, a^{2} f \cosh\left(f x + e\right)^{5} + 25 \, a^{2} f \cosh\left(f x + e\right)^{3} - 3 \, a^{2} f \cosh\left(f x + e\right)\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)^{3} - a^{2} f + 7 \, {\left(13 \, a^{2} f \cosh\left(f x + e\right)^{12} - 66 \, a^{2} f \cosh\left(f x + e\right)^{10} + 135 \, a^{2} f \cosh\left(f x + e\right)^{8} - 140 \, a^{2} f \cosh\left(f x + e\right)^{6} + 75 \, a^{2} f \cosh\left(f x + e\right)^{4} - 18 \, a^{2} f \cosh\left(f x + e\right)^{2} + a^{2} f + {\left(13 \, a^{2} f \cosh\left(f x + e\right)^{12} - 66 \, a^{2} f \cosh\left(f x + e\right)^{10} + 135 \, a^{2} f \cosh\left(f x + e\right)^{8} - 140 \, a^{2} f \cosh\left(f x + e\right)^{6} + 75 \, a^{2} f \cosh\left(f x + e\right)^{4} - 18 \, a^{2} f \cosh\left(f x + e\right)^{2} + a^{2} f\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)^{2} + {\left(a^{2} f \cosh\left(f x + e\right)^{14} - 7 \, a^{2} f \cosh\left(f x + e\right)^{12} + 21 \, a^{2} f \cosh\left(f x + e\right)^{10} - 35 \, a^{2} f \cosh\left(f x + e\right)^{8} + 35 \, a^{2} f \cosh\left(f x + e\right)^{6} - 21 \, a^{2} f \cosh\left(f x + e\right)^{4} + 7 \, a^{2} f \cosh\left(f x + e\right)^{2} - a^{2} f\right)} e^{\left(2 \, f x + 2 \, e\right)} + 14 \, {\left(a^{2} f \cosh\left(f x + e\right)^{13} - 6 \, a^{2} f \cosh\left(f x + e\right)^{11} + 15 \, a^{2} f \cosh\left(f x + e\right)^{9} - 20 \, a^{2} f \cosh\left(f x + e\right)^{7} + 15 \, a^{2} f \cosh\left(f x + e\right)^{5} - 6 \, a^{2} f \cosh\left(f x + e\right)^{3} + a^{2} f \cosh\left(f x + e\right) + {\left(a^{2} f \cosh\left(f x + e\right)^{13} - 6 \, a^{2} f \cosh\left(f x + e\right)^{11} + 15 \, a^{2} f \cosh\left(f x + e\right)^{9} - 20 \, a^{2} f \cosh\left(f x + e\right)^{7} + 15 \, a^{2} f \cosh\left(f x + e\right)^{5} - 6 \, a^{2} f \cosh\left(f x + e\right)^{3} + a^{2} f \cosh\left(f x + e\right)\right)} e^{\left(2 \, f x + 2 \, e\right)}\right)} \sinh\left(f x + e\right)\right)}}"," ",0,"-8/105*(385*cosh(f*x + e)*e^(f*x + e)*sinh(f*x + e)^10 + 35*e^(f*x + e)*sinh(f*x + e)^11 + 7*(275*cosh(f*x + e)^2 + 4)*e^(f*x + e)*sinh(f*x + e)^9 + 21*(275*cosh(f*x + e)^3 + 12*cosh(f*x + e))*e^(f*x + e)*sinh(f*x + e)^8 + 6*(1925*cosh(f*x + e)^4 + 168*cosh(f*x + e)^2 + 19)*e^(f*x + e)*sinh(f*x + e)^7 + 42*(385*cosh(f*x + e)^5 + 56*cosh(f*x + e)^3 + 19*cosh(f*x + e))*e^(f*x + e)*sinh(f*x + e)^6 + 14*(1155*cosh(f*x + e)^6 + 252*cosh(f*x + e)^4 + 171*cosh(f*x + e)^2 + 2)*e^(f*x + e)*sinh(f*x + e)^5 + 14*(825*cosh(f*x + e)^7 + 252*cosh(f*x + e)^5 + 285*cosh(f*x + e)^3 + 10*cosh(f*x + e))*e^(f*x + e)*sinh(f*x + e)^4 + 7*(825*cosh(f*x + e)^8 + 336*cosh(f*x + e)^6 + 570*cosh(f*x + e)^4 + 40*cosh(f*x + e)^2 + 5)*e^(f*x + e)*sinh(f*x + e)^3 + 7*(275*cosh(f*x + e)^9 + 144*cosh(f*x + e)^7 + 342*cosh(f*x + e)^5 + 40*cosh(f*x + e)^3 + 15*cosh(f*x + e))*e^(f*x + e)*sinh(f*x + e)^2 + 7*(55*cosh(f*x + e)^10 + 36*cosh(f*x + e)^8 + 114*cosh(f*x + e)^6 + 20*cosh(f*x + e)^4 + 15*cosh(f*x + e)^2)*e^(f*x + e)*sinh(f*x + e) + (35*cosh(f*x + e)^11 + 28*cosh(f*x + e)^9 + 114*cosh(f*x + e)^7 + 28*cosh(f*x + e)^5 + 35*cosh(f*x + e)^3)*e^(f*x + e))*sqrt(a*e^(4*f*x + 4*e) + 2*a*e^(2*f*x + 2*e) + a)*e^(-f*x - e)/(a^2*f*cosh(f*x + e)^14 - 7*a^2*f*cosh(f*x + e)^12 + (a^2*f*e^(2*f*x + 2*e) + a^2*f)*sinh(f*x + e)^14 + 14*(a^2*f*cosh(f*x + e)*e^(2*f*x + 2*e) + a^2*f*cosh(f*x + e))*sinh(f*x + e)^13 + 21*a^2*f*cosh(f*x + e)^10 + 7*(13*a^2*f*cosh(f*x + e)^2 - a^2*f + (13*a^2*f*cosh(f*x + e)^2 - a^2*f)*e^(2*f*x + 2*e))*sinh(f*x + e)^12 + 28*(13*a^2*f*cosh(f*x + e)^3 - 3*a^2*f*cosh(f*x + e) + (13*a^2*f*cosh(f*x + e)^3 - 3*a^2*f*cosh(f*x + e))*e^(2*f*x + 2*e))*sinh(f*x + e)^11 - 35*a^2*f*cosh(f*x + e)^8 + 7*(143*a^2*f*cosh(f*x + e)^4 - 66*a^2*f*cosh(f*x + e)^2 + 3*a^2*f + (143*a^2*f*cosh(f*x + e)^4 - 66*a^2*f*cosh(f*x + e)^2 + 3*a^2*f)*e^(2*f*x + 2*e))*sinh(f*x + e)^10 + 14*(143*a^2*f*cosh(f*x + e)^5 - 110*a^2*f*cosh(f*x + e)^3 + 15*a^2*f*cosh(f*x + e) + (143*a^2*f*cosh(f*x + e)^5 - 110*a^2*f*cosh(f*x + e)^3 + 15*a^2*f*cosh(f*x + e))*e^(2*f*x + 2*e))*sinh(f*x + e)^9 + 35*a^2*f*cosh(f*x + e)^6 + 7*(429*a^2*f*cosh(f*x + e)^6 - 495*a^2*f*cosh(f*x + e)^4 + 135*a^2*f*cosh(f*x + e)^2 - 5*a^2*f + (429*a^2*f*cosh(f*x + e)^6 - 495*a^2*f*cosh(f*x + e)^4 + 135*a^2*f*cosh(f*x + e)^2 - 5*a^2*f)*e^(2*f*x + 2*e))*sinh(f*x + e)^8 + 8*(429*a^2*f*cosh(f*x + e)^7 - 693*a^2*f*cosh(f*x + e)^5 + 315*a^2*f*cosh(f*x + e)^3 - 35*a^2*f*cosh(f*x + e) + (429*a^2*f*cosh(f*x + e)^7 - 693*a^2*f*cosh(f*x + e)^5 + 315*a^2*f*cosh(f*x + e)^3 - 35*a^2*f*cosh(f*x + e))*e^(2*f*x + 2*e))*sinh(f*x + e)^7 - 21*a^2*f*cosh(f*x + e)^4 + 7*(429*a^2*f*cosh(f*x + e)^8 - 924*a^2*f*cosh(f*x + e)^6 + 630*a^2*f*cosh(f*x + e)^4 - 140*a^2*f*cosh(f*x + e)^2 + 5*a^2*f + (429*a^2*f*cosh(f*x + e)^8 - 924*a^2*f*cosh(f*x + e)^6 + 630*a^2*f*cosh(f*x + e)^4 - 140*a^2*f*cosh(f*x + e)^2 + 5*a^2*f)*e^(2*f*x + 2*e))*sinh(f*x + e)^6 + 14*(143*a^2*f*cosh(f*x + e)^9 - 396*a^2*f*cosh(f*x + e)^7 + 378*a^2*f*cosh(f*x + e)^5 - 140*a^2*f*cosh(f*x + e)^3 + 15*a^2*f*cosh(f*x + e) + (143*a^2*f*cosh(f*x + e)^9 - 396*a^2*f*cosh(f*x + e)^7 + 378*a^2*f*cosh(f*x + e)^5 - 140*a^2*f*cosh(f*x + e)^3 + 15*a^2*f*cosh(f*x + e))*e^(2*f*x + 2*e))*sinh(f*x + e)^5 + 7*a^2*f*cosh(f*x + e)^2 + 7*(143*a^2*f*cosh(f*x + e)^10 - 495*a^2*f*cosh(f*x + e)^8 + 630*a^2*f*cosh(f*x + e)^6 - 350*a^2*f*cosh(f*x + e)^4 + 75*a^2*f*cosh(f*x + e)^2 - 3*a^2*f + (143*a^2*f*cosh(f*x + e)^10 - 495*a^2*f*cosh(f*x + e)^8 + 630*a^2*f*cosh(f*x + e)^6 - 350*a^2*f*cosh(f*x + e)^4 + 75*a^2*f*cosh(f*x + e)^2 - 3*a^2*f)*e^(2*f*x + 2*e))*sinh(f*x + e)^4 + 28*(13*a^2*f*cosh(f*x + e)^11 - 55*a^2*f*cosh(f*x + e)^9 + 90*a^2*f*cosh(f*x + e)^7 - 70*a^2*f*cosh(f*x + e)^5 + 25*a^2*f*cosh(f*x + e)^3 - 3*a^2*f*cosh(f*x + e) + (13*a^2*f*cosh(f*x + e)^11 - 55*a^2*f*cosh(f*x + e)^9 + 90*a^2*f*cosh(f*x + e)^7 - 70*a^2*f*cosh(f*x + e)^5 + 25*a^2*f*cosh(f*x + e)^3 - 3*a^2*f*cosh(f*x + e))*e^(2*f*x + 2*e))*sinh(f*x + e)^3 - a^2*f + 7*(13*a^2*f*cosh(f*x + e)^12 - 66*a^2*f*cosh(f*x + e)^10 + 135*a^2*f*cosh(f*x + e)^8 - 140*a^2*f*cosh(f*x + e)^6 + 75*a^2*f*cosh(f*x + e)^4 - 18*a^2*f*cosh(f*x + e)^2 + a^2*f + (13*a^2*f*cosh(f*x + e)^12 - 66*a^2*f*cosh(f*x + e)^10 + 135*a^2*f*cosh(f*x + e)^8 - 140*a^2*f*cosh(f*x + e)^6 + 75*a^2*f*cosh(f*x + e)^4 - 18*a^2*f*cosh(f*x + e)^2 + a^2*f)*e^(2*f*x + 2*e))*sinh(f*x + e)^2 + (a^2*f*cosh(f*x + e)^14 - 7*a^2*f*cosh(f*x + e)^12 + 21*a^2*f*cosh(f*x + e)^10 - 35*a^2*f*cosh(f*x + e)^8 + 35*a^2*f*cosh(f*x + e)^6 - 21*a^2*f*cosh(f*x + e)^4 + 7*a^2*f*cosh(f*x + e)^2 - a^2*f)*e^(2*f*x + 2*e) + 14*(a^2*f*cosh(f*x + e)^13 - 6*a^2*f*cosh(f*x + e)^11 + 15*a^2*f*cosh(f*x + e)^9 - 20*a^2*f*cosh(f*x + e)^7 + 15*a^2*f*cosh(f*x + e)^5 - 6*a^2*f*cosh(f*x + e)^3 + a^2*f*cosh(f*x + e) + (a^2*f*cosh(f*x + e)^13 - 6*a^2*f*cosh(f*x + e)^11 + 15*a^2*f*cosh(f*x + e)^9 - 20*a^2*f*cosh(f*x + e)^7 + 15*a^2*f*cosh(f*x + e)^5 - 6*a^2*f*cosh(f*x + e)^3 + a^2*f*cosh(f*x + e))*e^(2*f*x + 2*e))*sinh(f*x + e))","B",0
457,1,4704,0,1.607137," ","integrate((a+b*sinh(f*x+e)^2)^(1/2)*tanh(f*x+e)^5,x, algorithm=""fricas"")","\left[-\frac{{\left({\left(8 \, a^{2} - 24 \, a b + 15 \, b^{2}\right)} \cosh\left(f x + e\right)^{9} + 9 \, {\left(8 \, a^{2} - 24 \, a b + 15 \, b^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{8} + {\left(8 \, a^{2} - 24 \, a b + 15 \, b^{2}\right)} \sinh\left(f x + e\right)^{9} + 4 \, {\left(8 \, a^{2} - 24 \, a b + 15 \, b^{2}\right)} \cosh\left(f x + e\right)^{7} + 4 \, {\left(9 \, {\left(8 \, a^{2} - 24 \, a b + 15 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + 8 \, a^{2} - 24 \, a b + 15 \, b^{2}\right)} \sinh\left(f x + e\right)^{7} + 28 \, {\left(3 \, {\left(8 \, a^{2} - 24 \, a b + 15 \, b^{2}\right)} \cosh\left(f x + e\right)^{3} + {\left(8 \, a^{2} - 24 \, a b + 15 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{6} + 6 \, {\left(8 \, a^{2} - 24 \, a b + 15 \, b^{2}\right)} \cosh\left(f x + e\right)^{5} + 6 \, {\left(21 \, {\left(8 \, a^{2} - 24 \, a b + 15 \, b^{2}\right)} \cosh\left(f x + e\right)^{4} + 14 \, {\left(8 \, a^{2} - 24 \, a b + 15 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + 8 \, a^{2} - 24 \, a b + 15 \, b^{2}\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(63 \, {\left(8 \, a^{2} - 24 \, a b + 15 \, b^{2}\right)} \cosh\left(f x + e\right)^{5} + 70 \, {\left(8 \, a^{2} - 24 \, a b + 15 \, b^{2}\right)} \cosh\left(f x + e\right)^{3} + 15 \, {\left(8 \, a^{2} - 24 \, a b + 15 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(8 \, a^{2} - 24 \, a b + 15 \, b^{2}\right)} \cosh\left(f x + e\right)^{3} + 4 \, {\left(21 \, {\left(8 \, a^{2} - 24 \, a b + 15 \, b^{2}\right)} \cosh\left(f x + e\right)^{6} + 35 \, {\left(8 \, a^{2} - 24 \, a b + 15 \, b^{2}\right)} \cosh\left(f x + e\right)^{4} + 15 \, {\left(8 \, a^{2} - 24 \, a b + 15 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + 8 \, a^{2} - 24 \, a b + 15 \, b^{2}\right)} \sinh\left(f x + e\right)^{3} + 12 \, {\left(3 \, {\left(8 \, a^{2} - 24 \, a b + 15 \, b^{2}\right)} \cosh\left(f x + e\right)^{7} + 7 \, {\left(8 \, a^{2} - 24 \, a b + 15 \, b^{2}\right)} \cosh\left(f x + e\right)^{5} + 5 \, {\left(8 \, a^{2} - 24 \, a b + 15 \, b^{2}\right)} \cosh\left(f x + e\right)^{3} + {\left(8 \, a^{2} - 24 \, a b + 15 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{2} + {\left(8 \, a^{2} - 24 \, a b + 15 \, b^{2}\right)} \cosh\left(f x + e\right) + {\left(9 \, {\left(8 \, a^{2} - 24 \, a b + 15 \, b^{2}\right)} \cosh\left(f x + e\right)^{8} + 28 \, {\left(8 \, a^{2} - 24 \, a b + 15 \, b^{2}\right)} \cosh\left(f x + e\right)^{6} + 30 \, {\left(8 \, a^{2} - 24 \, a b + 15 \, b^{2}\right)} \cosh\left(f x + e\right)^{4} + 12 \, {\left(8 \, a^{2} - 24 \, a b + 15 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + 8 \, a^{2} - 24 \, a b + 15 \, b^{2}\right)} \sinh\left(f x + e\right)\right)} \sqrt{a - b} \log\left(\frac{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(4 \, a - 3 \, b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + 4 \, a - 3 \, b\right)} \sinh\left(f x + e\right)^{2} + 4 \, \sqrt{2} \sqrt{a - b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} {\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right)\right)} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(4 \, a - 3 \, b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}{\cosh\left(f x + e\right)^{4} + 4 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + \sinh\left(f x + e\right)^{4} + 2 \, {\left(3 \, \cosh\left(f x + e\right)^{2} + 1\right)} \sinh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right)^{2} + 4 \, {\left(\cosh\left(f x + e\right)^{3} + \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + 1}\right) - 4 \, \sqrt{2} {\left(2 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{8} + 16 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + 2 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \sinh\left(f x + e\right)^{8} + {\left(16 \, a^{2} - 33 \, a b + 17 \, b^{2}\right)} \cosh\left(f x + e\right)^{6} + {\left(56 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{2} + 16 \, a^{2} - 33 \, a b + 17 \, b^{2}\right)} \sinh\left(f x + e\right)^{6} + 2 \, {\left(56 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(16 \, a^{2} - 33 \, a b + 17 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(10 \, a^{2} - 21 \, a b + 11 \, b^{2}\right)} \cosh\left(f x + e\right)^{4} + {\left(140 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{4} + 15 \, {\left(16 \, a^{2} - 33 \, a b + 17 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + 20 \, a^{2} - 42 \, a b + 22 \, b^{2}\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(28 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{5} + 5 \, {\left(16 \, a^{2} - 33 \, a b + 17 \, b^{2}\right)} \cosh\left(f x + e\right)^{3} + 2 \, {\left(10 \, a^{2} - 21 \, a b + 11 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + {\left(16 \, a^{2} - 33 \, a b + 17 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + {\left(56 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{6} + 15 \, {\left(16 \, a^{2} - 33 \, a b + 17 \, b^{2}\right)} \cosh\left(f x + e\right)^{4} + 12 \, {\left(10 \, a^{2} - 21 \, a b + 11 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + 16 \, a^{2} - 33 \, a b + 17 \, b^{2}\right)} \sinh\left(f x + e\right)^{2} + 2 \, a^{2} - 4 \, a b + 2 \, b^{2} + 2 \, {\left(8 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{7} + 3 \, {\left(16 \, a^{2} - 33 \, a b + 17 \, b^{2}\right)} \cosh\left(f x + e\right)^{5} + 4 \, {\left(10 \, a^{2} - 21 \, a b + 11 \, b^{2}\right)} \cosh\left(f x + e\right)^{3} + {\left(16 \, a^{2} - 33 \, a b + 17 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{16 \, {\left({\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{9} + 9 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{8} + {\left(a^{2} - 2 \, a b + b^{2}\right)} f \sinh\left(f x + e\right)^{9} + 4 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{7} + 4 \, {\left(9 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{2} + {\left(a^{2} - 2 \, a b + b^{2}\right)} f\right)} \sinh\left(f x + e\right)^{7} + 6 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{5} + 28 \, {\left(3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{3} + {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{6} + 6 \, {\left(21 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{4} + 14 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{2} + {\left(a^{2} - 2 \, a b + b^{2}\right)} f\right)} \sinh\left(f x + e\right)^{5} + 4 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{3} + 2 \, {\left(63 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{5} + 70 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{3} + 15 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(21 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{6} + 35 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{4} + 15 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{2} + {\left(a^{2} - 2 \, a b + b^{2}\right)} f\right)} \sinh\left(f x + e\right)^{3} + {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right) + 12 \, {\left(3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{7} + 7 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{5} + 5 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{3} + {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{2} + {\left(9 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{8} + 28 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{6} + 30 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{4} + 12 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{2} + {\left(a^{2} - 2 \, a b + b^{2}\right)} f\right)} \sinh\left(f x + e\right)\right)}}, -\frac{{\left({\left(8 \, a^{2} - 24 \, a b + 15 \, b^{2}\right)} \cosh\left(f x + e\right)^{9} + 9 \, {\left(8 \, a^{2} - 24 \, a b + 15 \, b^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{8} + {\left(8 \, a^{2} - 24 \, a b + 15 \, b^{2}\right)} \sinh\left(f x + e\right)^{9} + 4 \, {\left(8 \, a^{2} - 24 \, a b + 15 \, b^{2}\right)} \cosh\left(f x + e\right)^{7} + 4 \, {\left(9 \, {\left(8 \, a^{2} - 24 \, a b + 15 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + 8 \, a^{2} - 24 \, a b + 15 \, b^{2}\right)} \sinh\left(f x + e\right)^{7} + 28 \, {\left(3 \, {\left(8 \, a^{2} - 24 \, a b + 15 \, b^{2}\right)} \cosh\left(f x + e\right)^{3} + {\left(8 \, a^{2} - 24 \, a b + 15 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{6} + 6 \, {\left(8 \, a^{2} - 24 \, a b + 15 \, b^{2}\right)} \cosh\left(f x + e\right)^{5} + 6 \, {\left(21 \, {\left(8 \, a^{2} - 24 \, a b + 15 \, b^{2}\right)} \cosh\left(f x + e\right)^{4} + 14 \, {\left(8 \, a^{2} - 24 \, a b + 15 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + 8 \, a^{2} - 24 \, a b + 15 \, b^{2}\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(63 \, {\left(8 \, a^{2} - 24 \, a b + 15 \, b^{2}\right)} \cosh\left(f x + e\right)^{5} + 70 \, {\left(8 \, a^{2} - 24 \, a b + 15 \, b^{2}\right)} \cosh\left(f x + e\right)^{3} + 15 \, {\left(8 \, a^{2} - 24 \, a b + 15 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(8 \, a^{2} - 24 \, a b + 15 \, b^{2}\right)} \cosh\left(f x + e\right)^{3} + 4 \, {\left(21 \, {\left(8 \, a^{2} - 24 \, a b + 15 \, b^{2}\right)} \cosh\left(f x + e\right)^{6} + 35 \, {\left(8 \, a^{2} - 24 \, a b + 15 \, b^{2}\right)} \cosh\left(f x + e\right)^{4} + 15 \, {\left(8 \, a^{2} - 24 \, a b + 15 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + 8 \, a^{2} - 24 \, a b + 15 \, b^{2}\right)} \sinh\left(f x + e\right)^{3} + 12 \, {\left(3 \, {\left(8 \, a^{2} - 24 \, a b + 15 \, b^{2}\right)} \cosh\left(f x + e\right)^{7} + 7 \, {\left(8 \, a^{2} - 24 \, a b + 15 \, b^{2}\right)} \cosh\left(f x + e\right)^{5} + 5 \, {\left(8 \, a^{2} - 24 \, a b + 15 \, b^{2}\right)} \cosh\left(f x + e\right)^{3} + {\left(8 \, a^{2} - 24 \, a b + 15 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{2} + {\left(8 \, a^{2} - 24 \, a b + 15 \, b^{2}\right)} \cosh\left(f x + e\right) + {\left(9 \, {\left(8 \, a^{2} - 24 \, a b + 15 \, b^{2}\right)} \cosh\left(f x + e\right)^{8} + 28 \, {\left(8 \, a^{2} - 24 \, a b + 15 \, b^{2}\right)} \cosh\left(f x + e\right)^{6} + 30 \, {\left(8 \, a^{2} - 24 \, a b + 15 \, b^{2}\right)} \cosh\left(f x + e\right)^{4} + 12 \, {\left(8 \, a^{2} - 24 \, a b + 15 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + 8 \, a^{2} - 24 \, a b + 15 \, b^{2}\right)} \sinh\left(f x + e\right)\right)} \sqrt{-a + b} \arctan\left(-\frac{\sqrt{2} \sqrt{-a + b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{2 \, {\left({\left(a - b\right)} \cosh\left(f x + e\right) + {\left(a - b\right)} \sinh\left(f x + e\right)\right)}}\right) - 2 \, \sqrt{2} {\left(2 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{8} + 16 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + 2 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \sinh\left(f x + e\right)^{8} + {\left(16 \, a^{2} - 33 \, a b + 17 \, b^{2}\right)} \cosh\left(f x + e\right)^{6} + {\left(56 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{2} + 16 \, a^{2} - 33 \, a b + 17 \, b^{2}\right)} \sinh\left(f x + e\right)^{6} + 2 \, {\left(56 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(16 \, a^{2} - 33 \, a b + 17 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(10 \, a^{2} - 21 \, a b + 11 \, b^{2}\right)} \cosh\left(f x + e\right)^{4} + {\left(140 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{4} + 15 \, {\left(16 \, a^{2} - 33 \, a b + 17 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + 20 \, a^{2} - 42 \, a b + 22 \, b^{2}\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(28 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{5} + 5 \, {\left(16 \, a^{2} - 33 \, a b + 17 \, b^{2}\right)} \cosh\left(f x + e\right)^{3} + 2 \, {\left(10 \, a^{2} - 21 \, a b + 11 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + {\left(16 \, a^{2} - 33 \, a b + 17 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + {\left(56 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{6} + 15 \, {\left(16 \, a^{2} - 33 \, a b + 17 \, b^{2}\right)} \cosh\left(f x + e\right)^{4} + 12 \, {\left(10 \, a^{2} - 21 \, a b + 11 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + 16 \, a^{2} - 33 \, a b + 17 \, b^{2}\right)} \sinh\left(f x + e\right)^{2} + 2 \, a^{2} - 4 \, a b + 2 \, b^{2} + 2 \, {\left(8 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{7} + 3 \, {\left(16 \, a^{2} - 33 \, a b + 17 \, b^{2}\right)} \cosh\left(f x + e\right)^{5} + 4 \, {\left(10 \, a^{2} - 21 \, a b + 11 \, b^{2}\right)} \cosh\left(f x + e\right)^{3} + {\left(16 \, a^{2} - 33 \, a b + 17 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{8 \, {\left({\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{9} + 9 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{8} + {\left(a^{2} - 2 \, a b + b^{2}\right)} f \sinh\left(f x + e\right)^{9} + 4 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{7} + 4 \, {\left(9 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{2} + {\left(a^{2} - 2 \, a b + b^{2}\right)} f\right)} \sinh\left(f x + e\right)^{7} + 6 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{5} + 28 \, {\left(3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{3} + {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{6} + 6 \, {\left(21 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{4} + 14 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{2} + {\left(a^{2} - 2 \, a b + b^{2}\right)} f\right)} \sinh\left(f x + e\right)^{5} + 4 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{3} + 2 \, {\left(63 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{5} + 70 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{3} + 15 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(21 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{6} + 35 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{4} + 15 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{2} + {\left(a^{2} - 2 \, a b + b^{2}\right)} f\right)} \sinh\left(f x + e\right)^{3} + {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right) + 12 \, {\left(3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{7} + 7 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{5} + 5 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{3} + {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{2} + {\left(9 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{8} + 28 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{6} + 30 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{4} + 12 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{2} + {\left(a^{2} - 2 \, a b + b^{2}\right)} f\right)} \sinh\left(f x + e\right)\right)}}\right]"," ",0,"[-1/16*(((8*a^2 - 24*a*b + 15*b^2)*cosh(f*x + e)^9 + 9*(8*a^2 - 24*a*b + 15*b^2)*cosh(f*x + e)*sinh(f*x + e)^8 + (8*a^2 - 24*a*b + 15*b^2)*sinh(f*x + e)^9 + 4*(8*a^2 - 24*a*b + 15*b^2)*cosh(f*x + e)^7 + 4*(9*(8*a^2 - 24*a*b + 15*b^2)*cosh(f*x + e)^2 + 8*a^2 - 24*a*b + 15*b^2)*sinh(f*x + e)^7 + 28*(3*(8*a^2 - 24*a*b + 15*b^2)*cosh(f*x + e)^3 + (8*a^2 - 24*a*b + 15*b^2)*cosh(f*x + e))*sinh(f*x + e)^6 + 6*(8*a^2 - 24*a*b + 15*b^2)*cosh(f*x + e)^5 + 6*(21*(8*a^2 - 24*a*b + 15*b^2)*cosh(f*x + e)^4 + 14*(8*a^2 - 24*a*b + 15*b^2)*cosh(f*x + e)^2 + 8*a^2 - 24*a*b + 15*b^2)*sinh(f*x + e)^5 + 2*(63*(8*a^2 - 24*a*b + 15*b^2)*cosh(f*x + e)^5 + 70*(8*a^2 - 24*a*b + 15*b^2)*cosh(f*x + e)^3 + 15*(8*a^2 - 24*a*b + 15*b^2)*cosh(f*x + e))*sinh(f*x + e)^4 + 4*(8*a^2 - 24*a*b + 15*b^2)*cosh(f*x + e)^3 + 4*(21*(8*a^2 - 24*a*b + 15*b^2)*cosh(f*x + e)^6 + 35*(8*a^2 - 24*a*b + 15*b^2)*cosh(f*x + e)^4 + 15*(8*a^2 - 24*a*b + 15*b^2)*cosh(f*x + e)^2 + 8*a^2 - 24*a*b + 15*b^2)*sinh(f*x + e)^3 + 12*(3*(8*a^2 - 24*a*b + 15*b^2)*cosh(f*x + e)^7 + 7*(8*a^2 - 24*a*b + 15*b^2)*cosh(f*x + e)^5 + 5*(8*a^2 - 24*a*b + 15*b^2)*cosh(f*x + e)^3 + (8*a^2 - 24*a*b + 15*b^2)*cosh(f*x + e))*sinh(f*x + e)^2 + (8*a^2 - 24*a*b + 15*b^2)*cosh(f*x + e) + (9*(8*a^2 - 24*a*b + 15*b^2)*cosh(f*x + e)^8 + 28*(8*a^2 - 24*a*b + 15*b^2)*cosh(f*x + e)^6 + 30*(8*a^2 - 24*a*b + 15*b^2)*cosh(f*x + e)^4 + 12*(8*a^2 - 24*a*b + 15*b^2)*cosh(f*x + e)^2 + 8*a^2 - 24*a*b + 15*b^2)*sinh(f*x + e))*sqrt(a - b)*log((b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(4*a - 3*b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 4*a - 3*b)*sinh(f*x + e)^2 + 4*sqrt(2)*sqrt(a - b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))*(cosh(f*x + e) + sinh(f*x + e)) + 4*(b*cosh(f*x + e)^3 + (4*a - 3*b)*cosh(f*x + e))*sinh(f*x + e) + b)/(cosh(f*x + e)^4 + 4*cosh(f*x + e)*sinh(f*x + e)^3 + sinh(f*x + e)^4 + 2*(3*cosh(f*x + e)^2 + 1)*sinh(f*x + e)^2 + 2*cosh(f*x + e)^2 + 4*(cosh(f*x + e)^3 + cosh(f*x + e))*sinh(f*x + e) + 1)) - 4*sqrt(2)*(2*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^8 + 16*(a^2 - 2*a*b + b^2)*cosh(f*x + e)*sinh(f*x + e)^7 + 2*(a^2 - 2*a*b + b^2)*sinh(f*x + e)^8 + (16*a^2 - 33*a*b + 17*b^2)*cosh(f*x + e)^6 + (56*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^2 + 16*a^2 - 33*a*b + 17*b^2)*sinh(f*x + e)^6 + 2*(56*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^3 + 3*(16*a^2 - 33*a*b + 17*b^2)*cosh(f*x + e))*sinh(f*x + e)^5 + 2*(10*a^2 - 21*a*b + 11*b^2)*cosh(f*x + e)^4 + (140*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^4 + 15*(16*a^2 - 33*a*b + 17*b^2)*cosh(f*x + e)^2 + 20*a^2 - 42*a*b + 22*b^2)*sinh(f*x + e)^4 + 4*(28*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^5 + 5*(16*a^2 - 33*a*b + 17*b^2)*cosh(f*x + e)^3 + 2*(10*a^2 - 21*a*b + 11*b^2)*cosh(f*x + e))*sinh(f*x + e)^3 + (16*a^2 - 33*a*b + 17*b^2)*cosh(f*x + e)^2 + (56*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^6 + 15*(16*a^2 - 33*a*b + 17*b^2)*cosh(f*x + e)^4 + 12*(10*a^2 - 21*a*b + 11*b^2)*cosh(f*x + e)^2 + 16*a^2 - 33*a*b + 17*b^2)*sinh(f*x + e)^2 + 2*a^2 - 4*a*b + 2*b^2 + 2*(8*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^7 + 3*(16*a^2 - 33*a*b + 17*b^2)*cosh(f*x + e)^5 + 4*(10*a^2 - 21*a*b + 11*b^2)*cosh(f*x + e)^3 + (16*a^2 - 33*a*b + 17*b^2)*cosh(f*x + e))*sinh(f*x + e))*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/((a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^9 + 9*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)*sinh(f*x + e)^8 + (a^2 - 2*a*b + b^2)*f*sinh(f*x + e)^9 + 4*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^7 + 4*(9*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^2 + (a^2 - 2*a*b + b^2)*f)*sinh(f*x + e)^7 + 6*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^5 + 28*(3*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^3 + (a^2 - 2*a*b + b^2)*f*cosh(f*x + e))*sinh(f*x + e)^6 + 6*(21*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^4 + 14*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^2 + (a^2 - 2*a*b + b^2)*f)*sinh(f*x + e)^5 + 4*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^3 + 2*(63*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^5 + 70*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^3 + 15*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e))*sinh(f*x + e)^4 + 4*(21*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^6 + 35*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^4 + 15*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^2 + (a^2 - 2*a*b + b^2)*f)*sinh(f*x + e)^3 + (a^2 - 2*a*b + b^2)*f*cosh(f*x + e) + 12*(3*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^7 + 7*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^5 + 5*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^3 + (a^2 - 2*a*b + b^2)*f*cosh(f*x + e))*sinh(f*x + e)^2 + (9*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^8 + 28*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^6 + 30*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^4 + 12*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^2 + (a^2 - 2*a*b + b^2)*f)*sinh(f*x + e)), -1/8*(((8*a^2 - 24*a*b + 15*b^2)*cosh(f*x + e)^9 + 9*(8*a^2 - 24*a*b + 15*b^2)*cosh(f*x + e)*sinh(f*x + e)^8 + (8*a^2 - 24*a*b + 15*b^2)*sinh(f*x + e)^9 + 4*(8*a^2 - 24*a*b + 15*b^2)*cosh(f*x + e)^7 + 4*(9*(8*a^2 - 24*a*b + 15*b^2)*cosh(f*x + e)^2 + 8*a^2 - 24*a*b + 15*b^2)*sinh(f*x + e)^7 + 28*(3*(8*a^2 - 24*a*b + 15*b^2)*cosh(f*x + e)^3 + (8*a^2 - 24*a*b + 15*b^2)*cosh(f*x + e))*sinh(f*x + e)^6 + 6*(8*a^2 - 24*a*b + 15*b^2)*cosh(f*x + e)^5 + 6*(21*(8*a^2 - 24*a*b + 15*b^2)*cosh(f*x + e)^4 + 14*(8*a^2 - 24*a*b + 15*b^2)*cosh(f*x + e)^2 + 8*a^2 - 24*a*b + 15*b^2)*sinh(f*x + e)^5 + 2*(63*(8*a^2 - 24*a*b + 15*b^2)*cosh(f*x + e)^5 + 70*(8*a^2 - 24*a*b + 15*b^2)*cosh(f*x + e)^3 + 15*(8*a^2 - 24*a*b + 15*b^2)*cosh(f*x + e))*sinh(f*x + e)^4 + 4*(8*a^2 - 24*a*b + 15*b^2)*cosh(f*x + e)^3 + 4*(21*(8*a^2 - 24*a*b + 15*b^2)*cosh(f*x + e)^6 + 35*(8*a^2 - 24*a*b + 15*b^2)*cosh(f*x + e)^4 + 15*(8*a^2 - 24*a*b + 15*b^2)*cosh(f*x + e)^2 + 8*a^2 - 24*a*b + 15*b^2)*sinh(f*x + e)^3 + 12*(3*(8*a^2 - 24*a*b + 15*b^2)*cosh(f*x + e)^7 + 7*(8*a^2 - 24*a*b + 15*b^2)*cosh(f*x + e)^5 + 5*(8*a^2 - 24*a*b + 15*b^2)*cosh(f*x + e)^3 + (8*a^2 - 24*a*b + 15*b^2)*cosh(f*x + e))*sinh(f*x + e)^2 + (8*a^2 - 24*a*b + 15*b^2)*cosh(f*x + e) + (9*(8*a^2 - 24*a*b + 15*b^2)*cosh(f*x + e)^8 + 28*(8*a^2 - 24*a*b + 15*b^2)*cosh(f*x + e)^6 + 30*(8*a^2 - 24*a*b + 15*b^2)*cosh(f*x + e)^4 + 12*(8*a^2 - 24*a*b + 15*b^2)*cosh(f*x + e)^2 + 8*a^2 - 24*a*b + 15*b^2)*sinh(f*x + e))*sqrt(-a + b)*arctan(-1/2*sqrt(2)*sqrt(-a + b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/((a - b)*cosh(f*x + e) + (a - b)*sinh(f*x + e))) - 2*sqrt(2)*(2*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^8 + 16*(a^2 - 2*a*b + b^2)*cosh(f*x + e)*sinh(f*x + e)^7 + 2*(a^2 - 2*a*b + b^2)*sinh(f*x + e)^8 + (16*a^2 - 33*a*b + 17*b^2)*cosh(f*x + e)^6 + (56*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^2 + 16*a^2 - 33*a*b + 17*b^2)*sinh(f*x + e)^6 + 2*(56*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^3 + 3*(16*a^2 - 33*a*b + 17*b^2)*cosh(f*x + e))*sinh(f*x + e)^5 + 2*(10*a^2 - 21*a*b + 11*b^2)*cosh(f*x + e)^4 + (140*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^4 + 15*(16*a^2 - 33*a*b + 17*b^2)*cosh(f*x + e)^2 + 20*a^2 - 42*a*b + 22*b^2)*sinh(f*x + e)^4 + 4*(28*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^5 + 5*(16*a^2 - 33*a*b + 17*b^2)*cosh(f*x + e)^3 + 2*(10*a^2 - 21*a*b + 11*b^2)*cosh(f*x + e))*sinh(f*x + e)^3 + (16*a^2 - 33*a*b + 17*b^2)*cosh(f*x + e)^2 + (56*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^6 + 15*(16*a^2 - 33*a*b + 17*b^2)*cosh(f*x + e)^4 + 12*(10*a^2 - 21*a*b + 11*b^2)*cosh(f*x + e)^2 + 16*a^2 - 33*a*b + 17*b^2)*sinh(f*x + e)^2 + 2*a^2 - 4*a*b + 2*b^2 + 2*(8*(a^2 - 2*a*b + b^2)*cosh(f*x + e)^7 + 3*(16*a^2 - 33*a*b + 17*b^2)*cosh(f*x + e)^5 + 4*(10*a^2 - 21*a*b + 11*b^2)*cosh(f*x + e)^3 + (16*a^2 - 33*a*b + 17*b^2)*cosh(f*x + e))*sinh(f*x + e))*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/((a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^9 + 9*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)*sinh(f*x + e)^8 + (a^2 - 2*a*b + b^2)*f*sinh(f*x + e)^9 + 4*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^7 + 4*(9*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^2 + (a^2 - 2*a*b + b^2)*f)*sinh(f*x + e)^7 + 6*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^5 + 28*(3*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^3 + (a^2 - 2*a*b + b^2)*f*cosh(f*x + e))*sinh(f*x + e)^6 + 6*(21*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^4 + 14*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^2 + (a^2 - 2*a*b + b^2)*f)*sinh(f*x + e)^5 + 4*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^3 + 2*(63*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^5 + 70*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^3 + 15*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e))*sinh(f*x + e)^4 + 4*(21*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^6 + 35*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^4 + 15*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^2 + (a^2 - 2*a*b + b^2)*f)*sinh(f*x + e)^3 + (a^2 - 2*a*b + b^2)*f*cosh(f*x + e) + 12*(3*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^7 + 7*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^5 + 5*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^3 + (a^2 - 2*a*b + b^2)*f*cosh(f*x + e))*sinh(f*x + e)^2 + (9*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^8 + 28*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^6 + 30*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^4 + 12*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^2 + (a^2 - 2*a*b + b^2)*f)*sinh(f*x + e))]","B",0
458,1,1670,0,1.557550," ","integrate((a+b*sinh(f*x+e)^2)^(1/2)*tanh(f*x+e)^3,x, algorithm=""fricas"")","\left[-\frac{{\left({\left(2 \, a - 3 \, b\right)} \cosh\left(f x + e\right)^{5} + 5 \, {\left(2 \, a - 3 \, b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{4} + {\left(2 \, a - 3 \, b\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(2 \, a - 3 \, b\right)} \cosh\left(f x + e\right)^{3} + 2 \, {\left(5 \, {\left(2 \, a - 3 \, b\right)} \cosh\left(f x + e\right)^{2} + 2 \, a - 3 \, b\right)} \sinh\left(f x + e\right)^{3} + 2 \, {\left(5 \, {\left(2 \, a - 3 \, b\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(2 \, a - 3 \, b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{2} + {\left(2 \, a - 3 \, b\right)} \cosh\left(f x + e\right) + {\left(5 \, {\left(2 \, a - 3 \, b\right)} \cosh\left(f x + e\right)^{4} + 6 \, {\left(2 \, a - 3 \, b\right)} \cosh\left(f x + e\right)^{2} + 2 \, a - 3 \, b\right)} \sinh\left(f x + e\right)\right)} \sqrt{a - b} \log\left(\frac{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(4 \, a - 3 \, b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + 4 \, a - 3 \, b\right)} \sinh\left(f x + e\right)^{2} + 4 \, \sqrt{2} \sqrt{a - b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} {\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right)\right)} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(4 \, a - 3 \, b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}{\cosh\left(f x + e\right)^{4} + 4 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + \sinh\left(f x + e\right)^{4} + 2 \, {\left(3 \, \cosh\left(f x + e\right)^{2} + 1\right)} \sinh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right)^{2} + 4 \, {\left(\cosh\left(f x + e\right)^{3} + \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + 1}\right) - 2 \, \sqrt{2} {\left({\left(a - b\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left(a - b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(a - b\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, {\left(a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, a - 2 \, b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left({\left(a - b\right)} \cosh\left(f x + e\right)^{3} + 2 \, {\left(a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + a - b\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{4 \, {\left({\left(a - b\right)} f \cosh\left(f x + e\right)^{5} + 5 \, {\left(a - b\right)} f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{4} + {\left(a - b\right)} f \sinh\left(f x + e\right)^{5} + 2 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{3} + 2 \, {\left(5 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{2} + {\left(a - b\right)} f\right)} \sinh\left(f x + e\right)^{3} + {\left(a - b\right)} f \cosh\left(f x + e\right) + 2 \, {\left(5 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{3} + 3 \, {\left(a - b\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{2} + {\left(5 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{4} + 6 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{2} + {\left(a - b\right)} f\right)} \sinh\left(f x + e\right)\right)}}, -\frac{{\left({\left(2 \, a - 3 \, b\right)} \cosh\left(f x + e\right)^{5} + 5 \, {\left(2 \, a - 3 \, b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{4} + {\left(2 \, a - 3 \, b\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(2 \, a - 3 \, b\right)} \cosh\left(f x + e\right)^{3} + 2 \, {\left(5 \, {\left(2 \, a - 3 \, b\right)} \cosh\left(f x + e\right)^{2} + 2 \, a - 3 \, b\right)} \sinh\left(f x + e\right)^{3} + 2 \, {\left(5 \, {\left(2 \, a - 3 \, b\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(2 \, a - 3 \, b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{2} + {\left(2 \, a - 3 \, b\right)} \cosh\left(f x + e\right) + {\left(5 \, {\left(2 \, a - 3 \, b\right)} \cosh\left(f x + e\right)^{4} + 6 \, {\left(2 \, a - 3 \, b\right)} \cosh\left(f x + e\right)^{2} + 2 \, a - 3 \, b\right)} \sinh\left(f x + e\right)\right)} \sqrt{-a + b} \arctan\left(-\frac{\sqrt{2} \sqrt{-a + b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{2 \, {\left({\left(a - b\right)} \cosh\left(f x + e\right) + {\left(a - b\right)} \sinh\left(f x + e\right)\right)}}\right) - \sqrt{2} {\left({\left(a - b\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left(a - b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(a - b\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, {\left(a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, a - 2 \, b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left({\left(a - b\right)} \cosh\left(f x + e\right)^{3} + 2 \, {\left(a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + a - b\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{2 \, {\left({\left(a - b\right)} f \cosh\left(f x + e\right)^{5} + 5 \, {\left(a - b\right)} f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{4} + {\left(a - b\right)} f \sinh\left(f x + e\right)^{5} + 2 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{3} + 2 \, {\left(5 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{2} + {\left(a - b\right)} f\right)} \sinh\left(f x + e\right)^{3} + {\left(a - b\right)} f \cosh\left(f x + e\right) + 2 \, {\left(5 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{3} + 3 \, {\left(a - b\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{2} + {\left(5 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{4} + 6 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{2} + {\left(a - b\right)} f\right)} \sinh\left(f x + e\right)\right)}}\right]"," ",0,"[-1/4*(((2*a - 3*b)*cosh(f*x + e)^5 + 5*(2*a - 3*b)*cosh(f*x + e)*sinh(f*x + e)^4 + (2*a - 3*b)*sinh(f*x + e)^5 + 2*(2*a - 3*b)*cosh(f*x + e)^3 + 2*(5*(2*a - 3*b)*cosh(f*x + e)^2 + 2*a - 3*b)*sinh(f*x + e)^3 + 2*(5*(2*a - 3*b)*cosh(f*x + e)^3 + 3*(2*a - 3*b)*cosh(f*x + e))*sinh(f*x + e)^2 + (2*a - 3*b)*cosh(f*x + e) + (5*(2*a - 3*b)*cosh(f*x + e)^4 + 6*(2*a - 3*b)*cosh(f*x + e)^2 + 2*a - 3*b)*sinh(f*x + e))*sqrt(a - b)*log((b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(4*a - 3*b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 4*a - 3*b)*sinh(f*x + e)^2 + 4*sqrt(2)*sqrt(a - b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))*(cosh(f*x + e) + sinh(f*x + e)) + 4*(b*cosh(f*x + e)^3 + (4*a - 3*b)*cosh(f*x + e))*sinh(f*x + e) + b)/(cosh(f*x + e)^4 + 4*cosh(f*x + e)*sinh(f*x + e)^3 + sinh(f*x + e)^4 + 2*(3*cosh(f*x + e)^2 + 1)*sinh(f*x + e)^2 + 2*cosh(f*x + e)^2 + 4*(cosh(f*x + e)^3 + cosh(f*x + e))*sinh(f*x + e) + 1)) - 2*sqrt(2)*((a - b)*cosh(f*x + e)^4 + 4*(a - b)*cosh(f*x + e)*sinh(f*x + e)^3 + (a - b)*sinh(f*x + e)^4 + 4*(a - b)*cosh(f*x + e)^2 + 2*(3*(a - b)*cosh(f*x + e)^2 + 2*a - 2*b)*sinh(f*x + e)^2 + 4*((a - b)*cosh(f*x + e)^3 + 2*(a - b)*cosh(f*x + e))*sinh(f*x + e) + a - b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/((a - b)*f*cosh(f*x + e)^5 + 5*(a - b)*f*cosh(f*x + e)*sinh(f*x + e)^4 + (a - b)*f*sinh(f*x + e)^5 + 2*(a - b)*f*cosh(f*x + e)^3 + 2*(5*(a - b)*f*cosh(f*x + e)^2 + (a - b)*f)*sinh(f*x + e)^3 + (a - b)*f*cosh(f*x + e) + 2*(5*(a - b)*f*cosh(f*x + e)^3 + 3*(a - b)*f*cosh(f*x + e))*sinh(f*x + e)^2 + (5*(a - b)*f*cosh(f*x + e)^4 + 6*(a - b)*f*cosh(f*x + e)^2 + (a - b)*f)*sinh(f*x + e)), -1/2*(((2*a - 3*b)*cosh(f*x + e)^5 + 5*(2*a - 3*b)*cosh(f*x + e)*sinh(f*x + e)^4 + (2*a - 3*b)*sinh(f*x + e)^5 + 2*(2*a - 3*b)*cosh(f*x + e)^3 + 2*(5*(2*a - 3*b)*cosh(f*x + e)^2 + 2*a - 3*b)*sinh(f*x + e)^3 + 2*(5*(2*a - 3*b)*cosh(f*x + e)^3 + 3*(2*a - 3*b)*cosh(f*x + e))*sinh(f*x + e)^2 + (2*a - 3*b)*cosh(f*x + e) + (5*(2*a - 3*b)*cosh(f*x + e)^4 + 6*(2*a - 3*b)*cosh(f*x + e)^2 + 2*a - 3*b)*sinh(f*x + e))*sqrt(-a + b)*arctan(-1/2*sqrt(2)*sqrt(-a + b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/((a - b)*cosh(f*x + e) + (a - b)*sinh(f*x + e))) - sqrt(2)*((a - b)*cosh(f*x + e)^4 + 4*(a - b)*cosh(f*x + e)*sinh(f*x + e)^3 + (a - b)*sinh(f*x + e)^4 + 4*(a - b)*cosh(f*x + e)^2 + 2*(3*(a - b)*cosh(f*x + e)^2 + 2*a - 2*b)*sinh(f*x + e)^2 + 4*((a - b)*cosh(f*x + e)^3 + 2*(a - b)*cosh(f*x + e))*sinh(f*x + e) + a - b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/((a - b)*f*cosh(f*x + e)^5 + 5*(a - b)*f*cosh(f*x + e)*sinh(f*x + e)^4 + (a - b)*f*sinh(f*x + e)^5 + 2*(a - b)*f*cosh(f*x + e)^3 + 2*(5*(a - b)*f*cosh(f*x + e)^2 + (a - b)*f)*sinh(f*x + e)^3 + (a - b)*f*cosh(f*x + e) + 2*(5*(a - b)*f*cosh(f*x + e)^3 + 3*(a - b)*f*cosh(f*x + e))*sinh(f*x + e)^2 + (5*(a - b)*f*cosh(f*x + e)^4 + 6*(a - b)*f*cosh(f*x + e)^2 + (a - b)*f)*sinh(f*x + e))]","B",0
459,1,624,0,1.285340," ","integrate((a+b*sinh(f*x+e)^2)^(1/2)*tanh(f*x+e),x, algorithm=""fricas"")","\left[\frac{\sqrt{a - b} {\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right)\right)} \log\left(\frac{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(4 \, a - 3 \, b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + 4 \, a - 3 \, b\right)} \sinh\left(f x + e\right)^{2} - 4 \, \sqrt{2} \sqrt{a - b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} {\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right)\right)} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(4 \, a - 3 \, b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}{\cosh\left(f x + e\right)^{4} + 4 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + \sinh\left(f x + e\right)^{4} + 2 \, {\left(3 \, \cosh\left(f x + e\right)^{2} + 1\right)} \sinh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right)^{2} + 4 \, {\left(\cosh\left(f x + e\right)^{3} + \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + 1}\right) + \sqrt{2} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{2 \, {\left(f \cosh\left(f x + e\right) + f \sinh\left(f x + e\right)\right)}}, -\frac{2 \, \sqrt{-a + b} {\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right)\right)} \arctan\left(-\frac{\sqrt{2} \sqrt{-a + b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{2 \, {\left({\left(a - b\right)} \cosh\left(f x + e\right) + {\left(a - b\right)} \sinh\left(f x + e\right)\right)}}\right) - \sqrt{2} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{2 \, {\left(f \cosh\left(f x + e\right) + f \sinh\left(f x + e\right)\right)}}\right]"," ",0,"[1/2*(sqrt(a - b)*(cosh(f*x + e) + sinh(f*x + e))*log((b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(4*a - 3*b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 4*a - 3*b)*sinh(f*x + e)^2 - 4*sqrt(2)*sqrt(a - b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))*(cosh(f*x + e) + sinh(f*x + e)) + 4*(b*cosh(f*x + e)^3 + (4*a - 3*b)*cosh(f*x + e))*sinh(f*x + e) + b)/(cosh(f*x + e)^4 + 4*cosh(f*x + e)*sinh(f*x + e)^3 + sinh(f*x + e)^4 + 2*(3*cosh(f*x + e)^2 + 1)*sinh(f*x + e)^2 + 2*cosh(f*x + e)^2 + 4*(cosh(f*x + e)^3 + cosh(f*x + e))*sinh(f*x + e) + 1)) + sqrt(2)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/(f*cosh(f*x + e) + f*sinh(f*x + e)), -1/2*(2*sqrt(-a + b)*(cosh(f*x + e) + sinh(f*x + e))*arctan(-1/2*sqrt(2)*sqrt(-a + b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/((a - b)*cosh(f*x + e) + (a - b)*sinh(f*x + e))) - sqrt(2)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/(f*cosh(f*x + e) + f*sinh(f*x + e))]","B",0
460,1,605,0,0.821879," ","integrate(coth(f*x+e)*(a+b*sinh(f*x+e)^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{a} {\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right)\right)} \log\left(\frac{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(4 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + 4 \, a - b\right)} \sinh\left(f x + e\right)^{2} - 4 \, \sqrt{2} \sqrt{a} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} {\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right)\right)} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(4 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}{\cosh\left(f x + e\right)^{4} + 4 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + \sinh\left(f x + e\right)^{4} + 2 \, {\left(3 \, \cosh\left(f x + e\right)^{2} - 1\right)} \sinh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right)^{2} + 4 \, {\left(\cosh\left(f x + e\right)^{3} - \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + 1}\right) + \sqrt{2} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{2 \, {\left(f \cosh\left(f x + e\right) + f \sinh\left(f x + e\right)\right)}}, \frac{2 \, \sqrt{-a} {\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right)\right)} \arctan\left(\frac{\sqrt{2} \sqrt{-a} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{2 \, {\left(a \cosh\left(f x + e\right) + a \sinh\left(f x + e\right)\right)}}\right) + \sqrt{2} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{2 \, {\left(f \cosh\left(f x + e\right) + f \sinh\left(f x + e\right)\right)}}\right]"," ",0,"[1/2*(sqrt(a)*(cosh(f*x + e) + sinh(f*x + e))*log((b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(4*a - b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 4*a - b)*sinh(f*x + e)^2 - 4*sqrt(2)*sqrt(a)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))*(cosh(f*x + e) + sinh(f*x + e)) + 4*(b*cosh(f*x + e)^3 + (4*a - b)*cosh(f*x + e))*sinh(f*x + e) + b)/(cosh(f*x + e)^4 + 4*cosh(f*x + e)*sinh(f*x + e)^3 + sinh(f*x + e)^4 + 2*(3*cosh(f*x + e)^2 - 1)*sinh(f*x + e)^2 - 2*cosh(f*x + e)^2 + 4*(cosh(f*x + e)^3 - cosh(f*x + e))*sinh(f*x + e) + 1)) + sqrt(2)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/(f*cosh(f*x + e) + f*sinh(f*x + e)), 1/2*(2*sqrt(-a)*(cosh(f*x + e) + sinh(f*x + e))*arctan(1/2*sqrt(2)*sqrt(-a)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/(a*cosh(f*x + e) + a*sinh(f*x + e))) + sqrt(2)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/(f*cosh(f*x + e) + f*sinh(f*x + e))]","B",0
461,1,1445,0,0.915624," ","integrate(coth(f*x+e)^3*(a+b*sinh(f*x+e)^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(2 \, a + b\right)} \cosh\left(f x + e\right)^{5} + 5 \, {\left(2 \, a + b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{4} + {\left(2 \, a + b\right)} \sinh\left(f x + e\right)^{5} - 2 \, {\left(2 \, a + b\right)} \cosh\left(f x + e\right)^{3} + 2 \, {\left(5 \, {\left(2 \, a + b\right)} \cosh\left(f x + e\right)^{2} - 2 \, a - b\right)} \sinh\left(f x + e\right)^{3} + 2 \, {\left(5 \, {\left(2 \, a + b\right)} \cosh\left(f x + e\right)^{3} - 3 \, {\left(2 \, a + b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{2} + {\left(2 \, a + b\right)} \cosh\left(f x + e\right) + {\left(5 \, {\left(2 \, a + b\right)} \cosh\left(f x + e\right)^{4} - 6 \, {\left(2 \, a + b\right)} \cosh\left(f x + e\right)^{2} + 2 \, a + b\right)} \sinh\left(f x + e\right)\right)} \sqrt{a} \log\left(\frac{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(4 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + 4 \, a - b\right)} \sinh\left(f x + e\right)^{2} - 4 \, \sqrt{2} \sqrt{a} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} {\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right)\right)} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(4 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}{\cosh\left(f x + e\right)^{4} + 4 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + \sinh\left(f x + e\right)^{4} + 2 \, {\left(3 \, \cosh\left(f x + e\right)^{2} - 1\right)} \sinh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right)^{2} + 4 \, {\left(\cosh\left(f x + e\right)^{3} - \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + 1}\right) + 2 \, \sqrt{2} {\left(a \cosh\left(f x + e\right)^{4} + 4 \, a \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + a \sinh\left(f x + e\right)^{4} - 4 \, a \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, a \cosh\left(f x + e\right)^{2} - 2 \, a\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(a \cosh\left(f x + e\right)^{3} - 2 \, a \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + a\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{4 \, {\left(a f \cosh\left(f x + e\right)^{5} + 5 \, a f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{4} + a f \sinh\left(f x + e\right)^{5} - 2 \, a f \cosh\left(f x + e\right)^{3} + 2 \, {\left(5 \, a f \cosh\left(f x + e\right)^{2} - a f\right)} \sinh\left(f x + e\right)^{3} + a f \cosh\left(f x + e\right) + 2 \, {\left(5 \, a f \cosh\left(f x + e\right)^{3} - 3 \, a f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{2} + {\left(5 \, a f \cosh\left(f x + e\right)^{4} - 6 \, a f \cosh\left(f x + e\right)^{2} + a f\right)} \sinh\left(f x + e\right)\right)}}, \frac{{\left({\left(2 \, a + b\right)} \cosh\left(f x + e\right)^{5} + 5 \, {\left(2 \, a + b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{4} + {\left(2 \, a + b\right)} \sinh\left(f x + e\right)^{5} - 2 \, {\left(2 \, a + b\right)} \cosh\left(f x + e\right)^{3} + 2 \, {\left(5 \, {\left(2 \, a + b\right)} \cosh\left(f x + e\right)^{2} - 2 \, a - b\right)} \sinh\left(f x + e\right)^{3} + 2 \, {\left(5 \, {\left(2 \, a + b\right)} \cosh\left(f x + e\right)^{3} - 3 \, {\left(2 \, a + b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{2} + {\left(2 \, a + b\right)} \cosh\left(f x + e\right) + {\left(5 \, {\left(2 \, a + b\right)} \cosh\left(f x + e\right)^{4} - 6 \, {\left(2 \, a + b\right)} \cosh\left(f x + e\right)^{2} + 2 \, a + b\right)} \sinh\left(f x + e\right)\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{2} \sqrt{-a} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{2 \, {\left(a \cosh\left(f x + e\right) + a \sinh\left(f x + e\right)\right)}}\right) + \sqrt{2} {\left(a \cosh\left(f x + e\right)^{4} + 4 \, a \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + a \sinh\left(f x + e\right)^{4} - 4 \, a \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, a \cosh\left(f x + e\right)^{2} - 2 \, a\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(a \cosh\left(f x + e\right)^{3} - 2 \, a \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + a\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{2 \, {\left(a f \cosh\left(f x + e\right)^{5} + 5 \, a f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{4} + a f \sinh\left(f x + e\right)^{5} - 2 \, a f \cosh\left(f x + e\right)^{3} + 2 \, {\left(5 \, a f \cosh\left(f x + e\right)^{2} - a f\right)} \sinh\left(f x + e\right)^{3} + a f \cosh\left(f x + e\right) + 2 \, {\left(5 \, a f \cosh\left(f x + e\right)^{3} - 3 \, a f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{2} + {\left(5 \, a f \cosh\left(f x + e\right)^{4} - 6 \, a f \cosh\left(f x + e\right)^{2} + a f\right)} \sinh\left(f x + e\right)\right)}}\right]"," ",0,"[1/4*(((2*a + b)*cosh(f*x + e)^5 + 5*(2*a + b)*cosh(f*x + e)*sinh(f*x + e)^4 + (2*a + b)*sinh(f*x + e)^5 - 2*(2*a + b)*cosh(f*x + e)^3 + 2*(5*(2*a + b)*cosh(f*x + e)^2 - 2*a - b)*sinh(f*x + e)^3 + 2*(5*(2*a + b)*cosh(f*x + e)^3 - 3*(2*a + b)*cosh(f*x + e))*sinh(f*x + e)^2 + (2*a + b)*cosh(f*x + e) + (5*(2*a + b)*cosh(f*x + e)^4 - 6*(2*a + b)*cosh(f*x + e)^2 + 2*a + b)*sinh(f*x + e))*sqrt(a)*log((b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(4*a - b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 4*a - b)*sinh(f*x + e)^2 - 4*sqrt(2)*sqrt(a)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))*(cosh(f*x + e) + sinh(f*x + e)) + 4*(b*cosh(f*x + e)^3 + (4*a - b)*cosh(f*x + e))*sinh(f*x + e) + b)/(cosh(f*x + e)^4 + 4*cosh(f*x + e)*sinh(f*x + e)^3 + sinh(f*x + e)^4 + 2*(3*cosh(f*x + e)^2 - 1)*sinh(f*x + e)^2 - 2*cosh(f*x + e)^2 + 4*(cosh(f*x + e)^3 - cosh(f*x + e))*sinh(f*x + e) + 1)) + 2*sqrt(2)*(a*cosh(f*x + e)^4 + 4*a*cosh(f*x + e)*sinh(f*x + e)^3 + a*sinh(f*x + e)^4 - 4*a*cosh(f*x + e)^2 + 2*(3*a*cosh(f*x + e)^2 - 2*a)*sinh(f*x + e)^2 + 4*(a*cosh(f*x + e)^3 - 2*a*cosh(f*x + e))*sinh(f*x + e) + a)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/(a*f*cosh(f*x + e)^5 + 5*a*f*cosh(f*x + e)*sinh(f*x + e)^4 + a*f*sinh(f*x + e)^5 - 2*a*f*cosh(f*x + e)^3 + 2*(5*a*f*cosh(f*x + e)^2 - a*f)*sinh(f*x + e)^3 + a*f*cosh(f*x + e) + 2*(5*a*f*cosh(f*x + e)^3 - 3*a*f*cosh(f*x + e))*sinh(f*x + e)^2 + (5*a*f*cosh(f*x + e)^4 - 6*a*f*cosh(f*x + e)^2 + a*f)*sinh(f*x + e)), 1/2*(((2*a + b)*cosh(f*x + e)^5 + 5*(2*a + b)*cosh(f*x + e)*sinh(f*x + e)^4 + (2*a + b)*sinh(f*x + e)^5 - 2*(2*a + b)*cosh(f*x + e)^3 + 2*(5*(2*a + b)*cosh(f*x + e)^2 - 2*a - b)*sinh(f*x + e)^3 + 2*(5*(2*a + b)*cosh(f*x + e)^3 - 3*(2*a + b)*cosh(f*x + e))*sinh(f*x + e)^2 + (2*a + b)*cosh(f*x + e) + (5*(2*a + b)*cosh(f*x + e)^4 - 6*(2*a + b)*cosh(f*x + e)^2 + 2*a + b)*sinh(f*x + e))*sqrt(-a)*arctan(1/2*sqrt(2)*sqrt(-a)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/(a*cosh(f*x + e) + a*sinh(f*x + e))) + sqrt(2)*(a*cosh(f*x + e)^4 + 4*a*cosh(f*x + e)*sinh(f*x + e)^3 + a*sinh(f*x + e)^4 - 4*a*cosh(f*x + e)^2 + 2*(3*a*cosh(f*x + e)^2 - 2*a)*sinh(f*x + e)^2 + 4*(a*cosh(f*x + e)^3 - 2*a*cosh(f*x + e))*sinh(f*x + e) + a)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/(a*f*cosh(f*x + e)^5 + 5*a*f*cosh(f*x + e)*sinh(f*x + e)^4 + a*f*sinh(f*x + e)^5 - 2*a*f*cosh(f*x + e)^3 + 2*(5*a*f*cosh(f*x + e)^2 - a*f)*sinh(f*x + e)^3 + a*f*cosh(f*x + e) + 2*(5*a*f*cosh(f*x + e)^3 - 3*a*f*cosh(f*x + e))*sinh(f*x + e)^2 + (5*a*f*cosh(f*x + e)^4 - 6*a*f*cosh(f*x + e)^2 + a*f)*sinh(f*x + e))]","B",0
462,1,3880,0,1.356535," ","integrate(coth(f*x+e)^5*(a+b*sinh(f*x+e)^2)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left({\left(8 \, a^{2} + 8 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{9} + 9 \, {\left(8 \, a^{2} + 8 \, a b - b^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{8} + {\left(8 \, a^{2} + 8 \, a b - b^{2}\right)} \sinh\left(f x + e\right)^{9} - 4 \, {\left(8 \, a^{2} + 8 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{7} + 4 \, {\left(9 \, {\left(8 \, a^{2} + 8 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{2} - 8 \, a^{2} - 8 \, a b + b^{2}\right)} \sinh\left(f x + e\right)^{7} + 28 \, {\left(3 \, {\left(8 \, a^{2} + 8 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{3} - {\left(8 \, a^{2} + 8 \, a b - b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{6} + 6 \, {\left(8 \, a^{2} + 8 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{5} + 6 \, {\left(21 \, {\left(8 \, a^{2} + 8 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{4} - 14 \, {\left(8 \, a^{2} + 8 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{2} + 8 \, a^{2} + 8 \, a b - b^{2}\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(63 \, {\left(8 \, a^{2} + 8 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{5} - 70 \, {\left(8 \, a^{2} + 8 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{3} + 15 \, {\left(8 \, a^{2} + 8 \, a b - b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{4} - 4 \, {\left(8 \, a^{2} + 8 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{3} + 4 \, {\left(21 \, {\left(8 \, a^{2} + 8 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{6} - 35 \, {\left(8 \, a^{2} + 8 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{4} + 15 \, {\left(8 \, a^{2} + 8 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{2} - 8 \, a^{2} - 8 \, a b + b^{2}\right)} \sinh\left(f x + e\right)^{3} + 12 \, {\left(3 \, {\left(8 \, a^{2} + 8 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{7} - 7 \, {\left(8 \, a^{2} + 8 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{5} + 5 \, {\left(8 \, a^{2} + 8 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{3} - {\left(8 \, a^{2} + 8 \, a b - b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{2} + {\left(8 \, a^{2} + 8 \, a b - b^{2}\right)} \cosh\left(f x + e\right) + {\left(9 \, {\left(8 \, a^{2} + 8 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{8} - 28 \, {\left(8 \, a^{2} + 8 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{6} + 30 \, {\left(8 \, a^{2} + 8 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{4} - 12 \, {\left(8 \, a^{2} + 8 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{2} + 8 \, a^{2} + 8 \, a b - b^{2}\right)} \sinh\left(f x + e\right)\right)} \sqrt{a} \log\left(\frac{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(4 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + 4 \, a - b\right)} \sinh\left(f x + e\right)^{2} + 4 \, \sqrt{2} \sqrt{a} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} {\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right)\right)} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(4 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}{\cosh\left(f x + e\right)^{4} + 4 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + \sinh\left(f x + e\right)^{4} + 2 \, {\left(3 \, \cosh\left(f x + e\right)^{2} - 1\right)} \sinh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right)^{2} + 4 \, {\left(\cosh\left(f x + e\right)^{3} - \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + 1}\right) - 4 \, \sqrt{2} {\left(2 \, a^{2} \cosh\left(f x + e\right)^{8} + 16 \, a^{2} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + 2 \, a^{2} \sinh\left(f x + e\right)^{8} - {\left(16 \, a^{2} + a b\right)} \cosh\left(f x + e\right)^{6} + {\left(56 \, a^{2} \cosh\left(f x + e\right)^{2} - 16 \, a^{2} - a b\right)} \sinh\left(f x + e\right)^{6} + 2 \, {\left(56 \, a^{2} \cosh\left(f x + e\right)^{3} - 3 \, {\left(16 \, a^{2} + a b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(10 \, a^{2} + a b\right)} \cosh\left(f x + e\right)^{4} + {\left(140 \, a^{2} \cosh\left(f x + e\right)^{4} - 15 \, {\left(16 \, a^{2} + a b\right)} \cosh\left(f x + e\right)^{2} + 20 \, a^{2} + 2 \, a b\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(28 \, a^{2} \cosh\left(f x + e\right)^{5} - 5 \, {\left(16 \, a^{2} + a b\right)} \cosh\left(f x + e\right)^{3} + 2 \, {\left(10 \, a^{2} + a b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} - {\left(16 \, a^{2} + a b\right)} \cosh\left(f x + e\right)^{2} + {\left(56 \, a^{2} \cosh\left(f x + e\right)^{6} - 15 \, {\left(16 \, a^{2} + a b\right)} \cosh\left(f x + e\right)^{4} + 12 \, {\left(10 \, a^{2} + a b\right)} \cosh\left(f x + e\right)^{2} - 16 \, a^{2} - a b\right)} \sinh\left(f x + e\right)^{2} + 2 \, a^{2} + 2 \, {\left(8 \, a^{2} \cosh\left(f x + e\right)^{7} - 3 \, {\left(16 \, a^{2} + a b\right)} \cosh\left(f x + e\right)^{5} + 4 \, {\left(10 \, a^{2} + a b\right)} \cosh\left(f x + e\right)^{3} - {\left(16 \, a^{2} + a b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{16 \, {\left(a^{2} f \cosh\left(f x + e\right)^{9} + 9 \, a^{2} f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{8} + a^{2} f \sinh\left(f x + e\right)^{9} - 4 \, a^{2} f \cosh\left(f x + e\right)^{7} + 6 \, a^{2} f \cosh\left(f x + e\right)^{5} + 4 \, {\left(9 \, a^{2} f \cosh\left(f x + e\right)^{2} - a^{2} f\right)} \sinh\left(f x + e\right)^{7} + 28 \, {\left(3 \, a^{2} f \cosh\left(f x + e\right)^{3} - a^{2} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{6} - 4 \, a^{2} f \cosh\left(f x + e\right)^{3} + 6 \, {\left(21 \, a^{2} f \cosh\left(f x + e\right)^{4} - 14 \, a^{2} f \cosh\left(f x + e\right)^{2} + a^{2} f\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(63 \, a^{2} f \cosh\left(f x + e\right)^{5} - 70 \, a^{2} f \cosh\left(f x + e\right)^{3} + 15 \, a^{2} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{4} + a^{2} f \cosh\left(f x + e\right) + 4 \, {\left(21 \, a^{2} f \cosh\left(f x + e\right)^{6} - 35 \, a^{2} f \cosh\left(f x + e\right)^{4} + 15 \, a^{2} f \cosh\left(f x + e\right)^{2} - a^{2} f\right)} \sinh\left(f x + e\right)^{3} + 12 \, {\left(3 \, a^{2} f \cosh\left(f x + e\right)^{7} - 7 \, a^{2} f \cosh\left(f x + e\right)^{5} + 5 \, a^{2} f \cosh\left(f x + e\right)^{3} - a^{2} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{2} + {\left(9 \, a^{2} f \cosh\left(f x + e\right)^{8} - 28 \, a^{2} f \cosh\left(f x + e\right)^{6} + 30 \, a^{2} f \cosh\left(f x + e\right)^{4} - 12 \, a^{2} f \cosh\left(f x + e\right)^{2} + a^{2} f\right)} \sinh\left(f x + e\right)\right)}}, \frac{{\left({\left(8 \, a^{2} + 8 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{9} + 9 \, {\left(8 \, a^{2} + 8 \, a b - b^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{8} + {\left(8 \, a^{2} + 8 \, a b - b^{2}\right)} \sinh\left(f x + e\right)^{9} - 4 \, {\left(8 \, a^{2} + 8 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{7} + 4 \, {\left(9 \, {\left(8 \, a^{2} + 8 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{2} - 8 \, a^{2} - 8 \, a b + b^{2}\right)} \sinh\left(f x + e\right)^{7} + 28 \, {\left(3 \, {\left(8 \, a^{2} + 8 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{3} - {\left(8 \, a^{2} + 8 \, a b - b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{6} + 6 \, {\left(8 \, a^{2} + 8 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{5} + 6 \, {\left(21 \, {\left(8 \, a^{2} + 8 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{4} - 14 \, {\left(8 \, a^{2} + 8 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{2} + 8 \, a^{2} + 8 \, a b - b^{2}\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(63 \, {\left(8 \, a^{2} + 8 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{5} - 70 \, {\left(8 \, a^{2} + 8 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{3} + 15 \, {\left(8 \, a^{2} + 8 \, a b - b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{4} - 4 \, {\left(8 \, a^{2} + 8 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{3} + 4 \, {\left(21 \, {\left(8 \, a^{2} + 8 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{6} - 35 \, {\left(8 \, a^{2} + 8 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{4} + 15 \, {\left(8 \, a^{2} + 8 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{2} - 8 \, a^{2} - 8 \, a b + b^{2}\right)} \sinh\left(f x + e\right)^{3} + 12 \, {\left(3 \, {\left(8 \, a^{2} + 8 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{7} - 7 \, {\left(8 \, a^{2} + 8 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{5} + 5 \, {\left(8 \, a^{2} + 8 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{3} - {\left(8 \, a^{2} + 8 \, a b - b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{2} + {\left(8 \, a^{2} + 8 \, a b - b^{2}\right)} \cosh\left(f x + e\right) + {\left(9 \, {\left(8 \, a^{2} + 8 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{8} - 28 \, {\left(8 \, a^{2} + 8 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{6} + 30 \, {\left(8 \, a^{2} + 8 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{4} - 12 \, {\left(8 \, a^{2} + 8 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{2} + 8 \, a^{2} + 8 \, a b - b^{2}\right)} \sinh\left(f x + e\right)\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{2} \sqrt{-a} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{2 \, {\left(a \cosh\left(f x + e\right) + a \sinh\left(f x + e\right)\right)}}\right) + 2 \, \sqrt{2} {\left(2 \, a^{2} \cosh\left(f x + e\right)^{8} + 16 \, a^{2} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + 2 \, a^{2} \sinh\left(f x + e\right)^{8} - {\left(16 \, a^{2} + a b\right)} \cosh\left(f x + e\right)^{6} + {\left(56 \, a^{2} \cosh\left(f x + e\right)^{2} - 16 \, a^{2} - a b\right)} \sinh\left(f x + e\right)^{6} + 2 \, {\left(56 \, a^{2} \cosh\left(f x + e\right)^{3} - 3 \, {\left(16 \, a^{2} + a b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(10 \, a^{2} + a b\right)} \cosh\left(f x + e\right)^{4} + {\left(140 \, a^{2} \cosh\left(f x + e\right)^{4} - 15 \, {\left(16 \, a^{2} + a b\right)} \cosh\left(f x + e\right)^{2} + 20 \, a^{2} + 2 \, a b\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(28 \, a^{2} \cosh\left(f x + e\right)^{5} - 5 \, {\left(16 \, a^{2} + a b\right)} \cosh\left(f x + e\right)^{3} + 2 \, {\left(10 \, a^{2} + a b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} - {\left(16 \, a^{2} + a b\right)} \cosh\left(f x + e\right)^{2} + {\left(56 \, a^{2} \cosh\left(f x + e\right)^{6} - 15 \, {\left(16 \, a^{2} + a b\right)} \cosh\left(f x + e\right)^{4} + 12 \, {\left(10 \, a^{2} + a b\right)} \cosh\left(f x + e\right)^{2} - 16 \, a^{2} - a b\right)} \sinh\left(f x + e\right)^{2} + 2 \, a^{2} + 2 \, {\left(8 \, a^{2} \cosh\left(f x + e\right)^{7} - 3 \, {\left(16 \, a^{2} + a b\right)} \cosh\left(f x + e\right)^{5} + 4 \, {\left(10 \, a^{2} + a b\right)} \cosh\left(f x + e\right)^{3} - {\left(16 \, a^{2} + a b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{8 \, {\left(a^{2} f \cosh\left(f x + e\right)^{9} + 9 \, a^{2} f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{8} + a^{2} f \sinh\left(f x + e\right)^{9} - 4 \, a^{2} f \cosh\left(f x + e\right)^{7} + 6 \, a^{2} f \cosh\left(f x + e\right)^{5} + 4 \, {\left(9 \, a^{2} f \cosh\left(f x + e\right)^{2} - a^{2} f\right)} \sinh\left(f x + e\right)^{7} + 28 \, {\left(3 \, a^{2} f \cosh\left(f x + e\right)^{3} - a^{2} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{6} - 4 \, a^{2} f \cosh\left(f x + e\right)^{3} + 6 \, {\left(21 \, a^{2} f \cosh\left(f x + e\right)^{4} - 14 \, a^{2} f \cosh\left(f x + e\right)^{2} + a^{2} f\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(63 \, a^{2} f \cosh\left(f x + e\right)^{5} - 70 \, a^{2} f \cosh\left(f x + e\right)^{3} + 15 \, a^{2} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{4} + a^{2} f \cosh\left(f x + e\right) + 4 \, {\left(21 \, a^{2} f \cosh\left(f x + e\right)^{6} - 35 \, a^{2} f \cosh\left(f x + e\right)^{4} + 15 \, a^{2} f \cosh\left(f x + e\right)^{2} - a^{2} f\right)} \sinh\left(f x + e\right)^{3} + 12 \, {\left(3 \, a^{2} f \cosh\left(f x + e\right)^{7} - 7 \, a^{2} f \cosh\left(f x + e\right)^{5} + 5 \, a^{2} f \cosh\left(f x + e\right)^{3} - a^{2} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{2} + {\left(9 \, a^{2} f \cosh\left(f x + e\right)^{8} - 28 \, a^{2} f \cosh\left(f x + e\right)^{6} + 30 \, a^{2} f \cosh\left(f x + e\right)^{4} - 12 \, a^{2} f \cosh\left(f x + e\right)^{2} + a^{2} f\right)} \sinh\left(f x + e\right)\right)}}\right]"," ",0,"[-1/16*(((8*a^2 + 8*a*b - b^2)*cosh(f*x + e)^9 + 9*(8*a^2 + 8*a*b - b^2)*cosh(f*x + e)*sinh(f*x + e)^8 + (8*a^2 + 8*a*b - b^2)*sinh(f*x + e)^9 - 4*(8*a^2 + 8*a*b - b^2)*cosh(f*x + e)^7 + 4*(9*(8*a^2 + 8*a*b - b^2)*cosh(f*x + e)^2 - 8*a^2 - 8*a*b + b^2)*sinh(f*x + e)^7 + 28*(3*(8*a^2 + 8*a*b - b^2)*cosh(f*x + e)^3 - (8*a^2 + 8*a*b - b^2)*cosh(f*x + e))*sinh(f*x + e)^6 + 6*(8*a^2 + 8*a*b - b^2)*cosh(f*x + e)^5 + 6*(21*(8*a^2 + 8*a*b - b^2)*cosh(f*x + e)^4 - 14*(8*a^2 + 8*a*b - b^2)*cosh(f*x + e)^2 + 8*a^2 + 8*a*b - b^2)*sinh(f*x + e)^5 + 2*(63*(8*a^2 + 8*a*b - b^2)*cosh(f*x + e)^5 - 70*(8*a^2 + 8*a*b - b^2)*cosh(f*x + e)^3 + 15*(8*a^2 + 8*a*b - b^2)*cosh(f*x + e))*sinh(f*x + e)^4 - 4*(8*a^2 + 8*a*b - b^2)*cosh(f*x + e)^3 + 4*(21*(8*a^2 + 8*a*b - b^2)*cosh(f*x + e)^6 - 35*(8*a^2 + 8*a*b - b^2)*cosh(f*x + e)^4 + 15*(8*a^2 + 8*a*b - b^2)*cosh(f*x + e)^2 - 8*a^2 - 8*a*b + b^2)*sinh(f*x + e)^3 + 12*(3*(8*a^2 + 8*a*b - b^2)*cosh(f*x + e)^7 - 7*(8*a^2 + 8*a*b - b^2)*cosh(f*x + e)^5 + 5*(8*a^2 + 8*a*b - b^2)*cosh(f*x + e)^3 - (8*a^2 + 8*a*b - b^2)*cosh(f*x + e))*sinh(f*x + e)^2 + (8*a^2 + 8*a*b - b^2)*cosh(f*x + e) + (9*(8*a^2 + 8*a*b - b^2)*cosh(f*x + e)^8 - 28*(8*a^2 + 8*a*b - b^2)*cosh(f*x + e)^6 + 30*(8*a^2 + 8*a*b - b^2)*cosh(f*x + e)^4 - 12*(8*a^2 + 8*a*b - b^2)*cosh(f*x + e)^2 + 8*a^2 + 8*a*b - b^2)*sinh(f*x + e))*sqrt(a)*log((b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(4*a - b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 4*a - b)*sinh(f*x + e)^2 + 4*sqrt(2)*sqrt(a)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))*(cosh(f*x + e) + sinh(f*x + e)) + 4*(b*cosh(f*x + e)^3 + (4*a - b)*cosh(f*x + e))*sinh(f*x + e) + b)/(cosh(f*x + e)^4 + 4*cosh(f*x + e)*sinh(f*x + e)^3 + sinh(f*x + e)^4 + 2*(3*cosh(f*x + e)^2 - 1)*sinh(f*x + e)^2 - 2*cosh(f*x + e)^2 + 4*(cosh(f*x + e)^3 - cosh(f*x + e))*sinh(f*x + e) + 1)) - 4*sqrt(2)*(2*a^2*cosh(f*x + e)^8 + 16*a^2*cosh(f*x + e)*sinh(f*x + e)^7 + 2*a^2*sinh(f*x + e)^8 - (16*a^2 + a*b)*cosh(f*x + e)^6 + (56*a^2*cosh(f*x + e)^2 - 16*a^2 - a*b)*sinh(f*x + e)^6 + 2*(56*a^2*cosh(f*x + e)^3 - 3*(16*a^2 + a*b)*cosh(f*x + e))*sinh(f*x + e)^5 + 2*(10*a^2 + a*b)*cosh(f*x + e)^4 + (140*a^2*cosh(f*x + e)^4 - 15*(16*a^2 + a*b)*cosh(f*x + e)^2 + 20*a^2 + 2*a*b)*sinh(f*x + e)^4 + 4*(28*a^2*cosh(f*x + e)^5 - 5*(16*a^2 + a*b)*cosh(f*x + e)^3 + 2*(10*a^2 + a*b)*cosh(f*x + e))*sinh(f*x + e)^3 - (16*a^2 + a*b)*cosh(f*x + e)^2 + (56*a^2*cosh(f*x + e)^6 - 15*(16*a^2 + a*b)*cosh(f*x + e)^4 + 12*(10*a^2 + a*b)*cosh(f*x + e)^2 - 16*a^2 - a*b)*sinh(f*x + e)^2 + 2*a^2 + 2*(8*a^2*cosh(f*x + e)^7 - 3*(16*a^2 + a*b)*cosh(f*x + e)^5 + 4*(10*a^2 + a*b)*cosh(f*x + e)^3 - (16*a^2 + a*b)*cosh(f*x + e))*sinh(f*x + e))*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/(a^2*f*cosh(f*x + e)^9 + 9*a^2*f*cosh(f*x + e)*sinh(f*x + e)^8 + a^2*f*sinh(f*x + e)^9 - 4*a^2*f*cosh(f*x + e)^7 + 6*a^2*f*cosh(f*x + e)^5 + 4*(9*a^2*f*cosh(f*x + e)^2 - a^2*f)*sinh(f*x + e)^7 + 28*(3*a^2*f*cosh(f*x + e)^3 - a^2*f*cosh(f*x + e))*sinh(f*x + e)^6 - 4*a^2*f*cosh(f*x + e)^3 + 6*(21*a^2*f*cosh(f*x + e)^4 - 14*a^2*f*cosh(f*x + e)^2 + a^2*f)*sinh(f*x + e)^5 + 2*(63*a^2*f*cosh(f*x + e)^5 - 70*a^2*f*cosh(f*x + e)^3 + 15*a^2*f*cosh(f*x + e))*sinh(f*x + e)^4 + a^2*f*cosh(f*x + e) + 4*(21*a^2*f*cosh(f*x + e)^6 - 35*a^2*f*cosh(f*x + e)^4 + 15*a^2*f*cosh(f*x + e)^2 - a^2*f)*sinh(f*x + e)^3 + 12*(3*a^2*f*cosh(f*x + e)^7 - 7*a^2*f*cosh(f*x + e)^5 + 5*a^2*f*cosh(f*x + e)^3 - a^2*f*cosh(f*x + e))*sinh(f*x + e)^2 + (9*a^2*f*cosh(f*x + e)^8 - 28*a^2*f*cosh(f*x + e)^6 + 30*a^2*f*cosh(f*x + e)^4 - 12*a^2*f*cosh(f*x + e)^2 + a^2*f)*sinh(f*x + e)), 1/8*(((8*a^2 + 8*a*b - b^2)*cosh(f*x + e)^9 + 9*(8*a^2 + 8*a*b - b^2)*cosh(f*x + e)*sinh(f*x + e)^8 + (8*a^2 + 8*a*b - b^2)*sinh(f*x + e)^9 - 4*(8*a^2 + 8*a*b - b^2)*cosh(f*x + e)^7 + 4*(9*(8*a^2 + 8*a*b - b^2)*cosh(f*x + e)^2 - 8*a^2 - 8*a*b + b^2)*sinh(f*x + e)^7 + 28*(3*(8*a^2 + 8*a*b - b^2)*cosh(f*x + e)^3 - (8*a^2 + 8*a*b - b^2)*cosh(f*x + e))*sinh(f*x + e)^6 + 6*(8*a^2 + 8*a*b - b^2)*cosh(f*x + e)^5 + 6*(21*(8*a^2 + 8*a*b - b^2)*cosh(f*x + e)^4 - 14*(8*a^2 + 8*a*b - b^2)*cosh(f*x + e)^2 + 8*a^2 + 8*a*b - b^2)*sinh(f*x + e)^5 + 2*(63*(8*a^2 + 8*a*b - b^2)*cosh(f*x + e)^5 - 70*(8*a^2 + 8*a*b - b^2)*cosh(f*x + e)^3 + 15*(8*a^2 + 8*a*b - b^2)*cosh(f*x + e))*sinh(f*x + e)^4 - 4*(8*a^2 + 8*a*b - b^2)*cosh(f*x + e)^3 + 4*(21*(8*a^2 + 8*a*b - b^2)*cosh(f*x + e)^6 - 35*(8*a^2 + 8*a*b - b^2)*cosh(f*x + e)^4 + 15*(8*a^2 + 8*a*b - b^2)*cosh(f*x + e)^2 - 8*a^2 - 8*a*b + b^2)*sinh(f*x + e)^3 + 12*(3*(8*a^2 + 8*a*b - b^2)*cosh(f*x + e)^7 - 7*(8*a^2 + 8*a*b - b^2)*cosh(f*x + e)^5 + 5*(8*a^2 + 8*a*b - b^2)*cosh(f*x + e)^3 - (8*a^2 + 8*a*b - b^2)*cosh(f*x + e))*sinh(f*x + e)^2 + (8*a^2 + 8*a*b - b^2)*cosh(f*x + e) + (9*(8*a^2 + 8*a*b - b^2)*cosh(f*x + e)^8 - 28*(8*a^2 + 8*a*b - b^2)*cosh(f*x + e)^6 + 30*(8*a^2 + 8*a*b - b^2)*cosh(f*x + e)^4 - 12*(8*a^2 + 8*a*b - b^2)*cosh(f*x + e)^2 + 8*a^2 + 8*a*b - b^2)*sinh(f*x + e))*sqrt(-a)*arctan(1/2*sqrt(2)*sqrt(-a)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/(a*cosh(f*x + e) + a*sinh(f*x + e))) + 2*sqrt(2)*(2*a^2*cosh(f*x + e)^8 + 16*a^2*cosh(f*x + e)*sinh(f*x + e)^7 + 2*a^2*sinh(f*x + e)^8 - (16*a^2 + a*b)*cosh(f*x + e)^6 + (56*a^2*cosh(f*x + e)^2 - 16*a^2 - a*b)*sinh(f*x + e)^6 + 2*(56*a^2*cosh(f*x + e)^3 - 3*(16*a^2 + a*b)*cosh(f*x + e))*sinh(f*x + e)^5 + 2*(10*a^2 + a*b)*cosh(f*x + e)^4 + (140*a^2*cosh(f*x + e)^4 - 15*(16*a^2 + a*b)*cosh(f*x + e)^2 + 20*a^2 + 2*a*b)*sinh(f*x + e)^4 + 4*(28*a^2*cosh(f*x + e)^5 - 5*(16*a^2 + a*b)*cosh(f*x + e)^3 + 2*(10*a^2 + a*b)*cosh(f*x + e))*sinh(f*x + e)^3 - (16*a^2 + a*b)*cosh(f*x + e)^2 + (56*a^2*cosh(f*x + e)^6 - 15*(16*a^2 + a*b)*cosh(f*x + e)^4 + 12*(10*a^2 + a*b)*cosh(f*x + e)^2 - 16*a^2 - a*b)*sinh(f*x + e)^2 + 2*a^2 + 2*(8*a^2*cosh(f*x + e)^7 - 3*(16*a^2 + a*b)*cosh(f*x + e)^5 + 4*(10*a^2 + a*b)*cosh(f*x + e)^3 - (16*a^2 + a*b)*cosh(f*x + e))*sinh(f*x + e))*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/(a^2*f*cosh(f*x + e)^9 + 9*a^2*f*cosh(f*x + e)*sinh(f*x + e)^8 + a^2*f*sinh(f*x + e)^9 - 4*a^2*f*cosh(f*x + e)^7 + 6*a^2*f*cosh(f*x + e)^5 + 4*(9*a^2*f*cosh(f*x + e)^2 - a^2*f)*sinh(f*x + e)^7 + 28*(3*a^2*f*cosh(f*x + e)^3 - a^2*f*cosh(f*x + e))*sinh(f*x + e)^6 - 4*a^2*f*cosh(f*x + e)^3 + 6*(21*a^2*f*cosh(f*x + e)^4 - 14*a^2*f*cosh(f*x + e)^2 + a^2*f)*sinh(f*x + e)^5 + 2*(63*a^2*f*cosh(f*x + e)^5 - 70*a^2*f*cosh(f*x + e)^3 + 15*a^2*f*cosh(f*x + e))*sinh(f*x + e)^4 + a^2*f*cosh(f*x + e) + 4*(21*a^2*f*cosh(f*x + e)^6 - 35*a^2*f*cosh(f*x + e)^4 + 15*a^2*f*cosh(f*x + e)^2 - a^2*f)*sinh(f*x + e)^3 + 12*(3*a^2*f*cosh(f*x + e)^7 - 7*a^2*f*cosh(f*x + e)^5 + 5*a^2*f*cosh(f*x + e)^3 - a^2*f*cosh(f*x + e))*sinh(f*x + e)^2 + (9*a^2*f*cosh(f*x + e)^8 - 28*a^2*f*cosh(f*x + e)^6 + 30*a^2*f*cosh(f*x + e)^4 - 12*a^2*f*cosh(f*x + e)^2 + a^2*f)*sinh(f*x + e))]","B",0
463,0,0,0,0.611321," ","integrate((a+b*sinh(f*x+e)^2)^(1/2)*tanh(f*x+e)^4,x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{b \sinh\left(f x + e\right)^{2} + a} \tanh\left(f x + e\right)^{4}, x\right)"," ",0,"integral(sqrt(b*sinh(f*x + e)^2 + a)*tanh(f*x + e)^4, x)","F",0
464,0,0,0,0.579044," ","integrate((a+b*sinh(f*x+e)^2)^(1/2)*tanh(f*x+e)^2,x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{b \sinh\left(f x + e\right)^{2} + a} \tanh\left(f x + e\right)^{2}, x\right)"," ",0,"integral(sqrt(b*sinh(f*x + e)^2 + a)*tanh(f*x + e)^2, x)","F",0
465,0,0,0,0.519498," ","integrate((a+b*sinh(f*x+e)^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{b \sinh\left(f x + e\right)^{2} + a}, x\right)"," ",0,"integral(sqrt(b*sinh(f*x + e)^2 + a), x)","F",0
466,0,0,0,0.627431," ","integrate(coth(f*x+e)^2*(a+b*sinh(f*x+e)^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{b \sinh\left(f x + e\right)^{2} + a} \coth\left(f x + e\right)^{2}, x\right)"," ",0,"integral(sqrt(b*sinh(f*x + e)^2 + a)*coth(f*x + e)^2, x)","F",0
467,0,0,0,0.660859," ","integrate(coth(f*x+e)^4*(a+b*sinh(f*x+e)^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\sqrt{b \sinh\left(f x + e\right)^{2} + a} \coth\left(f x + e\right)^{4}, x\right)"," ",0,"integral(sqrt(b*sinh(f*x + e)^2 + a)*coth(f*x + e)^4, x)","F",0
468,1,6380,0,1.293740," ","integrate((a+b*sinh(f*x+e)^2)^(3/2)*tanh(f*x+e)^5,x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(8 \, a^{2} - 40 \, a b + 35 \, b^{2}\right)} \cosh\left(f x + e\right)^{11} + 11 \, {\left(8 \, a^{2} - 40 \, a b + 35 \, b^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{10} + {\left(8 \, a^{2} - 40 \, a b + 35 \, b^{2}\right)} \sinh\left(f x + e\right)^{11} + 4 \, {\left(8 \, a^{2} - 40 \, a b + 35 \, b^{2}\right)} \cosh\left(f x + e\right)^{9} + {\left(55 \, {\left(8 \, a^{2} - 40 \, a b + 35 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + 32 \, a^{2} - 160 \, a b + 140 \, b^{2}\right)} \sinh\left(f x + e\right)^{9} + 3 \, {\left(55 \, {\left(8 \, a^{2} - 40 \, a b + 35 \, b^{2}\right)} \cosh\left(f x + e\right)^{3} + 12 \, {\left(8 \, a^{2} - 40 \, a b + 35 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{8} + 6 \, {\left(8 \, a^{2} - 40 \, a b + 35 \, b^{2}\right)} \cosh\left(f x + e\right)^{7} + 6 \, {\left(55 \, {\left(8 \, a^{2} - 40 \, a b + 35 \, b^{2}\right)} \cosh\left(f x + e\right)^{4} + 24 \, {\left(8 \, a^{2} - 40 \, a b + 35 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + 8 \, a^{2} - 40 \, a b + 35 \, b^{2}\right)} \sinh\left(f x + e\right)^{7} + 42 \, {\left(11 \, {\left(8 \, a^{2} - 40 \, a b + 35 \, b^{2}\right)} \cosh\left(f x + e\right)^{5} + 8 \, {\left(8 \, a^{2} - 40 \, a b + 35 \, b^{2}\right)} \cosh\left(f x + e\right)^{3} + {\left(8 \, a^{2} - 40 \, a b + 35 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{6} + 4 \, {\left(8 \, a^{2} - 40 \, a b + 35 \, b^{2}\right)} \cosh\left(f x + e\right)^{5} + 2 \, {\left(231 \, {\left(8 \, a^{2} - 40 \, a b + 35 \, b^{2}\right)} \cosh\left(f x + e\right)^{6} + 252 \, {\left(8 \, a^{2} - 40 \, a b + 35 \, b^{2}\right)} \cosh\left(f x + e\right)^{4} + 63 \, {\left(8 \, a^{2} - 40 \, a b + 35 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + 16 \, a^{2} - 80 \, a b + 70 \, b^{2}\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(165 \, {\left(8 \, a^{2} - 40 \, a b + 35 \, b^{2}\right)} \cosh\left(f x + e\right)^{7} + 252 \, {\left(8 \, a^{2} - 40 \, a b + 35 \, b^{2}\right)} \cosh\left(f x + e\right)^{5} + 105 \, {\left(8 \, a^{2} - 40 \, a b + 35 \, b^{2}\right)} \cosh\left(f x + e\right)^{3} + 10 \, {\left(8 \, a^{2} - 40 \, a b + 35 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{4} + {\left(8 \, a^{2} - 40 \, a b + 35 \, b^{2}\right)} \cosh\left(f x + e\right)^{3} + {\left(165 \, {\left(8 \, a^{2} - 40 \, a b + 35 \, b^{2}\right)} \cosh\left(f x + e\right)^{8} + 336 \, {\left(8 \, a^{2} - 40 \, a b + 35 \, b^{2}\right)} \cosh\left(f x + e\right)^{6} + 210 \, {\left(8 \, a^{2} - 40 \, a b + 35 \, b^{2}\right)} \cosh\left(f x + e\right)^{4} + 40 \, {\left(8 \, a^{2} - 40 \, a b + 35 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + 8 \, a^{2} - 40 \, a b + 35 \, b^{2}\right)} \sinh\left(f x + e\right)^{3} + {\left(55 \, {\left(8 \, a^{2} - 40 \, a b + 35 \, b^{2}\right)} \cosh\left(f x + e\right)^{9} + 144 \, {\left(8 \, a^{2} - 40 \, a b + 35 \, b^{2}\right)} \cosh\left(f x + e\right)^{7} + 126 \, {\left(8 \, a^{2} - 40 \, a b + 35 \, b^{2}\right)} \cosh\left(f x + e\right)^{5} + 40 \, {\left(8 \, a^{2} - 40 \, a b + 35 \, b^{2}\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(8 \, a^{2} - 40 \, a b + 35 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{2} + {\left(11 \, {\left(8 \, a^{2} - 40 \, a b + 35 \, b^{2}\right)} \cosh\left(f x + e\right)^{10} + 36 \, {\left(8 \, a^{2} - 40 \, a b + 35 \, b^{2}\right)} \cosh\left(f x + e\right)^{8} + 42 \, {\left(8 \, a^{2} - 40 \, a b + 35 \, b^{2}\right)} \cosh\left(f x + e\right)^{6} + 20 \, {\left(8 \, a^{2} - 40 \, a b + 35 \, b^{2}\right)} \cosh\left(f x + e\right)^{4} + 3 \, {\left(8 \, a^{2} - 40 \, a b + 35 \, b^{2}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)\right)} \sqrt{a - b} \log\left(\frac{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(4 \, a - 3 \, b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + 4 \, a - 3 \, b\right)} \sinh\left(f x + e\right)^{2} - 4 \, \sqrt{2} \sqrt{a - b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} {\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right)\right)} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(4 \, a - 3 \, b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}{\cosh\left(f x + e\right)^{4} + 4 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + \sinh\left(f x + e\right)^{4} + 2 \, {\left(3 \, \cosh\left(f x + e\right)^{2} + 1\right)} \sinh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right)^{2} + 4 \, {\left(\cosh\left(f x + e\right)^{3} + \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + 1}\right) + 2 \, \sqrt{2} {\left({\left(a b - b^{2}\right)} \cosh\left(f x + e\right)^{12} + 12 \, {\left(a b - b^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{11} + {\left(a b - b^{2}\right)} \sinh\left(f x + e\right)^{12} + 2 \, {\left(8 \, a^{2} - 25 \, a b + 17 \, b^{2}\right)} \cosh\left(f x + e\right)^{10} + 2 \, {\left(33 \, {\left(a b - b^{2}\right)} \cosh\left(f x + e\right)^{2} + 8 \, a^{2} - 25 \, a b + 17 \, b^{2}\right)} \sinh\left(f x + e\right)^{10} + 20 \, {\left(11 \, {\left(a b - b^{2}\right)} \cosh\left(f x + e\right)^{3} + {\left(8 \, a^{2} - 25 \, a b + 17 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{9} + {\left(112 \, a^{2} - 335 \, a b + 223 \, b^{2}\right)} \cosh\left(f x + e\right)^{8} + {\left(495 \, {\left(a b - b^{2}\right)} \cosh\left(f x + e\right)^{4} + 90 \, {\left(8 \, a^{2} - 25 \, a b + 17 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + 112 \, a^{2} - 335 \, a b + 223 \, b^{2}\right)} \sinh\left(f x + e\right)^{8} + 8 \, {\left(99 \, {\left(a b - b^{2}\right)} \cosh\left(f x + e\right)^{5} + 30 \, {\left(8 \, a^{2} - 25 \, a b + 17 \, b^{2}\right)} \cosh\left(f x + e\right)^{3} + {\left(112 \, a^{2} - 335 \, a b + 223 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{7} + 8 \, {\left(18 \, a^{2} - 59 \, a b + 41 \, b^{2}\right)} \cosh\left(f x + e\right)^{6} + 4 \, {\left(231 \, {\left(a b - b^{2}\right)} \cosh\left(f x + e\right)^{6} + 105 \, {\left(8 \, a^{2} - 25 \, a b + 17 \, b^{2}\right)} \cosh\left(f x + e\right)^{4} + 7 \, {\left(112 \, a^{2} - 335 \, a b + 223 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + 36 \, a^{2} - 118 \, a b + 82 \, b^{2}\right)} \sinh\left(f x + e\right)^{6} + 8 \, {\left(99 \, {\left(a b - b^{2}\right)} \cosh\left(f x + e\right)^{7} + 63 \, {\left(8 \, a^{2} - 25 \, a b + 17 \, b^{2}\right)} \cosh\left(f x + e\right)^{5} + 7 \, {\left(112 \, a^{2} - 335 \, a b + 223 \, b^{2}\right)} \cosh\left(f x + e\right)^{3} + 6 \, {\left(18 \, a^{2} - 59 \, a b + 41 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + {\left(112 \, a^{2} - 335 \, a b + 223 \, b^{2}\right)} \cosh\left(f x + e\right)^{4} + {\left(495 \, {\left(a b - b^{2}\right)} \cosh\left(f x + e\right)^{8} + 420 \, {\left(8 \, a^{2} - 25 \, a b + 17 \, b^{2}\right)} \cosh\left(f x + e\right)^{6} + 70 \, {\left(112 \, a^{2} - 335 \, a b + 223 \, b^{2}\right)} \cosh\left(f x + e\right)^{4} + 120 \, {\left(18 \, a^{2} - 59 \, a b + 41 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + 112 \, a^{2} - 335 \, a b + 223 \, b^{2}\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(55 \, {\left(a b - b^{2}\right)} \cosh\left(f x + e\right)^{9} + 60 \, {\left(8 \, a^{2} - 25 \, a b + 17 \, b^{2}\right)} \cosh\left(f x + e\right)^{7} + 14 \, {\left(112 \, a^{2} - 335 \, a b + 223 \, b^{2}\right)} \cosh\left(f x + e\right)^{5} + 40 \, {\left(18 \, a^{2} - 59 \, a b + 41 \, b^{2}\right)} \cosh\left(f x + e\right)^{3} + {\left(112 \, a^{2} - 335 \, a b + 223 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 2 \, {\left(8 \, a^{2} - 25 \, a b + 17 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(33 \, {\left(a b - b^{2}\right)} \cosh\left(f x + e\right)^{10} + 45 \, {\left(8 \, a^{2} - 25 \, a b + 17 \, b^{2}\right)} \cosh\left(f x + e\right)^{8} + 14 \, {\left(112 \, a^{2} - 335 \, a b + 223 \, b^{2}\right)} \cosh\left(f x + e\right)^{6} + 60 \, {\left(18 \, a^{2} - 59 \, a b + 41 \, b^{2}\right)} \cosh\left(f x + e\right)^{4} + 3 \, {\left(112 \, a^{2} - 335 \, a b + 223 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + 8 \, a^{2} - 25 \, a b + 17 \, b^{2}\right)} \sinh\left(f x + e\right)^{2} + a b - b^{2} + 4 \, {\left(3 \, {\left(a b - b^{2}\right)} \cosh\left(f x + e\right)^{11} + 5 \, {\left(8 \, a^{2} - 25 \, a b + 17 \, b^{2}\right)} \cosh\left(f x + e\right)^{9} + 2 \, {\left(112 \, a^{2} - 335 \, a b + 223 \, b^{2}\right)} \cosh\left(f x + e\right)^{7} + 12 \, {\left(18 \, a^{2} - 59 \, a b + 41 \, b^{2}\right)} \cosh\left(f x + e\right)^{5} + {\left(112 \, a^{2} - 335 \, a b + 223 \, b^{2}\right)} \cosh\left(f x + e\right)^{3} + {\left(8 \, a^{2} - 25 \, a b + 17 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{48 \, {\left({\left(a - b\right)} f \cosh\left(f x + e\right)^{11} + 11 \, {\left(a - b\right)} f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{10} + {\left(a - b\right)} f \sinh\left(f x + e\right)^{11} + 4 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{9} + {\left(55 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{2} + 4 \, {\left(a - b\right)} f\right)} \sinh\left(f x + e\right)^{9} + 6 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{7} + 3 \, {\left(55 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{3} + 12 \, {\left(a - b\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{8} + 6 \, {\left(55 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{4} + 24 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{2} + {\left(a - b\right)} f\right)} \sinh\left(f x + e\right)^{7} + 4 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{5} + 42 \, {\left(11 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{5} + 8 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{3} + {\left(a - b\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{6} + 2 \, {\left(231 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{6} + 252 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{4} + 63 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{2} + 2 \, {\left(a - b\right)} f\right)} \sinh\left(f x + e\right)^{5} + {\left(a - b\right)} f \cosh\left(f x + e\right)^{3} + 2 \, {\left(165 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{7} + 252 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{5} + 105 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{3} + 10 \, {\left(a - b\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{4} + {\left(165 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{8} + 336 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{6} + 210 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{4} + 40 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{2} + {\left(a - b\right)} f\right)} \sinh\left(f x + e\right)^{3} + {\left(55 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{9} + 144 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{7} + 126 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{5} + 40 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{3} + 3 \, {\left(a - b\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{2} + {\left(11 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{10} + 36 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{8} + 42 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{6} + 20 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{4} + 3 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)\right)}}, -\frac{3 \, {\left({\left(8 \, a^{2} - 40 \, a b + 35 \, b^{2}\right)} \cosh\left(f x + e\right)^{11} + 11 \, {\left(8 \, a^{2} - 40 \, a b + 35 \, b^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{10} + {\left(8 \, a^{2} - 40 \, a b + 35 \, b^{2}\right)} \sinh\left(f x + e\right)^{11} + 4 \, {\left(8 \, a^{2} - 40 \, a b + 35 \, b^{2}\right)} \cosh\left(f x + e\right)^{9} + {\left(55 \, {\left(8 \, a^{2} - 40 \, a b + 35 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + 32 \, a^{2} - 160 \, a b + 140 \, b^{2}\right)} \sinh\left(f x + e\right)^{9} + 3 \, {\left(55 \, {\left(8 \, a^{2} - 40 \, a b + 35 \, b^{2}\right)} \cosh\left(f x + e\right)^{3} + 12 \, {\left(8 \, a^{2} - 40 \, a b + 35 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{8} + 6 \, {\left(8 \, a^{2} - 40 \, a b + 35 \, b^{2}\right)} \cosh\left(f x + e\right)^{7} + 6 \, {\left(55 \, {\left(8 \, a^{2} - 40 \, a b + 35 \, b^{2}\right)} \cosh\left(f x + e\right)^{4} + 24 \, {\left(8 \, a^{2} - 40 \, a b + 35 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + 8 \, a^{2} - 40 \, a b + 35 \, b^{2}\right)} \sinh\left(f x + e\right)^{7} + 42 \, {\left(11 \, {\left(8 \, a^{2} - 40 \, a b + 35 \, b^{2}\right)} \cosh\left(f x + e\right)^{5} + 8 \, {\left(8 \, a^{2} - 40 \, a b + 35 \, b^{2}\right)} \cosh\left(f x + e\right)^{3} + {\left(8 \, a^{2} - 40 \, a b + 35 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{6} + 4 \, {\left(8 \, a^{2} - 40 \, a b + 35 \, b^{2}\right)} \cosh\left(f x + e\right)^{5} + 2 \, {\left(231 \, {\left(8 \, a^{2} - 40 \, a b + 35 \, b^{2}\right)} \cosh\left(f x + e\right)^{6} + 252 \, {\left(8 \, a^{2} - 40 \, a b + 35 \, b^{2}\right)} \cosh\left(f x + e\right)^{4} + 63 \, {\left(8 \, a^{2} - 40 \, a b + 35 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + 16 \, a^{2} - 80 \, a b + 70 \, b^{2}\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(165 \, {\left(8 \, a^{2} - 40 \, a b + 35 \, b^{2}\right)} \cosh\left(f x + e\right)^{7} + 252 \, {\left(8 \, a^{2} - 40 \, a b + 35 \, b^{2}\right)} \cosh\left(f x + e\right)^{5} + 105 \, {\left(8 \, a^{2} - 40 \, a b + 35 \, b^{2}\right)} \cosh\left(f x + e\right)^{3} + 10 \, {\left(8 \, a^{2} - 40 \, a b + 35 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{4} + {\left(8 \, a^{2} - 40 \, a b + 35 \, b^{2}\right)} \cosh\left(f x + e\right)^{3} + {\left(165 \, {\left(8 \, a^{2} - 40 \, a b + 35 \, b^{2}\right)} \cosh\left(f x + e\right)^{8} + 336 \, {\left(8 \, a^{2} - 40 \, a b + 35 \, b^{2}\right)} \cosh\left(f x + e\right)^{6} + 210 \, {\left(8 \, a^{2} - 40 \, a b + 35 \, b^{2}\right)} \cosh\left(f x + e\right)^{4} + 40 \, {\left(8 \, a^{2} - 40 \, a b + 35 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + 8 \, a^{2} - 40 \, a b + 35 \, b^{2}\right)} \sinh\left(f x + e\right)^{3} + {\left(55 \, {\left(8 \, a^{2} - 40 \, a b + 35 \, b^{2}\right)} \cosh\left(f x + e\right)^{9} + 144 \, {\left(8 \, a^{2} - 40 \, a b + 35 \, b^{2}\right)} \cosh\left(f x + e\right)^{7} + 126 \, {\left(8 \, a^{2} - 40 \, a b + 35 \, b^{2}\right)} \cosh\left(f x + e\right)^{5} + 40 \, {\left(8 \, a^{2} - 40 \, a b + 35 \, b^{2}\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(8 \, a^{2} - 40 \, a b + 35 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{2} + {\left(11 \, {\left(8 \, a^{2} - 40 \, a b + 35 \, b^{2}\right)} \cosh\left(f x + e\right)^{10} + 36 \, {\left(8 \, a^{2} - 40 \, a b + 35 \, b^{2}\right)} \cosh\left(f x + e\right)^{8} + 42 \, {\left(8 \, a^{2} - 40 \, a b + 35 \, b^{2}\right)} \cosh\left(f x + e\right)^{6} + 20 \, {\left(8 \, a^{2} - 40 \, a b + 35 \, b^{2}\right)} \cosh\left(f x + e\right)^{4} + 3 \, {\left(8 \, a^{2} - 40 \, a b + 35 \, b^{2}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)\right)} \sqrt{-a + b} \arctan\left(-\frac{\sqrt{2} \sqrt{-a + b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{2 \, {\left({\left(a - b\right)} \cosh\left(f x + e\right) + {\left(a - b\right)} \sinh\left(f x + e\right)\right)}}\right) - \sqrt{2} {\left({\left(a b - b^{2}\right)} \cosh\left(f x + e\right)^{12} + 12 \, {\left(a b - b^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{11} + {\left(a b - b^{2}\right)} \sinh\left(f x + e\right)^{12} + 2 \, {\left(8 \, a^{2} - 25 \, a b + 17 \, b^{2}\right)} \cosh\left(f x + e\right)^{10} + 2 \, {\left(33 \, {\left(a b - b^{2}\right)} \cosh\left(f x + e\right)^{2} + 8 \, a^{2} - 25 \, a b + 17 \, b^{2}\right)} \sinh\left(f x + e\right)^{10} + 20 \, {\left(11 \, {\left(a b - b^{2}\right)} \cosh\left(f x + e\right)^{3} + {\left(8 \, a^{2} - 25 \, a b + 17 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{9} + {\left(112 \, a^{2} - 335 \, a b + 223 \, b^{2}\right)} \cosh\left(f x + e\right)^{8} + {\left(495 \, {\left(a b - b^{2}\right)} \cosh\left(f x + e\right)^{4} + 90 \, {\left(8 \, a^{2} - 25 \, a b + 17 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + 112 \, a^{2} - 335 \, a b + 223 \, b^{2}\right)} \sinh\left(f x + e\right)^{8} + 8 \, {\left(99 \, {\left(a b - b^{2}\right)} \cosh\left(f x + e\right)^{5} + 30 \, {\left(8 \, a^{2} - 25 \, a b + 17 \, b^{2}\right)} \cosh\left(f x + e\right)^{3} + {\left(112 \, a^{2} - 335 \, a b + 223 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{7} + 8 \, {\left(18 \, a^{2} - 59 \, a b + 41 \, b^{2}\right)} \cosh\left(f x + e\right)^{6} + 4 \, {\left(231 \, {\left(a b - b^{2}\right)} \cosh\left(f x + e\right)^{6} + 105 \, {\left(8 \, a^{2} - 25 \, a b + 17 \, b^{2}\right)} \cosh\left(f x + e\right)^{4} + 7 \, {\left(112 \, a^{2} - 335 \, a b + 223 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + 36 \, a^{2} - 118 \, a b + 82 \, b^{2}\right)} \sinh\left(f x + e\right)^{6} + 8 \, {\left(99 \, {\left(a b - b^{2}\right)} \cosh\left(f x + e\right)^{7} + 63 \, {\left(8 \, a^{2} - 25 \, a b + 17 \, b^{2}\right)} \cosh\left(f x + e\right)^{5} + 7 \, {\left(112 \, a^{2} - 335 \, a b + 223 \, b^{2}\right)} \cosh\left(f x + e\right)^{3} + 6 \, {\left(18 \, a^{2} - 59 \, a b + 41 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + {\left(112 \, a^{2} - 335 \, a b + 223 \, b^{2}\right)} \cosh\left(f x + e\right)^{4} + {\left(495 \, {\left(a b - b^{2}\right)} \cosh\left(f x + e\right)^{8} + 420 \, {\left(8 \, a^{2} - 25 \, a b + 17 \, b^{2}\right)} \cosh\left(f x + e\right)^{6} + 70 \, {\left(112 \, a^{2} - 335 \, a b + 223 \, b^{2}\right)} \cosh\left(f x + e\right)^{4} + 120 \, {\left(18 \, a^{2} - 59 \, a b + 41 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + 112 \, a^{2} - 335 \, a b + 223 \, b^{2}\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(55 \, {\left(a b - b^{2}\right)} \cosh\left(f x + e\right)^{9} + 60 \, {\left(8 \, a^{2} - 25 \, a b + 17 \, b^{2}\right)} \cosh\left(f x + e\right)^{7} + 14 \, {\left(112 \, a^{2} - 335 \, a b + 223 \, b^{2}\right)} \cosh\left(f x + e\right)^{5} + 40 \, {\left(18 \, a^{2} - 59 \, a b + 41 \, b^{2}\right)} \cosh\left(f x + e\right)^{3} + {\left(112 \, a^{2} - 335 \, a b + 223 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 2 \, {\left(8 \, a^{2} - 25 \, a b + 17 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(33 \, {\left(a b - b^{2}\right)} \cosh\left(f x + e\right)^{10} + 45 \, {\left(8 \, a^{2} - 25 \, a b + 17 \, b^{2}\right)} \cosh\left(f x + e\right)^{8} + 14 \, {\left(112 \, a^{2} - 335 \, a b + 223 \, b^{2}\right)} \cosh\left(f x + e\right)^{6} + 60 \, {\left(18 \, a^{2} - 59 \, a b + 41 \, b^{2}\right)} \cosh\left(f x + e\right)^{4} + 3 \, {\left(112 \, a^{2} - 335 \, a b + 223 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + 8 \, a^{2} - 25 \, a b + 17 \, b^{2}\right)} \sinh\left(f x + e\right)^{2} + a b - b^{2} + 4 \, {\left(3 \, {\left(a b - b^{2}\right)} \cosh\left(f x + e\right)^{11} + 5 \, {\left(8 \, a^{2} - 25 \, a b + 17 \, b^{2}\right)} \cosh\left(f x + e\right)^{9} + 2 \, {\left(112 \, a^{2} - 335 \, a b + 223 \, b^{2}\right)} \cosh\left(f x + e\right)^{7} + 12 \, {\left(18 \, a^{2} - 59 \, a b + 41 \, b^{2}\right)} \cosh\left(f x + e\right)^{5} + {\left(112 \, a^{2} - 335 \, a b + 223 \, b^{2}\right)} \cosh\left(f x + e\right)^{3} + {\left(8 \, a^{2} - 25 \, a b + 17 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{24 \, {\left({\left(a - b\right)} f \cosh\left(f x + e\right)^{11} + 11 \, {\left(a - b\right)} f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{10} + {\left(a - b\right)} f \sinh\left(f x + e\right)^{11} + 4 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{9} + {\left(55 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{2} + 4 \, {\left(a - b\right)} f\right)} \sinh\left(f x + e\right)^{9} + 6 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{7} + 3 \, {\left(55 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{3} + 12 \, {\left(a - b\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{8} + 6 \, {\left(55 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{4} + 24 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{2} + {\left(a - b\right)} f\right)} \sinh\left(f x + e\right)^{7} + 4 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{5} + 42 \, {\left(11 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{5} + 8 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{3} + {\left(a - b\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{6} + 2 \, {\left(231 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{6} + 252 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{4} + 63 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{2} + 2 \, {\left(a - b\right)} f\right)} \sinh\left(f x + e\right)^{5} + {\left(a - b\right)} f \cosh\left(f x + e\right)^{3} + 2 \, {\left(165 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{7} + 252 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{5} + 105 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{3} + 10 \, {\left(a - b\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{4} + {\left(165 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{8} + 336 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{6} + 210 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{4} + 40 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{2} + {\left(a - b\right)} f\right)} \sinh\left(f x + e\right)^{3} + {\left(55 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{9} + 144 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{7} + 126 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{5} + 40 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{3} + 3 \, {\left(a - b\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{2} + {\left(11 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{10} + 36 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{8} + 42 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{6} + 20 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{4} + 3 \, {\left(a - b\right)} f \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)\right)}}\right]"," ",0,"[1/48*(3*((8*a^2 - 40*a*b + 35*b^2)*cosh(f*x + e)^11 + 11*(8*a^2 - 40*a*b + 35*b^2)*cosh(f*x + e)*sinh(f*x + e)^10 + (8*a^2 - 40*a*b + 35*b^2)*sinh(f*x + e)^11 + 4*(8*a^2 - 40*a*b + 35*b^2)*cosh(f*x + e)^9 + (55*(8*a^2 - 40*a*b + 35*b^2)*cosh(f*x + e)^2 + 32*a^2 - 160*a*b + 140*b^2)*sinh(f*x + e)^9 + 3*(55*(8*a^2 - 40*a*b + 35*b^2)*cosh(f*x + e)^3 + 12*(8*a^2 - 40*a*b + 35*b^2)*cosh(f*x + e))*sinh(f*x + e)^8 + 6*(8*a^2 - 40*a*b + 35*b^2)*cosh(f*x + e)^7 + 6*(55*(8*a^2 - 40*a*b + 35*b^2)*cosh(f*x + e)^4 + 24*(8*a^2 - 40*a*b + 35*b^2)*cosh(f*x + e)^2 + 8*a^2 - 40*a*b + 35*b^2)*sinh(f*x + e)^7 + 42*(11*(8*a^2 - 40*a*b + 35*b^2)*cosh(f*x + e)^5 + 8*(8*a^2 - 40*a*b + 35*b^2)*cosh(f*x + e)^3 + (8*a^2 - 40*a*b + 35*b^2)*cosh(f*x + e))*sinh(f*x + e)^6 + 4*(8*a^2 - 40*a*b + 35*b^2)*cosh(f*x + e)^5 + 2*(231*(8*a^2 - 40*a*b + 35*b^2)*cosh(f*x + e)^6 + 252*(8*a^2 - 40*a*b + 35*b^2)*cosh(f*x + e)^4 + 63*(8*a^2 - 40*a*b + 35*b^2)*cosh(f*x + e)^2 + 16*a^2 - 80*a*b + 70*b^2)*sinh(f*x + e)^5 + 2*(165*(8*a^2 - 40*a*b + 35*b^2)*cosh(f*x + e)^7 + 252*(8*a^2 - 40*a*b + 35*b^2)*cosh(f*x + e)^5 + 105*(8*a^2 - 40*a*b + 35*b^2)*cosh(f*x + e)^3 + 10*(8*a^2 - 40*a*b + 35*b^2)*cosh(f*x + e))*sinh(f*x + e)^4 + (8*a^2 - 40*a*b + 35*b^2)*cosh(f*x + e)^3 + (165*(8*a^2 - 40*a*b + 35*b^2)*cosh(f*x + e)^8 + 336*(8*a^2 - 40*a*b + 35*b^2)*cosh(f*x + e)^6 + 210*(8*a^2 - 40*a*b + 35*b^2)*cosh(f*x + e)^4 + 40*(8*a^2 - 40*a*b + 35*b^2)*cosh(f*x + e)^2 + 8*a^2 - 40*a*b + 35*b^2)*sinh(f*x + e)^3 + (55*(8*a^2 - 40*a*b + 35*b^2)*cosh(f*x + e)^9 + 144*(8*a^2 - 40*a*b + 35*b^2)*cosh(f*x + e)^7 + 126*(8*a^2 - 40*a*b + 35*b^2)*cosh(f*x + e)^5 + 40*(8*a^2 - 40*a*b + 35*b^2)*cosh(f*x + e)^3 + 3*(8*a^2 - 40*a*b + 35*b^2)*cosh(f*x + e))*sinh(f*x + e)^2 + (11*(8*a^2 - 40*a*b + 35*b^2)*cosh(f*x + e)^10 + 36*(8*a^2 - 40*a*b + 35*b^2)*cosh(f*x + e)^8 + 42*(8*a^2 - 40*a*b + 35*b^2)*cosh(f*x + e)^6 + 20*(8*a^2 - 40*a*b + 35*b^2)*cosh(f*x + e)^4 + 3*(8*a^2 - 40*a*b + 35*b^2)*cosh(f*x + e)^2)*sinh(f*x + e))*sqrt(a - b)*log((b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(4*a - 3*b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 4*a - 3*b)*sinh(f*x + e)^2 - 4*sqrt(2)*sqrt(a - b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))*(cosh(f*x + e) + sinh(f*x + e)) + 4*(b*cosh(f*x + e)^3 + (4*a - 3*b)*cosh(f*x + e))*sinh(f*x + e) + b)/(cosh(f*x + e)^4 + 4*cosh(f*x + e)*sinh(f*x + e)^3 + sinh(f*x + e)^4 + 2*(3*cosh(f*x + e)^2 + 1)*sinh(f*x + e)^2 + 2*cosh(f*x + e)^2 + 4*(cosh(f*x + e)^3 + cosh(f*x + e))*sinh(f*x + e) + 1)) + 2*sqrt(2)*((a*b - b^2)*cosh(f*x + e)^12 + 12*(a*b - b^2)*cosh(f*x + e)*sinh(f*x + e)^11 + (a*b - b^2)*sinh(f*x + e)^12 + 2*(8*a^2 - 25*a*b + 17*b^2)*cosh(f*x + e)^10 + 2*(33*(a*b - b^2)*cosh(f*x + e)^2 + 8*a^2 - 25*a*b + 17*b^2)*sinh(f*x + e)^10 + 20*(11*(a*b - b^2)*cosh(f*x + e)^3 + (8*a^2 - 25*a*b + 17*b^2)*cosh(f*x + e))*sinh(f*x + e)^9 + (112*a^2 - 335*a*b + 223*b^2)*cosh(f*x + e)^8 + (495*(a*b - b^2)*cosh(f*x + e)^4 + 90*(8*a^2 - 25*a*b + 17*b^2)*cosh(f*x + e)^2 + 112*a^2 - 335*a*b + 223*b^2)*sinh(f*x + e)^8 + 8*(99*(a*b - b^2)*cosh(f*x + e)^5 + 30*(8*a^2 - 25*a*b + 17*b^2)*cosh(f*x + e)^3 + (112*a^2 - 335*a*b + 223*b^2)*cosh(f*x + e))*sinh(f*x + e)^7 + 8*(18*a^2 - 59*a*b + 41*b^2)*cosh(f*x + e)^6 + 4*(231*(a*b - b^2)*cosh(f*x + e)^6 + 105*(8*a^2 - 25*a*b + 17*b^2)*cosh(f*x + e)^4 + 7*(112*a^2 - 335*a*b + 223*b^2)*cosh(f*x + e)^2 + 36*a^2 - 118*a*b + 82*b^2)*sinh(f*x + e)^6 + 8*(99*(a*b - b^2)*cosh(f*x + e)^7 + 63*(8*a^2 - 25*a*b + 17*b^2)*cosh(f*x + e)^5 + 7*(112*a^2 - 335*a*b + 223*b^2)*cosh(f*x + e)^3 + 6*(18*a^2 - 59*a*b + 41*b^2)*cosh(f*x + e))*sinh(f*x + e)^5 + (112*a^2 - 335*a*b + 223*b^2)*cosh(f*x + e)^4 + (495*(a*b - b^2)*cosh(f*x + e)^8 + 420*(8*a^2 - 25*a*b + 17*b^2)*cosh(f*x + e)^6 + 70*(112*a^2 - 335*a*b + 223*b^2)*cosh(f*x + e)^4 + 120*(18*a^2 - 59*a*b + 41*b^2)*cosh(f*x + e)^2 + 112*a^2 - 335*a*b + 223*b^2)*sinh(f*x + e)^4 + 4*(55*(a*b - b^2)*cosh(f*x + e)^9 + 60*(8*a^2 - 25*a*b + 17*b^2)*cosh(f*x + e)^7 + 14*(112*a^2 - 335*a*b + 223*b^2)*cosh(f*x + e)^5 + 40*(18*a^2 - 59*a*b + 41*b^2)*cosh(f*x + e)^3 + (112*a^2 - 335*a*b + 223*b^2)*cosh(f*x + e))*sinh(f*x + e)^3 + 2*(8*a^2 - 25*a*b + 17*b^2)*cosh(f*x + e)^2 + 2*(33*(a*b - b^2)*cosh(f*x + e)^10 + 45*(8*a^2 - 25*a*b + 17*b^2)*cosh(f*x + e)^8 + 14*(112*a^2 - 335*a*b + 223*b^2)*cosh(f*x + e)^6 + 60*(18*a^2 - 59*a*b + 41*b^2)*cosh(f*x + e)^4 + 3*(112*a^2 - 335*a*b + 223*b^2)*cosh(f*x + e)^2 + 8*a^2 - 25*a*b + 17*b^2)*sinh(f*x + e)^2 + a*b - b^2 + 4*(3*(a*b - b^2)*cosh(f*x + e)^11 + 5*(8*a^2 - 25*a*b + 17*b^2)*cosh(f*x + e)^9 + 2*(112*a^2 - 335*a*b + 223*b^2)*cosh(f*x + e)^7 + 12*(18*a^2 - 59*a*b + 41*b^2)*cosh(f*x + e)^5 + (112*a^2 - 335*a*b + 223*b^2)*cosh(f*x + e)^3 + (8*a^2 - 25*a*b + 17*b^2)*cosh(f*x + e))*sinh(f*x + e))*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/((a - b)*f*cosh(f*x + e)^11 + 11*(a - b)*f*cosh(f*x + e)*sinh(f*x + e)^10 + (a - b)*f*sinh(f*x + e)^11 + 4*(a - b)*f*cosh(f*x + e)^9 + (55*(a - b)*f*cosh(f*x + e)^2 + 4*(a - b)*f)*sinh(f*x + e)^9 + 6*(a - b)*f*cosh(f*x + e)^7 + 3*(55*(a - b)*f*cosh(f*x + e)^3 + 12*(a - b)*f*cosh(f*x + e))*sinh(f*x + e)^8 + 6*(55*(a - b)*f*cosh(f*x + e)^4 + 24*(a - b)*f*cosh(f*x + e)^2 + (a - b)*f)*sinh(f*x + e)^7 + 4*(a - b)*f*cosh(f*x + e)^5 + 42*(11*(a - b)*f*cosh(f*x + e)^5 + 8*(a - b)*f*cosh(f*x + e)^3 + (a - b)*f*cosh(f*x + e))*sinh(f*x + e)^6 + 2*(231*(a - b)*f*cosh(f*x + e)^6 + 252*(a - b)*f*cosh(f*x + e)^4 + 63*(a - b)*f*cosh(f*x + e)^2 + 2*(a - b)*f)*sinh(f*x + e)^5 + (a - b)*f*cosh(f*x + e)^3 + 2*(165*(a - b)*f*cosh(f*x + e)^7 + 252*(a - b)*f*cosh(f*x + e)^5 + 105*(a - b)*f*cosh(f*x + e)^3 + 10*(a - b)*f*cosh(f*x + e))*sinh(f*x + e)^4 + (165*(a - b)*f*cosh(f*x + e)^8 + 336*(a - b)*f*cosh(f*x + e)^6 + 210*(a - b)*f*cosh(f*x + e)^4 + 40*(a - b)*f*cosh(f*x + e)^2 + (a - b)*f)*sinh(f*x + e)^3 + (55*(a - b)*f*cosh(f*x + e)^9 + 144*(a - b)*f*cosh(f*x + e)^7 + 126*(a - b)*f*cosh(f*x + e)^5 + 40*(a - b)*f*cosh(f*x + e)^3 + 3*(a - b)*f*cosh(f*x + e))*sinh(f*x + e)^2 + (11*(a - b)*f*cosh(f*x + e)^10 + 36*(a - b)*f*cosh(f*x + e)^8 + 42*(a - b)*f*cosh(f*x + e)^6 + 20*(a - b)*f*cosh(f*x + e)^4 + 3*(a - b)*f*cosh(f*x + e)^2)*sinh(f*x + e)), -1/24*(3*((8*a^2 - 40*a*b + 35*b^2)*cosh(f*x + e)^11 + 11*(8*a^2 - 40*a*b + 35*b^2)*cosh(f*x + e)*sinh(f*x + e)^10 + (8*a^2 - 40*a*b + 35*b^2)*sinh(f*x + e)^11 + 4*(8*a^2 - 40*a*b + 35*b^2)*cosh(f*x + e)^9 + (55*(8*a^2 - 40*a*b + 35*b^2)*cosh(f*x + e)^2 + 32*a^2 - 160*a*b + 140*b^2)*sinh(f*x + e)^9 + 3*(55*(8*a^2 - 40*a*b + 35*b^2)*cosh(f*x + e)^3 + 12*(8*a^2 - 40*a*b + 35*b^2)*cosh(f*x + e))*sinh(f*x + e)^8 + 6*(8*a^2 - 40*a*b + 35*b^2)*cosh(f*x + e)^7 + 6*(55*(8*a^2 - 40*a*b + 35*b^2)*cosh(f*x + e)^4 + 24*(8*a^2 - 40*a*b + 35*b^2)*cosh(f*x + e)^2 + 8*a^2 - 40*a*b + 35*b^2)*sinh(f*x + e)^7 + 42*(11*(8*a^2 - 40*a*b + 35*b^2)*cosh(f*x + e)^5 + 8*(8*a^2 - 40*a*b + 35*b^2)*cosh(f*x + e)^3 + (8*a^2 - 40*a*b + 35*b^2)*cosh(f*x + e))*sinh(f*x + e)^6 + 4*(8*a^2 - 40*a*b + 35*b^2)*cosh(f*x + e)^5 + 2*(231*(8*a^2 - 40*a*b + 35*b^2)*cosh(f*x + e)^6 + 252*(8*a^2 - 40*a*b + 35*b^2)*cosh(f*x + e)^4 + 63*(8*a^2 - 40*a*b + 35*b^2)*cosh(f*x + e)^2 + 16*a^2 - 80*a*b + 70*b^2)*sinh(f*x + e)^5 + 2*(165*(8*a^2 - 40*a*b + 35*b^2)*cosh(f*x + e)^7 + 252*(8*a^2 - 40*a*b + 35*b^2)*cosh(f*x + e)^5 + 105*(8*a^2 - 40*a*b + 35*b^2)*cosh(f*x + e)^3 + 10*(8*a^2 - 40*a*b + 35*b^2)*cosh(f*x + e))*sinh(f*x + e)^4 + (8*a^2 - 40*a*b + 35*b^2)*cosh(f*x + e)^3 + (165*(8*a^2 - 40*a*b + 35*b^2)*cosh(f*x + e)^8 + 336*(8*a^2 - 40*a*b + 35*b^2)*cosh(f*x + e)^6 + 210*(8*a^2 - 40*a*b + 35*b^2)*cosh(f*x + e)^4 + 40*(8*a^2 - 40*a*b + 35*b^2)*cosh(f*x + e)^2 + 8*a^2 - 40*a*b + 35*b^2)*sinh(f*x + e)^3 + (55*(8*a^2 - 40*a*b + 35*b^2)*cosh(f*x + e)^9 + 144*(8*a^2 - 40*a*b + 35*b^2)*cosh(f*x + e)^7 + 126*(8*a^2 - 40*a*b + 35*b^2)*cosh(f*x + e)^5 + 40*(8*a^2 - 40*a*b + 35*b^2)*cosh(f*x + e)^3 + 3*(8*a^2 - 40*a*b + 35*b^2)*cosh(f*x + e))*sinh(f*x + e)^2 + (11*(8*a^2 - 40*a*b + 35*b^2)*cosh(f*x + e)^10 + 36*(8*a^2 - 40*a*b + 35*b^2)*cosh(f*x + e)^8 + 42*(8*a^2 - 40*a*b + 35*b^2)*cosh(f*x + e)^6 + 20*(8*a^2 - 40*a*b + 35*b^2)*cosh(f*x + e)^4 + 3*(8*a^2 - 40*a*b + 35*b^2)*cosh(f*x + e)^2)*sinh(f*x + e))*sqrt(-a + b)*arctan(-1/2*sqrt(2)*sqrt(-a + b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/((a - b)*cosh(f*x + e) + (a - b)*sinh(f*x + e))) - sqrt(2)*((a*b - b^2)*cosh(f*x + e)^12 + 12*(a*b - b^2)*cosh(f*x + e)*sinh(f*x + e)^11 + (a*b - b^2)*sinh(f*x + e)^12 + 2*(8*a^2 - 25*a*b + 17*b^2)*cosh(f*x + e)^10 + 2*(33*(a*b - b^2)*cosh(f*x + e)^2 + 8*a^2 - 25*a*b + 17*b^2)*sinh(f*x + e)^10 + 20*(11*(a*b - b^2)*cosh(f*x + e)^3 + (8*a^2 - 25*a*b + 17*b^2)*cosh(f*x + e))*sinh(f*x + e)^9 + (112*a^2 - 335*a*b + 223*b^2)*cosh(f*x + e)^8 + (495*(a*b - b^2)*cosh(f*x + e)^4 + 90*(8*a^2 - 25*a*b + 17*b^2)*cosh(f*x + e)^2 + 112*a^2 - 335*a*b + 223*b^2)*sinh(f*x + e)^8 + 8*(99*(a*b - b^2)*cosh(f*x + e)^5 + 30*(8*a^2 - 25*a*b + 17*b^2)*cosh(f*x + e)^3 + (112*a^2 - 335*a*b + 223*b^2)*cosh(f*x + e))*sinh(f*x + e)^7 + 8*(18*a^2 - 59*a*b + 41*b^2)*cosh(f*x + e)^6 + 4*(231*(a*b - b^2)*cosh(f*x + e)^6 + 105*(8*a^2 - 25*a*b + 17*b^2)*cosh(f*x + e)^4 + 7*(112*a^2 - 335*a*b + 223*b^2)*cosh(f*x + e)^2 + 36*a^2 - 118*a*b + 82*b^2)*sinh(f*x + e)^6 + 8*(99*(a*b - b^2)*cosh(f*x + e)^7 + 63*(8*a^2 - 25*a*b + 17*b^2)*cosh(f*x + e)^5 + 7*(112*a^2 - 335*a*b + 223*b^2)*cosh(f*x + e)^3 + 6*(18*a^2 - 59*a*b + 41*b^2)*cosh(f*x + e))*sinh(f*x + e)^5 + (112*a^2 - 335*a*b + 223*b^2)*cosh(f*x + e)^4 + (495*(a*b - b^2)*cosh(f*x + e)^8 + 420*(8*a^2 - 25*a*b + 17*b^2)*cosh(f*x + e)^6 + 70*(112*a^2 - 335*a*b + 223*b^2)*cosh(f*x + e)^4 + 120*(18*a^2 - 59*a*b + 41*b^2)*cosh(f*x + e)^2 + 112*a^2 - 335*a*b + 223*b^2)*sinh(f*x + e)^4 + 4*(55*(a*b - b^2)*cosh(f*x + e)^9 + 60*(8*a^2 - 25*a*b + 17*b^2)*cosh(f*x + e)^7 + 14*(112*a^2 - 335*a*b + 223*b^2)*cosh(f*x + e)^5 + 40*(18*a^2 - 59*a*b + 41*b^2)*cosh(f*x + e)^3 + (112*a^2 - 335*a*b + 223*b^2)*cosh(f*x + e))*sinh(f*x + e)^3 + 2*(8*a^2 - 25*a*b + 17*b^2)*cosh(f*x + e)^2 + 2*(33*(a*b - b^2)*cosh(f*x + e)^10 + 45*(8*a^2 - 25*a*b + 17*b^2)*cosh(f*x + e)^8 + 14*(112*a^2 - 335*a*b + 223*b^2)*cosh(f*x + e)^6 + 60*(18*a^2 - 59*a*b + 41*b^2)*cosh(f*x + e)^4 + 3*(112*a^2 - 335*a*b + 223*b^2)*cosh(f*x + e)^2 + 8*a^2 - 25*a*b + 17*b^2)*sinh(f*x + e)^2 + a*b - b^2 + 4*(3*(a*b - b^2)*cosh(f*x + e)^11 + 5*(8*a^2 - 25*a*b + 17*b^2)*cosh(f*x + e)^9 + 2*(112*a^2 - 335*a*b + 223*b^2)*cosh(f*x + e)^7 + 12*(18*a^2 - 59*a*b + 41*b^2)*cosh(f*x + e)^5 + (112*a^2 - 335*a*b + 223*b^2)*cosh(f*x + e)^3 + (8*a^2 - 25*a*b + 17*b^2)*cosh(f*x + e))*sinh(f*x + e))*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/((a - b)*f*cosh(f*x + e)^11 + 11*(a - b)*f*cosh(f*x + e)*sinh(f*x + e)^10 + (a - b)*f*sinh(f*x + e)^11 + 4*(a - b)*f*cosh(f*x + e)^9 + (55*(a - b)*f*cosh(f*x + e)^2 + 4*(a - b)*f)*sinh(f*x + e)^9 + 6*(a - b)*f*cosh(f*x + e)^7 + 3*(55*(a - b)*f*cosh(f*x + e)^3 + 12*(a - b)*f*cosh(f*x + e))*sinh(f*x + e)^8 + 6*(55*(a - b)*f*cosh(f*x + e)^4 + 24*(a - b)*f*cosh(f*x + e)^2 + (a - b)*f)*sinh(f*x + e)^7 + 4*(a - b)*f*cosh(f*x + e)^5 + 42*(11*(a - b)*f*cosh(f*x + e)^5 + 8*(a - b)*f*cosh(f*x + e)^3 + (a - b)*f*cosh(f*x + e))*sinh(f*x + e)^6 + 2*(231*(a - b)*f*cosh(f*x + e)^6 + 252*(a - b)*f*cosh(f*x + e)^4 + 63*(a - b)*f*cosh(f*x + e)^2 + 2*(a - b)*f)*sinh(f*x + e)^5 + (a - b)*f*cosh(f*x + e)^3 + 2*(165*(a - b)*f*cosh(f*x + e)^7 + 252*(a - b)*f*cosh(f*x + e)^5 + 105*(a - b)*f*cosh(f*x + e)^3 + 10*(a - b)*f*cosh(f*x + e))*sinh(f*x + e)^4 + (165*(a - b)*f*cosh(f*x + e)^8 + 336*(a - b)*f*cosh(f*x + e)^6 + 210*(a - b)*f*cosh(f*x + e)^4 + 40*(a - b)*f*cosh(f*x + e)^2 + (a - b)*f)*sinh(f*x + e)^3 + (55*(a - b)*f*cosh(f*x + e)^9 + 144*(a - b)*f*cosh(f*x + e)^7 + 126*(a - b)*f*cosh(f*x + e)^5 + 40*(a - b)*f*cosh(f*x + e)^3 + 3*(a - b)*f*cosh(f*x + e))*sinh(f*x + e)^2 + (11*(a - b)*f*cosh(f*x + e)^10 + 36*(a - b)*f*cosh(f*x + e)^8 + 42*(a - b)*f*cosh(f*x + e)^6 + 20*(a - b)*f*cosh(f*x + e)^4 + 3*(a - b)*f*cosh(f*x + e)^2)*sinh(f*x + e))]","B",0
469,1,2454,0,1.176226," ","integrate((a+b*sinh(f*x+e)^2)^(3/2)*tanh(f*x+e)^3,x, algorithm=""fricas"")","\left[-\frac{6 \, {\left({\left(2 \, a - 5 \, b\right)} \cosh\left(f x + e\right)^{7} + 7 \, {\left(2 \, a - 5 \, b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{6} + {\left(2 \, a - 5 \, b\right)} \sinh\left(f x + e\right)^{7} + 2 \, {\left(2 \, a - 5 \, b\right)} \cosh\left(f x + e\right)^{5} + {\left(21 \, {\left(2 \, a - 5 \, b\right)} \cosh\left(f x + e\right)^{2} + 4 \, a - 10 \, b\right)} \sinh\left(f x + e\right)^{5} + 5 \, {\left(7 \, {\left(2 \, a - 5 \, b\right)} \cosh\left(f x + e\right)^{3} + 2 \, {\left(2 \, a - 5 \, b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{4} + {\left(2 \, a - 5 \, b\right)} \cosh\left(f x + e\right)^{3} + {\left(35 \, {\left(2 \, a - 5 \, b\right)} \cosh\left(f x + e\right)^{4} + 20 \, {\left(2 \, a - 5 \, b\right)} \cosh\left(f x + e\right)^{2} + 2 \, a - 5 \, b\right)} \sinh\left(f x + e\right)^{3} + {\left(21 \, {\left(2 \, a - 5 \, b\right)} \cosh\left(f x + e\right)^{5} + 20 \, {\left(2 \, a - 5 \, b\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(2 \, a - 5 \, b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{2} + {\left(7 \, {\left(2 \, a - 5 \, b\right)} \cosh\left(f x + e\right)^{6} + 10 \, {\left(2 \, a - 5 \, b\right)} \cosh\left(f x + e\right)^{4} + 3 \, {\left(2 \, a - 5 \, b\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)\right)} \sqrt{a - b} \log\left(\frac{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(4 \, a - 3 \, b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + 4 \, a - 3 \, b\right)} \sinh\left(f x + e\right)^{2} + 4 \, \sqrt{2} \sqrt{a - b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} {\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right)\right)} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(4 \, a - 3 \, b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}{\cosh\left(f x + e\right)^{4} + 4 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + \sinh\left(f x + e\right)^{4} + 2 \, {\left(3 \, \cosh\left(f x + e\right)^{2} + 1\right)} \sinh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right)^{2} + 4 \, {\left(\cosh\left(f x + e\right)^{3} + \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + 1}\right) - \sqrt{2} {\left(b \cosh\left(f x + e\right)^{8} + 8 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + b \sinh\left(f x + e\right)^{8} + 8 \, {\left(2 \, a - 3 \, b\right)} \cosh\left(f x + e\right)^{6} + 4 \, {\left(7 \, b \cosh\left(f x + e\right)^{2} + 4 \, a - 6 \, b\right)} \sinh\left(f x + e\right)^{6} + 8 \, {\left(7 \, b \cosh\left(f x + e\right)^{3} + 6 \, {\left(2 \, a - 3 \, b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(28 \, a - 37 \, b\right)} \cosh\left(f x + e\right)^{4} + 2 \, {\left(35 \, b \cosh\left(f x + e\right)^{4} + 60 \, {\left(2 \, a - 3 \, b\right)} \cosh\left(f x + e\right)^{2} + 28 \, a - 37 \, b\right)} \sinh\left(f x + e\right)^{4} + 8 \, {\left(7 \, b \cosh\left(f x + e\right)^{5} + 20 \, {\left(2 \, a - 3 \, b\right)} \cosh\left(f x + e\right)^{3} + {\left(28 \, a - 37 \, b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 8 \, {\left(2 \, a - 3 \, b\right)} \cosh\left(f x + e\right)^{2} + 4 \, {\left(7 \, b \cosh\left(f x + e\right)^{6} + 30 \, {\left(2 \, a - 3 \, b\right)} \cosh\left(f x + e\right)^{4} + 3 \, {\left(28 \, a - 37 \, b\right)} \cosh\left(f x + e\right)^{2} + 4 \, a - 6 \, b\right)} \sinh\left(f x + e\right)^{2} + 8 \, {\left(b \cosh\left(f x + e\right)^{7} + 6 \, {\left(2 \, a - 3 \, b\right)} \cosh\left(f x + e\right)^{5} + {\left(28 \, a - 37 \, b\right)} \cosh\left(f x + e\right)^{3} + 2 \, {\left(2 \, a - 3 \, b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{24 \, {\left(f \cosh\left(f x + e\right)^{7} + 7 \, f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{6} + f \sinh\left(f x + e\right)^{7} + 2 \, f \cosh\left(f x + e\right)^{5} + {\left(21 \, f \cosh\left(f x + e\right)^{2} + 2 \, f\right)} \sinh\left(f x + e\right)^{5} + 5 \, {\left(7 \, f \cosh\left(f x + e\right)^{3} + 2 \, f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{4} + f \cosh\left(f x + e\right)^{3} + {\left(35 \, f \cosh\left(f x + e\right)^{4} + 20 \, f \cosh\left(f x + e\right)^{2} + f\right)} \sinh\left(f x + e\right)^{3} + {\left(21 \, f \cosh\left(f x + e\right)^{5} + 20 \, f \cosh\left(f x + e\right)^{3} + 3 \, f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{2} + {\left(7 \, f \cosh\left(f x + e\right)^{6} + 10 \, f \cosh\left(f x + e\right)^{4} + 3 \, f \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)\right)}}, -\frac{12 \, {\left({\left(2 \, a - 5 \, b\right)} \cosh\left(f x + e\right)^{7} + 7 \, {\left(2 \, a - 5 \, b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{6} + {\left(2 \, a - 5 \, b\right)} \sinh\left(f x + e\right)^{7} + 2 \, {\left(2 \, a - 5 \, b\right)} \cosh\left(f x + e\right)^{5} + {\left(21 \, {\left(2 \, a - 5 \, b\right)} \cosh\left(f x + e\right)^{2} + 4 \, a - 10 \, b\right)} \sinh\left(f x + e\right)^{5} + 5 \, {\left(7 \, {\left(2 \, a - 5 \, b\right)} \cosh\left(f x + e\right)^{3} + 2 \, {\left(2 \, a - 5 \, b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{4} + {\left(2 \, a - 5 \, b\right)} \cosh\left(f x + e\right)^{3} + {\left(35 \, {\left(2 \, a - 5 \, b\right)} \cosh\left(f x + e\right)^{4} + 20 \, {\left(2 \, a - 5 \, b\right)} \cosh\left(f x + e\right)^{2} + 2 \, a - 5 \, b\right)} \sinh\left(f x + e\right)^{3} + {\left(21 \, {\left(2 \, a - 5 \, b\right)} \cosh\left(f x + e\right)^{5} + 20 \, {\left(2 \, a - 5 \, b\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(2 \, a - 5 \, b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{2} + {\left(7 \, {\left(2 \, a - 5 \, b\right)} \cosh\left(f x + e\right)^{6} + 10 \, {\left(2 \, a - 5 \, b\right)} \cosh\left(f x + e\right)^{4} + 3 \, {\left(2 \, a - 5 \, b\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)\right)} \sqrt{-a + b} \arctan\left(-\frac{\sqrt{2} \sqrt{-a + b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{2 \, {\left({\left(a - b\right)} \cosh\left(f x + e\right) + {\left(a - b\right)} \sinh\left(f x + e\right)\right)}}\right) - \sqrt{2} {\left(b \cosh\left(f x + e\right)^{8} + 8 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + b \sinh\left(f x + e\right)^{8} + 8 \, {\left(2 \, a - 3 \, b\right)} \cosh\left(f x + e\right)^{6} + 4 \, {\left(7 \, b \cosh\left(f x + e\right)^{2} + 4 \, a - 6 \, b\right)} \sinh\left(f x + e\right)^{6} + 8 \, {\left(7 \, b \cosh\left(f x + e\right)^{3} + 6 \, {\left(2 \, a - 3 \, b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(28 \, a - 37 \, b\right)} \cosh\left(f x + e\right)^{4} + 2 \, {\left(35 \, b \cosh\left(f x + e\right)^{4} + 60 \, {\left(2 \, a - 3 \, b\right)} \cosh\left(f x + e\right)^{2} + 28 \, a - 37 \, b\right)} \sinh\left(f x + e\right)^{4} + 8 \, {\left(7 \, b \cosh\left(f x + e\right)^{5} + 20 \, {\left(2 \, a - 3 \, b\right)} \cosh\left(f x + e\right)^{3} + {\left(28 \, a - 37 \, b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 8 \, {\left(2 \, a - 3 \, b\right)} \cosh\left(f x + e\right)^{2} + 4 \, {\left(7 \, b \cosh\left(f x + e\right)^{6} + 30 \, {\left(2 \, a - 3 \, b\right)} \cosh\left(f x + e\right)^{4} + 3 \, {\left(28 \, a - 37 \, b\right)} \cosh\left(f x + e\right)^{2} + 4 \, a - 6 \, b\right)} \sinh\left(f x + e\right)^{2} + 8 \, {\left(b \cosh\left(f x + e\right)^{7} + 6 \, {\left(2 \, a - 3 \, b\right)} \cosh\left(f x + e\right)^{5} + {\left(28 \, a - 37 \, b\right)} \cosh\left(f x + e\right)^{3} + 2 \, {\left(2 \, a - 3 \, b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{24 \, {\left(f \cosh\left(f x + e\right)^{7} + 7 \, f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{6} + f \sinh\left(f x + e\right)^{7} + 2 \, f \cosh\left(f x + e\right)^{5} + {\left(21 \, f \cosh\left(f x + e\right)^{2} + 2 \, f\right)} \sinh\left(f x + e\right)^{5} + 5 \, {\left(7 \, f \cosh\left(f x + e\right)^{3} + 2 \, f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{4} + f \cosh\left(f x + e\right)^{3} + {\left(35 \, f \cosh\left(f x + e\right)^{4} + 20 \, f \cosh\left(f x + e\right)^{2} + f\right)} \sinh\left(f x + e\right)^{3} + {\left(21 \, f \cosh\left(f x + e\right)^{5} + 20 \, f \cosh\left(f x + e\right)^{3} + 3 \, f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{2} + {\left(7 \, f \cosh\left(f x + e\right)^{6} + 10 \, f \cosh\left(f x + e\right)^{4} + 3 \, f \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)\right)}}\right]"," ",0,"[-1/24*(6*((2*a - 5*b)*cosh(f*x + e)^7 + 7*(2*a - 5*b)*cosh(f*x + e)*sinh(f*x + e)^6 + (2*a - 5*b)*sinh(f*x + e)^7 + 2*(2*a - 5*b)*cosh(f*x + e)^5 + (21*(2*a - 5*b)*cosh(f*x + e)^2 + 4*a - 10*b)*sinh(f*x + e)^5 + 5*(7*(2*a - 5*b)*cosh(f*x + e)^3 + 2*(2*a - 5*b)*cosh(f*x + e))*sinh(f*x + e)^4 + (2*a - 5*b)*cosh(f*x + e)^3 + (35*(2*a - 5*b)*cosh(f*x + e)^4 + 20*(2*a - 5*b)*cosh(f*x + e)^2 + 2*a - 5*b)*sinh(f*x + e)^3 + (21*(2*a - 5*b)*cosh(f*x + e)^5 + 20*(2*a - 5*b)*cosh(f*x + e)^3 + 3*(2*a - 5*b)*cosh(f*x + e))*sinh(f*x + e)^2 + (7*(2*a - 5*b)*cosh(f*x + e)^6 + 10*(2*a - 5*b)*cosh(f*x + e)^4 + 3*(2*a - 5*b)*cosh(f*x + e)^2)*sinh(f*x + e))*sqrt(a - b)*log((b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(4*a - 3*b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 4*a - 3*b)*sinh(f*x + e)^2 + 4*sqrt(2)*sqrt(a - b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))*(cosh(f*x + e) + sinh(f*x + e)) + 4*(b*cosh(f*x + e)^3 + (4*a - 3*b)*cosh(f*x + e))*sinh(f*x + e) + b)/(cosh(f*x + e)^4 + 4*cosh(f*x + e)*sinh(f*x + e)^3 + sinh(f*x + e)^4 + 2*(3*cosh(f*x + e)^2 + 1)*sinh(f*x + e)^2 + 2*cosh(f*x + e)^2 + 4*(cosh(f*x + e)^3 + cosh(f*x + e))*sinh(f*x + e) + 1)) - sqrt(2)*(b*cosh(f*x + e)^8 + 8*b*cosh(f*x + e)*sinh(f*x + e)^7 + b*sinh(f*x + e)^8 + 8*(2*a - 3*b)*cosh(f*x + e)^6 + 4*(7*b*cosh(f*x + e)^2 + 4*a - 6*b)*sinh(f*x + e)^6 + 8*(7*b*cosh(f*x + e)^3 + 6*(2*a - 3*b)*cosh(f*x + e))*sinh(f*x + e)^5 + 2*(28*a - 37*b)*cosh(f*x + e)^4 + 2*(35*b*cosh(f*x + e)^4 + 60*(2*a - 3*b)*cosh(f*x + e)^2 + 28*a - 37*b)*sinh(f*x + e)^4 + 8*(7*b*cosh(f*x + e)^5 + 20*(2*a - 3*b)*cosh(f*x + e)^3 + (28*a - 37*b)*cosh(f*x + e))*sinh(f*x + e)^3 + 8*(2*a - 3*b)*cosh(f*x + e)^2 + 4*(7*b*cosh(f*x + e)^6 + 30*(2*a - 3*b)*cosh(f*x + e)^4 + 3*(28*a - 37*b)*cosh(f*x + e)^2 + 4*a - 6*b)*sinh(f*x + e)^2 + 8*(b*cosh(f*x + e)^7 + 6*(2*a - 3*b)*cosh(f*x + e)^5 + (28*a - 37*b)*cosh(f*x + e)^3 + 2*(2*a - 3*b)*cosh(f*x + e))*sinh(f*x + e) + b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/(f*cosh(f*x + e)^7 + 7*f*cosh(f*x + e)*sinh(f*x + e)^6 + f*sinh(f*x + e)^7 + 2*f*cosh(f*x + e)^5 + (21*f*cosh(f*x + e)^2 + 2*f)*sinh(f*x + e)^5 + 5*(7*f*cosh(f*x + e)^3 + 2*f*cosh(f*x + e))*sinh(f*x + e)^4 + f*cosh(f*x + e)^3 + (35*f*cosh(f*x + e)^4 + 20*f*cosh(f*x + e)^2 + f)*sinh(f*x + e)^3 + (21*f*cosh(f*x + e)^5 + 20*f*cosh(f*x + e)^3 + 3*f*cosh(f*x + e))*sinh(f*x + e)^2 + (7*f*cosh(f*x + e)^6 + 10*f*cosh(f*x + e)^4 + 3*f*cosh(f*x + e)^2)*sinh(f*x + e)), -1/24*(12*((2*a - 5*b)*cosh(f*x + e)^7 + 7*(2*a - 5*b)*cosh(f*x + e)*sinh(f*x + e)^6 + (2*a - 5*b)*sinh(f*x + e)^7 + 2*(2*a - 5*b)*cosh(f*x + e)^5 + (21*(2*a - 5*b)*cosh(f*x + e)^2 + 4*a - 10*b)*sinh(f*x + e)^5 + 5*(7*(2*a - 5*b)*cosh(f*x + e)^3 + 2*(2*a - 5*b)*cosh(f*x + e))*sinh(f*x + e)^4 + (2*a - 5*b)*cosh(f*x + e)^3 + (35*(2*a - 5*b)*cosh(f*x + e)^4 + 20*(2*a - 5*b)*cosh(f*x + e)^2 + 2*a - 5*b)*sinh(f*x + e)^3 + (21*(2*a - 5*b)*cosh(f*x + e)^5 + 20*(2*a - 5*b)*cosh(f*x + e)^3 + 3*(2*a - 5*b)*cosh(f*x + e))*sinh(f*x + e)^2 + (7*(2*a - 5*b)*cosh(f*x + e)^6 + 10*(2*a - 5*b)*cosh(f*x + e)^4 + 3*(2*a - 5*b)*cosh(f*x + e)^2)*sinh(f*x + e))*sqrt(-a + b)*arctan(-1/2*sqrt(2)*sqrt(-a + b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/((a - b)*cosh(f*x + e) + (a - b)*sinh(f*x + e))) - sqrt(2)*(b*cosh(f*x + e)^8 + 8*b*cosh(f*x + e)*sinh(f*x + e)^7 + b*sinh(f*x + e)^8 + 8*(2*a - 3*b)*cosh(f*x + e)^6 + 4*(7*b*cosh(f*x + e)^2 + 4*a - 6*b)*sinh(f*x + e)^6 + 8*(7*b*cosh(f*x + e)^3 + 6*(2*a - 3*b)*cosh(f*x + e))*sinh(f*x + e)^5 + 2*(28*a - 37*b)*cosh(f*x + e)^4 + 2*(35*b*cosh(f*x + e)^4 + 60*(2*a - 3*b)*cosh(f*x + e)^2 + 28*a - 37*b)*sinh(f*x + e)^4 + 8*(7*b*cosh(f*x + e)^5 + 20*(2*a - 3*b)*cosh(f*x + e)^3 + (28*a - 37*b)*cosh(f*x + e))*sinh(f*x + e)^3 + 8*(2*a - 3*b)*cosh(f*x + e)^2 + 4*(7*b*cosh(f*x + e)^6 + 30*(2*a - 3*b)*cosh(f*x + e)^4 + 3*(28*a - 37*b)*cosh(f*x + e)^2 + 4*a - 6*b)*sinh(f*x + e)^2 + 8*(b*cosh(f*x + e)^7 + 6*(2*a - 3*b)*cosh(f*x + e)^5 + (28*a - 37*b)*cosh(f*x + e)^3 + 2*(2*a - 3*b)*cosh(f*x + e))*sinh(f*x + e) + b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/(f*cosh(f*x + e)^7 + 7*f*cosh(f*x + e)*sinh(f*x + e)^6 + f*sinh(f*x + e)^7 + 2*f*cosh(f*x + e)^5 + (21*f*cosh(f*x + e)^2 + 2*f)*sinh(f*x + e)^5 + 5*(7*f*cosh(f*x + e)^3 + 2*f*cosh(f*x + e))*sinh(f*x + e)^4 + f*cosh(f*x + e)^3 + (35*f*cosh(f*x + e)^4 + 20*f*cosh(f*x + e)^2 + f)*sinh(f*x + e)^3 + (21*f*cosh(f*x + e)^5 + 20*f*cosh(f*x + e)^3 + 3*f*cosh(f*x + e))*sinh(f*x + e)^2 + (7*f*cosh(f*x + e)^6 + 10*f*cosh(f*x + e)^4 + 3*f*cosh(f*x + e)^2)*sinh(f*x + e))]","B",0
470,1,1052,0,1.109275," ","integrate((a+b*sinh(f*x+e)^2)^(3/2)*tanh(f*x+e),x, algorithm=""fricas"")","\left[-\frac{12 \, {\left({\left(a - b\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(a - b\right)} \cosh\left(f x + e\right)^{2} \sinh\left(f x + e\right) + 3 \, {\left(a - b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{2} + {\left(a - b\right)} \sinh\left(f x + e\right)^{3}\right)} \sqrt{a - b} \log\left(\frac{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(4 \, a - 3 \, b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + 4 \, a - 3 \, b\right)} \sinh\left(f x + e\right)^{2} + 4 \, \sqrt{2} \sqrt{a - b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} {\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right)\right)} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(4 \, a - 3 \, b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}{\cosh\left(f x + e\right)^{4} + 4 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + \sinh\left(f x + e\right)^{4} + 2 \, {\left(3 \, \cosh\left(f x + e\right)^{2} + 1\right)} \sinh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right)^{2} + 4 \, {\left(\cosh\left(f x + e\right)^{3} + \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + 1}\right) - \sqrt{2} {\left(b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(8 \, a - 7 \, b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + 8 \, a - 7 \, b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(8 \, a - 7 \, b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{24 \, {\left(f \cosh\left(f x + e\right)^{3} + 3 \, f \cosh\left(f x + e\right)^{2} \sinh\left(f x + e\right) + 3 \, f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{2} + f \sinh\left(f x + e\right)^{3}\right)}}, -\frac{24 \, {\left({\left(a - b\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(a - b\right)} \cosh\left(f x + e\right)^{2} \sinh\left(f x + e\right) + 3 \, {\left(a - b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{2} + {\left(a - b\right)} \sinh\left(f x + e\right)^{3}\right)} \sqrt{-a + b} \arctan\left(-\frac{\sqrt{2} \sqrt{-a + b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{2 \, {\left({\left(a - b\right)} \cosh\left(f x + e\right) + {\left(a - b\right)} \sinh\left(f x + e\right)\right)}}\right) - \sqrt{2} {\left(b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(8 \, a - 7 \, b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + 8 \, a - 7 \, b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(8 \, a - 7 \, b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{24 \, {\left(f \cosh\left(f x + e\right)^{3} + 3 \, f \cosh\left(f x + e\right)^{2} \sinh\left(f x + e\right) + 3 \, f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{2} + f \sinh\left(f x + e\right)^{3}\right)}}\right]"," ",0,"[-1/24*(12*((a - b)*cosh(f*x + e)^3 + 3*(a - b)*cosh(f*x + e)^2*sinh(f*x + e) + 3*(a - b)*cosh(f*x + e)*sinh(f*x + e)^2 + (a - b)*sinh(f*x + e)^3)*sqrt(a - b)*log((b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(4*a - 3*b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 4*a - 3*b)*sinh(f*x + e)^2 + 4*sqrt(2)*sqrt(a - b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))*(cosh(f*x + e) + sinh(f*x + e)) + 4*(b*cosh(f*x + e)^3 + (4*a - 3*b)*cosh(f*x + e))*sinh(f*x + e) + b)/(cosh(f*x + e)^4 + 4*cosh(f*x + e)*sinh(f*x + e)^3 + sinh(f*x + e)^4 + 2*(3*cosh(f*x + e)^2 + 1)*sinh(f*x + e)^2 + 2*cosh(f*x + e)^2 + 4*(cosh(f*x + e)^3 + cosh(f*x + e))*sinh(f*x + e) + 1)) - sqrt(2)*(b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(8*a - 7*b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 8*a - 7*b)*sinh(f*x + e)^2 + 4*(b*cosh(f*x + e)^3 + (8*a - 7*b)*cosh(f*x + e))*sinh(f*x + e) + b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/(f*cosh(f*x + e)^3 + 3*f*cosh(f*x + e)^2*sinh(f*x + e) + 3*f*cosh(f*x + e)*sinh(f*x + e)^2 + f*sinh(f*x + e)^3), -1/24*(24*((a - b)*cosh(f*x + e)^3 + 3*(a - b)*cosh(f*x + e)^2*sinh(f*x + e) + 3*(a - b)*cosh(f*x + e)*sinh(f*x + e)^2 + (a - b)*sinh(f*x + e)^3)*sqrt(-a + b)*arctan(-1/2*sqrt(2)*sqrt(-a + b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/((a - b)*cosh(f*x + e) + (a - b)*sinh(f*x + e))) - sqrt(2)*(b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(8*a - 7*b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 8*a - 7*b)*sinh(f*x + e)^2 + 4*(b*cosh(f*x + e)^3 + (8*a - 7*b)*cosh(f*x + e))*sinh(f*x + e) + b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/(f*cosh(f*x + e)^3 + 3*f*cosh(f*x + e)^2*sinh(f*x + e) + 3*f*cosh(f*x + e)*sinh(f*x + e)^2 + f*sinh(f*x + e)^3)]","B",0
471,1,1000,0,0.748361," ","integrate(coth(f*x+e)*(a+b*sinh(f*x+e)^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{12 \, {\left(a \cosh\left(f x + e\right)^{3} + 3 \, a \cosh\left(f x + e\right)^{2} \sinh\left(f x + e\right) + 3 \, a \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{2} + a \sinh\left(f x + e\right)^{3}\right)} \sqrt{a} \log\left(\frac{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(4 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + 4 \, a - b\right)} \sinh\left(f x + e\right)^{2} - 4 \, \sqrt{2} \sqrt{a} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} {\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right)\right)} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(4 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}{\cosh\left(f x + e\right)^{4} + 4 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + \sinh\left(f x + e\right)^{4} + 2 \, {\left(3 \, \cosh\left(f x + e\right)^{2} - 1\right)} \sinh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right)^{2} + 4 \, {\left(\cosh\left(f x + e\right)^{3} - \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + 1}\right) + \sqrt{2} {\left(b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(8 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + 8 \, a - b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(8 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{24 \, {\left(f \cosh\left(f x + e\right)^{3} + 3 \, f \cosh\left(f x + e\right)^{2} \sinh\left(f x + e\right) + 3 \, f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{2} + f \sinh\left(f x + e\right)^{3}\right)}}, \frac{24 \, {\left(a \cosh\left(f x + e\right)^{3} + 3 \, a \cosh\left(f x + e\right)^{2} \sinh\left(f x + e\right) + 3 \, a \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{2} + a \sinh\left(f x + e\right)^{3}\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{2} \sqrt{-a} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{2 \, {\left(a \cosh\left(f x + e\right) + a \sinh\left(f x + e\right)\right)}}\right) + \sqrt{2} {\left(b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(8 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + 8 \, a - b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(8 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{24 \, {\left(f \cosh\left(f x + e\right)^{3} + 3 \, f \cosh\left(f x + e\right)^{2} \sinh\left(f x + e\right) + 3 \, f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{2} + f \sinh\left(f x + e\right)^{3}\right)}}\right]"," ",0,"[1/24*(12*(a*cosh(f*x + e)^3 + 3*a*cosh(f*x + e)^2*sinh(f*x + e) + 3*a*cosh(f*x + e)*sinh(f*x + e)^2 + a*sinh(f*x + e)^3)*sqrt(a)*log((b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(4*a - b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 4*a - b)*sinh(f*x + e)^2 - 4*sqrt(2)*sqrt(a)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))*(cosh(f*x + e) + sinh(f*x + e)) + 4*(b*cosh(f*x + e)^3 + (4*a - b)*cosh(f*x + e))*sinh(f*x + e) + b)/(cosh(f*x + e)^4 + 4*cosh(f*x + e)*sinh(f*x + e)^3 + sinh(f*x + e)^4 + 2*(3*cosh(f*x + e)^2 - 1)*sinh(f*x + e)^2 - 2*cosh(f*x + e)^2 + 4*(cosh(f*x + e)^3 - cosh(f*x + e))*sinh(f*x + e) + 1)) + sqrt(2)*(b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(8*a - b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 8*a - b)*sinh(f*x + e)^2 + 4*(b*cosh(f*x + e)^3 + (8*a - b)*cosh(f*x + e))*sinh(f*x + e) + b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/(f*cosh(f*x + e)^3 + 3*f*cosh(f*x + e)^2*sinh(f*x + e) + 3*f*cosh(f*x + e)*sinh(f*x + e)^2 + f*sinh(f*x + e)^3), 1/24*(24*(a*cosh(f*x + e)^3 + 3*a*cosh(f*x + e)^2*sinh(f*x + e) + 3*a*cosh(f*x + e)*sinh(f*x + e)^2 + a*sinh(f*x + e)^3)*sqrt(-a)*arctan(1/2*sqrt(2)*sqrt(-a)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/(a*cosh(f*x + e) + a*sinh(f*x + e))) + sqrt(2)*(b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(8*a - b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 8*a - b)*sinh(f*x + e)^2 + 4*(b*cosh(f*x + e)^3 + (8*a - b)*cosh(f*x + e))*sinh(f*x + e) + b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/(f*cosh(f*x + e)^3 + 3*f*cosh(f*x + e)^2*sinh(f*x + e) + 3*f*cosh(f*x + e)*sinh(f*x + e)^2 + f*sinh(f*x + e)^3)]","B",0
472,1,2406,0,1.020819," ","integrate(coth(f*x+e)^3*(a+b*sinh(f*x+e)^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{6 \, {\left({\left(2 \, a + 3 \, b\right)} \cosh\left(f x + e\right)^{7} + 7 \, {\left(2 \, a + 3 \, b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{6} + {\left(2 \, a + 3 \, b\right)} \sinh\left(f x + e\right)^{7} - 2 \, {\left(2 \, a + 3 \, b\right)} \cosh\left(f x + e\right)^{5} + {\left(21 \, {\left(2 \, a + 3 \, b\right)} \cosh\left(f x + e\right)^{2} - 4 \, a - 6 \, b\right)} \sinh\left(f x + e\right)^{5} + 5 \, {\left(7 \, {\left(2 \, a + 3 \, b\right)} \cosh\left(f x + e\right)^{3} - 2 \, {\left(2 \, a + 3 \, b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{4} + {\left(2 \, a + 3 \, b\right)} \cosh\left(f x + e\right)^{3} + {\left(35 \, {\left(2 \, a + 3 \, b\right)} \cosh\left(f x + e\right)^{4} - 20 \, {\left(2 \, a + 3 \, b\right)} \cosh\left(f x + e\right)^{2} + 2 \, a + 3 \, b\right)} \sinh\left(f x + e\right)^{3} + {\left(21 \, {\left(2 \, a + 3 \, b\right)} \cosh\left(f x + e\right)^{5} - 20 \, {\left(2 \, a + 3 \, b\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(2 \, a + 3 \, b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{2} + {\left(7 \, {\left(2 \, a + 3 \, b\right)} \cosh\left(f x + e\right)^{6} - 10 \, {\left(2 \, a + 3 \, b\right)} \cosh\left(f x + e\right)^{4} + 3 \, {\left(2 \, a + 3 \, b\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)\right)} \sqrt{a} \log\left(\frac{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(4 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + 4 \, a - b\right)} \sinh\left(f x + e\right)^{2} - 4 \, \sqrt{2} \sqrt{a} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} {\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right)\right)} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(4 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}{\cosh\left(f x + e\right)^{4} + 4 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + \sinh\left(f x + e\right)^{4} + 2 \, {\left(3 \, \cosh\left(f x + e\right)^{2} - 1\right)} \sinh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right)^{2} + 4 \, {\left(\cosh\left(f x + e\right)^{3} - \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + 1}\right) + \sqrt{2} {\left(b \cosh\left(f x + e\right)^{8} + 8 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + b \sinh\left(f x + e\right)^{8} + 8 \, {\left(2 \, a + b\right)} \cosh\left(f x + e\right)^{6} + 4 \, {\left(7 \, b \cosh\left(f x + e\right)^{2} + 4 \, a + 2 \, b\right)} \sinh\left(f x + e\right)^{6} + 8 \, {\left(7 \, b \cosh\left(f x + e\right)^{3} + 6 \, {\left(2 \, a + b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} - 2 \, {\left(28 \, a + 9 \, b\right)} \cosh\left(f x + e\right)^{4} + 2 \, {\left(35 \, b \cosh\left(f x + e\right)^{4} + 60 \, {\left(2 \, a + b\right)} \cosh\left(f x + e\right)^{2} - 28 \, a - 9 \, b\right)} \sinh\left(f x + e\right)^{4} + 8 \, {\left(7 \, b \cosh\left(f x + e\right)^{5} + 20 \, {\left(2 \, a + b\right)} \cosh\left(f x + e\right)^{3} - {\left(28 \, a + 9 \, b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 8 \, {\left(2 \, a + b\right)} \cosh\left(f x + e\right)^{2} + 4 \, {\left(7 \, b \cosh\left(f x + e\right)^{6} + 30 \, {\left(2 \, a + b\right)} \cosh\left(f x + e\right)^{4} - 3 \, {\left(28 \, a + 9 \, b\right)} \cosh\left(f x + e\right)^{2} + 4 \, a + 2 \, b\right)} \sinh\left(f x + e\right)^{2} + 8 \, {\left(b \cosh\left(f x + e\right)^{7} + 6 \, {\left(2 \, a + b\right)} \cosh\left(f x + e\right)^{5} - {\left(28 \, a + 9 \, b\right)} \cosh\left(f x + e\right)^{3} + 2 \, {\left(2 \, a + b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{24 \, {\left(f \cosh\left(f x + e\right)^{7} + 7 \, f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{6} + f \sinh\left(f x + e\right)^{7} - 2 \, f \cosh\left(f x + e\right)^{5} + {\left(21 \, f \cosh\left(f x + e\right)^{2} - 2 \, f\right)} \sinh\left(f x + e\right)^{5} + 5 \, {\left(7 \, f \cosh\left(f x + e\right)^{3} - 2 \, f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{4} + f \cosh\left(f x + e\right)^{3} + {\left(35 \, f \cosh\left(f x + e\right)^{4} - 20 \, f \cosh\left(f x + e\right)^{2} + f\right)} \sinh\left(f x + e\right)^{3} + {\left(21 \, f \cosh\left(f x + e\right)^{5} - 20 \, f \cosh\left(f x + e\right)^{3} + 3 \, f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{2} + {\left(7 \, f \cosh\left(f x + e\right)^{6} - 10 \, f \cosh\left(f x + e\right)^{4} + 3 \, f \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)\right)}}, \frac{12 \, {\left({\left(2 \, a + 3 \, b\right)} \cosh\left(f x + e\right)^{7} + 7 \, {\left(2 \, a + 3 \, b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{6} + {\left(2 \, a + 3 \, b\right)} \sinh\left(f x + e\right)^{7} - 2 \, {\left(2 \, a + 3 \, b\right)} \cosh\left(f x + e\right)^{5} + {\left(21 \, {\left(2 \, a + 3 \, b\right)} \cosh\left(f x + e\right)^{2} - 4 \, a - 6 \, b\right)} \sinh\left(f x + e\right)^{5} + 5 \, {\left(7 \, {\left(2 \, a + 3 \, b\right)} \cosh\left(f x + e\right)^{3} - 2 \, {\left(2 \, a + 3 \, b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{4} + {\left(2 \, a + 3 \, b\right)} \cosh\left(f x + e\right)^{3} + {\left(35 \, {\left(2 \, a + 3 \, b\right)} \cosh\left(f x + e\right)^{4} - 20 \, {\left(2 \, a + 3 \, b\right)} \cosh\left(f x + e\right)^{2} + 2 \, a + 3 \, b\right)} \sinh\left(f x + e\right)^{3} + {\left(21 \, {\left(2 \, a + 3 \, b\right)} \cosh\left(f x + e\right)^{5} - 20 \, {\left(2 \, a + 3 \, b\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(2 \, a + 3 \, b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{2} + {\left(7 \, {\left(2 \, a + 3 \, b\right)} \cosh\left(f x + e\right)^{6} - 10 \, {\left(2 \, a + 3 \, b\right)} \cosh\left(f x + e\right)^{4} + 3 \, {\left(2 \, a + 3 \, b\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{2} \sqrt{-a} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{2 \, {\left(a \cosh\left(f x + e\right) + a \sinh\left(f x + e\right)\right)}}\right) + \sqrt{2} {\left(b \cosh\left(f x + e\right)^{8} + 8 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + b \sinh\left(f x + e\right)^{8} + 8 \, {\left(2 \, a + b\right)} \cosh\left(f x + e\right)^{6} + 4 \, {\left(7 \, b \cosh\left(f x + e\right)^{2} + 4 \, a + 2 \, b\right)} \sinh\left(f x + e\right)^{6} + 8 \, {\left(7 \, b \cosh\left(f x + e\right)^{3} + 6 \, {\left(2 \, a + b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} - 2 \, {\left(28 \, a + 9 \, b\right)} \cosh\left(f x + e\right)^{4} + 2 \, {\left(35 \, b \cosh\left(f x + e\right)^{4} + 60 \, {\left(2 \, a + b\right)} \cosh\left(f x + e\right)^{2} - 28 \, a - 9 \, b\right)} \sinh\left(f x + e\right)^{4} + 8 \, {\left(7 \, b \cosh\left(f x + e\right)^{5} + 20 \, {\left(2 \, a + b\right)} \cosh\left(f x + e\right)^{3} - {\left(28 \, a + 9 \, b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 8 \, {\left(2 \, a + b\right)} \cosh\left(f x + e\right)^{2} + 4 \, {\left(7 \, b \cosh\left(f x + e\right)^{6} + 30 \, {\left(2 \, a + b\right)} \cosh\left(f x + e\right)^{4} - 3 \, {\left(28 \, a + 9 \, b\right)} \cosh\left(f x + e\right)^{2} + 4 \, a + 2 \, b\right)} \sinh\left(f x + e\right)^{2} + 8 \, {\left(b \cosh\left(f x + e\right)^{7} + 6 \, {\left(2 \, a + b\right)} \cosh\left(f x + e\right)^{5} - {\left(28 \, a + 9 \, b\right)} \cosh\left(f x + e\right)^{3} + 2 \, {\left(2 \, a + b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{24 \, {\left(f \cosh\left(f x + e\right)^{7} + 7 \, f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{6} + f \sinh\left(f x + e\right)^{7} - 2 \, f \cosh\left(f x + e\right)^{5} + {\left(21 \, f \cosh\left(f x + e\right)^{2} - 2 \, f\right)} \sinh\left(f x + e\right)^{5} + 5 \, {\left(7 \, f \cosh\left(f x + e\right)^{3} - 2 \, f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{4} + f \cosh\left(f x + e\right)^{3} + {\left(35 \, f \cosh\left(f x + e\right)^{4} - 20 \, f \cosh\left(f x + e\right)^{2} + f\right)} \sinh\left(f x + e\right)^{3} + {\left(21 \, f \cosh\left(f x + e\right)^{5} - 20 \, f \cosh\left(f x + e\right)^{3} + 3 \, f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{2} + {\left(7 \, f \cosh\left(f x + e\right)^{6} - 10 \, f \cosh\left(f x + e\right)^{4} + 3 \, f \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)\right)}}\right]"," ",0,"[1/24*(6*((2*a + 3*b)*cosh(f*x + e)^7 + 7*(2*a + 3*b)*cosh(f*x + e)*sinh(f*x + e)^6 + (2*a + 3*b)*sinh(f*x + e)^7 - 2*(2*a + 3*b)*cosh(f*x + e)^5 + (21*(2*a + 3*b)*cosh(f*x + e)^2 - 4*a - 6*b)*sinh(f*x + e)^5 + 5*(7*(2*a + 3*b)*cosh(f*x + e)^3 - 2*(2*a + 3*b)*cosh(f*x + e))*sinh(f*x + e)^4 + (2*a + 3*b)*cosh(f*x + e)^3 + (35*(2*a + 3*b)*cosh(f*x + e)^4 - 20*(2*a + 3*b)*cosh(f*x + e)^2 + 2*a + 3*b)*sinh(f*x + e)^3 + (21*(2*a + 3*b)*cosh(f*x + e)^5 - 20*(2*a + 3*b)*cosh(f*x + e)^3 + 3*(2*a + 3*b)*cosh(f*x + e))*sinh(f*x + e)^2 + (7*(2*a + 3*b)*cosh(f*x + e)^6 - 10*(2*a + 3*b)*cosh(f*x + e)^4 + 3*(2*a + 3*b)*cosh(f*x + e)^2)*sinh(f*x + e))*sqrt(a)*log((b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(4*a - b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 4*a - b)*sinh(f*x + e)^2 - 4*sqrt(2)*sqrt(a)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))*(cosh(f*x + e) + sinh(f*x + e)) + 4*(b*cosh(f*x + e)^3 + (4*a - b)*cosh(f*x + e))*sinh(f*x + e) + b)/(cosh(f*x + e)^4 + 4*cosh(f*x + e)*sinh(f*x + e)^3 + sinh(f*x + e)^4 + 2*(3*cosh(f*x + e)^2 - 1)*sinh(f*x + e)^2 - 2*cosh(f*x + e)^2 + 4*(cosh(f*x + e)^3 - cosh(f*x + e))*sinh(f*x + e) + 1)) + sqrt(2)*(b*cosh(f*x + e)^8 + 8*b*cosh(f*x + e)*sinh(f*x + e)^7 + b*sinh(f*x + e)^8 + 8*(2*a + b)*cosh(f*x + e)^6 + 4*(7*b*cosh(f*x + e)^2 + 4*a + 2*b)*sinh(f*x + e)^6 + 8*(7*b*cosh(f*x + e)^3 + 6*(2*a + b)*cosh(f*x + e))*sinh(f*x + e)^5 - 2*(28*a + 9*b)*cosh(f*x + e)^4 + 2*(35*b*cosh(f*x + e)^4 + 60*(2*a + b)*cosh(f*x + e)^2 - 28*a - 9*b)*sinh(f*x + e)^4 + 8*(7*b*cosh(f*x + e)^5 + 20*(2*a + b)*cosh(f*x + e)^3 - (28*a + 9*b)*cosh(f*x + e))*sinh(f*x + e)^3 + 8*(2*a + b)*cosh(f*x + e)^2 + 4*(7*b*cosh(f*x + e)^6 + 30*(2*a + b)*cosh(f*x + e)^4 - 3*(28*a + 9*b)*cosh(f*x + e)^2 + 4*a + 2*b)*sinh(f*x + e)^2 + 8*(b*cosh(f*x + e)^7 + 6*(2*a + b)*cosh(f*x + e)^5 - (28*a + 9*b)*cosh(f*x + e)^3 + 2*(2*a + b)*cosh(f*x + e))*sinh(f*x + e) + b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/(f*cosh(f*x + e)^7 + 7*f*cosh(f*x + e)*sinh(f*x + e)^6 + f*sinh(f*x + e)^7 - 2*f*cosh(f*x + e)^5 + (21*f*cosh(f*x + e)^2 - 2*f)*sinh(f*x + e)^5 + 5*(7*f*cosh(f*x + e)^3 - 2*f*cosh(f*x + e))*sinh(f*x + e)^4 + f*cosh(f*x + e)^3 + (35*f*cosh(f*x + e)^4 - 20*f*cosh(f*x + e)^2 + f)*sinh(f*x + e)^3 + (21*f*cosh(f*x + e)^5 - 20*f*cosh(f*x + e)^3 + 3*f*cosh(f*x + e))*sinh(f*x + e)^2 + (7*f*cosh(f*x + e)^6 - 10*f*cosh(f*x + e)^4 + 3*f*cosh(f*x + e)^2)*sinh(f*x + e)), 1/24*(12*((2*a + 3*b)*cosh(f*x + e)^7 + 7*(2*a + 3*b)*cosh(f*x + e)*sinh(f*x + e)^6 + (2*a + 3*b)*sinh(f*x + e)^7 - 2*(2*a + 3*b)*cosh(f*x + e)^5 + (21*(2*a + 3*b)*cosh(f*x + e)^2 - 4*a - 6*b)*sinh(f*x + e)^5 + 5*(7*(2*a + 3*b)*cosh(f*x + e)^3 - 2*(2*a + 3*b)*cosh(f*x + e))*sinh(f*x + e)^4 + (2*a + 3*b)*cosh(f*x + e)^3 + (35*(2*a + 3*b)*cosh(f*x + e)^4 - 20*(2*a + 3*b)*cosh(f*x + e)^2 + 2*a + 3*b)*sinh(f*x + e)^3 + (21*(2*a + 3*b)*cosh(f*x + e)^5 - 20*(2*a + 3*b)*cosh(f*x + e)^3 + 3*(2*a + 3*b)*cosh(f*x + e))*sinh(f*x + e)^2 + (7*(2*a + 3*b)*cosh(f*x + e)^6 - 10*(2*a + 3*b)*cosh(f*x + e)^4 + 3*(2*a + 3*b)*cosh(f*x + e)^2)*sinh(f*x + e))*sqrt(-a)*arctan(1/2*sqrt(2)*sqrt(-a)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/(a*cosh(f*x + e) + a*sinh(f*x + e))) + sqrt(2)*(b*cosh(f*x + e)^8 + 8*b*cosh(f*x + e)*sinh(f*x + e)^7 + b*sinh(f*x + e)^8 + 8*(2*a + b)*cosh(f*x + e)^6 + 4*(7*b*cosh(f*x + e)^2 + 4*a + 2*b)*sinh(f*x + e)^6 + 8*(7*b*cosh(f*x + e)^3 + 6*(2*a + b)*cosh(f*x + e))*sinh(f*x + e)^5 - 2*(28*a + 9*b)*cosh(f*x + e)^4 + 2*(35*b*cosh(f*x + e)^4 + 60*(2*a + b)*cosh(f*x + e)^2 - 28*a - 9*b)*sinh(f*x + e)^4 + 8*(7*b*cosh(f*x + e)^5 + 20*(2*a + b)*cosh(f*x + e)^3 - (28*a + 9*b)*cosh(f*x + e))*sinh(f*x + e)^3 + 8*(2*a + b)*cosh(f*x + e)^2 + 4*(7*b*cosh(f*x + e)^6 + 30*(2*a + b)*cosh(f*x + e)^4 - 3*(28*a + 9*b)*cosh(f*x + e)^2 + 4*a + 2*b)*sinh(f*x + e)^2 + 8*(b*cosh(f*x + e)^7 + 6*(2*a + b)*cosh(f*x + e)^5 - (28*a + 9*b)*cosh(f*x + e)^3 + 2*(2*a + b)*cosh(f*x + e))*sinh(f*x + e) + b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/(f*cosh(f*x + e)^7 + 7*f*cosh(f*x + e)*sinh(f*x + e)^6 + f*sinh(f*x + e)^7 - 2*f*cosh(f*x + e)^5 + (21*f*cosh(f*x + e)^2 - 2*f)*sinh(f*x + e)^5 + 5*(7*f*cosh(f*x + e)^3 - 2*f*cosh(f*x + e))*sinh(f*x + e)^4 + f*cosh(f*x + e)^3 + (35*f*cosh(f*x + e)^4 - 20*f*cosh(f*x + e)^2 + f)*sinh(f*x + e)^3 + (21*f*cosh(f*x + e)^5 - 20*f*cosh(f*x + e)^3 + 3*f*cosh(f*x + e))*sinh(f*x + e)^2 + (7*f*cosh(f*x + e)^6 - 10*f*cosh(f*x + e)^4 + 3*f*cosh(f*x + e)^2)*sinh(f*x + e))]","B",0
473,1,5509,0,1.207935," ","integrate(coth(f*x+e)^5*(a+b*sinh(f*x+e)^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(8 \, a^{2} + 24 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{11} + 11 \, {\left(8 \, a^{2} + 24 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{10} + {\left(8 \, a^{2} + 24 \, a b + 3 \, b^{2}\right)} \sinh\left(f x + e\right)^{11} - 4 \, {\left(8 \, a^{2} + 24 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{9} + {\left(55 \, {\left(8 \, a^{2} + 24 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} - 32 \, a^{2} - 96 \, a b - 12 \, b^{2}\right)} \sinh\left(f x + e\right)^{9} + 3 \, {\left(55 \, {\left(8 \, a^{2} + 24 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{3} - 12 \, {\left(8 \, a^{2} + 24 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{8} + 6 \, {\left(8 \, a^{2} + 24 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{7} + 6 \, {\left(55 \, {\left(8 \, a^{2} + 24 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{4} - 24 \, {\left(8 \, a^{2} + 24 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + 8 \, a^{2} + 24 \, a b + 3 \, b^{2}\right)} \sinh\left(f x + e\right)^{7} + 42 \, {\left(11 \, {\left(8 \, a^{2} + 24 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{5} - 8 \, {\left(8 \, a^{2} + 24 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{3} + {\left(8 \, a^{2} + 24 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{6} - 4 \, {\left(8 \, a^{2} + 24 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{5} + 2 \, {\left(231 \, {\left(8 \, a^{2} + 24 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{6} - 252 \, {\left(8 \, a^{2} + 24 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{4} + 63 \, {\left(8 \, a^{2} + 24 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} - 16 \, a^{2} - 48 \, a b - 6 \, b^{2}\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(165 \, {\left(8 \, a^{2} + 24 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{7} - 252 \, {\left(8 \, a^{2} + 24 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{5} + 105 \, {\left(8 \, a^{2} + 24 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{3} - 10 \, {\left(8 \, a^{2} + 24 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{4} + {\left(8 \, a^{2} + 24 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{3} + {\left(165 \, {\left(8 \, a^{2} + 24 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{8} - 336 \, {\left(8 \, a^{2} + 24 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{6} + 210 \, {\left(8 \, a^{2} + 24 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{4} - 40 \, {\left(8 \, a^{2} + 24 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + 8 \, a^{2} + 24 \, a b + 3 \, b^{2}\right)} \sinh\left(f x + e\right)^{3} + {\left(55 \, {\left(8 \, a^{2} + 24 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{9} - 144 \, {\left(8 \, a^{2} + 24 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{7} + 126 \, {\left(8 \, a^{2} + 24 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{5} - 40 \, {\left(8 \, a^{2} + 24 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(8 \, a^{2} + 24 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{2} + {\left(11 \, {\left(8 \, a^{2} + 24 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{10} - 36 \, {\left(8 \, a^{2} + 24 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{8} + 42 \, {\left(8 \, a^{2} + 24 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{6} - 20 \, {\left(8 \, a^{2} + 24 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{4} + 3 \, {\left(8 \, a^{2} + 24 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)\right)} \sqrt{a} \log\left(\frac{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(4 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + 4 \, a - b\right)} \sinh\left(f x + e\right)^{2} - 4 \, \sqrt{2} \sqrt{a} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} {\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right)\right)} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(4 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}{\cosh\left(f x + e\right)^{4} + 4 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + \sinh\left(f x + e\right)^{4} + 2 \, {\left(3 \, \cosh\left(f x + e\right)^{2} - 1\right)} \sinh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right)^{2} + 4 \, {\left(\cosh\left(f x + e\right)^{3} - \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + 1}\right) + 2 \, \sqrt{2} {\left(a b \cosh\left(f x + e\right)^{12} + 12 \, a b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{11} + a b \sinh\left(f x + e\right)^{12} + 2 \, {\left(8 \, a^{2} + 9 \, a b\right)} \cosh\left(f x + e\right)^{10} + 2 \, {\left(33 \, a b \cosh\left(f x + e\right)^{2} + 8 \, a^{2} + 9 \, a b\right)} \sinh\left(f x + e\right)^{10} + 20 \, {\left(11 \, a b \cosh\left(f x + e\right)^{3} + {\left(8 \, a^{2} + 9 \, a b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{9} - {\left(112 \, a^{2} + 111 \, a b\right)} \cosh\left(f x + e\right)^{8} + {\left(495 \, a b \cosh\left(f x + e\right)^{4} + 90 \, {\left(8 \, a^{2} + 9 \, a b\right)} \cosh\left(f x + e\right)^{2} - 112 \, a^{2} - 111 \, a b\right)} \sinh\left(f x + e\right)^{8} + 8 \, {\left(99 \, a b \cosh\left(f x + e\right)^{5} + 30 \, {\left(8 \, a^{2} + 9 \, a b\right)} \cosh\left(f x + e\right)^{3} - {\left(112 \, a^{2} + 111 \, a b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{7} + 8 \, {\left(18 \, a^{2} + 23 \, a b\right)} \cosh\left(f x + e\right)^{6} + 4 \, {\left(231 \, a b \cosh\left(f x + e\right)^{6} + 105 \, {\left(8 \, a^{2} + 9 \, a b\right)} \cosh\left(f x + e\right)^{4} - 7 \, {\left(112 \, a^{2} + 111 \, a b\right)} \cosh\left(f x + e\right)^{2} + 36 \, a^{2} + 46 \, a b\right)} \sinh\left(f x + e\right)^{6} + 8 \, {\left(99 \, a b \cosh\left(f x + e\right)^{7} + 63 \, {\left(8 \, a^{2} + 9 \, a b\right)} \cosh\left(f x + e\right)^{5} - 7 \, {\left(112 \, a^{2} + 111 \, a b\right)} \cosh\left(f x + e\right)^{3} + 6 \, {\left(18 \, a^{2} + 23 \, a b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} - {\left(112 \, a^{2} + 111 \, a b\right)} \cosh\left(f x + e\right)^{4} + {\left(495 \, a b \cosh\left(f x + e\right)^{8} + 420 \, {\left(8 \, a^{2} + 9 \, a b\right)} \cosh\left(f x + e\right)^{6} - 70 \, {\left(112 \, a^{2} + 111 \, a b\right)} \cosh\left(f x + e\right)^{4} + 120 \, {\left(18 \, a^{2} + 23 \, a b\right)} \cosh\left(f x + e\right)^{2} - 112 \, a^{2} - 111 \, a b\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(55 \, a b \cosh\left(f x + e\right)^{9} + 60 \, {\left(8 \, a^{2} + 9 \, a b\right)} \cosh\left(f x + e\right)^{7} - 14 \, {\left(112 \, a^{2} + 111 \, a b\right)} \cosh\left(f x + e\right)^{5} + 40 \, {\left(18 \, a^{2} + 23 \, a b\right)} \cosh\left(f x + e\right)^{3} - {\left(112 \, a^{2} + 111 \, a b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 2 \, {\left(8 \, a^{2} + 9 \, a b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(33 \, a b \cosh\left(f x + e\right)^{10} + 45 \, {\left(8 \, a^{2} + 9 \, a b\right)} \cosh\left(f x + e\right)^{8} - 14 \, {\left(112 \, a^{2} + 111 \, a b\right)} \cosh\left(f x + e\right)^{6} + 60 \, {\left(18 \, a^{2} + 23 \, a b\right)} \cosh\left(f x + e\right)^{4} - 3 \, {\left(112 \, a^{2} + 111 \, a b\right)} \cosh\left(f x + e\right)^{2} + 8 \, a^{2} + 9 \, a b\right)} \sinh\left(f x + e\right)^{2} + a b + 4 \, {\left(3 \, a b \cosh\left(f x + e\right)^{11} + 5 \, {\left(8 \, a^{2} + 9 \, a b\right)} \cosh\left(f x + e\right)^{9} - 2 \, {\left(112 \, a^{2} + 111 \, a b\right)} \cosh\left(f x + e\right)^{7} + 12 \, {\left(18 \, a^{2} + 23 \, a b\right)} \cosh\left(f x + e\right)^{5} - {\left(112 \, a^{2} + 111 \, a b\right)} \cosh\left(f x + e\right)^{3} + {\left(8 \, a^{2} + 9 \, a b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{48 \, {\left(a f \cosh\left(f x + e\right)^{11} + 11 \, a f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{10} + a f \sinh\left(f x + e\right)^{11} - 4 \, a f \cosh\left(f x + e\right)^{9} + {\left(55 \, a f \cosh\left(f x + e\right)^{2} - 4 \, a f\right)} \sinh\left(f x + e\right)^{9} + 6 \, a f \cosh\left(f x + e\right)^{7} + 3 \, {\left(55 \, a f \cosh\left(f x + e\right)^{3} - 12 \, a f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{8} + 6 \, {\left(55 \, a f \cosh\left(f x + e\right)^{4} - 24 \, a f \cosh\left(f x + e\right)^{2} + a f\right)} \sinh\left(f x + e\right)^{7} - 4 \, a f \cosh\left(f x + e\right)^{5} + 42 \, {\left(11 \, a f \cosh\left(f x + e\right)^{5} - 8 \, a f \cosh\left(f x + e\right)^{3} + a f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{6} + 2 \, {\left(231 \, a f \cosh\left(f x + e\right)^{6} - 252 \, a f \cosh\left(f x + e\right)^{4} + 63 \, a f \cosh\left(f x + e\right)^{2} - 2 \, a f\right)} \sinh\left(f x + e\right)^{5} + a f \cosh\left(f x + e\right)^{3} + 2 \, {\left(165 \, a f \cosh\left(f x + e\right)^{7} - 252 \, a f \cosh\left(f x + e\right)^{5} + 105 \, a f \cosh\left(f x + e\right)^{3} - 10 \, a f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{4} + {\left(165 \, a f \cosh\left(f x + e\right)^{8} - 336 \, a f \cosh\left(f x + e\right)^{6} + 210 \, a f \cosh\left(f x + e\right)^{4} - 40 \, a f \cosh\left(f x + e\right)^{2} + a f\right)} \sinh\left(f x + e\right)^{3} + {\left(55 \, a f \cosh\left(f x + e\right)^{9} - 144 \, a f \cosh\left(f x + e\right)^{7} + 126 \, a f \cosh\left(f x + e\right)^{5} - 40 \, a f \cosh\left(f x + e\right)^{3} + 3 \, a f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{2} + {\left(11 \, a f \cosh\left(f x + e\right)^{10} - 36 \, a f \cosh\left(f x + e\right)^{8} + 42 \, a f \cosh\left(f x + e\right)^{6} - 20 \, a f \cosh\left(f x + e\right)^{4} + 3 \, a f \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)\right)}}, \frac{3 \, {\left({\left(8 \, a^{2} + 24 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{11} + 11 \, {\left(8 \, a^{2} + 24 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{10} + {\left(8 \, a^{2} + 24 \, a b + 3 \, b^{2}\right)} \sinh\left(f x + e\right)^{11} - 4 \, {\left(8 \, a^{2} + 24 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{9} + {\left(55 \, {\left(8 \, a^{2} + 24 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} - 32 \, a^{2} - 96 \, a b - 12 \, b^{2}\right)} \sinh\left(f x + e\right)^{9} + 3 \, {\left(55 \, {\left(8 \, a^{2} + 24 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{3} - 12 \, {\left(8 \, a^{2} + 24 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{8} + 6 \, {\left(8 \, a^{2} + 24 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{7} + 6 \, {\left(55 \, {\left(8 \, a^{2} + 24 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{4} - 24 \, {\left(8 \, a^{2} + 24 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + 8 \, a^{2} + 24 \, a b + 3 \, b^{2}\right)} \sinh\left(f x + e\right)^{7} + 42 \, {\left(11 \, {\left(8 \, a^{2} + 24 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{5} - 8 \, {\left(8 \, a^{2} + 24 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{3} + {\left(8 \, a^{2} + 24 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{6} - 4 \, {\left(8 \, a^{2} + 24 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{5} + 2 \, {\left(231 \, {\left(8 \, a^{2} + 24 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{6} - 252 \, {\left(8 \, a^{2} + 24 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{4} + 63 \, {\left(8 \, a^{2} + 24 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} - 16 \, a^{2} - 48 \, a b - 6 \, b^{2}\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(165 \, {\left(8 \, a^{2} + 24 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{7} - 252 \, {\left(8 \, a^{2} + 24 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{5} + 105 \, {\left(8 \, a^{2} + 24 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{3} - 10 \, {\left(8 \, a^{2} + 24 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{4} + {\left(8 \, a^{2} + 24 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{3} + {\left(165 \, {\left(8 \, a^{2} + 24 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{8} - 336 \, {\left(8 \, a^{2} + 24 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{6} + 210 \, {\left(8 \, a^{2} + 24 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{4} - 40 \, {\left(8 \, a^{2} + 24 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + 8 \, a^{2} + 24 \, a b + 3 \, b^{2}\right)} \sinh\left(f x + e\right)^{3} + {\left(55 \, {\left(8 \, a^{2} + 24 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{9} - 144 \, {\left(8 \, a^{2} + 24 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{7} + 126 \, {\left(8 \, a^{2} + 24 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{5} - 40 \, {\left(8 \, a^{2} + 24 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(8 \, a^{2} + 24 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{2} + {\left(11 \, {\left(8 \, a^{2} + 24 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{10} - 36 \, {\left(8 \, a^{2} + 24 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{8} + 42 \, {\left(8 \, a^{2} + 24 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{6} - 20 \, {\left(8 \, a^{2} + 24 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{4} + 3 \, {\left(8 \, a^{2} + 24 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{2} \sqrt{-a} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{2 \, {\left(a \cosh\left(f x + e\right) + a \sinh\left(f x + e\right)\right)}}\right) + \sqrt{2} {\left(a b \cosh\left(f x + e\right)^{12} + 12 \, a b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{11} + a b \sinh\left(f x + e\right)^{12} + 2 \, {\left(8 \, a^{2} + 9 \, a b\right)} \cosh\left(f x + e\right)^{10} + 2 \, {\left(33 \, a b \cosh\left(f x + e\right)^{2} + 8 \, a^{2} + 9 \, a b\right)} \sinh\left(f x + e\right)^{10} + 20 \, {\left(11 \, a b \cosh\left(f x + e\right)^{3} + {\left(8 \, a^{2} + 9 \, a b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{9} - {\left(112 \, a^{2} + 111 \, a b\right)} \cosh\left(f x + e\right)^{8} + {\left(495 \, a b \cosh\left(f x + e\right)^{4} + 90 \, {\left(8 \, a^{2} + 9 \, a b\right)} \cosh\left(f x + e\right)^{2} - 112 \, a^{2} - 111 \, a b\right)} \sinh\left(f x + e\right)^{8} + 8 \, {\left(99 \, a b \cosh\left(f x + e\right)^{5} + 30 \, {\left(8 \, a^{2} + 9 \, a b\right)} \cosh\left(f x + e\right)^{3} - {\left(112 \, a^{2} + 111 \, a b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{7} + 8 \, {\left(18 \, a^{2} + 23 \, a b\right)} \cosh\left(f x + e\right)^{6} + 4 \, {\left(231 \, a b \cosh\left(f x + e\right)^{6} + 105 \, {\left(8 \, a^{2} + 9 \, a b\right)} \cosh\left(f x + e\right)^{4} - 7 \, {\left(112 \, a^{2} + 111 \, a b\right)} \cosh\left(f x + e\right)^{2} + 36 \, a^{2} + 46 \, a b\right)} \sinh\left(f x + e\right)^{6} + 8 \, {\left(99 \, a b \cosh\left(f x + e\right)^{7} + 63 \, {\left(8 \, a^{2} + 9 \, a b\right)} \cosh\left(f x + e\right)^{5} - 7 \, {\left(112 \, a^{2} + 111 \, a b\right)} \cosh\left(f x + e\right)^{3} + 6 \, {\left(18 \, a^{2} + 23 \, a b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} - {\left(112 \, a^{2} + 111 \, a b\right)} \cosh\left(f x + e\right)^{4} + {\left(495 \, a b \cosh\left(f x + e\right)^{8} + 420 \, {\left(8 \, a^{2} + 9 \, a b\right)} \cosh\left(f x + e\right)^{6} - 70 \, {\left(112 \, a^{2} + 111 \, a b\right)} \cosh\left(f x + e\right)^{4} + 120 \, {\left(18 \, a^{2} + 23 \, a b\right)} \cosh\left(f x + e\right)^{2} - 112 \, a^{2} - 111 \, a b\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(55 \, a b \cosh\left(f x + e\right)^{9} + 60 \, {\left(8 \, a^{2} + 9 \, a b\right)} \cosh\left(f x + e\right)^{7} - 14 \, {\left(112 \, a^{2} + 111 \, a b\right)} \cosh\left(f x + e\right)^{5} + 40 \, {\left(18 \, a^{2} + 23 \, a b\right)} \cosh\left(f x + e\right)^{3} - {\left(112 \, a^{2} + 111 \, a b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 2 \, {\left(8 \, a^{2} + 9 \, a b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(33 \, a b \cosh\left(f x + e\right)^{10} + 45 \, {\left(8 \, a^{2} + 9 \, a b\right)} \cosh\left(f x + e\right)^{8} - 14 \, {\left(112 \, a^{2} + 111 \, a b\right)} \cosh\left(f x + e\right)^{6} + 60 \, {\left(18 \, a^{2} + 23 \, a b\right)} \cosh\left(f x + e\right)^{4} - 3 \, {\left(112 \, a^{2} + 111 \, a b\right)} \cosh\left(f x + e\right)^{2} + 8 \, a^{2} + 9 \, a b\right)} \sinh\left(f x + e\right)^{2} + a b + 4 \, {\left(3 \, a b \cosh\left(f x + e\right)^{11} + 5 \, {\left(8 \, a^{2} + 9 \, a b\right)} \cosh\left(f x + e\right)^{9} - 2 \, {\left(112 \, a^{2} + 111 \, a b\right)} \cosh\left(f x + e\right)^{7} + 12 \, {\left(18 \, a^{2} + 23 \, a b\right)} \cosh\left(f x + e\right)^{5} - {\left(112 \, a^{2} + 111 \, a b\right)} \cosh\left(f x + e\right)^{3} + {\left(8 \, a^{2} + 9 \, a b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{24 \, {\left(a f \cosh\left(f x + e\right)^{11} + 11 \, a f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{10} + a f \sinh\left(f x + e\right)^{11} - 4 \, a f \cosh\left(f x + e\right)^{9} + {\left(55 \, a f \cosh\left(f x + e\right)^{2} - 4 \, a f\right)} \sinh\left(f x + e\right)^{9} + 6 \, a f \cosh\left(f x + e\right)^{7} + 3 \, {\left(55 \, a f \cosh\left(f x + e\right)^{3} - 12 \, a f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{8} + 6 \, {\left(55 \, a f \cosh\left(f x + e\right)^{4} - 24 \, a f \cosh\left(f x + e\right)^{2} + a f\right)} \sinh\left(f x + e\right)^{7} - 4 \, a f \cosh\left(f x + e\right)^{5} + 42 \, {\left(11 \, a f \cosh\left(f x + e\right)^{5} - 8 \, a f \cosh\left(f x + e\right)^{3} + a f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{6} + 2 \, {\left(231 \, a f \cosh\left(f x + e\right)^{6} - 252 \, a f \cosh\left(f x + e\right)^{4} + 63 \, a f \cosh\left(f x + e\right)^{2} - 2 \, a f\right)} \sinh\left(f x + e\right)^{5} + a f \cosh\left(f x + e\right)^{3} + 2 \, {\left(165 \, a f \cosh\left(f x + e\right)^{7} - 252 \, a f \cosh\left(f x + e\right)^{5} + 105 \, a f \cosh\left(f x + e\right)^{3} - 10 \, a f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{4} + {\left(165 \, a f \cosh\left(f x + e\right)^{8} - 336 \, a f \cosh\left(f x + e\right)^{6} + 210 \, a f \cosh\left(f x + e\right)^{4} - 40 \, a f \cosh\left(f x + e\right)^{2} + a f\right)} \sinh\left(f x + e\right)^{3} + {\left(55 \, a f \cosh\left(f x + e\right)^{9} - 144 \, a f \cosh\left(f x + e\right)^{7} + 126 \, a f \cosh\left(f x + e\right)^{5} - 40 \, a f \cosh\left(f x + e\right)^{3} + 3 \, a f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{2} + {\left(11 \, a f \cosh\left(f x + e\right)^{10} - 36 \, a f \cosh\left(f x + e\right)^{8} + 42 \, a f \cosh\left(f x + e\right)^{6} - 20 \, a f \cosh\left(f x + e\right)^{4} + 3 \, a f \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)\right)}}\right]"," ",0,"[1/48*(3*((8*a^2 + 24*a*b + 3*b^2)*cosh(f*x + e)^11 + 11*(8*a^2 + 24*a*b + 3*b^2)*cosh(f*x + e)*sinh(f*x + e)^10 + (8*a^2 + 24*a*b + 3*b^2)*sinh(f*x + e)^11 - 4*(8*a^2 + 24*a*b + 3*b^2)*cosh(f*x + e)^9 + (55*(8*a^2 + 24*a*b + 3*b^2)*cosh(f*x + e)^2 - 32*a^2 - 96*a*b - 12*b^2)*sinh(f*x + e)^9 + 3*(55*(8*a^2 + 24*a*b + 3*b^2)*cosh(f*x + e)^3 - 12*(8*a^2 + 24*a*b + 3*b^2)*cosh(f*x + e))*sinh(f*x + e)^8 + 6*(8*a^2 + 24*a*b + 3*b^2)*cosh(f*x + e)^7 + 6*(55*(8*a^2 + 24*a*b + 3*b^2)*cosh(f*x + e)^4 - 24*(8*a^2 + 24*a*b + 3*b^2)*cosh(f*x + e)^2 + 8*a^2 + 24*a*b + 3*b^2)*sinh(f*x + e)^7 + 42*(11*(8*a^2 + 24*a*b + 3*b^2)*cosh(f*x + e)^5 - 8*(8*a^2 + 24*a*b + 3*b^2)*cosh(f*x + e)^3 + (8*a^2 + 24*a*b + 3*b^2)*cosh(f*x + e))*sinh(f*x + e)^6 - 4*(8*a^2 + 24*a*b + 3*b^2)*cosh(f*x + e)^5 + 2*(231*(8*a^2 + 24*a*b + 3*b^2)*cosh(f*x + e)^6 - 252*(8*a^2 + 24*a*b + 3*b^2)*cosh(f*x + e)^4 + 63*(8*a^2 + 24*a*b + 3*b^2)*cosh(f*x + e)^2 - 16*a^2 - 48*a*b - 6*b^2)*sinh(f*x + e)^5 + 2*(165*(8*a^2 + 24*a*b + 3*b^2)*cosh(f*x + e)^7 - 252*(8*a^2 + 24*a*b + 3*b^2)*cosh(f*x + e)^5 + 105*(8*a^2 + 24*a*b + 3*b^2)*cosh(f*x + e)^3 - 10*(8*a^2 + 24*a*b + 3*b^2)*cosh(f*x + e))*sinh(f*x + e)^4 + (8*a^2 + 24*a*b + 3*b^2)*cosh(f*x + e)^3 + (165*(8*a^2 + 24*a*b + 3*b^2)*cosh(f*x + e)^8 - 336*(8*a^2 + 24*a*b + 3*b^2)*cosh(f*x + e)^6 + 210*(8*a^2 + 24*a*b + 3*b^2)*cosh(f*x + e)^4 - 40*(8*a^2 + 24*a*b + 3*b^2)*cosh(f*x + e)^2 + 8*a^2 + 24*a*b + 3*b^2)*sinh(f*x + e)^3 + (55*(8*a^2 + 24*a*b + 3*b^2)*cosh(f*x + e)^9 - 144*(8*a^2 + 24*a*b + 3*b^2)*cosh(f*x + e)^7 + 126*(8*a^2 + 24*a*b + 3*b^2)*cosh(f*x + e)^5 - 40*(8*a^2 + 24*a*b + 3*b^2)*cosh(f*x + e)^3 + 3*(8*a^2 + 24*a*b + 3*b^2)*cosh(f*x + e))*sinh(f*x + e)^2 + (11*(8*a^2 + 24*a*b + 3*b^2)*cosh(f*x + e)^10 - 36*(8*a^2 + 24*a*b + 3*b^2)*cosh(f*x + e)^8 + 42*(8*a^2 + 24*a*b + 3*b^2)*cosh(f*x + e)^6 - 20*(8*a^2 + 24*a*b + 3*b^2)*cosh(f*x + e)^4 + 3*(8*a^2 + 24*a*b + 3*b^2)*cosh(f*x + e)^2)*sinh(f*x + e))*sqrt(a)*log((b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(4*a - b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 4*a - b)*sinh(f*x + e)^2 - 4*sqrt(2)*sqrt(a)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))*(cosh(f*x + e) + sinh(f*x + e)) + 4*(b*cosh(f*x + e)^3 + (4*a - b)*cosh(f*x + e))*sinh(f*x + e) + b)/(cosh(f*x + e)^4 + 4*cosh(f*x + e)*sinh(f*x + e)^3 + sinh(f*x + e)^4 + 2*(3*cosh(f*x + e)^2 - 1)*sinh(f*x + e)^2 - 2*cosh(f*x + e)^2 + 4*(cosh(f*x + e)^3 - cosh(f*x + e))*sinh(f*x + e) + 1)) + 2*sqrt(2)*(a*b*cosh(f*x + e)^12 + 12*a*b*cosh(f*x + e)*sinh(f*x + e)^11 + a*b*sinh(f*x + e)^12 + 2*(8*a^2 + 9*a*b)*cosh(f*x + e)^10 + 2*(33*a*b*cosh(f*x + e)^2 + 8*a^2 + 9*a*b)*sinh(f*x + e)^10 + 20*(11*a*b*cosh(f*x + e)^3 + (8*a^2 + 9*a*b)*cosh(f*x + e))*sinh(f*x + e)^9 - (112*a^2 + 111*a*b)*cosh(f*x + e)^8 + (495*a*b*cosh(f*x + e)^4 + 90*(8*a^2 + 9*a*b)*cosh(f*x + e)^2 - 112*a^2 - 111*a*b)*sinh(f*x + e)^8 + 8*(99*a*b*cosh(f*x + e)^5 + 30*(8*a^2 + 9*a*b)*cosh(f*x + e)^3 - (112*a^2 + 111*a*b)*cosh(f*x + e))*sinh(f*x + e)^7 + 8*(18*a^2 + 23*a*b)*cosh(f*x + e)^6 + 4*(231*a*b*cosh(f*x + e)^6 + 105*(8*a^2 + 9*a*b)*cosh(f*x + e)^4 - 7*(112*a^2 + 111*a*b)*cosh(f*x + e)^2 + 36*a^2 + 46*a*b)*sinh(f*x + e)^6 + 8*(99*a*b*cosh(f*x + e)^7 + 63*(8*a^2 + 9*a*b)*cosh(f*x + e)^5 - 7*(112*a^2 + 111*a*b)*cosh(f*x + e)^3 + 6*(18*a^2 + 23*a*b)*cosh(f*x + e))*sinh(f*x + e)^5 - (112*a^2 + 111*a*b)*cosh(f*x + e)^4 + (495*a*b*cosh(f*x + e)^8 + 420*(8*a^2 + 9*a*b)*cosh(f*x + e)^6 - 70*(112*a^2 + 111*a*b)*cosh(f*x + e)^4 + 120*(18*a^2 + 23*a*b)*cosh(f*x + e)^2 - 112*a^2 - 111*a*b)*sinh(f*x + e)^4 + 4*(55*a*b*cosh(f*x + e)^9 + 60*(8*a^2 + 9*a*b)*cosh(f*x + e)^7 - 14*(112*a^2 + 111*a*b)*cosh(f*x + e)^5 + 40*(18*a^2 + 23*a*b)*cosh(f*x + e)^3 - (112*a^2 + 111*a*b)*cosh(f*x + e))*sinh(f*x + e)^3 + 2*(8*a^2 + 9*a*b)*cosh(f*x + e)^2 + 2*(33*a*b*cosh(f*x + e)^10 + 45*(8*a^2 + 9*a*b)*cosh(f*x + e)^8 - 14*(112*a^2 + 111*a*b)*cosh(f*x + e)^6 + 60*(18*a^2 + 23*a*b)*cosh(f*x + e)^4 - 3*(112*a^2 + 111*a*b)*cosh(f*x + e)^2 + 8*a^2 + 9*a*b)*sinh(f*x + e)^2 + a*b + 4*(3*a*b*cosh(f*x + e)^11 + 5*(8*a^2 + 9*a*b)*cosh(f*x + e)^9 - 2*(112*a^2 + 111*a*b)*cosh(f*x + e)^7 + 12*(18*a^2 + 23*a*b)*cosh(f*x + e)^5 - (112*a^2 + 111*a*b)*cosh(f*x + e)^3 + (8*a^2 + 9*a*b)*cosh(f*x + e))*sinh(f*x + e))*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/(a*f*cosh(f*x + e)^11 + 11*a*f*cosh(f*x + e)*sinh(f*x + e)^10 + a*f*sinh(f*x + e)^11 - 4*a*f*cosh(f*x + e)^9 + (55*a*f*cosh(f*x + e)^2 - 4*a*f)*sinh(f*x + e)^9 + 6*a*f*cosh(f*x + e)^7 + 3*(55*a*f*cosh(f*x + e)^3 - 12*a*f*cosh(f*x + e))*sinh(f*x + e)^8 + 6*(55*a*f*cosh(f*x + e)^4 - 24*a*f*cosh(f*x + e)^2 + a*f)*sinh(f*x + e)^7 - 4*a*f*cosh(f*x + e)^5 + 42*(11*a*f*cosh(f*x + e)^5 - 8*a*f*cosh(f*x + e)^3 + a*f*cosh(f*x + e))*sinh(f*x + e)^6 + 2*(231*a*f*cosh(f*x + e)^6 - 252*a*f*cosh(f*x + e)^4 + 63*a*f*cosh(f*x + e)^2 - 2*a*f)*sinh(f*x + e)^5 + a*f*cosh(f*x + e)^3 + 2*(165*a*f*cosh(f*x + e)^7 - 252*a*f*cosh(f*x + e)^5 + 105*a*f*cosh(f*x + e)^3 - 10*a*f*cosh(f*x + e))*sinh(f*x + e)^4 + (165*a*f*cosh(f*x + e)^8 - 336*a*f*cosh(f*x + e)^6 + 210*a*f*cosh(f*x + e)^4 - 40*a*f*cosh(f*x + e)^2 + a*f)*sinh(f*x + e)^3 + (55*a*f*cosh(f*x + e)^9 - 144*a*f*cosh(f*x + e)^7 + 126*a*f*cosh(f*x + e)^5 - 40*a*f*cosh(f*x + e)^3 + 3*a*f*cosh(f*x + e))*sinh(f*x + e)^2 + (11*a*f*cosh(f*x + e)^10 - 36*a*f*cosh(f*x + e)^8 + 42*a*f*cosh(f*x + e)^6 - 20*a*f*cosh(f*x + e)^4 + 3*a*f*cosh(f*x + e)^2)*sinh(f*x + e)), 1/24*(3*((8*a^2 + 24*a*b + 3*b^2)*cosh(f*x + e)^11 + 11*(8*a^2 + 24*a*b + 3*b^2)*cosh(f*x + e)*sinh(f*x + e)^10 + (8*a^2 + 24*a*b + 3*b^2)*sinh(f*x + e)^11 - 4*(8*a^2 + 24*a*b + 3*b^2)*cosh(f*x + e)^9 + (55*(8*a^2 + 24*a*b + 3*b^2)*cosh(f*x + e)^2 - 32*a^2 - 96*a*b - 12*b^2)*sinh(f*x + e)^9 + 3*(55*(8*a^2 + 24*a*b + 3*b^2)*cosh(f*x + e)^3 - 12*(8*a^2 + 24*a*b + 3*b^2)*cosh(f*x + e))*sinh(f*x + e)^8 + 6*(8*a^2 + 24*a*b + 3*b^2)*cosh(f*x + e)^7 + 6*(55*(8*a^2 + 24*a*b + 3*b^2)*cosh(f*x + e)^4 - 24*(8*a^2 + 24*a*b + 3*b^2)*cosh(f*x + e)^2 + 8*a^2 + 24*a*b + 3*b^2)*sinh(f*x + e)^7 + 42*(11*(8*a^2 + 24*a*b + 3*b^2)*cosh(f*x + e)^5 - 8*(8*a^2 + 24*a*b + 3*b^2)*cosh(f*x + e)^3 + (8*a^2 + 24*a*b + 3*b^2)*cosh(f*x + e))*sinh(f*x + e)^6 - 4*(8*a^2 + 24*a*b + 3*b^2)*cosh(f*x + e)^5 + 2*(231*(8*a^2 + 24*a*b + 3*b^2)*cosh(f*x + e)^6 - 252*(8*a^2 + 24*a*b + 3*b^2)*cosh(f*x + e)^4 + 63*(8*a^2 + 24*a*b + 3*b^2)*cosh(f*x + e)^2 - 16*a^2 - 48*a*b - 6*b^2)*sinh(f*x + e)^5 + 2*(165*(8*a^2 + 24*a*b + 3*b^2)*cosh(f*x + e)^7 - 252*(8*a^2 + 24*a*b + 3*b^2)*cosh(f*x + e)^5 + 105*(8*a^2 + 24*a*b + 3*b^2)*cosh(f*x + e)^3 - 10*(8*a^2 + 24*a*b + 3*b^2)*cosh(f*x + e))*sinh(f*x + e)^4 + (8*a^2 + 24*a*b + 3*b^2)*cosh(f*x + e)^3 + (165*(8*a^2 + 24*a*b + 3*b^2)*cosh(f*x + e)^8 - 336*(8*a^2 + 24*a*b + 3*b^2)*cosh(f*x + e)^6 + 210*(8*a^2 + 24*a*b + 3*b^2)*cosh(f*x + e)^4 - 40*(8*a^2 + 24*a*b + 3*b^2)*cosh(f*x + e)^2 + 8*a^2 + 24*a*b + 3*b^2)*sinh(f*x + e)^3 + (55*(8*a^2 + 24*a*b + 3*b^2)*cosh(f*x + e)^9 - 144*(8*a^2 + 24*a*b + 3*b^2)*cosh(f*x + e)^7 + 126*(8*a^2 + 24*a*b + 3*b^2)*cosh(f*x + e)^5 - 40*(8*a^2 + 24*a*b + 3*b^2)*cosh(f*x + e)^3 + 3*(8*a^2 + 24*a*b + 3*b^2)*cosh(f*x + e))*sinh(f*x + e)^2 + (11*(8*a^2 + 24*a*b + 3*b^2)*cosh(f*x + e)^10 - 36*(8*a^2 + 24*a*b + 3*b^2)*cosh(f*x + e)^8 + 42*(8*a^2 + 24*a*b + 3*b^2)*cosh(f*x + e)^6 - 20*(8*a^2 + 24*a*b + 3*b^2)*cosh(f*x + e)^4 + 3*(8*a^2 + 24*a*b + 3*b^2)*cosh(f*x + e)^2)*sinh(f*x + e))*sqrt(-a)*arctan(1/2*sqrt(2)*sqrt(-a)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/(a*cosh(f*x + e) + a*sinh(f*x + e))) + sqrt(2)*(a*b*cosh(f*x + e)^12 + 12*a*b*cosh(f*x + e)*sinh(f*x + e)^11 + a*b*sinh(f*x + e)^12 + 2*(8*a^2 + 9*a*b)*cosh(f*x + e)^10 + 2*(33*a*b*cosh(f*x + e)^2 + 8*a^2 + 9*a*b)*sinh(f*x + e)^10 + 20*(11*a*b*cosh(f*x + e)^3 + (8*a^2 + 9*a*b)*cosh(f*x + e))*sinh(f*x + e)^9 - (112*a^2 + 111*a*b)*cosh(f*x + e)^8 + (495*a*b*cosh(f*x + e)^4 + 90*(8*a^2 + 9*a*b)*cosh(f*x + e)^2 - 112*a^2 - 111*a*b)*sinh(f*x + e)^8 + 8*(99*a*b*cosh(f*x + e)^5 + 30*(8*a^2 + 9*a*b)*cosh(f*x + e)^3 - (112*a^2 + 111*a*b)*cosh(f*x + e))*sinh(f*x + e)^7 + 8*(18*a^2 + 23*a*b)*cosh(f*x + e)^6 + 4*(231*a*b*cosh(f*x + e)^6 + 105*(8*a^2 + 9*a*b)*cosh(f*x + e)^4 - 7*(112*a^2 + 111*a*b)*cosh(f*x + e)^2 + 36*a^2 + 46*a*b)*sinh(f*x + e)^6 + 8*(99*a*b*cosh(f*x + e)^7 + 63*(8*a^2 + 9*a*b)*cosh(f*x + e)^5 - 7*(112*a^2 + 111*a*b)*cosh(f*x + e)^3 + 6*(18*a^2 + 23*a*b)*cosh(f*x + e))*sinh(f*x + e)^5 - (112*a^2 + 111*a*b)*cosh(f*x + e)^4 + (495*a*b*cosh(f*x + e)^8 + 420*(8*a^2 + 9*a*b)*cosh(f*x + e)^6 - 70*(112*a^2 + 111*a*b)*cosh(f*x + e)^4 + 120*(18*a^2 + 23*a*b)*cosh(f*x + e)^2 - 112*a^2 - 111*a*b)*sinh(f*x + e)^4 + 4*(55*a*b*cosh(f*x + e)^9 + 60*(8*a^2 + 9*a*b)*cosh(f*x + e)^7 - 14*(112*a^2 + 111*a*b)*cosh(f*x + e)^5 + 40*(18*a^2 + 23*a*b)*cosh(f*x + e)^3 - (112*a^2 + 111*a*b)*cosh(f*x + e))*sinh(f*x + e)^3 + 2*(8*a^2 + 9*a*b)*cosh(f*x + e)^2 + 2*(33*a*b*cosh(f*x + e)^10 + 45*(8*a^2 + 9*a*b)*cosh(f*x + e)^8 - 14*(112*a^2 + 111*a*b)*cosh(f*x + e)^6 + 60*(18*a^2 + 23*a*b)*cosh(f*x + e)^4 - 3*(112*a^2 + 111*a*b)*cosh(f*x + e)^2 + 8*a^2 + 9*a*b)*sinh(f*x + e)^2 + a*b + 4*(3*a*b*cosh(f*x + e)^11 + 5*(8*a^2 + 9*a*b)*cosh(f*x + e)^9 - 2*(112*a^2 + 111*a*b)*cosh(f*x + e)^7 + 12*(18*a^2 + 23*a*b)*cosh(f*x + e)^5 - (112*a^2 + 111*a*b)*cosh(f*x + e)^3 + (8*a^2 + 9*a*b)*cosh(f*x + e))*sinh(f*x + e))*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/(a*f*cosh(f*x + e)^11 + 11*a*f*cosh(f*x + e)*sinh(f*x + e)^10 + a*f*sinh(f*x + e)^11 - 4*a*f*cosh(f*x + e)^9 + (55*a*f*cosh(f*x + e)^2 - 4*a*f)*sinh(f*x + e)^9 + 6*a*f*cosh(f*x + e)^7 + 3*(55*a*f*cosh(f*x + e)^3 - 12*a*f*cosh(f*x + e))*sinh(f*x + e)^8 + 6*(55*a*f*cosh(f*x + e)^4 - 24*a*f*cosh(f*x + e)^2 + a*f)*sinh(f*x + e)^7 - 4*a*f*cosh(f*x + e)^5 + 42*(11*a*f*cosh(f*x + e)^5 - 8*a*f*cosh(f*x + e)^3 + a*f*cosh(f*x + e))*sinh(f*x + e)^6 + 2*(231*a*f*cosh(f*x + e)^6 - 252*a*f*cosh(f*x + e)^4 + 63*a*f*cosh(f*x + e)^2 - 2*a*f)*sinh(f*x + e)^5 + a*f*cosh(f*x + e)^3 + 2*(165*a*f*cosh(f*x + e)^7 - 252*a*f*cosh(f*x + e)^5 + 105*a*f*cosh(f*x + e)^3 - 10*a*f*cosh(f*x + e))*sinh(f*x + e)^4 + (165*a*f*cosh(f*x + e)^8 - 336*a*f*cosh(f*x + e)^6 + 210*a*f*cosh(f*x + e)^4 - 40*a*f*cosh(f*x + e)^2 + a*f)*sinh(f*x + e)^3 + (55*a*f*cosh(f*x + e)^9 - 144*a*f*cosh(f*x + e)^7 + 126*a*f*cosh(f*x + e)^5 - 40*a*f*cosh(f*x + e)^3 + 3*a*f*cosh(f*x + e))*sinh(f*x + e)^2 + (11*a*f*cosh(f*x + e)^10 - 36*a*f*cosh(f*x + e)^8 + 42*a*f*cosh(f*x + e)^6 - 20*a*f*cosh(f*x + e)^4 + 3*a*f*cosh(f*x + e)^2)*sinh(f*x + e))]","B",0
474,0,0,0,0.478113," ","integrate((a+b*sinh(f*x+e)^2)^(3/2)*tanh(f*x+e)^4,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sinh\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} \tanh\left(f x + e\right)^{4}, x\right)"," ",0,"integral((b*sinh(f*x + e)^2 + a)^(3/2)*tanh(f*x + e)^4, x)","F",0
475,0,0,0,0.642041," ","integrate((a+b*sinh(f*x+e)^2)^(3/2)*tanh(f*x+e)^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sinh\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}} \tanh\left(f x + e\right)^{2}, x\right)"," ",0,"integral((b*sinh(f*x + e)^2 + a)^(3/2)*tanh(f*x + e)^2, x)","F",0
476,0,0,0,0.427204," ","integrate((a+b*sinh(f*x+e)^2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sinh\left(f x + e\right)^{2} + a\right)}^{\frac{3}{2}}, x\right)"," ",0,"integral((b*sinh(f*x + e)^2 + a)^(3/2), x)","F",0
477,0,0,0,0.537989," ","integrate(coth(f*x+e)^2*(a+b*sinh(f*x+e)^2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \coth\left(f x + e\right)^{2} \sinh\left(f x + e\right)^{2} + a \coth\left(f x + e\right)^{2}\right)} \sqrt{b \sinh\left(f x + e\right)^{2} + a}, x\right)"," ",0,"integral((b*coth(f*x + e)^2*sinh(f*x + e)^2 + a*coth(f*x + e)^2)*sqrt(b*sinh(f*x + e)^2 + a), x)","F",0
478,0,0,0,0.691711," ","integrate(coth(f*x+e)^4*(a+b*sinh(f*x+e)^2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \coth\left(f x + e\right)^{4} \sinh\left(f x + e\right)^{2} + a \coth\left(f x + e\right)^{4}\right)} \sqrt{b \sinh\left(f x + e\right)^{2} + a}, x\right)"," ",0,"integral((b*coth(f*x + e)^4*sinh(f*x + e)^2 + a*coth(f*x + e)^4)*sqrt(b*sinh(f*x + e)^2 + a), x)","F",0
479,1,4100,0,0.999188," ","integrate(tanh(f*x+e)^5/(a+b*sinh(f*x+e)^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{8} + 8 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \sinh\left(f x + e\right)^{8} + 4 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{6} + 4 \, {\left(7 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + 8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \sinh\left(f x + e\right)^{6} + 8 \, {\left(7 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + 6 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{4} + 2 \, {\left(35 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{4} + 30 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + 24 \, a^{2} - 24 \, a b + 9 \, b^{2}\right)} \sinh\left(f x + e\right)^{4} + 8 \, {\left(7 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{5} + 10 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 4 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + 4 \, {\left(7 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{6} + 15 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{4} + 9 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + 8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \sinh\left(f x + e\right)^{2} + 8 \, a^{2} - 8 \, a b + 3 \, b^{2} + 8 \, {\left({\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{7} + 3 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{5} + 3 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{3} + {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{a - b} \log\left(\frac{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(4 \, a - 3 \, b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + 4 \, a - 3 \, b\right)} \sinh\left(f x + e\right)^{2} - 4 \, \sqrt{2} \sqrt{a - b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} {\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right)\right)} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(4 \, a - 3 \, b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}{\cosh\left(f x + e\right)^{4} + 4 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + \sinh\left(f x + e\right)^{4} + 2 \, {\left(3 \, \cosh\left(f x + e\right)^{2} + 1\right)} \sinh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right)^{2} + 4 \, {\left(\cosh\left(f x + e\right)^{3} + \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + 1}\right) + 4 \, \sqrt{2} {\left({\left(8 \, a^{2} - 13 \, a b + 5 \, b^{2}\right)} \cosh\left(f x + e\right)^{5} + 5 \, {\left(8 \, a^{2} - 13 \, a b + 5 \, b^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{4} + {\left(8 \, a^{2} - 13 \, a b + 5 \, b^{2}\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(4 \, a^{2} - 5 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{3} + 2 \, {\left(5 \, {\left(8 \, a^{2} - 13 \, a b + 5 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + 4 \, a^{2} - 5 \, a b + b^{2}\right)} \sinh\left(f x + e\right)^{3} + 2 \, {\left(5 \, {\left(8 \, a^{2} - 13 \, a b + 5 \, b^{2}\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(4 \, a^{2} - 5 \, a b + b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{2} + {\left(8 \, a^{2} - 13 \, a b + 5 \, b^{2}\right)} \cosh\left(f x + e\right) + {\left(5 \, {\left(8 \, a^{2} - 13 \, a b + 5 \, b^{2}\right)} \cosh\left(f x + e\right)^{4} + 6 \, {\left(4 \, a^{2} - 5 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{2} + 8 \, a^{2} - 13 \, a b + 5 \, b^{2}\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{16 \, {\left({\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} f \cosh\left(f x + e\right)^{8} + 8 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} f \sinh\left(f x + e\right)^{8} + 4 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} f \cosh\left(f x + e\right)^{6} + 4 \, {\left(7 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} f \cosh\left(f x + e\right)^{2} + {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} f\right)} \sinh\left(f x + e\right)^{6} + 6 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} f \cosh\left(f x + e\right)^{4} + 8 \, {\left(7 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} f \cosh\left(f x + e\right)^{3} + 3 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(35 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} f \cosh\left(f x + e\right)^{4} + 30 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} f \cosh\left(f x + e\right)^{2} + 3 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} f\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} f \cosh\left(f x + e\right)^{2} + 8 \, {\left(7 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} f \cosh\left(f x + e\right)^{5} + 10 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} f \cosh\left(f x + e\right)^{3} + 3 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 4 \, {\left(7 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} f \cosh\left(f x + e\right)^{6} + 15 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} f \cosh\left(f x + e\right)^{4} + 9 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} f \cosh\left(f x + e\right)^{2} + {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} f\right)} \sinh\left(f x + e\right)^{2} + {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} f + 8 \, {\left({\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} f \cosh\left(f x + e\right)^{7} + 3 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} f \cosh\left(f x + e\right)^{5} + 3 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} f \cosh\left(f x + e\right)^{3} + {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)}}, -\frac{{\left({\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{8} + 8 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \sinh\left(f x + e\right)^{8} + 4 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{6} + 4 \, {\left(7 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + 8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \sinh\left(f x + e\right)^{6} + 8 \, {\left(7 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + 6 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{4} + 2 \, {\left(35 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{4} + 30 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + 24 \, a^{2} - 24 \, a b + 9 \, b^{2}\right)} \sinh\left(f x + e\right)^{4} + 8 \, {\left(7 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{5} + 10 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 4 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + 4 \, {\left(7 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{6} + 15 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{4} + 9 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + 8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \sinh\left(f x + e\right)^{2} + 8 \, a^{2} - 8 \, a b + 3 \, b^{2} + 8 \, {\left({\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{7} + 3 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{5} + 3 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{3} + {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{-a + b} \arctan\left(-\frac{\sqrt{2} \sqrt{-a + b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{2 \, {\left({\left(a - b\right)} \cosh\left(f x + e\right) + {\left(a - b\right)} \sinh\left(f x + e\right)\right)}}\right) - 2 \, \sqrt{2} {\left({\left(8 \, a^{2} - 13 \, a b + 5 \, b^{2}\right)} \cosh\left(f x + e\right)^{5} + 5 \, {\left(8 \, a^{2} - 13 \, a b + 5 \, b^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{4} + {\left(8 \, a^{2} - 13 \, a b + 5 \, b^{2}\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(4 \, a^{2} - 5 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{3} + 2 \, {\left(5 \, {\left(8 \, a^{2} - 13 \, a b + 5 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + 4 \, a^{2} - 5 \, a b + b^{2}\right)} \sinh\left(f x + e\right)^{3} + 2 \, {\left(5 \, {\left(8 \, a^{2} - 13 \, a b + 5 \, b^{2}\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(4 \, a^{2} - 5 \, a b + b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{2} + {\left(8 \, a^{2} - 13 \, a b + 5 \, b^{2}\right)} \cosh\left(f x + e\right) + {\left(5 \, {\left(8 \, a^{2} - 13 \, a b + 5 \, b^{2}\right)} \cosh\left(f x + e\right)^{4} + 6 \, {\left(4 \, a^{2} - 5 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{2} + 8 \, a^{2} - 13 \, a b + 5 \, b^{2}\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{8 \, {\left({\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} f \cosh\left(f x + e\right)^{8} + 8 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} f \sinh\left(f x + e\right)^{8} + 4 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} f \cosh\left(f x + e\right)^{6} + 4 \, {\left(7 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} f \cosh\left(f x + e\right)^{2} + {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} f\right)} \sinh\left(f x + e\right)^{6} + 6 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} f \cosh\left(f x + e\right)^{4} + 8 \, {\left(7 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} f \cosh\left(f x + e\right)^{3} + 3 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(35 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} f \cosh\left(f x + e\right)^{4} + 30 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} f \cosh\left(f x + e\right)^{2} + 3 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} f\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} f \cosh\left(f x + e\right)^{2} + 8 \, {\left(7 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} f \cosh\left(f x + e\right)^{5} + 10 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} f \cosh\left(f x + e\right)^{3} + 3 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 4 \, {\left(7 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} f \cosh\left(f x + e\right)^{6} + 15 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} f \cosh\left(f x + e\right)^{4} + 9 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} f \cosh\left(f x + e\right)^{2} + {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} f\right)} \sinh\left(f x + e\right)^{2} + {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} f + 8 \, {\left({\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} f \cosh\left(f x + e\right)^{7} + 3 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} f \cosh\left(f x + e\right)^{5} + 3 \, {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} f \cosh\left(f x + e\right)^{3} + {\left(a^{3} - 3 \, a^{2} b + 3 \, a b^{2} - b^{3}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)}}\right]"," ",0,"[1/16*(((8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e)^8 + 8*(8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e)*sinh(f*x + e)^7 + (8*a^2 - 8*a*b + 3*b^2)*sinh(f*x + e)^8 + 4*(8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e)^6 + 4*(7*(8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e)^2 + 8*a^2 - 8*a*b + 3*b^2)*sinh(f*x + e)^6 + 8*(7*(8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e)^3 + 3*(8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e))*sinh(f*x + e)^5 + 6*(8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e)^4 + 2*(35*(8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e)^4 + 30*(8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e)^2 + 24*a^2 - 24*a*b + 9*b^2)*sinh(f*x + e)^4 + 8*(7*(8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e)^5 + 10*(8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e)^3 + 3*(8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e))*sinh(f*x + e)^3 + 4*(8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e)^2 + 4*(7*(8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e)^6 + 15*(8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e)^4 + 9*(8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e)^2 + 8*a^2 - 8*a*b + 3*b^2)*sinh(f*x + e)^2 + 8*a^2 - 8*a*b + 3*b^2 + 8*((8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e)^7 + 3*(8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e)^5 + 3*(8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e)^3 + (8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e))*sinh(f*x + e))*sqrt(a - b)*log((b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(4*a - 3*b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 4*a - 3*b)*sinh(f*x + e)^2 - 4*sqrt(2)*sqrt(a - b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))*(cosh(f*x + e) + sinh(f*x + e)) + 4*(b*cosh(f*x + e)^3 + (4*a - 3*b)*cosh(f*x + e))*sinh(f*x + e) + b)/(cosh(f*x + e)^4 + 4*cosh(f*x + e)*sinh(f*x + e)^3 + sinh(f*x + e)^4 + 2*(3*cosh(f*x + e)^2 + 1)*sinh(f*x + e)^2 + 2*cosh(f*x + e)^2 + 4*(cosh(f*x + e)^3 + cosh(f*x + e))*sinh(f*x + e) + 1)) + 4*sqrt(2)*((8*a^2 - 13*a*b + 5*b^2)*cosh(f*x + e)^5 + 5*(8*a^2 - 13*a*b + 5*b^2)*cosh(f*x + e)*sinh(f*x + e)^4 + (8*a^2 - 13*a*b + 5*b^2)*sinh(f*x + e)^5 + 2*(4*a^2 - 5*a*b + b^2)*cosh(f*x + e)^3 + 2*(5*(8*a^2 - 13*a*b + 5*b^2)*cosh(f*x + e)^2 + 4*a^2 - 5*a*b + b^2)*sinh(f*x + e)^3 + 2*(5*(8*a^2 - 13*a*b + 5*b^2)*cosh(f*x + e)^3 + 3*(4*a^2 - 5*a*b + b^2)*cosh(f*x + e))*sinh(f*x + e)^2 + (8*a^2 - 13*a*b + 5*b^2)*cosh(f*x + e) + (5*(8*a^2 - 13*a*b + 5*b^2)*cosh(f*x + e)^4 + 6*(4*a^2 - 5*a*b + b^2)*cosh(f*x + e)^2 + 8*a^2 - 13*a*b + 5*b^2)*sinh(f*x + e))*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/((a^3 - 3*a^2*b + 3*a*b^2 - b^3)*f*cosh(f*x + e)^8 + 8*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*f*cosh(f*x + e)*sinh(f*x + e)^7 + (a^3 - 3*a^2*b + 3*a*b^2 - b^3)*f*sinh(f*x + e)^8 + 4*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*f*cosh(f*x + e)^6 + 4*(7*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*f*cosh(f*x + e)^2 + (a^3 - 3*a^2*b + 3*a*b^2 - b^3)*f)*sinh(f*x + e)^6 + 6*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*f*cosh(f*x + e)^4 + 8*(7*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*f*cosh(f*x + e)^3 + 3*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*f*cosh(f*x + e))*sinh(f*x + e)^5 + 2*(35*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*f*cosh(f*x + e)^4 + 30*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*f*cosh(f*x + e)^2 + 3*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*f)*sinh(f*x + e)^4 + 4*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*f*cosh(f*x + e)^2 + 8*(7*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*f*cosh(f*x + e)^5 + 10*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*f*cosh(f*x + e)^3 + 3*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*f*cosh(f*x + e))*sinh(f*x + e)^3 + 4*(7*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*f*cosh(f*x + e)^6 + 15*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*f*cosh(f*x + e)^4 + 9*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*f*cosh(f*x + e)^2 + (a^3 - 3*a^2*b + 3*a*b^2 - b^3)*f)*sinh(f*x + e)^2 + (a^3 - 3*a^2*b + 3*a*b^2 - b^3)*f + 8*((a^3 - 3*a^2*b + 3*a*b^2 - b^3)*f*cosh(f*x + e)^7 + 3*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*f*cosh(f*x + e)^5 + 3*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*f*cosh(f*x + e)^3 + (a^3 - 3*a^2*b + 3*a*b^2 - b^3)*f*cosh(f*x + e))*sinh(f*x + e)), -1/8*(((8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e)^8 + 8*(8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e)*sinh(f*x + e)^7 + (8*a^2 - 8*a*b + 3*b^2)*sinh(f*x + e)^8 + 4*(8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e)^6 + 4*(7*(8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e)^2 + 8*a^2 - 8*a*b + 3*b^2)*sinh(f*x + e)^6 + 8*(7*(8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e)^3 + 3*(8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e))*sinh(f*x + e)^5 + 6*(8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e)^4 + 2*(35*(8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e)^4 + 30*(8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e)^2 + 24*a^2 - 24*a*b + 9*b^2)*sinh(f*x + e)^4 + 8*(7*(8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e)^5 + 10*(8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e)^3 + 3*(8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e))*sinh(f*x + e)^3 + 4*(8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e)^2 + 4*(7*(8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e)^6 + 15*(8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e)^4 + 9*(8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e)^2 + 8*a^2 - 8*a*b + 3*b^2)*sinh(f*x + e)^2 + 8*a^2 - 8*a*b + 3*b^2 + 8*((8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e)^7 + 3*(8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e)^5 + 3*(8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e)^3 + (8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e))*sinh(f*x + e))*sqrt(-a + b)*arctan(-1/2*sqrt(2)*sqrt(-a + b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/((a - b)*cosh(f*x + e) + (a - b)*sinh(f*x + e))) - 2*sqrt(2)*((8*a^2 - 13*a*b + 5*b^2)*cosh(f*x + e)^5 + 5*(8*a^2 - 13*a*b + 5*b^2)*cosh(f*x + e)*sinh(f*x + e)^4 + (8*a^2 - 13*a*b + 5*b^2)*sinh(f*x + e)^5 + 2*(4*a^2 - 5*a*b + b^2)*cosh(f*x + e)^3 + 2*(5*(8*a^2 - 13*a*b + 5*b^2)*cosh(f*x + e)^2 + 4*a^2 - 5*a*b + b^2)*sinh(f*x + e)^3 + 2*(5*(8*a^2 - 13*a*b + 5*b^2)*cosh(f*x + e)^3 + 3*(4*a^2 - 5*a*b + b^2)*cosh(f*x + e))*sinh(f*x + e)^2 + (8*a^2 - 13*a*b + 5*b^2)*cosh(f*x + e) + (5*(8*a^2 - 13*a*b + 5*b^2)*cosh(f*x + e)^4 + 6*(4*a^2 - 5*a*b + b^2)*cosh(f*x + e)^2 + 8*a^2 - 13*a*b + 5*b^2)*sinh(f*x + e))*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/((a^3 - 3*a^2*b + 3*a*b^2 - b^3)*f*cosh(f*x + e)^8 + 8*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*f*cosh(f*x + e)*sinh(f*x + e)^7 + (a^3 - 3*a^2*b + 3*a*b^2 - b^3)*f*sinh(f*x + e)^8 + 4*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*f*cosh(f*x + e)^6 + 4*(7*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*f*cosh(f*x + e)^2 + (a^3 - 3*a^2*b + 3*a*b^2 - b^3)*f)*sinh(f*x + e)^6 + 6*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*f*cosh(f*x + e)^4 + 8*(7*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*f*cosh(f*x + e)^3 + 3*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*f*cosh(f*x + e))*sinh(f*x + e)^5 + 2*(35*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*f*cosh(f*x + e)^4 + 30*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*f*cosh(f*x + e)^2 + 3*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*f)*sinh(f*x + e)^4 + 4*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*f*cosh(f*x + e)^2 + 8*(7*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*f*cosh(f*x + e)^5 + 10*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*f*cosh(f*x + e)^3 + 3*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*f*cosh(f*x + e))*sinh(f*x + e)^3 + 4*(7*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*f*cosh(f*x + e)^6 + 15*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*f*cosh(f*x + e)^4 + 9*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*f*cosh(f*x + e)^2 + (a^3 - 3*a^2*b + 3*a*b^2 - b^3)*f)*sinh(f*x + e)^2 + (a^3 - 3*a^2*b + 3*a*b^2 - b^3)*f + 8*((a^3 - 3*a^2*b + 3*a*b^2 - b^3)*f*cosh(f*x + e)^7 + 3*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*f*cosh(f*x + e)^5 + 3*(a^3 - 3*a^2*b + 3*a*b^2 - b^3)*f*cosh(f*x + e)^3 + (a^3 - 3*a^2*b + 3*a*b^2 - b^3)*f*cosh(f*x + e))*sinh(f*x + e))]","B",0
480,1,1320,0,0.647526," ","integrate(tanh(f*x+e)^3/(a+b*sinh(f*x+e)^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(2 \, a - b\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left(2 \, a - b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(2 \, a - b\right)} \sinh\left(f x + e\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, {\left(2 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, a - b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left({\left(2 \, a - b\right)} \cosh\left(f x + e\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + 2 \, a - b\right)} \sqrt{a - b} \log\left(\frac{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(4 \, a - 3 \, b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + 4 \, a - 3 \, b\right)} \sinh\left(f x + e\right)^{2} - 4 \, \sqrt{2} \sqrt{a - b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} {\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right)\right)} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(4 \, a - 3 \, b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}{\cosh\left(f x + e\right)^{4} + 4 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + \sinh\left(f x + e\right)^{4} + 2 \, {\left(3 \, \cosh\left(f x + e\right)^{2} + 1\right)} \sinh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right)^{2} + 4 \, {\left(\cosh\left(f x + e\right)^{3} + \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + 1}\right) + 4 \, \sqrt{2} {\left({\left(a - b\right)} \cosh\left(f x + e\right) + {\left(a - b\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{4 \, {\left({\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{4} + 4 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(a^{2} - 2 \, a b + b^{2}\right)} f \sinh\left(f x + e\right)^{4} + 2 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{2} + {\left(a^{2} - 2 \, a b + b^{2}\right)} f\right)} \sinh\left(f x + e\right)^{2} + {\left(a^{2} - 2 \, a b + b^{2}\right)} f + 4 \, {\left({\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{3} + {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)}}, -\frac{{\left({\left(2 \, a - b\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left(2 \, a - b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(2 \, a - b\right)} \sinh\left(f x + e\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, {\left(2 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, a - b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left({\left(2 \, a - b\right)} \cosh\left(f x + e\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + 2 \, a - b\right)} \sqrt{-a + b} \arctan\left(-\frac{\sqrt{2} \sqrt{-a + b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{2 \, {\left({\left(a - b\right)} \cosh\left(f x + e\right) + {\left(a - b\right)} \sinh\left(f x + e\right)\right)}}\right) - 2 \, \sqrt{2} {\left({\left(a - b\right)} \cosh\left(f x + e\right) + {\left(a - b\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{2 \, {\left({\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{4} + 4 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(a^{2} - 2 \, a b + b^{2}\right)} f \sinh\left(f x + e\right)^{4} + 2 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{2} + {\left(a^{2} - 2 \, a b + b^{2}\right)} f\right)} \sinh\left(f x + e\right)^{2} + {\left(a^{2} - 2 \, a b + b^{2}\right)} f + 4 \, {\left({\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)^{3} + {\left(a^{2} - 2 \, a b + b^{2}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)}}\right]"," ",0,"[1/4*(((2*a - b)*cosh(f*x + e)^4 + 4*(2*a - b)*cosh(f*x + e)*sinh(f*x + e)^3 + (2*a - b)*sinh(f*x + e)^4 + 2*(2*a - b)*cosh(f*x + e)^2 + 2*(3*(2*a - b)*cosh(f*x + e)^2 + 2*a - b)*sinh(f*x + e)^2 + 4*((2*a - b)*cosh(f*x + e)^3 + (2*a - b)*cosh(f*x + e))*sinh(f*x + e) + 2*a - b)*sqrt(a - b)*log((b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(4*a - 3*b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 4*a - 3*b)*sinh(f*x + e)^2 - 4*sqrt(2)*sqrt(a - b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))*(cosh(f*x + e) + sinh(f*x + e)) + 4*(b*cosh(f*x + e)^3 + (4*a - 3*b)*cosh(f*x + e))*sinh(f*x + e) + b)/(cosh(f*x + e)^4 + 4*cosh(f*x + e)*sinh(f*x + e)^3 + sinh(f*x + e)^4 + 2*(3*cosh(f*x + e)^2 + 1)*sinh(f*x + e)^2 + 2*cosh(f*x + e)^2 + 4*(cosh(f*x + e)^3 + cosh(f*x + e))*sinh(f*x + e) + 1)) + 4*sqrt(2)*((a - b)*cosh(f*x + e) + (a - b)*sinh(f*x + e))*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/((a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^4 + 4*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)*sinh(f*x + e)^3 + (a^2 - 2*a*b + b^2)*f*sinh(f*x + e)^4 + 2*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^2 + 2*(3*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^2 + (a^2 - 2*a*b + b^2)*f)*sinh(f*x + e)^2 + (a^2 - 2*a*b + b^2)*f + 4*((a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^3 + (a^2 - 2*a*b + b^2)*f*cosh(f*x + e))*sinh(f*x + e)), -1/2*(((2*a - b)*cosh(f*x + e)^4 + 4*(2*a - b)*cosh(f*x + e)*sinh(f*x + e)^3 + (2*a - b)*sinh(f*x + e)^4 + 2*(2*a - b)*cosh(f*x + e)^2 + 2*(3*(2*a - b)*cosh(f*x + e)^2 + 2*a - b)*sinh(f*x + e)^2 + 4*((2*a - b)*cosh(f*x + e)^3 + (2*a - b)*cosh(f*x + e))*sinh(f*x + e) + 2*a - b)*sqrt(-a + b)*arctan(-1/2*sqrt(2)*sqrt(-a + b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/((a - b)*cosh(f*x + e) + (a - b)*sinh(f*x + e))) - 2*sqrt(2)*((a - b)*cosh(f*x + e) + (a - b)*sinh(f*x + e))*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/((a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^4 + 4*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)*sinh(f*x + e)^3 + (a^2 - 2*a*b + b^2)*f*sinh(f*x + e)^4 + 2*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^2 + 2*(3*(a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^2 + (a^2 - 2*a*b + b^2)*f)*sinh(f*x + e)^2 + (a^2 - 2*a*b + b^2)*f + 4*((a^2 - 2*a*b + b^2)*f*cosh(f*x + e)^3 + (a^2 - 2*a*b + b^2)*f*cosh(f*x + e))*sinh(f*x + e))]","B",0
481,1,433,0,0.826749," ","integrate(tanh(f*x+e)/(a+b*sinh(f*x+e)^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{\log\left(\frac{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(4 \, a - 3 \, b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + 4 \, a - 3 \, b\right)} \sinh\left(f x + e\right)^{2} - 4 \, \sqrt{2} \sqrt{a - b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} {\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right)\right)} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(4 \, a - 3 \, b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}{\cosh\left(f x + e\right)^{4} + 4 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + \sinh\left(f x + e\right)^{4} + 2 \, {\left(3 \, \cosh\left(f x + e\right)^{2} + 1\right)} \sinh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right)^{2} + 4 \, {\left(\cosh\left(f x + e\right)^{3} + \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + 1}\right)}{2 \, \sqrt{a - b} f}, -\frac{\sqrt{-a + b} \arctan\left(-\frac{\sqrt{2} \sqrt{-a + b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{2 \, {\left({\left(a - b\right)} \cosh\left(f x + e\right) + {\left(a - b\right)} \sinh\left(f x + e\right)\right)}}\right)}{{\left(a - b\right)} f}\right]"," ",0,"[1/2*log((b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(4*a - 3*b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 4*a - 3*b)*sinh(f*x + e)^2 - 4*sqrt(2)*sqrt(a - b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))*(cosh(f*x + e) + sinh(f*x + e)) + 4*(b*cosh(f*x + e)^3 + (4*a - 3*b)*cosh(f*x + e))*sinh(f*x + e) + b)/(cosh(f*x + e)^4 + 4*cosh(f*x + e)*sinh(f*x + e)^3 + sinh(f*x + e)^4 + 2*(3*cosh(f*x + e)^2 + 1)*sinh(f*x + e)^2 + 2*cosh(f*x + e)^2 + 4*(cosh(f*x + e)^3 + cosh(f*x + e))*sinh(f*x + e) + 1))/(sqrt(a - b)*f), -sqrt(-a + b)*arctan(-1/2*sqrt(2)*sqrt(-a + b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/((a - b)*cosh(f*x + e) + (a - b)*sinh(f*x + e)))/((a - b)*f)]","B",0
482,1,410,0,0.545382," ","integrate(coth(f*x+e)/(a+b*sinh(f*x+e)^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{\log\left(\frac{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(4 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + 4 \, a - b\right)} \sinh\left(f x + e\right)^{2} - 4 \, \sqrt{2} \sqrt{a} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} {\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right)\right)} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(4 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}{\cosh\left(f x + e\right)^{4} + 4 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + \sinh\left(f x + e\right)^{4} + 2 \, {\left(3 \, \cosh\left(f x + e\right)^{2} - 1\right)} \sinh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right)^{2} + 4 \, {\left(\cosh\left(f x + e\right)^{3} - \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + 1}\right)}{2 \, \sqrt{a} f}, \frac{\sqrt{-a} \arctan\left(\frac{\sqrt{2} \sqrt{-a} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{2 \, {\left(a \cosh\left(f x + e\right) + a \sinh\left(f x + e\right)\right)}}\right)}{a f}\right]"," ",0,"[1/2*log((b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(4*a - b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 4*a - b)*sinh(f*x + e)^2 - 4*sqrt(2)*sqrt(a)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))*(cosh(f*x + e) + sinh(f*x + e)) + 4*(b*cosh(f*x + e)^3 + (4*a - b)*cosh(f*x + e))*sinh(f*x + e) + b)/(cosh(f*x + e)^4 + 4*cosh(f*x + e)*sinh(f*x + e)^3 + sinh(f*x + e)^4 + 2*(3*cosh(f*x + e)^2 - 1)*sinh(f*x + e)^2 - 2*cosh(f*x + e)^2 + 4*(cosh(f*x + e)^3 - cosh(f*x + e))*sinh(f*x + e) + 1))/(sqrt(a)*f), sqrt(-a)*arctan(1/2*sqrt(2)*sqrt(-a)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/(a*cosh(f*x + e) + a*sinh(f*x + e)))/(a*f)]","B",0
483,1,1144,0,0.800714," ","integrate(coth(f*x+e)^3/(a+b*sinh(f*x+e)^2)^(1/2),x, algorithm=""fricas"")","\left[-\frac{{\left({\left(2 \, a - b\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left(2 \, a - b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(2 \, a - b\right)} \sinh\left(f x + e\right)^{4} - 2 \, {\left(2 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, {\left(2 \, a - b\right)} \cosh\left(f x + e\right)^{2} - 2 \, a + b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left({\left(2 \, a - b\right)} \cosh\left(f x + e\right)^{3} - {\left(2 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + 2 \, a - b\right)} \sqrt{a} \log\left(\frac{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(4 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + 4 \, a - b\right)} \sinh\left(f x + e\right)^{2} + 4 \, \sqrt{2} \sqrt{a} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} {\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right)\right)} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(4 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}{\cosh\left(f x + e\right)^{4} + 4 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + \sinh\left(f x + e\right)^{4} + 2 \, {\left(3 \, \cosh\left(f x + e\right)^{2} - 1\right)} \sinh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right)^{2} + 4 \, {\left(\cosh\left(f x + e\right)^{3} - \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + 1}\right) + 4 \, \sqrt{2} {\left(a \cosh\left(f x + e\right) + a \sinh\left(f x + e\right)\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{4 \, {\left(a^{2} f \cosh\left(f x + e\right)^{4} + 4 \, a^{2} f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + a^{2} f \sinh\left(f x + e\right)^{4} - 2 \, a^{2} f \cosh\left(f x + e\right)^{2} + a^{2} f + 2 \, {\left(3 \, a^{2} f \cosh\left(f x + e\right)^{2} - a^{2} f\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(a^{2} f \cosh\left(f x + e\right)^{3} - a^{2} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)}}, \frac{{\left({\left(2 \, a - b\right)} \cosh\left(f x + e\right)^{4} + 4 \, {\left(2 \, a - b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(2 \, a - b\right)} \sinh\left(f x + e\right)^{4} - 2 \, {\left(2 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, {\left(2 \, a - b\right)} \cosh\left(f x + e\right)^{2} - 2 \, a + b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left({\left(2 \, a - b\right)} \cosh\left(f x + e\right)^{3} - {\left(2 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + 2 \, a - b\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{2} \sqrt{-a} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{2 \, {\left(a \cosh\left(f x + e\right) + a \sinh\left(f x + e\right)\right)}}\right) - 2 \, \sqrt{2} {\left(a \cosh\left(f x + e\right) + a \sinh\left(f x + e\right)\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{2 \, {\left(a^{2} f \cosh\left(f x + e\right)^{4} + 4 \, a^{2} f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + a^{2} f \sinh\left(f x + e\right)^{4} - 2 \, a^{2} f \cosh\left(f x + e\right)^{2} + a^{2} f + 2 \, {\left(3 \, a^{2} f \cosh\left(f x + e\right)^{2} - a^{2} f\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(a^{2} f \cosh\left(f x + e\right)^{3} - a^{2} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)}}\right]"," ",0,"[-1/4*(((2*a - b)*cosh(f*x + e)^4 + 4*(2*a - b)*cosh(f*x + e)*sinh(f*x + e)^3 + (2*a - b)*sinh(f*x + e)^4 - 2*(2*a - b)*cosh(f*x + e)^2 + 2*(3*(2*a - b)*cosh(f*x + e)^2 - 2*a + b)*sinh(f*x + e)^2 + 4*((2*a - b)*cosh(f*x + e)^3 - (2*a - b)*cosh(f*x + e))*sinh(f*x + e) + 2*a - b)*sqrt(a)*log((b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(4*a - b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 4*a - b)*sinh(f*x + e)^2 + 4*sqrt(2)*sqrt(a)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))*(cosh(f*x + e) + sinh(f*x + e)) + 4*(b*cosh(f*x + e)^3 + (4*a - b)*cosh(f*x + e))*sinh(f*x + e) + b)/(cosh(f*x + e)^4 + 4*cosh(f*x + e)*sinh(f*x + e)^3 + sinh(f*x + e)^4 + 2*(3*cosh(f*x + e)^2 - 1)*sinh(f*x + e)^2 - 2*cosh(f*x + e)^2 + 4*(cosh(f*x + e)^3 - cosh(f*x + e))*sinh(f*x + e) + 1)) + 4*sqrt(2)*(a*cosh(f*x + e) + a*sinh(f*x + e))*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/(a^2*f*cosh(f*x + e)^4 + 4*a^2*f*cosh(f*x + e)*sinh(f*x + e)^3 + a^2*f*sinh(f*x + e)^4 - 2*a^2*f*cosh(f*x + e)^2 + a^2*f + 2*(3*a^2*f*cosh(f*x + e)^2 - a^2*f)*sinh(f*x + e)^2 + 4*(a^2*f*cosh(f*x + e)^3 - a^2*f*cosh(f*x + e))*sinh(f*x + e)), 1/2*(((2*a - b)*cosh(f*x + e)^4 + 4*(2*a - b)*cosh(f*x + e)*sinh(f*x + e)^3 + (2*a - b)*sinh(f*x + e)^4 - 2*(2*a - b)*cosh(f*x + e)^2 + 2*(3*(2*a - b)*cosh(f*x + e)^2 - 2*a + b)*sinh(f*x + e)^2 + 4*((2*a - b)*cosh(f*x + e)^3 - (2*a - b)*cosh(f*x + e))*sinh(f*x + e) + 2*a - b)*sqrt(-a)*arctan(1/2*sqrt(2)*sqrt(-a)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/(a*cosh(f*x + e) + a*sinh(f*x + e))) - 2*sqrt(2)*(a*cosh(f*x + e) + a*sinh(f*x + e))*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/(a^2*f*cosh(f*x + e)^4 + 4*a^2*f*cosh(f*x + e)*sinh(f*x + e)^3 + a^2*f*sinh(f*x + e)^4 - 2*a^2*f*cosh(f*x + e)^2 + a^2*f + 2*(3*a^2*f*cosh(f*x + e)^2 - a^2*f)*sinh(f*x + e)^2 + 4*(a^2*f*cosh(f*x + e)^3 - a^2*f*cosh(f*x + e))*sinh(f*x + e))]","B",0
484,1,3086,0,0.774508," ","integrate(coth(f*x+e)^5/(a+b*sinh(f*x+e)^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{8} + 8 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \sinh\left(f x + e\right)^{8} - 4 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{6} + 4 \, {\left(7 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} - 8 \, a^{2} + 8 \, a b - 3 \, b^{2}\right)} \sinh\left(f x + e\right)^{6} + 8 \, {\left(7 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{3} - 3 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + 6 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{4} + 2 \, {\left(35 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{4} - 30 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + 24 \, a^{2} - 24 \, a b + 9 \, b^{2}\right)} \sinh\left(f x + e\right)^{4} + 8 \, {\left(7 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{5} - 10 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} - 4 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + 4 \, {\left(7 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{6} - 15 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{4} + 9 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} - 8 \, a^{2} + 8 \, a b - 3 \, b^{2}\right)} \sinh\left(f x + e\right)^{2} + 8 \, a^{2} - 8 \, a b + 3 \, b^{2} + 8 \, {\left({\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{7} - 3 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{5} + 3 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{3} - {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{a} \log\left(\frac{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(4 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + 4 \, a - b\right)} \sinh\left(f x + e\right)^{2} - 4 \, \sqrt{2} \sqrt{a} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} {\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right)\right)} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(4 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}{\cosh\left(f x + e\right)^{4} + 4 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + \sinh\left(f x + e\right)^{4} + 2 \, {\left(3 \, \cosh\left(f x + e\right)^{2} - 1\right)} \sinh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right)^{2} + 4 \, {\left(\cosh\left(f x + e\right)^{3} - \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + 1}\right) - 4 \, \sqrt{2} {\left({\left(8 \, a^{2} - 3 \, a b\right)} \cosh\left(f x + e\right)^{5} + 5 \, {\left(8 \, a^{2} - 3 \, a b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{4} + {\left(8 \, a^{2} - 3 \, a b\right)} \sinh\left(f x + e\right)^{5} - 2 \, {\left(4 \, a^{2} - 3 \, a b\right)} \cosh\left(f x + e\right)^{3} + 2 \, {\left(5 \, {\left(8 \, a^{2} - 3 \, a b\right)} \cosh\left(f x + e\right)^{2} - 4 \, a^{2} + 3 \, a b\right)} \sinh\left(f x + e\right)^{3} + 2 \, {\left(5 \, {\left(8 \, a^{2} - 3 \, a b\right)} \cosh\left(f x + e\right)^{3} - 3 \, {\left(4 \, a^{2} - 3 \, a b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{2} + {\left(8 \, a^{2} - 3 \, a b\right)} \cosh\left(f x + e\right) + {\left(5 \, {\left(8 \, a^{2} - 3 \, a b\right)} \cosh\left(f x + e\right)^{4} - 6 \, {\left(4 \, a^{2} - 3 \, a b\right)} \cosh\left(f x + e\right)^{2} + 8 \, a^{2} - 3 \, a b\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{16 \, {\left(a^{3} f \cosh\left(f x + e\right)^{8} + 8 \, a^{3} f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + a^{3} f \sinh\left(f x + e\right)^{8} - 4 \, a^{3} f \cosh\left(f x + e\right)^{6} + 6 \, a^{3} f \cosh\left(f x + e\right)^{4} + 4 \, {\left(7 \, a^{3} f \cosh\left(f x + e\right)^{2} - a^{3} f\right)} \sinh\left(f x + e\right)^{6} - 4 \, a^{3} f \cosh\left(f x + e\right)^{2} + 8 \, {\left(7 \, a^{3} f \cosh\left(f x + e\right)^{3} - 3 \, a^{3} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(35 \, a^{3} f \cosh\left(f x + e\right)^{4} - 30 \, a^{3} f \cosh\left(f x + e\right)^{2} + 3 \, a^{3} f\right)} \sinh\left(f x + e\right)^{4} + a^{3} f + 8 \, {\left(7 \, a^{3} f \cosh\left(f x + e\right)^{5} - 10 \, a^{3} f \cosh\left(f x + e\right)^{3} + 3 \, a^{3} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 4 \, {\left(7 \, a^{3} f \cosh\left(f x + e\right)^{6} - 15 \, a^{3} f \cosh\left(f x + e\right)^{4} + 9 \, a^{3} f \cosh\left(f x + e\right)^{2} - a^{3} f\right)} \sinh\left(f x + e\right)^{2} + 8 \, {\left(a^{3} f \cosh\left(f x + e\right)^{7} - 3 \, a^{3} f \cosh\left(f x + e\right)^{5} + 3 \, a^{3} f \cosh\left(f x + e\right)^{3} - a^{3} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)}}, \frac{{\left({\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{8} + 8 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \sinh\left(f x + e\right)^{8} - 4 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{6} + 4 \, {\left(7 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} - 8 \, a^{2} + 8 \, a b - 3 \, b^{2}\right)} \sinh\left(f x + e\right)^{6} + 8 \, {\left(7 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{3} - 3 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + 6 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{4} + 2 \, {\left(35 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{4} - 30 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + 24 \, a^{2} - 24 \, a b + 9 \, b^{2}\right)} \sinh\left(f x + e\right)^{4} + 8 \, {\left(7 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{5} - 10 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} - 4 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + 4 \, {\left(7 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{6} - 15 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{4} + 9 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} - 8 \, a^{2} + 8 \, a b - 3 \, b^{2}\right)} \sinh\left(f x + e\right)^{2} + 8 \, a^{2} - 8 \, a b + 3 \, b^{2} + 8 \, {\left({\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{7} - 3 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{5} + 3 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{3} - {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{2} \sqrt{-a} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{2 \, {\left(a \cosh\left(f x + e\right) + a \sinh\left(f x + e\right)\right)}}\right) - 2 \, \sqrt{2} {\left({\left(8 \, a^{2} - 3 \, a b\right)} \cosh\left(f x + e\right)^{5} + 5 \, {\left(8 \, a^{2} - 3 \, a b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{4} + {\left(8 \, a^{2} - 3 \, a b\right)} \sinh\left(f x + e\right)^{5} - 2 \, {\left(4 \, a^{2} - 3 \, a b\right)} \cosh\left(f x + e\right)^{3} + 2 \, {\left(5 \, {\left(8 \, a^{2} - 3 \, a b\right)} \cosh\left(f x + e\right)^{2} - 4 \, a^{2} + 3 \, a b\right)} \sinh\left(f x + e\right)^{3} + 2 \, {\left(5 \, {\left(8 \, a^{2} - 3 \, a b\right)} \cosh\left(f x + e\right)^{3} - 3 \, {\left(4 \, a^{2} - 3 \, a b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{2} + {\left(8 \, a^{2} - 3 \, a b\right)} \cosh\left(f x + e\right) + {\left(5 \, {\left(8 \, a^{2} - 3 \, a b\right)} \cosh\left(f x + e\right)^{4} - 6 \, {\left(4 \, a^{2} - 3 \, a b\right)} \cosh\left(f x + e\right)^{2} + 8 \, a^{2} - 3 \, a b\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{8 \, {\left(a^{3} f \cosh\left(f x + e\right)^{8} + 8 \, a^{3} f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + a^{3} f \sinh\left(f x + e\right)^{8} - 4 \, a^{3} f \cosh\left(f x + e\right)^{6} + 6 \, a^{3} f \cosh\left(f x + e\right)^{4} + 4 \, {\left(7 \, a^{3} f \cosh\left(f x + e\right)^{2} - a^{3} f\right)} \sinh\left(f x + e\right)^{6} - 4 \, a^{3} f \cosh\left(f x + e\right)^{2} + 8 \, {\left(7 \, a^{3} f \cosh\left(f x + e\right)^{3} - 3 \, a^{3} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(35 \, a^{3} f \cosh\left(f x + e\right)^{4} - 30 \, a^{3} f \cosh\left(f x + e\right)^{2} + 3 \, a^{3} f\right)} \sinh\left(f x + e\right)^{4} + a^{3} f + 8 \, {\left(7 \, a^{3} f \cosh\left(f x + e\right)^{5} - 10 \, a^{3} f \cosh\left(f x + e\right)^{3} + 3 \, a^{3} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 4 \, {\left(7 \, a^{3} f \cosh\left(f x + e\right)^{6} - 15 \, a^{3} f \cosh\left(f x + e\right)^{4} + 9 \, a^{3} f \cosh\left(f x + e\right)^{2} - a^{3} f\right)} \sinh\left(f x + e\right)^{2} + 8 \, {\left(a^{3} f \cosh\left(f x + e\right)^{7} - 3 \, a^{3} f \cosh\left(f x + e\right)^{5} + 3 \, a^{3} f \cosh\left(f x + e\right)^{3} - a^{3} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)}}\right]"," ",0,"[1/16*(((8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e)^8 + 8*(8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e)*sinh(f*x + e)^7 + (8*a^2 - 8*a*b + 3*b^2)*sinh(f*x + e)^8 - 4*(8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e)^6 + 4*(7*(8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e)^2 - 8*a^2 + 8*a*b - 3*b^2)*sinh(f*x + e)^6 + 8*(7*(8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e)^3 - 3*(8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e))*sinh(f*x + e)^5 + 6*(8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e)^4 + 2*(35*(8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e)^4 - 30*(8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e)^2 + 24*a^2 - 24*a*b + 9*b^2)*sinh(f*x + e)^4 + 8*(7*(8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e)^5 - 10*(8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e)^3 + 3*(8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e))*sinh(f*x + e)^3 - 4*(8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e)^2 + 4*(7*(8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e)^6 - 15*(8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e)^4 + 9*(8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e)^2 - 8*a^2 + 8*a*b - 3*b^2)*sinh(f*x + e)^2 + 8*a^2 - 8*a*b + 3*b^2 + 8*((8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e)^7 - 3*(8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e)^5 + 3*(8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e)^3 - (8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e))*sinh(f*x + e))*sqrt(a)*log((b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(4*a - b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 4*a - b)*sinh(f*x + e)^2 - 4*sqrt(2)*sqrt(a)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))*(cosh(f*x + e) + sinh(f*x + e)) + 4*(b*cosh(f*x + e)^3 + (4*a - b)*cosh(f*x + e))*sinh(f*x + e) + b)/(cosh(f*x + e)^4 + 4*cosh(f*x + e)*sinh(f*x + e)^3 + sinh(f*x + e)^4 + 2*(3*cosh(f*x + e)^2 - 1)*sinh(f*x + e)^2 - 2*cosh(f*x + e)^2 + 4*(cosh(f*x + e)^3 - cosh(f*x + e))*sinh(f*x + e) + 1)) - 4*sqrt(2)*((8*a^2 - 3*a*b)*cosh(f*x + e)^5 + 5*(8*a^2 - 3*a*b)*cosh(f*x + e)*sinh(f*x + e)^4 + (8*a^2 - 3*a*b)*sinh(f*x + e)^5 - 2*(4*a^2 - 3*a*b)*cosh(f*x + e)^3 + 2*(5*(8*a^2 - 3*a*b)*cosh(f*x + e)^2 - 4*a^2 + 3*a*b)*sinh(f*x + e)^3 + 2*(5*(8*a^2 - 3*a*b)*cosh(f*x + e)^3 - 3*(4*a^2 - 3*a*b)*cosh(f*x + e))*sinh(f*x + e)^2 + (8*a^2 - 3*a*b)*cosh(f*x + e) + (5*(8*a^2 - 3*a*b)*cosh(f*x + e)^4 - 6*(4*a^2 - 3*a*b)*cosh(f*x + e)^2 + 8*a^2 - 3*a*b)*sinh(f*x + e))*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/(a^3*f*cosh(f*x + e)^8 + 8*a^3*f*cosh(f*x + e)*sinh(f*x + e)^7 + a^3*f*sinh(f*x + e)^8 - 4*a^3*f*cosh(f*x + e)^6 + 6*a^3*f*cosh(f*x + e)^4 + 4*(7*a^3*f*cosh(f*x + e)^2 - a^3*f)*sinh(f*x + e)^6 - 4*a^3*f*cosh(f*x + e)^2 + 8*(7*a^3*f*cosh(f*x + e)^3 - 3*a^3*f*cosh(f*x + e))*sinh(f*x + e)^5 + 2*(35*a^3*f*cosh(f*x + e)^4 - 30*a^3*f*cosh(f*x + e)^2 + 3*a^3*f)*sinh(f*x + e)^4 + a^3*f + 8*(7*a^3*f*cosh(f*x + e)^5 - 10*a^3*f*cosh(f*x + e)^3 + 3*a^3*f*cosh(f*x + e))*sinh(f*x + e)^3 + 4*(7*a^3*f*cosh(f*x + e)^6 - 15*a^3*f*cosh(f*x + e)^4 + 9*a^3*f*cosh(f*x + e)^2 - a^3*f)*sinh(f*x + e)^2 + 8*(a^3*f*cosh(f*x + e)^7 - 3*a^3*f*cosh(f*x + e)^5 + 3*a^3*f*cosh(f*x + e)^3 - a^3*f*cosh(f*x + e))*sinh(f*x + e)), 1/8*(((8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e)^8 + 8*(8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e)*sinh(f*x + e)^7 + (8*a^2 - 8*a*b + 3*b^2)*sinh(f*x + e)^8 - 4*(8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e)^6 + 4*(7*(8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e)^2 - 8*a^2 + 8*a*b - 3*b^2)*sinh(f*x + e)^6 + 8*(7*(8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e)^3 - 3*(8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e))*sinh(f*x + e)^5 + 6*(8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e)^4 + 2*(35*(8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e)^4 - 30*(8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e)^2 + 24*a^2 - 24*a*b + 9*b^2)*sinh(f*x + e)^4 + 8*(7*(8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e)^5 - 10*(8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e)^3 + 3*(8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e))*sinh(f*x + e)^3 - 4*(8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e)^2 + 4*(7*(8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e)^6 - 15*(8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e)^4 + 9*(8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e)^2 - 8*a^2 + 8*a*b - 3*b^2)*sinh(f*x + e)^2 + 8*a^2 - 8*a*b + 3*b^2 + 8*((8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e)^7 - 3*(8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e)^5 + 3*(8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e)^3 - (8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e))*sinh(f*x + e))*sqrt(-a)*arctan(1/2*sqrt(2)*sqrt(-a)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/(a*cosh(f*x + e) + a*sinh(f*x + e))) - 2*sqrt(2)*((8*a^2 - 3*a*b)*cosh(f*x + e)^5 + 5*(8*a^2 - 3*a*b)*cosh(f*x + e)*sinh(f*x + e)^4 + (8*a^2 - 3*a*b)*sinh(f*x + e)^5 - 2*(4*a^2 - 3*a*b)*cosh(f*x + e)^3 + 2*(5*(8*a^2 - 3*a*b)*cosh(f*x + e)^2 - 4*a^2 + 3*a*b)*sinh(f*x + e)^3 + 2*(5*(8*a^2 - 3*a*b)*cosh(f*x + e)^3 - 3*(4*a^2 - 3*a*b)*cosh(f*x + e))*sinh(f*x + e)^2 + (8*a^2 - 3*a*b)*cosh(f*x + e) + (5*(8*a^2 - 3*a*b)*cosh(f*x + e)^4 - 6*(4*a^2 - 3*a*b)*cosh(f*x + e)^2 + 8*a^2 - 3*a*b)*sinh(f*x + e))*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/(a^3*f*cosh(f*x + e)^8 + 8*a^3*f*cosh(f*x + e)*sinh(f*x + e)^7 + a^3*f*sinh(f*x + e)^8 - 4*a^3*f*cosh(f*x + e)^6 + 6*a^3*f*cosh(f*x + e)^4 + 4*(7*a^3*f*cosh(f*x + e)^2 - a^3*f)*sinh(f*x + e)^6 - 4*a^3*f*cosh(f*x + e)^2 + 8*(7*a^3*f*cosh(f*x + e)^3 - 3*a^3*f*cosh(f*x + e))*sinh(f*x + e)^5 + 2*(35*a^3*f*cosh(f*x + e)^4 - 30*a^3*f*cosh(f*x + e)^2 + 3*a^3*f)*sinh(f*x + e)^4 + a^3*f + 8*(7*a^3*f*cosh(f*x + e)^5 - 10*a^3*f*cosh(f*x + e)^3 + 3*a^3*f*cosh(f*x + e))*sinh(f*x + e)^3 + 4*(7*a^3*f*cosh(f*x + e)^6 - 15*a^3*f*cosh(f*x + e)^4 + 9*a^3*f*cosh(f*x + e)^2 - a^3*f)*sinh(f*x + e)^2 + 8*(a^3*f*cosh(f*x + e)^7 - 3*a^3*f*cosh(f*x + e)^5 + 3*a^3*f*cosh(f*x + e)^3 - a^3*f*cosh(f*x + e))*sinh(f*x + e))]","B",0
485,0,0,0,0.541643," ","integrate(tanh(f*x+e)^4/(a+b*sinh(f*x+e)^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\tanh\left(f x + e\right)^{4}}{\sqrt{b \sinh\left(f x + e\right)^{2} + a}}, x\right)"," ",0,"integral(tanh(f*x + e)^4/sqrt(b*sinh(f*x + e)^2 + a), x)","F",0
486,0,0,0,0.467155," ","integrate(tanh(f*x+e)^2/(a+b*sinh(f*x+e)^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\tanh\left(f x + e\right)^{2}}{\sqrt{b \sinh\left(f x + e\right)^{2} + a}}, x\right)"," ",0,"integral(tanh(f*x + e)^2/sqrt(b*sinh(f*x + e)^2 + a), x)","F",0
487,0,0,0,0.744545," ","integrate(1/(a+b*sinh(f*x+e)^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{1}{\sqrt{b \sinh\left(f x + e\right)^{2} + a}}, x\right)"," ",0,"integral(1/sqrt(b*sinh(f*x + e)^2 + a), x)","F",0
488,0,0,0,0.494452," ","integrate(coth(f*x+e)^2/(a+b*sinh(f*x+e)^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\coth\left(f x + e\right)^{2}}{\sqrt{b \sinh\left(f x + e\right)^{2} + a}}, x\right)"," ",0,"integral(coth(f*x + e)^2/sqrt(b*sinh(f*x + e)^2 + a), x)","F",0
489,0,0,0,0.509592," ","integrate(coth(f*x+e)^4/(a+b*sinh(f*x+e)^2)^(1/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\coth\left(f x + e\right)^{4}}{\sqrt{b \sinh\left(f x + e\right)^{2} + a}}, x\right)"," ",0,"integral(coth(f*x + e)^4/sqrt(b*sinh(f*x + e)^2 + a), x)","F",0
490,1,10168,0,1.146971," ","integrate(tanh(f*x+e)^5/(a+b*sinh(f*x+e)^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(8 \, a^{2} b + 8 \, a b^{2} - b^{3}\right)} \cosh\left(f x + e\right)^{12} + 12 \, {\left(8 \, a^{2} b + 8 \, a b^{2} - b^{3}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{11} + {\left(8 \, a^{2} b + 8 \, a b^{2} - b^{3}\right)} \sinh\left(f x + e\right)^{12} + 2 \, {\left(16 \, a^{3} + 24 \, a^{2} b + 6 \, a b^{2} - b^{3}\right)} \cosh\left(f x + e\right)^{10} + 2 \, {\left(16 \, a^{3} + 24 \, a^{2} b + 6 \, a b^{2} - b^{3} + 33 \, {\left(8 \, a^{2} b + 8 \, a b^{2} - b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{10} + 20 \, {\left(11 \, {\left(8 \, a^{2} b + 8 \, a b^{2} - b^{3}\right)} \cosh\left(f x + e\right)^{3} + {\left(16 \, a^{3} + 24 \, a^{2} b + 6 \, a b^{2} - b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{9} + {\left(128 \, a^{3} + 120 \, a^{2} b - 24 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{8} + {\left(495 \, {\left(8 \, a^{2} b + 8 \, a b^{2} - b^{3}\right)} \cosh\left(f x + e\right)^{4} + 128 \, a^{3} + 120 \, a^{2} b - 24 \, a b^{2} + b^{3} + 90 \, {\left(16 \, a^{3} + 24 \, a^{2} b + 6 \, a b^{2} - b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{8} + 8 \, {\left(99 \, {\left(8 \, a^{2} b + 8 \, a b^{2} - b^{3}\right)} \cosh\left(f x + e\right)^{5} + 30 \, {\left(16 \, a^{3} + 24 \, a^{2} b + 6 \, a b^{2} - b^{3}\right)} \cosh\left(f x + e\right)^{3} + {\left(128 \, a^{3} + 120 \, a^{2} b - 24 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{7} + 4 \, {\left(48 \, a^{3} + 40 \, a^{2} b - 14 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{6} + 4 \, {\left(231 \, {\left(8 \, a^{2} b + 8 \, a b^{2} - b^{3}\right)} \cosh\left(f x + e\right)^{6} + 105 \, {\left(16 \, a^{3} + 24 \, a^{2} b + 6 \, a b^{2} - b^{3}\right)} \cosh\left(f x + e\right)^{4} + 48 \, a^{3} + 40 \, a^{2} b - 14 \, a b^{2} + b^{3} + 7 \, {\left(128 \, a^{3} + 120 \, a^{2} b - 24 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{6} + 8 \, {\left(99 \, {\left(8 \, a^{2} b + 8 \, a b^{2} - b^{3}\right)} \cosh\left(f x + e\right)^{7} + 63 \, {\left(16 \, a^{3} + 24 \, a^{2} b + 6 \, a b^{2} - b^{3}\right)} \cosh\left(f x + e\right)^{5} + 7 \, {\left(128 \, a^{3} + 120 \, a^{2} b - 24 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(48 \, a^{3} + 40 \, a^{2} b - 14 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + {\left(128 \, a^{3} + 120 \, a^{2} b - 24 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{4} + {\left(495 \, {\left(8 \, a^{2} b + 8 \, a b^{2} - b^{3}\right)} \cosh\left(f x + e\right)^{8} + 420 \, {\left(16 \, a^{3} + 24 \, a^{2} b + 6 \, a b^{2} - b^{3}\right)} \cosh\left(f x + e\right)^{6} + 70 \, {\left(128 \, a^{3} + 120 \, a^{2} b - 24 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{4} + 128 \, a^{3} + 120 \, a^{2} b - 24 \, a b^{2} + b^{3} + 60 \, {\left(48 \, a^{3} + 40 \, a^{2} b - 14 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(55 \, {\left(8 \, a^{2} b + 8 \, a b^{2} - b^{3}\right)} \cosh\left(f x + e\right)^{9} + 60 \, {\left(16 \, a^{3} + 24 \, a^{2} b + 6 \, a b^{2} - b^{3}\right)} \cosh\left(f x + e\right)^{7} + 14 \, {\left(128 \, a^{3} + 120 \, a^{2} b - 24 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{5} + 20 \, {\left(48 \, a^{3} + 40 \, a^{2} b - 14 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{3} + {\left(128 \, a^{3} + 120 \, a^{2} b - 24 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 8 \, a^{2} b + 8 \, a b^{2} - b^{3} + 2 \, {\left(16 \, a^{3} + 24 \, a^{2} b + 6 \, a b^{2} - b^{3}\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(33 \, {\left(8 \, a^{2} b + 8 \, a b^{2} - b^{3}\right)} \cosh\left(f x + e\right)^{10} + 45 \, {\left(16 \, a^{3} + 24 \, a^{2} b + 6 \, a b^{2} - b^{3}\right)} \cosh\left(f x + e\right)^{8} + 14 \, {\left(128 \, a^{3} + 120 \, a^{2} b - 24 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{6} + 30 \, {\left(48 \, a^{3} + 40 \, a^{2} b - 14 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{4} + 16 \, a^{3} + 24 \, a^{2} b + 6 \, a b^{2} - b^{3} + 3 \, {\left(128 \, a^{3} + 120 \, a^{2} b - 24 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(3 \, {\left(8 \, a^{2} b + 8 \, a b^{2} - b^{3}\right)} \cosh\left(f x + e\right)^{11} + 5 \, {\left(16 \, a^{3} + 24 \, a^{2} b + 6 \, a b^{2} - b^{3}\right)} \cosh\left(f x + e\right)^{9} + 2 \, {\left(128 \, a^{3} + 120 \, a^{2} b - 24 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{7} + 6 \, {\left(48 \, a^{3} + 40 \, a^{2} b - 14 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{5} + {\left(128 \, a^{3} + 120 \, a^{2} b - 24 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{3} + {\left(16 \, a^{3} + 24 \, a^{2} b + 6 \, a b^{2} - b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{a - b} \log\left(\frac{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(4 \, a - 3 \, b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + 4 \, a - 3 \, b\right)} \sinh\left(f x + e\right)^{2} - 4 \, \sqrt{2} \sqrt{a - b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} {\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right)\right)} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(4 \, a - 3 \, b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}{\cosh\left(f x + e\right)^{4} + 4 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + \sinh\left(f x + e\right)^{4} + 2 \, {\left(3 \, \cosh\left(f x + e\right)^{2} + 1\right)} \sinh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right)^{2} + 4 \, {\left(\cosh\left(f x + e\right)^{3} + \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + 1}\right) + 4 \, \sqrt{2} {\left({\left(8 \, a^{3} - 9 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{9} + 9 \, {\left(8 \, a^{3} - 9 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{8} + {\left(8 \, a^{3} - 9 \, a b^{2} + b^{3}\right)} \sinh\left(f x + e\right)^{9} + 4 \, {\left(16 \, a^{3} - 19 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{7} + 4 \, {\left(16 \, a^{3} - 19 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3} + 9 \, {\left(8 \, a^{3} - 9 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{7} + 28 \, {\left(3 \, {\left(8 \, a^{3} - 9 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{3} + {\left(16 \, a^{3} - 19 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{6} + 2 \, {\left(40 \, a^{3} - 28 \, a^{2} b - 19 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(f x + e\right)^{5} + 2 \, {\left(63 \, {\left(8 \, a^{3} - 9 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{4} + 40 \, a^{3} - 28 \, a^{2} b - 19 \, a b^{2} + 7 \, b^{3} + 42 \, {\left(16 \, a^{3} - 19 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(63 \, {\left(8 \, a^{3} - 9 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{5} + 70 \, {\left(16 \, a^{3} - 19 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} + 5 \, {\left(40 \, a^{3} - 28 \, a^{2} b - 19 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(16 \, a^{3} - 19 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} + 4 \, {\left(21 \, {\left(8 \, a^{3} - 9 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{6} + 35 \, {\left(16 \, a^{3} - 19 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} + 16 \, a^{3} - 19 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3} + 5 \, {\left(40 \, a^{3} - 28 \, a^{2} b - 19 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{3} + 4 \, {\left(9 \, {\left(8 \, a^{3} - 9 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{7} + 21 \, {\left(16 \, a^{3} - 19 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{5} + 5 \, {\left(40 \, a^{3} - 28 \, a^{2} b - 19 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(16 \, a^{3} - 19 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{2} + {\left(8 \, a^{3} - 9 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right) + {\left(9 \, {\left(8 \, a^{3} - 9 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{8} + 28 \, {\left(16 \, a^{3} - 19 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{6} + 10 \, {\left(40 \, a^{3} - 28 \, a^{2} b - 19 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} + 8 \, a^{3} - 9 \, a b^{2} + b^{3} + 12 \, {\left(16 \, a^{3} - 19 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{16 \, {\left({\left(a^{4} b - 4 \, a^{3} b^{2} + 6 \, a^{2} b^{3} - 4 \, a b^{4} + b^{5}\right)} f \cosh\left(f x + e\right)^{12} + 12 \, {\left(a^{4} b - 4 \, a^{3} b^{2} + 6 \, a^{2} b^{3} - 4 \, a b^{4} + b^{5}\right)} f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{11} + {\left(a^{4} b - 4 \, a^{3} b^{2} + 6 \, a^{2} b^{3} - 4 \, a b^{4} + b^{5}\right)} f \sinh\left(f x + e\right)^{12} + 2 \, {\left(2 \, a^{5} - 7 \, a^{4} b + 8 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 2 \, a b^{4} + b^{5}\right)} f \cosh\left(f x + e\right)^{10} + 2 \, {\left(33 \, {\left(a^{4} b - 4 \, a^{3} b^{2} + 6 \, a^{2} b^{3} - 4 \, a b^{4} + b^{5}\right)} f \cosh\left(f x + e\right)^{2} + {\left(2 \, a^{5} - 7 \, a^{4} b + 8 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 2 \, a b^{4} + b^{5}\right)} f\right)} \sinh\left(f x + e\right)^{10} + {\left(16 \, a^{5} - 65 \, a^{4} b + 100 \, a^{3} b^{2} - 70 \, a^{2} b^{3} + 20 \, a b^{4} - b^{5}\right)} f \cosh\left(f x + e\right)^{8} + 20 \, {\left(11 \, {\left(a^{4} b - 4 \, a^{3} b^{2} + 6 \, a^{2} b^{3} - 4 \, a b^{4} + b^{5}\right)} f \cosh\left(f x + e\right)^{3} + {\left(2 \, a^{5} - 7 \, a^{4} b + 8 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 2 \, a b^{4} + b^{5}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{9} + {\left(495 \, {\left(a^{4} b - 4 \, a^{3} b^{2} + 6 \, a^{2} b^{3} - 4 \, a b^{4} + b^{5}\right)} f \cosh\left(f x + e\right)^{4} + 90 \, {\left(2 \, a^{5} - 7 \, a^{4} b + 8 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 2 \, a b^{4} + b^{5}\right)} f \cosh\left(f x + e\right)^{2} + {\left(16 \, a^{5} - 65 \, a^{4} b + 100 \, a^{3} b^{2} - 70 \, a^{2} b^{3} + 20 \, a b^{4} - b^{5}\right)} f\right)} \sinh\left(f x + e\right)^{8} + 4 \, {\left(6 \, a^{5} - 25 \, a^{4} b + 40 \, a^{3} b^{2} - 30 \, a^{2} b^{3} + 10 \, a b^{4} - b^{5}\right)} f \cosh\left(f x + e\right)^{6} + 8 \, {\left(99 \, {\left(a^{4} b - 4 \, a^{3} b^{2} + 6 \, a^{2} b^{3} - 4 \, a b^{4} + b^{5}\right)} f \cosh\left(f x + e\right)^{5} + 30 \, {\left(2 \, a^{5} - 7 \, a^{4} b + 8 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 2 \, a b^{4} + b^{5}\right)} f \cosh\left(f x + e\right)^{3} + {\left(16 \, a^{5} - 65 \, a^{4} b + 100 \, a^{3} b^{2} - 70 \, a^{2} b^{3} + 20 \, a b^{4} - b^{5}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{7} + 4 \, {\left(231 \, {\left(a^{4} b - 4 \, a^{3} b^{2} + 6 \, a^{2} b^{3} - 4 \, a b^{4} + b^{5}\right)} f \cosh\left(f x + e\right)^{6} + 105 \, {\left(2 \, a^{5} - 7 \, a^{4} b + 8 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 2 \, a b^{4} + b^{5}\right)} f \cosh\left(f x + e\right)^{4} + 7 \, {\left(16 \, a^{5} - 65 \, a^{4} b + 100 \, a^{3} b^{2} - 70 \, a^{2} b^{3} + 20 \, a b^{4} - b^{5}\right)} f \cosh\left(f x + e\right)^{2} + {\left(6 \, a^{5} - 25 \, a^{4} b + 40 \, a^{3} b^{2} - 30 \, a^{2} b^{3} + 10 \, a b^{4} - b^{5}\right)} f\right)} \sinh\left(f x + e\right)^{6} + {\left(16 \, a^{5} - 65 \, a^{4} b + 100 \, a^{3} b^{2} - 70 \, a^{2} b^{3} + 20 \, a b^{4} - b^{5}\right)} f \cosh\left(f x + e\right)^{4} + 8 \, {\left(99 \, {\left(a^{4} b - 4 \, a^{3} b^{2} + 6 \, a^{2} b^{3} - 4 \, a b^{4} + b^{5}\right)} f \cosh\left(f x + e\right)^{7} + 63 \, {\left(2 \, a^{5} - 7 \, a^{4} b + 8 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 2 \, a b^{4} + b^{5}\right)} f \cosh\left(f x + e\right)^{5} + 7 \, {\left(16 \, a^{5} - 65 \, a^{4} b + 100 \, a^{3} b^{2} - 70 \, a^{2} b^{3} + 20 \, a b^{4} - b^{5}\right)} f \cosh\left(f x + e\right)^{3} + 3 \, {\left(6 \, a^{5} - 25 \, a^{4} b + 40 \, a^{3} b^{2} - 30 \, a^{2} b^{3} + 10 \, a b^{4} - b^{5}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + {\left(495 \, {\left(a^{4} b - 4 \, a^{3} b^{2} + 6 \, a^{2} b^{3} - 4 \, a b^{4} + b^{5}\right)} f \cosh\left(f x + e\right)^{8} + 420 \, {\left(2 \, a^{5} - 7 \, a^{4} b + 8 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 2 \, a b^{4} + b^{5}\right)} f \cosh\left(f x + e\right)^{6} + 70 \, {\left(16 \, a^{5} - 65 \, a^{4} b + 100 \, a^{3} b^{2} - 70 \, a^{2} b^{3} + 20 \, a b^{4} - b^{5}\right)} f \cosh\left(f x + e\right)^{4} + 60 \, {\left(6 \, a^{5} - 25 \, a^{4} b + 40 \, a^{3} b^{2} - 30 \, a^{2} b^{3} + 10 \, a b^{4} - b^{5}\right)} f \cosh\left(f x + e\right)^{2} + {\left(16 \, a^{5} - 65 \, a^{4} b + 100 \, a^{3} b^{2} - 70 \, a^{2} b^{3} + 20 \, a b^{4} - b^{5}\right)} f\right)} \sinh\left(f x + e\right)^{4} + 2 \, {\left(2 \, a^{5} - 7 \, a^{4} b + 8 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 2 \, a b^{4} + b^{5}\right)} f \cosh\left(f x + e\right)^{2} + 4 \, {\left(55 \, {\left(a^{4} b - 4 \, a^{3} b^{2} + 6 \, a^{2} b^{3} - 4 \, a b^{4} + b^{5}\right)} f \cosh\left(f x + e\right)^{9} + 60 \, {\left(2 \, a^{5} - 7 \, a^{4} b + 8 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 2 \, a b^{4} + b^{5}\right)} f \cosh\left(f x + e\right)^{7} + 14 \, {\left(16 \, a^{5} - 65 \, a^{4} b + 100 \, a^{3} b^{2} - 70 \, a^{2} b^{3} + 20 \, a b^{4} - b^{5}\right)} f \cosh\left(f x + e\right)^{5} + 20 \, {\left(6 \, a^{5} - 25 \, a^{4} b + 40 \, a^{3} b^{2} - 30 \, a^{2} b^{3} + 10 \, a b^{4} - b^{5}\right)} f \cosh\left(f x + e\right)^{3} + {\left(16 \, a^{5} - 65 \, a^{4} b + 100 \, a^{3} b^{2} - 70 \, a^{2} b^{3} + 20 \, a b^{4} - b^{5}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 2 \, {\left(33 \, {\left(a^{4} b - 4 \, a^{3} b^{2} + 6 \, a^{2} b^{3} - 4 \, a b^{4} + b^{5}\right)} f \cosh\left(f x + e\right)^{10} + 45 \, {\left(2 \, a^{5} - 7 \, a^{4} b + 8 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 2 \, a b^{4} + b^{5}\right)} f \cosh\left(f x + e\right)^{8} + 14 \, {\left(16 \, a^{5} - 65 \, a^{4} b + 100 \, a^{3} b^{2} - 70 \, a^{2} b^{3} + 20 \, a b^{4} - b^{5}\right)} f \cosh\left(f x + e\right)^{6} + 30 \, {\left(6 \, a^{5} - 25 \, a^{4} b + 40 \, a^{3} b^{2} - 30 \, a^{2} b^{3} + 10 \, a b^{4} - b^{5}\right)} f \cosh\left(f x + e\right)^{4} + 3 \, {\left(16 \, a^{5} - 65 \, a^{4} b + 100 \, a^{3} b^{2} - 70 \, a^{2} b^{3} + 20 \, a b^{4} - b^{5}\right)} f \cosh\left(f x + e\right)^{2} + {\left(2 \, a^{5} - 7 \, a^{4} b + 8 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 2 \, a b^{4} + b^{5}\right)} f\right)} \sinh\left(f x + e\right)^{2} + {\left(a^{4} b - 4 \, a^{3} b^{2} + 6 \, a^{2} b^{3} - 4 \, a b^{4} + b^{5}\right)} f + 4 \, {\left(3 \, {\left(a^{4} b - 4 \, a^{3} b^{2} + 6 \, a^{2} b^{3} - 4 \, a b^{4} + b^{5}\right)} f \cosh\left(f x + e\right)^{11} + 5 \, {\left(2 \, a^{5} - 7 \, a^{4} b + 8 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 2 \, a b^{4} + b^{5}\right)} f \cosh\left(f x + e\right)^{9} + 2 \, {\left(16 \, a^{5} - 65 \, a^{4} b + 100 \, a^{3} b^{2} - 70 \, a^{2} b^{3} + 20 \, a b^{4} - b^{5}\right)} f \cosh\left(f x + e\right)^{7} + 6 \, {\left(6 \, a^{5} - 25 \, a^{4} b + 40 \, a^{3} b^{2} - 30 \, a^{2} b^{3} + 10 \, a b^{4} - b^{5}\right)} f \cosh\left(f x + e\right)^{5} + {\left(16 \, a^{5} - 65 \, a^{4} b + 100 \, a^{3} b^{2} - 70 \, a^{2} b^{3} + 20 \, a b^{4} - b^{5}\right)} f \cosh\left(f x + e\right)^{3} + {\left(2 \, a^{5} - 7 \, a^{4} b + 8 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 2 \, a b^{4} + b^{5}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)}}, -\frac{{\left({\left(8 \, a^{2} b + 8 \, a b^{2} - b^{3}\right)} \cosh\left(f x + e\right)^{12} + 12 \, {\left(8 \, a^{2} b + 8 \, a b^{2} - b^{3}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{11} + {\left(8 \, a^{2} b + 8 \, a b^{2} - b^{3}\right)} \sinh\left(f x + e\right)^{12} + 2 \, {\left(16 \, a^{3} + 24 \, a^{2} b + 6 \, a b^{2} - b^{3}\right)} \cosh\left(f x + e\right)^{10} + 2 \, {\left(16 \, a^{3} + 24 \, a^{2} b + 6 \, a b^{2} - b^{3} + 33 \, {\left(8 \, a^{2} b + 8 \, a b^{2} - b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{10} + 20 \, {\left(11 \, {\left(8 \, a^{2} b + 8 \, a b^{2} - b^{3}\right)} \cosh\left(f x + e\right)^{3} + {\left(16 \, a^{3} + 24 \, a^{2} b + 6 \, a b^{2} - b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{9} + {\left(128 \, a^{3} + 120 \, a^{2} b - 24 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{8} + {\left(495 \, {\left(8 \, a^{2} b + 8 \, a b^{2} - b^{3}\right)} \cosh\left(f x + e\right)^{4} + 128 \, a^{3} + 120 \, a^{2} b - 24 \, a b^{2} + b^{3} + 90 \, {\left(16 \, a^{3} + 24 \, a^{2} b + 6 \, a b^{2} - b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{8} + 8 \, {\left(99 \, {\left(8 \, a^{2} b + 8 \, a b^{2} - b^{3}\right)} \cosh\left(f x + e\right)^{5} + 30 \, {\left(16 \, a^{3} + 24 \, a^{2} b + 6 \, a b^{2} - b^{3}\right)} \cosh\left(f x + e\right)^{3} + {\left(128 \, a^{3} + 120 \, a^{2} b - 24 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{7} + 4 \, {\left(48 \, a^{3} + 40 \, a^{2} b - 14 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{6} + 4 \, {\left(231 \, {\left(8 \, a^{2} b + 8 \, a b^{2} - b^{3}\right)} \cosh\left(f x + e\right)^{6} + 105 \, {\left(16 \, a^{3} + 24 \, a^{2} b + 6 \, a b^{2} - b^{3}\right)} \cosh\left(f x + e\right)^{4} + 48 \, a^{3} + 40 \, a^{2} b - 14 \, a b^{2} + b^{3} + 7 \, {\left(128 \, a^{3} + 120 \, a^{2} b - 24 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{6} + 8 \, {\left(99 \, {\left(8 \, a^{2} b + 8 \, a b^{2} - b^{3}\right)} \cosh\left(f x + e\right)^{7} + 63 \, {\left(16 \, a^{3} + 24 \, a^{2} b + 6 \, a b^{2} - b^{3}\right)} \cosh\left(f x + e\right)^{5} + 7 \, {\left(128 \, a^{3} + 120 \, a^{2} b - 24 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(48 \, a^{3} + 40 \, a^{2} b - 14 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + {\left(128 \, a^{3} + 120 \, a^{2} b - 24 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{4} + {\left(495 \, {\left(8 \, a^{2} b + 8 \, a b^{2} - b^{3}\right)} \cosh\left(f x + e\right)^{8} + 420 \, {\left(16 \, a^{3} + 24 \, a^{2} b + 6 \, a b^{2} - b^{3}\right)} \cosh\left(f x + e\right)^{6} + 70 \, {\left(128 \, a^{3} + 120 \, a^{2} b - 24 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{4} + 128 \, a^{3} + 120 \, a^{2} b - 24 \, a b^{2} + b^{3} + 60 \, {\left(48 \, a^{3} + 40 \, a^{2} b - 14 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(55 \, {\left(8 \, a^{2} b + 8 \, a b^{2} - b^{3}\right)} \cosh\left(f x + e\right)^{9} + 60 \, {\left(16 \, a^{3} + 24 \, a^{2} b + 6 \, a b^{2} - b^{3}\right)} \cosh\left(f x + e\right)^{7} + 14 \, {\left(128 \, a^{3} + 120 \, a^{2} b - 24 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{5} + 20 \, {\left(48 \, a^{3} + 40 \, a^{2} b - 14 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{3} + {\left(128 \, a^{3} + 120 \, a^{2} b - 24 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 8 \, a^{2} b + 8 \, a b^{2} - b^{3} + 2 \, {\left(16 \, a^{3} + 24 \, a^{2} b + 6 \, a b^{2} - b^{3}\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(33 \, {\left(8 \, a^{2} b + 8 \, a b^{2} - b^{3}\right)} \cosh\left(f x + e\right)^{10} + 45 \, {\left(16 \, a^{3} + 24 \, a^{2} b + 6 \, a b^{2} - b^{3}\right)} \cosh\left(f x + e\right)^{8} + 14 \, {\left(128 \, a^{3} + 120 \, a^{2} b - 24 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{6} + 30 \, {\left(48 \, a^{3} + 40 \, a^{2} b - 14 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{4} + 16 \, a^{3} + 24 \, a^{2} b + 6 \, a b^{2} - b^{3} + 3 \, {\left(128 \, a^{3} + 120 \, a^{2} b - 24 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(3 \, {\left(8 \, a^{2} b + 8 \, a b^{2} - b^{3}\right)} \cosh\left(f x + e\right)^{11} + 5 \, {\left(16 \, a^{3} + 24 \, a^{2} b + 6 \, a b^{2} - b^{3}\right)} \cosh\left(f x + e\right)^{9} + 2 \, {\left(128 \, a^{3} + 120 \, a^{2} b - 24 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{7} + 6 \, {\left(48 \, a^{3} + 40 \, a^{2} b - 14 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{5} + {\left(128 \, a^{3} + 120 \, a^{2} b - 24 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{3} + {\left(16 \, a^{3} + 24 \, a^{2} b + 6 \, a b^{2} - b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{-a + b} \arctan\left(-\frac{\sqrt{2} \sqrt{-a + b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{2 \, {\left({\left(a - b\right)} \cosh\left(f x + e\right) + {\left(a - b\right)} \sinh\left(f x + e\right)\right)}}\right) - 2 \, \sqrt{2} {\left({\left(8 \, a^{3} - 9 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{9} + 9 \, {\left(8 \, a^{3} - 9 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{8} + {\left(8 \, a^{3} - 9 \, a b^{2} + b^{3}\right)} \sinh\left(f x + e\right)^{9} + 4 \, {\left(16 \, a^{3} - 19 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{7} + 4 \, {\left(16 \, a^{3} - 19 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3} + 9 \, {\left(8 \, a^{3} - 9 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{7} + 28 \, {\left(3 \, {\left(8 \, a^{3} - 9 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{3} + {\left(16 \, a^{3} - 19 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{6} + 2 \, {\left(40 \, a^{3} - 28 \, a^{2} b - 19 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(f x + e\right)^{5} + 2 \, {\left(63 \, {\left(8 \, a^{3} - 9 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{4} + 40 \, a^{3} - 28 \, a^{2} b - 19 \, a b^{2} + 7 \, b^{3} + 42 \, {\left(16 \, a^{3} - 19 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(63 \, {\left(8 \, a^{3} - 9 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{5} + 70 \, {\left(16 \, a^{3} - 19 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} + 5 \, {\left(40 \, a^{3} - 28 \, a^{2} b - 19 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(16 \, a^{3} - 19 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} + 4 \, {\left(21 \, {\left(8 \, a^{3} - 9 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{6} + 35 \, {\left(16 \, a^{3} - 19 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} + 16 \, a^{3} - 19 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3} + 5 \, {\left(40 \, a^{3} - 28 \, a^{2} b - 19 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{3} + 4 \, {\left(9 \, {\left(8 \, a^{3} - 9 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{7} + 21 \, {\left(16 \, a^{3} - 19 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{5} + 5 \, {\left(40 \, a^{3} - 28 \, a^{2} b - 19 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(16 \, a^{3} - 19 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{2} + {\left(8 \, a^{3} - 9 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right) + {\left(9 \, {\left(8 \, a^{3} - 9 \, a b^{2} + b^{3}\right)} \cosh\left(f x + e\right)^{8} + 28 \, {\left(16 \, a^{3} - 19 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{6} + 10 \, {\left(40 \, a^{3} - 28 \, a^{2} b - 19 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} + 8 \, a^{3} - 9 \, a b^{2} + b^{3} + 12 \, {\left(16 \, a^{3} - 19 \, a^{2} b + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{8 \, {\left({\left(a^{4} b - 4 \, a^{3} b^{2} + 6 \, a^{2} b^{3} - 4 \, a b^{4} + b^{5}\right)} f \cosh\left(f x + e\right)^{12} + 12 \, {\left(a^{4} b - 4 \, a^{3} b^{2} + 6 \, a^{2} b^{3} - 4 \, a b^{4} + b^{5}\right)} f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{11} + {\left(a^{4} b - 4 \, a^{3} b^{2} + 6 \, a^{2} b^{3} - 4 \, a b^{4} + b^{5}\right)} f \sinh\left(f x + e\right)^{12} + 2 \, {\left(2 \, a^{5} - 7 \, a^{4} b + 8 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 2 \, a b^{4} + b^{5}\right)} f \cosh\left(f x + e\right)^{10} + 2 \, {\left(33 \, {\left(a^{4} b - 4 \, a^{3} b^{2} + 6 \, a^{2} b^{3} - 4 \, a b^{4} + b^{5}\right)} f \cosh\left(f x + e\right)^{2} + {\left(2 \, a^{5} - 7 \, a^{4} b + 8 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 2 \, a b^{4} + b^{5}\right)} f\right)} \sinh\left(f x + e\right)^{10} + {\left(16 \, a^{5} - 65 \, a^{4} b + 100 \, a^{3} b^{2} - 70 \, a^{2} b^{3} + 20 \, a b^{4} - b^{5}\right)} f \cosh\left(f x + e\right)^{8} + 20 \, {\left(11 \, {\left(a^{4} b - 4 \, a^{3} b^{2} + 6 \, a^{2} b^{3} - 4 \, a b^{4} + b^{5}\right)} f \cosh\left(f x + e\right)^{3} + {\left(2 \, a^{5} - 7 \, a^{4} b + 8 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 2 \, a b^{4} + b^{5}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{9} + {\left(495 \, {\left(a^{4} b - 4 \, a^{3} b^{2} + 6 \, a^{2} b^{3} - 4 \, a b^{4} + b^{5}\right)} f \cosh\left(f x + e\right)^{4} + 90 \, {\left(2 \, a^{5} - 7 \, a^{4} b + 8 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 2 \, a b^{4} + b^{5}\right)} f \cosh\left(f x + e\right)^{2} + {\left(16 \, a^{5} - 65 \, a^{4} b + 100 \, a^{3} b^{2} - 70 \, a^{2} b^{3} + 20 \, a b^{4} - b^{5}\right)} f\right)} \sinh\left(f x + e\right)^{8} + 4 \, {\left(6 \, a^{5} - 25 \, a^{4} b + 40 \, a^{3} b^{2} - 30 \, a^{2} b^{3} + 10 \, a b^{4} - b^{5}\right)} f \cosh\left(f x + e\right)^{6} + 8 \, {\left(99 \, {\left(a^{4} b - 4 \, a^{3} b^{2} + 6 \, a^{2} b^{3} - 4 \, a b^{4} + b^{5}\right)} f \cosh\left(f x + e\right)^{5} + 30 \, {\left(2 \, a^{5} - 7 \, a^{4} b + 8 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 2 \, a b^{4} + b^{5}\right)} f \cosh\left(f x + e\right)^{3} + {\left(16 \, a^{5} - 65 \, a^{4} b + 100 \, a^{3} b^{2} - 70 \, a^{2} b^{3} + 20 \, a b^{4} - b^{5}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{7} + 4 \, {\left(231 \, {\left(a^{4} b - 4 \, a^{3} b^{2} + 6 \, a^{2} b^{3} - 4 \, a b^{4} + b^{5}\right)} f \cosh\left(f x + e\right)^{6} + 105 \, {\left(2 \, a^{5} - 7 \, a^{4} b + 8 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 2 \, a b^{4} + b^{5}\right)} f \cosh\left(f x + e\right)^{4} + 7 \, {\left(16 \, a^{5} - 65 \, a^{4} b + 100 \, a^{3} b^{2} - 70 \, a^{2} b^{3} + 20 \, a b^{4} - b^{5}\right)} f \cosh\left(f x + e\right)^{2} + {\left(6 \, a^{5} - 25 \, a^{4} b + 40 \, a^{3} b^{2} - 30 \, a^{2} b^{3} + 10 \, a b^{4} - b^{5}\right)} f\right)} \sinh\left(f x + e\right)^{6} + {\left(16 \, a^{5} - 65 \, a^{4} b + 100 \, a^{3} b^{2} - 70 \, a^{2} b^{3} + 20 \, a b^{4} - b^{5}\right)} f \cosh\left(f x + e\right)^{4} + 8 \, {\left(99 \, {\left(a^{4} b - 4 \, a^{3} b^{2} + 6 \, a^{2} b^{3} - 4 \, a b^{4} + b^{5}\right)} f \cosh\left(f x + e\right)^{7} + 63 \, {\left(2 \, a^{5} - 7 \, a^{4} b + 8 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 2 \, a b^{4} + b^{5}\right)} f \cosh\left(f x + e\right)^{5} + 7 \, {\left(16 \, a^{5} - 65 \, a^{4} b + 100 \, a^{3} b^{2} - 70 \, a^{2} b^{3} + 20 \, a b^{4} - b^{5}\right)} f \cosh\left(f x + e\right)^{3} + 3 \, {\left(6 \, a^{5} - 25 \, a^{4} b + 40 \, a^{3} b^{2} - 30 \, a^{2} b^{3} + 10 \, a b^{4} - b^{5}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + {\left(495 \, {\left(a^{4} b - 4 \, a^{3} b^{2} + 6 \, a^{2} b^{3} - 4 \, a b^{4} + b^{5}\right)} f \cosh\left(f x + e\right)^{8} + 420 \, {\left(2 \, a^{5} - 7 \, a^{4} b + 8 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 2 \, a b^{4} + b^{5}\right)} f \cosh\left(f x + e\right)^{6} + 70 \, {\left(16 \, a^{5} - 65 \, a^{4} b + 100 \, a^{3} b^{2} - 70 \, a^{2} b^{3} + 20 \, a b^{4} - b^{5}\right)} f \cosh\left(f x + e\right)^{4} + 60 \, {\left(6 \, a^{5} - 25 \, a^{4} b + 40 \, a^{3} b^{2} - 30 \, a^{2} b^{3} + 10 \, a b^{4} - b^{5}\right)} f \cosh\left(f x + e\right)^{2} + {\left(16 \, a^{5} - 65 \, a^{4} b + 100 \, a^{3} b^{2} - 70 \, a^{2} b^{3} + 20 \, a b^{4} - b^{5}\right)} f\right)} \sinh\left(f x + e\right)^{4} + 2 \, {\left(2 \, a^{5} - 7 \, a^{4} b + 8 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 2 \, a b^{4} + b^{5}\right)} f \cosh\left(f x + e\right)^{2} + 4 \, {\left(55 \, {\left(a^{4} b - 4 \, a^{3} b^{2} + 6 \, a^{2} b^{3} - 4 \, a b^{4} + b^{5}\right)} f \cosh\left(f x + e\right)^{9} + 60 \, {\left(2 \, a^{5} - 7 \, a^{4} b + 8 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 2 \, a b^{4} + b^{5}\right)} f \cosh\left(f x + e\right)^{7} + 14 \, {\left(16 \, a^{5} - 65 \, a^{4} b + 100 \, a^{3} b^{2} - 70 \, a^{2} b^{3} + 20 \, a b^{4} - b^{5}\right)} f \cosh\left(f x + e\right)^{5} + 20 \, {\left(6 \, a^{5} - 25 \, a^{4} b + 40 \, a^{3} b^{2} - 30 \, a^{2} b^{3} + 10 \, a b^{4} - b^{5}\right)} f \cosh\left(f x + e\right)^{3} + {\left(16 \, a^{5} - 65 \, a^{4} b + 100 \, a^{3} b^{2} - 70 \, a^{2} b^{3} + 20 \, a b^{4} - b^{5}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 2 \, {\left(33 \, {\left(a^{4} b - 4 \, a^{3} b^{2} + 6 \, a^{2} b^{3} - 4 \, a b^{4} + b^{5}\right)} f \cosh\left(f x + e\right)^{10} + 45 \, {\left(2 \, a^{5} - 7 \, a^{4} b + 8 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 2 \, a b^{4} + b^{5}\right)} f \cosh\left(f x + e\right)^{8} + 14 \, {\left(16 \, a^{5} - 65 \, a^{4} b + 100 \, a^{3} b^{2} - 70 \, a^{2} b^{3} + 20 \, a b^{4} - b^{5}\right)} f \cosh\left(f x + e\right)^{6} + 30 \, {\left(6 \, a^{5} - 25 \, a^{4} b + 40 \, a^{3} b^{2} - 30 \, a^{2} b^{3} + 10 \, a b^{4} - b^{5}\right)} f \cosh\left(f x + e\right)^{4} + 3 \, {\left(16 \, a^{5} - 65 \, a^{4} b + 100 \, a^{3} b^{2} - 70 \, a^{2} b^{3} + 20 \, a b^{4} - b^{5}\right)} f \cosh\left(f x + e\right)^{2} + {\left(2 \, a^{5} - 7 \, a^{4} b + 8 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 2 \, a b^{4} + b^{5}\right)} f\right)} \sinh\left(f x + e\right)^{2} + {\left(a^{4} b - 4 \, a^{3} b^{2} + 6 \, a^{2} b^{3} - 4 \, a b^{4} + b^{5}\right)} f + 4 \, {\left(3 \, {\left(a^{4} b - 4 \, a^{3} b^{2} + 6 \, a^{2} b^{3} - 4 \, a b^{4} + b^{5}\right)} f \cosh\left(f x + e\right)^{11} + 5 \, {\left(2 \, a^{5} - 7 \, a^{4} b + 8 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 2 \, a b^{4} + b^{5}\right)} f \cosh\left(f x + e\right)^{9} + 2 \, {\left(16 \, a^{5} - 65 \, a^{4} b + 100 \, a^{3} b^{2} - 70 \, a^{2} b^{3} + 20 \, a b^{4} - b^{5}\right)} f \cosh\left(f x + e\right)^{7} + 6 \, {\left(6 \, a^{5} - 25 \, a^{4} b + 40 \, a^{3} b^{2} - 30 \, a^{2} b^{3} + 10 \, a b^{4} - b^{5}\right)} f \cosh\left(f x + e\right)^{5} + {\left(16 \, a^{5} - 65 \, a^{4} b + 100 \, a^{3} b^{2} - 70 \, a^{2} b^{3} + 20 \, a b^{4} - b^{5}\right)} f \cosh\left(f x + e\right)^{3} + {\left(2 \, a^{5} - 7 \, a^{4} b + 8 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 2 \, a b^{4} + b^{5}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)}}\right]"," ",0,"[1/16*(((8*a^2*b + 8*a*b^2 - b^3)*cosh(f*x + e)^12 + 12*(8*a^2*b + 8*a*b^2 - b^3)*cosh(f*x + e)*sinh(f*x + e)^11 + (8*a^2*b + 8*a*b^2 - b^3)*sinh(f*x + e)^12 + 2*(16*a^3 + 24*a^2*b + 6*a*b^2 - b^3)*cosh(f*x + e)^10 + 2*(16*a^3 + 24*a^2*b + 6*a*b^2 - b^3 + 33*(8*a^2*b + 8*a*b^2 - b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^10 + 20*(11*(8*a^2*b + 8*a*b^2 - b^3)*cosh(f*x + e)^3 + (16*a^3 + 24*a^2*b + 6*a*b^2 - b^3)*cosh(f*x + e))*sinh(f*x + e)^9 + (128*a^3 + 120*a^2*b - 24*a*b^2 + b^3)*cosh(f*x + e)^8 + (495*(8*a^2*b + 8*a*b^2 - b^3)*cosh(f*x + e)^4 + 128*a^3 + 120*a^2*b - 24*a*b^2 + b^3 + 90*(16*a^3 + 24*a^2*b + 6*a*b^2 - b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^8 + 8*(99*(8*a^2*b + 8*a*b^2 - b^3)*cosh(f*x + e)^5 + 30*(16*a^3 + 24*a^2*b + 6*a*b^2 - b^3)*cosh(f*x + e)^3 + (128*a^3 + 120*a^2*b - 24*a*b^2 + b^3)*cosh(f*x + e))*sinh(f*x + e)^7 + 4*(48*a^3 + 40*a^2*b - 14*a*b^2 + b^3)*cosh(f*x + e)^6 + 4*(231*(8*a^2*b + 8*a*b^2 - b^3)*cosh(f*x + e)^6 + 105*(16*a^3 + 24*a^2*b + 6*a*b^2 - b^3)*cosh(f*x + e)^4 + 48*a^3 + 40*a^2*b - 14*a*b^2 + b^3 + 7*(128*a^3 + 120*a^2*b - 24*a*b^2 + b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^6 + 8*(99*(8*a^2*b + 8*a*b^2 - b^3)*cosh(f*x + e)^7 + 63*(16*a^3 + 24*a^2*b + 6*a*b^2 - b^3)*cosh(f*x + e)^5 + 7*(128*a^3 + 120*a^2*b - 24*a*b^2 + b^3)*cosh(f*x + e)^3 + 3*(48*a^3 + 40*a^2*b - 14*a*b^2 + b^3)*cosh(f*x + e))*sinh(f*x + e)^5 + (128*a^3 + 120*a^2*b - 24*a*b^2 + b^3)*cosh(f*x + e)^4 + (495*(8*a^2*b + 8*a*b^2 - b^3)*cosh(f*x + e)^8 + 420*(16*a^3 + 24*a^2*b + 6*a*b^2 - b^3)*cosh(f*x + e)^6 + 70*(128*a^3 + 120*a^2*b - 24*a*b^2 + b^3)*cosh(f*x + e)^4 + 128*a^3 + 120*a^2*b - 24*a*b^2 + b^3 + 60*(48*a^3 + 40*a^2*b - 14*a*b^2 + b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^4 + 4*(55*(8*a^2*b + 8*a*b^2 - b^3)*cosh(f*x + e)^9 + 60*(16*a^3 + 24*a^2*b + 6*a*b^2 - b^3)*cosh(f*x + e)^7 + 14*(128*a^3 + 120*a^2*b - 24*a*b^2 + b^3)*cosh(f*x + e)^5 + 20*(48*a^3 + 40*a^2*b - 14*a*b^2 + b^3)*cosh(f*x + e)^3 + (128*a^3 + 120*a^2*b - 24*a*b^2 + b^3)*cosh(f*x + e))*sinh(f*x + e)^3 + 8*a^2*b + 8*a*b^2 - b^3 + 2*(16*a^3 + 24*a^2*b + 6*a*b^2 - b^3)*cosh(f*x + e)^2 + 2*(33*(8*a^2*b + 8*a*b^2 - b^3)*cosh(f*x + e)^10 + 45*(16*a^3 + 24*a^2*b + 6*a*b^2 - b^3)*cosh(f*x + e)^8 + 14*(128*a^3 + 120*a^2*b - 24*a*b^2 + b^3)*cosh(f*x + e)^6 + 30*(48*a^3 + 40*a^2*b - 14*a*b^2 + b^3)*cosh(f*x + e)^4 + 16*a^3 + 24*a^2*b + 6*a*b^2 - b^3 + 3*(128*a^3 + 120*a^2*b - 24*a*b^2 + b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^2 + 4*(3*(8*a^2*b + 8*a*b^2 - b^3)*cosh(f*x + e)^11 + 5*(16*a^3 + 24*a^2*b + 6*a*b^2 - b^3)*cosh(f*x + e)^9 + 2*(128*a^3 + 120*a^2*b - 24*a*b^2 + b^3)*cosh(f*x + e)^7 + 6*(48*a^3 + 40*a^2*b - 14*a*b^2 + b^3)*cosh(f*x + e)^5 + (128*a^3 + 120*a^2*b - 24*a*b^2 + b^3)*cosh(f*x + e)^3 + (16*a^3 + 24*a^2*b + 6*a*b^2 - b^3)*cosh(f*x + e))*sinh(f*x + e))*sqrt(a - b)*log((b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(4*a - 3*b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 4*a - 3*b)*sinh(f*x + e)^2 - 4*sqrt(2)*sqrt(a - b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))*(cosh(f*x + e) + sinh(f*x + e)) + 4*(b*cosh(f*x + e)^3 + (4*a - 3*b)*cosh(f*x + e))*sinh(f*x + e) + b)/(cosh(f*x + e)^4 + 4*cosh(f*x + e)*sinh(f*x + e)^3 + sinh(f*x + e)^4 + 2*(3*cosh(f*x + e)^2 + 1)*sinh(f*x + e)^2 + 2*cosh(f*x + e)^2 + 4*(cosh(f*x + e)^3 + cosh(f*x + e))*sinh(f*x + e) + 1)) + 4*sqrt(2)*((8*a^3 - 9*a*b^2 + b^3)*cosh(f*x + e)^9 + 9*(8*a^3 - 9*a*b^2 + b^3)*cosh(f*x + e)*sinh(f*x + e)^8 + (8*a^3 - 9*a*b^2 + b^3)*sinh(f*x + e)^9 + 4*(16*a^3 - 19*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e)^7 + 4*(16*a^3 - 19*a^2*b + 5*a*b^2 - 2*b^3 + 9*(8*a^3 - 9*a*b^2 + b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^7 + 28*(3*(8*a^3 - 9*a*b^2 + b^3)*cosh(f*x + e)^3 + (16*a^3 - 19*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e))*sinh(f*x + e)^6 + 2*(40*a^3 - 28*a^2*b - 19*a*b^2 + 7*b^3)*cosh(f*x + e)^5 + 2*(63*(8*a^3 - 9*a*b^2 + b^3)*cosh(f*x + e)^4 + 40*a^3 - 28*a^2*b - 19*a*b^2 + 7*b^3 + 42*(16*a^3 - 19*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^5 + 2*(63*(8*a^3 - 9*a*b^2 + b^3)*cosh(f*x + e)^5 + 70*(16*a^3 - 19*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e)^3 + 5*(40*a^3 - 28*a^2*b - 19*a*b^2 + 7*b^3)*cosh(f*x + e))*sinh(f*x + e)^4 + 4*(16*a^3 - 19*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e)^3 + 4*(21*(8*a^3 - 9*a*b^2 + b^3)*cosh(f*x + e)^6 + 35*(16*a^3 - 19*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e)^4 + 16*a^3 - 19*a^2*b + 5*a*b^2 - 2*b^3 + 5*(40*a^3 - 28*a^2*b - 19*a*b^2 + 7*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^3 + 4*(9*(8*a^3 - 9*a*b^2 + b^3)*cosh(f*x + e)^7 + 21*(16*a^3 - 19*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e)^5 + 5*(40*a^3 - 28*a^2*b - 19*a*b^2 + 7*b^3)*cosh(f*x + e)^3 + 3*(16*a^3 - 19*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e))*sinh(f*x + e)^2 + (8*a^3 - 9*a*b^2 + b^3)*cosh(f*x + e) + (9*(8*a^3 - 9*a*b^2 + b^3)*cosh(f*x + e)^8 + 28*(16*a^3 - 19*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e)^6 + 10*(40*a^3 - 28*a^2*b - 19*a*b^2 + 7*b^3)*cosh(f*x + e)^4 + 8*a^3 - 9*a*b^2 + b^3 + 12*(16*a^3 - 19*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e)^2)*sinh(f*x + e))*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/((a^4*b - 4*a^3*b^2 + 6*a^2*b^3 - 4*a*b^4 + b^5)*f*cosh(f*x + e)^12 + 12*(a^4*b - 4*a^3*b^2 + 6*a^2*b^3 - 4*a*b^4 + b^5)*f*cosh(f*x + e)*sinh(f*x + e)^11 + (a^4*b - 4*a^3*b^2 + 6*a^2*b^3 - 4*a*b^4 + b^5)*f*sinh(f*x + e)^12 + 2*(2*a^5 - 7*a^4*b + 8*a^3*b^2 - 2*a^2*b^3 - 2*a*b^4 + b^5)*f*cosh(f*x + e)^10 + 2*(33*(a^4*b - 4*a^3*b^2 + 6*a^2*b^3 - 4*a*b^4 + b^5)*f*cosh(f*x + e)^2 + (2*a^5 - 7*a^4*b + 8*a^3*b^2 - 2*a^2*b^3 - 2*a*b^4 + b^5)*f)*sinh(f*x + e)^10 + (16*a^5 - 65*a^4*b + 100*a^3*b^2 - 70*a^2*b^3 + 20*a*b^4 - b^5)*f*cosh(f*x + e)^8 + 20*(11*(a^4*b - 4*a^3*b^2 + 6*a^2*b^3 - 4*a*b^4 + b^5)*f*cosh(f*x + e)^3 + (2*a^5 - 7*a^4*b + 8*a^3*b^2 - 2*a^2*b^3 - 2*a*b^4 + b^5)*f*cosh(f*x + e))*sinh(f*x + e)^9 + (495*(a^4*b - 4*a^3*b^2 + 6*a^2*b^3 - 4*a*b^4 + b^5)*f*cosh(f*x + e)^4 + 90*(2*a^5 - 7*a^4*b + 8*a^3*b^2 - 2*a^2*b^3 - 2*a*b^4 + b^5)*f*cosh(f*x + e)^2 + (16*a^5 - 65*a^4*b + 100*a^3*b^2 - 70*a^2*b^3 + 20*a*b^4 - b^5)*f)*sinh(f*x + e)^8 + 4*(6*a^5 - 25*a^4*b + 40*a^3*b^2 - 30*a^2*b^3 + 10*a*b^4 - b^5)*f*cosh(f*x + e)^6 + 8*(99*(a^4*b - 4*a^3*b^2 + 6*a^2*b^3 - 4*a*b^4 + b^5)*f*cosh(f*x + e)^5 + 30*(2*a^5 - 7*a^4*b + 8*a^3*b^2 - 2*a^2*b^3 - 2*a*b^4 + b^5)*f*cosh(f*x + e)^3 + (16*a^5 - 65*a^4*b + 100*a^3*b^2 - 70*a^2*b^3 + 20*a*b^4 - b^5)*f*cosh(f*x + e))*sinh(f*x + e)^7 + 4*(231*(a^4*b - 4*a^3*b^2 + 6*a^2*b^3 - 4*a*b^4 + b^5)*f*cosh(f*x + e)^6 + 105*(2*a^5 - 7*a^4*b + 8*a^3*b^2 - 2*a^2*b^3 - 2*a*b^4 + b^5)*f*cosh(f*x + e)^4 + 7*(16*a^5 - 65*a^4*b + 100*a^3*b^2 - 70*a^2*b^3 + 20*a*b^4 - b^5)*f*cosh(f*x + e)^2 + (6*a^5 - 25*a^4*b + 40*a^3*b^2 - 30*a^2*b^3 + 10*a*b^4 - b^5)*f)*sinh(f*x + e)^6 + (16*a^5 - 65*a^4*b + 100*a^3*b^2 - 70*a^2*b^3 + 20*a*b^4 - b^5)*f*cosh(f*x + e)^4 + 8*(99*(a^4*b - 4*a^3*b^2 + 6*a^2*b^3 - 4*a*b^4 + b^5)*f*cosh(f*x + e)^7 + 63*(2*a^5 - 7*a^4*b + 8*a^3*b^2 - 2*a^2*b^3 - 2*a*b^4 + b^5)*f*cosh(f*x + e)^5 + 7*(16*a^5 - 65*a^4*b + 100*a^3*b^2 - 70*a^2*b^3 + 20*a*b^4 - b^5)*f*cosh(f*x + e)^3 + 3*(6*a^5 - 25*a^4*b + 40*a^3*b^2 - 30*a^2*b^3 + 10*a*b^4 - b^5)*f*cosh(f*x + e))*sinh(f*x + e)^5 + (495*(a^4*b - 4*a^3*b^2 + 6*a^2*b^3 - 4*a*b^4 + b^5)*f*cosh(f*x + e)^8 + 420*(2*a^5 - 7*a^4*b + 8*a^3*b^2 - 2*a^2*b^3 - 2*a*b^4 + b^5)*f*cosh(f*x + e)^6 + 70*(16*a^5 - 65*a^4*b + 100*a^3*b^2 - 70*a^2*b^3 + 20*a*b^4 - b^5)*f*cosh(f*x + e)^4 + 60*(6*a^5 - 25*a^4*b + 40*a^3*b^2 - 30*a^2*b^3 + 10*a*b^4 - b^5)*f*cosh(f*x + e)^2 + (16*a^5 - 65*a^4*b + 100*a^3*b^2 - 70*a^2*b^3 + 20*a*b^4 - b^5)*f)*sinh(f*x + e)^4 + 2*(2*a^5 - 7*a^4*b + 8*a^3*b^2 - 2*a^2*b^3 - 2*a*b^4 + b^5)*f*cosh(f*x + e)^2 + 4*(55*(a^4*b - 4*a^3*b^2 + 6*a^2*b^3 - 4*a*b^4 + b^5)*f*cosh(f*x + e)^9 + 60*(2*a^5 - 7*a^4*b + 8*a^3*b^2 - 2*a^2*b^3 - 2*a*b^4 + b^5)*f*cosh(f*x + e)^7 + 14*(16*a^5 - 65*a^4*b + 100*a^3*b^2 - 70*a^2*b^3 + 20*a*b^4 - b^5)*f*cosh(f*x + e)^5 + 20*(6*a^5 - 25*a^4*b + 40*a^3*b^2 - 30*a^2*b^3 + 10*a*b^4 - b^5)*f*cosh(f*x + e)^3 + (16*a^5 - 65*a^4*b + 100*a^3*b^2 - 70*a^2*b^3 + 20*a*b^4 - b^5)*f*cosh(f*x + e))*sinh(f*x + e)^3 + 2*(33*(a^4*b - 4*a^3*b^2 + 6*a^2*b^3 - 4*a*b^4 + b^5)*f*cosh(f*x + e)^10 + 45*(2*a^5 - 7*a^4*b + 8*a^3*b^2 - 2*a^2*b^3 - 2*a*b^4 + b^5)*f*cosh(f*x + e)^8 + 14*(16*a^5 - 65*a^4*b + 100*a^3*b^2 - 70*a^2*b^3 + 20*a*b^4 - b^5)*f*cosh(f*x + e)^6 + 30*(6*a^5 - 25*a^4*b + 40*a^3*b^2 - 30*a^2*b^3 + 10*a*b^4 - b^5)*f*cosh(f*x + e)^4 + 3*(16*a^5 - 65*a^4*b + 100*a^3*b^2 - 70*a^2*b^3 + 20*a*b^4 - b^5)*f*cosh(f*x + e)^2 + (2*a^5 - 7*a^4*b + 8*a^3*b^2 - 2*a^2*b^3 - 2*a*b^4 + b^5)*f)*sinh(f*x + e)^2 + (a^4*b - 4*a^3*b^2 + 6*a^2*b^3 - 4*a*b^4 + b^5)*f + 4*(3*(a^4*b - 4*a^3*b^2 + 6*a^2*b^3 - 4*a*b^4 + b^5)*f*cosh(f*x + e)^11 + 5*(2*a^5 - 7*a^4*b + 8*a^3*b^2 - 2*a^2*b^3 - 2*a*b^4 + b^5)*f*cosh(f*x + e)^9 + 2*(16*a^5 - 65*a^4*b + 100*a^3*b^2 - 70*a^2*b^3 + 20*a*b^4 - b^5)*f*cosh(f*x + e)^7 + 6*(6*a^5 - 25*a^4*b + 40*a^3*b^2 - 30*a^2*b^3 + 10*a*b^4 - b^5)*f*cosh(f*x + e)^5 + (16*a^5 - 65*a^4*b + 100*a^3*b^2 - 70*a^2*b^3 + 20*a*b^4 - b^5)*f*cosh(f*x + e)^3 + (2*a^5 - 7*a^4*b + 8*a^3*b^2 - 2*a^2*b^3 - 2*a*b^4 + b^5)*f*cosh(f*x + e))*sinh(f*x + e)), -1/8*(((8*a^2*b + 8*a*b^2 - b^3)*cosh(f*x + e)^12 + 12*(8*a^2*b + 8*a*b^2 - b^3)*cosh(f*x + e)*sinh(f*x + e)^11 + (8*a^2*b + 8*a*b^2 - b^3)*sinh(f*x + e)^12 + 2*(16*a^3 + 24*a^2*b + 6*a*b^2 - b^3)*cosh(f*x + e)^10 + 2*(16*a^3 + 24*a^2*b + 6*a*b^2 - b^3 + 33*(8*a^2*b + 8*a*b^2 - b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^10 + 20*(11*(8*a^2*b + 8*a*b^2 - b^3)*cosh(f*x + e)^3 + (16*a^3 + 24*a^2*b + 6*a*b^2 - b^3)*cosh(f*x + e))*sinh(f*x + e)^9 + (128*a^3 + 120*a^2*b - 24*a*b^2 + b^3)*cosh(f*x + e)^8 + (495*(8*a^2*b + 8*a*b^2 - b^3)*cosh(f*x + e)^4 + 128*a^3 + 120*a^2*b - 24*a*b^2 + b^3 + 90*(16*a^3 + 24*a^2*b + 6*a*b^2 - b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^8 + 8*(99*(8*a^2*b + 8*a*b^2 - b^3)*cosh(f*x + e)^5 + 30*(16*a^3 + 24*a^2*b + 6*a*b^2 - b^3)*cosh(f*x + e)^3 + (128*a^3 + 120*a^2*b - 24*a*b^2 + b^3)*cosh(f*x + e))*sinh(f*x + e)^7 + 4*(48*a^3 + 40*a^2*b - 14*a*b^2 + b^3)*cosh(f*x + e)^6 + 4*(231*(8*a^2*b + 8*a*b^2 - b^3)*cosh(f*x + e)^6 + 105*(16*a^3 + 24*a^2*b + 6*a*b^2 - b^3)*cosh(f*x + e)^4 + 48*a^3 + 40*a^2*b - 14*a*b^2 + b^3 + 7*(128*a^3 + 120*a^2*b - 24*a*b^2 + b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^6 + 8*(99*(8*a^2*b + 8*a*b^2 - b^3)*cosh(f*x + e)^7 + 63*(16*a^3 + 24*a^2*b + 6*a*b^2 - b^3)*cosh(f*x + e)^5 + 7*(128*a^3 + 120*a^2*b - 24*a*b^2 + b^3)*cosh(f*x + e)^3 + 3*(48*a^3 + 40*a^2*b - 14*a*b^2 + b^3)*cosh(f*x + e))*sinh(f*x + e)^5 + (128*a^3 + 120*a^2*b - 24*a*b^2 + b^3)*cosh(f*x + e)^4 + (495*(8*a^2*b + 8*a*b^2 - b^3)*cosh(f*x + e)^8 + 420*(16*a^3 + 24*a^2*b + 6*a*b^2 - b^3)*cosh(f*x + e)^6 + 70*(128*a^3 + 120*a^2*b - 24*a*b^2 + b^3)*cosh(f*x + e)^4 + 128*a^3 + 120*a^2*b - 24*a*b^2 + b^3 + 60*(48*a^3 + 40*a^2*b - 14*a*b^2 + b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^4 + 4*(55*(8*a^2*b + 8*a*b^2 - b^3)*cosh(f*x + e)^9 + 60*(16*a^3 + 24*a^2*b + 6*a*b^2 - b^3)*cosh(f*x + e)^7 + 14*(128*a^3 + 120*a^2*b - 24*a*b^2 + b^3)*cosh(f*x + e)^5 + 20*(48*a^3 + 40*a^2*b - 14*a*b^2 + b^3)*cosh(f*x + e)^3 + (128*a^3 + 120*a^2*b - 24*a*b^2 + b^3)*cosh(f*x + e))*sinh(f*x + e)^3 + 8*a^2*b + 8*a*b^2 - b^3 + 2*(16*a^3 + 24*a^2*b + 6*a*b^2 - b^3)*cosh(f*x + e)^2 + 2*(33*(8*a^2*b + 8*a*b^2 - b^3)*cosh(f*x + e)^10 + 45*(16*a^3 + 24*a^2*b + 6*a*b^2 - b^3)*cosh(f*x + e)^8 + 14*(128*a^3 + 120*a^2*b - 24*a*b^2 + b^3)*cosh(f*x + e)^6 + 30*(48*a^3 + 40*a^2*b - 14*a*b^2 + b^3)*cosh(f*x + e)^4 + 16*a^3 + 24*a^2*b + 6*a*b^2 - b^3 + 3*(128*a^3 + 120*a^2*b - 24*a*b^2 + b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^2 + 4*(3*(8*a^2*b + 8*a*b^2 - b^3)*cosh(f*x + e)^11 + 5*(16*a^3 + 24*a^2*b + 6*a*b^2 - b^3)*cosh(f*x + e)^9 + 2*(128*a^3 + 120*a^2*b - 24*a*b^2 + b^3)*cosh(f*x + e)^7 + 6*(48*a^3 + 40*a^2*b - 14*a*b^2 + b^3)*cosh(f*x + e)^5 + (128*a^3 + 120*a^2*b - 24*a*b^2 + b^3)*cosh(f*x + e)^3 + (16*a^3 + 24*a^2*b + 6*a*b^2 - b^3)*cosh(f*x + e))*sinh(f*x + e))*sqrt(-a + b)*arctan(-1/2*sqrt(2)*sqrt(-a + b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/((a - b)*cosh(f*x + e) + (a - b)*sinh(f*x + e))) - 2*sqrt(2)*((8*a^3 - 9*a*b^2 + b^3)*cosh(f*x + e)^9 + 9*(8*a^3 - 9*a*b^2 + b^3)*cosh(f*x + e)*sinh(f*x + e)^8 + (8*a^3 - 9*a*b^2 + b^3)*sinh(f*x + e)^9 + 4*(16*a^3 - 19*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e)^7 + 4*(16*a^3 - 19*a^2*b + 5*a*b^2 - 2*b^3 + 9*(8*a^3 - 9*a*b^2 + b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^7 + 28*(3*(8*a^3 - 9*a*b^2 + b^3)*cosh(f*x + e)^3 + (16*a^3 - 19*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e))*sinh(f*x + e)^6 + 2*(40*a^3 - 28*a^2*b - 19*a*b^2 + 7*b^3)*cosh(f*x + e)^5 + 2*(63*(8*a^3 - 9*a*b^2 + b^3)*cosh(f*x + e)^4 + 40*a^3 - 28*a^2*b - 19*a*b^2 + 7*b^3 + 42*(16*a^3 - 19*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^5 + 2*(63*(8*a^3 - 9*a*b^2 + b^3)*cosh(f*x + e)^5 + 70*(16*a^3 - 19*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e)^3 + 5*(40*a^3 - 28*a^2*b - 19*a*b^2 + 7*b^3)*cosh(f*x + e))*sinh(f*x + e)^4 + 4*(16*a^3 - 19*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e)^3 + 4*(21*(8*a^3 - 9*a*b^2 + b^3)*cosh(f*x + e)^6 + 35*(16*a^3 - 19*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e)^4 + 16*a^3 - 19*a^2*b + 5*a*b^2 - 2*b^3 + 5*(40*a^3 - 28*a^2*b - 19*a*b^2 + 7*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^3 + 4*(9*(8*a^3 - 9*a*b^2 + b^3)*cosh(f*x + e)^7 + 21*(16*a^3 - 19*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e)^5 + 5*(40*a^3 - 28*a^2*b - 19*a*b^2 + 7*b^3)*cosh(f*x + e)^3 + 3*(16*a^3 - 19*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e))*sinh(f*x + e)^2 + (8*a^3 - 9*a*b^2 + b^3)*cosh(f*x + e) + (9*(8*a^3 - 9*a*b^2 + b^3)*cosh(f*x + e)^8 + 28*(16*a^3 - 19*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e)^6 + 10*(40*a^3 - 28*a^2*b - 19*a*b^2 + 7*b^3)*cosh(f*x + e)^4 + 8*a^3 - 9*a*b^2 + b^3 + 12*(16*a^3 - 19*a^2*b + 5*a*b^2 - 2*b^3)*cosh(f*x + e)^2)*sinh(f*x + e))*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/((a^4*b - 4*a^3*b^2 + 6*a^2*b^3 - 4*a*b^4 + b^5)*f*cosh(f*x + e)^12 + 12*(a^4*b - 4*a^3*b^2 + 6*a^2*b^3 - 4*a*b^4 + b^5)*f*cosh(f*x + e)*sinh(f*x + e)^11 + (a^4*b - 4*a^3*b^2 + 6*a^2*b^3 - 4*a*b^4 + b^5)*f*sinh(f*x + e)^12 + 2*(2*a^5 - 7*a^4*b + 8*a^3*b^2 - 2*a^2*b^3 - 2*a*b^4 + b^5)*f*cosh(f*x + e)^10 + 2*(33*(a^4*b - 4*a^3*b^2 + 6*a^2*b^3 - 4*a*b^4 + b^5)*f*cosh(f*x + e)^2 + (2*a^5 - 7*a^4*b + 8*a^3*b^2 - 2*a^2*b^3 - 2*a*b^4 + b^5)*f)*sinh(f*x + e)^10 + (16*a^5 - 65*a^4*b + 100*a^3*b^2 - 70*a^2*b^3 + 20*a*b^4 - b^5)*f*cosh(f*x + e)^8 + 20*(11*(a^4*b - 4*a^3*b^2 + 6*a^2*b^3 - 4*a*b^4 + b^5)*f*cosh(f*x + e)^3 + (2*a^5 - 7*a^4*b + 8*a^3*b^2 - 2*a^2*b^3 - 2*a*b^4 + b^5)*f*cosh(f*x + e))*sinh(f*x + e)^9 + (495*(a^4*b - 4*a^3*b^2 + 6*a^2*b^3 - 4*a*b^4 + b^5)*f*cosh(f*x + e)^4 + 90*(2*a^5 - 7*a^4*b + 8*a^3*b^2 - 2*a^2*b^3 - 2*a*b^4 + b^5)*f*cosh(f*x + e)^2 + (16*a^5 - 65*a^4*b + 100*a^3*b^2 - 70*a^2*b^3 + 20*a*b^4 - b^5)*f)*sinh(f*x + e)^8 + 4*(6*a^5 - 25*a^4*b + 40*a^3*b^2 - 30*a^2*b^3 + 10*a*b^4 - b^5)*f*cosh(f*x + e)^6 + 8*(99*(a^4*b - 4*a^3*b^2 + 6*a^2*b^3 - 4*a*b^4 + b^5)*f*cosh(f*x + e)^5 + 30*(2*a^5 - 7*a^4*b + 8*a^3*b^2 - 2*a^2*b^3 - 2*a*b^4 + b^5)*f*cosh(f*x + e)^3 + (16*a^5 - 65*a^4*b + 100*a^3*b^2 - 70*a^2*b^3 + 20*a*b^4 - b^5)*f*cosh(f*x + e))*sinh(f*x + e)^7 + 4*(231*(a^4*b - 4*a^3*b^2 + 6*a^2*b^3 - 4*a*b^4 + b^5)*f*cosh(f*x + e)^6 + 105*(2*a^5 - 7*a^4*b + 8*a^3*b^2 - 2*a^2*b^3 - 2*a*b^4 + b^5)*f*cosh(f*x + e)^4 + 7*(16*a^5 - 65*a^4*b + 100*a^3*b^2 - 70*a^2*b^3 + 20*a*b^4 - b^5)*f*cosh(f*x + e)^2 + (6*a^5 - 25*a^4*b + 40*a^3*b^2 - 30*a^2*b^3 + 10*a*b^4 - b^5)*f)*sinh(f*x + e)^6 + (16*a^5 - 65*a^4*b + 100*a^3*b^2 - 70*a^2*b^3 + 20*a*b^4 - b^5)*f*cosh(f*x + e)^4 + 8*(99*(a^4*b - 4*a^3*b^2 + 6*a^2*b^3 - 4*a*b^4 + b^5)*f*cosh(f*x + e)^7 + 63*(2*a^5 - 7*a^4*b + 8*a^3*b^2 - 2*a^2*b^3 - 2*a*b^4 + b^5)*f*cosh(f*x + e)^5 + 7*(16*a^5 - 65*a^4*b + 100*a^3*b^2 - 70*a^2*b^3 + 20*a*b^4 - b^5)*f*cosh(f*x + e)^3 + 3*(6*a^5 - 25*a^4*b + 40*a^3*b^2 - 30*a^2*b^3 + 10*a*b^4 - b^5)*f*cosh(f*x + e))*sinh(f*x + e)^5 + (495*(a^4*b - 4*a^3*b^2 + 6*a^2*b^3 - 4*a*b^4 + b^5)*f*cosh(f*x + e)^8 + 420*(2*a^5 - 7*a^4*b + 8*a^3*b^2 - 2*a^2*b^3 - 2*a*b^4 + b^5)*f*cosh(f*x + e)^6 + 70*(16*a^5 - 65*a^4*b + 100*a^3*b^2 - 70*a^2*b^3 + 20*a*b^4 - b^5)*f*cosh(f*x + e)^4 + 60*(6*a^5 - 25*a^4*b + 40*a^3*b^2 - 30*a^2*b^3 + 10*a*b^4 - b^5)*f*cosh(f*x + e)^2 + (16*a^5 - 65*a^4*b + 100*a^3*b^2 - 70*a^2*b^3 + 20*a*b^4 - b^5)*f)*sinh(f*x + e)^4 + 2*(2*a^5 - 7*a^4*b + 8*a^3*b^2 - 2*a^2*b^3 - 2*a*b^4 + b^5)*f*cosh(f*x + e)^2 + 4*(55*(a^4*b - 4*a^3*b^2 + 6*a^2*b^3 - 4*a*b^4 + b^5)*f*cosh(f*x + e)^9 + 60*(2*a^5 - 7*a^4*b + 8*a^3*b^2 - 2*a^2*b^3 - 2*a*b^4 + b^5)*f*cosh(f*x + e)^7 + 14*(16*a^5 - 65*a^4*b + 100*a^3*b^2 - 70*a^2*b^3 + 20*a*b^4 - b^5)*f*cosh(f*x + e)^5 + 20*(6*a^5 - 25*a^4*b + 40*a^3*b^2 - 30*a^2*b^3 + 10*a*b^4 - b^5)*f*cosh(f*x + e)^3 + (16*a^5 - 65*a^4*b + 100*a^3*b^2 - 70*a^2*b^3 + 20*a*b^4 - b^5)*f*cosh(f*x + e))*sinh(f*x + e)^3 + 2*(33*(a^4*b - 4*a^3*b^2 + 6*a^2*b^3 - 4*a*b^4 + b^5)*f*cosh(f*x + e)^10 + 45*(2*a^5 - 7*a^4*b + 8*a^3*b^2 - 2*a^2*b^3 - 2*a*b^4 + b^5)*f*cosh(f*x + e)^8 + 14*(16*a^5 - 65*a^4*b + 100*a^3*b^2 - 70*a^2*b^3 + 20*a*b^4 - b^5)*f*cosh(f*x + e)^6 + 30*(6*a^5 - 25*a^4*b + 40*a^3*b^2 - 30*a^2*b^3 + 10*a*b^4 - b^5)*f*cosh(f*x + e)^4 + 3*(16*a^5 - 65*a^4*b + 100*a^3*b^2 - 70*a^2*b^3 + 20*a*b^4 - b^5)*f*cosh(f*x + e)^2 + (2*a^5 - 7*a^4*b + 8*a^3*b^2 - 2*a^2*b^3 - 2*a*b^4 + b^5)*f)*sinh(f*x + e)^2 + (a^4*b - 4*a^3*b^2 + 6*a^2*b^3 - 4*a*b^4 + b^5)*f + 4*(3*(a^4*b - 4*a^3*b^2 + 6*a^2*b^3 - 4*a*b^4 + b^5)*f*cosh(f*x + e)^11 + 5*(2*a^5 - 7*a^4*b + 8*a^3*b^2 - 2*a^2*b^3 - 2*a*b^4 + b^5)*f*cosh(f*x + e)^9 + 2*(16*a^5 - 65*a^4*b + 100*a^3*b^2 - 70*a^2*b^3 + 20*a*b^4 - b^5)*f*cosh(f*x + e)^7 + 6*(6*a^5 - 25*a^4*b + 40*a^3*b^2 - 30*a^2*b^3 + 10*a*b^4 - b^5)*f*cosh(f*x + e)^5 + (16*a^5 - 65*a^4*b + 100*a^3*b^2 - 70*a^2*b^3 + 20*a*b^4 - b^5)*f*cosh(f*x + e)^3 + (2*a^5 - 7*a^4*b + 8*a^3*b^2 - 2*a^2*b^3 - 2*a*b^4 + b^5)*f*cosh(f*x + e))*sinh(f*x + e))]","B",0
491,1,4050,0,0.738146," ","integrate(tanh(f*x+e)^3/(a+b*sinh(f*x+e)^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{8} + 8 \, {\left(2 \, a b + b^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + {\left(2 \, a b + b^{2}\right)} \sinh\left(f x + e\right)^{8} + 4 \, {\left(2 \, a^{2} + a b\right)} \cosh\left(f x + e\right)^{6} + 4 \, {\left(7 \, {\left(2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{2} + 2 \, a^{2} + a b\right)} \sinh\left(f x + e\right)^{6} + 8 \, {\left(7 \, {\left(2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(2 \, a^{2} + a b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(8 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{4} + 2 \, {\left(35 \, {\left(2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{4} + 30 \, {\left(2 \, a^{2} + a b\right)} \cosh\left(f x + e\right)^{2} + 8 \, a^{2} + 2 \, a b - b^{2}\right)} \sinh\left(f x + e\right)^{4} + 8 \, {\left(7 \, {\left(2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{5} + 10 \, {\left(2 \, a^{2} + a b\right)} \cosh\left(f x + e\right)^{3} + {\left(8 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 4 \, {\left(2 \, a^{2} + a b\right)} \cosh\left(f x + e\right)^{2} + 4 \, {\left(7 \, {\left(2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{6} + 15 \, {\left(2 \, a^{2} + a b\right)} \cosh\left(f x + e\right)^{4} + 3 \, {\left(8 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{2} + 2 \, a^{2} + a b\right)} \sinh\left(f x + e\right)^{2} + 2 \, a b + b^{2} + 8 \, {\left({\left(2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{7} + 3 \, {\left(2 \, a^{2} + a b\right)} \cosh\left(f x + e\right)^{5} + {\left(8 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{3} + {\left(2 \, a^{2} + a b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{a - b} \log\left(\frac{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(4 \, a - 3 \, b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + 4 \, a - 3 \, b\right)} \sinh\left(f x + e\right)^{2} - 4 \, \sqrt{2} \sqrt{a - b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} {\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right)\right)} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(4 \, a - 3 \, b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}{\cosh\left(f x + e\right)^{4} + 4 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + \sinh\left(f x + e\right)^{4} + 2 \, {\left(3 \, \cosh\left(f x + e\right)^{2} + 1\right)} \sinh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right)^{2} + 4 \, {\left(\cosh\left(f x + e\right)^{3} + \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + 1}\right) + 4 \, \sqrt{2} {\left({\left(2 \, a^{2} - a b - b^{2}\right)} \cosh\left(f x + e\right)^{5} + 5 \, {\left(2 \, a^{2} - a b - b^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{4} + {\left(2 \, a^{2} - a b - b^{2}\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(4 \, a^{2} - 5 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{3} + 2 \, {\left(5 \, {\left(2 \, a^{2} - a b - b^{2}\right)} \cosh\left(f x + e\right)^{2} + 4 \, a^{2} - 5 \, a b + b^{2}\right)} \sinh\left(f x + e\right)^{3} + 2 \, {\left(5 \, {\left(2 \, a^{2} - a b - b^{2}\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(4 \, a^{2} - 5 \, a b + b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{2} + {\left(2 \, a^{2} - a b - b^{2}\right)} \cosh\left(f x + e\right) + {\left(5 \, {\left(2 \, a^{2} - a b - b^{2}\right)} \cosh\left(f x + e\right)^{4} + 6 \, {\left(4 \, a^{2} - 5 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{2} + 2 \, a^{2} - a b - b^{2}\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{4 \, {\left({\left(a^{3} b - 3 \, a^{2} b^{2} + 3 \, a b^{3} - b^{4}\right)} f \cosh\left(f x + e\right)^{8} + 8 \, {\left(a^{3} b - 3 \, a^{2} b^{2} + 3 \, a b^{3} - b^{4}\right)} f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + {\left(a^{3} b - 3 \, a^{2} b^{2} + 3 \, a b^{3} - b^{4}\right)} f \sinh\left(f x + e\right)^{8} + 4 \, {\left(a^{4} - 3 \, a^{3} b + 3 \, a^{2} b^{2} - a b^{3}\right)} f \cosh\left(f x + e\right)^{6} + 4 \, {\left(7 \, {\left(a^{3} b - 3 \, a^{2} b^{2} + 3 \, a b^{3} - b^{4}\right)} f \cosh\left(f x + e\right)^{2} + {\left(a^{4} - 3 \, a^{3} b + 3 \, a^{2} b^{2} - a b^{3}\right)} f\right)} \sinh\left(f x + e\right)^{6} + 2 \, {\left(4 \, a^{4} - 13 \, a^{3} b + 15 \, a^{2} b^{2} - 7 \, a b^{3} + b^{4}\right)} f \cosh\left(f x + e\right)^{4} + 8 \, {\left(7 \, {\left(a^{3} b - 3 \, a^{2} b^{2} + 3 \, a b^{3} - b^{4}\right)} f \cosh\left(f x + e\right)^{3} + 3 \, {\left(a^{4} - 3 \, a^{3} b + 3 \, a^{2} b^{2} - a b^{3}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(35 \, {\left(a^{3} b - 3 \, a^{2} b^{2} + 3 \, a b^{3} - b^{4}\right)} f \cosh\left(f x + e\right)^{4} + 30 \, {\left(a^{4} - 3 \, a^{3} b + 3 \, a^{2} b^{2} - a b^{3}\right)} f \cosh\left(f x + e\right)^{2} + {\left(4 \, a^{4} - 13 \, a^{3} b + 15 \, a^{2} b^{2} - 7 \, a b^{3} + b^{4}\right)} f\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(a^{4} - 3 \, a^{3} b + 3 \, a^{2} b^{2} - a b^{3}\right)} f \cosh\left(f x + e\right)^{2} + 8 \, {\left(7 \, {\left(a^{3} b - 3 \, a^{2} b^{2} + 3 \, a b^{3} - b^{4}\right)} f \cosh\left(f x + e\right)^{5} + 10 \, {\left(a^{4} - 3 \, a^{3} b + 3 \, a^{2} b^{2} - a b^{3}\right)} f \cosh\left(f x + e\right)^{3} + {\left(4 \, a^{4} - 13 \, a^{3} b + 15 \, a^{2} b^{2} - 7 \, a b^{3} + b^{4}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 4 \, {\left(7 \, {\left(a^{3} b - 3 \, a^{2} b^{2} + 3 \, a b^{3} - b^{4}\right)} f \cosh\left(f x + e\right)^{6} + 15 \, {\left(a^{4} - 3 \, a^{3} b + 3 \, a^{2} b^{2} - a b^{3}\right)} f \cosh\left(f x + e\right)^{4} + 3 \, {\left(4 \, a^{4} - 13 \, a^{3} b + 15 \, a^{2} b^{2} - 7 \, a b^{3} + b^{4}\right)} f \cosh\left(f x + e\right)^{2} + {\left(a^{4} - 3 \, a^{3} b + 3 \, a^{2} b^{2} - a b^{3}\right)} f\right)} \sinh\left(f x + e\right)^{2} + {\left(a^{3} b - 3 \, a^{2} b^{2} + 3 \, a b^{3} - b^{4}\right)} f + 8 \, {\left({\left(a^{3} b - 3 \, a^{2} b^{2} + 3 \, a b^{3} - b^{4}\right)} f \cosh\left(f x + e\right)^{7} + 3 \, {\left(a^{4} - 3 \, a^{3} b + 3 \, a^{2} b^{2} - a b^{3}\right)} f \cosh\left(f x + e\right)^{5} + {\left(4 \, a^{4} - 13 \, a^{3} b + 15 \, a^{2} b^{2} - 7 \, a b^{3} + b^{4}\right)} f \cosh\left(f x + e\right)^{3} + {\left(a^{4} - 3 \, a^{3} b + 3 \, a^{2} b^{2} - a b^{3}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)}}, -\frac{{\left({\left(2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{8} + 8 \, {\left(2 \, a b + b^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + {\left(2 \, a b + b^{2}\right)} \sinh\left(f x + e\right)^{8} + 4 \, {\left(2 \, a^{2} + a b\right)} \cosh\left(f x + e\right)^{6} + 4 \, {\left(7 \, {\left(2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{2} + 2 \, a^{2} + a b\right)} \sinh\left(f x + e\right)^{6} + 8 \, {\left(7 \, {\left(2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(2 \, a^{2} + a b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(8 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{4} + 2 \, {\left(35 \, {\left(2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{4} + 30 \, {\left(2 \, a^{2} + a b\right)} \cosh\left(f x + e\right)^{2} + 8 \, a^{2} + 2 \, a b - b^{2}\right)} \sinh\left(f x + e\right)^{4} + 8 \, {\left(7 \, {\left(2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{5} + 10 \, {\left(2 \, a^{2} + a b\right)} \cosh\left(f x + e\right)^{3} + {\left(8 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 4 \, {\left(2 \, a^{2} + a b\right)} \cosh\left(f x + e\right)^{2} + 4 \, {\left(7 \, {\left(2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{6} + 15 \, {\left(2 \, a^{2} + a b\right)} \cosh\left(f x + e\right)^{4} + 3 \, {\left(8 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{2} + 2 \, a^{2} + a b\right)} \sinh\left(f x + e\right)^{2} + 2 \, a b + b^{2} + 8 \, {\left({\left(2 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{7} + 3 \, {\left(2 \, a^{2} + a b\right)} \cosh\left(f x + e\right)^{5} + {\left(8 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{3} + {\left(2 \, a^{2} + a b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{-a + b} \arctan\left(-\frac{\sqrt{2} \sqrt{-a + b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{2 \, {\left({\left(a - b\right)} \cosh\left(f x + e\right) + {\left(a - b\right)} \sinh\left(f x + e\right)\right)}}\right) - 2 \, \sqrt{2} {\left({\left(2 \, a^{2} - a b - b^{2}\right)} \cosh\left(f x + e\right)^{5} + 5 \, {\left(2 \, a^{2} - a b - b^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{4} + {\left(2 \, a^{2} - a b - b^{2}\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(4 \, a^{2} - 5 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{3} + 2 \, {\left(5 \, {\left(2 \, a^{2} - a b - b^{2}\right)} \cosh\left(f x + e\right)^{2} + 4 \, a^{2} - 5 \, a b + b^{2}\right)} \sinh\left(f x + e\right)^{3} + 2 \, {\left(5 \, {\left(2 \, a^{2} - a b - b^{2}\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(4 \, a^{2} - 5 \, a b + b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{2} + {\left(2 \, a^{2} - a b - b^{2}\right)} \cosh\left(f x + e\right) + {\left(5 \, {\left(2 \, a^{2} - a b - b^{2}\right)} \cosh\left(f x + e\right)^{4} + 6 \, {\left(4 \, a^{2} - 5 \, a b + b^{2}\right)} \cosh\left(f x + e\right)^{2} + 2 \, a^{2} - a b - b^{2}\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{2 \, {\left({\left(a^{3} b - 3 \, a^{2} b^{2} + 3 \, a b^{3} - b^{4}\right)} f \cosh\left(f x + e\right)^{8} + 8 \, {\left(a^{3} b - 3 \, a^{2} b^{2} + 3 \, a b^{3} - b^{4}\right)} f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + {\left(a^{3} b - 3 \, a^{2} b^{2} + 3 \, a b^{3} - b^{4}\right)} f \sinh\left(f x + e\right)^{8} + 4 \, {\left(a^{4} - 3 \, a^{3} b + 3 \, a^{2} b^{2} - a b^{3}\right)} f \cosh\left(f x + e\right)^{6} + 4 \, {\left(7 \, {\left(a^{3} b - 3 \, a^{2} b^{2} + 3 \, a b^{3} - b^{4}\right)} f \cosh\left(f x + e\right)^{2} + {\left(a^{4} - 3 \, a^{3} b + 3 \, a^{2} b^{2} - a b^{3}\right)} f\right)} \sinh\left(f x + e\right)^{6} + 2 \, {\left(4 \, a^{4} - 13 \, a^{3} b + 15 \, a^{2} b^{2} - 7 \, a b^{3} + b^{4}\right)} f \cosh\left(f x + e\right)^{4} + 8 \, {\left(7 \, {\left(a^{3} b - 3 \, a^{2} b^{2} + 3 \, a b^{3} - b^{4}\right)} f \cosh\left(f x + e\right)^{3} + 3 \, {\left(a^{4} - 3 \, a^{3} b + 3 \, a^{2} b^{2} - a b^{3}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(35 \, {\left(a^{3} b - 3 \, a^{2} b^{2} + 3 \, a b^{3} - b^{4}\right)} f \cosh\left(f x + e\right)^{4} + 30 \, {\left(a^{4} - 3 \, a^{3} b + 3 \, a^{2} b^{2} - a b^{3}\right)} f \cosh\left(f x + e\right)^{2} + {\left(4 \, a^{4} - 13 \, a^{3} b + 15 \, a^{2} b^{2} - 7 \, a b^{3} + b^{4}\right)} f\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(a^{4} - 3 \, a^{3} b + 3 \, a^{2} b^{2} - a b^{3}\right)} f \cosh\left(f x + e\right)^{2} + 8 \, {\left(7 \, {\left(a^{3} b - 3 \, a^{2} b^{2} + 3 \, a b^{3} - b^{4}\right)} f \cosh\left(f x + e\right)^{5} + 10 \, {\left(a^{4} - 3 \, a^{3} b + 3 \, a^{2} b^{2} - a b^{3}\right)} f \cosh\left(f x + e\right)^{3} + {\left(4 \, a^{4} - 13 \, a^{3} b + 15 \, a^{2} b^{2} - 7 \, a b^{3} + b^{4}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 4 \, {\left(7 \, {\left(a^{3} b - 3 \, a^{2} b^{2} + 3 \, a b^{3} - b^{4}\right)} f \cosh\left(f x + e\right)^{6} + 15 \, {\left(a^{4} - 3 \, a^{3} b + 3 \, a^{2} b^{2} - a b^{3}\right)} f \cosh\left(f x + e\right)^{4} + 3 \, {\left(4 \, a^{4} - 13 \, a^{3} b + 15 \, a^{2} b^{2} - 7 \, a b^{3} + b^{4}\right)} f \cosh\left(f x + e\right)^{2} + {\left(a^{4} - 3 \, a^{3} b + 3 \, a^{2} b^{2} - a b^{3}\right)} f\right)} \sinh\left(f x + e\right)^{2} + {\left(a^{3} b - 3 \, a^{2} b^{2} + 3 \, a b^{3} - b^{4}\right)} f + 8 \, {\left({\left(a^{3} b - 3 \, a^{2} b^{2} + 3 \, a b^{3} - b^{4}\right)} f \cosh\left(f x + e\right)^{7} + 3 \, {\left(a^{4} - 3 \, a^{3} b + 3 \, a^{2} b^{2} - a b^{3}\right)} f \cosh\left(f x + e\right)^{5} + {\left(4 \, a^{4} - 13 \, a^{3} b + 15 \, a^{2} b^{2} - 7 \, a b^{3} + b^{4}\right)} f \cosh\left(f x + e\right)^{3} + {\left(a^{4} - 3 \, a^{3} b + 3 \, a^{2} b^{2} - a b^{3}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)}}\right]"," ",0,"[1/4*(((2*a*b + b^2)*cosh(f*x + e)^8 + 8*(2*a*b + b^2)*cosh(f*x + e)*sinh(f*x + e)^7 + (2*a*b + b^2)*sinh(f*x + e)^8 + 4*(2*a^2 + a*b)*cosh(f*x + e)^6 + 4*(7*(2*a*b + b^2)*cosh(f*x + e)^2 + 2*a^2 + a*b)*sinh(f*x + e)^6 + 8*(7*(2*a*b + b^2)*cosh(f*x + e)^3 + 3*(2*a^2 + a*b)*cosh(f*x + e))*sinh(f*x + e)^5 + 2*(8*a^2 + 2*a*b - b^2)*cosh(f*x + e)^4 + 2*(35*(2*a*b + b^2)*cosh(f*x + e)^4 + 30*(2*a^2 + a*b)*cosh(f*x + e)^2 + 8*a^2 + 2*a*b - b^2)*sinh(f*x + e)^4 + 8*(7*(2*a*b + b^2)*cosh(f*x + e)^5 + 10*(2*a^2 + a*b)*cosh(f*x + e)^3 + (8*a^2 + 2*a*b - b^2)*cosh(f*x + e))*sinh(f*x + e)^3 + 4*(2*a^2 + a*b)*cosh(f*x + e)^2 + 4*(7*(2*a*b + b^2)*cosh(f*x + e)^6 + 15*(2*a^2 + a*b)*cosh(f*x + e)^4 + 3*(8*a^2 + 2*a*b - b^2)*cosh(f*x + e)^2 + 2*a^2 + a*b)*sinh(f*x + e)^2 + 2*a*b + b^2 + 8*((2*a*b + b^2)*cosh(f*x + e)^7 + 3*(2*a^2 + a*b)*cosh(f*x + e)^5 + (8*a^2 + 2*a*b - b^2)*cosh(f*x + e)^3 + (2*a^2 + a*b)*cosh(f*x + e))*sinh(f*x + e))*sqrt(a - b)*log((b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(4*a - 3*b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 4*a - 3*b)*sinh(f*x + e)^2 - 4*sqrt(2)*sqrt(a - b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))*(cosh(f*x + e) + sinh(f*x + e)) + 4*(b*cosh(f*x + e)^3 + (4*a - 3*b)*cosh(f*x + e))*sinh(f*x + e) + b)/(cosh(f*x + e)^4 + 4*cosh(f*x + e)*sinh(f*x + e)^3 + sinh(f*x + e)^4 + 2*(3*cosh(f*x + e)^2 + 1)*sinh(f*x + e)^2 + 2*cosh(f*x + e)^2 + 4*(cosh(f*x + e)^3 + cosh(f*x + e))*sinh(f*x + e) + 1)) + 4*sqrt(2)*((2*a^2 - a*b - b^2)*cosh(f*x + e)^5 + 5*(2*a^2 - a*b - b^2)*cosh(f*x + e)*sinh(f*x + e)^4 + (2*a^2 - a*b - b^2)*sinh(f*x + e)^5 + 2*(4*a^2 - 5*a*b + b^2)*cosh(f*x + e)^3 + 2*(5*(2*a^2 - a*b - b^2)*cosh(f*x + e)^2 + 4*a^2 - 5*a*b + b^2)*sinh(f*x + e)^3 + 2*(5*(2*a^2 - a*b - b^2)*cosh(f*x + e)^3 + 3*(4*a^2 - 5*a*b + b^2)*cosh(f*x + e))*sinh(f*x + e)^2 + (2*a^2 - a*b - b^2)*cosh(f*x + e) + (5*(2*a^2 - a*b - b^2)*cosh(f*x + e)^4 + 6*(4*a^2 - 5*a*b + b^2)*cosh(f*x + e)^2 + 2*a^2 - a*b - b^2)*sinh(f*x + e))*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/((a^3*b - 3*a^2*b^2 + 3*a*b^3 - b^4)*f*cosh(f*x + e)^8 + 8*(a^3*b - 3*a^2*b^2 + 3*a*b^3 - b^4)*f*cosh(f*x + e)*sinh(f*x + e)^7 + (a^3*b - 3*a^2*b^2 + 3*a*b^3 - b^4)*f*sinh(f*x + e)^8 + 4*(a^4 - 3*a^3*b + 3*a^2*b^2 - a*b^3)*f*cosh(f*x + e)^6 + 4*(7*(a^3*b - 3*a^2*b^2 + 3*a*b^3 - b^4)*f*cosh(f*x + e)^2 + (a^4 - 3*a^3*b + 3*a^2*b^2 - a*b^3)*f)*sinh(f*x + e)^6 + 2*(4*a^4 - 13*a^3*b + 15*a^2*b^2 - 7*a*b^3 + b^4)*f*cosh(f*x + e)^4 + 8*(7*(a^3*b - 3*a^2*b^2 + 3*a*b^3 - b^4)*f*cosh(f*x + e)^3 + 3*(a^4 - 3*a^3*b + 3*a^2*b^2 - a*b^3)*f*cosh(f*x + e))*sinh(f*x + e)^5 + 2*(35*(a^3*b - 3*a^2*b^2 + 3*a*b^3 - b^4)*f*cosh(f*x + e)^4 + 30*(a^4 - 3*a^3*b + 3*a^2*b^2 - a*b^3)*f*cosh(f*x + e)^2 + (4*a^4 - 13*a^3*b + 15*a^2*b^2 - 7*a*b^3 + b^4)*f)*sinh(f*x + e)^4 + 4*(a^4 - 3*a^3*b + 3*a^2*b^2 - a*b^3)*f*cosh(f*x + e)^2 + 8*(7*(a^3*b - 3*a^2*b^2 + 3*a*b^3 - b^4)*f*cosh(f*x + e)^5 + 10*(a^4 - 3*a^3*b + 3*a^2*b^2 - a*b^3)*f*cosh(f*x + e)^3 + (4*a^4 - 13*a^3*b + 15*a^2*b^2 - 7*a*b^3 + b^4)*f*cosh(f*x + e))*sinh(f*x + e)^3 + 4*(7*(a^3*b - 3*a^2*b^2 + 3*a*b^3 - b^4)*f*cosh(f*x + e)^6 + 15*(a^4 - 3*a^3*b + 3*a^2*b^2 - a*b^3)*f*cosh(f*x + e)^4 + 3*(4*a^4 - 13*a^3*b + 15*a^2*b^2 - 7*a*b^3 + b^4)*f*cosh(f*x + e)^2 + (a^4 - 3*a^3*b + 3*a^2*b^2 - a*b^3)*f)*sinh(f*x + e)^2 + (a^3*b - 3*a^2*b^2 + 3*a*b^3 - b^4)*f + 8*((a^3*b - 3*a^2*b^2 + 3*a*b^3 - b^4)*f*cosh(f*x + e)^7 + 3*(a^4 - 3*a^3*b + 3*a^2*b^2 - a*b^3)*f*cosh(f*x + e)^5 + (4*a^4 - 13*a^3*b + 15*a^2*b^2 - 7*a*b^3 + b^4)*f*cosh(f*x + e)^3 + (a^4 - 3*a^3*b + 3*a^2*b^2 - a*b^3)*f*cosh(f*x + e))*sinh(f*x + e)), -1/2*(((2*a*b + b^2)*cosh(f*x + e)^8 + 8*(2*a*b + b^2)*cosh(f*x + e)*sinh(f*x + e)^7 + (2*a*b + b^2)*sinh(f*x + e)^8 + 4*(2*a^2 + a*b)*cosh(f*x + e)^6 + 4*(7*(2*a*b + b^2)*cosh(f*x + e)^2 + 2*a^2 + a*b)*sinh(f*x + e)^6 + 8*(7*(2*a*b + b^2)*cosh(f*x + e)^3 + 3*(2*a^2 + a*b)*cosh(f*x + e))*sinh(f*x + e)^5 + 2*(8*a^2 + 2*a*b - b^2)*cosh(f*x + e)^4 + 2*(35*(2*a*b + b^2)*cosh(f*x + e)^4 + 30*(2*a^2 + a*b)*cosh(f*x + e)^2 + 8*a^2 + 2*a*b - b^2)*sinh(f*x + e)^4 + 8*(7*(2*a*b + b^2)*cosh(f*x + e)^5 + 10*(2*a^2 + a*b)*cosh(f*x + e)^3 + (8*a^2 + 2*a*b - b^2)*cosh(f*x + e))*sinh(f*x + e)^3 + 4*(2*a^2 + a*b)*cosh(f*x + e)^2 + 4*(7*(2*a*b + b^2)*cosh(f*x + e)^6 + 15*(2*a^2 + a*b)*cosh(f*x + e)^4 + 3*(8*a^2 + 2*a*b - b^2)*cosh(f*x + e)^2 + 2*a^2 + a*b)*sinh(f*x + e)^2 + 2*a*b + b^2 + 8*((2*a*b + b^2)*cosh(f*x + e)^7 + 3*(2*a^2 + a*b)*cosh(f*x + e)^5 + (8*a^2 + 2*a*b - b^2)*cosh(f*x + e)^3 + (2*a^2 + a*b)*cosh(f*x + e))*sinh(f*x + e))*sqrt(-a + b)*arctan(-1/2*sqrt(2)*sqrt(-a + b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/((a - b)*cosh(f*x + e) + (a - b)*sinh(f*x + e))) - 2*sqrt(2)*((2*a^2 - a*b - b^2)*cosh(f*x + e)^5 + 5*(2*a^2 - a*b - b^2)*cosh(f*x + e)*sinh(f*x + e)^4 + (2*a^2 - a*b - b^2)*sinh(f*x + e)^5 + 2*(4*a^2 - 5*a*b + b^2)*cosh(f*x + e)^3 + 2*(5*(2*a^2 - a*b - b^2)*cosh(f*x + e)^2 + 4*a^2 - 5*a*b + b^2)*sinh(f*x + e)^3 + 2*(5*(2*a^2 - a*b - b^2)*cosh(f*x + e)^3 + 3*(4*a^2 - 5*a*b + b^2)*cosh(f*x + e))*sinh(f*x + e)^2 + (2*a^2 - a*b - b^2)*cosh(f*x + e) + (5*(2*a^2 - a*b - b^2)*cosh(f*x + e)^4 + 6*(4*a^2 - 5*a*b + b^2)*cosh(f*x + e)^2 + 2*a^2 - a*b - b^2)*sinh(f*x + e))*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/((a^3*b - 3*a^2*b^2 + 3*a*b^3 - b^4)*f*cosh(f*x + e)^8 + 8*(a^3*b - 3*a^2*b^2 + 3*a*b^3 - b^4)*f*cosh(f*x + e)*sinh(f*x + e)^7 + (a^3*b - 3*a^2*b^2 + 3*a*b^3 - b^4)*f*sinh(f*x + e)^8 + 4*(a^4 - 3*a^3*b + 3*a^2*b^2 - a*b^3)*f*cosh(f*x + e)^6 + 4*(7*(a^3*b - 3*a^2*b^2 + 3*a*b^3 - b^4)*f*cosh(f*x + e)^2 + (a^4 - 3*a^3*b + 3*a^2*b^2 - a*b^3)*f)*sinh(f*x + e)^6 + 2*(4*a^4 - 13*a^3*b + 15*a^2*b^2 - 7*a*b^3 + b^4)*f*cosh(f*x + e)^4 + 8*(7*(a^3*b - 3*a^2*b^2 + 3*a*b^3 - b^4)*f*cosh(f*x + e)^3 + 3*(a^4 - 3*a^3*b + 3*a^2*b^2 - a*b^3)*f*cosh(f*x + e))*sinh(f*x + e)^5 + 2*(35*(a^3*b - 3*a^2*b^2 + 3*a*b^3 - b^4)*f*cosh(f*x + e)^4 + 30*(a^4 - 3*a^3*b + 3*a^2*b^2 - a*b^3)*f*cosh(f*x + e)^2 + (4*a^4 - 13*a^3*b + 15*a^2*b^2 - 7*a*b^3 + b^4)*f)*sinh(f*x + e)^4 + 4*(a^4 - 3*a^3*b + 3*a^2*b^2 - a*b^3)*f*cosh(f*x + e)^2 + 8*(7*(a^3*b - 3*a^2*b^2 + 3*a*b^3 - b^4)*f*cosh(f*x + e)^5 + 10*(a^4 - 3*a^3*b + 3*a^2*b^2 - a*b^3)*f*cosh(f*x + e)^3 + (4*a^4 - 13*a^3*b + 15*a^2*b^2 - 7*a*b^3 + b^4)*f*cosh(f*x + e))*sinh(f*x + e)^3 + 4*(7*(a^3*b - 3*a^2*b^2 + 3*a*b^3 - b^4)*f*cosh(f*x + e)^6 + 15*(a^4 - 3*a^3*b + 3*a^2*b^2 - a*b^3)*f*cosh(f*x + e)^4 + 3*(4*a^4 - 13*a^3*b + 15*a^2*b^2 - 7*a*b^3 + b^4)*f*cosh(f*x + e)^2 + (a^4 - 3*a^3*b + 3*a^2*b^2 - a*b^3)*f)*sinh(f*x + e)^2 + (a^3*b - 3*a^2*b^2 + 3*a*b^3 - b^4)*f + 8*((a^3*b - 3*a^2*b^2 + 3*a*b^3 - b^4)*f*cosh(f*x + e)^7 + 3*(a^4 - 3*a^3*b + 3*a^2*b^2 - a*b^3)*f*cosh(f*x + e)^5 + (4*a^4 - 13*a^3*b + 15*a^2*b^2 - 7*a*b^3 + b^4)*f*cosh(f*x + e)^3 + (a^4 - 3*a^3*b + 3*a^2*b^2 - a*b^3)*f*cosh(f*x + e))*sinh(f*x + e))]","B",0
492,1,1370,0,0.656941," ","integrate(tanh(f*x+e)/(a+b*sinh(f*x+e)^2)^(3/2),x, algorithm=""fricas"")","\left[-\frac{{\left(b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + 2 \, a - b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b\right)} \sqrt{a - b} \log\left(\frac{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(4 \, a - 3 \, b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + 4 \, a - 3 \, b\right)} \sinh\left(f x + e\right)^{2} + 4 \, \sqrt{2} \sqrt{a - b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} {\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right)\right)} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(4 \, a - 3 \, b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}{\cosh\left(f x + e\right)^{4} + 4 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + \sinh\left(f x + e\right)^{4} + 2 \, {\left(3 \, \cosh\left(f x + e\right)^{2} + 1\right)} \sinh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right)^{2} + 4 \, {\left(\cosh\left(f x + e\right)^{3} + \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + 1}\right) - 4 \, \sqrt{2} {\left({\left(a - b\right)} \cosh\left(f x + e\right) + {\left(a - b\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{2 \, {\left({\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} f \cosh\left(f x + e\right)^{4} + 4 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} f \sinh\left(f x + e\right)^{4} + 2 \, {\left(2 \, a^{3} - 5 \, a^{2} b + 4 \, a b^{2} - b^{3}\right)} f \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} f \cosh\left(f x + e\right)^{2} + {\left(2 \, a^{3} - 5 \, a^{2} b + 4 \, a b^{2} - b^{3}\right)} f\right)} \sinh\left(f x + e\right)^{2} + {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} f + 4 \, {\left({\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} f \cosh\left(f x + e\right)^{3} + {\left(2 \, a^{3} - 5 \, a^{2} b + 4 \, a b^{2} - b^{3}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)}}, -\frac{{\left(b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + 2 \, a - b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b\right)} \sqrt{-a + b} \arctan\left(-\frac{\sqrt{2} \sqrt{-a + b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{2 \, {\left({\left(a - b\right)} \cosh\left(f x + e\right) + {\left(a - b\right)} \sinh\left(f x + e\right)\right)}}\right) - 2 \, \sqrt{2} {\left({\left(a - b\right)} \cosh\left(f x + e\right) + {\left(a - b\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{{\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} f \cosh\left(f x + e\right)^{4} + 4 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} f \sinh\left(f x + e\right)^{4} + 2 \, {\left(2 \, a^{3} - 5 \, a^{2} b + 4 \, a b^{2} - b^{3}\right)} f \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} f \cosh\left(f x + e\right)^{2} + {\left(2 \, a^{3} - 5 \, a^{2} b + 4 \, a b^{2} - b^{3}\right)} f\right)} \sinh\left(f x + e\right)^{2} + {\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} f + 4 \, {\left({\left(a^{2} b - 2 \, a b^{2} + b^{3}\right)} f \cosh\left(f x + e\right)^{3} + {\left(2 \, a^{3} - 5 \, a^{2} b + 4 \, a b^{2} - b^{3}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)}\right]"," ",0,"[-1/2*((b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(2*a - b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 2*a - b)*sinh(f*x + e)^2 + 4*(b*cosh(f*x + e)^3 + (2*a - b)*cosh(f*x + e))*sinh(f*x + e) + b)*sqrt(a - b)*log((b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(4*a - 3*b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 4*a - 3*b)*sinh(f*x + e)^2 + 4*sqrt(2)*sqrt(a - b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))*(cosh(f*x + e) + sinh(f*x + e)) + 4*(b*cosh(f*x + e)^3 + (4*a - 3*b)*cosh(f*x + e))*sinh(f*x + e) + b)/(cosh(f*x + e)^4 + 4*cosh(f*x + e)*sinh(f*x + e)^3 + sinh(f*x + e)^4 + 2*(3*cosh(f*x + e)^2 + 1)*sinh(f*x + e)^2 + 2*cosh(f*x + e)^2 + 4*(cosh(f*x + e)^3 + cosh(f*x + e))*sinh(f*x + e) + 1)) - 4*sqrt(2)*((a - b)*cosh(f*x + e) + (a - b)*sinh(f*x + e))*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/((a^2*b - 2*a*b^2 + b^3)*f*cosh(f*x + e)^4 + 4*(a^2*b - 2*a*b^2 + b^3)*f*cosh(f*x + e)*sinh(f*x + e)^3 + (a^2*b - 2*a*b^2 + b^3)*f*sinh(f*x + e)^4 + 2*(2*a^3 - 5*a^2*b + 4*a*b^2 - b^3)*f*cosh(f*x + e)^2 + 2*(3*(a^2*b - 2*a*b^2 + b^3)*f*cosh(f*x + e)^2 + (2*a^3 - 5*a^2*b + 4*a*b^2 - b^3)*f)*sinh(f*x + e)^2 + (a^2*b - 2*a*b^2 + b^3)*f + 4*((a^2*b - 2*a*b^2 + b^3)*f*cosh(f*x + e)^3 + (2*a^3 - 5*a^2*b + 4*a*b^2 - b^3)*f*cosh(f*x + e))*sinh(f*x + e)), -((b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(2*a - b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 2*a - b)*sinh(f*x + e)^2 + 4*(b*cosh(f*x + e)^3 + (2*a - b)*cosh(f*x + e))*sinh(f*x + e) + b)*sqrt(-a + b)*arctan(-1/2*sqrt(2)*sqrt(-a + b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/((a - b)*cosh(f*x + e) + (a - b)*sinh(f*x + e))) - 2*sqrt(2)*((a - b)*cosh(f*x + e) + (a - b)*sinh(f*x + e))*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/((a^2*b - 2*a*b^2 + b^3)*f*cosh(f*x + e)^4 + 4*(a^2*b - 2*a*b^2 + b^3)*f*cosh(f*x + e)*sinh(f*x + e)^3 + (a^2*b - 2*a*b^2 + b^3)*f*sinh(f*x + e)^4 + 2*(2*a^3 - 5*a^2*b + 4*a*b^2 - b^3)*f*cosh(f*x + e)^2 + 2*(3*(a^2*b - 2*a*b^2 + b^3)*f*cosh(f*x + e)^2 + (2*a^3 - 5*a^2*b + 4*a*b^2 - b^3)*f)*sinh(f*x + e)^2 + (a^2*b - 2*a*b^2 + b^3)*f + 4*((a^2*b - 2*a*b^2 + b^3)*f*cosh(f*x + e)^3 + (2*a^3 - 5*a^2*b + 4*a*b^2 - b^3)*f*cosh(f*x + e))*sinh(f*x + e))]","B",0
493,1,1137,0,0.547641," ","integrate(coth(f*x+e)/(a+b*sinh(f*x+e)^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left(b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + 2 \, a - b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b\right)} \sqrt{a} \log\left(\frac{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(4 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + 4 \, a - b\right)} \sinh\left(f x + e\right)^{2} - 4 \, \sqrt{2} \sqrt{a} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} {\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right)\right)} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(4 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}{\cosh\left(f x + e\right)^{4} + 4 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + \sinh\left(f x + e\right)^{4} + 2 \, {\left(3 \, \cosh\left(f x + e\right)^{2} - 1\right)} \sinh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right)^{2} + 4 \, {\left(\cosh\left(f x + e\right)^{3} - \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + 1}\right) + 4 \, \sqrt{2} {\left(a \cosh\left(f x + e\right) + a \sinh\left(f x + e\right)\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{2 \, {\left(a^{2} b f \cosh\left(f x + e\right)^{4} + 4 \, a^{2} b f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + a^{2} b f \sinh\left(f x + e\right)^{4} + a^{2} b f + 2 \, {\left(2 \, a^{3} - a^{2} b\right)} f \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, a^{2} b f \cosh\left(f x + e\right)^{2} + {\left(2 \, a^{3} - a^{2} b\right)} f\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(a^{2} b f \cosh\left(f x + e\right)^{3} + {\left(2 \, a^{3} - a^{2} b\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)}}, \frac{{\left(b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + 2 \, a - b\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{2} \sqrt{-a} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{2 \, {\left(a \cosh\left(f x + e\right) + a \sinh\left(f x + e\right)\right)}}\right) + 2 \, \sqrt{2} {\left(a \cosh\left(f x + e\right) + a \sinh\left(f x + e\right)\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{a^{2} b f \cosh\left(f x + e\right)^{4} + 4 \, a^{2} b f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + a^{2} b f \sinh\left(f x + e\right)^{4} + a^{2} b f + 2 \, {\left(2 \, a^{3} - a^{2} b\right)} f \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, a^{2} b f \cosh\left(f x + e\right)^{2} + {\left(2 \, a^{3} - a^{2} b\right)} f\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(a^{2} b f \cosh\left(f x + e\right)^{3} + {\left(2 \, a^{3} - a^{2} b\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)}\right]"," ",0,"[1/2*((b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(2*a - b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 2*a - b)*sinh(f*x + e)^2 + 4*(b*cosh(f*x + e)^3 + (2*a - b)*cosh(f*x + e))*sinh(f*x + e) + b)*sqrt(a)*log((b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(4*a - b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 4*a - b)*sinh(f*x + e)^2 - 4*sqrt(2)*sqrt(a)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))*(cosh(f*x + e) + sinh(f*x + e)) + 4*(b*cosh(f*x + e)^3 + (4*a - b)*cosh(f*x + e))*sinh(f*x + e) + b)/(cosh(f*x + e)^4 + 4*cosh(f*x + e)*sinh(f*x + e)^3 + sinh(f*x + e)^4 + 2*(3*cosh(f*x + e)^2 - 1)*sinh(f*x + e)^2 - 2*cosh(f*x + e)^2 + 4*(cosh(f*x + e)^3 - cosh(f*x + e))*sinh(f*x + e) + 1)) + 4*sqrt(2)*(a*cosh(f*x + e) + a*sinh(f*x + e))*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/(a^2*b*f*cosh(f*x + e)^4 + 4*a^2*b*f*cosh(f*x + e)*sinh(f*x + e)^3 + a^2*b*f*sinh(f*x + e)^4 + a^2*b*f + 2*(2*a^3 - a^2*b)*f*cosh(f*x + e)^2 + 2*(3*a^2*b*f*cosh(f*x + e)^2 + (2*a^3 - a^2*b)*f)*sinh(f*x + e)^2 + 4*(a^2*b*f*cosh(f*x + e)^3 + (2*a^3 - a^2*b)*f*cosh(f*x + e))*sinh(f*x + e)), ((b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(2*a - b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 2*a - b)*sinh(f*x + e)^2 + 4*(b*cosh(f*x + e)^3 + (2*a - b)*cosh(f*x + e))*sinh(f*x + e) + b)*sqrt(-a)*arctan(1/2*sqrt(2)*sqrt(-a)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/(a*cosh(f*x + e) + a*sinh(f*x + e))) + 2*sqrt(2)*(a*cosh(f*x + e) + a*sinh(f*x + e))*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/(a^2*b*f*cosh(f*x + e)^4 + 4*a^2*b*f*cosh(f*x + e)*sinh(f*x + e)^3 + a^2*b*f*sinh(f*x + e)^4 + a^2*b*f + 2*(2*a^3 - a^2*b)*f*cosh(f*x + e)^2 + 2*(3*a^2*b*f*cosh(f*x + e)^2 + (2*a^3 - a^2*b)*f)*sinh(f*x + e)^2 + 4*(a^2*b*f*cosh(f*x + e)^3 + (2*a^3 - a^2*b)*f*cosh(f*x + e))*sinh(f*x + e))]","B",0
494,1,3228,0,0.679995," ","integrate(coth(f*x+e)^3/(a+b*sinh(f*x+e)^2)^(3/2),x, algorithm=""fricas"")","\left[-\frac{{\left({\left(2 \, a b - 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{8} + 8 \, {\left(2 \, a b - 3 \, b^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + {\left(2 \, a b - 3 \, b^{2}\right)} \sinh\left(f x + e\right)^{8} + 4 \, {\left(2 \, a^{2} - 5 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{6} + 4 \, {\left(7 \, {\left(2 \, a b - 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + 2 \, a^{2} - 5 \, a b + 3 \, b^{2}\right)} \sinh\left(f x + e\right)^{6} + 8 \, {\left(7 \, {\left(2 \, a b - 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(2 \, a^{2} - 5 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} - 2 \, {\left(8 \, a^{2} - 18 \, a b + 9 \, b^{2}\right)} \cosh\left(f x + e\right)^{4} + 2 \, {\left(35 \, {\left(2 \, a b - 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{4} + 30 \, {\left(2 \, a^{2} - 5 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} - 8 \, a^{2} + 18 \, a b - 9 \, b^{2}\right)} \sinh\left(f x + e\right)^{4} + 8 \, {\left(7 \, {\left(2 \, a b - 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{5} + 10 \, {\left(2 \, a^{2} - 5 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{3} - {\left(8 \, a^{2} - 18 \, a b + 9 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 4 \, {\left(2 \, a^{2} - 5 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + 4 \, {\left(7 \, {\left(2 \, a b - 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{6} + 15 \, {\left(2 \, a^{2} - 5 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{4} - 3 \, {\left(8 \, a^{2} - 18 \, a b + 9 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + 2 \, a^{2} - 5 \, a b + 3 \, b^{2}\right)} \sinh\left(f x + e\right)^{2} + 2 \, a b - 3 \, b^{2} + 8 \, {\left({\left(2 \, a b - 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{7} + 3 \, {\left(2 \, a^{2} - 5 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{5} - {\left(8 \, a^{2} - 18 \, a b + 9 \, b^{2}\right)} \cosh\left(f x + e\right)^{3} + {\left(2 \, a^{2} - 5 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{a} \log\left(\frac{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(4 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + 4 \, a - b\right)} \sinh\left(f x + e\right)^{2} + 4 \, \sqrt{2} \sqrt{a} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} {\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right)\right)} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(4 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}{\cosh\left(f x + e\right)^{4} + 4 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + \sinh\left(f x + e\right)^{4} + 2 \, {\left(3 \, \cosh\left(f x + e\right)^{2} - 1\right)} \sinh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right)^{2} + 4 \, {\left(\cosh\left(f x + e\right)^{3} - \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + 1}\right) - 4 \, \sqrt{2} {\left({\left(2 \, a^{2} - 3 \, a b\right)} \cosh\left(f x + e\right)^{5} + 5 \, {\left(2 \, a^{2} - 3 \, a b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{4} + {\left(2 \, a^{2} - 3 \, a b\right)} \sinh\left(f x + e\right)^{5} - 2 \, {\left(4 \, a^{2} - 3 \, a b\right)} \cosh\left(f x + e\right)^{3} + 2 \, {\left(5 \, {\left(2 \, a^{2} - 3 \, a b\right)} \cosh\left(f x + e\right)^{2} - 4 \, a^{2} + 3 \, a b\right)} \sinh\left(f x + e\right)^{3} + 2 \, {\left(5 \, {\left(2 \, a^{2} - 3 \, a b\right)} \cosh\left(f x + e\right)^{3} - 3 \, {\left(4 \, a^{2} - 3 \, a b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{2} + {\left(2 \, a^{2} - 3 \, a b\right)} \cosh\left(f x + e\right) + {\left(5 \, {\left(2 \, a^{2} - 3 \, a b\right)} \cosh\left(f x + e\right)^{4} - 6 \, {\left(4 \, a^{2} - 3 \, a b\right)} \cosh\left(f x + e\right)^{2} + 2 \, a^{2} - 3 \, a b\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{4 \, {\left(a^{3} b f \cosh\left(f x + e\right)^{8} + 8 \, a^{3} b f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + a^{3} b f \sinh\left(f x + e\right)^{8} + 4 \, {\left(a^{4} - a^{3} b\right)} f \cosh\left(f x + e\right)^{6} + 4 \, {\left(7 \, a^{3} b f \cosh\left(f x + e\right)^{2} + {\left(a^{4} - a^{3} b\right)} f\right)} \sinh\left(f x + e\right)^{6} - 2 \, {\left(4 \, a^{4} - 3 \, a^{3} b\right)} f \cosh\left(f x + e\right)^{4} + 8 \, {\left(7 \, a^{3} b f \cosh\left(f x + e\right)^{3} + 3 \, {\left(a^{4} - a^{3} b\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + a^{3} b f + 2 \, {\left(35 \, a^{3} b f \cosh\left(f x + e\right)^{4} + 30 \, {\left(a^{4} - a^{3} b\right)} f \cosh\left(f x + e\right)^{2} - {\left(4 \, a^{4} - 3 \, a^{3} b\right)} f\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(a^{4} - a^{3} b\right)} f \cosh\left(f x + e\right)^{2} + 8 \, {\left(7 \, a^{3} b f \cosh\left(f x + e\right)^{5} + 10 \, {\left(a^{4} - a^{3} b\right)} f \cosh\left(f x + e\right)^{3} - {\left(4 \, a^{4} - 3 \, a^{3} b\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 4 \, {\left(7 \, a^{3} b f \cosh\left(f x + e\right)^{6} + 15 \, {\left(a^{4} - a^{3} b\right)} f \cosh\left(f x + e\right)^{4} - 3 \, {\left(4 \, a^{4} - 3 \, a^{3} b\right)} f \cosh\left(f x + e\right)^{2} + {\left(a^{4} - a^{3} b\right)} f\right)} \sinh\left(f x + e\right)^{2} + 8 \, {\left(a^{3} b f \cosh\left(f x + e\right)^{7} + 3 \, {\left(a^{4} - a^{3} b\right)} f \cosh\left(f x + e\right)^{5} - {\left(4 \, a^{4} - 3 \, a^{3} b\right)} f \cosh\left(f x + e\right)^{3} + {\left(a^{4} - a^{3} b\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)}}, \frac{{\left({\left(2 \, a b - 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{8} + 8 \, {\left(2 \, a b - 3 \, b^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + {\left(2 \, a b - 3 \, b^{2}\right)} \sinh\left(f x + e\right)^{8} + 4 \, {\left(2 \, a^{2} - 5 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{6} + 4 \, {\left(7 \, {\left(2 \, a b - 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + 2 \, a^{2} - 5 \, a b + 3 \, b^{2}\right)} \sinh\left(f x + e\right)^{6} + 8 \, {\left(7 \, {\left(2 \, a b - 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(2 \, a^{2} - 5 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} - 2 \, {\left(8 \, a^{2} - 18 \, a b + 9 \, b^{2}\right)} \cosh\left(f x + e\right)^{4} + 2 \, {\left(35 \, {\left(2 \, a b - 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{4} + 30 \, {\left(2 \, a^{2} - 5 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} - 8 \, a^{2} + 18 \, a b - 9 \, b^{2}\right)} \sinh\left(f x + e\right)^{4} + 8 \, {\left(7 \, {\left(2 \, a b - 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{5} + 10 \, {\left(2 \, a^{2} - 5 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{3} - {\left(8 \, a^{2} - 18 \, a b + 9 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 4 \, {\left(2 \, a^{2} - 5 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + 4 \, {\left(7 \, {\left(2 \, a b - 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{6} + 15 \, {\left(2 \, a^{2} - 5 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{4} - 3 \, {\left(8 \, a^{2} - 18 \, a b + 9 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + 2 \, a^{2} - 5 \, a b + 3 \, b^{2}\right)} \sinh\left(f x + e\right)^{2} + 2 \, a b - 3 \, b^{2} + 8 \, {\left({\left(2 \, a b - 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{7} + 3 \, {\left(2 \, a^{2} - 5 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{5} - {\left(8 \, a^{2} - 18 \, a b + 9 \, b^{2}\right)} \cosh\left(f x + e\right)^{3} + {\left(2 \, a^{2} - 5 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{2} \sqrt{-a} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{2 \, {\left(a \cosh\left(f x + e\right) + a \sinh\left(f x + e\right)\right)}}\right) + 2 \, \sqrt{2} {\left({\left(2 \, a^{2} - 3 \, a b\right)} \cosh\left(f x + e\right)^{5} + 5 \, {\left(2 \, a^{2} - 3 \, a b\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{4} + {\left(2 \, a^{2} - 3 \, a b\right)} \sinh\left(f x + e\right)^{5} - 2 \, {\left(4 \, a^{2} - 3 \, a b\right)} \cosh\left(f x + e\right)^{3} + 2 \, {\left(5 \, {\left(2 \, a^{2} - 3 \, a b\right)} \cosh\left(f x + e\right)^{2} - 4 \, a^{2} + 3 \, a b\right)} \sinh\left(f x + e\right)^{3} + 2 \, {\left(5 \, {\left(2 \, a^{2} - 3 \, a b\right)} \cosh\left(f x + e\right)^{3} - 3 \, {\left(4 \, a^{2} - 3 \, a b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{2} + {\left(2 \, a^{2} - 3 \, a b\right)} \cosh\left(f x + e\right) + {\left(5 \, {\left(2 \, a^{2} - 3 \, a b\right)} \cosh\left(f x + e\right)^{4} - 6 \, {\left(4 \, a^{2} - 3 \, a b\right)} \cosh\left(f x + e\right)^{2} + 2 \, a^{2} - 3 \, a b\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{2 \, {\left(a^{3} b f \cosh\left(f x + e\right)^{8} + 8 \, a^{3} b f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + a^{3} b f \sinh\left(f x + e\right)^{8} + 4 \, {\left(a^{4} - a^{3} b\right)} f \cosh\left(f x + e\right)^{6} + 4 \, {\left(7 \, a^{3} b f \cosh\left(f x + e\right)^{2} + {\left(a^{4} - a^{3} b\right)} f\right)} \sinh\left(f x + e\right)^{6} - 2 \, {\left(4 \, a^{4} - 3 \, a^{3} b\right)} f \cosh\left(f x + e\right)^{4} + 8 \, {\left(7 \, a^{3} b f \cosh\left(f x + e\right)^{3} + 3 \, {\left(a^{4} - a^{3} b\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + a^{3} b f + 2 \, {\left(35 \, a^{3} b f \cosh\left(f x + e\right)^{4} + 30 \, {\left(a^{4} - a^{3} b\right)} f \cosh\left(f x + e\right)^{2} - {\left(4 \, a^{4} - 3 \, a^{3} b\right)} f\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(a^{4} - a^{3} b\right)} f \cosh\left(f x + e\right)^{2} + 8 \, {\left(7 \, a^{3} b f \cosh\left(f x + e\right)^{5} + 10 \, {\left(a^{4} - a^{3} b\right)} f \cosh\left(f x + e\right)^{3} - {\left(4 \, a^{4} - 3 \, a^{3} b\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 4 \, {\left(7 \, a^{3} b f \cosh\left(f x + e\right)^{6} + 15 \, {\left(a^{4} - a^{3} b\right)} f \cosh\left(f x + e\right)^{4} - 3 \, {\left(4 \, a^{4} - 3 \, a^{3} b\right)} f \cosh\left(f x + e\right)^{2} + {\left(a^{4} - a^{3} b\right)} f\right)} \sinh\left(f x + e\right)^{2} + 8 \, {\left(a^{3} b f \cosh\left(f x + e\right)^{7} + 3 \, {\left(a^{4} - a^{3} b\right)} f \cosh\left(f x + e\right)^{5} - {\left(4 \, a^{4} - 3 \, a^{3} b\right)} f \cosh\left(f x + e\right)^{3} + {\left(a^{4} - a^{3} b\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)}}\right]"," ",0,"[-1/4*(((2*a*b - 3*b^2)*cosh(f*x + e)^8 + 8*(2*a*b - 3*b^2)*cosh(f*x + e)*sinh(f*x + e)^7 + (2*a*b - 3*b^2)*sinh(f*x + e)^8 + 4*(2*a^2 - 5*a*b + 3*b^2)*cosh(f*x + e)^6 + 4*(7*(2*a*b - 3*b^2)*cosh(f*x + e)^2 + 2*a^2 - 5*a*b + 3*b^2)*sinh(f*x + e)^6 + 8*(7*(2*a*b - 3*b^2)*cosh(f*x + e)^3 + 3*(2*a^2 - 5*a*b + 3*b^2)*cosh(f*x + e))*sinh(f*x + e)^5 - 2*(8*a^2 - 18*a*b + 9*b^2)*cosh(f*x + e)^4 + 2*(35*(2*a*b - 3*b^2)*cosh(f*x + e)^4 + 30*(2*a^2 - 5*a*b + 3*b^2)*cosh(f*x + e)^2 - 8*a^2 + 18*a*b - 9*b^2)*sinh(f*x + e)^4 + 8*(7*(2*a*b - 3*b^2)*cosh(f*x + e)^5 + 10*(2*a^2 - 5*a*b + 3*b^2)*cosh(f*x + e)^3 - (8*a^2 - 18*a*b + 9*b^2)*cosh(f*x + e))*sinh(f*x + e)^3 + 4*(2*a^2 - 5*a*b + 3*b^2)*cosh(f*x + e)^2 + 4*(7*(2*a*b - 3*b^2)*cosh(f*x + e)^6 + 15*(2*a^2 - 5*a*b + 3*b^2)*cosh(f*x + e)^4 - 3*(8*a^2 - 18*a*b + 9*b^2)*cosh(f*x + e)^2 + 2*a^2 - 5*a*b + 3*b^2)*sinh(f*x + e)^2 + 2*a*b - 3*b^2 + 8*((2*a*b - 3*b^2)*cosh(f*x + e)^7 + 3*(2*a^2 - 5*a*b + 3*b^2)*cosh(f*x + e)^5 - (8*a^2 - 18*a*b + 9*b^2)*cosh(f*x + e)^3 + (2*a^2 - 5*a*b + 3*b^2)*cosh(f*x + e))*sinh(f*x + e))*sqrt(a)*log((b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(4*a - b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 4*a - b)*sinh(f*x + e)^2 + 4*sqrt(2)*sqrt(a)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))*(cosh(f*x + e) + sinh(f*x + e)) + 4*(b*cosh(f*x + e)^3 + (4*a - b)*cosh(f*x + e))*sinh(f*x + e) + b)/(cosh(f*x + e)^4 + 4*cosh(f*x + e)*sinh(f*x + e)^3 + sinh(f*x + e)^4 + 2*(3*cosh(f*x + e)^2 - 1)*sinh(f*x + e)^2 - 2*cosh(f*x + e)^2 + 4*(cosh(f*x + e)^3 - cosh(f*x + e))*sinh(f*x + e) + 1)) - 4*sqrt(2)*((2*a^2 - 3*a*b)*cosh(f*x + e)^5 + 5*(2*a^2 - 3*a*b)*cosh(f*x + e)*sinh(f*x + e)^4 + (2*a^2 - 3*a*b)*sinh(f*x + e)^5 - 2*(4*a^2 - 3*a*b)*cosh(f*x + e)^3 + 2*(5*(2*a^2 - 3*a*b)*cosh(f*x + e)^2 - 4*a^2 + 3*a*b)*sinh(f*x + e)^3 + 2*(5*(2*a^2 - 3*a*b)*cosh(f*x + e)^3 - 3*(4*a^2 - 3*a*b)*cosh(f*x + e))*sinh(f*x + e)^2 + (2*a^2 - 3*a*b)*cosh(f*x + e) + (5*(2*a^2 - 3*a*b)*cosh(f*x + e)^4 - 6*(4*a^2 - 3*a*b)*cosh(f*x + e)^2 + 2*a^2 - 3*a*b)*sinh(f*x + e))*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/(a^3*b*f*cosh(f*x + e)^8 + 8*a^3*b*f*cosh(f*x + e)*sinh(f*x + e)^7 + a^3*b*f*sinh(f*x + e)^8 + 4*(a^4 - a^3*b)*f*cosh(f*x + e)^6 + 4*(7*a^3*b*f*cosh(f*x + e)^2 + (a^4 - a^3*b)*f)*sinh(f*x + e)^6 - 2*(4*a^4 - 3*a^3*b)*f*cosh(f*x + e)^4 + 8*(7*a^3*b*f*cosh(f*x + e)^3 + 3*(a^4 - a^3*b)*f*cosh(f*x + e))*sinh(f*x + e)^5 + a^3*b*f + 2*(35*a^3*b*f*cosh(f*x + e)^4 + 30*(a^4 - a^3*b)*f*cosh(f*x + e)^2 - (4*a^4 - 3*a^3*b)*f)*sinh(f*x + e)^4 + 4*(a^4 - a^3*b)*f*cosh(f*x + e)^2 + 8*(7*a^3*b*f*cosh(f*x + e)^5 + 10*(a^4 - a^3*b)*f*cosh(f*x + e)^3 - (4*a^4 - 3*a^3*b)*f*cosh(f*x + e))*sinh(f*x + e)^3 + 4*(7*a^3*b*f*cosh(f*x + e)^6 + 15*(a^4 - a^3*b)*f*cosh(f*x + e)^4 - 3*(4*a^4 - 3*a^3*b)*f*cosh(f*x + e)^2 + (a^4 - a^3*b)*f)*sinh(f*x + e)^2 + 8*(a^3*b*f*cosh(f*x + e)^7 + 3*(a^4 - a^3*b)*f*cosh(f*x + e)^5 - (4*a^4 - 3*a^3*b)*f*cosh(f*x + e)^3 + (a^4 - a^3*b)*f*cosh(f*x + e))*sinh(f*x + e)), 1/2*(((2*a*b - 3*b^2)*cosh(f*x + e)^8 + 8*(2*a*b - 3*b^2)*cosh(f*x + e)*sinh(f*x + e)^7 + (2*a*b - 3*b^2)*sinh(f*x + e)^8 + 4*(2*a^2 - 5*a*b + 3*b^2)*cosh(f*x + e)^6 + 4*(7*(2*a*b - 3*b^2)*cosh(f*x + e)^2 + 2*a^2 - 5*a*b + 3*b^2)*sinh(f*x + e)^6 + 8*(7*(2*a*b - 3*b^2)*cosh(f*x + e)^3 + 3*(2*a^2 - 5*a*b + 3*b^2)*cosh(f*x + e))*sinh(f*x + e)^5 - 2*(8*a^2 - 18*a*b + 9*b^2)*cosh(f*x + e)^4 + 2*(35*(2*a*b - 3*b^2)*cosh(f*x + e)^4 + 30*(2*a^2 - 5*a*b + 3*b^2)*cosh(f*x + e)^2 - 8*a^2 + 18*a*b - 9*b^2)*sinh(f*x + e)^4 + 8*(7*(2*a*b - 3*b^2)*cosh(f*x + e)^5 + 10*(2*a^2 - 5*a*b + 3*b^2)*cosh(f*x + e)^3 - (8*a^2 - 18*a*b + 9*b^2)*cosh(f*x + e))*sinh(f*x + e)^3 + 4*(2*a^2 - 5*a*b + 3*b^2)*cosh(f*x + e)^2 + 4*(7*(2*a*b - 3*b^2)*cosh(f*x + e)^6 + 15*(2*a^2 - 5*a*b + 3*b^2)*cosh(f*x + e)^4 - 3*(8*a^2 - 18*a*b + 9*b^2)*cosh(f*x + e)^2 + 2*a^2 - 5*a*b + 3*b^2)*sinh(f*x + e)^2 + 2*a*b - 3*b^2 + 8*((2*a*b - 3*b^2)*cosh(f*x + e)^7 + 3*(2*a^2 - 5*a*b + 3*b^2)*cosh(f*x + e)^5 - (8*a^2 - 18*a*b + 9*b^2)*cosh(f*x + e)^3 + (2*a^2 - 5*a*b + 3*b^2)*cosh(f*x + e))*sinh(f*x + e))*sqrt(-a)*arctan(1/2*sqrt(2)*sqrt(-a)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/(a*cosh(f*x + e) + a*sinh(f*x + e))) + 2*sqrt(2)*((2*a^2 - 3*a*b)*cosh(f*x + e)^5 + 5*(2*a^2 - 3*a*b)*cosh(f*x + e)*sinh(f*x + e)^4 + (2*a^2 - 3*a*b)*sinh(f*x + e)^5 - 2*(4*a^2 - 3*a*b)*cosh(f*x + e)^3 + 2*(5*(2*a^2 - 3*a*b)*cosh(f*x + e)^2 - 4*a^2 + 3*a*b)*sinh(f*x + e)^3 + 2*(5*(2*a^2 - 3*a*b)*cosh(f*x + e)^3 - 3*(4*a^2 - 3*a*b)*cosh(f*x + e))*sinh(f*x + e)^2 + (2*a^2 - 3*a*b)*cosh(f*x + e) + (5*(2*a^2 - 3*a*b)*cosh(f*x + e)^4 - 6*(4*a^2 - 3*a*b)*cosh(f*x + e)^2 + 2*a^2 - 3*a*b)*sinh(f*x + e))*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/(a^3*b*f*cosh(f*x + e)^8 + 8*a^3*b*f*cosh(f*x + e)*sinh(f*x + e)^7 + a^3*b*f*sinh(f*x + e)^8 + 4*(a^4 - a^3*b)*f*cosh(f*x + e)^6 + 4*(7*a^3*b*f*cosh(f*x + e)^2 + (a^4 - a^3*b)*f)*sinh(f*x + e)^6 - 2*(4*a^4 - 3*a^3*b)*f*cosh(f*x + e)^4 + 8*(7*a^3*b*f*cosh(f*x + e)^3 + 3*(a^4 - a^3*b)*f*cosh(f*x + e))*sinh(f*x + e)^5 + a^3*b*f + 2*(35*a^3*b*f*cosh(f*x + e)^4 + 30*(a^4 - a^3*b)*f*cosh(f*x + e)^2 - (4*a^4 - 3*a^3*b)*f)*sinh(f*x + e)^4 + 4*(a^4 - a^3*b)*f*cosh(f*x + e)^2 + 8*(7*a^3*b*f*cosh(f*x + e)^5 + 10*(a^4 - a^3*b)*f*cosh(f*x + e)^3 - (4*a^4 - 3*a^3*b)*f*cosh(f*x + e))*sinh(f*x + e)^3 + 4*(7*a^3*b*f*cosh(f*x + e)^6 + 15*(a^4 - a^3*b)*f*cosh(f*x + e)^4 - 3*(4*a^4 - 3*a^3*b)*f*cosh(f*x + e)^2 + (a^4 - a^3*b)*f)*sinh(f*x + e)^2 + 8*(a^3*b*f*cosh(f*x + e)^7 + 3*(a^4 - a^3*b)*f*cosh(f*x + e)^5 - (4*a^4 - 3*a^3*b)*f*cosh(f*x + e)^3 + (a^4 - a^3*b)*f*cosh(f*x + e))*sinh(f*x + e))]","B",0
495,1,7562,0,0.869204," ","integrate(coth(f*x+e)^5/(a+b*sinh(f*x+e)^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(8 \, a^{2} b - 24 \, a b^{2} + 15 \, b^{3}\right)} \cosh\left(f x + e\right)^{12} + 12 \, {\left(8 \, a^{2} b - 24 \, a b^{2} + 15 \, b^{3}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{11} + {\left(8 \, a^{2} b - 24 \, a b^{2} + 15 \, b^{3}\right)} \sinh\left(f x + e\right)^{12} + 2 \, {\left(16 \, a^{3} - 72 \, a^{2} b + 102 \, a b^{2} - 45 \, b^{3}\right)} \cosh\left(f x + e\right)^{10} + 2 \, {\left(16 \, a^{3} - 72 \, a^{2} b + 102 \, a b^{2} - 45 \, b^{3} + 33 \, {\left(8 \, a^{2} b - 24 \, a b^{2} + 15 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{10} + 20 \, {\left(11 \, {\left(8 \, a^{2} b - 24 \, a b^{2} + 15 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} + {\left(16 \, a^{3} - 72 \, a^{2} b + 102 \, a b^{2} - 45 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{9} - {\left(128 \, a^{3} - 504 \, a^{2} b + 600 \, a b^{2} - 225 \, b^{3}\right)} \cosh\left(f x + e\right)^{8} + {\left(495 \, {\left(8 \, a^{2} b - 24 \, a b^{2} + 15 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} - 128 \, a^{3} + 504 \, a^{2} b - 600 \, a b^{2} + 225 \, b^{3} + 90 \, {\left(16 \, a^{3} - 72 \, a^{2} b + 102 \, a b^{2} - 45 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{8} + 8 \, {\left(99 \, {\left(8 \, a^{2} b - 24 \, a b^{2} + 15 \, b^{3}\right)} \cosh\left(f x + e\right)^{5} + 30 \, {\left(16 \, a^{3} - 72 \, a^{2} b + 102 \, a b^{2} - 45 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} - {\left(128 \, a^{3} - 504 \, a^{2} b + 600 \, a b^{2} - 225 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{7} + 4 \, {\left(48 \, a^{3} - 184 \, a^{2} b + 210 \, a b^{2} - 75 \, b^{3}\right)} \cosh\left(f x + e\right)^{6} + 4 \, {\left(231 \, {\left(8 \, a^{2} b - 24 \, a b^{2} + 15 \, b^{3}\right)} \cosh\left(f x + e\right)^{6} + 105 \, {\left(16 \, a^{3} - 72 \, a^{2} b + 102 \, a b^{2} - 45 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} + 48 \, a^{3} - 184 \, a^{2} b + 210 \, a b^{2} - 75 \, b^{3} - 7 \, {\left(128 \, a^{3} - 504 \, a^{2} b + 600 \, a b^{2} - 225 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{6} + 8 \, {\left(99 \, {\left(8 \, a^{2} b - 24 \, a b^{2} + 15 \, b^{3}\right)} \cosh\left(f x + e\right)^{7} + 63 \, {\left(16 \, a^{3} - 72 \, a^{2} b + 102 \, a b^{2} - 45 \, b^{3}\right)} \cosh\left(f x + e\right)^{5} - 7 \, {\left(128 \, a^{3} - 504 \, a^{2} b + 600 \, a b^{2} - 225 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(48 \, a^{3} - 184 \, a^{2} b + 210 \, a b^{2} - 75 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} - {\left(128 \, a^{3} - 504 \, a^{2} b + 600 \, a b^{2} - 225 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} + {\left(495 \, {\left(8 \, a^{2} b - 24 \, a b^{2} + 15 \, b^{3}\right)} \cosh\left(f x + e\right)^{8} + 420 \, {\left(16 \, a^{3} - 72 \, a^{2} b + 102 \, a b^{2} - 45 \, b^{3}\right)} \cosh\left(f x + e\right)^{6} - 70 \, {\left(128 \, a^{3} - 504 \, a^{2} b + 600 \, a b^{2} - 225 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} - 128 \, a^{3} + 504 \, a^{2} b - 600 \, a b^{2} + 225 \, b^{3} + 60 \, {\left(48 \, a^{3} - 184 \, a^{2} b + 210 \, a b^{2} - 75 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(55 \, {\left(8 \, a^{2} b - 24 \, a b^{2} + 15 \, b^{3}\right)} \cosh\left(f x + e\right)^{9} + 60 \, {\left(16 \, a^{3} - 72 \, a^{2} b + 102 \, a b^{2} - 45 \, b^{3}\right)} \cosh\left(f x + e\right)^{7} - 14 \, {\left(128 \, a^{3} - 504 \, a^{2} b + 600 \, a b^{2} - 225 \, b^{3}\right)} \cosh\left(f x + e\right)^{5} + 20 \, {\left(48 \, a^{3} - 184 \, a^{2} b + 210 \, a b^{2} - 75 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} - {\left(128 \, a^{3} - 504 \, a^{2} b + 600 \, a b^{2} - 225 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 8 \, a^{2} b - 24 \, a b^{2} + 15 \, b^{3} + 2 \, {\left(16 \, a^{3} - 72 \, a^{2} b + 102 \, a b^{2} - 45 \, b^{3}\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(33 \, {\left(8 \, a^{2} b - 24 \, a b^{2} + 15 \, b^{3}\right)} \cosh\left(f x + e\right)^{10} + 45 \, {\left(16 \, a^{3} - 72 \, a^{2} b + 102 \, a b^{2} - 45 \, b^{3}\right)} \cosh\left(f x + e\right)^{8} - 14 \, {\left(128 \, a^{3} - 504 \, a^{2} b + 600 \, a b^{2} - 225 \, b^{3}\right)} \cosh\left(f x + e\right)^{6} + 30 \, {\left(48 \, a^{3} - 184 \, a^{2} b + 210 \, a b^{2} - 75 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} + 16 \, a^{3} - 72 \, a^{2} b + 102 \, a b^{2} - 45 \, b^{3} - 3 \, {\left(128 \, a^{3} - 504 \, a^{2} b + 600 \, a b^{2} - 225 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(3 \, {\left(8 \, a^{2} b - 24 \, a b^{2} + 15 \, b^{3}\right)} \cosh\left(f x + e\right)^{11} + 5 \, {\left(16 \, a^{3} - 72 \, a^{2} b + 102 \, a b^{2} - 45 \, b^{3}\right)} \cosh\left(f x + e\right)^{9} - 2 \, {\left(128 \, a^{3} - 504 \, a^{2} b + 600 \, a b^{2} - 225 \, b^{3}\right)} \cosh\left(f x + e\right)^{7} + 6 \, {\left(48 \, a^{3} - 184 \, a^{2} b + 210 \, a b^{2} - 75 \, b^{3}\right)} \cosh\left(f x + e\right)^{5} - {\left(128 \, a^{3} - 504 \, a^{2} b + 600 \, a b^{2} - 225 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} + {\left(16 \, a^{3} - 72 \, a^{2} b + 102 \, a b^{2} - 45 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{a} \log\left(\frac{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(4 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + 4 \, a - b\right)} \sinh\left(f x + e\right)^{2} - 4 \, \sqrt{2} \sqrt{a} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} {\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right)\right)} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(4 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}{\cosh\left(f x + e\right)^{4} + 4 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + \sinh\left(f x + e\right)^{4} + 2 \, {\left(3 \, \cosh\left(f x + e\right)^{2} - 1\right)} \sinh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right)^{2} + 4 \, {\left(\cosh\left(f x + e\right)^{3} - \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + 1}\right) + 4 \, \sqrt{2} {\left({\left(8 \, a^{3} - 24 \, a^{2} b + 15 \, a b^{2}\right)} \cosh\left(f x + e\right)^{9} + 9 \, {\left(8 \, a^{3} - 24 \, a^{2} b + 15 \, a b^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{8} + {\left(8 \, a^{3} - 24 \, a^{2} b + 15 \, a b^{2}\right)} \sinh\left(f x + e\right)^{9} - 4 \, {\left(16 \, a^{3} - 29 \, a^{2} b + 15 \, a b^{2}\right)} \cosh\left(f x + e\right)^{7} - 4 \, {\left(16 \, a^{3} - 29 \, a^{2} b + 15 \, a b^{2} - 9 \, {\left(8 \, a^{3} - 24 \, a^{2} b + 15 \, a b^{2}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{7} + 28 \, {\left(3 \, {\left(8 \, a^{3} - 24 \, a^{2} b + 15 \, a b^{2}\right)} \cosh\left(f x + e\right)^{3} - {\left(16 \, a^{3} - 29 \, a^{2} b + 15 \, a b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{6} + 2 \, {\left(40 \, a^{3} - 92 \, a^{2} b + 45 \, a b^{2}\right)} \cosh\left(f x + e\right)^{5} + 2 \, {\left(63 \, {\left(8 \, a^{3} - 24 \, a^{2} b + 15 \, a b^{2}\right)} \cosh\left(f x + e\right)^{4} + 40 \, a^{3} - 92 \, a^{2} b + 45 \, a b^{2} - 42 \, {\left(16 \, a^{3} - 29 \, a^{2} b + 15 \, a b^{2}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(63 \, {\left(8 \, a^{3} - 24 \, a^{2} b + 15 \, a b^{2}\right)} \cosh\left(f x + e\right)^{5} - 70 \, {\left(16 \, a^{3} - 29 \, a^{2} b + 15 \, a b^{2}\right)} \cosh\left(f x + e\right)^{3} + 5 \, {\left(40 \, a^{3} - 92 \, a^{2} b + 45 \, a b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{4} - 4 \, {\left(16 \, a^{3} - 29 \, a^{2} b + 15 \, a b^{2}\right)} \cosh\left(f x + e\right)^{3} + 4 \, {\left(21 \, {\left(8 \, a^{3} - 24 \, a^{2} b + 15 \, a b^{2}\right)} \cosh\left(f x + e\right)^{6} - 35 \, {\left(16 \, a^{3} - 29 \, a^{2} b + 15 \, a b^{2}\right)} \cosh\left(f x + e\right)^{4} - 16 \, a^{3} + 29 \, a^{2} b - 15 \, a b^{2} + 5 \, {\left(40 \, a^{3} - 92 \, a^{2} b + 45 \, a b^{2}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{3} + 4 \, {\left(9 \, {\left(8 \, a^{3} - 24 \, a^{2} b + 15 \, a b^{2}\right)} \cosh\left(f x + e\right)^{7} - 21 \, {\left(16 \, a^{3} - 29 \, a^{2} b + 15 \, a b^{2}\right)} \cosh\left(f x + e\right)^{5} + 5 \, {\left(40 \, a^{3} - 92 \, a^{2} b + 45 \, a b^{2}\right)} \cosh\left(f x + e\right)^{3} - 3 \, {\left(16 \, a^{3} - 29 \, a^{2} b + 15 \, a b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{2} + {\left(8 \, a^{3} - 24 \, a^{2} b + 15 \, a b^{2}\right)} \cosh\left(f x + e\right) + {\left(9 \, {\left(8 \, a^{3} - 24 \, a^{2} b + 15 \, a b^{2}\right)} \cosh\left(f x + e\right)^{8} - 28 \, {\left(16 \, a^{3} - 29 \, a^{2} b + 15 \, a b^{2}\right)} \cosh\left(f x + e\right)^{6} + 10 \, {\left(40 \, a^{3} - 92 \, a^{2} b + 45 \, a b^{2}\right)} \cosh\left(f x + e\right)^{4} + 8 \, a^{3} - 24 \, a^{2} b + 15 \, a b^{2} - 12 \, {\left(16 \, a^{3} - 29 \, a^{2} b + 15 \, a b^{2}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{16 \, {\left(a^{4} b f \cosh\left(f x + e\right)^{12} + 12 \, a^{4} b f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{11} + a^{4} b f \sinh\left(f x + e\right)^{12} + 2 \, {\left(2 \, a^{5} - 3 \, a^{4} b\right)} f \cosh\left(f x + e\right)^{10} + 2 \, {\left(33 \, a^{4} b f \cosh\left(f x + e\right)^{2} + {\left(2 \, a^{5} - 3 \, a^{4} b\right)} f\right)} \sinh\left(f x + e\right)^{10} - {\left(16 \, a^{5} - 15 \, a^{4} b\right)} f \cosh\left(f x + e\right)^{8} + 20 \, {\left(11 \, a^{4} b f \cosh\left(f x + e\right)^{3} + {\left(2 \, a^{5} - 3 \, a^{4} b\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{9} + {\left(495 \, a^{4} b f \cosh\left(f x + e\right)^{4} + 90 \, {\left(2 \, a^{5} - 3 \, a^{4} b\right)} f \cosh\left(f x + e\right)^{2} - {\left(16 \, a^{5} - 15 \, a^{4} b\right)} f\right)} \sinh\left(f x + e\right)^{8} + 4 \, {\left(6 \, a^{5} - 5 \, a^{4} b\right)} f \cosh\left(f x + e\right)^{6} + 8 \, {\left(99 \, a^{4} b f \cosh\left(f x + e\right)^{5} + 30 \, {\left(2 \, a^{5} - 3 \, a^{4} b\right)} f \cosh\left(f x + e\right)^{3} - {\left(16 \, a^{5} - 15 \, a^{4} b\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{7} + 4 \, {\left(231 \, a^{4} b f \cosh\left(f x + e\right)^{6} + 105 \, {\left(2 \, a^{5} - 3 \, a^{4} b\right)} f \cosh\left(f x + e\right)^{4} - 7 \, {\left(16 \, a^{5} - 15 \, a^{4} b\right)} f \cosh\left(f x + e\right)^{2} + {\left(6 \, a^{5} - 5 \, a^{4} b\right)} f\right)} \sinh\left(f x + e\right)^{6} + a^{4} b f - {\left(16 \, a^{5} - 15 \, a^{4} b\right)} f \cosh\left(f x + e\right)^{4} + 8 \, {\left(99 \, a^{4} b f \cosh\left(f x + e\right)^{7} + 63 \, {\left(2 \, a^{5} - 3 \, a^{4} b\right)} f \cosh\left(f x + e\right)^{5} - 7 \, {\left(16 \, a^{5} - 15 \, a^{4} b\right)} f \cosh\left(f x + e\right)^{3} + 3 \, {\left(6 \, a^{5} - 5 \, a^{4} b\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + {\left(495 \, a^{4} b f \cosh\left(f x + e\right)^{8} + 420 \, {\left(2 \, a^{5} - 3 \, a^{4} b\right)} f \cosh\left(f x + e\right)^{6} - 70 \, {\left(16 \, a^{5} - 15 \, a^{4} b\right)} f \cosh\left(f x + e\right)^{4} + 60 \, {\left(6 \, a^{5} - 5 \, a^{4} b\right)} f \cosh\left(f x + e\right)^{2} - {\left(16 \, a^{5} - 15 \, a^{4} b\right)} f\right)} \sinh\left(f x + e\right)^{4} + 2 \, {\left(2 \, a^{5} - 3 \, a^{4} b\right)} f \cosh\left(f x + e\right)^{2} + 4 \, {\left(55 \, a^{4} b f \cosh\left(f x + e\right)^{9} + 60 \, {\left(2 \, a^{5} - 3 \, a^{4} b\right)} f \cosh\left(f x + e\right)^{7} - 14 \, {\left(16 \, a^{5} - 15 \, a^{4} b\right)} f \cosh\left(f x + e\right)^{5} + 20 \, {\left(6 \, a^{5} - 5 \, a^{4} b\right)} f \cosh\left(f x + e\right)^{3} - {\left(16 \, a^{5} - 15 \, a^{4} b\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 2 \, {\left(33 \, a^{4} b f \cosh\left(f x + e\right)^{10} + 45 \, {\left(2 \, a^{5} - 3 \, a^{4} b\right)} f \cosh\left(f x + e\right)^{8} - 14 \, {\left(16 \, a^{5} - 15 \, a^{4} b\right)} f \cosh\left(f x + e\right)^{6} + 30 \, {\left(6 \, a^{5} - 5 \, a^{4} b\right)} f \cosh\left(f x + e\right)^{4} - 3 \, {\left(16 \, a^{5} - 15 \, a^{4} b\right)} f \cosh\left(f x + e\right)^{2} + {\left(2 \, a^{5} - 3 \, a^{4} b\right)} f\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(3 \, a^{4} b f \cosh\left(f x + e\right)^{11} + 5 \, {\left(2 \, a^{5} - 3 \, a^{4} b\right)} f \cosh\left(f x + e\right)^{9} - 2 \, {\left(16 \, a^{5} - 15 \, a^{4} b\right)} f \cosh\left(f x + e\right)^{7} + 6 \, {\left(6 \, a^{5} - 5 \, a^{4} b\right)} f \cosh\left(f x + e\right)^{5} - {\left(16 \, a^{5} - 15 \, a^{4} b\right)} f \cosh\left(f x + e\right)^{3} + {\left(2 \, a^{5} - 3 \, a^{4} b\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)}}, \frac{{\left({\left(8 \, a^{2} b - 24 \, a b^{2} + 15 \, b^{3}\right)} \cosh\left(f x + e\right)^{12} + 12 \, {\left(8 \, a^{2} b - 24 \, a b^{2} + 15 \, b^{3}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{11} + {\left(8 \, a^{2} b - 24 \, a b^{2} + 15 \, b^{3}\right)} \sinh\left(f x + e\right)^{12} + 2 \, {\left(16 \, a^{3} - 72 \, a^{2} b + 102 \, a b^{2} - 45 \, b^{3}\right)} \cosh\left(f x + e\right)^{10} + 2 \, {\left(16 \, a^{3} - 72 \, a^{2} b + 102 \, a b^{2} - 45 \, b^{3} + 33 \, {\left(8 \, a^{2} b - 24 \, a b^{2} + 15 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{10} + 20 \, {\left(11 \, {\left(8 \, a^{2} b - 24 \, a b^{2} + 15 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} + {\left(16 \, a^{3} - 72 \, a^{2} b + 102 \, a b^{2} - 45 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{9} - {\left(128 \, a^{3} - 504 \, a^{2} b + 600 \, a b^{2} - 225 \, b^{3}\right)} \cosh\left(f x + e\right)^{8} + {\left(495 \, {\left(8 \, a^{2} b - 24 \, a b^{2} + 15 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} - 128 \, a^{3} + 504 \, a^{2} b - 600 \, a b^{2} + 225 \, b^{3} + 90 \, {\left(16 \, a^{3} - 72 \, a^{2} b + 102 \, a b^{2} - 45 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{8} + 8 \, {\left(99 \, {\left(8 \, a^{2} b - 24 \, a b^{2} + 15 \, b^{3}\right)} \cosh\left(f x + e\right)^{5} + 30 \, {\left(16 \, a^{3} - 72 \, a^{2} b + 102 \, a b^{2} - 45 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} - {\left(128 \, a^{3} - 504 \, a^{2} b + 600 \, a b^{2} - 225 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{7} + 4 \, {\left(48 \, a^{3} - 184 \, a^{2} b + 210 \, a b^{2} - 75 \, b^{3}\right)} \cosh\left(f x + e\right)^{6} + 4 \, {\left(231 \, {\left(8 \, a^{2} b - 24 \, a b^{2} + 15 \, b^{3}\right)} \cosh\left(f x + e\right)^{6} + 105 \, {\left(16 \, a^{3} - 72 \, a^{2} b + 102 \, a b^{2} - 45 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} + 48 \, a^{3} - 184 \, a^{2} b + 210 \, a b^{2} - 75 \, b^{3} - 7 \, {\left(128 \, a^{3} - 504 \, a^{2} b + 600 \, a b^{2} - 225 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{6} + 8 \, {\left(99 \, {\left(8 \, a^{2} b - 24 \, a b^{2} + 15 \, b^{3}\right)} \cosh\left(f x + e\right)^{7} + 63 \, {\left(16 \, a^{3} - 72 \, a^{2} b + 102 \, a b^{2} - 45 \, b^{3}\right)} \cosh\left(f x + e\right)^{5} - 7 \, {\left(128 \, a^{3} - 504 \, a^{2} b + 600 \, a b^{2} - 225 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(48 \, a^{3} - 184 \, a^{2} b + 210 \, a b^{2} - 75 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} - {\left(128 \, a^{3} - 504 \, a^{2} b + 600 \, a b^{2} - 225 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} + {\left(495 \, {\left(8 \, a^{2} b - 24 \, a b^{2} + 15 \, b^{3}\right)} \cosh\left(f x + e\right)^{8} + 420 \, {\left(16 \, a^{3} - 72 \, a^{2} b + 102 \, a b^{2} - 45 \, b^{3}\right)} \cosh\left(f x + e\right)^{6} - 70 \, {\left(128 \, a^{3} - 504 \, a^{2} b + 600 \, a b^{2} - 225 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} - 128 \, a^{3} + 504 \, a^{2} b - 600 \, a b^{2} + 225 \, b^{3} + 60 \, {\left(48 \, a^{3} - 184 \, a^{2} b + 210 \, a b^{2} - 75 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(55 \, {\left(8 \, a^{2} b - 24 \, a b^{2} + 15 \, b^{3}\right)} \cosh\left(f x + e\right)^{9} + 60 \, {\left(16 \, a^{3} - 72 \, a^{2} b + 102 \, a b^{2} - 45 \, b^{3}\right)} \cosh\left(f x + e\right)^{7} - 14 \, {\left(128 \, a^{3} - 504 \, a^{2} b + 600 \, a b^{2} - 225 \, b^{3}\right)} \cosh\left(f x + e\right)^{5} + 20 \, {\left(48 \, a^{3} - 184 \, a^{2} b + 210 \, a b^{2} - 75 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} - {\left(128 \, a^{3} - 504 \, a^{2} b + 600 \, a b^{2} - 225 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 8 \, a^{2} b - 24 \, a b^{2} + 15 \, b^{3} + 2 \, {\left(16 \, a^{3} - 72 \, a^{2} b + 102 \, a b^{2} - 45 \, b^{3}\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(33 \, {\left(8 \, a^{2} b - 24 \, a b^{2} + 15 \, b^{3}\right)} \cosh\left(f x + e\right)^{10} + 45 \, {\left(16 \, a^{3} - 72 \, a^{2} b + 102 \, a b^{2} - 45 \, b^{3}\right)} \cosh\left(f x + e\right)^{8} - 14 \, {\left(128 \, a^{3} - 504 \, a^{2} b + 600 \, a b^{2} - 225 \, b^{3}\right)} \cosh\left(f x + e\right)^{6} + 30 \, {\left(48 \, a^{3} - 184 \, a^{2} b + 210 \, a b^{2} - 75 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} + 16 \, a^{3} - 72 \, a^{2} b + 102 \, a b^{2} - 45 \, b^{3} - 3 \, {\left(128 \, a^{3} - 504 \, a^{2} b + 600 \, a b^{2} - 225 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(3 \, {\left(8 \, a^{2} b - 24 \, a b^{2} + 15 \, b^{3}\right)} \cosh\left(f x + e\right)^{11} + 5 \, {\left(16 \, a^{3} - 72 \, a^{2} b + 102 \, a b^{2} - 45 \, b^{3}\right)} \cosh\left(f x + e\right)^{9} - 2 \, {\left(128 \, a^{3} - 504 \, a^{2} b + 600 \, a b^{2} - 225 \, b^{3}\right)} \cosh\left(f x + e\right)^{7} + 6 \, {\left(48 \, a^{3} - 184 \, a^{2} b + 210 \, a b^{2} - 75 \, b^{3}\right)} \cosh\left(f x + e\right)^{5} - {\left(128 \, a^{3} - 504 \, a^{2} b + 600 \, a b^{2} - 225 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} + {\left(16 \, a^{3} - 72 \, a^{2} b + 102 \, a b^{2} - 45 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{2} \sqrt{-a} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{2 \, {\left(a \cosh\left(f x + e\right) + a \sinh\left(f x + e\right)\right)}}\right) + 2 \, \sqrt{2} {\left({\left(8 \, a^{3} - 24 \, a^{2} b + 15 \, a b^{2}\right)} \cosh\left(f x + e\right)^{9} + 9 \, {\left(8 \, a^{3} - 24 \, a^{2} b + 15 \, a b^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{8} + {\left(8 \, a^{3} - 24 \, a^{2} b + 15 \, a b^{2}\right)} \sinh\left(f x + e\right)^{9} - 4 \, {\left(16 \, a^{3} - 29 \, a^{2} b + 15 \, a b^{2}\right)} \cosh\left(f x + e\right)^{7} - 4 \, {\left(16 \, a^{3} - 29 \, a^{2} b + 15 \, a b^{2} - 9 \, {\left(8 \, a^{3} - 24 \, a^{2} b + 15 \, a b^{2}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{7} + 28 \, {\left(3 \, {\left(8 \, a^{3} - 24 \, a^{2} b + 15 \, a b^{2}\right)} \cosh\left(f x + e\right)^{3} - {\left(16 \, a^{3} - 29 \, a^{2} b + 15 \, a b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{6} + 2 \, {\left(40 \, a^{3} - 92 \, a^{2} b + 45 \, a b^{2}\right)} \cosh\left(f x + e\right)^{5} + 2 \, {\left(63 \, {\left(8 \, a^{3} - 24 \, a^{2} b + 15 \, a b^{2}\right)} \cosh\left(f x + e\right)^{4} + 40 \, a^{3} - 92 \, a^{2} b + 45 \, a b^{2} - 42 \, {\left(16 \, a^{3} - 29 \, a^{2} b + 15 \, a b^{2}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(63 \, {\left(8 \, a^{3} - 24 \, a^{2} b + 15 \, a b^{2}\right)} \cosh\left(f x + e\right)^{5} - 70 \, {\left(16 \, a^{3} - 29 \, a^{2} b + 15 \, a b^{2}\right)} \cosh\left(f x + e\right)^{3} + 5 \, {\left(40 \, a^{3} - 92 \, a^{2} b + 45 \, a b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{4} - 4 \, {\left(16 \, a^{3} - 29 \, a^{2} b + 15 \, a b^{2}\right)} \cosh\left(f x + e\right)^{3} + 4 \, {\left(21 \, {\left(8 \, a^{3} - 24 \, a^{2} b + 15 \, a b^{2}\right)} \cosh\left(f x + e\right)^{6} - 35 \, {\left(16 \, a^{3} - 29 \, a^{2} b + 15 \, a b^{2}\right)} \cosh\left(f x + e\right)^{4} - 16 \, a^{3} + 29 \, a^{2} b - 15 \, a b^{2} + 5 \, {\left(40 \, a^{3} - 92 \, a^{2} b + 45 \, a b^{2}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{3} + 4 \, {\left(9 \, {\left(8 \, a^{3} - 24 \, a^{2} b + 15 \, a b^{2}\right)} \cosh\left(f x + e\right)^{7} - 21 \, {\left(16 \, a^{3} - 29 \, a^{2} b + 15 \, a b^{2}\right)} \cosh\left(f x + e\right)^{5} + 5 \, {\left(40 \, a^{3} - 92 \, a^{2} b + 45 \, a b^{2}\right)} \cosh\left(f x + e\right)^{3} - 3 \, {\left(16 \, a^{3} - 29 \, a^{2} b + 15 \, a b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{2} + {\left(8 \, a^{3} - 24 \, a^{2} b + 15 \, a b^{2}\right)} \cosh\left(f x + e\right) + {\left(9 \, {\left(8 \, a^{3} - 24 \, a^{2} b + 15 \, a b^{2}\right)} \cosh\left(f x + e\right)^{8} - 28 \, {\left(16 \, a^{3} - 29 \, a^{2} b + 15 \, a b^{2}\right)} \cosh\left(f x + e\right)^{6} + 10 \, {\left(40 \, a^{3} - 92 \, a^{2} b + 45 \, a b^{2}\right)} \cosh\left(f x + e\right)^{4} + 8 \, a^{3} - 24 \, a^{2} b + 15 \, a b^{2} - 12 \, {\left(16 \, a^{3} - 29 \, a^{2} b + 15 \, a b^{2}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{8 \, {\left(a^{4} b f \cosh\left(f x + e\right)^{12} + 12 \, a^{4} b f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{11} + a^{4} b f \sinh\left(f x + e\right)^{12} + 2 \, {\left(2 \, a^{5} - 3 \, a^{4} b\right)} f \cosh\left(f x + e\right)^{10} + 2 \, {\left(33 \, a^{4} b f \cosh\left(f x + e\right)^{2} + {\left(2 \, a^{5} - 3 \, a^{4} b\right)} f\right)} \sinh\left(f x + e\right)^{10} - {\left(16 \, a^{5} - 15 \, a^{4} b\right)} f \cosh\left(f x + e\right)^{8} + 20 \, {\left(11 \, a^{4} b f \cosh\left(f x + e\right)^{3} + {\left(2 \, a^{5} - 3 \, a^{4} b\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{9} + {\left(495 \, a^{4} b f \cosh\left(f x + e\right)^{4} + 90 \, {\left(2 \, a^{5} - 3 \, a^{4} b\right)} f \cosh\left(f x + e\right)^{2} - {\left(16 \, a^{5} - 15 \, a^{4} b\right)} f\right)} \sinh\left(f x + e\right)^{8} + 4 \, {\left(6 \, a^{5} - 5 \, a^{4} b\right)} f \cosh\left(f x + e\right)^{6} + 8 \, {\left(99 \, a^{4} b f \cosh\left(f x + e\right)^{5} + 30 \, {\left(2 \, a^{5} - 3 \, a^{4} b\right)} f \cosh\left(f x + e\right)^{3} - {\left(16 \, a^{5} - 15 \, a^{4} b\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{7} + 4 \, {\left(231 \, a^{4} b f \cosh\left(f x + e\right)^{6} + 105 \, {\left(2 \, a^{5} - 3 \, a^{4} b\right)} f \cosh\left(f x + e\right)^{4} - 7 \, {\left(16 \, a^{5} - 15 \, a^{4} b\right)} f \cosh\left(f x + e\right)^{2} + {\left(6 \, a^{5} - 5 \, a^{4} b\right)} f\right)} \sinh\left(f x + e\right)^{6} + a^{4} b f - {\left(16 \, a^{5} - 15 \, a^{4} b\right)} f \cosh\left(f x + e\right)^{4} + 8 \, {\left(99 \, a^{4} b f \cosh\left(f x + e\right)^{7} + 63 \, {\left(2 \, a^{5} - 3 \, a^{4} b\right)} f \cosh\left(f x + e\right)^{5} - 7 \, {\left(16 \, a^{5} - 15 \, a^{4} b\right)} f \cosh\left(f x + e\right)^{3} + 3 \, {\left(6 \, a^{5} - 5 \, a^{4} b\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + {\left(495 \, a^{4} b f \cosh\left(f x + e\right)^{8} + 420 \, {\left(2 \, a^{5} - 3 \, a^{4} b\right)} f \cosh\left(f x + e\right)^{6} - 70 \, {\left(16 \, a^{5} - 15 \, a^{4} b\right)} f \cosh\left(f x + e\right)^{4} + 60 \, {\left(6 \, a^{5} - 5 \, a^{4} b\right)} f \cosh\left(f x + e\right)^{2} - {\left(16 \, a^{5} - 15 \, a^{4} b\right)} f\right)} \sinh\left(f x + e\right)^{4} + 2 \, {\left(2 \, a^{5} - 3 \, a^{4} b\right)} f \cosh\left(f x + e\right)^{2} + 4 \, {\left(55 \, a^{4} b f \cosh\left(f x + e\right)^{9} + 60 \, {\left(2 \, a^{5} - 3 \, a^{4} b\right)} f \cosh\left(f x + e\right)^{7} - 14 \, {\left(16 \, a^{5} - 15 \, a^{4} b\right)} f \cosh\left(f x + e\right)^{5} + 20 \, {\left(6 \, a^{5} - 5 \, a^{4} b\right)} f \cosh\left(f x + e\right)^{3} - {\left(16 \, a^{5} - 15 \, a^{4} b\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 2 \, {\left(33 \, a^{4} b f \cosh\left(f x + e\right)^{10} + 45 \, {\left(2 \, a^{5} - 3 \, a^{4} b\right)} f \cosh\left(f x + e\right)^{8} - 14 \, {\left(16 \, a^{5} - 15 \, a^{4} b\right)} f \cosh\left(f x + e\right)^{6} + 30 \, {\left(6 \, a^{5} - 5 \, a^{4} b\right)} f \cosh\left(f x + e\right)^{4} - 3 \, {\left(16 \, a^{5} - 15 \, a^{4} b\right)} f \cosh\left(f x + e\right)^{2} + {\left(2 \, a^{5} - 3 \, a^{4} b\right)} f\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(3 \, a^{4} b f \cosh\left(f x + e\right)^{11} + 5 \, {\left(2 \, a^{5} - 3 \, a^{4} b\right)} f \cosh\left(f x + e\right)^{9} - 2 \, {\left(16 \, a^{5} - 15 \, a^{4} b\right)} f \cosh\left(f x + e\right)^{7} + 6 \, {\left(6 \, a^{5} - 5 \, a^{4} b\right)} f \cosh\left(f x + e\right)^{5} - {\left(16 \, a^{5} - 15 \, a^{4} b\right)} f \cosh\left(f x + e\right)^{3} + {\left(2 \, a^{5} - 3 \, a^{4} b\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)}}\right]"," ",0,"[1/16*(((8*a^2*b - 24*a*b^2 + 15*b^3)*cosh(f*x + e)^12 + 12*(8*a^2*b - 24*a*b^2 + 15*b^3)*cosh(f*x + e)*sinh(f*x + e)^11 + (8*a^2*b - 24*a*b^2 + 15*b^3)*sinh(f*x + e)^12 + 2*(16*a^3 - 72*a^2*b + 102*a*b^2 - 45*b^3)*cosh(f*x + e)^10 + 2*(16*a^3 - 72*a^2*b + 102*a*b^2 - 45*b^3 + 33*(8*a^2*b - 24*a*b^2 + 15*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^10 + 20*(11*(8*a^2*b - 24*a*b^2 + 15*b^3)*cosh(f*x + e)^3 + (16*a^3 - 72*a^2*b + 102*a*b^2 - 45*b^3)*cosh(f*x + e))*sinh(f*x + e)^9 - (128*a^3 - 504*a^2*b + 600*a*b^2 - 225*b^3)*cosh(f*x + e)^8 + (495*(8*a^2*b - 24*a*b^2 + 15*b^3)*cosh(f*x + e)^4 - 128*a^3 + 504*a^2*b - 600*a*b^2 + 225*b^3 + 90*(16*a^3 - 72*a^2*b + 102*a*b^2 - 45*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^8 + 8*(99*(8*a^2*b - 24*a*b^2 + 15*b^3)*cosh(f*x + e)^5 + 30*(16*a^3 - 72*a^2*b + 102*a*b^2 - 45*b^3)*cosh(f*x + e)^3 - (128*a^3 - 504*a^2*b + 600*a*b^2 - 225*b^3)*cosh(f*x + e))*sinh(f*x + e)^7 + 4*(48*a^3 - 184*a^2*b + 210*a*b^2 - 75*b^3)*cosh(f*x + e)^6 + 4*(231*(8*a^2*b - 24*a*b^2 + 15*b^3)*cosh(f*x + e)^6 + 105*(16*a^3 - 72*a^2*b + 102*a*b^2 - 45*b^3)*cosh(f*x + e)^4 + 48*a^3 - 184*a^2*b + 210*a*b^2 - 75*b^3 - 7*(128*a^3 - 504*a^2*b + 600*a*b^2 - 225*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^6 + 8*(99*(8*a^2*b - 24*a*b^2 + 15*b^3)*cosh(f*x + e)^7 + 63*(16*a^3 - 72*a^2*b + 102*a*b^2 - 45*b^3)*cosh(f*x + e)^5 - 7*(128*a^3 - 504*a^2*b + 600*a*b^2 - 225*b^3)*cosh(f*x + e)^3 + 3*(48*a^3 - 184*a^2*b + 210*a*b^2 - 75*b^3)*cosh(f*x + e))*sinh(f*x + e)^5 - (128*a^3 - 504*a^2*b + 600*a*b^2 - 225*b^3)*cosh(f*x + e)^4 + (495*(8*a^2*b - 24*a*b^2 + 15*b^3)*cosh(f*x + e)^8 + 420*(16*a^3 - 72*a^2*b + 102*a*b^2 - 45*b^3)*cosh(f*x + e)^6 - 70*(128*a^3 - 504*a^2*b + 600*a*b^2 - 225*b^3)*cosh(f*x + e)^4 - 128*a^3 + 504*a^2*b - 600*a*b^2 + 225*b^3 + 60*(48*a^3 - 184*a^2*b + 210*a*b^2 - 75*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^4 + 4*(55*(8*a^2*b - 24*a*b^2 + 15*b^3)*cosh(f*x + e)^9 + 60*(16*a^3 - 72*a^2*b + 102*a*b^2 - 45*b^3)*cosh(f*x + e)^7 - 14*(128*a^3 - 504*a^2*b + 600*a*b^2 - 225*b^3)*cosh(f*x + e)^5 + 20*(48*a^3 - 184*a^2*b + 210*a*b^2 - 75*b^3)*cosh(f*x + e)^3 - (128*a^3 - 504*a^2*b + 600*a*b^2 - 225*b^3)*cosh(f*x + e))*sinh(f*x + e)^3 + 8*a^2*b - 24*a*b^2 + 15*b^3 + 2*(16*a^3 - 72*a^2*b + 102*a*b^2 - 45*b^3)*cosh(f*x + e)^2 + 2*(33*(8*a^2*b - 24*a*b^2 + 15*b^3)*cosh(f*x + e)^10 + 45*(16*a^3 - 72*a^2*b + 102*a*b^2 - 45*b^3)*cosh(f*x + e)^8 - 14*(128*a^3 - 504*a^2*b + 600*a*b^2 - 225*b^3)*cosh(f*x + e)^6 + 30*(48*a^3 - 184*a^2*b + 210*a*b^2 - 75*b^3)*cosh(f*x + e)^4 + 16*a^3 - 72*a^2*b + 102*a*b^2 - 45*b^3 - 3*(128*a^3 - 504*a^2*b + 600*a*b^2 - 225*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^2 + 4*(3*(8*a^2*b - 24*a*b^2 + 15*b^3)*cosh(f*x + e)^11 + 5*(16*a^3 - 72*a^2*b + 102*a*b^2 - 45*b^3)*cosh(f*x + e)^9 - 2*(128*a^3 - 504*a^2*b + 600*a*b^2 - 225*b^3)*cosh(f*x + e)^7 + 6*(48*a^3 - 184*a^2*b + 210*a*b^2 - 75*b^3)*cosh(f*x + e)^5 - (128*a^3 - 504*a^2*b + 600*a*b^2 - 225*b^3)*cosh(f*x + e)^3 + (16*a^3 - 72*a^2*b + 102*a*b^2 - 45*b^3)*cosh(f*x + e))*sinh(f*x + e))*sqrt(a)*log((b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(4*a - b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 4*a - b)*sinh(f*x + e)^2 - 4*sqrt(2)*sqrt(a)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))*(cosh(f*x + e) + sinh(f*x + e)) + 4*(b*cosh(f*x + e)^3 + (4*a - b)*cosh(f*x + e))*sinh(f*x + e) + b)/(cosh(f*x + e)^4 + 4*cosh(f*x + e)*sinh(f*x + e)^3 + sinh(f*x + e)^4 + 2*(3*cosh(f*x + e)^2 - 1)*sinh(f*x + e)^2 - 2*cosh(f*x + e)^2 + 4*(cosh(f*x + e)^3 - cosh(f*x + e))*sinh(f*x + e) + 1)) + 4*sqrt(2)*((8*a^3 - 24*a^2*b + 15*a*b^2)*cosh(f*x + e)^9 + 9*(8*a^3 - 24*a^2*b + 15*a*b^2)*cosh(f*x + e)*sinh(f*x + e)^8 + (8*a^3 - 24*a^2*b + 15*a*b^2)*sinh(f*x + e)^9 - 4*(16*a^3 - 29*a^2*b + 15*a*b^2)*cosh(f*x + e)^7 - 4*(16*a^3 - 29*a^2*b + 15*a*b^2 - 9*(8*a^3 - 24*a^2*b + 15*a*b^2)*cosh(f*x + e)^2)*sinh(f*x + e)^7 + 28*(3*(8*a^3 - 24*a^2*b + 15*a*b^2)*cosh(f*x + e)^3 - (16*a^3 - 29*a^2*b + 15*a*b^2)*cosh(f*x + e))*sinh(f*x + e)^6 + 2*(40*a^3 - 92*a^2*b + 45*a*b^2)*cosh(f*x + e)^5 + 2*(63*(8*a^3 - 24*a^2*b + 15*a*b^2)*cosh(f*x + e)^4 + 40*a^3 - 92*a^2*b + 45*a*b^2 - 42*(16*a^3 - 29*a^2*b + 15*a*b^2)*cosh(f*x + e)^2)*sinh(f*x + e)^5 + 2*(63*(8*a^3 - 24*a^2*b + 15*a*b^2)*cosh(f*x + e)^5 - 70*(16*a^3 - 29*a^2*b + 15*a*b^2)*cosh(f*x + e)^3 + 5*(40*a^3 - 92*a^2*b + 45*a*b^2)*cosh(f*x + e))*sinh(f*x + e)^4 - 4*(16*a^3 - 29*a^2*b + 15*a*b^2)*cosh(f*x + e)^3 + 4*(21*(8*a^3 - 24*a^2*b + 15*a*b^2)*cosh(f*x + e)^6 - 35*(16*a^3 - 29*a^2*b + 15*a*b^2)*cosh(f*x + e)^4 - 16*a^3 + 29*a^2*b - 15*a*b^2 + 5*(40*a^3 - 92*a^2*b + 45*a*b^2)*cosh(f*x + e)^2)*sinh(f*x + e)^3 + 4*(9*(8*a^3 - 24*a^2*b + 15*a*b^2)*cosh(f*x + e)^7 - 21*(16*a^3 - 29*a^2*b + 15*a*b^2)*cosh(f*x + e)^5 + 5*(40*a^3 - 92*a^2*b + 45*a*b^2)*cosh(f*x + e)^3 - 3*(16*a^3 - 29*a^2*b + 15*a*b^2)*cosh(f*x + e))*sinh(f*x + e)^2 + (8*a^3 - 24*a^2*b + 15*a*b^2)*cosh(f*x + e) + (9*(8*a^3 - 24*a^2*b + 15*a*b^2)*cosh(f*x + e)^8 - 28*(16*a^3 - 29*a^2*b + 15*a*b^2)*cosh(f*x + e)^6 + 10*(40*a^3 - 92*a^2*b + 45*a*b^2)*cosh(f*x + e)^4 + 8*a^3 - 24*a^2*b + 15*a*b^2 - 12*(16*a^3 - 29*a^2*b + 15*a*b^2)*cosh(f*x + e)^2)*sinh(f*x + e))*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/(a^4*b*f*cosh(f*x + e)^12 + 12*a^4*b*f*cosh(f*x + e)*sinh(f*x + e)^11 + a^4*b*f*sinh(f*x + e)^12 + 2*(2*a^5 - 3*a^4*b)*f*cosh(f*x + e)^10 + 2*(33*a^4*b*f*cosh(f*x + e)^2 + (2*a^5 - 3*a^4*b)*f)*sinh(f*x + e)^10 - (16*a^5 - 15*a^4*b)*f*cosh(f*x + e)^8 + 20*(11*a^4*b*f*cosh(f*x + e)^3 + (2*a^5 - 3*a^4*b)*f*cosh(f*x + e))*sinh(f*x + e)^9 + (495*a^4*b*f*cosh(f*x + e)^4 + 90*(2*a^5 - 3*a^4*b)*f*cosh(f*x + e)^2 - (16*a^5 - 15*a^4*b)*f)*sinh(f*x + e)^8 + 4*(6*a^5 - 5*a^4*b)*f*cosh(f*x + e)^6 + 8*(99*a^4*b*f*cosh(f*x + e)^5 + 30*(2*a^5 - 3*a^4*b)*f*cosh(f*x + e)^3 - (16*a^5 - 15*a^4*b)*f*cosh(f*x + e))*sinh(f*x + e)^7 + 4*(231*a^4*b*f*cosh(f*x + e)^6 + 105*(2*a^5 - 3*a^4*b)*f*cosh(f*x + e)^4 - 7*(16*a^5 - 15*a^4*b)*f*cosh(f*x + e)^2 + (6*a^5 - 5*a^4*b)*f)*sinh(f*x + e)^6 + a^4*b*f - (16*a^5 - 15*a^4*b)*f*cosh(f*x + e)^4 + 8*(99*a^4*b*f*cosh(f*x + e)^7 + 63*(2*a^5 - 3*a^4*b)*f*cosh(f*x + e)^5 - 7*(16*a^5 - 15*a^4*b)*f*cosh(f*x + e)^3 + 3*(6*a^5 - 5*a^4*b)*f*cosh(f*x + e))*sinh(f*x + e)^5 + (495*a^4*b*f*cosh(f*x + e)^8 + 420*(2*a^5 - 3*a^4*b)*f*cosh(f*x + e)^6 - 70*(16*a^5 - 15*a^4*b)*f*cosh(f*x + e)^4 + 60*(6*a^5 - 5*a^4*b)*f*cosh(f*x + e)^2 - (16*a^5 - 15*a^4*b)*f)*sinh(f*x + e)^4 + 2*(2*a^5 - 3*a^4*b)*f*cosh(f*x + e)^2 + 4*(55*a^4*b*f*cosh(f*x + e)^9 + 60*(2*a^5 - 3*a^4*b)*f*cosh(f*x + e)^7 - 14*(16*a^5 - 15*a^4*b)*f*cosh(f*x + e)^5 + 20*(6*a^5 - 5*a^4*b)*f*cosh(f*x + e)^3 - (16*a^5 - 15*a^4*b)*f*cosh(f*x + e))*sinh(f*x + e)^3 + 2*(33*a^4*b*f*cosh(f*x + e)^10 + 45*(2*a^5 - 3*a^4*b)*f*cosh(f*x + e)^8 - 14*(16*a^5 - 15*a^4*b)*f*cosh(f*x + e)^6 + 30*(6*a^5 - 5*a^4*b)*f*cosh(f*x + e)^4 - 3*(16*a^5 - 15*a^4*b)*f*cosh(f*x + e)^2 + (2*a^5 - 3*a^4*b)*f)*sinh(f*x + e)^2 + 4*(3*a^4*b*f*cosh(f*x + e)^11 + 5*(2*a^5 - 3*a^4*b)*f*cosh(f*x + e)^9 - 2*(16*a^5 - 15*a^4*b)*f*cosh(f*x + e)^7 + 6*(6*a^5 - 5*a^4*b)*f*cosh(f*x + e)^5 - (16*a^5 - 15*a^4*b)*f*cosh(f*x + e)^3 + (2*a^5 - 3*a^4*b)*f*cosh(f*x + e))*sinh(f*x + e)), 1/8*(((8*a^2*b - 24*a*b^2 + 15*b^3)*cosh(f*x + e)^12 + 12*(8*a^2*b - 24*a*b^2 + 15*b^3)*cosh(f*x + e)*sinh(f*x + e)^11 + (8*a^2*b - 24*a*b^2 + 15*b^3)*sinh(f*x + e)^12 + 2*(16*a^3 - 72*a^2*b + 102*a*b^2 - 45*b^3)*cosh(f*x + e)^10 + 2*(16*a^3 - 72*a^2*b + 102*a*b^2 - 45*b^3 + 33*(8*a^2*b - 24*a*b^2 + 15*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^10 + 20*(11*(8*a^2*b - 24*a*b^2 + 15*b^3)*cosh(f*x + e)^3 + (16*a^3 - 72*a^2*b + 102*a*b^2 - 45*b^3)*cosh(f*x + e))*sinh(f*x + e)^9 - (128*a^3 - 504*a^2*b + 600*a*b^2 - 225*b^3)*cosh(f*x + e)^8 + (495*(8*a^2*b - 24*a*b^2 + 15*b^3)*cosh(f*x + e)^4 - 128*a^3 + 504*a^2*b - 600*a*b^2 + 225*b^3 + 90*(16*a^3 - 72*a^2*b + 102*a*b^2 - 45*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^8 + 8*(99*(8*a^2*b - 24*a*b^2 + 15*b^3)*cosh(f*x + e)^5 + 30*(16*a^3 - 72*a^2*b + 102*a*b^2 - 45*b^3)*cosh(f*x + e)^3 - (128*a^3 - 504*a^2*b + 600*a*b^2 - 225*b^3)*cosh(f*x + e))*sinh(f*x + e)^7 + 4*(48*a^3 - 184*a^2*b + 210*a*b^2 - 75*b^3)*cosh(f*x + e)^6 + 4*(231*(8*a^2*b - 24*a*b^2 + 15*b^3)*cosh(f*x + e)^6 + 105*(16*a^3 - 72*a^2*b + 102*a*b^2 - 45*b^3)*cosh(f*x + e)^4 + 48*a^3 - 184*a^2*b + 210*a*b^2 - 75*b^3 - 7*(128*a^3 - 504*a^2*b + 600*a*b^2 - 225*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^6 + 8*(99*(8*a^2*b - 24*a*b^2 + 15*b^3)*cosh(f*x + e)^7 + 63*(16*a^3 - 72*a^2*b + 102*a*b^2 - 45*b^3)*cosh(f*x + e)^5 - 7*(128*a^3 - 504*a^2*b + 600*a*b^2 - 225*b^3)*cosh(f*x + e)^3 + 3*(48*a^3 - 184*a^2*b + 210*a*b^2 - 75*b^3)*cosh(f*x + e))*sinh(f*x + e)^5 - (128*a^3 - 504*a^2*b + 600*a*b^2 - 225*b^3)*cosh(f*x + e)^4 + (495*(8*a^2*b - 24*a*b^2 + 15*b^3)*cosh(f*x + e)^8 + 420*(16*a^3 - 72*a^2*b + 102*a*b^2 - 45*b^3)*cosh(f*x + e)^6 - 70*(128*a^3 - 504*a^2*b + 600*a*b^2 - 225*b^3)*cosh(f*x + e)^4 - 128*a^3 + 504*a^2*b - 600*a*b^2 + 225*b^3 + 60*(48*a^3 - 184*a^2*b + 210*a*b^2 - 75*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^4 + 4*(55*(8*a^2*b - 24*a*b^2 + 15*b^3)*cosh(f*x + e)^9 + 60*(16*a^3 - 72*a^2*b + 102*a*b^2 - 45*b^3)*cosh(f*x + e)^7 - 14*(128*a^3 - 504*a^2*b + 600*a*b^2 - 225*b^3)*cosh(f*x + e)^5 + 20*(48*a^3 - 184*a^2*b + 210*a*b^2 - 75*b^3)*cosh(f*x + e)^3 - (128*a^3 - 504*a^2*b + 600*a*b^2 - 225*b^3)*cosh(f*x + e))*sinh(f*x + e)^3 + 8*a^2*b - 24*a*b^2 + 15*b^3 + 2*(16*a^3 - 72*a^2*b + 102*a*b^2 - 45*b^3)*cosh(f*x + e)^2 + 2*(33*(8*a^2*b - 24*a*b^2 + 15*b^3)*cosh(f*x + e)^10 + 45*(16*a^3 - 72*a^2*b + 102*a*b^2 - 45*b^3)*cosh(f*x + e)^8 - 14*(128*a^3 - 504*a^2*b + 600*a*b^2 - 225*b^3)*cosh(f*x + e)^6 + 30*(48*a^3 - 184*a^2*b + 210*a*b^2 - 75*b^3)*cosh(f*x + e)^4 + 16*a^3 - 72*a^2*b + 102*a*b^2 - 45*b^3 - 3*(128*a^3 - 504*a^2*b + 600*a*b^2 - 225*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^2 + 4*(3*(8*a^2*b - 24*a*b^2 + 15*b^3)*cosh(f*x + e)^11 + 5*(16*a^3 - 72*a^2*b + 102*a*b^2 - 45*b^3)*cosh(f*x + e)^9 - 2*(128*a^3 - 504*a^2*b + 600*a*b^2 - 225*b^3)*cosh(f*x + e)^7 + 6*(48*a^3 - 184*a^2*b + 210*a*b^2 - 75*b^3)*cosh(f*x + e)^5 - (128*a^3 - 504*a^2*b + 600*a*b^2 - 225*b^3)*cosh(f*x + e)^3 + (16*a^3 - 72*a^2*b + 102*a*b^2 - 45*b^3)*cosh(f*x + e))*sinh(f*x + e))*sqrt(-a)*arctan(1/2*sqrt(2)*sqrt(-a)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/(a*cosh(f*x + e) + a*sinh(f*x + e))) + 2*sqrt(2)*((8*a^3 - 24*a^2*b + 15*a*b^2)*cosh(f*x + e)^9 + 9*(8*a^3 - 24*a^2*b + 15*a*b^2)*cosh(f*x + e)*sinh(f*x + e)^8 + (8*a^3 - 24*a^2*b + 15*a*b^2)*sinh(f*x + e)^9 - 4*(16*a^3 - 29*a^2*b + 15*a*b^2)*cosh(f*x + e)^7 - 4*(16*a^3 - 29*a^2*b + 15*a*b^2 - 9*(8*a^3 - 24*a^2*b + 15*a*b^2)*cosh(f*x + e)^2)*sinh(f*x + e)^7 + 28*(3*(8*a^3 - 24*a^2*b + 15*a*b^2)*cosh(f*x + e)^3 - (16*a^3 - 29*a^2*b + 15*a*b^2)*cosh(f*x + e))*sinh(f*x + e)^6 + 2*(40*a^3 - 92*a^2*b + 45*a*b^2)*cosh(f*x + e)^5 + 2*(63*(8*a^3 - 24*a^2*b + 15*a*b^2)*cosh(f*x + e)^4 + 40*a^3 - 92*a^2*b + 45*a*b^2 - 42*(16*a^3 - 29*a^2*b + 15*a*b^2)*cosh(f*x + e)^2)*sinh(f*x + e)^5 + 2*(63*(8*a^3 - 24*a^2*b + 15*a*b^2)*cosh(f*x + e)^5 - 70*(16*a^3 - 29*a^2*b + 15*a*b^2)*cosh(f*x + e)^3 + 5*(40*a^3 - 92*a^2*b + 45*a*b^2)*cosh(f*x + e))*sinh(f*x + e)^4 - 4*(16*a^3 - 29*a^2*b + 15*a*b^2)*cosh(f*x + e)^3 + 4*(21*(8*a^3 - 24*a^2*b + 15*a*b^2)*cosh(f*x + e)^6 - 35*(16*a^3 - 29*a^2*b + 15*a*b^2)*cosh(f*x + e)^4 - 16*a^3 + 29*a^2*b - 15*a*b^2 + 5*(40*a^3 - 92*a^2*b + 45*a*b^2)*cosh(f*x + e)^2)*sinh(f*x + e)^3 + 4*(9*(8*a^3 - 24*a^2*b + 15*a*b^2)*cosh(f*x + e)^7 - 21*(16*a^3 - 29*a^2*b + 15*a*b^2)*cosh(f*x + e)^5 + 5*(40*a^3 - 92*a^2*b + 45*a*b^2)*cosh(f*x + e)^3 - 3*(16*a^3 - 29*a^2*b + 15*a*b^2)*cosh(f*x + e))*sinh(f*x + e)^2 + (8*a^3 - 24*a^2*b + 15*a*b^2)*cosh(f*x + e) + (9*(8*a^3 - 24*a^2*b + 15*a*b^2)*cosh(f*x + e)^8 - 28*(16*a^3 - 29*a^2*b + 15*a*b^2)*cosh(f*x + e)^6 + 10*(40*a^3 - 92*a^2*b + 45*a*b^2)*cosh(f*x + e)^4 + 8*a^3 - 24*a^2*b + 15*a*b^2 - 12*(16*a^3 - 29*a^2*b + 15*a*b^2)*cosh(f*x + e)^2)*sinh(f*x + e))*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/(a^4*b*f*cosh(f*x + e)^12 + 12*a^4*b*f*cosh(f*x + e)*sinh(f*x + e)^11 + a^4*b*f*sinh(f*x + e)^12 + 2*(2*a^5 - 3*a^4*b)*f*cosh(f*x + e)^10 + 2*(33*a^4*b*f*cosh(f*x + e)^2 + (2*a^5 - 3*a^4*b)*f)*sinh(f*x + e)^10 - (16*a^5 - 15*a^4*b)*f*cosh(f*x + e)^8 + 20*(11*a^4*b*f*cosh(f*x + e)^3 + (2*a^5 - 3*a^4*b)*f*cosh(f*x + e))*sinh(f*x + e)^9 + (495*a^4*b*f*cosh(f*x + e)^4 + 90*(2*a^5 - 3*a^4*b)*f*cosh(f*x + e)^2 - (16*a^5 - 15*a^4*b)*f)*sinh(f*x + e)^8 + 4*(6*a^5 - 5*a^4*b)*f*cosh(f*x + e)^6 + 8*(99*a^4*b*f*cosh(f*x + e)^5 + 30*(2*a^5 - 3*a^4*b)*f*cosh(f*x + e)^3 - (16*a^5 - 15*a^4*b)*f*cosh(f*x + e))*sinh(f*x + e)^7 + 4*(231*a^4*b*f*cosh(f*x + e)^6 + 105*(2*a^5 - 3*a^4*b)*f*cosh(f*x + e)^4 - 7*(16*a^5 - 15*a^4*b)*f*cosh(f*x + e)^2 + (6*a^5 - 5*a^4*b)*f)*sinh(f*x + e)^6 + a^4*b*f - (16*a^5 - 15*a^4*b)*f*cosh(f*x + e)^4 + 8*(99*a^4*b*f*cosh(f*x + e)^7 + 63*(2*a^5 - 3*a^4*b)*f*cosh(f*x + e)^5 - 7*(16*a^5 - 15*a^4*b)*f*cosh(f*x + e)^3 + 3*(6*a^5 - 5*a^4*b)*f*cosh(f*x + e))*sinh(f*x + e)^5 + (495*a^4*b*f*cosh(f*x + e)^8 + 420*(2*a^5 - 3*a^4*b)*f*cosh(f*x + e)^6 - 70*(16*a^5 - 15*a^4*b)*f*cosh(f*x + e)^4 + 60*(6*a^5 - 5*a^4*b)*f*cosh(f*x + e)^2 - (16*a^5 - 15*a^4*b)*f)*sinh(f*x + e)^4 + 2*(2*a^5 - 3*a^4*b)*f*cosh(f*x + e)^2 + 4*(55*a^4*b*f*cosh(f*x + e)^9 + 60*(2*a^5 - 3*a^4*b)*f*cosh(f*x + e)^7 - 14*(16*a^5 - 15*a^4*b)*f*cosh(f*x + e)^5 + 20*(6*a^5 - 5*a^4*b)*f*cosh(f*x + e)^3 - (16*a^5 - 15*a^4*b)*f*cosh(f*x + e))*sinh(f*x + e)^3 + 2*(33*a^4*b*f*cosh(f*x + e)^10 + 45*(2*a^5 - 3*a^4*b)*f*cosh(f*x + e)^8 - 14*(16*a^5 - 15*a^4*b)*f*cosh(f*x + e)^6 + 30*(6*a^5 - 5*a^4*b)*f*cosh(f*x + e)^4 - 3*(16*a^5 - 15*a^4*b)*f*cosh(f*x + e)^2 + (2*a^5 - 3*a^4*b)*f)*sinh(f*x + e)^2 + 4*(3*a^4*b*f*cosh(f*x + e)^11 + 5*(2*a^5 - 3*a^4*b)*f*cosh(f*x + e)^9 - 2*(16*a^5 - 15*a^4*b)*f*cosh(f*x + e)^7 + 6*(6*a^5 - 5*a^4*b)*f*cosh(f*x + e)^5 - (16*a^5 - 15*a^4*b)*f*cosh(f*x + e)^3 + (2*a^5 - 3*a^4*b)*f*cosh(f*x + e))*sinh(f*x + e))]","B",0
496,0,0,0,0.476959," ","integrate(tanh(f*x+e)^4/(a+b*sinh(f*x+e)^2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sinh\left(f x + e\right)^{2} + a} \tanh\left(f x + e\right)^{4}}{b^{2} \sinh\left(f x + e\right)^{4} + 2 \, a b \sinh\left(f x + e\right)^{2} + a^{2}}, x\right)"," ",0,"integral(sqrt(b*sinh(f*x + e)^2 + a)*tanh(f*x + e)^4/(b^2*sinh(f*x + e)^4 + 2*a*b*sinh(f*x + e)^2 + a^2), x)","F",0
497,0,0,0,0.481387," ","integrate(tanh(f*x+e)^2/(a+b*sinh(f*x+e)^2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sinh\left(f x + e\right)^{2} + a} \tanh\left(f x + e\right)^{2}}{b^{2} \sinh\left(f x + e\right)^{4} + 2 \, a b \sinh\left(f x + e\right)^{2} + a^{2}}, x\right)"," ",0,"integral(sqrt(b*sinh(f*x + e)^2 + a)*tanh(f*x + e)^2/(b^2*sinh(f*x + e)^4 + 2*a*b*sinh(f*x + e)^2 + a^2), x)","F",0
498,0,0,0,0.528410," ","integrate(1/(a+b*sinh(f*x+e)^2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sinh\left(f x + e\right)^{2} + a}}{b^{2} \sinh\left(f x + e\right)^{4} + 2 \, a b \sinh\left(f x + e\right)^{2} + a^{2}}, x\right)"," ",0,"integral(sqrt(b*sinh(f*x + e)^2 + a)/(b^2*sinh(f*x + e)^4 + 2*a*b*sinh(f*x + e)^2 + a^2), x)","F",0
499,0,0,0,0.462514," ","integrate(coth(f*x+e)^2/(a+b*sinh(f*x+e)^2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sinh\left(f x + e\right)^{2} + a} \coth\left(f x + e\right)^{2}}{b^{2} \sinh\left(f x + e\right)^{4} + 2 \, a b \sinh\left(f x + e\right)^{2} + a^{2}}, x\right)"," ",0,"integral(sqrt(b*sinh(f*x + e)^2 + a)*coth(f*x + e)^2/(b^2*sinh(f*x + e)^4 + 2*a*b*sinh(f*x + e)^2 + a^2), x)","F",0
500,0,0,0,0.501563," ","integrate(coth(f*x+e)^4/(a+b*sinh(f*x+e)^2)^(3/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sinh\left(f x + e\right)^{2} + a} \coth\left(f x + e\right)^{4}}{b^{2} \sinh\left(f x + e\right)^{4} + 2 \, a b \sinh\left(f x + e\right)^{2} + a^{2}}, x\right)"," ",0,"integral(sqrt(b*sinh(f*x + e)^2 + a)*coth(f*x + e)^4/(b^2*sinh(f*x + e)^4 + 2*a*b*sinh(f*x + e)^2 + a^2), x)","F",0
501,-1,0,0,0.000000," ","integrate(tanh(f*x+e)^5/(a+b*sinh(f*x+e)^2)^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
502,1,10506,0,1.389768," ","integrate(tanh(f*x+e)^3/(a+b*sinh(f*x+e)^2)^(5/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left({\left(2 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{12} + 12 \, {\left(2 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{11} + {\left(2 \, a b^{2} + 3 \, b^{3}\right)} \sinh\left(f x + e\right)^{12} + 2 \, {\left(8 \, a^{2} b + 10 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{10} + 2 \, {\left(8 \, a^{2} b + 10 \, a b^{2} - 3 \, b^{3} + 33 \, {\left(2 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{10} + 20 \, {\left(11 \, {\left(2 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} + {\left(8 \, a^{2} b + 10 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{9} + {\left(32 \, a^{3} + 48 \, a^{2} b - 2 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{8} + {\left(495 \, {\left(2 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} + 32 \, a^{3} + 48 \, a^{2} b - 2 \, a b^{2} - 3 \, b^{3} + 90 \, {\left(8 \, a^{2} b + 10 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{8} + 8 \, {\left(99 \, {\left(2 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{5} + 30 \, {\left(8 \, a^{2} b + 10 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} + {\left(32 \, a^{3} + 48 \, a^{2} b - 2 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{7} + 4 \, {\left(16 \, a^{3} + 16 \, a^{2} b - 10 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{6} + 4 \, {\left(231 \, {\left(2 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{6} + 105 \, {\left(8 \, a^{2} b + 10 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} + 16 \, a^{3} + 16 \, a^{2} b - 10 \, a b^{2} + 3 \, b^{3} + 7 \, {\left(32 \, a^{3} + 48 \, a^{2} b - 2 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{6} + 8 \, {\left(99 \, {\left(2 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{7} + 63 \, {\left(8 \, a^{2} b + 10 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{5} + 7 \, {\left(32 \, a^{3} + 48 \, a^{2} b - 2 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(16 \, a^{3} + 16 \, a^{2} b - 10 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + {\left(32 \, a^{3} + 48 \, a^{2} b - 2 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} + {\left(495 \, {\left(2 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{8} + 420 \, {\left(8 \, a^{2} b + 10 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{6} + 70 \, {\left(32 \, a^{3} + 48 \, a^{2} b - 2 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} + 32 \, a^{3} + 48 \, a^{2} b - 2 \, a b^{2} - 3 \, b^{3} + 60 \, {\left(16 \, a^{3} + 16 \, a^{2} b - 10 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(55 \, {\left(2 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{9} + 60 \, {\left(8 \, a^{2} b + 10 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{7} + 14 \, {\left(32 \, a^{3} + 48 \, a^{2} b - 2 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{5} + 20 \, {\left(16 \, a^{3} + 16 \, a^{2} b - 10 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} + {\left(32 \, a^{3} + 48 \, a^{2} b - 2 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 2 \, a b^{2} + 3 \, b^{3} + 2 \, {\left(8 \, a^{2} b + 10 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(33 \, {\left(2 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{10} + 45 \, {\left(8 \, a^{2} b + 10 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{8} + 14 \, {\left(32 \, a^{3} + 48 \, a^{2} b - 2 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{6} + 30 \, {\left(16 \, a^{3} + 16 \, a^{2} b - 10 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} + 8 \, a^{2} b + 10 \, a b^{2} - 3 \, b^{3} + 3 \, {\left(32 \, a^{3} + 48 \, a^{2} b - 2 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(3 \, {\left(2 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{11} + 5 \, {\left(8 \, a^{2} b + 10 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{9} + 2 \, {\left(32 \, a^{3} + 48 \, a^{2} b - 2 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{7} + 6 \, {\left(16 \, a^{3} + 16 \, a^{2} b - 10 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{5} + {\left(32 \, a^{3} + 48 \, a^{2} b - 2 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} + {\left(8 \, a^{2} b + 10 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{a - b} \log\left(\frac{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(4 \, a - 3 \, b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + 4 \, a - 3 \, b\right)} \sinh\left(f x + e\right)^{2} + 4 \, \sqrt{2} \sqrt{a - b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} {\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right)\right)} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(4 \, a - 3 \, b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}{\cosh\left(f x + e\right)^{4} + 4 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + \sinh\left(f x + e\right)^{4} + 2 \, {\left(3 \, \cosh\left(f x + e\right)^{2} + 1\right)} \sinh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right)^{2} + 4 \, {\left(\cosh\left(f x + e\right)^{3} + \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + 1}\right) - 4 \, \sqrt{2} {\left(3 \, {\left(2 \, a^{2} b + a b^{2} - 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{9} + 27 \, {\left(2 \, a^{2} b + a b^{2} - 3 \, b^{3}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{8} + 3 \, {\left(2 \, a^{2} b + a b^{2} - 3 \, b^{3}\right)} \sinh\left(f x + e\right)^{9} + 4 \, {\left(8 \, a^{3} + 2 \, a^{2} b - 13 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{7} + 4 \, {\left(8 \, a^{3} + 2 \, a^{2} b - 13 \, a b^{2} + 3 \, b^{3} + 27 \, {\left(2 \, a^{2} b + a b^{2} - 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{7} + 28 \, {\left(9 \, {\left(2 \, a^{2} b + a b^{2} - 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} + {\left(8 \, a^{3} + 2 \, a^{2} b - 13 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{6} + 2 \, {\left(56 \, a^{3} - 70 \, a^{2} b + 17 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{5} + 2 \, {\left(189 \, {\left(2 \, a^{2} b + a b^{2} - 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} + 56 \, a^{3} - 70 \, a^{2} b + 17 \, a b^{2} - 3 \, b^{3} + 42 \, {\left(8 \, a^{3} + 2 \, a^{2} b - 13 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(189 \, {\left(2 \, a^{2} b + a b^{2} - 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{5} + 70 \, {\left(8 \, a^{3} + 2 \, a^{2} b - 13 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} + 5 \, {\left(56 \, a^{3} - 70 \, a^{2} b + 17 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(8 \, a^{3} + 2 \, a^{2} b - 13 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} + 4 \, {\left(63 \, {\left(2 \, a^{2} b + a b^{2} - 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{6} + 35 \, {\left(8 \, a^{3} + 2 \, a^{2} b - 13 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} + 8 \, a^{3} + 2 \, a^{2} b - 13 \, a b^{2} + 3 \, b^{3} + 5 \, {\left(56 \, a^{3} - 70 \, a^{2} b + 17 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{3} + 4 \, {\left(27 \, {\left(2 \, a^{2} b + a b^{2} - 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{7} + 21 \, {\left(8 \, a^{3} + 2 \, a^{2} b - 13 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{5} + 5 \, {\left(56 \, a^{3} - 70 \, a^{2} b + 17 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(8 \, a^{3} + 2 \, a^{2} b - 13 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{2} + 3 \, {\left(2 \, a^{2} b + a b^{2} - 3 \, b^{3}\right)} \cosh\left(f x + e\right) + {\left(27 \, {\left(2 \, a^{2} b + a b^{2} - 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{8} + 28 \, {\left(8 \, a^{3} + 2 \, a^{2} b - 13 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{6} + 10 \, {\left(56 \, a^{3} - 70 \, a^{2} b + 17 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} + 6 \, a^{2} b + 3 \, a b^{2} - 9 \, b^{3} + 12 \, {\left(8 \, a^{3} + 2 \, a^{2} b - 13 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{12 \, {\left({\left(a^{4} b^{2} - 4 \, a^{3} b^{3} + 6 \, a^{2} b^{4} - 4 \, a b^{5} + b^{6}\right)} f \cosh\left(f x + e\right)^{12} + 12 \, {\left(a^{4} b^{2} - 4 \, a^{3} b^{3} + 6 \, a^{2} b^{4} - 4 \, a b^{5} + b^{6}\right)} f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{11} + {\left(a^{4} b^{2} - 4 \, a^{3} b^{3} + 6 \, a^{2} b^{4} - 4 \, a b^{5} + b^{6}\right)} f \sinh\left(f x + e\right)^{12} + 2 \, {\left(4 \, a^{5} b - 17 \, a^{4} b^{2} + 28 \, a^{3} b^{3} - 22 \, a^{2} b^{4} + 8 \, a b^{5} - b^{6}\right)} f \cosh\left(f x + e\right)^{10} + 2 \, {\left(33 \, {\left(a^{4} b^{2} - 4 \, a^{3} b^{3} + 6 \, a^{2} b^{4} - 4 \, a b^{5} + b^{6}\right)} f \cosh\left(f x + e\right)^{2} + {\left(4 \, a^{5} b - 17 \, a^{4} b^{2} + 28 \, a^{3} b^{3} - 22 \, a^{2} b^{4} + 8 \, a b^{5} - b^{6}\right)} f\right)} \sinh\left(f x + e\right)^{10} + {\left(16 \, a^{6} - 64 \, a^{5} b + 95 \, a^{4} b^{2} - 60 \, a^{3} b^{3} + 10 \, a^{2} b^{4} + 4 \, a b^{5} - b^{6}\right)} f \cosh\left(f x + e\right)^{8} + 20 \, {\left(11 \, {\left(a^{4} b^{2} - 4 \, a^{3} b^{3} + 6 \, a^{2} b^{4} - 4 \, a b^{5} + b^{6}\right)} f \cosh\left(f x + e\right)^{3} + {\left(4 \, a^{5} b - 17 \, a^{4} b^{2} + 28 \, a^{3} b^{3} - 22 \, a^{2} b^{4} + 8 \, a b^{5} - b^{6}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{9} + {\left(495 \, {\left(a^{4} b^{2} - 4 \, a^{3} b^{3} + 6 \, a^{2} b^{4} - 4 \, a b^{5} + b^{6}\right)} f \cosh\left(f x + e\right)^{4} + 90 \, {\left(4 \, a^{5} b - 17 \, a^{4} b^{2} + 28 \, a^{3} b^{3} - 22 \, a^{2} b^{4} + 8 \, a b^{5} - b^{6}\right)} f \cosh\left(f x + e\right)^{2} + {\left(16 \, a^{6} - 64 \, a^{5} b + 95 \, a^{4} b^{2} - 60 \, a^{3} b^{3} + 10 \, a^{2} b^{4} + 4 \, a b^{5} - b^{6}\right)} f\right)} \sinh\left(f x + e\right)^{8} + 4 \, {\left(8 \, a^{6} - 36 \, a^{5} b + 65 \, a^{4} b^{2} - 60 \, a^{3} b^{3} + 30 \, a^{2} b^{4} - 8 \, a b^{5} + b^{6}\right)} f \cosh\left(f x + e\right)^{6} + 8 \, {\left(99 \, {\left(a^{4} b^{2} - 4 \, a^{3} b^{3} + 6 \, a^{2} b^{4} - 4 \, a b^{5} + b^{6}\right)} f \cosh\left(f x + e\right)^{5} + 30 \, {\left(4 \, a^{5} b - 17 \, a^{4} b^{2} + 28 \, a^{3} b^{3} - 22 \, a^{2} b^{4} + 8 \, a b^{5} - b^{6}\right)} f \cosh\left(f x + e\right)^{3} + {\left(16 \, a^{6} - 64 \, a^{5} b + 95 \, a^{4} b^{2} - 60 \, a^{3} b^{3} + 10 \, a^{2} b^{4} + 4 \, a b^{5} - b^{6}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{7} + 4 \, {\left(231 \, {\left(a^{4} b^{2} - 4 \, a^{3} b^{3} + 6 \, a^{2} b^{4} - 4 \, a b^{5} + b^{6}\right)} f \cosh\left(f x + e\right)^{6} + 105 \, {\left(4 \, a^{5} b - 17 \, a^{4} b^{2} + 28 \, a^{3} b^{3} - 22 \, a^{2} b^{4} + 8 \, a b^{5} - b^{6}\right)} f \cosh\left(f x + e\right)^{4} + 7 \, {\left(16 \, a^{6} - 64 \, a^{5} b + 95 \, a^{4} b^{2} - 60 \, a^{3} b^{3} + 10 \, a^{2} b^{4} + 4 \, a b^{5} - b^{6}\right)} f \cosh\left(f x + e\right)^{2} + {\left(8 \, a^{6} - 36 \, a^{5} b + 65 \, a^{4} b^{2} - 60 \, a^{3} b^{3} + 30 \, a^{2} b^{4} - 8 \, a b^{5} + b^{6}\right)} f\right)} \sinh\left(f x + e\right)^{6} + {\left(16 \, a^{6} - 64 \, a^{5} b + 95 \, a^{4} b^{2} - 60 \, a^{3} b^{3} + 10 \, a^{2} b^{4} + 4 \, a b^{5} - b^{6}\right)} f \cosh\left(f x + e\right)^{4} + 8 \, {\left(99 \, {\left(a^{4} b^{2} - 4 \, a^{3} b^{3} + 6 \, a^{2} b^{4} - 4 \, a b^{5} + b^{6}\right)} f \cosh\left(f x + e\right)^{7} + 63 \, {\left(4 \, a^{5} b - 17 \, a^{4} b^{2} + 28 \, a^{3} b^{3} - 22 \, a^{2} b^{4} + 8 \, a b^{5} - b^{6}\right)} f \cosh\left(f x + e\right)^{5} + 7 \, {\left(16 \, a^{6} - 64 \, a^{5} b + 95 \, a^{4} b^{2} - 60 \, a^{3} b^{3} + 10 \, a^{2} b^{4} + 4 \, a b^{5} - b^{6}\right)} f \cosh\left(f x + e\right)^{3} + 3 \, {\left(8 \, a^{6} - 36 \, a^{5} b + 65 \, a^{4} b^{2} - 60 \, a^{3} b^{3} + 30 \, a^{2} b^{4} - 8 \, a b^{5} + b^{6}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + {\left(495 \, {\left(a^{4} b^{2} - 4 \, a^{3} b^{3} + 6 \, a^{2} b^{4} - 4 \, a b^{5} + b^{6}\right)} f \cosh\left(f x + e\right)^{8} + 420 \, {\left(4 \, a^{5} b - 17 \, a^{4} b^{2} + 28 \, a^{3} b^{3} - 22 \, a^{2} b^{4} + 8 \, a b^{5} - b^{6}\right)} f \cosh\left(f x + e\right)^{6} + 70 \, {\left(16 \, a^{6} - 64 \, a^{5} b + 95 \, a^{4} b^{2} - 60 \, a^{3} b^{3} + 10 \, a^{2} b^{4} + 4 \, a b^{5} - b^{6}\right)} f \cosh\left(f x + e\right)^{4} + 60 \, {\left(8 \, a^{6} - 36 \, a^{5} b + 65 \, a^{4} b^{2} - 60 \, a^{3} b^{3} + 30 \, a^{2} b^{4} - 8 \, a b^{5} + b^{6}\right)} f \cosh\left(f x + e\right)^{2} + {\left(16 \, a^{6} - 64 \, a^{5} b + 95 \, a^{4} b^{2} - 60 \, a^{3} b^{3} + 10 \, a^{2} b^{4} + 4 \, a b^{5} - b^{6}\right)} f\right)} \sinh\left(f x + e\right)^{4} + 2 \, {\left(4 \, a^{5} b - 17 \, a^{4} b^{2} + 28 \, a^{3} b^{3} - 22 \, a^{2} b^{4} + 8 \, a b^{5} - b^{6}\right)} f \cosh\left(f x + e\right)^{2} + 4 \, {\left(55 \, {\left(a^{4} b^{2} - 4 \, a^{3} b^{3} + 6 \, a^{2} b^{4} - 4 \, a b^{5} + b^{6}\right)} f \cosh\left(f x + e\right)^{9} + 60 \, {\left(4 \, a^{5} b - 17 \, a^{4} b^{2} + 28 \, a^{3} b^{3} - 22 \, a^{2} b^{4} + 8 \, a b^{5} - b^{6}\right)} f \cosh\left(f x + e\right)^{7} + 14 \, {\left(16 \, a^{6} - 64 \, a^{5} b + 95 \, a^{4} b^{2} - 60 \, a^{3} b^{3} + 10 \, a^{2} b^{4} + 4 \, a b^{5} - b^{6}\right)} f \cosh\left(f x + e\right)^{5} + 20 \, {\left(8 \, a^{6} - 36 \, a^{5} b + 65 \, a^{4} b^{2} - 60 \, a^{3} b^{3} + 30 \, a^{2} b^{4} - 8 \, a b^{5} + b^{6}\right)} f \cosh\left(f x + e\right)^{3} + {\left(16 \, a^{6} - 64 \, a^{5} b + 95 \, a^{4} b^{2} - 60 \, a^{3} b^{3} + 10 \, a^{2} b^{4} + 4 \, a b^{5} - b^{6}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 2 \, {\left(33 \, {\left(a^{4} b^{2} - 4 \, a^{3} b^{3} + 6 \, a^{2} b^{4} - 4 \, a b^{5} + b^{6}\right)} f \cosh\left(f x + e\right)^{10} + 45 \, {\left(4 \, a^{5} b - 17 \, a^{4} b^{2} + 28 \, a^{3} b^{3} - 22 \, a^{2} b^{4} + 8 \, a b^{5} - b^{6}\right)} f \cosh\left(f x + e\right)^{8} + 14 \, {\left(16 \, a^{6} - 64 \, a^{5} b + 95 \, a^{4} b^{2} - 60 \, a^{3} b^{3} + 10 \, a^{2} b^{4} + 4 \, a b^{5} - b^{6}\right)} f \cosh\left(f x + e\right)^{6} + 30 \, {\left(8 \, a^{6} - 36 \, a^{5} b + 65 \, a^{4} b^{2} - 60 \, a^{3} b^{3} + 30 \, a^{2} b^{4} - 8 \, a b^{5} + b^{6}\right)} f \cosh\left(f x + e\right)^{4} + 3 \, {\left(16 \, a^{6} - 64 \, a^{5} b + 95 \, a^{4} b^{2} - 60 \, a^{3} b^{3} + 10 \, a^{2} b^{4} + 4 \, a b^{5} - b^{6}\right)} f \cosh\left(f x + e\right)^{2} + {\left(4 \, a^{5} b - 17 \, a^{4} b^{2} + 28 \, a^{3} b^{3} - 22 \, a^{2} b^{4} + 8 \, a b^{5} - b^{6}\right)} f\right)} \sinh\left(f x + e\right)^{2} + {\left(a^{4} b^{2} - 4 \, a^{3} b^{3} + 6 \, a^{2} b^{4} - 4 \, a b^{5} + b^{6}\right)} f + 4 \, {\left(3 \, {\left(a^{4} b^{2} - 4 \, a^{3} b^{3} + 6 \, a^{2} b^{4} - 4 \, a b^{5} + b^{6}\right)} f \cosh\left(f x + e\right)^{11} + 5 \, {\left(4 \, a^{5} b - 17 \, a^{4} b^{2} + 28 \, a^{3} b^{3} - 22 \, a^{2} b^{4} + 8 \, a b^{5} - b^{6}\right)} f \cosh\left(f x + e\right)^{9} + 2 \, {\left(16 \, a^{6} - 64 \, a^{5} b + 95 \, a^{4} b^{2} - 60 \, a^{3} b^{3} + 10 \, a^{2} b^{4} + 4 \, a b^{5} - b^{6}\right)} f \cosh\left(f x + e\right)^{7} + 6 \, {\left(8 \, a^{6} - 36 \, a^{5} b + 65 \, a^{4} b^{2} - 60 \, a^{3} b^{3} + 30 \, a^{2} b^{4} - 8 \, a b^{5} + b^{6}\right)} f \cosh\left(f x + e\right)^{5} + {\left(16 \, a^{6} - 64 \, a^{5} b + 95 \, a^{4} b^{2} - 60 \, a^{3} b^{3} + 10 \, a^{2} b^{4} + 4 \, a b^{5} - b^{6}\right)} f \cosh\left(f x + e\right)^{3} + {\left(4 \, a^{5} b - 17 \, a^{4} b^{2} + 28 \, a^{3} b^{3} - 22 \, a^{2} b^{4} + 8 \, a b^{5} - b^{6}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)}}, -\frac{3 \, {\left({\left(2 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{12} + 12 \, {\left(2 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{11} + {\left(2 \, a b^{2} + 3 \, b^{3}\right)} \sinh\left(f x + e\right)^{12} + 2 \, {\left(8 \, a^{2} b + 10 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{10} + 2 \, {\left(8 \, a^{2} b + 10 \, a b^{2} - 3 \, b^{3} + 33 \, {\left(2 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{10} + 20 \, {\left(11 \, {\left(2 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} + {\left(8 \, a^{2} b + 10 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{9} + {\left(32 \, a^{3} + 48 \, a^{2} b - 2 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{8} + {\left(495 \, {\left(2 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} + 32 \, a^{3} + 48 \, a^{2} b - 2 \, a b^{2} - 3 \, b^{3} + 90 \, {\left(8 \, a^{2} b + 10 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{8} + 8 \, {\left(99 \, {\left(2 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{5} + 30 \, {\left(8 \, a^{2} b + 10 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} + {\left(32 \, a^{3} + 48 \, a^{2} b - 2 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{7} + 4 \, {\left(16 \, a^{3} + 16 \, a^{2} b - 10 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{6} + 4 \, {\left(231 \, {\left(2 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{6} + 105 \, {\left(8 \, a^{2} b + 10 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} + 16 \, a^{3} + 16 \, a^{2} b - 10 \, a b^{2} + 3 \, b^{3} + 7 \, {\left(32 \, a^{3} + 48 \, a^{2} b - 2 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{6} + 8 \, {\left(99 \, {\left(2 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{7} + 63 \, {\left(8 \, a^{2} b + 10 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{5} + 7 \, {\left(32 \, a^{3} + 48 \, a^{2} b - 2 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(16 \, a^{3} + 16 \, a^{2} b - 10 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + {\left(32 \, a^{3} + 48 \, a^{2} b - 2 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} + {\left(495 \, {\left(2 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{8} + 420 \, {\left(8 \, a^{2} b + 10 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{6} + 70 \, {\left(32 \, a^{3} + 48 \, a^{2} b - 2 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} + 32 \, a^{3} + 48 \, a^{2} b - 2 \, a b^{2} - 3 \, b^{3} + 60 \, {\left(16 \, a^{3} + 16 \, a^{2} b - 10 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(55 \, {\left(2 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{9} + 60 \, {\left(8 \, a^{2} b + 10 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{7} + 14 \, {\left(32 \, a^{3} + 48 \, a^{2} b - 2 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{5} + 20 \, {\left(16 \, a^{3} + 16 \, a^{2} b - 10 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} + {\left(32 \, a^{3} + 48 \, a^{2} b - 2 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 2 \, a b^{2} + 3 \, b^{3} + 2 \, {\left(8 \, a^{2} b + 10 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(33 \, {\left(2 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{10} + 45 \, {\left(8 \, a^{2} b + 10 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{8} + 14 \, {\left(32 \, a^{3} + 48 \, a^{2} b - 2 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{6} + 30 \, {\left(16 \, a^{3} + 16 \, a^{2} b - 10 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} + 8 \, a^{2} b + 10 \, a b^{2} - 3 \, b^{3} + 3 \, {\left(32 \, a^{3} + 48 \, a^{2} b - 2 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(3 \, {\left(2 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{11} + 5 \, {\left(8 \, a^{2} b + 10 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{9} + 2 \, {\left(32 \, a^{3} + 48 \, a^{2} b - 2 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{7} + 6 \, {\left(16 \, a^{3} + 16 \, a^{2} b - 10 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{5} + {\left(32 \, a^{3} + 48 \, a^{2} b - 2 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} + {\left(8 \, a^{2} b + 10 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{-a + b} \arctan\left(-\frac{\sqrt{2} \sqrt{-a + b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{2 \, {\left({\left(a - b\right)} \cosh\left(f x + e\right) + {\left(a - b\right)} \sinh\left(f x + e\right)\right)}}\right) - 2 \, \sqrt{2} {\left(3 \, {\left(2 \, a^{2} b + a b^{2} - 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{9} + 27 \, {\left(2 \, a^{2} b + a b^{2} - 3 \, b^{3}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{8} + 3 \, {\left(2 \, a^{2} b + a b^{2} - 3 \, b^{3}\right)} \sinh\left(f x + e\right)^{9} + 4 \, {\left(8 \, a^{3} + 2 \, a^{2} b - 13 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{7} + 4 \, {\left(8 \, a^{3} + 2 \, a^{2} b - 13 \, a b^{2} + 3 \, b^{3} + 27 \, {\left(2 \, a^{2} b + a b^{2} - 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{7} + 28 \, {\left(9 \, {\left(2 \, a^{2} b + a b^{2} - 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} + {\left(8 \, a^{3} + 2 \, a^{2} b - 13 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{6} + 2 \, {\left(56 \, a^{3} - 70 \, a^{2} b + 17 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{5} + 2 \, {\left(189 \, {\left(2 \, a^{2} b + a b^{2} - 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} + 56 \, a^{3} - 70 \, a^{2} b + 17 \, a b^{2} - 3 \, b^{3} + 42 \, {\left(8 \, a^{3} + 2 \, a^{2} b - 13 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(189 \, {\left(2 \, a^{2} b + a b^{2} - 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{5} + 70 \, {\left(8 \, a^{3} + 2 \, a^{2} b - 13 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} + 5 \, {\left(56 \, a^{3} - 70 \, a^{2} b + 17 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(8 \, a^{3} + 2 \, a^{2} b - 13 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} + 4 \, {\left(63 \, {\left(2 \, a^{2} b + a b^{2} - 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{6} + 35 \, {\left(8 \, a^{3} + 2 \, a^{2} b - 13 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} + 8 \, a^{3} + 2 \, a^{2} b - 13 \, a b^{2} + 3 \, b^{3} + 5 \, {\left(56 \, a^{3} - 70 \, a^{2} b + 17 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{3} + 4 \, {\left(27 \, {\left(2 \, a^{2} b + a b^{2} - 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{7} + 21 \, {\left(8 \, a^{3} + 2 \, a^{2} b - 13 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{5} + 5 \, {\left(56 \, a^{3} - 70 \, a^{2} b + 17 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(8 \, a^{3} + 2 \, a^{2} b - 13 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{2} + 3 \, {\left(2 \, a^{2} b + a b^{2} - 3 \, b^{3}\right)} \cosh\left(f x + e\right) + {\left(27 \, {\left(2 \, a^{2} b + a b^{2} - 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{8} + 28 \, {\left(8 \, a^{3} + 2 \, a^{2} b - 13 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{6} + 10 \, {\left(56 \, a^{3} - 70 \, a^{2} b + 17 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} + 6 \, a^{2} b + 3 \, a b^{2} - 9 \, b^{3} + 12 \, {\left(8 \, a^{3} + 2 \, a^{2} b - 13 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{6 \, {\left({\left(a^{4} b^{2} - 4 \, a^{3} b^{3} + 6 \, a^{2} b^{4} - 4 \, a b^{5} + b^{6}\right)} f \cosh\left(f x + e\right)^{12} + 12 \, {\left(a^{4} b^{2} - 4 \, a^{3} b^{3} + 6 \, a^{2} b^{4} - 4 \, a b^{5} + b^{6}\right)} f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{11} + {\left(a^{4} b^{2} - 4 \, a^{3} b^{3} + 6 \, a^{2} b^{4} - 4 \, a b^{5} + b^{6}\right)} f \sinh\left(f x + e\right)^{12} + 2 \, {\left(4 \, a^{5} b - 17 \, a^{4} b^{2} + 28 \, a^{3} b^{3} - 22 \, a^{2} b^{4} + 8 \, a b^{5} - b^{6}\right)} f \cosh\left(f x + e\right)^{10} + 2 \, {\left(33 \, {\left(a^{4} b^{2} - 4 \, a^{3} b^{3} + 6 \, a^{2} b^{4} - 4 \, a b^{5} + b^{6}\right)} f \cosh\left(f x + e\right)^{2} + {\left(4 \, a^{5} b - 17 \, a^{4} b^{2} + 28 \, a^{3} b^{3} - 22 \, a^{2} b^{4} + 8 \, a b^{5} - b^{6}\right)} f\right)} \sinh\left(f x + e\right)^{10} + {\left(16 \, a^{6} - 64 \, a^{5} b + 95 \, a^{4} b^{2} - 60 \, a^{3} b^{3} + 10 \, a^{2} b^{4} + 4 \, a b^{5} - b^{6}\right)} f \cosh\left(f x + e\right)^{8} + 20 \, {\left(11 \, {\left(a^{4} b^{2} - 4 \, a^{3} b^{3} + 6 \, a^{2} b^{4} - 4 \, a b^{5} + b^{6}\right)} f \cosh\left(f x + e\right)^{3} + {\left(4 \, a^{5} b - 17 \, a^{4} b^{2} + 28 \, a^{3} b^{3} - 22 \, a^{2} b^{4} + 8 \, a b^{5} - b^{6}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{9} + {\left(495 \, {\left(a^{4} b^{2} - 4 \, a^{3} b^{3} + 6 \, a^{2} b^{4} - 4 \, a b^{5} + b^{6}\right)} f \cosh\left(f x + e\right)^{4} + 90 \, {\left(4 \, a^{5} b - 17 \, a^{4} b^{2} + 28 \, a^{3} b^{3} - 22 \, a^{2} b^{4} + 8 \, a b^{5} - b^{6}\right)} f \cosh\left(f x + e\right)^{2} + {\left(16 \, a^{6} - 64 \, a^{5} b + 95 \, a^{4} b^{2} - 60 \, a^{3} b^{3} + 10 \, a^{2} b^{4} + 4 \, a b^{5} - b^{6}\right)} f\right)} \sinh\left(f x + e\right)^{8} + 4 \, {\left(8 \, a^{6} - 36 \, a^{5} b + 65 \, a^{4} b^{2} - 60 \, a^{3} b^{3} + 30 \, a^{2} b^{4} - 8 \, a b^{5} + b^{6}\right)} f \cosh\left(f x + e\right)^{6} + 8 \, {\left(99 \, {\left(a^{4} b^{2} - 4 \, a^{3} b^{3} + 6 \, a^{2} b^{4} - 4 \, a b^{5} + b^{6}\right)} f \cosh\left(f x + e\right)^{5} + 30 \, {\left(4 \, a^{5} b - 17 \, a^{4} b^{2} + 28 \, a^{3} b^{3} - 22 \, a^{2} b^{4} + 8 \, a b^{5} - b^{6}\right)} f \cosh\left(f x + e\right)^{3} + {\left(16 \, a^{6} - 64 \, a^{5} b + 95 \, a^{4} b^{2} - 60 \, a^{3} b^{3} + 10 \, a^{2} b^{4} + 4 \, a b^{5} - b^{6}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{7} + 4 \, {\left(231 \, {\left(a^{4} b^{2} - 4 \, a^{3} b^{3} + 6 \, a^{2} b^{4} - 4 \, a b^{5} + b^{6}\right)} f \cosh\left(f x + e\right)^{6} + 105 \, {\left(4 \, a^{5} b - 17 \, a^{4} b^{2} + 28 \, a^{3} b^{3} - 22 \, a^{2} b^{4} + 8 \, a b^{5} - b^{6}\right)} f \cosh\left(f x + e\right)^{4} + 7 \, {\left(16 \, a^{6} - 64 \, a^{5} b + 95 \, a^{4} b^{2} - 60 \, a^{3} b^{3} + 10 \, a^{2} b^{4} + 4 \, a b^{5} - b^{6}\right)} f \cosh\left(f x + e\right)^{2} + {\left(8 \, a^{6} - 36 \, a^{5} b + 65 \, a^{4} b^{2} - 60 \, a^{3} b^{3} + 30 \, a^{2} b^{4} - 8 \, a b^{5} + b^{6}\right)} f\right)} \sinh\left(f x + e\right)^{6} + {\left(16 \, a^{6} - 64 \, a^{5} b + 95 \, a^{4} b^{2} - 60 \, a^{3} b^{3} + 10 \, a^{2} b^{4} + 4 \, a b^{5} - b^{6}\right)} f \cosh\left(f x + e\right)^{4} + 8 \, {\left(99 \, {\left(a^{4} b^{2} - 4 \, a^{3} b^{3} + 6 \, a^{2} b^{4} - 4 \, a b^{5} + b^{6}\right)} f \cosh\left(f x + e\right)^{7} + 63 \, {\left(4 \, a^{5} b - 17 \, a^{4} b^{2} + 28 \, a^{3} b^{3} - 22 \, a^{2} b^{4} + 8 \, a b^{5} - b^{6}\right)} f \cosh\left(f x + e\right)^{5} + 7 \, {\left(16 \, a^{6} - 64 \, a^{5} b + 95 \, a^{4} b^{2} - 60 \, a^{3} b^{3} + 10 \, a^{2} b^{4} + 4 \, a b^{5} - b^{6}\right)} f \cosh\left(f x + e\right)^{3} + 3 \, {\left(8 \, a^{6} - 36 \, a^{5} b + 65 \, a^{4} b^{2} - 60 \, a^{3} b^{3} + 30 \, a^{2} b^{4} - 8 \, a b^{5} + b^{6}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + {\left(495 \, {\left(a^{4} b^{2} - 4 \, a^{3} b^{3} + 6 \, a^{2} b^{4} - 4 \, a b^{5} + b^{6}\right)} f \cosh\left(f x + e\right)^{8} + 420 \, {\left(4 \, a^{5} b - 17 \, a^{4} b^{2} + 28 \, a^{3} b^{3} - 22 \, a^{2} b^{4} + 8 \, a b^{5} - b^{6}\right)} f \cosh\left(f x + e\right)^{6} + 70 \, {\left(16 \, a^{6} - 64 \, a^{5} b + 95 \, a^{4} b^{2} - 60 \, a^{3} b^{3} + 10 \, a^{2} b^{4} + 4 \, a b^{5} - b^{6}\right)} f \cosh\left(f x + e\right)^{4} + 60 \, {\left(8 \, a^{6} - 36 \, a^{5} b + 65 \, a^{4} b^{2} - 60 \, a^{3} b^{3} + 30 \, a^{2} b^{4} - 8 \, a b^{5} + b^{6}\right)} f \cosh\left(f x + e\right)^{2} + {\left(16 \, a^{6} - 64 \, a^{5} b + 95 \, a^{4} b^{2} - 60 \, a^{3} b^{3} + 10 \, a^{2} b^{4} + 4 \, a b^{5} - b^{6}\right)} f\right)} \sinh\left(f x + e\right)^{4} + 2 \, {\left(4 \, a^{5} b - 17 \, a^{4} b^{2} + 28 \, a^{3} b^{3} - 22 \, a^{2} b^{4} + 8 \, a b^{5} - b^{6}\right)} f \cosh\left(f x + e\right)^{2} + 4 \, {\left(55 \, {\left(a^{4} b^{2} - 4 \, a^{3} b^{3} + 6 \, a^{2} b^{4} - 4 \, a b^{5} + b^{6}\right)} f \cosh\left(f x + e\right)^{9} + 60 \, {\left(4 \, a^{5} b - 17 \, a^{4} b^{2} + 28 \, a^{3} b^{3} - 22 \, a^{2} b^{4} + 8 \, a b^{5} - b^{6}\right)} f \cosh\left(f x + e\right)^{7} + 14 \, {\left(16 \, a^{6} - 64 \, a^{5} b + 95 \, a^{4} b^{2} - 60 \, a^{3} b^{3} + 10 \, a^{2} b^{4} + 4 \, a b^{5} - b^{6}\right)} f \cosh\left(f x + e\right)^{5} + 20 \, {\left(8 \, a^{6} - 36 \, a^{5} b + 65 \, a^{4} b^{2} - 60 \, a^{3} b^{3} + 30 \, a^{2} b^{4} - 8 \, a b^{5} + b^{6}\right)} f \cosh\left(f x + e\right)^{3} + {\left(16 \, a^{6} - 64 \, a^{5} b + 95 \, a^{4} b^{2} - 60 \, a^{3} b^{3} + 10 \, a^{2} b^{4} + 4 \, a b^{5} - b^{6}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 2 \, {\left(33 \, {\left(a^{4} b^{2} - 4 \, a^{3} b^{3} + 6 \, a^{2} b^{4} - 4 \, a b^{5} + b^{6}\right)} f \cosh\left(f x + e\right)^{10} + 45 \, {\left(4 \, a^{5} b - 17 \, a^{4} b^{2} + 28 \, a^{3} b^{3} - 22 \, a^{2} b^{4} + 8 \, a b^{5} - b^{6}\right)} f \cosh\left(f x + e\right)^{8} + 14 \, {\left(16 \, a^{6} - 64 \, a^{5} b + 95 \, a^{4} b^{2} - 60 \, a^{3} b^{3} + 10 \, a^{2} b^{4} + 4 \, a b^{5} - b^{6}\right)} f \cosh\left(f x + e\right)^{6} + 30 \, {\left(8 \, a^{6} - 36 \, a^{5} b + 65 \, a^{4} b^{2} - 60 \, a^{3} b^{3} + 30 \, a^{2} b^{4} - 8 \, a b^{5} + b^{6}\right)} f \cosh\left(f x + e\right)^{4} + 3 \, {\left(16 \, a^{6} - 64 \, a^{5} b + 95 \, a^{4} b^{2} - 60 \, a^{3} b^{3} + 10 \, a^{2} b^{4} + 4 \, a b^{5} - b^{6}\right)} f \cosh\left(f x + e\right)^{2} + {\left(4 \, a^{5} b - 17 \, a^{4} b^{2} + 28 \, a^{3} b^{3} - 22 \, a^{2} b^{4} + 8 \, a b^{5} - b^{6}\right)} f\right)} \sinh\left(f x + e\right)^{2} + {\left(a^{4} b^{2} - 4 \, a^{3} b^{3} + 6 \, a^{2} b^{4} - 4 \, a b^{5} + b^{6}\right)} f + 4 \, {\left(3 \, {\left(a^{4} b^{2} - 4 \, a^{3} b^{3} + 6 \, a^{2} b^{4} - 4 \, a b^{5} + b^{6}\right)} f \cosh\left(f x + e\right)^{11} + 5 \, {\left(4 \, a^{5} b - 17 \, a^{4} b^{2} + 28 \, a^{3} b^{3} - 22 \, a^{2} b^{4} + 8 \, a b^{5} - b^{6}\right)} f \cosh\left(f x + e\right)^{9} + 2 \, {\left(16 \, a^{6} - 64 \, a^{5} b + 95 \, a^{4} b^{2} - 60 \, a^{3} b^{3} + 10 \, a^{2} b^{4} + 4 \, a b^{5} - b^{6}\right)} f \cosh\left(f x + e\right)^{7} + 6 \, {\left(8 \, a^{6} - 36 \, a^{5} b + 65 \, a^{4} b^{2} - 60 \, a^{3} b^{3} + 30 \, a^{2} b^{4} - 8 \, a b^{5} + b^{6}\right)} f \cosh\left(f x + e\right)^{5} + {\left(16 \, a^{6} - 64 \, a^{5} b + 95 \, a^{4} b^{2} - 60 \, a^{3} b^{3} + 10 \, a^{2} b^{4} + 4 \, a b^{5} - b^{6}\right)} f \cosh\left(f x + e\right)^{3} + {\left(4 \, a^{5} b - 17 \, a^{4} b^{2} + 28 \, a^{3} b^{3} - 22 \, a^{2} b^{4} + 8 \, a b^{5} - b^{6}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)}}\right]"," ",0,"[-1/12*(3*((2*a*b^2 + 3*b^3)*cosh(f*x + e)^12 + 12*(2*a*b^2 + 3*b^3)*cosh(f*x + e)*sinh(f*x + e)^11 + (2*a*b^2 + 3*b^3)*sinh(f*x + e)^12 + 2*(8*a^2*b + 10*a*b^2 - 3*b^3)*cosh(f*x + e)^10 + 2*(8*a^2*b + 10*a*b^2 - 3*b^3 + 33*(2*a*b^2 + 3*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^10 + 20*(11*(2*a*b^2 + 3*b^3)*cosh(f*x + e)^3 + (8*a^2*b + 10*a*b^2 - 3*b^3)*cosh(f*x + e))*sinh(f*x + e)^9 + (32*a^3 + 48*a^2*b - 2*a*b^2 - 3*b^3)*cosh(f*x + e)^8 + (495*(2*a*b^2 + 3*b^3)*cosh(f*x + e)^4 + 32*a^3 + 48*a^2*b - 2*a*b^2 - 3*b^3 + 90*(8*a^2*b + 10*a*b^2 - 3*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^8 + 8*(99*(2*a*b^2 + 3*b^3)*cosh(f*x + e)^5 + 30*(8*a^2*b + 10*a*b^2 - 3*b^3)*cosh(f*x + e)^3 + (32*a^3 + 48*a^2*b - 2*a*b^2 - 3*b^3)*cosh(f*x + e))*sinh(f*x + e)^7 + 4*(16*a^3 + 16*a^2*b - 10*a*b^2 + 3*b^3)*cosh(f*x + e)^6 + 4*(231*(2*a*b^2 + 3*b^3)*cosh(f*x + e)^6 + 105*(8*a^2*b + 10*a*b^2 - 3*b^3)*cosh(f*x + e)^4 + 16*a^3 + 16*a^2*b - 10*a*b^2 + 3*b^3 + 7*(32*a^3 + 48*a^2*b - 2*a*b^2 - 3*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^6 + 8*(99*(2*a*b^2 + 3*b^3)*cosh(f*x + e)^7 + 63*(8*a^2*b + 10*a*b^2 - 3*b^3)*cosh(f*x + e)^5 + 7*(32*a^3 + 48*a^2*b - 2*a*b^2 - 3*b^3)*cosh(f*x + e)^3 + 3*(16*a^3 + 16*a^2*b - 10*a*b^2 + 3*b^3)*cosh(f*x + e))*sinh(f*x + e)^5 + (32*a^3 + 48*a^2*b - 2*a*b^2 - 3*b^3)*cosh(f*x + e)^4 + (495*(2*a*b^2 + 3*b^3)*cosh(f*x + e)^8 + 420*(8*a^2*b + 10*a*b^2 - 3*b^3)*cosh(f*x + e)^6 + 70*(32*a^3 + 48*a^2*b - 2*a*b^2 - 3*b^3)*cosh(f*x + e)^4 + 32*a^3 + 48*a^2*b - 2*a*b^2 - 3*b^3 + 60*(16*a^3 + 16*a^2*b - 10*a*b^2 + 3*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^4 + 4*(55*(2*a*b^2 + 3*b^3)*cosh(f*x + e)^9 + 60*(8*a^2*b + 10*a*b^2 - 3*b^3)*cosh(f*x + e)^7 + 14*(32*a^3 + 48*a^2*b - 2*a*b^2 - 3*b^3)*cosh(f*x + e)^5 + 20*(16*a^3 + 16*a^2*b - 10*a*b^2 + 3*b^3)*cosh(f*x + e)^3 + (32*a^3 + 48*a^2*b - 2*a*b^2 - 3*b^3)*cosh(f*x + e))*sinh(f*x + e)^3 + 2*a*b^2 + 3*b^3 + 2*(8*a^2*b + 10*a*b^2 - 3*b^3)*cosh(f*x + e)^2 + 2*(33*(2*a*b^2 + 3*b^3)*cosh(f*x + e)^10 + 45*(8*a^2*b + 10*a*b^2 - 3*b^3)*cosh(f*x + e)^8 + 14*(32*a^3 + 48*a^2*b - 2*a*b^2 - 3*b^3)*cosh(f*x + e)^6 + 30*(16*a^3 + 16*a^2*b - 10*a*b^2 + 3*b^3)*cosh(f*x + e)^4 + 8*a^2*b + 10*a*b^2 - 3*b^3 + 3*(32*a^3 + 48*a^2*b - 2*a*b^2 - 3*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^2 + 4*(3*(2*a*b^2 + 3*b^3)*cosh(f*x + e)^11 + 5*(8*a^2*b + 10*a*b^2 - 3*b^3)*cosh(f*x + e)^9 + 2*(32*a^3 + 48*a^2*b - 2*a*b^2 - 3*b^3)*cosh(f*x + e)^7 + 6*(16*a^3 + 16*a^2*b - 10*a*b^2 + 3*b^3)*cosh(f*x + e)^5 + (32*a^3 + 48*a^2*b - 2*a*b^2 - 3*b^3)*cosh(f*x + e)^3 + (8*a^2*b + 10*a*b^2 - 3*b^3)*cosh(f*x + e))*sinh(f*x + e))*sqrt(a - b)*log((b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(4*a - 3*b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 4*a - 3*b)*sinh(f*x + e)^2 + 4*sqrt(2)*sqrt(a - b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))*(cosh(f*x + e) + sinh(f*x + e)) + 4*(b*cosh(f*x + e)^3 + (4*a - 3*b)*cosh(f*x + e))*sinh(f*x + e) + b)/(cosh(f*x + e)^4 + 4*cosh(f*x + e)*sinh(f*x + e)^3 + sinh(f*x + e)^4 + 2*(3*cosh(f*x + e)^2 + 1)*sinh(f*x + e)^2 + 2*cosh(f*x + e)^2 + 4*(cosh(f*x + e)^3 + cosh(f*x + e))*sinh(f*x + e) + 1)) - 4*sqrt(2)*(3*(2*a^2*b + a*b^2 - 3*b^3)*cosh(f*x + e)^9 + 27*(2*a^2*b + a*b^2 - 3*b^3)*cosh(f*x + e)*sinh(f*x + e)^8 + 3*(2*a^2*b + a*b^2 - 3*b^3)*sinh(f*x + e)^9 + 4*(8*a^3 + 2*a^2*b - 13*a*b^2 + 3*b^3)*cosh(f*x + e)^7 + 4*(8*a^3 + 2*a^2*b - 13*a*b^2 + 3*b^3 + 27*(2*a^2*b + a*b^2 - 3*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^7 + 28*(9*(2*a^2*b + a*b^2 - 3*b^3)*cosh(f*x + e)^3 + (8*a^3 + 2*a^2*b - 13*a*b^2 + 3*b^3)*cosh(f*x + e))*sinh(f*x + e)^6 + 2*(56*a^3 - 70*a^2*b + 17*a*b^2 - 3*b^3)*cosh(f*x + e)^5 + 2*(189*(2*a^2*b + a*b^2 - 3*b^3)*cosh(f*x + e)^4 + 56*a^3 - 70*a^2*b + 17*a*b^2 - 3*b^3 + 42*(8*a^3 + 2*a^2*b - 13*a*b^2 + 3*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^5 + 2*(189*(2*a^2*b + a*b^2 - 3*b^3)*cosh(f*x + e)^5 + 70*(8*a^3 + 2*a^2*b - 13*a*b^2 + 3*b^3)*cosh(f*x + e)^3 + 5*(56*a^3 - 70*a^2*b + 17*a*b^2 - 3*b^3)*cosh(f*x + e))*sinh(f*x + e)^4 + 4*(8*a^3 + 2*a^2*b - 13*a*b^2 + 3*b^3)*cosh(f*x + e)^3 + 4*(63*(2*a^2*b + a*b^2 - 3*b^3)*cosh(f*x + e)^6 + 35*(8*a^3 + 2*a^2*b - 13*a*b^2 + 3*b^3)*cosh(f*x + e)^4 + 8*a^3 + 2*a^2*b - 13*a*b^2 + 3*b^3 + 5*(56*a^3 - 70*a^2*b + 17*a*b^2 - 3*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^3 + 4*(27*(2*a^2*b + a*b^2 - 3*b^3)*cosh(f*x + e)^7 + 21*(8*a^3 + 2*a^2*b - 13*a*b^2 + 3*b^3)*cosh(f*x + e)^5 + 5*(56*a^3 - 70*a^2*b + 17*a*b^2 - 3*b^3)*cosh(f*x + e)^3 + 3*(8*a^3 + 2*a^2*b - 13*a*b^2 + 3*b^3)*cosh(f*x + e))*sinh(f*x + e)^2 + 3*(2*a^2*b + a*b^2 - 3*b^3)*cosh(f*x + e) + (27*(2*a^2*b + a*b^2 - 3*b^3)*cosh(f*x + e)^8 + 28*(8*a^3 + 2*a^2*b - 13*a*b^2 + 3*b^3)*cosh(f*x + e)^6 + 10*(56*a^3 - 70*a^2*b + 17*a*b^2 - 3*b^3)*cosh(f*x + e)^4 + 6*a^2*b + 3*a*b^2 - 9*b^3 + 12*(8*a^3 + 2*a^2*b - 13*a*b^2 + 3*b^3)*cosh(f*x + e)^2)*sinh(f*x + e))*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/((a^4*b^2 - 4*a^3*b^3 + 6*a^2*b^4 - 4*a*b^5 + b^6)*f*cosh(f*x + e)^12 + 12*(a^4*b^2 - 4*a^3*b^3 + 6*a^2*b^4 - 4*a*b^5 + b^6)*f*cosh(f*x + e)*sinh(f*x + e)^11 + (a^4*b^2 - 4*a^3*b^3 + 6*a^2*b^4 - 4*a*b^5 + b^6)*f*sinh(f*x + e)^12 + 2*(4*a^5*b - 17*a^4*b^2 + 28*a^3*b^3 - 22*a^2*b^4 + 8*a*b^5 - b^6)*f*cosh(f*x + e)^10 + 2*(33*(a^4*b^2 - 4*a^3*b^3 + 6*a^2*b^4 - 4*a*b^5 + b^6)*f*cosh(f*x + e)^2 + (4*a^5*b - 17*a^4*b^2 + 28*a^3*b^3 - 22*a^2*b^4 + 8*a*b^5 - b^6)*f)*sinh(f*x + e)^10 + (16*a^6 - 64*a^5*b + 95*a^4*b^2 - 60*a^3*b^3 + 10*a^2*b^4 + 4*a*b^5 - b^6)*f*cosh(f*x + e)^8 + 20*(11*(a^4*b^2 - 4*a^3*b^3 + 6*a^2*b^4 - 4*a*b^5 + b^6)*f*cosh(f*x + e)^3 + (4*a^5*b - 17*a^4*b^2 + 28*a^3*b^3 - 22*a^2*b^4 + 8*a*b^5 - b^6)*f*cosh(f*x + e))*sinh(f*x + e)^9 + (495*(a^4*b^2 - 4*a^3*b^3 + 6*a^2*b^4 - 4*a*b^5 + b^6)*f*cosh(f*x + e)^4 + 90*(4*a^5*b - 17*a^4*b^2 + 28*a^3*b^3 - 22*a^2*b^4 + 8*a*b^5 - b^6)*f*cosh(f*x + e)^2 + (16*a^6 - 64*a^5*b + 95*a^4*b^2 - 60*a^3*b^3 + 10*a^2*b^4 + 4*a*b^5 - b^6)*f)*sinh(f*x + e)^8 + 4*(8*a^6 - 36*a^5*b + 65*a^4*b^2 - 60*a^3*b^3 + 30*a^2*b^4 - 8*a*b^5 + b^6)*f*cosh(f*x + e)^6 + 8*(99*(a^4*b^2 - 4*a^3*b^3 + 6*a^2*b^4 - 4*a*b^5 + b^6)*f*cosh(f*x + e)^5 + 30*(4*a^5*b - 17*a^4*b^2 + 28*a^3*b^3 - 22*a^2*b^4 + 8*a*b^5 - b^6)*f*cosh(f*x + e)^3 + (16*a^6 - 64*a^5*b + 95*a^4*b^2 - 60*a^3*b^3 + 10*a^2*b^4 + 4*a*b^5 - b^6)*f*cosh(f*x + e))*sinh(f*x + e)^7 + 4*(231*(a^4*b^2 - 4*a^3*b^3 + 6*a^2*b^4 - 4*a*b^5 + b^6)*f*cosh(f*x + e)^6 + 105*(4*a^5*b - 17*a^4*b^2 + 28*a^3*b^3 - 22*a^2*b^4 + 8*a*b^5 - b^6)*f*cosh(f*x + e)^4 + 7*(16*a^6 - 64*a^5*b + 95*a^4*b^2 - 60*a^3*b^3 + 10*a^2*b^4 + 4*a*b^5 - b^6)*f*cosh(f*x + e)^2 + (8*a^6 - 36*a^5*b + 65*a^4*b^2 - 60*a^3*b^3 + 30*a^2*b^4 - 8*a*b^5 + b^6)*f)*sinh(f*x + e)^6 + (16*a^6 - 64*a^5*b + 95*a^4*b^2 - 60*a^3*b^3 + 10*a^2*b^4 + 4*a*b^5 - b^6)*f*cosh(f*x + e)^4 + 8*(99*(a^4*b^2 - 4*a^3*b^3 + 6*a^2*b^4 - 4*a*b^5 + b^6)*f*cosh(f*x + e)^7 + 63*(4*a^5*b - 17*a^4*b^2 + 28*a^3*b^3 - 22*a^2*b^4 + 8*a*b^5 - b^6)*f*cosh(f*x + e)^5 + 7*(16*a^6 - 64*a^5*b + 95*a^4*b^2 - 60*a^3*b^3 + 10*a^2*b^4 + 4*a*b^5 - b^6)*f*cosh(f*x + e)^3 + 3*(8*a^6 - 36*a^5*b + 65*a^4*b^2 - 60*a^3*b^3 + 30*a^2*b^4 - 8*a*b^5 + b^6)*f*cosh(f*x + e))*sinh(f*x + e)^5 + (495*(a^4*b^2 - 4*a^3*b^3 + 6*a^2*b^4 - 4*a*b^5 + b^6)*f*cosh(f*x + e)^8 + 420*(4*a^5*b - 17*a^4*b^2 + 28*a^3*b^3 - 22*a^2*b^4 + 8*a*b^5 - b^6)*f*cosh(f*x + e)^6 + 70*(16*a^6 - 64*a^5*b + 95*a^4*b^2 - 60*a^3*b^3 + 10*a^2*b^4 + 4*a*b^5 - b^6)*f*cosh(f*x + e)^4 + 60*(8*a^6 - 36*a^5*b + 65*a^4*b^2 - 60*a^3*b^3 + 30*a^2*b^4 - 8*a*b^5 + b^6)*f*cosh(f*x + e)^2 + (16*a^6 - 64*a^5*b + 95*a^4*b^2 - 60*a^3*b^3 + 10*a^2*b^4 + 4*a*b^5 - b^6)*f)*sinh(f*x + e)^4 + 2*(4*a^5*b - 17*a^4*b^2 + 28*a^3*b^3 - 22*a^2*b^4 + 8*a*b^5 - b^6)*f*cosh(f*x + e)^2 + 4*(55*(a^4*b^2 - 4*a^3*b^3 + 6*a^2*b^4 - 4*a*b^5 + b^6)*f*cosh(f*x + e)^9 + 60*(4*a^5*b - 17*a^4*b^2 + 28*a^3*b^3 - 22*a^2*b^4 + 8*a*b^5 - b^6)*f*cosh(f*x + e)^7 + 14*(16*a^6 - 64*a^5*b + 95*a^4*b^2 - 60*a^3*b^3 + 10*a^2*b^4 + 4*a*b^5 - b^6)*f*cosh(f*x + e)^5 + 20*(8*a^6 - 36*a^5*b + 65*a^4*b^2 - 60*a^3*b^3 + 30*a^2*b^4 - 8*a*b^5 + b^6)*f*cosh(f*x + e)^3 + (16*a^6 - 64*a^5*b + 95*a^4*b^2 - 60*a^3*b^3 + 10*a^2*b^4 + 4*a*b^5 - b^6)*f*cosh(f*x + e))*sinh(f*x + e)^3 + 2*(33*(a^4*b^2 - 4*a^3*b^3 + 6*a^2*b^4 - 4*a*b^5 + b^6)*f*cosh(f*x + e)^10 + 45*(4*a^5*b - 17*a^4*b^2 + 28*a^3*b^3 - 22*a^2*b^4 + 8*a*b^5 - b^6)*f*cosh(f*x + e)^8 + 14*(16*a^6 - 64*a^5*b + 95*a^4*b^2 - 60*a^3*b^3 + 10*a^2*b^4 + 4*a*b^5 - b^6)*f*cosh(f*x + e)^6 + 30*(8*a^6 - 36*a^5*b + 65*a^4*b^2 - 60*a^3*b^3 + 30*a^2*b^4 - 8*a*b^5 + b^6)*f*cosh(f*x + e)^4 + 3*(16*a^6 - 64*a^5*b + 95*a^4*b^2 - 60*a^3*b^3 + 10*a^2*b^4 + 4*a*b^5 - b^6)*f*cosh(f*x + e)^2 + (4*a^5*b - 17*a^4*b^2 + 28*a^3*b^3 - 22*a^2*b^4 + 8*a*b^5 - b^6)*f)*sinh(f*x + e)^2 + (a^4*b^2 - 4*a^3*b^3 + 6*a^2*b^4 - 4*a*b^5 + b^6)*f + 4*(3*(a^4*b^2 - 4*a^3*b^3 + 6*a^2*b^4 - 4*a*b^5 + b^6)*f*cosh(f*x + e)^11 + 5*(4*a^5*b - 17*a^4*b^2 + 28*a^3*b^3 - 22*a^2*b^4 + 8*a*b^5 - b^6)*f*cosh(f*x + e)^9 + 2*(16*a^6 - 64*a^5*b + 95*a^4*b^2 - 60*a^3*b^3 + 10*a^2*b^4 + 4*a*b^5 - b^6)*f*cosh(f*x + e)^7 + 6*(8*a^6 - 36*a^5*b + 65*a^4*b^2 - 60*a^3*b^3 + 30*a^2*b^4 - 8*a*b^5 + b^6)*f*cosh(f*x + e)^5 + (16*a^6 - 64*a^5*b + 95*a^4*b^2 - 60*a^3*b^3 + 10*a^2*b^4 + 4*a*b^5 - b^6)*f*cosh(f*x + e)^3 + (4*a^5*b - 17*a^4*b^2 + 28*a^3*b^3 - 22*a^2*b^4 + 8*a*b^5 - b^6)*f*cosh(f*x + e))*sinh(f*x + e)), -1/6*(3*((2*a*b^2 + 3*b^3)*cosh(f*x + e)^12 + 12*(2*a*b^2 + 3*b^3)*cosh(f*x + e)*sinh(f*x + e)^11 + (2*a*b^2 + 3*b^3)*sinh(f*x + e)^12 + 2*(8*a^2*b + 10*a*b^2 - 3*b^3)*cosh(f*x + e)^10 + 2*(8*a^2*b + 10*a*b^2 - 3*b^3 + 33*(2*a*b^2 + 3*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^10 + 20*(11*(2*a*b^2 + 3*b^3)*cosh(f*x + e)^3 + (8*a^2*b + 10*a*b^2 - 3*b^3)*cosh(f*x + e))*sinh(f*x + e)^9 + (32*a^3 + 48*a^2*b - 2*a*b^2 - 3*b^3)*cosh(f*x + e)^8 + (495*(2*a*b^2 + 3*b^3)*cosh(f*x + e)^4 + 32*a^3 + 48*a^2*b - 2*a*b^2 - 3*b^3 + 90*(8*a^2*b + 10*a*b^2 - 3*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^8 + 8*(99*(2*a*b^2 + 3*b^3)*cosh(f*x + e)^5 + 30*(8*a^2*b + 10*a*b^2 - 3*b^3)*cosh(f*x + e)^3 + (32*a^3 + 48*a^2*b - 2*a*b^2 - 3*b^3)*cosh(f*x + e))*sinh(f*x + e)^7 + 4*(16*a^3 + 16*a^2*b - 10*a*b^2 + 3*b^3)*cosh(f*x + e)^6 + 4*(231*(2*a*b^2 + 3*b^3)*cosh(f*x + e)^6 + 105*(8*a^2*b + 10*a*b^2 - 3*b^3)*cosh(f*x + e)^4 + 16*a^3 + 16*a^2*b - 10*a*b^2 + 3*b^3 + 7*(32*a^3 + 48*a^2*b - 2*a*b^2 - 3*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^6 + 8*(99*(2*a*b^2 + 3*b^3)*cosh(f*x + e)^7 + 63*(8*a^2*b + 10*a*b^2 - 3*b^3)*cosh(f*x + e)^5 + 7*(32*a^3 + 48*a^2*b - 2*a*b^2 - 3*b^3)*cosh(f*x + e)^3 + 3*(16*a^3 + 16*a^2*b - 10*a*b^2 + 3*b^3)*cosh(f*x + e))*sinh(f*x + e)^5 + (32*a^3 + 48*a^2*b - 2*a*b^2 - 3*b^3)*cosh(f*x + e)^4 + (495*(2*a*b^2 + 3*b^3)*cosh(f*x + e)^8 + 420*(8*a^2*b + 10*a*b^2 - 3*b^3)*cosh(f*x + e)^6 + 70*(32*a^3 + 48*a^2*b - 2*a*b^2 - 3*b^3)*cosh(f*x + e)^4 + 32*a^3 + 48*a^2*b - 2*a*b^2 - 3*b^3 + 60*(16*a^3 + 16*a^2*b - 10*a*b^2 + 3*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^4 + 4*(55*(2*a*b^2 + 3*b^3)*cosh(f*x + e)^9 + 60*(8*a^2*b + 10*a*b^2 - 3*b^3)*cosh(f*x + e)^7 + 14*(32*a^3 + 48*a^2*b - 2*a*b^2 - 3*b^3)*cosh(f*x + e)^5 + 20*(16*a^3 + 16*a^2*b - 10*a*b^2 + 3*b^3)*cosh(f*x + e)^3 + (32*a^3 + 48*a^2*b - 2*a*b^2 - 3*b^3)*cosh(f*x + e))*sinh(f*x + e)^3 + 2*a*b^2 + 3*b^3 + 2*(8*a^2*b + 10*a*b^2 - 3*b^3)*cosh(f*x + e)^2 + 2*(33*(2*a*b^2 + 3*b^3)*cosh(f*x + e)^10 + 45*(8*a^2*b + 10*a*b^2 - 3*b^3)*cosh(f*x + e)^8 + 14*(32*a^3 + 48*a^2*b - 2*a*b^2 - 3*b^3)*cosh(f*x + e)^6 + 30*(16*a^3 + 16*a^2*b - 10*a*b^2 + 3*b^3)*cosh(f*x + e)^4 + 8*a^2*b + 10*a*b^2 - 3*b^3 + 3*(32*a^3 + 48*a^2*b - 2*a*b^2 - 3*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^2 + 4*(3*(2*a*b^2 + 3*b^3)*cosh(f*x + e)^11 + 5*(8*a^2*b + 10*a*b^2 - 3*b^3)*cosh(f*x + e)^9 + 2*(32*a^3 + 48*a^2*b - 2*a*b^2 - 3*b^3)*cosh(f*x + e)^7 + 6*(16*a^3 + 16*a^2*b - 10*a*b^2 + 3*b^3)*cosh(f*x + e)^5 + (32*a^3 + 48*a^2*b - 2*a*b^2 - 3*b^3)*cosh(f*x + e)^3 + (8*a^2*b + 10*a*b^2 - 3*b^3)*cosh(f*x + e))*sinh(f*x + e))*sqrt(-a + b)*arctan(-1/2*sqrt(2)*sqrt(-a + b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/((a - b)*cosh(f*x + e) + (a - b)*sinh(f*x + e))) - 2*sqrt(2)*(3*(2*a^2*b + a*b^2 - 3*b^3)*cosh(f*x + e)^9 + 27*(2*a^2*b + a*b^2 - 3*b^3)*cosh(f*x + e)*sinh(f*x + e)^8 + 3*(2*a^2*b + a*b^2 - 3*b^3)*sinh(f*x + e)^9 + 4*(8*a^3 + 2*a^2*b - 13*a*b^2 + 3*b^3)*cosh(f*x + e)^7 + 4*(8*a^3 + 2*a^2*b - 13*a*b^2 + 3*b^3 + 27*(2*a^2*b + a*b^2 - 3*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^7 + 28*(9*(2*a^2*b + a*b^2 - 3*b^3)*cosh(f*x + e)^3 + (8*a^3 + 2*a^2*b - 13*a*b^2 + 3*b^3)*cosh(f*x + e))*sinh(f*x + e)^6 + 2*(56*a^3 - 70*a^2*b + 17*a*b^2 - 3*b^3)*cosh(f*x + e)^5 + 2*(189*(2*a^2*b + a*b^2 - 3*b^3)*cosh(f*x + e)^4 + 56*a^3 - 70*a^2*b + 17*a*b^2 - 3*b^3 + 42*(8*a^3 + 2*a^2*b - 13*a*b^2 + 3*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^5 + 2*(189*(2*a^2*b + a*b^2 - 3*b^3)*cosh(f*x + e)^5 + 70*(8*a^3 + 2*a^2*b - 13*a*b^2 + 3*b^3)*cosh(f*x + e)^3 + 5*(56*a^3 - 70*a^2*b + 17*a*b^2 - 3*b^3)*cosh(f*x + e))*sinh(f*x + e)^4 + 4*(8*a^3 + 2*a^2*b - 13*a*b^2 + 3*b^3)*cosh(f*x + e)^3 + 4*(63*(2*a^2*b + a*b^2 - 3*b^3)*cosh(f*x + e)^6 + 35*(8*a^3 + 2*a^2*b - 13*a*b^2 + 3*b^3)*cosh(f*x + e)^4 + 8*a^3 + 2*a^2*b - 13*a*b^2 + 3*b^3 + 5*(56*a^3 - 70*a^2*b + 17*a*b^2 - 3*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^3 + 4*(27*(2*a^2*b + a*b^2 - 3*b^3)*cosh(f*x + e)^7 + 21*(8*a^3 + 2*a^2*b - 13*a*b^2 + 3*b^3)*cosh(f*x + e)^5 + 5*(56*a^3 - 70*a^2*b + 17*a*b^2 - 3*b^3)*cosh(f*x + e)^3 + 3*(8*a^3 + 2*a^2*b - 13*a*b^2 + 3*b^3)*cosh(f*x + e))*sinh(f*x + e)^2 + 3*(2*a^2*b + a*b^2 - 3*b^3)*cosh(f*x + e) + (27*(2*a^2*b + a*b^2 - 3*b^3)*cosh(f*x + e)^8 + 28*(8*a^3 + 2*a^2*b - 13*a*b^2 + 3*b^3)*cosh(f*x + e)^6 + 10*(56*a^3 - 70*a^2*b + 17*a*b^2 - 3*b^3)*cosh(f*x + e)^4 + 6*a^2*b + 3*a*b^2 - 9*b^3 + 12*(8*a^3 + 2*a^2*b - 13*a*b^2 + 3*b^3)*cosh(f*x + e)^2)*sinh(f*x + e))*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/((a^4*b^2 - 4*a^3*b^3 + 6*a^2*b^4 - 4*a*b^5 + b^6)*f*cosh(f*x + e)^12 + 12*(a^4*b^2 - 4*a^3*b^3 + 6*a^2*b^4 - 4*a*b^5 + b^6)*f*cosh(f*x + e)*sinh(f*x + e)^11 + (a^4*b^2 - 4*a^3*b^3 + 6*a^2*b^4 - 4*a*b^5 + b^6)*f*sinh(f*x + e)^12 + 2*(4*a^5*b - 17*a^4*b^2 + 28*a^3*b^3 - 22*a^2*b^4 + 8*a*b^5 - b^6)*f*cosh(f*x + e)^10 + 2*(33*(a^4*b^2 - 4*a^3*b^3 + 6*a^2*b^4 - 4*a*b^5 + b^6)*f*cosh(f*x + e)^2 + (4*a^5*b - 17*a^4*b^2 + 28*a^3*b^3 - 22*a^2*b^4 + 8*a*b^5 - b^6)*f)*sinh(f*x + e)^10 + (16*a^6 - 64*a^5*b + 95*a^4*b^2 - 60*a^3*b^3 + 10*a^2*b^4 + 4*a*b^5 - b^6)*f*cosh(f*x + e)^8 + 20*(11*(a^4*b^2 - 4*a^3*b^3 + 6*a^2*b^4 - 4*a*b^5 + b^6)*f*cosh(f*x + e)^3 + (4*a^5*b - 17*a^4*b^2 + 28*a^3*b^3 - 22*a^2*b^4 + 8*a*b^5 - b^6)*f*cosh(f*x + e))*sinh(f*x + e)^9 + (495*(a^4*b^2 - 4*a^3*b^3 + 6*a^2*b^4 - 4*a*b^5 + b^6)*f*cosh(f*x + e)^4 + 90*(4*a^5*b - 17*a^4*b^2 + 28*a^3*b^3 - 22*a^2*b^4 + 8*a*b^5 - b^6)*f*cosh(f*x + e)^2 + (16*a^6 - 64*a^5*b + 95*a^4*b^2 - 60*a^3*b^3 + 10*a^2*b^4 + 4*a*b^5 - b^6)*f)*sinh(f*x + e)^8 + 4*(8*a^6 - 36*a^5*b + 65*a^4*b^2 - 60*a^3*b^3 + 30*a^2*b^4 - 8*a*b^5 + b^6)*f*cosh(f*x + e)^6 + 8*(99*(a^4*b^2 - 4*a^3*b^3 + 6*a^2*b^4 - 4*a*b^5 + b^6)*f*cosh(f*x + e)^5 + 30*(4*a^5*b - 17*a^4*b^2 + 28*a^3*b^3 - 22*a^2*b^4 + 8*a*b^5 - b^6)*f*cosh(f*x + e)^3 + (16*a^6 - 64*a^5*b + 95*a^4*b^2 - 60*a^3*b^3 + 10*a^2*b^4 + 4*a*b^5 - b^6)*f*cosh(f*x + e))*sinh(f*x + e)^7 + 4*(231*(a^4*b^2 - 4*a^3*b^3 + 6*a^2*b^4 - 4*a*b^5 + b^6)*f*cosh(f*x + e)^6 + 105*(4*a^5*b - 17*a^4*b^2 + 28*a^3*b^3 - 22*a^2*b^4 + 8*a*b^5 - b^6)*f*cosh(f*x + e)^4 + 7*(16*a^6 - 64*a^5*b + 95*a^4*b^2 - 60*a^3*b^3 + 10*a^2*b^4 + 4*a*b^5 - b^6)*f*cosh(f*x + e)^2 + (8*a^6 - 36*a^5*b + 65*a^4*b^2 - 60*a^3*b^3 + 30*a^2*b^4 - 8*a*b^5 + b^6)*f)*sinh(f*x + e)^6 + (16*a^6 - 64*a^5*b + 95*a^4*b^2 - 60*a^3*b^3 + 10*a^2*b^4 + 4*a*b^5 - b^6)*f*cosh(f*x + e)^4 + 8*(99*(a^4*b^2 - 4*a^3*b^3 + 6*a^2*b^4 - 4*a*b^5 + b^6)*f*cosh(f*x + e)^7 + 63*(4*a^5*b - 17*a^4*b^2 + 28*a^3*b^3 - 22*a^2*b^4 + 8*a*b^5 - b^6)*f*cosh(f*x + e)^5 + 7*(16*a^6 - 64*a^5*b + 95*a^4*b^2 - 60*a^3*b^3 + 10*a^2*b^4 + 4*a*b^5 - b^6)*f*cosh(f*x + e)^3 + 3*(8*a^6 - 36*a^5*b + 65*a^4*b^2 - 60*a^3*b^3 + 30*a^2*b^4 - 8*a*b^5 + b^6)*f*cosh(f*x + e))*sinh(f*x + e)^5 + (495*(a^4*b^2 - 4*a^3*b^3 + 6*a^2*b^4 - 4*a*b^5 + b^6)*f*cosh(f*x + e)^8 + 420*(4*a^5*b - 17*a^4*b^2 + 28*a^3*b^3 - 22*a^2*b^4 + 8*a*b^5 - b^6)*f*cosh(f*x + e)^6 + 70*(16*a^6 - 64*a^5*b + 95*a^4*b^2 - 60*a^3*b^3 + 10*a^2*b^4 + 4*a*b^5 - b^6)*f*cosh(f*x + e)^4 + 60*(8*a^6 - 36*a^5*b + 65*a^4*b^2 - 60*a^3*b^3 + 30*a^2*b^4 - 8*a*b^5 + b^6)*f*cosh(f*x + e)^2 + (16*a^6 - 64*a^5*b + 95*a^4*b^2 - 60*a^3*b^3 + 10*a^2*b^4 + 4*a*b^5 - b^6)*f)*sinh(f*x + e)^4 + 2*(4*a^5*b - 17*a^4*b^2 + 28*a^3*b^3 - 22*a^2*b^4 + 8*a*b^5 - b^6)*f*cosh(f*x + e)^2 + 4*(55*(a^4*b^2 - 4*a^3*b^3 + 6*a^2*b^4 - 4*a*b^5 + b^6)*f*cosh(f*x + e)^9 + 60*(4*a^5*b - 17*a^4*b^2 + 28*a^3*b^3 - 22*a^2*b^4 + 8*a*b^5 - b^6)*f*cosh(f*x + e)^7 + 14*(16*a^6 - 64*a^5*b + 95*a^4*b^2 - 60*a^3*b^3 + 10*a^2*b^4 + 4*a*b^5 - b^6)*f*cosh(f*x + e)^5 + 20*(8*a^6 - 36*a^5*b + 65*a^4*b^2 - 60*a^3*b^3 + 30*a^2*b^4 - 8*a*b^5 + b^6)*f*cosh(f*x + e)^3 + (16*a^6 - 64*a^5*b + 95*a^4*b^2 - 60*a^3*b^3 + 10*a^2*b^4 + 4*a*b^5 - b^6)*f*cosh(f*x + e))*sinh(f*x + e)^3 + 2*(33*(a^4*b^2 - 4*a^3*b^3 + 6*a^2*b^4 - 4*a*b^5 + b^6)*f*cosh(f*x + e)^10 + 45*(4*a^5*b - 17*a^4*b^2 + 28*a^3*b^3 - 22*a^2*b^4 + 8*a*b^5 - b^6)*f*cosh(f*x + e)^8 + 14*(16*a^6 - 64*a^5*b + 95*a^4*b^2 - 60*a^3*b^3 + 10*a^2*b^4 + 4*a*b^5 - b^6)*f*cosh(f*x + e)^6 + 30*(8*a^6 - 36*a^5*b + 65*a^4*b^2 - 60*a^3*b^3 + 30*a^2*b^4 - 8*a*b^5 + b^6)*f*cosh(f*x + e)^4 + 3*(16*a^6 - 64*a^5*b + 95*a^4*b^2 - 60*a^3*b^3 + 10*a^2*b^4 + 4*a*b^5 - b^6)*f*cosh(f*x + e)^2 + (4*a^5*b - 17*a^4*b^2 + 28*a^3*b^3 - 22*a^2*b^4 + 8*a*b^5 - b^6)*f)*sinh(f*x + e)^2 + (a^4*b^2 - 4*a^3*b^3 + 6*a^2*b^4 - 4*a*b^5 + b^6)*f + 4*(3*(a^4*b^2 - 4*a^3*b^3 + 6*a^2*b^4 - 4*a*b^5 + b^6)*f*cosh(f*x + e)^11 + 5*(4*a^5*b - 17*a^4*b^2 + 28*a^3*b^3 - 22*a^2*b^4 + 8*a*b^5 - b^6)*f*cosh(f*x + e)^9 + 2*(16*a^6 - 64*a^5*b + 95*a^4*b^2 - 60*a^3*b^3 + 10*a^2*b^4 + 4*a*b^5 - b^6)*f*cosh(f*x + e)^7 + 6*(8*a^6 - 36*a^5*b + 65*a^4*b^2 - 60*a^3*b^3 + 30*a^2*b^4 - 8*a*b^5 + b^6)*f*cosh(f*x + e)^5 + (16*a^6 - 64*a^5*b + 95*a^4*b^2 - 60*a^3*b^3 + 10*a^2*b^4 + 4*a*b^5 - b^6)*f*cosh(f*x + e)^3 + (4*a^5*b - 17*a^4*b^2 + 28*a^3*b^3 - 22*a^2*b^4 + 8*a*b^5 - b^6)*f*cosh(f*x + e))*sinh(f*x + e))]","B",0
503,1,4200,0,0.697668," ","integrate(tanh(f*x+e)/(a+b*sinh(f*x+e)^2)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(b^{2} \cosh\left(f x + e\right)^{8} + 8 \, b^{2} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + b^{2} \sinh\left(f x + e\right)^{8} + 4 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{6} + 4 \, {\left(7 \, b^{2} \cosh\left(f x + e\right)^{2} + 2 \, a b - b^{2}\right)} \sinh\left(f x + e\right)^{6} + 8 \, {\left(7 \, b^{2} \cosh\left(f x + e\right)^{3} + 3 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{4} + 2 \, {\left(35 \, b^{2} \cosh\left(f x + e\right)^{4} + 30 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{2} + 8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \sinh\left(f x + e\right)^{4} + 8 \, {\left(7 \, b^{2} \cosh\left(f x + e\right)^{5} + 10 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{3} + {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 4 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{2} + 4 \, {\left(7 \, b^{2} \cosh\left(f x + e\right)^{6} + 15 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{4} + 3 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + 2 \, a b - b^{2}\right)} \sinh\left(f x + e\right)^{2} + b^{2} + 8 \, {\left(b^{2} \cosh\left(f x + e\right)^{7} + 3 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{5} + {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{3} + {\left(2 \, a b - b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{a - b} \log\left(\frac{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(4 \, a - 3 \, b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + 4 \, a - 3 \, b\right)} \sinh\left(f x + e\right)^{2} - 4 \, \sqrt{2} \sqrt{a - b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} {\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right)\right)} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(4 \, a - 3 \, b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}{\cosh\left(f x + e\right)^{4} + 4 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + \sinh\left(f x + e\right)^{4} + 2 \, {\left(3 \, \cosh\left(f x + e\right)^{2} + 1\right)} \sinh\left(f x + e\right)^{2} + 2 \, \cosh\left(f x + e\right)^{2} + 4 \, {\left(\cosh\left(f x + e\right)^{3} + \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + 1}\right) + 4 \, \sqrt{2} {\left(3 \, {\left(a b - b^{2}\right)} \cosh\left(f x + e\right)^{5} + 15 \, {\left(a b - b^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{4} + 3 \, {\left(a b - b^{2}\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(8 \, a^{2} - 13 \, a b + 5 \, b^{2}\right)} \cosh\left(f x + e\right)^{3} + 2 \, {\left(15 \, {\left(a b - b^{2}\right)} \cosh\left(f x + e\right)^{2} + 8 \, a^{2} - 13 \, a b + 5 \, b^{2}\right)} \sinh\left(f x + e\right)^{3} + 6 \, {\left(5 \, {\left(a b - b^{2}\right)} \cosh\left(f x + e\right)^{3} + {\left(8 \, a^{2} - 13 \, a b + 5 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{2} + 3 \, {\left(a b - b^{2}\right)} \cosh\left(f x + e\right) + 3 \, {\left(5 \, {\left(a b - b^{2}\right)} \cosh\left(f x + e\right)^{4} + 2 \, {\left(8 \, a^{2} - 13 \, a b + 5 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + a b - b^{2}\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{6 \, {\left({\left(a^{3} b^{2} - 3 \, a^{2} b^{3} + 3 \, a b^{4} - b^{5}\right)} f \cosh\left(f x + e\right)^{8} + 8 \, {\left(a^{3} b^{2} - 3 \, a^{2} b^{3} + 3 \, a b^{4} - b^{5}\right)} f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + {\left(a^{3} b^{2} - 3 \, a^{2} b^{3} + 3 \, a b^{4} - b^{5}\right)} f \sinh\left(f x + e\right)^{8} + 4 \, {\left(2 \, a^{4} b - 7 \, a^{3} b^{2} + 9 \, a^{2} b^{3} - 5 \, a b^{4} + b^{5}\right)} f \cosh\left(f x + e\right)^{6} + 4 \, {\left(7 \, {\left(a^{3} b^{2} - 3 \, a^{2} b^{3} + 3 \, a b^{4} - b^{5}\right)} f \cosh\left(f x + e\right)^{2} + {\left(2 \, a^{4} b - 7 \, a^{3} b^{2} + 9 \, a^{2} b^{3} - 5 \, a b^{4} + b^{5}\right)} f\right)} \sinh\left(f x + e\right)^{6} + 2 \, {\left(8 \, a^{5} - 32 \, a^{4} b + 51 \, a^{3} b^{2} - 41 \, a^{2} b^{3} + 17 \, a b^{4} - 3 \, b^{5}\right)} f \cosh\left(f x + e\right)^{4} + 8 \, {\left(7 \, {\left(a^{3} b^{2} - 3 \, a^{2} b^{3} + 3 \, a b^{4} - b^{5}\right)} f \cosh\left(f x + e\right)^{3} + 3 \, {\left(2 \, a^{4} b - 7 \, a^{3} b^{2} + 9 \, a^{2} b^{3} - 5 \, a b^{4} + b^{5}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(35 \, {\left(a^{3} b^{2} - 3 \, a^{2} b^{3} + 3 \, a b^{4} - b^{5}\right)} f \cosh\left(f x + e\right)^{4} + 30 \, {\left(2 \, a^{4} b - 7 \, a^{3} b^{2} + 9 \, a^{2} b^{3} - 5 \, a b^{4} + b^{5}\right)} f \cosh\left(f x + e\right)^{2} + {\left(8 \, a^{5} - 32 \, a^{4} b + 51 \, a^{3} b^{2} - 41 \, a^{2} b^{3} + 17 \, a b^{4} - 3 \, b^{5}\right)} f\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(2 \, a^{4} b - 7 \, a^{3} b^{2} + 9 \, a^{2} b^{3} - 5 \, a b^{4} + b^{5}\right)} f \cosh\left(f x + e\right)^{2} + 8 \, {\left(7 \, {\left(a^{3} b^{2} - 3 \, a^{2} b^{3} + 3 \, a b^{4} - b^{5}\right)} f \cosh\left(f x + e\right)^{5} + 10 \, {\left(2 \, a^{4} b - 7 \, a^{3} b^{2} + 9 \, a^{2} b^{3} - 5 \, a b^{4} + b^{5}\right)} f \cosh\left(f x + e\right)^{3} + {\left(8 \, a^{5} - 32 \, a^{4} b + 51 \, a^{3} b^{2} - 41 \, a^{2} b^{3} + 17 \, a b^{4} - 3 \, b^{5}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 4 \, {\left(7 \, {\left(a^{3} b^{2} - 3 \, a^{2} b^{3} + 3 \, a b^{4} - b^{5}\right)} f \cosh\left(f x + e\right)^{6} + 15 \, {\left(2 \, a^{4} b - 7 \, a^{3} b^{2} + 9 \, a^{2} b^{3} - 5 \, a b^{4} + b^{5}\right)} f \cosh\left(f x + e\right)^{4} + 3 \, {\left(8 \, a^{5} - 32 \, a^{4} b + 51 \, a^{3} b^{2} - 41 \, a^{2} b^{3} + 17 \, a b^{4} - 3 \, b^{5}\right)} f \cosh\left(f x + e\right)^{2} + {\left(2 \, a^{4} b - 7 \, a^{3} b^{2} + 9 \, a^{2} b^{3} - 5 \, a b^{4} + b^{5}\right)} f\right)} \sinh\left(f x + e\right)^{2} + {\left(a^{3} b^{2} - 3 \, a^{2} b^{3} + 3 \, a b^{4} - b^{5}\right)} f + 8 \, {\left({\left(a^{3} b^{2} - 3 \, a^{2} b^{3} + 3 \, a b^{4} - b^{5}\right)} f \cosh\left(f x + e\right)^{7} + 3 \, {\left(2 \, a^{4} b - 7 \, a^{3} b^{2} + 9 \, a^{2} b^{3} - 5 \, a b^{4} + b^{5}\right)} f \cosh\left(f x + e\right)^{5} + {\left(8 \, a^{5} - 32 \, a^{4} b + 51 \, a^{3} b^{2} - 41 \, a^{2} b^{3} + 17 \, a b^{4} - 3 \, b^{5}\right)} f \cosh\left(f x + e\right)^{3} + {\left(2 \, a^{4} b - 7 \, a^{3} b^{2} + 9 \, a^{2} b^{3} - 5 \, a b^{4} + b^{5}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)}}, -\frac{3 \, {\left(b^{2} \cosh\left(f x + e\right)^{8} + 8 \, b^{2} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + b^{2} \sinh\left(f x + e\right)^{8} + 4 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{6} + 4 \, {\left(7 \, b^{2} \cosh\left(f x + e\right)^{2} + 2 \, a b - b^{2}\right)} \sinh\left(f x + e\right)^{6} + 8 \, {\left(7 \, b^{2} \cosh\left(f x + e\right)^{3} + 3 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{4} + 2 \, {\left(35 \, b^{2} \cosh\left(f x + e\right)^{4} + 30 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{2} + 8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \sinh\left(f x + e\right)^{4} + 8 \, {\left(7 \, b^{2} \cosh\left(f x + e\right)^{5} + 10 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{3} + {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 4 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{2} + 4 \, {\left(7 \, b^{2} \cosh\left(f x + e\right)^{6} + 15 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{4} + 3 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + 2 \, a b - b^{2}\right)} \sinh\left(f x + e\right)^{2} + b^{2} + 8 \, {\left(b^{2} \cosh\left(f x + e\right)^{7} + 3 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{5} + {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{3} + {\left(2 \, a b - b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{-a + b} \arctan\left(-\frac{\sqrt{2} \sqrt{-a + b} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{2 \, {\left({\left(a - b\right)} \cosh\left(f x + e\right) + {\left(a - b\right)} \sinh\left(f x + e\right)\right)}}\right) - 2 \, \sqrt{2} {\left(3 \, {\left(a b - b^{2}\right)} \cosh\left(f x + e\right)^{5} + 15 \, {\left(a b - b^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{4} + 3 \, {\left(a b - b^{2}\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(8 \, a^{2} - 13 \, a b + 5 \, b^{2}\right)} \cosh\left(f x + e\right)^{3} + 2 \, {\left(15 \, {\left(a b - b^{2}\right)} \cosh\left(f x + e\right)^{2} + 8 \, a^{2} - 13 \, a b + 5 \, b^{2}\right)} \sinh\left(f x + e\right)^{3} + 6 \, {\left(5 \, {\left(a b - b^{2}\right)} \cosh\left(f x + e\right)^{3} + {\left(8 \, a^{2} - 13 \, a b + 5 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{2} + 3 \, {\left(a b - b^{2}\right)} \cosh\left(f x + e\right) + 3 \, {\left(5 \, {\left(a b - b^{2}\right)} \cosh\left(f x + e\right)^{4} + 2 \, {\left(8 \, a^{2} - 13 \, a b + 5 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + a b - b^{2}\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{3 \, {\left({\left(a^{3} b^{2} - 3 \, a^{2} b^{3} + 3 \, a b^{4} - b^{5}\right)} f \cosh\left(f x + e\right)^{8} + 8 \, {\left(a^{3} b^{2} - 3 \, a^{2} b^{3} + 3 \, a b^{4} - b^{5}\right)} f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + {\left(a^{3} b^{2} - 3 \, a^{2} b^{3} + 3 \, a b^{4} - b^{5}\right)} f \sinh\left(f x + e\right)^{8} + 4 \, {\left(2 \, a^{4} b - 7 \, a^{3} b^{2} + 9 \, a^{2} b^{3} - 5 \, a b^{4} + b^{5}\right)} f \cosh\left(f x + e\right)^{6} + 4 \, {\left(7 \, {\left(a^{3} b^{2} - 3 \, a^{2} b^{3} + 3 \, a b^{4} - b^{5}\right)} f \cosh\left(f x + e\right)^{2} + {\left(2 \, a^{4} b - 7 \, a^{3} b^{2} + 9 \, a^{2} b^{3} - 5 \, a b^{4} + b^{5}\right)} f\right)} \sinh\left(f x + e\right)^{6} + 2 \, {\left(8 \, a^{5} - 32 \, a^{4} b + 51 \, a^{3} b^{2} - 41 \, a^{2} b^{3} + 17 \, a b^{4} - 3 \, b^{5}\right)} f \cosh\left(f x + e\right)^{4} + 8 \, {\left(7 \, {\left(a^{3} b^{2} - 3 \, a^{2} b^{3} + 3 \, a b^{4} - b^{5}\right)} f \cosh\left(f x + e\right)^{3} + 3 \, {\left(2 \, a^{4} b - 7 \, a^{3} b^{2} + 9 \, a^{2} b^{3} - 5 \, a b^{4} + b^{5}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(35 \, {\left(a^{3} b^{2} - 3 \, a^{2} b^{3} + 3 \, a b^{4} - b^{5}\right)} f \cosh\left(f x + e\right)^{4} + 30 \, {\left(2 \, a^{4} b - 7 \, a^{3} b^{2} + 9 \, a^{2} b^{3} - 5 \, a b^{4} + b^{5}\right)} f \cosh\left(f x + e\right)^{2} + {\left(8 \, a^{5} - 32 \, a^{4} b + 51 \, a^{3} b^{2} - 41 \, a^{2} b^{3} + 17 \, a b^{4} - 3 \, b^{5}\right)} f\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(2 \, a^{4} b - 7 \, a^{3} b^{2} + 9 \, a^{2} b^{3} - 5 \, a b^{4} + b^{5}\right)} f \cosh\left(f x + e\right)^{2} + 8 \, {\left(7 \, {\left(a^{3} b^{2} - 3 \, a^{2} b^{3} + 3 \, a b^{4} - b^{5}\right)} f \cosh\left(f x + e\right)^{5} + 10 \, {\left(2 \, a^{4} b - 7 \, a^{3} b^{2} + 9 \, a^{2} b^{3} - 5 \, a b^{4} + b^{5}\right)} f \cosh\left(f x + e\right)^{3} + {\left(8 \, a^{5} - 32 \, a^{4} b + 51 \, a^{3} b^{2} - 41 \, a^{2} b^{3} + 17 \, a b^{4} - 3 \, b^{5}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 4 \, {\left(7 \, {\left(a^{3} b^{2} - 3 \, a^{2} b^{3} + 3 \, a b^{4} - b^{5}\right)} f \cosh\left(f x + e\right)^{6} + 15 \, {\left(2 \, a^{4} b - 7 \, a^{3} b^{2} + 9 \, a^{2} b^{3} - 5 \, a b^{4} + b^{5}\right)} f \cosh\left(f x + e\right)^{4} + 3 \, {\left(8 \, a^{5} - 32 \, a^{4} b + 51 \, a^{3} b^{2} - 41 \, a^{2} b^{3} + 17 \, a b^{4} - 3 \, b^{5}\right)} f \cosh\left(f x + e\right)^{2} + {\left(2 \, a^{4} b - 7 \, a^{3} b^{2} + 9 \, a^{2} b^{3} - 5 \, a b^{4} + b^{5}\right)} f\right)} \sinh\left(f x + e\right)^{2} + {\left(a^{3} b^{2} - 3 \, a^{2} b^{3} + 3 \, a b^{4} - b^{5}\right)} f + 8 \, {\left({\left(a^{3} b^{2} - 3 \, a^{2} b^{3} + 3 \, a b^{4} - b^{5}\right)} f \cosh\left(f x + e\right)^{7} + 3 \, {\left(2 \, a^{4} b - 7 \, a^{3} b^{2} + 9 \, a^{2} b^{3} - 5 \, a b^{4} + b^{5}\right)} f \cosh\left(f x + e\right)^{5} + {\left(8 \, a^{5} - 32 \, a^{4} b + 51 \, a^{3} b^{2} - 41 \, a^{2} b^{3} + 17 \, a b^{4} - 3 \, b^{5}\right)} f \cosh\left(f x + e\right)^{3} + {\left(2 \, a^{4} b - 7 \, a^{3} b^{2} + 9 \, a^{2} b^{3} - 5 \, a b^{4} + b^{5}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)}}\right]"," ",0,"[1/6*(3*(b^2*cosh(f*x + e)^8 + 8*b^2*cosh(f*x + e)*sinh(f*x + e)^7 + b^2*sinh(f*x + e)^8 + 4*(2*a*b - b^2)*cosh(f*x + e)^6 + 4*(7*b^2*cosh(f*x + e)^2 + 2*a*b - b^2)*sinh(f*x + e)^6 + 8*(7*b^2*cosh(f*x + e)^3 + 3*(2*a*b - b^2)*cosh(f*x + e))*sinh(f*x + e)^5 + 2*(8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e)^4 + 2*(35*b^2*cosh(f*x + e)^4 + 30*(2*a*b - b^2)*cosh(f*x + e)^2 + 8*a^2 - 8*a*b + 3*b^2)*sinh(f*x + e)^4 + 8*(7*b^2*cosh(f*x + e)^5 + 10*(2*a*b - b^2)*cosh(f*x + e)^3 + (8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e))*sinh(f*x + e)^3 + 4*(2*a*b - b^2)*cosh(f*x + e)^2 + 4*(7*b^2*cosh(f*x + e)^6 + 15*(2*a*b - b^2)*cosh(f*x + e)^4 + 3*(8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e)^2 + 2*a*b - b^2)*sinh(f*x + e)^2 + b^2 + 8*(b^2*cosh(f*x + e)^7 + 3*(2*a*b - b^2)*cosh(f*x + e)^5 + (8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e)^3 + (2*a*b - b^2)*cosh(f*x + e))*sinh(f*x + e))*sqrt(a - b)*log((b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(4*a - 3*b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 4*a - 3*b)*sinh(f*x + e)^2 - 4*sqrt(2)*sqrt(a - b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))*(cosh(f*x + e) + sinh(f*x + e)) + 4*(b*cosh(f*x + e)^3 + (4*a - 3*b)*cosh(f*x + e))*sinh(f*x + e) + b)/(cosh(f*x + e)^4 + 4*cosh(f*x + e)*sinh(f*x + e)^3 + sinh(f*x + e)^4 + 2*(3*cosh(f*x + e)^2 + 1)*sinh(f*x + e)^2 + 2*cosh(f*x + e)^2 + 4*(cosh(f*x + e)^3 + cosh(f*x + e))*sinh(f*x + e) + 1)) + 4*sqrt(2)*(3*(a*b - b^2)*cosh(f*x + e)^5 + 15*(a*b - b^2)*cosh(f*x + e)*sinh(f*x + e)^4 + 3*(a*b - b^2)*sinh(f*x + e)^5 + 2*(8*a^2 - 13*a*b + 5*b^2)*cosh(f*x + e)^3 + 2*(15*(a*b - b^2)*cosh(f*x + e)^2 + 8*a^2 - 13*a*b + 5*b^2)*sinh(f*x + e)^3 + 6*(5*(a*b - b^2)*cosh(f*x + e)^3 + (8*a^2 - 13*a*b + 5*b^2)*cosh(f*x + e))*sinh(f*x + e)^2 + 3*(a*b - b^2)*cosh(f*x + e) + 3*(5*(a*b - b^2)*cosh(f*x + e)^4 + 2*(8*a^2 - 13*a*b + 5*b^2)*cosh(f*x + e)^2 + a*b - b^2)*sinh(f*x + e))*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/((a^3*b^2 - 3*a^2*b^3 + 3*a*b^4 - b^5)*f*cosh(f*x + e)^8 + 8*(a^3*b^2 - 3*a^2*b^3 + 3*a*b^4 - b^5)*f*cosh(f*x + e)*sinh(f*x + e)^7 + (a^3*b^2 - 3*a^2*b^3 + 3*a*b^4 - b^5)*f*sinh(f*x + e)^8 + 4*(2*a^4*b - 7*a^3*b^2 + 9*a^2*b^3 - 5*a*b^4 + b^5)*f*cosh(f*x + e)^6 + 4*(7*(a^3*b^2 - 3*a^2*b^3 + 3*a*b^4 - b^5)*f*cosh(f*x + e)^2 + (2*a^4*b - 7*a^3*b^2 + 9*a^2*b^3 - 5*a*b^4 + b^5)*f)*sinh(f*x + e)^6 + 2*(8*a^5 - 32*a^4*b + 51*a^3*b^2 - 41*a^2*b^3 + 17*a*b^4 - 3*b^5)*f*cosh(f*x + e)^4 + 8*(7*(a^3*b^2 - 3*a^2*b^3 + 3*a*b^4 - b^5)*f*cosh(f*x + e)^3 + 3*(2*a^4*b - 7*a^3*b^2 + 9*a^2*b^3 - 5*a*b^4 + b^5)*f*cosh(f*x + e))*sinh(f*x + e)^5 + 2*(35*(a^3*b^2 - 3*a^2*b^3 + 3*a*b^4 - b^5)*f*cosh(f*x + e)^4 + 30*(2*a^4*b - 7*a^3*b^2 + 9*a^2*b^3 - 5*a*b^4 + b^5)*f*cosh(f*x + e)^2 + (8*a^5 - 32*a^4*b + 51*a^3*b^2 - 41*a^2*b^3 + 17*a*b^4 - 3*b^5)*f)*sinh(f*x + e)^4 + 4*(2*a^4*b - 7*a^3*b^2 + 9*a^2*b^3 - 5*a*b^4 + b^5)*f*cosh(f*x + e)^2 + 8*(7*(a^3*b^2 - 3*a^2*b^3 + 3*a*b^4 - b^5)*f*cosh(f*x + e)^5 + 10*(2*a^4*b - 7*a^3*b^2 + 9*a^2*b^3 - 5*a*b^4 + b^5)*f*cosh(f*x + e)^3 + (8*a^5 - 32*a^4*b + 51*a^3*b^2 - 41*a^2*b^3 + 17*a*b^4 - 3*b^5)*f*cosh(f*x + e))*sinh(f*x + e)^3 + 4*(7*(a^3*b^2 - 3*a^2*b^3 + 3*a*b^4 - b^5)*f*cosh(f*x + e)^6 + 15*(2*a^4*b - 7*a^3*b^2 + 9*a^2*b^3 - 5*a*b^4 + b^5)*f*cosh(f*x + e)^4 + 3*(8*a^5 - 32*a^4*b + 51*a^3*b^2 - 41*a^2*b^3 + 17*a*b^4 - 3*b^5)*f*cosh(f*x + e)^2 + (2*a^4*b - 7*a^3*b^2 + 9*a^2*b^3 - 5*a*b^4 + b^5)*f)*sinh(f*x + e)^2 + (a^3*b^2 - 3*a^2*b^3 + 3*a*b^4 - b^5)*f + 8*((a^3*b^2 - 3*a^2*b^3 + 3*a*b^4 - b^5)*f*cosh(f*x + e)^7 + 3*(2*a^4*b - 7*a^3*b^2 + 9*a^2*b^3 - 5*a*b^4 + b^5)*f*cosh(f*x + e)^5 + (8*a^5 - 32*a^4*b + 51*a^3*b^2 - 41*a^2*b^3 + 17*a*b^4 - 3*b^5)*f*cosh(f*x + e)^3 + (2*a^4*b - 7*a^3*b^2 + 9*a^2*b^3 - 5*a*b^4 + b^5)*f*cosh(f*x + e))*sinh(f*x + e)), -1/3*(3*(b^2*cosh(f*x + e)^8 + 8*b^2*cosh(f*x + e)*sinh(f*x + e)^7 + b^2*sinh(f*x + e)^8 + 4*(2*a*b - b^2)*cosh(f*x + e)^6 + 4*(7*b^2*cosh(f*x + e)^2 + 2*a*b - b^2)*sinh(f*x + e)^6 + 8*(7*b^2*cosh(f*x + e)^3 + 3*(2*a*b - b^2)*cosh(f*x + e))*sinh(f*x + e)^5 + 2*(8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e)^4 + 2*(35*b^2*cosh(f*x + e)^4 + 30*(2*a*b - b^2)*cosh(f*x + e)^2 + 8*a^2 - 8*a*b + 3*b^2)*sinh(f*x + e)^4 + 8*(7*b^2*cosh(f*x + e)^5 + 10*(2*a*b - b^2)*cosh(f*x + e)^3 + (8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e))*sinh(f*x + e)^3 + 4*(2*a*b - b^2)*cosh(f*x + e)^2 + 4*(7*b^2*cosh(f*x + e)^6 + 15*(2*a*b - b^2)*cosh(f*x + e)^4 + 3*(8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e)^2 + 2*a*b - b^2)*sinh(f*x + e)^2 + b^2 + 8*(b^2*cosh(f*x + e)^7 + 3*(2*a*b - b^2)*cosh(f*x + e)^5 + (8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e)^3 + (2*a*b - b^2)*cosh(f*x + e))*sinh(f*x + e))*sqrt(-a + b)*arctan(-1/2*sqrt(2)*sqrt(-a + b)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/((a - b)*cosh(f*x + e) + (a - b)*sinh(f*x + e))) - 2*sqrt(2)*(3*(a*b - b^2)*cosh(f*x + e)^5 + 15*(a*b - b^2)*cosh(f*x + e)*sinh(f*x + e)^4 + 3*(a*b - b^2)*sinh(f*x + e)^5 + 2*(8*a^2 - 13*a*b + 5*b^2)*cosh(f*x + e)^3 + 2*(15*(a*b - b^2)*cosh(f*x + e)^2 + 8*a^2 - 13*a*b + 5*b^2)*sinh(f*x + e)^3 + 6*(5*(a*b - b^2)*cosh(f*x + e)^3 + (8*a^2 - 13*a*b + 5*b^2)*cosh(f*x + e))*sinh(f*x + e)^2 + 3*(a*b - b^2)*cosh(f*x + e) + 3*(5*(a*b - b^2)*cosh(f*x + e)^4 + 2*(8*a^2 - 13*a*b + 5*b^2)*cosh(f*x + e)^2 + a*b - b^2)*sinh(f*x + e))*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/((a^3*b^2 - 3*a^2*b^3 + 3*a*b^4 - b^5)*f*cosh(f*x + e)^8 + 8*(a^3*b^2 - 3*a^2*b^3 + 3*a*b^4 - b^5)*f*cosh(f*x + e)*sinh(f*x + e)^7 + (a^3*b^2 - 3*a^2*b^3 + 3*a*b^4 - b^5)*f*sinh(f*x + e)^8 + 4*(2*a^4*b - 7*a^3*b^2 + 9*a^2*b^3 - 5*a*b^4 + b^5)*f*cosh(f*x + e)^6 + 4*(7*(a^3*b^2 - 3*a^2*b^3 + 3*a*b^4 - b^5)*f*cosh(f*x + e)^2 + (2*a^4*b - 7*a^3*b^2 + 9*a^2*b^3 - 5*a*b^4 + b^5)*f)*sinh(f*x + e)^6 + 2*(8*a^5 - 32*a^4*b + 51*a^3*b^2 - 41*a^2*b^3 + 17*a*b^4 - 3*b^5)*f*cosh(f*x + e)^4 + 8*(7*(a^3*b^2 - 3*a^2*b^3 + 3*a*b^4 - b^5)*f*cosh(f*x + e)^3 + 3*(2*a^4*b - 7*a^3*b^2 + 9*a^2*b^3 - 5*a*b^4 + b^5)*f*cosh(f*x + e))*sinh(f*x + e)^5 + 2*(35*(a^3*b^2 - 3*a^2*b^3 + 3*a*b^4 - b^5)*f*cosh(f*x + e)^4 + 30*(2*a^4*b - 7*a^3*b^2 + 9*a^2*b^3 - 5*a*b^4 + b^5)*f*cosh(f*x + e)^2 + (8*a^5 - 32*a^4*b + 51*a^3*b^2 - 41*a^2*b^3 + 17*a*b^4 - 3*b^5)*f)*sinh(f*x + e)^4 + 4*(2*a^4*b - 7*a^3*b^2 + 9*a^2*b^3 - 5*a*b^4 + b^5)*f*cosh(f*x + e)^2 + 8*(7*(a^3*b^2 - 3*a^2*b^3 + 3*a*b^4 - b^5)*f*cosh(f*x + e)^5 + 10*(2*a^4*b - 7*a^3*b^2 + 9*a^2*b^3 - 5*a*b^4 + b^5)*f*cosh(f*x + e)^3 + (8*a^5 - 32*a^4*b + 51*a^3*b^2 - 41*a^2*b^3 + 17*a*b^4 - 3*b^5)*f*cosh(f*x + e))*sinh(f*x + e)^3 + 4*(7*(a^3*b^2 - 3*a^2*b^3 + 3*a*b^4 - b^5)*f*cosh(f*x + e)^6 + 15*(2*a^4*b - 7*a^3*b^2 + 9*a^2*b^3 - 5*a*b^4 + b^5)*f*cosh(f*x + e)^4 + 3*(8*a^5 - 32*a^4*b + 51*a^3*b^2 - 41*a^2*b^3 + 17*a*b^4 - 3*b^5)*f*cosh(f*x + e)^2 + (2*a^4*b - 7*a^3*b^2 + 9*a^2*b^3 - 5*a*b^4 + b^5)*f)*sinh(f*x + e)^2 + (a^3*b^2 - 3*a^2*b^3 + 3*a*b^4 - b^5)*f + 8*((a^3*b^2 - 3*a^2*b^3 + 3*a*b^4 - b^5)*f*cosh(f*x + e)^7 + 3*(2*a^4*b - 7*a^3*b^2 + 9*a^2*b^3 - 5*a*b^4 + b^5)*f*cosh(f*x + e)^5 + (8*a^5 - 32*a^4*b + 51*a^3*b^2 - 41*a^2*b^3 + 17*a*b^4 - 3*b^5)*f*cosh(f*x + e)^3 + (2*a^4*b - 7*a^3*b^2 + 9*a^2*b^3 - 5*a*b^4 + b^5)*f*cosh(f*x + e))*sinh(f*x + e))]","B",0
504,1,3084,0,0.624790," ","integrate(coth(f*x+e)/(a+b*sinh(f*x+e)^2)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(b^{2} \cosh\left(f x + e\right)^{8} + 8 \, b^{2} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + b^{2} \sinh\left(f x + e\right)^{8} + 4 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{6} + 4 \, {\left(7 \, b^{2} \cosh\left(f x + e\right)^{2} + 2 \, a b - b^{2}\right)} \sinh\left(f x + e\right)^{6} + 8 \, {\left(7 \, b^{2} \cosh\left(f x + e\right)^{3} + 3 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{4} + 2 \, {\left(35 \, b^{2} \cosh\left(f x + e\right)^{4} + 30 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{2} + 8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \sinh\left(f x + e\right)^{4} + 8 \, {\left(7 \, b^{2} \cosh\left(f x + e\right)^{5} + 10 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{3} + {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 4 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{2} + 4 \, {\left(7 \, b^{2} \cosh\left(f x + e\right)^{6} + 15 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{4} + 3 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + 2 \, a b - b^{2}\right)} \sinh\left(f x + e\right)^{2} + b^{2} + 8 \, {\left(b^{2} \cosh\left(f x + e\right)^{7} + 3 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{5} + {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{3} + {\left(2 \, a b - b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{a} \log\left(\frac{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(4 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + 4 \, a - b\right)} \sinh\left(f x + e\right)^{2} - 4 \, \sqrt{2} \sqrt{a} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} {\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right)\right)} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(4 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}{\cosh\left(f x + e\right)^{4} + 4 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + \sinh\left(f x + e\right)^{4} + 2 \, {\left(3 \, \cosh\left(f x + e\right)^{2} - 1\right)} \sinh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right)^{2} + 4 \, {\left(\cosh\left(f x + e\right)^{3} - \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + 1}\right) + 4 \, \sqrt{2} {\left(3 \, a b \cosh\left(f x + e\right)^{5} + 15 \, a b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{4} + 3 \, a b \sinh\left(f x + e\right)^{5} + 2 \, {\left(8 \, a^{2} - 3 \, a b\right)} \cosh\left(f x + e\right)^{3} + 2 \, {\left(15 \, a b \cosh\left(f x + e\right)^{2} + 8 \, a^{2} - 3 \, a b\right)} \sinh\left(f x + e\right)^{3} + 3 \, a b \cosh\left(f x + e\right) + 6 \, {\left(5 \, a b \cosh\left(f x + e\right)^{3} + {\left(8 \, a^{2} - 3 \, a b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{2} + 3 \, {\left(5 \, a b \cosh\left(f x + e\right)^{4} + 2 \, {\left(8 \, a^{2} - 3 \, a b\right)} \cosh\left(f x + e\right)^{2} + a b\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{6 \, {\left(a^{3} b^{2} f \cosh\left(f x + e\right)^{8} + 8 \, a^{3} b^{2} f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + a^{3} b^{2} f \sinh\left(f x + e\right)^{8} + 4 \, {\left(2 \, a^{4} b - a^{3} b^{2}\right)} f \cosh\left(f x + e\right)^{6} + 4 \, {\left(7 \, a^{3} b^{2} f \cosh\left(f x + e\right)^{2} + {\left(2 \, a^{4} b - a^{3} b^{2}\right)} f\right)} \sinh\left(f x + e\right)^{6} + a^{3} b^{2} f + 2 \, {\left(8 \, a^{5} - 8 \, a^{4} b + 3 \, a^{3} b^{2}\right)} f \cosh\left(f x + e\right)^{4} + 8 \, {\left(7 \, a^{3} b^{2} f \cosh\left(f x + e\right)^{3} + 3 \, {\left(2 \, a^{4} b - a^{3} b^{2}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(35 \, a^{3} b^{2} f \cosh\left(f x + e\right)^{4} + 30 \, {\left(2 \, a^{4} b - a^{3} b^{2}\right)} f \cosh\left(f x + e\right)^{2} + {\left(8 \, a^{5} - 8 \, a^{4} b + 3 \, a^{3} b^{2}\right)} f\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(2 \, a^{4} b - a^{3} b^{2}\right)} f \cosh\left(f x + e\right)^{2} + 8 \, {\left(7 \, a^{3} b^{2} f \cosh\left(f x + e\right)^{5} + 10 \, {\left(2 \, a^{4} b - a^{3} b^{2}\right)} f \cosh\left(f x + e\right)^{3} + {\left(8 \, a^{5} - 8 \, a^{4} b + 3 \, a^{3} b^{2}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 4 \, {\left(7 \, a^{3} b^{2} f \cosh\left(f x + e\right)^{6} + 15 \, {\left(2 \, a^{4} b - a^{3} b^{2}\right)} f \cosh\left(f x + e\right)^{4} + 3 \, {\left(8 \, a^{5} - 8 \, a^{4} b + 3 \, a^{3} b^{2}\right)} f \cosh\left(f x + e\right)^{2} + {\left(2 \, a^{4} b - a^{3} b^{2}\right)} f\right)} \sinh\left(f x + e\right)^{2} + 8 \, {\left(a^{3} b^{2} f \cosh\left(f x + e\right)^{7} + 3 \, {\left(2 \, a^{4} b - a^{3} b^{2}\right)} f \cosh\left(f x + e\right)^{5} + {\left(8 \, a^{5} - 8 \, a^{4} b + 3 \, a^{3} b^{2}\right)} f \cosh\left(f x + e\right)^{3} + {\left(2 \, a^{4} b - a^{3} b^{2}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)}}, \frac{3 \, {\left(b^{2} \cosh\left(f x + e\right)^{8} + 8 \, b^{2} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + b^{2} \sinh\left(f x + e\right)^{8} + 4 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{6} + 4 \, {\left(7 \, b^{2} \cosh\left(f x + e\right)^{2} + 2 \, a b - b^{2}\right)} \sinh\left(f x + e\right)^{6} + 8 \, {\left(7 \, b^{2} \cosh\left(f x + e\right)^{3} + 3 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{4} + 2 \, {\left(35 \, b^{2} \cosh\left(f x + e\right)^{4} + 30 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{2} + 8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \sinh\left(f x + e\right)^{4} + 8 \, {\left(7 \, b^{2} \cosh\left(f x + e\right)^{5} + 10 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{3} + {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 4 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{2} + 4 \, {\left(7 \, b^{2} \cosh\left(f x + e\right)^{6} + 15 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{4} + 3 \, {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{2} + 2 \, a b - b^{2}\right)} \sinh\left(f x + e\right)^{2} + b^{2} + 8 \, {\left(b^{2} \cosh\left(f x + e\right)^{7} + 3 \, {\left(2 \, a b - b^{2}\right)} \cosh\left(f x + e\right)^{5} + {\left(8 \, a^{2} - 8 \, a b + 3 \, b^{2}\right)} \cosh\left(f x + e\right)^{3} + {\left(2 \, a b - b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{2} \sqrt{-a} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{2 \, {\left(a \cosh\left(f x + e\right) + a \sinh\left(f x + e\right)\right)}}\right) + 2 \, \sqrt{2} {\left(3 \, a b \cosh\left(f x + e\right)^{5} + 15 \, a b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{4} + 3 \, a b \sinh\left(f x + e\right)^{5} + 2 \, {\left(8 \, a^{2} - 3 \, a b\right)} \cosh\left(f x + e\right)^{3} + 2 \, {\left(15 \, a b \cosh\left(f x + e\right)^{2} + 8 \, a^{2} - 3 \, a b\right)} \sinh\left(f x + e\right)^{3} + 3 \, a b \cosh\left(f x + e\right) + 6 \, {\left(5 \, a b \cosh\left(f x + e\right)^{3} + {\left(8 \, a^{2} - 3 \, a b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{2} + 3 \, {\left(5 \, a b \cosh\left(f x + e\right)^{4} + 2 \, {\left(8 \, a^{2} - 3 \, a b\right)} \cosh\left(f x + e\right)^{2} + a b\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{3 \, {\left(a^{3} b^{2} f \cosh\left(f x + e\right)^{8} + 8 \, a^{3} b^{2} f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{7} + a^{3} b^{2} f \sinh\left(f x + e\right)^{8} + 4 \, {\left(2 \, a^{4} b - a^{3} b^{2}\right)} f \cosh\left(f x + e\right)^{6} + 4 \, {\left(7 \, a^{3} b^{2} f \cosh\left(f x + e\right)^{2} + {\left(2 \, a^{4} b - a^{3} b^{2}\right)} f\right)} \sinh\left(f x + e\right)^{6} + a^{3} b^{2} f + 2 \, {\left(8 \, a^{5} - 8 \, a^{4} b + 3 \, a^{3} b^{2}\right)} f \cosh\left(f x + e\right)^{4} + 8 \, {\left(7 \, a^{3} b^{2} f \cosh\left(f x + e\right)^{3} + 3 \, {\left(2 \, a^{4} b - a^{3} b^{2}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(35 \, a^{3} b^{2} f \cosh\left(f x + e\right)^{4} + 30 \, {\left(2 \, a^{4} b - a^{3} b^{2}\right)} f \cosh\left(f x + e\right)^{2} + {\left(8 \, a^{5} - 8 \, a^{4} b + 3 \, a^{3} b^{2}\right)} f\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(2 \, a^{4} b - a^{3} b^{2}\right)} f \cosh\left(f x + e\right)^{2} + 8 \, {\left(7 \, a^{3} b^{2} f \cosh\left(f x + e\right)^{5} + 10 \, {\left(2 \, a^{4} b - a^{3} b^{2}\right)} f \cosh\left(f x + e\right)^{3} + {\left(8 \, a^{5} - 8 \, a^{4} b + 3 \, a^{3} b^{2}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 4 \, {\left(7 \, a^{3} b^{2} f \cosh\left(f x + e\right)^{6} + 15 \, {\left(2 \, a^{4} b - a^{3} b^{2}\right)} f \cosh\left(f x + e\right)^{4} + 3 \, {\left(8 \, a^{5} - 8 \, a^{4} b + 3 \, a^{3} b^{2}\right)} f \cosh\left(f x + e\right)^{2} + {\left(2 \, a^{4} b - a^{3} b^{2}\right)} f\right)} \sinh\left(f x + e\right)^{2} + 8 \, {\left(a^{3} b^{2} f \cosh\left(f x + e\right)^{7} + 3 \, {\left(2 \, a^{4} b - a^{3} b^{2}\right)} f \cosh\left(f x + e\right)^{5} + {\left(8 \, a^{5} - 8 \, a^{4} b + 3 \, a^{3} b^{2}\right)} f \cosh\left(f x + e\right)^{3} + {\left(2 \, a^{4} b - a^{3} b^{2}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)}}\right]"," ",0,"[1/6*(3*(b^2*cosh(f*x + e)^8 + 8*b^2*cosh(f*x + e)*sinh(f*x + e)^7 + b^2*sinh(f*x + e)^8 + 4*(2*a*b - b^2)*cosh(f*x + e)^6 + 4*(7*b^2*cosh(f*x + e)^2 + 2*a*b - b^2)*sinh(f*x + e)^6 + 8*(7*b^2*cosh(f*x + e)^3 + 3*(2*a*b - b^2)*cosh(f*x + e))*sinh(f*x + e)^5 + 2*(8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e)^4 + 2*(35*b^2*cosh(f*x + e)^4 + 30*(2*a*b - b^2)*cosh(f*x + e)^2 + 8*a^2 - 8*a*b + 3*b^2)*sinh(f*x + e)^4 + 8*(7*b^2*cosh(f*x + e)^5 + 10*(2*a*b - b^2)*cosh(f*x + e)^3 + (8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e))*sinh(f*x + e)^3 + 4*(2*a*b - b^2)*cosh(f*x + e)^2 + 4*(7*b^2*cosh(f*x + e)^6 + 15*(2*a*b - b^2)*cosh(f*x + e)^4 + 3*(8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e)^2 + 2*a*b - b^2)*sinh(f*x + e)^2 + b^2 + 8*(b^2*cosh(f*x + e)^7 + 3*(2*a*b - b^2)*cosh(f*x + e)^5 + (8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e)^3 + (2*a*b - b^2)*cosh(f*x + e))*sinh(f*x + e))*sqrt(a)*log((b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(4*a - b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 4*a - b)*sinh(f*x + e)^2 - 4*sqrt(2)*sqrt(a)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))*(cosh(f*x + e) + sinh(f*x + e)) + 4*(b*cosh(f*x + e)^3 + (4*a - b)*cosh(f*x + e))*sinh(f*x + e) + b)/(cosh(f*x + e)^4 + 4*cosh(f*x + e)*sinh(f*x + e)^3 + sinh(f*x + e)^4 + 2*(3*cosh(f*x + e)^2 - 1)*sinh(f*x + e)^2 - 2*cosh(f*x + e)^2 + 4*(cosh(f*x + e)^3 - cosh(f*x + e))*sinh(f*x + e) + 1)) + 4*sqrt(2)*(3*a*b*cosh(f*x + e)^5 + 15*a*b*cosh(f*x + e)*sinh(f*x + e)^4 + 3*a*b*sinh(f*x + e)^5 + 2*(8*a^2 - 3*a*b)*cosh(f*x + e)^3 + 2*(15*a*b*cosh(f*x + e)^2 + 8*a^2 - 3*a*b)*sinh(f*x + e)^3 + 3*a*b*cosh(f*x + e) + 6*(5*a*b*cosh(f*x + e)^3 + (8*a^2 - 3*a*b)*cosh(f*x + e))*sinh(f*x + e)^2 + 3*(5*a*b*cosh(f*x + e)^4 + 2*(8*a^2 - 3*a*b)*cosh(f*x + e)^2 + a*b)*sinh(f*x + e))*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/(a^3*b^2*f*cosh(f*x + e)^8 + 8*a^3*b^2*f*cosh(f*x + e)*sinh(f*x + e)^7 + a^3*b^2*f*sinh(f*x + e)^8 + 4*(2*a^4*b - a^3*b^2)*f*cosh(f*x + e)^6 + 4*(7*a^3*b^2*f*cosh(f*x + e)^2 + (2*a^4*b - a^3*b^2)*f)*sinh(f*x + e)^6 + a^3*b^2*f + 2*(8*a^5 - 8*a^4*b + 3*a^3*b^2)*f*cosh(f*x + e)^4 + 8*(7*a^3*b^2*f*cosh(f*x + e)^3 + 3*(2*a^4*b - a^3*b^2)*f*cosh(f*x + e))*sinh(f*x + e)^5 + 2*(35*a^3*b^2*f*cosh(f*x + e)^4 + 30*(2*a^4*b - a^3*b^2)*f*cosh(f*x + e)^2 + (8*a^5 - 8*a^4*b + 3*a^3*b^2)*f)*sinh(f*x + e)^4 + 4*(2*a^4*b - a^3*b^2)*f*cosh(f*x + e)^2 + 8*(7*a^3*b^2*f*cosh(f*x + e)^5 + 10*(2*a^4*b - a^3*b^2)*f*cosh(f*x + e)^3 + (8*a^5 - 8*a^4*b + 3*a^3*b^2)*f*cosh(f*x + e))*sinh(f*x + e)^3 + 4*(7*a^3*b^2*f*cosh(f*x + e)^6 + 15*(2*a^4*b - a^3*b^2)*f*cosh(f*x + e)^4 + 3*(8*a^5 - 8*a^4*b + 3*a^3*b^2)*f*cosh(f*x + e)^2 + (2*a^4*b - a^3*b^2)*f)*sinh(f*x + e)^2 + 8*(a^3*b^2*f*cosh(f*x + e)^7 + 3*(2*a^4*b - a^3*b^2)*f*cosh(f*x + e)^5 + (8*a^5 - 8*a^4*b + 3*a^3*b^2)*f*cosh(f*x + e)^3 + (2*a^4*b - a^3*b^2)*f*cosh(f*x + e))*sinh(f*x + e)), 1/3*(3*(b^2*cosh(f*x + e)^8 + 8*b^2*cosh(f*x + e)*sinh(f*x + e)^7 + b^2*sinh(f*x + e)^8 + 4*(2*a*b - b^2)*cosh(f*x + e)^6 + 4*(7*b^2*cosh(f*x + e)^2 + 2*a*b - b^2)*sinh(f*x + e)^6 + 8*(7*b^2*cosh(f*x + e)^3 + 3*(2*a*b - b^2)*cosh(f*x + e))*sinh(f*x + e)^5 + 2*(8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e)^4 + 2*(35*b^2*cosh(f*x + e)^4 + 30*(2*a*b - b^2)*cosh(f*x + e)^2 + 8*a^2 - 8*a*b + 3*b^2)*sinh(f*x + e)^4 + 8*(7*b^2*cosh(f*x + e)^5 + 10*(2*a*b - b^2)*cosh(f*x + e)^3 + (8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e))*sinh(f*x + e)^3 + 4*(2*a*b - b^2)*cosh(f*x + e)^2 + 4*(7*b^2*cosh(f*x + e)^6 + 15*(2*a*b - b^2)*cosh(f*x + e)^4 + 3*(8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e)^2 + 2*a*b - b^2)*sinh(f*x + e)^2 + b^2 + 8*(b^2*cosh(f*x + e)^7 + 3*(2*a*b - b^2)*cosh(f*x + e)^5 + (8*a^2 - 8*a*b + 3*b^2)*cosh(f*x + e)^3 + (2*a*b - b^2)*cosh(f*x + e))*sinh(f*x + e))*sqrt(-a)*arctan(1/2*sqrt(2)*sqrt(-a)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/(a*cosh(f*x + e) + a*sinh(f*x + e))) + 2*sqrt(2)*(3*a*b*cosh(f*x + e)^5 + 15*a*b*cosh(f*x + e)*sinh(f*x + e)^4 + 3*a*b*sinh(f*x + e)^5 + 2*(8*a^2 - 3*a*b)*cosh(f*x + e)^3 + 2*(15*a*b*cosh(f*x + e)^2 + 8*a^2 - 3*a*b)*sinh(f*x + e)^3 + 3*a*b*cosh(f*x + e) + 6*(5*a*b*cosh(f*x + e)^3 + (8*a^2 - 3*a*b)*cosh(f*x + e))*sinh(f*x + e)^2 + 3*(5*a*b*cosh(f*x + e)^4 + 2*(8*a^2 - 3*a*b)*cosh(f*x + e)^2 + a*b)*sinh(f*x + e))*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/(a^3*b^2*f*cosh(f*x + e)^8 + 8*a^3*b^2*f*cosh(f*x + e)*sinh(f*x + e)^7 + a^3*b^2*f*sinh(f*x + e)^8 + 4*(2*a^4*b - a^3*b^2)*f*cosh(f*x + e)^6 + 4*(7*a^3*b^2*f*cosh(f*x + e)^2 + (2*a^4*b - a^3*b^2)*f)*sinh(f*x + e)^6 + a^3*b^2*f + 2*(8*a^5 - 8*a^4*b + 3*a^3*b^2)*f*cosh(f*x + e)^4 + 8*(7*a^3*b^2*f*cosh(f*x + e)^3 + 3*(2*a^4*b - a^3*b^2)*f*cosh(f*x + e))*sinh(f*x + e)^5 + 2*(35*a^3*b^2*f*cosh(f*x + e)^4 + 30*(2*a^4*b - a^3*b^2)*f*cosh(f*x + e)^2 + (8*a^5 - 8*a^4*b + 3*a^3*b^2)*f)*sinh(f*x + e)^4 + 4*(2*a^4*b - a^3*b^2)*f*cosh(f*x + e)^2 + 8*(7*a^3*b^2*f*cosh(f*x + e)^5 + 10*(2*a^4*b - a^3*b^2)*f*cosh(f*x + e)^3 + (8*a^5 - 8*a^4*b + 3*a^3*b^2)*f*cosh(f*x + e))*sinh(f*x + e)^3 + 4*(7*a^3*b^2*f*cosh(f*x + e)^6 + 15*(2*a^4*b - a^3*b^2)*f*cosh(f*x + e)^4 + 3*(8*a^5 - 8*a^4*b + 3*a^3*b^2)*f*cosh(f*x + e)^2 + (2*a^4*b - a^3*b^2)*f)*sinh(f*x + e)^2 + 8*(a^3*b^2*f*cosh(f*x + e)^7 + 3*(2*a^4*b - a^3*b^2)*f*cosh(f*x + e)^5 + (8*a^5 - 8*a^4*b + 3*a^3*b^2)*f*cosh(f*x + e)^3 + (2*a^4*b - a^3*b^2)*f*cosh(f*x + e))*sinh(f*x + e))]","B",0
505,1,7594,0,0.813489," ","integrate(coth(f*x+e)^3/(a+b*sinh(f*x+e)^2)^(5/2),x, algorithm=""fricas"")","\left[-\frac{3 \, {\left({\left(2 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(f x + e\right)^{12} + 12 \, {\left(2 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{11} + {\left(2 \, a b^{2} - 5 \, b^{3}\right)} \sinh\left(f x + e\right)^{12} + 2 \, {\left(8 \, a^{2} b - 26 \, a b^{2} + 15 \, b^{3}\right)} \cosh\left(f x + e\right)^{10} + 2 \, {\left(8 \, a^{2} b - 26 \, a b^{2} + 15 \, b^{3} + 33 \, {\left(2 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{10} + 20 \, {\left(11 \, {\left(2 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} + {\left(8 \, a^{2} b - 26 \, a b^{2} + 15 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{9} + {\left(32 \, a^{3} - 144 \, a^{2} b + 190 \, a b^{2} - 75 \, b^{3}\right)} \cosh\left(f x + e\right)^{8} + {\left(495 \, {\left(2 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} + 32 \, a^{3} - 144 \, a^{2} b + 190 \, a b^{2} - 75 \, b^{3} + 90 \, {\left(8 \, a^{2} b - 26 \, a b^{2} + 15 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{8} + 8 \, {\left(99 \, {\left(2 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(f x + e\right)^{5} + 30 \, {\left(8 \, a^{2} b - 26 \, a b^{2} + 15 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} + {\left(32 \, a^{3} - 144 \, a^{2} b + 190 \, a b^{2} - 75 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{7} - 4 \, {\left(16 \, a^{3} - 64 \, a^{2} b + 70 \, a b^{2} - 25 \, b^{3}\right)} \cosh\left(f x + e\right)^{6} + 4 \, {\left(231 \, {\left(2 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(f x + e\right)^{6} + 105 \, {\left(8 \, a^{2} b - 26 \, a b^{2} + 15 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} - 16 \, a^{3} + 64 \, a^{2} b - 70 \, a b^{2} + 25 \, b^{3} + 7 \, {\left(32 \, a^{3} - 144 \, a^{2} b + 190 \, a b^{2} - 75 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{6} + 8 \, {\left(99 \, {\left(2 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(f x + e\right)^{7} + 63 \, {\left(8 \, a^{2} b - 26 \, a b^{2} + 15 \, b^{3}\right)} \cosh\left(f x + e\right)^{5} + 7 \, {\left(32 \, a^{3} - 144 \, a^{2} b + 190 \, a b^{2} - 75 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} - 3 \, {\left(16 \, a^{3} - 64 \, a^{2} b + 70 \, a b^{2} - 25 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + {\left(32 \, a^{3} - 144 \, a^{2} b + 190 \, a b^{2} - 75 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} + {\left(495 \, {\left(2 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(f x + e\right)^{8} + 420 \, {\left(8 \, a^{2} b - 26 \, a b^{2} + 15 \, b^{3}\right)} \cosh\left(f x + e\right)^{6} + 70 \, {\left(32 \, a^{3} - 144 \, a^{2} b + 190 \, a b^{2} - 75 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} + 32 \, a^{3} - 144 \, a^{2} b + 190 \, a b^{2} - 75 \, b^{3} - 60 \, {\left(16 \, a^{3} - 64 \, a^{2} b + 70 \, a b^{2} - 25 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(55 \, {\left(2 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(f x + e\right)^{9} + 60 \, {\left(8 \, a^{2} b - 26 \, a b^{2} + 15 \, b^{3}\right)} \cosh\left(f x + e\right)^{7} + 14 \, {\left(32 \, a^{3} - 144 \, a^{2} b + 190 \, a b^{2} - 75 \, b^{3}\right)} \cosh\left(f x + e\right)^{5} - 20 \, {\left(16 \, a^{3} - 64 \, a^{2} b + 70 \, a b^{2} - 25 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} + {\left(32 \, a^{3} - 144 \, a^{2} b + 190 \, a b^{2} - 75 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 2 \, a b^{2} - 5 \, b^{3} + 2 \, {\left(8 \, a^{2} b - 26 \, a b^{2} + 15 \, b^{3}\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(33 \, {\left(2 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(f x + e\right)^{10} + 45 \, {\left(8 \, a^{2} b - 26 \, a b^{2} + 15 \, b^{3}\right)} \cosh\left(f x + e\right)^{8} + 14 \, {\left(32 \, a^{3} - 144 \, a^{2} b + 190 \, a b^{2} - 75 \, b^{3}\right)} \cosh\left(f x + e\right)^{6} - 30 \, {\left(16 \, a^{3} - 64 \, a^{2} b + 70 \, a b^{2} - 25 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} + 8 \, a^{2} b - 26 \, a b^{2} + 15 \, b^{3} + 3 \, {\left(32 \, a^{3} - 144 \, a^{2} b + 190 \, a b^{2} - 75 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(3 \, {\left(2 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(f x + e\right)^{11} + 5 \, {\left(8 \, a^{2} b - 26 \, a b^{2} + 15 \, b^{3}\right)} \cosh\left(f x + e\right)^{9} + 2 \, {\left(32 \, a^{3} - 144 \, a^{2} b + 190 \, a b^{2} - 75 \, b^{3}\right)} \cosh\left(f x + e\right)^{7} - 6 \, {\left(16 \, a^{3} - 64 \, a^{2} b + 70 \, a b^{2} - 25 \, b^{3}\right)} \cosh\left(f x + e\right)^{5} + {\left(32 \, a^{3} - 144 \, a^{2} b + 190 \, a b^{2} - 75 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} + {\left(8 \, a^{2} b - 26 \, a b^{2} + 15 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{a} \log\left(\frac{b \cosh\left(f x + e\right)^{4} + 4 \, b \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + b \sinh\left(f x + e\right)^{4} + 2 \, {\left(4 \, a - b\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(3 \, b \cosh\left(f x + e\right)^{2} + 4 \, a - b\right)} \sinh\left(f x + e\right)^{2} + 4 \, \sqrt{2} \sqrt{a} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}} {\left(\cosh\left(f x + e\right) + \sinh\left(f x + e\right)\right)} + 4 \, {\left(b \cosh\left(f x + e\right)^{3} + {\left(4 \, a - b\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + b}{\cosh\left(f x + e\right)^{4} + 4 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{3} + \sinh\left(f x + e\right)^{4} + 2 \, {\left(3 \, \cosh\left(f x + e\right)^{2} - 1\right)} \sinh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right)^{2} + 4 \, {\left(\cosh\left(f x + e\right)^{3} - \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right) + 1}\right) - 4 \, \sqrt{2} {\left(3 \, {\left(2 \, a^{2} b - 5 \, a b^{2}\right)} \cosh\left(f x + e\right)^{9} + 27 \, {\left(2 \, a^{2} b - 5 \, a b^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{8} + 3 \, {\left(2 \, a^{2} b - 5 \, a b^{2}\right)} \sinh\left(f x + e\right)^{9} + 4 \, {\left(8 \, a^{3} - 26 \, a^{2} b + 15 \, a b^{2}\right)} \cosh\left(f x + e\right)^{7} + 4 \, {\left(8 \, a^{3} - 26 \, a^{2} b + 15 \, a b^{2} + 27 \, {\left(2 \, a^{2} b - 5 \, a b^{2}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{7} + 28 \, {\left(9 \, {\left(2 \, a^{2} b - 5 \, a b^{2}\right)} \cosh\left(f x + e\right)^{3} + {\left(8 \, a^{3} - 26 \, a^{2} b + 15 \, a b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{6} - 2 \, {\left(56 \, a^{3} - 98 \, a^{2} b + 45 \, a b^{2}\right)} \cosh\left(f x + e\right)^{5} + 2 \, {\left(189 \, {\left(2 \, a^{2} b - 5 \, a b^{2}\right)} \cosh\left(f x + e\right)^{4} - 56 \, a^{3} + 98 \, a^{2} b - 45 \, a b^{2} + 42 \, {\left(8 \, a^{3} - 26 \, a^{2} b + 15 \, a b^{2}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(189 \, {\left(2 \, a^{2} b - 5 \, a b^{2}\right)} \cosh\left(f x + e\right)^{5} + 70 \, {\left(8 \, a^{3} - 26 \, a^{2} b + 15 \, a b^{2}\right)} \cosh\left(f x + e\right)^{3} - 5 \, {\left(56 \, a^{3} - 98 \, a^{2} b + 45 \, a b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(8 \, a^{3} - 26 \, a^{2} b + 15 \, a b^{2}\right)} \cosh\left(f x + e\right)^{3} + 4 \, {\left(63 \, {\left(2 \, a^{2} b - 5 \, a b^{2}\right)} \cosh\left(f x + e\right)^{6} + 35 \, {\left(8 \, a^{3} - 26 \, a^{2} b + 15 \, a b^{2}\right)} \cosh\left(f x + e\right)^{4} + 8 \, a^{3} - 26 \, a^{2} b + 15 \, a b^{2} - 5 \, {\left(56 \, a^{3} - 98 \, a^{2} b + 45 \, a b^{2}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{3} + 4 \, {\left(27 \, {\left(2 \, a^{2} b - 5 \, a b^{2}\right)} \cosh\left(f x + e\right)^{7} + 21 \, {\left(8 \, a^{3} - 26 \, a^{2} b + 15 \, a b^{2}\right)} \cosh\left(f x + e\right)^{5} - 5 \, {\left(56 \, a^{3} - 98 \, a^{2} b + 45 \, a b^{2}\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(8 \, a^{3} - 26 \, a^{2} b + 15 \, a b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{2} + 3 \, {\left(2 \, a^{2} b - 5 \, a b^{2}\right)} \cosh\left(f x + e\right) + {\left(27 \, {\left(2 \, a^{2} b - 5 \, a b^{2}\right)} \cosh\left(f x + e\right)^{8} + 28 \, {\left(8 \, a^{3} - 26 \, a^{2} b + 15 \, a b^{2}\right)} \cosh\left(f x + e\right)^{6} - 10 \, {\left(56 \, a^{3} - 98 \, a^{2} b + 45 \, a b^{2}\right)} \cosh\left(f x + e\right)^{4} + 6 \, a^{2} b - 15 \, a b^{2} + 12 \, {\left(8 \, a^{3} - 26 \, a^{2} b + 15 \, a b^{2}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{12 \, {\left(a^{4} b^{2} f \cosh\left(f x + e\right)^{12} + 12 \, a^{4} b^{2} f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{11} + a^{4} b^{2} f \sinh\left(f x + e\right)^{12} + 2 \, {\left(4 \, a^{5} b - 3 \, a^{4} b^{2}\right)} f \cosh\left(f x + e\right)^{10} + 2 \, {\left(33 \, a^{4} b^{2} f \cosh\left(f x + e\right)^{2} + {\left(4 \, a^{5} b - 3 \, a^{4} b^{2}\right)} f\right)} \sinh\left(f x + e\right)^{10} + {\left(16 \, a^{6} - 32 \, a^{5} b + 15 \, a^{4} b^{2}\right)} f \cosh\left(f x + e\right)^{8} + 20 \, {\left(11 \, a^{4} b^{2} f \cosh\left(f x + e\right)^{3} + {\left(4 \, a^{5} b - 3 \, a^{4} b^{2}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{9} + {\left(495 \, a^{4} b^{2} f \cosh\left(f x + e\right)^{4} + 90 \, {\left(4 \, a^{5} b - 3 \, a^{4} b^{2}\right)} f \cosh\left(f x + e\right)^{2} + {\left(16 \, a^{6} - 32 \, a^{5} b + 15 \, a^{4} b^{2}\right)} f\right)} \sinh\left(f x + e\right)^{8} - 4 \, {\left(8 \, a^{6} - 12 \, a^{5} b + 5 \, a^{4} b^{2}\right)} f \cosh\left(f x + e\right)^{6} + 8 \, {\left(99 \, a^{4} b^{2} f \cosh\left(f x + e\right)^{5} + 30 \, {\left(4 \, a^{5} b - 3 \, a^{4} b^{2}\right)} f \cosh\left(f x + e\right)^{3} + {\left(16 \, a^{6} - 32 \, a^{5} b + 15 \, a^{4} b^{2}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{7} + a^{4} b^{2} f + 4 \, {\left(231 \, a^{4} b^{2} f \cosh\left(f x + e\right)^{6} + 105 \, {\left(4 \, a^{5} b - 3 \, a^{4} b^{2}\right)} f \cosh\left(f x + e\right)^{4} + 7 \, {\left(16 \, a^{6} - 32 \, a^{5} b + 15 \, a^{4} b^{2}\right)} f \cosh\left(f x + e\right)^{2} - {\left(8 \, a^{6} - 12 \, a^{5} b + 5 \, a^{4} b^{2}\right)} f\right)} \sinh\left(f x + e\right)^{6} + {\left(16 \, a^{6} - 32 \, a^{5} b + 15 \, a^{4} b^{2}\right)} f \cosh\left(f x + e\right)^{4} + 8 \, {\left(99 \, a^{4} b^{2} f \cosh\left(f x + e\right)^{7} + 63 \, {\left(4 \, a^{5} b - 3 \, a^{4} b^{2}\right)} f \cosh\left(f x + e\right)^{5} + 7 \, {\left(16 \, a^{6} - 32 \, a^{5} b + 15 \, a^{4} b^{2}\right)} f \cosh\left(f x + e\right)^{3} - 3 \, {\left(8 \, a^{6} - 12 \, a^{5} b + 5 \, a^{4} b^{2}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + {\left(495 \, a^{4} b^{2} f \cosh\left(f x + e\right)^{8} + 420 \, {\left(4 \, a^{5} b - 3 \, a^{4} b^{2}\right)} f \cosh\left(f x + e\right)^{6} + 70 \, {\left(16 \, a^{6} - 32 \, a^{5} b + 15 \, a^{4} b^{2}\right)} f \cosh\left(f x + e\right)^{4} - 60 \, {\left(8 \, a^{6} - 12 \, a^{5} b + 5 \, a^{4} b^{2}\right)} f \cosh\left(f x + e\right)^{2} + {\left(16 \, a^{6} - 32 \, a^{5} b + 15 \, a^{4} b^{2}\right)} f\right)} \sinh\left(f x + e\right)^{4} + 2 \, {\left(4 \, a^{5} b - 3 \, a^{4} b^{2}\right)} f \cosh\left(f x + e\right)^{2} + 4 \, {\left(55 \, a^{4} b^{2} f \cosh\left(f x + e\right)^{9} + 60 \, {\left(4 \, a^{5} b - 3 \, a^{4} b^{2}\right)} f \cosh\left(f x + e\right)^{7} + 14 \, {\left(16 \, a^{6} - 32 \, a^{5} b + 15 \, a^{4} b^{2}\right)} f \cosh\left(f x + e\right)^{5} - 20 \, {\left(8 \, a^{6} - 12 \, a^{5} b + 5 \, a^{4} b^{2}\right)} f \cosh\left(f x + e\right)^{3} + {\left(16 \, a^{6} - 32 \, a^{5} b + 15 \, a^{4} b^{2}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 2 \, {\left(33 \, a^{4} b^{2} f \cosh\left(f x + e\right)^{10} + 45 \, {\left(4 \, a^{5} b - 3 \, a^{4} b^{2}\right)} f \cosh\left(f x + e\right)^{8} + 14 \, {\left(16 \, a^{6} - 32 \, a^{5} b + 15 \, a^{4} b^{2}\right)} f \cosh\left(f x + e\right)^{6} - 30 \, {\left(8 \, a^{6} - 12 \, a^{5} b + 5 \, a^{4} b^{2}\right)} f \cosh\left(f x + e\right)^{4} + 3 \, {\left(16 \, a^{6} - 32 \, a^{5} b + 15 \, a^{4} b^{2}\right)} f \cosh\left(f x + e\right)^{2} + {\left(4 \, a^{5} b - 3 \, a^{4} b^{2}\right)} f\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(3 \, a^{4} b^{2} f \cosh\left(f x + e\right)^{11} + 5 \, {\left(4 \, a^{5} b - 3 \, a^{4} b^{2}\right)} f \cosh\left(f x + e\right)^{9} + 2 \, {\left(16 \, a^{6} - 32 \, a^{5} b + 15 \, a^{4} b^{2}\right)} f \cosh\left(f x + e\right)^{7} - 6 \, {\left(8 \, a^{6} - 12 \, a^{5} b + 5 \, a^{4} b^{2}\right)} f \cosh\left(f x + e\right)^{5} + {\left(16 \, a^{6} - 32 \, a^{5} b + 15 \, a^{4} b^{2}\right)} f \cosh\left(f x + e\right)^{3} + {\left(4 \, a^{5} b - 3 \, a^{4} b^{2}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)}}, \frac{3 \, {\left({\left(2 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(f x + e\right)^{12} + 12 \, {\left(2 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{11} + {\left(2 \, a b^{2} - 5 \, b^{3}\right)} \sinh\left(f x + e\right)^{12} + 2 \, {\left(8 \, a^{2} b - 26 \, a b^{2} + 15 \, b^{3}\right)} \cosh\left(f x + e\right)^{10} + 2 \, {\left(8 \, a^{2} b - 26 \, a b^{2} + 15 \, b^{3} + 33 \, {\left(2 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{10} + 20 \, {\left(11 \, {\left(2 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} + {\left(8 \, a^{2} b - 26 \, a b^{2} + 15 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{9} + {\left(32 \, a^{3} - 144 \, a^{2} b + 190 \, a b^{2} - 75 \, b^{3}\right)} \cosh\left(f x + e\right)^{8} + {\left(495 \, {\left(2 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} + 32 \, a^{3} - 144 \, a^{2} b + 190 \, a b^{2} - 75 \, b^{3} + 90 \, {\left(8 \, a^{2} b - 26 \, a b^{2} + 15 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{8} + 8 \, {\left(99 \, {\left(2 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(f x + e\right)^{5} + 30 \, {\left(8 \, a^{2} b - 26 \, a b^{2} + 15 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} + {\left(32 \, a^{3} - 144 \, a^{2} b + 190 \, a b^{2} - 75 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{7} - 4 \, {\left(16 \, a^{3} - 64 \, a^{2} b + 70 \, a b^{2} - 25 \, b^{3}\right)} \cosh\left(f x + e\right)^{6} + 4 \, {\left(231 \, {\left(2 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(f x + e\right)^{6} + 105 \, {\left(8 \, a^{2} b - 26 \, a b^{2} + 15 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} - 16 \, a^{3} + 64 \, a^{2} b - 70 \, a b^{2} + 25 \, b^{3} + 7 \, {\left(32 \, a^{3} - 144 \, a^{2} b + 190 \, a b^{2} - 75 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{6} + 8 \, {\left(99 \, {\left(2 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(f x + e\right)^{7} + 63 \, {\left(8 \, a^{2} b - 26 \, a b^{2} + 15 \, b^{3}\right)} \cosh\left(f x + e\right)^{5} + 7 \, {\left(32 \, a^{3} - 144 \, a^{2} b + 190 \, a b^{2} - 75 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} - 3 \, {\left(16 \, a^{3} - 64 \, a^{2} b + 70 \, a b^{2} - 25 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + {\left(32 \, a^{3} - 144 \, a^{2} b + 190 \, a b^{2} - 75 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} + {\left(495 \, {\left(2 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(f x + e\right)^{8} + 420 \, {\left(8 \, a^{2} b - 26 \, a b^{2} + 15 \, b^{3}\right)} \cosh\left(f x + e\right)^{6} + 70 \, {\left(32 \, a^{3} - 144 \, a^{2} b + 190 \, a b^{2} - 75 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} + 32 \, a^{3} - 144 \, a^{2} b + 190 \, a b^{2} - 75 \, b^{3} - 60 \, {\left(16 \, a^{3} - 64 \, a^{2} b + 70 \, a b^{2} - 25 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(55 \, {\left(2 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(f x + e\right)^{9} + 60 \, {\left(8 \, a^{2} b - 26 \, a b^{2} + 15 \, b^{3}\right)} \cosh\left(f x + e\right)^{7} + 14 \, {\left(32 \, a^{3} - 144 \, a^{2} b + 190 \, a b^{2} - 75 \, b^{3}\right)} \cosh\left(f x + e\right)^{5} - 20 \, {\left(16 \, a^{3} - 64 \, a^{2} b + 70 \, a b^{2} - 25 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} + {\left(32 \, a^{3} - 144 \, a^{2} b + 190 \, a b^{2} - 75 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 2 \, a b^{2} - 5 \, b^{3} + 2 \, {\left(8 \, a^{2} b - 26 \, a b^{2} + 15 \, b^{3}\right)} \cosh\left(f x + e\right)^{2} + 2 \, {\left(33 \, {\left(2 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(f x + e\right)^{10} + 45 \, {\left(8 \, a^{2} b - 26 \, a b^{2} + 15 \, b^{3}\right)} \cosh\left(f x + e\right)^{8} + 14 \, {\left(32 \, a^{3} - 144 \, a^{2} b + 190 \, a b^{2} - 75 \, b^{3}\right)} \cosh\left(f x + e\right)^{6} - 30 \, {\left(16 \, a^{3} - 64 \, a^{2} b + 70 \, a b^{2} - 25 \, b^{3}\right)} \cosh\left(f x + e\right)^{4} + 8 \, a^{2} b - 26 \, a b^{2} + 15 \, b^{3} + 3 \, {\left(32 \, a^{3} - 144 \, a^{2} b + 190 \, a b^{2} - 75 \, b^{3}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(3 \, {\left(2 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(f x + e\right)^{11} + 5 \, {\left(8 \, a^{2} b - 26 \, a b^{2} + 15 \, b^{3}\right)} \cosh\left(f x + e\right)^{9} + 2 \, {\left(32 \, a^{3} - 144 \, a^{2} b + 190 \, a b^{2} - 75 \, b^{3}\right)} \cosh\left(f x + e\right)^{7} - 6 \, {\left(16 \, a^{3} - 64 \, a^{2} b + 70 \, a b^{2} - 25 \, b^{3}\right)} \cosh\left(f x + e\right)^{5} + {\left(32 \, a^{3} - 144 \, a^{2} b + 190 \, a b^{2} - 75 \, b^{3}\right)} \cosh\left(f x + e\right)^{3} + {\left(8 \, a^{2} b - 26 \, a b^{2} + 15 \, b^{3}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{2} \sqrt{-a} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{2 \, {\left(a \cosh\left(f x + e\right) + a \sinh\left(f x + e\right)\right)}}\right) + 2 \, \sqrt{2} {\left(3 \, {\left(2 \, a^{2} b - 5 \, a b^{2}\right)} \cosh\left(f x + e\right)^{9} + 27 \, {\left(2 \, a^{2} b - 5 \, a b^{2}\right)} \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{8} + 3 \, {\left(2 \, a^{2} b - 5 \, a b^{2}\right)} \sinh\left(f x + e\right)^{9} + 4 \, {\left(8 \, a^{3} - 26 \, a^{2} b + 15 \, a b^{2}\right)} \cosh\left(f x + e\right)^{7} + 4 \, {\left(8 \, a^{3} - 26 \, a^{2} b + 15 \, a b^{2} + 27 \, {\left(2 \, a^{2} b - 5 \, a b^{2}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{7} + 28 \, {\left(9 \, {\left(2 \, a^{2} b - 5 \, a b^{2}\right)} \cosh\left(f x + e\right)^{3} + {\left(8 \, a^{3} - 26 \, a^{2} b + 15 \, a b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{6} - 2 \, {\left(56 \, a^{3} - 98 \, a^{2} b + 45 \, a b^{2}\right)} \cosh\left(f x + e\right)^{5} + 2 \, {\left(189 \, {\left(2 \, a^{2} b - 5 \, a b^{2}\right)} \cosh\left(f x + e\right)^{4} - 56 \, a^{3} + 98 \, a^{2} b - 45 \, a b^{2} + 42 \, {\left(8 \, a^{3} - 26 \, a^{2} b + 15 \, a b^{2}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{5} + 2 \, {\left(189 \, {\left(2 \, a^{2} b - 5 \, a b^{2}\right)} \cosh\left(f x + e\right)^{5} + 70 \, {\left(8 \, a^{3} - 26 \, a^{2} b + 15 \, a b^{2}\right)} \cosh\left(f x + e\right)^{3} - 5 \, {\left(56 \, a^{3} - 98 \, a^{2} b + 45 \, a b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{4} + 4 \, {\left(8 \, a^{3} - 26 \, a^{2} b + 15 \, a b^{2}\right)} \cosh\left(f x + e\right)^{3} + 4 \, {\left(63 \, {\left(2 \, a^{2} b - 5 \, a b^{2}\right)} \cosh\left(f x + e\right)^{6} + 35 \, {\left(8 \, a^{3} - 26 \, a^{2} b + 15 \, a b^{2}\right)} \cosh\left(f x + e\right)^{4} + 8 \, a^{3} - 26 \, a^{2} b + 15 \, a b^{2} - 5 \, {\left(56 \, a^{3} - 98 \, a^{2} b + 45 \, a b^{2}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)^{3} + 4 \, {\left(27 \, {\left(2 \, a^{2} b - 5 \, a b^{2}\right)} \cosh\left(f x + e\right)^{7} + 21 \, {\left(8 \, a^{3} - 26 \, a^{2} b + 15 \, a b^{2}\right)} \cosh\left(f x + e\right)^{5} - 5 \, {\left(56 \, a^{3} - 98 \, a^{2} b + 45 \, a b^{2}\right)} \cosh\left(f x + e\right)^{3} + 3 \, {\left(8 \, a^{3} - 26 \, a^{2} b + 15 \, a b^{2}\right)} \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{2} + 3 \, {\left(2 \, a^{2} b - 5 \, a b^{2}\right)} \cosh\left(f x + e\right) + {\left(27 \, {\left(2 \, a^{2} b - 5 \, a b^{2}\right)} \cosh\left(f x + e\right)^{8} + 28 \, {\left(8 \, a^{3} - 26 \, a^{2} b + 15 \, a b^{2}\right)} \cosh\left(f x + e\right)^{6} - 10 \, {\left(56 \, a^{3} - 98 \, a^{2} b + 45 \, a b^{2}\right)} \cosh\left(f x + e\right)^{4} + 6 \, a^{2} b - 15 \, a b^{2} + 12 \, {\left(8 \, a^{3} - 26 \, a^{2} b + 15 \, a b^{2}\right)} \cosh\left(f x + e\right)^{2}\right)} \sinh\left(f x + e\right)\right)} \sqrt{\frac{b \cosh\left(f x + e\right)^{2} + b \sinh\left(f x + e\right)^{2} + 2 \, a - b}{\cosh\left(f x + e\right)^{2} - 2 \, \cosh\left(f x + e\right) \sinh\left(f x + e\right) + \sinh\left(f x + e\right)^{2}}}}{6 \, {\left(a^{4} b^{2} f \cosh\left(f x + e\right)^{12} + 12 \, a^{4} b^{2} f \cosh\left(f x + e\right) \sinh\left(f x + e\right)^{11} + a^{4} b^{2} f \sinh\left(f x + e\right)^{12} + 2 \, {\left(4 \, a^{5} b - 3 \, a^{4} b^{2}\right)} f \cosh\left(f x + e\right)^{10} + 2 \, {\left(33 \, a^{4} b^{2} f \cosh\left(f x + e\right)^{2} + {\left(4 \, a^{5} b - 3 \, a^{4} b^{2}\right)} f\right)} \sinh\left(f x + e\right)^{10} + {\left(16 \, a^{6} - 32 \, a^{5} b + 15 \, a^{4} b^{2}\right)} f \cosh\left(f x + e\right)^{8} + 20 \, {\left(11 \, a^{4} b^{2} f \cosh\left(f x + e\right)^{3} + {\left(4 \, a^{5} b - 3 \, a^{4} b^{2}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{9} + {\left(495 \, a^{4} b^{2} f \cosh\left(f x + e\right)^{4} + 90 \, {\left(4 \, a^{5} b - 3 \, a^{4} b^{2}\right)} f \cosh\left(f x + e\right)^{2} + {\left(16 \, a^{6} - 32 \, a^{5} b + 15 \, a^{4} b^{2}\right)} f\right)} \sinh\left(f x + e\right)^{8} - 4 \, {\left(8 \, a^{6} - 12 \, a^{5} b + 5 \, a^{4} b^{2}\right)} f \cosh\left(f x + e\right)^{6} + 8 \, {\left(99 \, a^{4} b^{2} f \cosh\left(f x + e\right)^{5} + 30 \, {\left(4 \, a^{5} b - 3 \, a^{4} b^{2}\right)} f \cosh\left(f x + e\right)^{3} + {\left(16 \, a^{6} - 32 \, a^{5} b + 15 \, a^{4} b^{2}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{7} + a^{4} b^{2} f + 4 \, {\left(231 \, a^{4} b^{2} f \cosh\left(f x + e\right)^{6} + 105 \, {\left(4 \, a^{5} b - 3 \, a^{4} b^{2}\right)} f \cosh\left(f x + e\right)^{4} + 7 \, {\left(16 \, a^{6} - 32 \, a^{5} b + 15 \, a^{4} b^{2}\right)} f \cosh\left(f x + e\right)^{2} - {\left(8 \, a^{6} - 12 \, a^{5} b + 5 \, a^{4} b^{2}\right)} f\right)} \sinh\left(f x + e\right)^{6} + {\left(16 \, a^{6} - 32 \, a^{5} b + 15 \, a^{4} b^{2}\right)} f \cosh\left(f x + e\right)^{4} + 8 \, {\left(99 \, a^{4} b^{2} f \cosh\left(f x + e\right)^{7} + 63 \, {\left(4 \, a^{5} b - 3 \, a^{4} b^{2}\right)} f \cosh\left(f x + e\right)^{5} + 7 \, {\left(16 \, a^{6} - 32 \, a^{5} b + 15 \, a^{4} b^{2}\right)} f \cosh\left(f x + e\right)^{3} - 3 \, {\left(8 \, a^{6} - 12 \, a^{5} b + 5 \, a^{4} b^{2}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{5} + {\left(495 \, a^{4} b^{2} f \cosh\left(f x + e\right)^{8} + 420 \, {\left(4 \, a^{5} b - 3 \, a^{4} b^{2}\right)} f \cosh\left(f x + e\right)^{6} + 70 \, {\left(16 \, a^{6} - 32 \, a^{5} b + 15 \, a^{4} b^{2}\right)} f \cosh\left(f x + e\right)^{4} - 60 \, {\left(8 \, a^{6} - 12 \, a^{5} b + 5 \, a^{4} b^{2}\right)} f \cosh\left(f x + e\right)^{2} + {\left(16 \, a^{6} - 32 \, a^{5} b + 15 \, a^{4} b^{2}\right)} f\right)} \sinh\left(f x + e\right)^{4} + 2 \, {\left(4 \, a^{5} b - 3 \, a^{4} b^{2}\right)} f \cosh\left(f x + e\right)^{2} + 4 \, {\left(55 \, a^{4} b^{2} f \cosh\left(f x + e\right)^{9} + 60 \, {\left(4 \, a^{5} b - 3 \, a^{4} b^{2}\right)} f \cosh\left(f x + e\right)^{7} + 14 \, {\left(16 \, a^{6} - 32 \, a^{5} b + 15 \, a^{4} b^{2}\right)} f \cosh\left(f x + e\right)^{5} - 20 \, {\left(8 \, a^{6} - 12 \, a^{5} b + 5 \, a^{4} b^{2}\right)} f \cosh\left(f x + e\right)^{3} + {\left(16 \, a^{6} - 32 \, a^{5} b + 15 \, a^{4} b^{2}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)^{3} + 2 \, {\left(33 \, a^{4} b^{2} f \cosh\left(f x + e\right)^{10} + 45 \, {\left(4 \, a^{5} b - 3 \, a^{4} b^{2}\right)} f \cosh\left(f x + e\right)^{8} + 14 \, {\left(16 \, a^{6} - 32 \, a^{5} b + 15 \, a^{4} b^{2}\right)} f \cosh\left(f x + e\right)^{6} - 30 \, {\left(8 \, a^{6} - 12 \, a^{5} b + 5 \, a^{4} b^{2}\right)} f \cosh\left(f x + e\right)^{4} + 3 \, {\left(16 \, a^{6} - 32 \, a^{5} b + 15 \, a^{4} b^{2}\right)} f \cosh\left(f x + e\right)^{2} + {\left(4 \, a^{5} b - 3 \, a^{4} b^{2}\right)} f\right)} \sinh\left(f x + e\right)^{2} + 4 \, {\left(3 \, a^{4} b^{2} f \cosh\left(f x + e\right)^{11} + 5 \, {\left(4 \, a^{5} b - 3 \, a^{4} b^{2}\right)} f \cosh\left(f x + e\right)^{9} + 2 \, {\left(16 \, a^{6} - 32 \, a^{5} b + 15 \, a^{4} b^{2}\right)} f \cosh\left(f x + e\right)^{7} - 6 \, {\left(8 \, a^{6} - 12 \, a^{5} b + 5 \, a^{4} b^{2}\right)} f \cosh\left(f x + e\right)^{5} + {\left(16 \, a^{6} - 32 \, a^{5} b + 15 \, a^{4} b^{2}\right)} f \cosh\left(f x + e\right)^{3} + {\left(4 \, a^{5} b - 3 \, a^{4} b^{2}\right)} f \cosh\left(f x + e\right)\right)} \sinh\left(f x + e\right)\right)}}\right]"," ",0,"[-1/12*(3*((2*a*b^2 - 5*b^3)*cosh(f*x + e)^12 + 12*(2*a*b^2 - 5*b^3)*cosh(f*x + e)*sinh(f*x + e)^11 + (2*a*b^2 - 5*b^3)*sinh(f*x + e)^12 + 2*(8*a^2*b - 26*a*b^2 + 15*b^3)*cosh(f*x + e)^10 + 2*(8*a^2*b - 26*a*b^2 + 15*b^3 + 33*(2*a*b^2 - 5*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^10 + 20*(11*(2*a*b^2 - 5*b^3)*cosh(f*x + e)^3 + (8*a^2*b - 26*a*b^2 + 15*b^3)*cosh(f*x + e))*sinh(f*x + e)^9 + (32*a^3 - 144*a^2*b + 190*a*b^2 - 75*b^3)*cosh(f*x + e)^8 + (495*(2*a*b^2 - 5*b^3)*cosh(f*x + e)^4 + 32*a^3 - 144*a^2*b + 190*a*b^2 - 75*b^3 + 90*(8*a^2*b - 26*a*b^2 + 15*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^8 + 8*(99*(2*a*b^2 - 5*b^3)*cosh(f*x + e)^5 + 30*(8*a^2*b - 26*a*b^2 + 15*b^3)*cosh(f*x + e)^3 + (32*a^3 - 144*a^2*b + 190*a*b^2 - 75*b^3)*cosh(f*x + e))*sinh(f*x + e)^7 - 4*(16*a^3 - 64*a^2*b + 70*a*b^2 - 25*b^3)*cosh(f*x + e)^6 + 4*(231*(2*a*b^2 - 5*b^3)*cosh(f*x + e)^6 + 105*(8*a^2*b - 26*a*b^2 + 15*b^3)*cosh(f*x + e)^4 - 16*a^3 + 64*a^2*b - 70*a*b^2 + 25*b^3 + 7*(32*a^3 - 144*a^2*b + 190*a*b^2 - 75*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^6 + 8*(99*(2*a*b^2 - 5*b^3)*cosh(f*x + e)^7 + 63*(8*a^2*b - 26*a*b^2 + 15*b^3)*cosh(f*x + e)^5 + 7*(32*a^3 - 144*a^2*b + 190*a*b^2 - 75*b^3)*cosh(f*x + e)^3 - 3*(16*a^3 - 64*a^2*b + 70*a*b^2 - 25*b^3)*cosh(f*x + e))*sinh(f*x + e)^5 + (32*a^3 - 144*a^2*b + 190*a*b^2 - 75*b^3)*cosh(f*x + e)^4 + (495*(2*a*b^2 - 5*b^3)*cosh(f*x + e)^8 + 420*(8*a^2*b - 26*a*b^2 + 15*b^3)*cosh(f*x + e)^6 + 70*(32*a^3 - 144*a^2*b + 190*a*b^2 - 75*b^3)*cosh(f*x + e)^4 + 32*a^3 - 144*a^2*b + 190*a*b^2 - 75*b^3 - 60*(16*a^3 - 64*a^2*b + 70*a*b^2 - 25*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^4 + 4*(55*(2*a*b^2 - 5*b^3)*cosh(f*x + e)^9 + 60*(8*a^2*b - 26*a*b^2 + 15*b^3)*cosh(f*x + e)^7 + 14*(32*a^3 - 144*a^2*b + 190*a*b^2 - 75*b^3)*cosh(f*x + e)^5 - 20*(16*a^3 - 64*a^2*b + 70*a*b^2 - 25*b^3)*cosh(f*x + e)^3 + (32*a^3 - 144*a^2*b + 190*a*b^2 - 75*b^3)*cosh(f*x + e))*sinh(f*x + e)^3 + 2*a*b^2 - 5*b^3 + 2*(8*a^2*b - 26*a*b^2 + 15*b^3)*cosh(f*x + e)^2 + 2*(33*(2*a*b^2 - 5*b^3)*cosh(f*x + e)^10 + 45*(8*a^2*b - 26*a*b^2 + 15*b^3)*cosh(f*x + e)^8 + 14*(32*a^3 - 144*a^2*b + 190*a*b^2 - 75*b^3)*cosh(f*x + e)^6 - 30*(16*a^3 - 64*a^2*b + 70*a*b^2 - 25*b^3)*cosh(f*x + e)^4 + 8*a^2*b - 26*a*b^2 + 15*b^3 + 3*(32*a^3 - 144*a^2*b + 190*a*b^2 - 75*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^2 + 4*(3*(2*a*b^2 - 5*b^3)*cosh(f*x + e)^11 + 5*(8*a^2*b - 26*a*b^2 + 15*b^3)*cosh(f*x + e)^9 + 2*(32*a^3 - 144*a^2*b + 190*a*b^2 - 75*b^3)*cosh(f*x + e)^7 - 6*(16*a^3 - 64*a^2*b + 70*a*b^2 - 25*b^3)*cosh(f*x + e)^5 + (32*a^3 - 144*a^2*b + 190*a*b^2 - 75*b^3)*cosh(f*x + e)^3 + (8*a^2*b - 26*a*b^2 + 15*b^3)*cosh(f*x + e))*sinh(f*x + e))*sqrt(a)*log((b*cosh(f*x + e)^4 + 4*b*cosh(f*x + e)*sinh(f*x + e)^3 + b*sinh(f*x + e)^4 + 2*(4*a - b)*cosh(f*x + e)^2 + 2*(3*b*cosh(f*x + e)^2 + 4*a - b)*sinh(f*x + e)^2 + 4*sqrt(2)*sqrt(a)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))*(cosh(f*x + e) + sinh(f*x + e)) + 4*(b*cosh(f*x + e)^3 + (4*a - b)*cosh(f*x + e))*sinh(f*x + e) + b)/(cosh(f*x + e)^4 + 4*cosh(f*x + e)*sinh(f*x + e)^3 + sinh(f*x + e)^4 + 2*(3*cosh(f*x + e)^2 - 1)*sinh(f*x + e)^2 - 2*cosh(f*x + e)^2 + 4*(cosh(f*x + e)^3 - cosh(f*x + e))*sinh(f*x + e) + 1)) - 4*sqrt(2)*(3*(2*a^2*b - 5*a*b^2)*cosh(f*x + e)^9 + 27*(2*a^2*b - 5*a*b^2)*cosh(f*x + e)*sinh(f*x + e)^8 + 3*(2*a^2*b - 5*a*b^2)*sinh(f*x + e)^9 + 4*(8*a^3 - 26*a^2*b + 15*a*b^2)*cosh(f*x + e)^7 + 4*(8*a^3 - 26*a^2*b + 15*a*b^2 + 27*(2*a^2*b - 5*a*b^2)*cosh(f*x + e)^2)*sinh(f*x + e)^7 + 28*(9*(2*a^2*b - 5*a*b^2)*cosh(f*x + e)^3 + (8*a^3 - 26*a^2*b + 15*a*b^2)*cosh(f*x + e))*sinh(f*x + e)^6 - 2*(56*a^3 - 98*a^2*b + 45*a*b^2)*cosh(f*x + e)^5 + 2*(189*(2*a^2*b - 5*a*b^2)*cosh(f*x + e)^4 - 56*a^3 + 98*a^2*b - 45*a*b^2 + 42*(8*a^3 - 26*a^2*b + 15*a*b^2)*cosh(f*x + e)^2)*sinh(f*x + e)^5 + 2*(189*(2*a^2*b - 5*a*b^2)*cosh(f*x + e)^5 + 70*(8*a^3 - 26*a^2*b + 15*a*b^2)*cosh(f*x + e)^3 - 5*(56*a^3 - 98*a^2*b + 45*a*b^2)*cosh(f*x + e))*sinh(f*x + e)^4 + 4*(8*a^3 - 26*a^2*b + 15*a*b^2)*cosh(f*x + e)^3 + 4*(63*(2*a^2*b - 5*a*b^2)*cosh(f*x + e)^6 + 35*(8*a^3 - 26*a^2*b + 15*a*b^2)*cosh(f*x + e)^4 + 8*a^3 - 26*a^2*b + 15*a*b^2 - 5*(56*a^3 - 98*a^2*b + 45*a*b^2)*cosh(f*x + e)^2)*sinh(f*x + e)^3 + 4*(27*(2*a^2*b - 5*a*b^2)*cosh(f*x + e)^7 + 21*(8*a^3 - 26*a^2*b + 15*a*b^2)*cosh(f*x + e)^5 - 5*(56*a^3 - 98*a^2*b + 45*a*b^2)*cosh(f*x + e)^3 + 3*(8*a^3 - 26*a^2*b + 15*a*b^2)*cosh(f*x + e))*sinh(f*x + e)^2 + 3*(2*a^2*b - 5*a*b^2)*cosh(f*x + e) + (27*(2*a^2*b - 5*a*b^2)*cosh(f*x + e)^8 + 28*(8*a^3 - 26*a^2*b + 15*a*b^2)*cosh(f*x + e)^6 - 10*(56*a^3 - 98*a^2*b + 45*a*b^2)*cosh(f*x + e)^4 + 6*a^2*b - 15*a*b^2 + 12*(8*a^3 - 26*a^2*b + 15*a*b^2)*cosh(f*x + e)^2)*sinh(f*x + e))*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/(a^4*b^2*f*cosh(f*x + e)^12 + 12*a^4*b^2*f*cosh(f*x + e)*sinh(f*x + e)^11 + a^4*b^2*f*sinh(f*x + e)^12 + 2*(4*a^5*b - 3*a^4*b^2)*f*cosh(f*x + e)^10 + 2*(33*a^4*b^2*f*cosh(f*x + e)^2 + (4*a^5*b - 3*a^4*b^2)*f)*sinh(f*x + e)^10 + (16*a^6 - 32*a^5*b + 15*a^4*b^2)*f*cosh(f*x + e)^8 + 20*(11*a^4*b^2*f*cosh(f*x + e)^3 + (4*a^5*b - 3*a^4*b^2)*f*cosh(f*x + e))*sinh(f*x + e)^9 + (495*a^4*b^2*f*cosh(f*x + e)^4 + 90*(4*a^5*b - 3*a^4*b^2)*f*cosh(f*x + e)^2 + (16*a^6 - 32*a^5*b + 15*a^4*b^2)*f)*sinh(f*x + e)^8 - 4*(8*a^6 - 12*a^5*b + 5*a^4*b^2)*f*cosh(f*x + e)^6 + 8*(99*a^4*b^2*f*cosh(f*x + e)^5 + 30*(4*a^5*b - 3*a^4*b^2)*f*cosh(f*x + e)^3 + (16*a^6 - 32*a^5*b + 15*a^4*b^2)*f*cosh(f*x + e))*sinh(f*x + e)^7 + a^4*b^2*f + 4*(231*a^4*b^2*f*cosh(f*x + e)^6 + 105*(4*a^5*b - 3*a^4*b^2)*f*cosh(f*x + e)^4 + 7*(16*a^6 - 32*a^5*b + 15*a^4*b^2)*f*cosh(f*x + e)^2 - (8*a^6 - 12*a^5*b + 5*a^4*b^2)*f)*sinh(f*x + e)^6 + (16*a^6 - 32*a^5*b + 15*a^4*b^2)*f*cosh(f*x + e)^4 + 8*(99*a^4*b^2*f*cosh(f*x + e)^7 + 63*(4*a^5*b - 3*a^4*b^2)*f*cosh(f*x + e)^5 + 7*(16*a^6 - 32*a^5*b + 15*a^4*b^2)*f*cosh(f*x + e)^3 - 3*(8*a^6 - 12*a^5*b + 5*a^4*b^2)*f*cosh(f*x + e))*sinh(f*x + e)^5 + (495*a^4*b^2*f*cosh(f*x + e)^8 + 420*(4*a^5*b - 3*a^4*b^2)*f*cosh(f*x + e)^6 + 70*(16*a^6 - 32*a^5*b + 15*a^4*b^2)*f*cosh(f*x + e)^4 - 60*(8*a^6 - 12*a^5*b + 5*a^4*b^2)*f*cosh(f*x + e)^2 + (16*a^6 - 32*a^5*b + 15*a^4*b^2)*f)*sinh(f*x + e)^4 + 2*(4*a^5*b - 3*a^4*b^2)*f*cosh(f*x + e)^2 + 4*(55*a^4*b^2*f*cosh(f*x + e)^9 + 60*(4*a^5*b - 3*a^4*b^2)*f*cosh(f*x + e)^7 + 14*(16*a^6 - 32*a^5*b + 15*a^4*b^2)*f*cosh(f*x + e)^5 - 20*(8*a^6 - 12*a^5*b + 5*a^4*b^2)*f*cosh(f*x + e)^3 + (16*a^6 - 32*a^5*b + 15*a^4*b^2)*f*cosh(f*x + e))*sinh(f*x + e)^3 + 2*(33*a^4*b^2*f*cosh(f*x + e)^10 + 45*(4*a^5*b - 3*a^4*b^2)*f*cosh(f*x + e)^8 + 14*(16*a^6 - 32*a^5*b + 15*a^4*b^2)*f*cosh(f*x + e)^6 - 30*(8*a^6 - 12*a^5*b + 5*a^4*b^2)*f*cosh(f*x + e)^4 + 3*(16*a^6 - 32*a^5*b + 15*a^4*b^2)*f*cosh(f*x + e)^2 + (4*a^5*b - 3*a^4*b^2)*f)*sinh(f*x + e)^2 + 4*(3*a^4*b^2*f*cosh(f*x + e)^11 + 5*(4*a^5*b - 3*a^4*b^2)*f*cosh(f*x + e)^9 + 2*(16*a^6 - 32*a^5*b + 15*a^4*b^2)*f*cosh(f*x + e)^7 - 6*(8*a^6 - 12*a^5*b + 5*a^4*b^2)*f*cosh(f*x + e)^5 + (16*a^6 - 32*a^5*b + 15*a^4*b^2)*f*cosh(f*x + e)^3 + (4*a^5*b - 3*a^4*b^2)*f*cosh(f*x + e))*sinh(f*x + e)), 1/6*(3*((2*a*b^2 - 5*b^3)*cosh(f*x + e)^12 + 12*(2*a*b^2 - 5*b^3)*cosh(f*x + e)*sinh(f*x + e)^11 + (2*a*b^2 - 5*b^3)*sinh(f*x + e)^12 + 2*(8*a^2*b - 26*a*b^2 + 15*b^3)*cosh(f*x + e)^10 + 2*(8*a^2*b - 26*a*b^2 + 15*b^3 + 33*(2*a*b^2 - 5*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^10 + 20*(11*(2*a*b^2 - 5*b^3)*cosh(f*x + e)^3 + (8*a^2*b - 26*a*b^2 + 15*b^3)*cosh(f*x + e))*sinh(f*x + e)^9 + (32*a^3 - 144*a^2*b + 190*a*b^2 - 75*b^3)*cosh(f*x + e)^8 + (495*(2*a*b^2 - 5*b^3)*cosh(f*x + e)^4 + 32*a^3 - 144*a^2*b + 190*a*b^2 - 75*b^3 + 90*(8*a^2*b - 26*a*b^2 + 15*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^8 + 8*(99*(2*a*b^2 - 5*b^3)*cosh(f*x + e)^5 + 30*(8*a^2*b - 26*a*b^2 + 15*b^3)*cosh(f*x + e)^3 + (32*a^3 - 144*a^2*b + 190*a*b^2 - 75*b^3)*cosh(f*x + e))*sinh(f*x + e)^7 - 4*(16*a^3 - 64*a^2*b + 70*a*b^2 - 25*b^3)*cosh(f*x + e)^6 + 4*(231*(2*a*b^2 - 5*b^3)*cosh(f*x + e)^6 + 105*(8*a^2*b - 26*a*b^2 + 15*b^3)*cosh(f*x + e)^4 - 16*a^3 + 64*a^2*b - 70*a*b^2 + 25*b^3 + 7*(32*a^3 - 144*a^2*b + 190*a*b^2 - 75*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^6 + 8*(99*(2*a*b^2 - 5*b^3)*cosh(f*x + e)^7 + 63*(8*a^2*b - 26*a*b^2 + 15*b^3)*cosh(f*x + e)^5 + 7*(32*a^3 - 144*a^2*b + 190*a*b^2 - 75*b^3)*cosh(f*x + e)^3 - 3*(16*a^3 - 64*a^2*b + 70*a*b^2 - 25*b^3)*cosh(f*x + e))*sinh(f*x + e)^5 + (32*a^3 - 144*a^2*b + 190*a*b^2 - 75*b^3)*cosh(f*x + e)^4 + (495*(2*a*b^2 - 5*b^3)*cosh(f*x + e)^8 + 420*(8*a^2*b - 26*a*b^2 + 15*b^3)*cosh(f*x + e)^6 + 70*(32*a^3 - 144*a^2*b + 190*a*b^2 - 75*b^3)*cosh(f*x + e)^4 + 32*a^3 - 144*a^2*b + 190*a*b^2 - 75*b^3 - 60*(16*a^3 - 64*a^2*b + 70*a*b^2 - 25*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^4 + 4*(55*(2*a*b^2 - 5*b^3)*cosh(f*x + e)^9 + 60*(8*a^2*b - 26*a*b^2 + 15*b^3)*cosh(f*x + e)^7 + 14*(32*a^3 - 144*a^2*b + 190*a*b^2 - 75*b^3)*cosh(f*x + e)^5 - 20*(16*a^3 - 64*a^2*b + 70*a*b^2 - 25*b^3)*cosh(f*x + e)^3 + (32*a^3 - 144*a^2*b + 190*a*b^2 - 75*b^3)*cosh(f*x + e))*sinh(f*x + e)^3 + 2*a*b^2 - 5*b^3 + 2*(8*a^2*b - 26*a*b^2 + 15*b^3)*cosh(f*x + e)^2 + 2*(33*(2*a*b^2 - 5*b^3)*cosh(f*x + e)^10 + 45*(8*a^2*b - 26*a*b^2 + 15*b^3)*cosh(f*x + e)^8 + 14*(32*a^3 - 144*a^2*b + 190*a*b^2 - 75*b^3)*cosh(f*x + e)^6 - 30*(16*a^3 - 64*a^2*b + 70*a*b^2 - 25*b^3)*cosh(f*x + e)^4 + 8*a^2*b - 26*a*b^2 + 15*b^3 + 3*(32*a^3 - 144*a^2*b + 190*a*b^2 - 75*b^3)*cosh(f*x + e)^2)*sinh(f*x + e)^2 + 4*(3*(2*a*b^2 - 5*b^3)*cosh(f*x + e)^11 + 5*(8*a^2*b - 26*a*b^2 + 15*b^3)*cosh(f*x + e)^9 + 2*(32*a^3 - 144*a^2*b + 190*a*b^2 - 75*b^3)*cosh(f*x + e)^7 - 6*(16*a^3 - 64*a^2*b + 70*a*b^2 - 25*b^3)*cosh(f*x + e)^5 + (32*a^3 - 144*a^2*b + 190*a*b^2 - 75*b^3)*cosh(f*x + e)^3 + (8*a^2*b - 26*a*b^2 + 15*b^3)*cosh(f*x + e))*sinh(f*x + e))*sqrt(-a)*arctan(1/2*sqrt(2)*sqrt(-a)*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2))/(a*cosh(f*x + e) + a*sinh(f*x + e))) + 2*sqrt(2)*(3*(2*a^2*b - 5*a*b^2)*cosh(f*x + e)^9 + 27*(2*a^2*b - 5*a*b^2)*cosh(f*x + e)*sinh(f*x + e)^8 + 3*(2*a^2*b - 5*a*b^2)*sinh(f*x + e)^9 + 4*(8*a^3 - 26*a^2*b + 15*a*b^2)*cosh(f*x + e)^7 + 4*(8*a^3 - 26*a^2*b + 15*a*b^2 + 27*(2*a^2*b - 5*a*b^2)*cosh(f*x + e)^2)*sinh(f*x + e)^7 + 28*(9*(2*a^2*b - 5*a*b^2)*cosh(f*x + e)^3 + (8*a^3 - 26*a^2*b + 15*a*b^2)*cosh(f*x + e))*sinh(f*x + e)^6 - 2*(56*a^3 - 98*a^2*b + 45*a*b^2)*cosh(f*x + e)^5 + 2*(189*(2*a^2*b - 5*a*b^2)*cosh(f*x + e)^4 - 56*a^3 + 98*a^2*b - 45*a*b^2 + 42*(8*a^3 - 26*a^2*b + 15*a*b^2)*cosh(f*x + e)^2)*sinh(f*x + e)^5 + 2*(189*(2*a^2*b - 5*a*b^2)*cosh(f*x + e)^5 + 70*(8*a^3 - 26*a^2*b + 15*a*b^2)*cosh(f*x + e)^3 - 5*(56*a^3 - 98*a^2*b + 45*a*b^2)*cosh(f*x + e))*sinh(f*x + e)^4 + 4*(8*a^3 - 26*a^2*b + 15*a*b^2)*cosh(f*x + e)^3 + 4*(63*(2*a^2*b - 5*a*b^2)*cosh(f*x + e)^6 + 35*(8*a^3 - 26*a^2*b + 15*a*b^2)*cosh(f*x + e)^4 + 8*a^3 - 26*a^2*b + 15*a*b^2 - 5*(56*a^3 - 98*a^2*b + 45*a*b^2)*cosh(f*x + e)^2)*sinh(f*x + e)^3 + 4*(27*(2*a^2*b - 5*a*b^2)*cosh(f*x + e)^7 + 21*(8*a^3 - 26*a^2*b + 15*a*b^2)*cosh(f*x + e)^5 - 5*(56*a^3 - 98*a^2*b + 45*a*b^2)*cosh(f*x + e)^3 + 3*(8*a^3 - 26*a^2*b + 15*a*b^2)*cosh(f*x + e))*sinh(f*x + e)^2 + 3*(2*a^2*b - 5*a*b^2)*cosh(f*x + e) + (27*(2*a^2*b - 5*a*b^2)*cosh(f*x + e)^8 + 28*(8*a^3 - 26*a^2*b + 15*a*b^2)*cosh(f*x + e)^6 - 10*(56*a^3 - 98*a^2*b + 45*a*b^2)*cosh(f*x + e)^4 + 6*a^2*b - 15*a*b^2 + 12*(8*a^3 - 26*a^2*b + 15*a*b^2)*cosh(f*x + e)^2)*sinh(f*x + e))*sqrt((b*cosh(f*x + e)^2 + b*sinh(f*x + e)^2 + 2*a - b)/(cosh(f*x + e)^2 - 2*cosh(f*x + e)*sinh(f*x + e) + sinh(f*x + e)^2)))/(a^4*b^2*f*cosh(f*x + e)^12 + 12*a^4*b^2*f*cosh(f*x + e)*sinh(f*x + e)^11 + a^4*b^2*f*sinh(f*x + e)^12 + 2*(4*a^5*b - 3*a^4*b^2)*f*cosh(f*x + e)^10 + 2*(33*a^4*b^2*f*cosh(f*x + e)^2 + (4*a^5*b - 3*a^4*b^2)*f)*sinh(f*x + e)^10 + (16*a^6 - 32*a^5*b + 15*a^4*b^2)*f*cosh(f*x + e)^8 + 20*(11*a^4*b^2*f*cosh(f*x + e)^3 + (4*a^5*b - 3*a^4*b^2)*f*cosh(f*x + e))*sinh(f*x + e)^9 + (495*a^4*b^2*f*cosh(f*x + e)^4 + 90*(4*a^5*b - 3*a^4*b^2)*f*cosh(f*x + e)^2 + (16*a^6 - 32*a^5*b + 15*a^4*b^2)*f)*sinh(f*x + e)^8 - 4*(8*a^6 - 12*a^5*b + 5*a^4*b^2)*f*cosh(f*x + e)^6 + 8*(99*a^4*b^2*f*cosh(f*x + e)^5 + 30*(4*a^5*b - 3*a^4*b^2)*f*cosh(f*x + e)^3 + (16*a^6 - 32*a^5*b + 15*a^4*b^2)*f*cosh(f*x + e))*sinh(f*x + e)^7 + a^4*b^2*f + 4*(231*a^4*b^2*f*cosh(f*x + e)^6 + 105*(4*a^5*b - 3*a^4*b^2)*f*cosh(f*x + e)^4 + 7*(16*a^6 - 32*a^5*b + 15*a^4*b^2)*f*cosh(f*x + e)^2 - (8*a^6 - 12*a^5*b + 5*a^4*b^2)*f)*sinh(f*x + e)^6 + (16*a^6 - 32*a^5*b + 15*a^4*b^2)*f*cosh(f*x + e)^4 + 8*(99*a^4*b^2*f*cosh(f*x + e)^7 + 63*(4*a^5*b - 3*a^4*b^2)*f*cosh(f*x + e)^5 + 7*(16*a^6 - 32*a^5*b + 15*a^4*b^2)*f*cosh(f*x + e)^3 - 3*(8*a^6 - 12*a^5*b + 5*a^4*b^2)*f*cosh(f*x + e))*sinh(f*x + e)^5 + (495*a^4*b^2*f*cosh(f*x + e)^8 + 420*(4*a^5*b - 3*a^4*b^2)*f*cosh(f*x + e)^6 + 70*(16*a^6 - 32*a^5*b + 15*a^4*b^2)*f*cosh(f*x + e)^4 - 60*(8*a^6 - 12*a^5*b + 5*a^4*b^2)*f*cosh(f*x + e)^2 + (16*a^6 - 32*a^5*b + 15*a^4*b^2)*f)*sinh(f*x + e)^4 + 2*(4*a^5*b - 3*a^4*b^2)*f*cosh(f*x + e)^2 + 4*(55*a^4*b^2*f*cosh(f*x + e)^9 + 60*(4*a^5*b - 3*a^4*b^2)*f*cosh(f*x + e)^7 + 14*(16*a^6 - 32*a^5*b + 15*a^4*b^2)*f*cosh(f*x + e)^5 - 20*(8*a^6 - 12*a^5*b + 5*a^4*b^2)*f*cosh(f*x + e)^3 + (16*a^6 - 32*a^5*b + 15*a^4*b^2)*f*cosh(f*x + e))*sinh(f*x + e)^3 + 2*(33*a^4*b^2*f*cosh(f*x + e)^10 + 45*(4*a^5*b - 3*a^4*b^2)*f*cosh(f*x + e)^8 + 14*(16*a^6 - 32*a^5*b + 15*a^4*b^2)*f*cosh(f*x + e)^6 - 30*(8*a^6 - 12*a^5*b + 5*a^4*b^2)*f*cosh(f*x + e)^4 + 3*(16*a^6 - 32*a^5*b + 15*a^4*b^2)*f*cosh(f*x + e)^2 + (4*a^5*b - 3*a^4*b^2)*f)*sinh(f*x + e)^2 + 4*(3*a^4*b^2*f*cosh(f*x + e)^11 + 5*(4*a^5*b - 3*a^4*b^2)*f*cosh(f*x + e)^9 + 2*(16*a^6 - 32*a^5*b + 15*a^4*b^2)*f*cosh(f*x + e)^7 - 6*(8*a^6 - 12*a^5*b + 5*a^4*b^2)*f*cosh(f*x + e)^5 + (16*a^6 - 32*a^5*b + 15*a^4*b^2)*f*cosh(f*x + e)^3 + (4*a^5*b - 3*a^4*b^2)*f*cosh(f*x + e))*sinh(f*x + e))]","B",0
506,-1,0,0,0.000000," ","integrate(coth(f*x+e)^5/(a+b*sinh(f*x+e)^2)^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
507,0,0,0,0.562066," ","integrate(tanh(f*x+e)^4/(a+b*sinh(f*x+e)^2)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sinh\left(f x + e\right)^{2} + a} \tanh\left(f x + e\right)^{4}}{b^{3} \sinh\left(f x + e\right)^{6} + 3 \, a b^{2} \sinh\left(f x + e\right)^{4} + 3 \, a^{2} b \sinh\left(f x + e\right)^{2} + a^{3}}, x\right)"," ",0,"integral(sqrt(b*sinh(f*x + e)^2 + a)*tanh(f*x + e)^4/(b^3*sinh(f*x + e)^6 + 3*a*b^2*sinh(f*x + e)^4 + 3*a^2*b*sinh(f*x + e)^2 + a^3), x)","F",0
508,0,0,0,0.514416," ","integrate(tanh(f*x+e)^2/(a+b*sinh(f*x+e)^2)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sinh\left(f x + e\right)^{2} + a} \tanh\left(f x + e\right)^{2}}{b^{3} \sinh\left(f x + e\right)^{6} + 3 \, a b^{2} \sinh\left(f x + e\right)^{4} + 3 \, a^{2} b \sinh\left(f x + e\right)^{2} + a^{3}}, x\right)"," ",0,"integral(sqrt(b*sinh(f*x + e)^2 + a)*tanh(f*x + e)^2/(b^3*sinh(f*x + e)^6 + 3*a*b^2*sinh(f*x + e)^4 + 3*a^2*b*sinh(f*x + e)^2 + a^3), x)","F",0
509,0,0,0,0.539212," ","integrate(1/(a+b*sinh(f*x+e)^2)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sinh\left(f x + e\right)^{2} + a}}{b^{3} \sinh\left(f x + e\right)^{6} + 3 \, a b^{2} \sinh\left(f x + e\right)^{4} + 3 \, a^{2} b \sinh\left(f x + e\right)^{2} + a^{3}}, x\right)"," ",0,"integral(sqrt(b*sinh(f*x + e)^2 + a)/(b^3*sinh(f*x + e)^6 + 3*a*b^2*sinh(f*x + e)^4 + 3*a^2*b*sinh(f*x + e)^2 + a^3), x)","F",0
510,0,0,0,0.704420," ","integrate(coth(f*x+e)^2/(a+b*sinh(f*x+e)^2)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sinh\left(f x + e\right)^{2} + a} \coth\left(f x + e\right)^{2}}{b^{3} \sinh\left(f x + e\right)^{6} + 3 \, a b^{2} \sinh\left(f x + e\right)^{4} + 3 \, a^{2} b \sinh\left(f x + e\right)^{2} + a^{3}}, x\right)"," ",0,"integral(sqrt(b*sinh(f*x + e)^2 + a)*coth(f*x + e)^2/(b^3*sinh(f*x + e)^6 + 3*a*b^2*sinh(f*x + e)^4 + 3*a^2*b*sinh(f*x + e)^2 + a^3), x)","F",0
511,0,0,0,0.585915," ","integrate(coth(f*x+e)^4/(a+b*sinh(f*x+e)^2)^(5/2),x, algorithm=""fricas"")","{\rm integral}\left(\frac{\sqrt{b \sinh\left(f x + e\right)^{2} + a} \coth\left(f x + e\right)^{4}}{b^{3} \sinh\left(f x + e\right)^{6} + 3 \, a b^{2} \sinh\left(f x + e\right)^{4} + 3 \, a^{2} b \sinh\left(f x + e\right)^{2} + a^{3}}, x\right)"," ",0,"integral(sqrt(b*sinh(f*x + e)^2 + a)*coth(f*x + e)^4/(b^3*sinh(f*x + e)^6 + 3*a*b^2*sinh(f*x + e)^4 + 3*a^2*b*sinh(f*x + e)^2 + a^3), x)","F",0
512,0,0,0,1.183749," ","integrate((a+b*sinh(f*x+e)^2)^p*(d*tanh(f*x+e))^m,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sinh\left(f x + e\right)^{2} + a\right)}^{p} \left(d \tanh\left(f x + e\right)\right)^{m}, x\right)"," ",0,"integral((b*sinh(f*x + e)^2 + a)^p*(d*tanh(f*x + e))^m, x)","F",0
513,0,0,0,2.043822," ","integrate((a+b*sinh(d*x+c)^2)^p*tanh(d*x+c)^3,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sinh\left(d x + c\right)^{2} + a\right)}^{p} \tanh\left(d x + c\right)^{3}, x\right)"," ",0,"integral((b*sinh(d*x + c)^2 + a)^p*tanh(d*x + c)^3, x)","F",0
514,0,0,0,2.064285," ","integrate((a+b*sinh(d*x+c)^2)^p*tanh(d*x+c),x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sinh\left(d x + c\right)^{2} + a\right)}^{p} \tanh\left(d x + c\right), x\right)"," ",0,"integral((b*sinh(d*x + c)^2 + a)^p*tanh(d*x + c), x)","F",0
515,0,0,0,0.593877," ","integrate(coth(d*x+c)*(a+b*sinh(d*x+c)^2)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sinh\left(d x + c\right)^{2} + a\right)}^{p} \coth\left(d x + c\right), x\right)"," ",0,"integral((b*sinh(d*x + c)^2 + a)^p*coth(d*x + c), x)","F",0
516,0,0,0,1.517912," ","integrate(coth(d*x+c)^3*(a+b*sinh(d*x+c)^2)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sinh\left(d x + c\right)^{2} + a\right)}^{p} \coth\left(d x + c\right)^{3}, x\right)"," ",0,"integral((b*sinh(d*x + c)^2 + a)^p*coth(d*x + c)^3, x)","F",0
517,0,0,0,0.604156," ","integrate((a+b*sinh(d*x+c)^2)^p*tanh(d*x+c)^4,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sinh\left(d x + c\right)^{2} + a\right)}^{p} \tanh\left(d x + c\right)^{4}, x\right)"," ",0,"integral((b*sinh(d*x + c)^2 + a)^p*tanh(d*x + c)^4, x)","F",0
518,0,0,0,0.643961," ","integrate((a+b*sinh(d*x+c)^2)^p*tanh(d*x+c)^2,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sinh\left(d x + c\right)^{2} + a\right)}^{p} \tanh\left(d x + c\right)^{2}, x\right)"," ",0,"integral((b*sinh(d*x + c)^2 + a)^p*tanh(d*x + c)^2, x)","F",0
519,0,0,0,0.787607," ","integrate(coth(d*x+c)^2*(a+b*sinh(d*x+c)^2)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sinh\left(d x + c\right)^{2} + a\right)}^{p} \coth\left(d x + c\right)^{2}, x\right)"," ",0,"integral((b*sinh(d*x + c)^2 + a)^p*coth(d*x + c)^2, x)","F",0
520,0,0,0,1.244560," ","integrate(coth(d*x+c)^4*(a+b*sinh(d*x+c)^2)^p,x, algorithm=""fricas"")","{\rm integral}\left({\left(b \sinh\left(d x + c\right)^{2} + a\right)}^{p} \coth\left(d x + c\right)^{4}, x\right)"," ",0,"integral((b*sinh(d*x + c)^2 + a)^p*coth(d*x + c)^4, x)","F",0
521,1,1115,0,4.050375," ","integrate(coth(x)^3/(a+b*sinh(x)^3),x, algorithm=""fricas"")","-\frac{12 \, \sqrt{\frac{1}{3}} {\left(a e^{\left(4 \, x\right)} - 2 \, a e^{\left(2 \, x\right)} + a\right)} \sqrt{\frac{{\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} {\left(\frac{1}{a^{3}} + \frac{b^{2}}{a^{5}} - \frac{a^{2} + b^{2}}{a^{5}}\right)}^{\frac{1}{3}} + \frac{2}{a}\right)}^{2} a^{2} - 4 \, {\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} {\left(\frac{1}{a^{3}} + \frac{b^{2}}{a^{5}} - \frac{a^{2} + b^{2}}{a^{5}}\right)}^{\frac{1}{3}} + \frac{2}{a}\right)} a + 4}{a^{2}}} \arctan\left(-\frac{{\left(2 \, \sqrt{\frac{1}{3}} \sqrt{{\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} {\left(\frac{1}{a^{3}} + \frac{b^{2}}{a^{5}} - \frac{a^{2} + b^{2}}{a^{5}}\right)}^{\frac{1}{3}} + \frac{2}{a}\right)}^{2} a^{4} e^{\left(2 \, x\right)} + b^{2} e^{\left(4 \, x\right)} + 2 \, a b e^{\left(3 \, x\right)} - 2 \, a b e^{x} - {\left(a^{2} b e^{\left(3 \, x\right)} + 4 \, a^{3} e^{\left(2 \, x\right)} - a^{2} b e^{x}\right)} {\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} {\left(\frac{1}{a^{3}} + \frac{b^{2}}{a^{5}} - \frac{a^{2} + b^{2}}{a^{5}}\right)}^{\frac{1}{3}} + \frac{2}{a}\right)} + b^{2} + 2 \, {\left(2 \, a^{2} - b^{2}\right)} e^{\left(2 \, x\right)}} {\left({\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} {\left(\frac{1}{a^{3}} + \frac{b^{2}}{a^{5}} - \frac{a^{2} + b^{2}}{a^{5}}\right)}^{\frac{1}{3}} + \frac{2}{a}\right)} a^{3} - 2 \, a^{2}\right)} \sqrt{\frac{{\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} {\left(\frac{1}{a^{3}} + \frac{b^{2}}{a^{5}} - \frac{a^{2} + b^{2}}{a^{5}}\right)}^{\frac{1}{3}} + \frac{2}{a}\right)}^{2} a^{2} - 4 \, {\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} {\left(\frac{1}{a^{3}} + \frac{b^{2}}{a^{5}} - \frac{a^{2} + b^{2}}{a^{5}}\right)}^{\frac{1}{3}} + \frac{2}{a}\right)} a + 4}{a^{2}}} + \sqrt{\frac{1}{3}} {\left({\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} {\left(\frac{1}{a^{3}} + \frac{b^{2}}{a^{5}} - \frac{a^{2} + b^{2}}{a^{5}}\right)}^{\frac{1}{3}} + \frac{2}{a}\right)}^{2} a^{5} e^{x} + 4 \, a^{2} b e^{\left(2 \, x\right)} + 4 \, a^{3} e^{x} - 4 \, a^{2} b - 2 \, {\left(a^{3} b e^{\left(2 \, x\right)} + 2 \, a^{4} e^{x} - a^{3} b\right)} {\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} {\left(\frac{1}{a^{3}} + \frac{b^{2}}{a^{5}} - \frac{a^{2} + b^{2}}{a^{5}}\right)}^{\frac{1}{3}} + \frac{2}{a}\right)}\right)} \sqrt{\frac{{\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} {\left(\frac{1}{a^{3}} + \frac{b^{2}}{a^{5}} - \frac{a^{2} + b^{2}}{a^{5}}\right)}^{\frac{1}{3}} + \frac{2}{a}\right)}^{2} a^{2} - 4 \, {\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} {\left(\frac{1}{a^{3}} + \frac{b^{2}}{a^{5}} - \frac{a^{2} + b^{2}}{a^{5}}\right)}^{\frac{1}{3}} + \frac{2}{a}\right)} a + 4}{a^{2}}}\right)} e^{\left(-x\right)}}{8 \, b^{2}}\right) + 2 \, {\left(a e^{\left(4 \, x\right)} - 2 \, a e^{\left(2 \, x\right)} + a\right)} {\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} {\left(\frac{1}{a^{3}} + \frac{b^{2}}{a^{5}} - \frac{a^{2} + b^{2}}{a^{5}}\right)}^{\frac{1}{3}} + \frac{2}{a}\right)} \log\left({\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} {\left(\frac{1}{a^{3}} + \frac{b^{2}}{a^{5}} - \frac{a^{2} + b^{2}}{a^{5}}\right)}^{\frac{1}{3}} + \frac{2}{a}\right)} a^{2} e^{x} + b e^{\left(2 \, x\right)} - 2 \, a e^{x} - b\right) - {\left({\left(a e^{\left(4 \, x\right)} - 2 \, a e^{\left(2 \, x\right)} + a\right)} {\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} {\left(\frac{1}{a^{3}} + \frac{b^{2}}{a^{5}} - \frac{a^{2} + b^{2}}{a^{5}}\right)}^{\frac{1}{3}} + \frac{2}{a}\right)} - 6 \, e^{\left(4 \, x\right)} + 12 \, e^{\left(2 \, x\right)} - 6\right)} \log\left({\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} {\left(\frac{1}{a^{3}} + \frac{b^{2}}{a^{5}} - \frac{a^{2} + b^{2}}{a^{5}}\right)}^{\frac{1}{3}} + \frac{2}{a}\right)}^{2} a^{4} e^{\left(2 \, x\right)} + b^{2} e^{\left(4 \, x\right)} + 2 \, a b e^{\left(3 \, x\right)} - 2 \, a b e^{x} - {\left(a^{2} b e^{\left(3 \, x\right)} + 4 \, a^{3} e^{\left(2 \, x\right)} - a^{2} b e^{x}\right)} {\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} {\left(\frac{1}{a^{3}} + \frac{b^{2}}{a^{5}} - \frac{a^{2} + b^{2}}{a^{5}}\right)}^{\frac{1}{3}} + \frac{2}{a}\right)} + b^{2} + 2 \, {\left(2 \, a^{2} - b^{2}\right)} e^{\left(2 \, x\right)}\right) - 12 \, {\left(e^{\left(4 \, x\right)} - 2 \, e^{\left(2 \, x\right)} + 1\right)} \log\left(e^{\left(2 \, x\right)} - 1\right) + 24 \, e^{\left(2 \, x\right)}}{12 \, {\left(a e^{\left(4 \, x\right)} - 2 \, a e^{\left(2 \, x\right)} + a\right)}}"," ",0,"-1/12*(12*sqrt(1/3)*(a*e^(4*x) - 2*a*e^(2*x) + a)*sqrt((((1/2)^(1/3)*(I*sqrt(3) + 1)*(1/a^3 + b^2/a^5 - (a^2 + b^2)/a^5)^(1/3) + 2/a)^2*a^2 - 4*((1/2)^(1/3)*(I*sqrt(3) + 1)*(1/a^3 + b^2/a^5 - (a^2 + b^2)/a^5)^(1/3) + 2/a)*a + 4)/a^2)*arctan(-1/8*(2*sqrt(1/3)*sqrt(((1/2)^(1/3)*(I*sqrt(3) + 1)*(1/a^3 + b^2/a^5 - (a^2 + b^2)/a^5)^(1/3) + 2/a)^2*a^4*e^(2*x) + b^2*e^(4*x) + 2*a*b*e^(3*x) - 2*a*b*e^x - (a^2*b*e^(3*x) + 4*a^3*e^(2*x) - a^2*b*e^x)*((1/2)^(1/3)*(I*sqrt(3) + 1)*(1/a^3 + b^2/a^5 - (a^2 + b^2)/a^5)^(1/3) + 2/a) + b^2 + 2*(2*a^2 - b^2)*e^(2*x))*(((1/2)^(1/3)*(I*sqrt(3) + 1)*(1/a^3 + b^2/a^5 - (a^2 + b^2)/a^5)^(1/3) + 2/a)*a^3 - 2*a^2)*sqrt((((1/2)^(1/3)*(I*sqrt(3) + 1)*(1/a^3 + b^2/a^5 - (a^2 + b^2)/a^5)^(1/3) + 2/a)^2*a^2 - 4*((1/2)^(1/3)*(I*sqrt(3) + 1)*(1/a^3 + b^2/a^5 - (a^2 + b^2)/a^5)^(1/3) + 2/a)*a + 4)/a^2) + sqrt(1/3)*(((1/2)^(1/3)*(I*sqrt(3) + 1)*(1/a^3 + b^2/a^5 - (a^2 + b^2)/a^5)^(1/3) + 2/a)^2*a^5*e^x + 4*a^2*b*e^(2*x) + 4*a^3*e^x - 4*a^2*b - 2*(a^3*b*e^(2*x) + 2*a^4*e^x - a^3*b)*((1/2)^(1/3)*(I*sqrt(3) + 1)*(1/a^3 + b^2/a^5 - (a^2 + b^2)/a^5)^(1/3) + 2/a))*sqrt((((1/2)^(1/3)*(I*sqrt(3) + 1)*(1/a^3 + b^2/a^5 - (a^2 + b^2)/a^5)^(1/3) + 2/a)^2*a^2 - 4*((1/2)^(1/3)*(I*sqrt(3) + 1)*(1/a^3 + b^2/a^5 - (a^2 + b^2)/a^5)^(1/3) + 2/a)*a + 4)/a^2))*e^(-x)/b^2) + 2*(a*e^(4*x) - 2*a*e^(2*x) + a)*((1/2)^(1/3)*(I*sqrt(3) + 1)*(1/a^3 + b^2/a^5 - (a^2 + b^2)/a^5)^(1/3) + 2/a)*log(((1/2)^(1/3)*(I*sqrt(3) + 1)*(1/a^3 + b^2/a^5 - (a^2 + b^2)/a^5)^(1/3) + 2/a)*a^2*e^x + b*e^(2*x) - 2*a*e^x - b) - ((a*e^(4*x) - 2*a*e^(2*x) + a)*((1/2)^(1/3)*(I*sqrt(3) + 1)*(1/a^3 + b^2/a^5 - (a^2 + b^2)/a^5)^(1/3) + 2/a) - 6*e^(4*x) + 12*e^(2*x) - 6)*log(((1/2)^(1/3)*(I*sqrt(3) + 1)*(1/a^3 + b^2/a^5 - (a^2 + b^2)/a^5)^(1/3) + 2/a)^2*a^4*e^(2*x) + b^2*e^(4*x) + 2*a*b*e^(3*x) - 2*a*b*e^x - (a^2*b*e^(3*x) + 4*a^3*e^(2*x) - a^2*b*e^x)*((1/2)^(1/3)*(I*sqrt(3) + 1)*(1/a^3 + b^2/a^5 - (a^2 + b^2)/a^5)^(1/3) + 2/a) + b^2 + 2*(2*a^2 - b^2)*e^(2*x)) - 12*(e^(4*x) - 2*e^(2*x) + 1)*log(e^(2*x) - 1) + 24*e^(2*x))/(a*e^(4*x) - 2*a*e^(2*x) + a)","C",0
522,-2,0,0,0.000000," ","integrate(coth(x)/(a+b*sinh(x)^3)^(1/2),x, algorithm=""fricas"")","\text{Exception raised: TypeError}"," ",0,"Exception raised: TypeError >>  Error detected within library code:   failed of mode Union(SparseUnivariatePolynomial(Expression(Integer)),failed) cannot be coerced to mode SparseUnivariatePolynomial(Expression(Integer))","F(-2)",0
523,1,1663,0,6.284570," ","integrate(coth(x)*(a+b*sinh(x)^3)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{a} {\left(\cosh\left(x\right) + \sinh\left(x\right)\right)} \log\left(-\frac{b^{2} \cosh\left(x\right)^{12} + 12 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{11} + b^{2} \sinh\left(x\right)^{12} - 6 \, b^{2} \cosh\left(x\right)^{10} + 64 \, a b \cosh\left(x\right)^{9} + 6 \, {\left(11 \, b^{2} \cosh\left(x\right)^{2} - b^{2}\right)} \sinh\left(x\right)^{10} + 15 \, b^{2} \cosh\left(x\right)^{8} + 4 \, {\left(55 \, b^{2} \cosh\left(x\right)^{3} - 15 \, b^{2} \cosh\left(x\right) + 16 \, a b\right)} \sinh\left(x\right)^{9} - 192 \, a b \cosh\left(x\right)^{7} + 3 \, {\left(165 \, b^{2} \cosh\left(x\right)^{4} - 90 \, b^{2} \cosh\left(x\right)^{2} + 192 \, a b \cosh\left(x\right) + 5 \, b^{2}\right)} \sinh\left(x\right)^{8} + 24 \, {\left(33 \, b^{2} \cosh\left(x\right)^{5} - 30 \, b^{2} \cosh\left(x\right)^{3} + 96 \, a b \cosh\left(x\right)^{2} + 5 \, b^{2} \cosh\left(x\right) - 8 \, a b\right)} \sinh\left(x\right)^{7} + 192 \, a b \cosh\left(x\right)^{5} + 4 \, {\left(128 \, a^{2} - 5 \, b^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(231 \, b^{2} \cosh\left(x\right)^{6} - 315 \, b^{2} \cosh\left(x\right)^{4} + 1344 \, a b \cosh\left(x\right)^{3} + 105 \, b^{2} \cosh\left(x\right)^{2} - 336 \, a b \cosh\left(x\right) + 128 \, a^{2} - 5 \, b^{2}\right)} \sinh\left(x\right)^{6} + 15 \, b^{2} \cosh\left(x\right)^{4} + 24 \, {\left(33 \, b^{2} \cosh\left(x\right)^{7} - 63 \, b^{2} \cosh\left(x\right)^{5} + 336 \, a b \cosh\left(x\right)^{4} + 35 \, b^{2} \cosh\left(x\right)^{3} - 168 \, a b \cosh\left(x\right)^{2} + 8 \, a b + {\left(128 \, a^{2} - 5 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} - 64 \, a b \cosh\left(x\right)^{3} + 3 \, {\left(165 \, b^{2} \cosh\left(x\right)^{8} - 420 \, b^{2} \cosh\left(x\right)^{6} + 2688 \, a b \cosh\left(x\right)^{5} + 350 \, b^{2} \cosh\left(x\right)^{4} - 2240 \, a b \cosh\left(x\right)^{3} + 320 \, a b \cosh\left(x\right) + 20 \, {\left(128 \, a^{2} - 5 \, b^{2}\right)} \cosh\left(x\right)^{2} + 5 \, b^{2}\right)} \sinh\left(x\right)^{4} - 6 \, b^{2} \cosh\left(x\right)^{2} + 4 \, {\left(55 \, b^{2} \cosh\left(x\right)^{9} - 180 \, b^{2} \cosh\left(x\right)^{7} + 1344 \, a b \cosh\left(x\right)^{6} + 210 \, b^{2} \cosh\left(x\right)^{5} - 1680 \, a b \cosh\left(x\right)^{4} + 480 \, a b \cosh\left(x\right)^{2} + 20 \, {\left(128 \, a^{2} - 5 \, b^{2}\right)} \cosh\left(x\right)^{3} + 15 \, b^{2} \cosh\left(x\right) - 16 \, a b\right)} \sinh\left(x\right)^{3} + 6 \, {\left(11 \, b^{2} \cosh\left(x\right)^{10} - 45 \, b^{2} \cosh\left(x\right)^{8} + 384 \, a b \cosh\left(x\right)^{7} + 70 \, b^{2} \cosh\left(x\right)^{6} - 672 \, a b \cosh\left(x\right)^{5} + 320 \, a b \cosh\left(x\right)^{3} + 10 \, {\left(128 \, a^{2} - 5 \, b^{2}\right)} \cosh\left(x\right)^{4} + 15 \, b^{2} \cosh\left(x\right)^{2} - 32 \, a b \cosh\left(x\right) - b^{2}\right)} \sinh\left(x\right)^{2} + b^{2} - 16 \, {\left(b \cosh\left(x\right)^{8} + 8 \, b \cosh\left(x\right) \sinh\left(x\right)^{7} + b \sinh\left(x\right)^{8} - 3 \, b \cosh\left(x\right)^{6} + {\left(28 \, b \cosh\left(x\right)^{2} - 3 \, b\right)} \sinh\left(x\right)^{6} + 16 \, a \cosh\left(x\right)^{5} + 2 \, {\left(28 \, b \cosh\left(x\right)^{3} - 9 \, b \cosh\left(x\right) + 8 \, a\right)} \sinh\left(x\right)^{5} + 3 \, b \cosh\left(x\right)^{4} + {\left(70 \, b \cosh\left(x\right)^{4} - 45 \, b \cosh\left(x\right)^{2} + 80 \, a \cosh\left(x\right) + 3 \, b\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, b \cosh\left(x\right)^{5} - 15 \, b \cosh\left(x\right)^{3} + 40 \, a \cosh\left(x\right)^{2} + 3 \, b \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - b \cosh\left(x\right)^{2} + {\left(28 \, b \cosh\left(x\right)^{6} - 45 \, b \cosh\left(x\right)^{4} + 160 \, a \cosh\left(x\right)^{3} + 18 \, b \cosh\left(x\right)^{2} - b\right)} \sinh\left(x\right)^{2} + 2 \, {\left(4 \, b \cosh\left(x\right)^{7} - 9 \, b \cosh\left(x\right)^{5} + 40 \, a \cosh\left(x\right)^{4} + 6 \, b \cosh\left(x\right)^{3} - b \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \sqrt{\frac{b \sinh\left(x\right)^{3} + 3 \, {\left(b \cosh\left(x\right)^{2} - b\right)} \sinh\left(x\right) + 4 \, a}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 12 \, {\left(b^{2} \cosh\left(x\right)^{11} - 5 \, b^{2} \cosh\left(x\right)^{9} + 48 \, a b \cosh\left(x\right)^{8} + 10 \, b^{2} \cosh\left(x\right)^{7} - 112 \, a b \cosh\left(x\right)^{6} + 80 \, a b \cosh\left(x\right)^{4} + 2 \, {\left(128 \, a^{2} - 5 \, b^{2}\right)} \cosh\left(x\right)^{5} + 5 \, b^{2} \cosh\left(x\right)^{3} - 16 \, a b \cosh\left(x\right)^{2} - b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{12} + 12 \, \cosh\left(x\right) \sinh\left(x\right)^{11} + \sinh\left(x\right)^{12} + 6 \, {\left(11 \, \cosh\left(x\right)^{2} - 1\right)} \sinh\left(x\right)^{10} - 6 \, \cosh\left(x\right)^{10} + 20 \, {\left(11 \, \cosh\left(x\right)^{3} - 3 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{9} + 15 \, {\left(33 \, \cosh\left(x\right)^{4} - 18 \, \cosh\left(x\right)^{2} + 1\right)} \sinh\left(x\right)^{8} + 15 \, \cosh\left(x\right)^{8} + 24 \, {\left(33 \, \cosh\left(x\right)^{5} - 30 \, \cosh\left(x\right)^{3} + 5 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{7} + 4 \, {\left(231 \, \cosh\left(x\right)^{6} - 315 \, \cosh\left(x\right)^{4} + 105 \, \cosh\left(x\right)^{2} - 5\right)} \sinh\left(x\right)^{6} - 20 \, \cosh\left(x\right)^{6} + 24 \, {\left(33 \, \cosh\left(x\right)^{7} - 63 \, \cosh\left(x\right)^{5} + 35 \, \cosh\left(x\right)^{3} - 5 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 15 \, {\left(33 \, \cosh\left(x\right)^{8} - 84 \, \cosh\left(x\right)^{6} + 70 \, \cosh\left(x\right)^{4} - 20 \, \cosh\left(x\right)^{2} + 1\right)} \sinh\left(x\right)^{4} + 15 \, \cosh\left(x\right)^{4} + 20 \, {\left(11 \, \cosh\left(x\right)^{9} - 36 \, \cosh\left(x\right)^{7} + 42 \, \cosh\left(x\right)^{5} - 20 \, \cosh\left(x\right)^{3} + 3 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 6 \, {\left(11 \, \cosh\left(x\right)^{10} - 45 \, \cosh\left(x\right)^{8} + 70 \, \cosh\left(x\right)^{6} - 50 \, \cosh\left(x\right)^{4} + 15 \, \cosh\left(x\right)^{2} - 1\right)} \sinh\left(x\right)^{2} - 6 \, \cosh\left(x\right)^{2} + 12 \, {\left(\cosh\left(x\right)^{11} - 5 \, \cosh\left(x\right)^{9} + 10 \, \cosh\left(x\right)^{7} - 10 \, \cosh\left(x\right)^{5} + 5 \, \cosh\left(x\right)^{3} - \cosh\left(x\right)\right)} \sinh\left(x\right) + 1}\right) + 2 \, \sqrt{\frac{b \sinh\left(x\right)^{3} + 3 \, {\left(b \cosh\left(x\right)^{2} - b\right)} \sinh\left(x\right) + 4 \, a}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{6 \, {\left(\cosh\left(x\right) + \sinh\left(x\right)\right)}}, \frac{\sqrt{-a} {\left(\cosh\left(x\right) + \sinh\left(x\right)\right)} \arctan\left(\frac{8 \, {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}\right)} \sqrt{-a} \sqrt{\frac{b \sinh\left(x\right)^{3} + 3 \, {\left(b \cosh\left(x\right)^{2} - b\right)} \sinh\left(x\right) + 4 \, a}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{b \cosh\left(x\right)^{6} + 6 \, b \cosh\left(x\right) \sinh\left(x\right)^{5} + b \sinh\left(x\right)^{6} - 3 \, b \cosh\left(x\right)^{4} + 3 \, {\left(5 \, b \cosh\left(x\right)^{2} - b\right)} \sinh\left(x\right)^{4} + 16 \, a \cosh\left(x\right)^{3} + 4 \, {\left(5 \, b \cosh\left(x\right)^{3} - 3 \, b \cosh\left(x\right) + 4 \, a\right)} \sinh\left(x\right)^{3} + 3 \, b \cosh\left(x\right)^{2} + 3 \, {\left(5 \, b \cosh\left(x\right)^{4} - 6 \, b \cosh\left(x\right)^{2} + 16 \, a \cosh\left(x\right) + b\right)} \sinh\left(x\right)^{2} + 6 \, {\left(b \cosh\left(x\right)^{5} - 2 \, b \cosh\left(x\right)^{3} + 8 \, a \cosh\left(x\right)^{2} + b \cosh\left(x\right)\right)} \sinh\left(x\right) - b}\right) + \sqrt{\frac{b \sinh\left(x\right)^{3} + 3 \, {\left(b \cosh\left(x\right)^{2} - b\right)} \sinh\left(x\right) + 4 \, a}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{3 \, {\left(\cosh\left(x\right) + \sinh\left(x\right)\right)}}\right]"," ",0,"[1/6*(sqrt(a)*(cosh(x) + sinh(x))*log(-(b^2*cosh(x)^12 + 12*b^2*cosh(x)*sinh(x)^11 + b^2*sinh(x)^12 - 6*b^2*cosh(x)^10 + 64*a*b*cosh(x)^9 + 6*(11*b^2*cosh(x)^2 - b^2)*sinh(x)^10 + 15*b^2*cosh(x)^8 + 4*(55*b^2*cosh(x)^3 - 15*b^2*cosh(x) + 16*a*b)*sinh(x)^9 - 192*a*b*cosh(x)^7 + 3*(165*b^2*cosh(x)^4 - 90*b^2*cosh(x)^2 + 192*a*b*cosh(x) + 5*b^2)*sinh(x)^8 + 24*(33*b^2*cosh(x)^5 - 30*b^2*cosh(x)^3 + 96*a*b*cosh(x)^2 + 5*b^2*cosh(x) - 8*a*b)*sinh(x)^7 + 192*a*b*cosh(x)^5 + 4*(128*a^2 - 5*b^2)*cosh(x)^6 + 4*(231*b^2*cosh(x)^6 - 315*b^2*cosh(x)^4 + 1344*a*b*cosh(x)^3 + 105*b^2*cosh(x)^2 - 336*a*b*cosh(x) + 128*a^2 - 5*b^2)*sinh(x)^6 + 15*b^2*cosh(x)^4 + 24*(33*b^2*cosh(x)^7 - 63*b^2*cosh(x)^5 + 336*a*b*cosh(x)^4 + 35*b^2*cosh(x)^3 - 168*a*b*cosh(x)^2 + 8*a*b + (128*a^2 - 5*b^2)*cosh(x))*sinh(x)^5 - 64*a*b*cosh(x)^3 + 3*(165*b^2*cosh(x)^8 - 420*b^2*cosh(x)^6 + 2688*a*b*cosh(x)^5 + 350*b^2*cosh(x)^4 - 2240*a*b*cosh(x)^3 + 320*a*b*cosh(x) + 20*(128*a^2 - 5*b^2)*cosh(x)^2 + 5*b^2)*sinh(x)^4 - 6*b^2*cosh(x)^2 + 4*(55*b^2*cosh(x)^9 - 180*b^2*cosh(x)^7 + 1344*a*b*cosh(x)^6 + 210*b^2*cosh(x)^5 - 1680*a*b*cosh(x)^4 + 480*a*b*cosh(x)^2 + 20*(128*a^2 - 5*b^2)*cosh(x)^3 + 15*b^2*cosh(x) - 16*a*b)*sinh(x)^3 + 6*(11*b^2*cosh(x)^10 - 45*b^2*cosh(x)^8 + 384*a*b*cosh(x)^7 + 70*b^2*cosh(x)^6 - 672*a*b*cosh(x)^5 + 320*a*b*cosh(x)^3 + 10*(128*a^2 - 5*b^2)*cosh(x)^4 + 15*b^2*cosh(x)^2 - 32*a*b*cosh(x) - b^2)*sinh(x)^2 + b^2 - 16*(b*cosh(x)^8 + 8*b*cosh(x)*sinh(x)^7 + b*sinh(x)^8 - 3*b*cosh(x)^6 + (28*b*cosh(x)^2 - 3*b)*sinh(x)^6 + 16*a*cosh(x)^5 + 2*(28*b*cosh(x)^3 - 9*b*cosh(x) + 8*a)*sinh(x)^5 + 3*b*cosh(x)^4 + (70*b*cosh(x)^4 - 45*b*cosh(x)^2 + 80*a*cosh(x) + 3*b)*sinh(x)^4 + 4*(14*b*cosh(x)^5 - 15*b*cosh(x)^3 + 40*a*cosh(x)^2 + 3*b*cosh(x))*sinh(x)^3 - b*cosh(x)^2 + (28*b*cosh(x)^6 - 45*b*cosh(x)^4 + 160*a*cosh(x)^3 + 18*b*cosh(x)^2 - b)*sinh(x)^2 + 2*(4*b*cosh(x)^7 - 9*b*cosh(x)^5 + 40*a*cosh(x)^4 + 6*b*cosh(x)^3 - b*cosh(x))*sinh(x))*sqrt(a)*sqrt((b*sinh(x)^3 + 3*(b*cosh(x)^2 - b)*sinh(x) + 4*a)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 12*(b^2*cosh(x)^11 - 5*b^2*cosh(x)^9 + 48*a*b*cosh(x)^8 + 10*b^2*cosh(x)^7 - 112*a*b*cosh(x)^6 + 80*a*b*cosh(x)^4 + 2*(128*a^2 - 5*b^2)*cosh(x)^5 + 5*b^2*cosh(x)^3 - 16*a*b*cosh(x)^2 - b^2*cosh(x))*sinh(x))/(cosh(x)^12 + 12*cosh(x)*sinh(x)^11 + sinh(x)^12 + 6*(11*cosh(x)^2 - 1)*sinh(x)^10 - 6*cosh(x)^10 + 20*(11*cosh(x)^3 - 3*cosh(x))*sinh(x)^9 + 15*(33*cosh(x)^4 - 18*cosh(x)^2 + 1)*sinh(x)^8 + 15*cosh(x)^8 + 24*(33*cosh(x)^5 - 30*cosh(x)^3 + 5*cosh(x))*sinh(x)^7 + 4*(231*cosh(x)^6 - 315*cosh(x)^4 + 105*cosh(x)^2 - 5)*sinh(x)^6 - 20*cosh(x)^6 + 24*(33*cosh(x)^7 - 63*cosh(x)^5 + 35*cosh(x)^3 - 5*cosh(x))*sinh(x)^5 + 15*(33*cosh(x)^8 - 84*cosh(x)^6 + 70*cosh(x)^4 - 20*cosh(x)^2 + 1)*sinh(x)^4 + 15*cosh(x)^4 + 20*(11*cosh(x)^9 - 36*cosh(x)^7 + 42*cosh(x)^5 - 20*cosh(x)^3 + 3*cosh(x))*sinh(x)^3 + 6*(11*cosh(x)^10 - 45*cosh(x)^8 + 70*cosh(x)^6 - 50*cosh(x)^4 + 15*cosh(x)^2 - 1)*sinh(x)^2 - 6*cosh(x)^2 + 12*(cosh(x)^11 - 5*cosh(x)^9 + 10*cosh(x)^7 - 10*cosh(x)^5 + 5*cosh(x)^3 - cosh(x))*sinh(x) + 1)) + 2*sqrt((b*sinh(x)^3 + 3*(b*cosh(x)^2 - b)*sinh(x) + 4*a)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(cosh(x) + sinh(x)), 1/3*(sqrt(-a)*(cosh(x) + sinh(x))*arctan(8*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)*sqrt(-a)*sqrt((b*sinh(x)^3 + 3*(b*cosh(x)^2 - b)*sinh(x) + 4*a)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/(b*cosh(x)^6 + 6*b*cosh(x)*sinh(x)^5 + b*sinh(x)^6 - 3*b*cosh(x)^4 + 3*(5*b*cosh(x)^2 - b)*sinh(x)^4 + 16*a*cosh(x)^3 + 4*(5*b*cosh(x)^3 - 3*b*cosh(x) + 4*a)*sinh(x)^3 + 3*b*cosh(x)^2 + 3*(5*b*cosh(x)^4 - 6*b*cosh(x)^2 + 16*a*cosh(x) + b)*sinh(x)^2 + 6*(b*cosh(x)^5 - 2*b*cosh(x)^3 + 8*a*cosh(x)^2 + b*cosh(x))*sinh(x) - b)) + sqrt((b*sinh(x)^3 + 3*(b*cosh(x)^2 - b)*sinh(x) + 4*a)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(cosh(x) + sinh(x))]","B",0
524,1,113,0,2.246731," ","integrate(coth(x)/(a+b*sinh(x)^n)^(1/2),x, algorithm=""fricas"")","\left[\frac{\log\left(\frac{b \cosh\left(n \log\left(\sinh\left(x\right)\right)\right) + b \sinh\left(n \log\left(\sinh\left(x\right)\right)\right) - 2 \, \sqrt{b \cosh\left(n \log\left(\sinh\left(x\right)\right)\right) + b \sinh\left(n \log\left(\sinh\left(x\right)\right)\right) + a} \sqrt{a} + 2 \, a}{\cosh\left(n \log\left(\sinh\left(x\right)\right)\right) + \sinh\left(n \log\left(\sinh\left(x\right)\right)\right)}\right)}{\sqrt{a} n}, \frac{2 \, \sqrt{-a} \arctan\left(\frac{\sqrt{b \cosh\left(n \log\left(\sinh\left(x\right)\right)\right) + b \sinh\left(n \log\left(\sinh\left(x\right)\right)\right) + a} \sqrt{-a}}{a}\right)}{a n}\right]"," ",0,"[log((b*cosh(n*log(sinh(x))) + b*sinh(n*log(sinh(x))) - 2*sqrt(b*cosh(n*log(sinh(x))) + b*sinh(n*log(sinh(x))) + a)*sqrt(a) + 2*a)/(cosh(n*log(sinh(x))) + sinh(n*log(sinh(x)))))/(sqrt(a)*n), 2*sqrt(-a)*arctan(sqrt(b*cosh(n*log(sinh(x))) + b*sinh(n*log(sinh(x))) + a)*sqrt(-a)/a)/(a*n)]","A",0
525,1,156,0,0.480378," ","integrate(coth(x)*(a+b*sinh(x)^n)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{a} \log\left(\frac{b \cosh\left(n \log\left(\sinh\left(x\right)\right)\right) + b \sinh\left(n \log\left(\sinh\left(x\right)\right)\right) - 2 \, \sqrt{b \cosh\left(n \log\left(\sinh\left(x\right)\right)\right) + b \sinh\left(n \log\left(\sinh\left(x\right)\right)\right) + a} \sqrt{a} + 2 \, a}{\cosh\left(n \log\left(\sinh\left(x\right)\right)\right) + \sinh\left(n \log\left(\sinh\left(x\right)\right)\right)}\right) + 2 \, \sqrt{b \cosh\left(n \log\left(\sinh\left(x\right)\right)\right) + b \sinh\left(n \log\left(\sinh\left(x\right)\right)\right) + a}}{n}, \frac{2 \, {\left(\sqrt{-a} \arctan\left(\frac{\sqrt{b \cosh\left(n \log\left(\sinh\left(x\right)\right)\right) + b \sinh\left(n \log\left(\sinh\left(x\right)\right)\right) + a} \sqrt{-a}}{a}\right) + \sqrt{b \cosh\left(n \log\left(\sinh\left(x\right)\right)\right) + b \sinh\left(n \log\left(\sinh\left(x\right)\right)\right) + a}\right)}}{n}\right]"," ",0,"[(sqrt(a)*log((b*cosh(n*log(sinh(x))) + b*sinh(n*log(sinh(x))) - 2*sqrt(b*cosh(n*log(sinh(x))) + b*sinh(n*log(sinh(x))) + a)*sqrt(a) + 2*a)/(cosh(n*log(sinh(x))) + sinh(n*log(sinh(x))))) + 2*sqrt(b*cosh(n*log(sinh(x))) + b*sinh(n*log(sinh(x))) + a))/n, 2*(sqrt(-a)*arctan(sqrt(b*cosh(n*log(sinh(x))) + b*sinh(n*log(sinh(x))) + a)*sqrt(-a)/a) + sqrt(b*cosh(n*log(sinh(x))) + b*sinh(n*log(sinh(x))) + a))/n]","A",0
