1,1,120,0,0.511823," ","integrate(sinh(d*x+c)^4*(a+b*tanh(d*x+c)^2),x, algorithm=""fricas"")","\frac{{\left(a + b\right)} \sinh\left(d x + c\right)^{5} + {\left(10 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} - 7 \, a - 15 \, b\right)} \sinh\left(d x + c\right)^{3} + 8 \, {\left(3 \, {\left(a + 5 \, b\right)} d x + 8 \, b\right)} \cosh\left(d x + c\right) + {\left(5 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{4} - 3 \, {\left(7 \, a + 15 \, b\right)} \cosh\left(d x + c\right)^{2} - 8 \, a - 80 \, b\right)} \sinh\left(d x + c\right)}{64 \, d \cosh\left(d x + c\right)}"," ",0,"1/64*((a + b)*sinh(d*x + c)^5 + (10*(a + b)*cosh(d*x + c)^2 - 7*a - 15*b)*sinh(d*x + c)^3 + 8*(3*(a + 5*b)*d*x + 8*b)*cosh(d*x + c) + (5*(a + b)*cosh(d*x + c)^4 - 3*(7*a + 15*b)*cosh(d*x + c)^2 - 8*a - 80*b)*sinh(d*x + c))/(d*cosh(d*x + c))","A",0
2,1,91,0,0.784945," ","integrate(sinh(d*x+c)^3*(a+b*tanh(d*x+c)^2),x, algorithm=""fricas"")","\frac{{\left(a + b\right)} \cosh\left(d x + c\right)^{4} + {\left(a + b\right)} \sinh\left(d x + c\right)^{4} - 4 \, {\left(2 \, a + 5 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} - 4 \, a - 10 \, b\right)} \sinh\left(d x + c\right)^{2} - 9 \, a - 45 \, b}{24 \, d \cosh\left(d x + c\right)}"," ",0,"1/24*((a + b)*cosh(d*x + c)^4 + (a + b)*sinh(d*x + c)^4 - 4*(2*a + 5*b)*cosh(d*x + c)^2 + 2*(3*(a + b)*cosh(d*x + c)^2 - 4*a - 10*b)*sinh(d*x + c)^2 - 9*a - 45*b)/(d*cosh(d*x + c))","B",0
3,1,71,0,0.651047," ","integrate(sinh(d*x+c)^2*(a+b*tanh(d*x+c)^2),x, algorithm=""fricas"")","\frac{{\left(a + b\right)} \sinh\left(d x + c\right)^{3} - 4 \, {\left({\left(a + 3 \, b\right)} d x + 2 \, b\right)} \cosh\left(d x + c\right) + {\left(3 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} + a + 9 \, b\right)} \sinh\left(d x + c\right)}{8 \, d \cosh\left(d x + c\right)}"," ",0,"1/8*((a + b)*sinh(d*x + c)^3 - 4*((a + 3*b)*d*x + 2*b)*cosh(d*x + c) + (3*(a + b)*cosh(d*x + c)^2 + a + 9*b)*sinh(d*x + c))/(d*cosh(d*x + c))","A",0
4,1,42,0,0.563140," ","integrate(sinh(d*x+c)*(a+b*tanh(d*x+c)^2),x, algorithm=""fricas"")","\frac{{\left(a + b\right)} \cosh\left(d x + c\right)^{2} + {\left(a + b\right)} \sinh\left(d x + c\right)^{2} + a + 3 \, b}{2 \, d \cosh\left(d x + c\right)}"," ",0,"1/2*((a + b)*cosh(d*x + c)^2 + (a + b)*sinh(d*x + c)^2 + a + 3*b)/(d*cosh(d*x + c))","A",0
5,1,167,0,0.744738," ","integrate(csch(d*x+c)*(a+b*tanh(d*x+c)^2),x, algorithm=""fricas"")","-\frac{2 \, b \cosh\left(d x + c\right) + {\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} + 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)^{2} + 2 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a \sinh\left(d x + c\right)^{2} + a\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) + 2 \, b \sinh\left(d x + c\right)}{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} + d}"," ",0,"-(2*b*cosh(d*x + c) + (a*cosh(d*x + c)^2 + 2*a*cosh(d*x + c)*sinh(d*x + c) + a*sinh(d*x + c)^2 + a)*log(cosh(d*x + c) + sinh(d*x + c) + 1) - (a*cosh(d*x + c)^2 + 2*a*cosh(d*x + c)*sinh(d*x + c) + a*sinh(d*x + c)^2 + a)*log(cosh(d*x + c) + sinh(d*x + c) - 1) + 2*b*sinh(d*x + c))/(d*cosh(d*x + c)^2 + 2*d*cosh(d*x + c)*sinh(d*x + c) + d*sinh(d*x + c)^2 + d)","B",0
6,1,88,0,0.471185," ","integrate(csch(d*x+c)^2*(a+b*tanh(d*x+c)^2),x, algorithm=""fricas"")","-\frac{4 \, {\left(a \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)}}{d \cosh\left(d x + c\right)^{3} + 3 \, d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + d \sinh\left(d x + c\right)^{3} - d \cosh\left(d x + c\right) + {\left(3 \, d \cosh\left(d x + c\right)^{2} + d\right)} \sinh\left(d x + c\right)}"," ",0,"-4*(a*cosh(d*x + c) + b*sinh(d*x + c))/(d*cosh(d*x + c)^3 + 3*d*cosh(d*x + c)*sinh(d*x + c)^2 + d*sinh(d*x + c)^3 - d*cosh(d*x + c) + (3*d*cosh(d*x + c)^2 + d)*sinh(d*x + c))","B",0
7,1,924,0,0.659686," ","integrate(csch(d*x+c)^3*(a+b*tanh(d*x+c)^2),x, algorithm=""fricas"")","-\frac{2 \, {\left(a - 2 \, b\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(a - 2 \, b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} + 2 \, {\left(a - 2 \, b\right)} \sinh\left(d x + c\right)^{5} + 4 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(5 \, {\left(a - 2 \, b\right)} \cosh\left(d x + c\right)^{2} + a + 2 \, b\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(5 \, {\left(a - 2 \, b\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(a - 2 \, b\right)} \cosh\left(d x + c\right) - {\left({\left(a - 2 \, b\right)} \cosh\left(d x + c\right)^{6} + 6 \, {\left(a - 2 \, b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(a - 2 \, b\right)} \sinh\left(d x + c\right)^{6} - {\left(a - 2 \, b\right)} \cosh\left(d x + c\right)^{4} + {\left(15 \, {\left(a - 2 \, b\right)} \cosh\left(d x + c\right)^{2} - a + 2 \, b\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, {\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)^{3} - {\left(a - 2 \, b\right)} \cosh\left(d x + c\right)^{2} + {\left(15 \, {\left(a - 2 \, b\right)} \cosh\left(d x + c\right)^{4} - 6 \, {\left(a - 2 \, b\right)} \cosh\left(d x + c\right)^{2} - a + 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a - 2 \, b\right)} \cosh\left(d x + c\right)^{5} - 2 \, {\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)^{6} + 6 \, {\left(a - 2 \, b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(a - 2 \, b\right)} \sinh\left(d x + c\right)^{6} - {\left(a - 2 \, b\right)} \cosh\left(d x + c\right)^{4} + {\left(15 \, {\left(a - 2 \, b\right)} \cosh\left(d x + c\right)^{2} - a + 2 \, b\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, {\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)^{3} - {\left(a - 2 \, b\right)} \cosh\left(d x + c\right)^{2} + {\left(15 \, {\left(a - 2 \, b\right)} \cosh\left(d x + c\right)^{4} - 6 \, {\left(a - 2 \, b\right)} \cosh\left(d x + c\right)^{2} - a + 2 \, b\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a - 2 \, b\right)} \cosh\left(d x + c\right)^{5} - 2 \, {\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(5 \, {\left(a - 2 \, b\right)} \cosh\left(d x + c\right)^{4} + 6 \, {\left(a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + a - 2 \, b\right)} \sinh\left(d x + c\right)}{2 \, {\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} - d \cosh\left(d x + c\right)^{4} + {\left(15 \, 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} - d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - d \cosh\left(d x + c\right)^{2} + {\left(15 \, 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} + 2 \, {\left(3 \, 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,"-1/2*(2*(a - 2*b)*cosh(d*x + c)^5 + 10*(a - 2*b)*cosh(d*x + c)*sinh(d*x + c)^4 + 2*(a - 2*b)*sinh(d*x + c)^5 + 4*(a + 2*b)*cosh(d*x + c)^3 + 4*(5*(a - 2*b)*cosh(d*x + c)^2 + a + 2*b)*sinh(d*x + c)^3 + 4*(5*(a - 2*b)*cosh(d*x + c)^3 + 3*(a + 2*b)*cosh(d*x + c))*sinh(d*x + c)^2 + 2*(a - 2*b)*cosh(d*x + c) - ((a - 2*b)*cosh(d*x + c)^6 + 6*(a - 2*b)*cosh(d*x + c)*sinh(d*x + c)^5 + (a - 2*b)*sinh(d*x + c)^6 - (a - 2*b)*cosh(d*x + c)^4 + (15*(a - 2*b)*cosh(d*x + c)^2 - a + 2*b)*sinh(d*x + c)^4 + 4*(5*(a - 2*b)*cosh(d*x + c)^3 - (a - 2*b)*cosh(d*x + c))*sinh(d*x + c)^3 - (a - 2*b)*cosh(d*x + c)^2 + (15*(a - 2*b)*cosh(d*x + c)^4 - 6*(a - 2*b)*cosh(d*x + c)^2 - a + 2*b)*sinh(d*x + c)^2 + 2*(3*(a - 2*b)*cosh(d*x + c)^5 - 2*(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)^6 + 6*(a - 2*b)*cosh(d*x + c)*sinh(d*x + c)^5 + (a - 2*b)*sinh(d*x + c)^6 - (a - 2*b)*cosh(d*x + c)^4 + (15*(a - 2*b)*cosh(d*x + c)^2 - a + 2*b)*sinh(d*x + c)^4 + 4*(5*(a - 2*b)*cosh(d*x + c)^3 - (a - 2*b)*cosh(d*x + c))*sinh(d*x + c)^3 - (a - 2*b)*cosh(d*x + c)^2 + (15*(a - 2*b)*cosh(d*x + c)^4 - 6*(a - 2*b)*cosh(d*x + c)^2 - a + 2*b)*sinh(d*x + c)^2 + 2*(3*(a - 2*b)*cosh(d*x + c)^5 - 2*(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*(5*(a - 2*b)*cosh(d*x + c)^4 + 6*(a + 2*b)*cosh(d*x + c)^2 + a - 2*b)*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 - d*cosh(d*x + c)^4 + (15*d*cosh(d*x + c)^2 - d)*sinh(d*x + c)^4 + 4*(5*d*cosh(d*x + c)^3 - d*cosh(d*x + c))*sinh(d*x + c)^3 - d*cosh(d*x + c)^2 + (15*d*cosh(d*x + c)^4 - 6*d*cosh(d*x + c)^2 - d)*sinh(d*x + c)^2 + 2*(3*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
8,1,244,0,0.722680," ","integrate(csch(d*x+c)^4*(a+b*tanh(d*x+c)^2),x, algorithm=""fricas"")","-\frac{8 \, {\left({\left(a + 3 \, b\right)} \cosh\left(d x + c\right)^{2} + 4 \, 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} + a - 3 \, b\right)}}{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} - 2 \, d \cosh\left(d x + c\right)^{4} + {\left(15 \, 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} - 2 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - d \cosh\left(d x + c\right)^{2} + {\left(15 \, 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} + 2 \, {\left(3 \, 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) + 2 \, d\right)}}"," ",0,"-8/3*((a + 3*b)*cosh(d*x + c)^2 + 4*a*cosh(d*x + c)*sinh(d*x + c) + (a + 3*b)*sinh(d*x + c)^2 + a - 3*b)/(d*cosh(d*x + c)^6 + 6*d*cosh(d*x + c)*sinh(d*x + c)^5 + d*sinh(d*x + c)^6 - 2*d*cosh(d*x + c)^4 + (15*d*cosh(d*x + c)^2 - 2*d)*sinh(d*x + c)^4 + 4*(5*d*cosh(d*x + c)^3 - 2*d*cosh(d*x + c))*sinh(d*x + c)^3 - d*cosh(d*x + c)^2 + (15*d*cosh(d*x + c)^4 - 12*d*cosh(d*x + c)^2 - d)*sinh(d*x + c)^2 + 2*(3*d*cosh(d*x + c)^5 - 4*d*cosh(d*x + c)^3 + d*cosh(d*x + c))*sinh(d*x + c) + 2*d)","B",0
9,1,394,0,0.610487," ","integrate(sinh(d*x+c)^4*(a+b*tanh(d*x+c)^2)^2,x, algorithm=""fricas"")","\frac{3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{7} + 3 \, {\left(21 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} - 5 \, a^{2} - 26 \, a b - 21 \, b^{2}\right)} \sinh\left(d x + c\right)^{5} + 8 \, {\left(3 \, {\left(3 \, a^{2} + 30 \, a b + 35 \, b^{2}\right)} d x + 48 \, a b + 80 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 24 \, {\left(3 \, {\left(3 \, a^{2} + 30 \, a b + 35 \, b^{2}\right)} d x + 48 \, a b + 80 \, b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + {\left(105 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} - 30 \, {\left(5 \, a^{2} + 26 \, a b + 21 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 63 \, a^{2} - 654 \, a b - 847 \, b^{2}\right)} \sinh\left(d x + c\right)^{3} + 24 \, {\left(3 \, {\left(3 \, a^{2} + 30 \, a b + 35 \, b^{2}\right)} d x + 48 \, a b + 80 \, b^{2}\right)} \cosh\left(d x + c\right) + 3 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{6} - 5 \, {\left(5 \, a^{2} + 26 \, a b + 21 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} - {\left(63 \, a^{2} + 654 \, a b + 847 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 15 \, a^{2} - 190 \, a b - 175 \, b^{2}\right)} \sinh\left(d x + c\right)}{192 \, {\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,"1/192*(3*(a^2 + 2*a*b + b^2)*sinh(d*x + c)^7 + 3*(21*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 - 5*a^2 - 26*a*b - 21*b^2)*sinh(d*x + c)^5 + 8*(3*(3*a^2 + 30*a*b + 35*b^2)*d*x + 48*a*b + 80*b^2)*cosh(d*x + c)^3 + 24*(3*(3*a^2 + 30*a*b + 35*b^2)*d*x + 48*a*b + 80*b^2)*cosh(d*x + c)*sinh(d*x + c)^2 + (105*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 - 30*(5*a^2 + 26*a*b + 21*b^2)*cosh(d*x + c)^2 - 63*a^2 - 654*a*b - 847*b^2)*sinh(d*x + c)^3 + 24*(3*(3*a^2 + 30*a*b + 35*b^2)*d*x + 48*a*b + 80*b^2)*cosh(d*x + c) + 3*(7*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^6 - 5*(5*a^2 + 26*a*b + 21*b^2)*cosh(d*x + c)^4 - (63*a^2 + 654*a*b + 847*b^2)*cosh(d*x + c)^2 - 15*a^2 - 190*a*b - 175*b^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
10,1,259,0,0.523639," ","integrate(sinh(d*x+c)^3*(a+b*tanh(d*x+c)^2)^2,x, algorithm=""fricas"")","\frac{{\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{6} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{6} - 6 \, {\left(a^{2} + 6 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(5 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, a^{2} - 12 \, a b - 10 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} - 3 \, {\left(11 \, a^{2} + 86 \, a b + 91 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 3 \, {\left(5 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} - 12 \, {\left(a^{2} + 6 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 11 \, a^{2} - 86 \, a b - 91 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} - 26 \, a^{2} - 220 \, a b - 210 \, b^{2}}{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*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^6 + (a^2 + 2*a*b + b^2)*sinh(d*x + c)^6 - 6*(a^2 + 6*a*b + 5*b^2)*cosh(d*x + c)^4 + 3*(5*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 - 2*a^2 - 12*a*b - 10*b^2)*sinh(d*x + c)^4 - 3*(11*a^2 + 86*a*b + 91*b^2)*cosh(d*x + c)^2 + 3*(5*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 - 12*(a^2 + 6*a*b + 5*b^2)*cosh(d*x + c)^2 - 11*a^2 - 86*a*b - 91*b^2)*sinh(d*x + c)^2 - 26*a^2 - 220*a*b - 210*b^2)/(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
11,1,291,0,0.475628," ","integrate(sinh(d*x+c)^2*(a+b*tanh(d*x+c)^2)^2,x, algorithm=""fricas"")","\frac{3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{5} - 4 \, {\left(3 \, {\left(a^{2} + 6 \, a b + 5 \, b^{2}\right)} d x + 12 \, a b + 14 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - 12 \, {\left(3 \, {\left(a^{2} + 6 \, a b + 5 \, b^{2}\right)} d x + 12 \, a b + 14 \, b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + {\left(30 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 9 \, a^{2} + 66 \, a b + 65 \, b^{2}\right)} \sinh\left(d x + c\right)^{3} - 12 \, {\left(3 \, {\left(a^{2} + 6 \, a b + 5 \, b^{2}\right)} d x + 12 \, a b + 14 \, b^{2}\right)} \cosh\left(d x + c\right) + 3 \, {\left(5 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(9 \, a^{2} + 66 \, a b + 65 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, a^{2} + 20 \, a b + 10 \, b^{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*(a^2 + 2*a*b + b^2)*sinh(d*x + c)^5 - 4*(3*(a^2 + 6*a*b + 5*b^2)*d*x + 12*a*b + 14*b^2)*cosh(d*x + c)^3 - 12*(3*(a^2 + 6*a*b + 5*b^2)*d*x + 12*a*b + 14*b^2)*cosh(d*x + c)*sinh(d*x + c)^2 + (30*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + 9*a^2 + 66*a*b + 65*b^2)*sinh(d*x + c)^3 - 12*(3*(a^2 + 6*a*b + 5*b^2)*d*x + 12*a*b + 14*b^2)*cosh(d*x + c) + 3*(5*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 + (9*a^2 + 66*a*b + 65*b^2)*cosh(d*x + c)^2 + 2*a^2 + 20*a*b + 10*b^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
12,1,167,0,0.544940," ","integrate(sinh(d*x+c)*(a+b*tanh(d*x+c)^2)^2,x, algorithm=""fricas"")","\frac{3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{4} + 12 \, {\left(a^{2} + 4 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 6 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, a^{2} + 8 \, a b + 6 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} + 9 \, a^{2} + 42 \, a b + 25 \, b^{2}}{6 \, {\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,"1/6*(3*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 + 3*(a^2 + 2*a*b + b^2)*sinh(d*x + c)^4 + 12*(a^2 + 4*a*b + 3*b^2)*cosh(d*x + c)^2 + 6*(3*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + 2*a^2 + 8*a*b + 6*b^2)*sinh(d*x + c)^2 + 9*a^2 + 42*a*b + 25*b^2)/(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
13,1,890,0,0.896807," ","integrate(csch(d*x+c)*(a+b*tanh(d*x+c)^2)^2,x, algorithm=""fricas"")","-\frac{6 \, {\left(2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{5} + 30 \, {\left(2 \, a b + b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} + 6 \, {\left(2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{5} + 4 \, {\left(6 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(15 \, {\left(2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 6 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{3} + 12 \, {\left(5 \, {\left(2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(6 \, a b + b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 6 \, {\left(2 \, a b + b^{2}\right)} \cosh\left(d x + c\right) + 3 \, {\left(a^{2} \cosh\left(d x + c\right)^{6} + 6 \, a^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + a^{2} \sinh\left(d x + c\right)^{6} + 3 \, a^{2} \cosh\left(d x + c\right)^{4} + 3 \, {\left(5 \, a^{2} \cosh\left(d x + c\right)^{2} + a^{2}\right)} \sinh\left(d x + c\right)^{4} + 3 \, a^{2} \cosh\left(d x + c\right)^{2} + 4 \, {\left(5 \, 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)^{3} + 3 \, {\left(5 \, a^{2} \cosh\left(d x + c\right)^{4} + 6 \, a^{2} \cosh\left(d x + c\right)^{2} + a^{2}\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 6 \, {\left(a^{2} \cosh\left(d x + c\right)^{5} + 2 \, a^{2} \cosh\left(d x + c\right)^{3} + a^{2} \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(a^{2} \cosh\left(d x + c\right)^{6} + 6 \, a^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + a^{2} \sinh\left(d x + c\right)^{6} + 3 \, a^{2} \cosh\left(d x + c\right)^{4} + 3 \, {\left(5 \, a^{2} \cosh\left(d x + c\right)^{2} + a^{2}\right)} \sinh\left(d x + c\right)^{4} + 3 \, a^{2} \cosh\left(d x + c\right)^{2} + 4 \, {\left(5 \, 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)^{3} + 3 \, {\left(5 \, a^{2} \cosh\left(d x + c\right)^{4} + 6 \, a^{2} \cosh\left(d x + c\right)^{2} + a^{2}\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 6 \, {\left(a^{2} \cosh\left(d x + c\right)^{5} + 2 \, a^{2} \cosh\left(d x + c\right)^{3} + a^{2} \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(5 \, {\left(2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(6 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)}{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*(6*(2*a*b + b^2)*cosh(d*x + c)^5 + 30*(2*a*b + b^2)*cosh(d*x + c)*sinh(d*x + c)^4 + 6*(2*a*b + b^2)*sinh(d*x + c)^5 + 4*(6*a*b + b^2)*cosh(d*x + c)^3 + 4*(15*(2*a*b + b^2)*cosh(d*x + c)^2 + 6*a*b + b^2)*sinh(d*x + c)^3 + 12*(5*(2*a*b + b^2)*cosh(d*x + c)^3 + (6*a*b + b^2)*cosh(d*x + c))*sinh(d*x + c)^2 + 6*(2*a*b + b^2)*cosh(d*x + c) + 3*(a^2*cosh(d*x + c)^6 + 6*a^2*cosh(d*x + c)*sinh(d*x + c)^5 + a^2*sinh(d*x + c)^6 + 3*a^2*cosh(d*x + c)^4 + 3*(5*a^2*cosh(d*x + c)^2 + a^2)*sinh(d*x + c)^4 + 3*a^2*cosh(d*x + c)^2 + 4*(5*a^2*cosh(d*x + c)^3 + 3*a^2*cosh(d*x + c))*sinh(d*x + c)^3 + 3*(5*a^2*cosh(d*x + c)^4 + 6*a^2*cosh(d*x + c)^2 + a^2)*sinh(d*x + c)^2 + a^2 + 6*(a^2*cosh(d*x + c)^5 + 2*a^2*cosh(d*x + c)^3 + a^2*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) + 1) - 3*(a^2*cosh(d*x + c)^6 + 6*a^2*cosh(d*x + c)*sinh(d*x + c)^5 + a^2*sinh(d*x + c)^6 + 3*a^2*cosh(d*x + c)^4 + 3*(5*a^2*cosh(d*x + c)^2 + a^2)*sinh(d*x + c)^4 + 3*a^2*cosh(d*x + c)^2 + 4*(5*a^2*cosh(d*x + c)^3 + 3*a^2*cosh(d*x + c))*sinh(d*x + c)^3 + 3*(5*a^2*cosh(d*x + c)^4 + 6*a^2*cosh(d*x + c)^2 + a^2)*sinh(d*x + c)^2 + a^2 + 6*(a^2*cosh(d*x + c)^5 + 2*a^2*cosh(d*x + c)^3 + a^2*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) - 1) + 6*(5*(2*a*b + b^2)*cosh(d*x + c)^4 + 2*(6*a*b + b^2)*cosh(d*x + c)^2 + 2*a*b + b^2)*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 + 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
14,1,264,0,0.516098," ","integrate(csch(d*x+c)^2*(a+b*tanh(d*x+c)^2)^2,x, algorithm=""fricas"")","-\frac{4 \, {\left({\left(3 \, a^{2} + b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(3 \, a^{2} + b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{3} + {\left(9 \, a^{2} - b^{2}\right)} \cosh\left(d x + c\right) + 2 \, {\left(3 \, {\left(3 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 3 \, a b - b^{2}\right)} \sinh\left(d x + c\right)\right)}}{3 \, {\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} + d \cosh\left(d x + c\right)^{3} + {\left(10 \, d \cosh\left(d x + c\right)^{2} + 3 \, d\right)} \sinh\left(d x + c\right)^{3} + {\left(10 \, d \cosh\left(d x + c\right)^{3} + 3 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 2 \, d \cosh\left(d x + c\right) + {\left(5 \, d \cosh\left(d x + c\right)^{4} + 9 \, d \cosh\left(d x + c\right)^{2} + 2 \, d\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"-4/3*((3*a^2 + b^2)*cosh(d*x + c)^3 + 3*(3*a^2 + b^2)*cosh(d*x + c)*sinh(d*x + c)^2 + 2*(3*a*b + b^2)*sinh(d*x + c)^3 + (9*a^2 - b^2)*cosh(d*x + c) + 2*(3*(3*a*b + b^2)*cosh(d*x + c)^2 + 3*a*b - b^2)*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 + d*cosh(d*x + c)^3 + (10*d*cosh(d*x + c)^2 + 3*d)*sinh(d*x + c)^3 + (10*d*cosh(d*x + c)^3 + 3*d*cosh(d*x + c))*sinh(d*x + c)^2 - 2*d*cosh(d*x + c) + (5*d*cosh(d*x + c)^4 + 9*d*cosh(d*x + c)^2 + 2*d)*sinh(d*x + c))","B",0
15,1,2462,0,0.514323," ","integrate(csch(d*x+c)^3*(a+b*tanh(d*x+c)^2)^2,x, algorithm=""fricas"")","-\frac{6 \, {\left(a^{2} - 4 \, a b\right)} \cosh\left(d x + c\right)^{9} + 54 \, {\left(a^{2} - 4 \, a b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{8} + 6 \, {\left(a^{2} - 4 \, a b\right)} \sinh\left(d x + c\right)^{9} + 8 \, {\left(3 \, a^{2} + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} + 8 \, {\left(27 \, {\left(a^{2} - 4 \, a b\right)} \cosh\left(d x + c\right)^{2} + 3 \, a^{2} + 2 \, b^{2}\right)} \sinh\left(d x + c\right)^{7} + 56 \, {\left(9 \, {\left(a^{2} - 4 \, a b\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{2} + 2 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(9 \, a^{2} + 12 \, a b - 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 4 \, {\left(189 \, {\left(a^{2} - 4 \, a b\right)} \cosh\left(d x + c\right)^{4} + 42 \, {\left(3 \, a^{2} + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 9 \, a^{2} + 12 \, a b - 8 \, b^{2}\right)} \sinh\left(d x + c\right)^{5} + 4 \, {\left(189 \, {\left(a^{2} - 4 \, a b\right)} \cosh\left(d x + c\right)^{5} + 70 \, {\left(3 \, a^{2} + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 5 \, {\left(9 \, a^{2} + 12 \, a b - 8 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(3 \, a^{2} + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 8 \, {\left(63 \, {\left(a^{2} - 4 \, a b\right)} \cosh\left(d x + c\right)^{6} + 35 \, {\left(3 \, a^{2} + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 5 \, {\left(9 \, a^{2} + 12 \, a b - 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 3 \, a^{2} + 2 \, b^{2}\right)} \sinh\left(d x + c\right)^{3} + 8 \, {\left(27 \, {\left(a^{2} - 4 \, a b\right)} \cosh\left(d x + c\right)^{7} + 21 \, {\left(3 \, a^{2} + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(9 \, a^{2} + 12 \, a b - 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(3 \, a^{2} + 2 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 6 \, {\left(a^{2} - 4 \, a b\right)} \cosh\left(d x + c\right) - 3 \, {\left({\left(a^{2} - 4 \, a b\right)} \cosh\left(d x + c\right)^{10} + 10 \, {\left(a^{2} - 4 \, a b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + {\left(a^{2} - 4 \, a b\right)} \sinh\left(d x + c\right)^{10} + {\left(a^{2} - 4 \, a b\right)} \cosh\left(d x + c\right)^{8} + {\left(45 \, {\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)^{8} + 8 \, {\left(15 \, {\left(a^{2} - 4 \, a b\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} - 4 \, a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} - 2 \, {\left(a^{2} - 4 \, a b\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(105 \, {\left(a^{2} - 4 \, a b\right)} \cosh\left(d x + c\right)^{4} + 14 \, {\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)^{6} + 4 \, {\left(63 \, {\left(a^{2} - 4 \, a b\right)} \cosh\left(d x + c\right)^{5} + 14 \, {\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)^{5} - 2 \, {\left(a^{2} - 4 \, a b\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(105 \, {\left(a^{2} - 4 \, a b\right)} \cosh\left(d x + c\right)^{6} + 35 \, {\left(a^{2} - 4 \, a b\right)} \cosh\left(d x + c\right)^{4} - 15 \, {\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)^{4} + 8 \, {\left(15 \, {\left(a^{2} - 4 \, a b\right)} \cosh\left(d x + c\right)^{7} + 7 \, {\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)^{3} - {\left(a^{2} - 4 \, a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(a^{2} - 4 \, a b\right)} \cosh\left(d x + c\right)^{2} + {\left(45 \, {\left(a^{2} - 4 \, a b\right)} \cosh\left(d x + c\right)^{8} + 28 \, {\left(a^{2} - 4 \, a b\right)} \cosh\left(d x + c\right)^{6} - 30 \, {\left(a^{2} - 4 \, a b\right)} \cosh\left(d x + c\right)^{4} - 12 \, {\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)^{2} + a^{2} - 4 \, a b + 2 \, {\left(5 \, {\left(a^{2} - 4 \, a b\right)} \cosh\left(d x + c\right)^{9} + 4 \, {\left(a^{2} - 4 \, a b\right)} \cosh\left(d x + c\right)^{7} - 6 \, {\left(a^{2} - 4 \, a b\right)} \cosh\left(d x + c\right)^{5} - 4 \, {\left(a^{2} - 4 \, a b\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} - 4 \, a b\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(a^{2} - 4 \, a b\right)} \cosh\left(d x + c\right)^{10} + 10 \, {\left(a^{2} - 4 \, a b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + {\left(a^{2} - 4 \, a b\right)} \sinh\left(d x + c\right)^{10} + {\left(a^{2} - 4 \, a b\right)} \cosh\left(d x + c\right)^{8} + {\left(45 \, {\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)^{8} + 8 \, {\left(15 \, {\left(a^{2} - 4 \, a b\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} - 4 \, a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} - 2 \, {\left(a^{2} - 4 \, a b\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(105 \, {\left(a^{2} - 4 \, a b\right)} \cosh\left(d x + c\right)^{4} + 14 \, {\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)^{6} + 4 \, {\left(63 \, {\left(a^{2} - 4 \, a b\right)} \cosh\left(d x + c\right)^{5} + 14 \, {\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)^{5} - 2 \, {\left(a^{2} - 4 \, a b\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(105 \, {\left(a^{2} - 4 \, a b\right)} \cosh\left(d x + c\right)^{6} + 35 \, {\left(a^{2} - 4 \, a b\right)} \cosh\left(d x + c\right)^{4} - 15 \, {\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)^{4} + 8 \, {\left(15 \, {\left(a^{2} - 4 \, a b\right)} \cosh\left(d x + c\right)^{7} + 7 \, {\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)^{3} - {\left(a^{2} - 4 \, a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(a^{2} - 4 \, a b\right)} \cosh\left(d x + c\right)^{2} + {\left(45 \, {\left(a^{2} - 4 \, a b\right)} \cosh\left(d x + c\right)^{8} + 28 \, {\left(a^{2} - 4 \, a b\right)} \cosh\left(d x + c\right)^{6} - 30 \, {\left(a^{2} - 4 \, a b\right)} \cosh\left(d x + c\right)^{4} - 12 \, {\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)^{2} + a^{2} - 4 \, a b + 2 \, {\left(5 \, {\left(a^{2} - 4 \, a b\right)} \cosh\left(d x + c\right)^{9} + 4 \, {\left(a^{2} - 4 \, a b\right)} \cosh\left(d x + c\right)^{7} - 6 \, {\left(a^{2} - 4 \, a b\right)} \cosh\left(d x + c\right)^{5} - 4 \, {\left(a^{2} - 4 \, a b\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} - 4 \, a b\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(27 \, {\left(a^{2} - 4 \, a b\right)} \cosh\left(d x + c\right)^{8} + 28 \, {\left(3 \, a^{2} + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 10 \, {\left(9 \, a^{2} + 12 \, a b - 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 12 \, {\left(3 \, a^{2} + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 3 \, a^{2} - 12 \, a b\right)} \sinh\left(d x + c\right)}{6 \, {\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} + d \cosh\left(d x + c\right)^{8} + {\left(45 \, d \cosh\left(d x + c\right)^{2} + d\right)} \sinh\left(d x + c\right)^{8} + 8 \, {\left(15 \, d \cosh\left(d x + c\right)^{3} + d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} - 2 \, d \cosh\left(d x + c\right)^{6} + 2 \, {\left(105 \, 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} + 14 \, d \cosh\left(d x + c\right)^{3} - 3 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 2 \, d \cosh\left(d x + c\right)^{4} + 2 \, {\left(105 \, 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} + 8 \, {\left(15 \, 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} + d \cosh\left(d x + c\right)^{2} + {\left(45 \, 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} + 2 \, {\left(5 \, 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,"-1/6*(6*(a^2 - 4*a*b)*cosh(d*x + c)^9 + 54*(a^2 - 4*a*b)*cosh(d*x + c)*sinh(d*x + c)^8 + 6*(a^2 - 4*a*b)*sinh(d*x + c)^9 + 8*(3*a^2 + 2*b^2)*cosh(d*x + c)^7 + 8*(27*(a^2 - 4*a*b)*cosh(d*x + c)^2 + 3*a^2 + 2*b^2)*sinh(d*x + c)^7 + 56*(9*(a^2 - 4*a*b)*cosh(d*x + c)^3 + (3*a^2 + 2*b^2)*cosh(d*x + c))*sinh(d*x + c)^6 + 4*(9*a^2 + 12*a*b - 8*b^2)*cosh(d*x + c)^5 + 4*(189*(a^2 - 4*a*b)*cosh(d*x + c)^4 + 42*(3*a^2 + 2*b^2)*cosh(d*x + c)^2 + 9*a^2 + 12*a*b - 8*b^2)*sinh(d*x + c)^5 + 4*(189*(a^2 - 4*a*b)*cosh(d*x + c)^5 + 70*(3*a^2 + 2*b^2)*cosh(d*x + c)^3 + 5*(9*a^2 + 12*a*b - 8*b^2)*cosh(d*x + c))*sinh(d*x + c)^4 + 8*(3*a^2 + 2*b^2)*cosh(d*x + c)^3 + 8*(63*(a^2 - 4*a*b)*cosh(d*x + c)^6 + 35*(3*a^2 + 2*b^2)*cosh(d*x + c)^4 + 5*(9*a^2 + 12*a*b - 8*b^2)*cosh(d*x + c)^2 + 3*a^2 + 2*b^2)*sinh(d*x + c)^3 + 8*(27*(a^2 - 4*a*b)*cosh(d*x + c)^7 + 21*(3*a^2 + 2*b^2)*cosh(d*x + c)^5 + 5*(9*a^2 + 12*a*b - 8*b^2)*cosh(d*x + c)^3 + 3*(3*a^2 + 2*b^2)*cosh(d*x + c))*sinh(d*x + c)^2 + 6*(a^2 - 4*a*b)*cosh(d*x + c) - 3*((a^2 - 4*a*b)*cosh(d*x + c)^10 + 10*(a^2 - 4*a*b)*cosh(d*x + c)*sinh(d*x + c)^9 + (a^2 - 4*a*b)*sinh(d*x + c)^10 + (a^2 - 4*a*b)*cosh(d*x + c)^8 + (45*(a^2 - 4*a*b)*cosh(d*x + c)^2 + a^2 - 4*a*b)*sinh(d*x + c)^8 + 8*(15*(a^2 - 4*a*b)*cosh(d*x + c)^3 + (a^2 - 4*a*b)*cosh(d*x + c))*sinh(d*x + c)^7 - 2*(a^2 - 4*a*b)*cosh(d*x + c)^6 + 2*(105*(a^2 - 4*a*b)*cosh(d*x + c)^4 + 14*(a^2 - 4*a*b)*cosh(d*x + c)^2 - a^2 + 4*a*b)*sinh(d*x + c)^6 + 4*(63*(a^2 - 4*a*b)*cosh(d*x + c)^5 + 14*(a^2 - 4*a*b)*cosh(d*x + c)^3 - 3*(a^2 - 4*a*b)*cosh(d*x + c))*sinh(d*x + c)^5 - 2*(a^2 - 4*a*b)*cosh(d*x + c)^4 + 2*(105*(a^2 - 4*a*b)*cosh(d*x + c)^6 + 35*(a^2 - 4*a*b)*cosh(d*x + c)^4 - 15*(a^2 - 4*a*b)*cosh(d*x + c)^2 - a^2 + 4*a*b)*sinh(d*x + c)^4 + 8*(15*(a^2 - 4*a*b)*cosh(d*x + c)^7 + 7*(a^2 - 4*a*b)*cosh(d*x + c)^5 - 5*(a^2 - 4*a*b)*cosh(d*x + c)^3 - (a^2 - 4*a*b)*cosh(d*x + c))*sinh(d*x + c)^3 + (a^2 - 4*a*b)*cosh(d*x + c)^2 + (45*(a^2 - 4*a*b)*cosh(d*x + c)^8 + 28*(a^2 - 4*a*b)*cosh(d*x + c)^6 - 30*(a^2 - 4*a*b)*cosh(d*x + c)^4 - 12*(a^2 - 4*a*b)*cosh(d*x + c)^2 + a^2 - 4*a*b)*sinh(d*x + c)^2 + a^2 - 4*a*b + 2*(5*(a^2 - 4*a*b)*cosh(d*x + c)^9 + 4*(a^2 - 4*a*b)*cosh(d*x + c)^7 - 6*(a^2 - 4*a*b)*cosh(d*x + c)^5 - 4*(a^2 - 4*a*b)*cosh(d*x + c)^3 + (a^2 - 4*a*b)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) + 1) + 3*((a^2 - 4*a*b)*cosh(d*x + c)^10 + 10*(a^2 - 4*a*b)*cosh(d*x + c)*sinh(d*x + c)^9 + (a^2 - 4*a*b)*sinh(d*x + c)^10 + (a^2 - 4*a*b)*cosh(d*x + c)^8 + (45*(a^2 - 4*a*b)*cosh(d*x + c)^2 + a^2 - 4*a*b)*sinh(d*x + c)^8 + 8*(15*(a^2 - 4*a*b)*cosh(d*x + c)^3 + (a^2 - 4*a*b)*cosh(d*x + c))*sinh(d*x + c)^7 - 2*(a^2 - 4*a*b)*cosh(d*x + c)^6 + 2*(105*(a^2 - 4*a*b)*cosh(d*x + c)^4 + 14*(a^2 - 4*a*b)*cosh(d*x + c)^2 - a^2 + 4*a*b)*sinh(d*x + c)^6 + 4*(63*(a^2 - 4*a*b)*cosh(d*x + c)^5 + 14*(a^2 - 4*a*b)*cosh(d*x + c)^3 - 3*(a^2 - 4*a*b)*cosh(d*x + c))*sinh(d*x + c)^5 - 2*(a^2 - 4*a*b)*cosh(d*x + c)^4 + 2*(105*(a^2 - 4*a*b)*cosh(d*x + c)^6 + 35*(a^2 - 4*a*b)*cosh(d*x + c)^4 - 15*(a^2 - 4*a*b)*cosh(d*x + c)^2 - a^2 + 4*a*b)*sinh(d*x + c)^4 + 8*(15*(a^2 - 4*a*b)*cosh(d*x + c)^7 + 7*(a^2 - 4*a*b)*cosh(d*x + c)^5 - 5*(a^2 - 4*a*b)*cosh(d*x + c)^3 - (a^2 - 4*a*b)*cosh(d*x + c))*sinh(d*x + c)^3 + (a^2 - 4*a*b)*cosh(d*x + c)^2 + (45*(a^2 - 4*a*b)*cosh(d*x + c)^8 + 28*(a^2 - 4*a*b)*cosh(d*x + c)^6 - 30*(a^2 - 4*a*b)*cosh(d*x + c)^4 - 12*(a^2 - 4*a*b)*cosh(d*x + c)^2 + a^2 - 4*a*b)*sinh(d*x + c)^2 + a^2 - 4*a*b + 2*(5*(a^2 - 4*a*b)*cosh(d*x + c)^9 + 4*(a^2 - 4*a*b)*cosh(d*x + c)^7 - 6*(a^2 - 4*a*b)*cosh(d*x + c)^5 - 4*(a^2 - 4*a*b)*cosh(d*x + c)^3 + (a^2 - 4*a*b)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) - 1) + 2*(27*(a^2 - 4*a*b)*cosh(d*x + c)^8 + 28*(3*a^2 + 2*b^2)*cosh(d*x + c)^6 + 10*(9*a^2 + 12*a*b - 8*b^2)*cosh(d*x + c)^4 + 12*(3*a^2 + 2*b^2)*cosh(d*x + c)^2 + 3*a^2 - 12*a*b)*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 + d*cosh(d*x + c)^8 + (45*d*cosh(d*x + c)^2 + d)*sinh(d*x + c)^8 + 8*(15*d*cosh(d*x + c)^3 + d*cosh(d*x + c))*sinh(d*x + c)^7 - 2*d*cosh(d*x + c)^6 + 2*(105*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 + 14*d*cosh(d*x + c)^3 - 3*d*cosh(d*x + c))*sinh(d*x + c)^5 - 2*d*cosh(d*x + c)^4 + 2*(105*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 + 8*(15*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 + d*cosh(d*x + c)^2 + (45*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 + 2*(5*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
16,1,393,0,0.713579," ","integrate(csch(d*x+c)^4*(a+b*tanh(d*x+c)^2)^2,x, algorithm=""fricas"")","-\frac{8 \, {\left({\left(a^{2} + 6 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + 8 \, {\left(a^{2} + b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{2} + 6 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} + 6 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, a^{2} - 2 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} + 3 \, a^{2} - 6 \, a b + 3 \, b^{2} + 8 \, {\left({\left(a^{2} + b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}{3 \, {\left(d \cosh\left(d x + c\right)^{8} + 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} - 4 \, d \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, d \cosh\left(d x + c\right)^{4} - 2 \, d\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, d \cosh\left(d x + c\right)^{5} - d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, d \cosh\left(d x + c\right)^{6} - 6 \, d \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left(d \cosh\left(d x + c\right)^{7} - d \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right) + 3 \, d\right)}}"," ",0,"-8/3*((a^2 + 6*a*b + b^2)*cosh(d*x + c)^4 + 8*(a^2 + b^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (a^2 + 6*a*b + b^2)*sinh(d*x + c)^4 + 4*(a^2 - b^2)*cosh(d*x + c)^2 + 2*(3*(a^2 + 6*a*b + b^2)*cosh(d*x + c)^2 + 2*a^2 - 2*b^2)*sinh(d*x + c)^2 + 3*a^2 - 6*a*b + 3*b^2 + 8*((a^2 + b^2)*cosh(d*x + c)^3 + (a^2 - b^2)*cosh(d*x + c))*sinh(d*x + c))/(d*cosh(d*x + c)^8 + 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 - 4*d*cosh(d*x + c)^4 + 2*(35*d*cosh(d*x + c)^4 - 2*d)*sinh(d*x + c)^4 + 8*(7*d*cosh(d*x + c)^5 - d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*d*cosh(d*x + c)^6 - 6*d*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*(d*cosh(d*x + c)^7 - d*cosh(d*x + c)^3)*sinh(d*x + c) + 3*d)","B",0
17,1,879,0,0.551476," ","integrate(sinh(d*x+c)^4*(a+b*tanh(d*x+c)^2)^3,x, algorithm=""fricas"")","\frac{5 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \sinh\left(d x + c\right)^{9} - 15 \, {\left(a^{3} + 11 \, a^{2} b + 19 \, a b^{2} + 9 \, b^{3} - 12 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{7} + 8 \, {\left(120 \, a^{2} b + 400 \, a b^{2} + 288 \, b^{3} + 15 \, {\left(a^{3} + 15 \, a^{2} b + 35 \, a b^{2} + 21 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{5} + 40 \, {\left(120 \, a^{2} b + 400 \, a b^{2} + 288 \, b^{3} + 15 \, {\left(a^{3} + 15 \, a^{2} b + 35 \, a b^{2} + 21 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} + {\left(630 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{4} - 150 \, a^{3} - 2010 \, a^{2} b - 4850 \, a b^{2} - 3054 \, b^{3} - 315 \, {\left(a^{3} + 11 \, a^{2} b + 19 \, a b^{2} + 9 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{5} + 40 \, {\left(120 \, a^{2} b + 400 \, a b^{2} + 288 \, b^{3} + 15 \, {\left(a^{3} + 15 \, a^{2} b + 35 \, a b^{2} + 21 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + 5 \, {\left(84 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{6} - 105 \, {\left(a^{3} + 11 \, a^{2} b + 19 \, a b^{2} + 9 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 62 \, a^{3} - 978 \, a^{2} b - 2282 \, a b^{2} - 1302 \, b^{3} - 4 \, {\left(75 \, a^{3} + 1005 \, a^{2} b + 2425 \, a b^{2} + 1527 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + 40 \, {\left(2 \, {\left(120 \, a^{2} b + 400 \, a b^{2} + 288 \, b^{3} + 15 \, {\left(a^{3} + 15 \, a^{2} b + 35 \, a b^{2} + 21 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(120 \, a^{2} b + 400 \, a b^{2} + 288 \, b^{3} + 15 \, {\left(a^{3} + 15 \, a^{2} b + 35 \, a b^{2} + 21 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 80 \, {\left(120 \, a^{2} b + 400 \, a b^{2} + 288 \, b^{3} + 15 \, {\left(a^{3} + 15 \, a^{2} b + 35 \, a b^{2} + 21 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right) + 5 \, {\left(9 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{8} - 21 \, {\left(a^{3} + 11 \, a^{2} b + 19 \, a b^{2} + 9 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} - 2 \, {\left(75 \, a^{3} + 1005 \, a^{2} b + 2425 \, a b^{2} + 1527 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 36 \, a^{3} - 612 \, a^{2} b - 1372 \, a b^{2} - 924 \, b^{3} - 6 \, {\left(31 \, a^{3} + 489 \, a^{2} b + 1141 \, a b^{2} + 651 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)}{320 \, {\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,"1/320*(5*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*sinh(d*x + c)^9 - 15*(a^3 + 11*a^2*b + 19*a*b^2 + 9*b^3 - 12*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^7 + 8*(120*a^2*b + 400*a*b^2 + 288*b^3 + 15*(a^3 + 15*a^2*b + 35*a*b^2 + 21*b^3)*d*x)*cosh(d*x + c)^5 + 40*(120*a^2*b + 400*a*b^2 + 288*b^3 + 15*(a^3 + 15*a^2*b + 35*a*b^2 + 21*b^3)*d*x)*cosh(d*x + c)*sinh(d*x + c)^4 + (630*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^4 - 150*a^3 - 2010*a^2*b - 4850*a*b^2 - 3054*b^3 - 315*(a^3 + 11*a^2*b + 19*a*b^2 + 9*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 40*(120*a^2*b + 400*a*b^2 + 288*b^3 + 15*(a^3 + 15*a^2*b + 35*a*b^2 + 21*b^3)*d*x)*cosh(d*x + c)^3 + 5*(84*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^6 - 105*(a^3 + 11*a^2*b + 19*a*b^2 + 9*b^3)*cosh(d*x + c)^4 - 62*a^3 - 978*a^2*b - 2282*a*b^2 - 1302*b^3 - 4*(75*a^3 + 1005*a^2*b + 2425*a*b^2 + 1527*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 40*(2*(120*a^2*b + 400*a*b^2 + 288*b^3 + 15*(a^3 + 15*a^2*b + 35*a*b^2 + 21*b^3)*d*x)*cosh(d*x + c)^3 + 3*(120*a^2*b + 400*a*b^2 + 288*b^3 + 15*(a^3 + 15*a^2*b + 35*a*b^2 + 21*b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c)^2 + 80*(120*a^2*b + 400*a*b^2 + 288*b^3 + 15*(a^3 + 15*a^2*b + 35*a*b^2 + 21*b^3)*d*x)*cosh(d*x + c) + 5*(9*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^8 - 21*(a^3 + 11*a^2*b + 19*a*b^2 + 9*b^3)*cosh(d*x + c)^6 - 2*(75*a^3 + 1005*a^2*b + 2425*a*b^2 + 1527*b^3)*cosh(d*x + c)^4 - 36*a^3 - 612*a^2*b - 1372*a*b^2 - 924*b^3 - 6*(31*a^3 + 489*a^2*b + 1141*a*b^2 + 651*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
18,1,540,0,0.588091," ","integrate(sinh(d*x+c)^3*(a+b*tanh(d*x+c)^2)^3,x, algorithm=""fricas"")","\frac{5 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{8} + 5 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \sinh\left(d x + c\right)^{8} - 20 \, {\left(a^{3} + 12 \, a^{2} b + 21 \, a b^{2} + 10 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} - 20 \, {\left(a^{3} + 12 \, a^{2} b + 21 \, a b^{2} + 10 \, b^{3} - 7 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} - 20 \, {\left(11 \, a^{3} + 123 \, a^{2} b + 249 \, a b^{2} + 137 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 10 \, {\left(35 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{4} - 22 \, a^{3} - 246 \, a^{2} b - 498 \, a b^{2} - 274 \, b^{3} - 30 \, {\left(a^{3} + 12 \, a^{2} b + 21 \, a b^{2} + 10 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} - 425 \, a^{3} - 5235 \, a^{2} b - 10395 \, a b^{2} - 5649 \, b^{3} - 20 \, {\left(31 \, a^{3} + 372 \, a^{2} b + 747 \, a b^{2} + 390 \, b^{3}\right)} \cosh\left(d x + c\right)^{2} + 20 \, {\left(7 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{6} - 15 \, {\left(a^{3} + 12 \, a^{2} b + 21 \, a b^{2} + 10 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 31 \, a^{3} - 372 \, a^{2} b - 747 \, a b^{2} - 390 \, b^{3} - 6 \, {\left(11 \, a^{3} + 123 \, a^{2} b + 249 \, a b^{2} + 137 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2}}{120 \, {\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,"1/120*(5*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^8 + 5*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*sinh(d*x + c)^8 - 20*(a^3 + 12*a^2*b + 21*a*b^2 + 10*b^3)*cosh(d*x + c)^6 - 20*(a^3 + 12*a^2*b + 21*a*b^2 + 10*b^3 - 7*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^6 - 20*(11*a^3 + 123*a^2*b + 249*a*b^2 + 137*b^3)*cosh(d*x + c)^4 + 10*(35*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^4 - 22*a^3 - 246*a^2*b - 498*a*b^2 - 274*b^3 - 30*(a^3 + 12*a^2*b + 21*a*b^2 + 10*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 - 425*a^3 - 5235*a^2*b - 10395*a*b^2 - 5649*b^3 - 20*(31*a^3 + 372*a^2*b + 747*a*b^2 + 390*b^3)*cosh(d*x + c)^2 + 20*(7*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^6 - 15*(a^3 + 12*a^2*b + 21*a*b^2 + 10*b^3)*cosh(d*x + c)^4 - 31*a^3 - 372*a^2*b - 747*a*b^2 - 390*b^3 - 6*(11*a^3 + 123*a^2*b + 249*a*b^2 + 137*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2)/(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
19,1,725,0,0.874920," ","integrate(sinh(d*x+c)^2*(a+b*tanh(d*x+c)^2)^3,x, algorithm=""fricas"")","\frac{15 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \sinh\left(d x + c\right)^{7} - 4 \, {\left(90 \, a^{2} b + 210 \, a b^{2} + 116 \, b^{3} + 15 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{5} - 20 \, {\left(90 \, a^{2} b + 210 \, a b^{2} + 116 \, b^{3} + 15 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} + {\left(75 \, a^{3} + 585 \, a^{2} b + 1065 \, a b^{2} + 539 \, b^{3} + 315 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{5} - 20 \, {\left(90 \, a^{2} b + 210 \, a b^{2} + 116 \, b^{3} + 15 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + 5 \, {\left(105 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{4} + 27 \, a^{3} + 297 \, a^{2} b + 489 \, a b^{2} + 203 \, b^{3} + 2 \, {\left(75 \, a^{3} + 585 \, a^{2} b + 1065 \, a b^{2} + 539 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} - 20 \, {\left(2 \, {\left(90 \, a^{2} b + 210 \, a b^{2} + 116 \, b^{3} + 15 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(90 \, a^{2} b + 210 \, a b^{2} + 116 \, b^{3} + 15 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 40 \, {\left(90 \, a^{2} b + 210 \, a b^{2} + 116 \, b^{3} + 15 \, {\left(a^{3} + 9 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right) + 5 \, {\left(21 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{6} + {\left(75 \, a^{3} + 585 \, a^{2} b + 1065 \, a b^{2} + 539 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 15 \, a^{3} + 189 \, a^{2} b + 285 \, a b^{2} + 175 \, b^{3} + 3 \, {\left(27 \, a^{3} + 297 \, a^{2} b + 489 \, a b^{2} + 203 \, b^{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)^{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,"1/120*(15*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*sinh(d*x + c)^7 - 4*(90*a^2*b + 210*a*b^2 + 116*b^3 + 15*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*d*x)*cosh(d*x + c)^5 - 20*(90*a^2*b + 210*a*b^2 + 116*b^3 + 15*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*d*x)*cosh(d*x + c)*sinh(d*x + c)^4 + (75*a^3 + 585*a^2*b + 1065*a*b^2 + 539*b^3 + 315*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^5 - 20*(90*a^2*b + 210*a*b^2 + 116*b^3 + 15*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*d*x)*cosh(d*x + c)^3 + 5*(105*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^4 + 27*a^3 + 297*a^2*b + 489*a*b^2 + 203*b^3 + 2*(75*a^3 + 585*a^2*b + 1065*a*b^2 + 539*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^3 - 20*(2*(90*a^2*b + 210*a*b^2 + 116*b^3 + 15*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*d*x)*cosh(d*x + c)^3 + 3*(90*a^2*b + 210*a*b^2 + 116*b^3 + 15*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c)^2 - 40*(90*a^2*b + 210*a*b^2 + 116*b^3 + 15*(a^3 + 9*a^2*b + 15*a*b^2 + 7*b^3)*d*x)*cosh(d*x + c) + 5*(21*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^6 + (75*a^3 + 585*a^2*b + 1065*a*b^2 + 539*b^3)*cosh(d*x + c)^4 + 15*a^3 + 189*a^2*b + 285*a*b^2 + 175*b^3 + 3*(27*a^3 + 297*a^2*b + 489*a*b^2 + 203*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
20,1,383,0,0.635767," ","integrate(sinh(d*x+c)*(a+b*tanh(d*x+c)^2)^3,x, algorithm=""fricas"")","\frac{5 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{6} + 5 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \sinh\left(d x + c\right)^{6} + 30 \, {\left(a^{3} + 5 \, a^{2} b + 7 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 15 \, {\left(2 \, a^{3} + 10 \, a^{2} b + 14 \, a b^{2} + 6 \, b^{3} + 5 \, {\left(a^{3} + 3 \, 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} + 50 \, a^{3} + 330 \, a^{2} b + 430 \, a b^{2} + 182 \, b^{3} + 5 \, {\left(15 \, a^{3} + 93 \, a^{2} b + 125 \, a b^{2} + 47 \, b^{3}\right)} \cosh\left(d x + c\right)^{2} + 5 \, {\left(15 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{4} + 15 \, a^{3} + 93 \, a^{2} b + 125 \, a b^{2} + 47 \, b^{3} + 36 \, {\left(a^{3} + 5 \, a^{2} b + 7 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2}}{10 \, {\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,"1/10*(5*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^6 + 5*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*sinh(d*x + c)^6 + 30*(a^3 + 5*a^2*b + 7*a*b^2 + 3*b^3)*cosh(d*x + c)^4 + 15*(2*a^3 + 10*a^2*b + 14*a*b^2 + 6*b^3 + 5*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 50*a^3 + 330*a^2*b + 430*a*b^2 + 182*b^3 + 5*(15*a^3 + 93*a^2*b + 125*a*b^2 + 47*b^3)*cosh(d*x + c)^2 + 5*(15*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^4 + 15*a^3 + 93*a^2*b + 125*a*b^2 + 47*b^3 + 36*(a^3 + 5*a^2*b + 7*a*b^2 + 3*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2)/(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
21,1,2277,0,0.792505," ","integrate(csch(d*x+c)*(a+b*tanh(d*x+c)^2)^3,x, algorithm=""fricas"")","-\frac{30 \, {\left(3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{9} + 270 \, {\left(3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{8} + 30 \, {\left(3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \sinh\left(d x + c\right)^{9} + 40 \, {\left(9 \, a^{2} b + 6 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{7} + 40 \, {\left(9 \, a^{2} b + 6 \, a b^{2} + b^{3} + 27 \, {\left(3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{7} + 280 \, {\left(9 \, {\left(3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(9 \, a^{2} b + 6 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(135 \, a^{2} b + 75 \, a b^{2} + 29 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 4 \, {\left(945 \, {\left(3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{4} + 135 \, a^{2} b + 75 \, a b^{2} + 29 \, b^{3} + 210 \, {\left(9 \, a^{2} b + 6 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{5} + 20 \, {\left(189 \, {\left(3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{5} + 70 \, {\left(9 \, a^{2} b + 6 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(135 \, a^{2} b + 75 \, a b^{2} + 29 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 40 \, {\left(9 \, a^{2} b + 6 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{3} + 40 \, {\left(63 \, {\left(3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{6} + 35 \, {\left(9 \, a^{2} b + 6 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{4} + 9 \, a^{2} b + 6 \, a b^{2} + b^{3} + {\left(135 \, a^{2} b + 75 \, a b^{2} + 29 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + 40 \, {\left(27 \, {\left(3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{7} + 21 \, {\left(9 \, a^{2} b + 6 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{5} + {\left(135 \, a^{2} b + 75 \, a b^{2} + 29 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(9 \, a^{2} b + 6 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 30 \, {\left(3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right) + 15 \, {\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} + 5 \, a^{3} \cosh\left(d x + c\right)^{8} + 10 \, a^{3} \cosh\left(d x + c\right)^{6} + 5 \, {\left(9 \, a^{3} \cosh\left(d x + c\right)^{2} + a^{3}\right)} \sinh\left(d x + c\right)^{8} + 40 \, {\left(3 \, a^{3} \cosh\left(d x + c\right)^{3} + a^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 10 \, a^{3} \cosh\left(d x + c\right)^{4} + 10 \, {\left(21 \, a^{3} \cosh\left(d x + c\right)^{4} + 14 \, a^{3} \cosh\left(d x + c\right)^{2} + a^{3}\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(63 \, a^{3} \cosh\left(d x + c\right)^{5} + 70 \, a^{3} \cosh\left(d x + c\right)^{3} + 15 \, a^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 5 \, a^{3} \cosh\left(d x + c\right)^{2} + 10 \, {\left(21 \, a^{3} \cosh\left(d x + c\right)^{6} + 35 \, a^{3} \cosh\left(d x + c\right)^{4} + 15 \, a^{3} \cosh\left(d x + c\right)^{2} + a^{3}\right)} \sinh\left(d x + c\right)^{4} + 40 \, {\left(3 \, a^{3} \cosh\left(d x + c\right)^{7} + 7 \, a^{3} \cosh\left(d x + c\right)^{5} + 5 \, 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} + a^{3} + 5 \, {\left(9 \, a^{3} \cosh\left(d x + c\right)^{8} + 28 \, a^{3} \cosh\left(d x + c\right)^{6} + 30 \, a^{3} \cosh\left(d x + c\right)^{4} + 12 \, a^{3} \cosh\left(d x + c\right)^{2} + a^{3}\right)} \sinh\left(d x + c\right)^{2} + 10 \, {\left(a^{3} \cosh\left(d x + c\right)^{9} + 4 \, a^{3} \cosh\left(d x + c\right)^{7} + 6 \, a^{3} \cosh\left(d x + c\right)^{5} + 4 \, a^{3} \cosh\left(d x + c\right)^{3} + a^{3} \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^{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} + 5 \, a^{3} \cosh\left(d x + c\right)^{8} + 10 \, a^{3} \cosh\left(d x + c\right)^{6} + 5 \, {\left(9 \, a^{3} \cosh\left(d x + c\right)^{2} + a^{3}\right)} \sinh\left(d x + c\right)^{8} + 40 \, {\left(3 \, a^{3} \cosh\left(d x + c\right)^{3} + a^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 10 \, a^{3} \cosh\left(d x + c\right)^{4} + 10 \, {\left(21 \, a^{3} \cosh\left(d x + c\right)^{4} + 14 \, a^{3} \cosh\left(d x + c\right)^{2} + a^{3}\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(63 \, a^{3} \cosh\left(d x + c\right)^{5} + 70 \, a^{3} \cosh\left(d x + c\right)^{3} + 15 \, a^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 5 \, a^{3} \cosh\left(d x + c\right)^{2} + 10 \, {\left(21 \, a^{3} \cosh\left(d x + c\right)^{6} + 35 \, a^{3} \cosh\left(d x + c\right)^{4} + 15 \, a^{3} \cosh\left(d x + c\right)^{2} + a^{3}\right)} \sinh\left(d x + c\right)^{4} + 40 \, {\left(3 \, a^{3} \cosh\left(d x + c\right)^{7} + 7 \, a^{3} \cosh\left(d x + c\right)^{5} + 5 \, 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} + a^{3} + 5 \, {\left(9 \, a^{3} \cosh\left(d x + c\right)^{8} + 28 \, a^{3} \cosh\left(d x + c\right)^{6} + 30 \, a^{3} \cosh\left(d x + c\right)^{4} + 12 \, a^{3} \cosh\left(d x + c\right)^{2} + a^{3}\right)} \sinh\left(d x + c\right)^{2} + 10 \, {\left(a^{3} \cosh\left(d x + c\right)^{9} + 4 \, a^{3} \cosh\left(d x + c\right)^{7} + 6 \, a^{3} \cosh\left(d x + c\right)^{5} + 4 \, a^{3} \cosh\left(d x + c\right)^{3} + a^{3} \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(27 \, {\left(3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{8} + 28 \, {\left(9 \, a^{2} b + 6 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(135 \, a^{2} b + 75 \, a b^{2} + 29 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 9 \, a^{2} b + 9 \, a b^{2} + 3 \, b^{3} + 12 \, {\left(9 \, a^{2} b + 6 \, a b^{2} + 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)^{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*(30*(3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^9 + 270*(3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)*sinh(d*x + c)^8 + 30*(3*a^2*b + 3*a*b^2 + b^3)*sinh(d*x + c)^9 + 40*(9*a^2*b + 6*a*b^2 + b^3)*cosh(d*x + c)^7 + 40*(9*a^2*b + 6*a*b^2 + b^3 + 27*(3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^7 + 280*(9*(3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^3 + (9*a^2*b + 6*a*b^2 + b^3)*cosh(d*x + c))*sinh(d*x + c)^6 + 4*(135*a^2*b + 75*a*b^2 + 29*b^3)*cosh(d*x + c)^5 + 4*(945*(3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^4 + 135*a^2*b + 75*a*b^2 + 29*b^3 + 210*(9*a^2*b + 6*a*b^2 + b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 20*(189*(3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^5 + 70*(9*a^2*b + 6*a*b^2 + b^3)*cosh(d*x + c)^3 + (135*a^2*b + 75*a*b^2 + 29*b^3)*cosh(d*x + c))*sinh(d*x + c)^4 + 40*(9*a^2*b + 6*a*b^2 + b^3)*cosh(d*x + c)^3 + 40*(63*(3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^6 + 35*(9*a^2*b + 6*a*b^2 + b^3)*cosh(d*x + c)^4 + 9*a^2*b + 6*a*b^2 + b^3 + (135*a^2*b + 75*a*b^2 + 29*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 40*(27*(3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^7 + 21*(9*a^2*b + 6*a*b^2 + b^3)*cosh(d*x + c)^5 + (135*a^2*b + 75*a*b^2 + 29*b^3)*cosh(d*x + c)^3 + 3*(9*a^2*b + 6*a*b^2 + b^3)*cosh(d*x + c))*sinh(d*x + c)^2 + 30*(3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c) + 15*(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 + 5*a^3*cosh(d*x + c)^8 + 10*a^3*cosh(d*x + c)^6 + 5*(9*a^3*cosh(d*x + c)^2 + a^3)*sinh(d*x + c)^8 + 40*(3*a^3*cosh(d*x + c)^3 + a^3*cosh(d*x + c))*sinh(d*x + c)^7 + 10*a^3*cosh(d*x + c)^4 + 10*(21*a^3*cosh(d*x + c)^4 + 14*a^3*cosh(d*x + c)^2 + a^3)*sinh(d*x + c)^6 + 4*(63*a^3*cosh(d*x + c)^5 + 70*a^3*cosh(d*x + c)^3 + 15*a^3*cosh(d*x + c))*sinh(d*x + c)^5 + 5*a^3*cosh(d*x + c)^2 + 10*(21*a^3*cosh(d*x + c)^6 + 35*a^3*cosh(d*x + c)^4 + 15*a^3*cosh(d*x + c)^2 + a^3)*sinh(d*x + c)^4 + 40*(3*a^3*cosh(d*x + c)^7 + 7*a^3*cosh(d*x + c)^5 + 5*a^3*cosh(d*x + c)^3 + a^3*cosh(d*x + c))*sinh(d*x + c)^3 + a^3 + 5*(9*a^3*cosh(d*x + c)^8 + 28*a^3*cosh(d*x + c)^6 + 30*a^3*cosh(d*x + c)^4 + 12*a^3*cosh(d*x + c)^2 + a^3)*sinh(d*x + c)^2 + 10*(a^3*cosh(d*x + c)^9 + 4*a^3*cosh(d*x + c)^7 + 6*a^3*cosh(d*x + c)^5 + 4*a^3*cosh(d*x + c)^3 + a^3*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) + 1) - 15*(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 + 5*a^3*cosh(d*x + c)^8 + 10*a^3*cosh(d*x + c)^6 + 5*(9*a^3*cosh(d*x + c)^2 + a^3)*sinh(d*x + c)^8 + 40*(3*a^3*cosh(d*x + c)^3 + a^3*cosh(d*x + c))*sinh(d*x + c)^7 + 10*a^3*cosh(d*x + c)^4 + 10*(21*a^3*cosh(d*x + c)^4 + 14*a^3*cosh(d*x + c)^2 + a^3)*sinh(d*x + c)^6 + 4*(63*a^3*cosh(d*x + c)^5 + 70*a^3*cosh(d*x + c)^3 + 15*a^3*cosh(d*x + c))*sinh(d*x + c)^5 + 5*a^3*cosh(d*x + c)^2 + 10*(21*a^3*cosh(d*x + c)^6 + 35*a^3*cosh(d*x + c)^4 + 15*a^3*cosh(d*x + c)^2 + a^3)*sinh(d*x + c)^4 + 40*(3*a^3*cosh(d*x + c)^7 + 7*a^3*cosh(d*x + c)^5 + 5*a^3*cosh(d*x + c)^3 + a^3*cosh(d*x + c))*sinh(d*x + c)^3 + a^3 + 5*(9*a^3*cosh(d*x + c)^8 + 28*a^3*cosh(d*x + c)^6 + 30*a^3*cosh(d*x + c)^4 + 12*a^3*cosh(d*x + c)^2 + a^3)*sinh(d*x + c)^2 + 10*(a^3*cosh(d*x + c)^9 + 4*a^3*cosh(d*x + c)^7 + 6*a^3*cosh(d*x + c)^5 + 4*a^3*cosh(d*x + c)^3 + a^3*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) - 1) + 10*(27*(3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^8 + 28*(9*a^2*b + 6*a*b^2 + b^3)*cosh(d*x + c)^6 + 2*(135*a^2*b + 75*a*b^2 + 29*b^3)*cosh(d*x + c)^4 + 9*a^2*b + 9*a*b^2 + 3*b^3 + 12*(9*a^2*b + 6*a*b^2 + b^3)*cosh(d*x + c)^2)*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
22,1,572,0,0.487486," ","integrate(csch(d*x+c)^2*(a+b*tanh(d*x+c)^2)^3,x, algorithm=""fricas"")","-\frac{4 \, {\left({\left(5 \, a^{3} + 5 \, a b^{2} + 2 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(5 \, a^{3} + 5 \, a b^{2} + 2 \, b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} + {\left(15 \, a^{2} b + 10 \, a b^{2} + 3 \, b^{3}\right)} \sinh\left(d x + c\right)^{5} + {\left(25 \, a^{3} + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(45 \, a^{2} b + 10 \, a b^{2} - 3 \, b^{3} + 10 \, {\left(15 \, a^{2} b + 10 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + {\left(10 \, {\left(5 \, a^{3} + 5 \, a b^{2} + 2 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(25 \, a^{3} + 5 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 10 \, {\left(5 \, a^{3} - a b^{2}\right)} \cosh\left(d x + c\right) + {\left(5 \, {\left(15 \, a^{2} b + 10 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 30 \, a^{2} b + 10 \, b^{3} + 3 \, {\left(45 \, a^{2} b + 10 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)\right)}}{5 \, {\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} + 3 \, 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} + 3 \, 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} + 50 \, d \cosh\left(d x + c\right)^{2} + 9 \, d\right)} \sinh\left(d x + c\right)^{3} + 3 \, {\left(7 \, d \cosh\left(d x + c\right)^{5} + 10 \, d \cosh\left(d x + c\right)^{3} + d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 5 \, 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,"-4/5*((5*a^3 + 5*a*b^2 + 2*b^3)*cosh(d*x + c)^5 + 5*(5*a^3 + 5*a*b^2 + 2*b^3)*cosh(d*x + c)*sinh(d*x + c)^4 + (15*a^2*b + 10*a*b^2 + 3*b^3)*sinh(d*x + c)^5 + (25*a^3 + 5*a*b^2 - 2*b^3)*cosh(d*x + c)^3 + (45*a^2*b + 10*a*b^2 - 3*b^3 + 10*(15*a^2*b + 10*a*b^2 + 3*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + (10*(5*a^3 + 5*a*b^2 + 2*b^3)*cosh(d*x + c)^3 + 3*(25*a^3 + 5*a*b^2 - 2*b^3)*cosh(d*x + c))*sinh(d*x + c)^2 + 10*(5*a^3 - a*b^2)*cosh(d*x + c) + (5*(15*a^2*b + 10*a*b^2 + 3*b^3)*cosh(d*x + c)^4 + 30*a^2*b + 10*b^3 + 3*(45*a^2*b + 10*a*b^2 - 3*b^3)*cosh(d*x + c)^2)*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 + 3*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 + 3*d*cosh(d*x + c))*sinh(d*x + c)^4 + 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 + 3*(7*d*cosh(d*x + c)^5 + 10*d*cosh(d*x + c)^3 + d*cosh(d*x + c))*sinh(d*x + c)^2 - 5*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
23,1,5037,0,0.966948," ","integrate(csch(d*x+c)^3*(a+b*tanh(d*x+c)^2)^3,x, algorithm=""fricas"")","-\frac{30 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{13} + 390 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{12} + 30 \, {\left(a^{3} - 6 \, a^{2} b\right)} \sinh\left(d x + c\right)^{13} + 20 \, {\left(9 \, a^{3} - 18 \, a^{2} b + 12 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} + 20 \, {\left(9 \, a^{3} - 18 \, a^{2} b + 12 \, a b^{2} + 4 \, b^{3} + 117 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{11} + 220 \, {\left(39 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{3} + {\left(9 \, a^{3} - 18 \, a^{2} b + 12 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{10} + 6 \, {\left(75 \, a^{3} + 30 \, a^{2} b - 32 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + 2 \, {\left(10725 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{4} + 225 \, a^{3} + 90 \, a^{2} b - 96 \, b^{3} + 550 \, {\left(9 \, a^{3} - 18 \, a^{2} b + 12 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{9} + 6 \, {\left(6435 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{5} + 550 \, {\left(9 \, a^{3} - 18 \, a^{2} b + 12 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 9 \, {\left(75 \, a^{3} + 30 \, a^{2} b - 32 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{8} + 8 \, {\left(75 \, a^{3} + 90 \, a^{2} b - 60 \, a b^{2} + 28 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 8 \, {\left(6435 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{6} + 825 \, {\left(9 \, a^{3} - 18 \, a^{2} b + 12 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 75 \, a^{3} + 90 \, a^{2} b - 60 \, a b^{2} + 28 \, b^{3} + 27 \, {\left(75 \, a^{3} + 30 \, a^{2} b - 32 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{7} + 8 \, {\left(6435 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{7} + 1155 \, {\left(9 \, a^{3} - 18 \, a^{2} b + 12 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 63 \, {\left(75 \, a^{3} + 30 \, a^{2} b - 32 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 7 \, {\left(75 \, a^{3} + 90 \, a^{2} b - 60 \, a b^{2} + 28 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} + 6 \, {\left(75 \, a^{3} + 30 \, a^{2} b - 32 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 6 \, {\left(6435 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{8} + 1540 \, {\left(9 \, a^{3} - 18 \, a^{2} b + 12 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 126 \, {\left(75 \, a^{3} + 30 \, a^{2} b - 32 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 75 \, a^{3} + 30 \, a^{2} b - 32 \, b^{3} + 28 \, {\left(75 \, a^{3} + 90 \, a^{2} b - 60 \, a b^{2} + 28 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(10725 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{9} + 3300 \, {\left(9 \, a^{3} - 18 \, a^{2} b + 12 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 378 \, {\left(75 \, a^{3} + 30 \, a^{2} b - 32 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 140 \, {\left(75 \, a^{3} + 90 \, a^{2} b - 60 \, a b^{2} + 28 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 15 \, {\left(75 \, a^{3} + 30 \, a^{2} b - 32 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 20 \, {\left(9 \, a^{3} - 18 \, a^{2} b + 12 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(2145 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{10} + 825 \, {\left(9 \, a^{3} - 18 \, a^{2} b + 12 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 126 \, {\left(75 \, a^{3} + 30 \, a^{2} b - 32 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 70 \, {\left(75 \, a^{3} + 90 \, a^{2} b - 60 \, a b^{2} + 28 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 45 \, a^{3} - 90 \, a^{2} b + 60 \, a b^{2} + 20 \, b^{3} + 15 \, {\left(75 \, a^{3} + 30 \, a^{2} b - 32 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(585 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{11} + 275 \, {\left(9 \, a^{3} - 18 \, a^{2} b + 12 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + 54 \, {\left(75 \, a^{3} + 30 \, a^{2} b - 32 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 42 \, {\left(75 \, a^{3} + 90 \, a^{2} b - 60 \, a b^{2} + 28 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 15 \, {\left(75 \, a^{3} + 30 \, a^{2} b - 32 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 15 \, {\left(9 \, a^{3} - 18 \, a^{2} b + 12 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 30 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right) - 15 \, {\left({\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{14} + 14 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{13} + {\left(a^{3} - 6 \, a^{2} b\right)} \sinh\left(d x + c\right)^{14} + 3 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{12} + {\left(3 \, a^{3} - 18 \, a^{2} b + 91 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{12} + 4 \, {\left(91 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{3} + 9 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{11} + {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{10} + {\left(1001 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{4} + a^{3} - 6 \, a^{2} b + 198 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{10} + 2 \, {\left(1001 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{5} + 330 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{3} + 5 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} - 5 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{8} + {\left(3003 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{6} + 1485 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{4} - 5 \, a^{3} + 30 \, a^{2} b + 45 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{8} + 8 \, {\left(429 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{7} + 297 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{5} + 15 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{3} - 5 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} - 5 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{6} + {\left(3003 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{8} + 2772 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{6} + 210 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{4} - 5 \, a^{3} + 30 \, a^{2} b - 140 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(1001 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{9} + 1188 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{7} + 126 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{5} - 140 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{3} - 15 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{4} + {\left(1001 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{10} + 1485 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{8} + 210 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{6} - 350 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{4} + a^{3} - 6 \, a^{2} b - 75 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(91 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{11} + 165 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{9} + 30 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{7} - 70 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{5} - 25 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + a^{3} - 6 \, a^{2} b + 3 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{2} + {\left(91 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{12} + 198 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{10} + 45 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{8} - 140 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{6} - 75 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{4} + 3 \, a^{3} - 18 \, a^{2} b + 6 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(7 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{13} + 18 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{11} + 5 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{9} - 20 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{7} - 15 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\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)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) + 15 \, {\left({\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{14} + 14 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{13} + {\left(a^{3} - 6 \, a^{2} b\right)} \sinh\left(d x + c\right)^{14} + 3 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{12} + {\left(3 \, a^{3} - 18 \, a^{2} b + 91 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{12} + 4 \, {\left(91 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{3} + 9 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{11} + {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{10} + {\left(1001 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{4} + a^{3} - 6 \, a^{2} b + 198 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{10} + 2 \, {\left(1001 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{5} + 330 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{3} + 5 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} - 5 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{8} + {\left(3003 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{6} + 1485 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{4} - 5 \, a^{3} + 30 \, a^{2} b + 45 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{8} + 8 \, {\left(429 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{7} + 297 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{5} + 15 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{3} - 5 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} - 5 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{6} + {\left(3003 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{8} + 2772 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{6} + 210 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{4} - 5 \, a^{3} + 30 \, a^{2} b - 140 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(1001 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{9} + 1188 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{7} + 126 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{5} - 140 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{3} - 15 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{4} + {\left(1001 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{10} + 1485 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{8} + 210 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{6} - 350 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{4} + a^{3} - 6 \, a^{2} b - 75 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(91 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{11} + 165 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{9} + 30 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{7} - 70 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{5} - 25 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + a^{3} - 6 \, a^{2} b + 3 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{2} + {\left(91 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{12} + 198 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{10} + 45 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{8} - 140 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{6} - 75 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{4} + 3 \, a^{3} - 18 \, a^{2} b + 6 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(7 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{13} + 18 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{11} + 5 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{9} - 20 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{7} - 15 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\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)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) + 2 \, {\left(195 \, {\left(a^{3} - 6 \, a^{2} b\right)} \cosh\left(d x + c\right)^{12} + 110 \, {\left(9 \, a^{3} - 18 \, a^{2} b + 12 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} + 27 \, {\left(75 \, a^{3} + 30 \, a^{2} b - 32 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 28 \, {\left(75 \, a^{3} + 90 \, a^{2} b - 60 \, a b^{2} + 28 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(75 \, a^{3} + 30 \, a^{2} b - 32 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 15 \, a^{3} - 90 \, a^{2} b + 30 \, {\left(9 \, a^{3} - 18 \, a^{2} b + 12 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)}{30 \, {\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} + 3 \, d \cosh\left(d x + c\right)^{12} + {\left(91 \, d \cosh\left(d x + c\right)^{2} + 3 \, d\right)} \sinh\left(d x + c\right)^{12} + 4 \, {\left(91 \, d \cosh\left(d x + c\right)^{3} + 9 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{11} + d \cosh\left(d x + c\right)^{10} + {\left(1001 \, d \cosh\left(d x + c\right)^{4} + 198 \, d \cosh\left(d x + c\right)^{2} + d\right)} \sinh\left(d x + c\right)^{10} + 2 \, {\left(1001 \, d \cosh\left(d x + c\right)^{5} + 330 \, d \cosh\left(d x + c\right)^{3} + 5 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} - 5 \, d \cosh\left(d x + c\right)^{8} + {\left(3003 \, d \cosh\left(d x + c\right)^{6} + 1485 \, d \cosh\left(d x + c\right)^{4} + 45 \, d \cosh\left(d x + c\right)^{2} - 5 \, d\right)} \sinh\left(d x + c\right)^{8} + 8 \, {\left(429 \, d \cosh\left(d x + c\right)^{7} + 297 \, d \cosh\left(d x + c\right)^{5} + 15 \, d \cosh\left(d x + c\right)^{3} - 5 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} - 5 \, d \cosh\left(d x + c\right)^{6} + {\left(3003 \, d \cosh\left(d x + c\right)^{8} + 2772 \, d \cosh\left(d x + c\right)^{6} + 210 \, 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)^{6} + 2 \, {\left(1001 \, d \cosh\left(d x + c\right)^{9} + 1188 \, d \cosh\left(d x + c\right)^{7} + 126 \, 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)^{5} + d \cosh\left(d x + c\right)^{4} + {\left(1001 \, d \cosh\left(d x + c\right)^{10} + 1485 \, d \cosh\left(d x + c\right)^{8} + 210 \, 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} + d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(91 \, d \cosh\left(d x + c\right)^{11} + 165 \, d \cosh\left(d x + c\right)^{9} + 30 \, 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} + d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 3 \, d \cosh\left(d x + c\right)^{2} + {\left(91 \, d \cosh\left(d x + c\right)^{12} + 198 \, d \cosh\left(d x + c\right)^{10} + 45 \, 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} + 6 \, d \cosh\left(d x + c\right)^{2} + 3 \, d\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(7 \, d \cosh\left(d x + c\right)^{13} + 18 \, d \cosh\left(d x + c\right)^{11} + 5 \, d \cosh\left(d x + c\right)^{9} - 20 \, d \cosh\left(d x + c\right)^{7} - 15 \, d \cosh\left(d x + c\right)^{5} + 2 \, d \cosh\left(d x + c\right)^{3} + 3 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + d\right)}}"," ",0,"-1/30*(30*(a^3 - 6*a^2*b)*cosh(d*x + c)^13 + 390*(a^3 - 6*a^2*b)*cosh(d*x + c)*sinh(d*x + c)^12 + 30*(a^3 - 6*a^2*b)*sinh(d*x + c)^13 + 20*(9*a^3 - 18*a^2*b + 12*a*b^2 + 4*b^3)*cosh(d*x + c)^11 + 20*(9*a^3 - 18*a^2*b + 12*a*b^2 + 4*b^3 + 117*(a^3 - 6*a^2*b)*cosh(d*x + c)^2)*sinh(d*x + c)^11 + 220*(39*(a^3 - 6*a^2*b)*cosh(d*x + c)^3 + (9*a^3 - 18*a^2*b + 12*a*b^2 + 4*b^3)*cosh(d*x + c))*sinh(d*x + c)^10 + 6*(75*a^3 + 30*a^2*b - 32*b^3)*cosh(d*x + c)^9 + 2*(10725*(a^3 - 6*a^2*b)*cosh(d*x + c)^4 + 225*a^3 + 90*a^2*b - 96*b^3 + 550*(9*a^3 - 18*a^2*b + 12*a*b^2 + 4*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^9 + 6*(6435*(a^3 - 6*a^2*b)*cosh(d*x + c)^5 + 550*(9*a^3 - 18*a^2*b + 12*a*b^2 + 4*b^3)*cosh(d*x + c)^3 + 9*(75*a^3 + 30*a^2*b - 32*b^3)*cosh(d*x + c))*sinh(d*x + c)^8 + 8*(75*a^3 + 90*a^2*b - 60*a*b^2 + 28*b^3)*cosh(d*x + c)^7 + 8*(6435*(a^3 - 6*a^2*b)*cosh(d*x + c)^6 + 825*(9*a^3 - 18*a^2*b + 12*a*b^2 + 4*b^3)*cosh(d*x + c)^4 + 75*a^3 + 90*a^2*b - 60*a*b^2 + 28*b^3 + 27*(75*a^3 + 30*a^2*b - 32*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^7 + 8*(6435*(a^3 - 6*a^2*b)*cosh(d*x + c)^7 + 1155*(9*a^3 - 18*a^2*b + 12*a*b^2 + 4*b^3)*cosh(d*x + c)^5 + 63*(75*a^3 + 30*a^2*b - 32*b^3)*cosh(d*x + c)^3 + 7*(75*a^3 + 90*a^2*b - 60*a*b^2 + 28*b^3)*cosh(d*x + c))*sinh(d*x + c)^6 + 6*(75*a^3 + 30*a^2*b - 32*b^3)*cosh(d*x + c)^5 + 6*(6435*(a^3 - 6*a^2*b)*cosh(d*x + c)^8 + 1540*(9*a^3 - 18*a^2*b + 12*a*b^2 + 4*b^3)*cosh(d*x + c)^6 + 126*(75*a^3 + 30*a^2*b - 32*b^3)*cosh(d*x + c)^4 + 75*a^3 + 30*a^2*b - 32*b^3 + 28*(75*a^3 + 90*a^2*b - 60*a*b^2 + 28*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 2*(10725*(a^3 - 6*a^2*b)*cosh(d*x + c)^9 + 3300*(9*a^3 - 18*a^2*b + 12*a*b^2 + 4*b^3)*cosh(d*x + c)^7 + 378*(75*a^3 + 30*a^2*b - 32*b^3)*cosh(d*x + c)^5 + 140*(75*a^3 + 90*a^2*b - 60*a*b^2 + 28*b^3)*cosh(d*x + c)^3 + 15*(75*a^3 + 30*a^2*b - 32*b^3)*cosh(d*x + c))*sinh(d*x + c)^4 + 20*(9*a^3 - 18*a^2*b + 12*a*b^2 + 4*b^3)*cosh(d*x + c)^3 + 4*(2145*(a^3 - 6*a^2*b)*cosh(d*x + c)^10 + 825*(9*a^3 - 18*a^2*b + 12*a*b^2 + 4*b^3)*cosh(d*x + c)^8 + 126*(75*a^3 + 30*a^2*b - 32*b^3)*cosh(d*x + c)^6 + 70*(75*a^3 + 90*a^2*b - 60*a*b^2 + 28*b^3)*cosh(d*x + c)^4 + 45*a^3 - 90*a^2*b + 60*a*b^2 + 20*b^3 + 15*(75*a^3 + 30*a^2*b - 32*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 4*(585*(a^3 - 6*a^2*b)*cosh(d*x + c)^11 + 275*(9*a^3 - 18*a^2*b + 12*a*b^2 + 4*b^3)*cosh(d*x + c)^9 + 54*(75*a^3 + 30*a^2*b - 32*b^3)*cosh(d*x + c)^7 + 42*(75*a^3 + 90*a^2*b - 60*a*b^2 + 28*b^3)*cosh(d*x + c)^5 + 15*(75*a^3 + 30*a^2*b - 32*b^3)*cosh(d*x + c)^3 + 15*(9*a^3 - 18*a^2*b + 12*a*b^2 + 4*b^3)*cosh(d*x + c))*sinh(d*x + c)^2 + 30*(a^3 - 6*a^2*b)*cosh(d*x + c) - 15*((a^3 - 6*a^2*b)*cosh(d*x + c)^14 + 14*(a^3 - 6*a^2*b)*cosh(d*x + c)*sinh(d*x + c)^13 + (a^3 - 6*a^2*b)*sinh(d*x + c)^14 + 3*(a^3 - 6*a^2*b)*cosh(d*x + c)^12 + (3*a^3 - 18*a^2*b + 91*(a^3 - 6*a^2*b)*cosh(d*x + c)^2)*sinh(d*x + c)^12 + 4*(91*(a^3 - 6*a^2*b)*cosh(d*x + c)^3 + 9*(a^3 - 6*a^2*b)*cosh(d*x + c))*sinh(d*x + c)^11 + (a^3 - 6*a^2*b)*cosh(d*x + c)^10 + (1001*(a^3 - 6*a^2*b)*cosh(d*x + c)^4 + a^3 - 6*a^2*b + 198*(a^3 - 6*a^2*b)*cosh(d*x + c)^2)*sinh(d*x + c)^10 + 2*(1001*(a^3 - 6*a^2*b)*cosh(d*x + c)^5 + 330*(a^3 - 6*a^2*b)*cosh(d*x + c)^3 + 5*(a^3 - 6*a^2*b)*cosh(d*x + c))*sinh(d*x + c)^9 - 5*(a^3 - 6*a^2*b)*cosh(d*x + c)^8 + (3003*(a^3 - 6*a^2*b)*cosh(d*x + c)^6 + 1485*(a^3 - 6*a^2*b)*cosh(d*x + c)^4 - 5*a^3 + 30*a^2*b + 45*(a^3 - 6*a^2*b)*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 8*(429*(a^3 - 6*a^2*b)*cosh(d*x + c)^7 + 297*(a^3 - 6*a^2*b)*cosh(d*x + c)^5 + 15*(a^3 - 6*a^2*b)*cosh(d*x + c)^3 - 5*(a^3 - 6*a^2*b)*cosh(d*x + c))*sinh(d*x + c)^7 - 5*(a^3 - 6*a^2*b)*cosh(d*x + c)^6 + (3003*(a^3 - 6*a^2*b)*cosh(d*x + c)^8 + 2772*(a^3 - 6*a^2*b)*cosh(d*x + c)^6 + 210*(a^3 - 6*a^2*b)*cosh(d*x + c)^4 - 5*a^3 + 30*a^2*b - 140*(a^3 - 6*a^2*b)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 2*(1001*(a^3 - 6*a^2*b)*cosh(d*x + c)^9 + 1188*(a^3 - 6*a^2*b)*cosh(d*x + c)^7 + 126*(a^3 - 6*a^2*b)*cosh(d*x + c)^5 - 140*(a^3 - 6*a^2*b)*cosh(d*x + c)^3 - 15*(a^3 - 6*a^2*b)*cosh(d*x + c))*sinh(d*x + c)^5 + (a^3 - 6*a^2*b)*cosh(d*x + c)^4 + (1001*(a^3 - 6*a^2*b)*cosh(d*x + c)^10 + 1485*(a^3 - 6*a^2*b)*cosh(d*x + c)^8 + 210*(a^3 - 6*a^2*b)*cosh(d*x + c)^6 - 350*(a^3 - 6*a^2*b)*cosh(d*x + c)^4 + a^3 - 6*a^2*b - 75*(a^3 - 6*a^2*b)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 4*(91*(a^3 - 6*a^2*b)*cosh(d*x + c)^11 + 165*(a^3 - 6*a^2*b)*cosh(d*x + c)^9 + 30*(a^3 - 6*a^2*b)*cosh(d*x + c)^7 - 70*(a^3 - 6*a^2*b)*cosh(d*x + c)^5 - 25*(a^3 - 6*a^2*b)*cosh(d*x + c)^3 + (a^3 - 6*a^2*b)*cosh(d*x + c))*sinh(d*x + c)^3 + a^3 - 6*a^2*b + 3*(a^3 - 6*a^2*b)*cosh(d*x + c)^2 + (91*(a^3 - 6*a^2*b)*cosh(d*x + c)^12 + 198*(a^3 - 6*a^2*b)*cosh(d*x + c)^10 + 45*(a^3 - 6*a^2*b)*cosh(d*x + c)^8 - 140*(a^3 - 6*a^2*b)*cosh(d*x + c)^6 - 75*(a^3 - 6*a^2*b)*cosh(d*x + c)^4 + 3*a^3 - 18*a^2*b + 6*(a^3 - 6*a^2*b)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 2*(7*(a^3 - 6*a^2*b)*cosh(d*x + c)^13 + 18*(a^3 - 6*a^2*b)*cosh(d*x + c)^11 + 5*(a^3 - 6*a^2*b)*cosh(d*x + c)^9 - 20*(a^3 - 6*a^2*b)*cosh(d*x + c)^7 - 15*(a^3 - 6*a^2*b)*cosh(d*x + c)^5 + 2*(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))*log(cosh(d*x + c) + sinh(d*x + c) + 1) + 15*((a^3 - 6*a^2*b)*cosh(d*x + c)^14 + 14*(a^3 - 6*a^2*b)*cosh(d*x + c)*sinh(d*x + c)^13 + (a^3 - 6*a^2*b)*sinh(d*x + c)^14 + 3*(a^3 - 6*a^2*b)*cosh(d*x + c)^12 + (3*a^3 - 18*a^2*b + 91*(a^3 - 6*a^2*b)*cosh(d*x + c)^2)*sinh(d*x + c)^12 + 4*(91*(a^3 - 6*a^2*b)*cosh(d*x + c)^3 + 9*(a^3 - 6*a^2*b)*cosh(d*x + c))*sinh(d*x + c)^11 + (a^3 - 6*a^2*b)*cosh(d*x + c)^10 + (1001*(a^3 - 6*a^2*b)*cosh(d*x + c)^4 + a^3 - 6*a^2*b + 198*(a^3 - 6*a^2*b)*cosh(d*x + c)^2)*sinh(d*x + c)^10 + 2*(1001*(a^3 - 6*a^2*b)*cosh(d*x + c)^5 + 330*(a^3 - 6*a^2*b)*cosh(d*x + c)^3 + 5*(a^3 - 6*a^2*b)*cosh(d*x + c))*sinh(d*x + c)^9 - 5*(a^3 - 6*a^2*b)*cosh(d*x + c)^8 + (3003*(a^3 - 6*a^2*b)*cosh(d*x + c)^6 + 1485*(a^3 - 6*a^2*b)*cosh(d*x + c)^4 - 5*a^3 + 30*a^2*b + 45*(a^3 - 6*a^2*b)*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 8*(429*(a^3 - 6*a^2*b)*cosh(d*x + c)^7 + 297*(a^3 - 6*a^2*b)*cosh(d*x + c)^5 + 15*(a^3 - 6*a^2*b)*cosh(d*x + c)^3 - 5*(a^3 - 6*a^2*b)*cosh(d*x + c))*sinh(d*x + c)^7 - 5*(a^3 - 6*a^2*b)*cosh(d*x + c)^6 + (3003*(a^3 - 6*a^2*b)*cosh(d*x + c)^8 + 2772*(a^3 - 6*a^2*b)*cosh(d*x + c)^6 + 210*(a^3 - 6*a^2*b)*cosh(d*x + c)^4 - 5*a^3 + 30*a^2*b - 140*(a^3 - 6*a^2*b)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 2*(1001*(a^3 - 6*a^2*b)*cosh(d*x + c)^9 + 1188*(a^3 - 6*a^2*b)*cosh(d*x + c)^7 + 126*(a^3 - 6*a^2*b)*cosh(d*x + c)^5 - 140*(a^3 - 6*a^2*b)*cosh(d*x + c)^3 - 15*(a^3 - 6*a^2*b)*cosh(d*x + c))*sinh(d*x + c)^5 + (a^3 - 6*a^2*b)*cosh(d*x + c)^4 + (1001*(a^3 - 6*a^2*b)*cosh(d*x + c)^10 + 1485*(a^3 - 6*a^2*b)*cosh(d*x + c)^8 + 210*(a^3 - 6*a^2*b)*cosh(d*x + c)^6 - 350*(a^3 - 6*a^2*b)*cosh(d*x + c)^4 + a^3 - 6*a^2*b - 75*(a^3 - 6*a^2*b)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 4*(91*(a^3 - 6*a^2*b)*cosh(d*x + c)^11 + 165*(a^3 - 6*a^2*b)*cosh(d*x + c)^9 + 30*(a^3 - 6*a^2*b)*cosh(d*x + c)^7 - 70*(a^3 - 6*a^2*b)*cosh(d*x + c)^5 - 25*(a^3 - 6*a^2*b)*cosh(d*x + c)^3 + (a^3 - 6*a^2*b)*cosh(d*x + c))*sinh(d*x + c)^3 + a^3 - 6*a^2*b + 3*(a^3 - 6*a^2*b)*cosh(d*x + c)^2 + (91*(a^3 - 6*a^2*b)*cosh(d*x + c)^12 + 198*(a^3 - 6*a^2*b)*cosh(d*x + c)^10 + 45*(a^3 - 6*a^2*b)*cosh(d*x + c)^8 - 140*(a^3 - 6*a^2*b)*cosh(d*x + c)^6 - 75*(a^3 - 6*a^2*b)*cosh(d*x + c)^4 + 3*a^3 - 18*a^2*b + 6*(a^3 - 6*a^2*b)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 2*(7*(a^3 - 6*a^2*b)*cosh(d*x + c)^13 + 18*(a^3 - 6*a^2*b)*cosh(d*x + c)^11 + 5*(a^3 - 6*a^2*b)*cosh(d*x + c)^9 - 20*(a^3 - 6*a^2*b)*cosh(d*x + c)^7 - 15*(a^3 - 6*a^2*b)*cosh(d*x + c)^5 + 2*(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))*log(cosh(d*x + c) + sinh(d*x + c) - 1) + 2*(195*(a^3 - 6*a^2*b)*cosh(d*x + c)^12 + 110*(9*a^3 - 18*a^2*b + 12*a*b^2 + 4*b^3)*cosh(d*x + c)^10 + 27*(75*a^3 + 30*a^2*b - 32*b^3)*cosh(d*x + c)^8 + 28*(75*a^3 + 90*a^2*b - 60*a*b^2 + 28*b^3)*cosh(d*x + c)^6 + 15*(75*a^3 + 30*a^2*b - 32*b^3)*cosh(d*x + c)^4 + 15*a^3 - 90*a^2*b + 30*(9*a^3 - 18*a^2*b + 12*a*b^2 + 4*b^3)*cosh(d*x + c)^2)*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 + 3*d*cosh(d*x + c)^12 + (91*d*cosh(d*x + c)^2 + 3*d)*sinh(d*x + c)^12 + 4*(91*d*cosh(d*x + c)^3 + 9*d*cosh(d*x + c))*sinh(d*x + c)^11 + d*cosh(d*x + c)^10 + (1001*d*cosh(d*x + c)^4 + 198*d*cosh(d*x + c)^2 + d)*sinh(d*x + c)^10 + 2*(1001*d*cosh(d*x + c)^5 + 330*d*cosh(d*x + c)^3 + 5*d*cosh(d*x + c))*sinh(d*x + c)^9 - 5*d*cosh(d*x + c)^8 + (3003*d*cosh(d*x + c)^6 + 1485*d*cosh(d*x + c)^4 + 45*d*cosh(d*x + c)^2 - 5*d)*sinh(d*x + c)^8 + 8*(429*d*cosh(d*x + c)^7 + 297*d*cosh(d*x + c)^5 + 15*d*cosh(d*x + c)^3 - 5*d*cosh(d*x + c))*sinh(d*x + c)^7 - 5*d*cosh(d*x + c)^6 + (3003*d*cosh(d*x + c)^8 + 2772*d*cosh(d*x + c)^6 + 210*d*cosh(d*x + c)^4 - 140*d*cosh(d*x + c)^2 - 5*d)*sinh(d*x + c)^6 + 2*(1001*d*cosh(d*x + c)^9 + 1188*d*cosh(d*x + c)^7 + 126*d*cosh(d*x + c)^5 - 140*d*cosh(d*x + c)^3 - 15*d*cosh(d*x + c))*sinh(d*x + c)^5 + d*cosh(d*x + c)^4 + (1001*d*cosh(d*x + c)^10 + 1485*d*cosh(d*x + c)^8 + 210*d*cosh(d*x + c)^6 - 350*d*cosh(d*x + c)^4 - 75*d*cosh(d*x + c)^2 + d)*sinh(d*x + c)^4 + 4*(91*d*cosh(d*x + c)^11 + 165*d*cosh(d*x + c)^9 + 30*d*cosh(d*x + c)^7 - 70*d*cosh(d*x + c)^5 - 25*d*cosh(d*x + c)^3 + d*cosh(d*x + c))*sinh(d*x + c)^3 + 3*d*cosh(d*x + c)^2 + (91*d*cosh(d*x + c)^12 + 198*d*cosh(d*x + c)^10 + 45*d*cosh(d*x + c)^8 - 140*d*cosh(d*x + c)^6 - 75*d*cosh(d*x + c)^4 + 6*d*cosh(d*x + c)^2 + 3*d)*sinh(d*x + c)^2 + 2*(7*d*cosh(d*x + c)^13 + 18*d*cosh(d*x + c)^11 + 5*d*cosh(d*x + c)^9 - 20*d*cosh(d*x + c)^7 - 15*d*cosh(d*x + c)^5 + 2*d*cosh(d*x + c)^3 + 3*d*cosh(d*x + c))*sinh(d*x + c) + d)","B",0
24,1,925,0,0.594409," ","integrate(csch(d*x+c)^4*(a+b*tanh(d*x+c)^2)^3,x, algorithm=""fricas"")","-\frac{8 \, {\left({\left(5 \, a^{3} + 45 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 12 \, {\left(5 \, a^{3} + 15 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(5 \, a^{3} + 45 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(15 \, a^{3} + 45 \, a^{2} b - 15 \, a b^{2} - 13 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + {\left(30 \, a^{3} + 90 \, a^{2} b - 30 \, a b^{2} - 26 \, b^{3} + 15 \, {\left(5 \, a^{3} + 45 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(5 \, {\left(5 \, a^{3} + 15 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(5 \, a^{3} - 3 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 50 \, a^{3} - 90 \, a^{2} b + 30 \, a b^{2} - 22 \, b^{3} + {\left(75 \, a^{3} - 45 \, a^{2} b - 15 \, a b^{2} + 41 \, b^{3}\right)} \cosh\left(d x + c\right)^{2} + {\left(15 \, {\left(5 \, a^{3} + 45 \, a^{2} b + 15 \, a b^{2} + 7 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 75 \, a^{3} - 45 \, a^{2} b - 15 \, a b^{2} + 41 \, b^{3} + 12 \, {\left(15 \, a^{3} + 45 \, a^{2} b - 15 \, a b^{2} - 13 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(3 \, {\left(5 \, a^{3} + 15 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 8 \, {\left(5 \, a^{3} - 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(25 \, a^{3} - 45 \, a b^{2} + 12 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\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} + 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} - 3 \, 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} - 3 \, 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} - 8 \, d \cosh\left(d x + c\right)^{4} + {\left(210 \, d \cosh\left(d x + c\right)^{6} + 140 \, d \cosh\left(d x + c\right)^{4} - 45 \, d \cosh\left(d x + c\right)^{2} - 8 \, d\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} - 4 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 2 \, d \cosh\left(d x + c\right)^{2} + {\left(45 \, d \cosh\left(d x + c\right)^{8} + 56 \, d \cosh\left(d x + c\right)^{6} - 45 \, d \cosh\left(d x + c\right)^{4} - 48 \, d \cosh\left(d x + c\right)^{2} + 2 \, d\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} - 8 \, d \cosh\left(d x + c\right)^{3} - 2 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + 6 \, d\right)}}"," ",0,"-8/15*((5*a^3 + 45*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^6 + 12*(5*a^3 + 15*a*b^2 + 4*b^3)*cosh(d*x + c)*sinh(d*x + c)^5 + (5*a^3 + 45*a^2*b + 15*a*b^2 + 7*b^3)*sinh(d*x + c)^6 + 2*(15*a^3 + 45*a^2*b - 15*a*b^2 - 13*b^3)*cosh(d*x + c)^4 + (30*a^3 + 90*a^2*b - 30*a*b^2 - 26*b^3 + 15*(5*a^3 + 45*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(5*(5*a^3 + 15*a*b^2 + 4*b^3)*cosh(d*x + c)^3 + 4*(5*a^3 - 3*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 + 50*a^3 - 90*a^2*b + 30*a*b^2 - 22*b^3 + (75*a^3 - 45*a^2*b - 15*a*b^2 + 41*b^3)*cosh(d*x + c)^2 + (15*(5*a^3 + 45*a^2*b + 15*a*b^2 + 7*b^3)*cosh(d*x + c)^4 + 75*a^3 - 45*a^2*b - 15*a*b^2 + 41*b^3 + 12*(15*a^3 + 45*a^2*b - 15*a*b^2 - 13*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*(3*(5*a^3 + 15*a*b^2 + 4*b^3)*cosh(d*x + c)^5 + 8*(5*a^3 - 3*b^3)*cosh(d*x + c)^3 + (25*a^3 - 45*a*b^2 + 12*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 - 3*d*cosh(d*x + c)^6 + (210*d*cosh(d*x + c)^4 + 56*d*cosh(d*x + c)^2 - 3*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 - 8*d*cosh(d*x + c)^4 + (210*d*cosh(d*x + c)^6 + 140*d*cosh(d*x + c)^4 - 45*d*cosh(d*x + c)^2 - 8*d)*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 - 4*d*cosh(d*x + c))*sinh(d*x + c)^3 + 2*d*cosh(d*x + c)^2 + (45*d*cosh(d*x + c)^8 + 56*d*cosh(d*x + c)^6 - 45*d*cosh(d*x + c)^4 - 48*d*cosh(d*x + c)^2 + 2*d)*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 - 8*d*cosh(d*x + c)^3 - 2*d*cosh(d*x + c))*sinh(d*x + c) + 6*d)","B",0
25,1,2024,0,0.801620," ","integrate(sinh(d*x+c)^4/(a+b*tanh(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{{\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{8} + 8 \, {\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} d x \cosh\left(d x + c\right)^{4} - 8 \, {\left(a^{2} + a b\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, a^{2} - 2 \, a b\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} - 6 \, {\left(a^{2} + a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} d x - 60 \, {\left(a^{2} + a b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{5} + 4 \, {\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} d x \cosh\left(d x + c\right) - 20 \, {\left(a^{2} + a b\right)} \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right)^{3} + 8 \, {\left(a^{2} + a b\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{6} + 12 \, {\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} d x \cosh\left(d x + c\right)^{2} - 30 \, {\left(a^{2} + a b\right)} \cosh\left(d x + c\right)^{4} + 2 \, a^{2} + 2 \, a b\right)} \sinh\left(d x + c\right)^{2} + 32 \, {\left(a \cosh\left(d x + c\right)^{4} + 4 \, a \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, a \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a \sinh\left(d x + c\right)^{4}\right)} \sqrt{-a b} \log\left(\frac{{\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) \sinh\left(d x + c\right)^{3} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{2} + a^{2} - 6 \, a b + b^{2} + 4 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} - b^{2}\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)^{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} + a - b\right)} \sqrt{-a b}}{{\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) - a^{2} - 2 \, a b - b^{2} + 8 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{7} + 4 \, {\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} d x \cosh\left(d x + c\right)^{3} - 6 \, {\left(a^{2} + a b\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(a^{2} + a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{64 \, {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d \cosh\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)^{3} \sinh\left(d x + c\right) + 6 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, {\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)^{3} + {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d \sinh\left(d x + c\right)^{4}\right)}}, \frac{{\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{8} + 8 \, {\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} d x \cosh\left(d x + c\right)^{4} - 8 \, {\left(a^{2} + a b\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, a^{2} - 2 \, a b\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} - 6 \, {\left(a^{2} + a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} d x - 60 \, {\left(a^{2} + a b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{5} + 4 \, {\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} d x \cosh\left(d x + c\right) - 20 \, {\left(a^{2} + a b\right)} \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right)^{3} + 8 \, {\left(a^{2} + a b\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{6} + 12 \, {\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} d x \cosh\left(d x + c\right)^{2} - 30 \, {\left(a^{2} + a b\right)} \cosh\left(d x + c\right)^{4} + 2 \, a^{2} + 2 \, a b\right)} \sinh\left(d x + c\right)^{2} + 64 \, {\left(a \cosh\left(d x + c\right)^{4} + 4 \, a \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, a \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + a \sinh\left(d x + c\right)^{4}\right)} \sqrt{a b} \arctan\left(\frac{{\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} + a - b\right)} \sqrt{a b}}{2 \, a b}\right) - a^{2} - 2 \, a b - b^{2} + 8 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{7} + 4 \, {\left(3 \, a^{2} - 6 \, a b - b^{2}\right)} d x \cosh\left(d x + c\right)^{3} - 6 \, {\left(a^{2} + a b\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(a^{2} + a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{64 \, {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d \cosh\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)^{3} \sinh\left(d x + c\right) + 6 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, {\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)^{3} + {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d \sinh\left(d x + c\right)^{4}\right)}}\right]"," ",0,"[1/64*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^8 + 8*(a^2 + 2*a*b + b^2)*cosh(d*x + c)*sinh(d*x + c)^7 + (a^2 + 2*a*b + b^2)*sinh(d*x + c)^8 + 8*(3*a^2 - 6*a*b - b^2)*d*x*cosh(d*x + c)^4 - 8*(a^2 + a*b)*cosh(d*x + c)^6 + 4*(7*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 - 2*a^2 - 2*a*b)*sinh(d*x + c)^6 + 8*(7*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 - 6*(a^2 + a*b)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 + 4*(3*a^2 - 6*a*b - b^2)*d*x - 60*(a^2 + a*b)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(7*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^5 + 4*(3*a^2 - 6*a*b - b^2)*d*x*cosh(d*x + c) - 20*(a^2 + a*b)*cosh(d*x + c)^3)*sinh(d*x + c)^3 + 8*(a^2 + a*b)*cosh(d*x + c)^2 + 4*(7*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^6 + 12*(3*a^2 - 6*a*b - b^2)*d*x*cosh(d*x + c)^2 - 30*(a^2 + a*b)*cosh(d*x + c)^4 + 2*a^2 + 2*a*b)*sinh(d*x + c)^2 + 32*(a*cosh(d*x + c)^4 + 4*a*cosh(d*x + c)^3*sinh(d*x + c) + 6*a*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*a*cosh(d*x + c)*sinh(d*x + c)^3 + a*sinh(d*x + c)^4)*sqrt(-a*b)*log(((a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 + 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 + 2*(a^2 - b^2)*cosh(d*x + c)^2 + 2*(3*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + a^2 - b^2)*sinh(d*x + c)^2 + a^2 - 6*a*b + b^2 + 4*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 + (a^2 - 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 + a - b)*sqrt(-a*b))/((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)) - a^2 - 2*a*b - b^2 + 8*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^7 + 4*(3*a^2 - 6*a*b - b^2)*d*x*cosh(d*x + c)^3 - 6*(a^2 + a*b)*cosh(d*x + c)^5 + 2*(a^2 + a*b)*cosh(d*x + c))*sinh(d*x + c))/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*cosh(d*x + c)^4 + 4*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*cosh(d*x + c)^3*sinh(d*x + c) + 6*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*cosh(d*x + c)*sinh(d*x + c)^3 + (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*sinh(d*x + c)^4), 1/64*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^8 + 8*(a^2 + 2*a*b + b^2)*cosh(d*x + c)*sinh(d*x + c)^7 + (a^2 + 2*a*b + b^2)*sinh(d*x + c)^8 + 8*(3*a^2 - 6*a*b - b^2)*d*x*cosh(d*x + c)^4 - 8*(a^2 + a*b)*cosh(d*x + c)^6 + 4*(7*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 - 2*a^2 - 2*a*b)*sinh(d*x + c)^6 + 8*(7*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 - 6*(a^2 + a*b)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 + 4*(3*a^2 - 6*a*b - b^2)*d*x - 60*(a^2 + a*b)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(7*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^5 + 4*(3*a^2 - 6*a*b - b^2)*d*x*cosh(d*x + c) - 20*(a^2 + a*b)*cosh(d*x + c)^3)*sinh(d*x + c)^3 + 8*(a^2 + a*b)*cosh(d*x + c)^2 + 4*(7*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^6 + 12*(3*a^2 - 6*a*b - b^2)*d*x*cosh(d*x + c)^2 - 30*(a^2 + a*b)*cosh(d*x + c)^4 + 2*a^2 + 2*a*b)*sinh(d*x + c)^2 + 64*(a*cosh(d*x + c)^4 + 4*a*cosh(d*x + c)^3*sinh(d*x + c) + 6*a*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*a*cosh(d*x + c)*sinh(d*x + c)^3 + a*sinh(d*x + c)^4)*sqrt(a*b)*arctan(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 + a - b)*sqrt(a*b)/(a*b)) - a^2 - 2*a*b - b^2 + 8*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^7 + 4*(3*a^2 - 6*a*b - b^2)*d*x*cosh(d*x + c)^3 - 6*(a^2 + a*b)*cosh(d*x + c)^5 + 2*(a^2 + a*b)*cosh(d*x + c))*sinh(d*x + c))/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*cosh(d*x + c)^4 + 4*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*cosh(d*x + c)^3*sinh(d*x + c) + 6*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*cosh(d*x + c)*sinh(d*x + c)^3 + (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*sinh(d*x + c)^4)]","B",0
26,1,1367,0,0.650074," ","integrate(sinh(d*x+c)^3/(a+b*tanh(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{{\left(a + b\right)} \cosh\left(d x + c\right)^{6} + 6 \, {\left(a + b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(a + b\right)} \sinh\left(d x + c\right)^{6} - 3 \, {\left(3 \, a - b\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(5 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} - 3 \, a + b\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, {\left(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} - 3 \, {\left(3 \, a - b\right)} \cosh\left(d x + c\right)^{2} + 3 \, {\left(5 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{4} - 6 \, {\left(3 \, a - b\right)} \cosh\left(d x + c\right)^{2} - 3 \, a + b\right)} \sinh\left(d x + c\right)^{2} + 12 \, {\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)} \sqrt{\frac{b}{a + b}} \log\left(\frac{{\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 + 3 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} + a + 3 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a + 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) + 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}} + a + b}{{\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) + 6 \, {\left({\left(a + b\right)} \cosh\left(d x + c\right)^{5} - 2 \, {\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) + a + b}{24 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + {\left(a^{2} + 2 \, a b + b^{2}\right)} d \sinh\left(d x + c\right)^{3}\right)}}, \frac{{\left(a + b\right)} \cosh\left(d x + c\right)^{6} + 6 \, {\left(a + b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(a + b\right)} \sinh\left(d x + c\right)^{6} - 3 \, {\left(3 \, a - b\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(5 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} - 3 \, a + b\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, {\left(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} - 3 \, {\left(3 \, a - b\right)} \cosh\left(d x + c\right)^{2} + 3 \, {\left(5 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{4} - 6 \, {\left(3 \, a - b\right)} \cosh\left(d x + c\right)^{2} - 3 \, a + 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)} \sqrt{-\frac{b}{a + b}} \arctan\left(\frac{{\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 - 3 \, b\right)} \cosh\left(d x + c\right) + {\left(3 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} + a - 3 \, b\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{b}{a + b}}}{2 \, b}\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)} \sqrt{-\frac{b}{a + b}} \arctan\left(\frac{{\left({\left(a + b\right)} \cosh\left(d x + c\right) + {\left(a + b\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{b}{a + b}}}{2 \, b}\right) + 6 \, {\left({\left(a + b\right)} \cosh\left(d x + c\right)^{5} - 2 \, {\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) + a + b}{24 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + {\left(a^{2} + 2 \, a b + b^{2}\right)} d \sinh\left(d x + c\right)^{3}\right)}}\right]"," ",0,"[1/24*((a + b)*cosh(d*x + c)^6 + 6*(a + b)*cosh(d*x + c)*sinh(d*x + c)^5 + (a + b)*sinh(d*x + c)^6 - 3*(3*a - b)*cosh(d*x + c)^4 + 3*(5*(a + b)*cosh(d*x + c)^2 - 3*a + b)*sinh(d*x + c)^4 + 4*(5*(a + b)*cosh(d*x + c)^3 - 3*(3*a - b)*cosh(d*x + c))*sinh(d*x + c)^3 - 3*(3*a - b)*cosh(d*x + c)^2 + 3*(5*(a + b)*cosh(d*x + c)^4 - 6*(3*a - b)*cosh(d*x + c)^2 - 3*a + b)*sinh(d*x + c)^2 + 12*(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)*sqrt(b/(a + b))*log(((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 + 3*b)*cosh(d*x + c)^2 + 2*(3*(a + b)*cosh(d*x + c)^2 + a + 3*b)*sinh(d*x + c)^2 + 4*((a + b)*cosh(d*x + c)^3 + (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)) + a + b)/((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)) + 6*((a + b)*cosh(d*x + c)^5 - 2*(3*a - b)*cosh(d*x + c)^3 - (3*a - b)*cosh(d*x + c))*sinh(d*x + c) + a + b)/((a^2 + 2*a*b + b^2)*d*cosh(d*x + c)^3 + 3*(a^2 + 2*a*b + b^2)*d*cosh(d*x + c)^2*sinh(d*x + c) + 3*(a^2 + 2*a*b + b^2)*d*cosh(d*x + c)*sinh(d*x + c)^2 + (a^2 + 2*a*b + b^2)*d*sinh(d*x + c)^3), 1/24*((a + b)*cosh(d*x + c)^6 + 6*(a + b)*cosh(d*x + c)*sinh(d*x + c)^5 + (a + b)*sinh(d*x + c)^6 - 3*(3*a - b)*cosh(d*x + c)^4 + 3*(5*(a + b)*cosh(d*x + c)^2 - 3*a + b)*sinh(d*x + c)^4 + 4*(5*(a + b)*cosh(d*x + c)^3 - 3*(3*a - b)*cosh(d*x + c))*sinh(d*x + c)^3 - 3*(3*a - b)*cosh(d*x + c)^2 + 3*(5*(a + b)*cosh(d*x + c)^4 - 6*(3*a - b)*cosh(d*x + c)^2 - 3*a + 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)*sqrt(-b/(a + b))*arctan(1/2*((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 - 3*b)*cosh(d*x + c) + (3*(a + b)*cosh(d*x + c)^2 + a - 3*b)*sinh(d*x + c))*sqrt(-b/(a + b))/b) - 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)*sqrt(-b/(a + b))*arctan(1/2*((a + b)*cosh(d*x + c) + (a + b)*sinh(d*x + c))*sqrt(-b/(a + b))/b) + 6*((a + b)*cosh(d*x + c)^5 - 2*(3*a - b)*cosh(d*x + c)^3 - (3*a - b)*cosh(d*x + c))*sinh(d*x + c) + a + b)/((a^2 + 2*a*b + b^2)*d*cosh(d*x + c)^3 + 3*(a^2 + 2*a*b + b^2)*d*cosh(d*x + c)^2*sinh(d*x + c) + 3*(a^2 + 2*a*b + b^2)*d*cosh(d*x + c)*sinh(d*x + c)^2 + (a^2 + 2*a*b + b^2)*d*sinh(d*x + c)^3)]","B",0
27,1,916,0,0.565868," ","integrate(sinh(d*x+c)^2/(a+b*tanh(d*x+c)^2),x, algorithm=""fricas"")","\left[-\frac{4 \, {\left(a - b\right)} d x \cosh\left(d x + c\right)^{2} - {\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(2 \, {\left(a - b\right)} d x - 3 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} - 4 \, \sqrt{-a b} {\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}\right)} \log\left(\frac{{\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) \sinh\left(d x + c\right)^{3} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{2} + a^{2} - 6 \, a b + b^{2} + 4 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} - b^{2}\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)^{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} + a - b\right)} \sqrt{-a b}}{{\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) + 4 \, {\left(2 \, {\left(a - b\right)} d x \cosh\left(d x + c\right) - {\left(a + b\right)} \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right) + a + b}{8 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} + 2 \, a b + b^{2}\right)} d \sinh\left(d x + c\right)^{2}\right)}}, -\frac{4 \, {\left(a - b\right)} d x \cosh\left(d x + c\right)^{2} - {\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(2 \, {\left(a - b\right)} d x - 3 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, \sqrt{a b} {\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}\right)} \arctan\left(\frac{{\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} + a - b\right)} \sqrt{a b}}{2 \, a b}\right) + 4 \, {\left(2 \, {\left(a - b\right)} d x \cosh\left(d x + c\right) - {\left(a + b\right)} \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right) + a + b}{8 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} + 2 \, a b + b^{2}\right)} d \sinh\left(d x + c\right)^{2}\right)}}\right]"," ",0,"[-1/8*(4*(a - b)*d*x*cosh(d*x + c)^2 - (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 - b)*d*x - 3*(a + b)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - 4*sqrt(-a*b)*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)*log(((a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 + 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 + 2*(a^2 - b^2)*cosh(d*x + c)^2 + 2*(3*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + a^2 - b^2)*sinh(d*x + c)^2 + a^2 - 6*a*b + b^2 + 4*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 + (a^2 - 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 + a - b)*sqrt(-a*b))/((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)) + 4*(2*(a - b)*d*x*cosh(d*x + c) - (a + b)*cosh(d*x + c)^3)*sinh(d*x + c) + a + b)/((a^2 + 2*a*b + b^2)*d*cosh(d*x + c)^2 + 2*(a^2 + 2*a*b + b^2)*d*cosh(d*x + c)*sinh(d*x + c) + (a^2 + 2*a*b + b^2)*d*sinh(d*x + c)^2), -1/8*(4*(a - b)*d*x*cosh(d*x + c)^2 - (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 - b)*d*x - 3*(a + b)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*sqrt(a*b)*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)*arctan(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 + a - b)*sqrt(a*b)/(a*b)) + 4*(2*(a - b)*d*x*cosh(d*x + c) - (a + b)*cosh(d*x + c)^3)*sinh(d*x + c) + a + b)/((a^2 + 2*a*b + b^2)*d*cosh(d*x + c)^2 + 2*(a^2 + 2*a*b + b^2)*d*cosh(d*x + c)*sinh(d*x + c) + (a^2 + 2*a*b + b^2)*d*sinh(d*x + c)^2)]","B",0
28,1,666,0,0.915062," ","integrate(sinh(d*x+c)/(a+b*tanh(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{\sqrt{\frac{b}{a + b}} {\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right)} \log\left(\frac{{\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 + 3 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} + a + 3 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a + 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) - 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}} + a + b}{{\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) + \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} + 1}{2 \, {\left({\left(a + b\right)} d \cosh\left(d x + c\right) + {\left(a + b\right)} d \sinh\left(d x + c\right)\right)}}, -\frac{2 \, \sqrt{-\frac{b}{a + b}} {\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right)} \arctan\left(\frac{{\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 - 3 \, b\right)} \cosh\left(d x + c\right) + {\left(3 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} + a - 3 \, b\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{b}{a + b}}}{2 \, b}\right) - 2 \, \sqrt{-\frac{b}{a + b}} {\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right)} \arctan\left(\frac{{\left({\left(a + b\right)} \cosh\left(d x + c\right) + {\left(a + b\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{b}{a + b}}}{2 \, b}\right) - \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} - 1}{2 \, {\left({\left(a + b\right)} d \cosh\left(d x + c\right) + {\left(a + b\right)} d \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[1/2*(sqrt(b/(a + b))*(cosh(d*x + c) + sinh(d*x + c))*log(((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 + 3*b)*cosh(d*x + c)^2 + 2*(3*(a + b)*cosh(d*x + c)^2 + a + 3*b)*sinh(d*x + c)^2 + 4*((a + b)*cosh(d*x + c)^3 + (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)) + a + b)/((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)) + cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 + 1)/((a + b)*d*cosh(d*x + c) + (a + b)*d*sinh(d*x + c)), -1/2*(2*sqrt(-b/(a + b))*(cosh(d*x + c) + sinh(d*x + c))*arctan(1/2*((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 - 3*b)*cosh(d*x + c) + (3*(a + b)*cosh(d*x + c)^2 + a - 3*b)*sinh(d*x + c))*sqrt(-b/(a + b))/b) - 2*sqrt(-b/(a + b))*(cosh(d*x + c) + sinh(d*x + c))*arctan(1/2*((a + b)*cosh(d*x + c) + (a + b)*sinh(d*x + c))*sqrt(-b/(a + b))/b) - cosh(d*x + c)^2 - 2*cosh(d*x + c)*sinh(d*x + c) - sinh(d*x + c)^2 - 1)/((a + b)*d*cosh(d*x + c) + (a + b)*d*sinh(d*x + c))]","B",0
29,1,587,0,0.550746," ","integrate(csch(d*x+c)/(a+b*tanh(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{\sqrt{\frac{b}{a + b}} \log\left(\frac{{\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 + 3 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} + a + 3 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a + 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) + 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}} + a + b}{{\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) - 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{{\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 - 3 \, b\right)} \cosh\left(d x + c\right) + {\left(3 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} + a - 3 \, b\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{b}{a + b}}}{2 \, b}\right) - \sqrt{-\frac{b}{a + b}} \arctan\left(\frac{{\left({\left(a + b\right)} \cosh\left(d x + c\right) + {\left(a + 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(((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 + 3*b)*cosh(d*x + c)^2 + 2*(3*(a + b)*cosh(d*x + c)^2 + a + 3*b)*sinh(d*x + c)^2 + 4*((a + b)*cosh(d*x + c)^3 + (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)) + a + b)/((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)) - 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*((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 - 3*b)*cosh(d*x + c) + (3*(a + b)*cosh(d*x + c)^2 + a - 3*b)*sinh(d*x + c))*sqrt(-b/(a + b))/b) - sqrt(-b/(a + b))*arctan(1/2*((a + b)*cosh(d*x + c) + (a + 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
30,1,618,0,0.538323," ","integrate(csch(d*x+c)^2/(a+b*tanh(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{{\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} - 1\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{{\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) \sinh\left(d x + c\right)^{3} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{2} + a^{2} - 6 \, a b + b^{2} + 4 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) - 4 \, {\left({\left(a^{2} + a b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} + a b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} + a b\right)} \sinh\left(d x + c\right)^{2} + a^{2} - a b\right)} \sqrt{-\frac{b}{a}}}{{\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) - 4}{2 \, {\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)}}, -\frac{{\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} - 1\right)} \sqrt{\frac{b}{a}} \arctan\left(\frac{{\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} + a - b\right)} \sqrt{\frac{b}{a}}}{2 \, b}\right) + 2}{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,"[1/2*((cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 1)*sqrt(-b/a)*log(((a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 + 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 + 2*(a^2 - b^2)*cosh(d*x + c)^2 + 2*(3*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + a^2 - b^2)*sinh(d*x + c)^2 + a^2 - 6*a*b + b^2 + 4*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 + (a^2 - b^2)*cosh(d*x + c))*sinh(d*x + c) - 4*((a^2 + a*b)*cosh(d*x + c)^2 + 2*(a^2 + a*b)*cosh(d*x + c)*sinh(d*x + c) + (a^2 + a*b)*sinh(d*x + c)^2 + a^2 - a*b)*sqrt(-b/a))/((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)) - 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), -((cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 1)*sqrt(b/a)*arctan(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 + a - b)*sqrt(b/a)/b) + 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)]","B",0
31,1,1790,0,1.272101," ","integrate(csch(d*x+c)^3/(a+b*tanh(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(\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)} \sqrt{a b + b^{2}} \log\left(\frac{{\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 + 3 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} + a + 3 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a + 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) - 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}} + a + b}{{\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) + 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(\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)} \sqrt{-a b - b^{2}} \arctan\left(\frac{{\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 - 3 \, b\right)} \cosh\left(d x + c\right) + {\left(3 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} + a - 3 \, b\right)} \sinh\left(d x + c\right)\right)} \sqrt{-a b - b^{2}}}{2 \, {\left(a b + b^{2}\right)}}\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)} \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 \, 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 - (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)*sqrt(a*b + b^2)*log(((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 + 3*b)*cosh(d*x + c)^2 + 2*(3*(a + b)*cosh(d*x + c)^2 + a + 3*b)*sinh(d*x + c)^2 + 4*((a + b)*cosh(d*x + c)^3 + (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) + a + b)/((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)) + 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*(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)*sqrt(-a*b - b^2)*arctan(1/2*((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 - 3*b)*cosh(d*x + c) + (3*(a + b)*cosh(d*x + c)^2 + a - 3*b)*sinh(d*x + c))*sqrt(-a*b - b^2)/(a*b + b^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)*sqrt(-a*b - b^2)*arctan(1/2*sqrt(-a*b - b^2)*(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))]","B",0
32,1,1628,0,0.624785," ","integrate(csch(d*x+c)^4/(a+b*tanh(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{12 \, b \cosh\left(d x + c\right)^{4} + 48 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + 12 \, b \sinh\left(d x + c\right)^{4} - 24 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} + 24 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} - a - b\right)} \sinh\left(d x + c\right)^{2} + 3 \, {\left({\left(a + b\right)} \cosh\left(d x + c\right)^{6} + 6 \, {\left(a + b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(a + b\right)} \sinh\left(d x + c\right)^{6} - 3 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(5 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} - a - b\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(a + b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 3 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} + 3 \, {\left(5 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{4} - 6 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} + a + b\right)} \sinh\left(d x + c\right)^{2} + 6 \, {\left({\left(a + b\right)} \cosh\left(d x + c\right)^{5} - 2 \, {\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)} \sqrt{-\frac{b}{a}} \log\left(\frac{{\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) \sinh\left(d x + c\right)^{3} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{2} + a^{2} - 6 \, a b + b^{2} + 4 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + 4 \, {\left({\left(a^{2} + a b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} + a b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} + a b\right)} \sinh\left(d x + c\right)^{2} + a^{2} - a b\right)} \sqrt{-\frac{b}{a}}}{{\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) + 48 \, {\left(b \cosh\left(d x + c\right)^{3} - {\left(a + b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + 8 \, a + 12 \, b}{6 \, {\left(a^{2} d \cosh\left(d x + c\right)^{6} + 6 \, a^{2} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + a^{2} d \sinh\left(d x + c\right)^{6} - 3 \, a^{2} d \cosh\left(d x + c\right)^{4} + 3 \, a^{2} d \cosh\left(d x + c\right)^{2} + 3 \, {\left(5 \, a^{2} d \cosh\left(d x + c\right)^{2} - a^{2} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, a^{2} d \cosh\left(d x + c\right)^{3} - 3 \, a^{2} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - a^{2} d + 3 \, {\left(5 \, a^{2} d \cosh\left(d x + c\right)^{4} - 6 \, a^{2} d \cosh\left(d x + c\right)^{2} + a^{2} d\right)} \sinh\left(d x + c\right)^{2} + 6 \, {\left(a^{2} d \cosh\left(d x + c\right)^{5} - 2 \, 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{6 \, b \cosh\left(d x + c\right)^{4} + 24 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + 6 \, b \sinh\left(d x + c\right)^{4} - 12 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} + 12 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} - a - b\right)} \sinh\left(d x + c\right)^{2} + 3 \, {\left({\left(a + b\right)} \cosh\left(d x + c\right)^{6} + 6 \, {\left(a + b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(a + b\right)} \sinh\left(d x + c\right)^{6} - 3 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(5 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} - a - b\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(a + b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 3 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} + 3 \, {\left(5 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{4} - 6 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} + a + b\right)} \sinh\left(d x + c\right)^{2} + 6 \, {\left({\left(a + b\right)} \cosh\left(d x + c\right)^{5} - 2 \, {\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)} \sqrt{\frac{b}{a}} \arctan\left(\frac{{\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} + a - b\right)} \sqrt{\frac{b}{a}}}{2 \, b}\right) + 24 \, {\left(b \cosh\left(d x + c\right)^{3} - {\left(a + b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + 4 \, a + 6 \, b}{3 \, {\left(a^{2} d \cosh\left(d x + c\right)^{6} + 6 \, a^{2} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + a^{2} d \sinh\left(d x + c\right)^{6} - 3 \, a^{2} d \cosh\left(d x + c\right)^{4} + 3 \, a^{2} d \cosh\left(d x + c\right)^{2} + 3 \, {\left(5 \, a^{2} d \cosh\left(d x + c\right)^{2} - a^{2} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, a^{2} d \cosh\left(d x + c\right)^{3} - 3 \, a^{2} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - a^{2} d + 3 \, {\left(5 \, a^{2} d \cosh\left(d x + c\right)^{4} - 6 \, a^{2} d \cosh\left(d x + c\right)^{2} + a^{2} d\right)} \sinh\left(d x + c\right)^{2} + 6 \, {\left(a^{2} d \cosh\left(d x + c\right)^{5} - 2 \, 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,"[1/6*(12*b*cosh(d*x + c)^4 + 48*b*cosh(d*x + c)*sinh(d*x + c)^3 + 12*b*sinh(d*x + c)^4 - 24*(a + b)*cosh(d*x + c)^2 + 24*(3*b*cosh(d*x + c)^2 - a - b)*sinh(d*x + c)^2 + 3*((a + b)*cosh(d*x + c)^6 + 6*(a + b)*cosh(d*x + c)*sinh(d*x + c)^5 + (a + b)*sinh(d*x + c)^6 - 3*(a + b)*cosh(d*x + c)^4 + 3*(5*(a + b)*cosh(d*x + c)^2 - a - b)*sinh(d*x + c)^4 + 4*(5*(a + b)*cosh(d*x + c)^3 - 3*(a + b)*cosh(d*x + c))*sinh(d*x + c)^3 + 3*(a + b)*cosh(d*x + c)^2 + 3*(5*(a + b)*cosh(d*x + c)^4 - 6*(a + b)*cosh(d*x + c)^2 + a + b)*sinh(d*x + c)^2 + 6*((a + b)*cosh(d*x + c)^5 - 2*(a + b)*cosh(d*x + c)^3 + (a + b)*cosh(d*x + c))*sinh(d*x + c) - a - b)*sqrt(-b/a)*log(((a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 + 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 + 2*(a^2 - b^2)*cosh(d*x + c)^2 + 2*(3*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + a^2 - b^2)*sinh(d*x + c)^2 + a^2 - 6*a*b + b^2 + 4*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 + (a^2 - b^2)*cosh(d*x + c))*sinh(d*x + c) + 4*((a^2 + a*b)*cosh(d*x + c)^2 + 2*(a^2 + a*b)*cosh(d*x + c)*sinh(d*x + c) + (a^2 + a*b)*sinh(d*x + c)^2 + a^2 - a*b)*sqrt(-b/a))/((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)) + 48*(b*cosh(d*x + c)^3 - (a + b)*cosh(d*x + c))*sinh(d*x + c) + 8*a + 12*b)/(a^2*d*cosh(d*x + c)^6 + 6*a^2*d*cosh(d*x + c)*sinh(d*x + c)^5 + a^2*d*sinh(d*x + c)^6 - 3*a^2*d*cosh(d*x + c)^4 + 3*a^2*d*cosh(d*x + c)^2 + 3*(5*a^2*d*cosh(d*x + c)^2 - a^2*d)*sinh(d*x + c)^4 + 4*(5*a^2*d*cosh(d*x + c)^3 - 3*a^2*d*cosh(d*x + c))*sinh(d*x + c)^3 - a^2*d + 3*(5*a^2*d*cosh(d*x + c)^4 - 6*a^2*d*cosh(d*x + c)^2 + a^2*d)*sinh(d*x + c)^2 + 6*(a^2*d*cosh(d*x + c)^5 - 2*a^2*d*cosh(d*x + c)^3 + a^2*d*cosh(d*x + c))*sinh(d*x + c)), 1/3*(6*b*cosh(d*x + c)^4 + 24*b*cosh(d*x + c)*sinh(d*x + c)^3 + 6*b*sinh(d*x + c)^4 - 12*(a + b)*cosh(d*x + c)^2 + 12*(3*b*cosh(d*x + c)^2 - a - b)*sinh(d*x + c)^2 + 3*((a + b)*cosh(d*x + c)^6 + 6*(a + b)*cosh(d*x + c)*sinh(d*x + c)^5 + (a + b)*sinh(d*x + c)^6 - 3*(a + b)*cosh(d*x + c)^4 + 3*(5*(a + b)*cosh(d*x + c)^2 - a - b)*sinh(d*x + c)^4 + 4*(5*(a + b)*cosh(d*x + c)^3 - 3*(a + b)*cosh(d*x + c))*sinh(d*x + c)^3 + 3*(a + b)*cosh(d*x + c)^2 + 3*(5*(a + b)*cosh(d*x + c)^4 - 6*(a + b)*cosh(d*x + c)^2 + a + b)*sinh(d*x + c)^2 + 6*((a + b)*cosh(d*x + c)^5 - 2*(a + b)*cosh(d*x + c)^3 + (a + b)*cosh(d*x + c))*sinh(d*x + c) - a - b)*sqrt(b/a)*arctan(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 + a - b)*sqrt(b/a)/b) + 24*(b*cosh(d*x + c)^3 - (a + b)*cosh(d*x + c))*sinh(d*x + c) + 4*a + 6*b)/(a^2*d*cosh(d*x + c)^6 + 6*a^2*d*cosh(d*x + c)*sinh(d*x + c)^5 + a^2*d*sinh(d*x + c)^6 - 3*a^2*d*cosh(d*x + c)^4 + 3*a^2*d*cosh(d*x + c)^2 + 3*(5*a^2*d*cosh(d*x + c)^2 - a^2*d)*sinh(d*x + c)^4 + 4*(5*a^2*d*cosh(d*x + c)^3 - 3*a^2*d*cosh(d*x + c))*sinh(d*x + c)^3 - a^2*d + 3*(5*a^2*d*cosh(d*x + c)^4 - 6*a^2*d*cosh(d*x + c)^2 + a^2*d)*sinh(d*x + c)^2 + 6*(a^2*d*cosh(d*x + c)^5 - 2*a^2*d*cosh(d*x + c)^3 + a^2*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
33,1,7366,0,1.077933," ","integrate(sinh(d*x+c)^4/(a+b*tanh(d*x+c)^2)^2,x, algorithm=""fricas"")","\left[\frac{{\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{12} + 12 \, {\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)^{11} + {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \sinh\left(d x + c\right)^{12} - 6 \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{10} - 6 \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3} - 11 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{10} + 20 \, {\left(11 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} - {\left(15 \, a^{3} - 19 \, a^{2} b - 19 \, a b^{2} + 15 \, b^{3} - 24 \, {\left(a^{3} - 5 \, a^{2} b - 5 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{8} + {\left(495 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{4} - 15 \, a^{3} + 19 \, a^{2} b + 19 \, a b^{2} - 15 \, b^{3} + 24 \, {\left(a^{3} - 5 \, a^{2} b - 5 \, a b^{2} + b^{3}\right)} d x - 270 \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{8} + 8 \, {\left(99 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{5} - 90 \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{3} - {\left(15 \, a^{3} - 19 \, a^{2} b - 19 \, a b^{2} + 15 \, b^{3} - 24 \, {\left(a^{3} - 5 \, a^{2} b - 5 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} - 16 \, {\left(4 \, a^{2} b - 4 \, a b^{2} - 3 \, {\left(a^{3} - 7 \, a^{2} b + 7 \, a b^{2} - b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(231 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{6} - 315 \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{4} - 16 \, a^{2} b + 16 \, a b^{2} + 12 \, {\left(a^{3} - 7 \, a^{2} b + 7 \, a b^{2} - b^{3}\right)} d x - 7 \, {\left(15 \, a^{3} - 19 \, a^{2} b - 19 \, a b^{2} + 15 \, b^{3} - 24 \, {\left(a^{3} - 5 \, a^{2} b - 5 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(99 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{7} - 189 \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{5} - 7 \, {\left(15 \, a^{3} - 19 \, a^{2} b - 19 \, a b^{2} + 15 \, b^{3} - 24 \, {\left(a^{3} - 5 \, a^{2} b - 5 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - 12 \, {\left(4 \, a^{2} b - 4 \, a b^{2} - 3 \, {\left(a^{3} - 7 \, a^{2} b + 7 \, a b^{2} - b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + {\left(15 \, a^{3} - 83 \, a^{2} b - 83 \, a b^{2} + 15 \, b^{3} + 24 \, {\left(a^{3} - 5 \, a^{2} b - 5 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + {\left(495 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{8} - 1260 \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{6} - 70 \, {\left(15 \, a^{3} - 19 \, a^{2} b - 19 \, a b^{2} + 15 \, b^{3} - 24 \, {\left(a^{3} - 5 \, a^{2} b - 5 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 15 \, a^{3} - 83 \, a^{2} b - 83 \, a b^{2} + 15 \, b^{3} + 24 \, {\left(a^{3} - 5 \, a^{2} b - 5 \, a b^{2} + b^{3}\right)} d x - 240 \, {\left(4 \, a^{2} b - 4 \, a b^{2} - 3 \, {\left(a^{3} - 7 \, a^{2} b + 7 \, a b^{2} - b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(55 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{9} - 180 \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{7} - 14 \, {\left(15 \, a^{3} - 19 \, a^{2} b - 19 \, a b^{2} + 15 \, b^{3} - 24 \, {\left(a^{3} - 5 \, a^{2} b - 5 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{5} - 80 \, {\left(4 \, a^{2} b - 4 \, a b^{2} - 3 \, {\left(a^{3} - 7 \, a^{2} b + 7 \, a b^{2} - b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + {\left(15 \, a^{3} - 83 \, a^{2} b - 83 \, a b^{2} + 15 \, b^{3} + 24 \, {\left(a^{3} - 5 \, a^{2} b - 5 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - a^{3} - 3 \, a^{2} b - 3 \, a b^{2} - b^{3} + 6 \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(33 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{10} - 135 \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{8} - 14 \, {\left(15 \, a^{3} - 19 \, a^{2} b - 19 \, a b^{2} + 15 \, b^{3} - 24 \, {\left(a^{3} - 5 \, a^{2} b - 5 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{6} - 120 \, {\left(4 \, a^{2} b - 4 \, a b^{2} - 3 \, {\left(a^{3} - 7 \, a^{2} b + 7 \, a b^{2} - b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 3 \, a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - 3 \, b^{3} + 3 \, {\left(15 \, a^{3} - 83 \, a^{2} b - 83 \, a b^{2} + 15 \, b^{3} + 24 \, {\left(a^{3} - 5 \, a^{2} b - 5 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} - 48 \, {\left({\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{8} + 2 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(14 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} - 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(14 \, {\left(a^{2} - 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)\right)} \sinh\left(d x + c\right)^{5} + {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(70 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{4} + 30 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(14 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(14 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(2 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{5} + {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right)\right)} \sqrt{-a b} \log\left(\frac{{\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) \sinh\left(d x + c\right)^{3} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{2} + a^{2} - 6 \, a b + b^{2} + 4 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} - b^{2}\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)^{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} + a - b\right)} \sqrt{-a b}}{{\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) + 4 \, {\left(3 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{11} - 15 \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{9} - 2 \, {\left(15 \, a^{3} - 19 \, a^{2} b - 19 \, a b^{2} + 15 \, b^{3} - 24 \, {\left(a^{3} - 5 \, a^{2} b - 5 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{7} - 24 \, {\left(4 \, a^{2} b - 4 \, a b^{2} - 3 \, {\left(a^{3} - 7 \, a^{2} b + 7 \, a b^{2} - b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{5} + {\left(15 \, a^{3} - 83 \, a^{2} b - 83 \, a b^{2} + 15 \, b^{3} + 24 \, {\left(a^{3} - 5 \, a^{2} b - 5 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{64 \, {\left({\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d \sinh\left(d x + c\right)^{8} + 2 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} d \cosh\left(d x + c\right)^{6} + 2 \, {\left(14 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{6} + {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(14 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + {\left(70 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 30 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(14 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(14 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(2 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} d \cosh\left(d x + c\right)^{5} + {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right)\right)}}, \frac{{\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{12} + 12 \, {\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)^{11} + {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \sinh\left(d x + c\right)^{12} - 6 \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{10} - 6 \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3} - 11 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{10} + 20 \, {\left(11 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} - {\left(15 \, a^{3} - 19 \, a^{2} b - 19 \, a b^{2} + 15 \, b^{3} - 24 \, {\left(a^{3} - 5 \, a^{2} b - 5 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{8} + {\left(495 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{4} - 15 \, a^{3} + 19 \, a^{2} b + 19 \, a b^{2} - 15 \, b^{3} + 24 \, {\left(a^{3} - 5 \, a^{2} b - 5 \, a b^{2} + b^{3}\right)} d x - 270 \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{8} + 8 \, {\left(99 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{5} - 90 \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{3} - {\left(15 \, a^{3} - 19 \, a^{2} b - 19 \, a b^{2} + 15 \, b^{3} - 24 \, {\left(a^{3} - 5 \, a^{2} b - 5 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} - 16 \, {\left(4 \, a^{2} b - 4 \, a b^{2} - 3 \, {\left(a^{3} - 7 \, a^{2} b + 7 \, a b^{2} - b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(231 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{6} - 315 \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{4} - 16 \, a^{2} b + 16 \, a b^{2} + 12 \, {\left(a^{3} - 7 \, a^{2} b + 7 \, a b^{2} - b^{3}\right)} d x - 7 \, {\left(15 \, a^{3} - 19 \, a^{2} b - 19 \, a b^{2} + 15 \, b^{3} - 24 \, {\left(a^{3} - 5 \, a^{2} b - 5 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(99 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{7} - 189 \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{5} - 7 \, {\left(15 \, a^{3} - 19 \, a^{2} b - 19 \, a b^{2} + 15 \, b^{3} - 24 \, {\left(a^{3} - 5 \, a^{2} b - 5 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - 12 \, {\left(4 \, a^{2} b - 4 \, a b^{2} - 3 \, {\left(a^{3} - 7 \, a^{2} b + 7 \, a b^{2} - b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + {\left(15 \, a^{3} - 83 \, a^{2} b - 83 \, a b^{2} + 15 \, b^{3} + 24 \, {\left(a^{3} - 5 \, a^{2} b - 5 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + {\left(495 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{8} - 1260 \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{6} - 70 \, {\left(15 \, a^{3} - 19 \, a^{2} b - 19 \, a b^{2} + 15 \, b^{3} - 24 \, {\left(a^{3} - 5 \, a^{2} b - 5 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 15 \, a^{3} - 83 \, a^{2} b - 83 \, a b^{2} + 15 \, b^{3} + 24 \, {\left(a^{3} - 5 \, a^{2} b - 5 \, a b^{2} + b^{3}\right)} d x - 240 \, {\left(4 \, a^{2} b - 4 \, a b^{2} - 3 \, {\left(a^{3} - 7 \, a^{2} b + 7 \, a b^{2} - b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(55 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{9} - 180 \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{7} - 14 \, {\left(15 \, a^{3} - 19 \, a^{2} b - 19 \, a b^{2} + 15 \, b^{3} - 24 \, {\left(a^{3} - 5 \, a^{2} b - 5 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{5} - 80 \, {\left(4 \, a^{2} b - 4 \, a b^{2} - 3 \, {\left(a^{3} - 7 \, a^{2} b + 7 \, a b^{2} - b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + {\left(15 \, a^{3} - 83 \, a^{2} b - 83 \, a b^{2} + 15 \, b^{3} + 24 \, {\left(a^{3} - 5 \, a^{2} b - 5 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - a^{3} - 3 \, a^{2} b - 3 \, a b^{2} - b^{3} + 6 \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(33 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{10} - 135 \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{8} - 14 \, {\left(15 \, a^{3} - 19 \, a^{2} b - 19 \, a b^{2} + 15 \, b^{3} - 24 \, {\left(a^{3} - 5 \, a^{2} b - 5 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{6} - 120 \, {\left(4 \, a^{2} b - 4 \, a b^{2} - 3 \, {\left(a^{3} - 7 \, a^{2} b + 7 \, a b^{2} - b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 3 \, a^{3} + 3 \, a^{2} b - 3 \, a b^{2} - 3 \, b^{3} + 3 \, {\left(15 \, a^{3} - 83 \, a^{2} b - 83 \, a b^{2} + 15 \, b^{3} + 24 \, {\left(a^{3} - 5 \, a^{2} b - 5 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 96 \, {\left({\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{8} + 2 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(14 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} - 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(14 \, {\left(a^{2} - 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)\right)} \sinh\left(d x + c\right)^{5} + {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(70 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{4} + 30 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(14 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(14 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(2 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{5} + {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right)\right)} \sqrt{a b} \arctan\left(\frac{{\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} + a - b\right)} \sqrt{a b}}{2 \, a b}\right) + 4 \, {\left(3 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{11} - 15 \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{9} - 2 \, {\left(15 \, a^{3} - 19 \, a^{2} b - 19 \, a b^{2} + 15 \, b^{3} - 24 \, {\left(a^{3} - 5 \, a^{2} b - 5 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{7} - 24 \, {\left(4 \, a^{2} b - 4 \, a b^{2} - 3 \, {\left(a^{3} - 7 \, a^{2} b + 7 \, a b^{2} - b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{5} + {\left(15 \, a^{3} - 83 \, a^{2} b - 83 \, a b^{2} + 15 \, b^{3} + 24 \, {\left(a^{3} - 5 \, a^{2} b - 5 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{64 \, {\left({\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d \sinh\left(d x + c\right)^{8} + 2 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} d \cosh\left(d x + c\right)^{6} + 2 \, {\left(14 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{6} + {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(14 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + {\left(70 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 30 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(14 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(14 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(2 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} d \cosh\left(d x + c\right)^{5} + {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[1/64*((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^12 + 12*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)*sinh(d*x + c)^11 + (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*sinh(d*x + c)^12 - 6*(a^3 + a^2*b - a*b^2 - b^3)*cosh(d*x + c)^10 - 6*(a^3 + a^2*b - a*b^2 - b^3 - 11*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^10 + 20*(11*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^3 - 3*(a^3 + a^2*b - a*b^2 - b^3)*cosh(d*x + c))*sinh(d*x + c)^9 - (15*a^3 - 19*a^2*b - 19*a*b^2 + 15*b^3 - 24*(a^3 - 5*a^2*b - 5*a*b^2 + b^3)*d*x)*cosh(d*x + c)^8 + (495*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^4 - 15*a^3 + 19*a^2*b + 19*a*b^2 - 15*b^3 + 24*(a^3 - 5*a^2*b - 5*a*b^2 + b^3)*d*x - 270*(a^3 + a^2*b - a*b^2 - b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 8*(99*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^5 - 90*(a^3 + a^2*b - a*b^2 - b^3)*cosh(d*x + c)^3 - (15*a^3 - 19*a^2*b - 19*a*b^2 + 15*b^3 - 24*(a^3 - 5*a^2*b - 5*a*b^2 + b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c)^7 - 16*(4*a^2*b - 4*a*b^2 - 3*(a^3 - 7*a^2*b + 7*a*b^2 - b^3)*d*x)*cosh(d*x + c)^6 + 4*(231*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^6 - 315*(a^3 + a^2*b - a*b^2 - b^3)*cosh(d*x + c)^4 - 16*a^2*b + 16*a*b^2 + 12*(a^3 - 7*a^2*b + 7*a*b^2 - b^3)*d*x - 7*(15*a^3 - 19*a^2*b - 19*a*b^2 + 15*b^3 - 24*(a^3 - 5*a^2*b - 5*a*b^2 + b^3)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(99*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^7 - 189*(a^3 + a^2*b - a*b^2 - b^3)*cosh(d*x + c)^5 - 7*(15*a^3 - 19*a^2*b - 19*a*b^2 + 15*b^3 - 24*(a^3 - 5*a^2*b - 5*a*b^2 + b^3)*d*x)*cosh(d*x + c)^3 - 12*(4*a^2*b - 4*a*b^2 - 3*(a^3 - 7*a^2*b + 7*a*b^2 - b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c)^5 + (15*a^3 - 83*a^2*b - 83*a*b^2 + 15*b^3 + 24*(a^3 - 5*a^2*b - 5*a*b^2 + b^3)*d*x)*cosh(d*x + c)^4 + (495*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^8 - 1260*(a^3 + a^2*b - a*b^2 - b^3)*cosh(d*x + c)^6 - 70*(15*a^3 - 19*a^2*b - 19*a*b^2 + 15*b^3 - 24*(a^3 - 5*a^2*b - 5*a*b^2 + b^3)*d*x)*cosh(d*x + c)^4 + 15*a^3 - 83*a^2*b - 83*a*b^2 + 15*b^3 + 24*(a^3 - 5*a^2*b - 5*a*b^2 + b^3)*d*x - 240*(4*a^2*b - 4*a*b^2 - 3*(a^3 - 7*a^2*b + 7*a*b^2 - b^3)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 4*(55*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^9 - 180*(a^3 + a^2*b - a*b^2 - b^3)*cosh(d*x + c)^7 - 14*(15*a^3 - 19*a^2*b - 19*a*b^2 + 15*b^3 - 24*(a^3 - 5*a^2*b - 5*a*b^2 + b^3)*d*x)*cosh(d*x + c)^5 - 80*(4*a^2*b - 4*a*b^2 - 3*(a^3 - 7*a^2*b + 7*a*b^2 - b^3)*d*x)*cosh(d*x + c)^3 + (15*a^3 - 83*a^2*b - 83*a*b^2 + 15*b^3 + 24*(a^3 - 5*a^2*b - 5*a*b^2 + b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c)^3 - a^3 - 3*a^2*b - 3*a*b^2 - b^3 + 6*(a^3 + a^2*b - a*b^2 - b^3)*cosh(d*x + c)^2 + 2*(33*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^10 - 135*(a^3 + a^2*b - a*b^2 - b^3)*cosh(d*x + c)^8 - 14*(15*a^3 - 19*a^2*b - 19*a*b^2 + 15*b^3 - 24*(a^3 - 5*a^2*b - 5*a*b^2 + b^3)*d*x)*cosh(d*x + c)^6 - 120*(4*a^2*b - 4*a*b^2 - 3*(a^3 - 7*a^2*b + 7*a*b^2 - b^3)*d*x)*cosh(d*x + c)^4 + 3*a^3 + 3*a^2*b - 3*a*b^2 - 3*b^3 + 3*(15*a^3 - 83*a^2*b - 83*a*b^2 + 15*b^3 + 24*(a^3 - 5*a^2*b - 5*a*b^2 + b^3)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - 48*((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 + 2*(a^2 - 2*a*b + b^2)*cosh(d*x + c)^6 + 2*(14*(a^2 - b^2)*cosh(d*x + c)^2 + a^2 - 2*a*b + b^2)*sinh(d*x + c)^6 + 4*(14*(a^2 - b^2)*cosh(d*x + c)^3 + 3*(a^2 - 2*a*b + b^2)*cosh(d*x + c))*sinh(d*x + c)^5 + (a^2 - b^2)*cosh(d*x + c)^4 + (70*(a^2 - b^2)*cosh(d*x + c)^4 + 30*(a^2 - 2*a*b + b^2)*cosh(d*x + c)^2 + a^2 - b^2)*sinh(d*x + c)^4 + 4*(14*(a^2 - b^2)*cosh(d*x + c)^5 + 10*(a^2 - 2*a*b + b^2)*cosh(d*x + c)^3 + (a^2 - b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 2*(14*(a^2 - b^2)*cosh(d*x + c)^6 + 15*(a^2 - 2*a*b + b^2)*cosh(d*x + c)^4 + 3*(a^2 - b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*(2*(a^2 - b^2)*cosh(d*x + c)^7 + 3*(a^2 - 2*a*b + b^2)*cosh(d*x + c)^5 + (a^2 - b^2)*cosh(d*x + c)^3)*sinh(d*x + c))*sqrt(-a*b)*log(((a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 + 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 + 2*(a^2 - b^2)*cosh(d*x + c)^2 + 2*(3*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + a^2 - b^2)*sinh(d*x + c)^2 + a^2 - 6*a*b + b^2 + 4*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 + (a^2 - 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 + a - b)*sqrt(-a*b))/((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)) + 4*(3*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^11 - 15*(a^3 + a^2*b - a*b^2 - b^3)*cosh(d*x + c)^9 - 2*(15*a^3 - 19*a^2*b - 19*a*b^2 + 15*b^3 - 24*(a^3 - 5*a^2*b - 5*a*b^2 + b^3)*d*x)*cosh(d*x + c)^7 - 24*(4*a^2*b - 4*a*b^2 - 3*(a^3 - 7*a^2*b + 7*a*b^2 - b^3)*d*x)*cosh(d*x + c)^5 + (15*a^3 - 83*a^2*b - 83*a*b^2 + 15*b^3 + 24*(a^3 - 5*a^2*b - 5*a*b^2 + b^3)*d*x)*cosh(d*x + c)^3 + 3*(a^3 + a^2*b - a*b^2 - b^3)*cosh(d*x + c))*sinh(d*x + c))/((a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*cosh(d*x + c)^8 + 8*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*sinh(d*x + c)^8 + 2*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*d*cosh(d*x + c)^6 + 2*(14*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*cosh(d*x + c)^2 + (a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*d)*sinh(d*x + c)^6 + (a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*cosh(d*x + c)^4 + 4*(14*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*cosh(d*x + c)^3 + 3*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*d*cosh(d*x + c))*sinh(d*x + c)^5 + (70*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*cosh(d*x + c)^4 + 30*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*d*cosh(d*x + c)^2 + (a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d)*sinh(d*x + c)^4 + 4*(14*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*cosh(d*x + c)^5 + 10*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*d*cosh(d*x + c)^3 + (a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 2*(14*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*cosh(d*x + c)^6 + 15*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*d*cosh(d*x + c)^4 + 3*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*(2*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*cosh(d*x + c)^7 + 3*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*d*cosh(d*x + c)^5 + (a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*cosh(d*x + c)^3)*sinh(d*x + c)), 1/64*((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^12 + 12*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)*sinh(d*x + c)^11 + (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*sinh(d*x + c)^12 - 6*(a^3 + a^2*b - a*b^2 - b^3)*cosh(d*x + c)^10 - 6*(a^3 + a^2*b - a*b^2 - b^3 - 11*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^10 + 20*(11*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^3 - 3*(a^3 + a^2*b - a*b^2 - b^3)*cosh(d*x + c))*sinh(d*x + c)^9 - (15*a^3 - 19*a^2*b - 19*a*b^2 + 15*b^3 - 24*(a^3 - 5*a^2*b - 5*a*b^2 + b^3)*d*x)*cosh(d*x + c)^8 + (495*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^4 - 15*a^3 + 19*a^2*b + 19*a*b^2 - 15*b^3 + 24*(a^3 - 5*a^2*b - 5*a*b^2 + b^3)*d*x - 270*(a^3 + a^2*b - a*b^2 - b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 8*(99*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^5 - 90*(a^3 + a^2*b - a*b^2 - b^3)*cosh(d*x + c)^3 - (15*a^3 - 19*a^2*b - 19*a*b^2 + 15*b^3 - 24*(a^3 - 5*a^2*b - 5*a*b^2 + b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c)^7 - 16*(4*a^2*b - 4*a*b^2 - 3*(a^3 - 7*a^2*b + 7*a*b^2 - b^3)*d*x)*cosh(d*x + c)^6 + 4*(231*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^6 - 315*(a^3 + a^2*b - a*b^2 - b^3)*cosh(d*x + c)^4 - 16*a^2*b + 16*a*b^2 + 12*(a^3 - 7*a^2*b + 7*a*b^2 - b^3)*d*x - 7*(15*a^3 - 19*a^2*b - 19*a*b^2 + 15*b^3 - 24*(a^3 - 5*a^2*b - 5*a*b^2 + b^3)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(99*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^7 - 189*(a^3 + a^2*b - a*b^2 - b^3)*cosh(d*x + c)^5 - 7*(15*a^3 - 19*a^2*b - 19*a*b^2 + 15*b^3 - 24*(a^3 - 5*a^2*b - 5*a*b^2 + b^3)*d*x)*cosh(d*x + c)^3 - 12*(4*a^2*b - 4*a*b^2 - 3*(a^3 - 7*a^2*b + 7*a*b^2 - b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c)^5 + (15*a^3 - 83*a^2*b - 83*a*b^2 + 15*b^3 + 24*(a^3 - 5*a^2*b - 5*a*b^2 + b^3)*d*x)*cosh(d*x + c)^4 + (495*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^8 - 1260*(a^3 + a^2*b - a*b^2 - b^3)*cosh(d*x + c)^6 - 70*(15*a^3 - 19*a^2*b - 19*a*b^2 + 15*b^3 - 24*(a^3 - 5*a^2*b - 5*a*b^2 + b^3)*d*x)*cosh(d*x + c)^4 + 15*a^3 - 83*a^2*b - 83*a*b^2 + 15*b^3 + 24*(a^3 - 5*a^2*b - 5*a*b^2 + b^3)*d*x - 240*(4*a^2*b - 4*a*b^2 - 3*(a^3 - 7*a^2*b + 7*a*b^2 - b^3)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 4*(55*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^9 - 180*(a^3 + a^2*b - a*b^2 - b^3)*cosh(d*x + c)^7 - 14*(15*a^3 - 19*a^2*b - 19*a*b^2 + 15*b^3 - 24*(a^3 - 5*a^2*b - 5*a*b^2 + b^3)*d*x)*cosh(d*x + c)^5 - 80*(4*a^2*b - 4*a*b^2 - 3*(a^3 - 7*a^2*b + 7*a*b^2 - b^3)*d*x)*cosh(d*x + c)^3 + (15*a^3 - 83*a^2*b - 83*a*b^2 + 15*b^3 + 24*(a^3 - 5*a^2*b - 5*a*b^2 + b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c)^3 - a^3 - 3*a^2*b - 3*a*b^2 - b^3 + 6*(a^3 + a^2*b - a*b^2 - b^3)*cosh(d*x + c)^2 + 2*(33*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^10 - 135*(a^3 + a^2*b - a*b^2 - b^3)*cosh(d*x + c)^8 - 14*(15*a^3 - 19*a^2*b - 19*a*b^2 + 15*b^3 - 24*(a^3 - 5*a^2*b - 5*a*b^2 + b^3)*d*x)*cosh(d*x + c)^6 - 120*(4*a^2*b - 4*a*b^2 - 3*(a^3 - 7*a^2*b + 7*a*b^2 - b^3)*d*x)*cosh(d*x + c)^4 + 3*a^3 + 3*a^2*b - 3*a*b^2 - 3*b^3 + 3*(15*a^3 - 83*a^2*b - 83*a*b^2 + 15*b^3 + 24*(a^3 - 5*a^2*b - 5*a*b^2 + b^3)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 96*((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 + 2*(a^2 - 2*a*b + b^2)*cosh(d*x + c)^6 + 2*(14*(a^2 - b^2)*cosh(d*x + c)^2 + a^2 - 2*a*b + b^2)*sinh(d*x + c)^6 + 4*(14*(a^2 - b^2)*cosh(d*x + c)^3 + 3*(a^2 - 2*a*b + b^2)*cosh(d*x + c))*sinh(d*x + c)^5 + (a^2 - b^2)*cosh(d*x + c)^4 + (70*(a^2 - b^2)*cosh(d*x + c)^4 + 30*(a^2 - 2*a*b + b^2)*cosh(d*x + c)^2 + a^2 - b^2)*sinh(d*x + c)^4 + 4*(14*(a^2 - b^2)*cosh(d*x + c)^5 + 10*(a^2 - 2*a*b + b^2)*cosh(d*x + c)^3 + (a^2 - b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 2*(14*(a^2 - b^2)*cosh(d*x + c)^6 + 15*(a^2 - 2*a*b + b^2)*cosh(d*x + c)^4 + 3*(a^2 - b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*(2*(a^2 - b^2)*cosh(d*x + c)^7 + 3*(a^2 - 2*a*b + b^2)*cosh(d*x + c)^5 + (a^2 - b^2)*cosh(d*x + c)^3)*sinh(d*x + c))*sqrt(a*b)*arctan(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 + a - b)*sqrt(a*b)/(a*b)) + 4*(3*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^11 - 15*(a^3 + a^2*b - a*b^2 - b^3)*cosh(d*x + c)^9 - 2*(15*a^3 - 19*a^2*b - 19*a*b^2 + 15*b^3 - 24*(a^3 - 5*a^2*b - 5*a*b^2 + b^3)*d*x)*cosh(d*x + c)^7 - 24*(4*a^2*b - 4*a*b^2 - 3*(a^3 - 7*a^2*b + 7*a*b^2 - b^3)*d*x)*cosh(d*x + c)^5 + (15*a^3 - 83*a^2*b - 83*a*b^2 + 15*b^3 + 24*(a^3 - 5*a^2*b - 5*a*b^2 + b^3)*d*x)*cosh(d*x + c)^3 + 3*(a^3 + a^2*b - a*b^2 - b^3)*cosh(d*x + c))*sinh(d*x + c))/((a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*cosh(d*x + c)^8 + 8*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*sinh(d*x + c)^8 + 2*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*d*cosh(d*x + c)^6 + 2*(14*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*cosh(d*x + c)^2 + (a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*d)*sinh(d*x + c)^6 + (a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*cosh(d*x + c)^4 + 4*(14*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*cosh(d*x + c)^3 + 3*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*d*cosh(d*x + c))*sinh(d*x + c)^5 + (70*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*cosh(d*x + c)^4 + 30*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*d*cosh(d*x + c)^2 + (a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d)*sinh(d*x + c)^4 + 4*(14*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*cosh(d*x + c)^5 + 10*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*d*cosh(d*x + c)^3 + (a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 2*(14*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*cosh(d*x + c)^6 + 15*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*d*cosh(d*x + c)^4 + 3*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*(2*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*cosh(d*x + c)^7 + 3*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*d*cosh(d*x + c)^5 + (a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*cosh(d*x + c)^3)*sinh(d*x + c))]","B",0
34,1,5025,0,0.754724," ","integrate(sinh(d*x+c)^3/(a+b*tanh(d*x+c)^2)^2,x, algorithm=""fricas"")","\left[\frac{{\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{10} + 10 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{10} - {\left(7 \, a^{2} - 6 \, a b - 13 \, b^{2}\right)} \cosh\left(d x + c\right)^{8} + {\left(45 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} - 7 \, a^{2} + 6 \, a b + 13 \, b^{2}\right)} \sinh\left(d x + c\right)^{8} + 8 \, {\left(15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(7 \, a^{2} - 6 \, a b - 13 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} - 2 \, {\left(13 \, a^{2} - 40 \, a b + 7 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(105 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} - 14 \, {\left(7 \, a^{2} - 6 \, a b - 13 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 13 \, a^{2} + 40 \, a b - 7 \, b^{2}\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(63 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{5} - 14 \, {\left(7 \, a^{2} - 6 \, a b - 13 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(13 \, a^{2} - 40 \, a b + 7 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 2 \, {\left(13 \, a^{2} - 40 \, a b + 7 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(105 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{6} - 35 \, {\left(7 \, a^{2} - 6 \, a b - 13 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} - 15 \, {\left(13 \, a^{2} - 40 \, a b + 7 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 13 \, a^{2} + 40 \, a b - 7 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{7} - 7 \, {\left(7 \, a^{2} - 6 \, a b - 13 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} - 5 \, {\left(13 \, a^{2} - 40 \, a b + 7 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(13 \, a^{2} - 40 \, a b + 7 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - {\left(7 \, a^{2} - 6 \, a b - 13 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(45 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{8} - 28 \, {\left(7 \, a^{2} - 6 \, a b - 13 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} - 30 \, {\left(13 \, a^{2} - 40 \, a b + 7 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} - 12 \, {\left(13 \, a^{2} - 40 \, a b + 7 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 7 \, a^{2} + 6 \, a b + 13 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} - 6 \, {\left({\left(3 \, a^{2} + a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} + 7 \, {\left(3 \, a^{2} + a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + {\left(3 \, a^{2} + a b - 2 \, b^{2}\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(3 \, a^{2} - 5 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + {\left(21 \, {\left(3 \, a^{2} + a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 6 \, a^{2} - 10 \, a b + 4 \, b^{2}\right)} \sinh\left(d x + c\right)^{5} + 5 \, {\left(7 \, {\left(3 \, a^{2} + a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(3 \, a^{2} - 5 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + {\left(3 \, a^{2} + a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(35 \, {\left(3 \, a^{2} + a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 20 \, {\left(3 \, a^{2} - 5 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 3 \, a^{2} + a b - 2 \, b^{2}\right)} \sinh\left(d x + c\right)^{3} + {\left(21 \, {\left(3 \, a^{2} + a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 20 \, {\left(3 \, a^{2} - 5 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(3 \, a^{2} + a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(7 \, {\left(3 \, a^{2} + a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 10 \, {\left(3 \, a^{2} - 5 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{2} + a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{b}{a + b}} \log\left(\frac{{\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 + 3 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} + a + 3 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a + 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) - 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}} + a + b}{{\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) + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(5 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{9} - 4 \, {\left(7 \, a^{2} - 6 \, a b - 13 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} - 6 \, {\left(13 \, a^{2} - 40 \, a b + 7 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} - 4 \, {\left(13 \, a^{2} - 40 \, a b + 7 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(7 \, a^{2} - 6 \, a b - 13 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{24 \, {\left({\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} d \cosh\left(d x + c\right)^{7} + 7 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} d \sinh\left(d x + c\right)^{7} + 2 \, {\left(a^{4} + 2 \, a^{3} b - 2 \, a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{5} + {\left(21 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{4} + 2 \, a^{3} b - 2 \, a b^{3} - b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{5} + {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} d \cosh\left(d x + c\right)^{3} + 5 \, {\left(7 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} d \cosh\left(d x + c\right)^{3} + 2 \, {\left(a^{4} + 2 \, a^{3} b - 2 \, a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + {\left(35 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 20 \, {\left(a^{4} + 2 \, a^{3} b - 2 \, a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{3} + {\left(21 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} d \cosh\left(d x + c\right)^{5} + 20 \, {\left(a^{4} + 2 \, a^{3} b - 2 \, a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, 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)^{2} + {\left(7 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} d \cosh\left(d x + c\right)^{6} + 10 \, {\left(a^{4} + 2 \, a^{3} b - 2 \, a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} d \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)\right)}}, \frac{{\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{10} + 10 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{10} - {\left(7 \, a^{2} - 6 \, a b - 13 \, b^{2}\right)} \cosh\left(d x + c\right)^{8} + {\left(45 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} - 7 \, a^{2} + 6 \, a b + 13 \, b^{2}\right)} \sinh\left(d x + c\right)^{8} + 8 \, {\left(15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(7 \, a^{2} - 6 \, a b - 13 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} - 2 \, {\left(13 \, a^{2} - 40 \, a b + 7 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(105 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} - 14 \, {\left(7 \, a^{2} - 6 \, a b - 13 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 13 \, a^{2} + 40 \, a b - 7 \, b^{2}\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(63 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{5} - 14 \, {\left(7 \, a^{2} - 6 \, a b - 13 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(13 \, a^{2} - 40 \, a b + 7 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 2 \, {\left(13 \, a^{2} - 40 \, a b + 7 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(105 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{6} - 35 \, {\left(7 \, a^{2} - 6 \, a b - 13 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} - 15 \, {\left(13 \, a^{2} - 40 \, a b + 7 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 13 \, a^{2} + 40 \, a b - 7 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{7} - 7 \, {\left(7 \, a^{2} - 6 \, a b - 13 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} - 5 \, {\left(13 \, a^{2} - 40 \, a b + 7 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(13 \, a^{2} - 40 \, a b + 7 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - {\left(7 \, a^{2} - 6 \, a b - 13 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(45 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{8} - 28 \, {\left(7 \, a^{2} - 6 \, a b - 13 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} - 30 \, {\left(13 \, a^{2} - 40 \, a b + 7 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} - 12 \, {\left(13 \, a^{2} - 40 \, a b + 7 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 7 \, a^{2} + 6 \, a b + 13 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} + 12 \, {\left({\left(3 \, a^{2} + a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} + 7 \, {\left(3 \, a^{2} + a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + {\left(3 \, a^{2} + a b - 2 \, b^{2}\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(3 \, a^{2} - 5 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + {\left(21 \, {\left(3 \, a^{2} + a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 6 \, a^{2} - 10 \, a b + 4 \, b^{2}\right)} \sinh\left(d x + c\right)^{5} + 5 \, {\left(7 \, {\left(3 \, a^{2} + a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(3 \, a^{2} - 5 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + {\left(3 \, a^{2} + a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(35 \, {\left(3 \, a^{2} + a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 20 \, {\left(3 \, a^{2} - 5 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 3 \, a^{2} + a b - 2 \, b^{2}\right)} \sinh\left(d x + c\right)^{3} + {\left(21 \, {\left(3 \, a^{2} + a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 20 \, {\left(3 \, a^{2} - 5 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(3 \, a^{2} + a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(7 \, {\left(3 \, a^{2} + a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 10 \, {\left(3 \, a^{2} - 5 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{2} + a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{b}{a + b}} \arctan\left(\frac{{\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 - 3 \, b\right)} \cosh\left(d x + c\right) + {\left(3 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} + a - 3 \, b\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{b}{a + b}}}{2 \, b}\right) - 12 \, {\left({\left(3 \, a^{2} + a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} + 7 \, {\left(3 \, a^{2} + a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + {\left(3 \, a^{2} + a b - 2 \, b^{2}\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(3 \, a^{2} - 5 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + {\left(21 \, {\left(3 \, a^{2} + a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 6 \, a^{2} - 10 \, a b + 4 \, b^{2}\right)} \sinh\left(d x + c\right)^{5} + 5 \, {\left(7 \, {\left(3 \, a^{2} + a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(3 \, a^{2} - 5 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + {\left(3 \, a^{2} + a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(35 \, {\left(3 \, a^{2} + a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 20 \, {\left(3 \, a^{2} - 5 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 3 \, a^{2} + a b - 2 \, b^{2}\right)} \sinh\left(d x + c\right)^{3} + {\left(21 \, {\left(3 \, a^{2} + a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 20 \, {\left(3 \, a^{2} - 5 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(3 \, a^{2} + a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(7 \, {\left(3 \, a^{2} + a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 10 \, {\left(3 \, a^{2} - 5 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{2} + a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{b}{a + b}} \arctan\left(\frac{{\left({\left(a + b\right)} \cosh\left(d x + c\right) + {\left(a + b\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{b}{a + b}}}{2 \, b}\right) + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(5 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{9} - 4 \, {\left(7 \, a^{2} - 6 \, a b - 13 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} - 6 \, {\left(13 \, a^{2} - 40 \, a b + 7 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} - 4 \, {\left(13 \, a^{2} - 40 \, a b + 7 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(7 \, a^{2} - 6 \, a b - 13 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{24 \, {\left({\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} d \cosh\left(d x + c\right)^{7} + 7 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} d \sinh\left(d x + c\right)^{7} + 2 \, {\left(a^{4} + 2 \, a^{3} b - 2 \, a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{5} + {\left(21 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{4} + 2 \, a^{3} b - 2 \, a b^{3} - b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{5} + {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} d \cosh\left(d x + c\right)^{3} + 5 \, {\left(7 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} d \cosh\left(d x + c\right)^{3} + 2 \, {\left(a^{4} + 2 \, a^{3} b - 2 \, a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + {\left(35 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 20 \, {\left(a^{4} + 2 \, a^{3} b - 2 \, a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{3} + {\left(21 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} d \cosh\left(d x + c\right)^{5} + 20 \, {\left(a^{4} + 2 \, a^{3} b - 2 \, a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, 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)^{2} + {\left(7 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} d \cosh\left(d x + c\right)^{6} + 10 \, {\left(a^{4} + 2 \, a^{3} b - 2 \, a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} d \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[1/24*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^10 + 10*(a^2 + 2*a*b + b^2)*cosh(d*x + c)*sinh(d*x + c)^9 + (a^2 + 2*a*b + b^2)*sinh(d*x + c)^10 - (7*a^2 - 6*a*b - 13*b^2)*cosh(d*x + c)^8 + (45*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 - 7*a^2 + 6*a*b + 13*b^2)*sinh(d*x + c)^8 + 8*(15*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 - (7*a^2 - 6*a*b - 13*b^2)*cosh(d*x + c))*sinh(d*x + c)^7 - 2*(13*a^2 - 40*a*b + 7*b^2)*cosh(d*x + c)^6 + 2*(105*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 - 14*(7*a^2 - 6*a*b - 13*b^2)*cosh(d*x + c)^2 - 13*a^2 + 40*a*b - 7*b^2)*sinh(d*x + c)^6 + 4*(63*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^5 - 14*(7*a^2 - 6*a*b - 13*b^2)*cosh(d*x + c)^3 - 3*(13*a^2 - 40*a*b + 7*b^2)*cosh(d*x + c))*sinh(d*x + c)^5 - 2*(13*a^2 - 40*a*b + 7*b^2)*cosh(d*x + c)^4 + 2*(105*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^6 - 35*(7*a^2 - 6*a*b - 13*b^2)*cosh(d*x + c)^4 - 15*(13*a^2 - 40*a*b + 7*b^2)*cosh(d*x + c)^2 - 13*a^2 + 40*a*b - 7*b^2)*sinh(d*x + c)^4 + 8*(15*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^7 - 7*(7*a^2 - 6*a*b - 13*b^2)*cosh(d*x + c)^5 - 5*(13*a^2 - 40*a*b + 7*b^2)*cosh(d*x + c)^3 - (13*a^2 - 40*a*b + 7*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 - (7*a^2 - 6*a*b - 13*b^2)*cosh(d*x + c)^2 + (45*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^8 - 28*(7*a^2 - 6*a*b - 13*b^2)*cosh(d*x + c)^6 - 30*(13*a^2 - 40*a*b + 7*b^2)*cosh(d*x + c)^4 - 12*(13*a^2 - 40*a*b + 7*b^2)*cosh(d*x + c)^2 - 7*a^2 + 6*a*b + 13*b^2)*sinh(d*x + c)^2 - 6*((3*a^2 + a*b - 2*b^2)*cosh(d*x + c)^7 + 7*(3*a^2 + a*b - 2*b^2)*cosh(d*x + c)*sinh(d*x + c)^6 + (3*a^2 + a*b - 2*b^2)*sinh(d*x + c)^7 + 2*(3*a^2 - 5*a*b + 2*b^2)*cosh(d*x + c)^5 + (21*(3*a^2 + a*b - 2*b^2)*cosh(d*x + c)^2 + 6*a^2 - 10*a*b + 4*b^2)*sinh(d*x + c)^5 + 5*(7*(3*a^2 + a*b - 2*b^2)*cosh(d*x + c)^3 + 2*(3*a^2 - 5*a*b + 2*b^2)*cosh(d*x + c))*sinh(d*x + c)^4 + (3*a^2 + a*b - 2*b^2)*cosh(d*x + c)^3 + (35*(3*a^2 + a*b - 2*b^2)*cosh(d*x + c)^4 + 20*(3*a^2 - 5*a*b + 2*b^2)*cosh(d*x + c)^2 + 3*a^2 + a*b - 2*b^2)*sinh(d*x + c)^3 + (21*(3*a^2 + a*b - 2*b^2)*cosh(d*x + c)^5 + 20*(3*a^2 - 5*a*b + 2*b^2)*cosh(d*x + c)^3 + 3*(3*a^2 + a*b - 2*b^2)*cosh(d*x + c))*sinh(d*x + c)^2 + (7*(3*a^2 + a*b - 2*b^2)*cosh(d*x + c)^6 + 10*(3*a^2 - 5*a*b + 2*b^2)*cosh(d*x + c)^4 + 3*(3*a^2 + a*b - 2*b^2)*cosh(d*x + c)^2)*sinh(d*x + c))*sqrt(b/(a + b))*log(((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 + 3*b)*cosh(d*x + c)^2 + 2*(3*(a + b)*cosh(d*x + c)^2 + a + 3*b)*sinh(d*x + c)^2 + 4*((a + b)*cosh(d*x + c)^3 + (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)) + a + b)/((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)) + a^2 + 2*a*b + b^2 + 2*(5*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^9 - 4*(7*a^2 - 6*a*b - 13*b^2)*cosh(d*x + c)^7 - 6*(13*a^2 - 40*a*b + 7*b^2)*cosh(d*x + c)^5 - 4*(13*a^2 - 40*a*b + 7*b^2)*cosh(d*x + c)^3 - (7*a^2 - 6*a*b - 13*b^2)*cosh(d*x + c))*sinh(d*x + c))/((a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*d*cosh(d*x + c)^7 + 7*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*d*cosh(d*x + c)*sinh(d*x + c)^6 + (a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*d*sinh(d*x + c)^7 + 2*(a^4 + 2*a^3*b - 2*a*b^3 - b^4)*d*cosh(d*x + c)^5 + (21*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*d*cosh(d*x + c)^2 + 2*(a^4 + 2*a^3*b - 2*a*b^3 - b^4)*d)*sinh(d*x + c)^5 + (a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*d*cosh(d*x + c)^3 + 5*(7*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*d*cosh(d*x + c)^3 + 2*(a^4 + 2*a^3*b - 2*a*b^3 - b^4)*d*cosh(d*x + c))*sinh(d*x + c)^4 + (35*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*d*cosh(d*x + c)^4 + 20*(a^4 + 2*a^3*b - 2*a*b^3 - b^4)*d*cosh(d*x + c)^2 + (a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*d)*sinh(d*x + c)^3 + (21*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*d*cosh(d*x + c)^5 + 20*(a^4 + 2*a^3*b - 2*a*b^3 - b^4)*d*cosh(d*x + c)^3 + 3*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*d*cosh(d*x + c))*sinh(d*x + c)^2 + (7*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*d*cosh(d*x + c)^6 + 10*(a^4 + 2*a^3*b - 2*a*b^3 - b^4)*d*cosh(d*x + c)^4 + 3*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*d*cosh(d*x + c)^2)*sinh(d*x + c)), 1/24*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^10 + 10*(a^2 + 2*a*b + b^2)*cosh(d*x + c)*sinh(d*x + c)^9 + (a^2 + 2*a*b + b^2)*sinh(d*x + c)^10 - (7*a^2 - 6*a*b - 13*b^2)*cosh(d*x + c)^8 + (45*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 - 7*a^2 + 6*a*b + 13*b^2)*sinh(d*x + c)^8 + 8*(15*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 - (7*a^2 - 6*a*b - 13*b^2)*cosh(d*x + c))*sinh(d*x + c)^7 - 2*(13*a^2 - 40*a*b + 7*b^2)*cosh(d*x + c)^6 + 2*(105*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 - 14*(7*a^2 - 6*a*b - 13*b^2)*cosh(d*x + c)^2 - 13*a^2 + 40*a*b - 7*b^2)*sinh(d*x + c)^6 + 4*(63*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^5 - 14*(7*a^2 - 6*a*b - 13*b^2)*cosh(d*x + c)^3 - 3*(13*a^2 - 40*a*b + 7*b^2)*cosh(d*x + c))*sinh(d*x + c)^5 - 2*(13*a^2 - 40*a*b + 7*b^2)*cosh(d*x + c)^4 + 2*(105*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^6 - 35*(7*a^2 - 6*a*b - 13*b^2)*cosh(d*x + c)^4 - 15*(13*a^2 - 40*a*b + 7*b^2)*cosh(d*x + c)^2 - 13*a^2 + 40*a*b - 7*b^2)*sinh(d*x + c)^4 + 8*(15*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^7 - 7*(7*a^2 - 6*a*b - 13*b^2)*cosh(d*x + c)^5 - 5*(13*a^2 - 40*a*b + 7*b^2)*cosh(d*x + c)^3 - (13*a^2 - 40*a*b + 7*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 - (7*a^2 - 6*a*b - 13*b^2)*cosh(d*x + c)^2 + (45*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^8 - 28*(7*a^2 - 6*a*b - 13*b^2)*cosh(d*x + c)^6 - 30*(13*a^2 - 40*a*b + 7*b^2)*cosh(d*x + c)^4 - 12*(13*a^2 - 40*a*b + 7*b^2)*cosh(d*x + c)^2 - 7*a^2 + 6*a*b + 13*b^2)*sinh(d*x + c)^2 + 12*((3*a^2 + a*b - 2*b^2)*cosh(d*x + c)^7 + 7*(3*a^2 + a*b - 2*b^2)*cosh(d*x + c)*sinh(d*x + c)^6 + (3*a^2 + a*b - 2*b^2)*sinh(d*x + c)^7 + 2*(3*a^2 - 5*a*b + 2*b^2)*cosh(d*x + c)^5 + (21*(3*a^2 + a*b - 2*b^2)*cosh(d*x + c)^2 + 6*a^2 - 10*a*b + 4*b^2)*sinh(d*x + c)^5 + 5*(7*(3*a^2 + a*b - 2*b^2)*cosh(d*x + c)^3 + 2*(3*a^2 - 5*a*b + 2*b^2)*cosh(d*x + c))*sinh(d*x + c)^4 + (3*a^2 + a*b - 2*b^2)*cosh(d*x + c)^3 + (35*(3*a^2 + a*b - 2*b^2)*cosh(d*x + c)^4 + 20*(3*a^2 - 5*a*b + 2*b^2)*cosh(d*x + c)^2 + 3*a^2 + a*b - 2*b^2)*sinh(d*x + c)^3 + (21*(3*a^2 + a*b - 2*b^2)*cosh(d*x + c)^5 + 20*(3*a^2 - 5*a*b + 2*b^2)*cosh(d*x + c)^3 + 3*(3*a^2 + a*b - 2*b^2)*cosh(d*x + c))*sinh(d*x + c)^2 + (7*(3*a^2 + a*b - 2*b^2)*cosh(d*x + c)^6 + 10*(3*a^2 - 5*a*b + 2*b^2)*cosh(d*x + c)^4 + 3*(3*a^2 + a*b - 2*b^2)*cosh(d*x + c)^2)*sinh(d*x + c))*sqrt(-b/(a + b))*arctan(1/2*((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 - 3*b)*cosh(d*x + c) + (3*(a + b)*cosh(d*x + c)^2 + a - 3*b)*sinh(d*x + c))*sqrt(-b/(a + b))/b) - 12*((3*a^2 + a*b - 2*b^2)*cosh(d*x + c)^7 + 7*(3*a^2 + a*b - 2*b^2)*cosh(d*x + c)*sinh(d*x + c)^6 + (3*a^2 + a*b - 2*b^2)*sinh(d*x + c)^7 + 2*(3*a^2 - 5*a*b + 2*b^2)*cosh(d*x + c)^5 + (21*(3*a^2 + a*b - 2*b^2)*cosh(d*x + c)^2 + 6*a^2 - 10*a*b + 4*b^2)*sinh(d*x + c)^5 + 5*(7*(3*a^2 + a*b - 2*b^2)*cosh(d*x + c)^3 + 2*(3*a^2 - 5*a*b + 2*b^2)*cosh(d*x + c))*sinh(d*x + c)^4 + (3*a^2 + a*b - 2*b^2)*cosh(d*x + c)^3 + (35*(3*a^2 + a*b - 2*b^2)*cosh(d*x + c)^4 + 20*(3*a^2 - 5*a*b + 2*b^2)*cosh(d*x + c)^2 + 3*a^2 + a*b - 2*b^2)*sinh(d*x + c)^3 + (21*(3*a^2 + a*b - 2*b^2)*cosh(d*x + c)^5 + 20*(3*a^2 - 5*a*b + 2*b^2)*cosh(d*x + c)^3 + 3*(3*a^2 + a*b - 2*b^2)*cosh(d*x + c))*sinh(d*x + c)^2 + (7*(3*a^2 + a*b - 2*b^2)*cosh(d*x + c)^6 + 10*(3*a^2 - 5*a*b + 2*b^2)*cosh(d*x + c)^4 + 3*(3*a^2 + a*b - 2*b^2)*cosh(d*x + c)^2)*sinh(d*x + c))*sqrt(-b/(a + b))*arctan(1/2*((a + b)*cosh(d*x + c) + (a + b)*sinh(d*x + c))*sqrt(-b/(a + b))/b) + a^2 + 2*a*b + b^2 + 2*(5*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^9 - 4*(7*a^2 - 6*a*b - 13*b^2)*cosh(d*x + c)^7 - 6*(13*a^2 - 40*a*b + 7*b^2)*cosh(d*x + c)^5 - 4*(13*a^2 - 40*a*b + 7*b^2)*cosh(d*x + c)^3 - (7*a^2 - 6*a*b - 13*b^2)*cosh(d*x + c))*sinh(d*x + c))/((a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*d*cosh(d*x + c)^7 + 7*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*d*cosh(d*x + c)*sinh(d*x + c)^6 + (a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*d*sinh(d*x + c)^7 + 2*(a^4 + 2*a^3*b - 2*a*b^3 - b^4)*d*cosh(d*x + c)^5 + (21*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*d*cosh(d*x + c)^2 + 2*(a^4 + 2*a^3*b - 2*a*b^3 - b^4)*d)*sinh(d*x + c)^5 + (a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*d*cosh(d*x + c)^3 + 5*(7*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*d*cosh(d*x + c)^3 + 2*(a^4 + 2*a^3*b - 2*a*b^3 - b^4)*d*cosh(d*x + c))*sinh(d*x + c)^4 + (35*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*d*cosh(d*x + c)^4 + 20*(a^4 + 2*a^3*b - 2*a*b^3 - b^4)*d*cosh(d*x + c)^2 + (a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*d)*sinh(d*x + c)^3 + (21*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*d*cosh(d*x + c)^5 + 20*(a^4 + 2*a^3*b - 2*a*b^3 - b^4)*d*cosh(d*x + c)^3 + 3*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*d*cosh(d*x + c))*sinh(d*x + c)^2 + (7*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*d*cosh(d*x + c)^6 + 10*(a^4 + 2*a^3*b - 2*a*b^3 - b^4)*d*cosh(d*x + c)^4 + 3*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*d*cosh(d*x + c)^2)*sinh(d*x + c))]","B",0
35,1,3918,0,0.811503," ","integrate(sinh(d*x+c)^2/(a+b*tanh(d*x+c)^2)^2,x, algorithm=""fricas"")","\left[\frac{{\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{8} - 2 \, {\left(2 \, {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} d x - a^{2} + b^{2}\right)} \cosh\left(d x + c\right)^{6} - 2 \, {\left(2 \, {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} d x - 14 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} - a^{2} + b^{2}\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(14 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(2 \, {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} d x - a^{2} + b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 8 \, {\left({\left(a^{2} - 4 \, a b + 3 \, b^{2}\right)} d x - a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} - 4 \, {\left(a^{2} - 4 \, a b + 3 \, b^{2}\right)} d x - 15 \, {\left(2 \, {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} d x - a^{2} + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, a b - 4 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{5} - 5 \, {\left(2 \, {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} d x - a^{2} + b^{2}\right)} \cosh\left(d x + c\right)^{3} - 4 \, {\left({\left(a^{2} - 4 \, a b + 3 \, b^{2}\right)} d x - a b + b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 2 \, {\left(2 \, {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} d x + a^{2} - 4 \, a b - 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(14 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{6} - 15 \, {\left(2 \, {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} d x - a^{2} + b^{2}\right)} \cosh\left(d x + c\right)^{4} - 2 \, {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} d x - 24 \, {\left({\left(a^{2} - 4 \, a b + 3 \, b^{2}\right)} d x - a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} - a^{2} + 4 \, a b + 5 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} - 2 \, {\left({\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{6} + 6 \, {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(3 \, a^{2} - 4 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(15 \, {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 6 \, a^{2} - 8 \, a b + 2 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(3 \, a^{2} - 4 \, a b + b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(15 \, {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{4} + 12 \, {\left(3 \, a^{2} - 4 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 3 \, a^{2} + 2 \, a b - b^{2}\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{5} + 4 \, {\left(3 \, a^{2} - 4 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{2} + 2 \, 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{{\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) \sinh\left(d x + c\right)^{3} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{2} + a^{2} - 6 \, a b + b^{2} + 4 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + 4 \, {\left({\left(a^{2} + a b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} + a b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} + a b\right)} \sinh\left(d x + c\right)^{2} + a^{2} - a b\right)} \sqrt{-\frac{b}{a}}}{{\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) - a^{2} - 2 \, a b - b^{2} + 4 \, {\left(2 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{7} - 3 \, {\left(2 \, {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} d x - a^{2} + b^{2}\right)} \cosh\left(d x + c\right)^{5} - 8 \, {\left({\left(a^{2} - 4 \, a b + 3 \, b^{2}\right)} d x - a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(2 \, {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} d x + a^{2} - 4 \, a b - 5 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{8 \, {\left({\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} d \cosh\left(d x + c\right)^{6} + 6 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} d \sinh\left(d x + c\right)^{6} + 2 \, {\left(a^{4} + 2 \, a^{3} b - 2 \, a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{4} + {\left(15 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{4} + 2 \, a^{3} b - 2 \, a b^{3} - b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{4} + {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} d \cosh\left(d x + c\right)^{2} + 4 \, {\left(5 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} d \cosh\left(d x + c\right)^{3} + 2 \, {\left(a^{4} + 2 \, a^{3} b - 2 \, a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(15 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 12 \, {\left(a^{4} + 2 \, a^{3} b - 2 \, a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} d \cosh\left(d x + c\right)^{5} + 4 \, {\left(a^{4} + 2 \, a^{3} b - 2 \, a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{4} + 4 \, a^{3} b + 6 \, 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{{\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{8} - 2 \, {\left(2 \, {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} d x - a^{2} + b^{2}\right)} \cosh\left(d x + c\right)^{6} - 2 \, {\left(2 \, {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} d x - 14 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} - a^{2} + b^{2}\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(14 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(2 \, {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} d x - a^{2} + b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 8 \, {\left({\left(a^{2} - 4 \, a b + 3 \, b^{2}\right)} d x - a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} - 4 \, {\left(a^{2} - 4 \, a b + 3 \, b^{2}\right)} d x - 15 \, {\left(2 \, {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} d x - a^{2} + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, a b - 4 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{5} - 5 \, {\left(2 \, {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} d x - a^{2} + b^{2}\right)} \cosh\left(d x + c\right)^{3} - 4 \, {\left({\left(a^{2} - 4 \, a b + 3 \, b^{2}\right)} d x - a b + b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 2 \, {\left(2 \, {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} d x + a^{2} - 4 \, a b - 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(14 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{6} - 15 \, {\left(2 \, {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} d x - a^{2} + b^{2}\right)} \cosh\left(d x + c\right)^{4} - 2 \, {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} d x - 24 \, {\left({\left(a^{2} - 4 \, a b + 3 \, b^{2}\right)} d x - a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} - a^{2} + 4 \, a b + 5 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} - 4 \, {\left({\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{6} + 6 \, {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(3 \, a^{2} - 4 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(15 \, {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 6 \, a^{2} - 8 \, a b + 2 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(3 \, a^{2} - 4 \, a b + b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(15 \, {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{4} + 12 \, {\left(3 \, a^{2} - 4 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 3 \, a^{2} + 2 \, a b - b^{2}\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{5} + 4 \, {\left(3 \, a^{2} - 4 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{2} + 2 \, 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({\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} + a - b\right)} \sqrt{\frac{b}{a}}}{2 \, b}\right) - a^{2} - 2 \, a b - b^{2} + 4 \, {\left(2 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{7} - 3 \, {\left(2 \, {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} d x - a^{2} + b^{2}\right)} \cosh\left(d x + c\right)^{5} - 8 \, {\left({\left(a^{2} - 4 \, a b + 3 \, b^{2}\right)} d x - a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(2 \, {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} d x + a^{2} - 4 \, a b - 5 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{8 \, {\left({\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} d \cosh\left(d x + c\right)^{6} + 6 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} d \sinh\left(d x + c\right)^{6} + 2 \, {\left(a^{4} + 2 \, a^{3} b - 2 \, a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{4} + {\left(15 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{4} + 2 \, a^{3} b - 2 \, a b^{3} - b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{4} + {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} d \cosh\left(d x + c\right)^{2} + 4 \, {\left(5 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} d \cosh\left(d x + c\right)^{3} + 2 \, {\left(a^{4} + 2 \, a^{3} b - 2 \, a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(15 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 12 \, {\left(a^{4} + 2 \, a^{3} b - 2 \, a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} d \cosh\left(d x + c\right)^{5} + 4 \, {\left(a^{4} + 2 \, a^{3} b - 2 \, a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{4} + 4 \, a^{3} b + 6 \, 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,"[1/8*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^8 + 8*(a^2 + 2*a*b + b^2)*cosh(d*x + c)*sinh(d*x + c)^7 + (a^2 + 2*a*b + b^2)*sinh(d*x + c)^8 - 2*(2*(a^2 - 2*a*b - 3*b^2)*d*x - a^2 + b^2)*cosh(d*x + c)^6 - 2*(2*(a^2 - 2*a*b - 3*b^2)*d*x - 14*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 - a^2 + b^2)*sinh(d*x + c)^6 + 4*(14*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 - 3*(2*(a^2 - 2*a*b - 3*b^2)*d*x - a^2 + b^2)*cosh(d*x + c))*sinh(d*x + c)^5 - 8*((a^2 - 4*a*b + 3*b^2)*d*x - a*b + b^2)*cosh(d*x + c)^4 + 2*(35*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 - 4*(a^2 - 4*a*b + 3*b^2)*d*x - 15*(2*(a^2 - 2*a*b - 3*b^2)*d*x - a^2 + b^2)*cosh(d*x + c)^2 + 4*a*b - 4*b^2)*sinh(d*x + c)^4 + 8*(7*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^5 - 5*(2*(a^2 - 2*a*b - 3*b^2)*d*x - a^2 + b^2)*cosh(d*x + c)^3 - 4*((a^2 - 4*a*b + 3*b^2)*d*x - a*b + b^2)*cosh(d*x + c))*sinh(d*x + c)^3 - 2*(2*(a^2 - 2*a*b - 3*b^2)*d*x + a^2 - 4*a*b - 5*b^2)*cosh(d*x + c)^2 + 2*(14*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^6 - 15*(2*(a^2 - 2*a*b - 3*b^2)*d*x - a^2 + b^2)*cosh(d*x + c)^4 - 2*(a^2 - 2*a*b - 3*b^2)*d*x - 24*((a^2 - 4*a*b + 3*b^2)*d*x - a*b + b^2)*cosh(d*x + c)^2 - a^2 + 4*a*b + 5*b^2)*sinh(d*x + c)^2 - 2*((3*a^2 + 2*a*b - b^2)*cosh(d*x + c)^6 + 6*(3*a^2 + 2*a*b - b^2)*cosh(d*x + c)*sinh(d*x + c)^5 + (3*a^2 + 2*a*b - b^2)*sinh(d*x + c)^6 + 2*(3*a^2 - 4*a*b + b^2)*cosh(d*x + c)^4 + (15*(3*a^2 + 2*a*b - b^2)*cosh(d*x + c)^2 + 6*a^2 - 8*a*b + 2*b^2)*sinh(d*x + c)^4 + 4*(5*(3*a^2 + 2*a*b - b^2)*cosh(d*x + c)^3 + 2*(3*a^2 - 4*a*b + b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + (3*a^2 + 2*a*b - b^2)*cosh(d*x + c)^2 + (15*(3*a^2 + 2*a*b - b^2)*cosh(d*x + c)^4 + 12*(3*a^2 - 4*a*b + b^2)*cosh(d*x + c)^2 + 3*a^2 + 2*a*b - b^2)*sinh(d*x + c)^2 + 2*(3*(3*a^2 + 2*a*b - b^2)*cosh(d*x + c)^5 + 4*(3*a^2 - 4*a*b + b^2)*cosh(d*x + c)^3 + (3*a^2 + 2*a*b - b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-b/a)*log(((a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 + 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 + 2*(a^2 - b^2)*cosh(d*x + c)^2 + 2*(3*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + a^2 - b^2)*sinh(d*x + c)^2 + a^2 - 6*a*b + b^2 + 4*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 + (a^2 - b^2)*cosh(d*x + c))*sinh(d*x + c) + 4*((a^2 + a*b)*cosh(d*x + c)^2 + 2*(a^2 + a*b)*cosh(d*x + c)*sinh(d*x + c) + (a^2 + a*b)*sinh(d*x + c)^2 + a^2 - a*b)*sqrt(-b/a))/((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)) - a^2 - 2*a*b - b^2 + 4*(2*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^7 - 3*(2*(a^2 - 2*a*b - 3*b^2)*d*x - a^2 + b^2)*cosh(d*x + c)^5 - 8*((a^2 - 4*a*b + 3*b^2)*d*x - a*b + b^2)*cosh(d*x + c)^3 - (2*(a^2 - 2*a*b - 3*b^2)*d*x + a^2 - 4*a*b - 5*b^2)*cosh(d*x + c))*sinh(d*x + c))/((a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*d*cosh(d*x + c)^6 + 6*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*d*cosh(d*x + c)*sinh(d*x + c)^5 + (a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*d*sinh(d*x + c)^6 + 2*(a^4 + 2*a^3*b - 2*a*b^3 - b^4)*d*cosh(d*x + c)^4 + (15*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*d*cosh(d*x + c)^2 + 2*(a^4 + 2*a^3*b - 2*a*b^3 - b^4)*d)*sinh(d*x + c)^4 + (a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*d*cosh(d*x + c)^2 + 4*(5*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*d*cosh(d*x + c)^3 + 2*(a^4 + 2*a^3*b - 2*a*b^3 - b^4)*d*cosh(d*x + c))*sinh(d*x + c)^3 + (15*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*d*cosh(d*x + c)^4 + 12*(a^4 + 2*a^3*b - 2*a*b^3 - b^4)*d*cosh(d*x + c)^2 + (a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*d)*sinh(d*x + c)^2 + 2*(3*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*d*cosh(d*x + c)^5 + 4*(a^4 + 2*a^3*b - 2*a*b^3 - b^4)*d*cosh(d*x + c)^3 + (a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*d*cosh(d*x + c))*sinh(d*x + c)), 1/8*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^8 + 8*(a^2 + 2*a*b + b^2)*cosh(d*x + c)*sinh(d*x + c)^7 + (a^2 + 2*a*b + b^2)*sinh(d*x + c)^8 - 2*(2*(a^2 - 2*a*b - 3*b^2)*d*x - a^2 + b^2)*cosh(d*x + c)^6 - 2*(2*(a^2 - 2*a*b - 3*b^2)*d*x - 14*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 - a^2 + b^2)*sinh(d*x + c)^6 + 4*(14*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 - 3*(2*(a^2 - 2*a*b - 3*b^2)*d*x - a^2 + b^2)*cosh(d*x + c))*sinh(d*x + c)^5 - 8*((a^2 - 4*a*b + 3*b^2)*d*x - a*b + b^2)*cosh(d*x + c)^4 + 2*(35*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 - 4*(a^2 - 4*a*b + 3*b^2)*d*x - 15*(2*(a^2 - 2*a*b - 3*b^2)*d*x - a^2 + b^2)*cosh(d*x + c)^2 + 4*a*b - 4*b^2)*sinh(d*x + c)^4 + 8*(7*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^5 - 5*(2*(a^2 - 2*a*b - 3*b^2)*d*x - a^2 + b^2)*cosh(d*x + c)^3 - 4*((a^2 - 4*a*b + 3*b^2)*d*x - a*b + b^2)*cosh(d*x + c))*sinh(d*x + c)^3 - 2*(2*(a^2 - 2*a*b - 3*b^2)*d*x + a^2 - 4*a*b - 5*b^2)*cosh(d*x + c)^2 + 2*(14*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^6 - 15*(2*(a^2 - 2*a*b - 3*b^2)*d*x - a^2 + b^2)*cosh(d*x + c)^4 - 2*(a^2 - 2*a*b - 3*b^2)*d*x - 24*((a^2 - 4*a*b + 3*b^2)*d*x - a*b + b^2)*cosh(d*x + c)^2 - a^2 + 4*a*b + 5*b^2)*sinh(d*x + c)^2 - 4*((3*a^2 + 2*a*b - b^2)*cosh(d*x + c)^6 + 6*(3*a^2 + 2*a*b - b^2)*cosh(d*x + c)*sinh(d*x + c)^5 + (3*a^2 + 2*a*b - b^2)*sinh(d*x + c)^6 + 2*(3*a^2 - 4*a*b + b^2)*cosh(d*x + c)^4 + (15*(3*a^2 + 2*a*b - b^2)*cosh(d*x + c)^2 + 6*a^2 - 8*a*b + 2*b^2)*sinh(d*x + c)^4 + 4*(5*(3*a^2 + 2*a*b - b^2)*cosh(d*x + c)^3 + 2*(3*a^2 - 4*a*b + b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + (3*a^2 + 2*a*b - b^2)*cosh(d*x + c)^2 + (15*(3*a^2 + 2*a*b - b^2)*cosh(d*x + c)^4 + 12*(3*a^2 - 4*a*b + b^2)*cosh(d*x + c)^2 + 3*a^2 + 2*a*b - b^2)*sinh(d*x + c)^2 + 2*(3*(3*a^2 + 2*a*b - b^2)*cosh(d*x + c)^5 + 4*(3*a^2 - 4*a*b + b^2)*cosh(d*x + c)^3 + (3*a^2 + 2*a*b - b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(b/a)*arctan(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 + a - b)*sqrt(b/a)/b) - a^2 - 2*a*b - b^2 + 4*(2*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^7 - 3*(2*(a^2 - 2*a*b - 3*b^2)*d*x - a^2 + b^2)*cosh(d*x + c)^5 - 8*((a^2 - 4*a*b + 3*b^2)*d*x - a*b + b^2)*cosh(d*x + c)^3 - (2*(a^2 - 2*a*b - 3*b^2)*d*x + a^2 - 4*a*b - 5*b^2)*cosh(d*x + c))*sinh(d*x + c))/((a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*d*cosh(d*x + c)^6 + 6*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*d*cosh(d*x + c)*sinh(d*x + c)^5 + (a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*d*sinh(d*x + c)^6 + 2*(a^4 + 2*a^3*b - 2*a*b^3 - b^4)*d*cosh(d*x + c)^4 + (15*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*d*cosh(d*x + c)^2 + 2*(a^4 + 2*a^3*b - 2*a*b^3 - b^4)*d)*sinh(d*x + c)^4 + (a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*d*cosh(d*x + c)^2 + 4*(5*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*d*cosh(d*x + c)^3 + 2*(a^4 + 2*a^3*b - 2*a*b^3 - b^4)*d*cosh(d*x + c))*sinh(d*x + c)^3 + (15*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*d*cosh(d*x + c)^4 + 12*(a^4 + 2*a^3*b - 2*a*b^3 - b^4)*d*cosh(d*x + c)^2 + (a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*d)*sinh(d*x + c)^2 + 2*(3*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*d*cosh(d*x + c)^5 + 4*(a^4 + 2*a^3*b - 2*a*b^3 - b^4)*d*cosh(d*x + c)^3 + (a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
36,1,2252,0,0.613198," ","integrate(sinh(d*x+c)/(a+b*tanh(d*x+c)^2)^2,x, algorithm=""fricas"")","\left[\frac{2 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{6} + 12 \, {\left(a + b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + 2 \, {\left(a + b\right)} \sinh\left(d x + c\right)^{6} + 6 \, {\left(a - b\right)} \cosh\left(d x + c\right)^{4} + 6 \, {\left(5 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} + a - b\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(5 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 6 \, {\left(a - b\right)} \cosh\left(d x + c\right)^{2} + 6 \, {\left(5 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{4} + 6 \, {\left(a - b\right)} \cosh\left(d x + c\right)^{2} + a - b\right)} \sinh\left(d x + c\right)^{2} + 3 \, {\left({\left(a + b\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(a + b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} + {\left(a + b\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(a - b\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(5 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} + a - b\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(5 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(a + b\right)} \cosh\left(d x + c\right) + {\left(5 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{4} + 6 \, {\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}} \log\left(\frac{{\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 + 3 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} + a + 3 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a + 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) - 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}} + a + b}{{\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) + 12 \, {\left({\left(a + b\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\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) + 2 \, a + 2 \, b}{4 \, {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d \cosh\left(d x + c\right)^{5} + 5 \, {\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)^{4} + {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d \sinh\left(d x + c\right)^{5} + 2 \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{3} + 2 \, {\left(5 \, {\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} + a^{2} b - a b^{2} - b^{3}\right)} d\right)} \sinh\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) + 2 \, {\left(5 \, {\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} + a^{2} b - a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(5 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 6 \, {\left(a^{3} + a^{2} b - 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)\right)}}, \frac{{\left(a + b\right)} \cosh\left(d x + c\right)^{6} + 6 \, {\left(a + b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(a + b\right)} \sinh\left(d x + c\right)^{6} + 3 \, {\left(a - b\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(5 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} + a - b\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 3 \, {\left(a - b\right)} \cosh\left(d x + c\right)^{2} + 3 \, {\left(5 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{4} + 6 \, {\left(a - b\right)} \cosh\left(d x + c\right)^{2} + a - b\right)} \sinh\left(d x + c\right)^{2} - 3 \, {\left({\left(a + b\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(a + b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} + {\left(a + b\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(a - b\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(5 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} + a - b\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(5 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(a + b\right)} \cosh\left(d x + c\right) + {\left(5 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{4} + 6 \, {\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}} \arctan\left(\frac{{\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 - 3 \, b\right)} \cosh\left(d x + c\right) + {\left(3 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} + a - 3 \, b\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{b}{a + b}}}{2 \, b}\right) + 3 \, {\left({\left(a + b\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(a + b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} + {\left(a + b\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(a - b\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(5 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} + a - b\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(5 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(a + b\right)} \cosh\left(d x + c\right) + {\left(5 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{4} + 6 \, {\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}} \arctan\left(\frac{{\left({\left(a + b\right)} \cosh\left(d x + c\right) + {\left(a + b\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{b}{a + b}}}{2 \, b}\right) + 6 \, {\left({\left(a + b\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\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}{2 \, {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d \cosh\left(d x + c\right)^{5} + 5 \, {\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)^{4} + {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d \sinh\left(d x + c\right)^{5} + 2 \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{3} + 2 \, {\left(5 \, {\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} + a^{2} b - a b^{2} - b^{3}\right)} d\right)} \sinh\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) + 2 \, {\left(5 \, {\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} + a^{2} b - a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(5 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 6 \, {\left(a^{3} + a^{2} b - 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)\right)}}\right]"," ",0,"[1/4*(2*(a + b)*cosh(d*x + c)^6 + 12*(a + b)*cosh(d*x + c)*sinh(d*x + c)^5 + 2*(a + b)*sinh(d*x + c)^6 + 6*(a - b)*cosh(d*x + c)^4 + 6*(5*(a + b)*cosh(d*x + c)^2 + a - b)*sinh(d*x + c)^4 + 8*(5*(a + b)*cosh(d*x + c)^3 + 3*(a - b)*cosh(d*x + c))*sinh(d*x + c)^3 + 6*(a - b)*cosh(d*x + c)^2 + 6*(5*(a + b)*cosh(d*x + c)^4 + 6*(a - b)*cosh(d*x + c)^2 + a - b)*sinh(d*x + c)^2 + 3*((a + b)*cosh(d*x + c)^5 + 5*(a + b)*cosh(d*x + c)*sinh(d*x + c)^4 + (a + b)*sinh(d*x + c)^5 + 2*(a - b)*cosh(d*x + c)^3 + 2*(5*(a + b)*cosh(d*x + c)^2 + a - b)*sinh(d*x + c)^3 + 2*(5*(a + b)*cosh(d*x + c)^3 + 3*(a - b)*cosh(d*x + c))*sinh(d*x + c)^2 + (a + b)*cosh(d*x + c) + (5*(a + b)*cosh(d*x + c)^4 + 6*(a - b)*cosh(d*x + c)^2 + a + b)*sinh(d*x + c))*sqrt(b/(a + b))*log(((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 + 3*b)*cosh(d*x + c)^2 + 2*(3*(a + b)*cosh(d*x + c)^2 + a + 3*b)*sinh(d*x + c)^2 + 4*((a + b)*cosh(d*x + c)^3 + (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)) + a + b)/((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)) + 12*((a + b)*cosh(d*x + c)^5 + 2*(a - b)*cosh(d*x + c)^3 + (a - b)*cosh(d*x + c))*sinh(d*x + c) + 2*a + 2*b)/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*cosh(d*x + c)^5 + 5*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*cosh(d*x + c)*sinh(d*x + c)^4 + (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*sinh(d*x + c)^5 + 2*(a^3 + a^2*b - a*b^2 - b^3)*d*cosh(d*x + c)^3 + 2*(5*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*cosh(d*x + c)^2 + (a^3 + a^2*b - a*b^2 - b^3)*d)*sinh(d*x + c)^3 + (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*cosh(d*x + c) + 2*(5*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*cosh(d*x + c)^3 + 3*(a^3 + a^2*b - a*b^2 - b^3)*d*cosh(d*x + c))*sinh(d*x + c)^2 + (5*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*cosh(d*x + c)^4 + 6*(a^3 + a^2*b - 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)), 1/2*((a + b)*cosh(d*x + c)^6 + 6*(a + b)*cosh(d*x + c)*sinh(d*x + c)^5 + (a + b)*sinh(d*x + c)^6 + 3*(a - b)*cosh(d*x + c)^4 + 3*(5*(a + b)*cosh(d*x + c)^2 + a - b)*sinh(d*x + c)^4 + 4*(5*(a + b)*cosh(d*x + c)^3 + 3*(a - b)*cosh(d*x + c))*sinh(d*x + c)^3 + 3*(a - b)*cosh(d*x + c)^2 + 3*(5*(a + b)*cosh(d*x + c)^4 + 6*(a - b)*cosh(d*x + c)^2 + a - b)*sinh(d*x + c)^2 - 3*((a + b)*cosh(d*x + c)^5 + 5*(a + b)*cosh(d*x + c)*sinh(d*x + c)^4 + (a + b)*sinh(d*x + c)^5 + 2*(a - b)*cosh(d*x + c)^3 + 2*(5*(a + b)*cosh(d*x + c)^2 + a - b)*sinh(d*x + c)^3 + 2*(5*(a + b)*cosh(d*x + c)^3 + 3*(a - b)*cosh(d*x + c))*sinh(d*x + c)^2 + (a + b)*cosh(d*x + c) + (5*(a + b)*cosh(d*x + c)^4 + 6*(a - b)*cosh(d*x + c)^2 + a + b)*sinh(d*x + c))*sqrt(-b/(a + b))*arctan(1/2*((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 - 3*b)*cosh(d*x + c) + (3*(a + b)*cosh(d*x + c)^2 + a - 3*b)*sinh(d*x + c))*sqrt(-b/(a + b))/b) + 3*((a + b)*cosh(d*x + c)^5 + 5*(a + b)*cosh(d*x + c)*sinh(d*x + c)^4 + (a + b)*sinh(d*x + c)^5 + 2*(a - b)*cosh(d*x + c)^3 + 2*(5*(a + b)*cosh(d*x + c)^2 + a - b)*sinh(d*x + c)^3 + 2*(5*(a + b)*cosh(d*x + c)^3 + 3*(a - b)*cosh(d*x + c))*sinh(d*x + c)^2 + (a + b)*cosh(d*x + c) + (5*(a + b)*cosh(d*x + c)^4 + 6*(a - b)*cosh(d*x + c)^2 + a + b)*sinh(d*x + c))*sqrt(-b/(a + b))*arctan(1/2*((a + b)*cosh(d*x + c) + (a + b)*sinh(d*x + c))*sqrt(-b/(a + b))/b) + 6*((a + b)*cosh(d*x + c)^5 + 2*(a - b)*cosh(d*x + c)^3 + (a - b)*cosh(d*x + c))*sinh(d*x + c) + a + b)/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*cosh(d*x + c)^5 + 5*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*cosh(d*x + c)*sinh(d*x + c)^4 + (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*sinh(d*x + c)^5 + 2*(a^3 + a^2*b - a*b^2 - b^3)*d*cosh(d*x + c)^3 + 2*(5*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*cosh(d*x + c)^2 + (a^3 + a^2*b - a*b^2 - b^3)*d)*sinh(d*x + c)^3 + (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*cosh(d*x + c) + 2*(5*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*cosh(d*x + c)^3 + 3*(a^3 + a^2*b - a*b^2 - b^3)*d*cosh(d*x + c))*sinh(d*x + c)^2 + (5*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*cosh(d*x + c)^4 + 6*(a^3 + a^2*b - 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))]","B",0
37,1,2614,0,1.094322," ","integrate(csch(d*x+c)/(a+b*tanh(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^{2} + 5 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(3 \, a^{2} + 5 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(3 \, a^{2} + 5 \, a b + 2 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(3 \, a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(3 \, a^{2} + 5 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 3 \, a^{2} - a b - 2 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} + 3 \, a^{2} + 5 \, a b + 2 \, b^{2} + 4 \, {\left({\left(3 \, a^{2} + 5 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{2} - 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{{\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 + 3 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} + a + 3 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a + 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) + 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}} + a + b}{{\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) - 4 \, {\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) \sinh\left(d x + c\right)^{3} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 2 \, a b + b^{2} + 4 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} - 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^{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) \sinh\left(d x + c\right)^{3} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 2 \, a b + b^{2} + 4 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} - 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^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} d \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{4} - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{4} - a^{2} b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} d + 4 \, {\left({\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{4} - 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^{2} + 5 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(3 \, a^{2} + 5 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(3 \, a^{2} + 5 \, a b + 2 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(3 \, a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(3 \, a^{2} + 5 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 3 \, a^{2} - a b - 2 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} + 3 \, a^{2} + 5 \, a b + 2 \, b^{2} + 4 \, {\left({\left(3 \, a^{2} + 5 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{2} - 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({\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 - 3 \, b\right)} \cosh\left(d x + c\right) + {\left(3 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} + a - 3 \, b\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{b}{a + b}}}{2 \, b}\right) - {\left({\left(3 \, a^{2} + 5 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(3 \, a^{2} + 5 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(3 \, a^{2} + 5 \, a b + 2 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(3 \, a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(3 \, a^{2} + 5 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 3 \, a^{2} - a b - 2 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} + 3 \, a^{2} + 5 \, a b + 2 \, b^{2} + 4 \, {\left({\left(3 \, a^{2} + 5 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{2} - 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({\left(a + b\right)} \cosh\left(d x + c\right) + {\left(a + b\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{b}{a + b}}}{2 \, b}\right) - 2 \, {\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) \sinh\left(d x + c\right)^{3} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 2 \, a b + b^{2} + 4 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} - 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^{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) \sinh\left(d x + c\right)^{3} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 2 \, a b + b^{2} + 4 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} - 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^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} d \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{4} - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{4} - a^{2} b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} d + 4 \, {\left({\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{4} - 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^2 + 5*a*b + 2*b^2)*cosh(d*x + c)^4 + 4*(3*a^2 + 5*a*b + 2*b^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (3*a^2 + 5*a*b + 2*b^2)*sinh(d*x + c)^4 + 2*(3*a^2 - a*b - 2*b^2)*cosh(d*x + c)^2 + 2*(3*(3*a^2 + 5*a*b + 2*b^2)*cosh(d*x + c)^2 + 3*a^2 - a*b - 2*b^2)*sinh(d*x + c)^2 + 3*a^2 + 5*a*b + 2*b^2 + 4*((3*a^2 + 5*a*b + 2*b^2)*cosh(d*x + c)^3 + (3*a^2 - a*b - 2*b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(b/(a + b))*log(((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 + 3*b)*cosh(d*x + c)^2 + 2*(3*(a + b)*cosh(d*x + c)^2 + a + 3*b)*sinh(d*x + c)^2 + 4*((a + b)*cosh(d*x + c)^3 + (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)) + a + b)/((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)) - 4*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 + 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 + 2*(a^2 - b^2)*cosh(d*x + c)^2 + 2*(3*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + a^2 - b^2)*sinh(d*x + c)^2 + a^2 + 2*a*b + b^2 + 4*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 + (a^2 - b^2)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) + 1) + 4*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 + 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 + 2*(a^2 - b^2)*cosh(d*x + c)^2 + 2*(3*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + a^2 - b^2)*sinh(d*x + c)^2 + a^2 + 2*a*b + b^2 + 4*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 + (a^2 - 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^4 + 2*a^3*b + a^2*b^2)*d*cosh(d*x + c)^4 + 4*(a^4 + 2*a^3*b + a^2*b^2)*d*cosh(d*x + c)*sinh(d*x + c)^3 + (a^4 + 2*a^3*b + a^2*b^2)*d*sinh(d*x + c)^4 + 2*(a^4 - a^2*b^2)*d*cosh(d*x + c)^2 + 2*(3*(a^4 + 2*a^3*b + a^2*b^2)*d*cosh(d*x + c)^2 + (a^4 - a^2*b^2)*d)*sinh(d*x + c)^2 + (a^4 + 2*a^3*b + a^2*b^2)*d + 4*((a^4 + 2*a^3*b + a^2*b^2)*d*cosh(d*x + c)^3 + (a^4 - 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^2 + 5*a*b + 2*b^2)*cosh(d*x + c)^4 + 4*(3*a^2 + 5*a*b + 2*b^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (3*a^2 + 5*a*b + 2*b^2)*sinh(d*x + c)^4 + 2*(3*a^2 - a*b - 2*b^2)*cosh(d*x + c)^2 + 2*(3*(3*a^2 + 5*a*b + 2*b^2)*cosh(d*x + c)^2 + 3*a^2 - a*b - 2*b^2)*sinh(d*x + c)^2 + 3*a^2 + 5*a*b + 2*b^2 + 4*((3*a^2 + 5*a*b + 2*b^2)*cosh(d*x + c)^3 + (3*a^2 - a*b - 2*b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-b/(a + b))*arctan(1/2*((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 - 3*b)*cosh(d*x + c) + (3*(a + b)*cosh(d*x + c)^2 + a - 3*b)*sinh(d*x + c))*sqrt(-b/(a + b))/b) - ((3*a^2 + 5*a*b + 2*b^2)*cosh(d*x + c)^4 + 4*(3*a^2 + 5*a*b + 2*b^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (3*a^2 + 5*a*b + 2*b^2)*sinh(d*x + c)^4 + 2*(3*a^2 - a*b - 2*b^2)*cosh(d*x + c)^2 + 2*(3*(3*a^2 + 5*a*b + 2*b^2)*cosh(d*x + c)^2 + 3*a^2 - a*b - 2*b^2)*sinh(d*x + c)^2 + 3*a^2 + 5*a*b + 2*b^2 + 4*((3*a^2 + 5*a*b + 2*b^2)*cosh(d*x + c)^3 + (3*a^2 - a*b - 2*b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-b/(a + b))*arctan(1/2*((a + b)*cosh(d*x + c) + (a + b)*sinh(d*x + c))*sqrt(-b/(a + b))/b) - 2*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 + 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 + 2*(a^2 - b^2)*cosh(d*x + c)^2 + 2*(3*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + a^2 - b^2)*sinh(d*x + c)^2 + a^2 + 2*a*b + b^2 + 4*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 + (a^2 - b^2)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) + 1) + 2*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 + 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 + 2*(a^2 - b^2)*cosh(d*x + c)^2 + 2*(3*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + a^2 - b^2)*sinh(d*x + c)^2 + a^2 + 2*a*b + b^2 + 4*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 + (a^2 - 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^4 + 2*a^3*b + a^2*b^2)*d*cosh(d*x + c)^4 + 4*(a^4 + 2*a^3*b + a^2*b^2)*d*cosh(d*x + c)*sinh(d*x + c)^3 + (a^4 + 2*a^3*b + a^2*b^2)*d*sinh(d*x + c)^4 + 2*(a^4 - a^2*b^2)*d*cosh(d*x + c)^2 + 2*(3*(a^4 + 2*a^3*b + a^2*b^2)*d*cosh(d*x + c)^2 + (a^4 - a^2*b^2)*d)*sinh(d*x + c)^2 + (a^4 + 2*a^3*b + a^2*b^2)*d + 4*((a^4 + 2*a^3*b + a^2*b^2)*d*cosh(d*x + c)^3 + (a^4 - a^2*b^2)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
38,1,2562,0,0.632576," ","integrate(csch(d*x+c)^2/(a+b*tanh(d*x+c)^2)^2,x, algorithm=""fricas"")","\left[-\frac{4 \, {\left(2 \, a^{2} + 3 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 16 \, {\left(2 \, a^{2} + 3 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + 4 \, {\left(2 \, a^{2} + 3 \, a b + 3 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(2 \, a^{2} - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 8 \, {\left(3 \, {\left(2 \, a^{2} + 3 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, a^{2} - 3 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} - 3 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{6} + 6 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{6} + {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(15 \, {\left(a^{2} + 2 \, a b + 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)^{4} + 4 \, {\left(5 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(15 \, {\left(a^{2} + 2 \, a b + 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)^{2} - a^{2} - 2 \, a b - b^{2} + 2 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{{\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) \sinh\left(d x + c\right)^{3} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{2} + a^{2} - 6 \, a b + b^{2} + 4 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) - 4 \, {\left({\left(a^{2} + a b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} + a b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} + a b\right)} \sinh\left(d x + c\right)^{2} + a^{2} - a b\right)} \sqrt{-\frac{b}{a}}}{{\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) + 8 \, a^{2} + 20 \, a b + 12 \, b^{2} + 16 \, {\left({\left(2 \, a^{2} + 3 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{2} - 3 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{4 \, {\left({\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{6} + 6 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} d \sinh\left(d x + c\right)^{6} + {\left(a^{4} - 2 \, a^{3} b - 3 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{4} + {\left(15 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{4} - 2 \, a^{3} b - 3 \, a^{2} b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{4} - {\left(a^{4} - 2 \, a^{3} b - 3 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{2} + 4 \, {\left(5 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{4} - 2 \, a^{3} b - 3 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(15 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{4} + 6 \, {\left(a^{4} - 2 \, a^{3} b - 3 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{4} - 2 \, a^{3} b - 3 \, a^{2} b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{2} - {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} d + 2 \, {\left(3 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{5} + 2 \, {\left(a^{4} - 2 \, a^{3} b - 3 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a^{4} - 2 \, a^{3} b - 3 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}, -\frac{2 \, {\left(2 \, a^{2} + 3 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 8 \, {\left(2 \, a^{2} + 3 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + 2 \, {\left(2 \, a^{2} + 3 \, a b + 3 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(2 \, a^{2} - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(3 \, {\left(2 \, a^{2} + 3 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, a^{2} - 3 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} + 3 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{6} + 6 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{6} + {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(15 \, {\left(a^{2} + 2 \, a b + 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)^{4} + 4 \, {\left(5 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(15 \, {\left(a^{2} + 2 \, a b + 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)^{2} - a^{2} - 2 \, a b - b^{2} + 2 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(a^{2} - 2 \, a b - 3 \, 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({\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} + a - b\right)} \sqrt{\frac{b}{a}}}{2 \, b}\right) + 4 \, a^{2} + 10 \, a b + 6 \, b^{2} + 8 \, {\left({\left(2 \, a^{2} + 3 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{2} - 3 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{2 \, {\left({\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{6} + 6 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} d \sinh\left(d x + c\right)^{6} + {\left(a^{4} - 2 \, a^{3} b - 3 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{4} + {\left(15 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{4} - 2 \, a^{3} b - 3 \, a^{2} b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{4} - {\left(a^{4} - 2 \, a^{3} b - 3 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{2} + 4 \, {\left(5 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{4} - 2 \, a^{3} b - 3 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(15 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{4} + 6 \, {\left(a^{4} - 2 \, a^{3} b - 3 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{4} - 2 \, a^{3} b - 3 \, a^{2} b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{2} - {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} d + 2 \, {\left(3 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{5} + 2 \, {\left(a^{4} - 2 \, a^{3} b - 3 \, a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a^{4} - 2 \, a^{3} b - 3 \, 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*(2*a^2 + 3*a*b + 3*b^2)*cosh(d*x + c)^4 + 16*(2*a^2 + 3*a*b + 3*b^2)*cosh(d*x + c)*sinh(d*x + c)^3 + 4*(2*a^2 + 3*a*b + 3*b^2)*sinh(d*x + c)^4 + 8*(2*a^2 - 3*b^2)*cosh(d*x + c)^2 + 8*(3*(2*a^2 + 3*a*b + 3*b^2)*cosh(d*x + c)^2 + 2*a^2 - 3*b^2)*sinh(d*x + c)^2 - 3*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^6 + 6*(a^2 + 2*a*b + b^2)*cosh(d*x + c)*sinh(d*x + c)^5 + (a^2 + 2*a*b + b^2)*sinh(d*x + c)^6 + (a^2 - 2*a*b - 3*b^2)*cosh(d*x + c)^4 + (15*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + a^2 - 2*a*b - 3*b^2)*sinh(d*x + c)^4 + 4*(5*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 + (a^2 - 2*a*b - 3*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 - (a^2 - 2*a*b - 3*b^2)*cosh(d*x + c)^2 + (15*(a^2 + 2*a*b + 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)^2 - a^2 - 2*a*b - b^2 + 2*(3*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^5 + 2*(a^2 - 2*a*b - 3*b^2)*cosh(d*x + c)^3 - (a^2 - 2*a*b - 3*b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-b/a)*log(((a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 + 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 + 2*(a^2 - b^2)*cosh(d*x + c)^2 + 2*(3*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + a^2 - b^2)*sinh(d*x + c)^2 + a^2 - 6*a*b + b^2 + 4*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 + (a^2 - b^2)*cosh(d*x + c))*sinh(d*x + c) - 4*((a^2 + a*b)*cosh(d*x + c)^2 + 2*(a^2 + a*b)*cosh(d*x + c)*sinh(d*x + c) + (a^2 + a*b)*sinh(d*x + c)^2 + a^2 - a*b)*sqrt(-b/a))/((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)) + 8*a^2 + 20*a*b + 12*b^2 + 16*((2*a^2 + 3*a*b + 3*b^2)*cosh(d*x + c)^3 + (2*a^2 - 3*b^2)*cosh(d*x + c))*sinh(d*x + c))/((a^4 + 2*a^3*b + a^2*b^2)*d*cosh(d*x + c)^6 + 6*(a^4 + 2*a^3*b + a^2*b^2)*d*cosh(d*x + c)*sinh(d*x + c)^5 + (a^4 + 2*a^3*b + a^2*b^2)*d*sinh(d*x + c)^6 + (a^4 - 2*a^3*b - 3*a^2*b^2)*d*cosh(d*x + c)^4 + (15*(a^4 + 2*a^3*b + a^2*b^2)*d*cosh(d*x + c)^2 + (a^4 - 2*a^3*b - 3*a^2*b^2)*d)*sinh(d*x + c)^4 - (a^4 - 2*a^3*b - 3*a^2*b^2)*d*cosh(d*x + c)^2 + 4*(5*(a^4 + 2*a^3*b + a^2*b^2)*d*cosh(d*x + c)^3 + (a^4 - 2*a^3*b - 3*a^2*b^2)*d*cosh(d*x + c))*sinh(d*x + c)^3 + (15*(a^4 + 2*a^3*b + a^2*b^2)*d*cosh(d*x + c)^4 + 6*(a^4 - 2*a^3*b - 3*a^2*b^2)*d*cosh(d*x + c)^2 - (a^4 - 2*a^3*b - 3*a^2*b^2)*d)*sinh(d*x + c)^2 - (a^4 + 2*a^3*b + a^2*b^2)*d + 2*(3*(a^4 + 2*a^3*b + a^2*b^2)*d*cosh(d*x + c)^5 + 2*(a^4 - 2*a^3*b - 3*a^2*b^2)*d*cosh(d*x + c)^3 - (a^4 - 2*a^3*b - 3*a^2*b^2)*d*cosh(d*x + c))*sinh(d*x + c)), -1/2*(2*(2*a^2 + 3*a*b + 3*b^2)*cosh(d*x + c)^4 + 8*(2*a^2 + 3*a*b + 3*b^2)*cosh(d*x + c)*sinh(d*x + c)^3 + 2*(2*a^2 + 3*a*b + 3*b^2)*sinh(d*x + c)^4 + 4*(2*a^2 - 3*b^2)*cosh(d*x + c)^2 + 4*(3*(2*a^2 + 3*a*b + 3*b^2)*cosh(d*x + c)^2 + 2*a^2 - 3*b^2)*sinh(d*x + c)^2 + 3*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^6 + 6*(a^2 + 2*a*b + b^2)*cosh(d*x + c)*sinh(d*x + c)^5 + (a^2 + 2*a*b + b^2)*sinh(d*x + c)^6 + (a^2 - 2*a*b - 3*b^2)*cosh(d*x + c)^4 + (15*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + a^2 - 2*a*b - 3*b^2)*sinh(d*x + c)^4 + 4*(5*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 + (a^2 - 2*a*b - 3*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 - (a^2 - 2*a*b - 3*b^2)*cosh(d*x + c)^2 + (15*(a^2 + 2*a*b + 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)^2 - a^2 - 2*a*b - b^2 + 2*(3*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^5 + 2*(a^2 - 2*a*b - 3*b^2)*cosh(d*x + c)^3 - (a^2 - 2*a*b - 3*b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(b/a)*arctan(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 + a - b)*sqrt(b/a)/b) + 4*a^2 + 10*a*b + 6*b^2 + 8*((2*a^2 + 3*a*b + 3*b^2)*cosh(d*x + c)^3 + (2*a^2 - 3*b^2)*cosh(d*x + c))*sinh(d*x + c))/((a^4 + 2*a^3*b + a^2*b^2)*d*cosh(d*x + c)^6 + 6*(a^4 + 2*a^3*b + a^2*b^2)*d*cosh(d*x + c)*sinh(d*x + c)^5 + (a^4 + 2*a^3*b + a^2*b^2)*d*sinh(d*x + c)^6 + (a^4 - 2*a^3*b - 3*a^2*b^2)*d*cosh(d*x + c)^4 + (15*(a^4 + 2*a^3*b + a^2*b^2)*d*cosh(d*x + c)^2 + (a^4 - 2*a^3*b - 3*a^2*b^2)*d)*sinh(d*x + c)^4 - (a^4 - 2*a^3*b - 3*a^2*b^2)*d*cosh(d*x + c)^2 + 4*(5*(a^4 + 2*a^3*b + a^2*b^2)*d*cosh(d*x + c)^3 + (a^4 - 2*a^3*b - 3*a^2*b^2)*d*cosh(d*x + c))*sinh(d*x + c)^3 + (15*(a^4 + 2*a^3*b + a^2*b^2)*d*cosh(d*x + c)^4 + 6*(a^4 - 2*a^3*b - 3*a^2*b^2)*d*cosh(d*x + c)^2 - (a^4 - 2*a^3*b - 3*a^2*b^2)*d)*sinh(d*x + c)^2 - (a^4 + 2*a^3*b + a^2*b^2)*d + 2*(3*(a^4 + 2*a^3*b + a^2*b^2)*d*cosh(d*x + c)^5 + 2*(a^4 - 2*a^3*b - 3*a^2*b^2)*d*cosh(d*x + c)^3 - (a^4 - 2*a^3*b - 3*a^2*b^2)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
39,1,6335,0,0.732838," ","integrate(csch(d*x+c)^3/(a+b*tanh(d*x+c)^2)^2,x, algorithm=""fricas"")","\left[\frac{4 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{7} + 28 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + 4 \, {\left(a^{2} + 2 \, a b\right)} \sinh\left(d x + c\right)^{7} + 4 \, {\left(3 \, a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right)^{5} + 4 \, {\left(21 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{2} + 3 \, a^{2} - 2 \, a b\right)} \sinh\left(d x + c\right)^{5} + 20 \, {\left(7 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(3 \, a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(35 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{4} + 10 \, {\left(3 \, a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right)^{2} + 3 \, a^{2} - 2 \, a b\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(21 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(3 \, a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(3 \, a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - {\left({\left(3 \, a^{2} + 7 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(3 \, a^{2} + 7 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(3 \, a^{2} + 7 \, a b + 4 \, b^{2}\right)} \sinh\left(d x + c\right)^{8} - 4 \, {\left(3 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(3 \, a^{2} + 7 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 3 \, a b - 4 \, b^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(3 \, a^{2} + 7 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(3 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 2 \, {\left(3 \, a^{2} - 5 \, a b - 12 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(3 \, a^{2} + 7 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} - 30 \, {\left(3 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 3 \, a^{2} + 5 \, a b + 12 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(3 \, a^{2} + 7 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} - 10 \, {\left(3 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(3 \, a^{2} - 5 \, a b - 12 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 4 \, {\left(3 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(3 \, a^{2} + 7 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} - 15 \, {\left(3 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} - 3 \, {\left(3 \, a^{2} - 5 \, a b - 12 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 3 \, a b - 4 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} + 3 \, a^{2} + 7 \, a b + 4 \, b^{2} + 8 \, {\left({\left(3 \, a^{2} + 7 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} - 3 \, {\left(3 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} - {\left(3 \, a^{2} - 5 \, a b - 12 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(3 \, a b + 4 \, 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{{\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 + 3 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} + a + 3 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a + 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) - 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}} + a + b}{{\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) + 4 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right) - 2 \, {\left({\left(a^{2} + 5 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{2} + 5 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{2} + 5 \, a b + 4 \, b^{2}\right)} \sinh\left(d x + c\right)^{8} - 4 \, {\left(a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} + 5 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - a b - 4 \, b^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} + 5 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 2 \, {\left(a^{2} + a b - 12 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} + 5 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} - 30 \, {\left(a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - a^{2} - a b + 12 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} + 5 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} - 10 \, {\left(a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(a^{2} + a b - 12 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 4 \, {\left(a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} + 5 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} - 15 \, {\left(a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} - 3 \, {\left(a^{2} + a b - 12 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - a b - 4 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 5 \, a b + 4 \, b^{2} + 8 \, {\left({\left(a^{2} + 5 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} - 3 \, {\left(a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} - {\left(a^{2} + a b - 12 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(a b + 4 \, 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^{2} + 5 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{2} + 5 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{2} + 5 \, a b + 4 \, b^{2}\right)} \sinh\left(d x + c\right)^{8} - 4 \, {\left(a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} + 5 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - a b - 4 \, b^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} + 5 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 2 \, {\left(a^{2} + a b - 12 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} + 5 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} - 30 \, {\left(a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - a^{2} - a b + 12 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} + 5 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} - 10 \, {\left(a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(a^{2} + a b - 12 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 4 \, {\left(a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} + 5 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} - 15 \, {\left(a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} - 3 \, {\left(a^{2} + a b - 12 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - a b - 4 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 5 \, a b + 4 \, b^{2} + 8 \, {\left({\left(a^{2} + 5 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} - 3 \, {\left(a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} - {\left(a^{2} + a b - 12 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(a b + 4 \, 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(7 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{6} + 5 \, {\left(3 \, a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right)^{2} + a^{2} + 2 \, a b\right)} \sinh\left(d x + c\right)}{4 \, {\left(4 \, a^{3} b d \cosh\left(d x + c\right)^{6} - {\left(a^{4} + a^{3} b\right)} d \cosh\left(d x + c\right)^{8} - 8 \, {\left(a^{4} + a^{3} b\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} - {\left(a^{4} + a^{3} b\right)} d \sinh\left(d x + c\right)^{8} + 4 \, a^{3} b d \cosh\left(d x + c\right)^{2} + 4 \, {\left(a^{3} b d - 7 \, {\left(a^{4} + a^{3} b\right)} d \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(a^{4} - 3 \, a^{3} b\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(3 \, a^{3} b d \cosh\left(d x + c\right) - 7 \, {\left(a^{4} + a^{3} b\right)} d \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(30 \, a^{3} b d \cosh\left(d x + c\right)^{2} - 35 \, {\left(a^{4} + a^{3} b\right)} d \cosh\left(d x + c\right)^{4} + {\left(a^{4} - 3 \, a^{3} b\right)} d\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(10 \, a^{3} b d \cosh\left(d x + c\right)^{3} - 7 \, {\left(a^{4} + a^{3} b\right)} d \cosh\left(d x + c\right)^{5} + {\left(a^{4} - 3 \, a^{3} b\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(15 \, a^{3} b d \cosh\left(d x + c\right)^{4} - 7 \, {\left(a^{4} + a^{3} b\right)} d \cosh\left(d x + c\right)^{6} + a^{3} b d + 3 \, {\left(a^{4} - 3 \, a^{3} b\right)} d \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} - {\left(a^{4} + a^{3} b\right)} d + 8 \, {\left(3 \, a^{3} b d \cosh\left(d x + c\right)^{5} - {\left(a^{4} + a^{3} b\right)} d \cosh\left(d x + c\right)^{7} + a^{3} b d \cosh\left(d x + c\right) + {\left(a^{4} - 3 \, a^{3} b\right)} d \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right)\right)}}, \frac{2 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{7} + 14 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + 2 \, {\left(a^{2} + 2 \, a b\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(3 \, a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(21 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{2} + 3 \, a^{2} - 2 \, a b\right)} \sinh\left(d x + c\right)^{5} + 10 \, {\left(7 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(3 \, a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(35 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{4} + 10 \, {\left(3 \, a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right)^{2} + 3 \, a^{2} - 2 \, a b\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(21 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(3 \, a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(3 \, a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(3 \, a^{2} + 7 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(3 \, a^{2} + 7 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(3 \, a^{2} + 7 \, a b + 4 \, b^{2}\right)} \sinh\left(d x + c\right)^{8} - 4 \, {\left(3 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(3 \, a^{2} + 7 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 3 \, a b - 4 \, b^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(3 \, a^{2} + 7 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(3 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 2 \, {\left(3 \, a^{2} - 5 \, a b - 12 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(3 \, a^{2} + 7 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} - 30 \, {\left(3 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 3 \, a^{2} + 5 \, a b + 12 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(3 \, a^{2} + 7 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} - 10 \, {\left(3 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(3 \, a^{2} - 5 \, a b - 12 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 4 \, {\left(3 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(3 \, a^{2} + 7 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} - 15 \, {\left(3 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} - 3 \, {\left(3 \, a^{2} - 5 \, a b - 12 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 3 \, a b - 4 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} + 3 \, a^{2} + 7 \, a b + 4 \, b^{2} + 8 \, {\left({\left(3 \, a^{2} + 7 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} - 3 \, {\left(3 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} - {\left(3 \, a^{2} - 5 \, a b - 12 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(3 \, a b + 4 \, 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({\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 - 3 \, b\right)} \cosh\left(d x + c\right) + {\left(3 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} + a - 3 \, b\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{b}{a + b}}}{2 \, b}\right) - {\left({\left(3 \, a^{2} + 7 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(3 \, a^{2} + 7 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(3 \, a^{2} + 7 \, a b + 4 \, b^{2}\right)} \sinh\left(d x + c\right)^{8} - 4 \, {\left(3 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(3 \, a^{2} + 7 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 3 \, a b - 4 \, b^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(3 \, a^{2} + 7 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(3 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 2 \, {\left(3 \, a^{2} - 5 \, a b - 12 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(3 \, a^{2} + 7 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} - 30 \, {\left(3 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 3 \, a^{2} + 5 \, a b + 12 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(3 \, a^{2} + 7 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} - 10 \, {\left(3 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(3 \, a^{2} - 5 \, a b - 12 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 4 \, {\left(3 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(3 \, a^{2} + 7 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} - 15 \, {\left(3 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} - 3 \, {\left(3 \, a^{2} - 5 \, a b - 12 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 3 \, a b - 4 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} + 3 \, a^{2} + 7 \, a b + 4 \, b^{2} + 8 \, {\left({\left(3 \, a^{2} + 7 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} - 3 \, {\left(3 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} - {\left(3 \, a^{2} - 5 \, a b - 12 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(3 \, a b + 4 \, 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({\left(a + b\right)} \cosh\left(d x + c\right) + {\left(a + b\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{b}{a + b}}}{2 \, b}\right) + 2 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right) - {\left({\left(a^{2} + 5 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{2} + 5 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{2} + 5 \, a b + 4 \, b^{2}\right)} \sinh\left(d x + c\right)^{8} - 4 \, {\left(a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} + 5 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - a b - 4 \, b^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} + 5 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 2 \, {\left(a^{2} + a b - 12 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} + 5 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} - 30 \, {\left(a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - a^{2} - a b + 12 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} + 5 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} - 10 \, {\left(a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(a^{2} + a b - 12 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 4 \, {\left(a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} + 5 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} - 15 \, {\left(a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} - 3 \, {\left(a^{2} + a b - 12 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - a b - 4 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 5 \, a b + 4 \, b^{2} + 8 \, {\left({\left(a^{2} + 5 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} - 3 \, {\left(a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} - {\left(a^{2} + a b - 12 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(a b + 4 \, 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(a^{2} + 5 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{2} + 5 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{2} + 5 \, a b + 4 \, b^{2}\right)} \sinh\left(d x + c\right)^{8} - 4 \, {\left(a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} + 5 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - a b - 4 \, b^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} + 5 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 2 \, {\left(a^{2} + a b - 12 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} + 5 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} - 30 \, {\left(a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - a^{2} - a b + 12 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} + 5 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} - 10 \, {\left(a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(a^{2} + a b - 12 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 4 \, {\left(a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} + 5 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} - 15 \, {\left(a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} - 3 \, {\left(a^{2} + a b - 12 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - a b - 4 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 5 \, a b + 4 \, b^{2} + 8 \, {\left({\left(a^{2} + 5 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} - 3 \, {\left(a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} - {\left(a^{2} + a b - 12 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(a b + 4 \, 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(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{6} + 5 \, {\left(3 \, a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right)^{2} + a^{2} + 2 \, a b\right)} \sinh\left(d x + c\right)}{2 \, {\left(4 \, a^{3} b d \cosh\left(d x + c\right)^{6} - {\left(a^{4} + a^{3} b\right)} d \cosh\left(d x + c\right)^{8} - 8 \, {\left(a^{4} + a^{3} b\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} - {\left(a^{4} + a^{3} b\right)} d \sinh\left(d x + c\right)^{8} + 4 \, a^{3} b d \cosh\left(d x + c\right)^{2} + 4 \, {\left(a^{3} b d - 7 \, {\left(a^{4} + a^{3} b\right)} d \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(a^{4} - 3 \, a^{3} b\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(3 \, a^{3} b d \cosh\left(d x + c\right) - 7 \, {\left(a^{4} + a^{3} b\right)} d \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(30 \, a^{3} b d \cosh\left(d x + c\right)^{2} - 35 \, {\left(a^{4} + a^{3} b\right)} d \cosh\left(d x + c\right)^{4} + {\left(a^{4} - 3 \, a^{3} b\right)} d\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(10 \, a^{3} b d \cosh\left(d x + c\right)^{3} - 7 \, {\left(a^{4} + a^{3} b\right)} d \cosh\left(d x + c\right)^{5} + {\left(a^{4} - 3 \, a^{3} b\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(15 \, a^{3} b d \cosh\left(d x + c\right)^{4} - 7 \, {\left(a^{4} + a^{3} b\right)} d \cosh\left(d x + c\right)^{6} + a^{3} b d + 3 \, {\left(a^{4} - 3 \, a^{3} b\right)} d \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} - {\left(a^{4} + a^{3} b\right)} d + 8 \, {\left(3 \, a^{3} b d \cosh\left(d x + c\right)^{5} - {\left(a^{4} + a^{3} b\right)} d \cosh\left(d x + c\right)^{7} + a^{3} b d \cosh\left(d x + c\right) + {\left(a^{4} - 3 \, a^{3} b\right)} d \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[1/4*(4*(a^2 + 2*a*b)*cosh(d*x + c)^7 + 28*(a^2 + 2*a*b)*cosh(d*x + c)*sinh(d*x + c)^6 + 4*(a^2 + 2*a*b)*sinh(d*x + c)^7 + 4*(3*a^2 - 2*a*b)*cosh(d*x + c)^5 + 4*(21*(a^2 + 2*a*b)*cosh(d*x + c)^2 + 3*a^2 - 2*a*b)*sinh(d*x + c)^5 + 20*(7*(a^2 + 2*a*b)*cosh(d*x + c)^3 + (3*a^2 - 2*a*b)*cosh(d*x + c))*sinh(d*x + c)^4 + 4*(3*a^2 - 2*a*b)*cosh(d*x + c)^3 + 4*(35*(a^2 + 2*a*b)*cosh(d*x + c)^4 + 10*(3*a^2 - 2*a*b)*cosh(d*x + c)^2 + 3*a^2 - 2*a*b)*sinh(d*x + c)^3 + 4*(21*(a^2 + 2*a*b)*cosh(d*x + c)^5 + 10*(3*a^2 - 2*a*b)*cosh(d*x + c)^3 + 3*(3*a^2 - 2*a*b)*cosh(d*x + c))*sinh(d*x + c)^2 - ((3*a^2 + 7*a*b + 4*b^2)*cosh(d*x + c)^8 + 8*(3*a^2 + 7*a*b + 4*b^2)*cosh(d*x + c)*sinh(d*x + c)^7 + (3*a^2 + 7*a*b + 4*b^2)*sinh(d*x + c)^8 - 4*(3*a*b + 4*b^2)*cosh(d*x + c)^6 + 4*(7*(3*a^2 + 7*a*b + 4*b^2)*cosh(d*x + c)^2 - 3*a*b - 4*b^2)*sinh(d*x + c)^6 + 8*(7*(3*a^2 + 7*a*b + 4*b^2)*cosh(d*x + c)^3 - 3*(3*a*b + 4*b^2)*cosh(d*x + c))*sinh(d*x + c)^5 - 2*(3*a^2 - 5*a*b - 12*b^2)*cosh(d*x + c)^4 + 2*(35*(3*a^2 + 7*a*b + 4*b^2)*cosh(d*x + c)^4 - 30*(3*a*b + 4*b^2)*cosh(d*x + c)^2 - 3*a^2 + 5*a*b + 12*b^2)*sinh(d*x + c)^4 + 8*(7*(3*a^2 + 7*a*b + 4*b^2)*cosh(d*x + c)^5 - 10*(3*a*b + 4*b^2)*cosh(d*x + c)^3 - (3*a^2 - 5*a*b - 12*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 - 4*(3*a*b + 4*b^2)*cosh(d*x + c)^2 + 4*(7*(3*a^2 + 7*a*b + 4*b^2)*cosh(d*x + c)^6 - 15*(3*a*b + 4*b^2)*cosh(d*x + c)^4 - 3*(3*a^2 - 5*a*b - 12*b^2)*cosh(d*x + c)^2 - 3*a*b - 4*b^2)*sinh(d*x + c)^2 + 3*a^2 + 7*a*b + 4*b^2 + 8*((3*a^2 + 7*a*b + 4*b^2)*cosh(d*x + c)^7 - 3*(3*a*b + 4*b^2)*cosh(d*x + c)^5 - (3*a^2 - 5*a*b - 12*b^2)*cosh(d*x + c)^3 - (3*a*b + 4*b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(b/(a + b))*log(((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 + 3*b)*cosh(d*x + c)^2 + 2*(3*(a + b)*cosh(d*x + c)^2 + a + 3*b)*sinh(d*x + c)^2 + 4*((a + b)*cosh(d*x + c)^3 + (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)) + a + b)/((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)) + 4*(a^2 + 2*a*b)*cosh(d*x + c) - 2*((a^2 + 5*a*b + 4*b^2)*cosh(d*x + c)^8 + 8*(a^2 + 5*a*b + 4*b^2)*cosh(d*x + c)*sinh(d*x + c)^7 + (a^2 + 5*a*b + 4*b^2)*sinh(d*x + c)^8 - 4*(a*b + 4*b^2)*cosh(d*x + c)^6 + 4*(7*(a^2 + 5*a*b + 4*b^2)*cosh(d*x + c)^2 - a*b - 4*b^2)*sinh(d*x + c)^6 + 8*(7*(a^2 + 5*a*b + 4*b^2)*cosh(d*x + c)^3 - 3*(a*b + 4*b^2)*cosh(d*x + c))*sinh(d*x + c)^5 - 2*(a^2 + a*b - 12*b^2)*cosh(d*x + c)^4 + 2*(35*(a^2 + 5*a*b + 4*b^2)*cosh(d*x + c)^4 - 30*(a*b + 4*b^2)*cosh(d*x + c)^2 - a^2 - a*b + 12*b^2)*sinh(d*x + c)^4 + 8*(7*(a^2 + 5*a*b + 4*b^2)*cosh(d*x + c)^5 - 10*(a*b + 4*b^2)*cosh(d*x + c)^3 - (a^2 + a*b - 12*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 - 4*(a*b + 4*b^2)*cosh(d*x + c)^2 + 4*(7*(a^2 + 5*a*b + 4*b^2)*cosh(d*x + c)^6 - 15*(a*b + 4*b^2)*cosh(d*x + c)^4 - 3*(a^2 + a*b - 12*b^2)*cosh(d*x + c)^2 - a*b - 4*b^2)*sinh(d*x + c)^2 + a^2 + 5*a*b + 4*b^2 + 8*((a^2 + 5*a*b + 4*b^2)*cosh(d*x + c)^7 - 3*(a*b + 4*b^2)*cosh(d*x + c)^5 - (a^2 + a*b - 12*b^2)*cosh(d*x + c)^3 - (a*b + 4*b^2)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) + 1) + 2*((a^2 + 5*a*b + 4*b^2)*cosh(d*x + c)^8 + 8*(a^2 + 5*a*b + 4*b^2)*cosh(d*x + c)*sinh(d*x + c)^7 + (a^2 + 5*a*b + 4*b^2)*sinh(d*x + c)^8 - 4*(a*b + 4*b^2)*cosh(d*x + c)^6 + 4*(7*(a^2 + 5*a*b + 4*b^2)*cosh(d*x + c)^2 - a*b - 4*b^2)*sinh(d*x + c)^6 + 8*(7*(a^2 + 5*a*b + 4*b^2)*cosh(d*x + c)^3 - 3*(a*b + 4*b^2)*cosh(d*x + c))*sinh(d*x + c)^5 - 2*(a^2 + a*b - 12*b^2)*cosh(d*x + c)^4 + 2*(35*(a^2 + 5*a*b + 4*b^2)*cosh(d*x + c)^4 - 30*(a*b + 4*b^2)*cosh(d*x + c)^2 - a^2 - a*b + 12*b^2)*sinh(d*x + c)^4 + 8*(7*(a^2 + 5*a*b + 4*b^2)*cosh(d*x + c)^5 - 10*(a*b + 4*b^2)*cosh(d*x + c)^3 - (a^2 + a*b - 12*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 - 4*(a*b + 4*b^2)*cosh(d*x + c)^2 + 4*(7*(a^2 + 5*a*b + 4*b^2)*cosh(d*x + c)^6 - 15*(a*b + 4*b^2)*cosh(d*x + c)^4 - 3*(a^2 + a*b - 12*b^2)*cosh(d*x + c)^2 - a*b - 4*b^2)*sinh(d*x + c)^2 + a^2 + 5*a*b + 4*b^2 + 8*((a^2 + 5*a*b + 4*b^2)*cosh(d*x + c)^7 - 3*(a*b + 4*b^2)*cosh(d*x + c)^5 - (a^2 + a*b - 12*b^2)*cosh(d*x + c)^3 - (a*b + 4*b^2)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) - 1) + 4*(7*(a^2 + 2*a*b)*cosh(d*x + c)^6 + 5*(3*a^2 - 2*a*b)*cosh(d*x + c)^4 + 3*(3*a^2 - 2*a*b)*cosh(d*x + c)^2 + a^2 + 2*a*b)*sinh(d*x + c))/(4*a^3*b*d*cosh(d*x + c)^6 - (a^4 + a^3*b)*d*cosh(d*x + c)^8 - 8*(a^4 + a^3*b)*d*cosh(d*x + c)*sinh(d*x + c)^7 - (a^4 + a^3*b)*d*sinh(d*x + c)^8 + 4*a^3*b*d*cosh(d*x + c)^2 + 4*(a^3*b*d - 7*(a^4 + a^3*b)*d*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 2*(a^4 - 3*a^3*b)*d*cosh(d*x + c)^4 + 8*(3*a^3*b*d*cosh(d*x + c) - 7*(a^4 + a^3*b)*d*cosh(d*x + c)^3)*sinh(d*x + c)^5 + 2*(30*a^3*b*d*cosh(d*x + c)^2 - 35*(a^4 + a^3*b)*d*cosh(d*x + c)^4 + (a^4 - 3*a^3*b)*d)*sinh(d*x + c)^4 + 8*(10*a^3*b*d*cosh(d*x + c)^3 - 7*(a^4 + a^3*b)*d*cosh(d*x + c)^5 + (a^4 - 3*a^3*b)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(15*a^3*b*d*cosh(d*x + c)^4 - 7*(a^4 + a^3*b)*d*cosh(d*x + c)^6 + a^3*b*d + 3*(a^4 - 3*a^3*b)*d*cosh(d*x + c)^2)*sinh(d*x + c)^2 - (a^4 + a^3*b)*d + 8*(3*a^3*b*d*cosh(d*x + c)^5 - (a^4 + a^3*b)*d*cosh(d*x + c)^7 + a^3*b*d*cosh(d*x + c) + (a^4 - 3*a^3*b)*d*cosh(d*x + c)^3)*sinh(d*x + c)), 1/2*(2*(a^2 + 2*a*b)*cosh(d*x + c)^7 + 14*(a^2 + 2*a*b)*cosh(d*x + c)*sinh(d*x + c)^6 + 2*(a^2 + 2*a*b)*sinh(d*x + c)^7 + 2*(3*a^2 - 2*a*b)*cosh(d*x + c)^5 + 2*(21*(a^2 + 2*a*b)*cosh(d*x + c)^2 + 3*a^2 - 2*a*b)*sinh(d*x + c)^5 + 10*(7*(a^2 + 2*a*b)*cosh(d*x + c)^3 + (3*a^2 - 2*a*b)*cosh(d*x + c))*sinh(d*x + c)^4 + 2*(3*a^2 - 2*a*b)*cosh(d*x + c)^3 + 2*(35*(a^2 + 2*a*b)*cosh(d*x + c)^4 + 10*(3*a^2 - 2*a*b)*cosh(d*x + c)^2 + 3*a^2 - 2*a*b)*sinh(d*x + c)^3 + 2*(21*(a^2 + 2*a*b)*cosh(d*x + c)^5 + 10*(3*a^2 - 2*a*b)*cosh(d*x + c)^3 + 3*(3*a^2 - 2*a*b)*cosh(d*x + c))*sinh(d*x + c)^2 + ((3*a^2 + 7*a*b + 4*b^2)*cosh(d*x + c)^8 + 8*(3*a^2 + 7*a*b + 4*b^2)*cosh(d*x + c)*sinh(d*x + c)^7 + (3*a^2 + 7*a*b + 4*b^2)*sinh(d*x + c)^8 - 4*(3*a*b + 4*b^2)*cosh(d*x + c)^6 + 4*(7*(3*a^2 + 7*a*b + 4*b^2)*cosh(d*x + c)^2 - 3*a*b - 4*b^2)*sinh(d*x + c)^6 + 8*(7*(3*a^2 + 7*a*b + 4*b^2)*cosh(d*x + c)^3 - 3*(3*a*b + 4*b^2)*cosh(d*x + c))*sinh(d*x + c)^5 - 2*(3*a^2 - 5*a*b - 12*b^2)*cosh(d*x + c)^4 + 2*(35*(3*a^2 + 7*a*b + 4*b^2)*cosh(d*x + c)^4 - 30*(3*a*b + 4*b^2)*cosh(d*x + c)^2 - 3*a^2 + 5*a*b + 12*b^2)*sinh(d*x + c)^4 + 8*(7*(3*a^2 + 7*a*b + 4*b^2)*cosh(d*x + c)^5 - 10*(3*a*b + 4*b^2)*cosh(d*x + c)^3 - (3*a^2 - 5*a*b - 12*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 - 4*(3*a*b + 4*b^2)*cosh(d*x + c)^2 + 4*(7*(3*a^2 + 7*a*b + 4*b^2)*cosh(d*x + c)^6 - 15*(3*a*b + 4*b^2)*cosh(d*x + c)^4 - 3*(3*a^2 - 5*a*b - 12*b^2)*cosh(d*x + c)^2 - 3*a*b - 4*b^2)*sinh(d*x + c)^2 + 3*a^2 + 7*a*b + 4*b^2 + 8*((3*a^2 + 7*a*b + 4*b^2)*cosh(d*x + c)^7 - 3*(3*a*b + 4*b^2)*cosh(d*x + c)^5 - (3*a^2 - 5*a*b - 12*b^2)*cosh(d*x + c)^3 - (3*a*b + 4*b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-b/(a + b))*arctan(1/2*((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 - 3*b)*cosh(d*x + c) + (3*(a + b)*cosh(d*x + c)^2 + a - 3*b)*sinh(d*x + c))*sqrt(-b/(a + b))/b) - ((3*a^2 + 7*a*b + 4*b^2)*cosh(d*x + c)^8 + 8*(3*a^2 + 7*a*b + 4*b^2)*cosh(d*x + c)*sinh(d*x + c)^7 + (3*a^2 + 7*a*b + 4*b^2)*sinh(d*x + c)^8 - 4*(3*a*b + 4*b^2)*cosh(d*x + c)^6 + 4*(7*(3*a^2 + 7*a*b + 4*b^2)*cosh(d*x + c)^2 - 3*a*b - 4*b^2)*sinh(d*x + c)^6 + 8*(7*(3*a^2 + 7*a*b + 4*b^2)*cosh(d*x + c)^3 - 3*(3*a*b + 4*b^2)*cosh(d*x + c))*sinh(d*x + c)^5 - 2*(3*a^2 - 5*a*b - 12*b^2)*cosh(d*x + c)^4 + 2*(35*(3*a^2 + 7*a*b + 4*b^2)*cosh(d*x + c)^4 - 30*(3*a*b + 4*b^2)*cosh(d*x + c)^2 - 3*a^2 + 5*a*b + 12*b^2)*sinh(d*x + c)^4 + 8*(7*(3*a^2 + 7*a*b + 4*b^2)*cosh(d*x + c)^5 - 10*(3*a*b + 4*b^2)*cosh(d*x + c)^3 - (3*a^2 - 5*a*b - 12*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 - 4*(3*a*b + 4*b^2)*cosh(d*x + c)^2 + 4*(7*(3*a^2 + 7*a*b + 4*b^2)*cosh(d*x + c)^6 - 15*(3*a*b + 4*b^2)*cosh(d*x + c)^4 - 3*(3*a^2 - 5*a*b - 12*b^2)*cosh(d*x + c)^2 - 3*a*b - 4*b^2)*sinh(d*x + c)^2 + 3*a^2 + 7*a*b + 4*b^2 + 8*((3*a^2 + 7*a*b + 4*b^2)*cosh(d*x + c)^7 - 3*(3*a*b + 4*b^2)*cosh(d*x + c)^5 - (3*a^2 - 5*a*b - 12*b^2)*cosh(d*x + c)^3 - (3*a*b + 4*b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-b/(a + b))*arctan(1/2*((a + b)*cosh(d*x + c) + (a + b)*sinh(d*x + c))*sqrt(-b/(a + b))/b) + 2*(a^2 + 2*a*b)*cosh(d*x + c) - ((a^2 + 5*a*b + 4*b^2)*cosh(d*x + c)^8 + 8*(a^2 + 5*a*b + 4*b^2)*cosh(d*x + c)*sinh(d*x + c)^7 + (a^2 + 5*a*b + 4*b^2)*sinh(d*x + c)^8 - 4*(a*b + 4*b^2)*cosh(d*x + c)^6 + 4*(7*(a^2 + 5*a*b + 4*b^2)*cosh(d*x + c)^2 - a*b - 4*b^2)*sinh(d*x + c)^6 + 8*(7*(a^2 + 5*a*b + 4*b^2)*cosh(d*x + c)^3 - 3*(a*b + 4*b^2)*cosh(d*x + c))*sinh(d*x + c)^5 - 2*(a^2 + a*b - 12*b^2)*cosh(d*x + c)^4 + 2*(35*(a^2 + 5*a*b + 4*b^2)*cosh(d*x + c)^4 - 30*(a*b + 4*b^2)*cosh(d*x + c)^2 - a^2 - a*b + 12*b^2)*sinh(d*x + c)^4 + 8*(7*(a^2 + 5*a*b + 4*b^2)*cosh(d*x + c)^5 - 10*(a*b + 4*b^2)*cosh(d*x + c)^3 - (a^2 + a*b - 12*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 - 4*(a*b + 4*b^2)*cosh(d*x + c)^2 + 4*(7*(a^2 + 5*a*b + 4*b^2)*cosh(d*x + c)^6 - 15*(a*b + 4*b^2)*cosh(d*x + c)^4 - 3*(a^2 + a*b - 12*b^2)*cosh(d*x + c)^2 - a*b - 4*b^2)*sinh(d*x + c)^2 + a^2 + 5*a*b + 4*b^2 + 8*((a^2 + 5*a*b + 4*b^2)*cosh(d*x + c)^7 - 3*(a*b + 4*b^2)*cosh(d*x + c)^5 - (a^2 + a*b - 12*b^2)*cosh(d*x + c)^3 - (a*b + 4*b^2)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) + 1) + ((a^2 + 5*a*b + 4*b^2)*cosh(d*x + c)^8 + 8*(a^2 + 5*a*b + 4*b^2)*cosh(d*x + c)*sinh(d*x + c)^7 + (a^2 + 5*a*b + 4*b^2)*sinh(d*x + c)^8 - 4*(a*b + 4*b^2)*cosh(d*x + c)^6 + 4*(7*(a^2 + 5*a*b + 4*b^2)*cosh(d*x + c)^2 - a*b - 4*b^2)*sinh(d*x + c)^6 + 8*(7*(a^2 + 5*a*b + 4*b^2)*cosh(d*x + c)^3 - 3*(a*b + 4*b^2)*cosh(d*x + c))*sinh(d*x + c)^5 - 2*(a^2 + a*b - 12*b^2)*cosh(d*x + c)^4 + 2*(35*(a^2 + 5*a*b + 4*b^2)*cosh(d*x + c)^4 - 30*(a*b + 4*b^2)*cosh(d*x + c)^2 - a^2 - a*b + 12*b^2)*sinh(d*x + c)^4 + 8*(7*(a^2 + 5*a*b + 4*b^2)*cosh(d*x + c)^5 - 10*(a*b + 4*b^2)*cosh(d*x + c)^3 - (a^2 + a*b - 12*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 - 4*(a*b + 4*b^2)*cosh(d*x + c)^2 + 4*(7*(a^2 + 5*a*b + 4*b^2)*cosh(d*x + c)^6 - 15*(a*b + 4*b^2)*cosh(d*x + c)^4 - 3*(a^2 + a*b - 12*b^2)*cosh(d*x + c)^2 - a*b - 4*b^2)*sinh(d*x + c)^2 + a^2 + 5*a*b + 4*b^2 + 8*((a^2 + 5*a*b + 4*b^2)*cosh(d*x + c)^7 - 3*(a*b + 4*b^2)*cosh(d*x + c)^5 - (a^2 + a*b - 12*b^2)*cosh(d*x + c)^3 - (a*b + 4*b^2)*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) - 1) + 2*(7*(a^2 + 2*a*b)*cosh(d*x + c)^6 + 5*(3*a^2 - 2*a*b)*cosh(d*x + c)^4 + 3*(3*a^2 - 2*a*b)*cosh(d*x + c)^2 + a^2 + 2*a*b)*sinh(d*x + c))/(4*a^3*b*d*cosh(d*x + c)^6 - (a^4 + a^3*b)*d*cosh(d*x + c)^8 - 8*(a^4 + a^3*b)*d*cosh(d*x + c)*sinh(d*x + c)^7 - (a^4 + a^3*b)*d*sinh(d*x + c)^8 + 4*a^3*b*d*cosh(d*x + c)^2 + 4*(a^3*b*d - 7*(a^4 + a^3*b)*d*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 2*(a^4 - 3*a^3*b)*d*cosh(d*x + c)^4 + 8*(3*a^3*b*d*cosh(d*x + c) - 7*(a^4 + a^3*b)*d*cosh(d*x + c)^3)*sinh(d*x + c)^5 + 2*(30*a^3*b*d*cosh(d*x + c)^2 - 35*(a^4 + a^3*b)*d*cosh(d*x + c)^4 + (a^4 - 3*a^3*b)*d)*sinh(d*x + c)^4 + 8*(10*a^3*b*d*cosh(d*x + c)^3 - 7*(a^4 + a^3*b)*d*cosh(d*x + c)^5 + (a^4 - 3*a^3*b)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(15*a^3*b*d*cosh(d*x + c)^4 - 7*(a^4 + a^3*b)*d*cosh(d*x + c)^6 + a^3*b*d + 3*(a^4 - 3*a^3*b)*d*cosh(d*x + c)^2)*sinh(d*x + c)^2 - (a^4 + a^3*b)*d + 8*(3*a^3*b*d*cosh(d*x + c)^5 - (a^4 + a^3*b)*d*cosh(d*x + c)^7 + a^3*b*d*cosh(d*x + c) + (a^4 - 3*a^3*b)*d*cosh(d*x + c)^3)*sinh(d*x + c))]","B",0
40,1,5062,0,0.859162," ","integrate(csch(d*x+c)^4/(a+b*tanh(d*x+c)^2)^2,x, algorithm=""fricas"")","\left[\frac{12 \, {\left(3 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{8} + 96 \, {\left(3 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + 12 \, {\left(3 \, a b + 5 \, b^{2}\right)} \sinh\left(d x + c\right)^{8} - 24 \, {\left(2 \, a^{2} + a b + 10 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 24 \, {\left(14 \, {\left(3 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, a^{2} - a b - 10 \, b^{2}\right)} \sinh\left(d x + c\right)^{6} + 48 \, {\left(14 \, {\left(3 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(2 \, a^{2} + a b + 10 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 8 \, {\left(10 \, a^{2} - 2 \, a b - 45 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 8 \, {\left(105 \, {\left(3 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} - 45 \, {\left(2 \, a^{2} + a b + 10 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 10 \, a^{2} + 2 \, a b + 45 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 32 \, {\left(21 \, {\left(3 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} - 15 \, {\left(2 \, a^{2} + a b + 10 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(10 \, a^{2} - 2 \, a b - 45 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 8 \, {\left(2 \, a^{2} + 13 \, a b + 30 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 8 \, {\left(42 \, {\left(3 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} - 45 \, {\left(2 \, a^{2} + a b + 10 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} - 6 \, {\left(10 \, a^{2} - 2 \, a b - 45 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, a^{2} - 13 \, a b - 30 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} + 3 \, {\left({\left(3 \, a^{2} + 8 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{10} + 10 \, {\left(3 \, a^{2} + 8 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + {\left(3 \, a^{2} + 8 \, a b + 5 \, b^{2}\right)} \sinh\left(d x + c\right)^{10} - {\left(3 \, a^{2} + 20 \, a b + 25 \, b^{2}\right)} \cosh\left(d x + c\right)^{8} + {\left(45 \, {\left(3 \, a^{2} + 8 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 3 \, a^{2} - 20 \, a b - 25 \, b^{2}\right)} \sinh\left(d x + c\right)^{8} + 8 \, {\left(15 \, {\left(3 \, a^{2} + 8 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(3 \, a^{2} + 20 \, a b + 25 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} - 2 \, {\left(3 \, a^{2} - 10 \, a b - 25 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(105 \, {\left(3 \, a^{2} + 8 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} - 14 \, {\left(3 \, a^{2} + 20 \, a b + 25 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 3 \, a^{2} + 10 \, a b + 25 \, b^{2}\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(63 \, {\left(3 \, a^{2} + 8 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} - 14 \, {\left(3 \, a^{2} + 20 \, a b + 25 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(3 \, a^{2} - 10 \, a b - 25 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(3 \, a^{2} - 10 \, a b - 25 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(105 \, {\left(3 \, a^{2} + 8 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} - 35 \, {\left(3 \, a^{2} + 20 \, a b + 25 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} - 15 \, {\left(3 \, a^{2} - 10 \, a b - 25 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 3 \, a^{2} - 10 \, a b - 25 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(15 \, {\left(3 \, a^{2} + 8 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} - 7 \, {\left(3 \, a^{2} + 20 \, a b + 25 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} - 5 \, {\left(3 \, a^{2} - 10 \, a b - 25 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{2} - 10 \, a b - 25 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(3 \, a^{2} + 20 \, a b + 25 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(45 \, {\left(3 \, a^{2} + 8 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{8} - 28 \, {\left(3 \, a^{2} + 20 \, a b + 25 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} - 30 \, {\left(3 \, a^{2} - 10 \, a b - 25 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 12 \, {\left(3 \, a^{2} - 10 \, a b - 25 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 3 \, a^{2} + 20 \, a b + 25 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} - 3 \, a^{2} - 8 \, a b - 5 \, b^{2} + 2 \, {\left(5 \, {\left(3 \, a^{2} + 8 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{9} - 4 \, {\left(3 \, a^{2} + 20 \, a b + 25 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} - 6 \, {\left(3 \, a^{2} - 10 \, a b - 25 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 4 \, {\left(3 \, a^{2} - 10 \, a b - 25 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{2} + 20 \, a b + 25 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{{\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) \sinh\left(d x + c\right)^{3} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{2} + a^{2} - 6 \, a b + b^{2} + 4 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + 4 \, {\left({\left(a^{2} + a b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} + a b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} + a b\right)} \sinh\left(d x + c\right)^{2} + a^{2} - a b\right)} \sqrt{-\frac{b}{a}}}{{\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) + 16 \, a^{2} + 76 \, a b + 60 \, b^{2} + 16 \, {\left(6 \, {\left(3 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} - 9 \, {\left(2 \, a^{2} + a b + 10 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} - 2 \, {\left(10 \, a^{2} - 2 \, a b - 45 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(2 \, a^{2} + 13 \, a b + 30 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{12 \, {\left({\left(a^{4} + a^{3} b\right)} d \cosh\left(d x + c\right)^{10} + 10 \, {\left(a^{4} + a^{3} b\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + {\left(a^{4} + a^{3} b\right)} d \sinh\left(d x + c\right)^{10} - {\left(a^{4} + 5 \, a^{3} b\right)} d \cosh\left(d x + c\right)^{8} + {\left(45 \, {\left(a^{4} + a^{3} b\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{4} + 5 \, a^{3} b\right)} d\right)} \sinh\left(d x + c\right)^{8} - 2 \, {\left(a^{4} - 5 \, a^{3} b\right)} d \cosh\left(d x + c\right)^{6} + 8 \, {\left(15 \, {\left(a^{4} + a^{3} b\right)} d \cosh\left(d x + c\right)^{3} - {\left(a^{4} + 5 \, a^{3} b\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(105 \, {\left(a^{4} + a^{3} b\right)} d \cosh\left(d x + c\right)^{4} - 14 \, {\left(a^{4} + 5 \, a^{3} b\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{4} - 5 \, a^{3} b\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(a^{4} - 5 \, a^{3} b\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(63 \, {\left(a^{4} + a^{3} b\right)} d \cosh\left(d x + c\right)^{5} - 14 \, {\left(a^{4} + 5 \, a^{3} b\right)} d \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{4} - 5 \, a^{3} b\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(105 \, {\left(a^{4} + a^{3} b\right)} d \cosh\left(d x + c\right)^{6} - 35 \, {\left(a^{4} + 5 \, a^{3} b\right)} d \cosh\left(d x + c\right)^{4} - 15 \, {\left(a^{4} - 5 \, a^{3} b\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{4} - 5 \, a^{3} b\right)} d\right)} \sinh\left(d x + c\right)^{4} + {\left(a^{4} + 5 \, a^{3} b\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(15 \, {\left(a^{4} + a^{3} b\right)} d \cosh\left(d x + c\right)^{7} - 7 \, {\left(a^{4} + 5 \, a^{3} b\right)} d \cosh\left(d x + c\right)^{5} - 5 \, {\left(a^{4} - 5 \, a^{3} b\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{4} - 5 \, a^{3} b\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(45 \, {\left(a^{4} + a^{3} b\right)} d \cosh\left(d x + c\right)^{8} - 28 \, {\left(a^{4} + 5 \, a^{3} b\right)} d \cosh\left(d x + c\right)^{6} - 30 \, {\left(a^{4} - 5 \, a^{3} b\right)} d \cosh\left(d x + c\right)^{4} + 12 \, {\left(a^{4} - 5 \, a^{3} b\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{4} + 5 \, a^{3} b\right)} d\right)} \sinh\left(d x + c\right)^{2} - {\left(a^{4} + a^{3} b\right)} d + 2 \, {\left(5 \, {\left(a^{4} + a^{3} b\right)} d \cosh\left(d x + c\right)^{9} - 4 \, {\left(a^{4} + 5 \, a^{3} b\right)} d \cosh\left(d x + c\right)^{7} - 6 \, {\left(a^{4} - 5 \, a^{3} b\right)} d \cosh\left(d x + c\right)^{5} + 4 \, {\left(a^{4} - 5 \, a^{3} b\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{4} + 5 \, a^{3} b\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}, \frac{6 \, {\left(3 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{8} + 48 \, {\left(3 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + 6 \, {\left(3 \, a b + 5 \, b^{2}\right)} \sinh\left(d x + c\right)^{8} - 12 \, {\left(2 \, a^{2} + a b + 10 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 12 \, {\left(14 \, {\left(3 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, a^{2} - a b - 10 \, b^{2}\right)} \sinh\left(d x + c\right)^{6} + 24 \, {\left(14 \, {\left(3 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(2 \, a^{2} + a b + 10 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 4 \, {\left(10 \, a^{2} - 2 \, a b - 45 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(105 \, {\left(3 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} - 45 \, {\left(2 \, a^{2} + a b + 10 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 10 \, a^{2} + 2 \, a b + 45 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 16 \, {\left(21 \, {\left(3 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} - 15 \, {\left(2 \, a^{2} + a b + 10 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(10 \, a^{2} - 2 \, a b - 45 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 4 \, {\left(2 \, a^{2} + 13 \, a b + 30 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(42 \, {\left(3 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} - 45 \, {\left(2 \, a^{2} + a b + 10 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} - 6 \, {\left(10 \, a^{2} - 2 \, a b - 45 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, a^{2} - 13 \, a b - 30 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} + 3 \, {\left({\left(3 \, a^{2} + 8 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{10} + 10 \, {\left(3 \, a^{2} + 8 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + {\left(3 \, a^{2} + 8 \, a b + 5 \, b^{2}\right)} \sinh\left(d x + c\right)^{10} - {\left(3 \, a^{2} + 20 \, a b + 25 \, b^{2}\right)} \cosh\left(d x + c\right)^{8} + {\left(45 \, {\left(3 \, a^{2} + 8 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 3 \, a^{2} - 20 \, a b - 25 \, b^{2}\right)} \sinh\left(d x + c\right)^{8} + 8 \, {\left(15 \, {\left(3 \, a^{2} + 8 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(3 \, a^{2} + 20 \, a b + 25 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} - 2 \, {\left(3 \, a^{2} - 10 \, a b - 25 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(105 \, {\left(3 \, a^{2} + 8 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} - 14 \, {\left(3 \, a^{2} + 20 \, a b + 25 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 3 \, a^{2} + 10 \, a b + 25 \, b^{2}\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(63 \, {\left(3 \, a^{2} + 8 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} - 14 \, {\left(3 \, a^{2} + 20 \, a b + 25 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(3 \, a^{2} - 10 \, a b - 25 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(3 \, a^{2} - 10 \, a b - 25 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(105 \, {\left(3 \, a^{2} + 8 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} - 35 \, {\left(3 \, a^{2} + 20 \, a b + 25 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} - 15 \, {\left(3 \, a^{2} - 10 \, a b - 25 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 3 \, a^{2} - 10 \, a b - 25 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(15 \, {\left(3 \, a^{2} + 8 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} - 7 \, {\left(3 \, a^{2} + 20 \, a b + 25 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} - 5 \, {\left(3 \, a^{2} - 10 \, a b - 25 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{2} - 10 \, a b - 25 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(3 \, a^{2} + 20 \, a b + 25 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(45 \, {\left(3 \, a^{2} + 8 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{8} - 28 \, {\left(3 \, a^{2} + 20 \, a b + 25 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} - 30 \, {\left(3 \, a^{2} - 10 \, a b - 25 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 12 \, {\left(3 \, a^{2} - 10 \, a b - 25 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 3 \, a^{2} + 20 \, a b + 25 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} - 3 \, a^{2} - 8 \, a b - 5 \, b^{2} + 2 \, {\left(5 \, {\left(3 \, a^{2} + 8 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{9} - 4 \, {\left(3 \, a^{2} + 20 \, a b + 25 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} - 6 \, {\left(3 \, a^{2} - 10 \, a b - 25 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 4 \, {\left(3 \, a^{2} - 10 \, a b - 25 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{2} + 20 \, a b + 25 \, 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({\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} + a - b\right)} \sqrt{\frac{b}{a}}}{2 \, b}\right) + 8 \, a^{2} + 38 \, a b + 30 \, b^{2} + 8 \, {\left(6 \, {\left(3 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} - 9 \, {\left(2 \, a^{2} + a b + 10 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} - 2 \, {\left(10 \, a^{2} - 2 \, a b - 45 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(2 \, a^{2} + 13 \, a b + 30 \, 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)^{10} + 10 \, {\left(a^{4} + a^{3} b\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + {\left(a^{4} + a^{3} b\right)} d \sinh\left(d x + c\right)^{10} - {\left(a^{4} + 5 \, a^{3} b\right)} d \cosh\left(d x + c\right)^{8} + {\left(45 \, {\left(a^{4} + a^{3} b\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{4} + 5 \, a^{3} b\right)} d\right)} \sinh\left(d x + c\right)^{8} - 2 \, {\left(a^{4} - 5 \, a^{3} b\right)} d \cosh\left(d x + c\right)^{6} + 8 \, {\left(15 \, {\left(a^{4} + a^{3} b\right)} d \cosh\left(d x + c\right)^{3} - {\left(a^{4} + 5 \, a^{3} b\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(105 \, {\left(a^{4} + a^{3} b\right)} d \cosh\left(d x + c\right)^{4} - 14 \, {\left(a^{4} + 5 \, a^{3} b\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{4} - 5 \, a^{3} b\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(a^{4} - 5 \, a^{3} b\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(63 \, {\left(a^{4} + a^{3} b\right)} d \cosh\left(d x + c\right)^{5} - 14 \, {\left(a^{4} + 5 \, a^{3} b\right)} d \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{4} - 5 \, a^{3} b\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(105 \, {\left(a^{4} + a^{3} b\right)} d \cosh\left(d x + c\right)^{6} - 35 \, {\left(a^{4} + 5 \, a^{3} b\right)} d \cosh\left(d x + c\right)^{4} - 15 \, {\left(a^{4} - 5 \, a^{3} b\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{4} - 5 \, a^{3} b\right)} d\right)} \sinh\left(d x + c\right)^{4} + {\left(a^{4} + 5 \, a^{3} b\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(15 \, {\left(a^{4} + a^{3} b\right)} d \cosh\left(d x + c\right)^{7} - 7 \, {\left(a^{4} + 5 \, a^{3} b\right)} d \cosh\left(d x + c\right)^{5} - 5 \, {\left(a^{4} - 5 \, a^{3} b\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{4} - 5 \, a^{3} b\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(45 \, {\left(a^{4} + a^{3} b\right)} d \cosh\left(d x + c\right)^{8} - 28 \, {\left(a^{4} + 5 \, a^{3} b\right)} d \cosh\left(d x + c\right)^{6} - 30 \, {\left(a^{4} - 5 \, a^{3} b\right)} d \cosh\left(d x + c\right)^{4} + 12 \, {\left(a^{4} - 5 \, a^{3} b\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{4} + 5 \, a^{3} b\right)} d\right)} \sinh\left(d x + c\right)^{2} - {\left(a^{4} + a^{3} b\right)} d + 2 \, {\left(5 \, {\left(a^{4} + a^{3} b\right)} d \cosh\left(d x + c\right)^{9} - 4 \, {\left(a^{4} + 5 \, a^{3} b\right)} d \cosh\left(d x + c\right)^{7} - 6 \, {\left(a^{4} - 5 \, a^{3} b\right)} d \cosh\left(d x + c\right)^{5} + 4 \, {\left(a^{4} - 5 \, a^{3} b\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{4} + 5 \, a^{3} b\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[1/12*(12*(3*a*b + 5*b^2)*cosh(d*x + c)^8 + 96*(3*a*b + 5*b^2)*cosh(d*x + c)*sinh(d*x + c)^7 + 12*(3*a*b + 5*b^2)*sinh(d*x + c)^8 - 24*(2*a^2 + a*b + 10*b^2)*cosh(d*x + c)^6 + 24*(14*(3*a*b + 5*b^2)*cosh(d*x + c)^2 - 2*a^2 - a*b - 10*b^2)*sinh(d*x + c)^6 + 48*(14*(3*a*b + 5*b^2)*cosh(d*x + c)^3 - 3*(2*a^2 + a*b + 10*b^2)*cosh(d*x + c))*sinh(d*x + c)^5 - 8*(10*a^2 - 2*a*b - 45*b^2)*cosh(d*x + c)^4 + 8*(105*(3*a*b + 5*b^2)*cosh(d*x + c)^4 - 45*(2*a^2 + a*b + 10*b^2)*cosh(d*x + c)^2 - 10*a^2 + 2*a*b + 45*b^2)*sinh(d*x + c)^4 + 32*(21*(3*a*b + 5*b^2)*cosh(d*x + c)^5 - 15*(2*a^2 + a*b + 10*b^2)*cosh(d*x + c)^3 - (10*a^2 - 2*a*b - 45*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 - 8*(2*a^2 + 13*a*b + 30*b^2)*cosh(d*x + c)^2 + 8*(42*(3*a*b + 5*b^2)*cosh(d*x + c)^6 - 45*(2*a^2 + a*b + 10*b^2)*cosh(d*x + c)^4 - 6*(10*a^2 - 2*a*b - 45*b^2)*cosh(d*x + c)^2 - 2*a^2 - 13*a*b - 30*b^2)*sinh(d*x + c)^2 + 3*((3*a^2 + 8*a*b + 5*b^2)*cosh(d*x + c)^10 + 10*(3*a^2 + 8*a*b + 5*b^2)*cosh(d*x + c)*sinh(d*x + c)^9 + (3*a^2 + 8*a*b + 5*b^2)*sinh(d*x + c)^10 - (3*a^2 + 20*a*b + 25*b^2)*cosh(d*x + c)^8 + (45*(3*a^2 + 8*a*b + 5*b^2)*cosh(d*x + c)^2 - 3*a^2 - 20*a*b - 25*b^2)*sinh(d*x + c)^8 + 8*(15*(3*a^2 + 8*a*b + 5*b^2)*cosh(d*x + c)^3 - (3*a^2 + 20*a*b + 25*b^2)*cosh(d*x + c))*sinh(d*x + c)^7 - 2*(3*a^2 - 10*a*b - 25*b^2)*cosh(d*x + c)^6 + 2*(105*(3*a^2 + 8*a*b + 5*b^2)*cosh(d*x + c)^4 - 14*(3*a^2 + 20*a*b + 25*b^2)*cosh(d*x + c)^2 - 3*a^2 + 10*a*b + 25*b^2)*sinh(d*x + c)^6 + 4*(63*(3*a^2 + 8*a*b + 5*b^2)*cosh(d*x + c)^5 - 14*(3*a^2 + 20*a*b + 25*b^2)*cosh(d*x + c)^3 - 3*(3*a^2 - 10*a*b - 25*b^2)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(3*a^2 - 10*a*b - 25*b^2)*cosh(d*x + c)^4 + 2*(105*(3*a^2 + 8*a*b + 5*b^2)*cosh(d*x + c)^6 - 35*(3*a^2 + 20*a*b + 25*b^2)*cosh(d*x + c)^4 - 15*(3*a^2 - 10*a*b - 25*b^2)*cosh(d*x + c)^2 + 3*a^2 - 10*a*b - 25*b^2)*sinh(d*x + c)^4 + 8*(15*(3*a^2 + 8*a*b + 5*b^2)*cosh(d*x + c)^7 - 7*(3*a^2 + 20*a*b + 25*b^2)*cosh(d*x + c)^5 - 5*(3*a^2 - 10*a*b - 25*b^2)*cosh(d*x + c)^3 + (3*a^2 - 10*a*b - 25*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + (3*a^2 + 20*a*b + 25*b^2)*cosh(d*x + c)^2 + (45*(3*a^2 + 8*a*b + 5*b^2)*cosh(d*x + c)^8 - 28*(3*a^2 + 20*a*b + 25*b^2)*cosh(d*x + c)^6 - 30*(3*a^2 - 10*a*b - 25*b^2)*cosh(d*x + c)^4 + 12*(3*a^2 - 10*a*b - 25*b^2)*cosh(d*x + c)^2 + 3*a^2 + 20*a*b + 25*b^2)*sinh(d*x + c)^2 - 3*a^2 - 8*a*b - 5*b^2 + 2*(5*(3*a^2 + 8*a*b + 5*b^2)*cosh(d*x + c)^9 - 4*(3*a^2 + 20*a*b + 25*b^2)*cosh(d*x + c)^7 - 6*(3*a^2 - 10*a*b - 25*b^2)*cosh(d*x + c)^5 + 4*(3*a^2 - 10*a*b - 25*b^2)*cosh(d*x + c)^3 + (3*a^2 + 20*a*b + 25*b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-b/a)*log(((a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 + 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 + 2*(a^2 - b^2)*cosh(d*x + c)^2 + 2*(3*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + a^2 - b^2)*sinh(d*x + c)^2 + a^2 - 6*a*b + b^2 + 4*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 + (a^2 - b^2)*cosh(d*x + c))*sinh(d*x + c) + 4*((a^2 + a*b)*cosh(d*x + c)^2 + 2*(a^2 + a*b)*cosh(d*x + c)*sinh(d*x + c) + (a^2 + a*b)*sinh(d*x + c)^2 + a^2 - a*b)*sqrt(-b/a))/((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)) + 16*a^2 + 76*a*b + 60*b^2 + 16*(6*(3*a*b + 5*b^2)*cosh(d*x + c)^7 - 9*(2*a^2 + a*b + 10*b^2)*cosh(d*x + c)^5 - 2*(10*a^2 - 2*a*b - 45*b^2)*cosh(d*x + c)^3 - (2*a^2 + 13*a*b + 30*b^2)*cosh(d*x + c))*sinh(d*x + c))/((a^4 + a^3*b)*d*cosh(d*x + c)^10 + 10*(a^4 + a^3*b)*d*cosh(d*x + c)*sinh(d*x + c)^9 + (a^4 + a^3*b)*d*sinh(d*x + c)^10 - (a^4 + 5*a^3*b)*d*cosh(d*x + c)^8 + (45*(a^4 + a^3*b)*d*cosh(d*x + c)^2 - (a^4 + 5*a^3*b)*d)*sinh(d*x + c)^8 - 2*(a^4 - 5*a^3*b)*d*cosh(d*x + c)^6 + 8*(15*(a^4 + a^3*b)*d*cosh(d*x + c)^3 - (a^4 + 5*a^3*b)*d*cosh(d*x + c))*sinh(d*x + c)^7 + 2*(105*(a^4 + a^3*b)*d*cosh(d*x + c)^4 - 14*(a^4 + 5*a^3*b)*d*cosh(d*x + c)^2 - (a^4 - 5*a^3*b)*d)*sinh(d*x + c)^6 + 2*(a^4 - 5*a^3*b)*d*cosh(d*x + c)^4 + 4*(63*(a^4 + a^3*b)*d*cosh(d*x + c)^5 - 14*(a^4 + 5*a^3*b)*d*cosh(d*x + c)^3 - 3*(a^4 - 5*a^3*b)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(105*(a^4 + a^3*b)*d*cosh(d*x + c)^6 - 35*(a^4 + 5*a^3*b)*d*cosh(d*x + c)^4 - 15*(a^4 - 5*a^3*b)*d*cosh(d*x + c)^2 + (a^4 - 5*a^3*b)*d)*sinh(d*x + c)^4 + (a^4 + 5*a^3*b)*d*cosh(d*x + c)^2 + 8*(15*(a^4 + a^3*b)*d*cosh(d*x + c)^7 - 7*(a^4 + 5*a^3*b)*d*cosh(d*x + c)^5 - 5*(a^4 - 5*a^3*b)*d*cosh(d*x + c)^3 + (a^4 - 5*a^3*b)*d*cosh(d*x + c))*sinh(d*x + c)^3 + (45*(a^4 + a^3*b)*d*cosh(d*x + c)^8 - 28*(a^4 + 5*a^3*b)*d*cosh(d*x + c)^6 - 30*(a^4 - 5*a^3*b)*d*cosh(d*x + c)^4 + 12*(a^4 - 5*a^3*b)*d*cosh(d*x + c)^2 + (a^4 + 5*a^3*b)*d)*sinh(d*x + c)^2 - (a^4 + a^3*b)*d + 2*(5*(a^4 + a^3*b)*d*cosh(d*x + c)^9 - 4*(a^4 + 5*a^3*b)*d*cosh(d*x + c)^7 - 6*(a^4 - 5*a^3*b)*d*cosh(d*x + c)^5 + 4*(a^4 - 5*a^3*b)*d*cosh(d*x + c)^3 + (a^4 + 5*a^3*b)*d*cosh(d*x + c))*sinh(d*x + c)), 1/6*(6*(3*a*b + 5*b^2)*cosh(d*x + c)^8 + 48*(3*a*b + 5*b^2)*cosh(d*x + c)*sinh(d*x + c)^7 + 6*(3*a*b + 5*b^2)*sinh(d*x + c)^8 - 12*(2*a^2 + a*b + 10*b^2)*cosh(d*x + c)^6 + 12*(14*(3*a*b + 5*b^2)*cosh(d*x + c)^2 - 2*a^2 - a*b - 10*b^2)*sinh(d*x + c)^6 + 24*(14*(3*a*b + 5*b^2)*cosh(d*x + c)^3 - 3*(2*a^2 + a*b + 10*b^2)*cosh(d*x + c))*sinh(d*x + c)^5 - 4*(10*a^2 - 2*a*b - 45*b^2)*cosh(d*x + c)^4 + 4*(105*(3*a*b + 5*b^2)*cosh(d*x + c)^4 - 45*(2*a^2 + a*b + 10*b^2)*cosh(d*x + c)^2 - 10*a^2 + 2*a*b + 45*b^2)*sinh(d*x + c)^4 + 16*(21*(3*a*b + 5*b^2)*cosh(d*x + c)^5 - 15*(2*a^2 + a*b + 10*b^2)*cosh(d*x + c)^3 - (10*a^2 - 2*a*b - 45*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 - 4*(2*a^2 + 13*a*b + 30*b^2)*cosh(d*x + c)^2 + 4*(42*(3*a*b + 5*b^2)*cosh(d*x + c)^6 - 45*(2*a^2 + a*b + 10*b^2)*cosh(d*x + c)^4 - 6*(10*a^2 - 2*a*b - 45*b^2)*cosh(d*x + c)^2 - 2*a^2 - 13*a*b - 30*b^2)*sinh(d*x + c)^2 + 3*((3*a^2 + 8*a*b + 5*b^2)*cosh(d*x + c)^10 + 10*(3*a^2 + 8*a*b + 5*b^2)*cosh(d*x + c)*sinh(d*x + c)^9 + (3*a^2 + 8*a*b + 5*b^2)*sinh(d*x + c)^10 - (3*a^2 + 20*a*b + 25*b^2)*cosh(d*x + c)^8 + (45*(3*a^2 + 8*a*b + 5*b^2)*cosh(d*x + c)^2 - 3*a^2 - 20*a*b - 25*b^2)*sinh(d*x + c)^8 + 8*(15*(3*a^2 + 8*a*b + 5*b^2)*cosh(d*x + c)^3 - (3*a^2 + 20*a*b + 25*b^2)*cosh(d*x + c))*sinh(d*x + c)^7 - 2*(3*a^2 - 10*a*b - 25*b^2)*cosh(d*x + c)^6 + 2*(105*(3*a^2 + 8*a*b + 5*b^2)*cosh(d*x + c)^4 - 14*(3*a^2 + 20*a*b + 25*b^2)*cosh(d*x + c)^2 - 3*a^2 + 10*a*b + 25*b^2)*sinh(d*x + c)^6 + 4*(63*(3*a^2 + 8*a*b + 5*b^2)*cosh(d*x + c)^5 - 14*(3*a^2 + 20*a*b + 25*b^2)*cosh(d*x + c)^3 - 3*(3*a^2 - 10*a*b - 25*b^2)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(3*a^2 - 10*a*b - 25*b^2)*cosh(d*x + c)^4 + 2*(105*(3*a^2 + 8*a*b + 5*b^2)*cosh(d*x + c)^6 - 35*(3*a^2 + 20*a*b + 25*b^2)*cosh(d*x + c)^4 - 15*(3*a^2 - 10*a*b - 25*b^2)*cosh(d*x + c)^2 + 3*a^2 - 10*a*b - 25*b^2)*sinh(d*x + c)^4 + 8*(15*(3*a^2 + 8*a*b + 5*b^2)*cosh(d*x + c)^7 - 7*(3*a^2 + 20*a*b + 25*b^2)*cosh(d*x + c)^5 - 5*(3*a^2 - 10*a*b - 25*b^2)*cosh(d*x + c)^3 + (3*a^2 - 10*a*b - 25*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + (3*a^2 + 20*a*b + 25*b^2)*cosh(d*x + c)^2 + (45*(3*a^2 + 8*a*b + 5*b^2)*cosh(d*x + c)^8 - 28*(3*a^2 + 20*a*b + 25*b^2)*cosh(d*x + c)^6 - 30*(3*a^2 - 10*a*b - 25*b^2)*cosh(d*x + c)^4 + 12*(3*a^2 - 10*a*b - 25*b^2)*cosh(d*x + c)^2 + 3*a^2 + 20*a*b + 25*b^2)*sinh(d*x + c)^2 - 3*a^2 - 8*a*b - 5*b^2 + 2*(5*(3*a^2 + 8*a*b + 5*b^2)*cosh(d*x + c)^9 - 4*(3*a^2 + 20*a*b + 25*b^2)*cosh(d*x + c)^7 - 6*(3*a^2 - 10*a*b - 25*b^2)*cosh(d*x + c)^5 + 4*(3*a^2 - 10*a*b - 25*b^2)*cosh(d*x + c)^3 + (3*a^2 + 20*a*b + 25*b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(b/a)*arctan(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 + a - b)*sqrt(b/a)/b) + 8*a^2 + 38*a*b + 30*b^2 + 8*(6*(3*a*b + 5*b^2)*cosh(d*x + c)^7 - 9*(2*a^2 + a*b + 10*b^2)*cosh(d*x + c)^5 - 2*(10*a^2 - 2*a*b - 45*b^2)*cosh(d*x + c)^3 - (2*a^2 + 13*a*b + 30*b^2)*cosh(d*x + c))*sinh(d*x + c))/((a^4 + a^3*b)*d*cosh(d*x + c)^10 + 10*(a^4 + a^3*b)*d*cosh(d*x + c)*sinh(d*x + c)^9 + (a^4 + a^3*b)*d*sinh(d*x + c)^10 - (a^4 + 5*a^3*b)*d*cosh(d*x + c)^8 + (45*(a^4 + a^3*b)*d*cosh(d*x + c)^2 - (a^4 + 5*a^3*b)*d)*sinh(d*x + c)^8 - 2*(a^4 - 5*a^3*b)*d*cosh(d*x + c)^6 + 8*(15*(a^4 + a^3*b)*d*cosh(d*x + c)^3 - (a^4 + 5*a^3*b)*d*cosh(d*x + c))*sinh(d*x + c)^7 + 2*(105*(a^4 + a^3*b)*d*cosh(d*x + c)^4 - 14*(a^4 + 5*a^3*b)*d*cosh(d*x + c)^2 - (a^4 - 5*a^3*b)*d)*sinh(d*x + c)^6 + 2*(a^4 - 5*a^3*b)*d*cosh(d*x + c)^4 + 4*(63*(a^4 + a^3*b)*d*cosh(d*x + c)^5 - 14*(a^4 + 5*a^3*b)*d*cosh(d*x + c)^3 - 3*(a^4 - 5*a^3*b)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(105*(a^4 + a^3*b)*d*cosh(d*x + c)^6 - 35*(a^4 + 5*a^3*b)*d*cosh(d*x + c)^4 - 15*(a^4 - 5*a^3*b)*d*cosh(d*x + c)^2 + (a^4 - 5*a^3*b)*d)*sinh(d*x + c)^4 + (a^4 + 5*a^3*b)*d*cosh(d*x + c)^2 + 8*(15*(a^4 + a^3*b)*d*cosh(d*x + c)^7 - 7*(a^4 + 5*a^3*b)*d*cosh(d*x + c)^5 - 5*(a^4 - 5*a^3*b)*d*cosh(d*x + c)^3 + (a^4 - 5*a^3*b)*d*cosh(d*x + c))*sinh(d*x + c)^3 + (45*(a^4 + a^3*b)*d*cosh(d*x + c)^8 - 28*(a^4 + 5*a^3*b)*d*cosh(d*x + c)^6 - 30*(a^4 - 5*a^3*b)*d*cosh(d*x + c)^4 + 12*(a^4 - 5*a^3*b)*d*cosh(d*x + c)^2 + (a^4 + 5*a^3*b)*d)*sinh(d*x + c)^2 - (a^4 + a^3*b)*d + 2*(5*(a^4 + a^3*b)*d*cosh(d*x + c)^9 - 4*(a^4 + 5*a^3*b)*d*cosh(d*x + c)^7 - 6*(a^4 - 5*a^3*b)*d*cosh(d*x + c)^5 + 4*(a^4 - 5*a^3*b)*d*cosh(d*x + c)^3 + (a^4 + 5*a^3*b)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
41,-1,0,0,0.000000," ","integrate(sinh(d*x+c)^4/(a+b*tanh(d*x+c)^2)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
42,-1,0,0,0.000000," ","integrate(sinh(d*x+c)^3/(a+b*tanh(d*x+c)^2)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
43,1,12965,0,1.712344," ","integrate(sinh(d*x+c)^2/(a+b*tanh(d*x+c)^2)^3,x, algorithm=""fricas"")","\left[\frac{2 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(d x + c\right)^{12} + 24 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{11} + 2 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \sinh\left(d x + c\right)^{12} + 8 \, {\left(a^{4} + a^{3} b - a^{2} b^{2} - a b^{3} - {\left(a^{4} - 3 \, a^{3} b - 9 \, a^{2} b^{2} - 5 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{10} + 4 \, {\left(2 \, a^{4} + 2 \, a^{3} b - 2 \, a^{2} b^{2} - 2 \, a b^{3} - 2 \, {\left(a^{4} - 3 \, a^{3} b - 9 \, a^{2} b^{2} - 5 \, a b^{3}\right)} d x + 33 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{10} + 40 \, {\left(11 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(a^{4} + a^{3} b - a^{2} b^{2} - a b^{3} - {\left(a^{4} - 3 \, a^{3} b - 9 \, a^{2} b^{2} - 5 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} + 2 \, {\left(5 \, a^{4} + 17 \, a^{3} b - 11 \, a^{2} b^{2} - 21 \, a b^{3} + 2 \, b^{4} - 16 \, {\left(a^{4} - 5 \, a^{3} b - a^{2} b^{2} + 5 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{8} + 2 \, {\left(495 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(d x + c\right)^{4} + 5 \, a^{4} + 17 \, a^{3} b - 11 \, a^{2} b^{2} - 21 \, a b^{3} + 2 \, b^{4} - 16 \, {\left(a^{4} - 5 \, a^{3} b - a^{2} b^{2} + 5 \, a b^{3}\right)} d x + 180 \, {\left(a^{4} + a^{3} b - a^{2} b^{2} - a b^{3} - {\left(a^{4} - 3 \, a^{3} b - 9 \, a^{2} b^{2} - 5 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{8} + 16 \, {\left(99 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(d x + c\right)^{5} + 60 \, {\left(a^{4} + a^{3} b - a^{2} b^{2} - a b^{3} - {\left(a^{4} - 3 \, a^{3} b - 9 \, a^{2} b^{2} - 5 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + {\left(5 \, a^{4} + 17 \, a^{3} b - 11 \, a^{2} b^{2} - 21 \, a b^{3} + 2 \, b^{4} - 16 \, {\left(a^{4} - 5 \, a^{3} b - a^{2} b^{2} + 5 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 4 \, {\left(27 \, a^{3} b - 21 \, a^{2} b^{2} + 29 \, a b^{3} - 3 \, b^{4} - 4 \, {\left(3 \, a^{4} - 17 \, a^{3} b + 13 \, a^{2} b^{2} - 15 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(462 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(d x + c\right)^{6} + 420 \, {\left(a^{4} + a^{3} b - a^{2} b^{2} - a b^{3} - {\left(a^{4} - 3 \, a^{3} b - 9 \, a^{2} b^{2} - 5 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 27 \, a^{3} b - 21 \, a^{2} b^{2} + 29 \, a b^{3} - 3 \, b^{4} - 4 \, {\left(3 \, a^{4} - 17 \, a^{3} b + 13 \, a^{2} b^{2} - 15 \, a b^{3}\right)} d x + 14 \, {\left(5 \, a^{4} + 17 \, a^{3} b - 11 \, a^{2} b^{2} - 21 \, a b^{3} + 2 \, b^{4} - 16 \, {\left(a^{4} - 5 \, a^{3} b - a^{2} b^{2} + 5 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(198 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(d x + c\right)^{7} + 252 \, {\left(a^{4} + a^{3} b - a^{2} b^{2} - a b^{3} - {\left(a^{4} - 3 \, a^{3} b - 9 \, a^{2} b^{2} - 5 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{5} + 14 \, {\left(5 \, a^{4} + 17 \, a^{3} b - 11 \, a^{2} b^{2} - 21 \, a b^{3} + 2 \, b^{4} - 16 \, {\left(a^{4} - 5 \, a^{3} b - a^{2} b^{2} + 5 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(27 \, a^{3} b - 21 \, a^{2} b^{2} + 29 \, a b^{3} - 3 \, b^{4} - 4 \, {\left(3 \, a^{4} - 17 \, a^{3} b + 13 \, a^{2} b^{2} - 15 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 2 \, {\left(5 \, a^{4} - 55 \, a^{3} b - 3 \, a^{2} b^{2} + 51 \, a b^{3} - 6 \, b^{4} + 16 \, {\left(a^{4} - 5 \, a^{3} b - a^{2} b^{2} + 5 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(495 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(d x + c\right)^{8} + 840 \, {\left(a^{4} + a^{3} b - a^{2} b^{2} - a b^{3} - {\left(a^{4} - 3 \, a^{3} b - 9 \, a^{2} b^{2} - 5 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{6} + 70 \, {\left(5 \, a^{4} + 17 \, a^{3} b - 11 \, a^{2} b^{2} - 21 \, a b^{3} + 2 \, b^{4} - 16 \, {\left(a^{4} - 5 \, a^{3} b - a^{2} b^{2} + 5 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{4} - 5 \, a^{4} + 55 \, a^{3} b + 3 \, a^{2} b^{2} - 51 \, a b^{3} + 6 \, b^{4} - 16 \, {\left(a^{4} - 5 \, a^{3} b - a^{2} b^{2} + 5 \, a b^{3}\right)} d x + 30 \, {\left(27 \, a^{3} b - 21 \, a^{2} b^{2} + 29 \, a b^{3} - 3 \, b^{4} - 4 \, {\left(3 \, a^{4} - 17 \, a^{3} b + 13 \, a^{2} b^{2} - 15 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} - 2 \, a^{4} - 6 \, a^{3} b - 6 \, a^{2} b^{2} - 2 \, a b^{3} + 8 \, {\left(55 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(d x + c\right)^{9} + 120 \, {\left(a^{4} + a^{3} b - a^{2} b^{2} - a b^{3} - {\left(a^{4} - 3 \, a^{3} b - 9 \, a^{2} b^{2} - 5 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{7} + 14 \, {\left(5 \, a^{4} + 17 \, a^{3} b - 11 \, a^{2} b^{2} - 21 \, a b^{3} + 2 \, b^{4} - 16 \, {\left(a^{4} - 5 \, a^{3} b - a^{2} b^{2} + 5 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(27 \, a^{3} b - 21 \, a^{2} b^{2} + 29 \, a b^{3} - 3 \, b^{4} - 4 \, {\left(3 \, a^{4} - 17 \, a^{3} b + 13 \, a^{2} b^{2} - 15 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - {\left(5 \, a^{4} - 55 \, a^{3} b - 3 \, a^{2} b^{2} + 51 \, a b^{3} - 6 \, b^{4} + 16 \, {\left(a^{4} - 5 \, a^{3} b - a^{2} b^{2} + 5 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 4 \, {\left(2 \, a^{4} - 7 \, a^{3} b - 19 \, a^{2} b^{2} - 9 \, a b^{3} + b^{4} + 2 \, {\left(a^{4} - 3 \, a^{3} b - 9 \, a^{2} b^{2} - 5 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(33 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(d x + c\right)^{10} + 90 \, {\left(a^{4} + a^{3} b - a^{2} b^{2} - a b^{3} - {\left(a^{4} - 3 \, a^{3} b - 9 \, a^{2} b^{2} - 5 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{8} + 14 \, {\left(5 \, a^{4} + 17 \, a^{3} b - 11 \, a^{2} b^{2} - 21 \, a b^{3} + 2 \, b^{4} - 16 \, {\left(a^{4} - 5 \, a^{3} b - a^{2} b^{2} + 5 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(27 \, a^{3} b - 21 \, a^{2} b^{2} + 29 \, a b^{3} - 3 \, b^{4} - 4 \, {\left(3 \, a^{4} - 17 \, a^{3} b + 13 \, a^{2} b^{2} - 15 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{4} - 2 \, a^{4} + 7 \, a^{3} b + 19 \, a^{2} b^{2} + 9 \, a b^{3} - b^{4} - 2 \, {\left(a^{4} - 3 \, a^{3} b - 9 \, a^{2} b^{2} - 5 \, a b^{3}\right)} d x - 3 \, {\left(5 \, a^{4} - 55 \, a^{3} b - 3 \, a^{2} b^{2} + 51 \, a b^{3} - 6 \, b^{4} + 16 \, {\left(a^{4} - 5 \, a^{3} b - a^{2} b^{2} + 5 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} - {\left({\left(15 \, a^{4} + 20 \, a^{3} b - 6 \, a^{2} b^{2} - 12 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{10} + 10 \, {\left(15 \, a^{4} + 20 \, a^{3} b - 6 \, a^{2} b^{2} - 12 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + {\left(15 \, a^{4} + 20 \, a^{3} b - 6 \, a^{2} b^{2} - 12 \, a b^{3} - b^{4}\right)} \sinh\left(d x + c\right)^{10} + 4 \, {\left(15 \, a^{4} - 10 \, a^{3} b - 16 \, a^{2} b^{2} + 10 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{8} + {\left(60 \, a^{4} - 40 \, a^{3} b - 64 \, a^{2} b^{2} + 40 \, a b^{3} + 4 \, b^{4} + 45 \, {\left(15 \, a^{4} + 20 \, a^{3} b - 6 \, 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)^{8} + 8 \, {\left(15 \, {\left(15 \, a^{4} + 20 \, a^{3} b - 6 \, a^{2} b^{2} - 12 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(15 \, a^{4} - 10 \, a^{3} b - 16 \, a^{2} b^{2} + 10 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(45 \, a^{4} - 60 \, a^{3} b + 62 \, a^{2} b^{2} - 28 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(105 \, {\left(15 \, a^{4} + 20 \, a^{3} b - 6 \, a^{2} b^{2} - 12 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{4} + 45 \, a^{4} - 60 \, a^{3} b + 62 \, a^{2} b^{2} - 28 \, a b^{3} - 3 \, b^{4} + 56 \, {\left(15 \, a^{4} - 10 \, a^{3} b - 16 \, a^{2} b^{2} + 10 \, 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(15 \, a^{4} + 20 \, a^{3} b - 6 \, a^{2} b^{2} - 12 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{5} + 56 \, {\left(15 \, a^{4} - 10 \, a^{3} b - 16 \, a^{2} b^{2} + 10 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(45 \, a^{4} - 60 \, a^{3} b + 62 \, a^{2} b^{2} - 28 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 4 \, {\left(15 \, a^{4} - 10 \, a^{3} b - 16 \, a^{2} b^{2} + 10 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(105 \, {\left(15 \, a^{4} + 20 \, a^{3} b - 6 \, a^{2} b^{2} - 12 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{6} + 140 \, {\left(15 \, a^{4} - 10 \, a^{3} b - 16 \, a^{2} b^{2} + 10 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{4} + 30 \, a^{4} - 20 \, a^{3} b - 32 \, a^{2} b^{2} + 20 \, a b^{3} + 2 \, b^{4} + 15 \, {\left(45 \, a^{4} - 60 \, a^{3} b + 62 \, a^{2} b^{2} - 28 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(15 \, {\left(15 \, a^{4} + 20 \, a^{3} b - 6 \, a^{2} b^{2} - 12 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{7} + 28 \, {\left(15 \, a^{4} - 10 \, a^{3} b - 16 \, a^{2} b^{2} + 10 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(45 \, a^{4} - 60 \, a^{3} b + 62 \, a^{2} b^{2} - 28 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(15 \, a^{4} - 10 \, a^{3} b - 16 \, a^{2} b^{2} + 10 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(15 \, a^{4} + 20 \, a^{3} b - 6 \, a^{2} b^{2} - 12 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{2} + {\left(45 \, {\left(15 \, a^{4} + 20 \, a^{3} b - 6 \, a^{2} b^{2} - 12 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{8} + 112 \, {\left(15 \, a^{4} - 10 \, a^{3} b - 16 \, a^{2} b^{2} + 10 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{6} + 30 \, {\left(45 \, a^{4} - 60 \, a^{3} b + 62 \, a^{2} b^{2} - 28 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 15 \, a^{4} + 20 \, a^{3} b - 6 \, a^{2} b^{2} - 12 \, a b^{3} - b^{4} + 24 \, {\left(15 \, a^{4} - 10 \, a^{3} b - 16 \, a^{2} b^{2} + 10 \, 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(15 \, a^{4} + 20 \, a^{3} b - 6 \, a^{2} b^{2} - 12 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{9} + 16 \, {\left(15 \, a^{4} - 10 \, a^{3} b - 16 \, a^{2} b^{2} + 10 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{7} + 6 \, {\left(45 \, a^{4} - 60 \, a^{3} b + 62 \, a^{2} b^{2} - 28 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + 8 \, {\left(15 \, a^{4} - 10 \, a^{3} b - 16 \, a^{2} b^{2} + 10 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(15 \, a^{4} + 20 \, a^{3} b - 6 \, a^{2} b^{2} - 12 \, a b^{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{{\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) \sinh\left(d x + c\right)^{3} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{2} + a^{2} - 6 \, a b + b^{2} + 4 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + 4 \, {\left({\left(a^{2} + a b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} + a b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} + a b\right)} \sinh\left(d x + c\right)^{2} + a^{2} - a b\right)} \sqrt{-\frac{b}{a}}}{{\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) + 8 \, {\left(3 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(d x + c\right)^{11} + 10 \, {\left(a^{4} + a^{3} b - a^{2} b^{2} - a b^{3} - {\left(a^{4} - 3 \, a^{3} b - 9 \, a^{2} b^{2} - 5 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{9} + 2 \, {\left(5 \, a^{4} + 17 \, a^{3} b - 11 \, a^{2} b^{2} - 21 \, a b^{3} + 2 \, b^{4} - 16 \, {\left(a^{4} - 5 \, a^{3} b - a^{2} b^{2} + 5 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(27 \, a^{3} b - 21 \, a^{2} b^{2} + 29 \, a b^{3} - 3 \, b^{4} - 4 \, {\left(3 \, a^{4} - 17 \, a^{3} b + 13 \, a^{2} b^{2} - 15 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{5} - {\left(5 \, a^{4} - 55 \, a^{3} b - 3 \, a^{2} b^{2} + 51 \, a b^{3} - 6 \, b^{4} + 16 \, {\left(a^{4} - 5 \, a^{3} b - a^{2} b^{2} + 5 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - {\left(2 \, a^{4} - 7 \, a^{3} b - 19 \, a^{2} b^{2} - 9 \, a b^{3} + b^{4} + 2 \, {\left(a^{4} - 3 \, a^{3} b - 9 \, a^{2} b^{2} - 5 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{16 \, {\left({\left(a^{7} + 6 \, a^{6} b + 15 \, a^{5} b^{2} + 20 \, a^{4} b^{3} + 15 \, a^{3} b^{4} + 6 \, a^{2} b^{5} + a b^{6}\right)} d \cosh\left(d x + c\right)^{10} + 10 \, {\left(a^{7} + 6 \, a^{6} b + 15 \, a^{5} b^{2} + 20 \, a^{4} b^{3} + 15 \, a^{3} b^{4} + 6 \, a^{2} b^{5} + a b^{6}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + {\left(a^{7} + 6 \, a^{6} b + 15 \, a^{5} b^{2} + 20 \, a^{4} b^{3} + 15 \, a^{3} b^{4} + 6 \, a^{2} b^{5} + a b^{6}\right)} d \sinh\left(d x + c\right)^{10} + 4 \, {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} - 5 \, a^{3} b^{4} - 4 \, a^{2} b^{5} - a b^{6}\right)} d \cosh\left(d x + c\right)^{8} + {\left(45 \, {\left(a^{7} + 6 \, a^{6} b + 15 \, a^{5} b^{2} + 20 \, a^{4} b^{3} + 15 \, a^{3} b^{4} + 6 \, a^{2} b^{5} + a b^{6}\right)} d \cosh\left(d x + c\right)^{2} + 4 \, {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} - 5 \, a^{3} b^{4} - 4 \, a^{2} b^{5} - a b^{6}\right)} d\right)} \sinh\left(d x + c\right)^{8} + 2 \, {\left(3 \, a^{7} + 10 \, a^{6} b + 13 \, a^{5} b^{2} + 12 \, a^{4} b^{3} + 13 \, a^{3} b^{4} + 10 \, a^{2} b^{5} + 3 \, a b^{6}\right)} d \cosh\left(d x + c\right)^{6} + 8 \, {\left(15 \, {\left(a^{7} + 6 \, a^{6} b + 15 \, a^{5} b^{2} + 20 \, a^{4} b^{3} + 15 \, a^{3} b^{4} + 6 \, a^{2} b^{5} + a b^{6}\right)} d \cosh\left(d x + c\right)^{3} + 4 \, {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} - 5 \, a^{3} b^{4} - 4 \, a^{2} b^{5} - a b^{6}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(105 \, {\left(a^{7} + 6 \, a^{6} b + 15 \, a^{5} b^{2} + 20 \, a^{4} b^{3} + 15 \, a^{3} b^{4} + 6 \, a^{2} b^{5} + a b^{6}\right)} d \cosh\left(d x + c\right)^{4} + 56 \, {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} - 5 \, a^{3} b^{4} - 4 \, a^{2} b^{5} - a b^{6}\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{7} + 10 \, a^{6} b + 13 \, a^{5} b^{2} + 12 \, a^{4} b^{3} + 13 \, a^{3} b^{4} + 10 \, a^{2} b^{5} + 3 \, a b^{6}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} - 5 \, a^{3} b^{4} - 4 \, a^{2} b^{5} - a b^{6}\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(63 \, {\left(a^{7} + 6 \, a^{6} b + 15 \, a^{5} b^{2} + 20 \, a^{4} b^{3} + 15 \, a^{3} b^{4} + 6 \, a^{2} b^{5} + a b^{6}\right)} d \cosh\left(d x + c\right)^{5} + 56 \, {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} - 5 \, a^{3} b^{4} - 4 \, a^{2} b^{5} - a b^{6}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(3 \, a^{7} + 10 \, a^{6} b + 13 \, a^{5} b^{2} + 12 \, a^{4} b^{3} + 13 \, a^{3} b^{4} + 10 \, a^{2} b^{5} + 3 \, a b^{6}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(105 \, {\left(a^{7} + 6 \, a^{6} b + 15 \, a^{5} b^{2} + 20 \, a^{4} b^{3} + 15 \, a^{3} b^{4} + 6 \, a^{2} b^{5} + a b^{6}\right)} d \cosh\left(d x + c\right)^{6} + 140 \, {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} - 5 \, a^{3} b^{4} - 4 \, a^{2} b^{5} - a b^{6}\right)} d \cosh\left(d x + c\right)^{4} + 15 \, {\left(3 \, a^{7} + 10 \, a^{6} b + 13 \, a^{5} b^{2} + 12 \, a^{4} b^{3} + 13 \, a^{3} b^{4} + 10 \, a^{2} b^{5} + 3 \, a b^{6}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} - 5 \, a^{3} b^{4} - 4 \, a^{2} b^{5} - a b^{6}\right)} d\right)} \sinh\left(d x + c\right)^{4} + {\left(a^{7} + 6 \, a^{6} b + 15 \, a^{5} b^{2} + 20 \, a^{4} b^{3} + 15 \, a^{3} b^{4} + 6 \, a^{2} b^{5} + a b^{6}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(15 \, {\left(a^{7} + 6 \, a^{6} b + 15 \, a^{5} b^{2} + 20 \, a^{4} b^{3} + 15 \, a^{3} b^{4} + 6 \, a^{2} b^{5} + a b^{6}\right)} d \cosh\left(d x + c\right)^{7} + 28 \, {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} - 5 \, a^{3} b^{4} - 4 \, a^{2} b^{5} - a b^{6}\right)} d \cosh\left(d x + c\right)^{5} + 5 \, {\left(3 \, a^{7} + 10 \, a^{6} b + 13 \, a^{5} b^{2} + 12 \, a^{4} b^{3} + 13 \, a^{3} b^{4} + 10 \, a^{2} b^{5} + 3 \, a b^{6}\right)} d \cosh\left(d x + c\right)^{3} + 2 \, {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} - 5 \, a^{3} b^{4} - 4 \, a^{2} b^{5} - a b^{6}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(45 \, {\left(a^{7} + 6 \, a^{6} b + 15 \, a^{5} b^{2} + 20 \, a^{4} b^{3} + 15 \, a^{3} b^{4} + 6 \, a^{2} b^{5} + a b^{6}\right)} d \cosh\left(d x + c\right)^{8} + 112 \, {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} - 5 \, a^{3} b^{4} - 4 \, a^{2} b^{5} - a b^{6}\right)} d \cosh\left(d x + c\right)^{6} + 30 \, {\left(3 \, a^{7} + 10 \, a^{6} b + 13 \, a^{5} b^{2} + 12 \, a^{4} b^{3} + 13 \, a^{3} b^{4} + 10 \, a^{2} b^{5} + 3 \, a b^{6}\right)} d \cosh\left(d x + c\right)^{4} + 24 \, {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} - 5 \, a^{3} b^{4} - 4 \, a^{2} b^{5} - a b^{6}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{7} + 6 \, a^{6} b + 15 \, a^{5} b^{2} + 20 \, a^{4} b^{3} + 15 \, a^{3} b^{4} + 6 \, a^{2} b^{5} + a b^{6}\right)} d\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(5 \, {\left(a^{7} + 6 \, a^{6} b + 15 \, a^{5} b^{2} + 20 \, a^{4} b^{3} + 15 \, a^{3} b^{4} + 6 \, a^{2} b^{5} + a b^{6}\right)} d \cosh\left(d x + c\right)^{9} + 16 \, {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} - 5 \, a^{3} b^{4} - 4 \, a^{2} b^{5} - a b^{6}\right)} d \cosh\left(d x + c\right)^{7} + 6 \, {\left(3 \, a^{7} + 10 \, a^{6} b + 13 \, a^{5} b^{2} + 12 \, a^{4} b^{3} + 13 \, a^{3} b^{4} + 10 \, a^{2} b^{5} + 3 \, a b^{6}\right)} d \cosh\left(d x + c\right)^{5} + 8 \, {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} - 5 \, a^{3} b^{4} - 4 \, a^{2} b^{5} - a b^{6}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{7} + 6 \, a^{6} b + 15 \, a^{5} b^{2} + 20 \, a^{4} b^{3} + 15 \, a^{3} b^{4} + 6 \, a^{2} b^{5} + a b^{6}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}, \frac{{\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(d x + c\right)^{12} + 12 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{11} + {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \sinh\left(d x + c\right)^{12} + 4 \, {\left(a^{4} + a^{3} b - a^{2} b^{2} - a b^{3} - {\left(a^{4} - 3 \, a^{3} b - 9 \, a^{2} b^{2} - 5 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{10} + 2 \, {\left(2 \, a^{4} + 2 \, a^{3} b - 2 \, a^{2} b^{2} - 2 \, a b^{3} - 2 \, {\left(a^{4} - 3 \, a^{3} b - 9 \, a^{2} b^{2} - 5 \, a b^{3}\right)} d x + 33 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{10} + 20 \, {\left(11 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(a^{4} + a^{3} b - a^{2} b^{2} - a b^{3} - {\left(a^{4} - 3 \, a^{3} b - 9 \, a^{2} b^{2} - 5 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} + {\left(5 \, a^{4} + 17 \, a^{3} b - 11 \, a^{2} b^{2} - 21 \, a b^{3} + 2 \, b^{4} - 16 \, {\left(a^{4} - 5 \, a^{3} b - a^{2} b^{2} + 5 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{8} + {\left(495 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(d x + c\right)^{4} + 5 \, a^{4} + 17 \, a^{3} b - 11 \, a^{2} b^{2} - 21 \, a b^{3} + 2 \, b^{4} - 16 \, {\left(a^{4} - 5 \, a^{3} b - a^{2} b^{2} + 5 \, a b^{3}\right)} d x + 180 \, {\left(a^{4} + a^{3} b - a^{2} b^{2} - a b^{3} - {\left(a^{4} - 3 \, a^{3} b - 9 \, a^{2} b^{2} - 5 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{8} + 8 \, {\left(99 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(d x + c\right)^{5} + 60 \, {\left(a^{4} + a^{3} b - a^{2} b^{2} - a b^{3} - {\left(a^{4} - 3 \, a^{3} b - 9 \, a^{2} b^{2} - 5 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + {\left(5 \, a^{4} + 17 \, a^{3} b - 11 \, a^{2} b^{2} - 21 \, a b^{3} + 2 \, b^{4} - 16 \, {\left(a^{4} - 5 \, a^{3} b - a^{2} b^{2} + 5 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(27 \, a^{3} b - 21 \, a^{2} b^{2} + 29 \, a b^{3} - 3 \, b^{4} - 4 \, {\left(3 \, a^{4} - 17 \, a^{3} b + 13 \, a^{2} b^{2} - 15 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(462 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(d x + c\right)^{6} + 420 \, {\left(a^{4} + a^{3} b - a^{2} b^{2} - a b^{3} - {\left(a^{4} - 3 \, a^{3} b - 9 \, a^{2} b^{2} - 5 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 27 \, a^{3} b - 21 \, a^{2} b^{2} + 29 \, a b^{3} - 3 \, b^{4} - 4 \, {\left(3 \, a^{4} - 17 \, a^{3} b + 13 \, a^{2} b^{2} - 15 \, a b^{3}\right)} d x + 14 \, {\left(5 \, a^{4} + 17 \, a^{3} b - 11 \, a^{2} b^{2} - 21 \, a b^{3} + 2 \, b^{4} - 16 \, {\left(a^{4} - 5 \, a^{3} b - a^{2} b^{2} + 5 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(198 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(d x + c\right)^{7} + 252 \, {\left(a^{4} + a^{3} b - a^{2} b^{2} - a b^{3} - {\left(a^{4} - 3 \, a^{3} b - 9 \, a^{2} b^{2} - 5 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{5} + 14 \, {\left(5 \, a^{4} + 17 \, a^{3} b - 11 \, a^{2} b^{2} - 21 \, a b^{3} + 2 \, b^{4} - 16 \, {\left(a^{4} - 5 \, a^{3} b - a^{2} b^{2} + 5 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(27 \, a^{3} b - 21 \, a^{2} b^{2} + 29 \, a b^{3} - 3 \, b^{4} - 4 \, {\left(3 \, a^{4} - 17 \, a^{3} b + 13 \, a^{2} b^{2} - 15 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - {\left(5 \, a^{4} - 55 \, a^{3} b - 3 \, a^{2} b^{2} + 51 \, a b^{3} - 6 \, b^{4} + 16 \, {\left(a^{4} - 5 \, a^{3} b - a^{2} b^{2} + 5 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + {\left(495 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(d x + c\right)^{8} + 840 \, {\left(a^{4} + a^{3} b - a^{2} b^{2} - a b^{3} - {\left(a^{4} - 3 \, a^{3} b - 9 \, a^{2} b^{2} - 5 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{6} + 70 \, {\left(5 \, a^{4} + 17 \, a^{3} b - 11 \, a^{2} b^{2} - 21 \, a b^{3} + 2 \, b^{4} - 16 \, {\left(a^{4} - 5 \, a^{3} b - a^{2} b^{2} + 5 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{4} - 5 \, a^{4} + 55 \, a^{3} b + 3 \, a^{2} b^{2} - 51 \, a b^{3} + 6 \, b^{4} - 16 \, {\left(a^{4} - 5 \, a^{3} b - a^{2} b^{2} + 5 \, a b^{3}\right)} d x + 30 \, {\left(27 \, a^{3} b - 21 \, a^{2} b^{2} + 29 \, a b^{3} - 3 \, b^{4} - 4 \, {\left(3 \, a^{4} - 17 \, a^{3} b + 13 \, a^{2} b^{2} - 15 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} - a^{4} - 3 \, a^{3} b - 3 \, a^{2} b^{2} - a b^{3} + 4 \, {\left(55 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(d x + c\right)^{9} + 120 \, {\left(a^{4} + a^{3} b - a^{2} b^{2} - a b^{3} - {\left(a^{4} - 3 \, a^{3} b - 9 \, a^{2} b^{2} - 5 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{7} + 14 \, {\left(5 \, a^{4} + 17 \, a^{3} b - 11 \, a^{2} b^{2} - 21 \, a b^{3} + 2 \, b^{4} - 16 \, {\left(a^{4} - 5 \, a^{3} b - a^{2} b^{2} + 5 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(27 \, a^{3} b - 21 \, a^{2} b^{2} + 29 \, a b^{3} - 3 \, b^{4} - 4 \, {\left(3 \, a^{4} - 17 \, a^{3} b + 13 \, a^{2} b^{2} - 15 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - {\left(5 \, a^{4} - 55 \, a^{3} b - 3 \, a^{2} b^{2} + 51 \, a b^{3} - 6 \, b^{4} + 16 \, {\left(a^{4} - 5 \, a^{3} b - a^{2} b^{2} + 5 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 2 \, {\left(2 \, a^{4} - 7 \, a^{3} b - 19 \, a^{2} b^{2} - 9 \, a b^{3} + b^{4} + 2 \, {\left(a^{4} - 3 \, a^{3} b - 9 \, a^{2} b^{2} - 5 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(33 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(d x + c\right)^{10} + 90 \, {\left(a^{4} + a^{3} b - a^{2} b^{2} - a b^{3} - {\left(a^{4} - 3 \, a^{3} b - 9 \, a^{2} b^{2} - 5 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{8} + 14 \, {\left(5 \, a^{4} + 17 \, a^{3} b - 11 \, a^{2} b^{2} - 21 \, a b^{3} + 2 \, b^{4} - 16 \, {\left(a^{4} - 5 \, a^{3} b - a^{2} b^{2} + 5 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(27 \, a^{3} b - 21 \, a^{2} b^{2} + 29 \, a b^{3} - 3 \, b^{4} - 4 \, {\left(3 \, a^{4} - 17 \, a^{3} b + 13 \, a^{2} b^{2} - 15 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{4} - 2 \, a^{4} + 7 \, a^{3} b + 19 \, a^{2} b^{2} + 9 \, a b^{3} - b^{4} - 2 \, {\left(a^{4} - 3 \, a^{3} b - 9 \, a^{2} b^{2} - 5 \, a b^{3}\right)} d x - 3 \, {\left(5 \, a^{4} - 55 \, a^{3} b - 3 \, a^{2} b^{2} + 51 \, a b^{3} - 6 \, b^{4} + 16 \, {\left(a^{4} - 5 \, a^{3} b - a^{2} b^{2} + 5 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} - {\left({\left(15 \, a^{4} + 20 \, a^{3} b - 6 \, a^{2} b^{2} - 12 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{10} + 10 \, {\left(15 \, a^{4} + 20 \, a^{3} b - 6 \, a^{2} b^{2} - 12 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + {\left(15 \, a^{4} + 20 \, a^{3} b - 6 \, a^{2} b^{2} - 12 \, a b^{3} - b^{4}\right)} \sinh\left(d x + c\right)^{10} + 4 \, {\left(15 \, a^{4} - 10 \, a^{3} b - 16 \, a^{2} b^{2} + 10 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{8} + {\left(60 \, a^{4} - 40 \, a^{3} b - 64 \, a^{2} b^{2} + 40 \, a b^{3} + 4 \, b^{4} + 45 \, {\left(15 \, a^{4} + 20 \, a^{3} b - 6 \, 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)^{8} + 8 \, {\left(15 \, {\left(15 \, a^{4} + 20 \, a^{3} b - 6 \, a^{2} b^{2} - 12 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(15 \, a^{4} - 10 \, a^{3} b - 16 \, a^{2} b^{2} + 10 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(45 \, a^{4} - 60 \, a^{3} b + 62 \, a^{2} b^{2} - 28 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(105 \, {\left(15 \, a^{4} + 20 \, a^{3} b - 6 \, a^{2} b^{2} - 12 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{4} + 45 \, a^{4} - 60 \, a^{3} b + 62 \, a^{2} b^{2} - 28 \, a b^{3} - 3 \, b^{4} + 56 \, {\left(15 \, a^{4} - 10 \, a^{3} b - 16 \, a^{2} b^{2} + 10 \, 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(15 \, a^{4} + 20 \, a^{3} b - 6 \, a^{2} b^{2} - 12 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{5} + 56 \, {\left(15 \, a^{4} - 10 \, a^{3} b - 16 \, a^{2} b^{2} + 10 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(45 \, a^{4} - 60 \, a^{3} b + 62 \, a^{2} b^{2} - 28 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 4 \, {\left(15 \, a^{4} - 10 \, a^{3} b - 16 \, a^{2} b^{2} + 10 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(105 \, {\left(15 \, a^{4} + 20 \, a^{3} b - 6 \, a^{2} b^{2} - 12 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{6} + 140 \, {\left(15 \, a^{4} - 10 \, a^{3} b - 16 \, a^{2} b^{2} + 10 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{4} + 30 \, a^{4} - 20 \, a^{3} b - 32 \, a^{2} b^{2} + 20 \, a b^{3} + 2 \, b^{4} + 15 \, {\left(45 \, a^{4} - 60 \, a^{3} b + 62 \, a^{2} b^{2} - 28 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(15 \, {\left(15 \, a^{4} + 20 \, a^{3} b - 6 \, a^{2} b^{2} - 12 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{7} + 28 \, {\left(15 \, a^{4} - 10 \, a^{3} b - 16 \, a^{2} b^{2} + 10 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(45 \, a^{4} - 60 \, a^{3} b + 62 \, a^{2} b^{2} - 28 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(15 \, a^{4} - 10 \, a^{3} b - 16 \, a^{2} b^{2} + 10 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(15 \, a^{4} + 20 \, a^{3} b - 6 \, a^{2} b^{2} - 12 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{2} + {\left(45 \, {\left(15 \, a^{4} + 20 \, a^{3} b - 6 \, a^{2} b^{2} - 12 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{8} + 112 \, {\left(15 \, a^{4} - 10 \, a^{3} b - 16 \, a^{2} b^{2} + 10 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{6} + 30 \, {\left(45 \, a^{4} - 60 \, a^{3} b + 62 \, a^{2} b^{2} - 28 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 15 \, a^{4} + 20 \, a^{3} b - 6 \, a^{2} b^{2} - 12 \, a b^{3} - b^{4} + 24 \, {\left(15 \, a^{4} - 10 \, a^{3} b - 16 \, a^{2} b^{2} + 10 \, 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(15 \, a^{4} + 20 \, a^{3} b - 6 \, a^{2} b^{2} - 12 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{9} + 16 \, {\left(15 \, a^{4} - 10 \, a^{3} b - 16 \, a^{2} b^{2} + 10 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{7} + 6 \, {\left(45 \, a^{4} - 60 \, a^{3} b + 62 \, a^{2} b^{2} - 28 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + 8 \, {\left(15 \, a^{4} - 10 \, a^{3} b - 16 \, a^{2} b^{2} + 10 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(15 \, a^{4} + 20 \, a^{3} b - 6 \, a^{2} b^{2} - 12 \, a b^{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({\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} + a - b\right)} \sqrt{\frac{b}{a}}}{2 \, b}\right) + 4 \, {\left(3 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(d x + c\right)^{11} + 10 \, {\left(a^{4} + a^{3} b - a^{2} b^{2} - a b^{3} - {\left(a^{4} - 3 \, a^{3} b - 9 \, a^{2} b^{2} - 5 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{9} + 2 \, {\left(5 \, a^{4} + 17 \, a^{3} b - 11 \, a^{2} b^{2} - 21 \, a b^{3} + 2 \, b^{4} - 16 \, {\left(a^{4} - 5 \, a^{3} b - a^{2} b^{2} + 5 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(27 \, a^{3} b - 21 \, a^{2} b^{2} + 29 \, a b^{3} - 3 \, b^{4} - 4 \, {\left(3 \, a^{4} - 17 \, a^{3} b + 13 \, a^{2} b^{2} - 15 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{5} - {\left(5 \, a^{4} - 55 \, a^{3} b - 3 \, a^{2} b^{2} + 51 \, a b^{3} - 6 \, b^{4} + 16 \, {\left(a^{4} - 5 \, a^{3} b - a^{2} b^{2} + 5 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - {\left(2 \, a^{4} - 7 \, a^{3} b - 19 \, a^{2} b^{2} - 9 \, a b^{3} + b^{4} + 2 \, {\left(a^{4} - 3 \, a^{3} b - 9 \, a^{2} b^{2} - 5 \, a b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{8 \, {\left({\left(a^{7} + 6 \, a^{6} b + 15 \, a^{5} b^{2} + 20 \, a^{4} b^{3} + 15 \, a^{3} b^{4} + 6 \, a^{2} b^{5} + a b^{6}\right)} d \cosh\left(d x + c\right)^{10} + 10 \, {\left(a^{7} + 6 \, a^{6} b + 15 \, a^{5} b^{2} + 20 \, a^{4} b^{3} + 15 \, a^{3} b^{4} + 6 \, a^{2} b^{5} + a b^{6}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + {\left(a^{7} + 6 \, a^{6} b + 15 \, a^{5} b^{2} + 20 \, a^{4} b^{3} + 15 \, a^{3} b^{4} + 6 \, a^{2} b^{5} + a b^{6}\right)} d \sinh\left(d x + c\right)^{10} + 4 \, {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} - 5 \, a^{3} b^{4} - 4 \, a^{2} b^{5} - a b^{6}\right)} d \cosh\left(d x + c\right)^{8} + {\left(45 \, {\left(a^{7} + 6 \, a^{6} b + 15 \, a^{5} b^{2} + 20 \, a^{4} b^{3} + 15 \, a^{3} b^{4} + 6 \, a^{2} b^{5} + a b^{6}\right)} d \cosh\left(d x + c\right)^{2} + 4 \, {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} - 5 \, a^{3} b^{4} - 4 \, a^{2} b^{5} - a b^{6}\right)} d\right)} \sinh\left(d x + c\right)^{8} + 2 \, {\left(3 \, a^{7} + 10 \, a^{6} b + 13 \, a^{5} b^{2} + 12 \, a^{4} b^{3} + 13 \, a^{3} b^{4} + 10 \, a^{2} b^{5} + 3 \, a b^{6}\right)} d \cosh\left(d x + c\right)^{6} + 8 \, {\left(15 \, {\left(a^{7} + 6 \, a^{6} b + 15 \, a^{5} b^{2} + 20 \, a^{4} b^{3} + 15 \, a^{3} b^{4} + 6 \, a^{2} b^{5} + a b^{6}\right)} d \cosh\left(d x + c\right)^{3} + 4 \, {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} - 5 \, a^{3} b^{4} - 4 \, a^{2} b^{5} - a b^{6}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(105 \, {\left(a^{7} + 6 \, a^{6} b + 15 \, a^{5} b^{2} + 20 \, a^{4} b^{3} + 15 \, a^{3} b^{4} + 6 \, a^{2} b^{5} + a b^{6}\right)} d \cosh\left(d x + c\right)^{4} + 56 \, {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} - 5 \, a^{3} b^{4} - 4 \, a^{2} b^{5} - a b^{6}\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{7} + 10 \, a^{6} b + 13 \, a^{5} b^{2} + 12 \, a^{4} b^{3} + 13 \, a^{3} b^{4} + 10 \, a^{2} b^{5} + 3 \, a b^{6}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} - 5 \, a^{3} b^{4} - 4 \, a^{2} b^{5} - a b^{6}\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(63 \, {\left(a^{7} + 6 \, a^{6} b + 15 \, a^{5} b^{2} + 20 \, a^{4} b^{3} + 15 \, a^{3} b^{4} + 6 \, a^{2} b^{5} + a b^{6}\right)} d \cosh\left(d x + c\right)^{5} + 56 \, {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} - 5 \, a^{3} b^{4} - 4 \, a^{2} b^{5} - a b^{6}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(3 \, a^{7} + 10 \, a^{6} b + 13 \, a^{5} b^{2} + 12 \, a^{4} b^{3} + 13 \, a^{3} b^{4} + 10 \, a^{2} b^{5} + 3 \, a b^{6}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(105 \, {\left(a^{7} + 6 \, a^{6} b + 15 \, a^{5} b^{2} + 20 \, a^{4} b^{3} + 15 \, a^{3} b^{4} + 6 \, a^{2} b^{5} + a b^{6}\right)} d \cosh\left(d x + c\right)^{6} + 140 \, {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} - 5 \, a^{3} b^{4} - 4 \, a^{2} b^{5} - a b^{6}\right)} d \cosh\left(d x + c\right)^{4} + 15 \, {\left(3 \, a^{7} + 10 \, a^{6} b + 13 \, a^{5} b^{2} + 12 \, a^{4} b^{3} + 13 \, a^{3} b^{4} + 10 \, a^{2} b^{5} + 3 \, a b^{6}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} - 5 \, a^{3} b^{4} - 4 \, a^{2} b^{5} - a b^{6}\right)} d\right)} \sinh\left(d x + c\right)^{4} + {\left(a^{7} + 6 \, a^{6} b + 15 \, a^{5} b^{2} + 20 \, a^{4} b^{3} + 15 \, a^{3} b^{4} + 6 \, a^{2} b^{5} + a b^{6}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(15 \, {\left(a^{7} + 6 \, a^{6} b + 15 \, a^{5} b^{2} + 20 \, a^{4} b^{3} + 15 \, a^{3} b^{4} + 6 \, a^{2} b^{5} + a b^{6}\right)} d \cosh\left(d x + c\right)^{7} + 28 \, {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} - 5 \, a^{3} b^{4} - 4 \, a^{2} b^{5} - a b^{6}\right)} d \cosh\left(d x + c\right)^{5} + 5 \, {\left(3 \, a^{7} + 10 \, a^{6} b + 13 \, a^{5} b^{2} + 12 \, a^{4} b^{3} + 13 \, a^{3} b^{4} + 10 \, a^{2} b^{5} + 3 \, a b^{6}\right)} d \cosh\left(d x + c\right)^{3} + 2 \, {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} - 5 \, a^{3} b^{4} - 4 \, a^{2} b^{5} - a b^{6}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(45 \, {\left(a^{7} + 6 \, a^{6} b + 15 \, a^{5} b^{2} + 20 \, a^{4} b^{3} + 15 \, a^{3} b^{4} + 6 \, a^{2} b^{5} + a b^{6}\right)} d \cosh\left(d x + c\right)^{8} + 112 \, {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} - 5 \, a^{3} b^{4} - 4 \, a^{2} b^{5} - a b^{6}\right)} d \cosh\left(d x + c\right)^{6} + 30 \, {\left(3 \, a^{7} + 10 \, a^{6} b + 13 \, a^{5} b^{2} + 12 \, a^{4} b^{3} + 13 \, a^{3} b^{4} + 10 \, a^{2} b^{5} + 3 \, a b^{6}\right)} d \cosh\left(d x + c\right)^{4} + 24 \, {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} - 5 \, a^{3} b^{4} - 4 \, a^{2} b^{5} - a b^{6}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{7} + 6 \, a^{6} b + 15 \, a^{5} b^{2} + 20 \, a^{4} b^{3} + 15 \, a^{3} b^{4} + 6 \, a^{2} b^{5} + a b^{6}\right)} d\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(5 \, {\left(a^{7} + 6 \, a^{6} b + 15 \, a^{5} b^{2} + 20 \, a^{4} b^{3} + 15 \, a^{3} b^{4} + 6 \, a^{2} b^{5} + a b^{6}\right)} d \cosh\left(d x + c\right)^{9} + 16 \, {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} - 5 \, a^{3} b^{4} - 4 \, a^{2} b^{5} - a b^{6}\right)} d \cosh\left(d x + c\right)^{7} + 6 \, {\left(3 \, a^{7} + 10 \, a^{6} b + 13 \, a^{5} b^{2} + 12 \, a^{4} b^{3} + 13 \, a^{3} b^{4} + 10 \, a^{2} b^{5} + 3 \, a b^{6}\right)} d \cosh\left(d x + c\right)^{5} + 8 \, {\left(a^{7} + 4 \, a^{6} b + 5 \, a^{5} b^{2} - 5 \, a^{3} b^{4} - 4 \, a^{2} b^{5} - a b^{6}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{7} + 6 \, a^{6} b + 15 \, a^{5} b^{2} + 20 \, a^{4} b^{3} + 15 \, a^{3} b^{4} + 6 \, a^{2} b^{5} + a b^{6}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[1/16*(2*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(d*x + c)^12 + 24*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(d*x + c)*sinh(d*x + c)^11 + 2*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*sinh(d*x + c)^12 + 8*(a^4 + a^3*b - a^2*b^2 - a*b^3 - (a^4 - 3*a^3*b - 9*a^2*b^2 - 5*a*b^3)*d*x)*cosh(d*x + c)^10 + 4*(2*a^4 + 2*a^3*b - 2*a^2*b^2 - 2*a*b^3 - 2*(a^4 - 3*a^3*b - 9*a^2*b^2 - 5*a*b^3)*d*x + 33*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^10 + 40*(11*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(d*x + c)^3 + 2*(a^4 + a^3*b - a^2*b^2 - a*b^3 - (a^4 - 3*a^3*b - 9*a^2*b^2 - 5*a*b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c)^9 + 2*(5*a^4 + 17*a^3*b - 11*a^2*b^2 - 21*a*b^3 + 2*b^4 - 16*(a^4 - 5*a^3*b - a^2*b^2 + 5*a*b^3)*d*x)*cosh(d*x + c)^8 + 2*(495*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(d*x + c)^4 + 5*a^4 + 17*a^3*b - 11*a^2*b^2 - 21*a*b^3 + 2*b^4 - 16*(a^4 - 5*a^3*b - a^2*b^2 + 5*a*b^3)*d*x + 180*(a^4 + a^3*b - a^2*b^2 - a*b^3 - (a^4 - 3*a^3*b - 9*a^2*b^2 - 5*a*b^3)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 16*(99*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(d*x + c)^5 + 60*(a^4 + a^3*b - a^2*b^2 - a*b^3 - (a^4 - 3*a^3*b - 9*a^2*b^2 - 5*a*b^3)*d*x)*cosh(d*x + c)^3 + (5*a^4 + 17*a^3*b - 11*a^2*b^2 - 21*a*b^3 + 2*b^4 - 16*(a^4 - 5*a^3*b - a^2*b^2 + 5*a*b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c)^7 + 4*(27*a^3*b - 21*a^2*b^2 + 29*a*b^3 - 3*b^4 - 4*(3*a^4 - 17*a^3*b + 13*a^2*b^2 - 15*a*b^3)*d*x)*cosh(d*x + c)^6 + 4*(462*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(d*x + c)^6 + 420*(a^4 + a^3*b - a^2*b^2 - a*b^3 - (a^4 - 3*a^3*b - 9*a^2*b^2 - 5*a*b^3)*d*x)*cosh(d*x + c)^4 + 27*a^3*b - 21*a^2*b^2 + 29*a*b^3 - 3*b^4 - 4*(3*a^4 - 17*a^3*b + 13*a^2*b^2 - 15*a*b^3)*d*x + 14*(5*a^4 + 17*a^3*b - 11*a^2*b^2 - 21*a*b^3 + 2*b^4 - 16*(a^4 - 5*a^3*b - a^2*b^2 + 5*a*b^3)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(198*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(d*x + c)^7 + 252*(a^4 + a^3*b - a^2*b^2 - a*b^3 - (a^4 - 3*a^3*b - 9*a^2*b^2 - 5*a*b^3)*d*x)*cosh(d*x + c)^5 + 14*(5*a^4 + 17*a^3*b - 11*a^2*b^2 - 21*a*b^3 + 2*b^4 - 16*(a^4 - 5*a^3*b - a^2*b^2 + 5*a*b^3)*d*x)*cosh(d*x + c)^3 + 3*(27*a^3*b - 21*a^2*b^2 + 29*a*b^3 - 3*b^4 - 4*(3*a^4 - 17*a^3*b + 13*a^2*b^2 - 15*a*b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c)^5 - 2*(5*a^4 - 55*a^3*b - 3*a^2*b^2 + 51*a*b^3 - 6*b^4 + 16*(a^4 - 5*a^3*b - a^2*b^2 + 5*a*b^3)*d*x)*cosh(d*x + c)^4 + 2*(495*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(d*x + c)^8 + 840*(a^4 + a^3*b - a^2*b^2 - a*b^3 - (a^4 - 3*a^3*b - 9*a^2*b^2 - 5*a*b^3)*d*x)*cosh(d*x + c)^6 + 70*(5*a^4 + 17*a^3*b - 11*a^2*b^2 - 21*a*b^3 + 2*b^4 - 16*(a^4 - 5*a^3*b - a^2*b^2 + 5*a*b^3)*d*x)*cosh(d*x + c)^4 - 5*a^4 + 55*a^3*b + 3*a^2*b^2 - 51*a*b^3 + 6*b^4 - 16*(a^4 - 5*a^3*b - a^2*b^2 + 5*a*b^3)*d*x + 30*(27*a^3*b - 21*a^2*b^2 + 29*a*b^3 - 3*b^4 - 4*(3*a^4 - 17*a^3*b + 13*a^2*b^2 - 15*a*b^3)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^4 - 2*a^4 - 6*a^3*b - 6*a^2*b^2 - 2*a*b^3 + 8*(55*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(d*x + c)^9 + 120*(a^4 + a^3*b - a^2*b^2 - a*b^3 - (a^4 - 3*a^3*b - 9*a^2*b^2 - 5*a*b^3)*d*x)*cosh(d*x + c)^7 + 14*(5*a^4 + 17*a^3*b - 11*a^2*b^2 - 21*a*b^3 + 2*b^4 - 16*(a^4 - 5*a^3*b - a^2*b^2 + 5*a*b^3)*d*x)*cosh(d*x + c)^5 + 10*(27*a^3*b - 21*a^2*b^2 + 29*a*b^3 - 3*b^4 - 4*(3*a^4 - 17*a^3*b + 13*a^2*b^2 - 15*a*b^3)*d*x)*cosh(d*x + c)^3 - (5*a^4 - 55*a^3*b - 3*a^2*b^2 + 51*a*b^3 - 6*b^4 + 16*(a^4 - 5*a^3*b - a^2*b^2 + 5*a*b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c)^3 - 4*(2*a^4 - 7*a^3*b - 19*a^2*b^2 - 9*a*b^3 + b^4 + 2*(a^4 - 3*a^3*b - 9*a^2*b^2 - 5*a*b^3)*d*x)*cosh(d*x + c)^2 + 4*(33*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(d*x + c)^10 + 90*(a^4 + a^3*b - a^2*b^2 - a*b^3 - (a^4 - 3*a^3*b - 9*a^2*b^2 - 5*a*b^3)*d*x)*cosh(d*x + c)^8 + 14*(5*a^4 + 17*a^3*b - 11*a^2*b^2 - 21*a*b^3 + 2*b^4 - 16*(a^4 - 5*a^3*b - a^2*b^2 + 5*a*b^3)*d*x)*cosh(d*x + c)^6 + 15*(27*a^3*b - 21*a^2*b^2 + 29*a*b^3 - 3*b^4 - 4*(3*a^4 - 17*a^3*b + 13*a^2*b^2 - 15*a*b^3)*d*x)*cosh(d*x + c)^4 - 2*a^4 + 7*a^3*b + 19*a^2*b^2 + 9*a*b^3 - b^4 - 2*(a^4 - 3*a^3*b - 9*a^2*b^2 - 5*a*b^3)*d*x - 3*(5*a^4 - 55*a^3*b - 3*a^2*b^2 + 51*a*b^3 - 6*b^4 + 16*(a^4 - 5*a^3*b - a^2*b^2 + 5*a*b^3)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - ((15*a^4 + 20*a^3*b - 6*a^2*b^2 - 12*a*b^3 - b^4)*cosh(d*x + c)^10 + 10*(15*a^4 + 20*a^3*b - 6*a^2*b^2 - 12*a*b^3 - b^4)*cosh(d*x + c)*sinh(d*x + c)^9 + (15*a^4 + 20*a^3*b - 6*a^2*b^2 - 12*a*b^3 - b^4)*sinh(d*x + c)^10 + 4*(15*a^4 - 10*a^3*b - 16*a^2*b^2 + 10*a*b^3 + b^4)*cosh(d*x + c)^8 + (60*a^4 - 40*a^3*b - 64*a^2*b^2 + 40*a*b^3 + 4*b^4 + 45*(15*a^4 + 20*a^3*b - 6*a^2*b^2 - 12*a*b^3 - b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 8*(15*(15*a^4 + 20*a^3*b - 6*a^2*b^2 - 12*a*b^3 - b^4)*cosh(d*x + c)^3 + 4*(15*a^4 - 10*a^3*b - 16*a^2*b^2 + 10*a*b^3 + b^4)*cosh(d*x + c))*sinh(d*x + c)^7 + 2*(45*a^4 - 60*a^3*b + 62*a^2*b^2 - 28*a*b^3 - 3*b^4)*cosh(d*x + c)^6 + 2*(105*(15*a^4 + 20*a^3*b - 6*a^2*b^2 - 12*a*b^3 - b^4)*cosh(d*x + c)^4 + 45*a^4 - 60*a^3*b + 62*a^2*b^2 - 28*a*b^3 - 3*b^4 + 56*(15*a^4 - 10*a^3*b - 16*a^2*b^2 + 10*a*b^3 + b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 4*(63*(15*a^4 + 20*a^3*b - 6*a^2*b^2 - 12*a*b^3 - b^4)*cosh(d*x + c)^5 + 56*(15*a^4 - 10*a^3*b - 16*a^2*b^2 + 10*a*b^3 + b^4)*cosh(d*x + c)^3 + 3*(45*a^4 - 60*a^3*b + 62*a^2*b^2 - 28*a*b^3 - 3*b^4)*cosh(d*x + c))*sinh(d*x + c)^5 + 4*(15*a^4 - 10*a^3*b - 16*a^2*b^2 + 10*a*b^3 + b^4)*cosh(d*x + c)^4 + 2*(105*(15*a^4 + 20*a^3*b - 6*a^2*b^2 - 12*a*b^3 - b^4)*cosh(d*x + c)^6 + 140*(15*a^4 - 10*a^3*b - 16*a^2*b^2 + 10*a*b^3 + b^4)*cosh(d*x + c)^4 + 30*a^4 - 20*a^3*b - 32*a^2*b^2 + 20*a*b^3 + 2*b^4 + 15*(45*a^4 - 60*a^3*b + 62*a^2*b^2 - 28*a*b^3 - 3*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(15*(15*a^4 + 20*a^3*b - 6*a^2*b^2 - 12*a*b^3 - b^4)*cosh(d*x + c)^7 + 28*(15*a^4 - 10*a^3*b - 16*a^2*b^2 + 10*a*b^3 + b^4)*cosh(d*x + c)^5 + 5*(45*a^4 - 60*a^3*b + 62*a^2*b^2 - 28*a*b^3 - 3*b^4)*cosh(d*x + c)^3 + 2*(15*a^4 - 10*a^3*b - 16*a^2*b^2 + 10*a*b^3 + b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + (15*a^4 + 20*a^3*b - 6*a^2*b^2 - 12*a*b^3 - b^4)*cosh(d*x + c)^2 + (45*(15*a^4 + 20*a^3*b - 6*a^2*b^2 - 12*a*b^3 - b^4)*cosh(d*x + c)^8 + 112*(15*a^4 - 10*a^3*b - 16*a^2*b^2 + 10*a*b^3 + b^4)*cosh(d*x + c)^6 + 30*(45*a^4 - 60*a^3*b + 62*a^2*b^2 - 28*a*b^3 - 3*b^4)*cosh(d*x + c)^4 + 15*a^4 + 20*a^3*b - 6*a^2*b^2 - 12*a*b^3 - b^4 + 24*(15*a^4 - 10*a^3*b - 16*a^2*b^2 + 10*a*b^3 + b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 2*(5*(15*a^4 + 20*a^3*b - 6*a^2*b^2 - 12*a*b^3 - b^4)*cosh(d*x + c)^9 + 16*(15*a^4 - 10*a^3*b - 16*a^2*b^2 + 10*a*b^3 + b^4)*cosh(d*x + c)^7 + 6*(45*a^4 - 60*a^3*b + 62*a^2*b^2 - 28*a*b^3 - 3*b^4)*cosh(d*x + c)^5 + 8*(15*a^4 - 10*a^3*b - 16*a^2*b^2 + 10*a*b^3 + b^4)*cosh(d*x + c)^3 + (15*a^4 + 20*a^3*b - 6*a^2*b^2 - 12*a*b^3 - b^4)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-b/a)*log(((a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 + 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 + 2*(a^2 - b^2)*cosh(d*x + c)^2 + 2*(3*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + a^2 - b^2)*sinh(d*x + c)^2 + a^2 - 6*a*b + b^2 + 4*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 + (a^2 - b^2)*cosh(d*x + c))*sinh(d*x + c) + 4*((a^2 + a*b)*cosh(d*x + c)^2 + 2*(a^2 + a*b)*cosh(d*x + c)*sinh(d*x + c) + (a^2 + a*b)*sinh(d*x + c)^2 + a^2 - a*b)*sqrt(-b/a))/((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)) + 8*(3*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(d*x + c)^11 + 10*(a^4 + a^3*b - a^2*b^2 - a*b^3 - (a^4 - 3*a^3*b - 9*a^2*b^2 - 5*a*b^3)*d*x)*cosh(d*x + c)^9 + 2*(5*a^4 + 17*a^3*b - 11*a^2*b^2 - 21*a*b^3 + 2*b^4 - 16*(a^4 - 5*a^3*b - a^2*b^2 + 5*a*b^3)*d*x)*cosh(d*x + c)^7 + 3*(27*a^3*b - 21*a^2*b^2 + 29*a*b^3 - 3*b^4 - 4*(3*a^4 - 17*a^3*b + 13*a^2*b^2 - 15*a*b^3)*d*x)*cosh(d*x + c)^5 - (5*a^4 - 55*a^3*b - 3*a^2*b^2 + 51*a*b^3 - 6*b^4 + 16*(a^4 - 5*a^3*b - a^2*b^2 + 5*a*b^3)*d*x)*cosh(d*x + c)^3 - (2*a^4 - 7*a^3*b - 19*a^2*b^2 - 9*a*b^3 + b^4 + 2*(a^4 - 3*a^3*b - 9*a^2*b^2 - 5*a*b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c))/((a^7 + 6*a^6*b + 15*a^5*b^2 + 20*a^4*b^3 + 15*a^3*b^4 + 6*a^2*b^5 + a*b^6)*d*cosh(d*x + c)^10 + 10*(a^7 + 6*a^6*b + 15*a^5*b^2 + 20*a^4*b^3 + 15*a^3*b^4 + 6*a^2*b^5 + a*b^6)*d*cosh(d*x + c)*sinh(d*x + c)^9 + (a^7 + 6*a^6*b + 15*a^5*b^2 + 20*a^4*b^3 + 15*a^3*b^4 + 6*a^2*b^5 + a*b^6)*d*sinh(d*x + c)^10 + 4*(a^7 + 4*a^6*b + 5*a^5*b^2 - 5*a^3*b^4 - 4*a^2*b^5 - a*b^6)*d*cosh(d*x + c)^8 + (45*(a^7 + 6*a^6*b + 15*a^5*b^2 + 20*a^4*b^3 + 15*a^3*b^4 + 6*a^2*b^5 + a*b^6)*d*cosh(d*x + c)^2 + 4*(a^7 + 4*a^6*b + 5*a^5*b^2 - 5*a^3*b^4 - 4*a^2*b^5 - a*b^6)*d)*sinh(d*x + c)^8 + 2*(3*a^7 + 10*a^6*b + 13*a^5*b^2 + 12*a^4*b^3 + 13*a^3*b^4 + 10*a^2*b^5 + 3*a*b^6)*d*cosh(d*x + c)^6 + 8*(15*(a^7 + 6*a^6*b + 15*a^5*b^2 + 20*a^4*b^3 + 15*a^3*b^4 + 6*a^2*b^5 + a*b^6)*d*cosh(d*x + c)^3 + 4*(a^7 + 4*a^6*b + 5*a^5*b^2 - 5*a^3*b^4 - 4*a^2*b^5 - a*b^6)*d*cosh(d*x + c))*sinh(d*x + c)^7 + 2*(105*(a^7 + 6*a^6*b + 15*a^5*b^2 + 20*a^4*b^3 + 15*a^3*b^4 + 6*a^2*b^5 + a*b^6)*d*cosh(d*x + c)^4 + 56*(a^7 + 4*a^6*b + 5*a^5*b^2 - 5*a^3*b^4 - 4*a^2*b^5 - a*b^6)*d*cosh(d*x + c)^2 + (3*a^7 + 10*a^6*b + 13*a^5*b^2 + 12*a^4*b^3 + 13*a^3*b^4 + 10*a^2*b^5 + 3*a*b^6)*d)*sinh(d*x + c)^6 + 4*(a^7 + 4*a^6*b + 5*a^5*b^2 - 5*a^3*b^4 - 4*a^2*b^5 - a*b^6)*d*cosh(d*x + c)^4 + 4*(63*(a^7 + 6*a^6*b + 15*a^5*b^2 + 20*a^4*b^3 + 15*a^3*b^4 + 6*a^2*b^5 + a*b^6)*d*cosh(d*x + c)^5 + 56*(a^7 + 4*a^6*b + 5*a^5*b^2 - 5*a^3*b^4 - 4*a^2*b^5 - a*b^6)*d*cosh(d*x + c)^3 + 3*(3*a^7 + 10*a^6*b + 13*a^5*b^2 + 12*a^4*b^3 + 13*a^3*b^4 + 10*a^2*b^5 + 3*a*b^6)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(105*(a^7 + 6*a^6*b + 15*a^5*b^2 + 20*a^4*b^3 + 15*a^3*b^4 + 6*a^2*b^5 + a*b^6)*d*cosh(d*x + c)^6 + 140*(a^7 + 4*a^6*b + 5*a^5*b^2 - 5*a^3*b^4 - 4*a^2*b^5 - a*b^6)*d*cosh(d*x + c)^4 + 15*(3*a^7 + 10*a^6*b + 13*a^5*b^2 + 12*a^4*b^3 + 13*a^3*b^4 + 10*a^2*b^5 + 3*a*b^6)*d*cosh(d*x + c)^2 + 2*(a^7 + 4*a^6*b + 5*a^5*b^2 - 5*a^3*b^4 - 4*a^2*b^5 - a*b^6)*d)*sinh(d*x + c)^4 + (a^7 + 6*a^6*b + 15*a^5*b^2 + 20*a^4*b^3 + 15*a^3*b^4 + 6*a^2*b^5 + a*b^6)*d*cosh(d*x + c)^2 + 8*(15*(a^7 + 6*a^6*b + 15*a^5*b^2 + 20*a^4*b^3 + 15*a^3*b^4 + 6*a^2*b^5 + a*b^6)*d*cosh(d*x + c)^7 + 28*(a^7 + 4*a^6*b + 5*a^5*b^2 - 5*a^3*b^4 - 4*a^2*b^5 - a*b^6)*d*cosh(d*x + c)^5 + 5*(3*a^7 + 10*a^6*b + 13*a^5*b^2 + 12*a^4*b^3 + 13*a^3*b^4 + 10*a^2*b^5 + 3*a*b^6)*d*cosh(d*x + c)^3 + 2*(a^7 + 4*a^6*b + 5*a^5*b^2 - 5*a^3*b^4 - 4*a^2*b^5 - a*b^6)*d*cosh(d*x + c))*sinh(d*x + c)^3 + (45*(a^7 + 6*a^6*b + 15*a^5*b^2 + 20*a^4*b^3 + 15*a^3*b^4 + 6*a^2*b^5 + a*b^6)*d*cosh(d*x + c)^8 + 112*(a^7 + 4*a^6*b + 5*a^5*b^2 - 5*a^3*b^4 - 4*a^2*b^5 - a*b^6)*d*cosh(d*x + c)^6 + 30*(3*a^7 + 10*a^6*b + 13*a^5*b^2 + 12*a^4*b^3 + 13*a^3*b^4 + 10*a^2*b^5 + 3*a*b^6)*d*cosh(d*x + c)^4 + 24*(a^7 + 4*a^6*b + 5*a^5*b^2 - 5*a^3*b^4 - 4*a^2*b^5 - a*b^6)*d*cosh(d*x + c)^2 + (a^7 + 6*a^6*b + 15*a^5*b^2 + 20*a^4*b^3 + 15*a^3*b^4 + 6*a^2*b^5 + a*b^6)*d)*sinh(d*x + c)^2 + 2*(5*(a^7 + 6*a^6*b + 15*a^5*b^2 + 20*a^4*b^3 + 15*a^3*b^4 + 6*a^2*b^5 + a*b^6)*d*cosh(d*x + c)^9 + 16*(a^7 + 4*a^6*b + 5*a^5*b^2 - 5*a^3*b^4 - 4*a^2*b^5 - a*b^6)*d*cosh(d*x + c)^7 + 6*(3*a^7 + 10*a^6*b + 13*a^5*b^2 + 12*a^4*b^3 + 13*a^3*b^4 + 10*a^2*b^5 + 3*a*b^6)*d*cosh(d*x + c)^5 + 8*(a^7 + 4*a^6*b + 5*a^5*b^2 - 5*a^3*b^4 - 4*a^2*b^5 - a*b^6)*d*cosh(d*x + c)^3 + (a^7 + 6*a^6*b + 15*a^5*b^2 + 20*a^4*b^3 + 15*a^3*b^4 + 6*a^2*b^5 + a*b^6)*d*cosh(d*x + c))*sinh(d*x + c)), 1/8*((a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(d*x + c)^12 + 12*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(d*x + c)*sinh(d*x + c)^11 + (a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*sinh(d*x + c)^12 + 4*(a^4 + a^3*b - a^2*b^2 - a*b^3 - (a^4 - 3*a^3*b - 9*a^2*b^2 - 5*a*b^3)*d*x)*cosh(d*x + c)^10 + 2*(2*a^4 + 2*a^3*b - 2*a^2*b^2 - 2*a*b^3 - 2*(a^4 - 3*a^3*b - 9*a^2*b^2 - 5*a*b^3)*d*x + 33*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^10 + 20*(11*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(d*x + c)^3 + 2*(a^4 + a^3*b - a^2*b^2 - a*b^3 - (a^4 - 3*a^3*b - 9*a^2*b^2 - 5*a*b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c)^9 + (5*a^4 + 17*a^3*b - 11*a^2*b^2 - 21*a*b^3 + 2*b^4 - 16*(a^4 - 5*a^3*b - a^2*b^2 + 5*a*b^3)*d*x)*cosh(d*x + c)^8 + (495*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(d*x + c)^4 + 5*a^4 + 17*a^3*b - 11*a^2*b^2 - 21*a*b^3 + 2*b^4 - 16*(a^4 - 5*a^3*b - a^2*b^2 + 5*a*b^3)*d*x + 180*(a^4 + a^3*b - a^2*b^2 - a*b^3 - (a^4 - 3*a^3*b - 9*a^2*b^2 - 5*a*b^3)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 8*(99*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(d*x + c)^5 + 60*(a^4 + a^3*b - a^2*b^2 - a*b^3 - (a^4 - 3*a^3*b - 9*a^2*b^2 - 5*a*b^3)*d*x)*cosh(d*x + c)^3 + (5*a^4 + 17*a^3*b - 11*a^2*b^2 - 21*a*b^3 + 2*b^4 - 16*(a^4 - 5*a^3*b - a^2*b^2 + 5*a*b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c)^7 + 2*(27*a^3*b - 21*a^2*b^2 + 29*a*b^3 - 3*b^4 - 4*(3*a^4 - 17*a^3*b + 13*a^2*b^2 - 15*a*b^3)*d*x)*cosh(d*x + c)^6 + 2*(462*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(d*x + c)^6 + 420*(a^4 + a^3*b - a^2*b^2 - a*b^3 - (a^4 - 3*a^3*b - 9*a^2*b^2 - 5*a*b^3)*d*x)*cosh(d*x + c)^4 + 27*a^3*b - 21*a^2*b^2 + 29*a*b^3 - 3*b^4 - 4*(3*a^4 - 17*a^3*b + 13*a^2*b^2 - 15*a*b^3)*d*x + 14*(5*a^4 + 17*a^3*b - 11*a^2*b^2 - 21*a*b^3 + 2*b^4 - 16*(a^4 - 5*a^3*b - a^2*b^2 + 5*a*b^3)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 4*(198*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(d*x + c)^7 + 252*(a^4 + a^3*b - a^2*b^2 - a*b^3 - (a^4 - 3*a^3*b - 9*a^2*b^2 - 5*a*b^3)*d*x)*cosh(d*x + c)^5 + 14*(5*a^4 + 17*a^3*b - 11*a^2*b^2 - 21*a*b^3 + 2*b^4 - 16*(a^4 - 5*a^3*b - a^2*b^2 + 5*a*b^3)*d*x)*cosh(d*x + c)^3 + 3*(27*a^3*b - 21*a^2*b^2 + 29*a*b^3 - 3*b^4 - 4*(3*a^4 - 17*a^3*b + 13*a^2*b^2 - 15*a*b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c)^5 - (5*a^4 - 55*a^3*b - 3*a^2*b^2 + 51*a*b^3 - 6*b^4 + 16*(a^4 - 5*a^3*b - a^2*b^2 + 5*a*b^3)*d*x)*cosh(d*x + c)^4 + (495*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(d*x + c)^8 + 840*(a^4 + a^3*b - a^2*b^2 - a*b^3 - (a^4 - 3*a^3*b - 9*a^2*b^2 - 5*a*b^3)*d*x)*cosh(d*x + c)^6 + 70*(5*a^4 + 17*a^3*b - 11*a^2*b^2 - 21*a*b^3 + 2*b^4 - 16*(a^4 - 5*a^3*b - a^2*b^2 + 5*a*b^3)*d*x)*cosh(d*x + c)^4 - 5*a^4 + 55*a^3*b + 3*a^2*b^2 - 51*a*b^3 + 6*b^4 - 16*(a^4 - 5*a^3*b - a^2*b^2 + 5*a*b^3)*d*x + 30*(27*a^3*b - 21*a^2*b^2 + 29*a*b^3 - 3*b^4 - 4*(3*a^4 - 17*a^3*b + 13*a^2*b^2 - 15*a*b^3)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^4 - a^4 - 3*a^3*b - 3*a^2*b^2 - a*b^3 + 4*(55*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(d*x + c)^9 + 120*(a^4 + a^3*b - a^2*b^2 - a*b^3 - (a^4 - 3*a^3*b - 9*a^2*b^2 - 5*a*b^3)*d*x)*cosh(d*x + c)^7 + 14*(5*a^4 + 17*a^3*b - 11*a^2*b^2 - 21*a*b^3 + 2*b^4 - 16*(a^4 - 5*a^3*b - a^2*b^2 + 5*a*b^3)*d*x)*cosh(d*x + c)^5 + 10*(27*a^3*b - 21*a^2*b^2 + 29*a*b^3 - 3*b^4 - 4*(3*a^4 - 17*a^3*b + 13*a^2*b^2 - 15*a*b^3)*d*x)*cosh(d*x + c)^3 - (5*a^4 - 55*a^3*b - 3*a^2*b^2 + 51*a*b^3 - 6*b^4 + 16*(a^4 - 5*a^3*b - a^2*b^2 + 5*a*b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c)^3 - 2*(2*a^4 - 7*a^3*b - 19*a^2*b^2 - 9*a*b^3 + b^4 + 2*(a^4 - 3*a^3*b - 9*a^2*b^2 - 5*a*b^3)*d*x)*cosh(d*x + c)^2 + 2*(33*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(d*x + c)^10 + 90*(a^4 + a^3*b - a^2*b^2 - a*b^3 - (a^4 - 3*a^3*b - 9*a^2*b^2 - 5*a*b^3)*d*x)*cosh(d*x + c)^8 + 14*(5*a^4 + 17*a^3*b - 11*a^2*b^2 - 21*a*b^3 + 2*b^4 - 16*(a^4 - 5*a^3*b - a^2*b^2 + 5*a*b^3)*d*x)*cosh(d*x + c)^6 + 15*(27*a^3*b - 21*a^2*b^2 + 29*a*b^3 - 3*b^4 - 4*(3*a^4 - 17*a^3*b + 13*a^2*b^2 - 15*a*b^3)*d*x)*cosh(d*x + c)^4 - 2*a^4 + 7*a^3*b + 19*a^2*b^2 + 9*a*b^3 - b^4 - 2*(a^4 - 3*a^3*b - 9*a^2*b^2 - 5*a*b^3)*d*x - 3*(5*a^4 - 55*a^3*b - 3*a^2*b^2 + 51*a*b^3 - 6*b^4 + 16*(a^4 - 5*a^3*b - a^2*b^2 + 5*a*b^3)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - ((15*a^4 + 20*a^3*b - 6*a^2*b^2 - 12*a*b^3 - b^4)*cosh(d*x + c)^10 + 10*(15*a^4 + 20*a^3*b - 6*a^2*b^2 - 12*a*b^3 - b^4)*cosh(d*x + c)*sinh(d*x + c)^9 + (15*a^4 + 20*a^3*b - 6*a^2*b^2 - 12*a*b^3 - b^4)*sinh(d*x + c)^10 + 4*(15*a^4 - 10*a^3*b - 16*a^2*b^2 + 10*a*b^3 + b^4)*cosh(d*x + c)^8 + (60*a^4 - 40*a^3*b - 64*a^2*b^2 + 40*a*b^3 + 4*b^4 + 45*(15*a^4 + 20*a^3*b - 6*a^2*b^2 - 12*a*b^3 - b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 8*(15*(15*a^4 + 20*a^3*b - 6*a^2*b^2 - 12*a*b^3 - b^4)*cosh(d*x + c)^3 + 4*(15*a^4 - 10*a^3*b - 16*a^2*b^2 + 10*a*b^3 + b^4)*cosh(d*x + c))*sinh(d*x + c)^7 + 2*(45*a^4 - 60*a^3*b + 62*a^2*b^2 - 28*a*b^3 - 3*b^4)*cosh(d*x + c)^6 + 2*(105*(15*a^4 + 20*a^3*b - 6*a^2*b^2 - 12*a*b^3 - b^4)*cosh(d*x + c)^4 + 45*a^4 - 60*a^3*b + 62*a^2*b^2 - 28*a*b^3 - 3*b^4 + 56*(15*a^4 - 10*a^3*b - 16*a^2*b^2 + 10*a*b^3 + b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 4*(63*(15*a^4 + 20*a^3*b - 6*a^2*b^2 - 12*a*b^3 - b^4)*cosh(d*x + c)^5 + 56*(15*a^4 - 10*a^3*b - 16*a^2*b^2 + 10*a*b^3 + b^4)*cosh(d*x + c)^3 + 3*(45*a^4 - 60*a^3*b + 62*a^2*b^2 - 28*a*b^3 - 3*b^4)*cosh(d*x + c))*sinh(d*x + c)^5 + 4*(15*a^4 - 10*a^3*b - 16*a^2*b^2 + 10*a*b^3 + b^4)*cosh(d*x + c)^4 + 2*(105*(15*a^4 + 20*a^3*b - 6*a^2*b^2 - 12*a*b^3 - b^4)*cosh(d*x + c)^6 + 140*(15*a^4 - 10*a^3*b - 16*a^2*b^2 + 10*a*b^3 + b^4)*cosh(d*x + c)^4 + 30*a^4 - 20*a^3*b - 32*a^2*b^2 + 20*a*b^3 + 2*b^4 + 15*(45*a^4 - 60*a^3*b + 62*a^2*b^2 - 28*a*b^3 - 3*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(15*(15*a^4 + 20*a^3*b - 6*a^2*b^2 - 12*a*b^3 - b^4)*cosh(d*x + c)^7 + 28*(15*a^4 - 10*a^3*b - 16*a^2*b^2 + 10*a*b^3 + b^4)*cosh(d*x + c)^5 + 5*(45*a^4 - 60*a^3*b + 62*a^2*b^2 - 28*a*b^3 - 3*b^4)*cosh(d*x + c)^3 + 2*(15*a^4 - 10*a^3*b - 16*a^2*b^2 + 10*a*b^3 + b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + (15*a^4 + 20*a^3*b - 6*a^2*b^2 - 12*a*b^3 - b^4)*cosh(d*x + c)^2 + (45*(15*a^4 + 20*a^3*b - 6*a^2*b^2 - 12*a*b^3 - b^4)*cosh(d*x + c)^8 + 112*(15*a^4 - 10*a^3*b - 16*a^2*b^2 + 10*a*b^3 + b^4)*cosh(d*x + c)^6 + 30*(45*a^4 - 60*a^3*b + 62*a^2*b^2 - 28*a*b^3 - 3*b^4)*cosh(d*x + c)^4 + 15*a^4 + 20*a^3*b - 6*a^2*b^2 - 12*a*b^3 - b^4 + 24*(15*a^4 - 10*a^3*b - 16*a^2*b^2 + 10*a*b^3 + b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 2*(5*(15*a^4 + 20*a^3*b - 6*a^2*b^2 - 12*a*b^3 - b^4)*cosh(d*x + c)^9 + 16*(15*a^4 - 10*a^3*b - 16*a^2*b^2 + 10*a*b^3 + b^4)*cosh(d*x + c)^7 + 6*(45*a^4 - 60*a^3*b + 62*a^2*b^2 - 28*a*b^3 - 3*b^4)*cosh(d*x + c)^5 + 8*(15*a^4 - 10*a^3*b - 16*a^2*b^2 + 10*a*b^3 + b^4)*cosh(d*x + c)^3 + (15*a^4 + 20*a^3*b - 6*a^2*b^2 - 12*a*b^3 - b^4)*cosh(d*x + c))*sinh(d*x + c))*sqrt(b/a)*arctan(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 + a - b)*sqrt(b/a)/b) + 4*(3*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(d*x + c)^11 + 10*(a^4 + a^3*b - a^2*b^2 - a*b^3 - (a^4 - 3*a^3*b - 9*a^2*b^2 - 5*a*b^3)*d*x)*cosh(d*x + c)^9 + 2*(5*a^4 + 17*a^3*b - 11*a^2*b^2 - 21*a*b^3 + 2*b^4 - 16*(a^4 - 5*a^3*b - a^2*b^2 + 5*a*b^3)*d*x)*cosh(d*x + c)^7 + 3*(27*a^3*b - 21*a^2*b^2 + 29*a*b^3 - 3*b^4 - 4*(3*a^4 - 17*a^3*b + 13*a^2*b^2 - 15*a*b^3)*d*x)*cosh(d*x + c)^5 - (5*a^4 - 55*a^3*b - 3*a^2*b^2 + 51*a*b^3 - 6*b^4 + 16*(a^4 - 5*a^3*b - a^2*b^2 + 5*a*b^3)*d*x)*cosh(d*x + c)^3 - (2*a^4 - 7*a^3*b - 19*a^2*b^2 - 9*a*b^3 + b^4 + 2*(a^4 - 3*a^3*b - 9*a^2*b^2 - 5*a*b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c))/((a^7 + 6*a^6*b + 15*a^5*b^2 + 20*a^4*b^3 + 15*a^3*b^4 + 6*a^2*b^5 + a*b^6)*d*cosh(d*x + c)^10 + 10*(a^7 + 6*a^6*b + 15*a^5*b^2 + 20*a^4*b^3 + 15*a^3*b^4 + 6*a^2*b^5 + a*b^6)*d*cosh(d*x + c)*sinh(d*x + c)^9 + (a^7 + 6*a^6*b + 15*a^5*b^2 + 20*a^4*b^3 + 15*a^3*b^4 + 6*a^2*b^5 + a*b^6)*d*sinh(d*x + c)^10 + 4*(a^7 + 4*a^6*b + 5*a^5*b^2 - 5*a^3*b^4 - 4*a^2*b^5 - a*b^6)*d*cosh(d*x + c)^8 + (45*(a^7 + 6*a^6*b + 15*a^5*b^2 + 20*a^4*b^3 + 15*a^3*b^4 + 6*a^2*b^5 + a*b^6)*d*cosh(d*x + c)^2 + 4*(a^7 + 4*a^6*b + 5*a^5*b^2 - 5*a^3*b^4 - 4*a^2*b^5 - a*b^6)*d)*sinh(d*x + c)^8 + 2*(3*a^7 + 10*a^6*b + 13*a^5*b^2 + 12*a^4*b^3 + 13*a^3*b^4 + 10*a^2*b^5 + 3*a*b^6)*d*cosh(d*x + c)^6 + 8*(15*(a^7 + 6*a^6*b + 15*a^5*b^2 + 20*a^4*b^3 + 15*a^3*b^4 + 6*a^2*b^5 + a*b^6)*d*cosh(d*x + c)^3 + 4*(a^7 + 4*a^6*b + 5*a^5*b^2 - 5*a^3*b^4 - 4*a^2*b^5 - a*b^6)*d*cosh(d*x + c))*sinh(d*x + c)^7 + 2*(105*(a^7 + 6*a^6*b + 15*a^5*b^2 + 20*a^4*b^3 + 15*a^3*b^4 + 6*a^2*b^5 + a*b^6)*d*cosh(d*x + c)^4 + 56*(a^7 + 4*a^6*b + 5*a^5*b^2 - 5*a^3*b^4 - 4*a^2*b^5 - a*b^6)*d*cosh(d*x + c)^2 + (3*a^7 + 10*a^6*b + 13*a^5*b^2 + 12*a^4*b^3 + 13*a^3*b^4 + 10*a^2*b^5 + 3*a*b^6)*d)*sinh(d*x + c)^6 + 4*(a^7 + 4*a^6*b + 5*a^5*b^2 - 5*a^3*b^4 - 4*a^2*b^5 - a*b^6)*d*cosh(d*x + c)^4 + 4*(63*(a^7 + 6*a^6*b + 15*a^5*b^2 + 20*a^4*b^3 + 15*a^3*b^4 + 6*a^2*b^5 + a*b^6)*d*cosh(d*x + c)^5 + 56*(a^7 + 4*a^6*b + 5*a^5*b^2 - 5*a^3*b^4 - 4*a^2*b^5 - a*b^6)*d*cosh(d*x + c)^3 + 3*(3*a^7 + 10*a^6*b + 13*a^5*b^2 + 12*a^4*b^3 + 13*a^3*b^4 + 10*a^2*b^5 + 3*a*b^6)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(105*(a^7 + 6*a^6*b + 15*a^5*b^2 + 20*a^4*b^3 + 15*a^3*b^4 + 6*a^2*b^5 + a*b^6)*d*cosh(d*x + c)^6 + 140*(a^7 + 4*a^6*b + 5*a^5*b^2 - 5*a^3*b^4 - 4*a^2*b^5 - a*b^6)*d*cosh(d*x + c)^4 + 15*(3*a^7 + 10*a^6*b + 13*a^5*b^2 + 12*a^4*b^3 + 13*a^3*b^4 + 10*a^2*b^5 + 3*a*b^6)*d*cosh(d*x + c)^2 + 2*(a^7 + 4*a^6*b + 5*a^5*b^2 - 5*a^3*b^4 - 4*a^2*b^5 - a*b^6)*d)*sinh(d*x + c)^4 + (a^7 + 6*a^6*b + 15*a^5*b^2 + 20*a^4*b^3 + 15*a^3*b^4 + 6*a^2*b^5 + a*b^6)*d*cosh(d*x + c)^2 + 8*(15*(a^7 + 6*a^6*b + 15*a^5*b^2 + 20*a^4*b^3 + 15*a^3*b^4 + 6*a^2*b^5 + a*b^6)*d*cosh(d*x + c)^7 + 28*(a^7 + 4*a^6*b + 5*a^5*b^2 - 5*a^3*b^4 - 4*a^2*b^5 - a*b^6)*d*cosh(d*x + c)^5 + 5*(3*a^7 + 10*a^6*b + 13*a^5*b^2 + 12*a^4*b^3 + 13*a^3*b^4 + 10*a^2*b^5 + 3*a*b^6)*d*cosh(d*x + c)^3 + 2*(a^7 + 4*a^6*b + 5*a^5*b^2 - 5*a^3*b^4 - 4*a^2*b^5 - a*b^6)*d*cosh(d*x + c))*sinh(d*x + c)^3 + (45*(a^7 + 6*a^6*b + 15*a^5*b^2 + 20*a^4*b^3 + 15*a^3*b^4 + 6*a^2*b^5 + a*b^6)*d*cosh(d*x + c)^8 + 112*(a^7 + 4*a^6*b + 5*a^5*b^2 - 5*a^3*b^4 - 4*a^2*b^5 - a*b^6)*d*cosh(d*x + c)^6 + 30*(3*a^7 + 10*a^6*b + 13*a^5*b^2 + 12*a^4*b^3 + 13*a^3*b^4 + 10*a^2*b^5 + 3*a*b^6)*d*cosh(d*x + c)^4 + 24*(a^7 + 4*a^6*b + 5*a^5*b^2 - 5*a^3*b^4 - 4*a^2*b^5 - a*b^6)*d*cosh(d*x + c)^2 + (a^7 + 6*a^6*b + 15*a^5*b^2 + 20*a^4*b^3 + 15*a^3*b^4 + 6*a^2*b^5 + a*b^6)*d)*sinh(d*x + c)^2 + 2*(5*(a^7 + 6*a^6*b + 15*a^5*b^2 + 20*a^4*b^3 + 15*a^3*b^4 + 6*a^2*b^5 + a*b^6)*d*cosh(d*x + c)^9 + 16*(a^7 + 4*a^6*b + 5*a^5*b^2 - 5*a^3*b^4 - 4*a^2*b^5 - a*b^6)*d*cosh(d*x + c)^7 + 6*(3*a^7 + 10*a^6*b + 13*a^5*b^2 + 12*a^4*b^3 + 13*a^3*b^4 + 10*a^2*b^5 + 3*a*b^6)*d*cosh(d*x + c)^5 + 8*(a^7 + 4*a^6*b + 5*a^5*b^2 - 5*a^3*b^4 - 4*a^2*b^5 - a*b^6)*d*cosh(d*x + c)^3 + (a^7 + 6*a^6*b + 15*a^5*b^2 + 20*a^4*b^3 + 15*a^3*b^4 + 6*a^2*b^5 + a*b^6)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
44,1,7119,0,1.381018," ","integrate(sinh(d*x+c)/(a+b*tanh(d*x+c)^2)^3,x, algorithm=""fricas"")","\left[\frac{8 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{10} + 80 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + 8 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{10} + 20 \, {\left(2 \, a^{2} - a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{8} + 20 \, {\left(18 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, a^{2} - a b - 3 \, b^{2}\right)} \sinh\left(d x + c\right)^{8} + 160 \, {\left(6 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{2} - a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 20 \, {\left(4 \, a^{2} - 7 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{6} + 20 \, {\left(84 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + 28 \, {\left(2 \, a^{2} - a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, a^{2} - 7 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(252 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{5} + 140 \, {\left(2 \, a^{2} - a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 15 \, {\left(4 \, a^{2} - 7 \, a b + b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 20 \, {\left(4 \, a^{2} - 7 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + 20 \, {\left(84 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{6} + 70 \, {\left(2 \, a^{2} - a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 15 \, {\left(4 \, a^{2} - 7 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, a^{2} - 7 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{4} + 80 \, {\left(12 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{7} + 14 \, {\left(2 \, a^{2} - a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(4 \, a^{2} - 7 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(4 \, a^{2} - 7 \, a b + b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 20 \, {\left(2 \, a^{2} - a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 20 \, {\left(18 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{8} + 28 \, {\left(2 \, a^{2} - a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(4 \, a^{2} - 7 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + 6 \, {\left(4 \, a^{2} - 7 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, a^{2} - a b - 3 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} + 15 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{9} + 9 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{8} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{9} + 4 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{7} + 4 \, {\left(9 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{7} + 28 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(63 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + 42 \, {\left(a^{2} - 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)^{5} + 2 \, {\left(63 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{5} + 70 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{3} + 5 \, {\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(21 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{6} + 35 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{4} + 5 \, {\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(9 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{7} + 21 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right) + {\left(9 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{8} + 28 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{6} + 10 \, {\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 12 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{b}{a + b}} \log\left(\frac{{\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 + 3 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} + a + 3 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a + 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) - 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}} + a + b}{{\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) + 8 \, a^{2} + 16 \, a b + 8 \, b^{2} + 40 \, {\left(2 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{9} + 4 \, {\left(2 \, a^{2} - a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(4 \, a^{2} - 7 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(4 \, a^{2} - 7 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{2} - a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{16 \, {\left({\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right)^{9} + 9 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{8} + {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d \sinh\left(d x + c\right)^{9} + 4 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} d \cosh\left(d x + c\right)^{7} + 4 \, {\left(9 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(3 \, a^{5} + 7 \, a^{4} b + 6 \, a^{3} b^{2} + 6 \, a^{2} b^{3} + 7 \, a b^{4} + 3 \, b^{5}\right)} d \cosh\left(d x + c\right)^{5} + 28 \, {\left(3 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(63 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 42 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{5} + 7 \, a^{4} b + 6 \, a^{3} b^{2} + 6 \, a^{2} b^{3} + 7 \, a b^{4} + 3 \, b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{5} + 4 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} d \cosh\left(d x + c\right)^{3} + 2 \, {\left(63 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right)^{5} + 70 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} d \cosh\left(d x + c\right)^{3} + 5 \, {\left(3 \, a^{5} + 7 \, a^{4} b + 6 \, a^{3} b^{2} + 6 \, a^{2} b^{3} + 7 \, a b^{4} + 3 \, b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(21 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right)^{6} + 35 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 5 \, {\left(3 \, a^{5} + 7 \, a^{4} b + 6 \, a^{3} b^{2} + 6 \, a^{2} b^{3} + 7 \, a b^{4} + 3 \, b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{3} + {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right) + 4 \, {\left(9 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right)^{7} + 21 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} d \cosh\left(d x + c\right)^{5} + 5 \, {\left(3 \, a^{5} + 7 \, a^{4} b + 6 \, a^{3} b^{2} + 6 \, a^{2} b^{3} + 7 \, a b^{4} + 3 \, b^{5}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(9 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right)^{8} + 28 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} d \cosh\left(d x + c\right)^{6} + 10 \, {\left(3 \, a^{5} + 7 \, a^{4} b + 6 \, a^{3} b^{2} + 6 \, a^{2} b^{3} + 7 \, a b^{4} + 3 \, b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 12 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d\right)} \sinh\left(d x + c\right)\right)}}, \frac{4 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{10} + 40 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + 4 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{10} + 10 \, {\left(2 \, a^{2} - a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{8} + 10 \, {\left(18 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, a^{2} - a b - 3 \, b^{2}\right)} \sinh\left(d x + c\right)^{8} + 80 \, {\left(6 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{2} - a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 10 \, {\left(4 \, a^{2} - 7 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{6} + 10 \, {\left(84 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + 28 \, {\left(2 \, a^{2} - a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, a^{2} - 7 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(252 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{5} + 140 \, {\left(2 \, a^{2} - a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 15 \, {\left(4 \, a^{2} - 7 \, a b + b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 10 \, {\left(4 \, a^{2} - 7 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + 10 \, {\left(84 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{6} + 70 \, {\left(2 \, a^{2} - a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 15 \, {\left(4 \, a^{2} - 7 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, a^{2} - 7 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{4} + 40 \, {\left(12 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{7} + 14 \, {\left(2 \, a^{2} - a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(4 \, a^{2} - 7 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(4 \, a^{2} - 7 \, a b + b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 10 \, {\left(2 \, a^{2} - a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 10 \, {\left(18 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{8} + 28 \, {\left(2 \, a^{2} - a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(4 \, a^{2} - 7 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + 6 \, {\left(4 \, a^{2} - 7 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, a^{2} - a b - 3 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} - 15 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{9} + 9 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{8} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{9} + 4 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{7} + 4 \, {\left(9 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{7} + 28 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(63 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + 42 \, {\left(a^{2} - 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)^{5} + 2 \, {\left(63 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{5} + 70 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{3} + 5 \, {\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(21 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{6} + 35 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{4} + 5 \, {\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(9 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{7} + 21 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right) + {\left(9 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{8} + 28 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{6} + 10 \, {\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 12 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{b}{a + b}} \arctan\left(\frac{{\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 - 3 \, b\right)} \cosh\left(d x + c\right) + {\left(3 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} + a - 3 \, b\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{b}{a + b}}}{2 \, b}\right) + 15 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{9} + 9 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{8} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{9} + 4 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{7} + 4 \, {\left(9 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{7} + 28 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(63 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + 42 \, {\left(a^{2} - 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)^{5} + 2 \, {\left(63 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{5} + 70 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{3} + 5 \, {\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(21 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{6} + 35 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{4} + 5 \, {\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(9 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{7} + 21 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right) + {\left(9 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{8} + 28 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{6} + 10 \, {\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 12 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{b}{a + b}} \arctan\left(\frac{{\left({\left(a + b\right)} \cosh\left(d x + c\right) + {\left(a + b\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{b}{a + b}}}{2 \, b}\right) + 4 \, a^{2} + 8 \, a b + 4 \, b^{2} + 20 \, {\left(2 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{9} + 4 \, {\left(2 \, a^{2} - a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(4 \, a^{2} - 7 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(4 \, a^{2} - 7 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{2} - a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{8 \, {\left({\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right)^{9} + 9 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{8} + {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d \sinh\left(d x + c\right)^{9} + 4 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} d \cosh\left(d x + c\right)^{7} + 4 \, {\left(9 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(3 \, a^{5} + 7 \, a^{4} b + 6 \, a^{3} b^{2} + 6 \, a^{2} b^{3} + 7 \, a b^{4} + 3 \, b^{5}\right)} d \cosh\left(d x + c\right)^{5} + 28 \, {\left(3 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(63 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 42 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{5} + 7 \, a^{4} b + 6 \, a^{3} b^{2} + 6 \, a^{2} b^{3} + 7 \, a b^{4} + 3 \, b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{5} + 4 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} d \cosh\left(d x + c\right)^{3} + 2 \, {\left(63 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right)^{5} + 70 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} d \cosh\left(d x + c\right)^{3} + 5 \, {\left(3 \, a^{5} + 7 \, a^{4} b + 6 \, a^{3} b^{2} + 6 \, a^{2} b^{3} + 7 \, a b^{4} + 3 \, b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(21 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right)^{6} + 35 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 5 \, {\left(3 \, a^{5} + 7 \, a^{4} b + 6 \, a^{3} b^{2} + 6 \, a^{2} b^{3} + 7 \, a b^{4} + 3 \, b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{3} + {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right) + 4 \, {\left(9 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right)^{7} + 21 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} d \cosh\left(d x + c\right)^{5} + 5 \, {\left(3 \, a^{5} + 7 \, a^{4} b + 6 \, a^{3} b^{2} + 6 \, a^{2} b^{3} + 7 \, a b^{4} + 3 \, b^{5}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(9 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right)^{8} + 28 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} d \cosh\left(d x + c\right)^{6} + 10 \, {\left(3 \, a^{5} + 7 \, a^{4} b + 6 \, a^{3} b^{2} + 6 \, a^{2} b^{3} + 7 \, a b^{4} + 3 \, b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 12 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d\right)} \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[1/16*(8*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^10 + 80*(a^2 + 2*a*b + b^2)*cosh(d*x + c)*sinh(d*x + c)^9 + 8*(a^2 + 2*a*b + b^2)*sinh(d*x + c)^10 + 20*(2*a^2 - a*b - 3*b^2)*cosh(d*x + c)^8 + 20*(18*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + 2*a^2 - a*b - 3*b^2)*sinh(d*x + c)^8 + 160*(6*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 + (2*a^2 - a*b - 3*b^2)*cosh(d*x + c))*sinh(d*x + c)^7 + 20*(4*a^2 - 7*a*b + b^2)*cosh(d*x + c)^6 + 20*(84*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 + 28*(2*a^2 - a*b - 3*b^2)*cosh(d*x + c)^2 + 4*a^2 - 7*a*b + b^2)*sinh(d*x + c)^6 + 8*(252*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^5 + 140*(2*a^2 - a*b - 3*b^2)*cosh(d*x + c)^3 + 15*(4*a^2 - 7*a*b + b^2)*cosh(d*x + c))*sinh(d*x + c)^5 + 20*(4*a^2 - 7*a*b + b^2)*cosh(d*x + c)^4 + 20*(84*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^6 + 70*(2*a^2 - a*b - 3*b^2)*cosh(d*x + c)^4 + 15*(4*a^2 - 7*a*b + b^2)*cosh(d*x + c)^2 + 4*a^2 - 7*a*b + b^2)*sinh(d*x + c)^4 + 80*(12*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^7 + 14*(2*a^2 - a*b - 3*b^2)*cosh(d*x + c)^5 + 5*(4*a^2 - 7*a*b + b^2)*cosh(d*x + c)^3 + (4*a^2 - 7*a*b + b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 20*(2*a^2 - a*b - 3*b^2)*cosh(d*x + c)^2 + 20*(18*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^8 + 28*(2*a^2 - a*b - 3*b^2)*cosh(d*x + c)^6 + 15*(4*a^2 - 7*a*b + b^2)*cosh(d*x + c)^4 + 6*(4*a^2 - 7*a*b + b^2)*cosh(d*x + c)^2 + 2*a^2 - a*b - 3*b^2)*sinh(d*x + c)^2 + 15*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^9 + 9*(a^2 + 2*a*b + b^2)*cosh(d*x + c)*sinh(d*x + c)^8 + (a^2 + 2*a*b + b^2)*sinh(d*x + c)^9 + 4*(a^2 - b^2)*cosh(d*x + c)^7 + 4*(9*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + a^2 - b^2)*sinh(d*x + c)^7 + 28*(3*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 + (a^2 - b^2)*cosh(d*x + c))*sinh(d*x + c)^6 + 2*(3*a^2 - 2*a*b + 3*b^2)*cosh(d*x + c)^5 + 2*(63*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 + 42*(a^2 - b^2)*cosh(d*x + c)^2 + 3*a^2 - 2*a*b + 3*b^2)*sinh(d*x + c)^5 + 2*(63*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^5 + 70*(a^2 - b^2)*cosh(d*x + c)^3 + 5*(3*a^2 - 2*a*b + 3*b^2)*cosh(d*x + c))*sinh(d*x + c)^4 + 4*(a^2 - b^2)*cosh(d*x + c)^3 + 4*(21*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^6 + 35*(a^2 - b^2)*cosh(d*x + c)^4 + 5*(3*a^2 - 2*a*b + 3*b^2)*cosh(d*x + c)^2 + a^2 - b^2)*sinh(d*x + c)^3 + 4*(9*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^7 + 21*(a^2 - b^2)*cosh(d*x + c)^5 + 5*(3*a^2 - 2*a*b + 3*b^2)*cosh(d*x + c)^3 + 3*(a^2 - b^2)*cosh(d*x + c))*sinh(d*x + c)^2 + (a^2 + 2*a*b + b^2)*cosh(d*x + c) + (9*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^8 + 28*(a^2 - b^2)*cosh(d*x + c)^6 + 10*(3*a^2 - 2*a*b + 3*b^2)*cosh(d*x + c)^4 + 12*(a^2 - b^2)*cosh(d*x + c)^2 + a^2 + 2*a*b + b^2)*sinh(d*x + c))*sqrt(b/(a + b))*log(((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 + 3*b)*cosh(d*x + c)^2 + 2*(3*(a + b)*cosh(d*x + c)^2 + a + 3*b)*sinh(d*x + c)^2 + 4*((a + b)*cosh(d*x + c)^3 + (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)) + a + b)/((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)) + 8*a^2 + 16*a*b + 8*b^2 + 40*(2*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^9 + 4*(2*a^2 - a*b - 3*b^2)*cosh(d*x + c)^7 + 3*(4*a^2 - 7*a*b + b^2)*cosh(d*x + c)^5 + 2*(4*a^2 - 7*a*b + b^2)*cosh(d*x + c)^3 + (2*a^2 - a*b - 3*b^2)*cosh(d*x + c))*sinh(d*x + c))/((a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*cosh(d*x + c)^9 + 9*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*cosh(d*x + c)*sinh(d*x + c)^8 + (a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*sinh(d*x + c)^9 + 4*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*d*cosh(d*x + c)^7 + 4*(9*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*cosh(d*x + c)^2 + (a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*d)*sinh(d*x + c)^7 + 2*(3*a^5 + 7*a^4*b + 6*a^3*b^2 + 6*a^2*b^3 + 7*a*b^4 + 3*b^5)*d*cosh(d*x + c)^5 + 28*(3*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*cosh(d*x + c)^3 + (a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*d*cosh(d*x + c))*sinh(d*x + c)^6 + 2*(63*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*cosh(d*x + c)^4 + 42*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*d*cosh(d*x + c)^2 + (3*a^5 + 7*a^4*b + 6*a^3*b^2 + 6*a^2*b^3 + 7*a*b^4 + 3*b^5)*d)*sinh(d*x + c)^5 + 4*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*d*cosh(d*x + c)^3 + 2*(63*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*cosh(d*x + c)^5 + 70*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*d*cosh(d*x + c)^3 + 5*(3*a^5 + 7*a^4*b + 6*a^3*b^2 + 6*a^2*b^3 + 7*a*b^4 + 3*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^4 + 4*(21*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*cosh(d*x + c)^6 + 35*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*d*cosh(d*x + c)^4 + 5*(3*a^5 + 7*a^4*b + 6*a^3*b^2 + 6*a^2*b^3 + 7*a*b^4 + 3*b^5)*d*cosh(d*x + c)^2 + (a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*d)*sinh(d*x + c)^3 + (a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*cosh(d*x + c) + 4*(9*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*cosh(d*x + c)^7 + 21*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*d*cosh(d*x + c)^5 + 5*(3*a^5 + 7*a^4*b + 6*a^3*b^2 + 6*a^2*b^3 + 7*a*b^4 + 3*b^5)*d*cosh(d*x + c)^3 + 3*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*d*cosh(d*x + c))*sinh(d*x + c)^2 + (9*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*cosh(d*x + c)^8 + 28*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*d*cosh(d*x + c)^6 + 10*(3*a^5 + 7*a^4*b + 6*a^3*b^2 + 6*a^2*b^3 + 7*a*b^4 + 3*b^5)*d*cosh(d*x + c)^4 + 12*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*d*cosh(d*x + c)^2 + (a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d)*sinh(d*x + c)), 1/8*(4*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^10 + 40*(a^2 + 2*a*b + b^2)*cosh(d*x + c)*sinh(d*x + c)^9 + 4*(a^2 + 2*a*b + b^2)*sinh(d*x + c)^10 + 10*(2*a^2 - a*b - 3*b^2)*cosh(d*x + c)^8 + 10*(18*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + 2*a^2 - a*b - 3*b^2)*sinh(d*x + c)^8 + 80*(6*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 + (2*a^2 - a*b - 3*b^2)*cosh(d*x + c))*sinh(d*x + c)^7 + 10*(4*a^2 - 7*a*b + b^2)*cosh(d*x + c)^6 + 10*(84*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 + 28*(2*a^2 - a*b - 3*b^2)*cosh(d*x + c)^2 + 4*a^2 - 7*a*b + b^2)*sinh(d*x + c)^6 + 4*(252*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^5 + 140*(2*a^2 - a*b - 3*b^2)*cosh(d*x + c)^3 + 15*(4*a^2 - 7*a*b + b^2)*cosh(d*x + c))*sinh(d*x + c)^5 + 10*(4*a^2 - 7*a*b + b^2)*cosh(d*x + c)^4 + 10*(84*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^6 + 70*(2*a^2 - a*b - 3*b^2)*cosh(d*x + c)^4 + 15*(4*a^2 - 7*a*b + b^2)*cosh(d*x + c)^2 + 4*a^2 - 7*a*b + b^2)*sinh(d*x + c)^4 + 40*(12*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^7 + 14*(2*a^2 - a*b - 3*b^2)*cosh(d*x + c)^5 + 5*(4*a^2 - 7*a*b + b^2)*cosh(d*x + c)^3 + (4*a^2 - 7*a*b + b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 10*(2*a^2 - a*b - 3*b^2)*cosh(d*x + c)^2 + 10*(18*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^8 + 28*(2*a^2 - a*b - 3*b^2)*cosh(d*x + c)^6 + 15*(4*a^2 - 7*a*b + b^2)*cosh(d*x + c)^4 + 6*(4*a^2 - 7*a*b + b^2)*cosh(d*x + c)^2 + 2*a^2 - a*b - 3*b^2)*sinh(d*x + c)^2 - 15*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^9 + 9*(a^2 + 2*a*b + b^2)*cosh(d*x + c)*sinh(d*x + c)^8 + (a^2 + 2*a*b + b^2)*sinh(d*x + c)^9 + 4*(a^2 - b^2)*cosh(d*x + c)^7 + 4*(9*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + a^2 - b^2)*sinh(d*x + c)^7 + 28*(3*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 + (a^2 - b^2)*cosh(d*x + c))*sinh(d*x + c)^6 + 2*(3*a^2 - 2*a*b + 3*b^2)*cosh(d*x + c)^5 + 2*(63*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 + 42*(a^2 - b^2)*cosh(d*x + c)^2 + 3*a^2 - 2*a*b + 3*b^2)*sinh(d*x + c)^5 + 2*(63*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^5 + 70*(a^2 - b^2)*cosh(d*x + c)^3 + 5*(3*a^2 - 2*a*b + 3*b^2)*cosh(d*x + c))*sinh(d*x + c)^4 + 4*(a^2 - b^2)*cosh(d*x + c)^3 + 4*(21*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^6 + 35*(a^2 - b^2)*cosh(d*x + c)^4 + 5*(3*a^2 - 2*a*b + 3*b^2)*cosh(d*x + c)^2 + a^2 - b^2)*sinh(d*x + c)^3 + 4*(9*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^7 + 21*(a^2 - b^2)*cosh(d*x + c)^5 + 5*(3*a^2 - 2*a*b + 3*b^2)*cosh(d*x + c)^3 + 3*(a^2 - b^2)*cosh(d*x + c))*sinh(d*x + c)^2 + (a^2 + 2*a*b + b^2)*cosh(d*x + c) + (9*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^8 + 28*(a^2 - b^2)*cosh(d*x + c)^6 + 10*(3*a^2 - 2*a*b + 3*b^2)*cosh(d*x + c)^4 + 12*(a^2 - b^2)*cosh(d*x + c)^2 + a^2 + 2*a*b + b^2)*sinh(d*x + c))*sqrt(-b/(a + b))*arctan(1/2*((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 - 3*b)*cosh(d*x + c) + (3*(a + b)*cosh(d*x + c)^2 + a - 3*b)*sinh(d*x + c))*sqrt(-b/(a + b))/b) + 15*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^9 + 9*(a^2 + 2*a*b + b^2)*cosh(d*x + c)*sinh(d*x + c)^8 + (a^2 + 2*a*b + b^2)*sinh(d*x + c)^9 + 4*(a^2 - b^2)*cosh(d*x + c)^7 + 4*(9*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + a^2 - b^2)*sinh(d*x + c)^7 + 28*(3*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 + (a^2 - b^2)*cosh(d*x + c))*sinh(d*x + c)^6 + 2*(3*a^2 - 2*a*b + 3*b^2)*cosh(d*x + c)^5 + 2*(63*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 + 42*(a^2 - b^2)*cosh(d*x + c)^2 + 3*a^2 - 2*a*b + 3*b^2)*sinh(d*x + c)^5 + 2*(63*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^5 + 70*(a^2 - b^2)*cosh(d*x + c)^3 + 5*(3*a^2 - 2*a*b + 3*b^2)*cosh(d*x + c))*sinh(d*x + c)^4 + 4*(a^2 - b^2)*cosh(d*x + c)^3 + 4*(21*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^6 + 35*(a^2 - b^2)*cosh(d*x + c)^4 + 5*(3*a^2 - 2*a*b + 3*b^2)*cosh(d*x + c)^2 + a^2 - b^2)*sinh(d*x + c)^3 + 4*(9*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^7 + 21*(a^2 - b^2)*cosh(d*x + c)^5 + 5*(3*a^2 - 2*a*b + 3*b^2)*cosh(d*x + c)^3 + 3*(a^2 - b^2)*cosh(d*x + c))*sinh(d*x + c)^2 + (a^2 + 2*a*b + b^2)*cosh(d*x + c) + (9*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^8 + 28*(a^2 - b^2)*cosh(d*x + c)^6 + 10*(3*a^2 - 2*a*b + 3*b^2)*cosh(d*x + c)^4 + 12*(a^2 - b^2)*cosh(d*x + c)^2 + a^2 + 2*a*b + b^2)*sinh(d*x + c))*sqrt(-b/(a + b))*arctan(1/2*((a + b)*cosh(d*x + c) + (a + b)*sinh(d*x + c))*sqrt(-b/(a + b))/b) + 4*a^2 + 8*a*b + 4*b^2 + 20*(2*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^9 + 4*(2*a^2 - a*b - 3*b^2)*cosh(d*x + c)^7 + 3*(4*a^2 - 7*a*b + b^2)*cosh(d*x + c)^5 + 2*(4*a^2 - 7*a*b + b^2)*cosh(d*x + c)^3 + (2*a^2 - a*b - 3*b^2)*cosh(d*x + c))*sinh(d*x + c))/((a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*cosh(d*x + c)^9 + 9*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*cosh(d*x + c)*sinh(d*x + c)^8 + (a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*sinh(d*x + c)^9 + 4*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*d*cosh(d*x + c)^7 + 4*(9*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*cosh(d*x + c)^2 + (a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*d)*sinh(d*x + c)^7 + 2*(3*a^5 + 7*a^4*b + 6*a^3*b^2 + 6*a^2*b^3 + 7*a*b^4 + 3*b^5)*d*cosh(d*x + c)^5 + 28*(3*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*cosh(d*x + c)^3 + (a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*d*cosh(d*x + c))*sinh(d*x + c)^6 + 2*(63*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*cosh(d*x + c)^4 + 42*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*d*cosh(d*x + c)^2 + (3*a^5 + 7*a^4*b + 6*a^3*b^2 + 6*a^2*b^3 + 7*a*b^4 + 3*b^5)*d)*sinh(d*x + c)^5 + 4*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*d*cosh(d*x + c)^3 + 2*(63*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*cosh(d*x + c)^5 + 70*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*d*cosh(d*x + c)^3 + 5*(3*a^5 + 7*a^4*b + 6*a^3*b^2 + 6*a^2*b^3 + 7*a*b^4 + 3*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^4 + 4*(21*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*cosh(d*x + c)^6 + 35*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*d*cosh(d*x + c)^4 + 5*(3*a^5 + 7*a^4*b + 6*a^3*b^2 + 6*a^2*b^3 + 7*a*b^4 + 3*b^5)*d*cosh(d*x + c)^2 + (a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*d)*sinh(d*x + c)^3 + (a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*cosh(d*x + c) + 4*(9*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*cosh(d*x + c)^7 + 21*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*d*cosh(d*x + c)^5 + 5*(3*a^5 + 7*a^4*b + 6*a^3*b^2 + 6*a^2*b^3 + 7*a*b^4 + 3*b^5)*d*cosh(d*x + c)^3 + 3*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*d*cosh(d*x + c))*sinh(d*x + c)^2 + (9*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*cosh(d*x + c)^8 + 28*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*d*cosh(d*x + c)^6 + 10*(3*a^5 + 7*a^4*b + 6*a^3*b^2 + 6*a^2*b^3 + 7*a*b^4 + 3*b^5)*d*cosh(d*x + c)^4 + 12*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*d*cosh(d*x + c)^2 + (a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d)*sinh(d*x + c))]","B",0
45,1,10716,0,1.774965," ","integrate(csch(d*x+c)/(a+b*tanh(d*x+c)^2)^3,x, algorithm=""fricas"")","\left[\frac{4 \, {\left(9 \, a^{3} b + 13 \, a^{2} b^{2} + 4 \, a b^{3}\right)} \cosh\left(d x + c\right)^{7} + 28 \, {\left(9 \, a^{3} b + 13 \, a^{2} b^{2} + 4 \, a b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + 4 \, {\left(9 \, a^{3} b + 13 \, a^{2} b^{2} + 4 \, a b^{3}\right)} \sinh\left(d x + c\right)^{7} + 4 \, {\left(27 \, a^{3} b + 11 \, a^{2} b^{2} - 4 \, a b^{3}\right)} \cosh\left(d x + c\right)^{5} + 4 \, {\left(27 \, a^{3} b + 11 \, a^{2} b^{2} - 4 \, a b^{3} + 21 \, {\left(9 \, a^{3} b + 13 \, 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(9 \, a^{3} b + 13 \, a^{2} b^{2} + 4 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(27 \, a^{3} b + 11 \, 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(27 \, a^{3} b + 11 \, a^{2} b^{2} - 4 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(35 \, {\left(9 \, a^{3} b + 13 \, a^{2} b^{2} + 4 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} + 27 \, a^{3} b + 11 \, a^{2} b^{2} - 4 \, a b^{3} + 10 \, {\left(27 \, a^{3} b + 11 \, 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(9 \, a^{3} b + 13 \, a^{2} b^{2} + 4 \, a b^{3}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(27 \, a^{3} b + 11 \, a^{2} b^{2} - 4 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(27 \, a^{3} b + 11 \, 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^{4} + 50 \, a^{3} b + 63 \, a^{2} b^{2} + 36 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(15 \, a^{4} + 50 \, a^{3} b + 63 \, a^{2} b^{2} + 36 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(15 \, a^{4} + 50 \, a^{3} b + 63 \, a^{2} b^{2} + 36 \, a b^{3} + 8 \, b^{4}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(15 \, a^{4} + 20 \, a^{3} b - 7 \, a^{2} b^{2} - 20 \, a b^{3} - 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(15 \, a^{4} + 20 \, a^{3} b - 7 \, a^{2} b^{2} - 20 \, a b^{3} - 8 \, b^{4} + 7 \, {\left(15 \, a^{4} + 50 \, a^{3} b + 63 \, 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)^{6} + 8 \, {\left(7 \, {\left(15 \, a^{4} + 50 \, a^{3} b + 63 \, a^{2} b^{2} + 36 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(15 \, a^{4} + 20 \, a^{3} b - 7 \, a^{2} b^{2} - 20 \, a b^{3} - 8 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(45 \, a^{4} + 30 \, a^{3} b + 29 \, a^{2} b^{2} + 44 \, a b^{3} + 24 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(15 \, a^{4} + 50 \, a^{3} b + 63 \, a^{2} b^{2} + 36 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 45 \, a^{4} + 30 \, a^{3} b + 29 \, a^{2} b^{2} + 44 \, a b^{3} + 24 \, b^{4} + 30 \, {\left(15 \, a^{4} + 20 \, a^{3} b - 7 \, 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)^{4} + 15 \, a^{4} + 50 \, a^{3} b + 63 \, a^{2} b^{2} + 36 \, a b^{3} + 8 \, b^{4} + 8 \, {\left(7 \, {\left(15 \, a^{4} + 50 \, a^{3} b + 63 \, a^{2} b^{2} + 36 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(15 \, a^{4} + 20 \, a^{3} b - 7 \, a^{2} b^{2} - 20 \, a b^{3} - 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(45 \, a^{4} + 30 \, a^{3} b + 29 \, a^{2} b^{2} + 44 \, a b^{3} + 24 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(15 \, a^{4} + 20 \, a^{3} b - 7 \, a^{2} b^{2} - 20 \, a b^{3} - 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(15 \, a^{4} + 50 \, a^{3} b + 63 \, a^{2} b^{2} + 36 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(15 \, a^{4} + 20 \, a^{3} b - 7 \, a^{2} b^{2} - 20 \, a b^{3} - 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 15 \, a^{4} + 20 \, a^{3} b - 7 \, a^{2} b^{2} - 20 \, a b^{3} - 8 \, b^{4} + 3 \, {\left(45 \, a^{4} + 30 \, a^{3} b + 29 \, a^{2} b^{2} + 44 \, 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^{4} + 50 \, a^{3} b + 63 \, a^{2} b^{2} + 36 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(15 \, a^{4} + 20 \, a^{3} b - 7 \, a^{2} b^{2} - 20 \, a b^{3} - 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + {\left(45 \, a^{4} + 30 \, a^{3} b + 29 \, a^{2} b^{2} + 44 \, a b^{3} + 24 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(15 \, a^{4} + 20 \, a^{3} b - 7 \, a^{2} b^{2} - 20 \, 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{{\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 + 3 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} + a + 3 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a + 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) + 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}} + a + b}{{\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) + 4 \, {\left(9 \, a^{3} b + 13 \, a^{2} b^{2} + 4 \, a b^{3}\right)} \cosh\left(d x + c\right) - 16 \, {\left({\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{4} + 2 \, a^{3} b - 2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(a^{4} + 2 \, a^{3} b - 2 \, a b^{3} - b^{4} + 7 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, 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)^{6} + 8 \, {\left(7 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{4} + 2 \, a^{3} b - 2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(3 \, a^{4} + 4 \, a^{3} b + 2 \, a^{2} b^{2} + 4 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{4} + 3 \, a^{4} + 4 \, a^{3} b + 2 \, a^{2} b^{2} + 4 \, a b^{3} + 3 \, b^{4} + 30 \, {\left(a^{4} + 2 \, a^{3} b - 2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4} + 8 \, {\left(7 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{4} + 2 \, a^{3} b - 2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{4} + 4 \, a^{3} b + 2 \, 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)^{3} + 4 \, {\left(a^{4} + 2 \, a^{3} b - 2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{4} + 2 \, a^{3} b - 2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{4} + a^{4} + 2 \, a^{3} b - 2 \, a b^{3} - b^{4} + 3 \, {\left(3 \, a^{4} + 4 \, a^{3} b + 2 \, 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)^{2} + 8 \, {\left({\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{4} + 2 \, a^{3} b - 2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{4} + 4 \, a^{3} b + 2 \, a^{2} b^{2} + 4 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{4} + 2 \, a^{3} b - 2 \, 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^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{4} + 2 \, a^{3} b - 2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(a^{4} + 2 \, a^{3} b - 2 \, a b^{3} - b^{4} + 7 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, 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)^{6} + 8 \, {\left(7 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{4} + 2 \, a^{3} b - 2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(3 \, a^{4} + 4 \, a^{3} b + 2 \, a^{2} b^{2} + 4 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{4} + 3 \, a^{4} + 4 \, a^{3} b + 2 \, a^{2} b^{2} + 4 \, a b^{3} + 3 \, b^{4} + 30 \, {\left(a^{4} + 2 \, a^{3} b - 2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4} + 8 \, {\left(7 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{4} + 2 \, a^{3} b - 2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{4} + 4 \, a^{3} b + 2 \, 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)^{3} + 4 \, {\left(a^{4} + 2 \, a^{3} b - 2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{4} + 2 \, a^{3} b - 2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{4} + a^{4} + 2 \, a^{3} b - 2 \, a b^{3} - b^{4} + 3 \, {\left(3 \, a^{4} + 4 \, a^{3} b + 2 \, 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)^{2} + 8 \, {\left({\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{4} + 2 \, a^{3} b - 2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{4} + 4 \, a^{3} b + 2 \, a^{2} b^{2} + 4 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{4} + 2 \, a^{3} b - 2 \, 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(9 \, a^{3} b + 13 \, a^{2} b^{2} + 4 \, a b^{3}\right)} \cosh\left(d x + c\right)^{6} + 5 \, {\left(27 \, a^{3} b + 11 \, a^{2} b^{2} - 4 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} + 9 \, a^{3} b + 13 \, a^{2} b^{2} + 4 \, a b^{3} + 3 \, {\left(27 \, a^{3} b + 11 \, 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^{7} + 4 \, a^{6} b + 6 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{7} + 4 \, a^{6} b + 6 \, a^{5} b^{2} + 4 \, 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^{7} + 4 \, a^{6} b + 6 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + a^{3} b^{4}\right)} d \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{7} + 2 \, a^{6} b - 2 \, a^{4} b^{3} - a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{7} + 4 \, a^{6} b + 6 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{7} + 2 \, a^{6} b - 2 \, a^{4} b^{3} - a^{3} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(3 \, a^{7} + 4 \, a^{6} b + 2 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + 3 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{7} + 4 \, a^{6} b + 6 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{7} + 2 \, a^{6} b - 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 \, {\left(a^{7} + 4 \, a^{6} b + 6 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 30 \, {\left(a^{7} + 2 \, a^{6} b - 2 \, a^{4} b^{3} - a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{7} + 4 \, a^{6} b + 2 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + 3 \, a^{3} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{7} + 2 \, a^{6} b - 2 \, a^{4} b^{3} - a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a^{7} + 4 \, a^{6} b + 6 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{7} + 2 \, a^{6} b - 2 \, a^{4} b^{3} - a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{7} + 4 \, a^{6} b + 2 \, a^{5} b^{2} + 4 \, 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^{7} + 4 \, a^{6} b + 6 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{7} + 2 \, a^{6} b - 2 \, a^{4} b^{3} - a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{7} + 4 \, a^{6} b + 2 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + 3 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{7} + 2 \, a^{6} b - 2 \, a^{4} b^{3} - a^{3} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{7} + 4 \, a^{6} b + 6 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + a^{3} b^{4}\right)} d + 8 \, {\left({\left(a^{7} + 4 \, a^{6} b + 6 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{7} + 2 \, a^{6} b - 2 \, a^{4} b^{3} - a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{7} + 4 \, a^{6} b + 2 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + 3 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{7} + 2 \, a^{6} b - 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(9 \, a^{3} b + 13 \, a^{2} b^{2} + 4 \, a b^{3}\right)} \cosh\left(d x + c\right)^{7} + 14 \, {\left(9 \, a^{3} b + 13 \, a^{2} b^{2} + 4 \, a b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + 2 \, {\left(9 \, a^{3} b + 13 \, a^{2} b^{2} + 4 \, a b^{3}\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(27 \, a^{3} b + 11 \, a^{2} b^{2} - 4 \, a b^{3}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(27 \, a^{3} b + 11 \, a^{2} b^{2} - 4 \, a b^{3} + 21 \, {\left(9 \, a^{3} b + 13 \, 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(9 \, a^{3} b + 13 \, a^{2} b^{2} + 4 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(27 \, a^{3} b + 11 \, 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(27 \, a^{3} b + 11 \, a^{2} b^{2} - 4 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(35 \, {\left(9 \, a^{3} b + 13 \, a^{2} b^{2} + 4 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} + 27 \, a^{3} b + 11 \, a^{2} b^{2} - 4 \, a b^{3} + 10 \, {\left(27 \, a^{3} b + 11 \, 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(9 \, a^{3} b + 13 \, a^{2} b^{2} + 4 \, a b^{3}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(27 \, a^{3} b + 11 \, a^{2} b^{2} - 4 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(27 \, a^{3} b + 11 \, 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^{4} + 50 \, a^{3} b + 63 \, a^{2} b^{2} + 36 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(15 \, a^{4} + 50 \, a^{3} b + 63 \, a^{2} b^{2} + 36 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(15 \, a^{4} + 50 \, a^{3} b + 63 \, a^{2} b^{2} + 36 \, a b^{3} + 8 \, b^{4}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(15 \, a^{4} + 20 \, a^{3} b - 7 \, a^{2} b^{2} - 20 \, a b^{3} - 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(15 \, a^{4} + 20 \, a^{3} b - 7 \, a^{2} b^{2} - 20 \, a b^{3} - 8 \, b^{4} + 7 \, {\left(15 \, a^{4} + 50 \, a^{3} b + 63 \, 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)^{6} + 8 \, {\left(7 \, {\left(15 \, a^{4} + 50 \, a^{3} b + 63 \, a^{2} b^{2} + 36 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(15 \, a^{4} + 20 \, a^{3} b - 7 \, a^{2} b^{2} - 20 \, a b^{3} - 8 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(45 \, a^{4} + 30 \, a^{3} b + 29 \, a^{2} b^{2} + 44 \, a b^{3} + 24 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(15 \, a^{4} + 50 \, a^{3} b + 63 \, a^{2} b^{2} + 36 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 45 \, a^{4} + 30 \, a^{3} b + 29 \, a^{2} b^{2} + 44 \, a b^{3} + 24 \, b^{4} + 30 \, {\left(15 \, a^{4} + 20 \, a^{3} b - 7 \, 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)^{4} + 15 \, a^{4} + 50 \, a^{3} b + 63 \, a^{2} b^{2} + 36 \, a b^{3} + 8 \, b^{4} + 8 \, {\left(7 \, {\left(15 \, a^{4} + 50 \, a^{3} b + 63 \, a^{2} b^{2} + 36 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(15 \, a^{4} + 20 \, a^{3} b - 7 \, a^{2} b^{2} - 20 \, a b^{3} - 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(45 \, a^{4} + 30 \, a^{3} b + 29 \, a^{2} b^{2} + 44 \, a b^{3} + 24 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(15 \, a^{4} + 20 \, a^{3} b - 7 \, a^{2} b^{2} - 20 \, a b^{3} - 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(15 \, a^{4} + 50 \, a^{3} b + 63 \, a^{2} b^{2} + 36 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(15 \, a^{4} + 20 \, a^{3} b - 7 \, a^{2} b^{2} - 20 \, a b^{3} - 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 15 \, a^{4} + 20 \, a^{3} b - 7 \, a^{2} b^{2} - 20 \, a b^{3} - 8 \, b^{4} + 3 \, {\left(45 \, a^{4} + 30 \, a^{3} b + 29 \, a^{2} b^{2} + 44 \, 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^{4} + 50 \, a^{3} b + 63 \, a^{2} b^{2} + 36 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(15 \, a^{4} + 20 \, a^{3} b - 7 \, a^{2} b^{2} - 20 \, a b^{3} - 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + {\left(45 \, a^{4} + 30 \, a^{3} b + 29 \, a^{2} b^{2} + 44 \, a b^{3} + 24 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(15 \, a^{4} + 20 \, a^{3} b - 7 \, a^{2} b^{2} - 20 \, 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({\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 - 3 \, b\right)} \cosh\left(d x + c\right) + {\left(3 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} + a - 3 \, b\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{b}{a + b}}}{2 \, b}\right) - {\left({\left(15 \, a^{4} + 50 \, a^{3} b + 63 \, a^{2} b^{2} + 36 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(15 \, a^{4} + 50 \, a^{3} b + 63 \, a^{2} b^{2} + 36 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(15 \, a^{4} + 50 \, a^{3} b + 63 \, a^{2} b^{2} + 36 \, a b^{3} + 8 \, b^{4}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(15 \, a^{4} + 20 \, a^{3} b - 7 \, a^{2} b^{2} - 20 \, a b^{3} - 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(15 \, a^{4} + 20 \, a^{3} b - 7 \, a^{2} b^{2} - 20 \, a b^{3} - 8 \, b^{4} + 7 \, {\left(15 \, a^{4} + 50 \, a^{3} b + 63 \, 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)^{6} + 8 \, {\left(7 \, {\left(15 \, a^{4} + 50 \, a^{3} b + 63 \, a^{2} b^{2} + 36 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(15 \, a^{4} + 20 \, a^{3} b - 7 \, a^{2} b^{2} - 20 \, a b^{3} - 8 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(45 \, a^{4} + 30 \, a^{3} b + 29 \, a^{2} b^{2} + 44 \, a b^{3} + 24 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(15 \, a^{4} + 50 \, a^{3} b + 63 \, a^{2} b^{2} + 36 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 45 \, a^{4} + 30 \, a^{3} b + 29 \, a^{2} b^{2} + 44 \, a b^{3} + 24 \, b^{4} + 30 \, {\left(15 \, a^{4} + 20 \, a^{3} b - 7 \, 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)^{4} + 15 \, a^{4} + 50 \, a^{3} b + 63 \, a^{2} b^{2} + 36 \, a b^{3} + 8 \, b^{4} + 8 \, {\left(7 \, {\left(15 \, a^{4} + 50 \, a^{3} b + 63 \, a^{2} b^{2} + 36 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(15 \, a^{4} + 20 \, a^{3} b - 7 \, a^{2} b^{2} - 20 \, a b^{3} - 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(45 \, a^{4} + 30 \, a^{3} b + 29 \, a^{2} b^{2} + 44 \, a b^{3} + 24 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(15 \, a^{4} + 20 \, a^{3} b - 7 \, a^{2} b^{2} - 20 \, a b^{3} - 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(15 \, a^{4} + 50 \, a^{3} b + 63 \, a^{2} b^{2} + 36 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(15 \, a^{4} + 20 \, a^{3} b - 7 \, a^{2} b^{2} - 20 \, a b^{3} - 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 15 \, a^{4} + 20 \, a^{3} b - 7 \, a^{2} b^{2} - 20 \, a b^{3} - 8 \, b^{4} + 3 \, {\left(45 \, a^{4} + 30 \, a^{3} b + 29 \, a^{2} b^{2} + 44 \, 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^{4} + 50 \, a^{3} b + 63 \, a^{2} b^{2} + 36 \, a b^{3} + 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(15 \, a^{4} + 20 \, a^{3} b - 7 \, a^{2} b^{2} - 20 \, a b^{3} - 8 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + {\left(45 \, a^{4} + 30 \, a^{3} b + 29 \, a^{2} b^{2} + 44 \, a b^{3} + 24 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(15 \, a^{4} + 20 \, a^{3} b - 7 \, a^{2} b^{2} - 20 \, 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({\left(a + b\right)} \cosh\left(d x + c\right) + {\left(a + b\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{b}{a + b}}}{2 \, b}\right) + 2 \, {\left(9 \, a^{3} b + 13 \, a^{2} b^{2} + 4 \, a b^{3}\right)} \cosh\left(d x + c\right) - 8 \, {\left({\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{4} + 2 \, a^{3} b - 2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(a^{4} + 2 \, a^{3} b - 2 \, a b^{3} - b^{4} + 7 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, 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)^{6} + 8 \, {\left(7 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{4} + 2 \, a^{3} b - 2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(3 \, a^{4} + 4 \, a^{3} b + 2 \, a^{2} b^{2} + 4 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{4} + 3 \, a^{4} + 4 \, a^{3} b + 2 \, a^{2} b^{2} + 4 \, a b^{3} + 3 \, b^{4} + 30 \, {\left(a^{4} + 2 \, a^{3} b - 2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4} + 8 \, {\left(7 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{4} + 2 \, a^{3} b - 2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{4} + 4 \, a^{3} b + 2 \, 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)^{3} + 4 \, {\left(a^{4} + 2 \, a^{3} b - 2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{4} + 2 \, a^{3} b - 2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{4} + a^{4} + 2 \, a^{3} b - 2 \, a b^{3} - b^{4} + 3 \, {\left(3 \, a^{4} + 4 \, a^{3} b + 2 \, 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)^{2} + 8 \, {\left({\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{4} + 2 \, a^{3} b - 2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{4} + 4 \, a^{3} b + 2 \, a^{2} b^{2} + 4 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{4} + 2 \, a^{3} b - 2 \, 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^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{4} + 2 \, a^{3} b - 2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(a^{4} + 2 \, a^{3} b - 2 \, a b^{3} - b^{4} + 7 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, 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)^{6} + 8 \, {\left(7 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{4} + 2 \, a^{3} b - 2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(3 \, a^{4} + 4 \, a^{3} b + 2 \, a^{2} b^{2} + 4 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{4} + 3 \, a^{4} + 4 \, a^{3} b + 2 \, a^{2} b^{2} + 4 \, a b^{3} + 3 \, b^{4} + 30 \, {\left(a^{4} + 2 \, a^{3} b - 2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4} + 8 \, {\left(7 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{4} + 2 \, a^{3} b - 2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{4} + 4 \, a^{3} b + 2 \, 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)^{3} + 4 \, {\left(a^{4} + 2 \, a^{3} b - 2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{4} + 2 \, a^{3} b - 2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{4} + a^{4} + 2 \, a^{3} b - 2 \, a b^{3} - b^{4} + 3 \, {\left(3 \, a^{4} + 4 \, a^{3} b + 2 \, 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)^{2} + 8 \, {\left({\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{4} + 2 \, a^{3} b - 2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{4} + 4 \, a^{3} b + 2 \, a^{2} b^{2} + 4 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{4} + 2 \, a^{3} b - 2 \, 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(9 \, a^{3} b + 13 \, a^{2} b^{2} + 4 \, a b^{3}\right)} \cosh\left(d x + c\right)^{6} + 5 \, {\left(27 \, a^{3} b + 11 \, a^{2} b^{2} - 4 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} + 9 \, a^{3} b + 13 \, a^{2} b^{2} + 4 \, a b^{3} + 3 \, {\left(27 \, a^{3} b + 11 \, 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^{7} + 4 \, a^{6} b + 6 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{7} + 4 \, a^{6} b + 6 \, a^{5} b^{2} + 4 \, 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^{7} + 4 \, a^{6} b + 6 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + a^{3} b^{4}\right)} d \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{7} + 2 \, a^{6} b - 2 \, a^{4} b^{3} - a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{7} + 4 \, a^{6} b + 6 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{7} + 2 \, a^{6} b - 2 \, a^{4} b^{3} - a^{3} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(3 \, a^{7} + 4 \, a^{6} b + 2 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + 3 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{7} + 4 \, a^{6} b + 6 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{7} + 2 \, a^{6} b - 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 \, {\left(a^{7} + 4 \, a^{6} b + 6 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 30 \, {\left(a^{7} + 2 \, a^{6} b - 2 \, a^{4} b^{3} - a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{7} + 4 \, a^{6} b + 2 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + 3 \, a^{3} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{7} + 2 \, a^{6} b - 2 \, a^{4} b^{3} - a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a^{7} + 4 \, a^{6} b + 6 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{7} + 2 \, a^{6} b - 2 \, a^{4} b^{3} - a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{7} + 4 \, a^{6} b + 2 \, a^{5} b^{2} + 4 \, 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^{7} + 4 \, a^{6} b + 6 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{7} + 2 \, a^{6} b - 2 \, a^{4} b^{3} - a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{7} + 4 \, a^{6} b + 2 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + 3 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{7} + 2 \, a^{6} b - 2 \, a^{4} b^{3} - a^{3} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{7} + 4 \, a^{6} b + 6 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + a^{3} b^{4}\right)} d + 8 \, {\left({\left(a^{7} + 4 \, a^{6} b + 6 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{7} + 2 \, a^{6} b - 2 \, a^{4} b^{3} - a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{7} + 4 \, a^{6} b + 2 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + 3 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{7} + 2 \, a^{6} b - 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*(9*a^3*b + 13*a^2*b^2 + 4*a*b^3)*cosh(d*x + c)^7 + 28*(9*a^3*b + 13*a^2*b^2 + 4*a*b^3)*cosh(d*x + c)*sinh(d*x + c)^6 + 4*(9*a^3*b + 13*a^2*b^2 + 4*a*b^3)*sinh(d*x + c)^7 + 4*(27*a^3*b + 11*a^2*b^2 - 4*a*b^3)*cosh(d*x + c)^5 + 4*(27*a^3*b + 11*a^2*b^2 - 4*a*b^3 + 21*(9*a^3*b + 13*a^2*b^2 + 4*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 20*(7*(9*a^3*b + 13*a^2*b^2 + 4*a*b^3)*cosh(d*x + c)^3 + (27*a^3*b + 11*a^2*b^2 - 4*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^4 + 4*(27*a^3*b + 11*a^2*b^2 - 4*a*b^3)*cosh(d*x + c)^3 + 4*(35*(9*a^3*b + 13*a^2*b^2 + 4*a*b^3)*cosh(d*x + c)^4 + 27*a^3*b + 11*a^2*b^2 - 4*a*b^3 + 10*(27*a^3*b + 11*a^2*b^2 - 4*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 4*(21*(9*a^3*b + 13*a^2*b^2 + 4*a*b^3)*cosh(d*x + c)^5 + 10*(27*a^3*b + 11*a^2*b^2 - 4*a*b^3)*cosh(d*x + c)^3 + 3*(27*a^3*b + 11*a^2*b^2 - 4*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^2 + ((15*a^4 + 50*a^3*b + 63*a^2*b^2 + 36*a*b^3 + 8*b^4)*cosh(d*x + c)^8 + 8*(15*a^4 + 50*a^3*b + 63*a^2*b^2 + 36*a*b^3 + 8*b^4)*cosh(d*x + c)*sinh(d*x + c)^7 + (15*a^4 + 50*a^3*b + 63*a^2*b^2 + 36*a*b^3 + 8*b^4)*sinh(d*x + c)^8 + 4*(15*a^4 + 20*a^3*b - 7*a^2*b^2 - 20*a*b^3 - 8*b^4)*cosh(d*x + c)^6 + 4*(15*a^4 + 20*a^3*b - 7*a^2*b^2 - 20*a*b^3 - 8*b^4 + 7*(15*a^4 + 50*a^3*b + 63*a^2*b^2 + 36*a*b^3 + 8*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(15*a^4 + 50*a^3*b + 63*a^2*b^2 + 36*a*b^3 + 8*b^4)*cosh(d*x + c)^3 + 3*(15*a^4 + 20*a^3*b - 7*a^2*b^2 - 20*a*b^3 - 8*b^4)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(45*a^4 + 30*a^3*b + 29*a^2*b^2 + 44*a*b^3 + 24*b^4)*cosh(d*x + c)^4 + 2*(35*(15*a^4 + 50*a^3*b + 63*a^2*b^2 + 36*a*b^3 + 8*b^4)*cosh(d*x + c)^4 + 45*a^4 + 30*a^3*b + 29*a^2*b^2 + 44*a*b^3 + 24*b^4 + 30*(15*a^4 + 20*a^3*b - 7*a^2*b^2 - 20*a*b^3 - 8*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 15*a^4 + 50*a^3*b + 63*a^2*b^2 + 36*a*b^3 + 8*b^4 + 8*(7*(15*a^4 + 50*a^3*b + 63*a^2*b^2 + 36*a*b^3 + 8*b^4)*cosh(d*x + c)^5 + 10*(15*a^4 + 20*a^3*b - 7*a^2*b^2 - 20*a*b^3 - 8*b^4)*cosh(d*x + c)^3 + (45*a^4 + 30*a^3*b + 29*a^2*b^2 + 44*a*b^3 + 24*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(15*a^4 + 20*a^3*b - 7*a^2*b^2 - 20*a*b^3 - 8*b^4)*cosh(d*x + c)^2 + 4*(7*(15*a^4 + 50*a^3*b + 63*a^2*b^2 + 36*a*b^3 + 8*b^4)*cosh(d*x + c)^6 + 15*(15*a^4 + 20*a^3*b - 7*a^2*b^2 - 20*a*b^3 - 8*b^4)*cosh(d*x + c)^4 + 15*a^4 + 20*a^3*b - 7*a^2*b^2 - 20*a*b^3 - 8*b^4 + 3*(45*a^4 + 30*a^3*b + 29*a^2*b^2 + 44*a*b^3 + 24*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((15*a^4 + 50*a^3*b + 63*a^2*b^2 + 36*a*b^3 + 8*b^4)*cosh(d*x + c)^7 + 3*(15*a^4 + 20*a^3*b - 7*a^2*b^2 - 20*a*b^3 - 8*b^4)*cosh(d*x + c)^5 + (45*a^4 + 30*a^3*b + 29*a^2*b^2 + 44*a*b^3 + 24*b^4)*cosh(d*x + c)^3 + (15*a^4 + 20*a^3*b - 7*a^2*b^2 - 20*a*b^3 - 8*b^4)*cosh(d*x + c))*sinh(d*x + c))*sqrt(b/(a + b))*log(((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 + 3*b)*cosh(d*x + c)^2 + 2*(3*(a + b)*cosh(d*x + c)^2 + a + 3*b)*sinh(d*x + c)^2 + 4*((a + b)*cosh(d*x + c)^3 + (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)) + a + b)/((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)) + 4*(9*a^3*b + 13*a^2*b^2 + 4*a*b^3)*cosh(d*x + c) - 16*((a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*cosh(d*x + c)^8 + 8*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*cosh(d*x + c)*sinh(d*x + c)^7 + (a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*sinh(d*x + c)^8 + 4*(a^4 + 2*a^3*b - 2*a*b^3 - b^4)*cosh(d*x + c)^6 + 4*(a^4 + 2*a^3*b - 2*a*b^3 - b^4 + 7*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*cosh(d*x + c)^3 + 3*(a^4 + 2*a^3*b - 2*a*b^3 - b^4)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(3*a^4 + 4*a^3*b + 2*a^2*b^2 + 4*a*b^3 + 3*b^4)*cosh(d*x + c)^4 + 2*(35*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*cosh(d*x + c)^4 + 3*a^4 + 4*a^3*b + 2*a^2*b^2 + 4*a*b^3 + 3*b^4 + 30*(a^4 + 2*a^3*b - 2*a*b^3 - b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4 + 8*(7*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*cosh(d*x + c)^5 + 10*(a^4 + 2*a^3*b - 2*a*b^3 - b^4)*cosh(d*x + c)^3 + (3*a^4 + 4*a^3*b + 2*a^2*b^2 + 4*a*b^3 + 3*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(a^4 + 2*a^3*b - 2*a*b^3 - b^4)*cosh(d*x + c)^2 + 4*(7*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*cosh(d*x + c)^6 + 15*(a^4 + 2*a^3*b - 2*a*b^3 - b^4)*cosh(d*x + c)^4 + a^4 + 2*a^3*b - 2*a*b^3 - b^4 + 3*(3*a^4 + 4*a^3*b + 2*a^2*b^2 + 4*a*b^3 + 3*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*cosh(d*x + c)^7 + 3*(a^4 + 2*a^3*b - 2*a*b^3 - b^4)*cosh(d*x + c)^5 + (3*a^4 + 4*a^3*b + 2*a^2*b^2 + 4*a*b^3 + 3*b^4)*cosh(d*x + c)^3 + (a^4 + 2*a^3*b - 2*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^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*cosh(d*x + c)^8 + 8*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*cosh(d*x + c)*sinh(d*x + c)^7 + (a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*sinh(d*x + c)^8 + 4*(a^4 + 2*a^3*b - 2*a*b^3 - b^4)*cosh(d*x + c)^6 + 4*(a^4 + 2*a^3*b - 2*a*b^3 - b^4 + 7*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*cosh(d*x + c)^3 + 3*(a^4 + 2*a^3*b - 2*a*b^3 - b^4)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(3*a^4 + 4*a^3*b + 2*a^2*b^2 + 4*a*b^3 + 3*b^4)*cosh(d*x + c)^4 + 2*(35*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*cosh(d*x + c)^4 + 3*a^4 + 4*a^3*b + 2*a^2*b^2 + 4*a*b^3 + 3*b^4 + 30*(a^4 + 2*a^3*b - 2*a*b^3 - b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4 + 8*(7*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*cosh(d*x + c)^5 + 10*(a^4 + 2*a^3*b - 2*a*b^3 - b^4)*cosh(d*x + c)^3 + (3*a^4 + 4*a^3*b + 2*a^2*b^2 + 4*a*b^3 + 3*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(a^4 + 2*a^3*b - 2*a*b^3 - b^4)*cosh(d*x + c)^2 + 4*(7*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*cosh(d*x + c)^6 + 15*(a^4 + 2*a^3*b - 2*a*b^3 - b^4)*cosh(d*x + c)^4 + a^4 + 2*a^3*b - 2*a*b^3 - b^4 + 3*(3*a^4 + 4*a^3*b + 2*a^2*b^2 + 4*a*b^3 + 3*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*cosh(d*x + c)^7 + 3*(a^4 + 2*a^3*b - 2*a*b^3 - b^4)*cosh(d*x + c)^5 + (3*a^4 + 4*a^3*b + 2*a^2*b^2 + 4*a*b^3 + 3*b^4)*cosh(d*x + c)^3 + (a^4 + 2*a^3*b - 2*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*(9*a^3*b + 13*a^2*b^2 + 4*a*b^3)*cosh(d*x + c)^6 + 5*(27*a^3*b + 11*a^2*b^2 - 4*a*b^3)*cosh(d*x + c)^4 + 9*a^3*b + 13*a^2*b^2 + 4*a*b^3 + 3*(27*a^3*b + 11*a^2*b^2 - 4*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c))/((a^7 + 4*a^6*b + 6*a^5*b^2 + 4*a^4*b^3 + a^3*b^4)*d*cosh(d*x + c)^8 + 8*(a^7 + 4*a^6*b + 6*a^5*b^2 + 4*a^4*b^3 + a^3*b^4)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^7 + 4*a^6*b + 6*a^5*b^2 + 4*a^4*b^3 + a^3*b^4)*d*sinh(d*x + c)^8 + 4*(a^7 + 2*a^6*b - 2*a^4*b^3 - a^3*b^4)*d*cosh(d*x + c)^6 + 4*(7*(a^7 + 4*a^6*b + 6*a^5*b^2 + 4*a^4*b^3 + a^3*b^4)*d*cosh(d*x + c)^2 + (a^7 + 2*a^6*b - 2*a^4*b^3 - a^3*b^4)*d)*sinh(d*x + c)^6 + 2*(3*a^7 + 4*a^6*b + 2*a^5*b^2 + 4*a^4*b^3 + 3*a^3*b^4)*d*cosh(d*x + c)^4 + 8*(7*(a^7 + 4*a^6*b + 6*a^5*b^2 + 4*a^4*b^3 + a^3*b^4)*d*cosh(d*x + c)^3 + 3*(a^7 + 2*a^6*b - 2*a^4*b^3 - a^3*b^4)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^7 + 4*a^6*b + 6*a^5*b^2 + 4*a^4*b^3 + a^3*b^4)*d*cosh(d*x + c)^4 + 30*(a^7 + 2*a^6*b - 2*a^4*b^3 - a^3*b^4)*d*cosh(d*x + c)^2 + (3*a^7 + 4*a^6*b + 2*a^5*b^2 + 4*a^4*b^3 + 3*a^3*b^4)*d)*sinh(d*x + c)^4 + 4*(a^7 + 2*a^6*b - 2*a^4*b^3 - a^3*b^4)*d*cosh(d*x + c)^2 + 8*(7*(a^7 + 4*a^6*b + 6*a^5*b^2 + 4*a^4*b^3 + a^3*b^4)*d*cosh(d*x + c)^5 + 10*(a^7 + 2*a^6*b - 2*a^4*b^3 - a^3*b^4)*d*cosh(d*x + c)^3 + (3*a^7 + 4*a^6*b + 2*a^5*b^2 + 4*a^4*b^3 + 3*a^3*b^4)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^7 + 4*a^6*b + 6*a^5*b^2 + 4*a^4*b^3 + a^3*b^4)*d*cosh(d*x + c)^6 + 15*(a^7 + 2*a^6*b - 2*a^4*b^3 - a^3*b^4)*d*cosh(d*x + c)^4 + 3*(3*a^7 + 4*a^6*b + 2*a^5*b^2 + 4*a^4*b^3 + 3*a^3*b^4)*d*cosh(d*x + c)^2 + (a^7 + 2*a^6*b - 2*a^4*b^3 - a^3*b^4)*d)*sinh(d*x + c)^2 + (a^7 + 4*a^6*b + 6*a^5*b^2 + 4*a^4*b^3 + a^3*b^4)*d + 8*((a^7 + 4*a^6*b + 6*a^5*b^2 + 4*a^4*b^3 + a^3*b^4)*d*cosh(d*x + c)^7 + 3*(a^7 + 2*a^6*b - 2*a^4*b^3 - a^3*b^4)*d*cosh(d*x + c)^5 + (3*a^7 + 4*a^6*b + 2*a^5*b^2 + 4*a^4*b^3 + 3*a^3*b^4)*d*cosh(d*x + c)^3 + (a^7 + 2*a^6*b - 2*a^4*b^3 - a^3*b^4)*d*cosh(d*x + c))*sinh(d*x + c)), 1/8*(2*(9*a^3*b + 13*a^2*b^2 + 4*a*b^3)*cosh(d*x + c)^7 + 14*(9*a^3*b + 13*a^2*b^2 + 4*a*b^3)*cosh(d*x + c)*sinh(d*x + c)^6 + 2*(9*a^3*b + 13*a^2*b^2 + 4*a*b^3)*sinh(d*x + c)^7 + 2*(27*a^3*b + 11*a^2*b^2 - 4*a*b^3)*cosh(d*x + c)^5 + 2*(27*a^3*b + 11*a^2*b^2 - 4*a*b^3 + 21*(9*a^3*b + 13*a^2*b^2 + 4*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 10*(7*(9*a^3*b + 13*a^2*b^2 + 4*a*b^3)*cosh(d*x + c)^3 + (27*a^3*b + 11*a^2*b^2 - 4*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^4 + 2*(27*a^3*b + 11*a^2*b^2 - 4*a*b^3)*cosh(d*x + c)^3 + 2*(35*(9*a^3*b + 13*a^2*b^2 + 4*a*b^3)*cosh(d*x + c)^4 + 27*a^3*b + 11*a^2*b^2 - 4*a*b^3 + 10*(27*a^3*b + 11*a^2*b^2 - 4*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 2*(21*(9*a^3*b + 13*a^2*b^2 + 4*a*b^3)*cosh(d*x + c)^5 + 10*(27*a^3*b + 11*a^2*b^2 - 4*a*b^3)*cosh(d*x + c)^3 + 3*(27*a^3*b + 11*a^2*b^2 - 4*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^2 + ((15*a^4 + 50*a^3*b + 63*a^2*b^2 + 36*a*b^3 + 8*b^4)*cosh(d*x + c)^8 + 8*(15*a^4 + 50*a^3*b + 63*a^2*b^2 + 36*a*b^3 + 8*b^4)*cosh(d*x + c)*sinh(d*x + c)^7 + (15*a^4 + 50*a^3*b + 63*a^2*b^2 + 36*a*b^3 + 8*b^4)*sinh(d*x + c)^8 + 4*(15*a^4 + 20*a^3*b - 7*a^2*b^2 - 20*a*b^3 - 8*b^4)*cosh(d*x + c)^6 + 4*(15*a^4 + 20*a^3*b - 7*a^2*b^2 - 20*a*b^3 - 8*b^4 + 7*(15*a^4 + 50*a^3*b + 63*a^2*b^2 + 36*a*b^3 + 8*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(15*a^4 + 50*a^3*b + 63*a^2*b^2 + 36*a*b^3 + 8*b^4)*cosh(d*x + c)^3 + 3*(15*a^4 + 20*a^3*b - 7*a^2*b^2 - 20*a*b^3 - 8*b^4)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(45*a^4 + 30*a^3*b + 29*a^2*b^2 + 44*a*b^3 + 24*b^4)*cosh(d*x + c)^4 + 2*(35*(15*a^4 + 50*a^3*b + 63*a^2*b^2 + 36*a*b^3 + 8*b^4)*cosh(d*x + c)^4 + 45*a^4 + 30*a^3*b + 29*a^2*b^2 + 44*a*b^3 + 24*b^4 + 30*(15*a^4 + 20*a^3*b - 7*a^2*b^2 - 20*a*b^3 - 8*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 15*a^4 + 50*a^3*b + 63*a^2*b^2 + 36*a*b^3 + 8*b^4 + 8*(7*(15*a^4 + 50*a^3*b + 63*a^2*b^2 + 36*a*b^3 + 8*b^4)*cosh(d*x + c)^5 + 10*(15*a^4 + 20*a^3*b - 7*a^2*b^2 - 20*a*b^3 - 8*b^4)*cosh(d*x + c)^3 + (45*a^4 + 30*a^3*b + 29*a^2*b^2 + 44*a*b^3 + 24*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(15*a^4 + 20*a^3*b - 7*a^2*b^2 - 20*a*b^3 - 8*b^4)*cosh(d*x + c)^2 + 4*(7*(15*a^4 + 50*a^3*b + 63*a^2*b^2 + 36*a*b^3 + 8*b^4)*cosh(d*x + c)^6 + 15*(15*a^4 + 20*a^3*b - 7*a^2*b^2 - 20*a*b^3 - 8*b^4)*cosh(d*x + c)^4 + 15*a^4 + 20*a^3*b - 7*a^2*b^2 - 20*a*b^3 - 8*b^4 + 3*(45*a^4 + 30*a^3*b + 29*a^2*b^2 + 44*a*b^3 + 24*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((15*a^4 + 50*a^3*b + 63*a^2*b^2 + 36*a*b^3 + 8*b^4)*cosh(d*x + c)^7 + 3*(15*a^4 + 20*a^3*b - 7*a^2*b^2 - 20*a*b^3 - 8*b^4)*cosh(d*x + c)^5 + (45*a^4 + 30*a^3*b + 29*a^2*b^2 + 44*a*b^3 + 24*b^4)*cosh(d*x + c)^3 + (15*a^4 + 20*a^3*b - 7*a^2*b^2 - 20*a*b^3 - 8*b^4)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-b/(a + b))*arctan(1/2*((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 - 3*b)*cosh(d*x + c) + (3*(a + b)*cosh(d*x + c)^2 + a - 3*b)*sinh(d*x + c))*sqrt(-b/(a + b))/b) - ((15*a^4 + 50*a^3*b + 63*a^2*b^2 + 36*a*b^3 + 8*b^4)*cosh(d*x + c)^8 + 8*(15*a^4 + 50*a^3*b + 63*a^2*b^2 + 36*a*b^3 + 8*b^4)*cosh(d*x + c)*sinh(d*x + c)^7 + (15*a^4 + 50*a^3*b + 63*a^2*b^2 + 36*a*b^3 + 8*b^4)*sinh(d*x + c)^8 + 4*(15*a^4 + 20*a^3*b - 7*a^2*b^2 - 20*a*b^3 - 8*b^4)*cosh(d*x + c)^6 + 4*(15*a^4 + 20*a^3*b - 7*a^2*b^2 - 20*a*b^3 - 8*b^4 + 7*(15*a^4 + 50*a^3*b + 63*a^2*b^2 + 36*a*b^3 + 8*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(15*a^4 + 50*a^3*b + 63*a^2*b^2 + 36*a*b^3 + 8*b^4)*cosh(d*x + c)^3 + 3*(15*a^4 + 20*a^3*b - 7*a^2*b^2 - 20*a*b^3 - 8*b^4)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(45*a^4 + 30*a^3*b + 29*a^2*b^2 + 44*a*b^3 + 24*b^4)*cosh(d*x + c)^4 + 2*(35*(15*a^4 + 50*a^3*b + 63*a^2*b^2 + 36*a*b^3 + 8*b^4)*cosh(d*x + c)^4 + 45*a^4 + 30*a^3*b + 29*a^2*b^2 + 44*a*b^3 + 24*b^4 + 30*(15*a^4 + 20*a^3*b - 7*a^2*b^2 - 20*a*b^3 - 8*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 15*a^4 + 50*a^3*b + 63*a^2*b^2 + 36*a*b^3 + 8*b^4 + 8*(7*(15*a^4 + 50*a^3*b + 63*a^2*b^2 + 36*a*b^3 + 8*b^4)*cosh(d*x + c)^5 + 10*(15*a^4 + 20*a^3*b - 7*a^2*b^2 - 20*a*b^3 - 8*b^4)*cosh(d*x + c)^3 + (45*a^4 + 30*a^3*b + 29*a^2*b^2 + 44*a*b^3 + 24*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(15*a^4 + 20*a^3*b - 7*a^2*b^2 - 20*a*b^3 - 8*b^4)*cosh(d*x + c)^2 + 4*(7*(15*a^4 + 50*a^3*b + 63*a^2*b^2 + 36*a*b^3 + 8*b^4)*cosh(d*x + c)^6 + 15*(15*a^4 + 20*a^3*b - 7*a^2*b^2 - 20*a*b^3 - 8*b^4)*cosh(d*x + c)^4 + 15*a^4 + 20*a^3*b - 7*a^2*b^2 - 20*a*b^3 - 8*b^4 + 3*(45*a^4 + 30*a^3*b + 29*a^2*b^2 + 44*a*b^3 + 24*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((15*a^4 + 50*a^3*b + 63*a^2*b^2 + 36*a*b^3 + 8*b^4)*cosh(d*x + c)^7 + 3*(15*a^4 + 20*a^3*b - 7*a^2*b^2 - 20*a*b^3 - 8*b^4)*cosh(d*x + c)^5 + (45*a^4 + 30*a^3*b + 29*a^2*b^2 + 44*a*b^3 + 24*b^4)*cosh(d*x + c)^3 + (15*a^4 + 20*a^3*b - 7*a^2*b^2 - 20*a*b^3 - 8*b^4)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-b/(a + b))*arctan(1/2*((a + b)*cosh(d*x + c) + (a + b)*sinh(d*x + c))*sqrt(-b/(a + b))/b) + 2*(9*a^3*b + 13*a^2*b^2 + 4*a*b^3)*cosh(d*x + c) - 8*((a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*cosh(d*x + c)^8 + 8*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*cosh(d*x + c)*sinh(d*x + c)^7 + (a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*sinh(d*x + c)^8 + 4*(a^4 + 2*a^3*b - 2*a*b^3 - b^4)*cosh(d*x + c)^6 + 4*(a^4 + 2*a^3*b - 2*a*b^3 - b^4 + 7*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*cosh(d*x + c)^3 + 3*(a^4 + 2*a^3*b - 2*a*b^3 - b^4)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(3*a^4 + 4*a^3*b + 2*a^2*b^2 + 4*a*b^3 + 3*b^4)*cosh(d*x + c)^4 + 2*(35*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*cosh(d*x + c)^4 + 3*a^4 + 4*a^3*b + 2*a^2*b^2 + 4*a*b^3 + 3*b^4 + 30*(a^4 + 2*a^3*b - 2*a*b^3 - b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4 + 8*(7*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*cosh(d*x + c)^5 + 10*(a^4 + 2*a^3*b - 2*a*b^3 - b^4)*cosh(d*x + c)^3 + (3*a^4 + 4*a^3*b + 2*a^2*b^2 + 4*a*b^3 + 3*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(a^4 + 2*a^3*b - 2*a*b^3 - b^4)*cosh(d*x + c)^2 + 4*(7*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*cosh(d*x + c)^6 + 15*(a^4 + 2*a^3*b - 2*a*b^3 - b^4)*cosh(d*x + c)^4 + a^4 + 2*a^3*b - 2*a*b^3 - b^4 + 3*(3*a^4 + 4*a^3*b + 2*a^2*b^2 + 4*a*b^3 + 3*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*cosh(d*x + c)^7 + 3*(a^4 + 2*a^3*b - 2*a*b^3 - b^4)*cosh(d*x + c)^5 + (3*a^4 + 4*a^3*b + 2*a^2*b^2 + 4*a*b^3 + 3*b^4)*cosh(d*x + c)^3 + (a^4 + 2*a^3*b - 2*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^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*cosh(d*x + c)^8 + 8*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*cosh(d*x + c)*sinh(d*x + c)^7 + (a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*sinh(d*x + c)^8 + 4*(a^4 + 2*a^3*b - 2*a*b^3 - b^4)*cosh(d*x + c)^6 + 4*(a^4 + 2*a^3*b - 2*a*b^3 - b^4 + 7*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*cosh(d*x + c)^3 + 3*(a^4 + 2*a^3*b - 2*a*b^3 - b^4)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(3*a^4 + 4*a^3*b + 2*a^2*b^2 + 4*a*b^3 + 3*b^4)*cosh(d*x + c)^4 + 2*(35*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*cosh(d*x + c)^4 + 3*a^4 + 4*a^3*b + 2*a^2*b^2 + 4*a*b^3 + 3*b^4 + 30*(a^4 + 2*a^3*b - 2*a*b^3 - b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4 + 8*(7*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*cosh(d*x + c)^5 + 10*(a^4 + 2*a^3*b - 2*a*b^3 - b^4)*cosh(d*x + c)^3 + (3*a^4 + 4*a^3*b + 2*a^2*b^2 + 4*a*b^3 + 3*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(a^4 + 2*a^3*b - 2*a*b^3 - b^4)*cosh(d*x + c)^2 + 4*(7*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*cosh(d*x + c)^6 + 15*(a^4 + 2*a^3*b - 2*a*b^3 - b^4)*cosh(d*x + c)^4 + a^4 + 2*a^3*b - 2*a*b^3 - b^4 + 3*(3*a^4 + 4*a^3*b + 2*a^2*b^2 + 4*a*b^3 + 3*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*cosh(d*x + c)^7 + 3*(a^4 + 2*a^3*b - 2*a*b^3 - b^4)*cosh(d*x + c)^5 + (3*a^4 + 4*a^3*b + 2*a^2*b^2 + 4*a*b^3 + 3*b^4)*cosh(d*x + c)^3 + (a^4 + 2*a^3*b - 2*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*(9*a^3*b + 13*a^2*b^2 + 4*a*b^3)*cosh(d*x + c)^6 + 5*(27*a^3*b + 11*a^2*b^2 - 4*a*b^3)*cosh(d*x + c)^4 + 9*a^3*b + 13*a^2*b^2 + 4*a*b^3 + 3*(27*a^3*b + 11*a^2*b^2 - 4*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c))/((a^7 + 4*a^6*b + 6*a^5*b^2 + 4*a^4*b^3 + a^3*b^4)*d*cosh(d*x + c)^8 + 8*(a^7 + 4*a^6*b + 6*a^5*b^2 + 4*a^4*b^3 + a^3*b^4)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^7 + 4*a^6*b + 6*a^5*b^2 + 4*a^4*b^3 + a^3*b^4)*d*sinh(d*x + c)^8 + 4*(a^7 + 2*a^6*b - 2*a^4*b^3 - a^3*b^4)*d*cosh(d*x + c)^6 + 4*(7*(a^7 + 4*a^6*b + 6*a^5*b^2 + 4*a^4*b^3 + a^3*b^4)*d*cosh(d*x + c)^2 + (a^7 + 2*a^6*b - 2*a^4*b^3 - a^3*b^4)*d)*sinh(d*x + c)^6 + 2*(3*a^7 + 4*a^6*b + 2*a^5*b^2 + 4*a^4*b^3 + 3*a^3*b^4)*d*cosh(d*x + c)^4 + 8*(7*(a^7 + 4*a^6*b + 6*a^5*b^2 + 4*a^4*b^3 + a^3*b^4)*d*cosh(d*x + c)^3 + 3*(a^7 + 2*a^6*b - 2*a^4*b^3 - a^3*b^4)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^7 + 4*a^6*b + 6*a^5*b^2 + 4*a^4*b^3 + a^3*b^4)*d*cosh(d*x + c)^4 + 30*(a^7 + 2*a^6*b - 2*a^4*b^3 - a^3*b^4)*d*cosh(d*x + c)^2 + (3*a^7 + 4*a^6*b + 2*a^5*b^2 + 4*a^4*b^3 + 3*a^3*b^4)*d)*sinh(d*x + c)^4 + 4*(a^7 + 2*a^6*b - 2*a^4*b^3 - a^3*b^4)*d*cosh(d*x + c)^2 + 8*(7*(a^7 + 4*a^6*b + 6*a^5*b^2 + 4*a^4*b^3 + a^3*b^4)*d*cosh(d*x + c)^5 + 10*(a^7 + 2*a^6*b - 2*a^4*b^3 - a^3*b^4)*d*cosh(d*x + c)^3 + (3*a^7 + 4*a^6*b + 2*a^5*b^2 + 4*a^4*b^3 + 3*a^3*b^4)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^7 + 4*a^6*b + 6*a^5*b^2 + 4*a^4*b^3 + a^3*b^4)*d*cosh(d*x + c)^6 + 15*(a^7 + 2*a^6*b - 2*a^4*b^3 - a^3*b^4)*d*cosh(d*x + c)^4 + 3*(3*a^7 + 4*a^6*b + 2*a^5*b^2 + 4*a^4*b^3 + 3*a^3*b^4)*d*cosh(d*x + c)^2 + (a^7 + 2*a^6*b - 2*a^4*b^3 - a^3*b^4)*d)*sinh(d*x + c)^2 + (a^7 + 4*a^6*b + 6*a^5*b^2 + 4*a^4*b^3 + a^3*b^4)*d + 8*((a^7 + 4*a^6*b + 6*a^5*b^2 + 4*a^4*b^3 + a^3*b^4)*d*cosh(d*x + c)^7 + 3*(a^7 + 2*a^6*b - 2*a^4*b^3 - a^3*b^4)*d*cosh(d*x + c)^5 + (3*a^7 + 4*a^6*b + 2*a^5*b^2 + 4*a^4*b^3 + 3*a^3*b^4)*d*cosh(d*x + c)^3 + (a^7 + 2*a^6*b - 2*a^4*b^3 - a^3*b^4)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
46,1,8312,0,0.674560," ","integrate(csch(d*x+c)^2/(a+b*tanh(d*x+c)^2)^3,x, algorithm=""fricas"")","\left[-\frac{4 \, {\left(8 \, a^{4} + 23 \, a^{3} b + 45 \, a^{2} b^{2} + 45 \, a b^{3} + 15 \, b^{4}\right)} \cosh\left(d x + c\right)^{8} + 32 \, {\left(8 \, a^{4} + 23 \, a^{3} b + 45 \, a^{2} b^{2} + 45 \, a b^{3} + 15 \, b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + 4 \, {\left(8 \, a^{4} + 23 \, a^{3} b + 45 \, a^{2} b^{2} + 45 \, a b^{3} + 15 \, b^{4}\right)} \sinh\left(d x + c\right)^{8} + 8 \, {\left(16 \, a^{4} + 23 \, a^{3} b - 45 \, a b^{3} - 30 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 8 \, {\left(16 \, a^{4} + 23 \, a^{3} b - 45 \, a b^{3} - 30 \, b^{4} + 14 \, {\left(8 \, a^{4} + 23 \, a^{3} b + 45 \, a^{2} b^{2} + 45 \, a b^{3} + 15 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 16 \, {\left(14 \, {\left(8 \, a^{4} + 23 \, a^{3} b + 45 \, a^{2} b^{2} + 45 \, a b^{3} + 15 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(16 \, a^{4} + 23 \, a^{3} b - 45 \, a b^{3} - 30 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 8 \, {\left(24 \, a^{4} + 32 \, a^{3} b + 5 \, a^{2} b^{2} + 50 \, a b^{3} + 45 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 8 \, {\left(35 \, {\left(8 \, a^{4} + 23 \, a^{3} b + 45 \, a^{2} b^{2} + 45 \, a b^{3} + 15 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 24 \, a^{4} + 32 \, a^{3} b + 5 \, a^{2} b^{2} + 50 \, a b^{3} + 45 \, b^{4} + 15 \, {\left(16 \, a^{4} + 23 \, a^{3} b - 45 \, a b^{3} - 30 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 32 \, a^{4} + 164 \, a^{3} b + 292 \, a^{2} b^{2} + 220 \, a b^{3} + 60 \, b^{4} + 32 \, {\left(7 \, {\left(8 \, a^{4} + 23 \, a^{3} b + 45 \, a^{2} b^{2} + 45 \, a b^{3} + 15 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(16 \, a^{4} + 23 \, a^{3} b - 45 \, a b^{3} - 30 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(24 \, a^{4} + 32 \, a^{3} b + 5 \, a^{2} b^{2} + 50 \, a b^{3} + 45 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 8 \, {\left(16 \, a^{4} + 41 \, a^{3} b - 55 \, a b^{3} - 30 \, b^{4}\right)} \cosh\left(d x + c\right)^{2} + 8 \, {\left(14 \, {\left(8 \, a^{4} + 23 \, a^{3} b + 45 \, a^{2} b^{2} + 45 \, a b^{3} + 15 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(16 \, a^{4} + 23 \, a^{3} b - 45 \, a b^{3} - 30 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 16 \, a^{4} + 41 \, a^{3} b - 55 \, a b^{3} - 30 \, b^{4} + 6 \, {\left(24 \, a^{4} + 32 \, a^{3} b + 5 \, a^{2} b^{2} + 50 \, a b^{3} + 45 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} - 15 \, {\left({\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{10} + 10 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} \sinh\left(d x + c\right)^{10} + {\left(3 \, a^{4} + 4 \, a^{3} b - 6 \, a^{2} b^{2} - 12 \, a b^{3} - 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{8} + {\left(3 \, a^{4} + 4 \, a^{3} b - 6 \, a^{2} b^{2} - 12 \, a b^{3} - 5 \, b^{4} + 45 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, 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)^{8} + 8 \, {\left(15 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{4} + 4 \, a^{3} b - 6 \, a^{2} b^{2} - 12 \, a b^{3} - 5 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + 8 \, a b^{3} + 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(105 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{4} + a^{4} + 2 \, a^{2} b^{2} + 8 \, a b^{3} + 5 \, b^{4} + 14 \, {\left(3 \, a^{4} + 4 \, a^{3} b - 6 \, a^{2} b^{2} - 12 \, a b^{3} - 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(63 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{5} + 14 \, {\left(3 \, a^{4} + 4 \, a^{3} b - 6 \, a^{2} b^{2} - 12 \, a b^{3} - 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{4} + 2 \, a^{2} b^{2} + 8 \, a b^{3} + 5 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + 8 \, a b^{3} + 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(105 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{6} + 35 \, {\left(3 \, a^{4} + 4 \, a^{3} b - 6 \, a^{2} b^{2} - 12 \, a b^{3} - 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} - a^{4} - 2 \, a^{2} b^{2} - 8 \, a b^{3} - 5 \, b^{4} + 15 \, {\left(a^{4} + 2 \, a^{2} b^{2} + 8 \, a b^{3} + 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} - a^{4} - 4 \, a^{3} b - 6 \, a^{2} b^{2} - 4 \, a b^{3} - b^{4} + 8 \, {\left(15 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{7} + 7 \, {\left(3 \, a^{4} + 4 \, a^{3} b - 6 \, a^{2} b^{2} - 12 \, a b^{3} - 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(a^{4} + 2 \, a^{2} b^{2} + 8 \, a b^{3} + 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} - {\left(a^{4} + 2 \, a^{2} b^{2} + 8 \, a b^{3} + 5 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - {\left(3 \, a^{4} + 4 \, a^{3} b - 6 \, a^{2} b^{2} - 12 \, a b^{3} - 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{2} + {\left(45 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{8} + 28 \, {\left(3 \, a^{4} + 4 \, a^{3} b - 6 \, a^{2} b^{2} - 12 \, a b^{3} - 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 30 \, {\left(a^{4} + 2 \, a^{2} b^{2} + 8 \, a b^{3} + 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} - 3 \, a^{4} - 4 \, a^{3} b + 6 \, a^{2} b^{2} + 12 \, a b^{3} + 5 \, b^{4} - 12 \, {\left(a^{4} + 2 \, a^{2} b^{2} + 8 \, a b^{3} + 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(5 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{9} + 4 \, {\left(3 \, a^{4} + 4 \, a^{3} b - 6 \, a^{2} b^{2} - 12 \, a b^{3} - 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{7} + 6 \, {\left(a^{4} + 2 \, a^{2} b^{2} + 8 \, a b^{3} + 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} - 4 \, {\left(a^{4} + 2 \, a^{2} b^{2} + 8 \, a b^{3} + 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} - {\left(3 \, a^{4} + 4 \, a^{3} b - 6 \, a^{2} b^{2} - 12 \, a b^{3} - 5 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{{\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) \sinh\left(d x + c\right)^{3} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{2} + a^{2} - 6 \, a b + b^{2} + 4 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) - 4 \, {\left({\left(a^{2} + a b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} + a b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} + a b\right)} \sinh\left(d x + c\right)^{2} + a^{2} - a b\right)} \sqrt{-\frac{b}{a}}}{{\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) + 16 \, {\left(2 \, {\left(8 \, a^{4} + 23 \, a^{3} b + 45 \, a^{2} b^{2} + 45 \, a b^{3} + 15 \, b^{4}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(16 \, a^{4} + 23 \, a^{3} b - 45 \, a b^{3} - 30 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(24 \, a^{4} + 32 \, a^{3} b + 5 \, a^{2} b^{2} + 50 \, a b^{3} + 45 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(16 \, a^{4} + 41 \, a^{3} b - 55 \, a b^{3} - 30 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{16 \, {\left({\left(a^{7} + 4 \, a^{6} b + 6 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{10} + 10 \, {\left(a^{7} + 4 \, a^{6} b + 6 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + a^{3} b^{4}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + {\left(a^{7} + 4 \, a^{6} b + 6 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + a^{3} b^{4}\right)} d \sinh\left(d x + c\right)^{10} + {\left(3 \, a^{7} + 4 \, a^{6} b - 6 \, a^{5} b^{2} - 12 \, a^{4} b^{3} - 5 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{8} + {\left(45 \, {\left(a^{7} + 4 \, a^{6} b + 6 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{7} + 4 \, a^{6} b - 6 \, a^{5} b^{2} - 12 \, a^{4} b^{3} - 5 \, a^{3} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{8} + 2 \, {\left(a^{7} + 2 \, a^{5} b^{2} + 8 \, a^{4} b^{3} + 5 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{6} + 8 \, {\left(15 \, {\left(a^{7} + 4 \, a^{6} b + 6 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{7} + 4 \, a^{6} b - 6 \, a^{5} b^{2} - 12 \, a^{4} b^{3} - 5 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(105 \, {\left(a^{7} + 4 \, a^{6} b + 6 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 14 \, {\left(3 \, a^{7} + 4 \, a^{6} b - 6 \, a^{5} b^{2} - 12 \, a^{4} b^{3} - 5 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{7} + 2 \, a^{5} b^{2} + 8 \, a^{4} b^{3} + 5 \, a^{3} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{6} - 2 \, {\left(a^{7} + 2 \, a^{5} b^{2} + 8 \, a^{4} b^{3} + 5 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(63 \, {\left(a^{7} + 4 \, a^{6} b + 6 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{5} + 14 \, {\left(3 \, a^{7} + 4 \, a^{6} b - 6 \, a^{5} b^{2} - 12 \, a^{4} b^{3} - 5 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{7} + 2 \, a^{5} b^{2} + 8 \, a^{4} b^{3} + 5 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(105 \, {\left(a^{7} + 4 \, a^{6} b + 6 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{6} + 35 \, {\left(3 \, a^{7} + 4 \, a^{6} b - 6 \, a^{5} b^{2} - 12 \, a^{4} b^{3} - 5 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 15 \, {\left(a^{7} + 2 \, a^{5} b^{2} + 8 \, a^{4} b^{3} + 5 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{7} + 2 \, a^{5} b^{2} + 8 \, a^{4} b^{3} + 5 \, a^{3} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{4} - {\left(3 \, a^{7} + 4 \, a^{6} b - 6 \, a^{5} b^{2} - 12 \, a^{4} b^{3} - 5 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(15 \, {\left(a^{7} + 4 \, a^{6} b + 6 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{7} + 7 \, {\left(3 \, a^{7} + 4 \, a^{6} b - 6 \, a^{5} b^{2} - 12 \, a^{4} b^{3} - 5 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{5} + 5 \, {\left(a^{7} + 2 \, a^{5} b^{2} + 8 \, a^{4} b^{3} + 5 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a^{7} + 2 \, a^{5} b^{2} + 8 \, a^{4} b^{3} + 5 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(45 \, {\left(a^{7} + 4 \, a^{6} b + 6 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{8} + 28 \, {\left(3 \, a^{7} + 4 \, a^{6} b - 6 \, a^{5} b^{2} - 12 \, a^{4} b^{3} - 5 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{6} + 30 \, {\left(a^{7} + 2 \, a^{5} b^{2} + 8 \, a^{4} b^{3} + 5 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{4} - 12 \, {\left(a^{7} + 2 \, a^{5} b^{2} + 8 \, a^{4} b^{3} + 5 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{2} - {\left(3 \, a^{7} + 4 \, a^{6} b - 6 \, a^{5} b^{2} - 12 \, a^{4} b^{3} - 5 \, a^{3} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{2} - {\left(a^{7} + 4 \, a^{6} b + 6 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + a^{3} b^{4}\right)} d + 2 \, {\left(5 \, {\left(a^{7} + 4 \, a^{6} b + 6 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{9} + 4 \, {\left(3 \, a^{7} + 4 \, a^{6} b - 6 \, a^{5} b^{2} - 12 \, a^{4} b^{3} - 5 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{7} + 6 \, {\left(a^{7} + 2 \, a^{5} b^{2} + 8 \, a^{4} b^{3} + 5 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{5} - 4 \, {\left(a^{7} + 2 \, a^{5} b^{2} + 8 \, a^{4} b^{3} + 5 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{3} - {\left(3 \, a^{7} + 4 \, a^{6} b - 6 \, a^{5} b^{2} - 12 \, a^{4} b^{3} - 5 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}, -\frac{2 \, {\left(8 \, a^{4} + 23 \, a^{3} b + 45 \, a^{2} b^{2} + 45 \, a b^{3} + 15 \, b^{4}\right)} \cosh\left(d x + c\right)^{8} + 16 \, {\left(8 \, a^{4} + 23 \, a^{3} b + 45 \, a^{2} b^{2} + 45 \, a b^{3} + 15 \, b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + 2 \, {\left(8 \, a^{4} + 23 \, a^{3} b + 45 \, a^{2} b^{2} + 45 \, a b^{3} + 15 \, b^{4}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(16 \, a^{4} + 23 \, a^{3} b - 45 \, a b^{3} - 30 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(16 \, a^{4} + 23 \, a^{3} b - 45 \, a b^{3} - 30 \, b^{4} + 14 \, {\left(8 \, a^{4} + 23 \, a^{3} b + 45 \, a^{2} b^{2} + 45 \, a b^{3} + 15 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(14 \, {\left(8 \, a^{4} + 23 \, a^{3} b + 45 \, a^{2} b^{2} + 45 \, a b^{3} + 15 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(16 \, a^{4} + 23 \, a^{3} b - 45 \, a b^{3} - 30 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 4 \, {\left(24 \, a^{4} + 32 \, a^{3} b + 5 \, a^{2} b^{2} + 50 \, a b^{3} + 45 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(35 \, {\left(8 \, a^{4} + 23 \, a^{3} b + 45 \, a^{2} b^{2} + 45 \, a b^{3} + 15 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 24 \, a^{4} + 32 \, a^{3} b + 5 \, a^{2} b^{2} + 50 \, a b^{3} + 45 \, b^{4} + 15 \, {\left(16 \, a^{4} + 23 \, a^{3} b - 45 \, a b^{3} - 30 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 16 \, a^{4} + 82 \, a^{3} b + 146 \, a^{2} b^{2} + 110 \, a b^{3} + 30 \, b^{4} + 16 \, {\left(7 \, {\left(8 \, a^{4} + 23 \, a^{3} b + 45 \, a^{2} b^{2} + 45 \, a b^{3} + 15 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(16 \, a^{4} + 23 \, a^{3} b - 45 \, a b^{3} - 30 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(24 \, a^{4} + 32 \, a^{3} b + 5 \, a^{2} b^{2} + 50 \, a b^{3} + 45 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(16 \, a^{4} + 41 \, a^{3} b - 55 \, a b^{3} - 30 \, b^{4}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(14 \, {\left(8 \, a^{4} + 23 \, a^{3} b + 45 \, a^{2} b^{2} + 45 \, a b^{3} + 15 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(16 \, a^{4} + 23 \, a^{3} b - 45 \, a b^{3} - 30 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 16 \, a^{4} + 41 \, a^{3} b - 55 \, a b^{3} - 30 \, b^{4} + 6 \, {\left(24 \, a^{4} + 32 \, a^{3} b + 5 \, a^{2} b^{2} + 50 \, a b^{3} + 45 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 15 \, {\left({\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{10} + 10 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} \sinh\left(d x + c\right)^{10} + {\left(3 \, a^{4} + 4 \, a^{3} b - 6 \, a^{2} b^{2} - 12 \, a b^{3} - 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{8} + {\left(3 \, a^{4} + 4 \, a^{3} b - 6 \, a^{2} b^{2} - 12 \, a b^{3} - 5 \, b^{4} + 45 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, 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)^{8} + 8 \, {\left(15 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{4} + 4 \, a^{3} b - 6 \, a^{2} b^{2} - 12 \, a b^{3} - 5 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + 8 \, a b^{3} + 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(105 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{4} + a^{4} + 2 \, a^{2} b^{2} + 8 \, a b^{3} + 5 \, b^{4} + 14 \, {\left(3 \, a^{4} + 4 \, a^{3} b - 6 \, a^{2} b^{2} - 12 \, a b^{3} - 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(63 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{5} + 14 \, {\left(3 \, a^{4} + 4 \, a^{3} b - 6 \, a^{2} b^{2} - 12 \, a b^{3} - 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{4} + 2 \, a^{2} b^{2} + 8 \, a b^{3} + 5 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 2 \, {\left(a^{4} + 2 \, a^{2} b^{2} + 8 \, a b^{3} + 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(105 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{6} + 35 \, {\left(3 \, a^{4} + 4 \, a^{3} b - 6 \, a^{2} b^{2} - 12 \, a b^{3} - 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} - a^{4} - 2 \, a^{2} b^{2} - 8 \, a b^{3} - 5 \, b^{4} + 15 \, {\left(a^{4} + 2 \, a^{2} b^{2} + 8 \, a b^{3} + 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} - a^{4} - 4 \, a^{3} b - 6 \, a^{2} b^{2} - 4 \, a b^{3} - b^{4} + 8 \, {\left(15 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{7} + 7 \, {\left(3 \, a^{4} + 4 \, a^{3} b - 6 \, a^{2} b^{2} - 12 \, a b^{3} - 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(a^{4} + 2 \, a^{2} b^{2} + 8 \, a b^{3} + 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} - {\left(a^{4} + 2 \, a^{2} b^{2} + 8 \, a b^{3} + 5 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - {\left(3 \, a^{4} + 4 \, a^{3} b - 6 \, a^{2} b^{2} - 12 \, a b^{3} - 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{2} + {\left(45 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{8} + 28 \, {\left(3 \, a^{4} + 4 \, a^{3} b - 6 \, a^{2} b^{2} - 12 \, a b^{3} - 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 30 \, {\left(a^{4} + 2 \, a^{2} b^{2} + 8 \, a b^{3} + 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} - 3 \, a^{4} - 4 \, a^{3} b + 6 \, a^{2} b^{2} + 12 \, a b^{3} + 5 \, b^{4} - 12 \, {\left(a^{4} + 2 \, a^{2} b^{2} + 8 \, a b^{3} + 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(5 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{9} + 4 \, {\left(3 \, a^{4} + 4 \, a^{3} b - 6 \, a^{2} b^{2} - 12 \, a b^{3} - 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{7} + 6 \, {\left(a^{4} + 2 \, a^{2} b^{2} + 8 \, a b^{3} + 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} - 4 \, {\left(a^{4} + 2 \, a^{2} b^{2} + 8 \, a b^{3} + 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} - {\left(3 \, a^{4} + 4 \, a^{3} b - 6 \, a^{2} b^{2} - 12 \, a b^{3} - 5 \, 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({\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} + a - b\right)} \sqrt{\frac{b}{a}}}{2 \, b}\right) + 8 \, {\left(2 \, {\left(8 \, a^{4} + 23 \, a^{3} b + 45 \, a^{2} b^{2} + 45 \, a b^{3} + 15 \, b^{4}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(16 \, a^{4} + 23 \, a^{3} b - 45 \, a b^{3} - 30 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(24 \, a^{4} + 32 \, a^{3} b + 5 \, a^{2} b^{2} + 50 \, a b^{3} + 45 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(16 \, a^{4} + 41 \, a^{3} b - 55 \, a b^{3} - 30 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{8 \, {\left({\left(a^{7} + 4 \, a^{6} b + 6 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{10} + 10 \, {\left(a^{7} + 4 \, a^{6} b + 6 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + a^{3} b^{4}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + {\left(a^{7} + 4 \, a^{6} b + 6 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + a^{3} b^{4}\right)} d \sinh\left(d x + c\right)^{10} + {\left(3 \, a^{7} + 4 \, a^{6} b - 6 \, a^{5} b^{2} - 12 \, a^{4} b^{3} - 5 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{8} + {\left(45 \, {\left(a^{7} + 4 \, a^{6} b + 6 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{7} + 4 \, a^{6} b - 6 \, a^{5} b^{2} - 12 \, a^{4} b^{3} - 5 \, a^{3} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{8} + 2 \, {\left(a^{7} + 2 \, a^{5} b^{2} + 8 \, a^{4} b^{3} + 5 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{6} + 8 \, {\left(15 \, {\left(a^{7} + 4 \, a^{6} b + 6 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{7} + 4 \, a^{6} b - 6 \, a^{5} b^{2} - 12 \, a^{4} b^{3} - 5 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(105 \, {\left(a^{7} + 4 \, a^{6} b + 6 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 14 \, {\left(3 \, a^{7} + 4 \, a^{6} b - 6 \, a^{5} b^{2} - 12 \, a^{4} b^{3} - 5 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{7} + 2 \, a^{5} b^{2} + 8 \, a^{4} b^{3} + 5 \, a^{3} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{6} - 2 \, {\left(a^{7} + 2 \, a^{5} b^{2} + 8 \, a^{4} b^{3} + 5 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(63 \, {\left(a^{7} + 4 \, a^{6} b + 6 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{5} + 14 \, {\left(3 \, a^{7} + 4 \, a^{6} b - 6 \, a^{5} b^{2} - 12 \, a^{4} b^{3} - 5 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{7} + 2 \, a^{5} b^{2} + 8 \, a^{4} b^{3} + 5 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(105 \, {\left(a^{7} + 4 \, a^{6} b + 6 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{6} + 35 \, {\left(3 \, a^{7} + 4 \, a^{6} b - 6 \, a^{5} b^{2} - 12 \, a^{4} b^{3} - 5 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 15 \, {\left(a^{7} + 2 \, a^{5} b^{2} + 8 \, a^{4} b^{3} + 5 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{7} + 2 \, a^{5} b^{2} + 8 \, a^{4} b^{3} + 5 \, a^{3} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{4} - {\left(3 \, a^{7} + 4 \, a^{6} b - 6 \, a^{5} b^{2} - 12 \, a^{4} b^{3} - 5 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(15 \, {\left(a^{7} + 4 \, a^{6} b + 6 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{7} + 7 \, {\left(3 \, a^{7} + 4 \, a^{6} b - 6 \, a^{5} b^{2} - 12 \, a^{4} b^{3} - 5 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{5} + 5 \, {\left(a^{7} + 2 \, a^{5} b^{2} + 8 \, a^{4} b^{3} + 5 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a^{7} + 2 \, a^{5} b^{2} + 8 \, a^{4} b^{3} + 5 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(45 \, {\left(a^{7} + 4 \, a^{6} b + 6 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{8} + 28 \, {\left(3 \, a^{7} + 4 \, a^{6} b - 6 \, a^{5} b^{2} - 12 \, a^{4} b^{3} - 5 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{6} + 30 \, {\left(a^{7} + 2 \, a^{5} b^{2} + 8 \, a^{4} b^{3} + 5 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{4} - 12 \, {\left(a^{7} + 2 \, a^{5} b^{2} + 8 \, a^{4} b^{3} + 5 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{2} - {\left(3 \, a^{7} + 4 \, a^{6} b - 6 \, a^{5} b^{2} - 12 \, a^{4} b^{3} - 5 \, a^{3} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{2} - {\left(a^{7} + 4 \, a^{6} b + 6 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + a^{3} b^{4}\right)} d + 2 \, {\left(5 \, {\left(a^{7} + 4 \, a^{6} b + 6 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{9} + 4 \, {\left(3 \, a^{7} + 4 \, a^{6} b - 6 \, a^{5} b^{2} - 12 \, a^{4} b^{3} - 5 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{7} + 6 \, {\left(a^{7} + 2 \, a^{5} b^{2} + 8 \, a^{4} b^{3} + 5 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{5} - 4 \, {\left(a^{7} + 2 \, a^{5} b^{2} + 8 \, a^{4} b^{3} + 5 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{3} - {\left(3 \, a^{7} + 4 \, a^{6} b - 6 \, a^{5} b^{2} - 12 \, a^{4} b^{3} - 5 \, 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*(8*a^4 + 23*a^3*b + 45*a^2*b^2 + 45*a*b^3 + 15*b^4)*cosh(d*x + c)^8 + 32*(8*a^4 + 23*a^3*b + 45*a^2*b^2 + 45*a*b^3 + 15*b^4)*cosh(d*x + c)*sinh(d*x + c)^7 + 4*(8*a^4 + 23*a^3*b + 45*a^2*b^2 + 45*a*b^3 + 15*b^4)*sinh(d*x + c)^8 + 8*(16*a^4 + 23*a^3*b - 45*a*b^3 - 30*b^4)*cosh(d*x + c)^6 + 8*(16*a^4 + 23*a^3*b - 45*a*b^3 - 30*b^4 + 14*(8*a^4 + 23*a^3*b + 45*a^2*b^2 + 45*a*b^3 + 15*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 16*(14*(8*a^4 + 23*a^3*b + 45*a^2*b^2 + 45*a*b^3 + 15*b^4)*cosh(d*x + c)^3 + 3*(16*a^4 + 23*a^3*b - 45*a*b^3 - 30*b^4)*cosh(d*x + c))*sinh(d*x + c)^5 + 8*(24*a^4 + 32*a^3*b + 5*a^2*b^2 + 50*a*b^3 + 45*b^4)*cosh(d*x + c)^4 + 8*(35*(8*a^4 + 23*a^3*b + 45*a^2*b^2 + 45*a*b^3 + 15*b^4)*cosh(d*x + c)^4 + 24*a^4 + 32*a^3*b + 5*a^2*b^2 + 50*a*b^3 + 45*b^4 + 15*(16*a^4 + 23*a^3*b - 45*a*b^3 - 30*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 32*a^4 + 164*a^3*b + 292*a^2*b^2 + 220*a*b^3 + 60*b^4 + 32*(7*(8*a^4 + 23*a^3*b + 45*a^2*b^2 + 45*a*b^3 + 15*b^4)*cosh(d*x + c)^5 + 5*(16*a^4 + 23*a^3*b - 45*a*b^3 - 30*b^4)*cosh(d*x + c)^3 + (24*a^4 + 32*a^3*b + 5*a^2*b^2 + 50*a*b^3 + 45*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 8*(16*a^4 + 41*a^3*b - 55*a*b^3 - 30*b^4)*cosh(d*x + c)^2 + 8*(14*(8*a^4 + 23*a^3*b + 45*a^2*b^2 + 45*a*b^3 + 15*b^4)*cosh(d*x + c)^6 + 15*(16*a^4 + 23*a^3*b - 45*a*b^3 - 30*b^4)*cosh(d*x + c)^4 + 16*a^4 + 41*a^3*b - 55*a*b^3 - 30*b^4 + 6*(24*a^4 + 32*a^3*b + 5*a^2*b^2 + 50*a*b^3 + 45*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - 15*((a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*cosh(d*x + c)^10 + 10*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*cosh(d*x + c)*sinh(d*x + c)^9 + (a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*sinh(d*x + c)^10 + (3*a^4 + 4*a^3*b - 6*a^2*b^2 - 12*a*b^3 - 5*b^4)*cosh(d*x + c)^8 + (3*a^4 + 4*a^3*b - 6*a^2*b^2 - 12*a*b^3 - 5*b^4 + 45*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 8*(15*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*cosh(d*x + c)^3 + (3*a^4 + 4*a^3*b - 6*a^2*b^2 - 12*a*b^3 - 5*b^4)*cosh(d*x + c))*sinh(d*x + c)^7 + 2*(a^4 + 2*a^2*b^2 + 8*a*b^3 + 5*b^4)*cosh(d*x + c)^6 + 2*(105*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*cosh(d*x + c)^4 + a^4 + 2*a^2*b^2 + 8*a*b^3 + 5*b^4 + 14*(3*a^4 + 4*a^3*b - 6*a^2*b^2 - 12*a*b^3 - 5*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 4*(63*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*cosh(d*x + c)^5 + 14*(3*a^4 + 4*a^3*b - 6*a^2*b^2 - 12*a*b^3 - 5*b^4)*cosh(d*x + c)^3 + 3*(a^4 + 2*a^2*b^2 + 8*a*b^3 + 5*b^4)*cosh(d*x + c))*sinh(d*x + c)^5 - 2*(a^4 + 2*a^2*b^2 + 8*a*b^3 + 5*b^4)*cosh(d*x + c)^4 + 2*(105*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*cosh(d*x + c)^6 + 35*(3*a^4 + 4*a^3*b - 6*a^2*b^2 - 12*a*b^3 - 5*b^4)*cosh(d*x + c)^4 - a^4 - 2*a^2*b^2 - 8*a*b^3 - 5*b^4 + 15*(a^4 + 2*a^2*b^2 + 8*a*b^3 + 5*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 - a^4 - 4*a^3*b - 6*a^2*b^2 - 4*a*b^3 - b^4 + 8*(15*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*cosh(d*x + c)^7 + 7*(3*a^4 + 4*a^3*b - 6*a^2*b^2 - 12*a*b^3 - 5*b^4)*cosh(d*x + c)^5 + 5*(a^4 + 2*a^2*b^2 + 8*a*b^3 + 5*b^4)*cosh(d*x + c)^3 - (a^4 + 2*a^2*b^2 + 8*a*b^3 + 5*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 - (3*a^4 + 4*a^3*b - 6*a^2*b^2 - 12*a*b^3 - 5*b^4)*cosh(d*x + c)^2 + (45*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*cosh(d*x + c)^8 + 28*(3*a^4 + 4*a^3*b - 6*a^2*b^2 - 12*a*b^3 - 5*b^4)*cosh(d*x + c)^6 + 30*(a^4 + 2*a^2*b^2 + 8*a*b^3 + 5*b^4)*cosh(d*x + c)^4 - 3*a^4 - 4*a^3*b + 6*a^2*b^2 + 12*a*b^3 + 5*b^4 - 12*(a^4 + 2*a^2*b^2 + 8*a*b^3 + 5*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 2*(5*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*cosh(d*x + c)^9 + 4*(3*a^4 + 4*a^3*b - 6*a^2*b^2 - 12*a*b^3 - 5*b^4)*cosh(d*x + c)^7 + 6*(a^4 + 2*a^2*b^2 + 8*a*b^3 + 5*b^4)*cosh(d*x + c)^5 - 4*(a^4 + 2*a^2*b^2 + 8*a*b^3 + 5*b^4)*cosh(d*x + c)^3 - (3*a^4 + 4*a^3*b - 6*a^2*b^2 - 12*a*b^3 - 5*b^4)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-b/a)*log(((a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 + 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 + 2*(a^2 - b^2)*cosh(d*x + c)^2 + 2*(3*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + a^2 - b^2)*sinh(d*x + c)^2 + a^2 - 6*a*b + b^2 + 4*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 + (a^2 - b^2)*cosh(d*x + c))*sinh(d*x + c) - 4*((a^2 + a*b)*cosh(d*x + c)^2 + 2*(a^2 + a*b)*cosh(d*x + c)*sinh(d*x + c) + (a^2 + a*b)*sinh(d*x + c)^2 + a^2 - a*b)*sqrt(-b/a))/((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)) + 16*(2*(8*a^4 + 23*a^3*b + 45*a^2*b^2 + 45*a*b^3 + 15*b^4)*cosh(d*x + c)^7 + 3*(16*a^4 + 23*a^3*b - 45*a*b^3 - 30*b^4)*cosh(d*x + c)^5 + 2*(24*a^4 + 32*a^3*b + 5*a^2*b^2 + 50*a*b^3 + 45*b^4)*cosh(d*x + c)^3 + (16*a^4 + 41*a^3*b - 55*a*b^3 - 30*b^4)*cosh(d*x + c))*sinh(d*x + c))/((a^7 + 4*a^6*b + 6*a^5*b^2 + 4*a^4*b^3 + a^3*b^4)*d*cosh(d*x + c)^10 + 10*(a^7 + 4*a^6*b + 6*a^5*b^2 + 4*a^4*b^3 + a^3*b^4)*d*cosh(d*x + c)*sinh(d*x + c)^9 + (a^7 + 4*a^6*b + 6*a^5*b^2 + 4*a^4*b^3 + a^3*b^4)*d*sinh(d*x + c)^10 + (3*a^7 + 4*a^6*b - 6*a^5*b^2 - 12*a^4*b^3 - 5*a^3*b^4)*d*cosh(d*x + c)^8 + (45*(a^7 + 4*a^6*b + 6*a^5*b^2 + 4*a^4*b^3 + a^3*b^4)*d*cosh(d*x + c)^2 + (3*a^7 + 4*a^6*b - 6*a^5*b^2 - 12*a^4*b^3 - 5*a^3*b^4)*d)*sinh(d*x + c)^8 + 2*(a^7 + 2*a^5*b^2 + 8*a^4*b^3 + 5*a^3*b^4)*d*cosh(d*x + c)^6 + 8*(15*(a^7 + 4*a^6*b + 6*a^5*b^2 + 4*a^4*b^3 + a^3*b^4)*d*cosh(d*x + c)^3 + (3*a^7 + 4*a^6*b - 6*a^5*b^2 - 12*a^4*b^3 - 5*a^3*b^4)*d*cosh(d*x + c))*sinh(d*x + c)^7 + 2*(105*(a^7 + 4*a^6*b + 6*a^5*b^2 + 4*a^4*b^3 + a^3*b^4)*d*cosh(d*x + c)^4 + 14*(3*a^7 + 4*a^6*b - 6*a^5*b^2 - 12*a^4*b^3 - 5*a^3*b^4)*d*cosh(d*x + c)^2 + (a^7 + 2*a^5*b^2 + 8*a^4*b^3 + 5*a^3*b^4)*d)*sinh(d*x + c)^6 - 2*(a^7 + 2*a^5*b^2 + 8*a^4*b^3 + 5*a^3*b^4)*d*cosh(d*x + c)^4 + 4*(63*(a^7 + 4*a^6*b + 6*a^5*b^2 + 4*a^4*b^3 + a^3*b^4)*d*cosh(d*x + c)^5 + 14*(3*a^7 + 4*a^6*b - 6*a^5*b^2 - 12*a^4*b^3 - 5*a^3*b^4)*d*cosh(d*x + c)^3 + 3*(a^7 + 2*a^5*b^2 + 8*a^4*b^3 + 5*a^3*b^4)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(105*(a^7 + 4*a^6*b + 6*a^5*b^2 + 4*a^4*b^3 + a^3*b^4)*d*cosh(d*x + c)^6 + 35*(3*a^7 + 4*a^6*b - 6*a^5*b^2 - 12*a^4*b^3 - 5*a^3*b^4)*d*cosh(d*x + c)^4 + 15*(a^7 + 2*a^5*b^2 + 8*a^4*b^3 + 5*a^3*b^4)*d*cosh(d*x + c)^2 - (a^7 + 2*a^5*b^2 + 8*a^4*b^3 + 5*a^3*b^4)*d)*sinh(d*x + c)^4 - (3*a^7 + 4*a^6*b - 6*a^5*b^2 - 12*a^4*b^3 - 5*a^3*b^4)*d*cosh(d*x + c)^2 + 8*(15*(a^7 + 4*a^6*b + 6*a^5*b^2 + 4*a^4*b^3 + a^3*b^4)*d*cosh(d*x + c)^7 + 7*(3*a^7 + 4*a^6*b - 6*a^5*b^2 - 12*a^4*b^3 - 5*a^3*b^4)*d*cosh(d*x + c)^5 + 5*(a^7 + 2*a^5*b^2 + 8*a^4*b^3 + 5*a^3*b^4)*d*cosh(d*x + c)^3 - (a^7 + 2*a^5*b^2 + 8*a^4*b^3 + 5*a^3*b^4)*d*cosh(d*x + c))*sinh(d*x + c)^3 + (45*(a^7 + 4*a^6*b + 6*a^5*b^2 + 4*a^4*b^3 + a^3*b^4)*d*cosh(d*x + c)^8 + 28*(3*a^7 + 4*a^6*b - 6*a^5*b^2 - 12*a^4*b^3 - 5*a^3*b^4)*d*cosh(d*x + c)^6 + 30*(a^7 + 2*a^5*b^2 + 8*a^4*b^3 + 5*a^3*b^4)*d*cosh(d*x + c)^4 - 12*(a^7 + 2*a^5*b^2 + 8*a^4*b^3 + 5*a^3*b^4)*d*cosh(d*x + c)^2 - (3*a^7 + 4*a^6*b - 6*a^5*b^2 - 12*a^4*b^3 - 5*a^3*b^4)*d)*sinh(d*x + c)^2 - (a^7 + 4*a^6*b + 6*a^5*b^2 + 4*a^4*b^3 + a^3*b^4)*d + 2*(5*(a^7 + 4*a^6*b + 6*a^5*b^2 + 4*a^4*b^3 + a^3*b^4)*d*cosh(d*x + c)^9 + 4*(3*a^7 + 4*a^6*b - 6*a^5*b^2 - 12*a^4*b^3 - 5*a^3*b^4)*d*cosh(d*x + c)^7 + 6*(a^7 + 2*a^5*b^2 + 8*a^4*b^3 + 5*a^3*b^4)*d*cosh(d*x + c)^5 - 4*(a^7 + 2*a^5*b^2 + 8*a^4*b^3 + 5*a^3*b^4)*d*cosh(d*x + c)^3 - (3*a^7 + 4*a^6*b - 6*a^5*b^2 - 12*a^4*b^3 - 5*a^3*b^4)*d*cosh(d*x + c))*sinh(d*x + c)), -1/8*(2*(8*a^4 + 23*a^3*b + 45*a^2*b^2 + 45*a*b^3 + 15*b^4)*cosh(d*x + c)^8 + 16*(8*a^4 + 23*a^3*b + 45*a^2*b^2 + 45*a*b^3 + 15*b^4)*cosh(d*x + c)*sinh(d*x + c)^7 + 2*(8*a^4 + 23*a^3*b + 45*a^2*b^2 + 45*a*b^3 + 15*b^4)*sinh(d*x + c)^8 + 4*(16*a^4 + 23*a^3*b - 45*a*b^3 - 30*b^4)*cosh(d*x + c)^6 + 4*(16*a^4 + 23*a^3*b - 45*a*b^3 - 30*b^4 + 14*(8*a^4 + 23*a^3*b + 45*a^2*b^2 + 45*a*b^3 + 15*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(14*(8*a^4 + 23*a^3*b + 45*a^2*b^2 + 45*a*b^3 + 15*b^4)*cosh(d*x + c)^3 + 3*(16*a^4 + 23*a^3*b - 45*a*b^3 - 30*b^4)*cosh(d*x + c))*sinh(d*x + c)^5 + 4*(24*a^4 + 32*a^3*b + 5*a^2*b^2 + 50*a*b^3 + 45*b^4)*cosh(d*x + c)^4 + 4*(35*(8*a^4 + 23*a^3*b + 45*a^2*b^2 + 45*a*b^3 + 15*b^4)*cosh(d*x + c)^4 + 24*a^4 + 32*a^3*b + 5*a^2*b^2 + 50*a*b^3 + 45*b^4 + 15*(16*a^4 + 23*a^3*b - 45*a*b^3 - 30*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 16*a^4 + 82*a^3*b + 146*a^2*b^2 + 110*a*b^3 + 30*b^4 + 16*(7*(8*a^4 + 23*a^3*b + 45*a^2*b^2 + 45*a*b^3 + 15*b^4)*cosh(d*x + c)^5 + 5*(16*a^4 + 23*a^3*b - 45*a*b^3 - 30*b^4)*cosh(d*x + c)^3 + (24*a^4 + 32*a^3*b + 5*a^2*b^2 + 50*a*b^3 + 45*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(16*a^4 + 41*a^3*b - 55*a*b^3 - 30*b^4)*cosh(d*x + c)^2 + 4*(14*(8*a^4 + 23*a^3*b + 45*a^2*b^2 + 45*a*b^3 + 15*b^4)*cosh(d*x + c)^6 + 15*(16*a^4 + 23*a^3*b - 45*a*b^3 - 30*b^4)*cosh(d*x + c)^4 + 16*a^4 + 41*a^3*b - 55*a*b^3 - 30*b^4 + 6*(24*a^4 + 32*a^3*b + 5*a^2*b^2 + 50*a*b^3 + 45*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 15*((a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*cosh(d*x + c)^10 + 10*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*cosh(d*x + c)*sinh(d*x + c)^9 + (a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*sinh(d*x + c)^10 + (3*a^4 + 4*a^3*b - 6*a^2*b^2 - 12*a*b^3 - 5*b^4)*cosh(d*x + c)^8 + (3*a^4 + 4*a^3*b - 6*a^2*b^2 - 12*a*b^3 - 5*b^4 + 45*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 8*(15*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*cosh(d*x + c)^3 + (3*a^4 + 4*a^3*b - 6*a^2*b^2 - 12*a*b^3 - 5*b^4)*cosh(d*x + c))*sinh(d*x + c)^7 + 2*(a^4 + 2*a^2*b^2 + 8*a*b^3 + 5*b^4)*cosh(d*x + c)^6 + 2*(105*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*cosh(d*x + c)^4 + a^4 + 2*a^2*b^2 + 8*a*b^3 + 5*b^4 + 14*(3*a^4 + 4*a^3*b - 6*a^2*b^2 - 12*a*b^3 - 5*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 4*(63*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*cosh(d*x + c)^5 + 14*(3*a^4 + 4*a^3*b - 6*a^2*b^2 - 12*a*b^3 - 5*b^4)*cosh(d*x + c)^3 + 3*(a^4 + 2*a^2*b^2 + 8*a*b^3 + 5*b^4)*cosh(d*x + c))*sinh(d*x + c)^5 - 2*(a^4 + 2*a^2*b^2 + 8*a*b^3 + 5*b^4)*cosh(d*x + c)^4 + 2*(105*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*cosh(d*x + c)^6 + 35*(3*a^4 + 4*a^3*b - 6*a^2*b^2 - 12*a*b^3 - 5*b^4)*cosh(d*x + c)^4 - a^4 - 2*a^2*b^2 - 8*a*b^3 - 5*b^4 + 15*(a^4 + 2*a^2*b^2 + 8*a*b^3 + 5*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 - a^4 - 4*a^3*b - 6*a^2*b^2 - 4*a*b^3 - b^4 + 8*(15*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*cosh(d*x + c)^7 + 7*(3*a^4 + 4*a^3*b - 6*a^2*b^2 - 12*a*b^3 - 5*b^4)*cosh(d*x + c)^5 + 5*(a^4 + 2*a^2*b^2 + 8*a*b^3 + 5*b^4)*cosh(d*x + c)^3 - (a^4 + 2*a^2*b^2 + 8*a*b^3 + 5*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 - (3*a^4 + 4*a^3*b - 6*a^2*b^2 - 12*a*b^3 - 5*b^4)*cosh(d*x + c)^2 + (45*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*cosh(d*x + c)^8 + 28*(3*a^4 + 4*a^3*b - 6*a^2*b^2 - 12*a*b^3 - 5*b^4)*cosh(d*x + c)^6 + 30*(a^4 + 2*a^2*b^2 + 8*a*b^3 + 5*b^4)*cosh(d*x + c)^4 - 3*a^4 - 4*a^3*b + 6*a^2*b^2 + 12*a*b^3 + 5*b^4 - 12*(a^4 + 2*a^2*b^2 + 8*a*b^3 + 5*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 2*(5*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*cosh(d*x + c)^9 + 4*(3*a^4 + 4*a^3*b - 6*a^2*b^2 - 12*a*b^3 - 5*b^4)*cosh(d*x + c)^7 + 6*(a^4 + 2*a^2*b^2 + 8*a*b^3 + 5*b^4)*cosh(d*x + c)^5 - 4*(a^4 + 2*a^2*b^2 + 8*a*b^3 + 5*b^4)*cosh(d*x + c)^3 - (3*a^4 + 4*a^3*b - 6*a^2*b^2 - 12*a*b^3 - 5*b^4)*cosh(d*x + c))*sinh(d*x + c))*sqrt(b/a)*arctan(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 + a - b)*sqrt(b/a)/b) + 8*(2*(8*a^4 + 23*a^3*b + 45*a^2*b^2 + 45*a*b^3 + 15*b^4)*cosh(d*x + c)^7 + 3*(16*a^4 + 23*a^3*b - 45*a*b^3 - 30*b^4)*cosh(d*x + c)^5 + 2*(24*a^4 + 32*a^3*b + 5*a^2*b^2 + 50*a*b^3 + 45*b^4)*cosh(d*x + c)^3 + (16*a^4 + 41*a^3*b - 55*a*b^3 - 30*b^4)*cosh(d*x + c))*sinh(d*x + c))/((a^7 + 4*a^6*b + 6*a^5*b^2 + 4*a^4*b^3 + a^3*b^4)*d*cosh(d*x + c)^10 + 10*(a^7 + 4*a^6*b + 6*a^5*b^2 + 4*a^4*b^3 + a^3*b^4)*d*cosh(d*x + c)*sinh(d*x + c)^9 + (a^7 + 4*a^6*b + 6*a^5*b^2 + 4*a^4*b^3 + a^3*b^4)*d*sinh(d*x + c)^10 + (3*a^7 + 4*a^6*b - 6*a^5*b^2 - 12*a^4*b^3 - 5*a^3*b^4)*d*cosh(d*x + c)^8 + (45*(a^7 + 4*a^6*b + 6*a^5*b^2 + 4*a^4*b^3 + a^3*b^4)*d*cosh(d*x + c)^2 + (3*a^7 + 4*a^6*b - 6*a^5*b^2 - 12*a^4*b^3 - 5*a^3*b^4)*d)*sinh(d*x + c)^8 + 2*(a^7 + 2*a^5*b^2 + 8*a^4*b^3 + 5*a^3*b^4)*d*cosh(d*x + c)^6 + 8*(15*(a^7 + 4*a^6*b + 6*a^5*b^2 + 4*a^4*b^3 + a^3*b^4)*d*cosh(d*x + c)^3 + (3*a^7 + 4*a^6*b - 6*a^5*b^2 - 12*a^4*b^3 - 5*a^3*b^4)*d*cosh(d*x + c))*sinh(d*x + c)^7 + 2*(105*(a^7 + 4*a^6*b + 6*a^5*b^2 + 4*a^4*b^3 + a^3*b^4)*d*cosh(d*x + c)^4 + 14*(3*a^7 + 4*a^6*b - 6*a^5*b^2 - 12*a^4*b^3 - 5*a^3*b^4)*d*cosh(d*x + c)^2 + (a^7 + 2*a^5*b^2 + 8*a^4*b^3 + 5*a^3*b^4)*d)*sinh(d*x + c)^6 - 2*(a^7 + 2*a^5*b^2 + 8*a^4*b^3 + 5*a^3*b^4)*d*cosh(d*x + c)^4 + 4*(63*(a^7 + 4*a^6*b + 6*a^5*b^2 + 4*a^4*b^3 + a^3*b^4)*d*cosh(d*x + c)^5 + 14*(3*a^7 + 4*a^6*b - 6*a^5*b^2 - 12*a^4*b^3 - 5*a^3*b^4)*d*cosh(d*x + c)^3 + 3*(a^7 + 2*a^5*b^2 + 8*a^4*b^3 + 5*a^3*b^4)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(105*(a^7 + 4*a^6*b + 6*a^5*b^2 + 4*a^4*b^3 + a^3*b^4)*d*cosh(d*x + c)^6 + 35*(3*a^7 + 4*a^6*b - 6*a^5*b^2 - 12*a^4*b^3 - 5*a^3*b^4)*d*cosh(d*x + c)^4 + 15*(a^7 + 2*a^5*b^2 + 8*a^4*b^3 + 5*a^3*b^4)*d*cosh(d*x + c)^2 - (a^7 + 2*a^5*b^2 + 8*a^4*b^3 + 5*a^3*b^4)*d)*sinh(d*x + c)^4 - (3*a^7 + 4*a^6*b - 6*a^5*b^2 - 12*a^4*b^3 - 5*a^3*b^4)*d*cosh(d*x + c)^2 + 8*(15*(a^7 + 4*a^6*b + 6*a^5*b^2 + 4*a^4*b^3 + a^3*b^4)*d*cosh(d*x + c)^7 + 7*(3*a^7 + 4*a^6*b - 6*a^5*b^2 - 12*a^4*b^3 - 5*a^3*b^4)*d*cosh(d*x + c)^5 + 5*(a^7 + 2*a^5*b^2 + 8*a^4*b^3 + 5*a^3*b^4)*d*cosh(d*x + c)^3 - (a^7 + 2*a^5*b^2 + 8*a^4*b^3 + 5*a^3*b^4)*d*cosh(d*x + c))*sinh(d*x + c)^3 + (45*(a^7 + 4*a^6*b + 6*a^5*b^2 + 4*a^4*b^3 + a^3*b^4)*d*cosh(d*x + c)^8 + 28*(3*a^7 + 4*a^6*b - 6*a^5*b^2 - 12*a^4*b^3 - 5*a^3*b^4)*d*cosh(d*x + c)^6 + 30*(a^7 + 2*a^5*b^2 + 8*a^4*b^3 + 5*a^3*b^4)*d*cosh(d*x + c)^4 - 12*(a^7 + 2*a^5*b^2 + 8*a^4*b^3 + 5*a^3*b^4)*d*cosh(d*x + c)^2 - (3*a^7 + 4*a^6*b - 6*a^5*b^2 - 12*a^4*b^3 - 5*a^3*b^4)*d)*sinh(d*x + c)^2 - (a^7 + 4*a^6*b + 6*a^5*b^2 + 4*a^4*b^3 + a^3*b^4)*d + 2*(5*(a^7 + 4*a^6*b + 6*a^5*b^2 + 4*a^4*b^3 + a^3*b^4)*d*cosh(d*x + c)^9 + 4*(3*a^7 + 4*a^6*b - 6*a^5*b^2 - 12*a^4*b^3 - 5*a^3*b^4)*d*cosh(d*x + c)^7 + 6*(a^7 + 2*a^5*b^2 + 8*a^4*b^3 + 5*a^3*b^4)*d*cosh(d*x + c)^5 - 4*(a^7 + 2*a^5*b^2 + 8*a^4*b^3 + 5*a^3*b^4)*d*cosh(d*x + c)^3 - (3*a^7 + 4*a^6*b - 6*a^5*b^2 - 12*a^4*b^3 - 5*a^3*b^4)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
47,-1,0,0,0.000000," ","integrate(csch(d*x+c)^3/(a+b*tanh(d*x+c)^2)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
48,-1,0,0,0.000000," ","integrate(csch(d*x+c)^4/(a+b*tanh(d*x+c)^2)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
49,1,1530,0,0.571027," ","integrate(sinh(d*x+c)^4*(a+b*tanh(d*x+c)^3),x, algorithm=""fricas"")","\frac{{\left(a + b\right)} \cosh\left(d x + c\right)^{12} + 12 \, {\left(a + b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{11} + {\left(a + b\right)} \sinh\left(d x + c\right)^{12} - 6 \, {\left(a + 3 \, b\right)} \cosh\left(d x + c\right)^{10} + 6 \, {\left(11 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} - a - 3 \, b\right)} \sinh\left(d x + c\right)^{10} + 20 \, {\left(11 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(a + 3 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} + 3 \, {\left(8 \, {\left(a - 8 \, b\right)} d x - 5 \, a - 13 \, b\right)} \cosh\left(d x + c\right)^{8} + 3 \, {\left(165 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{4} + 8 \, {\left(a - 8 \, b\right)} d x - 90 \, {\left(a + 3 \, b\right)} \cosh\left(d x + c\right)^{2} - 5 \, a - 13 \, b\right)} \sinh\left(d x + c\right)^{8} + 24 \, {\left(33 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{5} - 30 \, {\left(a + 3 \, b\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, {\left(a - 8 \, b\right)} d x - 5 \, a - 13 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 8 \, {\left(6 \, {\left(a - 8 \, b\right)} d x + 11 \, b\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(231 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{6} - 315 \, {\left(a + 3 \, b\right)} \cosh\left(d x + c\right)^{4} + 12 \, {\left(a - 8 \, b\right)} d x + 21 \, {\left(8 \, {\left(a - 8 \, b\right)} d x - 5 \, a - 13 \, b\right)} \cosh\left(d x + c\right)^{2} + 22 \, b\right)} \sinh\left(d x + c\right)^{6} + 24 \, {\left(33 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{7} - 63 \, {\left(a + 3 \, b\right)} \cosh\left(d x + c\right)^{5} + 7 \, {\left(8 \, {\left(a - 8 \, b\right)} d x - 5 \, a - 13 \, b\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(6 \, {\left(a - 8 \, b\right)} d x + 11 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 3 \, {\left(8 \, {\left(a - 8 \, b\right)} d x + 5 \, a - 13 \, b\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(165 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{8} - 420 \, {\left(a + 3 \, b\right)} \cosh\left(d x + c\right)^{6} + 70 \, {\left(8 \, {\left(a - 8 \, b\right)} d x - 5 \, a - 13 \, b\right)} \cosh\left(d x + c\right)^{4} + 8 \, {\left(a - 8 \, b\right)} d x + 40 \, {\left(6 \, {\left(a - 8 \, b\right)} d x + 11 \, b\right)} \cosh\left(d x + c\right)^{2} + 5 \, a - 13 \, b\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(55 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{9} - 180 \, {\left(a + 3 \, b\right)} \cosh\left(d x + c\right)^{7} + 42 \, {\left(8 \, {\left(a - 8 \, b\right)} d x - 5 \, a - 13 \, b\right)} \cosh\left(d x + c\right)^{5} + 40 \, {\left(6 \, {\left(a - 8 \, b\right)} d x + 11 \, b\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(8 \, {\left(a - 8 \, b\right)} d x + 5 \, a - 13 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 6 \, {\left(a - 3 \, b\right)} \cosh\left(d x + c\right)^{2} + 6 \, {\left(11 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{10} - 45 \, {\left(a + 3 \, b\right)} \cosh\left(d x + c\right)^{8} + 14 \, {\left(8 \, {\left(a - 8 \, b\right)} d x - 5 \, a - 13 \, b\right)} \cosh\left(d x + c\right)^{6} + 20 \, {\left(6 \, {\left(a - 8 \, b\right)} d x + 11 \, b\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(8 \, {\left(a - 8 \, b\right)} d x + 5 \, a - 13 \, b\right)} \cosh\left(d x + c\right)^{2} + a - 3 \, b\right)} \sinh\left(d x + c\right)^{2} + 192 \, {\left(b \cosh\left(d x + c\right)^{8} + 8 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + b \sinh\left(d x + c\right)^{8} + 2 \, b \cosh\left(d x + c\right)^{6} + 2 \, {\left(14 \, b \cosh\left(d x + c\right)^{2} + b\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(14 \, b \cosh\left(d x + c\right)^{3} + 3 \, b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + b \cosh\left(d x + c\right)^{4} + {\left(70 \, b \cosh\left(d x + c\right)^{4} + 30 \, b \cosh\left(d x + c\right)^{2} + b\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(14 \, b \cosh\left(d x + c\right)^{5} + 10 \, b \cosh\left(d x + c\right)^{3} + b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(14 \, b \cosh\left(d x + c\right)^{6} + 15 \, b \cosh\left(d x + c\right)^{4} + 3 \, b \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(2 \, b \cosh\left(d x + c\right)^{7} + 3 \, b \cosh\left(d x + c\right)^{5} + b \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right)\right)} \log\left(\frac{2 \, \cosh\left(d x + c\right)}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) + 12 \, {\left({\left(a + b\right)} \cosh\left(d x + c\right)^{11} - 5 \, {\left(a + 3 \, b\right)} \cosh\left(d x + c\right)^{9} + 2 \, {\left(8 \, {\left(a - 8 \, b\right)} d x - 5 \, a - 13 \, b\right)} \cosh\left(d x + c\right)^{7} + 4 \, {\left(6 \, {\left(a - 8 \, b\right)} d x + 11 \, b\right)} \cosh\left(d x + c\right)^{5} + {\left(8 \, {\left(a - 8 \, b\right)} d x + 5 \, a - 13 \, 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 + b}{64 \, {\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} + 2 \, d \cosh\left(d x + c\right)^{6} + 2 \, {\left(14 \, d \cosh\left(d x + c\right)^{2} + d\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(14 \, d \cosh\left(d x + c\right)^{3} + 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(70 \, d \cosh\left(d x + c\right)^{4} + 30 \, d \cosh\left(d x + c\right)^{2} + d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(14 \, d \cosh\left(d x + c\right)^{5} + 10 \, d \cosh\left(d x + c\right)^{3} + d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(14 \, d \cosh\left(d x + c\right)^{6} + 15 \, d \cosh\left(d x + c\right)^{4} + 3 \, d \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(2 \, d \cosh\left(d x + c\right)^{7} + 3 \, 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*((a + b)*cosh(d*x + c)^12 + 12*(a + b)*cosh(d*x + c)*sinh(d*x + c)^11 + (a + b)*sinh(d*x + c)^12 - 6*(a + 3*b)*cosh(d*x + c)^10 + 6*(11*(a + b)*cosh(d*x + c)^2 - a - 3*b)*sinh(d*x + c)^10 + 20*(11*(a + b)*cosh(d*x + c)^3 - 3*(a + 3*b)*cosh(d*x + c))*sinh(d*x + c)^9 + 3*(8*(a - 8*b)*d*x - 5*a - 13*b)*cosh(d*x + c)^8 + 3*(165*(a + b)*cosh(d*x + c)^4 + 8*(a - 8*b)*d*x - 90*(a + 3*b)*cosh(d*x + c)^2 - 5*a - 13*b)*sinh(d*x + c)^8 + 24*(33*(a + b)*cosh(d*x + c)^5 - 30*(a + 3*b)*cosh(d*x + c)^3 + (8*(a - 8*b)*d*x - 5*a - 13*b)*cosh(d*x + c))*sinh(d*x + c)^7 + 8*(6*(a - 8*b)*d*x + 11*b)*cosh(d*x + c)^6 + 4*(231*(a + b)*cosh(d*x + c)^6 - 315*(a + 3*b)*cosh(d*x + c)^4 + 12*(a - 8*b)*d*x + 21*(8*(a - 8*b)*d*x - 5*a - 13*b)*cosh(d*x + c)^2 + 22*b)*sinh(d*x + c)^6 + 24*(33*(a + b)*cosh(d*x + c)^7 - 63*(a + 3*b)*cosh(d*x + c)^5 + 7*(8*(a - 8*b)*d*x - 5*a - 13*b)*cosh(d*x + c)^3 + 2*(6*(a - 8*b)*d*x + 11*b)*cosh(d*x + c))*sinh(d*x + c)^5 + 3*(8*(a - 8*b)*d*x + 5*a - 13*b)*cosh(d*x + c)^4 + 3*(165*(a + b)*cosh(d*x + c)^8 - 420*(a + 3*b)*cosh(d*x + c)^6 + 70*(8*(a - 8*b)*d*x - 5*a - 13*b)*cosh(d*x + c)^4 + 8*(a - 8*b)*d*x + 40*(6*(a - 8*b)*d*x + 11*b)*cosh(d*x + c)^2 + 5*a - 13*b)*sinh(d*x + c)^4 + 4*(55*(a + b)*cosh(d*x + c)^9 - 180*(a + 3*b)*cosh(d*x + c)^7 + 42*(8*(a - 8*b)*d*x - 5*a - 13*b)*cosh(d*x + c)^5 + 40*(6*(a - 8*b)*d*x + 11*b)*cosh(d*x + c)^3 + 3*(8*(a - 8*b)*d*x + 5*a - 13*b)*cosh(d*x + c))*sinh(d*x + c)^3 + 6*(a - 3*b)*cosh(d*x + c)^2 + 6*(11*(a + b)*cosh(d*x + c)^10 - 45*(a + 3*b)*cosh(d*x + c)^8 + 14*(8*(a - 8*b)*d*x - 5*a - 13*b)*cosh(d*x + c)^6 + 20*(6*(a - 8*b)*d*x + 11*b)*cosh(d*x + c)^4 + 3*(8*(a - 8*b)*d*x + 5*a - 13*b)*cosh(d*x + c)^2 + a - 3*b)*sinh(d*x + c)^2 + 192*(b*cosh(d*x + c)^8 + 8*b*cosh(d*x + c)*sinh(d*x + c)^7 + b*sinh(d*x + c)^8 + 2*b*cosh(d*x + c)^6 + 2*(14*b*cosh(d*x + c)^2 + b)*sinh(d*x + c)^6 + 4*(14*b*cosh(d*x + c)^3 + 3*b*cosh(d*x + c))*sinh(d*x + c)^5 + b*cosh(d*x + c)^4 + (70*b*cosh(d*x + c)^4 + 30*b*cosh(d*x + c)^2 + b)*sinh(d*x + c)^4 + 4*(14*b*cosh(d*x + c)^5 + 10*b*cosh(d*x + c)^3 + b*cosh(d*x + c))*sinh(d*x + c)^3 + 2*(14*b*cosh(d*x + c)^6 + 15*b*cosh(d*x + c)^4 + 3*b*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*(2*b*cosh(d*x + c)^7 + 3*b*cosh(d*x + c)^5 + b*cosh(d*x + c)^3)*sinh(d*x + c))*log(2*cosh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))) + 12*((a + b)*cosh(d*x + c)^11 - 5*(a + 3*b)*cosh(d*x + c)^9 + 2*(8*(a - 8*b)*d*x - 5*a - 13*b)*cosh(d*x + c)^7 + 4*(6*(a - 8*b)*d*x + 11*b)*cosh(d*x + c)^5 + (8*(a - 8*b)*d*x + 5*a - 13*b)*cosh(d*x + c)^3 + (a - 3*b)*cosh(d*x + c))*sinh(d*x + c) - a + b)/(d*cosh(d*x + c)^8 + 8*d*cosh(d*x + c)*sinh(d*x + c)^7 + d*sinh(d*x + c)^8 + 2*d*cosh(d*x + c)^6 + 2*(14*d*cosh(d*x + c)^2 + d)*sinh(d*x + c)^6 + 4*(14*d*cosh(d*x + c)^3 + 3*d*cosh(d*x + c))*sinh(d*x + c)^5 + d*cosh(d*x + c)^4 + (70*d*cosh(d*x + c)^4 + 30*d*cosh(d*x + c)^2 + d)*sinh(d*x + c)^4 + 4*(14*d*cosh(d*x + c)^5 + 10*d*cosh(d*x + c)^3 + d*cosh(d*x + c))*sinh(d*x + c)^3 + 2*(14*d*cosh(d*x + c)^6 + 15*d*cosh(d*x + c)^4 + 3*d*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*(2*d*cosh(d*x + c)^7 + 3*d*cosh(d*x + c)^5 + d*cosh(d*x + c)^3)*sinh(d*x + c))","B",0
50,1,1070,0,0.739511," ","integrate(sinh(d*x+c)^3*(a+b*tanh(d*x+c)^3),x, algorithm=""fricas"")","\frac{{\left(a + b\right)} \cosh\left(d x + c\right)^{10} + 10 \, {\left(a + b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + {\left(a + b\right)} \sinh\left(d x + c\right)^{10} - {\left(7 \, a + 25 \, b\right)} \cosh\left(d x + c\right)^{8} + {\left(45 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} - 7 \, a - 25 \, b\right)} \sinh\left(d x + c\right)^{8} + 8 \, {\left(15 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{3} - {\left(7 \, a + 25 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} - 2 \, {\left(13 \, a + 25 \, b\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(105 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{4} - 14 \, {\left(7 \, a + 25 \, b\right)} \cosh\left(d x + c\right)^{2} - 13 \, a - 25 \, b\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(63 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{5} - 14 \, {\left(7 \, a + 25 \, b\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(13 \, a + 25 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 2 \, {\left(13 \, a - 25 \, b\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(105 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{6} - 35 \, {\left(7 \, a + 25 \, b\right)} \cosh\left(d x + c\right)^{4} - 15 \, {\left(13 \, a + 25 \, b\right)} \cosh\left(d x + c\right)^{2} - 13 \, a + 25 \, b\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(15 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{7} - 7 \, {\left(7 \, a + 25 \, b\right)} \cosh\left(d x + c\right)^{5} - 5 \, {\left(13 \, a + 25 \, b\right)} \cosh\left(d x + c\right)^{3} - {\left(13 \, a - 25 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - {\left(7 \, a - 25 \, b\right)} \cosh\left(d x + c\right)^{2} + {\left(45 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{8} - 28 \, {\left(7 \, a + 25 \, b\right)} \cosh\left(d x + c\right)^{6} - 30 \, {\left(13 \, a + 25 \, b\right)} \cosh\left(d x + c\right)^{4} - 12 \, {\left(13 \, a - 25 \, b\right)} \cosh\left(d x + c\right)^{2} - 7 \, a + 25 \, b\right)} \sinh\left(d x + c\right)^{2} + 120 \, {\left(b \cosh\left(d x + c\right)^{7} + 7 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + b \sinh\left(d x + c\right)^{7} + 2 \, b \cosh\left(d x + c\right)^{5} + {\left(21 \, b \cosh\left(d x + c\right)^{2} + 2 \, b\right)} \sinh\left(d x + c\right)^{5} + 5 \, {\left(7 \, b \cosh\left(d x + c\right)^{3} + 2 \, b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + b \cosh\left(d x + c\right)^{3} + {\left(35 \, b \cosh\left(d x + c\right)^{4} + 20 \, b \cosh\left(d x + c\right)^{2} + b\right)} \sinh\left(d x + c\right)^{3} + {\left(21 \, b \cosh\left(d x + c\right)^{5} + 20 \, b \cosh\left(d x + c\right)^{3} + 3 \, b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(7 \, b \cosh\left(d x + c\right)^{6} + 10 \, b \cosh\left(d x + c\right)^{4} + 3 \, b \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 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{9} - 4 \, {\left(7 \, a + 25 \, b\right)} \cosh\left(d x + c\right)^{7} - 6 \, {\left(13 \, a + 25 \, b\right)} \cosh\left(d x + c\right)^{5} - 4 \, {\left(13 \, a - 25 \, b\right)} \cosh\left(d x + c\right)^{3} - {\left(7 \, a - 25 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + a - b}{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*((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 - (7*a + 25*b)*cosh(d*x + c)^8 + (45*(a + b)*cosh(d*x + c)^2 - 7*a - 25*b)*sinh(d*x + c)^8 + 8*(15*(a + b)*cosh(d*x + c)^3 - (7*a + 25*b)*cosh(d*x + c))*sinh(d*x + c)^7 - 2*(13*a + 25*b)*cosh(d*x + c)^6 + 2*(105*(a + b)*cosh(d*x + c)^4 - 14*(7*a + 25*b)*cosh(d*x + c)^2 - 13*a - 25*b)*sinh(d*x + c)^6 + 4*(63*(a + b)*cosh(d*x + c)^5 - 14*(7*a + 25*b)*cosh(d*x + c)^3 - 3*(13*a + 25*b)*cosh(d*x + c))*sinh(d*x + c)^5 - 2*(13*a - 25*b)*cosh(d*x + c)^4 + 2*(105*(a + b)*cosh(d*x + c)^6 - 35*(7*a + 25*b)*cosh(d*x + c)^4 - 15*(13*a + 25*b)*cosh(d*x + c)^2 - 13*a + 25*b)*sinh(d*x + c)^4 + 8*(15*(a + b)*cosh(d*x + c)^7 - 7*(7*a + 25*b)*cosh(d*x + c)^5 - 5*(13*a + 25*b)*cosh(d*x + c)^3 - (13*a - 25*b)*cosh(d*x + c))*sinh(d*x + c)^3 - (7*a - 25*b)*cosh(d*x + c)^2 + (45*(a + b)*cosh(d*x + c)^8 - 28*(7*a + 25*b)*cosh(d*x + c)^6 - 30*(13*a + 25*b)*cosh(d*x + c)^4 - 12*(13*a - 25*b)*cosh(d*x + c)^2 - 7*a + 25*b)*sinh(d*x + c)^2 + 120*(b*cosh(d*x + c)^7 + 7*b*cosh(d*x + c)*sinh(d*x + c)^6 + b*sinh(d*x + c)^7 + 2*b*cosh(d*x + c)^5 + (21*b*cosh(d*x + c)^2 + 2*b)*sinh(d*x + c)^5 + 5*(7*b*cosh(d*x + c)^3 + 2*b*cosh(d*x + c))*sinh(d*x + c)^4 + b*cosh(d*x + c)^3 + (35*b*cosh(d*x + c)^4 + 20*b*cosh(d*x + c)^2 + b)*sinh(d*x + c)^3 + (21*b*cosh(d*x + c)^5 + 20*b*cosh(d*x + c)^3 + 3*b*cosh(d*x + c))*sinh(d*x + c)^2 + (7*b*cosh(d*x + c)^6 + 10*b*cosh(d*x + c)^4 + 3*b*cosh(d*x + c)^2)*sinh(d*x + c))*arctan(cosh(d*x + c) + sinh(d*x + c)) + 2*(5*(a + b)*cosh(d*x + c)^9 - 4*(7*a + 25*b)*cosh(d*x + c)^7 - 6*(13*a + 25*b)*cosh(d*x + c)^5 - 4*(13*a - 25*b)*cosh(d*x + c)^3 - (7*a - 25*b)*cosh(d*x + c))*sinh(d*x + c) + a - b)/(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
51,1,924,0,0.590321," ","integrate(sinh(d*x+c)^2*(a+b*tanh(d*x+c)^3),x, algorithm=""fricas"")","\frac{{\left(a + b\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(a + b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a + b\right)} \sinh\left(d x + c\right)^{8} - 2 \, {\left(2 \, {\left(a - 4 \, b\right)} d x - a - b\right)} \cosh\left(d x + c\right)^{6} - 2 \, {\left(2 \, {\left(a - 4 \, b\right)} d x - 14 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} - a - b\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(14 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(2 \, {\left(a - 4 \, b\right)} d x - a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 2 \, {\left(4 \, {\left(a - 4 \, b\right)} d x + 7 \, b\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{4} - 4 \, {\left(a - 4 \, b\right)} d x - 15 \, {\left(2 \, {\left(a - 4 \, b\right)} d x - a - b\right)} \cosh\left(d x + c\right)^{2} - 7 \, b\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{5} - 5 \, {\left(2 \, {\left(a - 4 \, b\right)} d x - a - b\right)} \cosh\left(d x + c\right)^{3} - {\left(4 \, {\left(a - 4 \, b\right)} d x + 7 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 2 \, {\left(2 \, {\left(a - 4 \, b\right)} d x + a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(14 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{6} - 15 \, {\left(2 \, {\left(a - 4 \, b\right)} d x - a - b\right)} \cosh\left(d x + c\right)^{4} - 2 \, {\left(a - 4 \, b\right)} d x - 6 \, {\left(4 \, {\left(a - 4 \, b\right)} d x + 7 \, b\right)} \cosh\left(d x + c\right)^{2} - a + b\right)} \sinh\left(d x + c\right)^{2} - 16 \, {\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} + 2 \, b \cosh\left(d x + c\right)^{4} + {\left(15 \, b \cosh\left(d x + c\right)^{2} + 2 \, b\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, b \cosh\left(d x + c\right)^{3} + 2 \, b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + b \cosh\left(d x + c\right)^{2} + {\left(15 \, b \cosh\left(d x + c\right)^{4} + 12 \, b \cosh\left(d x + c\right)^{2} + b\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{5} + 4 \, b \cosh\left(d x + c\right)^{3} + b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\frac{2 \, \cosh\left(d x + c\right)}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) + 4 \, {\left(2 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{7} - 3 \, {\left(2 \, {\left(a - 4 \, b\right)} d x - a - b\right)} \cosh\left(d x + c\right)^{5} - 2 \, {\left(4 \, {\left(a - 4 \, b\right)} d x + 7 \, b\right)} \cosh\left(d x + c\right)^{3} - {\left(2 \, {\left(a - 4 \, b\right)} d x + a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) - a + b}{8 \, {\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} + 2 \, d \cosh\left(d x + c\right)^{4} + {\left(15 \, 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} + 2 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + d \cosh\left(d x + c\right)^{2} + {\left(15 \, 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} + 2 \, {\left(3 \, 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)\right)}}"," ",0,"1/8*((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 - 2*(2*(a - 4*b)*d*x - a - b)*cosh(d*x + c)^6 - 2*(2*(a - 4*b)*d*x - 14*(a + b)*cosh(d*x + c)^2 - a - b)*sinh(d*x + c)^6 + 4*(14*(a + b)*cosh(d*x + c)^3 - 3*(2*(a - 4*b)*d*x - a - b)*cosh(d*x + c))*sinh(d*x + c)^5 - 2*(4*(a - 4*b)*d*x + 7*b)*cosh(d*x + c)^4 + 2*(35*(a + b)*cosh(d*x + c)^4 - 4*(a - 4*b)*d*x - 15*(2*(a - 4*b)*d*x - a - b)*cosh(d*x + c)^2 - 7*b)*sinh(d*x + c)^4 + 8*(7*(a + b)*cosh(d*x + c)^5 - 5*(2*(a - 4*b)*d*x - a - b)*cosh(d*x + c)^3 - (4*(a - 4*b)*d*x + 7*b)*cosh(d*x + c))*sinh(d*x + c)^3 - 2*(2*(a - 4*b)*d*x + a - b)*cosh(d*x + c)^2 + 2*(14*(a + b)*cosh(d*x + c)^6 - 15*(2*(a - 4*b)*d*x - a - b)*cosh(d*x + c)^4 - 2*(a - 4*b)*d*x - 6*(4*(a - 4*b)*d*x + 7*b)*cosh(d*x + c)^2 - a + b)*sinh(d*x + c)^2 - 16*(b*cosh(d*x + c)^6 + 6*b*cosh(d*x + c)*sinh(d*x + c)^5 + b*sinh(d*x + c)^6 + 2*b*cosh(d*x + c)^4 + (15*b*cosh(d*x + c)^2 + 2*b)*sinh(d*x + c)^4 + 4*(5*b*cosh(d*x + c)^3 + 2*b*cosh(d*x + c))*sinh(d*x + c)^3 + b*cosh(d*x + c)^2 + (15*b*cosh(d*x + c)^4 + 12*b*cosh(d*x + c)^2 + b)*sinh(d*x + c)^2 + 2*(3*b*cosh(d*x + c)^5 + 4*b*cosh(d*x + c)^3 + b*cosh(d*x + c))*sinh(d*x + c))*log(2*cosh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))) + 4*(2*(a + b)*cosh(d*x + c)^7 - 3*(2*(a - 4*b)*d*x - a - b)*cosh(d*x + c)^5 - 2*(4*(a - 4*b)*d*x + 7*b)*cosh(d*x + c)^3 - (2*(a - 4*b)*d*x + a - b)*cosh(d*x + c))*sinh(d*x + c) - a + b)/(d*cosh(d*x + c)^6 + 6*d*cosh(d*x + c)*sinh(d*x + c)^5 + d*sinh(d*x + c)^6 + 2*d*cosh(d*x + c)^4 + (15*d*cosh(d*x + c)^2 + 2*d)*sinh(d*x + c)^4 + 4*(5*d*cosh(d*x + c)^3 + 2*d*cosh(d*x + c))*sinh(d*x + c)^3 + d*cosh(d*x + c)^2 + (15*d*cosh(d*x + c)^4 + 12*d*cosh(d*x + c)^2 + d)*sinh(d*x + c)^2 + 2*(3*d*cosh(d*x + c)^5 + 4*d*cosh(d*x + c)^3 + d*cosh(d*x + c))*sinh(d*x + c))","B",0
52,1,528,0,0.947690," ","integrate(sinh(d*x+c)*(a+b*tanh(d*x+c)^3),x, algorithm=""fricas"")","\frac{{\left(a + b\right)} \cosh\left(d x + c\right)^{6} + 6 \, {\left(a + b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(a + b\right)} \sinh\left(d x + c\right)^{6} + 3 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(5 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} + a + b\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a + b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 3 \, {\left(a - b\right)} \cosh\left(d x + c\right)^{2} + 3 \, {\left(5 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{4} + 6 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} + a - b\right)} \sinh\left(d x + c\right)^{2} - 6 \, {\left(b \cosh\left(d x + c\right)^{5} + 5 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} + b \sinh\left(d x + c\right)^{5} + 2 \, b \cosh\left(d x + c\right)^{3} + 2 \, {\left(5 \, b \cosh\left(d x + c\right)^{2} + b\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\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)^{2} + b \cosh\left(d x + c\right) + {\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)\right)} \arctan\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) + 6 \, {\left({\left(a + b\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\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}{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*((a + b)*cosh(d*x + c)^6 + 6*(a + b)*cosh(d*x + c)*sinh(d*x + c)^5 + (a + b)*sinh(d*x + c)^6 + 3*(a + b)*cosh(d*x + c)^4 + 3*(5*(a + b)*cosh(d*x + c)^2 + a + b)*sinh(d*x + c)^4 + 4*(5*(a + b)*cosh(d*x + c)^3 + 3*(a + b)*cosh(d*x + c))*sinh(d*x + c)^3 + 3*(a - b)*cosh(d*x + c)^2 + 3*(5*(a + b)*cosh(d*x + c)^4 + 6*(a + b)*cosh(d*x + c)^2 + a - b)*sinh(d*x + c)^2 - 6*(b*cosh(d*x + c)^5 + 5*b*cosh(d*x + c)*sinh(d*x + c)^4 + b*sinh(d*x + c)^5 + 2*b*cosh(d*x + c)^3 + 2*(5*b*cosh(d*x + c)^2 + b)*sinh(d*x + c)^3 + 2*(5*b*cosh(d*x + c)^3 + 3*b*cosh(d*x + c))*sinh(d*x + c)^2 + b*cosh(d*x + c) + (5*b*cosh(d*x + c)^4 + 6*b*cosh(d*x + c)^2 + b)*sinh(d*x + c))*arctan(cosh(d*x + c) + sinh(d*x + c)) + 6*((a + b)*cosh(d*x + c)^5 + 2*(a + b)*cosh(d*x + c)^3 + (a - b)*cosh(d*x + c))*sinh(d*x + c) + a - 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
53,1,522,0,0.958351," ","integrate(csch(d*x+c)*(a+b*tanh(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} + b \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)} \arctan\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) - b \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) + {\left(3 \, b \cosh\left(d x + c\right)^{2} - 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,"-(b*cosh(d*x + c)^3 + 3*b*cosh(d*x + c)*sinh(d*x + c)^2 + 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)*arctan(cosh(d*x + c) + sinh(d*x + c)) - b*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) + (3*b*cosh(d*x + c)^2 - 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
54,1,141,0,1.299193," ","integrate(csch(d*x+c)^2*(a+b*tanh(d*x+c)^3),x, algorithm=""fricas"")","-\frac{2 \, {\left({\left(2 \, a + b\right)} \cosh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(2 \, a + b\right)} \sinh\left(d x + c\right)^{2} + 2 \, a - b\right)}}{d \cosh\left(d x + c\right)^{4} + 6 \, d \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + d \sinh\left(d x + c\right)^{4} + 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,"-2*((2*a + b)*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + (2*a + b)*sinh(d*x + c)^2 + 2*a - b)/(d*cosh(d*x + c)^4 + 6*d*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*d*cosh(d*x + c)*sinh(d*x + c)^3 + d*sinh(d*x + c)^4 + 4*(d*cosh(d*x + c)^3 + d*cosh(d*x + c))*sinh(d*x + c) - d)","B",0
55,1,1188,0,1.683026," ","integrate(csch(d*x+c)^3*(a+b*tanh(d*x+c)^3),x, algorithm=""fricas"")","-\frac{2 \, {\left(a - b\right)} \cosh\left(d x + c\right)^{7} + 14 \, {\left(a - b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + 2 \, {\left(a - b\right)} \sinh\left(d x + c\right)^{7} + 6 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{5} + 6 \, {\left(7 \, {\left(a - b\right)} \cosh\left(d x + c\right)^{2} + a + b\right)} \sinh\left(d x + c\right)^{5} + 10 \, {\left(7 \, {\left(a - b\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a + b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 6 \, {\left(a - b\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(35 \, {\left(a - b\right)} \cosh\left(d x + c\right)^{4} + 30 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} + 3 \, a - 3 \, b\right)} \sinh\left(d x + c\right)^{3} + 6 \, {\left(7 \, {\left(a - b\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 2 \, {\left(b \cosh\left(d x + c\right)^{8} + 56 \, b \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right)^{5} + 28 \, b \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{6} + 8 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + b \sinh\left(d x + c\right)^{8} - 2 \, b \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, b \cosh\left(d x + c\right)^{4} - b\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, b \cosh\left(d x + c\right)^{5} - b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, b \cosh\left(d x + c\right)^{6} - 3 \, b \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left(b \cosh\left(d x + c\right)^{7} - b \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right) + 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) - {\left(a \cosh\left(d x + c\right)^{8} + 56 \, a \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right)^{5} + 28 \, a \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{6} + 8 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + a \sinh\left(d x + c\right)^{8} - 2 \, a \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, a \cosh\left(d x + c\right)^{4} - a\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, a \cosh\left(d x + c\right)^{5} - a \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, a \cosh\left(d x + c\right)^{6} - 3 \, a \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left(a \cosh\left(d x + c\right)^{7} - a \cosh\left(d x + c\right)^{3}\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)^{8} + 56 \, a \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right)^{5} + 28 \, a \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{6} + 8 \, a \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + a \sinh\left(d x + c\right)^{8} - 2 \, a \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, a \cosh\left(d x + c\right)^{4} - a\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, a \cosh\left(d x + c\right)^{5} - a \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, a \cosh\left(d x + c\right)^{6} - 3 \, a \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left(a \cosh\left(d x + c\right)^{7} - a \cosh\left(d x + c\right)^{3}\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(7 \, {\left(a - b\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{4} + 9 \, {\left(a - b\right)} \cosh\left(d x + c\right)^{2} + a + b\right)} \sinh\left(d x + c\right)}{2 \, {\left(d \cosh\left(d x + c\right)^{8} + 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} - 2 \, d \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, d \cosh\left(d x + c\right)^{4} - d\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, d \cosh\left(d x + c\right)^{5} - d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, d \cosh\left(d x + c\right)^{6} - 3 \, d \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left(d \cosh\left(d x + c\right)^{7} - d \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right) + d\right)}}"," ",0,"-1/2*(2*(a - b)*cosh(d*x + c)^7 + 14*(a - b)*cosh(d*x + c)*sinh(d*x + c)^6 + 2*(a - b)*sinh(d*x + c)^7 + 6*(a + b)*cosh(d*x + c)^5 + 6*(7*(a - b)*cosh(d*x + c)^2 + a + b)*sinh(d*x + c)^5 + 10*(7*(a - b)*cosh(d*x + c)^3 + 3*(a + b)*cosh(d*x + c))*sinh(d*x + c)^4 + 6*(a - b)*cosh(d*x + c)^3 + 2*(35*(a - b)*cosh(d*x + c)^4 + 30*(a + b)*cosh(d*x + c)^2 + 3*a - 3*b)*sinh(d*x + c)^3 + 6*(7*(a - b)*cosh(d*x + c)^5 + 10*(a + b)*cosh(d*x + c)^3 + 3*(a - b)*cosh(d*x + c))*sinh(d*x + c)^2 - 2*(b*cosh(d*x + c)^8 + 56*b*cosh(d*x + c)^3*sinh(d*x + c)^5 + 28*b*cosh(d*x + c)^2*sinh(d*x + c)^6 + 8*b*cosh(d*x + c)*sinh(d*x + c)^7 + b*sinh(d*x + c)^8 - 2*b*cosh(d*x + c)^4 + 2*(35*b*cosh(d*x + c)^4 - b)*sinh(d*x + c)^4 + 8*(7*b*cosh(d*x + c)^5 - b*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*b*cosh(d*x + c)^6 - 3*b*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*(b*cosh(d*x + c)^7 - b*cosh(d*x + c)^3)*sinh(d*x + c) + b)*arctan(cosh(d*x + c) + sinh(d*x + c)) + 2*(a + b)*cosh(d*x + c) - (a*cosh(d*x + c)^8 + 56*a*cosh(d*x + c)^3*sinh(d*x + c)^5 + 28*a*cosh(d*x + c)^2*sinh(d*x + c)^6 + 8*a*cosh(d*x + c)*sinh(d*x + c)^7 + a*sinh(d*x + c)^8 - 2*a*cosh(d*x + c)^4 + 2*(35*a*cosh(d*x + c)^4 - a)*sinh(d*x + c)^4 + 8*(7*a*cosh(d*x + c)^5 - a*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*a*cosh(d*x + c)^6 - 3*a*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*(a*cosh(d*x + c)^7 - a*cosh(d*x + c)^3)*sinh(d*x + c) + a)*log(cosh(d*x + c) + sinh(d*x + c) + 1) + (a*cosh(d*x + c)^8 + 56*a*cosh(d*x + c)^3*sinh(d*x + c)^5 + 28*a*cosh(d*x + c)^2*sinh(d*x + c)^6 + 8*a*cosh(d*x + c)*sinh(d*x + c)^7 + a*sinh(d*x + c)^8 - 2*a*cosh(d*x + c)^4 + 2*(35*a*cosh(d*x + c)^4 - a)*sinh(d*x + c)^4 + 8*(7*a*cosh(d*x + c)^5 - a*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*a*cosh(d*x + c)^6 - 3*a*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*(a*cosh(d*x + c)^7 - a*cosh(d*x + c)^3)*sinh(d*x + c) + a)*log(cosh(d*x + c) + sinh(d*x + c) - 1) + 2*(7*(a - b)*cosh(d*x + c)^6 + 15*(a + b)*cosh(d*x + c)^4 + 9*(a - b)*cosh(d*x + c)^2 + a + b)*sinh(d*x + c))/(d*cosh(d*x + c)^8 + 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 - 2*d*cosh(d*x + c)^4 + 2*(35*d*cosh(d*x + c)^4 - d)*sinh(d*x + c)^4 + 8*(7*d*cosh(d*x + c)^5 - d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*d*cosh(d*x + c)^6 - 3*d*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*(d*cosh(d*x + c)^7 - d*cosh(d*x + c)^3)*sinh(d*x + c) + d)","B",0
56,1,1739,0,0.739210," ","integrate(csch(d*x+c)^4*(a+b*tanh(d*x+c)^3),x, algorithm=""fricas"")","\frac{6 \, b \cosh\left(d x + c\right)^{8} + 48 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + 6 \, b \sinh\left(d x + c\right)^{8} - 6 \, {\left(2 \, a + 3 \, b\right)} \cosh\left(d x + c\right)^{6} + 6 \, {\left(28 \, b \cosh\left(d x + c\right)^{2} - 2 \, a - 3 \, b\right)} \sinh\left(d x + c\right)^{6} + 12 \, {\left(28 \, 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)^{5} - 2 \, {\left(10 \, a - 9 \, b\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(210 \, b \cosh\left(d x + c\right)^{4} - 45 \, {\left(2 \, a + 3 \, b\right)} \cosh\left(d x + c\right)^{2} - 10 \, a + 9 \, b\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(42 \, b \cosh\left(d x + c\right)^{5} - 15 \, {\left(2 \, a + 3 \, b\right)} \cosh\left(d x + c\right)^{3} - {\left(10 \, a - 9 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 2 \, {\left(2 \, a + 3 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(84 \, b \cosh\left(d x + c\right)^{6} - 45 \, {\left(2 \, a + 3 \, b\right)} \cosh\left(d x + c\right)^{4} - 6 \, {\left(10 \, a - 9 \, b\right)} \cosh\left(d x + c\right)^{2} - 2 \, a - 3 \, b\right)} \sinh\left(d x + c\right)^{2} - 3 \, {\left(b \cosh\left(d x + c\right)^{10} + 10 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + b \sinh\left(d x + c\right)^{10} - b \cosh\left(d x + c\right)^{8} + {\left(45 \, b \cosh\left(d x + c\right)^{2} - b\right)} \sinh\left(d x + c\right)^{8} + 8 \, {\left(15 \, b \cosh\left(d x + c\right)^{3} - b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} - 2 \, b \cosh\left(d x + c\right)^{6} + 2 \, {\left(105 \, b \cosh\left(d x + c\right)^{4} - 14 \, b \cosh\left(d x + c\right)^{2} - b\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(63 \, b \cosh\left(d x + c\right)^{5} - 14 \, b \cosh\left(d x + c\right)^{3} - 3 \, b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, b \cosh\left(d x + c\right)^{4} + 2 \, {\left(105 \, b \cosh\left(d x + c\right)^{6} - 35 \, b \cosh\left(d x + c\right)^{4} - 15 \, b \cosh\left(d x + c\right)^{2} + b\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(15 \, b \cosh\left(d x + c\right)^{7} - 7 \, b \cosh\left(d x + c\right)^{5} - 5 \, b \cosh\left(d x + c\right)^{3} + b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + b \cosh\left(d x + c\right)^{2} + {\left(45 \, b \cosh\left(d x + c\right)^{8} - 28 \, b \cosh\left(d x + c\right)^{6} - 30 \, b \cosh\left(d x + c\right)^{4} + 12 \, b \cosh\left(d x + c\right)^{2} + b\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(5 \, b \cosh\left(d x + c\right)^{9} - 4 \, b \cosh\left(d x + c\right)^{7} - 6 \, b \cosh\left(d x + c\right)^{5} + 4 \, 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(\frac{2 \, \cosh\left(d x + c\right)}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) + 3 \, {\left(b \cosh\left(d x + c\right)^{10} + 10 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + b \sinh\left(d x + c\right)^{10} - b \cosh\left(d x + c\right)^{8} + {\left(45 \, b \cosh\left(d x + c\right)^{2} - b\right)} \sinh\left(d x + c\right)^{8} + 8 \, {\left(15 \, b \cosh\left(d x + c\right)^{3} - b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} - 2 \, b \cosh\left(d x + c\right)^{6} + 2 \, {\left(105 \, b \cosh\left(d x + c\right)^{4} - 14 \, b \cosh\left(d x + c\right)^{2} - b\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(63 \, b \cosh\left(d x + c\right)^{5} - 14 \, b \cosh\left(d x + c\right)^{3} - 3 \, b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, b \cosh\left(d x + c\right)^{4} + 2 \, {\left(105 \, b \cosh\left(d x + c\right)^{6} - 35 \, b \cosh\left(d x + c\right)^{4} - 15 \, b \cosh\left(d x + c\right)^{2} + b\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(15 \, b \cosh\left(d x + c\right)^{7} - 7 \, b \cosh\left(d x + c\right)^{5} - 5 \, b \cosh\left(d x + c\right)^{3} + b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + b \cosh\left(d x + c\right)^{2} + {\left(45 \, b \cosh\left(d x + c\right)^{8} - 28 \, b \cosh\left(d x + c\right)^{6} - 30 \, b \cosh\left(d x + c\right)^{4} + 12 \, b \cosh\left(d x + c\right)^{2} + b\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(5 \, b \cosh\left(d x + c\right)^{9} - 4 \, b \cosh\left(d x + c\right)^{7} - 6 \, b \cosh\left(d x + c\right)^{5} + 4 \, 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(\frac{2 \, \sinh\left(d x + c\right)}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) + 4 \, {\left(12 \, b \cosh\left(d x + c\right)^{7} - 9 \, {\left(2 \, a + 3 \, b\right)} \cosh\left(d x + c\right)^{5} - 2 \, {\left(10 \, a - 9 \, 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) + 4 \, a}{3 \, {\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} - d \cosh\left(d x + c\right)^{8} + {\left(45 \, d \cosh\left(d x + c\right)^{2} - d\right)} \sinh\left(d x + c\right)^{8} + 8 \, {\left(15 \, d \cosh\left(d x + c\right)^{3} - d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} - 2 \, d \cosh\left(d x + c\right)^{6} + 2 \, {\left(105 \, 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} - 14 \, d \cosh\left(d x + c\right)^{3} - 3 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, d \cosh\left(d x + c\right)^{4} + 2 \, {\left(105 \, 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} + 8 \, {\left(15 \, 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} + d \cosh\left(d x + c\right)^{2} + {\left(45 \, 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} + 2 \, {\left(5 \, 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,"1/3*(6*b*cosh(d*x + c)^8 + 48*b*cosh(d*x + c)*sinh(d*x + c)^7 + 6*b*sinh(d*x + c)^8 - 6*(2*a + 3*b)*cosh(d*x + c)^6 + 6*(28*b*cosh(d*x + c)^2 - 2*a - 3*b)*sinh(d*x + c)^6 + 12*(28*b*cosh(d*x + c)^3 - 3*(2*a + 3*b)*cosh(d*x + c))*sinh(d*x + c)^5 - 2*(10*a - 9*b)*cosh(d*x + c)^4 + 2*(210*b*cosh(d*x + c)^4 - 45*(2*a + 3*b)*cosh(d*x + c)^2 - 10*a + 9*b)*sinh(d*x + c)^4 + 8*(42*b*cosh(d*x + c)^5 - 15*(2*a + 3*b)*cosh(d*x + c)^3 - (10*a - 9*b)*cosh(d*x + c))*sinh(d*x + c)^3 - 2*(2*a + 3*b)*cosh(d*x + c)^2 + 2*(84*b*cosh(d*x + c)^6 - 45*(2*a + 3*b)*cosh(d*x + c)^4 - 6*(10*a - 9*b)*cosh(d*x + c)^2 - 2*a - 3*b)*sinh(d*x + c)^2 - 3*(b*cosh(d*x + c)^10 + 10*b*cosh(d*x + c)*sinh(d*x + c)^9 + b*sinh(d*x + c)^10 - b*cosh(d*x + c)^8 + (45*b*cosh(d*x + c)^2 - b)*sinh(d*x + c)^8 + 8*(15*b*cosh(d*x + c)^3 - b*cosh(d*x + c))*sinh(d*x + c)^7 - 2*b*cosh(d*x + c)^6 + 2*(105*b*cosh(d*x + c)^4 - 14*b*cosh(d*x + c)^2 - b)*sinh(d*x + c)^6 + 4*(63*b*cosh(d*x + c)^5 - 14*b*cosh(d*x + c)^3 - 3*b*cosh(d*x + c))*sinh(d*x + c)^5 + 2*b*cosh(d*x + c)^4 + 2*(105*b*cosh(d*x + c)^6 - 35*b*cosh(d*x + c)^4 - 15*b*cosh(d*x + c)^2 + b)*sinh(d*x + c)^4 + 8*(15*b*cosh(d*x + c)^7 - 7*b*cosh(d*x + c)^5 - 5*b*cosh(d*x + c)^3 + b*cosh(d*x + c))*sinh(d*x + c)^3 + b*cosh(d*x + c)^2 + (45*b*cosh(d*x + c)^8 - 28*b*cosh(d*x + c)^6 - 30*b*cosh(d*x + c)^4 + 12*b*cosh(d*x + c)^2 + b)*sinh(d*x + c)^2 + 2*(5*b*cosh(d*x + c)^9 - 4*b*cosh(d*x + c)^7 - 6*b*cosh(d*x + c)^5 + 4*b*cosh(d*x + c)^3 + b*cosh(d*x + c))*sinh(d*x + c) - b)*log(2*cosh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))) + 3*(b*cosh(d*x + c)^10 + 10*b*cosh(d*x + c)*sinh(d*x + c)^9 + b*sinh(d*x + c)^10 - b*cosh(d*x + c)^8 + (45*b*cosh(d*x + c)^2 - b)*sinh(d*x + c)^8 + 8*(15*b*cosh(d*x + c)^3 - b*cosh(d*x + c))*sinh(d*x + c)^7 - 2*b*cosh(d*x + c)^6 + 2*(105*b*cosh(d*x + c)^4 - 14*b*cosh(d*x + c)^2 - b)*sinh(d*x + c)^6 + 4*(63*b*cosh(d*x + c)^5 - 14*b*cosh(d*x + c)^3 - 3*b*cosh(d*x + c))*sinh(d*x + c)^5 + 2*b*cosh(d*x + c)^4 + 2*(105*b*cosh(d*x + c)^6 - 35*b*cosh(d*x + c)^4 - 15*b*cosh(d*x + c)^2 + b)*sinh(d*x + c)^4 + 8*(15*b*cosh(d*x + c)^7 - 7*b*cosh(d*x + c)^5 - 5*b*cosh(d*x + c)^3 + b*cosh(d*x + c))*sinh(d*x + c)^3 + b*cosh(d*x + c)^2 + (45*b*cosh(d*x + c)^8 - 28*b*cosh(d*x + c)^6 - 30*b*cosh(d*x + c)^4 + 12*b*cosh(d*x + c)^2 + b)*sinh(d*x + c)^2 + 2*(5*b*cosh(d*x + c)^9 - 4*b*cosh(d*x + c)^7 - 6*b*cosh(d*x + c)^5 + 4*b*cosh(d*x + c)^3 + b*cosh(d*x + c))*sinh(d*x + c) - b)*log(2*sinh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))) + 4*(12*b*cosh(d*x + c)^7 - 9*(2*a + 3*b)*cosh(d*x + c)^5 - 2*(10*a - 9*b)*cosh(d*x + c)^3 - (2*a + 3*b)*cosh(d*x + c))*sinh(d*x + c) + 4*a)/(d*cosh(d*x + c)^10 + 10*d*cosh(d*x + c)*sinh(d*x + c)^9 + d*sinh(d*x + c)^10 - d*cosh(d*x + c)^8 + (45*d*cosh(d*x + c)^2 - d)*sinh(d*x + c)^8 + 8*(15*d*cosh(d*x + c)^3 - d*cosh(d*x + c))*sinh(d*x + c)^7 - 2*d*cosh(d*x + c)^6 + 2*(105*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 - 14*d*cosh(d*x + c)^3 - 3*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*d*cosh(d*x + c)^4 + 2*(105*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 + 8*(15*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 + d*cosh(d*x + c)^2 + (45*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 + 2*(5*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
57,1,5034,0,0.749118," ","integrate(sinh(d*x+c)^4*(a+b*tanh(d*x+c)^3)^2,x, algorithm=""fricas"")","\frac{5 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{18} + 90 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{17} + 5 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{18} - 15 \, {\left(a^{2} + 10 \, a b + 9 \, b^{2}\right)} \cosh\left(d x + c\right)^{16} + 15 \, {\left(51 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} - a^{2} - 10 \, a b - 9 \, b^{2}\right)} \sinh\left(d x + c\right)^{16} + 240 \, {\left(17 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(a^{2} + 10 \, a b + 9 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{15} + 30 \, {\left(4 \, {\left(a^{2} - 16 \, a b + 21 \, b^{2}\right)} d x - 5 \, a^{2} - 30 \, a b - 25 \, b^{2}\right)} \cosh\left(d x + c\right)^{14} + 30 \, {\left(510 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{2} - 16 \, a b + 21 \, b^{2}\right)} d x - 60 \, {\left(a^{2} + 10 \, a b + 9 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 5 \, a^{2} - 30 \, a b - 25 \, b^{2}\right)} \sinh\left(d x + c\right)^{14} + 420 \, {\left(102 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{5} - 20 \, {\left(a^{2} + 10 \, a b + 9 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(4 \, {\left(a^{2} - 16 \, a b + 21 \, b^{2}\right)} d x - 5 \, a^{2} - 30 \, a b - 25 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{13} + 10 \, {\left(60 \, {\left(a^{2} - 16 \, a b + 21 \, b^{2}\right)} d x - 31 \, a^{2} - 82 \, a b + 501 \, b^{2}\right)} \cosh\left(d x + c\right)^{12} + 10 \, {\left(9282 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{6} - 2730 \, {\left(a^{2} + 10 \, a b + 9 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 60 \, {\left(a^{2} - 16 \, a b + 21 \, b^{2}\right)} d x + 273 \, {\left(4 \, {\left(a^{2} - 16 \, a b + 21 \, b^{2}\right)} d x - 5 \, a^{2} - 30 \, a b - 25 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 31 \, a^{2} - 82 \, a b + 501 \, b^{2}\right)} \sinh\left(d x + c\right)^{12} + 120 \, {\left(1326 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{7} - 546 \, {\left(a^{2} + 10 \, a b + 9 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 91 \, {\left(4 \, {\left(a^{2} - 16 \, a b + 21 \, b^{2}\right)} d x - 5 \, a^{2} - 30 \, a b - 25 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(60 \, {\left(a^{2} - 16 \, a b + 21 \, b^{2}\right)} d x - 31 \, a^{2} - 82 \, a b + 501 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{11} + 60 \, {\left(20 \, {\left(a^{2} - 16 \, a b + 21 \, b^{2}\right)} d x - 3 \, a^{2} + 15 \, a b + 307 \, b^{2}\right)} \cosh\left(d x + c\right)^{10} + 30 \, {\left(7293 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{8} - 4004 \, {\left(a^{2} + 10 \, a b + 9 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 1001 \, {\left(4 \, {\left(a^{2} - 16 \, a b + 21 \, b^{2}\right)} d x - 5 \, a^{2} - 30 \, a b - 25 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 40 \, {\left(a^{2} - 16 \, a b + 21 \, b^{2}\right)} d x + 22 \, {\left(60 \, {\left(a^{2} - 16 \, a b + 21 \, b^{2}\right)} d x - 31 \, a^{2} - 82 \, a b + 501 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 6 \, a^{2} + 30 \, a b + 614 \, b^{2}\right)} \sinh\left(d x + c\right)^{10} + 20 \, {\left(12155 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{9} - 8580 \, {\left(a^{2} + 10 \, a b + 9 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} + 3003 \, {\left(4 \, {\left(a^{2} - 16 \, a b + 21 \, b^{2}\right)} d x - 5 \, a^{2} - 30 \, a b - 25 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 110 \, {\left(60 \, {\left(a^{2} - 16 \, a b + 21 \, b^{2}\right)} d x - 31 \, a^{2} - 82 \, a b + 501 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 30 \, {\left(20 \, {\left(a^{2} - 16 \, a b + 21 \, b^{2}\right)} d x - 3 \, a^{2} + 15 \, a b + 307 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} + 60 \, {\left(20 \, {\left(a^{2} - 16 \, a b + 21 \, b^{2}\right)} d x + 3 \, a^{2} + 15 \, a b + 461 \, b^{2}\right)} \cosh\left(d x + c\right)^{8} + 30 \, {\left(7293 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{10} - 6435 \, {\left(a^{2} + 10 \, a b + 9 \, b^{2}\right)} \cosh\left(d x + c\right)^{8} + 3003 \, {\left(4 \, {\left(a^{2} - 16 \, a b + 21 \, b^{2}\right)} d x - 5 \, a^{2} - 30 \, a b - 25 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 165 \, {\left(60 \, {\left(a^{2} - 16 \, a b + 21 \, b^{2}\right)} d x - 31 \, a^{2} - 82 \, a b + 501 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 40 \, {\left(a^{2} - 16 \, a b + 21 \, b^{2}\right)} d x + 90 \, {\left(20 \, {\left(a^{2} - 16 \, a b + 21 \, b^{2}\right)} d x - 3 \, a^{2} + 15 \, a b + 307 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 6 \, a^{2} + 30 \, a b + 922 \, b^{2}\right)} \sinh\left(d x + c\right)^{8} + 240 \, {\left(663 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{11} - 715 \, {\left(a^{2} + 10 \, a b + 9 \, b^{2}\right)} \cosh\left(d x + c\right)^{9} + 429 \, {\left(4 \, {\left(a^{2} - 16 \, a b + 21 \, b^{2}\right)} d x - 5 \, a^{2} - 30 \, a b - 25 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} + 33 \, {\left(60 \, {\left(a^{2} - 16 \, a b + 21 \, b^{2}\right)} d x - 31 \, a^{2} - 82 \, a b + 501 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 30 \, {\left(20 \, {\left(a^{2} - 16 \, a b + 21 \, b^{2}\right)} d x - 3 \, a^{2} + 15 \, a b + 307 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(20 \, {\left(a^{2} - 16 \, a b + 21 \, b^{2}\right)} d x + 3 \, a^{2} + 15 \, a b + 461 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 10 \, {\left(60 \, {\left(a^{2} - 16 \, a b + 21 \, b^{2}\right)} d x + 31 \, a^{2} - 82 \, a b + 1803 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 10 \, {\left(9282 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{12} - 12012 \, {\left(a^{2} + 10 \, a b + 9 \, b^{2}\right)} \cosh\left(d x + c\right)^{10} + 9009 \, {\left(4 \, {\left(a^{2} - 16 \, a b + 21 \, b^{2}\right)} d x - 5 \, a^{2} - 30 \, a b - 25 \, b^{2}\right)} \cosh\left(d x + c\right)^{8} + 924 \, {\left(60 \, {\left(a^{2} - 16 \, a b + 21 \, b^{2}\right)} d x - 31 \, a^{2} - 82 \, a b + 501 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 1260 \, {\left(20 \, {\left(a^{2} - 16 \, a b + 21 \, b^{2}\right)} d x - 3 \, a^{2} + 15 \, a b + 307 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 60 \, {\left(a^{2} - 16 \, a b + 21 \, b^{2}\right)} d x + 168 \, {\left(20 \, {\left(a^{2} - 16 \, a b + 21 \, b^{2}\right)} d x + 3 \, a^{2} + 15 \, a b + 461 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 31 \, a^{2} - 82 \, a b + 1803 \, b^{2}\right)} \sinh\left(d x + c\right)^{6} + 60 \, {\left(714 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{13} - 1092 \, {\left(a^{2} + 10 \, a b + 9 \, b^{2}\right)} \cosh\left(d x + c\right)^{11} + 1001 \, {\left(4 \, {\left(a^{2} - 16 \, a b + 21 \, b^{2}\right)} d x - 5 \, a^{2} - 30 \, a b - 25 \, b^{2}\right)} \cosh\left(d x + c\right)^{9} + 132 \, {\left(60 \, {\left(a^{2} - 16 \, a b + 21 \, b^{2}\right)} d x - 31 \, a^{2} - 82 \, a b + 501 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} + 252 \, {\left(20 \, {\left(a^{2} - 16 \, a b + 21 \, b^{2}\right)} d x - 3 \, a^{2} + 15 \, a b + 307 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 56 \, {\left(20 \, {\left(a^{2} - 16 \, a b + 21 \, b^{2}\right)} d x + 3 \, a^{2} + 15 \, a b + 461 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(60 \, {\left(a^{2} - 16 \, a b + 21 \, b^{2}\right)} d x + 31 \, a^{2} - 82 \, a b + 1803 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 6 \, {\left(20 \, {\left(a^{2} - 16 \, a b + 21 \, b^{2}\right)} d x + 25 \, a^{2} - 150 \, a b + 893 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 6 \, {\left(2550 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{14} - 4550 \, {\left(a^{2} + 10 \, a b + 9 \, b^{2}\right)} \cosh\left(d x + c\right)^{12} + 5005 \, {\left(4 \, {\left(a^{2} - 16 \, a b + 21 \, b^{2}\right)} d x - 5 \, a^{2} - 30 \, a b - 25 \, b^{2}\right)} \cosh\left(d x + c\right)^{10} + 825 \, {\left(60 \, {\left(a^{2} - 16 \, a b + 21 \, b^{2}\right)} d x - 31 \, a^{2} - 82 \, a b + 501 \, b^{2}\right)} \cosh\left(d x + c\right)^{8} + 2100 \, {\left(20 \, {\left(a^{2} - 16 \, a b + 21 \, b^{2}\right)} d x - 3 \, a^{2} + 15 \, a b + 307 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 700 \, {\left(20 \, {\left(a^{2} - 16 \, a b + 21 \, b^{2}\right)} d x + 3 \, a^{2} + 15 \, a b + 461 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 20 \, {\left(a^{2} - 16 \, a b + 21 \, b^{2}\right)} d x + 25 \, {\left(60 \, {\left(a^{2} - 16 \, a b + 21 \, b^{2}\right)} d x + 31 \, a^{2} - 82 \, a b + 1803 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 25 \, a^{2} - 150 \, a b + 893 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(510 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{15} - 1050 \, {\left(a^{2} + 10 \, a b + 9 \, b^{2}\right)} \cosh\left(d x + c\right)^{13} + 1365 \, {\left(4 \, {\left(a^{2} - 16 \, a b + 21 \, b^{2}\right)} d x - 5 \, a^{2} - 30 \, a b - 25 \, b^{2}\right)} \cosh\left(d x + c\right)^{11} + 275 \, {\left(60 \, {\left(a^{2} - 16 \, a b + 21 \, b^{2}\right)} d x - 31 \, a^{2} - 82 \, a b + 501 \, b^{2}\right)} \cosh\left(d x + c\right)^{9} + 900 \, {\left(20 \, {\left(a^{2} - 16 \, a b + 21 \, b^{2}\right)} d x - 3 \, a^{2} + 15 \, a b + 307 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} + 420 \, {\left(20 \, {\left(a^{2} - 16 \, a b + 21 \, b^{2}\right)} d x + 3 \, a^{2} + 15 \, a b + 461 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 25 \, {\left(60 \, {\left(a^{2} - 16 \, a b + 21 \, b^{2}\right)} d x + 31 \, a^{2} - 82 \, a b + 1803 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(20 \, {\left(a^{2} - 16 \, a b + 21 \, b^{2}\right)} d x + 25 \, a^{2} - 150 \, a b + 893 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 15 \, {\left(a^{2} - 10 \, a b + 9 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 3 \, {\left(255 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{16} - 600 \, {\left(a^{2} + 10 \, a b + 9 \, b^{2}\right)} \cosh\left(d x + c\right)^{14} + 910 \, {\left(4 \, {\left(a^{2} - 16 \, a b + 21 \, b^{2}\right)} d x - 5 \, a^{2} - 30 \, a b - 25 \, b^{2}\right)} \cosh\left(d x + c\right)^{12} + 220 \, {\left(60 \, {\left(a^{2} - 16 \, a b + 21 \, b^{2}\right)} d x - 31 \, a^{2} - 82 \, a b + 501 \, b^{2}\right)} \cosh\left(d x + c\right)^{10} + 900 \, {\left(20 \, {\left(a^{2} - 16 \, a b + 21 \, b^{2}\right)} d x - 3 \, a^{2} + 15 \, a b + 307 \, b^{2}\right)} \cosh\left(d x + c\right)^{8} + 560 \, {\left(20 \, {\left(a^{2} - 16 \, a b + 21 \, b^{2}\right)} d x + 3 \, a^{2} + 15 \, a b + 461 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 50 \, {\left(60 \, {\left(a^{2} - 16 \, a b + 21 \, b^{2}\right)} d x + 31 \, a^{2} - 82 \, a b + 1803 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 12 \, {\left(20 \, {\left(a^{2} - 16 \, a b + 21 \, b^{2}\right)} d x + 25 \, a^{2} - 150 \, a b + 893 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 5 \, a^{2} - 50 \, a b + 45 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} - 5 \, a^{2} + 10 \, a b - 5 \, b^{2} + 1920 \, {\left(a b \cosh\left(d x + c\right)^{14} + 14 \, a b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{13} + a b \sinh\left(d x + c\right)^{14} + 5 \, a b \cosh\left(d x + c\right)^{12} + {\left(91 \, a b \cosh\left(d x + c\right)^{2} + 5 \, a b\right)} \sinh\left(d x + c\right)^{12} + 10 \, a b \cosh\left(d x + c\right)^{10} + 4 \, {\left(91 \, 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)^{11} + {\left(1001 \, a b \cosh\left(d x + c\right)^{4} + 330 \, a b \cosh\left(d x + c\right)^{2} + 10 \, a b\right)} \sinh\left(d x + c\right)^{10} + 10 \, a b \cosh\left(d x + c\right)^{8} + 2 \, {\left(1001 \, a b \cosh\left(d x + c\right)^{5} + 550 \, a b \cosh\left(d x + c\right)^{3} + 50 \, a b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} + {\left(3003 \, a b \cosh\left(d x + c\right)^{6} + 2475 \, a b \cosh\left(d x + c\right)^{4} + 450 \, a b \cosh\left(d x + c\right)^{2} + 10 \, a b\right)} \sinh\left(d x + c\right)^{8} + 5 \, a b \cosh\left(d x + c\right)^{6} + 8 \, {\left(429 \, a b \cosh\left(d x + c\right)^{7} + 495 \, a b \cosh\left(d x + c\right)^{5} + 150 \, a b \cosh\left(d x + c\right)^{3} + 10 \, a b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + {\left(3003 \, a b \cosh\left(d x + c\right)^{8} + 4620 \, a b \cosh\left(d x + c\right)^{6} + 2100 \, a b \cosh\left(d x + c\right)^{4} + 280 \, a b \cosh\left(d x + c\right)^{2} + 5 \, a b\right)} \sinh\left(d x + c\right)^{6} + a b \cosh\left(d x + c\right)^{4} + 2 \, {\left(1001 \, a b \cosh\left(d x + c\right)^{9} + 1980 \, a b \cosh\left(d x + c\right)^{7} + 1260 \, a b \cosh\left(d x + c\right)^{5} + 280 \, 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} + {\left(1001 \, a b \cosh\left(d x + c\right)^{10} + 2475 \, a b \cosh\left(d x + c\right)^{8} + 2100 \, a b \cosh\left(d x + c\right)^{6} + 700 \, a b \cosh\left(d x + c\right)^{4} + 75 \, a b \cosh\left(d x + c\right)^{2} + a b\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(91 \, a b \cosh\left(d x + c\right)^{11} + 275 \, a b \cosh\left(d x + c\right)^{9} + 300 \, a b \cosh\left(d x + c\right)^{7} + 140 \, a b \cosh\left(d x + c\right)^{5} + 25 \, 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} + {\left(91 \, a b \cosh\left(d x + c\right)^{12} + 330 \, a b \cosh\left(d x + c\right)^{10} + 450 \, a b \cosh\left(d x + c\right)^{8} + 280 \, a b \cosh\left(d x + c\right)^{6} + 75 \, a b \cosh\left(d x + c\right)^{4} + 6 \, a b \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(7 \, a b \cosh\left(d x + c\right)^{13} + 30 \, a b \cosh\left(d x + c\right)^{11} + 50 \, a b \cosh\left(d x + c\right)^{9} + 40 \, a b \cosh\left(d x + c\right)^{7} + 15 \, a b \cosh\left(d x + c\right)^{5} + 2 \, a b \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right)\right)} \log\left(\frac{2 \, \cosh\left(d x + c\right)}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) + 6 \, {\left(15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{17} - 40 \, {\left(a^{2} + 10 \, a b + 9 \, b^{2}\right)} \cosh\left(d x + c\right)^{15} + 70 \, {\left(4 \, {\left(a^{2} - 16 \, a b + 21 \, b^{2}\right)} d x - 5 \, a^{2} - 30 \, a b - 25 \, b^{2}\right)} \cosh\left(d x + c\right)^{13} + 20 \, {\left(60 \, {\left(a^{2} - 16 \, a b + 21 \, b^{2}\right)} d x - 31 \, a^{2} - 82 \, a b + 501 \, b^{2}\right)} \cosh\left(d x + c\right)^{11} + 100 \, {\left(20 \, {\left(a^{2} - 16 \, a b + 21 \, b^{2}\right)} d x - 3 \, a^{2} + 15 \, a b + 307 \, b^{2}\right)} \cosh\left(d x + c\right)^{9} + 80 \, {\left(20 \, {\left(a^{2} - 16 \, a b + 21 \, b^{2}\right)} d x + 3 \, a^{2} + 15 \, a b + 461 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} + 10 \, {\left(60 \, {\left(a^{2} - 16 \, a b + 21 \, b^{2}\right)} d x + 31 \, a^{2} - 82 \, a b + 1803 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 4 \, {\left(20 \, {\left(a^{2} - 16 \, a b + 21 \, b^{2}\right)} d x + 25 \, a^{2} - 150 \, a b + 893 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 5 \, {\left(a^{2} - 10 \, a b + 9 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{320 \, {\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} + 5 \, d \cosh\left(d x + c\right)^{12} + {\left(91 \, d \cosh\left(d x + c\right)^{2} + 5 \, d\right)} \sinh\left(d x + c\right)^{12} + 4 \, {\left(91 \, d \cosh\left(d x + c\right)^{3} + 15 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{11} + 10 \, d \cosh\left(d x + c\right)^{10} + {\left(1001 \, d \cosh\left(d x + c\right)^{4} + 330 \, d \cosh\left(d x + c\right)^{2} + 10 \, d\right)} \sinh\left(d x + c\right)^{10} + 2 \, {\left(1001 \, d \cosh\left(d x + c\right)^{5} + 550 \, d \cosh\left(d x + c\right)^{3} + 50 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} + 10 \, d \cosh\left(d x + c\right)^{8} + {\left(3003 \, d \cosh\left(d x + c\right)^{6} + 2475 \, d \cosh\left(d x + c\right)^{4} + 450 \, d \cosh\left(d x + c\right)^{2} + 10 \, d\right)} \sinh\left(d x + c\right)^{8} + 8 \, {\left(429 \, d \cosh\left(d x + c\right)^{7} + 495 \, d \cosh\left(d x + c\right)^{5} + 150 \, d \cosh\left(d x + c\right)^{3} + 10 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 5 \, d \cosh\left(d x + c\right)^{6} + {\left(3003 \, d \cosh\left(d x + c\right)^{8} + 4620 \, d \cosh\left(d x + c\right)^{6} + 2100 \, d \cosh\left(d x + c\right)^{4} + 280 \, d \cosh\left(d x + c\right)^{2} + 5 \, d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(1001 \, d \cosh\left(d x + c\right)^{9} + 1980 \, d \cosh\left(d x + c\right)^{7} + 1260 \, d \cosh\left(d x + c\right)^{5} + 280 \, d \cosh\left(d x + c\right)^{3} + 15 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + d \cosh\left(d x + c\right)^{4} + {\left(1001 \, d \cosh\left(d x + c\right)^{10} + 2475 \, d \cosh\left(d x + c\right)^{8} + 2100 \, d \cosh\left(d x + c\right)^{6} + 700 \, d \cosh\left(d x + c\right)^{4} + 75 \, d \cosh\left(d x + c\right)^{2} + d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(91 \, d \cosh\left(d x + c\right)^{11} + 275 \, d \cosh\left(d x + c\right)^{9} + 300 \, d \cosh\left(d x + c\right)^{7} + 140 \, d \cosh\left(d x + c\right)^{5} + 25 \, d \cosh\left(d x + c\right)^{3} + d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(91 \, d \cosh\left(d x + c\right)^{12} + 330 \, d \cosh\left(d x + c\right)^{10} + 450 \, d \cosh\left(d x + c\right)^{8} + 280 \, d \cosh\left(d x + c\right)^{6} + 75 \, d \cosh\left(d x + c\right)^{4} + 6 \, d \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(7 \, d \cosh\left(d x + c\right)^{13} + 30 \, d \cosh\left(d x + c\right)^{11} + 50 \, d \cosh\left(d x + c\right)^{9} + 40 \, d \cosh\left(d x + c\right)^{7} + 15 \, d \cosh\left(d x + c\right)^{5} + 2 \, d \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"1/320*(5*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^18 + 90*(a^2 + 2*a*b + b^2)*cosh(d*x + c)*sinh(d*x + c)^17 + 5*(a^2 + 2*a*b + b^2)*sinh(d*x + c)^18 - 15*(a^2 + 10*a*b + 9*b^2)*cosh(d*x + c)^16 + 15*(51*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 - a^2 - 10*a*b - 9*b^2)*sinh(d*x + c)^16 + 240*(17*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 - (a^2 + 10*a*b + 9*b^2)*cosh(d*x + c))*sinh(d*x + c)^15 + 30*(4*(a^2 - 16*a*b + 21*b^2)*d*x - 5*a^2 - 30*a*b - 25*b^2)*cosh(d*x + c)^14 + 30*(510*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 + 4*(a^2 - 16*a*b + 21*b^2)*d*x - 60*(a^2 + 10*a*b + 9*b^2)*cosh(d*x + c)^2 - 5*a^2 - 30*a*b - 25*b^2)*sinh(d*x + c)^14 + 420*(102*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^5 - 20*(a^2 + 10*a*b + 9*b^2)*cosh(d*x + c)^3 + (4*(a^2 - 16*a*b + 21*b^2)*d*x - 5*a^2 - 30*a*b - 25*b^2)*cosh(d*x + c))*sinh(d*x + c)^13 + 10*(60*(a^2 - 16*a*b + 21*b^2)*d*x - 31*a^2 - 82*a*b + 501*b^2)*cosh(d*x + c)^12 + 10*(9282*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^6 - 2730*(a^2 + 10*a*b + 9*b^2)*cosh(d*x + c)^4 + 60*(a^2 - 16*a*b + 21*b^2)*d*x + 273*(4*(a^2 - 16*a*b + 21*b^2)*d*x - 5*a^2 - 30*a*b - 25*b^2)*cosh(d*x + c)^2 - 31*a^2 - 82*a*b + 501*b^2)*sinh(d*x + c)^12 + 120*(1326*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^7 - 546*(a^2 + 10*a*b + 9*b^2)*cosh(d*x + c)^5 + 91*(4*(a^2 - 16*a*b + 21*b^2)*d*x - 5*a^2 - 30*a*b - 25*b^2)*cosh(d*x + c)^3 + (60*(a^2 - 16*a*b + 21*b^2)*d*x - 31*a^2 - 82*a*b + 501*b^2)*cosh(d*x + c))*sinh(d*x + c)^11 + 60*(20*(a^2 - 16*a*b + 21*b^2)*d*x - 3*a^2 + 15*a*b + 307*b^2)*cosh(d*x + c)^10 + 30*(7293*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^8 - 4004*(a^2 + 10*a*b + 9*b^2)*cosh(d*x + c)^6 + 1001*(4*(a^2 - 16*a*b + 21*b^2)*d*x - 5*a^2 - 30*a*b - 25*b^2)*cosh(d*x + c)^4 + 40*(a^2 - 16*a*b + 21*b^2)*d*x + 22*(60*(a^2 - 16*a*b + 21*b^2)*d*x - 31*a^2 - 82*a*b + 501*b^2)*cosh(d*x + c)^2 - 6*a^2 + 30*a*b + 614*b^2)*sinh(d*x + c)^10 + 20*(12155*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^9 - 8580*(a^2 + 10*a*b + 9*b^2)*cosh(d*x + c)^7 + 3003*(4*(a^2 - 16*a*b + 21*b^2)*d*x - 5*a^2 - 30*a*b - 25*b^2)*cosh(d*x + c)^5 + 110*(60*(a^2 - 16*a*b + 21*b^2)*d*x - 31*a^2 - 82*a*b + 501*b^2)*cosh(d*x + c)^3 + 30*(20*(a^2 - 16*a*b + 21*b^2)*d*x - 3*a^2 + 15*a*b + 307*b^2)*cosh(d*x + c))*sinh(d*x + c)^9 + 60*(20*(a^2 - 16*a*b + 21*b^2)*d*x + 3*a^2 + 15*a*b + 461*b^2)*cosh(d*x + c)^8 + 30*(7293*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^10 - 6435*(a^2 + 10*a*b + 9*b^2)*cosh(d*x + c)^8 + 3003*(4*(a^2 - 16*a*b + 21*b^2)*d*x - 5*a^2 - 30*a*b - 25*b^2)*cosh(d*x + c)^6 + 165*(60*(a^2 - 16*a*b + 21*b^2)*d*x - 31*a^2 - 82*a*b + 501*b^2)*cosh(d*x + c)^4 + 40*(a^2 - 16*a*b + 21*b^2)*d*x + 90*(20*(a^2 - 16*a*b + 21*b^2)*d*x - 3*a^2 + 15*a*b + 307*b^2)*cosh(d*x + c)^2 + 6*a^2 + 30*a*b + 922*b^2)*sinh(d*x + c)^8 + 240*(663*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^11 - 715*(a^2 + 10*a*b + 9*b^2)*cosh(d*x + c)^9 + 429*(4*(a^2 - 16*a*b + 21*b^2)*d*x - 5*a^2 - 30*a*b - 25*b^2)*cosh(d*x + c)^7 + 33*(60*(a^2 - 16*a*b + 21*b^2)*d*x - 31*a^2 - 82*a*b + 501*b^2)*cosh(d*x + c)^5 + 30*(20*(a^2 - 16*a*b + 21*b^2)*d*x - 3*a^2 + 15*a*b + 307*b^2)*cosh(d*x + c)^3 + 2*(20*(a^2 - 16*a*b + 21*b^2)*d*x + 3*a^2 + 15*a*b + 461*b^2)*cosh(d*x + c))*sinh(d*x + c)^7 + 10*(60*(a^2 - 16*a*b + 21*b^2)*d*x + 31*a^2 - 82*a*b + 1803*b^2)*cosh(d*x + c)^6 + 10*(9282*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^12 - 12012*(a^2 + 10*a*b + 9*b^2)*cosh(d*x + c)^10 + 9009*(4*(a^2 - 16*a*b + 21*b^2)*d*x - 5*a^2 - 30*a*b - 25*b^2)*cosh(d*x + c)^8 + 924*(60*(a^2 - 16*a*b + 21*b^2)*d*x - 31*a^2 - 82*a*b + 501*b^2)*cosh(d*x + c)^6 + 1260*(20*(a^2 - 16*a*b + 21*b^2)*d*x - 3*a^2 + 15*a*b + 307*b^2)*cosh(d*x + c)^4 + 60*(a^2 - 16*a*b + 21*b^2)*d*x + 168*(20*(a^2 - 16*a*b + 21*b^2)*d*x + 3*a^2 + 15*a*b + 461*b^2)*cosh(d*x + c)^2 + 31*a^2 - 82*a*b + 1803*b^2)*sinh(d*x + c)^6 + 60*(714*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^13 - 1092*(a^2 + 10*a*b + 9*b^2)*cosh(d*x + c)^11 + 1001*(4*(a^2 - 16*a*b + 21*b^2)*d*x - 5*a^2 - 30*a*b - 25*b^2)*cosh(d*x + c)^9 + 132*(60*(a^2 - 16*a*b + 21*b^2)*d*x - 31*a^2 - 82*a*b + 501*b^2)*cosh(d*x + c)^7 + 252*(20*(a^2 - 16*a*b + 21*b^2)*d*x - 3*a^2 + 15*a*b + 307*b^2)*cosh(d*x + c)^5 + 56*(20*(a^2 - 16*a*b + 21*b^2)*d*x + 3*a^2 + 15*a*b + 461*b^2)*cosh(d*x + c)^3 + (60*(a^2 - 16*a*b + 21*b^2)*d*x + 31*a^2 - 82*a*b + 1803*b^2)*cosh(d*x + c))*sinh(d*x + c)^5 + 6*(20*(a^2 - 16*a*b + 21*b^2)*d*x + 25*a^2 - 150*a*b + 893*b^2)*cosh(d*x + c)^4 + 6*(2550*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^14 - 4550*(a^2 + 10*a*b + 9*b^2)*cosh(d*x + c)^12 + 5005*(4*(a^2 - 16*a*b + 21*b^2)*d*x - 5*a^2 - 30*a*b - 25*b^2)*cosh(d*x + c)^10 + 825*(60*(a^2 - 16*a*b + 21*b^2)*d*x - 31*a^2 - 82*a*b + 501*b^2)*cosh(d*x + c)^8 + 2100*(20*(a^2 - 16*a*b + 21*b^2)*d*x - 3*a^2 + 15*a*b + 307*b^2)*cosh(d*x + c)^6 + 700*(20*(a^2 - 16*a*b + 21*b^2)*d*x + 3*a^2 + 15*a*b + 461*b^2)*cosh(d*x + c)^4 + 20*(a^2 - 16*a*b + 21*b^2)*d*x + 25*(60*(a^2 - 16*a*b + 21*b^2)*d*x + 31*a^2 - 82*a*b + 1803*b^2)*cosh(d*x + c)^2 + 25*a^2 - 150*a*b + 893*b^2)*sinh(d*x + c)^4 + 8*(510*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^15 - 1050*(a^2 + 10*a*b + 9*b^2)*cosh(d*x + c)^13 + 1365*(4*(a^2 - 16*a*b + 21*b^2)*d*x - 5*a^2 - 30*a*b - 25*b^2)*cosh(d*x + c)^11 + 275*(60*(a^2 - 16*a*b + 21*b^2)*d*x - 31*a^2 - 82*a*b + 501*b^2)*cosh(d*x + c)^9 + 900*(20*(a^2 - 16*a*b + 21*b^2)*d*x - 3*a^2 + 15*a*b + 307*b^2)*cosh(d*x + c)^7 + 420*(20*(a^2 - 16*a*b + 21*b^2)*d*x + 3*a^2 + 15*a*b + 461*b^2)*cosh(d*x + c)^5 + 25*(60*(a^2 - 16*a*b + 21*b^2)*d*x + 31*a^2 - 82*a*b + 1803*b^2)*cosh(d*x + c)^3 + 3*(20*(a^2 - 16*a*b + 21*b^2)*d*x + 25*a^2 - 150*a*b + 893*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 15*(a^2 - 10*a*b + 9*b^2)*cosh(d*x + c)^2 + 3*(255*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^16 - 600*(a^2 + 10*a*b + 9*b^2)*cosh(d*x + c)^14 + 910*(4*(a^2 - 16*a*b + 21*b^2)*d*x - 5*a^2 - 30*a*b - 25*b^2)*cosh(d*x + c)^12 + 220*(60*(a^2 - 16*a*b + 21*b^2)*d*x - 31*a^2 - 82*a*b + 501*b^2)*cosh(d*x + c)^10 + 900*(20*(a^2 - 16*a*b + 21*b^2)*d*x - 3*a^2 + 15*a*b + 307*b^2)*cosh(d*x + c)^8 + 560*(20*(a^2 - 16*a*b + 21*b^2)*d*x + 3*a^2 + 15*a*b + 461*b^2)*cosh(d*x + c)^6 + 50*(60*(a^2 - 16*a*b + 21*b^2)*d*x + 31*a^2 - 82*a*b + 1803*b^2)*cosh(d*x + c)^4 + 12*(20*(a^2 - 16*a*b + 21*b^2)*d*x + 25*a^2 - 150*a*b + 893*b^2)*cosh(d*x + c)^2 + 5*a^2 - 50*a*b + 45*b^2)*sinh(d*x + c)^2 - 5*a^2 + 10*a*b - 5*b^2 + 1920*(a*b*cosh(d*x + c)^14 + 14*a*b*cosh(d*x + c)*sinh(d*x + c)^13 + a*b*sinh(d*x + c)^14 + 5*a*b*cosh(d*x + c)^12 + (91*a*b*cosh(d*x + c)^2 + 5*a*b)*sinh(d*x + c)^12 + 10*a*b*cosh(d*x + c)^10 + 4*(91*a*b*cosh(d*x + c)^3 + 15*a*b*cosh(d*x + c))*sinh(d*x + c)^11 + (1001*a*b*cosh(d*x + c)^4 + 330*a*b*cosh(d*x + c)^2 + 10*a*b)*sinh(d*x + c)^10 + 10*a*b*cosh(d*x + c)^8 + 2*(1001*a*b*cosh(d*x + c)^5 + 550*a*b*cosh(d*x + c)^3 + 50*a*b*cosh(d*x + c))*sinh(d*x + c)^9 + (3003*a*b*cosh(d*x + c)^6 + 2475*a*b*cosh(d*x + c)^4 + 450*a*b*cosh(d*x + c)^2 + 10*a*b)*sinh(d*x + c)^8 + 5*a*b*cosh(d*x + c)^6 + 8*(429*a*b*cosh(d*x + c)^7 + 495*a*b*cosh(d*x + c)^5 + 150*a*b*cosh(d*x + c)^3 + 10*a*b*cosh(d*x + c))*sinh(d*x + c)^7 + (3003*a*b*cosh(d*x + c)^8 + 4620*a*b*cosh(d*x + c)^6 + 2100*a*b*cosh(d*x + c)^4 + 280*a*b*cosh(d*x + c)^2 + 5*a*b)*sinh(d*x + c)^6 + a*b*cosh(d*x + c)^4 + 2*(1001*a*b*cosh(d*x + c)^9 + 1980*a*b*cosh(d*x + c)^7 + 1260*a*b*cosh(d*x + c)^5 + 280*a*b*cosh(d*x + c)^3 + 15*a*b*cosh(d*x + c))*sinh(d*x + c)^5 + (1001*a*b*cosh(d*x + c)^10 + 2475*a*b*cosh(d*x + c)^8 + 2100*a*b*cosh(d*x + c)^6 + 700*a*b*cosh(d*x + c)^4 + 75*a*b*cosh(d*x + c)^2 + a*b)*sinh(d*x + c)^4 + 4*(91*a*b*cosh(d*x + c)^11 + 275*a*b*cosh(d*x + c)^9 + 300*a*b*cosh(d*x + c)^7 + 140*a*b*cosh(d*x + c)^5 + 25*a*b*cosh(d*x + c)^3 + a*b*cosh(d*x + c))*sinh(d*x + c)^3 + (91*a*b*cosh(d*x + c)^12 + 330*a*b*cosh(d*x + c)^10 + 450*a*b*cosh(d*x + c)^8 + 280*a*b*cosh(d*x + c)^6 + 75*a*b*cosh(d*x + c)^4 + 6*a*b*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 2*(7*a*b*cosh(d*x + c)^13 + 30*a*b*cosh(d*x + c)^11 + 50*a*b*cosh(d*x + c)^9 + 40*a*b*cosh(d*x + c)^7 + 15*a*b*cosh(d*x + c)^5 + 2*a*b*cosh(d*x + c)^3)*sinh(d*x + c))*log(2*cosh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))) + 6*(15*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^17 - 40*(a^2 + 10*a*b + 9*b^2)*cosh(d*x + c)^15 + 70*(4*(a^2 - 16*a*b + 21*b^2)*d*x - 5*a^2 - 30*a*b - 25*b^2)*cosh(d*x + c)^13 + 20*(60*(a^2 - 16*a*b + 21*b^2)*d*x - 31*a^2 - 82*a*b + 501*b^2)*cosh(d*x + c)^11 + 100*(20*(a^2 - 16*a*b + 21*b^2)*d*x - 3*a^2 + 15*a*b + 307*b^2)*cosh(d*x + c)^9 + 80*(20*(a^2 - 16*a*b + 21*b^2)*d*x + 3*a^2 + 15*a*b + 461*b^2)*cosh(d*x + c)^7 + 10*(60*(a^2 - 16*a*b + 21*b^2)*d*x + 31*a^2 - 82*a*b + 1803*b^2)*cosh(d*x + c)^5 + 4*(20*(a^2 - 16*a*b + 21*b^2)*d*x + 25*a^2 - 150*a*b + 893*b^2)*cosh(d*x + c)^3 + 5*(a^2 - 10*a*b + 9*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 + 5*d*cosh(d*x + c)^12 + (91*d*cosh(d*x + c)^2 + 5*d)*sinh(d*x + c)^12 + 4*(91*d*cosh(d*x + c)^3 + 15*d*cosh(d*x + c))*sinh(d*x + c)^11 + 10*d*cosh(d*x + c)^10 + (1001*d*cosh(d*x + c)^4 + 330*d*cosh(d*x + c)^2 + 10*d)*sinh(d*x + c)^10 + 2*(1001*d*cosh(d*x + c)^5 + 550*d*cosh(d*x + c)^3 + 50*d*cosh(d*x + c))*sinh(d*x + c)^9 + 10*d*cosh(d*x + c)^8 + (3003*d*cosh(d*x + c)^6 + 2475*d*cosh(d*x + c)^4 + 450*d*cosh(d*x + c)^2 + 10*d)*sinh(d*x + c)^8 + 8*(429*d*cosh(d*x + c)^7 + 495*d*cosh(d*x + c)^5 + 150*d*cosh(d*x + c)^3 + 10*d*cosh(d*x + c))*sinh(d*x + c)^7 + 5*d*cosh(d*x + c)^6 + (3003*d*cosh(d*x + c)^8 + 4620*d*cosh(d*x + c)^6 + 2100*d*cosh(d*x + c)^4 + 280*d*cosh(d*x + c)^2 + 5*d)*sinh(d*x + c)^6 + 2*(1001*d*cosh(d*x + c)^9 + 1980*d*cosh(d*x + c)^7 + 1260*d*cosh(d*x + c)^5 + 280*d*cosh(d*x + c)^3 + 15*d*cosh(d*x + c))*sinh(d*x + c)^5 + d*cosh(d*x + c)^4 + (1001*d*cosh(d*x + c)^10 + 2475*d*cosh(d*x + c)^8 + 2100*d*cosh(d*x + c)^6 + 700*d*cosh(d*x + c)^4 + 75*d*cosh(d*x + c)^2 + d)*sinh(d*x + c)^4 + 4*(91*d*cosh(d*x + c)^11 + 275*d*cosh(d*x + c)^9 + 300*d*cosh(d*x + c)^7 + 140*d*cosh(d*x + c)^5 + 25*d*cosh(d*x + c)^3 + d*cosh(d*x + c))*sinh(d*x + c)^3 + (91*d*cosh(d*x + c)^12 + 330*d*cosh(d*x + c)^10 + 450*d*cosh(d*x + c)^8 + 280*d*cosh(d*x + c)^6 + 75*d*cosh(d*x + c)^4 + 6*d*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 2*(7*d*cosh(d*x + c)^13 + 30*d*cosh(d*x + c)^11 + 50*d*cosh(d*x + c)^9 + 40*d*cosh(d*x + c)^7 + 15*d*cosh(d*x + c)^5 + 2*d*cosh(d*x + c)^3)*sinh(d*x + c))","B",0
58,1,3341,0,0.659574," ","integrate(sinh(d*x+c)^3*(a+b*tanh(d*x+c)^3)^2,x, algorithm=""fricas"")","\frac{5 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{16} + 80 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{15} + 5 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{16} - 20 \, {\left(a^{2} + 11 \, a b + 10 \, b^{2}\right)} \cosh\left(d x + c\right)^{14} + 20 \, {\left(30 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} - a^{2} - 11 \, a b - 10 \, b^{2}\right)} \sinh\left(d x + c\right)^{14} + 280 \, {\left(10 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(a^{2} + 11 \, a b + 10 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{13} - 20 \, {\left(11 \, a^{2} + 61 \, a b + 137 \, b^{2}\right)} \cosh\left(d x + c\right)^{12} + 20 \, {\left(455 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} - 91 \, {\left(a^{2} + 11 \, a b + 10 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 11 \, a^{2} - 61 \, a b - 137 \, b^{2}\right)} \sinh\left(d x + c\right)^{12} + 80 \, {\left(273 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{5} - 91 \, {\left(a^{2} + 11 \, a b + 10 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(11 \, a^{2} + 61 \, a b + 137 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{11} - 20 \, {\left(31 \, a^{2} + 87 \, a b + 390 \, b^{2}\right)} \cosh\left(d x + c\right)^{10} + 20 \, {\left(2002 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{6} - 1001 \, {\left(a^{2} + 11 \, a b + 10 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} - 66 \, {\left(11 \, a^{2} + 61 \, a b + 137 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 31 \, a^{2} - 87 \, a b - 390 \, b^{2}\right)} \sinh\left(d x + c\right)^{10} + 40 \, {\left(1430 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{7} - 1001 \, {\left(a^{2} + 11 \, a b + 10 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} - 110 \, {\left(11 \, a^{2} + 61 \, a b + 137 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - 5 \, {\left(31 \, a^{2} + 87 \, a b + 390 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} - 2 \, {\left(425 \, a^{2} + 5649 \, b^{2}\right)} \cosh\left(d x + c\right)^{8} + 2 \, {\left(32175 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{8} - 30030 \, {\left(a^{2} + 11 \, a b + 10 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} - 4950 \, {\left(11 \, a^{2} + 61 \, a b + 137 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} - 450 \, {\left(31 \, a^{2} + 87 \, a b + 390 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 425 \, a^{2} - 5649 \, b^{2}\right)} \sinh\left(d x + c\right)^{8} + 16 \, {\left(3575 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{9} - 4290 \, {\left(a^{2} + 11 \, a b + 10 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} - 990 \, {\left(11 \, a^{2} + 61 \, a b + 137 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} - 150 \, {\left(31 \, a^{2} + 87 \, a b + 390 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(425 \, a^{2} + 5649 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} - 20 \, {\left(31 \, a^{2} - 87 \, a b + 390 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(10010 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{10} - 15015 \, {\left(a^{2} + 11 \, a b + 10 \, b^{2}\right)} \cosh\left(d x + c\right)^{8} - 4620 \, {\left(11 \, a^{2} + 61 \, a b + 137 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} - 1050 \, {\left(31 \, a^{2} + 87 \, a b + 390 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} - 14 \, {\left(425 \, a^{2} + 5649 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 155 \, a^{2} + 435 \, a b - 1950 \, b^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(2730 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{11} - 5005 \, {\left(a^{2} + 11 \, a b + 10 \, b^{2}\right)} \cosh\left(d x + c\right)^{9} - 1980 \, {\left(11 \, a^{2} + 61 \, a b + 137 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} - 630 \, {\left(31 \, a^{2} + 87 \, a b + 390 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} - 14 \, {\left(425 \, a^{2} + 5649 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - 15 \, {\left(31 \, a^{2} - 87 \, a b + 390 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 20 \, {\left(11 \, a^{2} - 61 \, a b + 137 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 20 \, {\left(455 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{12} - 1001 \, {\left(a^{2} + 11 \, a b + 10 \, b^{2}\right)} \cosh\left(d x + c\right)^{10} - 495 \, {\left(11 \, a^{2} + 61 \, a b + 137 \, b^{2}\right)} \cosh\left(d x + c\right)^{8} - 210 \, {\left(31 \, a^{2} + 87 \, a b + 390 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} - 7 \, {\left(425 \, a^{2} + 5649 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} - 15 \, {\left(31 \, a^{2} - 87 \, a b + 390 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 11 \, a^{2} + 61 \, a b - 137 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 16 \, {\left(175 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{13} - 455 \, {\left(a^{2} + 11 \, a b + 10 \, b^{2}\right)} \cosh\left(d x + c\right)^{11} - 275 \, {\left(11 \, a^{2} + 61 \, a b + 137 \, b^{2}\right)} \cosh\left(d x + c\right)^{9} - 150 \, {\left(31 \, a^{2} + 87 \, a b + 390 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} - 7 \, {\left(425 \, a^{2} + 5649 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} - 25 \, {\left(31 \, a^{2} - 87 \, a b + 390 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - 5 \, {\left(11 \, a^{2} - 61 \, a b + 137 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 20 \, {\left(a^{2} - 11 \, a b + 10 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(150 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{14} - 455 \, {\left(a^{2} + 11 \, a b + 10 \, b^{2}\right)} \cosh\left(d x + c\right)^{12} - 330 \, {\left(11 \, a^{2} + 61 \, a b + 137 \, b^{2}\right)} \cosh\left(d x + c\right)^{10} - 225 \, {\left(31 \, a^{2} + 87 \, a b + 390 \, b^{2}\right)} \cosh\left(d x + c\right)^{8} - 14 \, {\left(425 \, a^{2} + 5649 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} - 75 \, {\left(31 \, a^{2} - 87 \, a b + 390 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} - 30 \, {\left(11 \, a^{2} - 61 \, a b + 137 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 5 \, a^{2} + 55 \, a b - 50 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} + 5 \, a^{2} - 10 \, a b + 5 \, b^{2} + 1200 \, {\left(a b \cosh\left(d x + c\right)^{13} + 13 \, a b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{12} + a b \sinh\left(d x + c\right)^{13} + 5 \, a b \cosh\left(d x + c\right)^{11} + {\left(78 \, a b \cosh\left(d x + c\right)^{2} + 5 \, a b\right)} \sinh\left(d x + c\right)^{11} + 10 \, a b \cosh\left(d x + c\right)^{9} + 11 \, {\left(26 \, 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)^{10} + 5 \, {\left(143 \, a b \cosh\left(d x + c\right)^{4} + 55 \, a b \cosh\left(d x + c\right)^{2} + 2 \, a b\right)} \sinh\left(d x + c\right)^{9} + 10 \, a b \cosh\left(d x + c\right)^{7} + 3 \, {\left(429 \, a b \cosh\left(d x + c\right)^{5} + 275 \, a b \cosh\left(d x + c\right)^{3} + 30 \, a b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{8} + 2 \, {\left(858 \, a b \cosh\left(d x + c\right)^{6} + 825 \, a b \cosh\left(d x + c\right)^{4} + 180 \, a b \cosh\left(d x + c\right)^{2} + 5 \, a b\right)} \sinh\left(d x + c\right)^{7} + 5 \, a b \cosh\left(d x + c\right)^{5} + 2 \, {\left(858 \, a b \cosh\left(d x + c\right)^{7} + 1155 \, a b \cosh\left(d x + c\right)^{5} + 420 \, a b \cosh\left(d x + c\right)^{3} + 35 \, a b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} + {\left(1287 \, a b \cosh\left(d x + c\right)^{8} + 2310 \, a b \cosh\left(d x + c\right)^{6} + 1260 \, a b \cosh\left(d x + c\right)^{4} + 210 \, a b \cosh\left(d x + c\right)^{2} + 5 \, a b\right)} \sinh\left(d x + c\right)^{5} + a b \cosh\left(d x + c\right)^{3} + 5 \, {\left(143 \, a b \cosh\left(d x + c\right)^{9} + 330 \, a b \cosh\left(d x + c\right)^{7} + 252 \, a b \cosh\left(d x + c\right)^{5} + 70 \, 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} + {\left(286 \, a b \cosh\left(d x + c\right)^{10} + 825 \, a b \cosh\left(d x + c\right)^{8} + 840 \, a b \cosh\left(d x + c\right)^{6} + 350 \, a b \cosh\left(d x + c\right)^{4} + 50 \, a b \cosh\left(d x + c\right)^{2} + a b\right)} \sinh\left(d x + c\right)^{3} + {\left(78 \, a b \cosh\left(d x + c\right)^{11} + 275 \, a b \cosh\left(d x + c\right)^{9} + 360 \, a b \cosh\left(d x + c\right)^{7} + 210 \, a b \cosh\left(d x + c\right)^{5} + 50 \, 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)^{2} + {\left(13 \, a b \cosh\left(d x + c\right)^{12} + 55 \, a b \cosh\left(d x + c\right)^{10} + 90 \, a b \cosh\left(d x + c\right)^{8} + 70 \, a b \cosh\left(d x + c\right)^{6} + 25 \, a b \cosh\left(d x + c\right)^{4} + 3 \, a b \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) + 8 \, {\left(10 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{15} - 35 \, {\left(a^{2} + 11 \, a b + 10 \, b^{2}\right)} \cosh\left(d x + c\right)^{13} - 30 \, {\left(11 \, a^{2} + 61 \, a b + 137 \, b^{2}\right)} \cosh\left(d x + c\right)^{11} - 25 \, {\left(31 \, a^{2} + 87 \, a b + 390 \, b^{2}\right)} \cosh\left(d x + c\right)^{9} - 2 \, {\left(425 \, a^{2} + 5649 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} - 15 \, {\left(31 \, a^{2} - 87 \, a b + 390 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} - 10 \, {\left(11 \, a^{2} - 61 \, a b + 137 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - 5 \, {\left(a^{2} - 11 \, a b + 10 \, b^{2}\right)} \cosh\left(d x + c\right)\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*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^16 + 80*(a^2 + 2*a*b + b^2)*cosh(d*x + c)*sinh(d*x + c)^15 + 5*(a^2 + 2*a*b + b^2)*sinh(d*x + c)^16 - 20*(a^2 + 11*a*b + 10*b^2)*cosh(d*x + c)^14 + 20*(30*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 - a^2 - 11*a*b - 10*b^2)*sinh(d*x + c)^14 + 280*(10*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 - (a^2 + 11*a*b + 10*b^2)*cosh(d*x + c))*sinh(d*x + c)^13 - 20*(11*a^2 + 61*a*b + 137*b^2)*cosh(d*x + c)^12 + 20*(455*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 - 91*(a^2 + 11*a*b + 10*b^2)*cosh(d*x + c)^2 - 11*a^2 - 61*a*b - 137*b^2)*sinh(d*x + c)^12 + 80*(273*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^5 - 91*(a^2 + 11*a*b + 10*b^2)*cosh(d*x + c)^3 - 3*(11*a^2 + 61*a*b + 137*b^2)*cosh(d*x + c))*sinh(d*x + c)^11 - 20*(31*a^2 + 87*a*b + 390*b^2)*cosh(d*x + c)^10 + 20*(2002*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^6 - 1001*(a^2 + 11*a*b + 10*b^2)*cosh(d*x + c)^4 - 66*(11*a^2 + 61*a*b + 137*b^2)*cosh(d*x + c)^2 - 31*a^2 - 87*a*b - 390*b^2)*sinh(d*x + c)^10 + 40*(1430*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^7 - 1001*(a^2 + 11*a*b + 10*b^2)*cosh(d*x + c)^5 - 110*(11*a^2 + 61*a*b + 137*b^2)*cosh(d*x + c)^3 - 5*(31*a^2 + 87*a*b + 390*b^2)*cosh(d*x + c))*sinh(d*x + c)^9 - 2*(425*a^2 + 5649*b^2)*cosh(d*x + c)^8 + 2*(32175*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^8 - 30030*(a^2 + 11*a*b + 10*b^2)*cosh(d*x + c)^6 - 4950*(11*a^2 + 61*a*b + 137*b^2)*cosh(d*x + c)^4 - 450*(31*a^2 + 87*a*b + 390*b^2)*cosh(d*x + c)^2 - 425*a^2 - 5649*b^2)*sinh(d*x + c)^8 + 16*(3575*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^9 - 4290*(a^2 + 11*a*b + 10*b^2)*cosh(d*x + c)^7 - 990*(11*a^2 + 61*a*b + 137*b^2)*cosh(d*x + c)^5 - 150*(31*a^2 + 87*a*b + 390*b^2)*cosh(d*x + c)^3 - (425*a^2 + 5649*b^2)*cosh(d*x + c))*sinh(d*x + c)^7 - 20*(31*a^2 - 87*a*b + 390*b^2)*cosh(d*x + c)^6 + 4*(10010*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^10 - 15015*(a^2 + 11*a*b + 10*b^2)*cosh(d*x + c)^8 - 4620*(11*a^2 + 61*a*b + 137*b^2)*cosh(d*x + c)^6 - 1050*(31*a^2 + 87*a*b + 390*b^2)*cosh(d*x + c)^4 - 14*(425*a^2 + 5649*b^2)*cosh(d*x + c)^2 - 155*a^2 + 435*a*b - 1950*b^2)*sinh(d*x + c)^6 + 8*(2730*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^11 - 5005*(a^2 + 11*a*b + 10*b^2)*cosh(d*x + c)^9 - 1980*(11*a^2 + 61*a*b + 137*b^2)*cosh(d*x + c)^7 - 630*(31*a^2 + 87*a*b + 390*b^2)*cosh(d*x + c)^5 - 14*(425*a^2 + 5649*b^2)*cosh(d*x + c)^3 - 15*(31*a^2 - 87*a*b + 390*b^2)*cosh(d*x + c))*sinh(d*x + c)^5 - 20*(11*a^2 - 61*a*b + 137*b^2)*cosh(d*x + c)^4 + 20*(455*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^12 - 1001*(a^2 + 11*a*b + 10*b^2)*cosh(d*x + c)^10 - 495*(11*a^2 + 61*a*b + 137*b^2)*cosh(d*x + c)^8 - 210*(31*a^2 + 87*a*b + 390*b^2)*cosh(d*x + c)^6 - 7*(425*a^2 + 5649*b^2)*cosh(d*x + c)^4 - 15*(31*a^2 - 87*a*b + 390*b^2)*cosh(d*x + c)^2 - 11*a^2 + 61*a*b - 137*b^2)*sinh(d*x + c)^4 + 16*(175*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^13 - 455*(a^2 + 11*a*b + 10*b^2)*cosh(d*x + c)^11 - 275*(11*a^2 + 61*a*b + 137*b^2)*cosh(d*x + c)^9 - 150*(31*a^2 + 87*a*b + 390*b^2)*cosh(d*x + c)^7 - 7*(425*a^2 + 5649*b^2)*cosh(d*x + c)^5 - 25*(31*a^2 - 87*a*b + 390*b^2)*cosh(d*x + c)^3 - 5*(11*a^2 - 61*a*b + 137*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 - 20*(a^2 - 11*a*b + 10*b^2)*cosh(d*x + c)^2 + 4*(150*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^14 - 455*(a^2 + 11*a*b + 10*b^2)*cosh(d*x + c)^12 - 330*(11*a^2 + 61*a*b + 137*b^2)*cosh(d*x + c)^10 - 225*(31*a^2 + 87*a*b + 390*b^2)*cosh(d*x + c)^8 - 14*(425*a^2 + 5649*b^2)*cosh(d*x + c)^6 - 75*(31*a^2 - 87*a*b + 390*b^2)*cosh(d*x + c)^4 - 30*(11*a^2 - 61*a*b + 137*b^2)*cosh(d*x + c)^2 - 5*a^2 + 55*a*b - 50*b^2)*sinh(d*x + c)^2 + 5*a^2 - 10*a*b + 5*b^2 + 1200*(a*b*cosh(d*x + c)^13 + 13*a*b*cosh(d*x + c)*sinh(d*x + c)^12 + a*b*sinh(d*x + c)^13 + 5*a*b*cosh(d*x + c)^11 + (78*a*b*cosh(d*x + c)^2 + 5*a*b)*sinh(d*x + c)^11 + 10*a*b*cosh(d*x + c)^9 + 11*(26*a*b*cosh(d*x + c)^3 + 5*a*b*cosh(d*x + c))*sinh(d*x + c)^10 + 5*(143*a*b*cosh(d*x + c)^4 + 55*a*b*cosh(d*x + c)^2 + 2*a*b)*sinh(d*x + c)^9 + 10*a*b*cosh(d*x + c)^7 + 3*(429*a*b*cosh(d*x + c)^5 + 275*a*b*cosh(d*x + c)^3 + 30*a*b*cosh(d*x + c))*sinh(d*x + c)^8 + 2*(858*a*b*cosh(d*x + c)^6 + 825*a*b*cosh(d*x + c)^4 + 180*a*b*cosh(d*x + c)^2 + 5*a*b)*sinh(d*x + c)^7 + 5*a*b*cosh(d*x + c)^5 + 2*(858*a*b*cosh(d*x + c)^7 + 1155*a*b*cosh(d*x + c)^5 + 420*a*b*cosh(d*x + c)^3 + 35*a*b*cosh(d*x + c))*sinh(d*x + c)^6 + (1287*a*b*cosh(d*x + c)^8 + 2310*a*b*cosh(d*x + c)^6 + 1260*a*b*cosh(d*x + c)^4 + 210*a*b*cosh(d*x + c)^2 + 5*a*b)*sinh(d*x + c)^5 + a*b*cosh(d*x + c)^3 + 5*(143*a*b*cosh(d*x + c)^9 + 330*a*b*cosh(d*x + c)^7 + 252*a*b*cosh(d*x + c)^5 + 70*a*b*cosh(d*x + c)^3 + 5*a*b*cosh(d*x + c))*sinh(d*x + c)^4 + (286*a*b*cosh(d*x + c)^10 + 825*a*b*cosh(d*x + c)^8 + 840*a*b*cosh(d*x + c)^6 + 350*a*b*cosh(d*x + c)^4 + 50*a*b*cosh(d*x + c)^2 + a*b)*sinh(d*x + c)^3 + (78*a*b*cosh(d*x + c)^11 + 275*a*b*cosh(d*x + c)^9 + 360*a*b*cosh(d*x + c)^7 + 210*a*b*cosh(d*x + c)^5 + 50*a*b*cosh(d*x + c)^3 + 3*a*b*cosh(d*x + c))*sinh(d*x + c)^2 + (13*a*b*cosh(d*x + c)^12 + 55*a*b*cosh(d*x + c)^10 + 90*a*b*cosh(d*x + c)^8 + 70*a*b*cosh(d*x + c)^6 + 25*a*b*cosh(d*x + c)^4 + 3*a*b*cosh(d*x + c)^2)*sinh(d*x + c))*arctan(cosh(d*x + c) + sinh(d*x + c)) + 8*(10*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^15 - 35*(a^2 + 11*a*b + 10*b^2)*cosh(d*x + c)^13 - 30*(11*a^2 + 61*a*b + 137*b^2)*cosh(d*x + c)^11 - 25*(31*a^2 + 87*a*b + 390*b^2)*cosh(d*x + c)^9 - 2*(425*a^2 + 5649*b^2)*cosh(d*x + c)^7 - 15*(31*a^2 - 87*a*b + 390*b^2)*cosh(d*x + c)^5 - 10*(11*a^2 - 61*a*b + 137*b^2)*cosh(d*x + c)^3 - 5*(a^2 - 11*a*b + 10*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 + 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
59,1,3649,0,0.741528," ","integrate(sinh(d*x+c)^2*(a+b*tanh(d*x+c)^3)^2,x, algorithm=""fricas"")","\frac{15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{14} + 210 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{13} + 15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{14} - 15 \, {\left(4 \, {\left(a^{2} - 8 \, a b + 7 \, b^{2}\right)} d x - 5 \, a^{2} - 10 \, a b - 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{12} - 15 \, {\left(4 \, {\left(a^{2} - 8 \, a b + 7 \, b^{2}\right)} d x - 91 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} - 5 \, a^{2} - 10 \, a b - 5 \, b^{2}\right)} \sinh\left(d x + c\right)^{12} + 60 \, {\left(91 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(4 \, {\left(a^{2} - 8 \, a b + 7 \, b^{2}\right)} d x - 5 \, a^{2} - 10 \, a b - 5 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{11} - 15 \, {\left(20 \, {\left(a^{2} - 8 \, a b + 7 \, b^{2}\right)} d x - 9 \, a^{2} + 10 \, a b + 87 \, b^{2}\right)} \cosh\left(d x + c\right)^{10} + 15 \, {\left(1001 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} - 20 \, {\left(a^{2} - 8 \, a b + 7 \, b^{2}\right)} d x - 66 \, {\left(4 \, {\left(a^{2} - 8 \, a b + 7 \, b^{2}\right)} d x - 5 \, a^{2} - 10 \, a b - 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 9 \, a^{2} - 10 \, a b - 87 \, b^{2}\right)} \sinh\left(d x + c\right)^{10} + 30 \, {\left(1001 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{5} - 110 \, {\left(4 \, {\left(a^{2} - 8 \, a b + 7 \, b^{2}\right)} d x - 5 \, a^{2} - 10 \, a b - 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - 5 \, {\left(20 \, {\left(a^{2} - 8 \, a b + 7 \, b^{2}\right)} d x - 9 \, a^{2} + 10 \, a b + 87 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} - 15 \, {\left(40 \, {\left(a^{2} - 8 \, a b + 7 \, b^{2}\right)} d x - 5 \, a^{2} + 66 \, a b + 251 \, b^{2}\right)} \cosh\left(d x + c\right)^{8} + 15 \, {\left(3003 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{6} - 495 \, {\left(4 \, {\left(a^{2} - 8 \, a b + 7 \, b^{2}\right)} d x - 5 \, a^{2} - 10 \, a b - 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} - 40 \, {\left(a^{2} - 8 \, a b + 7 \, b^{2}\right)} d x - 45 \, {\left(20 \, {\left(a^{2} - 8 \, a b + 7 \, b^{2}\right)} d x - 9 \, a^{2} + 10 \, a b + 87 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 5 \, a^{2} - 66 \, a b - 251 \, b^{2}\right)} \sinh\left(d x + c\right)^{8} + 120 \, {\left(429 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{7} - 99 \, {\left(4 \, {\left(a^{2} - 8 \, a b + 7 \, b^{2}\right)} d x - 5 \, a^{2} - 10 \, a b - 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} - 15 \, {\left(20 \, {\left(a^{2} - 8 \, a b + 7 \, b^{2}\right)} d x - 9 \, a^{2} + 10 \, a b + 87 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(40 \, {\left(a^{2} - 8 \, a b + 7 \, b^{2}\right)} d x - 5 \, a^{2} + 66 \, a b + 251 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} - 5 \, {\left(120 \, {\left(a^{2} - 8 \, a b + 7 \, b^{2}\right)} d x + 15 \, a^{2} + 198 \, a b + 1103 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 5 \, {\left(9009 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{8} - 2772 \, {\left(4 \, {\left(a^{2} - 8 \, a b + 7 \, b^{2}\right)} d x - 5 \, a^{2} - 10 \, a b - 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} - 630 \, {\left(20 \, {\left(a^{2} - 8 \, a b + 7 \, b^{2}\right)} d x - 9 \, a^{2} + 10 \, a b + 87 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} - 120 \, {\left(a^{2} - 8 \, a b + 7 \, b^{2}\right)} d x - 84 \, {\left(40 \, {\left(a^{2} - 8 \, a b + 7 \, b^{2}\right)} d x - 5 \, a^{2} + 66 \, a b + 251 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 15 \, a^{2} - 198 \, a b - 1103 \, b^{2}\right)} \sinh\left(d x + c\right)^{6} + 30 \, {\left(1001 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{9} - 396 \, {\left(4 \, {\left(a^{2} - 8 \, a b + 7 \, b^{2}\right)} d x - 5 \, a^{2} - 10 \, a b - 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} - 126 \, {\left(20 \, {\left(a^{2} - 8 \, a b + 7 \, b^{2}\right)} d x - 9 \, a^{2} + 10 \, a b + 87 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} - 28 \, {\left(40 \, {\left(a^{2} - 8 \, a b + 7 \, b^{2}\right)} d x - 5 \, a^{2} + 66 \, a b + 251 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(120 \, {\left(a^{2} - 8 \, a b + 7 \, b^{2}\right)} d x + 15 \, a^{2} + 198 \, a b + 1103 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 5 \, {\left(60 \, {\left(a^{2} - 8 \, a b + 7 \, b^{2}\right)} d x + 27 \, a^{2} + 30 \, a b + 667 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 5 \, {\left(3003 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{10} - 1485 \, {\left(4 \, {\left(a^{2} - 8 \, a b + 7 \, b^{2}\right)} d x - 5 \, a^{2} - 10 \, a b - 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{8} - 630 \, {\left(20 \, {\left(a^{2} - 8 \, a b + 7 \, b^{2}\right)} d x - 9 \, a^{2} + 10 \, a b + 87 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} - 210 \, {\left(40 \, {\left(a^{2} - 8 \, a b + 7 \, b^{2}\right)} d x - 5 \, a^{2} + 66 \, a b + 251 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} - 60 \, {\left(a^{2} - 8 \, a b + 7 \, b^{2}\right)} d x - 15 \, {\left(120 \, {\left(a^{2} - 8 \, a b + 7 \, b^{2}\right)} d x + 15 \, a^{2} + 198 \, a b + 1103 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 27 \, a^{2} - 30 \, a b - 667 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 20 \, {\left(273 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{11} - 165 \, {\left(4 \, {\left(a^{2} - 8 \, a b + 7 \, b^{2}\right)} d x - 5 \, a^{2} - 10 \, a b - 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{9} - 90 \, {\left(20 \, {\left(a^{2} - 8 \, a b + 7 \, b^{2}\right)} d x - 9 \, a^{2} + 10 \, a b + 87 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} - 42 \, {\left(40 \, {\left(a^{2} - 8 \, a b + 7 \, b^{2}\right)} d x - 5 \, a^{2} + 66 \, a b + 251 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} - 5 \, {\left(120 \, {\left(a^{2} - 8 \, a b + 7 \, b^{2}\right)} d x + 15 \, a^{2} + 198 \, a b + 1103 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(60 \, {\left(a^{2} - 8 \, a b + 7 \, b^{2}\right)} d x + 27 \, a^{2} + 30 \, a b + 667 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - {\left(60 \, {\left(a^{2} - 8 \, a b + 7 \, b^{2}\right)} d x + 75 \, a^{2} - 150 \, a b + 1003 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(1365 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{12} - 990 \, {\left(4 \, {\left(a^{2} - 8 \, a b + 7 \, b^{2}\right)} d x - 5 \, a^{2} - 10 \, a b - 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{10} - 675 \, {\left(20 \, {\left(a^{2} - 8 \, a b + 7 \, b^{2}\right)} d x - 9 \, a^{2} + 10 \, a b + 87 \, b^{2}\right)} \cosh\left(d x + c\right)^{8} - 420 \, {\left(40 \, {\left(a^{2} - 8 \, a b + 7 \, b^{2}\right)} d x - 5 \, a^{2} + 66 \, a b + 251 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} - 75 \, {\left(120 \, {\left(a^{2} - 8 \, a b + 7 \, b^{2}\right)} d x + 15 \, a^{2} + 198 \, a b + 1103 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} - 60 \, {\left(a^{2} - 8 \, a b + 7 \, b^{2}\right)} d x - 30 \, {\left(60 \, {\left(a^{2} - 8 \, a b + 7 \, b^{2}\right)} d x + 27 \, a^{2} + 30 \, a b + 667 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 75 \, a^{2} + 150 \, a b - 1003 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} - 15 \, a^{2} + 30 \, a b - 15 \, b^{2} - 480 \, {\left(a b \cosh\left(d x + c\right)^{12} + 12 \, a b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{11} + a b \sinh\left(d x + c\right)^{12} + 5 \, a b \cosh\left(d x + c\right)^{10} + {\left(66 \, a b \cosh\left(d x + c\right)^{2} + 5 \, a b\right)} \sinh\left(d x + c\right)^{10} + 10 \, a b \cosh\left(d x + c\right)^{8} + 10 \, {\left(22 \, 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)^{9} + 5 \, {\left(99 \, a b \cosh\left(d x + c\right)^{4} + 45 \, a b \cosh\left(d x + c\right)^{2} + 2 \, a b\right)} \sinh\left(d x + c\right)^{8} + 10 \, a b \cosh\left(d x + c\right)^{6} + 8 \, {\left(99 \, a b \cosh\left(d x + c\right)^{5} + 75 \, a b \cosh\left(d x + c\right)^{3} + 10 \, a b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(462 \, a b \cosh\left(d x + c\right)^{6} + 525 \, a b \cosh\left(d x + c\right)^{4} + 140 \, a b \cosh\left(d x + c\right)^{2} + 5 \, a b\right)} \sinh\left(d x + c\right)^{6} + 5 \, a b \cosh\left(d x + c\right)^{4} + 4 \, {\left(198 \, a b \cosh\left(d x + c\right)^{7} + 315 \, a b \cosh\left(d x + c\right)^{5} + 140 \, 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} + 5 \, {\left(99 \, a b \cosh\left(d x + c\right)^{8} + 210 \, a b \cosh\left(d x + c\right)^{6} + 140 \, a b \cosh\left(d x + c\right)^{4} + 30 \, a b \cosh\left(d x + c\right)^{2} + a b\right)} \sinh\left(d x + c\right)^{4} + a b \cosh\left(d x + c\right)^{2} + 20 \, {\left(11 \, a b \cosh\left(d x + c\right)^{9} + 30 \, a b \cosh\left(d x + c\right)^{7} + 28 \, a b \cosh\left(d x + c\right)^{5} + 10 \, 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} + {\left(66 \, a b \cosh\left(d x + c\right)^{10} + 225 \, a b \cosh\left(d x + c\right)^{8} + 280 \, a b \cosh\left(d x + c\right)^{6} + 150 \, a b \cosh\left(d x + c\right)^{4} + 30 \, a b \cosh\left(d x + c\right)^{2} + a b\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(6 \, a b \cosh\left(d x + c\right)^{11} + 25 \, a b \cosh\left(d x + c\right)^{9} + 40 \, a b \cosh\left(d x + c\right)^{7} + 30 \, a b \cosh\left(d x + c\right)^{5} + 10 \, 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(\frac{2 \, \cosh\left(d x + c\right)}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) + 2 \, {\left(105 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{13} - 90 \, {\left(4 \, {\left(a^{2} - 8 \, a b + 7 \, b^{2}\right)} d x - 5 \, a^{2} - 10 \, a b - 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{11} - 75 \, {\left(20 \, {\left(a^{2} - 8 \, a b + 7 \, b^{2}\right)} d x - 9 \, a^{2} + 10 \, a b + 87 \, b^{2}\right)} \cosh\left(d x + c\right)^{9} - 60 \, {\left(40 \, {\left(a^{2} - 8 \, a b + 7 \, b^{2}\right)} d x - 5 \, a^{2} + 66 \, a b + 251 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} - 15 \, {\left(120 \, {\left(a^{2} - 8 \, a b + 7 \, b^{2}\right)} d x + 15 \, a^{2} + 198 \, a b + 1103 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} - 10 \, {\left(60 \, {\left(a^{2} - 8 \, a b + 7 \, b^{2}\right)} d x + 27 \, a^{2} + 30 \, a b + 667 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(60 \, {\left(a^{2} - 8 \, a b + 7 \, b^{2}\right)} d x + 75 \, a^{2} - 150 \, a b + 1003 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{120 \, {\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} + 5 \, d \cosh\left(d x + c\right)^{10} + {\left(66 \, d \cosh\left(d x + c\right)^{2} + 5 \, d\right)} \sinh\left(d x + c\right)^{10} + 10 \, {\left(22 \, d \cosh\left(d x + c\right)^{3} + 5 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} + 10 \, d \cosh\left(d x + c\right)^{8} + 5 \, {\left(99 \, d \cosh\left(d x + c\right)^{4} + 45 \, d \cosh\left(d x + c\right)^{2} + 2 \, d\right)} \sinh\left(d x + c\right)^{8} + 8 \, {\left(99 \, d \cosh\left(d x + c\right)^{5} + 75 \, d \cosh\left(d x + c\right)^{3} + 10 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 10 \, d \cosh\left(d x + c\right)^{6} + 2 \, {\left(462 \, d \cosh\left(d x + c\right)^{6} + 525 \, 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)^{6} + 4 \, {\left(198 \, d \cosh\left(d x + c\right)^{7} + 315 \, 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)^{5} + 5 \, d \cosh\left(d x + c\right)^{4} + 5 \, {\left(99 \, d \cosh\left(d x + c\right)^{8} + 210 \, d \cosh\left(d x + c\right)^{6} + 140 \, d \cosh\left(d x + c\right)^{4} + 30 \, 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} + 30 \, d \cosh\left(d x + c\right)^{7} + 28 \, d \cosh\left(d x + c\right)^{5} + 10 \, d \cosh\left(d x + c\right)^{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(66 \, d \cosh\left(d x + c\right)^{10} + 225 \, d \cosh\left(d x + c\right)^{8} + 280 \, d \cosh\left(d x + c\right)^{6} + 150 \, d \cosh\left(d x + c\right)^{4} + 30 \, d \cosh\left(d x + c\right)^{2} + d\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(6 \, d \cosh\left(d x + c\right)^{11} + 25 \, d \cosh\left(d x + c\right)^{9} + 40 \, d \cosh\left(d x + c\right)^{7} + 30 \, d \cosh\left(d x + c\right)^{5} + 10 \, d \cosh\left(d x + c\right)^{3} + d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"1/120*(15*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^14 + 210*(a^2 + 2*a*b + b^2)*cosh(d*x + c)*sinh(d*x + c)^13 + 15*(a^2 + 2*a*b + b^2)*sinh(d*x + c)^14 - 15*(4*(a^2 - 8*a*b + 7*b^2)*d*x - 5*a^2 - 10*a*b - 5*b^2)*cosh(d*x + c)^12 - 15*(4*(a^2 - 8*a*b + 7*b^2)*d*x - 91*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 - 5*a^2 - 10*a*b - 5*b^2)*sinh(d*x + c)^12 + 60*(91*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 - 3*(4*(a^2 - 8*a*b + 7*b^2)*d*x - 5*a^2 - 10*a*b - 5*b^2)*cosh(d*x + c))*sinh(d*x + c)^11 - 15*(20*(a^2 - 8*a*b + 7*b^2)*d*x - 9*a^2 + 10*a*b + 87*b^2)*cosh(d*x + c)^10 + 15*(1001*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 - 20*(a^2 - 8*a*b + 7*b^2)*d*x - 66*(4*(a^2 - 8*a*b + 7*b^2)*d*x - 5*a^2 - 10*a*b - 5*b^2)*cosh(d*x + c)^2 + 9*a^2 - 10*a*b - 87*b^2)*sinh(d*x + c)^10 + 30*(1001*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^5 - 110*(4*(a^2 - 8*a*b + 7*b^2)*d*x - 5*a^2 - 10*a*b - 5*b^2)*cosh(d*x + c)^3 - 5*(20*(a^2 - 8*a*b + 7*b^2)*d*x - 9*a^2 + 10*a*b + 87*b^2)*cosh(d*x + c))*sinh(d*x + c)^9 - 15*(40*(a^2 - 8*a*b + 7*b^2)*d*x - 5*a^2 + 66*a*b + 251*b^2)*cosh(d*x + c)^8 + 15*(3003*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^6 - 495*(4*(a^2 - 8*a*b + 7*b^2)*d*x - 5*a^2 - 10*a*b - 5*b^2)*cosh(d*x + c)^4 - 40*(a^2 - 8*a*b + 7*b^2)*d*x - 45*(20*(a^2 - 8*a*b + 7*b^2)*d*x - 9*a^2 + 10*a*b + 87*b^2)*cosh(d*x + c)^2 + 5*a^2 - 66*a*b - 251*b^2)*sinh(d*x + c)^8 + 120*(429*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^7 - 99*(4*(a^2 - 8*a*b + 7*b^2)*d*x - 5*a^2 - 10*a*b - 5*b^2)*cosh(d*x + c)^5 - 15*(20*(a^2 - 8*a*b + 7*b^2)*d*x - 9*a^2 + 10*a*b + 87*b^2)*cosh(d*x + c)^3 - (40*(a^2 - 8*a*b + 7*b^2)*d*x - 5*a^2 + 66*a*b + 251*b^2)*cosh(d*x + c))*sinh(d*x + c)^7 - 5*(120*(a^2 - 8*a*b + 7*b^2)*d*x + 15*a^2 + 198*a*b + 1103*b^2)*cosh(d*x + c)^6 + 5*(9009*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^8 - 2772*(4*(a^2 - 8*a*b + 7*b^2)*d*x - 5*a^2 - 10*a*b - 5*b^2)*cosh(d*x + c)^6 - 630*(20*(a^2 - 8*a*b + 7*b^2)*d*x - 9*a^2 + 10*a*b + 87*b^2)*cosh(d*x + c)^4 - 120*(a^2 - 8*a*b + 7*b^2)*d*x - 84*(40*(a^2 - 8*a*b + 7*b^2)*d*x - 5*a^2 + 66*a*b + 251*b^2)*cosh(d*x + c)^2 - 15*a^2 - 198*a*b - 1103*b^2)*sinh(d*x + c)^6 + 30*(1001*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^9 - 396*(4*(a^2 - 8*a*b + 7*b^2)*d*x - 5*a^2 - 10*a*b - 5*b^2)*cosh(d*x + c)^7 - 126*(20*(a^2 - 8*a*b + 7*b^2)*d*x - 9*a^2 + 10*a*b + 87*b^2)*cosh(d*x + c)^5 - 28*(40*(a^2 - 8*a*b + 7*b^2)*d*x - 5*a^2 + 66*a*b + 251*b^2)*cosh(d*x + c)^3 - (120*(a^2 - 8*a*b + 7*b^2)*d*x + 15*a^2 + 198*a*b + 1103*b^2)*cosh(d*x + c))*sinh(d*x + c)^5 - 5*(60*(a^2 - 8*a*b + 7*b^2)*d*x + 27*a^2 + 30*a*b + 667*b^2)*cosh(d*x + c)^4 + 5*(3003*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^10 - 1485*(4*(a^2 - 8*a*b + 7*b^2)*d*x - 5*a^2 - 10*a*b - 5*b^2)*cosh(d*x + c)^8 - 630*(20*(a^2 - 8*a*b + 7*b^2)*d*x - 9*a^2 + 10*a*b + 87*b^2)*cosh(d*x + c)^6 - 210*(40*(a^2 - 8*a*b + 7*b^2)*d*x - 5*a^2 + 66*a*b + 251*b^2)*cosh(d*x + c)^4 - 60*(a^2 - 8*a*b + 7*b^2)*d*x - 15*(120*(a^2 - 8*a*b + 7*b^2)*d*x + 15*a^2 + 198*a*b + 1103*b^2)*cosh(d*x + c)^2 - 27*a^2 - 30*a*b - 667*b^2)*sinh(d*x + c)^4 + 20*(273*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^11 - 165*(4*(a^2 - 8*a*b + 7*b^2)*d*x - 5*a^2 - 10*a*b - 5*b^2)*cosh(d*x + c)^9 - 90*(20*(a^2 - 8*a*b + 7*b^2)*d*x - 9*a^2 + 10*a*b + 87*b^2)*cosh(d*x + c)^7 - 42*(40*(a^2 - 8*a*b + 7*b^2)*d*x - 5*a^2 + 66*a*b + 251*b^2)*cosh(d*x + c)^5 - 5*(120*(a^2 - 8*a*b + 7*b^2)*d*x + 15*a^2 + 198*a*b + 1103*b^2)*cosh(d*x + c)^3 - (60*(a^2 - 8*a*b + 7*b^2)*d*x + 27*a^2 + 30*a*b + 667*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 - (60*(a^2 - 8*a*b + 7*b^2)*d*x + 75*a^2 - 150*a*b + 1003*b^2)*cosh(d*x + c)^2 + (1365*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^12 - 990*(4*(a^2 - 8*a*b + 7*b^2)*d*x - 5*a^2 - 10*a*b - 5*b^2)*cosh(d*x + c)^10 - 675*(20*(a^2 - 8*a*b + 7*b^2)*d*x - 9*a^2 + 10*a*b + 87*b^2)*cosh(d*x + c)^8 - 420*(40*(a^2 - 8*a*b + 7*b^2)*d*x - 5*a^2 + 66*a*b + 251*b^2)*cosh(d*x + c)^6 - 75*(120*(a^2 - 8*a*b + 7*b^2)*d*x + 15*a^2 + 198*a*b + 1103*b^2)*cosh(d*x + c)^4 - 60*(a^2 - 8*a*b + 7*b^2)*d*x - 30*(60*(a^2 - 8*a*b + 7*b^2)*d*x + 27*a^2 + 30*a*b + 667*b^2)*cosh(d*x + c)^2 - 75*a^2 + 150*a*b - 1003*b^2)*sinh(d*x + c)^2 - 15*a^2 + 30*a*b - 15*b^2 - 480*(a*b*cosh(d*x + c)^12 + 12*a*b*cosh(d*x + c)*sinh(d*x + c)^11 + a*b*sinh(d*x + c)^12 + 5*a*b*cosh(d*x + c)^10 + (66*a*b*cosh(d*x + c)^2 + 5*a*b)*sinh(d*x + c)^10 + 10*a*b*cosh(d*x + c)^8 + 10*(22*a*b*cosh(d*x + c)^3 + 5*a*b*cosh(d*x + c))*sinh(d*x + c)^9 + 5*(99*a*b*cosh(d*x + c)^4 + 45*a*b*cosh(d*x + c)^2 + 2*a*b)*sinh(d*x + c)^8 + 10*a*b*cosh(d*x + c)^6 + 8*(99*a*b*cosh(d*x + c)^5 + 75*a*b*cosh(d*x + c)^3 + 10*a*b*cosh(d*x + c))*sinh(d*x + c)^7 + 2*(462*a*b*cosh(d*x + c)^6 + 525*a*b*cosh(d*x + c)^4 + 140*a*b*cosh(d*x + c)^2 + 5*a*b)*sinh(d*x + c)^6 + 5*a*b*cosh(d*x + c)^4 + 4*(198*a*b*cosh(d*x + c)^7 + 315*a*b*cosh(d*x + c)^5 + 140*a*b*cosh(d*x + c)^3 + 15*a*b*cosh(d*x + c))*sinh(d*x + c)^5 + 5*(99*a*b*cosh(d*x + c)^8 + 210*a*b*cosh(d*x + c)^6 + 140*a*b*cosh(d*x + c)^4 + 30*a*b*cosh(d*x + c)^2 + a*b)*sinh(d*x + c)^4 + a*b*cosh(d*x + c)^2 + 20*(11*a*b*cosh(d*x + c)^9 + 30*a*b*cosh(d*x + c)^7 + 28*a*b*cosh(d*x + c)^5 + 10*a*b*cosh(d*x + c)^3 + a*b*cosh(d*x + c))*sinh(d*x + c)^3 + (66*a*b*cosh(d*x + c)^10 + 225*a*b*cosh(d*x + c)^8 + 280*a*b*cosh(d*x + c)^6 + 150*a*b*cosh(d*x + c)^4 + 30*a*b*cosh(d*x + c)^2 + a*b)*sinh(d*x + c)^2 + 2*(6*a*b*cosh(d*x + c)^11 + 25*a*b*cosh(d*x + c)^9 + 40*a*b*cosh(d*x + c)^7 + 30*a*b*cosh(d*x + c)^5 + 10*a*b*cosh(d*x + c)^3 + a*b*cosh(d*x + c))*sinh(d*x + c))*log(2*cosh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))) + 2*(105*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^13 - 90*(4*(a^2 - 8*a*b + 7*b^2)*d*x - 5*a^2 - 10*a*b - 5*b^2)*cosh(d*x + c)^11 - 75*(20*(a^2 - 8*a*b + 7*b^2)*d*x - 9*a^2 + 10*a*b + 87*b^2)*cosh(d*x + c)^9 - 60*(40*(a^2 - 8*a*b + 7*b^2)*d*x - 5*a^2 + 66*a*b + 251*b^2)*cosh(d*x + c)^7 - 15*(120*(a^2 - 8*a*b + 7*b^2)*d*x + 15*a^2 + 198*a*b + 1103*b^2)*cosh(d*x + c)^5 - 10*(60*(a^2 - 8*a*b + 7*b^2)*d*x + 27*a^2 + 30*a*b + 667*b^2)*cosh(d*x + c)^3 - (60*(a^2 - 8*a*b + 7*b^2)*d*x + 75*a^2 - 150*a*b + 1003*b^2)*cosh(d*x + c))*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 + 5*d*cosh(d*x + c)^10 + (66*d*cosh(d*x + c)^2 + 5*d)*sinh(d*x + c)^10 + 10*(22*d*cosh(d*x + c)^3 + 5*d*cosh(d*x + c))*sinh(d*x + c)^9 + 10*d*cosh(d*x + c)^8 + 5*(99*d*cosh(d*x + c)^4 + 45*d*cosh(d*x + c)^2 + 2*d)*sinh(d*x + c)^8 + 8*(99*d*cosh(d*x + c)^5 + 75*d*cosh(d*x + c)^3 + 10*d*cosh(d*x + c))*sinh(d*x + c)^7 + 10*d*cosh(d*x + c)^6 + 2*(462*d*cosh(d*x + c)^6 + 525*d*cosh(d*x + c)^4 + 140*d*cosh(d*x + c)^2 + 5*d)*sinh(d*x + c)^6 + 4*(198*d*cosh(d*x + c)^7 + 315*d*cosh(d*x + c)^5 + 140*d*cosh(d*x + c)^3 + 15*d*cosh(d*x + c))*sinh(d*x + c)^5 + 5*d*cosh(d*x + c)^4 + 5*(99*d*cosh(d*x + c)^8 + 210*d*cosh(d*x + c)^6 + 140*d*cosh(d*x + c)^4 + 30*d*cosh(d*x + c)^2 + d)*sinh(d*x + c)^4 + 20*(11*d*cosh(d*x + c)^9 + 30*d*cosh(d*x + c)^7 + 28*d*cosh(d*x + c)^5 + 10*d*cosh(d*x + c)^3 + d*cosh(d*x + c))*sinh(d*x + c)^3 + d*cosh(d*x + c)^2 + (66*d*cosh(d*x + c)^10 + 225*d*cosh(d*x + c)^8 + 280*d*cosh(d*x + c)^6 + 150*d*cosh(d*x + c)^4 + 30*d*cosh(d*x + c)^2 + d)*sinh(d*x + c)^2 + 2*(6*d*cosh(d*x + c)^11 + 25*d*cosh(d*x + c)^9 + 40*d*cosh(d*x + c)^7 + 30*d*cosh(d*x + c)^5 + 10*d*cosh(d*x + c)^3 + d*cosh(d*x + c))*sinh(d*x + c))","B",0
60,1,2230,0,0.720252," ","integrate(sinh(d*x+c)*(a+b*tanh(d*x+c)^3)^2,x, algorithm=""fricas"")","\frac{5 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{12} + 60 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{11} + 5 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{12} + 30 \, {\left(a^{2} + 2 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{10} + 30 \, {\left(11 \, {\left(a^{2} + 2 \, a b + 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)^{10} + 100 \, {\left(11 \, {\left(a^{2} + 2 \, a b + 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)^{9} + 5 \, {\left(15 \, a^{2} + 18 \, a b + 47 \, b^{2}\right)} \cosh\left(d x + c\right)^{8} + 5 \, {\left(495 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + 270 \, {\left(a^{2} + 2 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 15 \, a^{2} + 18 \, a b + 47 \, b^{2}\right)} \sinh\left(d x + c\right)^{8} + 40 \, {\left(99 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{5} + 90 \, {\left(a^{2} + 2 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(15 \, a^{2} + 18 \, a b + 47 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 4 \, {\left(25 \, a^{2} + 91 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(1155 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{6} + 1575 \, {\left(a^{2} + 2 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 35 \, {\left(15 \, a^{2} + 18 \, a b + 47 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 25 \, a^{2} + 91 \, b^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(495 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{7} + 945 \, {\left(a^{2} + 2 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 35 \, {\left(15 \, a^{2} + 18 \, a b + 47 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(25 \, a^{2} + 91 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 5 \, {\left(15 \, a^{2} - 18 \, a b + 47 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 5 \, {\left(495 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{8} + 1260 \, {\left(a^{2} + 2 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 70 \, {\left(15 \, a^{2} + 18 \, a b + 47 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 12 \, {\left(25 \, a^{2} + 91 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 15 \, a^{2} - 18 \, a b + 47 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 20 \, {\left(55 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{9} + 180 \, {\left(a^{2} + 2 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} + 14 \, {\left(15 \, a^{2} + 18 \, a b + 47 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 4 \, {\left(25 \, a^{2} + 91 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(15 \, a^{2} - 18 \, a b + 47 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 30 \, {\left(a^{2} - 2 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 10 \, {\left(33 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{10} + 135 \, {\left(a^{2} + 2 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{8} + 14 \, {\left(15 \, a^{2} + 18 \, a b + 47 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 6 \, {\left(25 \, a^{2} + 91 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(15 \, a^{2} - 18 \, a b + 47 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 3 \, a^{2} - 6 \, a b + 9 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} + 5 \, a^{2} - 10 \, a b + 5 \, b^{2} - 60 \, {\left(a b \cosh\left(d x + c\right)^{11} + 11 \, a b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{10} + a b \sinh\left(d x + c\right)^{11} + 5 \, a b \cosh\left(d x + c\right)^{9} + 5 \, {\left(11 \, a b \cosh\left(d x + c\right)^{2} + a b\right)} \sinh\left(d x + c\right)^{9} + 10 \, a b \cosh\left(d x + c\right)^{7} + 15 \, {\left(11 \, 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)^{8} + 10 \, {\left(33 \, 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)^{7} + 10 \, a b \cosh\left(d x + c\right)^{5} + 14 \, {\left(33 \, a b \cosh\left(d x + c\right)^{5} + 30 \, 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)^{6} + 2 \, {\left(231 \, a b \cosh\left(d x + c\right)^{6} + 315 \, a b \cosh\left(d x + c\right)^{4} + 105 \, a b \cosh\left(d x + c\right)^{2} + 5 \, a b\right)} \sinh\left(d x + c\right)^{5} + 5 \, a b \cosh\left(d x + c\right)^{3} + 10 \, {\left(33 \, a b \cosh\left(d x + c\right)^{7} + 63 \, a b \cosh\left(d x + c\right)^{5} + 35 \, 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} + 5 \, {\left(33 \, a b \cosh\left(d x + c\right)^{8} + 84 \, a b \cosh\left(d x + c\right)^{6} + 70 \, a b \cosh\left(d x + c\right)^{4} + 20 \, a b \cosh\left(d x + c\right)^{2} + a b\right)} \sinh\left(d x + c\right)^{3} + a b \cosh\left(d x + c\right) + 5 \, {\left(11 \, a b \cosh\left(d x + c\right)^{9} + 36 \, a b \cosh\left(d x + c\right)^{7} + 42 \, a b \cosh\left(d x + c\right)^{5} + 20 \, 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)^{2} + {\left(11 \, a b \cosh\left(d x + c\right)^{10} + 45 \, a b \cosh\left(d x + c\right)^{8} + 70 \, a b \cosh\left(d x + c\right)^{6} + 50 \, 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)\right)} \arctan\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) + 4 \, {\left(15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{11} + 75 \, {\left(a^{2} + 2 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{9} + 10 \, {\left(15 \, a^{2} + 18 \, a b + 47 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} + 6 \, {\left(25 \, a^{2} + 91 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(15 \, a^{2} - 18 \, a b + 47 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 15 \, {\left(a^{2} - 2 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{10 \, {\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} + 5 \, d \cosh\left(d x + c\right)^{9} + 5 \, {\left(11 \, d \cosh\left(d x + c\right)^{2} + d\right)} \sinh\left(d x + c\right)^{9} + 15 \, {\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)^{8} + 10 \, d \cosh\left(d x + c\right)^{7} + 10 \, {\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)^{7} + 14 \, {\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)^{6} + 10 \, d \cosh\left(d x + c\right)^{5} + 2 \, {\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)^{5} + 10 \, {\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)^{4} + 5 \, d \cosh\left(d x + c\right)^{3} + 5 \, {\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)^{3} + 5 \, {\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)^{2} + d \cosh\left(d x + c\right) + {\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)\right)}}"," ",0,"1/10*(5*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^12 + 60*(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 + 30*(a^2 + 2*a*b + 3*b^2)*cosh(d*x + c)^10 + 30*(11*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + a^2 + 2*a*b + 3*b^2)*sinh(d*x + c)^10 + 100*(11*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 + 3*(a^2 + 2*a*b + 3*b^2)*cosh(d*x + c))*sinh(d*x + c)^9 + 5*(15*a^2 + 18*a*b + 47*b^2)*cosh(d*x + c)^8 + 5*(495*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 + 270*(a^2 + 2*a*b + 3*b^2)*cosh(d*x + c)^2 + 15*a^2 + 18*a*b + 47*b^2)*sinh(d*x + c)^8 + 40*(99*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^5 + 90*(a^2 + 2*a*b + 3*b^2)*cosh(d*x + c)^3 + (15*a^2 + 18*a*b + 47*b^2)*cosh(d*x + c))*sinh(d*x + c)^7 + 4*(25*a^2 + 91*b^2)*cosh(d*x + c)^6 + 4*(1155*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^6 + 1575*(a^2 + 2*a*b + 3*b^2)*cosh(d*x + c)^4 + 35*(15*a^2 + 18*a*b + 47*b^2)*cosh(d*x + c)^2 + 25*a^2 + 91*b^2)*sinh(d*x + c)^6 + 8*(495*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^7 + 945*(a^2 + 2*a*b + 3*b^2)*cosh(d*x + c)^5 + 35*(15*a^2 + 18*a*b + 47*b^2)*cosh(d*x + c)^3 + 3*(25*a^2 + 91*b^2)*cosh(d*x + c))*sinh(d*x + c)^5 + 5*(15*a^2 - 18*a*b + 47*b^2)*cosh(d*x + c)^4 + 5*(495*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^8 + 1260*(a^2 + 2*a*b + 3*b^2)*cosh(d*x + c)^6 + 70*(15*a^2 + 18*a*b + 47*b^2)*cosh(d*x + c)^4 + 12*(25*a^2 + 91*b^2)*cosh(d*x + c)^2 + 15*a^2 - 18*a*b + 47*b^2)*sinh(d*x + c)^4 + 20*(55*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^9 + 180*(a^2 + 2*a*b + 3*b^2)*cosh(d*x + c)^7 + 14*(15*a^2 + 18*a*b + 47*b^2)*cosh(d*x + c)^5 + 4*(25*a^2 + 91*b^2)*cosh(d*x + c)^3 + (15*a^2 - 18*a*b + 47*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 30*(a^2 - 2*a*b + 3*b^2)*cosh(d*x + c)^2 + 10*(33*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^10 + 135*(a^2 + 2*a*b + 3*b^2)*cosh(d*x + c)^8 + 14*(15*a^2 + 18*a*b + 47*b^2)*cosh(d*x + c)^6 + 6*(25*a^2 + 91*b^2)*cosh(d*x + c)^4 + 3*(15*a^2 - 18*a*b + 47*b^2)*cosh(d*x + c)^2 + 3*a^2 - 6*a*b + 9*b^2)*sinh(d*x + c)^2 + 5*a^2 - 10*a*b + 5*b^2 - 60*(a*b*cosh(d*x + c)^11 + 11*a*b*cosh(d*x + c)*sinh(d*x + c)^10 + a*b*sinh(d*x + c)^11 + 5*a*b*cosh(d*x + c)^9 + 5*(11*a*b*cosh(d*x + c)^2 + a*b)*sinh(d*x + c)^9 + 10*a*b*cosh(d*x + c)^7 + 15*(11*a*b*cosh(d*x + c)^3 + 3*a*b*cosh(d*x + c))*sinh(d*x + c)^8 + 10*(33*a*b*cosh(d*x + c)^4 + 18*a*b*cosh(d*x + c)^2 + a*b)*sinh(d*x + c)^7 + 10*a*b*cosh(d*x + c)^5 + 14*(33*a*b*cosh(d*x + c)^5 + 30*a*b*cosh(d*x + c)^3 + 5*a*b*cosh(d*x + c))*sinh(d*x + c)^6 + 2*(231*a*b*cosh(d*x + c)^6 + 315*a*b*cosh(d*x + c)^4 + 105*a*b*cosh(d*x + c)^2 + 5*a*b)*sinh(d*x + c)^5 + 5*a*b*cosh(d*x + c)^3 + 10*(33*a*b*cosh(d*x + c)^7 + 63*a*b*cosh(d*x + c)^5 + 35*a*b*cosh(d*x + c)^3 + 5*a*b*cosh(d*x + c))*sinh(d*x + c)^4 + 5*(33*a*b*cosh(d*x + c)^8 + 84*a*b*cosh(d*x + c)^6 + 70*a*b*cosh(d*x + c)^4 + 20*a*b*cosh(d*x + c)^2 + a*b)*sinh(d*x + c)^3 + a*b*cosh(d*x + c) + 5*(11*a*b*cosh(d*x + c)^9 + 36*a*b*cosh(d*x + c)^7 + 42*a*b*cosh(d*x + c)^5 + 20*a*b*cosh(d*x + c)^3 + 3*a*b*cosh(d*x + c))*sinh(d*x + c)^2 + (11*a*b*cosh(d*x + c)^10 + 45*a*b*cosh(d*x + c)^8 + 70*a*b*cosh(d*x + c)^6 + 50*a*b*cosh(d*x + c)^4 + 15*a*b*cosh(d*x + c)^2 + a*b)*sinh(d*x + c))*arctan(cosh(d*x + c) + sinh(d*x + c)) + 4*(15*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^11 + 75*(a^2 + 2*a*b + 3*b^2)*cosh(d*x + c)^9 + 10*(15*a^2 + 18*a*b + 47*b^2)*cosh(d*x + c)^7 + 6*(25*a^2 + 91*b^2)*cosh(d*x + c)^5 + 5*(15*a^2 - 18*a*b + 47*b^2)*cosh(d*x + c)^3 + 15*(a^2 - 2*a*b + 3*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 + 5*d*cosh(d*x + c)^9 + 5*(11*d*cosh(d*x + c)^2 + d)*sinh(d*x + c)^9 + 15*(11*d*cosh(d*x + c)^3 + 3*d*cosh(d*x + c))*sinh(d*x + c)^8 + 10*d*cosh(d*x + c)^7 + 10*(33*d*cosh(d*x + c)^4 + 18*d*cosh(d*x + c)^2 + d)*sinh(d*x + c)^7 + 14*(33*d*cosh(d*x + c)^5 + 30*d*cosh(d*x + c)^3 + 5*d*cosh(d*x + c))*sinh(d*x + c)^6 + 10*d*cosh(d*x + c)^5 + 2*(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)^5 + 10*(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)^4 + 5*d*cosh(d*x + c)^3 + 5*(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)^3 + 5*(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)^2 + d*cosh(d*x + c) + (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))","B",0
61,1,2498,0,0.774592," ","integrate(csch(d*x+c)*(a+b*tanh(d*x+c)^3)^2,x, algorithm=""fricas"")","-\frac{30 \, {\left(a b + b^{2}\right)} \cosh\left(d x + c\right)^{9} + 270 \, {\left(a b + b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{8} + 30 \, {\left(a b + b^{2}\right)} \sinh\left(d x + c\right)^{9} + 20 \, {\left(3 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} + 20 \, {\left(54 \, {\left(a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 3 \, a b + 2 \, b^{2}\right)} \sinh\left(d x + c\right)^{7} + 116 \, b^{2} \cosh\left(d x + c\right)^{5} + 140 \, {\left(18 \, {\left(a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(945 \, {\left(a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + 105 \, {\left(3 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 29 \, b^{2}\right)} \sinh\left(d x + c\right)^{5} + 20 \, {\left(189 \, {\left(a b + b^{2}\right)} \cosh\left(d x + c\right)^{5} + 35 \, {\left(3 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 29 \, b^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} - 20 \, {\left(3 \, a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 20 \, {\left(126 \, {\left(a b + b^{2}\right)} \cosh\left(d x + c\right)^{6} + 35 \, {\left(3 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 58 \, b^{2} \cosh\left(d x + c\right)^{2} - 3 \, a b + 2 \, b^{2}\right)} \sinh\left(d x + c\right)^{3} + 20 \, {\left(54 \, {\left(a b + b^{2}\right)} \cosh\left(d x + c\right)^{7} + 21 \, {\left(3 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 58 \, b^{2} \cosh\left(d x + c\right)^{3} - 3 \, {\left(3 \, a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 30 \, {\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)} \arctan\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) - 30 \, {\left(a b - b^{2}\right)} \cosh\left(d x + c\right) + 15 \, {\left(a^{2} \cosh\left(d x + c\right)^{10} + 10 \, a^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + a^{2} \sinh\left(d x + c\right)^{10} + 5 \, a^{2} \cosh\left(d x + c\right)^{8} + 5 \, {\left(9 \, a^{2} \cosh\left(d x + c\right)^{2} + a^{2}\right)} \sinh\left(d x + c\right)^{8} + 10 \, a^{2} \cosh\left(d x + c\right)^{6} + 40 \, {\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)^{7} + 10 \, {\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)^{6} + 10 \, a^{2} \cosh\left(d x + c\right)^{4} + 4 \, {\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)^{5} + 10 \, {\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)^{4} + 5 \, a^{2} \cosh\left(d x + c\right)^{2} + 40 \, {\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)^{3} + 5 \, {\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)^{2} + a^{2} + 10 \, {\left(a^{2} \cosh\left(d x + c\right)^{9} + 4 \, a^{2} \cosh\left(d x + c\right)^{7} + 6 \, a^{2} \cosh\left(d x + c\right)^{5} + 4 \, a^{2} \cosh\left(d x + c\right)^{3} + a^{2} \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^{2} \cosh\left(d x + c\right)^{10} + 10 \, a^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + a^{2} \sinh\left(d x + c\right)^{10} + 5 \, a^{2} \cosh\left(d x + c\right)^{8} + 5 \, {\left(9 \, a^{2} \cosh\left(d x + c\right)^{2} + a^{2}\right)} \sinh\left(d x + c\right)^{8} + 10 \, a^{2} \cosh\left(d x + c\right)^{6} + 40 \, {\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)^{7} + 10 \, {\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)^{6} + 10 \, a^{2} \cosh\left(d x + c\right)^{4} + 4 \, {\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)^{5} + 10 \, {\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)^{4} + 5 \, a^{2} \cosh\left(d x + c\right)^{2} + 40 \, {\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)^{3} + 5 \, {\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)^{2} + a^{2} + 10 \, {\left(a^{2} \cosh\left(d x + c\right)^{9} + 4 \, a^{2} \cosh\left(d x + c\right)^{7} + 6 \, a^{2} \cosh\left(d x + c\right)^{5} + 4 \, a^{2} \cosh\left(d x + c\right)^{3} + a^{2} \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(27 \, {\left(a b + b^{2}\right)} \cosh\left(d x + c\right)^{8} + 14 \, {\left(3 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 58 \, b^{2} \cosh\left(d x + c\right)^{4} - 6 \, {\left(3 \, a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 3 \, a b + 3 \, b^{2}\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*(30*(a*b + b^2)*cosh(d*x + c)^9 + 270*(a*b + b^2)*cosh(d*x + c)*sinh(d*x + c)^8 + 30*(a*b + b^2)*sinh(d*x + c)^9 + 20*(3*a*b + 2*b^2)*cosh(d*x + c)^7 + 20*(54*(a*b + b^2)*cosh(d*x + c)^2 + 3*a*b + 2*b^2)*sinh(d*x + c)^7 + 116*b^2*cosh(d*x + c)^5 + 140*(18*(a*b + b^2)*cosh(d*x + c)^3 + (3*a*b + 2*b^2)*cosh(d*x + c))*sinh(d*x + c)^6 + 4*(945*(a*b + b^2)*cosh(d*x + c)^4 + 105*(3*a*b + 2*b^2)*cosh(d*x + c)^2 + 29*b^2)*sinh(d*x + c)^5 + 20*(189*(a*b + b^2)*cosh(d*x + c)^5 + 35*(3*a*b + 2*b^2)*cosh(d*x + c)^3 + 29*b^2*cosh(d*x + c))*sinh(d*x + c)^4 - 20*(3*a*b - 2*b^2)*cosh(d*x + c)^3 + 20*(126*(a*b + b^2)*cosh(d*x + c)^6 + 35*(3*a*b + 2*b^2)*cosh(d*x + c)^4 + 58*b^2*cosh(d*x + c)^2 - 3*a*b + 2*b^2)*sinh(d*x + c)^3 + 20*(54*(a*b + b^2)*cosh(d*x + c)^7 + 21*(3*a*b + 2*b^2)*cosh(d*x + c)^5 + 58*b^2*cosh(d*x + c)^3 - 3*(3*a*b - 2*b^2)*cosh(d*x + c))*sinh(d*x + c)^2 - 30*(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))*arctan(cosh(d*x + c) + sinh(d*x + c)) - 30*(a*b - b^2)*cosh(d*x + c) + 15*(a^2*cosh(d*x + c)^10 + 10*a^2*cosh(d*x + c)*sinh(d*x + c)^9 + a^2*sinh(d*x + c)^10 + 5*a^2*cosh(d*x + c)^8 + 5*(9*a^2*cosh(d*x + c)^2 + a^2)*sinh(d*x + c)^8 + 10*a^2*cosh(d*x + c)^6 + 40*(3*a^2*cosh(d*x + c)^3 + a^2*cosh(d*x + c))*sinh(d*x + c)^7 + 10*(21*a^2*cosh(d*x + c)^4 + 14*a^2*cosh(d*x + c)^2 + a^2)*sinh(d*x + c)^6 + 10*a^2*cosh(d*x + c)^4 + 4*(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)^5 + 10*(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)^4 + 5*a^2*cosh(d*x + c)^2 + 40*(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)^3 + 5*(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)^2 + a^2 + 10*(a^2*cosh(d*x + c)^9 + 4*a^2*cosh(d*x + c)^7 + 6*a^2*cosh(d*x + c)^5 + 4*a^2*cosh(d*x + c)^3 + a^2*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) + 1) - 15*(a^2*cosh(d*x + c)^10 + 10*a^2*cosh(d*x + c)*sinh(d*x + c)^9 + a^2*sinh(d*x + c)^10 + 5*a^2*cosh(d*x + c)^8 + 5*(9*a^2*cosh(d*x + c)^2 + a^2)*sinh(d*x + c)^8 + 10*a^2*cosh(d*x + c)^6 + 40*(3*a^2*cosh(d*x + c)^3 + a^2*cosh(d*x + c))*sinh(d*x + c)^7 + 10*(21*a^2*cosh(d*x + c)^4 + 14*a^2*cosh(d*x + c)^2 + a^2)*sinh(d*x + c)^6 + 10*a^2*cosh(d*x + c)^4 + 4*(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)^5 + 10*(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)^4 + 5*a^2*cosh(d*x + c)^2 + 40*(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)^3 + 5*(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)^2 + a^2 + 10*(a^2*cosh(d*x + c)^9 + 4*a^2*cosh(d*x + c)^7 + 6*a^2*cosh(d*x + c)^5 + 4*a^2*cosh(d*x + c)^3 + a^2*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) - 1) + 10*(27*(a*b + b^2)*cosh(d*x + c)^8 + 14*(3*a*b + 2*b^2)*cosh(d*x + c)^6 + 58*b^2*cosh(d*x + c)^4 - 6*(3*a*b - 2*b^2)*cosh(d*x + c)^2 - 3*a*b + 3*b^2)*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
62,1,518,0,0.565701," ","integrate(csch(d*x+c)^2*(a+b*tanh(d*x+c)^3)^2,x, algorithm=""fricas"")","-\frac{4 \, {\left({\left(5 \, a^{2} + 5 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(5 \, a^{2} + 5 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} + {\left(5 \, a b + 3 \, b^{2}\right)} \sinh\left(d x + c\right)^{5} + {\left(25 \, a^{2} + 5 \, a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(10 \, {\left(5 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 15 \, a b - 3 \, b^{2}\right)} \sinh\left(d x + c\right)^{3} + {\left(10 \, {\left(5 \, a^{2} + 5 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(25 \, a^{2} + 5 \, a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 10 \, {\left(5 \, a^{2} - a b\right)} \cosh\left(d x + c\right) + {\left(5 \, {\left(5 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 9 \, {\left(5 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 10 \, a b + 10 \, b^{2}\right)} \sinh\left(d x + c\right)\right)}}{5 \, {\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} + 3 \, 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} + 3 \, 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} + 50 \, d \cosh\left(d x + c\right)^{2} + 9 \, d\right)} \sinh\left(d x + c\right)^{3} + 3 \, {\left(7 \, d \cosh\left(d x + c\right)^{5} + 10 \, d \cosh\left(d x + c\right)^{3} + d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 5 \, 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,"-4/5*((5*a^2 + 5*a*b + 2*b^2)*cosh(d*x + c)^5 + 5*(5*a^2 + 5*a*b + 2*b^2)*cosh(d*x + c)*sinh(d*x + c)^4 + (5*a*b + 3*b^2)*sinh(d*x + c)^5 + (25*a^2 + 5*a*b - 2*b^2)*cosh(d*x + c)^3 + (10*(5*a*b + 3*b^2)*cosh(d*x + c)^2 + 15*a*b - 3*b^2)*sinh(d*x + c)^3 + (10*(5*a^2 + 5*a*b + 2*b^2)*cosh(d*x + c)^3 + 3*(25*a^2 + 5*a*b - 2*b^2)*cosh(d*x + c))*sinh(d*x + c)^2 + 10*(5*a^2 - a*b)*cosh(d*x + c) + (5*(5*a*b + 3*b^2)*cosh(d*x + c)^4 + 9*(5*a*b - b^2)*cosh(d*x + c)^2 + 10*a*b + 10*b^2)*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 + 3*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 + 3*d*cosh(d*x + c))*sinh(d*x + c)^4 + 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 + 3*(7*d*cosh(d*x + c)^5 + 10*d*cosh(d*x + c)^3 + d*cosh(d*x + c))*sinh(d*x + c)^2 - 5*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
63,1,4642,0,1.007217," ","integrate(csch(d*x+c)^3*(a+b*tanh(d*x+c)^3)^2,x, algorithm=""fricas"")","-\frac{30 \, {\left(a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right)^{13} + 390 \, {\left(a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{12} + 30 \, {\left(a^{2} - 2 \, a b\right)} \sinh\left(d x + c\right)^{13} + 20 \, {\left(9 \, a^{2} + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{11} + 20 \, {\left(117 \, {\left(a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right)^{2} + 9 \, a^{2} + 4 \, b^{2}\right)} \sinh\left(d x + c\right)^{11} + 220 \, {\left(39 \, {\left(a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right)^{3} + {\left(9 \, a^{2} + 4 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{10} + 6 \, {\left(75 \, a^{2} + 30 \, a b - 32 \, b^{2}\right)} \cosh\left(d x + c\right)^{9} + 2 \, {\left(10725 \, {\left(a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right)^{4} + 550 \, {\left(9 \, a^{2} + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 225 \, a^{2} + 90 \, a b - 96 \, b^{2}\right)} \sinh\left(d x + c\right)^{9} + 6 \, {\left(6435 \, {\left(a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right)^{5} + 550 \, {\left(9 \, a^{2} + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 9 \, {\left(75 \, a^{2} + 30 \, a b - 32 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{8} + 8 \, {\left(75 \, a^{2} + 28 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} + 8 \, {\left(6435 \, {\left(a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right)^{6} + 825 \, {\left(9 \, a^{2} + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 27 \, {\left(75 \, a^{2} + 30 \, a b - 32 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 75 \, a^{2} + 28 \, b^{2}\right)} \sinh\left(d x + c\right)^{7} + 8 \, {\left(6435 \, {\left(a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right)^{7} + 1155 \, {\left(9 \, a^{2} + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 63 \, {\left(75 \, a^{2} + 30 \, a b - 32 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 7 \, {\left(75 \, a^{2} + 28 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} + 6 \, {\left(75 \, a^{2} - 30 \, a b - 32 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 6 \, {\left(6435 \, {\left(a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right)^{8} + 1540 \, {\left(9 \, a^{2} + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 126 \, {\left(75 \, a^{2} + 30 \, a b - 32 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 28 \, {\left(75 \, a^{2} + 28 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 75 \, a^{2} - 30 \, a b - 32 \, b^{2}\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(10725 \, {\left(a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right)^{9} + 3300 \, {\left(9 \, a^{2} + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} + 378 \, {\left(75 \, a^{2} + 30 \, a b - 32 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 140 \, {\left(75 \, a^{2} + 28 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 15 \, {\left(75 \, a^{2} - 30 \, a b - 32 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 20 \, {\left(9 \, a^{2} + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(2145 \, {\left(a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right)^{10} + 825 \, {\left(9 \, a^{2} + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{8} + 126 \, {\left(75 \, a^{2} + 30 \, a b - 32 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 70 \, {\left(75 \, a^{2} + 28 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 15 \, {\left(75 \, a^{2} - 30 \, a b - 32 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 45 \, a^{2} + 20 \, b^{2}\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(585 \, {\left(a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right)^{11} + 275 \, {\left(9 \, a^{2} + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{9} + 54 \, {\left(75 \, a^{2} + 30 \, a b - 32 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} + 42 \, {\left(75 \, a^{2} + 28 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 15 \, {\left(75 \, a^{2} - 30 \, a b - 32 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 15 \, {\left(9 \, a^{2} + 4 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 60 \, {\left(a b \cosh\left(d x + c\right)^{14} + 14 \, a b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{13} + a b \sinh\left(d x + c\right)^{14} + 3 \, a b \cosh\left(d x + c\right)^{12} + {\left(91 \, a b \cosh\left(d x + c\right)^{2} + 3 \, a b\right)} \sinh\left(d x + c\right)^{12} + a b \cosh\left(d x + c\right)^{10} + 4 \, {\left(91 \, 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)^{11} + {\left(1001 \, a b \cosh\left(d x + c\right)^{4} + 198 \, a b \cosh\left(d x + c\right)^{2} + a b\right)} \sinh\left(d x + c\right)^{10} - 5 \, a b \cosh\left(d x + c\right)^{8} + 2 \, {\left(1001 \, a b \cosh\left(d x + c\right)^{5} + 330 \, 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)^{9} + {\left(3003 \, a b \cosh\left(d x + c\right)^{6} + 1485 \, a b \cosh\left(d x + c\right)^{4} + 45 \, a b \cosh\left(d x + c\right)^{2} - 5 \, a b\right)} \sinh\left(d x + c\right)^{8} - 5 \, a b \cosh\left(d x + c\right)^{6} + 8 \, {\left(429 \, a b \cosh\left(d x + c\right)^{7} + 297 \, a b \cosh\left(d x + c\right)^{5} + 15 \, 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)^{7} + {\left(3003 \, a b \cosh\left(d x + c\right)^{8} + 2772 \, a b \cosh\left(d x + c\right)^{6} + 210 \, a b \cosh\left(d x + c\right)^{4} - 140 \, a b \cosh\left(d x + c\right)^{2} - 5 \, a b\right)} \sinh\left(d x + c\right)^{6} + a b \cosh\left(d x + c\right)^{4} + 2 \, {\left(1001 \, a b \cosh\left(d x + c\right)^{9} + 1188 \, a b \cosh\left(d x + c\right)^{7} + 126 \, a b \cosh\left(d x + c\right)^{5} - 140 \, 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} + {\left(1001 \, a b \cosh\left(d x + c\right)^{10} + 1485 \, a b \cosh\left(d x + c\right)^{8} + 210 \, a b \cosh\left(d x + c\right)^{6} - 350 \, a b \cosh\left(d x + c\right)^{4} - 75 \, a b \cosh\left(d x + c\right)^{2} + a b\right)} \sinh\left(d x + c\right)^{4} + 3 \, a b \cosh\left(d x + c\right)^{2} + 4 \, {\left(91 \, a b \cosh\left(d x + c\right)^{11} + 165 \, a b \cosh\left(d x + c\right)^{9} + 30 \, a b \cosh\left(d x + c\right)^{7} - 70 \, a b \cosh\left(d x + c\right)^{5} - 25 \, 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} + {\left(91 \, a b \cosh\left(d x + c\right)^{12} + 198 \, a b \cosh\left(d x + c\right)^{10} + 45 \, a b \cosh\left(d x + c\right)^{8} - 140 \, a b \cosh\left(d x + c\right)^{6} - 75 \, a b \cosh\left(d x + c\right)^{4} + 6 \, a b \cosh\left(d x + c\right)^{2} + 3 \, a b\right)} \sinh\left(d x + c\right)^{2} + a b + 2 \, {\left(7 \, a b \cosh\left(d x + c\right)^{13} + 18 \, a b \cosh\left(d x + c\right)^{11} + 5 \, a b \cosh\left(d x + c\right)^{9} - 20 \, a b \cosh\left(d x + c\right)^{7} - 15 \, a b \cosh\left(d x + c\right)^{5} + 2 \, 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)\right)} \arctan\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) + 30 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right) - 15 \, {\left(a^{2} \cosh\left(d x + c\right)^{14} + 14 \, a^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{13} + a^{2} \sinh\left(d x + c\right)^{14} + 3 \, a^{2} \cosh\left(d x + c\right)^{12} + {\left(91 \, a^{2} \cosh\left(d x + c\right)^{2} + 3 \, a^{2}\right)} \sinh\left(d x + c\right)^{12} + a^{2} \cosh\left(d x + c\right)^{10} + 4 \, {\left(91 \, a^{2} \cosh\left(d x + c\right)^{3} + 9 \, a^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{11} + {\left(1001 \, a^{2} \cosh\left(d x + c\right)^{4} + 198 \, a^{2} \cosh\left(d x + c\right)^{2} + a^{2}\right)} \sinh\left(d x + c\right)^{10} - 5 \, a^{2} \cosh\left(d x + c\right)^{8} + 2 \, {\left(1001 \, a^{2} \cosh\left(d x + c\right)^{5} + 330 \, 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)^{9} + {\left(3003 \, a^{2} \cosh\left(d x + c\right)^{6} + 1485 \, a^{2} \cosh\left(d x + c\right)^{4} + 45 \, a^{2} \cosh\left(d x + c\right)^{2} - 5 \, a^{2}\right)} \sinh\left(d x + c\right)^{8} - 5 \, a^{2} \cosh\left(d x + c\right)^{6} + 8 \, {\left(429 \, a^{2} \cosh\left(d x + c\right)^{7} + 297 \, a^{2} \cosh\left(d x + c\right)^{5} + 15 \, 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)^{7} + {\left(3003 \, a^{2} \cosh\left(d x + c\right)^{8} + 2772 \, a^{2} \cosh\left(d x + c\right)^{6} + 210 \, a^{2} \cosh\left(d x + c\right)^{4} - 140 \, a^{2} \cosh\left(d x + c\right)^{2} - 5 \, a^{2}\right)} \sinh\left(d x + c\right)^{6} + a^{2} \cosh\left(d x + c\right)^{4} + 2 \, {\left(1001 \, a^{2} \cosh\left(d x + c\right)^{9} + 1188 \, a^{2} \cosh\left(d x + c\right)^{7} + 126 \, a^{2} \cosh\left(d x + c\right)^{5} - 140 \, 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)^{5} + {\left(1001 \, a^{2} \cosh\left(d x + c\right)^{10} + 1485 \, a^{2} \cosh\left(d x + c\right)^{8} + 210 \, a^{2} \cosh\left(d x + c\right)^{6} - 350 \, a^{2} \cosh\left(d x + c\right)^{4} - 75 \, a^{2} \cosh\left(d x + c\right)^{2} + a^{2}\right)} \sinh\left(d x + c\right)^{4} + 3 \, a^{2} \cosh\left(d x + c\right)^{2} + 4 \, {\left(91 \, a^{2} \cosh\left(d x + c\right)^{11} + 165 \, a^{2} \cosh\left(d x + c\right)^{9} + 30 \, a^{2} \cosh\left(d x + c\right)^{7} - 70 \, a^{2} \cosh\left(d x + c\right)^{5} - 25 \, a^{2} \cosh\left(d x + c\right)^{3} + a^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(91 \, a^{2} \cosh\left(d x + c\right)^{12} + 198 \, a^{2} \cosh\left(d x + c\right)^{10} + 45 \, a^{2} \cosh\left(d x + c\right)^{8} - 140 \, a^{2} \cosh\left(d x + c\right)^{6} - 75 \, a^{2} \cosh\left(d x + c\right)^{4} + 6 \, a^{2} \cosh\left(d x + c\right)^{2} + 3 \, a^{2}\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 2 \, {\left(7 \, a^{2} \cosh\left(d x + c\right)^{13} + 18 \, a^{2} \cosh\left(d x + c\right)^{11} + 5 \, a^{2} \cosh\left(d x + c\right)^{9} - 20 \, a^{2} \cosh\left(d x + c\right)^{7} - 15 \, a^{2} \cosh\left(d x + c\right)^{5} + 2 \, 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)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) + 1\right) + 15 \, {\left(a^{2} \cosh\left(d x + c\right)^{14} + 14 \, a^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{13} + a^{2} \sinh\left(d x + c\right)^{14} + 3 \, a^{2} \cosh\left(d x + c\right)^{12} + {\left(91 \, a^{2} \cosh\left(d x + c\right)^{2} + 3 \, a^{2}\right)} \sinh\left(d x + c\right)^{12} + a^{2} \cosh\left(d x + c\right)^{10} + 4 \, {\left(91 \, a^{2} \cosh\left(d x + c\right)^{3} + 9 \, a^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{11} + {\left(1001 \, a^{2} \cosh\left(d x + c\right)^{4} + 198 \, a^{2} \cosh\left(d x + c\right)^{2} + a^{2}\right)} \sinh\left(d x + c\right)^{10} - 5 \, a^{2} \cosh\left(d x + c\right)^{8} + 2 \, {\left(1001 \, a^{2} \cosh\left(d x + c\right)^{5} + 330 \, 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)^{9} + {\left(3003 \, a^{2} \cosh\left(d x + c\right)^{6} + 1485 \, a^{2} \cosh\left(d x + c\right)^{4} + 45 \, a^{2} \cosh\left(d x + c\right)^{2} - 5 \, a^{2}\right)} \sinh\left(d x + c\right)^{8} - 5 \, a^{2} \cosh\left(d x + c\right)^{6} + 8 \, {\left(429 \, a^{2} \cosh\left(d x + c\right)^{7} + 297 \, a^{2} \cosh\left(d x + c\right)^{5} + 15 \, 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)^{7} + {\left(3003 \, a^{2} \cosh\left(d x + c\right)^{8} + 2772 \, a^{2} \cosh\left(d x + c\right)^{6} + 210 \, a^{2} \cosh\left(d x + c\right)^{4} - 140 \, a^{2} \cosh\left(d x + c\right)^{2} - 5 \, a^{2}\right)} \sinh\left(d x + c\right)^{6} + a^{2} \cosh\left(d x + c\right)^{4} + 2 \, {\left(1001 \, a^{2} \cosh\left(d x + c\right)^{9} + 1188 \, a^{2} \cosh\left(d x + c\right)^{7} + 126 \, a^{2} \cosh\left(d x + c\right)^{5} - 140 \, 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)^{5} + {\left(1001 \, a^{2} \cosh\left(d x + c\right)^{10} + 1485 \, a^{2} \cosh\left(d x + c\right)^{8} + 210 \, a^{2} \cosh\left(d x + c\right)^{6} - 350 \, a^{2} \cosh\left(d x + c\right)^{4} - 75 \, a^{2} \cosh\left(d x + c\right)^{2} + a^{2}\right)} \sinh\left(d x + c\right)^{4} + 3 \, a^{2} \cosh\left(d x + c\right)^{2} + 4 \, {\left(91 \, a^{2} \cosh\left(d x + c\right)^{11} + 165 \, a^{2} \cosh\left(d x + c\right)^{9} + 30 \, a^{2} \cosh\left(d x + c\right)^{7} - 70 \, a^{2} \cosh\left(d x + c\right)^{5} - 25 \, a^{2} \cosh\left(d x + c\right)^{3} + a^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(91 \, a^{2} \cosh\left(d x + c\right)^{12} + 198 \, a^{2} \cosh\left(d x + c\right)^{10} + 45 \, a^{2} \cosh\left(d x + c\right)^{8} - 140 \, a^{2} \cosh\left(d x + c\right)^{6} - 75 \, a^{2} \cosh\left(d x + c\right)^{4} + 6 \, a^{2} \cosh\left(d x + c\right)^{2} + 3 \, a^{2}\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 2 \, {\left(7 \, a^{2} \cosh\left(d x + c\right)^{13} + 18 \, a^{2} \cosh\left(d x + c\right)^{11} + 5 \, a^{2} \cosh\left(d x + c\right)^{9} - 20 \, a^{2} \cosh\left(d x + c\right)^{7} - 15 \, a^{2} \cosh\left(d x + c\right)^{5} + 2 \, 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)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) + 2 \, {\left(195 \, {\left(a^{2} - 2 \, a b\right)} \cosh\left(d x + c\right)^{12} + 110 \, {\left(9 \, a^{2} + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{10} + 27 \, {\left(75 \, a^{2} + 30 \, a b - 32 \, b^{2}\right)} \cosh\left(d x + c\right)^{8} + 28 \, {\left(75 \, a^{2} + 28 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(75 \, a^{2} - 30 \, a b - 32 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 30 \, {\left(9 \, a^{2} + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 15 \, a^{2} + 30 \, a b\right)} \sinh\left(d x + c\right)}{30 \, {\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} + 3 \, d \cosh\left(d x + c\right)^{12} + {\left(91 \, d \cosh\left(d x + c\right)^{2} + 3 \, d\right)} \sinh\left(d x + c\right)^{12} + 4 \, {\left(91 \, d \cosh\left(d x + c\right)^{3} + 9 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{11} + d \cosh\left(d x + c\right)^{10} + {\left(1001 \, d \cosh\left(d x + c\right)^{4} + 198 \, d \cosh\left(d x + c\right)^{2} + d\right)} \sinh\left(d x + c\right)^{10} + 2 \, {\left(1001 \, d \cosh\left(d x + c\right)^{5} + 330 \, d \cosh\left(d x + c\right)^{3} + 5 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} - 5 \, d \cosh\left(d x + c\right)^{8} + {\left(3003 \, d \cosh\left(d x + c\right)^{6} + 1485 \, d \cosh\left(d x + c\right)^{4} + 45 \, d \cosh\left(d x + c\right)^{2} - 5 \, d\right)} \sinh\left(d x + c\right)^{8} + 8 \, {\left(429 \, d \cosh\left(d x + c\right)^{7} + 297 \, d \cosh\left(d x + c\right)^{5} + 15 \, d \cosh\left(d x + c\right)^{3} - 5 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} - 5 \, d \cosh\left(d x + c\right)^{6} + {\left(3003 \, d \cosh\left(d x + c\right)^{8} + 2772 \, d \cosh\left(d x + c\right)^{6} + 210 \, 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)^{6} + 2 \, {\left(1001 \, d \cosh\left(d x + c\right)^{9} + 1188 \, d \cosh\left(d x + c\right)^{7} + 126 \, 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)^{5} + d \cosh\left(d x + c\right)^{4} + {\left(1001 \, d \cosh\left(d x + c\right)^{10} + 1485 \, d \cosh\left(d x + c\right)^{8} + 210 \, 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} + d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(91 \, d \cosh\left(d x + c\right)^{11} + 165 \, d \cosh\left(d x + c\right)^{9} + 30 \, 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} + d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 3 \, d \cosh\left(d x + c\right)^{2} + {\left(91 \, d \cosh\left(d x + c\right)^{12} + 198 \, d \cosh\left(d x + c\right)^{10} + 45 \, 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} + 6 \, d \cosh\left(d x + c\right)^{2} + 3 \, d\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(7 \, d \cosh\left(d x + c\right)^{13} + 18 \, d \cosh\left(d x + c\right)^{11} + 5 \, d \cosh\left(d x + c\right)^{9} - 20 \, d \cosh\left(d x + c\right)^{7} - 15 \, d \cosh\left(d x + c\right)^{5} + 2 \, d \cosh\left(d x + c\right)^{3} + 3 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + d\right)}}"," ",0,"-1/30*(30*(a^2 - 2*a*b)*cosh(d*x + c)^13 + 390*(a^2 - 2*a*b)*cosh(d*x + c)*sinh(d*x + c)^12 + 30*(a^2 - 2*a*b)*sinh(d*x + c)^13 + 20*(9*a^2 + 4*b^2)*cosh(d*x + c)^11 + 20*(117*(a^2 - 2*a*b)*cosh(d*x + c)^2 + 9*a^2 + 4*b^2)*sinh(d*x + c)^11 + 220*(39*(a^2 - 2*a*b)*cosh(d*x + c)^3 + (9*a^2 + 4*b^2)*cosh(d*x + c))*sinh(d*x + c)^10 + 6*(75*a^2 + 30*a*b - 32*b^2)*cosh(d*x + c)^9 + 2*(10725*(a^2 - 2*a*b)*cosh(d*x + c)^4 + 550*(9*a^2 + 4*b^2)*cosh(d*x + c)^2 + 225*a^2 + 90*a*b - 96*b^2)*sinh(d*x + c)^9 + 6*(6435*(a^2 - 2*a*b)*cosh(d*x + c)^5 + 550*(9*a^2 + 4*b^2)*cosh(d*x + c)^3 + 9*(75*a^2 + 30*a*b - 32*b^2)*cosh(d*x + c))*sinh(d*x + c)^8 + 8*(75*a^2 + 28*b^2)*cosh(d*x + c)^7 + 8*(6435*(a^2 - 2*a*b)*cosh(d*x + c)^6 + 825*(9*a^2 + 4*b^2)*cosh(d*x + c)^4 + 27*(75*a^2 + 30*a*b - 32*b^2)*cosh(d*x + c)^2 + 75*a^2 + 28*b^2)*sinh(d*x + c)^7 + 8*(6435*(a^2 - 2*a*b)*cosh(d*x + c)^7 + 1155*(9*a^2 + 4*b^2)*cosh(d*x + c)^5 + 63*(75*a^2 + 30*a*b - 32*b^2)*cosh(d*x + c)^3 + 7*(75*a^2 + 28*b^2)*cosh(d*x + c))*sinh(d*x + c)^6 + 6*(75*a^2 - 30*a*b - 32*b^2)*cosh(d*x + c)^5 + 6*(6435*(a^2 - 2*a*b)*cosh(d*x + c)^8 + 1540*(9*a^2 + 4*b^2)*cosh(d*x + c)^6 + 126*(75*a^2 + 30*a*b - 32*b^2)*cosh(d*x + c)^4 + 28*(75*a^2 + 28*b^2)*cosh(d*x + c)^2 + 75*a^2 - 30*a*b - 32*b^2)*sinh(d*x + c)^5 + 2*(10725*(a^2 - 2*a*b)*cosh(d*x + c)^9 + 3300*(9*a^2 + 4*b^2)*cosh(d*x + c)^7 + 378*(75*a^2 + 30*a*b - 32*b^2)*cosh(d*x + c)^5 + 140*(75*a^2 + 28*b^2)*cosh(d*x + c)^3 + 15*(75*a^2 - 30*a*b - 32*b^2)*cosh(d*x + c))*sinh(d*x + c)^4 + 20*(9*a^2 + 4*b^2)*cosh(d*x + c)^3 + 4*(2145*(a^2 - 2*a*b)*cosh(d*x + c)^10 + 825*(9*a^2 + 4*b^2)*cosh(d*x + c)^8 + 126*(75*a^2 + 30*a*b - 32*b^2)*cosh(d*x + c)^6 + 70*(75*a^2 + 28*b^2)*cosh(d*x + c)^4 + 15*(75*a^2 - 30*a*b - 32*b^2)*cosh(d*x + c)^2 + 45*a^2 + 20*b^2)*sinh(d*x + c)^3 + 4*(585*(a^2 - 2*a*b)*cosh(d*x + c)^11 + 275*(9*a^2 + 4*b^2)*cosh(d*x + c)^9 + 54*(75*a^2 + 30*a*b - 32*b^2)*cosh(d*x + c)^7 + 42*(75*a^2 + 28*b^2)*cosh(d*x + c)^5 + 15*(75*a^2 - 30*a*b - 32*b^2)*cosh(d*x + c)^3 + 15*(9*a^2 + 4*b^2)*cosh(d*x + c))*sinh(d*x + c)^2 - 60*(a*b*cosh(d*x + c)^14 + 14*a*b*cosh(d*x + c)*sinh(d*x + c)^13 + a*b*sinh(d*x + c)^14 + 3*a*b*cosh(d*x + c)^12 + (91*a*b*cosh(d*x + c)^2 + 3*a*b)*sinh(d*x + c)^12 + a*b*cosh(d*x + c)^10 + 4*(91*a*b*cosh(d*x + c)^3 + 9*a*b*cosh(d*x + c))*sinh(d*x + c)^11 + (1001*a*b*cosh(d*x + c)^4 + 198*a*b*cosh(d*x + c)^2 + a*b)*sinh(d*x + c)^10 - 5*a*b*cosh(d*x + c)^8 + 2*(1001*a*b*cosh(d*x + c)^5 + 330*a*b*cosh(d*x + c)^3 + 5*a*b*cosh(d*x + c))*sinh(d*x + c)^9 + (3003*a*b*cosh(d*x + c)^6 + 1485*a*b*cosh(d*x + c)^4 + 45*a*b*cosh(d*x + c)^2 - 5*a*b)*sinh(d*x + c)^8 - 5*a*b*cosh(d*x + c)^6 + 8*(429*a*b*cosh(d*x + c)^7 + 297*a*b*cosh(d*x + c)^5 + 15*a*b*cosh(d*x + c)^3 - 5*a*b*cosh(d*x + c))*sinh(d*x + c)^7 + (3003*a*b*cosh(d*x + c)^8 + 2772*a*b*cosh(d*x + c)^6 + 210*a*b*cosh(d*x + c)^4 - 140*a*b*cosh(d*x + c)^2 - 5*a*b)*sinh(d*x + c)^6 + a*b*cosh(d*x + c)^4 + 2*(1001*a*b*cosh(d*x + c)^9 + 1188*a*b*cosh(d*x + c)^7 + 126*a*b*cosh(d*x + c)^5 - 140*a*b*cosh(d*x + c)^3 - 15*a*b*cosh(d*x + c))*sinh(d*x + c)^5 + (1001*a*b*cosh(d*x + c)^10 + 1485*a*b*cosh(d*x + c)^8 + 210*a*b*cosh(d*x + c)^6 - 350*a*b*cosh(d*x + c)^4 - 75*a*b*cosh(d*x + c)^2 + a*b)*sinh(d*x + c)^4 + 3*a*b*cosh(d*x + c)^2 + 4*(91*a*b*cosh(d*x + c)^11 + 165*a*b*cosh(d*x + c)^9 + 30*a*b*cosh(d*x + c)^7 - 70*a*b*cosh(d*x + c)^5 - 25*a*b*cosh(d*x + c)^3 + a*b*cosh(d*x + c))*sinh(d*x + c)^3 + (91*a*b*cosh(d*x + c)^12 + 198*a*b*cosh(d*x + c)^10 + 45*a*b*cosh(d*x + c)^8 - 140*a*b*cosh(d*x + c)^6 - 75*a*b*cosh(d*x + c)^4 + 6*a*b*cosh(d*x + c)^2 + 3*a*b)*sinh(d*x + c)^2 + a*b + 2*(7*a*b*cosh(d*x + c)^13 + 18*a*b*cosh(d*x + c)^11 + 5*a*b*cosh(d*x + c)^9 - 20*a*b*cosh(d*x + c)^7 - 15*a*b*cosh(d*x + c)^5 + 2*a*b*cosh(d*x + c)^3 + 3*a*b*cosh(d*x + c))*sinh(d*x + c))*arctan(cosh(d*x + c) + sinh(d*x + c)) + 30*(a^2 + 2*a*b)*cosh(d*x + c) - 15*(a^2*cosh(d*x + c)^14 + 14*a^2*cosh(d*x + c)*sinh(d*x + c)^13 + a^2*sinh(d*x + c)^14 + 3*a^2*cosh(d*x + c)^12 + (91*a^2*cosh(d*x + c)^2 + 3*a^2)*sinh(d*x + c)^12 + a^2*cosh(d*x + c)^10 + 4*(91*a^2*cosh(d*x + c)^3 + 9*a^2*cosh(d*x + c))*sinh(d*x + c)^11 + (1001*a^2*cosh(d*x + c)^4 + 198*a^2*cosh(d*x + c)^2 + a^2)*sinh(d*x + c)^10 - 5*a^2*cosh(d*x + c)^8 + 2*(1001*a^2*cosh(d*x + c)^5 + 330*a^2*cosh(d*x + c)^3 + 5*a^2*cosh(d*x + c))*sinh(d*x + c)^9 + (3003*a^2*cosh(d*x + c)^6 + 1485*a^2*cosh(d*x + c)^4 + 45*a^2*cosh(d*x + c)^2 - 5*a^2)*sinh(d*x + c)^8 - 5*a^2*cosh(d*x + c)^6 + 8*(429*a^2*cosh(d*x + c)^7 + 297*a^2*cosh(d*x + c)^5 + 15*a^2*cosh(d*x + c)^3 - 5*a^2*cosh(d*x + c))*sinh(d*x + c)^7 + (3003*a^2*cosh(d*x + c)^8 + 2772*a^2*cosh(d*x + c)^6 + 210*a^2*cosh(d*x + c)^4 - 140*a^2*cosh(d*x + c)^2 - 5*a^2)*sinh(d*x + c)^6 + a^2*cosh(d*x + c)^4 + 2*(1001*a^2*cosh(d*x + c)^9 + 1188*a^2*cosh(d*x + c)^7 + 126*a^2*cosh(d*x + c)^5 - 140*a^2*cosh(d*x + c)^3 - 15*a^2*cosh(d*x + c))*sinh(d*x + c)^5 + (1001*a^2*cosh(d*x + c)^10 + 1485*a^2*cosh(d*x + c)^8 + 210*a^2*cosh(d*x + c)^6 - 350*a^2*cosh(d*x + c)^4 - 75*a^2*cosh(d*x + c)^2 + a^2)*sinh(d*x + c)^4 + 3*a^2*cosh(d*x + c)^2 + 4*(91*a^2*cosh(d*x + c)^11 + 165*a^2*cosh(d*x + c)^9 + 30*a^2*cosh(d*x + c)^7 - 70*a^2*cosh(d*x + c)^5 - 25*a^2*cosh(d*x + c)^3 + a^2*cosh(d*x + c))*sinh(d*x + c)^3 + (91*a^2*cosh(d*x + c)^12 + 198*a^2*cosh(d*x + c)^10 + 45*a^2*cosh(d*x + c)^8 - 140*a^2*cosh(d*x + c)^6 - 75*a^2*cosh(d*x + c)^4 + 6*a^2*cosh(d*x + c)^2 + 3*a^2)*sinh(d*x + c)^2 + a^2 + 2*(7*a^2*cosh(d*x + c)^13 + 18*a^2*cosh(d*x + c)^11 + 5*a^2*cosh(d*x + c)^9 - 20*a^2*cosh(d*x + c)^7 - 15*a^2*cosh(d*x + c)^5 + 2*a^2*cosh(d*x + c)^3 + 3*a^2*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) + 1) + 15*(a^2*cosh(d*x + c)^14 + 14*a^2*cosh(d*x + c)*sinh(d*x + c)^13 + a^2*sinh(d*x + c)^14 + 3*a^2*cosh(d*x + c)^12 + (91*a^2*cosh(d*x + c)^2 + 3*a^2)*sinh(d*x + c)^12 + a^2*cosh(d*x + c)^10 + 4*(91*a^2*cosh(d*x + c)^3 + 9*a^2*cosh(d*x + c))*sinh(d*x + c)^11 + (1001*a^2*cosh(d*x + c)^4 + 198*a^2*cosh(d*x + c)^2 + a^2)*sinh(d*x + c)^10 - 5*a^2*cosh(d*x + c)^8 + 2*(1001*a^2*cosh(d*x + c)^5 + 330*a^2*cosh(d*x + c)^3 + 5*a^2*cosh(d*x + c))*sinh(d*x + c)^9 + (3003*a^2*cosh(d*x + c)^6 + 1485*a^2*cosh(d*x + c)^4 + 45*a^2*cosh(d*x + c)^2 - 5*a^2)*sinh(d*x + c)^8 - 5*a^2*cosh(d*x + c)^6 + 8*(429*a^2*cosh(d*x + c)^7 + 297*a^2*cosh(d*x + c)^5 + 15*a^2*cosh(d*x + c)^3 - 5*a^2*cosh(d*x + c))*sinh(d*x + c)^7 + (3003*a^2*cosh(d*x + c)^8 + 2772*a^2*cosh(d*x + c)^6 + 210*a^2*cosh(d*x + c)^4 - 140*a^2*cosh(d*x + c)^2 - 5*a^2)*sinh(d*x + c)^6 + a^2*cosh(d*x + c)^4 + 2*(1001*a^2*cosh(d*x + c)^9 + 1188*a^2*cosh(d*x + c)^7 + 126*a^2*cosh(d*x + c)^5 - 140*a^2*cosh(d*x + c)^3 - 15*a^2*cosh(d*x + c))*sinh(d*x + c)^5 + (1001*a^2*cosh(d*x + c)^10 + 1485*a^2*cosh(d*x + c)^8 + 210*a^2*cosh(d*x + c)^6 - 350*a^2*cosh(d*x + c)^4 - 75*a^2*cosh(d*x + c)^2 + a^2)*sinh(d*x + c)^4 + 3*a^2*cosh(d*x + c)^2 + 4*(91*a^2*cosh(d*x + c)^11 + 165*a^2*cosh(d*x + c)^9 + 30*a^2*cosh(d*x + c)^7 - 70*a^2*cosh(d*x + c)^5 - 25*a^2*cosh(d*x + c)^3 + a^2*cosh(d*x + c))*sinh(d*x + c)^3 + (91*a^2*cosh(d*x + c)^12 + 198*a^2*cosh(d*x + c)^10 + 45*a^2*cosh(d*x + c)^8 - 140*a^2*cosh(d*x + c)^6 - 75*a^2*cosh(d*x + c)^4 + 6*a^2*cosh(d*x + c)^2 + 3*a^2)*sinh(d*x + c)^2 + a^2 + 2*(7*a^2*cosh(d*x + c)^13 + 18*a^2*cosh(d*x + c)^11 + 5*a^2*cosh(d*x + c)^9 - 20*a^2*cosh(d*x + c)^7 - 15*a^2*cosh(d*x + c)^5 + 2*a^2*cosh(d*x + c)^3 + 3*a^2*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) - 1) + 2*(195*(a^2 - 2*a*b)*cosh(d*x + c)^12 + 110*(9*a^2 + 4*b^2)*cosh(d*x + c)^10 + 27*(75*a^2 + 30*a*b - 32*b^2)*cosh(d*x + c)^8 + 28*(75*a^2 + 28*b^2)*cosh(d*x + c)^6 + 15*(75*a^2 - 30*a*b - 32*b^2)*cosh(d*x + c)^4 + 30*(9*a^2 + 4*b^2)*cosh(d*x + c)^2 + 15*a^2 + 30*a*b)*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 + 3*d*cosh(d*x + c)^12 + (91*d*cosh(d*x + c)^2 + 3*d)*sinh(d*x + c)^12 + 4*(91*d*cosh(d*x + c)^3 + 9*d*cosh(d*x + c))*sinh(d*x + c)^11 + d*cosh(d*x + c)^10 + (1001*d*cosh(d*x + c)^4 + 198*d*cosh(d*x + c)^2 + d)*sinh(d*x + c)^10 + 2*(1001*d*cosh(d*x + c)^5 + 330*d*cosh(d*x + c)^3 + 5*d*cosh(d*x + c))*sinh(d*x + c)^9 - 5*d*cosh(d*x + c)^8 + (3003*d*cosh(d*x + c)^6 + 1485*d*cosh(d*x + c)^4 + 45*d*cosh(d*x + c)^2 - 5*d)*sinh(d*x + c)^8 + 8*(429*d*cosh(d*x + c)^7 + 297*d*cosh(d*x + c)^5 + 15*d*cosh(d*x + c)^3 - 5*d*cosh(d*x + c))*sinh(d*x + c)^7 - 5*d*cosh(d*x + c)^6 + (3003*d*cosh(d*x + c)^8 + 2772*d*cosh(d*x + c)^6 + 210*d*cosh(d*x + c)^4 - 140*d*cosh(d*x + c)^2 - 5*d)*sinh(d*x + c)^6 + 2*(1001*d*cosh(d*x + c)^9 + 1188*d*cosh(d*x + c)^7 + 126*d*cosh(d*x + c)^5 - 140*d*cosh(d*x + c)^3 - 15*d*cosh(d*x + c))*sinh(d*x + c)^5 + d*cosh(d*x + c)^4 + (1001*d*cosh(d*x + c)^10 + 1485*d*cosh(d*x + c)^8 + 210*d*cosh(d*x + c)^6 - 350*d*cosh(d*x + c)^4 - 75*d*cosh(d*x + c)^2 + d)*sinh(d*x + c)^4 + 4*(91*d*cosh(d*x + c)^11 + 165*d*cosh(d*x + c)^9 + 30*d*cosh(d*x + c)^7 - 70*d*cosh(d*x + c)^5 - 25*d*cosh(d*x + c)^3 + d*cosh(d*x + c))*sinh(d*x + c)^3 + 3*d*cosh(d*x + c)^2 + (91*d*cosh(d*x + c)^12 + 198*d*cosh(d*x + c)^10 + 45*d*cosh(d*x + c)^8 - 140*d*cosh(d*x + c)^6 - 75*d*cosh(d*x + c)^4 + 6*d*cosh(d*x + c)^2 + 3*d)*sinh(d*x + c)^2 + 2*(7*d*cosh(d*x + c)^13 + 18*d*cosh(d*x + c)^11 + 5*d*cosh(d*x + c)^9 - 20*d*cosh(d*x + c)^7 - 15*d*cosh(d*x + c)^5 + 2*d*cosh(d*x + c)^3 + 3*d*cosh(d*x + c))*sinh(d*x + c) + d)","B",0
64,1,4125,0,0.617037," ","integrate(csch(d*x+c)^4*(a+b*tanh(d*x+c)^3)^2,x, algorithm=""fricas"")","\frac{2 \, {\left(30 \, a b \cosh\left(d x + c\right)^{14} + 420 \, a b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{13} + 30 \, a b \sinh\left(d x + c\right)^{14} - 30 \, {\left(a^{2} + b^{2}\right)} \cosh\left(d x + c\right)^{12} + 30 \, {\left(91 \, a b \cosh\left(d x + c\right)^{2} - a^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{12} + 120 \, {\left(91 \, a b \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{2} + b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{11} - 10 \, {\left(14 \, a^{2} + 9 \, a b - 10 \, b^{2}\right)} \cosh\left(d x + c\right)^{10} + 10 \, {\left(3003 \, a b \cosh\left(d x + c\right)^{4} - 198 \, {\left(a^{2} + b^{2}\right)} \cosh\left(d x + c\right)^{2} - 14 \, a^{2} - 9 \, a b + 10 \, b^{2}\right)} \sinh\left(d x + c\right)^{10} + 20 \, {\left(3003 \, a b \cosh\left(d x + c\right)^{5} - 330 \, {\left(a^{2} + b^{2}\right)} \cosh\left(d x + c\right)^{3} - 5 \, {\left(14 \, a^{2} + 9 \, a b - 10 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} - 10 \, {\left(25 \, a^{2} + 13 \, b^{2}\right)} \cosh\left(d x + c\right)^{8} + 10 \, {\left(9009 \, a b \cosh\left(d x + c\right)^{6} - 1485 \, {\left(a^{2} + b^{2}\right)} \cosh\left(d x + c\right)^{4} - 45 \, {\left(14 \, a^{2} + 9 \, a b - 10 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 25 \, a^{2} - 13 \, b^{2}\right)} \sinh\left(d x + c\right)^{8} + 80 \, {\left(1287 \, a b \cosh\left(d x + c\right)^{7} - 297 \, {\left(a^{2} + b^{2}\right)} \cosh\left(d x + c\right)^{5} - 15 \, {\left(14 \, a^{2} + 9 \, a b - 10 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(25 \, a^{2} + 13 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} - 2 \, {\left(100 \, a^{2} - 45 \, a b - 44 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(45045 \, a b \cosh\left(d x + c\right)^{8} - 13860 \, {\left(a^{2} + b^{2}\right)} \cosh\left(d x + c\right)^{6} - 1050 \, {\left(14 \, a^{2} + 9 \, a b - 10 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} - 140 \, {\left(25 \, a^{2} + 13 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 100 \, a^{2} + 45 \, a b + 44 \, b^{2}\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(15015 \, a b \cosh\left(d x + c\right)^{9} - 5940 \, {\left(a^{2} + b^{2}\right)} \cosh\left(d x + c\right)^{7} - 630 \, {\left(14 \, a^{2} + 9 \, a b - 10 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} - 140 \, {\left(25 \, a^{2} + 13 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(100 \, a^{2} - 45 \, a b - 44 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 2 \, {\left(25 \, a^{2} + 17 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(15015 \, a b \cosh\left(d x + c\right)^{10} - 7425 \, {\left(a^{2} + b^{2}\right)} \cosh\left(d x + c\right)^{8} - 1050 \, {\left(14 \, a^{2} + 9 \, a b - 10 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} - 350 \, {\left(25 \, a^{2} + 13 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} - 15 \, {\left(100 \, a^{2} - 45 \, a b - 44 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 25 \, a^{2} - 17 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(1365 \, a b \cosh\left(d x + c\right)^{11} - 825 \, {\left(a^{2} + b^{2}\right)} \cosh\left(d x + c\right)^{9} - 150 \, {\left(14 \, a^{2} + 9 \, a b - 10 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} - 70 \, {\left(25 \, a^{2} + 13 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} - 5 \, {\left(100 \, a^{2} - 45 \, a b - 44 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(25 \, a^{2} + 17 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(10 \, a^{2} - 15 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(1365 \, a b \cosh\left(d x + c\right)^{12} - 990 \, {\left(a^{2} + b^{2}\right)} \cosh\left(d x + c\right)^{10} - 225 \, {\left(14 \, a^{2} + 9 \, a b - 10 \, b^{2}\right)} \cosh\left(d x + c\right)^{8} - 140 \, {\left(25 \, a^{2} + 13 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} - 15 \, {\left(100 \, a^{2} - 45 \, a b - 44 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} - 6 \, {\left(25 \, a^{2} + 17 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 10 \, a^{2} - 15 \, a b + 2 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} + 10 \, a^{2} + 2 \, b^{2} - 15 \, {\left(a b \cosh\left(d x + c\right)^{16} + 16 \, a b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{15} + a b \sinh\left(d x + c\right)^{16} + 2 \, a b \cosh\left(d x + c\right)^{14} + 2 \, {\left(60 \, a b \cosh\left(d x + c\right)^{2} + a b\right)} \sinh\left(d x + c\right)^{14} - 2 \, a b \cosh\left(d x + c\right)^{12} + 28 \, {\left(20 \, a b \cosh\left(d x + c\right)^{3} + a b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{13} + 2 \, {\left(910 \, a b \cosh\left(d x + c\right)^{4} + 91 \, a b \cosh\left(d x + c\right)^{2} - a b\right)} \sinh\left(d x + c\right)^{12} - 6 \, a b \cosh\left(d x + c\right)^{10} + 8 \, {\left(546 \, a b \cosh\left(d x + c\right)^{5} + 91 \, 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)^{11} + 2 \, {\left(4004 \, a b \cosh\left(d x + c\right)^{6} + 1001 \, a b \cosh\left(d x + c\right)^{4} - 66 \, a b \cosh\left(d x + c\right)^{2} - 3 \, a b\right)} \sinh\left(d x + c\right)^{10} + 4 \, {\left(2860 \, a b \cosh\left(d x + c\right)^{7} + 1001 \, a b \cosh\left(d x + c\right)^{5} - 110 \, 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)^{9} + 6 \, {\left(2145 \, a b \cosh\left(d x + c\right)^{8} + 1001 \, a b \cosh\left(d x + c\right)^{6} - 165 \, a b \cosh\left(d x + c\right)^{4} - 45 \, a b \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{8} + 6 \, a b \cosh\left(d x + c\right)^{6} + 16 \, {\left(715 \, a b \cosh\left(d x + c\right)^{9} + 429 \, a b \cosh\left(d x + c\right)^{7} - 99 \, a b \cosh\left(d x + c\right)^{5} - 45 \, a b \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(4004 \, a b \cosh\left(d x + c\right)^{10} + 3003 \, a b \cosh\left(d x + c\right)^{8} - 924 \, a b \cosh\left(d x + c\right)^{6} - 630 \, a b \cosh\left(d x + c\right)^{4} + 3 \, a b\right)} \sinh\left(d x + c\right)^{6} + 2 \, a b \cosh\left(d x + c\right)^{4} + 4 \, {\left(1092 \, a b \cosh\left(d x + c\right)^{11} + 1001 \, a b \cosh\left(d x + c\right)^{9} - 396 \, a b \cosh\left(d x + c\right)^{7} - 378 \, a b \cosh\left(d x + c\right)^{5} + 9 \, a b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(910 \, a b \cosh\left(d x + c\right)^{12} + 1001 \, a b \cosh\left(d x + c\right)^{10} - 495 \, a b \cosh\left(d x + c\right)^{8} - 630 \, a b \cosh\left(d x + c\right)^{6} + 45 \, a b \cosh\left(d x + c\right)^{2} + a b\right)} \sinh\left(d x + c\right)^{4} - 2 \, a b \cosh\left(d x + c\right)^{2} + 8 \, {\left(70 \, a b \cosh\left(d x + c\right)^{13} + 91 \, a b \cosh\left(d x + c\right)^{11} - 55 \, a b \cosh\left(d x + c\right)^{9} - 90 \, a b \cosh\left(d x + c\right)^{7} + 15 \, 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} + 2 \, {\left(60 \, a b \cosh\left(d x + c\right)^{14} + 91 \, a b \cosh\left(d x + c\right)^{12} - 66 \, a b \cosh\left(d x + c\right)^{10} - 135 \, a b \cosh\left(d x + c\right)^{8} + 45 \, a b \cosh\left(d x + c\right)^{4} + 6 \, a b \cosh\left(d x + c\right)^{2} - a b\right)} \sinh\left(d x + c\right)^{2} - a b + 4 \, {\left(4 \, a b \cosh\left(d x + c\right)^{15} + 7 \, a b \cosh\left(d x + c\right)^{13} - 6 \, a b \cosh\left(d x + c\right)^{11} - 15 \, a b \cosh\left(d x + c\right)^{9} + 9 \, a b \cosh\left(d x + c\right)^{5} + 2 \, 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(\frac{2 \, \cosh\left(d x + c\right)}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) + 15 \, {\left(a b \cosh\left(d x + c\right)^{16} + 16 \, a b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{15} + a b \sinh\left(d x + c\right)^{16} + 2 \, a b \cosh\left(d x + c\right)^{14} + 2 \, {\left(60 \, a b \cosh\left(d x + c\right)^{2} + a b\right)} \sinh\left(d x + c\right)^{14} - 2 \, a b \cosh\left(d x + c\right)^{12} + 28 \, {\left(20 \, a b \cosh\left(d x + c\right)^{3} + a b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{13} + 2 \, {\left(910 \, a b \cosh\left(d x + c\right)^{4} + 91 \, a b \cosh\left(d x + c\right)^{2} - a b\right)} \sinh\left(d x + c\right)^{12} - 6 \, a b \cosh\left(d x + c\right)^{10} + 8 \, {\left(546 \, a b \cosh\left(d x + c\right)^{5} + 91 \, 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)^{11} + 2 \, {\left(4004 \, a b \cosh\left(d x + c\right)^{6} + 1001 \, a b \cosh\left(d x + c\right)^{4} - 66 \, a b \cosh\left(d x + c\right)^{2} - 3 \, a b\right)} \sinh\left(d x + c\right)^{10} + 4 \, {\left(2860 \, a b \cosh\left(d x + c\right)^{7} + 1001 \, a b \cosh\left(d x + c\right)^{5} - 110 \, 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)^{9} + 6 \, {\left(2145 \, a b \cosh\left(d x + c\right)^{8} + 1001 \, a b \cosh\left(d x + c\right)^{6} - 165 \, a b \cosh\left(d x + c\right)^{4} - 45 \, a b \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{8} + 6 \, a b \cosh\left(d x + c\right)^{6} + 16 \, {\left(715 \, a b \cosh\left(d x + c\right)^{9} + 429 \, a b \cosh\left(d x + c\right)^{7} - 99 \, a b \cosh\left(d x + c\right)^{5} - 45 \, a b \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(4004 \, a b \cosh\left(d x + c\right)^{10} + 3003 \, a b \cosh\left(d x + c\right)^{8} - 924 \, a b \cosh\left(d x + c\right)^{6} - 630 \, a b \cosh\left(d x + c\right)^{4} + 3 \, a b\right)} \sinh\left(d x + c\right)^{6} + 2 \, a b \cosh\left(d x + c\right)^{4} + 4 \, {\left(1092 \, a b \cosh\left(d x + c\right)^{11} + 1001 \, a b \cosh\left(d x + c\right)^{9} - 396 \, a b \cosh\left(d x + c\right)^{7} - 378 \, a b \cosh\left(d x + c\right)^{5} + 9 \, a b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(910 \, a b \cosh\left(d x + c\right)^{12} + 1001 \, a b \cosh\left(d x + c\right)^{10} - 495 \, a b \cosh\left(d x + c\right)^{8} - 630 \, a b \cosh\left(d x + c\right)^{6} + 45 \, a b \cosh\left(d x + c\right)^{2} + a b\right)} \sinh\left(d x + c\right)^{4} - 2 \, a b \cosh\left(d x + c\right)^{2} + 8 \, {\left(70 \, a b \cosh\left(d x + c\right)^{13} + 91 \, a b \cosh\left(d x + c\right)^{11} - 55 \, a b \cosh\left(d x + c\right)^{9} - 90 \, a b \cosh\left(d x + c\right)^{7} + 15 \, 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} + 2 \, {\left(60 \, a b \cosh\left(d x + c\right)^{14} + 91 \, a b \cosh\left(d x + c\right)^{12} - 66 \, a b \cosh\left(d x + c\right)^{10} - 135 \, a b \cosh\left(d x + c\right)^{8} + 45 \, a b \cosh\left(d x + c\right)^{4} + 6 \, a b \cosh\left(d x + c\right)^{2} - a b\right)} \sinh\left(d x + c\right)^{2} - a b + 4 \, {\left(4 \, a b \cosh\left(d x + c\right)^{15} + 7 \, a b \cosh\left(d x + c\right)^{13} - 6 \, a b \cosh\left(d x + c\right)^{11} - 15 \, a b \cosh\left(d x + c\right)^{9} + 9 \, a b \cosh\left(d x + c\right)^{5} + 2 \, 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(\frac{2 \, \sinh\left(d x + c\right)}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) + 4 \, {\left(105 \, a b \cosh\left(d x + c\right)^{13} - 90 \, {\left(a^{2} + b^{2}\right)} \cosh\left(d x + c\right)^{11} - 25 \, {\left(14 \, a^{2} + 9 \, a b - 10 \, b^{2}\right)} \cosh\left(d x + c\right)^{9} - 20 \, {\left(25 \, a^{2} + 13 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} - 3 \, {\left(100 \, a^{2} - 45 \, a b - 44 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} - 2 \, {\left(25 \, a^{2} + 17 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(10 \, a^{2} - 15 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}{15 \, {\left(d \cosh\left(d x + c\right)^{16} + 16 \, d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{15} + d \sinh\left(d x + c\right)^{16} + 2 \, d \cosh\left(d x + c\right)^{14} + 2 \, {\left(60 \, d \cosh\left(d x + c\right)^{2} + d\right)} \sinh\left(d x + c\right)^{14} + 28 \, {\left(20 \, d \cosh\left(d x + c\right)^{3} + d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{13} - 2 \, d \cosh\left(d x + c\right)^{12} + 2 \, {\left(910 \, d \cosh\left(d x + c\right)^{4} + 91 \, d \cosh\left(d x + c\right)^{2} - d\right)} \sinh\left(d x + c\right)^{12} + 8 \, {\left(546 \, d \cosh\left(d x + c\right)^{5} + 91 \, d \cosh\left(d x + c\right)^{3} - 3 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{11} - 6 \, d \cosh\left(d x + c\right)^{10} + 2 \, {\left(4004 \, d \cosh\left(d x + c\right)^{6} + 1001 \, 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)^{10} + 4 \, {\left(2860 \, d \cosh\left(d x + c\right)^{7} + 1001 \, 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)^{9} + 6 \, {\left(2145 \, d \cosh\left(d x + c\right)^{8} + 1001 \, d \cosh\left(d x + c\right)^{6} - 165 \, d \cosh\left(d x + c\right)^{4} - 45 \, d \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{8} + 16 \, {\left(715 \, d \cosh\left(d x + c\right)^{9} + 429 \, d \cosh\left(d x + c\right)^{7} - 99 \, d \cosh\left(d x + c\right)^{5} - 45 \, d \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right)^{7} + 6 \, d \cosh\left(d x + c\right)^{6} + 2 \, {\left(4004 \, d \cosh\left(d x + c\right)^{10} + 3003 \, 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} + 3 \, d\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(1092 \, d \cosh\left(d x + c\right)^{11} + 1001 \, 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} + 9 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, d \cosh\left(d x + c\right)^{4} + 2 \, {\left(910 \, d \cosh\left(d x + c\right)^{12} + 1001 \, 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} + 45 \, d \cosh\left(d x + c\right)^{2} + d\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(70 \, d \cosh\left(d x + c\right)^{13} + 91 \, 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} + 15 \, d \cosh\left(d x + c\right)^{3} + d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 2 \, d \cosh\left(d x + c\right)^{2} + 2 \, {\left(60 \, d \cosh\left(d x + c\right)^{14} + 91 \, 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} + 45 \, 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} + 4 \, {\left(4 \, d \cosh\left(d x + c\right)^{15} + 7 \, d \cosh\left(d x + c\right)^{13} - 6 \, d \cosh\left(d x + c\right)^{11} - 15 \, d \cosh\left(d x + c\right)^{9} + 9 \, 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,"2/15*(30*a*b*cosh(d*x + c)^14 + 420*a*b*cosh(d*x + c)*sinh(d*x + c)^13 + 30*a*b*sinh(d*x + c)^14 - 30*(a^2 + b^2)*cosh(d*x + c)^12 + 30*(91*a*b*cosh(d*x + c)^2 - a^2 - b^2)*sinh(d*x + c)^12 + 120*(91*a*b*cosh(d*x + c)^3 - 3*(a^2 + b^2)*cosh(d*x + c))*sinh(d*x + c)^11 - 10*(14*a^2 + 9*a*b - 10*b^2)*cosh(d*x + c)^10 + 10*(3003*a*b*cosh(d*x + c)^4 - 198*(a^2 + b^2)*cosh(d*x + c)^2 - 14*a^2 - 9*a*b + 10*b^2)*sinh(d*x + c)^10 + 20*(3003*a*b*cosh(d*x + c)^5 - 330*(a^2 + b^2)*cosh(d*x + c)^3 - 5*(14*a^2 + 9*a*b - 10*b^2)*cosh(d*x + c))*sinh(d*x + c)^9 - 10*(25*a^2 + 13*b^2)*cosh(d*x + c)^8 + 10*(9009*a*b*cosh(d*x + c)^6 - 1485*(a^2 + b^2)*cosh(d*x + c)^4 - 45*(14*a^2 + 9*a*b - 10*b^2)*cosh(d*x + c)^2 - 25*a^2 - 13*b^2)*sinh(d*x + c)^8 + 80*(1287*a*b*cosh(d*x + c)^7 - 297*(a^2 + b^2)*cosh(d*x + c)^5 - 15*(14*a^2 + 9*a*b - 10*b^2)*cosh(d*x + c)^3 - (25*a^2 + 13*b^2)*cosh(d*x + c))*sinh(d*x + c)^7 - 2*(100*a^2 - 45*a*b - 44*b^2)*cosh(d*x + c)^6 + 2*(45045*a*b*cosh(d*x + c)^8 - 13860*(a^2 + b^2)*cosh(d*x + c)^6 - 1050*(14*a^2 + 9*a*b - 10*b^2)*cosh(d*x + c)^4 - 140*(25*a^2 + 13*b^2)*cosh(d*x + c)^2 - 100*a^2 + 45*a*b + 44*b^2)*sinh(d*x + c)^6 + 4*(15015*a*b*cosh(d*x + c)^9 - 5940*(a^2 + b^2)*cosh(d*x + c)^7 - 630*(14*a^2 + 9*a*b - 10*b^2)*cosh(d*x + c)^5 - 140*(25*a^2 + 13*b^2)*cosh(d*x + c)^3 - 3*(100*a^2 - 45*a*b - 44*b^2)*cosh(d*x + c))*sinh(d*x + c)^5 - 2*(25*a^2 + 17*b^2)*cosh(d*x + c)^4 + 2*(15015*a*b*cosh(d*x + c)^10 - 7425*(a^2 + b^2)*cosh(d*x + c)^8 - 1050*(14*a^2 + 9*a*b - 10*b^2)*cosh(d*x + c)^6 - 350*(25*a^2 + 13*b^2)*cosh(d*x + c)^4 - 15*(100*a^2 - 45*a*b - 44*b^2)*cosh(d*x + c)^2 - 25*a^2 - 17*b^2)*sinh(d*x + c)^4 + 8*(1365*a*b*cosh(d*x + c)^11 - 825*(a^2 + b^2)*cosh(d*x + c)^9 - 150*(14*a^2 + 9*a*b - 10*b^2)*cosh(d*x + c)^7 - 70*(25*a^2 + 13*b^2)*cosh(d*x + c)^5 - 5*(100*a^2 - 45*a*b - 44*b^2)*cosh(d*x + c)^3 - (25*a^2 + 17*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 2*(10*a^2 - 15*a*b + 2*b^2)*cosh(d*x + c)^2 + 2*(1365*a*b*cosh(d*x + c)^12 - 990*(a^2 + b^2)*cosh(d*x + c)^10 - 225*(14*a^2 + 9*a*b - 10*b^2)*cosh(d*x + c)^8 - 140*(25*a^2 + 13*b^2)*cosh(d*x + c)^6 - 15*(100*a^2 - 45*a*b - 44*b^2)*cosh(d*x + c)^4 - 6*(25*a^2 + 17*b^2)*cosh(d*x + c)^2 + 10*a^2 - 15*a*b + 2*b^2)*sinh(d*x + c)^2 + 10*a^2 + 2*b^2 - 15*(a*b*cosh(d*x + c)^16 + 16*a*b*cosh(d*x + c)*sinh(d*x + c)^15 + a*b*sinh(d*x + c)^16 + 2*a*b*cosh(d*x + c)^14 + 2*(60*a*b*cosh(d*x + c)^2 + a*b)*sinh(d*x + c)^14 - 2*a*b*cosh(d*x + c)^12 + 28*(20*a*b*cosh(d*x + c)^3 + a*b*cosh(d*x + c))*sinh(d*x + c)^13 + 2*(910*a*b*cosh(d*x + c)^4 + 91*a*b*cosh(d*x + c)^2 - a*b)*sinh(d*x + c)^12 - 6*a*b*cosh(d*x + c)^10 + 8*(546*a*b*cosh(d*x + c)^5 + 91*a*b*cosh(d*x + c)^3 - 3*a*b*cosh(d*x + c))*sinh(d*x + c)^11 + 2*(4004*a*b*cosh(d*x + c)^6 + 1001*a*b*cosh(d*x + c)^4 - 66*a*b*cosh(d*x + c)^2 - 3*a*b)*sinh(d*x + c)^10 + 4*(2860*a*b*cosh(d*x + c)^7 + 1001*a*b*cosh(d*x + c)^5 - 110*a*b*cosh(d*x + c)^3 - 15*a*b*cosh(d*x + c))*sinh(d*x + c)^9 + 6*(2145*a*b*cosh(d*x + c)^8 + 1001*a*b*cosh(d*x + c)^6 - 165*a*b*cosh(d*x + c)^4 - 45*a*b*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 6*a*b*cosh(d*x + c)^6 + 16*(715*a*b*cosh(d*x + c)^9 + 429*a*b*cosh(d*x + c)^7 - 99*a*b*cosh(d*x + c)^5 - 45*a*b*cosh(d*x + c)^3)*sinh(d*x + c)^7 + 2*(4004*a*b*cosh(d*x + c)^10 + 3003*a*b*cosh(d*x + c)^8 - 924*a*b*cosh(d*x + c)^6 - 630*a*b*cosh(d*x + c)^4 + 3*a*b)*sinh(d*x + c)^6 + 2*a*b*cosh(d*x + c)^4 + 4*(1092*a*b*cosh(d*x + c)^11 + 1001*a*b*cosh(d*x + c)^9 - 396*a*b*cosh(d*x + c)^7 - 378*a*b*cosh(d*x + c)^5 + 9*a*b*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(910*a*b*cosh(d*x + c)^12 + 1001*a*b*cosh(d*x + c)^10 - 495*a*b*cosh(d*x + c)^8 - 630*a*b*cosh(d*x + c)^6 + 45*a*b*cosh(d*x + c)^2 + a*b)*sinh(d*x + c)^4 - 2*a*b*cosh(d*x + c)^2 + 8*(70*a*b*cosh(d*x + c)^13 + 91*a*b*cosh(d*x + c)^11 - 55*a*b*cosh(d*x + c)^9 - 90*a*b*cosh(d*x + c)^7 + 15*a*b*cosh(d*x + c)^3 + a*b*cosh(d*x + c))*sinh(d*x + c)^3 + 2*(60*a*b*cosh(d*x + c)^14 + 91*a*b*cosh(d*x + c)^12 - 66*a*b*cosh(d*x + c)^10 - 135*a*b*cosh(d*x + c)^8 + 45*a*b*cosh(d*x + c)^4 + 6*a*b*cosh(d*x + c)^2 - a*b)*sinh(d*x + c)^2 - a*b + 4*(4*a*b*cosh(d*x + c)^15 + 7*a*b*cosh(d*x + c)^13 - 6*a*b*cosh(d*x + c)^11 - 15*a*b*cosh(d*x + c)^9 + 9*a*b*cosh(d*x + c)^5 + 2*a*b*cosh(d*x + c)^3 - a*b*cosh(d*x + c))*sinh(d*x + c))*log(2*cosh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))) + 15*(a*b*cosh(d*x + c)^16 + 16*a*b*cosh(d*x + c)*sinh(d*x + c)^15 + a*b*sinh(d*x + c)^16 + 2*a*b*cosh(d*x + c)^14 + 2*(60*a*b*cosh(d*x + c)^2 + a*b)*sinh(d*x + c)^14 - 2*a*b*cosh(d*x + c)^12 + 28*(20*a*b*cosh(d*x + c)^3 + a*b*cosh(d*x + c))*sinh(d*x + c)^13 + 2*(910*a*b*cosh(d*x + c)^4 + 91*a*b*cosh(d*x + c)^2 - a*b)*sinh(d*x + c)^12 - 6*a*b*cosh(d*x + c)^10 + 8*(546*a*b*cosh(d*x + c)^5 + 91*a*b*cosh(d*x + c)^3 - 3*a*b*cosh(d*x + c))*sinh(d*x + c)^11 + 2*(4004*a*b*cosh(d*x + c)^6 + 1001*a*b*cosh(d*x + c)^4 - 66*a*b*cosh(d*x + c)^2 - 3*a*b)*sinh(d*x + c)^10 + 4*(2860*a*b*cosh(d*x + c)^7 + 1001*a*b*cosh(d*x + c)^5 - 110*a*b*cosh(d*x + c)^3 - 15*a*b*cosh(d*x + c))*sinh(d*x + c)^9 + 6*(2145*a*b*cosh(d*x + c)^8 + 1001*a*b*cosh(d*x + c)^6 - 165*a*b*cosh(d*x + c)^4 - 45*a*b*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 6*a*b*cosh(d*x + c)^6 + 16*(715*a*b*cosh(d*x + c)^9 + 429*a*b*cosh(d*x + c)^7 - 99*a*b*cosh(d*x + c)^5 - 45*a*b*cosh(d*x + c)^3)*sinh(d*x + c)^7 + 2*(4004*a*b*cosh(d*x + c)^10 + 3003*a*b*cosh(d*x + c)^8 - 924*a*b*cosh(d*x + c)^6 - 630*a*b*cosh(d*x + c)^4 + 3*a*b)*sinh(d*x + c)^6 + 2*a*b*cosh(d*x + c)^4 + 4*(1092*a*b*cosh(d*x + c)^11 + 1001*a*b*cosh(d*x + c)^9 - 396*a*b*cosh(d*x + c)^7 - 378*a*b*cosh(d*x + c)^5 + 9*a*b*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(910*a*b*cosh(d*x + c)^12 + 1001*a*b*cosh(d*x + c)^10 - 495*a*b*cosh(d*x + c)^8 - 630*a*b*cosh(d*x + c)^6 + 45*a*b*cosh(d*x + c)^2 + a*b)*sinh(d*x + c)^4 - 2*a*b*cosh(d*x + c)^2 + 8*(70*a*b*cosh(d*x + c)^13 + 91*a*b*cosh(d*x + c)^11 - 55*a*b*cosh(d*x + c)^9 - 90*a*b*cosh(d*x + c)^7 + 15*a*b*cosh(d*x + c)^3 + a*b*cosh(d*x + c))*sinh(d*x + c)^3 + 2*(60*a*b*cosh(d*x + c)^14 + 91*a*b*cosh(d*x + c)^12 - 66*a*b*cosh(d*x + c)^10 - 135*a*b*cosh(d*x + c)^8 + 45*a*b*cosh(d*x + c)^4 + 6*a*b*cosh(d*x + c)^2 - a*b)*sinh(d*x + c)^2 - a*b + 4*(4*a*b*cosh(d*x + c)^15 + 7*a*b*cosh(d*x + c)^13 - 6*a*b*cosh(d*x + c)^11 - 15*a*b*cosh(d*x + c)^9 + 9*a*b*cosh(d*x + c)^5 + 2*a*b*cosh(d*x + c)^3 - a*b*cosh(d*x + c))*sinh(d*x + c))*log(2*sinh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))) + 4*(105*a*b*cosh(d*x + c)^13 - 90*(a^2 + b^2)*cosh(d*x + c)^11 - 25*(14*a^2 + 9*a*b - 10*b^2)*cosh(d*x + c)^9 - 20*(25*a^2 + 13*b^2)*cosh(d*x + c)^7 - 3*(100*a^2 - 45*a*b - 44*b^2)*cosh(d*x + c)^5 - 2*(25*a^2 + 17*b^2)*cosh(d*x + c)^3 + (10*a^2 - 15*a*b + 2*b^2)*cosh(d*x + c))*sinh(d*x + c))/(d*cosh(d*x + c)^16 + 16*d*cosh(d*x + c)*sinh(d*x + c)^15 + d*sinh(d*x + c)^16 + 2*d*cosh(d*x + c)^14 + 2*(60*d*cosh(d*x + c)^2 + d)*sinh(d*x + c)^14 + 28*(20*d*cosh(d*x + c)^3 + d*cosh(d*x + c))*sinh(d*x + c)^13 - 2*d*cosh(d*x + c)^12 + 2*(910*d*cosh(d*x + c)^4 + 91*d*cosh(d*x + c)^2 - d)*sinh(d*x + c)^12 + 8*(546*d*cosh(d*x + c)^5 + 91*d*cosh(d*x + c)^3 - 3*d*cosh(d*x + c))*sinh(d*x + c)^11 - 6*d*cosh(d*x + c)^10 + 2*(4004*d*cosh(d*x + c)^6 + 1001*d*cosh(d*x + c)^4 - 66*d*cosh(d*x + c)^2 - 3*d)*sinh(d*x + c)^10 + 4*(2860*d*cosh(d*x + c)^7 + 1001*d*cosh(d*x + c)^5 - 110*d*cosh(d*x + c)^3 - 15*d*cosh(d*x + c))*sinh(d*x + c)^9 + 6*(2145*d*cosh(d*x + c)^8 + 1001*d*cosh(d*x + c)^6 - 165*d*cosh(d*x + c)^4 - 45*d*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 16*(715*d*cosh(d*x + c)^9 + 429*d*cosh(d*x + c)^7 - 99*d*cosh(d*x + c)^5 - 45*d*cosh(d*x + c)^3)*sinh(d*x + c)^7 + 6*d*cosh(d*x + c)^6 + 2*(4004*d*cosh(d*x + c)^10 + 3003*d*cosh(d*x + c)^8 - 924*d*cosh(d*x + c)^6 - 630*d*cosh(d*x + c)^4 + 3*d)*sinh(d*x + c)^6 + 4*(1092*d*cosh(d*x + c)^11 + 1001*d*cosh(d*x + c)^9 - 396*d*cosh(d*x + c)^7 - 378*d*cosh(d*x + c)^5 + 9*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*d*cosh(d*x + c)^4 + 2*(910*d*cosh(d*x + c)^12 + 1001*d*cosh(d*x + c)^10 - 495*d*cosh(d*x + c)^8 - 630*d*cosh(d*x + c)^6 + 45*d*cosh(d*x + c)^2 + d)*sinh(d*x + c)^4 + 8*(70*d*cosh(d*x + c)^13 + 91*d*cosh(d*x + c)^11 - 55*d*cosh(d*x + c)^9 - 90*d*cosh(d*x + c)^7 + 15*d*cosh(d*x + c)^3 + d*cosh(d*x + c))*sinh(d*x + c)^3 - 2*d*cosh(d*x + c)^2 + 2*(60*d*cosh(d*x + c)^14 + 91*d*cosh(d*x + c)^12 - 66*d*cosh(d*x + c)^10 - 135*d*cosh(d*x + c)^8 + 45*d*cosh(d*x + c)^4 + 6*d*cosh(d*x + c)^2 - d)*sinh(d*x + c)^2 + 4*(4*d*cosh(d*x + c)^15 + 7*d*cosh(d*x + c)^13 - 6*d*cosh(d*x + c)^11 - 15*d*cosh(d*x + c)^9 + 9*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
65,-1,0,0,0.000000," ","integrate(sinh(d*x+c)^4*(a+b*tanh(d*x+c)^3)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
66,1,8462,0,0.603467," ","integrate(sinh(d*x+c)^3*(a+b*tanh(d*x+c)^3)^3,x, algorithm=""fricas"")","\frac{40 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{22} + 880 \, {\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)^{21} + 40 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \sinh\left(d x + c\right)^{22} - 40 \, {\left(a^{3} + 57 \, a^{2} b + 111 \, a b^{2} + 55 \, b^{3}\right)} \cosh\left(d x + c\right)^{20} - 40 \, {\left(a^{3} + 57 \, a^{2} b + 111 \, a b^{2} + 55 \, b^{3} - 231 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{20} + 800 \, {\left(77 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{3} - {\left(a^{3} + 57 \, a^{2} b + 111 \, a b^{2} + 55 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{19} - 5 \, {\left(424 \, a^{3} + 4440 \, a^{2} b + 15960 \, a b^{2} + 5599 \, b^{3}\right)} \cosh\left(d x + c\right)^{18} + 5 \, {\left(58520 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{4} - 424 \, a^{3} - 4440 \, a^{2} b - 15960 \, a b^{2} - 5599 \, b^{3} - 1520 \, {\left(a^{3} + 57 \, a^{2} b + 111 \, a b^{2} + 55 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{18} + 30 \, {\left(35112 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{5} - 1520 \, {\left(a^{3} + 57 \, a^{2} b + 111 \, a b^{2} + 55 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(424 \, a^{3} + 4440 \, a^{2} b + 15960 \, a b^{2} + 5599 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{17} - 15 \, {\left(712 \, a^{3} + 4840 \, a^{2} b + 26584 \, a b^{2} + 5665 \, b^{3}\right)} \cosh\left(d x + c\right)^{16} + 15 \, {\left(198968 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{6} - 12920 \, {\left(a^{3} + 57 \, a^{2} b + 111 \, a b^{2} + 55 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 712 \, a^{3} - 4840 \, a^{2} b - 26584 \, a b^{2} - 5665 \, b^{3} - 51 \, {\left(424 \, a^{3} + 4440 \, a^{2} b + 15960 \, a b^{2} + 5599 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{16} + 240 \, {\left(28424 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{7} - 2584 \, {\left(a^{3} + 57 \, a^{2} b + 111 \, a b^{2} + 55 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 17 \, {\left(424 \, a^{3} + 4440 \, a^{2} b + 15960 \, a b^{2} + 5599 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - {\left(712 \, a^{3} + 4840 \, a^{2} b + 26584 \, a b^{2} + 5665 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{15} - 3 \, {\left(9040 \, a^{3} + 36400 \, a^{2} b + 344944 \, a b^{2} + 45265 \, b^{3}\right)} \cosh\left(d x + c\right)^{14} + 3 \, {\left(4263600 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{8} - 516800 \, {\left(a^{3} + 57 \, a^{2} b + 111 \, a b^{2} + 55 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} - 5100 \, {\left(424 \, a^{3} + 4440 \, a^{2} b + 15960 \, a b^{2} + 5599 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 9040 \, a^{3} - 36400 \, a^{2} b - 344944 \, a b^{2} - 45265 \, b^{3} - 600 \, {\left(712 \, a^{3} + 4840 \, a^{2} b + 26584 \, a b^{2} + 5665 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{14} + 2 \, {\left(9948400 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{9} - 1550400 \, {\left(a^{3} + 57 \, a^{2} b + 111 \, a b^{2} + 55 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} - 21420 \, {\left(424 \, a^{3} + 4440 \, a^{2} b + 15960 \, a b^{2} + 5599 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 4200 \, {\left(712 \, a^{3} + 4840 \, a^{2} b + 26584 \, a b^{2} + 5665 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 21 \, {\left(9040 \, a^{3} + 36400 \, a^{2} b + 344944 \, a b^{2} + 45265 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{13} - 3 \, {\left(14000 \, a^{3} + 18800 \, a^{2} b + 542672 \, a b^{2} + 20405 \, b^{3}\right)} \cosh\left(d x + c\right)^{12} + {\left(25865840 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{10} - 5038800 \, {\left(a^{3} + 57 \, a^{2} b + 111 \, a b^{2} + 55 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} - 92820 \, {\left(424 \, a^{3} + 4440 \, a^{2} b + 15960 \, a b^{2} + 5599 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} - 27300 \, {\left(712 \, a^{3} + 4840 \, a^{2} b + 26584 \, a b^{2} + 5665 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 42000 \, a^{3} - 56400 \, a^{2} b - 1628016 \, a b^{2} - 61215 \, b^{3} - 273 \, {\left(9040 \, a^{3} + 36400 \, a^{2} b + 344944 \, a b^{2} + 45265 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{12} + 4 \, {\left(7054320 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{11} - 1679600 \, {\left(a^{3} + 57 \, a^{2} b + 111 \, a b^{2} + 55 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} - 39780 \, {\left(424 \, a^{3} + 4440 \, a^{2} b + 15960 \, a b^{2} + 5599 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} - 16380 \, {\left(712 \, a^{3} + 4840 \, a^{2} b + 26584 \, a b^{2} + 5665 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 273 \, {\left(9040 \, a^{3} + 36400 \, a^{2} b + 344944 \, a b^{2} + 45265 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 9 \, {\left(14000 \, a^{3} + 18800 \, a^{2} b + 542672 \, a b^{2} + 20405 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{11} - 3 \, {\left(14000 \, a^{3} - 18800 \, a^{2} b + 542672 \, a b^{2} - 20405 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} + {\left(25865840 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{12} - 7390240 \, {\left(a^{3} + 57 \, a^{2} b + 111 \, a b^{2} + 55 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} - 218790 \, {\left(424 \, a^{3} + 4440 \, a^{2} b + 15960 \, a b^{2} + 5599 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} - 120120 \, {\left(712 \, a^{3} + 4840 \, a^{2} b + 26584 \, a b^{2} + 5665 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} - 3003 \, {\left(9040 \, a^{3} + 36400 \, a^{2} b + 344944 \, a b^{2} + 45265 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 42000 \, a^{3} + 56400 \, a^{2} b - 1628016 \, a b^{2} + 61215 \, b^{3} - 198 \, {\left(14000 \, a^{3} + 18800 \, a^{2} b + 542672 \, a b^{2} + 20405 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{10} + 2 \, {\left(9948400 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{13} - 3359200 \, {\left(a^{3} + 57 \, a^{2} b + 111 \, a b^{2} + 55 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} - 121550 \, {\left(424 \, a^{3} + 4440 \, a^{2} b + 15960 \, a b^{2} + 5599 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} - 85800 \, {\left(712 \, a^{3} + 4840 \, a^{2} b + 26584 \, a b^{2} + 5665 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} - 3003 \, {\left(9040 \, a^{3} + 36400 \, a^{2} b + 344944 \, a b^{2} + 45265 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 330 \, {\left(14000 \, a^{3} + 18800 \, a^{2} b + 542672 \, a b^{2} + 20405 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 15 \, {\left(14000 \, a^{3} - 18800 \, a^{2} b + 542672 \, a b^{2} - 20405 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} - 3 \, {\left(9040 \, a^{3} - 36400 \, a^{2} b + 344944 \, a b^{2} - 45265 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 3 \, {\left(4263600 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{14} - 1679600 \, {\left(a^{3} + 57 \, a^{2} b + 111 \, a b^{2} + 55 \, b^{3}\right)} \cosh\left(d x + c\right)^{12} - 72930 \, {\left(424 \, a^{3} + 4440 \, a^{2} b + 15960 \, a b^{2} + 5599 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} - 64350 \, {\left(712 \, a^{3} + 4840 \, a^{2} b + 26584 \, a b^{2} + 5665 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} - 3003 \, {\left(9040 \, a^{3} + 36400 \, a^{2} b + 344944 \, a b^{2} + 45265 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} - 495 \, {\left(14000 \, a^{3} + 18800 \, a^{2} b + 542672 \, a b^{2} + 20405 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 9040 \, a^{3} + 36400 \, a^{2} b - 344944 \, a b^{2} + 45265 \, b^{3} - 45 \, {\left(14000 \, a^{3} - 18800 \, a^{2} b + 542672 \, a b^{2} - 20405 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{8} + 24 \, {\left(284240 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{15} - 129200 \, {\left(a^{3} + 57 \, a^{2} b + 111 \, a b^{2} + 55 \, b^{3}\right)} \cosh\left(d x + c\right)^{13} - 6630 \, {\left(424 \, a^{3} + 4440 \, a^{2} b + 15960 \, a b^{2} + 5599 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} - 7150 \, {\left(712 \, a^{3} + 4840 \, a^{2} b + 26584 \, a b^{2} + 5665 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} - 429 \, {\left(9040 \, a^{3} + 36400 \, a^{2} b + 344944 \, a b^{2} + 45265 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} - 99 \, {\left(14000 \, a^{3} + 18800 \, a^{2} b + 542672 \, a b^{2} + 20405 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 15 \, {\left(14000 \, a^{3} - 18800 \, a^{2} b + 542672 \, a b^{2} - 20405 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - {\left(9040 \, a^{3} - 36400 \, a^{2} b + 344944 \, a b^{2} - 45265 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} - 15 \, {\left(712 \, a^{3} - 4840 \, a^{2} b + 26584 \, a b^{2} - 5665 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 3 \, {\left(994840 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{16} - 516800 \, {\left(a^{3} + 57 \, a^{2} b + 111 \, a b^{2} + 55 \, b^{3}\right)} \cosh\left(d x + c\right)^{14} - 30940 \, {\left(424 \, a^{3} + 4440 \, a^{2} b + 15960 \, a b^{2} + 5599 \, b^{3}\right)} \cosh\left(d x + c\right)^{12} - 40040 \, {\left(712 \, a^{3} + 4840 \, a^{2} b + 26584 \, a b^{2} + 5665 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} - 3003 \, {\left(9040 \, a^{3} + 36400 \, a^{2} b + 344944 \, a b^{2} + 45265 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} - 924 \, {\left(14000 \, a^{3} + 18800 \, a^{2} b + 542672 \, a b^{2} + 20405 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} - 210 \, {\left(14000 \, a^{3} - 18800 \, a^{2} b + 542672 \, a b^{2} - 20405 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 3560 \, a^{3} + 24200 \, a^{2} b - 132920 \, a b^{2} + 28325 \, b^{3} - 28 \, {\left(9040 \, a^{3} - 36400 \, a^{2} b + 344944 \, a b^{2} - 45265 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 6 \, {\left(175560 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{17} - 103360 \, {\left(a^{3} + 57 \, a^{2} b + 111 \, a b^{2} + 55 \, b^{3}\right)} \cosh\left(d x + c\right)^{15} - 7140 \, {\left(424 \, a^{3} + 4440 \, a^{2} b + 15960 \, a b^{2} + 5599 \, b^{3}\right)} \cosh\left(d x + c\right)^{13} - 10920 \, {\left(712 \, a^{3} + 4840 \, a^{2} b + 26584 \, a b^{2} + 5665 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} - 1001 \, {\left(9040 \, a^{3} + 36400 \, a^{2} b + 344944 \, a b^{2} + 45265 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} - 396 \, {\left(14000 \, a^{3} + 18800 \, a^{2} b + 542672 \, a b^{2} + 20405 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} - 126 \, {\left(14000 \, a^{3} - 18800 \, a^{2} b + 542672 \, a b^{2} - 20405 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 28 \, {\left(9040 \, a^{3} - 36400 \, a^{2} b + 344944 \, a b^{2} - 45265 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 15 \, {\left(712 \, a^{3} - 4840 \, a^{2} b + 26584 \, a b^{2} - 5665 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 5 \, {\left(424 \, a^{3} - 4440 \, a^{2} b + 15960 \, a b^{2} - 5599 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + {\left(292600 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{18} - 193800 \, {\left(a^{3} + 57 \, a^{2} b + 111 \, a b^{2} + 55 \, b^{3}\right)} \cosh\left(d x + c\right)^{16} - 15300 \, {\left(424 \, a^{3} + 4440 \, a^{2} b + 15960 \, a b^{2} + 5599 \, b^{3}\right)} \cosh\left(d x + c\right)^{14} - 27300 \, {\left(712 \, a^{3} + 4840 \, a^{2} b + 26584 \, a b^{2} + 5665 \, b^{3}\right)} \cosh\left(d x + c\right)^{12} - 3003 \, {\left(9040 \, a^{3} + 36400 \, a^{2} b + 344944 \, a b^{2} + 45265 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} - 1485 \, {\left(14000 \, a^{3} + 18800 \, a^{2} b + 542672 \, a b^{2} + 20405 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} - 630 \, {\left(14000 \, a^{3} - 18800 \, a^{2} b + 542672 \, a b^{2} - 20405 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} - 210 \, {\left(9040 \, a^{3} - 36400 \, a^{2} b + 344944 \, a b^{2} - 45265 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 2120 \, a^{3} + 22200 \, a^{2} b - 79800 \, a b^{2} + 27995 \, b^{3} - 225 \, {\left(712 \, a^{3} - 4840 \, a^{2} b + 26584 \, a b^{2} - 5665 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(15400 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{19} - 11400 \, {\left(a^{3} + 57 \, a^{2} b + 111 \, a b^{2} + 55 \, b^{3}\right)} \cosh\left(d x + c\right)^{17} - 1020 \, {\left(424 \, a^{3} + 4440 \, a^{2} b + 15960 \, a b^{2} + 5599 \, b^{3}\right)} \cosh\left(d x + c\right)^{15} - 2100 \, {\left(712 \, a^{3} + 4840 \, a^{2} b + 26584 \, a b^{2} + 5665 \, b^{3}\right)} \cosh\left(d x + c\right)^{13} - 273 \, {\left(9040 \, a^{3} + 36400 \, a^{2} b + 344944 \, a b^{2} + 45265 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} - 165 \, {\left(14000 \, a^{3} + 18800 \, a^{2} b + 542672 \, a b^{2} + 20405 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} - 90 \, {\left(14000 \, a^{3} - 18800 \, a^{2} b + 542672 \, a b^{2} - 20405 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} - 42 \, {\left(9040 \, a^{3} - 36400 \, a^{2} b + 344944 \, a b^{2} - 45265 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 75 \, {\left(712 \, a^{3} - 4840 \, a^{2} b + 26584 \, a b^{2} - 5665 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 5 \, {\left(424 \, a^{3} - 4440 \, a^{2} b + 15960 \, a b^{2} - 5599 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 40 \, a^{3} - 120 \, a^{2} b + 120 \, a b^{2} - 40 \, b^{3} - 40 \, {\left(a^{3} - 57 \, a^{2} b + 111 \, a b^{2} - 55 \, b^{3}\right)} \cosh\left(d x + c\right)^{2} + {\left(9240 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{20} - 7600 \, {\left(a^{3} + 57 \, a^{2} b + 111 \, a b^{2} + 55 \, b^{3}\right)} \cosh\left(d x + c\right)^{18} - 765 \, {\left(424 \, a^{3} + 4440 \, a^{2} b + 15960 \, a b^{2} + 5599 \, b^{3}\right)} \cosh\left(d x + c\right)^{16} - 1800 \, {\left(712 \, a^{3} + 4840 \, a^{2} b + 26584 \, a b^{2} + 5665 \, b^{3}\right)} \cosh\left(d x + c\right)^{14} - 273 \, {\left(9040 \, a^{3} + 36400 \, a^{2} b + 344944 \, a b^{2} + 45265 \, b^{3}\right)} \cosh\left(d x + c\right)^{12} - 198 \, {\left(14000 \, a^{3} + 18800 \, a^{2} b + 542672 \, a b^{2} + 20405 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} - 135 \, {\left(14000 \, a^{3} - 18800 \, a^{2} b + 542672 \, a b^{2} - 20405 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} - 84 \, {\left(9040 \, a^{3} - 36400 \, a^{2} b + 344944 \, a b^{2} - 45265 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} - 225 \, {\left(712 \, a^{3} - 4840 \, a^{2} b + 26584 \, a b^{2} - 5665 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 40 \, a^{3} + 2280 \, a^{2} b - 4440 \, a b^{2} + 2200 \, b^{3} - 30 \, {\left(424 \, a^{3} - 4440 \, a^{2} b + 15960 \, a b^{2} - 5599 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 225 \, {\left({\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{19} + 19 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{18} + {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \sinh\left(d x + c\right)^{19} + 8 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{17} + {\left(512 \, a^{2} b + 616 \, b^{3} + 171 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{17} + 17 \, {\left(57 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 8 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{16} + 28 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{15} + 4 \, {\left(969 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 448 \, a^{2} b + 539 \, b^{3} + 272 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{15} + 4 \, {\left(2907 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 1360 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 105 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{14} + 56 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{13} + 28 \, {\left(969 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 680 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 128 \, a^{2} b + 154 \, b^{3} + 105 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{13} + 52 \, {\left(969 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 952 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 245 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 14 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{12} + 70 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} + 2 \, {\left(37791 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 49504 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 19110 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 2240 \, a^{2} b + 2695 \, b^{3} + 2184 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{11} + 22 \, {\left(4199 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + 7072 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 3822 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 728 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 35 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{10} + 56 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + 2 \, {\left(46189 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} + 97240 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 70070 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 20020 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 1792 \, a^{2} b + 2156 \, b^{3} + 1925 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{9} + 2 \, {\left(37791 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} + 97240 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + 90090 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 36036 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 5775 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 252 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{8} + 28 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 4 \, {\left(12597 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{12} + 38896 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} + 45045 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 24024 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 5775 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 448 \, a^{2} b + 539 \, b^{3} + 504 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{7} + 28 \, {\left(969 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{13} + 3536 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} + 5005 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + 3432 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 1155 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 168 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 7 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 4 \, {\left(2907 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{14} + 12376 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{12} + 21021 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} + 18018 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 8085 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 1764 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 128 \, a^{2} b + 154 \, b^{3} + 147 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{5} + 4 \, {\left(969 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{15} + 4760 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{13} + 9555 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} + 10010 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + 5775 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 1764 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 245 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 10 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(969 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{16} + 5440 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{14} + 12740 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{12} + 16016 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} + 11550 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 4704 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 980 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 64 \, a^{2} b + 77 \, b^{3} + 80 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + {\left(171 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{17} + 1088 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{15} + 2940 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{13} + 4368 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} + 3850 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + 2016 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 588 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 80 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(19 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{18} + 136 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{16} + 420 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{14} + 728 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{12} + 770 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} + 504 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 196 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 40 \, {\left(64 \, a^{2} b + 77 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(64 \, a^{2} b + 77 \, 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(440 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{21} - 400 \, {\left(a^{3} + 57 \, a^{2} b + 111 \, a b^{2} + 55 \, b^{3}\right)} \cosh\left(d x + c\right)^{19} - 45 \, {\left(424 \, a^{3} + 4440 \, a^{2} b + 15960 \, a b^{2} + 5599 \, b^{3}\right)} \cosh\left(d x + c\right)^{17} - 120 \, {\left(712 \, a^{3} + 4840 \, a^{2} b + 26584 \, a b^{2} + 5665 \, b^{3}\right)} \cosh\left(d x + c\right)^{15} - 21 \, {\left(9040 \, a^{3} + 36400 \, a^{2} b + 344944 \, a b^{2} + 45265 \, b^{3}\right)} \cosh\left(d x + c\right)^{13} - 18 \, {\left(14000 \, a^{3} + 18800 \, a^{2} b + 542672 \, a b^{2} + 20405 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} - 15 \, {\left(14000 \, a^{3} - 18800 \, a^{2} b + 542672 \, a b^{2} - 20405 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} - 12 \, {\left(9040 \, a^{3} - 36400 \, a^{2} b + 344944 \, a b^{2} - 45265 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} - 45 \, {\left(712 \, a^{3} - 4840 \, a^{2} b + 26584 \, a b^{2} - 5665 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 10 \, {\left(424 \, a^{3} - 4440 \, a^{2} b + 15960 \, a b^{2} - 5599 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 40 \, {\left(a^{3} - 57 \, a^{2} b + 111 \, a b^{2} - 55 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{960 \, {\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,"1/960*(40*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^22 + 880*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)*sinh(d*x + c)^21 + 40*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*sinh(d*x + c)^22 - 40*(a^3 + 57*a^2*b + 111*a*b^2 + 55*b^3)*cosh(d*x + c)^20 - 40*(a^3 + 57*a^2*b + 111*a*b^2 + 55*b^3 - 231*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^20 + 800*(77*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^3 - (a^3 + 57*a^2*b + 111*a*b^2 + 55*b^3)*cosh(d*x + c))*sinh(d*x + c)^19 - 5*(424*a^3 + 4440*a^2*b + 15960*a*b^2 + 5599*b^3)*cosh(d*x + c)^18 + 5*(58520*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^4 - 424*a^3 - 4440*a^2*b - 15960*a*b^2 - 5599*b^3 - 1520*(a^3 + 57*a^2*b + 111*a*b^2 + 55*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^18 + 30*(35112*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^5 - 1520*(a^3 + 57*a^2*b + 111*a*b^2 + 55*b^3)*cosh(d*x + c)^3 - 3*(424*a^3 + 4440*a^2*b + 15960*a*b^2 + 5599*b^3)*cosh(d*x + c))*sinh(d*x + c)^17 - 15*(712*a^3 + 4840*a^2*b + 26584*a*b^2 + 5665*b^3)*cosh(d*x + c)^16 + 15*(198968*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^6 - 12920*(a^3 + 57*a^2*b + 111*a*b^2 + 55*b^3)*cosh(d*x + c)^4 - 712*a^3 - 4840*a^2*b - 26584*a*b^2 - 5665*b^3 - 51*(424*a^3 + 4440*a^2*b + 15960*a*b^2 + 5599*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^16 + 240*(28424*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^7 - 2584*(a^3 + 57*a^2*b + 111*a*b^2 + 55*b^3)*cosh(d*x + c)^5 - 17*(424*a^3 + 4440*a^2*b + 15960*a*b^2 + 5599*b^3)*cosh(d*x + c)^3 - (712*a^3 + 4840*a^2*b + 26584*a*b^2 + 5665*b^3)*cosh(d*x + c))*sinh(d*x + c)^15 - 3*(9040*a^3 + 36400*a^2*b + 344944*a*b^2 + 45265*b^3)*cosh(d*x + c)^14 + 3*(4263600*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^8 - 516800*(a^3 + 57*a^2*b + 111*a*b^2 + 55*b^3)*cosh(d*x + c)^6 - 5100*(424*a^3 + 4440*a^2*b + 15960*a*b^2 + 5599*b^3)*cosh(d*x + c)^4 - 9040*a^3 - 36400*a^2*b - 344944*a*b^2 - 45265*b^3 - 600*(712*a^3 + 4840*a^2*b + 26584*a*b^2 + 5665*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^14 + 2*(9948400*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^9 - 1550400*(a^3 + 57*a^2*b + 111*a*b^2 + 55*b^3)*cosh(d*x + c)^7 - 21420*(424*a^3 + 4440*a^2*b + 15960*a*b^2 + 5599*b^3)*cosh(d*x + c)^5 - 4200*(712*a^3 + 4840*a^2*b + 26584*a*b^2 + 5665*b^3)*cosh(d*x + c)^3 - 21*(9040*a^3 + 36400*a^2*b + 344944*a*b^2 + 45265*b^3)*cosh(d*x + c))*sinh(d*x + c)^13 - 3*(14000*a^3 + 18800*a^2*b + 542672*a*b^2 + 20405*b^3)*cosh(d*x + c)^12 + (25865840*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^10 - 5038800*(a^3 + 57*a^2*b + 111*a*b^2 + 55*b^3)*cosh(d*x + c)^8 - 92820*(424*a^3 + 4440*a^2*b + 15960*a*b^2 + 5599*b^3)*cosh(d*x + c)^6 - 27300*(712*a^3 + 4840*a^2*b + 26584*a*b^2 + 5665*b^3)*cosh(d*x + c)^4 - 42000*a^3 - 56400*a^2*b - 1628016*a*b^2 - 61215*b^3 - 273*(9040*a^3 + 36400*a^2*b + 344944*a*b^2 + 45265*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^12 + 4*(7054320*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^11 - 1679600*(a^3 + 57*a^2*b + 111*a*b^2 + 55*b^3)*cosh(d*x + c)^9 - 39780*(424*a^3 + 4440*a^2*b + 15960*a*b^2 + 5599*b^3)*cosh(d*x + c)^7 - 16380*(712*a^3 + 4840*a^2*b + 26584*a*b^2 + 5665*b^3)*cosh(d*x + c)^5 - 273*(9040*a^3 + 36400*a^2*b + 344944*a*b^2 + 45265*b^3)*cosh(d*x + c)^3 - 9*(14000*a^3 + 18800*a^2*b + 542672*a*b^2 + 20405*b^3)*cosh(d*x + c))*sinh(d*x + c)^11 - 3*(14000*a^3 - 18800*a^2*b + 542672*a*b^2 - 20405*b^3)*cosh(d*x + c)^10 + (25865840*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^12 - 7390240*(a^3 + 57*a^2*b + 111*a*b^2 + 55*b^3)*cosh(d*x + c)^10 - 218790*(424*a^3 + 4440*a^2*b + 15960*a*b^2 + 5599*b^3)*cosh(d*x + c)^8 - 120120*(712*a^3 + 4840*a^2*b + 26584*a*b^2 + 5665*b^3)*cosh(d*x + c)^6 - 3003*(9040*a^3 + 36400*a^2*b + 344944*a*b^2 + 45265*b^3)*cosh(d*x + c)^4 - 42000*a^3 + 56400*a^2*b - 1628016*a*b^2 + 61215*b^3 - 198*(14000*a^3 + 18800*a^2*b + 542672*a*b^2 + 20405*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^10 + 2*(9948400*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^13 - 3359200*(a^3 + 57*a^2*b + 111*a*b^2 + 55*b^3)*cosh(d*x + c)^11 - 121550*(424*a^3 + 4440*a^2*b + 15960*a*b^2 + 5599*b^3)*cosh(d*x + c)^9 - 85800*(712*a^3 + 4840*a^2*b + 26584*a*b^2 + 5665*b^3)*cosh(d*x + c)^7 - 3003*(9040*a^3 + 36400*a^2*b + 344944*a*b^2 + 45265*b^3)*cosh(d*x + c)^5 - 330*(14000*a^3 + 18800*a^2*b + 542672*a*b^2 + 20405*b^3)*cosh(d*x + c)^3 - 15*(14000*a^3 - 18800*a^2*b + 542672*a*b^2 - 20405*b^3)*cosh(d*x + c))*sinh(d*x + c)^9 - 3*(9040*a^3 - 36400*a^2*b + 344944*a*b^2 - 45265*b^3)*cosh(d*x + c)^8 + 3*(4263600*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^14 - 1679600*(a^3 + 57*a^2*b + 111*a*b^2 + 55*b^3)*cosh(d*x + c)^12 - 72930*(424*a^3 + 4440*a^2*b + 15960*a*b^2 + 5599*b^3)*cosh(d*x + c)^10 - 64350*(712*a^3 + 4840*a^2*b + 26584*a*b^2 + 5665*b^3)*cosh(d*x + c)^8 - 3003*(9040*a^3 + 36400*a^2*b + 344944*a*b^2 + 45265*b^3)*cosh(d*x + c)^6 - 495*(14000*a^3 + 18800*a^2*b + 542672*a*b^2 + 20405*b^3)*cosh(d*x + c)^4 - 9040*a^3 + 36400*a^2*b - 344944*a*b^2 + 45265*b^3 - 45*(14000*a^3 - 18800*a^2*b + 542672*a*b^2 - 20405*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 24*(284240*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^15 - 129200*(a^3 + 57*a^2*b + 111*a*b^2 + 55*b^3)*cosh(d*x + c)^13 - 6630*(424*a^3 + 4440*a^2*b + 15960*a*b^2 + 5599*b^3)*cosh(d*x + c)^11 - 7150*(712*a^3 + 4840*a^2*b + 26584*a*b^2 + 5665*b^3)*cosh(d*x + c)^9 - 429*(9040*a^3 + 36400*a^2*b + 344944*a*b^2 + 45265*b^3)*cosh(d*x + c)^7 - 99*(14000*a^3 + 18800*a^2*b + 542672*a*b^2 + 20405*b^3)*cosh(d*x + c)^5 - 15*(14000*a^3 - 18800*a^2*b + 542672*a*b^2 - 20405*b^3)*cosh(d*x + c)^3 - (9040*a^3 - 36400*a^2*b + 344944*a*b^2 - 45265*b^3)*cosh(d*x + c))*sinh(d*x + c)^7 - 15*(712*a^3 - 4840*a^2*b + 26584*a*b^2 - 5665*b^3)*cosh(d*x + c)^6 + 3*(994840*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^16 - 516800*(a^3 + 57*a^2*b + 111*a*b^2 + 55*b^3)*cosh(d*x + c)^14 - 30940*(424*a^3 + 4440*a^2*b + 15960*a*b^2 + 5599*b^3)*cosh(d*x + c)^12 - 40040*(712*a^3 + 4840*a^2*b + 26584*a*b^2 + 5665*b^3)*cosh(d*x + c)^10 - 3003*(9040*a^3 + 36400*a^2*b + 344944*a*b^2 + 45265*b^3)*cosh(d*x + c)^8 - 924*(14000*a^3 + 18800*a^2*b + 542672*a*b^2 + 20405*b^3)*cosh(d*x + c)^6 - 210*(14000*a^3 - 18800*a^2*b + 542672*a*b^2 - 20405*b^3)*cosh(d*x + c)^4 - 3560*a^3 + 24200*a^2*b - 132920*a*b^2 + 28325*b^3 - 28*(9040*a^3 - 36400*a^2*b + 344944*a*b^2 - 45265*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 6*(175560*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^17 - 103360*(a^3 + 57*a^2*b + 111*a*b^2 + 55*b^3)*cosh(d*x + c)^15 - 7140*(424*a^3 + 4440*a^2*b + 15960*a*b^2 + 5599*b^3)*cosh(d*x + c)^13 - 10920*(712*a^3 + 4840*a^2*b + 26584*a*b^2 + 5665*b^3)*cosh(d*x + c)^11 - 1001*(9040*a^3 + 36400*a^2*b + 344944*a*b^2 + 45265*b^3)*cosh(d*x + c)^9 - 396*(14000*a^3 + 18800*a^2*b + 542672*a*b^2 + 20405*b^3)*cosh(d*x + c)^7 - 126*(14000*a^3 - 18800*a^2*b + 542672*a*b^2 - 20405*b^3)*cosh(d*x + c)^5 - 28*(9040*a^3 - 36400*a^2*b + 344944*a*b^2 - 45265*b^3)*cosh(d*x + c)^3 - 15*(712*a^3 - 4840*a^2*b + 26584*a*b^2 - 5665*b^3)*cosh(d*x + c))*sinh(d*x + c)^5 - 5*(424*a^3 - 4440*a^2*b + 15960*a*b^2 - 5599*b^3)*cosh(d*x + c)^4 + (292600*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^18 - 193800*(a^3 + 57*a^2*b + 111*a*b^2 + 55*b^3)*cosh(d*x + c)^16 - 15300*(424*a^3 + 4440*a^2*b + 15960*a*b^2 + 5599*b^3)*cosh(d*x + c)^14 - 27300*(712*a^3 + 4840*a^2*b + 26584*a*b^2 + 5665*b^3)*cosh(d*x + c)^12 - 3003*(9040*a^3 + 36400*a^2*b + 344944*a*b^2 + 45265*b^3)*cosh(d*x + c)^10 - 1485*(14000*a^3 + 18800*a^2*b + 542672*a*b^2 + 20405*b^3)*cosh(d*x + c)^8 - 630*(14000*a^3 - 18800*a^2*b + 542672*a*b^2 - 20405*b^3)*cosh(d*x + c)^6 - 210*(9040*a^3 - 36400*a^2*b + 344944*a*b^2 - 45265*b^3)*cosh(d*x + c)^4 - 2120*a^3 + 22200*a^2*b - 79800*a*b^2 + 27995*b^3 - 225*(712*a^3 - 4840*a^2*b + 26584*a*b^2 - 5665*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 4*(15400*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^19 - 11400*(a^3 + 57*a^2*b + 111*a*b^2 + 55*b^3)*cosh(d*x + c)^17 - 1020*(424*a^3 + 4440*a^2*b + 15960*a*b^2 + 5599*b^3)*cosh(d*x + c)^15 - 2100*(712*a^3 + 4840*a^2*b + 26584*a*b^2 + 5665*b^3)*cosh(d*x + c)^13 - 273*(9040*a^3 + 36400*a^2*b + 344944*a*b^2 + 45265*b^3)*cosh(d*x + c)^11 - 165*(14000*a^3 + 18800*a^2*b + 542672*a*b^2 + 20405*b^3)*cosh(d*x + c)^9 - 90*(14000*a^3 - 18800*a^2*b + 542672*a*b^2 - 20405*b^3)*cosh(d*x + c)^7 - 42*(9040*a^3 - 36400*a^2*b + 344944*a*b^2 - 45265*b^3)*cosh(d*x + c)^5 - 75*(712*a^3 - 4840*a^2*b + 26584*a*b^2 - 5665*b^3)*cosh(d*x + c)^3 - 5*(424*a^3 - 4440*a^2*b + 15960*a*b^2 - 5599*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 + 40*a^3 - 120*a^2*b + 120*a*b^2 - 40*b^3 - 40*(a^3 - 57*a^2*b + 111*a*b^2 - 55*b^3)*cosh(d*x + c)^2 + (9240*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^20 - 7600*(a^3 + 57*a^2*b + 111*a*b^2 + 55*b^3)*cosh(d*x + c)^18 - 765*(424*a^3 + 4440*a^2*b + 15960*a*b^2 + 5599*b^3)*cosh(d*x + c)^16 - 1800*(712*a^3 + 4840*a^2*b + 26584*a*b^2 + 5665*b^3)*cosh(d*x + c)^14 - 273*(9040*a^3 + 36400*a^2*b + 344944*a*b^2 + 45265*b^3)*cosh(d*x + c)^12 - 198*(14000*a^3 + 18800*a^2*b + 542672*a*b^2 + 20405*b^3)*cosh(d*x + c)^10 - 135*(14000*a^3 - 18800*a^2*b + 542672*a*b^2 - 20405*b^3)*cosh(d*x + c)^8 - 84*(9040*a^3 - 36400*a^2*b + 344944*a*b^2 - 45265*b^3)*cosh(d*x + c)^6 - 225*(712*a^3 - 4840*a^2*b + 26584*a*b^2 - 5665*b^3)*cosh(d*x + c)^4 - 40*a^3 + 2280*a^2*b - 4440*a*b^2 + 2200*b^3 - 30*(424*a^3 - 4440*a^2*b + 15960*a*b^2 - 5599*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 225*((64*a^2*b + 77*b^3)*cosh(d*x + c)^19 + 19*(64*a^2*b + 77*b^3)*cosh(d*x + c)*sinh(d*x + c)^18 + (64*a^2*b + 77*b^3)*sinh(d*x + c)^19 + 8*(64*a^2*b + 77*b^3)*cosh(d*x + c)^17 + (512*a^2*b + 616*b^3 + 171*(64*a^2*b + 77*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^17 + 17*(57*(64*a^2*b + 77*b^3)*cosh(d*x + c)^3 + 8*(64*a^2*b + 77*b^3)*cosh(d*x + c))*sinh(d*x + c)^16 + 28*(64*a^2*b + 77*b^3)*cosh(d*x + c)^15 + 4*(969*(64*a^2*b + 77*b^3)*cosh(d*x + c)^4 + 448*a^2*b + 539*b^3 + 272*(64*a^2*b + 77*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^15 + 4*(2907*(64*a^2*b + 77*b^3)*cosh(d*x + c)^5 + 1360*(64*a^2*b + 77*b^3)*cosh(d*x + c)^3 + 105*(64*a^2*b + 77*b^3)*cosh(d*x + c))*sinh(d*x + c)^14 + 56*(64*a^2*b + 77*b^3)*cosh(d*x + c)^13 + 28*(969*(64*a^2*b + 77*b^3)*cosh(d*x + c)^6 + 680*(64*a^2*b + 77*b^3)*cosh(d*x + c)^4 + 128*a^2*b + 154*b^3 + 105*(64*a^2*b + 77*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^13 + 52*(969*(64*a^2*b + 77*b^3)*cosh(d*x + c)^7 + 952*(64*a^2*b + 77*b^3)*cosh(d*x + c)^5 + 245*(64*a^2*b + 77*b^3)*cosh(d*x + c)^3 + 14*(64*a^2*b + 77*b^3)*cosh(d*x + c))*sinh(d*x + c)^12 + 70*(64*a^2*b + 77*b^3)*cosh(d*x + c)^11 + 2*(37791*(64*a^2*b + 77*b^3)*cosh(d*x + c)^8 + 49504*(64*a^2*b + 77*b^3)*cosh(d*x + c)^6 + 19110*(64*a^2*b + 77*b^3)*cosh(d*x + c)^4 + 2240*a^2*b + 2695*b^3 + 2184*(64*a^2*b + 77*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^11 + 22*(4199*(64*a^2*b + 77*b^3)*cosh(d*x + c)^9 + 7072*(64*a^2*b + 77*b^3)*cosh(d*x + c)^7 + 3822*(64*a^2*b + 77*b^3)*cosh(d*x + c)^5 + 728*(64*a^2*b + 77*b^3)*cosh(d*x + c)^3 + 35*(64*a^2*b + 77*b^3)*cosh(d*x + c))*sinh(d*x + c)^10 + 56*(64*a^2*b + 77*b^3)*cosh(d*x + c)^9 + 2*(46189*(64*a^2*b + 77*b^3)*cosh(d*x + c)^10 + 97240*(64*a^2*b + 77*b^3)*cosh(d*x + c)^8 + 70070*(64*a^2*b + 77*b^3)*cosh(d*x + c)^6 + 20020*(64*a^2*b + 77*b^3)*cosh(d*x + c)^4 + 1792*a^2*b + 2156*b^3 + 1925*(64*a^2*b + 77*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^9 + 2*(37791*(64*a^2*b + 77*b^3)*cosh(d*x + c)^11 + 97240*(64*a^2*b + 77*b^3)*cosh(d*x + c)^9 + 90090*(64*a^2*b + 77*b^3)*cosh(d*x + c)^7 + 36036*(64*a^2*b + 77*b^3)*cosh(d*x + c)^5 + 5775*(64*a^2*b + 77*b^3)*cosh(d*x + c)^3 + 252*(64*a^2*b + 77*b^3)*cosh(d*x + c))*sinh(d*x + c)^8 + 28*(64*a^2*b + 77*b^3)*cosh(d*x + c)^7 + 4*(12597*(64*a^2*b + 77*b^3)*cosh(d*x + c)^12 + 38896*(64*a^2*b + 77*b^3)*cosh(d*x + c)^10 + 45045*(64*a^2*b + 77*b^3)*cosh(d*x + c)^8 + 24024*(64*a^2*b + 77*b^3)*cosh(d*x + c)^6 + 5775*(64*a^2*b + 77*b^3)*cosh(d*x + c)^4 + 448*a^2*b + 539*b^3 + 504*(64*a^2*b + 77*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^7 + 28*(969*(64*a^2*b + 77*b^3)*cosh(d*x + c)^13 + 3536*(64*a^2*b + 77*b^3)*cosh(d*x + c)^11 + 5005*(64*a^2*b + 77*b^3)*cosh(d*x + c)^9 + 3432*(64*a^2*b + 77*b^3)*cosh(d*x + c)^7 + 1155*(64*a^2*b + 77*b^3)*cosh(d*x + c)^5 + 168*(64*a^2*b + 77*b^3)*cosh(d*x + c)^3 + 7*(64*a^2*b + 77*b^3)*cosh(d*x + c))*sinh(d*x + c)^6 + 8*(64*a^2*b + 77*b^3)*cosh(d*x + c)^5 + 4*(2907*(64*a^2*b + 77*b^3)*cosh(d*x + c)^14 + 12376*(64*a^2*b + 77*b^3)*cosh(d*x + c)^12 + 21021*(64*a^2*b + 77*b^3)*cosh(d*x + c)^10 + 18018*(64*a^2*b + 77*b^3)*cosh(d*x + c)^8 + 8085*(64*a^2*b + 77*b^3)*cosh(d*x + c)^6 + 1764*(64*a^2*b + 77*b^3)*cosh(d*x + c)^4 + 128*a^2*b + 154*b^3 + 147*(64*a^2*b + 77*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 4*(969*(64*a^2*b + 77*b^3)*cosh(d*x + c)^15 + 4760*(64*a^2*b + 77*b^3)*cosh(d*x + c)^13 + 9555*(64*a^2*b + 77*b^3)*cosh(d*x + c)^11 + 10010*(64*a^2*b + 77*b^3)*cosh(d*x + c)^9 + 5775*(64*a^2*b + 77*b^3)*cosh(d*x + c)^7 + 1764*(64*a^2*b + 77*b^3)*cosh(d*x + c)^5 + 245*(64*a^2*b + 77*b^3)*cosh(d*x + c)^3 + 10*(64*a^2*b + 77*b^3)*cosh(d*x + c))*sinh(d*x + c)^4 + (64*a^2*b + 77*b^3)*cosh(d*x + c)^3 + (969*(64*a^2*b + 77*b^3)*cosh(d*x + c)^16 + 5440*(64*a^2*b + 77*b^3)*cosh(d*x + c)^14 + 12740*(64*a^2*b + 77*b^3)*cosh(d*x + c)^12 + 16016*(64*a^2*b + 77*b^3)*cosh(d*x + c)^10 + 11550*(64*a^2*b + 77*b^3)*cosh(d*x + c)^8 + 4704*(64*a^2*b + 77*b^3)*cosh(d*x + c)^6 + 980*(64*a^2*b + 77*b^3)*cosh(d*x + c)^4 + 64*a^2*b + 77*b^3 + 80*(64*a^2*b + 77*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + (171*(64*a^2*b + 77*b^3)*cosh(d*x + c)^17 + 1088*(64*a^2*b + 77*b^3)*cosh(d*x + c)^15 + 2940*(64*a^2*b + 77*b^3)*cosh(d*x + c)^13 + 4368*(64*a^2*b + 77*b^3)*cosh(d*x + c)^11 + 3850*(64*a^2*b + 77*b^3)*cosh(d*x + c)^9 + 2016*(64*a^2*b + 77*b^3)*cosh(d*x + c)^7 + 588*(64*a^2*b + 77*b^3)*cosh(d*x + c)^5 + 80*(64*a^2*b + 77*b^3)*cosh(d*x + c)^3 + 3*(64*a^2*b + 77*b^3)*cosh(d*x + c))*sinh(d*x + c)^2 + (19*(64*a^2*b + 77*b^3)*cosh(d*x + c)^18 + 136*(64*a^2*b + 77*b^3)*cosh(d*x + c)^16 + 420*(64*a^2*b + 77*b^3)*cosh(d*x + c)^14 + 728*(64*a^2*b + 77*b^3)*cosh(d*x + c)^12 + 770*(64*a^2*b + 77*b^3)*cosh(d*x + c)^10 + 504*(64*a^2*b + 77*b^3)*cosh(d*x + c)^8 + 196*(64*a^2*b + 77*b^3)*cosh(d*x + c)^6 + 40*(64*a^2*b + 77*b^3)*cosh(d*x + c)^4 + 3*(64*a^2*b + 77*b^3)*cosh(d*x + c)^2)*sinh(d*x + c))*arctan(cosh(d*x + c) + sinh(d*x + c)) + 2*(440*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^21 - 400*(a^3 + 57*a^2*b + 111*a*b^2 + 55*b^3)*cosh(d*x + c)^19 - 45*(424*a^3 + 4440*a^2*b + 15960*a*b^2 + 5599*b^3)*cosh(d*x + c)^17 - 120*(712*a^3 + 4840*a^2*b + 26584*a*b^2 + 5665*b^3)*cosh(d*x + c)^15 - 21*(9040*a^3 + 36400*a^2*b + 344944*a*b^2 + 45265*b^3)*cosh(d*x + c)^13 - 18*(14000*a^3 + 18800*a^2*b + 542672*a*b^2 + 20405*b^3)*cosh(d*x + c)^11 - 15*(14000*a^3 - 18800*a^2*b + 542672*a*b^2 - 20405*b^3)*cosh(d*x + c)^9 - 12*(9040*a^3 - 36400*a^2*b + 344944*a*b^2 - 45265*b^3)*cosh(d*x + c)^7 - 45*(712*a^3 - 4840*a^2*b + 26584*a*b^2 - 5665*b^3)*cosh(d*x + c)^5 - 10*(424*a^3 - 4440*a^2*b + 15960*a*b^2 - 5599*b^3)*cosh(d*x + c)^3 - 40*(a^3 - 57*a^2*b + 111*a*b^2 - 55*b^3)*cosh(d*x + c))*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
67,1,9862,0,0.637345," ","integrate(sinh(d*x+c)^2*(a+b*tanh(d*x+c)^3)^3,x, algorithm=""fricas"")","\frac{15 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{20} + 300 \, {\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)^{19} + 15 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \sinh\left(d x + c\right)^{20} + 60 \, {\left(2 \, a^{3} + 6 \, a^{2} b + 6 \, a b^{2} + 2 \, b^{3} - {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{18} + 30 \, {\left(4 \, a^{3} + 12 \, a^{2} b + 12 \, a b^{2} + 4 \, b^{3} - 2 \, {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x + 95 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{18} + 180 \, {\left(95 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{3} + 6 \, {\left(2 \, a^{3} + 6 \, a^{2} b + 6 \, a b^{2} + 2 \, b^{3} - {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{17} + 15 \, {\left(27 \, a^{3} + 39 \, a^{2} b - 207 \, a b^{2} - 131 \, b^{3} - 32 \, {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{16} + 15 \, {\left(4845 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{4} + 27 \, a^{3} + 39 \, a^{2} b - 207 \, a b^{2} - 131 \, b^{3} - 32 \, {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x + 612 \, {\left(2 \, a^{3} + 6 \, a^{2} b + 6 \, a b^{2} + 2 \, b^{3} - {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{16} + 240 \, {\left(969 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{5} + 204 \, {\left(2 \, a^{3} + 6 \, a^{2} b + 6 \, a b^{2} + 2 \, b^{3} - {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + {\left(27 \, a^{3} + 39 \, a^{2} b - 207 \, a b^{2} - 131 \, b^{3} - 32 \, {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{15} + 240 \, {\left(3 \, a^{3} - 6 \, a^{2} b - 93 \, a b^{2} - 36 \, b^{3} - 7 \, {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{14} + 120 \, {\left(4845 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{6} + 1530 \, {\left(2 \, a^{3} + 6 \, a^{2} b + 6 \, a b^{2} + 2 \, b^{3} - {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 6 \, a^{3} - 12 \, a^{2} b - 186 \, a b^{2} - 72 \, b^{3} - 14 \, {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x + 15 \, {\left(27 \, a^{3} + 39 \, a^{2} b - 207 \, a b^{2} - 131 \, b^{3} - 32 \, {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{14} + 240 \, {\left(4845 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{7} + 2142 \, {\left(2 \, a^{3} + 6 \, a^{2} b + 6 \, a b^{2} + 2 \, b^{3} - {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{5} + 35 \, {\left(27 \, a^{3} + 39 \, a^{2} b - 207 \, a b^{2} - 131 \, b^{3} - 32 \, {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + 14 \, {\left(3 \, a^{3} - 6 \, a^{2} b - 93 \, a b^{2} - 36 \, b^{3} - 7 \, {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{13} + 10 \, {\left(63 \, a^{3} - 639 \, a^{2} b - 6195 \, a b^{2} - 2173 \, b^{3} - 336 \, {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{12} + 10 \, {\left(188955 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{8} + 111384 \, {\left(2 \, a^{3} + 6 \, a^{2} b + 6 \, a b^{2} + 2 \, b^{3} - {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{6} + 2730 \, {\left(27 \, a^{3} + 39 \, a^{2} b - 207 \, a b^{2} - 131 \, b^{3} - 32 \, {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 63 \, a^{3} - 639 \, a^{2} b - 6195 \, a b^{2} - 2173 \, b^{3} - 336 \, {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x + 2184 \, {\left(3 \, a^{3} - 6 \, a^{2} b - 93 \, a b^{2} - 36 \, b^{3} - 7 \, {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{12} + 120 \, {\left(20995 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{9} + 15912 \, {\left(2 \, a^{3} + 6 \, a^{2} b + 6 \, a b^{2} + 2 \, b^{3} - {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{7} + 546 \, {\left(27 \, a^{3} + 39 \, a^{2} b - 207 \, a b^{2} - 131 \, b^{3} - 32 \, {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{5} + 728 \, {\left(3 \, a^{3} - 6 \, a^{2} b - 93 \, a b^{2} - 36 \, b^{3} - 7 \, {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + {\left(63 \, a^{3} - 639 \, a^{2} b - 6195 \, a b^{2} - 2173 \, b^{3} - 336 \, {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{11} - 40 \, {\left(234 \, a^{2} b + 2436 \, a b^{2} + 662 \, b^{3} + 105 \, {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{10} + 20 \, {\left(138567 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{10} + 131274 \, {\left(2 \, a^{3} + 6 \, a^{2} b + 6 \, a b^{2} + 2 \, b^{3} - {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{8} + 6006 \, {\left(27 \, a^{3} + 39 \, a^{2} b - 207 \, a b^{2} - 131 \, b^{3} - 32 \, {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{6} + 12012 \, {\left(3 \, a^{3} - 6 \, a^{2} b - 93 \, a b^{2} - 36 \, b^{3} - 7 \, {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{4} - 468 \, a^{2} b - 4872 \, a b^{2} - 1324 \, b^{3} - 210 \, {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x + 33 \, {\left(63 \, a^{3} - 639 \, a^{2} b - 6195 \, a b^{2} - 2173 \, b^{3} - 336 \, {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{10} + 40 \, {\left(62985 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{11} + 72930 \, {\left(2 \, a^{3} + 6 \, a^{2} b + 6 \, a b^{2} + 2 \, b^{3} - {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{9} + 4290 \, {\left(27 \, a^{3} + 39 \, a^{2} b - 207 \, a b^{2} - 131 \, b^{3} - 32 \, {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{7} + 12012 \, {\left(3 \, a^{3} - 6 \, a^{2} b - 93 \, a b^{2} - 36 \, b^{3} - 7 \, {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{5} + 55 \, {\left(63 \, a^{3} - 639 \, a^{2} b - 6195 \, a b^{2} - 2173 \, b^{3} - 336 \, {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - 10 \, {\left(234 \, a^{2} b + 2436 \, a b^{2} + 662 \, b^{3} + 105 \, {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} - 2 \, {\left(315 \, a^{3} + 3195 \, a^{2} b + 46977 \, a b^{2} + 10865 \, b^{3} + 1680 \, {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{8} + 2 \, {\left(944775 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{12} + 1312740 \, {\left(2 \, a^{3} + 6 \, a^{2} b + 6 \, a b^{2} + 2 \, b^{3} - {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{10} + 96525 \, {\left(27 \, a^{3} + 39 \, a^{2} b - 207 \, a b^{2} - 131 \, b^{3} - 32 \, {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{8} + 360360 \, {\left(3 \, a^{3} - 6 \, a^{2} b - 93 \, a b^{2} - 36 \, b^{3} - 7 \, {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{6} + 2475 \, {\left(63 \, a^{3} - 639 \, a^{2} b - 6195 \, a b^{2} - 2173 \, b^{3} - 336 \, {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{4} - 315 \, a^{3} - 3195 \, a^{2} b - 46977 \, a b^{2} - 10865 \, b^{3} - 1680 \, {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x - 900 \, {\left(234 \, a^{2} b + 2436 \, a b^{2} + 662 \, b^{3} + 105 \, {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{8} + 16 \, {\left(72675 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{13} + 119340 \, {\left(2 \, a^{3} + 6 \, a^{2} b + 6 \, a b^{2} + 2 \, b^{3} - {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{11} + 10725 \, {\left(27 \, a^{3} + 39 \, a^{2} b - 207 \, a b^{2} - 131 \, b^{3} - 32 \, {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{9} + 51480 \, {\left(3 \, a^{3} - 6 \, a^{2} b - 93 \, a b^{2} - 36 \, b^{3} - 7 \, {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{7} + 495 \, {\left(63 \, a^{3} - 639 \, a^{2} b - 6195 \, a b^{2} - 2173 \, b^{3} - 336 \, {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{5} - 300 \, {\left(234 \, a^{2} b + 2436 \, a b^{2} + 662 \, b^{3} + 105 \, {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - {\left(315 \, a^{3} + 3195 \, a^{2} b + 46977 \, a b^{2} + 10865 \, b^{3} + 1680 \, {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} - 48 \, {\left(15 \, a^{3} + 30 \, a^{2} b + 1159 \, a b^{2} + 180 \, b^{3} + 35 \, {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{6} + 8 \, {\left(72675 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{14} + 139230 \, {\left(2 \, a^{3} + 6 \, a^{2} b + 6 \, a b^{2} + 2 \, b^{3} - {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{12} + 15015 \, {\left(27 \, a^{3} + 39 \, a^{2} b - 207 \, a b^{2} - 131 \, b^{3} - 32 \, {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{10} + 90090 \, {\left(3 \, a^{3} - 6 \, a^{2} b - 93 \, a b^{2} - 36 \, b^{3} - 7 \, {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{8} + 1155 \, {\left(63 \, a^{3} - 639 \, a^{2} b - 6195 \, a b^{2} - 2173 \, b^{3} - 336 \, {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{6} - 1050 \, {\left(234 \, a^{2} b + 2436 \, a b^{2} + 662 \, b^{3} + 105 \, {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{4} - 90 \, a^{3} - 180 \, a^{2} b - 6954 \, a b^{2} - 1080 \, b^{3} - 210 \, {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x - 7 \, {\left(315 \, a^{3} + 3195 \, a^{2} b + 46977 \, a b^{2} + 10865 \, b^{3} + 1680 \, {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 16 \, {\left(14535 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{15} + 32130 \, {\left(2 \, a^{3} + 6 \, a^{2} b + 6 \, a b^{2} + 2 \, b^{3} - {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{13} + 4095 \, {\left(27 \, a^{3} + 39 \, a^{2} b - 207 \, a b^{2} - 131 \, b^{3} - 32 \, {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{11} + 30030 \, {\left(3 \, a^{3} - 6 \, a^{2} b - 93 \, a b^{2} - 36 \, b^{3} - 7 \, {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{9} + 495 \, {\left(63 \, a^{3} - 639 \, a^{2} b - 6195 \, a b^{2} - 2173 \, b^{3} - 336 \, {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{7} - 630 \, {\left(234 \, a^{2} b + 2436 \, a b^{2} + 662 \, b^{3} + 105 \, {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{5} - 7 \, {\left(315 \, a^{3} + 3195 \, a^{2} b + 46977 \, a b^{2} + 10865 \, b^{3} + 1680 \, {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - 18 \, {\left(15 \, a^{3} + 30 \, a^{2} b + 1159 \, a b^{2} + 180 \, b^{3} + 35 \, {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 3 \, {\left(135 \, a^{3} - 195 \, a^{2} b + 6389 \, a b^{2} + 655 \, b^{3} + 160 \, {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + {\left(72675 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{16} + 183600 \, {\left(2 \, a^{3} + 6 \, a^{2} b + 6 \, a b^{2} + 2 \, b^{3} - {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{14} + 27300 \, {\left(27 \, a^{3} + 39 \, a^{2} b - 207 \, a b^{2} - 131 \, b^{3} - 32 \, {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{12} + 240240 \, {\left(3 \, a^{3} - 6 \, a^{2} b - 93 \, a b^{2} - 36 \, b^{3} - 7 \, {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{10} + 4950 \, {\left(63 \, a^{3} - 639 \, a^{2} b - 6195 \, a b^{2} - 2173 \, b^{3} - 336 \, {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{8} - 8400 \, {\left(234 \, a^{2} b + 2436 \, a b^{2} + 662 \, b^{3} + 105 \, {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{6} - 140 \, {\left(315 \, a^{3} + 3195 \, a^{2} b + 46977 \, a b^{2} + 10865 \, b^{3} + 1680 \, {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{4} - 405 \, a^{3} + 585 \, a^{2} b - 19167 \, a b^{2} - 1965 \, b^{3} - 480 \, {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x - 720 \, {\left(15 \, a^{3} + 30 \, a^{2} b + 1159 \, a b^{2} + 180 \, b^{3} + 35 \, {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(4275 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{17} + 12240 \, {\left(2 \, a^{3} + 6 \, a^{2} b + 6 \, a b^{2} + 2 \, b^{3} - {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{15} + 2100 \, {\left(27 \, a^{3} + 39 \, a^{2} b - 207 \, a b^{2} - 131 \, b^{3} - 32 \, {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{13} + 21840 \, {\left(3 \, a^{3} - 6 \, a^{2} b - 93 \, a b^{2} - 36 \, b^{3} - 7 \, {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{11} + 550 \, {\left(63 \, a^{3} - 639 \, a^{2} b - 6195 \, a b^{2} - 2173 \, b^{3} - 336 \, {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{9} - 1200 \, {\left(234 \, a^{2} b + 2436 \, a b^{2} + 662 \, b^{3} + 105 \, {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{7} - 28 \, {\left(315 \, a^{3} + 3195 \, a^{2} b + 46977 \, a b^{2} + 10865 \, b^{3} + 1680 \, {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{5} - 240 \, {\left(15 \, a^{3} + 30 \, a^{2} b + 1159 \, a b^{2} + 180 \, b^{3} + 35 \, {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(135 \, a^{3} - 195 \, a^{2} b + 6389 \, a b^{2} + 655 \, b^{3} + 160 \, {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 15 \, a^{3} + 45 \, a^{2} b - 45 \, a b^{2} + 15 \, b^{3} - 12 \, {\left(10 \, a^{3} - 30 \, a^{2} b + 262 \, a b^{2} - 10 \, b^{3} + 5 \, {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(1425 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{18} + 4590 \, {\left(2 \, a^{3} + 6 \, a^{2} b + 6 \, a b^{2} + 2 \, b^{3} - {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{16} + 900 \, {\left(27 \, a^{3} + 39 \, a^{2} b - 207 \, a b^{2} - 131 \, b^{3} - 32 \, {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{14} + 10920 \, {\left(3 \, a^{3} - 6 \, a^{2} b - 93 \, a b^{2} - 36 \, b^{3} - 7 \, {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{12} + 330 \, {\left(63 \, a^{3} - 639 \, a^{2} b - 6195 \, a b^{2} - 2173 \, b^{3} - 336 \, {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{10} - 900 \, {\left(234 \, a^{2} b + 2436 \, a b^{2} + 662 \, b^{3} + 105 \, {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{8} - 28 \, {\left(315 \, a^{3} + 3195 \, a^{2} b + 46977 \, a b^{2} + 10865 \, b^{3} + 1680 \, {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{6} - 360 \, {\left(15 \, a^{3} + 30 \, a^{2} b + 1159 \, a b^{2} + 180 \, b^{3} + 35 \, {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{4} - 60 \, a^{3} + 180 \, a^{2} b - 1572 \, a b^{2} + 60 \, b^{3} - 30 \, {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x - 9 \, {\left(135 \, a^{3} - 195 \, a^{2} b + 6389 \, a b^{2} + 655 \, b^{3} + 160 \, {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} - 120 \, {\left({\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{18} + 18 \, {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{17} + {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \sinh\left(d x + c\right)^{18} + 8 \, {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{16} + {\left(48 \, a^{2} b + 40 \, b^{3} + 153 \, {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{16} + 16 \, {\left(51 \, {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 8 \, {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{15} + 28 \, {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{14} + 4 \, {\left(765 \, {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 42 \, a^{2} b + 35 \, b^{3} + 240 \, {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{14} + 56 \, {\left(153 \, {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 80 \, {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 7 \, {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{13} + 56 \, {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{12} + 28 \, {\left(663 \, {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 520 \, {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 12 \, a^{2} b + 10 \, b^{3} + 91 \, {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{12} + 16 \, {\left(1989 \, {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 2184 \, {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 637 \, {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 42 \, {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{11} + 70 \, {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} + 2 \, {\left(21879 \, {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 32032 \, {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 14014 \, {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 210 \, a^{2} b + 175 \, b^{3} + 1848 \, {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{10} + 4 \, {\left(12155 \, {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + 22880 \, {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 14014 \, {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 3080 \, {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 175 \, {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} + 56 \, {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 2 \, {\left(21879 \, {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} + 51480 \, {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 42042 \, {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 13860 \, {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 168 \, a^{2} b + 140 \, b^{3} + 1575 \, {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{8} + 16 \, {\left(1989 \, {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} + 5720 \, {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + 6006 \, {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 2772 \, {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 525 \, {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 28 \, {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 28 \, {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 28 \, {\left(663 \, {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{12} + 2288 \, {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} + 3003 \, {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 1848 \, {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 525 \, {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 6 \, a^{2} b + 5 \, b^{3} + 56 \, {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 56 \, {\left(153 \, {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{13} + 624 \, {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} + 1001 \, {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + 792 \, {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 315 \, {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 56 \, {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 8 \, {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(765 \, {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{14} + 3640 \, {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{12} + 7007 \, {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} + 6930 \, {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 3675 \, {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 980 \, {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 12 \, a^{2} b + 10 \, b^{3} + 105 \, {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 16 \, {\left(51 \, {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{15} + 280 \, {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{13} + 637 \, {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} + 770 \, {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + 525 \, {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 196 \, {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 35 \, {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{2} + {\left(153 \, {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{16} + 960 \, {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{14} + 2548 \, {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{12} + 3696 \, {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} + 3150 \, {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 1568 \, {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 420 \, {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 6 \, a^{2} b + 5 \, b^{3} + 48 \, {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(9 \, {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{17} + 64 \, {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{15} + 196 \, {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{13} + 336 \, {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} + 350 \, {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + 224 \, {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 84 \, {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 16 \, {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(6 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\frac{2 \, \cosh\left(d x + c\right)}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) + 4 \, {\left(75 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{19} + 270 \, {\left(2 \, a^{3} + 6 \, a^{2} b + 6 \, a b^{2} + 2 \, b^{3} - {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{17} + 60 \, {\left(27 \, a^{3} + 39 \, a^{2} b - 207 \, a b^{2} - 131 \, b^{3} - 32 \, {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{15} + 840 \, {\left(3 \, a^{3} - 6 \, a^{2} b - 93 \, a b^{2} - 36 \, b^{3} - 7 \, {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{13} + 30 \, {\left(63 \, a^{3} - 639 \, a^{2} b - 6195 \, a b^{2} - 2173 \, b^{3} - 336 \, {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{11} - 100 \, {\left(234 \, a^{2} b + 2436 \, a b^{2} + 662 \, b^{3} + 105 \, {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{9} - 4 \, {\left(315 \, a^{3} + 3195 \, a^{2} b + 46977 \, a b^{2} + 10865 \, b^{3} + 1680 \, {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{7} - 72 \, {\left(15 \, a^{3} + 30 \, a^{2} b + 1159 \, a b^{2} + 180 \, b^{3} + 35 \, {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{5} - 3 \, {\left(135 \, a^{3} - 195 \, a^{2} b + 6389 \, a b^{2} + 655 \, b^{3} + 160 \, {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - 6 \, {\left(10 \, a^{3} - 30 \, a^{2} b + 262 \, a b^{2} - 10 \, b^{3} + 5 \, {\left(a^{3} - 12 \, a^{2} b + 21 \, a b^{2} - 10 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{120 \, {\left(d \cosh\left(d x + c\right)^{18} + 18 \, d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{17} + d \sinh\left(d x + c\right)^{18} + 8 \, d \cosh\left(d x + c\right)^{16} + {\left(153 \, d \cosh\left(d x + c\right)^{2} + 8 \, d\right)} \sinh\left(d x + c\right)^{16} + 16 \, {\left(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} + 28 \, d \cosh\left(d x + c\right)^{14} + 4 \, {\left(765 \, d \cosh\left(d x + c\right)^{4} + 240 \, d \cosh\left(d x + c\right)^{2} + 7 \, d\right)} \sinh\left(d x + c\right)^{14} + 56 \, {\left(153 \, d \cosh\left(d x + c\right)^{5} + 80 \, d \cosh\left(d x + c\right)^{3} + 7 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{13} + 56 \, d \cosh\left(d x + c\right)^{12} + 28 \, {\left(663 \, d \cosh\left(d x + c\right)^{6} + 520 \, d \cosh\left(d x + c\right)^{4} + 91 \, d \cosh\left(d x + c\right)^{2} + 2 \, d\right)} \sinh\left(d x + c\right)^{12} + 16 \, {\left(1989 \, d \cosh\left(d x + c\right)^{7} + 2184 \, d \cosh\left(d x + c\right)^{5} + 637 \, d \cosh\left(d x + c\right)^{3} + 42 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{11} + 70 \, d \cosh\left(d x + c\right)^{10} + 2 \, {\left(21879 \, d \cosh\left(d x + c\right)^{8} + 32032 \, d \cosh\left(d x + c\right)^{6} + 14014 \, d \cosh\left(d x + c\right)^{4} + 1848 \, d \cosh\left(d x + c\right)^{2} + 35 \, d\right)} \sinh\left(d x + c\right)^{10} + 4 \, {\left(12155 \, d \cosh\left(d x + c\right)^{9} + 22880 \, d \cosh\left(d x + c\right)^{7} + 14014 \, d \cosh\left(d x + c\right)^{5} + 3080 \, d \cosh\left(d x + c\right)^{3} + 175 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} + 56 \, d \cosh\left(d x + c\right)^{8} + 2 \, {\left(21879 \, d \cosh\left(d x + c\right)^{10} + 51480 \, d \cosh\left(d x + c\right)^{8} + 42042 \, d \cosh\left(d x + c\right)^{6} + 13860 \, d \cosh\left(d x + c\right)^{4} + 1575 \, d \cosh\left(d x + c\right)^{2} + 28 \, d\right)} \sinh\left(d x + c\right)^{8} + 16 \, {\left(1989 \, d \cosh\left(d x + c\right)^{11} + 5720 \, d \cosh\left(d x + c\right)^{9} + 6006 \, d \cosh\left(d x + c\right)^{7} + 2772 \, d \cosh\left(d x + c\right)^{5} + 525 \, d \cosh\left(d x + c\right)^{3} + 28 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 28 \, d \cosh\left(d x + c\right)^{6} + 28 \, {\left(663 \, d \cosh\left(d x + c\right)^{12} + 2288 \, d \cosh\left(d x + c\right)^{10} + 3003 \, d \cosh\left(d x + c\right)^{8} + 1848 \, d \cosh\left(d x + c\right)^{6} + 525 \, 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} + 56 \, {\left(153 \, d \cosh\left(d x + c\right)^{13} + 624 \, d \cosh\left(d x + c\right)^{11} + 1001 \, d \cosh\left(d x + c\right)^{9} + 792 \, d \cosh\left(d x + c\right)^{7} + 315 \, 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} + 8 \, d \cosh\left(d x + c\right)^{4} + 4 \, {\left(765 \, d \cosh\left(d x + c\right)^{14} + 3640 \, d \cosh\left(d x + c\right)^{12} + 7007 \, d \cosh\left(d x + c\right)^{10} + 6930 \, d \cosh\left(d x + c\right)^{8} + 3675 \, d \cosh\left(d x + c\right)^{6} + 980 \, 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)^{4} + 16 \, {\left(51 \, d \cosh\left(d x + c\right)^{15} + 280 \, d \cosh\left(d x + c\right)^{13} + 637 \, d \cosh\left(d x + c\right)^{11} + 770 \, d \cosh\left(d x + c\right)^{9} + 525 \, d \cosh\left(d x + c\right)^{7} + 196 \, d \cosh\left(d x + c\right)^{5} + 35 \, d \cosh\left(d x + c\right)^{3} + 2 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + d \cosh\left(d x + c\right)^{2} + {\left(153 \, d \cosh\left(d x + c\right)^{16} + 960 \, d \cosh\left(d x + c\right)^{14} + 2548 \, d \cosh\left(d x + c\right)^{12} + 3696 \, d \cosh\left(d x + c\right)^{10} + 3150 \, d \cosh\left(d x + c\right)^{8} + 1568 \, d \cosh\left(d x + c\right)^{6} + 420 \, d \cosh\left(d x + c\right)^{4} + 48 \, d \cosh\left(d x + c\right)^{2} + d\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(9 \, d \cosh\left(d x + c\right)^{17} + 64 \, d \cosh\left(d x + c\right)^{15} + 196 \, d \cosh\left(d x + c\right)^{13} + 336 \, d \cosh\left(d x + c\right)^{11} + 350 \, d \cosh\left(d x + c\right)^{9} + 224 \, d \cosh\left(d x + c\right)^{7} + 84 \, d \cosh\left(d x + c\right)^{5} + 16 \, d \cosh\left(d x + c\right)^{3} + d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"1/120*(15*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^20 + 300*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)*sinh(d*x + c)^19 + 15*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*sinh(d*x + c)^20 + 60*(2*a^3 + 6*a^2*b + 6*a*b^2 + 2*b^3 - (a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x)*cosh(d*x + c)^18 + 30*(4*a^3 + 12*a^2*b + 12*a*b^2 + 4*b^3 - 2*(a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x + 95*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^18 + 180*(95*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^3 + 6*(2*a^3 + 6*a^2*b + 6*a*b^2 + 2*b^3 - (a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c)^17 + 15*(27*a^3 + 39*a^2*b - 207*a*b^2 - 131*b^3 - 32*(a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x)*cosh(d*x + c)^16 + 15*(4845*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^4 + 27*a^3 + 39*a^2*b - 207*a*b^2 - 131*b^3 - 32*(a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x + 612*(2*a^3 + 6*a^2*b + 6*a*b^2 + 2*b^3 - (a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^16 + 240*(969*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^5 + 204*(2*a^3 + 6*a^2*b + 6*a*b^2 + 2*b^3 - (a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x)*cosh(d*x + c)^3 + (27*a^3 + 39*a^2*b - 207*a*b^2 - 131*b^3 - 32*(a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c)^15 + 240*(3*a^3 - 6*a^2*b - 93*a*b^2 - 36*b^3 - 7*(a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x)*cosh(d*x + c)^14 + 120*(4845*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^6 + 1530*(2*a^3 + 6*a^2*b + 6*a*b^2 + 2*b^3 - (a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x)*cosh(d*x + c)^4 + 6*a^3 - 12*a^2*b - 186*a*b^2 - 72*b^3 - 14*(a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x + 15*(27*a^3 + 39*a^2*b - 207*a*b^2 - 131*b^3 - 32*(a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^14 + 240*(4845*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^7 + 2142*(2*a^3 + 6*a^2*b + 6*a*b^2 + 2*b^3 - (a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x)*cosh(d*x + c)^5 + 35*(27*a^3 + 39*a^2*b - 207*a*b^2 - 131*b^3 - 32*(a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x)*cosh(d*x + c)^3 + 14*(3*a^3 - 6*a^2*b - 93*a*b^2 - 36*b^3 - 7*(a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c)^13 + 10*(63*a^3 - 639*a^2*b - 6195*a*b^2 - 2173*b^3 - 336*(a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x)*cosh(d*x + c)^12 + 10*(188955*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^8 + 111384*(2*a^3 + 6*a^2*b + 6*a*b^2 + 2*b^3 - (a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x)*cosh(d*x + c)^6 + 2730*(27*a^3 + 39*a^2*b - 207*a*b^2 - 131*b^3 - 32*(a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x)*cosh(d*x + c)^4 + 63*a^3 - 639*a^2*b - 6195*a*b^2 - 2173*b^3 - 336*(a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x + 2184*(3*a^3 - 6*a^2*b - 93*a*b^2 - 36*b^3 - 7*(a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^12 + 120*(20995*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^9 + 15912*(2*a^3 + 6*a^2*b + 6*a*b^2 + 2*b^3 - (a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x)*cosh(d*x + c)^7 + 546*(27*a^3 + 39*a^2*b - 207*a*b^2 - 131*b^3 - 32*(a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x)*cosh(d*x + c)^5 + 728*(3*a^3 - 6*a^2*b - 93*a*b^2 - 36*b^3 - 7*(a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x)*cosh(d*x + c)^3 + (63*a^3 - 639*a^2*b - 6195*a*b^2 - 2173*b^3 - 336*(a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c)^11 - 40*(234*a^2*b + 2436*a*b^2 + 662*b^3 + 105*(a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x)*cosh(d*x + c)^10 + 20*(138567*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^10 + 131274*(2*a^3 + 6*a^2*b + 6*a*b^2 + 2*b^3 - (a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x)*cosh(d*x + c)^8 + 6006*(27*a^3 + 39*a^2*b - 207*a*b^2 - 131*b^3 - 32*(a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x)*cosh(d*x + c)^6 + 12012*(3*a^3 - 6*a^2*b - 93*a*b^2 - 36*b^3 - 7*(a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x)*cosh(d*x + c)^4 - 468*a^2*b - 4872*a*b^2 - 1324*b^3 - 210*(a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x + 33*(63*a^3 - 639*a^2*b - 6195*a*b^2 - 2173*b^3 - 336*(a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^10 + 40*(62985*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^11 + 72930*(2*a^3 + 6*a^2*b + 6*a*b^2 + 2*b^3 - (a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x)*cosh(d*x + c)^9 + 4290*(27*a^3 + 39*a^2*b - 207*a*b^2 - 131*b^3 - 32*(a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x)*cosh(d*x + c)^7 + 12012*(3*a^3 - 6*a^2*b - 93*a*b^2 - 36*b^3 - 7*(a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x)*cosh(d*x + c)^5 + 55*(63*a^3 - 639*a^2*b - 6195*a*b^2 - 2173*b^3 - 336*(a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x)*cosh(d*x + c)^3 - 10*(234*a^2*b + 2436*a*b^2 + 662*b^3 + 105*(a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c)^9 - 2*(315*a^3 + 3195*a^2*b + 46977*a*b^2 + 10865*b^3 + 1680*(a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x)*cosh(d*x + c)^8 + 2*(944775*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^12 + 1312740*(2*a^3 + 6*a^2*b + 6*a*b^2 + 2*b^3 - (a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x)*cosh(d*x + c)^10 + 96525*(27*a^3 + 39*a^2*b - 207*a*b^2 - 131*b^3 - 32*(a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x)*cosh(d*x + c)^8 + 360360*(3*a^3 - 6*a^2*b - 93*a*b^2 - 36*b^3 - 7*(a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x)*cosh(d*x + c)^6 + 2475*(63*a^3 - 639*a^2*b - 6195*a*b^2 - 2173*b^3 - 336*(a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x)*cosh(d*x + c)^4 - 315*a^3 - 3195*a^2*b - 46977*a*b^2 - 10865*b^3 - 1680*(a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x - 900*(234*a^2*b + 2436*a*b^2 + 662*b^3 + 105*(a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 16*(72675*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^13 + 119340*(2*a^3 + 6*a^2*b + 6*a*b^2 + 2*b^3 - (a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x)*cosh(d*x + c)^11 + 10725*(27*a^3 + 39*a^2*b - 207*a*b^2 - 131*b^3 - 32*(a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x)*cosh(d*x + c)^9 + 51480*(3*a^3 - 6*a^2*b - 93*a*b^2 - 36*b^3 - 7*(a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x)*cosh(d*x + c)^7 + 495*(63*a^3 - 639*a^2*b - 6195*a*b^2 - 2173*b^3 - 336*(a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x)*cosh(d*x + c)^5 - 300*(234*a^2*b + 2436*a*b^2 + 662*b^3 + 105*(a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x)*cosh(d*x + c)^3 - (315*a^3 + 3195*a^2*b + 46977*a*b^2 + 10865*b^3 + 1680*(a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c)^7 - 48*(15*a^3 + 30*a^2*b + 1159*a*b^2 + 180*b^3 + 35*(a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x)*cosh(d*x + c)^6 + 8*(72675*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^14 + 139230*(2*a^3 + 6*a^2*b + 6*a*b^2 + 2*b^3 - (a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x)*cosh(d*x + c)^12 + 15015*(27*a^3 + 39*a^2*b - 207*a*b^2 - 131*b^3 - 32*(a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x)*cosh(d*x + c)^10 + 90090*(3*a^3 - 6*a^2*b - 93*a*b^2 - 36*b^3 - 7*(a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x)*cosh(d*x + c)^8 + 1155*(63*a^3 - 639*a^2*b - 6195*a*b^2 - 2173*b^3 - 336*(a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x)*cosh(d*x + c)^6 - 1050*(234*a^2*b + 2436*a*b^2 + 662*b^3 + 105*(a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x)*cosh(d*x + c)^4 - 90*a^3 - 180*a^2*b - 6954*a*b^2 - 1080*b^3 - 210*(a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x - 7*(315*a^3 + 3195*a^2*b + 46977*a*b^2 + 10865*b^3 + 1680*(a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 16*(14535*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^15 + 32130*(2*a^3 + 6*a^2*b + 6*a*b^2 + 2*b^3 - (a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x)*cosh(d*x + c)^13 + 4095*(27*a^3 + 39*a^2*b - 207*a*b^2 - 131*b^3 - 32*(a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x)*cosh(d*x + c)^11 + 30030*(3*a^3 - 6*a^2*b - 93*a*b^2 - 36*b^3 - 7*(a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x)*cosh(d*x + c)^9 + 495*(63*a^3 - 639*a^2*b - 6195*a*b^2 - 2173*b^3 - 336*(a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x)*cosh(d*x + c)^7 - 630*(234*a^2*b + 2436*a*b^2 + 662*b^3 + 105*(a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x)*cosh(d*x + c)^5 - 7*(315*a^3 + 3195*a^2*b + 46977*a*b^2 + 10865*b^3 + 1680*(a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x)*cosh(d*x + c)^3 - 18*(15*a^3 + 30*a^2*b + 1159*a*b^2 + 180*b^3 + 35*(a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c)^5 - 3*(135*a^3 - 195*a^2*b + 6389*a*b^2 + 655*b^3 + 160*(a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x)*cosh(d*x + c)^4 + (72675*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^16 + 183600*(2*a^3 + 6*a^2*b + 6*a*b^2 + 2*b^3 - (a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x)*cosh(d*x + c)^14 + 27300*(27*a^3 + 39*a^2*b - 207*a*b^2 - 131*b^3 - 32*(a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x)*cosh(d*x + c)^12 + 240240*(3*a^3 - 6*a^2*b - 93*a*b^2 - 36*b^3 - 7*(a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x)*cosh(d*x + c)^10 + 4950*(63*a^3 - 639*a^2*b - 6195*a*b^2 - 2173*b^3 - 336*(a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x)*cosh(d*x + c)^8 - 8400*(234*a^2*b + 2436*a*b^2 + 662*b^3 + 105*(a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x)*cosh(d*x + c)^6 - 140*(315*a^3 + 3195*a^2*b + 46977*a*b^2 + 10865*b^3 + 1680*(a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x)*cosh(d*x + c)^4 - 405*a^3 + 585*a^2*b - 19167*a*b^2 - 1965*b^3 - 480*(a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x - 720*(15*a^3 + 30*a^2*b + 1159*a*b^2 + 180*b^3 + 35*(a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 4*(4275*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^17 + 12240*(2*a^3 + 6*a^2*b + 6*a*b^2 + 2*b^3 - (a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x)*cosh(d*x + c)^15 + 2100*(27*a^3 + 39*a^2*b - 207*a*b^2 - 131*b^3 - 32*(a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x)*cosh(d*x + c)^13 + 21840*(3*a^3 - 6*a^2*b - 93*a*b^2 - 36*b^3 - 7*(a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x)*cosh(d*x + c)^11 + 550*(63*a^3 - 639*a^2*b - 6195*a*b^2 - 2173*b^3 - 336*(a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x)*cosh(d*x + c)^9 - 1200*(234*a^2*b + 2436*a*b^2 + 662*b^3 + 105*(a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x)*cosh(d*x + c)^7 - 28*(315*a^3 + 3195*a^2*b + 46977*a*b^2 + 10865*b^3 + 1680*(a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x)*cosh(d*x + c)^5 - 240*(15*a^3 + 30*a^2*b + 1159*a*b^2 + 180*b^3 + 35*(a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x)*cosh(d*x + c)^3 - 3*(135*a^3 - 195*a^2*b + 6389*a*b^2 + 655*b^3 + 160*(a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c)^3 - 15*a^3 + 45*a^2*b - 45*a*b^2 + 15*b^3 - 12*(10*a^3 - 30*a^2*b + 262*a*b^2 - 10*b^3 + 5*(a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x)*cosh(d*x + c)^2 + 2*(1425*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^18 + 4590*(2*a^3 + 6*a^2*b + 6*a*b^2 + 2*b^3 - (a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x)*cosh(d*x + c)^16 + 900*(27*a^3 + 39*a^2*b - 207*a*b^2 - 131*b^3 - 32*(a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x)*cosh(d*x + c)^14 + 10920*(3*a^3 - 6*a^2*b - 93*a*b^2 - 36*b^3 - 7*(a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x)*cosh(d*x + c)^12 + 330*(63*a^3 - 639*a^2*b - 6195*a*b^2 - 2173*b^3 - 336*(a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x)*cosh(d*x + c)^10 - 900*(234*a^2*b + 2436*a*b^2 + 662*b^3 + 105*(a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x)*cosh(d*x + c)^8 - 28*(315*a^3 + 3195*a^2*b + 46977*a*b^2 + 10865*b^3 + 1680*(a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x)*cosh(d*x + c)^6 - 360*(15*a^3 + 30*a^2*b + 1159*a*b^2 + 180*b^3 + 35*(a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x)*cosh(d*x + c)^4 - 60*a^3 + 180*a^2*b - 1572*a*b^2 + 60*b^3 - 30*(a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x - 9*(135*a^3 - 195*a^2*b + 6389*a*b^2 + 655*b^3 + 160*(a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - 120*((6*a^2*b + 5*b^3)*cosh(d*x + c)^18 + 18*(6*a^2*b + 5*b^3)*cosh(d*x + c)*sinh(d*x + c)^17 + (6*a^2*b + 5*b^3)*sinh(d*x + c)^18 + 8*(6*a^2*b + 5*b^3)*cosh(d*x + c)^16 + (48*a^2*b + 40*b^3 + 153*(6*a^2*b + 5*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^16 + 16*(51*(6*a^2*b + 5*b^3)*cosh(d*x + c)^3 + 8*(6*a^2*b + 5*b^3)*cosh(d*x + c))*sinh(d*x + c)^15 + 28*(6*a^2*b + 5*b^3)*cosh(d*x + c)^14 + 4*(765*(6*a^2*b + 5*b^3)*cosh(d*x + c)^4 + 42*a^2*b + 35*b^3 + 240*(6*a^2*b + 5*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^14 + 56*(153*(6*a^2*b + 5*b^3)*cosh(d*x + c)^5 + 80*(6*a^2*b + 5*b^3)*cosh(d*x + c)^3 + 7*(6*a^2*b + 5*b^3)*cosh(d*x + c))*sinh(d*x + c)^13 + 56*(6*a^2*b + 5*b^3)*cosh(d*x + c)^12 + 28*(663*(6*a^2*b + 5*b^3)*cosh(d*x + c)^6 + 520*(6*a^2*b + 5*b^3)*cosh(d*x + c)^4 + 12*a^2*b + 10*b^3 + 91*(6*a^2*b + 5*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^12 + 16*(1989*(6*a^2*b + 5*b^3)*cosh(d*x + c)^7 + 2184*(6*a^2*b + 5*b^3)*cosh(d*x + c)^5 + 637*(6*a^2*b + 5*b^3)*cosh(d*x + c)^3 + 42*(6*a^2*b + 5*b^3)*cosh(d*x + c))*sinh(d*x + c)^11 + 70*(6*a^2*b + 5*b^3)*cosh(d*x + c)^10 + 2*(21879*(6*a^2*b + 5*b^3)*cosh(d*x + c)^8 + 32032*(6*a^2*b + 5*b^3)*cosh(d*x + c)^6 + 14014*(6*a^2*b + 5*b^3)*cosh(d*x + c)^4 + 210*a^2*b + 175*b^3 + 1848*(6*a^2*b + 5*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^10 + 4*(12155*(6*a^2*b + 5*b^3)*cosh(d*x + c)^9 + 22880*(6*a^2*b + 5*b^3)*cosh(d*x + c)^7 + 14014*(6*a^2*b + 5*b^3)*cosh(d*x + c)^5 + 3080*(6*a^2*b + 5*b^3)*cosh(d*x + c)^3 + 175*(6*a^2*b + 5*b^3)*cosh(d*x + c))*sinh(d*x + c)^9 + 56*(6*a^2*b + 5*b^3)*cosh(d*x + c)^8 + 2*(21879*(6*a^2*b + 5*b^3)*cosh(d*x + c)^10 + 51480*(6*a^2*b + 5*b^3)*cosh(d*x + c)^8 + 42042*(6*a^2*b + 5*b^3)*cosh(d*x + c)^6 + 13860*(6*a^2*b + 5*b^3)*cosh(d*x + c)^4 + 168*a^2*b + 140*b^3 + 1575*(6*a^2*b + 5*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 16*(1989*(6*a^2*b + 5*b^3)*cosh(d*x + c)^11 + 5720*(6*a^2*b + 5*b^3)*cosh(d*x + c)^9 + 6006*(6*a^2*b + 5*b^3)*cosh(d*x + c)^7 + 2772*(6*a^2*b + 5*b^3)*cosh(d*x + c)^5 + 525*(6*a^2*b + 5*b^3)*cosh(d*x + c)^3 + 28*(6*a^2*b + 5*b^3)*cosh(d*x + c))*sinh(d*x + c)^7 + 28*(6*a^2*b + 5*b^3)*cosh(d*x + c)^6 + 28*(663*(6*a^2*b + 5*b^3)*cosh(d*x + c)^12 + 2288*(6*a^2*b + 5*b^3)*cosh(d*x + c)^10 + 3003*(6*a^2*b + 5*b^3)*cosh(d*x + c)^8 + 1848*(6*a^2*b + 5*b^3)*cosh(d*x + c)^6 + 525*(6*a^2*b + 5*b^3)*cosh(d*x + c)^4 + 6*a^2*b + 5*b^3 + 56*(6*a^2*b + 5*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 56*(153*(6*a^2*b + 5*b^3)*cosh(d*x + c)^13 + 624*(6*a^2*b + 5*b^3)*cosh(d*x + c)^11 + 1001*(6*a^2*b + 5*b^3)*cosh(d*x + c)^9 + 792*(6*a^2*b + 5*b^3)*cosh(d*x + c)^7 + 315*(6*a^2*b + 5*b^3)*cosh(d*x + c)^5 + 56*(6*a^2*b + 5*b^3)*cosh(d*x + c)^3 + 3*(6*a^2*b + 5*b^3)*cosh(d*x + c))*sinh(d*x + c)^5 + 8*(6*a^2*b + 5*b^3)*cosh(d*x + c)^4 + 4*(765*(6*a^2*b + 5*b^3)*cosh(d*x + c)^14 + 3640*(6*a^2*b + 5*b^3)*cosh(d*x + c)^12 + 7007*(6*a^2*b + 5*b^3)*cosh(d*x + c)^10 + 6930*(6*a^2*b + 5*b^3)*cosh(d*x + c)^8 + 3675*(6*a^2*b + 5*b^3)*cosh(d*x + c)^6 + 980*(6*a^2*b + 5*b^3)*cosh(d*x + c)^4 + 12*a^2*b + 10*b^3 + 105*(6*a^2*b + 5*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 16*(51*(6*a^2*b + 5*b^3)*cosh(d*x + c)^15 + 280*(6*a^2*b + 5*b^3)*cosh(d*x + c)^13 + 637*(6*a^2*b + 5*b^3)*cosh(d*x + c)^11 + 770*(6*a^2*b + 5*b^3)*cosh(d*x + c)^9 + 525*(6*a^2*b + 5*b^3)*cosh(d*x + c)^7 + 196*(6*a^2*b + 5*b^3)*cosh(d*x + c)^5 + 35*(6*a^2*b + 5*b^3)*cosh(d*x + c)^3 + 2*(6*a^2*b + 5*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 + (6*a^2*b + 5*b^3)*cosh(d*x + c)^2 + (153*(6*a^2*b + 5*b^3)*cosh(d*x + c)^16 + 960*(6*a^2*b + 5*b^3)*cosh(d*x + c)^14 + 2548*(6*a^2*b + 5*b^3)*cosh(d*x + c)^12 + 3696*(6*a^2*b + 5*b^3)*cosh(d*x + c)^10 + 3150*(6*a^2*b + 5*b^3)*cosh(d*x + c)^8 + 1568*(6*a^2*b + 5*b^3)*cosh(d*x + c)^6 + 420*(6*a^2*b + 5*b^3)*cosh(d*x + c)^4 + 6*a^2*b + 5*b^3 + 48*(6*a^2*b + 5*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 2*(9*(6*a^2*b + 5*b^3)*cosh(d*x + c)^17 + 64*(6*a^2*b + 5*b^3)*cosh(d*x + c)^15 + 196*(6*a^2*b + 5*b^3)*cosh(d*x + c)^13 + 336*(6*a^2*b + 5*b^3)*cosh(d*x + c)^11 + 350*(6*a^2*b + 5*b^3)*cosh(d*x + c)^9 + 224*(6*a^2*b + 5*b^3)*cosh(d*x + c)^7 + 84*(6*a^2*b + 5*b^3)*cosh(d*x + c)^5 + 16*(6*a^2*b + 5*b^3)*cosh(d*x + c)^3 + (6*a^2*b + 5*b^3)*cosh(d*x + c))*sinh(d*x + c))*log(2*cosh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))) + 4*(75*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^19 + 270*(2*a^3 + 6*a^2*b + 6*a*b^2 + 2*b^3 - (a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x)*cosh(d*x + c)^17 + 60*(27*a^3 + 39*a^2*b - 207*a*b^2 - 131*b^3 - 32*(a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x)*cosh(d*x + c)^15 + 840*(3*a^3 - 6*a^2*b - 93*a*b^2 - 36*b^3 - 7*(a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x)*cosh(d*x + c)^13 + 30*(63*a^3 - 639*a^2*b - 6195*a*b^2 - 2173*b^3 - 336*(a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x)*cosh(d*x + c)^11 - 100*(234*a^2*b + 2436*a*b^2 + 662*b^3 + 105*(a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x)*cosh(d*x + c)^9 - 4*(315*a^3 + 3195*a^2*b + 46977*a*b^2 + 10865*b^3 + 1680*(a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x)*cosh(d*x + c)^7 - 72*(15*a^3 + 30*a^2*b + 1159*a*b^2 + 180*b^3 + 35*(a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x)*cosh(d*x + c)^5 - 3*(135*a^3 - 195*a^2*b + 6389*a*b^2 + 655*b^3 + 160*(a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x)*cosh(d*x + c)^3 - 6*(10*a^3 - 30*a^2*b + 262*a*b^2 - 10*b^3 + 5*(a^3 - 12*a^2*b + 21*a*b^2 - 10*b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c))/(d*cosh(d*x + c)^18 + 18*d*cosh(d*x + c)*sinh(d*x + c)^17 + d*sinh(d*x + c)^18 + 8*d*cosh(d*x + c)^16 + (153*d*cosh(d*x + c)^2 + 8*d)*sinh(d*x + c)^16 + 16*(51*d*cosh(d*x + c)^3 + 8*d*cosh(d*x + c))*sinh(d*x + c)^15 + 28*d*cosh(d*x + c)^14 + 4*(765*d*cosh(d*x + c)^4 + 240*d*cosh(d*x + c)^2 + 7*d)*sinh(d*x + c)^14 + 56*(153*d*cosh(d*x + c)^5 + 80*d*cosh(d*x + c)^3 + 7*d*cosh(d*x + c))*sinh(d*x + c)^13 + 56*d*cosh(d*x + c)^12 + 28*(663*d*cosh(d*x + c)^6 + 520*d*cosh(d*x + c)^4 + 91*d*cosh(d*x + c)^2 + 2*d)*sinh(d*x + c)^12 + 16*(1989*d*cosh(d*x + c)^7 + 2184*d*cosh(d*x + c)^5 + 637*d*cosh(d*x + c)^3 + 42*d*cosh(d*x + c))*sinh(d*x + c)^11 + 70*d*cosh(d*x + c)^10 + 2*(21879*d*cosh(d*x + c)^8 + 32032*d*cosh(d*x + c)^6 + 14014*d*cosh(d*x + c)^4 + 1848*d*cosh(d*x + c)^2 + 35*d)*sinh(d*x + c)^10 + 4*(12155*d*cosh(d*x + c)^9 + 22880*d*cosh(d*x + c)^7 + 14014*d*cosh(d*x + c)^5 + 3080*d*cosh(d*x + c)^3 + 175*d*cosh(d*x + c))*sinh(d*x + c)^9 + 56*d*cosh(d*x + c)^8 + 2*(21879*d*cosh(d*x + c)^10 + 51480*d*cosh(d*x + c)^8 + 42042*d*cosh(d*x + c)^6 + 13860*d*cosh(d*x + c)^4 + 1575*d*cosh(d*x + c)^2 + 28*d)*sinh(d*x + c)^8 + 16*(1989*d*cosh(d*x + c)^11 + 5720*d*cosh(d*x + c)^9 + 6006*d*cosh(d*x + c)^7 + 2772*d*cosh(d*x + c)^5 + 525*d*cosh(d*x + c)^3 + 28*d*cosh(d*x + c))*sinh(d*x + c)^7 + 28*d*cosh(d*x + c)^6 + 28*(663*d*cosh(d*x + c)^12 + 2288*d*cosh(d*x + c)^10 + 3003*d*cosh(d*x + c)^8 + 1848*d*cosh(d*x + c)^6 + 525*d*cosh(d*x + c)^4 + 56*d*cosh(d*x + c)^2 + d)*sinh(d*x + c)^6 + 56*(153*d*cosh(d*x + c)^13 + 624*d*cosh(d*x + c)^11 + 1001*d*cosh(d*x + c)^9 + 792*d*cosh(d*x + c)^7 + 315*d*cosh(d*x + c)^5 + 56*d*cosh(d*x + c)^3 + 3*d*cosh(d*x + c))*sinh(d*x + c)^5 + 8*d*cosh(d*x + c)^4 + 4*(765*d*cosh(d*x + c)^14 + 3640*d*cosh(d*x + c)^12 + 7007*d*cosh(d*x + c)^10 + 6930*d*cosh(d*x + c)^8 + 3675*d*cosh(d*x + c)^6 + 980*d*cosh(d*x + c)^4 + 105*d*cosh(d*x + c)^2 + 2*d)*sinh(d*x + c)^4 + 16*(51*d*cosh(d*x + c)^15 + 280*d*cosh(d*x + c)^13 + 637*d*cosh(d*x + c)^11 + 770*d*cosh(d*x + c)^9 + 525*d*cosh(d*x + c)^7 + 196*d*cosh(d*x + c)^5 + 35*d*cosh(d*x + c)^3 + 2*d*cosh(d*x + c))*sinh(d*x + c)^3 + d*cosh(d*x + c)^2 + (153*d*cosh(d*x + c)^16 + 960*d*cosh(d*x + c)^14 + 2548*d*cosh(d*x + c)^12 + 3696*d*cosh(d*x + c)^10 + 3150*d*cosh(d*x + c)^8 + 1568*d*cosh(d*x + c)^6 + 420*d*cosh(d*x + c)^4 + 48*d*cosh(d*x + c)^2 + d)*sinh(d*x + c)^2 + 2*(9*d*cosh(d*x + c)^17 + 64*d*cosh(d*x + c)^15 + 196*d*cosh(d*x + c)^13 + 336*d*cosh(d*x + c)^11 + 350*d*cosh(d*x + c)^9 + 224*d*cosh(d*x + c)^7 + 84*d*cosh(d*x + c)^5 + 16*d*cosh(d*x + c)^3 + d*cosh(d*x + c))*sinh(d*x + c))","B",0
68,1,6410,0,0.524892," ","integrate(sinh(d*x+c)*(a+b*tanh(d*x+c)^3)^3,x, algorithm=""fricas"")","\frac{160 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{18} + 2880 \, {\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)^{17} + 160 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \sinh\left(d x + c\right)^{18} + 45 \, {\left(32 \, a^{3} + 96 \, a^{2} b + 224 \, a b^{2} + 61 \, b^{3}\right)} \cosh\left(d x + c\right)^{16} + 45 \, {\left(32 \, a^{3} + 96 \, a^{2} b + 224 \, a b^{2} + 61 \, b^{3} + 544 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{16} + 240 \, {\left(544 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(32 \, a^{3} + 96 \, a^{2} b + 224 \, a b^{2} + 61 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{15} + 15 \, {\left(384 \, a^{3} + 960 \, a^{2} b + 3328 \, a b^{2} + 475 \, b^{3}\right)} \cosh\left(d x + c\right)^{14} + 15 \, {\left(32640 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{4} + 384 \, a^{3} + 960 \, a^{2} b + 3328 \, a b^{2} + 475 \, b^{3} + 360 \, {\left(32 \, a^{3} + 96 \, a^{2} b + 224 \, a b^{2} + 61 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{14} + 210 \, {\left(6528 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{5} + 120 \, {\left(32 \, a^{3} + 96 \, a^{2} b + 224 \, a b^{2} + 61 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(384 \, a^{3} + 960 \, a^{2} b + 3328 \, a b^{2} + 475 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{13} + 3 \, {\left(4480 \, a^{3} + 7360 \, a^{2} b + 43008 \, a b^{2} + 4515 \, b^{3}\right)} \cosh\left(d x + c\right)^{12} + 3 \, {\left(990080 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{6} + 27300 \, {\left(32 \, a^{3} + 96 \, a^{2} b + 224 \, a b^{2} + 61 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 4480 \, a^{3} + 7360 \, a^{2} b + 43008 \, a b^{2} + 4515 \, b^{3} + 455 \, {\left(384 \, a^{3} + 960 \, a^{2} b + 3328 \, a b^{2} + 475 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{12} + 12 \, {\left(424320 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{7} + 16380 \, {\left(32 \, a^{3} + 96 \, a^{2} b + 224 \, a b^{2} + 61 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 455 \, {\left(384 \, a^{3} + 960 \, a^{2} b + 3328 \, a b^{2} + 475 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(4480 \, a^{3} + 7360 \, a^{2} b + 43008 \, a b^{2} + 4515 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{11} + 3 \, {\left(6720 \, a^{3} + 3840 \, a^{2} b + 67904 \, a b^{2} + 1295 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} + 3 \, {\left(2333760 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{8} + 120120 \, {\left(32 \, a^{3} + 96 \, a^{2} b + 224 \, a b^{2} + 61 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 5005 \, {\left(384 \, a^{3} + 960 \, a^{2} b + 3328 \, a b^{2} + 475 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 6720 \, a^{3} + 3840 \, a^{2} b + 67904 \, a b^{2} + 1295 \, b^{3} + 66 \, {\left(4480 \, a^{3} + 7360 \, a^{2} b + 43008 \, a b^{2} + 4515 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{10} + 10 \, {\left(777920 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{9} + 51480 \, {\left(32 \, a^{3} + 96 \, a^{2} b + 224 \, a b^{2} + 61 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 3003 \, {\left(384 \, a^{3} + 960 \, a^{2} b + 3328 \, a b^{2} + 475 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 66 \, {\left(4480 \, a^{3} + 7360 \, a^{2} b + 43008 \, a b^{2} + 4515 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(6720 \, a^{3} + 3840 \, a^{2} b + 67904 \, a b^{2} + 1295 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} + 3 \, {\left(6720 \, a^{3} - 3840 \, a^{2} b + 67904 \, a b^{2} - 1295 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 3 \, {\left(2333760 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{10} + 193050 \, {\left(32 \, a^{3} + 96 \, a^{2} b + 224 \, a b^{2} + 61 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 15015 \, {\left(384 \, a^{3} + 960 \, a^{2} b + 3328 \, a b^{2} + 475 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 495 \, {\left(4480 \, a^{3} + 7360 \, a^{2} b + 43008 \, a b^{2} + 4515 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 6720 \, a^{3} - 3840 \, a^{2} b + 67904 \, a b^{2} - 1295 \, b^{3} + 45 \, {\left(6720 \, a^{3} + 3840 \, a^{2} b + 67904 \, a b^{2} + 1295 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{8} + 24 \, {\left(212160 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{11} + 21450 \, {\left(32 \, a^{3} + 96 \, a^{2} b + 224 \, a b^{2} + 61 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + 2145 \, {\left(384 \, a^{3} + 960 \, a^{2} b + 3328 \, a b^{2} + 475 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 99 \, {\left(4480 \, a^{3} + 7360 \, a^{2} b + 43008 \, a b^{2} + 4515 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 15 \, {\left(6720 \, a^{3} + 3840 \, a^{2} b + 67904 \, a b^{2} + 1295 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(6720 \, a^{3} - 3840 \, a^{2} b + 67904 \, a b^{2} - 1295 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 3 \, {\left(4480 \, a^{3} - 7360 \, a^{2} b + 43008 \, a b^{2} - 4515 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 3 \, {\left(990080 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{12} + 120120 \, {\left(32 \, a^{3} + 96 \, a^{2} b + 224 \, a b^{2} + 61 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} + 15015 \, {\left(384 \, a^{3} + 960 \, a^{2} b + 3328 \, a b^{2} + 475 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 924 \, {\left(4480 \, a^{3} + 7360 \, a^{2} b + 43008 \, a b^{2} + 4515 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 210 \, {\left(6720 \, a^{3} + 3840 \, a^{2} b + 67904 \, a b^{2} + 1295 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 4480 \, a^{3} - 7360 \, a^{2} b + 43008 \, a b^{2} - 4515 \, b^{3} + 28 \, {\left(6720 \, a^{3} - 3840 \, a^{2} b + 67904 \, a b^{2} - 1295 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 6 \, {\left(228480 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{13} + 32760 \, {\left(32 \, a^{3} + 96 \, a^{2} b + 224 \, a b^{2} + 61 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} + 5005 \, {\left(384 \, a^{3} + 960 \, a^{2} b + 3328 \, a b^{2} + 475 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + 396 \, {\left(4480 \, a^{3} + 7360 \, a^{2} b + 43008 \, a b^{2} + 4515 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 126 \, {\left(6720 \, a^{3} + 3840 \, a^{2} b + 67904 \, a b^{2} + 1295 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 28 \, {\left(6720 \, a^{3} - 3840 \, a^{2} b + 67904 \, a b^{2} - 1295 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(4480 \, a^{3} - 7360 \, a^{2} b + 43008 \, a b^{2} - 4515 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 15 \, {\left(384 \, a^{3} - 960 \, a^{2} b + 3328 \, a b^{2} - 475 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 15 \, {\left(32640 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{14} + 5460 \, {\left(32 \, a^{3} + 96 \, a^{2} b + 224 \, a b^{2} + 61 \, b^{3}\right)} \cosh\left(d x + c\right)^{12} + 1001 \, {\left(384 \, a^{3} + 960 \, a^{2} b + 3328 \, a b^{2} + 475 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} + 99 \, {\left(4480 \, a^{3} + 7360 \, a^{2} b + 43008 \, a b^{2} + 4515 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 42 \, {\left(6720 \, a^{3} + 3840 \, a^{2} b + 67904 \, a b^{2} + 1295 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 14 \, {\left(6720 \, a^{3} - 3840 \, a^{2} b + 67904 \, a b^{2} - 1295 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 384 \, a^{3} - 960 \, a^{2} b + 3328 \, a b^{2} - 475 \, b^{3} + 3 \, {\left(4480 \, a^{3} - 7360 \, a^{2} b + 43008 \, a b^{2} - 4515 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 12 \, {\left(10880 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{15} + 2100 \, {\left(32 \, a^{3} + 96 \, a^{2} b + 224 \, a b^{2} + 61 \, b^{3}\right)} \cosh\left(d x + c\right)^{13} + 455 \, {\left(384 \, a^{3} + 960 \, a^{2} b + 3328 \, a b^{2} + 475 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} + 55 \, {\left(4480 \, a^{3} + 7360 \, a^{2} b + 43008 \, a b^{2} + 4515 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + 30 \, {\left(6720 \, a^{3} + 3840 \, a^{2} b + 67904 \, a b^{2} + 1295 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 14 \, {\left(6720 \, a^{3} - 3840 \, a^{2} b + 67904 \, a b^{2} - 1295 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(4480 \, a^{3} - 7360 \, a^{2} b + 43008 \, a b^{2} - 4515 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 5 \, {\left(384 \, a^{3} - 960 \, a^{2} b + 3328 \, a b^{2} - 475 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 160 \, a^{3} - 480 \, a^{2} b + 480 \, a b^{2} - 160 \, b^{3} + 45 \, {\left(32 \, a^{3} - 96 \, a^{2} b + 224 \, a b^{2} - 61 \, b^{3}\right)} \cosh\left(d x + c\right)^{2} + 3 \, {\left(8160 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{16} + 1800 \, {\left(32 \, a^{3} + 96 \, a^{2} b + 224 \, a b^{2} + 61 \, b^{3}\right)} \cosh\left(d x + c\right)^{14} + 455 \, {\left(384 \, a^{3} + 960 \, a^{2} b + 3328 \, a b^{2} + 475 \, b^{3}\right)} \cosh\left(d x + c\right)^{12} + 66 \, {\left(4480 \, a^{3} + 7360 \, a^{2} b + 43008 \, a b^{2} + 4515 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} + 45 \, {\left(6720 \, a^{3} + 3840 \, a^{2} b + 67904 \, a b^{2} + 1295 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 28 \, {\left(6720 \, a^{3} - 3840 \, a^{2} b + 67904 \, a b^{2} - 1295 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(4480 \, a^{3} - 7360 \, a^{2} b + 43008 \, a b^{2} - 4515 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 480 \, a^{3} - 1440 \, a^{2} b + 3360 \, a b^{2} - 915 \, b^{3} + 30 \, {\left(384 \, a^{3} - 960 \, a^{2} b + 3328 \, a b^{2} - 475 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} - 45 \, {\left({\left(64 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{17} + 17 \, {\left(64 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{16} + {\left(64 \, a^{2} b + 35 \, b^{3}\right)} \sinh\left(d x + c\right)^{17} + 8 \, {\left(64 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{15} + 8 \, {\left(64 \, a^{2} b + 35 \, b^{3} + 17 \, {\left(64 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{15} + 40 \, {\left(17 \, {\left(64 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(64 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{14} + 28 \, {\left(64 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{13} + 28 \, {\left(85 \, {\left(64 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 64 \, a^{2} b + 35 \, b^{3} + 30 \, {\left(64 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{13} + 364 \, {\left(17 \, {\left(64 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(64 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(64 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{12} + 56 \, {\left(64 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} + 56 \, {\left(221 \, {\left(64 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 195 \, {\left(64 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 64 \, a^{2} b + 35 \, b^{3} + 39 \, {\left(64 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{11} + 88 \, {\left(221 \, {\left(64 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 273 \, {\left(64 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 91 \, {\left(64 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 7 \, {\left(64 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{10} + 70 \, {\left(64 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + 10 \, {\left(2431 \, {\left(64 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 4004 \, {\left(64 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 2002 \, {\left(64 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 448 \, a^{2} b + 245 \, b^{3} + 308 \, {\left(64 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{9} + 2 \, {\left(12155 \, {\left(64 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + 25740 \, {\left(64 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 18018 \, {\left(64 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 4620 \, {\left(64 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 315 \, {\left(64 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{8} + 56 \, {\left(64 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 8 \, {\left(2431 \, {\left(64 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} + 6435 \, {\left(64 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 6006 \, {\left(64 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 2310 \, {\left(64 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 448 \, a^{2} b + 245 \, b^{3} + 315 \, {\left(64 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{7} + 56 \, {\left(221 \, {\left(64 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} + 715 \, {\left(64 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + 858 \, {\left(64 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 462 \, {\left(64 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 105 \, {\left(64 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 7 \, {\left(64 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} + 28 \, {\left(64 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 28 \, {\left(221 \, {\left(64 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{12} + 858 \, {\left(64 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} + 1287 \, {\left(64 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 924 \, {\left(64 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 315 \, {\left(64 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 64 \, a^{2} b + 35 \, b^{3} + 42 \, {\left(64 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{5} + 140 \, {\left(17 \, {\left(64 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{13} + 78 \, {\left(64 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} + 143 \, {\left(64 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + 132 \, {\left(64 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 63 \, {\left(64 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 14 \, {\left(64 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(64 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(64 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 8 \, {\left(85 \, {\left(64 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{14} + 455 \, {\left(64 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{12} + 1001 \, {\left(64 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} + 1155 \, {\left(64 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 735 \, {\left(64 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 245 \, {\left(64 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 64 \, a^{2} b + 35 \, b^{3} + 35 \, {\left(64 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + 8 \, {\left(17 \, {\left(64 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{15} + 105 \, {\left(64 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{13} + 273 \, {\left(64 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} + 385 \, {\left(64 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + 315 \, {\left(64 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 147 \, {\left(64 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 35 \, {\left(64 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(64 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(64 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right) + {\left(17 \, {\left(64 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{16} + 120 \, {\left(64 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{14} + 364 \, {\left(64 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{12} + 616 \, {\left(64 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} + 630 \, {\left(64 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 392 \, {\left(64 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 140 \, {\left(64 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 64 \, a^{2} b + 35 \, b^{3} + 24 \, {\left(64 \, a^{2} b + 35 \, 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) + 6 \, {\left(480 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{17} + 120 \, {\left(32 \, a^{3} + 96 \, a^{2} b + 224 \, a b^{2} + 61 \, b^{3}\right)} \cosh\left(d x + c\right)^{15} + 35 \, {\left(384 \, a^{3} + 960 \, a^{2} b + 3328 \, a b^{2} + 475 \, b^{3}\right)} \cosh\left(d x + c\right)^{13} + 6 \, {\left(4480 \, a^{3} + 7360 \, a^{2} b + 43008 \, a b^{2} + 4515 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} + 5 \, {\left(6720 \, a^{3} + 3840 \, a^{2} b + 67904 \, a b^{2} + 1295 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + 4 \, {\left(6720 \, a^{3} - 3840 \, a^{2} b + 67904 \, a b^{2} - 1295 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(4480 \, a^{3} - 7360 \, a^{2} b + 43008 \, a b^{2} - 4515 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(384 \, a^{3} - 960 \, a^{2} b + 3328 \, a b^{2} - 475 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 15 \, {\left(32 \, a^{3} - 96 \, a^{2} b + 224 \, a b^{2} - 61 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{320 \, {\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} + 8 \, d \cosh\left(d x + c\right)^{15} + 8 \, {\left(17 \, d \cosh\left(d x + c\right)^{2} + d\right)} \sinh\left(d x + c\right)^{15} + 40 \, {\left(17 \, d \cosh\left(d x + c\right)^{3} + 3 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{14} + 28 \, d \cosh\left(d x + c\right)^{13} + 28 \, {\left(85 \, d \cosh\left(d x + c\right)^{4} + 30 \, d \cosh\left(d x + c\right)^{2} + d\right)} \sinh\left(d x + c\right)^{13} + 364 \, {\left(17 \, d \cosh\left(d x + c\right)^{5} + 10 \, d \cosh\left(d x + c\right)^{3} + d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{12} + 56 \, d \cosh\left(d x + c\right)^{11} + 56 \, {\left(221 \, d \cosh\left(d x + c\right)^{6} + 195 \, d \cosh\left(d x + c\right)^{4} + 39 \, d \cosh\left(d x + c\right)^{2} + d\right)} \sinh\left(d x + c\right)^{11} + 88 \, {\left(221 \, d \cosh\left(d x + c\right)^{7} + 273 \, d \cosh\left(d x + c\right)^{5} + 91 \, d \cosh\left(d x + c\right)^{3} + 7 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{10} + 70 \, d \cosh\left(d x + c\right)^{9} + 10 \, {\left(2431 \, d \cosh\left(d x + c\right)^{8} + 4004 \, d \cosh\left(d x + c\right)^{6} + 2002 \, d \cosh\left(d x + c\right)^{4} + 308 \, d \cosh\left(d x + c\right)^{2} + 7 \, d\right)} \sinh\left(d x + c\right)^{9} + 2 \, {\left(12155 \, d \cosh\left(d x + c\right)^{9} + 25740 \, d \cosh\left(d x + c\right)^{7} + 18018 \, d \cosh\left(d x + c\right)^{5} + 4620 \, d \cosh\left(d x + c\right)^{3} + 315 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{8} + 56 \, d \cosh\left(d x + c\right)^{7} + 8 \, {\left(2431 \, d \cosh\left(d x + c\right)^{10} + 6435 \, d \cosh\left(d x + c\right)^{8} + 6006 \, d \cosh\left(d x + c\right)^{6} + 2310 \, d \cosh\left(d x + c\right)^{4} + 315 \, d \cosh\left(d x + c\right)^{2} + 7 \, d\right)} \sinh\left(d x + c\right)^{7} + 56 \, {\left(221 \, d \cosh\left(d x + c\right)^{11} + 715 \, d \cosh\left(d x + c\right)^{9} + 858 \, d \cosh\left(d x + c\right)^{7} + 462 \, d \cosh\left(d x + c\right)^{5} + 105 \, d \cosh\left(d x + c\right)^{3} + 7 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} + 28 \, d \cosh\left(d x + c\right)^{5} + 28 \, {\left(221 \, d \cosh\left(d x + c\right)^{12} + 858 \, d \cosh\left(d x + c\right)^{10} + 1287 \, d \cosh\left(d x + c\right)^{8} + 924 \, d \cosh\left(d x + c\right)^{6} + 315 \, 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} + 140 \, {\left(17 \, d \cosh\left(d x + c\right)^{13} + 78 \, d \cosh\left(d x + c\right)^{11} + 143 \, d \cosh\left(d x + c\right)^{9} + 132 \, d \cosh\left(d x + c\right)^{7} + 63 \, 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)^{4} + 8 \, d \cosh\left(d x + c\right)^{3} + 8 \, {\left(85 \, d \cosh\left(d x + c\right)^{14} + 455 \, d \cosh\left(d x + c\right)^{12} + 1001 \, d \cosh\left(d x + c\right)^{10} + 1155 \, d \cosh\left(d x + c\right)^{8} + 735 \, d \cosh\left(d x + c\right)^{6} + 245 \, d \cosh\left(d x + c\right)^{4} + 35 \, d \cosh\left(d x + c\right)^{2} + d\right)} \sinh\left(d x + c\right)^{3} + 8 \, {\left(17 \, d \cosh\left(d x + c\right)^{15} + 105 \, d \cosh\left(d x + c\right)^{13} + 273 \, d \cosh\left(d x + c\right)^{11} + 385 \, d \cosh\left(d x + c\right)^{9} + 315 \, d \cosh\left(d x + c\right)^{7} + 147 \, d \cosh\left(d x + c\right)^{5} + 35 \, 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(17 \, d \cosh\left(d x + c\right)^{16} + 120 \, d \cosh\left(d x + c\right)^{14} + 364 \, d \cosh\left(d x + c\right)^{12} + 616 \, d \cosh\left(d x + c\right)^{10} + 630 \, d \cosh\left(d x + c\right)^{8} + 392 \, d \cosh\left(d x + c\right)^{6} + 140 \, 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)\right)}}"," ",0,"1/320*(160*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^18 + 2880*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)*sinh(d*x + c)^17 + 160*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*sinh(d*x + c)^18 + 45*(32*a^3 + 96*a^2*b + 224*a*b^2 + 61*b^3)*cosh(d*x + c)^16 + 45*(32*a^3 + 96*a^2*b + 224*a*b^2 + 61*b^3 + 544*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^16 + 240*(544*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^3 + 3*(32*a^3 + 96*a^2*b + 224*a*b^2 + 61*b^3)*cosh(d*x + c))*sinh(d*x + c)^15 + 15*(384*a^3 + 960*a^2*b + 3328*a*b^2 + 475*b^3)*cosh(d*x + c)^14 + 15*(32640*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^4 + 384*a^3 + 960*a^2*b + 3328*a*b^2 + 475*b^3 + 360*(32*a^3 + 96*a^2*b + 224*a*b^2 + 61*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^14 + 210*(6528*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^5 + 120*(32*a^3 + 96*a^2*b + 224*a*b^2 + 61*b^3)*cosh(d*x + c)^3 + (384*a^3 + 960*a^2*b + 3328*a*b^2 + 475*b^3)*cosh(d*x + c))*sinh(d*x + c)^13 + 3*(4480*a^3 + 7360*a^2*b + 43008*a*b^2 + 4515*b^3)*cosh(d*x + c)^12 + 3*(990080*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^6 + 27300*(32*a^3 + 96*a^2*b + 224*a*b^2 + 61*b^3)*cosh(d*x + c)^4 + 4480*a^3 + 7360*a^2*b + 43008*a*b^2 + 4515*b^3 + 455*(384*a^3 + 960*a^2*b + 3328*a*b^2 + 475*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^12 + 12*(424320*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^7 + 16380*(32*a^3 + 96*a^2*b + 224*a*b^2 + 61*b^3)*cosh(d*x + c)^5 + 455*(384*a^3 + 960*a^2*b + 3328*a*b^2 + 475*b^3)*cosh(d*x + c)^3 + 3*(4480*a^3 + 7360*a^2*b + 43008*a*b^2 + 4515*b^3)*cosh(d*x + c))*sinh(d*x + c)^11 + 3*(6720*a^3 + 3840*a^2*b + 67904*a*b^2 + 1295*b^3)*cosh(d*x + c)^10 + 3*(2333760*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^8 + 120120*(32*a^3 + 96*a^2*b + 224*a*b^2 + 61*b^3)*cosh(d*x + c)^6 + 5005*(384*a^3 + 960*a^2*b + 3328*a*b^2 + 475*b^3)*cosh(d*x + c)^4 + 6720*a^3 + 3840*a^2*b + 67904*a*b^2 + 1295*b^3 + 66*(4480*a^3 + 7360*a^2*b + 43008*a*b^2 + 4515*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^10 + 10*(777920*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^9 + 51480*(32*a^3 + 96*a^2*b + 224*a*b^2 + 61*b^3)*cosh(d*x + c)^7 + 3003*(384*a^3 + 960*a^2*b + 3328*a*b^2 + 475*b^3)*cosh(d*x + c)^5 + 66*(4480*a^3 + 7360*a^2*b + 43008*a*b^2 + 4515*b^3)*cosh(d*x + c)^3 + 3*(6720*a^3 + 3840*a^2*b + 67904*a*b^2 + 1295*b^3)*cosh(d*x + c))*sinh(d*x + c)^9 + 3*(6720*a^3 - 3840*a^2*b + 67904*a*b^2 - 1295*b^3)*cosh(d*x + c)^8 + 3*(2333760*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^10 + 193050*(32*a^3 + 96*a^2*b + 224*a*b^2 + 61*b^3)*cosh(d*x + c)^8 + 15015*(384*a^3 + 960*a^2*b + 3328*a*b^2 + 475*b^3)*cosh(d*x + c)^6 + 495*(4480*a^3 + 7360*a^2*b + 43008*a*b^2 + 4515*b^3)*cosh(d*x + c)^4 + 6720*a^3 - 3840*a^2*b + 67904*a*b^2 - 1295*b^3 + 45*(6720*a^3 + 3840*a^2*b + 67904*a*b^2 + 1295*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 24*(212160*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^11 + 21450*(32*a^3 + 96*a^2*b + 224*a*b^2 + 61*b^3)*cosh(d*x + c)^9 + 2145*(384*a^3 + 960*a^2*b + 3328*a*b^2 + 475*b^3)*cosh(d*x + c)^7 + 99*(4480*a^3 + 7360*a^2*b + 43008*a*b^2 + 4515*b^3)*cosh(d*x + c)^5 + 15*(6720*a^3 + 3840*a^2*b + 67904*a*b^2 + 1295*b^3)*cosh(d*x + c)^3 + (6720*a^3 - 3840*a^2*b + 67904*a*b^2 - 1295*b^3)*cosh(d*x + c))*sinh(d*x + c)^7 + 3*(4480*a^3 - 7360*a^2*b + 43008*a*b^2 - 4515*b^3)*cosh(d*x + c)^6 + 3*(990080*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^12 + 120120*(32*a^3 + 96*a^2*b + 224*a*b^2 + 61*b^3)*cosh(d*x + c)^10 + 15015*(384*a^3 + 960*a^2*b + 3328*a*b^2 + 475*b^3)*cosh(d*x + c)^8 + 924*(4480*a^3 + 7360*a^2*b + 43008*a*b^2 + 4515*b^3)*cosh(d*x + c)^6 + 210*(6720*a^3 + 3840*a^2*b + 67904*a*b^2 + 1295*b^3)*cosh(d*x + c)^4 + 4480*a^3 - 7360*a^2*b + 43008*a*b^2 - 4515*b^3 + 28*(6720*a^3 - 3840*a^2*b + 67904*a*b^2 - 1295*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 6*(228480*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^13 + 32760*(32*a^3 + 96*a^2*b + 224*a*b^2 + 61*b^3)*cosh(d*x + c)^11 + 5005*(384*a^3 + 960*a^2*b + 3328*a*b^2 + 475*b^3)*cosh(d*x + c)^9 + 396*(4480*a^3 + 7360*a^2*b + 43008*a*b^2 + 4515*b^3)*cosh(d*x + c)^7 + 126*(6720*a^3 + 3840*a^2*b + 67904*a*b^2 + 1295*b^3)*cosh(d*x + c)^5 + 28*(6720*a^3 - 3840*a^2*b + 67904*a*b^2 - 1295*b^3)*cosh(d*x + c)^3 + 3*(4480*a^3 - 7360*a^2*b + 43008*a*b^2 - 4515*b^3)*cosh(d*x + c))*sinh(d*x + c)^5 + 15*(384*a^3 - 960*a^2*b + 3328*a*b^2 - 475*b^3)*cosh(d*x + c)^4 + 15*(32640*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^14 + 5460*(32*a^3 + 96*a^2*b + 224*a*b^2 + 61*b^3)*cosh(d*x + c)^12 + 1001*(384*a^3 + 960*a^2*b + 3328*a*b^2 + 475*b^3)*cosh(d*x + c)^10 + 99*(4480*a^3 + 7360*a^2*b + 43008*a*b^2 + 4515*b^3)*cosh(d*x + c)^8 + 42*(6720*a^3 + 3840*a^2*b + 67904*a*b^2 + 1295*b^3)*cosh(d*x + c)^6 + 14*(6720*a^3 - 3840*a^2*b + 67904*a*b^2 - 1295*b^3)*cosh(d*x + c)^4 + 384*a^3 - 960*a^2*b + 3328*a*b^2 - 475*b^3 + 3*(4480*a^3 - 7360*a^2*b + 43008*a*b^2 - 4515*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 12*(10880*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^15 + 2100*(32*a^3 + 96*a^2*b + 224*a*b^2 + 61*b^3)*cosh(d*x + c)^13 + 455*(384*a^3 + 960*a^2*b + 3328*a*b^2 + 475*b^3)*cosh(d*x + c)^11 + 55*(4480*a^3 + 7360*a^2*b + 43008*a*b^2 + 4515*b^3)*cosh(d*x + c)^9 + 30*(6720*a^3 + 3840*a^2*b + 67904*a*b^2 + 1295*b^3)*cosh(d*x + c)^7 + 14*(6720*a^3 - 3840*a^2*b + 67904*a*b^2 - 1295*b^3)*cosh(d*x + c)^5 + 5*(4480*a^3 - 7360*a^2*b + 43008*a*b^2 - 4515*b^3)*cosh(d*x + c)^3 + 5*(384*a^3 - 960*a^2*b + 3328*a*b^2 - 475*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 + 160*a^3 - 480*a^2*b + 480*a*b^2 - 160*b^3 + 45*(32*a^3 - 96*a^2*b + 224*a*b^2 - 61*b^3)*cosh(d*x + c)^2 + 3*(8160*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^16 + 1800*(32*a^3 + 96*a^2*b + 224*a*b^2 + 61*b^3)*cosh(d*x + c)^14 + 455*(384*a^3 + 960*a^2*b + 3328*a*b^2 + 475*b^3)*cosh(d*x + c)^12 + 66*(4480*a^3 + 7360*a^2*b + 43008*a*b^2 + 4515*b^3)*cosh(d*x + c)^10 + 45*(6720*a^3 + 3840*a^2*b + 67904*a*b^2 + 1295*b^3)*cosh(d*x + c)^8 + 28*(6720*a^3 - 3840*a^2*b + 67904*a*b^2 - 1295*b^3)*cosh(d*x + c)^6 + 15*(4480*a^3 - 7360*a^2*b + 43008*a*b^2 - 4515*b^3)*cosh(d*x + c)^4 + 480*a^3 - 1440*a^2*b + 3360*a*b^2 - 915*b^3 + 30*(384*a^3 - 960*a^2*b + 3328*a*b^2 - 475*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - 45*((64*a^2*b + 35*b^3)*cosh(d*x + c)^17 + 17*(64*a^2*b + 35*b^3)*cosh(d*x + c)*sinh(d*x + c)^16 + (64*a^2*b + 35*b^3)*sinh(d*x + c)^17 + 8*(64*a^2*b + 35*b^3)*cosh(d*x + c)^15 + 8*(64*a^2*b + 35*b^3 + 17*(64*a^2*b + 35*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^15 + 40*(17*(64*a^2*b + 35*b^3)*cosh(d*x + c)^3 + 3*(64*a^2*b + 35*b^3)*cosh(d*x + c))*sinh(d*x + c)^14 + 28*(64*a^2*b + 35*b^3)*cosh(d*x + c)^13 + 28*(85*(64*a^2*b + 35*b^3)*cosh(d*x + c)^4 + 64*a^2*b + 35*b^3 + 30*(64*a^2*b + 35*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^13 + 364*(17*(64*a^2*b + 35*b^3)*cosh(d*x + c)^5 + 10*(64*a^2*b + 35*b^3)*cosh(d*x + c)^3 + (64*a^2*b + 35*b^3)*cosh(d*x + c))*sinh(d*x + c)^12 + 56*(64*a^2*b + 35*b^3)*cosh(d*x + c)^11 + 56*(221*(64*a^2*b + 35*b^3)*cosh(d*x + c)^6 + 195*(64*a^2*b + 35*b^3)*cosh(d*x + c)^4 + 64*a^2*b + 35*b^3 + 39*(64*a^2*b + 35*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^11 + 88*(221*(64*a^2*b + 35*b^3)*cosh(d*x + c)^7 + 273*(64*a^2*b + 35*b^3)*cosh(d*x + c)^5 + 91*(64*a^2*b + 35*b^3)*cosh(d*x + c)^3 + 7*(64*a^2*b + 35*b^3)*cosh(d*x + c))*sinh(d*x + c)^10 + 70*(64*a^2*b + 35*b^3)*cosh(d*x + c)^9 + 10*(2431*(64*a^2*b + 35*b^3)*cosh(d*x + c)^8 + 4004*(64*a^2*b + 35*b^3)*cosh(d*x + c)^6 + 2002*(64*a^2*b + 35*b^3)*cosh(d*x + c)^4 + 448*a^2*b + 245*b^3 + 308*(64*a^2*b + 35*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^9 + 2*(12155*(64*a^2*b + 35*b^3)*cosh(d*x + c)^9 + 25740*(64*a^2*b + 35*b^3)*cosh(d*x + c)^7 + 18018*(64*a^2*b + 35*b^3)*cosh(d*x + c)^5 + 4620*(64*a^2*b + 35*b^3)*cosh(d*x + c)^3 + 315*(64*a^2*b + 35*b^3)*cosh(d*x + c))*sinh(d*x + c)^8 + 56*(64*a^2*b + 35*b^3)*cosh(d*x + c)^7 + 8*(2431*(64*a^2*b + 35*b^3)*cosh(d*x + c)^10 + 6435*(64*a^2*b + 35*b^3)*cosh(d*x + c)^8 + 6006*(64*a^2*b + 35*b^3)*cosh(d*x + c)^6 + 2310*(64*a^2*b + 35*b^3)*cosh(d*x + c)^4 + 448*a^2*b + 245*b^3 + 315*(64*a^2*b + 35*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^7 + 56*(221*(64*a^2*b + 35*b^3)*cosh(d*x + c)^11 + 715*(64*a^2*b + 35*b^3)*cosh(d*x + c)^9 + 858*(64*a^2*b + 35*b^3)*cosh(d*x + c)^7 + 462*(64*a^2*b + 35*b^3)*cosh(d*x + c)^5 + 105*(64*a^2*b + 35*b^3)*cosh(d*x + c)^3 + 7*(64*a^2*b + 35*b^3)*cosh(d*x + c))*sinh(d*x + c)^6 + 28*(64*a^2*b + 35*b^3)*cosh(d*x + c)^5 + 28*(221*(64*a^2*b + 35*b^3)*cosh(d*x + c)^12 + 858*(64*a^2*b + 35*b^3)*cosh(d*x + c)^10 + 1287*(64*a^2*b + 35*b^3)*cosh(d*x + c)^8 + 924*(64*a^2*b + 35*b^3)*cosh(d*x + c)^6 + 315*(64*a^2*b + 35*b^3)*cosh(d*x + c)^4 + 64*a^2*b + 35*b^3 + 42*(64*a^2*b + 35*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 140*(17*(64*a^2*b + 35*b^3)*cosh(d*x + c)^13 + 78*(64*a^2*b + 35*b^3)*cosh(d*x + c)^11 + 143*(64*a^2*b + 35*b^3)*cosh(d*x + c)^9 + 132*(64*a^2*b + 35*b^3)*cosh(d*x + c)^7 + 63*(64*a^2*b + 35*b^3)*cosh(d*x + c)^5 + 14*(64*a^2*b + 35*b^3)*cosh(d*x + c)^3 + (64*a^2*b + 35*b^3)*cosh(d*x + c))*sinh(d*x + c)^4 + 8*(64*a^2*b + 35*b^3)*cosh(d*x + c)^3 + 8*(85*(64*a^2*b + 35*b^3)*cosh(d*x + c)^14 + 455*(64*a^2*b + 35*b^3)*cosh(d*x + c)^12 + 1001*(64*a^2*b + 35*b^3)*cosh(d*x + c)^10 + 1155*(64*a^2*b + 35*b^3)*cosh(d*x + c)^8 + 735*(64*a^2*b + 35*b^3)*cosh(d*x + c)^6 + 245*(64*a^2*b + 35*b^3)*cosh(d*x + c)^4 + 64*a^2*b + 35*b^3 + 35*(64*a^2*b + 35*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 8*(17*(64*a^2*b + 35*b^3)*cosh(d*x + c)^15 + 105*(64*a^2*b + 35*b^3)*cosh(d*x + c)^13 + 273*(64*a^2*b + 35*b^3)*cosh(d*x + c)^11 + 385*(64*a^2*b + 35*b^3)*cosh(d*x + c)^9 + 315*(64*a^2*b + 35*b^3)*cosh(d*x + c)^7 + 147*(64*a^2*b + 35*b^3)*cosh(d*x + c)^5 + 35*(64*a^2*b + 35*b^3)*cosh(d*x + c)^3 + 3*(64*a^2*b + 35*b^3)*cosh(d*x + c))*sinh(d*x + c)^2 + (64*a^2*b + 35*b^3)*cosh(d*x + c) + (17*(64*a^2*b + 35*b^3)*cosh(d*x + c)^16 + 120*(64*a^2*b + 35*b^3)*cosh(d*x + c)^14 + 364*(64*a^2*b + 35*b^3)*cosh(d*x + c)^12 + 616*(64*a^2*b + 35*b^3)*cosh(d*x + c)^10 + 630*(64*a^2*b + 35*b^3)*cosh(d*x + c)^8 + 392*(64*a^2*b + 35*b^3)*cosh(d*x + c)^6 + 140*(64*a^2*b + 35*b^3)*cosh(d*x + c)^4 + 64*a^2*b + 35*b^3 + 24*(64*a^2*b + 35*b^3)*cosh(d*x + c)^2)*sinh(d*x + c))*arctan(cosh(d*x + c) + sinh(d*x + c)) + 6*(480*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^17 + 120*(32*a^3 + 96*a^2*b + 224*a*b^2 + 61*b^3)*cosh(d*x + c)^15 + 35*(384*a^3 + 960*a^2*b + 3328*a*b^2 + 475*b^3)*cosh(d*x + c)^13 + 6*(4480*a^3 + 7360*a^2*b + 43008*a*b^2 + 4515*b^3)*cosh(d*x + c)^11 + 5*(6720*a^3 + 3840*a^2*b + 67904*a*b^2 + 1295*b^3)*cosh(d*x + c)^9 + 4*(6720*a^3 - 3840*a^2*b + 67904*a*b^2 - 1295*b^3)*cosh(d*x + c)^7 + 3*(4480*a^3 - 7360*a^2*b + 43008*a*b^2 - 4515*b^3)*cosh(d*x + c)^5 + 10*(384*a^3 - 960*a^2*b + 3328*a*b^2 - 475*b^3)*cosh(d*x + c)^3 + 15*(32*a^3 - 96*a^2*b + 224*a*b^2 - 61*b^3)*cosh(d*x + c))*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 + 8*d*cosh(d*x + c)^15 + 8*(17*d*cosh(d*x + c)^2 + d)*sinh(d*x + c)^15 + 40*(17*d*cosh(d*x + c)^3 + 3*d*cosh(d*x + c))*sinh(d*x + c)^14 + 28*d*cosh(d*x + c)^13 + 28*(85*d*cosh(d*x + c)^4 + 30*d*cosh(d*x + c)^2 + d)*sinh(d*x + c)^13 + 364*(17*d*cosh(d*x + c)^5 + 10*d*cosh(d*x + c)^3 + d*cosh(d*x + c))*sinh(d*x + c)^12 + 56*d*cosh(d*x + c)^11 + 56*(221*d*cosh(d*x + c)^6 + 195*d*cosh(d*x + c)^4 + 39*d*cosh(d*x + c)^2 + d)*sinh(d*x + c)^11 + 88*(221*d*cosh(d*x + c)^7 + 273*d*cosh(d*x + c)^5 + 91*d*cosh(d*x + c)^3 + 7*d*cosh(d*x + c))*sinh(d*x + c)^10 + 70*d*cosh(d*x + c)^9 + 10*(2431*d*cosh(d*x + c)^8 + 4004*d*cosh(d*x + c)^6 + 2002*d*cosh(d*x + c)^4 + 308*d*cosh(d*x + c)^2 + 7*d)*sinh(d*x + c)^9 + 2*(12155*d*cosh(d*x + c)^9 + 25740*d*cosh(d*x + c)^7 + 18018*d*cosh(d*x + c)^5 + 4620*d*cosh(d*x + c)^3 + 315*d*cosh(d*x + c))*sinh(d*x + c)^8 + 56*d*cosh(d*x + c)^7 + 8*(2431*d*cosh(d*x + c)^10 + 6435*d*cosh(d*x + c)^8 + 6006*d*cosh(d*x + c)^6 + 2310*d*cosh(d*x + c)^4 + 315*d*cosh(d*x + c)^2 + 7*d)*sinh(d*x + c)^7 + 56*(221*d*cosh(d*x + c)^11 + 715*d*cosh(d*x + c)^9 + 858*d*cosh(d*x + c)^7 + 462*d*cosh(d*x + c)^5 + 105*d*cosh(d*x + c)^3 + 7*d*cosh(d*x + c))*sinh(d*x + c)^6 + 28*d*cosh(d*x + c)^5 + 28*(221*d*cosh(d*x + c)^12 + 858*d*cosh(d*x + c)^10 + 1287*d*cosh(d*x + c)^8 + 924*d*cosh(d*x + c)^6 + 315*d*cosh(d*x + c)^4 + 42*d*cosh(d*x + c)^2 + d)*sinh(d*x + c)^5 + 140*(17*d*cosh(d*x + c)^13 + 78*d*cosh(d*x + c)^11 + 143*d*cosh(d*x + c)^9 + 132*d*cosh(d*x + c)^7 + 63*d*cosh(d*x + c)^5 + 14*d*cosh(d*x + c)^3 + d*cosh(d*x + c))*sinh(d*x + c)^4 + 8*d*cosh(d*x + c)^3 + 8*(85*d*cosh(d*x + c)^14 + 455*d*cosh(d*x + c)^12 + 1001*d*cosh(d*x + c)^10 + 1155*d*cosh(d*x + c)^8 + 735*d*cosh(d*x + c)^6 + 245*d*cosh(d*x + c)^4 + 35*d*cosh(d*x + c)^2 + d)*sinh(d*x + c)^3 + 8*(17*d*cosh(d*x + c)^15 + 105*d*cosh(d*x + c)^13 + 273*d*cosh(d*x + c)^11 + 385*d*cosh(d*x + c)^9 + 315*d*cosh(d*x + c)^7 + 147*d*cosh(d*x + c)^5 + 35*d*cosh(d*x + c)^3 + 3*d*cosh(d*x + c))*sinh(d*x + c)^2 + d*cosh(d*x + c) + (17*d*cosh(d*x + c)^16 + 120*d*cosh(d*x + c)^14 + 364*d*cosh(d*x + c)^12 + 616*d*cosh(d*x + c)^10 + 630*d*cosh(d*x + c)^8 + 392*d*cosh(d*x + c)^6 + 140*d*cosh(d*x + c)^4 + 24*d*cosh(d*x + c)^2 + d)*sinh(d*x + c))","B",0
69,1,7127,0,0.550234," ","integrate(csch(d*x+c)*(a+b*tanh(d*x+c)^3)^3,x, algorithm=""fricas"")","-\frac{45 \, {\left(64 \, a^{2} b + 128 \, a b^{2} + 31 \, b^{3}\right)} \cosh\left(d x + c\right)^{15} + 675 \, {\left(64 \, a^{2} b + 128 \, a b^{2} + 31 \, b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{14} + 45 \, {\left(64 \, a^{2} b + 128 \, a b^{2} + 31 \, b^{3}\right)} \sinh\left(d x + c\right)^{15} + 5 \, {\left(2880 \, a^{2} b + 4992 \, a b^{2} + 91 \, b^{3}\right)} \cosh\left(d x + c\right)^{13} + 5 \, {\left(2880 \, a^{2} b + 4992 \, a b^{2} + 91 \, b^{3} + 945 \, {\left(64 \, a^{2} b + 128 \, a b^{2} + 31 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{13} + 65 \, {\left(315 \, {\left(64 \, a^{2} b + 128 \, a b^{2} + 31 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(2880 \, a^{2} b + 4992 \, a b^{2} + 91 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{12} + {\left(25920 \, a^{2} b + 62592 \, a b^{2} + 8995 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} + {\left(61425 \, {\left(64 \, a^{2} b + 128 \, a b^{2} + 31 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 25920 \, a^{2} b + 62592 \, a b^{2} + 8995 \, b^{3} + 390 \, {\left(2880 \, a^{2} b + 4992 \, a b^{2} + 91 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{11} + 11 \, {\left(12285 \, {\left(64 \, a^{2} b + 128 \, a b^{2} + 31 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 130 \, {\left(2880 \, a^{2} b + 4992 \, a b^{2} + 91 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(25920 \, a^{2} b + 62592 \, a b^{2} + 8995 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{10} + {\left(14400 \, a^{2} b + 103296 \, a b^{2} - 5425 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + {\left(225225 \, {\left(64 \, a^{2} b + 128 \, a b^{2} + 31 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 3575 \, {\left(2880 \, a^{2} b + 4992 \, a b^{2} + 91 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 14400 \, a^{2} b + 103296 \, a b^{2} - 5425 \, b^{3} + 55 \, {\left(25920 \, a^{2} b + 62592 \, a b^{2} + 8995 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{9} + 3 \, {\left(96525 \, {\left(64 \, a^{2} b + 128 \, a b^{2} + 31 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 2145 \, {\left(2880 \, a^{2} b + 4992 \, a b^{2} + 91 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 55 \, {\left(25920 \, a^{2} b + 62592 \, a b^{2} + 8995 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(14400 \, a^{2} b + 103296 \, a b^{2} - 5425 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{8} - {\left(14400 \, a^{2} b - 103296 \, a b^{2} - 5425 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + {\left(289575 \, {\left(64 \, a^{2} b + 128 \, a b^{2} + 31 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 8580 \, {\left(2880 \, a^{2} b + 4992 \, a b^{2} + 91 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 330 \, {\left(25920 \, a^{2} b + 62592 \, a b^{2} + 8995 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 14400 \, a^{2} b + 103296 \, a b^{2} + 5425 \, b^{3} + 36 \, {\left(14400 \, a^{2} b + 103296 \, a b^{2} - 5425 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{7} + {\left(225225 \, {\left(64 \, a^{2} b + 128 \, a b^{2} + 31 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + 8580 \, {\left(2880 \, a^{2} b + 4992 \, a b^{2} + 91 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 462 \, {\left(25920 \, a^{2} b + 62592 \, a b^{2} + 8995 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 84 \, {\left(14400 \, a^{2} b + 103296 \, a b^{2} - 5425 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 7 \, {\left(14400 \, a^{2} b - 103296 \, a b^{2} - 5425 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} - {\left(25920 \, a^{2} b - 62592 \, a b^{2} + 8995 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + {\left(135135 \, {\left(64 \, a^{2} b + 128 \, a b^{2} + 31 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} + 6435 \, {\left(2880 \, a^{2} b + 4992 \, a b^{2} + 91 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 462 \, {\left(25920 \, a^{2} b + 62592 \, a b^{2} + 8995 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 126 \, {\left(14400 \, a^{2} b + 103296 \, a b^{2} - 5425 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 25920 \, a^{2} b + 62592 \, a b^{2} - 8995 \, b^{3} - 21 \, {\left(14400 \, a^{2} b - 103296 \, a b^{2} - 5425 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{5} + {\left(61425 \, {\left(64 \, a^{2} b + 128 \, a b^{2} + 31 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} + 3575 \, {\left(2880 \, a^{2} b + 4992 \, a b^{2} + 91 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + 330 \, {\left(25920 \, a^{2} b + 62592 \, a b^{2} + 8995 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 126 \, {\left(14400 \, a^{2} b + 103296 \, a b^{2} - 5425 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 35 \, {\left(14400 \, a^{2} b - 103296 \, a b^{2} - 5425 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 5 \, {\left(25920 \, a^{2} b - 62592 \, a b^{2} + 8995 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} - 5 \, {\left(2880 \, a^{2} b - 4992 \, a b^{2} + 91 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(20475 \, {\left(64 \, a^{2} b + 128 \, a b^{2} + 31 \, b^{3}\right)} \cosh\left(d x + c\right)^{12} + 1430 \, {\left(2880 \, a^{2} b + 4992 \, a b^{2} + 91 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} + 165 \, {\left(25920 \, a^{2} b + 62592 \, a b^{2} + 8995 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 84 \, {\left(14400 \, a^{2} b + 103296 \, a b^{2} - 5425 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} - 35 \, {\left(14400 \, a^{2} b - 103296 \, a b^{2} - 5425 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 14400 \, a^{2} b + 24960 \, a b^{2} - 455 \, b^{3} - 10 \, {\left(25920 \, a^{2} b - 62592 \, a b^{2} + 8995 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + {\left(4725 \, {\left(64 \, a^{2} b + 128 \, a b^{2} + 31 \, b^{3}\right)} \cosh\left(d x + c\right)^{13} + 390 \, {\left(2880 \, a^{2} b + 4992 \, a b^{2} + 91 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} + 55 \, {\left(25920 \, a^{2} b + 62592 \, a b^{2} + 8995 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + 36 \, {\left(14400 \, a^{2} b + 103296 \, a b^{2} - 5425 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} - 21 \, {\left(14400 \, a^{2} b - 103296 \, a b^{2} - 5425 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 10 \, {\left(25920 \, a^{2} b - 62592 \, a b^{2} + 8995 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 15 \, {\left(2880 \, a^{2} b - 4992 \, a b^{2} + 91 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 15 \, {\left({\left(192 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{16} + 16 \, {\left(192 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{15} + {\left(192 \, a^{2} b + 35 \, b^{3}\right)} \sinh\left(d x + c\right)^{16} + 8 \, {\left(192 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{14} + 8 \, {\left(192 \, a^{2} b + 35 \, b^{3} + 15 \, {\left(192 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{14} + 112 \, {\left(5 \, {\left(192 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(192 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{13} + 28 \, {\left(192 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{12} + 28 \, {\left(65 \, {\left(192 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 192 \, a^{2} b + 35 \, b^{3} + 26 \, {\left(192 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{12} + 112 \, {\left(39 \, {\left(192 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 26 \, {\left(192 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(192 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{11} + 56 \, {\left(192 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} + 56 \, {\left(143 \, {\left(192 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 143 \, {\left(192 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 192 \, a^{2} b + 35 \, b^{3} + 33 \, {\left(192 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{10} + 16 \, {\left(715 \, {\left(192 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 1001 \, {\left(192 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 385 \, {\left(192 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 35 \, {\left(192 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} + 70 \, {\left(192 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 2 \, {\left(6435 \, {\left(192 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 12012 \, {\left(192 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 6930 \, {\left(192 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 6720 \, a^{2} b + 1225 \, b^{3} + 1260 \, {\left(192 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{8} + 16 \, {\left(715 \, {\left(192 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + 1716 \, {\left(192 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 1386 \, {\left(192 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 420 \, {\left(192 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 35 \, {\left(192 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 56 \, {\left(192 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 56 \, {\left(143 \, {\left(192 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} + 429 \, {\left(192 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 462 \, {\left(192 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 210 \, {\left(192 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 192 \, a^{2} b + 35 \, b^{3} + 35 \, {\left(192 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 112 \, {\left(39 \, {\left(192 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} + 143 \, {\left(192 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + 198 \, {\left(192 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 126 \, {\left(192 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 35 \, {\left(192 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(192 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 28 \, {\left(192 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 28 \, {\left(65 \, {\left(192 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{12} + 286 \, {\left(192 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} + 495 \, {\left(192 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 420 \, {\left(192 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 175 \, {\left(192 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 192 \, a^{2} b + 35 \, b^{3} + 30 \, {\left(192 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 112 \, {\left(5 \, {\left(192 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{13} + 26 \, {\left(192 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} + 55 \, {\left(192 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + 60 \, {\left(192 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 35 \, {\left(192 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(192 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(192 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 192 \, a^{2} b + 35 \, b^{3} + 8 \, {\left(192 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{2} + 8 \, {\left(15 \, {\left(192 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{14} + 91 \, {\left(192 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{12} + 231 \, {\left(192 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} + 315 \, {\left(192 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 245 \, {\left(192 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 105 \, {\left(192 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 192 \, a^{2} b + 35 \, b^{3} + 21 \, {\left(192 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 16 \, {\left({\left(192 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{15} + 7 \, {\left(192 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{13} + 21 \, {\left(192 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} + 35 \, {\left(192 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + 35 \, {\left(192 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 21 \, {\left(192 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 7 \, {\left(192 \, a^{2} b + 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(192 \, a^{2} b + 35 \, 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) - 45 \, {\left(64 \, a^{2} b - 128 \, a b^{2} + 31 \, b^{3}\right)} \cosh\left(d x + c\right) + 960 \, {\left(a^{3} \cosh\left(d x + c\right)^{16} + 16 \, a^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{15} + a^{3} \sinh\left(d x + c\right)^{16} + 8 \, a^{3} \cosh\left(d x + c\right)^{14} + 28 \, a^{3} \cosh\left(d x + c\right)^{12} + 8 \, {\left(15 \, a^{3} \cosh\left(d x + c\right)^{2} + a^{3}\right)} \sinh\left(d x + c\right)^{14} + 112 \, {\left(5 \, a^{3} \cosh\left(d x + c\right)^{3} + a^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{13} + 56 \, a^{3} \cosh\left(d x + c\right)^{10} + 28 \, {\left(65 \, a^{3} \cosh\left(d x + c\right)^{4} + 26 \, a^{3} \cosh\left(d x + c\right)^{2} + a^{3}\right)} \sinh\left(d x + c\right)^{12} + 112 \, {\left(39 \, a^{3} \cosh\left(d x + c\right)^{5} + 26 \, 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)^{11} + 70 \, a^{3} \cosh\left(d x + c\right)^{8} + 56 \, {\left(143 \, a^{3} \cosh\left(d x + c\right)^{6} + 143 \, a^{3} \cosh\left(d x + c\right)^{4} + 33 \, a^{3} \cosh\left(d x + c\right)^{2} + a^{3}\right)} \sinh\left(d x + c\right)^{10} + 16 \, {\left(715 \, a^{3} \cosh\left(d x + c\right)^{7} + 1001 \, a^{3} \cosh\left(d x + c\right)^{5} + 385 \, a^{3} \cosh\left(d x + c\right)^{3} + 35 \, a^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} + 56 \, a^{3} \cosh\left(d x + c\right)^{6} + 2 \, {\left(6435 \, a^{3} \cosh\left(d x + c\right)^{8} + 12012 \, a^{3} \cosh\left(d x + c\right)^{6} + 6930 \, a^{3} \cosh\left(d x + c\right)^{4} + 1260 \, a^{3} \cosh\left(d x + c\right)^{2} + 35 \, a^{3}\right)} \sinh\left(d x + c\right)^{8} + 16 \, {\left(715 \, a^{3} \cosh\left(d x + c\right)^{9} + 1716 \, a^{3} \cosh\left(d x + c\right)^{7} + 1386 \, a^{3} \cosh\left(d x + c\right)^{5} + 420 \, a^{3} \cosh\left(d x + c\right)^{3} + 35 \, a^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 28 \, a^{3} \cosh\left(d x + c\right)^{4} + 56 \, {\left(143 \, a^{3} \cosh\left(d x + c\right)^{10} + 429 \, a^{3} \cosh\left(d x + c\right)^{8} + 462 \, a^{3} \cosh\left(d x + c\right)^{6} + 210 \, a^{3} \cosh\left(d x + c\right)^{4} + 35 \, a^{3} \cosh\left(d x + c\right)^{2} + a^{3}\right)} \sinh\left(d x + c\right)^{6} + 112 \, {\left(39 \, a^{3} \cosh\left(d x + c\right)^{11} + 143 \, a^{3} \cosh\left(d x + c\right)^{9} + 198 \, a^{3} \cosh\left(d x + c\right)^{7} + 126 \, a^{3} \cosh\left(d x + c\right)^{5} + 35 \, 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} + 8 \, a^{3} \cosh\left(d x + c\right)^{2} + 28 \, {\left(65 \, a^{3} \cosh\left(d x + c\right)^{12} + 286 \, a^{3} \cosh\left(d x + c\right)^{10} + 495 \, a^{3} \cosh\left(d x + c\right)^{8} + 420 \, a^{3} \cosh\left(d x + c\right)^{6} + 175 \, a^{3} \cosh\left(d x + c\right)^{4} + 30 \, a^{3} \cosh\left(d x + c\right)^{2} + a^{3}\right)} \sinh\left(d x + c\right)^{4} + 112 \, {\left(5 \, a^{3} \cosh\left(d x + c\right)^{13} + 26 \, a^{3} \cosh\left(d x + c\right)^{11} + 55 \, a^{3} \cosh\left(d x + c\right)^{9} + 60 \, a^{3} \cosh\left(d x + c\right)^{7} + 35 \, a^{3} \cosh\left(d x + c\right)^{5} + 10 \, 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} + a^{3} + 8 \, {\left(15 \, a^{3} \cosh\left(d x + c\right)^{14} + 91 \, a^{3} \cosh\left(d x + c\right)^{12} + 231 \, a^{3} \cosh\left(d x + c\right)^{10} + 315 \, a^{3} \cosh\left(d x + c\right)^{8} + 245 \, a^{3} \cosh\left(d x + c\right)^{6} + 105 \, a^{3} \cosh\left(d x + c\right)^{4} + 21 \, a^{3} \cosh\left(d x + c\right)^{2} + a^{3}\right)} \sinh\left(d x + c\right)^{2} + 16 \, {\left(a^{3} \cosh\left(d x + c\right)^{15} + 7 \, a^{3} \cosh\left(d x + c\right)^{13} + 21 \, a^{3} \cosh\left(d x + c\right)^{11} + 35 \, a^{3} \cosh\left(d x + c\right)^{9} + 35 \, a^{3} \cosh\left(d x + c\right)^{7} + 21 \, a^{3} \cosh\left(d x + c\right)^{5} + 7 \, a^{3} \cosh\left(d x + c\right)^{3} + a^{3} \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) - 960 \, {\left(a^{3} \cosh\left(d x + c\right)^{16} + 16 \, a^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{15} + a^{3} \sinh\left(d x + c\right)^{16} + 8 \, a^{3} \cosh\left(d x + c\right)^{14} + 28 \, a^{3} \cosh\left(d x + c\right)^{12} + 8 \, {\left(15 \, a^{3} \cosh\left(d x + c\right)^{2} + a^{3}\right)} \sinh\left(d x + c\right)^{14} + 112 \, {\left(5 \, a^{3} \cosh\left(d x + c\right)^{3} + a^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{13} + 56 \, a^{3} \cosh\left(d x + c\right)^{10} + 28 \, {\left(65 \, a^{3} \cosh\left(d x + c\right)^{4} + 26 \, a^{3} \cosh\left(d x + c\right)^{2} + a^{3}\right)} \sinh\left(d x + c\right)^{12} + 112 \, {\left(39 \, a^{3} \cosh\left(d x + c\right)^{5} + 26 \, 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)^{11} + 70 \, a^{3} \cosh\left(d x + c\right)^{8} + 56 \, {\left(143 \, a^{3} \cosh\left(d x + c\right)^{6} + 143 \, a^{3} \cosh\left(d x + c\right)^{4} + 33 \, a^{3} \cosh\left(d x + c\right)^{2} + a^{3}\right)} \sinh\left(d x + c\right)^{10} + 16 \, {\left(715 \, a^{3} \cosh\left(d x + c\right)^{7} + 1001 \, a^{3} \cosh\left(d x + c\right)^{5} + 385 \, a^{3} \cosh\left(d x + c\right)^{3} + 35 \, a^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} + 56 \, a^{3} \cosh\left(d x + c\right)^{6} + 2 \, {\left(6435 \, a^{3} \cosh\left(d x + c\right)^{8} + 12012 \, a^{3} \cosh\left(d x + c\right)^{6} + 6930 \, a^{3} \cosh\left(d x + c\right)^{4} + 1260 \, a^{3} \cosh\left(d x + c\right)^{2} + 35 \, a^{3}\right)} \sinh\left(d x + c\right)^{8} + 16 \, {\left(715 \, a^{3} \cosh\left(d x + c\right)^{9} + 1716 \, a^{3} \cosh\left(d x + c\right)^{7} + 1386 \, a^{3} \cosh\left(d x + c\right)^{5} + 420 \, a^{3} \cosh\left(d x + c\right)^{3} + 35 \, a^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 28 \, a^{3} \cosh\left(d x + c\right)^{4} + 56 \, {\left(143 \, a^{3} \cosh\left(d x + c\right)^{10} + 429 \, a^{3} \cosh\left(d x + c\right)^{8} + 462 \, a^{3} \cosh\left(d x + c\right)^{6} + 210 \, a^{3} \cosh\left(d x + c\right)^{4} + 35 \, a^{3} \cosh\left(d x + c\right)^{2} + a^{3}\right)} \sinh\left(d x + c\right)^{6} + 112 \, {\left(39 \, a^{3} \cosh\left(d x + c\right)^{11} + 143 \, a^{3} \cosh\left(d x + c\right)^{9} + 198 \, a^{3} \cosh\left(d x + c\right)^{7} + 126 \, a^{3} \cosh\left(d x + c\right)^{5} + 35 \, 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} + 8 \, a^{3} \cosh\left(d x + c\right)^{2} + 28 \, {\left(65 \, a^{3} \cosh\left(d x + c\right)^{12} + 286 \, a^{3} \cosh\left(d x + c\right)^{10} + 495 \, a^{3} \cosh\left(d x + c\right)^{8} + 420 \, a^{3} \cosh\left(d x + c\right)^{6} + 175 \, a^{3} \cosh\left(d x + c\right)^{4} + 30 \, a^{3} \cosh\left(d x + c\right)^{2} + a^{3}\right)} \sinh\left(d x + c\right)^{4} + 112 \, {\left(5 \, a^{3} \cosh\left(d x + c\right)^{13} + 26 \, a^{3} \cosh\left(d x + c\right)^{11} + 55 \, a^{3} \cosh\left(d x + c\right)^{9} + 60 \, a^{3} \cosh\left(d x + c\right)^{7} + 35 \, a^{3} \cosh\left(d x + c\right)^{5} + 10 \, 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} + a^{3} + 8 \, {\left(15 \, a^{3} \cosh\left(d x + c\right)^{14} + 91 \, a^{3} \cosh\left(d x + c\right)^{12} + 231 \, a^{3} \cosh\left(d x + c\right)^{10} + 315 \, a^{3} \cosh\left(d x + c\right)^{8} + 245 \, a^{3} \cosh\left(d x + c\right)^{6} + 105 \, a^{3} \cosh\left(d x + c\right)^{4} + 21 \, a^{3} \cosh\left(d x + c\right)^{2} + a^{3}\right)} \sinh\left(d x + c\right)^{2} + 16 \, {\left(a^{3} \cosh\left(d x + c\right)^{15} + 7 \, a^{3} \cosh\left(d x + c\right)^{13} + 21 \, a^{3} \cosh\left(d x + c\right)^{11} + 35 \, a^{3} \cosh\left(d x + c\right)^{9} + 35 \, a^{3} \cosh\left(d x + c\right)^{7} + 21 \, a^{3} \cosh\left(d x + c\right)^{5} + 7 \, a^{3} \cosh\left(d x + c\right)^{3} + a^{3} \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(675 \, {\left(64 \, a^{2} b + 128 \, a b^{2} + 31 \, b^{3}\right)} \cosh\left(d x + c\right)^{14} + 65 \, {\left(2880 \, a^{2} b + 4992 \, a b^{2} + 91 \, b^{3}\right)} \cosh\left(d x + c\right)^{12} + 11 \, {\left(25920 \, a^{2} b + 62592 \, a b^{2} + 8995 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} + 9 \, {\left(14400 \, a^{2} b + 103296 \, a b^{2} - 5425 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} - 7 \, {\left(14400 \, a^{2} b - 103296 \, a b^{2} - 5425 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} - 5 \, {\left(25920 \, a^{2} b - 62592 \, a b^{2} + 8995 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 2880 \, a^{2} b + 5760 \, a b^{2} - 1395 \, b^{3} - 15 \, {\left(2880 \, a^{2} b - 4992 \, a b^{2} + 91 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)}{960 \, {\left(d \cosh\left(d x + c\right)^{16} + 16 \, d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{15} + d \sinh\left(d x + c\right)^{16} + 8 \, d \cosh\left(d x + c\right)^{14} + 8 \, {\left(15 \, d \cosh\left(d x + c\right)^{2} + d\right)} \sinh\left(d x + c\right)^{14} + 112 \, {\left(5 \, d \cosh\left(d x + c\right)^{3} + d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{13} + 28 \, d \cosh\left(d x + c\right)^{12} + 28 \, {\left(65 \, d \cosh\left(d x + c\right)^{4} + 26 \, d \cosh\left(d x + c\right)^{2} + d\right)} \sinh\left(d x + c\right)^{12} + 112 \, {\left(39 \, d \cosh\left(d x + c\right)^{5} + 26 \, d \cosh\left(d x + c\right)^{3} + 3 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{11} + 56 \, d \cosh\left(d x + c\right)^{10} + 56 \, {\left(143 \, d \cosh\left(d x + c\right)^{6} + 143 \, d \cosh\left(d x + c\right)^{4} + 33 \, d \cosh\left(d x + c\right)^{2} + d\right)} \sinh\left(d x + c\right)^{10} + 16 \, {\left(715 \, d \cosh\left(d x + c\right)^{7} + 1001 \, d \cosh\left(d x + c\right)^{5} + 385 \, d \cosh\left(d x + c\right)^{3} + 35 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} + 70 \, d \cosh\left(d x + c\right)^{8} + 2 \, {\left(6435 \, d \cosh\left(d x + c\right)^{8} + 12012 \, d \cosh\left(d x + c\right)^{6} + 6930 \, d \cosh\left(d x + c\right)^{4} + 1260 \, d \cosh\left(d x + c\right)^{2} + 35 \, d\right)} \sinh\left(d x + c\right)^{8} + 16 \, {\left(715 \, d \cosh\left(d x + c\right)^{9} + 1716 \, d \cosh\left(d x + c\right)^{7} + 1386 \, 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)^{7} + 56 \, d \cosh\left(d x + c\right)^{6} + 56 \, {\left(143 \, d \cosh\left(d x + c\right)^{10} + 429 \, d \cosh\left(d x + c\right)^{8} + 462 \, d \cosh\left(d x + c\right)^{6} + 210 \, d \cosh\left(d x + c\right)^{4} + 35 \, d \cosh\left(d x + c\right)^{2} + d\right)} \sinh\left(d x + c\right)^{6} + 112 \, {\left(39 \, d \cosh\left(d x + c\right)^{11} + 143 \, d \cosh\left(d x + c\right)^{9} + 198 \, d \cosh\left(d x + c\right)^{7} + 126 \, d \cosh\left(d x + c\right)^{5} + 35 \, d \cosh\left(d x + c\right)^{3} + 3 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 28 \, d \cosh\left(d x + c\right)^{4} + 28 \, {\left(65 \, d \cosh\left(d x + c\right)^{12} + 286 \, d \cosh\left(d x + c\right)^{10} + 495 \, d \cosh\left(d x + c\right)^{8} + 420 \, d \cosh\left(d x + c\right)^{6} + 175 \, d \cosh\left(d x + c\right)^{4} + 30 \, d \cosh\left(d x + c\right)^{2} + d\right)} \sinh\left(d x + c\right)^{4} + 112 \, {\left(5 \, d \cosh\left(d x + c\right)^{13} + 26 \, d \cosh\left(d x + c\right)^{11} + 55 \, d \cosh\left(d x + c\right)^{9} + 60 \, d \cosh\left(d x + c\right)^{7} + 35 \, d \cosh\left(d x + c\right)^{5} + 10 \, d \cosh\left(d x + c\right)^{3} + d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 8 \, d \cosh\left(d x + c\right)^{2} + 8 \, {\left(15 \, d \cosh\left(d x + c\right)^{14} + 91 \, d \cosh\left(d x + c\right)^{12} + 231 \, d \cosh\left(d x + c\right)^{10} + 315 \, d \cosh\left(d x + c\right)^{8} + 245 \, d \cosh\left(d x + c\right)^{6} + 105 \, d \cosh\left(d x + c\right)^{4} + 21 \, d \cosh\left(d x + c\right)^{2} + d\right)} \sinh\left(d x + c\right)^{2} + 16 \, {\left(d \cosh\left(d x + c\right)^{15} + 7 \, d \cosh\left(d x + c\right)^{13} + 21 \, d \cosh\left(d x + c\right)^{11} + 35 \, d \cosh\left(d x + c\right)^{9} + 35 \, d \cosh\left(d x + c\right)^{7} + 21 \, d \cosh\left(d x + c\right)^{5} + 7 \, 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,"-1/960*(45*(64*a^2*b + 128*a*b^2 + 31*b^3)*cosh(d*x + c)^15 + 675*(64*a^2*b + 128*a*b^2 + 31*b^3)*cosh(d*x + c)*sinh(d*x + c)^14 + 45*(64*a^2*b + 128*a*b^2 + 31*b^3)*sinh(d*x + c)^15 + 5*(2880*a^2*b + 4992*a*b^2 + 91*b^3)*cosh(d*x + c)^13 + 5*(2880*a^2*b + 4992*a*b^2 + 91*b^3 + 945*(64*a^2*b + 128*a*b^2 + 31*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^13 + 65*(315*(64*a^2*b + 128*a*b^2 + 31*b^3)*cosh(d*x + c)^3 + (2880*a^2*b + 4992*a*b^2 + 91*b^3)*cosh(d*x + c))*sinh(d*x + c)^12 + (25920*a^2*b + 62592*a*b^2 + 8995*b^3)*cosh(d*x + c)^11 + (61425*(64*a^2*b + 128*a*b^2 + 31*b^3)*cosh(d*x + c)^4 + 25920*a^2*b + 62592*a*b^2 + 8995*b^3 + 390*(2880*a^2*b + 4992*a*b^2 + 91*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^11 + 11*(12285*(64*a^2*b + 128*a*b^2 + 31*b^3)*cosh(d*x + c)^5 + 130*(2880*a^2*b + 4992*a*b^2 + 91*b^3)*cosh(d*x + c)^3 + (25920*a^2*b + 62592*a*b^2 + 8995*b^3)*cosh(d*x + c))*sinh(d*x + c)^10 + (14400*a^2*b + 103296*a*b^2 - 5425*b^3)*cosh(d*x + c)^9 + (225225*(64*a^2*b + 128*a*b^2 + 31*b^3)*cosh(d*x + c)^6 + 3575*(2880*a^2*b + 4992*a*b^2 + 91*b^3)*cosh(d*x + c)^4 + 14400*a^2*b + 103296*a*b^2 - 5425*b^3 + 55*(25920*a^2*b + 62592*a*b^2 + 8995*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^9 + 3*(96525*(64*a^2*b + 128*a*b^2 + 31*b^3)*cosh(d*x + c)^7 + 2145*(2880*a^2*b + 4992*a*b^2 + 91*b^3)*cosh(d*x + c)^5 + 55*(25920*a^2*b + 62592*a*b^2 + 8995*b^3)*cosh(d*x + c)^3 + 3*(14400*a^2*b + 103296*a*b^2 - 5425*b^3)*cosh(d*x + c))*sinh(d*x + c)^8 - (14400*a^2*b - 103296*a*b^2 - 5425*b^3)*cosh(d*x + c)^7 + (289575*(64*a^2*b + 128*a*b^2 + 31*b^3)*cosh(d*x + c)^8 + 8580*(2880*a^2*b + 4992*a*b^2 + 91*b^3)*cosh(d*x + c)^6 + 330*(25920*a^2*b + 62592*a*b^2 + 8995*b^3)*cosh(d*x + c)^4 - 14400*a^2*b + 103296*a*b^2 + 5425*b^3 + 36*(14400*a^2*b + 103296*a*b^2 - 5425*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^7 + (225225*(64*a^2*b + 128*a*b^2 + 31*b^3)*cosh(d*x + c)^9 + 8580*(2880*a^2*b + 4992*a*b^2 + 91*b^3)*cosh(d*x + c)^7 + 462*(25920*a^2*b + 62592*a*b^2 + 8995*b^3)*cosh(d*x + c)^5 + 84*(14400*a^2*b + 103296*a*b^2 - 5425*b^3)*cosh(d*x + c)^3 - 7*(14400*a^2*b - 103296*a*b^2 - 5425*b^3)*cosh(d*x + c))*sinh(d*x + c)^6 - (25920*a^2*b - 62592*a*b^2 + 8995*b^3)*cosh(d*x + c)^5 + (135135*(64*a^2*b + 128*a*b^2 + 31*b^3)*cosh(d*x + c)^10 + 6435*(2880*a^2*b + 4992*a*b^2 + 91*b^3)*cosh(d*x + c)^8 + 462*(25920*a^2*b + 62592*a*b^2 + 8995*b^3)*cosh(d*x + c)^6 + 126*(14400*a^2*b + 103296*a*b^2 - 5425*b^3)*cosh(d*x + c)^4 - 25920*a^2*b + 62592*a*b^2 - 8995*b^3 - 21*(14400*a^2*b - 103296*a*b^2 - 5425*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + (61425*(64*a^2*b + 128*a*b^2 + 31*b^3)*cosh(d*x + c)^11 + 3575*(2880*a^2*b + 4992*a*b^2 + 91*b^3)*cosh(d*x + c)^9 + 330*(25920*a^2*b + 62592*a*b^2 + 8995*b^3)*cosh(d*x + c)^7 + 126*(14400*a^2*b + 103296*a*b^2 - 5425*b^3)*cosh(d*x + c)^5 - 35*(14400*a^2*b - 103296*a*b^2 - 5425*b^3)*cosh(d*x + c)^3 - 5*(25920*a^2*b - 62592*a*b^2 + 8995*b^3)*cosh(d*x + c))*sinh(d*x + c)^4 - 5*(2880*a^2*b - 4992*a*b^2 + 91*b^3)*cosh(d*x + c)^3 + (20475*(64*a^2*b + 128*a*b^2 + 31*b^3)*cosh(d*x + c)^12 + 1430*(2880*a^2*b + 4992*a*b^2 + 91*b^3)*cosh(d*x + c)^10 + 165*(25920*a^2*b + 62592*a*b^2 + 8995*b^3)*cosh(d*x + c)^8 + 84*(14400*a^2*b + 103296*a*b^2 - 5425*b^3)*cosh(d*x + c)^6 - 35*(14400*a^2*b - 103296*a*b^2 - 5425*b^3)*cosh(d*x + c)^4 - 14400*a^2*b + 24960*a*b^2 - 455*b^3 - 10*(25920*a^2*b - 62592*a*b^2 + 8995*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + (4725*(64*a^2*b + 128*a*b^2 + 31*b^3)*cosh(d*x + c)^13 + 390*(2880*a^2*b + 4992*a*b^2 + 91*b^3)*cosh(d*x + c)^11 + 55*(25920*a^2*b + 62592*a*b^2 + 8995*b^3)*cosh(d*x + c)^9 + 36*(14400*a^2*b + 103296*a*b^2 - 5425*b^3)*cosh(d*x + c)^7 - 21*(14400*a^2*b - 103296*a*b^2 - 5425*b^3)*cosh(d*x + c)^5 - 10*(25920*a^2*b - 62592*a*b^2 + 8995*b^3)*cosh(d*x + c)^3 - 15*(2880*a^2*b - 4992*a*b^2 + 91*b^3)*cosh(d*x + c))*sinh(d*x + c)^2 - 15*((192*a^2*b + 35*b^3)*cosh(d*x + c)^16 + 16*(192*a^2*b + 35*b^3)*cosh(d*x + c)*sinh(d*x + c)^15 + (192*a^2*b + 35*b^3)*sinh(d*x + c)^16 + 8*(192*a^2*b + 35*b^3)*cosh(d*x + c)^14 + 8*(192*a^2*b + 35*b^3 + 15*(192*a^2*b + 35*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^14 + 112*(5*(192*a^2*b + 35*b^3)*cosh(d*x + c)^3 + (192*a^2*b + 35*b^3)*cosh(d*x + c))*sinh(d*x + c)^13 + 28*(192*a^2*b + 35*b^3)*cosh(d*x + c)^12 + 28*(65*(192*a^2*b + 35*b^3)*cosh(d*x + c)^4 + 192*a^2*b + 35*b^3 + 26*(192*a^2*b + 35*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^12 + 112*(39*(192*a^2*b + 35*b^3)*cosh(d*x + c)^5 + 26*(192*a^2*b + 35*b^3)*cosh(d*x + c)^3 + 3*(192*a^2*b + 35*b^3)*cosh(d*x + c))*sinh(d*x + c)^11 + 56*(192*a^2*b + 35*b^3)*cosh(d*x + c)^10 + 56*(143*(192*a^2*b + 35*b^3)*cosh(d*x + c)^6 + 143*(192*a^2*b + 35*b^3)*cosh(d*x + c)^4 + 192*a^2*b + 35*b^3 + 33*(192*a^2*b + 35*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^10 + 16*(715*(192*a^2*b + 35*b^3)*cosh(d*x + c)^7 + 1001*(192*a^2*b + 35*b^3)*cosh(d*x + c)^5 + 385*(192*a^2*b + 35*b^3)*cosh(d*x + c)^3 + 35*(192*a^2*b + 35*b^3)*cosh(d*x + c))*sinh(d*x + c)^9 + 70*(192*a^2*b + 35*b^3)*cosh(d*x + c)^8 + 2*(6435*(192*a^2*b + 35*b^3)*cosh(d*x + c)^8 + 12012*(192*a^2*b + 35*b^3)*cosh(d*x + c)^6 + 6930*(192*a^2*b + 35*b^3)*cosh(d*x + c)^4 + 6720*a^2*b + 1225*b^3 + 1260*(192*a^2*b + 35*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 16*(715*(192*a^2*b + 35*b^3)*cosh(d*x + c)^9 + 1716*(192*a^2*b + 35*b^3)*cosh(d*x + c)^7 + 1386*(192*a^2*b + 35*b^3)*cosh(d*x + c)^5 + 420*(192*a^2*b + 35*b^3)*cosh(d*x + c)^3 + 35*(192*a^2*b + 35*b^3)*cosh(d*x + c))*sinh(d*x + c)^7 + 56*(192*a^2*b + 35*b^3)*cosh(d*x + c)^6 + 56*(143*(192*a^2*b + 35*b^3)*cosh(d*x + c)^10 + 429*(192*a^2*b + 35*b^3)*cosh(d*x + c)^8 + 462*(192*a^2*b + 35*b^3)*cosh(d*x + c)^6 + 210*(192*a^2*b + 35*b^3)*cosh(d*x + c)^4 + 192*a^2*b + 35*b^3 + 35*(192*a^2*b + 35*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 112*(39*(192*a^2*b + 35*b^3)*cosh(d*x + c)^11 + 143*(192*a^2*b + 35*b^3)*cosh(d*x + c)^9 + 198*(192*a^2*b + 35*b^3)*cosh(d*x + c)^7 + 126*(192*a^2*b + 35*b^3)*cosh(d*x + c)^5 + 35*(192*a^2*b + 35*b^3)*cosh(d*x + c)^3 + 3*(192*a^2*b + 35*b^3)*cosh(d*x + c))*sinh(d*x + c)^5 + 28*(192*a^2*b + 35*b^3)*cosh(d*x + c)^4 + 28*(65*(192*a^2*b + 35*b^3)*cosh(d*x + c)^12 + 286*(192*a^2*b + 35*b^3)*cosh(d*x + c)^10 + 495*(192*a^2*b + 35*b^3)*cosh(d*x + c)^8 + 420*(192*a^2*b + 35*b^3)*cosh(d*x + c)^6 + 175*(192*a^2*b + 35*b^3)*cosh(d*x + c)^4 + 192*a^2*b + 35*b^3 + 30*(192*a^2*b + 35*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 112*(5*(192*a^2*b + 35*b^3)*cosh(d*x + c)^13 + 26*(192*a^2*b + 35*b^3)*cosh(d*x + c)^11 + 55*(192*a^2*b + 35*b^3)*cosh(d*x + c)^9 + 60*(192*a^2*b + 35*b^3)*cosh(d*x + c)^7 + 35*(192*a^2*b + 35*b^3)*cosh(d*x + c)^5 + 10*(192*a^2*b + 35*b^3)*cosh(d*x + c)^3 + (192*a^2*b + 35*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 + 192*a^2*b + 35*b^3 + 8*(192*a^2*b + 35*b^3)*cosh(d*x + c)^2 + 8*(15*(192*a^2*b + 35*b^3)*cosh(d*x + c)^14 + 91*(192*a^2*b + 35*b^3)*cosh(d*x + c)^12 + 231*(192*a^2*b + 35*b^3)*cosh(d*x + c)^10 + 315*(192*a^2*b + 35*b^3)*cosh(d*x + c)^8 + 245*(192*a^2*b + 35*b^3)*cosh(d*x + c)^6 + 105*(192*a^2*b + 35*b^3)*cosh(d*x + c)^4 + 192*a^2*b + 35*b^3 + 21*(192*a^2*b + 35*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 16*((192*a^2*b + 35*b^3)*cosh(d*x + c)^15 + 7*(192*a^2*b + 35*b^3)*cosh(d*x + c)^13 + 21*(192*a^2*b + 35*b^3)*cosh(d*x + c)^11 + 35*(192*a^2*b + 35*b^3)*cosh(d*x + c)^9 + 35*(192*a^2*b + 35*b^3)*cosh(d*x + c)^7 + 21*(192*a^2*b + 35*b^3)*cosh(d*x + c)^5 + 7*(192*a^2*b + 35*b^3)*cosh(d*x + c)^3 + (192*a^2*b + 35*b^3)*cosh(d*x + c))*sinh(d*x + c))*arctan(cosh(d*x + c) + sinh(d*x + c)) - 45*(64*a^2*b - 128*a*b^2 + 31*b^3)*cosh(d*x + c) + 960*(a^3*cosh(d*x + c)^16 + 16*a^3*cosh(d*x + c)*sinh(d*x + c)^15 + a^3*sinh(d*x + c)^16 + 8*a^3*cosh(d*x + c)^14 + 28*a^3*cosh(d*x + c)^12 + 8*(15*a^3*cosh(d*x + c)^2 + a^3)*sinh(d*x + c)^14 + 112*(5*a^3*cosh(d*x + c)^3 + a^3*cosh(d*x + c))*sinh(d*x + c)^13 + 56*a^3*cosh(d*x + c)^10 + 28*(65*a^3*cosh(d*x + c)^4 + 26*a^3*cosh(d*x + c)^2 + a^3)*sinh(d*x + c)^12 + 112*(39*a^3*cosh(d*x + c)^5 + 26*a^3*cosh(d*x + c)^3 + 3*a^3*cosh(d*x + c))*sinh(d*x + c)^11 + 70*a^3*cosh(d*x + c)^8 + 56*(143*a^3*cosh(d*x + c)^6 + 143*a^3*cosh(d*x + c)^4 + 33*a^3*cosh(d*x + c)^2 + a^3)*sinh(d*x + c)^10 + 16*(715*a^3*cosh(d*x + c)^7 + 1001*a^3*cosh(d*x + c)^5 + 385*a^3*cosh(d*x + c)^3 + 35*a^3*cosh(d*x + c))*sinh(d*x + c)^9 + 56*a^3*cosh(d*x + c)^6 + 2*(6435*a^3*cosh(d*x + c)^8 + 12012*a^3*cosh(d*x + c)^6 + 6930*a^3*cosh(d*x + c)^4 + 1260*a^3*cosh(d*x + c)^2 + 35*a^3)*sinh(d*x + c)^8 + 16*(715*a^3*cosh(d*x + c)^9 + 1716*a^3*cosh(d*x + c)^7 + 1386*a^3*cosh(d*x + c)^5 + 420*a^3*cosh(d*x + c)^3 + 35*a^3*cosh(d*x + c))*sinh(d*x + c)^7 + 28*a^3*cosh(d*x + c)^4 + 56*(143*a^3*cosh(d*x + c)^10 + 429*a^3*cosh(d*x + c)^8 + 462*a^3*cosh(d*x + c)^6 + 210*a^3*cosh(d*x + c)^4 + 35*a^3*cosh(d*x + c)^2 + a^3)*sinh(d*x + c)^6 + 112*(39*a^3*cosh(d*x + c)^11 + 143*a^3*cosh(d*x + c)^9 + 198*a^3*cosh(d*x + c)^7 + 126*a^3*cosh(d*x + c)^5 + 35*a^3*cosh(d*x + c)^3 + 3*a^3*cosh(d*x + c))*sinh(d*x + c)^5 + 8*a^3*cosh(d*x + c)^2 + 28*(65*a^3*cosh(d*x + c)^12 + 286*a^3*cosh(d*x + c)^10 + 495*a^3*cosh(d*x + c)^8 + 420*a^3*cosh(d*x + c)^6 + 175*a^3*cosh(d*x + c)^4 + 30*a^3*cosh(d*x + c)^2 + a^3)*sinh(d*x + c)^4 + 112*(5*a^3*cosh(d*x + c)^13 + 26*a^3*cosh(d*x + c)^11 + 55*a^3*cosh(d*x + c)^9 + 60*a^3*cosh(d*x + c)^7 + 35*a^3*cosh(d*x + c)^5 + 10*a^3*cosh(d*x + c)^3 + a^3*cosh(d*x + c))*sinh(d*x + c)^3 + a^3 + 8*(15*a^3*cosh(d*x + c)^14 + 91*a^3*cosh(d*x + c)^12 + 231*a^3*cosh(d*x + c)^10 + 315*a^3*cosh(d*x + c)^8 + 245*a^3*cosh(d*x + c)^6 + 105*a^3*cosh(d*x + c)^4 + 21*a^3*cosh(d*x + c)^2 + a^3)*sinh(d*x + c)^2 + 16*(a^3*cosh(d*x + c)^15 + 7*a^3*cosh(d*x + c)^13 + 21*a^3*cosh(d*x + c)^11 + 35*a^3*cosh(d*x + c)^9 + 35*a^3*cosh(d*x + c)^7 + 21*a^3*cosh(d*x + c)^5 + 7*a^3*cosh(d*x + c)^3 + a^3*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) + 1) - 960*(a^3*cosh(d*x + c)^16 + 16*a^3*cosh(d*x + c)*sinh(d*x + c)^15 + a^3*sinh(d*x + c)^16 + 8*a^3*cosh(d*x + c)^14 + 28*a^3*cosh(d*x + c)^12 + 8*(15*a^3*cosh(d*x + c)^2 + a^3)*sinh(d*x + c)^14 + 112*(5*a^3*cosh(d*x + c)^3 + a^3*cosh(d*x + c))*sinh(d*x + c)^13 + 56*a^3*cosh(d*x + c)^10 + 28*(65*a^3*cosh(d*x + c)^4 + 26*a^3*cosh(d*x + c)^2 + a^3)*sinh(d*x + c)^12 + 112*(39*a^3*cosh(d*x + c)^5 + 26*a^3*cosh(d*x + c)^3 + 3*a^3*cosh(d*x + c))*sinh(d*x + c)^11 + 70*a^3*cosh(d*x + c)^8 + 56*(143*a^3*cosh(d*x + c)^6 + 143*a^3*cosh(d*x + c)^4 + 33*a^3*cosh(d*x + c)^2 + a^3)*sinh(d*x + c)^10 + 16*(715*a^3*cosh(d*x + c)^7 + 1001*a^3*cosh(d*x + c)^5 + 385*a^3*cosh(d*x + c)^3 + 35*a^3*cosh(d*x + c))*sinh(d*x + c)^9 + 56*a^3*cosh(d*x + c)^6 + 2*(6435*a^3*cosh(d*x + c)^8 + 12012*a^3*cosh(d*x + c)^6 + 6930*a^3*cosh(d*x + c)^4 + 1260*a^3*cosh(d*x + c)^2 + 35*a^3)*sinh(d*x + c)^8 + 16*(715*a^3*cosh(d*x + c)^9 + 1716*a^3*cosh(d*x + c)^7 + 1386*a^3*cosh(d*x + c)^5 + 420*a^3*cosh(d*x + c)^3 + 35*a^3*cosh(d*x + c))*sinh(d*x + c)^7 + 28*a^3*cosh(d*x + c)^4 + 56*(143*a^3*cosh(d*x + c)^10 + 429*a^3*cosh(d*x + c)^8 + 462*a^3*cosh(d*x + c)^6 + 210*a^3*cosh(d*x + c)^4 + 35*a^3*cosh(d*x + c)^2 + a^3)*sinh(d*x + c)^6 + 112*(39*a^3*cosh(d*x + c)^11 + 143*a^3*cosh(d*x + c)^9 + 198*a^3*cosh(d*x + c)^7 + 126*a^3*cosh(d*x + c)^5 + 35*a^3*cosh(d*x + c)^3 + 3*a^3*cosh(d*x + c))*sinh(d*x + c)^5 + 8*a^3*cosh(d*x + c)^2 + 28*(65*a^3*cosh(d*x + c)^12 + 286*a^3*cosh(d*x + c)^10 + 495*a^3*cosh(d*x + c)^8 + 420*a^3*cosh(d*x + c)^6 + 175*a^3*cosh(d*x + c)^4 + 30*a^3*cosh(d*x + c)^2 + a^3)*sinh(d*x + c)^4 + 112*(5*a^3*cosh(d*x + c)^13 + 26*a^3*cosh(d*x + c)^11 + 55*a^3*cosh(d*x + c)^9 + 60*a^3*cosh(d*x + c)^7 + 35*a^3*cosh(d*x + c)^5 + 10*a^3*cosh(d*x + c)^3 + a^3*cosh(d*x + c))*sinh(d*x + c)^3 + a^3 + 8*(15*a^3*cosh(d*x + c)^14 + 91*a^3*cosh(d*x + c)^12 + 231*a^3*cosh(d*x + c)^10 + 315*a^3*cosh(d*x + c)^8 + 245*a^3*cosh(d*x + c)^6 + 105*a^3*cosh(d*x + c)^4 + 21*a^3*cosh(d*x + c)^2 + a^3)*sinh(d*x + c)^2 + 16*(a^3*cosh(d*x + c)^15 + 7*a^3*cosh(d*x + c)^13 + 21*a^3*cosh(d*x + c)^11 + 35*a^3*cosh(d*x + c)^9 + 35*a^3*cosh(d*x + c)^7 + 21*a^3*cosh(d*x + c)^5 + 7*a^3*cosh(d*x + c)^3 + a^3*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) - 1) + (675*(64*a^2*b + 128*a*b^2 + 31*b^3)*cosh(d*x + c)^14 + 65*(2880*a^2*b + 4992*a*b^2 + 91*b^3)*cosh(d*x + c)^12 + 11*(25920*a^2*b + 62592*a*b^2 + 8995*b^3)*cosh(d*x + c)^10 + 9*(14400*a^2*b + 103296*a*b^2 - 5425*b^3)*cosh(d*x + c)^8 - 7*(14400*a^2*b - 103296*a*b^2 - 5425*b^3)*cosh(d*x + c)^6 - 5*(25920*a^2*b - 62592*a*b^2 + 8995*b^3)*cosh(d*x + c)^4 - 2880*a^2*b + 5760*a*b^2 - 1395*b^3 - 15*(2880*a^2*b - 4992*a*b^2 + 91*b^3)*cosh(d*x + c)^2)*sinh(d*x + c))/(d*cosh(d*x + c)^16 + 16*d*cosh(d*x + c)*sinh(d*x + c)^15 + d*sinh(d*x + c)^16 + 8*d*cosh(d*x + c)^14 + 8*(15*d*cosh(d*x + c)^2 + d)*sinh(d*x + c)^14 + 112*(5*d*cosh(d*x + c)^3 + d*cosh(d*x + c))*sinh(d*x + c)^13 + 28*d*cosh(d*x + c)^12 + 28*(65*d*cosh(d*x + c)^4 + 26*d*cosh(d*x + c)^2 + d)*sinh(d*x + c)^12 + 112*(39*d*cosh(d*x + c)^5 + 26*d*cosh(d*x + c)^3 + 3*d*cosh(d*x + c))*sinh(d*x + c)^11 + 56*d*cosh(d*x + c)^10 + 56*(143*d*cosh(d*x + c)^6 + 143*d*cosh(d*x + c)^4 + 33*d*cosh(d*x + c)^2 + d)*sinh(d*x + c)^10 + 16*(715*d*cosh(d*x + c)^7 + 1001*d*cosh(d*x + c)^5 + 385*d*cosh(d*x + c)^3 + 35*d*cosh(d*x + c))*sinh(d*x + c)^9 + 70*d*cosh(d*x + c)^8 + 2*(6435*d*cosh(d*x + c)^8 + 12012*d*cosh(d*x + c)^6 + 6930*d*cosh(d*x + c)^4 + 1260*d*cosh(d*x + c)^2 + 35*d)*sinh(d*x + c)^8 + 16*(715*d*cosh(d*x + c)^9 + 1716*d*cosh(d*x + c)^7 + 1386*d*cosh(d*x + c)^5 + 420*d*cosh(d*x + c)^3 + 35*d*cosh(d*x + c))*sinh(d*x + c)^7 + 56*d*cosh(d*x + c)^6 + 56*(143*d*cosh(d*x + c)^10 + 429*d*cosh(d*x + c)^8 + 462*d*cosh(d*x + c)^6 + 210*d*cosh(d*x + c)^4 + 35*d*cosh(d*x + c)^2 + d)*sinh(d*x + c)^6 + 112*(39*d*cosh(d*x + c)^11 + 143*d*cosh(d*x + c)^9 + 198*d*cosh(d*x + c)^7 + 126*d*cosh(d*x + c)^5 + 35*d*cosh(d*x + c)^3 + 3*d*cosh(d*x + c))*sinh(d*x + c)^5 + 28*d*cosh(d*x + c)^4 + 28*(65*d*cosh(d*x + c)^12 + 286*d*cosh(d*x + c)^10 + 495*d*cosh(d*x + c)^8 + 420*d*cosh(d*x + c)^6 + 175*d*cosh(d*x + c)^4 + 30*d*cosh(d*x + c)^2 + d)*sinh(d*x + c)^4 + 112*(5*d*cosh(d*x + c)^13 + 26*d*cosh(d*x + c)^11 + 55*d*cosh(d*x + c)^9 + 60*d*cosh(d*x + c)^7 + 35*d*cosh(d*x + c)^5 + 10*d*cosh(d*x + c)^3 + d*cosh(d*x + c))*sinh(d*x + c)^3 + 8*d*cosh(d*x + c)^2 + 8*(15*d*cosh(d*x + c)^14 + 91*d*cosh(d*x + c)^12 + 231*d*cosh(d*x + c)^10 + 315*d*cosh(d*x + c)^8 + 245*d*cosh(d*x + c)^6 + 105*d*cosh(d*x + c)^4 + 21*d*cosh(d*x + c)^2 + d)*sinh(d*x + c)^2 + 16*(d*cosh(d*x + c)^15 + 7*d*cosh(d*x + c)^13 + 21*d*cosh(d*x + c)^11 + 35*d*cosh(d*x + c)^9 + 35*d*cosh(d*x + c)^7 + 21*d*cosh(d*x + c)^5 + 7*d*cosh(d*x + c)^3 + d*cosh(d*x + c))*sinh(d*x + c) + d)","B",0
70,1,1192,0,0.404074," ","integrate(csch(d*x+c)^2*(a+b*tanh(d*x+c)^3)^3,x, algorithm=""fricas"")","-\frac{2 \, {\left({\left(10 \, a^{3} + 15 \, a^{2} b + 12 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(15 \, a^{2} b + 18 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(10 \, a^{3} + 15 \, a^{2} b + 12 \, a b^{2} + 5 \, b^{3}\right)} \sinh\left(d x + c\right)^{8} + 2 \, {\left(40 \, a^{3} + 30 \, a^{2} b + 12 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(40 \, a^{3} + 30 \, a^{2} b + 12 \, a b^{2} - 5 \, b^{3} + 14 \, {\left(10 \, a^{3} + 15 \, a^{2} b + 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(14 \, {\left(15 \, a^{2} b + 18 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 27 \, {\left(5 \, a^{2} b + 2 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 20 \, {\left(14 \, a^{3} + 3 \, a^{2} b + 2 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 10 \, {\left(7 \, {\left(10 \, a^{3} + 15 \, a^{2} b + 12 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 28 \, a^{3} + 6 \, a^{2} b + 4 \, b^{3} + 3 \, {\left(40 \, a^{3} + 30 \, a^{2} b + 12 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(15 \, a^{2} b + 18 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 45 \, {\left(5 \, a^{2} b + 2 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} + 15 \, {\left(7 \, a^{2} b + 2 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 350 \, a^{3} - 75 \, a^{2} b - 12 \, a b^{2} + 35 \, b^{3} + 2 \, {\left(280 \, a^{3} - 30 \, a^{2} b - 12 \, a b^{2} - 35 \, b^{3}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(14 \, {\left(10 \, a^{3} + 15 \, a^{2} b + 12 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(40 \, a^{3} + 30 \, a^{2} b + 12 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 280 \, a^{3} - 30 \, a^{2} b - 12 \, a b^{2} - 35 \, b^{3} + 60 \, {\left(14 \, a^{3} + 3 \, a^{2} b + 2 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(2 \, {\left(15 \, a^{2} b + 18 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 27 \, {\left(5 \, a^{2} b + 2 \, a b^{2}\right)} \cosh\left(d x + c\right)^{5} + 30 \, {\left(7 \, a^{2} b + 2 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{3} + 21 \, {\left(5 \, a^{2} b + 2 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}{5 \, {\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} + 6 \, d \cosh\left(d x + c\right)^{8} + 3 \, {\left(15 \, 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} + 8 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 13 \, d \cosh\left(d x + c\right)^{6} + {\left(210 \, d \cosh\left(d x + c\right)^{4} + 168 \, d \cosh\left(d x + c\right)^{2} + 13 \, d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(126 \, d \cosh\left(d x + c\right)^{5} + 224 \, d \cosh\left(d x + c\right)^{3} + 81 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 8 \, d \cosh\left(d x + c\right)^{4} + {\left(210 \, d \cosh\left(d x + c\right)^{6} + 420 \, d \cosh\left(d x + c\right)^{4} + 195 \, d \cosh\left(d x + c\right)^{2} + 8 \, d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(30 \, d \cosh\left(d x + c\right)^{7} + 112 \, d \cosh\left(d x + c\right)^{5} + 135 \, d \cosh\left(d x + c\right)^{3} + 48 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 14 \, d \cosh\left(d x + c\right)^{2} + {\left(45 \, d \cosh\left(d x + c\right)^{8} + 168 \, d \cosh\left(d x + c\right)^{6} + 195 \, d \cosh\left(d x + c\right)^{4} + 48 \, d \cosh\left(d x + c\right)^{2} - 14 \, d\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(5 \, d \cosh\left(d x + c\right)^{9} + 32 \, d \cosh\left(d x + c\right)^{7} + 81 \, d \cosh\left(d x + c\right)^{5} + 96 \, d \cosh\left(d x + c\right)^{3} + 42 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) - 14 \, d\right)}}"," ",0,"-2/5*((10*a^3 + 15*a^2*b + 12*a*b^2 + 5*b^3)*cosh(d*x + c)^8 + 8*(15*a^2*b + 18*a*b^2 + 5*b^3)*cosh(d*x + c)*sinh(d*x + c)^7 + (10*a^3 + 15*a^2*b + 12*a*b^2 + 5*b^3)*sinh(d*x + c)^8 + 2*(40*a^3 + 30*a^2*b + 12*a*b^2 - 5*b^3)*cosh(d*x + c)^6 + 2*(40*a^3 + 30*a^2*b + 12*a*b^2 - 5*b^3 + 14*(10*a^3 + 15*a^2*b + 12*a*b^2 + 5*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 4*(14*(15*a^2*b + 18*a*b^2 + 5*b^3)*cosh(d*x + c)^3 + 27*(5*a^2*b + 2*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^5 + 20*(14*a^3 + 3*a^2*b + 2*b^3)*cosh(d*x + c)^4 + 10*(7*(10*a^3 + 15*a^2*b + 12*a*b^2 + 5*b^3)*cosh(d*x + c)^4 + 28*a^3 + 6*a^2*b + 4*b^3 + 3*(40*a^3 + 30*a^2*b + 12*a*b^2 - 5*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(7*(15*a^2*b + 18*a*b^2 + 5*b^3)*cosh(d*x + c)^5 + 45*(5*a^2*b + 2*a*b^2)*cosh(d*x + c)^3 + 15*(7*a^2*b + 2*a*b^2 + b^3)*cosh(d*x + c))*sinh(d*x + c)^3 + 350*a^3 - 75*a^2*b - 12*a*b^2 + 35*b^3 + 2*(280*a^3 - 30*a^2*b - 12*a*b^2 - 35*b^3)*cosh(d*x + c)^2 + 2*(14*(10*a^3 + 15*a^2*b + 12*a*b^2 + 5*b^3)*cosh(d*x + c)^6 + 15*(40*a^3 + 30*a^2*b + 12*a*b^2 - 5*b^3)*cosh(d*x + c)^4 + 280*a^3 - 30*a^2*b - 12*a*b^2 - 35*b^3 + 60*(14*a^3 + 3*a^2*b + 2*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*(2*(15*a^2*b + 18*a*b^2 + 5*b^3)*cosh(d*x + c)^7 + 27*(5*a^2*b + 2*a*b^2)*cosh(d*x + c)^5 + 30*(7*a^2*b + 2*a*b^2 + b^3)*cosh(d*x + c)^3 + 21*(5*a^2*b + 2*a*b^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 + 6*d*cosh(d*x + c)^8 + 3*(15*d*cosh(d*x + c)^2 + 2*d)*sinh(d*x + c)^8 + 8*(15*d*cosh(d*x + c)^3 + 8*d*cosh(d*x + c))*sinh(d*x + c)^7 + 13*d*cosh(d*x + c)^6 + (210*d*cosh(d*x + c)^4 + 168*d*cosh(d*x + c)^2 + 13*d)*sinh(d*x + c)^6 + 2*(126*d*cosh(d*x + c)^5 + 224*d*cosh(d*x + c)^3 + 81*d*cosh(d*x + c))*sinh(d*x + c)^5 + 8*d*cosh(d*x + c)^4 + (210*d*cosh(d*x + c)^6 + 420*d*cosh(d*x + c)^4 + 195*d*cosh(d*x + c)^2 + 8*d)*sinh(d*x + c)^4 + 4*(30*d*cosh(d*x + c)^7 + 112*d*cosh(d*x + c)^5 + 135*d*cosh(d*x + c)^3 + 48*d*cosh(d*x + c))*sinh(d*x + c)^3 - 14*d*cosh(d*x + c)^2 + (45*d*cosh(d*x + c)^8 + 168*d*cosh(d*x + c)^6 + 195*d*cosh(d*x + c)^4 + 48*d*cosh(d*x + c)^2 - 14*d)*sinh(d*x + c)^2 + 2*(5*d*cosh(d*x + c)^9 + 32*d*cosh(d*x + c)^7 + 81*d*cosh(d*x + c)^5 + 96*d*cosh(d*x + c)^3 + 42*d*cosh(d*x + c))*sinh(d*x + c) - 14*d)","B",0
71,1,10985,0,0.605807," ","integrate(csch(d*x+c)^3*(a+b*tanh(d*x+c)^3)^3,x, algorithm=""fricas"")","-\frac{15 \, {\left(64 \, a^{3} - 192 \, a^{2} b - 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{19} + 285 \, {\left(64 \, a^{3} - 192 \, a^{2} b - 5 \, b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{18} + 15 \, {\left(64 \, a^{3} - 192 \, a^{2} b - 5 \, b^{3}\right)} \sinh\left(d x + c\right)^{19} + 5 \, {\left(1728 \, a^{3} - 1728 \, a^{2} b + 1536 \, a b^{2} + 427 \, b^{3}\right)} \cosh\left(d x + c\right)^{17} + 5 \, {\left(1728 \, a^{3} - 1728 \, a^{2} b + 1536 \, a b^{2} + 427 \, b^{3} + 513 \, {\left(64 \, a^{3} - 192 \, a^{2} b - 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{17} + 85 \, {\left(171 \, {\left(64 \, a^{3} - 192 \, a^{2} b - 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(1728 \, a^{3} - 1728 \, a^{2} b + 1536 \, a b^{2} + 427 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{16} + 24 \, {\left(1440 \, a^{3} + 192 \, a b^{2} - 355 \, b^{3}\right)} \cosh\left(d x + c\right)^{15} + 4 \, {\left(14535 \, {\left(64 \, a^{3} - 192 \, a^{2} b - 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 8640 \, a^{3} + 1152 \, a b^{2} - 2130 \, b^{3} + 170 \, {\left(1728 \, a^{3} - 1728 \, a^{2} b + 1536 \, a b^{2} + 427 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{15} + 20 \, {\left(8721 \, {\left(64 \, a^{3} - 192 \, a^{2} b - 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 170 \, {\left(1728 \, a^{3} - 1728 \, a^{2} b + 1536 \, a b^{2} + 427 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 18 \, {\left(1440 \, a^{3} + 192 \, a b^{2} - 355 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{14} + 16 \, {\left(5040 \, a^{3} + 1440 \, a^{2} b - 672 \, a b^{2} + 1235 \, b^{3}\right)} \cosh\left(d x + c\right)^{13} + 4 \, {\left(101745 \, {\left(64 \, a^{3} - 192 \, a^{2} b - 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 2975 \, {\left(1728 \, a^{3} - 1728 \, a^{2} b + 1536 \, a b^{2} + 427 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 20160 \, a^{3} + 5760 \, a^{2} b - 2688 \, a b^{2} + 4940 \, b^{3} + 630 \, {\left(1440 \, a^{3} + 192 \, a b^{2} - 355 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{13} + 52 \, {\left(14535 \, {\left(64 \, a^{3} - 192 \, a^{2} b - 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 595 \, {\left(1728 \, a^{3} - 1728 \, a^{2} b + 1536 \, a b^{2} + 427 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 210 \, {\left(1440 \, a^{3} + 192 \, a b^{2} - 355 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(5040 \, a^{3} + 1440 \, a^{2} b - 672 \, a b^{2} + 1235 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{12} + 2 \, {\left(60480 \, a^{3} + 8640 \, a^{2} b - 768 \, a b^{2} - 15475 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} + 2 \, {\left(566865 \, {\left(64 \, a^{3} - 192 \, a^{2} b - 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 30940 \, {\left(1728 \, a^{3} - 1728 \, a^{2} b + 1536 \, a b^{2} + 427 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 16380 \, {\left(1440 \, a^{3} + 192 \, a b^{2} - 355 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 60480 \, a^{3} + 8640 \, a^{2} b - 768 \, a b^{2} - 15475 \, b^{3} + 624 \, {\left(5040 \, a^{3} + 1440 \, a^{2} b - 672 \, a b^{2} + 1235 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{11} + 22 \, {\left(62985 \, {\left(64 \, a^{3} - 192 \, a^{2} b - 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + 4420 \, {\left(1728 \, a^{3} - 1728 \, a^{2} b + 1536 \, a b^{2} + 427 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 3276 \, {\left(1440 \, a^{3} + 192 \, a b^{2} - 355 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 208 \, {\left(5040 \, a^{3} + 1440 \, a^{2} b - 672 \, a b^{2} + 1235 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(60480 \, a^{3} + 8640 \, a^{2} b - 768 \, a b^{2} - 15475 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{10} + 2 \, {\left(60480 \, a^{3} - 8640 \, a^{2} b - 768 \, a b^{2} + 15475 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + 2 \, {\left(692835 \, {\left(64 \, a^{3} - 192 \, a^{2} b - 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} + 60775 \, {\left(1728 \, a^{3} - 1728 \, a^{2} b + 1536 \, a b^{2} + 427 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 60060 \, {\left(1440 \, a^{3} + 192 \, a b^{2} - 355 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 5720 \, {\left(5040 \, a^{3} + 1440 \, a^{2} b - 672 \, a b^{2} + 1235 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 60480 \, a^{3} - 8640 \, a^{2} b - 768 \, a b^{2} + 15475 \, b^{3} + 55 \, {\left(60480 \, a^{3} + 8640 \, a^{2} b - 768 \, a b^{2} - 15475 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{9} + 2 \, {\left(566865 \, {\left(64 \, a^{3} - 192 \, a^{2} b - 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} + 60775 \, {\left(1728 \, a^{3} - 1728 \, a^{2} b + 1536 \, a b^{2} + 427 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + 77220 \, {\left(1440 \, a^{3} + 192 \, a b^{2} - 355 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 10296 \, {\left(5040 \, a^{3} + 1440 \, a^{2} b - 672 \, a b^{2} + 1235 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 165 \, {\left(60480 \, a^{3} + 8640 \, a^{2} b - 768 \, a b^{2} - 15475 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 9 \, {\left(60480 \, a^{3} - 8640 \, a^{2} b - 768 \, a b^{2} + 15475 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{8} + 16 \, {\left(5040 \, a^{3} - 1440 \, a^{2} b - 672 \, a b^{2} - 1235 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 4 \, {\left(188955 \, {\left(64 \, a^{3} - 192 \, a^{2} b - 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{12} + 24310 \, {\left(1728 \, a^{3} - 1728 \, a^{2} b + 1536 \, a b^{2} + 427 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} + 38610 \, {\left(1440 \, a^{3} + 192 \, a b^{2} - 355 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 6864 \, {\left(5040 \, a^{3} + 1440 \, a^{2} b - 672 \, a b^{2} + 1235 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 165 \, {\left(60480 \, a^{3} + 8640 \, a^{2} b - 768 \, a b^{2} - 15475 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 20160 \, a^{3} - 5760 \, a^{2} b - 2688 \, a b^{2} - 4940 \, b^{3} + 18 \, {\left(60480 \, a^{3} - 8640 \, a^{2} b - 768 \, a b^{2} + 15475 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{7} + 4 \, {\left(101745 \, {\left(64 \, a^{3} - 192 \, a^{2} b - 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{13} + 15470 \, {\left(1728 \, a^{3} - 1728 \, a^{2} b + 1536 \, a b^{2} + 427 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} + 30030 \, {\left(1440 \, a^{3} + 192 \, a b^{2} - 355 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + 6864 \, {\left(5040 \, a^{3} + 1440 \, a^{2} b - 672 \, a b^{2} + 1235 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 231 \, {\left(60480 \, a^{3} + 8640 \, a^{2} b - 768 \, a b^{2} - 15475 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 42 \, {\left(60480 \, a^{3} - 8640 \, a^{2} b - 768 \, a b^{2} + 15475 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 28 \, {\left(5040 \, a^{3} - 1440 \, a^{2} b - 672 \, a b^{2} - 1235 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} + 24 \, {\left(1440 \, a^{3} + 192 \, a b^{2} + 355 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 4 \, {\left(43605 \, {\left(64 \, a^{3} - 192 \, a^{2} b - 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{14} + 7735 \, {\left(1728 \, a^{3} - 1728 \, a^{2} b + 1536 \, a b^{2} + 427 \, b^{3}\right)} \cosh\left(d x + c\right)^{12} + 18018 \, {\left(1440 \, a^{3} + 192 \, a b^{2} - 355 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} + 5148 \, {\left(5040 \, a^{3} + 1440 \, a^{2} b - 672 \, a b^{2} + 1235 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 231 \, {\left(60480 \, a^{3} + 8640 \, a^{2} b - 768 \, a b^{2} - 15475 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 63 \, {\left(60480 \, a^{3} - 8640 \, a^{2} b - 768 \, a b^{2} + 15475 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 8640 \, a^{3} + 1152 \, a b^{2} + 2130 \, b^{3} + 84 \, {\left(5040 \, a^{3} - 1440 \, a^{2} b - 672 \, a b^{2} - 1235 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{5} + 4 \, {\left(14535 \, {\left(64 \, a^{3} - 192 \, a^{2} b - 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{15} + 2975 \, {\left(1728 \, a^{3} - 1728 \, a^{2} b + 1536 \, a b^{2} + 427 \, b^{3}\right)} \cosh\left(d x + c\right)^{13} + 8190 \, {\left(1440 \, a^{3} + 192 \, a b^{2} - 355 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} + 2860 \, {\left(5040 \, a^{3} + 1440 \, a^{2} b - 672 \, a b^{2} + 1235 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + 165 \, {\left(60480 \, a^{3} + 8640 \, a^{2} b - 768 \, a b^{2} - 15475 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 63 \, {\left(60480 \, a^{3} - 8640 \, a^{2} b - 768 \, a b^{2} + 15475 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 140 \, {\left(5040 \, a^{3} - 1440 \, a^{2} b - 672 \, a b^{2} - 1235 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 30 \, {\left(1440 \, a^{3} + 192 \, a b^{2} + 355 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 5 \, {\left(1728 \, a^{3} + 1728 \, a^{2} b + 1536 \, a b^{2} - 427 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(14535 \, {\left(64 \, a^{3} - 192 \, a^{2} b - 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{16} + 3400 \, {\left(1728 \, a^{3} - 1728 \, a^{2} b + 1536 \, a b^{2} + 427 \, b^{3}\right)} \cosh\left(d x + c\right)^{14} + 10920 \, {\left(1440 \, a^{3} + 192 \, a b^{2} - 355 \, b^{3}\right)} \cosh\left(d x + c\right)^{12} + 4576 \, {\left(5040 \, a^{3} + 1440 \, a^{2} b - 672 \, a b^{2} + 1235 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} + 330 \, {\left(60480 \, a^{3} + 8640 \, a^{2} b - 768 \, a b^{2} - 15475 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 168 \, {\left(60480 \, a^{3} - 8640 \, a^{2} b - 768 \, a b^{2} + 15475 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 560 \, {\left(5040 \, a^{3} - 1440 \, a^{2} b - 672 \, a b^{2} - 1235 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 8640 \, a^{3} + 8640 \, a^{2} b + 7680 \, a b^{2} - 2135 \, b^{3} + 240 \, {\left(1440 \, a^{3} + 192 \, a b^{2} + 355 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + {\left(2565 \, {\left(64 \, a^{3} - 192 \, a^{2} b - 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{17} + 680 \, {\left(1728 \, a^{3} - 1728 \, a^{2} b + 1536 \, a b^{2} + 427 \, b^{3}\right)} \cosh\left(d x + c\right)^{15} + 2520 \, {\left(1440 \, a^{3} + 192 \, a b^{2} - 355 \, b^{3}\right)} \cosh\left(d x + c\right)^{13} + 1248 \, {\left(5040 \, a^{3} + 1440 \, a^{2} b - 672 \, a b^{2} + 1235 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} + 110 \, {\left(60480 \, a^{3} + 8640 \, a^{2} b - 768 \, a b^{2} - 15475 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + 72 \, {\left(60480 \, a^{3} - 8640 \, a^{2} b - 768 \, a b^{2} + 15475 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 336 \, {\left(5040 \, a^{3} - 1440 \, a^{2} b - 672 \, a b^{2} - 1235 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 240 \, {\left(1440 \, a^{3} + 192 \, a b^{2} + 355 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 15 \, {\left(1728 \, a^{3} + 1728 \, a^{2} b + 1536 \, a b^{2} - 427 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 15 \, {\left({\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{20} + 20 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{19} + {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \sinh\left(d x + c\right)^{20} + 6 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{18} + 2 \, {\left(576 \, a^{2} b + 15 \, b^{3} + 95 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{18} + 12 \, {\left(95 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 9 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{17} + 13 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{16} + {\left(4845 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 2496 \, a^{2} b + 65 \, b^{3} + 918 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{16} + 16 \, {\left(969 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 306 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 13 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{15} + 8 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{14} + 8 \, {\left(4845 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 2295 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 192 \, a^{2} b + 5 \, b^{3} + 195 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{14} + 16 \, {\left(4845 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 3213 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 455 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 7 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{13} - 14 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{12} + 2 \, {\left(62985 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 55692 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 11830 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 1344 \, a^{2} b - 35 \, b^{3} + 364 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{12} + 8 \, {\left(20995 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + 23868 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 7098 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 364 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 21 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{11} - 28 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} + 4 \, {\left(46189 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} + 65637 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 26026 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 2002 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 1344 \, a^{2} b - 35 \, b^{3} - 231 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{10} + 8 \, {\left(20995 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} + 36465 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + 18590 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 2002 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 385 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 35 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} - 14 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 2 \, {\left(62985 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{12} + 131274 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} + 83655 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 12012 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} - 3465 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 1344 \, a^{2} b - 35 \, b^{3} - 630 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{8} + 16 \, {\left(4845 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{13} + 11934 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} + 9295 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + 1716 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} - 693 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 210 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 7 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 8 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 8 \, {\left(4845 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{14} + 13923 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{12} + 13013 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} + 3003 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} - 1617 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} - 735 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 192 \, a^{2} b + 5 \, b^{3} - 49 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 16 \, {\left(969 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{15} + 3213 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{13} + 3549 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} + 1001 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} - 693 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} - 441 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 49 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 13 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + {\left(4845 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{16} + 18360 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{14} + 23660 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{12} + 8008 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} - 6930 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} - 5880 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} - 980 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 2496 \, a^{2} b + 65 \, b^{3} + 120 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(285 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{17} + 1224 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{15} + 1820 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{13} + 728 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} - 770 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} - 840 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} - 196 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 40 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 13 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 192 \, a^{2} b + 5 \, b^{3} + 6 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(95 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{18} + 459 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{16} + 780 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{14} + 364 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{12} - 462 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} - 630 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} - 196 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 60 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 576 \, a^{2} b + 15 \, b^{3} + 39 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(5 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{19} + 27 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{17} + 52 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{15} + 28 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{13} - 42 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} - 70 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} - 28 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 12 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 13 \, {\left(192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(192 \, a^{2} b + 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) + 15 \, {\left(64 \, a^{3} + 192 \, a^{2} b + 5 \, b^{3}\right)} \cosh\left(d x + c\right) - 480 \, {\left(a^{3} \cosh\left(d x + c\right)^{20} + 20 \, a^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{19} + a^{3} \sinh\left(d x + c\right)^{20} + 6 \, a^{3} \cosh\left(d x + c\right)^{18} + 13 \, a^{3} \cosh\left(d x + c\right)^{16} + 2 \, {\left(95 \, a^{3} \cosh\left(d x + c\right)^{2} + 3 \, a^{3}\right)} \sinh\left(d x + c\right)^{18} + 12 \, {\left(95 \, a^{3} \cosh\left(d x + c\right)^{3} + 9 \, a^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{17} + 8 \, a^{3} \cosh\left(d x + c\right)^{14} + {\left(4845 \, a^{3} \cosh\left(d x + c\right)^{4} + 918 \, a^{3} \cosh\left(d x + c\right)^{2} + 13 \, a^{3}\right)} \sinh\left(d x + c\right)^{16} + 16 \, {\left(969 \, a^{3} \cosh\left(d x + c\right)^{5} + 306 \, a^{3} \cosh\left(d x + c\right)^{3} + 13 \, a^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{15} - 14 \, a^{3} \cosh\left(d x + c\right)^{12} + 8 \, {\left(4845 \, a^{3} \cosh\left(d x + c\right)^{6} + 2295 \, a^{3} \cosh\left(d x + c\right)^{4} + 195 \, a^{3} \cosh\left(d x + c\right)^{2} + a^{3}\right)} \sinh\left(d x + c\right)^{14} + 16 \, {\left(4845 \, a^{3} \cosh\left(d x + c\right)^{7} + 3213 \, a^{3} \cosh\left(d x + c\right)^{5} + 455 \, a^{3} \cosh\left(d x + c\right)^{3} + 7 \, a^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{13} - 28 \, a^{3} \cosh\left(d x + c\right)^{10} + 2 \, {\left(62985 \, a^{3} \cosh\left(d x + c\right)^{8} + 55692 \, a^{3} \cosh\left(d x + c\right)^{6} + 11830 \, a^{3} \cosh\left(d x + c\right)^{4} + 364 \, a^{3} \cosh\left(d x + c\right)^{2} - 7 \, a^{3}\right)} \sinh\left(d x + c\right)^{12} + 8 \, {\left(20995 \, a^{3} \cosh\left(d x + c\right)^{9} + 23868 \, a^{3} \cosh\left(d x + c\right)^{7} + 7098 \, a^{3} \cosh\left(d x + c\right)^{5} + 364 \, a^{3} \cosh\left(d x + c\right)^{3} - 21 \, a^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{11} - 14 \, a^{3} \cosh\left(d x + c\right)^{8} + 4 \, {\left(46189 \, a^{3} \cosh\left(d x + c\right)^{10} + 65637 \, a^{3} \cosh\left(d x + c\right)^{8} + 26026 \, a^{3} \cosh\left(d x + c\right)^{6} + 2002 \, a^{3} \cosh\left(d x + c\right)^{4} - 231 \, a^{3} \cosh\left(d x + c\right)^{2} - 7 \, a^{3}\right)} \sinh\left(d x + c\right)^{10} + 8 \, {\left(20995 \, a^{3} \cosh\left(d x + c\right)^{11} + 36465 \, a^{3} \cosh\left(d x + c\right)^{9} + 18590 \, a^{3} \cosh\left(d x + c\right)^{7} + 2002 \, a^{3} \cosh\left(d x + c\right)^{5} - 385 \, a^{3} \cosh\left(d x + c\right)^{3} - 35 \, a^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} + 8 \, a^{3} \cosh\left(d x + c\right)^{6} + 2 \, {\left(62985 \, a^{3} \cosh\left(d x + c\right)^{12} + 131274 \, a^{3} \cosh\left(d x + c\right)^{10} + 83655 \, a^{3} \cosh\left(d x + c\right)^{8} + 12012 \, a^{3} \cosh\left(d x + c\right)^{6} - 3465 \, a^{3} \cosh\left(d x + c\right)^{4} - 630 \, a^{3} \cosh\left(d x + c\right)^{2} - 7 \, a^{3}\right)} \sinh\left(d x + c\right)^{8} + 16 \, {\left(4845 \, a^{3} \cosh\left(d x + c\right)^{13} + 11934 \, a^{3} \cosh\left(d x + c\right)^{11} + 9295 \, a^{3} \cosh\left(d x + c\right)^{9} + 1716 \, a^{3} \cosh\left(d x + c\right)^{7} - 693 \, a^{3} \cosh\left(d x + c\right)^{5} - 210 \, a^{3} \cosh\left(d x + c\right)^{3} - 7 \, a^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 13 \, a^{3} \cosh\left(d x + c\right)^{4} + 8 \, {\left(4845 \, a^{3} \cosh\left(d x + c\right)^{14} + 13923 \, a^{3} \cosh\left(d x + c\right)^{12} + 13013 \, a^{3} \cosh\left(d x + c\right)^{10} + 3003 \, a^{3} \cosh\left(d x + c\right)^{8} - 1617 \, a^{3} \cosh\left(d x + c\right)^{6} - 735 \, a^{3} \cosh\left(d x + c\right)^{4} - 49 \, a^{3} \cosh\left(d x + c\right)^{2} + a^{3}\right)} \sinh\left(d x + c\right)^{6} + 16 \, {\left(969 \, a^{3} \cosh\left(d x + c\right)^{15} + 3213 \, a^{3} \cosh\left(d x + c\right)^{13} + 3549 \, a^{3} \cosh\left(d x + c\right)^{11} + 1001 \, a^{3} \cosh\left(d x + c\right)^{9} - 693 \, a^{3} \cosh\left(d x + c\right)^{7} - 441 \, a^{3} \cosh\left(d x + c\right)^{5} - 49 \, 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} + 6 \, a^{3} \cosh\left(d x + c\right)^{2} + {\left(4845 \, a^{3} \cosh\left(d x + c\right)^{16} + 18360 \, a^{3} \cosh\left(d x + c\right)^{14} + 23660 \, a^{3} \cosh\left(d x + c\right)^{12} + 8008 \, a^{3} \cosh\left(d x + c\right)^{10} - 6930 \, a^{3} \cosh\left(d x + c\right)^{8} - 5880 \, a^{3} \cosh\left(d x + c\right)^{6} - 980 \, a^{3} \cosh\left(d x + c\right)^{4} + 120 \, a^{3} \cosh\left(d x + c\right)^{2} + 13 \, a^{3}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(285 \, a^{3} \cosh\left(d x + c\right)^{17} + 1224 \, a^{3} \cosh\left(d x + c\right)^{15} + 1820 \, a^{3} \cosh\left(d x + c\right)^{13} + 728 \, a^{3} \cosh\left(d x + c\right)^{11} - 770 \, a^{3} \cosh\left(d x + c\right)^{9} - 840 \, a^{3} \cosh\left(d x + c\right)^{7} - 196 \, a^{3} \cosh\left(d x + c\right)^{5} + 40 \, a^{3} \cosh\left(d x + c\right)^{3} + 13 \, a^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + a^{3} + 2 \, {\left(95 \, a^{3} \cosh\left(d x + c\right)^{18} + 459 \, a^{3} \cosh\left(d x + c\right)^{16} + 780 \, a^{3} \cosh\left(d x + c\right)^{14} + 364 \, a^{3} \cosh\left(d x + c\right)^{12} - 462 \, a^{3} \cosh\left(d x + c\right)^{10} - 630 \, a^{3} \cosh\left(d x + c\right)^{8} - 196 \, a^{3} \cosh\left(d x + c\right)^{6} + 60 \, a^{3} \cosh\left(d x + c\right)^{4} + 39 \, a^{3} \cosh\left(d x + c\right)^{2} + 3 \, a^{3}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(5 \, a^{3} \cosh\left(d x + c\right)^{19} + 27 \, a^{3} \cosh\left(d x + c\right)^{17} + 52 \, a^{3} \cosh\left(d x + c\right)^{15} + 28 \, a^{3} \cosh\left(d x + c\right)^{13} - 42 \, a^{3} \cosh\left(d x + c\right)^{11} - 70 \, a^{3} \cosh\left(d x + c\right)^{9} - 28 \, a^{3} \cosh\left(d x + c\right)^{7} + 12 \, a^{3} \cosh\left(d x + c\right)^{5} + 13 \, 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)\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)^{20} + 20 \, a^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{19} + a^{3} \sinh\left(d x + c\right)^{20} + 6 \, a^{3} \cosh\left(d x + c\right)^{18} + 13 \, a^{3} \cosh\left(d x + c\right)^{16} + 2 \, {\left(95 \, a^{3} \cosh\left(d x + c\right)^{2} + 3 \, a^{3}\right)} \sinh\left(d x + c\right)^{18} + 12 \, {\left(95 \, a^{3} \cosh\left(d x + c\right)^{3} + 9 \, a^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{17} + 8 \, a^{3} \cosh\left(d x + c\right)^{14} + {\left(4845 \, a^{3} \cosh\left(d x + c\right)^{4} + 918 \, a^{3} \cosh\left(d x + c\right)^{2} + 13 \, a^{3}\right)} \sinh\left(d x + c\right)^{16} + 16 \, {\left(969 \, a^{3} \cosh\left(d x + c\right)^{5} + 306 \, a^{3} \cosh\left(d x + c\right)^{3} + 13 \, a^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{15} - 14 \, a^{3} \cosh\left(d x + c\right)^{12} + 8 \, {\left(4845 \, a^{3} \cosh\left(d x + c\right)^{6} + 2295 \, a^{3} \cosh\left(d x + c\right)^{4} + 195 \, a^{3} \cosh\left(d x + c\right)^{2} + a^{3}\right)} \sinh\left(d x + c\right)^{14} + 16 \, {\left(4845 \, a^{3} \cosh\left(d x + c\right)^{7} + 3213 \, a^{3} \cosh\left(d x + c\right)^{5} + 455 \, a^{3} \cosh\left(d x + c\right)^{3} + 7 \, a^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{13} - 28 \, a^{3} \cosh\left(d x + c\right)^{10} + 2 \, {\left(62985 \, a^{3} \cosh\left(d x + c\right)^{8} + 55692 \, a^{3} \cosh\left(d x + c\right)^{6} + 11830 \, a^{3} \cosh\left(d x + c\right)^{4} + 364 \, a^{3} \cosh\left(d x + c\right)^{2} - 7 \, a^{3}\right)} \sinh\left(d x + c\right)^{12} + 8 \, {\left(20995 \, a^{3} \cosh\left(d x + c\right)^{9} + 23868 \, a^{3} \cosh\left(d x + c\right)^{7} + 7098 \, a^{3} \cosh\left(d x + c\right)^{5} + 364 \, a^{3} \cosh\left(d x + c\right)^{3} - 21 \, a^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{11} - 14 \, a^{3} \cosh\left(d x + c\right)^{8} + 4 \, {\left(46189 \, a^{3} \cosh\left(d x + c\right)^{10} + 65637 \, a^{3} \cosh\left(d x + c\right)^{8} + 26026 \, a^{3} \cosh\left(d x + c\right)^{6} + 2002 \, a^{3} \cosh\left(d x + c\right)^{4} - 231 \, a^{3} \cosh\left(d x + c\right)^{2} - 7 \, a^{3}\right)} \sinh\left(d x + c\right)^{10} + 8 \, {\left(20995 \, a^{3} \cosh\left(d x + c\right)^{11} + 36465 \, a^{3} \cosh\left(d x + c\right)^{9} + 18590 \, a^{3} \cosh\left(d x + c\right)^{7} + 2002 \, a^{3} \cosh\left(d x + c\right)^{5} - 385 \, a^{3} \cosh\left(d x + c\right)^{3} - 35 \, a^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} + 8 \, a^{3} \cosh\left(d x + c\right)^{6} + 2 \, {\left(62985 \, a^{3} \cosh\left(d x + c\right)^{12} + 131274 \, a^{3} \cosh\left(d x + c\right)^{10} + 83655 \, a^{3} \cosh\left(d x + c\right)^{8} + 12012 \, a^{3} \cosh\left(d x + c\right)^{6} - 3465 \, a^{3} \cosh\left(d x + c\right)^{4} - 630 \, a^{3} \cosh\left(d x + c\right)^{2} - 7 \, a^{3}\right)} \sinh\left(d x + c\right)^{8} + 16 \, {\left(4845 \, a^{3} \cosh\left(d x + c\right)^{13} + 11934 \, a^{3} \cosh\left(d x + c\right)^{11} + 9295 \, a^{3} \cosh\left(d x + c\right)^{9} + 1716 \, a^{3} \cosh\left(d x + c\right)^{7} - 693 \, a^{3} \cosh\left(d x + c\right)^{5} - 210 \, a^{3} \cosh\left(d x + c\right)^{3} - 7 \, a^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 13 \, a^{3} \cosh\left(d x + c\right)^{4} + 8 \, {\left(4845 \, a^{3} \cosh\left(d x + c\right)^{14} + 13923 \, a^{3} \cosh\left(d x + c\right)^{12} + 13013 \, a^{3} \cosh\left(d x + c\right)^{10} + 3003 \, a^{3} \cosh\left(d x + c\right)^{8} - 1617 \, a^{3} \cosh\left(d x + c\right)^{6} - 735 \, a^{3} \cosh\left(d x + c\right)^{4} - 49 \, a^{3} \cosh\left(d x + c\right)^{2} + a^{3}\right)} \sinh\left(d x + c\right)^{6} + 16 \, {\left(969 \, a^{3} \cosh\left(d x + c\right)^{15} + 3213 \, a^{3} \cosh\left(d x + c\right)^{13} + 3549 \, a^{3} \cosh\left(d x + c\right)^{11} + 1001 \, a^{3} \cosh\left(d x + c\right)^{9} - 693 \, a^{3} \cosh\left(d x + c\right)^{7} - 441 \, a^{3} \cosh\left(d x + c\right)^{5} - 49 \, 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} + 6 \, a^{3} \cosh\left(d x + c\right)^{2} + {\left(4845 \, a^{3} \cosh\left(d x + c\right)^{16} + 18360 \, a^{3} \cosh\left(d x + c\right)^{14} + 23660 \, a^{3} \cosh\left(d x + c\right)^{12} + 8008 \, a^{3} \cosh\left(d x + c\right)^{10} - 6930 \, a^{3} \cosh\left(d x + c\right)^{8} - 5880 \, a^{3} \cosh\left(d x + c\right)^{6} - 980 \, a^{3} \cosh\left(d x + c\right)^{4} + 120 \, a^{3} \cosh\left(d x + c\right)^{2} + 13 \, a^{3}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(285 \, a^{3} \cosh\left(d x + c\right)^{17} + 1224 \, a^{3} \cosh\left(d x + c\right)^{15} + 1820 \, a^{3} \cosh\left(d x + c\right)^{13} + 728 \, a^{3} \cosh\left(d x + c\right)^{11} - 770 \, a^{3} \cosh\left(d x + c\right)^{9} - 840 \, a^{3} \cosh\left(d x + c\right)^{7} - 196 \, a^{3} \cosh\left(d x + c\right)^{5} + 40 \, a^{3} \cosh\left(d x + c\right)^{3} + 13 \, a^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + a^{3} + 2 \, {\left(95 \, a^{3} \cosh\left(d x + c\right)^{18} + 459 \, a^{3} \cosh\left(d x + c\right)^{16} + 780 \, a^{3} \cosh\left(d x + c\right)^{14} + 364 \, a^{3} \cosh\left(d x + c\right)^{12} - 462 \, a^{3} \cosh\left(d x + c\right)^{10} - 630 \, a^{3} \cosh\left(d x + c\right)^{8} - 196 \, a^{3} \cosh\left(d x + c\right)^{6} + 60 \, a^{3} \cosh\left(d x + c\right)^{4} + 39 \, a^{3} \cosh\left(d x + c\right)^{2} + 3 \, a^{3}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(5 \, a^{3} \cosh\left(d x + c\right)^{19} + 27 \, a^{3} \cosh\left(d x + c\right)^{17} + 52 \, a^{3} \cosh\left(d x + c\right)^{15} + 28 \, a^{3} \cosh\left(d x + c\right)^{13} - 42 \, a^{3} \cosh\left(d x + c\right)^{11} - 70 \, a^{3} \cosh\left(d x + c\right)^{9} - 28 \, a^{3} \cosh\left(d x + c\right)^{7} + 12 \, a^{3} \cosh\left(d x + c\right)^{5} + 13 \, 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)\right)} \log\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right) - 1\right) + {\left(285 \, {\left(64 \, a^{3} - 192 \, a^{2} b - 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{18} + 85 \, {\left(1728 \, a^{3} - 1728 \, a^{2} b + 1536 \, a b^{2} + 427 \, b^{3}\right)} \cosh\left(d x + c\right)^{16} + 360 \, {\left(1440 \, a^{3} + 192 \, a b^{2} - 355 \, b^{3}\right)} \cosh\left(d x + c\right)^{14} + 208 \, {\left(5040 \, a^{3} + 1440 \, a^{2} b - 672 \, a b^{2} + 1235 \, b^{3}\right)} \cosh\left(d x + c\right)^{12} + 22 \, {\left(60480 \, a^{3} + 8640 \, a^{2} b - 768 \, a b^{2} - 15475 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} + 18 \, {\left(60480 \, a^{3} - 8640 \, a^{2} b - 768 \, a b^{2} + 15475 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 112 \, {\left(5040 \, a^{3} - 1440 \, a^{2} b - 672 \, a b^{2} - 1235 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 120 \, {\left(1440 \, a^{3} + 192 \, a b^{2} + 355 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 960 \, a^{3} + 2880 \, a^{2} b + 75 \, b^{3} + 15 \, {\left(1728 \, a^{3} + 1728 \, a^{2} b + 1536 \, a b^{2} - 427 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)}{960 \, {\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} + 6 \, d \cosh\left(d x + c\right)^{18} + 2 \, {\left(95 \, d \cosh\left(d x + c\right)^{2} + 3 \, d\right)} \sinh\left(d x + c\right)^{18} + 12 \, {\left(95 \, d \cosh\left(d x + c\right)^{3} + 9 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{17} + 13 \, d \cosh\left(d x + c\right)^{16} + {\left(4845 \, d \cosh\left(d x + c\right)^{4} + 918 \, d \cosh\left(d x + c\right)^{2} + 13 \, d\right)} \sinh\left(d x + c\right)^{16} + 16 \, {\left(969 \, d \cosh\left(d x + c\right)^{5} + 306 \, d \cosh\left(d x + c\right)^{3} + 13 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{15} + 8 \, d \cosh\left(d x + c\right)^{14} + 8 \, {\left(4845 \, d \cosh\left(d x + c\right)^{6} + 2295 \, d \cosh\left(d x + c\right)^{4} + 195 \, d \cosh\left(d x + c\right)^{2} + d\right)} \sinh\left(d x + c\right)^{14} + 16 \, {\left(4845 \, d \cosh\left(d x + c\right)^{7} + 3213 \, d \cosh\left(d x + c\right)^{5} + 455 \, d \cosh\left(d x + c\right)^{3} + 7 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{13} - 14 \, d \cosh\left(d x + c\right)^{12} + 2 \, {\left(62985 \, d \cosh\left(d x + c\right)^{8} + 55692 \, d \cosh\left(d x + c\right)^{6} + 11830 \, d \cosh\left(d x + c\right)^{4} + 364 \, d \cosh\left(d x + c\right)^{2} - 7 \, d\right)} \sinh\left(d x + c\right)^{12} + 8 \, {\left(20995 \, d \cosh\left(d x + c\right)^{9} + 23868 \, d \cosh\left(d x + c\right)^{7} + 7098 \, d \cosh\left(d x + c\right)^{5} + 364 \, d \cosh\left(d x + c\right)^{3} - 21 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{11} - 28 \, d \cosh\left(d x + c\right)^{10} + 4 \, {\left(46189 \, d \cosh\left(d x + c\right)^{10} + 65637 \, d \cosh\left(d x + c\right)^{8} + 26026 \, d \cosh\left(d x + c\right)^{6} + 2002 \, d \cosh\left(d x + c\right)^{4} - 231 \, d \cosh\left(d x + c\right)^{2} - 7 \, d\right)} \sinh\left(d x + c\right)^{10} + 8 \, {\left(20995 \, d \cosh\left(d x + c\right)^{11} + 36465 \, d \cosh\left(d x + c\right)^{9} + 18590 \, d \cosh\left(d x + c\right)^{7} + 2002 \, d \cosh\left(d x + c\right)^{5} - 385 \, d \cosh\left(d x + c\right)^{3} - 35 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} - 14 \, d \cosh\left(d x + c\right)^{8} + 2 \, {\left(62985 \, d \cosh\left(d x + c\right)^{12} + 131274 \, d \cosh\left(d x + c\right)^{10} + 83655 \, d \cosh\left(d x + c\right)^{8} + 12012 \, d \cosh\left(d x + c\right)^{6} - 3465 \, d \cosh\left(d x + c\right)^{4} - 630 \, d \cosh\left(d x + c\right)^{2} - 7 \, d\right)} \sinh\left(d x + c\right)^{8} + 16 \, {\left(4845 \, d \cosh\left(d x + c\right)^{13} + 11934 \, d \cosh\left(d x + c\right)^{11} + 9295 \, d \cosh\left(d x + c\right)^{9} + 1716 \, d \cosh\left(d x + c\right)^{7} - 693 \, d \cosh\left(d x + c\right)^{5} - 210 \, d \cosh\left(d x + c\right)^{3} - 7 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 8 \, d \cosh\left(d x + c\right)^{6} + 8 \, {\left(4845 \, d \cosh\left(d x + c\right)^{14} + 13923 \, d \cosh\left(d x + c\right)^{12} + 13013 \, d \cosh\left(d x + c\right)^{10} + 3003 \, d \cosh\left(d x + c\right)^{8} - 1617 \, d \cosh\left(d x + c\right)^{6} - 735 \, d \cosh\left(d x + c\right)^{4} - 49 \, d \cosh\left(d x + c\right)^{2} + d\right)} \sinh\left(d x + c\right)^{6} + 16 \, {\left(969 \, d \cosh\left(d x + c\right)^{15} + 3213 \, d \cosh\left(d x + c\right)^{13} + 3549 \, d \cosh\left(d x + c\right)^{11} + 1001 \, d \cosh\left(d x + c\right)^{9} - 693 \, d \cosh\left(d x + c\right)^{7} - 441 \, d \cosh\left(d x + c\right)^{5} - 49 \, d \cosh\left(d x + c\right)^{3} + 3 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 13 \, d \cosh\left(d x + c\right)^{4} + {\left(4845 \, d \cosh\left(d x + c\right)^{16} + 18360 \, d \cosh\left(d x + c\right)^{14} + 23660 \, d \cosh\left(d x + c\right)^{12} + 8008 \, d \cosh\left(d x + c\right)^{10} - 6930 \, d \cosh\left(d x + c\right)^{8} - 5880 \, d \cosh\left(d x + c\right)^{6} - 980 \, d \cosh\left(d x + c\right)^{4} + 120 \, d \cosh\left(d x + c\right)^{2} + 13 \, d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(285 \, d \cosh\left(d x + c\right)^{17} + 1224 \, d \cosh\left(d x + c\right)^{15} + 1820 \, d \cosh\left(d x + c\right)^{13} + 728 \, d \cosh\left(d x + c\right)^{11} - 770 \, d \cosh\left(d x + c\right)^{9} - 840 \, d \cosh\left(d x + c\right)^{7} - 196 \, d \cosh\left(d x + c\right)^{5} + 40 \, d \cosh\left(d x + c\right)^{3} + 13 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 6 \, d \cosh\left(d x + c\right)^{2} + 2 \, {\left(95 \, d \cosh\left(d x + c\right)^{18} + 459 \, d \cosh\left(d x + c\right)^{16} + 780 \, d \cosh\left(d x + c\right)^{14} + 364 \, d \cosh\left(d x + c\right)^{12} - 462 \, d \cosh\left(d x + c\right)^{10} - 630 \, d \cosh\left(d x + c\right)^{8} - 196 \, d \cosh\left(d x + c\right)^{6} + 60 \, d \cosh\left(d x + c\right)^{4} + 39 \, d \cosh\left(d x + c\right)^{2} + 3 \, d\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(5 \, d \cosh\left(d x + c\right)^{19} + 27 \, d \cosh\left(d x + c\right)^{17} + 52 \, d \cosh\left(d x + c\right)^{15} + 28 \, d \cosh\left(d x + c\right)^{13} - 42 \, d \cosh\left(d x + c\right)^{11} - 70 \, d \cosh\left(d x + c\right)^{9} - 28 \, d \cosh\left(d x + c\right)^{7} + 12 \, d \cosh\left(d x + c\right)^{5} + 13 \, d \cosh\left(d x + c\right)^{3} + 3 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + d\right)}}"," ",0,"-1/960*(15*(64*a^3 - 192*a^2*b - 5*b^3)*cosh(d*x + c)^19 + 285*(64*a^3 - 192*a^2*b - 5*b^3)*cosh(d*x + c)*sinh(d*x + c)^18 + 15*(64*a^3 - 192*a^2*b - 5*b^3)*sinh(d*x + c)^19 + 5*(1728*a^3 - 1728*a^2*b + 1536*a*b^2 + 427*b^3)*cosh(d*x + c)^17 + 5*(1728*a^3 - 1728*a^2*b + 1536*a*b^2 + 427*b^3 + 513*(64*a^3 - 192*a^2*b - 5*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^17 + 85*(171*(64*a^3 - 192*a^2*b - 5*b^3)*cosh(d*x + c)^3 + (1728*a^3 - 1728*a^2*b + 1536*a*b^2 + 427*b^3)*cosh(d*x + c))*sinh(d*x + c)^16 + 24*(1440*a^3 + 192*a*b^2 - 355*b^3)*cosh(d*x + c)^15 + 4*(14535*(64*a^3 - 192*a^2*b - 5*b^3)*cosh(d*x + c)^4 + 8640*a^3 + 1152*a*b^2 - 2130*b^3 + 170*(1728*a^3 - 1728*a^2*b + 1536*a*b^2 + 427*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^15 + 20*(8721*(64*a^3 - 192*a^2*b - 5*b^3)*cosh(d*x + c)^5 + 170*(1728*a^3 - 1728*a^2*b + 1536*a*b^2 + 427*b^3)*cosh(d*x + c)^3 + 18*(1440*a^3 + 192*a*b^2 - 355*b^3)*cosh(d*x + c))*sinh(d*x + c)^14 + 16*(5040*a^3 + 1440*a^2*b - 672*a*b^2 + 1235*b^3)*cosh(d*x + c)^13 + 4*(101745*(64*a^3 - 192*a^2*b - 5*b^3)*cosh(d*x + c)^6 + 2975*(1728*a^3 - 1728*a^2*b + 1536*a*b^2 + 427*b^3)*cosh(d*x + c)^4 + 20160*a^3 + 5760*a^2*b - 2688*a*b^2 + 4940*b^3 + 630*(1440*a^3 + 192*a*b^2 - 355*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^13 + 52*(14535*(64*a^3 - 192*a^2*b - 5*b^3)*cosh(d*x + c)^7 + 595*(1728*a^3 - 1728*a^2*b + 1536*a*b^2 + 427*b^3)*cosh(d*x + c)^5 + 210*(1440*a^3 + 192*a*b^2 - 355*b^3)*cosh(d*x + c)^3 + 4*(5040*a^3 + 1440*a^2*b - 672*a*b^2 + 1235*b^3)*cosh(d*x + c))*sinh(d*x + c)^12 + 2*(60480*a^3 + 8640*a^2*b - 768*a*b^2 - 15475*b^3)*cosh(d*x + c)^11 + 2*(566865*(64*a^3 - 192*a^2*b - 5*b^3)*cosh(d*x + c)^8 + 30940*(1728*a^3 - 1728*a^2*b + 1536*a*b^2 + 427*b^3)*cosh(d*x + c)^6 + 16380*(1440*a^3 + 192*a*b^2 - 355*b^3)*cosh(d*x + c)^4 + 60480*a^3 + 8640*a^2*b - 768*a*b^2 - 15475*b^3 + 624*(5040*a^3 + 1440*a^2*b - 672*a*b^2 + 1235*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^11 + 22*(62985*(64*a^3 - 192*a^2*b - 5*b^3)*cosh(d*x + c)^9 + 4420*(1728*a^3 - 1728*a^2*b + 1536*a*b^2 + 427*b^3)*cosh(d*x + c)^7 + 3276*(1440*a^3 + 192*a*b^2 - 355*b^3)*cosh(d*x + c)^5 + 208*(5040*a^3 + 1440*a^2*b - 672*a*b^2 + 1235*b^3)*cosh(d*x + c)^3 + (60480*a^3 + 8640*a^2*b - 768*a*b^2 - 15475*b^3)*cosh(d*x + c))*sinh(d*x + c)^10 + 2*(60480*a^3 - 8640*a^2*b - 768*a*b^2 + 15475*b^3)*cosh(d*x + c)^9 + 2*(692835*(64*a^3 - 192*a^2*b - 5*b^3)*cosh(d*x + c)^10 + 60775*(1728*a^3 - 1728*a^2*b + 1536*a*b^2 + 427*b^3)*cosh(d*x + c)^8 + 60060*(1440*a^3 + 192*a*b^2 - 355*b^3)*cosh(d*x + c)^6 + 5720*(5040*a^3 + 1440*a^2*b - 672*a*b^2 + 1235*b^3)*cosh(d*x + c)^4 + 60480*a^3 - 8640*a^2*b - 768*a*b^2 + 15475*b^3 + 55*(60480*a^3 + 8640*a^2*b - 768*a*b^2 - 15475*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^9 + 2*(566865*(64*a^3 - 192*a^2*b - 5*b^3)*cosh(d*x + c)^11 + 60775*(1728*a^3 - 1728*a^2*b + 1536*a*b^2 + 427*b^3)*cosh(d*x + c)^9 + 77220*(1440*a^3 + 192*a*b^2 - 355*b^3)*cosh(d*x + c)^7 + 10296*(5040*a^3 + 1440*a^2*b - 672*a*b^2 + 1235*b^3)*cosh(d*x + c)^5 + 165*(60480*a^3 + 8640*a^2*b - 768*a*b^2 - 15475*b^3)*cosh(d*x + c)^3 + 9*(60480*a^3 - 8640*a^2*b - 768*a*b^2 + 15475*b^3)*cosh(d*x + c))*sinh(d*x + c)^8 + 16*(5040*a^3 - 1440*a^2*b - 672*a*b^2 - 1235*b^3)*cosh(d*x + c)^7 + 4*(188955*(64*a^3 - 192*a^2*b - 5*b^3)*cosh(d*x + c)^12 + 24310*(1728*a^3 - 1728*a^2*b + 1536*a*b^2 + 427*b^3)*cosh(d*x + c)^10 + 38610*(1440*a^3 + 192*a*b^2 - 355*b^3)*cosh(d*x + c)^8 + 6864*(5040*a^3 + 1440*a^2*b - 672*a*b^2 + 1235*b^3)*cosh(d*x + c)^6 + 165*(60480*a^3 + 8640*a^2*b - 768*a*b^2 - 15475*b^3)*cosh(d*x + c)^4 + 20160*a^3 - 5760*a^2*b - 2688*a*b^2 - 4940*b^3 + 18*(60480*a^3 - 8640*a^2*b - 768*a*b^2 + 15475*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^7 + 4*(101745*(64*a^3 - 192*a^2*b - 5*b^3)*cosh(d*x + c)^13 + 15470*(1728*a^3 - 1728*a^2*b + 1536*a*b^2 + 427*b^3)*cosh(d*x + c)^11 + 30030*(1440*a^3 + 192*a*b^2 - 355*b^3)*cosh(d*x + c)^9 + 6864*(5040*a^3 + 1440*a^2*b - 672*a*b^2 + 1235*b^3)*cosh(d*x + c)^7 + 231*(60480*a^3 + 8640*a^2*b - 768*a*b^2 - 15475*b^3)*cosh(d*x + c)^5 + 42*(60480*a^3 - 8640*a^2*b - 768*a*b^2 + 15475*b^3)*cosh(d*x + c)^3 + 28*(5040*a^3 - 1440*a^2*b - 672*a*b^2 - 1235*b^3)*cosh(d*x + c))*sinh(d*x + c)^6 + 24*(1440*a^3 + 192*a*b^2 + 355*b^3)*cosh(d*x + c)^5 + 4*(43605*(64*a^3 - 192*a^2*b - 5*b^3)*cosh(d*x + c)^14 + 7735*(1728*a^3 - 1728*a^2*b + 1536*a*b^2 + 427*b^3)*cosh(d*x + c)^12 + 18018*(1440*a^3 + 192*a*b^2 - 355*b^3)*cosh(d*x + c)^10 + 5148*(5040*a^3 + 1440*a^2*b - 672*a*b^2 + 1235*b^3)*cosh(d*x + c)^8 + 231*(60480*a^3 + 8640*a^2*b - 768*a*b^2 - 15475*b^3)*cosh(d*x + c)^6 + 63*(60480*a^3 - 8640*a^2*b - 768*a*b^2 + 15475*b^3)*cosh(d*x + c)^4 + 8640*a^3 + 1152*a*b^2 + 2130*b^3 + 84*(5040*a^3 - 1440*a^2*b - 672*a*b^2 - 1235*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 4*(14535*(64*a^3 - 192*a^2*b - 5*b^3)*cosh(d*x + c)^15 + 2975*(1728*a^3 - 1728*a^2*b + 1536*a*b^2 + 427*b^3)*cosh(d*x + c)^13 + 8190*(1440*a^3 + 192*a*b^2 - 355*b^3)*cosh(d*x + c)^11 + 2860*(5040*a^3 + 1440*a^2*b - 672*a*b^2 + 1235*b^3)*cosh(d*x + c)^9 + 165*(60480*a^3 + 8640*a^2*b - 768*a*b^2 - 15475*b^3)*cosh(d*x + c)^7 + 63*(60480*a^3 - 8640*a^2*b - 768*a*b^2 + 15475*b^3)*cosh(d*x + c)^5 + 140*(5040*a^3 - 1440*a^2*b - 672*a*b^2 - 1235*b^3)*cosh(d*x + c)^3 + 30*(1440*a^3 + 192*a*b^2 + 355*b^3)*cosh(d*x + c))*sinh(d*x + c)^4 + 5*(1728*a^3 + 1728*a^2*b + 1536*a*b^2 - 427*b^3)*cosh(d*x + c)^3 + (14535*(64*a^3 - 192*a^2*b - 5*b^3)*cosh(d*x + c)^16 + 3400*(1728*a^3 - 1728*a^2*b + 1536*a*b^2 + 427*b^3)*cosh(d*x + c)^14 + 10920*(1440*a^3 + 192*a*b^2 - 355*b^3)*cosh(d*x + c)^12 + 4576*(5040*a^3 + 1440*a^2*b - 672*a*b^2 + 1235*b^3)*cosh(d*x + c)^10 + 330*(60480*a^3 + 8640*a^2*b - 768*a*b^2 - 15475*b^3)*cosh(d*x + c)^8 + 168*(60480*a^3 - 8640*a^2*b - 768*a*b^2 + 15475*b^3)*cosh(d*x + c)^6 + 560*(5040*a^3 - 1440*a^2*b - 672*a*b^2 - 1235*b^3)*cosh(d*x + c)^4 + 8640*a^3 + 8640*a^2*b + 7680*a*b^2 - 2135*b^3 + 240*(1440*a^3 + 192*a*b^2 + 355*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + (2565*(64*a^3 - 192*a^2*b - 5*b^3)*cosh(d*x + c)^17 + 680*(1728*a^3 - 1728*a^2*b + 1536*a*b^2 + 427*b^3)*cosh(d*x + c)^15 + 2520*(1440*a^3 + 192*a*b^2 - 355*b^3)*cosh(d*x + c)^13 + 1248*(5040*a^3 + 1440*a^2*b - 672*a*b^2 + 1235*b^3)*cosh(d*x + c)^11 + 110*(60480*a^3 + 8640*a^2*b - 768*a*b^2 - 15475*b^3)*cosh(d*x + c)^9 + 72*(60480*a^3 - 8640*a^2*b - 768*a*b^2 + 15475*b^3)*cosh(d*x + c)^7 + 336*(5040*a^3 - 1440*a^2*b - 672*a*b^2 - 1235*b^3)*cosh(d*x + c)^5 + 240*(1440*a^3 + 192*a*b^2 + 355*b^3)*cosh(d*x + c)^3 + 15*(1728*a^3 + 1728*a^2*b + 1536*a*b^2 - 427*b^3)*cosh(d*x + c))*sinh(d*x + c)^2 - 15*((192*a^2*b + 5*b^3)*cosh(d*x + c)^20 + 20*(192*a^2*b + 5*b^3)*cosh(d*x + c)*sinh(d*x + c)^19 + (192*a^2*b + 5*b^3)*sinh(d*x + c)^20 + 6*(192*a^2*b + 5*b^3)*cosh(d*x + c)^18 + 2*(576*a^2*b + 15*b^3 + 95*(192*a^2*b + 5*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^18 + 12*(95*(192*a^2*b + 5*b^3)*cosh(d*x + c)^3 + 9*(192*a^2*b + 5*b^3)*cosh(d*x + c))*sinh(d*x + c)^17 + 13*(192*a^2*b + 5*b^3)*cosh(d*x + c)^16 + (4845*(192*a^2*b + 5*b^3)*cosh(d*x + c)^4 + 2496*a^2*b + 65*b^3 + 918*(192*a^2*b + 5*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^16 + 16*(969*(192*a^2*b + 5*b^3)*cosh(d*x + c)^5 + 306*(192*a^2*b + 5*b^3)*cosh(d*x + c)^3 + 13*(192*a^2*b + 5*b^3)*cosh(d*x + c))*sinh(d*x + c)^15 + 8*(192*a^2*b + 5*b^3)*cosh(d*x + c)^14 + 8*(4845*(192*a^2*b + 5*b^3)*cosh(d*x + c)^6 + 2295*(192*a^2*b + 5*b^3)*cosh(d*x + c)^4 + 192*a^2*b + 5*b^3 + 195*(192*a^2*b + 5*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^14 + 16*(4845*(192*a^2*b + 5*b^3)*cosh(d*x + c)^7 + 3213*(192*a^2*b + 5*b^3)*cosh(d*x + c)^5 + 455*(192*a^2*b + 5*b^3)*cosh(d*x + c)^3 + 7*(192*a^2*b + 5*b^3)*cosh(d*x + c))*sinh(d*x + c)^13 - 14*(192*a^2*b + 5*b^3)*cosh(d*x + c)^12 + 2*(62985*(192*a^2*b + 5*b^3)*cosh(d*x + c)^8 + 55692*(192*a^2*b + 5*b^3)*cosh(d*x + c)^6 + 11830*(192*a^2*b + 5*b^3)*cosh(d*x + c)^4 - 1344*a^2*b - 35*b^3 + 364*(192*a^2*b + 5*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^12 + 8*(20995*(192*a^2*b + 5*b^3)*cosh(d*x + c)^9 + 23868*(192*a^2*b + 5*b^3)*cosh(d*x + c)^7 + 7098*(192*a^2*b + 5*b^3)*cosh(d*x + c)^5 + 364*(192*a^2*b + 5*b^3)*cosh(d*x + c)^3 - 21*(192*a^2*b + 5*b^3)*cosh(d*x + c))*sinh(d*x + c)^11 - 28*(192*a^2*b + 5*b^3)*cosh(d*x + c)^10 + 4*(46189*(192*a^2*b + 5*b^3)*cosh(d*x + c)^10 + 65637*(192*a^2*b + 5*b^3)*cosh(d*x + c)^8 + 26026*(192*a^2*b + 5*b^3)*cosh(d*x + c)^6 + 2002*(192*a^2*b + 5*b^3)*cosh(d*x + c)^4 - 1344*a^2*b - 35*b^3 - 231*(192*a^2*b + 5*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^10 + 8*(20995*(192*a^2*b + 5*b^3)*cosh(d*x + c)^11 + 36465*(192*a^2*b + 5*b^3)*cosh(d*x + c)^9 + 18590*(192*a^2*b + 5*b^3)*cosh(d*x + c)^7 + 2002*(192*a^2*b + 5*b^3)*cosh(d*x + c)^5 - 385*(192*a^2*b + 5*b^3)*cosh(d*x + c)^3 - 35*(192*a^2*b + 5*b^3)*cosh(d*x + c))*sinh(d*x + c)^9 - 14*(192*a^2*b + 5*b^3)*cosh(d*x + c)^8 + 2*(62985*(192*a^2*b + 5*b^3)*cosh(d*x + c)^12 + 131274*(192*a^2*b + 5*b^3)*cosh(d*x + c)^10 + 83655*(192*a^2*b + 5*b^3)*cosh(d*x + c)^8 + 12012*(192*a^2*b + 5*b^3)*cosh(d*x + c)^6 - 3465*(192*a^2*b + 5*b^3)*cosh(d*x + c)^4 - 1344*a^2*b - 35*b^3 - 630*(192*a^2*b + 5*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 16*(4845*(192*a^2*b + 5*b^3)*cosh(d*x + c)^13 + 11934*(192*a^2*b + 5*b^3)*cosh(d*x + c)^11 + 9295*(192*a^2*b + 5*b^3)*cosh(d*x + c)^9 + 1716*(192*a^2*b + 5*b^3)*cosh(d*x + c)^7 - 693*(192*a^2*b + 5*b^3)*cosh(d*x + c)^5 - 210*(192*a^2*b + 5*b^3)*cosh(d*x + c)^3 - 7*(192*a^2*b + 5*b^3)*cosh(d*x + c))*sinh(d*x + c)^7 + 8*(192*a^2*b + 5*b^3)*cosh(d*x + c)^6 + 8*(4845*(192*a^2*b + 5*b^3)*cosh(d*x + c)^14 + 13923*(192*a^2*b + 5*b^3)*cosh(d*x + c)^12 + 13013*(192*a^2*b + 5*b^3)*cosh(d*x + c)^10 + 3003*(192*a^2*b + 5*b^3)*cosh(d*x + c)^8 - 1617*(192*a^2*b + 5*b^3)*cosh(d*x + c)^6 - 735*(192*a^2*b + 5*b^3)*cosh(d*x + c)^4 + 192*a^2*b + 5*b^3 - 49*(192*a^2*b + 5*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 16*(969*(192*a^2*b + 5*b^3)*cosh(d*x + c)^15 + 3213*(192*a^2*b + 5*b^3)*cosh(d*x + c)^13 + 3549*(192*a^2*b + 5*b^3)*cosh(d*x + c)^11 + 1001*(192*a^2*b + 5*b^3)*cosh(d*x + c)^9 - 693*(192*a^2*b + 5*b^3)*cosh(d*x + c)^7 - 441*(192*a^2*b + 5*b^3)*cosh(d*x + c)^5 - 49*(192*a^2*b + 5*b^3)*cosh(d*x + c)^3 + 3*(192*a^2*b + 5*b^3)*cosh(d*x + c))*sinh(d*x + c)^5 + 13*(192*a^2*b + 5*b^3)*cosh(d*x + c)^4 + (4845*(192*a^2*b + 5*b^3)*cosh(d*x + c)^16 + 18360*(192*a^2*b + 5*b^3)*cosh(d*x + c)^14 + 23660*(192*a^2*b + 5*b^3)*cosh(d*x + c)^12 + 8008*(192*a^2*b + 5*b^3)*cosh(d*x + c)^10 - 6930*(192*a^2*b + 5*b^3)*cosh(d*x + c)^8 - 5880*(192*a^2*b + 5*b^3)*cosh(d*x + c)^6 - 980*(192*a^2*b + 5*b^3)*cosh(d*x + c)^4 + 2496*a^2*b + 65*b^3 + 120*(192*a^2*b + 5*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 4*(285*(192*a^2*b + 5*b^3)*cosh(d*x + c)^17 + 1224*(192*a^2*b + 5*b^3)*cosh(d*x + c)^15 + 1820*(192*a^2*b + 5*b^3)*cosh(d*x + c)^13 + 728*(192*a^2*b + 5*b^3)*cosh(d*x + c)^11 - 770*(192*a^2*b + 5*b^3)*cosh(d*x + c)^9 - 840*(192*a^2*b + 5*b^3)*cosh(d*x + c)^7 - 196*(192*a^2*b + 5*b^3)*cosh(d*x + c)^5 + 40*(192*a^2*b + 5*b^3)*cosh(d*x + c)^3 + 13*(192*a^2*b + 5*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 + 192*a^2*b + 5*b^3 + 6*(192*a^2*b + 5*b^3)*cosh(d*x + c)^2 + 2*(95*(192*a^2*b + 5*b^3)*cosh(d*x + c)^18 + 459*(192*a^2*b + 5*b^3)*cosh(d*x + c)^16 + 780*(192*a^2*b + 5*b^3)*cosh(d*x + c)^14 + 364*(192*a^2*b + 5*b^3)*cosh(d*x + c)^12 - 462*(192*a^2*b + 5*b^3)*cosh(d*x + c)^10 - 630*(192*a^2*b + 5*b^3)*cosh(d*x + c)^8 - 196*(192*a^2*b + 5*b^3)*cosh(d*x + c)^6 + 60*(192*a^2*b + 5*b^3)*cosh(d*x + c)^4 + 576*a^2*b + 15*b^3 + 39*(192*a^2*b + 5*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*(5*(192*a^2*b + 5*b^3)*cosh(d*x + c)^19 + 27*(192*a^2*b + 5*b^3)*cosh(d*x + c)^17 + 52*(192*a^2*b + 5*b^3)*cosh(d*x + c)^15 + 28*(192*a^2*b + 5*b^3)*cosh(d*x + c)^13 - 42*(192*a^2*b + 5*b^3)*cosh(d*x + c)^11 - 70*(192*a^2*b + 5*b^3)*cosh(d*x + c)^9 - 28*(192*a^2*b + 5*b^3)*cosh(d*x + c)^7 + 12*(192*a^2*b + 5*b^3)*cosh(d*x + c)^5 + 13*(192*a^2*b + 5*b^3)*cosh(d*x + c)^3 + 3*(192*a^2*b + 5*b^3)*cosh(d*x + c))*sinh(d*x + c))*arctan(cosh(d*x + c) + sinh(d*x + c)) + 15*(64*a^3 + 192*a^2*b + 5*b^3)*cosh(d*x + c) - 480*(a^3*cosh(d*x + c)^20 + 20*a^3*cosh(d*x + c)*sinh(d*x + c)^19 + a^3*sinh(d*x + c)^20 + 6*a^3*cosh(d*x + c)^18 + 13*a^3*cosh(d*x + c)^16 + 2*(95*a^3*cosh(d*x + c)^2 + 3*a^3)*sinh(d*x + c)^18 + 12*(95*a^3*cosh(d*x + c)^3 + 9*a^3*cosh(d*x + c))*sinh(d*x + c)^17 + 8*a^3*cosh(d*x + c)^14 + (4845*a^3*cosh(d*x + c)^4 + 918*a^3*cosh(d*x + c)^2 + 13*a^3)*sinh(d*x + c)^16 + 16*(969*a^3*cosh(d*x + c)^5 + 306*a^3*cosh(d*x + c)^3 + 13*a^3*cosh(d*x + c))*sinh(d*x + c)^15 - 14*a^3*cosh(d*x + c)^12 + 8*(4845*a^3*cosh(d*x + c)^6 + 2295*a^3*cosh(d*x + c)^4 + 195*a^3*cosh(d*x + c)^2 + a^3)*sinh(d*x + c)^14 + 16*(4845*a^3*cosh(d*x + c)^7 + 3213*a^3*cosh(d*x + c)^5 + 455*a^3*cosh(d*x + c)^3 + 7*a^3*cosh(d*x + c))*sinh(d*x + c)^13 - 28*a^3*cosh(d*x + c)^10 + 2*(62985*a^3*cosh(d*x + c)^8 + 55692*a^3*cosh(d*x + c)^6 + 11830*a^3*cosh(d*x + c)^4 + 364*a^3*cosh(d*x + c)^2 - 7*a^3)*sinh(d*x + c)^12 + 8*(20995*a^3*cosh(d*x + c)^9 + 23868*a^3*cosh(d*x + c)^7 + 7098*a^3*cosh(d*x + c)^5 + 364*a^3*cosh(d*x + c)^3 - 21*a^3*cosh(d*x + c))*sinh(d*x + c)^11 - 14*a^3*cosh(d*x + c)^8 + 4*(46189*a^3*cosh(d*x + c)^10 + 65637*a^3*cosh(d*x + c)^8 + 26026*a^3*cosh(d*x + c)^6 + 2002*a^3*cosh(d*x + c)^4 - 231*a^3*cosh(d*x + c)^2 - 7*a^3)*sinh(d*x + c)^10 + 8*(20995*a^3*cosh(d*x + c)^11 + 36465*a^3*cosh(d*x + c)^9 + 18590*a^3*cosh(d*x + c)^7 + 2002*a^3*cosh(d*x + c)^5 - 385*a^3*cosh(d*x + c)^3 - 35*a^3*cosh(d*x + c))*sinh(d*x + c)^9 + 8*a^3*cosh(d*x + c)^6 + 2*(62985*a^3*cosh(d*x + c)^12 + 131274*a^3*cosh(d*x + c)^10 + 83655*a^3*cosh(d*x + c)^8 + 12012*a^3*cosh(d*x + c)^6 - 3465*a^3*cosh(d*x + c)^4 - 630*a^3*cosh(d*x + c)^2 - 7*a^3)*sinh(d*x + c)^8 + 16*(4845*a^3*cosh(d*x + c)^13 + 11934*a^3*cosh(d*x + c)^11 + 9295*a^3*cosh(d*x + c)^9 + 1716*a^3*cosh(d*x + c)^7 - 693*a^3*cosh(d*x + c)^5 - 210*a^3*cosh(d*x + c)^3 - 7*a^3*cosh(d*x + c))*sinh(d*x + c)^7 + 13*a^3*cosh(d*x + c)^4 + 8*(4845*a^3*cosh(d*x + c)^14 + 13923*a^3*cosh(d*x + c)^12 + 13013*a^3*cosh(d*x + c)^10 + 3003*a^3*cosh(d*x + c)^8 - 1617*a^3*cosh(d*x + c)^6 - 735*a^3*cosh(d*x + c)^4 - 49*a^3*cosh(d*x + c)^2 + a^3)*sinh(d*x + c)^6 + 16*(969*a^3*cosh(d*x + c)^15 + 3213*a^3*cosh(d*x + c)^13 + 3549*a^3*cosh(d*x + c)^11 + 1001*a^3*cosh(d*x + c)^9 - 693*a^3*cosh(d*x + c)^7 - 441*a^3*cosh(d*x + c)^5 - 49*a^3*cosh(d*x + c)^3 + 3*a^3*cosh(d*x + c))*sinh(d*x + c)^5 + 6*a^3*cosh(d*x + c)^2 + (4845*a^3*cosh(d*x + c)^16 + 18360*a^3*cosh(d*x + c)^14 + 23660*a^3*cosh(d*x + c)^12 + 8008*a^3*cosh(d*x + c)^10 - 6930*a^3*cosh(d*x + c)^8 - 5880*a^3*cosh(d*x + c)^6 - 980*a^3*cosh(d*x + c)^4 + 120*a^3*cosh(d*x + c)^2 + 13*a^3)*sinh(d*x + c)^4 + 4*(285*a^3*cosh(d*x + c)^17 + 1224*a^3*cosh(d*x + c)^15 + 1820*a^3*cosh(d*x + c)^13 + 728*a^3*cosh(d*x + c)^11 - 770*a^3*cosh(d*x + c)^9 - 840*a^3*cosh(d*x + c)^7 - 196*a^3*cosh(d*x + c)^5 + 40*a^3*cosh(d*x + c)^3 + 13*a^3*cosh(d*x + c))*sinh(d*x + c)^3 + a^3 + 2*(95*a^3*cosh(d*x + c)^18 + 459*a^3*cosh(d*x + c)^16 + 780*a^3*cosh(d*x + c)^14 + 364*a^3*cosh(d*x + c)^12 - 462*a^3*cosh(d*x + c)^10 - 630*a^3*cosh(d*x + c)^8 - 196*a^3*cosh(d*x + c)^6 + 60*a^3*cosh(d*x + c)^4 + 39*a^3*cosh(d*x + c)^2 + 3*a^3)*sinh(d*x + c)^2 + 4*(5*a^3*cosh(d*x + c)^19 + 27*a^3*cosh(d*x + c)^17 + 52*a^3*cosh(d*x + c)^15 + 28*a^3*cosh(d*x + c)^13 - 42*a^3*cosh(d*x + c)^11 - 70*a^3*cosh(d*x + c)^9 - 28*a^3*cosh(d*x + c)^7 + 12*a^3*cosh(d*x + c)^5 + 13*a^3*cosh(d*x + c)^3 + 3*a^3*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) + 1) + 480*(a^3*cosh(d*x + c)^20 + 20*a^3*cosh(d*x + c)*sinh(d*x + c)^19 + a^3*sinh(d*x + c)^20 + 6*a^3*cosh(d*x + c)^18 + 13*a^3*cosh(d*x + c)^16 + 2*(95*a^3*cosh(d*x + c)^2 + 3*a^3)*sinh(d*x + c)^18 + 12*(95*a^3*cosh(d*x + c)^3 + 9*a^3*cosh(d*x + c))*sinh(d*x + c)^17 + 8*a^3*cosh(d*x + c)^14 + (4845*a^3*cosh(d*x + c)^4 + 918*a^3*cosh(d*x + c)^2 + 13*a^3)*sinh(d*x + c)^16 + 16*(969*a^3*cosh(d*x + c)^5 + 306*a^3*cosh(d*x + c)^3 + 13*a^3*cosh(d*x + c))*sinh(d*x + c)^15 - 14*a^3*cosh(d*x + c)^12 + 8*(4845*a^3*cosh(d*x + c)^6 + 2295*a^3*cosh(d*x + c)^4 + 195*a^3*cosh(d*x + c)^2 + a^3)*sinh(d*x + c)^14 + 16*(4845*a^3*cosh(d*x + c)^7 + 3213*a^3*cosh(d*x + c)^5 + 455*a^3*cosh(d*x + c)^3 + 7*a^3*cosh(d*x + c))*sinh(d*x + c)^13 - 28*a^3*cosh(d*x + c)^10 + 2*(62985*a^3*cosh(d*x + c)^8 + 55692*a^3*cosh(d*x + c)^6 + 11830*a^3*cosh(d*x + c)^4 + 364*a^3*cosh(d*x + c)^2 - 7*a^3)*sinh(d*x + c)^12 + 8*(20995*a^3*cosh(d*x + c)^9 + 23868*a^3*cosh(d*x + c)^7 + 7098*a^3*cosh(d*x + c)^5 + 364*a^3*cosh(d*x + c)^3 - 21*a^3*cosh(d*x + c))*sinh(d*x + c)^11 - 14*a^3*cosh(d*x + c)^8 + 4*(46189*a^3*cosh(d*x + c)^10 + 65637*a^3*cosh(d*x + c)^8 + 26026*a^3*cosh(d*x + c)^6 + 2002*a^3*cosh(d*x + c)^4 - 231*a^3*cosh(d*x + c)^2 - 7*a^3)*sinh(d*x + c)^10 + 8*(20995*a^3*cosh(d*x + c)^11 + 36465*a^3*cosh(d*x + c)^9 + 18590*a^3*cosh(d*x + c)^7 + 2002*a^3*cosh(d*x + c)^5 - 385*a^3*cosh(d*x + c)^3 - 35*a^3*cosh(d*x + c))*sinh(d*x + c)^9 + 8*a^3*cosh(d*x + c)^6 + 2*(62985*a^3*cosh(d*x + c)^12 + 131274*a^3*cosh(d*x + c)^10 + 83655*a^3*cosh(d*x + c)^8 + 12012*a^3*cosh(d*x + c)^6 - 3465*a^3*cosh(d*x + c)^4 - 630*a^3*cosh(d*x + c)^2 - 7*a^3)*sinh(d*x + c)^8 + 16*(4845*a^3*cosh(d*x + c)^13 + 11934*a^3*cosh(d*x + c)^11 + 9295*a^3*cosh(d*x + c)^9 + 1716*a^3*cosh(d*x + c)^7 - 693*a^3*cosh(d*x + c)^5 - 210*a^3*cosh(d*x + c)^3 - 7*a^3*cosh(d*x + c))*sinh(d*x + c)^7 + 13*a^3*cosh(d*x + c)^4 + 8*(4845*a^3*cosh(d*x + c)^14 + 13923*a^3*cosh(d*x + c)^12 + 13013*a^3*cosh(d*x + c)^10 + 3003*a^3*cosh(d*x + c)^8 - 1617*a^3*cosh(d*x + c)^6 - 735*a^3*cosh(d*x + c)^4 - 49*a^3*cosh(d*x + c)^2 + a^3)*sinh(d*x + c)^6 + 16*(969*a^3*cosh(d*x + c)^15 + 3213*a^3*cosh(d*x + c)^13 + 3549*a^3*cosh(d*x + c)^11 + 1001*a^3*cosh(d*x + c)^9 - 693*a^3*cosh(d*x + c)^7 - 441*a^3*cosh(d*x + c)^5 - 49*a^3*cosh(d*x + c)^3 + 3*a^3*cosh(d*x + c))*sinh(d*x + c)^5 + 6*a^3*cosh(d*x + c)^2 + (4845*a^3*cosh(d*x + c)^16 + 18360*a^3*cosh(d*x + c)^14 + 23660*a^3*cosh(d*x + c)^12 + 8008*a^3*cosh(d*x + c)^10 - 6930*a^3*cosh(d*x + c)^8 - 5880*a^3*cosh(d*x + c)^6 - 980*a^3*cosh(d*x + c)^4 + 120*a^3*cosh(d*x + c)^2 + 13*a^3)*sinh(d*x + c)^4 + 4*(285*a^3*cosh(d*x + c)^17 + 1224*a^3*cosh(d*x + c)^15 + 1820*a^3*cosh(d*x + c)^13 + 728*a^3*cosh(d*x + c)^11 - 770*a^3*cosh(d*x + c)^9 - 840*a^3*cosh(d*x + c)^7 - 196*a^3*cosh(d*x + c)^5 + 40*a^3*cosh(d*x + c)^3 + 13*a^3*cosh(d*x + c))*sinh(d*x + c)^3 + a^3 + 2*(95*a^3*cosh(d*x + c)^18 + 459*a^3*cosh(d*x + c)^16 + 780*a^3*cosh(d*x + c)^14 + 364*a^3*cosh(d*x + c)^12 - 462*a^3*cosh(d*x + c)^10 - 630*a^3*cosh(d*x + c)^8 - 196*a^3*cosh(d*x + c)^6 + 60*a^3*cosh(d*x + c)^4 + 39*a^3*cosh(d*x + c)^2 + 3*a^3)*sinh(d*x + c)^2 + 4*(5*a^3*cosh(d*x + c)^19 + 27*a^3*cosh(d*x + c)^17 + 52*a^3*cosh(d*x + c)^15 + 28*a^3*cosh(d*x + c)^13 - 42*a^3*cosh(d*x + c)^11 - 70*a^3*cosh(d*x + c)^9 - 28*a^3*cosh(d*x + c)^7 + 12*a^3*cosh(d*x + c)^5 + 13*a^3*cosh(d*x + c)^3 + 3*a^3*cosh(d*x + c))*sinh(d*x + c))*log(cosh(d*x + c) + sinh(d*x + c) - 1) + (285*(64*a^3 - 192*a^2*b - 5*b^3)*cosh(d*x + c)^18 + 85*(1728*a^3 - 1728*a^2*b + 1536*a*b^2 + 427*b^3)*cosh(d*x + c)^16 + 360*(1440*a^3 + 192*a*b^2 - 355*b^3)*cosh(d*x + c)^14 + 208*(5040*a^3 + 1440*a^2*b - 672*a*b^2 + 1235*b^3)*cosh(d*x + c)^12 + 22*(60480*a^3 + 8640*a^2*b - 768*a*b^2 - 15475*b^3)*cosh(d*x + c)^10 + 18*(60480*a^3 - 8640*a^2*b - 768*a*b^2 + 15475*b^3)*cosh(d*x + c)^8 + 112*(5040*a^3 - 1440*a^2*b - 672*a*b^2 - 1235*b^3)*cosh(d*x + c)^6 + 120*(1440*a^3 + 192*a*b^2 + 355*b^3)*cosh(d*x + c)^4 + 960*a^3 + 2880*a^2*b + 75*b^3 + 15*(1728*a^3 + 1728*a^2*b + 1536*a*b^2 - 427*b^3)*cosh(d*x + c)^2)*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 + 6*d*cosh(d*x + c)^18 + 2*(95*d*cosh(d*x + c)^2 + 3*d)*sinh(d*x + c)^18 + 12*(95*d*cosh(d*x + c)^3 + 9*d*cosh(d*x + c))*sinh(d*x + c)^17 + 13*d*cosh(d*x + c)^16 + (4845*d*cosh(d*x + c)^4 + 918*d*cosh(d*x + c)^2 + 13*d)*sinh(d*x + c)^16 + 16*(969*d*cosh(d*x + c)^5 + 306*d*cosh(d*x + c)^3 + 13*d*cosh(d*x + c))*sinh(d*x + c)^15 + 8*d*cosh(d*x + c)^14 + 8*(4845*d*cosh(d*x + c)^6 + 2295*d*cosh(d*x + c)^4 + 195*d*cosh(d*x + c)^2 + d)*sinh(d*x + c)^14 + 16*(4845*d*cosh(d*x + c)^7 + 3213*d*cosh(d*x + c)^5 + 455*d*cosh(d*x + c)^3 + 7*d*cosh(d*x + c))*sinh(d*x + c)^13 - 14*d*cosh(d*x + c)^12 + 2*(62985*d*cosh(d*x + c)^8 + 55692*d*cosh(d*x + c)^6 + 11830*d*cosh(d*x + c)^4 + 364*d*cosh(d*x + c)^2 - 7*d)*sinh(d*x + c)^12 + 8*(20995*d*cosh(d*x + c)^9 + 23868*d*cosh(d*x + c)^7 + 7098*d*cosh(d*x + c)^5 + 364*d*cosh(d*x + c)^3 - 21*d*cosh(d*x + c))*sinh(d*x + c)^11 - 28*d*cosh(d*x + c)^10 + 4*(46189*d*cosh(d*x + c)^10 + 65637*d*cosh(d*x + c)^8 + 26026*d*cosh(d*x + c)^6 + 2002*d*cosh(d*x + c)^4 - 231*d*cosh(d*x + c)^2 - 7*d)*sinh(d*x + c)^10 + 8*(20995*d*cosh(d*x + c)^11 + 36465*d*cosh(d*x + c)^9 + 18590*d*cosh(d*x + c)^7 + 2002*d*cosh(d*x + c)^5 - 385*d*cosh(d*x + c)^3 - 35*d*cosh(d*x + c))*sinh(d*x + c)^9 - 14*d*cosh(d*x + c)^8 + 2*(62985*d*cosh(d*x + c)^12 + 131274*d*cosh(d*x + c)^10 + 83655*d*cosh(d*x + c)^8 + 12012*d*cosh(d*x + c)^6 - 3465*d*cosh(d*x + c)^4 - 630*d*cosh(d*x + c)^2 - 7*d)*sinh(d*x + c)^8 + 16*(4845*d*cosh(d*x + c)^13 + 11934*d*cosh(d*x + c)^11 + 9295*d*cosh(d*x + c)^9 + 1716*d*cosh(d*x + c)^7 - 693*d*cosh(d*x + c)^5 - 210*d*cosh(d*x + c)^3 - 7*d*cosh(d*x + c))*sinh(d*x + c)^7 + 8*d*cosh(d*x + c)^6 + 8*(4845*d*cosh(d*x + c)^14 + 13923*d*cosh(d*x + c)^12 + 13013*d*cosh(d*x + c)^10 + 3003*d*cosh(d*x + c)^8 - 1617*d*cosh(d*x + c)^6 - 735*d*cosh(d*x + c)^4 - 49*d*cosh(d*x + c)^2 + d)*sinh(d*x + c)^6 + 16*(969*d*cosh(d*x + c)^15 + 3213*d*cosh(d*x + c)^13 + 3549*d*cosh(d*x + c)^11 + 1001*d*cosh(d*x + c)^9 - 693*d*cosh(d*x + c)^7 - 441*d*cosh(d*x + c)^5 - 49*d*cosh(d*x + c)^3 + 3*d*cosh(d*x + c))*sinh(d*x + c)^5 + 13*d*cosh(d*x + c)^4 + (4845*d*cosh(d*x + c)^16 + 18360*d*cosh(d*x + c)^14 + 23660*d*cosh(d*x + c)^12 + 8008*d*cosh(d*x + c)^10 - 6930*d*cosh(d*x + c)^8 - 5880*d*cosh(d*x + c)^6 - 980*d*cosh(d*x + c)^4 + 120*d*cosh(d*x + c)^2 + 13*d)*sinh(d*x + c)^4 + 4*(285*d*cosh(d*x + c)^17 + 1224*d*cosh(d*x + c)^15 + 1820*d*cosh(d*x + c)^13 + 728*d*cosh(d*x + c)^11 - 770*d*cosh(d*x + c)^9 - 840*d*cosh(d*x + c)^7 - 196*d*cosh(d*x + c)^5 + 40*d*cosh(d*x + c)^3 + 13*d*cosh(d*x + c))*sinh(d*x + c)^3 + 6*d*cosh(d*x + c)^2 + 2*(95*d*cosh(d*x + c)^18 + 459*d*cosh(d*x + c)^16 + 780*d*cosh(d*x + c)^14 + 364*d*cosh(d*x + c)^12 - 462*d*cosh(d*x + c)^10 - 630*d*cosh(d*x + c)^8 - 196*d*cosh(d*x + c)^6 + 60*d*cosh(d*x + c)^4 + 39*d*cosh(d*x + c)^2 + 3*d)*sinh(d*x + c)^2 + 4*(5*d*cosh(d*x + c)^19 + 27*d*cosh(d*x + c)^17 + 52*d*cosh(d*x + c)^15 + 28*d*cosh(d*x + c)^13 - 42*d*cosh(d*x + c)^11 - 70*d*cosh(d*x + c)^9 - 28*d*cosh(d*x + c)^7 + 12*d*cosh(d*x + c)^5 + 13*d*cosh(d*x + c)^3 + 3*d*cosh(d*x + c))*sinh(d*x + c) + d)","B",0
72,1,9459,0,0.582001," ","integrate(csch(d*x+c)^4*(a+b*tanh(d*x+c)^3)^3,x, algorithm=""fricas"")","\frac{90 \, a^{2} b \cosh\left(d x + c\right)^{20} + 1800 \, a^{2} b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{19} + 90 \, a^{2} b \sinh\left(d x + c\right)^{20} - 30 \, {\left(2 \, a^{3} - 9 \, a^{2} b + 6 \, a b^{2} + 2 \, b^{3}\right)} \cosh\left(d x + c\right)^{18} + 30 \, {\left(570 \, a^{2} b \cosh\left(d x + c\right)^{2} - 2 \, a^{3} + 9 \, a^{2} b - 6 \, a b^{2} - 2 \, b^{3}\right)} \sinh\left(d x + c\right)^{18} + 540 \, {\left(190 \, a^{2} b \cosh\left(d x + c\right)^{3} - {\left(2 \, a^{3} - 9 \, a^{2} b + 6 \, a b^{2} + 2 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{17} - 20 \, {\left(23 \, a^{3} - 3 \, a b^{2} - 13 \, b^{3}\right)} \cosh\left(d x + c\right)^{16} + 10 \, {\left(43605 \, a^{2} b \cosh\left(d x + c\right)^{4} - 46 \, a^{3} + 6 \, a b^{2} + 26 \, b^{3} - 459 \, {\left(2 \, a^{3} - 9 \, a^{2} b + 6 \, a b^{2} + 2 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{16} + 160 \, {\left(8721 \, a^{2} b \cosh\left(d x + c\right)^{5} - 153 \, {\left(2 \, a^{3} - 9 \, a^{2} b + 6 \, a b^{2} + 2 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 2 \, {\left(23 \, a^{3} - 3 \, a b^{2} - 13 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{15} - 20 \, {\left(76 \, a^{3} + 36 \, a^{2} b - 24 \, a b^{2} + 31 \, b^{3}\right)} \cosh\left(d x + c\right)^{14} + 20 \, {\left(174420 \, a^{2} b \cosh\left(d x + c\right)^{6} - 4590 \, {\left(2 \, a^{3} - 9 \, a^{2} b + 6 \, a b^{2} + 2 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 76 \, a^{3} - 36 \, a^{2} b + 24 \, a b^{2} - 31 \, b^{3} - 120 \, {\left(23 \, a^{3} - 3 \, a b^{2} - 13 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{14} + 40 \, {\left(174420 \, a^{2} b \cosh\left(d x + c\right)^{7} - 6426 \, {\left(2 \, a^{3} - 9 \, a^{2} b + 6 \, a b^{2} + 2 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 280 \, {\left(23 \, a^{3} - 3 \, a b^{2} - 13 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 7 \, {\left(76 \, a^{3} + 36 \, a^{2} b - 24 \, a b^{2} + 31 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{13} - 4 \, {\left(700 \, a^{3} + 135 \, a^{2} b + 48 \, a b^{2} - 245 \, b^{3}\right)} \cosh\left(d x + c\right)^{12} + 4 \, {\left(2834325 \, a^{2} b \cosh\left(d x + c\right)^{8} - 139230 \, {\left(2 \, a^{3} - 9 \, a^{2} b + 6 \, a b^{2} + 2 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} - 9100 \, {\left(23 \, a^{3} - 3 \, a b^{2} - 13 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 700 \, a^{3} - 135 \, a^{2} b - 48 \, a b^{2} + 245 \, b^{3} - 455 \, {\left(76 \, a^{3} + 36 \, a^{2} b - 24 \, a b^{2} + 31 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{12} + 16 \, {\left(944775 \, a^{2} b \cosh\left(d x + c\right)^{9} - 59670 \, {\left(2 \, a^{3} - 9 \, a^{2} b + 6 \, a b^{2} + 2 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} - 5460 \, {\left(23 \, a^{3} - 3 \, a b^{2} - 13 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 455 \, {\left(76 \, a^{3} + 36 \, a^{2} b - 24 \, a b^{2} + 31 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(700 \, a^{3} + 135 \, a^{2} b + 48 \, a b^{2} - 245 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{11} - 20 \, {\left(154 \, a^{3} - 27 \, a^{2} b + 18 \, a b^{2} + 49 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} + 4 \, {\left(4157010 \, a^{2} b \cosh\left(d x + c\right)^{10} - 328185 \, {\left(2 \, a^{3} - 9 \, a^{2} b + 6 \, a b^{2} + 2 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} - 40040 \, {\left(23 \, a^{3} - 3 \, a b^{2} - 13 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} - 5005 \, {\left(76 \, a^{3} + 36 \, a^{2} b - 24 \, a b^{2} + 31 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 770 \, a^{3} + 135 \, a^{2} b - 90 \, a b^{2} - 245 \, b^{3} - 66 \, {\left(700 \, a^{3} + 135 \, a^{2} b + 48 \, a b^{2} - 245 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{10} + 40 \, {\left(377910 \, a^{2} b \cosh\left(d x + c\right)^{11} - 36465 \, {\left(2 \, a^{3} - 9 \, a^{2} b + 6 \, a b^{2} + 2 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} - 5720 \, {\left(23 \, a^{3} - 3 \, a b^{2} - 13 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} - 1001 \, {\left(76 \, a^{3} + 36 \, a^{2} b - 24 \, a b^{2} + 31 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 22 \, {\left(700 \, a^{3} + 135 \, a^{2} b + 48 \, a b^{2} - 245 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 5 \, {\left(154 \, a^{3} - 27 \, a^{2} b + 18 \, a b^{2} + 49 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} - 4 \, {\left(490 \, a^{3} - 180 \, a^{2} b - 54 \, a b^{2} - 155 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 4 \, {\left(2834325 \, a^{2} b \cosh\left(d x + c\right)^{12} - 328185 \, {\left(2 \, a^{3} - 9 \, a^{2} b + 6 \, a b^{2} + 2 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} - 64350 \, {\left(23 \, a^{3} - 3 \, a b^{2} - 13 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} - 15015 \, {\left(76 \, a^{3} + 36 \, a^{2} b - 24 \, a b^{2} + 31 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} - 495 \, {\left(700 \, a^{3} + 135 \, a^{2} b + 48 \, a b^{2} - 245 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 490 \, a^{3} + 180 \, a^{2} b + 54 \, a b^{2} + 155 \, b^{3} - 225 \, {\left(154 \, a^{3} - 27 \, a^{2} b + 18 \, a b^{2} + 49 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{8} + 32 \, {\left(218025 \, a^{2} b \cosh\left(d x + c\right)^{13} - 29835 \, {\left(2 \, a^{3} - 9 \, a^{2} b + 6 \, a b^{2} + 2 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} - 7150 \, {\left(23 \, a^{3} - 3 \, a b^{2} - 13 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} - 2145 \, {\left(76 \, a^{3} + 36 \, a^{2} b - 24 \, a b^{2} + 31 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} - 99 \, {\left(700 \, a^{3} + 135 \, a^{2} b + 48 \, a b^{2} - 245 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 75 \, {\left(154 \, a^{3} - 27 \, a^{2} b + 18 \, a b^{2} + 49 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - {\left(490 \, a^{3} - 180 \, a^{2} b - 54 \, a b^{2} - 155 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} - 20 \, {\left(28 \, a^{3} + 13 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(872100 \, a^{2} b \cosh\left(d x + c\right)^{14} - 139230 \, {\left(2 \, a^{3} - 9 \, a^{2} b + 6 \, a b^{2} + 2 \, b^{3}\right)} \cosh\left(d x + c\right)^{12} - 40040 \, {\left(23 \, a^{3} - 3 \, a b^{2} - 13 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} - 15015 \, {\left(76 \, a^{3} + 36 \, a^{2} b - 24 \, a b^{2} + 31 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} - 924 \, {\left(700 \, a^{3} + 135 \, a^{2} b + 48 \, a b^{2} - 245 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} - 1050 \, {\left(154 \, a^{3} - 27 \, a^{2} b + 18 \, a b^{2} + 49 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 140 \, a^{3} - 65 \, b^{3} - 28 \, {\left(490 \, a^{3} - 180 \, a^{2} b - 54 \, a b^{2} - 155 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(174420 \, a^{2} b \cosh\left(d x + c\right)^{15} - 32130 \, {\left(2 \, a^{3} - 9 \, a^{2} b + 6 \, a b^{2} + 2 \, b^{3}\right)} \cosh\left(d x + c\right)^{13} - 10920 \, {\left(23 \, a^{3} - 3 \, a b^{2} - 13 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} - 5005 \, {\left(76 \, a^{3} + 36 \, a^{2} b - 24 \, a b^{2} + 31 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} - 396 \, {\left(700 \, a^{3} + 135 \, a^{2} b + 48 \, a b^{2} - 245 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} - 630 \, {\left(154 \, a^{3} - 27 \, a^{2} b + 18 \, a b^{2} + 49 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 28 \, {\left(490 \, a^{3} - 180 \, a^{2} b - 54 \, a b^{2} - 155 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 15 \, {\left(28 \, a^{3} + 13 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(40 \, a^{3} - 135 \, a^{2} b - 48 \, a b^{2} + 30 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(218025 \, a^{2} b \cosh\left(d x + c\right)^{16} - 45900 \, {\left(2 \, a^{3} - 9 \, a^{2} b + 6 \, a b^{2} + 2 \, b^{3}\right)} \cosh\left(d x + c\right)^{14} - 18200 \, {\left(23 \, a^{3} - 3 \, a b^{2} - 13 \, b^{3}\right)} \cosh\left(d x + c\right)^{12} - 10010 \, {\left(76 \, a^{3} + 36 \, a^{2} b - 24 \, a b^{2} + 31 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} - 990 \, {\left(700 \, a^{3} + 135 \, a^{2} b + 48 \, a b^{2} - 245 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} - 2100 \, {\left(154 \, a^{3} - 27 \, a^{2} b + 18 \, a b^{2} + 49 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} - 140 \, {\left(490 \, a^{3} - 180 \, a^{2} b - 54 \, a b^{2} - 155 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 40 \, a^{3} - 135 \, a^{2} b - 48 \, a b^{2} + 30 \, b^{3} - 150 \, {\left(28 \, a^{3} + 13 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(12825 \, a^{2} b \cosh\left(d x + c\right)^{17} - 3060 \, {\left(2 \, a^{3} - 9 \, a^{2} b + 6 \, a b^{2} + 2 \, b^{3}\right)} \cosh\left(d x + c\right)^{15} - 1400 \, {\left(23 \, a^{3} - 3 \, a b^{2} - 13 \, b^{3}\right)} \cosh\left(d x + c\right)^{13} - 910 \, {\left(76 \, a^{3} + 36 \, a^{2} b - 24 \, a b^{2} + 31 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} - 110 \, {\left(700 \, a^{3} + 135 \, a^{2} b + 48 \, a b^{2} - 245 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} - 300 \, {\left(154 \, a^{3} - 27 \, a^{2} b + 18 \, a b^{2} + 49 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} - 28 \, {\left(490 \, a^{3} - 180 \, a^{2} b - 54 \, a b^{2} - 155 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 50 \, {\left(28 \, a^{3} + 13 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(40 \, a^{3} - 135 \, a^{2} b - 48 \, a b^{2} + 30 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 20 \, a^{3} + 12 \, a b^{2} + 10 \, {\left(10 \, a^{3} - 9 \, a^{2} b + 6 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(8550 \, a^{2} b \cosh\left(d x + c\right)^{18} - 2295 \, {\left(2 \, a^{3} - 9 \, a^{2} b + 6 \, a b^{2} + 2 \, b^{3}\right)} \cosh\left(d x + c\right)^{16} - 1200 \, {\left(23 \, a^{3} - 3 \, a b^{2} - 13 \, b^{3}\right)} \cosh\left(d x + c\right)^{14} - 910 \, {\left(76 \, a^{3} + 36 \, a^{2} b - 24 \, a b^{2} + 31 \, b^{3}\right)} \cosh\left(d x + c\right)^{12} - 132 \, {\left(700 \, a^{3} + 135 \, a^{2} b + 48 \, a b^{2} - 245 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} - 450 \, {\left(154 \, a^{3} - 27 \, a^{2} b + 18 \, a b^{2} + 49 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} - 56 \, {\left(490 \, a^{3} - 180 \, a^{2} b - 54 \, a b^{2} - 155 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} - 150 \, {\left(28 \, a^{3} + 13 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 50 \, a^{3} - 45 \, a^{2} b + 30 \, a b^{2} + 6 \, {\left(40 \, a^{3} - 135 \, a^{2} b - 48 \, a b^{2} + 30 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} - 45 \, {\left(a^{2} b \cosh\left(d x + c\right)^{22} + 22 \, a^{2} b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{21} + a^{2} b \sinh\left(d x + c\right)^{22} + 5 \, a^{2} b \cosh\left(d x + c\right)^{20} + 7 \, a^{2} b \cosh\left(d x + c\right)^{18} + {\left(231 \, a^{2} b \cosh\left(d x + c\right)^{2} + 5 \, a^{2} b\right)} \sinh\left(d x + c\right)^{20} + 20 \, {\left(77 \, 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)^{19} - 5 \, a^{2} b \cosh\left(d x + c\right)^{16} + {\left(7315 \, a^{2} b \cosh\left(d x + c\right)^{4} + 950 \, a^{2} b \cosh\left(d x + c\right)^{2} + 7 \, a^{2} b\right)} \sinh\left(d x + c\right)^{18} + 6 \, {\left(4389 \, a^{2} b \cosh\left(d x + c\right)^{5} + 950 \, a^{2} b \cosh\left(d x + c\right)^{3} + 21 \, a^{2} b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{17} - 22 \, a^{2} b \cosh\left(d x + c\right)^{14} + {\left(74613 \, a^{2} b \cosh\left(d x + c\right)^{6} + 24225 \, a^{2} b \cosh\left(d x + c\right)^{4} + 1071 \, a^{2} b \cosh\left(d x + c\right)^{2} - 5 \, a^{2} b\right)} \sinh\left(d x + c\right)^{16} + 16 \, {\left(10659 \, a^{2} b \cosh\left(d x + c\right)^{7} + 4845 \, a^{2} b \cosh\left(d x + c\right)^{5} + 357 \, 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)^{15} - 14 \, a^{2} b \cosh\left(d x + c\right)^{12} + 2 \, {\left(159885 \, a^{2} b \cosh\left(d x + c\right)^{8} + 96900 \, a^{2} b \cosh\left(d x + c\right)^{6} + 10710 \, a^{2} b \cosh\left(d x + c\right)^{4} - 300 \, a^{2} b \cosh\left(d x + c\right)^{2} - 11 \, a^{2} b\right)} \sinh\left(d x + c\right)^{14} + 4 \, {\left(124355 \, a^{2} b \cosh\left(d x + c\right)^{9} + 96900 \, a^{2} b \cosh\left(d x + c\right)^{7} + 14994 \, a^{2} b \cosh\left(d x + c\right)^{5} - 700 \, a^{2} b \cosh\left(d x + c\right)^{3} - 77 \, a^{2} b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{13} + 14 \, a^{2} b \cosh\left(d x + c\right)^{10} + 2 \, {\left(323323 \, a^{2} b \cosh\left(d x + c\right)^{10} + 314925 \, a^{2} b \cosh\left(d x + c\right)^{8} + 64974 \, a^{2} b \cosh\left(d x + c\right)^{6} - 4550 \, a^{2} b \cosh\left(d x + c\right)^{4} - 1001 \, a^{2} b \cosh\left(d x + c\right)^{2} - 7 \, a^{2} b\right)} \sinh\left(d x + c\right)^{12} + 8 \, {\left(88179 \, a^{2} b \cosh\left(d x + c\right)^{11} + 104975 \, a^{2} b \cosh\left(d x + c\right)^{9} + 27846 \, a^{2} b \cosh\left(d x + c\right)^{7} - 2730 \, a^{2} b \cosh\left(d x + c\right)^{5} - 1001 \, a^{2} b \cosh\left(d x + c\right)^{3} - 21 \, a^{2} b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{11} + 22 \, a^{2} b \cosh\left(d x + c\right)^{8} + 2 \, {\left(323323 \, a^{2} b \cosh\left(d x + c\right)^{12} + 461890 \, a^{2} b \cosh\left(d x + c\right)^{10} + 153153 \, a^{2} b \cosh\left(d x + c\right)^{8} - 20020 \, a^{2} b \cosh\left(d x + c\right)^{6} - 11011 \, a^{2} b \cosh\left(d x + c\right)^{4} - 462 \, a^{2} b \cosh\left(d x + c\right)^{2} + 7 \, a^{2} b\right)} \sinh\left(d x + c\right)^{10} + 4 \, {\left(124355 \, a^{2} b \cosh\left(d x + c\right)^{13} + 209950 \, a^{2} b \cosh\left(d x + c\right)^{11} + 85085 \, a^{2} b \cosh\left(d x + c\right)^{9} - 14300 \, a^{2} b \cosh\left(d x + c\right)^{7} - 11011 \, a^{2} b \cosh\left(d x + c\right)^{5} - 770 \, 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)^{9} + 5 \, a^{2} b \cosh\left(d x + c\right)^{6} + 2 \, {\left(159885 \, a^{2} b \cosh\left(d x + c\right)^{14} + 314925 \, a^{2} b \cosh\left(d x + c\right)^{12} + 153153 \, a^{2} b \cosh\left(d x + c\right)^{10} - 32175 \, a^{2} b \cosh\left(d x + c\right)^{8} - 33033 \, a^{2} b \cosh\left(d x + c\right)^{6} - 3465 \, a^{2} b \cosh\left(d x + c\right)^{4} + 315 \, a^{2} b \cosh\left(d x + c\right)^{2} + 11 \, a^{2} b\right)} \sinh\left(d x + c\right)^{8} + 16 \, {\left(10659 \, a^{2} b \cosh\left(d x + c\right)^{15} + 24225 \, a^{2} b \cosh\left(d x + c\right)^{13} + 13923 \, a^{2} b \cosh\left(d x + c\right)^{11} - 3575 \, a^{2} b \cosh\left(d x + c\right)^{9} - 4719 \, a^{2} b \cosh\left(d x + c\right)^{7} - 693 \, a^{2} b \cosh\left(d x + c\right)^{5} + 105 \, a^{2} b \cosh\left(d x + c\right)^{3} + 11 \, a^{2} b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} - 7 \, a^{2} b \cosh\left(d x + c\right)^{4} + {\left(74613 \, a^{2} b \cosh\left(d x + c\right)^{16} + 193800 \, a^{2} b \cosh\left(d x + c\right)^{14} + 129948 \, a^{2} b \cosh\left(d x + c\right)^{12} - 40040 \, a^{2} b \cosh\left(d x + c\right)^{10} - 66066 \, a^{2} b \cosh\left(d x + c\right)^{8} - 12936 \, a^{2} b \cosh\left(d x + c\right)^{6} + 2940 \, a^{2} b \cosh\left(d x + c\right)^{4} + 616 \, a^{2} b \cosh\left(d x + c\right)^{2} + 5 \, a^{2} b\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(13167 \, a^{2} b \cosh\left(d x + c\right)^{17} + 38760 \, a^{2} b \cosh\left(d x + c\right)^{15} + 29988 \, a^{2} b \cosh\left(d x + c\right)^{13} - 10920 \, a^{2} b \cosh\left(d x + c\right)^{11} - 22022 \, a^{2} b \cosh\left(d x + c\right)^{9} - 5544 \, a^{2} b \cosh\left(d x + c\right)^{7} + 1764 \, a^{2} b \cosh\left(d x + c\right)^{5} + 616 \, a^{2} b \cosh\left(d x + c\right)^{3} + 15 \, a^{2} b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 5 \, a^{2} b \cosh\left(d x + c\right)^{2} + {\left(7315 \, a^{2} b \cosh\left(d x + c\right)^{18} + 24225 \, a^{2} b \cosh\left(d x + c\right)^{16} + 21420 \, a^{2} b \cosh\left(d x + c\right)^{14} - 9100 \, a^{2} b \cosh\left(d x + c\right)^{12} - 22022 \, a^{2} b \cosh\left(d x + c\right)^{10} - 6930 \, a^{2} b \cosh\left(d x + c\right)^{8} + 2940 \, a^{2} b \cosh\left(d x + c\right)^{6} + 1540 \, a^{2} b \cosh\left(d x + c\right)^{4} + 75 \, a^{2} b \cosh\left(d x + c\right)^{2} - 7 \, a^{2} b\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(385 \, a^{2} b \cosh\left(d x + c\right)^{19} + 1425 \, a^{2} b \cosh\left(d x + c\right)^{17} + 1428 \, a^{2} b \cosh\left(d x + c\right)^{15} - 700 \, a^{2} b \cosh\left(d x + c\right)^{13} - 2002 \, a^{2} b \cosh\left(d x + c\right)^{11} - 770 \, a^{2} b \cosh\left(d x + c\right)^{9} + 420 \, a^{2} b \cosh\left(d x + c\right)^{7} + 308 \, a^{2} b \cosh\left(d x + c\right)^{5} + 25 \, a^{2} b \cosh\left(d x + c\right)^{3} - 7 \, a^{2} b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - a^{2} b + {\left(231 \, a^{2} b \cosh\left(d x + c\right)^{20} + 950 \, a^{2} b \cosh\left(d x + c\right)^{18} + 1071 \, a^{2} b \cosh\left(d x + c\right)^{16} - 600 \, a^{2} b \cosh\left(d x + c\right)^{14} - 2002 \, a^{2} b \cosh\left(d x + c\right)^{12} - 924 \, a^{2} b \cosh\left(d x + c\right)^{10} + 630 \, a^{2} b \cosh\left(d x + c\right)^{8} + 616 \, a^{2} b \cosh\left(d x + c\right)^{6} + 75 \, a^{2} b \cosh\left(d x + c\right)^{4} - 42 \, a^{2} b \cosh\left(d x + c\right)^{2} - 5 \, a^{2} b\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(11 \, a^{2} b \cosh\left(d x + c\right)^{21} + 50 \, a^{2} b \cosh\left(d x + c\right)^{19} + 63 \, a^{2} b \cosh\left(d x + c\right)^{17} - 40 \, a^{2} b \cosh\left(d x + c\right)^{15} - 154 \, a^{2} b \cosh\left(d x + c\right)^{13} - 84 \, a^{2} b \cosh\left(d x + c\right)^{11} + 70 \, a^{2} b \cosh\left(d x + c\right)^{9} + 88 \, a^{2} b \cosh\left(d x + c\right)^{7} + 15 \, a^{2} b \cosh\left(d x + c\right)^{5} - 14 \, 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)\right)} \log\left(\frac{2 \, \cosh\left(d x + c\right)}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) + 45 \, {\left(a^{2} b \cosh\left(d x + c\right)^{22} + 22 \, a^{2} b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{21} + a^{2} b \sinh\left(d x + c\right)^{22} + 5 \, a^{2} b \cosh\left(d x + c\right)^{20} + 7 \, a^{2} b \cosh\left(d x + c\right)^{18} + {\left(231 \, a^{2} b \cosh\left(d x + c\right)^{2} + 5 \, a^{2} b\right)} \sinh\left(d x + c\right)^{20} + 20 \, {\left(77 \, 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)^{19} - 5 \, a^{2} b \cosh\left(d x + c\right)^{16} + {\left(7315 \, a^{2} b \cosh\left(d x + c\right)^{4} + 950 \, a^{2} b \cosh\left(d x + c\right)^{2} + 7 \, a^{2} b\right)} \sinh\left(d x + c\right)^{18} + 6 \, {\left(4389 \, a^{2} b \cosh\left(d x + c\right)^{5} + 950 \, a^{2} b \cosh\left(d x + c\right)^{3} + 21 \, a^{2} b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{17} - 22 \, a^{2} b \cosh\left(d x + c\right)^{14} + {\left(74613 \, a^{2} b \cosh\left(d x + c\right)^{6} + 24225 \, a^{2} b \cosh\left(d x + c\right)^{4} + 1071 \, a^{2} b \cosh\left(d x + c\right)^{2} - 5 \, a^{2} b\right)} \sinh\left(d x + c\right)^{16} + 16 \, {\left(10659 \, a^{2} b \cosh\left(d x + c\right)^{7} + 4845 \, a^{2} b \cosh\left(d x + c\right)^{5} + 357 \, 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)^{15} - 14 \, a^{2} b \cosh\left(d x + c\right)^{12} + 2 \, {\left(159885 \, a^{2} b \cosh\left(d x + c\right)^{8} + 96900 \, a^{2} b \cosh\left(d x + c\right)^{6} + 10710 \, a^{2} b \cosh\left(d x + c\right)^{4} - 300 \, a^{2} b \cosh\left(d x + c\right)^{2} - 11 \, a^{2} b\right)} \sinh\left(d x + c\right)^{14} + 4 \, {\left(124355 \, a^{2} b \cosh\left(d x + c\right)^{9} + 96900 \, a^{2} b \cosh\left(d x + c\right)^{7} + 14994 \, a^{2} b \cosh\left(d x + c\right)^{5} - 700 \, a^{2} b \cosh\left(d x + c\right)^{3} - 77 \, a^{2} b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{13} + 14 \, a^{2} b \cosh\left(d x + c\right)^{10} + 2 \, {\left(323323 \, a^{2} b \cosh\left(d x + c\right)^{10} + 314925 \, a^{2} b \cosh\left(d x + c\right)^{8} + 64974 \, a^{2} b \cosh\left(d x + c\right)^{6} - 4550 \, a^{2} b \cosh\left(d x + c\right)^{4} - 1001 \, a^{2} b \cosh\left(d x + c\right)^{2} - 7 \, a^{2} b\right)} \sinh\left(d x + c\right)^{12} + 8 \, {\left(88179 \, a^{2} b \cosh\left(d x + c\right)^{11} + 104975 \, a^{2} b \cosh\left(d x + c\right)^{9} + 27846 \, a^{2} b \cosh\left(d x + c\right)^{7} - 2730 \, a^{2} b \cosh\left(d x + c\right)^{5} - 1001 \, a^{2} b \cosh\left(d x + c\right)^{3} - 21 \, a^{2} b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{11} + 22 \, a^{2} b \cosh\left(d x + c\right)^{8} + 2 \, {\left(323323 \, a^{2} b \cosh\left(d x + c\right)^{12} + 461890 \, a^{2} b \cosh\left(d x + c\right)^{10} + 153153 \, a^{2} b \cosh\left(d x + c\right)^{8} - 20020 \, a^{2} b \cosh\left(d x + c\right)^{6} - 11011 \, a^{2} b \cosh\left(d x + c\right)^{4} - 462 \, a^{2} b \cosh\left(d x + c\right)^{2} + 7 \, a^{2} b\right)} \sinh\left(d x + c\right)^{10} + 4 \, {\left(124355 \, a^{2} b \cosh\left(d x + c\right)^{13} + 209950 \, a^{2} b \cosh\left(d x + c\right)^{11} + 85085 \, a^{2} b \cosh\left(d x + c\right)^{9} - 14300 \, a^{2} b \cosh\left(d x + c\right)^{7} - 11011 \, a^{2} b \cosh\left(d x + c\right)^{5} - 770 \, 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)^{9} + 5 \, a^{2} b \cosh\left(d x + c\right)^{6} + 2 \, {\left(159885 \, a^{2} b \cosh\left(d x + c\right)^{14} + 314925 \, a^{2} b \cosh\left(d x + c\right)^{12} + 153153 \, a^{2} b \cosh\left(d x + c\right)^{10} - 32175 \, a^{2} b \cosh\left(d x + c\right)^{8} - 33033 \, a^{2} b \cosh\left(d x + c\right)^{6} - 3465 \, a^{2} b \cosh\left(d x + c\right)^{4} + 315 \, a^{2} b \cosh\left(d x + c\right)^{2} + 11 \, a^{2} b\right)} \sinh\left(d x + c\right)^{8} + 16 \, {\left(10659 \, a^{2} b \cosh\left(d x + c\right)^{15} + 24225 \, a^{2} b \cosh\left(d x + c\right)^{13} + 13923 \, a^{2} b \cosh\left(d x + c\right)^{11} - 3575 \, a^{2} b \cosh\left(d x + c\right)^{9} - 4719 \, a^{2} b \cosh\left(d x + c\right)^{7} - 693 \, a^{2} b \cosh\left(d x + c\right)^{5} + 105 \, a^{2} b \cosh\left(d x + c\right)^{3} + 11 \, a^{2} b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} - 7 \, a^{2} b \cosh\left(d x + c\right)^{4} + {\left(74613 \, a^{2} b \cosh\left(d x + c\right)^{16} + 193800 \, a^{2} b \cosh\left(d x + c\right)^{14} + 129948 \, a^{2} b \cosh\left(d x + c\right)^{12} - 40040 \, a^{2} b \cosh\left(d x + c\right)^{10} - 66066 \, a^{2} b \cosh\left(d x + c\right)^{8} - 12936 \, a^{2} b \cosh\left(d x + c\right)^{6} + 2940 \, a^{2} b \cosh\left(d x + c\right)^{4} + 616 \, a^{2} b \cosh\left(d x + c\right)^{2} + 5 \, a^{2} b\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(13167 \, a^{2} b \cosh\left(d x + c\right)^{17} + 38760 \, a^{2} b \cosh\left(d x + c\right)^{15} + 29988 \, a^{2} b \cosh\left(d x + c\right)^{13} - 10920 \, a^{2} b \cosh\left(d x + c\right)^{11} - 22022 \, a^{2} b \cosh\left(d x + c\right)^{9} - 5544 \, a^{2} b \cosh\left(d x + c\right)^{7} + 1764 \, a^{2} b \cosh\left(d x + c\right)^{5} + 616 \, a^{2} b \cosh\left(d x + c\right)^{3} + 15 \, a^{2} b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 5 \, a^{2} b \cosh\left(d x + c\right)^{2} + {\left(7315 \, a^{2} b \cosh\left(d x + c\right)^{18} + 24225 \, a^{2} b \cosh\left(d x + c\right)^{16} + 21420 \, a^{2} b \cosh\left(d x + c\right)^{14} - 9100 \, a^{2} b \cosh\left(d x + c\right)^{12} - 22022 \, a^{2} b \cosh\left(d x + c\right)^{10} - 6930 \, a^{2} b \cosh\left(d x + c\right)^{8} + 2940 \, a^{2} b \cosh\left(d x + c\right)^{6} + 1540 \, a^{2} b \cosh\left(d x + c\right)^{4} + 75 \, a^{2} b \cosh\left(d x + c\right)^{2} - 7 \, a^{2} b\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(385 \, a^{2} b \cosh\left(d x + c\right)^{19} + 1425 \, a^{2} b \cosh\left(d x + c\right)^{17} + 1428 \, a^{2} b \cosh\left(d x + c\right)^{15} - 700 \, a^{2} b \cosh\left(d x + c\right)^{13} - 2002 \, a^{2} b \cosh\left(d x + c\right)^{11} - 770 \, a^{2} b \cosh\left(d x + c\right)^{9} + 420 \, a^{2} b \cosh\left(d x + c\right)^{7} + 308 \, a^{2} b \cosh\left(d x + c\right)^{5} + 25 \, a^{2} b \cosh\left(d x + c\right)^{3} - 7 \, a^{2} b \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - a^{2} b + {\left(231 \, a^{2} b \cosh\left(d x + c\right)^{20} + 950 \, a^{2} b \cosh\left(d x + c\right)^{18} + 1071 \, a^{2} b \cosh\left(d x + c\right)^{16} - 600 \, a^{2} b \cosh\left(d x + c\right)^{14} - 2002 \, a^{2} b \cosh\left(d x + c\right)^{12} - 924 \, a^{2} b \cosh\left(d x + c\right)^{10} + 630 \, a^{2} b \cosh\left(d x + c\right)^{8} + 616 \, a^{2} b \cosh\left(d x + c\right)^{6} + 75 \, a^{2} b \cosh\left(d x + c\right)^{4} - 42 \, a^{2} b \cosh\left(d x + c\right)^{2} - 5 \, a^{2} b\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(11 \, a^{2} b \cosh\left(d x + c\right)^{21} + 50 \, a^{2} b \cosh\left(d x + c\right)^{19} + 63 \, a^{2} b \cosh\left(d x + c\right)^{17} - 40 \, a^{2} b \cosh\left(d x + c\right)^{15} - 154 \, a^{2} b \cosh\left(d x + c\right)^{13} - 84 \, a^{2} b \cosh\left(d x + c\right)^{11} + 70 \, a^{2} b \cosh\left(d x + c\right)^{9} + 88 \, a^{2} b \cosh\left(d x + c\right)^{7} + 15 \, a^{2} b \cosh\left(d x + c\right)^{5} - 14 \, 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)\right)} \log\left(\frac{2 \, \sinh\left(d x + c\right)}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) + 4 \, {\left(450 \, a^{2} b \cosh\left(d x + c\right)^{19} - 135 \, {\left(2 \, a^{3} - 9 \, a^{2} b + 6 \, a b^{2} + 2 \, b^{3}\right)} \cosh\left(d x + c\right)^{17} - 80 \, {\left(23 \, a^{3} - 3 \, a b^{2} - 13 \, b^{3}\right)} \cosh\left(d x + c\right)^{15} - 70 \, {\left(76 \, a^{3} + 36 \, a^{2} b - 24 \, a b^{2} + 31 \, b^{3}\right)} \cosh\left(d x + c\right)^{13} - 12 \, {\left(700 \, a^{3} + 135 \, a^{2} b + 48 \, a b^{2} - 245 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} - 50 \, {\left(154 \, a^{3} - 27 \, a^{2} b + 18 \, a b^{2} + 49 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} - 8 \, {\left(490 \, a^{3} - 180 \, a^{2} b - 54 \, a b^{2} - 155 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} - 30 \, {\left(28 \, a^{3} + 13 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(40 \, a^{3} - 135 \, a^{2} b - 48 \, a b^{2} + 30 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 5 \, {\left(10 \, a^{3} - 9 \, a^{2} b + 6 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{15 \, {\left(d \cosh\left(d x + c\right)^{22} + 22 \, d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{21} + d \sinh\left(d x + c\right)^{22} + 5 \, d \cosh\left(d x + c\right)^{20} + {\left(231 \, d \cosh\left(d x + c\right)^{2} + 5 \, d\right)} \sinh\left(d x + c\right)^{20} + 20 \, {\left(77 \, d \cosh\left(d x + c\right)^{3} + 5 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{19} + 7 \, d \cosh\left(d x + c\right)^{18} + {\left(7315 \, d \cosh\left(d x + c\right)^{4} + 950 \, d \cosh\left(d x + c\right)^{2} + 7 \, d\right)} \sinh\left(d x + c\right)^{18} + 6 \, {\left(4389 \, d \cosh\left(d x + c\right)^{5} + 950 \, d \cosh\left(d x + c\right)^{3} + 21 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{17} - 5 \, d \cosh\left(d x + c\right)^{16} + {\left(74613 \, d \cosh\left(d x + c\right)^{6} + 24225 \, d \cosh\left(d x + c\right)^{4} + 1071 \, d \cosh\left(d x + c\right)^{2} - 5 \, d\right)} \sinh\left(d x + c\right)^{16} + 16 \, {\left(10659 \, d \cosh\left(d x + c\right)^{7} + 4845 \, d \cosh\left(d x + c\right)^{5} + 357 \, d \cosh\left(d x + c\right)^{3} - 5 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{15} - 22 \, d \cosh\left(d x + c\right)^{14} + 2 \, {\left(159885 \, d \cosh\left(d x + c\right)^{8} + 96900 \, d \cosh\left(d x + c\right)^{6} + 10710 \, d \cosh\left(d x + c\right)^{4} - 300 \, d \cosh\left(d x + c\right)^{2} - 11 \, d\right)} \sinh\left(d x + c\right)^{14} + 4 \, {\left(124355 \, d \cosh\left(d x + c\right)^{9} + 96900 \, d \cosh\left(d x + c\right)^{7} + 14994 \, d \cosh\left(d x + c\right)^{5} - 700 \, d \cosh\left(d x + c\right)^{3} - 77 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{13} - 14 \, d \cosh\left(d x + c\right)^{12} + 2 \, {\left(323323 \, d \cosh\left(d x + c\right)^{10} + 314925 \, d \cosh\left(d x + c\right)^{8} + 64974 \, d \cosh\left(d x + c\right)^{6} - 4550 \, d \cosh\left(d x + c\right)^{4} - 1001 \, d \cosh\left(d x + c\right)^{2} - 7 \, d\right)} \sinh\left(d x + c\right)^{12} + 8 \, {\left(88179 \, d \cosh\left(d x + c\right)^{11} + 104975 \, d \cosh\left(d x + c\right)^{9} + 27846 \, d \cosh\left(d x + c\right)^{7} - 2730 \, d \cosh\left(d x + c\right)^{5} - 1001 \, d \cosh\left(d x + c\right)^{3} - 21 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{11} + 14 \, d \cosh\left(d x + c\right)^{10} + 2 \, {\left(323323 \, d \cosh\left(d x + c\right)^{12} + 461890 \, d \cosh\left(d x + c\right)^{10} + 153153 \, d \cosh\left(d x + c\right)^{8} - 20020 \, d \cosh\left(d x + c\right)^{6} - 11011 \, d \cosh\left(d x + c\right)^{4} - 462 \, d \cosh\left(d x + c\right)^{2} + 7 \, d\right)} \sinh\left(d x + c\right)^{10} + 4 \, {\left(124355 \, d \cosh\left(d x + c\right)^{13} + 209950 \, d \cosh\left(d x + c\right)^{11} + 85085 \, d \cosh\left(d x + c\right)^{9} - 14300 \, d \cosh\left(d x + c\right)^{7} - 11011 \, d \cosh\left(d x + c\right)^{5} - 770 \, d \cosh\left(d x + c\right)^{3} + 35 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} + 22 \, d \cosh\left(d x + c\right)^{8} + 2 \, {\left(159885 \, d \cosh\left(d x + c\right)^{14} + 314925 \, d \cosh\left(d x + c\right)^{12} + 153153 \, d \cosh\left(d x + c\right)^{10} - 32175 \, d \cosh\left(d x + c\right)^{8} - 33033 \, d \cosh\left(d x + c\right)^{6} - 3465 \, d \cosh\left(d x + c\right)^{4} + 315 \, d \cosh\left(d x + c\right)^{2} + 11 \, d\right)} \sinh\left(d x + c\right)^{8} + 16 \, {\left(10659 \, d \cosh\left(d x + c\right)^{15} + 24225 \, d \cosh\left(d x + c\right)^{13} + 13923 \, d \cosh\left(d x + c\right)^{11} - 3575 \, d \cosh\left(d x + c\right)^{9} - 4719 \, d \cosh\left(d x + c\right)^{7} - 693 \, d \cosh\left(d x + c\right)^{5} + 105 \, d \cosh\left(d x + c\right)^{3} + 11 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 5 \, d \cosh\left(d x + c\right)^{6} + {\left(74613 \, d \cosh\left(d x + c\right)^{16} + 193800 \, d \cosh\left(d x + c\right)^{14} + 129948 \, d \cosh\left(d x + c\right)^{12} - 40040 \, d \cosh\left(d x + c\right)^{10} - 66066 \, d \cosh\left(d x + c\right)^{8} - 12936 \, d \cosh\left(d x + c\right)^{6} + 2940 \, d \cosh\left(d x + c\right)^{4} + 616 \, d \cosh\left(d x + c\right)^{2} + 5 \, d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(13167 \, d \cosh\left(d x + c\right)^{17} + 38760 \, d \cosh\left(d x + c\right)^{15} + 29988 \, d \cosh\left(d x + c\right)^{13} - 10920 \, d \cosh\left(d x + c\right)^{11} - 22022 \, d \cosh\left(d x + c\right)^{9} - 5544 \, d \cosh\left(d x + c\right)^{7} + 1764 \, d \cosh\left(d x + c\right)^{5} + 616 \, d \cosh\left(d x + c\right)^{3} + 15 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 7 \, d \cosh\left(d x + c\right)^{4} + {\left(7315 \, d \cosh\left(d x + c\right)^{18} + 24225 \, d \cosh\left(d x + c\right)^{16} + 21420 \, d \cosh\left(d x + c\right)^{14} - 9100 \, d \cosh\left(d x + c\right)^{12} - 22022 \, d \cosh\left(d x + c\right)^{10} - 6930 \, d \cosh\left(d x + c\right)^{8} + 2940 \, d \cosh\left(d x + c\right)^{6} + 1540 \, d \cosh\left(d x + c\right)^{4} + 75 \, d \cosh\left(d x + c\right)^{2} - 7 \, d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(385 \, d \cosh\left(d x + c\right)^{19} + 1425 \, d \cosh\left(d x + c\right)^{17} + 1428 \, d \cosh\left(d x + c\right)^{15} - 700 \, d \cosh\left(d x + c\right)^{13} - 2002 \, d \cosh\left(d x + c\right)^{11} - 770 \, d \cosh\left(d x + c\right)^{9} + 420 \, d \cosh\left(d x + c\right)^{7} + 308 \, d \cosh\left(d x + c\right)^{5} + 25 \, d \cosh\left(d x + c\right)^{3} - 7 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 5 \, d \cosh\left(d x + c\right)^{2} + {\left(231 \, d \cosh\left(d x + c\right)^{20} + 950 \, d \cosh\left(d x + c\right)^{18} + 1071 \, d \cosh\left(d x + c\right)^{16} - 600 \, d \cosh\left(d x + c\right)^{14} - 2002 \, d \cosh\left(d x + c\right)^{12} - 924 \, d \cosh\left(d x + c\right)^{10} + 630 \, d \cosh\left(d x + c\right)^{8} + 616 \, d \cosh\left(d x + c\right)^{6} + 75 \, d \cosh\left(d x + c\right)^{4} - 42 \, d \cosh\left(d x + c\right)^{2} - 5 \, d\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(11 \, d \cosh\left(d x + c\right)^{21} + 50 \, d \cosh\left(d x + c\right)^{19} + 63 \, d \cosh\left(d x + c\right)^{17} - 40 \, d \cosh\left(d x + c\right)^{15} - 154 \, d \cosh\left(d x + c\right)^{13} - 84 \, d \cosh\left(d x + c\right)^{11} + 70 \, d \cosh\left(d x + c\right)^{9} + 88 \, d \cosh\left(d x + c\right)^{7} + 15 \, d \cosh\left(d x + c\right)^{5} - 14 \, d \cosh\left(d x + c\right)^{3} - 5 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) - d\right)}}"," ",0,"1/15*(90*a^2*b*cosh(d*x + c)^20 + 1800*a^2*b*cosh(d*x + c)*sinh(d*x + c)^19 + 90*a^2*b*sinh(d*x + c)^20 - 30*(2*a^3 - 9*a^2*b + 6*a*b^2 + 2*b^3)*cosh(d*x + c)^18 + 30*(570*a^2*b*cosh(d*x + c)^2 - 2*a^3 + 9*a^2*b - 6*a*b^2 - 2*b^3)*sinh(d*x + c)^18 + 540*(190*a^2*b*cosh(d*x + c)^3 - (2*a^3 - 9*a^2*b + 6*a*b^2 + 2*b^3)*cosh(d*x + c))*sinh(d*x + c)^17 - 20*(23*a^3 - 3*a*b^2 - 13*b^3)*cosh(d*x + c)^16 + 10*(43605*a^2*b*cosh(d*x + c)^4 - 46*a^3 + 6*a*b^2 + 26*b^3 - 459*(2*a^3 - 9*a^2*b + 6*a*b^2 + 2*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^16 + 160*(8721*a^2*b*cosh(d*x + c)^5 - 153*(2*a^3 - 9*a^2*b + 6*a*b^2 + 2*b^3)*cosh(d*x + c)^3 - 2*(23*a^3 - 3*a*b^2 - 13*b^3)*cosh(d*x + c))*sinh(d*x + c)^15 - 20*(76*a^3 + 36*a^2*b - 24*a*b^2 + 31*b^3)*cosh(d*x + c)^14 + 20*(174420*a^2*b*cosh(d*x + c)^6 - 4590*(2*a^3 - 9*a^2*b + 6*a*b^2 + 2*b^3)*cosh(d*x + c)^4 - 76*a^3 - 36*a^2*b + 24*a*b^2 - 31*b^3 - 120*(23*a^3 - 3*a*b^2 - 13*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^14 + 40*(174420*a^2*b*cosh(d*x + c)^7 - 6426*(2*a^3 - 9*a^2*b + 6*a*b^2 + 2*b^3)*cosh(d*x + c)^5 - 280*(23*a^3 - 3*a*b^2 - 13*b^3)*cosh(d*x + c)^3 - 7*(76*a^3 + 36*a^2*b - 24*a*b^2 + 31*b^3)*cosh(d*x + c))*sinh(d*x + c)^13 - 4*(700*a^3 + 135*a^2*b + 48*a*b^2 - 245*b^3)*cosh(d*x + c)^12 + 4*(2834325*a^2*b*cosh(d*x + c)^8 - 139230*(2*a^3 - 9*a^2*b + 6*a*b^2 + 2*b^3)*cosh(d*x + c)^6 - 9100*(23*a^3 - 3*a*b^2 - 13*b^3)*cosh(d*x + c)^4 - 700*a^3 - 135*a^2*b - 48*a*b^2 + 245*b^3 - 455*(76*a^3 + 36*a^2*b - 24*a*b^2 + 31*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^12 + 16*(944775*a^2*b*cosh(d*x + c)^9 - 59670*(2*a^3 - 9*a^2*b + 6*a*b^2 + 2*b^3)*cosh(d*x + c)^7 - 5460*(23*a^3 - 3*a*b^2 - 13*b^3)*cosh(d*x + c)^5 - 455*(76*a^3 + 36*a^2*b - 24*a*b^2 + 31*b^3)*cosh(d*x + c)^3 - 3*(700*a^3 + 135*a^2*b + 48*a*b^2 - 245*b^3)*cosh(d*x + c))*sinh(d*x + c)^11 - 20*(154*a^3 - 27*a^2*b + 18*a*b^2 + 49*b^3)*cosh(d*x + c)^10 + 4*(4157010*a^2*b*cosh(d*x + c)^10 - 328185*(2*a^3 - 9*a^2*b + 6*a*b^2 + 2*b^3)*cosh(d*x + c)^8 - 40040*(23*a^3 - 3*a*b^2 - 13*b^3)*cosh(d*x + c)^6 - 5005*(76*a^3 + 36*a^2*b - 24*a*b^2 + 31*b^3)*cosh(d*x + c)^4 - 770*a^3 + 135*a^2*b - 90*a*b^2 - 245*b^3 - 66*(700*a^3 + 135*a^2*b + 48*a*b^2 - 245*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^10 + 40*(377910*a^2*b*cosh(d*x + c)^11 - 36465*(2*a^3 - 9*a^2*b + 6*a*b^2 + 2*b^3)*cosh(d*x + c)^9 - 5720*(23*a^3 - 3*a*b^2 - 13*b^3)*cosh(d*x + c)^7 - 1001*(76*a^3 + 36*a^2*b - 24*a*b^2 + 31*b^3)*cosh(d*x + c)^5 - 22*(700*a^3 + 135*a^2*b + 48*a*b^2 - 245*b^3)*cosh(d*x + c)^3 - 5*(154*a^3 - 27*a^2*b + 18*a*b^2 + 49*b^3)*cosh(d*x + c))*sinh(d*x + c)^9 - 4*(490*a^3 - 180*a^2*b - 54*a*b^2 - 155*b^3)*cosh(d*x + c)^8 + 4*(2834325*a^2*b*cosh(d*x + c)^12 - 328185*(2*a^3 - 9*a^2*b + 6*a*b^2 + 2*b^3)*cosh(d*x + c)^10 - 64350*(23*a^3 - 3*a*b^2 - 13*b^3)*cosh(d*x + c)^8 - 15015*(76*a^3 + 36*a^2*b - 24*a*b^2 + 31*b^3)*cosh(d*x + c)^6 - 495*(700*a^3 + 135*a^2*b + 48*a*b^2 - 245*b^3)*cosh(d*x + c)^4 - 490*a^3 + 180*a^2*b + 54*a*b^2 + 155*b^3 - 225*(154*a^3 - 27*a^2*b + 18*a*b^2 + 49*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 32*(218025*a^2*b*cosh(d*x + c)^13 - 29835*(2*a^3 - 9*a^2*b + 6*a*b^2 + 2*b^3)*cosh(d*x + c)^11 - 7150*(23*a^3 - 3*a*b^2 - 13*b^3)*cosh(d*x + c)^9 - 2145*(76*a^3 + 36*a^2*b - 24*a*b^2 + 31*b^3)*cosh(d*x + c)^7 - 99*(700*a^3 + 135*a^2*b + 48*a*b^2 - 245*b^3)*cosh(d*x + c)^5 - 75*(154*a^3 - 27*a^2*b + 18*a*b^2 + 49*b^3)*cosh(d*x + c)^3 - (490*a^3 - 180*a^2*b - 54*a*b^2 - 155*b^3)*cosh(d*x + c))*sinh(d*x + c)^7 - 20*(28*a^3 + 13*b^3)*cosh(d*x + c)^6 + 4*(872100*a^2*b*cosh(d*x + c)^14 - 139230*(2*a^3 - 9*a^2*b + 6*a*b^2 + 2*b^3)*cosh(d*x + c)^12 - 40040*(23*a^3 - 3*a*b^2 - 13*b^3)*cosh(d*x + c)^10 - 15015*(76*a^3 + 36*a^2*b - 24*a*b^2 + 31*b^3)*cosh(d*x + c)^8 - 924*(700*a^3 + 135*a^2*b + 48*a*b^2 - 245*b^3)*cosh(d*x + c)^6 - 1050*(154*a^3 - 27*a^2*b + 18*a*b^2 + 49*b^3)*cosh(d*x + c)^4 - 140*a^3 - 65*b^3 - 28*(490*a^3 - 180*a^2*b - 54*a*b^2 - 155*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(174420*a^2*b*cosh(d*x + c)^15 - 32130*(2*a^3 - 9*a^2*b + 6*a*b^2 + 2*b^3)*cosh(d*x + c)^13 - 10920*(23*a^3 - 3*a*b^2 - 13*b^3)*cosh(d*x + c)^11 - 5005*(76*a^3 + 36*a^2*b - 24*a*b^2 + 31*b^3)*cosh(d*x + c)^9 - 396*(700*a^3 + 135*a^2*b + 48*a*b^2 - 245*b^3)*cosh(d*x + c)^7 - 630*(154*a^3 - 27*a^2*b + 18*a*b^2 + 49*b^3)*cosh(d*x + c)^5 - 28*(490*a^3 - 180*a^2*b - 54*a*b^2 - 155*b^3)*cosh(d*x + c)^3 - 15*(28*a^3 + 13*b^3)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(40*a^3 - 135*a^2*b - 48*a*b^2 + 30*b^3)*cosh(d*x + c)^4 + 2*(218025*a^2*b*cosh(d*x + c)^16 - 45900*(2*a^3 - 9*a^2*b + 6*a*b^2 + 2*b^3)*cosh(d*x + c)^14 - 18200*(23*a^3 - 3*a*b^2 - 13*b^3)*cosh(d*x + c)^12 - 10010*(76*a^3 + 36*a^2*b - 24*a*b^2 + 31*b^3)*cosh(d*x + c)^10 - 990*(700*a^3 + 135*a^2*b + 48*a*b^2 - 245*b^3)*cosh(d*x + c)^8 - 2100*(154*a^3 - 27*a^2*b + 18*a*b^2 + 49*b^3)*cosh(d*x + c)^6 - 140*(490*a^3 - 180*a^2*b - 54*a*b^2 - 155*b^3)*cosh(d*x + c)^4 + 40*a^3 - 135*a^2*b - 48*a*b^2 + 30*b^3 - 150*(28*a^3 + 13*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(12825*a^2*b*cosh(d*x + c)^17 - 3060*(2*a^3 - 9*a^2*b + 6*a*b^2 + 2*b^3)*cosh(d*x + c)^15 - 1400*(23*a^3 - 3*a*b^2 - 13*b^3)*cosh(d*x + c)^13 - 910*(76*a^3 + 36*a^2*b - 24*a*b^2 + 31*b^3)*cosh(d*x + c)^11 - 110*(700*a^3 + 135*a^2*b + 48*a*b^2 - 245*b^3)*cosh(d*x + c)^9 - 300*(154*a^3 - 27*a^2*b + 18*a*b^2 + 49*b^3)*cosh(d*x + c)^7 - 28*(490*a^3 - 180*a^2*b - 54*a*b^2 - 155*b^3)*cosh(d*x + c)^5 - 50*(28*a^3 + 13*b^3)*cosh(d*x + c)^3 + (40*a^3 - 135*a^2*b - 48*a*b^2 + 30*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 + 20*a^3 + 12*a*b^2 + 10*(10*a^3 - 9*a^2*b + 6*a*b^2)*cosh(d*x + c)^2 + 2*(8550*a^2*b*cosh(d*x + c)^18 - 2295*(2*a^3 - 9*a^2*b + 6*a*b^2 + 2*b^3)*cosh(d*x + c)^16 - 1200*(23*a^3 - 3*a*b^2 - 13*b^3)*cosh(d*x + c)^14 - 910*(76*a^3 + 36*a^2*b - 24*a*b^2 + 31*b^3)*cosh(d*x + c)^12 - 132*(700*a^3 + 135*a^2*b + 48*a*b^2 - 245*b^3)*cosh(d*x + c)^10 - 450*(154*a^3 - 27*a^2*b + 18*a*b^2 + 49*b^3)*cosh(d*x + c)^8 - 56*(490*a^3 - 180*a^2*b - 54*a*b^2 - 155*b^3)*cosh(d*x + c)^6 - 150*(28*a^3 + 13*b^3)*cosh(d*x + c)^4 + 50*a^3 - 45*a^2*b + 30*a*b^2 + 6*(40*a^3 - 135*a^2*b - 48*a*b^2 + 30*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - 45*(a^2*b*cosh(d*x + c)^22 + 22*a^2*b*cosh(d*x + c)*sinh(d*x + c)^21 + a^2*b*sinh(d*x + c)^22 + 5*a^2*b*cosh(d*x + c)^20 + 7*a^2*b*cosh(d*x + c)^18 + (231*a^2*b*cosh(d*x + c)^2 + 5*a^2*b)*sinh(d*x + c)^20 + 20*(77*a^2*b*cosh(d*x + c)^3 + 5*a^2*b*cosh(d*x + c))*sinh(d*x + c)^19 - 5*a^2*b*cosh(d*x + c)^16 + (7315*a^2*b*cosh(d*x + c)^4 + 950*a^2*b*cosh(d*x + c)^2 + 7*a^2*b)*sinh(d*x + c)^18 + 6*(4389*a^2*b*cosh(d*x + c)^5 + 950*a^2*b*cosh(d*x + c)^3 + 21*a^2*b*cosh(d*x + c))*sinh(d*x + c)^17 - 22*a^2*b*cosh(d*x + c)^14 + (74613*a^2*b*cosh(d*x + c)^6 + 24225*a^2*b*cosh(d*x + c)^4 + 1071*a^2*b*cosh(d*x + c)^2 - 5*a^2*b)*sinh(d*x + c)^16 + 16*(10659*a^2*b*cosh(d*x + c)^7 + 4845*a^2*b*cosh(d*x + c)^5 + 357*a^2*b*cosh(d*x + c)^3 - 5*a^2*b*cosh(d*x + c))*sinh(d*x + c)^15 - 14*a^2*b*cosh(d*x + c)^12 + 2*(159885*a^2*b*cosh(d*x + c)^8 + 96900*a^2*b*cosh(d*x + c)^6 + 10710*a^2*b*cosh(d*x + c)^4 - 300*a^2*b*cosh(d*x + c)^2 - 11*a^2*b)*sinh(d*x + c)^14 + 4*(124355*a^2*b*cosh(d*x + c)^9 + 96900*a^2*b*cosh(d*x + c)^7 + 14994*a^2*b*cosh(d*x + c)^5 - 700*a^2*b*cosh(d*x + c)^3 - 77*a^2*b*cosh(d*x + c))*sinh(d*x + c)^13 + 14*a^2*b*cosh(d*x + c)^10 + 2*(323323*a^2*b*cosh(d*x + c)^10 + 314925*a^2*b*cosh(d*x + c)^8 + 64974*a^2*b*cosh(d*x + c)^6 - 4550*a^2*b*cosh(d*x + c)^4 - 1001*a^2*b*cosh(d*x + c)^2 - 7*a^2*b)*sinh(d*x + c)^12 + 8*(88179*a^2*b*cosh(d*x + c)^11 + 104975*a^2*b*cosh(d*x + c)^9 + 27846*a^2*b*cosh(d*x + c)^7 - 2730*a^2*b*cosh(d*x + c)^5 - 1001*a^2*b*cosh(d*x + c)^3 - 21*a^2*b*cosh(d*x + c))*sinh(d*x + c)^11 + 22*a^2*b*cosh(d*x + c)^8 + 2*(323323*a^2*b*cosh(d*x + c)^12 + 461890*a^2*b*cosh(d*x + c)^10 + 153153*a^2*b*cosh(d*x + c)^8 - 20020*a^2*b*cosh(d*x + c)^6 - 11011*a^2*b*cosh(d*x + c)^4 - 462*a^2*b*cosh(d*x + c)^2 + 7*a^2*b)*sinh(d*x + c)^10 + 4*(124355*a^2*b*cosh(d*x + c)^13 + 209950*a^2*b*cosh(d*x + c)^11 + 85085*a^2*b*cosh(d*x + c)^9 - 14300*a^2*b*cosh(d*x + c)^7 - 11011*a^2*b*cosh(d*x + c)^5 - 770*a^2*b*cosh(d*x + c)^3 + 35*a^2*b*cosh(d*x + c))*sinh(d*x + c)^9 + 5*a^2*b*cosh(d*x + c)^6 + 2*(159885*a^2*b*cosh(d*x + c)^14 + 314925*a^2*b*cosh(d*x + c)^12 + 153153*a^2*b*cosh(d*x + c)^10 - 32175*a^2*b*cosh(d*x + c)^8 - 33033*a^2*b*cosh(d*x + c)^6 - 3465*a^2*b*cosh(d*x + c)^4 + 315*a^2*b*cosh(d*x + c)^2 + 11*a^2*b)*sinh(d*x + c)^8 + 16*(10659*a^2*b*cosh(d*x + c)^15 + 24225*a^2*b*cosh(d*x + c)^13 + 13923*a^2*b*cosh(d*x + c)^11 - 3575*a^2*b*cosh(d*x + c)^9 - 4719*a^2*b*cosh(d*x + c)^7 - 693*a^2*b*cosh(d*x + c)^5 + 105*a^2*b*cosh(d*x + c)^3 + 11*a^2*b*cosh(d*x + c))*sinh(d*x + c)^7 - 7*a^2*b*cosh(d*x + c)^4 + (74613*a^2*b*cosh(d*x + c)^16 + 193800*a^2*b*cosh(d*x + c)^14 + 129948*a^2*b*cosh(d*x + c)^12 - 40040*a^2*b*cosh(d*x + c)^10 - 66066*a^2*b*cosh(d*x + c)^8 - 12936*a^2*b*cosh(d*x + c)^6 + 2940*a^2*b*cosh(d*x + c)^4 + 616*a^2*b*cosh(d*x + c)^2 + 5*a^2*b)*sinh(d*x + c)^6 + 2*(13167*a^2*b*cosh(d*x + c)^17 + 38760*a^2*b*cosh(d*x + c)^15 + 29988*a^2*b*cosh(d*x + c)^13 - 10920*a^2*b*cosh(d*x + c)^11 - 22022*a^2*b*cosh(d*x + c)^9 - 5544*a^2*b*cosh(d*x + c)^7 + 1764*a^2*b*cosh(d*x + c)^5 + 616*a^2*b*cosh(d*x + c)^3 + 15*a^2*b*cosh(d*x + c))*sinh(d*x + c)^5 - 5*a^2*b*cosh(d*x + c)^2 + (7315*a^2*b*cosh(d*x + c)^18 + 24225*a^2*b*cosh(d*x + c)^16 + 21420*a^2*b*cosh(d*x + c)^14 - 9100*a^2*b*cosh(d*x + c)^12 - 22022*a^2*b*cosh(d*x + c)^10 - 6930*a^2*b*cosh(d*x + c)^8 + 2940*a^2*b*cosh(d*x + c)^6 + 1540*a^2*b*cosh(d*x + c)^4 + 75*a^2*b*cosh(d*x + c)^2 - 7*a^2*b)*sinh(d*x + c)^4 + 4*(385*a^2*b*cosh(d*x + c)^19 + 1425*a^2*b*cosh(d*x + c)^17 + 1428*a^2*b*cosh(d*x + c)^15 - 700*a^2*b*cosh(d*x + c)^13 - 2002*a^2*b*cosh(d*x + c)^11 - 770*a^2*b*cosh(d*x + c)^9 + 420*a^2*b*cosh(d*x + c)^7 + 308*a^2*b*cosh(d*x + c)^5 + 25*a^2*b*cosh(d*x + c)^3 - 7*a^2*b*cosh(d*x + c))*sinh(d*x + c)^3 - a^2*b + (231*a^2*b*cosh(d*x + c)^20 + 950*a^2*b*cosh(d*x + c)^18 + 1071*a^2*b*cosh(d*x + c)^16 - 600*a^2*b*cosh(d*x + c)^14 - 2002*a^2*b*cosh(d*x + c)^12 - 924*a^2*b*cosh(d*x + c)^10 + 630*a^2*b*cosh(d*x + c)^8 + 616*a^2*b*cosh(d*x + c)^6 + 75*a^2*b*cosh(d*x + c)^4 - 42*a^2*b*cosh(d*x + c)^2 - 5*a^2*b)*sinh(d*x + c)^2 + 2*(11*a^2*b*cosh(d*x + c)^21 + 50*a^2*b*cosh(d*x + c)^19 + 63*a^2*b*cosh(d*x + c)^17 - 40*a^2*b*cosh(d*x + c)^15 - 154*a^2*b*cosh(d*x + c)^13 - 84*a^2*b*cosh(d*x + c)^11 + 70*a^2*b*cosh(d*x + c)^9 + 88*a^2*b*cosh(d*x + c)^7 + 15*a^2*b*cosh(d*x + c)^5 - 14*a^2*b*cosh(d*x + c)^3 - 5*a^2*b*cosh(d*x + c))*sinh(d*x + c))*log(2*cosh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))) + 45*(a^2*b*cosh(d*x + c)^22 + 22*a^2*b*cosh(d*x + c)*sinh(d*x + c)^21 + a^2*b*sinh(d*x + c)^22 + 5*a^2*b*cosh(d*x + c)^20 + 7*a^2*b*cosh(d*x + c)^18 + (231*a^2*b*cosh(d*x + c)^2 + 5*a^2*b)*sinh(d*x + c)^20 + 20*(77*a^2*b*cosh(d*x + c)^3 + 5*a^2*b*cosh(d*x + c))*sinh(d*x + c)^19 - 5*a^2*b*cosh(d*x + c)^16 + (7315*a^2*b*cosh(d*x + c)^4 + 950*a^2*b*cosh(d*x + c)^2 + 7*a^2*b)*sinh(d*x + c)^18 + 6*(4389*a^2*b*cosh(d*x + c)^5 + 950*a^2*b*cosh(d*x + c)^3 + 21*a^2*b*cosh(d*x + c))*sinh(d*x + c)^17 - 22*a^2*b*cosh(d*x + c)^14 + (74613*a^2*b*cosh(d*x + c)^6 + 24225*a^2*b*cosh(d*x + c)^4 + 1071*a^2*b*cosh(d*x + c)^2 - 5*a^2*b)*sinh(d*x + c)^16 + 16*(10659*a^2*b*cosh(d*x + c)^7 + 4845*a^2*b*cosh(d*x + c)^5 + 357*a^2*b*cosh(d*x + c)^3 - 5*a^2*b*cosh(d*x + c))*sinh(d*x + c)^15 - 14*a^2*b*cosh(d*x + c)^12 + 2*(159885*a^2*b*cosh(d*x + c)^8 + 96900*a^2*b*cosh(d*x + c)^6 + 10710*a^2*b*cosh(d*x + c)^4 - 300*a^2*b*cosh(d*x + c)^2 - 11*a^2*b)*sinh(d*x + c)^14 + 4*(124355*a^2*b*cosh(d*x + c)^9 + 96900*a^2*b*cosh(d*x + c)^7 + 14994*a^2*b*cosh(d*x + c)^5 - 700*a^2*b*cosh(d*x + c)^3 - 77*a^2*b*cosh(d*x + c))*sinh(d*x + c)^13 + 14*a^2*b*cosh(d*x + c)^10 + 2*(323323*a^2*b*cosh(d*x + c)^10 + 314925*a^2*b*cosh(d*x + c)^8 + 64974*a^2*b*cosh(d*x + c)^6 - 4550*a^2*b*cosh(d*x + c)^4 - 1001*a^2*b*cosh(d*x + c)^2 - 7*a^2*b)*sinh(d*x + c)^12 + 8*(88179*a^2*b*cosh(d*x + c)^11 + 104975*a^2*b*cosh(d*x + c)^9 + 27846*a^2*b*cosh(d*x + c)^7 - 2730*a^2*b*cosh(d*x + c)^5 - 1001*a^2*b*cosh(d*x + c)^3 - 21*a^2*b*cosh(d*x + c))*sinh(d*x + c)^11 + 22*a^2*b*cosh(d*x + c)^8 + 2*(323323*a^2*b*cosh(d*x + c)^12 + 461890*a^2*b*cosh(d*x + c)^10 + 153153*a^2*b*cosh(d*x + c)^8 - 20020*a^2*b*cosh(d*x + c)^6 - 11011*a^2*b*cosh(d*x + c)^4 - 462*a^2*b*cosh(d*x + c)^2 + 7*a^2*b)*sinh(d*x + c)^10 + 4*(124355*a^2*b*cosh(d*x + c)^13 + 209950*a^2*b*cosh(d*x + c)^11 + 85085*a^2*b*cosh(d*x + c)^9 - 14300*a^2*b*cosh(d*x + c)^7 - 11011*a^2*b*cosh(d*x + c)^5 - 770*a^2*b*cosh(d*x + c)^3 + 35*a^2*b*cosh(d*x + c))*sinh(d*x + c)^9 + 5*a^2*b*cosh(d*x + c)^6 + 2*(159885*a^2*b*cosh(d*x + c)^14 + 314925*a^2*b*cosh(d*x + c)^12 + 153153*a^2*b*cosh(d*x + c)^10 - 32175*a^2*b*cosh(d*x + c)^8 - 33033*a^2*b*cosh(d*x + c)^6 - 3465*a^2*b*cosh(d*x + c)^4 + 315*a^2*b*cosh(d*x + c)^2 + 11*a^2*b)*sinh(d*x + c)^8 + 16*(10659*a^2*b*cosh(d*x + c)^15 + 24225*a^2*b*cosh(d*x + c)^13 + 13923*a^2*b*cosh(d*x + c)^11 - 3575*a^2*b*cosh(d*x + c)^9 - 4719*a^2*b*cosh(d*x + c)^7 - 693*a^2*b*cosh(d*x + c)^5 + 105*a^2*b*cosh(d*x + c)^3 + 11*a^2*b*cosh(d*x + c))*sinh(d*x + c)^7 - 7*a^2*b*cosh(d*x + c)^4 + (74613*a^2*b*cosh(d*x + c)^16 + 193800*a^2*b*cosh(d*x + c)^14 + 129948*a^2*b*cosh(d*x + c)^12 - 40040*a^2*b*cosh(d*x + c)^10 - 66066*a^2*b*cosh(d*x + c)^8 - 12936*a^2*b*cosh(d*x + c)^6 + 2940*a^2*b*cosh(d*x + c)^4 + 616*a^2*b*cosh(d*x + c)^2 + 5*a^2*b)*sinh(d*x + c)^6 + 2*(13167*a^2*b*cosh(d*x + c)^17 + 38760*a^2*b*cosh(d*x + c)^15 + 29988*a^2*b*cosh(d*x + c)^13 - 10920*a^2*b*cosh(d*x + c)^11 - 22022*a^2*b*cosh(d*x + c)^9 - 5544*a^2*b*cosh(d*x + c)^7 + 1764*a^2*b*cosh(d*x + c)^5 + 616*a^2*b*cosh(d*x + c)^3 + 15*a^2*b*cosh(d*x + c))*sinh(d*x + c)^5 - 5*a^2*b*cosh(d*x + c)^2 + (7315*a^2*b*cosh(d*x + c)^18 + 24225*a^2*b*cosh(d*x + c)^16 + 21420*a^2*b*cosh(d*x + c)^14 - 9100*a^2*b*cosh(d*x + c)^12 - 22022*a^2*b*cosh(d*x + c)^10 - 6930*a^2*b*cosh(d*x + c)^8 + 2940*a^2*b*cosh(d*x + c)^6 + 1540*a^2*b*cosh(d*x + c)^4 + 75*a^2*b*cosh(d*x + c)^2 - 7*a^2*b)*sinh(d*x + c)^4 + 4*(385*a^2*b*cosh(d*x + c)^19 + 1425*a^2*b*cosh(d*x + c)^17 + 1428*a^2*b*cosh(d*x + c)^15 - 700*a^2*b*cosh(d*x + c)^13 - 2002*a^2*b*cosh(d*x + c)^11 - 770*a^2*b*cosh(d*x + c)^9 + 420*a^2*b*cosh(d*x + c)^7 + 308*a^2*b*cosh(d*x + c)^5 + 25*a^2*b*cosh(d*x + c)^3 - 7*a^2*b*cosh(d*x + c))*sinh(d*x + c)^3 - a^2*b + (231*a^2*b*cosh(d*x + c)^20 + 950*a^2*b*cosh(d*x + c)^18 + 1071*a^2*b*cosh(d*x + c)^16 - 600*a^2*b*cosh(d*x + c)^14 - 2002*a^2*b*cosh(d*x + c)^12 - 924*a^2*b*cosh(d*x + c)^10 + 630*a^2*b*cosh(d*x + c)^8 + 616*a^2*b*cosh(d*x + c)^6 + 75*a^2*b*cosh(d*x + c)^4 - 42*a^2*b*cosh(d*x + c)^2 - 5*a^2*b)*sinh(d*x + c)^2 + 2*(11*a^2*b*cosh(d*x + c)^21 + 50*a^2*b*cosh(d*x + c)^19 + 63*a^2*b*cosh(d*x + c)^17 - 40*a^2*b*cosh(d*x + c)^15 - 154*a^2*b*cosh(d*x + c)^13 - 84*a^2*b*cosh(d*x + c)^11 + 70*a^2*b*cosh(d*x + c)^9 + 88*a^2*b*cosh(d*x + c)^7 + 15*a^2*b*cosh(d*x + c)^5 - 14*a^2*b*cosh(d*x + c)^3 - 5*a^2*b*cosh(d*x + c))*sinh(d*x + c))*log(2*sinh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))) + 4*(450*a^2*b*cosh(d*x + c)^19 - 135*(2*a^3 - 9*a^2*b + 6*a*b^2 + 2*b^3)*cosh(d*x + c)^17 - 80*(23*a^3 - 3*a*b^2 - 13*b^3)*cosh(d*x + c)^15 - 70*(76*a^3 + 36*a^2*b - 24*a*b^2 + 31*b^3)*cosh(d*x + c)^13 - 12*(700*a^3 + 135*a^2*b + 48*a*b^2 - 245*b^3)*cosh(d*x + c)^11 - 50*(154*a^3 - 27*a^2*b + 18*a*b^2 + 49*b^3)*cosh(d*x + c)^9 - 8*(490*a^3 - 180*a^2*b - 54*a*b^2 - 155*b^3)*cosh(d*x + c)^7 - 30*(28*a^3 + 13*b^3)*cosh(d*x + c)^5 + 2*(40*a^3 - 135*a^2*b - 48*a*b^2 + 30*b^3)*cosh(d*x + c)^3 + 5*(10*a^3 - 9*a^2*b + 6*a*b^2)*cosh(d*x + c))*sinh(d*x + c))/(d*cosh(d*x + c)^22 + 22*d*cosh(d*x + c)*sinh(d*x + c)^21 + d*sinh(d*x + c)^22 + 5*d*cosh(d*x + c)^20 + (231*d*cosh(d*x + c)^2 + 5*d)*sinh(d*x + c)^20 + 20*(77*d*cosh(d*x + c)^3 + 5*d*cosh(d*x + c))*sinh(d*x + c)^19 + 7*d*cosh(d*x + c)^18 + (7315*d*cosh(d*x + c)^4 + 950*d*cosh(d*x + c)^2 + 7*d)*sinh(d*x + c)^18 + 6*(4389*d*cosh(d*x + c)^5 + 950*d*cosh(d*x + c)^3 + 21*d*cosh(d*x + c))*sinh(d*x + c)^17 - 5*d*cosh(d*x + c)^16 + (74613*d*cosh(d*x + c)^6 + 24225*d*cosh(d*x + c)^4 + 1071*d*cosh(d*x + c)^2 - 5*d)*sinh(d*x + c)^16 + 16*(10659*d*cosh(d*x + c)^7 + 4845*d*cosh(d*x + c)^5 + 357*d*cosh(d*x + c)^3 - 5*d*cosh(d*x + c))*sinh(d*x + c)^15 - 22*d*cosh(d*x + c)^14 + 2*(159885*d*cosh(d*x + c)^8 + 96900*d*cosh(d*x + c)^6 + 10710*d*cosh(d*x + c)^4 - 300*d*cosh(d*x + c)^2 - 11*d)*sinh(d*x + c)^14 + 4*(124355*d*cosh(d*x + c)^9 + 96900*d*cosh(d*x + c)^7 + 14994*d*cosh(d*x + c)^5 - 700*d*cosh(d*x + c)^3 - 77*d*cosh(d*x + c))*sinh(d*x + c)^13 - 14*d*cosh(d*x + c)^12 + 2*(323323*d*cosh(d*x + c)^10 + 314925*d*cosh(d*x + c)^8 + 64974*d*cosh(d*x + c)^6 - 4550*d*cosh(d*x + c)^4 - 1001*d*cosh(d*x + c)^2 - 7*d)*sinh(d*x + c)^12 + 8*(88179*d*cosh(d*x + c)^11 + 104975*d*cosh(d*x + c)^9 + 27846*d*cosh(d*x + c)^7 - 2730*d*cosh(d*x + c)^5 - 1001*d*cosh(d*x + c)^3 - 21*d*cosh(d*x + c))*sinh(d*x + c)^11 + 14*d*cosh(d*x + c)^10 + 2*(323323*d*cosh(d*x + c)^12 + 461890*d*cosh(d*x + c)^10 + 153153*d*cosh(d*x + c)^8 - 20020*d*cosh(d*x + c)^6 - 11011*d*cosh(d*x + c)^4 - 462*d*cosh(d*x + c)^2 + 7*d)*sinh(d*x + c)^10 + 4*(124355*d*cosh(d*x + c)^13 + 209950*d*cosh(d*x + c)^11 + 85085*d*cosh(d*x + c)^9 - 14300*d*cosh(d*x + c)^7 - 11011*d*cosh(d*x + c)^5 - 770*d*cosh(d*x + c)^3 + 35*d*cosh(d*x + c))*sinh(d*x + c)^9 + 22*d*cosh(d*x + c)^8 + 2*(159885*d*cosh(d*x + c)^14 + 314925*d*cosh(d*x + c)^12 + 153153*d*cosh(d*x + c)^10 - 32175*d*cosh(d*x + c)^8 - 33033*d*cosh(d*x + c)^6 - 3465*d*cosh(d*x + c)^4 + 315*d*cosh(d*x + c)^2 + 11*d)*sinh(d*x + c)^8 + 16*(10659*d*cosh(d*x + c)^15 + 24225*d*cosh(d*x + c)^13 + 13923*d*cosh(d*x + c)^11 - 3575*d*cosh(d*x + c)^9 - 4719*d*cosh(d*x + c)^7 - 693*d*cosh(d*x + c)^5 + 105*d*cosh(d*x + c)^3 + 11*d*cosh(d*x + c))*sinh(d*x + c)^7 + 5*d*cosh(d*x + c)^6 + (74613*d*cosh(d*x + c)^16 + 193800*d*cosh(d*x + c)^14 + 129948*d*cosh(d*x + c)^12 - 40040*d*cosh(d*x + c)^10 - 66066*d*cosh(d*x + c)^8 - 12936*d*cosh(d*x + c)^6 + 2940*d*cosh(d*x + c)^4 + 616*d*cosh(d*x + c)^2 + 5*d)*sinh(d*x + c)^6 + 2*(13167*d*cosh(d*x + c)^17 + 38760*d*cosh(d*x + c)^15 + 29988*d*cosh(d*x + c)^13 - 10920*d*cosh(d*x + c)^11 - 22022*d*cosh(d*x + c)^9 - 5544*d*cosh(d*x + c)^7 + 1764*d*cosh(d*x + c)^5 + 616*d*cosh(d*x + c)^3 + 15*d*cosh(d*x + c))*sinh(d*x + c)^5 - 7*d*cosh(d*x + c)^4 + (7315*d*cosh(d*x + c)^18 + 24225*d*cosh(d*x + c)^16 + 21420*d*cosh(d*x + c)^14 - 9100*d*cosh(d*x + c)^12 - 22022*d*cosh(d*x + c)^10 - 6930*d*cosh(d*x + c)^8 + 2940*d*cosh(d*x + c)^6 + 1540*d*cosh(d*x + c)^4 + 75*d*cosh(d*x + c)^2 - 7*d)*sinh(d*x + c)^4 + 4*(385*d*cosh(d*x + c)^19 + 1425*d*cosh(d*x + c)^17 + 1428*d*cosh(d*x + c)^15 - 700*d*cosh(d*x + c)^13 - 2002*d*cosh(d*x + c)^11 - 770*d*cosh(d*x + c)^9 + 420*d*cosh(d*x + c)^7 + 308*d*cosh(d*x + c)^5 + 25*d*cosh(d*x + c)^3 - 7*d*cosh(d*x + c))*sinh(d*x + c)^3 - 5*d*cosh(d*x + c)^2 + (231*d*cosh(d*x + c)^20 + 950*d*cosh(d*x + c)^18 + 1071*d*cosh(d*x + c)^16 - 600*d*cosh(d*x + c)^14 - 2002*d*cosh(d*x + c)^12 - 924*d*cosh(d*x + c)^10 + 630*d*cosh(d*x + c)^8 + 616*d*cosh(d*x + c)^6 + 75*d*cosh(d*x + c)^4 - 42*d*cosh(d*x + c)^2 - 5*d)*sinh(d*x + c)^2 + 2*(11*d*cosh(d*x + c)^21 + 50*d*cosh(d*x + c)^19 + 63*d*cosh(d*x + c)^17 - 40*d*cosh(d*x + c)^15 - 154*d*cosh(d*x + c)^13 - 84*d*cosh(d*x + c)^11 + 70*d*cosh(d*x + c)^9 + 88*d*cosh(d*x + c)^7 + 15*d*cosh(d*x + c)^5 - 14*d*cosh(d*x + c)^3 - 5*d*cosh(d*x + c))*sinh(d*x + c) - d)","B",0
73,-1,0,0,0.000000," ","integrate(sinh(d*x+c)^4/(a+b*tanh(d*x+c)^3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
74,-1,0,0,0.000000," ","integrate(sinh(d*x+c)^3/(a+b*tanh(d*x+c)^3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
75,1,10695,0,1.412886," ","integrate(sinh(d*x+c)^2/(a+b*tanh(d*x+c)^3),x, algorithm=""fricas"")","-\frac{36 \, {\left(a^{3} + 4 \, a^{2} b + 5 \, a b^{2} + 2 \, b^{3}\right)} d x \cosh\left(d x + c\right)^{2} - 9 \, {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{4} - 36 \, {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} - 9 \, {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} \sinh\left(d x + c\right)^{4} + 9 \, a^{3} + 9 \, a^{2} b - 9 \, a b^{2} - 9 \, b^{3} - 4 \, {\left({\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d \sinh\left(d x + c\right)^{2}\right)} {\left(\frac{{\left(\frac{b^{2}}{a^{4} d^{2} - 2 \, a^{2} b^{2} d^{2} + b^{4} d^{2}} - \frac{{\left(2 \, a^{2} b + b^{3}\right)}^{2}}{{\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}^{2}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(-\frac{{\left(2 \, a^{2} b + b^{3}\right)} b^{2}}{18 \, {\left(a^{4} d^{2} - 2 \, a^{2} b^{2} d^{2} + b^{4} d^{2}\right)} {\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}} + \frac{{\left(2 \, a^{2} b + b^{3}\right)}^{3}}{27 \, {\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}^{3}} + \frac{b}{54 \, {\left(a^{4} d^{3} - 2 \, a^{2} b^{2} d^{3} + b^{4} d^{3}\right)}} + \frac{{\left(a^{2} + 8 \, b^{2}\right)} a^{2} b}{54 \, {\left(a^{2} - b^{2}\right)}^{4} d^{3}}\right)}^{\frac{1}{3}}} - 9 \, {\left(-\frac{{\left(2 \, a^{2} b + b^{3}\right)} b^{2}}{18 \, {\left(a^{4} d^{2} - 2 \, a^{2} b^{2} d^{2} + b^{4} d^{2}\right)} {\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}} + \frac{{\left(2 \, a^{2} b + b^{3}\right)}^{3}}{27 \, {\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}^{3}} + \frac{b}{54 \, {\left(a^{4} d^{3} - 2 \, a^{2} b^{2} d^{3} + b^{4} d^{3}\right)}} + \frac{{\left(a^{2} + 8 \, b^{2}\right)} a^{2} b}{54 \, {\left(a^{2} - b^{2}\right)}^{4} d^{3}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + \frac{6 \, {\left(2 \, a^{2} b + b^{3}\right)}}{a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d}\right)} \log\left(\frac{1}{18} \, {\left(a^{5} + 2 \, a^{4} b - 2 \, a^{3} b^{2} - 4 \, a^{2} b^{3} + a b^{4} + 2 \, b^{5}\right)} {\left(\frac{{\left(\frac{b^{2}}{a^{4} d^{2} - 2 \, a^{2} b^{2} d^{2} + b^{4} d^{2}} - \frac{{\left(2 \, a^{2} b + b^{3}\right)}^{2}}{{\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}^{2}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(-\frac{{\left(2 \, a^{2} b + b^{3}\right)} b^{2}}{18 \, {\left(a^{4} d^{2} - 2 \, a^{2} b^{2} d^{2} + b^{4} d^{2}\right)} {\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}} + \frac{{\left(2 \, a^{2} b + b^{3}\right)}^{3}}{27 \, {\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}^{3}} + \frac{b}{54 \, {\left(a^{4} d^{3} - 2 \, a^{2} b^{2} d^{3} + b^{4} d^{3}\right)}} + \frac{{\left(a^{2} + 8 \, b^{2}\right)} a^{2} b}{54 \, {\left(a^{2} - b^{2}\right)}^{4} d^{3}}\right)}^{\frac{1}{3}}} - 9 \, {\left(-\frac{{\left(2 \, a^{2} b + b^{3}\right)} b^{2}}{18 \, {\left(a^{4} d^{2} - 2 \, a^{2} b^{2} d^{2} + b^{4} d^{2}\right)} {\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}} + \frac{{\left(2 \, a^{2} b + b^{3}\right)}^{3}}{27 \, {\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}^{3}} + \frac{b}{54 \, {\left(a^{4} d^{3} - 2 \, a^{2} b^{2} d^{3} + b^{4} d^{3}\right)}} + \frac{{\left(a^{2} + 8 \, b^{2}\right)} a^{2} b}{54 \, {\left(a^{2} - b^{2}\right)}^{4} d^{3}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + \frac{6 \, {\left(2 \, a^{2} b + b^{3}\right)}}{a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d}\right)}^{2} d^{2} + a^{3} + 2 \, a^{2} b + 2 \, a b^{2} + 4 \, b^{3} - \frac{1}{3} \, {\left(a^{4} + 3 \, a^{3} b + 13 \, a^{2} b^{2} + 6 \, a b^{3} + 4 \, b^{4}\right)} {\left(\frac{{\left(\frac{b^{2}}{a^{4} d^{2} - 2 \, a^{2} b^{2} d^{2} + b^{4} d^{2}} - \frac{{\left(2 \, a^{2} b + b^{3}\right)}^{2}}{{\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}^{2}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(-\frac{{\left(2 \, a^{2} b + b^{3}\right)} b^{2}}{18 \, {\left(a^{4} d^{2} - 2 \, a^{2} b^{2} d^{2} + b^{4} d^{2}\right)} {\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}} + \frac{{\left(2 \, a^{2} b + b^{3}\right)}^{3}}{27 \, {\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}^{3}} + \frac{b}{54 \, {\left(a^{4} d^{3} - 2 \, a^{2} b^{2} d^{3} + b^{4} d^{3}\right)}} + \frac{{\left(a^{2} + 8 \, b^{2}\right)} a^{2} b}{54 \, {\left(a^{2} - b^{2}\right)}^{4} d^{3}}\right)}^{\frac{1}{3}}} - 9 \, {\left(-\frac{{\left(2 \, a^{2} b + b^{3}\right)} b^{2}}{18 \, {\left(a^{4} d^{2} - 2 \, a^{2} b^{2} d^{2} + b^{4} d^{2}\right)} {\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}} + \frac{{\left(2 \, a^{2} b + b^{3}\right)}^{3}}{27 \, {\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}^{3}} + \frac{b}{54 \, {\left(a^{4} d^{3} - 2 \, a^{2} b^{2} d^{3} + b^{4} d^{3}\right)}} + \frac{{\left(a^{2} + 8 \, b^{2}\right)} a^{2} b}{54 \, {\left(a^{2} - b^{2}\right)}^{4} d^{3}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + \frac{6 \, {\left(2 \, a^{2} b + b^{3}\right)}}{a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d}\right)} d + {\left(a^{3} + 8 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{3} + 8 \, a b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{3} + 8 \, a b^{2}\right)} \sinh\left(d x + c\right)^{2}\right) + 18 \, {\left(2 \, {\left(a^{3} + 4 \, a^{2} b + 5 \, a b^{2} + 2 \, b^{3}\right)} d x - 3 \, {\left(a^{3} - 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(18 \, {\left(2 \, a^{2} b + b^{3}\right)} \cosh\left(d x + c\right)^{2} + 36 \, {\left(2 \, a^{2} b + b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + 18 \, {\left(2 \, a^{2} b + b^{3}\right)} \sinh\left(d x + c\right)^{2} - {\left({\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d \sinh\left(d x + c\right)^{2}\right)} {\left(\frac{{\left(\frac{b^{2}}{a^{4} d^{2} - 2 \, a^{2} b^{2} d^{2} + b^{4} d^{2}} - \frac{{\left(2 \, a^{2} b + b^{3}\right)}^{2}}{{\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}^{2}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(-\frac{{\left(2 \, a^{2} b + b^{3}\right)} b^{2}}{18 \, {\left(a^{4} d^{2} - 2 \, a^{2} b^{2} d^{2} + b^{4} d^{2}\right)} {\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}} + \frac{{\left(2 \, a^{2} b + b^{3}\right)}^{3}}{27 \, {\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}^{3}} + \frac{b}{54 \, {\left(a^{4} d^{3} - 2 \, a^{2} b^{2} d^{3} + b^{4} d^{3}\right)}} + \frac{{\left(a^{2} + 8 \, b^{2}\right)} a^{2} b}{54 \, {\left(a^{2} - b^{2}\right)}^{4} d^{3}}\right)}^{\frac{1}{3}}} - 9 \, {\left(-\frac{{\left(2 \, a^{2} b + b^{3}\right)} b^{2}}{18 \, {\left(a^{4} d^{2} - 2 \, a^{2} b^{2} d^{2} + b^{4} d^{2}\right)} {\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}} + \frac{{\left(2 \, a^{2} b + b^{3}\right)}^{3}}{27 \, {\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}^{3}} + \frac{b}{54 \, {\left(a^{4} d^{3} - 2 \, a^{2} b^{2} d^{3} + b^{4} d^{3}\right)}} + \frac{{\left(a^{2} + 8 \, b^{2}\right)} a^{2} b}{54 \, {\left(a^{2} - b^{2}\right)}^{4} d^{3}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + \frac{6 \, {\left(2 \, a^{2} b + b^{3}\right)}}{a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d}\right)} - 3 \, \sqrt{\frac{1}{3}} {\left({\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{288 \, a^{4} b^{2} + 720 \, a^{2} b^{4} - 36 \, b^{6} - {\left(a^{8} - 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} {\left(\frac{{\left(\frac{b^{2}}{a^{4} d^{2} - 2 \, a^{2} b^{2} d^{2} + b^{4} d^{2}} - \frac{{\left(2 \, a^{2} b + b^{3}\right)}^{2}}{{\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}^{2}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(-\frac{{\left(2 \, a^{2} b + b^{3}\right)} b^{2}}{18 \, {\left(a^{4} d^{2} - 2 \, a^{2} b^{2} d^{2} + b^{4} d^{2}\right)} {\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}} + \frac{{\left(2 \, a^{2} b + b^{3}\right)}^{3}}{27 \, {\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}^{3}} + \frac{b}{54 \, {\left(a^{4} d^{3} - 2 \, a^{2} b^{2} d^{3} + b^{4} d^{3}\right)}} + \frac{{\left(a^{2} + 8 \, b^{2}\right)} a^{2} b}{54 \, {\left(a^{2} - b^{2}\right)}^{4} d^{3}}\right)}^{\frac{1}{3}}} - 9 \, {\left(-\frac{{\left(2 \, a^{2} b + b^{3}\right)} b^{2}}{18 \, {\left(a^{4} d^{2} - 2 \, a^{2} b^{2} d^{2} + b^{4} d^{2}\right)} {\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}} + \frac{{\left(2 \, a^{2} b + b^{3}\right)}^{3}}{27 \, {\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}^{3}} + \frac{b}{54 \, {\left(a^{4} d^{3} - 2 \, a^{2} b^{2} d^{3} + b^{4} d^{3}\right)}} + \frac{{\left(a^{2} + 8 \, b^{2}\right)} a^{2} b}{54 \, {\left(a^{2} - b^{2}\right)}^{4} d^{3}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + \frac{6 \, {\left(2 \, a^{2} b + b^{3}\right)}}{a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d}\right)}^{2} d^{2} + 12 \, {\left(2 \, a^{6} b - 3 \, a^{4} b^{3} + b^{7}\right)} {\left(\frac{{\left(\frac{b^{2}}{a^{4} d^{2} - 2 \, a^{2} b^{2} d^{2} + b^{4} d^{2}} - \frac{{\left(2 \, a^{2} b + b^{3}\right)}^{2}}{{\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}^{2}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(-\frac{{\left(2 \, a^{2} b + b^{3}\right)} b^{2}}{18 \, {\left(a^{4} d^{2} - 2 \, a^{2} b^{2} d^{2} + b^{4} d^{2}\right)} {\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}} + \frac{{\left(2 \, a^{2} b + b^{3}\right)}^{3}}{27 \, {\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}^{3}} + \frac{b}{54 \, {\left(a^{4} d^{3} - 2 \, a^{2} b^{2} d^{3} + b^{4} d^{3}\right)}} + \frac{{\left(a^{2} + 8 \, b^{2}\right)} a^{2} b}{54 \, {\left(a^{2} - b^{2}\right)}^{4} d^{3}}\right)}^{\frac{1}{3}}} - 9 \, {\left(-\frac{{\left(2 \, a^{2} b + b^{3}\right)} b^{2}}{18 \, {\left(a^{4} d^{2} - 2 \, a^{2} b^{2} d^{2} + b^{4} d^{2}\right)} {\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}} + \frac{{\left(2 \, a^{2} b + b^{3}\right)}^{3}}{27 \, {\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}^{3}} + \frac{b}{54 \, {\left(a^{4} d^{3} - 2 \, a^{2} b^{2} d^{3} + b^{4} d^{3}\right)}} + \frac{{\left(a^{2} + 8 \, b^{2}\right)} a^{2} b}{54 \, {\left(a^{2} - b^{2}\right)}^{4} d^{3}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + \frac{6 \, {\left(2 \, a^{2} b + b^{3}\right)}}{a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d}\right)} d}{{\left(a^{8} - 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} d^{2}}}\right)} \log\left(-\frac{1}{36} \, {\left(a^{6} + 3 \, a^{5} b - 6 \, a^{3} b^{3} - 3 \, a^{2} b^{4} + 3 \, a b^{5} + 2 \, b^{6}\right)} {\left(\frac{{\left(\frac{b^{2}}{a^{4} d^{2} - 2 \, a^{2} b^{2} d^{2} + b^{4} d^{2}} - \frac{{\left(2 \, a^{2} b + b^{3}\right)}^{2}}{{\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}^{2}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(-\frac{{\left(2 \, a^{2} b + b^{3}\right)} b^{2}}{18 \, {\left(a^{4} d^{2} - 2 \, a^{2} b^{2} d^{2} + b^{4} d^{2}\right)} {\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}} + \frac{{\left(2 \, a^{2} b + b^{3}\right)}^{3}}{27 \, {\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}^{3}} + \frac{b}{54 \, {\left(a^{4} d^{3} - 2 \, a^{2} b^{2} d^{3} + b^{4} d^{3}\right)}} + \frac{{\left(a^{2} + 8 \, b^{2}\right)} a^{2} b}{54 \, {\left(a^{2} - b^{2}\right)}^{4} d^{3}}\right)}^{\frac{1}{3}}} - 9 \, {\left(-\frac{{\left(2 \, a^{2} b + b^{3}\right)} b^{2}}{18 \, {\left(a^{4} d^{2} - 2 \, a^{2} b^{2} d^{2} + b^{4} d^{2}\right)} {\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}} + \frac{{\left(2 \, a^{2} b + b^{3}\right)}^{3}}{27 \, {\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}^{3}} + \frac{b}{54 \, {\left(a^{4} d^{3} - 2 \, a^{2} b^{2} d^{3} + b^{4} d^{3}\right)}} + \frac{{\left(a^{2} + 8 \, b^{2}\right)} a^{2} b}{54 \, {\left(a^{2} - b^{2}\right)}^{4} d^{3}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + \frac{6 \, {\left(2 \, a^{2} b + b^{3}\right)}}{a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d}\right)}^{2} d^{2} + a^{4} - 3 \, a^{3} b + 10 \, a^{2} b^{2} - 15 \, a b^{3} - 2 \, b^{4} + \frac{1}{6} \, {\left(a^{5} + 4 \, a^{4} b + 16 \, a^{3} b^{2} + 19 \, a^{2} b^{3} + 10 \, a b^{4} + 4 \, b^{5}\right)} {\left(\frac{{\left(\frac{b^{2}}{a^{4} d^{2} - 2 \, a^{2} b^{2} d^{2} + b^{4} d^{2}} - \frac{{\left(2 \, a^{2} b + b^{3}\right)}^{2}}{{\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}^{2}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(-\frac{{\left(2 \, a^{2} b + b^{3}\right)} b^{2}}{18 \, {\left(a^{4} d^{2} - 2 \, a^{2} b^{2} d^{2} + b^{4} d^{2}\right)} {\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}} + \frac{{\left(2 \, a^{2} b + b^{3}\right)}^{3}}{27 \, {\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}^{3}} + \frac{b}{54 \, {\left(a^{4} d^{3} - 2 \, a^{2} b^{2} d^{3} + b^{4} d^{3}\right)}} + \frac{{\left(a^{2} + 8 \, b^{2}\right)} a^{2} b}{54 \, {\left(a^{2} - b^{2}\right)}^{4} d^{3}}\right)}^{\frac{1}{3}}} - 9 \, {\left(-\frac{{\left(2 \, a^{2} b + b^{3}\right)} b^{2}}{18 \, {\left(a^{4} d^{2} - 2 \, a^{2} b^{2} d^{2} + b^{4} d^{2}\right)} {\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}} + \frac{{\left(2 \, a^{2} b + b^{3}\right)}^{3}}{27 \, {\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}^{3}} + \frac{b}{54 \, {\left(a^{4} d^{3} - 2 \, a^{2} b^{2} d^{3} + b^{4} d^{3}\right)}} + \frac{{\left(a^{2} + 8 \, b^{2}\right)} a^{2} b}{54 \, {\left(a^{2} - b^{2}\right)}^{4} d^{3}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + \frac{6 \, {\left(2 \, a^{2} b + b^{3}\right)}}{a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d}\right)} d + {\left(a^{4} + a^{3} b + 8 \, a^{2} b^{2} + 8 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{4} + a^{3} b + 8 \, a^{2} b^{2} + 8 \, a b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{4} + a^{3} b + 8 \, a^{2} b^{2} + 8 \, a b^{3}\right)} \sinh\left(d x + c\right)^{2} + \frac{1}{12} \, \sqrt{\frac{1}{3}} {\left({\left(a^{6} + 3 \, a^{5} b - 6 \, a^{3} b^{3} - 3 \, a^{2} b^{4} + 3 \, a b^{5} + 2 \, b^{6}\right)} {\left(\frac{{\left(\frac{b^{2}}{a^{4} d^{2} - 2 \, a^{2} b^{2} d^{2} + b^{4} d^{2}} - \frac{{\left(2 \, a^{2} b + b^{3}\right)}^{2}}{{\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}^{2}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(-\frac{{\left(2 \, a^{2} b + b^{3}\right)} b^{2}}{18 \, {\left(a^{4} d^{2} - 2 \, a^{2} b^{2} d^{2} + b^{4} d^{2}\right)} {\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}} + \frac{{\left(2 \, a^{2} b + b^{3}\right)}^{3}}{27 \, {\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}^{3}} + \frac{b}{54 \, {\left(a^{4} d^{3} - 2 \, a^{2} b^{2} d^{3} + b^{4} d^{3}\right)}} + \frac{{\left(a^{2} + 8 \, b^{2}\right)} a^{2} b}{54 \, {\left(a^{2} - b^{2}\right)}^{4} d^{3}}\right)}^{\frac{1}{3}}} - 9 \, {\left(-\frac{{\left(2 \, a^{2} b + b^{3}\right)} b^{2}}{18 \, {\left(a^{4} d^{2} - 2 \, a^{2} b^{2} d^{2} + b^{4} d^{2}\right)} {\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}} + \frac{{\left(2 \, a^{2} b + b^{3}\right)}^{3}}{27 \, {\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}^{3}} + \frac{b}{54 \, {\left(a^{4} d^{3} - 2 \, a^{2} b^{2} d^{3} + b^{4} d^{3}\right)}} + \frac{{\left(a^{2} + 8 \, b^{2}\right)} a^{2} b}{54 \, {\left(a^{2} - b^{2}\right)}^{4} d^{3}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + \frac{6 \, {\left(2 \, a^{2} b + b^{3}\right)}}{a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d}\right)} d^{2} + 6 \, {\left(a^{5} - 2 \, a^{4} b - 2 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4} - 2 \, b^{5}\right)} d\right)} \sqrt{\frac{288 \, a^{4} b^{2} + 720 \, a^{2} b^{4} - 36 \, b^{6} - {\left(a^{8} - 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} {\left(\frac{{\left(\frac{b^{2}}{a^{4} d^{2} - 2 \, a^{2} b^{2} d^{2} + b^{4} d^{2}} - \frac{{\left(2 \, a^{2} b + b^{3}\right)}^{2}}{{\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}^{2}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(-\frac{{\left(2 \, a^{2} b + b^{3}\right)} b^{2}}{18 \, {\left(a^{4} d^{2} - 2 \, a^{2} b^{2} d^{2} + b^{4} d^{2}\right)} {\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}} + \frac{{\left(2 \, a^{2} b + b^{3}\right)}^{3}}{27 \, {\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}^{3}} + \frac{b}{54 \, {\left(a^{4} d^{3} - 2 \, a^{2} b^{2} d^{3} + b^{4} d^{3}\right)}} + \frac{{\left(a^{2} + 8 \, b^{2}\right)} a^{2} b}{54 \, {\left(a^{2} - b^{2}\right)}^{4} d^{3}}\right)}^{\frac{1}{3}}} - 9 \, {\left(-\frac{{\left(2 \, a^{2} b + b^{3}\right)} b^{2}}{18 \, {\left(a^{4} d^{2} - 2 \, a^{2} b^{2} d^{2} + b^{4} d^{2}\right)} {\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}} + \frac{{\left(2 \, a^{2} b + b^{3}\right)}^{3}}{27 \, {\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}^{3}} + \frac{b}{54 \, {\left(a^{4} d^{3} - 2 \, a^{2} b^{2} d^{3} + b^{4} d^{3}\right)}} + \frac{{\left(a^{2} + 8 \, b^{2}\right)} a^{2} b}{54 \, {\left(a^{2} - b^{2}\right)}^{4} d^{3}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + \frac{6 \, {\left(2 \, a^{2} b + b^{3}\right)}}{a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d}\right)}^{2} d^{2} + 12 \, {\left(2 \, a^{6} b - 3 \, a^{4} b^{3} + b^{7}\right)} {\left(\frac{{\left(\frac{b^{2}}{a^{4} d^{2} - 2 \, a^{2} b^{2} d^{2} + b^{4} d^{2}} - \frac{{\left(2 \, a^{2} b + b^{3}\right)}^{2}}{{\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}^{2}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(-\frac{{\left(2 \, a^{2} b + b^{3}\right)} b^{2}}{18 \, {\left(a^{4} d^{2} - 2 \, a^{2} b^{2} d^{2} + b^{4} d^{2}\right)} {\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}} + \frac{{\left(2 \, a^{2} b + b^{3}\right)}^{3}}{27 \, {\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}^{3}} + \frac{b}{54 \, {\left(a^{4} d^{3} - 2 \, a^{2} b^{2} d^{3} + b^{4} d^{3}\right)}} + \frac{{\left(a^{2} + 8 \, b^{2}\right)} a^{2} b}{54 \, {\left(a^{2} - b^{2}\right)}^{4} d^{3}}\right)}^{\frac{1}{3}}} - 9 \, {\left(-\frac{{\left(2 \, a^{2} b + b^{3}\right)} b^{2}}{18 \, {\left(a^{4} d^{2} - 2 \, a^{2} b^{2} d^{2} + b^{4} d^{2}\right)} {\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}} + \frac{{\left(2 \, a^{2} b + b^{3}\right)}^{3}}{27 \, {\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}^{3}} + \frac{b}{54 \, {\left(a^{4} d^{3} - 2 \, a^{2} b^{2} d^{3} + b^{4} d^{3}\right)}} + \frac{{\left(a^{2} + 8 \, b^{2}\right)} a^{2} b}{54 \, {\left(a^{2} - b^{2}\right)}^{4} d^{3}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + \frac{6 \, {\left(2 \, a^{2} b + b^{3}\right)}}{a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d}\right)} d}{{\left(a^{8} - 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} d^{2}}}\right) - 2 \, {\left(18 \, {\left(2 \, a^{2} b + b^{3}\right)} \cosh\left(d x + c\right)^{2} + 36 \, {\left(2 \, a^{2} b + b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + 18 \, {\left(2 \, a^{2} b + b^{3}\right)} \sinh\left(d x + c\right)^{2} - {\left({\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d \sinh\left(d x + c\right)^{2}\right)} {\left(\frac{{\left(\frac{b^{2}}{a^{4} d^{2} - 2 \, a^{2} b^{2} d^{2} + b^{4} d^{2}} - \frac{{\left(2 \, a^{2} b + b^{3}\right)}^{2}}{{\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}^{2}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(-\frac{{\left(2 \, a^{2} b + b^{3}\right)} b^{2}}{18 \, {\left(a^{4} d^{2} - 2 \, a^{2} b^{2} d^{2} + b^{4} d^{2}\right)} {\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}} + \frac{{\left(2 \, a^{2} b + b^{3}\right)}^{3}}{27 \, {\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}^{3}} + \frac{b}{54 \, {\left(a^{4} d^{3} - 2 \, a^{2} b^{2} d^{3} + b^{4} d^{3}\right)}} + \frac{{\left(a^{2} + 8 \, b^{2}\right)} a^{2} b}{54 \, {\left(a^{2} - b^{2}\right)}^{4} d^{3}}\right)}^{\frac{1}{3}}} - 9 \, {\left(-\frac{{\left(2 \, a^{2} b + b^{3}\right)} b^{2}}{18 \, {\left(a^{4} d^{2} - 2 \, a^{2} b^{2} d^{2} + b^{4} d^{2}\right)} {\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}} + \frac{{\left(2 \, a^{2} b + b^{3}\right)}^{3}}{27 \, {\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}^{3}} + \frac{b}{54 \, {\left(a^{4} d^{3} - 2 \, a^{2} b^{2} d^{3} + b^{4} d^{3}\right)}} + \frac{{\left(a^{2} + 8 \, b^{2}\right)} a^{2} b}{54 \, {\left(a^{2} - b^{2}\right)}^{4} d^{3}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + \frac{6 \, {\left(2 \, a^{2} b + b^{3}\right)}}{a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d}\right)} + 3 \, \sqrt{\frac{1}{3}} {\left({\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d \sinh\left(d x + c\right)^{2}\right)} \sqrt{\frac{288 \, a^{4} b^{2} + 720 \, a^{2} b^{4} - 36 \, b^{6} - {\left(a^{8} - 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} {\left(\frac{{\left(\frac{b^{2}}{a^{4} d^{2} - 2 \, a^{2} b^{2} d^{2} + b^{4} d^{2}} - \frac{{\left(2 \, a^{2} b + b^{3}\right)}^{2}}{{\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}^{2}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(-\frac{{\left(2 \, a^{2} b + b^{3}\right)} b^{2}}{18 \, {\left(a^{4} d^{2} - 2 \, a^{2} b^{2} d^{2} + b^{4} d^{2}\right)} {\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}} + \frac{{\left(2 \, a^{2} b + b^{3}\right)}^{3}}{27 \, {\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}^{3}} + \frac{b}{54 \, {\left(a^{4} d^{3} - 2 \, a^{2} b^{2} d^{3} + b^{4} d^{3}\right)}} + \frac{{\left(a^{2} + 8 \, b^{2}\right)} a^{2} b}{54 \, {\left(a^{2} - b^{2}\right)}^{4} d^{3}}\right)}^{\frac{1}{3}}} - 9 \, {\left(-\frac{{\left(2 \, a^{2} b + b^{3}\right)} b^{2}}{18 \, {\left(a^{4} d^{2} - 2 \, a^{2} b^{2} d^{2} + b^{4} d^{2}\right)} {\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}} + \frac{{\left(2 \, a^{2} b + b^{3}\right)}^{3}}{27 \, {\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}^{3}} + \frac{b}{54 \, {\left(a^{4} d^{3} - 2 \, a^{2} b^{2} d^{3} + b^{4} d^{3}\right)}} + \frac{{\left(a^{2} + 8 \, b^{2}\right)} a^{2} b}{54 \, {\left(a^{2} - b^{2}\right)}^{4} d^{3}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + \frac{6 \, {\left(2 \, a^{2} b + b^{3}\right)}}{a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d}\right)}^{2} d^{2} + 12 \, {\left(2 \, a^{6} b - 3 \, a^{4} b^{3} + b^{7}\right)} {\left(\frac{{\left(\frac{b^{2}}{a^{4} d^{2} - 2 \, a^{2} b^{2} d^{2} + b^{4} d^{2}} - \frac{{\left(2 \, a^{2} b + b^{3}\right)}^{2}}{{\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}^{2}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(-\frac{{\left(2 \, a^{2} b + b^{3}\right)} b^{2}}{18 \, {\left(a^{4} d^{2} - 2 \, a^{2} b^{2} d^{2} + b^{4} d^{2}\right)} {\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}} + \frac{{\left(2 \, a^{2} b + b^{3}\right)}^{3}}{27 \, {\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}^{3}} + \frac{b}{54 \, {\left(a^{4} d^{3} - 2 \, a^{2} b^{2} d^{3} + b^{4} d^{3}\right)}} + \frac{{\left(a^{2} + 8 \, b^{2}\right)} a^{2} b}{54 \, {\left(a^{2} - b^{2}\right)}^{4} d^{3}}\right)}^{\frac{1}{3}}} - 9 \, {\left(-\frac{{\left(2 \, a^{2} b + b^{3}\right)} b^{2}}{18 \, {\left(a^{4} d^{2} - 2 \, a^{2} b^{2} d^{2} + b^{4} d^{2}\right)} {\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}} + \frac{{\left(2 \, a^{2} b + b^{3}\right)}^{3}}{27 \, {\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}^{3}} + \frac{b}{54 \, {\left(a^{4} d^{3} - 2 \, a^{2} b^{2} d^{3} + b^{4} d^{3}\right)}} + \frac{{\left(a^{2} + 8 \, b^{2}\right)} a^{2} b}{54 \, {\left(a^{2} - b^{2}\right)}^{4} d^{3}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + \frac{6 \, {\left(2 \, a^{2} b + b^{3}\right)}}{a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d}\right)} d}{{\left(a^{8} - 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} d^{2}}}\right)} \log\left(-\frac{1}{36} \, {\left(a^{6} + 3 \, a^{5} b - 6 \, a^{3} b^{3} - 3 \, a^{2} b^{4} + 3 \, a b^{5} + 2 \, b^{6}\right)} {\left(\frac{{\left(\frac{b^{2}}{a^{4} d^{2} - 2 \, a^{2} b^{2} d^{2} + b^{4} d^{2}} - \frac{{\left(2 \, a^{2} b + b^{3}\right)}^{2}}{{\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}^{2}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(-\frac{{\left(2 \, a^{2} b + b^{3}\right)} b^{2}}{18 \, {\left(a^{4} d^{2} - 2 \, a^{2} b^{2} d^{2} + b^{4} d^{2}\right)} {\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}} + \frac{{\left(2 \, a^{2} b + b^{3}\right)}^{3}}{27 \, {\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}^{3}} + \frac{b}{54 \, {\left(a^{4} d^{3} - 2 \, a^{2} b^{2} d^{3} + b^{4} d^{3}\right)}} + \frac{{\left(a^{2} + 8 \, b^{2}\right)} a^{2} b}{54 \, {\left(a^{2} - b^{2}\right)}^{4} d^{3}}\right)}^{\frac{1}{3}}} - 9 \, {\left(-\frac{{\left(2 \, a^{2} b + b^{3}\right)} b^{2}}{18 \, {\left(a^{4} d^{2} - 2 \, a^{2} b^{2} d^{2} + b^{4} d^{2}\right)} {\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}} + \frac{{\left(2 \, a^{2} b + b^{3}\right)}^{3}}{27 \, {\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}^{3}} + \frac{b}{54 \, {\left(a^{4} d^{3} - 2 \, a^{2} b^{2} d^{3} + b^{4} d^{3}\right)}} + \frac{{\left(a^{2} + 8 \, b^{2}\right)} a^{2} b}{54 \, {\left(a^{2} - b^{2}\right)}^{4} d^{3}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + \frac{6 \, {\left(2 \, a^{2} b + b^{3}\right)}}{a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d}\right)}^{2} d^{2} + a^{4} - 3 \, a^{3} b + 10 \, a^{2} b^{2} - 15 \, a b^{3} - 2 \, b^{4} + \frac{1}{6} \, {\left(a^{5} + 4 \, a^{4} b + 16 \, a^{3} b^{2} + 19 \, a^{2} b^{3} + 10 \, a b^{4} + 4 \, b^{5}\right)} {\left(\frac{{\left(\frac{b^{2}}{a^{4} d^{2} - 2 \, a^{2} b^{2} d^{2} + b^{4} d^{2}} - \frac{{\left(2 \, a^{2} b + b^{3}\right)}^{2}}{{\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}^{2}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(-\frac{{\left(2 \, a^{2} b + b^{3}\right)} b^{2}}{18 \, {\left(a^{4} d^{2} - 2 \, a^{2} b^{2} d^{2} + b^{4} d^{2}\right)} {\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}} + \frac{{\left(2 \, a^{2} b + b^{3}\right)}^{3}}{27 \, {\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}^{3}} + \frac{b}{54 \, {\left(a^{4} d^{3} - 2 \, a^{2} b^{2} d^{3} + b^{4} d^{3}\right)}} + \frac{{\left(a^{2} + 8 \, b^{2}\right)} a^{2} b}{54 \, {\left(a^{2} - b^{2}\right)}^{4} d^{3}}\right)}^{\frac{1}{3}}} - 9 \, {\left(-\frac{{\left(2 \, a^{2} b + b^{3}\right)} b^{2}}{18 \, {\left(a^{4} d^{2} - 2 \, a^{2} b^{2} d^{2} + b^{4} d^{2}\right)} {\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}} + \frac{{\left(2 \, a^{2} b + b^{3}\right)}^{3}}{27 \, {\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}^{3}} + \frac{b}{54 \, {\left(a^{4} d^{3} - 2 \, a^{2} b^{2} d^{3} + b^{4} d^{3}\right)}} + \frac{{\left(a^{2} + 8 \, b^{2}\right)} a^{2} b}{54 \, {\left(a^{2} - b^{2}\right)}^{4} d^{3}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + \frac{6 \, {\left(2 \, a^{2} b + b^{3}\right)}}{a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d}\right)} d + {\left(a^{4} + a^{3} b + 8 \, a^{2} b^{2} + 8 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{4} + a^{3} b + 8 \, a^{2} b^{2} + 8 \, a b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{4} + a^{3} b + 8 \, a^{2} b^{2} + 8 \, a b^{3}\right)} \sinh\left(d x + c\right)^{2} - \frac{1}{12} \, \sqrt{\frac{1}{3}} {\left({\left(a^{6} + 3 \, a^{5} b - 6 \, a^{3} b^{3} - 3 \, a^{2} b^{4} + 3 \, a b^{5} + 2 \, b^{6}\right)} {\left(\frac{{\left(\frac{b^{2}}{a^{4} d^{2} - 2 \, a^{2} b^{2} d^{2} + b^{4} d^{2}} - \frac{{\left(2 \, a^{2} b + b^{3}\right)}^{2}}{{\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}^{2}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(-\frac{{\left(2 \, a^{2} b + b^{3}\right)} b^{2}}{18 \, {\left(a^{4} d^{2} - 2 \, a^{2} b^{2} d^{2} + b^{4} d^{2}\right)} {\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}} + \frac{{\left(2 \, a^{2} b + b^{3}\right)}^{3}}{27 \, {\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}^{3}} + \frac{b}{54 \, {\left(a^{4} d^{3} - 2 \, a^{2} b^{2} d^{3} + b^{4} d^{3}\right)}} + \frac{{\left(a^{2} + 8 \, b^{2}\right)} a^{2} b}{54 \, {\left(a^{2} - b^{2}\right)}^{4} d^{3}}\right)}^{\frac{1}{3}}} - 9 \, {\left(-\frac{{\left(2 \, a^{2} b + b^{3}\right)} b^{2}}{18 \, {\left(a^{4} d^{2} - 2 \, a^{2} b^{2} d^{2} + b^{4} d^{2}\right)} {\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}} + \frac{{\left(2 \, a^{2} b + b^{3}\right)}^{3}}{27 \, {\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}^{3}} + \frac{b}{54 \, {\left(a^{4} d^{3} - 2 \, a^{2} b^{2} d^{3} + b^{4} d^{3}\right)}} + \frac{{\left(a^{2} + 8 \, b^{2}\right)} a^{2} b}{54 \, {\left(a^{2} - b^{2}\right)}^{4} d^{3}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + \frac{6 \, {\left(2 \, a^{2} b + b^{3}\right)}}{a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d}\right)} d^{2} + 6 \, {\left(a^{5} - 2 \, a^{4} b - 2 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4} - 2 \, b^{5}\right)} d\right)} \sqrt{\frac{288 \, a^{4} b^{2} + 720 \, a^{2} b^{4} - 36 \, b^{6} - {\left(a^{8} - 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} {\left(\frac{{\left(\frac{b^{2}}{a^{4} d^{2} - 2 \, a^{2} b^{2} d^{2} + b^{4} d^{2}} - \frac{{\left(2 \, a^{2} b + b^{3}\right)}^{2}}{{\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}^{2}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(-\frac{{\left(2 \, a^{2} b + b^{3}\right)} b^{2}}{18 \, {\left(a^{4} d^{2} - 2 \, a^{2} b^{2} d^{2} + b^{4} d^{2}\right)} {\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}} + \frac{{\left(2 \, a^{2} b + b^{3}\right)}^{3}}{27 \, {\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}^{3}} + \frac{b}{54 \, {\left(a^{4} d^{3} - 2 \, a^{2} b^{2} d^{3} + b^{4} d^{3}\right)}} + \frac{{\left(a^{2} + 8 \, b^{2}\right)} a^{2} b}{54 \, {\left(a^{2} - b^{2}\right)}^{4} d^{3}}\right)}^{\frac{1}{3}}} - 9 \, {\left(-\frac{{\left(2 \, a^{2} b + b^{3}\right)} b^{2}}{18 \, {\left(a^{4} d^{2} - 2 \, a^{2} b^{2} d^{2} + b^{4} d^{2}\right)} {\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}} + \frac{{\left(2 \, a^{2} b + b^{3}\right)}^{3}}{27 \, {\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}^{3}} + \frac{b}{54 \, {\left(a^{4} d^{3} - 2 \, a^{2} b^{2} d^{3} + b^{4} d^{3}\right)}} + \frac{{\left(a^{2} + 8 \, b^{2}\right)} a^{2} b}{54 \, {\left(a^{2} - b^{2}\right)}^{4} d^{3}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + \frac{6 \, {\left(2 \, a^{2} b + b^{3}\right)}}{a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d}\right)}^{2} d^{2} + 12 \, {\left(2 \, a^{6} b - 3 \, a^{4} b^{3} + b^{7}\right)} {\left(\frac{{\left(\frac{b^{2}}{a^{4} d^{2} - 2 \, a^{2} b^{2} d^{2} + b^{4} d^{2}} - \frac{{\left(2 \, a^{2} b + b^{3}\right)}^{2}}{{\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}^{2}}\right)} {\left(-i \, \sqrt{3} + 1\right)}}{{\left(-\frac{{\left(2 \, a^{2} b + b^{3}\right)} b^{2}}{18 \, {\left(a^{4} d^{2} - 2 \, a^{2} b^{2} d^{2} + b^{4} d^{2}\right)} {\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}} + \frac{{\left(2 \, a^{2} b + b^{3}\right)}^{3}}{27 \, {\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}^{3}} + \frac{b}{54 \, {\left(a^{4} d^{3} - 2 \, a^{2} b^{2} d^{3} + b^{4} d^{3}\right)}} + \frac{{\left(a^{2} + 8 \, b^{2}\right)} a^{2} b}{54 \, {\left(a^{2} - b^{2}\right)}^{4} d^{3}}\right)}^{\frac{1}{3}}} - 9 \, {\left(-\frac{{\left(2 \, a^{2} b + b^{3}\right)} b^{2}}{18 \, {\left(a^{4} d^{2} - 2 \, a^{2} b^{2} d^{2} + b^{4} d^{2}\right)} {\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}} + \frac{{\left(2 \, a^{2} b + b^{3}\right)}^{3}}{27 \, {\left(a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d\right)}^{3}} + \frac{b}{54 \, {\left(a^{4} d^{3} - 2 \, a^{2} b^{2} d^{3} + b^{4} d^{3}\right)}} + \frac{{\left(a^{2} + 8 \, b^{2}\right)} a^{2} b}{54 \, {\left(a^{2} - b^{2}\right)}^{4} d^{3}}\right)}^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} + \frac{6 \, {\left(2 \, a^{2} b + b^{3}\right)}}{a^{4} d - 2 \, a^{2} b^{2} d + b^{4} d}\right)} d}{{\left(a^{8} - 4 \, a^{6} b^{2} + 6 \, a^{4} b^{4} - 4 \, a^{2} b^{6} + b^{8}\right)} d^{2}}}\right) + 36 \, {\left(2 \, {\left(a^{3} + 4 \, a^{2} b + 5 \, a b^{2} + 2 \, b^{3}\right)} d x \cosh\left(d x + c\right) - {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right)}{72 \, {\left({\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{4} - 2 \, a^{2} b^{2} + b^{4}\right)} d \sinh\left(d x + c\right)^{2}\right)}}"," ",0,"-1/72*(36*(a^3 + 4*a^2*b + 5*a*b^2 + 2*b^3)*d*x*cosh(d*x + c)^2 - 9*(a^3 - a^2*b - a*b^2 + b^3)*cosh(d*x + c)^4 - 36*(a^3 - a^2*b - a*b^2 + b^3)*cosh(d*x + c)*sinh(d*x + c)^3 - 9*(a^3 - a^2*b - a*b^2 + b^3)*sinh(d*x + c)^4 + 9*a^3 + 9*a^2*b - 9*a*b^2 - 9*b^3 - 4*((a^4 - 2*a^2*b^2 + b^4)*d*cosh(d*x + c)^2 + 2*(a^4 - 2*a^2*b^2 + b^4)*d*cosh(d*x + c)*sinh(d*x + c) + (a^4 - 2*a^2*b^2 + b^4)*d*sinh(d*x + c)^2)*((b^2/(a^4*d^2 - 2*a^2*b^2*d^2 + b^4*d^2) - (2*a^2*b + b^3)^2/(a^4*d - 2*a^2*b^2*d + b^4*d)^2)*(-I*sqrt(3) + 1)/(-1/18*(2*a^2*b + b^3)*b^2/((a^4*d^2 - 2*a^2*b^2*d^2 + b^4*d^2)*(a^4*d - 2*a^2*b^2*d + b^4*d)) + 1/27*(2*a^2*b + b^3)^3/(a^4*d - 2*a^2*b^2*d + b^4*d)^3 + 1/54*b/(a^4*d^3 - 2*a^2*b^2*d^3 + b^4*d^3) + 1/54*(a^2 + 8*b^2)*a^2*b/((a^2 - b^2)^4*d^3))^(1/3) - 9*(-1/18*(2*a^2*b + b^3)*b^2/((a^4*d^2 - 2*a^2*b^2*d^2 + b^4*d^2)*(a^4*d - 2*a^2*b^2*d + b^4*d)) + 1/27*(2*a^2*b + b^3)^3/(a^4*d - 2*a^2*b^2*d + b^4*d)^3 + 1/54*b/(a^4*d^3 - 2*a^2*b^2*d^3 + b^4*d^3) + 1/54*(a^2 + 8*b^2)*a^2*b/((a^2 - b^2)^4*d^3))^(1/3)*(I*sqrt(3) + 1) + 6*(2*a^2*b + b^3)/(a^4*d - 2*a^2*b^2*d + b^4*d))*log(1/18*(a^5 + 2*a^4*b - 2*a^3*b^2 - 4*a^2*b^3 + a*b^4 + 2*b^5)*((b^2/(a^4*d^2 - 2*a^2*b^2*d^2 + b^4*d^2) - (2*a^2*b + b^3)^2/(a^4*d - 2*a^2*b^2*d + b^4*d)^2)*(-I*sqrt(3) + 1)/(-1/18*(2*a^2*b + b^3)*b^2/((a^4*d^2 - 2*a^2*b^2*d^2 + b^4*d^2)*(a^4*d - 2*a^2*b^2*d + b^4*d)) + 1/27*(2*a^2*b + b^3)^3/(a^4*d - 2*a^2*b^2*d + b^4*d)^3 + 1/54*b/(a^4*d^3 - 2*a^2*b^2*d^3 + b^4*d^3) + 1/54*(a^2 + 8*b^2)*a^2*b/((a^2 - b^2)^4*d^3))^(1/3) - 9*(-1/18*(2*a^2*b + b^3)*b^2/((a^4*d^2 - 2*a^2*b^2*d^2 + b^4*d^2)*(a^4*d - 2*a^2*b^2*d + b^4*d)) + 1/27*(2*a^2*b + b^3)^3/(a^4*d - 2*a^2*b^2*d + b^4*d)^3 + 1/54*b/(a^4*d^3 - 2*a^2*b^2*d^3 + b^4*d^3) + 1/54*(a^2 + 8*b^2)*a^2*b/((a^2 - b^2)^4*d^3))^(1/3)*(I*sqrt(3) + 1) + 6*(2*a^2*b + b^3)/(a^4*d - 2*a^2*b^2*d + b^4*d))^2*d^2 + a^3 + 2*a^2*b + 2*a*b^2 + 4*b^3 - 1/3*(a^4 + 3*a^3*b + 13*a^2*b^2 + 6*a*b^3 + 4*b^4)*((b^2/(a^4*d^2 - 2*a^2*b^2*d^2 + b^4*d^2) - (2*a^2*b + b^3)^2/(a^4*d - 2*a^2*b^2*d + b^4*d)^2)*(-I*sqrt(3) + 1)/(-1/18*(2*a^2*b + b^3)*b^2/((a^4*d^2 - 2*a^2*b^2*d^2 + b^4*d^2)*(a^4*d - 2*a^2*b^2*d + b^4*d)) + 1/27*(2*a^2*b + b^3)^3/(a^4*d - 2*a^2*b^2*d + b^4*d)^3 + 1/54*b/(a^4*d^3 - 2*a^2*b^2*d^3 + b^4*d^3) + 1/54*(a^2 + 8*b^2)*a^2*b/((a^2 - b^2)^4*d^3))^(1/3) - 9*(-1/18*(2*a^2*b + b^3)*b^2/((a^4*d^2 - 2*a^2*b^2*d^2 + b^4*d^2)*(a^4*d - 2*a^2*b^2*d + b^4*d)) + 1/27*(2*a^2*b + b^3)^3/(a^4*d - 2*a^2*b^2*d + b^4*d)^3 + 1/54*b/(a^4*d^3 - 2*a^2*b^2*d^3 + b^4*d^3) + 1/54*(a^2 + 8*b^2)*a^2*b/((a^2 - b^2)^4*d^3))^(1/3)*(I*sqrt(3) + 1) + 6*(2*a^2*b + b^3)/(a^4*d - 2*a^2*b^2*d + b^4*d))*d + (a^3 + 8*a*b^2)*cosh(d*x + c)^2 + 2*(a^3 + 8*a*b^2)*cosh(d*x + c)*sinh(d*x + c) + (a^3 + 8*a*b^2)*sinh(d*x + c)^2) + 18*(2*(a^3 + 4*a^2*b + 5*a*b^2 + 2*b^3)*d*x - 3*(a^3 - a^2*b - a*b^2 + b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - 2*(18*(2*a^2*b + b^3)*cosh(d*x + c)^2 + 36*(2*a^2*b + b^3)*cosh(d*x + c)*sinh(d*x + c) + 18*(2*a^2*b + b^3)*sinh(d*x + c)^2 - ((a^4 - 2*a^2*b^2 + b^4)*d*cosh(d*x + c)^2 + 2*(a^4 - 2*a^2*b^2 + b^4)*d*cosh(d*x + c)*sinh(d*x + c) + (a^4 - 2*a^2*b^2 + b^4)*d*sinh(d*x + c)^2)*((b^2/(a^4*d^2 - 2*a^2*b^2*d^2 + b^4*d^2) - (2*a^2*b + b^3)^2/(a^4*d - 2*a^2*b^2*d + b^4*d)^2)*(-I*sqrt(3) + 1)/(-1/18*(2*a^2*b + b^3)*b^2/((a^4*d^2 - 2*a^2*b^2*d^2 + b^4*d^2)*(a^4*d - 2*a^2*b^2*d + b^4*d)) + 1/27*(2*a^2*b + b^3)^3/(a^4*d - 2*a^2*b^2*d + b^4*d)^3 + 1/54*b/(a^4*d^3 - 2*a^2*b^2*d^3 + b^4*d^3) + 1/54*(a^2 + 8*b^2)*a^2*b/((a^2 - b^2)^4*d^3))^(1/3) - 9*(-1/18*(2*a^2*b + b^3)*b^2/((a^4*d^2 - 2*a^2*b^2*d^2 + b^4*d^2)*(a^4*d - 2*a^2*b^2*d + b^4*d)) + 1/27*(2*a^2*b + b^3)^3/(a^4*d - 2*a^2*b^2*d + b^4*d)^3 + 1/54*b/(a^4*d^3 - 2*a^2*b^2*d^3 + b^4*d^3) + 1/54*(a^2 + 8*b^2)*a^2*b/((a^2 - b^2)^4*d^3))^(1/3)*(I*sqrt(3) + 1) + 6*(2*a^2*b + b^3)/(a^4*d - 2*a^2*b^2*d + b^4*d)) - 3*sqrt(1/3)*((a^4 - 2*a^2*b^2 + b^4)*d*cosh(d*x + c)^2 + 2*(a^4 - 2*a^2*b^2 + b^4)*d*cosh(d*x + c)*sinh(d*x + c) + (a^4 - 2*a^2*b^2 + b^4)*d*sinh(d*x + c)^2)*sqrt((288*a^4*b^2 + 720*a^2*b^4 - 36*b^6 - (a^8 - 4*a^6*b^2 + 6*a^4*b^4 - 4*a^2*b^6 + b^8)*((b^2/(a^4*d^2 - 2*a^2*b^2*d^2 + b^4*d^2) - (2*a^2*b + b^3)^2/(a^4*d - 2*a^2*b^2*d + b^4*d)^2)*(-I*sqrt(3) + 1)/(-1/18*(2*a^2*b + b^3)*b^2/((a^4*d^2 - 2*a^2*b^2*d^2 + b^4*d^2)*(a^4*d - 2*a^2*b^2*d + b^4*d)) + 1/27*(2*a^2*b + b^3)^3/(a^4*d - 2*a^2*b^2*d + b^4*d)^3 + 1/54*b/(a^4*d^3 - 2*a^2*b^2*d^3 + b^4*d^3) + 1/54*(a^2 + 8*b^2)*a^2*b/((a^2 - b^2)^4*d^3))^(1/3) - 9*(-1/18*(2*a^2*b + b^3)*b^2/((a^4*d^2 - 2*a^2*b^2*d^2 + b^4*d^2)*(a^4*d - 2*a^2*b^2*d + b^4*d)) + 1/27*(2*a^2*b + b^3)^3/(a^4*d - 2*a^2*b^2*d + b^4*d)^3 + 1/54*b/(a^4*d^3 - 2*a^2*b^2*d^3 + b^4*d^3) + 1/54*(a^2 + 8*b^2)*a^2*b/((a^2 - b^2)^4*d^3))^(1/3)*(I*sqrt(3) + 1) + 6*(2*a^2*b + b^3)/(a^4*d - 2*a^2*b^2*d + b^4*d))^2*d^2 + 12*(2*a^6*b - 3*a^4*b^3 + b^7)*((b^2/(a^4*d^2 - 2*a^2*b^2*d^2 + b^4*d^2) - (2*a^2*b + b^3)^2/(a^4*d - 2*a^2*b^2*d + b^4*d)^2)*(-I*sqrt(3) + 1)/(-1/18*(2*a^2*b + b^3)*b^2/((a^4*d^2 - 2*a^2*b^2*d^2 + b^4*d^2)*(a^4*d - 2*a^2*b^2*d + b^4*d)) + 1/27*(2*a^2*b + b^3)^3/(a^4*d - 2*a^2*b^2*d + b^4*d)^3 + 1/54*b/(a^4*d^3 - 2*a^2*b^2*d^3 + b^4*d^3) + 1/54*(a^2 + 8*b^2)*a^2*b/((a^2 - b^2)^4*d^3))^(1/3) - 9*(-1/18*(2*a^2*b + b^3)*b^2/((a^4*d^2 - 2*a^2*b^2*d^2 + b^4*d^2)*(a^4*d - 2*a^2*b^2*d + b^4*d)) + 1/27*(2*a^2*b + b^3)^3/(a^4*d - 2*a^2*b^2*d + b^4*d)^3 + 1/54*b/(a^4*d^3 - 2*a^2*b^2*d^3 + b^4*d^3) + 1/54*(a^2 + 8*b^2)*a^2*b/((a^2 - b^2)^4*d^3))^(1/3)*(I*sqrt(3) + 1) + 6*(2*a^2*b + b^3)/(a^4*d - 2*a^2*b^2*d + b^4*d))*d)/((a^8 - 4*a^6*b^2 + 6*a^4*b^4 - 4*a^2*b^6 + b^8)*d^2)))*log(-1/36*(a^6 + 3*a^5*b - 6*a^3*b^3 - 3*a^2*b^4 + 3*a*b^5 + 2*b^6)*((b^2/(a^4*d^2 - 2*a^2*b^2*d^2 + b^4*d^2) - (2*a^2*b + b^3)^2/(a^4*d - 2*a^2*b^2*d + b^4*d)^2)*(-I*sqrt(3) + 1)/(-1/18*(2*a^2*b + b^3)*b^2/((a^4*d^2 - 2*a^2*b^2*d^2 + b^4*d^2)*(a^4*d - 2*a^2*b^2*d + b^4*d)) + 1/27*(2*a^2*b + b^3)^3/(a^4*d - 2*a^2*b^2*d + b^4*d)^3 + 1/54*b/(a^4*d^3 - 2*a^2*b^2*d^3 + b^4*d^3) + 1/54*(a^2 + 8*b^2)*a^2*b/((a^2 - b^2)^4*d^3))^(1/3) - 9*(-1/18*(2*a^2*b + b^3)*b^2/((a^4*d^2 - 2*a^2*b^2*d^2 + b^4*d^2)*(a^4*d - 2*a^2*b^2*d + b^4*d)) + 1/27*(2*a^2*b + b^3)^3/(a^4*d - 2*a^2*b^2*d + b^4*d)^3 + 1/54*b/(a^4*d^3 - 2*a^2*b^2*d^3 + b^4*d^3) + 1/54*(a^2 + 8*b^2)*a^2*b/((a^2 - b^2)^4*d^3))^(1/3)*(I*sqrt(3) + 1) + 6*(2*a^2*b + b^3)/(a^4*d - 2*a^2*b^2*d + b^4*d))^2*d^2 + a^4 - 3*a^3*b + 10*a^2*b^2 - 15*a*b^3 - 2*b^4 + 1/6*(a^5 + 4*a^4*b + 16*a^3*b^2 + 19*a^2*b^3 + 10*a*b^4 + 4*b^5)*((b^2/(a^4*d^2 - 2*a^2*b^2*d^2 + b^4*d^2) - (2*a^2*b + b^3)^2/(a^4*d - 2*a^2*b^2*d + b^4*d)^2)*(-I*sqrt(3) + 1)/(-1/18*(2*a^2*b + b^3)*b^2/((a^4*d^2 - 2*a^2*b^2*d^2 + b^4*d^2)*(a^4*d - 2*a^2*b^2*d + b^4*d)) + 1/27*(2*a^2*b + b^3)^3/(a^4*d - 2*a^2*b^2*d + b^4*d)^3 + 1/54*b/(a^4*d^3 - 2*a^2*b^2*d^3 + b^4*d^3) + 1/54*(a^2 + 8*b^2)*a^2*b/((a^2 - b^2)^4*d^3))^(1/3) - 9*(-1/18*(2*a^2*b + b^3)*b^2/((a^4*d^2 - 2*a^2*b^2*d^2 + b^4*d^2)*(a^4*d - 2*a^2*b^2*d + b^4*d)) + 1/27*(2*a^2*b + b^3)^3/(a^4*d - 2*a^2*b^2*d + b^4*d)^3 + 1/54*b/(a^4*d^3 - 2*a^2*b^2*d^3 + b^4*d^3) + 1/54*(a^2 + 8*b^2)*a^2*b/((a^2 - b^2)^4*d^3))^(1/3)*(I*sqrt(3) + 1) + 6*(2*a^2*b + b^3)/(a^4*d - 2*a^2*b^2*d + b^4*d))*d + (a^4 + a^3*b + 8*a^2*b^2 + 8*a*b^3)*cosh(d*x + c)^2 + 2*(a^4 + a^3*b + 8*a^2*b^2 + 8*a*b^3)*cosh(d*x + c)*sinh(d*x + c) + (a^4 + a^3*b + 8*a^2*b^2 + 8*a*b^3)*sinh(d*x + c)^2 + 1/12*sqrt(1/3)*((a^6 + 3*a^5*b - 6*a^3*b^3 - 3*a^2*b^4 + 3*a*b^5 + 2*b^6)*((b^2/(a^4*d^2 - 2*a^2*b^2*d^2 + b^4*d^2) - (2*a^2*b + b^3)^2/(a^4*d - 2*a^2*b^2*d + b^4*d)^2)*(-I*sqrt(3) + 1)/(-1/18*(2*a^2*b + b^3)*b^2/((a^4*d^2 - 2*a^2*b^2*d^2 + b^4*d^2)*(a^4*d - 2*a^2*b^2*d + b^4*d)) + 1/27*(2*a^2*b + b^3)^3/(a^4*d - 2*a^2*b^2*d + b^4*d)^3 + 1/54*b/(a^4*d^3 - 2*a^2*b^2*d^3 + b^4*d^3) + 1/54*(a^2 + 8*b^2)*a^2*b/((a^2 - b^2)^4*d^3))^(1/3) - 9*(-1/18*(2*a^2*b + b^3)*b^2/((a^4*d^2 - 2*a^2*b^2*d^2 + b^4*d^2)*(a^4*d - 2*a^2*b^2*d + b^4*d)) + 1/27*(2*a^2*b + b^3)^3/(a^4*d - 2*a^2*b^2*d + b^4*d)^3 + 1/54*b/(a^4*d^3 - 2*a^2*b^2*d^3 + b^4*d^3) + 1/54*(a^2 + 8*b^2)*a^2*b/((a^2 - b^2)^4*d^3))^(1/3)*(I*sqrt(3) + 1) + 6*(2*a^2*b + b^3)/(a^4*d - 2*a^2*b^2*d + b^4*d))*d^2 + 6*(a^5 - 2*a^4*b - 2*a^3*b^2 + 4*a^2*b^3 + a*b^4 - 2*b^5)*d)*sqrt((288*a^4*b^2 + 720*a^2*b^4 - 36*b^6 - (a^8 - 4*a^6*b^2 + 6*a^4*b^4 - 4*a^2*b^6 + b^8)*((b^2/(a^4*d^2 - 2*a^2*b^2*d^2 + b^4*d^2) - (2*a^2*b + b^3)^2/(a^4*d - 2*a^2*b^2*d + b^4*d)^2)*(-I*sqrt(3) + 1)/(-1/18*(2*a^2*b + b^3)*b^2/((a^4*d^2 - 2*a^2*b^2*d^2 + b^4*d^2)*(a^4*d - 2*a^2*b^2*d + b^4*d)) + 1/27*(2*a^2*b + b^3)^3/(a^4*d - 2*a^2*b^2*d + b^4*d)^3 + 1/54*b/(a^4*d^3 - 2*a^2*b^2*d^3 + b^4*d^3) + 1/54*(a^2 + 8*b^2)*a^2*b/((a^2 - b^2)^4*d^3))^(1/3) - 9*(-1/18*(2*a^2*b + b^3)*b^2/((a^4*d^2 - 2*a^2*b^2*d^2 + b^4*d^2)*(a^4*d - 2*a^2*b^2*d + b^4*d)) + 1/27*(2*a^2*b + b^3)^3/(a^4*d - 2*a^2*b^2*d + b^4*d)^3 + 1/54*b/(a^4*d^3 - 2*a^2*b^2*d^3 + b^4*d^3) + 1/54*(a^2 + 8*b^2)*a^2*b/((a^2 - b^2)^4*d^3))^(1/3)*(I*sqrt(3) + 1) + 6*(2*a^2*b + b^3)/(a^4*d - 2*a^2*b^2*d + b^4*d))^2*d^2 + 12*(2*a^6*b - 3*a^4*b^3 + b^7)*((b^2/(a^4*d^2 - 2*a^2*b^2*d^2 + b^4*d^2) - (2*a^2*b + b^3)^2/(a^4*d - 2*a^2*b^2*d + b^4*d)^2)*(-I*sqrt(3) + 1)/(-1/18*(2*a^2*b + b^3)*b^2/((a^4*d^2 - 2*a^2*b^2*d^2 + b^4*d^2)*(a^4*d - 2*a^2*b^2*d + b^4*d)) + 1/27*(2*a^2*b + b^3)^3/(a^4*d - 2*a^2*b^2*d + b^4*d)^3 + 1/54*b/(a^4*d^3 - 2*a^2*b^2*d^3 + b^4*d^3) + 1/54*(a^2 + 8*b^2)*a^2*b/((a^2 - b^2)^4*d^3))^(1/3) - 9*(-1/18*(2*a^2*b + b^3)*b^2/((a^4*d^2 - 2*a^2*b^2*d^2 + b^4*d^2)*(a^4*d - 2*a^2*b^2*d + b^4*d)) + 1/27*(2*a^2*b + b^3)^3/(a^4*d - 2*a^2*b^2*d + b^4*d)^3 + 1/54*b/(a^4*d^3 - 2*a^2*b^2*d^3 + b^4*d^3) + 1/54*(a^2 + 8*b^2)*a^2*b/((a^2 - b^2)^4*d^3))^(1/3)*(I*sqrt(3) + 1) + 6*(2*a^2*b + b^3)/(a^4*d - 2*a^2*b^2*d + b^4*d))*d)/((a^8 - 4*a^6*b^2 + 6*a^4*b^4 - 4*a^2*b^6 + b^8)*d^2))) - 2*(18*(2*a^2*b + b^3)*cosh(d*x + c)^2 + 36*(2*a^2*b + b^3)*cosh(d*x + c)*sinh(d*x + c) + 18*(2*a^2*b + b^3)*sinh(d*x + c)^2 - ((a^4 - 2*a^2*b^2 + b^4)*d*cosh(d*x + c)^2 + 2*(a^4 - 2*a^2*b^2 + b^4)*d*cosh(d*x + c)*sinh(d*x + c) + (a^4 - 2*a^2*b^2 + b^4)*d*sinh(d*x + c)^2)*((b^2/(a^4*d^2 - 2*a^2*b^2*d^2 + b^4*d^2) - (2*a^2*b + b^3)^2/(a^4*d - 2*a^2*b^2*d + b^4*d)^2)*(-I*sqrt(3) + 1)/(-1/18*(2*a^2*b + b^3)*b^2/((a^4*d^2 - 2*a^2*b^2*d^2 + b^4*d^2)*(a^4*d - 2*a^2*b^2*d + b^4*d)) + 1/27*(2*a^2*b + b^3)^3/(a^4*d - 2*a^2*b^2*d + b^4*d)^3 + 1/54*b/(a^4*d^3 - 2*a^2*b^2*d^3 + b^4*d^3) + 1/54*(a^2 + 8*b^2)*a^2*b/((a^2 - b^2)^4*d^3))^(1/3) - 9*(-1/18*(2*a^2*b + b^3)*b^2/((a^4*d^2 - 2*a^2*b^2*d^2 + b^4*d^2)*(a^4*d - 2*a^2*b^2*d + b^4*d)) + 1/27*(2*a^2*b + b^3)^3/(a^4*d - 2*a^2*b^2*d + b^4*d)^3 + 1/54*b/(a^4*d^3 - 2*a^2*b^2*d^3 + b^4*d^3) + 1/54*(a^2 + 8*b^2)*a^2*b/((a^2 - b^2)^4*d^3))^(1/3)*(I*sqrt(3) + 1) + 6*(2*a^2*b + b^3)/(a^4*d - 2*a^2*b^2*d + b^4*d)) + 3*sqrt(1/3)*((a^4 - 2*a^2*b^2 + b^4)*d*cosh(d*x + c)^2 + 2*(a^4 - 2*a^2*b^2 + b^4)*d*cosh(d*x + c)*sinh(d*x + c) + (a^4 - 2*a^2*b^2 + b^4)*d*sinh(d*x + c)^2)*sqrt((288*a^4*b^2 + 720*a^2*b^4 - 36*b^6 - (a^8 - 4*a^6*b^2 + 6*a^4*b^4 - 4*a^2*b^6 + b^8)*((b^2/(a^4*d^2 - 2*a^2*b^2*d^2 + b^4*d^2) - (2*a^2*b + b^3)^2/(a^4*d - 2*a^2*b^2*d + b^4*d)^2)*(-I*sqrt(3) + 1)/(-1/18*(2*a^2*b + b^3)*b^2/((a^4*d^2 - 2*a^2*b^2*d^2 + b^4*d^2)*(a^4*d - 2*a^2*b^2*d + b^4*d)) + 1/27*(2*a^2*b + b^3)^3/(a^4*d - 2*a^2*b^2*d + b^4*d)^3 + 1/54*b/(a^4*d^3 - 2*a^2*b^2*d^3 + b^4*d^3) + 1/54*(a^2 + 8*b^2)*a^2*b/((a^2 - b^2)^4*d^3))^(1/3) - 9*(-1/18*(2*a^2*b + b^3)*b^2/((a^4*d^2 - 2*a^2*b^2*d^2 + b^4*d^2)*(a^4*d - 2*a^2*b^2*d + b^4*d)) + 1/27*(2*a^2*b + b^3)^3/(a^4*d - 2*a^2*b^2*d + b^4*d)^3 + 1/54*b/(a^4*d^3 - 2*a^2*b^2*d^3 + b^4*d^3) + 1/54*(a^2 + 8*b^2)*a^2*b/((a^2 - b^2)^4*d^3))^(1/3)*(I*sqrt(3) + 1) + 6*(2*a^2*b + b^3)/(a^4*d - 2*a^2*b^2*d + b^4*d))^2*d^2 + 12*(2*a^6*b - 3*a^4*b^3 + b^7)*((b^2/(a^4*d^2 - 2*a^2*b^2*d^2 + b^4*d^2) - (2*a^2*b + b^3)^2/(a^4*d - 2*a^2*b^2*d + b^4*d)^2)*(-I*sqrt(3) + 1)/(-1/18*(2*a^2*b + b^3)*b^2/((a^4*d^2 - 2*a^2*b^2*d^2 + b^4*d^2)*(a^4*d - 2*a^2*b^2*d + b^4*d)) + 1/27*(2*a^2*b + b^3)^3/(a^4*d - 2*a^2*b^2*d + b^4*d)^3 + 1/54*b/(a^4*d^3 - 2*a^2*b^2*d^3 + b^4*d^3) + 1/54*(a^2 + 8*b^2)*a^2*b/((a^2 - b^2)^4*d^3))^(1/3) - 9*(-1/18*(2*a^2*b + b^3)*b^2/((a^4*d^2 - 2*a^2*b^2*d^2 + b^4*d^2)*(a^4*d - 2*a^2*b^2*d + b^4*d)) + 1/27*(2*a^2*b + b^3)^3/(a^4*d - 2*a^2*b^2*d + b^4*d)^3 + 1/54*b/(a^4*d^3 - 2*a^2*b^2*d^3 + b^4*d^3) + 1/54*(a^2 + 8*b^2)*a^2*b/((a^2 - b^2)^4*d^3))^(1/3)*(I*sqrt(3) + 1) + 6*(2*a^2*b + b^3)/(a^4*d - 2*a^2*b^2*d + b^4*d))*d)/((a^8 - 4*a^6*b^2 + 6*a^4*b^4 - 4*a^2*b^6 + b^8)*d^2)))*log(-1/36*(a^6 + 3*a^5*b - 6*a^3*b^3 - 3*a^2*b^4 + 3*a*b^5 + 2*b^6)*((b^2/(a^4*d^2 - 2*a^2*b^2*d^2 + b^4*d^2) - (2*a^2*b + b^3)^2/(a^4*d - 2*a^2*b^2*d + b^4*d)^2)*(-I*sqrt(3) + 1)/(-1/18*(2*a^2*b + b^3)*b^2/((a^4*d^2 - 2*a^2*b^2*d^2 + b^4*d^2)*(a^4*d - 2*a^2*b^2*d + b^4*d)) + 1/27*(2*a^2*b + b^3)^3/(a^4*d - 2*a^2*b^2*d + b^4*d)^3 + 1/54*b/(a^4*d^3 - 2*a^2*b^2*d^3 + b^4*d^3) + 1/54*(a^2 + 8*b^2)*a^2*b/((a^2 - b^2)^4*d^3))^(1/3) - 9*(-1/18*(2*a^2*b + b^3)*b^2/((a^4*d^2 - 2*a^2*b^2*d^2 + b^4*d^2)*(a^4*d - 2*a^2*b^2*d + b^4*d)) + 1/27*(2*a^2*b + b^3)^3/(a^4*d - 2*a^2*b^2*d + b^4*d)^3 + 1/54*b/(a^4*d^3 - 2*a^2*b^2*d^3 + b^4*d^3) + 1/54*(a^2 + 8*b^2)*a^2*b/((a^2 - b^2)^4*d^3))^(1/3)*(I*sqrt(3) + 1) + 6*(2*a^2*b + b^3)/(a^4*d - 2*a^2*b^2*d + b^4*d))^2*d^2 + a^4 - 3*a^3*b + 10*a^2*b^2 - 15*a*b^3 - 2*b^4 + 1/6*(a^5 + 4*a^4*b + 16*a^3*b^2 + 19*a^2*b^3 + 10*a*b^4 + 4*b^5)*((b^2/(a^4*d^2 - 2*a^2*b^2*d^2 + b^4*d^2) - (2*a^2*b + b^3)^2/(a^4*d - 2*a^2*b^2*d + b^4*d)^2)*(-I*sqrt(3) + 1)/(-1/18*(2*a^2*b + b^3)*b^2/((a^4*d^2 - 2*a^2*b^2*d^2 + b^4*d^2)*(a^4*d - 2*a^2*b^2*d + b^4*d)) + 1/27*(2*a^2*b + b^3)^3/(a^4*d - 2*a^2*b^2*d + b^4*d)^3 + 1/54*b/(a^4*d^3 - 2*a^2*b^2*d^3 + b^4*d^3) + 1/54*(a^2 + 8*b^2)*a^2*b/((a^2 - b^2)^4*d^3))^(1/3) - 9*(-1/18*(2*a^2*b + b^3)*b^2/((a^4*d^2 - 2*a^2*b^2*d^2 + b^4*d^2)*(a^4*d - 2*a^2*b^2*d + b^4*d)) + 1/27*(2*a^2*b + b^3)^3/(a^4*d - 2*a^2*b^2*d + b^4*d)^3 + 1/54*b/(a^4*d^3 - 2*a^2*b^2*d^3 + b^4*d^3) + 1/54*(a^2 + 8*b^2)*a^2*b/((a^2 - b^2)^4*d^3))^(1/3)*(I*sqrt(3) + 1) + 6*(2*a^2*b + b^3)/(a^4*d - 2*a^2*b^2*d + b^4*d))*d + (a^4 + a^3*b + 8*a^2*b^2 + 8*a*b^3)*cosh(d*x + c)^2 + 2*(a^4 + a^3*b + 8*a^2*b^2 + 8*a*b^3)*cosh(d*x + c)*sinh(d*x + c) + (a^4 + a^3*b + 8*a^2*b^2 + 8*a*b^3)*sinh(d*x + c)^2 - 1/12*sqrt(1/3)*((a^6 + 3*a^5*b - 6*a^3*b^3 - 3*a^2*b^4 + 3*a*b^5 + 2*b^6)*((b^2/(a^4*d^2 - 2*a^2*b^2*d^2 + b^4*d^2) - (2*a^2*b + b^3)^2/(a^4*d - 2*a^2*b^2*d + b^4*d)^2)*(-I*sqrt(3) + 1)/(-1/18*(2*a^2*b + b^3)*b^2/((a^4*d^2 - 2*a^2*b^2*d^2 + b^4*d^2)*(a^4*d - 2*a^2*b^2*d + b^4*d)) + 1/27*(2*a^2*b + b^3)^3/(a^4*d - 2*a^2*b^2*d + b^4*d)^3 + 1/54*b/(a^4*d^3 - 2*a^2*b^2*d^3 + b^4*d^3) + 1/54*(a^2 + 8*b^2)*a^2*b/((a^2 - b^2)^4*d^3))^(1/3) - 9*(-1/18*(2*a^2*b + b^3)*b^2/((a^4*d^2 - 2*a^2*b^2*d^2 + b^4*d^2)*(a^4*d - 2*a^2*b^2*d + b^4*d)) + 1/27*(2*a^2*b + b^3)^3/(a^4*d - 2*a^2*b^2*d + b^4*d)^3 + 1/54*b/(a^4*d^3 - 2*a^2*b^2*d^3 + b^4*d^3) + 1/54*(a^2 + 8*b^2)*a^2*b/((a^2 - b^2)^4*d^3))^(1/3)*(I*sqrt(3) + 1) + 6*(2*a^2*b + b^3)/(a^4*d - 2*a^2*b^2*d + b^4*d))*d^2 + 6*(a^5 - 2*a^4*b - 2*a^3*b^2 + 4*a^2*b^3 + a*b^4 - 2*b^5)*d)*sqrt((288*a^4*b^2 + 720*a^2*b^4 - 36*b^6 - (a^8 - 4*a^6*b^2 + 6*a^4*b^4 - 4*a^2*b^6 + b^8)*((b^2/(a^4*d^2 - 2*a^2*b^2*d^2 + b^4*d^2) - (2*a^2*b + b^3)^2/(a^4*d - 2*a^2*b^2*d + b^4*d)^2)*(-I*sqrt(3) + 1)/(-1/18*(2*a^2*b + b^3)*b^2/((a^4*d^2 - 2*a^2*b^2*d^2 + b^4*d^2)*(a^4*d - 2*a^2*b^2*d + b^4*d)) + 1/27*(2*a^2*b + b^3)^3/(a^4*d - 2*a^2*b^2*d + b^4*d)^3 + 1/54*b/(a^4*d^3 - 2*a^2*b^2*d^3 + b^4*d^3) + 1/54*(a^2 + 8*b^2)*a^2*b/((a^2 - b^2)^4*d^3))^(1/3) - 9*(-1/18*(2*a^2*b + b^3)*b^2/((a^4*d^2 - 2*a^2*b^2*d^2 + b^4*d^2)*(a^4*d - 2*a^2*b^2*d + b^4*d)) + 1/27*(2*a^2*b + b^3)^3/(a^4*d - 2*a^2*b^2*d + b^4*d)^3 + 1/54*b/(a^4*d^3 - 2*a^2*b^2*d^3 + b^4*d^3) + 1/54*(a^2 + 8*b^2)*a^2*b/((a^2 - b^2)^4*d^3))^(1/3)*(I*sqrt(3) + 1) + 6*(2*a^2*b + b^3)/(a^4*d - 2*a^2*b^2*d + b^4*d))^2*d^2 + 12*(2*a^6*b - 3*a^4*b^3 + b^7)*((b^2/(a^4*d^2 - 2*a^2*b^2*d^2 + b^4*d^2) - (2*a^2*b + b^3)^2/(a^4*d - 2*a^2*b^2*d + b^4*d)^2)*(-I*sqrt(3) + 1)/(-1/18*(2*a^2*b + b^3)*b^2/((a^4*d^2 - 2*a^2*b^2*d^2 + b^4*d^2)*(a^4*d - 2*a^2*b^2*d + b^4*d)) + 1/27*(2*a^2*b + b^3)^3/(a^4*d - 2*a^2*b^2*d + b^4*d)^3 + 1/54*b/(a^4*d^3 - 2*a^2*b^2*d^3 + b^4*d^3) + 1/54*(a^2 + 8*b^2)*a^2*b/((a^2 - b^2)^4*d^3))^(1/3) - 9*(-1/18*(2*a^2*b + b^3)*b^2/((a^4*d^2 - 2*a^2*b^2*d^2 + b^4*d^2)*(a^4*d - 2*a^2*b^2*d + b^4*d)) + 1/27*(2*a^2*b + b^3)^3/(a^4*d - 2*a^2*b^2*d + b^4*d)^3 + 1/54*b/(a^4*d^3 - 2*a^2*b^2*d^3 + b^4*d^3) + 1/54*(a^2 + 8*b^2)*a^2*b/((a^2 - b^2)^4*d^3))^(1/3)*(I*sqrt(3) + 1) + 6*(2*a^2*b + b^3)/(a^4*d - 2*a^2*b^2*d + b^4*d))*d)/((a^8 - 4*a^6*b^2 + 6*a^4*b^4 - 4*a^2*b^6 + b^8)*d^2))) + 36*(2*(a^3 + 4*a^2*b + 5*a*b^2 + 2*b^3)*d*x*cosh(d*x + c) - (a^3 - a^2*b - a*b^2 + b^3)*cosh(d*x + c)^3)*sinh(d*x + c))/((a^4 - 2*a^2*b^2 + b^4)*d*cosh(d*x + c)^2 + 2*(a^4 - 2*a^2*b^2 + b^4)*d*cosh(d*x + c)*sinh(d*x + c) + (a^4 - 2*a^2*b^2 + b^4)*d*sinh(d*x + c)^2)","C",0
76,-1,0,0,0.000000," ","integrate(sinh(d*x+c)/(a+b*tanh(d*x+c)^3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
77,-1,0,0,0.000000," ","integrate(csch(d*x+c)/(a+b*tanh(d*x+c)^3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
78,1,640,0,0.719558," ","integrate(csch(d*x+c)^2/(a+b*tanh(d*x+c)^3),x, algorithm=""fricas"")","-\frac{2 \, {\left(\sqrt{3} \cosh\left(d x + c\right)^{2} + 2 \, \sqrt{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sqrt{3} \sinh\left(d x + c\right)^{2} - \sqrt{3}\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}} \arctan\left(-\frac{\sqrt{3} b \cosh\left(d x + c\right)^{2} + 2 \, \sqrt{3} b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sqrt{3} b \sinh\left(d x + c\right)^{2} - {\left(\sqrt{3} a \cosh\left(d x + c\right)^{2} + 2 \, \sqrt{3} a \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sqrt{3} a \sinh\left(d x + c\right)^{2} + \sqrt{3} a\right)} \left(\frac{b}{a}\right)^{\frac{2}{3}} - {\left(\sqrt{3} b \cosh\left(d x + c\right)^{2} + 2 \, \sqrt{3} b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + \sqrt{3} b \sinh\left(d x + c\right)^{2} - \sqrt{3} b\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}}}{3 \, b}\right) + {\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} - 1\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}} \log\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) - 2 \, {\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} - a\right)} \left(\frac{b}{a}\right)^{\frac{2}{3}} + 2 \, {\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} + a\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}} + a + b\right) - 2 \, {\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} - 1\right)} \left(\frac{b}{a}\right)^{\frac{1}{3}} \log\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} + 2 \, a \left(\frac{b}{a}\right)^{\frac{2}{3}} - 2 \, a \left(\frac{b}{a}\right)^{\frac{1}{3}} + a - b\right) + 12}{6 \, {\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,"-1/6*(2*(sqrt(3)*cosh(d*x + c)^2 + 2*sqrt(3)*cosh(d*x + c)*sinh(d*x + c) + sqrt(3)*sinh(d*x + c)^2 - sqrt(3))*(b/a)^(1/3)*arctan(-1/3*(sqrt(3)*b*cosh(d*x + c)^2 + 2*sqrt(3)*b*cosh(d*x + c)*sinh(d*x + c) + sqrt(3)*b*sinh(d*x + c)^2 - (sqrt(3)*a*cosh(d*x + c)^2 + 2*sqrt(3)*a*cosh(d*x + c)*sinh(d*x + c) + sqrt(3)*a*sinh(d*x + c)^2 + sqrt(3)*a)*(b/a)^(2/3) - (sqrt(3)*b*cosh(d*x + c)^2 + 2*sqrt(3)*b*cosh(d*x + c)*sinh(d*x + c) + sqrt(3)*b*sinh(d*x + c)^2 - sqrt(3)*b)*(b/a)^(1/3))/b) + (cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 1)*(b/a)^(1/3)*log((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) - 2*(a*cosh(d*x + c)^2 + 2*a*cosh(d*x + c)*sinh(d*x + c) + a*sinh(d*x + c)^2 - a)*(b/a)^(2/3) + 2*(a*cosh(d*x + c)^2 + 2*a*cosh(d*x + c)*sinh(d*x + c) + a*sinh(d*x + c)^2 + a)*(b/a)^(1/3) + a + b) - 2*(cosh(d*x + c)^2 + 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2 - 1)*(b/a)^(1/3)*log((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*(b/a)^(2/3) - 2*a*(b/a)^(1/3) + a - b) + 12)/(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
79,-1,0,0,0.000000," ","integrate(csch(d*x+c)^3/(a+b*tanh(d*x+c)^3),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
80,1,1954,0,1.868748," ","integrate(csch(d*x+c)^4/(a+b*tanh(d*x+c)^3),x, algorithm=""fricas"")","\frac{12 \, \sqrt{\frac{1}{3}} {\left(a^{2} d e^{\left(6 \, d x + 6 \, c\right)} - 3 \, a^{2} d e^{\left(4 \, d x + 4 \, c\right)} + 3 \, a^{2} d e^{\left(2 \, d x + 2 \, c\right)} - a^{2} d\right)} \sqrt{\frac{{\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} {\left(\frac{b}{a^{4} d^{3}} - \frac{b^{3}}{a^{6} d^{3}} - \frac{a^{2} b - b^{3}}{a^{6} d^{3}}\right)}^{\frac{1}{3}} - \frac{2 \, b}{a^{2} d}\right)}^{2} a^{4} d^{2} + 4 \, {\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} {\left(\frac{b}{a^{4} d^{3}} - \frac{b^{3}}{a^{6} d^{3}} - \frac{a^{2} b - b^{3}}{a^{6} d^{3}}\right)}^{\frac{1}{3}} - \frac{2 \, b}{a^{2} d}\right)} a^{2} b d + 4 \, b^{2}}{a^{4} d^{2}}} \arctan\left(-\frac{\sqrt{\frac{1}{3}} {\left({\left(a^{6} + a^{5} b\right)} {\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} {\left(\frac{b}{a^{4} d^{3}} - \frac{b^{3}}{a^{6} d^{3}} - \frac{a^{2} b - b^{3}}{a^{6} d^{3}}\right)}^{\frac{1}{3}} - \frac{2 \, b}{a^{2} d}\right)}^{2} d^{3} e^{\left(2 \, d x + 2 \, c\right)} - 4 \, {\left(2 \, a^{3} b + a^{2} b^{2} - a b^{3}\right)} d e^{\left(2 \, d x + 2 \, c\right)} - 2 \, {\left({\left(a^{5} - a^{4} b - 2 \, a^{3} b^{2}\right)} d^{2} e^{\left(2 \, d x + 2 \, c\right)} + {\left(a^{5} + a^{4} b\right)} d^{2}\right)} {\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} {\left(\frac{b}{a^{4} d^{3}} - \frac{b^{3}}{a^{6} d^{3}} - \frac{a^{2} b - b^{3}}{a^{6} d^{3}}\right)}^{\frac{1}{3}} - \frac{2 \, b}{a^{2} d}\right)} - {\left({\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} {\left(\frac{b}{a^{4} d^{3}} - \frac{b^{3}}{a^{6} d^{3}} - \frac{a^{2} b - b^{3}}{a^{6} d^{3}}\right)}^{\frac{1}{3}} - \frac{2 \, b}{a^{2} d}\right)}^{2} a^{4} d^{3} - 2 \, {\left(a^{3} - 2 \, a^{2} b\right)} {\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} {\left(\frac{b}{a^{4} d^{3}} - \frac{b^{3}}{a^{6} d^{3}} - \frac{a^{2} b - b^{3}}{a^{6} d^{3}}\right)}^{\frac{1}{3}} - \frac{2 \, b}{a^{2} d}\right)} d^{2} - 4 \, {\left(2 \, a b - b^{2}\right)} d\right)} \sqrt{a^{4} + 4 \, a^{3} b + 5 \, a^{2} b^{2} + 2 \, a b^{3} - \frac{1}{2} \, {\left({\left(a^{6} + a^{5} b\right)} d^{2} e^{\left(2 \, d x + 2 \, c\right)} - {\left(a^{6} + a^{5} b\right)} d^{2}\right)} {\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} {\left(\frac{b}{a^{4} d^{3}} - \frac{b^{3}}{a^{6} d^{3}} - \frac{a^{2} b - b^{3}}{a^{6} d^{3}}\right)}^{\frac{1}{3}} - \frac{2 \, b}{a^{2} d}\right)}^{2} + {\left({\left(a^{5} - a^{4} b - 2 \, a^{3} b^{2}\right)} d e^{\left(2 \, d x + 2 \, c\right)} + {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2}\right)} d\right)} {\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} {\left(\frac{b}{a^{4} d^{3}} - \frac{b^{3}}{a^{6} d^{3}} - \frac{a^{2} b - b^{3}}{a^{6} d^{3}}\right)}^{\frac{1}{3}} - \frac{2 \, b}{a^{2} d}\right)} + {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(a^{4} + a^{3} b - a^{2} b^{2} - a b^{3}\right)} e^{\left(2 \, d x + 2 \, c\right)}}\right)} \sqrt{\frac{{\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} {\left(\frac{b}{a^{4} d^{3}} - \frac{b^{3}}{a^{6} d^{3}} - \frac{a^{2} b - b^{3}}{a^{6} d^{3}}\right)}^{\frac{1}{3}} - \frac{2 \, b}{a^{2} d}\right)}^{2} a^{4} d^{2} + 4 \, {\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} {\left(\frac{b}{a^{4} d^{3}} - \frac{b^{3}}{a^{6} d^{3}} - \frac{a^{2} b - b^{3}}{a^{6} d^{3}}\right)}^{\frac{1}{3}} - \frac{2 \, b}{a^{2} d}\right)} a^{2} b d + 4 \, b^{2}}{a^{4} d^{2}}}}{8 \, {\left(a^{2} b + a b^{2}\right)}}\right) - 2 \, {\left(a^{2} d e^{\left(6 \, d x + 6 \, c\right)} - 3 \, a^{2} d e^{\left(4 \, d x + 4 \, c\right)} + 3 \, a^{2} d e^{\left(2 \, d x + 2 \, c\right)} - a^{2} d\right)} {\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} {\left(\frac{b}{a^{4} d^{3}} - \frac{b^{3}}{a^{6} d^{3}} - \frac{a^{2} b - b^{3}}{a^{6} d^{3}}\right)}^{\frac{1}{3}} - \frac{2 \, b}{a^{2} d}\right)} \log\left(\frac{1}{2} \, {\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} {\left(\frac{b}{a^{4} d^{3}} - \frac{b^{3}}{a^{6} d^{3}} - \frac{a^{2} b - b^{3}}{a^{6} d^{3}}\right)}^{\frac{1}{3}} - \frac{2 \, b}{a^{2} d}\right)}^{2} a^{4} d^{2} - {\left(a^{3} - 2 \, a^{2} b\right)} {\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} {\left(\frac{b}{a^{4} d^{3}} - \frac{b^{3}}{a^{6} d^{3}} - \frac{a^{2} b - b^{3}}{a^{6} d^{3}}\right)}^{\frac{1}{3}} - \frac{2 \, b}{a^{2} d}\right)} d + a^{2} - 3 \, a b + 2 \, b^{2} + {\left(a^{2} + a b\right)} e^{\left(2 \, d x + 2 \, c\right)}\right) - 48 \, a e^{\left(2 \, d x + 2 \, c\right)} + {\left({\left(a^{2} d e^{\left(6 \, d x + 6 \, c\right)} - 3 \, a^{2} d e^{\left(4 \, d x + 4 \, c\right)} + 3 \, a^{2} d e^{\left(2 \, d x + 2 \, c\right)} - a^{2} d\right)} {\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} {\left(\frac{b}{a^{4} d^{3}} - \frac{b^{3}}{a^{6} d^{3}} - \frac{a^{2} b - b^{3}}{a^{6} d^{3}}\right)}^{\frac{1}{3}} - \frac{2 \, b}{a^{2} d}\right)} + 6 \, b e^{\left(6 \, d x + 6 \, c\right)} - 18 \, b e^{\left(4 \, d x + 4 \, c\right)} + 18 \, b e^{\left(2 \, d x + 2 \, c\right)} - 6 \, b\right)} \log\left(a^{4} + 4 \, a^{3} b + 5 \, a^{2} b^{2} + 2 \, a b^{3} - \frac{1}{2} \, {\left({\left(a^{6} + a^{5} b\right)} d^{2} e^{\left(2 \, d x + 2 \, c\right)} - {\left(a^{6} + a^{5} b\right)} d^{2}\right)} {\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} {\left(\frac{b}{a^{4} d^{3}} - \frac{b^{3}}{a^{6} d^{3}} - \frac{a^{2} b - b^{3}}{a^{6} d^{3}}\right)}^{\frac{1}{3}} - \frac{2 \, b}{a^{2} d}\right)}^{2} + {\left({\left(a^{5} - a^{4} b - 2 \, a^{3} b^{2}\right)} d e^{\left(2 \, d x + 2 \, c\right)} + {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2}\right)} d\right)} {\left(\left(\frac{1}{2}\right)^{\frac{1}{3}} {\left(i \, \sqrt{3} + 1\right)} {\left(\frac{b}{a^{4} d^{3}} - \frac{b^{3}}{a^{6} d^{3}} - \frac{a^{2} b - b^{3}}{a^{6} d^{3}}\right)}^{\frac{1}{3}} - \frac{2 \, b}{a^{2} d}\right)} + {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} e^{\left(4 \, d x + 4 \, c\right)} + 2 \, {\left(a^{4} + a^{3} b - a^{2} b^{2} - a b^{3}\right)} e^{\left(2 \, d x + 2 \, c\right)}\right) - 12 \, {\left(b e^{\left(6 \, d x + 6 \, c\right)} - 3 \, b e^{\left(4 \, d x + 4 \, c\right)} + 3 \, b e^{\left(2 \, d x + 2 \, c\right)} - b\right)} \log\left(e^{\left(2 \, d x + 2 \, c\right)} - 1\right) + 16 \, a}{12 \, {\left(a^{2} d e^{\left(6 \, d x + 6 \, c\right)} - 3 \, a^{2} d e^{\left(4 \, d x + 4 \, c\right)} + 3 \, a^{2} d e^{\left(2 \, d x + 2 \, c\right)} - a^{2} d\right)}}"," ",0,"1/12*(12*sqrt(1/3)*(a^2*d*e^(6*d*x + 6*c) - 3*a^2*d*e^(4*d*x + 4*c) + 3*a^2*d*e^(2*d*x + 2*c) - a^2*d)*sqrt((((1/2)^(1/3)*(I*sqrt(3) + 1)*(b/(a^4*d^3) - b^3/(a^6*d^3) - (a^2*b - b^3)/(a^6*d^3))^(1/3) - 2*b/(a^2*d))^2*a^4*d^2 + 4*((1/2)^(1/3)*(I*sqrt(3) + 1)*(b/(a^4*d^3) - b^3/(a^6*d^3) - (a^2*b - b^3)/(a^6*d^3))^(1/3) - 2*b/(a^2*d))*a^2*b*d + 4*b^2)/(a^4*d^2))*arctan(-1/8*sqrt(1/3)*((a^6 + a^5*b)*((1/2)^(1/3)*(I*sqrt(3) + 1)*(b/(a^4*d^3) - b^3/(a^6*d^3) - (a^2*b - b^3)/(a^6*d^3))^(1/3) - 2*b/(a^2*d))^2*d^3*e^(2*d*x + 2*c) - 4*(2*a^3*b + a^2*b^2 - a*b^3)*d*e^(2*d*x + 2*c) - 2*((a^5 - a^4*b - 2*a^3*b^2)*d^2*e^(2*d*x + 2*c) + (a^5 + a^4*b)*d^2)*((1/2)^(1/3)*(I*sqrt(3) + 1)*(b/(a^4*d^3) - b^3/(a^6*d^3) - (a^2*b - b^3)/(a^6*d^3))^(1/3) - 2*b/(a^2*d)) - (((1/2)^(1/3)*(I*sqrt(3) + 1)*(b/(a^4*d^3) - b^3/(a^6*d^3) - (a^2*b - b^3)/(a^6*d^3))^(1/3) - 2*b/(a^2*d))^2*a^4*d^3 - 2*(a^3 - 2*a^2*b)*((1/2)^(1/3)*(I*sqrt(3) + 1)*(b/(a^4*d^3) - b^3/(a^6*d^3) - (a^2*b - b^3)/(a^6*d^3))^(1/3) - 2*b/(a^2*d))*d^2 - 4*(2*a*b - b^2)*d)*sqrt(a^4 + 4*a^3*b + 5*a^2*b^2 + 2*a*b^3 - 1/2*((a^6 + a^5*b)*d^2*e^(2*d*x + 2*c) - (a^6 + a^5*b)*d^2)*((1/2)^(1/3)*(I*sqrt(3) + 1)*(b/(a^4*d^3) - b^3/(a^6*d^3) - (a^2*b - b^3)/(a^6*d^3))^(1/3) - 2*b/(a^2*d))^2 + ((a^5 - a^4*b - 2*a^3*b^2)*d*e^(2*d*x + 2*c) + (a^5 + 3*a^4*b + 2*a^3*b^2)*d)*((1/2)^(1/3)*(I*sqrt(3) + 1)*(b/(a^4*d^3) - b^3/(a^6*d^3) - (a^2*b - b^3)/(a^6*d^3))^(1/3) - 2*b/(a^2*d)) + (a^4 + 2*a^3*b + a^2*b^2)*e^(4*d*x + 4*c) + 2*(a^4 + a^3*b - a^2*b^2 - a*b^3)*e^(2*d*x + 2*c)))*sqrt((((1/2)^(1/3)*(I*sqrt(3) + 1)*(b/(a^4*d^3) - b^3/(a^6*d^3) - (a^2*b - b^3)/(a^6*d^3))^(1/3) - 2*b/(a^2*d))^2*a^4*d^2 + 4*((1/2)^(1/3)*(I*sqrt(3) + 1)*(b/(a^4*d^3) - b^3/(a^6*d^3) - (a^2*b - b^3)/(a^6*d^3))^(1/3) - 2*b/(a^2*d))*a^2*b*d + 4*b^2)/(a^4*d^2))/(a^2*b + a*b^2)) - 2*(a^2*d*e^(6*d*x + 6*c) - 3*a^2*d*e^(4*d*x + 4*c) + 3*a^2*d*e^(2*d*x + 2*c) - a^2*d)*((1/2)^(1/3)*(I*sqrt(3) + 1)*(b/(a^4*d^3) - b^3/(a^6*d^3) - (a^2*b - b^3)/(a^6*d^3))^(1/3) - 2*b/(a^2*d))*log(1/2*((1/2)^(1/3)*(I*sqrt(3) + 1)*(b/(a^4*d^3) - b^3/(a^6*d^3) - (a^2*b - b^3)/(a^6*d^3))^(1/3) - 2*b/(a^2*d))^2*a^4*d^2 - (a^3 - 2*a^2*b)*((1/2)^(1/3)*(I*sqrt(3) + 1)*(b/(a^4*d^3) - b^3/(a^6*d^3) - (a^2*b - b^3)/(a^6*d^3))^(1/3) - 2*b/(a^2*d))*d + a^2 - 3*a*b + 2*b^2 + (a^2 + a*b)*e^(2*d*x + 2*c)) - 48*a*e^(2*d*x + 2*c) + ((a^2*d*e^(6*d*x + 6*c) - 3*a^2*d*e^(4*d*x + 4*c) + 3*a^2*d*e^(2*d*x + 2*c) - a^2*d)*((1/2)^(1/3)*(I*sqrt(3) + 1)*(b/(a^4*d^3) - b^3/(a^6*d^3) - (a^2*b - b^3)/(a^6*d^3))^(1/3) - 2*b/(a^2*d)) + 6*b*e^(6*d*x + 6*c) - 18*b*e^(4*d*x + 4*c) + 18*b*e^(2*d*x + 2*c) - 6*b)*log(a^4 + 4*a^3*b + 5*a^2*b^2 + 2*a*b^3 - 1/2*((a^6 + a^5*b)*d^2*e^(2*d*x + 2*c) - (a^6 + a^5*b)*d^2)*((1/2)^(1/3)*(I*sqrt(3) + 1)*(b/(a^4*d^3) - b^3/(a^6*d^3) - (a^2*b - b^3)/(a^6*d^3))^(1/3) - 2*b/(a^2*d))^2 + ((a^5 - a^4*b - 2*a^3*b^2)*d*e^(2*d*x + 2*c) + (a^5 + 3*a^4*b + 2*a^3*b^2)*d)*((1/2)^(1/3)*(I*sqrt(3) + 1)*(b/(a^4*d^3) - b^3/(a^6*d^3) - (a^2*b - b^3)/(a^6*d^3))^(1/3) - 2*b/(a^2*d)) + (a^4 + 2*a^3*b + a^2*b^2)*e^(4*d*x + 4*c) + 2*(a^4 + a^3*b - a^2*b^2 - a*b^3)*e^(2*d*x + 2*c)) - 12*(b*e^(6*d*x + 6*c) - 3*b*e^(4*d*x + 4*c) + 3*b*e^(2*d*x + 2*c) - b)*log(e^(2*d*x + 2*c) - 1) + 16*a)/(a^2*d*e^(6*d*x + 6*c) - 3*a^2*d*e^(4*d*x + 4*c) + 3*a^2*d*e^(2*d*x + 2*c) - a^2*d)","C",0
81,1,63,0,0.411766," ","integrate(cosh(d*x+c)^4*(a+b*tanh(d*x+c)^2),x, algorithm=""fricas"")","\frac{{\left(a + b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(3 \, a - b\right)} d x + {\left({\left(a + b\right)} \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*((a + b)*cosh(d*x + c)*sinh(d*x + c)^3 + (3*a - b)*d*x + ((a + b)*cosh(d*x + c)^3 + 4*a*cosh(d*x + c))*sinh(d*x + c))/d","A",0
82,1,45,0,0.391586," ","integrate(cosh(d*x+c)^3*(a+b*tanh(d*x+c)^2),x, algorithm=""fricas"")","\frac{{\left(a + b\right)} \sinh\left(d x + c\right)^{3} + 3 \, {\left({\left(a + b\right)} \cosh\left(d x + c\right)^{2} + 3 \, a - b\right)} \sinh\left(d x + c\right)}{12 \, d}"," ",0,"1/12*((a + b)*sinh(d*x + c)^3 + 3*((a + b)*cosh(d*x + c)^2 + 3*a - b)*sinh(d*x + c))/d","A",0
83,1,30,0,0.394243," ","integrate(cosh(d*x+c)^2*(a+b*tanh(d*x+c)^2),x, algorithm=""fricas"")","\frac{{\left(a - b\right)} d x + {\left(a + b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)}{2 \, d}"," ",0,"1/2*((a - b)*d*x + (a + b)*cosh(d*x + c)*sinh(d*x + c))/d","A",0
84,1,102,0,0.407942," ","integrate(cosh(d*x+c)*(a+b*tanh(d*x+c)^2),x, algorithm=""fricas"")","\frac{{\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} - 4 \, {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \arctan\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) - a - b}{2 \, {\left(d \cosh\left(d x + c\right) + d \sinh\left(d x + c\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 - 4*(b*cosh(d*x + c) + b*sinh(d*x + c))*arctan(cosh(d*x + c) + sinh(d*x + c)) - a - b)/(d*cosh(d*x + c) + d*sinh(d*x + c))","B",0
85,1,323,0,0.393188," ","integrate(sech(d*x+c)*(a+b*tanh(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} + b \sinh\left(d x + c\right)^{3} - {\left({\left(2 \, a + b\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(2 \, a + b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(2 \, a + b\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a + b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(2 \, a + b\right)} \cosh\left(d x + c\right)^{2} + 2 \, a + b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\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) + 2 \, a + b\right)} \arctan\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) - b \cosh\left(d x + c\right) + {\left(3 \, b \cosh\left(d x + c\right)^{2} - 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,"-(b*cosh(d*x + c)^3 + 3*b*cosh(d*x + c)*sinh(d*x + c)^2 + b*sinh(d*x + c)^3 - ((2*a + b)*cosh(d*x + c)^4 + 4*(2*a + b)*cosh(d*x + c)*sinh(d*x + c)^3 + (2*a + b)*sinh(d*x + c)^4 + 2*(2*a + b)*cosh(d*x + c)^2 + 2*(3*(2*a + b)*cosh(d*x + c)^2 + 2*a + b)*sinh(d*x + c)^2 + 4*((2*a + b)*cosh(d*x + c)^3 + (2*a + b)*cosh(d*x + c))*sinh(d*x + c) + 2*a + b)*arctan(cosh(d*x + c) + sinh(d*x + c)) - b*cosh(d*x + c) + (3*b*cosh(d*x + c)^2 - 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
86,1,159,0,0.382339," ","integrate(sech(d*x+c)^2*(a+b*tanh(d*x+c)^2),x, algorithm=""fricas"")","-\frac{4 \, {\left({\left(3 \, a + 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(3 \, 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*((3*a + 2*b)*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + (3*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
87,1,1046,0,0.401276," ","integrate(sech(d*x+c)^3*(a+b*tanh(d*x+c)^2),x, algorithm=""fricas"")","\frac{{\left(4 \, a + b\right)} \cosh\left(d x + c\right)^{7} + 7 \, {\left(4 \, a + b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + {\left(4 \, a + b\right)} \sinh\left(d x + c\right)^{7} + {\left(4 \, a - 7 \, b\right)} \cosh\left(d x + c\right)^{5} + {\left(21 \, {\left(4 \, a + b\right)} \cosh\left(d x + c\right)^{2} + 4 \, a - 7 \, b\right)} \sinh\left(d x + c\right)^{5} + 5 \, {\left(7 \, {\left(4 \, a + b\right)} \cosh\left(d x + c\right)^{3} + {\left(4 \, a - 7 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} - {\left(4 \, a - 7 \, b\right)} \cosh\left(d x + c\right)^{3} + {\left(35 \, {\left(4 \, a + b\right)} \cosh\left(d x + c\right)^{4} + 10 \, {\left(4 \, a - 7 \, b\right)} \cosh\left(d x + c\right)^{2} - 4 \, a + 7 \, b\right)} \sinh\left(d x + c\right)^{3} + {\left(21 \, {\left(4 \, a + b\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(4 \, a - 7 \, b\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(4 \, a - 7 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(4 \, a + b\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(4 \, a + b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(4 \, a + b\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(4 \, a + b\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(4 \, a + b\right)} \cosh\left(d x + c\right)^{2} + 4 \, a + b\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\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)^{5} + 6 \, {\left(4 \, a + b\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(4 \, a + b\right)} \cosh\left(d x + c\right)^{4} + 30 \, {\left(4 \, a + b\right)} \cosh\left(d x + c\right)^{2} + 12 \, a + 3 \, b\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(4 \, a + b\right)} \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)^{3} + 4 \, {\left(4 \, a + b\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(4 \, a + b\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(4 \, a + b\right)} \cosh\left(d x + c\right)^{4} + 9 \, {\left(4 \, a + b\right)} \cosh\left(d x + c\right)^{2} + 4 \, a + b\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left({\left(4 \, a + b\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(4 \, a + b\right)} \cosh\left(d x + c\right)^{5} + 3 \, {\left(4 \, a + b\right)} \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 \, a + b\right)} \arctan\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) - {\left(4 \, a + b\right)} \cosh\left(d x + c\right) + {\left(7 \, {\left(4 \, a + b\right)} \cosh\left(d x + c\right)^{6} + 5 \, {\left(4 \, a - 7 \, b\right)} \cosh\left(d x + c\right)^{4} - 3 \, {\left(4 \, a - 7 \, b\right)} \cosh\left(d x + c\right)^{2} - 4 \, 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*((4*a + b)*cosh(d*x + c)^7 + 7*(4*a + b)*cosh(d*x + c)*sinh(d*x + c)^6 + (4*a + b)*sinh(d*x + c)^7 + (4*a - 7*b)*cosh(d*x + c)^5 + (21*(4*a + b)*cosh(d*x + c)^2 + 4*a - 7*b)*sinh(d*x + c)^5 + 5*(7*(4*a + b)*cosh(d*x + c)^3 + (4*a - 7*b)*cosh(d*x + c))*sinh(d*x + c)^4 - (4*a - 7*b)*cosh(d*x + c)^3 + (35*(4*a + b)*cosh(d*x + c)^4 + 10*(4*a - 7*b)*cosh(d*x + c)^2 - 4*a + 7*b)*sinh(d*x + c)^3 + (21*(4*a + b)*cosh(d*x + c)^5 + 10*(4*a - 7*b)*cosh(d*x + c)^3 - 3*(4*a - 7*b)*cosh(d*x + c))*sinh(d*x + c)^2 + ((4*a + b)*cosh(d*x + c)^8 + 8*(4*a + b)*cosh(d*x + c)*sinh(d*x + c)^7 + (4*a + b)*sinh(d*x + c)^8 + 4*(4*a + b)*cosh(d*x + c)^6 + 4*(7*(4*a + b)*cosh(d*x + c)^2 + 4*a + b)*sinh(d*x + c)^6 + 8*(7*(4*a + b)*cosh(d*x + c)^3 + 3*(4*a + b)*cosh(d*x + c))*sinh(d*x + c)^5 + 6*(4*a + b)*cosh(d*x + c)^4 + 2*(35*(4*a + b)*cosh(d*x + c)^4 + 30*(4*a + b)*cosh(d*x + c)^2 + 12*a + 3*b)*sinh(d*x + c)^4 + 8*(7*(4*a + 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)^3 + 4*(4*a + b)*cosh(d*x + c)^2 + 4*(7*(4*a + b)*cosh(d*x + c)^6 + 15*(4*a + b)*cosh(d*x + c)^4 + 9*(4*a + b)*cosh(d*x + c)^2 + 4*a + b)*sinh(d*x + c)^2 + 8*((4*a + b)*cosh(d*x + c)^7 + 3*(4*a + b)*cosh(d*x + c)^5 + 3*(4*a + b)*cosh(d*x + c)^3 + (4*a + b)*cosh(d*x + c))*sinh(d*x + c) + 4*a + b)*arctan(cosh(d*x + c) + sinh(d*x + c)) - (4*a + b)*cosh(d*x + c) + (7*(4*a + b)*cosh(d*x + c)^6 + 5*(4*a - 7*b)*cosh(d*x + c)^4 - 3*(4*a - 7*b)*cosh(d*x + c)^2 - 4*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
88,1,345,0,0.392905," ","integrate(sech(d*x+c)^4*(a+b*tanh(d*x+c)^2),x, algorithm=""fricas"")","-\frac{8 \, {\left(2 \, {\left(5 \, a + 4 \, b\right)} \cosh\left(d x + c\right)^{3} + 6 \, {\left(5 \, a + 4 \, b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + {\left(5 \, a + 7 \, b\right)} \sinh\left(d x + c\right)^{3} + 30 \, a \cosh\left(d x + c\right) + {\left(3 \, {\left(5 \, a + 7 \, b\right)} \cosh\left(d x + c\right)^{2} + 5 \, 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*(5*a + 4*b)*cosh(d*x + c)^3 + 6*(5*a + 4*b)*cosh(d*x + c)*sinh(d*x + c)^2 + (5*a + 7*b)*sinh(d*x + c)^3 + 30*a*cosh(d*x + c) + (3*(5*a + 7*b)*cosh(d*x + c)^2 + 5*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
89,1,95,0,0.411865," ","integrate(cosh(d*x+c)^4*(a+b*tanh(d*x+c)^2)^2,x, algorithm=""fricas"")","\frac{{\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} d x + {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{8 \, d}"," ",0,"1/8*((a^2 + 2*a*b + b^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (3*a^2 - 2*a*b + 3*b^2)*d*x + ((a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 + 4*(a^2 - b^2)*cosh(d*x + c))*sinh(d*x + c))/d","A",0
90,1,519,0,0.418554," ","integrate(cosh(d*x+c)^3*(a+b*tanh(d*x+c)^2)^2,x, algorithm=""fricas"")","\frac{{\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{6} + 6 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{6} + 3 \, {\left(3 \, a^{2} - 2 \, a b - 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(5 \, {\left(a^{2} + 2 \, a b + 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} + 4 \, {\left(5 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(3 \, a^{2} - 2 \, a b - 5 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 3 \, {\left(3 \, a^{2} - 2 \, a b - 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 3 \, {\left(5 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + 6 \, {\left(3 \, a^{2} - 2 \, a b - 5 \, 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)^{2} - a^{2} - 2 \, a b - b^{2} + 48 \, {\left(b^{2} \cosh\left(d x + c\right)^{3} + 3 \, b^{2} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + b^{2} \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({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(3 \, a^{2} - 2 \, a b - 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(3 \, a^{2} - 2 \, 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*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^6 + 6*(a^2 + 2*a*b + b^2)*cosh(d*x + c)*sinh(d*x + c)^5 + (a^2 + 2*a*b + b^2)*sinh(d*x + c)^6 + 3*(3*a^2 - 2*a*b - 5*b^2)*cosh(d*x + c)^4 + 3*(5*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + 3*a^2 - 2*a*b - 5*b^2)*sinh(d*x + c)^4 + 4*(5*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 + 3*(3*a^2 - 2*a*b - 5*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 - 3*(3*a^2 - 2*a*b - 5*b^2)*cosh(d*x + c)^2 + 3*(5*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 + 6*(3*a^2 - 2*a*b - 5*b^2)*cosh(d*x + c)^2 - 3*a^2 + 2*a*b + 5*b^2)*sinh(d*x + c)^2 - a^2 - 2*a*b - b^2 + 48*(b^2*cosh(d*x + c)^3 + 3*b^2*cosh(d*x + c)^2*sinh(d*x + c) + 3*b^2*cosh(d*x + c)*sinh(d*x + c)^2 + b^2*sinh(d*x + c)^3)*arctan(cosh(d*x + c) + sinh(d*x + c)) + 6*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^5 + 2*(3*a^2 - 2*a*b - 5*b^2)*cosh(d*x + c)^3 - (3*a^2 - 2*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
91,1,105,0,0.427401," ","integrate(cosh(d*x+c)^2*(a+b*tanh(d*x+c)^2)^2,x, algorithm=""fricas"")","\frac{{\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left({\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} d x - 2 \, b^{2}\right)} \cosh\left(d x + c\right) + {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} + 2 \, a b + 9 \, b^{2}\right)} \sinh\left(d x + c\right)}{8 \, d \cosh\left(d x + c\right)}"," ",0,"1/8*((a^2 + 2*a*b + b^2)*sinh(d*x + c)^3 + 4*((a^2 - 2*a*b - 3*b^2)*d*x - 2*b^2)*cosh(d*x + c) + (3*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + a^2 + 2*a*b + 9*b^2)*sinh(d*x + c))/(d*cosh(d*x + c))","B",0
92,1,774,0,0.427619," ","integrate(cosh(d*x+c)*(a+b*tanh(d*x+c)^2)^2,x, algorithm=""fricas"")","\frac{{\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{6} + 6 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{6} + {\left(a^{2} + 2 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(15 \, {\left(a^{2} + 2 \, a b + 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)^{4} + 4 \, {\left(5 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} + 2 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - {\left(a^{2} + 2 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + {\left(15 \, {\left(a^{2} + 2 \, a b + 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)^{2} - a^{2} - 2 \, a b - b^{2} - 2 \, {\left({\left(4 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(4 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} + {\left(4 \, a b + 3 \, b^{2}\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(4 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(5 \, {\left(4 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, a b + 3 \, b^{2}\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(5 \, {\left(4 \, a b + 3 \, b^{2}\right)} \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)^{2} + {\left(4 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right) + {\left(5 \, {\left(4 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 6 \, {\left(4 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, 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 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(a^{2} + 2 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{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(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*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^6 + 6*(a^2 + 2*a*b + b^2)*cosh(d*x + c)*sinh(d*x + c)^5 + (a^2 + 2*a*b + b^2)*sinh(d*x + c)^6 + (a^2 + 2*a*b + 3*b^2)*cosh(d*x + c)^4 + (15*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + a^2 + 2*a*b + 3*b^2)*sinh(d*x + c)^4 + 4*(5*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 + (a^2 + 2*a*b + 3*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 - (a^2 + 2*a*b + 3*b^2)*cosh(d*x + c)^2 + (15*(a^2 + 2*a*b + 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)^2 - a^2 - 2*a*b - b^2 - 2*((4*a*b + 3*b^2)*cosh(d*x + c)^5 + 5*(4*a*b + 3*b^2)*cosh(d*x + c)*sinh(d*x + c)^4 + (4*a*b + 3*b^2)*sinh(d*x + c)^5 + 2*(4*a*b + 3*b^2)*cosh(d*x + c)^3 + 2*(5*(4*a*b + 3*b^2)*cosh(d*x + c)^2 + 4*a*b + 3*b^2)*sinh(d*x + c)^3 + 2*(5*(4*a*b + 3*b^2)*cosh(d*x + c)^3 + 3*(4*a*b + 3*b^2)*cosh(d*x + c))*sinh(d*x + c)^2 + (4*a*b + 3*b^2)*cosh(d*x + c) + (5*(4*a*b + 3*b^2)*cosh(d*x + c)^4 + 6*(4*a*b + 3*b^2)*cosh(d*x + c)^2 + 4*a*b + 3*b^2)*sinh(d*x + c))*arctan(cosh(d*x + c) + sinh(d*x + c)) + 2*(3*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^5 + 2*(a^2 + 2*a*b + 3*b^2)*cosh(d*x + c)^3 - (a^2 + 2*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
93,1,1373,0,0.417542," ","integrate(sech(d*x+c)*(a+b*tanh(d*x+c)^2)^2,x, algorithm=""fricas"")","-\frac{{\left(8 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} + 7 \, {\left(8 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + {\left(8 \, a b + 5 \, b^{2}\right)} \sinh\left(d x + c\right)^{7} + {\left(8 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + {\left(21 \, {\left(8 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 8 \, a b - 3 \, b^{2}\right)} \sinh\left(d x + c\right)^{5} + 5 \, {\left(7 \, {\left(8 \, a b + 5 \, 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)^{4} - {\left(8 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(35 \, {\left(8 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 10 \, {\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)^{3} + {\left(21 \, {\left(8 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(8 \, a b - 3 \, b^{2}\right)} \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)^{2} - {\left({\left(8 \, a^{2} + 8 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(8 \, a^{2} + 8 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(8 \, a^{2} + 8 \, a b + 3 \, b^{2}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(8 \, a^{2} + 8 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(8 \, a^{2} + 8 \, a b + 3 \, 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)^{6} + 8 \, {\left(7 \, {\left(8 \, a^{2} + 8 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 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)^{5} + 6 \, {\left(8 \, a^{2} + 8 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(8 \, a^{2} + 8 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 30 \, {\left(8 \, a^{2} + 8 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 24 \, a^{2} + 24 \, a b + 9 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(8 \, a^{2} + 8 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(8 \, a^{2} + 8 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 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(8 \, a^{2} + 8 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(8 \, a^{2} + 8 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(8 \, a^{2} + 8 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 9 \, {\left(8 \, a^{2} + 8 \, a b + 3 \, 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)^{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(d x + c\right)^{7} + 3 \, {\left(8 \, a^{2} + 8 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 3 \, {\left(8 \, a^{2} + 8 \, a b + 3 \, 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)\right)} \arctan\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) - {\left(8 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right) + {\left(7 \, {\left(8 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 5 \, {\left(8 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} - 3 \, {\left(8 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 8 \, 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*((8*a*b + 5*b^2)*cosh(d*x + c)^7 + 7*(8*a*b + 5*b^2)*cosh(d*x + c)*sinh(d*x + c)^6 + (8*a*b + 5*b^2)*sinh(d*x + c)^7 + (8*a*b - 3*b^2)*cosh(d*x + c)^5 + (21*(8*a*b + 5*b^2)*cosh(d*x + c)^2 + 8*a*b - 3*b^2)*sinh(d*x + c)^5 + 5*(7*(8*a*b + 5*b^2)*cosh(d*x + c)^3 + (8*a*b - 3*b^2)*cosh(d*x + c))*sinh(d*x + c)^4 - (8*a*b - 3*b^2)*cosh(d*x + c)^3 + (35*(8*a*b + 5*b^2)*cosh(d*x + c)^4 + 10*(8*a*b - 3*b^2)*cosh(d*x + c)^2 - 8*a*b + 3*b^2)*sinh(d*x + c)^3 + (21*(8*a*b + 5*b^2)*cosh(d*x + c)^5 + 10*(8*a*b - 3*b^2)*cosh(d*x + c)^3 - 3*(8*a*b - 3*b^2)*cosh(d*x + c))*sinh(d*x + c)^2 - ((8*a^2 + 8*a*b + 3*b^2)*cosh(d*x + c)^8 + 8*(8*a^2 + 8*a*b + 3*b^2)*cosh(d*x + c)*sinh(d*x + c)^7 + (8*a^2 + 8*a*b + 3*b^2)*sinh(d*x + c)^8 + 4*(8*a^2 + 8*a*b + 3*b^2)*cosh(d*x + c)^6 + 4*(7*(8*a^2 + 8*a*b + 3*b^2)*cosh(d*x + c)^2 + 8*a^2 + 8*a*b + 3*b^2)*sinh(d*x + c)^6 + 8*(7*(8*a^2 + 8*a*b + 3*b^2)*cosh(d*x + c)^3 + 3*(8*a^2 + 8*a*b + 3*b^2)*cosh(d*x + c))*sinh(d*x + c)^5 + 6*(8*a^2 + 8*a*b + 3*b^2)*cosh(d*x + c)^4 + 2*(35*(8*a^2 + 8*a*b + 3*b^2)*cosh(d*x + c)^4 + 30*(8*a^2 + 8*a*b + 3*b^2)*cosh(d*x + c)^2 + 24*a^2 + 24*a*b + 9*b^2)*sinh(d*x + c)^4 + 8*(7*(8*a^2 + 8*a*b + 3*b^2)*cosh(d*x + c)^5 + 10*(8*a^2 + 8*a*b + 3*b^2)*cosh(d*x + c)^3 + 3*(8*a^2 + 8*a*b + 3*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(8*a^2 + 8*a*b + 3*b^2)*cosh(d*x + c)^2 + 4*(7*(8*a^2 + 8*a*b + 3*b^2)*cosh(d*x + c)^6 + 15*(8*a^2 + 8*a*b + 3*b^2)*cosh(d*x + c)^4 + 9*(8*a^2 + 8*a*b + 3*b^2)*cosh(d*x + c)^2 + 8*a^2 + 8*a*b + 3*b^2)*sinh(d*x + c)^2 + 8*a^2 + 8*a*b + 3*b^2 + 8*((8*a^2 + 8*a*b + 3*b^2)*cosh(d*x + c)^7 + 3*(8*a^2 + 8*a*b + 3*b^2)*cosh(d*x + c)^5 + 3*(8*a^2 + 8*a*b + 3*b^2)*cosh(d*x + c)^3 + (8*a^2 + 8*a*b + 3*b^2)*cosh(d*x + c))*sinh(d*x + c))*arctan(cosh(d*x + c) + sinh(d*x + c)) - (8*a*b + 5*b^2)*cosh(d*x + c) + (7*(8*a*b + 5*b^2)*cosh(d*x + c)^6 + 5*(8*a*b - 3*b^2)*cosh(d*x + c)^4 - 3*(8*a*b - 3*b^2)*cosh(d*x + c)^2 - 8*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
94,1,391,0,0.401875," ","integrate(sech(d*x+c)^2*(a+b*tanh(d*x+c)^2)^2,x, algorithm=""fricas"")","-\frac{4 \, {\left({\left(15 \, a^{2} + 20 \, a b + 9 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 8 \, {\left(5 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(15 \, a^{2} + 20 \, a b + 9 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 20 \, {\left(3 \, a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(15 \, a^{2} + 20 \, a b + 9 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 30 \, a^{2} + 20 \, a b\right)} \sinh\left(d x + c\right)^{2} + 45 \, a^{2} + 20 \, a b + 15 \, b^{2} + 8 \, {\left({\left(5 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 5 \, a b \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*((15*a^2 + 20*a*b + 9*b^2)*cosh(d*x + c)^4 + 8*(5*a*b + 3*b^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (15*a^2 + 20*a*b + 9*b^2)*sinh(d*x + c)^4 + 20*(3*a^2 + 2*a*b)*cosh(d*x + c)^2 + 2*(3*(15*a^2 + 20*a*b + 9*b^2)*cosh(d*x + c)^2 + 30*a^2 + 20*a*b)*sinh(d*x + c)^2 + 45*a^2 + 20*a*b + 15*b^2 + 8*((5*a*b + 3*b^2)*cosh(d*x + c)^3 + 5*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
95,1,2824,0,0.469872," ","integrate(sech(d*x+c)^3*(a+b*tanh(d*x+c)^2)^2,x, algorithm=""fricas"")","\frac{3 \, {\left(8 \, a^{2} + 4 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{11} + 33 \, {\left(8 \, a^{2} + 4 \, a b + b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{10} + 3 \, {\left(8 \, a^{2} + 4 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{11} + {\left(72 \, a^{2} - 60 \, a b - 47 \, b^{2}\right)} \cosh\left(d x + c\right)^{9} + {\left(165 \, {\left(8 \, a^{2} + 4 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 72 \, a^{2} - 60 \, a b - 47 \, b^{2}\right)} \sinh\left(d x + c\right)^{9} + 9 \, {\left(55 \, {\left(8 \, a^{2} + 4 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(72 \, a^{2} - 60 \, a b - 47 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{8} + 6 \, {\left(8 \, a^{2} - 12 \, a b + 13 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} + 6 \, {\left(165 \, {\left(8 \, a^{2} + 4 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + 6 \, {\left(72 \, a^{2} - 60 \, a b - 47 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 8 \, a^{2} - 12 \, a b + 13 \, b^{2}\right)} \sinh\left(d x + c\right)^{7} + 42 \, {\left(33 \, {\left(8 \, a^{2} + 4 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(72 \, a^{2} - 60 \, a b - 47 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{2} - 12 \, a b + 13 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} - 6 \, {\left(8 \, a^{2} - 12 \, a b + 13 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 6 \, {\left(231 \, {\left(8 \, a^{2} + 4 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{6} + 21 \, {\left(72 \, a^{2} - 60 \, a b - 47 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 21 \, {\left(8 \, a^{2} - 12 \, a b + 13 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 8 \, a^{2} + 12 \, a b - 13 \, b^{2}\right)} \sinh\left(d x + c\right)^{5} + 6 \, {\left(165 \, {\left(8 \, a^{2} + 4 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{7} + 21 \, {\left(72 \, a^{2} - 60 \, a b - 47 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 35 \, {\left(8 \, a^{2} - 12 \, a b + 13 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - 5 \, {\left(8 \, a^{2} - 12 \, a b + 13 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} - {\left(72 \, a^{2} - 60 \, a b - 47 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(495 \, {\left(8 \, a^{2} + 4 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{8} + 84 \, {\left(72 \, a^{2} - 60 \, a b - 47 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 210 \, {\left(8 \, a^{2} - 12 \, a b + 13 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} - 60 \, {\left(8 \, a^{2} - 12 \, a b + 13 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 72 \, a^{2} + 60 \, a b + 47 \, b^{2}\right)} \sinh\left(d x + c\right)^{3} + 3 \, {\left(55 \, {\left(8 \, a^{2} + 4 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{9} + 12 \, {\left(72 \, a^{2} - 60 \, a b - 47 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} + 42 \, {\left(8 \, a^{2} - 12 \, a b + 13 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} - 20 \, {\left(8 \, a^{2} - 12 \, a b + 13 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(72 \, a^{2} - 60 \, a b - 47 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 3 \, {\left({\left(8 \, a^{2} + 4 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{12} + 12 \, {\left(8 \, a^{2} + 4 \, a b + b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{11} + {\left(8 \, a^{2} + 4 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{12} + 6 \, {\left(8 \, a^{2} + 4 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{10} + 6 \, {\left(11 \, {\left(8 \, a^{2} + 4 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 8 \, a^{2} + 4 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{10} + 20 \, {\left(11 \, {\left(8 \, a^{2} + 4 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(8 \, a^{2} + 4 \, a b + b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} + 15 \, {\left(8 \, a^{2} + 4 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{8} + 15 \, {\left(33 \, {\left(8 \, a^{2} + 4 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + 18 \, {\left(8 \, a^{2} + 4 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 8 \, a^{2} + 4 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{8} + 24 \, {\left(33 \, {\left(8 \, a^{2} + 4 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{5} + 30 \, {\left(8 \, a^{2} + 4 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + 5 \, {\left(8 \, a^{2} + 4 \, a b + b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 20 \, {\left(8 \, a^{2} + 4 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(231 \, {\left(8 \, a^{2} + 4 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{6} + 315 \, {\left(8 \, a^{2} + 4 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + 105 \, {\left(8 \, a^{2} + 4 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 40 \, a^{2} + 20 \, a b + 5 \, b^{2}\right)} \sinh\left(d x + c\right)^{6} + 24 \, {\left(33 \, {\left(8 \, a^{2} + 4 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{7} + 63 \, {\left(8 \, a^{2} + 4 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{5} + 35 \, {\left(8 \, a^{2} + 4 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + 5 \, {\left(8 \, a^{2} + 4 \, a b + b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 15 \, {\left(8 \, a^{2} + 4 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + 15 \, {\left(33 \, {\left(8 \, a^{2} + 4 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{8} + 84 \, {\left(8 \, a^{2} + 4 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{6} + 70 \, {\left(8 \, a^{2} + 4 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + 20 \, {\left(8 \, a^{2} + 4 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 8 \, a^{2} + 4 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{4} + 20 \, {\left(11 \, {\left(8 \, a^{2} + 4 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{9} + 36 \, {\left(8 \, a^{2} + 4 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{7} + 42 \, {\left(8 \, a^{2} + 4 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{5} + 20 \, {\left(8 \, a^{2} + 4 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(8 \, a^{2} + 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)} \cosh\left(d x + c\right)^{2} + 6 \, {\left(11 \, {\left(8 \, a^{2} + 4 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{10} + 45 \, {\left(8 \, a^{2} + 4 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{8} + 70 \, {\left(8 \, a^{2} + 4 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{6} + 50 \, {\left(8 \, a^{2} + 4 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + 15 \, {\left(8 \, a^{2} + 4 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 8 \, a^{2} + 4 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, a^{2} + 4 \, a b + b^{2} + 12 \, {\left({\left(8 \, a^{2} + 4 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{11} + 5 \, {\left(8 \, a^{2} + 4 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{9} + 10 \, {\left(8 \, a^{2} + 4 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{7} + 10 \, {\left(8 \, a^{2} + 4 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(8 \, a^{2} + 4 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{2} + 4 \, 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(8 \, a^{2} + 4 \, a b + b^{2}\right)} \cosh\left(d x + c\right) + 3 \, {\left(11 \, {\left(8 \, a^{2} + 4 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{10} + 3 \, {\left(72 \, a^{2} - 60 \, a b - 47 \, b^{2}\right)} \cosh\left(d x + c\right)^{8} + 14 \, {\left(8 \, a^{2} - 12 \, a b + 13 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} - 10 \, {\left(8 \, a^{2} - 12 \, a b + 13 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} - {\left(72 \, a^{2} - 60 \, a b - 47 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 8 \, a^{2} - 4 \, 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*(8*a^2 + 4*a*b + b^2)*cosh(d*x + c)^11 + 33*(8*a^2 + 4*a*b + b^2)*cosh(d*x + c)*sinh(d*x + c)^10 + 3*(8*a^2 + 4*a*b + b^2)*sinh(d*x + c)^11 + (72*a^2 - 60*a*b - 47*b^2)*cosh(d*x + c)^9 + (165*(8*a^2 + 4*a*b + b^2)*cosh(d*x + c)^2 + 72*a^2 - 60*a*b - 47*b^2)*sinh(d*x + c)^9 + 9*(55*(8*a^2 + 4*a*b + b^2)*cosh(d*x + c)^3 + (72*a^2 - 60*a*b - 47*b^2)*cosh(d*x + c))*sinh(d*x + c)^8 + 6*(8*a^2 - 12*a*b + 13*b^2)*cosh(d*x + c)^7 + 6*(165*(8*a^2 + 4*a*b + b^2)*cosh(d*x + c)^4 + 6*(72*a^2 - 60*a*b - 47*b^2)*cosh(d*x + c)^2 + 8*a^2 - 12*a*b + 13*b^2)*sinh(d*x + c)^7 + 42*(33*(8*a^2 + 4*a*b + b^2)*cosh(d*x + c)^5 + 2*(72*a^2 - 60*a*b - 47*b^2)*cosh(d*x + c)^3 + (8*a^2 - 12*a*b + 13*b^2)*cosh(d*x + c))*sinh(d*x + c)^6 - 6*(8*a^2 - 12*a*b + 13*b^2)*cosh(d*x + c)^5 + 6*(231*(8*a^2 + 4*a*b + b^2)*cosh(d*x + c)^6 + 21*(72*a^2 - 60*a*b - 47*b^2)*cosh(d*x + c)^4 + 21*(8*a^2 - 12*a*b + 13*b^2)*cosh(d*x + c)^2 - 8*a^2 + 12*a*b - 13*b^2)*sinh(d*x + c)^5 + 6*(165*(8*a^2 + 4*a*b + b^2)*cosh(d*x + c)^7 + 21*(72*a^2 - 60*a*b - 47*b^2)*cosh(d*x + c)^5 + 35*(8*a^2 - 12*a*b + 13*b^2)*cosh(d*x + c)^3 - 5*(8*a^2 - 12*a*b + 13*b^2)*cosh(d*x + c))*sinh(d*x + c)^4 - (72*a^2 - 60*a*b - 47*b^2)*cosh(d*x + c)^3 + (495*(8*a^2 + 4*a*b + b^2)*cosh(d*x + c)^8 + 84*(72*a^2 - 60*a*b - 47*b^2)*cosh(d*x + c)^6 + 210*(8*a^2 - 12*a*b + 13*b^2)*cosh(d*x + c)^4 - 60*(8*a^2 - 12*a*b + 13*b^2)*cosh(d*x + c)^2 - 72*a^2 + 60*a*b + 47*b^2)*sinh(d*x + c)^3 + 3*(55*(8*a^2 + 4*a*b + b^2)*cosh(d*x + c)^9 + 12*(72*a^2 - 60*a*b - 47*b^2)*cosh(d*x + c)^7 + 42*(8*a^2 - 12*a*b + 13*b^2)*cosh(d*x + c)^5 - 20*(8*a^2 - 12*a*b + 13*b^2)*cosh(d*x + c)^3 - (72*a^2 - 60*a*b - 47*b^2)*cosh(d*x + c))*sinh(d*x + c)^2 + 3*((8*a^2 + 4*a*b + b^2)*cosh(d*x + c)^12 + 12*(8*a^2 + 4*a*b + b^2)*cosh(d*x + c)*sinh(d*x + c)^11 + (8*a^2 + 4*a*b + b^2)*sinh(d*x + c)^12 + 6*(8*a^2 + 4*a*b + b^2)*cosh(d*x + c)^10 + 6*(11*(8*a^2 + 4*a*b + b^2)*cosh(d*x + c)^2 + 8*a^2 + 4*a*b + b^2)*sinh(d*x + c)^10 + 20*(11*(8*a^2 + 4*a*b + b^2)*cosh(d*x + c)^3 + 3*(8*a^2 + 4*a*b + b^2)*cosh(d*x + c))*sinh(d*x + c)^9 + 15*(8*a^2 + 4*a*b + b^2)*cosh(d*x + c)^8 + 15*(33*(8*a^2 + 4*a*b + b^2)*cosh(d*x + c)^4 + 18*(8*a^2 + 4*a*b + b^2)*cosh(d*x + c)^2 + 8*a^2 + 4*a*b + b^2)*sinh(d*x + c)^8 + 24*(33*(8*a^2 + 4*a*b + b^2)*cosh(d*x + c)^5 + 30*(8*a^2 + 4*a*b + b^2)*cosh(d*x + c)^3 + 5*(8*a^2 + 4*a*b + b^2)*cosh(d*x + c))*sinh(d*x + c)^7 + 20*(8*a^2 + 4*a*b + b^2)*cosh(d*x + c)^6 + 4*(231*(8*a^2 + 4*a*b + b^2)*cosh(d*x + c)^6 + 315*(8*a^2 + 4*a*b + b^2)*cosh(d*x + c)^4 + 105*(8*a^2 + 4*a*b + b^2)*cosh(d*x + c)^2 + 40*a^2 + 20*a*b + 5*b^2)*sinh(d*x + c)^6 + 24*(33*(8*a^2 + 4*a*b + b^2)*cosh(d*x + c)^7 + 63*(8*a^2 + 4*a*b + b^2)*cosh(d*x + c)^5 + 35*(8*a^2 + 4*a*b + b^2)*cosh(d*x + c)^3 + 5*(8*a^2 + 4*a*b + b^2)*cosh(d*x + c))*sinh(d*x + c)^5 + 15*(8*a^2 + 4*a*b + b^2)*cosh(d*x + c)^4 + 15*(33*(8*a^2 + 4*a*b + b^2)*cosh(d*x + c)^8 + 84*(8*a^2 + 4*a*b + b^2)*cosh(d*x + c)^6 + 70*(8*a^2 + 4*a*b + b^2)*cosh(d*x + c)^4 + 20*(8*a^2 + 4*a*b + b^2)*cosh(d*x + c)^2 + 8*a^2 + 4*a*b + b^2)*sinh(d*x + c)^4 + 20*(11*(8*a^2 + 4*a*b + b^2)*cosh(d*x + c)^9 + 36*(8*a^2 + 4*a*b + b^2)*cosh(d*x + c)^7 + 42*(8*a^2 + 4*a*b + b^2)*cosh(d*x + c)^5 + 20*(8*a^2 + 4*a*b + b^2)*cosh(d*x + c)^3 + 3*(8*a^2 + 4*a*b + b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 6*(8*a^2 + 4*a*b + b^2)*cosh(d*x + c)^2 + 6*(11*(8*a^2 + 4*a*b + b^2)*cosh(d*x + c)^10 + 45*(8*a^2 + 4*a*b + b^2)*cosh(d*x + c)^8 + 70*(8*a^2 + 4*a*b + b^2)*cosh(d*x + c)^6 + 50*(8*a^2 + 4*a*b + b^2)*cosh(d*x + c)^4 + 15*(8*a^2 + 4*a*b + b^2)*cosh(d*x + c)^2 + 8*a^2 + 4*a*b + b^2)*sinh(d*x + c)^2 + 8*a^2 + 4*a*b + b^2 + 12*((8*a^2 + 4*a*b + b^2)*cosh(d*x + c)^11 + 5*(8*a^2 + 4*a*b + b^2)*cosh(d*x + c)^9 + 10*(8*a^2 + 4*a*b + b^2)*cosh(d*x + c)^7 + 10*(8*a^2 + 4*a*b + b^2)*cosh(d*x + c)^5 + 5*(8*a^2 + 4*a*b + b^2)*cosh(d*x + c)^3 + (8*a^2 + 4*a*b + b^2)*cosh(d*x + c))*sinh(d*x + c))*arctan(cosh(d*x + c) + sinh(d*x + c)) - 3*(8*a^2 + 4*a*b + b^2)*cosh(d*x + c) + 3*(11*(8*a^2 + 4*a*b + b^2)*cosh(d*x + c)^10 + 3*(72*a^2 - 60*a*b - 47*b^2)*cosh(d*x + c)^8 + 14*(8*a^2 - 12*a*b + 13*b^2)*cosh(d*x + c)^6 - 10*(8*a^2 - 12*a*b + 13*b^2)*cosh(d*x + c)^4 - (72*a^2 - 60*a*b - 47*b^2)*cosh(d*x + c)^2 - 8*a^2 - 4*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
96,1,677,0,0.402982," ","integrate(sech(d*x+c)^4*(a+b*tanh(d*x+c)^2)^2,x, algorithm=""fricas"")","-\frac{8 \, {\left(2 \, {\left(35 \, a^{2} + 56 \, a b + 27 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(35 \, a^{2} + 56 \, a b + 27 \, b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} + {\left(35 \, a^{2} + 98 \, a b + 51 \, b^{2}\right)} \sinh\left(d x + c\right)^{5} + 14 \, {\left(25 \, a^{2} + 16 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(10 \, {\left(35 \, a^{2} + 98 \, a b + 51 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 105 \, a^{2} + 126 \, a b - 63 \, b^{2}\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(10 \, {\left(35 \, a^{2} + 56 \, a b + 27 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 21 \, {\left(25 \, a^{2} + 16 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 28 \, {\left(25 \, a^{2} + 4 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right) + {\left(5 \, {\left(35 \, a^{2} + 98 \, a b + 51 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 63 \, {\left(5 \, a^{2} + 6 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 70 \, a^{2} + 28 \, a b + 126 \, b^{2}\right)} \sinh\left(d x + c\right)\right)}}{105 \, {\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} + 7 \, d \cosh\left(d x + c\right)^{7} + {\left(36 \, d \cosh\left(d x + c\right)^{2} + 7 \, d\right)} \sinh\left(d x + c\right)^{7} + 7 \, {\left(12 \, d \cosh\left(d x + c\right)^{3} + 7 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} + 22 \, d \cosh\left(d x + c\right)^{5} + {\left(126 \, d \cosh\left(d x + c\right)^{4} + 147 \, d \cosh\left(d x + c\right)^{2} + 20 \, d\right)} \sinh\left(d x + c\right)^{5} + {\left(126 \, d \cosh\left(d x + c\right)^{5} + 245 \, d \cosh\left(d x + c\right)^{3} + 110 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 42 \, d \cosh\left(d x + c\right)^{3} + {\left(84 \, d \cosh\left(d x + c\right)^{6} + 245 \, d \cosh\left(d x + c\right)^{4} + 200 \, d \cosh\left(d x + c\right)^{2} + 28 \, d\right)} \sinh\left(d x + c\right)^{3} + {\left(36 \, d \cosh\left(d x + c\right)^{7} + 147 \, d \cosh\left(d x + c\right)^{5} + 220 \, d \cosh\left(d x + c\right)^{3} + 126 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 56 \, d \cosh\left(d x + c\right) + {\left(9 \, d \cosh\left(d x + c\right)^{8} + 49 \, d \cosh\left(d x + c\right)^{6} + 100 \, d \cosh\left(d x + c\right)^{4} + 84 \, d \cosh\left(d x + c\right)^{2} + 14 \, d\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"-8/105*(2*(35*a^2 + 56*a*b + 27*b^2)*cosh(d*x + c)^5 + 10*(35*a^2 + 56*a*b + 27*b^2)*cosh(d*x + c)*sinh(d*x + c)^4 + (35*a^2 + 98*a*b + 51*b^2)*sinh(d*x + c)^5 + 14*(25*a^2 + 16*a*b - 3*b^2)*cosh(d*x + c)^3 + (10*(35*a^2 + 98*a*b + 51*b^2)*cosh(d*x + c)^2 + 105*a^2 + 126*a*b - 63*b^2)*sinh(d*x + c)^3 + 2*(10*(35*a^2 + 56*a*b + 27*b^2)*cosh(d*x + c)^3 + 21*(25*a^2 + 16*a*b - 3*b^2)*cosh(d*x + c))*sinh(d*x + c)^2 + 28*(25*a^2 + 4*a*b + 3*b^2)*cosh(d*x + c) + (5*(35*a^2 + 98*a*b + 51*b^2)*cosh(d*x + c)^4 + 63*(5*a^2 + 6*a*b - 3*b^2)*cosh(d*x + c)^2 + 70*a^2 + 28*a*b + 126*b^2)*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 + 7*d*cosh(d*x + c)^7 + (36*d*cosh(d*x + c)^2 + 7*d)*sinh(d*x + c)^7 + 7*(12*d*cosh(d*x + c)^3 + 7*d*cosh(d*x + c))*sinh(d*x + c)^6 + 22*d*cosh(d*x + c)^5 + (126*d*cosh(d*x + c)^4 + 147*d*cosh(d*x + c)^2 + 20*d)*sinh(d*x + c)^5 + (126*d*cosh(d*x + c)^5 + 245*d*cosh(d*x + c)^3 + 110*d*cosh(d*x + c))*sinh(d*x + c)^4 + 42*d*cosh(d*x + c)^3 + (84*d*cosh(d*x + c)^6 + 245*d*cosh(d*x + c)^4 + 200*d*cosh(d*x + c)^2 + 28*d)*sinh(d*x + c)^3 + (36*d*cosh(d*x + c)^7 + 147*d*cosh(d*x + c)^5 + 220*d*cosh(d*x + c)^3 + 126*d*cosh(d*x + c))*sinh(d*x + c)^2 + 56*d*cosh(d*x + c) + (9*d*cosh(d*x + c)^8 + 49*d*cosh(d*x + c)^6 + 100*d*cosh(d*x + c)^4 + 84*d*cosh(d*x + c)^2 + 14*d)*sinh(d*x + c))","B",0
97,1,227,0,0.423498," ","integrate(cosh(d*x+c)^4*(a+b*tanh(d*x+c)^2)^3,x, algorithm=""fricas"")","\frac{{\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \sinh\left(d x + c\right)^{5} + {\left(9 \, a^{3} + 3 \, a^{2} b - 21 \, a b^{2} - 15 \, b^{3} + 10 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + 8 \, {\left(8 \, b^{3} + 3 \, {\left(a^{3} - a^{2} b + 3 \, a b^{2} + 5 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right) + {\left(5 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{4} + 8 \, a^{3} - 24 \, a b^{2} - 80 \, b^{3} + 9 \, {\left(3 \, a^{3} + a^{2} b - 7 \, 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*((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*sinh(d*x + c)^5 + (9*a^3 + 3*a^2*b - 21*a*b^2 - 15*b^3 + 10*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 8*(8*b^3 + 3*(a^3 - a^2*b + 3*a*b^2 + 5*b^3)*d*x)*cosh(d*x + c) + (5*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^4 + 8*a^3 - 24*a*b^2 - 80*b^3 + 9*(3*a^3 + a^2*b - 7*a*b^2 - 5*b^3)*cosh(d*x + c)^2)*sinh(d*x + c))/(d*cosh(d*x + c))","B",0
98,1,1840,0,0.450906," ","integrate(cosh(d*x+c)^3*(a+b*tanh(d*x+c)^2)^3,x, algorithm=""fricas"")","\frac{{\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{10} + 10 \, {\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)^{9} + {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \sinh\left(d x + c\right)^{10} + {\left(11 \, a^{3} - 3 \, a^{2} b - 39 \, a b^{2} - 25 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + {\left(11 \, a^{3} - 3 \, a^{2} b - 39 \, a b^{2} - 25 \, b^{3} + 45 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{8} + 8 \, {\left(15 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(11 \, a^{3} - 3 \, a^{2} b - 39 \, a b^{2} - 25 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(5 \, a^{3} - 3 \, a^{2} b - 21 \, a b^{2} - 25 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(105 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{4} + 5 \, a^{3} - 3 \, a^{2} b - 21 \, a b^{2} - 25 \, b^{3} + 14 \, {\left(11 \, a^{3} - 3 \, a^{2} b - 39 \, 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 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{5} + 14 \, {\left(11 \, a^{3} - 3 \, a^{2} b - 39 \, a b^{2} - 25 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(5 \, a^{3} - 3 \, a^{2} b - 21 \, a b^{2} - 25 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 2 \, {\left(5 \, a^{3} - 3 \, a^{2} b - 21 \, a b^{2} - 25 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(105 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{6} + 35 \, {\left(11 \, a^{3} - 3 \, a^{2} b - 39 \, a b^{2} - 25 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 5 \, a^{3} + 3 \, a^{2} b + 21 \, a b^{2} + 25 \, b^{3} + 15 \, {\left(5 \, a^{3} - 3 \, a^{2} b - 21 \, 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 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{7} + 7 \, {\left(11 \, a^{3} - 3 \, a^{2} b - 39 \, a b^{2} - 25 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(5 \, a^{3} - 3 \, a^{2} b - 21 \, a b^{2} - 25 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - {\left(5 \, a^{3} - 3 \, a^{2} b - 21 \, a b^{2} - 25 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - a^{3} - 3 \, a^{2} b - 3 \, a b^{2} - b^{3} - {\left(11 \, a^{3} - 3 \, a^{2} b - 39 \, a b^{2} - 25 \, b^{3}\right)} \cosh\left(d x + c\right)^{2} + {\left(45 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{8} + 28 \, {\left(11 \, a^{3} - 3 \, a^{2} b - 39 \, a b^{2} - 25 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 30 \, {\left(5 \, a^{3} - 3 \, a^{2} b - 21 \, a b^{2} - 25 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 11 \, a^{3} + 3 \, a^{2} b + 39 \, a b^{2} + 25 \, b^{3} - 12 \, {\left(5 \, a^{3} - 3 \, a^{2} b - 21 \, 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(6 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 7 \, {\left(6 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + {\left(6 \, a b^{2} + 5 \, b^{3}\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(6 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + {\left(12 \, a b^{2} + 10 \, b^{3} + 21 \, {\left(6 \, 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(6 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(6 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + {\left(6 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(35 \, {\left(6 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 6 \, a b^{2} + 5 \, b^{3} + 20 \, {\left(6 \, 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(6 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 20 \, {\left(6 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(6 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(7 \, {\left(6 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 10 \, {\left(6 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(6 \, 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 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{9} + 4 \, {\left(11 \, a^{3} - 3 \, a^{2} b - 39 \, a b^{2} - 25 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 6 \, {\left(5 \, a^{3} - 3 \, a^{2} b - 21 \, a b^{2} - 25 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 4 \, {\left(5 \, a^{3} - 3 \, a^{2} b - 21 \, a b^{2} - 25 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - {\left(11 \, a^{3} - 3 \, a^{2} b - 39 \, 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*((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^10 + 10*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)*sinh(d*x + c)^9 + (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*sinh(d*x + c)^10 + (11*a^3 - 3*a^2*b - 39*a*b^2 - 25*b^3)*cosh(d*x + c)^8 + (11*a^3 - 3*a^2*b - 39*a*b^2 - 25*b^3 + 45*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 8*(15*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^3 + (11*a^3 - 3*a^2*b - 39*a*b^2 - 25*b^3)*cosh(d*x + c))*sinh(d*x + c)^7 + 2*(5*a^3 - 3*a^2*b - 21*a*b^2 - 25*b^3)*cosh(d*x + c)^6 + 2*(105*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^4 + 5*a^3 - 3*a^2*b - 21*a*b^2 - 25*b^3 + 14*(11*a^3 - 3*a^2*b - 39*a*b^2 - 25*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 4*(63*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^5 + 14*(11*a^3 - 3*a^2*b - 39*a*b^2 - 25*b^3)*cosh(d*x + c)^3 + 3*(5*a^3 - 3*a^2*b - 21*a*b^2 - 25*b^3)*cosh(d*x + c))*sinh(d*x + c)^5 - 2*(5*a^3 - 3*a^2*b - 21*a*b^2 - 25*b^3)*cosh(d*x + c)^4 + 2*(105*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^6 + 35*(11*a^3 - 3*a^2*b - 39*a*b^2 - 25*b^3)*cosh(d*x + c)^4 - 5*a^3 + 3*a^2*b + 21*a*b^2 + 25*b^3 + 15*(5*a^3 - 3*a^2*b - 21*a*b^2 - 25*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(15*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^7 + 7*(11*a^3 - 3*a^2*b - 39*a*b^2 - 25*b^3)*cosh(d*x + c)^5 + 5*(5*a^3 - 3*a^2*b - 21*a*b^2 - 25*b^3)*cosh(d*x + c)^3 - (5*a^3 - 3*a^2*b - 21*a*b^2 - 25*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 - a^3 - 3*a^2*b - 3*a*b^2 - b^3 - (11*a^3 - 3*a^2*b - 39*a*b^2 - 25*b^3)*cosh(d*x + c)^2 + (45*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^8 + 28*(11*a^3 - 3*a^2*b - 39*a*b^2 - 25*b^3)*cosh(d*x + c)^6 + 30*(5*a^3 - 3*a^2*b - 21*a*b^2 - 25*b^3)*cosh(d*x + c)^4 - 11*a^3 + 3*a^2*b + 39*a*b^2 + 25*b^3 - 12*(5*a^3 - 3*a^2*b - 21*a*b^2 - 25*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 24*((6*a*b^2 + 5*b^3)*cosh(d*x + c)^7 + 7*(6*a*b^2 + 5*b^3)*cosh(d*x + c)*sinh(d*x + c)^6 + (6*a*b^2 + 5*b^3)*sinh(d*x + c)^7 + 2*(6*a*b^2 + 5*b^3)*cosh(d*x + c)^5 + (12*a*b^2 + 10*b^3 + 21*(6*a*b^2 + 5*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 5*(7*(6*a*b^2 + 5*b^3)*cosh(d*x + c)^3 + 2*(6*a*b^2 + 5*b^3)*cosh(d*x + c))*sinh(d*x + c)^4 + (6*a*b^2 + 5*b^3)*cosh(d*x + c)^3 + (35*(6*a*b^2 + 5*b^3)*cosh(d*x + c)^4 + 6*a*b^2 + 5*b^3 + 20*(6*a*b^2 + 5*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + (21*(6*a*b^2 + 5*b^3)*cosh(d*x + c)^5 + 20*(6*a*b^2 + 5*b^3)*cosh(d*x + c)^3 + 3*(6*a*b^2 + 5*b^3)*cosh(d*x + c))*sinh(d*x + c)^2 + (7*(6*a*b^2 + 5*b^3)*cosh(d*x + c)^6 + 10*(6*a*b^2 + 5*b^3)*cosh(d*x + c)^4 + 3*(6*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*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^9 + 4*(11*a^3 - 3*a^2*b - 39*a*b^2 - 25*b^3)*cosh(d*x + c)^7 + 6*(5*a^3 - 3*a^2*b - 21*a*b^2 - 25*b^3)*cosh(d*x + c)^5 - 4*(5*a^3 - 3*a^2*b - 21*a*b^2 - 25*b^3)*cosh(d*x + c)^3 - (11*a^3 - 3*a^2*b - 39*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
99,1,369,0,0.410791," ","integrate(cosh(d*x+c)^2*(a+b*tanh(d*x+c)^2)^3,x, algorithm=""fricas"")","\frac{3 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \sinh\left(d x + c\right)^{5} - 4 \, {\left(18 \, a b^{2} + 14 \, b^{3} - 3 \, {\left(a^{3} - 3 \, a^{2} b - 9 \, a b^{2} - 5 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - 12 \, {\left(18 \, a b^{2} + 14 \, b^{3} - 3 \, {\left(a^{3} - 3 \, a^{2} b - 9 \, a b^{2} - 5 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + {\left(9 \, a^{3} + 27 \, a^{2} b + 99 \, a b^{2} + 65 \, b^{3} + 30 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} - 12 \, {\left(18 \, a b^{2} + 14 \, b^{3} - 3 \, {\left(a^{3} - 3 \, a^{2} b - 9 \, a b^{2} - 5 \, b^{3}\right)} d x\right)} \cosh\left(d x + c\right) + 3 \, {\left(5 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{4} + 2 \, a^{3} + 6 \, a^{2} b + 30 \, a b^{2} + 10 \, b^{3} + {\left(9 \, a^{3} + 27 \, a^{2} b + 99 \, 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*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*sinh(d*x + c)^5 - 4*(18*a*b^2 + 14*b^3 - 3*(a^3 - 3*a^2*b - 9*a*b^2 - 5*b^3)*d*x)*cosh(d*x + c)^3 - 12*(18*a*b^2 + 14*b^3 - 3*(a^3 - 3*a^2*b - 9*a*b^2 - 5*b^3)*d*x)*cosh(d*x + c)*sinh(d*x + c)^2 + (9*a^3 + 27*a^2*b + 99*a*b^2 + 65*b^3 + 30*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^3 - 12*(18*a*b^2 + 14*b^3 - 3*(a^3 - 3*a^2*b - 9*a*b^2 - 5*b^3)*d*x)*cosh(d*x + c) + 3*(5*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^4 + 2*a^3 + 6*a^2*b + 30*a*b^2 + 10*b^3 + (9*a^3 + 27*a^2*b + 99*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
100,1,2411,0,0.451868," ","integrate(cosh(d*x+c)*(a+b*tanh(d*x+c)^2)^3,x, algorithm=""fricas"")","\frac{2 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{10} + 20 \, {\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)^{9} + 2 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \sinh\left(d x + c\right)^{10} + 3 \, {\left(2 \, a^{3} + 6 \, a^{2} b + 10 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 3 \, {\left(2 \, a^{3} + 6 \, a^{2} b + 10 \, a b^{2} + 5 \, b^{3} + 30 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{8} + 24 \, {\left(10 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{3} + 6 \, a^{2} b + 10 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + {\left(4 \, a^{3} + 12 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + {\left(420 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{4} + 4 \, a^{3} + 12 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3} + 84 \, {\left(2 \, a^{3} + 6 \, a^{2} b + 10 \, 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 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{5} + 28 \, {\left(2 \, a^{3} + 6 \, a^{2} b + 10 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(4 \, a^{3} + 12 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - {\left(4 \, a^{3} + 12 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + {\left(420 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{6} + 210 \, {\left(2 \, a^{3} + 6 \, a^{2} b + 10 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 4 \, a^{3} - 12 \, a^{2} b - 24 \, a b^{2} - 5 \, b^{3} + 15 \, {\left(4 \, a^{3} + 12 \, a^{2} b + 24 \, 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 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{7} + 42 \, {\left(2 \, a^{3} + 6 \, a^{2} b + 10 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(4 \, a^{3} + 12 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - {\left(4 \, a^{3} + 12 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 2 \, a^{3} - 6 \, a^{2} b - 6 \, a b^{2} - 2 \, b^{3} - 3 \, {\left(2 \, a^{3} + 6 \, a^{2} b + 10 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{2} + 3 \, {\left(30 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{8} + 28 \, {\left(2 \, a^{3} + 6 \, a^{2} b + 10 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 5 \, {\left(4 \, a^{3} + 12 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 2 \, a^{3} - 6 \, a^{2} b - 10 \, a b^{2} - 5 \, b^{3} - 2 \, {\left(4 \, a^{3} + 12 \, a^{2} b + 24 \, 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(8 \, a^{2} b + 12 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + 9 \, {\left(8 \, a^{2} b + 12 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{8} + {\left(8 \, a^{2} b + 12 \, a b^{2} + 5 \, b^{3}\right)} \sinh\left(d x + c\right)^{9} + 4 \, {\left(8 \, a^{2} b + 12 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 4 \, {\left(8 \, a^{2} b + 12 \, a b^{2} + 5 \, b^{3} + 9 \, {\left(8 \, a^{2} b + 12 \, 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(8 \, a^{2} b + 12 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{2} b + 12 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} + 6 \, {\left(8 \, a^{2} b + 12 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 6 \, {\left(21 \, {\left(8 \, a^{2} b + 12 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 8 \, a^{2} b + 12 \, a b^{2} + 5 \, b^{3} + 14 \, {\left(8 \, a^{2} b + 12 \, 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(8 \, a^{2} b + 12 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 70 \, {\left(8 \, a^{2} b + 12 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 15 \, {\left(8 \, a^{2} b + 12 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(8 \, a^{2} b + 12 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(21 \, {\left(8 \, a^{2} b + 12 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 35 \, {\left(8 \, a^{2} b + 12 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 8 \, a^{2} b + 12 \, a b^{2} + 5 \, b^{3} + 15 \, {\left(8 \, a^{2} b + 12 \, 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(8 \, a^{2} b + 12 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 7 \, {\left(8 \, a^{2} b + 12 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(8 \, a^{2} b + 12 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{2} b + 12 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(8 \, a^{2} b + 12 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right) + {\left(9 \, {\left(8 \, a^{2} b + 12 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 28 \, {\left(8 \, a^{2} b + 12 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 30 \, {\left(8 \, a^{2} b + 12 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 8 \, a^{2} b + 12 \, a b^{2} + 5 \, b^{3} + 12 \, {\left(8 \, a^{2} b + 12 \, 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 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{9} + 12 \, {\left(2 \, a^{3} + 6 \, a^{2} b + 10 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(4 \, a^{3} + 12 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 2 \, {\left(4 \, a^{3} + 12 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(2 \, a^{3} + 6 \, a^{2} b + 10 \, 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*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^10 + 20*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)*sinh(d*x + c)^9 + 2*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*sinh(d*x + c)^10 + 3*(2*a^3 + 6*a^2*b + 10*a*b^2 + 5*b^3)*cosh(d*x + c)^8 + 3*(2*a^3 + 6*a^2*b + 10*a*b^2 + 5*b^3 + 30*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 24*(10*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^3 + (2*a^3 + 6*a^2*b + 10*a*b^2 + 5*b^3)*cosh(d*x + c))*sinh(d*x + c)^7 + (4*a^3 + 12*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c)^6 + (420*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^4 + 4*a^3 + 12*a^2*b + 24*a*b^2 + 5*b^3 + 84*(2*a^3 + 6*a^2*b + 10*a*b^2 + 5*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 6*(84*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^5 + 28*(2*a^3 + 6*a^2*b + 10*a*b^2 + 5*b^3)*cosh(d*x + c)^3 + (4*a^3 + 12*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c))*sinh(d*x + c)^5 - (4*a^3 + 12*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c)^4 + (420*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^6 + 210*(2*a^3 + 6*a^2*b + 10*a*b^2 + 5*b^3)*cosh(d*x + c)^4 - 4*a^3 - 12*a^2*b - 24*a*b^2 - 5*b^3 + 15*(4*a^3 + 12*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 4*(60*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^7 + 42*(2*a^3 + 6*a^2*b + 10*a*b^2 + 5*b^3)*cosh(d*x + c)^5 + 5*(4*a^3 + 12*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c)^3 - (4*a^3 + 12*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 - 2*a^3 - 6*a^2*b - 6*a*b^2 - 2*b^3 - 3*(2*a^3 + 6*a^2*b + 10*a*b^2 + 5*b^3)*cosh(d*x + c)^2 + 3*(30*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^8 + 28*(2*a^3 + 6*a^2*b + 10*a*b^2 + 5*b^3)*cosh(d*x + c)^6 + 5*(4*a^3 + 12*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c)^4 - 2*a^3 - 6*a^2*b - 10*a*b^2 - 5*b^3 - 2*(4*a^3 + 12*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - 3*((8*a^2*b + 12*a*b^2 + 5*b^3)*cosh(d*x + c)^9 + 9*(8*a^2*b + 12*a*b^2 + 5*b^3)*cosh(d*x + c)*sinh(d*x + c)^8 + (8*a^2*b + 12*a*b^2 + 5*b^3)*sinh(d*x + c)^9 + 4*(8*a^2*b + 12*a*b^2 + 5*b^3)*cosh(d*x + c)^7 + 4*(8*a^2*b + 12*a*b^2 + 5*b^3 + 9*(8*a^2*b + 12*a*b^2 + 5*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^7 + 28*(3*(8*a^2*b + 12*a*b^2 + 5*b^3)*cosh(d*x + c)^3 + (8*a^2*b + 12*a*b^2 + 5*b^3)*cosh(d*x + c))*sinh(d*x + c)^6 + 6*(8*a^2*b + 12*a*b^2 + 5*b^3)*cosh(d*x + c)^5 + 6*(21*(8*a^2*b + 12*a*b^2 + 5*b^3)*cosh(d*x + c)^4 + 8*a^2*b + 12*a*b^2 + 5*b^3 + 14*(8*a^2*b + 12*a*b^2 + 5*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 2*(63*(8*a^2*b + 12*a*b^2 + 5*b^3)*cosh(d*x + c)^5 + 70*(8*a^2*b + 12*a*b^2 + 5*b^3)*cosh(d*x + c)^3 + 15*(8*a^2*b + 12*a*b^2 + 5*b^3)*cosh(d*x + c))*sinh(d*x + c)^4 + 4*(8*a^2*b + 12*a*b^2 + 5*b^3)*cosh(d*x + c)^3 + 4*(21*(8*a^2*b + 12*a*b^2 + 5*b^3)*cosh(d*x + c)^6 + 35*(8*a^2*b + 12*a*b^2 + 5*b^3)*cosh(d*x + c)^4 + 8*a^2*b + 12*a*b^2 + 5*b^3 + 15*(8*a^2*b + 12*a*b^2 + 5*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 12*(3*(8*a^2*b + 12*a*b^2 + 5*b^3)*cosh(d*x + c)^7 + 7*(8*a^2*b + 12*a*b^2 + 5*b^3)*cosh(d*x + c)^5 + 5*(8*a^2*b + 12*a*b^2 + 5*b^3)*cosh(d*x + c)^3 + (8*a^2*b + 12*a*b^2 + 5*b^3)*cosh(d*x + c))*sinh(d*x + c)^2 + (8*a^2*b + 12*a*b^2 + 5*b^3)*cosh(d*x + c) + (9*(8*a^2*b + 12*a*b^2 + 5*b^3)*cosh(d*x + c)^8 + 28*(8*a^2*b + 12*a*b^2 + 5*b^3)*cosh(d*x + c)^6 + 30*(8*a^2*b + 12*a*b^2 + 5*b^3)*cosh(d*x + c)^4 + 8*a^2*b + 12*a*b^2 + 5*b^3 + 12*(8*a^2*b + 12*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*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^9 + 12*(2*a^3 + 6*a^2*b + 10*a*b^2 + 5*b^3)*cosh(d*x + c)^7 + 3*(4*a^3 + 12*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c)^5 - 2*(4*a^3 + 12*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c)^3 - 3*(2*a^3 + 6*a^2*b + 10*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
101,1,3465,0,0.445627," ","integrate(sech(d*x+c)*(a+b*tanh(d*x+c)^2)^3,x, algorithm=""fricas"")","-\frac{3 \, {\left(24 \, a^{2} b + 30 \, a b^{2} + 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} + 33 \, {\left(24 \, a^{2} b + 30 \, a b^{2} + 11 \, b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{10} + 3 \, {\left(24 \, a^{2} b + 30 \, a b^{2} + 11 \, b^{3}\right)} \sinh\left(d x + c\right)^{11} + {\left(216 \, a^{2} b + 126 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + {\left(216 \, a^{2} b + 126 \, a b^{2} - 5 \, b^{3} + 165 \, {\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)^{9} + 9 \, {\left(55 \, {\left(24 \, a^{2} b + 30 \, a b^{2} + 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(216 \, a^{2} b + 126 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{8} + 18 \, {\left(8 \, a^{2} b + 2 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 18 \, {\left(55 \, {\left(24 \, a^{2} b + 30 \, a b^{2} + 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 8 \, a^{2} b + 2 \, a b^{2} + 5 \, b^{3} + 2 \, {\left(216 \, a^{2} b + 126 \, 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(24 \, a^{2} b + 30 \, a b^{2} + 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(216 \, a^{2} b + 126 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(8 \, a^{2} b + 2 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} - 18 \, {\left(8 \, a^{2} b + 2 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 18 \, {\left(77 \, {\left(24 \, a^{2} b + 30 \, a b^{2} + 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 7 \, {\left(216 \, a^{2} b + 126 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 8 \, a^{2} b - 2 \, a b^{2} - 5 \, b^{3} + 21 \, {\left(8 \, a^{2} b + 2 \, 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(24 \, a^{2} b + 30 \, a b^{2} + 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 7 \, {\left(216 \, a^{2} b + 126 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 35 \, {\left(8 \, a^{2} b + 2 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 5 \, {\left(8 \, a^{2} b + 2 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} - {\left(216 \, a^{2} b + 126 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(495 \, {\left(24 \, a^{2} b + 30 \, a b^{2} + 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 84 \, {\left(216 \, a^{2} b + 126 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 630 \, {\left(8 \, a^{2} b + 2 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 216 \, a^{2} b - 126 \, a b^{2} + 5 \, b^{3} - 180 \, {\left(8 \, a^{2} b + 2 \, 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(24 \, a^{2} b + 30 \, a b^{2} + 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + 12 \, {\left(216 \, a^{2} b + 126 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 126 \, {\left(8 \, a^{2} b + 2 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 60 \, {\left(8 \, a^{2} b + 2 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - {\left(216 \, a^{2} b + 126 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 3 \, {\left({\left(16 \, a^{3} + 24 \, a^{2} b + 18 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{12} + 12 \, {\left(16 \, a^{3} + 24 \, a^{2} b + 18 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{11} + {\left(16 \, a^{3} + 24 \, a^{2} b + 18 \, a b^{2} + 5 \, b^{3}\right)} \sinh\left(d x + c\right)^{12} + 6 \, {\left(16 \, a^{3} + 24 \, a^{2} b + 18 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} + 6 \, {\left(16 \, a^{3} + 24 \, a^{2} b + 18 \, a b^{2} + 5 \, b^{3} + 11 \, {\left(16 \, a^{3} + 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)^{10} + 20 \, {\left(11 \, {\left(16 \, a^{3} + 24 \, a^{2} b + 18 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(16 \, a^{3} + 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)^{9} + 15 \, {\left(16 \, a^{3} + 24 \, a^{2} b + 18 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 15 \, {\left(33 \, {\left(16 \, a^{3} + 24 \, a^{2} b + 18 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 16 \, a^{3} + 24 \, a^{2} b + 18 \, a b^{2} + 5 \, b^{3} + 18 \, {\left(16 \, a^{3} + 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)^{8} + 24 \, {\left(33 \, {\left(16 \, a^{3} + 24 \, a^{2} b + 18 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 30 \, {\left(16 \, a^{3} + 24 \, a^{2} b + 18 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 5 \, {\left(16 \, a^{3} + 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)^{7} + 20 \, {\left(16 \, a^{3} + 24 \, a^{2} b + 18 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(231 \, {\left(16 \, a^{3} + 24 \, a^{2} b + 18 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 315 \, {\left(16 \, a^{3} + 24 \, a^{2} b + 18 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 80 \, a^{3} + 120 \, a^{2} b + 90 \, a b^{2} + 25 \, b^{3} + 105 \, {\left(16 \, a^{3} + 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)^{6} + 24 \, {\left(33 \, {\left(16 \, a^{3} + 24 \, a^{2} b + 18 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 63 \, {\left(16 \, a^{3} + 24 \, a^{2} b + 18 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 35 \, {\left(16 \, a^{3} + 24 \, a^{2} b + 18 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 5 \, {\left(16 \, a^{3} + 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} + 15 \, {\left(16 \, a^{3} + 24 \, a^{2} b + 18 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 15 \, {\left(33 \, {\left(16 \, a^{3} + 24 \, a^{2} b + 18 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 84 \, {\left(16 \, a^{3} + 24 \, a^{2} b + 18 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 70 \, {\left(16 \, a^{3} + 24 \, a^{2} b + 18 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 16 \, a^{3} + 24 \, a^{2} b + 18 \, a b^{2} + 5 \, b^{3} + 20 \, {\left(16 \, a^{3} + 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} + 20 \, {\left(11 \, {\left(16 \, a^{3} + 24 \, a^{2} b + 18 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + 36 \, {\left(16 \, a^{3} + 24 \, a^{2} b + 18 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 42 \, {\left(16 \, a^{3} + 24 \, a^{2} b + 18 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 20 \, {\left(16 \, a^{3} + 24 \, a^{2} b + 18 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(16 \, a^{3} + 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} + 16 \, a^{3} + 24 \, a^{2} b + 18 \, a b^{2} + 5 \, b^{3} + 6 \, {\left(16 \, a^{3} + 24 \, a^{2} b + 18 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{2} + 6 \, {\left(11 \, {\left(16 \, a^{3} + 24 \, a^{2} b + 18 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} + 45 \, {\left(16 \, a^{3} + 24 \, a^{2} b + 18 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 70 \, {\left(16 \, a^{3} + 24 \, a^{2} b + 18 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 50 \, {\left(16 \, a^{3} + 24 \, a^{2} b + 18 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 16 \, a^{3} + 24 \, a^{2} b + 18 \, a b^{2} + 5 \, b^{3} + 15 \, {\left(16 \, a^{3} + 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} + 12 \, {\left({\left(16 \, a^{3} + 24 \, a^{2} b + 18 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} + 5 \, {\left(16 \, a^{3} + 24 \, a^{2} b + 18 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + 10 \, {\left(16 \, a^{3} + 24 \, a^{2} b + 18 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 10 \, {\left(16 \, a^{3} + 24 \, a^{2} b + 18 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(16 \, a^{3} + 24 \, a^{2} b + 18 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(16 \, a^{3} + 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)\right)} \arctan\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) - 3 \, {\left(24 \, a^{2} b + 30 \, a b^{2} + 11 \, b^{3}\right)} \cosh\left(d x + c\right) + 3 \, {\left(11 \, {\left(24 \, a^{2} b + 30 \, a b^{2} + 11 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} + 3 \, {\left(216 \, a^{2} b + 126 \, a b^{2} - 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 42 \, {\left(8 \, a^{2} b + 2 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} - 30 \, {\left(8 \, a^{2} b + 2 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 24 \, a^{2} b - 30 \, a b^{2} - 11 \, b^{3} - {\left(216 \, a^{2} b + 126 \, 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*(24*a^2*b + 30*a*b^2 + 11*b^3)*cosh(d*x + c)^11 + 33*(24*a^2*b + 30*a*b^2 + 11*b^3)*cosh(d*x + c)*sinh(d*x + c)^10 + 3*(24*a^2*b + 30*a*b^2 + 11*b^3)*sinh(d*x + c)^11 + (216*a^2*b + 126*a*b^2 - 5*b^3)*cosh(d*x + c)^9 + (216*a^2*b + 126*a*b^2 - 5*b^3 + 165*(24*a^2*b + 30*a*b^2 + 11*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^9 + 9*(55*(24*a^2*b + 30*a*b^2 + 11*b^3)*cosh(d*x + c)^3 + (216*a^2*b + 126*a*b^2 - 5*b^3)*cosh(d*x + c))*sinh(d*x + c)^8 + 18*(8*a^2*b + 2*a*b^2 + 5*b^3)*cosh(d*x + c)^7 + 18*(55*(24*a^2*b + 30*a*b^2 + 11*b^3)*cosh(d*x + c)^4 + 8*a^2*b + 2*a*b^2 + 5*b^3 + 2*(216*a^2*b + 126*a*b^2 - 5*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^7 + 42*(33*(24*a^2*b + 30*a*b^2 + 11*b^3)*cosh(d*x + c)^5 + 2*(216*a^2*b + 126*a*b^2 - 5*b^3)*cosh(d*x + c)^3 + 3*(8*a^2*b + 2*a*b^2 + 5*b^3)*cosh(d*x + c))*sinh(d*x + c)^6 - 18*(8*a^2*b + 2*a*b^2 + 5*b^3)*cosh(d*x + c)^5 + 18*(77*(24*a^2*b + 30*a*b^2 + 11*b^3)*cosh(d*x + c)^6 + 7*(216*a^2*b + 126*a*b^2 - 5*b^3)*cosh(d*x + c)^4 - 8*a^2*b - 2*a*b^2 - 5*b^3 + 21*(8*a^2*b + 2*a*b^2 + 5*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 18*(55*(24*a^2*b + 30*a*b^2 + 11*b^3)*cosh(d*x + c)^7 + 7*(216*a^2*b + 126*a*b^2 - 5*b^3)*cosh(d*x + c)^5 + 35*(8*a^2*b + 2*a*b^2 + 5*b^3)*cosh(d*x + c)^3 - 5*(8*a^2*b + 2*a*b^2 + 5*b^3)*cosh(d*x + c))*sinh(d*x + c)^4 - (216*a^2*b + 126*a*b^2 - 5*b^3)*cosh(d*x + c)^3 + (495*(24*a^2*b + 30*a*b^2 + 11*b^3)*cosh(d*x + c)^8 + 84*(216*a^2*b + 126*a*b^2 - 5*b^3)*cosh(d*x + c)^6 + 630*(8*a^2*b + 2*a*b^2 + 5*b^3)*cosh(d*x + c)^4 - 216*a^2*b - 126*a*b^2 + 5*b^3 - 180*(8*a^2*b + 2*a*b^2 + 5*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 3*(55*(24*a^2*b + 30*a*b^2 + 11*b^3)*cosh(d*x + c)^9 + 12*(216*a^2*b + 126*a*b^2 - 5*b^3)*cosh(d*x + c)^7 + 126*(8*a^2*b + 2*a*b^2 + 5*b^3)*cosh(d*x + c)^5 - 60*(8*a^2*b + 2*a*b^2 + 5*b^3)*cosh(d*x + c)^3 - (216*a^2*b + 126*a*b^2 - 5*b^3)*cosh(d*x + c))*sinh(d*x + c)^2 - 3*((16*a^3 + 24*a^2*b + 18*a*b^2 + 5*b^3)*cosh(d*x + c)^12 + 12*(16*a^3 + 24*a^2*b + 18*a*b^2 + 5*b^3)*cosh(d*x + c)*sinh(d*x + c)^11 + (16*a^3 + 24*a^2*b + 18*a*b^2 + 5*b^3)*sinh(d*x + c)^12 + 6*(16*a^3 + 24*a^2*b + 18*a*b^2 + 5*b^3)*cosh(d*x + c)^10 + 6*(16*a^3 + 24*a^2*b + 18*a*b^2 + 5*b^3 + 11*(16*a^3 + 24*a^2*b + 18*a*b^2 + 5*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^10 + 20*(11*(16*a^3 + 24*a^2*b + 18*a*b^2 + 5*b^3)*cosh(d*x + c)^3 + 3*(16*a^3 + 24*a^2*b + 18*a*b^2 + 5*b^3)*cosh(d*x + c))*sinh(d*x + c)^9 + 15*(16*a^3 + 24*a^2*b + 18*a*b^2 + 5*b^3)*cosh(d*x + c)^8 + 15*(33*(16*a^3 + 24*a^2*b + 18*a*b^2 + 5*b^3)*cosh(d*x + c)^4 + 16*a^3 + 24*a^2*b + 18*a*b^2 + 5*b^3 + 18*(16*a^3 + 24*a^2*b + 18*a*b^2 + 5*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 24*(33*(16*a^3 + 24*a^2*b + 18*a*b^2 + 5*b^3)*cosh(d*x + c)^5 + 30*(16*a^3 + 24*a^2*b + 18*a*b^2 + 5*b^3)*cosh(d*x + c)^3 + 5*(16*a^3 + 24*a^2*b + 18*a*b^2 + 5*b^3)*cosh(d*x + c))*sinh(d*x + c)^7 + 20*(16*a^3 + 24*a^2*b + 18*a*b^2 + 5*b^3)*cosh(d*x + c)^6 + 4*(231*(16*a^3 + 24*a^2*b + 18*a*b^2 + 5*b^3)*cosh(d*x + c)^6 + 315*(16*a^3 + 24*a^2*b + 18*a*b^2 + 5*b^3)*cosh(d*x + c)^4 + 80*a^3 + 120*a^2*b + 90*a*b^2 + 25*b^3 + 105*(16*a^3 + 24*a^2*b + 18*a*b^2 + 5*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 24*(33*(16*a^3 + 24*a^2*b + 18*a*b^2 + 5*b^3)*cosh(d*x + c)^7 + 63*(16*a^3 + 24*a^2*b + 18*a*b^2 + 5*b^3)*cosh(d*x + c)^5 + 35*(16*a^3 + 24*a^2*b + 18*a*b^2 + 5*b^3)*cosh(d*x + c)^3 + 5*(16*a^3 + 24*a^2*b + 18*a*b^2 + 5*b^3)*cosh(d*x + c))*sinh(d*x + c)^5 + 15*(16*a^3 + 24*a^2*b + 18*a*b^2 + 5*b^3)*cosh(d*x + c)^4 + 15*(33*(16*a^3 + 24*a^2*b + 18*a*b^2 + 5*b^3)*cosh(d*x + c)^8 + 84*(16*a^3 + 24*a^2*b + 18*a*b^2 + 5*b^3)*cosh(d*x + c)^6 + 70*(16*a^3 + 24*a^2*b + 18*a*b^2 + 5*b^3)*cosh(d*x + c)^4 + 16*a^3 + 24*a^2*b + 18*a*b^2 + 5*b^3 + 20*(16*a^3 + 24*a^2*b + 18*a*b^2 + 5*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 20*(11*(16*a^3 + 24*a^2*b + 18*a*b^2 + 5*b^3)*cosh(d*x + c)^9 + 36*(16*a^3 + 24*a^2*b + 18*a*b^2 + 5*b^3)*cosh(d*x + c)^7 + 42*(16*a^3 + 24*a^2*b + 18*a*b^2 + 5*b^3)*cosh(d*x + c)^5 + 20*(16*a^3 + 24*a^2*b + 18*a*b^2 + 5*b^3)*cosh(d*x + c)^3 + 3*(16*a^3 + 24*a^2*b + 18*a*b^2 + 5*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 + 16*a^3 + 24*a^2*b + 18*a*b^2 + 5*b^3 + 6*(16*a^3 + 24*a^2*b + 18*a*b^2 + 5*b^3)*cosh(d*x + c)^2 + 6*(11*(16*a^3 + 24*a^2*b + 18*a*b^2 + 5*b^3)*cosh(d*x + c)^10 + 45*(16*a^3 + 24*a^2*b + 18*a*b^2 + 5*b^3)*cosh(d*x + c)^8 + 70*(16*a^3 + 24*a^2*b + 18*a*b^2 + 5*b^3)*cosh(d*x + c)^6 + 50*(16*a^3 + 24*a^2*b + 18*a*b^2 + 5*b^3)*cosh(d*x + c)^4 + 16*a^3 + 24*a^2*b + 18*a*b^2 + 5*b^3 + 15*(16*a^3 + 24*a^2*b + 18*a*b^2 + 5*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 12*((16*a^3 + 24*a^2*b + 18*a*b^2 + 5*b^3)*cosh(d*x + c)^11 + 5*(16*a^3 + 24*a^2*b + 18*a*b^2 + 5*b^3)*cosh(d*x + c)^9 + 10*(16*a^3 + 24*a^2*b + 18*a*b^2 + 5*b^3)*cosh(d*x + c)^7 + 10*(16*a^3 + 24*a^2*b + 18*a*b^2 + 5*b^3)*cosh(d*x + c)^5 + 5*(16*a^3 + 24*a^2*b + 18*a*b^2 + 5*b^3)*cosh(d*x + c)^3 + (16*a^3 + 24*a^2*b + 18*a*b^2 + 5*b^3)*cosh(d*x + c))*sinh(d*x + c))*arctan(cosh(d*x + c) + sinh(d*x + c)) - 3*(24*a^2*b + 30*a*b^2 + 11*b^3)*cosh(d*x + c) + 3*(11*(24*a^2*b + 30*a*b^2 + 11*b^3)*cosh(d*x + c)^10 + 3*(216*a^2*b + 126*a*b^2 - 5*b^3)*cosh(d*x + c)^8 + 42*(8*a^2*b + 2*a*b^2 + 5*b^3)*cosh(d*x + c)^6 - 30*(8*a^2*b + 2*a*b^2 + 5*b^3)*cosh(d*x + c)^4 - 24*a^2*b - 30*a*b^2 - 11*b^3 - (216*a^2*b + 126*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
102,1,786,0,0.395511," ","integrate(sech(d*x+c)^2*(a+b*tanh(d*x+c)^2)^3,x, algorithm=""fricas"")","-\frac{4 \, {\left({\left(35 \, a^{3} + 70 \, a^{2} b + 63 \, a b^{2} + 20 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 6 \, {\left(35 \, a^{2} b + 42 \, a b^{2} + 15 \, b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(35 \, a^{3} + 70 \, a^{2} b + 63 \, a b^{2} + 20 \, b^{3}\right)} \sinh\left(d x + c\right)^{6} + 14 \, {\left(15 \, a^{3} + 20 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(210 \, a^{3} + 280 \, a^{2} b + 126 \, a b^{2} + 15 \, {\left(35 \, a^{3} + 70 \, a^{2} b + 63 \, 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(35 \, a^{2} b + 42 \, a b^{2} + 15 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 28 \, {\left(5 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 350 \, a^{3} + 280 \, a^{2} b + 210 \, a b^{2} + 7 \, {\left(75 \, a^{3} + 70 \, a^{2} b + 39 \, a b^{2} + 20 \, b^{3}\right)} \cosh\left(d x + c\right)^{2} + {\left(15 \, {\left(35 \, a^{3} + 70 \, a^{2} b + 63 \, a b^{2} + 20 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 525 \, a^{3} + 490 \, a^{2} b + 273 \, a b^{2} + 140 \, b^{3} + 84 \, {\left(15 \, a^{3} + 20 \, 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(35 \, a^{2} b + 42 \, a b^{2} + 15 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 56 \, {\left(5 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} + 7 \, {\left(25 \, a^{2} b + 6 \, 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*((35*a^3 + 70*a^2*b + 63*a*b^2 + 20*b^3)*cosh(d*x + c)^6 + 6*(35*a^2*b + 42*a*b^2 + 15*b^3)*cosh(d*x + c)*sinh(d*x + c)^5 + (35*a^3 + 70*a^2*b + 63*a*b^2 + 20*b^3)*sinh(d*x + c)^6 + 14*(15*a^3 + 20*a^2*b + 9*a*b^2)*cosh(d*x + c)^4 + (210*a^3 + 280*a^2*b + 126*a*b^2 + 15*(35*a^3 + 70*a^2*b + 63*a*b^2 + 20*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 4*(5*(35*a^2*b + 42*a*b^2 + 15*b^3)*cosh(d*x + c)^3 + 28*(5*a^2*b + 3*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 350*a^3 + 280*a^2*b + 210*a*b^2 + 7*(75*a^3 + 70*a^2*b + 39*a*b^2 + 20*b^3)*cosh(d*x + c)^2 + (15*(35*a^3 + 70*a^2*b + 63*a*b^2 + 20*b^3)*cosh(d*x + c)^4 + 525*a^3 + 490*a^2*b + 273*a*b^2 + 140*b^3 + 84*(15*a^3 + 20*a^2*b + 9*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 2*(3*(35*a^2*b + 42*a*b^2 + 15*b^3)*cosh(d*x + c)^5 + 56*(5*a^2*b + 3*a*b^2)*cosh(d*x + c)^3 + 7*(25*a^2*b + 6*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
103,1,6114,0,1.184006," ","integrate(sech(d*x+c)^3*(a+b*tanh(d*x+c)^2)^3,x, algorithm=""fricas"")","\frac{3 \, {\left(64 \, a^{3} + 48 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{15} + 45 \, {\left(64 \, a^{3} + 48 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{14} + 3 \, {\left(64 \, a^{3} + 48 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3}\right)} \sinh\left(d x + c\right)^{15} + {\left(960 \, a^{3} - 432 \, a^{2} b - 984 \, a b^{2} - 397 \, b^{3}\right)} \cosh\left(d x + c\right)^{13} + {\left(960 \, a^{3} - 432 \, a^{2} b - 984 \, a b^{2} - 397 \, b^{3} + 315 \, {\left(64 \, a^{3} + 48 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{13} + 13 \, {\left(105 \, {\left(64 \, a^{3} + 48 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(960 \, a^{3} - 432 \, a^{2} b - 984 \, a b^{2} - 397 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{12} + {\left(1728 \, a^{3} - 2160 \, a^{2} b - 312 \, a b^{2} + 895 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} + {\left(4095 \, {\left(64 \, a^{3} + 48 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 1728 \, a^{3} - 2160 \, a^{2} b - 312 \, a b^{2} + 895 \, b^{3} + 78 \, {\left(960 \, a^{3} - 432 \, a^{2} b - 984 \, a b^{2} - 397 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{11} + 11 \, {\left(819 \, {\left(64 \, a^{3} + 48 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 26 \, {\left(960 \, a^{3} - 432 \, a^{2} b - 984 \, a b^{2} - 397 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(1728 \, a^{3} - 2160 \, a^{2} b - 312 \, a b^{2} + 895 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{10} + {\left(960 \, a^{3} - 1584 \, a^{2} b + 744 \, a b^{2} - 1765 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + {\left(15015 \, {\left(64 \, a^{3} + 48 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 715 \, {\left(960 \, a^{3} - 432 \, a^{2} b - 984 \, a b^{2} - 397 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 960 \, a^{3} - 1584 \, a^{2} b + 744 \, a b^{2} - 1765 \, b^{3} + 55 \, {\left(1728 \, a^{3} - 2160 \, a^{2} b - 312 \, a b^{2} + 895 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{9} + 3 \, {\left(6435 \, {\left(64 \, a^{3} + 48 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 429 \, {\left(960 \, a^{3} - 432 \, a^{2} b - 984 \, a b^{2} - 397 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 55 \, {\left(1728 \, a^{3} - 2160 \, a^{2} b - 312 \, a b^{2} + 895 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(960 \, a^{3} - 1584 \, a^{2} b + 744 \, a b^{2} - 1765 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{8} - {\left(960 \, a^{3} - 1584 \, a^{2} b + 744 \, a b^{2} - 1765 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + {\left(19305 \, {\left(64 \, a^{3} + 48 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 1716 \, {\left(960 \, a^{3} - 432 \, a^{2} b - 984 \, a b^{2} - 397 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 330 \, {\left(1728 \, a^{3} - 2160 \, a^{2} b - 312 \, a b^{2} + 895 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 960 \, a^{3} + 1584 \, a^{2} b - 744 \, a b^{2} + 1765 \, b^{3} + 36 \, {\left(960 \, a^{3} - 1584 \, a^{2} b + 744 \, a b^{2} - 1765 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{7} + {\left(15015 \, {\left(64 \, a^{3} + 48 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + 1716 \, {\left(960 \, a^{3} - 432 \, a^{2} b - 984 \, a b^{2} - 397 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 462 \, {\left(1728 \, a^{3} - 2160 \, a^{2} b - 312 \, a b^{2} + 895 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 84 \, {\left(960 \, a^{3} - 1584 \, a^{2} b + 744 \, a b^{2} - 1765 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 7 \, {\left(960 \, a^{3} - 1584 \, a^{2} b + 744 \, a b^{2} - 1765 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} - {\left(1728 \, a^{3} - 2160 \, a^{2} b - 312 \, a b^{2} + 895 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + {\left(9009 \, {\left(64 \, a^{3} + 48 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} + 1287 \, {\left(960 \, a^{3} - 432 \, a^{2} b - 984 \, a b^{2} - 397 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 462 \, {\left(1728 \, a^{3} - 2160 \, a^{2} b - 312 \, a b^{2} + 895 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 126 \, {\left(960 \, a^{3} - 1584 \, a^{2} b + 744 \, a b^{2} - 1765 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 1728 \, a^{3} + 2160 \, a^{2} b + 312 \, a b^{2} - 895 \, b^{3} - 21 \, {\left(960 \, a^{3} - 1584 \, a^{2} b + 744 \, a b^{2} - 1765 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{5} + {\left(4095 \, {\left(64 \, a^{3} + 48 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} + 715 \, {\left(960 \, a^{3} - 432 \, a^{2} b - 984 \, a b^{2} - 397 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + 330 \, {\left(1728 \, a^{3} - 2160 \, a^{2} b - 312 \, a b^{2} + 895 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 126 \, {\left(960 \, a^{3} - 1584 \, a^{2} b + 744 \, a b^{2} - 1765 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 35 \, {\left(960 \, a^{3} - 1584 \, a^{2} b + 744 \, a b^{2} - 1765 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 5 \, {\left(1728 \, a^{3} - 2160 \, a^{2} b - 312 \, a b^{2} + 895 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} - {\left(960 \, a^{3} - 432 \, a^{2} b - 984 \, a b^{2} - 397 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(1365 \, {\left(64 \, a^{3} + 48 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{12} + 286 \, {\left(960 \, a^{3} - 432 \, a^{2} b - 984 \, a b^{2} - 397 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} + 165 \, {\left(1728 \, a^{3} - 2160 \, a^{2} b - 312 \, a b^{2} + 895 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 84 \, {\left(960 \, a^{3} - 1584 \, a^{2} b + 744 \, a b^{2} - 1765 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} - 35 \, {\left(960 \, a^{3} - 1584 \, a^{2} b + 744 \, a b^{2} - 1765 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 960 \, a^{3} + 432 \, a^{2} b + 984 \, a b^{2} + 397 \, b^{3} - 10 \, {\left(1728 \, a^{3} - 2160 \, a^{2} b - 312 \, a b^{2} + 895 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + {\left(315 \, {\left(64 \, a^{3} + 48 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{13} + 78 \, {\left(960 \, a^{3} - 432 \, a^{2} b - 984 \, a b^{2} - 397 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} + 55 \, {\left(1728 \, a^{3} - 2160 \, a^{2} b - 312 \, a b^{2} + 895 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + 36 \, {\left(960 \, a^{3} - 1584 \, a^{2} b + 744 \, a b^{2} - 1765 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} - 21 \, {\left(960 \, a^{3} - 1584 \, a^{2} b + 744 \, a b^{2} - 1765 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} - 10 \, {\left(1728 \, a^{3} - 2160 \, a^{2} b - 312 \, a b^{2} + 895 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(960 \, a^{3} - 432 \, a^{2} b - 984 \, a b^{2} - 397 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 3 \, {\left({\left(64 \, a^{3} + 48 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{16} + 16 \, {\left(64 \, a^{3} + 48 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{15} + {\left(64 \, a^{3} + 48 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3}\right)} \sinh\left(d x + c\right)^{16} + 8 \, {\left(64 \, a^{3} + 48 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{14} + 8 \, {\left(64 \, a^{3} + 48 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3} + 15 \, {\left(64 \, a^{3} + 48 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{14} + 112 \, {\left(5 \, {\left(64 \, a^{3} + 48 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(64 \, a^{3} + 48 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{13} + 28 \, {\left(64 \, a^{3} + 48 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{12} + 28 \, {\left(65 \, {\left(64 \, a^{3} + 48 \, a^{2} b + 24 \, 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} + 26 \, {\left(64 \, a^{3} + 48 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{12} + 112 \, {\left(39 \, {\left(64 \, a^{3} + 48 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 26 \, {\left(64 \, a^{3} + 48 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(64 \, a^{3} + 48 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{11} + 56 \, {\left(64 \, a^{3} + 48 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} + 56 \, {\left(143 \, {\left(64 \, a^{3} + 48 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 143 \, {\left(64 \, a^{3} + 48 \, a^{2} b + 24 \, 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} + 33 \, {\left(64 \, a^{3} + 48 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{10} + 16 \, {\left(715 \, {\left(64 \, a^{3} + 48 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 1001 \, {\left(64 \, a^{3} + 48 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 385 \, {\left(64 \, a^{3} + 48 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 35 \, {\left(64 \, a^{3} + 48 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} + 70 \, {\left(64 \, a^{3} + 48 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 2 \, {\left(6435 \, {\left(64 \, a^{3} + 48 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 12012 \, {\left(64 \, a^{3} + 48 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 6930 \, {\left(64 \, a^{3} + 48 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 2240 \, a^{3} + 1680 \, a^{2} b + 840 \, a b^{2} + 175 \, b^{3} + 1260 \, {\left(64 \, a^{3} + 48 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{8} + 16 \, {\left(715 \, {\left(64 \, a^{3} + 48 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + 1716 \, {\left(64 \, a^{3} + 48 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 1386 \, {\left(64 \, a^{3} + 48 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 420 \, {\left(64 \, a^{3} + 48 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 35 \, {\left(64 \, a^{3} + 48 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 56 \, {\left(64 \, a^{3} + 48 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 56 \, {\left(143 \, {\left(64 \, a^{3} + 48 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} + 429 \, {\left(64 \, a^{3} + 48 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 462 \, {\left(64 \, a^{3} + 48 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 210 \, {\left(64 \, a^{3} + 48 \, a^{2} b + 24 \, 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} + 35 \, {\left(64 \, a^{3} + 48 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 112 \, {\left(39 \, {\left(64 \, a^{3} + 48 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} + 143 \, {\left(64 \, a^{3} + 48 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + 198 \, {\left(64 \, a^{3} + 48 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 126 \, {\left(64 \, a^{3} + 48 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 35 \, {\left(64 \, a^{3} + 48 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(64 \, a^{3} + 48 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 28 \, {\left(64 \, a^{3} + 48 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 28 \, {\left(65 \, {\left(64 \, a^{3} + 48 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{12} + 286 \, {\left(64 \, a^{3} + 48 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} + 495 \, {\left(64 \, a^{3} + 48 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 420 \, {\left(64 \, a^{3} + 48 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 175 \, {\left(64 \, a^{3} + 48 \, a^{2} b + 24 \, 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} + 30 \, {\left(64 \, a^{3} + 48 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 112 \, {\left(5 \, {\left(64 \, a^{3} + 48 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{13} + 26 \, {\left(64 \, a^{3} + 48 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} + 55 \, {\left(64 \, a^{3} + 48 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + 60 \, {\left(64 \, a^{3} + 48 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 35 \, {\left(64 \, a^{3} + 48 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(64 \, a^{3} + 48 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(64 \, a^{3} + 48 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 64 \, a^{3} + 48 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3} + 8 \, {\left(64 \, a^{3} + 48 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{2} + 8 \, {\left(15 \, {\left(64 \, a^{3} + 48 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{14} + 91 \, {\left(64 \, a^{3} + 48 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{12} + 231 \, {\left(64 \, a^{3} + 48 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} + 315 \, {\left(64 \, a^{3} + 48 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 245 \, {\left(64 \, a^{3} + 48 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 105 \, {\left(64 \, a^{3} + 48 \, a^{2} b + 24 \, 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} + 21 \, {\left(64 \, a^{3} + 48 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 16 \, {\left({\left(64 \, a^{3} + 48 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{15} + 7 \, {\left(64 \, a^{3} + 48 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{13} + 21 \, {\left(64 \, a^{3} + 48 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{11} + 35 \, {\left(64 \, a^{3} + 48 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{9} + 35 \, {\left(64 \, a^{3} + 48 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 21 \, {\left(64 \, a^{3} + 48 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 7 \, {\left(64 \, a^{3} + 48 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(64 \, a^{3} + 48 \, a^{2} b + 24 \, 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(64 \, a^{3} + 48 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right) + {\left(45 \, {\left(64 \, a^{3} + 48 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3}\right)} \cosh\left(d x + c\right)^{14} + 13 \, {\left(960 \, a^{3} - 432 \, a^{2} b - 984 \, a b^{2} - 397 \, b^{3}\right)} \cosh\left(d x + c\right)^{12} + 11 \, {\left(1728 \, a^{3} - 2160 \, a^{2} b - 312 \, a b^{2} + 895 \, b^{3}\right)} \cosh\left(d x + c\right)^{10} + 9 \, {\left(960 \, a^{3} - 1584 \, a^{2} b + 744 \, a b^{2} - 1765 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} - 7 \, {\left(960 \, a^{3} - 1584 \, a^{2} b + 744 \, a b^{2} - 1765 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} - 5 \, {\left(1728 \, a^{3} - 2160 \, a^{2} b - 312 \, a b^{2} + 895 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 192 \, a^{3} - 144 \, a^{2} b - 72 \, a b^{2} - 15 \, b^{3} - 3 \, {\left(960 \, a^{3} - 432 \, a^{2} b - 984 \, a b^{2} - 397 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)}{192 \, {\left(d \cosh\left(d x + c\right)^{16} + 16 \, d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{15} + d \sinh\left(d x + c\right)^{16} + 8 \, d \cosh\left(d x + c\right)^{14} + 8 \, {\left(15 \, d \cosh\left(d x + c\right)^{2} + d\right)} \sinh\left(d x + c\right)^{14} + 112 \, {\left(5 \, d \cosh\left(d x + c\right)^{3} + d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{13} + 28 \, d \cosh\left(d x + c\right)^{12} + 28 \, {\left(65 \, d \cosh\left(d x + c\right)^{4} + 26 \, d \cosh\left(d x + c\right)^{2} + d\right)} \sinh\left(d x + c\right)^{12} + 112 \, {\left(39 \, d \cosh\left(d x + c\right)^{5} + 26 \, d \cosh\left(d x + c\right)^{3} + 3 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{11} + 56 \, d \cosh\left(d x + c\right)^{10} + 56 \, {\left(143 \, d \cosh\left(d x + c\right)^{6} + 143 \, d \cosh\left(d x + c\right)^{4} + 33 \, d \cosh\left(d x + c\right)^{2} + d\right)} \sinh\left(d x + c\right)^{10} + 16 \, {\left(715 \, d \cosh\left(d x + c\right)^{7} + 1001 \, d \cosh\left(d x + c\right)^{5} + 385 \, d \cosh\left(d x + c\right)^{3} + 35 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} + 70 \, d \cosh\left(d x + c\right)^{8} + 2 \, {\left(6435 \, d \cosh\left(d x + c\right)^{8} + 12012 \, d \cosh\left(d x + c\right)^{6} + 6930 \, d \cosh\left(d x + c\right)^{4} + 1260 \, d \cosh\left(d x + c\right)^{2} + 35 \, d\right)} \sinh\left(d x + c\right)^{8} + 16 \, {\left(715 \, d \cosh\left(d x + c\right)^{9} + 1716 \, d \cosh\left(d x + c\right)^{7} + 1386 \, 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)^{7} + 56 \, d \cosh\left(d x + c\right)^{6} + 56 \, {\left(143 \, d \cosh\left(d x + c\right)^{10} + 429 \, d \cosh\left(d x + c\right)^{8} + 462 \, d \cosh\left(d x + c\right)^{6} + 210 \, d \cosh\left(d x + c\right)^{4} + 35 \, d \cosh\left(d x + c\right)^{2} + d\right)} \sinh\left(d x + c\right)^{6} + 112 \, {\left(39 \, d \cosh\left(d x + c\right)^{11} + 143 \, d \cosh\left(d x + c\right)^{9} + 198 \, d \cosh\left(d x + c\right)^{7} + 126 \, d \cosh\left(d x + c\right)^{5} + 35 \, d \cosh\left(d x + c\right)^{3} + 3 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 28 \, d \cosh\left(d x + c\right)^{4} + 28 \, {\left(65 \, d \cosh\left(d x + c\right)^{12} + 286 \, d \cosh\left(d x + c\right)^{10} + 495 \, d \cosh\left(d x + c\right)^{8} + 420 \, d \cosh\left(d x + c\right)^{6} + 175 \, d \cosh\left(d x + c\right)^{4} + 30 \, d \cosh\left(d x + c\right)^{2} + d\right)} \sinh\left(d x + c\right)^{4} + 112 \, {\left(5 \, d \cosh\left(d x + c\right)^{13} + 26 \, d \cosh\left(d x + c\right)^{11} + 55 \, d \cosh\left(d x + c\right)^{9} + 60 \, d \cosh\left(d x + c\right)^{7} + 35 \, d \cosh\left(d x + c\right)^{5} + 10 \, d \cosh\left(d x + c\right)^{3} + d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 8 \, d \cosh\left(d x + c\right)^{2} + 8 \, {\left(15 \, d \cosh\left(d x + c\right)^{14} + 91 \, d \cosh\left(d x + c\right)^{12} + 231 \, d \cosh\left(d x + c\right)^{10} + 315 \, d \cosh\left(d x + c\right)^{8} + 245 \, d \cosh\left(d x + c\right)^{6} + 105 \, d \cosh\left(d x + c\right)^{4} + 21 \, d \cosh\left(d x + c\right)^{2} + d\right)} \sinh\left(d x + c\right)^{2} + 16 \, {\left(d \cosh\left(d x + c\right)^{15} + 7 \, d \cosh\left(d x + c\right)^{13} + 21 \, d \cosh\left(d x + c\right)^{11} + 35 \, d \cosh\left(d x + c\right)^{9} + 35 \, d \cosh\left(d x + c\right)^{7} + 21 \, d \cosh\left(d x + c\right)^{5} + 7 \, 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,"1/192*(3*(64*a^3 + 48*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c)^15 + 45*(64*a^3 + 48*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c)*sinh(d*x + c)^14 + 3*(64*a^3 + 48*a^2*b + 24*a*b^2 + 5*b^3)*sinh(d*x + c)^15 + (960*a^3 - 432*a^2*b - 984*a*b^2 - 397*b^3)*cosh(d*x + c)^13 + (960*a^3 - 432*a^2*b - 984*a*b^2 - 397*b^3 + 315*(64*a^3 + 48*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^13 + 13*(105*(64*a^3 + 48*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c)^3 + (960*a^3 - 432*a^2*b - 984*a*b^2 - 397*b^3)*cosh(d*x + c))*sinh(d*x + c)^12 + (1728*a^3 - 2160*a^2*b - 312*a*b^2 + 895*b^3)*cosh(d*x + c)^11 + (4095*(64*a^3 + 48*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c)^4 + 1728*a^3 - 2160*a^2*b - 312*a*b^2 + 895*b^3 + 78*(960*a^3 - 432*a^2*b - 984*a*b^2 - 397*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^11 + 11*(819*(64*a^3 + 48*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c)^5 + 26*(960*a^3 - 432*a^2*b - 984*a*b^2 - 397*b^3)*cosh(d*x + c)^3 + (1728*a^3 - 2160*a^2*b - 312*a*b^2 + 895*b^3)*cosh(d*x + c))*sinh(d*x + c)^10 + (960*a^3 - 1584*a^2*b + 744*a*b^2 - 1765*b^3)*cosh(d*x + c)^9 + (15015*(64*a^3 + 48*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c)^6 + 715*(960*a^3 - 432*a^2*b - 984*a*b^2 - 397*b^3)*cosh(d*x + c)^4 + 960*a^3 - 1584*a^2*b + 744*a*b^2 - 1765*b^3 + 55*(1728*a^3 - 2160*a^2*b - 312*a*b^2 + 895*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^9 + 3*(6435*(64*a^3 + 48*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c)^7 + 429*(960*a^3 - 432*a^2*b - 984*a*b^2 - 397*b^3)*cosh(d*x + c)^5 + 55*(1728*a^3 - 2160*a^2*b - 312*a*b^2 + 895*b^3)*cosh(d*x + c)^3 + 3*(960*a^3 - 1584*a^2*b + 744*a*b^2 - 1765*b^3)*cosh(d*x + c))*sinh(d*x + c)^8 - (960*a^3 - 1584*a^2*b + 744*a*b^2 - 1765*b^3)*cosh(d*x + c)^7 + (19305*(64*a^3 + 48*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c)^8 + 1716*(960*a^3 - 432*a^2*b - 984*a*b^2 - 397*b^3)*cosh(d*x + c)^6 + 330*(1728*a^3 - 2160*a^2*b - 312*a*b^2 + 895*b^3)*cosh(d*x + c)^4 - 960*a^3 + 1584*a^2*b - 744*a*b^2 + 1765*b^3 + 36*(960*a^3 - 1584*a^2*b + 744*a*b^2 - 1765*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^7 + (15015*(64*a^3 + 48*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c)^9 + 1716*(960*a^3 - 432*a^2*b - 984*a*b^2 - 397*b^3)*cosh(d*x + c)^7 + 462*(1728*a^3 - 2160*a^2*b - 312*a*b^2 + 895*b^3)*cosh(d*x + c)^5 + 84*(960*a^3 - 1584*a^2*b + 744*a*b^2 - 1765*b^3)*cosh(d*x + c)^3 - 7*(960*a^3 - 1584*a^2*b + 744*a*b^2 - 1765*b^3)*cosh(d*x + c))*sinh(d*x + c)^6 - (1728*a^3 - 2160*a^2*b - 312*a*b^2 + 895*b^3)*cosh(d*x + c)^5 + (9009*(64*a^3 + 48*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c)^10 + 1287*(960*a^3 - 432*a^2*b - 984*a*b^2 - 397*b^3)*cosh(d*x + c)^8 + 462*(1728*a^3 - 2160*a^2*b - 312*a*b^2 + 895*b^3)*cosh(d*x + c)^6 + 126*(960*a^3 - 1584*a^2*b + 744*a*b^2 - 1765*b^3)*cosh(d*x + c)^4 - 1728*a^3 + 2160*a^2*b + 312*a*b^2 - 895*b^3 - 21*(960*a^3 - 1584*a^2*b + 744*a*b^2 - 1765*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + (4095*(64*a^3 + 48*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c)^11 + 715*(960*a^3 - 432*a^2*b - 984*a*b^2 - 397*b^3)*cosh(d*x + c)^9 + 330*(1728*a^3 - 2160*a^2*b - 312*a*b^2 + 895*b^3)*cosh(d*x + c)^7 + 126*(960*a^3 - 1584*a^2*b + 744*a*b^2 - 1765*b^3)*cosh(d*x + c)^5 - 35*(960*a^3 - 1584*a^2*b + 744*a*b^2 - 1765*b^3)*cosh(d*x + c)^3 - 5*(1728*a^3 - 2160*a^2*b - 312*a*b^2 + 895*b^3)*cosh(d*x + c))*sinh(d*x + c)^4 - (960*a^3 - 432*a^2*b - 984*a*b^2 - 397*b^3)*cosh(d*x + c)^3 + (1365*(64*a^3 + 48*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c)^12 + 286*(960*a^3 - 432*a^2*b - 984*a*b^2 - 397*b^3)*cosh(d*x + c)^10 + 165*(1728*a^3 - 2160*a^2*b - 312*a*b^2 + 895*b^3)*cosh(d*x + c)^8 + 84*(960*a^3 - 1584*a^2*b + 744*a*b^2 - 1765*b^3)*cosh(d*x + c)^6 - 35*(960*a^3 - 1584*a^2*b + 744*a*b^2 - 1765*b^3)*cosh(d*x + c)^4 - 960*a^3 + 432*a^2*b + 984*a*b^2 + 397*b^3 - 10*(1728*a^3 - 2160*a^2*b - 312*a*b^2 + 895*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + (315*(64*a^3 + 48*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c)^13 + 78*(960*a^3 - 432*a^2*b - 984*a*b^2 - 397*b^3)*cosh(d*x + c)^11 + 55*(1728*a^3 - 2160*a^2*b - 312*a*b^2 + 895*b^3)*cosh(d*x + c)^9 + 36*(960*a^3 - 1584*a^2*b + 744*a*b^2 - 1765*b^3)*cosh(d*x + c)^7 - 21*(960*a^3 - 1584*a^2*b + 744*a*b^2 - 1765*b^3)*cosh(d*x + c)^5 - 10*(1728*a^3 - 2160*a^2*b - 312*a*b^2 + 895*b^3)*cosh(d*x + c)^3 - 3*(960*a^3 - 432*a^2*b - 984*a*b^2 - 397*b^3)*cosh(d*x + c))*sinh(d*x + c)^2 + 3*((64*a^3 + 48*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c)^16 + 16*(64*a^3 + 48*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c)*sinh(d*x + c)^15 + (64*a^3 + 48*a^2*b + 24*a*b^2 + 5*b^3)*sinh(d*x + c)^16 + 8*(64*a^3 + 48*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c)^14 + 8*(64*a^3 + 48*a^2*b + 24*a*b^2 + 5*b^3 + 15*(64*a^3 + 48*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^14 + 112*(5*(64*a^3 + 48*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c)^3 + (64*a^3 + 48*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c))*sinh(d*x + c)^13 + 28*(64*a^3 + 48*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c)^12 + 28*(65*(64*a^3 + 48*a^2*b + 24*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 + 26*(64*a^3 + 48*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^12 + 112*(39*(64*a^3 + 48*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c)^5 + 26*(64*a^3 + 48*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c)^3 + 3*(64*a^3 + 48*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c))*sinh(d*x + c)^11 + 56*(64*a^3 + 48*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c)^10 + 56*(143*(64*a^3 + 48*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c)^6 + 143*(64*a^3 + 48*a^2*b + 24*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 + 33*(64*a^3 + 48*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^10 + 16*(715*(64*a^3 + 48*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c)^7 + 1001*(64*a^3 + 48*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c)^5 + 385*(64*a^3 + 48*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c)^3 + 35*(64*a^3 + 48*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c))*sinh(d*x + c)^9 + 70*(64*a^3 + 48*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c)^8 + 2*(6435*(64*a^3 + 48*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c)^8 + 12012*(64*a^3 + 48*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c)^6 + 6930*(64*a^3 + 48*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c)^4 + 2240*a^3 + 1680*a^2*b + 840*a*b^2 + 175*b^3 + 1260*(64*a^3 + 48*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 16*(715*(64*a^3 + 48*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c)^9 + 1716*(64*a^3 + 48*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c)^7 + 1386*(64*a^3 + 48*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c)^5 + 420*(64*a^3 + 48*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c)^3 + 35*(64*a^3 + 48*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c))*sinh(d*x + c)^7 + 56*(64*a^3 + 48*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c)^6 + 56*(143*(64*a^3 + 48*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c)^10 + 429*(64*a^3 + 48*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c)^8 + 462*(64*a^3 + 48*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c)^6 + 210*(64*a^3 + 48*a^2*b + 24*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 + 35*(64*a^3 + 48*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 112*(39*(64*a^3 + 48*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c)^11 + 143*(64*a^3 + 48*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c)^9 + 198*(64*a^3 + 48*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c)^7 + 126*(64*a^3 + 48*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c)^5 + 35*(64*a^3 + 48*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c)^3 + 3*(64*a^3 + 48*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c))*sinh(d*x + c)^5 + 28*(64*a^3 + 48*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c)^4 + 28*(65*(64*a^3 + 48*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c)^12 + 286*(64*a^3 + 48*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c)^10 + 495*(64*a^3 + 48*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c)^8 + 420*(64*a^3 + 48*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c)^6 + 175*(64*a^3 + 48*a^2*b + 24*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 + 30*(64*a^3 + 48*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 112*(5*(64*a^3 + 48*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c)^13 + 26*(64*a^3 + 48*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c)^11 + 55*(64*a^3 + 48*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c)^9 + 60*(64*a^3 + 48*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c)^7 + 35*(64*a^3 + 48*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c)^5 + 10*(64*a^3 + 48*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c)^3 + (64*a^3 + 48*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 + 64*a^3 + 48*a^2*b + 24*a*b^2 + 5*b^3 + 8*(64*a^3 + 48*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c)^2 + 8*(15*(64*a^3 + 48*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c)^14 + 91*(64*a^3 + 48*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c)^12 + 231*(64*a^3 + 48*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c)^10 + 315*(64*a^3 + 48*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c)^8 + 245*(64*a^3 + 48*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c)^6 + 105*(64*a^3 + 48*a^2*b + 24*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 + 21*(64*a^3 + 48*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 16*((64*a^3 + 48*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c)^15 + 7*(64*a^3 + 48*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c)^13 + 21*(64*a^3 + 48*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c)^11 + 35*(64*a^3 + 48*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c)^9 + 35*(64*a^3 + 48*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c)^7 + 21*(64*a^3 + 48*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c)^5 + 7*(64*a^3 + 48*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c)^3 + (64*a^3 + 48*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c))*sinh(d*x + c))*arctan(cosh(d*x + c) + sinh(d*x + c)) - 3*(64*a^3 + 48*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c) + (45*(64*a^3 + 48*a^2*b + 24*a*b^2 + 5*b^3)*cosh(d*x + c)^14 + 13*(960*a^3 - 432*a^2*b - 984*a*b^2 - 397*b^3)*cosh(d*x + c)^12 + 11*(1728*a^3 - 2160*a^2*b - 312*a*b^2 + 895*b^3)*cosh(d*x + c)^10 + 9*(960*a^3 - 1584*a^2*b + 744*a*b^2 - 1765*b^3)*cosh(d*x + c)^8 - 7*(960*a^3 - 1584*a^2*b + 744*a*b^2 - 1765*b^3)*cosh(d*x + c)^6 - 5*(1728*a^3 - 2160*a^2*b - 312*a*b^2 + 895*b^3)*cosh(d*x + c)^4 - 192*a^3 - 144*a^2*b - 72*a*b^2 - 15*b^3 - 3*(960*a^3 - 432*a^2*b - 984*a*b^2 - 397*b^3)*cosh(d*x + c)^2)*sinh(d*x + c))/(d*cosh(d*x + c)^16 + 16*d*cosh(d*x + c)*sinh(d*x + c)^15 + d*sinh(d*x + c)^16 + 8*d*cosh(d*x + c)^14 + 8*(15*d*cosh(d*x + c)^2 + d)*sinh(d*x + c)^14 + 112*(5*d*cosh(d*x + c)^3 + d*cosh(d*x + c))*sinh(d*x + c)^13 + 28*d*cosh(d*x + c)^12 + 28*(65*d*cosh(d*x + c)^4 + 26*d*cosh(d*x + c)^2 + d)*sinh(d*x + c)^12 + 112*(39*d*cosh(d*x + c)^5 + 26*d*cosh(d*x + c)^3 + 3*d*cosh(d*x + c))*sinh(d*x + c)^11 + 56*d*cosh(d*x + c)^10 + 56*(143*d*cosh(d*x + c)^6 + 143*d*cosh(d*x + c)^4 + 33*d*cosh(d*x + c)^2 + d)*sinh(d*x + c)^10 + 16*(715*d*cosh(d*x + c)^7 + 1001*d*cosh(d*x + c)^5 + 385*d*cosh(d*x + c)^3 + 35*d*cosh(d*x + c))*sinh(d*x + c)^9 + 70*d*cosh(d*x + c)^8 + 2*(6435*d*cosh(d*x + c)^8 + 12012*d*cosh(d*x + c)^6 + 6930*d*cosh(d*x + c)^4 + 1260*d*cosh(d*x + c)^2 + 35*d)*sinh(d*x + c)^8 + 16*(715*d*cosh(d*x + c)^9 + 1716*d*cosh(d*x + c)^7 + 1386*d*cosh(d*x + c)^5 + 420*d*cosh(d*x + c)^3 + 35*d*cosh(d*x + c))*sinh(d*x + c)^7 + 56*d*cosh(d*x + c)^6 + 56*(143*d*cosh(d*x + c)^10 + 429*d*cosh(d*x + c)^8 + 462*d*cosh(d*x + c)^6 + 210*d*cosh(d*x + c)^4 + 35*d*cosh(d*x + c)^2 + d)*sinh(d*x + c)^6 + 112*(39*d*cosh(d*x + c)^11 + 143*d*cosh(d*x + c)^9 + 198*d*cosh(d*x + c)^7 + 126*d*cosh(d*x + c)^5 + 35*d*cosh(d*x + c)^3 + 3*d*cosh(d*x + c))*sinh(d*x + c)^5 + 28*d*cosh(d*x + c)^4 + 28*(65*d*cosh(d*x + c)^12 + 286*d*cosh(d*x + c)^10 + 495*d*cosh(d*x + c)^8 + 420*d*cosh(d*x + c)^6 + 175*d*cosh(d*x + c)^4 + 30*d*cosh(d*x + c)^2 + d)*sinh(d*x + c)^4 + 112*(5*d*cosh(d*x + c)^13 + 26*d*cosh(d*x + c)^11 + 55*d*cosh(d*x + c)^9 + 60*d*cosh(d*x + c)^7 + 35*d*cosh(d*x + c)^5 + 10*d*cosh(d*x + c)^3 + d*cosh(d*x + c))*sinh(d*x + c)^3 + 8*d*cosh(d*x + c)^2 + 8*(15*d*cosh(d*x + c)^14 + 91*d*cosh(d*x + c)^12 + 231*d*cosh(d*x + c)^10 + 315*d*cosh(d*x + c)^8 + 245*d*cosh(d*x + c)^6 + 105*d*cosh(d*x + c)^4 + 21*d*cosh(d*x + c)^2 + d)*sinh(d*x + c)^2 + 16*(d*cosh(d*x + c)^15 + 7*d*cosh(d*x + c)^13 + 21*d*cosh(d*x + c)^11 + 35*d*cosh(d*x + c)^9 + 35*d*cosh(d*x + c)^7 + 21*d*cosh(d*x + c)^5 + 7*d*cosh(d*x + c)^3 + d*cosh(d*x + c))*sinh(d*x + c) + d)","B",0
104,1,1185,0,0.401463," ","integrate(sech(d*x+c)^4*(a+b*tanh(d*x+c)^2)^3,x, algorithm=""fricas"")","-\frac{8 \, {\left(2 \, {\left(105 \, a^{3} + 252 \, a^{2} b + 243 \, a b^{2} + 80 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 14 \, {\left(105 \, a^{3} + 252 \, a^{2} b + 243 \, a b^{2} + 80 \, b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + {\left(105 \, a^{3} + 441 \, a^{2} b + 459 \, a b^{2} + 155 \, b^{3}\right)} \sinh\left(d x + c\right)^{7} + 6 \, {\left(245 \, a^{3} + 336 \, a^{2} b + 99 \, a b^{2} - 40 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 3 \, {\left(175 \, a^{3} + 483 \, a^{2} b + 117 \, a b^{2} - 95 \, b^{3} + 7 \, {\left(105 \, a^{3} + 441 \, a^{2} b + 459 \, a b^{2} + 155 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{5} + 10 \, {\left(7 \, {\left(105 \, a^{3} + 252 \, a^{2} b + 243 \, a b^{2} + 80 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(245 \, a^{3} + 336 \, a^{2} b + 99 \, a b^{2} - 40 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 18 \, {\left(245 \, a^{3} + 168 \, a^{2} b + 27 \, a b^{2} + 40 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(35 \, {\left(105 \, a^{3} + 441 \, a^{2} b + 459 \, a b^{2} + 155 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 945 \, a^{3} + 1701 \, a^{2} b + 459 \, a b^{2} + 855 \, b^{3} + 30 \, {\left(175 \, a^{3} + 483 \, a^{2} b + 117 \, a b^{2} - 95 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + 6 \, {\left(7 \, {\left(105 \, a^{3} + 252 \, a^{2} b + 243 \, a b^{2} + 80 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(245 \, a^{3} + 336 \, a^{2} b + 99 \, a b^{2} - 40 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 9 \, {\left(245 \, a^{3} + 168 \, a^{2} b + 27 \, a b^{2} + 40 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 210 \, {\left(35 \, a^{3} + 12 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(d x + c\right) + {\left(7 \, {\left(105 \, a^{3} + 441 \, a^{2} b + 459 \, a b^{2} + 155 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(175 \, a^{3} + 483 \, a^{2} b + 117 \, a b^{2} - 95 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 525 \, a^{3} + 693 \, a^{2} b + 567 \, a b^{2} - 945 \, b^{3} + 27 \, {\left(105 \, a^{3} + 189 \, a^{2} b + 51 \, a b^{2} + 95 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)\right)}}{315 \, {\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} + 9 \, d \cosh\left(d x + c\right)^{9} + {\left(55 \, d \cosh\left(d x + c\right)^{2} + 9 \, d\right)} \sinh\left(d x + c\right)^{9} + 3 \, {\left(55 \, d \cosh\left(d x + c\right)^{3} + 27 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{8} + 37 \, d \cosh\left(d x + c\right)^{7} + {\left(330 \, d \cosh\left(d x + c\right)^{4} + 324 \, d \cosh\left(d x + c\right)^{2} + 35 \, d\right)} \sinh\left(d x + c\right)^{7} + 7 \, {\left(66 \, d \cosh\left(d x + c\right)^{5} + 108 \, d \cosh\left(d x + c\right)^{3} + 37 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} + 93 \, d \cosh\left(d x + c\right)^{5} + 3 \, {\left(154 \, d \cosh\left(d x + c\right)^{6} + 378 \, d \cosh\left(d x + c\right)^{4} + 245 \, d \cosh\left(d x + c\right)^{2} + 25 \, d\right)} \sinh\left(d x + c\right)^{5} + {\left(330 \, d \cosh\left(d x + c\right)^{7} + 1134 \, d \cosh\left(d x + c\right)^{5} + 1295 \, d \cosh\left(d x + c\right)^{3} + 465 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 162 \, d \cosh\left(d x + c\right)^{3} + {\left(165 \, d \cosh\left(d x + c\right)^{8} + 756 \, d \cosh\left(d x + c\right)^{6} + 1225 \, d \cosh\left(d x + c\right)^{4} + 750 \, d \cosh\left(d x + c\right)^{2} + 90 \, d\right)} \sinh\left(d x + c\right)^{3} + {\left(55 \, d \cosh\left(d x + c\right)^{9} + 324 \, d \cosh\left(d x + c\right)^{7} + 777 \, d \cosh\left(d x + c\right)^{5} + 930 \, d \cosh\left(d x + c\right)^{3} + 486 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 210 \, d \cosh\left(d x + c\right) + {\left(11 \, d \cosh\left(d x + c\right)^{10} + 81 \, d \cosh\left(d x + c\right)^{8} + 245 \, d \cosh\left(d x + c\right)^{6} + 375 \, d \cosh\left(d x + c\right)^{4} + 270 \, d \cosh\left(d x + c\right)^{2} + 42 \, d\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"-8/315*(2*(105*a^3 + 252*a^2*b + 243*a*b^2 + 80*b^3)*cosh(d*x + c)^7 + 14*(105*a^3 + 252*a^2*b + 243*a*b^2 + 80*b^3)*cosh(d*x + c)*sinh(d*x + c)^6 + (105*a^3 + 441*a^2*b + 459*a*b^2 + 155*b^3)*sinh(d*x + c)^7 + 6*(245*a^3 + 336*a^2*b + 99*a*b^2 - 40*b^3)*cosh(d*x + c)^5 + 3*(175*a^3 + 483*a^2*b + 117*a*b^2 - 95*b^3 + 7*(105*a^3 + 441*a^2*b + 459*a*b^2 + 155*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 10*(7*(105*a^3 + 252*a^2*b + 243*a*b^2 + 80*b^3)*cosh(d*x + c)^3 + 3*(245*a^3 + 336*a^2*b + 99*a*b^2 - 40*b^3)*cosh(d*x + c))*sinh(d*x + c)^4 + 18*(245*a^3 + 168*a^2*b + 27*a*b^2 + 40*b^3)*cosh(d*x + c)^3 + (35*(105*a^3 + 441*a^2*b + 459*a*b^2 + 155*b^3)*cosh(d*x + c)^4 + 945*a^3 + 1701*a^2*b + 459*a*b^2 + 855*b^3 + 30*(175*a^3 + 483*a^2*b + 117*a*b^2 - 95*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 6*(7*(105*a^3 + 252*a^2*b + 243*a*b^2 + 80*b^3)*cosh(d*x + c)^5 + 10*(245*a^3 + 336*a^2*b + 99*a*b^2 - 40*b^3)*cosh(d*x + c)^3 + 9*(245*a^3 + 168*a^2*b + 27*a*b^2 + 40*b^3)*cosh(d*x + c))*sinh(d*x + c)^2 + 210*(35*a^3 + 12*a^2*b + 9*a*b^2)*cosh(d*x + c) + (7*(105*a^3 + 441*a^2*b + 459*a*b^2 + 155*b^3)*cosh(d*x + c)^6 + 15*(175*a^3 + 483*a^2*b + 117*a*b^2 - 95*b^3)*cosh(d*x + c)^4 + 525*a^3 + 693*a^2*b + 567*a*b^2 - 945*b^3 + 27*(105*a^3 + 189*a^2*b + 51*a*b^2 + 95*b^3)*cosh(d*x + c)^2)*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 + 9*d*cosh(d*x + c)^9 + (55*d*cosh(d*x + c)^2 + 9*d)*sinh(d*x + c)^9 + 3*(55*d*cosh(d*x + c)^3 + 27*d*cosh(d*x + c))*sinh(d*x + c)^8 + 37*d*cosh(d*x + c)^7 + (330*d*cosh(d*x + c)^4 + 324*d*cosh(d*x + c)^2 + 35*d)*sinh(d*x + c)^7 + 7*(66*d*cosh(d*x + c)^5 + 108*d*cosh(d*x + c)^3 + 37*d*cosh(d*x + c))*sinh(d*x + c)^6 + 93*d*cosh(d*x + c)^5 + 3*(154*d*cosh(d*x + c)^6 + 378*d*cosh(d*x + c)^4 + 245*d*cosh(d*x + c)^2 + 25*d)*sinh(d*x + c)^5 + (330*d*cosh(d*x + c)^7 + 1134*d*cosh(d*x + c)^5 + 1295*d*cosh(d*x + c)^3 + 465*d*cosh(d*x + c))*sinh(d*x + c)^4 + 162*d*cosh(d*x + c)^3 + (165*d*cosh(d*x + c)^8 + 756*d*cosh(d*x + c)^6 + 1225*d*cosh(d*x + c)^4 + 750*d*cosh(d*x + c)^2 + 90*d)*sinh(d*x + c)^3 + (55*d*cosh(d*x + c)^9 + 324*d*cosh(d*x + c)^7 + 777*d*cosh(d*x + c)^5 + 930*d*cosh(d*x + c)^3 + 486*d*cosh(d*x + c))*sinh(d*x + c)^2 + 210*d*cosh(d*x + c) + (11*d*cosh(d*x + c)^10 + 81*d*cosh(d*x + c)^8 + 245*d*cosh(d*x + c)^6 + 375*d*cosh(d*x + c)^4 + 270*d*cosh(d*x + c)^2 + 42*d)*sinh(d*x + c))","B",0
105,1,2180,0,0.482255," ","integrate(cosh(d*x+c)^4/(a+b*tanh(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{{\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{8} + 8 \, {\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} d x \cosh\left(d x + c\right)^{4} + 8 \, {\left(a^{2} + 3 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, a^{2} + 6 \, a b + 4 \, b^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + 6 \, {\left(a^{2} + 3 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} d x + 60 \, {\left(a^{2} + 3 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{5} + 4 \, {\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} d x \cosh\left(d x + c\right) + 20 \, {\left(a^{2} + 3 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right)^{3} - 8 \, {\left(a^{2} + 3 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{6} + 12 \, {\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} d x \cosh\left(d x + c\right)^{2} + 30 \, {\left(a^{2} + 3 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} - 2 \, a^{2} - 6 \, a b - 4 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} + 32 \, {\left(b^{2} \cosh\left(d x + c\right)^{4} + 4 \, b^{2} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, b^{2} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 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}\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{{\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) \sinh\left(d x + c\right)^{3} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{2} + a^{2} - 6 \, a b + b^{2} + 4 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + 4 \, {\left({\left(a^{2} + a b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} + a b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} + a b\right)} \sinh\left(d x + c\right)^{2} + a^{2} - a b\right)} \sqrt{-\frac{b}{a}}}{{\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) - a^{2} - 2 \, a b - b^{2} + 8 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{7} + 4 \, {\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} d x \cosh\left(d x + c\right)^{3} + 6 \, {\left(a^{2} + 3 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} - 2 \, {\left(a^{2} + 3 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{64 \, {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d \cosh\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)^{3} \sinh\left(d x + c\right) + 6 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, {\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)^{3} + {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d \sinh\left(d x + c\right)^{4}\right)}}, \frac{{\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{8} + 8 \, {\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} d x \cosh\left(d x + c\right)^{4} + 8 \, {\left(a^{2} + 3 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, a^{2} + 6 \, a b + 4 \, b^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + 6 \, {\left(a^{2} + 3 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} d x + 60 \, {\left(a^{2} + 3 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{5} + 4 \, {\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} d x \cosh\left(d x + c\right) + 20 \, {\left(a^{2} + 3 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right)^{3} - 8 \, {\left(a^{2} + 3 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{6} + 12 \, {\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} d x \cosh\left(d x + c\right)^{2} + 30 \, {\left(a^{2} + 3 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} - 2 \, a^{2} - 6 \, a b - 4 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} + 64 \, {\left(b^{2} \cosh\left(d x + c\right)^{4} + 4 \, b^{2} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right) + 6 \, b^{2} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 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}\right)} \sqrt{\frac{b}{a}} \arctan\left(\frac{{\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} + a - b\right)} \sqrt{\frac{b}{a}}}{2 \, b}\right) - a^{2} - 2 \, a b - b^{2} + 8 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{7} + 4 \, {\left(3 \, a^{2} + 10 \, a b + 15 \, b^{2}\right)} d x \cosh\left(d x + c\right)^{3} + 6 \, {\left(a^{2} + 3 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} - 2 \, {\left(a^{2} + 3 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{64 \, {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d \cosh\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)^{3} \sinh\left(d x + c\right) + 6 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{2} + 4 \, {\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)^{3} + {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d \sinh\left(d x + c\right)^{4}\right)}}\right]"," ",0,"[1/64*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^8 + 8*(a^2 + 2*a*b + b^2)*cosh(d*x + c)*sinh(d*x + c)^7 + (a^2 + 2*a*b + b^2)*sinh(d*x + c)^8 + 8*(3*a^2 + 10*a*b + 15*b^2)*d*x*cosh(d*x + c)^4 + 8*(a^2 + 3*a*b + 2*b^2)*cosh(d*x + c)^6 + 4*(7*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + 2*a^2 + 6*a*b + 4*b^2)*sinh(d*x + c)^6 + 8*(7*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 + 6*(a^2 + 3*a*b + 2*b^2)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 + 4*(3*a^2 + 10*a*b + 15*b^2)*d*x + 60*(a^2 + 3*a*b + 2*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(7*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^5 + 4*(3*a^2 + 10*a*b + 15*b^2)*d*x*cosh(d*x + c) + 20*(a^2 + 3*a*b + 2*b^2)*cosh(d*x + c)^3)*sinh(d*x + c)^3 - 8*(a^2 + 3*a*b + 2*b^2)*cosh(d*x + c)^2 + 4*(7*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^6 + 12*(3*a^2 + 10*a*b + 15*b^2)*d*x*cosh(d*x + c)^2 + 30*(a^2 + 3*a*b + 2*b^2)*cosh(d*x + c)^4 - 2*a^2 - 6*a*b - 4*b^2)*sinh(d*x + c)^2 + 32*(b^2*cosh(d*x + c)^4 + 4*b^2*cosh(d*x + c)^3*sinh(d*x + c) + 6*b^2*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*b^2*cosh(d*x + c)*sinh(d*x + c)^3 + b^2*sinh(d*x + c)^4)*sqrt(-b/a)*log(((a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 + 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 + 2*(a^2 - b^2)*cosh(d*x + c)^2 + 2*(3*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + a^2 - b^2)*sinh(d*x + c)^2 + a^2 - 6*a*b + b^2 + 4*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 + (a^2 - b^2)*cosh(d*x + c))*sinh(d*x + c) + 4*((a^2 + a*b)*cosh(d*x + c)^2 + 2*(a^2 + a*b)*cosh(d*x + c)*sinh(d*x + c) + (a^2 + a*b)*sinh(d*x + c)^2 + a^2 - a*b)*sqrt(-b/a))/((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)) - a^2 - 2*a*b - b^2 + 8*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^7 + 4*(3*a^2 + 10*a*b + 15*b^2)*d*x*cosh(d*x + c)^3 + 6*(a^2 + 3*a*b + 2*b^2)*cosh(d*x + c)^5 - 2*(a^2 + 3*a*b + 2*b^2)*cosh(d*x + c))*sinh(d*x + c))/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*cosh(d*x + c)^4 + 4*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*cosh(d*x + c)^3*sinh(d*x + c) + 6*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*cosh(d*x + c)*sinh(d*x + c)^3 + (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*sinh(d*x + c)^4), 1/64*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^8 + 8*(a^2 + 2*a*b + b^2)*cosh(d*x + c)*sinh(d*x + c)^7 + (a^2 + 2*a*b + b^2)*sinh(d*x + c)^8 + 8*(3*a^2 + 10*a*b + 15*b^2)*d*x*cosh(d*x + c)^4 + 8*(a^2 + 3*a*b + 2*b^2)*cosh(d*x + c)^6 + 4*(7*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + 2*a^2 + 6*a*b + 4*b^2)*sinh(d*x + c)^6 + 8*(7*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 + 6*(a^2 + 3*a*b + 2*b^2)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 + 4*(3*a^2 + 10*a*b + 15*b^2)*d*x + 60*(a^2 + 3*a*b + 2*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(7*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^5 + 4*(3*a^2 + 10*a*b + 15*b^2)*d*x*cosh(d*x + c) + 20*(a^2 + 3*a*b + 2*b^2)*cosh(d*x + c)^3)*sinh(d*x + c)^3 - 8*(a^2 + 3*a*b + 2*b^2)*cosh(d*x + c)^2 + 4*(7*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^6 + 12*(3*a^2 + 10*a*b + 15*b^2)*d*x*cosh(d*x + c)^2 + 30*(a^2 + 3*a*b + 2*b^2)*cosh(d*x + c)^4 - 2*a^2 - 6*a*b - 4*b^2)*sinh(d*x + c)^2 + 64*(b^2*cosh(d*x + c)^4 + 4*b^2*cosh(d*x + c)^3*sinh(d*x + c) + 6*b^2*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*b^2*cosh(d*x + c)*sinh(d*x + c)^3 + b^2*sinh(d*x + c)^4)*sqrt(b/a)*arctan(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 + a - b)*sqrt(b/a)/b) - a^2 - 2*a*b - b^2 + 8*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^7 + 4*(3*a^2 + 10*a*b + 15*b^2)*d*x*cosh(d*x + c)^3 + 6*(a^2 + 3*a*b + 2*b^2)*cosh(d*x + c)^5 - 2*(a^2 + 3*a*b + 2*b^2)*cosh(d*x + c))*sinh(d*x + c))/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*cosh(d*x + c)^4 + 4*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*cosh(d*x + c)^3*sinh(d*x + c) + 6*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*cosh(d*x + c)^2*sinh(d*x + c)^2 + 4*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*cosh(d*x + c)*sinh(d*x + c)^3 + (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*sinh(d*x + c)^4)]","B",0
106,1,1850,0,0.493464," ","integrate(cosh(d*x+c)^3/(a+b*tanh(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{{\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(d x + c\right)^{6} + 6 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \sinh\left(d x + c\right)^{6} + 3 \, {\left(3 \, a^{3} + 10 \, a^{2} b + 7 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{3} + 10 \, a^{2} b + 7 \, a b^{2} + 5 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(3 \, a^{3} + 10 \, a^{2} b + 7 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - a^{3} - 2 \, a^{2} b - a b^{2} - 3 \, {\left(3 \, a^{3} + 10 \, a^{2} b + 7 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2} + 3 \, {\left(5 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(d x + c\right)^{4} - 3 \, a^{3} - 10 \, a^{2} b - 7 \, a b^{2} + 6 \, {\left(3 \, a^{3} + 10 \, 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(b^{2} \cosh\left(d x + c\right)^{3} + 3 \, b^{2} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + b^{2} \sinh\left(d x + c\right)^{3}\right)} \sqrt{-a^{2} - a b} \log\left(\frac{{\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(3 \, a + b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} - 3 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(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) - 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^{2} - a b} + a + b}{{\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) + 6 \, {\left({\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(3 \, a^{3} + 10 \, a^{2} b + 7 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(3 \, a^{3} + 10 \, a^{2} b + 7 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{24 \, {\left({\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)^{2} \sinh\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) \sinh\left(d x + c\right)^{2} + {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} d \sinh\left(d x + c\right)^{3}\right)}}, \frac{{\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(d x + c\right)^{6} + 6 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \sinh\left(d x + c\right)^{6} + 3 \, {\left(3 \, a^{3} + 10 \, a^{2} b + 7 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{3} + 10 \, a^{2} b + 7 \, a b^{2} + 5 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(3 \, a^{3} + 10 \, a^{2} b + 7 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - a^{3} - 2 \, a^{2} b - a b^{2} - 3 \, {\left(3 \, a^{3} + 10 \, a^{2} b + 7 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2} + 3 \, {\left(5 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(d x + c\right)^{4} - 3 \, a^{3} - 10 \, a^{2} b - 7 \, a b^{2} + 6 \, {\left(3 \, a^{3} + 10 \, 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(b^{2} \cosh\left(d x + c\right)^{3} + 3 \, b^{2} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + b^{2} \sinh\left(d x + c\right)^{3}\right)} \sqrt{a^{2} + a b} \arctan\left(\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(3 \, a - b\right)} \cosh\left(d x + c\right) + {\left(3 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} + 3 \, a - b\right)} \sinh\left(d x + c\right)}{2 \, \sqrt{a^{2} + a b}}\right) + 24 \, {\left(b^{2} \cosh\left(d x + c\right)^{3} + 3 \, b^{2} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right) + 3 \, b^{2} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + b^{2} \sinh\left(d x + c\right)^{3}\right)} \sqrt{a^{2} + a b} \arctan\left(\frac{\sqrt{a^{2} + a b} {\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right)}}{2 \, a}\right) + 6 \, {\left({\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(3 \, a^{3} + 10 \, a^{2} b + 7 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(3 \, a^{3} + 10 \, a^{2} b + 7 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{24 \, {\left({\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)^{2} \sinh\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) \sinh\left(d x + c\right)^{2} + {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} d \sinh\left(d x + c\right)^{3}\right)}}\right]"," ",0,"[1/24*((a^3 + 2*a^2*b + a*b^2)*cosh(d*x + c)^6 + 6*(a^3 + 2*a^2*b + a*b^2)*cosh(d*x + c)*sinh(d*x + c)^5 + (a^3 + 2*a^2*b + a*b^2)*sinh(d*x + c)^6 + 3*(3*a^3 + 10*a^2*b + 7*a*b^2)*cosh(d*x + c)^4 + 3*(3*a^3 + 10*a^2*b + 7*a*b^2 + 5*(a^3 + 2*a^2*b + a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 4*(5*(a^3 + 2*a^2*b + a*b^2)*cosh(d*x + c)^3 + 3*(3*a^3 + 10*a^2*b + 7*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 - a^3 - 2*a^2*b - a*b^2 - 3*(3*a^3 + 10*a^2*b + 7*a*b^2)*cosh(d*x + c)^2 + 3*(5*(a^3 + 2*a^2*b + a*b^2)*cosh(d*x + c)^4 - 3*a^3 - 10*a^2*b - 7*a*b^2 + 6*(3*a^3 + 10*a^2*b + 7*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - 12*(b^2*cosh(d*x + c)^3 + 3*b^2*cosh(d*x + c)^2*sinh(d*x + c) + 3*b^2*cosh(d*x + c)*sinh(d*x + c)^2 + b^2*sinh(d*x + c)^3)*sqrt(-a^2 - a*b)*log(((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*(3*a + b)*cosh(d*x + c)^2 + 2*(3*(a + b)*cosh(d*x + c)^2 - 3*a - b)*sinh(d*x + c)^2 + 4*((a + b)*cosh(d*x + c)^3 - (3*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^2 - a*b) + a + b)/((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)) + 6*((a^3 + 2*a^2*b + a*b^2)*cosh(d*x + c)^5 + 2*(3*a^3 + 10*a^2*b + 7*a*b^2)*cosh(d*x + c)^3 - (3*a^3 + 10*a^2*b + 7*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)^3 + 3*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d*cosh(d*x + c)^2*sinh(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)^2 + (a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d*sinh(d*x + c)^3), 1/24*((a^3 + 2*a^2*b + a*b^2)*cosh(d*x + c)^6 + 6*(a^3 + 2*a^2*b + a*b^2)*cosh(d*x + c)*sinh(d*x + c)^5 + (a^3 + 2*a^2*b + a*b^2)*sinh(d*x + c)^6 + 3*(3*a^3 + 10*a^2*b + 7*a*b^2)*cosh(d*x + c)^4 + 3*(3*a^3 + 10*a^2*b + 7*a*b^2 + 5*(a^3 + 2*a^2*b + a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 4*(5*(a^3 + 2*a^2*b + a*b^2)*cosh(d*x + c)^3 + 3*(3*a^3 + 10*a^2*b + 7*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 - a^3 - 2*a^2*b - a*b^2 - 3*(3*a^3 + 10*a^2*b + 7*a*b^2)*cosh(d*x + c)^2 + 3*(5*(a^3 + 2*a^2*b + a*b^2)*cosh(d*x + c)^4 - 3*a^3 - 10*a^2*b - 7*a*b^2 + 6*(3*a^3 + 10*a^2*b + 7*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 24*(b^2*cosh(d*x + c)^3 + 3*b^2*cosh(d*x + c)^2*sinh(d*x + c) + 3*b^2*cosh(d*x + c)*sinh(d*x + c)^2 + b^2*sinh(d*x + c)^3)*sqrt(a^2 + a*b)*arctan(1/2*((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 + (3*a - b)*cosh(d*x + c) + (3*(a + b)*cosh(d*x + c)^2 + 3*a - b)*sinh(d*x + c))/sqrt(a^2 + a*b)) + 24*(b^2*cosh(d*x + c)^3 + 3*b^2*cosh(d*x + c)^2*sinh(d*x + c) + 3*b^2*cosh(d*x + c)*sinh(d*x + c)^2 + b^2*sinh(d*x + c)^3)*sqrt(a^2 + a*b)*arctan(1/2*sqrt(a^2 + a*b)*(cosh(d*x + c) + sinh(d*x + c))/a) + 6*((a^3 + 2*a^2*b + a*b^2)*cosh(d*x + c)^5 + 2*(3*a^3 + 10*a^2*b + 7*a*b^2)*cosh(d*x + c)^3 - (3*a^3 + 10*a^2*b + 7*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)^3 + 3*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d*cosh(d*x + c)^2*sinh(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)^2 + (a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d*sinh(d*x + c)^3)]","B",0
107,1,948,0,0.446996," ","integrate(cosh(d*x+c)^2/(a+b*tanh(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{4 \, {\left(a + 3 \, b\right)} d x \cosh\left(d x + c\right)^{2} + {\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(2 \, {\left(a + 3 \, b\right)} d x + 3 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 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}\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{{\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) \sinh\left(d x + c\right)^{3} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{2} + a^{2} - 6 \, a b + b^{2} + 4 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + 4 \, {\left({\left(a^{2} + a b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} + a b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} + a b\right)} \sinh\left(d x + c\right)^{2} + a^{2} - a b\right)} \sqrt{-\frac{b}{a}}}{{\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) + 4 \, {\left(2 \, {\left(a + 3 \, b\right)} d x \cosh\left(d x + c\right) + {\left(a + b\right)} \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right) - a - b}{8 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} + 2 \, a b + b^{2}\right)} d \sinh\left(d x + c\right)^{2}\right)}}, \frac{4 \, {\left(a + 3 \, b\right)} d x \cosh\left(d x + c\right)^{2} + {\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(2 \, {\left(a + 3 \, b\right)} d x + 3 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\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}\right)} \sqrt{\frac{b}{a}} \arctan\left(\frac{{\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} + a - b\right)} \sqrt{\frac{b}{a}}}{2 \, b}\right) + 4 \, {\left(2 \, {\left(a + 3 \, b\right)} d x \cosh\left(d x + c\right) + {\left(a + b\right)} \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right) - a - b}{8 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} + 2 \, a b + b^{2}\right)} d \sinh\left(d x + c\right)^{2}\right)}}\right]"," ",0,"[1/8*(4*(a + 3*b)*d*x*cosh(d*x + c)^2 + (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 + 3*b)*d*x + 3*(a + b)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2)*sqrt(-b/a)*log(((a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 + 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 + 2*(a^2 - b^2)*cosh(d*x + c)^2 + 2*(3*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + a^2 - b^2)*sinh(d*x + c)^2 + a^2 - 6*a*b + b^2 + 4*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 + (a^2 - b^2)*cosh(d*x + c))*sinh(d*x + c) + 4*((a^2 + a*b)*cosh(d*x + c)^2 + 2*(a^2 + a*b)*cosh(d*x + c)*sinh(d*x + c) + (a^2 + a*b)*sinh(d*x + c)^2 + a^2 - a*b)*sqrt(-b/a))/((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)) + 4*(2*(a + 3*b)*d*x*cosh(d*x + c) + (a + b)*cosh(d*x + c)^3)*sinh(d*x + c) - a - b)/((a^2 + 2*a*b + b^2)*d*cosh(d*x + c)^2 + 2*(a^2 + 2*a*b + b^2)*d*cosh(d*x + c)*sinh(d*x + c) + (a^2 + 2*a*b + b^2)*d*sinh(d*x + c)^2), 1/8*(4*(a + 3*b)*d*x*cosh(d*x + c)^2 + (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 + 3*b)*d*x + 3*(a + b)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*(b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2)*sqrt(b/a)*arctan(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 + a - b)*sqrt(b/a)/b) + 4*(2*(a + 3*b)*d*x*cosh(d*x + c) + (a + b)*cosh(d*x + c)^3)*sinh(d*x + c) - a - b)/((a^2 + 2*a*b + b^2)*d*cosh(d*x + c)^2 + 2*(a^2 + 2*a*b + b^2)*d*cosh(d*x + c)*sinh(d*x + c) + (a^2 + 2*a*b + b^2)*d*sinh(d*x + c)^2)]","B",0
108,1,766,0,0.451185," ","integrate(cosh(d*x+c)/(a+b*tanh(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{{\left(a^{2} + a b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} + a b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} + a b\right)} \sinh\left(d x + c\right)^{2} - \sqrt{-a^{2} - a b} {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \log\left(\frac{{\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(3 \, a + b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} - 3 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(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) - 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^{2} - a b} + a + b}{{\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) - a^{2} - a b}{2 \, {\left({\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} d \cosh\left(d x + c\right) + {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} d \sinh\left(d x + c\right)\right)}}, \frac{{\left(a^{2} + a b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} + a b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} + a b\right)} \sinh\left(d x + c\right)^{2} + 2 \, \sqrt{a^{2} + a b} {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \arctan\left(\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(3 \, a - b\right)} \cosh\left(d x + c\right) + {\left(3 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} + 3 \, a - b\right)} \sinh\left(d x + c\right)}{2 \, \sqrt{a^{2} + a b}}\right) + 2 \, \sqrt{a^{2} + a b} {\left(b \cosh\left(d x + c\right) + b \sinh\left(d x + c\right)\right)} \arctan\left(\frac{\sqrt{a^{2} + a b} {\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right)}}{2 \, a}\right) - a^{2} - a b}{2 \, {\left({\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} d \cosh\left(d x + c\right) + {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} d \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[1/2*((a^2 + a*b)*cosh(d*x + c)^2 + 2*(a^2 + a*b)*cosh(d*x + c)*sinh(d*x + c) + (a^2 + a*b)*sinh(d*x + c)^2 - sqrt(-a^2 - a*b)*(b*cosh(d*x + c) + b*sinh(d*x + c))*log(((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*(3*a + b)*cosh(d*x + c)^2 + 2*(3*(a + b)*cosh(d*x + c)^2 - 3*a - b)*sinh(d*x + c)^2 + 4*((a + b)*cosh(d*x + c)^3 - (3*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^2 - a*b) + a + b)/((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)) - a^2 - a*b)/((a^3 + 2*a^2*b + a*b^2)*d*cosh(d*x + c) + (a^3 + 2*a^2*b + a*b^2)*d*sinh(d*x + c)), 1/2*((a^2 + a*b)*cosh(d*x + c)^2 + 2*(a^2 + a*b)*cosh(d*x + c)*sinh(d*x + c) + (a^2 + a*b)*sinh(d*x + c)^2 + 2*sqrt(a^2 + a*b)*(b*cosh(d*x + c) + b*sinh(d*x + c))*arctan(1/2*((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 + (3*a - b)*cosh(d*x + c) + (3*(a + b)*cosh(d*x + c)^2 + 3*a - b)*sinh(d*x + c))/sqrt(a^2 + a*b)) + 2*sqrt(a^2 + a*b)*(b*cosh(d*x + c) + b*sinh(d*x + c))*arctan(1/2*sqrt(a^2 + a*b)*(cosh(d*x + c) + sinh(d*x + c))/a) - a^2 - a*b)/((a^3 + 2*a^2*b + a*b^2)*d*cosh(d*x + c) + (a^3 + 2*a^2*b + a*b^2)*d*sinh(d*x + c))]","B",0
109,1,511,0,0.423097," ","integrate(sech(d*x+c)/(a+b*tanh(d*x+c)^2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-a^{2} - a b} \log\left(\frac{{\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(3 \, a + b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} - 3 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(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) - 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^{2} - a b} + a + b}{{\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)}{2 \, {\left(a^{2} + a b\right)} d}, \frac{\sqrt{a^{2} + a b} \arctan\left(\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(3 \, a - b\right)} \cosh\left(d x + c\right) + {\left(3 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} + 3 \, a - b\right)} \sinh\left(d x + c\right)}{2 \, \sqrt{a^{2} + a b}}\right) + \sqrt{a^{2} + a b} \arctan\left(\frac{\sqrt{a^{2} + a b} {\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right)}}{2 \, a}\right)}{{\left(a^{2} + a b\right)} d}\right]"," ",0,"[-1/2*sqrt(-a^2 - a*b)*log(((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*(3*a + b)*cosh(d*x + c)^2 + 2*(3*(a + b)*cosh(d*x + c)^2 - 3*a - b)*sinh(d*x + c)^2 + 4*((a + b)*cosh(d*x + c)^3 - (3*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^2 - a*b) + a + b)/((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))/((a^2 + a*b)*d), (sqrt(a^2 + a*b)*arctan(1/2*((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 + (3*a - b)*cosh(d*x + c) + (3*(a + b)*cosh(d*x + c)^2 + 3*a - b)*sinh(d*x + c))/sqrt(a^2 + a*b)) + sqrt(a^2 + a*b)*arctan(1/2*sqrt(a^2 + a*b)*(cosh(d*x + c) + sinh(d*x + c))/a))/((a^2 + a*b)*d)]","B",0
110,1,455,0,0.455008," ","integrate(sech(d*x+c)^2/(a+b*tanh(d*x+c)^2),x, algorithm=""fricas"")","\left[-\frac{\sqrt{-a b} \log\left(\frac{{\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) \sinh\left(d x + c\right)^{3} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{2} + a^{2} - 6 \, a b + b^{2} + 4 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} - b^{2}\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)^{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} + a - b\right)} \sqrt{-a b}}{{\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)}{2 \, a b d}, \frac{\sqrt{a b} \arctan\left(\frac{{\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} + a - b\right)} \sqrt{a b}}{2 \, a b}\right)}{a b d}\right]"," ",0,"[-1/2*sqrt(-a*b)*log(((a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 + 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 + 2*(a^2 - b^2)*cosh(d*x + c)^2 + 2*(3*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + a^2 - b^2)*sinh(d*x + c)^2 + a^2 - 6*a*b + b^2 + 4*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 + (a^2 - 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 + a - b)*sqrt(-a*b))/((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))/(a*b*d), sqrt(a*b)*arctan(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 + a - b)*sqrt(a*b)/(a*b))/(a*b*d)]","B",0
111,1,540,0,0.448253," ","integrate(sech(d*x+c)^3/(a+b*tanh(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{\sqrt{-\frac{a + b}{a}} \log\left(\frac{{\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(3 \, a + b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} - 3 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(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) + 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{a + b}{a}} + a + b}{{\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) - 4 \, \arctan\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right)}{2 \, b d}, \frac{\sqrt{\frac{a + b}{a}} \arctan\left(\frac{1}{2} \, \sqrt{\frac{a + b}{a}} {\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right)}\right) + \sqrt{\frac{a + b}{a}} \arctan\left(\frac{{\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(3 \, a - b\right)} \cosh\left(d x + c\right) + {\left(3 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} + 3 \, a - b\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a + b}{a}}}{2 \, {\left(a + b\right)}}\right) - 2 \, \arctan\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right)}{b d}\right]"," ",0,"[1/2*(sqrt(-(a + b)/a)*log(((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*(3*a + b)*cosh(d*x + c)^2 + 2*(3*(a + b)*cosh(d*x + c)^2 - 3*a - b)*sinh(d*x + c)^2 + 4*((a + b)*cosh(d*x + c)^3 - (3*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(-(a + b)/a) + a + b)/((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)) - 4*arctan(cosh(d*x + c) + sinh(d*x + c)))/(b*d), (sqrt((a + b)/a)*arctan(1/2*sqrt((a + b)/a)*(cosh(d*x + c) + sinh(d*x + c))) + sqrt((a + b)/a)*arctan(1/2*((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 + (3*a - b)*cosh(d*x + c) + (3*(a + b)*cosh(d*x + c)^2 + 3*a - b)*sinh(d*x + c))*sqrt((a + b)/a)/(a + b)) - 2*arctan(cosh(d*x + c) + sinh(d*x + c)))/(b*d)]","B",0
112,1,649,0,0.439711," ","integrate(sech(d*x+c)^4/(a+b*tanh(d*x+c)^2),x, algorithm=""fricas"")","\left[-\frac{{\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} + a + b\right)} \sqrt{-a b} \log\left(\frac{{\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) \sinh\left(d x + c\right)^{3} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{2} + a^{2} - 6 \, a b + b^{2} + 4 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} - b^{2}\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)^{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} + a - b\right)} \sqrt{-a b}}{{\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) - 4 \, a b}{2 \, {\left(a b^{2} d \cosh\left(d x + c\right)^{2} + 2 \, a b^{2} d \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a b^{2} d \sinh\left(d x + c\right)^{2} + a b^{2} d\right)}}, \frac{{\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} + a + b\right)} \sqrt{a b} \arctan\left(\frac{{\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} + a - b\right)} \sqrt{a b}}{2 \, a b}\right) + 2 \, a b}{a b^{2} d \cosh\left(d x + c\right)^{2} + 2 \, a b^{2} d \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a b^{2} d \sinh\left(d x + c\right)^{2} + a b^{2} d}\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 + a + b)*sqrt(-a*b)*log(((a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 + 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 + 2*(a^2 - b^2)*cosh(d*x + c)^2 + 2*(3*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + a^2 - b^2)*sinh(d*x + c)^2 + a^2 - 6*a*b + b^2 + 4*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 + (a^2 - 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 + a - b)*sqrt(-a*b))/((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)) - 4*a*b)/(a*b^2*d*cosh(d*x + c)^2 + 2*a*b^2*d*cosh(d*x + c)*sinh(d*x + c) + a*b^2*d*sinh(d*x + c)^2 + a*b^2*d), (((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 + a + b)*sqrt(a*b)*arctan(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 + a - b)*sqrt(a*b)/(a*b)) + 2*a*b)/(a*b^2*d*cosh(d*x + c)^2 + 2*a*b^2*d*cosh(d*x + c)*sinh(d*x + c) + a*b^2*d*sinh(d*x + c)^2 + a*b^2*d)]","B",0
113,1,1584,0,0.471416," ","integrate(sech(d*x+c)^5/(a+b*tanh(d*x+c)^2),x, algorithm=""fricas"")","\left[-\frac{2 \, b \cosh\left(d x + c\right)^{3} + 6 \, b \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + 2 \, b \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)} \sqrt{-\frac{a + b}{a}} \log\left(\frac{{\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(3 \, a + b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} - 3 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(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) + 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{a + b}{a}} + a + b}{{\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) + 2 \, {\left({\left(2 \, a + 3 \, b\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(2 \, a + 3 \, b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(2 \, a + 3 \, b\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a + 3 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(2 \, a + 3 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, a + 3 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(2 \, 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) + 2 \, a + 3 \, b\right)} \arctan\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) - 2 \, b \cosh\left(d x + c\right) + 2 \, {\left(3 \, b \cosh\left(d x + c\right)^{2} - b\right)} \sinh\left(d x + c\right)}{2 \, {\left(b^{2} d \cosh\left(d x + c\right)^{4} + 4 \, b^{2} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{2} d \sinh\left(d x + c\right)^{4} + 2 \, b^{2} d \cosh\left(d x + c\right)^{2} + b^{2} d + 2 \, {\left(3 \, b^{2} d \cosh\left(d x + c\right)^{2} + b^{2} d\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b^{2} d \cosh\left(d x + c\right)^{3} + b^{2} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}, -\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({\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)} \sqrt{\frac{a + b}{a}} \arctan\left(\frac{1}{2} \, \sqrt{\frac{a + b}{a}} {\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right)}\right) - {\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)} \sqrt{\frac{a + b}{a}} \arctan\left(\frac{{\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(3 \, a - b\right)} \cosh\left(d x + c\right) + {\left(3 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} + 3 \, a - b\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a + b}{a}}}{2 \, {\left(a + b\right)}}\right) + {\left({\left(2 \, a + 3 \, b\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(2 \, a + 3 \, b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(2 \, a + 3 \, b\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(2 \, a + 3 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(2 \, a + 3 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, a + 3 \, b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(2 \, 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) + 2 \, a + 3 \, b\right)} \arctan\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right) - b \cosh\left(d x + c\right) + {\left(3 \, b \cosh\left(d x + c\right)^{2} - b\right)} \sinh\left(d x + c\right)}{b^{2} d \cosh\left(d x + c\right)^{4} + 4 \, b^{2} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + b^{2} d \sinh\left(d x + c\right)^{4} + 2 \, b^{2} d \cosh\left(d x + c\right)^{2} + b^{2} d + 2 \, {\left(3 \, b^{2} d \cosh\left(d x + c\right)^{2} + b^{2} d\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(b^{2} d \cosh\left(d x + c\right)^{3} + b^{2} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}\right]"," ",0,"[-1/2*(2*b*cosh(d*x + c)^3 + 6*b*cosh(d*x + c)*sinh(d*x + c)^2 + 2*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)*sqrt(-(a + b)/a)*log(((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*(3*a + b)*cosh(d*x + c)^2 + 2*(3*(a + b)*cosh(d*x + c)^2 - 3*a - b)*sinh(d*x + c)^2 + 4*((a + b)*cosh(d*x + c)^3 - (3*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(-(a + b)/a) + a + b)/((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)) + 2*((2*a + 3*b)*cosh(d*x + c)^4 + 4*(2*a + 3*b)*cosh(d*x + c)*sinh(d*x + c)^3 + (2*a + 3*b)*sinh(d*x + c)^4 + 2*(2*a + 3*b)*cosh(d*x + c)^2 + 2*(3*(2*a + 3*b)*cosh(d*x + c)^2 + 2*a + 3*b)*sinh(d*x + c)^2 + 4*((2*a + 3*b)*cosh(d*x + c)^3 + (2*a + 3*b)*cosh(d*x + c))*sinh(d*x + c) + 2*a + 3*b)*arctan(cosh(d*x + c) + sinh(d*x + c)) - 2*b*cosh(d*x + c) + 2*(3*b*cosh(d*x + c)^2 - b)*sinh(d*x + c))/(b^2*d*cosh(d*x + c)^4 + 4*b^2*d*cosh(d*x + c)*sinh(d*x + c)^3 + b^2*d*sinh(d*x + c)^4 + 2*b^2*d*cosh(d*x + c)^2 + b^2*d + 2*(3*b^2*d*cosh(d*x + c)^2 + b^2*d)*sinh(d*x + c)^2 + 4*(b^2*d*cosh(d*x + c)^3 + b^2*d*cosh(d*x + c))*sinh(d*x + c)), -(b*cosh(d*x + c)^3 + 3*b*cosh(d*x + c)*sinh(d*x + c)^2 + 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)*sqrt((a + b)/a)*arctan(1/2*sqrt((a + b)/a)*(cosh(d*x + c) + sinh(d*x + c))) - ((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)*sqrt((a + b)/a)*arctan(1/2*((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 + (3*a - b)*cosh(d*x + c) + (3*(a + b)*cosh(d*x + c)^2 + 3*a - b)*sinh(d*x + c))*sqrt((a + b)/a)/(a + b)) + ((2*a + 3*b)*cosh(d*x + c)^4 + 4*(2*a + 3*b)*cosh(d*x + c)*sinh(d*x + c)^3 + (2*a + 3*b)*sinh(d*x + c)^4 + 2*(2*a + 3*b)*cosh(d*x + c)^2 + 2*(3*(2*a + 3*b)*cosh(d*x + c)^2 + 2*a + 3*b)*sinh(d*x + c)^2 + 4*((2*a + 3*b)*cosh(d*x + c)^3 + (2*a + 3*b)*cosh(d*x + c))*sinh(d*x + c) + 2*a + 3*b)*arctan(cosh(d*x + c) + sinh(d*x + c)) - b*cosh(d*x + c) + (3*b*cosh(d*x + c)^2 - b)*sinh(d*x + c))/(b^2*d*cosh(d*x + c)^4 + 4*b^2*d*cosh(d*x + c)*sinh(d*x + c)^3 + b^2*d*sinh(d*x + c)^4 + 2*b^2*d*cosh(d*x + c)^2 + b^2*d + 2*(3*b^2*d*cosh(d*x + c)^2 + b^2*d)*sinh(d*x + c)^2 + 4*(b^2*d*cosh(d*x + c)^3 + b^2*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
114,1,2032,0,0.482491," ","integrate(sech(d*x+c)^6/(a+b*tanh(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} + 12 \, a^{2} b + 20 \, a b^{2} + 24 \, {\left(a^{2} b + 2 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2} + 24 \, {\left(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({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{6} + 6 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{6} + 3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(5 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, {\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)\right)} \sinh\left(d x + c\right)^{3} + 3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 3 \, {\left(5 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + 6 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 2 \, a b + b^{2} + 6 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} + 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{{\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) \sinh\left(d x + c\right)^{3} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{2} + a^{2} - 6 \, a b + b^{2} + 4 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} - b^{2}\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)^{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} + a - b\right)} \sqrt{-a b}}{{\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) + 48 \, {\left({\left(a^{2} b + a b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} b + 2 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{6 \, {\left(a b^{3} d \cosh\left(d x + c\right)^{6} + 6 \, a b^{3} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + a b^{3} d \sinh\left(d x + c\right)^{6} + 3 \, a b^{3} d \cosh\left(d x + c\right)^{4} + 3 \, a b^{3} d \cosh\left(d x + c\right)^{2} + a b^{3} d + 3 \, {\left(5 \, a b^{3} d \cosh\left(d x + c\right)^{2} + a b^{3} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, a b^{3} d \cosh\left(d x + c\right)^{3} + 3 \, a b^{3} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 3 \, {\left(5 \, a b^{3} d \cosh\left(d x + c\right)^{4} + 6 \, a b^{3} d \cosh\left(d x + c\right)^{2} + a b^{3} d\right)} \sinh\left(d x + c\right)^{2} + 6 \, {\left(a b^{3} d \cosh\left(d x + c\right)^{5} + 2 \, a b^{3} d \cosh\left(d x + c\right)^{3} + a b^{3} 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} + 6 \, a^{2} b + 10 \, a b^{2} + 12 \, {\left(a^{2} b + 2 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2} + 12 \, {\left(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({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{6} + 6 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{6} + 3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(5 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, {\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)\right)} \sinh\left(d x + c\right)^{3} + 3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 3 \, {\left(5 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + 6 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 2 \, a b + b^{2} + 6 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} + 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({\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} + a - b\right)} \sqrt{a b}}{2 \, a b}\right) + 24 \, {\left({\left(a^{2} b + a b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} b + 2 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{3 \, {\left(a b^{3} d \cosh\left(d x + c\right)^{6} + 6 \, a b^{3} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + a b^{3} d \sinh\left(d x + c\right)^{6} + 3 \, a b^{3} d \cosh\left(d x + c\right)^{4} + 3 \, a b^{3} d \cosh\left(d x + c\right)^{2} + a b^{3} d + 3 \, {\left(5 \, a b^{3} d \cosh\left(d x + c\right)^{2} + a b^{3} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(5 \, a b^{3} d \cosh\left(d x + c\right)^{3} + 3 \, a b^{3} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 3 \, {\left(5 \, a b^{3} d \cosh\left(d x + c\right)^{4} + 6 \, a b^{3} d \cosh\left(d x + c\right)^{2} + a b^{3} d\right)} \sinh\left(d x + c\right)^{2} + 6 \, {\left(a b^{3} d \cosh\left(d x + c\right)^{5} + 2 \, a b^{3} d \cosh\left(d x + c\right)^{3} + a b^{3} 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 + 12*a^2*b + 20*a*b^2 + 24*(a^2*b + 2*a*b^2)*cosh(d*x + c)^2 + 24*(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*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^6 + 6*(a^2 + 2*a*b + b^2)*cosh(d*x + c)*sinh(d*x + c)^5 + (a^2 + 2*a*b + b^2)*sinh(d*x + c)^6 + 3*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 + 3*(5*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + a^2 + 2*a*b + b^2)*sinh(d*x + c)^4 + 4*(5*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 + 3*(a^2 + 2*a*b + b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 3*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + 3*(5*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 + 6*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + a^2 + 2*a*b + b^2)*sinh(d*x + c)^2 + a^2 + 2*a*b + b^2 + 6*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^5 + 2*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 + (a^2 + 2*a*b + b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-a*b)*log(((a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 + 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 + 2*(a^2 - b^2)*cosh(d*x + c)^2 + 2*(3*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + a^2 - b^2)*sinh(d*x + c)^2 + a^2 - 6*a*b + b^2 + 4*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 + (a^2 - 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 + a - b)*sqrt(-a*b))/((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)) + 48*((a^2*b + a*b^2)*cosh(d*x + c)^3 + (a^2*b + 2*a*b^2)*cosh(d*x + c))*sinh(d*x + c))/(a*b^3*d*cosh(d*x + c)^6 + 6*a*b^3*d*cosh(d*x + c)*sinh(d*x + c)^5 + a*b^3*d*sinh(d*x + c)^6 + 3*a*b^3*d*cosh(d*x + c)^4 + 3*a*b^3*d*cosh(d*x + c)^2 + a*b^3*d + 3*(5*a*b^3*d*cosh(d*x + c)^2 + a*b^3*d)*sinh(d*x + c)^4 + 4*(5*a*b^3*d*cosh(d*x + c)^3 + 3*a*b^3*d*cosh(d*x + c))*sinh(d*x + c)^3 + 3*(5*a*b^3*d*cosh(d*x + c)^4 + 6*a*b^3*d*cosh(d*x + c)^2 + a*b^3*d)*sinh(d*x + c)^2 + 6*(a*b^3*d*cosh(d*x + c)^5 + 2*a*b^3*d*cosh(d*x + c)^3 + 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 + 6*a^2*b + 10*a*b^2 + 12*(a^2*b + 2*a*b^2)*cosh(d*x + c)^2 + 12*(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*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^6 + 6*(a^2 + 2*a*b + b^2)*cosh(d*x + c)*sinh(d*x + c)^5 + (a^2 + 2*a*b + b^2)*sinh(d*x + c)^6 + 3*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 + 3*(5*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + a^2 + 2*a*b + b^2)*sinh(d*x + c)^4 + 4*(5*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 + 3*(a^2 + 2*a*b + b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 3*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + 3*(5*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 + 6*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + a^2 + 2*a*b + b^2)*sinh(d*x + c)^2 + a^2 + 2*a*b + b^2 + 6*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^5 + 2*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 + (a^2 + 2*a*b + b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(a*b)*arctan(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 + a - b)*sqrt(a*b)/(a*b)) + 24*((a^2*b + a*b^2)*cosh(d*x + c)^3 + (a^2*b + 2*a*b^2)*cosh(d*x + c))*sinh(d*x + c))/(a*b^3*d*cosh(d*x + c)^6 + 6*a*b^3*d*cosh(d*x + c)*sinh(d*x + c)^5 + a*b^3*d*sinh(d*x + c)^6 + 3*a*b^3*d*cosh(d*x + c)^4 + 3*a*b^3*d*cosh(d*x + c)^2 + a*b^3*d + 3*(5*a*b^3*d*cosh(d*x + c)^2 + a*b^3*d)*sinh(d*x + c)^4 + 4*(5*a*b^3*d*cosh(d*x + c)^3 + 3*a*b^3*d*cosh(d*x + c))*sinh(d*x + c)^3 + 3*(5*a*b^3*d*cosh(d*x + c)^4 + 6*a*b^3*d*cosh(d*x + c)^2 + a*b^3*d)*sinh(d*x + c)^2 + 6*(a*b^3*d*cosh(d*x + c)^5 + 2*a*b^3*d*cosh(d*x + c)^3 + a*b^3*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
115,1,6934,0,0.563061," ","integrate(cosh(d*x+c)^3/(a+b*tanh(d*x+c)^2)^2,x, algorithm=""fricas"")","\left[\frac{{\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{10} + 10 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \sinh\left(d x + c\right)^{10} + {\left(11 \, a^{5} + 53 \, a^{4} b + 73 \, a^{3} b^{2} + 31 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{8} + {\left(11 \, a^{5} + 53 \, a^{4} b + 73 \, a^{3} b^{2} + 31 \, a^{2} b^{3} + 45 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{8} + 8 \, {\left(15 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(11 \, a^{5} + 53 \, a^{4} b + 73 \, a^{3} b^{2} + 31 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(5 \, a^{5} + 9 \, a^{4} b - 45 \, a^{3} b^{2} - 37 \, a^{2} b^{3} + 12 \, a b^{4}\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(5 \, a^{5} + 9 \, a^{4} b - 45 \, a^{3} b^{2} - 37 \, a^{2} b^{3} + 12 \, a b^{4} + 105 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{4} + 14 \, {\left(11 \, a^{5} + 53 \, a^{4} b + 73 \, a^{3} b^{2} + 31 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(63 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{5} + 14 \, {\left(11 \, a^{5} + 53 \, a^{4} b + 73 \, a^{3} b^{2} + 31 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(5 \, a^{5} + 9 \, a^{4} b - 45 \, a^{3} b^{2} - 37 \, a^{2} b^{3} + 12 \, a b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - a^{5} - 3 \, a^{4} b - 3 \, a^{3} b^{2} - a^{2} b^{3} - 2 \, {\left(5 \, a^{5} + 9 \, a^{4} b - 45 \, a^{3} b^{2} - 37 \, a^{2} b^{3} + 12 \, a b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(105 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{6} - 5 \, a^{5} - 9 \, a^{4} b + 45 \, a^{3} b^{2} + 37 \, a^{2} b^{3} - 12 \, a b^{4} + 35 \, {\left(11 \, a^{5} + 53 \, a^{4} b + 73 \, a^{3} b^{2} + 31 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{4} + 15 \, {\left(5 \, a^{5} + 9 \, a^{4} b - 45 \, a^{3} b^{2} - 37 \, a^{2} b^{3} + 12 \, a b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(15 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{7} + 7 \, {\left(11 \, a^{5} + 53 \, a^{4} b + 73 \, a^{3} b^{2} + 31 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(5 \, a^{5} + 9 \, a^{4} b - 45 \, a^{3} b^{2} - 37 \, a^{2} b^{3} + 12 \, a b^{4}\right)} \cosh\left(d x + c\right)^{3} - {\left(5 \, a^{5} + 9 \, a^{4} b - 45 \, a^{3} b^{2} - 37 \, a^{2} b^{3} + 12 \, a b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - {\left(11 \, a^{5} + 53 \, a^{4} b + 73 \, a^{3} b^{2} + 31 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{2} + {\left(45 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{8} + 28 \, {\left(11 \, a^{5} + 53 \, a^{4} b + 73 \, a^{3} b^{2} + 31 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{6} - 11 \, a^{5} - 53 \, a^{4} b - 73 \, a^{3} b^{2} - 31 \, a^{2} b^{3} + 30 \, {\left(5 \, a^{5} + 9 \, a^{4} b - 45 \, a^{3} b^{2} - 37 \, a^{2} b^{3} + 12 \, a b^{4}\right)} \cosh\left(d x + c\right)^{4} - 12 \, {\left(5 \, a^{5} + 9 \, a^{4} b - 45 \, a^{3} b^{2} - 37 \, a^{2} b^{3} + 12 \, a b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} - 6 \, {\left({\left(6 \, a^{2} b^{2} + 7 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{7} + 7 \, {\left(6 \, a^{2} b^{2} + 7 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + {\left(6 \, a^{2} b^{2} + 7 \, a b^{3} + b^{4}\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(6 \, a^{2} b^{2} - 5 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{5} + {\left(12 \, a^{2} b^{2} - 10 \, a b^{3} - 2 \, b^{4} + 21 \, {\left(6 \, a^{2} b^{2} + 7 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{5} + 5 \, {\left(7 \, {\left(6 \, a^{2} b^{2} + 7 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(6 \, a^{2} b^{2} - 5 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + {\left(6 \, a^{2} b^{2} + 7 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(35 \, {\left(6 \, a^{2} b^{2} + 7 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{4} + 6 \, a^{2} b^{2} + 7 \, a b^{3} + b^{4} + 20 \, {\left(6 \, a^{2} b^{2} - 5 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + {\left(21 \, {\left(6 \, a^{2} b^{2} + 7 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{5} + 20 \, {\left(6 \, a^{2} b^{2} - 5 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(6 \, a^{2} b^{2} + 7 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(7 \, {\left(6 \, a^{2} b^{2} + 7 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{6} + 10 \, {\left(6 \, a^{2} b^{2} - 5 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(6 \, a^{2} b^{2} + 7 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)\right)} \sqrt{-a^{2} - a b} \log\left(\frac{{\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(3 \, a + b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} - 3 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(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) - 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^{2} - a b} + a + b}{{\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) + 2 \, {\left(5 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{9} + 4 \, {\left(11 \, a^{5} + 53 \, a^{4} b + 73 \, a^{3} b^{2} + 31 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{7} + 6 \, {\left(5 \, a^{5} + 9 \, a^{4} b - 45 \, a^{3} b^{2} - 37 \, a^{2} b^{3} + 12 \, a b^{4}\right)} \cosh\left(d x + c\right)^{5} - 4 \, {\left(5 \, a^{5} + 9 \, a^{4} b - 45 \, a^{3} b^{2} - 37 \, a^{2} b^{3} + 12 \, a b^{4}\right)} \cosh\left(d x + c\right)^{3} - {\left(11 \, a^{5} + 53 \, a^{4} b + 73 \, a^{3} b^{2} + 31 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{24 \, {\left({\left(a^{7} + 5 \, a^{6} b + 10 \, a^{5} b^{2} + 10 \, a^{4} b^{3} + 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{7} + 7 \, {\left(a^{7} + 5 \, a^{6} b + 10 \, a^{5} b^{2} + 10 \, a^{4} b^{3} + 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + {\left(a^{7} + 5 \, a^{6} b + 10 \, a^{5} b^{2} + 10 \, a^{4} b^{3} + 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \sinh\left(d x + c\right)^{7} + 2 \, {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2} - 2 \, a^{4} b^{3} - 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{5} + {\left(21 \, {\left(a^{7} + 5 \, a^{6} b + 10 \, a^{5} b^{2} + 10 \, a^{4} b^{3} + 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2} - 2 \, a^{4} b^{3} - 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{5} + {\left(a^{7} + 5 \, a^{6} b + 10 \, a^{5} b^{2} + 10 \, a^{4} b^{3} + 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + 5 \, {\left(7 \, {\left(a^{7} + 5 \, a^{6} b + 10 \, a^{5} b^{2} + 10 \, a^{4} b^{3} + 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + 2 \, {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2} - 2 \, a^{4} b^{3} - 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + {\left(35 \, {\left(a^{7} + 5 \, a^{6} b + 10 \, a^{5} b^{2} + 10 \, a^{4} b^{3} + 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 20 \, {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2} - 2 \, a^{4} b^{3} - 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{7} + 5 \, a^{6} b + 10 \, a^{5} b^{2} + 10 \, a^{4} b^{3} + 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{3} + {\left(21 \, {\left(a^{7} + 5 \, a^{6} b + 10 \, a^{5} b^{2} + 10 \, a^{4} b^{3} + 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{5} + 20 \, {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2} - 2 \, a^{4} b^{3} - 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{7} + 5 \, a^{6} b + 10 \, a^{5} b^{2} + 10 \, a^{4} b^{3} + 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(7 \, {\left(a^{7} + 5 \, a^{6} b + 10 \, a^{5} b^{2} + 10 \, a^{4} b^{3} + 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{6} + 10 \, {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2} - 2 \, a^{4} b^{3} - 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(a^{7} + 5 \, a^{6} b + 10 \, a^{5} b^{2} + 10 \, a^{4} b^{3} + 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)\right)}}, \frac{{\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{10} + 10 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \sinh\left(d x + c\right)^{10} + {\left(11 \, a^{5} + 53 \, a^{4} b + 73 \, a^{3} b^{2} + 31 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{8} + {\left(11 \, a^{5} + 53 \, a^{4} b + 73 \, a^{3} b^{2} + 31 \, a^{2} b^{3} + 45 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{8} + 8 \, {\left(15 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(11 \, a^{5} + 53 \, a^{4} b + 73 \, a^{3} b^{2} + 31 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(5 \, a^{5} + 9 \, a^{4} b - 45 \, a^{3} b^{2} - 37 \, a^{2} b^{3} + 12 \, a b^{4}\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(5 \, a^{5} + 9 \, a^{4} b - 45 \, a^{3} b^{2} - 37 \, a^{2} b^{3} + 12 \, a b^{4} + 105 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{4} + 14 \, {\left(11 \, a^{5} + 53 \, a^{4} b + 73 \, a^{3} b^{2} + 31 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(63 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{5} + 14 \, {\left(11 \, a^{5} + 53 \, a^{4} b + 73 \, a^{3} b^{2} + 31 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(5 \, a^{5} + 9 \, a^{4} b - 45 \, a^{3} b^{2} - 37 \, a^{2} b^{3} + 12 \, a b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - a^{5} - 3 \, a^{4} b - 3 \, a^{3} b^{2} - a^{2} b^{3} - 2 \, {\left(5 \, a^{5} + 9 \, a^{4} b - 45 \, a^{3} b^{2} - 37 \, a^{2} b^{3} + 12 \, a b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(105 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{6} - 5 \, a^{5} - 9 \, a^{4} b + 45 \, a^{3} b^{2} + 37 \, a^{2} b^{3} - 12 \, a b^{4} + 35 \, {\left(11 \, a^{5} + 53 \, a^{4} b + 73 \, a^{3} b^{2} + 31 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{4} + 15 \, {\left(5 \, a^{5} + 9 \, a^{4} b - 45 \, a^{3} b^{2} - 37 \, a^{2} b^{3} + 12 \, a b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(15 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{7} + 7 \, {\left(11 \, a^{5} + 53 \, a^{4} b + 73 \, a^{3} b^{2} + 31 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(5 \, a^{5} + 9 \, a^{4} b - 45 \, a^{3} b^{2} - 37 \, a^{2} b^{3} + 12 \, a b^{4}\right)} \cosh\left(d x + c\right)^{3} - {\left(5 \, a^{5} + 9 \, a^{4} b - 45 \, a^{3} b^{2} - 37 \, a^{2} b^{3} + 12 \, a b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - {\left(11 \, a^{5} + 53 \, a^{4} b + 73 \, a^{3} b^{2} + 31 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{2} + {\left(45 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{8} + 28 \, {\left(11 \, a^{5} + 53 \, a^{4} b + 73 \, a^{3} b^{2} + 31 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{6} - 11 \, a^{5} - 53 \, a^{4} b - 73 \, a^{3} b^{2} - 31 \, a^{2} b^{3} + 30 \, {\left(5 \, a^{5} + 9 \, a^{4} b - 45 \, a^{3} b^{2} - 37 \, a^{2} b^{3} + 12 \, a b^{4}\right)} \cosh\left(d x + c\right)^{4} - 12 \, {\left(5 \, a^{5} + 9 \, a^{4} b - 45 \, a^{3} b^{2} - 37 \, a^{2} b^{3} + 12 \, a b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 12 \, {\left({\left(6 \, a^{2} b^{2} + 7 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{7} + 7 \, {\left(6 \, a^{2} b^{2} + 7 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + {\left(6 \, a^{2} b^{2} + 7 \, a b^{3} + b^{4}\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(6 \, a^{2} b^{2} - 5 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{5} + {\left(12 \, a^{2} b^{2} - 10 \, a b^{3} - 2 \, b^{4} + 21 \, {\left(6 \, a^{2} b^{2} + 7 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{5} + 5 \, {\left(7 \, {\left(6 \, a^{2} b^{2} + 7 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(6 \, a^{2} b^{2} - 5 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + {\left(6 \, a^{2} b^{2} + 7 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(35 \, {\left(6 \, a^{2} b^{2} + 7 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{4} + 6 \, a^{2} b^{2} + 7 \, a b^{3} + b^{4} + 20 \, {\left(6 \, a^{2} b^{2} - 5 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + {\left(21 \, {\left(6 \, a^{2} b^{2} + 7 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{5} + 20 \, {\left(6 \, a^{2} b^{2} - 5 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(6 \, a^{2} b^{2} + 7 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(7 \, {\left(6 \, a^{2} b^{2} + 7 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{6} + 10 \, {\left(6 \, a^{2} b^{2} - 5 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(6 \, a^{2} b^{2} + 7 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)\right)} \sqrt{a^{2} + a b} \arctan\left(\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(3 \, a - b\right)} \cosh\left(d x + c\right) + {\left(3 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} + 3 \, a - b\right)} \sinh\left(d x + c\right)}{2 \, \sqrt{a^{2} + a b}}\right) + 12 \, {\left({\left(6 \, a^{2} b^{2} + 7 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{7} + 7 \, {\left(6 \, a^{2} b^{2} + 7 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + {\left(6 \, a^{2} b^{2} + 7 \, a b^{3} + b^{4}\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(6 \, a^{2} b^{2} - 5 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{5} + {\left(12 \, a^{2} b^{2} - 10 \, a b^{3} - 2 \, b^{4} + 21 \, {\left(6 \, a^{2} b^{2} + 7 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{5} + 5 \, {\left(7 \, {\left(6 \, a^{2} b^{2} + 7 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(6 \, a^{2} b^{2} - 5 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + {\left(6 \, a^{2} b^{2} + 7 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(35 \, {\left(6 \, a^{2} b^{2} + 7 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{4} + 6 \, a^{2} b^{2} + 7 \, a b^{3} + b^{4} + 20 \, {\left(6 \, a^{2} b^{2} - 5 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + {\left(21 \, {\left(6 \, a^{2} b^{2} + 7 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{5} + 20 \, {\left(6 \, a^{2} b^{2} - 5 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(6 \, a^{2} b^{2} + 7 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(7 \, {\left(6 \, a^{2} b^{2} + 7 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{6} + 10 \, {\left(6 \, a^{2} b^{2} - 5 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(6 \, a^{2} b^{2} + 7 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)\right)} \sqrt{a^{2} + a b} \arctan\left(\frac{\sqrt{a^{2} + a b} {\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right)}}{2 \, a}\right) + 2 \, {\left(5 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{9} + 4 \, {\left(11 \, a^{5} + 53 \, a^{4} b + 73 \, a^{3} b^{2} + 31 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{7} + 6 \, {\left(5 \, a^{5} + 9 \, a^{4} b - 45 \, a^{3} b^{2} - 37 \, a^{2} b^{3} + 12 \, a b^{4}\right)} \cosh\left(d x + c\right)^{5} - 4 \, {\left(5 \, a^{5} + 9 \, a^{4} b - 45 \, a^{3} b^{2} - 37 \, a^{2} b^{3} + 12 \, a b^{4}\right)} \cosh\left(d x + c\right)^{3} - {\left(11 \, a^{5} + 53 \, a^{4} b + 73 \, a^{3} b^{2} + 31 \, a^{2} b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{24 \, {\left({\left(a^{7} + 5 \, a^{6} b + 10 \, a^{5} b^{2} + 10 \, a^{4} b^{3} + 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{7} + 7 \, {\left(a^{7} + 5 \, a^{6} b + 10 \, a^{5} b^{2} + 10 \, a^{4} b^{3} + 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + {\left(a^{7} + 5 \, a^{6} b + 10 \, a^{5} b^{2} + 10 \, a^{4} b^{3} + 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \sinh\left(d x + c\right)^{7} + 2 \, {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2} - 2 \, a^{4} b^{3} - 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{5} + {\left(21 \, {\left(a^{7} + 5 \, a^{6} b + 10 \, a^{5} b^{2} + 10 \, a^{4} b^{3} + 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2} - 2 \, a^{4} b^{3} - 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{5} + {\left(a^{7} + 5 \, a^{6} b + 10 \, a^{5} b^{2} + 10 \, a^{4} b^{3} + 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + 5 \, {\left(7 \, {\left(a^{7} + 5 \, a^{6} b + 10 \, a^{5} b^{2} + 10 \, a^{4} b^{3} + 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + 2 \, {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2} - 2 \, a^{4} b^{3} - 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + {\left(35 \, {\left(a^{7} + 5 \, a^{6} b + 10 \, a^{5} b^{2} + 10 \, a^{4} b^{3} + 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 20 \, {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2} - 2 \, a^{4} b^{3} - 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{7} + 5 \, a^{6} b + 10 \, a^{5} b^{2} + 10 \, a^{4} b^{3} + 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{3} + {\left(21 \, {\left(a^{7} + 5 \, a^{6} b + 10 \, a^{5} b^{2} + 10 \, a^{4} b^{3} + 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{5} + 20 \, {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2} - 2 \, a^{4} b^{3} - 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{7} + 5 \, a^{6} b + 10 \, a^{5} b^{2} + 10 \, a^{4} b^{3} + 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(7 \, {\left(a^{7} + 5 \, a^{6} b + 10 \, a^{5} b^{2} + 10 \, a^{4} b^{3} + 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{6} + 10 \, {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2} - 2 \, a^{4} b^{3} - 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(a^{7} + 5 \, a^{6} b + 10 \, a^{5} b^{2} + 10 \, a^{4} b^{3} + 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[1/24*((a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(d*x + c)^10 + 10*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(d*x + c)*sinh(d*x + c)^9 + (a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*sinh(d*x + c)^10 + (11*a^5 + 53*a^4*b + 73*a^3*b^2 + 31*a^2*b^3)*cosh(d*x + c)^8 + (11*a^5 + 53*a^4*b + 73*a^3*b^2 + 31*a^2*b^3 + 45*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 8*(15*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(d*x + c)^3 + (11*a^5 + 53*a^4*b + 73*a^3*b^2 + 31*a^2*b^3)*cosh(d*x + c))*sinh(d*x + c)^7 + 2*(5*a^5 + 9*a^4*b - 45*a^3*b^2 - 37*a^2*b^3 + 12*a*b^4)*cosh(d*x + c)^6 + 2*(5*a^5 + 9*a^4*b - 45*a^3*b^2 - 37*a^2*b^3 + 12*a*b^4 + 105*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(d*x + c)^4 + 14*(11*a^5 + 53*a^4*b + 73*a^3*b^2 + 31*a^2*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 4*(63*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(d*x + c)^5 + 14*(11*a^5 + 53*a^4*b + 73*a^3*b^2 + 31*a^2*b^3)*cosh(d*x + c)^3 + 3*(5*a^5 + 9*a^4*b - 45*a^3*b^2 - 37*a^2*b^3 + 12*a*b^4)*cosh(d*x + c))*sinh(d*x + c)^5 - a^5 - 3*a^4*b - 3*a^3*b^2 - a^2*b^3 - 2*(5*a^5 + 9*a^4*b - 45*a^3*b^2 - 37*a^2*b^3 + 12*a*b^4)*cosh(d*x + c)^4 + 2*(105*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(d*x + c)^6 - 5*a^5 - 9*a^4*b + 45*a^3*b^2 + 37*a^2*b^3 - 12*a*b^4 + 35*(11*a^5 + 53*a^4*b + 73*a^3*b^2 + 31*a^2*b^3)*cosh(d*x + c)^4 + 15*(5*a^5 + 9*a^4*b - 45*a^3*b^2 - 37*a^2*b^3 + 12*a*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(15*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(d*x + c)^7 + 7*(11*a^5 + 53*a^4*b + 73*a^3*b^2 + 31*a^2*b^3)*cosh(d*x + c)^5 + 5*(5*a^5 + 9*a^4*b - 45*a^3*b^2 - 37*a^2*b^3 + 12*a*b^4)*cosh(d*x + c)^3 - (5*a^5 + 9*a^4*b - 45*a^3*b^2 - 37*a^2*b^3 + 12*a*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 - (11*a^5 + 53*a^4*b + 73*a^3*b^2 + 31*a^2*b^3)*cosh(d*x + c)^2 + (45*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(d*x + c)^8 + 28*(11*a^5 + 53*a^4*b + 73*a^3*b^2 + 31*a^2*b^3)*cosh(d*x + c)^6 - 11*a^5 - 53*a^4*b - 73*a^3*b^2 - 31*a^2*b^3 + 30*(5*a^5 + 9*a^4*b - 45*a^3*b^2 - 37*a^2*b^3 + 12*a*b^4)*cosh(d*x + c)^4 - 12*(5*a^5 + 9*a^4*b - 45*a^3*b^2 - 37*a^2*b^3 + 12*a*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - 6*((6*a^2*b^2 + 7*a*b^3 + b^4)*cosh(d*x + c)^7 + 7*(6*a^2*b^2 + 7*a*b^3 + b^4)*cosh(d*x + c)*sinh(d*x + c)^6 + (6*a^2*b^2 + 7*a*b^3 + b^4)*sinh(d*x + c)^7 + 2*(6*a^2*b^2 - 5*a*b^3 - b^4)*cosh(d*x + c)^5 + (12*a^2*b^2 - 10*a*b^3 - 2*b^4 + 21*(6*a^2*b^2 + 7*a*b^3 + b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 5*(7*(6*a^2*b^2 + 7*a*b^3 + b^4)*cosh(d*x + c)^3 + 2*(6*a^2*b^2 - 5*a*b^3 - b^4)*cosh(d*x + c))*sinh(d*x + c)^4 + (6*a^2*b^2 + 7*a*b^3 + b^4)*cosh(d*x + c)^3 + (35*(6*a^2*b^2 + 7*a*b^3 + b^4)*cosh(d*x + c)^4 + 6*a^2*b^2 + 7*a*b^3 + b^4 + 20*(6*a^2*b^2 - 5*a*b^3 - b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + (21*(6*a^2*b^2 + 7*a*b^3 + b^4)*cosh(d*x + c)^5 + 20*(6*a^2*b^2 - 5*a*b^3 - b^4)*cosh(d*x + c)^3 + 3*(6*a^2*b^2 + 7*a*b^3 + b^4)*cosh(d*x + c))*sinh(d*x + c)^2 + (7*(6*a^2*b^2 + 7*a*b^3 + b^4)*cosh(d*x + c)^6 + 10*(6*a^2*b^2 - 5*a*b^3 - b^4)*cosh(d*x + c)^4 + 3*(6*a^2*b^2 + 7*a*b^3 + b^4)*cosh(d*x + c)^2)*sinh(d*x + c))*sqrt(-a^2 - a*b)*log(((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*(3*a + b)*cosh(d*x + c)^2 + 2*(3*(a + b)*cosh(d*x + c)^2 - 3*a - b)*sinh(d*x + c)^2 + 4*((a + b)*cosh(d*x + c)^3 - (3*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^2 - a*b) + a + b)/((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)) + 2*(5*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(d*x + c)^9 + 4*(11*a^5 + 53*a^4*b + 73*a^3*b^2 + 31*a^2*b^3)*cosh(d*x + c)^7 + 6*(5*a^5 + 9*a^4*b - 45*a^3*b^2 - 37*a^2*b^3 + 12*a*b^4)*cosh(d*x + c)^5 - 4*(5*a^5 + 9*a^4*b - 45*a^3*b^2 - 37*a^2*b^3 + 12*a*b^4)*cosh(d*x + c)^3 - (11*a^5 + 53*a^4*b + 73*a^3*b^2 + 31*a^2*b^3)*cosh(d*x + c))*sinh(d*x + c))/((a^7 + 5*a^6*b + 10*a^5*b^2 + 10*a^4*b^3 + 5*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)^7 + 7*(a^7 + 5*a^6*b + 10*a^5*b^2 + 10*a^4*b^3 + 5*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)*sinh(d*x + c)^6 + (a^7 + 5*a^6*b + 10*a^5*b^2 + 10*a^4*b^3 + 5*a^3*b^4 + a^2*b^5)*d*sinh(d*x + c)^7 + 2*(a^7 + 3*a^6*b + 2*a^5*b^2 - 2*a^4*b^3 - 3*a^3*b^4 - a^2*b^5)*d*cosh(d*x + c)^5 + (21*(a^7 + 5*a^6*b + 10*a^5*b^2 + 10*a^4*b^3 + 5*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)^2 + 2*(a^7 + 3*a^6*b + 2*a^5*b^2 - 2*a^4*b^3 - 3*a^3*b^4 - a^2*b^5)*d)*sinh(d*x + c)^5 + (a^7 + 5*a^6*b + 10*a^5*b^2 + 10*a^4*b^3 + 5*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)^3 + 5*(7*(a^7 + 5*a^6*b + 10*a^5*b^2 + 10*a^4*b^3 + 5*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)^3 + 2*(a^7 + 3*a^6*b + 2*a^5*b^2 - 2*a^4*b^3 - 3*a^3*b^4 - a^2*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^4 + (35*(a^7 + 5*a^6*b + 10*a^5*b^2 + 10*a^4*b^3 + 5*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)^4 + 20*(a^7 + 3*a^6*b + 2*a^5*b^2 - 2*a^4*b^3 - 3*a^3*b^4 - a^2*b^5)*d*cosh(d*x + c)^2 + (a^7 + 5*a^6*b + 10*a^5*b^2 + 10*a^4*b^3 + 5*a^3*b^4 + a^2*b^5)*d)*sinh(d*x + c)^3 + (21*(a^7 + 5*a^6*b + 10*a^5*b^2 + 10*a^4*b^3 + 5*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)^5 + 20*(a^7 + 3*a^6*b + 2*a^5*b^2 - 2*a^4*b^3 - 3*a^3*b^4 - a^2*b^5)*d*cosh(d*x + c)^3 + 3*(a^7 + 5*a^6*b + 10*a^5*b^2 + 10*a^4*b^3 + 5*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^2 + (7*(a^7 + 5*a^6*b + 10*a^5*b^2 + 10*a^4*b^3 + 5*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)^6 + 10*(a^7 + 3*a^6*b + 2*a^5*b^2 - 2*a^4*b^3 - 3*a^3*b^4 - a^2*b^5)*d*cosh(d*x + c)^4 + 3*(a^7 + 5*a^6*b + 10*a^5*b^2 + 10*a^4*b^3 + 5*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)^2)*sinh(d*x + c)), 1/24*((a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(d*x + c)^10 + 10*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(d*x + c)*sinh(d*x + c)^9 + (a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*sinh(d*x + c)^10 + (11*a^5 + 53*a^4*b + 73*a^3*b^2 + 31*a^2*b^3)*cosh(d*x + c)^8 + (11*a^5 + 53*a^4*b + 73*a^3*b^2 + 31*a^2*b^3 + 45*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 8*(15*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(d*x + c)^3 + (11*a^5 + 53*a^4*b + 73*a^3*b^2 + 31*a^2*b^3)*cosh(d*x + c))*sinh(d*x + c)^7 + 2*(5*a^5 + 9*a^4*b - 45*a^3*b^2 - 37*a^2*b^3 + 12*a*b^4)*cosh(d*x + c)^6 + 2*(5*a^5 + 9*a^4*b - 45*a^3*b^2 - 37*a^2*b^3 + 12*a*b^4 + 105*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(d*x + c)^4 + 14*(11*a^5 + 53*a^4*b + 73*a^3*b^2 + 31*a^2*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 4*(63*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(d*x + c)^5 + 14*(11*a^5 + 53*a^4*b + 73*a^3*b^2 + 31*a^2*b^3)*cosh(d*x + c)^3 + 3*(5*a^5 + 9*a^4*b - 45*a^3*b^2 - 37*a^2*b^3 + 12*a*b^4)*cosh(d*x + c))*sinh(d*x + c)^5 - a^5 - 3*a^4*b - 3*a^3*b^2 - a^2*b^3 - 2*(5*a^5 + 9*a^4*b - 45*a^3*b^2 - 37*a^2*b^3 + 12*a*b^4)*cosh(d*x + c)^4 + 2*(105*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(d*x + c)^6 - 5*a^5 - 9*a^4*b + 45*a^3*b^2 + 37*a^2*b^3 - 12*a*b^4 + 35*(11*a^5 + 53*a^4*b + 73*a^3*b^2 + 31*a^2*b^3)*cosh(d*x + c)^4 + 15*(5*a^5 + 9*a^4*b - 45*a^3*b^2 - 37*a^2*b^3 + 12*a*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(15*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(d*x + c)^7 + 7*(11*a^5 + 53*a^4*b + 73*a^3*b^2 + 31*a^2*b^3)*cosh(d*x + c)^5 + 5*(5*a^5 + 9*a^4*b - 45*a^3*b^2 - 37*a^2*b^3 + 12*a*b^4)*cosh(d*x + c)^3 - (5*a^5 + 9*a^4*b - 45*a^3*b^2 - 37*a^2*b^3 + 12*a*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 - (11*a^5 + 53*a^4*b + 73*a^3*b^2 + 31*a^2*b^3)*cosh(d*x + c)^2 + (45*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(d*x + c)^8 + 28*(11*a^5 + 53*a^4*b + 73*a^3*b^2 + 31*a^2*b^3)*cosh(d*x + c)^6 - 11*a^5 - 53*a^4*b - 73*a^3*b^2 - 31*a^2*b^3 + 30*(5*a^5 + 9*a^4*b - 45*a^3*b^2 - 37*a^2*b^3 + 12*a*b^4)*cosh(d*x + c)^4 - 12*(5*a^5 + 9*a^4*b - 45*a^3*b^2 - 37*a^2*b^3 + 12*a*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 12*((6*a^2*b^2 + 7*a*b^3 + b^4)*cosh(d*x + c)^7 + 7*(6*a^2*b^2 + 7*a*b^3 + b^4)*cosh(d*x + c)*sinh(d*x + c)^6 + (6*a^2*b^2 + 7*a*b^3 + b^4)*sinh(d*x + c)^7 + 2*(6*a^2*b^2 - 5*a*b^3 - b^4)*cosh(d*x + c)^5 + (12*a^2*b^2 - 10*a*b^3 - 2*b^4 + 21*(6*a^2*b^2 + 7*a*b^3 + b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 5*(7*(6*a^2*b^2 + 7*a*b^3 + b^4)*cosh(d*x + c)^3 + 2*(6*a^2*b^2 - 5*a*b^3 - b^4)*cosh(d*x + c))*sinh(d*x + c)^4 + (6*a^2*b^2 + 7*a*b^3 + b^4)*cosh(d*x + c)^3 + (35*(6*a^2*b^2 + 7*a*b^3 + b^4)*cosh(d*x + c)^4 + 6*a^2*b^2 + 7*a*b^3 + b^4 + 20*(6*a^2*b^2 - 5*a*b^3 - b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + (21*(6*a^2*b^2 + 7*a*b^3 + b^4)*cosh(d*x + c)^5 + 20*(6*a^2*b^2 - 5*a*b^3 - b^4)*cosh(d*x + c)^3 + 3*(6*a^2*b^2 + 7*a*b^3 + b^4)*cosh(d*x + c))*sinh(d*x + c)^2 + (7*(6*a^2*b^2 + 7*a*b^3 + b^4)*cosh(d*x + c)^6 + 10*(6*a^2*b^2 - 5*a*b^3 - b^4)*cosh(d*x + c)^4 + 3*(6*a^2*b^2 + 7*a*b^3 + b^4)*cosh(d*x + c)^2)*sinh(d*x + c))*sqrt(a^2 + a*b)*arctan(1/2*((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 + (3*a - b)*cosh(d*x + c) + (3*(a + b)*cosh(d*x + c)^2 + 3*a - b)*sinh(d*x + c))/sqrt(a^2 + a*b)) + 12*((6*a^2*b^2 + 7*a*b^3 + b^4)*cosh(d*x + c)^7 + 7*(6*a^2*b^2 + 7*a*b^3 + b^4)*cosh(d*x + c)*sinh(d*x + c)^6 + (6*a^2*b^2 + 7*a*b^3 + b^4)*sinh(d*x + c)^7 + 2*(6*a^2*b^2 - 5*a*b^3 - b^4)*cosh(d*x + c)^5 + (12*a^2*b^2 - 10*a*b^3 - 2*b^4 + 21*(6*a^2*b^2 + 7*a*b^3 + b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 5*(7*(6*a^2*b^2 + 7*a*b^3 + b^4)*cosh(d*x + c)^3 + 2*(6*a^2*b^2 - 5*a*b^3 - b^4)*cosh(d*x + c))*sinh(d*x + c)^4 + (6*a^2*b^2 + 7*a*b^3 + b^4)*cosh(d*x + c)^3 + (35*(6*a^2*b^2 + 7*a*b^3 + b^4)*cosh(d*x + c)^4 + 6*a^2*b^2 + 7*a*b^3 + b^4 + 20*(6*a^2*b^2 - 5*a*b^3 - b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + (21*(6*a^2*b^2 + 7*a*b^3 + b^4)*cosh(d*x + c)^5 + 20*(6*a^2*b^2 - 5*a*b^3 - b^4)*cosh(d*x + c)^3 + 3*(6*a^2*b^2 + 7*a*b^3 + b^4)*cosh(d*x + c))*sinh(d*x + c)^2 + (7*(6*a^2*b^2 + 7*a*b^3 + b^4)*cosh(d*x + c)^6 + 10*(6*a^2*b^2 - 5*a*b^3 - b^4)*cosh(d*x + c)^4 + 3*(6*a^2*b^2 + 7*a*b^3 + b^4)*cosh(d*x + c)^2)*sinh(d*x + c))*sqrt(a^2 + a*b)*arctan(1/2*sqrt(a^2 + a*b)*(cosh(d*x + c) + sinh(d*x + c))/a) + 2*(5*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(d*x + c)^9 + 4*(11*a^5 + 53*a^4*b + 73*a^3*b^2 + 31*a^2*b^3)*cosh(d*x + c)^7 + 6*(5*a^5 + 9*a^4*b - 45*a^3*b^2 - 37*a^2*b^3 + 12*a*b^4)*cosh(d*x + c)^5 - 4*(5*a^5 + 9*a^4*b - 45*a^3*b^2 - 37*a^2*b^3 + 12*a*b^4)*cosh(d*x + c)^3 - (11*a^5 + 53*a^4*b + 73*a^3*b^2 + 31*a^2*b^3)*cosh(d*x + c))*sinh(d*x + c))/((a^7 + 5*a^6*b + 10*a^5*b^2 + 10*a^4*b^3 + 5*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)^7 + 7*(a^7 + 5*a^6*b + 10*a^5*b^2 + 10*a^4*b^3 + 5*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)*sinh(d*x + c)^6 + (a^7 + 5*a^6*b + 10*a^5*b^2 + 10*a^4*b^3 + 5*a^3*b^4 + a^2*b^5)*d*sinh(d*x + c)^7 + 2*(a^7 + 3*a^6*b + 2*a^5*b^2 - 2*a^4*b^3 - 3*a^3*b^4 - a^2*b^5)*d*cosh(d*x + c)^5 + (21*(a^7 + 5*a^6*b + 10*a^5*b^2 + 10*a^4*b^3 + 5*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)^2 + 2*(a^7 + 3*a^6*b + 2*a^5*b^2 - 2*a^4*b^3 - 3*a^3*b^4 - a^2*b^5)*d)*sinh(d*x + c)^5 + (a^7 + 5*a^6*b + 10*a^5*b^2 + 10*a^4*b^3 + 5*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)^3 + 5*(7*(a^7 + 5*a^6*b + 10*a^5*b^2 + 10*a^4*b^3 + 5*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)^3 + 2*(a^7 + 3*a^6*b + 2*a^5*b^2 - 2*a^4*b^3 - 3*a^3*b^4 - a^2*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^4 + (35*(a^7 + 5*a^6*b + 10*a^5*b^2 + 10*a^4*b^3 + 5*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)^4 + 20*(a^7 + 3*a^6*b + 2*a^5*b^2 - 2*a^4*b^3 - 3*a^3*b^4 - a^2*b^5)*d*cosh(d*x + c)^2 + (a^7 + 5*a^6*b + 10*a^5*b^2 + 10*a^4*b^3 + 5*a^3*b^4 + a^2*b^5)*d)*sinh(d*x + c)^3 + (21*(a^7 + 5*a^6*b + 10*a^5*b^2 + 10*a^4*b^3 + 5*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)^5 + 20*(a^7 + 3*a^6*b + 2*a^5*b^2 - 2*a^4*b^3 - 3*a^3*b^4 - a^2*b^5)*d*cosh(d*x + c)^3 + 3*(a^7 + 5*a^6*b + 10*a^5*b^2 + 10*a^4*b^3 + 5*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^2 + (7*(a^7 + 5*a^6*b + 10*a^5*b^2 + 10*a^4*b^3 + 5*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)^6 + 10*(a^7 + 3*a^6*b + 2*a^5*b^2 - 2*a^4*b^3 - 3*a^3*b^4 - a^2*b^5)*d*cosh(d*x + c)^4 + 3*(a^7 + 5*a^6*b + 10*a^5*b^2 + 10*a^4*b^3 + 5*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)^2)*sinh(d*x + c))]","B",0
116,1,4324,0,0.525749," ","integrate(cosh(d*x+c)^2/(a+b*tanh(d*x+c)^2)^2,x, algorithm=""fricas"")","\left[\frac{{\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \sinh\left(d x + c\right)^{8} + 2 \, {\left(a^{3} - a b^{2} + 2 \, {\left(a^{3} + 6 \, a^{2} b + 5 \, a b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(a^{3} - a b^{2} + 2 \, {\left(a^{3} + 6 \, a^{2} b + 5 \, a b^{2}\right)} d x + 14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{3} - a b^{2} + 2 \, {\left(a^{3} + 6 \, 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(a b^{2} - b^{3} - {\left(a^{3} + 4 \, a^{2} b - 5 \, a b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(d x + c\right)^{4} - 4 \, a b^{2} + 4 \, b^{3} + 4 \, {\left(a^{3} + 4 \, a^{2} b - 5 \, a b^{2}\right)} d x + 15 \, {\left(a^{3} - a b^{2} + 2 \, {\left(a^{3} + 6 \, 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 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(a^{3} - a b^{2} + 2 \, {\left(a^{3} + 6 \, a^{2} b + 5 \, a b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - 4 \, {\left(a b^{2} - b^{3} - {\left(a^{3} + 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)^{3} - a^{3} - 2 \, a^{2} b - a b^{2} - 2 \, {\left(a^{3} + 3 \, a b^{2} + 4 \, b^{3} - 2 \, {\left(a^{3} + 6 \, a^{2} b + 5 \, a b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{3} - a b^{2} + 2 \, {\left(a^{3} + 6 \, a^{2} b + 5 \, a b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{4} - a^{3} - 3 \, a b^{2} - 4 \, b^{3} + 2 \, {\left(a^{3} + 6 \, a^{2} b + 5 \, a b^{2}\right)} d x - 24 \, {\left(a b^{2} - b^{3} - {\left(a^{3} + 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)^{2} + 2 \, {\left({\left(5 \, a^{2} b + 6 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{6} + 6 \, {\left(5 \, a^{2} b + 6 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(5 \, a^{2} b + 6 \, a b^{2} + b^{3}\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(5 \, a^{2} b - 4 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{4} + {\left(10 \, a^{2} b - 8 \, a b^{2} - 2 \, b^{3} + 15 \, {\left(5 \, a^{2} b + 6 \, 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(5 \, a^{2} b + 6 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(5 \, a^{2} b - 4 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(5 \, a^{2} b + 6 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{2} + {\left(15 \, {\left(5 \, a^{2} b + 6 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{4} + 5 \, a^{2} b + 6 \, a b^{2} + b^{3} + 12 \, {\left(5 \, 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} + 2 \, {\left(3 \, {\left(5 \, a^{2} b + 6 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{5} + 4 \, {\left(5 \, a^{2} b - 4 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(5 \, a^{2} b + 6 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{{\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) \sinh\left(d x + c\right)^{3} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{2} + a^{2} - 6 \, a b + b^{2} + 4 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + 4 \, {\left({\left(a^{2} + a b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} + a b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} + a b\right)} \sinh\left(d x + c\right)^{2} + a^{2} - a b\right)} \sqrt{-\frac{b}{a}}}{{\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) + 4 \, {\left(2 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{3} - a b^{2} + 2 \, {\left(a^{3} + 6 \, a^{2} b + 5 \, a b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{5} - 8 \, {\left(a b^{2} - b^{3} - {\left(a^{3} + 4 \, a^{2} b - 5 \, a b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - {\left(a^{3} + 3 \, a b^{2} + 4 \, b^{3} - 2 \, {\left(a^{3} + 6 \, 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({\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} + 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) \sinh\left(d x + c\right)^{5} + {\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)^{6} + 2 \, {\left(a^{5} + 2 \, a^{4} b - 2 \, a^{2} b^{3} - a b^{4}\right)} d \cosh\left(d x + c\right)^{4} + {\left(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} + 2 \, {\left(a^{5} + 2 \, a^{4} b - 2 \, a^{2} b^{3} - a b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{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)^{2} + 4 \, {\left(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} + 2 \, {\left(a^{5} + 2 \, a^{4} b - 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 \, {\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} + 2 \, a^{4} b - 2 \, 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} + 2 \, {\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)^{5} + 4 \, {\left(a^{5} + 2 \, a^{4} b - 2 \, 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{{\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \sinh\left(d x + c\right)^{8} + 2 \, {\left(a^{3} - a b^{2} + 2 \, {\left(a^{3} + 6 \, a^{2} b + 5 \, a b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(a^{3} - a b^{2} + 2 \, {\left(a^{3} + 6 \, a^{2} b + 5 \, a b^{2}\right)} d x + 14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{3} - a b^{2} + 2 \, {\left(a^{3} + 6 \, 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(a b^{2} - b^{3} - {\left(a^{3} + 4 \, a^{2} b - 5 \, a b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(d x + c\right)^{4} - 4 \, a b^{2} + 4 \, b^{3} + 4 \, {\left(a^{3} + 4 \, a^{2} b - 5 \, a b^{2}\right)} d x + 15 \, {\left(a^{3} - a b^{2} + 2 \, {\left(a^{3} + 6 \, 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 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(a^{3} - a b^{2} + 2 \, {\left(a^{3} + 6 \, a^{2} b + 5 \, a b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - 4 \, {\left(a b^{2} - b^{3} - {\left(a^{3} + 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)^{3} - a^{3} - 2 \, a^{2} b - a b^{2} - 2 \, {\left(a^{3} + 3 \, a b^{2} + 4 \, b^{3} - 2 \, {\left(a^{3} + 6 \, a^{2} b + 5 \, a b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(14 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{3} - a b^{2} + 2 \, {\left(a^{3} + 6 \, a^{2} b + 5 \, a b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{4} - a^{3} - 3 \, a b^{2} - 4 \, b^{3} + 2 \, {\left(a^{3} + 6 \, a^{2} b + 5 \, a b^{2}\right)} d x - 24 \, {\left(a b^{2} - b^{3} - {\left(a^{3} + 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)^{2} + 4 \, {\left({\left(5 \, a^{2} b + 6 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{6} + 6 \, {\left(5 \, a^{2} b + 6 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(5 \, a^{2} b + 6 \, a b^{2} + b^{3}\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(5 \, a^{2} b - 4 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{4} + {\left(10 \, a^{2} b - 8 \, a b^{2} - 2 \, b^{3} + 15 \, {\left(5 \, a^{2} b + 6 \, 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(5 \, a^{2} b + 6 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(5 \, a^{2} b - 4 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(5 \, a^{2} b + 6 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{2} + {\left(15 \, {\left(5 \, a^{2} b + 6 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{4} + 5 \, a^{2} b + 6 \, a b^{2} + b^{3} + 12 \, {\left(5 \, 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} + 2 \, {\left(3 \, {\left(5 \, a^{2} b + 6 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{5} + 4 \, {\left(5 \, a^{2} b - 4 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(5 \, a^{2} b + 6 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{b}{a}} \arctan\left(\frac{{\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} + a - b\right)} \sqrt{\frac{b}{a}}}{2 \, b}\right) + 4 \, {\left(2 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{3} - a b^{2} + 2 \, {\left(a^{3} + 6 \, a^{2} b + 5 \, a b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{5} - 8 \, {\left(a b^{2} - b^{3} - {\left(a^{3} + 4 \, a^{2} b - 5 \, a b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - {\left(a^{3} + 3 \, a b^{2} + 4 \, b^{3} - 2 \, {\left(a^{3} + 6 \, 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({\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} + 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) \sinh\left(d x + c\right)^{5} + {\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)^{6} + 2 \, {\left(a^{5} + 2 \, a^{4} b - 2 \, a^{2} b^{3} - a b^{4}\right)} d \cosh\left(d x + c\right)^{4} + {\left(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} + 2 \, {\left(a^{5} + 2 \, a^{4} b - 2 \, a^{2} b^{3} - a b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{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)^{2} + 4 \, {\left(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} + 2 \, {\left(a^{5} + 2 \, a^{4} b - 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 \, {\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} + 2 \, a^{4} b - 2 \, 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} + 2 \, {\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)^{5} + 4 \, {\left(a^{5} + 2 \, a^{4} b - 2 \, 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,"[1/8*((a^3 + 2*a^2*b + a*b^2)*cosh(d*x + c)^8 + 8*(a^3 + 2*a^2*b + a*b^2)*cosh(d*x + c)*sinh(d*x + c)^7 + (a^3 + 2*a^2*b + a*b^2)*sinh(d*x + c)^8 + 2*(a^3 - a*b^2 + 2*(a^3 + 6*a^2*b + 5*a*b^2)*d*x)*cosh(d*x + c)^6 + 2*(a^3 - a*b^2 + 2*(a^3 + 6*a^2*b + 5*a*b^2)*d*x + 14*(a^3 + 2*a^2*b + a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 4*(14*(a^3 + 2*a^2*b + a*b^2)*cosh(d*x + c)^3 + 3*(a^3 - a*b^2 + 2*(a^3 + 6*a^2*b + 5*a*b^2)*d*x)*cosh(d*x + c))*sinh(d*x + c)^5 - 8*(a*b^2 - b^3 - (a^3 + 4*a^2*b - 5*a*b^2)*d*x)*cosh(d*x + c)^4 + 2*(35*(a^3 + 2*a^2*b + a*b^2)*cosh(d*x + c)^4 - 4*a*b^2 + 4*b^3 + 4*(a^3 + 4*a^2*b - 5*a*b^2)*d*x + 15*(a^3 - a*b^2 + 2*(a^3 + 6*a^2*b + 5*a*b^2)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(7*(a^3 + 2*a^2*b + a*b^2)*cosh(d*x + c)^5 + 5*(a^3 - a*b^2 + 2*(a^3 + 6*a^2*b + 5*a*b^2)*d*x)*cosh(d*x + c)^3 - 4*(a*b^2 - b^3 - (a^3 + 4*a^2*b - 5*a*b^2)*d*x)*cosh(d*x + c))*sinh(d*x + c)^3 - a^3 - 2*a^2*b - a*b^2 - 2*(a^3 + 3*a*b^2 + 4*b^3 - 2*(a^3 + 6*a^2*b + 5*a*b^2)*d*x)*cosh(d*x + c)^2 + 2*(14*(a^3 + 2*a^2*b + a*b^2)*cosh(d*x + c)^6 + 15*(a^3 - a*b^2 + 2*(a^3 + 6*a^2*b + 5*a*b^2)*d*x)*cosh(d*x + c)^4 - a^3 - 3*a*b^2 - 4*b^3 + 2*(a^3 + 6*a^2*b + 5*a*b^2)*d*x - 24*(a*b^2 - b^3 - (a^3 + 4*a^2*b - 5*a*b^2)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 2*((5*a^2*b + 6*a*b^2 + b^3)*cosh(d*x + c)^6 + 6*(5*a^2*b + 6*a*b^2 + b^3)*cosh(d*x + c)*sinh(d*x + c)^5 + (5*a^2*b + 6*a*b^2 + b^3)*sinh(d*x + c)^6 + 2*(5*a^2*b - 4*a*b^2 - b^3)*cosh(d*x + c)^4 + (10*a^2*b - 8*a*b^2 - 2*b^3 + 15*(5*a^2*b + 6*a*b^2 + b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 4*(5*(5*a^2*b + 6*a*b^2 + b^3)*cosh(d*x + c)^3 + 2*(5*a^2*b - 4*a*b^2 - b^3)*cosh(d*x + c))*sinh(d*x + c)^3 + (5*a^2*b + 6*a*b^2 + b^3)*cosh(d*x + c)^2 + (15*(5*a^2*b + 6*a*b^2 + b^3)*cosh(d*x + c)^4 + 5*a^2*b + 6*a*b^2 + b^3 + 12*(5*a^2*b - 4*a*b^2 - b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 2*(3*(5*a^2*b + 6*a*b^2 + b^3)*cosh(d*x + c)^5 + 4*(5*a^2*b - 4*a*b^2 - b^3)*cosh(d*x + c)^3 + (5*a^2*b + 6*a*b^2 + b^3)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-b/a)*log(((a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 + 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 + 2*(a^2 - b^2)*cosh(d*x + c)^2 + 2*(3*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + a^2 - b^2)*sinh(d*x + c)^2 + a^2 - 6*a*b + b^2 + 4*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 + (a^2 - b^2)*cosh(d*x + c))*sinh(d*x + c) + 4*((a^2 + a*b)*cosh(d*x + c)^2 + 2*(a^2 + a*b)*cosh(d*x + c)*sinh(d*x + c) + (a^2 + a*b)*sinh(d*x + c)^2 + a^2 - a*b)*sqrt(-b/a))/((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)) + 4*(2*(a^3 + 2*a^2*b + a*b^2)*cosh(d*x + c)^7 + 3*(a^3 - a*b^2 + 2*(a^3 + 6*a^2*b + 5*a*b^2)*d*x)*cosh(d*x + c)^5 - 8*(a*b^2 - b^3 - (a^3 + 4*a^2*b - 5*a*b^2)*d*x)*cosh(d*x + c)^3 - (a^3 + 3*a*b^2 + 4*b^3 - 2*(a^3 + 6*a^2*b + 5*a*b^2)*d*x)*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)^6 + 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)*sinh(d*x + c)^5 + (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 + 2*(a^5 + 2*a^4*b - 2*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 + 2*(a^5 + 2*a^4*b - 2*a^2*b^3 - a*b^4)*d)*sinh(d*x + c)^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)^2 + 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)^3 + 2*(a^5 + 2*a^4*b - 2*a^2*b^3 - a*b^4)*d*cosh(d*x + c))*sinh(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)^4 + 12*(a^5 + 2*a^4*b - 2*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 + 2*(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)^5 + 4*(a^5 + 2*a^4*b - 2*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)), 1/8*((a^3 + 2*a^2*b + a*b^2)*cosh(d*x + c)^8 + 8*(a^3 + 2*a^2*b + a*b^2)*cosh(d*x + c)*sinh(d*x + c)^7 + (a^3 + 2*a^2*b + a*b^2)*sinh(d*x + c)^8 + 2*(a^3 - a*b^2 + 2*(a^3 + 6*a^2*b + 5*a*b^2)*d*x)*cosh(d*x + c)^6 + 2*(a^3 - a*b^2 + 2*(a^3 + 6*a^2*b + 5*a*b^2)*d*x + 14*(a^3 + 2*a^2*b + a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 4*(14*(a^3 + 2*a^2*b + a*b^2)*cosh(d*x + c)^3 + 3*(a^3 - a*b^2 + 2*(a^3 + 6*a^2*b + 5*a*b^2)*d*x)*cosh(d*x + c))*sinh(d*x + c)^5 - 8*(a*b^2 - b^3 - (a^3 + 4*a^2*b - 5*a*b^2)*d*x)*cosh(d*x + c)^4 + 2*(35*(a^3 + 2*a^2*b + a*b^2)*cosh(d*x + c)^4 - 4*a*b^2 + 4*b^3 + 4*(a^3 + 4*a^2*b - 5*a*b^2)*d*x + 15*(a^3 - a*b^2 + 2*(a^3 + 6*a^2*b + 5*a*b^2)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(7*(a^3 + 2*a^2*b + a*b^2)*cosh(d*x + c)^5 + 5*(a^3 - a*b^2 + 2*(a^3 + 6*a^2*b + 5*a*b^2)*d*x)*cosh(d*x + c)^3 - 4*(a*b^2 - b^3 - (a^3 + 4*a^2*b - 5*a*b^2)*d*x)*cosh(d*x + c))*sinh(d*x + c)^3 - a^3 - 2*a^2*b - a*b^2 - 2*(a^3 + 3*a*b^2 + 4*b^3 - 2*(a^3 + 6*a^2*b + 5*a*b^2)*d*x)*cosh(d*x + c)^2 + 2*(14*(a^3 + 2*a^2*b + a*b^2)*cosh(d*x + c)^6 + 15*(a^3 - a*b^2 + 2*(a^3 + 6*a^2*b + 5*a*b^2)*d*x)*cosh(d*x + c)^4 - a^3 - 3*a*b^2 - 4*b^3 + 2*(a^3 + 6*a^2*b + 5*a*b^2)*d*x - 24*(a*b^2 - b^3 - (a^3 + 4*a^2*b - 5*a*b^2)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((5*a^2*b + 6*a*b^2 + b^3)*cosh(d*x + c)^6 + 6*(5*a^2*b + 6*a*b^2 + b^3)*cosh(d*x + c)*sinh(d*x + c)^5 + (5*a^2*b + 6*a*b^2 + b^3)*sinh(d*x + c)^6 + 2*(5*a^2*b - 4*a*b^2 - b^3)*cosh(d*x + c)^4 + (10*a^2*b - 8*a*b^2 - 2*b^3 + 15*(5*a^2*b + 6*a*b^2 + b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 4*(5*(5*a^2*b + 6*a*b^2 + b^3)*cosh(d*x + c)^3 + 2*(5*a^2*b - 4*a*b^2 - b^3)*cosh(d*x + c))*sinh(d*x + c)^3 + (5*a^2*b + 6*a*b^2 + b^3)*cosh(d*x + c)^2 + (15*(5*a^2*b + 6*a*b^2 + b^3)*cosh(d*x + c)^4 + 5*a^2*b + 6*a*b^2 + b^3 + 12*(5*a^2*b - 4*a*b^2 - b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 2*(3*(5*a^2*b + 6*a*b^2 + b^3)*cosh(d*x + c)^5 + 4*(5*a^2*b - 4*a*b^2 - b^3)*cosh(d*x + c)^3 + (5*a^2*b + 6*a*b^2 + b^3)*cosh(d*x + c))*sinh(d*x + c))*sqrt(b/a)*arctan(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 + a - b)*sqrt(b/a)/b) + 4*(2*(a^3 + 2*a^2*b + a*b^2)*cosh(d*x + c)^7 + 3*(a^3 - a*b^2 + 2*(a^3 + 6*a^2*b + 5*a*b^2)*d*x)*cosh(d*x + c)^5 - 8*(a*b^2 - b^3 - (a^3 + 4*a^2*b - 5*a*b^2)*d*x)*cosh(d*x + c)^3 - (a^3 + 3*a*b^2 + 4*b^3 - 2*(a^3 + 6*a^2*b + 5*a*b^2)*d*x)*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)^6 + 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)*sinh(d*x + c)^5 + (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 + 2*(a^5 + 2*a^4*b - 2*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 + 2*(a^5 + 2*a^4*b - 2*a^2*b^3 - a*b^4)*d)*sinh(d*x + c)^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)^2 + 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)^3 + 2*(a^5 + 2*a^4*b - 2*a^2*b^3 - a*b^4)*d*cosh(d*x + c))*sinh(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)^4 + 12*(a^5 + 2*a^4*b - 2*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 + 2*(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)^5 + 4*(a^5 + 2*a^4*b - 2*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
117,1,3502,0,0.543221," ","integrate(cosh(d*x+c)/(a+b*tanh(d*x+c)^2)^2,x, algorithm=""fricas"")","\left[\frac{2 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{6} + 12 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + 2 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(a^{4} - 2 \, a^{3} b - a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(a^{4} - 2 \, a^{3} b - a^{2} b^{2} + 2 \, a b^{3} + 15 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} - 2 \, a^{4} - 4 \, a^{3} b - 2 \, a^{2} b^{2} + 8 \, {\left(5 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{4} - 2 \, 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)^{3} - 2 \, {\left(a^{4} - 2 \, a^{3} b - a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(15 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{4} - a^{4} + 2 \, a^{3} b + a^{2} b^{2} - 2 \, a b^{3} + 6 \, {\left(a^{4} - 2 \, 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)^{2} - {\left({\left(4 \, a^{2} b + 5 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(4 \, a^{2} b + 5 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} + {\left(4 \, a^{2} b + 5 \, a b^{2} + b^{3}\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(4 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(4 \, a^{2} b - 3 \, a b^{2} - b^{3} + 5 \, {\left(4 \, a^{2} b + 5 \, 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(4 \, a^{2} b + 5 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{3} + 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)^{2} + {\left(4 \, a^{2} b + 5 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right) + {\left(5 \, {\left(4 \, a^{2} b + 5 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{4} + 4 \, a^{2} b + 5 \, a b^{2} + b^{3} + 6 \, {\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)\right)} \sqrt{-a^{2} - a b} \log\left(\frac{{\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(3 \, a + b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} - 3 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(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) - 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^{2} - a b} + a + b}{{\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) + 4 \, {\left(3 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(a^{4} - 2 \, a^{3} b - a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} - {\left(a^{4} - 2 \, 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)}{4 \, {\left({\left(a^{6} + 4 \, a^{5} b + 6 \, a^{4} b^{2} + 4 \, a^{3} b^{3} + a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{5} + 5 \, {\left(a^{6} + 4 \, a^{5} b + 6 \, a^{4} b^{2} + 4 \, a^{3} b^{3} + a^{2} b^{4}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} + {\left(a^{6} + 4 \, a^{5} b + 6 \, a^{4} b^{2} + 4 \, a^{3} b^{3} + a^{2} b^{4}\right)} d \sinh\left(d x + c\right)^{5} + 2 \, {\left(a^{6} + 2 \, a^{5} b - 2 \, a^{3} b^{3} - a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{3} + 2 \, {\left(5 \, {\left(a^{6} + 4 \, a^{5} b + 6 \, a^{4} b^{2} + 4 \, a^{3} b^{3} + a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{6} + 2 \, a^{5} b - 2 \, a^{3} b^{3} - a^{2} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{3} + {\left(a^{6} + 4 \, a^{5} b + 6 \, a^{4} b^{2} + 4 \, a^{3} b^{3} + a^{2} b^{4}\right)} d \cosh\left(d x + c\right) + 2 \, {\left(5 \, {\left(a^{6} + 4 \, a^{5} b + 6 \, a^{4} b^{2} + 4 \, a^{3} b^{3} + a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{6} + 2 \, a^{5} b - 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 \, {\left(a^{6} + 4 \, a^{5} b + 6 \, a^{4} b^{2} + 4 \, a^{3} b^{3} + a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 6 \, {\left(a^{6} + 2 \, a^{5} b - 2 \, a^{3} b^{3} - a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{6} + 4 \, a^{5} b + 6 \, a^{4} b^{2} + 4 \, a^{3} b^{3} + a^{2} b^{4}\right)} d\right)} \sinh\left(d x + c\right)\right)}}, \frac{{\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{6} + 6 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} \sinh\left(d x + c\right)^{6} + {\left(a^{4} - 2 \, a^{3} b - a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} + {\left(a^{4} - 2 \, a^{3} b - a^{2} b^{2} + 2 \, a b^{3} + 15 \, {\left(a^{4} + 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^{4} - 2 \, a^{3} b - a^{2} b^{2} + 4 \, {\left(5 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{4} - 2 \, 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)^{3} - {\left(a^{4} - 2 \, a^{3} b - a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2} + {\left(15 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{4} - a^{4} + 2 \, a^{3} b + a^{2} b^{2} - 2 \, a b^{3} + 6 \, {\left(a^{4} - 2 \, 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)^{2} + {\left({\left(4 \, a^{2} b + 5 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(4 \, a^{2} b + 5 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} + {\left(4 \, a^{2} b + 5 \, a b^{2} + b^{3}\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(4 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(4 \, a^{2} b - 3 \, a b^{2} - b^{3} + 5 \, {\left(4 \, a^{2} b + 5 \, 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(4 \, a^{2} b + 5 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{3} + 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)^{2} + {\left(4 \, a^{2} b + 5 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right) + {\left(5 \, {\left(4 \, a^{2} b + 5 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{4} + 4 \, a^{2} b + 5 \, a b^{2} + b^{3} + 6 \, {\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)\right)} \sqrt{a^{2} + a b} \arctan\left(\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(3 \, a - b\right)} \cosh\left(d x + c\right) + {\left(3 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} + 3 \, a - b\right)} \sinh\left(d x + c\right)}{2 \, \sqrt{a^{2} + a b}}\right) + {\left({\left(4 \, a^{2} b + 5 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(4 \, a^{2} b + 5 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} + {\left(4 \, a^{2} b + 5 \, a b^{2} + b^{3}\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(4 \, a^{2} b - 3 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(4 \, a^{2} b - 3 \, a b^{2} - b^{3} + 5 \, {\left(4 \, a^{2} b + 5 \, 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(4 \, a^{2} b + 5 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{3} + 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)^{2} + {\left(4 \, a^{2} b + 5 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right) + {\left(5 \, {\left(4 \, a^{2} b + 5 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{4} + 4 \, a^{2} b + 5 \, a b^{2} + b^{3} + 6 \, {\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)\right)} \sqrt{a^{2} + a b} \arctan\left(\frac{\sqrt{a^{2} + a b} {\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right)}}{2 \, a}\right) + 2 \, {\left(3 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(a^{4} - 2 \, a^{3} b - a^{2} b^{2} + 2 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} - {\left(a^{4} - 2 \, 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)}{2 \, {\left({\left(a^{6} + 4 \, a^{5} b + 6 \, a^{4} b^{2} + 4 \, a^{3} b^{3} + a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{5} + 5 \, {\left(a^{6} + 4 \, a^{5} b + 6 \, a^{4} b^{2} + 4 \, a^{3} b^{3} + a^{2} b^{4}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} + {\left(a^{6} + 4 \, a^{5} b + 6 \, a^{4} b^{2} + 4 \, a^{3} b^{3} + a^{2} b^{4}\right)} d \sinh\left(d x + c\right)^{5} + 2 \, {\left(a^{6} + 2 \, a^{5} b - 2 \, a^{3} b^{3} - a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{3} + 2 \, {\left(5 \, {\left(a^{6} + 4 \, a^{5} b + 6 \, a^{4} b^{2} + 4 \, a^{3} b^{3} + a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{6} + 2 \, a^{5} b - 2 \, a^{3} b^{3} - a^{2} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{3} + {\left(a^{6} + 4 \, a^{5} b + 6 \, a^{4} b^{2} + 4 \, a^{3} b^{3} + a^{2} b^{4}\right)} d \cosh\left(d x + c\right) + 2 \, {\left(5 \, {\left(a^{6} + 4 \, a^{5} b + 6 \, a^{4} b^{2} + 4 \, a^{3} b^{3} + a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{6} + 2 \, a^{5} b - 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 \, {\left(a^{6} + 4 \, a^{5} b + 6 \, a^{4} b^{2} + 4 \, a^{3} b^{3} + a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 6 \, {\left(a^{6} + 2 \, a^{5} b - 2 \, a^{3} b^{3} - a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{6} + 4 \, a^{5} b + 6 \, a^{4} b^{2} + 4 \, a^{3} b^{3} + a^{2} b^{4}\right)} d\right)} \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[1/4*(2*(a^4 + 2*a^3*b + a^2*b^2)*cosh(d*x + c)^6 + 12*(a^4 + 2*a^3*b + a^2*b^2)*cosh(d*x + c)*sinh(d*x + c)^5 + 2*(a^4 + 2*a^3*b + a^2*b^2)*sinh(d*x + c)^6 + 2*(a^4 - 2*a^3*b - a^2*b^2 + 2*a*b^3)*cosh(d*x + c)^4 + 2*(a^4 - 2*a^3*b - a^2*b^2 + 2*a*b^3 + 15*(a^4 + 2*a^3*b + a^2*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^4 - 2*a^4 - 4*a^3*b - 2*a^2*b^2 + 8*(5*(a^4 + 2*a^3*b + a^2*b^2)*cosh(d*x + c)^3 + (a^4 - 2*a^3*b - a^2*b^2 + 2*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 - 2*(a^4 - 2*a^3*b - a^2*b^2 + 2*a*b^3)*cosh(d*x + c)^2 + 2*(15*(a^4 + 2*a^3*b + a^2*b^2)*cosh(d*x + c)^4 - a^4 + 2*a^3*b + a^2*b^2 - 2*a*b^3 + 6*(a^4 - 2*a^3*b - a^2*b^2 + 2*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - ((4*a^2*b + 5*a*b^2 + b^3)*cosh(d*x + c)^5 + 5*(4*a^2*b + 5*a*b^2 + b^3)*cosh(d*x + c)*sinh(d*x + c)^4 + (4*a^2*b + 5*a*b^2 + b^3)*sinh(d*x + c)^5 + 2*(4*a^2*b - 3*a*b^2 - b^3)*cosh(d*x + c)^3 + 2*(4*a^2*b - 3*a*b^2 - b^3 + 5*(4*a^2*b + 5*a*b^2 + b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 2*(5*(4*a^2*b + 5*a*b^2 + b^3)*cosh(d*x + c)^3 + 3*(4*a^2*b - 3*a*b^2 - b^3)*cosh(d*x + c))*sinh(d*x + c)^2 + (4*a^2*b + 5*a*b^2 + b^3)*cosh(d*x + c) + (5*(4*a^2*b + 5*a*b^2 + b^3)*cosh(d*x + c)^4 + 4*a^2*b + 5*a*b^2 + b^3 + 6*(4*a^2*b - 3*a*b^2 - b^3)*cosh(d*x + c)^2)*sinh(d*x + c))*sqrt(-a^2 - a*b)*log(((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*(3*a + b)*cosh(d*x + c)^2 + 2*(3*(a + b)*cosh(d*x + c)^2 - 3*a - b)*sinh(d*x + c)^2 + 4*((a + b)*cosh(d*x + c)^3 - (3*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^2 - a*b) + a + b)/((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)) + 4*(3*(a^4 + 2*a^3*b + a^2*b^2)*cosh(d*x + c)^5 + 2*(a^4 - 2*a^3*b - a^2*b^2 + 2*a*b^3)*cosh(d*x + c)^3 - (a^4 - 2*a^3*b - a^2*b^2 + 2*a*b^3)*cosh(d*x + c))*sinh(d*x + c))/((a^6 + 4*a^5*b + 6*a^4*b^2 + 4*a^3*b^3 + a^2*b^4)*d*cosh(d*x + c)^5 + 5*(a^6 + 4*a^5*b + 6*a^4*b^2 + 4*a^3*b^3 + a^2*b^4)*d*cosh(d*x + c)*sinh(d*x + c)^4 + (a^6 + 4*a^5*b + 6*a^4*b^2 + 4*a^3*b^3 + a^2*b^4)*d*sinh(d*x + c)^5 + 2*(a^6 + 2*a^5*b - 2*a^3*b^3 - a^2*b^4)*d*cosh(d*x + c)^3 + 2*(5*(a^6 + 4*a^5*b + 6*a^4*b^2 + 4*a^3*b^3 + a^2*b^4)*d*cosh(d*x + c)^2 + (a^6 + 2*a^5*b - 2*a^3*b^3 - a^2*b^4)*d)*sinh(d*x + c)^3 + (a^6 + 4*a^5*b + 6*a^4*b^2 + 4*a^3*b^3 + a^2*b^4)*d*cosh(d*x + c) + 2*(5*(a^6 + 4*a^5*b + 6*a^4*b^2 + 4*a^3*b^3 + a^2*b^4)*d*cosh(d*x + c)^3 + 3*(a^6 + 2*a^5*b - 2*a^3*b^3 - a^2*b^4)*d*cosh(d*x + c))*sinh(d*x + c)^2 + (5*(a^6 + 4*a^5*b + 6*a^4*b^2 + 4*a^3*b^3 + a^2*b^4)*d*cosh(d*x + c)^4 + 6*(a^6 + 2*a^5*b - 2*a^3*b^3 - a^2*b^4)*d*cosh(d*x + c)^2 + (a^6 + 4*a^5*b + 6*a^4*b^2 + 4*a^3*b^3 + a^2*b^4)*d)*sinh(d*x + c)), 1/2*((a^4 + 2*a^3*b + a^2*b^2)*cosh(d*x + c)^6 + 6*(a^4 + 2*a^3*b + a^2*b^2)*cosh(d*x + c)*sinh(d*x + c)^5 + (a^4 + 2*a^3*b + a^2*b^2)*sinh(d*x + c)^6 + (a^4 - 2*a^3*b - a^2*b^2 + 2*a*b^3)*cosh(d*x + c)^4 + (a^4 - 2*a^3*b - a^2*b^2 + 2*a*b^3 + 15*(a^4 + 2*a^3*b + a^2*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^4 - a^4 - 2*a^3*b - a^2*b^2 + 4*(5*(a^4 + 2*a^3*b + a^2*b^2)*cosh(d*x + c)^3 + (a^4 - 2*a^3*b - a^2*b^2 + 2*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 - (a^4 - 2*a^3*b - a^2*b^2 + 2*a*b^3)*cosh(d*x + c)^2 + (15*(a^4 + 2*a^3*b + a^2*b^2)*cosh(d*x + c)^4 - a^4 + 2*a^3*b + a^2*b^2 - 2*a*b^3 + 6*(a^4 - 2*a^3*b - a^2*b^2 + 2*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((4*a^2*b + 5*a*b^2 + b^3)*cosh(d*x + c)^5 + 5*(4*a^2*b + 5*a*b^2 + b^3)*cosh(d*x + c)*sinh(d*x + c)^4 + (4*a^2*b + 5*a*b^2 + b^3)*sinh(d*x + c)^5 + 2*(4*a^2*b - 3*a*b^2 - b^3)*cosh(d*x + c)^3 + 2*(4*a^2*b - 3*a*b^2 - b^3 + 5*(4*a^2*b + 5*a*b^2 + b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 2*(5*(4*a^2*b + 5*a*b^2 + b^3)*cosh(d*x + c)^3 + 3*(4*a^2*b - 3*a*b^2 - b^3)*cosh(d*x + c))*sinh(d*x + c)^2 + (4*a^2*b + 5*a*b^2 + b^3)*cosh(d*x + c) + (5*(4*a^2*b + 5*a*b^2 + b^3)*cosh(d*x + c)^4 + 4*a^2*b + 5*a*b^2 + b^3 + 6*(4*a^2*b - 3*a*b^2 - b^3)*cosh(d*x + c)^2)*sinh(d*x + c))*sqrt(a^2 + a*b)*arctan(1/2*((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 + (3*a - b)*cosh(d*x + c) + (3*(a + b)*cosh(d*x + c)^2 + 3*a - b)*sinh(d*x + c))/sqrt(a^2 + a*b)) + ((4*a^2*b + 5*a*b^2 + b^3)*cosh(d*x + c)^5 + 5*(4*a^2*b + 5*a*b^2 + b^3)*cosh(d*x + c)*sinh(d*x + c)^4 + (4*a^2*b + 5*a*b^2 + b^3)*sinh(d*x + c)^5 + 2*(4*a^2*b - 3*a*b^2 - b^3)*cosh(d*x + c)^3 + 2*(4*a^2*b - 3*a*b^2 - b^3 + 5*(4*a^2*b + 5*a*b^2 + b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 2*(5*(4*a^2*b + 5*a*b^2 + b^3)*cosh(d*x + c)^3 + 3*(4*a^2*b - 3*a*b^2 - b^3)*cosh(d*x + c))*sinh(d*x + c)^2 + (4*a^2*b + 5*a*b^2 + b^3)*cosh(d*x + c) + (5*(4*a^2*b + 5*a*b^2 + b^3)*cosh(d*x + c)^4 + 4*a^2*b + 5*a*b^2 + b^3 + 6*(4*a^2*b - 3*a*b^2 - b^3)*cosh(d*x + c)^2)*sinh(d*x + c))*sqrt(a^2 + a*b)*arctan(1/2*sqrt(a^2 + a*b)*(cosh(d*x + c) + sinh(d*x + c))/a) + 2*(3*(a^4 + 2*a^3*b + a^2*b^2)*cosh(d*x + c)^5 + 2*(a^4 - 2*a^3*b - a^2*b^2 + 2*a*b^3)*cosh(d*x + c)^3 - (a^4 - 2*a^3*b - a^2*b^2 + 2*a*b^3)*cosh(d*x + c))*sinh(d*x + c))/((a^6 + 4*a^5*b + 6*a^4*b^2 + 4*a^3*b^3 + a^2*b^4)*d*cosh(d*x + c)^5 + 5*(a^6 + 4*a^5*b + 6*a^4*b^2 + 4*a^3*b^3 + a^2*b^4)*d*cosh(d*x + c)*sinh(d*x + c)^4 + (a^6 + 4*a^5*b + 6*a^4*b^2 + 4*a^3*b^3 + a^2*b^4)*d*sinh(d*x + c)^5 + 2*(a^6 + 2*a^5*b - 2*a^3*b^3 - a^2*b^4)*d*cosh(d*x + c)^3 + 2*(5*(a^6 + 4*a^5*b + 6*a^4*b^2 + 4*a^3*b^3 + a^2*b^4)*d*cosh(d*x + c)^2 + (a^6 + 2*a^5*b - 2*a^3*b^3 - a^2*b^4)*d)*sinh(d*x + c)^3 + (a^6 + 4*a^5*b + 6*a^4*b^2 + 4*a^3*b^3 + a^2*b^4)*d*cosh(d*x + c) + 2*(5*(a^6 + 4*a^5*b + 6*a^4*b^2 + 4*a^3*b^3 + a^2*b^4)*d*cosh(d*x + c)^3 + 3*(a^6 + 2*a^5*b - 2*a^3*b^3 - a^2*b^4)*d*cosh(d*x + c))*sinh(d*x + c)^2 + (5*(a^6 + 4*a^5*b + 6*a^4*b^2 + 4*a^3*b^3 + a^2*b^4)*d*cosh(d*x + c)^4 + 6*(a^6 + 2*a^5*b - 2*a^3*b^3 - a^2*b^4)*d*cosh(d*x + c)^2 + (a^6 + 4*a^5*b + 6*a^4*b^2 + 4*a^3*b^3 + a^2*b^4)*d)*sinh(d*x + c))]","B",0
118,1,2041,0,0.463253," ","integrate(sech(d*x+c)/(a+b*tanh(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(2 \, a^{2} + 3 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(2 \, a^{2} + 3 \, a b + b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(2 \, a^{2} + 3 \, 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(2 \, a^{2} + 3 \, 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} + 2 \, a^{2} + 3 \, a b + b^{2} + 4 \, {\left({\left(2 \, a^{2} + 3 \, 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^{2} - a b} \log\left(\frac{{\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(3 \, a + b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} - 3 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(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) - 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^{2} - a b} + a + b}{{\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) - 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^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} d \cosh\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) \sinh\left(d x + c\right)^{3} + {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} d \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{5} + a^{4} b - a^{3} b^{2} - a^{2} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(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)^{2} + {\left(a^{5} + a^{4} b - a^{3} b^{2} - a^{2} b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} d + 4 \, {\left({\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(a^{5} + a^{4} b - 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(2 \, a^{2} + 3 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(2 \, a^{2} + 3 \, a b + b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(2 \, a^{2} + 3 \, 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(2 \, a^{2} + 3 \, 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} + 2 \, a^{2} + 3 \, a b + b^{2} + 4 \, {\left({\left(2 \, a^{2} + 3 \, 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^{2} + a b} \arctan\left(\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(3 \, a - b\right)} \cosh\left(d x + c\right) + {\left(3 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} + 3 \, a - b\right)} \sinh\left(d x + c\right)}{2 \, \sqrt{a^{2} + a b}}\right) + {\left({\left(2 \, a^{2} + 3 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(2 \, a^{2} + 3 \, a b + b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(2 \, a^{2} + 3 \, 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(2 \, a^{2} + 3 \, 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} + 2 \, a^{2} + 3 \, a b + b^{2} + 4 \, {\left({\left(2 \, a^{2} + 3 \, 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^{2} + a b} \arctan\left(\frac{\sqrt{a^{2} + a b} {\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right)}}{2 \, a}\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^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} d \cosh\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) \sinh\left(d x + c\right)^{3} + {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} d \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{5} + a^{4} b - a^{3} b^{2} - a^{2} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(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)^{2} + {\left(a^{5} + a^{4} b - a^{3} b^{2} - a^{2} b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} d + 4 \, {\left({\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(a^{5} + a^{4} b - 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 - ((2*a^2 + 3*a*b + b^2)*cosh(d*x + c)^4 + 4*(2*a^2 + 3*a*b + b^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (2*a^2 + 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*(2*a^2 + 3*a*b + b^2)*cosh(d*x + c)^2 + 2*a^2 - a*b - b^2)*sinh(d*x + c)^2 + 2*a^2 + 3*a*b + b^2 + 4*((2*a^2 + 3*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^2 - a*b)*log(((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*(3*a + b)*cosh(d*x + c)^2 + 2*(3*(a + b)*cosh(d*x + c)^2 - 3*a - b)*sinh(d*x + c)^2 + 4*((a + b)*cosh(d*x + c)^3 - (3*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^2 - a*b) + a + b)/((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)) - 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^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*d*cosh(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)*sinh(d*x + c)^3 + (a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*d*sinh(d*x + c)^4 + 2*(a^5 + a^4*b - a^3*b^2 - a^2*b^3)*d*cosh(d*x + c)^2 + 2*(3*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*d*cosh(d*x + c)^2 + (a^5 + a^4*b - a^3*b^2 - a^2*b^3)*d)*sinh(d*x + c)^2 + (a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*d + 4*((a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*d*cosh(d*x + c)^3 + (a^5 + a^4*b - 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 + ((2*a^2 + 3*a*b + b^2)*cosh(d*x + c)^4 + 4*(2*a^2 + 3*a*b + b^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (2*a^2 + 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*(2*a^2 + 3*a*b + b^2)*cosh(d*x + c)^2 + 2*a^2 - a*b - b^2)*sinh(d*x + c)^2 + 2*a^2 + 3*a*b + b^2 + 4*((2*a^2 + 3*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^2 + a*b)*arctan(1/2*((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 + (3*a - b)*cosh(d*x + c) + (3*(a + b)*cosh(d*x + c)^2 + 3*a - b)*sinh(d*x + c))/sqrt(a^2 + a*b)) + ((2*a^2 + 3*a*b + b^2)*cosh(d*x + c)^4 + 4*(2*a^2 + 3*a*b + b^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (2*a^2 + 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*(2*a^2 + 3*a*b + b^2)*cosh(d*x + c)^2 + 2*a^2 - a*b - b^2)*sinh(d*x + c)^2 + 2*a^2 + 3*a*b + b^2 + 4*((2*a^2 + 3*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^2 + a*b)*arctan(1/2*sqrt(a^2 + a*b)*(cosh(d*x + c) + sinh(d*x + c))/a) - 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^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*d*cosh(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)*sinh(d*x + c)^3 + (a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*d*sinh(d*x + c)^4 + 2*(a^5 + a^4*b - a^3*b^2 - a^2*b^3)*d*cosh(d*x + c)^2 + 2*(3*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*d*cosh(d*x + c)^2 + (a^5 + a^4*b - a^3*b^2 - a^2*b^3)*d)*sinh(d*x + c)^2 + (a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*d + 4*((a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*d*cosh(d*x + c)^3 + (a^5 + a^4*b - a^3*b^2 - a^2*b^3)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
119,1,1515,0,0.434790," ","integrate(sech(d*x+c)^2/(a+b*tanh(d*x+c)^2)^2,x, algorithm=""fricas"")","\left[-\frac{4 \, a^{2} b + 4 \, a b^{2} + 4 \, {\left(a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right)^{2} + 8 \, {\left(a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + 4 \, {\left(a^{2} b - a b^{2}\right)} \sinh\left(d x + c\right)^{2} + {\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) \sinh\left(d x + c\right)^{3} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 2 \, a b + b^{2} + 4 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-a b} \log\left(\frac{{\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) \sinh\left(d x + c\right)^{3} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{2} + a^{2} - 6 \, a b + b^{2} + 4 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} - b^{2}\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)^{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} + a - b\right)} \sqrt{-a b}}{{\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)}{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(a^{4} b - 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(a^{4} b - 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(a^{4} b - 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(a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + 2 \, {\left(a^{2} b - a b^{2}\right)} \sinh\left(d x + c\right)^{2} - {\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) \sinh\left(d x + c\right)^{3} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 2 \, a b + b^{2} + 4 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{a b} \arctan\left(\frac{{\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} + a - b\right)} \sqrt{a b}}{2 \, a b}\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(a^{4} b - 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(a^{4} b - 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(a^{4} b - 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*(a^2*b - a*b^2)*cosh(d*x + c)^2 + 8*(a^2*b - a*b^2)*cosh(d*x + c)*sinh(d*x + c) + 4*(a^2*b - a*b^2)*sinh(d*x + c)^2 + ((a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 + 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 + 2*(a^2 - b^2)*cosh(d*x + c)^2 + 2*(3*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + a^2 - b^2)*sinh(d*x + c)^2 + a^2 + 2*a*b + b^2 + 4*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 + (a^2 - b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-a*b)*log(((a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 + 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 + 2*(a^2 - b^2)*cosh(d*x + c)^2 + 2*(3*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + a^2 - b^2)*sinh(d*x + c)^2 + a^2 - 6*a*b + b^2 + 4*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 + (a^2 - 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 + a - b)*sqrt(-a*b))/((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)))/((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*(a^4*b - 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 + (a^4*b - 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 + (a^4*b - a^2*b^3)*d*cosh(d*x + c))*sinh(d*x + c)), -1/2*(2*a^2*b + 2*a*b^2 + 2*(a^2*b - a*b^2)*cosh(d*x + c)^2 + 4*(a^2*b - a*b^2)*cosh(d*x + c)*sinh(d*x + c) + 2*(a^2*b - a*b^2)*sinh(d*x + c)^2 - ((a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 + 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 + 2*(a^2 - b^2)*cosh(d*x + c)^2 + 2*(3*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + a^2 - b^2)*sinh(d*x + c)^2 + a^2 + 2*a*b + b^2 + 4*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 + (a^2 - b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(a*b)*arctan(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 + a - b)*sqrt(a*b)/(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*(a^4*b - 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 + (a^4*b - 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 + (a^4*b - a^2*b^3)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
120,1,1555,0,0.437855," ","integrate(sech(d*x+c)^3/(a+b*tanh(d*x+c)^2)^2,x, algorithm=""fricas"")","\left[\frac{4 \, {\left(a^{2} + a b\right)} \cosh\left(d x + c\right)^{3} + 12 \, {\left(a^{2} + a b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + 4 \, {\left(a^{2} + 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)} \sqrt{-a^{2} - a b} \log\left(\frac{{\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(3 \, a + b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} - 3 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(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) - 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^{2} - a b} + a + b}{{\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) - 4 \, {\left(a^{2} + a b\right)} \cosh\left(d x + c\right) + 4 \, {\left(3 \, {\left(a^{2} + a b\right)} \cosh\left(d x + c\right)^{2} - a^{2} - a b\right)} \sinh\left(d x + c\right)}{4 \, {\left({\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} d \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{4} - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{4} - a^{2} b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} d + 4 \, {\left({\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{4} - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}, \frac{2 \, {\left(a^{2} + a b\right)} \cosh\left(d x + c\right)^{3} + 6 \, {\left(a^{2} + a b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} + 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)} \sqrt{a^{2} + a b} \arctan\left(\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(3 \, a - b\right)} \cosh\left(d x + c\right) + {\left(3 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} + 3 \, a - b\right)} \sinh\left(d x + c\right)}{2 \, \sqrt{a^{2} + a b}}\right) + {\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)} \sqrt{a^{2} + a b} \arctan\left(\frac{\sqrt{a^{2} + a b} {\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right)}}{2 \, a}\right) - 2 \, {\left(a^{2} + a b\right)} \cosh\left(d x + c\right) + 2 \, {\left(3 \, {\left(a^{2} + a b\right)} \cosh\left(d x + c\right)^{2} - a^{2} - a b\right)} \sinh\left(d x + c\right)}{2 \, {\left({\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} d \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{4} - a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{4} - a^{2} b^{2}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} d + 4 \, {\left({\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{4} - 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^2 + a*b)*cosh(d*x + c)^3 + 12*(a^2 + a*b)*cosh(d*x + c)*sinh(d*x + c)^2 + 4*(a^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)*sqrt(-a^2 - a*b)*log(((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*(3*a + b)*cosh(d*x + c)^2 + 2*(3*(a + b)*cosh(d*x + c)^2 - 3*a - b)*sinh(d*x + c)^2 + 4*((a + b)*cosh(d*x + c)^3 - (3*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^2 - a*b) + a + b)/((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)) - 4*(a^2 + a*b)*cosh(d*x + c) + 4*(3*(a^2 + a*b)*cosh(d*x + c)^2 - a^2 - a*b)*sinh(d*x + c))/((a^4 + 2*a^3*b + a^2*b^2)*d*cosh(d*x + c)^4 + 4*(a^4 + 2*a^3*b + a^2*b^2)*d*cosh(d*x + c)*sinh(d*x + c)^3 + (a^4 + 2*a^3*b + a^2*b^2)*d*sinh(d*x + c)^4 + 2*(a^4 - a^2*b^2)*d*cosh(d*x + c)^2 + 2*(3*(a^4 + 2*a^3*b + a^2*b^2)*d*cosh(d*x + c)^2 + (a^4 - a^2*b^2)*d)*sinh(d*x + c)^2 + (a^4 + 2*a^3*b + a^2*b^2)*d + 4*((a^4 + 2*a^3*b + a^2*b^2)*d*cosh(d*x + c)^3 + (a^4 - a^2*b^2)*d*cosh(d*x + c))*sinh(d*x + c)), 1/2*(2*(a^2 + a*b)*cosh(d*x + c)^3 + 6*(a^2 + a*b)*cosh(d*x + c)*sinh(d*x + c)^2 + 2*(a^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)*sqrt(a^2 + a*b)*arctan(1/2*((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 + (3*a - b)*cosh(d*x + c) + (3*(a + b)*cosh(d*x + c)^2 + 3*a - b)*sinh(d*x + c))/sqrt(a^2 + a*b)) + ((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)*sqrt(a^2 + a*b)*arctan(1/2*sqrt(a^2 + a*b)*(cosh(d*x + c) + sinh(d*x + c))/a) - 2*(a^2 + a*b)*cosh(d*x + c) + 2*(3*(a^2 + a*b)*cosh(d*x + c)^2 - a^2 - a*b)*sinh(d*x + c))/((a^4 + 2*a^3*b + a^2*b^2)*d*cosh(d*x + c)^4 + 4*(a^4 + 2*a^3*b + a^2*b^2)*d*cosh(d*x + c)*sinh(d*x + c)^3 + (a^4 + 2*a^3*b + a^2*b^2)*d*sinh(d*x + c)^4 + 2*(a^4 - a^2*b^2)*d*cosh(d*x + c)^2 + 2*(3*(a^4 + 2*a^3*b + a^2*b^2)*d*cosh(d*x + c)^2 + (a^4 - a^2*b^2)*d)*sinh(d*x + c)^2 + (a^4 + 2*a^3*b + a^2*b^2)*d + 4*((a^4 + 2*a^3*b + a^2*b^2)*d*cosh(d*x + c)^3 + (a^4 - a^2*b^2)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
121,1,1443,0,0.444364," ","integrate(sech(d*x+c)^4/(a+b*tanh(d*x+c)^2)^2,x, algorithm=""fricas"")","\left[-\frac{4 \, a^{2} b + 4 \, a b^{2} + 4 \, {\left(a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right)^{2} + 8 \, {\left(a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + 4 \, {\left(a^{2} b - a b^{2}\right)} \sinh\left(d x + c\right)^{2} - {\left({\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} - 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{2} + a^{2} - b^{2} + 4 \, {\left({\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} - 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{{\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) \sinh\left(d x + c\right)^{3} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{2} + a^{2} - 6 \, a b + b^{2} + 4 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} - b^{2}\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)^{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} + a - b\right)} \sqrt{-a b}}{{\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)}{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(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(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(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(a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + 2 \, {\left(a^{2} b - a b^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} - 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{2} + a^{2} - b^{2} + 4 \, {\left({\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} - 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({\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} + a - b\right)} \sqrt{a b}}{2 \, a b}\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(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(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(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*(a^2*b - a*b^2)*cosh(d*x + c)^2 + 8*(a^2*b - a*b^2)*cosh(d*x + c)*sinh(d*x + c) + 4*(a^2*b - a*b^2)*sinh(d*x + c)^2 - ((a^2 - b^2)*cosh(d*x + c)^4 + 4*(a^2 - b^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (a^2 - b^2)*sinh(d*x + c)^4 + 2*(a^2 - 2*a*b + b^2)*cosh(d*x + c)^2 + 2*(3*(a^2 - b^2)*cosh(d*x + c)^2 + a^2 - 2*a*b + b^2)*sinh(d*x + c)^2 + a^2 - b^2 + 4*((a^2 - b^2)*cosh(d*x + c)^3 + (a^2 - 2*a*b + b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-a*b)*log(((a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 + 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 + 2*(a^2 - b^2)*cosh(d*x + c)^2 + 2*(3*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + a^2 - b^2)*sinh(d*x + c)^2 + a^2 - 6*a*b + b^2 + 4*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 + (a^2 - 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 + a - b)*sqrt(-a*b))/((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)))/((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*(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 + (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 + (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*(a^2*b - a*b^2)*cosh(d*x + c)^2 + 4*(a^2*b - a*b^2)*cosh(d*x + c)*sinh(d*x + c) + 2*(a^2*b - a*b^2)*sinh(d*x + c)^2 + ((a^2 - b^2)*cosh(d*x + c)^4 + 4*(a^2 - b^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (a^2 - b^2)*sinh(d*x + c)^4 + 2*(a^2 - 2*a*b + b^2)*cosh(d*x + c)^2 + 2*(3*(a^2 - b^2)*cosh(d*x + c)^2 + a^2 - 2*a*b + b^2)*sinh(d*x + c)^2 + a^2 - b^2 + 4*((a^2 - b^2)*cosh(d*x + c)^3 + (a^2 - 2*a*b + b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(a*b)*arctan(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 + a - b)*sqrt(a*b)/(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*(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 + (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 + (a^3*b^2 - a^2*b^3)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
122,1,2140,0,0.515884," ","integrate(sech(d*x+c)^5/(a+b*tanh(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(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(2 \, a^{2} + 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(2 \, a^{2} + 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} + 2 \, a^{2} + a b - b^{2} + 4 \, {\left({\left(2 \, a^{2} + 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)} \sqrt{-\frac{a + b}{a}} \log\left(\frac{{\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(3 \, a + b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} - 3 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(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) + 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{a + b}{a}} + a + b}{{\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) + 8 \, {\left({\left(a^{2} + a b\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{2} + a b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{2} + a b\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{2} - a b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} + a b\right)} \cosh\left(d x + c\right)^{2} + a^{2} - a b\right)} \sinh\left(d x + c\right)^{2} + a^{2} + a b + 4 \, {\left({\left(a^{2} + a b\right)} \cosh\left(d x + c\right)^{3} + {\left(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^{2} b^{2} + a b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{2} b^{2} + a b^{3}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{2} b^{2} + a b^{3}\right)} d \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{2} b^{2} - a b^{3}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} b^{2} + a b^{3}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{2} b^{2} - a b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{2} b^{2} + a b^{3}\right)} d + 4 \, {\left({\left(a^{2} b^{2} + a b^{3}\right)} d \cosh\left(d x + c\right)^{3} + {\left(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(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(2 \, a^{2} + 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(2 \, a^{2} + 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} + 2 \, a^{2} + a b - b^{2} + 4 \, {\left({\left(2 \, a^{2} + 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)} \sqrt{\frac{a + b}{a}} \arctan\left(\frac{1}{2} \, \sqrt{\frac{a + b}{a}} {\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right)}\right) - {\left({\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(2 \, a^{2} + 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(2 \, a^{2} + 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} + 2 \, a^{2} + a b - b^{2} + 4 \, {\left({\left(2 \, a^{2} + 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)} \sqrt{\frac{a + b}{a}} \arctan\left(\frac{{\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(3 \, a - b\right)} \cosh\left(d x + c\right) + {\left(3 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} + 3 \, a - b\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a + b}{a}}}{2 \, {\left(a + b\right)}}\right) + 4 \, {\left({\left(a^{2} + a b\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{2} + a b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{2} + a b\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{2} - a b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} + a b\right)} \cosh\left(d x + c\right)^{2} + a^{2} - a b\right)} \sinh\left(d x + c\right)^{2} + a^{2} + a b + 4 \, {\left({\left(a^{2} + a b\right)} \cosh\left(d x + c\right)^{3} + {\left(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^{2} b^{2} + a b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{2} b^{2} + a b^{3}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{2} b^{2} + a b^{3}\right)} d \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{2} b^{2} - a b^{3}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} b^{2} + a b^{3}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{2} b^{2} - a b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{2} b^{2} + a b^{3}\right)} d + 4 \, {\left({\left(a^{2} b^{2} + a b^{3}\right)} d \cosh\left(d x + c\right)^{3} + {\left(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 - ((2*a^2 + a*b - b^2)*cosh(d*x + c)^4 + 4*(2*a^2 + a*b - b^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (2*a^2 + 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*(2*a^2 + a*b - b^2)*cosh(d*x + c)^2 + 2*a^2 - 3*a*b + b^2)*sinh(d*x + c)^2 + 2*a^2 + a*b - b^2 + 4*((2*a^2 + 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))*sqrt(-(a + b)/a)*log(((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*(3*a + b)*cosh(d*x + c)^2 + 2*(3*(a + b)*cosh(d*x + c)^2 - 3*a - b)*sinh(d*x + c)^2 + 4*((a + b)*cosh(d*x + c)^3 - (3*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(-(a + b)/a) + a + b)/((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)) + 8*((a^2 + a*b)*cosh(d*x + c)^4 + 4*(a^2 + a*b)*cosh(d*x + c)*sinh(d*x + c)^3 + (a^2 + a*b)*sinh(d*x + c)^4 + 2*(a^2 - a*b)*cosh(d*x + c)^2 + 2*(3*(a^2 + a*b)*cosh(d*x + c)^2 + a^2 - a*b)*sinh(d*x + c)^2 + a^2 + a*b + 4*((a^2 + a*b)*cosh(d*x + c)^3 + (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^2*b^2 + a*b^3)*d*cosh(d*x + c)^4 + 4*(a^2*b^2 + a*b^3)*d*cosh(d*x + c)*sinh(d*x + c)^3 + (a^2*b^2 + a*b^3)*d*sinh(d*x + c)^4 + 2*(a^2*b^2 - a*b^3)*d*cosh(d*x + c)^2 + 2*(3*(a^2*b^2 + a*b^3)*d*cosh(d*x + c)^2 + (a^2*b^2 - a*b^3)*d)*sinh(d*x + c)^2 + (a^2*b^2 + a*b^3)*d + 4*((a^2*b^2 + a*b^3)*d*cosh(d*x + c)^3 + (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 - ((2*a^2 + a*b - b^2)*cosh(d*x + c)^4 + 4*(2*a^2 + a*b - b^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (2*a^2 + 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*(2*a^2 + a*b - b^2)*cosh(d*x + c)^2 + 2*a^2 - 3*a*b + b^2)*sinh(d*x + c)^2 + 2*a^2 + a*b - b^2 + 4*((2*a^2 + 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))*sqrt((a + b)/a)*arctan(1/2*sqrt((a + b)/a)*(cosh(d*x + c) + sinh(d*x + c))) - ((2*a^2 + a*b - b^2)*cosh(d*x + c)^4 + 4*(2*a^2 + a*b - b^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (2*a^2 + 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*(2*a^2 + a*b - b^2)*cosh(d*x + c)^2 + 2*a^2 - 3*a*b + b^2)*sinh(d*x + c)^2 + 2*a^2 + a*b - b^2 + 4*((2*a^2 + 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))*sqrt((a + b)/a)*arctan(1/2*((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 + (3*a - b)*cosh(d*x + c) + (3*(a + b)*cosh(d*x + c)^2 + 3*a - b)*sinh(d*x + c))*sqrt((a + b)/a)/(a + b)) + 4*((a^2 + a*b)*cosh(d*x + c)^4 + 4*(a^2 + a*b)*cosh(d*x + c)*sinh(d*x + c)^3 + (a^2 + a*b)*sinh(d*x + c)^4 + 2*(a^2 - a*b)*cosh(d*x + c)^2 + 2*(3*(a^2 + a*b)*cosh(d*x + c)^2 + a^2 - a*b)*sinh(d*x + c)^2 + a^2 + a*b + 4*((a^2 + a*b)*cosh(d*x + c)^3 + (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^2*b^2 + a*b^3)*d*cosh(d*x + c)^4 + 4*(a^2*b^2 + a*b^3)*d*cosh(d*x + c)*sinh(d*x + c)^3 + (a^2*b^2 + a*b^3)*d*sinh(d*x + c)^4 + 2*(a^2*b^2 - a*b^3)*d*cosh(d*x + c)^2 + 2*(3*(a^2*b^2 + a*b^3)*d*cosh(d*x + c)^2 + (a^2*b^2 - a*b^3)*d)*sinh(d*x + c)^2 + (a^2*b^2 + a*b^3)*d + 4*((a^2*b^2 + a*b^3)*d*cosh(d*x + c)^3 + (a^2*b^2 - a*b^3)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
123,1,2869,0,0.502418," ","integrate(sech(d*x+c)^6/(a+b*tanh(d*x+c)^2)^2,x, algorithm=""fricas"")","\left[-\frac{4 \, {\left(3 \, a^{3} b + 2 \, a^{2} b^{2} - a b^{3}\right)} \cosh\left(d x + c\right)^{4} + 16 \, {\left(3 \, a^{3} b + 2 \, a^{2} b^{2} - a b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + 4 \, {\left(3 \, a^{3} b + 2 \, a^{2} b^{2} - a b^{3}\right)} \sinh\left(d x + c\right)^{4} + 12 \, a^{3} b + 16 \, a^{2} b^{2} + 4 \, a b^{3} + 8 \, {\left(3 \, a^{3} b - a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{2} + 8 \, {\left(3 \, a^{3} b - a^{2} b^{2} + 3 \, {\left(3 \, a^{3} b + 2 \, 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(3 \, a^{3} + 5 \, a^{2} b + a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{6} + 6 \, {\left(3 \, a^{3} + 5 \, a^{2} b + a b^{2} - b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(3 \, a^{3} + 5 \, a^{2} b + a b^{2} - b^{3}\right)} \sinh\left(d x + c\right)^{6} + {\left(9 \, a^{3} + 3 \, a^{2} b - 5 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{4} + {\left(9 \, a^{3} + 3 \, a^{2} b - 5 \, a b^{2} + b^{3} + 15 \, {\left(3 \, a^{3} + 5 \, a^{2} b + 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(3 \, a^{3} + 5 \, a^{2} b + a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(9 \, a^{3} + 3 \, a^{2} b - 5 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 3 \, a^{3} + 5 \, a^{2} b + a b^{2} - b^{3} + {\left(9 \, a^{3} + 3 \, a^{2} b - 5 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{2} + {\left(15 \, {\left(3 \, a^{3} + 5 \, a^{2} b + a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{4} + 9 \, a^{3} + 3 \, a^{2} b - 5 \, a b^{2} + b^{3} + 6 \, {\left(9 \, a^{3} + 3 \, a^{2} b - 5 \, 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(3 \, a^{3} + 5 \, a^{2} b + a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(9 \, a^{3} + 3 \, a^{2} b - 5 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(9 \, a^{3} + 3 \, a^{2} b - 5 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-a b} \log\left(\frac{{\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) \sinh\left(d x + c\right)^{3} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{2} + a^{2} - 6 \, a b + b^{2} + 4 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} - b^{2}\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)^{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} + a - b\right)} \sqrt{-a b}}{{\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) + 16 \, {\left({\left(3 \, a^{3} b + 2 \, a^{2} b^{2} - a b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, 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^{3} b^{3} + a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{6} + 6 \, {\left(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^{3} b^{3} + a^{2} b^{4}\right)} d \sinh\left(d x + c\right)^{6} + {\left(3 \, a^{3} b^{3} - a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{4} + {\left(15 \, {\left(a^{3} b^{3} + a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{3} b^{3} - a^{2} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{4} + {\left(3 \, a^{3} b^{3} - a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + 4 \, {\left(5 \, {\left(a^{3} b^{3} + a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{3} + {\left(3 \, 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^{3} b^{3} + a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 6 \, {\left(3 \, a^{3} b^{3} - a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{3} b^{3} - a^{2} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{3} b^{3} + a^{2} b^{4}\right)} d + 2 \, {\left(3 \, {\left(a^{3} b^{3} + a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{5} + 2 \, {\left(3 \, a^{3} b^{3} - a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{3} + {\left(3 \, 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(3 \, a^{3} b + 2 \, a^{2} b^{2} - a b^{3}\right)} \cosh\left(d x + c\right)^{4} + 8 \, {\left(3 \, a^{3} b + 2 \, a^{2} b^{2} - a b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + 2 \, {\left(3 \, a^{3} b + 2 \, a^{2} b^{2} - a b^{3}\right)} \sinh\left(d x + c\right)^{4} + 6 \, a^{3} b + 8 \, a^{2} b^{2} + 2 \, a b^{3} + 4 \, {\left(3 \, a^{3} b - a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(3 \, a^{3} b - a^{2} b^{2} + 3 \, {\left(3 \, a^{3} b + 2 \, 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(3 \, a^{3} + 5 \, a^{2} b + a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{6} + 6 \, {\left(3 \, a^{3} + 5 \, a^{2} b + a b^{2} - b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(3 \, a^{3} + 5 \, a^{2} b + a b^{2} - b^{3}\right)} \sinh\left(d x + c\right)^{6} + {\left(9 \, a^{3} + 3 \, a^{2} b - 5 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{4} + {\left(9 \, a^{3} + 3 \, a^{2} b - 5 \, a b^{2} + b^{3} + 15 \, {\left(3 \, a^{3} + 5 \, a^{2} b + 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(3 \, a^{3} + 5 \, a^{2} b + a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(9 \, a^{3} + 3 \, a^{2} b - 5 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 3 \, a^{3} + 5 \, a^{2} b + a b^{2} - b^{3} + {\left(9 \, a^{3} + 3 \, a^{2} b - 5 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{2} + {\left(15 \, {\left(3 \, a^{3} + 5 \, a^{2} b + a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{4} + 9 \, a^{3} + 3 \, a^{2} b - 5 \, a b^{2} + b^{3} + 6 \, {\left(9 \, a^{3} + 3 \, a^{2} b - 5 \, 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(3 \, a^{3} + 5 \, a^{2} b + a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(9 \, a^{3} + 3 \, a^{2} b - 5 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(9 \, a^{3} + 3 \, a^{2} b - 5 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{a b} \arctan\left(\frac{{\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} + a - b\right)} \sqrt{a b}}{2 \, a b}\right) + 8 \, {\left({\left(3 \, a^{3} b + 2 \, a^{2} b^{2} - a b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, 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^{3} b^{3} + a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{6} + 6 \, {\left(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^{3} b^{3} + a^{2} b^{4}\right)} d \sinh\left(d x + c\right)^{6} + {\left(3 \, a^{3} b^{3} - a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{4} + {\left(15 \, {\left(a^{3} b^{3} + a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{3} b^{3} - a^{2} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{4} + {\left(3 \, a^{3} b^{3} - a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + 4 \, {\left(5 \, {\left(a^{3} b^{3} + a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{3} + {\left(3 \, 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^{3} b^{3} + a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 6 \, {\left(3 \, a^{3} b^{3} - a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{3} b^{3} - a^{2} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{3} b^{3} + a^{2} b^{4}\right)} d + 2 \, {\left(3 \, {\left(a^{3} b^{3} + a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{5} + 2 \, {\left(3 \, a^{3} b^{3} - a^{2} b^{4}\right)} d \cosh\left(d x + c\right)^{3} + {\left(3 \, 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*(3*a^3*b + 2*a^2*b^2 - a*b^3)*cosh(d*x + c)^4 + 16*(3*a^3*b + 2*a^2*b^2 - a*b^3)*cosh(d*x + c)*sinh(d*x + c)^3 + 4*(3*a^3*b + 2*a^2*b^2 - a*b^3)*sinh(d*x + c)^4 + 12*a^3*b + 16*a^2*b^2 + 4*a*b^3 + 8*(3*a^3*b - a^2*b^2)*cosh(d*x + c)^2 + 8*(3*a^3*b - a^2*b^2 + 3*(3*a^3*b + 2*a^2*b^2 - a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - ((3*a^3 + 5*a^2*b + a*b^2 - b^3)*cosh(d*x + c)^6 + 6*(3*a^3 + 5*a^2*b + a*b^2 - b^3)*cosh(d*x + c)*sinh(d*x + c)^5 + (3*a^3 + 5*a^2*b + a*b^2 - b^3)*sinh(d*x + c)^6 + (9*a^3 + 3*a^2*b - 5*a*b^2 + b^3)*cosh(d*x + c)^4 + (9*a^3 + 3*a^2*b - 5*a*b^2 + b^3 + 15*(3*a^3 + 5*a^2*b + a*b^2 - b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 4*(5*(3*a^3 + 5*a^2*b + a*b^2 - b^3)*cosh(d*x + c)^3 + (9*a^3 + 3*a^2*b - 5*a*b^2 + b^3)*cosh(d*x + c))*sinh(d*x + c)^3 + 3*a^3 + 5*a^2*b + a*b^2 - b^3 + (9*a^3 + 3*a^2*b - 5*a*b^2 + b^3)*cosh(d*x + c)^2 + (15*(3*a^3 + 5*a^2*b + a*b^2 - b^3)*cosh(d*x + c)^4 + 9*a^3 + 3*a^2*b - 5*a*b^2 + b^3 + 6*(9*a^3 + 3*a^2*b - 5*a*b^2 + b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 2*(3*(3*a^3 + 5*a^2*b + a*b^2 - b^3)*cosh(d*x + c)^5 + 2*(9*a^3 + 3*a^2*b - 5*a*b^2 + b^3)*cosh(d*x + c)^3 + (9*a^3 + 3*a^2*b - 5*a*b^2 + b^3)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-a*b)*log(((a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 + 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 + 2*(a^2 - b^2)*cosh(d*x + c)^2 + 2*(3*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + a^2 - b^2)*sinh(d*x + c)^2 + a^2 - 6*a*b + b^2 + 4*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 + (a^2 - 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 + a - b)*sqrt(-a*b))/((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)) + 16*((3*a^3*b + 2*a^2*b^2 - a*b^3)*cosh(d*x + c)^3 + (3*a^3*b - a^2*b^2)*cosh(d*x + c))*sinh(d*x + c))/((a^3*b^3 + a^2*b^4)*d*cosh(d*x + c)^6 + 6*(a^3*b^3 + a^2*b^4)*d*cosh(d*x + c)*sinh(d*x + c)^5 + (a^3*b^3 + a^2*b^4)*d*sinh(d*x + c)^6 + (3*a^3*b^3 - a^2*b^4)*d*cosh(d*x + c)^4 + (15*(a^3*b^3 + a^2*b^4)*d*cosh(d*x + c)^2 + (3*a^3*b^3 - a^2*b^4)*d)*sinh(d*x + c)^4 + (3*a^3*b^3 - a^2*b^4)*d*cosh(d*x + c)^2 + 4*(5*(a^3*b^3 + a^2*b^4)*d*cosh(d*x + c)^3 + (3*a^3*b^3 - a^2*b^4)*d*cosh(d*x + c))*sinh(d*x + c)^3 + (15*(a^3*b^3 + a^2*b^4)*d*cosh(d*x + c)^4 + 6*(3*a^3*b^3 - a^2*b^4)*d*cosh(d*x + c)^2 + (3*a^3*b^3 - a^2*b^4)*d)*sinh(d*x + c)^2 + (a^3*b^3 + a^2*b^4)*d + 2*(3*(a^3*b^3 + a^2*b^4)*d*cosh(d*x + c)^5 + 2*(3*a^3*b^3 - a^2*b^4)*d*cosh(d*x + c)^3 + (3*a^3*b^3 - a^2*b^4)*d*cosh(d*x + c))*sinh(d*x + c)), -1/2*(2*(3*a^3*b + 2*a^2*b^2 - a*b^3)*cosh(d*x + c)^4 + 8*(3*a^3*b + 2*a^2*b^2 - a*b^3)*cosh(d*x + c)*sinh(d*x + c)^3 + 2*(3*a^3*b + 2*a^2*b^2 - a*b^3)*sinh(d*x + c)^4 + 6*a^3*b + 8*a^2*b^2 + 2*a*b^3 + 4*(3*a^3*b - a^2*b^2)*cosh(d*x + c)^2 + 4*(3*a^3*b - a^2*b^2 + 3*(3*a^3*b + 2*a^2*b^2 - a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((3*a^3 + 5*a^2*b + a*b^2 - b^3)*cosh(d*x + c)^6 + 6*(3*a^3 + 5*a^2*b + a*b^2 - b^3)*cosh(d*x + c)*sinh(d*x + c)^5 + (3*a^3 + 5*a^2*b + a*b^2 - b^3)*sinh(d*x + c)^6 + (9*a^3 + 3*a^2*b - 5*a*b^2 + b^3)*cosh(d*x + c)^4 + (9*a^3 + 3*a^2*b - 5*a*b^2 + b^3 + 15*(3*a^3 + 5*a^2*b + a*b^2 - b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 4*(5*(3*a^3 + 5*a^2*b + a*b^2 - b^3)*cosh(d*x + c)^3 + (9*a^3 + 3*a^2*b - 5*a*b^2 + b^3)*cosh(d*x + c))*sinh(d*x + c)^3 + 3*a^3 + 5*a^2*b + a*b^2 - b^3 + (9*a^3 + 3*a^2*b - 5*a*b^2 + b^3)*cosh(d*x + c)^2 + (15*(3*a^3 + 5*a^2*b + a*b^2 - b^3)*cosh(d*x + c)^4 + 9*a^3 + 3*a^2*b - 5*a*b^2 + b^3 + 6*(9*a^3 + 3*a^2*b - 5*a*b^2 + b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 2*(3*(3*a^3 + 5*a^2*b + a*b^2 - b^3)*cosh(d*x + c)^5 + 2*(9*a^3 + 3*a^2*b - 5*a*b^2 + b^3)*cosh(d*x + c)^3 + (9*a^3 + 3*a^2*b - 5*a*b^2 + b^3)*cosh(d*x + c))*sinh(d*x + c))*sqrt(a*b)*arctan(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 + a - b)*sqrt(a*b)/(a*b)) + 8*((3*a^3*b + 2*a^2*b^2 - a*b^3)*cosh(d*x + c)^3 + (3*a^3*b - a^2*b^2)*cosh(d*x + c))*sinh(d*x + c))/((a^3*b^3 + a^2*b^4)*d*cosh(d*x + c)^6 + 6*(a^3*b^3 + a^2*b^4)*d*cosh(d*x + c)*sinh(d*x + c)^5 + (a^3*b^3 + a^2*b^4)*d*sinh(d*x + c)^6 + (3*a^3*b^3 - a^2*b^4)*d*cosh(d*x + c)^4 + (15*(a^3*b^3 + a^2*b^4)*d*cosh(d*x + c)^2 + (3*a^3*b^3 - a^2*b^4)*d)*sinh(d*x + c)^4 + (3*a^3*b^3 - a^2*b^4)*d*cosh(d*x + c)^2 + 4*(5*(a^3*b^3 + a^2*b^4)*d*cosh(d*x + c)^3 + (3*a^3*b^3 - a^2*b^4)*d*cosh(d*x + c))*sinh(d*x + c)^3 + (15*(a^3*b^3 + a^2*b^4)*d*cosh(d*x + c)^4 + 6*(3*a^3*b^3 - a^2*b^4)*d*cosh(d*x + c)^2 + (3*a^3*b^3 - a^2*b^4)*d)*sinh(d*x + c)^2 + (a^3*b^3 + a^2*b^4)*d + 2*(3*(a^3*b^3 + a^2*b^4)*d*cosh(d*x + c)^5 + 2*(3*a^3*b^3 - a^2*b^4)*d*cosh(d*x + c)^3 + (3*a^3*b^3 - a^2*b^4)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
124,1,6396,0,0.572847," ","integrate(sech(d*x+c)^7/(a+b*tanh(d*x+c)^2)^2,x, algorithm=""fricas"")","\left[\frac{4 \, {\left(2 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{7} + 28 \, {\left(2 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + 4 \, {\left(2 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \sinh\left(d x + c\right)^{7} + 4 \, {\left(2 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{5} + 4 \, {\left(2 \, a^{2} b - a b^{2} + b^{3} + 21 \, {\left(2 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{5} + 20 \, {\left(7 \, {\left(2 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} - 4 \, {\left(2 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(35 \, {\left(2 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{4} - 2 \, a^{2} b + a b^{2} - b^{3} + 10 \, {\left(2 \, a^{2} b - 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(2 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(2 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(2 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - {\left({\left(4 \, a^{3} + 7 \, a^{2} b + 2 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(4 \, a^{3} + 7 \, a^{2} b + 2 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(4 \, a^{3} + 7 \, a^{2} b + 2 \, a b^{2} - b^{3}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(4 \, a^{3} + 3 \, a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(4 \, a^{3} + 3 \, a^{2} b - a b^{2} + 7 \, {\left(4 \, a^{3} + 7 \, a^{2} b + 2 \, 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(4 \, a^{3} + 7 \, a^{2} b + 2 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(4 \, a^{3} + 3 \, a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(12 \, a^{3} + 5 \, a^{2} b - 6 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(4 \, a^{3} + 7 \, a^{2} b + 2 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{4} + 12 \, a^{3} + 5 \, a^{2} b - 6 \, a b^{2} + b^{3} + 30 \, {\left(4 \, a^{3} + 3 \, 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(4 \, a^{3} + 7 \, a^{2} b + 2 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(4 \, a^{3} + 3 \, a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(12 \, a^{3} + 5 \, a^{2} b - 6 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, a^{3} + 7 \, a^{2} b + 2 \, a b^{2} - b^{3} + 4 \, {\left(4 \, a^{3} + 3 \, a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(4 \, a^{3} + 7 \, a^{2} b + 2 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(4 \, a^{3} + 3 \, a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, a^{3} + 3 \, a^{2} b - a b^{2} + 3 \, {\left(12 \, a^{3} + 5 \, a^{2} b - 6 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left({\left(4 \, a^{3} + 7 \, a^{2} b + 2 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(4 \, a^{3} + 3 \, a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right)^{5} + {\left(12 \, a^{3} + 5 \, a^{2} b - 6 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(4 \, a^{3} + 3 \, a^{2} b - a 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{{\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(3 \, a + b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} - 3 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(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) + 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{a + b}{a}} + a + b}{{\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) + 4 \, {\left({\left(4 \, a^{3} + 9 \, a^{2} b + 5 \, a b^{2}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(4 \, a^{3} + 9 \, a^{2} b + 5 \, a b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(4 \, a^{3} + 9 \, a^{2} b + 5 \, a b^{2}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(4 \, a^{3} + 5 \, a^{2} b\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(4 \, a^{3} + 5 \, a^{2} b + 7 \, {\left(4 \, a^{3} + 9 \, 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(4 \, a^{3} + 9 \, a^{2} b + 5 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(4 \, a^{3} + 5 \, a^{2} b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(12 \, a^{3} + 11 \, a^{2} b - 5 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(4 \, a^{3} + 9 \, a^{2} b + 5 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} + 12 \, a^{3} + 11 \, a^{2} b - 5 \, a b^{2} + 30 \, {\left(4 \, 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(4 \, a^{3} + 9 \, a^{2} b + 5 \, a b^{2}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(4 \, a^{3} + 5 \, a^{2} b\right)} \cosh\left(d x + c\right)^{3} + {\left(12 \, a^{3} + 11 \, a^{2} b - 5 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, a^{3} + 9 \, a^{2} b + 5 \, a b^{2} + 4 \, {\left(4 \, a^{3} + 5 \, a^{2} b\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(4 \, a^{3} + 9 \, a^{2} b + 5 \, a b^{2}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(4 \, a^{3} + 5 \, a^{2} b\right)} \cosh\left(d x + c\right)^{4} + 4 \, a^{3} + 5 \, a^{2} b + 3 \, {\left(12 \, a^{3} + 11 \, 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(4 \, a^{3} + 9 \, a^{2} b + 5 \, a b^{2}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(4 \, a^{3} + 5 \, a^{2} b\right)} \cosh\left(d x + c\right)^{5} + {\left(12 \, a^{3} + 11 \, a^{2} b - 5 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(4 \, 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(2 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right) + 4 \, {\left(7 \, {\left(2 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{6} + 5 \, {\left(2 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{4} - 2 \, a^{2} b - 3 \, a b^{2} - b^{3} - 3 \, {\left(2 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)}{4 \, {\left(4 \, a^{2} b^{3} d \cosh\left(d x + c\right)^{6} + {\left(a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{2} b^{3} + a b^{4}\right)} d \sinh\left(d x + c\right)^{8} + 4 \, a^{2} b^{3} d \cosh\left(d x + c\right)^{2} + 4 \, {\left(a^{2} b^{3} d + 7 \, {\left(a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(3 \, a^{2} b^{3} - a b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(3 \, a^{2} b^{3} d \cosh\left(d x + c\right) + 7 \, {\left(a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(30 \, a^{2} b^{3} d \cosh\left(d x + c\right)^{2} + 35 \, {\left(a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)^{4} + {\left(3 \, a^{2} b^{3} - a b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(10 \, a^{2} b^{3} d \cosh\left(d x + c\right)^{3} + 7 \, {\left(a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)^{5} + {\left(3 \, 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(15 \, a^{2} b^{3} d \cosh\left(d x + c\right)^{4} + 7 \, {\left(a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)^{6} + a^{2} b^{3} d + 3 \, {\left(3 \, a^{2} b^{3} - a b^{4}\right)} d \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{2} b^{3} + a b^{4}\right)} d + 8 \, {\left(3 \, a^{2} b^{3} d \cosh\left(d x + c\right)^{5} + {\left(a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)^{7} + a^{2} b^{3} d \cosh\left(d x + c\right) + {\left(3 \, 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{2 \, {\left(2 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{7} + 14 \, {\left(2 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + 2 \, {\left(2 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(2 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(2 \, a^{2} b - a b^{2} + b^{3} + 21 \, {\left(2 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{5} + 10 \, {\left(7 \, {\left(2 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(2 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(35 \, {\left(2 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{4} - 2 \, a^{2} b + a b^{2} - b^{3} + 10 \, {\left(2 \, a^{2} b - 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(2 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(2 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(2 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - {\left({\left(4 \, a^{3} + 7 \, a^{2} b + 2 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(4 \, a^{3} + 7 \, a^{2} b + 2 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(4 \, a^{3} + 7 \, a^{2} b + 2 \, a b^{2} - b^{3}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(4 \, a^{3} + 3 \, a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(4 \, a^{3} + 3 \, a^{2} b - a b^{2} + 7 \, {\left(4 \, a^{3} + 7 \, a^{2} b + 2 \, 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(4 \, a^{3} + 7 \, a^{2} b + 2 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(4 \, a^{3} + 3 \, a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(12 \, a^{3} + 5 \, a^{2} b - 6 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(4 \, a^{3} + 7 \, a^{2} b + 2 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{4} + 12 \, a^{3} + 5 \, a^{2} b - 6 \, a b^{2} + b^{3} + 30 \, {\left(4 \, a^{3} + 3 \, 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(4 \, a^{3} + 7 \, a^{2} b + 2 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(4 \, a^{3} + 3 \, a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(12 \, a^{3} + 5 \, a^{2} b - 6 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, a^{3} + 7 \, a^{2} b + 2 \, a b^{2} - b^{3} + 4 \, {\left(4 \, a^{3} + 3 \, a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(4 \, a^{3} + 7 \, a^{2} b + 2 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(4 \, a^{3} + 3 \, a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, a^{3} + 3 \, a^{2} b - a b^{2} + 3 \, {\left(12 \, a^{3} + 5 \, a^{2} b - 6 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left({\left(4 \, a^{3} + 7 \, a^{2} b + 2 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(4 \, a^{3} + 3 \, a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right)^{5} + {\left(12 \, a^{3} + 5 \, a^{2} b - 6 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(4 \, a^{3} + 3 \, a^{2} b - a 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{1}{2} \, \sqrt{\frac{a + b}{a}} {\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right)}\right) - {\left({\left(4 \, a^{3} + 7 \, a^{2} b + 2 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(4 \, a^{3} + 7 \, a^{2} b + 2 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(4 \, a^{3} + 7 \, a^{2} b + 2 \, a b^{2} - b^{3}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(4 \, a^{3} + 3 \, a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(4 \, a^{3} + 3 \, a^{2} b - a b^{2} + 7 \, {\left(4 \, a^{3} + 7 \, a^{2} b + 2 \, 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(4 \, a^{3} + 7 \, a^{2} b + 2 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(4 \, a^{3} + 3 \, a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(12 \, a^{3} + 5 \, a^{2} b - 6 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(4 \, a^{3} + 7 \, a^{2} b + 2 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{4} + 12 \, a^{3} + 5 \, a^{2} b - 6 \, a b^{2} + b^{3} + 30 \, {\left(4 \, a^{3} + 3 \, 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(4 \, a^{3} + 7 \, a^{2} b + 2 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(4 \, a^{3} + 3 \, a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(12 \, a^{3} + 5 \, a^{2} b - 6 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, a^{3} + 7 \, a^{2} b + 2 \, a b^{2} - b^{3} + 4 \, {\left(4 \, a^{3} + 3 \, a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(4 \, a^{3} + 7 \, a^{2} b + 2 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(4 \, a^{3} + 3 \, a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, a^{3} + 3 \, a^{2} b - a b^{2} + 3 \, {\left(12 \, a^{3} + 5 \, a^{2} b - 6 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left({\left(4 \, a^{3} + 7 \, a^{2} b + 2 \, a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(4 \, a^{3} + 3 \, a^{2} b - a b^{2}\right)} \cosh\left(d x + c\right)^{5} + {\left(12 \, a^{3} + 5 \, a^{2} b - 6 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(4 \, a^{3} + 3 \, a^{2} b - a 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({\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(3 \, a - b\right)} \cosh\left(d x + c\right) + {\left(3 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} + 3 \, a - b\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a + b}{a}}}{2 \, {\left(a + b\right)}}\right) + 2 \, {\left({\left(4 \, a^{3} + 9 \, a^{2} b + 5 \, a b^{2}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(4 \, a^{3} + 9 \, a^{2} b + 5 \, a b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(4 \, a^{3} + 9 \, a^{2} b + 5 \, a b^{2}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(4 \, a^{3} + 5 \, a^{2} b\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(4 \, a^{3} + 5 \, a^{2} b + 7 \, {\left(4 \, a^{3} + 9 \, 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(4 \, a^{3} + 9 \, a^{2} b + 5 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(4 \, a^{3} + 5 \, a^{2} b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(12 \, a^{3} + 11 \, a^{2} b - 5 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(4 \, a^{3} + 9 \, a^{2} b + 5 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} + 12 \, a^{3} + 11 \, a^{2} b - 5 \, a b^{2} + 30 \, {\left(4 \, 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(4 \, a^{3} + 9 \, a^{2} b + 5 \, a b^{2}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(4 \, a^{3} + 5 \, a^{2} b\right)} \cosh\left(d x + c\right)^{3} + {\left(12 \, a^{3} + 11 \, a^{2} b - 5 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, a^{3} + 9 \, a^{2} b + 5 \, a b^{2} + 4 \, {\left(4 \, a^{3} + 5 \, a^{2} b\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(4 \, a^{3} + 9 \, a^{2} b + 5 \, a b^{2}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(4 \, a^{3} + 5 \, a^{2} b\right)} \cosh\left(d x + c\right)^{4} + 4 \, a^{3} + 5 \, a^{2} b + 3 \, {\left(12 \, a^{3} + 11 \, 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(4 \, a^{3} + 9 \, a^{2} b + 5 \, a b^{2}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(4 \, a^{3} + 5 \, a^{2} b\right)} \cosh\left(d x + c\right)^{5} + {\left(12 \, a^{3} + 11 \, a^{2} b - 5 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(4 \, 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(2 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right) + 2 \, {\left(7 \, {\left(2 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{6} + 5 \, {\left(2 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{4} - 2 \, a^{2} b - 3 \, a b^{2} - b^{3} - 3 \, {\left(2 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)}{2 \, {\left(4 \, a^{2} b^{3} d \cosh\left(d x + c\right)^{6} + {\left(a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{2} b^{3} + a b^{4}\right)} d \sinh\left(d x + c\right)^{8} + 4 \, a^{2} b^{3} d \cosh\left(d x + c\right)^{2} + 4 \, {\left(a^{2} b^{3} d + 7 \, {\left(a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(3 \, a^{2} b^{3} - a b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(3 \, a^{2} b^{3} d \cosh\left(d x + c\right) + 7 \, {\left(a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(30 \, a^{2} b^{3} d \cosh\left(d x + c\right)^{2} + 35 \, {\left(a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)^{4} + {\left(3 \, a^{2} b^{3} - a b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(10 \, a^{2} b^{3} d \cosh\left(d x + c\right)^{3} + 7 \, {\left(a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)^{5} + {\left(3 \, 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(15 \, a^{2} b^{3} d \cosh\left(d x + c\right)^{4} + 7 \, {\left(a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)^{6} + a^{2} b^{3} d + 3 \, {\left(3 \, a^{2} b^{3} - a b^{4}\right)} d \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{2} b^{3} + a b^{4}\right)} d + 8 \, {\left(3 \, a^{2} b^{3} d \cosh\left(d x + c\right)^{5} + {\left(a^{2} b^{3} + a b^{4}\right)} d \cosh\left(d x + c\right)^{7} + a^{2} b^{3} d \cosh\left(d x + c\right) + {\left(3 \, 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,"[1/4*(4*(2*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^7 + 28*(2*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)*sinh(d*x + c)^6 + 4*(2*a^2*b + 3*a*b^2 + b^3)*sinh(d*x + c)^7 + 4*(2*a^2*b - a*b^2 + b^3)*cosh(d*x + c)^5 + 4*(2*a^2*b - a*b^2 + b^3 + 21*(2*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 20*(7*(2*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^3 + (2*a^2*b - a*b^2 + b^3)*cosh(d*x + c))*sinh(d*x + c)^4 - 4*(2*a^2*b - a*b^2 + b^3)*cosh(d*x + c)^3 + 4*(35*(2*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^4 - 2*a^2*b + a*b^2 - b^3 + 10*(2*a^2*b - a*b^2 + b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 4*(21*(2*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^5 + 10*(2*a^2*b - a*b^2 + b^3)*cosh(d*x + c)^3 - 3*(2*a^2*b - a*b^2 + b^3)*cosh(d*x + c))*sinh(d*x + c)^2 - ((4*a^3 + 7*a^2*b + 2*a*b^2 - b^3)*cosh(d*x + c)^8 + 8*(4*a^3 + 7*a^2*b + 2*a*b^2 - b^3)*cosh(d*x + c)*sinh(d*x + c)^7 + (4*a^3 + 7*a^2*b + 2*a*b^2 - b^3)*sinh(d*x + c)^8 + 4*(4*a^3 + 3*a^2*b - a*b^2)*cosh(d*x + c)^6 + 4*(4*a^3 + 3*a^2*b - a*b^2 + 7*(4*a^3 + 7*a^2*b + 2*a*b^2 - b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(4*a^3 + 7*a^2*b + 2*a*b^2 - b^3)*cosh(d*x + c)^3 + 3*(4*a^3 + 3*a^2*b - a*b^2)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(12*a^3 + 5*a^2*b - 6*a*b^2 + b^3)*cosh(d*x + c)^4 + 2*(35*(4*a^3 + 7*a^2*b + 2*a*b^2 - b^3)*cosh(d*x + c)^4 + 12*a^3 + 5*a^2*b - 6*a*b^2 + b^3 + 30*(4*a^3 + 3*a^2*b - a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(7*(4*a^3 + 7*a^2*b + 2*a*b^2 - b^3)*cosh(d*x + c)^5 + 10*(4*a^3 + 3*a^2*b - a*b^2)*cosh(d*x + c)^3 + (12*a^3 + 5*a^2*b - 6*a*b^2 + b^3)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*a^3 + 7*a^2*b + 2*a*b^2 - b^3 + 4*(4*a^3 + 3*a^2*b - a*b^2)*cosh(d*x + c)^2 + 4*(7*(4*a^3 + 7*a^2*b + 2*a*b^2 - b^3)*cosh(d*x + c)^6 + 15*(4*a^3 + 3*a^2*b - a*b^2)*cosh(d*x + c)^4 + 4*a^3 + 3*a^2*b - a*b^2 + 3*(12*a^3 + 5*a^2*b - 6*a*b^2 + b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((4*a^3 + 7*a^2*b + 2*a*b^2 - b^3)*cosh(d*x + c)^7 + 3*(4*a^3 + 3*a^2*b - a*b^2)*cosh(d*x + c)^5 + (12*a^3 + 5*a^2*b - 6*a*b^2 + b^3)*cosh(d*x + c)^3 + (4*a^3 + 3*a^2*b - a*b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-(a + b)/a)*log(((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*(3*a + b)*cosh(d*x + c)^2 + 2*(3*(a + b)*cosh(d*x + c)^2 - 3*a - b)*sinh(d*x + c)^2 + 4*((a + b)*cosh(d*x + c)^3 - (3*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(-(a + b)/a) + a + b)/((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)) + 4*((4*a^3 + 9*a^2*b + 5*a*b^2)*cosh(d*x + c)^8 + 8*(4*a^3 + 9*a^2*b + 5*a*b^2)*cosh(d*x + c)*sinh(d*x + c)^7 + (4*a^3 + 9*a^2*b + 5*a*b^2)*sinh(d*x + c)^8 + 4*(4*a^3 + 5*a^2*b)*cosh(d*x + c)^6 + 4*(4*a^3 + 5*a^2*b + 7*(4*a^3 + 9*a^2*b + 5*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(4*a^3 + 9*a^2*b + 5*a*b^2)*cosh(d*x + c)^3 + 3*(4*a^3 + 5*a^2*b)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(12*a^3 + 11*a^2*b - 5*a*b^2)*cosh(d*x + c)^4 + 2*(35*(4*a^3 + 9*a^2*b + 5*a*b^2)*cosh(d*x + c)^4 + 12*a^3 + 11*a^2*b - 5*a*b^2 + 30*(4*a^3 + 5*a^2*b)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(7*(4*a^3 + 9*a^2*b + 5*a*b^2)*cosh(d*x + c)^5 + 10*(4*a^3 + 5*a^2*b)*cosh(d*x + c)^3 + (12*a^3 + 11*a^2*b - 5*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*a^3 + 9*a^2*b + 5*a*b^2 + 4*(4*a^3 + 5*a^2*b)*cosh(d*x + c)^2 + 4*(7*(4*a^3 + 9*a^2*b + 5*a*b^2)*cosh(d*x + c)^6 + 15*(4*a^3 + 5*a^2*b)*cosh(d*x + c)^4 + 4*a^3 + 5*a^2*b + 3*(12*a^3 + 11*a^2*b - 5*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((4*a^3 + 9*a^2*b + 5*a*b^2)*cosh(d*x + c)^7 + 3*(4*a^3 + 5*a^2*b)*cosh(d*x + c)^5 + (12*a^3 + 11*a^2*b - 5*a*b^2)*cosh(d*x + c)^3 + (4*a^3 + 5*a^2*b)*cosh(d*x + c))*sinh(d*x + c))*arctan(cosh(d*x + c) + sinh(d*x + c)) - 4*(2*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c) + 4*(7*(2*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^6 + 5*(2*a^2*b - a*b^2 + b^3)*cosh(d*x + c)^4 - 2*a^2*b - 3*a*b^2 - b^3 - 3*(2*a^2*b - a*b^2 + b^3)*cosh(d*x + c)^2)*sinh(d*x + c))/(4*a^2*b^3*d*cosh(d*x + c)^6 + (a^2*b^3 + a*b^4)*d*cosh(d*x + c)^8 + 8*(a^2*b^3 + a*b^4)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^2*b^3 + a*b^4)*d*sinh(d*x + c)^8 + 4*a^2*b^3*d*cosh(d*x + c)^2 + 4*(a^2*b^3*d + 7*(a^2*b^3 + a*b^4)*d*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 2*(3*a^2*b^3 - a*b^4)*d*cosh(d*x + c)^4 + 8*(3*a^2*b^3*d*cosh(d*x + c) + 7*(a^2*b^3 + a*b^4)*d*cosh(d*x + c)^3)*sinh(d*x + c)^5 + 2*(30*a^2*b^3*d*cosh(d*x + c)^2 + 35*(a^2*b^3 + a*b^4)*d*cosh(d*x + c)^4 + (3*a^2*b^3 - a*b^4)*d)*sinh(d*x + c)^4 + 8*(10*a^2*b^3*d*cosh(d*x + c)^3 + 7*(a^2*b^3 + a*b^4)*d*cosh(d*x + c)^5 + (3*a^2*b^3 - a*b^4)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(15*a^2*b^3*d*cosh(d*x + c)^4 + 7*(a^2*b^3 + a*b^4)*d*cosh(d*x + c)^6 + a^2*b^3*d + 3*(3*a^2*b^3 - a*b^4)*d*cosh(d*x + c)^2)*sinh(d*x + c)^2 + (a^2*b^3 + a*b^4)*d + 8*(3*a^2*b^3*d*cosh(d*x + c)^5 + (a^2*b^3 + a*b^4)*d*cosh(d*x + c)^7 + a^2*b^3*d*cosh(d*x + c) + (3*a^2*b^3 - a*b^4)*d*cosh(d*x + c)^3)*sinh(d*x + c)), 1/2*(2*(2*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^7 + 14*(2*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)*sinh(d*x + c)^6 + 2*(2*a^2*b + 3*a*b^2 + b^3)*sinh(d*x + c)^7 + 2*(2*a^2*b - a*b^2 + b^3)*cosh(d*x + c)^5 + 2*(2*a^2*b - a*b^2 + b^3 + 21*(2*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 10*(7*(2*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^3 + (2*a^2*b - a*b^2 + b^3)*cosh(d*x + c))*sinh(d*x + c)^4 - 2*(2*a^2*b - a*b^2 + b^3)*cosh(d*x + c)^3 + 2*(35*(2*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^4 - 2*a^2*b + a*b^2 - b^3 + 10*(2*a^2*b - a*b^2 + b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 2*(21*(2*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^5 + 10*(2*a^2*b - a*b^2 + b^3)*cosh(d*x + c)^3 - 3*(2*a^2*b - a*b^2 + b^3)*cosh(d*x + c))*sinh(d*x + c)^2 - ((4*a^3 + 7*a^2*b + 2*a*b^2 - b^3)*cosh(d*x + c)^8 + 8*(4*a^3 + 7*a^2*b + 2*a*b^2 - b^3)*cosh(d*x + c)*sinh(d*x + c)^7 + (4*a^3 + 7*a^2*b + 2*a*b^2 - b^3)*sinh(d*x + c)^8 + 4*(4*a^3 + 3*a^2*b - a*b^2)*cosh(d*x + c)^6 + 4*(4*a^3 + 3*a^2*b - a*b^2 + 7*(4*a^3 + 7*a^2*b + 2*a*b^2 - b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(4*a^3 + 7*a^2*b + 2*a*b^2 - b^3)*cosh(d*x + c)^3 + 3*(4*a^3 + 3*a^2*b - a*b^2)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(12*a^3 + 5*a^2*b - 6*a*b^2 + b^3)*cosh(d*x + c)^4 + 2*(35*(4*a^3 + 7*a^2*b + 2*a*b^2 - b^3)*cosh(d*x + c)^4 + 12*a^3 + 5*a^2*b - 6*a*b^2 + b^3 + 30*(4*a^3 + 3*a^2*b - a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(7*(4*a^3 + 7*a^2*b + 2*a*b^2 - b^3)*cosh(d*x + c)^5 + 10*(4*a^3 + 3*a^2*b - a*b^2)*cosh(d*x + c)^3 + (12*a^3 + 5*a^2*b - 6*a*b^2 + b^3)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*a^3 + 7*a^2*b + 2*a*b^2 - b^3 + 4*(4*a^3 + 3*a^2*b - a*b^2)*cosh(d*x + c)^2 + 4*(7*(4*a^3 + 7*a^2*b + 2*a*b^2 - b^3)*cosh(d*x + c)^6 + 15*(4*a^3 + 3*a^2*b - a*b^2)*cosh(d*x + c)^4 + 4*a^3 + 3*a^2*b - a*b^2 + 3*(12*a^3 + 5*a^2*b - 6*a*b^2 + b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((4*a^3 + 7*a^2*b + 2*a*b^2 - b^3)*cosh(d*x + c)^7 + 3*(4*a^3 + 3*a^2*b - a*b^2)*cosh(d*x + c)^5 + (12*a^3 + 5*a^2*b - 6*a*b^2 + b^3)*cosh(d*x + c)^3 + (4*a^3 + 3*a^2*b - a*b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a + b)/a)*arctan(1/2*sqrt((a + b)/a)*(cosh(d*x + c) + sinh(d*x + c))) - ((4*a^3 + 7*a^2*b + 2*a*b^2 - b^3)*cosh(d*x + c)^8 + 8*(4*a^3 + 7*a^2*b + 2*a*b^2 - b^3)*cosh(d*x + c)*sinh(d*x + c)^7 + (4*a^3 + 7*a^2*b + 2*a*b^2 - b^3)*sinh(d*x + c)^8 + 4*(4*a^3 + 3*a^2*b - a*b^2)*cosh(d*x + c)^6 + 4*(4*a^3 + 3*a^2*b - a*b^2 + 7*(4*a^3 + 7*a^2*b + 2*a*b^2 - b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(4*a^3 + 7*a^2*b + 2*a*b^2 - b^3)*cosh(d*x + c)^3 + 3*(4*a^3 + 3*a^2*b - a*b^2)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(12*a^3 + 5*a^2*b - 6*a*b^2 + b^3)*cosh(d*x + c)^4 + 2*(35*(4*a^3 + 7*a^2*b + 2*a*b^2 - b^3)*cosh(d*x + c)^4 + 12*a^3 + 5*a^2*b - 6*a*b^2 + b^3 + 30*(4*a^3 + 3*a^2*b - a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(7*(4*a^3 + 7*a^2*b + 2*a*b^2 - b^3)*cosh(d*x + c)^5 + 10*(4*a^3 + 3*a^2*b - a*b^2)*cosh(d*x + c)^3 + (12*a^3 + 5*a^2*b - 6*a*b^2 + b^3)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*a^3 + 7*a^2*b + 2*a*b^2 - b^3 + 4*(4*a^3 + 3*a^2*b - a*b^2)*cosh(d*x + c)^2 + 4*(7*(4*a^3 + 7*a^2*b + 2*a*b^2 - b^3)*cosh(d*x + c)^6 + 15*(4*a^3 + 3*a^2*b - a*b^2)*cosh(d*x + c)^4 + 4*a^3 + 3*a^2*b - a*b^2 + 3*(12*a^3 + 5*a^2*b - 6*a*b^2 + b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((4*a^3 + 7*a^2*b + 2*a*b^2 - b^3)*cosh(d*x + c)^7 + 3*(4*a^3 + 3*a^2*b - a*b^2)*cosh(d*x + c)^5 + (12*a^3 + 5*a^2*b - 6*a*b^2 + b^3)*cosh(d*x + c)^3 + (4*a^3 + 3*a^2*b - a*b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a + b)/a)*arctan(1/2*((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 + (3*a - b)*cosh(d*x + c) + (3*(a + b)*cosh(d*x + c)^2 + 3*a - b)*sinh(d*x + c))*sqrt((a + b)/a)/(a + b)) + 2*((4*a^3 + 9*a^2*b + 5*a*b^2)*cosh(d*x + c)^8 + 8*(4*a^3 + 9*a^2*b + 5*a*b^2)*cosh(d*x + c)*sinh(d*x + c)^7 + (4*a^3 + 9*a^2*b + 5*a*b^2)*sinh(d*x + c)^8 + 4*(4*a^3 + 5*a^2*b)*cosh(d*x + c)^6 + 4*(4*a^3 + 5*a^2*b + 7*(4*a^3 + 9*a^2*b + 5*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(4*a^3 + 9*a^2*b + 5*a*b^2)*cosh(d*x + c)^3 + 3*(4*a^3 + 5*a^2*b)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(12*a^3 + 11*a^2*b - 5*a*b^2)*cosh(d*x + c)^4 + 2*(35*(4*a^3 + 9*a^2*b + 5*a*b^2)*cosh(d*x + c)^4 + 12*a^3 + 11*a^2*b - 5*a*b^2 + 30*(4*a^3 + 5*a^2*b)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(7*(4*a^3 + 9*a^2*b + 5*a*b^2)*cosh(d*x + c)^5 + 10*(4*a^3 + 5*a^2*b)*cosh(d*x + c)^3 + (12*a^3 + 11*a^2*b - 5*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*a^3 + 9*a^2*b + 5*a*b^2 + 4*(4*a^3 + 5*a^2*b)*cosh(d*x + c)^2 + 4*(7*(4*a^3 + 9*a^2*b + 5*a*b^2)*cosh(d*x + c)^6 + 15*(4*a^3 + 5*a^2*b)*cosh(d*x + c)^4 + 4*a^3 + 5*a^2*b + 3*(12*a^3 + 11*a^2*b - 5*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((4*a^3 + 9*a^2*b + 5*a*b^2)*cosh(d*x + c)^7 + 3*(4*a^3 + 5*a^2*b)*cosh(d*x + c)^5 + (12*a^3 + 11*a^2*b - 5*a*b^2)*cosh(d*x + c)^3 + (4*a^3 + 5*a^2*b)*cosh(d*x + c))*sinh(d*x + c))*arctan(cosh(d*x + c) + sinh(d*x + c)) - 2*(2*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c) + 2*(7*(2*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^6 + 5*(2*a^2*b - a*b^2 + b^3)*cosh(d*x + c)^4 - 2*a^2*b - 3*a*b^2 - b^3 - 3*(2*a^2*b - a*b^2 + b^3)*cosh(d*x + c)^2)*sinh(d*x + c))/(4*a^2*b^3*d*cosh(d*x + c)^6 + (a^2*b^3 + a*b^4)*d*cosh(d*x + c)^8 + 8*(a^2*b^3 + a*b^4)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^2*b^3 + a*b^4)*d*sinh(d*x + c)^8 + 4*a^2*b^3*d*cosh(d*x + c)^2 + 4*(a^2*b^3*d + 7*(a^2*b^3 + a*b^4)*d*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 2*(3*a^2*b^3 - a*b^4)*d*cosh(d*x + c)^4 + 8*(3*a^2*b^3*d*cosh(d*x + c) + 7*(a^2*b^3 + a*b^4)*d*cosh(d*x + c)^3)*sinh(d*x + c)^5 + 2*(30*a^2*b^3*d*cosh(d*x + c)^2 + 35*(a^2*b^3 + a*b^4)*d*cosh(d*x + c)^4 + (3*a^2*b^3 - a*b^4)*d)*sinh(d*x + c)^4 + 8*(10*a^2*b^3*d*cosh(d*x + c)^3 + 7*(a^2*b^3 + a*b^4)*d*cosh(d*x + c)^5 + (3*a^2*b^3 - a*b^4)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(15*a^2*b^3*d*cosh(d*x + c)^4 + 7*(a^2*b^3 + a*b^4)*d*cosh(d*x + c)^6 + a^2*b^3*d + 3*(3*a^2*b^3 - a*b^4)*d*cosh(d*x + c)^2)*sinh(d*x + c)^2 + (a^2*b^3 + a*b^4)*d + 8*(3*a^2*b^3*d*cosh(d*x + c)^5 + (a^2*b^3 + a*b^4)*d*cosh(d*x + c)^7 + a^2*b^3*d*cosh(d*x + c) + (3*a^2*b^3 - a*b^4)*d*cosh(d*x + c)^3)*sinh(d*x + c))]","B",0
125,1,13887,0,0.713850," ","integrate(cosh(d*x+c)^2/(a+b*tanh(d*x+c)^2)^3,x, algorithm=""fricas"")","\left[\frac{2 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{12} + 24 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{11} + 2 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \sinh\left(d x + c\right)^{12} + 8 \, {\left(a^{5} + a^{4} b - a^{3} b^{2} - a^{2} b^{3} + {\left(a^{5} + 9 \, a^{4} b + 15 \, a^{3} b^{2} + 7 \, a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{10} + 4 \, {\left(2 \, a^{5} + 2 \, a^{4} b - 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} + 2 \, {\left(a^{5} + 9 \, a^{4} b + 15 \, a^{3} b^{2} + 7 \, a^{2} b^{3}\right)} d x + 33 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{10} + 40 \, {\left(11 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(a^{5} + a^{4} b - a^{3} b^{2} - a^{2} b^{3} + {\left(a^{5} + 9 \, a^{4} b + 15 \, a^{3} b^{2} + 7 \, a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} + 2 \, {\left(5 \, a^{5} - a^{4} b - 27 \, a^{3} b^{2} + 7 \, a^{2} b^{3} + 34 \, a b^{4} + 6 \, b^{5} + 16 \, {\left(a^{5} + 7 \, a^{4} b - a^{3} b^{2} - 7 \, a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{8} + 2 \, {\left(5 \, a^{5} - a^{4} b - 27 \, a^{3} b^{2} + 7 \, a^{2} b^{3} + 34 \, a b^{4} + 6 \, b^{5} + 495 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{4} + 16 \, {\left(a^{5} + 7 \, a^{4} b - a^{3} b^{2} - 7 \, a^{2} b^{3}\right)} d x + 180 \, {\left(a^{5} + a^{4} b - a^{3} b^{2} - a^{2} b^{3} + {\left(a^{5} + 9 \, a^{4} b + 15 \, a^{3} b^{2} + 7 \, a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{8} + 16 \, {\left(99 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{5} + 60 \, {\left(a^{5} + a^{4} b - a^{3} b^{2} - a^{2} b^{3} + {\left(a^{5} + 9 \, a^{4} b + 15 \, a^{3} b^{2} + 7 \, a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + {\left(5 \, a^{5} - a^{4} b - 27 \, a^{3} b^{2} + 7 \, a^{2} b^{3} + 34 \, a b^{4} + 6 \, b^{5} + 16 \, {\left(a^{5} + 7 \, a^{4} b - a^{3} b^{2} - 7 \, a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} - 4 \, {\left(39 \, a^{3} b^{2} - 17 \, a^{2} b^{3} + 33 \, a b^{4} + 9 \, b^{5} - 4 \, {\left(3 \, a^{5} + 19 \, a^{4} b - 11 \, a^{3} b^{2} + 21 \, a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(462 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{6} - 39 \, a^{3} b^{2} + 17 \, a^{2} b^{3} - 33 \, a b^{4} - 9 \, b^{5} + 420 \, {\left(a^{5} + a^{4} b - a^{3} b^{2} - a^{2} b^{3} + {\left(a^{5} + 9 \, a^{4} b + 15 \, a^{3} b^{2} + 7 \, a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(3 \, a^{5} + 19 \, a^{4} b - 11 \, a^{3} b^{2} + 21 \, a^{2} b^{3}\right)} d x + 14 \, {\left(5 \, a^{5} - a^{4} b - 27 \, a^{3} b^{2} + 7 \, a^{2} b^{3} + 34 \, a b^{4} + 6 \, b^{5} + 16 \, {\left(a^{5} + 7 \, a^{4} b - a^{3} b^{2} - 7 \, a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(198 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{7} + 252 \, {\left(a^{5} + a^{4} b - a^{3} b^{2} - a^{2} b^{3} + {\left(a^{5} + 9 \, a^{4} b + 15 \, a^{3} b^{2} + 7 \, a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{5} + 14 \, {\left(5 \, a^{5} - a^{4} b - 27 \, a^{3} b^{2} + 7 \, a^{2} b^{3} + 34 \, a b^{4} + 6 \, b^{5} + 16 \, {\left(a^{5} + 7 \, a^{4} b - a^{3} b^{2} - 7 \, a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(39 \, a^{3} b^{2} - 17 \, a^{2} b^{3} + 33 \, a b^{4} + 9 \, b^{5} - 4 \, {\left(3 \, a^{5} + 19 \, a^{4} b - 11 \, a^{3} b^{2} + 21 \, a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 2 \, a^{5} - 6 \, a^{4} b - 6 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 2 \, {\left(5 \, a^{5} - a^{4} b + 77 \, a^{3} b^{2} + 31 \, a^{2} b^{3} - 70 \, a b^{4} - 18 \, b^{5} - 16 \, {\left(a^{5} + 7 \, a^{4} b - a^{3} b^{2} - 7 \, a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(495 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{8} + 840 \, {\left(a^{5} + a^{4} b - a^{3} b^{2} - a^{2} b^{3} + {\left(a^{5} + 9 \, a^{4} b + 15 \, a^{3} b^{2} + 7 \, a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{6} - 5 \, a^{5} + a^{4} b - 77 \, a^{3} b^{2} - 31 \, a^{2} b^{3} + 70 \, a b^{4} + 18 \, b^{5} + 70 \, {\left(5 \, a^{5} - a^{4} b - 27 \, a^{3} b^{2} + 7 \, a^{2} b^{3} + 34 \, a b^{4} + 6 \, b^{5} + 16 \, {\left(a^{5} + 7 \, a^{4} b - a^{3} b^{2} - 7 \, a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 16 \, {\left(a^{5} + 7 \, a^{4} b - a^{3} b^{2} - 7 \, a^{2} b^{3}\right)} d x - 30 \, {\left(39 \, a^{3} b^{2} - 17 \, a^{2} b^{3} + 33 \, a b^{4} + 9 \, b^{5} - 4 \, {\left(3 \, a^{5} + 19 \, a^{4} b - 11 \, a^{3} b^{2} + 21 \, a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(55 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{9} + 120 \, {\left(a^{5} + a^{4} b - a^{3} b^{2} - a^{2} b^{3} + {\left(a^{5} + 9 \, a^{4} b + 15 \, a^{3} b^{2} + 7 \, a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{7} + 14 \, {\left(5 \, a^{5} - a^{4} b - 27 \, a^{3} b^{2} + 7 \, a^{2} b^{3} + 34 \, a b^{4} + 6 \, b^{5} + 16 \, {\left(a^{5} + 7 \, a^{4} b - a^{3} b^{2} - 7 \, a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{5} - 10 \, {\left(39 \, a^{3} b^{2} - 17 \, a^{2} b^{3} + 33 \, a b^{4} + 9 \, b^{5} - 4 \, {\left(3 \, a^{5} + 19 \, a^{4} b - 11 \, a^{3} b^{2} + 21 \, a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - {\left(5 \, a^{5} - a^{4} b + 77 \, a^{3} b^{2} + 31 \, a^{2} b^{3} - 70 \, a b^{4} - 18 \, b^{5} - 16 \, {\left(a^{5} + 7 \, a^{4} b - a^{3} b^{2} - 7 \, a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 4 \, {\left(2 \, a^{5} + 2 \, a^{4} b + 11 \, a^{3} b^{2} + 27 \, a^{2} b^{3} + 19 \, a b^{4} + 3 \, b^{5} - 2 \, {\left(a^{5} + 9 \, a^{4} b + 15 \, a^{3} b^{2} + 7 \, a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(33 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{10} + 90 \, {\left(a^{5} + a^{4} b - a^{3} b^{2} - a^{2} b^{3} + {\left(a^{5} + 9 \, a^{4} b + 15 \, a^{3} b^{2} + 7 \, a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{8} + 14 \, {\left(5 \, a^{5} - a^{4} b - 27 \, a^{3} b^{2} + 7 \, a^{2} b^{3} + 34 \, a b^{4} + 6 \, b^{5} + 16 \, {\left(a^{5} + 7 \, a^{4} b - a^{3} b^{2} - 7 \, a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{6} - 2 \, a^{5} - 2 \, a^{4} b - 11 \, a^{3} b^{2} - 27 \, a^{2} b^{3} - 19 \, a b^{4} - 3 \, b^{5} - 15 \, {\left(39 \, a^{3} b^{2} - 17 \, a^{2} b^{3} + 33 \, a b^{4} + 9 \, b^{5} - 4 \, {\left(3 \, a^{5} + 19 \, a^{4} b - 11 \, a^{3} b^{2} + 21 \, a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(a^{5} + 9 \, a^{4} b + 15 \, a^{3} b^{2} + 7 \, a^{2} b^{3}\right)} d x - 3 \, {\left(5 \, a^{5} - a^{4} b + 77 \, a^{3} b^{2} + 31 \, a^{2} b^{3} - 70 \, a b^{4} - 18 \, b^{5} - 16 \, {\left(a^{5} + 7 \, a^{4} b - a^{3} b^{2} - 7 \, a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(35 \, a^{4} b + 84 \, a^{3} b^{2} + 66 \, a^{2} b^{3} + 20 \, a b^{4} + 3 \, b^{5}\right)} \cosh\left(d x + c\right)^{10} + 10 \, {\left(35 \, a^{4} b + 84 \, a^{3} b^{2} + 66 \, a^{2} b^{3} + 20 \, a b^{4} + 3 \, b^{5}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + {\left(35 \, a^{4} b + 84 \, a^{3} b^{2} + 66 \, a^{2} b^{3} + 20 \, a b^{4} + 3 \, b^{5}\right)} \sinh\left(d x + c\right)^{10} + 4 \, {\left(35 \, a^{4} b + 14 \, a^{3} b^{2} - 32 \, a^{2} b^{3} - 14 \, a b^{4} - 3 \, b^{5}\right)} \cosh\left(d x + c\right)^{8} + {\left(140 \, a^{4} b + 56 \, a^{3} b^{2} - 128 \, a^{2} b^{3} - 56 \, a b^{4} - 12 \, b^{5} + 45 \, {\left(35 \, a^{4} b + 84 \, a^{3} b^{2} + 66 \, 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)^{8} + 8 \, {\left(15 \, {\left(35 \, a^{4} b + 84 \, a^{3} b^{2} + 66 \, a^{2} b^{3} + 20 \, a b^{4} + 3 \, b^{5}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(35 \, a^{4} b + 14 \, a^{3} b^{2} - 32 \, a^{2} b^{3} - 14 \, a b^{4} - 3 \, b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(105 \, a^{4} b - 28 \, a^{3} b^{2} + 86 \, a^{2} b^{3} + 36 \, a b^{4} + 9 \, b^{5}\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(105 \, a^{4} b - 28 \, a^{3} b^{2} + 86 \, a^{2} b^{3} + 36 \, a b^{4} + 9 \, b^{5} + 105 \, {\left(35 \, a^{4} b + 84 \, a^{3} b^{2} + 66 \, a^{2} b^{3} + 20 \, a b^{4} + 3 \, b^{5}\right)} \cosh\left(d x + c\right)^{4} + 56 \, {\left(35 \, a^{4} b + 14 \, a^{3} b^{2} - 32 \, a^{2} b^{3} - 14 \, 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(35 \, a^{4} b + 84 \, a^{3} b^{2} + 66 \, a^{2} b^{3} + 20 \, a b^{4} + 3 \, b^{5}\right)} \cosh\left(d x + c\right)^{5} + 56 \, {\left(35 \, a^{4} b + 14 \, a^{3} b^{2} - 32 \, a^{2} b^{3} - 14 \, a b^{4} - 3 \, b^{5}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(105 \, a^{4} b - 28 \, a^{3} b^{2} + 86 \, a^{2} b^{3} + 36 \, a b^{4} + 9 \, b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 4 \, {\left(35 \, a^{4} b + 14 \, a^{3} b^{2} - 32 \, a^{2} b^{3} - 14 \, a b^{4} - 3 \, b^{5}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(105 \, {\left(35 \, a^{4} b + 84 \, a^{3} b^{2} + 66 \, a^{2} b^{3} + 20 \, a b^{4} + 3 \, b^{5}\right)} \cosh\left(d x + c\right)^{6} + 70 \, a^{4} b + 28 \, a^{3} b^{2} - 64 \, a^{2} b^{3} - 28 \, a b^{4} - 6 \, b^{5} + 140 \, {\left(35 \, a^{4} b + 14 \, a^{3} b^{2} - 32 \, a^{2} b^{3} - 14 \, a b^{4} - 3 \, b^{5}\right)} \cosh\left(d x + c\right)^{4} + 15 \, {\left(105 \, a^{4} b - 28 \, a^{3} b^{2} + 86 \, a^{2} b^{3} + 36 \, a b^{4} + 9 \, b^{5}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(15 \, {\left(35 \, a^{4} b + 84 \, a^{3} b^{2} + 66 \, a^{2} b^{3} + 20 \, a b^{4} + 3 \, b^{5}\right)} \cosh\left(d x + c\right)^{7} + 28 \, {\left(35 \, a^{4} b + 14 \, a^{3} b^{2} - 32 \, a^{2} b^{3} - 14 \, a b^{4} - 3 \, b^{5}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(105 \, a^{4} b - 28 \, a^{3} b^{2} + 86 \, a^{2} b^{3} + 36 \, a b^{4} + 9 \, b^{5}\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(35 \, a^{4} b + 14 \, a^{3} b^{2} - 32 \, a^{2} b^{3} - 14 \, a b^{4} - 3 \, b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(35 \, a^{4} b + 84 \, a^{3} b^{2} + 66 \, a^{2} b^{3} + 20 \, a b^{4} + 3 \, b^{5}\right)} \cosh\left(d x + c\right)^{2} + {\left(45 \, {\left(35 \, a^{4} b + 84 \, a^{3} b^{2} + 66 \, a^{2} b^{3} + 20 \, a b^{4} + 3 \, b^{5}\right)} \cosh\left(d x + c\right)^{8} + 112 \, {\left(35 \, a^{4} b + 14 \, a^{3} b^{2} - 32 \, a^{2} b^{3} - 14 \, a b^{4} - 3 \, b^{5}\right)} \cosh\left(d x + c\right)^{6} + 35 \, a^{4} b + 84 \, a^{3} b^{2} + 66 \, a^{2} b^{3} + 20 \, a b^{4} + 3 \, b^{5} + 30 \, {\left(105 \, a^{4} b - 28 \, a^{3} b^{2} + 86 \, a^{2} b^{3} + 36 \, a b^{4} + 9 \, b^{5}\right)} \cosh\left(d x + c\right)^{4} + 24 \, {\left(35 \, a^{4} b + 14 \, a^{3} b^{2} - 32 \, a^{2} b^{3} - 14 \, a b^{4} - 3 \, b^{5}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(5 \, {\left(35 \, a^{4} b + 84 \, a^{3} b^{2} + 66 \, a^{2} b^{3} + 20 \, a b^{4} + 3 \, b^{5}\right)} \cosh\left(d x + c\right)^{9} + 16 \, {\left(35 \, a^{4} b + 14 \, a^{3} b^{2} - 32 \, a^{2} b^{3} - 14 \, a b^{4} - 3 \, b^{5}\right)} \cosh\left(d x + c\right)^{7} + 6 \, {\left(105 \, a^{4} b - 28 \, a^{3} b^{2} + 86 \, a^{2} b^{3} + 36 \, a b^{4} + 9 \, b^{5}\right)} \cosh\left(d x + c\right)^{5} + 8 \, {\left(35 \, a^{4} b + 14 \, a^{3} b^{2} - 32 \, a^{2} b^{3} - 14 \, a b^{4} - 3 \, b^{5}\right)} \cosh\left(d x + c\right)^{3} + {\left(35 \, a^{4} b + 84 \, a^{3} b^{2} + 66 \, 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{-\frac{b}{a}} \log\left(\frac{{\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) \sinh\left(d x + c\right)^{3} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{2} + a^{2} - 6 \, a b + b^{2} + 4 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + 4 \, {\left({\left(a^{2} + a b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} + a b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} + a b\right)} \sinh\left(d x + c\right)^{2} + a^{2} - a b\right)} \sqrt{-\frac{b}{a}}}{{\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) + 8 \, {\left(3 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{11} + 10 \, {\left(a^{5} + a^{4} b - a^{3} b^{2} - a^{2} b^{3} + {\left(a^{5} + 9 \, a^{4} b + 15 \, a^{3} b^{2} + 7 \, a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{9} + 2 \, {\left(5 \, a^{5} - a^{4} b - 27 \, a^{3} b^{2} + 7 \, a^{2} b^{3} + 34 \, a b^{4} + 6 \, b^{5} + 16 \, {\left(a^{5} + 7 \, a^{4} b - a^{3} b^{2} - 7 \, a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{7} - 3 \, {\left(39 \, a^{3} b^{2} - 17 \, a^{2} b^{3} + 33 \, a b^{4} + 9 \, b^{5} - 4 \, {\left(3 \, a^{5} + 19 \, a^{4} b - 11 \, a^{3} b^{2} + 21 \, a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{5} - {\left(5 \, a^{5} - a^{4} b + 77 \, a^{3} b^{2} + 31 \, a^{2} b^{3} - 70 \, a b^{4} - 18 \, b^{5} - 16 \, {\left(a^{5} + 7 \, a^{4} b - a^{3} b^{2} - 7 \, a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - {\left(2 \, a^{5} + 2 \, a^{4} b + 11 \, a^{3} b^{2} + 27 \, a^{2} b^{3} + 19 \, a b^{4} + 3 \, b^{5} - 2 \, {\left(a^{5} + 9 \, a^{4} b + 15 \, a^{3} b^{2} + 7 \, a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{16 \, {\left({\left(a^{8} + 6 \, a^{7} b + 15 \, a^{6} b^{2} + 20 \, a^{5} b^{3} + 15 \, a^{4} b^{4} + 6 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{10} + 10 \, {\left(a^{8} + 6 \, a^{7} b + 15 \, a^{6} b^{2} + 20 \, a^{5} b^{3} + 15 \, a^{4} b^{4} + 6 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + {\left(a^{8} + 6 \, a^{7} b + 15 \, a^{6} b^{2} + 20 \, a^{5} b^{3} + 15 \, a^{4} b^{4} + 6 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \sinh\left(d x + c\right)^{10} + 4 \, {\left(a^{8} + 4 \, a^{7} b + 5 \, a^{6} b^{2} - 5 \, a^{4} b^{4} - 4 \, a^{3} b^{5} - a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{8} + {\left(45 \, {\left(a^{8} + 6 \, a^{7} b + 15 \, a^{6} b^{2} + 20 \, a^{5} b^{3} + 15 \, a^{4} b^{4} + 6 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{2} + 4 \, {\left(a^{8} + 4 \, a^{7} b + 5 \, a^{6} b^{2} - 5 \, a^{4} b^{4} - 4 \, a^{3} b^{5} - a^{2} b^{6}\right)} d\right)} \sinh\left(d x + c\right)^{8} + 2 \, {\left(3 \, a^{8} + 10 \, a^{7} b + 13 \, a^{6} b^{2} + 12 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 10 \, a^{3} b^{5} + 3 \, a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{6} + 8 \, {\left(15 \, {\left(a^{8} + 6 \, a^{7} b + 15 \, a^{6} b^{2} + 20 \, a^{5} b^{3} + 15 \, a^{4} b^{4} + 6 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{3} + 4 \, {\left(a^{8} + 4 \, a^{7} b + 5 \, a^{6} b^{2} - 5 \, a^{4} b^{4} - 4 \, a^{3} b^{5} - a^{2} b^{6}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(105 \, {\left(a^{8} + 6 \, a^{7} b + 15 \, a^{6} b^{2} + 20 \, a^{5} b^{3} + 15 \, a^{4} b^{4} + 6 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{4} + 56 \, {\left(a^{8} + 4 \, a^{7} b + 5 \, a^{6} b^{2} - 5 \, a^{4} b^{4} - 4 \, a^{3} b^{5} - a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{8} + 10 \, a^{7} b + 13 \, a^{6} b^{2} + 12 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 10 \, a^{3} b^{5} + 3 \, a^{2} b^{6}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(a^{8} + 4 \, a^{7} b + 5 \, a^{6} b^{2} - 5 \, a^{4} b^{4} - 4 \, a^{3} b^{5} - a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(63 \, {\left(a^{8} + 6 \, a^{7} b + 15 \, a^{6} b^{2} + 20 \, a^{5} b^{3} + 15 \, a^{4} b^{4} + 6 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{5} + 56 \, {\left(a^{8} + 4 \, a^{7} b + 5 \, a^{6} b^{2} - 5 \, a^{4} b^{4} - 4 \, a^{3} b^{5} - a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(3 \, a^{8} + 10 \, a^{7} b + 13 \, a^{6} b^{2} + 12 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 10 \, a^{3} b^{5} + 3 \, a^{2} b^{6}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(105 \, {\left(a^{8} + 6 \, a^{7} b + 15 \, a^{6} b^{2} + 20 \, a^{5} b^{3} + 15 \, a^{4} b^{4} + 6 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{6} + 140 \, {\left(a^{8} + 4 \, a^{7} b + 5 \, a^{6} b^{2} - 5 \, a^{4} b^{4} - 4 \, a^{3} b^{5} - a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{4} + 15 \, {\left(3 \, a^{8} + 10 \, a^{7} b + 13 \, a^{6} b^{2} + 12 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 10 \, a^{3} b^{5} + 3 \, a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{8} + 4 \, a^{7} b + 5 \, a^{6} b^{2} - 5 \, a^{4} b^{4} - 4 \, a^{3} b^{5} - a^{2} b^{6}\right)} d\right)} \sinh\left(d x + c\right)^{4} + {\left(a^{8} + 6 \, a^{7} b + 15 \, a^{6} b^{2} + 20 \, a^{5} b^{3} + 15 \, a^{4} b^{4} + 6 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(15 \, {\left(a^{8} + 6 \, a^{7} b + 15 \, a^{6} b^{2} + 20 \, a^{5} b^{3} + 15 \, a^{4} b^{4} + 6 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{7} + 28 \, {\left(a^{8} + 4 \, a^{7} b + 5 \, a^{6} b^{2} - 5 \, a^{4} b^{4} - 4 \, a^{3} b^{5} - a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{5} + 5 \, {\left(3 \, a^{8} + 10 \, a^{7} b + 13 \, a^{6} b^{2} + 12 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 10 \, a^{3} b^{5} + 3 \, a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{3} + 2 \, {\left(a^{8} + 4 \, a^{7} b + 5 \, a^{6} b^{2} - 5 \, a^{4} b^{4} - 4 \, a^{3} b^{5} - a^{2} b^{6}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(45 \, {\left(a^{8} + 6 \, a^{7} b + 15 \, a^{6} b^{2} + 20 \, a^{5} b^{3} + 15 \, a^{4} b^{4} + 6 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{8} + 112 \, {\left(a^{8} + 4 \, a^{7} b + 5 \, a^{6} b^{2} - 5 \, a^{4} b^{4} - 4 \, a^{3} b^{5} - a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{6} + 30 \, {\left(3 \, a^{8} + 10 \, a^{7} b + 13 \, a^{6} b^{2} + 12 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 10 \, a^{3} b^{5} + 3 \, a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{4} + 24 \, {\left(a^{8} + 4 \, a^{7} b + 5 \, a^{6} b^{2} - 5 \, a^{4} b^{4} - 4 \, a^{3} b^{5} - a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{8} + 6 \, a^{7} b + 15 \, a^{6} b^{2} + 20 \, a^{5} b^{3} + 15 \, a^{4} b^{4} + 6 \, a^{3} b^{5} + a^{2} b^{6}\right)} d\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(5 \, {\left(a^{8} + 6 \, a^{7} b + 15 \, a^{6} b^{2} + 20 \, a^{5} b^{3} + 15 \, a^{4} b^{4} + 6 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{9} + 16 \, {\left(a^{8} + 4 \, a^{7} b + 5 \, a^{6} b^{2} - 5 \, a^{4} b^{4} - 4 \, a^{3} b^{5} - a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{7} + 6 \, {\left(3 \, a^{8} + 10 \, a^{7} b + 13 \, a^{6} b^{2} + 12 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 10 \, a^{3} b^{5} + 3 \, a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{5} + 8 \, {\left(a^{8} + 4 \, a^{7} b + 5 \, a^{6} b^{2} - 5 \, a^{4} b^{4} - 4 \, a^{3} b^{5} - a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{8} + 6 \, a^{7} b + 15 \, a^{6} b^{2} + 20 \, a^{5} b^{3} + 15 \, a^{4} b^{4} + 6 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}, \frac{{\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{12} + 12 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{11} + {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \sinh\left(d x + c\right)^{12} + 4 \, {\left(a^{5} + a^{4} b - a^{3} b^{2} - a^{2} b^{3} + {\left(a^{5} + 9 \, a^{4} b + 15 \, a^{3} b^{2} + 7 \, a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{10} + 2 \, {\left(2 \, a^{5} + 2 \, a^{4} b - 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} + 2 \, {\left(a^{5} + 9 \, a^{4} b + 15 \, a^{3} b^{2} + 7 \, a^{2} b^{3}\right)} d x + 33 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{10} + 20 \, {\left(11 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(a^{5} + a^{4} b - a^{3} b^{2} - a^{2} b^{3} + {\left(a^{5} + 9 \, a^{4} b + 15 \, a^{3} b^{2} + 7 \, a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} + {\left(5 \, a^{5} - a^{4} b - 27 \, a^{3} b^{2} + 7 \, a^{2} b^{3} + 34 \, a b^{4} + 6 \, b^{5} + 16 \, {\left(a^{5} + 7 \, a^{4} b - a^{3} b^{2} - 7 \, a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{8} + {\left(5 \, a^{5} - a^{4} b - 27 \, a^{3} b^{2} + 7 \, a^{2} b^{3} + 34 \, a b^{4} + 6 \, b^{5} + 495 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{4} + 16 \, {\left(a^{5} + 7 \, a^{4} b - a^{3} b^{2} - 7 \, a^{2} b^{3}\right)} d x + 180 \, {\left(a^{5} + a^{4} b - a^{3} b^{2} - a^{2} b^{3} + {\left(a^{5} + 9 \, a^{4} b + 15 \, a^{3} b^{2} + 7 \, a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{8} + 8 \, {\left(99 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{5} + 60 \, {\left(a^{5} + a^{4} b - a^{3} b^{2} - a^{2} b^{3} + {\left(a^{5} + 9 \, a^{4} b + 15 \, a^{3} b^{2} + 7 \, a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + {\left(5 \, a^{5} - a^{4} b - 27 \, a^{3} b^{2} + 7 \, a^{2} b^{3} + 34 \, a b^{4} + 6 \, b^{5} + 16 \, {\left(a^{5} + 7 \, a^{4} b - a^{3} b^{2} - 7 \, a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} - 2 \, {\left(39 \, a^{3} b^{2} - 17 \, a^{2} b^{3} + 33 \, a b^{4} + 9 \, b^{5} - 4 \, {\left(3 \, a^{5} + 19 \, a^{4} b - 11 \, a^{3} b^{2} + 21 \, a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(462 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{6} - 39 \, a^{3} b^{2} + 17 \, a^{2} b^{3} - 33 \, a b^{4} - 9 \, b^{5} + 420 \, {\left(a^{5} + a^{4} b - a^{3} b^{2} - a^{2} b^{3} + {\left(a^{5} + 9 \, a^{4} b + 15 \, a^{3} b^{2} + 7 \, a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(3 \, a^{5} + 19 \, a^{4} b - 11 \, a^{3} b^{2} + 21 \, a^{2} b^{3}\right)} d x + 14 \, {\left(5 \, a^{5} - a^{4} b - 27 \, a^{3} b^{2} + 7 \, a^{2} b^{3} + 34 \, a b^{4} + 6 \, b^{5} + 16 \, {\left(a^{5} + 7 \, a^{4} b - a^{3} b^{2} - 7 \, a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(198 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{7} + 252 \, {\left(a^{5} + a^{4} b - a^{3} b^{2} - a^{2} b^{3} + {\left(a^{5} + 9 \, a^{4} b + 15 \, a^{3} b^{2} + 7 \, a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{5} + 14 \, {\left(5 \, a^{5} - a^{4} b - 27 \, a^{3} b^{2} + 7 \, a^{2} b^{3} + 34 \, a b^{4} + 6 \, b^{5} + 16 \, {\left(a^{5} + 7 \, a^{4} b - a^{3} b^{2} - 7 \, a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(39 \, a^{3} b^{2} - 17 \, a^{2} b^{3} + 33 \, a b^{4} + 9 \, b^{5} - 4 \, {\left(3 \, a^{5} + 19 \, a^{4} b - 11 \, a^{3} b^{2} + 21 \, a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - a^{5} - 3 \, a^{4} b - 3 \, a^{3} b^{2} - a^{2} b^{3} - {\left(5 \, a^{5} - a^{4} b + 77 \, a^{3} b^{2} + 31 \, a^{2} b^{3} - 70 \, a b^{4} - 18 \, b^{5} - 16 \, {\left(a^{5} + 7 \, a^{4} b - a^{3} b^{2} - 7 \, a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + {\left(495 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{8} + 840 \, {\left(a^{5} + a^{4} b - a^{3} b^{2} - a^{2} b^{3} + {\left(a^{5} + 9 \, a^{4} b + 15 \, a^{3} b^{2} + 7 \, a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{6} - 5 \, a^{5} + a^{4} b - 77 \, a^{3} b^{2} - 31 \, a^{2} b^{3} + 70 \, a b^{4} + 18 \, b^{5} + 70 \, {\left(5 \, a^{5} - a^{4} b - 27 \, a^{3} b^{2} + 7 \, a^{2} b^{3} + 34 \, a b^{4} + 6 \, b^{5} + 16 \, {\left(a^{5} + 7 \, a^{4} b - a^{3} b^{2} - 7 \, a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 16 \, {\left(a^{5} + 7 \, a^{4} b - a^{3} b^{2} - 7 \, a^{2} b^{3}\right)} d x - 30 \, {\left(39 \, a^{3} b^{2} - 17 \, a^{2} b^{3} + 33 \, a b^{4} + 9 \, b^{5} - 4 \, {\left(3 \, a^{5} + 19 \, a^{4} b - 11 \, a^{3} b^{2} + 21 \, a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(55 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{9} + 120 \, {\left(a^{5} + a^{4} b - a^{3} b^{2} - a^{2} b^{3} + {\left(a^{5} + 9 \, a^{4} b + 15 \, a^{3} b^{2} + 7 \, a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{7} + 14 \, {\left(5 \, a^{5} - a^{4} b - 27 \, a^{3} b^{2} + 7 \, a^{2} b^{3} + 34 \, a b^{4} + 6 \, b^{5} + 16 \, {\left(a^{5} + 7 \, a^{4} b - a^{3} b^{2} - 7 \, a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{5} - 10 \, {\left(39 \, a^{3} b^{2} - 17 \, a^{2} b^{3} + 33 \, a b^{4} + 9 \, b^{5} - 4 \, {\left(3 \, a^{5} + 19 \, a^{4} b - 11 \, a^{3} b^{2} + 21 \, a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - {\left(5 \, a^{5} - a^{4} b + 77 \, a^{3} b^{2} + 31 \, a^{2} b^{3} - 70 \, a b^{4} - 18 \, b^{5} - 16 \, {\left(a^{5} + 7 \, a^{4} b - a^{3} b^{2} - 7 \, a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 2 \, {\left(2 \, a^{5} + 2 \, a^{4} b + 11 \, a^{3} b^{2} + 27 \, a^{2} b^{3} + 19 \, a b^{4} + 3 \, b^{5} - 2 \, {\left(a^{5} + 9 \, a^{4} b + 15 \, a^{3} b^{2} + 7 \, a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(33 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{10} + 90 \, {\left(a^{5} + a^{4} b - a^{3} b^{2} - a^{2} b^{3} + {\left(a^{5} + 9 \, a^{4} b + 15 \, a^{3} b^{2} + 7 \, a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{8} + 14 \, {\left(5 \, a^{5} - a^{4} b - 27 \, a^{3} b^{2} + 7 \, a^{2} b^{3} + 34 \, a b^{4} + 6 \, b^{5} + 16 \, {\left(a^{5} + 7 \, a^{4} b - a^{3} b^{2} - 7 \, a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{6} - 2 \, a^{5} - 2 \, a^{4} b - 11 \, a^{3} b^{2} - 27 \, a^{2} b^{3} - 19 \, a b^{4} - 3 \, b^{5} - 15 \, {\left(39 \, a^{3} b^{2} - 17 \, a^{2} b^{3} + 33 \, a b^{4} + 9 \, b^{5} - 4 \, {\left(3 \, a^{5} + 19 \, a^{4} b - 11 \, a^{3} b^{2} + 21 \, a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(a^{5} + 9 \, a^{4} b + 15 \, a^{3} b^{2} + 7 \, a^{2} b^{3}\right)} d x - 3 \, {\left(5 \, a^{5} - a^{4} b + 77 \, a^{3} b^{2} + 31 \, a^{2} b^{3} - 70 \, a b^{4} - 18 \, b^{5} - 16 \, {\left(a^{5} + 7 \, a^{4} b - a^{3} b^{2} - 7 \, a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(35 \, a^{4} b + 84 \, a^{3} b^{2} + 66 \, a^{2} b^{3} + 20 \, a b^{4} + 3 \, b^{5}\right)} \cosh\left(d x + c\right)^{10} + 10 \, {\left(35 \, a^{4} b + 84 \, a^{3} b^{2} + 66 \, a^{2} b^{3} + 20 \, a b^{4} + 3 \, b^{5}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + {\left(35 \, a^{4} b + 84 \, a^{3} b^{2} + 66 \, a^{2} b^{3} + 20 \, a b^{4} + 3 \, b^{5}\right)} \sinh\left(d x + c\right)^{10} + 4 \, {\left(35 \, a^{4} b + 14 \, a^{3} b^{2} - 32 \, a^{2} b^{3} - 14 \, a b^{4} - 3 \, b^{5}\right)} \cosh\left(d x + c\right)^{8} + {\left(140 \, a^{4} b + 56 \, a^{3} b^{2} - 128 \, a^{2} b^{3} - 56 \, a b^{4} - 12 \, b^{5} + 45 \, {\left(35 \, a^{4} b + 84 \, a^{3} b^{2} + 66 \, 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)^{8} + 8 \, {\left(15 \, {\left(35 \, a^{4} b + 84 \, a^{3} b^{2} + 66 \, a^{2} b^{3} + 20 \, a b^{4} + 3 \, b^{5}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(35 \, a^{4} b + 14 \, a^{3} b^{2} - 32 \, a^{2} b^{3} - 14 \, a b^{4} - 3 \, b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(105 \, a^{4} b - 28 \, a^{3} b^{2} + 86 \, a^{2} b^{3} + 36 \, a b^{4} + 9 \, b^{5}\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(105 \, a^{4} b - 28 \, a^{3} b^{2} + 86 \, a^{2} b^{3} + 36 \, a b^{4} + 9 \, b^{5} + 105 \, {\left(35 \, a^{4} b + 84 \, a^{3} b^{2} + 66 \, a^{2} b^{3} + 20 \, a b^{4} + 3 \, b^{5}\right)} \cosh\left(d x + c\right)^{4} + 56 \, {\left(35 \, a^{4} b + 14 \, a^{3} b^{2} - 32 \, a^{2} b^{3} - 14 \, 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(35 \, a^{4} b + 84 \, a^{3} b^{2} + 66 \, a^{2} b^{3} + 20 \, a b^{4} + 3 \, b^{5}\right)} \cosh\left(d x + c\right)^{5} + 56 \, {\left(35 \, a^{4} b + 14 \, a^{3} b^{2} - 32 \, a^{2} b^{3} - 14 \, a b^{4} - 3 \, b^{5}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(105 \, a^{4} b - 28 \, a^{3} b^{2} + 86 \, a^{2} b^{3} + 36 \, a b^{4} + 9 \, b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 4 \, {\left(35 \, a^{4} b + 14 \, a^{3} b^{2} - 32 \, a^{2} b^{3} - 14 \, a b^{4} - 3 \, b^{5}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(105 \, {\left(35 \, a^{4} b + 84 \, a^{3} b^{2} + 66 \, a^{2} b^{3} + 20 \, a b^{4} + 3 \, b^{5}\right)} \cosh\left(d x + c\right)^{6} + 70 \, a^{4} b + 28 \, a^{3} b^{2} - 64 \, a^{2} b^{3} - 28 \, a b^{4} - 6 \, b^{5} + 140 \, {\left(35 \, a^{4} b + 14 \, a^{3} b^{2} - 32 \, a^{2} b^{3} - 14 \, a b^{4} - 3 \, b^{5}\right)} \cosh\left(d x + c\right)^{4} + 15 \, {\left(105 \, a^{4} b - 28 \, a^{3} b^{2} + 86 \, a^{2} b^{3} + 36 \, a b^{4} + 9 \, b^{5}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(15 \, {\left(35 \, a^{4} b + 84 \, a^{3} b^{2} + 66 \, a^{2} b^{3} + 20 \, a b^{4} + 3 \, b^{5}\right)} \cosh\left(d x + c\right)^{7} + 28 \, {\left(35 \, a^{4} b + 14 \, a^{3} b^{2} - 32 \, a^{2} b^{3} - 14 \, a b^{4} - 3 \, b^{5}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(105 \, a^{4} b - 28 \, a^{3} b^{2} + 86 \, a^{2} b^{3} + 36 \, a b^{4} + 9 \, b^{5}\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(35 \, a^{4} b + 14 \, a^{3} b^{2} - 32 \, a^{2} b^{3} - 14 \, a b^{4} - 3 \, b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(35 \, a^{4} b + 84 \, a^{3} b^{2} + 66 \, a^{2} b^{3} + 20 \, a b^{4} + 3 \, b^{5}\right)} \cosh\left(d x + c\right)^{2} + {\left(45 \, {\left(35 \, a^{4} b + 84 \, a^{3} b^{2} + 66 \, a^{2} b^{3} + 20 \, a b^{4} + 3 \, b^{5}\right)} \cosh\left(d x + c\right)^{8} + 112 \, {\left(35 \, a^{4} b + 14 \, a^{3} b^{2} - 32 \, a^{2} b^{3} - 14 \, a b^{4} - 3 \, b^{5}\right)} \cosh\left(d x + c\right)^{6} + 35 \, a^{4} b + 84 \, a^{3} b^{2} + 66 \, a^{2} b^{3} + 20 \, a b^{4} + 3 \, b^{5} + 30 \, {\left(105 \, a^{4} b - 28 \, a^{3} b^{2} + 86 \, a^{2} b^{3} + 36 \, a b^{4} + 9 \, b^{5}\right)} \cosh\left(d x + c\right)^{4} + 24 \, {\left(35 \, a^{4} b + 14 \, a^{3} b^{2} - 32 \, a^{2} b^{3} - 14 \, a b^{4} - 3 \, b^{5}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(5 \, {\left(35 \, a^{4} b + 84 \, a^{3} b^{2} + 66 \, a^{2} b^{3} + 20 \, a b^{4} + 3 \, b^{5}\right)} \cosh\left(d x + c\right)^{9} + 16 \, {\left(35 \, a^{4} b + 14 \, a^{3} b^{2} - 32 \, a^{2} b^{3} - 14 \, a b^{4} - 3 \, b^{5}\right)} \cosh\left(d x + c\right)^{7} + 6 \, {\left(105 \, a^{4} b - 28 \, a^{3} b^{2} + 86 \, a^{2} b^{3} + 36 \, a b^{4} + 9 \, b^{5}\right)} \cosh\left(d x + c\right)^{5} + 8 \, {\left(35 \, a^{4} b + 14 \, a^{3} b^{2} - 32 \, a^{2} b^{3} - 14 \, a b^{4} - 3 \, b^{5}\right)} \cosh\left(d x + c\right)^{3} + {\left(35 \, a^{4} b + 84 \, a^{3} b^{2} + 66 \, 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{\frac{b}{a}} \arctan\left(\frac{{\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} + a - b\right)} \sqrt{\frac{b}{a}}}{2 \, b}\right) + 4 \, {\left(3 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(d x + c\right)^{11} + 10 \, {\left(a^{5} + a^{4} b - a^{3} b^{2} - a^{2} b^{3} + {\left(a^{5} + 9 \, a^{4} b + 15 \, a^{3} b^{2} + 7 \, a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{9} + 2 \, {\left(5 \, a^{5} - a^{4} b - 27 \, a^{3} b^{2} + 7 \, a^{2} b^{3} + 34 \, a b^{4} + 6 \, b^{5} + 16 \, {\left(a^{5} + 7 \, a^{4} b - a^{3} b^{2} - 7 \, a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{7} - 3 \, {\left(39 \, a^{3} b^{2} - 17 \, a^{2} b^{3} + 33 \, a b^{4} + 9 \, b^{5} - 4 \, {\left(3 \, a^{5} + 19 \, a^{4} b - 11 \, a^{3} b^{2} + 21 \, a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{5} - {\left(5 \, a^{5} - a^{4} b + 77 \, a^{3} b^{2} + 31 \, a^{2} b^{3} - 70 \, a b^{4} - 18 \, b^{5} - 16 \, {\left(a^{5} + 7 \, a^{4} b - a^{3} b^{2} - 7 \, a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - {\left(2 \, a^{5} + 2 \, a^{4} b + 11 \, a^{3} b^{2} + 27 \, a^{2} b^{3} + 19 \, a b^{4} + 3 \, b^{5} - 2 \, {\left(a^{5} + 9 \, a^{4} b + 15 \, a^{3} b^{2} + 7 \, a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{8 \, {\left({\left(a^{8} + 6 \, a^{7} b + 15 \, a^{6} b^{2} + 20 \, a^{5} b^{3} + 15 \, a^{4} b^{4} + 6 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{10} + 10 \, {\left(a^{8} + 6 \, a^{7} b + 15 \, a^{6} b^{2} + 20 \, a^{5} b^{3} + 15 \, a^{4} b^{4} + 6 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + {\left(a^{8} + 6 \, a^{7} b + 15 \, a^{6} b^{2} + 20 \, a^{5} b^{3} + 15 \, a^{4} b^{4} + 6 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \sinh\left(d x + c\right)^{10} + 4 \, {\left(a^{8} + 4 \, a^{7} b + 5 \, a^{6} b^{2} - 5 \, a^{4} b^{4} - 4 \, a^{3} b^{5} - a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{8} + {\left(45 \, {\left(a^{8} + 6 \, a^{7} b + 15 \, a^{6} b^{2} + 20 \, a^{5} b^{3} + 15 \, a^{4} b^{4} + 6 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{2} + 4 \, {\left(a^{8} + 4 \, a^{7} b + 5 \, a^{6} b^{2} - 5 \, a^{4} b^{4} - 4 \, a^{3} b^{5} - a^{2} b^{6}\right)} d\right)} \sinh\left(d x + c\right)^{8} + 2 \, {\left(3 \, a^{8} + 10 \, a^{7} b + 13 \, a^{6} b^{2} + 12 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 10 \, a^{3} b^{5} + 3 \, a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{6} + 8 \, {\left(15 \, {\left(a^{8} + 6 \, a^{7} b + 15 \, a^{6} b^{2} + 20 \, a^{5} b^{3} + 15 \, a^{4} b^{4} + 6 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{3} + 4 \, {\left(a^{8} + 4 \, a^{7} b + 5 \, a^{6} b^{2} - 5 \, a^{4} b^{4} - 4 \, a^{3} b^{5} - a^{2} b^{6}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(105 \, {\left(a^{8} + 6 \, a^{7} b + 15 \, a^{6} b^{2} + 20 \, a^{5} b^{3} + 15 \, a^{4} b^{4} + 6 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{4} + 56 \, {\left(a^{8} + 4 \, a^{7} b + 5 \, a^{6} b^{2} - 5 \, a^{4} b^{4} - 4 \, a^{3} b^{5} - a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{8} + 10 \, a^{7} b + 13 \, a^{6} b^{2} + 12 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 10 \, a^{3} b^{5} + 3 \, a^{2} b^{6}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(a^{8} + 4 \, a^{7} b + 5 \, a^{6} b^{2} - 5 \, a^{4} b^{4} - 4 \, a^{3} b^{5} - a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(63 \, {\left(a^{8} + 6 \, a^{7} b + 15 \, a^{6} b^{2} + 20 \, a^{5} b^{3} + 15 \, a^{4} b^{4} + 6 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{5} + 56 \, {\left(a^{8} + 4 \, a^{7} b + 5 \, a^{6} b^{2} - 5 \, a^{4} b^{4} - 4 \, a^{3} b^{5} - a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(3 \, a^{8} + 10 \, a^{7} b + 13 \, a^{6} b^{2} + 12 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 10 \, a^{3} b^{5} + 3 \, a^{2} b^{6}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(105 \, {\left(a^{8} + 6 \, a^{7} b + 15 \, a^{6} b^{2} + 20 \, a^{5} b^{3} + 15 \, a^{4} b^{4} + 6 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{6} + 140 \, {\left(a^{8} + 4 \, a^{7} b + 5 \, a^{6} b^{2} - 5 \, a^{4} b^{4} - 4 \, a^{3} b^{5} - a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{4} + 15 \, {\left(3 \, a^{8} + 10 \, a^{7} b + 13 \, a^{6} b^{2} + 12 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 10 \, a^{3} b^{5} + 3 \, a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{8} + 4 \, a^{7} b + 5 \, a^{6} b^{2} - 5 \, a^{4} b^{4} - 4 \, a^{3} b^{5} - a^{2} b^{6}\right)} d\right)} \sinh\left(d x + c\right)^{4} + {\left(a^{8} + 6 \, a^{7} b + 15 \, a^{6} b^{2} + 20 \, a^{5} b^{3} + 15 \, a^{4} b^{4} + 6 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(15 \, {\left(a^{8} + 6 \, a^{7} b + 15 \, a^{6} b^{2} + 20 \, a^{5} b^{3} + 15 \, a^{4} b^{4} + 6 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{7} + 28 \, {\left(a^{8} + 4 \, a^{7} b + 5 \, a^{6} b^{2} - 5 \, a^{4} b^{4} - 4 \, a^{3} b^{5} - a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{5} + 5 \, {\left(3 \, a^{8} + 10 \, a^{7} b + 13 \, a^{6} b^{2} + 12 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 10 \, a^{3} b^{5} + 3 \, a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{3} + 2 \, {\left(a^{8} + 4 \, a^{7} b + 5 \, a^{6} b^{2} - 5 \, a^{4} b^{4} - 4 \, a^{3} b^{5} - a^{2} b^{6}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(45 \, {\left(a^{8} + 6 \, a^{7} b + 15 \, a^{6} b^{2} + 20 \, a^{5} b^{3} + 15 \, a^{4} b^{4} + 6 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{8} + 112 \, {\left(a^{8} + 4 \, a^{7} b + 5 \, a^{6} b^{2} - 5 \, a^{4} b^{4} - 4 \, a^{3} b^{5} - a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{6} + 30 \, {\left(3 \, a^{8} + 10 \, a^{7} b + 13 \, a^{6} b^{2} + 12 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 10 \, a^{3} b^{5} + 3 \, a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{4} + 24 \, {\left(a^{8} + 4 \, a^{7} b + 5 \, a^{6} b^{2} - 5 \, a^{4} b^{4} - 4 \, a^{3} b^{5} - a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{8} + 6 \, a^{7} b + 15 \, a^{6} b^{2} + 20 \, a^{5} b^{3} + 15 \, a^{4} b^{4} + 6 \, a^{3} b^{5} + a^{2} b^{6}\right)} d\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(5 \, {\left(a^{8} + 6 \, a^{7} b + 15 \, a^{6} b^{2} + 20 \, a^{5} b^{3} + 15 \, a^{4} b^{4} + 6 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{9} + 16 \, {\left(a^{8} + 4 \, a^{7} b + 5 \, a^{6} b^{2} - 5 \, a^{4} b^{4} - 4 \, a^{3} b^{5} - a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{7} + 6 \, {\left(3 \, a^{8} + 10 \, a^{7} b + 13 \, a^{6} b^{2} + 12 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 10 \, a^{3} b^{5} + 3 \, a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{5} + 8 \, {\left(a^{8} + 4 \, a^{7} b + 5 \, a^{6} b^{2} - 5 \, a^{4} b^{4} - 4 \, a^{3} b^{5} - a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{8} + 6 \, a^{7} b + 15 \, a^{6} b^{2} + 20 \, a^{5} b^{3} + 15 \, a^{4} b^{4} + 6 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[1/16*(2*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(d*x + c)^12 + 24*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(d*x + c)*sinh(d*x + c)^11 + 2*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*sinh(d*x + c)^12 + 8*(a^5 + a^4*b - a^3*b^2 - a^2*b^3 + (a^5 + 9*a^4*b + 15*a^3*b^2 + 7*a^2*b^3)*d*x)*cosh(d*x + c)^10 + 4*(2*a^5 + 2*a^4*b - 2*a^3*b^2 - 2*a^2*b^3 + 2*(a^5 + 9*a^4*b + 15*a^3*b^2 + 7*a^2*b^3)*d*x + 33*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^10 + 40*(11*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(d*x + c)^3 + 2*(a^5 + a^4*b - a^3*b^2 - a^2*b^3 + (a^5 + 9*a^4*b + 15*a^3*b^2 + 7*a^2*b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c)^9 + 2*(5*a^5 - a^4*b - 27*a^3*b^2 + 7*a^2*b^3 + 34*a*b^4 + 6*b^5 + 16*(a^5 + 7*a^4*b - a^3*b^2 - 7*a^2*b^3)*d*x)*cosh(d*x + c)^8 + 2*(5*a^5 - a^4*b - 27*a^3*b^2 + 7*a^2*b^3 + 34*a*b^4 + 6*b^5 + 495*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(d*x + c)^4 + 16*(a^5 + 7*a^4*b - a^3*b^2 - 7*a^2*b^3)*d*x + 180*(a^5 + a^4*b - a^3*b^2 - a^2*b^3 + (a^5 + 9*a^4*b + 15*a^3*b^2 + 7*a^2*b^3)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 16*(99*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(d*x + c)^5 + 60*(a^5 + a^4*b - a^3*b^2 - a^2*b^3 + (a^5 + 9*a^4*b + 15*a^3*b^2 + 7*a^2*b^3)*d*x)*cosh(d*x + c)^3 + (5*a^5 - a^4*b - 27*a^3*b^2 + 7*a^2*b^3 + 34*a*b^4 + 6*b^5 + 16*(a^5 + 7*a^4*b - a^3*b^2 - 7*a^2*b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c)^7 - 4*(39*a^3*b^2 - 17*a^2*b^3 + 33*a*b^4 + 9*b^5 - 4*(3*a^5 + 19*a^4*b - 11*a^3*b^2 + 21*a^2*b^3)*d*x)*cosh(d*x + c)^6 + 4*(462*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(d*x + c)^6 - 39*a^3*b^2 + 17*a^2*b^3 - 33*a*b^4 - 9*b^5 + 420*(a^5 + a^4*b - a^3*b^2 - a^2*b^3 + (a^5 + 9*a^4*b + 15*a^3*b^2 + 7*a^2*b^3)*d*x)*cosh(d*x + c)^4 + 4*(3*a^5 + 19*a^4*b - 11*a^3*b^2 + 21*a^2*b^3)*d*x + 14*(5*a^5 - a^4*b - 27*a^3*b^2 + 7*a^2*b^3 + 34*a*b^4 + 6*b^5 + 16*(a^5 + 7*a^4*b - a^3*b^2 - 7*a^2*b^3)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(198*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(d*x + c)^7 + 252*(a^5 + a^4*b - a^3*b^2 - a^2*b^3 + (a^5 + 9*a^4*b + 15*a^3*b^2 + 7*a^2*b^3)*d*x)*cosh(d*x + c)^5 + 14*(5*a^5 - a^4*b - 27*a^3*b^2 + 7*a^2*b^3 + 34*a*b^4 + 6*b^5 + 16*(a^5 + 7*a^4*b - a^3*b^2 - 7*a^2*b^3)*d*x)*cosh(d*x + c)^3 - 3*(39*a^3*b^2 - 17*a^2*b^3 + 33*a*b^4 + 9*b^5 - 4*(3*a^5 + 19*a^4*b - 11*a^3*b^2 + 21*a^2*b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c)^5 - 2*a^5 - 6*a^4*b - 6*a^3*b^2 - 2*a^2*b^3 - 2*(5*a^5 - a^4*b + 77*a^3*b^2 + 31*a^2*b^3 - 70*a*b^4 - 18*b^5 - 16*(a^5 + 7*a^4*b - a^3*b^2 - 7*a^2*b^3)*d*x)*cosh(d*x + c)^4 + 2*(495*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(d*x + c)^8 + 840*(a^5 + a^4*b - a^3*b^2 - a^2*b^3 + (a^5 + 9*a^4*b + 15*a^3*b^2 + 7*a^2*b^3)*d*x)*cosh(d*x + c)^6 - 5*a^5 + a^4*b - 77*a^3*b^2 - 31*a^2*b^3 + 70*a*b^4 + 18*b^5 + 70*(5*a^5 - a^4*b - 27*a^3*b^2 + 7*a^2*b^3 + 34*a*b^4 + 6*b^5 + 16*(a^5 + 7*a^4*b - a^3*b^2 - 7*a^2*b^3)*d*x)*cosh(d*x + c)^4 + 16*(a^5 + 7*a^4*b - a^3*b^2 - 7*a^2*b^3)*d*x - 30*(39*a^3*b^2 - 17*a^2*b^3 + 33*a*b^4 + 9*b^5 - 4*(3*a^5 + 19*a^4*b - 11*a^3*b^2 + 21*a^2*b^3)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(55*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(d*x + c)^9 + 120*(a^5 + a^4*b - a^3*b^2 - a^2*b^3 + (a^5 + 9*a^4*b + 15*a^3*b^2 + 7*a^2*b^3)*d*x)*cosh(d*x + c)^7 + 14*(5*a^5 - a^4*b - 27*a^3*b^2 + 7*a^2*b^3 + 34*a*b^4 + 6*b^5 + 16*(a^5 + 7*a^4*b - a^3*b^2 - 7*a^2*b^3)*d*x)*cosh(d*x + c)^5 - 10*(39*a^3*b^2 - 17*a^2*b^3 + 33*a*b^4 + 9*b^5 - 4*(3*a^5 + 19*a^4*b - 11*a^3*b^2 + 21*a^2*b^3)*d*x)*cosh(d*x + c)^3 - (5*a^5 - a^4*b + 77*a^3*b^2 + 31*a^2*b^3 - 70*a*b^4 - 18*b^5 - 16*(a^5 + 7*a^4*b - a^3*b^2 - 7*a^2*b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c)^3 - 4*(2*a^5 + 2*a^4*b + 11*a^3*b^2 + 27*a^2*b^3 + 19*a*b^4 + 3*b^5 - 2*(a^5 + 9*a^4*b + 15*a^3*b^2 + 7*a^2*b^3)*d*x)*cosh(d*x + c)^2 + 4*(33*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(d*x + c)^10 + 90*(a^5 + a^4*b - a^3*b^2 - a^2*b^3 + (a^5 + 9*a^4*b + 15*a^3*b^2 + 7*a^2*b^3)*d*x)*cosh(d*x + c)^8 + 14*(5*a^5 - a^4*b - 27*a^3*b^2 + 7*a^2*b^3 + 34*a*b^4 + 6*b^5 + 16*(a^5 + 7*a^4*b - a^3*b^2 - 7*a^2*b^3)*d*x)*cosh(d*x + c)^6 - 2*a^5 - 2*a^4*b - 11*a^3*b^2 - 27*a^2*b^3 - 19*a*b^4 - 3*b^5 - 15*(39*a^3*b^2 - 17*a^2*b^3 + 33*a*b^4 + 9*b^5 - 4*(3*a^5 + 19*a^4*b - 11*a^3*b^2 + 21*a^2*b^3)*d*x)*cosh(d*x + c)^4 + 2*(a^5 + 9*a^4*b + 15*a^3*b^2 + 7*a^2*b^3)*d*x - 3*(5*a^5 - a^4*b + 77*a^3*b^2 + 31*a^2*b^3 - 70*a*b^4 - 18*b^5 - 16*(a^5 + 7*a^4*b - a^3*b^2 - 7*a^2*b^3)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((35*a^4*b + 84*a^3*b^2 + 66*a^2*b^3 + 20*a*b^4 + 3*b^5)*cosh(d*x + c)^10 + 10*(35*a^4*b + 84*a^3*b^2 + 66*a^2*b^3 + 20*a*b^4 + 3*b^5)*cosh(d*x + c)*sinh(d*x + c)^9 + (35*a^4*b + 84*a^3*b^2 + 66*a^2*b^3 + 20*a*b^4 + 3*b^5)*sinh(d*x + c)^10 + 4*(35*a^4*b + 14*a^3*b^2 - 32*a^2*b^3 - 14*a*b^4 - 3*b^5)*cosh(d*x + c)^8 + (140*a^4*b + 56*a^3*b^2 - 128*a^2*b^3 - 56*a*b^4 - 12*b^5 + 45*(35*a^4*b + 84*a^3*b^2 + 66*a^2*b^3 + 20*a*b^4 + 3*b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 8*(15*(35*a^4*b + 84*a^3*b^2 + 66*a^2*b^3 + 20*a*b^4 + 3*b^5)*cosh(d*x + c)^3 + 4*(35*a^4*b + 14*a^3*b^2 - 32*a^2*b^3 - 14*a*b^4 - 3*b^5)*cosh(d*x + c))*sinh(d*x + c)^7 + 2*(105*a^4*b - 28*a^3*b^2 + 86*a^2*b^3 + 36*a*b^4 + 9*b^5)*cosh(d*x + c)^6 + 2*(105*a^4*b - 28*a^3*b^2 + 86*a^2*b^3 + 36*a*b^4 + 9*b^5 + 105*(35*a^4*b + 84*a^3*b^2 + 66*a^2*b^3 + 20*a*b^4 + 3*b^5)*cosh(d*x + c)^4 + 56*(35*a^4*b + 14*a^3*b^2 - 32*a^2*b^3 - 14*a*b^4 - 3*b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 4*(63*(35*a^4*b + 84*a^3*b^2 + 66*a^2*b^3 + 20*a*b^4 + 3*b^5)*cosh(d*x + c)^5 + 56*(35*a^4*b + 14*a^3*b^2 - 32*a^2*b^3 - 14*a*b^4 - 3*b^5)*cosh(d*x + c)^3 + 3*(105*a^4*b - 28*a^3*b^2 + 86*a^2*b^3 + 36*a*b^4 + 9*b^5)*cosh(d*x + c))*sinh(d*x + c)^5 + 4*(35*a^4*b + 14*a^3*b^2 - 32*a^2*b^3 - 14*a*b^4 - 3*b^5)*cosh(d*x + c)^4 + 2*(105*(35*a^4*b + 84*a^3*b^2 + 66*a^2*b^3 + 20*a*b^4 + 3*b^5)*cosh(d*x + c)^6 + 70*a^4*b + 28*a^3*b^2 - 64*a^2*b^3 - 28*a*b^4 - 6*b^5 + 140*(35*a^4*b + 14*a^3*b^2 - 32*a^2*b^3 - 14*a*b^4 - 3*b^5)*cosh(d*x + c)^4 + 15*(105*a^4*b - 28*a^3*b^2 + 86*a^2*b^3 + 36*a*b^4 + 9*b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(15*(35*a^4*b + 84*a^3*b^2 + 66*a^2*b^3 + 20*a*b^4 + 3*b^5)*cosh(d*x + c)^7 + 28*(35*a^4*b + 14*a^3*b^2 - 32*a^2*b^3 - 14*a*b^4 - 3*b^5)*cosh(d*x + c)^5 + 5*(105*a^4*b - 28*a^3*b^2 + 86*a^2*b^3 + 36*a*b^4 + 9*b^5)*cosh(d*x + c)^3 + 2*(35*a^4*b + 14*a^3*b^2 - 32*a^2*b^3 - 14*a*b^4 - 3*b^5)*cosh(d*x + c))*sinh(d*x + c)^3 + (35*a^4*b + 84*a^3*b^2 + 66*a^2*b^3 + 20*a*b^4 + 3*b^5)*cosh(d*x + c)^2 + (45*(35*a^4*b + 84*a^3*b^2 + 66*a^2*b^3 + 20*a*b^4 + 3*b^5)*cosh(d*x + c)^8 + 112*(35*a^4*b + 14*a^3*b^2 - 32*a^2*b^3 - 14*a*b^4 - 3*b^5)*cosh(d*x + c)^6 + 35*a^4*b + 84*a^3*b^2 + 66*a^2*b^3 + 20*a*b^4 + 3*b^5 + 30*(105*a^4*b - 28*a^3*b^2 + 86*a^2*b^3 + 36*a*b^4 + 9*b^5)*cosh(d*x + c)^4 + 24*(35*a^4*b + 14*a^3*b^2 - 32*a^2*b^3 - 14*a*b^4 - 3*b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 2*(5*(35*a^4*b + 84*a^3*b^2 + 66*a^2*b^3 + 20*a*b^4 + 3*b^5)*cosh(d*x + c)^9 + 16*(35*a^4*b + 14*a^3*b^2 - 32*a^2*b^3 - 14*a*b^4 - 3*b^5)*cosh(d*x + c)^7 + 6*(105*a^4*b - 28*a^3*b^2 + 86*a^2*b^3 + 36*a*b^4 + 9*b^5)*cosh(d*x + c)^5 + 8*(35*a^4*b + 14*a^3*b^2 - 32*a^2*b^3 - 14*a*b^4 - 3*b^5)*cosh(d*x + c)^3 + (35*a^4*b + 84*a^3*b^2 + 66*a^2*b^3 + 20*a*b^4 + 3*b^5)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-b/a)*log(((a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 + 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 + 2*(a^2 - b^2)*cosh(d*x + c)^2 + 2*(3*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + a^2 - b^2)*sinh(d*x + c)^2 + a^2 - 6*a*b + b^2 + 4*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 + (a^2 - b^2)*cosh(d*x + c))*sinh(d*x + c) + 4*((a^2 + a*b)*cosh(d*x + c)^2 + 2*(a^2 + a*b)*cosh(d*x + c)*sinh(d*x + c) + (a^2 + a*b)*sinh(d*x + c)^2 + a^2 - a*b)*sqrt(-b/a))/((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)) + 8*(3*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(d*x + c)^11 + 10*(a^5 + a^4*b - a^3*b^2 - a^2*b^3 + (a^5 + 9*a^4*b + 15*a^3*b^2 + 7*a^2*b^3)*d*x)*cosh(d*x + c)^9 + 2*(5*a^5 - a^4*b - 27*a^3*b^2 + 7*a^2*b^3 + 34*a*b^4 + 6*b^5 + 16*(a^5 + 7*a^4*b - a^3*b^2 - 7*a^2*b^3)*d*x)*cosh(d*x + c)^7 - 3*(39*a^3*b^2 - 17*a^2*b^3 + 33*a*b^4 + 9*b^5 - 4*(3*a^5 + 19*a^4*b - 11*a^3*b^2 + 21*a^2*b^3)*d*x)*cosh(d*x + c)^5 - (5*a^5 - a^4*b + 77*a^3*b^2 + 31*a^2*b^3 - 70*a*b^4 - 18*b^5 - 16*(a^5 + 7*a^4*b - a^3*b^2 - 7*a^2*b^3)*d*x)*cosh(d*x + c)^3 - (2*a^5 + 2*a^4*b + 11*a^3*b^2 + 27*a^2*b^3 + 19*a*b^4 + 3*b^5 - 2*(a^5 + 9*a^4*b + 15*a^3*b^2 + 7*a^2*b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c))/((a^8 + 6*a^7*b + 15*a^6*b^2 + 20*a^5*b^3 + 15*a^4*b^4 + 6*a^3*b^5 + a^2*b^6)*d*cosh(d*x + c)^10 + 10*(a^8 + 6*a^7*b + 15*a^6*b^2 + 20*a^5*b^3 + 15*a^4*b^4 + 6*a^3*b^5 + a^2*b^6)*d*cosh(d*x + c)*sinh(d*x + c)^9 + (a^8 + 6*a^7*b + 15*a^6*b^2 + 20*a^5*b^3 + 15*a^4*b^4 + 6*a^3*b^5 + a^2*b^6)*d*sinh(d*x + c)^10 + 4*(a^8 + 4*a^7*b + 5*a^6*b^2 - 5*a^4*b^4 - 4*a^3*b^5 - a^2*b^6)*d*cosh(d*x + c)^8 + (45*(a^8 + 6*a^7*b + 15*a^6*b^2 + 20*a^5*b^3 + 15*a^4*b^4 + 6*a^3*b^5 + a^2*b^6)*d*cosh(d*x + c)^2 + 4*(a^8 + 4*a^7*b + 5*a^6*b^2 - 5*a^4*b^4 - 4*a^3*b^5 - a^2*b^6)*d)*sinh(d*x + c)^8 + 2*(3*a^8 + 10*a^7*b + 13*a^6*b^2 + 12*a^5*b^3 + 13*a^4*b^4 + 10*a^3*b^5 + 3*a^2*b^6)*d*cosh(d*x + c)^6 + 8*(15*(a^8 + 6*a^7*b + 15*a^6*b^2 + 20*a^5*b^3 + 15*a^4*b^4 + 6*a^3*b^5 + a^2*b^6)*d*cosh(d*x + c)^3 + 4*(a^8 + 4*a^7*b + 5*a^6*b^2 - 5*a^4*b^4 - 4*a^3*b^5 - a^2*b^6)*d*cosh(d*x + c))*sinh(d*x + c)^7 + 2*(105*(a^8 + 6*a^7*b + 15*a^6*b^2 + 20*a^5*b^3 + 15*a^4*b^4 + 6*a^3*b^5 + a^2*b^6)*d*cosh(d*x + c)^4 + 56*(a^8 + 4*a^7*b + 5*a^6*b^2 - 5*a^4*b^4 - 4*a^3*b^5 - a^2*b^6)*d*cosh(d*x + c)^2 + (3*a^8 + 10*a^7*b + 13*a^6*b^2 + 12*a^5*b^3 + 13*a^4*b^4 + 10*a^3*b^5 + 3*a^2*b^6)*d)*sinh(d*x + c)^6 + 4*(a^8 + 4*a^7*b + 5*a^6*b^2 - 5*a^4*b^4 - 4*a^3*b^5 - a^2*b^6)*d*cosh(d*x + c)^4 + 4*(63*(a^8 + 6*a^7*b + 15*a^6*b^2 + 20*a^5*b^3 + 15*a^4*b^4 + 6*a^3*b^5 + a^2*b^6)*d*cosh(d*x + c)^5 + 56*(a^8 + 4*a^7*b + 5*a^6*b^2 - 5*a^4*b^4 - 4*a^3*b^5 - a^2*b^6)*d*cosh(d*x + c)^3 + 3*(3*a^8 + 10*a^7*b + 13*a^6*b^2 + 12*a^5*b^3 + 13*a^4*b^4 + 10*a^3*b^5 + 3*a^2*b^6)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(105*(a^8 + 6*a^7*b + 15*a^6*b^2 + 20*a^5*b^3 + 15*a^4*b^4 + 6*a^3*b^5 + a^2*b^6)*d*cosh(d*x + c)^6 + 140*(a^8 + 4*a^7*b + 5*a^6*b^2 - 5*a^4*b^4 - 4*a^3*b^5 - a^2*b^6)*d*cosh(d*x + c)^4 + 15*(3*a^8 + 10*a^7*b + 13*a^6*b^2 + 12*a^5*b^3 + 13*a^4*b^4 + 10*a^3*b^5 + 3*a^2*b^6)*d*cosh(d*x + c)^2 + 2*(a^8 + 4*a^7*b + 5*a^6*b^2 - 5*a^4*b^4 - 4*a^3*b^5 - a^2*b^6)*d)*sinh(d*x + c)^4 + (a^8 + 6*a^7*b + 15*a^6*b^2 + 20*a^5*b^3 + 15*a^4*b^4 + 6*a^3*b^5 + a^2*b^6)*d*cosh(d*x + c)^2 + 8*(15*(a^8 + 6*a^7*b + 15*a^6*b^2 + 20*a^5*b^3 + 15*a^4*b^4 + 6*a^3*b^5 + a^2*b^6)*d*cosh(d*x + c)^7 + 28*(a^8 + 4*a^7*b + 5*a^6*b^2 - 5*a^4*b^4 - 4*a^3*b^5 - a^2*b^6)*d*cosh(d*x + c)^5 + 5*(3*a^8 + 10*a^7*b + 13*a^6*b^2 + 12*a^5*b^3 + 13*a^4*b^4 + 10*a^3*b^5 + 3*a^2*b^6)*d*cosh(d*x + c)^3 + 2*(a^8 + 4*a^7*b + 5*a^6*b^2 - 5*a^4*b^4 - 4*a^3*b^5 - a^2*b^6)*d*cosh(d*x + c))*sinh(d*x + c)^3 + (45*(a^8 + 6*a^7*b + 15*a^6*b^2 + 20*a^5*b^3 + 15*a^4*b^4 + 6*a^3*b^5 + a^2*b^6)*d*cosh(d*x + c)^8 + 112*(a^8 + 4*a^7*b + 5*a^6*b^2 - 5*a^4*b^4 - 4*a^3*b^5 - a^2*b^6)*d*cosh(d*x + c)^6 + 30*(3*a^8 + 10*a^7*b + 13*a^6*b^2 + 12*a^5*b^3 + 13*a^4*b^4 + 10*a^3*b^5 + 3*a^2*b^6)*d*cosh(d*x + c)^4 + 24*(a^8 + 4*a^7*b + 5*a^6*b^2 - 5*a^4*b^4 - 4*a^3*b^5 - a^2*b^6)*d*cosh(d*x + c)^2 + (a^8 + 6*a^7*b + 15*a^6*b^2 + 20*a^5*b^3 + 15*a^4*b^4 + 6*a^3*b^5 + a^2*b^6)*d)*sinh(d*x + c)^2 + 2*(5*(a^8 + 6*a^7*b + 15*a^6*b^2 + 20*a^5*b^3 + 15*a^4*b^4 + 6*a^3*b^5 + a^2*b^6)*d*cosh(d*x + c)^9 + 16*(a^8 + 4*a^7*b + 5*a^6*b^2 - 5*a^4*b^4 - 4*a^3*b^5 - a^2*b^6)*d*cosh(d*x + c)^7 + 6*(3*a^8 + 10*a^7*b + 13*a^6*b^2 + 12*a^5*b^3 + 13*a^4*b^4 + 10*a^3*b^5 + 3*a^2*b^6)*d*cosh(d*x + c)^5 + 8*(a^8 + 4*a^7*b + 5*a^6*b^2 - 5*a^4*b^4 - 4*a^3*b^5 - a^2*b^6)*d*cosh(d*x + c)^3 + (a^8 + 6*a^7*b + 15*a^6*b^2 + 20*a^5*b^3 + 15*a^4*b^4 + 6*a^3*b^5 + a^2*b^6)*d*cosh(d*x + c))*sinh(d*x + c)), 1/8*((a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(d*x + c)^12 + 12*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(d*x + c)*sinh(d*x + c)^11 + (a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*sinh(d*x + c)^12 + 4*(a^5 + a^4*b - a^3*b^2 - a^2*b^3 + (a^5 + 9*a^4*b + 15*a^3*b^2 + 7*a^2*b^3)*d*x)*cosh(d*x + c)^10 + 2*(2*a^5 + 2*a^4*b - 2*a^3*b^2 - 2*a^2*b^3 + 2*(a^5 + 9*a^4*b + 15*a^3*b^2 + 7*a^2*b^3)*d*x + 33*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^10 + 20*(11*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(d*x + c)^3 + 2*(a^5 + a^4*b - a^3*b^2 - a^2*b^3 + (a^5 + 9*a^4*b + 15*a^3*b^2 + 7*a^2*b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c)^9 + (5*a^5 - a^4*b - 27*a^3*b^2 + 7*a^2*b^3 + 34*a*b^4 + 6*b^5 + 16*(a^5 + 7*a^4*b - a^3*b^2 - 7*a^2*b^3)*d*x)*cosh(d*x + c)^8 + (5*a^5 - a^4*b - 27*a^3*b^2 + 7*a^2*b^3 + 34*a*b^4 + 6*b^5 + 495*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(d*x + c)^4 + 16*(a^5 + 7*a^4*b - a^3*b^2 - 7*a^2*b^3)*d*x + 180*(a^5 + a^4*b - a^3*b^2 - a^2*b^3 + (a^5 + 9*a^4*b + 15*a^3*b^2 + 7*a^2*b^3)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 8*(99*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(d*x + c)^5 + 60*(a^5 + a^4*b - a^3*b^2 - a^2*b^3 + (a^5 + 9*a^4*b + 15*a^3*b^2 + 7*a^2*b^3)*d*x)*cosh(d*x + c)^3 + (5*a^5 - a^4*b - 27*a^3*b^2 + 7*a^2*b^3 + 34*a*b^4 + 6*b^5 + 16*(a^5 + 7*a^4*b - a^3*b^2 - 7*a^2*b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c)^7 - 2*(39*a^3*b^2 - 17*a^2*b^3 + 33*a*b^4 + 9*b^5 - 4*(3*a^5 + 19*a^4*b - 11*a^3*b^2 + 21*a^2*b^3)*d*x)*cosh(d*x + c)^6 + 2*(462*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(d*x + c)^6 - 39*a^3*b^2 + 17*a^2*b^3 - 33*a*b^4 - 9*b^5 + 420*(a^5 + a^4*b - a^3*b^2 - a^2*b^3 + (a^5 + 9*a^4*b + 15*a^3*b^2 + 7*a^2*b^3)*d*x)*cosh(d*x + c)^4 + 4*(3*a^5 + 19*a^4*b - 11*a^3*b^2 + 21*a^2*b^3)*d*x + 14*(5*a^5 - a^4*b - 27*a^3*b^2 + 7*a^2*b^3 + 34*a*b^4 + 6*b^5 + 16*(a^5 + 7*a^4*b - a^3*b^2 - 7*a^2*b^3)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 4*(198*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(d*x + c)^7 + 252*(a^5 + a^4*b - a^3*b^2 - a^2*b^3 + (a^5 + 9*a^4*b + 15*a^3*b^2 + 7*a^2*b^3)*d*x)*cosh(d*x + c)^5 + 14*(5*a^5 - a^4*b - 27*a^3*b^2 + 7*a^2*b^3 + 34*a*b^4 + 6*b^5 + 16*(a^5 + 7*a^4*b - a^3*b^2 - 7*a^2*b^3)*d*x)*cosh(d*x + c)^3 - 3*(39*a^3*b^2 - 17*a^2*b^3 + 33*a*b^4 + 9*b^5 - 4*(3*a^5 + 19*a^4*b - 11*a^3*b^2 + 21*a^2*b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c)^5 - a^5 - 3*a^4*b - 3*a^3*b^2 - a^2*b^3 - (5*a^5 - a^4*b + 77*a^3*b^2 + 31*a^2*b^3 - 70*a*b^4 - 18*b^5 - 16*(a^5 + 7*a^4*b - a^3*b^2 - 7*a^2*b^3)*d*x)*cosh(d*x + c)^4 + (495*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(d*x + c)^8 + 840*(a^5 + a^4*b - a^3*b^2 - a^2*b^3 + (a^5 + 9*a^4*b + 15*a^3*b^2 + 7*a^2*b^3)*d*x)*cosh(d*x + c)^6 - 5*a^5 + a^4*b - 77*a^3*b^2 - 31*a^2*b^3 + 70*a*b^4 + 18*b^5 + 70*(5*a^5 - a^4*b - 27*a^3*b^2 + 7*a^2*b^3 + 34*a*b^4 + 6*b^5 + 16*(a^5 + 7*a^4*b - a^3*b^2 - 7*a^2*b^3)*d*x)*cosh(d*x + c)^4 + 16*(a^5 + 7*a^4*b - a^3*b^2 - 7*a^2*b^3)*d*x - 30*(39*a^3*b^2 - 17*a^2*b^3 + 33*a*b^4 + 9*b^5 - 4*(3*a^5 + 19*a^4*b - 11*a^3*b^2 + 21*a^2*b^3)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 4*(55*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(d*x + c)^9 + 120*(a^5 + a^4*b - a^3*b^2 - a^2*b^3 + (a^5 + 9*a^4*b + 15*a^3*b^2 + 7*a^2*b^3)*d*x)*cosh(d*x + c)^7 + 14*(5*a^5 - a^4*b - 27*a^3*b^2 + 7*a^2*b^3 + 34*a*b^4 + 6*b^5 + 16*(a^5 + 7*a^4*b - a^3*b^2 - 7*a^2*b^3)*d*x)*cosh(d*x + c)^5 - 10*(39*a^3*b^2 - 17*a^2*b^3 + 33*a*b^4 + 9*b^5 - 4*(3*a^5 + 19*a^4*b - 11*a^3*b^2 + 21*a^2*b^3)*d*x)*cosh(d*x + c)^3 - (5*a^5 - a^4*b + 77*a^3*b^2 + 31*a^2*b^3 - 70*a*b^4 - 18*b^5 - 16*(a^5 + 7*a^4*b - a^3*b^2 - 7*a^2*b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c)^3 - 2*(2*a^5 + 2*a^4*b + 11*a^3*b^2 + 27*a^2*b^3 + 19*a*b^4 + 3*b^5 - 2*(a^5 + 9*a^4*b + 15*a^3*b^2 + 7*a^2*b^3)*d*x)*cosh(d*x + c)^2 + 2*(33*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(d*x + c)^10 + 90*(a^5 + a^4*b - a^3*b^2 - a^2*b^3 + (a^5 + 9*a^4*b + 15*a^3*b^2 + 7*a^2*b^3)*d*x)*cosh(d*x + c)^8 + 14*(5*a^5 - a^4*b - 27*a^3*b^2 + 7*a^2*b^3 + 34*a*b^4 + 6*b^5 + 16*(a^5 + 7*a^4*b - a^3*b^2 - 7*a^2*b^3)*d*x)*cosh(d*x + c)^6 - 2*a^5 - 2*a^4*b - 11*a^3*b^2 - 27*a^2*b^3 - 19*a*b^4 - 3*b^5 - 15*(39*a^3*b^2 - 17*a^2*b^3 + 33*a*b^4 + 9*b^5 - 4*(3*a^5 + 19*a^4*b - 11*a^3*b^2 + 21*a^2*b^3)*d*x)*cosh(d*x + c)^4 + 2*(a^5 + 9*a^4*b + 15*a^3*b^2 + 7*a^2*b^3)*d*x - 3*(5*a^5 - a^4*b + 77*a^3*b^2 + 31*a^2*b^3 - 70*a*b^4 - 18*b^5 - 16*(a^5 + 7*a^4*b - a^3*b^2 - 7*a^2*b^3)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((35*a^4*b + 84*a^3*b^2 + 66*a^2*b^3 + 20*a*b^4 + 3*b^5)*cosh(d*x + c)^10 + 10*(35*a^4*b + 84*a^3*b^2 + 66*a^2*b^3 + 20*a*b^4 + 3*b^5)*cosh(d*x + c)*sinh(d*x + c)^9 + (35*a^4*b + 84*a^3*b^2 + 66*a^2*b^3 + 20*a*b^4 + 3*b^5)*sinh(d*x + c)^10 + 4*(35*a^4*b + 14*a^3*b^2 - 32*a^2*b^3 - 14*a*b^4 - 3*b^5)*cosh(d*x + c)^8 + (140*a^4*b + 56*a^3*b^2 - 128*a^2*b^3 - 56*a*b^4 - 12*b^5 + 45*(35*a^4*b + 84*a^3*b^2 + 66*a^2*b^3 + 20*a*b^4 + 3*b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 8*(15*(35*a^4*b + 84*a^3*b^2 + 66*a^2*b^3 + 20*a*b^4 + 3*b^5)*cosh(d*x + c)^3 + 4*(35*a^4*b + 14*a^3*b^2 - 32*a^2*b^3 - 14*a*b^4 - 3*b^5)*cosh(d*x + c))*sinh(d*x + c)^7 + 2*(105*a^4*b - 28*a^3*b^2 + 86*a^2*b^3 + 36*a*b^4 + 9*b^5)*cosh(d*x + c)^6 + 2*(105*a^4*b - 28*a^3*b^2 + 86*a^2*b^3 + 36*a*b^4 + 9*b^5 + 105*(35*a^4*b + 84*a^3*b^2 + 66*a^2*b^3 + 20*a*b^4 + 3*b^5)*cosh(d*x + c)^4 + 56*(35*a^4*b + 14*a^3*b^2 - 32*a^2*b^3 - 14*a*b^4 - 3*b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 4*(63*(35*a^4*b + 84*a^3*b^2 + 66*a^2*b^3 + 20*a*b^4 + 3*b^5)*cosh(d*x + c)^5 + 56*(35*a^4*b + 14*a^3*b^2 - 32*a^2*b^3 - 14*a*b^4 - 3*b^5)*cosh(d*x + c)^3 + 3*(105*a^4*b - 28*a^3*b^2 + 86*a^2*b^3 + 36*a*b^4 + 9*b^5)*cosh(d*x + c))*sinh(d*x + c)^5 + 4*(35*a^4*b + 14*a^3*b^2 - 32*a^2*b^3 - 14*a*b^4 - 3*b^5)*cosh(d*x + c)^4 + 2*(105*(35*a^4*b + 84*a^3*b^2 + 66*a^2*b^3 + 20*a*b^4 + 3*b^5)*cosh(d*x + c)^6 + 70*a^4*b + 28*a^3*b^2 - 64*a^2*b^3 - 28*a*b^4 - 6*b^5 + 140*(35*a^4*b + 14*a^3*b^2 - 32*a^2*b^3 - 14*a*b^4 - 3*b^5)*cosh(d*x + c)^4 + 15*(105*a^4*b - 28*a^3*b^2 + 86*a^2*b^3 + 36*a*b^4 + 9*b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(15*(35*a^4*b + 84*a^3*b^2 + 66*a^2*b^3 + 20*a*b^4 + 3*b^5)*cosh(d*x + c)^7 + 28*(35*a^4*b + 14*a^3*b^2 - 32*a^2*b^3 - 14*a*b^4 - 3*b^5)*cosh(d*x + c)^5 + 5*(105*a^4*b - 28*a^3*b^2 + 86*a^2*b^3 + 36*a*b^4 + 9*b^5)*cosh(d*x + c)^3 + 2*(35*a^4*b + 14*a^3*b^2 - 32*a^2*b^3 - 14*a*b^4 - 3*b^5)*cosh(d*x + c))*sinh(d*x + c)^3 + (35*a^4*b + 84*a^3*b^2 + 66*a^2*b^3 + 20*a*b^4 + 3*b^5)*cosh(d*x + c)^2 + (45*(35*a^4*b + 84*a^3*b^2 + 66*a^2*b^3 + 20*a*b^4 + 3*b^5)*cosh(d*x + c)^8 + 112*(35*a^4*b + 14*a^3*b^2 - 32*a^2*b^3 - 14*a*b^4 - 3*b^5)*cosh(d*x + c)^6 + 35*a^4*b + 84*a^3*b^2 + 66*a^2*b^3 + 20*a*b^4 + 3*b^5 + 30*(105*a^4*b - 28*a^3*b^2 + 86*a^2*b^3 + 36*a*b^4 + 9*b^5)*cosh(d*x + c)^4 + 24*(35*a^4*b + 14*a^3*b^2 - 32*a^2*b^3 - 14*a*b^4 - 3*b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 2*(5*(35*a^4*b + 84*a^3*b^2 + 66*a^2*b^3 + 20*a*b^4 + 3*b^5)*cosh(d*x + c)^9 + 16*(35*a^4*b + 14*a^3*b^2 - 32*a^2*b^3 - 14*a*b^4 - 3*b^5)*cosh(d*x + c)^7 + 6*(105*a^4*b - 28*a^3*b^2 + 86*a^2*b^3 + 36*a*b^4 + 9*b^5)*cosh(d*x + c)^5 + 8*(35*a^4*b + 14*a^3*b^2 - 32*a^2*b^3 - 14*a*b^4 - 3*b^5)*cosh(d*x + c)^3 + (35*a^4*b + 84*a^3*b^2 + 66*a^2*b^3 + 20*a*b^4 + 3*b^5)*cosh(d*x + c))*sinh(d*x + c))*sqrt(b/a)*arctan(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 + a - b)*sqrt(b/a)/b) + 4*(3*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(d*x + c)^11 + 10*(a^5 + a^4*b - a^3*b^2 - a^2*b^3 + (a^5 + 9*a^4*b + 15*a^3*b^2 + 7*a^2*b^3)*d*x)*cosh(d*x + c)^9 + 2*(5*a^5 - a^4*b - 27*a^3*b^2 + 7*a^2*b^3 + 34*a*b^4 + 6*b^5 + 16*(a^5 + 7*a^4*b - a^3*b^2 - 7*a^2*b^3)*d*x)*cosh(d*x + c)^7 - 3*(39*a^3*b^2 - 17*a^2*b^3 + 33*a*b^4 + 9*b^5 - 4*(3*a^5 + 19*a^4*b - 11*a^3*b^2 + 21*a^2*b^3)*d*x)*cosh(d*x + c)^5 - (5*a^5 - a^4*b + 77*a^3*b^2 + 31*a^2*b^3 - 70*a*b^4 - 18*b^5 - 16*(a^5 + 7*a^4*b - a^3*b^2 - 7*a^2*b^3)*d*x)*cosh(d*x + c)^3 - (2*a^5 + 2*a^4*b + 11*a^3*b^2 + 27*a^2*b^3 + 19*a*b^4 + 3*b^5 - 2*(a^5 + 9*a^4*b + 15*a^3*b^2 + 7*a^2*b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c))/((a^8 + 6*a^7*b + 15*a^6*b^2 + 20*a^5*b^3 + 15*a^4*b^4 + 6*a^3*b^5 + a^2*b^6)*d*cosh(d*x + c)^10 + 10*(a^8 + 6*a^7*b + 15*a^6*b^2 + 20*a^5*b^3 + 15*a^4*b^4 + 6*a^3*b^5 + a^2*b^6)*d*cosh(d*x + c)*sinh(d*x + c)^9 + (a^8 + 6*a^7*b + 15*a^6*b^2 + 20*a^5*b^3 + 15*a^4*b^4 + 6*a^3*b^5 + a^2*b^6)*d*sinh(d*x + c)^10 + 4*(a^8 + 4*a^7*b + 5*a^6*b^2 - 5*a^4*b^4 - 4*a^3*b^5 - a^2*b^6)*d*cosh(d*x + c)^8 + (45*(a^8 + 6*a^7*b + 15*a^6*b^2 + 20*a^5*b^3 + 15*a^4*b^4 + 6*a^3*b^5 + a^2*b^6)*d*cosh(d*x + c)^2 + 4*(a^8 + 4*a^7*b + 5*a^6*b^2 - 5*a^4*b^4 - 4*a^3*b^5 - a^2*b^6)*d)*sinh(d*x + c)^8 + 2*(3*a^8 + 10*a^7*b + 13*a^6*b^2 + 12*a^5*b^3 + 13*a^4*b^4 + 10*a^3*b^5 + 3*a^2*b^6)*d*cosh(d*x + c)^6 + 8*(15*(a^8 + 6*a^7*b + 15*a^6*b^2 + 20*a^5*b^3 + 15*a^4*b^4 + 6*a^3*b^5 + a^2*b^6)*d*cosh(d*x + c)^3 + 4*(a^8 + 4*a^7*b + 5*a^6*b^2 - 5*a^4*b^4 - 4*a^3*b^5 - a^2*b^6)*d*cosh(d*x + c))*sinh(d*x + c)^7 + 2*(105*(a^8 + 6*a^7*b + 15*a^6*b^2 + 20*a^5*b^3 + 15*a^4*b^4 + 6*a^3*b^5 + a^2*b^6)*d*cosh(d*x + c)^4 + 56*(a^8 + 4*a^7*b + 5*a^6*b^2 - 5*a^4*b^4 - 4*a^3*b^5 - a^2*b^6)*d*cosh(d*x + c)^2 + (3*a^8 + 10*a^7*b + 13*a^6*b^2 + 12*a^5*b^3 + 13*a^4*b^4 + 10*a^3*b^5 + 3*a^2*b^6)*d)*sinh(d*x + c)^6 + 4*(a^8 + 4*a^7*b + 5*a^6*b^2 - 5*a^4*b^4 - 4*a^3*b^5 - a^2*b^6)*d*cosh(d*x + c)^4 + 4*(63*(a^8 + 6*a^7*b + 15*a^6*b^2 + 20*a^5*b^3 + 15*a^4*b^4 + 6*a^3*b^5 + a^2*b^6)*d*cosh(d*x + c)^5 + 56*(a^8 + 4*a^7*b + 5*a^6*b^2 - 5*a^4*b^4 - 4*a^3*b^5 - a^2*b^6)*d*cosh(d*x + c)^3 + 3*(3*a^8 + 10*a^7*b + 13*a^6*b^2 + 12*a^5*b^3 + 13*a^4*b^4 + 10*a^3*b^5 + 3*a^2*b^6)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(105*(a^8 + 6*a^7*b + 15*a^6*b^2 + 20*a^5*b^3 + 15*a^4*b^4 + 6*a^3*b^5 + a^2*b^6)*d*cosh(d*x + c)^6 + 140*(a^8 + 4*a^7*b + 5*a^6*b^2 - 5*a^4*b^4 - 4*a^3*b^5 - a^2*b^6)*d*cosh(d*x + c)^4 + 15*(3*a^8 + 10*a^7*b + 13*a^6*b^2 + 12*a^5*b^3 + 13*a^4*b^4 + 10*a^3*b^5 + 3*a^2*b^6)*d*cosh(d*x + c)^2 + 2*(a^8 + 4*a^7*b + 5*a^6*b^2 - 5*a^4*b^4 - 4*a^3*b^5 - a^2*b^6)*d)*sinh(d*x + c)^4 + (a^8 + 6*a^7*b + 15*a^6*b^2 + 20*a^5*b^3 + 15*a^4*b^4 + 6*a^3*b^5 + a^2*b^6)*d*cosh(d*x + c)^2 + 8*(15*(a^8 + 6*a^7*b + 15*a^6*b^2 + 20*a^5*b^3 + 15*a^4*b^4 + 6*a^3*b^5 + a^2*b^6)*d*cosh(d*x + c)^7 + 28*(a^8 + 4*a^7*b + 5*a^6*b^2 - 5*a^4*b^4 - 4*a^3*b^5 - a^2*b^6)*d*cosh(d*x + c)^5 + 5*(3*a^8 + 10*a^7*b + 13*a^6*b^2 + 12*a^5*b^3 + 13*a^4*b^4 + 10*a^3*b^5 + 3*a^2*b^6)*d*cosh(d*x + c)^3 + 2*(a^8 + 4*a^7*b + 5*a^6*b^2 - 5*a^4*b^4 - 4*a^3*b^5 - a^2*b^6)*d*cosh(d*x + c))*sinh(d*x + c)^3 + (45*(a^8 + 6*a^7*b + 15*a^6*b^2 + 20*a^5*b^3 + 15*a^4*b^4 + 6*a^3*b^5 + a^2*b^6)*d*cosh(d*x + c)^8 + 112*(a^8 + 4*a^7*b + 5*a^6*b^2 - 5*a^4*b^4 - 4*a^3*b^5 - a^2*b^6)*d*cosh(d*x + c)^6 + 30*(3*a^8 + 10*a^7*b + 13*a^6*b^2 + 12*a^5*b^3 + 13*a^4*b^4 + 10*a^3*b^5 + 3*a^2*b^6)*d*cosh(d*x + c)^4 + 24*(a^8 + 4*a^7*b + 5*a^6*b^2 - 5*a^4*b^4 - 4*a^3*b^5 - a^2*b^6)*d*cosh(d*x + c)^2 + (a^8 + 6*a^7*b + 15*a^6*b^2 + 20*a^5*b^3 + 15*a^4*b^4 + 6*a^3*b^5 + a^2*b^6)*d)*sinh(d*x + c)^2 + 2*(5*(a^8 + 6*a^7*b + 15*a^6*b^2 + 20*a^5*b^3 + 15*a^4*b^4 + 6*a^3*b^5 + a^2*b^6)*d*cosh(d*x + c)^9 + 16*(a^8 + 4*a^7*b + 5*a^6*b^2 - 5*a^4*b^4 - 4*a^3*b^5 - a^2*b^6)*d*cosh(d*x + c)^7 + 6*(3*a^8 + 10*a^7*b + 13*a^6*b^2 + 12*a^5*b^3 + 13*a^4*b^4 + 10*a^3*b^5 + 3*a^2*b^6)*d*cosh(d*x + c)^5 + 8*(a^8 + 4*a^7*b + 5*a^6*b^2 - 5*a^4*b^4 - 4*a^3*b^5 - a^2*b^6)*d*cosh(d*x + c)^3 + (a^8 + 6*a^7*b + 15*a^6*b^2 + 20*a^5*b^3 + 15*a^4*b^4 + 6*a^3*b^5 + a^2*b^6)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
126,1,11392,0,0.651920," ","integrate(cosh(d*x+c)/(a+b*tanh(d*x+c)^2)^3,x, algorithm=""fricas"")","\left[\frac{8 \, {\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} \cosh\left(d x + c\right)^{10} + 80 \, {\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + 8 \, {\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} \sinh\left(d x + c\right)^{10} + 4 \, {\left(6 \, a^{6} + 2 \, a^{5} b - 2 \, a^{4} b^{2} + 17 \, a^{3} b^{3} + 18 \, a^{2} b^{4} + 3 \, a b^{5}\right)} \cosh\left(d x + c\right)^{8} + 4 \, {\left(6 \, a^{6} + 2 \, a^{5} b - 2 \, a^{4} b^{2} + 17 \, a^{3} b^{3} + 18 \, a^{2} b^{4} + 3 \, a b^{5} + 90 \, {\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{8} + 32 \, {\left(30 \, {\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(6 \, a^{6} + 2 \, a^{5} b - 2 \, a^{4} b^{2} + 17 \, a^{3} b^{3} + 18 \, a^{2} b^{4} + 3 \, a b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 4 \, {\left(4 \, a^{6} - 4 \, a^{5} b + 24 \, a^{4} b^{2} + 7 \, a^{3} b^{3} - 34 \, a^{2} b^{4} - 9 \, a b^{5}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(4 \, a^{6} - 4 \, a^{5} b + 24 \, a^{4} b^{2} + 7 \, a^{3} b^{3} - 34 \, a^{2} b^{4} - 9 \, a b^{5} + 420 \, {\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} \cosh\left(d x + c\right)^{4} + 28 \, {\left(6 \, a^{6} + 2 \, a^{5} b - 2 \, a^{4} b^{2} + 17 \, a^{3} b^{3} + 18 \, a^{2} b^{4} + 3 \, a b^{5}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} - 8 \, a^{6} - 24 \, a^{5} b - 24 \, a^{4} b^{2} - 8 \, a^{3} b^{3} + 8 \, {\left(252 \, {\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} \cosh\left(d x + c\right)^{5} + 28 \, {\left(6 \, a^{6} + 2 \, a^{5} b - 2 \, a^{4} b^{2} + 17 \, a^{3} b^{3} + 18 \, a^{2} b^{4} + 3 \, a b^{5}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(4 \, a^{6} - 4 \, a^{5} b + 24 \, a^{4} b^{2} + 7 \, a^{3} b^{3} - 34 \, a^{2} b^{4} - 9 \, a b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 4 \, {\left(4 \, a^{6} - 4 \, a^{5} b + 24 \, a^{4} b^{2} + 7 \, a^{3} b^{3} - 34 \, a^{2} b^{4} - 9 \, a b^{5}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(420 \, {\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} \cosh\left(d x + c\right)^{6} - 4 \, a^{6} + 4 \, a^{5} b - 24 \, a^{4} b^{2} - 7 \, a^{3} b^{3} + 34 \, a^{2} b^{4} + 9 \, a b^{5} + 70 \, {\left(6 \, a^{6} + 2 \, a^{5} b - 2 \, a^{4} b^{2} + 17 \, a^{3} b^{3} + 18 \, a^{2} b^{4} + 3 \, a b^{5}\right)} \cosh\left(d x + c\right)^{4} + 15 \, {\left(4 \, a^{6} - 4 \, a^{5} b + 24 \, a^{4} b^{2} + 7 \, a^{3} b^{3} - 34 \, a^{2} b^{4} - 9 \, a b^{5}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 16 \, {\left(60 \, {\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} \cosh\left(d x + c\right)^{7} + 14 \, {\left(6 \, a^{6} + 2 \, a^{5} b - 2 \, a^{4} b^{2} + 17 \, a^{3} b^{3} + 18 \, a^{2} b^{4} + 3 \, a b^{5}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(4 \, a^{6} - 4 \, a^{5} b + 24 \, a^{4} b^{2} + 7 \, a^{3} b^{3} - 34 \, a^{2} b^{4} - 9 \, a b^{5}\right)} \cosh\left(d x + c\right)^{3} - {\left(4 \, a^{6} - 4 \, a^{5} b + 24 \, a^{4} b^{2} + 7 \, a^{3} b^{3} - 34 \, a^{2} b^{4} - 9 \, a b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 4 \, {\left(6 \, a^{6} + 2 \, a^{5} b - 2 \, a^{4} b^{2} + 17 \, a^{3} b^{3} + 18 \, a^{2} b^{4} + 3 \, a b^{5}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(90 \, {\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} \cosh\left(d x + c\right)^{8} + 28 \, {\left(6 \, a^{6} + 2 \, a^{5} b - 2 \, a^{4} b^{2} + 17 \, a^{3} b^{3} + 18 \, a^{2} b^{4} + 3 \, a b^{5}\right)} \cosh\left(d x + c\right)^{6} - 6 \, a^{6} - 2 \, a^{5} b + 2 \, a^{4} b^{2} - 17 \, a^{3} b^{3} - 18 \, a^{2} b^{4} - 3 \, a b^{5} + 15 \, {\left(4 \, a^{6} - 4 \, a^{5} b + 24 \, a^{4} b^{2} + 7 \, a^{3} b^{3} - 34 \, a^{2} b^{4} - 9 \, a b^{5}\right)} \cosh\left(d x + c\right)^{4} - 6 \, {\left(4 \, a^{6} - 4 \, a^{5} b + 24 \, a^{4} b^{2} + 7 \, a^{3} b^{3} - 34 \, a^{2} b^{4} - 9 \, a b^{5}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} - 3 \, {\left({\left(8 \, a^{4} b + 20 \, a^{3} b^{2} + 17 \, a^{2} b^{3} + 6 \, a b^{4} + b^{5}\right)} \cosh\left(d x + c\right)^{9} + 9 \, {\left(8 \, a^{4} b + 20 \, a^{3} b^{2} + 17 \, a^{2} b^{3} + 6 \, a b^{4} + b^{5}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{8} + {\left(8 \, a^{4} b + 20 \, a^{3} b^{2} + 17 \, a^{2} b^{3} + 6 \, a b^{4} + b^{5}\right)} \sinh\left(d x + c\right)^{9} + 4 \, {\left(8 \, a^{4} b + 4 \, a^{3} b^{2} - 7 \, a^{2} b^{3} - 4 \, a b^{4} - b^{5}\right)} \cosh\left(d x + c\right)^{7} + 4 \, {\left(8 \, a^{4} b + 4 \, a^{3} b^{2} - 7 \, a^{2} b^{3} - 4 \, a b^{4} - b^{5} + 9 \, {\left(8 \, a^{4} b + 20 \, a^{3} b^{2} + 17 \, a^{2} b^{3} + 6 \, a b^{4} + b^{5}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{7} + 28 \, {\left(3 \, {\left(8 \, a^{4} b + 20 \, a^{3} b^{2} + 17 \, a^{2} b^{3} + 6 \, a b^{4} + b^{5}\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{4} b + 4 \, a^{3} b^{2} - 7 \, a^{2} b^{3} - 4 \, a b^{4} - b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(24 \, a^{4} b - 4 \, a^{3} b^{2} + 19 \, a^{2} b^{3} + 10 \, a b^{4} + 3 \, b^{5}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(24 \, a^{4} b - 4 \, a^{3} b^{2} + 19 \, a^{2} b^{3} + 10 \, a b^{4} + 3 \, b^{5} + 63 \, {\left(8 \, a^{4} b + 20 \, a^{3} b^{2} + 17 \, a^{2} b^{3} + 6 \, a b^{4} + b^{5}\right)} \cosh\left(d x + c\right)^{4} + 42 \, {\left(8 \, a^{4} b + 4 \, a^{3} b^{2} - 7 \, 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)^{5} + 2 \, {\left(63 \, {\left(8 \, a^{4} b + 20 \, a^{3} b^{2} + 17 \, a^{2} b^{3} + 6 \, a b^{4} + b^{5}\right)} \cosh\left(d x + c\right)^{5} + 70 \, {\left(8 \, a^{4} b + 4 \, a^{3} b^{2} - 7 \, a^{2} b^{3} - 4 \, a b^{4} - b^{5}\right)} \cosh\left(d x + c\right)^{3} + 5 \, {\left(24 \, a^{4} b - 4 \, a^{3} b^{2} + 19 \, a^{2} b^{3} + 10 \, a b^{4} + 3 \, b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(8 \, a^{4} b + 4 \, a^{3} b^{2} - 7 \, a^{2} b^{3} - 4 \, a b^{4} - b^{5}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(21 \, {\left(8 \, a^{4} b + 20 \, a^{3} b^{2} + 17 \, a^{2} b^{3} + 6 \, a b^{4} + b^{5}\right)} \cosh\left(d x + c\right)^{6} + 8 \, a^{4} b + 4 \, a^{3} b^{2} - 7 \, a^{2} b^{3} - 4 \, a b^{4} - b^{5} + 35 \, {\left(8 \, a^{4} b + 4 \, a^{3} b^{2} - 7 \, a^{2} b^{3} - 4 \, a b^{4} - b^{5}\right)} \cosh\left(d x + c\right)^{4} + 5 \, {\left(24 \, a^{4} b - 4 \, a^{3} b^{2} + 19 \, a^{2} b^{3} + 10 \, a b^{4} + 3 \, b^{5}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(9 \, {\left(8 \, a^{4} b + 20 \, a^{3} b^{2} + 17 \, a^{2} b^{3} + 6 \, a b^{4} + b^{5}\right)} \cosh\left(d x + c\right)^{7} + 21 \, {\left(8 \, a^{4} b + 4 \, a^{3} b^{2} - 7 \, a^{2} b^{3} - 4 \, a b^{4} - b^{5}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(24 \, a^{4} b - 4 \, a^{3} b^{2} + 19 \, a^{2} b^{3} + 10 \, a b^{4} + 3 \, b^{5}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(8 \, a^{4} b + 4 \, a^{3} b^{2} - 7 \, a^{2} b^{3} - 4 \, a b^{4} - b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(8 \, a^{4} b + 20 \, a^{3} b^{2} + 17 \, a^{2} b^{3} + 6 \, a b^{4} + b^{5}\right)} \cosh\left(d x + c\right) + {\left(9 \, {\left(8 \, a^{4} b + 20 \, a^{3} b^{2} + 17 \, a^{2} b^{3} + 6 \, a b^{4} + b^{5}\right)} \cosh\left(d x + c\right)^{8} + 28 \, {\left(8 \, a^{4} b + 4 \, a^{3} b^{2} - 7 \, a^{2} b^{3} - 4 \, a b^{4} - b^{5}\right)} \cosh\left(d x + c\right)^{6} + 8 \, a^{4} b + 20 \, a^{3} b^{2} + 17 \, a^{2} b^{3} + 6 \, a b^{4} + b^{5} + 10 \, {\left(24 \, a^{4} b - 4 \, a^{3} b^{2} + 19 \, a^{2} b^{3} + 10 \, a b^{4} + 3 \, b^{5}\right)} \cosh\left(d x + c\right)^{4} + 12 \, {\left(8 \, a^{4} b + 4 \, a^{3} b^{2} - 7 \, 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)\right)} \sqrt{-a^{2} - a b} \log\left(\frac{{\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(3 \, a + b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} - 3 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(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) - 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^{2} - a b} + a + b}{{\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) + 8 \, {\left(10 \, {\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} \cosh\left(d x + c\right)^{9} + 4 \, {\left(6 \, a^{6} + 2 \, a^{5} b - 2 \, a^{4} b^{2} + 17 \, a^{3} b^{3} + 18 \, a^{2} b^{4} + 3 \, a b^{5}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(4 \, a^{6} - 4 \, a^{5} b + 24 \, a^{4} b^{2} + 7 \, a^{3} b^{3} - 34 \, a^{2} b^{4} - 9 \, a b^{5}\right)} \cosh\left(d x + c\right)^{5} - 2 \, {\left(4 \, a^{6} - 4 \, a^{5} b + 24 \, a^{4} b^{2} + 7 \, a^{3} b^{3} - 34 \, a^{2} b^{4} - 9 \, a b^{5}\right)} \cosh\left(d x + c\right)^{3} - {\left(6 \, a^{6} + 2 \, a^{5} b - 2 \, a^{4} b^{2} + 17 \, a^{3} b^{3} + 18 \, 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^{9} + 6 \, a^{8} b + 15 \, a^{7} b^{2} + 20 \, a^{6} b^{3} + 15 \, a^{5} b^{4} + 6 \, a^{4} b^{5} + a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{9} + 9 \, {\left(a^{9} + 6 \, a^{8} b + 15 \, a^{7} b^{2} + 20 \, a^{6} b^{3} + 15 \, a^{5} b^{4} + 6 \, a^{4} b^{5} + a^{3} b^{6}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{8} + {\left(a^{9} + 6 \, a^{8} b + 15 \, a^{7} b^{2} + 20 \, a^{6} b^{3} + 15 \, a^{5} b^{4} + 6 \, a^{4} b^{5} + a^{3} b^{6}\right)} d \sinh\left(d x + c\right)^{9} + 4 \, {\left(a^{9} + 4 \, a^{8} b + 5 \, a^{7} b^{2} - 5 \, a^{5} b^{4} - 4 \, a^{4} b^{5} - a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{7} + 4 \, {\left(9 \, {\left(a^{9} + 6 \, a^{8} b + 15 \, a^{7} b^{2} + 20 \, a^{6} b^{3} + 15 \, a^{5} b^{4} + 6 \, a^{4} b^{5} + a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{9} + 4 \, a^{8} b + 5 \, a^{7} b^{2} - 5 \, a^{5} b^{4} - 4 \, a^{4} b^{5} - a^{3} b^{6}\right)} d\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(3 \, a^{9} + 10 \, a^{8} b + 13 \, a^{7} b^{2} + 12 \, a^{6} b^{3} + 13 \, a^{5} b^{4} + 10 \, a^{4} b^{5} + 3 \, a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{5} + 28 \, {\left(3 \, {\left(a^{9} + 6 \, a^{8} b + 15 \, a^{7} b^{2} + 20 \, a^{6} b^{3} + 15 \, a^{5} b^{4} + 6 \, a^{4} b^{5} + a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{9} + 4 \, a^{8} b + 5 \, a^{7} b^{2} - 5 \, a^{5} b^{4} - 4 \, a^{4} b^{5} - a^{3} b^{6}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(63 \, {\left(a^{9} + 6 \, a^{8} b + 15 \, a^{7} b^{2} + 20 \, a^{6} b^{3} + 15 \, a^{5} b^{4} + 6 \, a^{4} b^{5} + a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{4} + 42 \, {\left(a^{9} + 4 \, a^{8} b + 5 \, a^{7} b^{2} - 5 \, a^{5} b^{4} - 4 \, a^{4} b^{5} - a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{9} + 10 \, a^{8} b + 13 \, a^{7} b^{2} + 12 \, a^{6} b^{3} + 13 \, a^{5} b^{4} + 10 \, a^{4} b^{5} + 3 \, a^{3} b^{6}\right)} d\right)} \sinh\left(d x + c\right)^{5} + 4 \, {\left(a^{9} + 4 \, a^{8} b + 5 \, a^{7} b^{2} - 5 \, a^{5} b^{4} - 4 \, a^{4} b^{5} - a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{3} + 2 \, {\left(63 \, {\left(a^{9} + 6 \, a^{8} b + 15 \, a^{7} b^{2} + 20 \, a^{6} b^{3} + 15 \, a^{5} b^{4} + 6 \, a^{4} b^{5} + a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{5} + 70 \, {\left(a^{9} + 4 \, a^{8} b + 5 \, a^{7} b^{2} - 5 \, a^{5} b^{4} - 4 \, a^{4} b^{5} - a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{3} + 5 \, {\left(3 \, a^{9} + 10 \, a^{8} b + 13 \, a^{7} b^{2} + 12 \, a^{6} b^{3} + 13 \, a^{5} b^{4} + 10 \, a^{4} b^{5} + 3 \, a^{3} b^{6}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(21 \, {\left(a^{9} + 6 \, a^{8} b + 15 \, a^{7} b^{2} + 20 \, a^{6} b^{3} + 15 \, a^{5} b^{4} + 6 \, a^{4} b^{5} + a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{6} + 35 \, {\left(a^{9} + 4 \, a^{8} b + 5 \, a^{7} b^{2} - 5 \, a^{5} b^{4} - 4 \, a^{4} b^{5} - a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{4} + 5 \, {\left(3 \, a^{9} + 10 \, a^{8} b + 13 \, a^{7} b^{2} + 12 \, a^{6} b^{3} + 13 \, a^{5} b^{4} + 10 \, a^{4} b^{5} + 3 \, a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{9} + 4 \, a^{8} b + 5 \, a^{7} b^{2} - 5 \, a^{5} b^{4} - 4 \, a^{4} b^{5} - a^{3} b^{6}\right)} d\right)} \sinh\left(d x + c\right)^{3} + {\left(a^{9} + 6 \, a^{8} b + 15 \, a^{7} b^{2} + 20 \, a^{6} b^{3} + 15 \, a^{5} b^{4} + 6 \, a^{4} b^{5} + a^{3} b^{6}\right)} d \cosh\left(d x + c\right) + 4 \, {\left(9 \, {\left(a^{9} + 6 \, a^{8} b + 15 \, a^{7} b^{2} + 20 \, a^{6} b^{3} + 15 \, a^{5} b^{4} + 6 \, a^{4} b^{5} + a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{7} + 21 \, {\left(a^{9} + 4 \, a^{8} b + 5 \, a^{7} b^{2} - 5 \, a^{5} b^{4} - 4 \, a^{4} b^{5} - a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{5} + 5 \, {\left(3 \, a^{9} + 10 \, a^{8} b + 13 \, a^{7} b^{2} + 12 \, a^{6} b^{3} + 13 \, a^{5} b^{4} + 10 \, a^{4} b^{5} + 3 \, a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{9} + 4 \, a^{8} b + 5 \, a^{7} b^{2} - 5 \, a^{5} b^{4} - 4 \, a^{4} b^{5} - a^{3} b^{6}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(9 \, {\left(a^{9} + 6 \, a^{8} b + 15 \, a^{7} b^{2} + 20 \, a^{6} b^{3} + 15 \, a^{5} b^{4} + 6 \, a^{4} b^{5} + a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{8} + 28 \, {\left(a^{9} + 4 \, a^{8} b + 5 \, a^{7} b^{2} - 5 \, a^{5} b^{4} - 4 \, a^{4} b^{5} - a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{6} + 10 \, {\left(3 \, a^{9} + 10 \, a^{8} b + 13 \, a^{7} b^{2} + 12 \, a^{6} b^{3} + 13 \, a^{5} b^{4} + 10 \, a^{4} b^{5} + 3 \, a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{4} + 12 \, {\left(a^{9} + 4 \, a^{8} b + 5 \, a^{7} b^{2} - 5 \, a^{5} b^{4} - 4 \, a^{4} b^{5} - a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{9} + 6 \, a^{8} b + 15 \, a^{7} b^{2} + 20 \, a^{6} b^{3} + 15 \, a^{5} b^{4} + 6 \, a^{4} b^{5} + a^{3} b^{6}\right)} d\right)} \sinh\left(d x + c\right)\right)}}, \frac{4 \, {\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} \cosh\left(d x + c\right)^{10} + 40 \, {\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + 4 \, {\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} \sinh\left(d x + c\right)^{10} + 2 \, {\left(6 \, a^{6} + 2 \, a^{5} b - 2 \, a^{4} b^{2} + 17 \, a^{3} b^{3} + 18 \, a^{2} b^{4} + 3 \, a b^{5}\right)} \cosh\left(d x + c\right)^{8} + 2 \, {\left(6 \, a^{6} + 2 \, a^{5} b - 2 \, a^{4} b^{2} + 17 \, a^{3} b^{3} + 18 \, a^{2} b^{4} + 3 \, a b^{5} + 90 \, {\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{8} + 16 \, {\left(30 \, {\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(6 \, a^{6} + 2 \, a^{5} b - 2 \, a^{4} b^{2} + 17 \, a^{3} b^{3} + 18 \, a^{2} b^{4} + 3 \, a b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(4 \, a^{6} - 4 \, a^{5} b + 24 \, a^{4} b^{2} + 7 \, a^{3} b^{3} - 34 \, a^{2} b^{4} - 9 \, a b^{5}\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(4 \, a^{6} - 4 \, a^{5} b + 24 \, a^{4} b^{2} + 7 \, a^{3} b^{3} - 34 \, a^{2} b^{4} - 9 \, a b^{5} + 420 \, {\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} \cosh\left(d x + c\right)^{4} + 28 \, {\left(6 \, a^{6} + 2 \, a^{5} b - 2 \, a^{4} b^{2} + 17 \, a^{3} b^{3} + 18 \, a^{2} b^{4} + 3 \, a b^{5}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} - 4 \, a^{6} - 12 \, a^{5} b - 12 \, a^{4} b^{2} - 4 \, a^{3} b^{3} + 4 \, {\left(252 \, {\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} \cosh\left(d x + c\right)^{5} + 28 \, {\left(6 \, a^{6} + 2 \, a^{5} b - 2 \, a^{4} b^{2} + 17 \, a^{3} b^{3} + 18 \, a^{2} b^{4} + 3 \, a b^{5}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(4 \, a^{6} - 4 \, a^{5} b + 24 \, a^{4} b^{2} + 7 \, a^{3} b^{3} - 34 \, a^{2} b^{4} - 9 \, a b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 2 \, {\left(4 \, a^{6} - 4 \, a^{5} b + 24 \, a^{4} b^{2} + 7 \, a^{3} b^{3} - 34 \, a^{2} b^{4} - 9 \, a b^{5}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(420 \, {\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} \cosh\left(d x + c\right)^{6} - 4 \, a^{6} + 4 \, a^{5} b - 24 \, a^{4} b^{2} - 7 \, a^{3} b^{3} + 34 \, a^{2} b^{4} + 9 \, a b^{5} + 70 \, {\left(6 \, a^{6} + 2 \, a^{5} b - 2 \, a^{4} b^{2} + 17 \, a^{3} b^{3} + 18 \, a^{2} b^{4} + 3 \, a b^{5}\right)} \cosh\left(d x + c\right)^{4} + 15 \, {\left(4 \, a^{6} - 4 \, a^{5} b + 24 \, a^{4} b^{2} + 7 \, a^{3} b^{3} - 34 \, a^{2} b^{4} - 9 \, a b^{5}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(60 \, {\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} \cosh\left(d x + c\right)^{7} + 14 \, {\left(6 \, a^{6} + 2 \, a^{5} b - 2 \, a^{4} b^{2} + 17 \, a^{3} b^{3} + 18 \, a^{2} b^{4} + 3 \, a b^{5}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(4 \, a^{6} - 4 \, a^{5} b + 24 \, a^{4} b^{2} + 7 \, a^{3} b^{3} - 34 \, a^{2} b^{4} - 9 \, a b^{5}\right)} \cosh\left(d x + c\right)^{3} - {\left(4 \, a^{6} - 4 \, a^{5} b + 24 \, a^{4} b^{2} + 7 \, a^{3} b^{3} - 34 \, a^{2} b^{4} - 9 \, a b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 2 \, {\left(6 \, a^{6} + 2 \, a^{5} b - 2 \, a^{4} b^{2} + 17 \, a^{3} b^{3} + 18 \, a^{2} b^{4} + 3 \, a b^{5}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(90 \, {\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} \cosh\left(d x + c\right)^{8} + 28 \, {\left(6 \, a^{6} + 2 \, a^{5} b - 2 \, a^{4} b^{2} + 17 \, a^{3} b^{3} + 18 \, a^{2} b^{4} + 3 \, a b^{5}\right)} \cosh\left(d x + c\right)^{6} - 6 \, a^{6} - 2 \, a^{5} b + 2 \, a^{4} b^{2} - 17 \, a^{3} b^{3} - 18 \, a^{2} b^{4} - 3 \, a b^{5} + 15 \, {\left(4 \, a^{6} - 4 \, a^{5} b + 24 \, a^{4} b^{2} + 7 \, a^{3} b^{3} - 34 \, a^{2} b^{4} - 9 \, a b^{5}\right)} \cosh\left(d x + c\right)^{4} - 6 \, {\left(4 \, a^{6} - 4 \, a^{5} b + 24 \, a^{4} b^{2} + 7 \, a^{3} b^{3} - 34 \, a^{2} b^{4} - 9 \, a b^{5}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 3 \, {\left({\left(8 \, a^{4} b + 20 \, a^{3} b^{2} + 17 \, a^{2} b^{3} + 6 \, a b^{4} + b^{5}\right)} \cosh\left(d x + c\right)^{9} + 9 \, {\left(8 \, a^{4} b + 20 \, a^{3} b^{2} + 17 \, a^{2} b^{3} + 6 \, a b^{4} + b^{5}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{8} + {\left(8 \, a^{4} b + 20 \, a^{3} b^{2} + 17 \, a^{2} b^{3} + 6 \, a b^{4} + b^{5}\right)} \sinh\left(d x + c\right)^{9} + 4 \, {\left(8 \, a^{4} b + 4 \, a^{3} b^{2} - 7 \, a^{2} b^{3} - 4 \, a b^{4} - b^{5}\right)} \cosh\left(d x + c\right)^{7} + 4 \, {\left(8 \, a^{4} b + 4 \, a^{3} b^{2} - 7 \, a^{2} b^{3} - 4 \, a b^{4} - b^{5} + 9 \, {\left(8 \, a^{4} b + 20 \, a^{3} b^{2} + 17 \, a^{2} b^{3} + 6 \, a b^{4} + b^{5}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{7} + 28 \, {\left(3 \, {\left(8 \, a^{4} b + 20 \, a^{3} b^{2} + 17 \, a^{2} b^{3} + 6 \, a b^{4} + b^{5}\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{4} b + 4 \, a^{3} b^{2} - 7 \, a^{2} b^{3} - 4 \, a b^{4} - b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(24 \, a^{4} b - 4 \, a^{3} b^{2} + 19 \, a^{2} b^{3} + 10 \, a b^{4} + 3 \, b^{5}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(24 \, a^{4} b - 4 \, a^{3} b^{2} + 19 \, a^{2} b^{3} + 10 \, a b^{4} + 3 \, b^{5} + 63 \, {\left(8 \, a^{4} b + 20 \, a^{3} b^{2} + 17 \, a^{2} b^{3} + 6 \, a b^{4} + b^{5}\right)} \cosh\left(d x + c\right)^{4} + 42 \, {\left(8 \, a^{4} b + 4 \, a^{3} b^{2} - 7 \, 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)^{5} + 2 \, {\left(63 \, {\left(8 \, a^{4} b + 20 \, a^{3} b^{2} + 17 \, a^{2} b^{3} + 6 \, a b^{4} + b^{5}\right)} \cosh\left(d x + c\right)^{5} + 70 \, {\left(8 \, a^{4} b + 4 \, a^{3} b^{2} - 7 \, a^{2} b^{3} - 4 \, a b^{4} - b^{5}\right)} \cosh\left(d x + c\right)^{3} + 5 \, {\left(24 \, a^{4} b - 4 \, a^{3} b^{2} + 19 \, a^{2} b^{3} + 10 \, a b^{4} + 3 \, b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(8 \, a^{4} b + 4 \, a^{3} b^{2} - 7 \, a^{2} b^{3} - 4 \, a b^{4} - b^{5}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(21 \, {\left(8 \, a^{4} b + 20 \, a^{3} b^{2} + 17 \, a^{2} b^{3} + 6 \, a b^{4} + b^{5}\right)} \cosh\left(d x + c\right)^{6} + 8 \, a^{4} b + 4 \, a^{3} b^{2} - 7 \, a^{2} b^{3} - 4 \, a b^{4} - b^{5} + 35 \, {\left(8 \, a^{4} b + 4 \, a^{3} b^{2} - 7 \, a^{2} b^{3} - 4 \, a b^{4} - b^{5}\right)} \cosh\left(d x + c\right)^{4} + 5 \, {\left(24 \, a^{4} b - 4 \, a^{3} b^{2} + 19 \, a^{2} b^{3} + 10 \, a b^{4} + 3 \, b^{5}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(9 \, {\left(8 \, a^{4} b + 20 \, a^{3} b^{2} + 17 \, a^{2} b^{3} + 6 \, a b^{4} + b^{5}\right)} \cosh\left(d x + c\right)^{7} + 21 \, {\left(8 \, a^{4} b + 4 \, a^{3} b^{2} - 7 \, a^{2} b^{3} - 4 \, a b^{4} - b^{5}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(24 \, a^{4} b - 4 \, a^{3} b^{2} + 19 \, a^{2} b^{3} + 10 \, a b^{4} + 3 \, b^{5}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(8 \, a^{4} b + 4 \, a^{3} b^{2} - 7 \, a^{2} b^{3} - 4 \, a b^{4} - b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(8 \, a^{4} b + 20 \, a^{3} b^{2} + 17 \, a^{2} b^{3} + 6 \, a b^{4} + b^{5}\right)} \cosh\left(d x + c\right) + {\left(9 \, {\left(8 \, a^{4} b + 20 \, a^{3} b^{2} + 17 \, a^{2} b^{3} + 6 \, a b^{4} + b^{5}\right)} \cosh\left(d x + c\right)^{8} + 28 \, {\left(8 \, a^{4} b + 4 \, a^{3} b^{2} - 7 \, a^{2} b^{3} - 4 \, a b^{4} - b^{5}\right)} \cosh\left(d x + c\right)^{6} + 8 \, a^{4} b + 20 \, a^{3} b^{2} + 17 \, a^{2} b^{3} + 6 \, a b^{4} + b^{5} + 10 \, {\left(24 \, a^{4} b - 4 \, a^{3} b^{2} + 19 \, a^{2} b^{3} + 10 \, a b^{4} + 3 \, b^{5}\right)} \cosh\left(d x + c\right)^{4} + 12 \, {\left(8 \, a^{4} b + 4 \, a^{3} b^{2} - 7 \, 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)\right)} \sqrt{a^{2} + a b} \arctan\left(\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(3 \, a - b\right)} \cosh\left(d x + c\right) + {\left(3 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} + 3 \, a - b\right)} \sinh\left(d x + c\right)}{2 \, \sqrt{a^{2} + a b}}\right) + 3 \, {\left({\left(8 \, a^{4} b + 20 \, a^{3} b^{2} + 17 \, a^{2} b^{3} + 6 \, a b^{4} + b^{5}\right)} \cosh\left(d x + c\right)^{9} + 9 \, {\left(8 \, a^{4} b + 20 \, a^{3} b^{2} + 17 \, a^{2} b^{3} + 6 \, a b^{4} + b^{5}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{8} + {\left(8 \, a^{4} b + 20 \, a^{3} b^{2} + 17 \, a^{2} b^{3} + 6 \, a b^{4} + b^{5}\right)} \sinh\left(d x + c\right)^{9} + 4 \, {\left(8 \, a^{4} b + 4 \, a^{3} b^{2} - 7 \, a^{2} b^{3} - 4 \, a b^{4} - b^{5}\right)} \cosh\left(d x + c\right)^{7} + 4 \, {\left(8 \, a^{4} b + 4 \, a^{3} b^{2} - 7 \, a^{2} b^{3} - 4 \, a b^{4} - b^{5} + 9 \, {\left(8 \, a^{4} b + 20 \, a^{3} b^{2} + 17 \, a^{2} b^{3} + 6 \, a b^{4} + b^{5}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{7} + 28 \, {\left(3 \, {\left(8 \, a^{4} b + 20 \, a^{3} b^{2} + 17 \, a^{2} b^{3} + 6 \, a b^{4} + b^{5}\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{4} b + 4 \, a^{3} b^{2} - 7 \, a^{2} b^{3} - 4 \, a b^{4} - b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(24 \, a^{4} b - 4 \, a^{3} b^{2} + 19 \, a^{2} b^{3} + 10 \, a b^{4} + 3 \, b^{5}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(24 \, a^{4} b - 4 \, a^{3} b^{2} + 19 \, a^{2} b^{3} + 10 \, a b^{4} + 3 \, b^{5} + 63 \, {\left(8 \, a^{4} b + 20 \, a^{3} b^{2} + 17 \, a^{2} b^{3} + 6 \, a b^{4} + b^{5}\right)} \cosh\left(d x + c\right)^{4} + 42 \, {\left(8 \, a^{4} b + 4 \, a^{3} b^{2} - 7 \, 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)^{5} + 2 \, {\left(63 \, {\left(8 \, a^{4} b + 20 \, a^{3} b^{2} + 17 \, a^{2} b^{3} + 6 \, a b^{4} + b^{5}\right)} \cosh\left(d x + c\right)^{5} + 70 \, {\left(8 \, a^{4} b + 4 \, a^{3} b^{2} - 7 \, a^{2} b^{3} - 4 \, a b^{4} - b^{5}\right)} \cosh\left(d x + c\right)^{3} + 5 \, {\left(24 \, a^{4} b - 4 \, a^{3} b^{2} + 19 \, a^{2} b^{3} + 10 \, a b^{4} + 3 \, b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(8 \, a^{4} b + 4 \, a^{3} b^{2} - 7 \, a^{2} b^{3} - 4 \, a b^{4} - b^{5}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(21 \, {\left(8 \, a^{4} b + 20 \, a^{3} b^{2} + 17 \, a^{2} b^{3} + 6 \, a b^{4} + b^{5}\right)} \cosh\left(d x + c\right)^{6} + 8 \, a^{4} b + 4 \, a^{3} b^{2} - 7 \, a^{2} b^{3} - 4 \, a b^{4} - b^{5} + 35 \, {\left(8 \, a^{4} b + 4 \, a^{3} b^{2} - 7 \, a^{2} b^{3} - 4 \, a b^{4} - b^{5}\right)} \cosh\left(d x + c\right)^{4} + 5 \, {\left(24 \, a^{4} b - 4 \, a^{3} b^{2} + 19 \, a^{2} b^{3} + 10 \, a b^{4} + 3 \, b^{5}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(9 \, {\left(8 \, a^{4} b + 20 \, a^{3} b^{2} + 17 \, a^{2} b^{3} + 6 \, a b^{4} + b^{5}\right)} \cosh\left(d x + c\right)^{7} + 21 \, {\left(8 \, a^{4} b + 4 \, a^{3} b^{2} - 7 \, a^{2} b^{3} - 4 \, a b^{4} - b^{5}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(24 \, a^{4} b - 4 \, a^{3} b^{2} + 19 \, a^{2} b^{3} + 10 \, a b^{4} + 3 \, b^{5}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(8 \, a^{4} b + 4 \, a^{3} b^{2} - 7 \, a^{2} b^{3} - 4 \, a b^{4} - b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(8 \, a^{4} b + 20 \, a^{3} b^{2} + 17 \, a^{2} b^{3} + 6 \, a b^{4} + b^{5}\right)} \cosh\left(d x + c\right) + {\left(9 \, {\left(8 \, a^{4} b + 20 \, a^{3} b^{2} + 17 \, a^{2} b^{3} + 6 \, a b^{4} + b^{5}\right)} \cosh\left(d x + c\right)^{8} + 28 \, {\left(8 \, a^{4} b + 4 \, a^{3} b^{2} - 7 \, a^{2} b^{3} - 4 \, a b^{4} - b^{5}\right)} \cosh\left(d x + c\right)^{6} + 8 \, a^{4} b + 20 \, a^{3} b^{2} + 17 \, a^{2} b^{3} + 6 \, a b^{4} + b^{5} + 10 \, {\left(24 \, a^{4} b - 4 \, a^{3} b^{2} + 19 \, a^{2} b^{3} + 10 \, a b^{4} + 3 \, b^{5}\right)} \cosh\left(d x + c\right)^{4} + 12 \, {\left(8 \, a^{4} b + 4 \, a^{3} b^{2} - 7 \, 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)\right)} \sqrt{a^{2} + a b} \arctan\left(\frac{\sqrt{a^{2} + a b} {\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right)}}{2 \, a}\right) + 4 \, {\left(10 \, {\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} \cosh\left(d x + c\right)^{9} + 4 \, {\left(6 \, a^{6} + 2 \, a^{5} b - 2 \, a^{4} b^{2} + 17 \, a^{3} b^{3} + 18 \, a^{2} b^{4} + 3 \, a b^{5}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(4 \, a^{6} - 4 \, a^{5} b + 24 \, a^{4} b^{2} + 7 \, a^{3} b^{3} - 34 \, a^{2} b^{4} - 9 \, a b^{5}\right)} \cosh\left(d x + c\right)^{5} - 2 \, {\left(4 \, a^{6} - 4 \, a^{5} b + 24 \, a^{4} b^{2} + 7 \, a^{3} b^{3} - 34 \, a^{2} b^{4} - 9 \, a b^{5}\right)} \cosh\left(d x + c\right)^{3} - {\left(6 \, a^{6} + 2 \, a^{5} b - 2 \, a^{4} b^{2} + 17 \, a^{3} b^{3} + 18 \, 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^{9} + 6 \, a^{8} b + 15 \, a^{7} b^{2} + 20 \, a^{6} b^{3} + 15 \, a^{5} b^{4} + 6 \, a^{4} b^{5} + a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{9} + 9 \, {\left(a^{9} + 6 \, a^{8} b + 15 \, a^{7} b^{2} + 20 \, a^{6} b^{3} + 15 \, a^{5} b^{4} + 6 \, a^{4} b^{5} + a^{3} b^{6}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{8} + {\left(a^{9} + 6 \, a^{8} b + 15 \, a^{7} b^{2} + 20 \, a^{6} b^{3} + 15 \, a^{5} b^{4} + 6 \, a^{4} b^{5} + a^{3} b^{6}\right)} d \sinh\left(d x + c\right)^{9} + 4 \, {\left(a^{9} + 4 \, a^{8} b + 5 \, a^{7} b^{2} - 5 \, a^{5} b^{4} - 4 \, a^{4} b^{5} - a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{7} + 4 \, {\left(9 \, {\left(a^{9} + 6 \, a^{8} b + 15 \, a^{7} b^{2} + 20 \, a^{6} b^{3} + 15 \, a^{5} b^{4} + 6 \, a^{4} b^{5} + a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{9} + 4 \, a^{8} b + 5 \, a^{7} b^{2} - 5 \, a^{5} b^{4} - 4 \, a^{4} b^{5} - a^{3} b^{6}\right)} d\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(3 \, a^{9} + 10 \, a^{8} b + 13 \, a^{7} b^{2} + 12 \, a^{6} b^{3} + 13 \, a^{5} b^{4} + 10 \, a^{4} b^{5} + 3 \, a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{5} + 28 \, {\left(3 \, {\left(a^{9} + 6 \, a^{8} b + 15 \, a^{7} b^{2} + 20 \, a^{6} b^{3} + 15 \, a^{5} b^{4} + 6 \, a^{4} b^{5} + a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{9} + 4 \, a^{8} b + 5 \, a^{7} b^{2} - 5 \, a^{5} b^{4} - 4 \, a^{4} b^{5} - a^{3} b^{6}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(63 \, {\left(a^{9} + 6 \, a^{8} b + 15 \, a^{7} b^{2} + 20 \, a^{6} b^{3} + 15 \, a^{5} b^{4} + 6 \, a^{4} b^{5} + a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{4} + 42 \, {\left(a^{9} + 4 \, a^{8} b + 5 \, a^{7} b^{2} - 5 \, a^{5} b^{4} - 4 \, a^{4} b^{5} - a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{9} + 10 \, a^{8} b + 13 \, a^{7} b^{2} + 12 \, a^{6} b^{3} + 13 \, a^{5} b^{4} + 10 \, a^{4} b^{5} + 3 \, a^{3} b^{6}\right)} d\right)} \sinh\left(d x + c\right)^{5} + 4 \, {\left(a^{9} + 4 \, a^{8} b + 5 \, a^{7} b^{2} - 5 \, a^{5} b^{4} - 4 \, a^{4} b^{5} - a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{3} + 2 \, {\left(63 \, {\left(a^{9} + 6 \, a^{8} b + 15 \, a^{7} b^{2} + 20 \, a^{6} b^{3} + 15 \, a^{5} b^{4} + 6 \, a^{4} b^{5} + a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{5} + 70 \, {\left(a^{9} + 4 \, a^{8} b + 5 \, a^{7} b^{2} - 5 \, a^{5} b^{4} - 4 \, a^{4} b^{5} - a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{3} + 5 \, {\left(3 \, a^{9} + 10 \, a^{8} b + 13 \, a^{7} b^{2} + 12 \, a^{6} b^{3} + 13 \, a^{5} b^{4} + 10 \, a^{4} b^{5} + 3 \, a^{3} b^{6}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(21 \, {\left(a^{9} + 6 \, a^{8} b + 15 \, a^{7} b^{2} + 20 \, a^{6} b^{3} + 15 \, a^{5} b^{4} + 6 \, a^{4} b^{5} + a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{6} + 35 \, {\left(a^{9} + 4 \, a^{8} b + 5 \, a^{7} b^{2} - 5 \, a^{5} b^{4} - 4 \, a^{4} b^{5} - a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{4} + 5 \, {\left(3 \, a^{9} + 10 \, a^{8} b + 13 \, a^{7} b^{2} + 12 \, a^{6} b^{3} + 13 \, a^{5} b^{4} + 10 \, a^{4} b^{5} + 3 \, a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{9} + 4 \, a^{8} b + 5 \, a^{7} b^{2} - 5 \, a^{5} b^{4} - 4 \, a^{4} b^{5} - a^{3} b^{6}\right)} d\right)} \sinh\left(d x + c\right)^{3} + {\left(a^{9} + 6 \, a^{8} b + 15 \, a^{7} b^{2} + 20 \, a^{6} b^{3} + 15 \, a^{5} b^{4} + 6 \, a^{4} b^{5} + a^{3} b^{6}\right)} d \cosh\left(d x + c\right) + 4 \, {\left(9 \, {\left(a^{9} + 6 \, a^{8} b + 15 \, a^{7} b^{2} + 20 \, a^{6} b^{3} + 15 \, a^{5} b^{4} + 6 \, a^{4} b^{5} + a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{7} + 21 \, {\left(a^{9} + 4 \, a^{8} b + 5 \, a^{7} b^{2} - 5 \, a^{5} b^{4} - 4 \, a^{4} b^{5} - a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{5} + 5 \, {\left(3 \, a^{9} + 10 \, a^{8} b + 13 \, a^{7} b^{2} + 12 \, a^{6} b^{3} + 13 \, a^{5} b^{4} + 10 \, a^{4} b^{5} + 3 \, a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{9} + 4 \, a^{8} b + 5 \, a^{7} b^{2} - 5 \, a^{5} b^{4} - 4 \, a^{4} b^{5} - a^{3} b^{6}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + {\left(9 \, {\left(a^{9} + 6 \, a^{8} b + 15 \, a^{7} b^{2} + 20 \, a^{6} b^{3} + 15 \, a^{5} b^{4} + 6 \, a^{4} b^{5} + a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{8} + 28 \, {\left(a^{9} + 4 \, a^{8} b + 5 \, a^{7} b^{2} - 5 \, a^{5} b^{4} - 4 \, a^{4} b^{5} - a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{6} + 10 \, {\left(3 \, a^{9} + 10 \, a^{8} b + 13 \, a^{7} b^{2} + 12 \, a^{6} b^{3} + 13 \, a^{5} b^{4} + 10 \, a^{4} b^{5} + 3 \, a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{4} + 12 \, {\left(a^{9} + 4 \, a^{8} b + 5 \, a^{7} b^{2} - 5 \, a^{5} b^{4} - 4 \, a^{4} b^{5} - a^{3} b^{6}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{9} + 6 \, a^{8} b + 15 \, a^{7} b^{2} + 20 \, a^{6} b^{3} + 15 \, a^{5} b^{4} + 6 \, a^{4} b^{5} + a^{3} b^{6}\right)} d\right)} \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[1/16*(8*(a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*cosh(d*x + c)^10 + 80*(a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*cosh(d*x + c)*sinh(d*x + c)^9 + 8*(a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*sinh(d*x + c)^10 + 4*(6*a^6 + 2*a^5*b - 2*a^4*b^2 + 17*a^3*b^3 + 18*a^2*b^4 + 3*a*b^5)*cosh(d*x + c)^8 + 4*(6*a^6 + 2*a^5*b - 2*a^4*b^2 + 17*a^3*b^3 + 18*a^2*b^4 + 3*a*b^5 + 90*(a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 32*(30*(a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*cosh(d*x + c)^3 + (6*a^6 + 2*a^5*b - 2*a^4*b^2 + 17*a^3*b^3 + 18*a^2*b^4 + 3*a*b^5)*cosh(d*x + c))*sinh(d*x + c)^7 + 4*(4*a^6 - 4*a^5*b + 24*a^4*b^2 + 7*a^3*b^3 - 34*a^2*b^4 - 9*a*b^5)*cosh(d*x + c)^6 + 4*(4*a^6 - 4*a^5*b + 24*a^4*b^2 + 7*a^3*b^3 - 34*a^2*b^4 - 9*a*b^5 + 420*(a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*cosh(d*x + c)^4 + 28*(6*a^6 + 2*a^5*b - 2*a^4*b^2 + 17*a^3*b^3 + 18*a^2*b^4 + 3*a*b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^6 - 8*a^6 - 24*a^5*b - 24*a^4*b^2 - 8*a^3*b^3 + 8*(252*(a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*cosh(d*x + c)^5 + 28*(6*a^6 + 2*a^5*b - 2*a^4*b^2 + 17*a^3*b^3 + 18*a^2*b^4 + 3*a*b^5)*cosh(d*x + c)^3 + 3*(4*a^6 - 4*a^5*b + 24*a^4*b^2 + 7*a^3*b^3 - 34*a^2*b^4 - 9*a*b^5)*cosh(d*x + c))*sinh(d*x + c)^5 - 4*(4*a^6 - 4*a^5*b + 24*a^4*b^2 + 7*a^3*b^3 - 34*a^2*b^4 - 9*a*b^5)*cosh(d*x + c)^4 + 4*(420*(a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*cosh(d*x + c)^6 - 4*a^6 + 4*a^5*b - 24*a^4*b^2 - 7*a^3*b^3 + 34*a^2*b^4 + 9*a*b^5 + 70*(6*a^6 + 2*a^5*b - 2*a^4*b^2 + 17*a^3*b^3 + 18*a^2*b^4 + 3*a*b^5)*cosh(d*x + c)^4 + 15*(4*a^6 - 4*a^5*b + 24*a^4*b^2 + 7*a^3*b^3 - 34*a^2*b^4 - 9*a*b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 16*(60*(a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*cosh(d*x + c)^7 + 14*(6*a^6 + 2*a^5*b - 2*a^4*b^2 + 17*a^3*b^3 + 18*a^2*b^4 + 3*a*b^5)*cosh(d*x + c)^5 + 5*(4*a^6 - 4*a^5*b + 24*a^4*b^2 + 7*a^3*b^3 - 34*a^2*b^4 - 9*a*b^5)*cosh(d*x + c)^3 - (4*a^6 - 4*a^5*b + 24*a^4*b^2 + 7*a^3*b^3 - 34*a^2*b^4 - 9*a*b^5)*cosh(d*x + c))*sinh(d*x + c)^3 - 4*(6*a^6 + 2*a^5*b - 2*a^4*b^2 + 17*a^3*b^3 + 18*a^2*b^4 + 3*a*b^5)*cosh(d*x + c)^2 + 4*(90*(a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*cosh(d*x + c)^8 + 28*(6*a^6 + 2*a^5*b - 2*a^4*b^2 + 17*a^3*b^3 + 18*a^2*b^4 + 3*a*b^5)*cosh(d*x + c)^6 - 6*a^6 - 2*a^5*b + 2*a^4*b^2 - 17*a^3*b^3 - 18*a^2*b^4 - 3*a*b^5 + 15*(4*a^6 - 4*a^5*b + 24*a^4*b^2 + 7*a^3*b^3 - 34*a^2*b^4 - 9*a*b^5)*cosh(d*x + c)^4 - 6*(4*a^6 - 4*a^5*b + 24*a^4*b^2 + 7*a^3*b^3 - 34*a^2*b^4 - 9*a*b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - 3*((8*a^4*b + 20*a^3*b^2 + 17*a^2*b^3 + 6*a*b^4 + b^5)*cosh(d*x + c)^9 + 9*(8*a^4*b + 20*a^3*b^2 + 17*a^2*b^3 + 6*a*b^4 + b^5)*cosh(d*x + c)*sinh(d*x + c)^8 + (8*a^4*b + 20*a^3*b^2 + 17*a^2*b^3 + 6*a*b^4 + b^5)*sinh(d*x + c)^9 + 4*(8*a^4*b + 4*a^3*b^2 - 7*a^2*b^3 - 4*a*b^4 - b^5)*cosh(d*x + c)^7 + 4*(8*a^4*b + 4*a^3*b^2 - 7*a^2*b^3 - 4*a*b^4 - b^5 + 9*(8*a^4*b + 20*a^3*b^2 + 17*a^2*b^3 + 6*a*b^4 + b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^7 + 28*(3*(8*a^4*b + 20*a^3*b^2 + 17*a^2*b^3 + 6*a*b^4 + b^5)*cosh(d*x + c)^3 + (8*a^4*b + 4*a^3*b^2 - 7*a^2*b^3 - 4*a*b^4 - b^5)*cosh(d*x + c))*sinh(d*x + c)^6 + 2*(24*a^4*b - 4*a^3*b^2 + 19*a^2*b^3 + 10*a*b^4 + 3*b^5)*cosh(d*x + c)^5 + 2*(24*a^4*b - 4*a^3*b^2 + 19*a^2*b^3 + 10*a*b^4 + 3*b^5 + 63*(8*a^4*b + 20*a^3*b^2 + 17*a^2*b^3 + 6*a*b^4 + b^5)*cosh(d*x + c)^4 + 42*(8*a^4*b + 4*a^3*b^2 - 7*a^2*b^3 - 4*a*b^4 - b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 2*(63*(8*a^4*b + 20*a^3*b^2 + 17*a^2*b^3 + 6*a*b^4 + b^5)*cosh(d*x + c)^5 + 70*(8*a^4*b + 4*a^3*b^2 - 7*a^2*b^3 - 4*a*b^4 - b^5)*cosh(d*x + c)^3 + 5*(24*a^4*b - 4*a^3*b^2 + 19*a^2*b^3 + 10*a*b^4 + 3*b^5)*cosh(d*x + c))*sinh(d*x + c)^4 + 4*(8*a^4*b + 4*a^3*b^2 - 7*a^2*b^3 - 4*a*b^4 - b^5)*cosh(d*x + c)^3 + 4*(21*(8*a^4*b + 20*a^3*b^2 + 17*a^2*b^3 + 6*a*b^4 + b^5)*cosh(d*x + c)^6 + 8*a^4*b + 4*a^3*b^2 - 7*a^2*b^3 - 4*a*b^4 - b^5 + 35*(8*a^4*b + 4*a^3*b^2 - 7*a^2*b^3 - 4*a*b^4 - b^5)*cosh(d*x + c)^4 + 5*(24*a^4*b - 4*a^3*b^2 + 19*a^2*b^3 + 10*a*b^4 + 3*b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 4*(9*(8*a^4*b + 20*a^3*b^2 + 17*a^2*b^3 + 6*a*b^4 + b^5)*cosh(d*x + c)^7 + 21*(8*a^4*b + 4*a^3*b^2 - 7*a^2*b^3 - 4*a*b^4 - b^5)*cosh(d*x + c)^5 + 5*(24*a^4*b - 4*a^3*b^2 + 19*a^2*b^3 + 10*a*b^4 + 3*b^5)*cosh(d*x + c)^3 + 3*(8*a^4*b + 4*a^3*b^2 - 7*a^2*b^3 - 4*a*b^4 - b^5)*cosh(d*x + c))*sinh(d*x + c)^2 + (8*a^4*b + 20*a^3*b^2 + 17*a^2*b^3 + 6*a*b^4 + b^5)*cosh(d*x + c) + (9*(8*a^4*b + 20*a^3*b^2 + 17*a^2*b^3 + 6*a*b^4 + b^5)*cosh(d*x + c)^8 + 28*(8*a^4*b + 4*a^3*b^2 - 7*a^2*b^3 - 4*a*b^4 - b^5)*cosh(d*x + c)^6 + 8*a^4*b + 20*a^3*b^2 + 17*a^2*b^3 + 6*a*b^4 + b^5 + 10*(24*a^4*b - 4*a^3*b^2 + 19*a^2*b^3 + 10*a*b^4 + 3*b^5)*cosh(d*x + c)^4 + 12*(8*a^4*b + 4*a^3*b^2 - 7*a^2*b^3 - 4*a*b^4 - b^5)*cosh(d*x + c)^2)*sinh(d*x + c))*sqrt(-a^2 - a*b)*log(((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*(3*a + b)*cosh(d*x + c)^2 + 2*(3*(a + b)*cosh(d*x + c)^2 - 3*a - b)*sinh(d*x + c)^2 + 4*((a + b)*cosh(d*x + c)^3 - (3*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^2 - a*b) + a + b)/((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)) + 8*(10*(a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*cosh(d*x + c)^9 + 4*(6*a^6 + 2*a^5*b - 2*a^4*b^2 + 17*a^3*b^3 + 18*a^2*b^4 + 3*a*b^5)*cosh(d*x + c)^7 + 3*(4*a^6 - 4*a^5*b + 24*a^4*b^2 + 7*a^3*b^3 - 34*a^2*b^4 - 9*a*b^5)*cosh(d*x + c)^5 - 2*(4*a^6 - 4*a^5*b + 24*a^4*b^2 + 7*a^3*b^3 - 34*a^2*b^4 - 9*a*b^5)*cosh(d*x + c)^3 - (6*a^6 + 2*a^5*b - 2*a^4*b^2 + 17*a^3*b^3 + 18*a^2*b^4 + 3*a*b^5)*cosh(d*x + c))*sinh(d*x + c))/((a^9 + 6*a^8*b + 15*a^7*b^2 + 20*a^6*b^3 + 15*a^5*b^4 + 6*a^4*b^5 + a^3*b^6)*d*cosh(d*x + c)^9 + 9*(a^9 + 6*a^8*b + 15*a^7*b^2 + 20*a^6*b^3 + 15*a^5*b^4 + 6*a^4*b^5 + a^3*b^6)*d*cosh(d*x + c)*sinh(d*x + c)^8 + (a^9 + 6*a^8*b + 15*a^7*b^2 + 20*a^6*b^3 + 15*a^5*b^4 + 6*a^4*b^5 + a^3*b^6)*d*sinh(d*x + c)^9 + 4*(a^9 + 4*a^8*b + 5*a^7*b^2 - 5*a^5*b^4 - 4*a^4*b^5 - a^3*b^6)*d*cosh(d*x + c)^7 + 4*(9*(a^9 + 6*a^8*b + 15*a^7*b^2 + 20*a^6*b^3 + 15*a^5*b^4 + 6*a^4*b^5 + a^3*b^6)*d*cosh(d*x + c)^2 + (a^9 + 4*a^8*b + 5*a^7*b^2 - 5*a^5*b^4 - 4*a^4*b^5 - a^3*b^6)*d)*sinh(d*x + c)^7 + 2*(3*a^9 + 10*a^8*b + 13*a^7*b^2 + 12*a^6*b^3 + 13*a^5*b^4 + 10*a^4*b^5 + 3*a^3*b^6)*d*cosh(d*x + c)^5 + 28*(3*(a^9 + 6*a^8*b + 15*a^7*b^2 + 20*a^6*b^3 + 15*a^5*b^4 + 6*a^4*b^5 + a^3*b^6)*d*cosh(d*x + c)^3 + (a^9 + 4*a^8*b + 5*a^7*b^2 - 5*a^5*b^4 - 4*a^4*b^5 - a^3*b^6)*d*cosh(d*x + c))*sinh(d*x + c)^6 + 2*(63*(a^9 + 6*a^8*b + 15*a^7*b^2 + 20*a^6*b^3 + 15*a^5*b^4 + 6*a^4*b^5 + a^3*b^6)*d*cosh(d*x + c)^4 + 42*(a^9 + 4*a^8*b + 5*a^7*b^2 - 5*a^5*b^4 - 4*a^4*b^5 - a^3*b^6)*d*cosh(d*x + c)^2 + (3*a^9 + 10*a^8*b + 13*a^7*b^2 + 12*a^6*b^3 + 13*a^5*b^4 + 10*a^4*b^5 + 3*a^3*b^6)*d)*sinh(d*x + c)^5 + 4*(a^9 + 4*a^8*b + 5*a^7*b^2 - 5*a^5*b^4 - 4*a^4*b^5 - a^3*b^6)*d*cosh(d*x + c)^3 + 2*(63*(a^9 + 6*a^8*b + 15*a^7*b^2 + 20*a^6*b^3 + 15*a^5*b^4 + 6*a^4*b^5 + a^3*b^6)*d*cosh(d*x + c)^5 + 70*(a^9 + 4*a^8*b + 5*a^7*b^2 - 5*a^5*b^4 - 4*a^4*b^5 - a^3*b^6)*d*cosh(d*x + c)^3 + 5*(3*a^9 + 10*a^8*b + 13*a^7*b^2 + 12*a^6*b^3 + 13*a^5*b^4 + 10*a^4*b^5 + 3*a^3*b^6)*d*cosh(d*x + c))*sinh(d*x + c)^4 + 4*(21*(a^9 + 6*a^8*b + 15*a^7*b^2 + 20*a^6*b^3 + 15*a^5*b^4 + 6*a^4*b^5 + a^3*b^6)*d*cosh(d*x + c)^6 + 35*(a^9 + 4*a^8*b + 5*a^7*b^2 - 5*a^5*b^4 - 4*a^4*b^5 - a^3*b^6)*d*cosh(d*x + c)^4 + 5*(3*a^9 + 10*a^8*b + 13*a^7*b^2 + 12*a^6*b^3 + 13*a^5*b^4 + 10*a^4*b^5 + 3*a^3*b^6)*d*cosh(d*x + c)^2 + (a^9 + 4*a^8*b + 5*a^7*b^2 - 5*a^5*b^4 - 4*a^4*b^5 - a^3*b^6)*d)*sinh(d*x + c)^3 + (a^9 + 6*a^8*b + 15*a^7*b^2 + 20*a^6*b^3 + 15*a^5*b^4 + 6*a^4*b^5 + a^3*b^6)*d*cosh(d*x + c) + 4*(9*(a^9 + 6*a^8*b + 15*a^7*b^2 + 20*a^6*b^3 + 15*a^5*b^4 + 6*a^4*b^5 + a^3*b^6)*d*cosh(d*x + c)^7 + 21*(a^9 + 4*a^8*b + 5*a^7*b^2 - 5*a^5*b^4 - 4*a^4*b^5 - a^3*b^6)*d*cosh(d*x + c)^5 + 5*(3*a^9 + 10*a^8*b + 13*a^7*b^2 + 12*a^6*b^3 + 13*a^5*b^4 + 10*a^4*b^5 + 3*a^3*b^6)*d*cosh(d*x + c)^3 + 3*(a^9 + 4*a^8*b + 5*a^7*b^2 - 5*a^5*b^4 - 4*a^4*b^5 - a^3*b^6)*d*cosh(d*x + c))*sinh(d*x + c)^2 + (9*(a^9 + 6*a^8*b + 15*a^7*b^2 + 20*a^6*b^3 + 15*a^5*b^4 + 6*a^4*b^5 + a^3*b^6)*d*cosh(d*x + c)^8 + 28*(a^9 + 4*a^8*b + 5*a^7*b^2 - 5*a^5*b^4 - 4*a^4*b^5 - a^3*b^6)*d*cosh(d*x + c)^6 + 10*(3*a^9 + 10*a^8*b + 13*a^7*b^2 + 12*a^6*b^3 + 13*a^5*b^4 + 10*a^4*b^5 + 3*a^3*b^6)*d*cosh(d*x + c)^4 + 12*(a^9 + 4*a^8*b + 5*a^7*b^2 - 5*a^5*b^4 - 4*a^4*b^5 - a^3*b^6)*d*cosh(d*x + c)^2 + (a^9 + 6*a^8*b + 15*a^7*b^2 + 20*a^6*b^3 + 15*a^5*b^4 + 6*a^4*b^5 + a^3*b^6)*d)*sinh(d*x + c)), 1/8*(4*(a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*cosh(d*x + c)^10 + 40*(a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*cosh(d*x + c)*sinh(d*x + c)^9 + 4*(a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*sinh(d*x + c)^10 + 2*(6*a^6 + 2*a^5*b - 2*a^4*b^2 + 17*a^3*b^3 + 18*a^2*b^4 + 3*a*b^5)*cosh(d*x + c)^8 + 2*(6*a^6 + 2*a^5*b - 2*a^4*b^2 + 17*a^3*b^3 + 18*a^2*b^4 + 3*a*b^5 + 90*(a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 16*(30*(a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*cosh(d*x + c)^3 + (6*a^6 + 2*a^5*b - 2*a^4*b^2 + 17*a^3*b^3 + 18*a^2*b^4 + 3*a*b^5)*cosh(d*x + c))*sinh(d*x + c)^7 + 2*(4*a^6 - 4*a^5*b + 24*a^4*b^2 + 7*a^3*b^3 - 34*a^2*b^4 - 9*a*b^5)*cosh(d*x + c)^6 + 2*(4*a^6 - 4*a^5*b + 24*a^4*b^2 + 7*a^3*b^3 - 34*a^2*b^4 - 9*a*b^5 + 420*(a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*cosh(d*x + c)^4 + 28*(6*a^6 + 2*a^5*b - 2*a^4*b^2 + 17*a^3*b^3 + 18*a^2*b^4 + 3*a*b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^6 - 4*a^6 - 12*a^5*b - 12*a^4*b^2 - 4*a^3*b^3 + 4*(252*(a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*cosh(d*x + c)^5 + 28*(6*a^6 + 2*a^5*b - 2*a^4*b^2 + 17*a^3*b^3 + 18*a^2*b^4 + 3*a*b^5)*cosh(d*x + c)^3 + 3*(4*a^6 - 4*a^5*b + 24*a^4*b^2 + 7*a^3*b^3 - 34*a^2*b^4 - 9*a*b^5)*cosh(d*x + c))*sinh(d*x + c)^5 - 2*(4*a^6 - 4*a^5*b + 24*a^4*b^2 + 7*a^3*b^3 - 34*a^2*b^4 - 9*a*b^5)*cosh(d*x + c)^4 + 2*(420*(a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*cosh(d*x + c)^6 - 4*a^6 + 4*a^5*b - 24*a^4*b^2 - 7*a^3*b^3 + 34*a^2*b^4 + 9*a*b^5 + 70*(6*a^6 + 2*a^5*b - 2*a^4*b^2 + 17*a^3*b^3 + 18*a^2*b^4 + 3*a*b^5)*cosh(d*x + c)^4 + 15*(4*a^6 - 4*a^5*b + 24*a^4*b^2 + 7*a^3*b^3 - 34*a^2*b^4 - 9*a*b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(60*(a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*cosh(d*x + c)^7 + 14*(6*a^6 + 2*a^5*b - 2*a^4*b^2 + 17*a^3*b^3 + 18*a^2*b^4 + 3*a*b^5)*cosh(d*x + c)^5 + 5*(4*a^6 - 4*a^5*b + 24*a^4*b^2 + 7*a^3*b^3 - 34*a^2*b^4 - 9*a*b^5)*cosh(d*x + c)^3 - (4*a^6 - 4*a^5*b + 24*a^4*b^2 + 7*a^3*b^3 - 34*a^2*b^4 - 9*a*b^5)*cosh(d*x + c))*sinh(d*x + c)^3 - 2*(6*a^6 + 2*a^5*b - 2*a^4*b^2 + 17*a^3*b^3 + 18*a^2*b^4 + 3*a*b^5)*cosh(d*x + c)^2 + 2*(90*(a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*cosh(d*x + c)^8 + 28*(6*a^6 + 2*a^5*b - 2*a^4*b^2 + 17*a^3*b^3 + 18*a^2*b^4 + 3*a*b^5)*cosh(d*x + c)^6 - 6*a^6 - 2*a^5*b + 2*a^4*b^2 - 17*a^3*b^3 - 18*a^2*b^4 - 3*a*b^5 + 15*(4*a^6 - 4*a^5*b + 24*a^4*b^2 + 7*a^3*b^3 - 34*a^2*b^4 - 9*a*b^5)*cosh(d*x + c)^4 - 6*(4*a^6 - 4*a^5*b + 24*a^4*b^2 + 7*a^3*b^3 - 34*a^2*b^4 - 9*a*b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 3*((8*a^4*b + 20*a^3*b^2 + 17*a^2*b^3 + 6*a*b^4 + b^5)*cosh(d*x + c)^9 + 9*(8*a^4*b + 20*a^3*b^2 + 17*a^2*b^3 + 6*a*b^4 + b^5)*cosh(d*x + c)*sinh(d*x + c)^8 + (8*a^4*b + 20*a^3*b^2 + 17*a^2*b^3 + 6*a*b^4 + b^5)*sinh(d*x + c)^9 + 4*(8*a^4*b + 4*a^3*b^2 - 7*a^2*b^3 - 4*a*b^4 - b^5)*cosh(d*x + c)^7 + 4*(8*a^4*b + 4*a^3*b^2 - 7*a^2*b^3 - 4*a*b^4 - b^5 + 9*(8*a^4*b + 20*a^3*b^2 + 17*a^2*b^3 + 6*a*b^4 + b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^7 + 28*(3*(8*a^4*b + 20*a^3*b^2 + 17*a^2*b^3 + 6*a*b^4 + b^5)*cosh(d*x + c)^3 + (8*a^4*b + 4*a^3*b^2 - 7*a^2*b^3 - 4*a*b^4 - b^5)*cosh(d*x + c))*sinh(d*x + c)^6 + 2*(24*a^4*b - 4*a^3*b^2 + 19*a^2*b^3 + 10*a*b^4 + 3*b^5)*cosh(d*x + c)^5 + 2*(24*a^4*b - 4*a^3*b^2 + 19*a^2*b^3 + 10*a*b^4 + 3*b^5 + 63*(8*a^4*b + 20*a^3*b^2 + 17*a^2*b^3 + 6*a*b^4 + b^5)*cosh(d*x + c)^4 + 42*(8*a^4*b + 4*a^3*b^2 - 7*a^2*b^3 - 4*a*b^4 - b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 2*(63*(8*a^4*b + 20*a^3*b^2 + 17*a^2*b^3 + 6*a*b^4 + b^5)*cosh(d*x + c)^5 + 70*(8*a^4*b + 4*a^3*b^2 - 7*a^2*b^3 - 4*a*b^4 - b^5)*cosh(d*x + c)^3 + 5*(24*a^4*b - 4*a^3*b^2 + 19*a^2*b^3 + 10*a*b^4 + 3*b^5)*cosh(d*x + c))*sinh(d*x + c)^4 + 4*(8*a^4*b + 4*a^3*b^2 - 7*a^2*b^3 - 4*a*b^4 - b^5)*cosh(d*x + c)^3 + 4*(21*(8*a^4*b + 20*a^3*b^2 + 17*a^2*b^3 + 6*a*b^4 + b^5)*cosh(d*x + c)^6 + 8*a^4*b + 4*a^3*b^2 - 7*a^2*b^3 - 4*a*b^4 - b^5 + 35*(8*a^4*b + 4*a^3*b^2 - 7*a^2*b^3 - 4*a*b^4 - b^5)*cosh(d*x + c)^4 + 5*(24*a^4*b - 4*a^3*b^2 + 19*a^2*b^3 + 10*a*b^4 + 3*b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 4*(9*(8*a^4*b + 20*a^3*b^2 + 17*a^2*b^3 + 6*a*b^4 + b^5)*cosh(d*x + c)^7 + 21*(8*a^4*b + 4*a^3*b^2 - 7*a^2*b^3 - 4*a*b^4 - b^5)*cosh(d*x + c)^5 + 5*(24*a^4*b - 4*a^3*b^2 + 19*a^2*b^3 + 10*a*b^4 + 3*b^5)*cosh(d*x + c)^3 + 3*(8*a^4*b + 4*a^3*b^2 - 7*a^2*b^3 - 4*a*b^4 - b^5)*cosh(d*x + c))*sinh(d*x + c)^2 + (8*a^4*b + 20*a^3*b^2 + 17*a^2*b^3 + 6*a*b^4 + b^5)*cosh(d*x + c) + (9*(8*a^4*b + 20*a^3*b^2 + 17*a^2*b^3 + 6*a*b^4 + b^5)*cosh(d*x + c)^8 + 28*(8*a^4*b + 4*a^3*b^2 - 7*a^2*b^3 - 4*a*b^4 - b^5)*cosh(d*x + c)^6 + 8*a^4*b + 20*a^3*b^2 + 17*a^2*b^3 + 6*a*b^4 + b^5 + 10*(24*a^4*b - 4*a^3*b^2 + 19*a^2*b^3 + 10*a*b^4 + 3*b^5)*cosh(d*x + c)^4 + 12*(8*a^4*b + 4*a^3*b^2 - 7*a^2*b^3 - 4*a*b^4 - b^5)*cosh(d*x + c)^2)*sinh(d*x + c))*sqrt(a^2 + a*b)*arctan(1/2*((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 + (3*a - b)*cosh(d*x + c) + (3*(a + b)*cosh(d*x + c)^2 + 3*a - b)*sinh(d*x + c))/sqrt(a^2 + a*b)) + 3*((8*a^4*b + 20*a^3*b^2 + 17*a^2*b^3 + 6*a*b^4 + b^5)*cosh(d*x + c)^9 + 9*(8*a^4*b + 20*a^3*b^2 + 17*a^2*b^3 + 6*a*b^4 + b^5)*cosh(d*x + c)*sinh(d*x + c)^8 + (8*a^4*b + 20*a^3*b^2 + 17*a^2*b^3 + 6*a*b^4 + b^5)*sinh(d*x + c)^9 + 4*(8*a^4*b + 4*a^3*b^2 - 7*a^2*b^3 - 4*a*b^4 - b^5)*cosh(d*x + c)^7 + 4*(8*a^4*b + 4*a^3*b^2 - 7*a^2*b^3 - 4*a*b^4 - b^5 + 9*(8*a^4*b + 20*a^3*b^2 + 17*a^2*b^3 + 6*a*b^4 + b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^7 + 28*(3*(8*a^4*b + 20*a^3*b^2 + 17*a^2*b^3 + 6*a*b^4 + b^5)*cosh(d*x + c)^3 + (8*a^4*b + 4*a^3*b^2 - 7*a^2*b^3 - 4*a*b^4 - b^5)*cosh(d*x + c))*sinh(d*x + c)^6 + 2*(24*a^4*b - 4*a^3*b^2 + 19*a^2*b^3 + 10*a*b^4 + 3*b^5)*cosh(d*x + c)^5 + 2*(24*a^4*b - 4*a^3*b^2 + 19*a^2*b^3 + 10*a*b^4 + 3*b^5 + 63*(8*a^4*b + 20*a^3*b^2 + 17*a^2*b^3 + 6*a*b^4 + b^5)*cosh(d*x + c)^4 + 42*(8*a^4*b + 4*a^3*b^2 - 7*a^2*b^3 - 4*a*b^4 - b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 2*(63*(8*a^4*b + 20*a^3*b^2 + 17*a^2*b^3 + 6*a*b^4 + b^5)*cosh(d*x + c)^5 + 70*(8*a^4*b + 4*a^3*b^2 - 7*a^2*b^3 - 4*a*b^4 - b^5)*cosh(d*x + c)^3 + 5*(24*a^4*b - 4*a^3*b^2 + 19*a^2*b^3 + 10*a*b^4 + 3*b^5)*cosh(d*x + c))*sinh(d*x + c)^4 + 4*(8*a^4*b + 4*a^3*b^2 - 7*a^2*b^3 - 4*a*b^4 - b^5)*cosh(d*x + c)^3 + 4*(21*(8*a^4*b + 20*a^3*b^2 + 17*a^2*b^3 + 6*a*b^4 + b^5)*cosh(d*x + c)^6 + 8*a^4*b + 4*a^3*b^2 - 7*a^2*b^3 - 4*a*b^4 - b^5 + 35*(8*a^4*b + 4*a^3*b^2 - 7*a^2*b^3 - 4*a*b^4 - b^5)*cosh(d*x + c)^4 + 5*(24*a^4*b - 4*a^3*b^2 + 19*a^2*b^3 + 10*a*b^4 + 3*b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 4*(9*(8*a^4*b + 20*a^3*b^2 + 17*a^2*b^3 + 6*a*b^4 + b^5)*cosh(d*x + c)^7 + 21*(8*a^4*b + 4*a^3*b^2 - 7*a^2*b^3 - 4*a*b^4 - b^5)*cosh(d*x + c)^5 + 5*(24*a^4*b - 4*a^3*b^2 + 19*a^2*b^3 + 10*a*b^4 + 3*b^5)*cosh(d*x + c)^3 + 3*(8*a^4*b + 4*a^3*b^2 - 7*a^2*b^3 - 4*a*b^4 - b^5)*cosh(d*x + c))*sinh(d*x + c)^2 + (8*a^4*b + 20*a^3*b^2 + 17*a^2*b^3 + 6*a*b^4 + b^5)*cosh(d*x + c) + (9*(8*a^4*b + 20*a^3*b^2 + 17*a^2*b^3 + 6*a*b^4 + b^5)*cosh(d*x + c)^8 + 28*(8*a^4*b + 4*a^3*b^2 - 7*a^2*b^3 - 4*a*b^4 - b^5)*cosh(d*x + c)^6 + 8*a^4*b + 20*a^3*b^2 + 17*a^2*b^3 + 6*a*b^4 + b^5 + 10*(24*a^4*b - 4*a^3*b^2 + 19*a^2*b^3 + 10*a*b^4 + 3*b^5)*cosh(d*x + c)^4 + 12*(8*a^4*b + 4*a^3*b^2 - 7*a^2*b^3 - 4*a*b^4 - b^5)*cosh(d*x + c)^2)*sinh(d*x + c))*sqrt(a^2 + a*b)*arctan(1/2*sqrt(a^2 + a*b)*(cosh(d*x + c) + sinh(d*x + c))/a) + 4*(10*(a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*cosh(d*x + c)^9 + 4*(6*a^6 + 2*a^5*b - 2*a^4*b^2 + 17*a^3*b^3 + 18*a^2*b^4 + 3*a*b^5)*cosh(d*x + c)^7 + 3*(4*a^6 - 4*a^5*b + 24*a^4*b^2 + 7*a^3*b^3 - 34*a^2*b^4 - 9*a*b^5)*cosh(d*x + c)^5 - 2*(4*a^6 - 4*a^5*b + 24*a^4*b^2 + 7*a^3*b^3 - 34*a^2*b^4 - 9*a*b^5)*cosh(d*x + c)^3 - (6*a^6 + 2*a^5*b - 2*a^4*b^2 + 17*a^3*b^3 + 18*a^2*b^4 + 3*a*b^5)*cosh(d*x + c))*sinh(d*x + c))/((a^9 + 6*a^8*b + 15*a^7*b^2 + 20*a^6*b^3 + 15*a^5*b^4 + 6*a^4*b^5 + a^3*b^6)*d*cosh(d*x + c)^9 + 9*(a^9 + 6*a^8*b + 15*a^7*b^2 + 20*a^6*b^3 + 15*a^5*b^4 + 6*a^4*b^5 + a^3*b^6)*d*cosh(d*x + c)*sinh(d*x + c)^8 + (a^9 + 6*a^8*b + 15*a^7*b^2 + 20*a^6*b^3 + 15*a^5*b^4 + 6*a^4*b^5 + a^3*b^6)*d*sinh(d*x + c)^9 + 4*(a^9 + 4*a^8*b + 5*a^7*b^2 - 5*a^5*b^4 - 4*a^4*b^5 - a^3*b^6)*d*cosh(d*x + c)^7 + 4*(9*(a^9 + 6*a^8*b + 15*a^7*b^2 + 20*a^6*b^3 + 15*a^5*b^4 + 6*a^4*b^5 + a^3*b^6)*d*cosh(d*x + c)^2 + (a^9 + 4*a^8*b + 5*a^7*b^2 - 5*a^5*b^4 - 4*a^4*b^5 - a^3*b^6)*d)*sinh(d*x + c)^7 + 2*(3*a^9 + 10*a^8*b + 13*a^7*b^2 + 12*a^6*b^3 + 13*a^5*b^4 + 10*a^4*b^5 + 3*a^3*b^6)*d*cosh(d*x + c)^5 + 28*(3*(a^9 + 6*a^8*b + 15*a^7*b^2 + 20*a^6*b^3 + 15*a^5*b^4 + 6*a^4*b^5 + a^3*b^6)*d*cosh(d*x + c)^3 + (a^9 + 4*a^8*b + 5*a^7*b^2 - 5*a^5*b^4 - 4*a^4*b^5 - a^3*b^6)*d*cosh(d*x + c))*sinh(d*x + c)^6 + 2*(63*(a^9 + 6*a^8*b + 15*a^7*b^2 + 20*a^6*b^3 + 15*a^5*b^4 + 6*a^4*b^5 + a^3*b^6)*d*cosh(d*x + c)^4 + 42*(a^9 + 4*a^8*b + 5*a^7*b^2 - 5*a^5*b^4 - 4*a^4*b^5 - a^3*b^6)*d*cosh(d*x + c)^2 + (3*a^9 + 10*a^8*b + 13*a^7*b^2 + 12*a^6*b^3 + 13*a^5*b^4 + 10*a^4*b^5 + 3*a^3*b^6)*d)*sinh(d*x + c)^5 + 4*(a^9 + 4*a^8*b + 5*a^7*b^2 - 5*a^5*b^4 - 4*a^4*b^5 - a^3*b^6)*d*cosh(d*x + c)^3 + 2*(63*(a^9 + 6*a^8*b + 15*a^7*b^2 + 20*a^6*b^3 + 15*a^5*b^4 + 6*a^4*b^5 + a^3*b^6)*d*cosh(d*x + c)^5 + 70*(a^9 + 4*a^8*b + 5*a^7*b^2 - 5*a^5*b^4 - 4*a^4*b^5 - a^3*b^6)*d*cosh(d*x + c)^3 + 5*(3*a^9 + 10*a^8*b + 13*a^7*b^2 + 12*a^6*b^3 + 13*a^5*b^4 + 10*a^4*b^5 + 3*a^3*b^6)*d*cosh(d*x + c))*sinh(d*x + c)^4 + 4*(21*(a^9 + 6*a^8*b + 15*a^7*b^2 + 20*a^6*b^3 + 15*a^5*b^4 + 6*a^4*b^5 + a^3*b^6)*d*cosh(d*x + c)^6 + 35*(a^9 + 4*a^8*b + 5*a^7*b^2 - 5*a^5*b^4 - 4*a^4*b^5 - a^3*b^6)*d*cosh(d*x + c)^4 + 5*(3*a^9 + 10*a^8*b + 13*a^7*b^2 + 12*a^6*b^3 + 13*a^5*b^4 + 10*a^4*b^5 + 3*a^3*b^6)*d*cosh(d*x + c)^2 + (a^9 + 4*a^8*b + 5*a^7*b^2 - 5*a^5*b^4 - 4*a^4*b^5 - a^3*b^6)*d)*sinh(d*x + c)^3 + (a^9 + 6*a^8*b + 15*a^7*b^2 + 20*a^6*b^3 + 15*a^5*b^4 + 6*a^4*b^5 + a^3*b^6)*d*cosh(d*x + c) + 4*(9*(a^9 + 6*a^8*b + 15*a^7*b^2 + 20*a^6*b^3 + 15*a^5*b^4 + 6*a^4*b^5 + a^3*b^6)*d*cosh(d*x + c)^7 + 21*(a^9 + 4*a^8*b + 5*a^7*b^2 - 5*a^5*b^4 - 4*a^4*b^5 - a^3*b^6)*d*cosh(d*x + c)^5 + 5*(3*a^9 + 10*a^8*b + 13*a^7*b^2 + 12*a^6*b^3 + 13*a^5*b^4 + 10*a^4*b^5 + 3*a^3*b^6)*d*cosh(d*x + c)^3 + 3*(a^9 + 4*a^8*b + 5*a^7*b^2 - 5*a^5*b^4 - 4*a^4*b^5 - a^3*b^6)*d*cosh(d*x + c))*sinh(d*x + c)^2 + (9*(a^9 + 6*a^8*b + 15*a^7*b^2 + 20*a^6*b^3 + 15*a^5*b^4 + 6*a^4*b^5 + a^3*b^6)*d*cosh(d*x + c)^8 + 28*(a^9 + 4*a^8*b + 5*a^7*b^2 - 5*a^5*b^4 - 4*a^4*b^5 - a^3*b^6)*d*cosh(d*x + c)^6 + 10*(3*a^9 + 10*a^8*b + 13*a^7*b^2 + 12*a^6*b^3 + 13*a^5*b^4 + 10*a^4*b^5 + 3*a^3*b^6)*d*cosh(d*x + c)^4 + 12*(a^9 + 4*a^8*b + 5*a^7*b^2 - 5*a^5*b^4 - 4*a^4*b^5 - a^3*b^6)*d*cosh(d*x + c)^2 + (a^9 + 6*a^8*b + 15*a^7*b^2 + 20*a^6*b^3 + 15*a^5*b^4 + 6*a^4*b^5 + a^3*b^6)*d)*sinh(d*x + c))]","B",0
127,1,7909,0,0.564995," ","integrate(sech(d*x+c)/(a+b*tanh(d*x+c)^2)^3,x, algorithm=""fricas"")","\left[\frac{4 \, {\left(8 \, a^{4} b + 19 \, a^{3} b^{2} + 14 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{7} + 28 \, {\left(8 \, a^{4} b + 19 \, a^{3} b^{2} + 14 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + 4 \, {\left(8 \, a^{4} b + 19 \, a^{3} b^{2} + 14 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \sinh\left(d x + c\right)^{7} + 4 \, {\left(8 \, a^{4} b - 5 \, a^{3} b^{2} - 22 \, a^{2} b^{3} - 9 \, a b^{4}\right)} \cosh\left(d x + c\right)^{5} + 4 \, {\left(8 \, a^{4} b - 5 \, a^{3} b^{2} - 22 \, a^{2} b^{3} - 9 \, a b^{4} + 21 \, {\left(8 \, a^{4} b + 19 \, a^{3} b^{2} + 14 \, 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(8 \, a^{4} b + 19 \, a^{3} b^{2} + 14 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{4} b - 5 \, a^{3} b^{2} - 22 \, 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(8 \, a^{4} b - 5 \, a^{3} b^{2} - 22 \, a^{2} b^{3} - 9 \, a b^{4}\right)} \cosh\left(d x + c\right)^{3} - 4 \, {\left(8 \, a^{4} b - 5 \, a^{3} b^{2} - 22 \, a^{2} b^{3} - 9 \, a b^{4} - 35 \, {\left(8 \, a^{4} b + 19 \, a^{3} b^{2} + 14 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{4} - 10 \, {\left(8 \, a^{4} b - 5 \, a^{3} b^{2} - 22 \, 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(8 \, a^{4} b + 19 \, a^{3} b^{2} + 14 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(8 \, a^{4} b - 5 \, a^{3} b^{2} - 22 \, a^{2} b^{3} - 9 \, a b^{4}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(8 \, a^{4} b - 5 \, a^{3} b^{2} - 22 \, 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(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)^{8} + 8 \, {\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) \sinh\left(d x + c\right)^{7} + {\left(8 \, a^{4} + 24 \, a^{3} b + 27 \, a^{2} b^{2} + 14 \, a b^{3} + 3 \, b^{4}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(8 \, a^{4} + 8 \, a^{3} b - 5 \, a^{2} b^{2} - 8 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(8 \, a^{4} + 8 \, a^{3} b - 5 \, a^{2} b^{2} - 8 \, a b^{3} - 3 \, b^{4} + 7 \, {\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)^{6} + 8 \, {\left(7 \, {\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} + 3 \, {\left(8 \, a^{4} + 8 \, a^{3} b - 5 \, 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)^{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(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} + 24 \, a^{4} + 8 \, a^{3} b + 17 \, a^{2} b^{2} + 18 \, a b^{3} + 9 \, b^{4} + 30 \, {\left(8 \, a^{4} + 8 \, a^{3} b - 5 \, 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)^{4} + 8 \, a^{4} + 24 \, a^{3} b + 27 \, a^{2} b^{2} + 14 \, a b^{3} + 3 \, b^{4} + 8 \, {\left(7 \, {\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)^{5} + 10 \, {\left(8 \, a^{4} + 8 \, a^{3} b - 5 \, a^{2} b^{2} - 8 \, 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(8 \, a^{4} + 8 \, a^{3} b - 5 \, a^{2} b^{2} - 8 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\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)^{6} + 15 \, {\left(8 \, a^{4} + 8 \, a^{3} b - 5 \, a^{2} b^{2} - 8 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 8 \, a^{4} + 8 \, a^{3} b - 5 \, a^{2} b^{2} - 8 \, 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(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)^{7} + 3 \, {\left(8 \, a^{4} + 8 \, a^{3} b - 5 \, a^{2} b^{2} - 8 \, 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(8 \, a^{4} + 8 \, a^{3} b - 5 \, 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)\right)} \sqrt{-a^{2} - a b} \log\left(\frac{{\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(3 \, a + b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} - 3 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(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) - 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^{2} - a b} + a + b}{{\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) - 4 \, {\left(8 \, a^{4} b + 19 \, a^{3} b^{2} + 14 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(d x + c\right) + 4 \, {\left(7 \, {\left(8 \, a^{4} b + 19 \, a^{3} b^{2} + 14 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{6} - 8 \, a^{4} b - 19 \, a^{3} b^{2} - 14 \, a^{2} b^{3} - 3 \, a b^{4} + 5 \, {\left(8 \, a^{4} b - 5 \, a^{3} b^{2} - 22 \, a^{2} b^{3} - 9 \, a b^{4}\right)} \cosh\left(d x + c\right)^{4} - 3 \, {\left(8 \, a^{4} b - 5 \, a^{3} b^{2} - 22 \, 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({\left(a^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{8} + 3 \, a^{7} b + 2 \, a^{6} b^{2} - 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^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{8} + 3 \, a^{7} b + 2 \, a^{6} b^{2} - 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(3 \, a^{8} + 7 \, a^{7} b + 6 \, a^{6} b^{2} + 6 \, a^{5} b^{3} + 7 \, a^{4} b^{4} + 3 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{8} + 3 \, a^{7} b + 2 \, a^{6} b^{2} - 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^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 30 \, {\left(a^{8} + 3 \, a^{7} b + 2 \, a^{6} b^{2} - 2 \, a^{5} b^{3} - 3 \, a^{4} b^{4} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{8} + 7 \, a^{7} b + 6 \, a^{6} b^{2} + 6 \, a^{5} b^{3} + 7 \, a^{4} b^{4} + 3 \, a^{3} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{8} + 3 \, a^{7} b + 2 \, a^{6} b^{2} - 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^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{8} + 3 \, a^{7} b + 2 \, a^{6} b^{2} - 2 \, a^{5} b^{3} - 3 \, a^{4} b^{4} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{8} + 7 \, a^{7} b + 6 \, a^{6} b^{2} + 6 \, a^{5} b^{3} + 7 \, 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^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{8} + 3 \, a^{7} b + 2 \, a^{6} b^{2} - 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(3 \, a^{8} + 7 \, a^{7} b + 6 \, a^{6} b^{2} + 6 \, a^{5} b^{3} + 7 \, a^{4} b^{4} + 3 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{8} + 3 \, a^{7} b + 2 \, a^{6} b^{2} - 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^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} d + 8 \, {\left({\left(a^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{8} + 3 \, a^{7} b + 2 \, a^{6} b^{2} - 2 \, a^{5} b^{3} - 3 \, a^{4} b^{4} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{8} + 7 \, a^{7} b + 6 \, a^{6} b^{2} + 6 \, a^{5} b^{3} + 7 \, a^{4} b^{4} + 3 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{8} + 3 \, a^{7} b + 2 \, a^{6} b^{2} - 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 + 19 \, a^{3} b^{2} + 14 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{7} + 14 \, {\left(8 \, a^{4} b + 19 \, a^{3} b^{2} + 14 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + 2 \, {\left(8 \, a^{4} b + 19 \, a^{3} b^{2} + 14 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(8 \, a^{4} b - 5 \, a^{3} b^{2} - 22 \, a^{2} b^{3} - 9 \, a b^{4}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(8 \, a^{4} b - 5 \, a^{3} b^{2} - 22 \, a^{2} b^{3} - 9 \, a b^{4} + 21 \, {\left(8 \, a^{4} b + 19 \, a^{3} b^{2} + 14 \, 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(8 \, a^{4} b + 19 \, a^{3} b^{2} + 14 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{4} b - 5 \, a^{3} b^{2} - 22 \, 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(8 \, a^{4} b - 5 \, a^{3} b^{2} - 22 \, a^{2} b^{3} - 9 \, a b^{4}\right)} \cosh\left(d x + c\right)^{3} - 2 \, {\left(8 \, a^{4} b - 5 \, a^{3} b^{2} - 22 \, a^{2} b^{3} - 9 \, a b^{4} - 35 \, {\left(8 \, a^{4} b + 19 \, a^{3} b^{2} + 14 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{4} - 10 \, {\left(8 \, a^{4} b - 5 \, a^{3} b^{2} - 22 \, 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(8 \, a^{4} b + 19 \, a^{3} b^{2} + 14 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(8 \, a^{4} b - 5 \, a^{3} b^{2} - 22 \, a^{2} b^{3} - 9 \, a b^{4}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(8 \, a^{4} b - 5 \, a^{3} b^{2} - 22 \, 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(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)^{8} + 8 \, {\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) \sinh\left(d x + c\right)^{7} + {\left(8 \, a^{4} + 24 \, a^{3} b + 27 \, a^{2} b^{2} + 14 \, a b^{3} + 3 \, b^{4}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(8 \, a^{4} + 8 \, a^{3} b - 5 \, a^{2} b^{2} - 8 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(8 \, a^{4} + 8 \, a^{3} b - 5 \, a^{2} b^{2} - 8 \, a b^{3} - 3 \, b^{4} + 7 \, {\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)^{6} + 8 \, {\left(7 \, {\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} + 3 \, {\left(8 \, a^{4} + 8 \, a^{3} b - 5 \, 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)^{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(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} + 24 \, a^{4} + 8 \, a^{3} b + 17 \, a^{2} b^{2} + 18 \, a b^{3} + 9 \, b^{4} + 30 \, {\left(8 \, a^{4} + 8 \, a^{3} b - 5 \, 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)^{4} + 8 \, a^{4} + 24 \, a^{3} b + 27 \, a^{2} b^{2} + 14 \, a b^{3} + 3 \, b^{4} + 8 \, {\left(7 \, {\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)^{5} + 10 \, {\left(8 \, a^{4} + 8 \, a^{3} b - 5 \, a^{2} b^{2} - 8 \, 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(8 \, a^{4} + 8 \, a^{3} b - 5 \, a^{2} b^{2} - 8 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\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)^{6} + 15 \, {\left(8 \, a^{4} + 8 \, a^{3} b - 5 \, a^{2} b^{2} - 8 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 8 \, a^{4} + 8 \, a^{3} b - 5 \, a^{2} b^{2} - 8 \, 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(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)^{7} + 3 \, {\left(8 \, a^{4} + 8 \, a^{3} b - 5 \, a^{2} b^{2} - 8 \, 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(8 \, a^{4} + 8 \, a^{3} b - 5 \, 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)\right)} \sqrt{a^{2} + a b} \arctan\left(\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(3 \, a - b\right)} \cosh\left(d x + c\right) + {\left(3 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} + 3 \, a - b\right)} \sinh\left(d x + c\right)}{2 \, \sqrt{a^{2} + a b}}\right) + {\left({\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)^{8} + 8 \, {\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) \sinh\left(d x + c\right)^{7} + {\left(8 \, a^{4} + 24 \, a^{3} b + 27 \, a^{2} b^{2} + 14 \, a b^{3} + 3 \, b^{4}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(8 \, a^{4} + 8 \, a^{3} b - 5 \, a^{2} b^{2} - 8 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(8 \, a^{4} + 8 \, a^{3} b - 5 \, a^{2} b^{2} - 8 \, a b^{3} - 3 \, b^{4} + 7 \, {\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)^{6} + 8 \, {\left(7 \, {\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} + 3 \, {\left(8 \, a^{4} + 8 \, a^{3} b - 5 \, 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)^{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(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} + 24 \, a^{4} + 8 \, a^{3} b + 17 \, a^{2} b^{2} + 18 \, a b^{3} + 9 \, b^{4} + 30 \, {\left(8 \, a^{4} + 8 \, a^{3} b - 5 \, 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)^{4} + 8 \, a^{4} + 24 \, a^{3} b + 27 \, a^{2} b^{2} + 14 \, a b^{3} + 3 \, b^{4} + 8 \, {\left(7 \, {\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)^{5} + 10 \, {\left(8 \, a^{4} + 8 \, a^{3} b - 5 \, a^{2} b^{2} - 8 \, 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(8 \, a^{4} + 8 \, a^{3} b - 5 \, a^{2} b^{2} - 8 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\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)^{6} + 15 \, {\left(8 \, a^{4} + 8 \, a^{3} b - 5 \, a^{2} b^{2} - 8 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 8 \, a^{4} + 8 \, a^{3} b - 5 \, a^{2} b^{2} - 8 \, 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(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)^{7} + 3 \, {\left(8 \, a^{4} + 8 \, a^{3} b - 5 \, a^{2} b^{2} - 8 \, 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(8 \, a^{4} + 8 \, a^{3} b - 5 \, 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)\right)} \sqrt{a^{2} + a b} \arctan\left(\frac{\sqrt{a^{2} + a b} {\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right)}}{2 \, a}\right) - 2 \, {\left(8 \, a^{4} b + 19 \, a^{3} b^{2} + 14 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(d x + c\right) + 2 \, {\left(7 \, {\left(8 \, a^{4} b + 19 \, a^{3} b^{2} + 14 \, a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{6} - 8 \, a^{4} b - 19 \, a^{3} b^{2} - 14 \, a^{2} b^{3} - 3 \, a b^{4} + 5 \, {\left(8 \, a^{4} b - 5 \, a^{3} b^{2} - 22 \, a^{2} b^{3} - 9 \, a b^{4}\right)} \cosh\left(d x + c\right)^{4} - 3 \, {\left(8 \, a^{4} b - 5 \, a^{3} b^{2} - 22 \, 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({\left(a^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{8} + 3 \, a^{7} b + 2 \, a^{6} b^{2} - 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^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{8} + 3 \, a^{7} b + 2 \, a^{6} b^{2} - 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(3 \, a^{8} + 7 \, a^{7} b + 6 \, a^{6} b^{2} + 6 \, a^{5} b^{3} + 7 \, a^{4} b^{4} + 3 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{8} + 3 \, a^{7} b + 2 \, a^{6} b^{2} - 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^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 30 \, {\left(a^{8} + 3 \, a^{7} b + 2 \, a^{6} b^{2} - 2 \, a^{5} b^{3} - 3 \, a^{4} b^{4} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{8} + 7 \, a^{7} b + 6 \, a^{6} b^{2} + 6 \, a^{5} b^{3} + 7 \, a^{4} b^{4} + 3 \, a^{3} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{8} + 3 \, a^{7} b + 2 \, a^{6} b^{2} - 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^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{8} + 3 \, a^{7} b + 2 \, a^{6} b^{2} - 2 \, a^{5} b^{3} - 3 \, a^{4} b^{4} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{8} + 7 \, a^{7} b + 6 \, a^{6} b^{2} + 6 \, a^{5} b^{3} + 7 \, 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^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{8} + 3 \, a^{7} b + 2 \, a^{6} b^{2} - 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(3 \, a^{8} + 7 \, a^{7} b + 6 \, a^{6} b^{2} + 6 \, a^{5} b^{3} + 7 \, a^{4} b^{4} + 3 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{8} + 3 \, a^{7} b + 2 \, a^{6} b^{2} - 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^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} d + 8 \, {\left({\left(a^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{8} + 3 \, a^{7} b + 2 \, a^{6} b^{2} - 2 \, a^{5} b^{3} - 3 \, a^{4} b^{4} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{8} + 7 \, a^{7} b + 6 \, a^{6} b^{2} + 6 \, a^{5} b^{3} + 7 \, a^{4} b^{4} + 3 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{8} + 3 \, a^{7} b + 2 \, a^{6} b^{2} - 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 + 19*a^3*b^2 + 14*a^2*b^3 + 3*a*b^4)*cosh(d*x + c)^7 + 28*(8*a^4*b + 19*a^3*b^2 + 14*a^2*b^3 + 3*a*b^4)*cosh(d*x + c)*sinh(d*x + c)^6 + 4*(8*a^4*b + 19*a^3*b^2 + 14*a^2*b^3 + 3*a*b^4)*sinh(d*x + c)^7 + 4*(8*a^4*b - 5*a^3*b^2 - 22*a^2*b^3 - 9*a*b^4)*cosh(d*x + c)^5 + 4*(8*a^4*b - 5*a^3*b^2 - 22*a^2*b^3 - 9*a*b^4 + 21*(8*a^4*b + 19*a^3*b^2 + 14*a^2*b^3 + 3*a*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 20*(7*(8*a^4*b + 19*a^3*b^2 + 14*a^2*b^3 + 3*a*b^4)*cosh(d*x + c)^3 + (8*a^4*b - 5*a^3*b^2 - 22*a^2*b^3 - 9*a*b^4)*cosh(d*x + c))*sinh(d*x + c)^4 - 4*(8*a^4*b - 5*a^3*b^2 - 22*a^2*b^3 - 9*a*b^4)*cosh(d*x + c)^3 - 4*(8*a^4*b - 5*a^3*b^2 - 22*a^2*b^3 - 9*a*b^4 - 35*(8*a^4*b + 19*a^3*b^2 + 14*a^2*b^3 + 3*a*b^4)*cosh(d*x + c)^4 - 10*(8*a^4*b - 5*a^3*b^2 - 22*a^2*b^3 - 9*a*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 4*(21*(8*a^4*b + 19*a^3*b^2 + 14*a^2*b^3 + 3*a*b^4)*cosh(d*x + c)^5 + 10*(8*a^4*b - 5*a^3*b^2 - 22*a^2*b^3 - 9*a*b^4)*cosh(d*x + c)^3 - 3*(8*a^4*b - 5*a^3*b^2 - 22*a^2*b^3 - 9*a*b^4)*cosh(d*x + c))*sinh(d*x + c)^2 - ((8*a^4 + 24*a^3*b + 27*a^2*b^2 + 14*a*b^3 + 3*b^4)*cosh(d*x + c)^8 + 8*(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)^7 + (8*a^4 + 24*a^3*b + 27*a^2*b^2 + 14*a*b^3 + 3*b^4)*sinh(d*x + c)^8 + 4*(8*a^4 + 8*a^3*b - 5*a^2*b^2 - 8*a*b^3 - 3*b^4)*cosh(d*x + c)^6 + 4*(8*a^4 + 8*a^3*b - 5*a^2*b^2 - 8*a*b^3 - 3*b^4 + 7*(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)^6 + 8*(7*(8*a^4 + 24*a^3*b + 27*a^2*b^2 + 14*a*b^3 + 3*b^4)*cosh(d*x + c)^3 + 3*(8*a^4 + 8*a^3*b - 5*a^2*b^2 - 8*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*(8*a^4 + 24*a^3*b + 27*a^2*b^2 + 14*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*(8*a^4 + 8*a^3*b - 5*a^2*b^2 - 8*a*b^3 - 3*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*a^4 + 24*a^3*b + 27*a^2*b^2 + 14*a*b^3 + 3*b^4 + 8*(7*(8*a^4 + 24*a^3*b + 27*a^2*b^2 + 14*a*b^3 + 3*b^4)*cosh(d*x + c)^5 + 10*(8*a^4 + 8*a^3*b - 5*a^2*b^2 - 8*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*(8*a^4 + 8*a^3*b - 5*a^2*b^2 - 8*a*b^3 - 3*b^4)*cosh(d*x + c)^2 + 4*(7*(8*a^4 + 24*a^3*b + 27*a^2*b^2 + 14*a*b^3 + 3*b^4)*cosh(d*x + c)^6 + 15*(8*a^4 + 8*a^3*b - 5*a^2*b^2 - 8*a*b^3 - 3*b^4)*cosh(d*x + c)^4 + 8*a^4 + 8*a^3*b - 5*a^2*b^2 - 8*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*((8*a^4 + 24*a^3*b + 27*a^2*b^2 + 14*a*b^3 + 3*b^4)*cosh(d*x + c)^7 + 3*(8*a^4 + 8*a^3*b - 5*a^2*b^2 - 8*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 + (8*a^4 + 8*a^3*b - 5*a^2*b^2 - 8*a*b^3 - 3*b^4)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-a^2 - a*b)*log(((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*(3*a + b)*cosh(d*x + c)^2 + 2*(3*(a + b)*cosh(d*x + c)^2 - 3*a - b)*sinh(d*x + c)^2 + 4*((a + b)*cosh(d*x + c)^3 - (3*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^2 - a*b) + a + b)/((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)) - 4*(8*a^4*b + 19*a^3*b^2 + 14*a^2*b^3 + 3*a*b^4)*cosh(d*x + c) + 4*(7*(8*a^4*b + 19*a^3*b^2 + 14*a^2*b^3 + 3*a*b^4)*cosh(d*x + c)^6 - 8*a^4*b - 19*a^3*b^2 - 14*a^2*b^3 - 3*a*b^4 + 5*(8*a^4*b - 5*a^3*b^2 - 22*a^2*b^3 - 9*a*b^4)*cosh(d*x + c)^4 - 3*(8*a^4*b - 5*a^3*b^2 - 22*a^2*b^3 - 9*a*b^4)*cosh(d*x + c)^2)*sinh(d*x + c))/((a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)^8 + 8*(a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*d*sinh(d*x + c)^8 + 4*(a^8 + 3*a^7*b + 2*a^6*b^2 - 2*a^5*b^3 - 3*a^4*b^4 - a^3*b^5)*d*cosh(d*x + c)^6 + 4*(7*(a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)^2 + (a^8 + 3*a^7*b + 2*a^6*b^2 - 2*a^5*b^3 - 3*a^4*b^4 - a^3*b^5)*d)*sinh(d*x + c)^6 + 2*(3*a^8 + 7*a^7*b + 6*a^6*b^2 + 6*a^5*b^3 + 7*a^4*b^4 + 3*a^3*b^5)*d*cosh(d*x + c)^4 + 8*(7*(a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)^3 + 3*(a^8 + 3*a^7*b + 2*a^6*b^2 - 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^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)^4 + 30*(a^8 + 3*a^7*b + 2*a^6*b^2 - 2*a^5*b^3 - 3*a^4*b^4 - a^3*b^5)*d*cosh(d*x + c)^2 + (3*a^8 + 7*a^7*b + 6*a^6*b^2 + 6*a^5*b^3 + 7*a^4*b^4 + 3*a^3*b^5)*d)*sinh(d*x + c)^4 + 4*(a^8 + 3*a^7*b + 2*a^6*b^2 - 2*a^5*b^3 - 3*a^4*b^4 - a^3*b^5)*d*cosh(d*x + c)^2 + 8*(7*(a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)^5 + 10*(a^8 + 3*a^7*b + 2*a^6*b^2 - 2*a^5*b^3 - 3*a^4*b^4 - a^3*b^5)*d*cosh(d*x + c)^3 + (3*a^8 + 7*a^7*b + 6*a^6*b^2 + 6*a^5*b^3 + 7*a^4*b^4 + 3*a^3*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)^6 + 15*(a^8 + 3*a^7*b + 2*a^6*b^2 - 2*a^5*b^3 - 3*a^4*b^4 - a^3*b^5)*d*cosh(d*x + c)^4 + 3*(3*a^8 + 7*a^7*b + 6*a^6*b^2 + 6*a^5*b^3 + 7*a^4*b^4 + 3*a^3*b^5)*d*cosh(d*x + c)^2 + (a^8 + 3*a^7*b + 2*a^6*b^2 - 2*a^5*b^3 - 3*a^4*b^4 - a^3*b^5)*d)*sinh(d*x + c)^2 + (a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*d + 8*((a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)^7 + 3*(a^8 + 3*a^7*b + 2*a^6*b^2 - 2*a^5*b^3 - 3*a^4*b^4 - a^3*b^5)*d*cosh(d*x + c)^5 + (3*a^8 + 7*a^7*b + 6*a^6*b^2 + 6*a^5*b^3 + 7*a^4*b^4 + 3*a^3*b^5)*d*cosh(d*x + c)^3 + (a^8 + 3*a^7*b + 2*a^6*b^2 - 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 + 19*a^3*b^2 + 14*a^2*b^3 + 3*a*b^4)*cosh(d*x + c)^7 + 14*(8*a^4*b + 19*a^3*b^2 + 14*a^2*b^3 + 3*a*b^4)*cosh(d*x + c)*sinh(d*x + c)^6 + 2*(8*a^4*b + 19*a^3*b^2 + 14*a^2*b^3 + 3*a*b^4)*sinh(d*x + c)^7 + 2*(8*a^4*b - 5*a^3*b^2 - 22*a^2*b^3 - 9*a*b^4)*cosh(d*x + c)^5 + 2*(8*a^4*b - 5*a^3*b^2 - 22*a^2*b^3 - 9*a*b^4 + 21*(8*a^4*b + 19*a^3*b^2 + 14*a^2*b^3 + 3*a*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 10*(7*(8*a^4*b + 19*a^3*b^2 + 14*a^2*b^3 + 3*a*b^4)*cosh(d*x + c)^3 + (8*a^4*b - 5*a^3*b^2 - 22*a^2*b^3 - 9*a*b^4)*cosh(d*x + c))*sinh(d*x + c)^4 - 2*(8*a^4*b - 5*a^3*b^2 - 22*a^2*b^3 - 9*a*b^4)*cosh(d*x + c)^3 - 2*(8*a^4*b - 5*a^3*b^2 - 22*a^2*b^3 - 9*a*b^4 - 35*(8*a^4*b + 19*a^3*b^2 + 14*a^2*b^3 + 3*a*b^4)*cosh(d*x + c)^4 - 10*(8*a^4*b - 5*a^3*b^2 - 22*a^2*b^3 - 9*a*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 2*(21*(8*a^4*b + 19*a^3*b^2 + 14*a^2*b^3 + 3*a*b^4)*cosh(d*x + c)^5 + 10*(8*a^4*b - 5*a^3*b^2 - 22*a^2*b^3 - 9*a*b^4)*cosh(d*x + c)^3 - 3*(8*a^4*b - 5*a^3*b^2 - 22*a^2*b^3 - 9*a*b^4)*cosh(d*x + c))*sinh(d*x + c)^2 + ((8*a^4 + 24*a^3*b + 27*a^2*b^2 + 14*a*b^3 + 3*b^4)*cosh(d*x + c)^8 + 8*(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)^7 + (8*a^4 + 24*a^3*b + 27*a^2*b^2 + 14*a*b^3 + 3*b^4)*sinh(d*x + c)^8 + 4*(8*a^4 + 8*a^3*b - 5*a^2*b^2 - 8*a*b^3 - 3*b^4)*cosh(d*x + c)^6 + 4*(8*a^4 + 8*a^3*b - 5*a^2*b^2 - 8*a*b^3 - 3*b^4 + 7*(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)^6 + 8*(7*(8*a^4 + 24*a^3*b + 27*a^2*b^2 + 14*a*b^3 + 3*b^4)*cosh(d*x + c)^3 + 3*(8*a^4 + 8*a^3*b - 5*a^2*b^2 - 8*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*(8*a^4 + 24*a^3*b + 27*a^2*b^2 + 14*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*(8*a^4 + 8*a^3*b - 5*a^2*b^2 - 8*a*b^3 - 3*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*a^4 + 24*a^3*b + 27*a^2*b^2 + 14*a*b^3 + 3*b^4 + 8*(7*(8*a^4 + 24*a^3*b + 27*a^2*b^2 + 14*a*b^3 + 3*b^4)*cosh(d*x + c)^5 + 10*(8*a^4 + 8*a^3*b - 5*a^2*b^2 - 8*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*(8*a^4 + 8*a^3*b - 5*a^2*b^2 - 8*a*b^3 - 3*b^4)*cosh(d*x + c)^2 + 4*(7*(8*a^4 + 24*a^3*b + 27*a^2*b^2 + 14*a*b^3 + 3*b^4)*cosh(d*x + c)^6 + 15*(8*a^4 + 8*a^3*b - 5*a^2*b^2 - 8*a*b^3 - 3*b^4)*cosh(d*x + c)^4 + 8*a^4 + 8*a^3*b - 5*a^2*b^2 - 8*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*((8*a^4 + 24*a^3*b + 27*a^2*b^2 + 14*a*b^3 + 3*b^4)*cosh(d*x + c)^7 + 3*(8*a^4 + 8*a^3*b - 5*a^2*b^2 - 8*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 + (8*a^4 + 8*a^3*b - 5*a^2*b^2 - 8*a*b^3 - 3*b^4)*cosh(d*x + c))*sinh(d*x + c))*sqrt(a^2 + a*b)*arctan(1/2*((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 + (3*a - b)*cosh(d*x + c) + (3*(a + b)*cosh(d*x + c)^2 + 3*a - b)*sinh(d*x + c))/sqrt(a^2 + a*b)) + ((8*a^4 + 24*a^3*b + 27*a^2*b^2 + 14*a*b^3 + 3*b^4)*cosh(d*x + c)^8 + 8*(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)^7 + (8*a^4 + 24*a^3*b + 27*a^2*b^2 + 14*a*b^3 + 3*b^4)*sinh(d*x + c)^8 + 4*(8*a^4 + 8*a^3*b - 5*a^2*b^2 - 8*a*b^3 - 3*b^4)*cosh(d*x + c)^6 + 4*(8*a^4 + 8*a^3*b - 5*a^2*b^2 - 8*a*b^3 - 3*b^4 + 7*(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)^6 + 8*(7*(8*a^4 + 24*a^3*b + 27*a^2*b^2 + 14*a*b^3 + 3*b^4)*cosh(d*x + c)^3 + 3*(8*a^4 + 8*a^3*b - 5*a^2*b^2 - 8*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*(8*a^4 + 24*a^3*b + 27*a^2*b^2 + 14*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*(8*a^4 + 8*a^3*b - 5*a^2*b^2 - 8*a*b^3 - 3*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*a^4 + 24*a^3*b + 27*a^2*b^2 + 14*a*b^3 + 3*b^4 + 8*(7*(8*a^4 + 24*a^3*b + 27*a^2*b^2 + 14*a*b^3 + 3*b^4)*cosh(d*x + c)^5 + 10*(8*a^4 + 8*a^3*b - 5*a^2*b^2 - 8*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*(8*a^4 + 8*a^3*b - 5*a^2*b^2 - 8*a*b^3 - 3*b^4)*cosh(d*x + c)^2 + 4*(7*(8*a^4 + 24*a^3*b + 27*a^2*b^2 + 14*a*b^3 + 3*b^4)*cosh(d*x + c)^6 + 15*(8*a^4 + 8*a^3*b - 5*a^2*b^2 - 8*a*b^3 - 3*b^4)*cosh(d*x + c)^4 + 8*a^4 + 8*a^3*b - 5*a^2*b^2 - 8*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*((8*a^4 + 24*a^3*b + 27*a^2*b^2 + 14*a*b^3 + 3*b^4)*cosh(d*x + c)^7 + 3*(8*a^4 + 8*a^3*b - 5*a^2*b^2 - 8*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 + (8*a^4 + 8*a^3*b - 5*a^2*b^2 - 8*a*b^3 - 3*b^4)*cosh(d*x + c))*sinh(d*x + c))*sqrt(a^2 + a*b)*arctan(1/2*sqrt(a^2 + a*b)*(cosh(d*x + c) + sinh(d*x + c))/a) - 2*(8*a^4*b + 19*a^3*b^2 + 14*a^2*b^3 + 3*a*b^4)*cosh(d*x + c) + 2*(7*(8*a^4*b + 19*a^3*b^2 + 14*a^2*b^3 + 3*a*b^4)*cosh(d*x + c)^6 - 8*a^4*b - 19*a^3*b^2 - 14*a^2*b^3 - 3*a*b^4 + 5*(8*a^4*b - 5*a^3*b^2 - 22*a^2*b^3 - 9*a*b^4)*cosh(d*x + c)^4 - 3*(8*a^4*b - 5*a^3*b^2 - 22*a^2*b^3 - 9*a*b^4)*cosh(d*x + c)^2)*sinh(d*x + c))/((a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)^8 + 8*(a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*d*sinh(d*x + c)^8 + 4*(a^8 + 3*a^7*b + 2*a^6*b^2 - 2*a^5*b^3 - 3*a^4*b^4 - a^3*b^5)*d*cosh(d*x + c)^6 + 4*(7*(a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)^2 + (a^8 + 3*a^7*b + 2*a^6*b^2 - 2*a^5*b^3 - 3*a^4*b^4 - a^3*b^5)*d)*sinh(d*x + c)^6 + 2*(3*a^8 + 7*a^7*b + 6*a^6*b^2 + 6*a^5*b^3 + 7*a^4*b^4 + 3*a^3*b^5)*d*cosh(d*x + c)^4 + 8*(7*(a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)^3 + 3*(a^8 + 3*a^7*b + 2*a^6*b^2 - 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^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)^4 + 30*(a^8 + 3*a^7*b + 2*a^6*b^2 - 2*a^5*b^3 - 3*a^4*b^4 - a^3*b^5)*d*cosh(d*x + c)^2 + (3*a^8 + 7*a^7*b + 6*a^6*b^2 + 6*a^5*b^3 + 7*a^4*b^4 + 3*a^3*b^5)*d)*sinh(d*x + c)^4 + 4*(a^8 + 3*a^7*b + 2*a^6*b^2 - 2*a^5*b^3 - 3*a^4*b^4 - a^3*b^5)*d*cosh(d*x + c)^2 + 8*(7*(a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)^5 + 10*(a^8 + 3*a^7*b + 2*a^6*b^2 - 2*a^5*b^3 - 3*a^4*b^4 - a^3*b^5)*d*cosh(d*x + c)^3 + (3*a^8 + 7*a^7*b + 6*a^6*b^2 + 6*a^5*b^3 + 7*a^4*b^4 + 3*a^3*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)^6 + 15*(a^8 + 3*a^7*b + 2*a^6*b^2 - 2*a^5*b^3 - 3*a^4*b^4 - a^3*b^5)*d*cosh(d*x + c)^4 + 3*(3*a^8 + 7*a^7*b + 6*a^6*b^2 + 6*a^5*b^3 + 7*a^4*b^4 + 3*a^3*b^5)*d*cosh(d*x + c)^2 + (a^8 + 3*a^7*b + 2*a^6*b^2 - 2*a^5*b^3 - 3*a^4*b^4 - a^3*b^5)*d)*sinh(d*x + c)^2 + (a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*d + 8*((a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)^7 + 3*(a^8 + 3*a^7*b + 2*a^6*b^2 - 2*a^5*b^3 - 3*a^4*b^4 - a^3*b^5)*d*cosh(d*x + c)^5 + (3*a^8 + 7*a^7*b + 6*a^6*b^2 + 6*a^5*b^3 + 7*a^4*b^4 + 3*a^3*b^5)*d*cosh(d*x + c)^3 + (a^8 + 3*a^7*b + 2*a^6*b^2 - 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
128,1,5840,0,0.544122," ","integrate(sech(d*x+c)^2/(a+b*tanh(d*x+c)^2)^3,x, algorithm=""fricas"")","\left[-\frac{4 \, {\left(5 \, a^{4} b - a^{3} b^{2} - 9 \, a^{2} b^{3} - 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{6} + 24 \, {\left(5 \, a^{4} b - a^{3} b^{2} - 9 \, a^{2} b^{3} - 3 \, a b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + 4 \, {\left(5 \, a^{4} b - a^{3} b^{2} - 9 \, a^{2} b^{3} - 3 \, a b^{4}\right)} \sinh\left(d x + c\right)^{6} + 20 \, a^{4} b + 52 \, a^{3} b^{2} + 44 \, a^{2} b^{3} + 12 \, a b^{4} + 4 \, {\left(15 \, a^{4} b - a^{3} b^{2} + 9 \, a^{2} b^{3} + 9 \, a b^{4}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(15 \, a^{4} b - a^{3} b^{2} + 9 \, a^{2} b^{3} + 9 \, a b^{4} + 15 \, {\left(5 \, a^{4} b - a^{3} b^{2} - 9 \, 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(5 \, a^{4} b - a^{3} b^{2} - 9 \, a^{2} b^{3} - 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(15 \, a^{4} b - a^{3} b^{2} + 9 \, 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(15 \, a^{4} b + 13 \, a^{3} b^{2} - 11 \, a^{2} b^{3} - 9 \, a b^{4}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(15 \, a^{4} b + 13 \, a^{3} b^{2} - 11 \, a^{2} b^{3} - 9 \, a b^{4} + 15 \, {\left(5 \, a^{4} b - a^{3} b^{2} - 9 \, a^{2} b^{3} - 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{4} + 6 \, {\left(15 \, a^{4} b - a^{3} b^{2} + 9 \, 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({\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{4} + 2 \, a^{3} b - 2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(a^{4} + 2 \, a^{3} b - 2 \, a b^{3} - b^{4} + 7 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, 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)^{6} + 8 \, {\left(7 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{4} + 2 \, a^{3} b - 2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(3 \, a^{4} + 4 \, a^{3} b + 2 \, a^{2} b^{2} + 4 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{4} + 3 \, a^{4} + 4 \, a^{3} b + 2 \, a^{2} b^{2} + 4 \, a b^{3} + 3 \, b^{4} + 30 \, {\left(a^{4} + 2 \, a^{3} b - 2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4} + 8 \, {\left(7 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{4} + 2 \, a^{3} b - 2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{4} + 4 \, a^{3} b + 2 \, 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)^{3} + 4 \, {\left(a^{4} + 2 \, a^{3} b - 2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{4} + 2 \, a^{3} b - 2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{4} + a^{4} + 2 \, a^{3} b - 2 \, a b^{3} - b^{4} + 3 \, {\left(3 \, a^{4} + 4 \, a^{3} b + 2 \, 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)^{2} + 8 \, {\left({\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{4} + 2 \, a^{3} b - 2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{4} + 4 \, a^{3} b + 2 \, a^{2} b^{2} + 4 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{4} + 2 \, a^{3} b - 2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-a b} \log\left(\frac{{\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) \sinh\left(d x + c\right)^{3} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{2} + a^{2} - 6 \, a b + b^{2} + 4 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} - b^{2}\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)^{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} + a - b\right)} \sqrt{-a b}}{{\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) + 8 \, {\left(3 \, {\left(5 \, a^{4} b - a^{3} b^{2} - 9 \, a^{2} b^{3} - 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(15 \, a^{4} b - a^{3} b^{2} + 9 \, a^{2} b^{3} + 9 \, a b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(15 \, a^{4} b + 13 \, a^{3} b^{2} - 11 \, 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^{7} b + 4 \, a^{6} b^{2} + 6 \, a^{5} b^{3} + 4 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{7} b + 4 \, a^{6} b^{2} + 6 \, a^{5} b^{3} + 4 \, 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^{7} b + 4 \, a^{6} b^{2} + 6 \, a^{5} b^{3} + 4 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{7} b + 2 \, a^{6} b^{2} - 2 \, a^{4} b^{4} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{7} b + 4 \, a^{6} b^{2} + 6 \, a^{5} b^{3} + 4 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{7} b + 2 \, a^{6} b^{2} - 2 \, a^{4} b^{4} - a^{3} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(3 \, a^{7} b + 4 \, a^{6} b^{2} + 2 \, a^{5} b^{3} + 4 \, a^{4} b^{4} + 3 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{7} b + 4 \, a^{6} b^{2} + 6 \, a^{5} b^{3} + 4 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{7} b + 2 \, a^{6} b^{2} - 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 \, {\left(a^{7} b + 4 \, a^{6} b^{2} + 6 \, a^{5} b^{3} + 4 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 30 \, {\left(a^{7} b + 2 \, a^{6} b^{2} - 2 \, a^{4} b^{4} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{7} b + 4 \, a^{6} b^{2} + 2 \, a^{5} b^{3} + 4 \, a^{4} b^{4} + 3 \, a^{3} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{7} b + 2 \, a^{6} b^{2} - 2 \, a^{4} b^{4} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a^{7} b + 4 \, a^{6} b^{2} + 6 \, a^{5} b^{3} + 4 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{7} b + 2 \, a^{6} b^{2} - 2 \, a^{4} b^{4} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{7} b + 4 \, a^{6} b^{2} + 2 \, a^{5} b^{3} + 4 \, 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^{7} b + 4 \, a^{6} b^{2} + 6 \, a^{5} b^{3} + 4 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{7} b + 2 \, a^{6} b^{2} - 2 \, a^{4} b^{4} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{7} b + 4 \, a^{6} b^{2} + 2 \, a^{5} b^{3} + 4 \, a^{4} b^{4} + 3 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{7} b + 2 \, a^{6} b^{2} - 2 \, a^{4} b^{4} - a^{3} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{7} b + 4 \, a^{6} b^{2} + 6 \, a^{5} b^{3} + 4 \, a^{4} b^{4} + a^{3} b^{5}\right)} d + 8 \, {\left({\left(a^{7} b + 4 \, a^{6} b^{2} + 6 \, a^{5} b^{3} + 4 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{7} b + 2 \, a^{6} b^{2} - 2 \, a^{4} b^{4} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{7} b + 4 \, a^{6} b^{2} + 2 \, a^{5} b^{3} + 4 \, a^{4} b^{4} + 3 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{7} b + 2 \, a^{6} b^{2} - 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^{4} b - a^{3} b^{2} - 9 \, a^{2} b^{3} - 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{6} + 12 \, {\left(5 \, a^{4} b - a^{3} b^{2} - 9 \, a^{2} b^{3} - 3 \, a b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + 2 \, {\left(5 \, a^{4} b - a^{3} b^{2} - 9 \, a^{2} b^{3} - 3 \, a b^{4}\right)} \sinh\left(d x + c\right)^{6} + 10 \, a^{4} b + 26 \, a^{3} b^{2} + 22 \, a^{2} b^{3} + 6 \, a b^{4} + 2 \, {\left(15 \, a^{4} b - a^{3} b^{2} + 9 \, a^{2} b^{3} + 9 \, a b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(15 \, a^{4} b - a^{3} b^{2} + 9 \, a^{2} b^{3} + 9 \, a b^{4} + 15 \, {\left(5 \, a^{4} b - a^{3} b^{2} - 9 \, 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(5 \, a^{4} b - a^{3} b^{2} - 9 \, a^{2} b^{3} - 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(15 \, a^{4} b - a^{3} b^{2} + 9 \, 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(15 \, a^{4} b + 13 \, a^{3} b^{2} - 11 \, a^{2} b^{3} - 9 \, a b^{4}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(15 \, a^{4} b + 13 \, a^{3} b^{2} - 11 \, a^{2} b^{3} - 9 \, a b^{4} + 15 \, {\left(5 \, a^{4} b - a^{3} b^{2} - 9 \, a^{2} b^{3} - 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{4} + 6 \, {\left(15 \, a^{4} b - a^{3} b^{2} + 9 \, 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({\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{4} + 2 \, a^{3} b - 2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(a^{4} + 2 \, a^{3} b - 2 \, a b^{3} - b^{4} + 7 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, 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)^{6} + 8 \, {\left(7 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{4} + 2 \, a^{3} b - 2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(3 \, a^{4} + 4 \, a^{3} b + 2 \, a^{2} b^{2} + 4 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{4} + 3 \, a^{4} + 4 \, a^{3} b + 2 \, a^{2} b^{2} + 4 \, a b^{3} + 3 \, b^{4} + 30 \, {\left(a^{4} + 2 \, a^{3} b - 2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4} + 8 \, {\left(7 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{4} + 2 \, a^{3} b - 2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{4} + 4 \, a^{3} b + 2 \, 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)^{3} + 4 \, {\left(a^{4} + 2 \, a^{3} b - 2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{4} + 2 \, a^{3} b - 2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{4} + a^{4} + 2 \, a^{3} b - 2 \, a b^{3} - b^{4} + 3 \, {\left(3 \, a^{4} + 4 \, a^{3} b + 2 \, 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)^{2} + 8 \, {\left({\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{4} + 2 \, a^{3} b - 2 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{4} + 4 \, a^{3} b + 2 \, a^{2} b^{2} + 4 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{4} + 2 \, a^{3} b - 2 \, a b^{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({\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} + a - b\right)} \sqrt{a b}}{2 \, a b}\right) + 4 \, {\left(3 \, {\left(5 \, a^{4} b - a^{3} b^{2} - 9 \, a^{2} b^{3} - 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(15 \, a^{4} b - a^{3} b^{2} + 9 \, a^{2} b^{3} + 9 \, a b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(15 \, a^{4} b + 13 \, a^{3} b^{2} - 11 \, 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^{7} b + 4 \, a^{6} b^{2} + 6 \, a^{5} b^{3} + 4 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{7} b + 4 \, a^{6} b^{2} + 6 \, a^{5} b^{3} + 4 \, 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^{7} b + 4 \, a^{6} b^{2} + 6 \, a^{5} b^{3} + 4 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{7} b + 2 \, a^{6} b^{2} - 2 \, a^{4} b^{4} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{7} b + 4 \, a^{6} b^{2} + 6 \, a^{5} b^{3} + 4 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{7} b + 2 \, a^{6} b^{2} - 2 \, a^{4} b^{4} - a^{3} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(3 \, a^{7} b + 4 \, a^{6} b^{2} + 2 \, a^{5} b^{3} + 4 \, a^{4} b^{4} + 3 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{7} b + 4 \, a^{6} b^{2} + 6 \, a^{5} b^{3} + 4 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{7} b + 2 \, a^{6} b^{2} - 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 \, {\left(a^{7} b + 4 \, a^{6} b^{2} + 6 \, a^{5} b^{3} + 4 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 30 \, {\left(a^{7} b + 2 \, a^{6} b^{2} - 2 \, a^{4} b^{4} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{7} b + 4 \, a^{6} b^{2} + 2 \, a^{5} b^{3} + 4 \, a^{4} b^{4} + 3 \, a^{3} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{7} b + 2 \, a^{6} b^{2} - 2 \, a^{4} b^{4} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a^{7} b + 4 \, a^{6} b^{2} + 6 \, a^{5} b^{3} + 4 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{7} b + 2 \, a^{6} b^{2} - 2 \, a^{4} b^{4} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{7} b + 4 \, a^{6} b^{2} + 2 \, a^{5} b^{3} + 4 \, 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^{7} b + 4 \, a^{6} b^{2} + 6 \, a^{5} b^{3} + 4 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{7} b + 2 \, a^{6} b^{2} - 2 \, a^{4} b^{4} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{7} b + 4 \, a^{6} b^{2} + 2 \, a^{5} b^{3} + 4 \, a^{4} b^{4} + 3 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{7} b + 2 \, a^{6} b^{2} - 2 \, a^{4} b^{4} - a^{3} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{7} b + 4 \, a^{6} b^{2} + 6 \, a^{5} b^{3} + 4 \, a^{4} b^{4} + a^{3} b^{5}\right)} d + 8 \, {\left({\left(a^{7} b + 4 \, a^{6} b^{2} + 6 \, a^{5} b^{3} + 4 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{7} b + 2 \, a^{6} b^{2} - 2 \, a^{4} b^{4} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{7} b + 4 \, a^{6} b^{2} + 2 \, a^{5} b^{3} + 4 \, a^{4} b^{4} + 3 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{7} b + 2 \, a^{6} b^{2} - 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^4*b - a^3*b^2 - 9*a^2*b^3 - 3*a*b^4)*cosh(d*x + c)^6 + 24*(5*a^4*b - a^3*b^2 - 9*a^2*b^3 - 3*a*b^4)*cosh(d*x + c)*sinh(d*x + c)^5 + 4*(5*a^4*b - a^3*b^2 - 9*a^2*b^3 - 3*a*b^4)*sinh(d*x + c)^6 + 20*a^4*b + 52*a^3*b^2 + 44*a^2*b^3 + 12*a*b^4 + 4*(15*a^4*b - a^3*b^2 + 9*a^2*b^3 + 9*a*b^4)*cosh(d*x + c)^4 + 4*(15*a^4*b - a^3*b^2 + 9*a^2*b^3 + 9*a*b^4 + 15*(5*a^4*b - a^3*b^2 - 9*a^2*b^3 - 3*a*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 16*(5*(5*a^4*b - a^3*b^2 - 9*a^2*b^3 - 3*a*b^4)*cosh(d*x + c)^3 + (15*a^4*b - a^3*b^2 + 9*a^2*b^3 + 9*a*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(15*a^4*b + 13*a^3*b^2 - 11*a^2*b^3 - 9*a*b^4)*cosh(d*x + c)^2 + 4*(15*a^4*b + 13*a^3*b^2 - 11*a^2*b^3 - 9*a*b^4 + 15*(5*a^4*b - a^3*b^2 - 9*a^2*b^3 - 3*a*b^4)*cosh(d*x + c)^4 + 6*(15*a^4*b - a^3*b^2 + 9*a^2*b^3 + 9*a*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 3*((a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*cosh(d*x + c)^8 + 8*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*cosh(d*x + c)*sinh(d*x + c)^7 + (a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*sinh(d*x + c)^8 + 4*(a^4 + 2*a^3*b - 2*a*b^3 - b^4)*cosh(d*x + c)^6 + 4*(a^4 + 2*a^3*b - 2*a*b^3 - b^4 + 7*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*cosh(d*x + c)^3 + 3*(a^4 + 2*a^3*b - 2*a*b^3 - b^4)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(3*a^4 + 4*a^3*b + 2*a^2*b^2 + 4*a*b^3 + 3*b^4)*cosh(d*x + c)^4 + 2*(35*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*cosh(d*x + c)^4 + 3*a^4 + 4*a^3*b + 2*a^2*b^2 + 4*a*b^3 + 3*b^4 + 30*(a^4 + 2*a^3*b - 2*a*b^3 - b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4 + 8*(7*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*cosh(d*x + c)^5 + 10*(a^4 + 2*a^3*b - 2*a*b^3 - b^4)*cosh(d*x + c)^3 + (3*a^4 + 4*a^3*b + 2*a^2*b^2 + 4*a*b^3 + 3*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(a^4 + 2*a^3*b - 2*a*b^3 - b^4)*cosh(d*x + c)^2 + 4*(7*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*cosh(d*x + c)^6 + 15*(a^4 + 2*a^3*b - 2*a*b^3 - b^4)*cosh(d*x + c)^4 + a^4 + 2*a^3*b - 2*a*b^3 - b^4 + 3*(3*a^4 + 4*a^3*b + 2*a^2*b^2 + 4*a*b^3 + 3*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*cosh(d*x + c)^7 + 3*(a^4 + 2*a^3*b - 2*a*b^3 - b^4)*cosh(d*x + c)^5 + (3*a^4 + 4*a^3*b + 2*a^2*b^2 + 4*a*b^3 + 3*b^4)*cosh(d*x + c)^3 + (a^4 + 2*a^3*b - 2*a*b^3 - b^4)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-a*b)*log(((a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 + 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 + 2*(a^2 - b^2)*cosh(d*x + c)^2 + 2*(3*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + a^2 - b^2)*sinh(d*x + c)^2 + a^2 - 6*a*b + b^2 + 4*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 + (a^2 - 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 + a - b)*sqrt(-a*b))/((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)) + 8*(3*(5*a^4*b - a^3*b^2 - 9*a^2*b^3 - 3*a*b^4)*cosh(d*x + c)^5 + 2*(15*a^4*b - a^3*b^2 + 9*a^2*b^3 + 9*a*b^4)*cosh(d*x + c)^3 + (15*a^4*b + 13*a^3*b^2 - 11*a^2*b^3 - 9*a*b^4)*cosh(d*x + c))*sinh(d*x + c))/((a^7*b + 4*a^6*b^2 + 6*a^5*b^3 + 4*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)^8 + 8*(a^7*b + 4*a^6*b^2 + 6*a^5*b^3 + 4*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^7*b + 4*a^6*b^2 + 6*a^5*b^3 + 4*a^4*b^4 + a^3*b^5)*d*sinh(d*x + c)^8 + 4*(a^7*b + 2*a^6*b^2 - 2*a^4*b^4 - a^3*b^5)*d*cosh(d*x + c)^6 + 4*(7*(a^7*b + 4*a^6*b^2 + 6*a^5*b^3 + 4*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)^2 + (a^7*b + 2*a^6*b^2 - 2*a^4*b^4 - a^3*b^5)*d)*sinh(d*x + c)^6 + 2*(3*a^7*b + 4*a^6*b^2 + 2*a^5*b^3 + 4*a^4*b^4 + 3*a^3*b^5)*d*cosh(d*x + c)^4 + 8*(7*(a^7*b + 4*a^6*b^2 + 6*a^5*b^3 + 4*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)^3 + 3*(a^7*b + 2*a^6*b^2 - 2*a^4*b^4 - a^3*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^7*b + 4*a^6*b^2 + 6*a^5*b^3 + 4*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)^4 + 30*(a^7*b + 2*a^6*b^2 - 2*a^4*b^4 - a^3*b^5)*d*cosh(d*x + c)^2 + (3*a^7*b + 4*a^6*b^2 + 2*a^5*b^3 + 4*a^4*b^4 + 3*a^3*b^5)*d)*sinh(d*x + c)^4 + 4*(a^7*b + 2*a^6*b^2 - 2*a^4*b^4 - a^3*b^5)*d*cosh(d*x + c)^2 + 8*(7*(a^7*b + 4*a^6*b^2 + 6*a^5*b^3 + 4*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)^5 + 10*(a^7*b + 2*a^6*b^2 - 2*a^4*b^4 - a^3*b^5)*d*cosh(d*x + c)^3 + (3*a^7*b + 4*a^6*b^2 + 2*a^5*b^3 + 4*a^4*b^4 + 3*a^3*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^7*b + 4*a^6*b^2 + 6*a^5*b^3 + 4*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)^6 + 15*(a^7*b + 2*a^6*b^2 - 2*a^4*b^4 - a^3*b^5)*d*cosh(d*x + c)^4 + 3*(3*a^7*b + 4*a^6*b^2 + 2*a^5*b^3 + 4*a^4*b^4 + 3*a^3*b^5)*d*cosh(d*x + c)^2 + (a^7*b + 2*a^6*b^2 - 2*a^4*b^4 - a^3*b^5)*d)*sinh(d*x + c)^2 + (a^7*b + 4*a^6*b^2 + 6*a^5*b^3 + 4*a^4*b^4 + a^3*b^5)*d + 8*((a^7*b + 4*a^6*b^2 + 6*a^5*b^3 + 4*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)^7 + 3*(a^7*b + 2*a^6*b^2 - 2*a^4*b^4 - a^3*b^5)*d*cosh(d*x + c)^5 + (3*a^7*b + 4*a^6*b^2 + 2*a^5*b^3 + 4*a^4*b^4 + 3*a^3*b^5)*d*cosh(d*x + c)^3 + (a^7*b + 2*a^6*b^2 - 2*a^4*b^4 - a^3*b^5)*d*cosh(d*x + c))*sinh(d*x + c)), -1/8*(2*(5*a^4*b - a^3*b^2 - 9*a^2*b^3 - 3*a*b^4)*cosh(d*x + c)^6 + 12*(5*a^4*b - a^3*b^2 - 9*a^2*b^3 - 3*a*b^4)*cosh(d*x + c)*sinh(d*x + c)^5 + 2*(5*a^4*b - a^3*b^2 - 9*a^2*b^3 - 3*a*b^4)*sinh(d*x + c)^6 + 10*a^4*b + 26*a^3*b^2 + 22*a^2*b^3 + 6*a*b^4 + 2*(15*a^4*b - a^3*b^2 + 9*a^2*b^3 + 9*a*b^4)*cosh(d*x + c)^4 + 2*(15*a^4*b - a^3*b^2 + 9*a^2*b^3 + 9*a*b^4 + 15*(5*a^4*b - a^3*b^2 - 9*a^2*b^3 - 3*a*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(5*(5*a^4*b - a^3*b^2 - 9*a^2*b^3 - 3*a*b^4)*cosh(d*x + c)^3 + (15*a^4*b - a^3*b^2 + 9*a^2*b^3 + 9*a*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 2*(15*a^4*b + 13*a^3*b^2 - 11*a^2*b^3 - 9*a*b^4)*cosh(d*x + c)^2 + 2*(15*a^4*b + 13*a^3*b^2 - 11*a^2*b^3 - 9*a*b^4 + 15*(5*a^4*b - a^3*b^2 - 9*a^2*b^3 - 3*a*b^4)*cosh(d*x + c)^4 + 6*(15*a^4*b - a^3*b^2 + 9*a^2*b^3 + 9*a*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - 3*((a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*cosh(d*x + c)^8 + 8*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*cosh(d*x + c)*sinh(d*x + c)^7 + (a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*sinh(d*x + c)^8 + 4*(a^4 + 2*a^3*b - 2*a*b^3 - b^4)*cosh(d*x + c)^6 + 4*(a^4 + 2*a^3*b - 2*a*b^3 - b^4 + 7*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*cosh(d*x + c)^3 + 3*(a^4 + 2*a^3*b - 2*a*b^3 - b^4)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(3*a^4 + 4*a^3*b + 2*a^2*b^2 + 4*a*b^3 + 3*b^4)*cosh(d*x + c)^4 + 2*(35*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*cosh(d*x + c)^4 + 3*a^4 + 4*a^3*b + 2*a^2*b^2 + 4*a*b^3 + 3*b^4 + 30*(a^4 + 2*a^3*b - 2*a*b^3 - b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4 + 8*(7*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*cosh(d*x + c)^5 + 10*(a^4 + 2*a^3*b - 2*a*b^3 - b^4)*cosh(d*x + c)^3 + (3*a^4 + 4*a^3*b + 2*a^2*b^2 + 4*a*b^3 + 3*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(a^4 + 2*a^3*b - 2*a*b^3 - b^4)*cosh(d*x + c)^2 + 4*(7*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*cosh(d*x + c)^6 + 15*(a^4 + 2*a^3*b - 2*a*b^3 - b^4)*cosh(d*x + c)^4 + a^4 + 2*a^3*b - 2*a*b^3 - b^4 + 3*(3*a^4 + 4*a^3*b + 2*a^2*b^2 + 4*a*b^3 + 3*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*cosh(d*x + c)^7 + 3*(a^4 + 2*a^3*b - 2*a*b^3 - b^4)*cosh(d*x + c)^5 + (3*a^4 + 4*a^3*b + 2*a^2*b^2 + 4*a*b^3 + 3*b^4)*cosh(d*x + c)^3 + (a^4 + 2*a^3*b - 2*a*b^3 - b^4)*cosh(d*x + c))*sinh(d*x + c))*sqrt(a*b)*arctan(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 + a - b)*sqrt(a*b)/(a*b)) + 4*(3*(5*a^4*b - a^3*b^2 - 9*a^2*b^3 - 3*a*b^4)*cosh(d*x + c)^5 + 2*(15*a^4*b - a^3*b^2 + 9*a^2*b^3 + 9*a*b^4)*cosh(d*x + c)^3 + (15*a^4*b + 13*a^3*b^2 - 11*a^2*b^3 - 9*a*b^4)*cosh(d*x + c))*sinh(d*x + c))/((a^7*b + 4*a^6*b^2 + 6*a^5*b^3 + 4*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)^8 + 8*(a^7*b + 4*a^6*b^2 + 6*a^5*b^3 + 4*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^7*b + 4*a^6*b^2 + 6*a^5*b^3 + 4*a^4*b^4 + a^3*b^5)*d*sinh(d*x + c)^8 + 4*(a^7*b + 2*a^6*b^2 - 2*a^4*b^4 - a^3*b^5)*d*cosh(d*x + c)^6 + 4*(7*(a^7*b + 4*a^6*b^2 + 6*a^5*b^3 + 4*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)^2 + (a^7*b + 2*a^6*b^2 - 2*a^4*b^4 - a^3*b^5)*d)*sinh(d*x + c)^6 + 2*(3*a^7*b + 4*a^6*b^2 + 2*a^5*b^3 + 4*a^4*b^4 + 3*a^3*b^5)*d*cosh(d*x + c)^4 + 8*(7*(a^7*b + 4*a^6*b^2 + 6*a^5*b^3 + 4*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)^3 + 3*(a^7*b + 2*a^6*b^2 - 2*a^4*b^4 - a^3*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^7*b + 4*a^6*b^2 + 6*a^5*b^3 + 4*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)^4 + 30*(a^7*b + 2*a^6*b^2 - 2*a^4*b^4 - a^3*b^5)*d*cosh(d*x + c)^2 + (3*a^7*b + 4*a^6*b^2 + 2*a^5*b^3 + 4*a^4*b^4 + 3*a^3*b^5)*d)*sinh(d*x + c)^4 + 4*(a^7*b + 2*a^6*b^2 - 2*a^4*b^4 - a^3*b^5)*d*cosh(d*x + c)^2 + 8*(7*(a^7*b + 4*a^6*b^2 + 6*a^5*b^3 + 4*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)^5 + 10*(a^7*b + 2*a^6*b^2 - 2*a^4*b^4 - a^3*b^5)*d*cosh(d*x + c)^3 + (3*a^7*b + 4*a^6*b^2 + 2*a^5*b^3 + 4*a^4*b^4 + 3*a^3*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^7*b + 4*a^6*b^2 + 6*a^5*b^3 + 4*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)^6 + 15*(a^7*b + 2*a^6*b^2 - 2*a^4*b^4 - a^3*b^5)*d*cosh(d*x + c)^4 + 3*(3*a^7*b + 4*a^6*b^2 + 2*a^5*b^3 + 4*a^4*b^4 + 3*a^3*b^5)*d*cosh(d*x + c)^2 + (a^7*b + 2*a^6*b^2 - 2*a^4*b^4 - a^3*b^5)*d)*sinh(d*x + c)^2 + (a^7*b + 4*a^6*b^2 + 6*a^5*b^3 + 4*a^4*b^4 + a^3*b^5)*d + 8*((a^7*b + 4*a^6*b^2 + 6*a^5*b^3 + 4*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)^7 + 3*(a^7*b + 2*a^6*b^2 - 2*a^4*b^4 - a^3*b^5)*d*cosh(d*x + c)^5 + (3*a^7*b + 4*a^6*b^2 + 2*a^5*b^3 + 4*a^4*b^4 + 3*a^3*b^5)*d*cosh(d*x + c)^3 + (a^7*b + 2*a^6*b^2 - 2*a^4*b^4 - a^3*b^5)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
129,1,6614,0,0.566550," ","integrate(sech(d*x+c)^3/(a+b*tanh(d*x+c)^2)^3,x, algorithm=""fricas"")","\left[\frac{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)^{7} + 28 \, {\left(4 \, a^{4} + 11 \, a^{3} b + 10 \, a^{2} b^{2} + 3 \, a b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + 4 \, {\left(4 \, a^{4} + 11 \, a^{3} b + 10 \, a^{2} b^{2} + 3 \, a b^{3}\right)} \sinh\left(d x + c\right)^{7} + 4 \, {\left(4 \, a^{4} + 3 \, a^{3} b - 10 \, a^{2} b^{2} - 9 \, a b^{3}\right)} \cosh\left(d x + c\right)^{5} + 4 \, {\left(4 \, a^{4} + 3 \, a^{3} b - 10 \, a^{2} b^{2} - 9 \, a b^{3} + 21 \, {\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}\right)} \sinh\left(d x + c\right)^{5} + 20 \, {\left(7 \, {\left(4 \, a^{4} + 11 \, a^{3} b + 10 \, a^{2} b^{2} + 3 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(4 \, a^{4} + 3 \, a^{3} b - 10 \, 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^{4} + 3 \, a^{3} b - 10 \, a^{2} b^{2} - 9 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(35 \, {\left(4 \, a^{4} + 11 \, a^{3} b + 10 \, a^{2} b^{2} + 3 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} - 4 \, a^{4} - 3 \, a^{3} b + 10 \, a^{2} b^{2} + 9 \, a b^{3} + 10 \, {\left(4 \, a^{4} + 3 \, a^{3} b - 10 \, 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(4 \, a^{4} + 11 \, a^{3} b + 10 \, a^{2} b^{2} + 3 \, a b^{3}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(4 \, a^{4} + 3 \, a^{3} b - 10 \, a^{2} b^{2} - 9 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(4 \, a^{4} + 3 \, a^{3} b - 10 \, 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(4 \, a^{3} + 11 \, a^{2} b + 10 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(4 \, a^{3} + 11 \, a^{2} b + 10 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(4 \, a^{3} + 11 \, a^{2} b + 10 \, a b^{2} + 3 \, b^{3}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(4 \, a^{3} + 3 \, a^{2} b - 4 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(4 \, a^{3} + 3 \, a^{2} b - 4 \, a b^{2} - 3 \, b^{3} + 7 \, {\left(4 \, a^{3} + 11 \, a^{2} b + 10 \, 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(4 \, a^{3} + 11 \, a^{2} b + 10 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(4 \, a^{3} + 3 \, a^{2} b - 4 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(12 \, a^{3} + a^{2} b + 6 \, a b^{2} + 9 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(4 \, a^{3} + 11 \, a^{2} b + 10 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 12 \, a^{3} + a^{2} b + 6 \, a b^{2} + 9 \, b^{3} + 30 \, {\left(4 \, a^{3} + 3 \, a^{2} b - 4 \, 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(4 \, a^{3} + 11 \, a^{2} b + 10 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(4 \, a^{3} + 3 \, a^{2} b - 4 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(12 \, a^{3} + a^{2} b + 6 \, a b^{2} + 9 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, a^{3} + 11 \, a^{2} b + 10 \, a b^{2} + 3 \, b^{3} + 4 \, {\left(4 \, a^{3} + 3 \, a^{2} b - 4 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(4 \, a^{3} + 11 \, a^{2} b + 10 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(4 \, a^{3} + 3 \, a^{2} b - 4 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 4 \, a^{3} + 3 \, a^{2} b - 4 \, a b^{2} - 3 \, b^{3} + 3 \, {\left(12 \, a^{3} + a^{2} b + 6 \, 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(4 \, a^{3} + 11 \, a^{2} b + 10 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(4 \, a^{3} + 3 \, a^{2} b - 4 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + {\left(12 \, a^{3} + a^{2} b + 6 \, a b^{2} + 9 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(4 \, a^{3} + 3 \, a^{2} b - 4 \, a b^{2} - 3 \, 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{{\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(3 \, a + b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} - 3 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(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) - 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^{2} - a b} + a + b}{{\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) - 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) + 4 \, {\left(7 \, {\left(4 \, a^{4} + 11 \, a^{3} b + 10 \, a^{2} b^{2} + 3 \, a b^{3}\right)} \cosh\left(d x + c\right)^{6} + 5 \, {\left(4 \, a^{4} + 3 \, a^{3} b - 10 \, a^{2} b^{2} - 9 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} - 4 \, a^{4} - 11 \, a^{3} b - 10 \, a^{2} b^{2} - 3 \, a b^{3} - 3 \, {\left(4 \, a^{4} + 3 \, a^{3} b - 10 \, 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({\left(a^{7} + 4 \, a^{6} b + 6 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{7} + 4 \, a^{6} b + 6 \, a^{5} b^{2} + 4 \, 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^{7} + 4 \, a^{6} b + 6 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + a^{3} b^{4}\right)} d \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{7} + 2 \, a^{6} b - 2 \, a^{4} b^{3} - a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{7} + 4 \, a^{6} b + 6 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{7} + 2 \, a^{6} b - 2 \, a^{4} b^{3} - a^{3} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(3 \, a^{7} + 4 \, a^{6} b + 2 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + 3 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{7} + 4 \, a^{6} b + 6 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{7} + 2 \, a^{6} b - 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 \, {\left(a^{7} + 4 \, a^{6} b + 6 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 30 \, {\left(a^{7} + 2 \, a^{6} b - 2 \, a^{4} b^{3} - a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{7} + 4 \, a^{6} b + 2 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + 3 \, a^{3} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{7} + 2 \, a^{6} b - 2 \, a^{4} b^{3} - a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a^{7} + 4 \, a^{6} b + 6 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{7} + 2 \, a^{6} b - 2 \, a^{4} b^{3} - a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{7} + 4 \, a^{6} b + 2 \, a^{5} b^{2} + 4 \, 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^{7} + 4 \, a^{6} b + 6 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{7} + 2 \, a^{6} b - 2 \, a^{4} b^{3} - a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{7} + 4 \, a^{6} b + 2 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + 3 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{7} + 2 \, a^{6} b - 2 \, a^{4} b^{3} - a^{3} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{7} + 4 \, a^{6} b + 6 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + a^{3} b^{4}\right)} d + 8 \, {\left({\left(a^{7} + 4 \, a^{6} b + 6 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{7} + 2 \, a^{6} b - 2 \, a^{4} b^{3} - a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{7} + 4 \, a^{6} b + 2 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + 3 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{7} + 2 \, a^{6} b - 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(4 \, a^{4} + 11 \, a^{3} b + 10 \, a^{2} b^{2} + 3 \, a b^{3}\right)} \cosh\left(d x + c\right)^{7} + 14 \, {\left(4 \, a^{4} + 11 \, a^{3} b + 10 \, a^{2} b^{2} + 3 \, a b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + 2 \, {\left(4 \, a^{4} + 11 \, a^{3} b + 10 \, a^{2} b^{2} + 3 \, a b^{3}\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(4 \, a^{4} + 3 \, a^{3} b - 10 \, a^{2} b^{2} - 9 \, a b^{3}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(4 \, a^{4} + 3 \, a^{3} b - 10 \, a^{2} b^{2} - 9 \, a b^{3} + 21 \, {\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}\right)} \sinh\left(d x + c\right)^{5} + 10 \, {\left(7 \, {\left(4 \, a^{4} + 11 \, a^{3} b + 10 \, a^{2} b^{2} + 3 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(4 \, a^{4} + 3 \, a^{3} b - 10 \, 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^{4} + 3 \, a^{3} b - 10 \, a^{2} b^{2} - 9 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(35 \, {\left(4 \, a^{4} + 11 \, a^{3} b + 10 \, a^{2} b^{2} + 3 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} - 4 \, a^{4} - 3 \, a^{3} b + 10 \, a^{2} b^{2} + 9 \, a b^{3} + 10 \, {\left(4 \, a^{4} + 3 \, a^{3} b - 10 \, 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(4 \, a^{4} + 11 \, a^{3} b + 10 \, a^{2} b^{2} + 3 \, a b^{3}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(4 \, a^{4} + 3 \, a^{3} b - 10 \, a^{2} b^{2} - 9 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(4 \, a^{4} + 3 \, a^{3} b - 10 \, 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(4 \, a^{3} + 11 \, a^{2} b + 10 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(4 \, a^{3} + 11 \, a^{2} b + 10 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(4 \, a^{3} + 11 \, a^{2} b + 10 \, a b^{2} + 3 \, b^{3}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(4 \, a^{3} + 3 \, a^{2} b - 4 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(4 \, a^{3} + 3 \, a^{2} b - 4 \, a b^{2} - 3 \, b^{3} + 7 \, {\left(4 \, a^{3} + 11 \, a^{2} b + 10 \, 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(4 \, a^{3} + 11 \, a^{2} b + 10 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(4 \, a^{3} + 3 \, a^{2} b - 4 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(12 \, a^{3} + a^{2} b + 6 \, a b^{2} + 9 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(4 \, a^{3} + 11 \, a^{2} b + 10 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 12 \, a^{3} + a^{2} b + 6 \, a b^{2} + 9 \, b^{3} + 30 \, {\left(4 \, a^{3} + 3 \, a^{2} b - 4 \, 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(4 \, a^{3} + 11 \, a^{2} b + 10 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(4 \, a^{3} + 3 \, a^{2} b - 4 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(12 \, a^{3} + a^{2} b + 6 \, a b^{2} + 9 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, a^{3} + 11 \, a^{2} b + 10 \, a b^{2} + 3 \, b^{3} + 4 \, {\left(4 \, a^{3} + 3 \, a^{2} b - 4 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(4 \, a^{3} + 11 \, a^{2} b + 10 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(4 \, a^{3} + 3 \, a^{2} b - 4 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 4 \, a^{3} + 3 \, a^{2} b - 4 \, a b^{2} - 3 \, b^{3} + 3 \, {\left(12 \, a^{3} + a^{2} b + 6 \, 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(4 \, a^{3} + 11 \, a^{2} b + 10 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(4 \, a^{3} + 3 \, a^{2} b - 4 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + {\left(12 \, a^{3} + a^{2} b + 6 \, a b^{2} + 9 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(4 \, a^{3} + 3 \, a^{2} b - 4 \, a b^{2} - 3 \, 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(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(3 \, a - b\right)} \cosh\left(d x + c\right) + {\left(3 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} + 3 \, a - b\right)} \sinh\left(d x + c\right)}{2 \, \sqrt{a^{2} + a b}}\right) + {\left({\left(4 \, a^{3} + 11 \, a^{2} b + 10 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(4 \, a^{3} + 11 \, a^{2} b + 10 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(4 \, a^{3} + 11 \, a^{2} b + 10 \, a b^{2} + 3 \, b^{3}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(4 \, a^{3} + 3 \, a^{2} b - 4 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(4 \, a^{3} + 3 \, a^{2} b - 4 \, a b^{2} - 3 \, b^{3} + 7 \, {\left(4 \, a^{3} + 11 \, a^{2} b + 10 \, 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(4 \, a^{3} + 11 \, a^{2} b + 10 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(4 \, a^{3} + 3 \, a^{2} b - 4 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(12 \, a^{3} + a^{2} b + 6 \, a b^{2} + 9 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(4 \, a^{3} + 11 \, a^{2} b + 10 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 12 \, a^{3} + a^{2} b + 6 \, a b^{2} + 9 \, b^{3} + 30 \, {\left(4 \, a^{3} + 3 \, a^{2} b - 4 \, 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(4 \, a^{3} + 11 \, a^{2} b + 10 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(4 \, a^{3} + 3 \, a^{2} b - 4 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(12 \, a^{3} + a^{2} b + 6 \, a b^{2} + 9 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, a^{3} + 11 \, a^{2} b + 10 \, a b^{2} + 3 \, b^{3} + 4 \, {\left(4 \, a^{3} + 3 \, a^{2} b - 4 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(4 \, a^{3} + 11 \, a^{2} b + 10 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(4 \, a^{3} + 3 \, a^{2} b - 4 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 4 \, a^{3} + 3 \, a^{2} b - 4 \, a b^{2} - 3 \, b^{3} + 3 \, {\left(12 \, a^{3} + a^{2} b + 6 \, 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(4 \, a^{3} + 11 \, a^{2} b + 10 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(4 \, a^{3} + 3 \, a^{2} b - 4 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + {\left(12 \, a^{3} + a^{2} b + 6 \, a b^{2} + 9 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(4 \, a^{3} + 3 \, a^{2} b - 4 \, a b^{2} - 3 \, 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{\sqrt{a^{2} + a b} {\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right)}}{2 \, a}\right) - 2 \, {\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 \, {\left(7 \, {\left(4 \, a^{4} + 11 \, a^{3} b + 10 \, a^{2} b^{2} + 3 \, a b^{3}\right)} \cosh\left(d x + c\right)^{6} + 5 \, {\left(4 \, a^{4} + 3 \, a^{3} b - 10 \, a^{2} b^{2} - 9 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} - 4 \, a^{4} - 11 \, a^{3} b - 10 \, a^{2} b^{2} - 3 \, a b^{3} - 3 \, {\left(4 \, a^{4} + 3 \, a^{3} b - 10 \, 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({\left(a^{7} + 4 \, a^{6} b + 6 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{7} + 4 \, a^{6} b + 6 \, a^{5} b^{2} + 4 \, 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^{7} + 4 \, a^{6} b + 6 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + a^{3} b^{4}\right)} d \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{7} + 2 \, a^{6} b - 2 \, a^{4} b^{3} - a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{7} + 4 \, a^{6} b + 6 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{7} + 2 \, a^{6} b - 2 \, a^{4} b^{3} - a^{3} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(3 \, a^{7} + 4 \, a^{6} b + 2 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + 3 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{7} + 4 \, a^{6} b + 6 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{7} + 2 \, a^{6} b - 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 \, {\left(a^{7} + 4 \, a^{6} b + 6 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 30 \, {\left(a^{7} + 2 \, a^{6} b - 2 \, a^{4} b^{3} - a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{7} + 4 \, a^{6} b + 2 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + 3 \, a^{3} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{7} + 2 \, a^{6} b - 2 \, a^{4} b^{3} - a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a^{7} + 4 \, a^{6} b + 6 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{7} + 2 \, a^{6} b - 2 \, a^{4} b^{3} - a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{7} + 4 \, a^{6} b + 2 \, a^{5} b^{2} + 4 \, 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^{7} + 4 \, a^{6} b + 6 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{7} + 2 \, a^{6} b - 2 \, a^{4} b^{3} - a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{7} + 4 \, a^{6} b + 2 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + 3 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{7} + 2 \, a^{6} b - 2 \, a^{4} b^{3} - a^{3} b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{7} + 4 \, a^{6} b + 6 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + a^{3} b^{4}\right)} d + 8 \, {\left({\left(a^{7} + 4 \, a^{6} b + 6 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{7} + 2 \, a^{6} b - 2 \, a^{4} b^{3} - a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{7} + 4 \, a^{6} b + 2 \, a^{5} b^{2} + 4 \, a^{4} b^{3} + 3 \, a^{3} b^{4}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{7} + 2 \, a^{6} b - 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*(4*a^4 + 11*a^3*b + 10*a^2*b^2 + 3*a*b^3)*cosh(d*x + c)^7 + 28*(4*a^4 + 11*a^3*b + 10*a^2*b^2 + 3*a*b^3)*cosh(d*x + c)*sinh(d*x + c)^6 + 4*(4*a^4 + 11*a^3*b + 10*a^2*b^2 + 3*a*b^3)*sinh(d*x + c)^7 + 4*(4*a^4 + 3*a^3*b - 10*a^2*b^2 - 9*a*b^3)*cosh(d*x + c)^5 + 4*(4*a^4 + 3*a^3*b - 10*a^2*b^2 - 9*a*b^3 + 21*(4*a^4 + 11*a^3*b + 10*a^2*b^2 + 3*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 20*(7*(4*a^4 + 11*a^3*b + 10*a^2*b^2 + 3*a*b^3)*cosh(d*x + c)^3 + (4*a^4 + 3*a^3*b - 10*a^2*b^2 - 9*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^4 - 4*(4*a^4 + 3*a^3*b - 10*a^2*b^2 - 9*a*b^3)*cosh(d*x + c)^3 + 4*(35*(4*a^4 + 11*a^3*b + 10*a^2*b^2 + 3*a*b^3)*cosh(d*x + c)^4 - 4*a^4 - 3*a^3*b + 10*a^2*b^2 + 9*a*b^3 + 10*(4*a^4 + 3*a^3*b - 10*a^2*b^2 - 9*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 4*(21*(4*a^4 + 11*a^3*b + 10*a^2*b^2 + 3*a*b^3)*cosh(d*x + c)^5 + 10*(4*a^4 + 3*a^3*b - 10*a^2*b^2 - 9*a*b^3)*cosh(d*x + c)^3 - 3*(4*a^4 + 3*a^3*b - 10*a^2*b^2 - 9*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^2 - ((4*a^3 + 11*a^2*b + 10*a*b^2 + 3*b^3)*cosh(d*x + c)^8 + 8*(4*a^3 + 11*a^2*b + 10*a*b^2 + 3*b^3)*cosh(d*x + c)*sinh(d*x + c)^7 + (4*a^3 + 11*a^2*b + 10*a*b^2 + 3*b^3)*sinh(d*x + c)^8 + 4*(4*a^3 + 3*a^2*b - 4*a*b^2 - 3*b^3)*cosh(d*x + c)^6 + 4*(4*a^3 + 3*a^2*b - 4*a*b^2 - 3*b^3 + 7*(4*a^3 + 11*a^2*b + 10*a*b^2 + 3*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(4*a^3 + 11*a^2*b + 10*a*b^2 + 3*b^3)*cosh(d*x + c)^3 + 3*(4*a^3 + 3*a^2*b - 4*a*b^2 - 3*b^3)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(12*a^3 + a^2*b + 6*a*b^2 + 9*b^3)*cosh(d*x + c)^4 + 2*(35*(4*a^3 + 11*a^2*b + 10*a*b^2 + 3*b^3)*cosh(d*x + c)^4 + 12*a^3 + a^2*b + 6*a*b^2 + 9*b^3 + 30*(4*a^3 + 3*a^2*b - 4*a*b^2 - 3*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(7*(4*a^3 + 11*a^2*b + 10*a*b^2 + 3*b^3)*cosh(d*x + c)^5 + 10*(4*a^3 + 3*a^2*b - 4*a*b^2 - 3*b^3)*cosh(d*x + c)^3 + (12*a^3 + a^2*b + 6*a*b^2 + 9*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*a^3 + 11*a^2*b + 10*a*b^2 + 3*b^3 + 4*(4*a^3 + 3*a^2*b - 4*a*b^2 - 3*b^3)*cosh(d*x + c)^2 + 4*(7*(4*a^3 + 11*a^2*b + 10*a*b^2 + 3*b^3)*cosh(d*x + c)^6 + 15*(4*a^3 + 3*a^2*b - 4*a*b^2 - 3*b^3)*cosh(d*x + c)^4 + 4*a^3 + 3*a^2*b - 4*a*b^2 - 3*b^3 + 3*(12*a^3 + a^2*b + 6*a*b^2 + 9*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((4*a^3 + 11*a^2*b + 10*a*b^2 + 3*b^3)*cosh(d*x + c)^7 + 3*(4*a^3 + 3*a^2*b - 4*a*b^2 - 3*b^3)*cosh(d*x + c)^5 + (12*a^3 + a^2*b + 6*a*b^2 + 9*b^3)*cosh(d*x + c)^3 + (4*a^3 + 3*a^2*b - 4*a*b^2 - 3*b^3)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-a^2 - a*b)*log(((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*(3*a + b)*cosh(d*x + c)^2 + 2*(3*(a + b)*cosh(d*x + c)^2 - 3*a - b)*sinh(d*x + c)^2 + 4*((a + b)*cosh(d*x + c)^3 - (3*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^2 - a*b) + a + b)/((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)) - 4*(4*a^4 + 11*a^3*b + 10*a^2*b^2 + 3*a*b^3)*cosh(d*x + c) + 4*(7*(4*a^4 + 11*a^3*b + 10*a^2*b^2 + 3*a*b^3)*cosh(d*x + c)^6 + 5*(4*a^4 + 3*a^3*b - 10*a^2*b^2 - 9*a*b^3)*cosh(d*x + c)^4 - 4*a^4 - 11*a^3*b - 10*a^2*b^2 - 3*a*b^3 - 3*(4*a^4 + 3*a^3*b - 10*a^2*b^2 - 9*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c))/((a^7 + 4*a^6*b + 6*a^5*b^2 + 4*a^4*b^3 + a^3*b^4)*d*cosh(d*x + c)^8 + 8*(a^7 + 4*a^6*b + 6*a^5*b^2 + 4*a^4*b^3 + a^3*b^4)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^7 + 4*a^6*b + 6*a^5*b^2 + 4*a^4*b^3 + a^3*b^4)*d*sinh(d*x + c)^8 + 4*(a^7 + 2*a^6*b - 2*a^4*b^3 - a^3*b^4)*d*cosh(d*x + c)^6 + 4*(7*(a^7 + 4*a^6*b + 6*a^5*b^2 + 4*a^4*b^3 + a^3*b^4)*d*cosh(d*x + c)^2 + (a^7 + 2*a^6*b - 2*a^4*b^3 - a^3*b^4)*d)*sinh(d*x + c)^6 + 2*(3*a^7 + 4*a^6*b + 2*a^5*b^2 + 4*a^4*b^3 + 3*a^3*b^4)*d*cosh(d*x + c)^4 + 8*(7*(a^7 + 4*a^6*b + 6*a^5*b^2 + 4*a^4*b^3 + a^3*b^4)*d*cosh(d*x + c)^3 + 3*(a^7 + 2*a^6*b - 2*a^4*b^3 - a^3*b^4)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^7 + 4*a^6*b + 6*a^5*b^2 + 4*a^4*b^3 + a^3*b^4)*d*cosh(d*x + c)^4 + 30*(a^7 + 2*a^6*b - 2*a^4*b^3 - a^3*b^4)*d*cosh(d*x + c)^2 + (3*a^7 + 4*a^6*b + 2*a^5*b^2 + 4*a^4*b^3 + 3*a^3*b^4)*d)*sinh(d*x + c)^4 + 4*(a^7 + 2*a^6*b - 2*a^4*b^3 - a^3*b^4)*d*cosh(d*x + c)^2 + 8*(7*(a^7 + 4*a^6*b + 6*a^5*b^2 + 4*a^4*b^3 + a^3*b^4)*d*cosh(d*x + c)^5 + 10*(a^7 + 2*a^6*b - 2*a^4*b^3 - a^3*b^4)*d*cosh(d*x + c)^3 + (3*a^7 + 4*a^6*b + 2*a^5*b^2 + 4*a^4*b^3 + 3*a^3*b^4)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^7 + 4*a^6*b + 6*a^5*b^2 + 4*a^4*b^3 + a^3*b^4)*d*cosh(d*x + c)^6 + 15*(a^7 + 2*a^6*b - 2*a^4*b^3 - a^3*b^4)*d*cosh(d*x + c)^4 + 3*(3*a^7 + 4*a^6*b + 2*a^5*b^2 + 4*a^4*b^3 + 3*a^3*b^4)*d*cosh(d*x + c)^2 + (a^7 + 2*a^6*b - 2*a^4*b^3 - a^3*b^4)*d)*sinh(d*x + c)^2 + (a^7 + 4*a^6*b + 6*a^5*b^2 + 4*a^4*b^3 + a^3*b^4)*d + 8*((a^7 + 4*a^6*b + 6*a^5*b^2 + 4*a^4*b^3 + a^3*b^4)*d*cosh(d*x + c)^7 + 3*(a^7 + 2*a^6*b - 2*a^4*b^3 - a^3*b^4)*d*cosh(d*x + c)^5 + (3*a^7 + 4*a^6*b + 2*a^5*b^2 + 4*a^4*b^3 + 3*a^3*b^4)*d*cosh(d*x + c)^3 + (a^7 + 2*a^6*b - 2*a^4*b^3 - a^3*b^4)*d*cosh(d*x + c))*sinh(d*x + c)), 1/8*(2*(4*a^4 + 11*a^3*b + 10*a^2*b^2 + 3*a*b^3)*cosh(d*x + c)^7 + 14*(4*a^4 + 11*a^3*b + 10*a^2*b^2 + 3*a*b^3)*cosh(d*x + c)*sinh(d*x + c)^6 + 2*(4*a^4 + 11*a^3*b + 10*a^2*b^2 + 3*a*b^3)*sinh(d*x + c)^7 + 2*(4*a^4 + 3*a^3*b - 10*a^2*b^2 - 9*a*b^3)*cosh(d*x + c)^5 + 2*(4*a^4 + 3*a^3*b - 10*a^2*b^2 - 9*a*b^3 + 21*(4*a^4 + 11*a^3*b + 10*a^2*b^2 + 3*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 10*(7*(4*a^4 + 11*a^3*b + 10*a^2*b^2 + 3*a*b^3)*cosh(d*x + c)^3 + (4*a^4 + 3*a^3*b - 10*a^2*b^2 - 9*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^4 - 2*(4*a^4 + 3*a^3*b - 10*a^2*b^2 - 9*a*b^3)*cosh(d*x + c)^3 + 2*(35*(4*a^4 + 11*a^3*b + 10*a^2*b^2 + 3*a*b^3)*cosh(d*x + c)^4 - 4*a^4 - 3*a^3*b + 10*a^2*b^2 + 9*a*b^3 + 10*(4*a^4 + 3*a^3*b - 10*a^2*b^2 - 9*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 2*(21*(4*a^4 + 11*a^3*b + 10*a^2*b^2 + 3*a*b^3)*cosh(d*x + c)^5 + 10*(4*a^4 + 3*a^3*b - 10*a^2*b^2 - 9*a*b^3)*cosh(d*x + c)^3 - 3*(4*a^4 + 3*a^3*b - 10*a^2*b^2 - 9*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^2 + ((4*a^3 + 11*a^2*b + 10*a*b^2 + 3*b^3)*cosh(d*x + c)^8 + 8*(4*a^3 + 11*a^2*b + 10*a*b^2 + 3*b^3)*cosh(d*x + c)*sinh(d*x + c)^7 + (4*a^3 + 11*a^2*b + 10*a*b^2 + 3*b^3)*sinh(d*x + c)^8 + 4*(4*a^3 + 3*a^2*b - 4*a*b^2 - 3*b^3)*cosh(d*x + c)^6 + 4*(4*a^3 + 3*a^2*b - 4*a*b^2 - 3*b^3 + 7*(4*a^3 + 11*a^2*b + 10*a*b^2 + 3*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(4*a^3 + 11*a^2*b + 10*a*b^2 + 3*b^3)*cosh(d*x + c)^3 + 3*(4*a^3 + 3*a^2*b - 4*a*b^2 - 3*b^3)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(12*a^3 + a^2*b + 6*a*b^2 + 9*b^3)*cosh(d*x + c)^4 + 2*(35*(4*a^3 + 11*a^2*b + 10*a*b^2 + 3*b^3)*cosh(d*x + c)^4 + 12*a^3 + a^2*b + 6*a*b^2 + 9*b^3 + 30*(4*a^3 + 3*a^2*b - 4*a*b^2 - 3*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(7*(4*a^3 + 11*a^2*b + 10*a*b^2 + 3*b^3)*cosh(d*x + c)^5 + 10*(4*a^3 + 3*a^2*b - 4*a*b^2 - 3*b^3)*cosh(d*x + c)^3 + (12*a^3 + a^2*b + 6*a*b^2 + 9*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*a^3 + 11*a^2*b + 10*a*b^2 + 3*b^3 + 4*(4*a^3 + 3*a^2*b - 4*a*b^2 - 3*b^3)*cosh(d*x + c)^2 + 4*(7*(4*a^3 + 11*a^2*b + 10*a*b^2 + 3*b^3)*cosh(d*x + c)^6 + 15*(4*a^3 + 3*a^2*b - 4*a*b^2 - 3*b^3)*cosh(d*x + c)^4 + 4*a^3 + 3*a^2*b - 4*a*b^2 - 3*b^3 + 3*(12*a^3 + a^2*b + 6*a*b^2 + 9*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((4*a^3 + 11*a^2*b + 10*a*b^2 + 3*b^3)*cosh(d*x + c)^7 + 3*(4*a^3 + 3*a^2*b - 4*a*b^2 - 3*b^3)*cosh(d*x + c)^5 + (12*a^3 + a^2*b + 6*a*b^2 + 9*b^3)*cosh(d*x + c)^3 + (4*a^3 + 3*a^2*b - 4*a*b^2 - 3*b^3)*cosh(d*x + c))*sinh(d*x + c))*sqrt(a^2 + a*b)*arctan(1/2*((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 + (3*a - b)*cosh(d*x + c) + (3*(a + b)*cosh(d*x + c)^2 + 3*a - b)*sinh(d*x + c))/sqrt(a^2 + a*b)) + ((4*a^3 + 11*a^2*b + 10*a*b^2 + 3*b^3)*cosh(d*x + c)^8 + 8*(4*a^3 + 11*a^2*b + 10*a*b^2 + 3*b^3)*cosh(d*x + c)*sinh(d*x + c)^7 + (4*a^3 + 11*a^2*b + 10*a*b^2 + 3*b^3)*sinh(d*x + c)^8 + 4*(4*a^3 + 3*a^2*b - 4*a*b^2 - 3*b^3)*cosh(d*x + c)^6 + 4*(4*a^3 + 3*a^2*b - 4*a*b^2 - 3*b^3 + 7*(4*a^3 + 11*a^2*b + 10*a*b^2 + 3*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(4*a^3 + 11*a^2*b + 10*a*b^2 + 3*b^3)*cosh(d*x + c)^3 + 3*(4*a^3 + 3*a^2*b - 4*a*b^2 - 3*b^3)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(12*a^3 + a^2*b + 6*a*b^2 + 9*b^3)*cosh(d*x + c)^4 + 2*(35*(4*a^3 + 11*a^2*b + 10*a*b^2 + 3*b^3)*cosh(d*x + c)^4 + 12*a^3 + a^2*b + 6*a*b^2 + 9*b^3 + 30*(4*a^3 + 3*a^2*b - 4*a*b^2 - 3*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(7*(4*a^3 + 11*a^2*b + 10*a*b^2 + 3*b^3)*cosh(d*x + c)^5 + 10*(4*a^3 + 3*a^2*b - 4*a*b^2 - 3*b^3)*cosh(d*x + c)^3 + (12*a^3 + a^2*b + 6*a*b^2 + 9*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*a^3 + 11*a^2*b + 10*a*b^2 + 3*b^3 + 4*(4*a^3 + 3*a^2*b - 4*a*b^2 - 3*b^3)*cosh(d*x + c)^2 + 4*(7*(4*a^3 + 11*a^2*b + 10*a*b^2 + 3*b^3)*cosh(d*x + c)^6 + 15*(4*a^3 + 3*a^2*b - 4*a*b^2 - 3*b^3)*cosh(d*x + c)^4 + 4*a^3 + 3*a^2*b - 4*a*b^2 - 3*b^3 + 3*(12*a^3 + a^2*b + 6*a*b^2 + 9*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((4*a^3 + 11*a^2*b + 10*a*b^2 + 3*b^3)*cosh(d*x + c)^7 + 3*(4*a^3 + 3*a^2*b - 4*a*b^2 - 3*b^3)*cosh(d*x + c)^5 + (12*a^3 + a^2*b + 6*a*b^2 + 9*b^3)*cosh(d*x + c)^3 + (4*a^3 + 3*a^2*b - 4*a*b^2 - 3*b^3)*cosh(d*x + c))*sinh(d*x + c))*sqrt(a^2 + a*b)*arctan(1/2*sqrt(a^2 + a*b)*(cosh(d*x + c) + sinh(d*x + c))/a) - 2*(4*a^4 + 11*a^3*b + 10*a^2*b^2 + 3*a*b^3)*cosh(d*x + c) + 2*(7*(4*a^4 + 11*a^3*b + 10*a^2*b^2 + 3*a*b^3)*cosh(d*x + c)^6 + 5*(4*a^4 + 3*a^3*b - 10*a^2*b^2 - 9*a*b^3)*cosh(d*x + c)^4 - 4*a^4 - 11*a^3*b - 10*a^2*b^2 - 3*a*b^3 - 3*(4*a^4 + 3*a^3*b - 10*a^2*b^2 - 9*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c))/((a^7 + 4*a^6*b + 6*a^5*b^2 + 4*a^4*b^3 + a^3*b^4)*d*cosh(d*x + c)^8 + 8*(a^7 + 4*a^6*b + 6*a^5*b^2 + 4*a^4*b^3 + a^3*b^4)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^7 + 4*a^6*b + 6*a^5*b^2 + 4*a^4*b^3 + a^3*b^4)*d*sinh(d*x + c)^8 + 4*(a^7 + 2*a^6*b - 2*a^4*b^3 - a^3*b^4)*d*cosh(d*x + c)^6 + 4*(7*(a^7 + 4*a^6*b + 6*a^5*b^2 + 4*a^4*b^3 + a^3*b^4)*d*cosh(d*x + c)^2 + (a^7 + 2*a^6*b - 2*a^4*b^3 - a^3*b^4)*d)*sinh(d*x + c)^6 + 2*(3*a^7 + 4*a^6*b + 2*a^5*b^2 + 4*a^4*b^3 + 3*a^3*b^4)*d*cosh(d*x + c)^4 + 8*(7*(a^7 + 4*a^6*b + 6*a^5*b^2 + 4*a^4*b^3 + a^3*b^4)*d*cosh(d*x + c)^3 + 3*(a^7 + 2*a^6*b - 2*a^4*b^3 - a^3*b^4)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^7 + 4*a^6*b + 6*a^5*b^2 + 4*a^4*b^3 + a^3*b^4)*d*cosh(d*x + c)^4 + 30*(a^7 + 2*a^6*b - 2*a^4*b^3 - a^3*b^4)*d*cosh(d*x + c)^2 + (3*a^7 + 4*a^6*b + 2*a^5*b^2 + 4*a^4*b^3 + 3*a^3*b^4)*d)*sinh(d*x + c)^4 + 4*(a^7 + 2*a^6*b - 2*a^4*b^3 - a^3*b^4)*d*cosh(d*x + c)^2 + 8*(7*(a^7 + 4*a^6*b + 6*a^5*b^2 + 4*a^4*b^3 + a^3*b^4)*d*cosh(d*x + c)^5 + 10*(a^7 + 2*a^6*b - 2*a^4*b^3 - a^3*b^4)*d*cosh(d*x + c)^3 + (3*a^7 + 4*a^6*b + 2*a^5*b^2 + 4*a^4*b^3 + 3*a^3*b^4)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^7 + 4*a^6*b + 6*a^5*b^2 + 4*a^4*b^3 + a^3*b^4)*d*cosh(d*x + c)^6 + 15*(a^7 + 2*a^6*b - 2*a^4*b^3 - a^3*b^4)*d*cosh(d*x + c)^4 + 3*(3*a^7 + 4*a^6*b + 2*a^5*b^2 + 4*a^4*b^3 + 3*a^3*b^4)*d*cosh(d*x + c)^2 + (a^7 + 2*a^6*b - 2*a^4*b^3 - a^3*b^4)*d)*sinh(d*x + c)^2 + (a^7 + 4*a^6*b + 6*a^5*b^2 + 4*a^4*b^3 + a^3*b^4)*d + 8*((a^7 + 4*a^6*b + 6*a^5*b^2 + 4*a^4*b^3 + a^3*b^4)*d*cosh(d*x + c)^7 + 3*(a^7 + 2*a^6*b - 2*a^4*b^3 - a^3*b^4)*d*cosh(d*x + c)^5 + (3*a^7 + 4*a^6*b + 2*a^5*b^2 + 4*a^4*b^3 + 3*a^3*b^4)*d*cosh(d*x + c)^3 + (a^7 + 2*a^6*b - 2*a^4*b^3 - a^3*b^4)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
130,1,5659,0,0.533590," ","integrate(sech(d*x+c)^4/(a+b*tanh(d*x+c)^2)^3,x, algorithm=""fricas"")","\left[-\frac{4 \, {\left(a^{4} b - a^{3} b^{2} - 5 \, a^{2} b^{3} - 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{6} + 24 \, {\left(a^{4} b - a^{3} b^{2} - 5 \, a^{2} b^{3} - 3 \, a b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + 4 \, {\left(a^{4} b - a^{3} b^{2} - 5 \, a^{2} b^{3} - 3 \, a b^{4}\right)} \sinh\left(d x + c\right)^{6} + 4 \, a^{4} b + 20 \, a^{3} b^{2} + 28 \, a^{2} b^{3} + 12 \, a b^{4} + 4 \, {\left(3 \, a^{4} b + 7 \, a^{3} b^{2} - 3 \, a^{2} b^{3} + 9 \, a b^{4}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(3 \, a^{4} b + 7 \, a^{3} b^{2} - 3 \, a^{2} b^{3} + 9 \, a b^{4} + 15 \, {\left(a^{4} b - 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)^{4} + 16 \, {\left(5 \, {\left(a^{4} b - a^{3} b^{2} - 5 \, a^{2} b^{3} - 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{4} b + 7 \, a^{3} b^{2} - 3 \, 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(3 \, a^{4} b + 13 \, a^{3} b^{2} + a^{2} b^{3} - 9 \, a b^{4}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(3 \, a^{4} b + 13 \, a^{3} b^{2} + a^{2} b^{3} - 9 \, a b^{4} + 15 \, {\left(a^{4} b - a^{3} b^{2} - 5 \, a^{2} b^{3} - 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{4} + 6 \, {\left(3 \, a^{4} b + 7 \, a^{3} b^{2} - 3 \, 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(a^{4} - 6 \, a^{2} b^{2} - 8 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{4} - 6 \, 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(a^{4} - 6 \, a^{2} b^{2} - 8 \, a b^{3} - 3 \, b^{4}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{4} - 2 \, a^{3} b - 4 \, a^{2} b^{2} + 2 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(a^{4} - 2 \, a^{3} b - 4 \, a^{2} b^{2} + 2 \, a b^{3} + 3 \, b^{4} + 7 \, {\left(a^{4} - 6 \, 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(a^{4} - 6 \, a^{2} b^{2} - 8 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{4} - 2 \, a^{3} b - 4 \, a^{2} b^{2} + 2 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(3 \, a^{4} - 8 \, a^{3} b - 2 \, a^{2} b^{2} - 9 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(a^{4} - 6 \, a^{2} b^{2} - 8 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 3 \, a^{4} - 8 \, a^{3} b - 2 \, a^{2} b^{2} - 9 \, b^{4} + 30 \, {\left(a^{4} - 2 \, a^{3} b - 4 \, 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)^{4} + a^{4} - 6 \, a^{2} b^{2} - 8 \, a b^{3} - 3 \, b^{4} + 8 \, {\left(7 \, {\left(a^{4} - 6 \, a^{2} b^{2} - 8 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{4} - 2 \, a^{3} b - 4 \, a^{2} b^{2} + 2 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{4} - 8 \, a^{3} b - 2 \, a^{2} b^{2} - 9 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(a^{4} - 2 \, a^{3} b - 4 \, a^{2} b^{2} + 2 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(a^{4} - 6 \, a^{2} b^{2} - 8 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{4} - 2 \, a^{3} b - 4 \, a^{2} b^{2} + 2 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + a^{4} - 2 \, a^{3} b - 4 \, a^{2} b^{2} + 2 \, a b^{3} + 3 \, b^{4} + 3 \, {\left(3 \, a^{4} - 8 \, a^{3} b - 2 \, a^{2} b^{2} - 9 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left({\left(a^{4} - 6 \, a^{2} b^{2} - 8 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{4} - 2 \, a^{3} b - 4 \, a^{2} b^{2} + 2 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{4} - 8 \, a^{3} b - 2 \, a^{2} b^{2} - 9 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{4} - 2 \, a^{3} b - 4 \, a^{2} b^{2} + 2 \, 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{{\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) \sinh\left(d x + c\right)^{3} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{2} + a^{2} - 6 \, a b + b^{2} + 4 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} - b^{2}\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)^{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} + a - b\right)} \sqrt{-a b}}{{\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) + 8 \, {\left(3 \, {\left(a^{4} b - a^{3} b^{2} - 5 \, a^{2} b^{3} - 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(3 \, a^{4} b + 7 \, a^{3} b^{2} - 3 \, a^{2} b^{3} + 9 \, a b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{4} b + 13 \, a^{3} b^{2} + 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(a^{6} b^{2} + a^{5} b^{3} - 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(a^{6} b^{2} + a^{5} b^{3} - a^{4} b^{4} - a^{3} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(3 \, a^{6} b^{2} + a^{5} b^{3} + 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(a^{6} b^{2} + a^{5} b^{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^{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(a^{6} b^{2} + a^{5} b^{3} - a^{4} b^{4} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{6} b^{2} + a^{5} b^{3} + a^{4} b^{4} + 3 \, a^{3} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{6} b^{2} + a^{5} b^{3} - 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(a^{6} b^{2} + a^{5} b^{3} - a^{4} b^{4} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{6} b^{2} + a^{5} b^{3} + 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(a^{6} b^{2} + a^{5} b^{3} - a^{4} b^{4} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{6} b^{2} + a^{5} b^{3} + a^{4} b^{4} + 3 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{6} b^{2} + a^{5} b^{3} - 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(a^{6} b^{2} + a^{5} b^{3} - a^{4} b^{4} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{6} b^{2} + a^{5} b^{3} + a^{4} b^{4} + 3 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{6} b^{2} + a^{5} b^{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(a^{4} b - a^{3} b^{2} - 5 \, a^{2} b^{3} - 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{6} + 12 \, {\left(a^{4} b - a^{3} b^{2} - 5 \, a^{2} b^{3} - 3 \, a b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + 2 \, {\left(a^{4} b - a^{3} b^{2} - 5 \, a^{2} b^{3} - 3 \, a b^{4}\right)} \sinh\left(d x + c\right)^{6} + 2 \, a^{4} b + 10 \, a^{3} b^{2} + 14 \, a^{2} b^{3} + 6 \, a b^{4} + 2 \, {\left(3 \, a^{4} b + 7 \, a^{3} b^{2} - 3 \, a^{2} b^{3} + 9 \, a b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(3 \, a^{4} b + 7 \, a^{3} b^{2} - 3 \, a^{2} b^{3} + 9 \, a b^{4} + 15 \, {\left(a^{4} b - 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)^{4} + 8 \, {\left(5 \, {\left(a^{4} b - a^{3} b^{2} - 5 \, a^{2} b^{3} - 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{4} b + 7 \, a^{3} b^{2} - 3 \, 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(3 \, a^{4} b + 13 \, a^{3} b^{2} + a^{2} b^{3} - 9 \, a b^{4}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{4} b + 13 \, a^{3} b^{2} + a^{2} b^{3} - 9 \, a b^{4} + 15 \, {\left(a^{4} b - a^{3} b^{2} - 5 \, a^{2} b^{3} - 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{4} + 6 \, {\left(3 \, a^{4} b + 7 \, a^{3} b^{2} - 3 \, 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(a^{4} - 6 \, a^{2} b^{2} - 8 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{4} - 6 \, 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(a^{4} - 6 \, a^{2} b^{2} - 8 \, a b^{3} - 3 \, b^{4}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{4} - 2 \, a^{3} b - 4 \, a^{2} b^{2} + 2 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(a^{4} - 2 \, a^{3} b - 4 \, a^{2} b^{2} + 2 \, a b^{3} + 3 \, b^{4} + 7 \, {\left(a^{4} - 6 \, 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(a^{4} - 6 \, a^{2} b^{2} - 8 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{4} - 2 \, a^{3} b - 4 \, a^{2} b^{2} + 2 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(3 \, a^{4} - 8 \, a^{3} b - 2 \, a^{2} b^{2} - 9 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(a^{4} - 6 \, a^{2} b^{2} - 8 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 3 \, a^{4} - 8 \, a^{3} b - 2 \, a^{2} b^{2} - 9 \, b^{4} + 30 \, {\left(a^{4} - 2 \, a^{3} b - 4 \, 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)^{4} + a^{4} - 6 \, a^{2} b^{2} - 8 \, a b^{3} - 3 \, b^{4} + 8 \, {\left(7 \, {\left(a^{4} - 6 \, a^{2} b^{2} - 8 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{4} - 2 \, a^{3} b - 4 \, a^{2} b^{2} + 2 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{4} - 8 \, a^{3} b - 2 \, a^{2} b^{2} - 9 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(a^{4} - 2 \, a^{3} b - 4 \, a^{2} b^{2} + 2 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(a^{4} - 6 \, a^{2} b^{2} - 8 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{4} - 2 \, a^{3} b - 4 \, a^{2} b^{2} + 2 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + a^{4} - 2 \, a^{3} b - 4 \, a^{2} b^{2} + 2 \, a b^{3} + 3 \, b^{4} + 3 \, {\left(3 \, a^{4} - 8 \, a^{3} b - 2 \, a^{2} b^{2} - 9 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left({\left(a^{4} - 6 \, a^{2} b^{2} - 8 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{4} - 2 \, a^{3} b - 4 \, a^{2} b^{2} + 2 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{4} - 8 \, a^{3} b - 2 \, a^{2} b^{2} - 9 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{4} - 2 \, a^{3} b - 4 \, a^{2} b^{2} + 2 \, 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({\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} + a - b\right)} \sqrt{a b}}{2 \, a b}\right) + 4 \, {\left(3 \, {\left(a^{4} b - a^{3} b^{2} - 5 \, a^{2} b^{3} - 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(3 \, a^{4} b + 7 \, a^{3} b^{2} - 3 \, a^{2} b^{3} + 9 \, a b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{4} b + 13 \, a^{3} b^{2} + 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(a^{6} b^{2} + a^{5} b^{3} - 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(a^{6} b^{2} + a^{5} b^{3} - a^{4} b^{4} - a^{3} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(3 \, a^{6} b^{2} + a^{5} b^{3} + 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(a^{6} b^{2} + a^{5} b^{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^{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(a^{6} b^{2} + a^{5} b^{3} - a^{4} b^{4} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{6} b^{2} + a^{5} b^{3} + a^{4} b^{4} + 3 \, a^{3} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{6} b^{2} + a^{5} b^{3} - 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(a^{6} b^{2} + a^{5} b^{3} - a^{4} b^{4} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{6} b^{2} + a^{5} b^{3} + 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(a^{6} b^{2} + a^{5} b^{3} - a^{4} b^{4} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{6} b^{2} + a^{5} b^{3} + a^{4} b^{4} + 3 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{6} b^{2} + a^{5} b^{3} - 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(a^{6} b^{2} + a^{5} b^{3} - a^{4} b^{4} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{6} b^{2} + a^{5} b^{3} + a^{4} b^{4} + 3 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{6} b^{2} + a^{5} b^{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*(a^4*b - a^3*b^2 - 5*a^2*b^3 - 3*a*b^4)*cosh(d*x + c)^6 + 24*(a^4*b - a^3*b^2 - 5*a^2*b^3 - 3*a*b^4)*cosh(d*x + c)*sinh(d*x + c)^5 + 4*(a^4*b - a^3*b^2 - 5*a^2*b^3 - 3*a*b^4)*sinh(d*x + c)^6 + 4*a^4*b + 20*a^3*b^2 + 28*a^2*b^3 + 12*a*b^4 + 4*(3*a^4*b + 7*a^3*b^2 - 3*a^2*b^3 + 9*a*b^4)*cosh(d*x + c)^4 + 4*(3*a^4*b + 7*a^3*b^2 - 3*a^2*b^3 + 9*a*b^4 + 15*(a^4*b - a^3*b^2 - 5*a^2*b^3 - 3*a*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 16*(5*(a^4*b - a^3*b^2 - 5*a^2*b^3 - 3*a*b^4)*cosh(d*x + c)^3 + (3*a^4*b + 7*a^3*b^2 - 3*a^2*b^3 + 9*a*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(3*a^4*b + 13*a^3*b^2 + a^2*b^3 - 9*a*b^4)*cosh(d*x + c)^2 + 4*(3*a^4*b + 13*a^3*b^2 + a^2*b^3 - 9*a*b^4 + 15*(a^4*b - a^3*b^2 - 5*a^2*b^3 - 3*a*b^4)*cosh(d*x + c)^4 + 6*(3*a^4*b + 7*a^3*b^2 - 3*a^2*b^3 + 9*a*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - ((a^4 - 6*a^2*b^2 - 8*a*b^3 - 3*b^4)*cosh(d*x + c)^8 + 8*(a^4 - 6*a^2*b^2 - 8*a*b^3 - 3*b^4)*cosh(d*x + c)*sinh(d*x + c)^7 + (a^4 - 6*a^2*b^2 - 8*a*b^3 - 3*b^4)*sinh(d*x + c)^8 + 4*(a^4 - 2*a^3*b - 4*a^2*b^2 + 2*a*b^3 + 3*b^4)*cosh(d*x + c)^6 + 4*(a^4 - 2*a^3*b - 4*a^2*b^2 + 2*a*b^3 + 3*b^4 + 7*(a^4 - 6*a^2*b^2 - 8*a*b^3 - 3*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(a^4 - 6*a^2*b^2 - 8*a*b^3 - 3*b^4)*cosh(d*x + c)^3 + 3*(a^4 - 2*a^3*b - 4*a^2*b^2 + 2*a*b^3 + 3*b^4)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(3*a^4 - 8*a^3*b - 2*a^2*b^2 - 9*b^4)*cosh(d*x + c)^4 + 2*(35*(a^4 - 6*a^2*b^2 - 8*a*b^3 - 3*b^4)*cosh(d*x + c)^4 + 3*a^4 - 8*a^3*b - 2*a^2*b^2 - 9*b^4 + 30*(a^4 - 2*a^3*b - 4*a^2*b^2 + 2*a*b^3 + 3*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + a^4 - 6*a^2*b^2 - 8*a*b^3 - 3*b^4 + 8*(7*(a^4 - 6*a^2*b^2 - 8*a*b^3 - 3*b^4)*cosh(d*x + c)^5 + 10*(a^4 - 2*a^3*b - 4*a^2*b^2 + 2*a*b^3 + 3*b^4)*cosh(d*x + c)^3 + (3*a^4 - 8*a^3*b - 2*a^2*b^2 - 9*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(a^4 - 2*a^3*b - 4*a^2*b^2 + 2*a*b^3 + 3*b^4)*cosh(d*x + c)^2 + 4*(7*(a^4 - 6*a^2*b^2 - 8*a*b^3 - 3*b^4)*cosh(d*x + c)^6 + 15*(a^4 - 2*a^3*b - 4*a^2*b^2 + 2*a*b^3 + 3*b^4)*cosh(d*x + c)^4 + a^4 - 2*a^3*b - 4*a^2*b^2 + 2*a*b^3 + 3*b^4 + 3*(3*a^4 - 8*a^3*b - 2*a^2*b^2 - 9*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((a^4 - 6*a^2*b^2 - 8*a*b^3 - 3*b^4)*cosh(d*x + c)^7 + 3*(a^4 - 2*a^3*b - 4*a^2*b^2 + 2*a*b^3 + 3*b^4)*cosh(d*x + c)^5 + (3*a^4 - 8*a^3*b - 2*a^2*b^2 - 9*b^4)*cosh(d*x + c)^3 + (a^4 - 2*a^3*b - 4*a^2*b^2 + 2*a*b^3 + 3*b^4)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-a*b)*log(((a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 + 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 + 2*(a^2 - b^2)*cosh(d*x + c)^2 + 2*(3*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + a^2 - b^2)*sinh(d*x + c)^2 + a^2 - 6*a*b + b^2 + 4*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 + (a^2 - 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 + a - b)*sqrt(-a*b))/((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)) + 8*(3*(a^4*b - a^3*b^2 - 5*a^2*b^3 - 3*a*b^4)*cosh(d*x + c)^5 + 2*(3*a^4*b + 7*a^3*b^2 - 3*a^2*b^3 + 9*a*b^4)*cosh(d*x + c)^3 + (3*a^4*b + 13*a^3*b^2 + 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*(a^6*b^2 + a^5*b^3 - 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 + (a^6*b^2 + a^5*b^3 - a^4*b^4 - a^3*b^5)*d)*sinh(d*x + c)^6 + 2*(3*a^6*b^2 + a^5*b^3 + 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*(a^6*b^2 + a^5*b^3 - 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*(a^6*b^2 + a^5*b^3 - a^4*b^4 - a^3*b^5)*d*cosh(d*x + c)^2 + (3*a^6*b^2 + a^5*b^3 + a^4*b^4 + 3*a^3*b^5)*d)*sinh(d*x + c)^4 + 4*(a^6*b^2 + a^5*b^3 - 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*(a^6*b^2 + a^5*b^3 - a^4*b^4 - a^3*b^5)*d*cosh(d*x + c)^3 + (3*a^6*b^2 + a^5*b^3 + 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*(a^6*b^2 + a^5*b^3 - a^4*b^4 - a^3*b^5)*d*cosh(d*x + c)^4 + 3*(3*a^6*b^2 + a^5*b^3 + a^4*b^4 + 3*a^3*b^5)*d*cosh(d*x + c)^2 + (a^6*b^2 + a^5*b^3 - 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*(a^6*b^2 + a^5*b^3 - a^4*b^4 - a^3*b^5)*d*cosh(d*x + c)^5 + (3*a^6*b^2 + a^5*b^3 + a^4*b^4 + 3*a^3*b^5)*d*cosh(d*x + c)^3 + (a^6*b^2 + a^5*b^3 - a^4*b^4 - a^3*b^5)*d*cosh(d*x + c))*sinh(d*x + c)), -1/8*(2*(a^4*b - a^3*b^2 - 5*a^2*b^3 - 3*a*b^4)*cosh(d*x + c)^6 + 12*(a^4*b - a^3*b^2 - 5*a^2*b^3 - 3*a*b^4)*cosh(d*x + c)*sinh(d*x + c)^5 + 2*(a^4*b - a^3*b^2 - 5*a^2*b^3 - 3*a*b^4)*sinh(d*x + c)^6 + 2*a^4*b + 10*a^3*b^2 + 14*a^2*b^3 + 6*a*b^4 + 2*(3*a^4*b + 7*a^3*b^2 - 3*a^2*b^3 + 9*a*b^4)*cosh(d*x + c)^4 + 2*(3*a^4*b + 7*a^3*b^2 - 3*a^2*b^3 + 9*a*b^4 + 15*(a^4*b - a^3*b^2 - 5*a^2*b^3 - 3*a*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(5*(a^4*b - a^3*b^2 - 5*a^2*b^3 - 3*a*b^4)*cosh(d*x + c)^3 + (3*a^4*b + 7*a^3*b^2 - 3*a^2*b^3 + 9*a*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 2*(3*a^4*b + 13*a^3*b^2 + a^2*b^3 - 9*a*b^4)*cosh(d*x + c)^2 + 2*(3*a^4*b + 13*a^3*b^2 + a^2*b^3 - 9*a*b^4 + 15*(a^4*b - a^3*b^2 - 5*a^2*b^3 - 3*a*b^4)*cosh(d*x + c)^4 + 6*(3*a^4*b + 7*a^3*b^2 - 3*a^2*b^3 + 9*a*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((a^4 - 6*a^2*b^2 - 8*a*b^3 - 3*b^4)*cosh(d*x + c)^8 + 8*(a^4 - 6*a^2*b^2 - 8*a*b^3 - 3*b^4)*cosh(d*x + c)*sinh(d*x + c)^7 + (a^4 - 6*a^2*b^2 - 8*a*b^3 - 3*b^4)*sinh(d*x + c)^8 + 4*(a^4 - 2*a^3*b - 4*a^2*b^2 + 2*a*b^3 + 3*b^4)*cosh(d*x + c)^6 + 4*(a^4 - 2*a^3*b - 4*a^2*b^2 + 2*a*b^3 + 3*b^4 + 7*(a^4 - 6*a^2*b^2 - 8*a*b^3 - 3*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(a^4 - 6*a^2*b^2 - 8*a*b^3 - 3*b^4)*cosh(d*x + c)^3 + 3*(a^4 - 2*a^3*b - 4*a^2*b^2 + 2*a*b^3 + 3*b^4)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(3*a^4 - 8*a^3*b - 2*a^2*b^2 - 9*b^4)*cosh(d*x + c)^4 + 2*(35*(a^4 - 6*a^2*b^2 - 8*a*b^3 - 3*b^4)*cosh(d*x + c)^4 + 3*a^4 - 8*a^3*b - 2*a^2*b^2 - 9*b^4 + 30*(a^4 - 2*a^3*b - 4*a^2*b^2 + 2*a*b^3 + 3*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + a^4 - 6*a^2*b^2 - 8*a*b^3 - 3*b^4 + 8*(7*(a^4 - 6*a^2*b^2 - 8*a*b^3 - 3*b^4)*cosh(d*x + c)^5 + 10*(a^4 - 2*a^3*b - 4*a^2*b^2 + 2*a*b^3 + 3*b^4)*cosh(d*x + c)^3 + (3*a^4 - 8*a^3*b - 2*a^2*b^2 - 9*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(a^4 - 2*a^3*b - 4*a^2*b^2 + 2*a*b^3 + 3*b^4)*cosh(d*x + c)^2 + 4*(7*(a^4 - 6*a^2*b^2 - 8*a*b^3 - 3*b^4)*cosh(d*x + c)^6 + 15*(a^4 - 2*a^3*b - 4*a^2*b^2 + 2*a*b^3 + 3*b^4)*cosh(d*x + c)^4 + a^4 - 2*a^3*b - 4*a^2*b^2 + 2*a*b^3 + 3*b^4 + 3*(3*a^4 - 8*a^3*b - 2*a^2*b^2 - 9*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((a^4 - 6*a^2*b^2 - 8*a*b^3 - 3*b^4)*cosh(d*x + c)^7 + 3*(a^4 - 2*a^3*b - 4*a^2*b^2 + 2*a*b^3 + 3*b^4)*cosh(d*x + c)^5 + (3*a^4 - 8*a^3*b - 2*a^2*b^2 - 9*b^4)*cosh(d*x + c)^3 + (a^4 - 2*a^3*b - 4*a^2*b^2 + 2*a*b^3 + 3*b^4)*cosh(d*x + c))*sinh(d*x + c))*sqrt(a*b)*arctan(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 + a - b)*sqrt(a*b)/(a*b)) + 4*(3*(a^4*b - a^3*b^2 - 5*a^2*b^3 - 3*a*b^4)*cosh(d*x + c)^5 + 2*(3*a^4*b + 7*a^3*b^2 - 3*a^2*b^3 + 9*a*b^4)*cosh(d*x + c)^3 + (3*a^4*b + 13*a^3*b^2 + 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*(a^6*b^2 + a^5*b^3 - 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 + (a^6*b^2 + a^5*b^3 - a^4*b^4 - a^3*b^5)*d)*sinh(d*x + c)^6 + 2*(3*a^6*b^2 + a^5*b^3 + 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*(a^6*b^2 + a^5*b^3 - 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*(a^6*b^2 + a^5*b^3 - a^4*b^4 - a^3*b^5)*d*cosh(d*x + c)^2 + (3*a^6*b^2 + a^5*b^3 + a^4*b^4 + 3*a^3*b^5)*d)*sinh(d*x + c)^4 + 4*(a^6*b^2 + a^5*b^3 - 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*(a^6*b^2 + a^5*b^3 - a^4*b^4 - a^3*b^5)*d*cosh(d*x + c)^3 + (3*a^6*b^2 + a^5*b^3 + 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*(a^6*b^2 + a^5*b^3 - a^4*b^4 - a^3*b^5)*d*cosh(d*x + c)^4 + 3*(3*a^6*b^2 + a^5*b^3 + a^4*b^4 + 3*a^3*b^5)*d*cosh(d*x + c)^2 + (a^6*b^2 + a^5*b^3 - 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*(a^6*b^2 + a^5*b^3 - a^4*b^4 - a^3*b^5)*d*cosh(d*x + c)^5 + (3*a^6*b^2 + a^5*b^3 + a^4*b^4 + 3*a^3*b^5)*d*cosh(d*x + c)^3 + (a^6*b^2 + a^5*b^3 - a^4*b^4 - a^3*b^5)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
131,1,5077,0,0.516278," ","integrate(sech(d*x+c)^5/(a+b*tanh(d*x+c)^2)^3,x, algorithm=""fricas"")","\left[\frac{12 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(d x + c\right)^{7} + 84 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + 12 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \sinh\left(d x + c\right)^{7} + 4 \, {\left(11 \, a^{3} + 2 \, a^{2} b - 9 \, a b^{2}\right)} \cosh\left(d x + c\right)^{5} + 4 \, {\left(11 \, a^{3} + 2 \, a^{2} b - 9 \, a b^{2} + 63 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{5} + 20 \, {\left(21 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(11 \, a^{3} + 2 \, a^{2} b - 9 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} - 4 \, {\left(11 \, a^{3} + 2 \, a^{2} b - 9 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(105 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(d x + c\right)^{4} - 11 \, a^{3} - 2 \, a^{2} b + 9 \, a b^{2} + 10 \, {\left(11 \, 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)^{3} + 4 \, {\left(63 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(11 \, a^{3} + 2 \, a^{2} b - 9 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(11 \, a^{3} + 2 \, a^{2} b - 9 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - 3 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + 30 \, {\left(a^{2} - 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)^{4} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{2} - 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)^{3} + 4 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 2 \, a b + b^{2} + 8 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} - 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{{\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(3 \, a + b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} - 3 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(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) - 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^{2} - a b} + a + b}{{\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) - 12 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(d x + c\right) + 4 \, {\left(21 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(d x + c\right)^{6} + 5 \, {\left(11 \, a^{3} + 2 \, a^{2} b - 9 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} - 3 \, a^{3} - 6 \, a^{2} b - 3 \, a b^{2} - 3 \, {\left(11 \, 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)}{16 \, {\left({\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} d \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{6} + a^{5} b - a^{4} b^{2} - a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{6} + a^{5} b - a^{4} b^{2} - a^{3} b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(3 \, a^{6} + a^{5} b + a^{4} b^{2} + 3 \, a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{6} + a^{5} b - 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 \, {\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 30 \, {\left(a^{6} + a^{5} b - a^{4} b^{2} - a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{6} + a^{5} b + a^{4} b^{2} + 3 \, a^{3} b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{6} + a^{5} b - a^{4} b^{2} - a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{6} + a^{5} b - a^{4} b^{2} - a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{6} + a^{5} b + 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 \, {\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{6} + a^{5} b - a^{4} b^{2} - a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{6} + a^{5} b + a^{4} b^{2} + 3 \, a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{6} + a^{5} b - a^{4} b^{2} - a^{3} b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} d + 8 \, {\left({\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{6} + a^{5} b - a^{4} b^{2} - a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{6} + a^{5} b + a^{4} b^{2} + 3 \, a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{6} + a^{5} b - 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 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(d x + c\right)^{7} + 42 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + 6 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(11 \, a^{3} + 2 \, a^{2} b - 9 \, a b^{2}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(11 \, a^{3} + 2 \, a^{2} b - 9 \, a b^{2} + 63 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{5} + 10 \, {\left(21 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(11 \, a^{3} + 2 \, a^{2} b - 9 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(11 \, a^{3} + 2 \, a^{2} b - 9 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(105 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(d x + c\right)^{4} - 11 \, a^{3} - 2 \, a^{2} b + 9 \, a b^{2} + 10 \, {\left(11 \, 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)^{3} + 2 \, {\left(63 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(11 \, a^{3} + 2 \, a^{2} b - 9 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(11 \, a^{3} + 2 \, a^{2} b - 9 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 3 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + 30 \, {\left(a^{2} - 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)^{4} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{2} - 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)^{3} + 4 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 2 \, a b + b^{2} + 8 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} - 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(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(3 \, a - b\right)} \cosh\left(d x + c\right) + {\left(3 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} + 3 \, a - b\right)} \sinh\left(d x + c\right)}{2 \, \sqrt{a^{2} + a b}}\right) + 3 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + 30 \, {\left(a^{2} - 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)^{4} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{2} - 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)^{3} + 4 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 2 \, a b + b^{2} + 8 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} - 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{\sqrt{a^{2} + a b} {\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right)}}{2 \, a}\right) - 6 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(d x + c\right) + 2 \, {\left(21 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(d x + c\right)^{6} + 5 \, {\left(11 \, a^{3} + 2 \, a^{2} b - 9 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} - 3 \, a^{3} - 6 \, a^{2} b - 3 \, a b^{2} - 3 \, {\left(11 \, 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)}{8 \, {\left({\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} d \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{6} + a^{5} b - a^{4} b^{2} - a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{6} + a^{5} b - a^{4} b^{2} - a^{3} b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(3 \, a^{6} + a^{5} b + a^{4} b^{2} + 3 \, a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{6} + a^{5} b - 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 \, {\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 30 \, {\left(a^{6} + a^{5} b - a^{4} b^{2} - a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{6} + a^{5} b + a^{4} b^{2} + 3 \, a^{3} b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{6} + a^{5} b - a^{4} b^{2} - a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{6} + a^{5} b - a^{4} b^{2} - a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{6} + a^{5} b + 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 \, {\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{6} + a^{5} b - a^{4} b^{2} - a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{6} + a^{5} b + a^{4} b^{2} + 3 \, a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{6} + a^{5} b - a^{4} b^{2} - a^{3} b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} d + 8 \, {\left({\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{6} + a^{5} b - a^{4} b^{2} - a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{6} + a^{5} b + a^{4} b^{2} + 3 \, a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{6} + a^{5} b - 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^3 + 2*a^2*b + a*b^2)*cosh(d*x + c)^7 + 84*(a^3 + 2*a^2*b + a*b^2)*cosh(d*x + c)*sinh(d*x + c)^6 + 12*(a^3 + 2*a^2*b + a*b^2)*sinh(d*x + c)^7 + 4*(11*a^3 + 2*a^2*b - 9*a*b^2)*cosh(d*x + c)^5 + 4*(11*a^3 + 2*a^2*b - 9*a*b^2 + 63*(a^3 + 2*a^2*b + a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 20*(21*(a^3 + 2*a^2*b + a*b^2)*cosh(d*x + c)^3 + (11*a^3 + 2*a^2*b - 9*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^4 - 4*(11*a^3 + 2*a^2*b - 9*a*b^2)*cosh(d*x + c)^3 + 4*(105*(a^3 + 2*a^2*b + a*b^2)*cosh(d*x + c)^4 - 11*a^3 - 2*a^2*b + 9*a*b^2 + 10*(11*a^3 + 2*a^2*b - 9*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 4*(63*(a^3 + 2*a^2*b + a*b^2)*cosh(d*x + c)^5 + 10*(11*a^3 + 2*a^2*b - 9*a*b^2)*cosh(d*x + c)^3 - 3*(11*a^3 + 2*a^2*b - 9*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^2 - 3*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^8 + 8*(a^2 + 2*a*b + b^2)*cosh(d*x + c)*sinh(d*x + c)^7 + (a^2 + 2*a*b + b^2)*sinh(d*x + c)^8 + 4*(a^2 - b^2)*cosh(d*x + c)^6 + 4*(7*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + a^2 - b^2)*sinh(d*x + c)^6 + 8*(7*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 + 3*(a^2 - b^2)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(3*a^2 - 2*a*b + 3*b^2)*cosh(d*x + c)^4 + 2*(35*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 + 30*(a^2 - b^2)*cosh(d*x + c)^2 + 3*a^2 - 2*a*b + 3*b^2)*sinh(d*x + c)^4 + 8*(7*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^5 + 10*(a^2 - b^2)*cosh(d*x + c)^3 + (3*a^2 - 2*a*b + 3*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(a^2 - b^2)*cosh(d*x + c)^2 + 4*(7*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^6 + 15*(a^2 - b^2)*cosh(d*x + c)^4 + 3*(3*a^2 - 2*a*b + 3*b^2)*cosh(d*x + c)^2 + a^2 - b^2)*sinh(d*x + c)^2 + a^2 + 2*a*b + b^2 + 8*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^7 + 3*(a^2 - b^2)*cosh(d*x + c)^5 + (3*a^2 - 2*a*b + 3*b^2)*cosh(d*x + c)^3 + (a^2 - b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-a^2 - a*b)*log(((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*(3*a + b)*cosh(d*x + c)^2 + 2*(3*(a + b)*cosh(d*x + c)^2 - 3*a - b)*sinh(d*x + c)^2 + 4*((a + b)*cosh(d*x + c)^3 - (3*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^2 - a*b) + a + b)/((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)) - 12*(a^3 + 2*a^2*b + a*b^2)*cosh(d*x + c) + 4*(21*(a^3 + 2*a^2*b + a*b^2)*cosh(d*x + c)^6 + 5*(11*a^3 + 2*a^2*b - 9*a*b^2)*cosh(d*x + c)^4 - 3*a^3 - 6*a^2*b - 3*a*b^2 - 3*(11*a^3 + 2*a^2*b - 9*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c))/((a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*d*cosh(d*x + c)^8 + 8*(a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*d*sinh(d*x + c)^8 + 4*(a^6 + a^5*b - a^4*b^2 - a^3*b^3)*d*cosh(d*x + c)^6 + 4*(7*(a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*d*cosh(d*x + c)^2 + (a^6 + a^5*b - a^4*b^2 - a^3*b^3)*d)*sinh(d*x + c)^6 + 2*(3*a^6 + a^5*b + a^4*b^2 + 3*a^3*b^3)*d*cosh(d*x + c)^4 + 8*(7*(a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*d*cosh(d*x + c)^3 + 3*(a^6 + a^5*b - a^4*b^2 - a^3*b^3)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*d*cosh(d*x + c)^4 + 30*(a^6 + a^5*b - a^4*b^2 - a^3*b^3)*d*cosh(d*x + c)^2 + (3*a^6 + a^5*b + a^4*b^2 + 3*a^3*b^3)*d)*sinh(d*x + c)^4 + 4*(a^6 + a^5*b - a^4*b^2 - a^3*b^3)*d*cosh(d*x + c)^2 + 8*(7*(a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*d*cosh(d*x + c)^5 + 10*(a^6 + a^5*b - a^4*b^2 - a^3*b^3)*d*cosh(d*x + c)^3 + (3*a^6 + a^5*b + a^4*b^2 + 3*a^3*b^3)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*d*cosh(d*x + c)^6 + 15*(a^6 + a^5*b - a^4*b^2 - a^3*b^3)*d*cosh(d*x + c)^4 + 3*(3*a^6 + a^5*b + a^4*b^2 + 3*a^3*b^3)*d*cosh(d*x + c)^2 + (a^6 + a^5*b - a^4*b^2 - a^3*b^3)*d)*sinh(d*x + c)^2 + (a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*d + 8*((a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*d*cosh(d*x + c)^7 + 3*(a^6 + a^5*b - a^4*b^2 - a^3*b^3)*d*cosh(d*x + c)^5 + (3*a^6 + a^5*b + a^4*b^2 + 3*a^3*b^3)*d*cosh(d*x + c)^3 + (a^6 + a^5*b - a^4*b^2 - a^3*b^3)*d*cosh(d*x + c))*sinh(d*x + c)), 1/8*(6*(a^3 + 2*a^2*b + a*b^2)*cosh(d*x + c)^7 + 42*(a^3 + 2*a^2*b + a*b^2)*cosh(d*x + c)*sinh(d*x + c)^6 + 6*(a^3 + 2*a^2*b + a*b^2)*sinh(d*x + c)^7 + 2*(11*a^3 + 2*a^2*b - 9*a*b^2)*cosh(d*x + c)^5 + 2*(11*a^3 + 2*a^2*b - 9*a*b^2 + 63*(a^3 + 2*a^2*b + a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 10*(21*(a^3 + 2*a^2*b + a*b^2)*cosh(d*x + c)^3 + (11*a^3 + 2*a^2*b - 9*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^4 - 2*(11*a^3 + 2*a^2*b - 9*a*b^2)*cosh(d*x + c)^3 + 2*(105*(a^3 + 2*a^2*b + a*b^2)*cosh(d*x + c)^4 - 11*a^3 - 2*a^2*b + 9*a*b^2 + 10*(11*a^3 + 2*a^2*b - 9*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 2*(63*(a^3 + 2*a^2*b + a*b^2)*cosh(d*x + c)^5 + 10*(11*a^3 + 2*a^2*b - 9*a*b^2)*cosh(d*x + c)^3 - 3*(11*a^3 + 2*a^2*b - 9*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^2 + 3*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^8 + 8*(a^2 + 2*a*b + b^2)*cosh(d*x + c)*sinh(d*x + c)^7 + (a^2 + 2*a*b + b^2)*sinh(d*x + c)^8 + 4*(a^2 - b^2)*cosh(d*x + c)^6 + 4*(7*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + a^2 - b^2)*sinh(d*x + c)^6 + 8*(7*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 + 3*(a^2 - b^2)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(3*a^2 - 2*a*b + 3*b^2)*cosh(d*x + c)^4 + 2*(35*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 + 30*(a^2 - b^2)*cosh(d*x + c)^2 + 3*a^2 - 2*a*b + 3*b^2)*sinh(d*x + c)^4 + 8*(7*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^5 + 10*(a^2 - b^2)*cosh(d*x + c)^3 + (3*a^2 - 2*a*b + 3*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(a^2 - b^2)*cosh(d*x + c)^2 + 4*(7*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^6 + 15*(a^2 - b^2)*cosh(d*x + c)^4 + 3*(3*a^2 - 2*a*b + 3*b^2)*cosh(d*x + c)^2 + a^2 - b^2)*sinh(d*x + c)^2 + a^2 + 2*a*b + b^2 + 8*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^7 + 3*(a^2 - b^2)*cosh(d*x + c)^5 + (3*a^2 - 2*a*b + 3*b^2)*cosh(d*x + c)^3 + (a^2 - b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(a^2 + a*b)*arctan(1/2*((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 + (3*a - b)*cosh(d*x + c) + (3*(a + b)*cosh(d*x + c)^2 + 3*a - b)*sinh(d*x + c))/sqrt(a^2 + a*b)) + 3*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^8 + 8*(a^2 + 2*a*b + b^2)*cosh(d*x + c)*sinh(d*x + c)^7 + (a^2 + 2*a*b + b^2)*sinh(d*x + c)^8 + 4*(a^2 - b^2)*cosh(d*x + c)^6 + 4*(7*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + a^2 - b^2)*sinh(d*x + c)^6 + 8*(7*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 + 3*(a^2 - b^2)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(3*a^2 - 2*a*b + 3*b^2)*cosh(d*x + c)^4 + 2*(35*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 + 30*(a^2 - b^2)*cosh(d*x + c)^2 + 3*a^2 - 2*a*b + 3*b^2)*sinh(d*x + c)^4 + 8*(7*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^5 + 10*(a^2 - b^2)*cosh(d*x + c)^3 + (3*a^2 - 2*a*b + 3*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(a^2 - b^2)*cosh(d*x + c)^2 + 4*(7*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^6 + 15*(a^2 - b^2)*cosh(d*x + c)^4 + 3*(3*a^2 - 2*a*b + 3*b^2)*cosh(d*x + c)^2 + a^2 - b^2)*sinh(d*x + c)^2 + a^2 + 2*a*b + b^2 + 8*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^7 + 3*(a^2 - b^2)*cosh(d*x + c)^5 + (3*a^2 - 2*a*b + 3*b^2)*cosh(d*x + c)^3 + (a^2 - b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(a^2 + a*b)*arctan(1/2*sqrt(a^2 + a*b)*(cosh(d*x + c) + sinh(d*x + c))/a) - 6*(a^3 + 2*a^2*b + a*b^2)*cosh(d*x + c) + 2*(21*(a^3 + 2*a^2*b + a*b^2)*cosh(d*x + c)^6 + 5*(11*a^3 + 2*a^2*b - 9*a*b^2)*cosh(d*x + c)^4 - 3*a^3 - 6*a^2*b - 3*a*b^2 - 3*(11*a^3 + 2*a^2*b - 9*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c))/((a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*d*cosh(d*x + c)^8 + 8*(a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*d*sinh(d*x + c)^8 + 4*(a^6 + a^5*b - a^4*b^2 - a^3*b^3)*d*cosh(d*x + c)^6 + 4*(7*(a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*d*cosh(d*x + c)^2 + (a^6 + a^5*b - a^4*b^2 - a^3*b^3)*d)*sinh(d*x + c)^6 + 2*(3*a^6 + a^5*b + a^4*b^2 + 3*a^3*b^3)*d*cosh(d*x + c)^4 + 8*(7*(a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*d*cosh(d*x + c)^3 + 3*(a^6 + a^5*b - a^4*b^2 - a^3*b^3)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*d*cosh(d*x + c)^4 + 30*(a^6 + a^5*b - a^4*b^2 - a^3*b^3)*d*cosh(d*x + c)^2 + (3*a^6 + a^5*b + a^4*b^2 + 3*a^3*b^3)*d)*sinh(d*x + c)^4 + 4*(a^6 + a^5*b - a^4*b^2 - a^3*b^3)*d*cosh(d*x + c)^2 + 8*(7*(a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*d*cosh(d*x + c)^5 + 10*(a^6 + a^5*b - a^4*b^2 - a^3*b^3)*d*cosh(d*x + c)^3 + (3*a^6 + a^5*b + a^4*b^2 + 3*a^3*b^3)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*d*cosh(d*x + c)^6 + 15*(a^6 + a^5*b - a^4*b^2 - a^3*b^3)*d*cosh(d*x + c)^4 + 3*(3*a^6 + a^5*b + a^4*b^2 + 3*a^3*b^3)*d*cosh(d*x + c)^2 + (a^6 + a^5*b - a^4*b^2 - a^3*b^3)*d)*sinh(d*x + c)^2 + (a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*d + 8*((a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*d*cosh(d*x + c)^7 + 3*(a^6 + a^5*b - a^4*b^2 - a^3*b^3)*d*cosh(d*x + c)^5 + (3*a^6 + a^5*b + a^4*b^2 + 3*a^3*b^3)*d*cosh(d*x + c)^3 + (a^6 + a^5*b - a^4*b^2 - a^3*b^3)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
132,1,5233,0,0.545722," ","integrate(sech(d*x+c)^6/(a+b*tanh(d*x+c)^2)^3,x, algorithm=""fricas"")","\left[\frac{4 \, {\left(3 \, a^{4} b + a^{3} b^{2} + a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{6} + 24 \, {\left(3 \, a^{4} b + a^{3} b^{2} + a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + 4 \, {\left(3 \, a^{4} b + a^{3} b^{2} + a^{2} b^{3} + 3 \, a b^{4}\right)} \sinh\left(d x + c\right)^{6} + 12 \, a^{4} b + 12 \, a^{3} b^{2} - 12 \, a^{2} b^{3} - 12 \, a b^{4} + 12 \, {\left(3 \, a^{4} b - 5 \, a^{3} b^{2} + 5 \, a^{2} b^{3} - 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{4} + 12 \, {\left(3 \, a^{4} b - 5 \, a^{3} b^{2} + 5 \, a^{2} b^{3} - 3 \, a b^{4} + 5 \, {\left(3 \, a^{4} b + a^{3} b^{2} + 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(3 \, a^{4} b + a^{3} b^{2} + a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(3 \, a^{4} b - 5 \, 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(9 \, a^{4} b - 13 \, a^{3} b^{2} - 13 \, a^{2} b^{3} + 9 \, a b^{4}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(9 \, a^{4} b - 13 \, a^{3} b^{2} - 13 \, a^{2} b^{3} + 9 \, a b^{4} + 15 \, {\left(3 \, a^{4} b + a^{3} b^{2} + a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{4} + 18 \, {\left(3 \, a^{4} b - 5 \, 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(3 \, a^{4} + 4 \, a^{3} b + 2 \, a^{2} b^{2} + 4 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(3 \, a^{4} + 4 \, a^{3} b + 2 \, 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(3 \, a^{4} + 4 \, a^{3} b + 2 \, a^{2} b^{2} + 4 \, a b^{3} + 3 \, b^{4}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(3 \, a^{4} - 2 \, a^{3} b + 2 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(3 \, a^{4} - 2 \, a^{3} b + 2 \, a b^{3} - 3 \, b^{4} + 7 \, {\left(3 \, a^{4} + 4 \, a^{3} b + 2 \, 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(3 \, a^{4} + 4 \, a^{3} b + 2 \, a^{2} b^{2} + 4 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(3 \, a^{4} - 2 \, 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(9 \, a^{4} - 12 \, a^{3} b + 22 \, a^{2} b^{2} - 12 \, a b^{3} + 9 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(3 \, a^{4} + 4 \, a^{3} b + 2 \, a^{2} b^{2} + 4 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 9 \, a^{4} - 12 \, a^{3} b + 22 \, a^{2} b^{2} - 12 \, a b^{3} + 9 \, b^{4} + 30 \, {\left(3 \, a^{4} - 2 \, 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} + 3 \, a^{4} + 4 \, a^{3} b + 2 \, a^{2} b^{2} + 4 \, a b^{3} + 3 \, b^{4} + 8 \, {\left(7 \, {\left(3 \, a^{4} + 4 \, a^{3} b + 2 \, a^{2} b^{2} + 4 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(3 \, a^{4} - 2 \, a^{3} b + 2 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(9 \, a^{4} - 12 \, a^{3} b + 22 \, 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(3 \, a^{4} - 2 \, a^{3} b + 2 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(3 \, a^{4} + 4 \, a^{3} b + 2 \, a^{2} b^{2} + 4 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(3 \, a^{4} - 2 \, a^{3} b + 2 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 3 \, a^{4} - 2 \, a^{3} b + 2 \, a b^{3} - 3 \, b^{4} + 3 \, {\left(9 \, a^{4} - 12 \, a^{3} b + 22 \, 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(3 \, a^{4} + 4 \, a^{3} b + 2 \, a^{2} b^{2} + 4 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(3 \, a^{4} - 2 \, a^{3} b + 2 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + {\left(9 \, a^{4} - 12 \, a^{3} b + 22 \, a^{2} b^{2} - 12 \, a b^{3} + 9 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{4} - 2 \, 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{-a b} \log\left(\frac{{\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) \sinh\left(d x + c\right)^{3} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{2} + a^{2} - 6 \, a b + b^{2} + 4 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} - b^{2}\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)^{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} + a - b\right)} \sqrt{-a b}}{{\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) + 8 \, {\left(3 \, {\left(3 \, a^{4} b + a^{3} b^{2} + a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{5} + 6 \, {\left(3 \, a^{4} b - 5 \, a^{3} b^{2} + 5 \, a^{2} b^{3} - 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(9 \, a^{4} b - 13 \, a^{3} b^{2} - 13 \, 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(a^{5} b^{3} - 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(a^{5} b^{3} - a^{3} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(3 \, a^{5} b^{3} - 2 \, 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(a^{5} b^{3} - 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(a^{5} b^{3} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{5} b^{3} - 2 \, a^{4} b^{4} + 3 \, a^{3} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{5} b^{3} - 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(a^{5} b^{3} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{5} b^{3} - 2 \, 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(a^{5} b^{3} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{5} b^{3} - 2 \, a^{4} b^{4} + 3 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{5} b^{3} - 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(a^{5} b^{3} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{5} b^{3} - 2 \, a^{4} b^{4} + 3 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{5} b^{3} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}, \frac{2 \, {\left(3 \, a^{4} b + a^{3} b^{2} + a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{6} + 12 \, {\left(3 \, a^{4} b + a^{3} b^{2} + a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + 2 \, {\left(3 \, a^{4} b + a^{3} b^{2} + a^{2} b^{3} + 3 \, a b^{4}\right)} \sinh\left(d x + c\right)^{6} + 6 \, a^{4} b + 6 \, a^{3} b^{2} - 6 \, a^{2} b^{3} - 6 \, a b^{4} + 6 \, {\left(3 \, a^{4} b - 5 \, a^{3} b^{2} + 5 \, a^{2} b^{3} - 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{4} + 6 \, {\left(3 \, a^{4} b - 5 \, a^{3} b^{2} + 5 \, a^{2} b^{3} - 3 \, a b^{4} + 5 \, {\left(3 \, a^{4} b + a^{3} b^{2} + 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(3 \, a^{4} b + a^{3} b^{2} + a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(3 \, a^{4} b - 5 \, 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(9 \, a^{4} b - 13 \, a^{3} b^{2} - 13 \, a^{2} b^{3} + 9 \, a b^{4}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(9 \, a^{4} b - 13 \, a^{3} b^{2} - 13 \, a^{2} b^{3} + 9 \, a b^{4} + 15 \, {\left(3 \, a^{4} b + a^{3} b^{2} + a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{4} + 18 \, {\left(3 \, a^{4} b - 5 \, 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(3 \, a^{4} + 4 \, a^{3} b + 2 \, a^{2} b^{2} + 4 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(3 \, a^{4} + 4 \, a^{3} b + 2 \, 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(3 \, a^{4} + 4 \, a^{3} b + 2 \, a^{2} b^{2} + 4 \, a b^{3} + 3 \, b^{4}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(3 \, a^{4} - 2 \, a^{3} b + 2 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(3 \, a^{4} - 2 \, a^{3} b + 2 \, a b^{3} - 3 \, b^{4} + 7 \, {\left(3 \, a^{4} + 4 \, a^{3} b + 2 \, 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(3 \, a^{4} + 4 \, a^{3} b + 2 \, a^{2} b^{2} + 4 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(3 \, a^{4} - 2 \, 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(9 \, a^{4} - 12 \, a^{3} b + 22 \, a^{2} b^{2} - 12 \, a b^{3} + 9 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(3 \, a^{4} + 4 \, a^{3} b + 2 \, a^{2} b^{2} + 4 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 9 \, a^{4} - 12 \, a^{3} b + 22 \, a^{2} b^{2} - 12 \, a b^{3} + 9 \, b^{4} + 30 \, {\left(3 \, a^{4} - 2 \, 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} + 3 \, a^{4} + 4 \, a^{3} b + 2 \, a^{2} b^{2} + 4 \, a b^{3} + 3 \, b^{4} + 8 \, {\left(7 \, {\left(3 \, a^{4} + 4 \, a^{3} b + 2 \, a^{2} b^{2} + 4 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(3 \, a^{4} - 2 \, a^{3} b + 2 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(9 \, a^{4} - 12 \, a^{3} b + 22 \, 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(3 \, a^{4} - 2 \, a^{3} b + 2 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(3 \, a^{4} + 4 \, a^{3} b + 2 \, a^{2} b^{2} + 4 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(3 \, a^{4} - 2 \, a^{3} b + 2 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 3 \, a^{4} - 2 \, a^{3} b + 2 \, a b^{3} - 3 \, b^{4} + 3 \, {\left(9 \, a^{4} - 12 \, a^{3} b + 22 \, 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(3 \, a^{4} + 4 \, a^{3} b + 2 \, a^{2} b^{2} + 4 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(3 \, a^{4} - 2 \, a^{3} b + 2 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + {\left(9 \, a^{4} - 12 \, a^{3} b + 22 \, a^{2} b^{2} - 12 \, a b^{3} + 9 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{4} - 2 \, 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{a b} \arctan\left(\frac{{\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} + a - b\right)} \sqrt{a b}}{2 \, a b}\right) + 4 \, {\left(3 \, {\left(3 \, a^{4} b + a^{3} b^{2} + a^{2} b^{3} + 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{5} + 6 \, {\left(3 \, a^{4} b - 5 \, a^{3} b^{2} + 5 \, a^{2} b^{3} - 3 \, a b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(9 \, a^{4} b - 13 \, a^{3} b^{2} - 13 \, 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(a^{5} b^{3} - 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(a^{5} b^{3} - a^{3} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(3 \, a^{5} b^{3} - 2 \, 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(a^{5} b^{3} - 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(a^{5} b^{3} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{5} b^{3} - 2 \, a^{4} b^{4} + 3 \, a^{3} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{5} b^{3} - 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(a^{5} b^{3} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{5} b^{3} - 2 \, 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(a^{5} b^{3} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{5} b^{3} - 2 \, a^{4} b^{4} + 3 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{5} b^{3} - 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(a^{5} b^{3} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{5} b^{3} - 2 \, a^{4} b^{4} + 3 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{5} b^{3} - 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*(3*a^4*b + a^3*b^2 + a^2*b^3 + 3*a*b^4)*cosh(d*x + c)^6 + 24*(3*a^4*b + a^3*b^2 + a^2*b^3 + 3*a*b^4)*cosh(d*x + c)*sinh(d*x + c)^5 + 4*(3*a^4*b + a^3*b^2 + a^2*b^3 + 3*a*b^4)*sinh(d*x + c)^6 + 12*a^4*b + 12*a^3*b^2 - 12*a^2*b^3 - 12*a*b^4 + 12*(3*a^4*b - 5*a^3*b^2 + 5*a^2*b^3 - 3*a*b^4)*cosh(d*x + c)^4 + 12*(3*a^4*b - 5*a^3*b^2 + 5*a^2*b^3 - 3*a*b^4 + 5*(3*a^4*b + a^3*b^2 + a^2*b^3 + 3*a*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 16*(5*(3*a^4*b + a^3*b^2 + a^2*b^3 + 3*a*b^4)*cosh(d*x + c)^3 + 3*(3*a^4*b - 5*a^3*b^2 + 5*a^2*b^3 - 3*a*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(9*a^4*b - 13*a^3*b^2 - 13*a^2*b^3 + 9*a*b^4)*cosh(d*x + c)^2 + 4*(9*a^4*b - 13*a^3*b^2 - 13*a^2*b^3 + 9*a*b^4 + 15*(3*a^4*b + a^3*b^2 + a^2*b^3 + 3*a*b^4)*cosh(d*x + c)^4 + 18*(3*a^4*b - 5*a^3*b^2 + 5*a^2*b^3 - 3*a*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - ((3*a^4 + 4*a^3*b + 2*a^2*b^2 + 4*a*b^3 + 3*b^4)*cosh(d*x + c)^8 + 8*(3*a^4 + 4*a^3*b + 2*a^2*b^2 + 4*a*b^3 + 3*b^4)*cosh(d*x + c)*sinh(d*x + c)^7 + (3*a^4 + 4*a^3*b + 2*a^2*b^2 + 4*a*b^3 + 3*b^4)*sinh(d*x + c)^8 + 4*(3*a^4 - 2*a^3*b + 2*a*b^3 - 3*b^4)*cosh(d*x + c)^6 + 4*(3*a^4 - 2*a^3*b + 2*a*b^3 - 3*b^4 + 7*(3*a^4 + 4*a^3*b + 2*a^2*b^2 + 4*a*b^3 + 3*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(3*a^4 + 4*a^3*b + 2*a^2*b^2 + 4*a*b^3 + 3*b^4)*cosh(d*x + c)^3 + 3*(3*a^4 - 2*a^3*b + 2*a*b^3 - 3*b^4)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(9*a^4 - 12*a^3*b + 22*a^2*b^2 - 12*a*b^3 + 9*b^4)*cosh(d*x + c)^4 + 2*(35*(3*a^4 + 4*a^3*b + 2*a^2*b^2 + 4*a*b^3 + 3*b^4)*cosh(d*x + c)^4 + 9*a^4 - 12*a^3*b + 22*a^2*b^2 - 12*a*b^3 + 9*b^4 + 30*(3*a^4 - 2*a^3*b + 2*a*b^3 - 3*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 3*a^4 + 4*a^3*b + 2*a^2*b^2 + 4*a*b^3 + 3*b^4 + 8*(7*(3*a^4 + 4*a^3*b + 2*a^2*b^2 + 4*a*b^3 + 3*b^4)*cosh(d*x + c)^5 + 10*(3*a^4 - 2*a^3*b + 2*a*b^3 - 3*b^4)*cosh(d*x + c)^3 + (9*a^4 - 12*a^3*b + 22*a^2*b^2 - 12*a*b^3 + 9*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(3*a^4 - 2*a^3*b + 2*a*b^3 - 3*b^4)*cosh(d*x + c)^2 + 4*(7*(3*a^4 + 4*a^3*b + 2*a^2*b^2 + 4*a*b^3 + 3*b^4)*cosh(d*x + c)^6 + 15*(3*a^4 - 2*a^3*b + 2*a*b^3 - 3*b^4)*cosh(d*x + c)^4 + 3*a^4 - 2*a^3*b + 2*a*b^3 - 3*b^4 + 3*(9*a^4 - 12*a^3*b + 22*a^2*b^2 - 12*a*b^3 + 9*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((3*a^4 + 4*a^3*b + 2*a^2*b^2 + 4*a*b^3 + 3*b^4)*cosh(d*x + c)^7 + 3*(3*a^4 - 2*a^3*b + 2*a*b^3 - 3*b^4)*cosh(d*x + c)^5 + (9*a^4 - 12*a^3*b + 22*a^2*b^2 - 12*a*b^3 + 9*b^4)*cosh(d*x + c)^3 + (3*a^4 - 2*a^3*b + 2*a*b^3 - 3*b^4)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-a*b)*log(((a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 + 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 + 2*(a^2 - b^2)*cosh(d*x + c)^2 + 2*(3*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + a^2 - b^2)*sinh(d*x + c)^2 + a^2 - 6*a*b + b^2 + 4*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 + (a^2 - 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 + a - b)*sqrt(-a*b))/((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)) + 8*(3*(3*a^4*b + a^3*b^2 + a^2*b^3 + 3*a*b^4)*cosh(d*x + c)^5 + 6*(3*a^4*b - 5*a^3*b^2 + 5*a^2*b^3 - 3*a*b^4)*cosh(d*x + c)^3 + (9*a^4*b - 13*a^3*b^2 - 13*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*(a^5*b^3 - 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 + (a^5*b^3 - a^3*b^5)*d)*sinh(d*x + c)^6 + 2*(3*a^5*b^3 - 2*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*(a^5*b^3 - 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*(a^5*b^3 - a^3*b^5)*d*cosh(d*x + c)^2 + (3*a^5*b^3 - 2*a^4*b^4 + 3*a^3*b^5)*d)*sinh(d*x + c)^4 + 4*(a^5*b^3 - 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*(a^5*b^3 - a^3*b^5)*d*cosh(d*x + c)^3 + (3*a^5*b^3 - 2*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*(a^5*b^3 - a^3*b^5)*d*cosh(d*x + c)^4 + 3*(3*a^5*b^3 - 2*a^4*b^4 + 3*a^3*b^5)*d*cosh(d*x + c)^2 + (a^5*b^3 - 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*(a^5*b^3 - a^3*b^5)*d*cosh(d*x + c)^5 + (3*a^5*b^3 - 2*a^4*b^4 + 3*a^3*b^5)*d*cosh(d*x + c)^3 + (a^5*b^3 - a^3*b^5)*d*cosh(d*x + c))*sinh(d*x + c)), 1/8*(2*(3*a^4*b + a^3*b^2 + a^2*b^3 + 3*a*b^4)*cosh(d*x + c)^6 + 12*(3*a^4*b + a^3*b^2 + a^2*b^3 + 3*a*b^4)*cosh(d*x + c)*sinh(d*x + c)^5 + 2*(3*a^4*b + a^3*b^2 + a^2*b^3 + 3*a*b^4)*sinh(d*x + c)^6 + 6*a^4*b + 6*a^3*b^2 - 6*a^2*b^3 - 6*a*b^4 + 6*(3*a^4*b - 5*a^3*b^2 + 5*a^2*b^3 - 3*a*b^4)*cosh(d*x + c)^4 + 6*(3*a^4*b - 5*a^3*b^2 + 5*a^2*b^3 - 3*a*b^4 + 5*(3*a^4*b + a^3*b^2 + a^2*b^3 + 3*a*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(5*(3*a^4*b + a^3*b^2 + a^2*b^3 + 3*a*b^4)*cosh(d*x + c)^3 + 3*(3*a^4*b - 5*a^3*b^2 + 5*a^2*b^3 - 3*a*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 2*(9*a^4*b - 13*a^3*b^2 - 13*a^2*b^3 + 9*a*b^4)*cosh(d*x + c)^2 + 2*(9*a^4*b - 13*a^3*b^2 - 13*a^2*b^3 + 9*a*b^4 + 15*(3*a^4*b + a^3*b^2 + a^2*b^3 + 3*a*b^4)*cosh(d*x + c)^4 + 18*(3*a^4*b - 5*a^3*b^2 + 5*a^2*b^3 - 3*a*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((3*a^4 + 4*a^3*b + 2*a^2*b^2 + 4*a*b^3 + 3*b^4)*cosh(d*x + c)^8 + 8*(3*a^4 + 4*a^3*b + 2*a^2*b^2 + 4*a*b^3 + 3*b^4)*cosh(d*x + c)*sinh(d*x + c)^7 + (3*a^4 + 4*a^3*b + 2*a^2*b^2 + 4*a*b^3 + 3*b^4)*sinh(d*x + c)^8 + 4*(3*a^4 - 2*a^3*b + 2*a*b^3 - 3*b^4)*cosh(d*x + c)^6 + 4*(3*a^4 - 2*a^3*b + 2*a*b^3 - 3*b^4 + 7*(3*a^4 + 4*a^3*b + 2*a^2*b^2 + 4*a*b^3 + 3*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(3*a^4 + 4*a^3*b + 2*a^2*b^2 + 4*a*b^3 + 3*b^4)*cosh(d*x + c)^3 + 3*(3*a^4 - 2*a^3*b + 2*a*b^3 - 3*b^4)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(9*a^4 - 12*a^3*b + 22*a^2*b^2 - 12*a*b^3 + 9*b^4)*cosh(d*x + c)^4 + 2*(35*(3*a^4 + 4*a^3*b + 2*a^2*b^2 + 4*a*b^3 + 3*b^4)*cosh(d*x + c)^4 + 9*a^4 - 12*a^3*b + 22*a^2*b^2 - 12*a*b^3 + 9*b^4 + 30*(3*a^4 - 2*a^3*b + 2*a*b^3 - 3*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 3*a^4 + 4*a^3*b + 2*a^2*b^2 + 4*a*b^3 + 3*b^4 + 8*(7*(3*a^4 + 4*a^3*b + 2*a^2*b^2 + 4*a*b^3 + 3*b^4)*cosh(d*x + c)^5 + 10*(3*a^4 - 2*a^3*b + 2*a*b^3 - 3*b^4)*cosh(d*x + c)^3 + (9*a^4 - 12*a^3*b + 22*a^2*b^2 - 12*a*b^3 + 9*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(3*a^4 - 2*a^3*b + 2*a*b^3 - 3*b^4)*cosh(d*x + c)^2 + 4*(7*(3*a^4 + 4*a^3*b + 2*a^2*b^2 + 4*a*b^3 + 3*b^4)*cosh(d*x + c)^6 + 15*(3*a^4 - 2*a^3*b + 2*a*b^3 - 3*b^4)*cosh(d*x + c)^4 + 3*a^4 - 2*a^3*b + 2*a*b^3 - 3*b^4 + 3*(9*a^4 - 12*a^3*b + 22*a^2*b^2 - 12*a*b^3 + 9*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((3*a^4 + 4*a^3*b + 2*a^2*b^2 + 4*a*b^3 + 3*b^4)*cosh(d*x + c)^7 + 3*(3*a^4 - 2*a^3*b + 2*a*b^3 - 3*b^4)*cosh(d*x + c)^5 + (9*a^4 - 12*a^3*b + 22*a^2*b^2 - 12*a*b^3 + 9*b^4)*cosh(d*x + c)^3 + (3*a^4 - 2*a^3*b + 2*a*b^3 - 3*b^4)*cosh(d*x + c))*sinh(d*x + c))*sqrt(a*b)*arctan(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 + a - b)*sqrt(a*b)/(a*b)) + 4*(3*(3*a^4*b + a^3*b^2 + a^2*b^3 + 3*a*b^4)*cosh(d*x + c)^5 + 6*(3*a^4*b - 5*a^3*b^2 + 5*a^2*b^3 - 3*a*b^4)*cosh(d*x + c)^3 + (9*a^4*b - 13*a^3*b^2 - 13*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*(a^5*b^3 - 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 + (a^5*b^3 - a^3*b^5)*d)*sinh(d*x + c)^6 + 2*(3*a^5*b^3 - 2*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*(a^5*b^3 - 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*(a^5*b^3 - a^3*b^5)*d*cosh(d*x + c)^2 + (3*a^5*b^3 - 2*a^4*b^4 + 3*a^3*b^5)*d)*sinh(d*x + c)^4 + 4*(a^5*b^3 - 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*(a^5*b^3 - a^3*b^5)*d*cosh(d*x + c)^3 + (3*a^5*b^3 - 2*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*(a^5*b^3 - a^3*b^5)*d*cosh(d*x + c)^4 + 3*(3*a^5*b^3 - 2*a^4*b^4 + 3*a^3*b^5)*d*cosh(d*x + c)^2 + (a^5*b^3 - 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*(a^5*b^3 - a^3*b^5)*d*cosh(d*x + c)^5 + (3*a^5*b^3 - 2*a^4*b^4 + 3*a^3*b^5)*d*cosh(d*x + c)^3 + (a^5*b^3 - a^3*b^5)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
133,1,8070,0,0.598312," ","integrate(sech(d*x+c)^7/(a+b*tanh(d*x+c)^2)^3,x, algorithm=""fricas"")","\left[-\frac{4 \, {\left(4 \, a^{3} b + 5 \, a^{2} b^{2} - 2 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{7} + 28 \, {\left(4 \, a^{3} b + 5 \, a^{2} b^{2} - 2 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + 4 \, {\left(4 \, a^{3} b + 5 \, a^{2} b^{2} - 2 \, a b^{3} - 3 \, b^{4}\right)} \sinh\left(d x + c\right)^{7} + 4 \, {\left(4 \, a^{3} b - 19 \, a^{2} b^{2} - 14 \, a b^{3} + 9 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + 4 \, {\left(4 \, a^{3} b - 19 \, a^{2} b^{2} - 14 \, a b^{3} + 9 \, b^{4} + 21 \, {\left(4 \, a^{3} b + 5 \, 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)^{5} + 20 \, {\left(7 \, {\left(4 \, a^{3} b + 5 \, a^{2} b^{2} - 2 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(4 \, a^{3} b - 19 \, a^{2} b^{2} - 14 \, a b^{3} + 9 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} - 4 \, {\left(4 \, a^{3} b - 19 \, a^{2} b^{2} - 14 \, a b^{3} + 9 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + 4 \, {\left(35 \, {\left(4 \, a^{3} b + 5 \, a^{2} b^{2} - 2 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} - 4 \, a^{3} b + 19 \, a^{2} b^{2} + 14 \, a b^{3} - 9 \, b^{4} + 10 \, {\left(4 \, a^{3} b - 19 \, a^{2} b^{2} - 14 \, 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(4 \, a^{3} b + 5 \, a^{2} b^{2} - 2 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(4 \, a^{3} b - 19 \, a^{2} b^{2} - 14 \, a b^{3} + 9 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(4 \, a^{3} b - 19 \, a^{2} b^{2} - 14 \, a b^{3} + 9 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - {\left({\left(8 \, a^{4} + 12 \, a^{3} b + 3 \, a^{2} b^{2} + 2 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(8 \, a^{4} + 12 \, a^{3} b + 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(8 \, a^{4} + 12 \, a^{3} b + 3 \, a^{2} b^{2} + 2 \, a b^{3} + 3 \, b^{4}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(8 \, a^{4} - 4 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(8 \, a^{4} - 4 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - 3 \, b^{4} + 7 \, {\left(8 \, a^{4} + 12 \, a^{3} b + 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(8 \, a^{4} + 12 \, a^{3} b + 3 \, a^{2} b^{2} + 2 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(8 \, a^{4} - 4 \, a^{3} b - 5 \, 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} - 28 \, a^{3} b + 41 \, a^{2} b^{2} - 18 \, a b^{3} + 9 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(8 \, a^{4} + 12 \, a^{3} b + 3 \, a^{2} b^{2} + 2 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 24 \, a^{4} - 28 \, a^{3} b + 41 \, a^{2} b^{2} - 18 \, a b^{3} + 9 \, b^{4} + 30 \, {\left(8 \, a^{4} - 4 \, a^{3} b - 5 \, 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} + 8 \, a^{4} + 12 \, a^{3} b + 3 \, a^{2} b^{2} + 2 \, a b^{3} + 3 \, b^{4} + 8 \, {\left(7 \, {\left(8 \, a^{4} + 12 \, a^{3} b + 3 \, a^{2} b^{2} + 2 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(8 \, a^{4} - 4 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(24 \, a^{4} - 28 \, a^{3} b + 41 \, 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(8 \, a^{4} - 4 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(8 \, a^{4} + 12 \, a^{3} b + 3 \, a^{2} b^{2} + 2 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(8 \, a^{4} - 4 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 8 \, a^{4} - 4 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - 3 \, b^{4} + 3 \, {\left(24 \, a^{4} - 28 \, a^{3} b + 41 \, 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(8 \, a^{4} + 12 \, a^{3} b + 3 \, a^{2} b^{2} + 2 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(8 \, a^{4} - 4 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + {\left(24 \, a^{4} - 28 \, a^{3} b + 41 \, a^{2} b^{2} - 18 \, a b^{3} + 9 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{4} - 4 \, a^{3} b - 5 \, 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{-\frac{a + b}{a}} \log\left(\frac{{\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(3 \, a + b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} - 3 \, a - b\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(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) + 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{a + b}{a}} + a + b}{{\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) + 32 \, {\left({\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{4} - a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(a^{4} - a^{2} b^{2} + 7 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{4} - a^{2} b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(3 \, a^{4} - 2 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{4} + 3 \, a^{4} - 2 \, a^{3} b + 3 \, a^{2} b^{2} + 30 \, {\left(a^{4} - a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + a^{4} + 2 \, a^{3} b + a^{2} b^{2} + 8 \, {\left(7 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{4} - a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{4} - 2 \, 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(a^{4} - a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{4} - a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{4} + a^{4} - a^{2} b^{2} + 3 \, {\left(3 \, a^{4} - 2 \, 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({\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{4} - a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{4} - 2 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{4} - 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(4 \, a^{3} b + 5 \, a^{2} b^{2} - 2 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right) + 4 \, {\left(7 \, {\left(4 \, a^{3} b + 5 \, a^{2} b^{2} - 2 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 5 \, {\left(4 \, a^{3} b - 19 \, a^{2} b^{2} - 14 \, a b^{3} + 9 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} - 4 \, a^{3} b - 5 \, a^{2} b^{2} + 2 \, a b^{3} + 3 \, b^{4} - 3 \, {\left(4 \, a^{3} b - 19 \, a^{2} b^{2} - 14 \, 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^{4} b^{3} + 2 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{4} b^{3} + 2 \, 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^{4} b^{3} + 2 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{4} b^{3} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{4} b^{3} + 2 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{4} b^{3} - a^{2} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(3 \, a^{4} b^{3} - 2 \, a^{3} b^{4} + 3 \, a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{4} b^{3} + 2 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{4} b^{3} - 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^{4} b^{3} + 2 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 30 \, {\left(a^{4} b^{3} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{4} b^{3} - 2 \, a^{3} b^{4} + 3 \, a^{2} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{4} b^{3} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a^{4} b^{3} + 2 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{4} b^{3} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{4} b^{3} - 2 \, 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^{4} b^{3} + 2 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{4} b^{3} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{4} b^{3} - 2 \, a^{3} b^{4} + 3 \, a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{4} b^{3} - a^{2} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{4} b^{3} + 2 \, a^{3} b^{4} + a^{2} b^{5}\right)} d + 8 \, {\left({\left(a^{4} b^{3} + 2 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{4} b^{3} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{4} b^{3} - 2 \, a^{3} b^{4} + 3 \, a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(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{2 \, {\left(4 \, a^{3} b + 5 \, a^{2} b^{2} - 2 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{7} + 14 \, {\left(4 \, a^{3} b + 5 \, a^{2} b^{2} - 2 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + 2 \, {\left(4 \, a^{3} b + 5 \, a^{2} b^{2} - 2 \, a b^{3} - 3 \, b^{4}\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(4 \, a^{3} b - 19 \, a^{2} b^{2} - 14 \, a b^{3} + 9 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(4 \, a^{3} b - 19 \, a^{2} b^{2} - 14 \, a b^{3} + 9 \, b^{4} + 21 \, {\left(4 \, a^{3} b + 5 \, 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)^{5} + 10 \, {\left(7 \, {\left(4 \, a^{3} b + 5 \, a^{2} b^{2} - 2 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(4 \, a^{3} b - 19 \, a^{2} b^{2} - 14 \, a b^{3} + 9 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(4 \, a^{3} b - 19 \, a^{2} b^{2} - 14 \, a b^{3} + 9 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + 2 \, {\left(35 \, {\left(4 \, a^{3} b + 5 \, a^{2} b^{2} - 2 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} - 4 \, a^{3} b + 19 \, a^{2} b^{2} + 14 \, a b^{3} - 9 \, b^{4} + 10 \, {\left(4 \, a^{3} b - 19 \, a^{2} b^{2} - 14 \, 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(4 \, a^{3} b + 5 \, a^{2} b^{2} - 2 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(4 \, a^{3} b - 19 \, a^{2} b^{2} - 14 \, a b^{3} + 9 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(4 \, a^{3} b - 19 \, a^{2} b^{2} - 14 \, a b^{3} + 9 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} - {\left({\left(8 \, a^{4} + 12 \, a^{3} b + 3 \, a^{2} b^{2} + 2 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(8 \, a^{4} + 12 \, a^{3} b + 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(8 \, a^{4} + 12 \, a^{3} b + 3 \, a^{2} b^{2} + 2 \, a b^{3} + 3 \, b^{4}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(8 \, a^{4} - 4 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(8 \, a^{4} - 4 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - 3 \, b^{4} + 7 \, {\left(8 \, a^{4} + 12 \, a^{3} b + 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(8 \, a^{4} + 12 \, a^{3} b + 3 \, a^{2} b^{2} + 2 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(8 \, a^{4} - 4 \, a^{3} b - 5 \, 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} - 28 \, a^{3} b + 41 \, a^{2} b^{2} - 18 \, a b^{3} + 9 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(8 \, a^{4} + 12 \, a^{3} b + 3 \, a^{2} b^{2} + 2 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 24 \, a^{4} - 28 \, a^{3} b + 41 \, a^{2} b^{2} - 18 \, a b^{3} + 9 \, b^{4} + 30 \, {\left(8 \, a^{4} - 4 \, a^{3} b - 5 \, 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} + 8 \, a^{4} + 12 \, a^{3} b + 3 \, a^{2} b^{2} + 2 \, a b^{3} + 3 \, b^{4} + 8 \, {\left(7 \, {\left(8 \, a^{4} + 12 \, a^{3} b + 3 \, a^{2} b^{2} + 2 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(8 \, a^{4} - 4 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(24 \, a^{4} - 28 \, a^{3} b + 41 \, 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(8 \, a^{4} - 4 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(8 \, a^{4} + 12 \, a^{3} b + 3 \, a^{2} b^{2} + 2 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(8 \, a^{4} - 4 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 8 \, a^{4} - 4 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - 3 \, b^{4} + 3 \, {\left(24 \, a^{4} - 28 \, a^{3} b + 41 \, 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(8 \, a^{4} + 12 \, a^{3} b + 3 \, a^{2} b^{2} + 2 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(8 \, a^{4} - 4 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + {\left(24 \, a^{4} - 28 \, a^{3} b + 41 \, a^{2} b^{2} - 18 \, a b^{3} + 9 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{4} - 4 \, a^{3} b - 5 \, 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{\frac{a + b}{a}} \arctan\left(\frac{1}{2} \, \sqrt{\frac{a + b}{a}} {\left(\cosh\left(d x + c\right) + \sinh\left(d x + c\right)\right)}\right) - {\left({\left(8 \, a^{4} + 12 \, a^{3} b + 3 \, a^{2} b^{2} + 2 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(8 \, a^{4} + 12 \, a^{3} b + 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(8 \, a^{4} + 12 \, a^{3} b + 3 \, a^{2} b^{2} + 2 \, a b^{3} + 3 \, b^{4}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(8 \, a^{4} - 4 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(8 \, a^{4} - 4 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - 3 \, b^{4} + 7 \, {\left(8 \, a^{4} + 12 \, a^{3} b + 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(8 \, a^{4} + 12 \, a^{3} b + 3 \, a^{2} b^{2} + 2 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(8 \, a^{4} - 4 \, a^{3} b - 5 \, 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} - 28 \, a^{3} b + 41 \, a^{2} b^{2} - 18 \, a b^{3} + 9 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(8 \, a^{4} + 12 \, a^{3} b + 3 \, a^{2} b^{2} + 2 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 24 \, a^{4} - 28 \, a^{3} b + 41 \, a^{2} b^{2} - 18 \, a b^{3} + 9 \, b^{4} + 30 \, {\left(8 \, a^{4} - 4 \, a^{3} b - 5 \, 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} + 8 \, a^{4} + 12 \, a^{3} b + 3 \, a^{2} b^{2} + 2 \, a b^{3} + 3 \, b^{4} + 8 \, {\left(7 \, {\left(8 \, a^{4} + 12 \, a^{3} b + 3 \, a^{2} b^{2} + 2 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(8 \, a^{4} - 4 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(24 \, a^{4} - 28 \, a^{3} b + 41 \, 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(8 \, a^{4} - 4 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(8 \, a^{4} + 12 \, a^{3} b + 3 \, a^{2} b^{2} + 2 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(8 \, a^{4} - 4 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 8 \, a^{4} - 4 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - 3 \, b^{4} + 3 \, {\left(24 \, a^{4} - 28 \, a^{3} b + 41 \, 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(8 \, a^{4} + 12 \, a^{3} b + 3 \, a^{2} b^{2} + 2 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(8 \, a^{4} - 4 \, a^{3} b - 5 \, a^{2} b^{2} + 4 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + {\left(24 \, a^{4} - 28 \, a^{3} b + 41 \, a^{2} b^{2} - 18 \, a b^{3} + 9 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{4} - 4 \, a^{3} b - 5 \, 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{\frac{a + b}{a}} \arctan\left(\frac{{\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(3 \, a - b\right)} \cosh\left(d x + c\right) + {\left(3 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} + 3 \, a - b\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a + b}{a}}}{2 \, {\left(a + b\right)}}\right) + 16 \, {\left({\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{4} - a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(a^{4} - a^{2} b^{2} + 7 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{4} - a^{2} b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(3 \, a^{4} - 2 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{4} + 3 \, a^{4} - 2 \, a^{3} b + 3 \, a^{2} b^{2} + 30 \, {\left(a^{4} - a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + a^{4} + 2 \, a^{3} b + a^{2} b^{2} + 8 \, {\left(7 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{4} - a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{4} - 2 \, 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(a^{4} - a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{4} - a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{4} + a^{4} - a^{2} b^{2} + 3 \, {\left(3 \, a^{4} - 2 \, 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({\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{4} - a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{4} - 2 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{4} - 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(4 \, a^{3} b + 5 \, a^{2} b^{2} - 2 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right) + 2 \, {\left(7 \, {\left(4 \, a^{3} b + 5 \, a^{2} b^{2} - 2 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 5 \, {\left(4 \, a^{3} b - 19 \, a^{2} b^{2} - 14 \, a b^{3} + 9 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} - 4 \, a^{3} b - 5 \, a^{2} b^{2} + 2 \, a b^{3} + 3 \, b^{4} - 3 \, {\left(4 \, a^{3} b - 19 \, a^{2} b^{2} - 14 \, 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^{4} b^{3} + 2 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{4} b^{3} + 2 \, 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^{4} b^{3} + 2 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{4} b^{3} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{4} b^{3} + 2 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{4} b^{3} - a^{2} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(3 \, a^{4} b^{3} - 2 \, a^{3} b^{4} + 3 \, a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{4} b^{3} + 2 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{4} b^{3} - 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^{4} b^{3} + 2 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 30 \, {\left(a^{4} b^{3} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{4} b^{3} - 2 \, a^{3} b^{4} + 3 \, a^{2} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{4} b^{3} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a^{4} b^{3} + 2 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{4} b^{3} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{4} b^{3} - 2 \, 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^{4} b^{3} + 2 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{4} b^{3} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{4} b^{3} - 2 \, a^{3} b^{4} + 3 \, a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{4} b^{3} - a^{2} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{4} b^{3} + 2 \, a^{3} b^{4} + a^{2} b^{5}\right)} d + 8 \, {\left({\left(a^{4} b^{3} + 2 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{4} b^{3} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{4} b^{3} - 2 \, a^{3} b^{4} + 3 \, a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(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,"[-1/16*(4*(4*a^3*b + 5*a^2*b^2 - 2*a*b^3 - 3*b^4)*cosh(d*x + c)^7 + 28*(4*a^3*b + 5*a^2*b^2 - 2*a*b^3 - 3*b^4)*cosh(d*x + c)*sinh(d*x + c)^6 + 4*(4*a^3*b + 5*a^2*b^2 - 2*a*b^3 - 3*b^4)*sinh(d*x + c)^7 + 4*(4*a^3*b - 19*a^2*b^2 - 14*a*b^3 + 9*b^4)*cosh(d*x + c)^5 + 4*(4*a^3*b - 19*a^2*b^2 - 14*a*b^3 + 9*b^4 + 21*(4*a^3*b + 5*a^2*b^2 - 2*a*b^3 - 3*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 20*(7*(4*a^3*b + 5*a^2*b^2 - 2*a*b^3 - 3*b^4)*cosh(d*x + c)^3 + (4*a^3*b - 19*a^2*b^2 - 14*a*b^3 + 9*b^4)*cosh(d*x + c))*sinh(d*x + c)^4 - 4*(4*a^3*b - 19*a^2*b^2 - 14*a*b^3 + 9*b^4)*cosh(d*x + c)^3 + 4*(35*(4*a^3*b + 5*a^2*b^2 - 2*a*b^3 - 3*b^4)*cosh(d*x + c)^4 - 4*a^3*b + 19*a^2*b^2 + 14*a*b^3 - 9*b^4 + 10*(4*a^3*b - 19*a^2*b^2 - 14*a*b^3 + 9*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 4*(21*(4*a^3*b + 5*a^2*b^2 - 2*a*b^3 - 3*b^4)*cosh(d*x + c)^5 + 10*(4*a^3*b - 19*a^2*b^2 - 14*a*b^3 + 9*b^4)*cosh(d*x + c)^3 - 3*(4*a^3*b - 19*a^2*b^2 - 14*a*b^3 + 9*b^4)*cosh(d*x + c))*sinh(d*x + c)^2 - ((8*a^4 + 12*a^3*b + 3*a^2*b^2 + 2*a*b^3 + 3*b^4)*cosh(d*x + c)^8 + 8*(8*a^4 + 12*a^3*b + 3*a^2*b^2 + 2*a*b^3 + 3*b^4)*cosh(d*x + c)*sinh(d*x + c)^7 + (8*a^4 + 12*a^3*b + 3*a^2*b^2 + 2*a*b^3 + 3*b^4)*sinh(d*x + c)^8 + 4*(8*a^4 - 4*a^3*b - 5*a^2*b^2 + 4*a*b^3 - 3*b^4)*cosh(d*x + c)^6 + 4*(8*a^4 - 4*a^3*b - 5*a^2*b^2 + 4*a*b^3 - 3*b^4 + 7*(8*a^4 + 12*a^3*b + 3*a^2*b^2 + 2*a*b^3 + 3*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(8*a^4 + 12*a^3*b + 3*a^2*b^2 + 2*a*b^3 + 3*b^4)*cosh(d*x + c)^3 + 3*(8*a^4 - 4*a^3*b - 5*a^2*b^2 + 4*a*b^3 - 3*b^4)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(24*a^4 - 28*a^3*b + 41*a^2*b^2 - 18*a*b^3 + 9*b^4)*cosh(d*x + c)^4 + 2*(35*(8*a^4 + 12*a^3*b + 3*a^2*b^2 + 2*a*b^3 + 3*b^4)*cosh(d*x + c)^4 + 24*a^4 - 28*a^3*b + 41*a^2*b^2 - 18*a*b^3 + 9*b^4 + 30*(8*a^4 - 4*a^3*b - 5*a^2*b^2 + 4*a*b^3 - 3*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*a^4 + 12*a^3*b + 3*a^2*b^2 + 2*a*b^3 + 3*b^4 + 8*(7*(8*a^4 + 12*a^3*b + 3*a^2*b^2 + 2*a*b^3 + 3*b^4)*cosh(d*x + c)^5 + 10*(8*a^4 - 4*a^3*b - 5*a^2*b^2 + 4*a*b^3 - 3*b^4)*cosh(d*x + c)^3 + (24*a^4 - 28*a^3*b + 41*a^2*b^2 - 18*a*b^3 + 9*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(8*a^4 - 4*a^3*b - 5*a^2*b^2 + 4*a*b^3 - 3*b^4)*cosh(d*x + c)^2 + 4*(7*(8*a^4 + 12*a^3*b + 3*a^2*b^2 + 2*a*b^3 + 3*b^4)*cosh(d*x + c)^6 + 15*(8*a^4 - 4*a^3*b - 5*a^2*b^2 + 4*a*b^3 - 3*b^4)*cosh(d*x + c)^4 + 8*a^4 - 4*a^3*b - 5*a^2*b^2 + 4*a*b^3 - 3*b^4 + 3*(24*a^4 - 28*a^3*b + 41*a^2*b^2 - 18*a*b^3 + 9*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((8*a^4 + 12*a^3*b + 3*a^2*b^2 + 2*a*b^3 + 3*b^4)*cosh(d*x + c)^7 + 3*(8*a^4 - 4*a^3*b - 5*a^2*b^2 + 4*a*b^3 - 3*b^4)*cosh(d*x + c)^5 + (24*a^4 - 28*a^3*b + 41*a^2*b^2 - 18*a*b^3 + 9*b^4)*cosh(d*x + c)^3 + (8*a^4 - 4*a^3*b - 5*a^2*b^2 + 4*a*b^3 - 3*b^4)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-(a + b)/a)*log(((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*(3*a + b)*cosh(d*x + c)^2 + 2*(3*(a + b)*cosh(d*x + c)^2 - 3*a - b)*sinh(d*x + c)^2 + 4*((a + b)*cosh(d*x + c)^3 - (3*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(-(a + b)/a) + a + b)/((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)) + 32*((a^4 + 2*a^3*b + a^2*b^2)*cosh(d*x + c)^8 + 8*(a^4 + 2*a^3*b + a^2*b^2)*cosh(d*x + c)*sinh(d*x + c)^7 + (a^4 + 2*a^3*b + a^2*b^2)*sinh(d*x + c)^8 + 4*(a^4 - a^2*b^2)*cosh(d*x + c)^6 + 4*(a^4 - a^2*b^2 + 7*(a^4 + 2*a^3*b + a^2*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(a^4 + 2*a^3*b + a^2*b^2)*cosh(d*x + c)^3 + 3*(a^4 - a^2*b^2)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(3*a^4 - 2*a^3*b + 3*a^2*b^2)*cosh(d*x + c)^4 + 2*(35*(a^4 + 2*a^3*b + a^2*b^2)*cosh(d*x + c)^4 + 3*a^4 - 2*a^3*b + 3*a^2*b^2 + 30*(a^4 - a^2*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + a^4 + 2*a^3*b + a^2*b^2 + 8*(7*(a^4 + 2*a^3*b + a^2*b^2)*cosh(d*x + c)^5 + 10*(a^4 - a^2*b^2)*cosh(d*x + c)^3 + (3*a^4 - 2*a^3*b + 3*a^2*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(a^4 - a^2*b^2)*cosh(d*x + c)^2 + 4*(7*(a^4 + 2*a^3*b + a^2*b^2)*cosh(d*x + c)^6 + 15*(a^4 - a^2*b^2)*cosh(d*x + c)^4 + a^4 - a^2*b^2 + 3*(3*a^4 - 2*a^3*b + 3*a^2*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((a^4 + 2*a^3*b + a^2*b^2)*cosh(d*x + c)^7 + 3*(a^4 - a^2*b^2)*cosh(d*x + c)^5 + (3*a^4 - 2*a^3*b + 3*a^2*b^2)*cosh(d*x + c)^3 + (a^4 - a^2*b^2)*cosh(d*x + c))*sinh(d*x + c))*arctan(cosh(d*x + c) + sinh(d*x + c)) - 4*(4*a^3*b + 5*a^2*b^2 - 2*a*b^3 - 3*b^4)*cosh(d*x + c) + 4*(7*(4*a^3*b + 5*a^2*b^2 - 2*a*b^3 - 3*b^4)*cosh(d*x + c)^6 + 5*(4*a^3*b - 19*a^2*b^2 - 14*a*b^3 + 9*b^4)*cosh(d*x + c)^4 - 4*a^3*b - 5*a^2*b^2 + 2*a*b^3 + 3*b^4 - 3*(4*a^3*b - 19*a^2*b^2 - 14*a*b^3 + 9*b^4)*cosh(d*x + c)^2)*sinh(d*x + c))/((a^4*b^3 + 2*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)^8 + 8*(a^4*b^3 + 2*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^4*b^3 + 2*a^3*b^4 + a^2*b^5)*d*sinh(d*x + c)^8 + 4*(a^4*b^3 - a^2*b^5)*d*cosh(d*x + c)^6 + 4*(7*(a^4*b^3 + 2*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)^2 + (a^4*b^3 - a^2*b^5)*d)*sinh(d*x + c)^6 + 2*(3*a^4*b^3 - 2*a^3*b^4 + 3*a^2*b^5)*d*cosh(d*x + c)^4 + 8*(7*(a^4*b^3 + 2*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)^3 + 3*(a^4*b^3 - a^2*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^4*b^3 + 2*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)^4 + 30*(a^4*b^3 - a^2*b^5)*d*cosh(d*x + c)^2 + (3*a^4*b^3 - 2*a^3*b^4 + 3*a^2*b^5)*d)*sinh(d*x + c)^4 + 4*(a^4*b^3 - a^2*b^5)*d*cosh(d*x + c)^2 + 8*(7*(a^4*b^3 + 2*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)^5 + 10*(a^4*b^3 - a^2*b^5)*d*cosh(d*x + c)^3 + (3*a^4*b^3 - 2*a^3*b^4 + 3*a^2*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^4*b^3 + 2*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)^6 + 15*(a^4*b^3 - a^2*b^5)*d*cosh(d*x + c)^4 + 3*(3*a^4*b^3 - 2*a^3*b^4 + 3*a^2*b^5)*d*cosh(d*x + c)^2 + (a^4*b^3 - a^2*b^5)*d)*sinh(d*x + c)^2 + (a^4*b^3 + 2*a^3*b^4 + a^2*b^5)*d + 8*((a^4*b^3 + 2*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)^7 + 3*(a^4*b^3 - a^2*b^5)*d*cosh(d*x + c)^5 + (3*a^4*b^3 - 2*a^3*b^4 + 3*a^2*b^5)*d*cosh(d*x + c)^3 + (a^4*b^3 - a^2*b^5)*d*cosh(d*x + c))*sinh(d*x + c)), -1/8*(2*(4*a^3*b + 5*a^2*b^2 - 2*a*b^3 - 3*b^4)*cosh(d*x + c)^7 + 14*(4*a^3*b + 5*a^2*b^2 - 2*a*b^3 - 3*b^4)*cosh(d*x + c)*sinh(d*x + c)^6 + 2*(4*a^3*b + 5*a^2*b^2 - 2*a*b^3 - 3*b^4)*sinh(d*x + c)^7 + 2*(4*a^3*b - 19*a^2*b^2 - 14*a*b^3 + 9*b^4)*cosh(d*x + c)^5 + 2*(4*a^3*b - 19*a^2*b^2 - 14*a*b^3 + 9*b^4 + 21*(4*a^3*b + 5*a^2*b^2 - 2*a*b^3 - 3*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 10*(7*(4*a^3*b + 5*a^2*b^2 - 2*a*b^3 - 3*b^4)*cosh(d*x + c)^3 + (4*a^3*b - 19*a^2*b^2 - 14*a*b^3 + 9*b^4)*cosh(d*x + c))*sinh(d*x + c)^4 - 2*(4*a^3*b - 19*a^2*b^2 - 14*a*b^3 + 9*b^4)*cosh(d*x + c)^3 + 2*(35*(4*a^3*b + 5*a^2*b^2 - 2*a*b^3 - 3*b^4)*cosh(d*x + c)^4 - 4*a^3*b + 19*a^2*b^2 + 14*a*b^3 - 9*b^4 + 10*(4*a^3*b - 19*a^2*b^2 - 14*a*b^3 + 9*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 2*(21*(4*a^3*b + 5*a^2*b^2 - 2*a*b^3 - 3*b^4)*cosh(d*x + c)^5 + 10*(4*a^3*b - 19*a^2*b^2 - 14*a*b^3 + 9*b^4)*cosh(d*x + c)^3 - 3*(4*a^3*b - 19*a^2*b^2 - 14*a*b^3 + 9*b^4)*cosh(d*x + c))*sinh(d*x + c)^2 - ((8*a^4 + 12*a^3*b + 3*a^2*b^2 + 2*a*b^3 + 3*b^4)*cosh(d*x + c)^8 + 8*(8*a^4 + 12*a^3*b + 3*a^2*b^2 + 2*a*b^3 + 3*b^4)*cosh(d*x + c)*sinh(d*x + c)^7 + (8*a^4 + 12*a^3*b + 3*a^2*b^2 + 2*a*b^3 + 3*b^4)*sinh(d*x + c)^8 + 4*(8*a^4 - 4*a^3*b - 5*a^2*b^2 + 4*a*b^3 - 3*b^4)*cosh(d*x + c)^6 + 4*(8*a^4 - 4*a^3*b - 5*a^2*b^2 + 4*a*b^3 - 3*b^4 + 7*(8*a^4 + 12*a^3*b + 3*a^2*b^2 + 2*a*b^3 + 3*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(8*a^4 + 12*a^3*b + 3*a^2*b^2 + 2*a*b^3 + 3*b^4)*cosh(d*x + c)^3 + 3*(8*a^4 - 4*a^3*b - 5*a^2*b^2 + 4*a*b^3 - 3*b^4)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(24*a^4 - 28*a^3*b + 41*a^2*b^2 - 18*a*b^3 + 9*b^4)*cosh(d*x + c)^4 + 2*(35*(8*a^4 + 12*a^3*b + 3*a^2*b^2 + 2*a*b^3 + 3*b^4)*cosh(d*x + c)^4 + 24*a^4 - 28*a^3*b + 41*a^2*b^2 - 18*a*b^3 + 9*b^4 + 30*(8*a^4 - 4*a^3*b - 5*a^2*b^2 + 4*a*b^3 - 3*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*a^4 + 12*a^3*b + 3*a^2*b^2 + 2*a*b^3 + 3*b^4 + 8*(7*(8*a^4 + 12*a^3*b + 3*a^2*b^2 + 2*a*b^3 + 3*b^4)*cosh(d*x + c)^5 + 10*(8*a^4 - 4*a^3*b - 5*a^2*b^2 + 4*a*b^3 - 3*b^4)*cosh(d*x + c)^3 + (24*a^4 - 28*a^3*b + 41*a^2*b^2 - 18*a*b^3 + 9*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(8*a^4 - 4*a^3*b - 5*a^2*b^2 + 4*a*b^3 - 3*b^4)*cosh(d*x + c)^2 + 4*(7*(8*a^4 + 12*a^3*b + 3*a^2*b^2 + 2*a*b^3 + 3*b^4)*cosh(d*x + c)^6 + 15*(8*a^4 - 4*a^3*b - 5*a^2*b^2 + 4*a*b^3 - 3*b^4)*cosh(d*x + c)^4 + 8*a^4 - 4*a^3*b - 5*a^2*b^2 + 4*a*b^3 - 3*b^4 + 3*(24*a^4 - 28*a^3*b + 41*a^2*b^2 - 18*a*b^3 + 9*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((8*a^4 + 12*a^3*b + 3*a^2*b^2 + 2*a*b^3 + 3*b^4)*cosh(d*x + c)^7 + 3*(8*a^4 - 4*a^3*b - 5*a^2*b^2 + 4*a*b^3 - 3*b^4)*cosh(d*x + c)^5 + (24*a^4 - 28*a^3*b + 41*a^2*b^2 - 18*a*b^3 + 9*b^4)*cosh(d*x + c)^3 + (8*a^4 - 4*a^3*b - 5*a^2*b^2 + 4*a*b^3 - 3*b^4)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a + b)/a)*arctan(1/2*sqrt((a + b)/a)*(cosh(d*x + c) + sinh(d*x + c))) - ((8*a^4 + 12*a^3*b + 3*a^2*b^2 + 2*a*b^3 + 3*b^4)*cosh(d*x + c)^8 + 8*(8*a^4 + 12*a^3*b + 3*a^2*b^2 + 2*a*b^3 + 3*b^4)*cosh(d*x + c)*sinh(d*x + c)^7 + (8*a^4 + 12*a^3*b + 3*a^2*b^2 + 2*a*b^3 + 3*b^4)*sinh(d*x + c)^8 + 4*(8*a^4 - 4*a^3*b - 5*a^2*b^2 + 4*a*b^3 - 3*b^4)*cosh(d*x + c)^6 + 4*(8*a^4 - 4*a^3*b - 5*a^2*b^2 + 4*a*b^3 - 3*b^4 + 7*(8*a^4 + 12*a^3*b + 3*a^2*b^2 + 2*a*b^3 + 3*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(8*a^4 + 12*a^3*b + 3*a^2*b^2 + 2*a*b^3 + 3*b^4)*cosh(d*x + c)^3 + 3*(8*a^4 - 4*a^3*b - 5*a^2*b^2 + 4*a*b^3 - 3*b^4)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(24*a^4 - 28*a^3*b + 41*a^2*b^2 - 18*a*b^3 + 9*b^4)*cosh(d*x + c)^4 + 2*(35*(8*a^4 + 12*a^3*b + 3*a^2*b^2 + 2*a*b^3 + 3*b^4)*cosh(d*x + c)^4 + 24*a^4 - 28*a^3*b + 41*a^2*b^2 - 18*a*b^3 + 9*b^4 + 30*(8*a^4 - 4*a^3*b - 5*a^2*b^2 + 4*a*b^3 - 3*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*a^4 + 12*a^3*b + 3*a^2*b^2 + 2*a*b^3 + 3*b^4 + 8*(7*(8*a^4 + 12*a^3*b + 3*a^2*b^2 + 2*a*b^3 + 3*b^4)*cosh(d*x + c)^5 + 10*(8*a^4 - 4*a^3*b - 5*a^2*b^2 + 4*a*b^3 - 3*b^4)*cosh(d*x + c)^3 + (24*a^4 - 28*a^3*b + 41*a^2*b^2 - 18*a*b^3 + 9*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(8*a^4 - 4*a^3*b - 5*a^2*b^2 + 4*a*b^3 - 3*b^4)*cosh(d*x + c)^2 + 4*(7*(8*a^4 + 12*a^3*b + 3*a^2*b^2 + 2*a*b^3 + 3*b^4)*cosh(d*x + c)^6 + 15*(8*a^4 - 4*a^3*b - 5*a^2*b^2 + 4*a*b^3 - 3*b^4)*cosh(d*x + c)^4 + 8*a^4 - 4*a^3*b - 5*a^2*b^2 + 4*a*b^3 - 3*b^4 + 3*(24*a^4 - 28*a^3*b + 41*a^2*b^2 - 18*a*b^3 + 9*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((8*a^4 + 12*a^3*b + 3*a^2*b^2 + 2*a*b^3 + 3*b^4)*cosh(d*x + c)^7 + 3*(8*a^4 - 4*a^3*b - 5*a^2*b^2 + 4*a*b^3 - 3*b^4)*cosh(d*x + c)^5 + (24*a^4 - 28*a^3*b + 41*a^2*b^2 - 18*a*b^3 + 9*b^4)*cosh(d*x + c)^3 + (8*a^4 - 4*a^3*b - 5*a^2*b^2 + 4*a*b^3 - 3*b^4)*cosh(d*x + c))*sinh(d*x + c))*sqrt((a + b)/a)*arctan(1/2*((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 + (3*a - b)*cosh(d*x + c) + (3*(a + b)*cosh(d*x + c)^2 + 3*a - b)*sinh(d*x + c))*sqrt((a + b)/a)/(a + b)) + 16*((a^4 + 2*a^3*b + a^2*b^2)*cosh(d*x + c)^8 + 8*(a^4 + 2*a^3*b + a^2*b^2)*cosh(d*x + c)*sinh(d*x + c)^7 + (a^4 + 2*a^3*b + a^2*b^2)*sinh(d*x + c)^8 + 4*(a^4 - a^2*b^2)*cosh(d*x + c)^6 + 4*(a^4 - a^2*b^2 + 7*(a^4 + 2*a^3*b + a^2*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(a^4 + 2*a^3*b + a^2*b^2)*cosh(d*x + c)^3 + 3*(a^4 - a^2*b^2)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(3*a^4 - 2*a^3*b + 3*a^2*b^2)*cosh(d*x + c)^4 + 2*(35*(a^4 + 2*a^3*b + a^2*b^2)*cosh(d*x + c)^4 + 3*a^4 - 2*a^3*b + 3*a^2*b^2 + 30*(a^4 - a^2*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + a^4 + 2*a^3*b + a^2*b^2 + 8*(7*(a^4 + 2*a^3*b + a^2*b^2)*cosh(d*x + c)^5 + 10*(a^4 - a^2*b^2)*cosh(d*x + c)^3 + (3*a^4 - 2*a^3*b + 3*a^2*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(a^4 - a^2*b^2)*cosh(d*x + c)^2 + 4*(7*(a^4 + 2*a^3*b + a^2*b^2)*cosh(d*x + c)^6 + 15*(a^4 - a^2*b^2)*cosh(d*x + c)^4 + a^4 - a^2*b^2 + 3*(3*a^4 - 2*a^3*b + 3*a^2*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((a^4 + 2*a^3*b + a^2*b^2)*cosh(d*x + c)^7 + 3*(a^4 - a^2*b^2)*cosh(d*x + c)^5 + (3*a^4 - 2*a^3*b + 3*a^2*b^2)*cosh(d*x + c)^3 + (a^4 - a^2*b^2)*cosh(d*x + c))*sinh(d*x + c))*arctan(cosh(d*x + c) + sinh(d*x + c)) - 2*(4*a^3*b + 5*a^2*b^2 - 2*a*b^3 - 3*b^4)*cosh(d*x + c) + 2*(7*(4*a^3*b + 5*a^2*b^2 - 2*a*b^3 - 3*b^4)*cosh(d*x + c)^6 + 5*(4*a^3*b - 19*a^2*b^2 - 14*a*b^3 + 9*b^4)*cosh(d*x + c)^4 - 4*a^3*b - 5*a^2*b^2 + 2*a*b^3 + 3*b^4 - 3*(4*a^3*b - 19*a^2*b^2 - 14*a*b^3 + 9*b^4)*cosh(d*x + c)^2)*sinh(d*x + c))/((a^4*b^3 + 2*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)^8 + 8*(a^4*b^3 + 2*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^4*b^3 + 2*a^3*b^4 + a^2*b^5)*d*sinh(d*x + c)^8 + 4*(a^4*b^3 - a^2*b^5)*d*cosh(d*x + c)^6 + 4*(7*(a^4*b^3 + 2*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)^2 + (a^4*b^3 - a^2*b^5)*d)*sinh(d*x + c)^6 + 2*(3*a^4*b^3 - 2*a^3*b^4 + 3*a^2*b^5)*d*cosh(d*x + c)^4 + 8*(7*(a^4*b^3 + 2*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)^3 + 3*(a^4*b^3 - a^2*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^4*b^3 + 2*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)^4 + 30*(a^4*b^3 - a^2*b^5)*d*cosh(d*x + c)^2 + (3*a^4*b^3 - 2*a^3*b^4 + 3*a^2*b^5)*d)*sinh(d*x + c)^4 + 4*(a^4*b^3 - a^2*b^5)*d*cosh(d*x + c)^2 + 8*(7*(a^4*b^3 + 2*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)^5 + 10*(a^4*b^3 - a^2*b^5)*d*cosh(d*x + c)^3 + (3*a^4*b^3 - 2*a^3*b^4 + 3*a^2*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^4*b^3 + 2*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)^6 + 15*(a^4*b^3 - a^2*b^5)*d*cosh(d*x + c)^4 + 3*(3*a^4*b^3 - 2*a^3*b^4 + 3*a^2*b^5)*d*cosh(d*x + c)^2 + (a^4*b^3 - a^2*b^5)*d)*sinh(d*x + c)^2 + (a^4*b^3 + 2*a^3*b^4 + a^2*b^5)*d + 8*((a^4*b^3 + 2*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)^7 + 3*(a^4*b^3 - a^2*b^5)*d*cosh(d*x + c)^5 + (3*a^4*b^3 - 2*a^3*b^4 + 3*a^2*b^5)*d*cosh(d*x + c)^3 + (a^4*b^3 - a^2*b^5)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
134,1,339,0,0.411668," ","integrate(tanh(d*x+c)^4*(a+b*tanh(d*x+c)^2),x, algorithm=""fricas"")","\frac{{\left(15 \, {\left(a + b\right)} d x + 20 \, a + 23 \, b\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(15 \, {\left(a + b\right)} d x + 20 \, a + 23 \, b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} - {\left(20 \, a + 23 \, b\right)} \sinh\left(d x + c\right)^{5} + 5 \, {\left(15 \, {\left(a + b\right)} d x + 20 \, a + 23 \, b\right)} \cosh\left(d x + c\right)^{3} - 5 \, {\left(2 \, {\left(20 \, a + 23 \, b\right)} \cosh\left(d x + c\right)^{2} + 8 \, a + 5 \, b\right)} \sinh\left(d x + c\right)^{3} + 5 \, {\left(2 \, {\left(15 \, {\left(a + b\right)} d x + 20 \, a + 23 \, b\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(15 \, {\left(a + b\right)} d x + 20 \, a + 23 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 10 \, {\left(15 \, {\left(a + b\right)} d x + 20 \, a + 23 \, b\right)} \cosh\left(d x + c\right) - 5 \, {\left({\left(20 \, a + 23 \, b\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(8 \, a + 5 \, b\right)} \cosh\left(d x + c\right)^{2} + 4 \, a + 10 \, b\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*(a + b)*d*x + 20*a + 23*b)*cosh(d*x + c)^5 + 5*(15*(a + b)*d*x + 20*a + 23*b)*cosh(d*x + c)*sinh(d*x + c)^4 - (20*a + 23*b)*sinh(d*x + c)^5 + 5*(15*(a + b)*d*x + 20*a + 23*b)*cosh(d*x + c)^3 - 5*(2*(20*a + 23*b)*cosh(d*x + c)^2 + 8*a + 5*b)*sinh(d*x + c)^3 + 5*(2*(15*(a + b)*d*x + 20*a + 23*b)*cosh(d*x + c)^3 + 3*(15*(a + b)*d*x + 20*a + 23*b)*cosh(d*x + c))*sinh(d*x + c)^2 + 10*(15*(a + b)*d*x + 20*a + 23*b)*cosh(d*x + c) - 5*((20*a + 23*b)*cosh(d*x + c)^4 + 3*(8*a + 5*b)*cosh(d*x + c)^2 + 4*a + 10*b)*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
135,1,1205,0,0.444310," ","integrate(tanh(d*x+c)^3*(a+b*tanh(d*x+c)^2),x, algorithm=""fricas"")","-\frac{{\left(a + b\right)} d x \cosh\left(d x + c\right)^{8} + 8 \, {\left(a + b\right)} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a + b\right)} d x \sinh\left(d x + c\right)^{8} + 2 \, {\left(2 \, {\left(a + b\right)} d x - a - 2 \, b\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(14 \, {\left(a + b\right)} d x \cosh\left(d x + c\right)^{2} + 2 \, {\left(a + b\right)} d x - a - 2 \, b\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(14 \, {\left(a + b\right)} d x \cosh\left(d x + c\right)^{3} + 3 \, {\left(2 \, {\left(a + b\right)} d x - a - 2 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(3 \, {\left(a + b\right)} d x - 2 \, a - 2 \, b\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(a + b\right)} d x \cosh\left(d x + c\right)^{4} + 3 \, {\left(a + b\right)} d x + 15 \, {\left(2 \, {\left(a + b\right)} d x - a - 2 \, b\right)} \cosh\left(d x + c\right)^{2} - 2 \, a - 2 \, b\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a + b\right)} d x \cosh\left(d x + c\right)^{5} + 5 \, {\left(2 \, {\left(a + b\right)} d x - a - 2 \, b\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, {\left(a + b\right)} d x - 2 \, a - 2 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(a + b\right)} d x + 2 \, {\left(2 \, {\left(a + b\right)} d x - a - 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(14 \, {\left(a + b\right)} d x \cosh\left(d x + c\right)^{6} + 15 \, {\left(2 \, {\left(a + b\right)} d x - a - 2 \, b\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(a + b\right)} d x + 6 \, {\left(3 \, {\left(a + b\right)} d x - 2 \, a - 2 \, b\right)} \cosh\left(d x + c\right)^{2} - a - 2 \, b\right)} \sinh\left(d x + c\right)^{2} - {\left({\left(a + b\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(a + b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a + b\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} + a + b\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a + b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 6 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{4} + 30 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} + 3 \, a + 3 \, b\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a + b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{4} + 9 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} + a + b\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left({\left(a + b\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{5} + 3 \, {\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)} \log\left(\frac{2 \, \cosh\left(d x + c\right)}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) + 4 \, {\left(2 \, {\left(a + b\right)} d x \cosh\left(d x + c\right)^{7} + 3 \, {\left(2 \, {\left(a + b\right)} d x - a - 2 \, b\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(3 \, {\left(a + b\right)} d x - 2 \, a - 2 \, b\right)} \cosh\left(d x + c\right)^{3} + {\left(2 \, {\left(a + b\right)} d x - a - 2 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{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}"," ",0,"-((a + b)*d*x*cosh(d*x + c)^8 + 8*(a + b)*d*x*cosh(d*x + c)*sinh(d*x + c)^7 + (a + b)*d*x*sinh(d*x + c)^8 + 2*(2*(a + b)*d*x - a - 2*b)*cosh(d*x + c)^6 + 2*(14*(a + b)*d*x*cosh(d*x + c)^2 + 2*(a + b)*d*x - a - 2*b)*sinh(d*x + c)^6 + 4*(14*(a + b)*d*x*cosh(d*x + c)^3 + 3*(2*(a + b)*d*x - a - 2*b)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(3*(a + b)*d*x - 2*a - 2*b)*cosh(d*x + c)^4 + 2*(35*(a + b)*d*x*cosh(d*x + c)^4 + 3*(a + b)*d*x + 15*(2*(a + b)*d*x - a - 2*b)*cosh(d*x + c)^2 - 2*a - 2*b)*sinh(d*x + c)^4 + 8*(7*(a + b)*d*x*cosh(d*x + c)^5 + 5*(2*(a + b)*d*x - a - 2*b)*cosh(d*x + c)^3 + (3*(a + b)*d*x - 2*a - 2*b)*cosh(d*x + c))*sinh(d*x + c)^3 + (a + b)*d*x + 2*(2*(a + b)*d*x - a - 2*b)*cosh(d*x + c)^2 + 2*(14*(a + b)*d*x*cosh(d*x + c)^6 + 15*(2*(a + b)*d*x - a - 2*b)*cosh(d*x + c)^4 + 2*(a + b)*d*x + 6*(3*(a + b)*d*x - 2*a - 2*b)*cosh(d*x + c)^2 - a - 2*b)*sinh(d*x + c)^2 - ((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 + 4*(a + b)*cosh(d*x + c)^6 + 4*(7*(a + b)*cosh(d*x + c)^2 + a + b)*sinh(d*x + c)^6 + 8*(7*(a + b)*cosh(d*x + c)^3 + 3*(a + b)*cosh(d*x + c))*sinh(d*x + c)^5 + 6*(a + b)*cosh(d*x + c)^4 + 2*(35*(a + b)*cosh(d*x + c)^4 + 30*(a + b)*cosh(d*x + c)^2 + 3*a + 3*b)*sinh(d*x + c)^4 + 8*(7*(a + b)*cosh(d*x + c)^5 + 10*(a + b)*cosh(d*x + c)^3 + 3*(a + b)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(a + b)*cosh(d*x + c)^2 + 4*(7*(a + b)*cosh(d*x + c)^6 + 15*(a + b)*cosh(d*x + c)^4 + 9*(a + b)*cosh(d*x + c)^2 + a + b)*sinh(d*x + c)^2 + 8*((a + b)*cosh(d*x + c)^7 + 3*(a + b)*cosh(d*x + c)^5 + 3*(a + b)*cosh(d*x + c)^3 + (a + b)*cosh(d*x + c))*sinh(d*x + c) + a + b)*log(2*cosh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))) + 4*(2*(a + b)*d*x*cosh(d*x + c)^7 + 3*(2*(a + b)*d*x - a - 2*b)*cosh(d*x + c)^5 + 2*(3*(a + b)*d*x - 2*a - 2*b)*cosh(d*x + c)^3 + (2*(a + b)*d*x - a - 2*b)*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 + 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
136,1,160,0,0.410815," ","integrate(tanh(d*x+c)^2*(a+b*tanh(d*x+c)^2),x, algorithm=""fricas"")","\frac{{\left(3 \, {\left(a + b\right)} d x + 3 \, a + 4 \, b\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(3 \, {\left(a + b\right)} d x + 3 \, a + 4 \, b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} - {\left(3 \, a + 4 \, b\right)} \sinh\left(d x + c\right)^{3} + 3 \, {\left(3 \, {\left(a + b\right)} d x + 3 \, a + 4 \, b\right)} \cosh\left(d x + c\right) - 3 \, {\left({\left(3 \, a + 4 \, b\right)} \cosh\left(d x + c\right)^{2} + a\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*(a + b)*d*x + 3*a + 4*b)*cosh(d*x + c)^3 + 3*(3*(a + b)*d*x + 3*a + 4*b)*cosh(d*x + c)*sinh(d*x + c)^2 - (3*a + 4*b)*sinh(d*x + c)^3 + 3*(3*(a + b)*d*x + 3*a + 4*b)*cosh(d*x + c) - 3*((3*a + 4*b)*cosh(d*x + c)^2 + a)*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
137,1,399,0,0.442636," ","integrate(tanh(d*x+c)*(a+b*tanh(d*x+c)^2),x, algorithm=""fricas"")","-\frac{{\left(a + b\right)} d x \cosh\left(d x + c\right)^{4} + 4 \, {\left(a + b\right)} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a + b\right)} d x \sinh\left(d x + c\right)^{4} + {\left(a + b\right)} d x + 2 \, {\left({\left(a + b\right)} d x - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} d x \cosh\left(d x + c\right)^{2} + {\left(a + b\right)} d x - b\right)} \sinh\left(d x + c\right)^{2} - {\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)} \log\left(\frac{2 \, \cosh\left(d x + c\right)}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) + 4 \, {\left({\left(a + b\right)} d x \cosh\left(d x + c\right)^{3} + {\left({\left(a + b\right)} d x - b\right)} \cosh\left(d x + c\right)\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)*d*x*cosh(d*x + c)^4 + 4*(a + b)*d*x*cosh(d*x + c)*sinh(d*x + c)^3 + (a + b)*d*x*sinh(d*x + c)^4 + (a + b)*d*x + 2*((a + b)*d*x - b)*cosh(d*x + c)^2 + 2*(3*(a + b)*d*x*cosh(d*x + c)^2 + (a + b)*d*x - b)*sinh(d*x + c)^2 - ((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)*log(2*cosh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))) + 4*((a + b)*d*x*cosh(d*x + c)^3 + ((a + b)*d*x - b)*cosh(d*x + c))*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
138,1,37,0,0.403454," ","integrate(a+b*tanh(d*x+c)^2,x, algorithm=""fricas"")","\frac{{\left({\left(a + b\right)} d x + b\right)} \cosh\left(d x + c\right) - b \sinh\left(d x + c\right)}{d \cosh\left(d x + c\right)}"," ",0,"(((a + b)*d*x + b)*cosh(d*x + c) - b*sinh(d*x + c))/(d*cosh(d*x + c))","A",0
139,1,70,0,0.420549," ","integrate(coth(d*x+c)*(a+b*tanh(d*x+c)^2),x, algorithm=""fricas"")","-\frac{{\left(a + b\right)} d x - b \log\left(\frac{2 \, \cosh\left(d x + c\right)}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) - a \log\left(\frac{2 \, \sinh\left(d x + c\right)}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right)}{d}"," ",0,"-((a + b)*d*x - b*log(2*cosh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))) - a*log(2*sinh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))))/d","B",0
140,1,38,0,0.404085," ","integrate(coth(d*x+c)^2*(a+b*tanh(d*x+c)^2),x, algorithm=""fricas"")","-\frac{a \cosh\left(d x + c\right) - {\left({\left(a + b\right)} d x + a\right)} \sinh\left(d x + c\right)}{d \sinh\left(d x + c\right)}"," ",0,"-(a*cosh(d*x + c) - ((a + b)*d*x + a)*sinh(d*x + c))/(d*sinh(d*x + c))","B",0
141,1,407,0,0.426067," ","integrate(coth(d*x+c)^3*(a+b*tanh(d*x+c)^2),x, algorithm=""fricas"")","-\frac{{\left(a + b\right)} d x \cosh\left(d x + c\right)^{4} + 4 \, {\left(a + b\right)} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a + b\right)} d x \sinh\left(d x + c\right)^{4} + {\left(a + b\right)} d x - 2 \, {\left({\left(a + b\right)} d x - a\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} d x \cosh\left(d x + c\right)^{2} - {\left(a + b\right)} d x + a\right)} \sinh\left(d x + c\right)^{2} - {\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)} \log\left(\frac{2 \, \sinh\left(d x + c\right)}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) + 4 \, {\left({\left(a + b\right)} d x \cosh\left(d x + c\right)^{3} - {\left({\left(a + b\right)} d x - a\right)} \cosh\left(d x + c\right)\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)*d*x*cosh(d*x + c)^4 + 4*(a + b)*d*x*cosh(d*x + c)*sinh(d*x + c)^3 + (a + b)*d*x*sinh(d*x + c)^4 + (a + b)*d*x - 2*((a + b)*d*x - a)*cosh(d*x + c)^2 + 2*(3*(a + b)*d*x*cosh(d*x + c)^2 - (a + b)*d*x + a)*sinh(d*x + c)^2 - ((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)*log(2*sinh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))) + 4*((a + b)*d*x*cosh(d*x + c)^3 - ((a + b)*d*x - a)*cosh(d*x + c))*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
142,1,156,0,0.425172," ","integrate(coth(d*x+c)^4*(a+b*tanh(d*x+c)^2),x, algorithm=""fricas"")","-\frac{{\left(4 \, a + 3 \, b\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(4 \, a + 3 \, b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} - {\left(3 \, {\left(a + b\right)} d x + 4 \, a + 3 \, b\right)} \sinh\left(d x + c\right)^{3} - 3 \, b \cosh\left(d x + c\right) + 3 \, {\left(3 \, {\left(a + b\right)} d x - {\left(3 \, {\left(a + b\right)} d x + 4 \, a + 3 \, b\right)} \cosh\left(d x + c\right)^{2} + 4 \, a + 3 \, 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*((4*a + 3*b)*cosh(d*x + c)^3 + 3*(4*a + 3*b)*cosh(d*x + c)*sinh(d*x + c)^2 - (3*(a + b)*d*x + 4*a + 3*b)*sinh(d*x + c)^3 - 3*b*cosh(d*x + c) + 3*(3*(a + b)*d*x - (3*(a + b)*d*x + 4*a + 3*b)*cosh(d*x + c)^2 + 4*a + 3*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
143,1,1216,0,0.432343," ","integrate(coth(d*x+c)^5*(a+b*tanh(d*x+c)^2),x, algorithm=""fricas"")","-\frac{{\left(a + b\right)} d x \cosh\left(d x + c\right)^{8} + 8 \, {\left(a + b\right)} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a + b\right)} d x \sinh\left(d x + c\right)^{8} - 2 \, {\left(2 \, {\left(a + b\right)} d x - 2 \, a - b\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(14 \, {\left(a + b\right)} d x \cosh\left(d x + c\right)^{2} - 2 \, {\left(a + b\right)} d x + 2 \, a + b\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(14 \, {\left(a + b\right)} d x \cosh\left(d x + c\right)^{3} - 3 \, {\left(2 \, {\left(a + b\right)} d x - 2 \, a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(3 \, {\left(a + b\right)} d x - 2 \, a - 2 \, b\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(a + b\right)} d x \cosh\left(d x + c\right)^{4} + 3 \, {\left(a + b\right)} d x - 15 \, {\left(2 \, {\left(a + b\right)} d x - 2 \, a - b\right)} \cosh\left(d x + c\right)^{2} - 2 \, a - 2 \, b\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a + b\right)} d x \cosh\left(d x + c\right)^{5} - 5 \, {\left(2 \, {\left(a + b\right)} d x - 2 \, a - b\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, {\left(a + b\right)} d x - 2 \, a - 2 \, b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(a + b\right)} d x - 2 \, {\left(2 \, {\left(a + b\right)} d x - 2 \, a - b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(14 \, {\left(a + b\right)} d x \cosh\left(d x + c\right)^{6} - 15 \, {\left(2 \, {\left(a + b\right)} d x - 2 \, a - b\right)} \cosh\left(d x + c\right)^{4} - 2 \, {\left(a + b\right)} d x + 6 \, {\left(3 \, {\left(a + b\right)} d x - 2 \, a - 2 \, b\right)} \cosh\left(d x + c\right)^{2} + 2 \, a + b\right)} \sinh\left(d x + c\right)^{2} - {\left({\left(a + b\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(a + b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a + b\right)} \sinh\left(d x + c\right)^{8} - 4 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} - a - b\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(a + b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 6 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{4} - 30 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} + 3 \, a + 3 \, b\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{5} - 10 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a + b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 4 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{6} - 15 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{4} + 9 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{2} - a - b\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left({\left(a + b\right)} \cosh\left(d x + c\right)^{7} - 3 \, {\left(a + b\right)} \cosh\left(d x + c\right)^{5} + 3 \, {\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)} \log\left(\frac{2 \, \sinh\left(d x + c\right)}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) + 4 \, {\left(2 \, {\left(a + b\right)} d x \cosh\left(d x + c\right)^{7} - 3 \, {\left(2 \, {\left(a + b\right)} d x - 2 \, a - b\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(3 \, {\left(a + b\right)} d x - 2 \, a - 2 \, b\right)} \cosh\left(d x + c\right)^{3} - {\left(2 \, {\left(a + b\right)} d x - 2 \, a - b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{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}"," ",0,"-((a + b)*d*x*cosh(d*x + c)^8 + 8*(a + b)*d*x*cosh(d*x + c)*sinh(d*x + c)^7 + (a + b)*d*x*sinh(d*x + c)^8 - 2*(2*(a + b)*d*x - 2*a - b)*cosh(d*x + c)^6 + 2*(14*(a + b)*d*x*cosh(d*x + c)^2 - 2*(a + b)*d*x + 2*a + b)*sinh(d*x + c)^6 + 4*(14*(a + b)*d*x*cosh(d*x + c)^3 - 3*(2*(a + b)*d*x - 2*a - b)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(3*(a + b)*d*x - 2*a - 2*b)*cosh(d*x + c)^4 + 2*(35*(a + b)*d*x*cosh(d*x + c)^4 + 3*(a + b)*d*x - 15*(2*(a + b)*d*x - 2*a - b)*cosh(d*x + c)^2 - 2*a - 2*b)*sinh(d*x + c)^4 + 8*(7*(a + b)*d*x*cosh(d*x + c)^5 - 5*(2*(a + b)*d*x - 2*a - b)*cosh(d*x + c)^3 + (3*(a + b)*d*x - 2*a - 2*b)*cosh(d*x + c))*sinh(d*x + c)^3 + (a + b)*d*x - 2*(2*(a + b)*d*x - 2*a - b)*cosh(d*x + c)^2 + 2*(14*(a + b)*d*x*cosh(d*x + c)^6 - 15*(2*(a + b)*d*x - 2*a - b)*cosh(d*x + c)^4 - 2*(a + b)*d*x + 6*(3*(a + b)*d*x - 2*a - 2*b)*cosh(d*x + c)^2 + 2*a + b)*sinh(d*x + c)^2 - ((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 - 4*(a + b)*cosh(d*x + c)^6 + 4*(7*(a + b)*cosh(d*x + c)^2 - a - b)*sinh(d*x + c)^6 + 8*(7*(a + b)*cosh(d*x + c)^3 - 3*(a + b)*cosh(d*x + c))*sinh(d*x + c)^5 + 6*(a + b)*cosh(d*x + c)^4 + 2*(35*(a + b)*cosh(d*x + c)^4 - 30*(a + b)*cosh(d*x + c)^2 + 3*a + 3*b)*sinh(d*x + c)^4 + 8*(7*(a + b)*cosh(d*x + c)^5 - 10*(a + b)*cosh(d*x + c)^3 + 3*(a + b)*cosh(d*x + c))*sinh(d*x + c)^3 - 4*(a + b)*cosh(d*x + c)^2 + 4*(7*(a + b)*cosh(d*x + c)^6 - 15*(a + b)*cosh(d*x + c)^4 + 9*(a + b)*cosh(d*x + c)^2 - a - b)*sinh(d*x + c)^2 + 8*((a + b)*cosh(d*x + c)^7 - 3*(a + b)*cosh(d*x + c)^5 + 3*(a + b)*cosh(d*x + c)^3 - (a + b)*cosh(d*x + c))*sinh(d*x + c) + a + b)*log(2*sinh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))) + 4*(2*(a + b)*d*x*cosh(d*x + c)^7 - 3*(2*(a + b)*d*x - 2*a - b)*cosh(d*x + c)^5 + 2*(3*(a + b)*d*x - 2*a - 2*b)*cosh(d*x + c)^3 - (2*(a + b)*d*x - 2*a - b)*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 - 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
144,1,796,0,0.416418," ","integrate(tanh(d*x+c)^4*(a+b*tanh(d*x+c)^2)^2,x, algorithm=""fricas"")","\frac{{\left(105 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x + 140 \, a^{2} + 322 \, a b + 176 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} + 7 \, {\left(105 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x + 140 \, a^{2} + 322 \, a b + 176 \, b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} - 2 \, {\left(70 \, a^{2} + 161 \, a b + 88 \, b^{2}\right)} \sinh\left(d x + c\right)^{7} + 7 \, {\left(105 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x + 140 \, a^{2} + 322 \, a b + 176 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} - 14 \, {\left(3 \, {\left(70 \, a^{2} + 161 \, a b + 88 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 40 \, a^{2} + 71 \, a b + 28 \, b^{2}\right)} \sinh\left(d x + c\right)^{5} + 35 \, {\left({\left(105 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x + 140 \, a^{2} + 322 \, a b + 176 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(105 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x + 140 \, a^{2} + 322 \, a b + 176 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 21 \, {\left(105 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x + 140 \, a^{2} + 322 \, a b + 176 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - 14 \, {\left(5 \, {\left(70 \, a^{2} + 161 \, a b + 88 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 10 \, {\left(40 \, a^{2} + 71 \, a b + 28 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 60 \, a^{2} + 123 \, a b + 84 \, b^{2}\right)} \sinh\left(d x + c\right)^{3} + 7 \, {\left(3 \, {\left(105 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x + 140 \, a^{2} + 322 \, a b + 176 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(105 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x + 140 \, a^{2} + 322 \, a b + 176 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 9 \, {\left(105 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x + 140 \, a^{2} + 322 \, a b + 176 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 35 \, {\left(105 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x + 140 \, a^{2} + 322 \, a b + 176 \, b^{2}\right)} \cosh\left(d x + c\right) - 14 \, {\left({\left(70 \, a^{2} + 161 \, a b + 88 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 5 \, {\left(40 \, a^{2} + 71 \, a b + 28 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 9 \, {\left(20 \, a^{2} + 41 \, a b + 28 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 30 \, a^{2} + 75 \, a b\right)} \sinh\left(d x + c\right)}{105 \, {\left(d \cosh\left(d x + c\right)^{7} + 7 \, d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + 7 \, d \cosh\left(d x + c\right)^{5} + 35 \, {\left(d \cosh\left(d x + c\right)^{3} + d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 21 \, d \cosh\left(d x + c\right)^{3} + 7 \, {\left(3 \, d \cosh\left(d x + c\right)^{5} + 10 \, d \cosh\left(d x + c\right)^{3} + 9 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 35 \, d \cosh\left(d x + c\right)\right)}}"," ",0,"1/105*((105*(a^2 + 2*a*b + b^2)*d*x + 140*a^2 + 322*a*b + 176*b^2)*cosh(d*x + c)^7 + 7*(105*(a^2 + 2*a*b + b^2)*d*x + 140*a^2 + 322*a*b + 176*b^2)*cosh(d*x + c)*sinh(d*x + c)^6 - 2*(70*a^2 + 161*a*b + 88*b^2)*sinh(d*x + c)^7 + 7*(105*(a^2 + 2*a*b + b^2)*d*x + 140*a^2 + 322*a*b + 176*b^2)*cosh(d*x + c)^5 - 14*(3*(70*a^2 + 161*a*b + 88*b^2)*cosh(d*x + c)^2 + 40*a^2 + 71*a*b + 28*b^2)*sinh(d*x + c)^5 + 35*((105*(a^2 + 2*a*b + b^2)*d*x + 140*a^2 + 322*a*b + 176*b^2)*cosh(d*x + c)^3 + (105*(a^2 + 2*a*b + b^2)*d*x + 140*a^2 + 322*a*b + 176*b^2)*cosh(d*x + c))*sinh(d*x + c)^4 + 21*(105*(a^2 + 2*a*b + b^2)*d*x + 140*a^2 + 322*a*b + 176*b^2)*cosh(d*x + c)^3 - 14*(5*(70*a^2 + 161*a*b + 88*b^2)*cosh(d*x + c)^4 + 10*(40*a^2 + 71*a*b + 28*b^2)*cosh(d*x + c)^2 + 60*a^2 + 123*a*b + 84*b^2)*sinh(d*x + c)^3 + 7*(3*(105*(a^2 + 2*a*b + b^2)*d*x + 140*a^2 + 322*a*b + 176*b^2)*cosh(d*x + c)^5 + 10*(105*(a^2 + 2*a*b + b^2)*d*x + 140*a^2 + 322*a*b + 176*b^2)*cosh(d*x + c)^3 + 9*(105*(a^2 + 2*a*b + b^2)*d*x + 140*a^2 + 322*a*b + 176*b^2)*cosh(d*x + c))*sinh(d*x + c)^2 + 35*(105*(a^2 + 2*a*b + b^2)*d*x + 140*a^2 + 322*a*b + 176*b^2)*cosh(d*x + c) - 14*((70*a^2 + 161*a*b + 88*b^2)*cosh(d*x + c)^6 + 5*(40*a^2 + 71*a*b + 28*b^2)*cosh(d*x + c)^4 + 9*(20*a^2 + 41*a*b + 28*b^2)*cosh(d*x + c)^2 + 30*a^2 + 75*a*b)*sinh(d*x + c))/(d*cosh(d*x + c)^7 + 7*d*cosh(d*x + c)*sinh(d*x + c)^6 + 7*d*cosh(d*x + c)^5 + 35*(d*cosh(d*x + c)^3 + d*cosh(d*x + c))*sinh(d*x + c)^4 + 21*d*cosh(d*x + c)^3 + 7*(3*d*cosh(d*x + c)^5 + 10*d*cosh(d*x + c)^3 + 9*d*cosh(d*x + c))*sinh(d*x + c)^2 + 35*d*cosh(d*x + c))","B",0
145,1,3441,0,0.475085," ","integrate(tanh(d*x+c)^3*(a+b*tanh(d*x+c)^2)^2,x, algorithm=""fricas"")","-\frac{3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x \cosh\left(d x + c\right)^{12} + 36 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{11} + 3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x \sinh\left(d x + c\right)^{12} + 6 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x - a^{2} - 4 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{10} + 6 \, {\left(33 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x \cosh\left(d x + c\right)^{2} + 3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x - a^{2} - 4 \, a b - 3 \, b^{2}\right)} \sinh\left(d x + c\right)^{10} + 60 \, {\left(11 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x \cosh\left(d x + c\right)^{3} + {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x - a^{2} - 4 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} + 3 \, {\left(15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x - 8 \, a^{2} - 24 \, a b - 12 \, b^{2}\right)} \cosh\left(d x + c\right)^{8} + 3 \, {\left(495 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x \cosh\left(d x + c\right)^{4} + 15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x + 90 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x - a^{2} - 4 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 8 \, a^{2} - 24 \, a b - 12 \, b^{2}\right)} \sinh\left(d x + c\right)^{8} + 24 \, {\left(99 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x \cosh\left(d x + c\right)^{5} + 30 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x - a^{2} - 4 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x - 8 \, a^{2} - 24 \, a b - 12 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 4 \, {\left(15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x - 9 \, a^{2} - 24 \, a b - 17 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(693 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x \cosh\left(d x + c\right)^{6} + 315 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x - a^{2} - 4 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x + 21 \, {\left(15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x - 8 \, a^{2} - 24 \, a b - 12 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 9 \, a^{2} - 24 \, a b - 17 \, b^{2}\right)} \sinh\left(d x + c\right)^{6} + 24 \, {\left(99 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x \cosh\left(d x + c\right)^{7} + 63 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x - a^{2} - 4 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 7 \, {\left(15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x - 8 \, a^{2} - 24 \, a b - 12 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x - 9 \, a^{2} - 24 \, a b - 17 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 3 \, {\left(15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x - 8 \, a^{2} - 24 \, a b - 12 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(495 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x \cosh\left(d x + c\right)^{8} + 420 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x - a^{2} - 4 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 70 \, {\left(15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x - 8 \, a^{2} - 24 \, a b - 12 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x + 20 \, {\left(15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x - 9 \, a^{2} - 24 \, a b - 17 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 8 \, a^{2} - 24 \, a b - 12 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(165 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x \cosh\left(d x + c\right)^{9} + 180 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x - a^{2} - 4 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} + 42 \, {\left(15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x - 8 \, a^{2} - 24 \, a b - 12 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 20 \, {\left(15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x - 9 \, a^{2} - 24 \, a b - 17 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x - 8 \, a^{2} - 24 \, a b - 12 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x + 6 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x - a^{2} - 4 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 6 \, {\left(33 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x \cosh\left(d x + c\right)^{10} + 45 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x - a^{2} - 4 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{8} + 14 \, {\left(15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x - 8 \, a^{2} - 24 \, a b - 12 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 10 \, {\left(15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x - 9 \, a^{2} - 24 \, a b - 17 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x + 3 \, {\left(15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x - 8 \, a^{2} - 24 \, a b - 12 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - a^{2} - 4 \, a b - 3 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} - 3 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{12} + 12 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{11} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{12} + 6 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{10} + 6 \, {\left(11 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{10} + 20 \, {\left(11 \, {\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)\right)} \sinh\left(d x + c\right)^{9} + 15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{8} + 15 \, {\left(33 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + 18 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{8} + 24 \, {\left(33 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{5} + 30 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + 5 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 20 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(231 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{6} + 315 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + 105 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 5 \, a^{2} + 10 \, a b + 5 \, b^{2}\right)} \sinh\left(d x + c\right)^{6} + 24 \, {\left(33 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{7} + 63 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{5} + 35 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + 5 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + 15 \, {\left(33 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{8} + 84 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{6} + 70 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + 20 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{4} + 20 \, {\left(11 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{9} + 36 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{7} + 42 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{5} + 20 \, {\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)\right)} \sinh\left(d x + c\right)^{3} + 6 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 6 \, {\left(11 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{10} + 45 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{8} + 70 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{6} + 50 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + 15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 2 \, a b + b^{2} + 12 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{11} + 5 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{9} + 10 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{7} + 10 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\frac{2 \, \cosh\left(d x + c\right)}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) + 12 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x \cosh\left(d x + c\right)^{11} + 5 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x - a^{2} - 4 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{9} + 2 \, {\left(15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x - 8 \, a^{2} - 24 \, a b - 12 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} + 2 \, {\left(15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x - 9 \, a^{2} - 24 \, a b - 17 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + {\left(15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x - 8 \, a^{2} - 24 \, a b - 12 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x - a^{2} - 4 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{3 \, {\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,"-1/3*(3*(a^2 + 2*a*b + b^2)*d*x*cosh(d*x + c)^12 + 36*(a^2 + 2*a*b + b^2)*d*x*cosh(d*x + c)*sinh(d*x + c)^11 + 3*(a^2 + 2*a*b + b^2)*d*x*sinh(d*x + c)^12 + 6*(3*(a^2 + 2*a*b + b^2)*d*x - a^2 - 4*a*b - 3*b^2)*cosh(d*x + c)^10 + 6*(33*(a^2 + 2*a*b + b^2)*d*x*cosh(d*x + c)^2 + 3*(a^2 + 2*a*b + b^2)*d*x - a^2 - 4*a*b - 3*b^2)*sinh(d*x + c)^10 + 60*(11*(a^2 + 2*a*b + b^2)*d*x*cosh(d*x + c)^3 + (3*(a^2 + 2*a*b + b^2)*d*x - a^2 - 4*a*b - 3*b^2)*cosh(d*x + c))*sinh(d*x + c)^9 + 3*(15*(a^2 + 2*a*b + b^2)*d*x - 8*a^2 - 24*a*b - 12*b^2)*cosh(d*x + c)^8 + 3*(495*(a^2 + 2*a*b + b^2)*d*x*cosh(d*x + c)^4 + 15*(a^2 + 2*a*b + b^2)*d*x + 90*(3*(a^2 + 2*a*b + b^2)*d*x - a^2 - 4*a*b - 3*b^2)*cosh(d*x + c)^2 - 8*a^2 - 24*a*b - 12*b^2)*sinh(d*x + c)^8 + 24*(99*(a^2 + 2*a*b + b^2)*d*x*cosh(d*x + c)^5 + 30*(3*(a^2 + 2*a*b + b^2)*d*x - a^2 - 4*a*b - 3*b^2)*cosh(d*x + c)^3 + (15*(a^2 + 2*a*b + b^2)*d*x - 8*a^2 - 24*a*b - 12*b^2)*cosh(d*x + c))*sinh(d*x + c)^7 + 4*(15*(a^2 + 2*a*b + b^2)*d*x - 9*a^2 - 24*a*b - 17*b^2)*cosh(d*x + c)^6 + 4*(693*(a^2 + 2*a*b + b^2)*d*x*cosh(d*x + c)^6 + 315*(3*(a^2 + 2*a*b + b^2)*d*x - a^2 - 4*a*b - 3*b^2)*cosh(d*x + c)^4 + 15*(a^2 + 2*a*b + b^2)*d*x + 21*(15*(a^2 + 2*a*b + b^2)*d*x - 8*a^2 - 24*a*b - 12*b^2)*cosh(d*x + c)^2 - 9*a^2 - 24*a*b - 17*b^2)*sinh(d*x + c)^6 + 24*(99*(a^2 + 2*a*b + b^2)*d*x*cosh(d*x + c)^7 + 63*(3*(a^2 + 2*a*b + b^2)*d*x - a^2 - 4*a*b - 3*b^2)*cosh(d*x + c)^5 + 7*(15*(a^2 + 2*a*b + b^2)*d*x - 8*a^2 - 24*a*b - 12*b^2)*cosh(d*x + c)^3 + (15*(a^2 + 2*a*b + b^2)*d*x - 9*a^2 - 24*a*b - 17*b^2)*cosh(d*x + c))*sinh(d*x + c)^5 + 3*(15*(a^2 + 2*a*b + b^2)*d*x - 8*a^2 - 24*a*b - 12*b^2)*cosh(d*x + c)^4 + 3*(495*(a^2 + 2*a*b + b^2)*d*x*cosh(d*x + c)^8 + 420*(3*(a^2 + 2*a*b + b^2)*d*x - a^2 - 4*a*b - 3*b^2)*cosh(d*x + c)^6 + 70*(15*(a^2 + 2*a*b + b^2)*d*x - 8*a^2 - 24*a*b - 12*b^2)*cosh(d*x + c)^4 + 15*(a^2 + 2*a*b + b^2)*d*x + 20*(15*(a^2 + 2*a*b + b^2)*d*x - 9*a^2 - 24*a*b - 17*b^2)*cosh(d*x + c)^2 - 8*a^2 - 24*a*b - 12*b^2)*sinh(d*x + c)^4 + 4*(165*(a^2 + 2*a*b + b^2)*d*x*cosh(d*x + c)^9 + 180*(3*(a^2 + 2*a*b + b^2)*d*x - a^2 - 4*a*b - 3*b^2)*cosh(d*x + c)^7 + 42*(15*(a^2 + 2*a*b + b^2)*d*x - 8*a^2 - 24*a*b - 12*b^2)*cosh(d*x + c)^5 + 20*(15*(a^2 + 2*a*b + b^2)*d*x - 9*a^2 - 24*a*b - 17*b^2)*cosh(d*x + c)^3 + 3*(15*(a^2 + 2*a*b + b^2)*d*x - 8*a^2 - 24*a*b - 12*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 3*(a^2 + 2*a*b + b^2)*d*x + 6*(3*(a^2 + 2*a*b + b^2)*d*x - a^2 - 4*a*b - 3*b^2)*cosh(d*x + c)^2 + 6*(33*(a^2 + 2*a*b + b^2)*d*x*cosh(d*x + c)^10 + 45*(3*(a^2 + 2*a*b + b^2)*d*x - a^2 - 4*a*b - 3*b^2)*cosh(d*x + c)^8 + 14*(15*(a^2 + 2*a*b + b^2)*d*x - 8*a^2 - 24*a*b - 12*b^2)*cosh(d*x + c)^6 + 10*(15*(a^2 + 2*a*b + b^2)*d*x - 9*a^2 - 24*a*b - 17*b^2)*cosh(d*x + c)^4 + 3*(a^2 + 2*a*b + b^2)*d*x + 3*(15*(a^2 + 2*a*b + b^2)*d*x - 8*a^2 - 24*a*b - 12*b^2)*cosh(d*x + c)^2 - a^2 - 4*a*b - 3*b^2)*sinh(d*x + c)^2 - 3*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^12 + 12*(a^2 + 2*a*b + b^2)*cosh(d*x + c)*sinh(d*x + c)^11 + (a^2 + 2*a*b + b^2)*sinh(d*x + c)^12 + 6*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^10 + 6*(11*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + a^2 + 2*a*b + b^2)*sinh(d*x + c)^10 + 20*(11*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 + 3*(a^2 + 2*a*b + b^2)*cosh(d*x + c))*sinh(d*x + c)^9 + 15*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^8 + 15*(33*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 + 18*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + a^2 + 2*a*b + b^2)*sinh(d*x + c)^8 + 24*(33*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^5 + 30*(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)^7 + 20*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^6 + 4*(231*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^6 + 315*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 + 105*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + 5*a^2 + 10*a*b + 5*b^2)*sinh(d*x + c)^6 + 24*(33*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^7 + 63*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^5 + 35*(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)^5 + 15*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 + 15*(33*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^8 + 84*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^6 + 70*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 + 20*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + a^2 + 2*a*b + b^2)*sinh(d*x + c)^4 + 20*(11*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^9 + 36*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^7 + 42*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^5 + 20*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 + 3*(a^2 + 2*a*b + b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 6*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + 6*(11*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^10 + 45*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^8 + 70*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^6 + 50*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 + 15*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + a^2 + 2*a*b + b^2)*sinh(d*x + c)^2 + a^2 + 2*a*b + b^2 + 12*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^11 + 5*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^9 + 10*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^7 + 10*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^5 + 5*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 + (a^2 + 2*a*b + b^2)*cosh(d*x + c))*sinh(d*x + c))*log(2*cosh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))) + 12*(3*(a^2 + 2*a*b + b^2)*d*x*cosh(d*x + c)^11 + 5*(3*(a^2 + 2*a*b + b^2)*d*x - a^2 - 4*a*b - 3*b^2)*cosh(d*x + c)^9 + 2*(15*(a^2 + 2*a*b + b^2)*d*x - 8*a^2 - 24*a*b - 12*b^2)*cosh(d*x + c)^7 + 2*(15*(a^2 + 2*a*b + b^2)*d*x - 9*a^2 - 24*a*b - 17*b^2)*cosh(d*x + c)^5 + (15*(a^2 + 2*a*b + b^2)*d*x - 8*a^2 - 24*a*b - 12*b^2)*cosh(d*x + c)^3 + (3*(a^2 + 2*a*b + b^2)*d*x - a^2 - 4*a*b - 3*b^2)*cosh(d*x + c))*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
146,1,483,0,0.429014," ","integrate(tanh(d*x+c)^2*(a+b*tanh(d*x+c)^2)^2,x, algorithm=""fricas"")","\frac{{\left(15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x + 15 \, a^{2} + 40 \, a b + 23 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x + 15 \, a^{2} + 40 \, a b + 23 \, b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} - {\left(15 \, a^{2} + 40 \, a b + 23 \, b^{2}\right)} \sinh\left(d x + c\right)^{5} + 5 \, {\left(15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x + 15 \, a^{2} + 40 \, a b + 23 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - 5 \, {\left(2 \, {\left(15 \, a^{2} + 40 \, a b + 23 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 9 \, a^{2} + 16 \, a b + 5 \, b^{2}\right)} \sinh\left(d x + c\right)^{3} + 5 \, {\left(2 \, {\left(15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x + 15 \, a^{2} + 40 \, a b + 23 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x + 15 \, a^{2} + 40 \, a b + 23 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 10 \, {\left(15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x + 15 \, a^{2} + 40 \, a b + 23 \, b^{2}\right)} \cosh\left(d x + c\right) - 5 \, {\left({\left(15 \, a^{2} + 40 \, a b + 23 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(9 \, a^{2} + 16 \, a b + 5 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 6 \, a^{2} + 8 \, a b + 10 \, b^{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*(a^2 + 2*a*b + b^2)*d*x + 15*a^2 + 40*a*b + 23*b^2)*cosh(d*x + c)^5 + 5*(15*(a^2 + 2*a*b + b^2)*d*x + 15*a^2 + 40*a*b + 23*b^2)*cosh(d*x + c)*sinh(d*x + c)^4 - (15*a^2 + 40*a*b + 23*b^2)*sinh(d*x + c)^5 + 5*(15*(a^2 + 2*a*b + b^2)*d*x + 15*a^2 + 40*a*b + 23*b^2)*cosh(d*x + c)^3 - 5*(2*(15*a^2 + 40*a*b + 23*b^2)*cosh(d*x + c)^2 + 9*a^2 + 16*a*b + 5*b^2)*sinh(d*x + c)^3 + 5*(2*(15*(a^2 + 2*a*b + b^2)*d*x + 15*a^2 + 40*a*b + 23*b^2)*cosh(d*x + c)^3 + 3*(15*(a^2 + 2*a*b + b^2)*d*x + 15*a^2 + 40*a*b + 23*b^2)*cosh(d*x + c))*sinh(d*x + c)^2 + 10*(15*(a^2 + 2*a*b + b^2)*d*x + 15*a^2 + 40*a*b + 23*b^2)*cosh(d*x + c) - 5*((15*a^2 + 40*a*b + 23*b^2)*cosh(d*x + c)^4 + 3*(9*a^2 + 16*a*b + 5*b^2)*cosh(d*x + c)^2 + 6*a^2 + 8*a*b + 10*b^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
147,1,1638,0,0.430897," ","integrate(tanh(d*x+c)*(a+b*tanh(d*x+c)^2)^2,x, algorithm=""fricas"")","-\frac{{\left(a^{2} + 2 \, a b + b^{2}\right)} d x \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{2} + 2 \, a b + b^{2}\right)} d x \sinh\left(d x + c\right)^{8} + 4 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} d x - a b - b^{2}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x \cosh\left(d x + c\right)^{2} + {\left(a^{2} + 2 \, a b + b^{2}\right)} d x - a b - b^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x \cosh\left(d x + c\right)^{3} + 3 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} d x - a b - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x - 4 \, a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x \cosh\left(d x + c\right)^{4} + 3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x + 30 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} d x - a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} - 4 \, a b - 2 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x \cosh\left(d x + c\right)^{5} + 10 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} d x - a b - b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x - 4 \, a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(a^{2} + 2 \, a b + b^{2}\right)} d x + 4 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} d x - a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x \cosh\left(d x + c\right)^{6} + 15 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} d x - a b - b^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(a^{2} + 2 \, a b + b^{2}\right)} d x + 3 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x - 4 \, a b - 2 \, 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} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\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)\right)} \sinh\left(d x + c\right)^{5} + 6 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + 30 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 3 \, a^{2} + 6 \, a b + 3 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\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)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + 9 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 2 \, a b + b^{2} + 8 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{5} + 3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\frac{2 \, \cosh\left(d x + c\right)}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) + 8 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} d x \cosh\left(d x + c\right)^{7} + 3 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} d x - a b - b^{2}\right)} \cosh\left(d x + c\right)^{5} + {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x - 4 \, a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} d x - a b - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{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}"," ",0,"-((a^2 + 2*a*b + b^2)*d*x*cosh(d*x + c)^8 + 8*(a^2 + 2*a*b + b^2)*d*x*cosh(d*x + c)*sinh(d*x + c)^7 + (a^2 + 2*a*b + b^2)*d*x*sinh(d*x + c)^8 + 4*((a^2 + 2*a*b + b^2)*d*x - a*b - b^2)*cosh(d*x + c)^6 + 4*(7*(a^2 + 2*a*b + b^2)*d*x*cosh(d*x + c)^2 + (a^2 + 2*a*b + b^2)*d*x - a*b - b^2)*sinh(d*x + c)^6 + 8*(7*(a^2 + 2*a*b + b^2)*d*x*cosh(d*x + c)^3 + 3*((a^2 + 2*a*b + b^2)*d*x - a*b - b^2)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(3*(a^2 + 2*a*b + b^2)*d*x - 4*a*b - 2*b^2)*cosh(d*x + c)^4 + 2*(35*(a^2 + 2*a*b + b^2)*d*x*cosh(d*x + c)^4 + 3*(a^2 + 2*a*b + b^2)*d*x + 30*((a^2 + 2*a*b + b^2)*d*x - a*b - b^2)*cosh(d*x + c)^2 - 4*a*b - 2*b^2)*sinh(d*x + c)^4 + 8*(7*(a^2 + 2*a*b + b^2)*d*x*cosh(d*x + c)^5 + 10*((a^2 + 2*a*b + b^2)*d*x - a*b - b^2)*cosh(d*x + c)^3 + (3*(a^2 + 2*a*b + b^2)*d*x - 4*a*b - 2*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + (a^2 + 2*a*b + b^2)*d*x + 4*((a^2 + 2*a*b + b^2)*d*x - a*b - b^2)*cosh(d*x + c)^2 + 4*(7*(a^2 + 2*a*b + b^2)*d*x*cosh(d*x + c)^6 + 15*((a^2 + 2*a*b + b^2)*d*x - a*b - b^2)*cosh(d*x + c)^4 + (a^2 + 2*a*b + b^2)*d*x + 3*(3*(a^2 + 2*a*b + b^2)*d*x - 4*a*b - 2*b^2)*cosh(d*x + c)^2 - a*b - b^2)*sinh(d*x + c)^2 - ((a^2 + 2*a*b + b^2)*cosh(d*x + c)^8 + 8*(a^2 + 2*a*b + b^2)*cosh(d*x + c)*sinh(d*x + c)^7 + (a^2 + 2*a*b + b^2)*sinh(d*x + c)^8 + 4*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^6 + 4*(7*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + a^2 + 2*a*b + b^2)*sinh(d*x + c)^6 + 8*(7*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 + 3*(a^2 + 2*a*b + b^2)*cosh(d*x + c))*sinh(d*x + c)^5 + 6*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 + 2*(35*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 + 30*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + 3*a^2 + 6*a*b + 3*b^2)*sinh(d*x + c)^4 + 8*(7*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^5 + 10*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 + 3*(a^2 + 2*a*b + b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + 4*(7*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^6 + 15*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 + 9*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + a^2 + 2*a*b + b^2)*sinh(d*x + c)^2 + a^2 + 2*a*b + b^2 + 8*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^7 + 3*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^5 + 3*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 + (a^2 + 2*a*b + b^2)*cosh(d*x + c))*sinh(d*x + c))*log(2*cosh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))) + 8*((a^2 + 2*a*b + b^2)*d*x*cosh(d*x + c)^7 + 3*((a^2 + 2*a*b + b^2)*d*x - a*b - b^2)*cosh(d*x + c)^5 + (3*(a^2 + 2*a*b + b^2)*d*x - 4*a*b - 2*b^2)*cosh(d*x + c)^3 + ((a^2 + 2*a*b + b^2)*d*x - a*b - 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 + 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
148,1,201,0,0.396407," ","integrate((a+b*tanh(d*x+c)^2)^2,x, algorithm=""fricas"")","\frac{{\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x + 6 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x + 6 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} - 2 \, {\left(3 \, a b + 2 \, b^{2}\right)} \sinh\left(d x + c\right)^{3} + 3 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x + 6 \, a b + 4 \, b^{2}\right)} \cosh\left(d x + c\right) - 6 \, {\left({\left(3 \, a b + 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{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*(a^2 + 2*a*b + b^2)*d*x + 6*a*b + 4*b^2)*cosh(d*x + c)^3 + 3*(3*(a^2 + 2*a*b + b^2)*d*x + 6*a*b + 4*b^2)*cosh(d*x + c)*sinh(d*x + c)^2 - 2*(3*a*b + 2*b^2)*sinh(d*x + c)^3 + 3*(3*(a^2 + 2*a*b + b^2)*d*x + 6*a*b + 4*b^2)*cosh(d*x + c) - 6*((3*a*b + 2*b^2)*cosh(d*x + c)^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
149,1,668,0,0.417345," ","integrate(coth(d*x+c)*(a+b*tanh(d*x+c)^2)^2,x, algorithm=""fricas"")","-\frac{{\left(a^{2} + 2 \, a b + b^{2}\right)} d x \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{2} + 2 \, a b + b^{2}\right)} d x \sinh\left(d x + c\right)^{4} + {\left(a^{2} + 2 \, a b + b^{2}\right)} d x + 2 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} d x - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x \cosh\left(d x + c\right)^{2} + {\left(a^{2} + 2 \, a b + b^{2}\right)} d x - 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(2 \, 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} + 2 \, 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(2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\frac{2 \, \cosh\left(d x + c\right)}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) - {\left(a^{2} \cosh\left(d x + c\right)^{4} + 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} + 2 \, a^{2} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(d x + c\right)^{2} + a^{2}\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 4 \, {\left(a^{2} \cosh\left(d x + c\right)^{3} + a^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\frac{2 \, \sinh\left(d x + c\right)}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) + 4 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} d x \cosh\left(d x + c\right)^{3} + {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} d x - b^{2}\right)} \cosh\left(d x + c\right)\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^2 + 2*a*b + b^2)*d*x*cosh(d*x + c)^4 + 4*(a^2 + 2*a*b + b^2)*d*x*cosh(d*x + c)*sinh(d*x + c)^3 + (a^2 + 2*a*b + b^2)*d*x*sinh(d*x + c)^4 + (a^2 + 2*a*b + b^2)*d*x + 2*((a^2 + 2*a*b + b^2)*d*x - b^2)*cosh(d*x + c)^2 + 2*(3*(a^2 + 2*a*b + b^2)*d*x*cosh(d*x + c)^2 + (a^2 + 2*a*b + b^2)*d*x - 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*(2*a*b + b^2)*cosh(d*x + c)^2 + 2*(3*(2*a*b + b^2)*cosh(d*x + c)^2 + 2*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 + (2*a*b + b^2)*cosh(d*x + c))*sinh(d*x + c))*log(2*cosh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))) - (a^2*cosh(d*x + c)^4 + 4*a^2*cosh(d*x + c)*sinh(d*x + c)^3 + a^2*sinh(d*x + c)^4 + 2*a^2*cosh(d*x + c)^2 + 2*(3*a^2*cosh(d*x + c)^2 + a^2)*sinh(d*x + c)^2 + a^2 + 4*(a^2*cosh(d*x + c)^3 + a^2*cosh(d*x + c))*sinh(d*x + c))*log(2*sinh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))) + 4*((a^2 + 2*a*b + b^2)*d*x*cosh(d*x + c)^3 + ((a^2 + 2*a*b + b^2)*d*x - b^2)*cosh(d*x + c))*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
150,1,97,0,0.391020," ","integrate(coth(d*x+c)^2*(a+b*tanh(d*x+c)^2)^2,x, algorithm=""fricas"")","-\frac{{\left(a^{2} + b^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} d x + a^{2} + b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} + b^{2}\right)} \sinh\left(d x + c\right)^{2} + a^{2} - b^{2}}{2 \, d \cosh\left(d x + c\right) \sinh\left(d x + c\right)}"," ",0,"-1/2*((a^2 + b^2)*cosh(d*x + c)^2 - 2*((a^2 + 2*a*b + b^2)*d*x + a^2 + b^2)*cosh(d*x + c)*sinh(d*x + c) + (a^2 + b^2)*sinh(d*x + c)^2 + a^2 - b^2)/(d*cosh(d*x + c)*sinh(d*x + c))","B",0
151,1,677,0,0.433727," ","integrate(coth(d*x+c)^3*(a+b*tanh(d*x+c)^2)^2,x, algorithm=""fricas"")","-\frac{{\left(a^{2} + 2 \, a b + b^{2}\right)} d x \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{2} + 2 \, a b + b^{2}\right)} d x \sinh\left(d x + c\right)^{4} + {\left(a^{2} + 2 \, a b + b^{2}\right)} d x - 2 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} d x - a^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x \cosh\left(d x + c\right)^{2} - {\left(a^{2} + 2 \, a b + b^{2}\right)} d x + a^{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 \, b^{2} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(d x + c\right)^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{2} + b^{2} + 4 \, {\left(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)} \log\left(\frac{2 \, \cosh\left(d x + c\right)}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) - {\left({\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{2} + 2 \, a b\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{2} - a^{2} - 2 \, a b\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 2 \, a b + 4 \, {\left({\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)^{3} - {\left(a^{2} + 2 \, a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\frac{2 \, \sinh\left(d x + c\right)}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) + 4 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} d x \cosh\left(d x + c\right)^{3} - {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} d x - a^{2}\right)} \cosh\left(d x + c\right)\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^2 + 2*a*b + b^2)*d*x*cosh(d*x + c)^4 + 4*(a^2 + 2*a*b + b^2)*d*x*cosh(d*x + c)*sinh(d*x + c)^3 + (a^2 + 2*a*b + b^2)*d*x*sinh(d*x + c)^4 + (a^2 + 2*a*b + b^2)*d*x - 2*((a^2 + 2*a*b + b^2)*d*x - a^2)*cosh(d*x + c)^2 + 2*(3*(a^2 + 2*a*b + b^2)*d*x*cosh(d*x + c)^2 - (a^2 + 2*a*b + b^2)*d*x + a^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*b^2*cosh(d*x + c)^2 + 2*(3*b^2*cosh(d*x + c)^2 - b^2)*sinh(d*x + c)^2 + b^2 + 4*(b^2*cosh(d*x + c)^3 - b^2*cosh(d*x + c))*sinh(d*x + c))*log(2*cosh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))) - ((a^2 + 2*a*b)*cosh(d*x + c)^4 + 4*(a^2 + 2*a*b)*cosh(d*x + c)*sinh(d*x + c)^3 + (a^2 + 2*a*b)*sinh(d*x + c)^4 - 2*(a^2 + 2*a*b)*cosh(d*x + c)^2 + 2*(3*(a^2 + 2*a*b)*cosh(d*x + c)^2 - a^2 - 2*a*b)*sinh(d*x + c)^2 + a^2 + 2*a*b + 4*((a^2 + 2*a*b)*cosh(d*x + c)^3 - (a^2 + 2*a*b)*cosh(d*x + c))*sinh(d*x + c))*log(2*sinh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))) + 4*((a^2 + 2*a*b + b^2)*d*x*cosh(d*x + c)^3 - ((a^2 + 2*a*b + b^2)*d*x - a^2)*cosh(d*x + c))*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
152,1,197,0,0.403706," ","integrate(coth(d*x+c)^4*(a+b*tanh(d*x+c)^2)^2,x, algorithm=""fricas"")","-\frac{2 \, {\left(2 \, a^{2} + 3 \, a b\right)} \cosh\left(d x + c\right)^{3} + 6 \, {\left(2 \, a^{2} + 3 \, a b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{2} - {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x + 4 \, a^{2} + 6 \, a b\right)} \sinh\left(d x + c\right)^{3} - 6 \, a b \cosh\left(d x + c\right) + 3 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x - {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x + 4 \, a^{2} + 6 \, a b\right)} \cosh\left(d x + c\right)^{2} + 4 \, 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*(2*a^2 + 3*a*b)*cosh(d*x + c)^3 + 6*(2*a^2 + 3*a*b)*cosh(d*x + c)*sinh(d*x + c)^2 - (3*(a^2 + 2*a*b + b^2)*d*x + 4*a^2 + 6*a*b)*sinh(d*x + c)^3 - 6*a*b*cosh(d*x + c) + 3*(3*(a^2 + 2*a*b + b^2)*d*x - (3*(a^2 + 2*a*b + b^2)*d*x + 4*a^2 + 6*a*b)*cosh(d*x + c)^2 + 4*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
153,1,1649,0,0.464750," ","integrate(coth(d*x+c)^5*(a+b*tanh(d*x+c)^2)^2,x, algorithm=""fricas"")","-\frac{{\left(a^{2} + 2 \, a b + b^{2}\right)} d x \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{2} + 2 \, a b + b^{2}\right)} d x \sinh\left(d x + c\right)^{8} - 4 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} d x - a^{2} - a b\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x \cosh\left(d x + c\right)^{2} - {\left(a^{2} + 2 \, a b + b^{2}\right)} d x + a^{2} + a b\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x \cosh\left(d x + c\right)^{3} - 3 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} d x - a^{2} - a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x - 2 \, a^{2} - 4 \, a b\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x \cosh\left(d x + c\right)^{4} + 3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x - 30 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} d x - a^{2} - a b\right)} \cosh\left(d x + c\right)^{2} - 2 \, a^{2} - 4 \, a b\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x \cosh\left(d x + c\right)^{5} - 10 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} d x - a^{2} - a b\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x - 2 \, a^{2} - 4 \, a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(a^{2} + 2 \, a b + b^{2}\right)} d x - 4 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} d x - a^{2} - a b\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x \cosh\left(d x + c\right)^{6} - 15 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} d x - a^{2} - a b\right)} \cosh\left(d x + c\right)^{4} - {\left(a^{2} + 2 \, a b + b^{2}\right)} d x + 3 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x - 2 \, a^{2} - 4 \, a b\right)} \cosh\left(d x + c\right)^{2} + a^{2} + a b\right)} \sinh\left(d x + c\right)^{2} - {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{8} - 4 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} - a^{2} - 2 \, a b - b^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\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)\right)} \sinh\left(d x + c\right)^{5} + 6 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} - 30 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 3 \, a^{2} + 6 \, a b + 3 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{5} - 10 \, {\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)\right)} \sinh\left(d x + c\right)^{3} - 4 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{6} - 15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + 9 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} - a^{2} - 2 \, a b - b^{2}\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 2 \, a b + b^{2} + 8 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{7} - 3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{5} + 3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\frac{2 \, \sinh\left(d x + c\right)}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) + 8 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} d x \cosh\left(d x + c\right)^{7} - 3 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} d x - a^{2} - a b\right)} \cosh\left(d x + c\right)^{5} + {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x - 2 \, a^{2} - 4 \, a b\right)} \cosh\left(d x + c\right)^{3} - {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} d x - a^{2} - a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{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}"," ",0,"-((a^2 + 2*a*b + b^2)*d*x*cosh(d*x + c)^8 + 8*(a^2 + 2*a*b + b^2)*d*x*cosh(d*x + c)*sinh(d*x + c)^7 + (a^2 + 2*a*b + b^2)*d*x*sinh(d*x + c)^8 - 4*((a^2 + 2*a*b + b^2)*d*x - a^2 - a*b)*cosh(d*x + c)^6 + 4*(7*(a^2 + 2*a*b + b^2)*d*x*cosh(d*x + c)^2 - (a^2 + 2*a*b + b^2)*d*x + a^2 + a*b)*sinh(d*x + c)^6 + 8*(7*(a^2 + 2*a*b + b^2)*d*x*cosh(d*x + c)^3 - 3*((a^2 + 2*a*b + b^2)*d*x - a^2 - a*b)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(3*(a^2 + 2*a*b + b^2)*d*x - 2*a^2 - 4*a*b)*cosh(d*x + c)^4 + 2*(35*(a^2 + 2*a*b + b^2)*d*x*cosh(d*x + c)^4 + 3*(a^2 + 2*a*b + b^2)*d*x - 30*((a^2 + 2*a*b + b^2)*d*x - a^2 - a*b)*cosh(d*x + c)^2 - 2*a^2 - 4*a*b)*sinh(d*x + c)^4 + 8*(7*(a^2 + 2*a*b + b^2)*d*x*cosh(d*x + c)^5 - 10*((a^2 + 2*a*b + b^2)*d*x - a^2 - a*b)*cosh(d*x + c)^3 + (3*(a^2 + 2*a*b + b^2)*d*x - 2*a^2 - 4*a*b)*cosh(d*x + c))*sinh(d*x + c)^3 + (a^2 + 2*a*b + b^2)*d*x - 4*((a^2 + 2*a*b + b^2)*d*x - a^2 - a*b)*cosh(d*x + c)^2 + 4*(7*(a^2 + 2*a*b + b^2)*d*x*cosh(d*x + c)^6 - 15*((a^2 + 2*a*b + b^2)*d*x - a^2 - a*b)*cosh(d*x + c)^4 - (a^2 + 2*a*b + b^2)*d*x + 3*(3*(a^2 + 2*a*b + b^2)*d*x - 2*a^2 - 4*a*b)*cosh(d*x + c)^2 + a^2 + a*b)*sinh(d*x + c)^2 - ((a^2 + 2*a*b + b^2)*cosh(d*x + c)^8 + 8*(a^2 + 2*a*b + b^2)*cosh(d*x + c)*sinh(d*x + c)^7 + (a^2 + 2*a*b + b^2)*sinh(d*x + c)^8 - 4*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^6 + 4*(7*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 - a^2 - 2*a*b - b^2)*sinh(d*x + c)^6 + 8*(7*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 - 3*(a^2 + 2*a*b + b^2)*cosh(d*x + c))*sinh(d*x + c)^5 + 6*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 + 2*(35*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 - 30*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + 3*a^2 + 6*a*b + 3*b^2)*sinh(d*x + c)^4 + 8*(7*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^5 - 10*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 + 3*(a^2 + 2*a*b + b^2)*cosh(d*x + c))*sinh(d*x + c)^3 - 4*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + 4*(7*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^6 - 15*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 + 9*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 - a^2 - 2*a*b - b^2)*sinh(d*x + c)^2 + a^2 + 2*a*b + b^2 + 8*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^7 - 3*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^5 + 3*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 - (a^2 + 2*a*b + b^2)*cosh(d*x + c))*sinh(d*x + c))*log(2*sinh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))) + 8*((a^2 + 2*a*b + b^2)*d*x*cosh(d*x + c)^7 - 3*((a^2 + 2*a*b + b^2)*d*x - a^2 - a*b)*cosh(d*x + c)^5 + (3*(a^2 + 2*a*b + b^2)*d*x - 2*a^2 - 4*a*b)*cosh(d*x + c)^3 - ((a^2 + 2*a*b + b^2)*d*x - a^2 - a*b)*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 - 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
154,1,473,0,0.410229," ","integrate(coth(d*x+c)^6*(a+b*tanh(d*x+c)^2)^2,x, algorithm=""fricas"")","-\frac{{\left(23 \, a^{2} + 40 \, a b + 15 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(23 \, a^{2} + 40 \, a b + 15 \, b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} - {\left(15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x + 23 \, a^{2} + 40 \, a b + 15 \, b^{2}\right)} \sinh\left(d x + c\right)^{5} - 5 \, {\left(5 \, a^{2} + 16 \, a b + 9 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 5 \, {\left(15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x - 2 \, {\left(15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x + 23 \, a^{2} + 40 \, a b + 15 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 23 \, a^{2} + 40 \, a b + 15 \, b^{2}\right)} \sinh\left(d x + c\right)^{3} + 5 \, {\left(2 \, {\left(23 \, a^{2} + 40 \, a b + 15 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(5 \, a^{2} + 16 \, a b + 9 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 10 \, {\left(5 \, a^{2} + 4 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right) - 5 \, {\left({\left(15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x + 23 \, a^{2} + 40 \, a b + 15 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 30 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x - 3 \, {\left(15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x + 23 \, a^{2} + 40 \, a b + 15 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 46 \, a^{2} + 80 \, a b + 30 \, b^{2}\right)} \sinh\left(d x + c\right)}{15 \, {\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,"-1/15*((23*a^2 + 40*a*b + 15*b^2)*cosh(d*x + c)^5 + 5*(23*a^2 + 40*a*b + 15*b^2)*cosh(d*x + c)*sinh(d*x + c)^4 - (15*(a^2 + 2*a*b + b^2)*d*x + 23*a^2 + 40*a*b + 15*b^2)*sinh(d*x + c)^5 - 5*(5*a^2 + 16*a*b + 9*b^2)*cosh(d*x + c)^3 + 5*(15*(a^2 + 2*a*b + b^2)*d*x - 2*(15*(a^2 + 2*a*b + b^2)*d*x + 23*a^2 + 40*a*b + 15*b^2)*cosh(d*x + c)^2 + 23*a^2 + 40*a*b + 15*b^2)*sinh(d*x + c)^3 + 5*(2*(23*a^2 + 40*a*b + 15*b^2)*cosh(d*x + c)^3 - 3*(5*a^2 + 16*a*b + 9*b^2)*cosh(d*x + c))*sinh(d*x + c)^2 + 10*(5*a^2 + 4*a*b + 3*b^2)*cosh(d*x + c) - 5*((15*(a^2 + 2*a*b + b^2)*d*x + 23*a^2 + 40*a*b + 15*b^2)*cosh(d*x + c)^4 + 30*(a^2 + 2*a*b + b^2)*d*x - 3*(15*(a^2 + 2*a*b + b^2)*d*x + 23*a^2 + 40*a*b + 15*b^2)*cosh(d*x + c)^2 + 46*a^2 + 80*a*b + 30*b^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
155,1,3454,0,0.471742," ","integrate(coth(d*x+c)^7*(a+b*tanh(d*x+c)^2)^2,x, algorithm=""fricas"")","-\frac{3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x \cosh\left(d x + c\right)^{12} + 36 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{11} + 3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x \sinh\left(d x + c\right)^{12} - 6 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x - 3 \, a^{2} - 4 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{10} + 6 \, {\left(33 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x \cosh\left(d x + c\right)^{2} - 3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x + 3 \, a^{2} + 4 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{10} + 60 \, {\left(11 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x \cosh\left(d x + c\right)^{3} - {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x - 3 \, a^{2} - 4 \, a b - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} + 3 \, {\left(15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x - 12 \, a^{2} - 24 \, a b - 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{8} + 3 \, {\left(495 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x \cosh\left(d x + c\right)^{4} + 15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x - 90 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x - 3 \, a^{2} - 4 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} - 12 \, a^{2} - 24 \, a b - 8 \, b^{2}\right)} \sinh\left(d x + c\right)^{8} + 24 \, {\left(99 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x \cosh\left(d x + c\right)^{5} - 30 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x - 3 \, a^{2} - 4 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x - 12 \, a^{2} - 24 \, a b - 8 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} - 4 \, {\left(15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x - 17 \, a^{2} - 24 \, a b - 9 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(693 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x \cosh\left(d x + c\right)^{6} - 315 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x - 3 \, a^{2} - 4 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{4} - 15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x + 21 \, {\left(15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x - 12 \, a^{2} - 24 \, a b - 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 17 \, a^{2} + 24 \, a b + 9 \, b^{2}\right)} \sinh\left(d x + c\right)^{6} + 24 \, {\left(99 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x \cosh\left(d x + c\right)^{7} - 63 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x - 3 \, a^{2} - 4 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{5} + 7 \, {\left(15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x - 12 \, a^{2} - 24 \, a b - 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x - 17 \, a^{2} - 24 \, a b - 9 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 3 \, {\left(15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x - 12 \, a^{2} - 24 \, a b - 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(495 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x \cosh\left(d x + c\right)^{8} - 420 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x - 3 \, a^{2} - 4 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{6} + 70 \, {\left(15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x - 12 \, a^{2} - 24 \, a b - 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x - 20 \, {\left(15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x - 17 \, a^{2} - 24 \, a b - 9 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - 12 \, a^{2} - 24 \, a b - 8 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(165 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x \cosh\left(d x + c\right)^{9} - 180 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x - 3 \, a^{2} - 4 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{7} + 42 \, {\left(15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x - 12 \, a^{2} - 24 \, a b - 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} - 20 \, {\left(15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x - 17 \, a^{2} - 24 \, a b - 9 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x - 12 \, a^{2} - 24 \, a b - 8 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x - 6 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x - 3 \, a^{2} - 4 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 6 \, {\left(33 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x \cosh\left(d x + c\right)^{10} - 45 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x - 3 \, a^{2} - 4 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{8} + 14 \, {\left(15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x - 12 \, a^{2} - 24 \, a b - 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} - 10 \, {\left(15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x - 17 \, a^{2} - 24 \, a b - 9 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} - 3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x + 3 \, {\left(15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x - 12 \, a^{2} - 24 \, a b - 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 3 \, a^{2} + 4 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{2} - 3 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{12} + 12 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{11} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{12} - 6 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{10} + 6 \, {\left(11 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} - a^{2} - 2 \, a b - b^{2}\right)} \sinh\left(d x + c\right)^{10} + 20 \, {\left(11 \, {\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)\right)} \sinh\left(d x + c\right)^{9} + 15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{8} + 15 \, {\left(33 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} - 18 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{8} + 24 \, {\left(33 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{5} - 30 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + 5 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} - 20 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(231 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{6} - 315 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + 105 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} - 5 \, a^{2} - 10 \, a b - 5 \, b^{2}\right)} \sinh\left(d x + c\right)^{6} + 24 \, {\left(33 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{7} - 63 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{5} + 35 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} - 5 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + 15 \, {\left(33 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{8} - 84 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{6} + 70 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} - 20 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{4} + 20 \, {\left(11 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{9} - 36 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{7} + 42 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{5} - 20 \, {\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)\right)} \sinh\left(d x + c\right)^{3} - 6 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 6 \, {\left(11 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{10} - 45 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{8} + 70 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{6} - 50 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + 15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} - a^{2} - 2 \, a b - b^{2}\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 2 \, a b + b^{2} + 12 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{11} - 5 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{9} + 10 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{7} - 10 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\frac{2 \, \sinh\left(d x + c\right)}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) + 12 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x \cosh\left(d x + c\right)^{11} - 5 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x - 3 \, a^{2} - 4 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{9} + 2 \, {\left(15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x - 12 \, a^{2} - 24 \, a b - 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} - 2 \, {\left(15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x - 17 \, a^{2} - 24 \, a b - 9 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + {\left(15 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x - 12 \, a^{2} - 24 \, a b - 8 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x - 3 \, a^{2} - 4 \, a b - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{3 \, {\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,"-1/3*(3*(a^2 + 2*a*b + b^2)*d*x*cosh(d*x + c)^12 + 36*(a^2 + 2*a*b + b^2)*d*x*cosh(d*x + c)*sinh(d*x + c)^11 + 3*(a^2 + 2*a*b + b^2)*d*x*sinh(d*x + c)^12 - 6*(3*(a^2 + 2*a*b + b^2)*d*x - 3*a^2 - 4*a*b - b^2)*cosh(d*x + c)^10 + 6*(33*(a^2 + 2*a*b + b^2)*d*x*cosh(d*x + c)^2 - 3*(a^2 + 2*a*b + b^2)*d*x + 3*a^2 + 4*a*b + b^2)*sinh(d*x + c)^10 + 60*(11*(a^2 + 2*a*b + b^2)*d*x*cosh(d*x + c)^3 - (3*(a^2 + 2*a*b + b^2)*d*x - 3*a^2 - 4*a*b - b^2)*cosh(d*x + c))*sinh(d*x + c)^9 + 3*(15*(a^2 + 2*a*b + b^2)*d*x - 12*a^2 - 24*a*b - 8*b^2)*cosh(d*x + c)^8 + 3*(495*(a^2 + 2*a*b + b^2)*d*x*cosh(d*x + c)^4 + 15*(a^2 + 2*a*b + b^2)*d*x - 90*(3*(a^2 + 2*a*b + b^2)*d*x - 3*a^2 - 4*a*b - b^2)*cosh(d*x + c)^2 - 12*a^2 - 24*a*b - 8*b^2)*sinh(d*x + c)^8 + 24*(99*(a^2 + 2*a*b + b^2)*d*x*cosh(d*x + c)^5 - 30*(3*(a^2 + 2*a*b + b^2)*d*x - 3*a^2 - 4*a*b - b^2)*cosh(d*x + c)^3 + (15*(a^2 + 2*a*b + b^2)*d*x - 12*a^2 - 24*a*b - 8*b^2)*cosh(d*x + c))*sinh(d*x + c)^7 - 4*(15*(a^2 + 2*a*b + b^2)*d*x - 17*a^2 - 24*a*b - 9*b^2)*cosh(d*x + c)^6 + 4*(693*(a^2 + 2*a*b + b^2)*d*x*cosh(d*x + c)^6 - 315*(3*(a^2 + 2*a*b + b^2)*d*x - 3*a^2 - 4*a*b - b^2)*cosh(d*x + c)^4 - 15*(a^2 + 2*a*b + b^2)*d*x + 21*(15*(a^2 + 2*a*b + b^2)*d*x - 12*a^2 - 24*a*b - 8*b^2)*cosh(d*x + c)^2 + 17*a^2 + 24*a*b + 9*b^2)*sinh(d*x + c)^6 + 24*(99*(a^2 + 2*a*b + b^2)*d*x*cosh(d*x + c)^7 - 63*(3*(a^2 + 2*a*b + b^2)*d*x - 3*a^2 - 4*a*b - b^2)*cosh(d*x + c)^5 + 7*(15*(a^2 + 2*a*b + b^2)*d*x - 12*a^2 - 24*a*b - 8*b^2)*cosh(d*x + c)^3 - (15*(a^2 + 2*a*b + b^2)*d*x - 17*a^2 - 24*a*b - 9*b^2)*cosh(d*x + c))*sinh(d*x + c)^5 + 3*(15*(a^2 + 2*a*b + b^2)*d*x - 12*a^2 - 24*a*b - 8*b^2)*cosh(d*x + c)^4 + 3*(495*(a^2 + 2*a*b + b^2)*d*x*cosh(d*x + c)^8 - 420*(3*(a^2 + 2*a*b + b^2)*d*x - 3*a^2 - 4*a*b - b^2)*cosh(d*x + c)^6 + 70*(15*(a^2 + 2*a*b + b^2)*d*x - 12*a^2 - 24*a*b - 8*b^2)*cosh(d*x + c)^4 + 15*(a^2 + 2*a*b + b^2)*d*x - 20*(15*(a^2 + 2*a*b + b^2)*d*x - 17*a^2 - 24*a*b - 9*b^2)*cosh(d*x + c)^2 - 12*a^2 - 24*a*b - 8*b^2)*sinh(d*x + c)^4 + 4*(165*(a^2 + 2*a*b + b^2)*d*x*cosh(d*x + c)^9 - 180*(3*(a^2 + 2*a*b + b^2)*d*x - 3*a^2 - 4*a*b - b^2)*cosh(d*x + c)^7 + 42*(15*(a^2 + 2*a*b + b^2)*d*x - 12*a^2 - 24*a*b - 8*b^2)*cosh(d*x + c)^5 - 20*(15*(a^2 + 2*a*b + b^2)*d*x - 17*a^2 - 24*a*b - 9*b^2)*cosh(d*x + c)^3 + 3*(15*(a^2 + 2*a*b + b^2)*d*x - 12*a^2 - 24*a*b - 8*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 3*(a^2 + 2*a*b + b^2)*d*x - 6*(3*(a^2 + 2*a*b + b^2)*d*x - 3*a^2 - 4*a*b - b^2)*cosh(d*x + c)^2 + 6*(33*(a^2 + 2*a*b + b^2)*d*x*cosh(d*x + c)^10 - 45*(3*(a^2 + 2*a*b + b^2)*d*x - 3*a^2 - 4*a*b - b^2)*cosh(d*x + c)^8 + 14*(15*(a^2 + 2*a*b + b^2)*d*x - 12*a^2 - 24*a*b - 8*b^2)*cosh(d*x + c)^6 - 10*(15*(a^2 + 2*a*b + b^2)*d*x - 17*a^2 - 24*a*b - 9*b^2)*cosh(d*x + c)^4 - 3*(a^2 + 2*a*b + b^2)*d*x + 3*(15*(a^2 + 2*a*b + b^2)*d*x - 12*a^2 - 24*a*b - 8*b^2)*cosh(d*x + c)^2 + 3*a^2 + 4*a*b + b^2)*sinh(d*x + c)^2 - 3*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^12 + 12*(a^2 + 2*a*b + b^2)*cosh(d*x + c)*sinh(d*x + c)^11 + (a^2 + 2*a*b + b^2)*sinh(d*x + c)^12 - 6*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^10 + 6*(11*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 - a^2 - 2*a*b - b^2)*sinh(d*x + c)^10 + 20*(11*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 - 3*(a^2 + 2*a*b + b^2)*cosh(d*x + c))*sinh(d*x + c)^9 + 15*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^8 + 15*(33*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 - 18*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + a^2 + 2*a*b + b^2)*sinh(d*x + c)^8 + 24*(33*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^5 - 30*(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)^7 - 20*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^6 + 4*(231*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^6 - 315*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 + 105*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 - 5*a^2 - 10*a*b - 5*b^2)*sinh(d*x + c)^6 + 24*(33*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^7 - 63*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^5 + 35*(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)^5 + 15*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 + 15*(33*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^8 - 84*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^6 + 70*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 - 20*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + a^2 + 2*a*b + b^2)*sinh(d*x + c)^4 + 20*(11*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^9 - 36*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^7 + 42*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^5 - 20*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 + 3*(a^2 + 2*a*b + b^2)*cosh(d*x + c))*sinh(d*x + c)^3 - 6*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + 6*(11*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^10 - 45*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^8 + 70*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^6 - 50*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 + 15*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 - a^2 - 2*a*b - b^2)*sinh(d*x + c)^2 + a^2 + 2*a*b + b^2 + 12*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^11 - 5*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^9 + 10*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^7 - 10*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^5 + 5*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 - (a^2 + 2*a*b + b^2)*cosh(d*x + c))*sinh(d*x + c))*log(2*sinh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))) + 12*(3*(a^2 + 2*a*b + b^2)*d*x*cosh(d*x + c)^11 - 5*(3*(a^2 + 2*a*b + b^2)*d*x - 3*a^2 - 4*a*b - b^2)*cosh(d*x + c)^9 + 2*(15*(a^2 + 2*a*b + b^2)*d*x - 12*a^2 - 24*a*b - 8*b^2)*cosh(d*x + c)^7 - 2*(15*(a^2 + 2*a*b + b^2)*d*x - 17*a^2 - 24*a*b - 9*b^2)*cosh(d*x + c)^5 + (15*(a^2 + 2*a*b + b^2)*d*x - 12*a^2 - 24*a*b - 8*b^2)*cosh(d*x + c)^3 - (3*(a^2 + 2*a*b + b^2)*d*x - 3*a^2 - 4*a*b - b^2)*cosh(d*x + c))*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
156,1,1563,0,0.448857," ","integrate(tanh(d*x+c)^4*(a+b*tanh(d*x+c)^2)^3,x, algorithm=""fricas"")","\frac{{\left(420 \, a^{3} + 1449 \, a^{2} b + 1584 \, a b^{2} + 563 \, b^{3} + 315 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{9} + 9 \, {\left(420 \, a^{3} + 1449 \, a^{2} b + 1584 \, a b^{2} + 563 \, b^{3} + 315 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{8} - {\left(420 \, a^{3} + 1449 \, a^{2} b + 1584 \, a b^{2} + 563 \, b^{3}\right)} \sinh\left(d x + c\right)^{9} + 9 \, {\left(420 \, a^{3} + 1449 \, a^{2} b + 1584 \, a b^{2} + 563 \, b^{3} + 315 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{7} - 9 \, {\left(280 \, a^{3} + 819 \, a^{2} b + 744 \, a b^{2} + 213 \, b^{3} + 4 \, {\left(420 \, a^{3} + 1449 \, a^{2} b + 1584 \, a b^{2} + 563 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{7} + 21 \, {\left(4 \, {\left(420 \, a^{3} + 1449 \, a^{2} b + 1584 \, a b^{2} + 563 \, b^{3} + 315 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(420 \, a^{3} + 1449 \, a^{2} b + 1584 \, a b^{2} + 563 \, b^{3} + 315 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} + 36 \, {\left(420 \, a^{3} + 1449 \, a^{2} b + 1584 \, a b^{2} + 563 \, b^{3} + 315 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{5} - 9 \, {\left(14 \, {\left(420 \, a^{3} + 1449 \, a^{2} b + 1584 \, a b^{2} + 563 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 700 \, a^{3} + 2016 \, a^{2} b + 2136 \, a b^{2} + 852 \, b^{3} + 21 \, {\left(280 \, a^{3} + 819 \, a^{2} b + 744 \, a b^{2} + 213 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{5} + 9 \, {\left(14 \, {\left(420 \, a^{3} + 1449 \, a^{2} b + 1584 \, a b^{2} + 563 \, b^{3} + 315 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{5} + 35 \, {\left(420 \, a^{3} + 1449 \, a^{2} b + 1584 \, a b^{2} + 563 \, b^{3} + 315 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + 20 \, {\left(420 \, a^{3} + 1449 \, a^{2} b + 1584 \, a b^{2} + 563 \, b^{3} + 315 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 84 \, {\left(420 \, a^{3} + 1449 \, a^{2} b + 1584 \, a b^{2} + 563 \, b^{3} + 315 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(28 \, {\left(420 \, a^{3} + 1449 \, a^{2} b + 1584 \, a b^{2} + 563 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 105 \, {\left(280 \, a^{3} + 819 \, a^{2} b + 744 \, a b^{2} + 213 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 2660 \, a^{3} + 8232 \, a^{2} b + 8232 \, a b^{2} + 1764 \, b^{3} + 120 \, {\left(175 \, a^{3} + 504 \, a^{2} b + 534 \, a b^{2} + 213 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + 9 \, {\left(4 \, {\left(420 \, a^{3} + 1449 \, a^{2} b + 1584 \, a b^{2} + 563 \, b^{3} + 315 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{7} + 21 \, {\left(420 \, a^{3} + 1449 \, a^{2} b + 1584 \, a b^{2} + 563 \, b^{3} + 315 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{5} + 40 \, {\left(420 \, a^{3} + 1449 \, a^{2} b + 1584 \, a b^{2} + 563 \, b^{3} + 315 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + 28 \, {\left(420 \, a^{3} + 1449 \, a^{2} b + 1584 \, a b^{2} + 563 \, b^{3} + 315 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 126 \, {\left(420 \, a^{3} + 1449 \, a^{2} b + 1584 \, a b^{2} + 563 \, b^{3} + 315 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right) - 9 \, {\left({\left(420 \, a^{3} + 1449 \, a^{2} b + 1584 \, a b^{2} + 563 \, b^{3}\right)} \cosh\left(d x + c\right)^{8} + 7 \, {\left(280 \, a^{3} + 819 \, a^{2} b + 744 \, a b^{2} + 213 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 20 \, {\left(175 \, a^{3} + 504 \, a^{2} b + 534 \, a b^{2} + 213 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 420 \, a^{3} + 1386 \, a^{2} b + 1176 \, a b^{2} + 882 \, b^{3} + 28 \, {\left(95 \, a^{3} + 294 \, a^{2} b + 294 \, a b^{2} + 63 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)}{315 \, {\left(d \cosh\left(d x + c\right)^{9} + 9 \, d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{8} + 9 \, d \cosh\left(d x + c\right)^{7} + 21 \, {\left(4 \, d \cosh\left(d x + c\right)^{3} + 3 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} + 36 \, d \cosh\left(d x + c\right)^{5} + 9 \, {\left(14 \, d \cosh\left(d x + c\right)^{5} + 35 \, d \cosh\left(d x + c\right)^{3} + 20 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 84 \, d \cosh\left(d x + c\right)^{3} + 9 \, {\left(4 \, d \cosh\left(d x + c\right)^{7} + 21 \, d \cosh\left(d x + c\right)^{5} + 40 \, d \cosh\left(d x + c\right)^{3} + 28 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 126 \, d \cosh\left(d x + c\right)\right)}}"," ",0,"1/315*((420*a^3 + 1449*a^2*b + 1584*a*b^2 + 563*b^3 + 315*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^9 + 9*(420*a^3 + 1449*a^2*b + 1584*a*b^2 + 563*b^3 + 315*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)*sinh(d*x + c)^8 - (420*a^3 + 1449*a^2*b + 1584*a*b^2 + 563*b^3)*sinh(d*x + c)^9 + 9*(420*a^3 + 1449*a^2*b + 1584*a*b^2 + 563*b^3 + 315*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^7 - 9*(280*a^3 + 819*a^2*b + 744*a*b^2 + 213*b^3 + 4*(420*a^3 + 1449*a^2*b + 1584*a*b^2 + 563*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^7 + 21*(4*(420*a^3 + 1449*a^2*b + 1584*a*b^2 + 563*b^3 + 315*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^3 + 3*(420*a^3 + 1449*a^2*b + 1584*a*b^2 + 563*b^3 + 315*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c)^6 + 36*(420*a^3 + 1449*a^2*b + 1584*a*b^2 + 563*b^3 + 315*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^5 - 9*(14*(420*a^3 + 1449*a^2*b + 1584*a*b^2 + 563*b^3)*cosh(d*x + c)^4 + 700*a^3 + 2016*a^2*b + 2136*a*b^2 + 852*b^3 + 21*(280*a^3 + 819*a^2*b + 744*a*b^2 + 213*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 9*(14*(420*a^3 + 1449*a^2*b + 1584*a*b^2 + 563*b^3 + 315*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^5 + 35*(420*a^3 + 1449*a^2*b + 1584*a*b^2 + 563*b^3 + 315*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^3 + 20*(420*a^3 + 1449*a^2*b + 1584*a*b^2 + 563*b^3 + 315*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c)^4 + 84*(420*a^3 + 1449*a^2*b + 1584*a*b^2 + 563*b^3 + 315*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^3 - 3*(28*(420*a^3 + 1449*a^2*b + 1584*a*b^2 + 563*b^3)*cosh(d*x + c)^6 + 105*(280*a^3 + 819*a^2*b + 744*a*b^2 + 213*b^3)*cosh(d*x + c)^4 + 2660*a^3 + 8232*a^2*b + 8232*a*b^2 + 1764*b^3 + 120*(175*a^3 + 504*a^2*b + 534*a*b^2 + 213*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 9*(4*(420*a^3 + 1449*a^2*b + 1584*a*b^2 + 563*b^3 + 315*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^7 + 21*(420*a^3 + 1449*a^2*b + 1584*a*b^2 + 563*b^3 + 315*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^5 + 40*(420*a^3 + 1449*a^2*b + 1584*a*b^2 + 563*b^3 + 315*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^3 + 28*(420*a^3 + 1449*a^2*b + 1584*a*b^2 + 563*b^3 + 315*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c)^2 + 126*(420*a^3 + 1449*a^2*b + 1584*a*b^2 + 563*b^3 + 315*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c) - 9*((420*a^3 + 1449*a^2*b + 1584*a*b^2 + 563*b^3)*cosh(d*x + c)^8 + 7*(280*a^3 + 819*a^2*b + 744*a*b^2 + 213*b^3)*cosh(d*x + c)^6 + 20*(175*a^3 + 504*a^2*b + 534*a*b^2 + 213*b^3)*cosh(d*x + c)^4 + 420*a^3 + 1386*a^2*b + 1176*a*b^2 + 882*b^3 + 28*(95*a^3 + 294*a^2*b + 294*a*b^2 + 63*b^3)*cosh(d*x + c)^2)*sinh(d*x + c))/(d*cosh(d*x + c)^9 + 9*d*cosh(d*x + c)*sinh(d*x + c)^8 + 9*d*cosh(d*x + c)^7 + 21*(4*d*cosh(d*x + c)^3 + 3*d*cosh(d*x + c))*sinh(d*x + c)^6 + 36*d*cosh(d*x + c)^5 + 9*(14*d*cosh(d*x + c)^5 + 35*d*cosh(d*x + c)^3 + 20*d*cosh(d*x + c))*sinh(d*x + c)^4 + 84*d*cosh(d*x + c)^3 + 9*(4*d*cosh(d*x + c)^7 + 21*d*cosh(d*x + c)^5 + 40*d*cosh(d*x + c)^3 + 28*d*cosh(d*x + c))*sinh(d*x + c)^2 + 126*d*cosh(d*x + c))","B",0
157,1,7502,0,0.558285," ","integrate(tanh(d*x+c)^3*(a+b*tanh(d*x+c)^2)^3,x, algorithm=""fricas"")","-\frac{3 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x \cosh\left(d x + c\right)^{16} + 48 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{15} + 3 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x \sinh\left(d x + c\right)^{16} - 6 \, {\left(a^{3} + 6 \, a^{2} b + 9 \, a b^{2} + 4 \, b^{3} - 4 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{14} + 6 \, {\left(60 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x \cosh\left(d x + c\right)^{2} - a^{3} - 6 \, a^{2} b - 9 \, a b^{2} - 4 \, b^{3} + 4 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \sinh\left(d x + c\right)^{14} + 84 \, {\left(20 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x \cosh\left(d x + c\right)^{3} - {\left(a^{3} + 6 \, a^{2} b + 9 \, a b^{2} + 4 \, b^{3} - 4 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{13} - 12 \, {\left(3 \, a^{3} + 15 \, a^{2} b + 18 \, a b^{2} + 6 \, b^{3} - 7 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{12} + 6 \, {\left(910 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x \cosh\left(d x + c\right)^{4} - 6 \, a^{3} - 30 \, a^{2} b - 36 \, a b^{2} - 12 \, b^{3} + 14 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x - 91 \, {\left(a^{3} + 6 \, a^{2} b + 9 \, a b^{2} + 4 \, b^{3} - 4 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{12} + 24 \, {\left(546 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x \cosh\left(d x + c\right)^{5} - 91 \, {\left(a^{3} + 6 \, a^{2} b + 9 \, a b^{2} + 4 \, b^{3} - 4 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - 6 \, {\left(3 \, a^{3} + 15 \, a^{2} b + 18 \, a b^{2} + 6 \, b^{3} - 7 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{11} - 2 \, {\left(45 \, a^{3} + 198 \, a^{2} b + 237 \, a b^{2} + 100 \, b^{3} - 84 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{10} + 2 \, {\left(12012 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x \cosh\left(d x + c\right)^{6} - 3003 \, {\left(a^{3} + 6 \, a^{2} b + 9 \, a b^{2} + 4 \, b^{3} - 4 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{4} - 45 \, a^{3} - 198 \, a^{2} b - 237 \, a b^{2} - 100 \, b^{3} + 84 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x - 396 \, {\left(3 \, a^{3} + 15 \, a^{2} b + 18 \, a b^{2} + 6 \, b^{3} - 7 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{10} + 4 \, {\left(8580 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x \cosh\left(d x + c\right)^{7} - 3003 \, {\left(a^{3} + 6 \, a^{2} b + 9 \, a b^{2} + 4 \, b^{3} - 4 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{5} - 660 \, {\left(3 \, a^{3} + 15 \, a^{2} b + 18 \, a b^{2} + 6 \, b^{3} - 7 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - 5 \, {\left(45 \, a^{3} + 198 \, a^{2} b + 237 \, a b^{2} + 100 \, b^{3} - 84 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} - 2 \, {\left(60 \, a^{3} + 252 \, a^{2} b + 312 \, a b^{2} + 104 \, b^{3} - 105 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{8} + 2 \, {\left(19305 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x \cosh\left(d x + c\right)^{8} - 9009 \, {\left(a^{3} + 6 \, a^{2} b + 9 \, a b^{2} + 4 \, b^{3} - 4 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{6} - 2970 \, {\left(3 \, a^{3} + 15 \, a^{2} b + 18 \, a b^{2} + 6 \, b^{3} - 7 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{4} - 60 \, a^{3} - 252 \, a^{2} b - 312 \, a b^{2} - 104 \, b^{3} + 105 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x - 45 \, {\left(45 \, a^{3} + 198 \, a^{2} b + 237 \, a b^{2} + 100 \, b^{3} - 84 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{8} + 16 \, {\left(2145 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x \cosh\left(d x + c\right)^{9} - 1287 \, {\left(a^{3} + 6 \, a^{2} b + 9 \, a b^{2} + 4 \, b^{3} - 4 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{7} - 594 \, {\left(3 \, a^{3} + 15 \, a^{2} b + 18 \, a b^{2} + 6 \, b^{3} - 7 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{5} - 15 \, {\left(45 \, a^{3} + 198 \, a^{2} b + 237 \, a b^{2} + 100 \, b^{3} - 84 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - {\left(60 \, a^{3} + 252 \, a^{2} b + 312 \, a b^{2} + 104 \, b^{3} - 105 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} - 2 \, {\left(45 \, a^{3} + 198 \, a^{2} b + 237 \, a b^{2} + 100 \, b^{3} - 84 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(12012 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x \cosh\left(d x + c\right)^{10} - 9009 \, {\left(a^{3} + 6 \, a^{2} b + 9 \, a b^{2} + 4 \, b^{3} - 4 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{8} - 5544 \, {\left(3 \, a^{3} + 15 \, a^{2} b + 18 \, a b^{2} + 6 \, b^{3} - 7 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{6} - 210 \, {\left(45 \, a^{3} + 198 \, a^{2} b + 237 \, a b^{2} + 100 \, b^{3} - 84 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{4} - 45 \, a^{3} - 198 \, a^{2} b - 237 \, a b^{2} - 100 \, b^{3} + 84 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x - 28 \, {\left(60 \, a^{3} + 252 \, a^{2} b + 312 \, a b^{2} + 104 \, b^{3} - 105 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(3276 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x \cosh\left(d x + c\right)^{11} - 3003 \, {\left(a^{3} + 6 \, a^{2} b + 9 \, a b^{2} + 4 \, b^{3} - 4 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{9} - 2376 \, {\left(3 \, a^{3} + 15 \, a^{2} b + 18 \, a b^{2} + 6 \, b^{3} - 7 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{7} - 126 \, {\left(45 \, a^{3} + 198 \, a^{2} b + 237 \, a b^{2} + 100 \, b^{3} - 84 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{5} - 28 \, {\left(60 \, a^{3} + 252 \, a^{2} b + 312 \, a b^{2} + 104 \, b^{3} - 105 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(45 \, a^{3} + 198 \, a^{2} b + 237 \, a b^{2} + 100 \, b^{3} - 84 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 12 \, {\left(3 \, a^{3} + 15 \, a^{2} b + 18 \, a b^{2} + 6 \, b^{3} - 7 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(2730 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x \cosh\left(d x + c\right)^{12} - 3003 \, {\left(a^{3} + 6 \, a^{2} b + 9 \, a b^{2} + 4 \, b^{3} - 4 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{10} - 2970 \, {\left(3 \, a^{3} + 15 \, a^{2} b + 18 \, a b^{2} + 6 \, b^{3} - 7 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{8} - 210 \, {\left(45 \, a^{3} + 198 \, a^{2} b + 237 \, a b^{2} + 100 \, b^{3} - 84 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{6} - 70 \, {\left(60 \, a^{3} + 252 \, a^{2} b + 312 \, a b^{2} + 104 \, b^{3} - 105 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{4} - 18 \, a^{3} - 90 \, a^{2} b - 108 \, a b^{2} - 36 \, b^{3} + 42 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x - 15 \, {\left(45 \, a^{3} + 198 \, a^{2} b + 237 \, a b^{2} + 100 \, b^{3} - 84 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(210 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x \cosh\left(d x + c\right)^{13} - 273 \, {\left(a^{3} + 6 \, a^{2} b + 9 \, a b^{2} + 4 \, b^{3} - 4 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{11} - 330 \, {\left(3 \, a^{3} + 15 \, a^{2} b + 18 \, a b^{2} + 6 \, b^{3} - 7 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{9} - 30 \, {\left(45 \, a^{3} + 198 \, a^{2} b + 237 \, a b^{2} + 100 \, b^{3} - 84 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{7} - 14 \, {\left(60 \, a^{3} + 252 \, a^{2} b + 312 \, a b^{2} + 104 \, b^{3} - 105 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{5} - 5 \, {\left(45 \, a^{3} + 198 \, a^{2} b + 237 \, a b^{2} + 100 \, b^{3} - 84 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - 6 \, {\left(3 \, a^{3} + 15 \, a^{2} b + 18 \, a b^{2} + 6 \, b^{3} - 7 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 3 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x - 6 \, {\left(a^{3} + 6 \, a^{2} b + 9 \, a b^{2} + 4 \, b^{3} - 4 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(180 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x \cosh\left(d x + c\right)^{14} - 273 \, {\left(a^{3} + 6 \, a^{2} b + 9 \, a b^{2} + 4 \, b^{3} - 4 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{12} - 396 \, {\left(3 \, a^{3} + 15 \, a^{2} b + 18 \, a b^{2} + 6 \, b^{3} - 7 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{10} - 45 \, {\left(45 \, a^{3} + 198 \, a^{2} b + 237 \, a b^{2} + 100 \, b^{3} - 84 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{8} - 28 \, {\left(60 \, a^{3} + 252 \, a^{2} b + 312 \, a b^{2} + 104 \, b^{3} - 105 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{6} - 15 \, {\left(45 \, a^{3} + 198 \, a^{2} b + 237 \, a b^{2} + 100 \, b^{3} - 84 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{4} - 3 \, a^{3} - 18 \, a^{2} b - 27 \, a b^{2} - 12 \, b^{3} + 12 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x - 36 \, {\left(3 \, a^{3} + 15 \, a^{2} b + 18 \, a b^{2} + 6 \, b^{3} - 7 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} - 3 \, {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{16} + 16 \, {\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)^{15} + {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \sinh\left(d x + c\right)^{16} + 8 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{14} + 8 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} + 15 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{14} + 112 \, {\left(5 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{13} + 28 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{12} + 28 \, {\left(65 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{4} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} + 26 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{12} + 112 \, {\left(39 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{5} + 26 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{11} + 56 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{10} + 56 \, {\left(143 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{6} + 143 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{4} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} + 33 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{10} + 16 \, {\left(715 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{7} + 1001 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{5} + 385 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{3} + 35 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} + 70 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{8} + 2 \, {\left(6435 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{8} + 12012 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{6} + 6930 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{4} + 35 \, a^{3} + 105 \, a^{2} b + 105 \, a b^{2} + 35 \, b^{3} + 1260 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{8} + 16 \, {\left(715 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{9} + 1716 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{7} + 1386 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{5} + 420 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{3} + 35 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 56 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{6} + 56 \, {\left(143 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{10} + 429 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{8} + 462 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{6} + 210 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{4} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} + 35 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 112 \, {\left(39 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{11} + 143 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{9} + 198 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{7} + 126 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{5} + 35 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 28 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{4} + 28 \, {\left(65 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{12} + 286 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{10} + 495 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{8} + 420 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{6} + 175 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{4} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} + 30 \, {\left(a^{3} + 3 \, 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} + 112 \, {\left(5 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{13} + 26 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{11} + 55 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{9} + 60 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{7} + 35 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} + 8 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{2} + 8 \, {\left(15 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{14} + 91 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{12} + 231 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{10} + 315 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{8} + 245 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{6} + 105 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{4} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} + 21 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 16 \, {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{15} + 7 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{13} + 21 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{11} + 35 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{9} + 35 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{7} + 21 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{5} + 7 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\frac{2 \, \cosh\left(d x + c\right)}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) + 4 \, {\left(12 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x \cosh\left(d x + c\right)^{15} - 21 \, {\left(a^{3} + 6 \, a^{2} b + 9 \, a b^{2} + 4 \, b^{3} - 4 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{13} - 36 \, {\left(3 \, a^{3} + 15 \, a^{2} b + 18 \, a b^{2} + 6 \, b^{3} - 7 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{11} - 5 \, {\left(45 \, a^{3} + 198 \, a^{2} b + 237 \, a b^{2} + 100 \, b^{3} - 84 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{9} - 4 \, {\left(60 \, a^{3} + 252 \, a^{2} b + 312 \, a b^{2} + 104 \, b^{3} - 105 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{7} - 3 \, {\left(45 \, a^{3} + 198 \, a^{2} b + 237 \, a b^{2} + 100 \, b^{3} - 84 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{5} - 12 \, {\left(3 \, a^{3} + 15 \, a^{2} b + 18 \, a b^{2} + 6 \, b^{3} - 7 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{3} + 6 \, a^{2} b + 9 \, a b^{2} + 4 \, b^{3} - 4 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{3 \, {\left(d \cosh\left(d x + c\right)^{16} + 16 \, d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{15} + d \sinh\left(d x + c\right)^{16} + 8 \, d \cosh\left(d x + c\right)^{14} + 8 \, {\left(15 \, d \cosh\left(d x + c\right)^{2} + d\right)} \sinh\left(d x + c\right)^{14} + 112 \, {\left(5 \, d \cosh\left(d x + c\right)^{3} + d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{13} + 28 \, d \cosh\left(d x + c\right)^{12} + 28 \, {\left(65 \, d \cosh\left(d x + c\right)^{4} + 26 \, d \cosh\left(d x + c\right)^{2} + d\right)} \sinh\left(d x + c\right)^{12} + 112 \, {\left(39 \, d \cosh\left(d x + c\right)^{5} + 26 \, d \cosh\left(d x + c\right)^{3} + 3 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{11} + 56 \, d \cosh\left(d x + c\right)^{10} + 56 \, {\left(143 \, d \cosh\left(d x + c\right)^{6} + 143 \, d \cosh\left(d x + c\right)^{4} + 33 \, d \cosh\left(d x + c\right)^{2} + d\right)} \sinh\left(d x + c\right)^{10} + 16 \, {\left(715 \, d \cosh\left(d x + c\right)^{7} + 1001 \, d \cosh\left(d x + c\right)^{5} + 385 \, d \cosh\left(d x + c\right)^{3} + 35 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} + 70 \, d \cosh\left(d x + c\right)^{8} + 2 \, {\left(6435 \, d \cosh\left(d x + c\right)^{8} + 12012 \, d \cosh\left(d x + c\right)^{6} + 6930 \, d \cosh\left(d x + c\right)^{4} + 1260 \, d \cosh\left(d x + c\right)^{2} + 35 \, d\right)} \sinh\left(d x + c\right)^{8} + 16 \, {\left(715 \, d \cosh\left(d x + c\right)^{9} + 1716 \, d \cosh\left(d x + c\right)^{7} + 1386 \, 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)^{7} + 56 \, d \cosh\left(d x + c\right)^{6} + 56 \, {\left(143 \, d \cosh\left(d x + c\right)^{10} + 429 \, d \cosh\left(d x + c\right)^{8} + 462 \, d \cosh\left(d x + c\right)^{6} + 210 \, d \cosh\left(d x + c\right)^{4} + 35 \, d \cosh\left(d x + c\right)^{2} + d\right)} \sinh\left(d x + c\right)^{6} + 112 \, {\left(39 \, d \cosh\left(d x + c\right)^{11} + 143 \, d \cosh\left(d x + c\right)^{9} + 198 \, d \cosh\left(d x + c\right)^{7} + 126 \, d \cosh\left(d x + c\right)^{5} + 35 \, d \cosh\left(d x + c\right)^{3} + 3 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 28 \, d \cosh\left(d x + c\right)^{4} + 28 \, {\left(65 \, d \cosh\left(d x + c\right)^{12} + 286 \, d \cosh\left(d x + c\right)^{10} + 495 \, d \cosh\left(d x + c\right)^{8} + 420 \, d \cosh\left(d x + c\right)^{6} + 175 \, d \cosh\left(d x + c\right)^{4} + 30 \, d \cosh\left(d x + c\right)^{2} + d\right)} \sinh\left(d x + c\right)^{4} + 112 \, {\left(5 \, d \cosh\left(d x + c\right)^{13} + 26 \, d \cosh\left(d x + c\right)^{11} + 55 \, d \cosh\left(d x + c\right)^{9} + 60 \, d \cosh\left(d x + c\right)^{7} + 35 \, d \cosh\left(d x + c\right)^{5} + 10 \, d \cosh\left(d x + c\right)^{3} + d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 8 \, d \cosh\left(d x + c\right)^{2} + 8 \, {\left(15 \, d \cosh\left(d x + c\right)^{14} + 91 \, d \cosh\left(d x + c\right)^{12} + 231 \, d \cosh\left(d x + c\right)^{10} + 315 \, d \cosh\left(d x + c\right)^{8} + 245 \, d \cosh\left(d x + c\right)^{6} + 105 \, d \cosh\left(d x + c\right)^{4} + 21 \, d \cosh\left(d x + c\right)^{2} + d\right)} \sinh\left(d x + c\right)^{2} + 16 \, {\left(d \cosh\left(d x + c\right)^{15} + 7 \, d \cosh\left(d x + c\right)^{13} + 21 \, d \cosh\left(d x + c\right)^{11} + 35 \, d \cosh\left(d x + c\right)^{9} + 35 \, d \cosh\left(d x + c\right)^{7} + 21 \, d \cosh\left(d x + c\right)^{5} + 7 \, 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*(3*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x*cosh(d*x + c)^16 + 48*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x*cosh(d*x + c)*sinh(d*x + c)^15 + 3*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x*sinh(d*x + c)^16 - 6*(a^3 + 6*a^2*b + 9*a*b^2 + 4*b^3 - 4*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^14 + 6*(60*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x*cosh(d*x + c)^2 - a^3 - 6*a^2*b - 9*a*b^2 - 4*b^3 + 4*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*sinh(d*x + c)^14 + 84*(20*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x*cosh(d*x + c)^3 - (a^3 + 6*a^2*b + 9*a*b^2 + 4*b^3 - 4*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c)^13 - 12*(3*a^3 + 15*a^2*b + 18*a*b^2 + 6*b^3 - 7*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^12 + 6*(910*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x*cosh(d*x + c)^4 - 6*a^3 - 30*a^2*b - 36*a*b^2 - 12*b^3 + 14*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x - 91*(a^3 + 6*a^2*b + 9*a*b^2 + 4*b^3 - 4*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^12 + 24*(546*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x*cosh(d*x + c)^5 - 91*(a^3 + 6*a^2*b + 9*a*b^2 + 4*b^3 - 4*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^3 - 6*(3*a^3 + 15*a^2*b + 18*a*b^2 + 6*b^3 - 7*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c)^11 - 2*(45*a^3 + 198*a^2*b + 237*a*b^2 + 100*b^3 - 84*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^10 + 2*(12012*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x*cosh(d*x + c)^6 - 3003*(a^3 + 6*a^2*b + 9*a*b^2 + 4*b^3 - 4*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^4 - 45*a^3 - 198*a^2*b - 237*a*b^2 - 100*b^3 + 84*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x - 396*(3*a^3 + 15*a^2*b + 18*a*b^2 + 6*b^3 - 7*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^10 + 4*(8580*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x*cosh(d*x + c)^7 - 3003*(a^3 + 6*a^2*b + 9*a*b^2 + 4*b^3 - 4*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^5 - 660*(3*a^3 + 15*a^2*b + 18*a*b^2 + 6*b^3 - 7*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^3 - 5*(45*a^3 + 198*a^2*b + 237*a*b^2 + 100*b^3 - 84*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c)^9 - 2*(60*a^3 + 252*a^2*b + 312*a*b^2 + 104*b^3 - 105*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^8 + 2*(19305*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x*cosh(d*x + c)^8 - 9009*(a^3 + 6*a^2*b + 9*a*b^2 + 4*b^3 - 4*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^6 - 2970*(3*a^3 + 15*a^2*b + 18*a*b^2 + 6*b^3 - 7*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^4 - 60*a^3 - 252*a^2*b - 312*a*b^2 - 104*b^3 + 105*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x - 45*(45*a^3 + 198*a^2*b + 237*a*b^2 + 100*b^3 - 84*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 16*(2145*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x*cosh(d*x + c)^9 - 1287*(a^3 + 6*a^2*b + 9*a*b^2 + 4*b^3 - 4*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^7 - 594*(3*a^3 + 15*a^2*b + 18*a*b^2 + 6*b^3 - 7*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^5 - 15*(45*a^3 + 198*a^2*b + 237*a*b^2 + 100*b^3 - 84*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^3 - (60*a^3 + 252*a^2*b + 312*a*b^2 + 104*b^3 - 105*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c)^7 - 2*(45*a^3 + 198*a^2*b + 237*a*b^2 + 100*b^3 - 84*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^6 + 2*(12012*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x*cosh(d*x + c)^10 - 9009*(a^3 + 6*a^2*b + 9*a*b^2 + 4*b^3 - 4*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^8 - 5544*(3*a^3 + 15*a^2*b + 18*a*b^2 + 6*b^3 - 7*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^6 - 210*(45*a^3 + 198*a^2*b + 237*a*b^2 + 100*b^3 - 84*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^4 - 45*a^3 - 198*a^2*b - 237*a*b^2 - 100*b^3 + 84*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x - 28*(60*a^3 + 252*a^2*b + 312*a*b^2 + 104*b^3 - 105*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 4*(3276*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x*cosh(d*x + c)^11 - 3003*(a^3 + 6*a^2*b + 9*a*b^2 + 4*b^3 - 4*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^9 - 2376*(3*a^3 + 15*a^2*b + 18*a*b^2 + 6*b^3 - 7*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^7 - 126*(45*a^3 + 198*a^2*b + 237*a*b^2 + 100*b^3 - 84*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^5 - 28*(60*a^3 + 252*a^2*b + 312*a*b^2 + 104*b^3 - 105*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^3 - 3*(45*a^3 + 198*a^2*b + 237*a*b^2 + 100*b^3 - 84*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c)^5 - 12*(3*a^3 + 15*a^2*b + 18*a*b^2 + 6*b^3 - 7*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^4 + 2*(2730*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x*cosh(d*x + c)^12 - 3003*(a^3 + 6*a^2*b + 9*a*b^2 + 4*b^3 - 4*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^10 - 2970*(3*a^3 + 15*a^2*b + 18*a*b^2 + 6*b^3 - 7*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^8 - 210*(45*a^3 + 198*a^2*b + 237*a*b^2 + 100*b^3 - 84*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^6 - 70*(60*a^3 + 252*a^2*b + 312*a*b^2 + 104*b^3 - 105*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^4 - 18*a^3 - 90*a^2*b - 108*a*b^2 - 36*b^3 + 42*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x - 15*(45*a^3 + 198*a^2*b + 237*a*b^2 + 100*b^3 - 84*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(210*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x*cosh(d*x + c)^13 - 273*(a^3 + 6*a^2*b + 9*a*b^2 + 4*b^3 - 4*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^11 - 330*(3*a^3 + 15*a^2*b + 18*a*b^2 + 6*b^3 - 7*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^9 - 30*(45*a^3 + 198*a^2*b + 237*a*b^2 + 100*b^3 - 84*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^7 - 14*(60*a^3 + 252*a^2*b + 312*a*b^2 + 104*b^3 - 105*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^5 - 5*(45*a^3 + 198*a^2*b + 237*a*b^2 + 100*b^3 - 84*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^3 - 6*(3*a^3 + 15*a^2*b + 18*a*b^2 + 6*b^3 - 7*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c)^3 + 3*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x - 6*(a^3 + 6*a^2*b + 9*a*b^2 + 4*b^3 - 4*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^2 + 2*(180*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x*cosh(d*x + c)^14 - 273*(a^3 + 6*a^2*b + 9*a*b^2 + 4*b^3 - 4*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^12 - 396*(3*a^3 + 15*a^2*b + 18*a*b^2 + 6*b^3 - 7*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^10 - 45*(45*a^3 + 198*a^2*b + 237*a*b^2 + 100*b^3 - 84*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^8 - 28*(60*a^3 + 252*a^2*b + 312*a*b^2 + 104*b^3 - 105*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^6 - 15*(45*a^3 + 198*a^2*b + 237*a*b^2 + 100*b^3 - 84*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^4 - 3*a^3 - 18*a^2*b - 27*a*b^2 - 12*b^3 + 12*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x - 36*(3*a^3 + 15*a^2*b + 18*a*b^2 + 6*b^3 - 7*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - 3*((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^16 + 16*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)*sinh(d*x + c)^15 + (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*sinh(d*x + c)^16 + 8*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^14 + 8*(a^3 + 3*a^2*b + 3*a*b^2 + b^3 + 15*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^14 + 112*(5*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^3 + (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c))*sinh(d*x + c)^13 + 28*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^12 + 28*(65*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^4 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 + 26*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^12 + 112*(39*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^5 + 26*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^3 + 3*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c))*sinh(d*x + c)^11 + 56*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^10 + 56*(143*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^6 + 143*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^4 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 + 33*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^10 + 16*(715*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^7 + 1001*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^5 + 385*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^3 + 35*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c))*sinh(d*x + c)^9 + 70*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^8 + 2*(6435*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^8 + 12012*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^6 + 6930*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^4 + 35*a^3 + 105*a^2*b + 105*a*b^2 + 35*b^3 + 1260*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 16*(715*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^9 + 1716*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^7 + 1386*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^5 + 420*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^3 + 35*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c))*sinh(d*x + c)^7 + 56*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^6 + 56*(143*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^10 + 429*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^8 + 462*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^6 + 210*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^4 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 + 35*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 112*(39*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^11 + 143*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^9 + 198*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^7 + 126*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^5 + 35*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^3 + 3*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c))*sinh(d*x + c)^5 + 28*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^4 + 28*(65*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^12 + 286*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^10 + 495*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^8 + 420*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^6 + 175*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^4 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 + 30*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 112*(5*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^13 + 26*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^11 + 55*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^9 + 60*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^7 + 35*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^5 + 10*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^3 + (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c))*sinh(d*x + c)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 + 8*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^2 + 8*(15*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^14 + 91*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^12 + 231*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^10 + 315*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^8 + 245*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^6 + 105*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^4 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 + 21*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 16*((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^15 + 7*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^13 + 21*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^11 + 35*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^9 + 35*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^7 + 21*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^5 + 7*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^3 + (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c))*sinh(d*x + c))*log(2*cosh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))) + 4*(12*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x*cosh(d*x + c)^15 - 21*(a^3 + 6*a^2*b + 9*a*b^2 + 4*b^3 - 4*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^13 - 36*(3*a^3 + 15*a^2*b + 18*a*b^2 + 6*b^3 - 7*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^11 - 5*(45*a^3 + 198*a^2*b + 237*a*b^2 + 100*b^3 - 84*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^9 - 4*(60*a^3 + 252*a^2*b + 312*a*b^2 + 104*b^3 - 105*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^7 - 3*(45*a^3 + 198*a^2*b + 237*a*b^2 + 100*b^3 - 84*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^5 - 12*(3*a^3 + 15*a^2*b + 18*a*b^2 + 6*b^3 - 7*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^3 - 3*(a^3 + 6*a^2*b + 9*a*b^2 + 4*b^3 - 4*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c))/(d*cosh(d*x + c)^16 + 16*d*cosh(d*x + c)*sinh(d*x + c)^15 + d*sinh(d*x + c)^16 + 8*d*cosh(d*x + c)^14 + 8*(15*d*cosh(d*x + c)^2 + d)*sinh(d*x + c)^14 + 112*(5*d*cosh(d*x + c)^3 + d*cosh(d*x + c))*sinh(d*x + c)^13 + 28*d*cosh(d*x + c)^12 + 28*(65*d*cosh(d*x + c)^4 + 26*d*cosh(d*x + c)^2 + d)*sinh(d*x + c)^12 + 112*(39*d*cosh(d*x + c)^5 + 26*d*cosh(d*x + c)^3 + 3*d*cosh(d*x + c))*sinh(d*x + c)^11 + 56*d*cosh(d*x + c)^10 + 56*(143*d*cosh(d*x + c)^6 + 143*d*cosh(d*x + c)^4 + 33*d*cosh(d*x + c)^2 + d)*sinh(d*x + c)^10 + 16*(715*d*cosh(d*x + c)^7 + 1001*d*cosh(d*x + c)^5 + 385*d*cosh(d*x + c)^3 + 35*d*cosh(d*x + c))*sinh(d*x + c)^9 + 70*d*cosh(d*x + c)^8 + 2*(6435*d*cosh(d*x + c)^8 + 12012*d*cosh(d*x + c)^6 + 6930*d*cosh(d*x + c)^4 + 1260*d*cosh(d*x + c)^2 + 35*d)*sinh(d*x + c)^8 + 16*(715*d*cosh(d*x + c)^9 + 1716*d*cosh(d*x + c)^7 + 1386*d*cosh(d*x + c)^5 + 420*d*cosh(d*x + c)^3 + 35*d*cosh(d*x + c))*sinh(d*x + c)^7 + 56*d*cosh(d*x + c)^6 + 56*(143*d*cosh(d*x + c)^10 + 429*d*cosh(d*x + c)^8 + 462*d*cosh(d*x + c)^6 + 210*d*cosh(d*x + c)^4 + 35*d*cosh(d*x + c)^2 + d)*sinh(d*x + c)^6 + 112*(39*d*cosh(d*x + c)^11 + 143*d*cosh(d*x + c)^9 + 198*d*cosh(d*x + c)^7 + 126*d*cosh(d*x + c)^5 + 35*d*cosh(d*x + c)^3 + 3*d*cosh(d*x + c))*sinh(d*x + c)^5 + 28*d*cosh(d*x + c)^4 + 28*(65*d*cosh(d*x + c)^12 + 286*d*cosh(d*x + c)^10 + 495*d*cosh(d*x + c)^8 + 420*d*cosh(d*x + c)^6 + 175*d*cosh(d*x + c)^4 + 30*d*cosh(d*x + c)^2 + d)*sinh(d*x + c)^4 + 112*(5*d*cosh(d*x + c)^13 + 26*d*cosh(d*x + c)^11 + 55*d*cosh(d*x + c)^9 + 60*d*cosh(d*x + c)^7 + 35*d*cosh(d*x + c)^5 + 10*d*cosh(d*x + c)^3 + d*cosh(d*x + c))*sinh(d*x + c)^3 + 8*d*cosh(d*x + c)^2 + 8*(15*d*cosh(d*x + c)^14 + 91*d*cosh(d*x + c)^12 + 231*d*cosh(d*x + c)^10 + 315*d*cosh(d*x + c)^8 + 245*d*cosh(d*x + c)^6 + 105*d*cosh(d*x + c)^4 + 21*d*cosh(d*x + c)^2 + d)*sinh(d*x + c)^2 + 16*(d*cosh(d*x + c)^15 + 7*d*cosh(d*x + c)^13 + 21*d*cosh(d*x + c)^11 + 35*d*cosh(d*x + c)^9 + 35*d*cosh(d*x + c)^7 + 21*d*cosh(d*x + c)^5 + 7*d*cosh(d*x + c)^3 + d*cosh(d*x + c))*sinh(d*x + c) + d)","B",0
158,1,1036,0,0.430792," ","integrate(tanh(d*x+c)^2*(a+b*tanh(d*x+c)^2)^3,x, algorithm=""fricas"")","\frac{{\left(105 \, a^{3} + 420 \, a^{2} b + 483 \, a b^{2} + 176 \, b^{3} + 105 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{7} + 7 \, {\left(105 \, a^{3} + 420 \, a^{2} b + 483 \, a b^{2} + 176 \, b^{3} + 105 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} - {\left(105 \, a^{3} + 420 \, a^{2} b + 483 \, a b^{2} + 176 \, b^{3}\right)} \sinh\left(d x + c\right)^{7} + 7 \, {\left(105 \, a^{3} + 420 \, a^{2} b + 483 \, a b^{2} + 176 \, b^{3} + 105 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{5} - 7 \, {\left(75 \, a^{3} + 240 \, a^{2} b + 213 \, a b^{2} + 56 \, b^{3} + 3 \, {\left(105 \, a^{3} + 420 \, a^{2} b + 483 \, a b^{2} + 176 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{5} + 35 \, {\left({\left(105 \, a^{3} + 420 \, a^{2} b + 483 \, a b^{2} + 176 \, b^{3} + 105 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + {\left(105 \, a^{3} + 420 \, a^{2} b + 483 \, a b^{2} + 176 \, b^{3} + 105 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 21 \, {\left(105 \, a^{3} + 420 \, a^{2} b + 483 \, a b^{2} + 176 \, b^{3} + 105 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - 7 \, {\left(5 \, {\left(105 \, a^{3} + 420 \, a^{2} b + 483 \, a b^{2} + 176 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 135 \, a^{3} + 360 \, a^{2} b + 369 \, a b^{2} + 168 \, b^{3} + 10 \, {\left(75 \, a^{3} + 240 \, a^{2} b + 213 \, a b^{2} + 56 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + 7 \, {\left(3 \, {\left(105 \, a^{3} + 420 \, a^{2} b + 483 \, a b^{2} + 176 \, b^{3} + 105 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(105 \, a^{3} + 420 \, a^{2} b + 483 \, a b^{2} + 176 \, b^{3} + 105 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + 9 \, {\left(105 \, a^{3} + 420 \, a^{2} b + 483 \, a b^{2} + 176 \, b^{3} + 105 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 35 \, {\left(105 \, a^{3} + 420 \, a^{2} b + 483 \, a b^{2} + 176 \, b^{3} + 105 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right) - 7 \, {\left({\left(105 \, a^{3} + 420 \, a^{2} b + 483 \, a b^{2} + 176 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 5 \, {\left(75 \, a^{3} + 240 \, a^{2} b + 213 \, a b^{2} + 56 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 75 \, a^{3} + 180 \, a^{2} b + 225 \, a b^{2} + 9 \, {\left(45 \, a^{3} + 120 \, a^{2} b + 123 \, a b^{2} + 56 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)}{105 \, {\left(d \cosh\left(d x + c\right)^{7} + 7 \, d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + 7 \, d \cosh\left(d x + c\right)^{5} + 35 \, {\left(d \cosh\left(d x + c\right)^{3} + d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 21 \, d \cosh\left(d x + c\right)^{3} + 7 \, {\left(3 \, d \cosh\left(d x + c\right)^{5} + 10 \, d \cosh\left(d x + c\right)^{3} + 9 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 35 \, d \cosh\left(d x + c\right)\right)}}"," ",0,"1/105*((105*a^3 + 420*a^2*b + 483*a*b^2 + 176*b^3 + 105*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^7 + 7*(105*a^3 + 420*a^2*b + 483*a*b^2 + 176*b^3 + 105*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)*sinh(d*x + c)^6 - (105*a^3 + 420*a^2*b + 483*a*b^2 + 176*b^3)*sinh(d*x + c)^7 + 7*(105*a^3 + 420*a^2*b + 483*a*b^2 + 176*b^3 + 105*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^5 - 7*(75*a^3 + 240*a^2*b + 213*a*b^2 + 56*b^3 + 3*(105*a^3 + 420*a^2*b + 483*a*b^2 + 176*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 35*((105*a^3 + 420*a^2*b + 483*a*b^2 + 176*b^3 + 105*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^3 + (105*a^3 + 420*a^2*b + 483*a*b^2 + 176*b^3 + 105*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c)^4 + 21*(105*a^3 + 420*a^2*b + 483*a*b^2 + 176*b^3 + 105*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^3 - 7*(5*(105*a^3 + 420*a^2*b + 483*a*b^2 + 176*b^3)*cosh(d*x + c)^4 + 135*a^3 + 360*a^2*b + 369*a*b^2 + 168*b^3 + 10*(75*a^3 + 240*a^2*b + 213*a*b^2 + 56*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 7*(3*(105*a^3 + 420*a^2*b + 483*a*b^2 + 176*b^3 + 105*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^5 + 10*(105*a^3 + 420*a^2*b + 483*a*b^2 + 176*b^3 + 105*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^3 + 9*(105*a^3 + 420*a^2*b + 483*a*b^2 + 176*b^3 + 105*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c)^2 + 35*(105*a^3 + 420*a^2*b + 483*a*b^2 + 176*b^3 + 105*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c) - 7*((105*a^3 + 420*a^2*b + 483*a*b^2 + 176*b^3)*cosh(d*x + c)^6 + 5*(75*a^3 + 240*a^2*b + 213*a*b^2 + 56*b^3)*cosh(d*x + c)^4 + 75*a^3 + 180*a^2*b + 225*a*b^2 + 9*(45*a^3 + 120*a^2*b + 123*a*b^2 + 56*b^3)*cosh(d*x + c)^2)*sinh(d*x + c))/(d*cosh(d*x + c)^7 + 7*d*cosh(d*x + c)*sinh(d*x + c)^6 + 7*d*cosh(d*x + c)^5 + 35*(d*cosh(d*x + c)^3 + d*cosh(d*x + c))*sinh(d*x + c)^4 + 21*d*cosh(d*x + c)^3 + 7*(3*d*cosh(d*x + c)^5 + 10*d*cosh(d*x + c)^3 + 9*d*cosh(d*x + c))*sinh(d*x + c)^2 + 35*d*cosh(d*x + c))","B",0
159,1,4298,0,0.487901," ","integrate(tanh(d*x+c)*(a+b*tanh(d*x+c)^2)^3,x, algorithm=""fricas"")","-\frac{3 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x \cosh\left(d x + c\right)^{12} + 36 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{11} + 3 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x \sinh\left(d x + c\right)^{12} - 18 \, {\left(a^{2} b + 2 \, a b^{2} + b^{3} - {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{10} + 18 \, {\left(11 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x \cosh\left(d x + c\right)^{2} - a^{2} b - 2 \, a b^{2} - b^{3} + {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \sinh\left(d x + c\right)^{10} + 60 \, {\left(11 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{2} b + 2 \, a b^{2} + b^{3} - {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} - 9 \, {\left(8 \, a^{2} b + 12 \, a b^{2} + 4 \, b^{3} - 5 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{8} + 9 \, {\left(165 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x \cosh\left(d x + c\right)^{4} - 8 \, a^{2} b - 12 \, a b^{2} - 4 \, b^{3} + 5 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x - 90 \, {\left(a^{2} b + 2 \, a b^{2} + b^{3} - {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{8} + 72 \, {\left(33 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x \cosh\left(d x + c\right)^{5} - 30 \, {\left(a^{2} b + 2 \, a b^{2} + b^{3} - {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - {\left(8 \, a^{2} b + 12 \, a b^{2} + 4 \, b^{3} - 5 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} - 4 \, {\left(27 \, a^{2} b + 36 \, a b^{2} + 17 \, b^{3} - 15 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(693 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x \cosh\left(d x + c\right)^{6} - 945 \, {\left(a^{2} b + 2 \, a b^{2} + b^{3} - {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{4} - 27 \, a^{2} b - 36 \, a b^{2} - 17 \, b^{3} + 15 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x - 63 \, {\left(8 \, a^{2} b + 12 \, a b^{2} + 4 \, b^{3} - 5 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 24 \, {\left(99 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x \cosh\left(d x + c\right)^{7} - 189 \, {\left(a^{2} b + 2 \, a b^{2} + b^{3} - {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{5} - 21 \, {\left(8 \, a^{2} b + 12 \, a b^{2} + 4 \, b^{3} - 5 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - {\left(27 \, a^{2} b + 36 \, a b^{2} + 17 \, b^{3} - 15 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 9 \, {\left(8 \, a^{2} b + 12 \, a b^{2} + 4 \, b^{3} - 5 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(495 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x \cosh\left(d x + c\right)^{8} - 1260 \, {\left(a^{2} b + 2 \, a b^{2} + b^{3} - {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{6} - 210 \, {\left(8 \, a^{2} b + 12 \, a b^{2} + 4 \, b^{3} - 5 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{4} - 24 \, a^{2} b - 36 \, a b^{2} - 12 \, b^{3} + 15 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x - 20 \, {\left(27 \, a^{2} b + 36 \, a b^{2} + 17 \, b^{3} - 15 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(165 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x \cosh\left(d x + c\right)^{9} - 540 \, {\left(a^{2} b + 2 \, a b^{2} + b^{3} - {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{7} - 126 \, {\left(8 \, a^{2} b + 12 \, a b^{2} + 4 \, b^{3} - 5 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{5} - 20 \, {\left(27 \, a^{2} b + 36 \, a b^{2} + 17 \, b^{3} - 15 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - 9 \, {\left(8 \, a^{2} b + 12 \, a b^{2} + 4 \, b^{3} - 5 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 3 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x - 18 \, {\left(a^{2} b + 2 \, a b^{2} + b^{3} - {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2} + 6 \, {\left(33 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x \cosh\left(d x + c\right)^{10} - 135 \, {\left(a^{2} b + 2 \, a b^{2} + b^{3} - {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{8} - 42 \, {\left(8 \, a^{2} b + 12 \, a b^{2} + 4 \, b^{3} - 5 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{6} - 10 \, {\left(27 \, a^{2} b + 36 \, a b^{2} + 17 \, b^{3} - 15 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{4} - 3 \, a^{2} b - 6 \, a b^{2} - 3 \, b^{3} + 3 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x - 9 \, {\left(8 \, a^{2} b + 12 \, a b^{2} + 4 \, b^{3} - 5 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} - 3 \, {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{12} + 12 \, {\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)^{11} + {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \sinh\left(d x + c\right)^{12} + 6 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{10} + 6 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} + 11 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{10} + 20 \, {\left(11 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} + 15 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{8} + 15 \, {\left(33 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{4} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} + 18 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{8} + 24 \, {\left(33 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{5} + 30 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\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)\right)} \sinh\left(d x + c\right)^{7} + 20 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(231 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{6} + 315 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{4} + 5 \, a^{3} + 15 \, a^{2} b + 15 \, a b^{2} + 5 \, b^{3} + 105 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 24 \, {\left(33 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{7} + 63 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{5} + 35 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\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)\right)} \sinh\left(d x + c\right)^{5} + 15 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{4} + 15 \, {\left(33 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{8} + 84 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{6} + 70 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{4} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} + 20 \, {\left(a^{3} + 3 \, 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} + 20 \, {\left(11 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{9} + 36 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{7} + 42 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{5} + 20 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} + 6 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{2} + 6 \, {\left(11 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{10} + 45 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{8} + 70 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{6} + 50 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{4} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} + 15 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 12 \, {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{11} + 5 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{9} + 10 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{7} + 10 \, {\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)^{3} + {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\frac{2 \, \cosh\left(d x + c\right)}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) + 12 \, {\left(3 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x \cosh\left(d x + c\right)^{11} - 15 \, {\left(a^{2} b + 2 \, a b^{2} + b^{3} - {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{9} - 6 \, {\left(8 \, a^{2} b + 12 \, a b^{2} + 4 \, b^{3} - 5 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{7} - 2 \, {\left(27 \, a^{2} b + 36 \, a b^{2} + 17 \, b^{3} - 15 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{5} - 3 \, {\left(8 \, a^{2} b + 12 \, a b^{2} + 4 \, b^{3} - 5 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{2} b + 2 \, a b^{2} + b^{3} - {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{3 \, {\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,"-1/3*(3*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x*cosh(d*x + c)^12 + 36*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x*cosh(d*x + c)*sinh(d*x + c)^11 + 3*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x*sinh(d*x + c)^12 - 18*(a^2*b + 2*a*b^2 + b^3 - (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^10 + 18*(11*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x*cosh(d*x + c)^2 - a^2*b - 2*a*b^2 - b^3 + (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*sinh(d*x + c)^10 + 60*(11*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x*cosh(d*x + c)^3 - 3*(a^2*b + 2*a*b^2 + b^3 - (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c)^9 - 9*(8*a^2*b + 12*a*b^2 + 4*b^3 - 5*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^8 + 9*(165*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x*cosh(d*x + c)^4 - 8*a^2*b - 12*a*b^2 - 4*b^3 + 5*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x - 90*(a^2*b + 2*a*b^2 + b^3 - (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 72*(33*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x*cosh(d*x + c)^5 - 30*(a^2*b + 2*a*b^2 + b^3 - (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^3 - (8*a^2*b + 12*a*b^2 + 4*b^3 - 5*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c)^7 - 4*(27*a^2*b + 36*a*b^2 + 17*b^3 - 15*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^6 + 4*(693*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x*cosh(d*x + c)^6 - 945*(a^2*b + 2*a*b^2 + b^3 - (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^4 - 27*a^2*b - 36*a*b^2 - 17*b^3 + 15*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x - 63*(8*a^2*b + 12*a*b^2 + 4*b^3 - 5*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 24*(99*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x*cosh(d*x + c)^7 - 189*(a^2*b + 2*a*b^2 + b^3 - (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^5 - 21*(8*a^2*b + 12*a*b^2 + 4*b^3 - 5*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^3 - (27*a^2*b + 36*a*b^2 + 17*b^3 - 15*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c)^5 - 9*(8*a^2*b + 12*a*b^2 + 4*b^3 - 5*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^4 + 3*(495*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x*cosh(d*x + c)^8 - 1260*(a^2*b + 2*a*b^2 + b^3 - (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^6 - 210*(8*a^2*b + 12*a*b^2 + 4*b^3 - 5*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^4 - 24*a^2*b - 36*a*b^2 - 12*b^3 + 15*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x - 20*(27*a^2*b + 36*a*b^2 + 17*b^3 - 15*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 4*(165*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x*cosh(d*x + c)^9 - 540*(a^2*b + 2*a*b^2 + b^3 - (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^7 - 126*(8*a^2*b + 12*a*b^2 + 4*b^3 - 5*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^5 - 20*(27*a^2*b + 36*a*b^2 + 17*b^3 - 15*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^3 - 9*(8*a^2*b + 12*a*b^2 + 4*b^3 - 5*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c)^3 + 3*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x - 18*(a^2*b + 2*a*b^2 + b^3 - (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^2 + 6*(33*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x*cosh(d*x + c)^10 - 135*(a^2*b + 2*a*b^2 + b^3 - (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^8 - 42*(8*a^2*b + 12*a*b^2 + 4*b^3 - 5*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^6 - 10*(27*a^2*b + 36*a*b^2 + 17*b^3 - 15*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^4 - 3*a^2*b - 6*a*b^2 - 3*b^3 + 3*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x - 9*(8*a^2*b + 12*a*b^2 + 4*b^3 - 5*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - 3*((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^12 + 12*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)*sinh(d*x + c)^11 + (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*sinh(d*x + c)^12 + 6*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^10 + 6*(a^3 + 3*a^2*b + 3*a*b^2 + b^3 + 11*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^10 + 20*(11*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^3 + 3*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c))*sinh(d*x + c)^9 + 15*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^8 + 15*(33*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^4 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 + 18*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 24*(33*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^5 + 30*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(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)^7 + 20*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^6 + 4*(231*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^6 + 315*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^4 + 5*a^3 + 15*a^2*b + 15*a*b^2 + 5*b^3 + 105*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 24*(33*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^7 + 63*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^5 + 35*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(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)^5 + 15*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^4 + 15*(33*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^8 + 84*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^6 + 70*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^4 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 + 20*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 20*(11*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^9 + 36*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^7 + 42*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^5 + 20*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^3 + 3*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c))*sinh(d*x + c)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 + 6*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^2 + 6*(11*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^10 + 45*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^8 + 70*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^6 + 50*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^4 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 + 15*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 12*((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^11 + 5*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^9 + 10*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^7 + 10*(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)^3 + (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c))*sinh(d*x + c))*log(2*cosh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))) + 12*(3*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x*cosh(d*x + c)^11 - 15*(a^2*b + 2*a*b^2 + b^3 - (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^9 - 6*(8*a^2*b + 12*a*b^2 + 4*b^3 - 5*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^7 - 2*(27*a^2*b + 36*a*b^2 + 17*b^3 - 15*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^5 - 3*(8*a^2*b + 12*a*b^2 + 4*b^3 - 5*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^3 - 3*(a^2*b + 2*a*b^2 + b^3 - (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c))*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
160,1,567,0,0.410430," ","integrate((a+b*tanh(d*x+c)^2)^3,x, algorithm=""fricas"")","\frac{{\left(45 \, a^{2} b + 60 \, a b^{2} + 23 \, b^{3} + 15 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(45 \, a^{2} b + 60 \, a b^{2} + 23 \, b^{3} + 15 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} - {\left(45 \, a^{2} b + 60 \, a b^{2} + 23 \, b^{3}\right)} \sinh\left(d x + c\right)^{5} + 5 \, {\left(45 \, a^{2} b + 60 \, a b^{2} + 23 \, b^{3} + 15 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - 5 \, {\left(27 \, a^{2} b + 24 \, a b^{2} + 5 \, b^{3} + 2 \, {\left(45 \, a^{2} b + 60 \, 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(45 \, a^{2} b + 60 \, a b^{2} + 23 \, b^{3} + 15 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(45 \, a^{2} b + 60 \, a b^{2} + 23 \, b^{3} + 15 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 10 \, {\left(45 \, a^{2} b + 60 \, a b^{2} + 23 \, b^{3} + 15 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right) - 5 \, {\left({\left(45 \, a^{2} b + 60 \, a b^{2} + 23 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + 18 \, a^{2} b + 12 \, a b^{2} + 10 \, b^{3} + 3 \, {\left(27 \, a^{2} b + 24 \, 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*((45*a^2*b + 60*a*b^2 + 23*b^3 + 15*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^5 + 5*(45*a^2*b + 60*a*b^2 + 23*b^3 + 15*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)*sinh(d*x + c)^4 - (45*a^2*b + 60*a*b^2 + 23*b^3)*sinh(d*x + c)^5 + 5*(45*a^2*b + 60*a*b^2 + 23*b^3 + 15*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^3 - 5*(27*a^2*b + 24*a*b^2 + 5*b^3 + 2*(45*a^2*b + 60*a*b^2 + 23*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 5*(2*(45*a^2*b + 60*a*b^2 + 23*b^3 + 15*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^3 + 3*(45*a^2*b + 60*a*b^2 + 23*b^3 + 15*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c)^2 + 10*(45*a^2*b + 60*a*b^2 + 23*b^3 + 15*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c) - 5*((45*a^2*b + 60*a*b^2 + 23*b^3)*cosh(d*x + c)^4 + 18*a^2*b + 12*a*b^2 + 10*b^3 + 3*(27*a^2*b + 24*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
161,1,2381,0,0.468217," ","integrate(coth(d*x+c)*(a+b*tanh(d*x+c)^2)^3,x, algorithm=""fricas"")","-\frac{{\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x \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 x \sinh\left(d x + c\right)^{8} - 2 \, {\left(3 \, a b^{2} + 2 \, b^{3} - 2 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(14 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x \cosh\left(d x + c\right)^{2} - 3 \, a b^{2} - 2 \, b^{3} + 2 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(14 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x \cosh\left(d x + c\right)^{3} - 3 \, {\left(3 \, a b^{2} + 2 \, b^{3} - 2 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 2 \, {\left(6 \, a b^{2} + 2 \, b^{3} - 3 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x \cosh\left(d x + c\right)^{4} - 6 \, a b^{2} - 2 \, b^{3} + 3 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x - 15 \, {\left(3 \, a b^{2} + 2 \, b^{3} - 2 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x \cosh\left(d x + c\right)^{5} - 5 \, {\left(3 \, a b^{2} + 2 \, b^{3} - 2 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - {\left(6 \, a b^{2} + 2 \, b^{3} - 3 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x - 2 \, {\left(3 \, a b^{2} + 2 \, b^{3} - 2 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(14 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x \cosh\left(d x + c\right)^{6} - 15 \, {\left(3 \, a b^{2} + 2 \, b^{3} - 2 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{4} - 3 \, a b^{2} - 2 \, b^{3} + 2 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x - 6 \, {\left(6 \, a b^{2} + 2 \, b^{3} - 3 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} - {\left({\left(3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(3 \, a^{2} b + 3 \, a b^{2} + b^{3} + 7 \, {\left(3 \, a^{2} b + 3 \, 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(3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 6 \, {\left(3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{4} + 9 \, a^{2} b + 9 \, a b^{2} + 3 \, b^{3} + 30 \, {\left(3 \, 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} + 8 \, {\left(7 \, {\left(3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} + 4 \, {\left(3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{4} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} + 9 \, {\left(3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left({\left(3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{5} + 3 \, {\left(3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\frac{2 \, \cosh\left(d x + c\right)}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) - {\left(a^{3} \cosh\left(d x + c\right)^{8} + 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} + 4 \, a^{3} \cosh\left(d x + c\right)^{6} + 6 \, a^{3} \cosh\left(d x + c\right)^{4} + 4 \, {\left(7 \, a^{3} \cosh\left(d x + c\right)^{2} + a^{3}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, 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} + 4 \, a^{3} \cosh\left(d x + c\right)^{2} + 2 \, {\left(35 \, a^{3} \cosh\left(d x + c\right)^{4} + 30 \, a^{3} \cosh\left(d x + c\right)^{2} + 3 \, a^{3}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, a^{3} \cosh\left(d x + c\right)^{5} + 10 \, 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)^{3} + a^{3} + 4 \, {\left(7 \, a^{3} \cosh\left(d x + c\right)^{6} + 15 \, a^{3} \cosh\left(d x + c\right)^{4} + 9 \, a^{3} \cosh\left(d x + c\right)^{2} + a^{3}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left(a^{3} \cosh\left(d x + c\right)^{7} + 3 \, a^{3} \cosh\left(d x + c\right)^{5} + 3 \, a^{3} \cosh\left(d x + c\right)^{3} + a^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\frac{2 \, \sinh\left(d x + c\right)}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) + 4 \, {\left(2 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x \cosh\left(d x + c\right)^{7} - 3 \, {\left(3 \, a b^{2} + 2 \, b^{3} - 2 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{5} - 2 \, {\left(6 \, a b^{2} + 2 \, b^{3} - 3 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - {\left(3 \, a b^{2} + 2 \, b^{3} - 2 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{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}"," ",0,"-((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x*cosh(d*x + c)^8 + 8*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x*cosh(d*x + c)*sinh(d*x + c)^7 + (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x*sinh(d*x + c)^8 - 2*(3*a*b^2 + 2*b^3 - 2*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^6 + 2*(14*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x*cosh(d*x + c)^2 - 3*a*b^2 - 2*b^3 + 2*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*sinh(d*x + c)^6 + 4*(14*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x*cosh(d*x + c)^3 - 3*(3*a*b^2 + 2*b^3 - 2*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c)^5 - 2*(6*a*b^2 + 2*b^3 - 3*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^4 + 2*(35*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x*cosh(d*x + c)^4 - 6*a*b^2 - 2*b^3 + 3*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x - 15*(3*a*b^2 + 2*b^3 - 2*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(7*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x*cosh(d*x + c)^5 - 5*(3*a*b^2 + 2*b^3 - 2*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^3 - (6*a*b^2 + 2*b^3 - 3*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c)^3 + (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x - 2*(3*a*b^2 + 2*b^3 - 2*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^2 + 2*(14*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x*cosh(d*x + c)^6 - 15*(3*a*b^2 + 2*b^3 - 2*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^4 - 3*a*b^2 - 2*b^3 + 2*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x - 6*(6*a*b^2 + 2*b^3 - 3*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - ((3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^8 + 8*(3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)*sinh(d*x + c)^7 + (3*a^2*b + 3*a*b^2 + b^3)*sinh(d*x + c)^8 + 4*(3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^6 + 4*(3*a^2*b + 3*a*b^2 + b^3 + 7*(3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^3 + 3*(3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c))*sinh(d*x + c)^5 + 6*(3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^4 + 2*(35*(3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^4 + 9*a^2*b + 9*a*b^2 + 3*b^3 + 30*(3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(7*(3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^5 + 10*(3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^3 + 3*(3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c))*sinh(d*x + c)^3 + 3*a^2*b + 3*a*b^2 + b^3 + 4*(3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^2 + 4*(7*(3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^6 + 15*(3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^4 + 3*a^2*b + 3*a*b^2 + b^3 + 9*(3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^7 + 3*(3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^5 + 3*(3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^3 + (3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c))*sinh(d*x + c))*log(2*cosh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))) - (a^3*cosh(d*x + c)^8 + 8*a^3*cosh(d*x + c)*sinh(d*x + c)^7 + a^3*sinh(d*x + c)^8 + 4*a^3*cosh(d*x + c)^6 + 6*a^3*cosh(d*x + c)^4 + 4*(7*a^3*cosh(d*x + c)^2 + a^3)*sinh(d*x + c)^6 + 8*(7*a^3*cosh(d*x + c)^3 + 3*a^3*cosh(d*x + c))*sinh(d*x + c)^5 + 4*a^3*cosh(d*x + c)^2 + 2*(35*a^3*cosh(d*x + c)^4 + 30*a^3*cosh(d*x + c)^2 + 3*a^3)*sinh(d*x + c)^4 + 8*(7*a^3*cosh(d*x + c)^5 + 10*a^3*cosh(d*x + c)^3 + 3*a^3*cosh(d*x + c))*sinh(d*x + c)^3 + a^3 + 4*(7*a^3*cosh(d*x + c)^6 + 15*a^3*cosh(d*x + c)^4 + 9*a^3*cosh(d*x + c)^2 + a^3)*sinh(d*x + c)^2 + 8*(a^3*cosh(d*x + c)^7 + 3*a^3*cosh(d*x + c)^5 + 3*a^3*cosh(d*x + c)^3 + a^3*cosh(d*x + c))*sinh(d*x + c))*log(2*sinh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))) + 4*(2*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x*cosh(d*x + c)^7 - 3*(3*a*b^2 + 2*b^3 - 2*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^5 - 2*(6*a*b^2 + 2*b^3 - 3*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^3 - (3*a*b^2 + 2*b^3 - 2*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*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 + 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
162,1,341,0,0.427991," ","integrate(coth(d*x+c)^2*(a+b*tanh(d*x+c)^2)^3,x, algorithm=""fricas"")","-\frac{{\left(3 \, a^{3} + 9 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 4 \, {\left(3 \, a^{3} + 9 \, a b^{2} + 4 \, b^{3} + 3 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(3 \, a^{3} + 9 \, a b^{2} + 4 \, b^{3}\right)} \sinh\left(d x + c\right)^{4} + 9 \, a^{3} - 9 \, a b^{2} + 4 \, {\left(3 \, a^{3} - b^{3}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(6 \, a^{3} - 2 \, b^{3} + 3 \, {\left(3 \, a^{3} + 9 \, a b^{2} + 4 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} - 4 \, {\left({\left(3 \, a^{3} + 9 \, a b^{2} + 4 \, b^{3} + 3 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{3} + 9 \, a b^{2} + 4 \, b^{3} + 3 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{12 \, {\left(d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(d \cosh\left(d x + c\right)^{3} + d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"-1/12*((3*a^3 + 9*a*b^2 + 4*b^3)*cosh(d*x + c)^4 - 4*(3*a^3 + 9*a*b^2 + 4*b^3 + 3*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)*sinh(d*x + c)^3 + (3*a^3 + 9*a*b^2 + 4*b^3)*sinh(d*x + c)^4 + 9*a^3 - 9*a*b^2 + 4*(3*a^3 - b^3)*cosh(d*x + c)^2 + 2*(6*a^3 - 2*b^3 + 3*(3*a^3 + 9*a*b^2 + 4*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - 4*((3*a^3 + 9*a*b^2 + 4*b^3 + 3*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^3 + (3*a^3 + 9*a*b^2 + 4*b^3 + 3*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c))/(d*cosh(d*x + c)*sinh(d*x + c)^3 + (d*cosh(d*x + c)^3 + d*cosh(d*x + c))*sinh(d*x + c))","B",0
163,1,1686,0,0.445217," ","integrate(coth(d*x+c)^3*(a+b*tanh(d*x+c)^2)^3,x, algorithm=""fricas"")","-\frac{{\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x \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 x \sinh\left(d x + c\right)^{8} + 2 \, {\left(a^{3} - b^{3}\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(14 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x \cosh\left(d x + c\right)^{2} + a^{3} - b^{3}\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(14 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{3} - b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(2 \, a^{3} + 2 \, b^{3} - {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x \cosh\left(d x + c\right)^{4} + 2 \, a^{3} + 2 \, b^{3} - {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x + 15 \, {\left(a^{3} - b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x \cosh\left(d x + c\right)^{5} + 5 \, {\left(a^{3} - b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{3} + 2 \, b^{3} - {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x + 2 \, {\left(a^{3} - b^{3}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(14 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{3} - b^{3}\right)} \cosh\left(d x + c\right)^{4} + a^{3} - b^{3} + 6 \, {\left(2 \, a^{3} + 2 \, b^{3} - {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} - {\left({\left(3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{8} + 56 \, {\left(3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right)^{5} + 28 \, {\left(3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{6} + 8 \, {\left(3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(3 \, a b^{2} + b^{3}\right)} \sinh\left(d x + c\right)^{8} - 2 \, {\left(3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{4} - 3 \, a b^{2} - b^{3}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{5} - {\left(3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 3 \, a b^{2} + b^{3} + 4 \, {\left(7 \, {\left(3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{6} - 3 \, {\left(3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left({\left(3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{7} - {\left(3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right)\right)} \log\left(\frac{2 \, \cosh\left(d x + c\right)}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) - {\left({\left(a^{3} + 3 \, a^{2} b\right)} \cosh\left(d x + c\right)^{8} + 56 \, {\left(a^{3} + 3 \, a^{2} b\right)} \cosh\left(d x + c\right)^{3} \sinh\left(d x + c\right)^{5} + 28 \, {\left(a^{3} + 3 \, a^{2} b\right)} \cosh\left(d x + c\right)^{2} \sinh\left(d x + c\right)^{6} + 8 \, {\left(a^{3} + 3 \, a^{2} b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{3} + 3 \, a^{2} b\right)} \sinh\left(d x + c\right)^{8} - 2 \, {\left(a^{3} + 3 \, a^{2} b\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(a^{3} + 3 \, a^{2} b\right)} \cosh\left(d x + c\right)^{4} - a^{3} - 3 \, a^{2} b\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{3} + 3 \, a^{2} b\right)} \cosh\left(d x + c\right)^{5} - {\left(a^{3} + 3 \, a^{2} b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + a^{3} + 3 \, a^{2} b + 4 \, {\left(7 \, {\left(a^{3} + 3 \, a^{2} b\right)} \cosh\left(d x + c\right)^{6} - 3 \, {\left(a^{3} + 3 \, a^{2} b\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left({\left(a^{3} + 3 \, a^{2} b\right)} \cosh\left(d x + c\right)^{7} - {\left(a^{3} + 3 \, a^{2} b\right)} \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right)\right)} \log\left(\frac{2 \, \sinh\left(d x + c\right)}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) + 4 \, {\left(2 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{3} - b^{3}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(2 \, a^{3} + 2 \, b^{3} - {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{3} - b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{d \cosh\left(d x + c\right)^{8} + 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} - 2 \, d \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, d \cosh\left(d x + c\right)^{4} - d\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, d \cosh\left(d x + c\right)^{5} - d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, d \cosh\left(d x + c\right)^{6} - 3 \, d \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left(d \cosh\left(d x + c\right)^{7} - d \cosh\left(d x + c\right)^{3}\right)} \sinh\left(d x + c\right) + d}"," ",0,"-((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x*cosh(d*x + c)^8 + 8*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x*cosh(d*x + c)*sinh(d*x + c)^7 + (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x*sinh(d*x + c)^8 + 2*(a^3 - b^3)*cosh(d*x + c)^6 + 2*(14*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x*cosh(d*x + c)^2 + a^3 - b^3)*sinh(d*x + c)^6 + 4*(14*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x*cosh(d*x + c)^3 + 3*(a^3 - b^3)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(2*a^3 + 2*b^3 - (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^4 + 2*(35*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x*cosh(d*x + c)^4 + 2*a^3 + 2*b^3 - (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x + 15*(a^3 - b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(7*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x*cosh(d*x + c)^5 + 5*(a^3 - b^3)*cosh(d*x + c)^3 + (2*a^3 + 2*b^3 - (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c)^3 + (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x + 2*(a^3 - b^3)*cosh(d*x + c)^2 + 2*(14*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x*cosh(d*x + c)^6 + 15*(a^3 - b^3)*cosh(d*x + c)^4 + a^3 - b^3 + 6*(2*a^3 + 2*b^3 - (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - ((3*a*b^2 + b^3)*cosh(d*x + c)^8 + 56*(3*a*b^2 + b^3)*cosh(d*x + c)^3*sinh(d*x + c)^5 + 28*(3*a*b^2 + b^3)*cosh(d*x + c)^2*sinh(d*x + c)^6 + 8*(3*a*b^2 + b^3)*cosh(d*x + c)*sinh(d*x + c)^7 + (3*a*b^2 + b^3)*sinh(d*x + c)^8 - 2*(3*a*b^2 + b^3)*cosh(d*x + c)^4 + 2*(35*(3*a*b^2 + b^3)*cosh(d*x + c)^4 - 3*a*b^2 - b^3)*sinh(d*x + c)^4 + 8*(7*(3*a*b^2 + b^3)*cosh(d*x + c)^5 - (3*a*b^2 + b^3)*cosh(d*x + c))*sinh(d*x + c)^3 + 3*a*b^2 + b^3 + 4*(7*(3*a*b^2 + b^3)*cosh(d*x + c)^6 - 3*(3*a*b^2 + b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((3*a*b^2 + b^3)*cosh(d*x + c)^7 - (3*a*b^2 + b^3)*cosh(d*x + c)^3)*sinh(d*x + c))*log(2*cosh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))) - ((a^3 + 3*a^2*b)*cosh(d*x + c)^8 + 56*(a^3 + 3*a^2*b)*cosh(d*x + c)^3*sinh(d*x + c)^5 + 28*(a^3 + 3*a^2*b)*cosh(d*x + c)^2*sinh(d*x + c)^6 + 8*(a^3 + 3*a^2*b)*cosh(d*x + c)*sinh(d*x + c)^7 + (a^3 + 3*a^2*b)*sinh(d*x + c)^8 - 2*(a^3 + 3*a^2*b)*cosh(d*x + c)^4 + 2*(35*(a^3 + 3*a^2*b)*cosh(d*x + c)^4 - a^3 - 3*a^2*b)*sinh(d*x + c)^4 + 8*(7*(a^3 + 3*a^2*b)*cosh(d*x + c)^5 - (a^3 + 3*a^2*b)*cosh(d*x + c))*sinh(d*x + c)^3 + a^3 + 3*a^2*b + 4*(7*(a^3 + 3*a^2*b)*cosh(d*x + c)^6 - 3*(a^3 + 3*a^2*b)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((a^3 + 3*a^2*b)*cosh(d*x + c)^7 - (a^3 + 3*a^2*b)*cosh(d*x + c)^3)*sinh(d*x + c))*log(2*sinh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))) + 4*(2*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x*cosh(d*x + c)^7 + 3*(a^3 - b^3)*cosh(d*x + c)^5 + 2*(2*a^3 + 2*b^3 - (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^3 + (a^3 - b^3)*cosh(d*x + c))*sinh(d*x + c))/(d*cosh(d*x + c)^8 + 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 - 2*d*cosh(d*x + c)^4 + 2*(35*d*cosh(d*x + c)^4 - d)*sinh(d*x + c)^4 + 8*(7*d*cosh(d*x + c)^5 - d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*d*cosh(d*x + c)^6 - 3*d*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*(d*cosh(d*x + c)^7 - d*cosh(d*x + c)^3)*sinh(d*x + c) + d)","B",0
164,1,341,0,0.436938," ","integrate(coth(d*x+c)^4*(a+b*tanh(d*x+c)^2)^3,x, algorithm=""fricas"")","-\frac{{\left(4 \, a^{3} + 9 \, a^{2} b + 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 4 \, {\left(4 \, a^{3} + 9 \, a^{2} b + 3 \, b^{3} + 3 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(4 \, a^{3} + 9 \, a^{2} b + 3 \, b^{3}\right)} \sinh\left(d x + c\right)^{4} - 9 \, a^{2} b + 9 \, b^{3} + 4 \, {\left(a^{3} - 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(2 \, a^{3} - 6 \, b^{3} + 3 \, {\left(4 \, a^{3} + 9 \, a^{2} b + 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} - 4 \, {\left({\left(4 \, a^{3} + 9 \, a^{2} b + 3 \, b^{3} + 3 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - {\left(4 \, a^{3} + 9 \, a^{2} b + 3 \, b^{3} + 3 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{12 \, {\left(d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(d \cosh\left(d x + c\right)^{3} - d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"-1/12*((4*a^3 + 9*a^2*b + 3*b^3)*cosh(d*x + c)^4 - 4*(4*a^3 + 9*a^2*b + 3*b^3 + 3*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)*sinh(d*x + c)^3 + (4*a^3 + 9*a^2*b + 3*b^3)*sinh(d*x + c)^4 - 9*a^2*b + 9*b^3 + 4*(a^3 - 3*b^3)*cosh(d*x + c)^2 + 2*(2*a^3 - 6*b^3 + 3*(4*a^3 + 9*a^2*b + 3*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - 4*((4*a^3 + 9*a^2*b + 3*b^3 + 3*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^3 - (4*a^3 + 9*a^2*b + 3*b^3 + 3*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c))/(d*cosh(d*x + c)*sinh(d*x + c)^3 + (d*cosh(d*x + c)^3 - d*cosh(d*x + c))*sinh(d*x + c))","B",0
165,1,2393,0,0.461118," ","integrate(coth(d*x+c)^5*(a+b*tanh(d*x+c)^2)^3,x, algorithm=""fricas"")","-\frac{{\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x \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 x \sinh\left(d x + c\right)^{8} + 2 \, {\left(2 \, a^{3} + 3 \, a^{2} b - 2 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(14 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x \cosh\left(d x + c\right)^{2} + 2 \, a^{3} + 3 \, a^{2} b - 2 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(14 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x \cosh\left(d x + c\right)^{3} + 3 \, {\left(2 \, a^{3} + 3 \, a^{2} b - 2 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 2 \, {\left(2 \, a^{3} + 6 \, a^{2} b - 3 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x \cosh\left(d x + c\right)^{4} - 2 \, a^{3} - 6 \, a^{2} b + 3 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x + 15 \, {\left(2 \, a^{3} + 3 \, a^{2} b - 2 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x \cosh\left(d x + c\right)^{5} + 5 \, {\left(2 \, a^{3} + 3 \, a^{2} b - 2 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - {\left(2 \, a^{3} + 6 \, a^{2} b - 3 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x + 2 \, {\left(2 \, a^{3} + 3 \, a^{2} b - 2 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(14 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x \cosh\left(d x + c\right)^{6} + 15 \, {\left(2 \, a^{3} + 3 \, a^{2} b - 2 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 2 \, a^{3} + 3 \, a^{2} b - 2 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x - 6 \, {\left(2 \, a^{3} + 6 \, a^{2} b - 3 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} - {\left(b^{3} \cosh\left(d x + c\right)^{8} + 8 \, b^{3} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + b^{3} \sinh\left(d x + c\right)^{8} - 4 \, b^{3} \cosh\left(d x + c\right)^{6} + 6 \, b^{3} \cosh\left(d x + c\right)^{4} + 4 \, {\left(7 \, b^{3} \cosh\left(d x + c\right)^{2} - b^{3}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, b^{3} \cosh\left(d x + c\right)^{3} - 3 \, b^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 4 \, b^{3} \cosh\left(d x + c\right)^{2} + 2 \, {\left(35 \, b^{3} \cosh\left(d x + c\right)^{4} - 30 \, b^{3} \cosh\left(d x + c\right)^{2} + 3 \, b^{3}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, b^{3} \cosh\left(d x + c\right)^{5} - 10 \, b^{3} \cosh\left(d x + c\right)^{3} + 3 \, b^{3} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + b^{3} + 4 \, {\left(7 \, b^{3} \cosh\left(d x + c\right)^{6} - 15 \, b^{3} \cosh\left(d x + c\right)^{4} + 9 \, b^{3} \cosh\left(d x + c\right)^{2} - b^{3}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left(b^{3} \cosh\left(d x + c\right)^{7} - 3 \, b^{3} \cosh\left(d x + c\right)^{5} + 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)\right)} \log\left(\frac{2 \, \cosh\left(d x + c\right)}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) - {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2}\right)} \sinh\left(d x + c\right)^{8} - 4 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(d x + c\right)^{6} - 4 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} - 7 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 6 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} + 3 \, a^{3} + 9 \, a^{2} b + 9 \, a b^{2} - 30 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(d x + c\right)^{5} - 10 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} - 4 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(d x + c\right)^{6} - 15 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} - a^{3} - 3 \, a^{2} b - 3 \, a b^{2} + 9 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(d x + c\right)^{7} - 3 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(d x + c\right)^{5} + 3 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\frac{2 \, \sinh\left(d x + c\right)}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) + 4 \, {\left(2 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x \cosh\left(d x + c\right)^{7} + 3 \, {\left(2 \, a^{3} + 3 \, a^{2} b - 2 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{5} - 2 \, {\left(2 \, a^{3} + 6 \, a^{2} b - 3 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{3} + 3 \, a^{2} b - 2 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{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}"," ",0,"-((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x*cosh(d*x + c)^8 + 8*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x*cosh(d*x + c)*sinh(d*x + c)^7 + (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x*sinh(d*x + c)^8 + 2*(2*a^3 + 3*a^2*b - 2*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^6 + 2*(14*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x*cosh(d*x + c)^2 + 2*a^3 + 3*a^2*b - 2*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*sinh(d*x + c)^6 + 4*(14*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x*cosh(d*x + c)^3 + 3*(2*a^3 + 3*a^2*b - 2*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c)^5 - 2*(2*a^3 + 6*a^2*b - 3*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^4 + 2*(35*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x*cosh(d*x + c)^4 - 2*a^3 - 6*a^2*b + 3*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x + 15*(2*a^3 + 3*a^2*b - 2*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(7*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x*cosh(d*x + c)^5 + 5*(2*a^3 + 3*a^2*b - 2*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^3 - (2*a^3 + 6*a^2*b - 3*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c)^3 + (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x + 2*(2*a^3 + 3*a^2*b - 2*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^2 + 2*(14*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x*cosh(d*x + c)^6 + 15*(2*a^3 + 3*a^2*b - 2*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^4 + 2*a^3 + 3*a^2*b - 2*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x - 6*(2*a^3 + 6*a^2*b - 3*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - (b^3*cosh(d*x + c)^8 + 8*b^3*cosh(d*x + c)*sinh(d*x + c)^7 + b^3*sinh(d*x + c)^8 - 4*b^3*cosh(d*x + c)^6 + 6*b^3*cosh(d*x + c)^4 + 4*(7*b^3*cosh(d*x + c)^2 - b^3)*sinh(d*x + c)^6 + 8*(7*b^3*cosh(d*x + c)^3 - 3*b^3*cosh(d*x + c))*sinh(d*x + c)^5 - 4*b^3*cosh(d*x + c)^2 + 2*(35*b^3*cosh(d*x + c)^4 - 30*b^3*cosh(d*x + c)^2 + 3*b^3)*sinh(d*x + c)^4 + 8*(7*b^3*cosh(d*x + c)^5 - 10*b^3*cosh(d*x + c)^3 + 3*b^3*cosh(d*x + c))*sinh(d*x + c)^3 + b^3 + 4*(7*b^3*cosh(d*x + c)^6 - 15*b^3*cosh(d*x + c)^4 + 9*b^3*cosh(d*x + c)^2 - b^3)*sinh(d*x + c)^2 + 8*(b^3*cosh(d*x + c)^7 - 3*b^3*cosh(d*x + c)^5 + 3*b^3*cosh(d*x + c)^3 - b^3*cosh(d*x + c))*sinh(d*x + c))*log(2*cosh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))) - ((a^3 + 3*a^2*b + 3*a*b^2)*cosh(d*x + c)^8 + 8*(a^3 + 3*a^2*b + 3*a*b^2)*cosh(d*x + c)*sinh(d*x + c)^7 + (a^3 + 3*a^2*b + 3*a*b^2)*sinh(d*x + c)^8 - 4*(a^3 + 3*a^2*b + 3*a*b^2)*cosh(d*x + c)^6 - 4*(a^3 + 3*a^2*b + 3*a*b^2 - 7*(a^3 + 3*a^2*b + 3*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(a^3 + 3*a^2*b + 3*a*b^2)*cosh(d*x + c)^3 - 3*(a^3 + 3*a^2*b + 3*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^5 + 6*(a^3 + 3*a^2*b + 3*a*b^2)*cosh(d*x + c)^4 + 2*(35*(a^3 + 3*a^2*b + 3*a*b^2)*cosh(d*x + c)^4 + 3*a^3 + 9*a^2*b + 9*a*b^2 - 30*(a^3 + 3*a^2*b + 3*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(7*(a^3 + 3*a^2*b + 3*a*b^2)*cosh(d*x + c)^5 - 10*(a^3 + 3*a^2*b + 3*a*b^2)*cosh(d*x + c)^3 + 3*(a^3 + 3*a^2*b + 3*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + a^3 + 3*a^2*b + 3*a*b^2 - 4*(a^3 + 3*a^2*b + 3*a*b^2)*cosh(d*x + c)^2 + 4*(7*(a^3 + 3*a^2*b + 3*a*b^2)*cosh(d*x + c)^6 - 15*(a^3 + 3*a^2*b + 3*a*b^2)*cosh(d*x + c)^4 - a^3 - 3*a^2*b - 3*a*b^2 + 9*(a^3 + 3*a^2*b + 3*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((a^3 + 3*a^2*b + 3*a*b^2)*cosh(d*x + c)^7 - 3*(a^3 + 3*a^2*b + 3*a*b^2)*cosh(d*x + c)^5 + 3*(a^3 + 3*a^2*b + 3*a*b^2)*cosh(d*x + c)^3 - (a^3 + 3*a^2*b + 3*a*b^2)*cosh(d*x + c))*sinh(d*x + c))*log(2*sinh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))) + 4*(2*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x*cosh(d*x + c)^7 + 3*(2*a^3 + 3*a^2*b - 2*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^5 - 2*(2*a^3 + 6*a^2*b - 3*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^3 + (2*a^3 + 3*a^2*b - 2*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*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 - 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
166,1,557,0,0.440532," ","integrate(coth(d*x+c)^6*(a+b*tanh(d*x+c)^2)^3,x, algorithm=""fricas"")","-\frac{{\left(23 \, a^{3} + 60 \, a^{2} b + 45 \, a b^{2}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(23 \, a^{3} + 60 \, a^{2} b + 45 \, a b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{4} - {\left(23 \, a^{3} + 60 \, a^{2} b + 45 \, a b^{2} + 15 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \sinh\left(d x + c\right)^{5} - 5 \, {\left(5 \, a^{3} + 24 \, a^{2} b + 27 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} + 5 \, {\left(23 \, a^{3} + 60 \, a^{2} b + 45 \, a b^{2} + 15 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x - 2 \, {\left(23 \, a^{3} + 60 \, a^{2} b + 45 \, a b^{2} + 15 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + 5 \, {\left(2 \, {\left(23 \, a^{3} + 60 \, a^{2} b + 45 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(5 \, a^{3} + 24 \, a^{2} b + 27 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 10 \, {\left(5 \, a^{3} + 6 \, a^{2} b + 9 \, a b^{2}\right)} \cosh\left(d x + c\right) - 5 \, {\left({\left(23 \, a^{3} + 60 \, a^{2} b + 45 \, a b^{2} + 15 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 46 \, a^{3} + 120 \, a^{2} b + 90 \, a b^{2} + 30 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x - 3 \, {\left(23 \, a^{3} + 60 \, a^{2} b + 45 \, a b^{2} + 15 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)}{15 \, {\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,"-1/15*((23*a^3 + 60*a^2*b + 45*a*b^2)*cosh(d*x + c)^5 + 5*(23*a^3 + 60*a^2*b + 45*a*b^2)*cosh(d*x + c)*sinh(d*x + c)^4 - (23*a^3 + 60*a^2*b + 45*a*b^2 + 15*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*sinh(d*x + c)^5 - 5*(5*a^3 + 24*a^2*b + 27*a*b^2)*cosh(d*x + c)^3 + 5*(23*a^3 + 60*a^2*b + 45*a*b^2 + 15*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x - 2*(23*a^3 + 60*a^2*b + 45*a*b^2 + 15*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 5*(2*(23*a^3 + 60*a^2*b + 45*a*b^2)*cosh(d*x + c)^3 - 3*(5*a^3 + 24*a^2*b + 27*a*b^2)*cosh(d*x + c))*sinh(d*x + c)^2 + 10*(5*a^3 + 6*a^2*b + 9*a*b^2)*cosh(d*x + c) - 5*((23*a^3 + 60*a^2*b + 45*a*b^2 + 15*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^4 + 46*a^3 + 120*a^2*b + 90*a*b^2 + 30*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x - 3*(23*a^3 + 60*a^2*b + 45*a*b^2 + 15*(a^3 + 3*a^2*b + 3*a*b^2 + 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
167,1,4305,0,0.493167," ","integrate(coth(d*x+c)^7*(a+b*tanh(d*x+c)^2)^3,x, algorithm=""fricas"")","-\frac{3 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x \cosh\left(d x + c\right)^{12} + 36 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{11} + 3 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x \sinh\left(d x + c\right)^{12} + 18 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2} - {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{10} + 18 \, {\left(11 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x \cosh\left(d x + c\right)^{2} + a^{3} + 2 \, a^{2} b + a b^{2} - {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \sinh\left(d x + c\right)^{10} + 60 \, {\left(11 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2} - {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} - 9 \, {\left(4 \, a^{3} + 12 \, a^{2} b + 8 \, a b^{2} - 5 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{8} + 9 \, {\left(165 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x \cosh\left(d x + c\right)^{4} - 4 \, a^{3} - 12 \, a^{2} b - 8 \, a b^{2} + 5 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x + 90 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2} - {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{8} + 72 \, {\left(33 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x \cosh\left(d x + c\right)^{5} + 30 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2} - {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - {\left(4 \, a^{3} + 12 \, a^{2} b + 8 \, a b^{2} - 5 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 4 \, {\left(17 \, a^{3} + 36 \, a^{2} b + 27 \, a b^{2} - 15 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(693 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x \cosh\left(d x + c\right)^{6} + 945 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2} - {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 17 \, a^{3} + 36 \, a^{2} b + 27 \, a b^{2} - 15 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x - 63 \, {\left(4 \, a^{3} + 12 \, a^{2} b + 8 \, a b^{2} - 5 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 24 \, {\left(99 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x \cosh\left(d x + c\right)^{7} + 189 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2} - {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{5} - 21 \, {\left(4 \, a^{3} + 12 \, a^{2} b + 8 \, a b^{2} - 5 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + {\left(17 \, a^{3} + 36 \, a^{2} b + 27 \, a b^{2} - 15 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 9 \, {\left(4 \, a^{3} + 12 \, a^{2} b + 8 \, a b^{2} - 5 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(495 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x \cosh\left(d x + c\right)^{8} + 1260 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2} - {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{6} - 210 \, {\left(4 \, a^{3} + 12 \, a^{2} b + 8 \, a b^{2} - 5 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{4} - 12 \, a^{3} - 36 \, a^{2} b - 24 \, a b^{2} + 15 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x + 20 \, {\left(17 \, a^{3} + 36 \, a^{2} b + 27 \, a b^{2} - 15 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(165 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x \cosh\left(d x + c\right)^{9} + 540 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2} - {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{7} - 126 \, {\left(4 \, a^{3} + 12 \, a^{2} b + 8 \, a b^{2} - 5 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{5} + 20 \, {\left(17 \, a^{3} + 36 \, a^{2} b + 27 \, a b^{2} - 15 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - 9 \, {\left(4 \, a^{3} + 12 \, a^{2} b + 8 \, a b^{2} - 5 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 3 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x + 18 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2} - {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2} + 6 \, {\left(33 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x \cosh\left(d x + c\right)^{10} + 135 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2} - {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{8} - 42 \, {\left(4 \, a^{3} + 12 \, a^{2} b + 8 \, a b^{2} - 5 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{6} + 10 \, {\left(17 \, a^{3} + 36 \, a^{2} b + 27 \, a b^{2} - 15 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 3 \, a^{3} + 6 \, a^{2} b + 3 \, a b^{2} - 3 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x - 9 \, {\left(4 \, a^{3} + 12 \, a^{2} b + 8 \, a b^{2} - 5 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} - 3 \, {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{12} + 12 \, {\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)^{11} + {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \sinh\left(d x + c\right)^{12} - 6 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{10} - 6 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} - 11 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{10} + 20 \, {\left(11 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} + 15 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{8} + 15 \, {\left(33 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{4} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} - 18 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{8} + 24 \, {\left(33 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{5} - 30 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\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)\right)} \sinh\left(d x + c\right)^{7} - 20 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(231 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{6} - 315 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{4} - 5 \, a^{3} - 15 \, a^{2} b - 15 \, a b^{2} - 5 \, b^{3} + 105 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 24 \, {\left(33 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{7} - 63 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{5} + 35 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\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)\right)} \sinh\left(d x + c\right)^{5} + 15 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{4} + 15 \, {\left(33 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{8} - 84 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{6} + 70 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{4} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} - 20 \, {\left(a^{3} + 3 \, 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} + 20 \, {\left(11 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{9} - 36 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{7} + 42 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{5} - 20 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} - 6 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{2} + 6 \, {\left(11 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{10} - 45 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{8} + 70 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{6} - 50 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{4} - a^{3} - 3 \, a^{2} b - 3 \, a b^{2} - b^{3} + 15 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 12 \, {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{11} - 5 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{9} + 10 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{7} - 10 \, {\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)^{3} - {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\frac{2 \, \sinh\left(d x + c\right)}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) + 12 \, {\left(3 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x \cosh\left(d x + c\right)^{11} + 15 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2} - {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{9} - 6 \, {\left(4 \, a^{3} + 12 \, a^{2} b + 8 \, a b^{2} - 5 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{7} + 2 \, {\left(17 \, a^{3} + 36 \, a^{2} b + 27 \, a b^{2} - 15 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{5} - 3 \, {\left(4 \, a^{3} + 12 \, a^{2} b + 8 \, a b^{2} - 5 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2} - {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{3 \, {\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,"-1/3*(3*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x*cosh(d*x + c)^12 + 36*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x*cosh(d*x + c)*sinh(d*x + c)^11 + 3*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x*sinh(d*x + c)^12 + 18*(a^3 + 2*a^2*b + a*b^2 - (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^10 + 18*(11*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x*cosh(d*x + c)^2 + a^3 + 2*a^2*b + a*b^2 - (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*sinh(d*x + c)^10 + 60*(11*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x*cosh(d*x + c)^3 + 3*(a^3 + 2*a^2*b + a*b^2 - (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c)^9 - 9*(4*a^3 + 12*a^2*b + 8*a*b^2 - 5*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^8 + 9*(165*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x*cosh(d*x + c)^4 - 4*a^3 - 12*a^2*b - 8*a*b^2 + 5*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x + 90*(a^3 + 2*a^2*b + a*b^2 - (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 72*(33*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x*cosh(d*x + c)^5 + 30*(a^3 + 2*a^2*b + a*b^2 - (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^3 - (4*a^3 + 12*a^2*b + 8*a*b^2 - 5*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c)^7 + 4*(17*a^3 + 36*a^2*b + 27*a*b^2 - 15*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^6 + 4*(693*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x*cosh(d*x + c)^6 + 945*(a^3 + 2*a^2*b + a*b^2 - (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^4 + 17*a^3 + 36*a^2*b + 27*a*b^2 - 15*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x - 63*(4*a^3 + 12*a^2*b + 8*a*b^2 - 5*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 24*(99*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x*cosh(d*x + c)^7 + 189*(a^3 + 2*a^2*b + a*b^2 - (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^5 - 21*(4*a^3 + 12*a^2*b + 8*a*b^2 - 5*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^3 + (17*a^3 + 36*a^2*b + 27*a*b^2 - 15*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c)^5 - 9*(4*a^3 + 12*a^2*b + 8*a*b^2 - 5*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^4 + 3*(495*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x*cosh(d*x + c)^8 + 1260*(a^3 + 2*a^2*b + a*b^2 - (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^6 - 210*(4*a^3 + 12*a^2*b + 8*a*b^2 - 5*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^4 - 12*a^3 - 36*a^2*b - 24*a*b^2 + 15*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x + 20*(17*a^3 + 36*a^2*b + 27*a*b^2 - 15*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 4*(165*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x*cosh(d*x + c)^9 + 540*(a^3 + 2*a^2*b + a*b^2 - (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^7 - 126*(4*a^3 + 12*a^2*b + 8*a*b^2 - 5*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^5 + 20*(17*a^3 + 36*a^2*b + 27*a*b^2 - 15*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^3 - 9*(4*a^3 + 12*a^2*b + 8*a*b^2 - 5*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c)^3 + 3*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x + 18*(a^3 + 2*a^2*b + a*b^2 - (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^2 + 6*(33*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x*cosh(d*x + c)^10 + 135*(a^3 + 2*a^2*b + a*b^2 - (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^8 - 42*(4*a^3 + 12*a^2*b + 8*a*b^2 - 5*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^6 + 10*(17*a^3 + 36*a^2*b + 27*a*b^2 - 15*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^4 + 3*a^3 + 6*a^2*b + 3*a*b^2 - 3*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x - 9*(4*a^3 + 12*a^2*b + 8*a*b^2 - 5*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - 3*((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^12 + 12*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)*sinh(d*x + c)^11 + (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*sinh(d*x + c)^12 - 6*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^10 - 6*(a^3 + 3*a^2*b + 3*a*b^2 + b^3 - 11*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^10 + 20*(11*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^3 - 3*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c))*sinh(d*x + c)^9 + 15*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^8 + 15*(33*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^4 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 - 18*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 24*(33*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^5 - 30*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(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)^7 - 20*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^6 + 4*(231*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^6 - 315*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^4 - 5*a^3 - 15*a^2*b - 15*a*b^2 - 5*b^3 + 105*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 24*(33*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^7 - 63*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^5 + 35*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(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)^5 + 15*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^4 + 15*(33*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^8 - 84*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^6 + 70*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^4 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 - 20*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 20*(11*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^9 - 36*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^7 + 42*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^5 - 20*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^3 + 3*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c))*sinh(d*x + c)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 - 6*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^2 + 6*(11*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^10 - 45*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^8 + 70*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^6 - 50*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^4 - a^3 - 3*a^2*b - 3*a*b^2 - b^3 + 15*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 12*((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^11 - 5*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^9 + 10*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^7 - 10*(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)^3 - (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c))*sinh(d*x + c))*log(2*sinh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))) + 12*(3*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x*cosh(d*x + c)^11 + 15*(a^3 + 2*a^2*b + a*b^2 - (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^9 - 6*(4*a^3 + 12*a^2*b + 8*a*b^2 - 5*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^7 + 2*(17*a^3 + 36*a^2*b + 27*a*b^2 - 15*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^5 - 3*(4*a^3 + 12*a^2*b + 8*a*b^2 - 5*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c)^3 + 3*(a^3 + 2*a^2*b + a*b^2 - (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*x)*cosh(d*x + c))*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
168,1,1176,0,0.427465," ","integrate((a+b*tanh(d*x+c)^2)^4,x, algorithm=""fricas"")","\frac{{\left(420 \, a^{3} b + 840 \, a^{2} b^{2} + 644 \, a b^{3} + 176 \, b^{4} + 105 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{7} + 7 \, {\left(420 \, a^{3} b + 840 \, a^{2} b^{2} + 644 \, a b^{3} + 176 \, b^{4} + 105 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} d x\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} - 4 \, {\left(105 \, a^{3} b + 210 \, a^{2} b^{2} + 161 \, a b^{3} + 44 \, b^{4}\right)} \sinh\left(d x + c\right)^{7} + 7 \, {\left(420 \, a^{3} b + 840 \, a^{2} b^{2} + 644 \, a b^{3} + 176 \, b^{4} + 105 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{5} - 28 \, {\left(75 \, a^{3} b + 120 \, a^{2} b^{2} + 71 \, a b^{3} + 14 \, b^{4} + 3 \, {\left(105 \, a^{3} b + 210 \, a^{2} b^{2} + 161 \, a b^{3} + 44 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{5} + 35 \, {\left({\left(420 \, a^{3} b + 840 \, a^{2} b^{2} + 644 \, a b^{3} + 176 \, b^{4} + 105 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + {\left(420 \, a^{3} b + 840 \, a^{2} b^{2} + 644 \, a b^{3} + 176 \, b^{4} + 105 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 21 \, {\left(420 \, a^{3} b + 840 \, a^{2} b^{2} + 644 \, a b^{3} + 176 \, b^{4} + 105 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - 28 \, {\left(5 \, {\left(105 \, a^{3} b + 210 \, a^{2} b^{2} + 161 \, a b^{3} + 44 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 135 \, a^{3} b + 180 \, a^{2} b^{2} + 123 \, a b^{3} + 42 \, b^{4} + 10 \, {\left(75 \, a^{3} b + 120 \, a^{2} b^{2} + 71 \, a b^{3} + 14 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + 7 \, {\left(3 \, {\left(420 \, a^{3} b + 840 \, a^{2} b^{2} + 644 \, a b^{3} + 176 \, b^{4} + 105 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(420 \, a^{3} b + 840 \, a^{2} b^{2} + 644 \, a b^{3} + 176 \, b^{4} + 105 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + 9 \, {\left(420 \, a^{3} b + 840 \, a^{2} b^{2} + 644 \, a b^{3} + 176 \, b^{4} + 105 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 35 \, {\left(420 \, a^{3} b + 840 \, a^{2} b^{2} + 644 \, a b^{3} + 176 \, b^{4} + 105 \, {\left(a^{4} + 4 \, a^{3} b + 6 \, a^{2} b^{2} + 4 \, a b^{3} + b^{4}\right)} d x\right)} \cosh\left(d x + c\right) - 28 \, {\left({\left(105 \, a^{3} b + 210 \, a^{2} b^{2} + 161 \, a b^{3} + 44 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 5 \, {\left(75 \, a^{3} b + 120 \, a^{2} b^{2} + 71 \, a b^{3} + 14 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 75 \, a^{3} b + 90 \, a^{2} b^{2} + 75 \, a b^{3} + 9 \, {\left(45 \, a^{3} b + 60 \, a^{2} b^{2} + 41 \, a b^{3} + 14 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)}{105 \, {\left(d \cosh\left(d x + c\right)^{7} + 7 \, d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{6} + 7 \, d \cosh\left(d x + c\right)^{5} + 35 \, {\left(d \cosh\left(d x + c\right)^{3} + d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 21 \, d \cosh\left(d x + c\right)^{3} + 7 \, {\left(3 \, d \cosh\left(d x + c\right)^{5} + 10 \, d \cosh\left(d x + c\right)^{3} + 9 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 35 \, d \cosh\left(d x + c\right)\right)}}"," ",0,"1/105*((420*a^3*b + 840*a^2*b^2 + 644*a*b^3 + 176*b^4 + 105*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*d*x)*cosh(d*x + c)^7 + 7*(420*a^3*b + 840*a^2*b^2 + 644*a*b^3 + 176*b^4 + 105*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*d*x)*cosh(d*x + c)*sinh(d*x + c)^6 - 4*(105*a^3*b + 210*a^2*b^2 + 161*a*b^3 + 44*b^4)*sinh(d*x + c)^7 + 7*(420*a^3*b + 840*a^2*b^2 + 644*a*b^3 + 176*b^4 + 105*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*d*x)*cosh(d*x + c)^5 - 28*(75*a^3*b + 120*a^2*b^2 + 71*a*b^3 + 14*b^4 + 3*(105*a^3*b + 210*a^2*b^2 + 161*a*b^3 + 44*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 35*((420*a^3*b + 840*a^2*b^2 + 644*a*b^3 + 176*b^4 + 105*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*d*x)*cosh(d*x + c)^3 + (420*a^3*b + 840*a^2*b^2 + 644*a*b^3 + 176*b^4 + 105*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*d*x)*cosh(d*x + c))*sinh(d*x + c)^4 + 21*(420*a^3*b + 840*a^2*b^2 + 644*a*b^3 + 176*b^4 + 105*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*d*x)*cosh(d*x + c)^3 - 28*(5*(105*a^3*b + 210*a^2*b^2 + 161*a*b^3 + 44*b^4)*cosh(d*x + c)^4 + 135*a^3*b + 180*a^2*b^2 + 123*a*b^3 + 42*b^4 + 10*(75*a^3*b + 120*a^2*b^2 + 71*a*b^3 + 14*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 7*(3*(420*a^3*b + 840*a^2*b^2 + 644*a*b^3 + 176*b^4 + 105*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*d*x)*cosh(d*x + c)^5 + 10*(420*a^3*b + 840*a^2*b^2 + 644*a*b^3 + 176*b^4 + 105*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*d*x)*cosh(d*x + c)^3 + 9*(420*a^3*b + 840*a^2*b^2 + 644*a*b^3 + 176*b^4 + 105*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*d*x)*cosh(d*x + c))*sinh(d*x + c)^2 + 35*(420*a^3*b + 840*a^2*b^2 + 644*a*b^3 + 176*b^4 + 105*(a^4 + 4*a^3*b + 6*a^2*b^2 + 4*a*b^3 + b^4)*d*x)*cosh(d*x + c) - 28*((105*a^3*b + 210*a^2*b^2 + 161*a*b^3 + 44*b^4)*cosh(d*x + c)^6 + 5*(75*a^3*b + 120*a^2*b^2 + 71*a*b^3 + 14*b^4)*cosh(d*x + c)^4 + 75*a^3*b + 90*a^2*b^2 + 75*a*b^3 + 9*(45*a^3*b + 60*a^2*b^2 + 41*a*b^3 + 14*b^4)*cosh(d*x + c)^2)*sinh(d*x + c))/(d*cosh(d*x + c)^7 + 7*d*cosh(d*x + c)*sinh(d*x + c)^6 + 7*d*cosh(d*x + c)^5 + 35*(d*cosh(d*x + c)^3 + d*cosh(d*x + c))*sinh(d*x + c)^4 + 21*d*cosh(d*x + c)^3 + 7*(3*d*cosh(d*x + c)^5 + 10*d*cosh(d*x + c)^3 + 9*d*cosh(d*x + c))*sinh(d*x + c)^2 + 35*d*cosh(d*x + c))","B",0
169,1,2133,0,0.436575," ","integrate((a+b*tanh(d*x+c)^2)^5,x, algorithm=""fricas"")","\frac{{\left(1575 \, a^{4} b + 4200 \, a^{3} b^{2} + 4830 \, a^{2} b^{3} + 2640 \, a b^{4} + 563 \, b^{5} + 315 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d x\right)} \cosh\left(d x + c\right)^{9} + 9 \, {\left(1575 \, a^{4} b + 4200 \, a^{3} b^{2} + 4830 \, a^{2} b^{3} + 2640 \, a b^{4} + 563 \, b^{5} + 315 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d x\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{8} - {\left(1575 \, a^{4} b + 4200 \, a^{3} b^{2} + 4830 \, a^{2} b^{3} + 2640 \, a b^{4} + 563 \, b^{5}\right)} \sinh\left(d x + c\right)^{9} + 9 \, {\left(1575 \, a^{4} b + 4200 \, a^{3} b^{2} + 4830 \, a^{2} b^{3} + 2640 \, a b^{4} + 563 \, b^{5} + 315 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d x\right)} \cosh\left(d x + c\right)^{7} - 9 \, {\left(1225 \, a^{4} b + 2800 \, a^{3} b^{2} + 2730 \, a^{2} b^{3} + 1240 \, a b^{4} + 213 \, b^{5} + 4 \, {\left(1575 \, a^{4} b + 4200 \, a^{3} b^{2} + 4830 \, a^{2} b^{3} + 2640 \, a b^{4} + 563 \, b^{5}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{7} + 21 \, {\left(4 \, {\left(1575 \, a^{4} b + 4200 \, a^{3} b^{2} + 4830 \, a^{2} b^{3} + 2640 \, a b^{4} + 563 \, b^{5} + 315 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(1575 \, a^{4} b + 4200 \, a^{3} b^{2} + 4830 \, a^{2} b^{3} + 2640 \, a b^{4} + 563 \, b^{5} + 315 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} + 36 \, {\left(1575 \, a^{4} b + 4200 \, a^{3} b^{2} + 4830 \, a^{2} b^{3} + 2640 \, a b^{4} + 563 \, b^{5} + 315 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d x\right)} \cosh\left(d x + c\right)^{5} - 9 \, {\left(3500 \, a^{4} b + 7000 \, a^{3} b^{2} + 6720 \, a^{2} b^{3} + 3560 \, a b^{4} + 852 \, b^{5} + 14 \, {\left(1575 \, a^{4} b + 4200 \, a^{3} b^{2} + 4830 \, a^{2} b^{3} + 2640 \, a b^{4} + 563 \, b^{5}\right)} \cosh\left(d x + c\right)^{4} + 21 \, {\left(1225 \, a^{4} b + 2800 \, a^{3} b^{2} + 2730 \, a^{2} b^{3} + 1240 \, a b^{4} + 213 \, b^{5}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{5} + 9 \, {\left(14 \, {\left(1575 \, a^{4} b + 4200 \, a^{3} b^{2} + 4830 \, a^{2} b^{3} + 2640 \, a b^{4} + 563 \, b^{5} + 315 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d x\right)} \cosh\left(d x + c\right)^{5} + 35 \, {\left(1575 \, a^{4} b + 4200 \, a^{3} b^{2} + 4830 \, a^{2} b^{3} + 2640 \, a b^{4} + 563 \, b^{5} + 315 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + 20 \, {\left(1575 \, a^{4} b + 4200 \, a^{3} b^{2} + 4830 \, a^{2} b^{3} + 2640 \, a b^{4} + 563 \, b^{5} + 315 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 84 \, {\left(1575 \, a^{4} b + 4200 \, a^{3} b^{2} + 4830 \, a^{2} b^{3} + 2640 \, a b^{4} + 563 \, b^{5} + 315 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(28 \, {\left(1575 \, a^{4} b + 4200 \, a^{3} b^{2} + 4830 \, a^{2} b^{3} + 2640 \, a b^{4} + 563 \, b^{5}\right)} \cosh\left(d x + c\right)^{6} + 14700 \, a^{4} b + 26600 \, a^{3} b^{2} + 27440 \, a^{2} b^{3} + 13720 \, a b^{4} + 1764 \, b^{5} + 105 \, {\left(1225 \, a^{4} b + 2800 \, a^{3} b^{2} + 2730 \, a^{2} b^{3} + 1240 \, a b^{4} + 213 \, b^{5}\right)} \cosh\left(d x + c\right)^{4} + 120 \, {\left(875 \, a^{4} b + 1750 \, a^{3} b^{2} + 1680 \, a^{2} b^{3} + 890 \, a b^{4} + 213 \, b^{5}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{3} + 9 \, {\left(4 \, {\left(1575 \, a^{4} b + 4200 \, a^{3} b^{2} + 4830 \, a^{2} b^{3} + 2640 \, a b^{4} + 563 \, b^{5} + 315 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d x\right)} \cosh\left(d x + c\right)^{7} + 21 \, {\left(1575 \, a^{4} b + 4200 \, a^{3} b^{2} + 4830 \, a^{2} b^{3} + 2640 \, a b^{4} + 563 \, b^{5} + 315 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d x\right)} \cosh\left(d x + c\right)^{5} + 40 \, {\left(1575 \, a^{4} b + 4200 \, a^{3} b^{2} + 4830 \, a^{2} b^{3} + 2640 \, a b^{4} + 563 \, b^{5} + 315 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + 28 \, {\left(1575 \, a^{4} b + 4200 \, a^{3} b^{2} + 4830 \, a^{2} b^{3} + 2640 \, a b^{4} + 563 \, b^{5} + 315 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 126 \, {\left(1575 \, a^{4} b + 4200 \, a^{3} b^{2} + 4830 \, a^{2} b^{3} + 2640 \, a b^{4} + 563 \, b^{5} + 315 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d x\right)} \cosh\left(d x + c\right) - 9 \, {\left({\left(1575 \, a^{4} b + 4200 \, a^{3} b^{2} + 4830 \, a^{2} b^{3} + 2640 \, a b^{4} + 563 \, b^{5}\right)} \cosh\left(d x + c\right)^{8} + 7 \, {\left(1225 \, a^{4} b + 2800 \, a^{3} b^{2} + 2730 \, a^{2} b^{3} + 1240 \, a b^{4} + 213 \, b^{5}\right)} \cosh\left(d x + c\right)^{6} + 2450 \, a^{4} b + 4200 \, a^{3} b^{2} + 4620 \, a^{2} b^{3} + 1960 \, a b^{4} + 882 \, b^{5} + 20 \, {\left(875 \, a^{4} b + 1750 \, a^{3} b^{2} + 1680 \, a^{2} b^{3} + 890 \, a b^{4} + 213 \, b^{5}\right)} \cosh\left(d x + c\right)^{4} + 28 \, {\left(525 \, a^{4} b + 950 \, a^{3} b^{2} + 980 \, a^{2} b^{3} + 490 \, a b^{4} + 63 \, b^{5}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)}{315 \, {\left(d \cosh\left(d x + c\right)^{9} + 9 \, d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{8} + 9 \, d \cosh\left(d x + c\right)^{7} + 21 \, {\left(4 \, d \cosh\left(d x + c\right)^{3} + 3 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{6} + 36 \, d \cosh\left(d x + c\right)^{5} + 9 \, {\left(14 \, d \cosh\left(d x + c\right)^{5} + 35 \, d \cosh\left(d x + c\right)^{3} + 20 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{4} + 84 \, d \cosh\left(d x + c\right)^{3} + 9 \, {\left(4 \, d \cosh\left(d x + c\right)^{7} + 21 \, d \cosh\left(d x + c\right)^{5} + 40 \, d \cosh\left(d x + c\right)^{3} + 28 \, d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{2} + 126 \, d \cosh\left(d x + c\right)\right)}}"," ",0,"1/315*((1575*a^4*b + 4200*a^3*b^2 + 4830*a^2*b^3 + 2640*a*b^4 + 563*b^5 + 315*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*x)*cosh(d*x + c)^9 + 9*(1575*a^4*b + 4200*a^3*b^2 + 4830*a^2*b^3 + 2640*a*b^4 + 563*b^5 + 315*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*x)*cosh(d*x + c)*sinh(d*x + c)^8 - (1575*a^4*b + 4200*a^3*b^2 + 4830*a^2*b^3 + 2640*a*b^4 + 563*b^5)*sinh(d*x + c)^9 + 9*(1575*a^4*b + 4200*a^3*b^2 + 4830*a^2*b^3 + 2640*a*b^4 + 563*b^5 + 315*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*x)*cosh(d*x + c)^7 - 9*(1225*a^4*b + 2800*a^3*b^2 + 2730*a^2*b^3 + 1240*a*b^4 + 213*b^5 + 4*(1575*a^4*b + 4200*a^3*b^2 + 4830*a^2*b^3 + 2640*a*b^4 + 563*b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^7 + 21*(4*(1575*a^4*b + 4200*a^3*b^2 + 4830*a^2*b^3 + 2640*a*b^4 + 563*b^5 + 315*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*x)*cosh(d*x + c)^3 + 3*(1575*a^4*b + 4200*a^3*b^2 + 4830*a^2*b^3 + 2640*a*b^4 + 563*b^5 + 315*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*x)*cosh(d*x + c))*sinh(d*x + c)^6 + 36*(1575*a^4*b + 4200*a^3*b^2 + 4830*a^2*b^3 + 2640*a*b^4 + 563*b^5 + 315*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*x)*cosh(d*x + c)^5 - 9*(3500*a^4*b + 7000*a^3*b^2 + 6720*a^2*b^3 + 3560*a*b^4 + 852*b^5 + 14*(1575*a^4*b + 4200*a^3*b^2 + 4830*a^2*b^3 + 2640*a*b^4 + 563*b^5)*cosh(d*x + c)^4 + 21*(1225*a^4*b + 2800*a^3*b^2 + 2730*a^2*b^3 + 1240*a*b^4 + 213*b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^5 + 9*(14*(1575*a^4*b + 4200*a^3*b^2 + 4830*a^2*b^3 + 2640*a*b^4 + 563*b^5 + 315*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*x)*cosh(d*x + c)^5 + 35*(1575*a^4*b + 4200*a^3*b^2 + 4830*a^2*b^3 + 2640*a*b^4 + 563*b^5 + 315*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*x)*cosh(d*x + c)^3 + 20*(1575*a^4*b + 4200*a^3*b^2 + 4830*a^2*b^3 + 2640*a*b^4 + 563*b^5 + 315*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*x)*cosh(d*x + c))*sinh(d*x + c)^4 + 84*(1575*a^4*b + 4200*a^3*b^2 + 4830*a^2*b^3 + 2640*a*b^4 + 563*b^5 + 315*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*x)*cosh(d*x + c)^3 - 3*(28*(1575*a^4*b + 4200*a^3*b^2 + 4830*a^2*b^3 + 2640*a*b^4 + 563*b^5)*cosh(d*x + c)^6 + 14700*a^4*b + 26600*a^3*b^2 + 27440*a^2*b^3 + 13720*a*b^4 + 1764*b^5 + 105*(1225*a^4*b + 2800*a^3*b^2 + 2730*a^2*b^3 + 1240*a*b^4 + 213*b^5)*cosh(d*x + c)^4 + 120*(875*a^4*b + 1750*a^3*b^2 + 1680*a^2*b^3 + 890*a*b^4 + 213*b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^3 + 9*(4*(1575*a^4*b + 4200*a^3*b^2 + 4830*a^2*b^3 + 2640*a*b^4 + 563*b^5 + 315*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*x)*cosh(d*x + c)^7 + 21*(1575*a^4*b + 4200*a^3*b^2 + 4830*a^2*b^3 + 2640*a*b^4 + 563*b^5 + 315*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*x)*cosh(d*x + c)^5 + 40*(1575*a^4*b + 4200*a^3*b^2 + 4830*a^2*b^3 + 2640*a*b^4 + 563*b^5 + 315*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*x)*cosh(d*x + c)^3 + 28*(1575*a^4*b + 4200*a^3*b^2 + 4830*a^2*b^3 + 2640*a*b^4 + 563*b^5 + 315*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*x)*cosh(d*x + c))*sinh(d*x + c)^2 + 126*(1575*a^4*b + 4200*a^3*b^2 + 4830*a^2*b^3 + 2640*a*b^4 + 563*b^5 + 315*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*x)*cosh(d*x + c) - 9*((1575*a^4*b + 4200*a^3*b^2 + 4830*a^2*b^3 + 2640*a*b^4 + 563*b^5)*cosh(d*x + c)^8 + 7*(1225*a^4*b + 2800*a^3*b^2 + 2730*a^2*b^3 + 1240*a*b^4 + 213*b^5)*cosh(d*x + c)^6 + 2450*a^4*b + 4200*a^3*b^2 + 4620*a^2*b^3 + 1960*a*b^4 + 882*b^5 + 20*(875*a^4*b + 1750*a^3*b^2 + 1680*a^2*b^3 + 890*a*b^4 + 213*b^5)*cosh(d*x + c)^4 + 28*(525*a^4*b + 950*a^3*b^2 + 980*a^2*b^3 + 490*a*b^4 + 63*b^5)*cosh(d*x + c)^2)*sinh(d*x + c))/(d*cosh(d*x + c)^9 + 9*d*cosh(d*x + c)*sinh(d*x + c)^8 + 9*d*cosh(d*x + c)^7 + 21*(4*d*cosh(d*x + c)^3 + 3*d*cosh(d*x + c))*sinh(d*x + c)^6 + 36*d*cosh(d*x + c)^5 + 9*(14*d*cosh(d*x + c)^5 + 35*d*cosh(d*x + c)^3 + 20*d*cosh(d*x + c))*sinh(d*x + c)^4 + 84*d*cosh(d*x + c)^3 + 9*(4*d*cosh(d*x + c)^7 + 21*d*cosh(d*x + c)^5 + 40*d*cosh(d*x + c)^3 + 28*d*cosh(d*x + c))*sinh(d*x + c)^2 + 126*d*cosh(d*x + c))","B",0
170,1,742,0,0.519124," ","integrate(tanh(d*x+c)^5/(a+b*tanh(d*x+c)^2),x, algorithm=""fricas"")","-\frac{2 \, b^{2} d x \cosh\left(d x + c\right)^{4} + 8 \, b^{2} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + 2 \, b^{2} d x \sinh\left(d x + c\right)^{4} + 2 \, b^{2} d x + 4 \, {\left(b^{2} d x - a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(3 \, b^{2} d x \cosh\left(d x + c\right)^{2} + b^{2} d x - a b - b^{2}\right)} \sinh\left(d x + c\right)^{2} - {\left(a^{2} \cosh\left(d x + c\right)^{4} + 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} + 2 \, a^{2} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(d x + c\right)^{2} + a^{2}\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 4 \, {\left(a^{2} \cosh\left(d x + c\right)^{3} + a^{2} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\frac{2 \, {\left({\left(a + b\right)} \cosh\left(d x + c\right)^{2} + {\left(a + b\right)} \sinh\left(d x + c\right)^{2} + a - b\right)}}{\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}}\right) + 2 \, {\left({\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{2} + a^{2} - b^{2} + 4 \, {\left({\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\frac{2 \, \cosh\left(d x + c\right)}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) + 8 \, {\left(b^{2} d x \cosh\left(d x + c\right)^{3} + {\left(b^{2} d x - a b - b^{2}\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)^{4} + 4 \, {\left(a b^{2} + b^{3}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a b^{2} + b^{3}\right)} d \sinh\left(d x + c\right)^{4} + 2 \, {\left(a b^{2} + b^{3}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\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)^{2} + {\left(a b^{2} + b^{3}\right)} d + 4 \, {\left({\left(a b^{2} + 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,"-1/2*(2*b^2*d*x*cosh(d*x + c)^4 + 8*b^2*d*x*cosh(d*x + c)*sinh(d*x + c)^3 + 2*b^2*d*x*sinh(d*x + c)^4 + 2*b^2*d*x + 4*(b^2*d*x - a*b - b^2)*cosh(d*x + c)^2 + 4*(3*b^2*d*x*cosh(d*x + c)^2 + b^2*d*x - a*b - b^2)*sinh(d*x + c)^2 - (a^2*cosh(d*x + c)^4 + 4*a^2*cosh(d*x + c)*sinh(d*x + c)^3 + a^2*sinh(d*x + c)^4 + 2*a^2*cosh(d*x + c)^2 + 2*(3*a^2*cosh(d*x + c)^2 + a^2)*sinh(d*x + c)^2 + a^2 + 4*(a^2*cosh(d*x + c)^3 + a^2*cosh(d*x + c))*sinh(d*x + c))*log(2*((a + b)*cosh(d*x + c)^2 + (a + b)*sinh(d*x + c)^2 + a - b)/(cosh(d*x + c)^2 - 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)) + 2*((a^2 - b^2)*cosh(d*x + c)^4 + 4*(a^2 - b^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (a^2 - b^2)*sinh(d*x + c)^4 + 2*(a^2 - b^2)*cosh(d*x + c)^2 + 2*(3*(a^2 - b^2)*cosh(d*x + c)^2 + a^2 - b^2)*sinh(d*x + c)^2 + a^2 - b^2 + 4*((a^2 - b^2)*cosh(d*x + c)^3 + (a^2 - b^2)*cosh(d*x + c))*sinh(d*x + c))*log(2*cosh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))) + 8*(b^2*d*x*cosh(d*x + c)^3 + (b^2*d*x - a*b - b^2)*cosh(d*x + c))*sinh(d*x + c))/((a*b^2 + b^3)*d*cosh(d*x + c)^4 + 4*(a*b^2 + b^3)*d*cosh(d*x + c)*sinh(d*x + c)^3 + (a*b^2 + b^3)*d*sinh(d*x + c)^4 + 2*(a*b^2 + b^3)*d*cosh(d*x + c)^2 + 2*(3*(a*b^2 + 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 + 4*((a*b^2 + b^3)*d*cosh(d*x + c)^3 + (a*b^2 + b^3)*d*cosh(d*x + c))*sinh(d*x + c))","B",0
171,1,777,0,0.464924," ","integrate(tanh(d*x+c)^4/(a+b*tanh(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{2 \, b d x \cosh\left(d x + c\right)^{2} + 4 \, b d x \cosh\left(d x + c\right) \sinh\left(d x + c\right) + 2 \, b d x \sinh\left(d x + c\right)^{2} + 2 \, b d x + {\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} + a\right)} \sqrt{-\frac{a}{b}} \log\left(\frac{{\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) \sinh\left(d x + c\right)^{3} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{2} + a^{2} - 6 \, a b + b^{2} + 4 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} - 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} + a b - b^{2}\right)} \sqrt{-\frac{a}{b}}}{{\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) + 4 \, a + 4 \, b}{2 \, {\left({\left(a b + b^{2}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(a b + b^{2}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a b + b^{2}\right)} d \sinh\left(d x + c\right)^{2} + {\left(a b + b^{2}\right)} d\right)}}, \frac{b d x \cosh\left(d x + c\right)^{2} + 2 \, b d x \cosh\left(d x + c\right) \sinh\left(d x + c\right) + b d x \sinh\left(d x + c\right)^{2} + b d x + {\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} + a\right)} \sqrt{\frac{a}{b}} \arctan\left(\frac{{\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} + a - b\right)} \sqrt{\frac{a}{b}}}{2 \, a}\right) + 2 \, a + 2 \, b}{{\left(a b + b^{2}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(a b + b^{2}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a b + b^{2}\right)} d \sinh\left(d x + c\right)^{2} + {\left(a b + b^{2}\right)} d}\right]"," ",0,"[1/2*(2*b*d*x*cosh(d*x + c)^2 + 4*b*d*x*cosh(d*x + c)*sinh(d*x + c) + 2*b*d*x*sinh(d*x + c)^2 + 2*b*d*x + (a*cosh(d*x + c)^2 + 2*a*cosh(d*x + c)*sinh(d*x + c) + a*sinh(d*x + c)^2 + a)*sqrt(-a/b)*log(((a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 + 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 + 2*(a^2 - b^2)*cosh(d*x + c)^2 + 2*(3*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + a^2 - b^2)*sinh(d*x + c)^2 + a^2 - 6*a*b + b^2 + 4*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 + (a^2 - 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 + a*b - b^2)*sqrt(-a/b))/((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)) + 4*a + 4*b)/((a*b + b^2)*d*cosh(d*x + c)^2 + 2*(a*b + b^2)*d*cosh(d*x + c)*sinh(d*x + c) + (a*b + b^2)*d*sinh(d*x + c)^2 + (a*b + b^2)*d), (b*d*x*cosh(d*x + c)^2 + 2*b*d*x*cosh(d*x + c)*sinh(d*x + c) + b*d*x*sinh(d*x + c)^2 + b*d*x + (a*cosh(d*x + c)^2 + 2*a*cosh(d*x + c)*sinh(d*x + c) + a*sinh(d*x + c)^2 + a)*sqrt(a/b)*arctan(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 + a - b)*sqrt(a/b)/a) + 2*a + 2*b)/((a*b + b^2)*d*cosh(d*x + c)^2 + 2*(a*b + b^2)*d*cosh(d*x + c)*sinh(d*x + c) + (a*b + b^2)*d*sinh(d*x + c)^2 + (a*b + b^2)*d)]","B",0
172,1,118,0,0.461587," ","integrate(tanh(d*x+c)^3/(a+b*tanh(d*x+c)^2),x, algorithm=""fricas"")","-\frac{2 \, b d x + a \log\left(\frac{2 \, {\left({\left(a + b\right)} \cosh\left(d x + c\right)^{2} + {\left(a + b\right)} \sinh\left(d x + c\right)^{2} + a - b\right)}}{\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}}\right) - 2 \, {\left(a + b\right)} \log\left(\frac{2 \, \cosh\left(d x + c\right)}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right)}{2 \, {\left(a b + b^{2}\right)} d}"," ",0,"-1/2*(2*b*d*x + a*log(2*((a + b)*cosh(d*x + c)^2 + (a + b)*sinh(d*x + c)^2 + a - b)/(cosh(d*x + c)^2 - 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)) - 2*(a + b)*log(2*cosh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))))/((a*b + b^2)*d)","B",0
173,1,486,0,0.489149," ","integrate(tanh(d*x+c)^2/(a+b*tanh(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{2 \, d x + \sqrt{-\frac{a}{b}} \log\left(\frac{{\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) \sinh\left(d x + c\right)^{3} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{2} + a^{2} - 6 \, a b + b^{2} + 4 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} - 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} + a b - b^{2}\right)} \sqrt{-\frac{a}{b}}}{{\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)}{2 \, {\left(a + b\right)} d}, \frac{d x - \sqrt{\frac{a}{b}} \arctan\left(\frac{{\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} + a - b\right)} \sqrt{\frac{a}{b}}}{2 \, a}\right)}{{\left(a + b\right)} d}\right]"," ",0,"[1/2*(2*d*x + sqrt(-a/b)*log(((a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 + 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 + 2*(a^2 - b^2)*cosh(d*x + c)^2 + 2*(3*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + a^2 - b^2)*sinh(d*x + c)^2 + a^2 - 6*a*b + b^2 + 4*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 + (a^2 - 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 + a*b - b^2)*sqrt(-a/b))/((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)))/((a + b)*d), (d*x - sqrt(a/b)*arctan(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 + a - b)*sqrt(a/b)/a))/((a + b)*d)]","B",0
174,1,82,0,0.414944," ","integrate(tanh(d*x+c)/(a+b*tanh(d*x+c)^2),x, algorithm=""fricas"")","-\frac{2 \, d x - \log\left(\frac{2 \, {\left({\left(a + b\right)} \cosh\left(d x + c\right)^{2} + {\left(a + b\right)} \sinh\left(d x + c\right)^{2} + a - b\right)}}{\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}}\right)}{2 \, {\left(a + b\right)} d}"," ",0,"-1/2*(2*d*x - log(2*((a + b)*cosh(d*x + c)^2 + (a + b)*sinh(d*x + c)^2 + a - b)/(cosh(d*x + c)^2 - 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)))/((a + b)*d)","B",0
175,1,484,0,0.457739," ","integrate(1/(a+b*tanh(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{2 \, d x + \sqrt{-\frac{b}{a}} \log\left(\frac{{\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) \sinh\left(d x + c\right)^{3} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{2} + a^{2} - 6 \, a b + b^{2} + 4 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + 4 \, {\left({\left(a^{2} + a b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} + a b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} + a b\right)} \sinh\left(d x + c\right)^{2} + a^{2} - a b\right)} \sqrt{-\frac{b}{a}}}{{\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)}{2 \, {\left(a + b\right)} d}, \frac{d x + \sqrt{\frac{b}{a}} \arctan\left(\frac{{\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} + a - b\right)} \sqrt{\frac{b}{a}}}{2 \, b}\right)}{{\left(a + b\right)} d}\right]"," ",0,"[1/2*(2*d*x + sqrt(-b/a)*log(((a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 + 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 + 2*(a^2 - b^2)*cosh(d*x + c)^2 + 2*(3*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + a^2 - b^2)*sinh(d*x + c)^2 + a^2 - 6*a*b + b^2 + 4*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 + (a^2 - b^2)*cosh(d*x + c))*sinh(d*x + c) + 4*((a^2 + a*b)*cosh(d*x + c)^2 + 2*(a^2 + a*b)*cosh(d*x + c)*sinh(d*x + c) + (a^2 + a*b)*sinh(d*x + c)^2 + a^2 - a*b)*sqrt(-b/a))/((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)))/((a + b)*d), (d*x + sqrt(b/a)*arctan(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 + a - b)*sqrt(b/a)/b))/((a + b)*d)]","B",0
176,1,118,0,0.452722," ","integrate(coth(d*x+c)/(a+b*tanh(d*x+c)^2),x, algorithm=""fricas"")","-\frac{2 \, a d x + b \log\left(\frac{2 \, {\left({\left(a + b\right)} \cosh\left(d x + c\right)^{2} + {\left(a + b\right)} \sinh\left(d x + c\right)^{2} + a - b\right)}}{\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}}\right) - 2 \, {\left(a + b\right)} \log\left(\frac{2 \, \sinh\left(d x + c\right)}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right)}{2 \, {\left(a^{2} + a b\right)} d}"," ",0,"-1/2*(2*a*d*x + b*log(2*((a + b)*cosh(d*x + c)^2 + (a + b)*sinh(d*x + c)^2 + a - b)/(cosh(d*x + c)^2 - 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)) - 2*(a + b)*log(2*sinh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))))/((a^2 + a*b)*d)","B",0
177,1,784,0,0.453278," ","integrate(coth(d*x+c)^2/(a+b*tanh(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{2 \, a d x \cosh\left(d x + c\right)^{2} + 4 \, a d x \cosh\left(d x + c\right) \sinh\left(d x + c\right) + 2 \, a d x \sinh\left(d x + c\right)^{2} - 2 \, a d x + {\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{-\frac{b}{a}} \log\left(\frac{{\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) \sinh\left(d x + c\right)^{3} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{2} + a^{2} - 6 \, a b + b^{2} + 4 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) - 4 \, {\left({\left(a^{2} + a b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} + a b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} + a b\right)} \sinh\left(d x + c\right)^{2} + a^{2} - a b\right)} \sqrt{-\frac{b}{a}}}{{\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) - 4 \, a - 4 \, b}{2 \, {\left({\left(a^{2} + a b\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} + a b\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} + a b\right)} d \sinh\left(d x + c\right)^{2} - {\left(a^{2} + a b\right)} d\right)}}, \frac{a d x \cosh\left(d x + c\right)^{2} + 2 \, a d x \cosh\left(d x + c\right) \sinh\left(d x + c\right) + a d x \sinh\left(d x + c\right)^{2} - a d x - {\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{\frac{b}{a}} \arctan\left(\frac{{\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} + a - b\right)} \sqrt{\frac{b}{a}}}{2 \, b}\right) - 2 \, a - 2 \, b}{{\left(a^{2} + a b\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} + a b\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} + a b\right)} d \sinh\left(d x + c\right)^{2} - {\left(a^{2} + a b\right)} d}\right]"," ",0,"[1/2*(2*a*d*x*cosh(d*x + c)^2 + 4*a*d*x*cosh(d*x + c)*sinh(d*x + c) + 2*a*d*x*sinh(d*x + c)^2 - 2*a*d*x + (b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 - b)*sqrt(-b/a)*log(((a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 + 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 + 2*(a^2 - b^2)*cosh(d*x + c)^2 + 2*(3*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + a^2 - b^2)*sinh(d*x + c)^2 + a^2 - 6*a*b + b^2 + 4*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 + (a^2 - b^2)*cosh(d*x + c))*sinh(d*x + c) - 4*((a^2 + a*b)*cosh(d*x + c)^2 + 2*(a^2 + a*b)*cosh(d*x + c)*sinh(d*x + c) + (a^2 + a*b)*sinh(d*x + c)^2 + a^2 - a*b)*sqrt(-b/a))/((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)) - 4*a - 4*b)/((a^2 + a*b)*d*cosh(d*x + c)^2 + 2*(a^2 + a*b)*d*cosh(d*x + c)*sinh(d*x + c) + (a^2 + a*b)*d*sinh(d*x + c)^2 - (a^2 + a*b)*d), (a*d*x*cosh(d*x + c)^2 + 2*a*d*x*cosh(d*x + c)*sinh(d*x + c) + a*d*x*sinh(d*x + c)^2 - a*d*x - (b*cosh(d*x + c)^2 + 2*b*cosh(d*x + c)*sinh(d*x + c) + b*sinh(d*x + c)^2 - b)*sqrt(b/a)*arctan(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 + a - b)*sqrt(b/a)/b) - 2*a - 2*b)/((a^2 + a*b)*d*cosh(d*x + c)^2 + 2*(a^2 + a*b)*d*cosh(d*x + c)*sinh(d*x + c) + (a^2 + a*b)*d*sinh(d*x + c)^2 - (a^2 + a*b)*d)]","B",0
178,1,747,0,0.519294," ","integrate(coth(d*x+c)^3/(a+b*tanh(d*x+c)^2),x, algorithm=""fricas"")","-\frac{2 \, a^{2} d x \cosh\left(d x + c\right)^{4} + 8 \, a^{2} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + 2 \, a^{2} d x \sinh\left(d x + c\right)^{4} + 2 \, a^{2} d x - 4 \, {\left(a^{2} d x - a^{2} - a b\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(3 \, a^{2} d x \cosh\left(d x + c\right)^{2} - a^{2} d x + a^{2} + a b\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 \, b^{2} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(d x + c\right)^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{2} + b^{2} + 4 \, {\left(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)} \log\left(\frac{2 \, {\left({\left(a + b\right)} \cosh\left(d x + c\right)^{2} + {\left(a + b\right)} \sinh\left(d x + c\right)^{2} + a - b\right)}}{\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}}\right) - 2 \, {\left({\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{4} - 2 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{2} - a^{2} + b^{2}\right)} \sinh\left(d x + c\right)^{2} + a^{2} - b^{2} + 4 \, {\left({\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{3} - {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\frac{2 \, \sinh\left(d x + c\right)}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) + 8 \, {\left(a^{2} d x \cosh\left(d x + c\right)^{3} - {\left(a^{2} d x - a^{2} - a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{2 \, {\left({\left(a^{3} + a^{2} b\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{3} + a^{2} b\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{3} + a^{2} b\right)} d \sinh\left(d x + c\right)^{4} - 2 \, {\left(a^{3} + a^{2} b\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{3} + a^{2} b\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{3} + a^{2} b\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{3} + a^{2} b\right)} d + 4 \, {\left({\left(a^{3} + a^{2} b\right)} d \cosh\left(d x + c\right)^{3} - {\left(a^{3} + a^{2} b\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"-1/2*(2*a^2*d*x*cosh(d*x + c)^4 + 8*a^2*d*x*cosh(d*x + c)*sinh(d*x + c)^3 + 2*a^2*d*x*sinh(d*x + c)^4 + 2*a^2*d*x - 4*(a^2*d*x - a^2 - a*b)*cosh(d*x + c)^2 + 4*(3*a^2*d*x*cosh(d*x + c)^2 - a^2*d*x + a^2 + a*b)*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*b^2*cosh(d*x + c)^2 + 2*(3*b^2*cosh(d*x + c)^2 - b^2)*sinh(d*x + c)^2 + b^2 + 4*(b^2*cosh(d*x + c)^3 - b^2*cosh(d*x + c))*sinh(d*x + c))*log(2*((a + b)*cosh(d*x + c)^2 + (a + b)*sinh(d*x + c)^2 + a - b)/(cosh(d*x + c)^2 - 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)) - 2*((a^2 - b^2)*cosh(d*x + c)^4 + 4*(a^2 - b^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (a^2 - b^2)*sinh(d*x + c)^4 - 2*(a^2 - b^2)*cosh(d*x + c)^2 + 2*(3*(a^2 - b^2)*cosh(d*x + c)^2 - a^2 + b^2)*sinh(d*x + c)^2 + a^2 - b^2 + 4*((a^2 - b^2)*cosh(d*x + c)^3 - (a^2 - b^2)*cosh(d*x + c))*sinh(d*x + c))*log(2*sinh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))) + 8*(a^2*d*x*cosh(d*x + c)^3 - (a^2*d*x - a^2 - a*b)*cosh(d*x + c))*sinh(d*x + c))/((a^3 + a^2*b)*d*cosh(d*x + c)^4 + 4*(a^3 + a^2*b)*d*cosh(d*x + c)*sinh(d*x + c)^3 + (a^3 + a^2*b)*d*sinh(d*x + c)^4 - 2*(a^3 + a^2*b)*d*cosh(d*x + c)^2 + 2*(3*(a^3 + a^2*b)*d*cosh(d*x + c)^2 - (a^3 + a^2*b)*d)*sinh(d*x + c)^2 + (a^3 + a^2*b)*d + 4*((a^3 + a^2*b)*d*cosh(d*x + c)^3 - (a^3 + a^2*b)*d*cosh(d*x + c))*sinh(d*x + c))","B",0
179,1,2368,0,0.462288," ","integrate(coth(d*x+c)^4/(a+b*tanh(d*x+c)^2),x, algorithm=""fricas"")","\left[\frac{6 \, a^{2} d x \cosh\left(d x + c\right)^{6} + 36 \, a^{2} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + 6 \, a^{2} d x \sinh\left(d x + c\right)^{6} - 6 \, {\left(3 \, a^{2} d x + 4 \, a^{2} + 2 \, a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 6 \, {\left(15 \, a^{2} d x \cosh\left(d x + c\right)^{2} - 3 \, a^{2} d x - 4 \, a^{2} - 2 \, a b + 2 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} - 6 \, a^{2} d x + 24 \, {\left(5 \, a^{2} d x \cosh\left(d x + c\right)^{3} - {\left(3 \, a^{2} d x + 4 \, a^{2} + 2 \, a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 6 \, {\left(3 \, a^{2} d x + 4 \, a^{2} - 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 6 \, {\left(15 \, a^{2} d x \cosh\left(d x + c\right)^{4} + 3 \, a^{2} d x - 6 \, {\left(3 \, a^{2} d x + 4 \, a^{2} + 2 \, a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, a^{2} - 4 \, b^{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{-\frac{b}{a}} \log\left(\frac{{\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) \sinh\left(d x + c\right)^{3} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{2} + a^{2} - 6 \, a b + b^{2} + 4 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + 4 \, {\left({\left(a^{2} + a b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} + a b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} + a b\right)} \sinh\left(d x + c\right)^{2} + a^{2} - a b\right)} \sqrt{-\frac{b}{a}}}{{\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) - 16 \, a^{2} - 4 \, a b + 12 \, b^{2} + 12 \, {\left(3 \, a^{2} d x \cosh\left(d x + c\right)^{5} - 2 \, {\left(3 \, a^{2} d x + 4 \, a^{2} + 2 \, a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{2} d x + 4 \, a^{2} - 4 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{6 \, {\left({\left(a^{3} + a^{2} b\right)} d \cosh\left(d x + c\right)^{6} + 6 \, {\left(a^{3} + a^{2} b\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(a^{3} + a^{2} b\right)} d \sinh\left(d x + c\right)^{6} - 3 \, {\left(a^{3} + a^{2} b\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(5 \, {\left(a^{3} + a^{2} b\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{3} + a^{2} b\right)} d\right)} \sinh\left(d x + c\right)^{4} + 3 \, {\left(a^{3} + a^{2} b\right)} d \cosh\left(d x + c\right)^{2} + 4 \, {\left(5 \, {\left(a^{3} + a^{2} b\right)} d \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{3} + a^{2} b\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 3 \, {\left(5 \, {\left(a^{3} + a^{2} b\right)} d \cosh\left(d x + c\right)^{4} - 6 \, {\left(a^{3} + a^{2} b\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{3} + a^{2} b\right)} d\right)} \sinh\left(d x + c\right)^{2} - {\left(a^{3} + a^{2} b\right)} d + 6 \, {\left({\left(a^{3} + a^{2} b\right)} d \cosh\left(d x + c\right)^{5} - 2 \, {\left(a^{3} + a^{2} b\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{3} + a^{2} b\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}, \frac{3 \, a^{2} d x \cosh\left(d x + c\right)^{6} + 18 \, a^{2} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + 3 \, a^{2} d x \sinh\left(d x + c\right)^{6} - 3 \, {\left(3 \, a^{2} d x + 4 \, a^{2} + 2 \, a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(15 \, a^{2} d x \cosh\left(d x + c\right)^{2} - 3 \, a^{2} d x - 4 \, a^{2} - 2 \, a b + 2 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} - 3 \, a^{2} d x + 12 \, {\left(5 \, a^{2} d x \cosh\left(d x + c\right)^{3} - {\left(3 \, a^{2} d x + 4 \, a^{2} + 2 \, a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 3 \, {\left(3 \, a^{2} d x + 4 \, a^{2} - 4 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 3 \, {\left(15 \, a^{2} d x \cosh\left(d x + c\right)^{4} + 3 \, a^{2} d x - 6 \, {\left(3 \, a^{2} d x + 4 \, a^{2} + 2 \, a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, a^{2} - 4 \, b^{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{\frac{b}{a}} \arctan\left(\frac{{\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} + a - b\right)} \sqrt{\frac{b}{a}}}{2 \, b}\right) - 8 \, a^{2} - 2 \, a b + 6 \, b^{2} + 6 \, {\left(3 \, a^{2} d x \cosh\left(d x + c\right)^{5} - 2 \, {\left(3 \, a^{2} d x + 4 \, a^{2} + 2 \, a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{2} d x + 4 \, a^{2} - 4 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{3 \, {\left({\left(a^{3} + a^{2} b\right)} d \cosh\left(d x + c\right)^{6} + 6 \, {\left(a^{3} + a^{2} b\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(a^{3} + a^{2} b\right)} d \sinh\left(d x + c\right)^{6} - 3 \, {\left(a^{3} + a^{2} b\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(5 \, {\left(a^{3} + a^{2} b\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{3} + a^{2} b\right)} d\right)} \sinh\left(d x + c\right)^{4} + 3 \, {\left(a^{3} + a^{2} b\right)} d \cosh\left(d x + c\right)^{2} + 4 \, {\left(5 \, {\left(a^{3} + a^{2} b\right)} d \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{3} + a^{2} b\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 3 \, {\left(5 \, {\left(a^{3} + a^{2} b\right)} d \cosh\left(d x + c\right)^{4} - 6 \, {\left(a^{3} + a^{2} b\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{3} + a^{2} b\right)} d\right)} \sinh\left(d x + c\right)^{2} - {\left(a^{3} + a^{2} b\right)} d + 6 \, {\left({\left(a^{3} + a^{2} b\right)} d \cosh\left(d x + c\right)^{5} - 2 \, {\left(a^{3} + a^{2} b\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{3} + a^{2} b\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[1/6*(6*a^2*d*x*cosh(d*x + c)^6 + 36*a^2*d*x*cosh(d*x + c)*sinh(d*x + c)^5 + 6*a^2*d*x*sinh(d*x + c)^6 - 6*(3*a^2*d*x + 4*a^2 + 2*a*b - 2*b^2)*cosh(d*x + c)^4 + 6*(15*a^2*d*x*cosh(d*x + c)^2 - 3*a^2*d*x - 4*a^2 - 2*a*b + 2*b^2)*sinh(d*x + c)^4 - 6*a^2*d*x + 24*(5*a^2*d*x*cosh(d*x + c)^3 - (3*a^2*d*x + 4*a^2 + 2*a*b - 2*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 6*(3*a^2*d*x + 4*a^2 - 4*b^2)*cosh(d*x + c)^2 + 6*(15*a^2*d*x*cosh(d*x + c)^4 + 3*a^2*d*x - 6*(3*a^2*d*x + 4*a^2 + 2*a*b - 2*b^2)*cosh(d*x + c)^2 + 4*a^2 - 4*b^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(-b/a)*log(((a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 + 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 + 2*(a^2 - b^2)*cosh(d*x + c)^2 + 2*(3*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + a^2 - b^2)*sinh(d*x + c)^2 + a^2 - 6*a*b + b^2 + 4*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 + (a^2 - b^2)*cosh(d*x + c))*sinh(d*x + c) + 4*((a^2 + a*b)*cosh(d*x + c)^2 + 2*(a^2 + a*b)*cosh(d*x + c)*sinh(d*x + c) + (a^2 + a*b)*sinh(d*x + c)^2 + a^2 - a*b)*sqrt(-b/a))/((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)) - 16*a^2 - 4*a*b + 12*b^2 + 12*(3*a^2*d*x*cosh(d*x + c)^5 - 2*(3*a^2*d*x + 4*a^2 + 2*a*b - 2*b^2)*cosh(d*x + c)^3 + (3*a^2*d*x + 4*a^2 - 4*b^2)*cosh(d*x + c))*sinh(d*x + c))/((a^3 + a^2*b)*d*cosh(d*x + c)^6 + 6*(a^3 + a^2*b)*d*cosh(d*x + c)*sinh(d*x + c)^5 + (a^3 + a^2*b)*d*sinh(d*x + c)^6 - 3*(a^3 + a^2*b)*d*cosh(d*x + c)^4 + 3*(5*(a^3 + a^2*b)*d*cosh(d*x + c)^2 - (a^3 + a^2*b)*d)*sinh(d*x + c)^4 + 3*(a^3 + a^2*b)*d*cosh(d*x + c)^2 + 4*(5*(a^3 + a^2*b)*d*cosh(d*x + c)^3 - 3*(a^3 + a^2*b)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 3*(5*(a^3 + a^2*b)*d*cosh(d*x + c)^4 - 6*(a^3 + a^2*b)*d*cosh(d*x + c)^2 + (a^3 + a^2*b)*d)*sinh(d*x + c)^2 - (a^3 + a^2*b)*d + 6*((a^3 + a^2*b)*d*cosh(d*x + c)^5 - 2*(a^3 + a^2*b)*d*cosh(d*x + c)^3 + (a^3 + a^2*b)*d*cosh(d*x + c))*sinh(d*x + c)), 1/3*(3*a^2*d*x*cosh(d*x + c)^6 + 18*a^2*d*x*cosh(d*x + c)*sinh(d*x + c)^5 + 3*a^2*d*x*sinh(d*x + c)^6 - 3*(3*a^2*d*x + 4*a^2 + 2*a*b - 2*b^2)*cosh(d*x + c)^4 + 3*(15*a^2*d*x*cosh(d*x + c)^2 - 3*a^2*d*x - 4*a^2 - 2*a*b + 2*b^2)*sinh(d*x + c)^4 - 3*a^2*d*x + 12*(5*a^2*d*x*cosh(d*x + c)^3 - (3*a^2*d*x + 4*a^2 + 2*a*b - 2*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 3*(3*a^2*d*x + 4*a^2 - 4*b^2)*cosh(d*x + c)^2 + 3*(15*a^2*d*x*cosh(d*x + c)^4 + 3*a^2*d*x - 6*(3*a^2*d*x + 4*a^2 + 2*a*b - 2*b^2)*cosh(d*x + c)^2 + 4*a^2 - 4*b^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(b/a)*arctan(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 + a - b)*sqrt(b/a)/b) - 8*a^2 - 2*a*b + 6*b^2 + 6*(3*a^2*d*x*cosh(d*x + c)^5 - 2*(3*a^2*d*x + 4*a^2 + 2*a*b - 2*b^2)*cosh(d*x + c)^3 + (3*a^2*d*x + 4*a^2 - 4*b^2)*cosh(d*x + c))*sinh(d*x + c))/((a^3 + a^2*b)*d*cosh(d*x + c)^6 + 6*(a^3 + a^2*b)*d*cosh(d*x + c)*sinh(d*x + c)^5 + (a^3 + a^2*b)*d*sinh(d*x + c)^6 - 3*(a^3 + a^2*b)*d*cosh(d*x + c)^4 + 3*(5*(a^3 + a^2*b)*d*cosh(d*x + c)^2 - (a^3 + a^2*b)*d)*sinh(d*x + c)^4 + 3*(a^3 + a^2*b)*d*cosh(d*x + c)^2 + 4*(5*(a^3 + a^2*b)*d*cosh(d*x + c)^3 - 3*(a^3 + a^2*b)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 3*(5*(a^3 + a^2*b)*d*cosh(d*x + c)^4 - 6*(a^3 + a^2*b)*d*cosh(d*x + c)^2 + (a^3 + a^2*b)*d)*sinh(d*x + c)^2 - (a^3 + a^2*b)*d + 6*((a^3 + a^2*b)*d*cosh(d*x + c)^5 - 2*(a^3 + a^2*b)*d*cosh(d*x + c)^3 + (a^3 + a^2*b)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
180,1,1141,0,0.548930," ","integrate(tanh(d*x+c)^5/(a+b*tanh(d*x+c)^2)^2,x, algorithm=""fricas"")","-\frac{2 \, {\left(a b^{2} + b^{3}\right)} d x \cosh\left(d x + c\right)^{4} + 8 \, {\left(a b^{2} + b^{3}\right)} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + 2 \, {\left(a b^{2} + b^{3}\right)} d x \sinh\left(d x + c\right)^{4} + 2 \, {\left(a b^{2} + b^{3}\right)} d x + 4 \, {\left(a^{2} b + {\left(a b^{2} - b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(3 \, {\left(a b^{2} + b^{3}\right)} d x \cosh\left(d x + c\right)^{2} + a^{2} b + {\left(a b^{2} - b^{3}\right)} d x\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(a^{3} + 3 \, a^{2} b + 2 \, a b^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{3} + 3 \, a^{2} b + 2 \, a b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{3} + 3 \, a^{2} b + 2 \, a b^{2}\right)} \sinh\left(d x + c\right)^{4} + a^{3} + 3 \, a^{2} b + 2 \, a b^{2} + 2 \, {\left(a^{3} + a^{2} b - 2 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{3} + a^{2} b - 2 \, a b^{2} + 3 \, {\left(a^{3} + 3 \, a^{2} b + 2 \, a b^{2}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{3} + 3 \, a^{2} b + 2 \, a b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{3} + a^{2} b - 2 \, a b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\frac{2 \, {\left({\left(a + b\right)} \cosh\left(d x + c\right)^{2} + {\left(a + b\right)} \sinh\left(d x + c\right)^{2} + a - b\right)}}{\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}}\right) - 2 \, {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\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)^{3} + {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \sinh\left(d x + c\right)^{4} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} + 2 \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3} + 3 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\frac{2 \, \cosh\left(d x + c\right)}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) + 8 \, {\left({\left(a b^{2} + b^{3}\right)} d x \cosh\left(d x + c\right)^{3} + {\left(a^{2} b + {\left(a b^{2} - b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{2 \, {\left({\left(a^{3} b^{2} + 3 \, a^{2} b^{3} + 3 \, a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{3} b^{2} + 3 \, a^{2} b^{3} + 3 \, a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{3} b^{2} + 3 \, a^{2} b^{3} + 3 \, a b^{4} + b^{5}\right)} d \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{3} b^{2} + a^{2} b^{3} - a b^{4} - b^{5}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{3} b^{2} + 3 \, a^{2} b^{3} + 3 \, a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{3} b^{2} + a^{2} b^{3} - a b^{4} - b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{3} b^{2} + 3 \, a^{2} b^{3} + 3 \, a b^{4} + b^{5}\right)} d + 4 \, {\left({\left(a^{3} b^{2} + 3 \, a^{2} b^{3} + 3 \, a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{3} b^{2} + a^{2} b^{3} - a b^{4} - b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"-1/2*(2*(a*b^2 + b^3)*d*x*cosh(d*x + c)^4 + 8*(a*b^2 + b^3)*d*x*cosh(d*x + c)*sinh(d*x + c)^3 + 2*(a*b^2 + b^3)*d*x*sinh(d*x + c)^4 + 2*(a*b^2 + b^3)*d*x + 4*(a^2*b + (a*b^2 - b^3)*d*x)*cosh(d*x + c)^2 + 4*(3*(a*b^2 + b^3)*d*x*cosh(d*x + c)^2 + a^2*b + (a*b^2 - b^3)*d*x)*sinh(d*x + c)^2 + ((a^3 + 3*a^2*b + 2*a*b^2)*cosh(d*x + c)^4 + 4*(a^3 + 3*a^2*b + 2*a*b^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (a^3 + 3*a^2*b + 2*a*b^2)*sinh(d*x + c)^4 + a^3 + 3*a^2*b + 2*a*b^2 + 2*(a^3 + a^2*b - 2*a*b^2)*cosh(d*x + c)^2 + 2*(a^3 + a^2*b - 2*a*b^2 + 3*(a^3 + 3*a^2*b + 2*a*b^2)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((a^3 + 3*a^2*b + 2*a*b^2)*cosh(d*x + c)^3 + (a^3 + a^2*b - 2*a*b^2)*cosh(d*x + c))*sinh(d*x + c))*log(2*((a + b)*cosh(d*x + c)^2 + (a + b)*sinh(d*x + c)^2 + a - b)/(cosh(d*x + c)^2 - 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)) - 2*((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^4 + 4*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)*sinh(d*x + c)^3 + (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*sinh(d*x + c)^4 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 + 2*(a^3 + a^2*b - a*b^2 - b^3)*cosh(d*x + c)^2 + 2*(a^3 + a^2*b - a*b^2 - b^3 + 3*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^3 + (a^3 + a^2*b - a*b^2 - b^3)*cosh(d*x + c))*sinh(d*x + c))*log(2*cosh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))) + 8*((a*b^2 + b^3)*d*x*cosh(d*x + c)^3 + (a^2*b + (a*b^2 - b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c))/((a^3*b^2 + 3*a^2*b^3 + 3*a*b^4 + b^5)*d*cosh(d*x + c)^4 + 4*(a^3*b^2 + 3*a^2*b^3 + 3*a*b^4 + b^5)*d*cosh(d*x + c)*sinh(d*x + c)^3 + (a^3*b^2 + 3*a^2*b^3 + 3*a*b^4 + b^5)*d*sinh(d*x + c)^4 + 2*(a^3*b^2 + a^2*b^3 - a*b^4 - b^5)*d*cosh(d*x + c)^2 + 2*(3*(a^3*b^2 + 3*a^2*b^3 + 3*a*b^4 + b^5)*d*cosh(d*x + c)^2 + (a^3*b^2 + a^2*b^3 - a*b^4 - b^5)*d)*sinh(d*x + c)^2 + (a^3*b^2 + 3*a^2*b^3 + 3*a*b^4 + b^5)*d + 4*((a^3*b^2 + 3*a^2*b^3 + 3*a*b^4 + b^5)*d*cosh(d*x + c)^3 + (a^3*b^2 + a^2*b^3 - a*b^4 - b^5)*d*cosh(d*x + c))*sinh(d*x + c))","B",0
181,1,1950,0,0.477350," ","integrate(tanh(d*x+c)^4/(a+b*tanh(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(a b - b^{2}\right)} d x - 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(a b - b^{2}\right)} d x - a^{2} + a b\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(a^{2} + 4 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{2} + 4 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{2} + 4 \, a b + 3 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{2} + 2 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} + 4 \, 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)^{2} + a^{2} + 4 \, a b + 3 \, b^{2} + 4 \, {\left({\left(a^{2} + 4 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} + 2 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{a}{b}} \log\left(\frac{{\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) \sinh\left(d x + c\right)^{3} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{2} + a^{2} - 6 \, a b + b^{2} + 4 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} - 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} + a b - b^{2}\right)} \sqrt{-\frac{a}{b}}}{{\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) - 4 \, a^{2} - 4 \, a b + 8 \, {\left(2 \, {\left(a b + b^{2}\right)} d x \cosh\left(d x + c\right)^{3} + {\left(2 \, {\left(a b - b^{2}\right)} d x - a^{2} + a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{4 \, {\left({\left(a^{3} b + 3 \, a^{2} b^{2} + 3 \, a b^{3} + b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{3} b + 3 \, a^{2} b^{2} + 3 \, a b^{3} + b^{4}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{3} b + 3 \, a^{2} b^{2} + 3 \, a b^{3} + b^{4}\right)} d \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{3} b + a^{2} b^{2} - a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{3} b + 3 \, a^{2} b^{2} + 3 \, a b^{3} + b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{3} b + a^{2} b^{2} - a b^{3} - b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{3} b + 3 \, a^{2} b^{2} + 3 \, a b^{3} + b^{4}\right)} d + 4 \, {\left({\left(a^{3} b + 3 \, a^{2} b^{2} + 3 \, a b^{3} + b^{4}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{3} b + a^{2} b^{2} - 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(a b - b^{2}\right)} d x - 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(a b - b^{2}\right)} d x - a^{2} + a b\right)} \sinh\left(d x + c\right)^{2} - {\left({\left(a^{2} + 4 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{2} + 4 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{2} + 4 \, a b + 3 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{2} + 2 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} + 4 \, 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)^{2} + a^{2} + 4 \, a b + 3 \, b^{2} + 4 \, {\left({\left(a^{2} + 4 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} + 2 \, a b - 3 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a}{b}} \arctan\left(\frac{{\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} + a - b\right)} \sqrt{\frac{a}{b}}}{2 \, a}\right) - 2 \, a^{2} - 2 \, a b + 4 \, {\left(2 \, {\left(a b + b^{2}\right)} d x \cosh\left(d x + c\right)^{3} + {\left(2 \, {\left(a b - b^{2}\right)} d x - a^{2} + a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{2 \, {\left({\left(a^{3} b + 3 \, a^{2} b^{2} + 3 \, a b^{3} + b^{4}\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{3} b + 3 \, a^{2} b^{2} + 3 \, a b^{3} + b^{4}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{3} b + 3 \, a^{2} b^{2} + 3 \, a b^{3} + b^{4}\right)} d \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{3} b + a^{2} b^{2} - a b^{3} - b^{4}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{3} b + 3 \, a^{2} b^{2} + 3 \, a b^{3} + b^{4}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{3} b + a^{2} b^{2} - a b^{3} - b^{4}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{3} b + 3 \, a^{2} b^{2} + 3 \, a b^{3} + b^{4}\right)} d + 4 \, {\left({\left(a^{3} b + 3 \, a^{2} b^{2} + 3 \, a b^{3} + b^{4}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{3} b + a^{2} b^{2} - 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*(a*b - b^2)*d*x - a^2 + a*b)*cosh(d*x + c)^2 + 4*(6*(a*b + b^2)*d*x*cosh(d*x + c)^2 + 2*(a*b - b^2)*d*x - a^2 + a*b)*sinh(d*x + c)^2 + ((a^2 + 4*a*b + 3*b^2)*cosh(d*x + c)^4 + 4*(a^2 + 4*a*b + 3*b^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (a^2 + 4*a*b + 3*b^2)*sinh(d*x + c)^4 + 2*(a^2 + 2*a*b - 3*b^2)*cosh(d*x + c)^2 + 2*(3*(a^2 + 4*a*b + 3*b^2)*cosh(d*x + c)^2 + a^2 + 2*a*b - 3*b^2)*sinh(d*x + c)^2 + a^2 + 4*a*b + 3*b^2 + 4*((a^2 + 4*a*b + 3*b^2)*cosh(d*x + c)^3 + (a^2 + 2*a*b - 3*b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-a/b)*log(((a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 + 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 + 2*(a^2 - b^2)*cosh(d*x + c)^2 + 2*(3*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + a^2 - b^2)*sinh(d*x + c)^2 + a^2 - 6*a*b + b^2 + 4*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 + (a^2 - 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 + a*b - b^2)*sqrt(-a/b))/((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)) - 4*a^2 - 4*a*b + 8*(2*(a*b + b^2)*d*x*cosh(d*x + c)^3 + (2*(a*b - b^2)*d*x - a^2 + a*b)*cosh(d*x + c))*sinh(d*x + c))/((a^3*b + 3*a^2*b^2 + 3*a*b^3 + b^4)*d*cosh(d*x + c)^4 + 4*(a^3*b + 3*a^2*b^2 + 3*a*b^3 + b^4)*d*cosh(d*x + c)*sinh(d*x + c)^3 + (a^3*b + 3*a^2*b^2 + 3*a*b^3 + b^4)*d*sinh(d*x + c)^4 + 2*(a^3*b + a^2*b^2 - a*b^3 - b^4)*d*cosh(d*x + c)^2 + 2*(3*(a^3*b + 3*a^2*b^2 + 3*a*b^3 + b^4)*d*cosh(d*x + c)^2 + (a^3*b + a^2*b^2 - a*b^3 - b^4)*d)*sinh(d*x + c)^2 + (a^3*b + 3*a^2*b^2 + 3*a*b^3 + b^4)*d + 4*((a^3*b + 3*a^2*b^2 + 3*a*b^3 + b^4)*d*cosh(d*x + c)^3 + (a^3*b + a^2*b^2 - 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*(a*b - b^2)*d*x - a^2 + a*b)*cosh(d*x + c)^2 + 2*(6*(a*b + b^2)*d*x*cosh(d*x + c)^2 + 2*(a*b - b^2)*d*x - a^2 + a*b)*sinh(d*x + c)^2 - ((a^2 + 4*a*b + 3*b^2)*cosh(d*x + c)^4 + 4*(a^2 + 4*a*b + 3*b^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (a^2 + 4*a*b + 3*b^2)*sinh(d*x + c)^4 + 2*(a^2 + 2*a*b - 3*b^2)*cosh(d*x + c)^2 + 2*(3*(a^2 + 4*a*b + 3*b^2)*cosh(d*x + c)^2 + a^2 + 2*a*b - 3*b^2)*sinh(d*x + c)^2 + a^2 + 4*a*b + 3*b^2 + 4*((a^2 + 4*a*b + 3*b^2)*cosh(d*x + c)^3 + (a^2 + 2*a*b - 3*b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(a/b)*arctan(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 + a - b)*sqrt(a/b)/a) - 2*a^2 - 2*a*b + 4*(2*(a*b + b^2)*d*x*cosh(d*x + c)^3 + (2*(a*b - b^2)*d*x - a^2 + a*b)*cosh(d*x + c))*sinh(d*x + c))/((a^3*b + 3*a^2*b^2 + 3*a*b^3 + b^4)*d*cosh(d*x + c)^4 + 4*(a^3*b + 3*a^2*b^2 + 3*a*b^3 + b^4)*d*cosh(d*x + c)*sinh(d*x + c)^3 + (a^3*b + 3*a^2*b^2 + 3*a*b^3 + b^4)*d*sinh(d*x + c)^4 + 2*(a^3*b + a^2*b^2 - a*b^3 - b^4)*d*cosh(d*x + c)^2 + 2*(3*(a^3*b + 3*a^2*b^2 + 3*a*b^3 + b^4)*d*cosh(d*x + c)^2 + (a^3*b + a^2*b^2 - a*b^3 - b^4)*d)*sinh(d*x + c)^2 + (a^3*b + 3*a^2*b^2 + 3*a*b^3 + b^4)*d + 4*((a^3*b + 3*a^2*b^2 + 3*a*b^3 + b^4)*d*cosh(d*x + c)^3 + (a^3*b + a^2*b^2 - a*b^3 - b^4)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
182,1,629,0,0.466321," ","integrate(tanh(d*x+c)^3/(a+b*tanh(d*x+c)^2)^2,x, algorithm=""fricas"")","-\frac{2 \, {\left(a + b\right)} d x \cosh\left(d x + c\right)^{4} + 8 \, {\left(a + b\right)} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + 2 \, {\left(a + b\right)} d x \sinh\left(d x + c\right)^{4} + 2 \, {\left(a + b\right)} d x + 4 \, {\left({\left(a - b\right)} d x - a\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(3 \, {\left(a + b\right)} d x \cosh\left(d x + c\right)^{2} + {\left(a - b\right)} d x - a\right)} \sinh\left(d x + c\right)^{2} - {\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)} \log\left(\frac{2 \, {\left({\left(a + b\right)} \cosh\left(d x + c\right)^{2} + {\left(a + b\right)} \sinh\left(d x + c\right)^{2} + a - b\right)}}{\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}}\right) + 8 \, {\left({\left(a + b\right)} d x \cosh\left(d x + c\right)^{3} + {\left({\left(a - b\right)} d x - a\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{2 \, {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d \cosh\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) \sinh\left(d x + c\right)^{3} + {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\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} + a^{2} b - 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 + 4 \, {\left({\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} + a^{2} b - a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"-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 + 4*((a - b)*d*x - a)*cosh(d*x + c)^2 + 4*(3*(a + b)*d*x*cosh(d*x + c)^2 + (a - b)*d*x - a)*sinh(d*x + c)^2 - ((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)*log(2*((a + b)*cosh(d*x + c)^2 + (a + b)*sinh(d*x + c)^2 + a - b)/(cosh(d*x + c)^2 - 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)) + 8*((a + b)*d*x*cosh(d*x + c)^3 + ((a - b)*d*x - a)*cosh(d*x + c))*sinh(d*x + c))/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*cosh(d*x + c)^4 + 4*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*cosh(d*x + c)*sinh(d*x + c)^3 + (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*sinh(d*x + c)^4 + 2*(a^3 + a^2*b - a*b^2 - b^3)*d*cosh(d*x + c)^2 + 2*(3*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*cosh(d*x + c)^2 + (a^3 + a^2*b - a*b^2 - b^3)*d)*sinh(d*x + c)^2 + (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d + 4*((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*cosh(d*x + c)^3 + (a^3 + a^2*b - a*b^2 - b^3)*d*cosh(d*x + c))*sinh(d*x + c))","B",0
183,1,2025,0,0.461231," ","integrate(tanh(d*x+c)^2/(a+b*tanh(d*x+c)^2)^2,x, algorithm=""fricas"")","\left[\frac{4 \, {\left(a^{2} b + a b^{2}\right)} d x \cosh\left(d x + c\right)^{4} + 16 \, {\left(a^{2} b + a b^{2}\right)} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + 4 \, {\left(a^{2} b + a b^{2}\right)} d x \sinh\left(d x + c\right)^{4} + 4 \, a^{2} b + 4 \, a b^{2} + 4 \, {\left(a^{2} b + a b^{2}\right)} d x + 4 \, {\left(a^{2} b - a b^{2} + 2 \, {\left(a^{2} b - a b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(6 \, {\left(a^{2} b + a b^{2}\right)} d x \cosh\left(d x + c\right)^{2} + a^{2} b - a b^{2} + 2 \, {\left(a^{2} b - a b^{2}\right)} d x\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} - 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{2} + a^{2} - b^{2} + 4 \, {\left({\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} - 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{{\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) \sinh\left(d x + c\right)^{3} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{2} + a^{2} - 6 \, a b + b^{2} + 4 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} - b^{2}\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)^{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} + a - b\right)} \sqrt{-a b}}{{\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) + 8 \, {\left(2 \, {\left(a^{2} b + a b^{2}\right)} d x \cosh\left(d x + c\right)^{3} + {\left(a^{2} b - a b^{2} + 2 \, {\left(a^{2} b - a b^{2}\right)} d x\right)} \cosh\left(d x + c\right)\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)^{4} + 4 \, {\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)^{3} + {\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)^{4} + 2 \, {\left(a^{4} b + a^{3} b^{2} - a^{2} b^{3} - a b^{4}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\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^{4} b + a^{3} b^{2} - a^{2} b^{3} - a b^{4}\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 + 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)^{3} + {\left(a^{4} b + a^{3} b^{2} - 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 \, {\left(a^{2} b + a b^{2}\right)} d x \cosh\left(d x + c\right)^{4} + 8 \, {\left(a^{2} b + a b^{2}\right)} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + 2 \, {\left(a^{2} b + a b^{2}\right)} d x \sinh\left(d x + c\right)^{4} + 2 \, a^{2} b + 2 \, a b^{2} + 2 \, {\left(a^{2} b + a b^{2}\right)} d x + 2 \, {\left(a^{2} b - a b^{2} + 2 \, {\left(a^{2} b - a b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(6 \, {\left(a^{2} b + a b^{2}\right)} d x \cosh\left(d x + c\right)^{2} + a^{2} b - a b^{2} + 2 \, {\left(a^{2} b - a b^{2}\right)} d x\right)} \sinh\left(d x + c\right)^{2} - {\left({\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(a^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} - 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{2} + a^{2} - b^{2} + 4 \, {\left({\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} - 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({\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} + a - b\right)} \sqrt{a b}}{2 \, a b}\right) + 4 \, {\left(2 \, {\left(a^{2} b + a b^{2}\right)} d x \cosh\left(d x + c\right)^{3} + {\left(a^{2} b - a b^{2} + 2 \, {\left(a^{2} b - a b^{2}\right)} d x\right)} \cosh\left(d x + c\right)\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)^{4} + 4 \, {\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)^{3} + {\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)^{4} + 2 \, {\left(a^{4} b + a^{3} b^{2} - a^{2} b^{3} - a b^{4}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\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^{4} b + a^{3} b^{2} - a^{2} b^{3} - a b^{4}\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 + 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)^{3} + {\left(a^{4} b + a^{3} b^{2} - 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 + a*b^2)*d*x*cosh(d*x + c)^4 + 16*(a^2*b + a*b^2)*d*x*cosh(d*x + c)*sinh(d*x + c)^3 + 4*(a^2*b + a*b^2)*d*x*sinh(d*x + c)^4 + 4*a^2*b + 4*a*b^2 + 4*(a^2*b + a*b^2)*d*x + 4*(a^2*b - a*b^2 + 2*(a^2*b - a*b^2)*d*x)*cosh(d*x + c)^2 + 4*(6*(a^2*b + a*b^2)*d*x*cosh(d*x + c)^2 + a^2*b - a*b^2 + 2*(a^2*b - a*b^2)*d*x)*sinh(d*x + c)^2 + ((a^2 - b^2)*cosh(d*x + c)^4 + 4*(a^2 - b^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (a^2 - b^2)*sinh(d*x + c)^4 + 2*(a^2 - 2*a*b + b^2)*cosh(d*x + c)^2 + 2*(3*(a^2 - b^2)*cosh(d*x + c)^2 + a^2 - 2*a*b + b^2)*sinh(d*x + c)^2 + a^2 - b^2 + 4*((a^2 - b^2)*cosh(d*x + c)^3 + (a^2 - 2*a*b + b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-a*b)*log(((a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 + 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 + 2*(a^2 - b^2)*cosh(d*x + c)^2 + 2*(3*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + a^2 - b^2)*sinh(d*x + c)^2 + a^2 - 6*a*b + b^2 + 4*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 + (a^2 - 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 + a - b)*sqrt(-a*b))/((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)) + 8*(2*(a^2*b + a*b^2)*d*x*cosh(d*x + c)^3 + (a^2*b - a*b^2 + 2*(a^2*b - a*b^2)*d*x)*cosh(d*x + c))*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)^4 + 4*(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)^3 + (a^4*b + 3*a^3*b^2 + 3*a^2*b^3 + a*b^4)*d*sinh(d*x + c)^4 + 2*(a^4*b + a^3*b^2 - a^2*b^3 - a*b^4)*d*cosh(d*x + c)^2 + 2*(3*(a^4*b + 3*a^3*b^2 + 3*a^2*b^3 + a*b^4)*d*cosh(d*x + c)^2 + (a^4*b + a^3*b^2 - a^2*b^3 - a*b^4)*d)*sinh(d*x + c)^2 + (a^4*b + 3*a^3*b^2 + 3*a^2*b^3 + a*b^4)*d + 4*((a^4*b + 3*a^3*b^2 + 3*a^2*b^3 + a*b^4)*d*cosh(d*x + c)^3 + (a^4*b + a^3*b^2 - a^2*b^3 - a*b^4)*d*cosh(d*x + c))*sinh(d*x + c)), 1/2*(2*(a^2*b + a*b^2)*d*x*cosh(d*x + c)^4 + 8*(a^2*b + a*b^2)*d*x*cosh(d*x + c)*sinh(d*x + c)^3 + 2*(a^2*b + a*b^2)*d*x*sinh(d*x + c)^4 + 2*a^2*b + 2*a*b^2 + 2*(a^2*b + a*b^2)*d*x + 2*(a^2*b - a*b^2 + 2*(a^2*b - a*b^2)*d*x)*cosh(d*x + c)^2 + 2*(6*(a^2*b + a*b^2)*d*x*cosh(d*x + c)^2 + a^2*b - a*b^2 + 2*(a^2*b - a*b^2)*d*x)*sinh(d*x + c)^2 - ((a^2 - b^2)*cosh(d*x + c)^4 + 4*(a^2 - b^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (a^2 - b^2)*sinh(d*x + c)^4 + 2*(a^2 - 2*a*b + b^2)*cosh(d*x + c)^2 + 2*(3*(a^2 - b^2)*cosh(d*x + c)^2 + a^2 - 2*a*b + b^2)*sinh(d*x + c)^2 + a^2 - b^2 + 4*((a^2 - b^2)*cosh(d*x + c)^3 + (a^2 - 2*a*b + b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(a*b)*arctan(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 + a - b)*sqrt(a*b)/(a*b)) + 4*(2*(a^2*b + a*b^2)*d*x*cosh(d*x + c)^3 + (a^2*b - a*b^2 + 2*(a^2*b - a*b^2)*d*x)*cosh(d*x + c))*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)^4 + 4*(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)^3 + (a^4*b + 3*a^3*b^2 + 3*a^2*b^3 + a*b^4)*d*sinh(d*x + c)^4 + 2*(a^4*b + a^3*b^2 - a^2*b^3 - a*b^4)*d*cosh(d*x + c)^2 + 2*(3*(a^4*b + 3*a^3*b^2 + 3*a^2*b^3 + a*b^4)*d*cosh(d*x + c)^2 + (a^4*b + a^3*b^2 - a^2*b^3 - a*b^4)*d)*sinh(d*x + c)^2 + (a^4*b + 3*a^3*b^2 + 3*a^2*b^3 + a*b^4)*d + 4*((a^4*b + 3*a^3*b^2 + 3*a^2*b^3 + a*b^4)*d*cosh(d*x + c)^3 + (a^4*b + a^3*b^2 - a^2*b^3 - a*b^4)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
184,1,623,0,0.442580," ","integrate(tanh(d*x+c)/(a+b*tanh(d*x+c)^2)^2,x, algorithm=""fricas"")","-\frac{2 \, {\left(a + b\right)} d x \cosh\left(d x + c\right)^{4} + 8 \, {\left(a + b\right)} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + 2 \, {\left(a + b\right)} d x \sinh\left(d x + c\right)^{4} + 2 \, {\left(a + b\right)} d x + 4 \, {\left({\left(a - b\right)} d x + b\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(3 \, {\left(a + b\right)} d x \cosh\left(d x + c\right)^{2} + {\left(a - b\right)} d x + b\right)} \sinh\left(d x + c\right)^{2} - {\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)} \log\left(\frac{2 \, {\left({\left(a + b\right)} \cosh\left(d x + c\right)^{2} + {\left(a + b\right)} \sinh\left(d x + c\right)^{2} + a - b\right)}}{\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}}\right) + 8 \, {\left({\left(a + b\right)} d x \cosh\left(d x + c\right)^{3} + {\left({\left(a - b\right)} d x + b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{2 \, {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d \cosh\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) \sinh\left(d x + c\right)^{3} + {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} d \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\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} + a^{2} b - 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 + 4 \, {\left({\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} + a^{2} b - a b^{2} - b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"-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 + 4*((a - b)*d*x + b)*cosh(d*x + c)^2 + 4*(3*(a + b)*d*x*cosh(d*x + c)^2 + (a - b)*d*x + b)*sinh(d*x + c)^2 - ((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)*log(2*((a + b)*cosh(d*x + c)^2 + (a + b)*sinh(d*x + c)^2 + a - b)/(cosh(d*x + c)^2 - 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)) + 8*((a + b)*d*x*cosh(d*x + c)^3 + ((a - b)*d*x + b)*cosh(d*x + c))*sinh(d*x + c))/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*cosh(d*x + c)^4 + 4*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*cosh(d*x + c)*sinh(d*x + c)^3 + (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*sinh(d*x + c)^4 + 2*(a^3 + a^2*b - a*b^2 - b^3)*d*cosh(d*x + c)^2 + 2*(3*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*cosh(d*x + c)^2 + (a^3 + a^2*b - a*b^2 - b^3)*d)*sinh(d*x + c)^2 + (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d + 4*((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*d*cosh(d*x + c)^3 + (a^3 + a^2*b - a*b^2 - b^3)*d*cosh(d*x + c))*sinh(d*x + c))","B",0
185,1,1942,0,0.472891," ","integrate(1/(a+b*tanh(d*x+c)^2)^2,x, algorithm=""fricas"")","\left[\frac{4 \, {\left(a^{2} + a b\right)} d x \cosh\left(d x + c\right)^{4} + 16 \, {\left(a^{2} + a b\right)} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + 4 \, {\left(a^{2} + a b\right)} d x \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{2} + a b\right)} d x + 4 \, {\left(2 \, {\left(a^{2} - a b\right)} d x - a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(6 \, {\left(a^{2} + a b\right)} d x \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} - a b\right)} d x - a b + b^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(3 \, a^{2} + 4 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(3 \, a^{2} + 4 \, a b + b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(3 \, a^{2} + 4 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(3 \, a^{2} - 2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(3 \, a^{2} + 4 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 3 \, a^{2} - 2 \, a b - b^{2}\right)} \sinh\left(d x + c\right)^{2} + 3 \, a^{2} + 4 \, a b + b^{2} + 4 \, {\left({\left(3 \, a^{2} + 4 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{2} - 2 \, 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{{\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) \sinh\left(d x + c\right)^{3} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{2} + a^{2} - 6 \, a b + b^{2} + 4 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + 4 \, {\left({\left(a^{2} + a b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} + a b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} + a b\right)} \sinh\left(d x + c\right)^{2} + a^{2} - a b\right)} \sqrt{-\frac{b}{a}}}{{\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) - 4 \, a b - 4 \, b^{2} + 8 \, {\left(2 \, {\left(a^{2} + a b\right)} d x \cosh\left(d x + c\right)^{3} + {\left(2 \, {\left(a^{2} - a b\right)} d x - a b + b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{4 \, {\left({\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\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)^{3} + {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} d \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{4} + a^{3} b - a^{2} b^{2} - a b^{3}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(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} + {\left(a^{4} + a^{3} b - 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 + 4 \, {\left({\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} + a^{3} b - 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^{2} + a b\right)} d x \cosh\left(d x + c\right)^{4} + 8 \, {\left(a^{2} + a b\right)} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + 2 \, {\left(a^{2} + a b\right)} d x \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{2} + a b\right)} d x + 2 \, {\left(2 \, {\left(a^{2} - a b\right)} d x - a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(6 \, {\left(a^{2} + a b\right)} d x \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} - a b\right)} d x - a b + b^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(3 \, a^{2} + 4 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(3 \, a^{2} + 4 \, a b + b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(3 \, a^{2} + 4 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(3 \, a^{2} - 2 \, a b - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(3 \, a^{2} + 4 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 3 \, a^{2} - 2 \, a b - b^{2}\right)} \sinh\left(d x + c\right)^{2} + 3 \, a^{2} + 4 \, a b + b^{2} + 4 \, {\left({\left(3 \, a^{2} + 4 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{2} - 2 \, 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({\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} + a - b\right)} \sqrt{\frac{b}{a}}}{2 \, b}\right) - 2 \, a b - 2 \, b^{2} + 4 \, {\left(2 \, {\left(a^{2} + a b\right)} d x \cosh\left(d x + c\right)^{3} + {\left(2 \, {\left(a^{2} - a b\right)} d x - a b + b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{2 \, {\left({\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\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)^{3} + {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} d \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{4} + a^{3} b - a^{2} b^{2} - a b^{3}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(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} + {\left(a^{4} + a^{3} b - 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 + 4 \, {\left({\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} + a^{3} b - 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^2 + a*b)*d*x*cosh(d*x + c)^4 + 16*(a^2 + a*b)*d*x*cosh(d*x + c)*sinh(d*x + c)^3 + 4*(a^2 + a*b)*d*x*sinh(d*x + c)^4 + 4*(a^2 + a*b)*d*x + 4*(2*(a^2 - a*b)*d*x - a*b + b^2)*cosh(d*x + c)^2 + 4*(6*(a^2 + a*b)*d*x*cosh(d*x + c)^2 + 2*(a^2 - a*b)*d*x - a*b + b^2)*sinh(d*x + c)^2 + ((3*a^2 + 4*a*b + b^2)*cosh(d*x + c)^4 + 4*(3*a^2 + 4*a*b + b^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (3*a^2 + 4*a*b + b^2)*sinh(d*x + c)^4 + 2*(3*a^2 - 2*a*b - b^2)*cosh(d*x + c)^2 + 2*(3*(3*a^2 + 4*a*b + b^2)*cosh(d*x + c)^2 + 3*a^2 - 2*a*b - b^2)*sinh(d*x + c)^2 + 3*a^2 + 4*a*b + b^2 + 4*((3*a^2 + 4*a*b + b^2)*cosh(d*x + c)^3 + (3*a^2 - 2*a*b - b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-b/a)*log(((a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 + 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 + 2*(a^2 - b^2)*cosh(d*x + c)^2 + 2*(3*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + a^2 - b^2)*sinh(d*x + c)^2 + a^2 - 6*a*b + b^2 + 4*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 + (a^2 - b^2)*cosh(d*x + c))*sinh(d*x + c) + 4*((a^2 + a*b)*cosh(d*x + c)^2 + 2*(a^2 + a*b)*cosh(d*x + c)*sinh(d*x + c) + (a^2 + a*b)*sinh(d*x + c)^2 + a^2 - a*b)*sqrt(-b/a))/((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)) - 4*a*b - 4*b^2 + 8*(2*(a^2 + a*b)*d*x*cosh(d*x + c)^3 + (2*(a^2 - a*b)*d*x - a*b + 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)^4 + 4*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d*cosh(d*x + c)*sinh(d*x + c)^3 + (a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d*sinh(d*x + c)^4 + 2*(a^4 + a^3*b - a^2*b^2 - a*b^3)*d*cosh(d*x + c)^2 + 2*(3*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d*cosh(d*x + c)^2 + (a^4 + a^3*b - 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 + 4*((a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d*cosh(d*x + c)^3 + (a^4 + a^3*b - a^2*b^2 - a*b^3)*d*cosh(d*x + c))*sinh(d*x + c)), 1/2*(2*(a^2 + a*b)*d*x*cosh(d*x + c)^4 + 8*(a^2 + a*b)*d*x*cosh(d*x + c)*sinh(d*x + c)^3 + 2*(a^2 + a*b)*d*x*sinh(d*x + c)^4 + 2*(a^2 + a*b)*d*x + 2*(2*(a^2 - a*b)*d*x - a*b + b^2)*cosh(d*x + c)^2 + 2*(6*(a^2 + a*b)*d*x*cosh(d*x + c)^2 + 2*(a^2 - a*b)*d*x - a*b + b^2)*sinh(d*x + c)^2 + ((3*a^2 + 4*a*b + b^2)*cosh(d*x + c)^4 + 4*(3*a^2 + 4*a*b + b^2)*cosh(d*x + c)*sinh(d*x + c)^3 + (3*a^2 + 4*a*b + b^2)*sinh(d*x + c)^4 + 2*(3*a^2 - 2*a*b - b^2)*cosh(d*x + c)^2 + 2*(3*(3*a^2 + 4*a*b + b^2)*cosh(d*x + c)^2 + 3*a^2 - 2*a*b - b^2)*sinh(d*x + c)^2 + 3*a^2 + 4*a*b + b^2 + 4*((3*a^2 + 4*a*b + b^2)*cosh(d*x + c)^3 + (3*a^2 - 2*a*b - b^2)*cosh(d*x + c))*sinh(d*x + c))*sqrt(b/a)*arctan(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 + a - b)*sqrt(b/a)/b) - 2*a*b - 2*b^2 + 4*(2*(a^2 + a*b)*d*x*cosh(d*x + c)^3 + (2*(a^2 - a*b)*d*x - a*b + 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)^4 + 4*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d*cosh(d*x + c)*sinh(d*x + c)^3 + (a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d*sinh(d*x + c)^4 + 2*(a^4 + a^3*b - a^2*b^2 - a*b^3)*d*cosh(d*x + c)^2 + 2*(3*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d*cosh(d*x + c)^2 + (a^4 + a^3*b - 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 + 4*((a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*d*cosh(d*x + c)^3 + (a^4 + a^3*b - a^2*b^2 - a*b^3)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
186,1,1148,0,0.563218," ","integrate(coth(d*x+c)/(a+b*tanh(d*x+c)^2)^2,x, algorithm=""fricas"")","-\frac{2 \, {\left(a^{3} + a^{2} b\right)} d x \cosh\left(d x + c\right)^{4} + 8 \, {\left(a^{3} + a^{2} b\right)} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + 2 \, {\left(a^{3} + a^{2} b\right)} d x \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{3} + a^{2} b\right)} d x - 4 \, {\left(a b^{2} - {\left(a^{3} - a^{2} b\right)} d x\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(3 \, {\left(a^{3} + a^{2} b\right)} d x \cosh\left(d x + c\right)^{2} - a b^{2} + {\left(a^{3} - a^{2} b\right)} d x\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(2 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(2 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{3} + {\left(2 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \sinh\left(d x + c\right)^{4} + 2 \, a^{2} b + 3 \, a b^{2} + b^{3} + 2 \, {\left(2 \, a^{2} b - a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(2 \, a^{2} b - a b^{2} - b^{3} + 3 \, {\left(2 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(2 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{2} b - a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\frac{2 \, {\left({\left(a + b\right)} \cosh\left(d x + c\right)^{2} + {\left(a + b\right)} \sinh\left(d x + c\right)^{2} + a - b\right)}}{\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}}\right) - 2 \, {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\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)^{3} + {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \sinh\left(d x + c\right)^{4} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} + 2 \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3} + 3 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\frac{2 \, \sinh\left(d x + c\right)}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) + 8 \, {\left({\left(a^{3} + a^{2} b\right)} d x \cosh\left(d x + c\right)^{3} - {\left(a b^{2} - {\left(a^{3} - a^{2} b\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{2 \, {\left({\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} + 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) \sinh\left(d x + c\right)^{3} + {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} d \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{5} + a^{4} b - a^{3} b^{2} - a^{2} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + 2 \, {\left(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)^{2} + {\left(a^{5} + a^{4} b - a^{3} b^{2} - a^{2} b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} d + 4 \, {\left({\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(a^{5} + a^{4} b - a^{3} b^{2} - a^{2} b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"-1/2*(2*(a^3 + a^2*b)*d*x*cosh(d*x + c)^4 + 8*(a^3 + a^2*b)*d*x*cosh(d*x + c)*sinh(d*x + c)^3 + 2*(a^3 + a^2*b)*d*x*sinh(d*x + c)^4 + 2*(a^3 + a^2*b)*d*x - 4*(a*b^2 - (a^3 - a^2*b)*d*x)*cosh(d*x + c)^2 + 4*(3*(a^3 + a^2*b)*d*x*cosh(d*x + c)^2 - a*b^2 + (a^3 - a^2*b)*d*x)*sinh(d*x + c)^2 + ((2*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^4 + 4*(2*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)*sinh(d*x + c)^3 + (2*a^2*b + 3*a*b^2 + b^3)*sinh(d*x + c)^4 + 2*a^2*b + 3*a*b^2 + b^3 + 2*(2*a^2*b - a*b^2 - b^3)*cosh(d*x + c)^2 + 2*(2*a^2*b - a*b^2 - b^3 + 3*(2*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((2*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^3 + (2*a^2*b - a*b^2 - b^3)*cosh(d*x + c))*sinh(d*x + c))*log(2*((a + b)*cosh(d*x + c)^2 + (a + b)*sinh(d*x + c)^2 + a - b)/(cosh(d*x + c)^2 - 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)) - 2*((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^4 + 4*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)*sinh(d*x + c)^3 + (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*sinh(d*x + c)^4 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 + 2*(a^3 + a^2*b - a*b^2 - b^3)*cosh(d*x + c)^2 + 2*(a^3 + a^2*b - a*b^2 - b^3 + 3*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(d*x + c)^3 + (a^3 + a^2*b - a*b^2 - b^3)*cosh(d*x + c))*sinh(d*x + c))*log(2*sinh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))) + 8*((a^3 + a^2*b)*d*x*cosh(d*x + c)^3 - (a*b^2 - (a^3 - a^2*b)*d*x)*cosh(d*x + c))*sinh(d*x + c))/((a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*d*cosh(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)*sinh(d*x + c)^3 + (a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*d*sinh(d*x + c)^4 + 2*(a^5 + a^4*b - a^3*b^2 - a^2*b^3)*d*cosh(d*x + c)^2 + 2*(3*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*d*cosh(d*x + c)^2 + (a^5 + a^4*b - a^3*b^2 - a^2*b^3)*d)*sinh(d*x + c)^2 + (a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*d + 4*((a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*d*cosh(d*x + c)^3 + (a^5 + a^4*b - a^3*b^2 - a^2*b^3)*d*cosh(d*x + c))*sinh(d*x + c))","B",0
187,1,3725,0,0.502182," ","integrate(coth(d*x+c)^2/(a+b*tanh(d*x+c)^2)^2,x, algorithm=""fricas"")","\left[\frac{4 \, {\left(a^{3} + a^{2} b\right)} d x \cosh\left(d x + c\right)^{6} + 24 \, {\left(a^{3} + a^{2} b\right)} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + 4 \, {\left(a^{3} + a^{2} b\right)} d x \sinh\left(d x + c\right)^{6} - 4 \, {\left(2 \, a^{3} + 6 \, a^{2} b + 5 \, a b^{2} + 3 \, b^{3} - {\left(a^{3} - 3 \, a^{2} b\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(15 \, {\left(a^{3} + a^{2} b\right)} d x \cosh\left(d x + c\right)^{2} - 2 \, a^{3} - 6 \, a^{2} b - 5 \, a b^{2} - 3 \, b^{3} + {\left(a^{3} - 3 \, a^{2} b\right)} d x\right)} \sinh\left(d x + c\right)^{4} + 16 \, {\left(5 \, {\left(a^{3} + a^{2} b\right)} d x \cosh\left(d x + c\right)^{3} - {\left(2 \, a^{3} + 6 \, a^{2} b + 5 \, a b^{2} + 3 \, b^{3} - {\left(a^{3} - 3 \, a^{2} b\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 8 \, a^{3} - 24 \, a^{2} b - 28 \, a b^{2} - 12 \, b^{3} - 4 \, {\left(a^{3} + a^{2} b\right)} d x - 4 \, {\left(4 \, a^{3} + 4 \, a^{2} b - 4 \, a b^{2} - 6 \, b^{3} + {\left(a^{3} - 3 \, a^{2} b\right)} d x\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(15 \, {\left(a^{3} + a^{2} b\right)} d x \cosh\left(d x + c\right)^{4} - 4 \, a^{3} - 4 \, a^{2} b + 4 \, a b^{2} + 6 \, b^{3} - {\left(a^{3} - 3 \, a^{2} b\right)} d x - 6 \, {\left(2 \, a^{3} + 6 \, a^{2} b + 5 \, a b^{2} + 3 \, b^{3} - {\left(a^{3} - 3 \, a^{2} b\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(5 \, a^{2} b + 8 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 6 \, {\left(5 \, a^{2} b + 8 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(5 \, a^{2} b + 8 \, a b^{2} + 3 \, b^{3}\right)} \sinh\left(d x + c\right)^{6} + {\left(5 \, a^{2} b - 12 \, a b^{2} - 9 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + {\left(5 \, a^{2} b - 12 \, a b^{2} - 9 \, b^{3} + 15 \, {\left(5 \, a^{2} b + 8 \, 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(5 \, a^{2} b + 8 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(5 \, a^{2} b - 12 \, a b^{2} - 9 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 5 \, a^{2} b - 8 \, a b^{2} - 3 \, b^{3} - {\left(5 \, a^{2} b - 12 \, a b^{2} - 9 \, b^{3}\right)} \cosh\left(d x + c\right)^{2} + {\left(15 \, {\left(5 \, a^{2} b + 8 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 5 \, a^{2} b + 12 \, a b^{2} + 9 \, b^{3} + 6 \, {\left(5 \, a^{2} b - 12 \, 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(5 \, a^{2} b + 8 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(5 \, a^{2} b - 12 \, a b^{2} - 9 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - {\left(5 \, a^{2} b - 12 \, a b^{2} - 9 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{{\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) \sinh\left(d x + c\right)^{3} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{2} + a^{2} - 6 \, a b + b^{2} + 4 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) - 4 \, {\left({\left(a^{2} + a b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} + a b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} + a b\right)} \sinh\left(d x + c\right)^{2} + a^{2} - a b\right)} \sqrt{-\frac{b}{a}}}{{\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) + 8 \, {\left(3 \, {\left(a^{3} + a^{2} b\right)} d x \cosh\left(d x + c\right)^{5} - 2 \, {\left(2 \, a^{3} + 6 \, a^{2} b + 5 \, a b^{2} + 3 \, b^{3} - {\left(a^{3} - 3 \, a^{2} b\right)} d x\right)} \cosh\left(d x + c\right)^{3} - {\left(4 \, a^{3} + 4 \, a^{2} b - 4 \, a b^{2} - 6 \, b^{3} + {\left(a^{3} - 3 \, a^{2} b\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{4 \, {\left({\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} + 6 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} d \sinh\left(d x + c\right)^{6} + {\left(a^{5} - a^{4} b - 5 \, a^{3} b^{2} - 3 \, a^{2} b^{3}\right)} d \cosh\left(d x + c\right)^{4} + {\left(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)^{2} + {\left(a^{5} - a^{4} b - 5 \, a^{3} b^{2} - 3 \, a^{2} b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{4} - {\left(a^{5} - a^{4} b - 5 \, a^{3} b^{2} - 3 \, a^{2} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + 4 \, {\left(5 \, {\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(a^{5} - a^{4} b - 5 \, a^{3} b^{2} - 3 \, a^{2} b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(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} + 6 \, {\left(a^{5} - a^{4} b - 5 \, a^{3} b^{2} - 3 \, a^{2} b^{3}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{5} - a^{4} b - 5 \, a^{3} b^{2} - 3 \, a^{2} b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{2} - {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} d + 2 \, {\left(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} + 2 \, {\left(a^{5} - a^{4} b - 5 \, a^{3} b^{2} - 3 \, a^{2} b^{3}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a^{5} - a^{4} b - 5 \, a^{3} b^{2} - 3 \, a^{2} b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}, \frac{2 \, {\left(a^{3} + a^{2} b\right)} d x \cosh\left(d x + c\right)^{6} + 12 \, {\left(a^{3} + a^{2} b\right)} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + 2 \, {\left(a^{3} + a^{2} b\right)} d x \sinh\left(d x + c\right)^{6} - 2 \, {\left(2 \, a^{3} + 6 \, a^{2} b + 5 \, a b^{2} + 3 \, b^{3} - {\left(a^{3} - 3 \, a^{2} b\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(15 \, {\left(a^{3} + a^{2} b\right)} d x \cosh\left(d x + c\right)^{2} - 2 \, a^{3} - 6 \, a^{2} b - 5 \, a b^{2} - 3 \, b^{3} + {\left(a^{3} - 3 \, a^{2} b\right)} d x\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(5 \, {\left(a^{3} + a^{2} b\right)} d x \cosh\left(d x + c\right)^{3} - {\left(2 \, a^{3} + 6 \, a^{2} b + 5 \, a b^{2} + 3 \, b^{3} - {\left(a^{3} - 3 \, a^{2} b\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 4 \, a^{3} - 12 \, a^{2} b - 14 \, a b^{2} - 6 \, b^{3} - 2 \, {\left(a^{3} + a^{2} b\right)} d x - 2 \, {\left(4 \, a^{3} + 4 \, a^{2} b - 4 \, a b^{2} - 6 \, b^{3} + {\left(a^{3} - 3 \, a^{2} b\right)} d x\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(15 \, {\left(a^{3} + a^{2} b\right)} d x \cosh\left(d x + c\right)^{4} - 4 \, a^{3} - 4 \, a^{2} b + 4 \, a b^{2} + 6 \, b^{3} - {\left(a^{3} - 3 \, a^{2} b\right)} d x - 6 \, {\left(2 \, a^{3} + 6 \, a^{2} b + 5 \, a b^{2} + 3 \, b^{3} - {\left(a^{3} - 3 \, a^{2} b\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} - {\left({\left(5 \, a^{2} b + 8 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{6} + 6 \, {\left(5 \, a^{2} b + 8 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(5 \, a^{2} b + 8 \, a b^{2} + 3 \, b^{3}\right)} \sinh\left(d x + c\right)^{6} + {\left(5 \, a^{2} b - 12 \, a b^{2} - 9 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} + {\left(5 \, a^{2} b - 12 \, a b^{2} - 9 \, b^{3} + 15 \, {\left(5 \, a^{2} b + 8 \, 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(5 \, a^{2} b + 8 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(5 \, a^{2} b - 12 \, a b^{2} - 9 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 5 \, a^{2} b - 8 \, a b^{2} - 3 \, b^{3} - {\left(5 \, a^{2} b - 12 \, a b^{2} - 9 \, b^{3}\right)} \cosh\left(d x + c\right)^{2} + {\left(15 \, {\left(5 \, a^{2} b + 8 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{4} - 5 \, a^{2} b + 12 \, a b^{2} + 9 \, b^{3} + 6 \, {\left(5 \, a^{2} b - 12 \, 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(5 \, a^{2} b + 8 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(5 \, a^{2} b - 12 \, a b^{2} - 9 \, b^{3}\right)} \cosh\left(d x + c\right)^{3} - {\left(5 \, a^{2} b - 12 \, a b^{2} - 9 \, b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{b}{a}} \arctan\left(\frac{{\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} + a - b\right)} \sqrt{\frac{b}{a}}}{2 \, b}\right) + 4 \, {\left(3 \, {\left(a^{3} + a^{2} b\right)} d x \cosh\left(d x + c\right)^{5} - 2 \, {\left(2 \, a^{3} + 6 \, a^{2} b + 5 \, a b^{2} + 3 \, b^{3} - {\left(a^{3} - 3 \, a^{2} b\right)} d x\right)} \cosh\left(d x + c\right)^{3} - {\left(4 \, a^{3} + 4 \, a^{2} b - 4 \, a b^{2} - 6 \, b^{3} + {\left(a^{3} - 3 \, a^{2} b\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{2 \, {\left({\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} + 6 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{5} + {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} d \sinh\left(d x + c\right)^{6} + {\left(a^{5} - a^{4} b - 5 \, a^{3} b^{2} - 3 \, a^{2} b^{3}\right)} d \cosh\left(d x + c\right)^{4} + {\left(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)^{2} + {\left(a^{5} - a^{4} b - 5 \, a^{3} b^{2} - 3 \, a^{2} b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{4} - {\left(a^{5} - a^{4} b - 5 \, a^{3} b^{2} - 3 \, a^{2} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + 4 \, {\left(5 \, {\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(a^{5} - a^{4} b - 5 \, a^{3} b^{2} - 3 \, a^{2} b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(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} + 6 \, {\left(a^{5} - a^{4} b - 5 \, a^{3} b^{2} - 3 \, a^{2} b^{3}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{5} - a^{4} b - 5 \, a^{3} b^{2} - 3 \, a^{2} b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{2} - {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} d + 2 \, {\left(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} + 2 \, {\left(a^{5} - a^{4} b - 5 \, a^{3} b^{2} - 3 \, a^{2} b^{3}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a^{5} - a^{4} b - 5 \, a^{3} b^{2} - 3 \, 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^3 + a^2*b)*d*x*cosh(d*x + c)^6 + 24*(a^3 + a^2*b)*d*x*cosh(d*x + c)*sinh(d*x + c)^5 + 4*(a^3 + a^2*b)*d*x*sinh(d*x + c)^6 - 4*(2*a^3 + 6*a^2*b + 5*a*b^2 + 3*b^3 - (a^3 - 3*a^2*b)*d*x)*cosh(d*x + c)^4 + 4*(15*(a^3 + a^2*b)*d*x*cosh(d*x + c)^2 - 2*a^3 - 6*a^2*b - 5*a*b^2 - 3*b^3 + (a^3 - 3*a^2*b)*d*x)*sinh(d*x + c)^4 + 16*(5*(a^3 + a^2*b)*d*x*cosh(d*x + c)^3 - (2*a^3 + 6*a^2*b + 5*a*b^2 + 3*b^3 - (a^3 - 3*a^2*b)*d*x)*cosh(d*x + c))*sinh(d*x + c)^3 - 8*a^3 - 24*a^2*b - 28*a*b^2 - 12*b^3 - 4*(a^3 + a^2*b)*d*x - 4*(4*a^3 + 4*a^2*b - 4*a*b^2 - 6*b^3 + (a^3 - 3*a^2*b)*d*x)*cosh(d*x + c)^2 + 4*(15*(a^3 + a^2*b)*d*x*cosh(d*x + c)^4 - 4*a^3 - 4*a^2*b + 4*a*b^2 + 6*b^3 - (a^3 - 3*a^2*b)*d*x - 6*(2*a^3 + 6*a^2*b + 5*a*b^2 + 3*b^3 - (a^3 - 3*a^2*b)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((5*a^2*b + 8*a*b^2 + 3*b^3)*cosh(d*x + c)^6 + 6*(5*a^2*b + 8*a*b^2 + 3*b^3)*cosh(d*x + c)*sinh(d*x + c)^5 + (5*a^2*b + 8*a*b^2 + 3*b^3)*sinh(d*x + c)^6 + (5*a^2*b - 12*a*b^2 - 9*b^3)*cosh(d*x + c)^4 + (5*a^2*b - 12*a*b^2 - 9*b^3 + 15*(5*a^2*b + 8*a*b^2 + 3*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 4*(5*(5*a^2*b + 8*a*b^2 + 3*b^3)*cosh(d*x + c)^3 + (5*a^2*b - 12*a*b^2 - 9*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 - 5*a^2*b - 8*a*b^2 - 3*b^3 - (5*a^2*b - 12*a*b^2 - 9*b^3)*cosh(d*x + c)^2 + (15*(5*a^2*b + 8*a*b^2 + 3*b^3)*cosh(d*x + c)^4 - 5*a^2*b + 12*a*b^2 + 9*b^3 + 6*(5*a^2*b - 12*a*b^2 - 9*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 2*(3*(5*a^2*b + 8*a*b^2 + 3*b^3)*cosh(d*x + c)^5 + 2*(5*a^2*b - 12*a*b^2 - 9*b^3)*cosh(d*x + c)^3 - (5*a^2*b - 12*a*b^2 - 9*b^3)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-b/a)*log(((a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 + 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 + 2*(a^2 - b^2)*cosh(d*x + c)^2 + 2*(3*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + a^2 - b^2)*sinh(d*x + c)^2 + a^2 - 6*a*b + b^2 + 4*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 + (a^2 - b^2)*cosh(d*x + c))*sinh(d*x + c) - 4*((a^2 + a*b)*cosh(d*x + c)^2 + 2*(a^2 + a*b)*cosh(d*x + c)*sinh(d*x + c) + (a^2 + a*b)*sinh(d*x + c)^2 + a^2 - a*b)*sqrt(-b/a))/((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)) + 8*(3*(a^3 + a^2*b)*d*x*cosh(d*x + c)^5 - 2*(2*a^3 + 6*a^2*b + 5*a*b^2 + 3*b^3 - (a^3 - 3*a^2*b)*d*x)*cosh(d*x + c)^3 - (4*a^3 + 4*a^2*b - 4*a*b^2 - 6*b^3 + (a^3 - 3*a^2*b)*d*x)*cosh(d*x + c))*sinh(d*x + c))/((a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*d*cosh(d*x + c)^6 + 6*(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 + (a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*d*sinh(d*x + c)^6 + (a^5 - a^4*b - 5*a^3*b^2 - 3*a^2*b^3)*d*cosh(d*x + c)^4 + (15*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*d*cosh(d*x + c)^2 + (a^5 - a^4*b - 5*a^3*b^2 - 3*a^2*b^3)*d)*sinh(d*x + c)^4 - (a^5 - a^4*b - 5*a^3*b^2 - 3*a^2*b^3)*d*cosh(d*x + c)^2 + 4*(5*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*d*cosh(d*x + c)^3 + (a^5 - a^4*b - 5*a^3*b^2 - 3*a^2*b^3)*d*cosh(d*x + c))*sinh(d*x + c)^3 + (15*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*d*cosh(d*x + c)^4 + 6*(a^5 - a^4*b - 5*a^3*b^2 - 3*a^2*b^3)*d*cosh(d*x + c)^2 - (a^5 - a^4*b - 5*a^3*b^2 - 3*a^2*b^3)*d)*sinh(d*x + c)^2 - (a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*d + 2*(3*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*d*cosh(d*x + c)^5 + 2*(a^5 - a^4*b - 5*a^3*b^2 - 3*a^2*b^3)*d*cosh(d*x + c)^3 - (a^5 - a^4*b - 5*a^3*b^2 - 3*a^2*b^3)*d*cosh(d*x + c))*sinh(d*x + c)), 1/2*(2*(a^3 + a^2*b)*d*x*cosh(d*x + c)^6 + 12*(a^3 + a^2*b)*d*x*cosh(d*x + c)*sinh(d*x + c)^5 + 2*(a^3 + a^2*b)*d*x*sinh(d*x + c)^6 - 2*(2*a^3 + 6*a^2*b + 5*a*b^2 + 3*b^3 - (a^3 - 3*a^2*b)*d*x)*cosh(d*x + c)^4 + 2*(15*(a^3 + a^2*b)*d*x*cosh(d*x + c)^2 - 2*a^3 - 6*a^2*b - 5*a*b^2 - 3*b^3 + (a^3 - 3*a^2*b)*d*x)*sinh(d*x + c)^4 + 8*(5*(a^3 + a^2*b)*d*x*cosh(d*x + c)^3 - (2*a^3 + 6*a^2*b + 5*a*b^2 + 3*b^3 - (a^3 - 3*a^2*b)*d*x)*cosh(d*x + c))*sinh(d*x + c)^3 - 4*a^3 - 12*a^2*b - 14*a*b^2 - 6*b^3 - 2*(a^3 + a^2*b)*d*x - 2*(4*a^3 + 4*a^2*b - 4*a*b^2 - 6*b^3 + (a^3 - 3*a^2*b)*d*x)*cosh(d*x + c)^2 + 2*(15*(a^3 + a^2*b)*d*x*cosh(d*x + c)^4 - 4*a^3 - 4*a^2*b + 4*a*b^2 + 6*b^3 - (a^3 - 3*a^2*b)*d*x - 6*(2*a^3 + 6*a^2*b + 5*a*b^2 + 3*b^3 - (a^3 - 3*a^2*b)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - ((5*a^2*b + 8*a*b^2 + 3*b^3)*cosh(d*x + c)^6 + 6*(5*a^2*b + 8*a*b^2 + 3*b^3)*cosh(d*x + c)*sinh(d*x + c)^5 + (5*a^2*b + 8*a*b^2 + 3*b^3)*sinh(d*x + c)^6 + (5*a^2*b - 12*a*b^2 - 9*b^3)*cosh(d*x + c)^4 + (5*a^2*b - 12*a*b^2 - 9*b^3 + 15*(5*a^2*b + 8*a*b^2 + 3*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 4*(5*(5*a^2*b + 8*a*b^2 + 3*b^3)*cosh(d*x + c)^3 + (5*a^2*b - 12*a*b^2 - 9*b^3)*cosh(d*x + c))*sinh(d*x + c)^3 - 5*a^2*b - 8*a*b^2 - 3*b^3 - (5*a^2*b - 12*a*b^2 - 9*b^3)*cosh(d*x + c)^2 + (15*(5*a^2*b + 8*a*b^2 + 3*b^3)*cosh(d*x + c)^4 - 5*a^2*b + 12*a*b^2 + 9*b^3 + 6*(5*a^2*b - 12*a*b^2 - 9*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 2*(3*(5*a^2*b + 8*a*b^2 + 3*b^3)*cosh(d*x + c)^5 + 2*(5*a^2*b - 12*a*b^2 - 9*b^3)*cosh(d*x + c)^3 - (5*a^2*b - 12*a*b^2 - 9*b^3)*cosh(d*x + c))*sinh(d*x + c))*sqrt(b/a)*arctan(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 + a - b)*sqrt(b/a)/b) + 4*(3*(a^3 + a^2*b)*d*x*cosh(d*x + c)^5 - 2*(2*a^3 + 6*a^2*b + 5*a*b^2 + 3*b^3 - (a^3 - 3*a^2*b)*d*x)*cosh(d*x + c)^3 - (4*a^3 + 4*a^2*b - 4*a*b^2 - 6*b^3 + (a^3 - 3*a^2*b)*d*x)*cosh(d*x + c))*sinh(d*x + c))/((a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*d*cosh(d*x + c)^6 + 6*(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 + (a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*d*sinh(d*x + c)^6 + (a^5 - a^4*b - 5*a^3*b^2 - 3*a^2*b^3)*d*cosh(d*x + c)^4 + (15*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*d*cosh(d*x + c)^2 + (a^5 - a^4*b - 5*a^3*b^2 - 3*a^2*b^3)*d)*sinh(d*x + c)^4 - (a^5 - a^4*b - 5*a^3*b^2 - 3*a^2*b^3)*d*cosh(d*x + c)^2 + 4*(5*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*d*cosh(d*x + c)^3 + (a^5 - a^4*b - 5*a^3*b^2 - 3*a^2*b^3)*d*cosh(d*x + c))*sinh(d*x + c)^3 + (15*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*d*cosh(d*x + c)^4 + 6*(a^5 - a^4*b - 5*a^3*b^2 - 3*a^2*b^3)*d*cosh(d*x + c)^2 - (a^5 - a^4*b - 5*a^3*b^2 - 3*a^2*b^3)*d)*sinh(d*x + c)^2 - (a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*d + 2*(3*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*d*cosh(d*x + c)^5 + 2*(a^5 - a^4*b - 5*a^3*b^2 - 3*a^2*b^3)*d*cosh(d*x + c)^3 - (a^5 - a^4*b - 5*a^3*b^2 - 3*a^2*b^3)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
188,1,3468,0,0.670891," ","integrate(coth(d*x+c)^3/(a+b*tanh(d*x+c)^2)^2,x, algorithm=""fricas"")","-\frac{2 \, {\left(a^{4} + a^{3} b\right)} d x \cosh\left(d x + c\right)^{8} + 16 \, {\left(a^{4} + a^{3} b\right)} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + 2 \, {\left(a^{4} + a^{3} b\right)} d x \sinh\left(d x + c\right)^{8} - 4 \, {\left(2 \, a^{3} b d x - a^{4} - 3 \, a^{3} b - 3 \, a^{2} b^{2} - 2 \, a b^{3}\right)} \cosh\left(d x + c\right)^{6} - 4 \, {\left(2 \, a^{3} b d x - 14 \, {\left(a^{4} + a^{3} b\right)} d x \cosh\left(d x + c\right)^{2} - a^{4} - 3 \, a^{3} b - 3 \, a^{2} b^{2} - 2 \, a b^{3}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(14 \, {\left(a^{4} + a^{3} b\right)} d x \cosh\left(d x + c\right)^{3} - 3 \, {\left(2 \, a^{3} b d x - a^{4} - 3 \, a^{3} b - 3 \, a^{2} b^{2} - 2 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 4 \, {\left(2 \, a^{4} + 2 \, a^{3} b - 2 \, a^{2} b^{2} - 4 \, a b^{3} - {\left(a^{4} - 3 \, a^{3} b\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(35 \, {\left(a^{4} + a^{3} b\right)} d x \cosh\left(d x + c\right)^{4} + 2 \, a^{4} + 2 \, a^{3} b - 2 \, a^{2} b^{2} - 4 \, a b^{3} - {\left(a^{4} - 3 \, a^{3} b\right)} d x - 15 \, {\left(2 \, a^{3} b d x - a^{4} - 3 \, a^{3} b - 3 \, 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 \, {\left(7 \, {\left(a^{4} + a^{3} b\right)} d x \cosh\left(d x + c\right)^{5} - 5 \, {\left(2 \, a^{3} b d x - a^{4} - 3 \, a^{3} b - 3 \, a^{2} b^{2} - 2 \, a b^{3}\right)} \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{4} + 2 \, a^{3} b - 2 \, a^{2} b^{2} - 4 \, a b^{3} - {\left(a^{4} - 3 \, a^{3} b\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(a^{4} + a^{3} b\right)} d x - 4 \, {\left(2 \, a^{3} b d x - a^{4} - 3 \, a^{3} b - 3 \, a^{2} b^{2} - 2 \, a b^{3}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(14 \, {\left(a^{4} + a^{3} b\right)} d x \cosh\left(d x + c\right)^{6} - 2 \, a^{3} b d x - 15 \, {\left(2 \, a^{3} b d x - a^{4} - 3 \, a^{3} b - 3 \, a^{2} b^{2} - 2 \, a b^{3}\right)} \cosh\left(d x + c\right)^{4} + a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + 2 \, a b^{3} + 6 \, {\left(2 \, a^{4} + 2 \, a^{3} b - 2 \, a^{2} b^{2} - 4 \, a b^{3} - {\left(a^{4} - 3 \, a^{3} b\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} - {\left({\left(3 \, a^{2} b^{2} + 5 \, a b^{3} + 2 \, b^{4}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(3 \, a^{2} b^{2} + 5 \, a b^{3} + 2 \, b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(3 \, a^{2} b^{2} + 5 \, a b^{3} + 2 \, b^{4}\right)} \sinh\left(d x + c\right)^{8} - 4 \, {\left(3 \, a b^{3} + 2 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} - 4 \, {\left(3 \, a b^{3} + 2 \, b^{4} - 7 \, {\left(3 \, a^{2} b^{2} + 5 \, a b^{3} + 2 \, 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} + 5 \, a b^{3} + 2 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(3 \, a b^{3} + 2 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 2 \, {\left(3 \, a^{2} b^{2} - 7 \, a b^{3} - 6 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(3 \, a^{2} b^{2} + 5 \, a b^{3} + 2 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} - 3 \, a^{2} b^{2} + 7 \, a b^{3} + 6 \, b^{4} - 30 \, {\left(3 \, a b^{3} + 2 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 3 \, a^{2} b^{2} + 5 \, a b^{3} + 2 \, b^{4} + 8 \, {\left(7 \, {\left(3 \, a^{2} b^{2} + 5 \, a b^{3} + 2 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} - 10 \, {\left(3 \, a b^{3} + 2 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} - {\left(3 \, a^{2} b^{2} - 7 \, a b^{3} - 6 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 4 \, {\left(3 \, a b^{3} + 2 \, b^{4}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(3 \, a^{2} b^{2} + 5 \, a b^{3} + 2 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} - 15 \, {\left(3 \, a b^{3} + 2 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} - 3 \, a b^{3} - 2 \, b^{4} - 3 \, {\left(3 \, a^{2} b^{2} - 7 \, a b^{3} - 6 \, 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} + 5 \, a b^{3} + 2 \, b^{4}\right)} \cosh\left(d x + c\right)^{7} - 3 \, {\left(3 \, a b^{3} + 2 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} - {\left(3 \, a^{2} b^{2} - 7 \, a b^{3} - 6 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} - {\left(3 \, a b^{3} + 2 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\frac{2 \, {\left({\left(a + b\right)} \cosh\left(d x + c\right)^{2} + {\left(a + b\right)} \sinh\left(d x + c\right)^{2} + a - b\right)}}{\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}}\right) - 2 \, {\left({\left(a^{4} + a^{3} b - 3 \, a^{2} b^{2} - 5 \, a b^{3} - 2 \, b^{4}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{4} + a^{3} b - 3 \, a^{2} b^{2} - 5 \, a b^{3} - 2 \, b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{4} + a^{3} b - 3 \, a^{2} b^{2} - 5 \, a b^{3} - 2 \, b^{4}\right)} \sinh\left(d x + c\right)^{8} - 4 \, {\left(a^{3} b - 3 \, a b^{3} - 2 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} - 4 \, {\left(a^{3} b - 3 \, a b^{3} - 2 \, b^{4} - 7 \, {\left(a^{4} + a^{3} b - 3 \, a^{2} b^{2} - 5 \, a b^{3} - 2 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(a^{4} + a^{3} b - 3 \, a^{2} b^{2} - 5 \, a b^{3} - 2 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{3} b - 3 \, a b^{3} - 2 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 2 \, {\left(a^{4} - 3 \, a^{3} b - 3 \, a^{2} b^{2} + 7 \, a b^{3} + 6 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(a^{4} + a^{3} b - 3 \, a^{2} b^{2} - 5 \, a b^{3} - 2 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} - a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} - 7 \, a b^{3} - 6 \, b^{4} - 30 \, {\left(a^{3} b - 3 \, a b^{3} - 2 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + a^{4} + a^{3} b - 3 \, a^{2} b^{2} - 5 \, a b^{3} - 2 \, b^{4} + 8 \, {\left(7 \, {\left(a^{4} + a^{3} b - 3 \, a^{2} b^{2} - 5 \, a b^{3} - 2 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} - 10 \, {\left(a^{3} b - 3 \, a b^{3} - 2 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} - {\left(a^{4} - 3 \, a^{3} b - 3 \, a^{2} b^{2} + 7 \, a b^{3} + 6 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 4 \, {\left(a^{3} b - 3 \, a b^{3} - 2 \, b^{4}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(a^{4} + a^{3} b - 3 \, a^{2} b^{2} - 5 \, a b^{3} - 2 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} - 15 \, {\left(a^{3} b - 3 \, a b^{3} - 2 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} - a^{3} b + 3 \, a b^{3} + 2 \, b^{4} - 3 \, {\left(a^{4} - 3 \, a^{3} b - 3 \, a^{2} b^{2} + 7 \, a b^{3} + 6 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left({\left(a^{4} + a^{3} b - 3 \, a^{2} b^{2} - 5 \, a b^{3} - 2 \, b^{4}\right)} \cosh\left(d x + c\right)^{7} - 3 \, {\left(a^{3} b - 3 \, a b^{3} - 2 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} - {\left(a^{4} - 3 \, a^{3} b - 3 \, a^{2} b^{2} + 7 \, a b^{3} + 6 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} - {\left(a^{3} b - 3 \, a b^{3} - 2 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\frac{2 \, \sinh\left(d x + c\right)}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) + 8 \, {\left(2 \, {\left(a^{4} + a^{3} b\right)} d x \cosh\left(d x + c\right)^{7} - 3 \, {\left(2 \, a^{3} b d x - a^{4} - 3 \, a^{3} b - 3 \, a^{2} b^{2} - 2 \, a b^{3}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(2 \, a^{4} + 2 \, a^{3} b - 2 \, a^{2} b^{2} - 4 \, a b^{3} - {\left(a^{4} - 3 \, a^{3} b\right)} d x\right)} \cosh\left(d x + c\right)^{3} - {\left(2 \, a^{3} b d x - a^{4} - 3 \, a^{3} b - 3 \, a^{2} b^{2} - 2 \, a b^{3}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{2 \, {\left({\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} d \sinh\left(d x + c\right)^{8} - 4 \, {\left(a^{5} b + 2 \, a^{4} b^{2} + a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{5} b + 2 \, a^{4} b^{2} + a^{3} b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{6} - 2 \, {\left(a^{6} - a^{5} b - 5 \, a^{4} b^{2} - 3 \, a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{5} b + 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 \, {\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{4} - 30 \, {\left(a^{5} b + 2 \, a^{4} b^{2} + a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{6} - a^{5} b - 5 \, a^{4} b^{2} - 3 \, a^{3} b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{4} - 4 \, {\left(a^{5} b + 2 \, a^{4} b^{2} + a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{5} - 10 \, {\left(a^{5} b + 2 \, a^{4} b^{2} + a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a^{6} - a^{5} b - 5 \, 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 \, {\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{6} - 15 \, {\left(a^{5} b + 2 \, a^{4} b^{2} + a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{4} - 3 \, {\left(a^{6} - a^{5} b - 5 \, a^{4} b^{2} - 3 \, a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{5} b + 2 \, a^{4} b^{2} + a^{3} b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} d + 8 \, {\left({\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{7} - 3 \, {\left(a^{5} b + 2 \, a^{4} b^{2} + a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{5} - {\left(a^{6} - a^{5} b - 5 \, a^{4} b^{2} - 3 \, a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a^{5} b + 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)}}"," ",0,"-1/2*(2*(a^4 + a^3*b)*d*x*cosh(d*x + c)^8 + 16*(a^4 + a^3*b)*d*x*cosh(d*x + c)*sinh(d*x + c)^7 + 2*(a^4 + a^3*b)*d*x*sinh(d*x + c)^8 - 4*(2*a^3*b*d*x - a^4 - 3*a^3*b - 3*a^2*b^2 - 2*a*b^3)*cosh(d*x + c)^6 - 4*(2*a^3*b*d*x - 14*(a^4 + a^3*b)*d*x*cosh(d*x + c)^2 - a^4 - 3*a^3*b - 3*a^2*b^2 - 2*a*b^3)*sinh(d*x + c)^6 + 8*(14*(a^4 + a^3*b)*d*x*cosh(d*x + c)^3 - 3*(2*a^3*b*d*x - a^4 - 3*a^3*b - 3*a^2*b^2 - 2*a*b^3)*cosh(d*x + c))*sinh(d*x + c)^5 + 4*(2*a^4 + 2*a^3*b - 2*a^2*b^2 - 4*a*b^3 - (a^4 - 3*a^3*b)*d*x)*cosh(d*x + c)^4 + 4*(35*(a^4 + a^3*b)*d*x*cosh(d*x + c)^4 + 2*a^4 + 2*a^3*b - 2*a^2*b^2 - 4*a*b^3 - (a^4 - 3*a^3*b)*d*x - 15*(2*a^3*b*d*x - a^4 - 3*a^3*b - 3*a^2*b^2 - 2*a*b^3)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 16*(7*(a^4 + a^3*b)*d*x*cosh(d*x + c)^5 - 5*(2*a^3*b*d*x - a^4 - 3*a^3*b - 3*a^2*b^2 - 2*a*b^3)*cosh(d*x + c)^3 + (2*a^4 + 2*a^3*b - 2*a^2*b^2 - 4*a*b^3 - (a^4 - 3*a^3*b)*d*x)*cosh(d*x + c))*sinh(d*x + c)^3 + 2*(a^4 + a^3*b)*d*x - 4*(2*a^3*b*d*x - a^4 - 3*a^3*b - 3*a^2*b^2 - 2*a*b^3)*cosh(d*x + c)^2 + 4*(14*(a^4 + a^3*b)*d*x*cosh(d*x + c)^6 - 2*a^3*b*d*x - 15*(2*a^3*b*d*x - a^4 - 3*a^3*b - 3*a^2*b^2 - 2*a*b^3)*cosh(d*x + c)^4 + a^4 + 3*a^3*b + 3*a^2*b^2 + 2*a*b^3 + 6*(2*a^4 + 2*a^3*b - 2*a^2*b^2 - 4*a*b^3 - (a^4 - 3*a^3*b)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - ((3*a^2*b^2 + 5*a*b^3 + 2*b^4)*cosh(d*x + c)^8 + 8*(3*a^2*b^2 + 5*a*b^3 + 2*b^4)*cosh(d*x + c)*sinh(d*x + c)^7 + (3*a^2*b^2 + 5*a*b^3 + 2*b^4)*sinh(d*x + c)^8 - 4*(3*a*b^3 + 2*b^4)*cosh(d*x + c)^6 - 4*(3*a*b^3 + 2*b^4 - 7*(3*a^2*b^2 + 5*a*b^3 + 2*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(3*a^2*b^2 + 5*a*b^3 + 2*b^4)*cosh(d*x + c)^3 - 3*(3*a*b^3 + 2*b^4)*cosh(d*x + c))*sinh(d*x + c)^5 - 2*(3*a^2*b^2 - 7*a*b^3 - 6*b^4)*cosh(d*x + c)^4 + 2*(35*(3*a^2*b^2 + 5*a*b^3 + 2*b^4)*cosh(d*x + c)^4 - 3*a^2*b^2 + 7*a*b^3 + 6*b^4 - 30*(3*a*b^3 + 2*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 3*a^2*b^2 + 5*a*b^3 + 2*b^4 + 8*(7*(3*a^2*b^2 + 5*a*b^3 + 2*b^4)*cosh(d*x + c)^5 - 10*(3*a*b^3 + 2*b^4)*cosh(d*x + c)^3 - (3*a^2*b^2 - 7*a*b^3 - 6*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 - 4*(3*a*b^3 + 2*b^4)*cosh(d*x + c)^2 + 4*(7*(3*a^2*b^2 + 5*a*b^3 + 2*b^4)*cosh(d*x + c)^6 - 15*(3*a*b^3 + 2*b^4)*cosh(d*x + c)^4 - 3*a*b^3 - 2*b^4 - 3*(3*a^2*b^2 - 7*a*b^3 - 6*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((3*a^2*b^2 + 5*a*b^3 + 2*b^4)*cosh(d*x + c)^7 - 3*(3*a*b^3 + 2*b^4)*cosh(d*x + c)^5 - (3*a^2*b^2 - 7*a*b^3 - 6*b^4)*cosh(d*x + c)^3 - (3*a*b^3 + 2*b^4)*cosh(d*x + c))*sinh(d*x + c))*log(2*((a + b)*cosh(d*x + c)^2 + (a + b)*sinh(d*x + c)^2 + a - b)/(cosh(d*x + c)^2 - 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)) - 2*((a^4 + a^3*b - 3*a^2*b^2 - 5*a*b^3 - 2*b^4)*cosh(d*x + c)^8 + 8*(a^4 + a^3*b - 3*a^2*b^2 - 5*a*b^3 - 2*b^4)*cosh(d*x + c)*sinh(d*x + c)^7 + (a^4 + a^3*b - 3*a^2*b^2 - 5*a*b^3 - 2*b^4)*sinh(d*x + c)^8 - 4*(a^3*b - 3*a*b^3 - 2*b^4)*cosh(d*x + c)^6 - 4*(a^3*b - 3*a*b^3 - 2*b^4 - 7*(a^4 + a^3*b - 3*a^2*b^2 - 5*a*b^3 - 2*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(a^4 + a^3*b - 3*a^2*b^2 - 5*a*b^3 - 2*b^4)*cosh(d*x + c)^3 - 3*(a^3*b - 3*a*b^3 - 2*b^4)*cosh(d*x + c))*sinh(d*x + c)^5 - 2*(a^4 - 3*a^3*b - 3*a^2*b^2 + 7*a*b^3 + 6*b^4)*cosh(d*x + c)^4 + 2*(35*(a^4 + a^3*b - 3*a^2*b^2 - 5*a*b^3 - 2*b^4)*cosh(d*x + c)^4 - a^4 + 3*a^3*b + 3*a^2*b^2 - 7*a*b^3 - 6*b^4 - 30*(a^3*b - 3*a*b^3 - 2*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + a^4 + a^3*b - 3*a^2*b^2 - 5*a*b^3 - 2*b^4 + 8*(7*(a^4 + a^3*b - 3*a^2*b^2 - 5*a*b^3 - 2*b^4)*cosh(d*x + c)^5 - 10*(a^3*b - 3*a*b^3 - 2*b^4)*cosh(d*x + c)^3 - (a^4 - 3*a^3*b - 3*a^2*b^2 + 7*a*b^3 + 6*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 - 4*(a^3*b - 3*a*b^3 - 2*b^4)*cosh(d*x + c)^2 + 4*(7*(a^4 + a^3*b - 3*a^2*b^2 - 5*a*b^3 - 2*b^4)*cosh(d*x + c)^6 - 15*(a^3*b - 3*a*b^3 - 2*b^4)*cosh(d*x + c)^4 - a^3*b + 3*a*b^3 + 2*b^4 - 3*(a^4 - 3*a^3*b - 3*a^2*b^2 + 7*a*b^3 + 6*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((a^4 + a^3*b - 3*a^2*b^2 - 5*a*b^3 - 2*b^4)*cosh(d*x + c)^7 - 3*(a^3*b - 3*a*b^3 - 2*b^4)*cosh(d*x + c)^5 - (a^4 - 3*a^3*b - 3*a^2*b^2 + 7*a*b^3 + 6*b^4)*cosh(d*x + c)^3 - (a^3*b - 3*a*b^3 - 2*b^4)*cosh(d*x + c))*sinh(d*x + c))*log(2*sinh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))) + 8*(2*(a^4 + a^3*b)*d*x*cosh(d*x + c)^7 - 3*(2*a^3*b*d*x - a^4 - 3*a^3*b - 3*a^2*b^2 - 2*a*b^3)*cosh(d*x + c)^5 + 2*(2*a^4 + 2*a^3*b - 2*a^2*b^2 - 4*a*b^3 - (a^4 - 3*a^3*b)*d*x)*cosh(d*x + c)^3 - (2*a^3*b*d*x - a^4 - 3*a^3*b - 3*a^2*b^2 - 2*a*b^3)*cosh(d*x + c))*sinh(d*x + c))/((a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*d*cosh(d*x + c)^8 + 8*(a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*d*sinh(d*x + c)^8 - 4*(a^5*b + 2*a^4*b^2 + a^3*b^3)*d*cosh(d*x + c)^6 + 4*(7*(a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*d*cosh(d*x + c)^2 - (a^5*b + 2*a^4*b^2 + a^3*b^3)*d)*sinh(d*x + c)^6 - 2*(a^6 - a^5*b - 5*a^4*b^2 - 3*a^3*b^3)*d*cosh(d*x + c)^4 + 8*(7*(a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*d*cosh(d*x + c)^3 - 3*(a^5*b + 2*a^4*b^2 + a^3*b^3)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*d*cosh(d*x + c)^4 - 30*(a^5*b + 2*a^4*b^2 + a^3*b^3)*d*cosh(d*x + c)^2 - (a^6 - a^5*b - 5*a^4*b^2 - 3*a^3*b^3)*d)*sinh(d*x + c)^4 - 4*(a^5*b + 2*a^4*b^2 + a^3*b^3)*d*cosh(d*x + c)^2 + 8*(7*(a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*d*cosh(d*x + c)^5 - 10*(a^5*b + 2*a^4*b^2 + a^3*b^3)*d*cosh(d*x + c)^3 - (a^6 - a^5*b - 5*a^4*b^2 - 3*a^3*b^3)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*d*cosh(d*x + c)^6 - 15*(a^5*b + 2*a^4*b^2 + a^3*b^3)*d*cosh(d*x + c)^4 - 3*(a^6 - a^5*b - 5*a^4*b^2 - 3*a^3*b^3)*d*cosh(d*x + c)^2 - (a^5*b + 2*a^4*b^2 + a^3*b^3)*d)*sinh(d*x + c)^2 + (a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*d + 8*((a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*d*cosh(d*x + c)^7 - 3*(a^5*b + 2*a^4*b^2 + a^3*b^3)*d*cosh(d*x + c)^5 - (a^6 - a^5*b - 5*a^4*b^2 - 3*a^3*b^3)*d*cosh(d*x + c)^3 - (a^5*b + 2*a^4*b^2 + a^3*b^3)*d*cosh(d*x + c))*sinh(d*x + c))","B",0
189,1,8482,0,0.593279," ","integrate(coth(d*x+c)^4/(a+b*tanh(d*x+c)^2)^2,x, algorithm=""fricas"")","\left[\frac{12 \, {\left(a^{4} + a^{3} b\right)} d x \cosh\left(d x + c\right)^{10} + 120 \, {\left(a^{4} + a^{3} b\right)} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + 12 \, {\left(a^{4} + a^{3} b\right)} d x \sinh\left(d x + c\right)^{10} - 12 \, {\left(4 \, a^{4} + 8 \, a^{3} b - 7 \, a b^{3} - 5 \, b^{4} + {\left(a^{4} + 5 \, a^{3} b\right)} d x\right)} \cosh\left(d x + c\right)^{8} + 12 \, {\left(45 \, {\left(a^{4} + a^{3} b\right)} d x \cosh\left(d x + c\right)^{2} - 4 \, a^{4} - 8 \, a^{3} b + 7 \, a b^{3} + 5 \, b^{4} - {\left(a^{4} + 5 \, a^{3} b\right)} d x\right)} \sinh\left(d x + c\right)^{8} + 96 \, {\left(15 \, {\left(a^{4} + a^{3} b\right)} d x \cosh\left(d x + c\right)^{3} - {\left(4 \, a^{4} + 8 \, a^{3} b - 7 \, a b^{3} - 5 \, b^{4} + {\left(a^{4} + 5 \, a^{3} b\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} - 24 \, {\left(2 \, a^{4} - 2 \, a^{3} b - 2 \, a^{2} b^{2} + 9 \, a b^{3} + 10 \, b^{4} + {\left(a^{4} - 5 \, a^{3} b\right)} d x\right)} \cosh\left(d x + c\right)^{6} + 24 \, {\left(105 \, {\left(a^{4} + a^{3} b\right)} d x \cosh\left(d x + c\right)^{4} - 2 \, a^{4} + 2 \, a^{3} b + 2 \, a^{2} b^{2} - 9 \, a b^{3} - 10 \, b^{4} - {\left(a^{4} - 5 \, a^{3} b\right)} d x - 14 \, {\left(4 \, a^{4} + 8 \, a^{3} b - 7 \, a b^{3} - 5 \, b^{4} + {\left(a^{4} + 5 \, a^{3} b\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 48 \, {\left(63 \, {\left(a^{4} + a^{3} b\right)} d x \cosh\left(d x + c\right)^{5} - 14 \, {\left(4 \, a^{4} + 8 \, a^{3} b - 7 \, a b^{3} - 5 \, b^{4} + {\left(a^{4} + 5 \, a^{3} b\right)} d x\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(2 \, a^{4} - 2 \, a^{3} b - 2 \, a^{2} b^{2} + 9 \, a b^{3} + 10 \, b^{4} + {\left(a^{4} - 5 \, a^{3} b\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 8 \, {\left(2 \, a^{4} - 30 \, a^{3} b - 30 \, a^{2} b^{2} + 38 \, a b^{3} + 45 \, b^{4} + 3 \, {\left(a^{4} - 5 \, a^{3} b\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 8 \, {\left(315 \, {\left(a^{4} + a^{3} b\right)} d x \cosh\left(d x + c\right)^{6} - 105 \, {\left(4 \, a^{4} + 8 \, a^{3} b - 7 \, a b^{3} - 5 \, b^{4} + {\left(a^{4} + 5 \, a^{3} b\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 2 \, a^{4} - 30 \, a^{3} b - 30 \, a^{2} b^{2} + 38 \, a b^{3} + 45 \, b^{4} + 3 \, {\left(a^{4} - 5 \, a^{3} b\right)} d x - 45 \, {\left(2 \, a^{4} - 2 \, a^{3} b - 2 \, a^{2} b^{2} + 9 \, a b^{3} + 10 \, b^{4} + {\left(a^{4} - 5 \, a^{3} b\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} - 32 \, a^{4} - 48 \, a^{3} b + 48 \, a^{2} b^{2} + 124 \, a b^{3} + 60 \, b^{4} + 32 \, {\left(45 \, {\left(a^{4} + a^{3} b\right)} d x \cosh\left(d x + c\right)^{7} - 21 \, {\left(4 \, a^{4} + 8 \, a^{3} b - 7 \, a b^{3} - 5 \, b^{4} + {\left(a^{4} + 5 \, a^{3} b\right)} d x\right)} \cosh\left(d x + c\right)^{5} - 15 \, {\left(2 \, a^{4} - 2 \, a^{3} b - 2 \, a^{2} b^{2} + 9 \, a b^{3} + 10 \, b^{4} + {\left(a^{4} - 5 \, a^{3} b\right)} d x\right)} \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{4} - 30 \, a^{3} b - 30 \, a^{2} b^{2} + 38 \, a b^{3} + 45 \, b^{4} + 3 \, {\left(a^{4} - 5 \, a^{3} b\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 12 \, {\left(a^{4} + a^{3} b\right)} d x - 4 \, {\left(4 \, a^{4} - 20 \, a^{3} b - 4 \, a^{2} b^{2} + 74 \, a b^{3} + 60 \, b^{4} - 3 \, {\left(a^{4} + 5 \, a^{3} b\right)} d x\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(135 \, {\left(a^{4} + a^{3} b\right)} d x \cosh\left(d x + c\right)^{8} - 84 \, {\left(4 \, a^{4} + 8 \, a^{3} b - 7 \, a b^{3} - 5 \, b^{4} + {\left(a^{4} + 5 \, a^{3} b\right)} d x\right)} \cosh\left(d x + c\right)^{6} - 90 \, {\left(2 \, a^{4} - 2 \, a^{3} b - 2 \, a^{2} b^{2} + 9 \, a b^{3} + 10 \, b^{4} + {\left(a^{4} - 5 \, a^{3} b\right)} d x\right)} \cosh\left(d x + c\right)^{4} - 4 \, a^{4} + 20 \, a^{3} b + 4 \, a^{2} b^{2} - 74 \, a b^{3} - 60 \, b^{4} + 3 \, {\left(a^{4} + 5 \, a^{3} b\right)} d x + 12 \, {\left(2 \, a^{4} - 30 \, a^{3} b - 30 \, a^{2} b^{2} + 38 \, a b^{3} + 45 \, b^{4} + 3 \, {\left(a^{4} - 5 \, a^{3} b\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 3 \, {\left({\left(7 \, a^{2} b^{2} + 12 \, a b^{3} + 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{10} + 10 \, {\left(7 \, a^{2} b^{2} + 12 \, a b^{3} + 5 \, b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + {\left(7 \, a^{2} b^{2} + 12 \, a b^{3} + 5 \, b^{4}\right)} \sinh\left(d x + c\right)^{10} - {\left(7 \, a^{2} b^{2} + 40 \, a b^{3} + 25 \, b^{4}\right)} \cosh\left(d x + c\right)^{8} - {\left(7 \, a^{2} b^{2} + 40 \, a b^{3} + 25 \, b^{4} - 45 \, {\left(7 \, a^{2} b^{2} + 12 \, 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(7 \, a^{2} b^{2} + 12 \, a b^{3} + 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} - {\left(7 \, a^{2} b^{2} + 40 \, a b^{3} + 25 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} - 2 \, {\left(7 \, a^{2} b^{2} - 30 \, a b^{3} - 25 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(105 \, {\left(7 \, a^{2} b^{2} + 12 \, a b^{3} + 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} - 7 \, a^{2} b^{2} + 30 \, a b^{3} + 25 \, b^{4} - 14 \, {\left(7 \, a^{2} b^{2} + 40 \, 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(7 \, a^{2} b^{2} + 12 \, a b^{3} + 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} - 14 \, {\left(7 \, a^{2} b^{2} + 40 \, a b^{3} + 25 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(7 \, a^{2} b^{2} - 30 \, a b^{3} - 25 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(7 \, a^{2} b^{2} - 30 \, a b^{3} - 25 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(105 \, {\left(7 \, a^{2} b^{2} + 12 \, a b^{3} + 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} - 35 \, {\left(7 \, a^{2} b^{2} + 40 \, a b^{3} + 25 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 7 \, a^{2} b^{2} - 30 \, a b^{3} - 25 \, b^{4} - 15 \, {\left(7 \, a^{2} b^{2} - 30 \, a b^{3} - 25 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} - 7 \, a^{2} b^{2} - 12 \, a b^{3} - 5 \, b^{4} + 8 \, {\left(15 \, {\left(7 \, a^{2} b^{2} + 12 \, a b^{3} + 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{7} - 7 \, {\left(7 \, a^{2} b^{2} + 40 \, a b^{3} + 25 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} - 5 \, {\left(7 \, a^{2} b^{2} - 30 \, a b^{3} - 25 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(7 \, a^{2} b^{2} - 30 \, a b^{3} - 25 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(7 \, a^{2} b^{2} + 40 \, a b^{3} + 25 \, b^{4}\right)} \cosh\left(d x + c\right)^{2} + {\left(45 \, {\left(7 \, a^{2} b^{2} + 12 \, a b^{3} + 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{8} - 28 \, {\left(7 \, a^{2} b^{2} + 40 \, a b^{3} + 25 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} - 30 \, {\left(7 \, a^{2} b^{2} - 30 \, a b^{3} - 25 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 7 \, a^{2} b^{2} + 40 \, a b^{3} + 25 \, b^{4} + 12 \, {\left(7 \, a^{2} b^{2} - 30 \, 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(7 \, a^{2} b^{2} + 12 \, a b^{3} + 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{9} - 4 \, {\left(7 \, a^{2} b^{2} + 40 \, a b^{3} + 25 \, b^{4}\right)} \cosh\left(d x + c\right)^{7} - 6 \, {\left(7 \, a^{2} b^{2} - 30 \, a b^{3} - 25 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + 4 \, {\left(7 \, a^{2} b^{2} - 30 \, a b^{3} - 25 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(7 \, a^{2} b^{2} + 40 \, a b^{3} + 25 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{{\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) \sinh\left(d x + c\right)^{3} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{2} + a^{2} - 6 \, a b + b^{2} + 4 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + 4 \, {\left({\left(a^{2} + a b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} + a b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} + a b\right)} \sinh\left(d x + c\right)^{2} + a^{2} - a b\right)} \sqrt{-\frac{b}{a}}}{{\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) + 8 \, {\left(15 \, {\left(a^{4} + a^{3} b\right)} d x \cosh\left(d x + c\right)^{9} - 12 \, {\left(4 \, a^{4} + 8 \, a^{3} b - 7 \, a b^{3} - 5 \, b^{4} + {\left(a^{4} + 5 \, a^{3} b\right)} d x\right)} \cosh\left(d x + c\right)^{7} - 18 \, {\left(2 \, a^{4} - 2 \, a^{3} b - 2 \, a^{2} b^{2} + 9 \, a b^{3} + 10 \, b^{4} + {\left(a^{4} - 5 \, a^{3} b\right)} d x\right)} \cosh\left(d x + c\right)^{5} + 4 \, {\left(2 \, a^{4} - 30 \, a^{3} b - 30 \, a^{2} b^{2} + 38 \, a b^{3} + 45 \, b^{4} + 3 \, {\left(a^{4} - 5 \, a^{3} b\right)} d x\right)} \cosh\left(d x + c\right)^{3} - {\left(4 \, a^{4} - 20 \, a^{3} b - 4 \, a^{2} b^{2} + 74 \, a b^{3} + 60 \, b^{4} - 3 \, {\left(a^{4} + 5 \, a^{3} b\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{12 \, {\left({\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{10} + 10 \, {\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + {\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} d \sinh\left(d x + c\right)^{10} - {\left(a^{6} + 7 \, a^{5} b + 11 \, a^{4} b^{2} + 5 \, a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{8} + {\left(45 \, {\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{6} + 7 \, a^{5} b + 11 \, a^{4} b^{2} + 5 \, a^{3} b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{8} - 2 \, {\left(a^{6} - 3 \, a^{5} b - 9 \, a^{4} b^{2} - 5 \, a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{6} + 8 \, {\left(15 \, {\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a^{6} + 7 \, a^{5} b + 11 \, a^{4} b^{2} + 5 \, a^{3} b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(105 \, {\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{4} - 14 \, {\left(a^{6} + 7 \, a^{5} b + 11 \, a^{4} b^{2} + 5 \, a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{6} - 3 \, a^{5} b - 9 \, a^{4} b^{2} - 5 \, a^{3} b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(a^{6} - 3 \, a^{5} b - 9 \, a^{4} b^{2} - 5 \, a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(63 \, {\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{5} - 14 \, {\left(a^{6} + 7 \, a^{5} b + 11 \, a^{4} b^{2} + 5 \, a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{6} - 3 \, a^{5} b - 9 \, a^{4} b^{2} - 5 \, a^{3} b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(105 \, {\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{6} - 35 \, {\left(a^{6} + 7 \, a^{5} b + 11 \, a^{4} b^{2} + 5 \, a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{4} - 15 \, {\left(a^{6} - 3 \, a^{5} b - 9 \, a^{4} b^{2} - 5 \, a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{6} - 3 \, a^{5} b - 9 \, a^{4} b^{2} - 5 \, a^{3} b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{4} + {\left(a^{6} + 7 \, a^{5} b + 11 \, a^{4} b^{2} + 5 \, a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(15 \, {\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{7} - 7 \, {\left(a^{6} + 7 \, a^{5} b + 11 \, a^{4} b^{2} + 5 \, a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{5} - 5 \, {\left(a^{6} - 3 \, a^{5} b - 9 \, a^{4} b^{2} - 5 \, a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{6} - 3 \, a^{5} b - 9 \, a^{4} b^{2} - 5 \, a^{3} b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(45 \, {\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{8} - 28 \, {\left(a^{6} + 7 \, a^{5} b + 11 \, a^{4} b^{2} + 5 \, a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{6} - 30 \, {\left(a^{6} - 3 \, a^{5} b - 9 \, a^{4} b^{2} - 5 \, a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 12 \, {\left(a^{6} - 3 \, a^{5} b - 9 \, a^{4} b^{2} - 5 \, a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{6} + 7 \, a^{5} b + 11 \, a^{4} b^{2} + 5 \, a^{3} b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{2} - {\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} d + 2 \, {\left(5 \, {\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{9} - 4 \, {\left(a^{6} + 7 \, a^{5} b + 11 \, a^{4} b^{2} + 5 \, a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{7} - 6 \, {\left(a^{6} - 3 \, a^{5} b - 9 \, a^{4} b^{2} - 5 \, a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{5} + 4 \, {\left(a^{6} - 3 \, a^{5} b - 9 \, a^{4} b^{2} - 5 \, a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{6} + 7 \, a^{5} b + 11 \, a^{4} b^{2} + 5 \, a^{3} b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}, \frac{6 \, {\left(a^{4} + a^{3} b\right)} d x \cosh\left(d x + c\right)^{10} + 60 \, {\left(a^{4} + a^{3} b\right)} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + 6 \, {\left(a^{4} + a^{3} b\right)} d x \sinh\left(d x + c\right)^{10} - 6 \, {\left(4 \, a^{4} + 8 \, a^{3} b - 7 \, a b^{3} - 5 \, b^{4} + {\left(a^{4} + 5 \, a^{3} b\right)} d x\right)} \cosh\left(d x + c\right)^{8} + 6 \, {\left(45 \, {\left(a^{4} + a^{3} b\right)} d x \cosh\left(d x + c\right)^{2} - 4 \, a^{4} - 8 \, a^{3} b + 7 \, a b^{3} + 5 \, b^{4} - {\left(a^{4} + 5 \, a^{3} b\right)} d x\right)} \sinh\left(d x + c\right)^{8} + 48 \, {\left(15 \, {\left(a^{4} + a^{3} b\right)} d x \cosh\left(d x + c\right)^{3} - {\left(4 \, a^{4} + 8 \, a^{3} b - 7 \, a b^{3} - 5 \, b^{4} + {\left(a^{4} + 5 \, a^{3} b\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} - 12 \, {\left(2 \, a^{4} - 2 \, a^{3} b - 2 \, a^{2} b^{2} + 9 \, a b^{3} + 10 \, b^{4} + {\left(a^{4} - 5 \, a^{3} b\right)} d x\right)} \cosh\left(d x + c\right)^{6} + 12 \, {\left(105 \, {\left(a^{4} + a^{3} b\right)} d x \cosh\left(d x + c\right)^{4} - 2 \, a^{4} + 2 \, a^{3} b + 2 \, a^{2} b^{2} - 9 \, a b^{3} - 10 \, b^{4} - {\left(a^{4} - 5 \, a^{3} b\right)} d x - 14 \, {\left(4 \, a^{4} + 8 \, a^{3} b - 7 \, a b^{3} - 5 \, b^{4} + {\left(a^{4} + 5 \, a^{3} b\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 24 \, {\left(63 \, {\left(a^{4} + a^{3} b\right)} d x \cosh\left(d x + c\right)^{5} - 14 \, {\left(4 \, a^{4} + 8 \, a^{3} b - 7 \, a b^{3} - 5 \, b^{4} + {\left(a^{4} + 5 \, a^{3} b\right)} d x\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(2 \, a^{4} - 2 \, a^{3} b - 2 \, a^{2} b^{2} + 9 \, a b^{3} + 10 \, b^{4} + {\left(a^{4} - 5 \, a^{3} b\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 4 \, {\left(2 \, a^{4} - 30 \, a^{3} b - 30 \, a^{2} b^{2} + 38 \, a b^{3} + 45 \, b^{4} + 3 \, {\left(a^{4} - 5 \, a^{3} b\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(315 \, {\left(a^{4} + a^{3} b\right)} d x \cosh\left(d x + c\right)^{6} - 105 \, {\left(4 \, a^{4} + 8 \, a^{3} b - 7 \, a b^{3} - 5 \, b^{4} + {\left(a^{4} + 5 \, a^{3} b\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 2 \, a^{4} - 30 \, a^{3} b - 30 \, a^{2} b^{2} + 38 \, a b^{3} + 45 \, b^{4} + 3 \, {\left(a^{4} - 5 \, a^{3} b\right)} d x - 45 \, {\left(2 \, a^{4} - 2 \, a^{3} b - 2 \, a^{2} b^{2} + 9 \, a b^{3} + 10 \, b^{4} + {\left(a^{4} - 5 \, a^{3} b\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} - 16 \, a^{4} - 24 \, a^{3} b + 24 \, a^{2} b^{2} + 62 \, a b^{3} + 30 \, b^{4} + 16 \, {\left(45 \, {\left(a^{4} + a^{3} b\right)} d x \cosh\left(d x + c\right)^{7} - 21 \, {\left(4 \, a^{4} + 8 \, a^{3} b - 7 \, a b^{3} - 5 \, b^{4} + {\left(a^{4} + 5 \, a^{3} b\right)} d x\right)} \cosh\left(d x + c\right)^{5} - 15 \, {\left(2 \, a^{4} - 2 \, a^{3} b - 2 \, a^{2} b^{2} + 9 \, a b^{3} + 10 \, b^{4} + {\left(a^{4} - 5 \, a^{3} b\right)} d x\right)} \cosh\left(d x + c\right)^{3} + {\left(2 \, a^{4} - 30 \, a^{3} b - 30 \, a^{2} b^{2} + 38 \, a b^{3} + 45 \, b^{4} + 3 \, {\left(a^{4} - 5 \, a^{3} b\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 6 \, {\left(a^{4} + a^{3} b\right)} d x - 2 \, {\left(4 \, a^{4} - 20 \, a^{3} b - 4 \, a^{2} b^{2} + 74 \, a b^{3} + 60 \, b^{4} - 3 \, {\left(a^{4} + 5 \, a^{3} b\right)} d x\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(135 \, {\left(a^{4} + a^{3} b\right)} d x \cosh\left(d x + c\right)^{8} - 84 \, {\left(4 \, a^{4} + 8 \, a^{3} b - 7 \, a b^{3} - 5 \, b^{4} + {\left(a^{4} + 5 \, a^{3} b\right)} d x\right)} \cosh\left(d x + c\right)^{6} - 90 \, {\left(2 \, a^{4} - 2 \, a^{3} b - 2 \, a^{2} b^{2} + 9 \, a b^{3} + 10 \, b^{4} + {\left(a^{4} - 5 \, a^{3} b\right)} d x\right)} \cosh\left(d x + c\right)^{4} - 4 \, a^{4} + 20 \, a^{3} b + 4 \, a^{2} b^{2} - 74 \, a b^{3} - 60 \, b^{4} + 3 \, {\left(a^{4} + 5 \, a^{3} b\right)} d x + 12 \, {\left(2 \, a^{4} - 30 \, a^{3} b - 30 \, a^{2} b^{2} + 38 \, a b^{3} + 45 \, b^{4} + 3 \, {\left(a^{4} - 5 \, a^{3} b\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 3 \, {\left({\left(7 \, a^{2} b^{2} + 12 \, a b^{3} + 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{10} + 10 \, {\left(7 \, a^{2} b^{2} + 12 \, a b^{3} + 5 \, b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + {\left(7 \, a^{2} b^{2} + 12 \, a b^{3} + 5 \, b^{4}\right)} \sinh\left(d x + c\right)^{10} - {\left(7 \, a^{2} b^{2} + 40 \, a b^{3} + 25 \, b^{4}\right)} \cosh\left(d x + c\right)^{8} - {\left(7 \, a^{2} b^{2} + 40 \, a b^{3} + 25 \, b^{4} - 45 \, {\left(7 \, a^{2} b^{2} + 12 \, 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(7 \, a^{2} b^{2} + 12 \, a b^{3} + 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} - {\left(7 \, a^{2} b^{2} + 40 \, a b^{3} + 25 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} - 2 \, {\left(7 \, a^{2} b^{2} - 30 \, a b^{3} - 25 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(105 \, {\left(7 \, a^{2} b^{2} + 12 \, a b^{3} + 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} - 7 \, a^{2} b^{2} + 30 \, a b^{3} + 25 \, b^{4} - 14 \, {\left(7 \, a^{2} b^{2} + 40 \, 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(7 \, a^{2} b^{2} + 12 \, a b^{3} + 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} - 14 \, {\left(7 \, a^{2} b^{2} + 40 \, a b^{3} + 25 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(7 \, a^{2} b^{2} - 30 \, a b^{3} - 25 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(7 \, a^{2} b^{2} - 30 \, a b^{3} - 25 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(105 \, {\left(7 \, a^{2} b^{2} + 12 \, a b^{3} + 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} - 35 \, {\left(7 \, a^{2} b^{2} + 40 \, a b^{3} + 25 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 7 \, a^{2} b^{2} - 30 \, a b^{3} - 25 \, b^{4} - 15 \, {\left(7 \, a^{2} b^{2} - 30 \, a b^{3} - 25 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} - 7 \, a^{2} b^{2} - 12 \, a b^{3} - 5 \, b^{4} + 8 \, {\left(15 \, {\left(7 \, a^{2} b^{2} + 12 \, a b^{3} + 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{7} - 7 \, {\left(7 \, a^{2} b^{2} + 40 \, a b^{3} + 25 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} - 5 \, {\left(7 \, a^{2} b^{2} - 30 \, a b^{3} - 25 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(7 \, a^{2} b^{2} - 30 \, a b^{3} - 25 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(7 \, a^{2} b^{2} + 40 \, a b^{3} + 25 \, b^{4}\right)} \cosh\left(d x + c\right)^{2} + {\left(45 \, {\left(7 \, a^{2} b^{2} + 12 \, a b^{3} + 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{8} - 28 \, {\left(7 \, a^{2} b^{2} + 40 \, a b^{3} + 25 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} - 30 \, {\left(7 \, a^{2} b^{2} - 30 \, a b^{3} - 25 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 7 \, a^{2} b^{2} + 40 \, a b^{3} + 25 \, b^{4} + 12 \, {\left(7 \, a^{2} b^{2} - 30 \, 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(7 \, a^{2} b^{2} + 12 \, a b^{3} + 5 \, b^{4}\right)} \cosh\left(d x + c\right)^{9} - 4 \, {\left(7 \, a^{2} b^{2} + 40 \, a b^{3} + 25 \, b^{4}\right)} \cosh\left(d x + c\right)^{7} - 6 \, {\left(7 \, a^{2} b^{2} - 30 \, a b^{3} - 25 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + 4 \, {\left(7 \, a^{2} b^{2} - 30 \, a b^{3} - 25 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(7 \, a^{2} b^{2} + 40 \, a b^{3} + 25 \, 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({\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} + a - b\right)} \sqrt{\frac{b}{a}}}{2 \, b}\right) + 4 \, {\left(15 \, {\left(a^{4} + a^{3} b\right)} d x \cosh\left(d x + c\right)^{9} - 12 \, {\left(4 \, a^{4} + 8 \, a^{3} b - 7 \, a b^{3} - 5 \, b^{4} + {\left(a^{4} + 5 \, a^{3} b\right)} d x\right)} \cosh\left(d x + c\right)^{7} - 18 \, {\left(2 \, a^{4} - 2 \, a^{3} b - 2 \, a^{2} b^{2} + 9 \, a b^{3} + 10 \, b^{4} + {\left(a^{4} - 5 \, a^{3} b\right)} d x\right)} \cosh\left(d x + c\right)^{5} + 4 \, {\left(2 \, a^{4} - 30 \, a^{3} b - 30 \, a^{2} b^{2} + 38 \, a b^{3} + 45 \, b^{4} + 3 \, {\left(a^{4} - 5 \, a^{3} b\right)} d x\right)} \cosh\left(d x + c\right)^{3} - {\left(4 \, a^{4} - 20 \, a^{3} b - 4 \, a^{2} b^{2} + 74 \, a b^{3} + 60 \, b^{4} - 3 \, {\left(a^{4} + 5 \, a^{3} b\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{6 \, {\left({\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{10} + 10 \, {\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + {\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} d \sinh\left(d x + c\right)^{10} - {\left(a^{6} + 7 \, a^{5} b + 11 \, a^{4} b^{2} + 5 \, a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{8} + {\left(45 \, {\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{6} + 7 \, a^{5} b + 11 \, a^{4} b^{2} + 5 \, a^{3} b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{8} - 2 \, {\left(a^{6} - 3 \, a^{5} b - 9 \, a^{4} b^{2} - 5 \, a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{6} + 8 \, {\left(15 \, {\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a^{6} + 7 \, a^{5} b + 11 \, a^{4} b^{2} + 5 \, a^{3} b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(105 \, {\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{4} - 14 \, {\left(a^{6} + 7 \, a^{5} b + 11 \, a^{4} b^{2} + 5 \, a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{6} - 3 \, a^{5} b - 9 \, a^{4} b^{2} - 5 \, a^{3} b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(a^{6} - 3 \, a^{5} b - 9 \, a^{4} b^{2} - 5 \, a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(63 \, {\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{5} - 14 \, {\left(a^{6} + 7 \, a^{5} b + 11 \, a^{4} b^{2} + 5 \, a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{6} - 3 \, a^{5} b - 9 \, a^{4} b^{2} - 5 \, a^{3} b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(105 \, {\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{6} - 35 \, {\left(a^{6} + 7 \, a^{5} b + 11 \, a^{4} b^{2} + 5 \, a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{4} - 15 \, {\left(a^{6} - 3 \, a^{5} b - 9 \, a^{4} b^{2} - 5 \, a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{6} - 3 \, a^{5} b - 9 \, a^{4} b^{2} - 5 \, a^{3} b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{4} + {\left(a^{6} + 7 \, a^{5} b + 11 \, a^{4} b^{2} + 5 \, a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(15 \, {\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{7} - 7 \, {\left(a^{6} + 7 \, a^{5} b + 11 \, a^{4} b^{2} + 5 \, a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{5} - 5 \, {\left(a^{6} - 3 \, a^{5} b - 9 \, a^{4} b^{2} - 5 \, a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{6} - 3 \, a^{5} b - 9 \, a^{4} b^{2} - 5 \, a^{3} b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(45 \, {\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{8} - 28 \, {\left(a^{6} + 7 \, a^{5} b + 11 \, a^{4} b^{2} + 5 \, a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{6} - 30 \, {\left(a^{6} - 3 \, a^{5} b - 9 \, a^{4} b^{2} - 5 \, a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{4} + 12 \, {\left(a^{6} - 3 \, a^{5} b - 9 \, a^{4} b^{2} - 5 \, a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{6} + 7 \, a^{5} b + 11 \, a^{4} b^{2} + 5 \, a^{3} b^{3}\right)} d\right)} \sinh\left(d x + c\right)^{2} - {\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} d + 2 \, {\left(5 \, {\left(a^{6} + 3 \, a^{5} b + 3 \, a^{4} b^{2} + a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{9} - 4 \, {\left(a^{6} + 7 \, a^{5} b + 11 \, a^{4} b^{2} + 5 \, a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{7} - 6 \, {\left(a^{6} - 3 \, a^{5} b - 9 \, a^{4} b^{2} - 5 \, a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{5} + 4 \, {\left(a^{6} - 3 \, a^{5} b - 9 \, a^{4} b^{2} - 5 \, a^{3} b^{3}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{6} + 7 \, a^{5} b + 11 \, a^{4} b^{2} + 5 \, a^{3} b^{3}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[1/12*(12*(a^4 + a^3*b)*d*x*cosh(d*x + c)^10 + 120*(a^4 + a^3*b)*d*x*cosh(d*x + c)*sinh(d*x + c)^9 + 12*(a^4 + a^3*b)*d*x*sinh(d*x + c)^10 - 12*(4*a^4 + 8*a^3*b - 7*a*b^3 - 5*b^4 + (a^4 + 5*a^3*b)*d*x)*cosh(d*x + c)^8 + 12*(45*(a^4 + a^3*b)*d*x*cosh(d*x + c)^2 - 4*a^4 - 8*a^3*b + 7*a*b^3 + 5*b^4 - (a^4 + 5*a^3*b)*d*x)*sinh(d*x + c)^8 + 96*(15*(a^4 + a^3*b)*d*x*cosh(d*x + c)^3 - (4*a^4 + 8*a^3*b - 7*a*b^3 - 5*b^4 + (a^4 + 5*a^3*b)*d*x)*cosh(d*x + c))*sinh(d*x + c)^7 - 24*(2*a^4 - 2*a^3*b - 2*a^2*b^2 + 9*a*b^3 + 10*b^4 + (a^4 - 5*a^3*b)*d*x)*cosh(d*x + c)^6 + 24*(105*(a^4 + a^3*b)*d*x*cosh(d*x + c)^4 - 2*a^4 + 2*a^3*b + 2*a^2*b^2 - 9*a*b^3 - 10*b^4 - (a^4 - 5*a^3*b)*d*x - 14*(4*a^4 + 8*a^3*b - 7*a*b^3 - 5*b^4 + (a^4 + 5*a^3*b)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 48*(63*(a^4 + a^3*b)*d*x*cosh(d*x + c)^5 - 14*(4*a^4 + 8*a^3*b - 7*a*b^3 - 5*b^4 + (a^4 + 5*a^3*b)*d*x)*cosh(d*x + c)^3 - 3*(2*a^4 - 2*a^3*b - 2*a^2*b^2 + 9*a*b^3 + 10*b^4 + (a^4 - 5*a^3*b)*d*x)*cosh(d*x + c))*sinh(d*x + c)^5 + 8*(2*a^4 - 30*a^3*b - 30*a^2*b^2 + 38*a*b^3 + 45*b^4 + 3*(a^4 - 5*a^3*b)*d*x)*cosh(d*x + c)^4 + 8*(315*(a^4 + a^3*b)*d*x*cosh(d*x + c)^6 - 105*(4*a^4 + 8*a^3*b - 7*a*b^3 - 5*b^4 + (a^4 + 5*a^3*b)*d*x)*cosh(d*x + c)^4 + 2*a^4 - 30*a^3*b - 30*a^2*b^2 + 38*a*b^3 + 45*b^4 + 3*(a^4 - 5*a^3*b)*d*x - 45*(2*a^4 - 2*a^3*b - 2*a^2*b^2 + 9*a*b^3 + 10*b^4 + (a^4 - 5*a^3*b)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^4 - 32*a^4 - 48*a^3*b + 48*a^2*b^2 + 124*a*b^3 + 60*b^4 + 32*(45*(a^4 + a^3*b)*d*x*cosh(d*x + c)^7 - 21*(4*a^4 + 8*a^3*b - 7*a*b^3 - 5*b^4 + (a^4 + 5*a^3*b)*d*x)*cosh(d*x + c)^5 - 15*(2*a^4 - 2*a^3*b - 2*a^2*b^2 + 9*a*b^3 + 10*b^4 + (a^4 - 5*a^3*b)*d*x)*cosh(d*x + c)^3 + (2*a^4 - 30*a^3*b - 30*a^2*b^2 + 38*a*b^3 + 45*b^4 + 3*(a^4 - 5*a^3*b)*d*x)*cosh(d*x + c))*sinh(d*x + c)^3 - 12*(a^4 + a^3*b)*d*x - 4*(4*a^4 - 20*a^3*b - 4*a^2*b^2 + 74*a*b^3 + 60*b^4 - 3*(a^4 + 5*a^3*b)*d*x)*cosh(d*x + c)^2 + 4*(135*(a^4 + a^3*b)*d*x*cosh(d*x + c)^8 - 84*(4*a^4 + 8*a^3*b - 7*a*b^3 - 5*b^4 + (a^4 + 5*a^3*b)*d*x)*cosh(d*x + c)^6 - 90*(2*a^4 - 2*a^3*b - 2*a^2*b^2 + 9*a*b^3 + 10*b^4 + (a^4 - 5*a^3*b)*d*x)*cosh(d*x + c)^4 - 4*a^4 + 20*a^3*b + 4*a^2*b^2 - 74*a*b^3 - 60*b^4 + 3*(a^4 + 5*a^3*b)*d*x + 12*(2*a^4 - 30*a^3*b - 30*a^2*b^2 + 38*a*b^3 + 45*b^4 + 3*(a^4 - 5*a^3*b)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 3*((7*a^2*b^2 + 12*a*b^3 + 5*b^4)*cosh(d*x + c)^10 + 10*(7*a^2*b^2 + 12*a*b^3 + 5*b^4)*cosh(d*x + c)*sinh(d*x + c)^9 + (7*a^2*b^2 + 12*a*b^3 + 5*b^4)*sinh(d*x + c)^10 - (7*a^2*b^2 + 40*a*b^3 + 25*b^4)*cosh(d*x + c)^8 - (7*a^2*b^2 + 40*a*b^3 + 25*b^4 - 45*(7*a^2*b^2 + 12*a*b^3 + 5*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 8*(15*(7*a^2*b^2 + 12*a*b^3 + 5*b^4)*cosh(d*x + c)^3 - (7*a^2*b^2 + 40*a*b^3 + 25*b^4)*cosh(d*x + c))*sinh(d*x + c)^7 - 2*(7*a^2*b^2 - 30*a*b^3 - 25*b^4)*cosh(d*x + c)^6 + 2*(105*(7*a^2*b^2 + 12*a*b^3 + 5*b^4)*cosh(d*x + c)^4 - 7*a^2*b^2 + 30*a*b^3 + 25*b^4 - 14*(7*a^2*b^2 + 40*a*b^3 + 25*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 4*(63*(7*a^2*b^2 + 12*a*b^3 + 5*b^4)*cosh(d*x + c)^5 - 14*(7*a^2*b^2 + 40*a*b^3 + 25*b^4)*cosh(d*x + c)^3 - 3*(7*a^2*b^2 - 30*a*b^3 - 25*b^4)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(7*a^2*b^2 - 30*a*b^3 - 25*b^4)*cosh(d*x + c)^4 + 2*(105*(7*a^2*b^2 + 12*a*b^3 + 5*b^4)*cosh(d*x + c)^6 - 35*(7*a^2*b^2 + 40*a*b^3 + 25*b^4)*cosh(d*x + c)^4 + 7*a^2*b^2 - 30*a*b^3 - 25*b^4 - 15*(7*a^2*b^2 - 30*a*b^3 - 25*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 - 7*a^2*b^2 - 12*a*b^3 - 5*b^4 + 8*(15*(7*a^2*b^2 + 12*a*b^3 + 5*b^4)*cosh(d*x + c)^7 - 7*(7*a^2*b^2 + 40*a*b^3 + 25*b^4)*cosh(d*x + c)^5 - 5*(7*a^2*b^2 - 30*a*b^3 - 25*b^4)*cosh(d*x + c)^3 + (7*a^2*b^2 - 30*a*b^3 - 25*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + (7*a^2*b^2 + 40*a*b^3 + 25*b^4)*cosh(d*x + c)^2 + (45*(7*a^2*b^2 + 12*a*b^3 + 5*b^4)*cosh(d*x + c)^8 - 28*(7*a^2*b^2 + 40*a*b^3 + 25*b^4)*cosh(d*x + c)^6 - 30*(7*a^2*b^2 - 30*a*b^3 - 25*b^4)*cosh(d*x + c)^4 + 7*a^2*b^2 + 40*a*b^3 + 25*b^4 + 12*(7*a^2*b^2 - 30*a*b^3 - 25*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 2*(5*(7*a^2*b^2 + 12*a*b^3 + 5*b^4)*cosh(d*x + c)^9 - 4*(7*a^2*b^2 + 40*a*b^3 + 25*b^4)*cosh(d*x + c)^7 - 6*(7*a^2*b^2 - 30*a*b^3 - 25*b^4)*cosh(d*x + c)^5 + 4*(7*a^2*b^2 - 30*a*b^3 - 25*b^4)*cosh(d*x + c)^3 + (7*a^2*b^2 + 40*a*b^3 + 25*b^4)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-b/a)*log(((a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 + 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 + 2*(a^2 - b^2)*cosh(d*x + c)^2 + 2*(3*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + a^2 - b^2)*sinh(d*x + c)^2 + a^2 - 6*a*b + b^2 + 4*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 + (a^2 - b^2)*cosh(d*x + c))*sinh(d*x + c) + 4*((a^2 + a*b)*cosh(d*x + c)^2 + 2*(a^2 + a*b)*cosh(d*x + c)*sinh(d*x + c) + (a^2 + a*b)*sinh(d*x + c)^2 + a^2 - a*b)*sqrt(-b/a))/((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)) + 8*(15*(a^4 + a^3*b)*d*x*cosh(d*x + c)^9 - 12*(4*a^4 + 8*a^3*b - 7*a*b^3 - 5*b^4 + (a^4 + 5*a^3*b)*d*x)*cosh(d*x + c)^7 - 18*(2*a^4 - 2*a^3*b - 2*a^2*b^2 + 9*a*b^3 + 10*b^4 + (a^4 - 5*a^3*b)*d*x)*cosh(d*x + c)^5 + 4*(2*a^4 - 30*a^3*b - 30*a^2*b^2 + 38*a*b^3 + 45*b^4 + 3*(a^4 - 5*a^3*b)*d*x)*cosh(d*x + c)^3 - (4*a^4 - 20*a^3*b - 4*a^2*b^2 + 74*a*b^3 + 60*b^4 - 3*(a^4 + 5*a^3*b)*d*x)*cosh(d*x + c))*sinh(d*x + c))/((a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*d*cosh(d*x + c)^10 + 10*(a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*d*cosh(d*x + c)*sinh(d*x + c)^9 + (a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*d*sinh(d*x + c)^10 - (a^6 + 7*a^5*b + 11*a^4*b^2 + 5*a^3*b^3)*d*cosh(d*x + c)^8 + (45*(a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*d*cosh(d*x + c)^2 - (a^6 + 7*a^5*b + 11*a^4*b^2 + 5*a^3*b^3)*d)*sinh(d*x + c)^8 - 2*(a^6 - 3*a^5*b - 9*a^4*b^2 - 5*a^3*b^3)*d*cosh(d*x + c)^6 + 8*(15*(a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*d*cosh(d*x + c)^3 - (a^6 + 7*a^5*b + 11*a^4*b^2 + 5*a^3*b^3)*d*cosh(d*x + c))*sinh(d*x + c)^7 + 2*(105*(a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*d*cosh(d*x + c)^4 - 14*(a^6 + 7*a^5*b + 11*a^4*b^2 + 5*a^3*b^3)*d*cosh(d*x + c)^2 - (a^6 - 3*a^5*b - 9*a^4*b^2 - 5*a^3*b^3)*d)*sinh(d*x + c)^6 + 2*(a^6 - 3*a^5*b - 9*a^4*b^2 - 5*a^3*b^3)*d*cosh(d*x + c)^4 + 4*(63*(a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*d*cosh(d*x + c)^5 - 14*(a^6 + 7*a^5*b + 11*a^4*b^2 + 5*a^3*b^3)*d*cosh(d*x + c)^3 - 3*(a^6 - 3*a^5*b - 9*a^4*b^2 - 5*a^3*b^3)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(105*(a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*d*cosh(d*x + c)^6 - 35*(a^6 + 7*a^5*b + 11*a^4*b^2 + 5*a^3*b^3)*d*cosh(d*x + c)^4 - 15*(a^6 - 3*a^5*b - 9*a^4*b^2 - 5*a^3*b^3)*d*cosh(d*x + c)^2 + (a^6 - 3*a^5*b - 9*a^4*b^2 - 5*a^3*b^3)*d)*sinh(d*x + c)^4 + (a^6 + 7*a^5*b + 11*a^4*b^2 + 5*a^3*b^3)*d*cosh(d*x + c)^2 + 8*(15*(a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*d*cosh(d*x + c)^7 - 7*(a^6 + 7*a^5*b + 11*a^4*b^2 + 5*a^3*b^3)*d*cosh(d*x + c)^5 - 5*(a^6 - 3*a^5*b - 9*a^4*b^2 - 5*a^3*b^3)*d*cosh(d*x + c)^3 + (a^6 - 3*a^5*b - 9*a^4*b^2 - 5*a^3*b^3)*d*cosh(d*x + c))*sinh(d*x + c)^3 + (45*(a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*d*cosh(d*x + c)^8 - 28*(a^6 + 7*a^5*b + 11*a^4*b^2 + 5*a^3*b^3)*d*cosh(d*x + c)^6 - 30*(a^6 - 3*a^5*b - 9*a^4*b^2 - 5*a^3*b^3)*d*cosh(d*x + c)^4 + 12*(a^6 - 3*a^5*b - 9*a^4*b^2 - 5*a^3*b^3)*d*cosh(d*x + c)^2 + (a^6 + 7*a^5*b + 11*a^4*b^2 + 5*a^3*b^3)*d)*sinh(d*x + c)^2 - (a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*d + 2*(5*(a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*d*cosh(d*x + c)^9 - 4*(a^6 + 7*a^5*b + 11*a^4*b^2 + 5*a^3*b^3)*d*cosh(d*x + c)^7 - 6*(a^6 - 3*a^5*b - 9*a^4*b^2 - 5*a^3*b^3)*d*cosh(d*x + c)^5 + 4*(a^6 - 3*a^5*b - 9*a^4*b^2 - 5*a^3*b^3)*d*cosh(d*x + c)^3 + (a^6 + 7*a^5*b + 11*a^4*b^2 + 5*a^3*b^3)*d*cosh(d*x + c))*sinh(d*x + c)), 1/6*(6*(a^4 + a^3*b)*d*x*cosh(d*x + c)^10 + 60*(a^4 + a^3*b)*d*x*cosh(d*x + c)*sinh(d*x + c)^9 + 6*(a^4 + a^3*b)*d*x*sinh(d*x + c)^10 - 6*(4*a^4 + 8*a^3*b - 7*a*b^3 - 5*b^4 + (a^4 + 5*a^3*b)*d*x)*cosh(d*x + c)^8 + 6*(45*(a^4 + a^3*b)*d*x*cosh(d*x + c)^2 - 4*a^4 - 8*a^3*b + 7*a*b^3 + 5*b^4 - (a^4 + 5*a^3*b)*d*x)*sinh(d*x + c)^8 + 48*(15*(a^4 + a^3*b)*d*x*cosh(d*x + c)^3 - (4*a^4 + 8*a^3*b - 7*a*b^3 - 5*b^4 + (a^4 + 5*a^3*b)*d*x)*cosh(d*x + c))*sinh(d*x + c)^7 - 12*(2*a^4 - 2*a^3*b - 2*a^2*b^2 + 9*a*b^3 + 10*b^4 + (a^4 - 5*a^3*b)*d*x)*cosh(d*x + c)^6 + 12*(105*(a^4 + a^3*b)*d*x*cosh(d*x + c)^4 - 2*a^4 + 2*a^3*b + 2*a^2*b^2 - 9*a*b^3 - 10*b^4 - (a^4 - 5*a^3*b)*d*x - 14*(4*a^4 + 8*a^3*b - 7*a*b^3 - 5*b^4 + (a^4 + 5*a^3*b)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 24*(63*(a^4 + a^3*b)*d*x*cosh(d*x + c)^5 - 14*(4*a^4 + 8*a^3*b - 7*a*b^3 - 5*b^4 + (a^4 + 5*a^3*b)*d*x)*cosh(d*x + c)^3 - 3*(2*a^4 - 2*a^3*b - 2*a^2*b^2 + 9*a*b^3 + 10*b^4 + (a^4 - 5*a^3*b)*d*x)*cosh(d*x + c))*sinh(d*x + c)^5 + 4*(2*a^4 - 30*a^3*b - 30*a^2*b^2 + 38*a*b^3 + 45*b^4 + 3*(a^4 - 5*a^3*b)*d*x)*cosh(d*x + c)^4 + 4*(315*(a^4 + a^3*b)*d*x*cosh(d*x + c)^6 - 105*(4*a^4 + 8*a^3*b - 7*a*b^3 - 5*b^4 + (a^4 + 5*a^3*b)*d*x)*cosh(d*x + c)^4 + 2*a^4 - 30*a^3*b - 30*a^2*b^2 + 38*a*b^3 + 45*b^4 + 3*(a^4 - 5*a^3*b)*d*x - 45*(2*a^4 - 2*a^3*b - 2*a^2*b^2 + 9*a*b^3 + 10*b^4 + (a^4 - 5*a^3*b)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^4 - 16*a^4 - 24*a^3*b + 24*a^2*b^2 + 62*a*b^3 + 30*b^4 + 16*(45*(a^4 + a^3*b)*d*x*cosh(d*x + c)^7 - 21*(4*a^4 + 8*a^3*b - 7*a*b^3 - 5*b^4 + (a^4 + 5*a^3*b)*d*x)*cosh(d*x + c)^5 - 15*(2*a^4 - 2*a^3*b - 2*a^2*b^2 + 9*a*b^3 + 10*b^4 + (a^4 - 5*a^3*b)*d*x)*cosh(d*x + c)^3 + (2*a^4 - 30*a^3*b - 30*a^2*b^2 + 38*a*b^3 + 45*b^4 + 3*(a^4 - 5*a^3*b)*d*x)*cosh(d*x + c))*sinh(d*x + c)^3 - 6*(a^4 + a^3*b)*d*x - 2*(4*a^4 - 20*a^3*b - 4*a^2*b^2 + 74*a*b^3 + 60*b^4 - 3*(a^4 + 5*a^3*b)*d*x)*cosh(d*x + c)^2 + 2*(135*(a^4 + a^3*b)*d*x*cosh(d*x + c)^8 - 84*(4*a^4 + 8*a^3*b - 7*a*b^3 - 5*b^4 + (a^4 + 5*a^3*b)*d*x)*cosh(d*x + c)^6 - 90*(2*a^4 - 2*a^3*b - 2*a^2*b^2 + 9*a*b^3 + 10*b^4 + (a^4 - 5*a^3*b)*d*x)*cosh(d*x + c)^4 - 4*a^4 + 20*a^3*b + 4*a^2*b^2 - 74*a*b^3 - 60*b^4 + 3*(a^4 + 5*a^3*b)*d*x + 12*(2*a^4 - 30*a^3*b - 30*a^2*b^2 + 38*a*b^3 + 45*b^4 + 3*(a^4 - 5*a^3*b)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 3*((7*a^2*b^2 + 12*a*b^3 + 5*b^4)*cosh(d*x + c)^10 + 10*(7*a^2*b^2 + 12*a*b^3 + 5*b^4)*cosh(d*x + c)*sinh(d*x + c)^9 + (7*a^2*b^2 + 12*a*b^3 + 5*b^4)*sinh(d*x + c)^10 - (7*a^2*b^2 + 40*a*b^3 + 25*b^4)*cosh(d*x + c)^8 - (7*a^2*b^2 + 40*a*b^3 + 25*b^4 - 45*(7*a^2*b^2 + 12*a*b^3 + 5*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 8*(15*(7*a^2*b^2 + 12*a*b^3 + 5*b^4)*cosh(d*x + c)^3 - (7*a^2*b^2 + 40*a*b^3 + 25*b^4)*cosh(d*x + c))*sinh(d*x + c)^7 - 2*(7*a^2*b^2 - 30*a*b^3 - 25*b^4)*cosh(d*x + c)^6 + 2*(105*(7*a^2*b^2 + 12*a*b^3 + 5*b^4)*cosh(d*x + c)^4 - 7*a^2*b^2 + 30*a*b^3 + 25*b^4 - 14*(7*a^2*b^2 + 40*a*b^3 + 25*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 4*(63*(7*a^2*b^2 + 12*a*b^3 + 5*b^4)*cosh(d*x + c)^5 - 14*(7*a^2*b^2 + 40*a*b^3 + 25*b^4)*cosh(d*x + c)^3 - 3*(7*a^2*b^2 - 30*a*b^3 - 25*b^4)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(7*a^2*b^2 - 30*a*b^3 - 25*b^4)*cosh(d*x + c)^4 + 2*(105*(7*a^2*b^2 + 12*a*b^3 + 5*b^4)*cosh(d*x + c)^6 - 35*(7*a^2*b^2 + 40*a*b^3 + 25*b^4)*cosh(d*x + c)^4 + 7*a^2*b^2 - 30*a*b^3 - 25*b^4 - 15*(7*a^2*b^2 - 30*a*b^3 - 25*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 - 7*a^2*b^2 - 12*a*b^3 - 5*b^4 + 8*(15*(7*a^2*b^2 + 12*a*b^3 + 5*b^4)*cosh(d*x + c)^7 - 7*(7*a^2*b^2 + 40*a*b^3 + 25*b^4)*cosh(d*x + c)^5 - 5*(7*a^2*b^2 - 30*a*b^3 - 25*b^4)*cosh(d*x + c)^3 + (7*a^2*b^2 - 30*a*b^3 - 25*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + (7*a^2*b^2 + 40*a*b^3 + 25*b^4)*cosh(d*x + c)^2 + (45*(7*a^2*b^2 + 12*a*b^3 + 5*b^4)*cosh(d*x + c)^8 - 28*(7*a^2*b^2 + 40*a*b^3 + 25*b^4)*cosh(d*x + c)^6 - 30*(7*a^2*b^2 - 30*a*b^3 - 25*b^4)*cosh(d*x + c)^4 + 7*a^2*b^2 + 40*a*b^3 + 25*b^4 + 12*(7*a^2*b^2 - 30*a*b^3 - 25*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 2*(5*(7*a^2*b^2 + 12*a*b^3 + 5*b^4)*cosh(d*x + c)^9 - 4*(7*a^2*b^2 + 40*a*b^3 + 25*b^4)*cosh(d*x + c)^7 - 6*(7*a^2*b^2 - 30*a*b^3 - 25*b^4)*cosh(d*x + c)^5 + 4*(7*a^2*b^2 - 30*a*b^3 - 25*b^4)*cosh(d*x + c)^3 + (7*a^2*b^2 + 40*a*b^3 + 25*b^4)*cosh(d*x + c))*sinh(d*x + c))*sqrt(b/a)*arctan(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 + a - b)*sqrt(b/a)/b) + 4*(15*(a^4 + a^3*b)*d*x*cosh(d*x + c)^9 - 12*(4*a^4 + 8*a^3*b - 7*a*b^3 - 5*b^4 + (a^4 + 5*a^3*b)*d*x)*cosh(d*x + c)^7 - 18*(2*a^4 - 2*a^3*b - 2*a^2*b^2 + 9*a*b^3 + 10*b^4 + (a^4 - 5*a^3*b)*d*x)*cosh(d*x + c)^5 + 4*(2*a^4 - 30*a^3*b - 30*a^2*b^2 + 38*a*b^3 + 45*b^4 + 3*(a^4 - 5*a^3*b)*d*x)*cosh(d*x + c)^3 - (4*a^4 - 20*a^3*b - 4*a^2*b^2 + 74*a*b^3 + 60*b^4 - 3*(a^4 + 5*a^3*b)*d*x)*cosh(d*x + c))*sinh(d*x + c))/((a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*d*cosh(d*x + c)^10 + 10*(a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*d*cosh(d*x + c)*sinh(d*x + c)^9 + (a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*d*sinh(d*x + c)^10 - (a^6 + 7*a^5*b + 11*a^4*b^2 + 5*a^3*b^3)*d*cosh(d*x + c)^8 + (45*(a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*d*cosh(d*x + c)^2 - (a^6 + 7*a^5*b + 11*a^4*b^2 + 5*a^3*b^3)*d)*sinh(d*x + c)^8 - 2*(a^6 - 3*a^5*b - 9*a^4*b^2 - 5*a^3*b^3)*d*cosh(d*x + c)^6 + 8*(15*(a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*d*cosh(d*x + c)^3 - (a^6 + 7*a^5*b + 11*a^4*b^2 + 5*a^3*b^3)*d*cosh(d*x + c))*sinh(d*x + c)^7 + 2*(105*(a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*d*cosh(d*x + c)^4 - 14*(a^6 + 7*a^5*b + 11*a^4*b^2 + 5*a^3*b^3)*d*cosh(d*x + c)^2 - (a^6 - 3*a^5*b - 9*a^4*b^2 - 5*a^3*b^3)*d)*sinh(d*x + c)^6 + 2*(a^6 - 3*a^5*b - 9*a^4*b^2 - 5*a^3*b^3)*d*cosh(d*x + c)^4 + 4*(63*(a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*d*cosh(d*x + c)^5 - 14*(a^6 + 7*a^5*b + 11*a^4*b^2 + 5*a^3*b^3)*d*cosh(d*x + c)^3 - 3*(a^6 - 3*a^5*b - 9*a^4*b^2 - 5*a^3*b^3)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(105*(a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*d*cosh(d*x + c)^6 - 35*(a^6 + 7*a^5*b + 11*a^4*b^2 + 5*a^3*b^3)*d*cosh(d*x + c)^4 - 15*(a^6 - 3*a^5*b - 9*a^4*b^2 - 5*a^3*b^3)*d*cosh(d*x + c)^2 + (a^6 - 3*a^5*b - 9*a^4*b^2 - 5*a^3*b^3)*d)*sinh(d*x + c)^4 + (a^6 + 7*a^5*b + 11*a^4*b^2 + 5*a^3*b^3)*d*cosh(d*x + c)^2 + 8*(15*(a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*d*cosh(d*x + c)^7 - 7*(a^6 + 7*a^5*b + 11*a^4*b^2 + 5*a^3*b^3)*d*cosh(d*x + c)^5 - 5*(a^6 - 3*a^5*b - 9*a^4*b^2 - 5*a^3*b^3)*d*cosh(d*x + c)^3 + (a^6 - 3*a^5*b - 9*a^4*b^2 - 5*a^3*b^3)*d*cosh(d*x + c))*sinh(d*x + c)^3 + (45*(a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*d*cosh(d*x + c)^8 - 28*(a^6 + 7*a^5*b + 11*a^4*b^2 + 5*a^3*b^3)*d*cosh(d*x + c)^6 - 30*(a^6 - 3*a^5*b - 9*a^4*b^2 - 5*a^3*b^3)*d*cosh(d*x + c)^4 + 12*(a^6 - 3*a^5*b - 9*a^4*b^2 - 5*a^3*b^3)*d*cosh(d*x + c)^2 + (a^6 + 7*a^5*b + 11*a^4*b^2 + 5*a^3*b^3)*d)*sinh(d*x + c)^2 - (a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*d + 2*(5*(a^6 + 3*a^5*b + 3*a^4*b^2 + a^3*b^3)*d*cosh(d*x + c)^9 - 4*(a^6 + 7*a^5*b + 11*a^4*b^2 + 5*a^3*b^3)*d*cosh(d*x + c)^7 - 6*(a^6 - 3*a^5*b - 9*a^4*b^2 - 5*a^3*b^3)*d*cosh(d*x + c)^5 + 4*(a^6 - 3*a^5*b - 9*a^4*b^2 - 5*a^3*b^3)*d*cosh(d*x + c)^3 + (a^6 + 7*a^5*b + 11*a^4*b^2 + 5*a^3*b^3)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
190,1,7528,0,0.580974," ","integrate(tanh(d*x+c)^6/(a+b*tanh(d*x+c)^2)^3,x, algorithm=""fricas"")","\left[\frac{16 \, {\left(a^{2} b^{2} + 2 \, a b^{3} + b^{4}\right)} d x \cosh\left(d x + c\right)^{8} + 128 \, {\left(a^{2} b^{2} + 2 \, a b^{3} + b^{4}\right)} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + 16 \, {\left(a^{2} b^{2} + 2 \, a b^{3} + b^{4}\right)} d x \sinh\left(d x + c\right)^{8} - 4 \, {\left(3 \, a^{4} + 13 \, a^{3} b + a^{2} b^{2} - 9 \, a b^{3} - 16 \, {\left(a^{2} b^{2} - b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(112 \, {\left(a^{2} b^{2} + 2 \, a b^{3} + b^{4}\right)} d x \cosh\left(d x + c\right)^{2} - 3 \, a^{4} - 13 \, a^{3} b - a^{2} b^{2} + 9 \, a b^{3} + 16 \, {\left(a^{2} b^{2} - b^{4}\right)} d x\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(112 \, {\left(a^{2} b^{2} + 2 \, a b^{3} + b^{4}\right)} d x \cosh\left(d x + c\right)^{3} - 3 \, {\left(3 \, a^{4} + 13 \, a^{3} b + a^{2} b^{2} - 9 \, a b^{3} - 16 \, {\left(a^{2} b^{2} - b^{4}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 4 \, {\left(9 \, a^{4} + 21 \, a^{3} b - 9 \, a^{2} b^{2} + 27 \, a b^{3} - 8 \, {\left(3 \, a^{2} b^{2} - 2 \, a b^{3} + 3 \, b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(280 \, {\left(a^{2} b^{2} + 2 \, a b^{3} + b^{4}\right)} d x \cosh\left(d x + c\right)^{4} - 9 \, a^{4} - 21 \, a^{3} b + 9 \, a^{2} b^{2} - 27 \, a b^{3} + 8 \, {\left(3 \, a^{2} b^{2} - 2 \, a b^{3} + 3 \, b^{4}\right)} d x - 15 \, {\left(3 \, a^{4} + 13 \, a^{3} b + a^{2} b^{2} - 9 \, a b^{3} - 16 \, {\left(a^{2} b^{2} - b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} - 12 \, a^{4} - 60 \, a^{3} b - 84 \, a^{2} b^{2} - 36 \, a b^{3} + 16 \, {\left(56 \, {\left(a^{2} b^{2} + 2 \, a b^{3} + b^{4}\right)} d x \cosh\left(d x + c\right)^{5} - 5 \, {\left(3 \, a^{4} + 13 \, a^{3} b + a^{2} b^{2} - 9 \, a b^{3} - 16 \, {\left(a^{2} b^{2} - b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - {\left(9 \, a^{4} + 21 \, a^{3} b - 9 \, a^{2} b^{2} + 27 \, a b^{3} - 8 \, {\left(3 \, a^{2} b^{2} - 2 \, a b^{3} + 3 \, b^{4}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 16 \, {\left(a^{2} b^{2} + 2 \, a b^{3} + b^{4}\right)} d x - 4 \, {\left(9 \, a^{4} + 23 \, a^{3} b - 13 \, a^{2} b^{2} - 27 \, a b^{3} - 16 \, {\left(a^{2} b^{2} - b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(112 \, {\left(a^{2} b^{2} + 2 \, a b^{3} + b^{4}\right)} d x \cosh\left(d x + c\right)^{6} - 15 \, {\left(3 \, a^{4} + 13 \, a^{3} b + a^{2} b^{2} - 9 \, a b^{3} - 16 \, {\left(a^{2} b^{2} - b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{4} - 9 \, a^{4} - 23 \, a^{3} b + 13 \, a^{2} b^{2} + 27 \, a b^{3} + 16 \, {\left(a^{2} b^{2} - b^{4}\right)} d x - 6 \, {\left(9 \, a^{4} + 21 \, a^{3} b - 9 \, a^{2} b^{2} + 27 \, a b^{3} - 8 \, {\left(3 \, a^{2} b^{2} - 2 \, a b^{3} + 3 \, b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(3 \, a^{4} + 16 \, a^{3} b + 38 \, a^{2} b^{2} + 40 \, a b^{3} + 15 \, b^{4}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(3 \, a^{4} + 16 \, a^{3} b + 38 \, a^{2} b^{2} + 40 \, a b^{3} + 15 \, b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(3 \, a^{4} + 16 \, a^{3} b + 38 \, a^{2} b^{2} + 40 \, a b^{3} + 15 \, b^{4}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(3 \, a^{4} + 10 \, a^{3} b + 12 \, a^{2} b^{2} - 10 \, a b^{3} - 15 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(3 \, a^{4} + 10 \, a^{3} b + 12 \, a^{2} b^{2} - 10 \, a b^{3} - 15 \, b^{4} + 7 \, {\left(3 \, a^{4} + 16 \, a^{3} b + 38 \, a^{2} b^{2} + 40 \, a b^{3} + 15 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(3 \, a^{4} + 16 \, a^{3} b + 38 \, a^{2} b^{2} + 40 \, a b^{3} + 15 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(3 \, a^{4} + 10 \, a^{3} b + 12 \, a^{2} b^{2} - 10 \, a b^{3} - 15 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(9 \, a^{4} + 24 \, a^{3} b + 34 \, a^{2} b^{2} + 45 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(3 \, a^{4} + 16 \, a^{3} b + 38 \, a^{2} b^{2} + 40 \, a b^{3} + 15 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 9 \, a^{4} + 24 \, a^{3} b + 34 \, a^{2} b^{2} + 45 \, b^{4} + 30 \, {\left(3 \, a^{4} + 10 \, a^{3} b + 12 \, a^{2} b^{2} - 10 \, a b^{3} - 15 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 3 \, a^{4} + 16 \, a^{3} b + 38 \, a^{2} b^{2} + 40 \, a b^{3} + 15 \, b^{4} + 8 \, {\left(7 \, {\left(3 \, a^{4} + 16 \, a^{3} b + 38 \, a^{2} b^{2} + 40 \, a b^{3} + 15 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(3 \, a^{4} + 10 \, a^{3} b + 12 \, a^{2} b^{2} - 10 \, a b^{3} - 15 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(9 \, a^{4} + 24 \, a^{3} b + 34 \, a^{2} b^{2} + 45 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(3 \, a^{4} + 10 \, a^{3} b + 12 \, a^{2} b^{2} - 10 \, a b^{3} - 15 \, b^{4}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(3 \, a^{4} + 16 \, a^{3} b + 38 \, a^{2} b^{2} + 40 \, a b^{3} + 15 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(3 \, a^{4} + 10 \, a^{3} b + 12 \, a^{2} b^{2} - 10 \, a b^{3} - 15 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 3 \, a^{4} + 10 \, a^{3} b + 12 \, a^{2} b^{2} - 10 \, a b^{3} - 15 \, b^{4} + 3 \, {\left(9 \, a^{4} + 24 \, a^{3} b + 34 \, a^{2} b^{2} + 45 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left({\left(3 \, a^{4} + 16 \, a^{3} b + 38 \, a^{2} b^{2} + 40 \, a b^{3} + 15 \, b^{4}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(3 \, a^{4} + 10 \, a^{3} b + 12 \, a^{2} b^{2} - 10 \, a b^{3} - 15 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + {\left(9 \, a^{4} + 24 \, a^{3} b + 34 \, a^{2} b^{2} + 45 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{4} + 10 \, a^{3} b + 12 \, a^{2} b^{2} - 10 \, a b^{3} - 15 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{a}{b}} \log\left(\frac{{\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) \sinh\left(d x + c\right)^{3} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{2} + a^{2} - 6 \, a b + b^{2} + 4 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} - 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} + a b - b^{2}\right)} \sqrt{-\frac{a}{b}}}{{\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) + 8 \, {\left(16 \, {\left(a^{2} b^{2} + 2 \, a b^{3} + b^{4}\right)} d x \cosh\left(d x + c\right)^{7} - 3 \, {\left(3 \, a^{4} + 13 \, a^{3} b + a^{2} b^{2} - 9 \, a b^{3} - 16 \, {\left(a^{2} b^{2} - b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{5} - 2 \, {\left(9 \, a^{4} + 21 \, a^{3} b - 9 \, a^{2} b^{2} + 27 \, a b^{3} - 8 \, {\left(3 \, a^{2} b^{2} - 2 \, a b^{3} + 3 \, b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - {\left(9 \, a^{4} + 23 \, a^{3} b - 13 \, a^{2} b^{2} - 27 \, a b^{3} - 16 \, {\left(a^{2} b^{2} - b^{4}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{16 \, {\left({\left(a^{5} b^{2} + 5 \, a^{4} b^{3} + 10 \, a^{3} b^{4} + 10 \, a^{2} b^{5} + 5 \, a b^{6} + b^{7}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{5} b^{2} + 5 \, a^{4} b^{3} + 10 \, a^{3} b^{4} + 10 \, a^{2} b^{5} + 5 \, a b^{6} + b^{7}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{5} b^{2} + 5 \, a^{4} b^{3} + 10 \, a^{3} b^{4} + 10 \, a^{2} b^{5} + 5 \, a b^{6} + b^{7}\right)} d \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{5} b^{2} + 3 \, a^{4} b^{3} + 2 \, a^{3} b^{4} - 2 \, a^{2} b^{5} - 3 \, a b^{6} - b^{7}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{5} b^{2} + 5 \, a^{4} b^{3} + 10 \, a^{3} b^{4} + 10 \, a^{2} b^{5} + 5 \, a b^{6} + b^{7}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{5} b^{2} + 3 \, a^{4} b^{3} + 2 \, a^{3} b^{4} - 2 \, a^{2} b^{5} - 3 \, a b^{6} - b^{7}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(3 \, a^{5} b^{2} + 7 \, a^{4} b^{3} + 6 \, a^{3} b^{4} + 6 \, a^{2} b^{5} + 7 \, a b^{6} + 3 \, b^{7}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{5} b^{2} + 5 \, a^{4} b^{3} + 10 \, a^{3} b^{4} + 10 \, a^{2} b^{5} + 5 \, a b^{6} + b^{7}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{5} b^{2} + 3 \, a^{4} b^{3} + 2 \, a^{3} b^{4} - 2 \, a^{2} b^{5} - 3 \, 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^{5} b^{2} + 5 \, a^{4} b^{3} + 10 \, a^{3} b^{4} + 10 \, a^{2} b^{5} + 5 \, a b^{6} + b^{7}\right)} d \cosh\left(d x + c\right)^{4} + 30 \, {\left(a^{5} b^{2} + 3 \, a^{4} b^{3} + 2 \, a^{3} b^{4} - 2 \, a^{2} b^{5} - 3 \, a b^{6} - b^{7}\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{5} b^{2} + 7 \, a^{4} b^{3} + 6 \, a^{3} b^{4} + 6 \, a^{2} b^{5} + 7 \, a b^{6} + 3 \, b^{7}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{5} b^{2} + 3 \, a^{4} b^{3} + 2 \, a^{3} b^{4} - 2 \, a^{2} b^{5} - 3 \, a b^{6} - b^{7}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a^{5} b^{2} + 5 \, a^{4} b^{3} + 10 \, a^{3} b^{4} + 10 \, a^{2} b^{5} + 5 \, a b^{6} + b^{7}\right)} d \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{5} b^{2} + 3 \, a^{4} b^{3} + 2 \, a^{3} b^{4} - 2 \, a^{2} b^{5} - 3 \, a b^{6} - b^{7}\right)} d \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{5} b^{2} + 7 \, a^{4} b^{3} + 6 \, a^{3} b^{4} + 6 \, a^{2} b^{5} + 7 \, 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^{5} b^{2} + 5 \, a^{4} b^{3} + 10 \, a^{3} b^{4} + 10 \, a^{2} b^{5} + 5 \, a b^{6} + b^{7}\right)} d \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{5} b^{2} + 3 \, a^{4} b^{3} + 2 \, a^{3} b^{4} - 2 \, a^{2} b^{5} - 3 \, a b^{6} - b^{7}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{5} b^{2} + 7 \, a^{4} b^{3} + 6 \, a^{3} b^{4} + 6 \, a^{2} b^{5} + 7 \, a b^{6} + 3 \, b^{7}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{5} b^{2} + 3 \, a^{4} b^{3} + 2 \, a^{3} b^{4} - 2 \, a^{2} b^{5} - 3 \, a b^{6} - b^{7}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{5} b^{2} + 5 \, a^{4} b^{3} + 10 \, a^{3} b^{4} + 10 \, a^{2} b^{5} + 5 \, a b^{6} + b^{7}\right)} d + 8 \, {\left({\left(a^{5} b^{2} + 5 \, a^{4} b^{3} + 10 \, a^{3} b^{4} + 10 \, a^{2} b^{5} + 5 \, a b^{6} + b^{7}\right)} d \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{5} b^{2} + 3 \, a^{4} b^{3} + 2 \, a^{3} b^{4} - 2 \, a^{2} b^{5} - 3 \, a b^{6} - b^{7}\right)} d \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{5} b^{2} + 7 \, a^{4} b^{3} + 6 \, a^{3} b^{4} + 6 \, a^{2} b^{5} + 7 \, a b^{6} + 3 \, b^{7}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{5} b^{2} + 3 \, a^{4} b^{3} + 2 \, a^{3} b^{4} - 2 \, a^{2} b^{5} - 3 \, a b^{6} - b^{7}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}, \frac{8 \, {\left(a^{2} b^{2} + 2 \, a b^{3} + b^{4}\right)} d x \cosh\left(d x + c\right)^{8} + 64 \, {\left(a^{2} b^{2} + 2 \, a b^{3} + b^{4}\right)} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + 8 \, {\left(a^{2} b^{2} + 2 \, a b^{3} + b^{4}\right)} d x \sinh\left(d x + c\right)^{8} - 2 \, {\left(3 \, a^{4} + 13 \, a^{3} b + a^{2} b^{2} - 9 \, a b^{3} - 16 \, {\left(a^{2} b^{2} - b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(112 \, {\left(a^{2} b^{2} + 2 \, a b^{3} + b^{4}\right)} d x \cosh\left(d x + c\right)^{2} - 3 \, a^{4} - 13 \, a^{3} b - a^{2} b^{2} + 9 \, a b^{3} + 16 \, {\left(a^{2} b^{2} - b^{4}\right)} d x\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(112 \, {\left(a^{2} b^{2} + 2 \, a b^{3} + b^{4}\right)} d x \cosh\left(d x + c\right)^{3} - 3 \, {\left(3 \, a^{4} + 13 \, a^{3} b + a^{2} b^{2} - 9 \, a b^{3} - 16 \, {\left(a^{2} b^{2} - b^{4}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 2 \, {\left(9 \, a^{4} + 21 \, a^{3} b - 9 \, a^{2} b^{2} + 27 \, a b^{3} - 8 \, {\left(3 \, a^{2} b^{2} - 2 \, a b^{3} + 3 \, b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(280 \, {\left(a^{2} b^{2} + 2 \, a b^{3} + b^{4}\right)} d x \cosh\left(d x + c\right)^{4} - 9 \, a^{4} - 21 \, a^{3} b + 9 \, a^{2} b^{2} - 27 \, a b^{3} + 8 \, {\left(3 \, a^{2} b^{2} - 2 \, a b^{3} + 3 \, b^{4}\right)} d x - 15 \, {\left(3 \, a^{4} + 13 \, a^{3} b + a^{2} b^{2} - 9 \, a b^{3} - 16 \, {\left(a^{2} b^{2} - b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} - 6 \, a^{4} - 30 \, a^{3} b - 42 \, a^{2} b^{2} - 18 \, a b^{3} + 8 \, {\left(56 \, {\left(a^{2} b^{2} + 2 \, a b^{3} + b^{4}\right)} d x \cosh\left(d x + c\right)^{5} - 5 \, {\left(3 \, a^{4} + 13 \, a^{3} b + a^{2} b^{2} - 9 \, a b^{3} - 16 \, {\left(a^{2} b^{2} - b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - {\left(9 \, a^{4} + 21 \, a^{3} b - 9 \, a^{2} b^{2} + 27 \, a b^{3} - 8 \, {\left(3 \, a^{2} b^{2} - 2 \, a b^{3} + 3 \, b^{4}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 8 \, {\left(a^{2} b^{2} + 2 \, a b^{3} + b^{4}\right)} d x - 2 \, {\left(9 \, a^{4} + 23 \, a^{3} b - 13 \, a^{2} b^{2} - 27 \, a b^{3} - 16 \, {\left(a^{2} b^{2} - b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(112 \, {\left(a^{2} b^{2} + 2 \, a b^{3} + b^{4}\right)} d x \cosh\left(d x + c\right)^{6} - 15 \, {\left(3 \, a^{4} + 13 \, a^{3} b + a^{2} b^{2} - 9 \, a b^{3} - 16 \, {\left(a^{2} b^{2} - b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{4} - 9 \, a^{4} - 23 \, a^{3} b + 13 \, a^{2} b^{2} + 27 \, a b^{3} + 16 \, {\left(a^{2} b^{2} - b^{4}\right)} d x - 6 \, {\left(9 \, a^{4} + 21 \, a^{3} b - 9 \, a^{2} b^{2} + 27 \, a b^{3} - 8 \, {\left(3 \, a^{2} b^{2} - 2 \, a b^{3} + 3 \, b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} - {\left({\left(3 \, a^{4} + 16 \, a^{3} b + 38 \, a^{2} b^{2} + 40 \, a b^{3} + 15 \, b^{4}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(3 \, a^{4} + 16 \, a^{3} b + 38 \, a^{2} b^{2} + 40 \, a b^{3} + 15 \, b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(3 \, a^{4} + 16 \, a^{3} b + 38 \, a^{2} b^{2} + 40 \, a b^{3} + 15 \, b^{4}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(3 \, a^{4} + 10 \, a^{3} b + 12 \, a^{2} b^{2} - 10 \, a b^{3} - 15 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(3 \, a^{4} + 10 \, a^{3} b + 12 \, a^{2} b^{2} - 10 \, a b^{3} - 15 \, b^{4} + 7 \, {\left(3 \, a^{4} + 16 \, a^{3} b + 38 \, a^{2} b^{2} + 40 \, a b^{3} + 15 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(3 \, a^{4} + 16 \, a^{3} b + 38 \, a^{2} b^{2} + 40 \, a b^{3} + 15 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(3 \, a^{4} + 10 \, a^{3} b + 12 \, a^{2} b^{2} - 10 \, a b^{3} - 15 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(9 \, a^{4} + 24 \, a^{3} b + 34 \, a^{2} b^{2} + 45 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(3 \, a^{4} + 16 \, a^{3} b + 38 \, a^{2} b^{2} + 40 \, a b^{3} + 15 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 9 \, a^{4} + 24 \, a^{3} b + 34 \, a^{2} b^{2} + 45 \, b^{4} + 30 \, {\left(3 \, a^{4} + 10 \, a^{3} b + 12 \, a^{2} b^{2} - 10 \, a b^{3} - 15 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 3 \, a^{4} + 16 \, a^{3} b + 38 \, a^{2} b^{2} + 40 \, a b^{3} + 15 \, b^{4} + 8 \, {\left(7 \, {\left(3 \, a^{4} + 16 \, a^{3} b + 38 \, a^{2} b^{2} + 40 \, a b^{3} + 15 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(3 \, a^{4} + 10 \, a^{3} b + 12 \, a^{2} b^{2} - 10 \, a b^{3} - 15 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(9 \, a^{4} + 24 \, a^{3} b + 34 \, a^{2} b^{2} + 45 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(3 \, a^{4} + 10 \, a^{3} b + 12 \, a^{2} b^{2} - 10 \, a b^{3} - 15 \, b^{4}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(3 \, a^{4} + 16 \, a^{3} b + 38 \, a^{2} b^{2} + 40 \, a b^{3} + 15 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(3 \, a^{4} + 10 \, a^{3} b + 12 \, a^{2} b^{2} - 10 \, a b^{3} - 15 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 3 \, a^{4} + 10 \, a^{3} b + 12 \, a^{2} b^{2} - 10 \, a b^{3} - 15 \, b^{4} + 3 \, {\left(9 \, a^{4} + 24 \, a^{3} b + 34 \, a^{2} b^{2} + 45 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left({\left(3 \, a^{4} + 16 \, a^{3} b + 38 \, a^{2} b^{2} + 40 \, a b^{3} + 15 \, b^{4}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(3 \, a^{4} + 10 \, a^{3} b + 12 \, a^{2} b^{2} - 10 \, a b^{3} - 15 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + {\left(9 \, a^{4} + 24 \, a^{3} b + 34 \, a^{2} b^{2} + 45 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{4} + 10 \, a^{3} b + 12 \, a^{2} b^{2} - 10 \, a b^{3} - 15 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{a}{b}} \arctan\left(\frac{{\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} + a - b\right)} \sqrt{\frac{a}{b}}}{2 \, a}\right) + 4 \, {\left(16 \, {\left(a^{2} b^{2} + 2 \, a b^{3} + b^{4}\right)} d x \cosh\left(d x + c\right)^{7} - 3 \, {\left(3 \, a^{4} + 13 \, a^{3} b + a^{2} b^{2} - 9 \, a b^{3} - 16 \, {\left(a^{2} b^{2} - b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{5} - 2 \, {\left(9 \, a^{4} + 21 \, a^{3} b - 9 \, a^{2} b^{2} + 27 \, a b^{3} - 8 \, {\left(3 \, a^{2} b^{2} - 2 \, a b^{3} + 3 \, b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - {\left(9 \, a^{4} + 23 \, a^{3} b - 13 \, a^{2} b^{2} - 27 \, a b^{3} - 16 \, {\left(a^{2} b^{2} - b^{4}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{8 \, {\left({\left(a^{5} b^{2} + 5 \, a^{4} b^{3} + 10 \, a^{3} b^{4} + 10 \, a^{2} b^{5} + 5 \, a b^{6} + b^{7}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{5} b^{2} + 5 \, a^{4} b^{3} + 10 \, a^{3} b^{4} + 10 \, a^{2} b^{5} + 5 \, a b^{6} + b^{7}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{5} b^{2} + 5 \, a^{4} b^{3} + 10 \, a^{3} b^{4} + 10 \, a^{2} b^{5} + 5 \, a b^{6} + b^{7}\right)} d \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{5} b^{2} + 3 \, a^{4} b^{3} + 2 \, a^{3} b^{4} - 2 \, a^{2} b^{5} - 3 \, a b^{6} - b^{7}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{5} b^{2} + 5 \, a^{4} b^{3} + 10 \, a^{3} b^{4} + 10 \, a^{2} b^{5} + 5 \, a b^{6} + b^{7}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{5} b^{2} + 3 \, a^{4} b^{3} + 2 \, a^{3} b^{4} - 2 \, a^{2} b^{5} - 3 \, a b^{6} - b^{7}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(3 \, a^{5} b^{2} + 7 \, a^{4} b^{3} + 6 \, a^{3} b^{4} + 6 \, a^{2} b^{5} + 7 \, a b^{6} + 3 \, b^{7}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{5} b^{2} + 5 \, a^{4} b^{3} + 10 \, a^{3} b^{4} + 10 \, a^{2} b^{5} + 5 \, a b^{6} + b^{7}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{5} b^{2} + 3 \, a^{4} b^{3} + 2 \, a^{3} b^{4} - 2 \, a^{2} b^{5} - 3 \, 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^{5} b^{2} + 5 \, a^{4} b^{3} + 10 \, a^{3} b^{4} + 10 \, a^{2} b^{5} + 5 \, a b^{6} + b^{7}\right)} d \cosh\left(d x + c\right)^{4} + 30 \, {\left(a^{5} b^{2} + 3 \, a^{4} b^{3} + 2 \, a^{3} b^{4} - 2 \, a^{2} b^{5} - 3 \, a b^{6} - b^{7}\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{5} b^{2} + 7 \, a^{4} b^{3} + 6 \, a^{3} b^{4} + 6 \, a^{2} b^{5} + 7 \, a b^{6} + 3 \, b^{7}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{5} b^{2} + 3 \, a^{4} b^{3} + 2 \, a^{3} b^{4} - 2 \, a^{2} b^{5} - 3 \, a b^{6} - b^{7}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a^{5} b^{2} + 5 \, a^{4} b^{3} + 10 \, a^{3} b^{4} + 10 \, a^{2} b^{5} + 5 \, a b^{6} + b^{7}\right)} d \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{5} b^{2} + 3 \, a^{4} b^{3} + 2 \, a^{3} b^{4} - 2 \, a^{2} b^{5} - 3 \, a b^{6} - b^{7}\right)} d \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{5} b^{2} + 7 \, a^{4} b^{3} + 6 \, a^{3} b^{4} + 6 \, a^{2} b^{5} + 7 \, 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^{5} b^{2} + 5 \, a^{4} b^{3} + 10 \, a^{3} b^{4} + 10 \, a^{2} b^{5} + 5 \, a b^{6} + b^{7}\right)} d \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{5} b^{2} + 3 \, a^{4} b^{3} + 2 \, a^{3} b^{4} - 2 \, a^{2} b^{5} - 3 \, a b^{6} - b^{7}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{5} b^{2} + 7 \, a^{4} b^{3} + 6 \, a^{3} b^{4} + 6 \, a^{2} b^{5} + 7 \, a b^{6} + 3 \, b^{7}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{5} b^{2} + 3 \, a^{4} b^{3} + 2 \, a^{3} b^{4} - 2 \, a^{2} b^{5} - 3 \, a b^{6} - b^{7}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{5} b^{2} + 5 \, a^{4} b^{3} + 10 \, a^{3} b^{4} + 10 \, a^{2} b^{5} + 5 \, a b^{6} + b^{7}\right)} d + 8 \, {\left({\left(a^{5} b^{2} + 5 \, a^{4} b^{3} + 10 \, a^{3} b^{4} + 10 \, a^{2} b^{5} + 5 \, a b^{6} + b^{7}\right)} d \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{5} b^{2} + 3 \, a^{4} b^{3} + 2 \, a^{3} b^{4} - 2 \, a^{2} b^{5} - 3 \, a b^{6} - b^{7}\right)} d \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{5} b^{2} + 7 \, a^{4} b^{3} + 6 \, a^{3} b^{4} + 6 \, a^{2} b^{5} + 7 \, a b^{6} + 3 \, b^{7}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{5} b^{2} + 3 \, a^{4} b^{3} + 2 \, a^{3} b^{4} - 2 \, a^{2} b^{5} - 3 \, 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*(16*(a^2*b^2 + 2*a*b^3 + b^4)*d*x*cosh(d*x + c)^8 + 128*(a^2*b^2 + 2*a*b^3 + b^4)*d*x*cosh(d*x + c)*sinh(d*x + c)^7 + 16*(a^2*b^2 + 2*a*b^3 + b^4)*d*x*sinh(d*x + c)^8 - 4*(3*a^4 + 13*a^3*b + a^2*b^2 - 9*a*b^3 - 16*(a^2*b^2 - b^4)*d*x)*cosh(d*x + c)^6 + 4*(112*(a^2*b^2 + 2*a*b^3 + b^4)*d*x*cosh(d*x + c)^2 - 3*a^4 - 13*a^3*b - a^2*b^2 + 9*a*b^3 + 16*(a^2*b^2 - b^4)*d*x)*sinh(d*x + c)^6 + 8*(112*(a^2*b^2 + 2*a*b^3 + b^4)*d*x*cosh(d*x + c)^3 - 3*(3*a^4 + 13*a^3*b + a^2*b^2 - 9*a*b^3 - 16*(a^2*b^2 - b^4)*d*x)*cosh(d*x + c))*sinh(d*x + c)^5 - 4*(9*a^4 + 21*a^3*b - 9*a^2*b^2 + 27*a*b^3 - 8*(3*a^2*b^2 - 2*a*b^3 + 3*b^4)*d*x)*cosh(d*x + c)^4 + 4*(280*(a^2*b^2 + 2*a*b^3 + b^4)*d*x*cosh(d*x + c)^4 - 9*a^4 - 21*a^3*b + 9*a^2*b^2 - 27*a*b^3 + 8*(3*a^2*b^2 - 2*a*b^3 + 3*b^4)*d*x - 15*(3*a^4 + 13*a^3*b + a^2*b^2 - 9*a*b^3 - 16*(a^2*b^2 - b^4)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^4 - 12*a^4 - 60*a^3*b - 84*a^2*b^2 - 36*a*b^3 + 16*(56*(a^2*b^2 + 2*a*b^3 + b^4)*d*x*cosh(d*x + c)^5 - 5*(3*a^4 + 13*a^3*b + a^2*b^2 - 9*a*b^3 - 16*(a^2*b^2 - b^4)*d*x)*cosh(d*x + c)^3 - (9*a^4 + 21*a^3*b - 9*a^2*b^2 + 27*a*b^3 - 8*(3*a^2*b^2 - 2*a*b^3 + 3*b^4)*d*x)*cosh(d*x + c))*sinh(d*x + c)^3 + 16*(a^2*b^2 + 2*a*b^3 + b^4)*d*x - 4*(9*a^4 + 23*a^3*b - 13*a^2*b^2 - 27*a*b^3 - 16*(a^2*b^2 - b^4)*d*x)*cosh(d*x + c)^2 + 4*(112*(a^2*b^2 + 2*a*b^3 + b^4)*d*x*cosh(d*x + c)^6 - 15*(3*a^4 + 13*a^3*b + a^2*b^2 - 9*a*b^3 - 16*(a^2*b^2 - b^4)*d*x)*cosh(d*x + c)^4 - 9*a^4 - 23*a^3*b + 13*a^2*b^2 + 27*a*b^3 + 16*(a^2*b^2 - b^4)*d*x - 6*(9*a^4 + 21*a^3*b - 9*a^2*b^2 + 27*a*b^3 - 8*(3*a^2*b^2 - 2*a*b^3 + 3*b^4)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((3*a^4 + 16*a^3*b + 38*a^2*b^2 + 40*a*b^3 + 15*b^4)*cosh(d*x + c)^8 + 8*(3*a^4 + 16*a^3*b + 38*a^2*b^2 + 40*a*b^3 + 15*b^4)*cosh(d*x + c)*sinh(d*x + c)^7 + (3*a^4 + 16*a^3*b + 38*a^2*b^2 + 40*a*b^3 + 15*b^4)*sinh(d*x + c)^8 + 4*(3*a^4 + 10*a^3*b + 12*a^2*b^2 - 10*a*b^3 - 15*b^4)*cosh(d*x + c)^6 + 4*(3*a^4 + 10*a^3*b + 12*a^2*b^2 - 10*a*b^3 - 15*b^4 + 7*(3*a^4 + 16*a^3*b + 38*a^2*b^2 + 40*a*b^3 + 15*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(3*a^4 + 16*a^3*b + 38*a^2*b^2 + 40*a*b^3 + 15*b^4)*cosh(d*x + c)^3 + 3*(3*a^4 + 10*a^3*b + 12*a^2*b^2 - 10*a*b^3 - 15*b^4)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(9*a^4 + 24*a^3*b + 34*a^2*b^2 + 45*b^4)*cosh(d*x + c)^4 + 2*(35*(3*a^4 + 16*a^3*b + 38*a^2*b^2 + 40*a*b^3 + 15*b^4)*cosh(d*x + c)^4 + 9*a^4 + 24*a^3*b + 34*a^2*b^2 + 45*b^4 + 30*(3*a^4 + 10*a^3*b + 12*a^2*b^2 - 10*a*b^3 - 15*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 3*a^4 + 16*a^3*b + 38*a^2*b^2 + 40*a*b^3 + 15*b^4 + 8*(7*(3*a^4 + 16*a^3*b + 38*a^2*b^2 + 40*a*b^3 + 15*b^4)*cosh(d*x + c)^5 + 10*(3*a^4 + 10*a^3*b + 12*a^2*b^2 - 10*a*b^3 - 15*b^4)*cosh(d*x + c)^3 + (9*a^4 + 24*a^3*b + 34*a^2*b^2 + 45*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(3*a^4 + 10*a^3*b + 12*a^2*b^2 - 10*a*b^3 - 15*b^4)*cosh(d*x + c)^2 + 4*(7*(3*a^4 + 16*a^3*b + 38*a^2*b^2 + 40*a*b^3 + 15*b^4)*cosh(d*x + c)^6 + 15*(3*a^4 + 10*a^3*b + 12*a^2*b^2 - 10*a*b^3 - 15*b^4)*cosh(d*x + c)^4 + 3*a^4 + 10*a^3*b + 12*a^2*b^2 - 10*a*b^3 - 15*b^4 + 3*(9*a^4 + 24*a^3*b + 34*a^2*b^2 + 45*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((3*a^4 + 16*a^3*b + 38*a^2*b^2 + 40*a*b^3 + 15*b^4)*cosh(d*x + c)^7 + 3*(3*a^4 + 10*a^3*b + 12*a^2*b^2 - 10*a*b^3 - 15*b^4)*cosh(d*x + c)^5 + (9*a^4 + 24*a^3*b + 34*a^2*b^2 + 45*b^4)*cosh(d*x + c)^3 + (3*a^4 + 10*a^3*b + 12*a^2*b^2 - 10*a*b^3 - 15*b^4)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-a/b)*log(((a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 + 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 + 2*(a^2 - b^2)*cosh(d*x + c)^2 + 2*(3*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + a^2 - b^2)*sinh(d*x + c)^2 + a^2 - 6*a*b + b^2 + 4*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 + (a^2 - 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 + a*b - b^2)*sqrt(-a/b))/((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)) + 8*(16*(a^2*b^2 + 2*a*b^3 + b^4)*d*x*cosh(d*x + c)^7 - 3*(3*a^4 + 13*a^3*b + a^2*b^2 - 9*a*b^3 - 16*(a^2*b^2 - b^4)*d*x)*cosh(d*x + c)^5 - 2*(9*a^4 + 21*a^3*b - 9*a^2*b^2 + 27*a*b^3 - 8*(3*a^2*b^2 - 2*a*b^3 + 3*b^4)*d*x)*cosh(d*x + c)^3 - (9*a^4 + 23*a^3*b - 13*a^2*b^2 - 27*a*b^3 - 16*(a^2*b^2 - b^4)*d*x)*cosh(d*x + c))*sinh(d*x + c))/((a^5*b^2 + 5*a^4*b^3 + 10*a^3*b^4 + 10*a^2*b^5 + 5*a*b^6 + b^7)*d*cosh(d*x + c)^8 + 8*(a^5*b^2 + 5*a^4*b^3 + 10*a^3*b^4 + 10*a^2*b^5 + 5*a*b^6 + b^7)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^5*b^2 + 5*a^4*b^3 + 10*a^3*b^4 + 10*a^2*b^5 + 5*a*b^6 + b^7)*d*sinh(d*x + c)^8 + 4*(a^5*b^2 + 3*a^4*b^3 + 2*a^3*b^4 - 2*a^2*b^5 - 3*a*b^6 - b^7)*d*cosh(d*x + c)^6 + 4*(7*(a^5*b^2 + 5*a^4*b^3 + 10*a^3*b^4 + 10*a^2*b^5 + 5*a*b^6 + b^7)*d*cosh(d*x + c)^2 + (a^5*b^2 + 3*a^4*b^3 + 2*a^3*b^4 - 2*a^2*b^5 - 3*a*b^6 - b^7)*d)*sinh(d*x + c)^6 + 2*(3*a^5*b^2 + 7*a^4*b^3 + 6*a^3*b^4 + 6*a^2*b^5 + 7*a*b^6 + 3*b^7)*d*cosh(d*x + c)^4 + 8*(7*(a^5*b^2 + 5*a^4*b^3 + 10*a^3*b^4 + 10*a^2*b^5 + 5*a*b^6 + b^7)*d*cosh(d*x + c)^3 + 3*(a^5*b^2 + 3*a^4*b^3 + 2*a^3*b^4 - 2*a^2*b^5 - 3*a*b^6 - b^7)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^5*b^2 + 5*a^4*b^3 + 10*a^3*b^4 + 10*a^2*b^5 + 5*a*b^6 + b^7)*d*cosh(d*x + c)^4 + 30*(a^5*b^2 + 3*a^4*b^3 + 2*a^3*b^4 - 2*a^2*b^5 - 3*a*b^6 - b^7)*d*cosh(d*x + c)^2 + (3*a^5*b^2 + 7*a^4*b^3 + 6*a^3*b^4 + 6*a^2*b^5 + 7*a*b^6 + 3*b^7)*d)*sinh(d*x + c)^4 + 4*(a^5*b^2 + 3*a^4*b^3 + 2*a^3*b^4 - 2*a^2*b^5 - 3*a*b^6 - b^7)*d*cosh(d*x + c)^2 + 8*(7*(a^5*b^2 + 5*a^4*b^3 + 10*a^3*b^4 + 10*a^2*b^5 + 5*a*b^6 + b^7)*d*cosh(d*x + c)^5 + 10*(a^5*b^2 + 3*a^4*b^3 + 2*a^3*b^4 - 2*a^2*b^5 - 3*a*b^6 - b^7)*d*cosh(d*x + c)^3 + (3*a^5*b^2 + 7*a^4*b^3 + 6*a^3*b^4 + 6*a^2*b^5 + 7*a*b^6 + 3*b^7)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^5*b^2 + 5*a^4*b^3 + 10*a^3*b^4 + 10*a^2*b^5 + 5*a*b^6 + b^7)*d*cosh(d*x + c)^6 + 15*(a^5*b^2 + 3*a^4*b^3 + 2*a^3*b^4 - 2*a^2*b^5 - 3*a*b^6 - b^7)*d*cosh(d*x + c)^4 + 3*(3*a^5*b^2 + 7*a^4*b^3 + 6*a^3*b^4 + 6*a^2*b^5 + 7*a*b^6 + 3*b^7)*d*cosh(d*x + c)^2 + (a^5*b^2 + 3*a^4*b^3 + 2*a^3*b^4 - 2*a^2*b^5 - 3*a*b^6 - b^7)*d)*sinh(d*x + c)^2 + (a^5*b^2 + 5*a^4*b^3 + 10*a^3*b^4 + 10*a^2*b^5 + 5*a*b^6 + b^7)*d + 8*((a^5*b^2 + 5*a^4*b^3 + 10*a^3*b^4 + 10*a^2*b^5 + 5*a*b^6 + b^7)*d*cosh(d*x + c)^7 + 3*(a^5*b^2 + 3*a^4*b^3 + 2*a^3*b^4 - 2*a^2*b^5 - 3*a*b^6 - b^7)*d*cosh(d*x + c)^5 + (3*a^5*b^2 + 7*a^4*b^3 + 6*a^3*b^4 + 6*a^2*b^5 + 7*a*b^6 + 3*b^7)*d*cosh(d*x + c)^3 + (a^5*b^2 + 3*a^4*b^3 + 2*a^3*b^4 - 2*a^2*b^5 - 3*a*b^6 - b^7)*d*cosh(d*x + c))*sinh(d*x + c)), 1/8*(8*(a^2*b^2 + 2*a*b^3 + b^4)*d*x*cosh(d*x + c)^8 + 64*(a^2*b^2 + 2*a*b^3 + b^4)*d*x*cosh(d*x + c)*sinh(d*x + c)^7 + 8*(a^2*b^2 + 2*a*b^3 + b^4)*d*x*sinh(d*x + c)^8 - 2*(3*a^4 + 13*a^3*b + a^2*b^2 - 9*a*b^3 - 16*(a^2*b^2 - b^4)*d*x)*cosh(d*x + c)^6 + 2*(112*(a^2*b^2 + 2*a*b^3 + b^4)*d*x*cosh(d*x + c)^2 - 3*a^4 - 13*a^3*b - a^2*b^2 + 9*a*b^3 + 16*(a^2*b^2 - b^4)*d*x)*sinh(d*x + c)^6 + 4*(112*(a^2*b^2 + 2*a*b^3 + b^4)*d*x*cosh(d*x + c)^3 - 3*(3*a^4 + 13*a^3*b + a^2*b^2 - 9*a*b^3 - 16*(a^2*b^2 - b^4)*d*x)*cosh(d*x + c))*sinh(d*x + c)^5 - 2*(9*a^4 + 21*a^3*b - 9*a^2*b^2 + 27*a*b^3 - 8*(3*a^2*b^2 - 2*a*b^3 + 3*b^4)*d*x)*cosh(d*x + c)^4 + 2*(280*(a^2*b^2 + 2*a*b^3 + b^4)*d*x*cosh(d*x + c)^4 - 9*a^4 - 21*a^3*b + 9*a^2*b^2 - 27*a*b^3 + 8*(3*a^2*b^2 - 2*a*b^3 + 3*b^4)*d*x - 15*(3*a^4 + 13*a^3*b + a^2*b^2 - 9*a*b^3 - 16*(a^2*b^2 - b^4)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^4 - 6*a^4 - 30*a^3*b - 42*a^2*b^2 - 18*a*b^3 + 8*(56*(a^2*b^2 + 2*a*b^3 + b^4)*d*x*cosh(d*x + c)^5 - 5*(3*a^4 + 13*a^3*b + a^2*b^2 - 9*a*b^3 - 16*(a^2*b^2 - b^4)*d*x)*cosh(d*x + c)^3 - (9*a^4 + 21*a^3*b - 9*a^2*b^2 + 27*a*b^3 - 8*(3*a^2*b^2 - 2*a*b^3 + 3*b^4)*d*x)*cosh(d*x + c))*sinh(d*x + c)^3 + 8*(a^2*b^2 + 2*a*b^3 + b^4)*d*x - 2*(9*a^4 + 23*a^3*b - 13*a^2*b^2 - 27*a*b^3 - 16*(a^2*b^2 - b^4)*d*x)*cosh(d*x + c)^2 + 2*(112*(a^2*b^2 + 2*a*b^3 + b^4)*d*x*cosh(d*x + c)^6 - 15*(3*a^4 + 13*a^3*b + a^2*b^2 - 9*a*b^3 - 16*(a^2*b^2 - b^4)*d*x)*cosh(d*x + c)^4 - 9*a^4 - 23*a^3*b + 13*a^2*b^2 + 27*a*b^3 + 16*(a^2*b^2 - b^4)*d*x - 6*(9*a^4 + 21*a^3*b - 9*a^2*b^2 + 27*a*b^3 - 8*(3*a^2*b^2 - 2*a*b^3 + 3*b^4)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - ((3*a^4 + 16*a^3*b + 38*a^2*b^2 + 40*a*b^3 + 15*b^4)*cosh(d*x + c)^8 + 8*(3*a^4 + 16*a^3*b + 38*a^2*b^2 + 40*a*b^3 + 15*b^4)*cosh(d*x + c)*sinh(d*x + c)^7 + (3*a^4 + 16*a^3*b + 38*a^2*b^2 + 40*a*b^3 + 15*b^4)*sinh(d*x + c)^8 + 4*(3*a^4 + 10*a^3*b + 12*a^2*b^2 - 10*a*b^3 - 15*b^4)*cosh(d*x + c)^6 + 4*(3*a^4 + 10*a^3*b + 12*a^2*b^2 - 10*a*b^3 - 15*b^4 + 7*(3*a^4 + 16*a^3*b + 38*a^2*b^2 + 40*a*b^3 + 15*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(3*a^4 + 16*a^3*b + 38*a^2*b^2 + 40*a*b^3 + 15*b^4)*cosh(d*x + c)^3 + 3*(3*a^4 + 10*a^3*b + 12*a^2*b^2 - 10*a*b^3 - 15*b^4)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(9*a^4 + 24*a^3*b + 34*a^2*b^2 + 45*b^4)*cosh(d*x + c)^4 + 2*(35*(3*a^4 + 16*a^3*b + 38*a^2*b^2 + 40*a*b^3 + 15*b^4)*cosh(d*x + c)^4 + 9*a^4 + 24*a^3*b + 34*a^2*b^2 + 45*b^4 + 30*(3*a^4 + 10*a^3*b + 12*a^2*b^2 - 10*a*b^3 - 15*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 3*a^4 + 16*a^3*b + 38*a^2*b^2 + 40*a*b^3 + 15*b^4 + 8*(7*(3*a^4 + 16*a^3*b + 38*a^2*b^2 + 40*a*b^3 + 15*b^4)*cosh(d*x + c)^5 + 10*(3*a^4 + 10*a^3*b + 12*a^2*b^2 - 10*a*b^3 - 15*b^4)*cosh(d*x + c)^3 + (9*a^4 + 24*a^3*b + 34*a^2*b^2 + 45*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(3*a^4 + 10*a^3*b + 12*a^2*b^2 - 10*a*b^3 - 15*b^4)*cosh(d*x + c)^2 + 4*(7*(3*a^4 + 16*a^3*b + 38*a^2*b^2 + 40*a*b^3 + 15*b^4)*cosh(d*x + c)^6 + 15*(3*a^4 + 10*a^3*b + 12*a^2*b^2 - 10*a*b^3 - 15*b^4)*cosh(d*x + c)^4 + 3*a^4 + 10*a^3*b + 12*a^2*b^2 - 10*a*b^3 - 15*b^4 + 3*(9*a^4 + 24*a^3*b + 34*a^2*b^2 + 45*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((3*a^4 + 16*a^3*b + 38*a^2*b^2 + 40*a*b^3 + 15*b^4)*cosh(d*x + c)^7 + 3*(3*a^4 + 10*a^3*b + 12*a^2*b^2 - 10*a*b^3 - 15*b^4)*cosh(d*x + c)^5 + (9*a^4 + 24*a^3*b + 34*a^2*b^2 + 45*b^4)*cosh(d*x + c)^3 + (3*a^4 + 10*a^3*b + 12*a^2*b^2 - 10*a*b^3 - 15*b^4)*cosh(d*x + c))*sinh(d*x + c))*sqrt(a/b)*arctan(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 + a - b)*sqrt(a/b)/a) + 4*(16*(a^2*b^2 + 2*a*b^3 + b^4)*d*x*cosh(d*x + c)^7 - 3*(3*a^4 + 13*a^3*b + a^2*b^2 - 9*a*b^3 - 16*(a^2*b^2 - b^4)*d*x)*cosh(d*x + c)^5 - 2*(9*a^4 + 21*a^3*b - 9*a^2*b^2 + 27*a*b^3 - 8*(3*a^2*b^2 - 2*a*b^3 + 3*b^4)*d*x)*cosh(d*x + c)^3 - (9*a^4 + 23*a^3*b - 13*a^2*b^2 - 27*a*b^3 - 16*(a^2*b^2 - b^4)*d*x)*cosh(d*x + c))*sinh(d*x + c))/((a^5*b^2 + 5*a^4*b^3 + 10*a^3*b^4 + 10*a^2*b^5 + 5*a*b^6 + b^7)*d*cosh(d*x + c)^8 + 8*(a^5*b^2 + 5*a^4*b^3 + 10*a^3*b^4 + 10*a^2*b^5 + 5*a*b^6 + b^7)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^5*b^2 + 5*a^4*b^3 + 10*a^3*b^4 + 10*a^2*b^5 + 5*a*b^6 + b^7)*d*sinh(d*x + c)^8 + 4*(a^5*b^2 + 3*a^4*b^3 + 2*a^3*b^4 - 2*a^2*b^5 - 3*a*b^6 - b^7)*d*cosh(d*x + c)^6 + 4*(7*(a^5*b^2 + 5*a^4*b^3 + 10*a^3*b^4 + 10*a^2*b^5 + 5*a*b^6 + b^7)*d*cosh(d*x + c)^2 + (a^5*b^2 + 3*a^4*b^3 + 2*a^3*b^4 - 2*a^2*b^5 - 3*a*b^6 - b^7)*d)*sinh(d*x + c)^6 + 2*(3*a^5*b^2 + 7*a^4*b^3 + 6*a^3*b^4 + 6*a^2*b^5 + 7*a*b^6 + 3*b^7)*d*cosh(d*x + c)^4 + 8*(7*(a^5*b^2 + 5*a^4*b^3 + 10*a^3*b^4 + 10*a^2*b^5 + 5*a*b^6 + b^7)*d*cosh(d*x + c)^3 + 3*(a^5*b^2 + 3*a^4*b^3 + 2*a^3*b^4 - 2*a^2*b^5 - 3*a*b^6 - b^7)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^5*b^2 + 5*a^4*b^3 + 10*a^3*b^4 + 10*a^2*b^5 + 5*a*b^6 + b^7)*d*cosh(d*x + c)^4 + 30*(a^5*b^2 + 3*a^4*b^3 + 2*a^3*b^4 - 2*a^2*b^5 - 3*a*b^6 - b^7)*d*cosh(d*x + c)^2 + (3*a^5*b^2 + 7*a^4*b^3 + 6*a^3*b^4 + 6*a^2*b^5 + 7*a*b^6 + 3*b^7)*d)*sinh(d*x + c)^4 + 4*(a^5*b^2 + 3*a^4*b^3 + 2*a^3*b^4 - 2*a^2*b^5 - 3*a*b^6 - b^7)*d*cosh(d*x + c)^2 + 8*(7*(a^5*b^2 + 5*a^4*b^3 + 10*a^3*b^4 + 10*a^2*b^5 + 5*a*b^6 + b^7)*d*cosh(d*x + c)^5 + 10*(a^5*b^2 + 3*a^4*b^3 + 2*a^3*b^4 - 2*a^2*b^5 - 3*a*b^6 - b^7)*d*cosh(d*x + c)^3 + (3*a^5*b^2 + 7*a^4*b^3 + 6*a^3*b^4 + 6*a^2*b^5 + 7*a*b^6 + 3*b^7)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^5*b^2 + 5*a^4*b^3 + 10*a^3*b^4 + 10*a^2*b^5 + 5*a*b^6 + b^7)*d*cosh(d*x + c)^6 + 15*(a^5*b^2 + 3*a^4*b^3 + 2*a^3*b^4 - 2*a^2*b^5 - 3*a*b^6 - b^7)*d*cosh(d*x + c)^4 + 3*(3*a^5*b^2 + 7*a^4*b^3 + 6*a^3*b^4 + 6*a^2*b^5 + 7*a*b^6 + 3*b^7)*d*cosh(d*x + c)^2 + (a^5*b^2 + 3*a^4*b^3 + 2*a^3*b^4 - 2*a^2*b^5 - 3*a*b^6 - b^7)*d)*sinh(d*x + c)^2 + (a^5*b^2 + 5*a^4*b^3 + 10*a^3*b^4 + 10*a^2*b^5 + 5*a*b^6 + b^7)*d + 8*((a^5*b^2 + 5*a^4*b^3 + 10*a^3*b^4 + 10*a^2*b^5 + 5*a*b^6 + b^7)*d*cosh(d*x + c)^7 + 3*(a^5*b^2 + 3*a^4*b^3 + 2*a^3*b^4 - 2*a^2*b^5 - 3*a*b^6 - b^7)*d*cosh(d*x + c)^5 + (3*a^5*b^2 + 7*a^4*b^3 + 6*a^3*b^4 + 6*a^2*b^5 + 7*a*b^6 + 3*b^7)*d*cosh(d*x + c)^3 + (a^5*b^2 + 3*a^4*b^3 + 2*a^3*b^4 - 2*a^2*b^5 - 3*a*b^6 - b^7)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
191,1,2584,0,0.482029," ","integrate(tanh(d*x+c)^5/(a+b*tanh(d*x+c)^2)^3,x, algorithm=""fricas"")","-\frac{2 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x \cosh\left(d x + c\right)^{8} + 16 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + 2 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x \sinh\left(d x + c\right)^{8} + 8 \, {\left({\left(a^{2} - b^{2}\right)} d x - a^{2} - a b\right)} \cosh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x \cosh\left(d x + c\right)^{2} + {\left(a^{2} - b^{2}\right)} d x - a^{2} - a b\right)} \sinh\left(d x + c\right)^{6} + 16 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x \cosh\left(d x + c\right)^{3} + 3 \, {\left({\left(a^{2} - b^{2}\right)} d x - a^{2} - a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 4 \, {\left({\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} d x - 2 \, a^{2} + 4 \, a b\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(35 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x \cosh\left(d x + c\right)^{4} + {\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} d x + 30 \, {\left({\left(a^{2} - b^{2}\right)} d x - a^{2} - a b\right)} \cosh\left(d x + c\right)^{2} - 2 \, a^{2} + 4 \, a b\right)} \sinh\left(d x + c\right)^{4} + 16 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x \cosh\left(d x + c\right)^{5} + 10 \, {\left({\left(a^{2} - b^{2}\right)} d x - a^{2} - a b\right)} \cosh\left(d x + c\right)^{3} + {\left({\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} d x - 2 \, a^{2} + 4 \, a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x + 8 \, {\left({\left(a^{2} - b^{2}\right)} d x - a^{2} - a b\right)} \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x \cosh\left(d x + c\right)^{6} + 15 \, {\left({\left(a^{2} - b^{2}\right)} d x - a^{2} - a b\right)} \cosh\left(d x + c\right)^{4} + {\left(a^{2} - b^{2}\right)} d x + 3 \, {\left({\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} d x - 2 \, a^{2} + 4 \, a b\right)} \cosh\left(d x + c\right)^{2} - a^{2} - a b\right)} \sinh\left(d x + c\right)^{2} - {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + 30 \, {\left(a^{2} - 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)^{4} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{2} - 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)^{3} + 4 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 2 \, a b + b^{2} + 8 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\frac{2 \, {\left({\left(a + b\right)} \cosh\left(d x + c\right)^{2} + {\left(a + b\right)} \sinh\left(d x + c\right)^{2} + a - b\right)}}{\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}}\right) + 16 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} d x \cosh\left(d x + c\right)^{7} + 3 \, {\left({\left(a^{2} - b^{2}\right)} d x - a^{2} - a b\right)} \cosh\left(d x + c\right)^{5} + {\left({\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} d x - 2 \, a^{2} + 4 \, a b\right)} \cosh\left(d x + c\right)^{3} + {\left({\left(a^{2} - b^{2}\right)} d x - a^{2} - a b\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{2 \, {\left({\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(3 \, a^{5} + 7 \, a^{4} b + 6 \, a^{3} b^{2} + 6 \, a^{2} b^{3} + 7 \, a b^{4} + 3 \, b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 30 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{5} + 7 \, a^{4} b + 6 \, a^{3} b^{2} + 6 \, a^{2} b^{3} + 7 \, a b^{4} + 3 \, b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{5} + 7 \, a^{4} b + 6 \, a^{3} b^{2} + 6 \, a^{2} b^{3} + 7 \, a b^{4} + 3 \, b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{5} + 7 \, a^{4} b + 6 \, a^{3} b^{2} + 6 \, a^{2} b^{3} + 7 \, a b^{4} + 3 \, b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d + 8 \, {\left({\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} d \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{5} + 7 \, a^{4} b + 6 \, a^{3} b^{2} + 6 \, a^{2} b^{3} + 7 \, a b^{4} + 3 \, b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"-1/2*(2*(a^2 + 2*a*b + b^2)*d*x*cosh(d*x + c)^8 + 16*(a^2 + 2*a*b + b^2)*d*x*cosh(d*x + c)*sinh(d*x + c)^7 + 2*(a^2 + 2*a*b + b^2)*d*x*sinh(d*x + c)^8 + 8*((a^2 - b^2)*d*x - a^2 - a*b)*cosh(d*x + c)^6 + 8*(7*(a^2 + 2*a*b + b^2)*d*x*cosh(d*x + c)^2 + (a^2 - b^2)*d*x - a^2 - a*b)*sinh(d*x + c)^6 + 16*(7*(a^2 + 2*a*b + b^2)*d*x*cosh(d*x + c)^3 + 3*((a^2 - b^2)*d*x - a^2 - a*b)*cosh(d*x + c))*sinh(d*x + c)^5 + 4*((3*a^2 - 2*a*b + 3*b^2)*d*x - 2*a^2 + 4*a*b)*cosh(d*x + c)^4 + 4*(35*(a^2 + 2*a*b + b^2)*d*x*cosh(d*x + c)^4 + (3*a^2 - 2*a*b + 3*b^2)*d*x + 30*((a^2 - b^2)*d*x - a^2 - a*b)*cosh(d*x + c)^2 - 2*a^2 + 4*a*b)*sinh(d*x + c)^4 + 16*(7*(a^2 + 2*a*b + b^2)*d*x*cosh(d*x + c)^5 + 10*((a^2 - b^2)*d*x - a^2 - a*b)*cosh(d*x + c)^3 + ((3*a^2 - 2*a*b + 3*b^2)*d*x - 2*a^2 + 4*a*b)*cosh(d*x + c))*sinh(d*x + c)^3 + 2*(a^2 + 2*a*b + b^2)*d*x + 8*((a^2 - b^2)*d*x - a^2 - a*b)*cosh(d*x + c)^2 + 8*(7*(a^2 + 2*a*b + b^2)*d*x*cosh(d*x + c)^6 + 15*((a^2 - b^2)*d*x - a^2 - a*b)*cosh(d*x + c)^4 + (a^2 - b^2)*d*x + 3*((3*a^2 - 2*a*b + 3*b^2)*d*x - 2*a^2 + 4*a*b)*cosh(d*x + c)^2 - a^2 - a*b)*sinh(d*x + c)^2 - ((a^2 + 2*a*b + b^2)*cosh(d*x + c)^8 + 8*(a^2 + 2*a*b + b^2)*cosh(d*x + c)*sinh(d*x + c)^7 + (a^2 + 2*a*b + b^2)*sinh(d*x + c)^8 + 4*(a^2 - b^2)*cosh(d*x + c)^6 + 4*(7*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + a^2 - b^2)*sinh(d*x + c)^6 + 8*(7*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 + 3*(a^2 - b^2)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(3*a^2 - 2*a*b + 3*b^2)*cosh(d*x + c)^4 + 2*(35*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 + 30*(a^2 - b^2)*cosh(d*x + c)^2 + 3*a^2 - 2*a*b + 3*b^2)*sinh(d*x + c)^4 + 8*(7*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^5 + 10*(a^2 - b^2)*cosh(d*x + c)^3 + (3*a^2 - 2*a*b + 3*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(a^2 - b^2)*cosh(d*x + c)^2 + 4*(7*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^6 + 15*(a^2 - b^2)*cosh(d*x + c)^4 + 3*(3*a^2 - 2*a*b + 3*b^2)*cosh(d*x + c)^2 + a^2 - b^2)*sinh(d*x + c)^2 + a^2 + 2*a*b + b^2 + 8*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^7 + 3*(a^2 - b^2)*cosh(d*x + c)^5 + (3*a^2 - 2*a*b + 3*b^2)*cosh(d*x + c)^3 + (a^2 - b^2)*cosh(d*x + c))*sinh(d*x + c))*log(2*((a + b)*cosh(d*x + c)^2 + (a + b)*sinh(d*x + c)^2 + a - b)/(cosh(d*x + c)^2 - 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)) + 16*((a^2 + 2*a*b + b^2)*d*x*cosh(d*x + c)^7 + 3*((a^2 - b^2)*d*x - a^2 - a*b)*cosh(d*x + c)^5 + ((3*a^2 - 2*a*b + 3*b^2)*d*x - 2*a^2 + 4*a*b)*cosh(d*x + c)^3 + ((a^2 - b^2)*d*x - a^2 - a*b)*cosh(d*x + c))*sinh(d*x + c))/((a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*cosh(d*x + c)^8 + 8*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*sinh(d*x + c)^8 + 4*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*d*cosh(d*x + c)^6 + 4*(7*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*cosh(d*x + c)^2 + (a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*d)*sinh(d*x + c)^6 + 2*(3*a^5 + 7*a^4*b + 6*a^3*b^2 + 6*a^2*b^3 + 7*a*b^4 + 3*b^5)*d*cosh(d*x + c)^4 + 8*(7*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*cosh(d*x + c)^3 + 3*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*cosh(d*x + c)^4 + 30*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*d*cosh(d*x + c)^2 + (3*a^5 + 7*a^4*b + 6*a^3*b^2 + 6*a^2*b^3 + 7*a*b^4 + 3*b^5)*d)*sinh(d*x + c)^4 + 4*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*d*cosh(d*x + c)^2 + 8*(7*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*cosh(d*x + c)^5 + 10*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*d*cosh(d*x + c)^3 + (3*a^5 + 7*a^4*b + 6*a^3*b^2 + 6*a^2*b^3 + 7*a*b^4 + 3*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*cosh(d*x + c)^6 + 15*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*d*cosh(d*x + c)^4 + 3*(3*a^5 + 7*a^4*b + 6*a^3*b^2 + 6*a^2*b^3 + 7*a*b^4 + 3*b^5)*d*cosh(d*x + c)^2 + (a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*d)*sinh(d*x + c)^2 + (a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d + 8*((a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*cosh(d*x + c)^7 + 3*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*d*cosh(d*x + c)^5 + (3*a^5 + 7*a^4*b + 6*a^3*b^2 + 6*a^2*b^3 + 7*a*b^4 + 3*b^5)*d*cosh(d*x + c)^3 + (a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*d*cosh(d*x + c))*sinh(d*x + c))","B",0
192,1,7757,0,0.578200," ","integrate(tanh(d*x+c)^4/(a+b*tanh(d*x+c)^2)^3,x, algorithm=""fricas"")","\left[\frac{16 \, {\left(a^{3} b^{2} + 2 \, a^{2} b^{3} + a b^{4}\right)} d x \cosh\left(d x + c\right)^{8} + 128 \, {\left(a^{3} b^{2} + 2 \, a^{2} b^{3} + a b^{4}\right)} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + 16 \, {\left(a^{3} b^{2} + 2 \, a^{2} b^{3} + a b^{4}\right)} d x \sinh\left(d x + c\right)^{8} - 4 \, {\left(a^{4} b - 9 \, a^{3} b^{2} - 5 \, a^{2} b^{3} + 5 \, a b^{4} - 16 \, {\left(a^{3} b^{2} - a b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{6} - 4 \, {\left(a^{4} b - 9 \, a^{3} b^{2} - 5 \, a^{2} b^{3} + 5 \, a b^{4} - 112 \, {\left(a^{3} b^{2} + 2 \, a^{2} b^{3} + a b^{4}\right)} d x \cosh\left(d x + c\right)^{2} - 16 \, {\left(a^{3} b^{2} - a b^{4}\right)} d x\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(112 \, {\left(a^{3} b^{2} + 2 \, a^{2} b^{3} + a b^{4}\right)} d x \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{4} b - 9 \, a^{3} b^{2} - 5 \, a^{2} b^{3} + 5 \, a b^{4} - 16 \, {\left(a^{3} b^{2} - a b^{4}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 4 \, a^{4} b + 12 \, a^{3} b^{2} + 36 \, a^{2} b^{3} + 20 \, a b^{4} - 4 \, {\left(3 \, a^{4} b - 17 \, a^{3} b^{2} + 13 \, a^{2} b^{3} - 15 \, a b^{4} - 8 \, {\left(3 \, a^{3} b^{2} - 2 \, a^{2} b^{3} + 3 \, a b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(280 \, {\left(a^{3} b^{2} + 2 \, a^{2} b^{3} + a b^{4}\right)} d x \cosh\left(d x + c\right)^{4} - 3 \, a^{4} b + 17 \, a^{3} b^{2} - 13 \, a^{2} b^{3} + 15 \, a b^{4} + 8 \, {\left(3 \, a^{3} b^{2} - 2 \, a^{2} b^{3} + 3 \, a b^{4}\right)} d x - 15 \, {\left(a^{4} b - 9 \, a^{3} b^{2} - 5 \, a^{2} b^{3} + 5 \, a b^{4} - 16 \, {\left(a^{3} b^{2} - a b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 16 \, {\left(56 \, {\left(a^{3} b^{2} + 2 \, a^{2} b^{3} + a b^{4}\right)} d x \cosh\left(d x + c\right)^{5} - 5 \, {\left(a^{4} b - 9 \, a^{3} b^{2} - 5 \, a^{2} b^{3} + 5 \, a b^{4} - 16 \, {\left(a^{3} b^{2} - a b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - {\left(3 \, a^{4} b - 17 \, a^{3} b^{2} + 13 \, a^{2} b^{3} - 15 \, a b^{4} - 8 \, {\left(3 \, a^{3} b^{2} - 2 \, a^{2} b^{3} + 3 \, a b^{4}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 16 \, {\left(a^{3} b^{2} + 2 \, a^{2} b^{3} + a b^{4}\right)} d x - 4 \, {\left(3 \, a^{4} b - 11 \, a^{3} b^{2} + a^{2} b^{3} + 15 \, a b^{4} - 16 \, {\left(a^{3} b^{2} - a b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(112 \, {\left(a^{3} b^{2} + 2 \, a^{2} b^{3} + a b^{4}\right)} d x \cosh\left(d x + c\right)^{6} - 3 \, a^{4} b + 11 \, a^{3} b^{2} - a^{2} b^{3} - 15 \, a b^{4} - 15 \, {\left(a^{4} b - 9 \, a^{3} b^{2} - 5 \, a^{2} b^{3} + 5 \, a b^{4} - 16 \, {\left(a^{3} b^{2} - a b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 16 \, {\left(a^{3} b^{2} - a b^{4}\right)} d x - 6 \, {\left(3 \, a^{4} b - 17 \, a^{3} b^{2} + 13 \, a^{2} b^{3} - 15 \, a b^{4} - 8 \, {\left(3 \, a^{3} b^{2} - 2 \, a^{2} b^{3} + 3 \, a b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(a^{4} + 8 \, a^{3} b + 10 \, a^{2} b^{2} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{4} + 8 \, a^{3} b + 10 \, a^{2} b^{2} - 3 \, b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{4} + 8 \, a^{3} b + 10 \, a^{2} b^{2} - 3 \, b^{4}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{4} + 6 \, a^{3} b - 4 \, a^{2} b^{2} - 6 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(a^{4} + 6 \, a^{3} b - 4 \, a^{2} b^{2} - 6 \, a b^{3} + 3 \, b^{4} + 7 \, {\left(a^{4} + 8 \, a^{3} b + 10 \, a^{2} b^{2} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(a^{4} + 8 \, a^{3} b + 10 \, a^{2} b^{2} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{4} + 6 \, a^{3} b - 4 \, a^{2} b^{2} - 6 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(3 \, a^{4} + 16 \, a^{3} b - 18 \, a^{2} b^{2} + 24 \, a b^{3} - 9 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(a^{4} + 8 \, a^{3} b + 10 \, a^{2} b^{2} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 3 \, a^{4} + 16 \, a^{3} b - 18 \, a^{2} b^{2} + 24 \, a b^{3} - 9 \, b^{4} + 30 \, {\left(a^{4} + 6 \, a^{3} b - 4 \, a^{2} b^{2} - 6 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + a^{4} + 8 \, a^{3} b + 10 \, a^{2} b^{2} - 3 \, b^{4} + 8 \, {\left(7 \, {\left(a^{4} + 8 \, a^{3} b + 10 \, a^{2} b^{2} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{4} + 6 \, a^{3} b - 4 \, a^{2} b^{2} - 6 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{4} + 16 \, a^{3} b - 18 \, a^{2} b^{2} + 24 \, a b^{3} - 9 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(a^{4} + 6 \, a^{3} b - 4 \, a^{2} b^{2} - 6 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(a^{4} + 8 \, a^{3} b + 10 \, a^{2} b^{2} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{4} + 6 \, a^{3} b - 4 \, a^{2} b^{2} - 6 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + a^{4} + 6 \, a^{3} b - 4 \, a^{2} b^{2} - 6 \, a b^{3} + 3 \, b^{4} + 3 \, {\left(3 \, a^{4} + 16 \, a^{3} b - 18 \, a^{2} b^{2} + 24 \, 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(a^{4} + 8 \, a^{3} b + 10 \, a^{2} b^{2} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{4} + 6 \, a^{3} b - 4 \, a^{2} b^{2} - 6 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{4} + 16 \, a^{3} b - 18 \, a^{2} b^{2} + 24 \, a b^{3} - 9 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{4} + 6 \, a^{3} b - 4 \, a^{2} b^{2} - 6 \, 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{{\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) \sinh\left(d x + c\right)^{3} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{2} + a^{2} - 6 \, a b + b^{2} + 4 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} - b^{2}\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)^{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} + a - b\right)} \sqrt{-a b}}{{\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) + 8 \, {\left(16 \, {\left(a^{3} b^{2} + 2 \, a^{2} b^{3} + a b^{4}\right)} d x \cosh\left(d x + c\right)^{7} - 3 \, {\left(a^{4} b - 9 \, a^{3} b^{2} - 5 \, a^{2} b^{3} + 5 \, a b^{4} - 16 \, {\left(a^{3} b^{2} - a b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{5} - 2 \, {\left(3 \, a^{4} b - 17 \, a^{3} b^{2} + 13 \, a^{2} b^{3} - 15 \, a b^{4} - 8 \, {\left(3 \, a^{3} b^{2} - 2 \, a^{2} b^{3} + 3 \, a b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - {\left(3 \, a^{4} b - 11 \, a^{3} b^{2} + a^{2} b^{3} + 15 \, a b^{4} - 16 \, {\left(a^{3} b^{2} - a b^{4}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{16 \, {\left({\left(a^{6} b^{2} + 5 \, a^{5} b^{3} + 10 \, a^{4} b^{4} + 10 \, a^{3} b^{5} + 5 \, a^{2} b^{6} + a b^{7}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{6} b^{2} + 5 \, a^{5} b^{3} + 10 \, a^{4} b^{4} + 10 \, a^{3} b^{5} + 5 \, a^{2} b^{6} + a b^{7}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{6} b^{2} + 5 \, a^{5} b^{3} + 10 \, a^{4} b^{4} + 10 \, a^{3} b^{5} + 5 \, a^{2} b^{6} + a b^{7}\right)} d \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{6} b^{2} + 3 \, a^{5} b^{3} + 2 \, a^{4} b^{4} - 2 \, a^{3} b^{5} - 3 \, a^{2} b^{6} - a b^{7}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{6} b^{2} + 5 \, a^{5} b^{3} + 10 \, a^{4} b^{4} + 10 \, a^{3} b^{5} + 5 \, a^{2} b^{6} + a b^{7}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{6} b^{2} + 3 \, a^{5} b^{3} + 2 \, a^{4} b^{4} - 2 \, a^{3} b^{5} - 3 \, a^{2} b^{6} - a b^{7}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(3 \, a^{6} b^{2} + 7 \, a^{5} b^{3} + 6 \, a^{4} b^{4} + 6 \, a^{3} b^{5} + 7 \, a^{2} b^{6} + 3 \, a b^{7}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{6} b^{2} + 5 \, a^{5} b^{3} + 10 \, a^{4} b^{4} + 10 \, a^{3} b^{5} + 5 \, a^{2} b^{6} + a b^{7}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{6} b^{2} + 3 \, a^{5} b^{3} + 2 \, a^{4} b^{4} - 2 \, a^{3} b^{5} - 3 \, 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^{6} b^{2} + 5 \, a^{5} b^{3} + 10 \, a^{4} b^{4} + 10 \, a^{3} b^{5} + 5 \, a^{2} b^{6} + a b^{7}\right)} d \cosh\left(d x + c\right)^{4} + 30 \, {\left(a^{6} b^{2} + 3 \, a^{5} b^{3} + 2 \, a^{4} b^{4} - 2 \, a^{3} b^{5} - 3 \, a^{2} b^{6} - a b^{7}\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{6} b^{2} + 7 \, a^{5} b^{3} + 6 \, a^{4} b^{4} + 6 \, a^{3} b^{5} + 7 \, a^{2} b^{6} + 3 \, a b^{7}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{6} b^{2} + 3 \, a^{5} b^{3} + 2 \, a^{4} b^{4} - 2 \, a^{3} b^{5} - 3 \, a^{2} b^{6} - a b^{7}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a^{6} b^{2} + 5 \, a^{5} b^{3} + 10 \, a^{4} b^{4} + 10 \, a^{3} b^{5} + 5 \, a^{2} b^{6} + a b^{7}\right)} d \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{6} b^{2} + 3 \, a^{5} b^{3} + 2 \, a^{4} b^{4} - 2 \, a^{3} b^{5} - 3 \, a^{2} b^{6} - a b^{7}\right)} d \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{6} b^{2} + 7 \, a^{5} b^{3} + 6 \, a^{4} b^{4} + 6 \, a^{3} b^{5} + 7 \, 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^{6} b^{2} + 5 \, a^{5} b^{3} + 10 \, a^{4} b^{4} + 10 \, a^{3} b^{5} + 5 \, a^{2} b^{6} + a b^{7}\right)} d \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{6} b^{2} + 3 \, a^{5} b^{3} + 2 \, a^{4} b^{4} - 2 \, a^{3} b^{5} - 3 \, a^{2} b^{6} - a b^{7}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{6} b^{2} + 7 \, a^{5} b^{3} + 6 \, a^{4} b^{4} + 6 \, a^{3} b^{5} + 7 \, a^{2} b^{6} + 3 \, a b^{7}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{6} b^{2} + 3 \, a^{5} b^{3} + 2 \, a^{4} b^{4} - 2 \, a^{3} b^{5} - 3 \, a^{2} b^{6} - a b^{7}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{6} b^{2} + 5 \, a^{5} b^{3} + 10 \, a^{4} b^{4} + 10 \, a^{3} b^{5} + 5 \, a^{2} b^{6} + a b^{7}\right)} d + 8 \, {\left({\left(a^{6} b^{2} + 5 \, a^{5} b^{3} + 10 \, a^{4} b^{4} + 10 \, a^{3} b^{5} + 5 \, a^{2} b^{6} + a b^{7}\right)} d \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{6} b^{2} + 3 \, a^{5} b^{3} + 2 \, a^{4} b^{4} - 2 \, a^{3} b^{5} - 3 \, a^{2} b^{6} - a b^{7}\right)} d \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{6} b^{2} + 7 \, a^{5} b^{3} + 6 \, a^{4} b^{4} + 6 \, a^{3} b^{5} + 7 \, a^{2} b^{6} + 3 \, a b^{7}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{6} b^{2} + 3 \, a^{5} b^{3} + 2 \, a^{4} b^{4} - 2 \, a^{3} b^{5} - 3 \, a^{2} b^{6} - a b^{7}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}, \frac{8 \, {\left(a^{3} b^{2} + 2 \, a^{2} b^{3} + a b^{4}\right)} d x \cosh\left(d x + c\right)^{8} + 64 \, {\left(a^{3} b^{2} + 2 \, a^{2} b^{3} + a b^{4}\right)} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + 8 \, {\left(a^{3} b^{2} + 2 \, a^{2} b^{3} + a b^{4}\right)} d x \sinh\left(d x + c\right)^{8} - 2 \, {\left(a^{4} b - 9 \, a^{3} b^{2} - 5 \, a^{2} b^{3} + 5 \, a b^{4} - 16 \, {\left(a^{3} b^{2} - a b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{6} - 2 \, {\left(a^{4} b - 9 \, a^{3} b^{2} - 5 \, a^{2} b^{3} + 5 \, a b^{4} - 112 \, {\left(a^{3} b^{2} + 2 \, a^{2} b^{3} + a b^{4}\right)} d x \cosh\left(d x + c\right)^{2} - 16 \, {\left(a^{3} b^{2} - a b^{4}\right)} d x\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(112 \, {\left(a^{3} b^{2} + 2 \, a^{2} b^{3} + a b^{4}\right)} d x \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{4} b - 9 \, a^{3} b^{2} - 5 \, a^{2} b^{3} + 5 \, a b^{4} - 16 \, {\left(a^{3} b^{2} - a b^{4}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 2 \, a^{4} b + 6 \, a^{3} b^{2} + 18 \, a^{2} b^{3} + 10 \, a b^{4} - 2 \, {\left(3 \, a^{4} b - 17 \, a^{3} b^{2} + 13 \, a^{2} b^{3} - 15 \, a b^{4} - 8 \, {\left(3 \, a^{3} b^{2} - 2 \, a^{2} b^{3} + 3 \, a b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(280 \, {\left(a^{3} b^{2} + 2 \, a^{2} b^{3} + a b^{4}\right)} d x \cosh\left(d x + c\right)^{4} - 3 \, a^{4} b + 17 \, a^{3} b^{2} - 13 \, a^{2} b^{3} + 15 \, a b^{4} + 8 \, {\left(3 \, a^{3} b^{2} - 2 \, a^{2} b^{3} + 3 \, a b^{4}\right)} d x - 15 \, {\left(a^{4} b - 9 \, a^{3} b^{2} - 5 \, a^{2} b^{3} + 5 \, a b^{4} - 16 \, {\left(a^{3} b^{2} - a b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(56 \, {\left(a^{3} b^{2} + 2 \, a^{2} b^{3} + a b^{4}\right)} d x \cosh\left(d x + c\right)^{5} - 5 \, {\left(a^{4} b - 9 \, a^{3} b^{2} - 5 \, a^{2} b^{3} + 5 \, a b^{4} - 16 \, {\left(a^{3} b^{2} - a b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - {\left(3 \, a^{4} b - 17 \, a^{3} b^{2} + 13 \, a^{2} b^{3} - 15 \, a b^{4} - 8 \, {\left(3 \, a^{3} b^{2} - 2 \, a^{2} b^{3} + 3 \, a b^{4}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 8 \, {\left(a^{3} b^{2} + 2 \, a^{2} b^{3} + a b^{4}\right)} d x - 2 \, {\left(3 \, a^{4} b - 11 \, a^{3} b^{2} + a^{2} b^{3} + 15 \, a b^{4} - 16 \, {\left(a^{3} b^{2} - a b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(112 \, {\left(a^{3} b^{2} + 2 \, a^{2} b^{3} + a b^{4}\right)} d x \cosh\left(d x + c\right)^{6} - 3 \, a^{4} b + 11 \, a^{3} b^{2} - a^{2} b^{3} - 15 \, a b^{4} - 15 \, {\left(a^{4} b - 9 \, a^{3} b^{2} - 5 \, a^{2} b^{3} + 5 \, a b^{4} - 16 \, {\left(a^{3} b^{2} - a b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 16 \, {\left(a^{3} b^{2} - a b^{4}\right)} d x - 6 \, {\left(3 \, a^{4} b - 17 \, a^{3} b^{2} + 13 \, a^{2} b^{3} - 15 \, a b^{4} - 8 \, {\left(3 \, a^{3} b^{2} - 2 \, a^{2} b^{3} + 3 \, a b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} - {\left({\left(a^{4} + 8 \, a^{3} b + 10 \, a^{2} b^{2} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{4} + 8 \, a^{3} b + 10 \, a^{2} b^{2} - 3 \, b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{4} + 8 \, a^{3} b + 10 \, a^{2} b^{2} - 3 \, b^{4}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{4} + 6 \, a^{3} b - 4 \, a^{2} b^{2} - 6 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(a^{4} + 6 \, a^{3} b - 4 \, a^{2} b^{2} - 6 \, a b^{3} + 3 \, b^{4} + 7 \, {\left(a^{4} + 8 \, a^{3} b + 10 \, a^{2} b^{2} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(a^{4} + 8 \, a^{3} b + 10 \, a^{2} b^{2} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{4} + 6 \, a^{3} b - 4 \, a^{2} b^{2} - 6 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(3 \, a^{4} + 16 \, a^{3} b - 18 \, a^{2} b^{2} + 24 \, a b^{3} - 9 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(a^{4} + 8 \, a^{3} b + 10 \, a^{2} b^{2} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 3 \, a^{4} + 16 \, a^{3} b - 18 \, a^{2} b^{2} + 24 \, a b^{3} - 9 \, b^{4} + 30 \, {\left(a^{4} + 6 \, a^{3} b - 4 \, a^{2} b^{2} - 6 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + a^{4} + 8 \, a^{3} b + 10 \, a^{2} b^{2} - 3 \, b^{4} + 8 \, {\left(7 \, {\left(a^{4} + 8 \, a^{3} b + 10 \, a^{2} b^{2} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{4} + 6 \, a^{3} b - 4 \, a^{2} b^{2} - 6 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{4} + 16 \, a^{3} b - 18 \, a^{2} b^{2} + 24 \, a b^{3} - 9 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(a^{4} + 6 \, a^{3} b - 4 \, a^{2} b^{2} - 6 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(a^{4} + 8 \, a^{3} b + 10 \, a^{2} b^{2} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{4} + 6 \, a^{3} b - 4 \, a^{2} b^{2} - 6 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + a^{4} + 6 \, a^{3} b - 4 \, a^{2} b^{2} - 6 \, a b^{3} + 3 \, b^{4} + 3 \, {\left(3 \, a^{4} + 16 \, a^{3} b - 18 \, a^{2} b^{2} + 24 \, 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(a^{4} + 8 \, a^{3} b + 10 \, a^{2} b^{2} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{4} + 6 \, a^{3} b - 4 \, a^{2} b^{2} - 6 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{4} + 16 \, a^{3} b - 18 \, a^{2} b^{2} + 24 \, a b^{3} - 9 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{4} + 6 \, a^{3} b - 4 \, a^{2} b^{2} - 6 \, 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({\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} + a - b\right)} \sqrt{a b}}{2 \, a b}\right) + 4 \, {\left(16 \, {\left(a^{3} b^{2} + 2 \, a^{2} b^{3} + a b^{4}\right)} d x \cosh\left(d x + c\right)^{7} - 3 \, {\left(a^{4} b - 9 \, a^{3} b^{2} - 5 \, a^{2} b^{3} + 5 \, a b^{4} - 16 \, {\left(a^{3} b^{2} - a b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{5} - 2 \, {\left(3 \, a^{4} b - 17 \, a^{3} b^{2} + 13 \, a^{2} b^{3} - 15 \, a b^{4} - 8 \, {\left(3 \, a^{3} b^{2} - 2 \, a^{2} b^{3} + 3 \, a b^{4}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - {\left(3 \, a^{4} b - 11 \, a^{3} b^{2} + a^{2} b^{3} + 15 \, a b^{4} - 16 \, {\left(a^{3} b^{2} - a b^{4}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{8 \, {\left({\left(a^{6} b^{2} + 5 \, a^{5} b^{3} + 10 \, a^{4} b^{4} + 10 \, a^{3} b^{5} + 5 \, a^{2} b^{6} + a b^{7}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{6} b^{2} + 5 \, a^{5} b^{3} + 10 \, a^{4} b^{4} + 10 \, a^{3} b^{5} + 5 \, a^{2} b^{6} + a b^{7}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{6} b^{2} + 5 \, a^{5} b^{3} + 10 \, a^{4} b^{4} + 10 \, a^{3} b^{5} + 5 \, a^{2} b^{6} + a b^{7}\right)} d \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{6} b^{2} + 3 \, a^{5} b^{3} + 2 \, a^{4} b^{4} - 2 \, a^{3} b^{5} - 3 \, a^{2} b^{6} - a b^{7}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{6} b^{2} + 5 \, a^{5} b^{3} + 10 \, a^{4} b^{4} + 10 \, a^{3} b^{5} + 5 \, a^{2} b^{6} + a b^{7}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{6} b^{2} + 3 \, a^{5} b^{3} + 2 \, a^{4} b^{4} - 2 \, a^{3} b^{5} - 3 \, a^{2} b^{6} - a b^{7}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(3 \, a^{6} b^{2} + 7 \, a^{5} b^{3} + 6 \, a^{4} b^{4} + 6 \, a^{3} b^{5} + 7 \, a^{2} b^{6} + 3 \, a b^{7}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{6} b^{2} + 5 \, a^{5} b^{3} + 10 \, a^{4} b^{4} + 10 \, a^{3} b^{5} + 5 \, a^{2} b^{6} + a b^{7}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{6} b^{2} + 3 \, a^{5} b^{3} + 2 \, a^{4} b^{4} - 2 \, a^{3} b^{5} - 3 \, 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^{6} b^{2} + 5 \, a^{5} b^{3} + 10 \, a^{4} b^{4} + 10 \, a^{3} b^{5} + 5 \, a^{2} b^{6} + a b^{7}\right)} d \cosh\left(d x + c\right)^{4} + 30 \, {\left(a^{6} b^{2} + 3 \, a^{5} b^{3} + 2 \, a^{4} b^{4} - 2 \, a^{3} b^{5} - 3 \, a^{2} b^{6} - a b^{7}\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{6} b^{2} + 7 \, a^{5} b^{3} + 6 \, a^{4} b^{4} + 6 \, a^{3} b^{5} + 7 \, a^{2} b^{6} + 3 \, a b^{7}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{6} b^{2} + 3 \, a^{5} b^{3} + 2 \, a^{4} b^{4} - 2 \, a^{3} b^{5} - 3 \, a^{2} b^{6} - a b^{7}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a^{6} b^{2} + 5 \, a^{5} b^{3} + 10 \, a^{4} b^{4} + 10 \, a^{3} b^{5} + 5 \, a^{2} b^{6} + a b^{7}\right)} d \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{6} b^{2} + 3 \, a^{5} b^{3} + 2 \, a^{4} b^{4} - 2 \, a^{3} b^{5} - 3 \, a^{2} b^{6} - a b^{7}\right)} d \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{6} b^{2} + 7 \, a^{5} b^{3} + 6 \, a^{4} b^{4} + 6 \, a^{3} b^{5} + 7 \, 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^{6} b^{2} + 5 \, a^{5} b^{3} + 10 \, a^{4} b^{4} + 10 \, a^{3} b^{5} + 5 \, a^{2} b^{6} + a b^{7}\right)} d \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{6} b^{2} + 3 \, a^{5} b^{3} + 2 \, a^{4} b^{4} - 2 \, a^{3} b^{5} - 3 \, a^{2} b^{6} - a b^{7}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{6} b^{2} + 7 \, a^{5} b^{3} + 6 \, a^{4} b^{4} + 6 \, a^{3} b^{5} + 7 \, a^{2} b^{6} + 3 \, a b^{7}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{6} b^{2} + 3 \, a^{5} b^{3} + 2 \, a^{4} b^{4} - 2 \, a^{3} b^{5} - 3 \, a^{2} b^{6} - a b^{7}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{6} b^{2} + 5 \, a^{5} b^{3} + 10 \, a^{4} b^{4} + 10 \, a^{3} b^{5} + 5 \, a^{2} b^{6} + a b^{7}\right)} d + 8 \, {\left({\left(a^{6} b^{2} + 5 \, a^{5} b^{3} + 10 \, a^{4} b^{4} + 10 \, a^{3} b^{5} + 5 \, a^{2} b^{6} + a b^{7}\right)} d \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{6} b^{2} + 3 \, a^{5} b^{3} + 2 \, a^{4} b^{4} - 2 \, a^{3} b^{5} - 3 \, a^{2} b^{6} - a b^{7}\right)} d \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{6} b^{2} + 7 \, a^{5} b^{3} + 6 \, a^{4} b^{4} + 6 \, a^{3} b^{5} + 7 \, a^{2} b^{6} + 3 \, a b^{7}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{6} b^{2} + 3 \, a^{5} b^{3} + 2 \, a^{4} b^{4} - 2 \, a^{3} b^{5} - 3 \, 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*(16*(a^3*b^2 + 2*a^2*b^3 + a*b^4)*d*x*cosh(d*x + c)^8 + 128*(a^3*b^2 + 2*a^2*b^3 + a*b^4)*d*x*cosh(d*x + c)*sinh(d*x + c)^7 + 16*(a^3*b^2 + 2*a^2*b^3 + a*b^4)*d*x*sinh(d*x + c)^8 - 4*(a^4*b - 9*a^3*b^2 - 5*a^2*b^3 + 5*a*b^4 - 16*(a^3*b^2 - a*b^4)*d*x)*cosh(d*x + c)^6 - 4*(a^4*b - 9*a^3*b^2 - 5*a^2*b^3 + 5*a*b^4 - 112*(a^3*b^2 + 2*a^2*b^3 + a*b^4)*d*x*cosh(d*x + c)^2 - 16*(a^3*b^2 - a*b^4)*d*x)*sinh(d*x + c)^6 + 8*(112*(a^3*b^2 + 2*a^2*b^3 + a*b^4)*d*x*cosh(d*x + c)^3 - 3*(a^4*b - 9*a^3*b^2 - 5*a^2*b^3 + 5*a*b^4 - 16*(a^3*b^2 - a*b^4)*d*x)*cosh(d*x + c))*sinh(d*x + c)^5 - 4*a^4*b + 12*a^3*b^2 + 36*a^2*b^3 + 20*a*b^4 - 4*(3*a^4*b - 17*a^3*b^2 + 13*a^2*b^3 - 15*a*b^4 - 8*(3*a^3*b^2 - 2*a^2*b^3 + 3*a*b^4)*d*x)*cosh(d*x + c)^4 + 4*(280*(a^3*b^2 + 2*a^2*b^3 + a*b^4)*d*x*cosh(d*x + c)^4 - 3*a^4*b + 17*a^3*b^2 - 13*a^2*b^3 + 15*a*b^4 + 8*(3*a^3*b^2 - 2*a^2*b^3 + 3*a*b^4)*d*x - 15*(a^4*b - 9*a^3*b^2 - 5*a^2*b^3 + 5*a*b^4 - 16*(a^3*b^2 - a*b^4)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 16*(56*(a^3*b^2 + 2*a^2*b^3 + a*b^4)*d*x*cosh(d*x + c)^5 - 5*(a^4*b - 9*a^3*b^2 - 5*a^2*b^3 + 5*a*b^4 - 16*(a^3*b^2 - a*b^4)*d*x)*cosh(d*x + c)^3 - (3*a^4*b - 17*a^3*b^2 + 13*a^2*b^3 - 15*a*b^4 - 8*(3*a^3*b^2 - 2*a^2*b^3 + 3*a*b^4)*d*x)*cosh(d*x + c))*sinh(d*x + c)^3 + 16*(a^3*b^2 + 2*a^2*b^3 + a*b^4)*d*x - 4*(3*a^4*b - 11*a^3*b^2 + a^2*b^3 + 15*a*b^4 - 16*(a^3*b^2 - a*b^4)*d*x)*cosh(d*x + c)^2 + 4*(112*(a^3*b^2 + 2*a^2*b^3 + a*b^4)*d*x*cosh(d*x + c)^6 - 3*a^4*b + 11*a^3*b^2 - a^2*b^3 - 15*a*b^4 - 15*(a^4*b - 9*a^3*b^2 - 5*a^2*b^3 + 5*a*b^4 - 16*(a^3*b^2 - a*b^4)*d*x)*cosh(d*x + c)^4 + 16*(a^3*b^2 - a*b^4)*d*x - 6*(3*a^4*b - 17*a^3*b^2 + 13*a^2*b^3 - 15*a*b^4 - 8*(3*a^3*b^2 - 2*a^2*b^3 + 3*a*b^4)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((a^4 + 8*a^3*b + 10*a^2*b^2 - 3*b^4)*cosh(d*x + c)^8 + 8*(a^4 + 8*a^3*b + 10*a^2*b^2 - 3*b^4)*cosh(d*x + c)*sinh(d*x + c)^7 + (a^4 + 8*a^3*b + 10*a^2*b^2 - 3*b^4)*sinh(d*x + c)^8 + 4*(a^4 + 6*a^3*b - 4*a^2*b^2 - 6*a*b^3 + 3*b^4)*cosh(d*x + c)^6 + 4*(a^4 + 6*a^3*b - 4*a^2*b^2 - 6*a*b^3 + 3*b^4 + 7*(a^4 + 8*a^3*b + 10*a^2*b^2 - 3*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(a^4 + 8*a^3*b + 10*a^2*b^2 - 3*b^4)*cosh(d*x + c)^3 + 3*(a^4 + 6*a^3*b - 4*a^2*b^2 - 6*a*b^3 + 3*b^4)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(3*a^4 + 16*a^3*b - 18*a^2*b^2 + 24*a*b^3 - 9*b^4)*cosh(d*x + c)^4 + 2*(35*(a^4 + 8*a^3*b + 10*a^2*b^2 - 3*b^4)*cosh(d*x + c)^4 + 3*a^4 + 16*a^3*b - 18*a^2*b^2 + 24*a*b^3 - 9*b^4 + 30*(a^4 + 6*a^3*b - 4*a^2*b^2 - 6*a*b^3 + 3*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + a^4 + 8*a^3*b + 10*a^2*b^2 - 3*b^4 + 8*(7*(a^4 + 8*a^3*b + 10*a^2*b^2 - 3*b^4)*cosh(d*x + c)^5 + 10*(a^4 + 6*a^3*b - 4*a^2*b^2 - 6*a*b^3 + 3*b^4)*cosh(d*x + c)^3 + (3*a^4 + 16*a^3*b - 18*a^2*b^2 + 24*a*b^3 - 9*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(a^4 + 6*a^3*b - 4*a^2*b^2 - 6*a*b^3 + 3*b^4)*cosh(d*x + c)^2 + 4*(7*(a^4 + 8*a^3*b + 10*a^2*b^2 - 3*b^4)*cosh(d*x + c)^6 + 15*(a^4 + 6*a^3*b - 4*a^2*b^2 - 6*a*b^3 + 3*b^4)*cosh(d*x + c)^4 + a^4 + 6*a^3*b - 4*a^2*b^2 - 6*a*b^3 + 3*b^4 + 3*(3*a^4 + 16*a^3*b - 18*a^2*b^2 + 24*a*b^3 - 9*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((a^4 + 8*a^3*b + 10*a^2*b^2 - 3*b^4)*cosh(d*x + c)^7 + 3*(a^4 + 6*a^3*b - 4*a^2*b^2 - 6*a*b^3 + 3*b^4)*cosh(d*x + c)^5 + (3*a^4 + 16*a^3*b - 18*a^2*b^2 + 24*a*b^3 - 9*b^4)*cosh(d*x + c)^3 + (a^4 + 6*a^3*b - 4*a^2*b^2 - 6*a*b^3 + 3*b^4)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-a*b)*log(((a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 + 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 + 2*(a^2 - b^2)*cosh(d*x + c)^2 + 2*(3*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + a^2 - b^2)*sinh(d*x + c)^2 + a^2 - 6*a*b + b^2 + 4*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 + (a^2 - 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 + a - b)*sqrt(-a*b))/((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)) + 8*(16*(a^3*b^2 + 2*a^2*b^3 + a*b^4)*d*x*cosh(d*x + c)^7 - 3*(a^4*b - 9*a^3*b^2 - 5*a^2*b^3 + 5*a*b^4 - 16*(a^3*b^2 - a*b^4)*d*x)*cosh(d*x + c)^5 - 2*(3*a^4*b - 17*a^3*b^2 + 13*a^2*b^3 - 15*a*b^4 - 8*(3*a^3*b^2 - 2*a^2*b^3 + 3*a*b^4)*d*x)*cosh(d*x + c)^3 - (3*a^4*b - 11*a^3*b^2 + a^2*b^3 + 15*a*b^4 - 16*(a^3*b^2 - a*b^4)*d*x)*cosh(d*x + c))*sinh(d*x + c))/((a^6*b^2 + 5*a^5*b^3 + 10*a^4*b^4 + 10*a^3*b^5 + 5*a^2*b^6 + a*b^7)*d*cosh(d*x + c)^8 + 8*(a^6*b^2 + 5*a^5*b^3 + 10*a^4*b^4 + 10*a^3*b^5 + 5*a^2*b^6 + a*b^7)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^6*b^2 + 5*a^5*b^3 + 10*a^4*b^4 + 10*a^3*b^5 + 5*a^2*b^6 + a*b^7)*d*sinh(d*x + c)^8 + 4*(a^6*b^2 + 3*a^5*b^3 + 2*a^4*b^4 - 2*a^3*b^5 - 3*a^2*b^6 - a*b^7)*d*cosh(d*x + c)^6 + 4*(7*(a^6*b^2 + 5*a^5*b^3 + 10*a^4*b^4 + 10*a^3*b^5 + 5*a^2*b^6 + a*b^7)*d*cosh(d*x + c)^2 + (a^6*b^2 + 3*a^5*b^3 + 2*a^4*b^4 - 2*a^3*b^5 - 3*a^2*b^6 - a*b^7)*d)*sinh(d*x + c)^6 + 2*(3*a^6*b^2 + 7*a^5*b^3 + 6*a^4*b^4 + 6*a^3*b^5 + 7*a^2*b^6 + 3*a*b^7)*d*cosh(d*x + c)^4 + 8*(7*(a^6*b^2 + 5*a^5*b^3 + 10*a^4*b^4 + 10*a^3*b^5 + 5*a^2*b^6 + a*b^7)*d*cosh(d*x + c)^3 + 3*(a^6*b^2 + 3*a^5*b^3 + 2*a^4*b^4 - 2*a^3*b^5 - 3*a^2*b^6 - a*b^7)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^6*b^2 + 5*a^5*b^3 + 10*a^4*b^4 + 10*a^3*b^5 + 5*a^2*b^6 + a*b^7)*d*cosh(d*x + c)^4 + 30*(a^6*b^2 + 3*a^5*b^3 + 2*a^4*b^4 - 2*a^3*b^5 - 3*a^2*b^6 - a*b^7)*d*cosh(d*x + c)^2 + (3*a^6*b^2 + 7*a^5*b^3 + 6*a^4*b^4 + 6*a^3*b^5 + 7*a^2*b^6 + 3*a*b^7)*d)*sinh(d*x + c)^4 + 4*(a^6*b^2 + 3*a^5*b^3 + 2*a^4*b^4 - 2*a^3*b^5 - 3*a^2*b^6 - a*b^7)*d*cosh(d*x + c)^2 + 8*(7*(a^6*b^2 + 5*a^5*b^3 + 10*a^4*b^4 + 10*a^3*b^5 + 5*a^2*b^6 + a*b^7)*d*cosh(d*x + c)^5 + 10*(a^6*b^2 + 3*a^5*b^3 + 2*a^4*b^4 - 2*a^3*b^5 - 3*a^2*b^6 - a*b^7)*d*cosh(d*x + c)^3 + (3*a^6*b^2 + 7*a^5*b^3 + 6*a^4*b^4 + 6*a^3*b^5 + 7*a^2*b^6 + 3*a*b^7)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^6*b^2 + 5*a^5*b^3 + 10*a^4*b^4 + 10*a^3*b^5 + 5*a^2*b^6 + a*b^7)*d*cosh(d*x + c)^6 + 15*(a^6*b^2 + 3*a^5*b^3 + 2*a^4*b^4 - 2*a^3*b^5 - 3*a^2*b^6 - a*b^7)*d*cosh(d*x + c)^4 + 3*(3*a^6*b^2 + 7*a^5*b^3 + 6*a^4*b^4 + 6*a^3*b^5 + 7*a^2*b^6 + 3*a*b^7)*d*cosh(d*x + c)^2 + (a^6*b^2 + 3*a^5*b^3 + 2*a^4*b^4 - 2*a^3*b^5 - 3*a^2*b^6 - a*b^7)*d)*sinh(d*x + c)^2 + (a^6*b^2 + 5*a^5*b^3 + 10*a^4*b^4 + 10*a^3*b^5 + 5*a^2*b^6 + a*b^7)*d + 8*((a^6*b^2 + 5*a^5*b^3 + 10*a^4*b^4 + 10*a^3*b^5 + 5*a^2*b^6 + a*b^7)*d*cosh(d*x + c)^7 + 3*(a^6*b^2 + 3*a^5*b^3 + 2*a^4*b^4 - 2*a^3*b^5 - 3*a^2*b^6 - a*b^7)*d*cosh(d*x + c)^5 + (3*a^6*b^2 + 7*a^5*b^3 + 6*a^4*b^4 + 6*a^3*b^5 + 7*a^2*b^6 + 3*a*b^7)*d*cosh(d*x + c)^3 + (a^6*b^2 + 3*a^5*b^3 + 2*a^4*b^4 - 2*a^3*b^5 - 3*a^2*b^6 - a*b^7)*d*cosh(d*x + c))*sinh(d*x + c)), 1/8*(8*(a^3*b^2 + 2*a^2*b^3 + a*b^4)*d*x*cosh(d*x + c)^8 + 64*(a^3*b^2 + 2*a^2*b^3 + a*b^4)*d*x*cosh(d*x + c)*sinh(d*x + c)^7 + 8*(a^3*b^2 + 2*a^2*b^3 + a*b^4)*d*x*sinh(d*x + c)^8 - 2*(a^4*b - 9*a^3*b^2 - 5*a^2*b^3 + 5*a*b^4 - 16*(a^3*b^2 - a*b^4)*d*x)*cosh(d*x + c)^6 - 2*(a^4*b - 9*a^3*b^2 - 5*a^2*b^3 + 5*a*b^4 - 112*(a^3*b^2 + 2*a^2*b^3 + a*b^4)*d*x*cosh(d*x + c)^2 - 16*(a^3*b^2 - a*b^4)*d*x)*sinh(d*x + c)^6 + 4*(112*(a^3*b^2 + 2*a^2*b^3 + a*b^4)*d*x*cosh(d*x + c)^3 - 3*(a^4*b - 9*a^3*b^2 - 5*a^2*b^3 + 5*a*b^4 - 16*(a^3*b^2 - a*b^4)*d*x)*cosh(d*x + c))*sinh(d*x + c)^5 - 2*a^4*b + 6*a^3*b^2 + 18*a^2*b^3 + 10*a*b^4 - 2*(3*a^4*b - 17*a^3*b^2 + 13*a^2*b^3 - 15*a*b^4 - 8*(3*a^3*b^2 - 2*a^2*b^3 + 3*a*b^4)*d*x)*cosh(d*x + c)^4 + 2*(280*(a^3*b^2 + 2*a^2*b^3 + a*b^4)*d*x*cosh(d*x + c)^4 - 3*a^4*b + 17*a^3*b^2 - 13*a^2*b^3 + 15*a*b^4 + 8*(3*a^3*b^2 - 2*a^2*b^3 + 3*a*b^4)*d*x - 15*(a^4*b - 9*a^3*b^2 - 5*a^2*b^3 + 5*a*b^4 - 16*(a^3*b^2 - a*b^4)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(56*(a^3*b^2 + 2*a^2*b^3 + a*b^4)*d*x*cosh(d*x + c)^5 - 5*(a^4*b - 9*a^3*b^2 - 5*a^2*b^3 + 5*a*b^4 - 16*(a^3*b^2 - a*b^4)*d*x)*cosh(d*x + c)^3 - (3*a^4*b - 17*a^3*b^2 + 13*a^2*b^3 - 15*a*b^4 - 8*(3*a^3*b^2 - 2*a^2*b^3 + 3*a*b^4)*d*x)*cosh(d*x + c))*sinh(d*x + c)^3 + 8*(a^3*b^2 + 2*a^2*b^3 + a*b^4)*d*x - 2*(3*a^4*b - 11*a^3*b^2 + a^2*b^3 + 15*a*b^4 - 16*(a^3*b^2 - a*b^4)*d*x)*cosh(d*x + c)^2 + 2*(112*(a^3*b^2 + 2*a^2*b^3 + a*b^4)*d*x*cosh(d*x + c)^6 - 3*a^4*b + 11*a^3*b^2 - a^2*b^3 - 15*a*b^4 - 15*(a^4*b - 9*a^3*b^2 - 5*a^2*b^3 + 5*a*b^4 - 16*(a^3*b^2 - a*b^4)*d*x)*cosh(d*x + c)^4 + 16*(a^3*b^2 - a*b^4)*d*x - 6*(3*a^4*b - 17*a^3*b^2 + 13*a^2*b^3 - 15*a*b^4 - 8*(3*a^3*b^2 - 2*a^2*b^3 + 3*a*b^4)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - ((a^4 + 8*a^3*b + 10*a^2*b^2 - 3*b^4)*cosh(d*x + c)^8 + 8*(a^4 + 8*a^3*b + 10*a^2*b^2 - 3*b^4)*cosh(d*x + c)*sinh(d*x + c)^7 + (a^4 + 8*a^3*b + 10*a^2*b^2 - 3*b^4)*sinh(d*x + c)^8 + 4*(a^4 + 6*a^3*b - 4*a^2*b^2 - 6*a*b^3 + 3*b^4)*cosh(d*x + c)^6 + 4*(a^4 + 6*a^3*b - 4*a^2*b^2 - 6*a*b^3 + 3*b^4 + 7*(a^4 + 8*a^3*b + 10*a^2*b^2 - 3*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(a^4 + 8*a^3*b + 10*a^2*b^2 - 3*b^4)*cosh(d*x + c)^3 + 3*(a^4 + 6*a^3*b - 4*a^2*b^2 - 6*a*b^3 + 3*b^4)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(3*a^4 + 16*a^3*b - 18*a^2*b^2 + 24*a*b^3 - 9*b^4)*cosh(d*x + c)^4 + 2*(35*(a^4 + 8*a^3*b + 10*a^2*b^2 - 3*b^4)*cosh(d*x + c)^4 + 3*a^4 + 16*a^3*b - 18*a^2*b^2 + 24*a*b^3 - 9*b^4 + 30*(a^4 + 6*a^3*b - 4*a^2*b^2 - 6*a*b^3 + 3*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + a^4 + 8*a^3*b + 10*a^2*b^2 - 3*b^4 + 8*(7*(a^4 + 8*a^3*b + 10*a^2*b^2 - 3*b^4)*cosh(d*x + c)^5 + 10*(a^4 + 6*a^3*b - 4*a^2*b^2 - 6*a*b^3 + 3*b^4)*cosh(d*x + c)^3 + (3*a^4 + 16*a^3*b - 18*a^2*b^2 + 24*a*b^3 - 9*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(a^4 + 6*a^3*b - 4*a^2*b^2 - 6*a*b^3 + 3*b^4)*cosh(d*x + c)^2 + 4*(7*(a^4 + 8*a^3*b + 10*a^2*b^2 - 3*b^4)*cosh(d*x + c)^6 + 15*(a^4 + 6*a^3*b - 4*a^2*b^2 - 6*a*b^3 + 3*b^4)*cosh(d*x + c)^4 + a^4 + 6*a^3*b - 4*a^2*b^2 - 6*a*b^3 + 3*b^4 + 3*(3*a^4 + 16*a^3*b - 18*a^2*b^2 + 24*a*b^3 - 9*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((a^4 + 8*a^3*b + 10*a^2*b^2 - 3*b^4)*cosh(d*x + c)^7 + 3*(a^4 + 6*a^3*b - 4*a^2*b^2 - 6*a*b^3 + 3*b^4)*cosh(d*x + c)^5 + (3*a^4 + 16*a^3*b - 18*a^2*b^2 + 24*a*b^3 - 9*b^4)*cosh(d*x + c)^3 + (a^4 + 6*a^3*b - 4*a^2*b^2 - 6*a*b^3 + 3*b^4)*cosh(d*x + c))*sinh(d*x + c))*sqrt(a*b)*arctan(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 + a - b)*sqrt(a*b)/(a*b)) + 4*(16*(a^3*b^2 + 2*a^2*b^3 + a*b^4)*d*x*cosh(d*x + c)^7 - 3*(a^4*b - 9*a^3*b^2 - 5*a^2*b^3 + 5*a*b^4 - 16*(a^3*b^2 - a*b^4)*d*x)*cosh(d*x + c)^5 - 2*(3*a^4*b - 17*a^3*b^2 + 13*a^2*b^3 - 15*a*b^4 - 8*(3*a^3*b^2 - 2*a^2*b^3 + 3*a*b^4)*d*x)*cosh(d*x + c)^3 - (3*a^4*b - 11*a^3*b^2 + a^2*b^3 + 15*a*b^4 - 16*(a^3*b^2 - a*b^4)*d*x)*cosh(d*x + c))*sinh(d*x + c))/((a^6*b^2 + 5*a^5*b^3 + 10*a^4*b^4 + 10*a^3*b^5 + 5*a^2*b^6 + a*b^7)*d*cosh(d*x + c)^8 + 8*(a^6*b^2 + 5*a^5*b^3 + 10*a^4*b^4 + 10*a^3*b^5 + 5*a^2*b^6 + a*b^7)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^6*b^2 + 5*a^5*b^3 + 10*a^4*b^4 + 10*a^3*b^5 + 5*a^2*b^6 + a*b^7)*d*sinh(d*x + c)^8 + 4*(a^6*b^2 + 3*a^5*b^3 + 2*a^4*b^4 - 2*a^3*b^5 - 3*a^2*b^6 - a*b^7)*d*cosh(d*x + c)^6 + 4*(7*(a^6*b^2 + 5*a^5*b^3 + 10*a^4*b^4 + 10*a^3*b^5 + 5*a^2*b^6 + a*b^7)*d*cosh(d*x + c)^2 + (a^6*b^2 + 3*a^5*b^3 + 2*a^4*b^4 - 2*a^3*b^5 - 3*a^2*b^6 - a*b^7)*d)*sinh(d*x + c)^6 + 2*(3*a^6*b^2 + 7*a^5*b^3 + 6*a^4*b^4 + 6*a^3*b^5 + 7*a^2*b^6 + 3*a*b^7)*d*cosh(d*x + c)^4 + 8*(7*(a^6*b^2 + 5*a^5*b^3 + 10*a^4*b^4 + 10*a^3*b^5 + 5*a^2*b^6 + a*b^7)*d*cosh(d*x + c)^3 + 3*(a^6*b^2 + 3*a^5*b^3 + 2*a^4*b^4 - 2*a^3*b^5 - 3*a^2*b^6 - a*b^7)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^6*b^2 + 5*a^5*b^3 + 10*a^4*b^4 + 10*a^3*b^5 + 5*a^2*b^6 + a*b^7)*d*cosh(d*x + c)^4 + 30*(a^6*b^2 + 3*a^5*b^3 + 2*a^4*b^4 - 2*a^3*b^5 - 3*a^2*b^6 - a*b^7)*d*cosh(d*x + c)^2 + (3*a^6*b^2 + 7*a^5*b^3 + 6*a^4*b^4 + 6*a^3*b^5 + 7*a^2*b^6 + 3*a*b^7)*d)*sinh(d*x + c)^4 + 4*(a^6*b^2 + 3*a^5*b^3 + 2*a^4*b^4 - 2*a^3*b^5 - 3*a^2*b^6 - a*b^7)*d*cosh(d*x + c)^2 + 8*(7*(a^6*b^2 + 5*a^5*b^3 + 10*a^4*b^4 + 10*a^3*b^5 + 5*a^2*b^6 + a*b^7)*d*cosh(d*x + c)^5 + 10*(a^6*b^2 + 3*a^5*b^3 + 2*a^4*b^4 - 2*a^3*b^5 - 3*a^2*b^6 - a*b^7)*d*cosh(d*x + c)^3 + (3*a^6*b^2 + 7*a^5*b^3 + 6*a^4*b^4 + 6*a^3*b^5 + 7*a^2*b^6 + 3*a*b^7)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^6*b^2 + 5*a^5*b^3 + 10*a^4*b^4 + 10*a^3*b^5 + 5*a^2*b^6 + a*b^7)*d*cosh(d*x + c)^6 + 15*(a^6*b^2 + 3*a^5*b^3 + 2*a^4*b^4 - 2*a^3*b^5 - 3*a^2*b^6 - a*b^7)*d*cosh(d*x + c)^4 + 3*(3*a^6*b^2 + 7*a^5*b^3 + 6*a^4*b^4 + 6*a^3*b^5 + 7*a^2*b^6 + 3*a*b^7)*d*cosh(d*x + c)^2 + (a^6*b^2 + 3*a^5*b^3 + 2*a^4*b^4 - 2*a^3*b^5 - 3*a^2*b^6 - a*b^7)*d)*sinh(d*x + c)^2 + (a^6*b^2 + 5*a^5*b^3 + 10*a^4*b^4 + 10*a^3*b^5 + 5*a^2*b^6 + a*b^7)*d + 8*((a^6*b^2 + 5*a^5*b^3 + 10*a^4*b^4 + 10*a^3*b^5 + 5*a^2*b^6 + a*b^7)*d*cosh(d*x + c)^7 + 3*(a^6*b^2 + 3*a^5*b^3 + 2*a^4*b^4 - 2*a^3*b^5 - 3*a^2*b^6 - a*b^7)*d*cosh(d*x + c)^5 + (3*a^6*b^2 + 7*a^5*b^3 + 6*a^4*b^4 + 6*a^3*b^5 + 7*a^2*b^6 + 3*a*b^7)*d*cosh(d*x + c)^3 + (a^6*b^2 + 3*a^5*b^3 + 2*a^4*b^4 - 2*a^3*b^5 - 3*a^2*b^6 - a*b^7)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
193,1,2611,0,0.479673," ","integrate(tanh(d*x+c)^3/(a+b*tanh(d*x+c)^2)^3,x, algorithm=""fricas"")","-\frac{2 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x \cosh\left(d x + c\right)^{8} + 16 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + 2 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x \sinh\left(d x + c\right)^{8} + 4 \, {\left(2 \, {\left(a^{2} - b^{2}\right)} d x - a^{2} + b^{2}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(14 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} - b^{2}\right)} d x - a^{2} + b^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(14 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x \cosh\left(d x + c\right)^{3} + 3 \, {\left(2 \, {\left(a^{2} - b^{2}\right)} d x - a^{2} + b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 4 \, {\left({\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} d x - 2 \, a^{2} + 2 \, a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(35 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x \cosh\left(d x + c\right)^{4} + {\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} d x + 15 \, {\left(2 \, {\left(a^{2} - b^{2}\right)} d x - a^{2} + b^{2}\right)} \cosh\left(d x + c\right)^{2} - 2 \, a^{2} + 2 \, a b - 2 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 16 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x \cosh\left(d x + c\right)^{5} + 5 \, {\left(2 \, {\left(a^{2} - b^{2}\right)} d x - a^{2} + b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left({\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} d x - 2 \, a^{2} + 2 \, a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x + 4 \, {\left(2 \, {\left(a^{2} - b^{2}\right)} d x - a^{2} + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(14 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x \cosh\left(d x + c\right)^{6} + 15 \, {\left(2 \, {\left(a^{2} - b^{2}\right)} d x - a^{2} + b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(a^{2} - b^{2}\right)} d x + 6 \, {\left({\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} d x - 2 \, a^{2} + 2 \, a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} - a^{2} + b^{2}\right)} \sinh\left(d x + c\right)^{2} - {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + 30 \, {\left(a^{2} - 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)^{4} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{2} - 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)^{3} + 4 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 2 \, a b + b^{2} + 8 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\frac{2 \, {\left({\left(a + b\right)} \cosh\left(d x + c\right)^{2} + {\left(a + b\right)} \sinh\left(d x + c\right)^{2} + a - b\right)}}{\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}}\right) + 8 \, {\left(2 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x \cosh\left(d x + c\right)^{7} + 3 \, {\left(2 \, {\left(a^{2} - b^{2}\right)} d x - a^{2} + b^{2}\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left({\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} d x - 2 \, a^{2} + 2 \, a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(2 \, {\left(a^{2} - b^{2}\right)} d x - a^{2} + b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{2 \, {\left({\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(3 \, a^{5} + 7 \, a^{4} b + 6 \, a^{3} b^{2} + 6 \, a^{2} b^{3} + 7 \, a b^{4} + 3 \, b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 30 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{5} + 7 \, a^{4} b + 6 \, a^{3} b^{2} + 6 \, a^{2} b^{3} + 7 \, a b^{4} + 3 \, b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{5} + 7 \, a^{4} b + 6 \, a^{3} b^{2} + 6 \, a^{2} b^{3} + 7 \, a b^{4} + 3 \, b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{5} + 7 \, a^{4} b + 6 \, a^{3} b^{2} + 6 \, a^{2} b^{3} + 7 \, a b^{4} + 3 \, b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d + 8 \, {\left({\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} d \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{5} + 7 \, a^{4} b + 6 \, a^{3} b^{2} + 6 \, a^{2} b^{3} + 7 \, a b^{4} + 3 \, b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"-1/2*(2*(a^2 + 2*a*b + b^2)*d*x*cosh(d*x + c)^8 + 16*(a^2 + 2*a*b + b^2)*d*x*cosh(d*x + c)*sinh(d*x + c)^7 + 2*(a^2 + 2*a*b + b^2)*d*x*sinh(d*x + c)^8 + 4*(2*(a^2 - b^2)*d*x - a^2 + b^2)*cosh(d*x + c)^6 + 4*(14*(a^2 + 2*a*b + b^2)*d*x*cosh(d*x + c)^2 + 2*(a^2 - b^2)*d*x - a^2 + b^2)*sinh(d*x + c)^6 + 8*(14*(a^2 + 2*a*b + b^2)*d*x*cosh(d*x + c)^3 + 3*(2*(a^2 - b^2)*d*x - a^2 + b^2)*cosh(d*x + c))*sinh(d*x + c)^5 + 4*((3*a^2 - 2*a*b + 3*b^2)*d*x - 2*a^2 + 2*a*b - 2*b^2)*cosh(d*x + c)^4 + 4*(35*(a^2 + 2*a*b + b^2)*d*x*cosh(d*x + c)^4 + (3*a^2 - 2*a*b + 3*b^2)*d*x + 15*(2*(a^2 - b^2)*d*x - a^2 + b^2)*cosh(d*x + c)^2 - 2*a^2 + 2*a*b - 2*b^2)*sinh(d*x + c)^4 + 16*(7*(a^2 + 2*a*b + b^2)*d*x*cosh(d*x + c)^5 + 5*(2*(a^2 - b^2)*d*x - a^2 + b^2)*cosh(d*x + c)^3 + ((3*a^2 - 2*a*b + 3*b^2)*d*x - 2*a^2 + 2*a*b - 2*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 2*(a^2 + 2*a*b + b^2)*d*x + 4*(2*(a^2 - b^2)*d*x - a^2 + b^2)*cosh(d*x + c)^2 + 4*(14*(a^2 + 2*a*b + b^2)*d*x*cosh(d*x + c)^6 + 15*(2*(a^2 - b^2)*d*x - a^2 + b^2)*cosh(d*x + c)^4 + 2*(a^2 - b^2)*d*x + 6*((3*a^2 - 2*a*b + 3*b^2)*d*x - 2*a^2 + 2*a*b - 2*b^2)*cosh(d*x + c)^2 - a^2 + b^2)*sinh(d*x + c)^2 - ((a^2 + 2*a*b + b^2)*cosh(d*x + c)^8 + 8*(a^2 + 2*a*b + b^2)*cosh(d*x + c)*sinh(d*x + c)^7 + (a^2 + 2*a*b + b^2)*sinh(d*x + c)^8 + 4*(a^2 - b^2)*cosh(d*x + c)^6 + 4*(7*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + a^2 - b^2)*sinh(d*x + c)^6 + 8*(7*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 + 3*(a^2 - b^2)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(3*a^2 - 2*a*b + 3*b^2)*cosh(d*x + c)^4 + 2*(35*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 + 30*(a^2 - b^2)*cosh(d*x + c)^2 + 3*a^2 - 2*a*b + 3*b^2)*sinh(d*x + c)^4 + 8*(7*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^5 + 10*(a^2 - b^2)*cosh(d*x + c)^3 + (3*a^2 - 2*a*b + 3*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(a^2 - b^2)*cosh(d*x + c)^2 + 4*(7*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^6 + 15*(a^2 - b^2)*cosh(d*x + c)^4 + 3*(3*a^2 - 2*a*b + 3*b^2)*cosh(d*x + c)^2 + a^2 - b^2)*sinh(d*x + c)^2 + a^2 + 2*a*b + b^2 + 8*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^7 + 3*(a^2 - b^2)*cosh(d*x + c)^5 + (3*a^2 - 2*a*b + 3*b^2)*cosh(d*x + c)^3 + (a^2 - b^2)*cosh(d*x + c))*sinh(d*x + c))*log(2*((a + b)*cosh(d*x + c)^2 + (a + b)*sinh(d*x + c)^2 + a - b)/(cosh(d*x + c)^2 - 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)) + 8*(2*(a^2 + 2*a*b + b^2)*d*x*cosh(d*x + c)^7 + 3*(2*(a^2 - b^2)*d*x - a^2 + b^2)*cosh(d*x + c)^5 + 2*((3*a^2 - 2*a*b + 3*b^2)*d*x - 2*a^2 + 2*a*b - 2*b^2)*cosh(d*x + c)^3 + (2*(a^2 - b^2)*d*x - a^2 + b^2)*cosh(d*x + c))*sinh(d*x + c))/((a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*cosh(d*x + c)^8 + 8*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*sinh(d*x + c)^8 + 4*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*d*cosh(d*x + c)^6 + 4*(7*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*cosh(d*x + c)^2 + (a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*d)*sinh(d*x + c)^6 + 2*(3*a^5 + 7*a^4*b + 6*a^3*b^2 + 6*a^2*b^3 + 7*a*b^4 + 3*b^5)*d*cosh(d*x + c)^4 + 8*(7*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*cosh(d*x + c)^3 + 3*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*cosh(d*x + c)^4 + 30*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*d*cosh(d*x + c)^2 + (3*a^5 + 7*a^4*b + 6*a^3*b^2 + 6*a^2*b^3 + 7*a*b^4 + 3*b^5)*d)*sinh(d*x + c)^4 + 4*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*d*cosh(d*x + c)^2 + 8*(7*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*cosh(d*x + c)^5 + 10*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*d*cosh(d*x + c)^3 + (3*a^5 + 7*a^4*b + 6*a^3*b^2 + 6*a^2*b^3 + 7*a*b^4 + 3*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*cosh(d*x + c)^6 + 15*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*d*cosh(d*x + c)^4 + 3*(3*a^5 + 7*a^4*b + 6*a^3*b^2 + 6*a^2*b^3 + 7*a*b^4 + 3*b^5)*d*cosh(d*x + c)^2 + (a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*d)*sinh(d*x + c)^2 + (a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d + 8*((a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*cosh(d*x + c)^7 + 3*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*d*cosh(d*x + c)^5 + (3*a^5 + 7*a^4*b + 6*a^3*b^2 + 6*a^2*b^3 + 7*a*b^4 + 3*b^5)*d*cosh(d*x + c)^3 + (a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*d*cosh(d*x + c))*sinh(d*x + c))","B",0
194,1,7791,0,0.576883," ","integrate(tanh(d*x+c)^2/(a+b*tanh(d*x+c)^2)^3,x, algorithm=""fricas"")","\left[\frac{16 \, {\left(a^{4} b + 2 \, a^{3} b^{2} + a^{2} b^{3}\right)} d x \cosh\left(d x + c\right)^{8} + 128 \, {\left(a^{4} b + 2 \, a^{3} b^{2} + a^{2} b^{3}\right)} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + 16 \, {\left(a^{4} b + 2 \, a^{3} b^{2} + a^{2} b^{3}\right)} d x \sinh\left(d x + c\right)^{8} + 4 \, {\left(5 \, a^{4} b - 5 \, a^{3} b^{2} - 9 \, a^{2} b^{3} + a b^{4} + 16 \, {\left(a^{4} b - a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(5 \, a^{4} b - 5 \, a^{3} b^{2} - 9 \, a^{2} b^{3} + a b^{4} + 112 \, {\left(a^{4} b + 2 \, a^{3} b^{2} + a^{2} b^{3}\right)} d x \cosh\left(d x + c\right)^{2} + 16 \, {\left(a^{4} b - a^{2} b^{3}\right)} d x\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(112 \, {\left(a^{4} b + 2 \, a^{3} b^{2} + a^{2} b^{3}\right)} d x \cosh\left(d x + c\right)^{3} + 3 \, {\left(5 \, a^{4} b - 5 \, a^{3} b^{2} - 9 \, a^{2} b^{3} + a b^{4} + 16 \, {\left(a^{4} b - a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 20 \, a^{4} b + 36 \, a^{3} b^{2} + 12 \, a^{2} b^{3} - 4 \, a b^{4} + 4 \, {\left(15 \, a^{4} b - 13 \, a^{3} b^{2} + 17 \, a^{2} b^{3} - 3 \, a b^{4} + 8 \, {\left(3 \, a^{4} b - 2 \, a^{3} b^{2} + 3 \, a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(280 \, {\left(a^{4} b + 2 \, a^{3} b^{2} + a^{2} b^{3}\right)} d x \cosh\left(d x + c\right)^{4} + 15 \, a^{4} b - 13 \, a^{3} b^{2} + 17 \, a^{2} b^{3} - 3 \, a b^{4} + 8 \, {\left(3 \, a^{4} b - 2 \, a^{3} b^{2} + 3 \, a^{2} b^{3}\right)} d x + 15 \, {\left(5 \, a^{4} b - 5 \, a^{3} b^{2} - 9 \, a^{2} b^{3} + a b^{4} + 16 \, {\left(a^{4} b - a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 16 \, {\left(56 \, {\left(a^{4} b + 2 \, a^{3} b^{2} + a^{2} b^{3}\right)} d x \cosh\left(d x + c\right)^{5} + 5 \, {\left(5 \, a^{4} b - 5 \, a^{3} b^{2} - 9 \, a^{2} b^{3} + a b^{4} + 16 \, {\left(a^{4} b - a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + {\left(15 \, a^{4} b - 13 \, a^{3} b^{2} + 17 \, a^{2} b^{3} - 3 \, a b^{4} + 8 \, {\left(3 \, a^{4} b - 2 \, a^{3} b^{2} + 3 \, a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 16 \, {\left(a^{4} b + 2 \, a^{3} b^{2} + a^{2} b^{3}\right)} d x + 4 \, {\left(15 \, a^{4} b + a^{3} b^{2} - 11 \, a^{2} b^{3} + 3 \, a b^{4} + 16 \, {\left(a^{4} b - a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(112 \, {\left(a^{4} b + 2 \, a^{3} b^{2} + a^{2} b^{3}\right)} d x \cosh\left(d x + c\right)^{6} + 15 \, a^{4} b + a^{3} b^{2} - 11 \, a^{2} b^{3} + 3 \, a b^{4} + 15 \, {\left(5 \, a^{4} b - 5 \, a^{3} b^{2} - 9 \, a^{2} b^{3} + a b^{4} + 16 \, {\left(a^{4} b - a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 16 \, {\left(a^{4} b - a^{2} b^{3}\right)} d x + 6 \, {\left(15 \, a^{4} b - 13 \, a^{3} b^{2} + 17 \, a^{2} b^{3} - 3 \, a b^{4} + 8 \, {\left(3 \, a^{4} b - 2 \, a^{3} b^{2} + 3 \, a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(3 \, a^{4} - 10 \, a^{2} b^{2} - 8 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(3 \, a^{4} - 10 \, a^{2} b^{2} - 8 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(3 \, a^{4} - 10 \, a^{2} b^{2} - 8 \, a b^{3} - b^{4}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(3 \, a^{4} - 6 \, a^{3} b - 4 \, a^{2} b^{2} + 6 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(3 \, a^{4} - 6 \, a^{3} b - 4 \, a^{2} b^{2} + 6 \, a b^{3} + b^{4} + 7 \, {\left(3 \, a^{4} - 10 \, a^{2} b^{2} - 8 \, 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(3 \, a^{4} - 10 \, a^{2} b^{2} - 8 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(3 \, a^{4} - 6 \, a^{3} b - 4 \, 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(9 \, a^{4} - 24 \, a^{3} b + 18 \, a^{2} b^{2} - 16 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(3 \, a^{4} - 10 \, a^{2} b^{2} - 8 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{4} + 9 \, a^{4} - 24 \, a^{3} b + 18 \, a^{2} b^{2} - 16 \, a b^{3} - 3 \, b^{4} + 30 \, {\left(3 \, a^{4} - 6 \, a^{3} b - 4 \, 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} + 3 \, a^{4} - 10 \, a^{2} b^{2} - 8 \, a b^{3} - b^{4} + 8 \, {\left(7 \, {\left(3 \, a^{4} - 10 \, a^{2} b^{2} - 8 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(3 \, a^{4} - 6 \, a^{3} b - 4 \, a^{2} b^{2} + 6 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(9 \, a^{4} - 24 \, a^{3} b + 18 \, 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)^{3} + 4 \, {\left(3 \, a^{4} - 6 \, a^{3} b - 4 \, a^{2} b^{2} + 6 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(3 \, a^{4} - 10 \, a^{2} b^{2} - 8 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(3 \, a^{4} - 6 \, a^{3} b - 4 \, a^{2} b^{2} + 6 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{4} + 3 \, a^{4} - 6 \, a^{3} b - 4 \, a^{2} b^{2} + 6 \, a b^{3} + b^{4} + 3 \, {\left(9 \, a^{4} - 24 \, a^{3} b + 18 \, 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)^{2} + 8 \, {\left({\left(3 \, a^{4} - 10 \, a^{2} b^{2} - 8 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(3 \, a^{4} - 6 \, a^{3} b - 4 \, a^{2} b^{2} + 6 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{5} + {\left(9 \, a^{4} - 24 \, a^{3} b + 18 \, a^{2} b^{2} - 16 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{4} - 6 \, a^{3} b - 4 \, 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 b} \log\left(\frac{{\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) \sinh\left(d x + c\right)^{3} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{2} + a^{2} - 6 \, a b + b^{2} + 4 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} - b^{2}\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)^{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} + a - b\right)} \sqrt{-a b}}{{\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) + 8 \, {\left(16 \, {\left(a^{4} b + 2 \, a^{3} b^{2} + a^{2} b^{3}\right)} d x \cosh\left(d x + c\right)^{7} + 3 \, {\left(5 \, a^{4} b - 5 \, a^{3} b^{2} - 9 \, a^{2} b^{3} + a b^{4} + 16 \, {\left(a^{4} b - a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(15 \, a^{4} b - 13 \, a^{3} b^{2} + 17 \, a^{2} b^{3} - 3 \, a b^{4} + 8 \, {\left(3 \, a^{4} b - 2 \, a^{3} b^{2} + 3 \, a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + {\left(15 \, a^{4} b + a^{3} b^{2} - 11 \, a^{2} b^{3} + 3 \, a b^{4} + 16 \, {\left(a^{4} b - a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{16 \, {\left({\left(a^{7} b + 5 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 10 \, a^{4} b^{4} + 5 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{7} b + 5 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 10 \, a^{4} b^{4} + 5 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{7} b + 5 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 10 \, a^{4} b^{4} + 5 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{7} b + 3 \, a^{6} b^{2} + 2 \, a^{5} b^{3} - 2 \, a^{4} b^{4} - 3 \, a^{3} b^{5} - a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{7} b + 5 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 10 \, a^{4} b^{4} + 5 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{7} b + 3 \, a^{6} b^{2} + 2 \, a^{5} b^{3} - 2 \, a^{4} b^{4} - 3 \, a^{3} b^{5} - a^{2} b^{6}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(3 \, a^{7} b + 7 \, a^{6} b^{2} + 6 \, a^{5} b^{3} + 6 \, a^{4} b^{4} + 7 \, a^{3} b^{5} + 3 \, a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{7} b + 5 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 10 \, a^{4} b^{4} + 5 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{7} b + 3 \, a^{6} b^{2} + 2 \, a^{5} b^{3} - 2 \, a^{4} b^{4} - 3 \, a^{3} b^{5} - a^{2} b^{6}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a^{7} b + 5 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 10 \, a^{4} b^{4} + 5 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{4} + 30 \, {\left(a^{7} b + 3 \, a^{6} b^{2} + 2 \, a^{5} b^{3} - 2 \, a^{4} b^{4} - 3 \, a^{3} b^{5} - a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{7} b + 7 \, a^{6} b^{2} + 6 \, a^{5} b^{3} + 6 \, a^{4} b^{4} + 7 \, a^{3} b^{5} + 3 \, a^{2} b^{6}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{7} b + 3 \, a^{6} b^{2} + 2 \, a^{5} b^{3} - 2 \, a^{4} b^{4} - 3 \, a^{3} b^{5} - a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a^{7} b + 5 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 10 \, a^{4} b^{4} + 5 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{7} b + 3 \, a^{6} b^{2} + 2 \, a^{5} b^{3} - 2 \, a^{4} b^{4} - 3 \, a^{3} b^{5} - a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{7} b + 7 \, a^{6} b^{2} + 6 \, a^{5} b^{3} + 6 \, a^{4} b^{4} + 7 \, a^{3} b^{5} + 3 \, a^{2} b^{6}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a^{7} b + 5 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 10 \, a^{4} b^{4} + 5 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{7} b + 3 \, a^{6} b^{2} + 2 \, a^{5} b^{3} - 2 \, a^{4} b^{4} - 3 \, a^{3} b^{5} - a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{7} b + 7 \, a^{6} b^{2} + 6 \, a^{5} b^{3} + 6 \, a^{4} b^{4} + 7 \, a^{3} b^{5} + 3 \, a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{7} b + 3 \, a^{6} b^{2} + 2 \, a^{5} b^{3} - 2 \, a^{4} b^{4} - 3 \, a^{3} b^{5} - a^{2} b^{6}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{7} b + 5 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 10 \, a^{4} b^{4} + 5 \, a^{3} b^{5} + a^{2} b^{6}\right)} d + 8 \, {\left({\left(a^{7} b + 5 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 10 \, a^{4} b^{4} + 5 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{7} b + 3 \, a^{6} b^{2} + 2 \, a^{5} b^{3} - 2 \, a^{4} b^{4} - 3 \, a^{3} b^{5} - a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{7} b + 7 \, a^{6} b^{2} + 6 \, a^{5} b^{3} + 6 \, a^{4} b^{4} + 7 \, a^{3} b^{5} + 3 \, a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{7} b + 3 \, a^{6} b^{2} + 2 \, a^{5} b^{3} - 2 \, a^{4} b^{4} - 3 \, a^{3} b^{5} - a^{2} b^{6}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}, \frac{8 \, {\left(a^{4} b + 2 \, a^{3} b^{2} + a^{2} b^{3}\right)} d x \cosh\left(d x + c\right)^{8} + 64 \, {\left(a^{4} b + 2 \, a^{3} b^{2} + a^{2} b^{3}\right)} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + 8 \, {\left(a^{4} b + 2 \, a^{3} b^{2} + a^{2} b^{3}\right)} d x \sinh\left(d x + c\right)^{8} + 2 \, {\left(5 \, a^{4} b - 5 \, a^{3} b^{2} - 9 \, a^{2} b^{3} + a b^{4} + 16 \, {\left(a^{4} b - a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(5 \, a^{4} b - 5 \, a^{3} b^{2} - 9 \, a^{2} b^{3} + a b^{4} + 112 \, {\left(a^{4} b + 2 \, a^{3} b^{2} + a^{2} b^{3}\right)} d x \cosh\left(d x + c\right)^{2} + 16 \, {\left(a^{4} b - a^{2} b^{3}\right)} d x\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(112 \, {\left(a^{4} b + 2 \, a^{3} b^{2} + a^{2} b^{3}\right)} d x \cosh\left(d x + c\right)^{3} + 3 \, {\left(5 \, a^{4} b - 5 \, a^{3} b^{2} - 9 \, a^{2} b^{3} + a b^{4} + 16 \, {\left(a^{4} b - a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 10 \, a^{4} b + 18 \, a^{3} b^{2} + 6 \, a^{2} b^{3} - 2 \, a b^{4} + 2 \, {\left(15 \, a^{4} b - 13 \, a^{3} b^{2} + 17 \, a^{2} b^{3} - 3 \, a b^{4} + 8 \, {\left(3 \, a^{4} b - 2 \, a^{3} b^{2} + 3 \, a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(280 \, {\left(a^{4} b + 2 \, a^{3} b^{2} + a^{2} b^{3}\right)} d x \cosh\left(d x + c\right)^{4} + 15 \, a^{4} b - 13 \, a^{3} b^{2} + 17 \, a^{2} b^{3} - 3 \, a b^{4} + 8 \, {\left(3 \, a^{4} b - 2 \, a^{3} b^{2} + 3 \, a^{2} b^{3}\right)} d x + 15 \, {\left(5 \, a^{4} b - 5 \, a^{3} b^{2} - 9 \, a^{2} b^{3} + a b^{4} + 16 \, {\left(a^{4} b - a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(56 \, {\left(a^{4} b + 2 \, a^{3} b^{2} + a^{2} b^{3}\right)} d x \cosh\left(d x + c\right)^{5} + 5 \, {\left(5 \, a^{4} b - 5 \, a^{3} b^{2} - 9 \, a^{2} b^{3} + a b^{4} + 16 \, {\left(a^{4} b - a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + {\left(15 \, a^{4} b - 13 \, a^{3} b^{2} + 17 \, a^{2} b^{3} - 3 \, a b^{4} + 8 \, {\left(3 \, a^{4} b - 2 \, a^{3} b^{2} + 3 \, a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 8 \, {\left(a^{4} b + 2 \, a^{3} b^{2} + a^{2} b^{3}\right)} d x + 2 \, {\left(15 \, a^{4} b + a^{3} b^{2} - 11 \, a^{2} b^{3} + 3 \, a b^{4} + 16 \, {\left(a^{4} b - a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(112 \, {\left(a^{4} b + 2 \, a^{3} b^{2} + a^{2} b^{3}\right)} d x \cosh\left(d x + c\right)^{6} + 15 \, a^{4} b + a^{3} b^{2} - 11 \, a^{2} b^{3} + 3 \, a b^{4} + 15 \, {\left(5 \, a^{4} b - 5 \, a^{3} b^{2} - 9 \, a^{2} b^{3} + a b^{4} + 16 \, {\left(a^{4} b - a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 16 \, {\left(a^{4} b - a^{2} b^{3}\right)} d x + 6 \, {\left(15 \, a^{4} b - 13 \, a^{3} b^{2} + 17 \, a^{2} b^{3} - 3 \, a b^{4} + 8 \, {\left(3 \, a^{4} b - 2 \, a^{3} b^{2} + 3 \, a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} - {\left({\left(3 \, a^{4} - 10 \, a^{2} b^{2} - 8 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(3 \, a^{4} - 10 \, a^{2} b^{2} - 8 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(3 \, a^{4} - 10 \, a^{2} b^{2} - 8 \, a b^{3} - b^{4}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(3 \, a^{4} - 6 \, a^{3} b - 4 \, a^{2} b^{2} + 6 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(3 \, a^{4} - 6 \, a^{3} b - 4 \, a^{2} b^{2} + 6 \, a b^{3} + b^{4} + 7 \, {\left(3 \, a^{4} - 10 \, a^{2} b^{2} - 8 \, 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(3 \, a^{4} - 10 \, a^{2} b^{2} - 8 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(3 \, a^{4} - 6 \, a^{3} b - 4 \, 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(9 \, a^{4} - 24 \, a^{3} b + 18 \, a^{2} b^{2} - 16 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(3 \, a^{4} - 10 \, a^{2} b^{2} - 8 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{4} + 9 \, a^{4} - 24 \, a^{3} b + 18 \, a^{2} b^{2} - 16 \, a b^{3} - 3 \, b^{4} + 30 \, {\left(3 \, a^{4} - 6 \, a^{3} b - 4 \, 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} + 3 \, a^{4} - 10 \, a^{2} b^{2} - 8 \, a b^{3} - b^{4} + 8 \, {\left(7 \, {\left(3 \, a^{4} - 10 \, a^{2} b^{2} - 8 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(3 \, a^{4} - 6 \, a^{3} b - 4 \, a^{2} b^{2} + 6 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(9 \, a^{4} - 24 \, a^{3} b + 18 \, 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)^{3} + 4 \, {\left(3 \, a^{4} - 6 \, a^{3} b - 4 \, a^{2} b^{2} + 6 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(3 \, a^{4} - 10 \, a^{2} b^{2} - 8 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(3 \, a^{4} - 6 \, a^{3} b - 4 \, a^{2} b^{2} + 6 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{4} + 3 \, a^{4} - 6 \, a^{3} b - 4 \, a^{2} b^{2} + 6 \, a b^{3} + b^{4} + 3 \, {\left(9 \, a^{4} - 24 \, a^{3} b + 18 \, 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)^{2} + 8 \, {\left({\left(3 \, a^{4} - 10 \, a^{2} b^{2} - 8 \, a b^{3} - b^{4}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(3 \, a^{4} - 6 \, a^{3} b - 4 \, a^{2} b^{2} + 6 \, a b^{3} + b^{4}\right)} \cosh\left(d x + c\right)^{5} + {\left(9 \, a^{4} - 24 \, a^{3} b + 18 \, a^{2} b^{2} - 16 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{4} - 6 \, a^{3} b - 4 \, 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 b} \arctan\left(\frac{{\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} + a - b\right)} \sqrt{a b}}{2 \, a b}\right) + 4 \, {\left(16 \, {\left(a^{4} b + 2 \, a^{3} b^{2} + a^{2} b^{3}\right)} d x \cosh\left(d x + c\right)^{7} + 3 \, {\left(5 \, a^{4} b - 5 \, a^{3} b^{2} - 9 \, a^{2} b^{3} + a b^{4} + 16 \, {\left(a^{4} b - a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{5} + 2 \, {\left(15 \, a^{4} b - 13 \, a^{3} b^{2} + 17 \, a^{2} b^{3} - 3 \, a b^{4} + 8 \, {\left(3 \, a^{4} b - 2 \, a^{3} b^{2} + 3 \, a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + {\left(15 \, a^{4} b + a^{3} b^{2} - 11 \, a^{2} b^{3} + 3 \, a b^{4} + 16 \, {\left(a^{4} b - a^{2} b^{3}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{8 \, {\left({\left(a^{7} b + 5 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 10 \, a^{4} b^{4} + 5 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{7} b + 5 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 10 \, a^{4} b^{4} + 5 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{7} b + 5 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 10 \, a^{4} b^{4} + 5 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{7} b + 3 \, a^{6} b^{2} + 2 \, a^{5} b^{3} - 2 \, a^{4} b^{4} - 3 \, a^{3} b^{5} - a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{7} b + 5 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 10 \, a^{4} b^{4} + 5 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{7} b + 3 \, a^{6} b^{2} + 2 \, a^{5} b^{3} - 2 \, a^{4} b^{4} - 3 \, a^{3} b^{5} - a^{2} b^{6}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(3 \, a^{7} b + 7 \, a^{6} b^{2} + 6 \, a^{5} b^{3} + 6 \, a^{4} b^{4} + 7 \, a^{3} b^{5} + 3 \, a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{7} b + 5 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 10 \, a^{4} b^{4} + 5 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{7} b + 3 \, a^{6} b^{2} + 2 \, a^{5} b^{3} - 2 \, a^{4} b^{4} - 3 \, a^{3} b^{5} - a^{2} b^{6}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a^{7} b + 5 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 10 \, a^{4} b^{4} + 5 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{4} + 30 \, {\left(a^{7} b + 3 \, a^{6} b^{2} + 2 \, a^{5} b^{3} - 2 \, a^{4} b^{4} - 3 \, a^{3} b^{5} - a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{7} b + 7 \, a^{6} b^{2} + 6 \, a^{5} b^{3} + 6 \, a^{4} b^{4} + 7 \, a^{3} b^{5} + 3 \, a^{2} b^{6}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{7} b + 3 \, a^{6} b^{2} + 2 \, a^{5} b^{3} - 2 \, a^{4} b^{4} - 3 \, a^{3} b^{5} - a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a^{7} b + 5 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 10 \, a^{4} b^{4} + 5 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{7} b + 3 \, a^{6} b^{2} + 2 \, a^{5} b^{3} - 2 \, a^{4} b^{4} - 3 \, a^{3} b^{5} - a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{7} b + 7 \, a^{6} b^{2} + 6 \, a^{5} b^{3} + 6 \, a^{4} b^{4} + 7 \, a^{3} b^{5} + 3 \, a^{2} b^{6}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a^{7} b + 5 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 10 \, a^{4} b^{4} + 5 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{7} b + 3 \, a^{6} b^{2} + 2 \, a^{5} b^{3} - 2 \, a^{4} b^{4} - 3 \, a^{3} b^{5} - a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{7} b + 7 \, a^{6} b^{2} + 6 \, a^{5} b^{3} + 6 \, a^{4} b^{4} + 7 \, a^{3} b^{5} + 3 \, a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{7} b + 3 \, a^{6} b^{2} + 2 \, a^{5} b^{3} - 2 \, a^{4} b^{4} - 3 \, a^{3} b^{5} - a^{2} b^{6}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{7} b + 5 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 10 \, a^{4} b^{4} + 5 \, a^{3} b^{5} + a^{2} b^{6}\right)} d + 8 \, {\left({\left(a^{7} b + 5 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 10 \, a^{4} b^{4} + 5 \, a^{3} b^{5} + a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{7} b + 3 \, a^{6} b^{2} + 2 \, a^{5} b^{3} - 2 \, a^{4} b^{4} - 3 \, a^{3} b^{5} - a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{7} b + 7 \, a^{6} b^{2} + 6 \, a^{5} b^{3} + 6 \, a^{4} b^{4} + 7 \, a^{3} b^{5} + 3 \, a^{2} b^{6}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{7} b + 3 \, a^{6} b^{2} + 2 \, a^{5} b^{3} - 2 \, a^{4} b^{4} - 3 \, a^{3} b^{5} - a^{2} b^{6}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[1/16*(16*(a^4*b + 2*a^3*b^2 + a^2*b^3)*d*x*cosh(d*x + c)^8 + 128*(a^4*b + 2*a^3*b^2 + a^2*b^3)*d*x*cosh(d*x + c)*sinh(d*x + c)^7 + 16*(a^4*b + 2*a^3*b^2 + a^2*b^3)*d*x*sinh(d*x + c)^8 + 4*(5*a^4*b - 5*a^3*b^2 - 9*a^2*b^3 + a*b^4 + 16*(a^4*b - a^2*b^3)*d*x)*cosh(d*x + c)^6 + 4*(5*a^4*b - 5*a^3*b^2 - 9*a^2*b^3 + a*b^4 + 112*(a^4*b + 2*a^3*b^2 + a^2*b^3)*d*x*cosh(d*x + c)^2 + 16*(a^4*b - a^2*b^3)*d*x)*sinh(d*x + c)^6 + 8*(112*(a^4*b + 2*a^3*b^2 + a^2*b^3)*d*x*cosh(d*x + c)^3 + 3*(5*a^4*b - 5*a^3*b^2 - 9*a^2*b^3 + a*b^4 + 16*(a^4*b - a^2*b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c)^5 + 20*a^4*b + 36*a^3*b^2 + 12*a^2*b^3 - 4*a*b^4 + 4*(15*a^4*b - 13*a^3*b^2 + 17*a^2*b^3 - 3*a*b^4 + 8*(3*a^4*b - 2*a^3*b^2 + 3*a^2*b^3)*d*x)*cosh(d*x + c)^4 + 4*(280*(a^4*b + 2*a^3*b^2 + a^2*b^3)*d*x*cosh(d*x + c)^4 + 15*a^4*b - 13*a^3*b^2 + 17*a^2*b^3 - 3*a*b^4 + 8*(3*a^4*b - 2*a^3*b^2 + 3*a^2*b^3)*d*x + 15*(5*a^4*b - 5*a^3*b^2 - 9*a^2*b^3 + a*b^4 + 16*(a^4*b - a^2*b^3)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 16*(56*(a^4*b + 2*a^3*b^2 + a^2*b^3)*d*x*cosh(d*x + c)^5 + 5*(5*a^4*b - 5*a^3*b^2 - 9*a^2*b^3 + a*b^4 + 16*(a^4*b - a^2*b^3)*d*x)*cosh(d*x + c)^3 + (15*a^4*b - 13*a^3*b^2 + 17*a^2*b^3 - 3*a*b^4 + 8*(3*a^4*b - 2*a^3*b^2 + 3*a^2*b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c)^3 + 16*(a^4*b + 2*a^3*b^2 + a^2*b^3)*d*x + 4*(15*a^4*b + a^3*b^2 - 11*a^2*b^3 + 3*a*b^4 + 16*(a^4*b - a^2*b^3)*d*x)*cosh(d*x + c)^2 + 4*(112*(a^4*b + 2*a^3*b^2 + a^2*b^3)*d*x*cosh(d*x + c)^6 + 15*a^4*b + a^3*b^2 - 11*a^2*b^3 + 3*a*b^4 + 15*(5*a^4*b - 5*a^3*b^2 - 9*a^2*b^3 + a*b^4 + 16*(a^4*b - a^2*b^3)*d*x)*cosh(d*x + c)^4 + 16*(a^4*b - a^2*b^3)*d*x + 6*(15*a^4*b - 13*a^3*b^2 + 17*a^2*b^3 - 3*a*b^4 + 8*(3*a^4*b - 2*a^3*b^2 + 3*a^2*b^3)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((3*a^4 - 10*a^2*b^2 - 8*a*b^3 - b^4)*cosh(d*x + c)^8 + 8*(3*a^4 - 10*a^2*b^2 - 8*a*b^3 - b^4)*cosh(d*x + c)*sinh(d*x + c)^7 + (3*a^4 - 10*a^2*b^2 - 8*a*b^3 - b^4)*sinh(d*x + c)^8 + 4*(3*a^4 - 6*a^3*b - 4*a^2*b^2 + 6*a*b^3 + b^4)*cosh(d*x + c)^6 + 4*(3*a^4 - 6*a^3*b - 4*a^2*b^2 + 6*a*b^3 + b^4 + 7*(3*a^4 - 10*a^2*b^2 - 8*a*b^3 - b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(3*a^4 - 10*a^2*b^2 - 8*a*b^3 - b^4)*cosh(d*x + c)^3 + 3*(3*a^4 - 6*a^3*b - 4*a^2*b^2 + 6*a*b^3 + b^4)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(9*a^4 - 24*a^3*b + 18*a^2*b^2 - 16*a*b^3 - 3*b^4)*cosh(d*x + c)^4 + 2*(35*(3*a^4 - 10*a^2*b^2 - 8*a*b^3 - b^4)*cosh(d*x + c)^4 + 9*a^4 - 24*a^3*b + 18*a^2*b^2 - 16*a*b^3 - 3*b^4 + 30*(3*a^4 - 6*a^3*b - 4*a^2*b^2 + 6*a*b^3 + b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 3*a^4 - 10*a^2*b^2 - 8*a*b^3 - b^4 + 8*(7*(3*a^4 - 10*a^2*b^2 - 8*a*b^3 - b^4)*cosh(d*x + c)^5 + 10*(3*a^4 - 6*a^3*b - 4*a^2*b^2 + 6*a*b^3 + b^4)*cosh(d*x + c)^3 + (9*a^4 - 24*a^3*b + 18*a^2*b^2 - 16*a*b^3 - 3*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(3*a^4 - 6*a^3*b - 4*a^2*b^2 + 6*a*b^3 + b^4)*cosh(d*x + c)^2 + 4*(7*(3*a^4 - 10*a^2*b^2 - 8*a*b^3 - b^4)*cosh(d*x + c)^6 + 15*(3*a^4 - 6*a^3*b - 4*a^2*b^2 + 6*a*b^3 + b^4)*cosh(d*x + c)^4 + 3*a^4 - 6*a^3*b - 4*a^2*b^2 + 6*a*b^3 + b^4 + 3*(9*a^4 - 24*a^3*b + 18*a^2*b^2 - 16*a*b^3 - 3*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((3*a^4 - 10*a^2*b^2 - 8*a*b^3 - b^4)*cosh(d*x + c)^7 + 3*(3*a^4 - 6*a^3*b - 4*a^2*b^2 + 6*a*b^3 + b^4)*cosh(d*x + c)^5 + (9*a^4 - 24*a^3*b + 18*a^2*b^2 - 16*a*b^3 - 3*b^4)*cosh(d*x + c)^3 + (3*a^4 - 6*a^3*b - 4*a^2*b^2 + 6*a*b^3 + b^4)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-a*b)*log(((a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 + 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 + 2*(a^2 - b^2)*cosh(d*x + c)^2 + 2*(3*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + a^2 - b^2)*sinh(d*x + c)^2 + a^2 - 6*a*b + b^2 + 4*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 + (a^2 - 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 + a - b)*sqrt(-a*b))/((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)) + 8*(16*(a^4*b + 2*a^3*b^2 + a^2*b^3)*d*x*cosh(d*x + c)^7 + 3*(5*a^4*b - 5*a^3*b^2 - 9*a^2*b^3 + a*b^4 + 16*(a^4*b - a^2*b^3)*d*x)*cosh(d*x + c)^5 + 2*(15*a^4*b - 13*a^3*b^2 + 17*a^2*b^3 - 3*a*b^4 + 8*(3*a^4*b - 2*a^3*b^2 + 3*a^2*b^3)*d*x)*cosh(d*x + c)^3 + (15*a^4*b + a^3*b^2 - 11*a^2*b^3 + 3*a*b^4 + 16*(a^4*b - a^2*b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c))/((a^7*b + 5*a^6*b^2 + 10*a^5*b^3 + 10*a^4*b^4 + 5*a^3*b^5 + a^2*b^6)*d*cosh(d*x + c)^8 + 8*(a^7*b + 5*a^6*b^2 + 10*a^5*b^3 + 10*a^4*b^4 + 5*a^3*b^5 + a^2*b^6)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^7*b + 5*a^6*b^2 + 10*a^5*b^3 + 10*a^4*b^4 + 5*a^3*b^5 + a^2*b^6)*d*sinh(d*x + c)^8 + 4*(a^7*b + 3*a^6*b^2 + 2*a^5*b^3 - 2*a^4*b^4 - 3*a^3*b^5 - a^2*b^6)*d*cosh(d*x + c)^6 + 4*(7*(a^7*b + 5*a^6*b^2 + 10*a^5*b^3 + 10*a^4*b^4 + 5*a^3*b^5 + a^2*b^6)*d*cosh(d*x + c)^2 + (a^7*b + 3*a^6*b^2 + 2*a^5*b^3 - 2*a^4*b^4 - 3*a^3*b^5 - a^2*b^6)*d)*sinh(d*x + c)^6 + 2*(3*a^7*b + 7*a^6*b^2 + 6*a^5*b^3 + 6*a^4*b^4 + 7*a^3*b^5 + 3*a^2*b^6)*d*cosh(d*x + c)^4 + 8*(7*(a^7*b + 5*a^6*b^2 + 10*a^5*b^3 + 10*a^4*b^4 + 5*a^3*b^5 + a^2*b^6)*d*cosh(d*x + c)^3 + 3*(a^7*b + 3*a^6*b^2 + 2*a^5*b^3 - 2*a^4*b^4 - 3*a^3*b^5 - a^2*b^6)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^7*b + 5*a^6*b^2 + 10*a^5*b^3 + 10*a^4*b^4 + 5*a^3*b^5 + a^2*b^6)*d*cosh(d*x + c)^4 + 30*(a^7*b + 3*a^6*b^2 + 2*a^5*b^3 - 2*a^4*b^4 - 3*a^3*b^5 - a^2*b^6)*d*cosh(d*x + c)^2 + (3*a^7*b + 7*a^6*b^2 + 6*a^5*b^3 + 6*a^4*b^4 + 7*a^3*b^5 + 3*a^2*b^6)*d)*sinh(d*x + c)^4 + 4*(a^7*b + 3*a^6*b^2 + 2*a^5*b^3 - 2*a^4*b^4 - 3*a^3*b^5 - a^2*b^6)*d*cosh(d*x + c)^2 + 8*(7*(a^7*b + 5*a^6*b^2 + 10*a^5*b^3 + 10*a^4*b^4 + 5*a^3*b^5 + a^2*b^6)*d*cosh(d*x + c)^5 + 10*(a^7*b + 3*a^6*b^2 + 2*a^5*b^3 - 2*a^4*b^4 - 3*a^3*b^5 - a^2*b^6)*d*cosh(d*x + c)^3 + (3*a^7*b + 7*a^6*b^2 + 6*a^5*b^3 + 6*a^4*b^4 + 7*a^3*b^5 + 3*a^2*b^6)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^7*b + 5*a^6*b^2 + 10*a^5*b^3 + 10*a^4*b^4 + 5*a^3*b^5 + a^2*b^6)*d*cosh(d*x + c)^6 + 15*(a^7*b + 3*a^6*b^2 + 2*a^5*b^3 - 2*a^4*b^4 - 3*a^3*b^5 - a^2*b^6)*d*cosh(d*x + c)^4 + 3*(3*a^7*b + 7*a^6*b^2 + 6*a^5*b^3 + 6*a^4*b^4 + 7*a^3*b^5 + 3*a^2*b^6)*d*cosh(d*x + c)^2 + (a^7*b + 3*a^6*b^2 + 2*a^5*b^3 - 2*a^4*b^4 - 3*a^3*b^5 - a^2*b^6)*d)*sinh(d*x + c)^2 + (a^7*b + 5*a^6*b^2 + 10*a^5*b^3 + 10*a^4*b^4 + 5*a^3*b^5 + a^2*b^6)*d + 8*((a^7*b + 5*a^6*b^2 + 10*a^5*b^3 + 10*a^4*b^4 + 5*a^3*b^5 + a^2*b^6)*d*cosh(d*x + c)^7 + 3*(a^7*b + 3*a^6*b^2 + 2*a^5*b^3 - 2*a^4*b^4 - 3*a^3*b^5 - a^2*b^6)*d*cosh(d*x + c)^5 + (3*a^7*b + 7*a^6*b^2 + 6*a^5*b^3 + 6*a^4*b^4 + 7*a^3*b^5 + 3*a^2*b^6)*d*cosh(d*x + c)^3 + (a^7*b + 3*a^6*b^2 + 2*a^5*b^3 - 2*a^4*b^4 - 3*a^3*b^5 - a^2*b^6)*d*cosh(d*x + c))*sinh(d*x + c)), 1/8*(8*(a^4*b + 2*a^3*b^2 + a^2*b^3)*d*x*cosh(d*x + c)^8 + 64*(a^4*b + 2*a^3*b^2 + a^2*b^3)*d*x*cosh(d*x + c)*sinh(d*x + c)^7 + 8*(a^4*b + 2*a^3*b^2 + a^2*b^3)*d*x*sinh(d*x + c)^8 + 2*(5*a^4*b - 5*a^3*b^2 - 9*a^2*b^3 + a*b^4 + 16*(a^4*b - a^2*b^3)*d*x)*cosh(d*x + c)^6 + 2*(5*a^4*b - 5*a^3*b^2 - 9*a^2*b^3 + a*b^4 + 112*(a^4*b + 2*a^3*b^2 + a^2*b^3)*d*x*cosh(d*x + c)^2 + 16*(a^4*b - a^2*b^3)*d*x)*sinh(d*x + c)^6 + 4*(112*(a^4*b + 2*a^3*b^2 + a^2*b^3)*d*x*cosh(d*x + c)^3 + 3*(5*a^4*b - 5*a^3*b^2 - 9*a^2*b^3 + a*b^4 + 16*(a^4*b - a^2*b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c)^5 + 10*a^4*b + 18*a^3*b^2 + 6*a^2*b^3 - 2*a*b^4 + 2*(15*a^4*b - 13*a^3*b^2 + 17*a^2*b^3 - 3*a*b^4 + 8*(3*a^4*b - 2*a^3*b^2 + 3*a^2*b^3)*d*x)*cosh(d*x + c)^4 + 2*(280*(a^4*b + 2*a^3*b^2 + a^2*b^3)*d*x*cosh(d*x + c)^4 + 15*a^4*b - 13*a^3*b^2 + 17*a^2*b^3 - 3*a*b^4 + 8*(3*a^4*b - 2*a^3*b^2 + 3*a^2*b^3)*d*x + 15*(5*a^4*b - 5*a^3*b^2 - 9*a^2*b^3 + a*b^4 + 16*(a^4*b - a^2*b^3)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(56*(a^4*b + 2*a^3*b^2 + a^2*b^3)*d*x*cosh(d*x + c)^5 + 5*(5*a^4*b - 5*a^3*b^2 - 9*a^2*b^3 + a*b^4 + 16*(a^4*b - a^2*b^3)*d*x)*cosh(d*x + c)^3 + (15*a^4*b - 13*a^3*b^2 + 17*a^2*b^3 - 3*a*b^4 + 8*(3*a^4*b - 2*a^3*b^2 + 3*a^2*b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c)^3 + 8*(a^4*b + 2*a^3*b^2 + a^2*b^3)*d*x + 2*(15*a^4*b + a^3*b^2 - 11*a^2*b^3 + 3*a*b^4 + 16*(a^4*b - a^2*b^3)*d*x)*cosh(d*x + c)^2 + 2*(112*(a^4*b + 2*a^3*b^2 + a^2*b^3)*d*x*cosh(d*x + c)^6 + 15*a^4*b + a^3*b^2 - 11*a^2*b^3 + 3*a*b^4 + 15*(5*a^4*b - 5*a^3*b^2 - 9*a^2*b^3 + a*b^4 + 16*(a^4*b - a^2*b^3)*d*x)*cosh(d*x + c)^4 + 16*(a^4*b - a^2*b^3)*d*x + 6*(15*a^4*b - 13*a^3*b^2 + 17*a^2*b^3 - 3*a*b^4 + 8*(3*a^4*b - 2*a^3*b^2 + 3*a^2*b^3)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - ((3*a^4 - 10*a^2*b^2 - 8*a*b^3 - b^4)*cosh(d*x + c)^8 + 8*(3*a^4 - 10*a^2*b^2 - 8*a*b^3 - b^4)*cosh(d*x + c)*sinh(d*x + c)^7 + (3*a^4 - 10*a^2*b^2 - 8*a*b^3 - b^4)*sinh(d*x + c)^8 + 4*(3*a^4 - 6*a^3*b - 4*a^2*b^2 + 6*a*b^3 + b^4)*cosh(d*x + c)^6 + 4*(3*a^4 - 6*a^3*b - 4*a^2*b^2 + 6*a*b^3 + b^4 + 7*(3*a^4 - 10*a^2*b^2 - 8*a*b^3 - b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(3*a^4 - 10*a^2*b^2 - 8*a*b^3 - b^4)*cosh(d*x + c)^3 + 3*(3*a^4 - 6*a^3*b - 4*a^2*b^2 + 6*a*b^3 + b^4)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(9*a^4 - 24*a^3*b + 18*a^2*b^2 - 16*a*b^3 - 3*b^4)*cosh(d*x + c)^4 + 2*(35*(3*a^4 - 10*a^2*b^2 - 8*a*b^3 - b^4)*cosh(d*x + c)^4 + 9*a^4 - 24*a^3*b + 18*a^2*b^2 - 16*a*b^3 - 3*b^4 + 30*(3*a^4 - 6*a^3*b - 4*a^2*b^2 + 6*a*b^3 + b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 3*a^4 - 10*a^2*b^2 - 8*a*b^3 - b^4 + 8*(7*(3*a^4 - 10*a^2*b^2 - 8*a*b^3 - b^4)*cosh(d*x + c)^5 + 10*(3*a^4 - 6*a^3*b - 4*a^2*b^2 + 6*a*b^3 + b^4)*cosh(d*x + c)^3 + (9*a^4 - 24*a^3*b + 18*a^2*b^2 - 16*a*b^3 - 3*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(3*a^4 - 6*a^3*b - 4*a^2*b^2 + 6*a*b^3 + b^4)*cosh(d*x + c)^2 + 4*(7*(3*a^4 - 10*a^2*b^2 - 8*a*b^3 - b^4)*cosh(d*x + c)^6 + 15*(3*a^4 - 6*a^3*b - 4*a^2*b^2 + 6*a*b^3 + b^4)*cosh(d*x + c)^4 + 3*a^4 - 6*a^3*b - 4*a^2*b^2 + 6*a*b^3 + b^4 + 3*(9*a^4 - 24*a^3*b + 18*a^2*b^2 - 16*a*b^3 - 3*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((3*a^4 - 10*a^2*b^2 - 8*a*b^3 - b^4)*cosh(d*x + c)^7 + 3*(3*a^4 - 6*a^3*b - 4*a^2*b^2 + 6*a*b^3 + b^4)*cosh(d*x + c)^5 + (9*a^4 - 24*a^3*b + 18*a^2*b^2 - 16*a*b^3 - 3*b^4)*cosh(d*x + c)^3 + (3*a^4 - 6*a^3*b - 4*a^2*b^2 + 6*a*b^3 + b^4)*cosh(d*x + c))*sinh(d*x + c))*sqrt(a*b)*arctan(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 + a - b)*sqrt(a*b)/(a*b)) + 4*(16*(a^4*b + 2*a^3*b^2 + a^2*b^3)*d*x*cosh(d*x + c)^7 + 3*(5*a^4*b - 5*a^3*b^2 - 9*a^2*b^3 + a*b^4 + 16*(a^4*b - a^2*b^3)*d*x)*cosh(d*x + c)^5 + 2*(15*a^4*b - 13*a^3*b^2 + 17*a^2*b^3 - 3*a*b^4 + 8*(3*a^4*b - 2*a^3*b^2 + 3*a^2*b^3)*d*x)*cosh(d*x + c)^3 + (15*a^4*b + a^3*b^2 - 11*a^2*b^3 + 3*a*b^4 + 16*(a^4*b - a^2*b^3)*d*x)*cosh(d*x + c))*sinh(d*x + c))/((a^7*b + 5*a^6*b^2 + 10*a^5*b^3 + 10*a^4*b^4 + 5*a^3*b^5 + a^2*b^6)*d*cosh(d*x + c)^8 + 8*(a^7*b + 5*a^6*b^2 + 10*a^5*b^3 + 10*a^4*b^4 + 5*a^3*b^5 + a^2*b^6)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^7*b + 5*a^6*b^2 + 10*a^5*b^3 + 10*a^4*b^4 + 5*a^3*b^5 + a^2*b^6)*d*sinh(d*x + c)^8 + 4*(a^7*b + 3*a^6*b^2 + 2*a^5*b^3 - 2*a^4*b^4 - 3*a^3*b^5 - a^2*b^6)*d*cosh(d*x + c)^6 + 4*(7*(a^7*b + 5*a^6*b^2 + 10*a^5*b^3 + 10*a^4*b^4 + 5*a^3*b^5 + a^2*b^6)*d*cosh(d*x + c)^2 + (a^7*b + 3*a^6*b^2 + 2*a^5*b^3 - 2*a^4*b^4 - 3*a^3*b^5 - a^2*b^6)*d)*sinh(d*x + c)^6 + 2*(3*a^7*b + 7*a^6*b^2 + 6*a^5*b^3 + 6*a^4*b^4 + 7*a^3*b^5 + 3*a^2*b^6)*d*cosh(d*x + c)^4 + 8*(7*(a^7*b + 5*a^6*b^2 + 10*a^5*b^3 + 10*a^4*b^4 + 5*a^3*b^5 + a^2*b^6)*d*cosh(d*x + c)^3 + 3*(a^7*b + 3*a^6*b^2 + 2*a^5*b^3 - 2*a^4*b^4 - 3*a^3*b^5 - a^2*b^6)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^7*b + 5*a^6*b^2 + 10*a^5*b^3 + 10*a^4*b^4 + 5*a^3*b^5 + a^2*b^6)*d*cosh(d*x + c)^4 + 30*(a^7*b + 3*a^6*b^2 + 2*a^5*b^3 - 2*a^4*b^4 - 3*a^3*b^5 - a^2*b^6)*d*cosh(d*x + c)^2 + (3*a^7*b + 7*a^6*b^2 + 6*a^5*b^3 + 6*a^4*b^4 + 7*a^3*b^5 + 3*a^2*b^6)*d)*sinh(d*x + c)^4 + 4*(a^7*b + 3*a^6*b^2 + 2*a^5*b^3 - 2*a^4*b^4 - 3*a^3*b^5 - a^2*b^6)*d*cosh(d*x + c)^2 + 8*(7*(a^7*b + 5*a^6*b^2 + 10*a^5*b^3 + 10*a^4*b^4 + 5*a^3*b^5 + a^2*b^6)*d*cosh(d*x + c)^5 + 10*(a^7*b + 3*a^6*b^2 + 2*a^5*b^3 - 2*a^4*b^4 - 3*a^3*b^5 - a^2*b^6)*d*cosh(d*x + c)^3 + (3*a^7*b + 7*a^6*b^2 + 6*a^5*b^3 + 6*a^4*b^4 + 7*a^3*b^5 + 3*a^2*b^6)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^7*b + 5*a^6*b^2 + 10*a^5*b^3 + 10*a^4*b^4 + 5*a^3*b^5 + a^2*b^6)*d*cosh(d*x + c)^6 + 15*(a^7*b + 3*a^6*b^2 + 2*a^5*b^3 - 2*a^4*b^4 - 3*a^3*b^5 - a^2*b^6)*d*cosh(d*x + c)^4 + 3*(3*a^7*b + 7*a^6*b^2 + 6*a^5*b^3 + 6*a^4*b^4 + 7*a^3*b^5 + 3*a^2*b^6)*d*cosh(d*x + c)^2 + (a^7*b + 3*a^6*b^2 + 2*a^5*b^3 - 2*a^4*b^4 - 3*a^3*b^5 - a^2*b^6)*d)*sinh(d*x + c)^2 + (a^7*b + 5*a^6*b^2 + 10*a^5*b^3 + 10*a^4*b^4 + 5*a^3*b^5 + a^2*b^6)*d + 8*((a^7*b + 5*a^6*b^2 + 10*a^5*b^3 + 10*a^4*b^4 + 5*a^3*b^5 + a^2*b^6)*d*cosh(d*x + c)^7 + 3*(a^7*b + 3*a^6*b^2 + 2*a^5*b^3 - 2*a^4*b^4 - 3*a^3*b^5 - a^2*b^6)*d*cosh(d*x + c)^5 + (3*a^7*b + 7*a^6*b^2 + 6*a^5*b^3 + 6*a^4*b^4 + 7*a^3*b^5 + 3*a^2*b^6)*d*cosh(d*x + c)^3 + (a^7*b + 3*a^6*b^2 + 2*a^5*b^3 - 2*a^4*b^4 - 3*a^3*b^5 - a^2*b^6)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
195,1,2554,0,0.466979," ","integrate(tanh(d*x+c)/(a+b*tanh(d*x+c)^2)^3,x, algorithm=""fricas"")","-\frac{2 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x \cosh\left(d x + c\right)^{8} + 16 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + 2 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x \sinh\left(d x + c\right)^{8} + 8 \, {\left({\left(a^{2} - b^{2}\right)} d x + a b + b^{2}\right)} \cosh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x \cosh\left(d x + c\right)^{2} + {\left(a^{2} - b^{2}\right)} d x + a b + b^{2}\right)} \sinh\left(d x + c\right)^{6} + 16 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x \cosh\left(d x + c\right)^{3} + 3 \, {\left({\left(a^{2} - b^{2}\right)} d x + a b + b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 4 \, {\left({\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} d x + 4 \, a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(35 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x \cosh\left(d x + c\right)^{4} + {\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} d x + 30 \, {\left({\left(a^{2} - b^{2}\right)} d x + a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, a b - 2 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 16 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x \cosh\left(d x + c\right)^{5} + 10 \, {\left({\left(a^{2} - b^{2}\right)} d x + a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left({\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} d x + 4 \, a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x + 8 \, {\left({\left(a^{2} - b^{2}\right)} d x + a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} d x \cosh\left(d x + c\right)^{6} + 15 \, {\left({\left(a^{2} - b^{2}\right)} d x + a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + {\left(a^{2} - b^{2}\right)} d x + 3 \, {\left({\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} d x + 4 \, a b - 2 \, 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} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{4} + 30 \, {\left(a^{2} - 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)^{4} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{2} - 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)^{3} + 4 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{2} + a^{2} + 2 \, a b + b^{2} + 8 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\frac{2 \, {\left({\left(a + b\right)} \cosh\left(d x + c\right)^{2} + {\left(a + b\right)} \sinh\left(d x + c\right)^{2} + a - b\right)}}{\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}}\right) + 16 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} d x \cosh\left(d x + c\right)^{7} + 3 \, {\left({\left(a^{2} - b^{2}\right)} d x + a b + b^{2}\right)} \cosh\left(d x + c\right)^{5} + {\left({\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} d x + 4 \, a b - 2 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left({\left(a^{2} - b^{2}\right)} d x + a b + b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{2 \, {\left({\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(3 \, a^{5} + 7 \, a^{4} b + 6 \, a^{3} b^{2} + 6 \, a^{2} b^{3} + 7 \, a b^{4} + 3 \, b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 30 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{5} + 7 \, a^{4} b + 6 \, a^{3} b^{2} + 6 \, a^{2} b^{3} + 7 \, a b^{4} + 3 \, b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{5} + 7 \, a^{4} b + 6 \, a^{3} b^{2} + 6 \, a^{2} b^{3} + 7 \, a b^{4} + 3 \, b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{5} + 7 \, a^{4} b + 6 \, a^{3} b^{2} + 6 \, a^{2} b^{3} + 7 \, a b^{4} + 3 \, b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d + 8 \, {\left({\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} d \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} d \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{5} + 7 \, a^{4} b + 6 \, a^{3} b^{2} + 6 \, a^{2} b^{3} + 7 \, a b^{4} + 3 \, b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"-1/2*(2*(a^2 + 2*a*b + b^2)*d*x*cosh(d*x + c)^8 + 16*(a^2 + 2*a*b + b^2)*d*x*cosh(d*x + c)*sinh(d*x + c)^7 + 2*(a^2 + 2*a*b + b^2)*d*x*sinh(d*x + c)^8 + 8*((a^2 - b^2)*d*x + a*b + b^2)*cosh(d*x + c)^6 + 8*(7*(a^2 + 2*a*b + b^2)*d*x*cosh(d*x + c)^2 + (a^2 - b^2)*d*x + a*b + b^2)*sinh(d*x + c)^6 + 16*(7*(a^2 + 2*a*b + b^2)*d*x*cosh(d*x + c)^3 + 3*((a^2 - b^2)*d*x + a*b + b^2)*cosh(d*x + c))*sinh(d*x + c)^5 + 4*((3*a^2 - 2*a*b + 3*b^2)*d*x + 4*a*b - 2*b^2)*cosh(d*x + c)^4 + 4*(35*(a^2 + 2*a*b + b^2)*d*x*cosh(d*x + c)^4 + (3*a^2 - 2*a*b + 3*b^2)*d*x + 30*((a^2 - b^2)*d*x + a*b + b^2)*cosh(d*x + c)^2 + 4*a*b - 2*b^2)*sinh(d*x + c)^4 + 16*(7*(a^2 + 2*a*b + b^2)*d*x*cosh(d*x + c)^5 + 10*((a^2 - b^2)*d*x + a*b + b^2)*cosh(d*x + c)^3 + ((3*a^2 - 2*a*b + 3*b^2)*d*x + 4*a*b - 2*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 2*(a^2 + 2*a*b + b^2)*d*x + 8*((a^2 - b^2)*d*x + a*b + b^2)*cosh(d*x + c)^2 + 8*(7*(a^2 + 2*a*b + b^2)*d*x*cosh(d*x + c)^6 + 15*((a^2 - b^2)*d*x + a*b + b^2)*cosh(d*x + c)^4 + (a^2 - b^2)*d*x + 3*((3*a^2 - 2*a*b + 3*b^2)*d*x + 4*a*b - 2*b^2)*cosh(d*x + c)^2 + a*b + b^2)*sinh(d*x + c)^2 - ((a^2 + 2*a*b + b^2)*cosh(d*x + c)^8 + 8*(a^2 + 2*a*b + b^2)*cosh(d*x + c)*sinh(d*x + c)^7 + (a^2 + 2*a*b + b^2)*sinh(d*x + c)^8 + 4*(a^2 - b^2)*cosh(d*x + c)^6 + 4*(7*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + a^2 - b^2)*sinh(d*x + c)^6 + 8*(7*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 + 3*(a^2 - b^2)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(3*a^2 - 2*a*b + 3*b^2)*cosh(d*x + c)^4 + 2*(35*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 + 30*(a^2 - b^2)*cosh(d*x + c)^2 + 3*a^2 - 2*a*b + 3*b^2)*sinh(d*x + c)^4 + 8*(7*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^5 + 10*(a^2 - b^2)*cosh(d*x + c)^3 + (3*a^2 - 2*a*b + 3*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(a^2 - b^2)*cosh(d*x + c)^2 + 4*(7*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^6 + 15*(a^2 - b^2)*cosh(d*x + c)^4 + 3*(3*a^2 - 2*a*b + 3*b^2)*cosh(d*x + c)^2 + a^2 - b^2)*sinh(d*x + c)^2 + a^2 + 2*a*b + b^2 + 8*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^7 + 3*(a^2 - b^2)*cosh(d*x + c)^5 + (3*a^2 - 2*a*b + 3*b^2)*cosh(d*x + c)^3 + (a^2 - b^2)*cosh(d*x + c))*sinh(d*x + c))*log(2*((a + b)*cosh(d*x + c)^2 + (a + b)*sinh(d*x + c)^2 + a - b)/(cosh(d*x + c)^2 - 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)) + 16*((a^2 + 2*a*b + b^2)*d*x*cosh(d*x + c)^7 + 3*((a^2 - b^2)*d*x + a*b + b^2)*cosh(d*x + c)^5 + ((3*a^2 - 2*a*b + 3*b^2)*d*x + 4*a*b - 2*b^2)*cosh(d*x + c)^3 + ((a^2 - b^2)*d*x + a*b + b^2)*cosh(d*x + c))*sinh(d*x + c))/((a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*cosh(d*x + c)^8 + 8*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*sinh(d*x + c)^8 + 4*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*d*cosh(d*x + c)^6 + 4*(7*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*cosh(d*x + c)^2 + (a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*d)*sinh(d*x + c)^6 + 2*(3*a^5 + 7*a^4*b + 6*a^3*b^2 + 6*a^2*b^3 + 7*a*b^4 + 3*b^5)*d*cosh(d*x + c)^4 + 8*(7*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*cosh(d*x + c)^3 + 3*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*cosh(d*x + c)^4 + 30*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*d*cosh(d*x + c)^2 + (3*a^5 + 7*a^4*b + 6*a^3*b^2 + 6*a^2*b^3 + 7*a*b^4 + 3*b^5)*d)*sinh(d*x + c)^4 + 4*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*d*cosh(d*x + c)^2 + 8*(7*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*cosh(d*x + c)^5 + 10*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*d*cosh(d*x + c)^3 + (3*a^5 + 7*a^4*b + 6*a^3*b^2 + 6*a^2*b^3 + 7*a*b^4 + 3*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*cosh(d*x + c)^6 + 15*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*d*cosh(d*x + c)^4 + 3*(3*a^5 + 7*a^4*b + 6*a^3*b^2 + 6*a^2*b^3 + 7*a*b^4 + 3*b^5)*d*cosh(d*x + c)^2 + (a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*d)*sinh(d*x + c)^2 + (a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d + 8*((a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*d*cosh(d*x + c)^7 + 3*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*d*cosh(d*x + c)^5 + (3*a^5 + 7*a^4*b + 6*a^3*b^2 + 6*a^2*b^3 + 7*a*b^4 + 3*b^5)*d*cosh(d*x + c)^3 + (a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*d*cosh(d*x + c))*sinh(d*x + c))","B",0
196,1,7496,0,0.560480," ","integrate(1/(a+b*tanh(d*x+c)^2)^3,x, algorithm=""fricas"")","\left[\frac{16 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} d x \cosh\left(d x + c\right)^{8} + 128 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + 16 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} d x \sinh\left(d x + c\right)^{8} - 4 \, {\left(9 \, a^{3} b - a^{2} b^{2} - 13 \, a b^{3} - 3 \, b^{4} - 16 \, {\left(a^{4} - a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(112 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} d x \cosh\left(d x + c\right)^{2} - 9 \, a^{3} b + a^{2} b^{2} + 13 \, a b^{3} + 3 \, b^{4} + 16 \, {\left(a^{4} - a^{2} b^{2}\right)} d x\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(112 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} d x \cosh\left(d x + c\right)^{3} - 3 \, {\left(9 \, a^{3} b - a^{2} b^{2} - 13 \, a b^{3} - 3 \, b^{4} - 16 \, {\left(a^{4} - a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 4 \, {\left(27 \, a^{3} b - 9 \, a^{2} b^{2} + 21 \, a b^{3} + 9 \, b^{4} - 8 \, {\left(3 \, a^{4} - 2 \, a^{3} b + 3 \, a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(280 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} d x \cosh\left(d x + c\right)^{4} - 27 \, a^{3} b + 9 \, a^{2} b^{2} - 21 \, a b^{3} - 9 \, b^{4} + 8 \, {\left(3 \, a^{4} - 2 \, a^{3} b + 3 \, a^{2} b^{2}\right)} d x - 15 \, {\left(9 \, a^{3} b - a^{2} b^{2} - 13 \, a b^{3} - 3 \, b^{4} - 16 \, {\left(a^{4} - a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} - 36 \, a^{3} b - 84 \, a^{2} b^{2} - 60 \, a b^{3} - 12 \, b^{4} + 16 \, {\left(56 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} d x \cosh\left(d x + c\right)^{5} - 5 \, {\left(9 \, a^{3} b - a^{2} b^{2} - 13 \, a b^{3} - 3 \, b^{4} - 16 \, {\left(a^{4} - a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - {\left(27 \, a^{3} b - 9 \, a^{2} b^{2} + 21 \, a b^{3} + 9 \, b^{4} - 8 \, {\left(3 \, a^{4} - 2 \, 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} + 16 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} d x - 4 \, {\left(27 \, a^{3} b + 13 \, a^{2} b^{2} - 23 \, a b^{3} - 9 \, b^{4} - 16 \, {\left(a^{4} - a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(112 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} d x \cosh\left(d x + c\right)^{6} - 15 \, {\left(9 \, a^{3} b - a^{2} b^{2} - 13 \, a b^{3} - 3 \, b^{4} - 16 \, {\left(a^{4} - a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{4} - 27 \, a^{3} b - 13 \, a^{2} b^{2} + 23 \, a b^{3} + 9 \, b^{4} + 16 \, {\left(a^{4} - a^{2} b^{2}\right)} d x - 6 \, {\left(27 \, a^{3} b - 9 \, a^{2} b^{2} + 21 \, a b^{3} + 9 \, b^{4} - 8 \, {\left(3 \, a^{4} - 2 \, 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(15 \, a^{4} + 40 \, a^{3} b + 38 \, a^{2} b^{2} + 16 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(15 \, a^{4} + 40 \, a^{3} b + 38 \, a^{2} b^{2} + 16 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(15 \, a^{4} + 40 \, a^{3} b + 38 \, a^{2} b^{2} + 16 \, a b^{3} + 3 \, b^{4}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(15 \, a^{4} + 10 \, a^{3} b - 12 \, a^{2} b^{2} - 10 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(15 \, a^{4} + 10 \, a^{3} b - 12 \, a^{2} b^{2} - 10 \, a b^{3} - 3 \, b^{4} + 7 \, {\left(15 \, a^{4} + 40 \, a^{3} b + 38 \, 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)^{6} + 8 \, {\left(7 \, {\left(15 \, a^{4} + 40 \, a^{3} b + 38 \, a^{2} b^{2} + 16 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(15 \, a^{4} + 10 \, a^{3} b - 12 \, 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(45 \, a^{4} + 34 \, a^{2} b^{2} + 24 \, a b^{3} + 9 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(15 \, a^{4} + 40 \, a^{3} b + 38 \, a^{2} b^{2} + 16 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 45 \, a^{4} + 34 \, a^{2} b^{2} + 24 \, a b^{3} + 9 \, b^{4} + 30 \, {\left(15 \, a^{4} + 10 \, a^{3} b - 12 \, 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} + 15 \, a^{4} + 40 \, a^{3} b + 38 \, a^{2} b^{2} + 16 \, a b^{3} + 3 \, b^{4} + 8 \, {\left(7 \, {\left(15 \, a^{4} + 40 \, a^{3} b + 38 \, a^{2} b^{2} + 16 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(15 \, a^{4} + 10 \, a^{3} b - 12 \, a^{2} b^{2} - 10 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(45 \, a^{4} + 34 \, a^{2} b^{2} + 24 \, a b^{3} + 9 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(15 \, a^{4} + 10 \, a^{3} b - 12 \, a^{2} b^{2} - 10 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(15 \, a^{4} + 40 \, a^{3} b + 38 \, a^{2} b^{2} + 16 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(15 \, a^{4} + 10 \, a^{3} b - 12 \, a^{2} b^{2} - 10 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 15 \, a^{4} + 10 \, a^{3} b - 12 \, a^{2} b^{2} - 10 \, a b^{3} - 3 \, b^{4} + 3 \, {\left(45 \, a^{4} + 34 \, a^{2} b^{2} + 24 \, 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^{4} + 40 \, a^{3} b + 38 \, a^{2} b^{2} + 16 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(15 \, a^{4} + 10 \, a^{3} b - 12 \, a^{2} b^{2} - 10 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + {\left(45 \, a^{4} + 34 \, a^{2} b^{2} + 24 \, a b^{3} + 9 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(15 \, a^{4} + 10 \, a^{3} b - 12 \, 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{-\frac{b}{a}} \log\left(\frac{{\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) \sinh\left(d x + c\right)^{3} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{2} + a^{2} - 6 \, a b + b^{2} + 4 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) + 4 \, {\left({\left(a^{2} + a b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} + a b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} + a b\right)} \sinh\left(d x + c\right)^{2} + a^{2} - a b\right)} \sqrt{-\frac{b}{a}}}{{\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) + 8 \, {\left(16 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} d x \cosh\left(d x + c\right)^{7} - 3 \, {\left(9 \, a^{3} b - a^{2} b^{2} - 13 \, a b^{3} - 3 \, b^{4} - 16 \, {\left(a^{4} - a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{5} - 2 \, {\left(27 \, a^{3} b - 9 \, a^{2} b^{2} + 21 \, a b^{3} + 9 \, b^{4} - 8 \, {\left(3 \, a^{4} - 2 \, a^{3} b + 3 \, a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - {\left(27 \, a^{3} b + 13 \, a^{2} b^{2} - 23 \, a b^{3} - 9 \, b^{4} - 16 \, {\left(a^{4} - a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{16 \, {\left({\left(a^{7} + 5 \, a^{6} b + 10 \, a^{5} b^{2} + 10 \, a^{4} b^{3} + 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{7} + 5 \, a^{6} b + 10 \, a^{5} b^{2} + 10 \, a^{4} b^{3} + 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{7} + 5 \, a^{6} b + 10 \, a^{5} b^{2} + 10 \, a^{4} b^{3} + 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2} - 2 \, a^{4} b^{3} - 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{7} + 5 \, a^{6} b + 10 \, a^{5} b^{2} + 10 \, a^{4} b^{3} + 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2} - 2 \, a^{4} b^{3} - 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(3 \, a^{7} + 7 \, a^{6} b + 6 \, a^{5} b^{2} + 6 \, a^{4} b^{3} + 7 \, a^{3} b^{4} + 3 \, a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{7} + 5 \, a^{6} b + 10 \, a^{5} b^{2} + 10 \, a^{4} b^{3} + 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2} - 2 \, a^{4} b^{3} - 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a^{7} + 5 \, a^{6} b + 10 \, a^{5} b^{2} + 10 \, a^{4} b^{3} + 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 30 \, {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2} - 2 \, a^{4} b^{3} - 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{7} + 7 \, a^{6} b + 6 \, a^{5} b^{2} + 6 \, a^{4} b^{3} + 7 \, a^{3} b^{4} + 3 \, a^{2} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2} - 2 \, a^{4} b^{3} - 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a^{7} + 5 \, a^{6} b + 10 \, a^{5} b^{2} + 10 \, a^{4} b^{3} + 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2} - 2 \, a^{4} b^{3} - 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{7} + 7 \, a^{6} b + 6 \, a^{5} b^{2} + 6 \, a^{4} b^{3} + 7 \, a^{3} b^{4} + 3 \, a^{2} b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a^{7} + 5 \, a^{6} b + 10 \, a^{5} b^{2} + 10 \, a^{4} b^{3} + 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2} - 2 \, a^{4} b^{3} - 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{7} + 7 \, a^{6} b + 6 \, a^{5} b^{2} + 6 \, a^{4} b^{3} + 7 \, a^{3} b^{4} + 3 \, a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2} - 2 \, a^{4} b^{3} - 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{7} + 5 \, a^{6} b + 10 \, a^{5} b^{2} + 10 \, a^{4} b^{3} + 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} d + 8 \, {\left({\left(a^{7} + 5 \, a^{6} b + 10 \, a^{5} b^{2} + 10 \, a^{4} b^{3} + 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2} - 2 \, a^{4} b^{3} - 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{7} + 7 \, a^{6} b + 6 \, a^{5} b^{2} + 6 \, a^{4} b^{3} + 7 \, a^{3} b^{4} + 3 \, a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2} - 2 \, a^{4} b^{3} - 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}, \frac{8 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} d x \cosh\left(d x + c\right)^{8} + 64 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + 8 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} d x \sinh\left(d x + c\right)^{8} - 2 \, {\left(9 \, a^{3} b - a^{2} b^{2} - 13 \, a b^{3} - 3 \, b^{4} - 16 \, {\left(a^{4} - a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(112 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} d x \cosh\left(d x + c\right)^{2} - 9 \, a^{3} b + a^{2} b^{2} + 13 \, a b^{3} + 3 \, b^{4} + 16 \, {\left(a^{4} - a^{2} b^{2}\right)} d x\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(112 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} d x \cosh\left(d x + c\right)^{3} - 3 \, {\left(9 \, a^{3} b - a^{2} b^{2} - 13 \, a b^{3} - 3 \, b^{4} - 16 \, {\left(a^{4} - a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 2 \, {\left(27 \, a^{3} b - 9 \, a^{2} b^{2} + 21 \, a b^{3} + 9 \, b^{4} - 8 \, {\left(3 \, a^{4} - 2 \, a^{3} b + 3 \, a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(280 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} d x \cosh\left(d x + c\right)^{4} - 27 \, a^{3} b + 9 \, a^{2} b^{2} - 21 \, a b^{3} - 9 \, b^{4} + 8 \, {\left(3 \, a^{4} - 2 \, a^{3} b + 3 \, a^{2} b^{2}\right)} d x - 15 \, {\left(9 \, a^{3} b - a^{2} b^{2} - 13 \, a b^{3} - 3 \, b^{4} - 16 \, {\left(a^{4} - a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} - 18 \, a^{3} b - 42 \, a^{2} b^{2} - 30 \, a b^{3} - 6 \, b^{4} + 8 \, {\left(56 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} d x \cosh\left(d x + c\right)^{5} - 5 \, {\left(9 \, a^{3} b - a^{2} b^{2} - 13 \, a b^{3} - 3 \, b^{4} - 16 \, {\left(a^{4} - a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - {\left(27 \, a^{3} b - 9 \, a^{2} b^{2} + 21 \, a b^{3} + 9 \, b^{4} - 8 \, {\left(3 \, a^{4} - 2 \, 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} + 8 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} d x - 2 \, {\left(27 \, a^{3} b + 13 \, a^{2} b^{2} - 23 \, a b^{3} - 9 \, b^{4} - 16 \, {\left(a^{4} - a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(112 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} d x \cosh\left(d x + c\right)^{6} - 15 \, {\left(9 \, a^{3} b - a^{2} b^{2} - 13 \, a b^{3} - 3 \, b^{4} - 16 \, {\left(a^{4} - a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{4} - 27 \, a^{3} b - 13 \, a^{2} b^{2} + 23 \, a b^{3} + 9 \, b^{4} + 16 \, {\left(a^{4} - a^{2} b^{2}\right)} d x - 6 \, {\left(27 \, a^{3} b - 9 \, a^{2} b^{2} + 21 \, a b^{3} + 9 \, b^{4} - 8 \, {\left(3 \, a^{4} - 2 \, 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(15 \, a^{4} + 40 \, a^{3} b + 38 \, a^{2} b^{2} + 16 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(15 \, a^{4} + 40 \, a^{3} b + 38 \, a^{2} b^{2} + 16 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(15 \, a^{4} + 40 \, a^{3} b + 38 \, a^{2} b^{2} + 16 \, a b^{3} + 3 \, b^{4}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(15 \, a^{4} + 10 \, a^{3} b - 12 \, a^{2} b^{2} - 10 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(15 \, a^{4} + 10 \, a^{3} b - 12 \, a^{2} b^{2} - 10 \, a b^{3} - 3 \, b^{4} + 7 \, {\left(15 \, a^{4} + 40 \, a^{3} b + 38 \, 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)^{6} + 8 \, {\left(7 \, {\left(15 \, a^{4} + 40 \, a^{3} b + 38 \, a^{2} b^{2} + 16 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(15 \, a^{4} + 10 \, a^{3} b - 12 \, 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(45 \, a^{4} + 34 \, a^{2} b^{2} + 24 \, a b^{3} + 9 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(35 \, {\left(15 \, a^{4} + 40 \, a^{3} b + 38 \, a^{2} b^{2} + 16 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 45 \, a^{4} + 34 \, a^{2} b^{2} + 24 \, a b^{3} + 9 \, b^{4} + 30 \, {\left(15 \, a^{4} + 10 \, a^{3} b - 12 \, 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} + 15 \, a^{4} + 40 \, a^{3} b + 38 \, a^{2} b^{2} + 16 \, a b^{3} + 3 \, b^{4} + 8 \, {\left(7 \, {\left(15 \, a^{4} + 40 \, a^{3} b + 38 \, a^{2} b^{2} + 16 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(15 \, a^{4} + 10 \, a^{3} b - 12 \, a^{2} b^{2} - 10 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(45 \, a^{4} + 34 \, a^{2} b^{2} + 24 \, a b^{3} + 9 \, b^{4}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(15 \, a^{4} + 10 \, a^{3} b - 12 \, a^{2} b^{2} - 10 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(15 \, a^{4} + 40 \, a^{3} b + 38 \, a^{2} b^{2} + 16 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{6} + 15 \, {\left(15 \, a^{4} + 10 \, a^{3} b - 12 \, a^{2} b^{2} - 10 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{4} + 15 \, a^{4} + 10 \, a^{3} b - 12 \, a^{2} b^{2} - 10 \, a b^{3} - 3 \, b^{4} + 3 \, {\left(45 \, a^{4} + 34 \, a^{2} b^{2} + 24 \, 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^{4} + 40 \, a^{3} b + 38 \, a^{2} b^{2} + 16 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(15 \, a^{4} + 10 \, a^{3} b - 12 \, a^{2} b^{2} - 10 \, a b^{3} - 3 \, b^{4}\right)} \cosh\left(d x + c\right)^{5} + {\left(45 \, a^{4} + 34 \, a^{2} b^{2} + 24 \, a b^{3} + 9 \, b^{4}\right)} \cosh\left(d x + c\right)^{3} + {\left(15 \, a^{4} + 10 \, a^{3} b - 12 \, 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{\frac{b}{a}} \arctan\left(\frac{{\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} + a - b\right)} \sqrt{\frac{b}{a}}}{2 \, b}\right) + 4 \, {\left(16 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} d x \cosh\left(d x + c\right)^{7} - 3 \, {\left(9 \, a^{3} b - a^{2} b^{2} - 13 \, a b^{3} - 3 \, b^{4} - 16 \, {\left(a^{4} - a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{5} - 2 \, {\left(27 \, a^{3} b - 9 \, a^{2} b^{2} + 21 \, a b^{3} + 9 \, b^{4} - 8 \, {\left(3 \, a^{4} - 2 \, a^{3} b + 3 \, a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - {\left(27 \, a^{3} b + 13 \, a^{2} b^{2} - 23 \, a b^{3} - 9 \, b^{4} - 16 \, {\left(a^{4} - a^{2} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{8 \, {\left({\left(a^{7} + 5 \, a^{6} b + 10 \, a^{5} b^{2} + 10 \, a^{4} b^{3} + 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{7} + 5 \, a^{6} b + 10 \, a^{5} b^{2} + 10 \, a^{4} b^{3} + 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{7} + 5 \, a^{6} b + 10 \, a^{5} b^{2} + 10 \, a^{4} b^{3} + 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2} - 2 \, a^{4} b^{3} - 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{6} + 4 \, {\left(7 \, {\left(a^{7} + 5 \, a^{6} b + 10 \, a^{5} b^{2} + 10 \, a^{4} b^{3} + 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2} - 2 \, a^{4} b^{3} - 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{6} + 2 \, {\left(3 \, a^{7} + 7 \, a^{6} b + 6 \, a^{5} b^{2} + 6 \, a^{4} b^{3} + 7 \, a^{3} b^{4} + 3 \, a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{7} + 5 \, a^{6} b + 10 \, a^{5} b^{2} + 10 \, a^{4} b^{3} + 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2} - 2 \, a^{4} b^{3} - 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(35 \, {\left(a^{7} + 5 \, a^{6} b + 10 \, a^{5} b^{2} + 10 \, a^{4} b^{3} + 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 30 \, {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2} - 2 \, a^{4} b^{3} - 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{7} + 7 \, a^{6} b + 6 \, a^{5} b^{2} + 6 \, a^{4} b^{3} + 7 \, a^{3} b^{4} + 3 \, a^{2} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2} - 2 \, a^{4} b^{3} - 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(7 \, {\left(a^{7} + 5 \, a^{6} b + 10 \, a^{5} b^{2} + 10 \, a^{4} b^{3} + 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2} - 2 \, a^{4} b^{3} - 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{7} + 7 \, a^{6} b + 6 \, a^{5} b^{2} + 6 \, a^{4} b^{3} + 7 \, a^{3} b^{4} + 3 \, a^{2} b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(7 \, {\left(a^{7} + 5 \, a^{6} b + 10 \, a^{5} b^{2} + 10 \, a^{4} b^{3} + 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2} - 2 \, a^{4} b^{3} - 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{7} + 7 \, a^{6} b + 6 \, a^{5} b^{2} + 6 \, a^{4} b^{3} + 7 \, a^{3} b^{4} + 3 \, a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2} - 2 \, a^{4} b^{3} - 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{7} + 5 \, a^{6} b + 10 \, a^{5} b^{2} + 10 \, a^{4} b^{3} + 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} d + 8 \, {\left({\left(a^{7} + 5 \, a^{6} b + 10 \, a^{5} b^{2} + 10 \, a^{4} b^{3} + 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2} - 2 \, a^{4} b^{3} - 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{7} + 7 \, a^{6} b + 6 \, a^{5} b^{2} + 6 \, a^{4} b^{3} + 7 \, a^{3} b^{4} + 3 \, a^{2} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2} - 2 \, a^{4} b^{3} - 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[1/16*(16*(a^4 + 2*a^3*b + a^2*b^2)*d*x*cosh(d*x + c)^8 + 128*(a^4 + 2*a^3*b + a^2*b^2)*d*x*cosh(d*x + c)*sinh(d*x + c)^7 + 16*(a^4 + 2*a^3*b + a^2*b^2)*d*x*sinh(d*x + c)^8 - 4*(9*a^3*b - a^2*b^2 - 13*a*b^3 - 3*b^4 - 16*(a^4 - a^2*b^2)*d*x)*cosh(d*x + c)^6 + 4*(112*(a^4 + 2*a^3*b + a^2*b^2)*d*x*cosh(d*x + c)^2 - 9*a^3*b + a^2*b^2 + 13*a*b^3 + 3*b^4 + 16*(a^4 - a^2*b^2)*d*x)*sinh(d*x + c)^6 + 8*(112*(a^4 + 2*a^3*b + a^2*b^2)*d*x*cosh(d*x + c)^3 - 3*(9*a^3*b - a^2*b^2 - 13*a*b^3 - 3*b^4 - 16*(a^4 - a^2*b^2)*d*x)*cosh(d*x + c))*sinh(d*x + c)^5 - 4*(27*a^3*b - 9*a^2*b^2 + 21*a*b^3 + 9*b^4 - 8*(3*a^4 - 2*a^3*b + 3*a^2*b^2)*d*x)*cosh(d*x + c)^4 + 4*(280*(a^4 + 2*a^3*b + a^2*b^2)*d*x*cosh(d*x + c)^4 - 27*a^3*b + 9*a^2*b^2 - 21*a*b^3 - 9*b^4 + 8*(3*a^4 - 2*a^3*b + 3*a^2*b^2)*d*x - 15*(9*a^3*b - a^2*b^2 - 13*a*b^3 - 3*b^4 - 16*(a^4 - a^2*b^2)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^4 - 36*a^3*b - 84*a^2*b^2 - 60*a*b^3 - 12*b^4 + 16*(56*(a^4 + 2*a^3*b + a^2*b^2)*d*x*cosh(d*x + c)^5 - 5*(9*a^3*b - a^2*b^2 - 13*a*b^3 - 3*b^4 - 16*(a^4 - a^2*b^2)*d*x)*cosh(d*x + c)^3 - (27*a^3*b - 9*a^2*b^2 + 21*a*b^3 + 9*b^4 - 8*(3*a^4 - 2*a^3*b + 3*a^2*b^2)*d*x)*cosh(d*x + c))*sinh(d*x + c)^3 + 16*(a^4 + 2*a^3*b + a^2*b^2)*d*x - 4*(27*a^3*b + 13*a^2*b^2 - 23*a*b^3 - 9*b^4 - 16*(a^4 - a^2*b^2)*d*x)*cosh(d*x + c)^2 + 4*(112*(a^4 + 2*a^3*b + a^2*b^2)*d*x*cosh(d*x + c)^6 - 15*(9*a^3*b - a^2*b^2 - 13*a*b^3 - 3*b^4 - 16*(a^4 - a^2*b^2)*d*x)*cosh(d*x + c)^4 - 27*a^3*b - 13*a^2*b^2 + 23*a*b^3 + 9*b^4 + 16*(a^4 - a^2*b^2)*d*x - 6*(27*a^3*b - 9*a^2*b^2 + 21*a*b^3 + 9*b^4 - 8*(3*a^4 - 2*a^3*b + 3*a^2*b^2)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((15*a^4 + 40*a^3*b + 38*a^2*b^2 + 16*a*b^3 + 3*b^4)*cosh(d*x + c)^8 + 8*(15*a^4 + 40*a^3*b + 38*a^2*b^2 + 16*a*b^3 + 3*b^4)*cosh(d*x + c)*sinh(d*x + c)^7 + (15*a^4 + 40*a^3*b + 38*a^2*b^2 + 16*a*b^3 + 3*b^4)*sinh(d*x + c)^8 + 4*(15*a^4 + 10*a^3*b - 12*a^2*b^2 - 10*a*b^3 - 3*b^4)*cosh(d*x + c)^6 + 4*(15*a^4 + 10*a^3*b - 12*a^2*b^2 - 10*a*b^3 - 3*b^4 + 7*(15*a^4 + 40*a^3*b + 38*a^2*b^2 + 16*a*b^3 + 3*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(15*a^4 + 40*a^3*b + 38*a^2*b^2 + 16*a*b^3 + 3*b^4)*cosh(d*x + c)^3 + 3*(15*a^4 + 10*a^3*b - 12*a^2*b^2 - 10*a*b^3 - 3*b^4)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(45*a^4 + 34*a^2*b^2 + 24*a*b^3 + 9*b^4)*cosh(d*x + c)^4 + 2*(35*(15*a^4 + 40*a^3*b + 38*a^2*b^2 + 16*a*b^3 + 3*b^4)*cosh(d*x + c)^4 + 45*a^4 + 34*a^2*b^2 + 24*a*b^3 + 9*b^4 + 30*(15*a^4 + 10*a^3*b - 12*a^2*b^2 - 10*a*b^3 - 3*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 15*a^4 + 40*a^3*b + 38*a^2*b^2 + 16*a*b^3 + 3*b^4 + 8*(7*(15*a^4 + 40*a^3*b + 38*a^2*b^2 + 16*a*b^3 + 3*b^4)*cosh(d*x + c)^5 + 10*(15*a^4 + 10*a^3*b - 12*a^2*b^2 - 10*a*b^3 - 3*b^4)*cosh(d*x + c)^3 + (45*a^4 + 34*a^2*b^2 + 24*a*b^3 + 9*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(15*a^4 + 10*a^3*b - 12*a^2*b^2 - 10*a*b^3 - 3*b^4)*cosh(d*x + c)^2 + 4*(7*(15*a^4 + 40*a^3*b + 38*a^2*b^2 + 16*a*b^3 + 3*b^4)*cosh(d*x + c)^6 + 15*(15*a^4 + 10*a^3*b - 12*a^2*b^2 - 10*a*b^3 - 3*b^4)*cosh(d*x + c)^4 + 15*a^4 + 10*a^3*b - 12*a^2*b^2 - 10*a*b^3 - 3*b^4 + 3*(45*a^4 + 34*a^2*b^2 + 24*a*b^3 + 9*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((15*a^4 + 40*a^3*b + 38*a^2*b^2 + 16*a*b^3 + 3*b^4)*cosh(d*x + c)^7 + 3*(15*a^4 + 10*a^3*b - 12*a^2*b^2 - 10*a*b^3 - 3*b^4)*cosh(d*x + c)^5 + (45*a^4 + 34*a^2*b^2 + 24*a*b^3 + 9*b^4)*cosh(d*x + c)^3 + (15*a^4 + 10*a^3*b - 12*a^2*b^2 - 10*a*b^3 - 3*b^4)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-b/a)*log(((a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 + 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 + 2*(a^2 - b^2)*cosh(d*x + c)^2 + 2*(3*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + a^2 - b^2)*sinh(d*x + c)^2 + a^2 - 6*a*b + b^2 + 4*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 + (a^2 - b^2)*cosh(d*x + c))*sinh(d*x + c) + 4*((a^2 + a*b)*cosh(d*x + c)^2 + 2*(a^2 + a*b)*cosh(d*x + c)*sinh(d*x + c) + (a^2 + a*b)*sinh(d*x + c)^2 + a^2 - a*b)*sqrt(-b/a))/((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)) + 8*(16*(a^4 + 2*a^3*b + a^2*b^2)*d*x*cosh(d*x + c)^7 - 3*(9*a^3*b - a^2*b^2 - 13*a*b^3 - 3*b^4 - 16*(a^4 - a^2*b^2)*d*x)*cosh(d*x + c)^5 - 2*(27*a^3*b - 9*a^2*b^2 + 21*a*b^3 + 9*b^4 - 8*(3*a^4 - 2*a^3*b + 3*a^2*b^2)*d*x)*cosh(d*x + c)^3 - (27*a^3*b + 13*a^2*b^2 - 23*a*b^3 - 9*b^4 - 16*(a^4 - a^2*b^2)*d*x)*cosh(d*x + c))*sinh(d*x + c))/((a^7 + 5*a^6*b + 10*a^5*b^2 + 10*a^4*b^3 + 5*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)^8 + 8*(a^7 + 5*a^6*b + 10*a^5*b^2 + 10*a^4*b^3 + 5*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^7 + 5*a^6*b + 10*a^5*b^2 + 10*a^4*b^3 + 5*a^3*b^4 + a^2*b^5)*d*sinh(d*x + c)^8 + 4*(a^7 + 3*a^6*b + 2*a^5*b^2 - 2*a^4*b^3 - 3*a^3*b^4 - a^2*b^5)*d*cosh(d*x + c)^6 + 4*(7*(a^7 + 5*a^6*b + 10*a^5*b^2 + 10*a^4*b^3 + 5*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)^2 + (a^7 + 3*a^6*b + 2*a^5*b^2 - 2*a^4*b^3 - 3*a^3*b^4 - a^2*b^5)*d)*sinh(d*x + c)^6 + 2*(3*a^7 + 7*a^6*b + 6*a^5*b^2 + 6*a^4*b^3 + 7*a^3*b^4 + 3*a^2*b^5)*d*cosh(d*x + c)^4 + 8*(7*(a^7 + 5*a^6*b + 10*a^5*b^2 + 10*a^4*b^3 + 5*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)^3 + 3*(a^7 + 3*a^6*b + 2*a^5*b^2 - 2*a^4*b^3 - 3*a^3*b^4 - a^2*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^7 + 5*a^6*b + 10*a^5*b^2 + 10*a^4*b^3 + 5*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)^4 + 30*(a^7 + 3*a^6*b + 2*a^5*b^2 - 2*a^4*b^3 - 3*a^3*b^4 - a^2*b^5)*d*cosh(d*x + c)^2 + (3*a^7 + 7*a^6*b + 6*a^5*b^2 + 6*a^4*b^3 + 7*a^3*b^4 + 3*a^2*b^5)*d)*sinh(d*x + c)^4 + 4*(a^7 + 3*a^6*b + 2*a^5*b^2 - 2*a^4*b^3 - 3*a^3*b^4 - a^2*b^5)*d*cosh(d*x + c)^2 + 8*(7*(a^7 + 5*a^6*b + 10*a^5*b^2 + 10*a^4*b^3 + 5*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)^5 + 10*(a^7 + 3*a^6*b + 2*a^5*b^2 - 2*a^4*b^3 - 3*a^3*b^4 - a^2*b^5)*d*cosh(d*x + c)^3 + (3*a^7 + 7*a^6*b + 6*a^5*b^2 + 6*a^4*b^3 + 7*a^3*b^4 + 3*a^2*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^7 + 5*a^6*b + 10*a^5*b^2 + 10*a^4*b^3 + 5*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)^6 + 15*(a^7 + 3*a^6*b + 2*a^5*b^2 - 2*a^4*b^3 - 3*a^3*b^4 - a^2*b^5)*d*cosh(d*x + c)^4 + 3*(3*a^7 + 7*a^6*b + 6*a^5*b^2 + 6*a^4*b^3 + 7*a^3*b^4 + 3*a^2*b^5)*d*cosh(d*x + c)^2 + (a^7 + 3*a^6*b + 2*a^5*b^2 - 2*a^4*b^3 - 3*a^3*b^4 - a^2*b^5)*d)*sinh(d*x + c)^2 + (a^7 + 5*a^6*b + 10*a^5*b^2 + 10*a^4*b^3 + 5*a^3*b^4 + a^2*b^5)*d + 8*((a^7 + 5*a^6*b + 10*a^5*b^2 + 10*a^4*b^3 + 5*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)^7 + 3*(a^7 + 3*a^6*b + 2*a^5*b^2 - 2*a^4*b^3 - 3*a^3*b^4 - a^2*b^5)*d*cosh(d*x + c)^5 + (3*a^7 + 7*a^6*b + 6*a^5*b^2 + 6*a^4*b^3 + 7*a^3*b^4 + 3*a^2*b^5)*d*cosh(d*x + c)^3 + (a^7 + 3*a^6*b + 2*a^5*b^2 - 2*a^4*b^3 - 3*a^3*b^4 - a^2*b^5)*d*cosh(d*x + c))*sinh(d*x + c)), 1/8*(8*(a^4 + 2*a^3*b + a^2*b^2)*d*x*cosh(d*x + c)^8 + 64*(a^4 + 2*a^3*b + a^2*b^2)*d*x*cosh(d*x + c)*sinh(d*x + c)^7 + 8*(a^4 + 2*a^3*b + a^2*b^2)*d*x*sinh(d*x + c)^8 - 2*(9*a^3*b - a^2*b^2 - 13*a*b^3 - 3*b^4 - 16*(a^4 - a^2*b^2)*d*x)*cosh(d*x + c)^6 + 2*(112*(a^4 + 2*a^3*b + a^2*b^2)*d*x*cosh(d*x + c)^2 - 9*a^3*b + a^2*b^2 + 13*a*b^3 + 3*b^4 + 16*(a^4 - a^2*b^2)*d*x)*sinh(d*x + c)^6 + 4*(112*(a^4 + 2*a^3*b + a^2*b^2)*d*x*cosh(d*x + c)^3 - 3*(9*a^3*b - a^2*b^2 - 13*a*b^3 - 3*b^4 - 16*(a^4 - a^2*b^2)*d*x)*cosh(d*x + c))*sinh(d*x + c)^5 - 2*(27*a^3*b - 9*a^2*b^2 + 21*a*b^3 + 9*b^4 - 8*(3*a^4 - 2*a^3*b + 3*a^2*b^2)*d*x)*cosh(d*x + c)^4 + 2*(280*(a^4 + 2*a^3*b + a^2*b^2)*d*x*cosh(d*x + c)^4 - 27*a^3*b + 9*a^2*b^2 - 21*a*b^3 - 9*b^4 + 8*(3*a^4 - 2*a^3*b + 3*a^2*b^2)*d*x - 15*(9*a^3*b - a^2*b^2 - 13*a*b^3 - 3*b^4 - 16*(a^4 - a^2*b^2)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^4 - 18*a^3*b - 42*a^2*b^2 - 30*a*b^3 - 6*b^4 + 8*(56*(a^4 + 2*a^3*b + a^2*b^2)*d*x*cosh(d*x + c)^5 - 5*(9*a^3*b - a^2*b^2 - 13*a*b^3 - 3*b^4 - 16*(a^4 - a^2*b^2)*d*x)*cosh(d*x + c)^3 - (27*a^3*b - 9*a^2*b^2 + 21*a*b^3 + 9*b^4 - 8*(3*a^4 - 2*a^3*b + 3*a^2*b^2)*d*x)*cosh(d*x + c))*sinh(d*x + c)^3 + 8*(a^4 + 2*a^3*b + a^2*b^2)*d*x - 2*(27*a^3*b + 13*a^2*b^2 - 23*a*b^3 - 9*b^4 - 16*(a^4 - a^2*b^2)*d*x)*cosh(d*x + c)^2 + 2*(112*(a^4 + 2*a^3*b + a^2*b^2)*d*x*cosh(d*x + c)^6 - 15*(9*a^3*b - a^2*b^2 - 13*a*b^3 - 3*b^4 - 16*(a^4 - a^2*b^2)*d*x)*cosh(d*x + c)^4 - 27*a^3*b - 13*a^2*b^2 + 23*a*b^3 + 9*b^4 + 16*(a^4 - a^2*b^2)*d*x - 6*(27*a^3*b - 9*a^2*b^2 + 21*a*b^3 + 9*b^4 - 8*(3*a^4 - 2*a^3*b + 3*a^2*b^2)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((15*a^4 + 40*a^3*b + 38*a^2*b^2 + 16*a*b^3 + 3*b^4)*cosh(d*x + c)^8 + 8*(15*a^4 + 40*a^3*b + 38*a^2*b^2 + 16*a*b^3 + 3*b^4)*cosh(d*x + c)*sinh(d*x + c)^7 + (15*a^4 + 40*a^3*b + 38*a^2*b^2 + 16*a*b^3 + 3*b^4)*sinh(d*x + c)^8 + 4*(15*a^4 + 10*a^3*b - 12*a^2*b^2 - 10*a*b^3 - 3*b^4)*cosh(d*x + c)^6 + 4*(15*a^4 + 10*a^3*b - 12*a^2*b^2 - 10*a*b^3 - 3*b^4 + 7*(15*a^4 + 40*a^3*b + 38*a^2*b^2 + 16*a*b^3 + 3*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(15*a^4 + 40*a^3*b + 38*a^2*b^2 + 16*a*b^3 + 3*b^4)*cosh(d*x + c)^3 + 3*(15*a^4 + 10*a^3*b - 12*a^2*b^2 - 10*a*b^3 - 3*b^4)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(45*a^4 + 34*a^2*b^2 + 24*a*b^3 + 9*b^4)*cosh(d*x + c)^4 + 2*(35*(15*a^4 + 40*a^3*b + 38*a^2*b^2 + 16*a*b^3 + 3*b^4)*cosh(d*x + c)^4 + 45*a^4 + 34*a^2*b^2 + 24*a*b^3 + 9*b^4 + 30*(15*a^4 + 10*a^3*b - 12*a^2*b^2 - 10*a*b^3 - 3*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 15*a^4 + 40*a^3*b + 38*a^2*b^2 + 16*a*b^3 + 3*b^4 + 8*(7*(15*a^4 + 40*a^3*b + 38*a^2*b^2 + 16*a*b^3 + 3*b^4)*cosh(d*x + c)^5 + 10*(15*a^4 + 10*a^3*b - 12*a^2*b^2 - 10*a*b^3 - 3*b^4)*cosh(d*x + c)^3 + (45*a^4 + 34*a^2*b^2 + 24*a*b^3 + 9*b^4)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(15*a^4 + 10*a^3*b - 12*a^2*b^2 - 10*a*b^3 - 3*b^4)*cosh(d*x + c)^2 + 4*(7*(15*a^4 + 40*a^3*b + 38*a^2*b^2 + 16*a*b^3 + 3*b^4)*cosh(d*x + c)^6 + 15*(15*a^4 + 10*a^3*b - 12*a^2*b^2 - 10*a*b^3 - 3*b^4)*cosh(d*x + c)^4 + 15*a^4 + 10*a^3*b - 12*a^2*b^2 - 10*a*b^3 - 3*b^4 + 3*(45*a^4 + 34*a^2*b^2 + 24*a*b^3 + 9*b^4)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((15*a^4 + 40*a^3*b + 38*a^2*b^2 + 16*a*b^3 + 3*b^4)*cosh(d*x + c)^7 + 3*(15*a^4 + 10*a^3*b - 12*a^2*b^2 - 10*a*b^3 - 3*b^4)*cosh(d*x + c)^5 + (45*a^4 + 34*a^2*b^2 + 24*a*b^3 + 9*b^4)*cosh(d*x + c)^3 + (15*a^4 + 10*a^3*b - 12*a^2*b^2 - 10*a*b^3 - 3*b^4)*cosh(d*x + c))*sinh(d*x + c))*sqrt(b/a)*arctan(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 + a - b)*sqrt(b/a)/b) + 4*(16*(a^4 + 2*a^3*b + a^2*b^2)*d*x*cosh(d*x + c)^7 - 3*(9*a^3*b - a^2*b^2 - 13*a*b^3 - 3*b^4 - 16*(a^4 - a^2*b^2)*d*x)*cosh(d*x + c)^5 - 2*(27*a^3*b - 9*a^2*b^2 + 21*a*b^3 + 9*b^4 - 8*(3*a^4 - 2*a^3*b + 3*a^2*b^2)*d*x)*cosh(d*x + c)^3 - (27*a^3*b + 13*a^2*b^2 - 23*a*b^3 - 9*b^4 - 16*(a^4 - a^2*b^2)*d*x)*cosh(d*x + c))*sinh(d*x + c))/((a^7 + 5*a^6*b + 10*a^5*b^2 + 10*a^4*b^3 + 5*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)^8 + 8*(a^7 + 5*a^6*b + 10*a^5*b^2 + 10*a^4*b^3 + 5*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^7 + 5*a^6*b + 10*a^5*b^2 + 10*a^4*b^3 + 5*a^3*b^4 + a^2*b^5)*d*sinh(d*x + c)^8 + 4*(a^7 + 3*a^6*b + 2*a^5*b^2 - 2*a^4*b^3 - 3*a^3*b^4 - a^2*b^5)*d*cosh(d*x + c)^6 + 4*(7*(a^7 + 5*a^6*b + 10*a^5*b^2 + 10*a^4*b^3 + 5*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)^2 + (a^7 + 3*a^6*b + 2*a^5*b^2 - 2*a^4*b^3 - 3*a^3*b^4 - a^2*b^5)*d)*sinh(d*x + c)^6 + 2*(3*a^7 + 7*a^6*b + 6*a^5*b^2 + 6*a^4*b^3 + 7*a^3*b^4 + 3*a^2*b^5)*d*cosh(d*x + c)^4 + 8*(7*(a^7 + 5*a^6*b + 10*a^5*b^2 + 10*a^4*b^3 + 5*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)^3 + 3*(a^7 + 3*a^6*b + 2*a^5*b^2 - 2*a^4*b^3 - 3*a^3*b^4 - a^2*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(35*(a^7 + 5*a^6*b + 10*a^5*b^2 + 10*a^4*b^3 + 5*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)^4 + 30*(a^7 + 3*a^6*b + 2*a^5*b^2 - 2*a^4*b^3 - 3*a^3*b^4 - a^2*b^5)*d*cosh(d*x + c)^2 + (3*a^7 + 7*a^6*b + 6*a^5*b^2 + 6*a^4*b^3 + 7*a^3*b^4 + 3*a^2*b^5)*d)*sinh(d*x + c)^4 + 4*(a^7 + 3*a^6*b + 2*a^5*b^2 - 2*a^4*b^3 - 3*a^3*b^4 - a^2*b^5)*d*cosh(d*x + c)^2 + 8*(7*(a^7 + 5*a^6*b + 10*a^5*b^2 + 10*a^4*b^3 + 5*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)^5 + 10*(a^7 + 3*a^6*b + 2*a^5*b^2 - 2*a^4*b^3 - 3*a^3*b^4 - a^2*b^5)*d*cosh(d*x + c)^3 + (3*a^7 + 7*a^6*b + 6*a^5*b^2 + 6*a^4*b^3 + 7*a^3*b^4 + 3*a^2*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^7 + 5*a^6*b + 10*a^5*b^2 + 10*a^4*b^3 + 5*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)^6 + 15*(a^7 + 3*a^6*b + 2*a^5*b^2 - 2*a^4*b^3 - 3*a^3*b^4 - a^2*b^5)*d*cosh(d*x + c)^4 + 3*(3*a^7 + 7*a^6*b + 6*a^5*b^2 + 6*a^4*b^3 + 7*a^3*b^4 + 3*a^2*b^5)*d*cosh(d*x + c)^2 + (a^7 + 3*a^6*b + 2*a^5*b^2 - 2*a^4*b^3 - 3*a^3*b^4 - a^2*b^5)*d)*sinh(d*x + c)^2 + (a^7 + 5*a^6*b + 10*a^5*b^2 + 10*a^4*b^3 + 5*a^3*b^4 + a^2*b^5)*d + 8*((a^7 + 5*a^6*b + 10*a^5*b^2 + 10*a^4*b^3 + 5*a^3*b^4 + a^2*b^5)*d*cosh(d*x + c)^7 + 3*(a^7 + 3*a^6*b + 2*a^5*b^2 - 2*a^4*b^3 - 3*a^3*b^4 - a^2*b^5)*d*cosh(d*x + c)^5 + (3*a^7 + 7*a^6*b + 6*a^5*b^2 + 6*a^4*b^3 + 7*a^3*b^4 + 3*a^2*b^5)*d*cosh(d*x + c)^3 + (a^7 + 3*a^6*b + 2*a^5*b^2 - 2*a^4*b^3 - 3*a^3*b^4 - a^2*b^5)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
197,1,4800,0,0.873031," ","integrate(coth(d*x+c)/(a+b*tanh(d*x+c)^2)^3,x, algorithm=""fricas"")","-\frac{2 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} d x \cosh\left(d x + c\right)^{8} + 16 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + 2 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} d x \sinh\left(d x + c\right)^{8} - 4 \, {\left(3 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4} - 2 \, {\left(a^{5} - a^{3} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{6} - 4 \, {\left(3 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4} - 14 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} d x \cosh\left(d x + c\right)^{2} - 2 \, {\left(a^{5} - a^{3} b^{2}\right)} d x\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(14 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} d x \cosh\left(d x + c\right)^{3} - 3 \, {\left(3 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4} - 2 \, {\left(a^{5} - a^{3} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 4 \, {\left(6 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 2 \, a b^{4} - {\left(3 \, a^{5} - 2 \, a^{4} b + 3 \, a^{3} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(35 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} d x \cosh\left(d x + c\right)^{4} - 6 \, a^{3} b^{2} + 2 \, a^{2} b^{3} + 2 \, a b^{4} + {\left(3 \, a^{5} - 2 \, a^{4} b + 3 \, a^{3} b^{2}\right)} d x - 15 \, {\left(3 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4} - 2 \, {\left(a^{5} - a^{3} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 16 \, {\left(7 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} d x \cosh\left(d x + c\right)^{5} - 5 \, {\left(3 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4} - 2 \, {\left(a^{5} - a^{3} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - {\left(6 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 2 \, a b^{4} - {\left(3 \, a^{5} - 2 \, a^{4} b + 3 \, a^{3} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} d x - 4 \, {\left(3 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4} - 2 \, {\left(a^{5} - a^{3} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(14 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} d x \cosh\left(d x + c\right)^{6} - 3 \, a^{3} b^{2} - 4 \, a^{2} b^{3} - a b^{4} - 15 \, {\left(3 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4} - 2 \, {\left(a^{5} - a^{3} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(a^{5} - a^{3} b^{2}\right)} d x - 6 \, {\left(6 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 2 \, a b^{4} - {\left(3 \, a^{5} - 2 \, a^{4} b + 3 \, a^{3} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(3 \, a^{4} b + 9 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(3 \, a^{4} b + 9 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(3 \, a^{4} b + 9 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(3 \, a^{4} b + 3 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(3 \, a^{4} b + 3 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5} + 7 \, {\left(3 \, a^{4} b + 9 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(3 \, a^{4} b + 9 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(3 \, a^{4} b + 3 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 3 \, a^{4} b + 9 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5} + 2 \, {\left(9 \, a^{4} b + 3 \, a^{3} b^{2} + 6 \, a^{2} b^{3} + 7 \, a b^{4} + 3 \, b^{5}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(9 \, a^{4} b + 3 \, a^{3} b^{2} + 6 \, a^{2} b^{3} + 7 \, a b^{4} + 3 \, b^{5} + 35 \, {\left(3 \, a^{4} b + 9 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} \cosh\left(d x + c\right)^{4} + 30 \, {\left(3 \, a^{4} b + 3 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(3 \, a^{4} b + 9 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(3 \, a^{4} b + 3 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} \cosh\left(d x + c\right)^{3} + {\left(9 \, a^{4} b + 3 \, a^{3} b^{2} + 6 \, a^{2} b^{3} + 7 \, a b^{4} + 3 \, b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(3 \, a^{4} b + 3 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(3 \, a^{4} b + 9 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} \cosh\left(d x + c\right)^{6} + 3 \, a^{4} b + 3 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5} + 15 \, {\left(3 \, a^{4} b + 3 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(9 \, a^{4} b + 3 \, a^{3} b^{2} + 6 \, a^{2} b^{3} + 7 \, a b^{4} + 3 \, b^{5}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left({\left(3 \, a^{4} b + 9 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(3 \, a^{4} b + 3 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} \cosh\left(d x + c\right)^{5} + {\left(9 \, a^{4} b + 3 \, a^{3} b^{2} + 6 \, a^{2} b^{3} + 7 \, a b^{4} + 3 \, b^{5}\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{4} b + 3 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\frac{2 \, {\left({\left(a + b\right)} \cosh\left(d x + c\right)^{2} + {\left(a + b\right)} \sinh\left(d x + c\right)^{2} + a - b\right)}}{\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}}\right) - 2 \, {\left({\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5} + 7 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(7 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5} + 2 \, {\left(3 \, a^{5} + 7 \, a^{4} b + 6 \, a^{3} b^{2} + 6 \, a^{2} b^{3} + 7 \, a b^{4} + 3 \, b^{5}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(3 \, a^{5} + 7 \, a^{4} b + 6 \, a^{3} b^{2} + 6 \, a^{2} b^{3} + 7 \, a b^{4} + 3 \, b^{5} + 35 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} \cosh\left(d x + c\right)^{4} + 30 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{5} + 7 \, a^{4} b + 6 \, a^{3} b^{2} + 6 \, a^{2} b^{3} + 7 \, a b^{4} + 3 \, b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 4 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(7 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} \cosh\left(d x + c\right)^{6} + a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5} + 15 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} \cosh\left(d x + c\right)^{4} + 3 \, {\left(3 \, a^{5} + 7 \, a^{4} b + 6 \, a^{3} b^{2} + 6 \, a^{2} b^{3} + 7 \, a b^{4} + 3 \, b^{5}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 8 \, {\left({\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{5} + 7 \, a^{4} b + 6 \, a^{3} b^{2} + 6 \, a^{2} b^{3} + 7 \, a b^{4} + 3 \, b^{5}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\frac{2 \, \sinh\left(d x + c\right)}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) + 8 \, {\left(2 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} d x \cosh\left(d x + c\right)^{7} - 3 \, {\left(3 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4} - 2 \, {\left(a^{5} - a^{3} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{5} - 2 \, {\left(6 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 2 \, a b^{4} - {\left(3 \, a^{5} - 2 \, a^{4} b + 3 \, a^{3} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - {\left(3 \, a^{3} b^{2} + 4 \, a^{2} b^{3} + a b^{4} - 2 \, {\left(a^{5} - a^{3} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{2 \, {\left({\left(a^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{8} + 8 \, {\left(a^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{7} + {\left(a^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \sinh\left(d x + c\right)^{8} + 4 \, {\left(a^{8} + 3 \, a^{7} b + 2 \, a^{6} b^{2} - 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^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{8} + 3 \, a^{7} b + 2 \, a^{6} b^{2} - 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(3 \, a^{8} + 7 \, a^{7} b + 6 \, a^{6} b^{2} + 6 \, a^{5} b^{3} + 7 \, a^{4} b^{4} + 3 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(7 \, {\left(a^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{8} + 3 \, a^{7} b + 2 \, a^{6} b^{2} - 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^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 30 \, {\left(a^{8} + 3 \, a^{7} b + 2 \, a^{6} b^{2} - 2 \, a^{5} b^{3} - 3 \, a^{4} b^{4} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{8} + 7 \, a^{7} b + 6 \, a^{6} b^{2} + 6 \, a^{5} b^{3} + 7 \, a^{4} b^{4} + 3 \, a^{3} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(a^{8} + 3 \, a^{7} b + 2 \, a^{6} b^{2} - 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^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{5} + 10 \, {\left(a^{8} + 3 \, a^{7} b + 2 \, a^{6} b^{2} - 2 \, a^{5} b^{3} - 3 \, a^{4} b^{4} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{8} + 7 \, a^{7} b + 6 \, a^{6} b^{2} + 6 \, a^{5} b^{3} + 7 \, 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^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{6} + 15 \, {\left(a^{8} + 3 \, a^{7} b + 2 \, a^{6} b^{2} - 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(3 \, a^{8} + 7 \, a^{7} b + 6 \, a^{6} b^{2} + 6 \, a^{5} b^{3} + 7 \, a^{4} b^{4} + 3 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{8} + 3 \, a^{7} b + 2 \, a^{6} b^{2} - 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^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} d + 8 \, {\left({\left(a^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{7} + 3 \, {\left(a^{8} + 3 \, a^{7} b + 2 \, a^{6} b^{2} - 2 \, a^{5} b^{3} - 3 \, a^{4} b^{4} - a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{5} + {\left(3 \, a^{8} + 7 \, a^{7} b + 6 \, a^{6} b^{2} + 6 \, a^{5} b^{3} + 7 \, a^{4} b^{4} + 3 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{8} + 3 \, a^{7} b + 2 \, a^{6} b^{2} - 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)}}"," ",0,"-1/2*(2*(a^5 + 2*a^4*b + a^3*b^2)*d*x*cosh(d*x + c)^8 + 16*(a^5 + 2*a^4*b + a^3*b^2)*d*x*cosh(d*x + c)*sinh(d*x + c)^7 + 2*(a^5 + 2*a^4*b + a^3*b^2)*d*x*sinh(d*x + c)^8 - 4*(3*a^3*b^2 + 4*a^2*b^3 + a*b^4 - 2*(a^5 - a^3*b^2)*d*x)*cosh(d*x + c)^6 - 4*(3*a^3*b^2 + 4*a^2*b^3 + a*b^4 - 14*(a^5 + 2*a^4*b + a^3*b^2)*d*x*cosh(d*x + c)^2 - 2*(a^5 - a^3*b^2)*d*x)*sinh(d*x + c)^6 + 8*(14*(a^5 + 2*a^4*b + a^3*b^2)*d*x*cosh(d*x + c)^3 - 3*(3*a^3*b^2 + 4*a^2*b^3 + a*b^4 - 2*(a^5 - a^3*b^2)*d*x)*cosh(d*x + c))*sinh(d*x + c)^5 - 4*(6*a^3*b^2 - 2*a^2*b^3 - 2*a*b^4 - (3*a^5 - 2*a^4*b + 3*a^3*b^2)*d*x)*cosh(d*x + c)^4 + 4*(35*(a^5 + 2*a^4*b + a^3*b^2)*d*x*cosh(d*x + c)^4 - 6*a^3*b^2 + 2*a^2*b^3 + 2*a*b^4 + (3*a^5 - 2*a^4*b + 3*a^3*b^2)*d*x - 15*(3*a^3*b^2 + 4*a^2*b^3 + a*b^4 - 2*(a^5 - a^3*b^2)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 16*(7*(a^5 + 2*a^4*b + a^3*b^2)*d*x*cosh(d*x + c)^5 - 5*(3*a^3*b^2 + 4*a^2*b^3 + a*b^4 - 2*(a^5 - a^3*b^2)*d*x)*cosh(d*x + c)^3 - (6*a^3*b^2 - 2*a^2*b^3 - 2*a*b^4 - (3*a^5 - 2*a^4*b + 3*a^3*b^2)*d*x)*cosh(d*x + c))*sinh(d*x + c)^3 + 2*(a^5 + 2*a^4*b + a^3*b^2)*d*x - 4*(3*a^3*b^2 + 4*a^2*b^3 + a*b^4 - 2*(a^5 - a^3*b^2)*d*x)*cosh(d*x + c)^2 + 4*(14*(a^5 + 2*a^4*b + a^3*b^2)*d*x*cosh(d*x + c)^6 - 3*a^3*b^2 - 4*a^2*b^3 - a*b^4 - 15*(3*a^3*b^2 + 4*a^2*b^3 + a*b^4 - 2*(a^5 - a^3*b^2)*d*x)*cosh(d*x + c)^4 + 2*(a^5 - a^3*b^2)*d*x - 6*(6*a^3*b^2 - 2*a^2*b^3 - 2*a*b^4 - (3*a^5 - 2*a^4*b + 3*a^3*b^2)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((3*a^4*b + 9*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*cosh(d*x + c)^8 + 8*(3*a^4*b + 9*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*cosh(d*x + c)*sinh(d*x + c)^7 + (3*a^4*b + 9*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*sinh(d*x + c)^8 + 4*(3*a^4*b + 3*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*cosh(d*x + c)^6 + 4*(3*a^4*b + 3*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5 + 7*(3*a^4*b + 9*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(3*a^4*b + 9*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*cosh(d*x + c)^3 + 3*(3*a^4*b + 3*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*cosh(d*x + c))*sinh(d*x + c)^5 + 3*a^4*b + 9*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5 + 2*(9*a^4*b + 3*a^3*b^2 + 6*a^2*b^3 + 7*a*b^4 + 3*b^5)*cosh(d*x + c)^4 + 2*(9*a^4*b + 3*a^3*b^2 + 6*a^2*b^3 + 7*a*b^4 + 3*b^5 + 35*(3*a^4*b + 9*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*cosh(d*x + c)^4 + 30*(3*a^4*b + 3*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(7*(3*a^4*b + 9*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*cosh(d*x + c)^5 + 10*(3*a^4*b + 3*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*cosh(d*x + c)^3 + (9*a^4*b + 3*a^3*b^2 + 6*a^2*b^3 + 7*a*b^4 + 3*b^5)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(3*a^4*b + 3*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*cosh(d*x + c)^2 + 4*(7*(3*a^4*b + 9*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*cosh(d*x + c)^6 + 3*a^4*b + 3*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5 + 15*(3*a^4*b + 3*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*cosh(d*x + c)^4 + 3*(9*a^4*b + 3*a^3*b^2 + 6*a^2*b^3 + 7*a*b^4 + 3*b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((3*a^4*b + 9*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*cosh(d*x + c)^7 + 3*(3*a^4*b + 3*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*cosh(d*x + c)^5 + (9*a^4*b + 3*a^3*b^2 + 6*a^2*b^3 + 7*a*b^4 + 3*b^5)*cosh(d*x + c)^3 + (3*a^4*b + 3*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*cosh(d*x + c))*sinh(d*x + c))*log(2*((a + b)*cosh(d*x + c)^2 + (a + b)*sinh(d*x + c)^2 + a - b)/(cosh(d*x + c)^2 - 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)) - 2*((a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*cosh(d*x + c)^8 + 8*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*cosh(d*x + c)*sinh(d*x + c)^7 + (a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*sinh(d*x + c)^8 + 4*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*cosh(d*x + c)^6 + 4*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5 + 7*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(7*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*cosh(d*x + c)^3 + 3*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*cosh(d*x + c))*sinh(d*x + c)^5 + a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5 + 2*(3*a^5 + 7*a^4*b + 6*a^3*b^2 + 6*a^2*b^3 + 7*a*b^4 + 3*b^5)*cosh(d*x + c)^4 + 2*(3*a^5 + 7*a^4*b + 6*a^3*b^2 + 6*a^2*b^3 + 7*a*b^4 + 3*b^5 + 35*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*cosh(d*x + c)^4 + 30*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(7*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*cosh(d*x + c)^5 + 10*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*cosh(d*x + c)^3 + (3*a^5 + 7*a^4*b + 6*a^3*b^2 + 6*a^2*b^3 + 7*a*b^4 + 3*b^5)*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*cosh(d*x + c)^2 + 4*(7*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*cosh(d*x + c)^6 + a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5 + 15*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*cosh(d*x + c)^4 + 3*(3*a^5 + 7*a^4*b + 6*a^3*b^2 + 6*a^2*b^3 + 7*a*b^4 + 3*b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 8*((a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*cosh(d*x + c)^7 + 3*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*cosh(d*x + c)^5 + (3*a^5 + 7*a^4*b + 6*a^3*b^2 + 6*a^2*b^3 + 7*a*b^4 + 3*b^5)*cosh(d*x + c)^3 + (a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*cosh(d*x + c))*sinh(d*x + c))*log(2*sinh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))) + 8*(2*(a^5 + 2*a^4*b + a^3*b^2)*d*x*cosh(d*x + c)^7 - 3*(3*a^3*b^2 + 4*a^2*b^3 + a*b^4 - 2*(a^5 - a^3*b^2)*d*x)*cosh(d*x + c)^5 - 2*(6*a^3*b^2 - 2*a^2*b^3 - 2*a*b^4 - (3*a^5 - 2*a^4*b + 3*a^3*b^2)*d*x)*cosh(d*x + c)^3 - (3*a^3*b^2 + 4*a^2*b^3 + a*b^4 - 2*(a^5 - a^3*b^2)*d*x)*cosh(d*x + c))*sinh(d*x + c))/((a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)^8 + 8*(a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)*sinh(d*x + c)^7 + (a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*d*sinh(d*x + c)^8 + 4*(a^8 + 3*a^7*b + 2*a^6*b^2 - 2*a^5*b^3 - 3*a^4*b^4 - a^3*b^5)*d*cosh(d*x + c)^6 + 4*(7*(a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)^2 + (a^8 + 3*a^7*b + 2*a^6*b^2 - 2*a^5*b^3 - 3*a^4*b^4 - a^3*b^5)*d)*sinh(d*x + c)^6 + 2*(3*a^8 + 7*a^7*b + 6*a^6*b^2 + 6*a^5*b^3 + 7*a^4*b^4 + 3*a^3*b^5)*d*cosh(d*x + c)^4 + 8*(7*(a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)^3 + 3*(a^8 + 3*a^7*b + 2*a^6*b^2 - 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^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)^4 + 30*(a^8 + 3*a^7*b + 2*a^6*b^2 - 2*a^5*b^3 - 3*a^4*b^4 - a^3*b^5)*d*cosh(d*x + c)^2 + (3*a^8 + 7*a^7*b + 6*a^6*b^2 + 6*a^5*b^3 + 7*a^4*b^4 + 3*a^3*b^5)*d)*sinh(d*x + c)^4 + 4*(a^8 + 3*a^7*b + 2*a^6*b^2 - 2*a^5*b^3 - 3*a^4*b^4 - a^3*b^5)*d*cosh(d*x + c)^2 + 8*(7*(a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)^5 + 10*(a^8 + 3*a^7*b + 2*a^6*b^2 - 2*a^5*b^3 - 3*a^4*b^4 - a^3*b^5)*d*cosh(d*x + c)^3 + (3*a^8 + 7*a^7*b + 6*a^6*b^2 + 6*a^5*b^3 + 7*a^4*b^4 + 3*a^3*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 4*(7*(a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)^6 + 15*(a^8 + 3*a^7*b + 2*a^6*b^2 - 2*a^5*b^3 - 3*a^4*b^4 - a^3*b^5)*d*cosh(d*x + c)^4 + 3*(3*a^8 + 7*a^7*b + 6*a^6*b^2 + 6*a^5*b^3 + 7*a^4*b^4 + 3*a^3*b^5)*d*cosh(d*x + c)^2 + (a^8 + 3*a^7*b + 2*a^6*b^2 - 2*a^5*b^3 - 3*a^4*b^4 - a^3*b^5)*d)*sinh(d*x + c)^2 + (a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*d + 8*((a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)^7 + 3*(a^8 + 3*a^7*b + 2*a^6*b^2 - 2*a^5*b^3 - 3*a^4*b^4 - a^3*b^5)*d*cosh(d*x + c)^5 + (3*a^8 + 7*a^7*b + 6*a^6*b^2 + 6*a^5*b^3 + 7*a^4*b^4 + 3*a^3*b^5)*d*cosh(d*x + c)^3 + (a^8 + 3*a^7*b + 2*a^6*b^2 - 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
198,1,11865,0,0.680480," ","integrate(coth(d*x+c)^2/(a+b*tanh(d*x+c)^2)^3,x, algorithm=""fricas"")","\left[\frac{16 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} d x \cosh\left(d x + c\right)^{10} + 160 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + 16 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} d x \sinh\left(d x + c\right)^{10} - 4 \, {\left(8 \, a^{5} + 40 \, a^{4} b + 67 \, a^{3} b^{2} + 77 \, a^{2} b^{3} + 57 \, a b^{4} + 15 \, b^{5} - 4 \, {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{8} - 4 \, {\left(8 \, a^{5} + 40 \, a^{4} b + 67 \, a^{3} b^{2} + 77 \, a^{2} b^{3} + 57 \, a b^{4} + 15 \, b^{5} - 180 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} d x \cosh\left(d x + c\right)^{2} - 4 \, {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} d x\right)} \sinh\left(d x + c\right)^{8} + 32 \, {\left(60 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} d x \cosh\left(d x + c\right)^{3} - {\left(8 \, a^{5} + 40 \, a^{4} b + 67 \, a^{3} b^{2} + 77 \, a^{2} b^{3} + 57 \, a b^{4} + 15 \, b^{5} - 4 \, {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} - 8 \, {\left(16 \, a^{5} + 48 \, a^{4} b + 19 \, a^{3} b^{2} - 28 \, a^{2} b^{3} - 69 \, a b^{4} - 30 \, b^{5} - 4 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{6} + 8 \, {\left(420 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} d x \cosh\left(d x + c\right)^{4} - 16 \, a^{5} - 48 \, a^{4} b - 19 \, a^{3} b^{2} + 28 \, a^{2} b^{3} + 69 \, a b^{4} + 30 \, b^{5} + 4 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} d x - 14 \, {\left(8 \, a^{5} + 40 \, a^{4} b + 67 \, a^{3} b^{2} + 77 \, a^{2} b^{3} + 57 \, a b^{4} + 15 \, b^{5} - 4 \, {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 16 \, {\left(252 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} d x \cosh\left(d x + c\right)^{5} - 14 \, {\left(8 \, a^{5} + 40 \, a^{4} b + 67 \, a^{3} b^{2} + 77 \, a^{2} b^{3} + 57 \, a b^{4} + 15 \, b^{5} - 4 \, {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(16 \, a^{5} + 48 \, a^{4} b + 19 \, a^{3} b^{2} - 28 \, a^{2} b^{3} - 69 \, a b^{4} - 30 \, b^{5} - 4 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 32 \, a^{5} - 160 \, a^{4} b - 372 \, a^{3} b^{2} - 452 \, a^{2} b^{3} - 268 \, a b^{4} - 60 \, b^{5} - 8 \, {\left(24 \, a^{5} + 56 \, a^{4} b + 48 \, a^{3} b^{2} + 33 \, a^{2} b^{3} + 86 \, a b^{4} + 45 \, b^{5} + 4 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 8 \, {\left(420 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} d x \cosh\left(d x + c\right)^{6} - 24 \, a^{5} - 56 \, a^{4} b - 48 \, a^{3} b^{2} - 33 \, a^{2} b^{3} - 86 \, a b^{4} - 45 \, b^{5} - 35 \, {\left(8 \, a^{5} + 40 \, a^{4} b + 67 \, a^{3} b^{2} + 77 \, a^{2} b^{3} + 57 \, a b^{4} + 15 \, b^{5} - 4 \, {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{4} - 4 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} d x - 15 \, {\left(16 \, a^{5} + 48 \, a^{4} b + 19 \, a^{3} b^{2} - 28 \, a^{2} b^{3} - 69 \, a b^{4} - 30 \, b^{5} - 4 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 32 \, {\left(60 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} d x \cosh\left(d x + c\right)^{7} - 7 \, {\left(8 \, a^{5} + 40 \, a^{4} b + 67 \, a^{3} b^{2} + 77 \, a^{2} b^{3} + 57 \, a b^{4} + 15 \, b^{5} - 4 \, {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{5} - 5 \, {\left(16 \, a^{5} + 48 \, a^{4} b + 19 \, a^{3} b^{2} - 28 \, a^{2} b^{3} - 69 \, a b^{4} - 30 \, b^{5} - 4 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - {\left(24 \, a^{5} + 56 \, a^{4} b + 48 \, a^{3} b^{2} + 33 \, a^{2} b^{3} + 86 \, a b^{4} + 45 \, b^{5} + 4 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 16 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} d x - 8 \, {\left(16 \, a^{5} + 48 \, a^{4} b + 45 \, a^{3} b^{2} - 36 \, a^{2} b^{3} - 79 \, a b^{4} - 30 \, b^{5} + 2 \, {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{2} + 8 \, {\left(90 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} d x \cosh\left(d x + c\right)^{8} - 14 \, {\left(8 \, a^{5} + 40 \, a^{4} b + 67 \, a^{3} b^{2} + 77 \, a^{2} b^{3} + 57 \, a b^{4} + 15 \, b^{5} - 4 \, {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{6} - 16 \, a^{5} - 48 \, a^{4} b - 45 \, a^{3} b^{2} + 36 \, a^{2} b^{3} + 79 \, a b^{4} + 30 \, b^{5} - 15 \, {\left(16 \, a^{5} + 48 \, a^{4} b + 19 \, a^{3} b^{2} - 28 \, a^{2} b^{3} - 69 \, a b^{4} - 30 \, b^{5} - 4 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{4} - 2 \, {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} d x - 6 \, {\left(24 \, a^{5} + 56 \, a^{4} b + 48 \, a^{3} b^{2} + 33 \, a^{2} b^{3} + 86 \, a b^{4} + 45 \, b^{5} + 4 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + {\left({\left(35 \, a^{4} b + 112 \, a^{3} b^{2} + 134 \, a^{2} b^{3} + 72 \, a b^{4} + 15 \, b^{5}\right)} \cosh\left(d x + c\right)^{10} + 10 \, {\left(35 \, a^{4} b + 112 \, a^{3} b^{2} + 134 \, a^{2} b^{3} + 72 \, a b^{4} + 15 \, b^{5}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + {\left(35 \, a^{4} b + 112 \, a^{3} b^{2} + 134 \, a^{2} b^{3} + 72 \, a b^{4} + 15 \, b^{5}\right)} \sinh\left(d x + c\right)^{10} + {\left(105 \, a^{4} b + 56 \, a^{3} b^{2} - 214 \, a^{2} b^{3} - 240 \, a b^{4} - 75 \, b^{5}\right)} \cosh\left(d x + c\right)^{8} + {\left(105 \, a^{4} b + 56 \, a^{3} b^{2} - 214 \, a^{2} b^{3} - 240 \, a b^{4} - 75 \, b^{5} + 45 \, {\left(35 \, a^{4} b + 112 \, a^{3} b^{2} + 134 \, a^{2} b^{3} + 72 \, a b^{4} + 15 \, b^{5}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{8} + 8 \, {\left(15 \, {\left(35 \, a^{4} b + 112 \, a^{3} b^{2} + 134 \, a^{2} b^{3} + 72 \, a b^{4} + 15 \, b^{5}\right)} \cosh\left(d x + c\right)^{3} + {\left(105 \, a^{4} b + 56 \, a^{3} b^{2} - 214 \, a^{2} b^{3} - 240 \, a b^{4} - 75 \, b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(35 \, a^{4} b - 28 \, a^{3} b^{2} + 106 \, a^{2} b^{3} + 180 \, a b^{4} + 75 \, b^{5}\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(35 \, a^{4} b - 28 \, a^{3} b^{2} + 106 \, a^{2} b^{3} + 180 \, a b^{4} + 75 \, b^{5} + 105 \, {\left(35 \, a^{4} b + 112 \, a^{3} b^{2} + 134 \, a^{2} b^{3} + 72 \, a b^{4} + 15 \, b^{5}\right)} \cosh\left(d x + c\right)^{4} + 14 \, {\left(105 \, a^{4} b + 56 \, a^{3} b^{2} - 214 \, a^{2} b^{3} - 240 \, a b^{4} - 75 \, b^{5}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(63 \, {\left(35 \, a^{4} b + 112 \, a^{3} b^{2} + 134 \, a^{2} b^{3} + 72 \, a b^{4} + 15 \, b^{5}\right)} \cosh\left(d x + c\right)^{5} + 14 \, {\left(105 \, a^{4} b + 56 \, a^{3} b^{2} - 214 \, a^{2} b^{3} - 240 \, a b^{4} - 75 \, b^{5}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(35 \, a^{4} b - 28 \, a^{3} b^{2} + 106 \, a^{2} b^{3} + 180 \, a b^{4} + 75 \, b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 35 \, a^{4} b - 112 \, a^{3} b^{2} - 134 \, a^{2} b^{3} - 72 \, a b^{4} - 15 \, b^{5} - 2 \, {\left(35 \, a^{4} b - 28 \, a^{3} b^{2} + 106 \, a^{2} b^{3} + 180 \, a b^{4} + 75 \, b^{5}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(105 \, {\left(35 \, a^{4} b + 112 \, a^{3} b^{2} + 134 \, a^{2} b^{3} + 72 \, a b^{4} + 15 \, b^{5}\right)} \cosh\left(d x + c\right)^{6} - 35 \, a^{4} b + 28 \, a^{3} b^{2} - 106 \, a^{2} b^{3} - 180 \, a b^{4} - 75 \, b^{5} + 35 \, {\left(105 \, a^{4} b + 56 \, a^{3} b^{2} - 214 \, a^{2} b^{3} - 240 \, a b^{4} - 75 \, b^{5}\right)} \cosh\left(d x + c\right)^{4} + 15 \, {\left(35 \, a^{4} b - 28 \, a^{3} b^{2} + 106 \, a^{2} b^{3} + 180 \, a b^{4} + 75 \, b^{5}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(15 \, {\left(35 \, a^{4} b + 112 \, a^{3} b^{2} + 134 \, a^{2} b^{3} + 72 \, a b^{4} + 15 \, b^{5}\right)} \cosh\left(d x + c\right)^{7} + 7 \, {\left(105 \, a^{4} b + 56 \, a^{3} b^{2} - 214 \, a^{2} b^{3} - 240 \, a b^{4} - 75 \, b^{5}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(35 \, a^{4} b - 28 \, a^{3} b^{2} + 106 \, a^{2} b^{3} + 180 \, a b^{4} + 75 \, b^{5}\right)} \cosh\left(d x + c\right)^{3} - {\left(35 \, a^{4} b - 28 \, a^{3} b^{2} + 106 \, a^{2} b^{3} + 180 \, a b^{4} + 75 \, b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - {\left(105 \, a^{4} b + 56 \, a^{3} b^{2} - 214 \, a^{2} b^{3} - 240 \, a b^{4} - 75 \, b^{5}\right)} \cosh\left(d x + c\right)^{2} + {\left(45 \, {\left(35 \, a^{4} b + 112 \, a^{3} b^{2} + 134 \, a^{2} b^{3} + 72 \, a b^{4} + 15 \, b^{5}\right)} \cosh\left(d x + c\right)^{8} + 28 \, {\left(105 \, a^{4} b + 56 \, a^{3} b^{2} - 214 \, a^{2} b^{3} - 240 \, a b^{4} - 75 \, b^{5}\right)} \cosh\left(d x + c\right)^{6} - 105 \, a^{4} b - 56 \, a^{3} b^{2} + 214 \, a^{2} b^{3} + 240 \, a b^{4} + 75 \, b^{5} + 30 \, {\left(35 \, a^{4} b - 28 \, a^{3} b^{2} + 106 \, a^{2} b^{3} + 180 \, a b^{4} + 75 \, b^{5}\right)} \cosh\left(d x + c\right)^{4} - 12 \, {\left(35 \, a^{4} b - 28 \, a^{3} b^{2} + 106 \, a^{2} b^{3} + 180 \, a b^{4} + 75 \, b^{5}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(5 \, {\left(35 \, a^{4} b + 112 \, a^{3} b^{2} + 134 \, a^{2} b^{3} + 72 \, a b^{4} + 15 \, b^{5}\right)} \cosh\left(d x + c\right)^{9} + 4 \, {\left(105 \, a^{4} b + 56 \, a^{3} b^{2} - 214 \, a^{2} b^{3} - 240 \, a b^{4} - 75 \, b^{5}\right)} \cosh\left(d x + c\right)^{7} + 6 \, {\left(35 \, a^{4} b - 28 \, a^{3} b^{2} + 106 \, a^{2} b^{3} + 180 \, a b^{4} + 75 \, b^{5}\right)} \cosh\left(d x + c\right)^{5} - 4 \, {\left(35 \, a^{4} b - 28 \, a^{3} b^{2} + 106 \, a^{2} b^{3} + 180 \, a b^{4} + 75 \, b^{5}\right)} \cosh\left(d x + c\right)^{3} - {\left(105 \, a^{4} b + 56 \, a^{3} b^{2} - 214 \, a^{2} b^{3} - 240 \, a b^{4} - 75 \, b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{-\frac{b}{a}} \log\left(\frac{{\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) \sinh\left(d x + c\right)^{3} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(d x + c\right)^{2} + a^{2} - 6 \, a b + b^{2} + 4 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{2} - b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right) - 4 \, {\left({\left(a^{2} + a b\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(a^{2} + a b\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right) + {\left(a^{2} + a b\right)} \sinh\left(d x + c\right)^{2} + a^{2} - a b\right)} \sqrt{-\frac{b}{a}}}{{\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) + 16 \, {\left(10 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} d x \cosh\left(d x + c\right)^{9} - 2 \, {\left(8 \, a^{5} + 40 \, a^{4} b + 67 \, a^{3} b^{2} + 77 \, a^{2} b^{3} + 57 \, a b^{4} + 15 \, b^{5} - 4 \, {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{7} - 3 \, {\left(16 \, a^{5} + 48 \, a^{4} b + 19 \, a^{3} b^{2} - 28 \, a^{2} b^{3} - 69 \, a b^{4} - 30 \, b^{5} - 4 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{5} - 2 \, {\left(24 \, a^{5} + 56 \, a^{4} b + 48 \, a^{3} b^{2} + 33 \, a^{2} b^{3} + 86 \, a b^{4} + 45 \, b^{5} + 4 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - {\left(16 \, a^{5} + 48 \, a^{4} b + 45 \, a^{3} b^{2} - 36 \, a^{2} b^{3} - 79 \, a b^{4} - 30 \, b^{5} + 2 \, {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{16 \, {\left({\left(a^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{10} + 10 \, {\left(a^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + {\left(a^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \sinh\left(d x + c\right)^{10} + {\left(3 \, a^{8} + 7 \, a^{7} b - 2 \, a^{6} b^{2} - 18 \, a^{5} b^{3} - 17 \, a^{4} b^{4} - 5 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{8} + {\left(45 \, {\left(a^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{8} + 7 \, a^{7} b - 2 \, a^{6} b^{2} - 18 \, a^{5} b^{3} - 17 \, a^{4} b^{4} - 5 \, a^{3} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{8} + 2 \, {\left(a^{8} + a^{7} b + 2 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 5 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{6} + 8 \, {\left(15 \, {\left(a^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{8} + 7 \, a^{7} b - 2 \, a^{6} b^{2} - 18 \, a^{5} b^{3} - 17 \, a^{4} b^{4} - 5 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(105 \, {\left(a^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 14 \, {\left(3 \, a^{8} + 7 \, a^{7} b - 2 \, a^{6} b^{2} - 18 \, a^{5} b^{3} - 17 \, a^{4} b^{4} - 5 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{8} + a^{7} b + 2 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 5 \, a^{3} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{6} - 2 \, {\left(a^{8} + a^{7} b + 2 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 5 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(63 \, {\left(a^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{5} + 14 \, {\left(3 \, a^{8} + 7 \, a^{7} b - 2 \, a^{6} b^{2} - 18 \, a^{5} b^{3} - 17 \, a^{4} b^{4} - 5 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{8} + a^{7} b + 2 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 5 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(105 \, {\left(a^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{6} + 35 \, {\left(3 \, a^{8} + 7 \, a^{7} b - 2 \, a^{6} b^{2} - 18 \, a^{5} b^{3} - 17 \, a^{4} b^{4} - 5 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 15 \, {\left(a^{8} + a^{7} b + 2 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 5 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{8} + a^{7} b + 2 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 5 \, a^{3} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{4} - {\left(3 \, a^{8} + 7 \, a^{7} b - 2 \, a^{6} b^{2} - 18 \, a^{5} b^{3} - 17 \, a^{4} b^{4} - 5 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(15 \, {\left(a^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{7} + 7 \, {\left(3 \, a^{8} + 7 \, a^{7} b - 2 \, a^{6} b^{2} - 18 \, a^{5} b^{3} - 17 \, a^{4} b^{4} - 5 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{5} + 5 \, {\left(a^{8} + a^{7} b + 2 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 5 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a^{8} + a^{7} b + 2 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 5 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(45 \, {\left(a^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{8} + 28 \, {\left(3 \, a^{8} + 7 \, a^{7} b - 2 \, a^{6} b^{2} - 18 \, a^{5} b^{3} - 17 \, a^{4} b^{4} - 5 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{6} + 30 \, {\left(a^{8} + a^{7} b + 2 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 5 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{4} - 12 \, {\left(a^{8} + a^{7} b + 2 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 5 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{2} - {\left(3 \, a^{8} + 7 \, a^{7} b - 2 \, a^{6} b^{2} - 18 \, a^{5} b^{3} - 17 \, a^{4} b^{4} - 5 \, a^{3} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{2} - {\left(a^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} d + 2 \, {\left(5 \, {\left(a^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{9} + 4 \, {\left(3 \, a^{8} + 7 \, a^{7} b - 2 \, a^{6} b^{2} - 18 \, a^{5} b^{3} - 17 \, a^{4} b^{4} - 5 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{7} + 6 \, {\left(a^{8} + a^{7} b + 2 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 5 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{5} - 4 \, {\left(a^{8} + a^{7} b + 2 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 5 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{3} - {\left(3 \, a^{8} + 7 \, a^{7} b - 2 \, a^{6} b^{2} - 18 \, a^{5} b^{3} - 17 \, a^{4} b^{4} - 5 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}, \frac{8 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} d x \cosh\left(d x + c\right)^{10} + 80 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + 8 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} d x \sinh\left(d x + c\right)^{10} - 2 \, {\left(8 \, a^{5} + 40 \, a^{4} b + 67 \, a^{3} b^{2} + 77 \, a^{2} b^{3} + 57 \, a b^{4} + 15 \, b^{5} - 4 \, {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{8} - 2 \, {\left(8 \, a^{5} + 40 \, a^{4} b + 67 \, a^{3} b^{2} + 77 \, a^{2} b^{3} + 57 \, a b^{4} + 15 \, b^{5} - 180 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} d x \cosh\left(d x + c\right)^{2} - 4 \, {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} d x\right)} \sinh\left(d x + c\right)^{8} + 16 \, {\left(60 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} d x \cosh\left(d x + c\right)^{3} - {\left(8 \, a^{5} + 40 \, a^{4} b + 67 \, a^{3} b^{2} + 77 \, a^{2} b^{3} + 57 \, a b^{4} + 15 \, b^{5} - 4 \, {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} - 4 \, {\left(16 \, a^{5} + 48 \, a^{4} b + 19 \, a^{3} b^{2} - 28 \, a^{2} b^{3} - 69 \, a b^{4} - 30 \, b^{5} - 4 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(420 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} d x \cosh\left(d x + c\right)^{4} - 16 \, a^{5} - 48 \, a^{4} b - 19 \, a^{3} b^{2} + 28 \, a^{2} b^{3} + 69 \, a b^{4} + 30 \, b^{5} + 4 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} d x - 14 \, {\left(8 \, a^{5} + 40 \, a^{4} b + 67 \, a^{3} b^{2} + 77 \, a^{2} b^{3} + 57 \, a b^{4} + 15 \, b^{5} - 4 \, {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 8 \, {\left(252 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} d x \cosh\left(d x + c\right)^{5} - 14 \, {\left(8 \, a^{5} + 40 \, a^{4} b + 67 \, a^{3} b^{2} + 77 \, a^{2} b^{3} + 57 \, a b^{4} + 15 \, b^{5} - 4 \, {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(16 \, a^{5} + 48 \, a^{4} b + 19 \, a^{3} b^{2} - 28 \, a^{2} b^{3} - 69 \, a b^{4} - 30 \, b^{5} - 4 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 16 \, a^{5} - 80 \, a^{4} b - 186 \, a^{3} b^{2} - 226 \, a^{2} b^{3} - 134 \, a b^{4} - 30 \, b^{5} - 4 \, {\left(24 \, a^{5} + 56 \, a^{4} b + 48 \, a^{3} b^{2} + 33 \, a^{2} b^{3} + 86 \, a b^{4} + 45 \, b^{5} + 4 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 4 \, {\left(420 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} d x \cosh\left(d x + c\right)^{6} - 24 \, a^{5} - 56 \, a^{4} b - 48 \, a^{3} b^{2} - 33 \, a^{2} b^{3} - 86 \, a b^{4} - 45 \, b^{5} - 35 \, {\left(8 \, a^{5} + 40 \, a^{4} b + 67 \, a^{3} b^{2} + 77 \, a^{2} b^{3} + 57 \, a b^{4} + 15 \, b^{5} - 4 \, {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{4} - 4 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} d x - 15 \, {\left(16 \, a^{5} + 48 \, a^{4} b + 19 \, a^{3} b^{2} - 28 \, a^{2} b^{3} - 69 \, a b^{4} - 30 \, b^{5} - 4 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 16 \, {\left(60 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} d x \cosh\left(d x + c\right)^{7} - 7 \, {\left(8 \, a^{5} + 40 \, a^{4} b + 67 \, a^{3} b^{2} + 77 \, a^{2} b^{3} + 57 \, a b^{4} + 15 \, b^{5} - 4 \, {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{5} - 5 \, {\left(16 \, a^{5} + 48 \, a^{4} b + 19 \, a^{3} b^{2} - 28 \, a^{2} b^{3} - 69 \, a b^{4} - 30 \, b^{5} - 4 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - {\left(24 \, a^{5} + 56 \, a^{4} b + 48 \, a^{3} b^{2} + 33 \, a^{2} b^{3} + 86 \, a b^{4} + 45 \, b^{5} + 4 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - 8 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} d x - 4 \, {\left(16 \, a^{5} + 48 \, a^{4} b + 45 \, a^{3} b^{2} - 36 \, a^{2} b^{3} - 79 \, a b^{4} - 30 \, b^{5} + 2 \, {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(90 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} d x \cosh\left(d x + c\right)^{8} - 14 \, {\left(8 \, a^{5} + 40 \, a^{4} b + 67 \, a^{3} b^{2} + 77 \, a^{2} b^{3} + 57 \, a b^{4} + 15 \, b^{5} - 4 \, {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{6} - 16 \, a^{5} - 48 \, a^{4} b - 45 \, a^{3} b^{2} + 36 \, a^{2} b^{3} + 79 \, a b^{4} + 30 \, b^{5} - 15 \, {\left(16 \, a^{5} + 48 \, a^{4} b + 19 \, a^{3} b^{2} - 28 \, a^{2} b^{3} - 69 \, a b^{4} - 30 \, b^{5} - 4 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{4} - 2 \, {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} d x - 6 \, {\left(24 \, a^{5} + 56 \, a^{4} b + 48 \, a^{3} b^{2} + 33 \, a^{2} b^{3} + 86 \, a b^{4} + 45 \, b^{5} + 4 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} - {\left({\left(35 \, a^{4} b + 112 \, a^{3} b^{2} + 134 \, a^{2} b^{3} + 72 \, a b^{4} + 15 \, b^{5}\right)} \cosh\left(d x + c\right)^{10} + 10 \, {\left(35 \, a^{4} b + 112 \, a^{3} b^{2} + 134 \, a^{2} b^{3} + 72 \, a b^{4} + 15 \, b^{5}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + {\left(35 \, a^{4} b + 112 \, a^{3} b^{2} + 134 \, a^{2} b^{3} + 72 \, a b^{4} + 15 \, b^{5}\right)} \sinh\left(d x + c\right)^{10} + {\left(105 \, a^{4} b + 56 \, a^{3} b^{2} - 214 \, a^{2} b^{3} - 240 \, a b^{4} - 75 \, b^{5}\right)} \cosh\left(d x + c\right)^{8} + {\left(105 \, a^{4} b + 56 \, a^{3} b^{2} - 214 \, a^{2} b^{3} - 240 \, a b^{4} - 75 \, b^{5} + 45 \, {\left(35 \, a^{4} b + 112 \, a^{3} b^{2} + 134 \, a^{2} b^{3} + 72 \, a b^{4} + 15 \, b^{5}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{8} + 8 \, {\left(15 \, {\left(35 \, a^{4} b + 112 \, a^{3} b^{2} + 134 \, a^{2} b^{3} + 72 \, a b^{4} + 15 \, b^{5}\right)} \cosh\left(d x + c\right)^{3} + {\left(105 \, a^{4} b + 56 \, a^{3} b^{2} - 214 \, a^{2} b^{3} - 240 \, a b^{4} - 75 \, b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(35 \, a^{4} b - 28 \, a^{3} b^{2} + 106 \, a^{2} b^{3} + 180 \, a b^{4} + 75 \, b^{5}\right)} \cosh\left(d x + c\right)^{6} + 2 \, {\left(35 \, a^{4} b - 28 \, a^{3} b^{2} + 106 \, a^{2} b^{3} + 180 \, a b^{4} + 75 \, b^{5} + 105 \, {\left(35 \, a^{4} b + 112 \, a^{3} b^{2} + 134 \, a^{2} b^{3} + 72 \, a b^{4} + 15 \, b^{5}\right)} \cosh\left(d x + c\right)^{4} + 14 \, {\left(105 \, a^{4} b + 56 \, a^{3} b^{2} - 214 \, a^{2} b^{3} - 240 \, a b^{4} - 75 \, b^{5}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 4 \, {\left(63 \, {\left(35 \, a^{4} b + 112 \, a^{3} b^{2} + 134 \, a^{2} b^{3} + 72 \, a b^{4} + 15 \, b^{5}\right)} \cosh\left(d x + c\right)^{5} + 14 \, {\left(105 \, a^{4} b + 56 \, a^{3} b^{2} - 214 \, a^{2} b^{3} - 240 \, a b^{4} - 75 \, b^{5}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(35 \, a^{4} b - 28 \, a^{3} b^{2} + 106 \, a^{2} b^{3} + 180 \, a b^{4} + 75 \, b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - 35 \, a^{4} b - 112 \, a^{3} b^{2} - 134 \, a^{2} b^{3} - 72 \, a b^{4} - 15 \, b^{5} - 2 \, {\left(35 \, a^{4} b - 28 \, a^{3} b^{2} + 106 \, a^{2} b^{3} + 180 \, a b^{4} + 75 \, b^{5}\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(105 \, {\left(35 \, a^{4} b + 112 \, a^{3} b^{2} + 134 \, a^{2} b^{3} + 72 \, a b^{4} + 15 \, b^{5}\right)} \cosh\left(d x + c\right)^{6} - 35 \, a^{4} b + 28 \, a^{3} b^{2} - 106 \, a^{2} b^{3} - 180 \, a b^{4} - 75 \, b^{5} + 35 \, {\left(105 \, a^{4} b + 56 \, a^{3} b^{2} - 214 \, a^{2} b^{3} - 240 \, a b^{4} - 75 \, b^{5}\right)} \cosh\left(d x + c\right)^{4} + 15 \, {\left(35 \, a^{4} b - 28 \, a^{3} b^{2} + 106 \, a^{2} b^{3} + 180 \, a b^{4} + 75 \, b^{5}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(15 \, {\left(35 \, a^{4} b + 112 \, a^{3} b^{2} + 134 \, a^{2} b^{3} + 72 \, a b^{4} + 15 \, b^{5}\right)} \cosh\left(d x + c\right)^{7} + 7 \, {\left(105 \, a^{4} b + 56 \, a^{3} b^{2} - 214 \, a^{2} b^{3} - 240 \, a b^{4} - 75 \, b^{5}\right)} \cosh\left(d x + c\right)^{5} + 5 \, {\left(35 \, a^{4} b - 28 \, a^{3} b^{2} + 106 \, a^{2} b^{3} + 180 \, a b^{4} + 75 \, b^{5}\right)} \cosh\left(d x + c\right)^{3} - {\left(35 \, a^{4} b - 28 \, a^{3} b^{2} + 106 \, a^{2} b^{3} + 180 \, a b^{4} + 75 \, b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} - {\left(105 \, a^{4} b + 56 \, a^{3} b^{2} - 214 \, a^{2} b^{3} - 240 \, a b^{4} - 75 \, b^{5}\right)} \cosh\left(d x + c\right)^{2} + {\left(45 \, {\left(35 \, a^{4} b + 112 \, a^{3} b^{2} + 134 \, a^{2} b^{3} + 72 \, a b^{4} + 15 \, b^{5}\right)} \cosh\left(d x + c\right)^{8} + 28 \, {\left(105 \, a^{4} b + 56 \, a^{3} b^{2} - 214 \, a^{2} b^{3} - 240 \, a b^{4} - 75 \, b^{5}\right)} \cosh\left(d x + c\right)^{6} - 105 \, a^{4} b - 56 \, a^{3} b^{2} + 214 \, a^{2} b^{3} + 240 \, a b^{4} + 75 \, b^{5} + 30 \, {\left(35 \, a^{4} b - 28 \, a^{3} b^{2} + 106 \, a^{2} b^{3} + 180 \, a b^{4} + 75 \, b^{5}\right)} \cosh\left(d x + c\right)^{4} - 12 \, {\left(35 \, a^{4} b - 28 \, a^{3} b^{2} + 106 \, a^{2} b^{3} + 180 \, a b^{4} + 75 \, b^{5}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 2 \, {\left(5 \, {\left(35 \, a^{4} b + 112 \, a^{3} b^{2} + 134 \, a^{2} b^{3} + 72 \, a b^{4} + 15 \, b^{5}\right)} \cosh\left(d x + c\right)^{9} + 4 \, {\left(105 \, a^{4} b + 56 \, a^{3} b^{2} - 214 \, a^{2} b^{3} - 240 \, a b^{4} - 75 \, b^{5}\right)} \cosh\left(d x + c\right)^{7} + 6 \, {\left(35 \, a^{4} b - 28 \, a^{3} b^{2} + 106 \, a^{2} b^{3} + 180 \, a b^{4} + 75 \, b^{5}\right)} \cosh\left(d x + c\right)^{5} - 4 \, {\left(35 \, a^{4} b - 28 \, a^{3} b^{2} + 106 \, a^{2} b^{3} + 180 \, a b^{4} + 75 \, b^{5}\right)} \cosh\left(d x + c\right)^{3} - {\left(105 \, a^{4} b + 56 \, a^{3} b^{2} - 214 \, a^{2} b^{3} - 240 \, a b^{4} - 75 \, b^{5}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \sqrt{\frac{b}{a}} \arctan\left(\frac{{\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} + a - b\right)} \sqrt{\frac{b}{a}}}{2 \, b}\right) + 8 \, {\left(10 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} d x \cosh\left(d x + c\right)^{9} - 2 \, {\left(8 \, a^{5} + 40 \, a^{4} b + 67 \, a^{3} b^{2} + 77 \, a^{2} b^{3} + 57 \, a b^{4} + 15 \, b^{5} - 4 \, {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{7} - 3 \, {\left(16 \, a^{5} + 48 \, a^{4} b + 19 \, a^{3} b^{2} - 28 \, a^{2} b^{3} - 69 \, a b^{4} - 30 \, b^{5} - 4 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{5} - 2 \, {\left(24 \, a^{5} + 56 \, a^{4} b + 48 \, a^{3} b^{2} + 33 \, a^{2} b^{3} + 86 \, a b^{4} + 45 \, b^{5} + 4 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{3} - {\left(16 \, a^{5} + 48 \, a^{4} b + 45 \, a^{3} b^{2} - 36 \, a^{2} b^{3} - 79 \, a b^{4} - 30 \, b^{5} + 2 \, {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{8 \, {\left({\left(a^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{10} + 10 \, {\left(a^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + {\left(a^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \sinh\left(d x + c\right)^{10} + {\left(3 \, a^{8} + 7 \, a^{7} b - 2 \, a^{6} b^{2} - 18 \, a^{5} b^{3} - 17 \, a^{4} b^{4} - 5 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{8} + {\left(45 \, {\left(a^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(3 \, a^{8} + 7 \, a^{7} b - 2 \, a^{6} b^{2} - 18 \, a^{5} b^{3} - 17 \, a^{4} b^{4} - 5 \, a^{3} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{8} + 2 \, {\left(a^{8} + a^{7} b + 2 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 5 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{6} + 8 \, {\left(15 \, {\left(a^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(3 \, a^{8} + 7 \, a^{7} b - 2 \, a^{6} b^{2} - 18 \, a^{5} b^{3} - 17 \, a^{4} b^{4} - 5 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 2 \, {\left(105 \, {\left(a^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 14 \, {\left(3 \, a^{8} + 7 \, a^{7} b - 2 \, a^{6} b^{2} - 18 \, a^{5} b^{3} - 17 \, a^{4} b^{4} - 5 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{8} + a^{7} b + 2 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 5 \, a^{3} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{6} - 2 \, {\left(a^{8} + a^{7} b + 2 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 5 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 4 \, {\left(63 \, {\left(a^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{5} + 14 \, {\left(3 \, a^{8} + 7 \, a^{7} b - 2 \, a^{6} b^{2} - 18 \, a^{5} b^{3} - 17 \, a^{4} b^{4} - 5 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + 3 \, {\left(a^{8} + a^{7} b + 2 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 5 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(105 \, {\left(a^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{6} + 35 \, {\left(3 \, a^{8} + 7 \, a^{7} b - 2 \, a^{6} b^{2} - 18 \, a^{5} b^{3} - 17 \, a^{4} b^{4} - 5 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 15 \, {\left(a^{8} + a^{7} b + 2 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 5 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{8} + a^{7} b + 2 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 5 \, a^{3} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{4} - {\left(3 \, a^{8} + 7 \, a^{7} b - 2 \, a^{6} b^{2} - 18 \, a^{5} b^{3} - 17 \, a^{4} b^{4} - 5 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + 8 \, {\left(15 \, {\left(a^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{7} + 7 \, {\left(3 \, a^{8} + 7 \, a^{7} b - 2 \, a^{6} b^{2} - 18 \, a^{5} b^{3} - 17 \, a^{4} b^{4} - 5 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{5} + 5 \, {\left(a^{8} + a^{7} b + 2 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 5 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a^{8} + a^{7} b + 2 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 5 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + {\left(45 \, {\left(a^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{8} + 28 \, {\left(3 \, a^{8} + 7 \, a^{7} b - 2 \, a^{6} b^{2} - 18 \, a^{5} b^{3} - 17 \, a^{4} b^{4} - 5 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{6} + 30 \, {\left(a^{8} + a^{7} b + 2 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 5 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{4} - 12 \, {\left(a^{8} + a^{7} b + 2 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 5 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{2} - {\left(3 \, a^{8} + 7 \, a^{7} b - 2 \, a^{6} b^{2} - 18 \, a^{5} b^{3} - 17 \, a^{4} b^{4} - 5 \, a^{3} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{2} - {\left(a^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} d + 2 \, {\left(5 \, {\left(a^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{9} + 4 \, {\left(3 \, a^{8} + 7 \, a^{7} b - 2 \, a^{6} b^{2} - 18 \, a^{5} b^{3} - 17 \, a^{4} b^{4} - 5 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{7} + 6 \, {\left(a^{8} + a^{7} b + 2 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 5 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{5} - 4 \, {\left(a^{8} + a^{7} b + 2 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 5 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)^{3} - {\left(3 \, a^{8} + 7 \, a^{7} b - 2 \, a^{6} b^{2} - 18 \, a^{5} b^{3} - 17 \, a^{4} b^{4} - 5 \, a^{3} b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}\right]"," ",0,"[1/16*(16*(a^5 + 2*a^4*b + a^3*b^2)*d*x*cosh(d*x + c)^10 + 160*(a^5 + 2*a^4*b + a^3*b^2)*d*x*cosh(d*x + c)*sinh(d*x + c)^9 + 16*(a^5 + 2*a^4*b + a^3*b^2)*d*x*sinh(d*x + c)^10 - 4*(8*a^5 + 40*a^4*b + 67*a^3*b^2 + 77*a^2*b^3 + 57*a*b^4 + 15*b^5 - 4*(3*a^5 - 2*a^4*b - 5*a^3*b^2)*d*x)*cosh(d*x + c)^8 - 4*(8*a^5 + 40*a^4*b + 67*a^3*b^2 + 77*a^2*b^3 + 57*a*b^4 + 15*b^5 - 180*(a^5 + 2*a^4*b + a^3*b^2)*d*x*cosh(d*x + c)^2 - 4*(3*a^5 - 2*a^4*b - 5*a^3*b^2)*d*x)*sinh(d*x + c)^8 + 32*(60*(a^5 + 2*a^4*b + a^3*b^2)*d*x*cosh(d*x + c)^3 - (8*a^5 + 40*a^4*b + 67*a^3*b^2 + 77*a^2*b^3 + 57*a*b^4 + 15*b^5 - 4*(3*a^5 - 2*a^4*b - 5*a^3*b^2)*d*x)*cosh(d*x + c))*sinh(d*x + c)^7 - 8*(16*a^5 + 48*a^4*b + 19*a^3*b^2 - 28*a^2*b^3 - 69*a*b^4 - 30*b^5 - 4*(a^5 - 2*a^4*b + 5*a^3*b^2)*d*x)*cosh(d*x + c)^6 + 8*(420*(a^5 + 2*a^4*b + a^3*b^2)*d*x*cosh(d*x + c)^4 - 16*a^5 - 48*a^4*b - 19*a^3*b^2 + 28*a^2*b^3 + 69*a*b^4 + 30*b^5 + 4*(a^5 - 2*a^4*b + 5*a^3*b^2)*d*x - 14*(8*a^5 + 40*a^4*b + 67*a^3*b^2 + 77*a^2*b^3 + 57*a*b^4 + 15*b^5 - 4*(3*a^5 - 2*a^4*b - 5*a^3*b^2)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 16*(252*(a^5 + 2*a^4*b + a^3*b^2)*d*x*cosh(d*x + c)^5 - 14*(8*a^5 + 40*a^4*b + 67*a^3*b^2 + 77*a^2*b^3 + 57*a*b^4 + 15*b^5 - 4*(3*a^5 - 2*a^4*b - 5*a^3*b^2)*d*x)*cosh(d*x + c)^3 - 3*(16*a^5 + 48*a^4*b + 19*a^3*b^2 - 28*a^2*b^3 - 69*a*b^4 - 30*b^5 - 4*(a^5 - 2*a^4*b + 5*a^3*b^2)*d*x)*cosh(d*x + c))*sinh(d*x + c)^5 - 32*a^5 - 160*a^4*b - 372*a^3*b^2 - 452*a^2*b^3 - 268*a*b^4 - 60*b^5 - 8*(24*a^5 + 56*a^4*b + 48*a^3*b^2 + 33*a^2*b^3 + 86*a*b^4 + 45*b^5 + 4*(a^5 - 2*a^4*b + 5*a^3*b^2)*d*x)*cosh(d*x + c)^4 + 8*(420*(a^5 + 2*a^4*b + a^3*b^2)*d*x*cosh(d*x + c)^6 - 24*a^5 - 56*a^4*b - 48*a^3*b^2 - 33*a^2*b^3 - 86*a*b^4 - 45*b^5 - 35*(8*a^5 + 40*a^4*b + 67*a^3*b^2 + 77*a^2*b^3 + 57*a*b^4 + 15*b^5 - 4*(3*a^5 - 2*a^4*b - 5*a^3*b^2)*d*x)*cosh(d*x + c)^4 - 4*(a^5 - 2*a^4*b + 5*a^3*b^2)*d*x - 15*(16*a^5 + 48*a^4*b + 19*a^3*b^2 - 28*a^2*b^3 - 69*a*b^4 - 30*b^5 - 4*(a^5 - 2*a^4*b + 5*a^3*b^2)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 32*(60*(a^5 + 2*a^4*b + a^3*b^2)*d*x*cosh(d*x + c)^7 - 7*(8*a^5 + 40*a^4*b + 67*a^3*b^2 + 77*a^2*b^3 + 57*a*b^4 + 15*b^5 - 4*(3*a^5 - 2*a^4*b - 5*a^3*b^2)*d*x)*cosh(d*x + c)^5 - 5*(16*a^5 + 48*a^4*b + 19*a^3*b^2 - 28*a^2*b^3 - 69*a*b^4 - 30*b^5 - 4*(a^5 - 2*a^4*b + 5*a^3*b^2)*d*x)*cosh(d*x + c)^3 - (24*a^5 + 56*a^4*b + 48*a^3*b^2 + 33*a^2*b^3 + 86*a*b^4 + 45*b^5 + 4*(a^5 - 2*a^4*b + 5*a^3*b^2)*d*x)*cosh(d*x + c))*sinh(d*x + c)^3 - 16*(a^5 + 2*a^4*b + a^3*b^2)*d*x - 8*(16*a^5 + 48*a^4*b + 45*a^3*b^2 - 36*a^2*b^3 - 79*a*b^4 - 30*b^5 + 2*(3*a^5 - 2*a^4*b - 5*a^3*b^2)*d*x)*cosh(d*x + c)^2 + 8*(90*(a^5 + 2*a^4*b + a^3*b^2)*d*x*cosh(d*x + c)^8 - 14*(8*a^5 + 40*a^4*b + 67*a^3*b^2 + 77*a^2*b^3 + 57*a*b^4 + 15*b^5 - 4*(3*a^5 - 2*a^4*b - 5*a^3*b^2)*d*x)*cosh(d*x + c)^6 - 16*a^5 - 48*a^4*b - 45*a^3*b^2 + 36*a^2*b^3 + 79*a*b^4 + 30*b^5 - 15*(16*a^5 + 48*a^4*b + 19*a^3*b^2 - 28*a^2*b^3 - 69*a*b^4 - 30*b^5 - 4*(a^5 - 2*a^4*b + 5*a^3*b^2)*d*x)*cosh(d*x + c)^4 - 2*(3*a^5 - 2*a^4*b - 5*a^3*b^2)*d*x - 6*(24*a^5 + 56*a^4*b + 48*a^3*b^2 + 33*a^2*b^3 + 86*a*b^4 + 45*b^5 + 4*(a^5 - 2*a^4*b + 5*a^3*b^2)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + ((35*a^4*b + 112*a^3*b^2 + 134*a^2*b^3 + 72*a*b^4 + 15*b^5)*cosh(d*x + c)^10 + 10*(35*a^4*b + 112*a^3*b^2 + 134*a^2*b^3 + 72*a*b^4 + 15*b^5)*cosh(d*x + c)*sinh(d*x + c)^9 + (35*a^4*b + 112*a^3*b^2 + 134*a^2*b^3 + 72*a*b^4 + 15*b^5)*sinh(d*x + c)^10 + (105*a^4*b + 56*a^3*b^2 - 214*a^2*b^3 - 240*a*b^4 - 75*b^5)*cosh(d*x + c)^8 + (105*a^4*b + 56*a^3*b^2 - 214*a^2*b^3 - 240*a*b^4 - 75*b^5 + 45*(35*a^4*b + 112*a^3*b^2 + 134*a^2*b^3 + 72*a*b^4 + 15*b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 8*(15*(35*a^4*b + 112*a^3*b^2 + 134*a^2*b^3 + 72*a*b^4 + 15*b^5)*cosh(d*x + c)^3 + (105*a^4*b + 56*a^3*b^2 - 214*a^2*b^3 - 240*a*b^4 - 75*b^5)*cosh(d*x + c))*sinh(d*x + c)^7 + 2*(35*a^4*b - 28*a^3*b^2 + 106*a^2*b^3 + 180*a*b^4 + 75*b^5)*cosh(d*x + c)^6 + 2*(35*a^4*b - 28*a^3*b^2 + 106*a^2*b^3 + 180*a*b^4 + 75*b^5 + 105*(35*a^4*b + 112*a^3*b^2 + 134*a^2*b^3 + 72*a*b^4 + 15*b^5)*cosh(d*x + c)^4 + 14*(105*a^4*b + 56*a^3*b^2 - 214*a^2*b^3 - 240*a*b^4 - 75*b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 4*(63*(35*a^4*b + 112*a^3*b^2 + 134*a^2*b^3 + 72*a*b^4 + 15*b^5)*cosh(d*x + c)^5 + 14*(105*a^4*b + 56*a^3*b^2 - 214*a^2*b^3 - 240*a*b^4 - 75*b^5)*cosh(d*x + c)^3 + 3*(35*a^4*b - 28*a^3*b^2 + 106*a^2*b^3 + 180*a*b^4 + 75*b^5)*cosh(d*x + c))*sinh(d*x + c)^5 - 35*a^4*b - 112*a^3*b^2 - 134*a^2*b^3 - 72*a*b^4 - 15*b^5 - 2*(35*a^4*b - 28*a^3*b^2 + 106*a^2*b^3 + 180*a*b^4 + 75*b^5)*cosh(d*x + c)^4 + 2*(105*(35*a^4*b + 112*a^3*b^2 + 134*a^2*b^3 + 72*a*b^4 + 15*b^5)*cosh(d*x + c)^6 - 35*a^4*b + 28*a^3*b^2 - 106*a^2*b^3 - 180*a*b^4 - 75*b^5 + 35*(105*a^4*b + 56*a^3*b^2 - 214*a^2*b^3 - 240*a*b^4 - 75*b^5)*cosh(d*x + c)^4 + 15*(35*a^4*b - 28*a^3*b^2 + 106*a^2*b^3 + 180*a*b^4 + 75*b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(15*(35*a^4*b + 112*a^3*b^2 + 134*a^2*b^3 + 72*a*b^4 + 15*b^5)*cosh(d*x + c)^7 + 7*(105*a^4*b + 56*a^3*b^2 - 214*a^2*b^3 - 240*a*b^4 - 75*b^5)*cosh(d*x + c)^5 + 5*(35*a^4*b - 28*a^3*b^2 + 106*a^2*b^3 + 180*a*b^4 + 75*b^5)*cosh(d*x + c)^3 - (35*a^4*b - 28*a^3*b^2 + 106*a^2*b^3 + 180*a*b^4 + 75*b^5)*cosh(d*x + c))*sinh(d*x + c)^3 - (105*a^4*b + 56*a^3*b^2 - 214*a^2*b^3 - 240*a*b^4 - 75*b^5)*cosh(d*x + c)^2 + (45*(35*a^4*b + 112*a^3*b^2 + 134*a^2*b^3 + 72*a*b^4 + 15*b^5)*cosh(d*x + c)^8 + 28*(105*a^4*b + 56*a^3*b^2 - 214*a^2*b^3 - 240*a*b^4 - 75*b^5)*cosh(d*x + c)^6 - 105*a^4*b - 56*a^3*b^2 + 214*a^2*b^3 + 240*a*b^4 + 75*b^5 + 30*(35*a^4*b - 28*a^3*b^2 + 106*a^2*b^3 + 180*a*b^4 + 75*b^5)*cosh(d*x + c)^4 - 12*(35*a^4*b - 28*a^3*b^2 + 106*a^2*b^3 + 180*a*b^4 + 75*b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 2*(5*(35*a^4*b + 112*a^3*b^2 + 134*a^2*b^3 + 72*a*b^4 + 15*b^5)*cosh(d*x + c)^9 + 4*(105*a^4*b + 56*a^3*b^2 - 214*a^2*b^3 - 240*a*b^4 - 75*b^5)*cosh(d*x + c)^7 + 6*(35*a^4*b - 28*a^3*b^2 + 106*a^2*b^3 + 180*a*b^4 + 75*b^5)*cosh(d*x + c)^5 - 4*(35*a^4*b - 28*a^3*b^2 + 106*a^2*b^3 + 180*a*b^4 + 75*b^5)*cosh(d*x + c)^3 - (105*a^4*b + 56*a^3*b^2 - 214*a^2*b^3 - 240*a*b^4 - 75*b^5)*cosh(d*x + c))*sinh(d*x + c))*sqrt(-b/a)*log(((a^2 + 2*a*b + b^2)*cosh(d*x + c)^4 + 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 + 2*(a^2 - b^2)*cosh(d*x + c)^2 + 2*(3*(a^2 + 2*a*b + b^2)*cosh(d*x + c)^2 + a^2 - b^2)*sinh(d*x + c)^2 + a^2 - 6*a*b + b^2 + 4*((a^2 + 2*a*b + b^2)*cosh(d*x + c)^3 + (a^2 - b^2)*cosh(d*x + c))*sinh(d*x + c) - 4*((a^2 + a*b)*cosh(d*x + c)^2 + 2*(a^2 + a*b)*cosh(d*x + c)*sinh(d*x + c) + (a^2 + a*b)*sinh(d*x + c)^2 + a^2 - a*b)*sqrt(-b/a))/((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)) + 16*(10*(a^5 + 2*a^4*b + a^3*b^2)*d*x*cosh(d*x + c)^9 - 2*(8*a^5 + 40*a^4*b + 67*a^3*b^2 + 77*a^2*b^3 + 57*a*b^4 + 15*b^5 - 4*(3*a^5 - 2*a^4*b - 5*a^3*b^2)*d*x)*cosh(d*x + c)^7 - 3*(16*a^5 + 48*a^4*b + 19*a^3*b^2 - 28*a^2*b^3 - 69*a*b^4 - 30*b^5 - 4*(a^5 - 2*a^4*b + 5*a^3*b^2)*d*x)*cosh(d*x + c)^5 - 2*(24*a^5 + 56*a^4*b + 48*a^3*b^2 + 33*a^2*b^3 + 86*a*b^4 + 45*b^5 + 4*(a^5 - 2*a^4*b + 5*a^3*b^2)*d*x)*cosh(d*x + c)^3 - (16*a^5 + 48*a^4*b + 45*a^3*b^2 - 36*a^2*b^3 - 79*a*b^4 - 30*b^5 + 2*(3*a^5 - 2*a^4*b - 5*a^3*b^2)*d*x)*cosh(d*x + c))*sinh(d*x + c))/((a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)^10 + 10*(a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)*sinh(d*x + c)^9 + (a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*d*sinh(d*x + c)^10 + (3*a^8 + 7*a^7*b - 2*a^6*b^2 - 18*a^5*b^3 - 17*a^4*b^4 - 5*a^3*b^5)*d*cosh(d*x + c)^8 + (45*(a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)^2 + (3*a^8 + 7*a^7*b - 2*a^6*b^2 - 18*a^5*b^3 - 17*a^4*b^4 - 5*a^3*b^5)*d)*sinh(d*x + c)^8 + 2*(a^8 + a^7*b + 2*a^6*b^2 + 10*a^5*b^3 + 13*a^4*b^4 + 5*a^3*b^5)*d*cosh(d*x + c)^6 + 8*(15*(a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)^3 + (3*a^8 + 7*a^7*b - 2*a^6*b^2 - 18*a^5*b^3 - 17*a^4*b^4 - 5*a^3*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^7 + 2*(105*(a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)^4 + 14*(3*a^8 + 7*a^7*b - 2*a^6*b^2 - 18*a^5*b^3 - 17*a^4*b^4 - 5*a^3*b^5)*d*cosh(d*x + c)^2 + (a^8 + a^7*b + 2*a^6*b^2 + 10*a^5*b^3 + 13*a^4*b^4 + 5*a^3*b^5)*d)*sinh(d*x + c)^6 - 2*(a^8 + a^7*b + 2*a^6*b^2 + 10*a^5*b^3 + 13*a^4*b^4 + 5*a^3*b^5)*d*cosh(d*x + c)^4 + 4*(63*(a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)^5 + 14*(3*a^8 + 7*a^7*b - 2*a^6*b^2 - 18*a^5*b^3 - 17*a^4*b^4 - 5*a^3*b^5)*d*cosh(d*x + c)^3 + 3*(a^8 + a^7*b + 2*a^6*b^2 + 10*a^5*b^3 + 13*a^4*b^4 + 5*a^3*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(105*(a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)^6 + 35*(3*a^8 + 7*a^7*b - 2*a^6*b^2 - 18*a^5*b^3 - 17*a^4*b^4 - 5*a^3*b^5)*d*cosh(d*x + c)^4 + 15*(a^8 + a^7*b + 2*a^6*b^2 + 10*a^5*b^3 + 13*a^4*b^4 + 5*a^3*b^5)*d*cosh(d*x + c)^2 - (a^8 + a^7*b + 2*a^6*b^2 + 10*a^5*b^3 + 13*a^4*b^4 + 5*a^3*b^5)*d)*sinh(d*x + c)^4 - (3*a^8 + 7*a^7*b - 2*a^6*b^2 - 18*a^5*b^3 - 17*a^4*b^4 - 5*a^3*b^5)*d*cosh(d*x + c)^2 + 8*(15*(a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)^7 + 7*(3*a^8 + 7*a^7*b - 2*a^6*b^2 - 18*a^5*b^3 - 17*a^4*b^4 - 5*a^3*b^5)*d*cosh(d*x + c)^5 + 5*(a^8 + a^7*b + 2*a^6*b^2 + 10*a^5*b^3 + 13*a^4*b^4 + 5*a^3*b^5)*d*cosh(d*x + c)^3 - (a^8 + a^7*b + 2*a^6*b^2 + 10*a^5*b^3 + 13*a^4*b^4 + 5*a^3*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^3 + (45*(a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)^8 + 28*(3*a^8 + 7*a^7*b - 2*a^6*b^2 - 18*a^5*b^3 - 17*a^4*b^4 - 5*a^3*b^5)*d*cosh(d*x + c)^6 + 30*(a^8 + a^7*b + 2*a^6*b^2 + 10*a^5*b^3 + 13*a^4*b^4 + 5*a^3*b^5)*d*cosh(d*x + c)^4 - 12*(a^8 + a^7*b + 2*a^6*b^2 + 10*a^5*b^3 + 13*a^4*b^4 + 5*a^3*b^5)*d*cosh(d*x + c)^2 - (3*a^8 + 7*a^7*b - 2*a^6*b^2 - 18*a^5*b^3 - 17*a^4*b^4 - 5*a^3*b^5)*d)*sinh(d*x + c)^2 - (a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*d + 2*(5*(a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)^9 + 4*(3*a^8 + 7*a^7*b - 2*a^6*b^2 - 18*a^5*b^3 - 17*a^4*b^4 - 5*a^3*b^5)*d*cosh(d*x + c)^7 + 6*(a^8 + a^7*b + 2*a^6*b^2 + 10*a^5*b^3 + 13*a^4*b^4 + 5*a^3*b^5)*d*cosh(d*x + c)^5 - 4*(a^8 + a^7*b + 2*a^6*b^2 + 10*a^5*b^3 + 13*a^4*b^4 + 5*a^3*b^5)*d*cosh(d*x + c)^3 - (3*a^8 + 7*a^7*b - 2*a^6*b^2 - 18*a^5*b^3 - 17*a^4*b^4 - 5*a^3*b^5)*d*cosh(d*x + c))*sinh(d*x + c)), 1/8*(8*(a^5 + 2*a^4*b + a^3*b^2)*d*x*cosh(d*x + c)^10 + 80*(a^5 + 2*a^4*b + a^3*b^2)*d*x*cosh(d*x + c)*sinh(d*x + c)^9 + 8*(a^5 + 2*a^4*b + a^3*b^2)*d*x*sinh(d*x + c)^10 - 2*(8*a^5 + 40*a^4*b + 67*a^3*b^2 + 77*a^2*b^3 + 57*a*b^4 + 15*b^5 - 4*(3*a^5 - 2*a^4*b - 5*a^3*b^2)*d*x)*cosh(d*x + c)^8 - 2*(8*a^5 + 40*a^4*b + 67*a^3*b^2 + 77*a^2*b^3 + 57*a*b^4 + 15*b^5 - 180*(a^5 + 2*a^4*b + a^3*b^2)*d*x*cosh(d*x + c)^2 - 4*(3*a^5 - 2*a^4*b - 5*a^3*b^2)*d*x)*sinh(d*x + c)^8 + 16*(60*(a^5 + 2*a^4*b + a^3*b^2)*d*x*cosh(d*x + c)^3 - (8*a^5 + 40*a^4*b + 67*a^3*b^2 + 77*a^2*b^3 + 57*a*b^4 + 15*b^5 - 4*(3*a^5 - 2*a^4*b - 5*a^3*b^2)*d*x)*cosh(d*x + c))*sinh(d*x + c)^7 - 4*(16*a^5 + 48*a^4*b + 19*a^3*b^2 - 28*a^2*b^3 - 69*a*b^4 - 30*b^5 - 4*(a^5 - 2*a^4*b + 5*a^3*b^2)*d*x)*cosh(d*x + c)^6 + 4*(420*(a^5 + 2*a^4*b + a^3*b^2)*d*x*cosh(d*x + c)^4 - 16*a^5 - 48*a^4*b - 19*a^3*b^2 + 28*a^2*b^3 + 69*a*b^4 + 30*b^5 + 4*(a^5 - 2*a^4*b + 5*a^3*b^2)*d*x - 14*(8*a^5 + 40*a^4*b + 67*a^3*b^2 + 77*a^2*b^3 + 57*a*b^4 + 15*b^5 - 4*(3*a^5 - 2*a^4*b - 5*a^3*b^2)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 8*(252*(a^5 + 2*a^4*b + a^3*b^2)*d*x*cosh(d*x + c)^5 - 14*(8*a^5 + 40*a^4*b + 67*a^3*b^2 + 77*a^2*b^3 + 57*a*b^4 + 15*b^5 - 4*(3*a^5 - 2*a^4*b - 5*a^3*b^2)*d*x)*cosh(d*x + c)^3 - 3*(16*a^5 + 48*a^4*b + 19*a^3*b^2 - 28*a^2*b^3 - 69*a*b^4 - 30*b^5 - 4*(a^5 - 2*a^4*b + 5*a^3*b^2)*d*x)*cosh(d*x + c))*sinh(d*x + c)^5 - 16*a^5 - 80*a^4*b - 186*a^3*b^2 - 226*a^2*b^3 - 134*a*b^4 - 30*b^5 - 4*(24*a^5 + 56*a^4*b + 48*a^3*b^2 + 33*a^2*b^3 + 86*a*b^4 + 45*b^5 + 4*(a^5 - 2*a^4*b + 5*a^3*b^2)*d*x)*cosh(d*x + c)^4 + 4*(420*(a^5 + 2*a^4*b + a^3*b^2)*d*x*cosh(d*x + c)^6 - 24*a^5 - 56*a^4*b - 48*a^3*b^2 - 33*a^2*b^3 - 86*a*b^4 - 45*b^5 - 35*(8*a^5 + 40*a^4*b + 67*a^3*b^2 + 77*a^2*b^3 + 57*a*b^4 + 15*b^5 - 4*(3*a^5 - 2*a^4*b - 5*a^3*b^2)*d*x)*cosh(d*x + c)^4 - 4*(a^5 - 2*a^4*b + 5*a^3*b^2)*d*x - 15*(16*a^5 + 48*a^4*b + 19*a^3*b^2 - 28*a^2*b^3 - 69*a*b^4 - 30*b^5 - 4*(a^5 - 2*a^4*b + 5*a^3*b^2)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 16*(60*(a^5 + 2*a^4*b + a^3*b^2)*d*x*cosh(d*x + c)^7 - 7*(8*a^5 + 40*a^4*b + 67*a^3*b^2 + 77*a^2*b^3 + 57*a*b^4 + 15*b^5 - 4*(3*a^5 - 2*a^4*b - 5*a^3*b^2)*d*x)*cosh(d*x + c)^5 - 5*(16*a^5 + 48*a^4*b + 19*a^3*b^2 - 28*a^2*b^3 - 69*a*b^4 - 30*b^5 - 4*(a^5 - 2*a^4*b + 5*a^3*b^2)*d*x)*cosh(d*x + c)^3 - (24*a^5 + 56*a^4*b + 48*a^3*b^2 + 33*a^2*b^3 + 86*a*b^4 + 45*b^5 + 4*(a^5 - 2*a^4*b + 5*a^3*b^2)*d*x)*cosh(d*x + c))*sinh(d*x + c)^3 - 8*(a^5 + 2*a^4*b + a^3*b^2)*d*x - 4*(16*a^5 + 48*a^4*b + 45*a^3*b^2 - 36*a^2*b^3 - 79*a*b^4 - 30*b^5 + 2*(3*a^5 - 2*a^4*b - 5*a^3*b^2)*d*x)*cosh(d*x + c)^2 + 4*(90*(a^5 + 2*a^4*b + a^3*b^2)*d*x*cosh(d*x + c)^8 - 14*(8*a^5 + 40*a^4*b + 67*a^3*b^2 + 77*a^2*b^3 + 57*a*b^4 + 15*b^5 - 4*(3*a^5 - 2*a^4*b - 5*a^3*b^2)*d*x)*cosh(d*x + c)^6 - 16*a^5 - 48*a^4*b - 45*a^3*b^2 + 36*a^2*b^3 + 79*a*b^4 + 30*b^5 - 15*(16*a^5 + 48*a^4*b + 19*a^3*b^2 - 28*a^2*b^3 - 69*a*b^4 - 30*b^5 - 4*(a^5 - 2*a^4*b + 5*a^3*b^2)*d*x)*cosh(d*x + c)^4 - 2*(3*a^5 - 2*a^4*b - 5*a^3*b^2)*d*x - 6*(24*a^5 + 56*a^4*b + 48*a^3*b^2 + 33*a^2*b^3 + 86*a*b^4 + 45*b^5 + 4*(a^5 - 2*a^4*b + 5*a^3*b^2)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - ((35*a^4*b + 112*a^3*b^2 + 134*a^2*b^3 + 72*a*b^4 + 15*b^5)*cosh(d*x + c)^10 + 10*(35*a^4*b + 112*a^3*b^2 + 134*a^2*b^3 + 72*a*b^4 + 15*b^5)*cosh(d*x + c)*sinh(d*x + c)^9 + (35*a^4*b + 112*a^3*b^2 + 134*a^2*b^3 + 72*a*b^4 + 15*b^5)*sinh(d*x + c)^10 + (105*a^4*b + 56*a^3*b^2 - 214*a^2*b^3 - 240*a*b^4 - 75*b^5)*cosh(d*x + c)^8 + (105*a^4*b + 56*a^3*b^2 - 214*a^2*b^3 - 240*a*b^4 - 75*b^5 + 45*(35*a^4*b + 112*a^3*b^2 + 134*a^2*b^3 + 72*a*b^4 + 15*b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 8*(15*(35*a^4*b + 112*a^3*b^2 + 134*a^2*b^3 + 72*a*b^4 + 15*b^5)*cosh(d*x + c)^3 + (105*a^4*b + 56*a^3*b^2 - 214*a^2*b^3 - 240*a*b^4 - 75*b^5)*cosh(d*x + c))*sinh(d*x + c)^7 + 2*(35*a^4*b - 28*a^3*b^2 + 106*a^2*b^3 + 180*a*b^4 + 75*b^5)*cosh(d*x + c)^6 + 2*(35*a^4*b - 28*a^3*b^2 + 106*a^2*b^3 + 180*a*b^4 + 75*b^5 + 105*(35*a^4*b + 112*a^3*b^2 + 134*a^2*b^3 + 72*a*b^4 + 15*b^5)*cosh(d*x + c)^4 + 14*(105*a^4*b + 56*a^3*b^2 - 214*a^2*b^3 - 240*a*b^4 - 75*b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 4*(63*(35*a^4*b + 112*a^3*b^2 + 134*a^2*b^3 + 72*a*b^4 + 15*b^5)*cosh(d*x + c)^5 + 14*(105*a^4*b + 56*a^3*b^2 - 214*a^2*b^3 - 240*a*b^4 - 75*b^5)*cosh(d*x + c)^3 + 3*(35*a^4*b - 28*a^3*b^2 + 106*a^2*b^3 + 180*a*b^4 + 75*b^5)*cosh(d*x + c))*sinh(d*x + c)^5 - 35*a^4*b - 112*a^3*b^2 - 134*a^2*b^3 - 72*a*b^4 - 15*b^5 - 2*(35*a^4*b - 28*a^3*b^2 + 106*a^2*b^3 + 180*a*b^4 + 75*b^5)*cosh(d*x + c)^4 + 2*(105*(35*a^4*b + 112*a^3*b^2 + 134*a^2*b^3 + 72*a*b^4 + 15*b^5)*cosh(d*x + c)^6 - 35*a^4*b + 28*a^3*b^2 - 106*a^2*b^3 - 180*a*b^4 - 75*b^5 + 35*(105*a^4*b + 56*a^3*b^2 - 214*a^2*b^3 - 240*a*b^4 - 75*b^5)*cosh(d*x + c)^4 + 15*(35*a^4*b - 28*a^3*b^2 + 106*a^2*b^3 + 180*a*b^4 + 75*b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(15*(35*a^4*b + 112*a^3*b^2 + 134*a^2*b^3 + 72*a*b^4 + 15*b^5)*cosh(d*x + c)^7 + 7*(105*a^4*b + 56*a^3*b^2 - 214*a^2*b^3 - 240*a*b^4 - 75*b^5)*cosh(d*x + c)^5 + 5*(35*a^4*b - 28*a^3*b^2 + 106*a^2*b^3 + 180*a*b^4 + 75*b^5)*cosh(d*x + c)^3 - (35*a^4*b - 28*a^3*b^2 + 106*a^2*b^3 + 180*a*b^4 + 75*b^5)*cosh(d*x + c))*sinh(d*x + c)^3 - (105*a^4*b + 56*a^3*b^2 - 214*a^2*b^3 - 240*a*b^4 - 75*b^5)*cosh(d*x + c)^2 + (45*(35*a^4*b + 112*a^3*b^2 + 134*a^2*b^3 + 72*a*b^4 + 15*b^5)*cosh(d*x + c)^8 + 28*(105*a^4*b + 56*a^3*b^2 - 214*a^2*b^3 - 240*a*b^4 - 75*b^5)*cosh(d*x + c)^6 - 105*a^4*b - 56*a^3*b^2 + 214*a^2*b^3 + 240*a*b^4 + 75*b^5 + 30*(35*a^4*b - 28*a^3*b^2 + 106*a^2*b^3 + 180*a*b^4 + 75*b^5)*cosh(d*x + c)^4 - 12*(35*a^4*b - 28*a^3*b^2 + 106*a^2*b^3 + 180*a*b^4 + 75*b^5)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 2*(5*(35*a^4*b + 112*a^3*b^2 + 134*a^2*b^3 + 72*a*b^4 + 15*b^5)*cosh(d*x + c)^9 + 4*(105*a^4*b + 56*a^3*b^2 - 214*a^2*b^3 - 240*a*b^4 - 75*b^5)*cosh(d*x + c)^7 + 6*(35*a^4*b - 28*a^3*b^2 + 106*a^2*b^3 + 180*a*b^4 + 75*b^5)*cosh(d*x + c)^5 - 4*(35*a^4*b - 28*a^3*b^2 + 106*a^2*b^3 + 180*a*b^4 + 75*b^5)*cosh(d*x + c)^3 - (105*a^4*b + 56*a^3*b^2 - 214*a^2*b^3 - 240*a*b^4 - 75*b^5)*cosh(d*x + c))*sinh(d*x + c))*sqrt(b/a)*arctan(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 + a - b)*sqrt(b/a)/b) + 8*(10*(a^5 + 2*a^4*b + a^3*b^2)*d*x*cosh(d*x + c)^9 - 2*(8*a^5 + 40*a^4*b + 67*a^3*b^2 + 77*a^2*b^3 + 57*a*b^4 + 15*b^5 - 4*(3*a^5 - 2*a^4*b - 5*a^3*b^2)*d*x)*cosh(d*x + c)^7 - 3*(16*a^5 + 48*a^4*b + 19*a^3*b^2 - 28*a^2*b^3 - 69*a*b^4 - 30*b^5 - 4*(a^5 - 2*a^4*b + 5*a^3*b^2)*d*x)*cosh(d*x + c)^5 - 2*(24*a^5 + 56*a^4*b + 48*a^3*b^2 + 33*a^2*b^3 + 86*a*b^4 + 45*b^5 + 4*(a^5 - 2*a^4*b + 5*a^3*b^2)*d*x)*cosh(d*x + c)^3 - (16*a^5 + 48*a^4*b + 45*a^3*b^2 - 36*a^2*b^3 - 79*a*b^4 - 30*b^5 + 2*(3*a^5 - 2*a^4*b - 5*a^3*b^2)*d*x)*cosh(d*x + c))*sinh(d*x + c))/((a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)^10 + 10*(a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)*sinh(d*x + c)^9 + (a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*d*sinh(d*x + c)^10 + (3*a^8 + 7*a^7*b - 2*a^6*b^2 - 18*a^5*b^3 - 17*a^4*b^4 - 5*a^3*b^5)*d*cosh(d*x + c)^8 + (45*(a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)^2 + (3*a^8 + 7*a^7*b - 2*a^6*b^2 - 18*a^5*b^3 - 17*a^4*b^4 - 5*a^3*b^5)*d)*sinh(d*x + c)^8 + 2*(a^8 + a^7*b + 2*a^6*b^2 + 10*a^5*b^3 + 13*a^4*b^4 + 5*a^3*b^5)*d*cosh(d*x + c)^6 + 8*(15*(a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)^3 + (3*a^8 + 7*a^7*b - 2*a^6*b^2 - 18*a^5*b^3 - 17*a^4*b^4 - 5*a^3*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^7 + 2*(105*(a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)^4 + 14*(3*a^8 + 7*a^7*b - 2*a^6*b^2 - 18*a^5*b^3 - 17*a^4*b^4 - 5*a^3*b^5)*d*cosh(d*x + c)^2 + (a^8 + a^7*b + 2*a^6*b^2 + 10*a^5*b^3 + 13*a^4*b^4 + 5*a^3*b^5)*d)*sinh(d*x + c)^6 - 2*(a^8 + a^7*b + 2*a^6*b^2 + 10*a^5*b^3 + 13*a^4*b^4 + 5*a^3*b^5)*d*cosh(d*x + c)^4 + 4*(63*(a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)^5 + 14*(3*a^8 + 7*a^7*b - 2*a^6*b^2 - 18*a^5*b^3 - 17*a^4*b^4 - 5*a^3*b^5)*d*cosh(d*x + c)^3 + 3*(a^8 + a^7*b + 2*a^6*b^2 + 10*a^5*b^3 + 13*a^4*b^4 + 5*a^3*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(105*(a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)^6 + 35*(3*a^8 + 7*a^7*b - 2*a^6*b^2 - 18*a^5*b^3 - 17*a^4*b^4 - 5*a^3*b^5)*d*cosh(d*x + c)^4 + 15*(a^8 + a^7*b + 2*a^6*b^2 + 10*a^5*b^3 + 13*a^4*b^4 + 5*a^3*b^5)*d*cosh(d*x + c)^2 - (a^8 + a^7*b + 2*a^6*b^2 + 10*a^5*b^3 + 13*a^4*b^4 + 5*a^3*b^5)*d)*sinh(d*x + c)^4 - (3*a^8 + 7*a^7*b - 2*a^6*b^2 - 18*a^5*b^3 - 17*a^4*b^4 - 5*a^3*b^5)*d*cosh(d*x + c)^2 + 8*(15*(a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)^7 + 7*(3*a^8 + 7*a^7*b - 2*a^6*b^2 - 18*a^5*b^3 - 17*a^4*b^4 - 5*a^3*b^5)*d*cosh(d*x + c)^5 + 5*(a^8 + a^7*b + 2*a^6*b^2 + 10*a^5*b^3 + 13*a^4*b^4 + 5*a^3*b^5)*d*cosh(d*x + c)^3 - (a^8 + a^7*b + 2*a^6*b^2 + 10*a^5*b^3 + 13*a^4*b^4 + 5*a^3*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^3 + (45*(a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)^8 + 28*(3*a^8 + 7*a^7*b - 2*a^6*b^2 - 18*a^5*b^3 - 17*a^4*b^4 - 5*a^3*b^5)*d*cosh(d*x + c)^6 + 30*(a^8 + a^7*b + 2*a^6*b^2 + 10*a^5*b^3 + 13*a^4*b^4 + 5*a^3*b^5)*d*cosh(d*x + c)^4 - 12*(a^8 + a^7*b + 2*a^6*b^2 + 10*a^5*b^3 + 13*a^4*b^4 + 5*a^3*b^5)*d*cosh(d*x + c)^2 - (3*a^8 + 7*a^7*b - 2*a^6*b^2 - 18*a^5*b^3 - 17*a^4*b^4 - 5*a^3*b^5)*d)*sinh(d*x + c)^2 - (a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*d + 2*(5*(a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*d*cosh(d*x + c)^9 + 4*(3*a^8 + 7*a^7*b - 2*a^6*b^2 - 18*a^5*b^3 - 17*a^4*b^4 - 5*a^3*b^5)*d*cosh(d*x + c)^7 + 6*(a^8 + a^7*b + 2*a^6*b^2 + 10*a^5*b^3 + 13*a^4*b^4 + 5*a^3*b^5)*d*cosh(d*x + c)^5 - 4*(a^8 + a^7*b + 2*a^6*b^2 + 10*a^5*b^3 + 13*a^4*b^4 + 5*a^3*b^5)*d*cosh(d*x + c)^3 - (3*a^8 + 7*a^7*b - 2*a^6*b^2 - 18*a^5*b^3 - 17*a^4*b^4 - 5*a^3*b^5)*d*cosh(d*x + c))*sinh(d*x + c))]","B",0
199,1,10720,0,1.293065," ","integrate(coth(d*x+c)^3/(a+b*tanh(d*x+c)^2)^3,x, algorithm=""fricas"")","-\frac{2 \, {\left(a^{6} + 2 \, a^{5} b + a^{4} b^{2}\right)} d x \cosh\left(d x + c\right)^{12} + 24 \, {\left(a^{6} + 2 \, a^{5} b + a^{4} b^{2}\right)} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{11} + 2 \, {\left(a^{6} + 2 \, a^{5} b + a^{4} b^{2}\right)} d x \sinh\left(d x + c\right)^{12} + 4 \, {\left(a^{6} + 5 \, a^{5} b + 10 \, a^{4} b^{2} + 14 \, a^{3} b^{3} + 11 \, a^{2} b^{4} + 3 \, a b^{5} + {\left(a^{6} - 2 \, a^{5} b - 3 \, a^{4} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{10} + 4 \, {\left(a^{6} + 5 \, a^{5} b + 10 \, a^{4} b^{2} + 14 \, a^{3} b^{3} + 11 \, a^{2} b^{4} + 3 \, a b^{5} + 33 \, {\left(a^{6} + 2 \, a^{5} b + a^{4} b^{2}\right)} d x \cosh\left(d x + c\right)^{2} + {\left(a^{6} - 2 \, a^{5} b - 3 \, a^{4} b^{2}\right)} d x\right)} \sinh\left(d x + c\right)^{10} + 40 \, {\left(11 \, {\left(a^{6} + 2 \, a^{5} b + a^{4} b^{2}\right)} d x \cosh\left(d x + c\right)^{3} + {\left(a^{6} + 5 \, a^{5} b + 10 \, a^{4} b^{2} + 14 \, a^{3} b^{3} + 11 \, a^{2} b^{4} + 3 \, a b^{5} + {\left(a^{6} - 2 \, a^{5} b - 3 \, a^{4} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} + 2 \, {\left(8 \, a^{6} + 24 \, a^{5} b + 16 \, a^{4} b^{2} - 16 \, a^{3} b^{3} - 52 \, a^{2} b^{4} - 24 \, a b^{5} - {\left(a^{6} + 2 \, a^{5} b - 15 \, a^{4} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{8} + 2 \, {\left(495 \, {\left(a^{6} + 2 \, a^{5} b + a^{4} b^{2}\right)} d x \cosh\left(d x + c\right)^{4} + 8 \, a^{6} + 24 \, a^{5} b + 16 \, a^{4} b^{2} - 16 \, a^{3} b^{3} - 52 \, a^{2} b^{4} - 24 \, a b^{5} - {\left(a^{6} + 2 \, a^{5} b - 15 \, a^{4} b^{2}\right)} d x + 90 \, {\left(a^{6} + 5 \, a^{5} b + 10 \, a^{4} b^{2} + 14 \, a^{3} b^{3} + 11 \, a^{2} b^{4} + 3 \, a b^{5} + {\left(a^{6} - 2 \, a^{5} b - 3 \, a^{4} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{8} + 16 \, {\left(99 \, {\left(a^{6} + 2 \, a^{5} b + a^{4} b^{2}\right)} d x \cosh\left(d x + c\right)^{5} + 30 \, {\left(a^{6} + 5 \, a^{5} b + 10 \, a^{4} b^{2} + 14 \, a^{3} b^{3} + 11 \, a^{2} b^{4} + 3 \, a b^{5} + {\left(a^{6} - 2 \, a^{5} b - 3 \, a^{4} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{6} + 24 \, a^{5} b + 16 \, a^{4} b^{2} - 16 \, a^{3} b^{3} - 52 \, a^{2} b^{4} - 24 \, a b^{5} - {\left(a^{6} + 2 \, a^{5} b - 15 \, a^{4} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 8 \, {\left(3 \, a^{6} + 7 \, a^{5} b + 6 \, a^{4} b^{2} + 2 \, a^{3} b^{3} + 15 \, a^{2} b^{4} + 9 \, a b^{5} - {\left(a^{6} - 2 \, a^{5} b + 5 \, a^{4} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{6} + 8 \, {\left(231 \, {\left(a^{6} + 2 \, a^{5} b + a^{4} b^{2}\right)} d x \cosh\left(d x + c\right)^{6} + 3 \, a^{6} + 7 \, a^{5} b + 6 \, a^{4} b^{2} + 2 \, a^{3} b^{3} + 15 \, a^{2} b^{4} + 9 \, a b^{5} + 105 \, {\left(a^{6} + 5 \, a^{5} b + 10 \, a^{4} b^{2} + 14 \, a^{3} b^{3} + 11 \, a^{2} b^{4} + 3 \, a b^{5} + {\left(a^{6} - 2 \, a^{5} b - 3 \, a^{4} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{4} - {\left(a^{6} - 2 \, a^{5} b + 5 \, a^{4} b^{2}\right)} d x + 7 \, {\left(8 \, a^{6} + 24 \, a^{5} b + 16 \, a^{4} b^{2} - 16 \, a^{3} b^{3} - 52 \, a^{2} b^{4} - 24 \, a b^{5} - {\left(a^{6} + 2 \, a^{5} b - 15 \, a^{4} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 16 \, {\left(99 \, {\left(a^{6} + 2 \, a^{5} b + a^{4} b^{2}\right)} d x \cosh\left(d x + c\right)^{7} + 63 \, {\left(a^{6} + 5 \, a^{5} b + 10 \, a^{4} b^{2} + 14 \, a^{3} b^{3} + 11 \, a^{2} b^{4} + 3 \, a b^{5} + {\left(a^{6} - 2 \, a^{5} b - 3 \, a^{4} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{5} + 7 \, {\left(8 \, a^{6} + 24 \, a^{5} b + 16 \, a^{4} b^{2} - 16 \, a^{3} b^{3} - 52 \, a^{2} b^{4} - 24 \, a b^{5} - {\left(a^{6} + 2 \, a^{5} b - 15 \, a^{4} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(3 \, a^{6} + 7 \, a^{5} b + 6 \, a^{4} b^{2} + 2 \, a^{3} b^{3} + 15 \, a^{2} b^{4} + 9 \, a b^{5} - {\left(a^{6} - 2 \, a^{5} b + 5 \, a^{4} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 2 \, {\left(8 \, a^{6} + 24 \, a^{5} b + 16 \, a^{4} b^{2} - 16 \, a^{3} b^{3} - 52 \, a^{2} b^{4} - 24 \, a b^{5} - {\left(a^{6} + 2 \, a^{5} b - 15 \, a^{4} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + 2 \, {\left(495 \, {\left(a^{6} + 2 \, a^{5} b + a^{4} b^{2}\right)} d x \cosh\left(d x + c\right)^{8} + 420 \, {\left(a^{6} + 5 \, a^{5} b + 10 \, a^{4} b^{2} + 14 \, a^{3} b^{3} + 11 \, a^{2} b^{4} + 3 \, a b^{5} + {\left(a^{6} - 2 \, a^{5} b - 3 \, a^{4} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{6} + 8 \, a^{6} + 24 \, a^{5} b + 16 \, a^{4} b^{2} - 16 \, a^{3} b^{3} - 52 \, a^{2} b^{4} - 24 \, a b^{5} + 70 \, {\left(8 \, a^{6} + 24 \, a^{5} b + 16 \, a^{4} b^{2} - 16 \, a^{3} b^{3} - 52 \, a^{2} b^{4} - 24 \, a b^{5} - {\left(a^{6} + 2 \, a^{5} b - 15 \, a^{4} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{4} - {\left(a^{6} + 2 \, a^{5} b - 15 \, a^{4} b^{2}\right)} d x + 60 \, {\left(3 \, a^{6} + 7 \, a^{5} b + 6 \, a^{4} b^{2} + 2 \, a^{3} b^{3} + 15 \, a^{2} b^{4} + 9 \, a b^{5} - {\left(a^{6} - 2 \, a^{5} b + 5 \, a^{4} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 8 \, {\left(55 \, {\left(a^{6} + 2 \, a^{5} b + a^{4} b^{2}\right)} d x \cosh\left(d x + c\right)^{9} + 60 \, {\left(a^{6} + 5 \, a^{5} b + 10 \, a^{4} b^{2} + 14 \, a^{3} b^{3} + 11 \, a^{2} b^{4} + 3 \, a b^{5} + {\left(a^{6} - 2 \, a^{5} b - 3 \, a^{4} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{7} + 14 \, {\left(8 \, a^{6} + 24 \, a^{5} b + 16 \, a^{4} b^{2} - 16 \, a^{3} b^{3} - 52 \, a^{2} b^{4} - 24 \, a b^{5} - {\left(a^{6} + 2 \, a^{5} b - 15 \, a^{4} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{5} + 20 \, {\left(3 \, a^{6} + 7 \, a^{5} b + 6 \, a^{4} b^{2} + 2 \, a^{3} b^{3} + 15 \, a^{2} b^{4} + 9 \, a b^{5} - {\left(a^{6} - 2 \, a^{5} b + 5 \, a^{4} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + {\left(8 \, a^{6} + 24 \, a^{5} b + 16 \, a^{4} b^{2} - 16 \, a^{3} b^{3} - 52 \, a^{2} b^{4} - 24 \, a b^{5} - {\left(a^{6} + 2 \, a^{5} b - 15 \, a^{4} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(a^{6} + 2 \, a^{5} b + a^{4} b^{2}\right)} d x + 4 \, {\left(a^{6} + 5 \, a^{5} b + 10 \, a^{4} b^{2} + 14 \, a^{3} b^{3} + 11 \, a^{2} b^{4} + 3 \, a b^{5} + {\left(a^{6} - 2 \, a^{5} b - 3 \, a^{4} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{2} + 4 \, {\left(33 \, {\left(a^{6} + 2 \, a^{5} b + a^{4} b^{2}\right)} d x \cosh\left(d x + c\right)^{10} + 45 \, {\left(a^{6} + 5 \, a^{5} b + 10 \, a^{4} b^{2} + 14 \, a^{3} b^{3} + 11 \, a^{2} b^{4} + 3 \, a b^{5} + {\left(a^{6} - 2 \, a^{5} b - 3 \, a^{4} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{8} + 14 \, {\left(8 \, a^{6} + 24 \, a^{5} b + 16 \, a^{4} b^{2} - 16 \, a^{3} b^{3} - 52 \, a^{2} b^{4} - 24 \, a b^{5} - {\left(a^{6} + 2 \, a^{5} b - 15 \, a^{4} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{6} + a^{6} + 5 \, a^{5} b + 10 \, a^{4} b^{2} + 14 \, a^{3} b^{3} + 11 \, a^{2} b^{4} + 3 \, a b^{5} + 30 \, {\left(3 \, a^{6} + 7 \, a^{5} b + 6 \, a^{4} b^{2} + 2 \, a^{3} b^{3} + 15 \, a^{2} b^{4} + 9 \, a b^{5} - {\left(a^{6} - 2 \, a^{5} b + 5 \, a^{4} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{4} + {\left(a^{6} - 2 \, a^{5} b - 3 \, a^{4} b^{2}\right)} d x + 3 \, {\left(8 \, a^{6} + 24 \, a^{5} b + 16 \, a^{4} b^{2} - 16 \, a^{3} b^{3} - 52 \, a^{2} b^{4} - 24 \, a b^{5} - {\left(a^{6} + 2 \, a^{5} b - 15 \, a^{4} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} - {\left({\left(6 \, a^{4} b^{2} + 20 \, a^{3} b^{3} + 25 \, a^{2} b^{4} + 14 \, a b^{5} + 3 \, b^{6}\right)} \cosh\left(d x + c\right)^{12} + 12 \, {\left(6 \, a^{4} b^{2} + 20 \, a^{3} b^{3} + 25 \, a^{2} b^{4} + 14 \, a b^{5} + 3 \, b^{6}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{11} + {\left(6 \, a^{4} b^{2} + 20 \, a^{3} b^{3} + 25 \, a^{2} b^{4} + 14 \, a b^{5} + 3 \, b^{6}\right)} \sinh\left(d x + c\right)^{12} + 2 \, {\left(6 \, a^{4} b^{2} - 4 \, a^{3} b^{3} - 31 \, a^{2} b^{4} - 30 \, a b^{5} - 9 \, b^{6}\right)} \cosh\left(d x + c\right)^{10} + 2 \, {\left(6 \, a^{4} b^{2} - 4 \, a^{3} b^{3} - 31 \, a^{2} b^{4} - 30 \, a b^{5} - 9 \, b^{6} + 33 \, {\left(6 \, a^{4} b^{2} + 20 \, a^{3} b^{3} + 25 \, a^{2} b^{4} + 14 \, a b^{5} + 3 \, b^{6}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{10} + 20 \, {\left(11 \, {\left(6 \, a^{4} b^{2} + 20 \, a^{3} b^{3} + 25 \, a^{2} b^{4} + 14 \, a b^{5} + 3 \, b^{6}\right)} \cosh\left(d x + c\right)^{3} + {\left(6 \, a^{4} b^{2} - 4 \, a^{3} b^{3} - 31 \, a^{2} b^{4} - 30 \, a b^{5} - 9 \, b^{6}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} - {\left(6 \, a^{4} b^{2} + 20 \, a^{3} b^{3} - 71 \, a^{2} b^{4} - 114 \, a b^{5} - 45 \, b^{6}\right)} \cosh\left(d x + c\right)^{8} - {\left(6 \, a^{4} b^{2} + 20 \, a^{3} b^{3} - 71 \, a^{2} b^{4} - 114 \, a b^{5} - 45 \, b^{6} - 495 \, {\left(6 \, a^{4} b^{2} + 20 \, a^{3} b^{3} + 25 \, a^{2} b^{4} + 14 \, a b^{5} + 3 \, b^{6}\right)} \cosh\left(d x + c\right)^{4} - 90 \, {\left(6 \, a^{4} b^{2} - 4 \, a^{3} b^{3} - 31 \, a^{2} b^{4} - 30 \, a b^{5} - 9 \, b^{6}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{8} + 8 \, {\left(99 \, {\left(6 \, a^{4} b^{2} + 20 \, a^{3} b^{3} + 25 \, a^{2} b^{4} + 14 \, a b^{5} + 3 \, b^{6}\right)} \cosh\left(d x + c\right)^{5} + 30 \, {\left(6 \, a^{4} b^{2} - 4 \, a^{3} b^{3} - 31 \, a^{2} b^{4} - 30 \, a b^{5} - 9 \, b^{6}\right)} \cosh\left(d x + c\right)^{3} - {\left(6 \, a^{4} b^{2} + 20 \, a^{3} b^{3} - 71 \, a^{2} b^{4} - 114 \, a b^{5} - 45 \, b^{6}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} - 4 \, {\left(6 \, a^{4} b^{2} - 4 \, a^{3} b^{3} + 17 \, a^{2} b^{4} + 34 \, a b^{5} + 15 \, b^{6}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(231 \, {\left(6 \, a^{4} b^{2} + 20 \, a^{3} b^{3} + 25 \, a^{2} b^{4} + 14 \, a b^{5} + 3 \, b^{6}\right)} \cosh\left(d x + c\right)^{6} - 6 \, a^{4} b^{2} + 4 \, a^{3} b^{3} - 17 \, a^{2} b^{4} - 34 \, a b^{5} - 15 \, b^{6} + 105 \, {\left(6 \, a^{4} b^{2} - 4 \, a^{3} b^{3} - 31 \, a^{2} b^{4} - 30 \, a b^{5} - 9 \, b^{6}\right)} \cosh\left(d x + c\right)^{4} - 7 \, {\left(6 \, a^{4} b^{2} + 20 \, a^{3} b^{3} - 71 \, a^{2} b^{4} - 114 \, a b^{5} - 45 \, b^{6}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + 6 \, a^{4} b^{2} + 20 \, a^{3} b^{3} + 25 \, a^{2} b^{4} + 14 \, a b^{5} + 3 \, b^{6} + 8 \, {\left(99 \, {\left(6 \, a^{4} b^{2} + 20 \, a^{3} b^{3} + 25 \, a^{2} b^{4} + 14 \, a b^{5} + 3 \, b^{6}\right)} \cosh\left(d x + c\right)^{7} + 63 \, {\left(6 \, a^{4} b^{2} - 4 \, a^{3} b^{3} - 31 \, a^{2} b^{4} - 30 \, a b^{5} - 9 \, b^{6}\right)} \cosh\left(d x + c\right)^{5} - 7 \, {\left(6 \, a^{4} b^{2} + 20 \, a^{3} b^{3} - 71 \, a^{2} b^{4} - 114 \, a b^{5} - 45 \, b^{6}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(6 \, a^{4} b^{2} - 4 \, a^{3} b^{3} + 17 \, a^{2} b^{4} + 34 \, a b^{5} + 15 \, b^{6}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - {\left(6 \, a^{4} b^{2} + 20 \, a^{3} b^{3} - 71 \, a^{2} b^{4} - 114 \, a b^{5} - 45 \, b^{6}\right)} \cosh\left(d x + c\right)^{4} + {\left(495 \, {\left(6 \, a^{4} b^{2} + 20 \, a^{3} b^{3} + 25 \, a^{2} b^{4} + 14 \, a b^{5} + 3 \, b^{6}\right)} \cosh\left(d x + c\right)^{8} + 420 \, {\left(6 \, a^{4} b^{2} - 4 \, a^{3} b^{3} - 31 \, a^{2} b^{4} - 30 \, a b^{5} - 9 \, b^{6}\right)} \cosh\left(d x + c\right)^{6} - 6 \, a^{4} b^{2} - 20 \, a^{3} b^{3} + 71 \, a^{2} b^{4} + 114 \, a b^{5} + 45 \, b^{6} - 70 \, {\left(6 \, a^{4} b^{2} + 20 \, a^{3} b^{3} - 71 \, a^{2} b^{4} - 114 \, a b^{5} - 45 \, b^{6}\right)} \cosh\left(d x + c\right)^{4} - 60 \, {\left(6 \, a^{4} b^{2} - 4 \, a^{3} b^{3} + 17 \, a^{2} b^{4} + 34 \, a b^{5} + 15 \, b^{6}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(55 \, {\left(6 \, a^{4} b^{2} + 20 \, a^{3} b^{3} + 25 \, a^{2} b^{4} + 14 \, a b^{5} + 3 \, b^{6}\right)} \cosh\left(d x + c\right)^{9} + 60 \, {\left(6 \, a^{4} b^{2} - 4 \, a^{3} b^{3} - 31 \, a^{2} b^{4} - 30 \, a b^{5} - 9 \, b^{6}\right)} \cosh\left(d x + c\right)^{7} - 14 \, {\left(6 \, a^{4} b^{2} + 20 \, a^{3} b^{3} - 71 \, a^{2} b^{4} - 114 \, a b^{5} - 45 \, b^{6}\right)} \cosh\left(d x + c\right)^{5} - 20 \, {\left(6 \, a^{4} b^{2} - 4 \, a^{3} b^{3} + 17 \, a^{2} b^{4} + 34 \, a b^{5} + 15 \, b^{6}\right)} \cosh\left(d x + c\right)^{3} - {\left(6 \, a^{4} b^{2} + 20 \, a^{3} b^{3} - 71 \, a^{2} b^{4} - 114 \, a b^{5} - 45 \, b^{6}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(6 \, a^{4} b^{2} - 4 \, a^{3} b^{3} - 31 \, a^{2} b^{4} - 30 \, a b^{5} - 9 \, b^{6}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(33 \, {\left(6 \, a^{4} b^{2} + 20 \, a^{3} b^{3} + 25 \, a^{2} b^{4} + 14 \, a b^{5} + 3 \, b^{6}\right)} \cosh\left(d x + c\right)^{10} + 45 \, {\left(6 \, a^{4} b^{2} - 4 \, a^{3} b^{3} - 31 \, a^{2} b^{4} - 30 \, a b^{5} - 9 \, b^{6}\right)} \cosh\left(d x + c\right)^{8} - 14 \, {\left(6 \, a^{4} b^{2} + 20 \, a^{3} b^{3} - 71 \, a^{2} b^{4} - 114 \, a b^{5} - 45 \, b^{6}\right)} \cosh\left(d x + c\right)^{6} + 6 \, a^{4} b^{2} - 4 \, a^{3} b^{3} - 31 \, a^{2} b^{4} - 30 \, a b^{5} - 9 \, b^{6} - 30 \, {\left(6 \, a^{4} b^{2} - 4 \, a^{3} b^{3} + 17 \, a^{2} b^{4} + 34 \, a b^{5} + 15 \, b^{6}\right)} \cosh\left(d x + c\right)^{4} - 3 \, {\left(6 \, a^{4} b^{2} + 20 \, a^{3} b^{3} - 71 \, a^{2} b^{4} - 114 \, a b^{5} - 45 \, b^{6}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(3 \, {\left(6 \, a^{4} b^{2} + 20 \, a^{3} b^{3} + 25 \, a^{2} b^{4} + 14 \, a b^{5} + 3 \, b^{6}\right)} \cosh\left(d x + c\right)^{11} + 5 \, {\left(6 \, a^{4} b^{2} - 4 \, a^{3} b^{3} - 31 \, a^{2} b^{4} - 30 \, a b^{5} - 9 \, b^{6}\right)} \cosh\left(d x + c\right)^{9} - 2 \, {\left(6 \, a^{4} b^{2} + 20 \, a^{3} b^{3} - 71 \, a^{2} b^{4} - 114 \, a b^{5} - 45 \, b^{6}\right)} \cosh\left(d x + c\right)^{7} - 6 \, {\left(6 \, a^{4} b^{2} - 4 \, a^{3} b^{3} + 17 \, a^{2} b^{4} + 34 \, a b^{5} + 15 \, b^{6}\right)} \cosh\left(d x + c\right)^{5} - {\left(6 \, a^{4} b^{2} + 20 \, a^{3} b^{3} - 71 \, a^{2} b^{4} - 114 \, a b^{5} - 45 \, b^{6}\right)} \cosh\left(d x + c\right)^{3} + {\left(6 \, a^{4} b^{2} - 4 \, a^{3} b^{3} - 31 \, a^{2} b^{4} - 30 \, a b^{5} - 9 \, b^{6}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\frac{2 \, {\left({\left(a + b\right)} \cosh\left(d x + c\right)^{2} + {\left(a + b\right)} \sinh\left(d x + c\right)^{2} + a - b\right)}}{\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}}\right) - 2 \, {\left({\left(a^{6} + 2 \, a^{5} b - 5 \, a^{4} b^{2} - 20 \, a^{3} b^{3} - 25 \, a^{2} b^{4} - 14 \, a b^{5} - 3 \, b^{6}\right)} \cosh\left(d x + c\right)^{12} + 12 \, {\left(a^{6} + 2 \, a^{5} b - 5 \, a^{4} b^{2} - 20 \, a^{3} b^{3} - 25 \, a^{2} b^{4} - 14 \, a b^{5} - 3 \, b^{6}\right)} \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{11} + {\left(a^{6} + 2 \, a^{5} b - 5 \, a^{4} b^{2} - 20 \, a^{3} b^{3} - 25 \, a^{2} b^{4} - 14 \, a b^{5} - 3 \, b^{6}\right)} \sinh\left(d x + c\right)^{12} + 2 \, {\left(a^{6} - 2 \, a^{5} b - 9 \, a^{4} b^{2} + 4 \, a^{3} b^{3} + 31 \, a^{2} b^{4} + 30 \, a b^{5} + 9 \, b^{6}\right)} \cosh\left(d x + c\right)^{10} + 2 \, {\left(a^{6} - 2 \, a^{5} b - 9 \, a^{4} b^{2} + 4 \, a^{3} b^{3} + 31 \, a^{2} b^{4} + 30 \, a b^{5} + 9 \, b^{6} + 33 \, {\left(a^{6} + 2 \, a^{5} b - 5 \, a^{4} b^{2} - 20 \, a^{3} b^{3} - 25 \, a^{2} b^{4} - 14 \, a b^{5} - 3 \, b^{6}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{10} + 20 \, {\left(11 \, {\left(a^{6} + 2 \, a^{5} b - 5 \, a^{4} b^{2} - 20 \, a^{3} b^{3} - 25 \, a^{2} b^{4} - 14 \, a b^{5} - 3 \, b^{6}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{6} - 2 \, a^{5} b - 9 \, a^{4} b^{2} + 4 \, a^{3} b^{3} + 31 \, a^{2} b^{4} + 30 \, a b^{5} + 9 \, b^{6}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} - {\left(a^{6} + 2 \, a^{5} b - 21 \, a^{4} b^{2} - 20 \, a^{3} b^{3} + 71 \, a^{2} b^{4} + 114 \, a b^{5} + 45 \, b^{6}\right)} \cosh\left(d x + c\right)^{8} - {\left(a^{6} + 2 \, a^{5} b - 21 \, a^{4} b^{2} - 20 \, a^{3} b^{3} + 71 \, a^{2} b^{4} + 114 \, a b^{5} + 45 \, b^{6} - 495 \, {\left(a^{6} + 2 \, a^{5} b - 5 \, a^{4} b^{2} - 20 \, a^{3} b^{3} - 25 \, a^{2} b^{4} - 14 \, a b^{5} - 3 \, b^{6}\right)} \cosh\left(d x + c\right)^{4} - 90 \, {\left(a^{6} - 2 \, a^{5} b - 9 \, a^{4} b^{2} + 4 \, a^{3} b^{3} + 31 \, a^{2} b^{4} + 30 \, a b^{5} + 9 \, b^{6}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{8} + 8 \, {\left(99 \, {\left(a^{6} + 2 \, a^{5} b - 5 \, a^{4} b^{2} - 20 \, a^{3} b^{3} - 25 \, a^{2} b^{4} - 14 \, a b^{5} - 3 \, b^{6}\right)} \cosh\left(d x + c\right)^{5} + 30 \, {\left(a^{6} - 2 \, a^{5} b - 9 \, a^{4} b^{2} + 4 \, a^{3} b^{3} + 31 \, a^{2} b^{4} + 30 \, a b^{5} + 9 \, b^{6}\right)} \cosh\left(d x + c\right)^{3} - {\left(a^{6} + 2 \, a^{5} b - 21 \, a^{4} b^{2} - 20 \, a^{3} b^{3} + 71 \, a^{2} b^{4} + 114 \, a b^{5} + 45 \, b^{6}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} - 4 \, {\left(a^{6} - 2 \, a^{5} b - a^{4} b^{2} + 4 \, a^{3} b^{3} - 17 \, a^{2} b^{4} - 34 \, a b^{5} - 15 \, b^{6}\right)} \cosh\left(d x + c\right)^{6} + 4 \, {\left(231 \, {\left(a^{6} + 2 \, a^{5} b - 5 \, a^{4} b^{2} - 20 \, a^{3} b^{3} - 25 \, a^{2} b^{4} - 14 \, a b^{5} - 3 \, b^{6}\right)} \cosh\left(d x + c\right)^{6} - a^{6} + 2 \, a^{5} b + a^{4} b^{2} - 4 \, a^{3} b^{3} + 17 \, a^{2} b^{4} + 34 \, a b^{5} + 15 \, b^{6} + 105 \, {\left(a^{6} - 2 \, a^{5} b - 9 \, a^{4} b^{2} + 4 \, a^{3} b^{3} + 31 \, a^{2} b^{4} + 30 \, a b^{5} + 9 \, b^{6}\right)} \cosh\left(d x + c\right)^{4} - 7 \, {\left(a^{6} + 2 \, a^{5} b - 21 \, a^{4} b^{2} - 20 \, a^{3} b^{3} + 71 \, a^{2} b^{4} + 114 \, a b^{5} + 45 \, b^{6}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{6} + a^{6} + 2 \, a^{5} b - 5 \, a^{4} b^{2} - 20 \, a^{3} b^{3} - 25 \, a^{2} b^{4} - 14 \, a b^{5} - 3 \, b^{6} + 8 \, {\left(99 \, {\left(a^{6} + 2 \, a^{5} b - 5 \, a^{4} b^{2} - 20 \, a^{3} b^{3} - 25 \, a^{2} b^{4} - 14 \, a b^{5} - 3 \, b^{6}\right)} \cosh\left(d x + c\right)^{7} + 63 \, {\left(a^{6} - 2 \, a^{5} b - 9 \, a^{4} b^{2} + 4 \, a^{3} b^{3} + 31 \, a^{2} b^{4} + 30 \, a b^{5} + 9 \, b^{6}\right)} \cosh\left(d x + c\right)^{5} - 7 \, {\left(a^{6} + 2 \, a^{5} b - 21 \, a^{4} b^{2} - 20 \, a^{3} b^{3} + 71 \, a^{2} b^{4} + 114 \, a b^{5} + 45 \, b^{6}\right)} \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{6} - 2 \, a^{5} b - a^{4} b^{2} + 4 \, a^{3} b^{3} - 17 \, a^{2} b^{4} - 34 \, a b^{5} - 15 \, b^{6}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} - {\left(a^{6} + 2 \, a^{5} b - 21 \, a^{4} b^{2} - 20 \, a^{3} b^{3} + 71 \, a^{2} b^{4} + 114 \, a b^{5} + 45 \, b^{6}\right)} \cosh\left(d x + c\right)^{4} + {\left(495 \, {\left(a^{6} + 2 \, a^{5} b - 5 \, a^{4} b^{2} - 20 \, a^{3} b^{3} - 25 \, a^{2} b^{4} - 14 \, a b^{5} - 3 \, b^{6}\right)} \cosh\left(d x + c\right)^{8} + 420 \, {\left(a^{6} - 2 \, a^{5} b - 9 \, a^{4} b^{2} + 4 \, a^{3} b^{3} + 31 \, a^{2} b^{4} + 30 \, a b^{5} + 9 \, b^{6}\right)} \cosh\left(d x + c\right)^{6} - a^{6} - 2 \, a^{5} b + 21 \, a^{4} b^{2} + 20 \, a^{3} b^{3} - 71 \, a^{2} b^{4} - 114 \, a b^{5} - 45 \, b^{6} - 70 \, {\left(a^{6} + 2 \, a^{5} b - 21 \, a^{4} b^{2} - 20 \, a^{3} b^{3} + 71 \, a^{2} b^{4} + 114 \, a b^{5} + 45 \, b^{6}\right)} \cosh\left(d x + c\right)^{4} - 60 \, {\left(a^{6} - 2 \, a^{5} b - a^{4} b^{2} + 4 \, a^{3} b^{3} - 17 \, a^{2} b^{4} - 34 \, a b^{5} - 15 \, b^{6}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{4} + 4 \, {\left(55 \, {\left(a^{6} + 2 \, a^{5} b - 5 \, a^{4} b^{2} - 20 \, a^{3} b^{3} - 25 \, a^{2} b^{4} - 14 \, a b^{5} - 3 \, b^{6}\right)} \cosh\left(d x + c\right)^{9} + 60 \, {\left(a^{6} - 2 \, a^{5} b - 9 \, a^{4} b^{2} + 4 \, a^{3} b^{3} + 31 \, a^{2} b^{4} + 30 \, a b^{5} + 9 \, b^{6}\right)} \cosh\left(d x + c\right)^{7} - 14 \, {\left(a^{6} + 2 \, a^{5} b - 21 \, a^{4} b^{2} - 20 \, a^{3} b^{3} + 71 \, a^{2} b^{4} + 114 \, a b^{5} + 45 \, b^{6}\right)} \cosh\left(d x + c\right)^{5} - 20 \, {\left(a^{6} - 2 \, a^{5} b - a^{4} b^{2} + 4 \, a^{3} b^{3} - 17 \, a^{2} b^{4} - 34 \, a b^{5} - 15 \, b^{6}\right)} \cosh\left(d x + c\right)^{3} - {\left(a^{6} + 2 \, a^{5} b - 21 \, a^{4} b^{2} - 20 \, a^{3} b^{3} + 71 \, a^{2} b^{4} + 114 \, a b^{5} + 45 \, b^{6}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(a^{6} - 2 \, a^{5} b - 9 \, a^{4} b^{2} + 4 \, a^{3} b^{3} + 31 \, a^{2} b^{4} + 30 \, a b^{5} + 9 \, b^{6}\right)} \cosh\left(d x + c\right)^{2} + 2 \, {\left(33 \, {\left(a^{6} + 2 \, a^{5} b - 5 \, a^{4} b^{2} - 20 \, a^{3} b^{3} - 25 \, a^{2} b^{4} - 14 \, a b^{5} - 3 \, b^{6}\right)} \cosh\left(d x + c\right)^{10} + 45 \, {\left(a^{6} - 2 \, a^{5} b - 9 \, a^{4} b^{2} + 4 \, a^{3} b^{3} + 31 \, a^{2} b^{4} + 30 \, a b^{5} + 9 \, b^{6}\right)} \cosh\left(d x + c\right)^{8} - 14 \, {\left(a^{6} + 2 \, a^{5} b - 21 \, a^{4} b^{2} - 20 \, a^{3} b^{3} + 71 \, a^{2} b^{4} + 114 \, a b^{5} + 45 \, b^{6}\right)} \cosh\left(d x + c\right)^{6} + a^{6} - 2 \, a^{5} b - 9 \, a^{4} b^{2} + 4 \, a^{3} b^{3} + 31 \, a^{2} b^{4} + 30 \, a b^{5} + 9 \, b^{6} - 30 \, {\left(a^{6} - 2 \, a^{5} b - a^{4} b^{2} + 4 \, a^{3} b^{3} - 17 \, a^{2} b^{4} - 34 \, a b^{5} - 15 \, b^{6}\right)} \cosh\left(d x + c\right)^{4} - 3 \, {\left(a^{6} + 2 \, a^{5} b - 21 \, a^{4} b^{2} - 20 \, a^{3} b^{3} + 71 \, a^{2} b^{4} + 114 \, a b^{5} + 45 \, b^{6}\right)} \cosh\left(d x + c\right)^{2}\right)} \sinh\left(d x + c\right)^{2} + 4 \, {\left(3 \, {\left(a^{6} + 2 \, a^{5} b - 5 \, a^{4} b^{2} - 20 \, a^{3} b^{3} - 25 \, a^{2} b^{4} - 14 \, a b^{5} - 3 \, b^{6}\right)} \cosh\left(d x + c\right)^{11} + 5 \, {\left(a^{6} - 2 \, a^{5} b - 9 \, a^{4} b^{2} + 4 \, a^{3} b^{3} + 31 \, a^{2} b^{4} + 30 \, a b^{5} + 9 \, b^{6}\right)} \cosh\left(d x + c\right)^{9} - 2 \, {\left(a^{6} + 2 \, a^{5} b - 21 \, a^{4} b^{2} - 20 \, a^{3} b^{3} + 71 \, a^{2} b^{4} + 114 \, a b^{5} + 45 \, b^{6}\right)} \cosh\left(d x + c\right)^{7} - 6 \, {\left(a^{6} - 2 \, a^{5} b - a^{4} b^{2} + 4 \, a^{3} b^{3} - 17 \, a^{2} b^{4} - 34 \, a b^{5} - 15 \, b^{6}\right)} \cosh\left(d x + c\right)^{5} - {\left(a^{6} + 2 \, a^{5} b - 21 \, a^{4} b^{2} - 20 \, a^{3} b^{3} + 71 \, a^{2} b^{4} + 114 \, a b^{5} + 45 \, b^{6}\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{6} - 2 \, a^{5} b - 9 \, a^{4} b^{2} + 4 \, a^{3} b^{3} + 31 \, a^{2} b^{4} + 30 \, a b^{5} + 9 \, b^{6}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)} \log\left(\frac{2 \, \sinh\left(d x + c\right)}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) + 8 \, {\left(3 \, {\left(a^{6} + 2 \, a^{5} b + a^{4} b^{2}\right)} d x \cosh\left(d x + c\right)^{11} + 5 \, {\left(a^{6} + 5 \, a^{5} b + 10 \, a^{4} b^{2} + 14 \, a^{3} b^{3} + 11 \, a^{2} b^{4} + 3 \, a b^{5} + {\left(a^{6} - 2 \, a^{5} b - 3 \, a^{4} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{9} + 2 \, {\left(8 \, a^{6} + 24 \, a^{5} b + 16 \, a^{4} b^{2} - 16 \, a^{3} b^{3} - 52 \, a^{2} b^{4} - 24 \, a b^{5} - {\left(a^{6} + 2 \, a^{5} b - 15 \, a^{4} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{7} + 6 \, {\left(3 \, a^{6} + 7 \, a^{5} b + 6 \, a^{4} b^{2} + 2 \, a^{3} b^{3} + 15 \, a^{2} b^{4} + 9 \, a b^{5} - {\left(a^{6} - 2 \, a^{5} b + 5 \, a^{4} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{5} + {\left(8 \, a^{6} + 24 \, a^{5} b + 16 \, a^{4} b^{2} - 16 \, a^{3} b^{3} - 52 \, a^{2} b^{4} - 24 \, a b^{5} - {\left(a^{6} + 2 \, a^{5} b - 15 \, a^{4} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)^{3} + {\left(a^{6} + 5 \, a^{5} b + 10 \, a^{4} b^{2} + 14 \, a^{3} b^{3} + 11 \, a^{2} b^{4} + 3 \, a b^{5} + {\left(a^{6} - 2 \, a^{5} b - 3 \, a^{4} b^{2}\right)} d x\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)}{2 \, {\left({\left(a^{9} + 5 \, a^{8} b + 10 \, a^{7} b^{2} + 10 \, a^{6} b^{3} + 5 \, a^{5} b^{4} + a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{12} + 12 \, {\left(a^{9} + 5 \, a^{8} b + 10 \, a^{7} b^{2} + 10 \, a^{6} b^{3} + 5 \, a^{5} b^{4} + a^{4} b^{5}\right)} d \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{11} + {\left(a^{9} + 5 \, a^{8} b + 10 \, a^{7} b^{2} + 10 \, a^{6} b^{3} + 5 \, a^{5} b^{4} + a^{4} b^{5}\right)} d \sinh\left(d x + c\right)^{12} + 2 \, {\left(a^{9} + a^{8} b - 6 \, a^{7} b^{2} - 14 \, a^{6} b^{3} - 11 \, a^{5} b^{4} - 3 \, a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{10} + 2 \, {\left(33 \, {\left(a^{9} + 5 \, a^{8} b + 10 \, a^{7} b^{2} + 10 \, a^{6} b^{3} + 5 \, a^{5} b^{4} + a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{9} + a^{8} b - 6 \, a^{7} b^{2} - 14 \, a^{6} b^{3} - 11 \, a^{5} b^{4} - 3 \, a^{4} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{10} - {\left(a^{9} + 5 \, a^{8} b - 6 \, a^{7} b^{2} - 38 \, a^{6} b^{3} - 43 \, a^{5} b^{4} - 15 \, a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{8} + 20 \, {\left(11 \, {\left(a^{9} + 5 \, a^{8} b + 10 \, a^{7} b^{2} + 10 \, a^{6} b^{3} + 5 \, a^{5} b^{4} + a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{9} + a^{8} b - 6 \, a^{7} b^{2} - 14 \, a^{6} b^{3} - 11 \, a^{5} b^{4} - 3 \, a^{4} b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{9} + {\left(495 \, {\left(a^{9} + 5 \, a^{8} b + 10 \, a^{7} b^{2} + 10 \, a^{6} b^{3} + 5 \, a^{5} b^{4} + a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 90 \, {\left(a^{9} + a^{8} b - 6 \, a^{7} b^{2} - 14 \, a^{6} b^{3} - 11 \, a^{5} b^{4} - 3 \, a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{9} + 5 \, a^{8} b - 6 \, a^{7} b^{2} - 38 \, a^{6} b^{3} - 43 \, a^{5} b^{4} - 15 \, a^{4} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{8} - 4 \, {\left(a^{9} + a^{8} b + 2 \, a^{7} b^{2} + 10 \, a^{6} b^{3} + 13 \, a^{5} b^{4} + 5 \, a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{6} + 8 \, {\left(99 \, {\left(a^{9} + 5 \, a^{8} b + 10 \, a^{7} b^{2} + 10 \, a^{6} b^{3} + 5 \, a^{5} b^{4} + a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{5} + 30 \, {\left(a^{9} + a^{8} b - 6 \, a^{7} b^{2} - 14 \, a^{6} b^{3} - 11 \, a^{5} b^{4} - 3 \, a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a^{9} + 5 \, a^{8} b - 6 \, a^{7} b^{2} - 38 \, a^{6} b^{3} - 43 \, a^{5} b^{4} - 15 \, a^{4} b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 4 \, {\left(231 \, {\left(a^{9} + 5 \, a^{8} b + 10 \, a^{7} b^{2} + 10 \, a^{6} b^{3} + 5 \, a^{5} b^{4} + a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{6} + 105 \, {\left(a^{9} + a^{8} b - 6 \, a^{7} b^{2} - 14 \, a^{6} b^{3} - 11 \, a^{5} b^{4} - 3 \, a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{4} - 7 \, {\left(a^{9} + 5 \, a^{8} b - 6 \, a^{7} b^{2} - 38 \, a^{6} b^{3} - 43 \, a^{5} b^{4} - 15 \, a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{9} + a^{8} b + 2 \, a^{7} b^{2} + 10 \, a^{6} b^{3} + 13 \, a^{5} b^{4} + 5 \, a^{4} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{6} - {\left(a^{9} + 5 \, a^{8} b - 6 \, a^{7} b^{2} - 38 \, a^{6} b^{3} - 43 \, a^{5} b^{4} - 15 \, a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{4} + 8 \, {\left(99 \, {\left(a^{9} + 5 \, a^{8} b + 10 \, a^{7} b^{2} + 10 \, a^{6} b^{3} + 5 \, a^{5} b^{4} + a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{7} + 63 \, {\left(a^{9} + a^{8} b - 6 \, a^{7} b^{2} - 14 \, a^{6} b^{3} - 11 \, a^{5} b^{4} - 3 \, a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{5} - 7 \, {\left(a^{9} + 5 \, a^{8} b - 6 \, a^{7} b^{2} - 38 \, a^{6} b^{3} - 43 \, a^{5} b^{4} - 15 \, a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{3} - 3 \, {\left(a^{9} + a^{8} b + 2 \, a^{7} b^{2} + 10 \, a^{6} b^{3} + 13 \, 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} + {\left(495 \, {\left(a^{9} + 5 \, a^{8} b + 10 \, a^{7} b^{2} + 10 \, a^{6} b^{3} + 5 \, a^{5} b^{4} + a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{8} + 420 \, {\left(a^{9} + a^{8} b - 6 \, a^{7} b^{2} - 14 \, a^{6} b^{3} - 11 \, a^{5} b^{4} - 3 \, a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{6} - 70 \, {\left(a^{9} + 5 \, a^{8} b - 6 \, a^{7} b^{2} - 38 \, a^{6} b^{3} - 43 \, a^{5} b^{4} - 15 \, a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{4} - 60 \, {\left(a^{9} + a^{8} b + 2 \, a^{7} b^{2} + 10 \, a^{6} b^{3} + 13 \, a^{5} b^{4} + 5 \, a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{2} - {\left(a^{9} + 5 \, a^{8} b - 6 \, a^{7} b^{2} - 38 \, a^{6} b^{3} - 43 \, a^{5} b^{4} - 15 \, a^{4} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{4} + 2 \, {\left(a^{9} + a^{8} b - 6 \, a^{7} b^{2} - 14 \, a^{6} b^{3} - 11 \, a^{5} b^{4} - 3 \, a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + 4 \, {\left(55 \, {\left(a^{9} + 5 \, a^{8} b + 10 \, a^{7} b^{2} + 10 \, a^{6} b^{3} + 5 \, a^{5} b^{4} + a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{9} + 60 \, {\left(a^{9} + a^{8} b - 6 \, a^{7} b^{2} - 14 \, a^{6} b^{3} - 11 \, a^{5} b^{4} - 3 \, a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{7} - 14 \, {\left(a^{9} + 5 \, a^{8} b - 6 \, a^{7} b^{2} - 38 \, a^{6} b^{3} - 43 \, a^{5} b^{4} - 15 \, a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{5} - 20 \, {\left(a^{9} + a^{8} b + 2 \, a^{7} b^{2} + 10 \, a^{6} b^{3} + 13 \, a^{5} b^{4} + 5 \, a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{3} - {\left(a^{9} + 5 \, a^{8} b - 6 \, a^{7} b^{2} - 38 \, a^{6} b^{3} - 43 \, a^{5} b^{4} - 15 \, a^{4} b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 2 \, {\left(33 \, {\left(a^{9} + 5 \, a^{8} b + 10 \, a^{7} b^{2} + 10 \, a^{6} b^{3} + 5 \, a^{5} b^{4} + a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{10} + 45 \, {\left(a^{9} + a^{8} b - 6 \, a^{7} b^{2} - 14 \, a^{6} b^{3} - 11 \, a^{5} b^{4} - 3 \, a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{8} - 14 \, {\left(a^{9} + 5 \, a^{8} b - 6 \, a^{7} b^{2} - 38 \, a^{6} b^{3} - 43 \, a^{5} b^{4} - 15 \, a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{6} - 30 \, {\left(a^{9} + a^{8} b + 2 \, a^{7} b^{2} + 10 \, a^{6} b^{3} + 13 \, a^{5} b^{4} + 5 \, a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{4} - 3 \, {\left(a^{9} + 5 \, a^{8} b - 6 \, a^{7} b^{2} - 38 \, a^{6} b^{3} - 43 \, a^{5} b^{4} - 15 \, a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{2} + {\left(a^{9} + a^{8} b - 6 \, a^{7} b^{2} - 14 \, a^{6} b^{3} - 11 \, a^{5} b^{4} - 3 \, a^{4} b^{5}\right)} d\right)} \sinh\left(d x + c\right)^{2} + {\left(a^{9} + 5 \, a^{8} b + 10 \, a^{7} b^{2} + 10 \, a^{6} b^{3} + 5 \, a^{5} b^{4} + a^{4} b^{5}\right)} d + 4 \, {\left(3 \, {\left(a^{9} + 5 \, a^{8} b + 10 \, a^{7} b^{2} + 10 \, a^{6} b^{3} + 5 \, a^{5} b^{4} + a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{11} + 5 \, {\left(a^{9} + a^{8} b - 6 \, a^{7} b^{2} - 14 \, a^{6} b^{3} - 11 \, a^{5} b^{4} - 3 \, a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{9} - 2 \, {\left(a^{9} + 5 \, a^{8} b - 6 \, a^{7} b^{2} - 38 \, a^{6} b^{3} - 43 \, a^{5} b^{4} - 15 \, a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{7} - 6 \, {\left(a^{9} + a^{8} b + 2 \, a^{7} b^{2} + 10 \, a^{6} b^{3} + 13 \, a^{5} b^{4} + 5 \, a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{5} - {\left(a^{9} + 5 \, a^{8} b - 6 \, a^{7} b^{2} - 38 \, a^{6} b^{3} - 43 \, a^{5} b^{4} - 15 \, a^{4} b^{5}\right)} d \cosh\left(d x + c\right)^{3} + {\left(a^{9} + a^{8} b - 6 \, a^{7} b^{2} - 14 \, a^{6} b^{3} - 11 \, a^{5} b^{4} - 3 \, a^{4} b^{5}\right)} d \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)\right)}}"," ",0,"-1/2*(2*(a^6 + 2*a^5*b + a^4*b^2)*d*x*cosh(d*x + c)^12 + 24*(a^6 + 2*a^5*b + a^4*b^2)*d*x*cosh(d*x + c)*sinh(d*x + c)^11 + 2*(a^6 + 2*a^5*b + a^4*b^2)*d*x*sinh(d*x + c)^12 + 4*(a^6 + 5*a^5*b + 10*a^4*b^2 + 14*a^3*b^3 + 11*a^2*b^4 + 3*a*b^5 + (a^6 - 2*a^5*b - 3*a^4*b^2)*d*x)*cosh(d*x + c)^10 + 4*(a^6 + 5*a^5*b + 10*a^4*b^2 + 14*a^3*b^3 + 11*a^2*b^4 + 3*a*b^5 + 33*(a^6 + 2*a^5*b + a^4*b^2)*d*x*cosh(d*x + c)^2 + (a^6 - 2*a^5*b - 3*a^4*b^2)*d*x)*sinh(d*x + c)^10 + 40*(11*(a^6 + 2*a^5*b + a^4*b^2)*d*x*cosh(d*x + c)^3 + (a^6 + 5*a^5*b + 10*a^4*b^2 + 14*a^3*b^3 + 11*a^2*b^4 + 3*a*b^5 + (a^6 - 2*a^5*b - 3*a^4*b^2)*d*x)*cosh(d*x + c))*sinh(d*x + c)^9 + 2*(8*a^6 + 24*a^5*b + 16*a^4*b^2 - 16*a^3*b^3 - 52*a^2*b^4 - 24*a*b^5 - (a^6 + 2*a^5*b - 15*a^4*b^2)*d*x)*cosh(d*x + c)^8 + 2*(495*(a^6 + 2*a^5*b + a^4*b^2)*d*x*cosh(d*x + c)^4 + 8*a^6 + 24*a^5*b + 16*a^4*b^2 - 16*a^3*b^3 - 52*a^2*b^4 - 24*a*b^5 - (a^6 + 2*a^5*b - 15*a^4*b^2)*d*x + 90*(a^6 + 5*a^5*b + 10*a^4*b^2 + 14*a^3*b^3 + 11*a^2*b^4 + 3*a*b^5 + (a^6 - 2*a^5*b - 3*a^4*b^2)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 16*(99*(a^6 + 2*a^5*b + a^4*b^2)*d*x*cosh(d*x + c)^5 + 30*(a^6 + 5*a^5*b + 10*a^4*b^2 + 14*a^3*b^3 + 11*a^2*b^4 + 3*a*b^5 + (a^6 - 2*a^5*b - 3*a^4*b^2)*d*x)*cosh(d*x + c)^3 + (8*a^6 + 24*a^5*b + 16*a^4*b^2 - 16*a^3*b^3 - 52*a^2*b^4 - 24*a*b^5 - (a^6 + 2*a^5*b - 15*a^4*b^2)*d*x)*cosh(d*x + c))*sinh(d*x + c)^7 + 8*(3*a^6 + 7*a^5*b + 6*a^4*b^2 + 2*a^3*b^3 + 15*a^2*b^4 + 9*a*b^5 - (a^6 - 2*a^5*b + 5*a^4*b^2)*d*x)*cosh(d*x + c)^6 + 8*(231*(a^6 + 2*a^5*b + a^4*b^2)*d*x*cosh(d*x + c)^6 + 3*a^6 + 7*a^5*b + 6*a^4*b^2 + 2*a^3*b^3 + 15*a^2*b^4 + 9*a*b^5 + 105*(a^6 + 5*a^5*b + 10*a^4*b^2 + 14*a^3*b^3 + 11*a^2*b^4 + 3*a*b^5 + (a^6 - 2*a^5*b - 3*a^4*b^2)*d*x)*cosh(d*x + c)^4 - (a^6 - 2*a^5*b + 5*a^4*b^2)*d*x + 7*(8*a^6 + 24*a^5*b + 16*a^4*b^2 - 16*a^3*b^3 - 52*a^2*b^4 - 24*a*b^5 - (a^6 + 2*a^5*b - 15*a^4*b^2)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 16*(99*(a^6 + 2*a^5*b + a^4*b^2)*d*x*cosh(d*x + c)^7 + 63*(a^6 + 5*a^5*b + 10*a^4*b^2 + 14*a^3*b^3 + 11*a^2*b^4 + 3*a*b^5 + (a^6 - 2*a^5*b - 3*a^4*b^2)*d*x)*cosh(d*x + c)^5 + 7*(8*a^6 + 24*a^5*b + 16*a^4*b^2 - 16*a^3*b^3 - 52*a^2*b^4 - 24*a*b^5 - (a^6 + 2*a^5*b - 15*a^4*b^2)*d*x)*cosh(d*x + c)^3 + 3*(3*a^6 + 7*a^5*b + 6*a^4*b^2 + 2*a^3*b^3 + 15*a^2*b^4 + 9*a*b^5 - (a^6 - 2*a^5*b + 5*a^4*b^2)*d*x)*cosh(d*x + c))*sinh(d*x + c)^5 + 2*(8*a^6 + 24*a^5*b + 16*a^4*b^2 - 16*a^3*b^3 - 52*a^2*b^4 - 24*a*b^5 - (a^6 + 2*a^5*b - 15*a^4*b^2)*d*x)*cosh(d*x + c)^4 + 2*(495*(a^6 + 2*a^5*b + a^4*b^2)*d*x*cosh(d*x + c)^8 + 420*(a^6 + 5*a^5*b + 10*a^4*b^2 + 14*a^3*b^3 + 11*a^2*b^4 + 3*a*b^5 + (a^6 - 2*a^5*b - 3*a^4*b^2)*d*x)*cosh(d*x + c)^6 + 8*a^6 + 24*a^5*b + 16*a^4*b^2 - 16*a^3*b^3 - 52*a^2*b^4 - 24*a*b^5 + 70*(8*a^6 + 24*a^5*b + 16*a^4*b^2 - 16*a^3*b^3 - 52*a^2*b^4 - 24*a*b^5 - (a^6 + 2*a^5*b - 15*a^4*b^2)*d*x)*cosh(d*x + c)^4 - (a^6 + 2*a^5*b - 15*a^4*b^2)*d*x + 60*(3*a^6 + 7*a^5*b + 6*a^4*b^2 + 2*a^3*b^3 + 15*a^2*b^4 + 9*a*b^5 - (a^6 - 2*a^5*b + 5*a^4*b^2)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 8*(55*(a^6 + 2*a^5*b + a^4*b^2)*d*x*cosh(d*x + c)^9 + 60*(a^6 + 5*a^5*b + 10*a^4*b^2 + 14*a^3*b^3 + 11*a^2*b^4 + 3*a*b^5 + (a^6 - 2*a^5*b - 3*a^4*b^2)*d*x)*cosh(d*x + c)^7 + 14*(8*a^6 + 24*a^5*b + 16*a^4*b^2 - 16*a^3*b^3 - 52*a^2*b^4 - 24*a*b^5 - (a^6 + 2*a^5*b - 15*a^4*b^2)*d*x)*cosh(d*x + c)^5 + 20*(3*a^6 + 7*a^5*b + 6*a^4*b^2 + 2*a^3*b^3 + 15*a^2*b^4 + 9*a*b^5 - (a^6 - 2*a^5*b + 5*a^4*b^2)*d*x)*cosh(d*x + c)^3 + (8*a^6 + 24*a^5*b + 16*a^4*b^2 - 16*a^3*b^3 - 52*a^2*b^4 - 24*a*b^5 - (a^6 + 2*a^5*b - 15*a^4*b^2)*d*x)*cosh(d*x + c))*sinh(d*x + c)^3 + 2*(a^6 + 2*a^5*b + a^4*b^2)*d*x + 4*(a^6 + 5*a^5*b + 10*a^4*b^2 + 14*a^3*b^3 + 11*a^2*b^4 + 3*a*b^5 + (a^6 - 2*a^5*b - 3*a^4*b^2)*d*x)*cosh(d*x + c)^2 + 4*(33*(a^6 + 2*a^5*b + a^4*b^2)*d*x*cosh(d*x + c)^10 + 45*(a^6 + 5*a^5*b + 10*a^4*b^2 + 14*a^3*b^3 + 11*a^2*b^4 + 3*a*b^5 + (a^6 - 2*a^5*b - 3*a^4*b^2)*d*x)*cosh(d*x + c)^8 + 14*(8*a^6 + 24*a^5*b + 16*a^4*b^2 - 16*a^3*b^3 - 52*a^2*b^4 - 24*a*b^5 - (a^6 + 2*a^5*b - 15*a^4*b^2)*d*x)*cosh(d*x + c)^6 + a^6 + 5*a^5*b + 10*a^4*b^2 + 14*a^3*b^3 + 11*a^2*b^4 + 3*a*b^5 + 30*(3*a^6 + 7*a^5*b + 6*a^4*b^2 + 2*a^3*b^3 + 15*a^2*b^4 + 9*a*b^5 - (a^6 - 2*a^5*b + 5*a^4*b^2)*d*x)*cosh(d*x + c)^4 + (a^6 - 2*a^5*b - 3*a^4*b^2)*d*x + 3*(8*a^6 + 24*a^5*b + 16*a^4*b^2 - 16*a^3*b^3 - 52*a^2*b^4 - 24*a*b^5 - (a^6 + 2*a^5*b - 15*a^4*b^2)*d*x)*cosh(d*x + c)^2)*sinh(d*x + c)^2 - ((6*a^4*b^2 + 20*a^3*b^3 + 25*a^2*b^4 + 14*a*b^5 + 3*b^6)*cosh(d*x + c)^12 + 12*(6*a^4*b^2 + 20*a^3*b^3 + 25*a^2*b^4 + 14*a*b^5 + 3*b^6)*cosh(d*x + c)*sinh(d*x + c)^11 + (6*a^4*b^2 + 20*a^3*b^3 + 25*a^2*b^4 + 14*a*b^5 + 3*b^6)*sinh(d*x + c)^12 + 2*(6*a^4*b^2 - 4*a^3*b^3 - 31*a^2*b^4 - 30*a*b^5 - 9*b^6)*cosh(d*x + c)^10 + 2*(6*a^4*b^2 - 4*a^3*b^3 - 31*a^2*b^4 - 30*a*b^5 - 9*b^6 + 33*(6*a^4*b^2 + 20*a^3*b^3 + 25*a^2*b^4 + 14*a*b^5 + 3*b^6)*cosh(d*x + c)^2)*sinh(d*x + c)^10 + 20*(11*(6*a^4*b^2 + 20*a^3*b^3 + 25*a^2*b^4 + 14*a*b^5 + 3*b^6)*cosh(d*x + c)^3 + (6*a^4*b^2 - 4*a^3*b^3 - 31*a^2*b^4 - 30*a*b^5 - 9*b^6)*cosh(d*x + c))*sinh(d*x + c)^9 - (6*a^4*b^2 + 20*a^3*b^3 - 71*a^2*b^4 - 114*a*b^5 - 45*b^6)*cosh(d*x + c)^8 - (6*a^4*b^2 + 20*a^3*b^3 - 71*a^2*b^4 - 114*a*b^5 - 45*b^6 - 495*(6*a^4*b^2 + 20*a^3*b^3 + 25*a^2*b^4 + 14*a*b^5 + 3*b^6)*cosh(d*x + c)^4 - 90*(6*a^4*b^2 - 4*a^3*b^3 - 31*a^2*b^4 - 30*a*b^5 - 9*b^6)*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 8*(99*(6*a^4*b^2 + 20*a^3*b^3 + 25*a^2*b^4 + 14*a*b^5 + 3*b^6)*cosh(d*x + c)^5 + 30*(6*a^4*b^2 - 4*a^3*b^3 - 31*a^2*b^4 - 30*a*b^5 - 9*b^6)*cosh(d*x + c)^3 - (6*a^4*b^2 + 20*a^3*b^3 - 71*a^2*b^4 - 114*a*b^5 - 45*b^6)*cosh(d*x + c))*sinh(d*x + c)^7 - 4*(6*a^4*b^2 - 4*a^3*b^3 + 17*a^2*b^4 + 34*a*b^5 + 15*b^6)*cosh(d*x + c)^6 + 4*(231*(6*a^4*b^2 + 20*a^3*b^3 + 25*a^2*b^4 + 14*a*b^5 + 3*b^6)*cosh(d*x + c)^6 - 6*a^4*b^2 + 4*a^3*b^3 - 17*a^2*b^4 - 34*a*b^5 - 15*b^6 + 105*(6*a^4*b^2 - 4*a^3*b^3 - 31*a^2*b^4 - 30*a*b^5 - 9*b^6)*cosh(d*x + c)^4 - 7*(6*a^4*b^2 + 20*a^3*b^3 - 71*a^2*b^4 - 114*a*b^5 - 45*b^6)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + 6*a^4*b^2 + 20*a^3*b^3 + 25*a^2*b^4 + 14*a*b^5 + 3*b^6 + 8*(99*(6*a^4*b^2 + 20*a^3*b^3 + 25*a^2*b^4 + 14*a*b^5 + 3*b^6)*cosh(d*x + c)^7 + 63*(6*a^4*b^2 - 4*a^3*b^3 - 31*a^2*b^4 - 30*a*b^5 - 9*b^6)*cosh(d*x + c)^5 - 7*(6*a^4*b^2 + 20*a^3*b^3 - 71*a^2*b^4 - 114*a*b^5 - 45*b^6)*cosh(d*x + c)^3 - 3*(6*a^4*b^2 - 4*a^3*b^3 + 17*a^2*b^4 + 34*a*b^5 + 15*b^6)*cosh(d*x + c))*sinh(d*x + c)^5 - (6*a^4*b^2 + 20*a^3*b^3 - 71*a^2*b^4 - 114*a*b^5 - 45*b^6)*cosh(d*x + c)^4 + (495*(6*a^4*b^2 + 20*a^3*b^3 + 25*a^2*b^4 + 14*a*b^5 + 3*b^6)*cosh(d*x + c)^8 + 420*(6*a^4*b^2 - 4*a^3*b^3 - 31*a^2*b^4 - 30*a*b^5 - 9*b^6)*cosh(d*x + c)^6 - 6*a^4*b^2 - 20*a^3*b^3 + 71*a^2*b^4 + 114*a*b^5 + 45*b^6 - 70*(6*a^4*b^2 + 20*a^3*b^3 - 71*a^2*b^4 - 114*a*b^5 - 45*b^6)*cosh(d*x + c)^4 - 60*(6*a^4*b^2 - 4*a^3*b^3 + 17*a^2*b^4 + 34*a*b^5 + 15*b^6)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 4*(55*(6*a^4*b^2 + 20*a^3*b^3 + 25*a^2*b^4 + 14*a*b^5 + 3*b^6)*cosh(d*x + c)^9 + 60*(6*a^4*b^2 - 4*a^3*b^3 - 31*a^2*b^4 - 30*a*b^5 - 9*b^6)*cosh(d*x + c)^7 - 14*(6*a^4*b^2 + 20*a^3*b^3 - 71*a^2*b^4 - 114*a*b^5 - 45*b^6)*cosh(d*x + c)^5 - 20*(6*a^4*b^2 - 4*a^3*b^3 + 17*a^2*b^4 + 34*a*b^5 + 15*b^6)*cosh(d*x + c)^3 - (6*a^4*b^2 + 20*a^3*b^3 - 71*a^2*b^4 - 114*a*b^5 - 45*b^6)*cosh(d*x + c))*sinh(d*x + c)^3 + 2*(6*a^4*b^2 - 4*a^3*b^3 - 31*a^2*b^4 - 30*a*b^5 - 9*b^6)*cosh(d*x + c)^2 + 2*(33*(6*a^4*b^2 + 20*a^3*b^3 + 25*a^2*b^4 + 14*a*b^5 + 3*b^6)*cosh(d*x + c)^10 + 45*(6*a^4*b^2 - 4*a^3*b^3 - 31*a^2*b^4 - 30*a*b^5 - 9*b^6)*cosh(d*x + c)^8 - 14*(6*a^4*b^2 + 20*a^3*b^3 - 71*a^2*b^4 - 114*a*b^5 - 45*b^6)*cosh(d*x + c)^6 + 6*a^4*b^2 - 4*a^3*b^3 - 31*a^2*b^4 - 30*a*b^5 - 9*b^6 - 30*(6*a^4*b^2 - 4*a^3*b^3 + 17*a^2*b^4 + 34*a*b^5 + 15*b^6)*cosh(d*x + c)^4 - 3*(6*a^4*b^2 + 20*a^3*b^3 - 71*a^2*b^4 - 114*a*b^5 - 45*b^6)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*(3*(6*a^4*b^2 + 20*a^3*b^3 + 25*a^2*b^4 + 14*a*b^5 + 3*b^6)*cosh(d*x + c)^11 + 5*(6*a^4*b^2 - 4*a^3*b^3 - 31*a^2*b^4 - 30*a*b^5 - 9*b^6)*cosh(d*x + c)^9 - 2*(6*a^4*b^2 + 20*a^3*b^3 - 71*a^2*b^4 - 114*a*b^5 - 45*b^6)*cosh(d*x + c)^7 - 6*(6*a^4*b^2 - 4*a^3*b^3 + 17*a^2*b^4 + 34*a*b^5 + 15*b^6)*cosh(d*x + c)^5 - (6*a^4*b^2 + 20*a^3*b^3 - 71*a^2*b^4 - 114*a*b^5 - 45*b^6)*cosh(d*x + c)^3 + (6*a^4*b^2 - 4*a^3*b^3 - 31*a^2*b^4 - 30*a*b^5 - 9*b^6)*cosh(d*x + c))*sinh(d*x + c))*log(2*((a + b)*cosh(d*x + c)^2 + (a + b)*sinh(d*x + c)^2 + a - b)/(cosh(d*x + c)^2 - 2*cosh(d*x + c)*sinh(d*x + c) + sinh(d*x + c)^2)) - 2*((a^6 + 2*a^5*b - 5*a^4*b^2 - 20*a^3*b^3 - 25*a^2*b^4 - 14*a*b^5 - 3*b^6)*cosh(d*x + c)^12 + 12*(a^6 + 2*a^5*b - 5*a^4*b^2 - 20*a^3*b^3 - 25*a^2*b^4 - 14*a*b^5 - 3*b^6)*cosh(d*x + c)*sinh(d*x + c)^11 + (a^6 + 2*a^5*b - 5*a^4*b^2 - 20*a^3*b^3 - 25*a^2*b^4 - 14*a*b^5 - 3*b^6)*sinh(d*x + c)^12 + 2*(a^6 - 2*a^5*b - 9*a^4*b^2 + 4*a^3*b^3 + 31*a^2*b^4 + 30*a*b^5 + 9*b^6)*cosh(d*x + c)^10 + 2*(a^6 - 2*a^5*b - 9*a^4*b^2 + 4*a^3*b^3 + 31*a^2*b^4 + 30*a*b^5 + 9*b^6 + 33*(a^6 + 2*a^5*b - 5*a^4*b^2 - 20*a^3*b^3 - 25*a^2*b^4 - 14*a*b^5 - 3*b^6)*cosh(d*x + c)^2)*sinh(d*x + c)^10 + 20*(11*(a^6 + 2*a^5*b - 5*a^4*b^2 - 20*a^3*b^3 - 25*a^2*b^4 - 14*a*b^5 - 3*b^6)*cosh(d*x + c)^3 + (a^6 - 2*a^5*b - 9*a^4*b^2 + 4*a^3*b^3 + 31*a^2*b^4 + 30*a*b^5 + 9*b^6)*cosh(d*x + c))*sinh(d*x + c)^9 - (a^6 + 2*a^5*b - 21*a^4*b^2 - 20*a^3*b^3 + 71*a^2*b^4 + 114*a*b^5 + 45*b^6)*cosh(d*x + c)^8 - (a^6 + 2*a^5*b - 21*a^4*b^2 - 20*a^3*b^3 + 71*a^2*b^4 + 114*a*b^5 + 45*b^6 - 495*(a^6 + 2*a^5*b - 5*a^4*b^2 - 20*a^3*b^3 - 25*a^2*b^4 - 14*a*b^5 - 3*b^6)*cosh(d*x + c)^4 - 90*(a^6 - 2*a^5*b - 9*a^4*b^2 + 4*a^3*b^3 + 31*a^2*b^4 + 30*a*b^5 + 9*b^6)*cosh(d*x + c)^2)*sinh(d*x + c)^8 + 8*(99*(a^6 + 2*a^5*b - 5*a^4*b^2 - 20*a^3*b^3 - 25*a^2*b^4 - 14*a*b^5 - 3*b^6)*cosh(d*x + c)^5 + 30*(a^6 - 2*a^5*b - 9*a^4*b^2 + 4*a^3*b^3 + 31*a^2*b^4 + 30*a*b^5 + 9*b^6)*cosh(d*x + c)^3 - (a^6 + 2*a^5*b - 21*a^4*b^2 - 20*a^3*b^3 + 71*a^2*b^4 + 114*a*b^5 + 45*b^6)*cosh(d*x + c))*sinh(d*x + c)^7 - 4*(a^6 - 2*a^5*b - a^4*b^2 + 4*a^3*b^3 - 17*a^2*b^4 - 34*a*b^5 - 15*b^6)*cosh(d*x + c)^6 + 4*(231*(a^6 + 2*a^5*b - 5*a^4*b^2 - 20*a^3*b^3 - 25*a^2*b^4 - 14*a*b^5 - 3*b^6)*cosh(d*x + c)^6 - a^6 + 2*a^5*b + a^4*b^2 - 4*a^3*b^3 + 17*a^2*b^4 + 34*a*b^5 + 15*b^6 + 105*(a^6 - 2*a^5*b - 9*a^4*b^2 + 4*a^3*b^3 + 31*a^2*b^4 + 30*a*b^5 + 9*b^6)*cosh(d*x + c)^4 - 7*(a^6 + 2*a^5*b - 21*a^4*b^2 - 20*a^3*b^3 + 71*a^2*b^4 + 114*a*b^5 + 45*b^6)*cosh(d*x + c)^2)*sinh(d*x + c)^6 + a^6 + 2*a^5*b - 5*a^4*b^2 - 20*a^3*b^3 - 25*a^2*b^4 - 14*a*b^5 - 3*b^6 + 8*(99*(a^6 + 2*a^5*b - 5*a^4*b^2 - 20*a^3*b^3 - 25*a^2*b^4 - 14*a*b^5 - 3*b^6)*cosh(d*x + c)^7 + 63*(a^6 - 2*a^5*b - 9*a^4*b^2 + 4*a^3*b^3 + 31*a^2*b^4 + 30*a*b^5 + 9*b^6)*cosh(d*x + c)^5 - 7*(a^6 + 2*a^5*b - 21*a^4*b^2 - 20*a^3*b^3 + 71*a^2*b^4 + 114*a*b^5 + 45*b^6)*cosh(d*x + c)^3 - 3*(a^6 - 2*a^5*b - a^4*b^2 + 4*a^3*b^3 - 17*a^2*b^4 - 34*a*b^5 - 15*b^6)*cosh(d*x + c))*sinh(d*x + c)^5 - (a^6 + 2*a^5*b - 21*a^4*b^2 - 20*a^3*b^3 + 71*a^2*b^4 + 114*a*b^5 + 45*b^6)*cosh(d*x + c)^4 + (495*(a^6 + 2*a^5*b - 5*a^4*b^2 - 20*a^3*b^3 - 25*a^2*b^4 - 14*a*b^5 - 3*b^6)*cosh(d*x + c)^8 + 420*(a^6 - 2*a^5*b - 9*a^4*b^2 + 4*a^3*b^3 + 31*a^2*b^4 + 30*a*b^5 + 9*b^6)*cosh(d*x + c)^6 - a^6 - 2*a^5*b + 21*a^4*b^2 + 20*a^3*b^3 - 71*a^2*b^4 - 114*a*b^5 - 45*b^6 - 70*(a^6 + 2*a^5*b - 21*a^4*b^2 - 20*a^3*b^3 + 71*a^2*b^4 + 114*a*b^5 + 45*b^6)*cosh(d*x + c)^4 - 60*(a^6 - 2*a^5*b - a^4*b^2 + 4*a^3*b^3 - 17*a^2*b^4 - 34*a*b^5 - 15*b^6)*cosh(d*x + c)^2)*sinh(d*x + c)^4 + 4*(55*(a^6 + 2*a^5*b - 5*a^4*b^2 - 20*a^3*b^3 - 25*a^2*b^4 - 14*a*b^5 - 3*b^6)*cosh(d*x + c)^9 + 60*(a^6 - 2*a^5*b - 9*a^4*b^2 + 4*a^3*b^3 + 31*a^2*b^4 + 30*a*b^5 + 9*b^6)*cosh(d*x + c)^7 - 14*(a^6 + 2*a^5*b - 21*a^4*b^2 - 20*a^3*b^3 + 71*a^2*b^4 + 114*a*b^5 + 45*b^6)*cosh(d*x + c)^5 - 20*(a^6 - 2*a^5*b - a^4*b^2 + 4*a^3*b^3 - 17*a^2*b^4 - 34*a*b^5 - 15*b^6)*cosh(d*x + c)^3 - (a^6 + 2*a^5*b - 21*a^4*b^2 - 20*a^3*b^3 + 71*a^2*b^4 + 114*a*b^5 + 45*b^6)*cosh(d*x + c))*sinh(d*x + c)^3 + 2*(a^6 - 2*a^5*b - 9*a^4*b^2 + 4*a^3*b^3 + 31*a^2*b^4 + 30*a*b^5 + 9*b^6)*cosh(d*x + c)^2 + 2*(33*(a^6 + 2*a^5*b - 5*a^4*b^2 - 20*a^3*b^3 - 25*a^2*b^4 - 14*a*b^5 - 3*b^6)*cosh(d*x + c)^10 + 45*(a^6 - 2*a^5*b - 9*a^4*b^2 + 4*a^3*b^3 + 31*a^2*b^4 + 30*a*b^5 + 9*b^6)*cosh(d*x + c)^8 - 14*(a^6 + 2*a^5*b - 21*a^4*b^2 - 20*a^3*b^3 + 71*a^2*b^4 + 114*a*b^5 + 45*b^6)*cosh(d*x + c)^6 + a^6 - 2*a^5*b - 9*a^4*b^2 + 4*a^3*b^3 + 31*a^2*b^4 + 30*a*b^5 + 9*b^6 - 30*(a^6 - 2*a^5*b - a^4*b^2 + 4*a^3*b^3 - 17*a^2*b^4 - 34*a*b^5 - 15*b^6)*cosh(d*x + c)^4 - 3*(a^6 + 2*a^5*b - 21*a^4*b^2 - 20*a^3*b^3 + 71*a^2*b^4 + 114*a*b^5 + 45*b^6)*cosh(d*x + c)^2)*sinh(d*x + c)^2 + 4*(3*(a^6 + 2*a^5*b - 5*a^4*b^2 - 20*a^3*b^3 - 25*a^2*b^4 - 14*a*b^5 - 3*b^6)*cosh(d*x + c)^11 + 5*(a^6 - 2*a^5*b - 9*a^4*b^2 + 4*a^3*b^3 + 31*a^2*b^4 + 30*a*b^5 + 9*b^6)*cosh(d*x + c)^9 - 2*(a^6 + 2*a^5*b - 21*a^4*b^2 - 20*a^3*b^3 + 71*a^2*b^4 + 114*a*b^5 + 45*b^6)*cosh(d*x + c)^7 - 6*(a^6 - 2*a^5*b - a^4*b^2 + 4*a^3*b^3 - 17*a^2*b^4 - 34*a*b^5 - 15*b^6)*cosh(d*x + c)^5 - (a^6 + 2*a^5*b - 21*a^4*b^2 - 20*a^3*b^3 + 71*a^2*b^4 + 114*a*b^5 + 45*b^6)*cosh(d*x + c)^3 + (a^6 - 2*a^5*b - 9*a^4*b^2 + 4*a^3*b^3 + 31*a^2*b^4 + 30*a*b^5 + 9*b^6)*cosh(d*x + c))*sinh(d*x + c))*log(2*sinh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))) + 8*(3*(a^6 + 2*a^5*b + a^4*b^2)*d*x*cosh(d*x + c)^11 + 5*(a^6 + 5*a^5*b + 10*a^4*b^2 + 14*a^3*b^3 + 11*a^2*b^4 + 3*a*b^5 + (a^6 - 2*a^5*b - 3*a^4*b^2)*d*x)*cosh(d*x + c)^9 + 2*(8*a^6 + 24*a^5*b + 16*a^4*b^2 - 16*a^3*b^3 - 52*a^2*b^4 - 24*a*b^5 - (a^6 + 2*a^5*b - 15*a^4*b^2)*d*x)*cosh(d*x + c)^7 + 6*(3*a^6 + 7*a^5*b + 6*a^4*b^2 + 2*a^3*b^3 + 15*a^2*b^4 + 9*a*b^5 - (a^6 - 2*a^5*b + 5*a^4*b^2)*d*x)*cosh(d*x + c)^5 + (8*a^6 + 24*a^5*b + 16*a^4*b^2 - 16*a^3*b^3 - 52*a^2*b^4 - 24*a*b^5 - (a^6 + 2*a^5*b - 15*a^4*b^2)*d*x)*cosh(d*x + c)^3 + (a^6 + 5*a^5*b + 10*a^4*b^2 + 14*a^3*b^3 + 11*a^2*b^4 + 3*a*b^5 + (a^6 - 2*a^5*b - 3*a^4*b^2)*d*x)*cosh(d*x + c))*sinh(d*x + c))/((a^9 + 5*a^8*b + 10*a^7*b^2 + 10*a^6*b^3 + 5*a^5*b^4 + a^4*b^5)*d*cosh(d*x + c)^12 + 12*(a^9 + 5*a^8*b + 10*a^7*b^2 + 10*a^6*b^3 + 5*a^5*b^4 + a^4*b^5)*d*cosh(d*x + c)*sinh(d*x + c)^11 + (a^9 + 5*a^8*b + 10*a^7*b^2 + 10*a^6*b^3 + 5*a^5*b^4 + a^4*b^5)*d*sinh(d*x + c)^12 + 2*(a^9 + a^8*b - 6*a^7*b^2 - 14*a^6*b^3 - 11*a^5*b^4 - 3*a^4*b^5)*d*cosh(d*x + c)^10 + 2*(33*(a^9 + 5*a^8*b + 10*a^7*b^2 + 10*a^6*b^3 + 5*a^5*b^4 + a^4*b^5)*d*cosh(d*x + c)^2 + (a^9 + a^8*b - 6*a^7*b^2 - 14*a^6*b^3 - 11*a^5*b^4 - 3*a^4*b^5)*d)*sinh(d*x + c)^10 - (a^9 + 5*a^8*b - 6*a^7*b^2 - 38*a^6*b^3 - 43*a^5*b^4 - 15*a^4*b^5)*d*cosh(d*x + c)^8 + 20*(11*(a^9 + 5*a^8*b + 10*a^7*b^2 + 10*a^6*b^3 + 5*a^5*b^4 + a^4*b^5)*d*cosh(d*x + c)^3 + (a^9 + a^8*b - 6*a^7*b^2 - 14*a^6*b^3 - 11*a^5*b^4 - 3*a^4*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^9 + (495*(a^9 + 5*a^8*b + 10*a^7*b^2 + 10*a^6*b^3 + 5*a^5*b^4 + a^4*b^5)*d*cosh(d*x + c)^4 + 90*(a^9 + a^8*b - 6*a^7*b^2 - 14*a^6*b^3 - 11*a^5*b^4 - 3*a^4*b^5)*d*cosh(d*x + c)^2 - (a^9 + 5*a^8*b - 6*a^7*b^2 - 38*a^6*b^3 - 43*a^5*b^4 - 15*a^4*b^5)*d)*sinh(d*x + c)^8 - 4*(a^9 + a^8*b + 2*a^7*b^2 + 10*a^6*b^3 + 13*a^5*b^4 + 5*a^4*b^5)*d*cosh(d*x + c)^6 + 8*(99*(a^9 + 5*a^8*b + 10*a^7*b^2 + 10*a^6*b^3 + 5*a^5*b^4 + a^4*b^5)*d*cosh(d*x + c)^5 + 30*(a^9 + a^8*b - 6*a^7*b^2 - 14*a^6*b^3 - 11*a^5*b^4 - 3*a^4*b^5)*d*cosh(d*x + c)^3 - (a^9 + 5*a^8*b - 6*a^7*b^2 - 38*a^6*b^3 - 43*a^5*b^4 - 15*a^4*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^7 + 4*(231*(a^9 + 5*a^8*b + 10*a^7*b^2 + 10*a^6*b^3 + 5*a^5*b^4 + a^4*b^5)*d*cosh(d*x + c)^6 + 105*(a^9 + a^8*b - 6*a^7*b^2 - 14*a^6*b^3 - 11*a^5*b^4 - 3*a^4*b^5)*d*cosh(d*x + c)^4 - 7*(a^9 + 5*a^8*b - 6*a^7*b^2 - 38*a^6*b^3 - 43*a^5*b^4 - 15*a^4*b^5)*d*cosh(d*x + c)^2 - (a^9 + a^8*b + 2*a^7*b^2 + 10*a^6*b^3 + 13*a^5*b^4 + 5*a^4*b^5)*d)*sinh(d*x + c)^6 - (a^9 + 5*a^8*b - 6*a^7*b^2 - 38*a^6*b^3 - 43*a^5*b^4 - 15*a^4*b^5)*d*cosh(d*x + c)^4 + 8*(99*(a^9 + 5*a^8*b + 10*a^7*b^2 + 10*a^6*b^3 + 5*a^5*b^4 + a^4*b^5)*d*cosh(d*x + c)^7 + 63*(a^9 + a^8*b - 6*a^7*b^2 - 14*a^6*b^3 - 11*a^5*b^4 - 3*a^4*b^5)*d*cosh(d*x + c)^5 - 7*(a^9 + 5*a^8*b - 6*a^7*b^2 - 38*a^6*b^3 - 43*a^5*b^4 - 15*a^4*b^5)*d*cosh(d*x + c)^3 - 3*(a^9 + a^8*b + 2*a^7*b^2 + 10*a^6*b^3 + 13*a^5*b^4 + 5*a^4*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^5 + (495*(a^9 + 5*a^8*b + 10*a^7*b^2 + 10*a^6*b^3 + 5*a^5*b^4 + a^4*b^5)*d*cosh(d*x + c)^8 + 420*(a^9 + a^8*b - 6*a^7*b^2 - 14*a^6*b^3 - 11*a^5*b^4 - 3*a^4*b^5)*d*cosh(d*x + c)^6 - 70*(a^9 + 5*a^8*b - 6*a^7*b^2 - 38*a^6*b^3 - 43*a^5*b^4 - 15*a^4*b^5)*d*cosh(d*x + c)^4 - 60*(a^9 + a^8*b + 2*a^7*b^2 + 10*a^6*b^3 + 13*a^5*b^4 + 5*a^4*b^5)*d*cosh(d*x + c)^2 - (a^9 + 5*a^8*b - 6*a^7*b^2 - 38*a^6*b^3 - 43*a^5*b^4 - 15*a^4*b^5)*d)*sinh(d*x + c)^4 + 2*(a^9 + a^8*b - 6*a^7*b^2 - 14*a^6*b^3 - 11*a^5*b^4 - 3*a^4*b^5)*d*cosh(d*x + c)^2 + 4*(55*(a^9 + 5*a^8*b + 10*a^7*b^2 + 10*a^6*b^3 + 5*a^5*b^4 + a^4*b^5)*d*cosh(d*x + c)^9 + 60*(a^9 + a^8*b - 6*a^7*b^2 - 14*a^6*b^3 - 11*a^5*b^4 - 3*a^4*b^5)*d*cosh(d*x + c)^7 - 14*(a^9 + 5*a^8*b - 6*a^7*b^2 - 38*a^6*b^3 - 43*a^5*b^4 - 15*a^4*b^5)*d*cosh(d*x + c)^5 - 20*(a^9 + a^8*b + 2*a^7*b^2 + 10*a^6*b^3 + 13*a^5*b^4 + 5*a^4*b^5)*d*cosh(d*x + c)^3 - (a^9 + 5*a^8*b - 6*a^7*b^2 - 38*a^6*b^3 - 43*a^5*b^4 - 15*a^4*b^5)*d*cosh(d*x + c))*sinh(d*x + c)^3 + 2*(33*(a^9 + 5*a^8*b + 10*a^7*b^2 + 10*a^6*b^3 + 5*a^5*b^4 + a^4*b^5)*d*cosh(d*x + c)^10 + 45*(a^9 + a^8*b - 6*a^7*b^2 - 14*a^6*b^3 - 11*a^5*b^4 - 3*a^4*b^5)*d*cosh(d*x + c)^8 - 14*(a^9 + 5*a^8*b - 6*a^7*b^2 - 38*a^6*b^3 - 43*a^5*b^4 - 15*a^4*b^5)*d*cosh(d*x + c)^6 - 30*(a^9 + a^8*b + 2*a^7*b^2 + 10*a^6*b^3 + 13*a^5*b^4 + 5*a^4*b^5)*d*cosh(d*x + c)^4 - 3*(a^9 + 5*a^8*b - 6*a^7*b^2 - 38*a^6*b^3 - 43*a^5*b^4 - 15*a^4*b^5)*d*cosh(d*x + c)^2 + (a^9 + a^8*b - 6*a^7*b^2 - 14*a^6*b^3 - 11*a^5*b^4 - 3*a^4*b^5)*d)*sinh(d*x + c)^2 + (a^9 + 5*a^8*b + 10*a^7*b^2 + 10*a^6*b^3 + 5*a^5*b^4 + a^4*b^5)*d + 4*(3*(a^9 + 5*a^8*b + 10*a^7*b^2 + 10*a^6*b^3 + 5*a^5*b^4 + a^4*b^5)*d*cosh(d*x + c)^11 + 5*(a^9 + a^8*b - 6*a^7*b^2 - 14*a^6*b^3 - 11*a^5*b^4 - 3*a^4*b^5)*d*cosh(d*x + c)^9 - 2*(a^9 + 5*a^8*b - 6*a^7*b^2 - 38*a^6*b^3 - 43*a^5*b^4 - 15*a^4*b^5)*d*cosh(d*x + c)^7 - 6*(a^9 + a^8*b + 2*a^7*b^2 + 10*a^6*b^3 + 13*a^5*b^4 + 5*a^4*b^5)*d*cosh(d*x + c)^5 - (a^9 + 5*a^8*b - 6*a^7*b^2 - 38*a^6*b^3 - 43*a^5*b^4 - 15*a^4*b^5)*d*cosh(d*x + c)^3 + (a^9 + a^8*b - 6*a^7*b^2 - 14*a^6*b^3 - 11*a^5*b^4 - 3*a^4*b^5)*d*cosh(d*x + c))*sinh(d*x + c))","B",0
200,-1,0,0,0.000000," ","integrate(coth(d*x+c)^4/(a+b*tanh(d*x+c)^2)^3,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
201,-1,0,0,0.000000," ","integrate(1/(a+b*tanh(d*x+c)^2)^4,x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
202,1,8,0,0.743759," ","integrate((1-tanh(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))","B",0
203,1,1,0,2.082027," ","integrate((-1+tanh(x)^2)^(1/2),x, algorithm=""fricas"")","0"," ",0,"0","A",0
204,1,140,0,0.450889," ","integrate((1-tanh(x)^2)^(3/2),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)}{\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}"," ",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))/(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)","B",0
205,1,1,0,0.612664," ","integrate((-1+tanh(x)^2)^(3/2),x, algorithm=""fricas"")","0"," ",0,"0","A",0
206,1,2,0,0.551841," ","integrate(1/(1-tanh(x)^2)^(1/2),x, algorithm=""fricas"")","\sinh\left(x\right)"," ",0,"sinh(x)","A",0
207,1,1,0,0.460823," ","integrate(1/(-1+tanh(x)^2)^(1/2),x, algorithm=""fricas"")","0"," ",0,"0","A",0
208,1,4529,0,0.866970," ","integrate((a+b*tanh(x)^2)^(1/2)*tanh(x)^5,x, algorithm=""fricas"")","\left[\frac{15 \, {\left(b^{2} \cosh\left(x\right)^{10} + 10 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{9} + b^{2} \sinh\left(x\right)^{10} + 5 \, b^{2} \cosh\left(x\right)^{8} + 5 \, {\left(9 \, b^{2} \cosh\left(x\right)^{2} + b^{2}\right)} \sinh\left(x\right)^{8} + 10 \, b^{2} \cosh\left(x\right)^{6} + 40 \, {\left(3 \, b^{2} \cosh\left(x\right)^{3} + b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{7} + 10 \, {\left(21 \, b^{2} \cosh\left(x\right)^{4} + 14 \, b^{2} \cosh\left(x\right)^{2} + b^{2}\right)} \sinh\left(x\right)^{6} + 10 \, b^{2} \cosh\left(x\right)^{4} + 4 \, {\left(63 \, b^{2} \cosh\left(x\right)^{5} + 70 \, b^{2} \cosh\left(x\right)^{3} + 15 \, b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 10 \, {\left(21 \, b^{2} \cosh\left(x\right)^{6} + 35 \, b^{2} \cosh\left(x\right)^{4} + 15 \, b^{2} \cosh\left(x\right)^{2} + b^{2}\right)} \sinh\left(x\right)^{4} + 5 \, b^{2} \cosh\left(x\right)^{2} + 40 \, {\left(3 \, b^{2} \cosh\left(x\right)^{7} + 7 \, b^{2} \cosh\left(x\right)^{5} + 5 \, b^{2} \cosh\left(x\right)^{3} + b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 5 \, {\left(9 \, b^{2} \cosh\left(x\right)^{8} + 28 \, b^{2} \cosh\left(x\right)^{6} + 30 \, b^{2} \cosh\left(x\right)^{4} + 12 \, b^{2} \cosh\left(x\right)^{2} + b^{2}\right)} \sinh\left(x\right)^{2} + b^{2} + 10 \, {\left(b^{2} \cosh\left(x\right)^{9} + 4 \, b^{2} \cosh\left(x\right)^{7} + 6 \, b^{2} \cosh\left(x\right)^{5} + 4 \, b^{2} \cosh\left(x\right)^{3} + b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \log\left(\frac{{\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{3} + a^{2} b\right)} \sinh\left(x\right)^{8} + 2 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} + 2 \, {\left(2 \, a^{3} + a^{2} b + 14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} + 3 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3} + 30 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} + 10 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} + 2 \, {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} + 15 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 2 \, a^{3} + 3 \, a^{2} b - b^{3} + 3 \, {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(a^{2} \cosh\left(x\right)^{6} + 6 \, a^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + a^{2} \sinh\left(x\right)^{6} + 3 \, a^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, a^{2} \cosh\left(x\right)^{2} + a^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, a^{2} \cosh\left(x\right)^{3} + 3 \, a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, a^{2} \cosh\left(x\right)^{4} + 18 \, a^{2} \cosh\left(x\right)^{2} + 3 \, a^{2} + 2 \, a b - b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(x\right)^{5} + 6 \, a^{2} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{7} + 3 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) + 15 \, {\left(b^{2} \cosh\left(x\right)^{10} + 10 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{9} + b^{2} \sinh\left(x\right)^{10} + 5 \, b^{2} \cosh\left(x\right)^{8} + 5 \, {\left(9 \, b^{2} \cosh\left(x\right)^{2} + b^{2}\right)} \sinh\left(x\right)^{8} + 10 \, b^{2} \cosh\left(x\right)^{6} + 40 \, {\left(3 \, b^{2} \cosh\left(x\right)^{3} + b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{7} + 10 \, {\left(21 \, b^{2} \cosh\left(x\right)^{4} + 14 \, b^{2} \cosh\left(x\right)^{2} + b^{2}\right)} \sinh\left(x\right)^{6} + 10 \, b^{2} \cosh\left(x\right)^{4} + 4 \, {\left(63 \, b^{2} \cosh\left(x\right)^{5} + 70 \, b^{2} \cosh\left(x\right)^{3} + 15 \, b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 10 \, {\left(21 \, b^{2} \cosh\left(x\right)^{6} + 35 \, b^{2} \cosh\left(x\right)^{4} + 15 \, b^{2} \cosh\left(x\right)^{2} + b^{2}\right)} \sinh\left(x\right)^{4} + 5 \, b^{2} \cosh\left(x\right)^{2} + 40 \, {\left(3 \, b^{2} \cosh\left(x\right)^{7} + 7 \, b^{2} \cosh\left(x\right)^{5} + 5 \, b^{2} \cosh\left(x\right)^{3} + b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 5 \, {\left(9 \, b^{2} \cosh\left(x\right)^{8} + 28 \, b^{2} \cosh\left(x\right)^{6} + 30 \, b^{2} \cosh\left(x\right)^{4} + 12 \, b^{2} \cosh\left(x\right)^{2} + b^{2}\right)} \sinh\left(x\right)^{2} + b^{2} + 10 \, {\left(b^{2} \cosh\left(x\right)^{9} + 4 \, b^{2} \cosh\left(x\right)^{7} + 6 \, b^{2} \cosh\left(x\right)^{5} + 4 \, b^{2} \cosh\left(x\right)^{3} + b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \log\left(-\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - b\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - b \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right) + 4 \, \sqrt{2} {\left({\left(2 \, a^{2} - 6 \, a b - 23 \, b^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(2 \, a^{2} - 6 \, a b - 23 \, b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(2 \, a^{2} - 6 \, a b - 23 \, b^{2}\right)} \sinh\left(x\right)^{8} + 4 \, {\left(2 \, a^{2} - 5 \, a b - 12 \, b^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(2 \, a^{2} - 6 \, a b - 23 \, b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, a^{2} - 5 \, a b - 12 \, b^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(2 \, a^{2} - 6 \, a b - 23 \, b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(2 \, a^{2} - 5 \, a b - 12 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(6 \, a^{2} - 14 \, a b - 49 \, b^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(2 \, a^{2} - 6 \, a b - 23 \, b^{2}\right)} \cosh\left(x\right)^{4} + 30 \, {\left(2 \, a^{2} - 5 \, a b - 12 \, b^{2}\right)} \cosh\left(x\right)^{2} + 6 \, a^{2} - 14 \, a b - 49 \, b^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(2 \, a^{2} - 6 \, a b - 23 \, b^{2}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(2 \, a^{2} - 5 \, a b - 12 \, b^{2}\right)} \cosh\left(x\right)^{3} + {\left(6 \, a^{2} - 14 \, a b - 49 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(2 \, a^{2} - 5 \, a b - 12 \, b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(2 \, a^{2} - 6 \, a b - 23 \, b^{2}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(2 \, a^{2} - 5 \, a b - 12 \, b^{2}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(6 \, a^{2} - 14 \, a b - 49 \, b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, a^{2} - 5 \, a b - 12 \, b^{2}\right)} \sinh\left(x\right)^{2} + 2 \, a^{2} - 6 \, a b - 23 \, b^{2} + 8 \, {\left({\left(2 \, a^{2} - 6 \, a b - 23 \, b^{2}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(2 \, a^{2} - 5 \, a b - 12 \, b^{2}\right)} \cosh\left(x\right)^{5} + {\left(6 \, a^{2} - 14 \, a b - 49 \, b^{2}\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{2} - 5 \, a b - 12 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{60 \, {\left(b^{2} \cosh\left(x\right)^{10} + 10 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{9} + b^{2} \sinh\left(x\right)^{10} + 5 \, b^{2} \cosh\left(x\right)^{8} + 5 \, {\left(9 \, b^{2} \cosh\left(x\right)^{2} + b^{2}\right)} \sinh\left(x\right)^{8} + 10 \, b^{2} \cosh\left(x\right)^{6} + 40 \, {\left(3 \, b^{2} \cosh\left(x\right)^{3} + b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{7} + 10 \, {\left(21 \, b^{2} \cosh\left(x\right)^{4} + 14 \, b^{2} \cosh\left(x\right)^{2} + b^{2}\right)} \sinh\left(x\right)^{6} + 10 \, b^{2} \cosh\left(x\right)^{4} + 4 \, {\left(63 \, b^{2} \cosh\left(x\right)^{5} + 70 \, b^{2} \cosh\left(x\right)^{3} + 15 \, b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 10 \, {\left(21 \, b^{2} \cosh\left(x\right)^{6} + 35 \, b^{2} \cosh\left(x\right)^{4} + 15 \, b^{2} \cosh\left(x\right)^{2} + b^{2}\right)} \sinh\left(x\right)^{4} + 5 \, b^{2} \cosh\left(x\right)^{2} + 40 \, {\left(3 \, b^{2} \cosh\left(x\right)^{7} + 7 \, b^{2} \cosh\left(x\right)^{5} + 5 \, b^{2} \cosh\left(x\right)^{3} + b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 5 \, {\left(9 \, b^{2} \cosh\left(x\right)^{8} + 28 \, b^{2} \cosh\left(x\right)^{6} + 30 \, b^{2} \cosh\left(x\right)^{4} + 12 \, b^{2} \cosh\left(x\right)^{2} + b^{2}\right)} \sinh\left(x\right)^{2} + b^{2} + 10 \, {\left(b^{2} \cosh\left(x\right)^{9} + 4 \, b^{2} \cosh\left(x\right)^{7} + 6 \, b^{2} \cosh\left(x\right)^{5} + 4 \, b^{2} \cosh\left(x\right)^{3} + b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}, -\frac{15 \, {\left(b^{2} \cosh\left(x\right)^{10} + 10 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{9} + b^{2} \sinh\left(x\right)^{10} + 5 \, b^{2} \cosh\left(x\right)^{8} + 5 \, {\left(9 \, b^{2} \cosh\left(x\right)^{2} + b^{2}\right)} \sinh\left(x\right)^{8} + 10 \, b^{2} \cosh\left(x\right)^{6} + 40 \, {\left(3 \, b^{2} \cosh\left(x\right)^{3} + b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{7} + 10 \, {\left(21 \, b^{2} \cosh\left(x\right)^{4} + 14 \, b^{2} \cosh\left(x\right)^{2} + b^{2}\right)} \sinh\left(x\right)^{6} + 10 \, b^{2} \cosh\left(x\right)^{4} + 4 \, {\left(63 \, b^{2} \cosh\left(x\right)^{5} + 70 \, b^{2} \cosh\left(x\right)^{3} + 15 \, b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 10 \, {\left(21 \, b^{2} \cosh\left(x\right)^{6} + 35 \, b^{2} \cosh\left(x\right)^{4} + 15 \, b^{2} \cosh\left(x\right)^{2} + b^{2}\right)} \sinh\left(x\right)^{4} + 5 \, b^{2} \cosh\left(x\right)^{2} + 40 \, {\left(3 \, b^{2} \cosh\left(x\right)^{7} + 7 \, b^{2} \cosh\left(x\right)^{5} + 5 \, b^{2} \cosh\left(x\right)^{3} + b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 5 \, {\left(9 \, b^{2} \cosh\left(x\right)^{8} + 28 \, b^{2} \cosh\left(x\right)^{6} + 30 \, b^{2} \cosh\left(x\right)^{4} + 12 \, b^{2} \cosh\left(x\right)^{2} + b^{2}\right)} \sinh\left(x\right)^{2} + b^{2} + 10 \, {\left(b^{2} \cosh\left(x\right)^{9} + 4 \, b^{2} \cosh\left(x\right)^{7} + 6 \, b^{2} \cosh\left(x\right)^{5} + 4 \, b^{2} \cosh\left(x\right)^{3} + b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(a \cosh\left(x\right)^{2} + 2 \, a \cosh\left(x\right) \sinh\left(x\right) + a \sinh\left(x\right)^{2} + a + b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a^{2} + a b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{2} + a b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{2} + a b\right)} \sinh\left(x\right)^{4} + {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} + 2 \, a^{2} + a b - b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(2 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + 15 \, {\left(b^{2} \cosh\left(x\right)^{10} + 10 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{9} + b^{2} \sinh\left(x\right)^{10} + 5 \, b^{2} \cosh\left(x\right)^{8} + 5 \, {\left(9 \, b^{2} \cosh\left(x\right)^{2} + b^{2}\right)} \sinh\left(x\right)^{8} + 10 \, b^{2} \cosh\left(x\right)^{6} + 40 \, {\left(3 \, b^{2} \cosh\left(x\right)^{3} + b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{7} + 10 \, {\left(21 \, b^{2} \cosh\left(x\right)^{4} + 14 \, b^{2} \cosh\left(x\right)^{2} + b^{2}\right)} \sinh\left(x\right)^{6} + 10 \, b^{2} \cosh\left(x\right)^{4} + 4 \, {\left(63 \, b^{2} \cosh\left(x\right)^{5} + 70 \, b^{2} \cosh\left(x\right)^{3} + 15 \, b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 10 \, {\left(21 \, b^{2} \cosh\left(x\right)^{6} + 35 \, b^{2} \cosh\left(x\right)^{4} + 15 \, b^{2} \cosh\left(x\right)^{2} + b^{2}\right)} \sinh\left(x\right)^{4} + 5 \, b^{2} \cosh\left(x\right)^{2} + 40 \, {\left(3 \, b^{2} \cosh\left(x\right)^{7} + 7 \, b^{2} \cosh\left(x\right)^{5} + 5 \, b^{2} \cosh\left(x\right)^{3} + b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 5 \, {\left(9 \, b^{2} \cosh\left(x\right)^{8} + 28 \, b^{2} \cosh\left(x\right)^{6} + 30 \, b^{2} \cosh\left(x\right)^{4} + 12 \, b^{2} \cosh\left(x\right)^{2} + b^{2}\right)} \sinh\left(x\right)^{2} + b^{2} + 10 \, {\left(b^{2} \cosh\left(x\right)^{9} + 4 \, b^{2} \cosh\left(x\right)^{7} + 6 \, b^{2} \cosh\left(x\right)^{5} + 4 \, b^{2} \cosh\left(x\right)^{3} + b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) - 2 \, \sqrt{2} {\left({\left(2 \, a^{2} - 6 \, a b - 23 \, b^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(2 \, a^{2} - 6 \, a b - 23 \, b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(2 \, a^{2} - 6 \, a b - 23 \, b^{2}\right)} \sinh\left(x\right)^{8} + 4 \, {\left(2 \, a^{2} - 5 \, a b - 12 \, b^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(2 \, a^{2} - 6 \, a b - 23 \, b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, a^{2} - 5 \, a b - 12 \, b^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(2 \, a^{2} - 6 \, a b - 23 \, b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(2 \, a^{2} - 5 \, a b - 12 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(6 \, a^{2} - 14 \, a b - 49 \, b^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(2 \, a^{2} - 6 \, a b - 23 \, b^{2}\right)} \cosh\left(x\right)^{4} + 30 \, {\left(2 \, a^{2} - 5 \, a b - 12 \, b^{2}\right)} \cosh\left(x\right)^{2} + 6 \, a^{2} - 14 \, a b - 49 \, b^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(2 \, a^{2} - 6 \, a b - 23 \, b^{2}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(2 \, a^{2} - 5 \, a b - 12 \, b^{2}\right)} \cosh\left(x\right)^{3} + {\left(6 \, a^{2} - 14 \, a b - 49 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(2 \, a^{2} - 5 \, a b - 12 \, b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(2 \, a^{2} - 6 \, a b - 23 \, b^{2}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(2 \, a^{2} - 5 \, a b - 12 \, b^{2}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(6 \, a^{2} - 14 \, a b - 49 \, b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, a^{2} - 5 \, a b - 12 \, b^{2}\right)} \sinh\left(x\right)^{2} + 2 \, a^{2} - 6 \, a b - 23 \, b^{2} + 8 \, {\left({\left(2 \, a^{2} - 6 \, a b - 23 \, b^{2}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(2 \, a^{2} - 5 \, a b - 12 \, b^{2}\right)} \cosh\left(x\right)^{5} + {\left(6 \, a^{2} - 14 \, a b - 49 \, b^{2}\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{2} - 5 \, a b - 12 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{30 \, {\left(b^{2} \cosh\left(x\right)^{10} + 10 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{9} + b^{2} \sinh\left(x\right)^{10} + 5 \, b^{2} \cosh\left(x\right)^{8} + 5 \, {\left(9 \, b^{2} \cosh\left(x\right)^{2} + b^{2}\right)} \sinh\left(x\right)^{8} + 10 \, b^{2} \cosh\left(x\right)^{6} + 40 \, {\left(3 \, b^{2} \cosh\left(x\right)^{3} + b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{7} + 10 \, {\left(21 \, b^{2} \cosh\left(x\right)^{4} + 14 \, b^{2} \cosh\left(x\right)^{2} + b^{2}\right)} \sinh\left(x\right)^{6} + 10 \, b^{2} \cosh\left(x\right)^{4} + 4 \, {\left(63 \, b^{2} \cosh\left(x\right)^{5} + 70 \, b^{2} \cosh\left(x\right)^{3} + 15 \, b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 10 \, {\left(21 \, b^{2} \cosh\left(x\right)^{6} + 35 \, b^{2} \cosh\left(x\right)^{4} + 15 \, b^{2} \cosh\left(x\right)^{2} + b^{2}\right)} \sinh\left(x\right)^{4} + 5 \, b^{2} \cosh\left(x\right)^{2} + 40 \, {\left(3 \, b^{2} \cosh\left(x\right)^{7} + 7 \, b^{2} \cosh\left(x\right)^{5} + 5 \, b^{2} \cosh\left(x\right)^{3} + b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 5 \, {\left(9 \, b^{2} \cosh\left(x\right)^{8} + 28 \, b^{2} \cosh\left(x\right)^{6} + 30 \, b^{2} \cosh\left(x\right)^{4} + 12 \, b^{2} \cosh\left(x\right)^{2} + b^{2}\right)} \sinh\left(x\right)^{2} + b^{2} + 10 \, {\left(b^{2} \cosh\left(x\right)^{9} + 4 \, b^{2} \cosh\left(x\right)^{7} + 6 \, b^{2} \cosh\left(x\right)^{5} + 4 \, b^{2} \cosh\left(x\right)^{3} + b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}\right]"," ",0,"[1/60*(15*(b^2*cosh(x)^10 + 10*b^2*cosh(x)*sinh(x)^9 + b^2*sinh(x)^10 + 5*b^2*cosh(x)^8 + 5*(9*b^2*cosh(x)^2 + b^2)*sinh(x)^8 + 10*b^2*cosh(x)^6 + 40*(3*b^2*cosh(x)^3 + b^2*cosh(x))*sinh(x)^7 + 10*(21*b^2*cosh(x)^4 + 14*b^2*cosh(x)^2 + b^2)*sinh(x)^6 + 10*b^2*cosh(x)^4 + 4*(63*b^2*cosh(x)^5 + 70*b^2*cosh(x)^3 + 15*b^2*cosh(x))*sinh(x)^5 + 10*(21*b^2*cosh(x)^6 + 35*b^2*cosh(x)^4 + 15*b^2*cosh(x)^2 + b^2)*sinh(x)^4 + 5*b^2*cosh(x)^2 + 40*(3*b^2*cosh(x)^7 + 7*b^2*cosh(x)^5 + 5*b^2*cosh(x)^3 + b^2*cosh(x))*sinh(x)^3 + 5*(9*b^2*cosh(x)^8 + 28*b^2*cosh(x)^6 + 30*b^2*cosh(x)^4 + 12*b^2*cosh(x)^2 + b^2)*sinh(x)^2 + b^2 + 10*(b^2*cosh(x)^9 + 4*b^2*cosh(x)^7 + 6*b^2*cosh(x)^5 + 4*b^2*cosh(x)^3 + b^2*cosh(x))*sinh(x))*sqrt(a + b)*log(((a^3 + a^2*b)*cosh(x)^8 + 8*(a^3 + a^2*b)*cosh(x)*sinh(x)^7 + (a^3 + a^2*b)*sinh(x)^8 + 2*(2*a^3 + a^2*b)*cosh(x)^6 + 2*(2*a^3 + a^2*b + 14*(a^3 + a^2*b)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a^3 + a^2*b)*cosh(x)^3 + 3*(2*a^3 + a^2*b)*cosh(x))*sinh(x)^5 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^4 + (70*(a^3 + a^2*b)*cosh(x)^4 + 6*a^3 + 4*a^2*b - a*b^2 + b^3 + 30*(2*a^3 + a^2*b)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a^3 + a^2*b)*cosh(x)^5 + 10*(2*a^3 + a^2*b)*cosh(x)^3 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x))*sinh(x)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 + 2*(2*a^3 + 3*a^2*b - b^3)*cosh(x)^2 + 2*(14*(a^3 + a^2*b)*cosh(x)^6 + 15*(2*a^3 + a^2*b)*cosh(x)^4 + 2*a^3 + 3*a^2*b - b^3 + 3*(6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^2)*sinh(x)^2 + sqrt(2)*(a^2*cosh(x)^6 + 6*a^2*cosh(x)*sinh(x)^5 + a^2*sinh(x)^6 + 3*a^2*cosh(x)^4 + 3*(5*a^2*cosh(x)^2 + a^2)*sinh(x)^4 + 4*(5*a^2*cosh(x)^3 + 3*a^2*cosh(x))*sinh(x)^3 + (3*a^2 + 2*a*b - b^2)*cosh(x)^2 + (15*a^2*cosh(x)^4 + 18*a^2*cosh(x)^2 + 3*a^2 + 2*a*b - b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(3*a^2*cosh(x)^5 + 6*a^2*cosh(x)^3 + (3*a^2 + 2*a*b - b^2)*cosh(x))*sinh(x))*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a^3 + a^2*b)*cosh(x)^7 + 3*(2*a^3 + a^2*b)*cosh(x)^5 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^3 + (2*a^3 + 3*a^2*b - b^3)*cosh(x))*sinh(x))/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) + 15*(b^2*cosh(x)^10 + 10*b^2*cosh(x)*sinh(x)^9 + b^2*sinh(x)^10 + 5*b^2*cosh(x)^8 + 5*(9*b^2*cosh(x)^2 + b^2)*sinh(x)^8 + 10*b^2*cosh(x)^6 + 40*(3*b^2*cosh(x)^3 + b^2*cosh(x))*sinh(x)^7 + 10*(21*b^2*cosh(x)^4 + 14*b^2*cosh(x)^2 + b^2)*sinh(x)^6 + 10*b^2*cosh(x)^4 + 4*(63*b^2*cosh(x)^5 + 70*b^2*cosh(x)^3 + 15*b^2*cosh(x))*sinh(x)^5 + 10*(21*b^2*cosh(x)^6 + 35*b^2*cosh(x)^4 + 15*b^2*cosh(x)^2 + b^2)*sinh(x)^4 + 5*b^2*cosh(x)^2 + 40*(3*b^2*cosh(x)^7 + 7*b^2*cosh(x)^5 + 5*b^2*cosh(x)^3 + b^2*cosh(x))*sinh(x)^3 + 5*(9*b^2*cosh(x)^8 + 28*b^2*cosh(x)^6 + 30*b^2*cosh(x)^4 + 12*b^2*cosh(x)^2 + b^2)*sinh(x)^2 + b^2 + 10*(b^2*cosh(x)^9 + 4*b^2*cosh(x)^7 + 6*b^2*cosh(x)^5 + 4*b^2*cosh(x)^3 + b^2*cosh(x))*sinh(x))*sqrt(a + b)*log(-((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*b*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + b)*cosh(x)^3 - b*cosh(x))*sinh(x) + a + b)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*sqrt(2)*((2*a^2 - 6*a*b - 23*b^2)*cosh(x)^8 + 8*(2*a^2 - 6*a*b - 23*b^2)*cosh(x)*sinh(x)^7 + (2*a^2 - 6*a*b - 23*b^2)*sinh(x)^8 + 4*(2*a^2 - 5*a*b - 12*b^2)*cosh(x)^6 + 4*(7*(2*a^2 - 6*a*b - 23*b^2)*cosh(x)^2 + 2*a^2 - 5*a*b - 12*b^2)*sinh(x)^6 + 8*(7*(2*a^2 - 6*a*b - 23*b^2)*cosh(x)^3 + 3*(2*a^2 - 5*a*b - 12*b^2)*cosh(x))*sinh(x)^5 + 2*(6*a^2 - 14*a*b - 49*b^2)*cosh(x)^4 + 2*(35*(2*a^2 - 6*a*b - 23*b^2)*cosh(x)^4 + 30*(2*a^2 - 5*a*b - 12*b^2)*cosh(x)^2 + 6*a^2 - 14*a*b - 49*b^2)*sinh(x)^4 + 8*(7*(2*a^2 - 6*a*b - 23*b^2)*cosh(x)^5 + 10*(2*a^2 - 5*a*b - 12*b^2)*cosh(x)^3 + (6*a^2 - 14*a*b - 49*b^2)*cosh(x))*sinh(x)^3 + 4*(2*a^2 - 5*a*b - 12*b^2)*cosh(x)^2 + 4*(7*(2*a^2 - 6*a*b - 23*b^2)*cosh(x)^6 + 15*(2*a^2 - 5*a*b - 12*b^2)*cosh(x)^4 + 3*(6*a^2 - 14*a*b - 49*b^2)*cosh(x)^2 + 2*a^2 - 5*a*b - 12*b^2)*sinh(x)^2 + 2*a^2 - 6*a*b - 23*b^2 + 8*((2*a^2 - 6*a*b - 23*b^2)*cosh(x)^7 + 3*(2*a^2 - 5*a*b - 12*b^2)*cosh(x)^5 + (6*a^2 - 14*a*b - 49*b^2)*cosh(x)^3 + (2*a^2 - 5*a*b - 12*b^2)*cosh(x))*sinh(x))*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(b^2*cosh(x)^10 + 10*b^2*cosh(x)*sinh(x)^9 + b^2*sinh(x)^10 + 5*b^2*cosh(x)^8 + 5*(9*b^2*cosh(x)^2 + b^2)*sinh(x)^8 + 10*b^2*cosh(x)^6 + 40*(3*b^2*cosh(x)^3 + b^2*cosh(x))*sinh(x)^7 + 10*(21*b^2*cosh(x)^4 + 14*b^2*cosh(x)^2 + b^2)*sinh(x)^6 + 10*b^2*cosh(x)^4 + 4*(63*b^2*cosh(x)^5 + 70*b^2*cosh(x)^3 + 15*b^2*cosh(x))*sinh(x)^5 + 10*(21*b^2*cosh(x)^6 + 35*b^2*cosh(x)^4 + 15*b^2*cosh(x)^2 + b^2)*sinh(x)^4 + 5*b^2*cosh(x)^2 + 40*(3*b^2*cosh(x)^7 + 7*b^2*cosh(x)^5 + 5*b^2*cosh(x)^3 + b^2*cosh(x))*sinh(x)^3 + 5*(9*b^2*cosh(x)^8 + 28*b^2*cosh(x)^6 + 30*b^2*cosh(x)^4 + 12*b^2*cosh(x)^2 + b^2)*sinh(x)^2 + b^2 + 10*(b^2*cosh(x)^9 + 4*b^2*cosh(x)^7 + 6*b^2*cosh(x)^5 + 4*b^2*cosh(x)^3 + b^2*cosh(x))*sinh(x)), -1/30*(15*(b^2*cosh(x)^10 + 10*b^2*cosh(x)*sinh(x)^9 + b^2*sinh(x)^10 + 5*b^2*cosh(x)^8 + 5*(9*b^2*cosh(x)^2 + b^2)*sinh(x)^8 + 10*b^2*cosh(x)^6 + 40*(3*b^2*cosh(x)^3 + b^2*cosh(x))*sinh(x)^7 + 10*(21*b^2*cosh(x)^4 + 14*b^2*cosh(x)^2 + b^2)*sinh(x)^6 + 10*b^2*cosh(x)^4 + 4*(63*b^2*cosh(x)^5 + 70*b^2*cosh(x)^3 + 15*b^2*cosh(x))*sinh(x)^5 + 10*(21*b^2*cosh(x)^6 + 35*b^2*cosh(x)^4 + 15*b^2*cosh(x)^2 + b^2)*sinh(x)^4 + 5*b^2*cosh(x)^2 + 40*(3*b^2*cosh(x)^7 + 7*b^2*cosh(x)^5 + 5*b^2*cosh(x)^3 + b^2*cosh(x))*sinh(x)^3 + 5*(9*b^2*cosh(x)^8 + 28*b^2*cosh(x)^6 + 30*b^2*cosh(x)^4 + 12*b^2*cosh(x)^2 + b^2)*sinh(x)^2 + b^2 + 10*(b^2*cosh(x)^9 + 4*b^2*cosh(x)^7 + 6*b^2*cosh(x)^5 + 4*b^2*cosh(x)^3 + b^2*cosh(x))*sinh(x))*sqrt(-a - b)*arctan(sqrt(2)*(a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 + a + b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a^2 + a*b)*cosh(x)^4 + 4*(a^2 + a*b)*cosh(x)*sinh(x)^3 + (a^2 + a*b)*sinh(x)^4 + (2*a^2 + a*b - b^2)*cosh(x)^2 + (6*(a^2 + a*b)*cosh(x)^2 + 2*a^2 + a*b - b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(2*(a^2 + a*b)*cosh(x)^3 + (2*a^2 + a*b - b^2)*cosh(x))*sinh(x))) + 15*(b^2*cosh(x)^10 + 10*b^2*cosh(x)*sinh(x)^9 + b^2*sinh(x)^10 + 5*b^2*cosh(x)^8 + 5*(9*b^2*cosh(x)^2 + b^2)*sinh(x)^8 + 10*b^2*cosh(x)^6 + 40*(3*b^2*cosh(x)^3 + b^2*cosh(x))*sinh(x)^7 + 10*(21*b^2*cosh(x)^4 + 14*b^2*cosh(x)^2 + b^2)*sinh(x)^6 + 10*b^2*cosh(x)^4 + 4*(63*b^2*cosh(x)^5 + 70*b^2*cosh(x)^3 + 15*b^2*cosh(x))*sinh(x)^5 + 10*(21*b^2*cosh(x)^6 + 35*b^2*cosh(x)^4 + 15*b^2*cosh(x)^2 + b^2)*sinh(x)^4 + 5*b^2*cosh(x)^2 + 40*(3*b^2*cosh(x)^7 + 7*b^2*cosh(x)^5 + 5*b^2*cosh(x)^3 + b^2*cosh(x))*sinh(x)^3 + 5*(9*b^2*cosh(x)^8 + 28*b^2*cosh(x)^6 + 30*b^2*cosh(x)^4 + 12*b^2*cosh(x)^2 + b^2)*sinh(x)^2 + b^2 + 10*(b^2*cosh(x)^9 + 4*b^2*cosh(x)^7 + 6*b^2*cosh(x)^5 + 4*b^2*cosh(x)^3 + b^2*cosh(x))*sinh(x))*sqrt(-a - b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a - b)*cosh(x))*sinh(x) + a + b)) - 2*sqrt(2)*((2*a^2 - 6*a*b - 23*b^2)*cosh(x)^8 + 8*(2*a^2 - 6*a*b - 23*b^2)*cosh(x)*sinh(x)^7 + (2*a^2 - 6*a*b - 23*b^2)*sinh(x)^8 + 4*(2*a^2 - 5*a*b - 12*b^2)*cosh(x)^6 + 4*(7*(2*a^2 - 6*a*b - 23*b^2)*cosh(x)^2 + 2*a^2 - 5*a*b - 12*b^2)*sinh(x)^6 + 8*(7*(2*a^2 - 6*a*b - 23*b^2)*cosh(x)^3 + 3*(2*a^2 - 5*a*b - 12*b^2)*cosh(x))*sinh(x)^5 + 2*(6*a^2 - 14*a*b - 49*b^2)*cosh(x)^4 + 2*(35*(2*a^2 - 6*a*b - 23*b^2)*cosh(x)^4 + 30*(2*a^2 - 5*a*b - 12*b^2)*cosh(x)^2 + 6*a^2 - 14*a*b - 49*b^2)*sinh(x)^4 + 8*(7*(2*a^2 - 6*a*b - 23*b^2)*cosh(x)^5 + 10*(2*a^2 - 5*a*b - 12*b^2)*cosh(x)^3 + (6*a^2 - 14*a*b - 49*b^2)*cosh(x))*sinh(x)^3 + 4*(2*a^2 - 5*a*b - 12*b^2)*cosh(x)^2 + 4*(7*(2*a^2 - 6*a*b - 23*b^2)*cosh(x)^6 + 15*(2*a^2 - 5*a*b - 12*b^2)*cosh(x)^4 + 3*(6*a^2 - 14*a*b - 49*b^2)*cosh(x)^2 + 2*a^2 - 5*a*b - 12*b^2)*sinh(x)^2 + 2*a^2 - 6*a*b - 23*b^2 + 8*((2*a^2 - 6*a*b - 23*b^2)*cosh(x)^7 + 3*(2*a^2 - 5*a*b - 12*b^2)*cosh(x)^5 + (6*a^2 - 14*a*b - 49*b^2)*cosh(x)^3 + (2*a^2 - 5*a*b - 12*b^2)*cosh(x))*sinh(x))*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(b^2*cosh(x)^10 + 10*b^2*cosh(x)*sinh(x)^9 + b^2*sinh(x)^10 + 5*b^2*cosh(x)^8 + 5*(9*b^2*cosh(x)^2 + b^2)*sinh(x)^8 + 10*b^2*cosh(x)^6 + 40*(3*b^2*cosh(x)^3 + b^2*cosh(x))*sinh(x)^7 + 10*(21*b^2*cosh(x)^4 + 14*b^2*cosh(x)^2 + b^2)*sinh(x)^6 + 10*b^2*cosh(x)^4 + 4*(63*b^2*cosh(x)^5 + 70*b^2*cosh(x)^3 + 15*b^2*cosh(x))*sinh(x)^5 + 10*(21*b^2*cosh(x)^6 + 35*b^2*cosh(x)^4 + 15*b^2*cosh(x)^2 + b^2)*sinh(x)^4 + 5*b^2*cosh(x)^2 + 40*(3*b^2*cosh(x)^7 + 7*b^2*cosh(x)^5 + 5*b^2*cosh(x)^3 + b^2*cosh(x))*sinh(x)^3 + 5*(9*b^2*cosh(x)^8 + 28*b^2*cosh(x)^6 + 30*b^2*cosh(x)^4 + 12*b^2*cosh(x)^2 + b^2)*sinh(x)^2 + b^2 + 10*(b^2*cosh(x)^9 + 4*b^2*cosh(x)^7 + 6*b^2*cosh(x)^5 + 4*b^2*cosh(x)^3 + b^2*cosh(x))*sinh(x))]","B",0
209,1,9360,0,0.951260," ","integrate((a+b*tanh(x)^2)^(1/2)*tanh(x)^4,x, algorithm=""fricas"")","\left[\frac{4 \, {\left(b^{2} \cosh\left(x\right)^{8} + 8 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{7} + b^{2} \sinh\left(x\right)^{8} + 4 \, b^{2} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, b^{2} \cosh\left(x\right)^{2} + b^{2}\right)} \sinh\left(x\right)^{6} + 6 \, b^{2} \cosh\left(x\right)^{4} + 8 \, {\left(7 \, b^{2} \cosh\left(x\right)^{3} + 3 \, b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(35 \, b^{2} \cosh\left(x\right)^{4} + 30 \, b^{2} \cosh\left(x\right)^{2} + 3 \, b^{2}\right)} \sinh\left(x\right)^{4} + 4 \, b^{2} \cosh\left(x\right)^{2} + 8 \, {\left(7 \, b^{2} \cosh\left(x\right)^{5} + 10 \, b^{2} \cosh\left(x\right)^{3} + 3 \, b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(7 \, b^{2} \cosh\left(x\right)^{6} + 15 \, b^{2} \cosh\left(x\right)^{4} + 9 \, b^{2} \cosh\left(x\right)^{2} + b^{2}\right)} \sinh\left(x\right)^{2} + b^{2} + 8 \, {\left(b^{2} \cosh\left(x\right)^{7} + 3 \, b^{2} \cosh\left(x\right)^{5} + 3 \, b^{2} \cosh\left(x\right)^{3} + b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \log\left(-\frac{{\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a b^{2} + b^{3}\right)} \sinh\left(x\right)^{8} - 2 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{6} - 2 \, {\left(a b^{2} + 2 \, b^{3} - 14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3} - 30 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} + 2 \, {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} - 3 \, a b^{2} - 2 \, b^{3} + 3 \, {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(b^{2} \cosh\left(x\right)^{6} + 6 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + b^{2} \sinh\left(x\right)^{6} - 3 \, b^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, b^{2} \cosh\left(x\right)^{2} - b^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, b^{2} \cosh\left(x\right)^{3} - 3 \, b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, b^{2} \cosh\left(x\right)^{4} - 18 \, b^{2} \cosh\left(x\right)^{2} - a^{2} + 2 \, a b + 3 \, b^{2}\right)} \sinh\left(x\right)^{2} - a^{2} - 2 \, a b - b^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{5} - 6 \, b^{2} \cosh\left(x\right)^{3} - {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{5} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) - {\left({\left(a^{2} - 4 \, a b - 8 \, b^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{2} - 4 \, a b - 8 \, b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{2} - 4 \, a b - 8 \, b^{2}\right)} \sinh\left(x\right)^{8} + 4 \, {\left(a^{2} - 4 \, a b - 8 \, b^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} - 4 \, a b - 8 \, b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} - 4 \, a b - 8 \, b^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} - 4 \, a b - 8 \, b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{2} - 4 \, a b - 8 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 6 \, {\left(a^{2} - 4 \, a b - 8 \, b^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} - 4 \, a b - 8 \, b^{2}\right)} \cosh\left(x\right)^{4} + 30 \, {\left(a^{2} - 4 \, a b - 8 \, b^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} - 12 \, a b - 24 \, b^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} - 4 \, a b - 8 \, b^{2}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(a^{2} - 4 \, a b - 8 \, b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{2} - 4 \, a b - 8 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(a^{2} - 4 \, a b - 8 \, b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} - 4 \, a b - 8 \, b^{2}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(a^{2} - 4 \, a b - 8 \, b^{2}\right)} \cosh\left(x\right)^{4} + 9 \, {\left(a^{2} - 4 \, a b - 8 \, b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} - 4 \, a b - 8 \, b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} - 4 \, a b - 8 \, b^{2} + 8 \, {\left({\left(a^{2} - 4 \, a b - 8 \, b^{2}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(a^{2} - 4 \, a b - 8 \, b^{2}\right)} \cosh\left(x\right)^{5} + 3 \, {\left(a^{2} - 4 \, a b - 8 \, b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{2} - 4 \, a b - 8 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{b} \log\left(-\frac{{\left(a + 2 \, b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + 2 \, b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + a - 2 \, b\right)} \sinh\left(x\right)^{2} - 2 \, \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + 2 \, b\right)} \cosh\left(x\right)^{3} + {\left(a - 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + 2 \, b}{\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) + 4 \, {\left(b^{2} \cosh\left(x\right)^{8} + 8 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{7} + b^{2} \sinh\left(x\right)^{8} + 4 \, b^{2} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, b^{2} \cosh\left(x\right)^{2} + b^{2}\right)} \sinh\left(x\right)^{6} + 6 \, b^{2} \cosh\left(x\right)^{4} + 8 \, {\left(7 \, b^{2} \cosh\left(x\right)^{3} + 3 \, b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(35 \, b^{2} \cosh\left(x\right)^{4} + 30 \, b^{2} \cosh\left(x\right)^{2} + 3 \, b^{2}\right)} \sinh\left(x\right)^{4} + 4 \, b^{2} \cosh\left(x\right)^{2} + 8 \, {\left(7 \, b^{2} \cosh\left(x\right)^{5} + 10 \, b^{2} \cosh\left(x\right)^{3} + 3 \, b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(7 \, b^{2} \cosh\left(x\right)^{6} + 15 \, b^{2} \cosh\left(x\right)^{4} + 9 \, b^{2} \cosh\left(x\right)^{2} + b^{2}\right)} \sinh\left(x\right)^{2} + b^{2} + 8 \, {\left(b^{2} \cosh\left(x\right)^{7} + 3 \, b^{2} \cosh\left(x\right)^{5} + 3 \, b^{2} \cosh\left(x\right)^{3} + b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \log\left(\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, a \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + a \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right) - 2 \, \sqrt{2} {\left({\left(a b + 6 \, b^{2}\right)} \cosh\left(x\right)^{6} + 6 \, {\left(a b + 6 \, b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(a b + 6 \, b^{2}\right)} \sinh\left(x\right)^{6} + {\left(a b - 2 \, b^{2}\right)} \cosh\left(x\right)^{4} + {\left(15 \, {\left(a b + 6 \, b^{2}\right)} \cosh\left(x\right)^{2} + a b - 2 \, b^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, {\left(a b + 6 \, b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a b - 2 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - {\left(a b - 2 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, {\left(a b + 6 \, b^{2}\right)} \cosh\left(x\right)^{4} + 6 \, {\left(a b - 2 \, b^{2}\right)} \cosh\left(x\right)^{2} - a b + 2 \, b^{2}\right)} \sinh\left(x\right)^{2} - a b - 6 \, b^{2} + 2 \, {\left(3 \, {\left(a b + 6 \, b^{2}\right)} \cosh\left(x\right)^{5} + 2 \, {\left(a b - 2 \, b^{2}\right)} \cosh\left(x\right)^{3} - {\left(a b - 2 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{16 \, {\left(b^{2} \cosh\left(x\right)^{8} + 8 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{7} + b^{2} \sinh\left(x\right)^{8} + 4 \, b^{2} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, b^{2} \cosh\left(x\right)^{2} + b^{2}\right)} \sinh\left(x\right)^{6} + 6 \, b^{2} \cosh\left(x\right)^{4} + 8 \, {\left(7 \, b^{2} \cosh\left(x\right)^{3} + 3 \, b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(35 \, b^{2} \cosh\left(x\right)^{4} + 30 \, b^{2} \cosh\left(x\right)^{2} + 3 \, b^{2}\right)} \sinh\left(x\right)^{4} + 4 \, b^{2} \cosh\left(x\right)^{2} + 8 \, {\left(7 \, b^{2} \cosh\left(x\right)^{5} + 10 \, b^{2} \cosh\left(x\right)^{3} + 3 \, b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(7 \, b^{2} \cosh\left(x\right)^{6} + 15 \, b^{2} \cosh\left(x\right)^{4} + 9 \, b^{2} \cosh\left(x\right)^{2} + b^{2}\right)} \sinh\left(x\right)^{2} + b^{2} + 8 \, {\left(b^{2} \cosh\left(x\right)^{7} + 3 \, b^{2} \cosh\left(x\right)^{5} + 3 \, b^{2} \cosh\left(x\right)^{3} + b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}, -\frac{{\left({\left(a^{2} - 4 \, a b - 8 \, b^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{2} - 4 \, a b - 8 \, b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{2} - 4 \, a b - 8 \, b^{2}\right)} \sinh\left(x\right)^{8} + 4 \, {\left(a^{2} - 4 \, a b - 8 \, b^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} - 4 \, a b - 8 \, b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} - 4 \, a b - 8 \, b^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} - 4 \, a b - 8 \, b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{2} - 4 \, a b - 8 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 6 \, {\left(a^{2} - 4 \, a b - 8 \, b^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} - 4 \, a b - 8 \, b^{2}\right)} \cosh\left(x\right)^{4} + 30 \, {\left(a^{2} - 4 \, a b - 8 \, b^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} - 12 \, a b - 24 \, b^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} - 4 \, a b - 8 \, b^{2}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(a^{2} - 4 \, a b - 8 \, b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{2} - 4 \, a b - 8 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(a^{2} - 4 \, a b - 8 \, b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} - 4 \, a b - 8 \, b^{2}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(a^{2} - 4 \, a b - 8 \, b^{2}\right)} \cosh\left(x\right)^{4} + 9 \, {\left(a^{2} - 4 \, a b - 8 \, b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} - 4 \, a b - 8 \, b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} - 4 \, a b - 8 \, b^{2} + 8 \, {\left({\left(a^{2} - 4 \, a b - 8 \, b^{2}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(a^{2} - 4 \, a b - 8 \, b^{2}\right)} \cosh\left(x\right)^{5} + 3 \, {\left(a^{2} - 4 \, a b - 8 \, b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{2} - 4 \, a b - 8 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{-b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) - 2 \, {\left(b^{2} \cosh\left(x\right)^{8} + 8 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{7} + b^{2} \sinh\left(x\right)^{8} + 4 \, b^{2} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, b^{2} \cosh\left(x\right)^{2} + b^{2}\right)} \sinh\left(x\right)^{6} + 6 \, b^{2} \cosh\left(x\right)^{4} + 8 \, {\left(7 \, b^{2} \cosh\left(x\right)^{3} + 3 \, b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(35 \, b^{2} \cosh\left(x\right)^{4} + 30 \, b^{2} \cosh\left(x\right)^{2} + 3 \, b^{2}\right)} \sinh\left(x\right)^{4} + 4 \, b^{2} \cosh\left(x\right)^{2} + 8 \, {\left(7 \, b^{2} \cosh\left(x\right)^{5} + 10 \, b^{2} \cosh\left(x\right)^{3} + 3 \, b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(7 \, b^{2} \cosh\left(x\right)^{6} + 15 \, b^{2} \cosh\left(x\right)^{4} + 9 \, b^{2} \cosh\left(x\right)^{2} + b^{2}\right)} \sinh\left(x\right)^{2} + b^{2} + 8 \, {\left(b^{2} \cosh\left(x\right)^{7} + 3 \, b^{2} \cosh\left(x\right)^{5} + 3 \, b^{2} \cosh\left(x\right)^{3} + b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \log\left(-\frac{{\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a b^{2} + b^{3}\right)} \sinh\left(x\right)^{8} - 2 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{6} - 2 \, {\left(a b^{2} + 2 \, b^{3} - 14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3} - 30 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} + 2 \, {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} - 3 \, a b^{2} - 2 \, b^{3} + 3 \, {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(b^{2} \cosh\left(x\right)^{6} + 6 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + b^{2} \sinh\left(x\right)^{6} - 3 \, b^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, b^{2} \cosh\left(x\right)^{2} - b^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, b^{2} \cosh\left(x\right)^{3} - 3 \, b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, b^{2} \cosh\left(x\right)^{4} - 18 \, b^{2} \cosh\left(x\right)^{2} - a^{2} + 2 \, a b + 3 \, b^{2}\right)} \sinh\left(x\right)^{2} - a^{2} - 2 \, a b - b^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{5} - 6 \, b^{2} \cosh\left(x\right)^{3} - {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{5} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) - 2 \, {\left(b^{2} \cosh\left(x\right)^{8} + 8 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{7} + b^{2} \sinh\left(x\right)^{8} + 4 \, b^{2} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, b^{2} \cosh\left(x\right)^{2} + b^{2}\right)} \sinh\left(x\right)^{6} + 6 \, b^{2} \cosh\left(x\right)^{4} + 8 \, {\left(7 \, b^{2} \cosh\left(x\right)^{3} + 3 \, b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(35 \, b^{2} \cosh\left(x\right)^{4} + 30 \, b^{2} \cosh\left(x\right)^{2} + 3 \, b^{2}\right)} \sinh\left(x\right)^{4} + 4 \, b^{2} \cosh\left(x\right)^{2} + 8 \, {\left(7 \, b^{2} \cosh\left(x\right)^{5} + 10 \, b^{2} \cosh\left(x\right)^{3} + 3 \, b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(7 \, b^{2} \cosh\left(x\right)^{6} + 15 \, b^{2} \cosh\left(x\right)^{4} + 9 \, b^{2} \cosh\left(x\right)^{2} + b^{2}\right)} \sinh\left(x\right)^{2} + b^{2} + 8 \, {\left(b^{2} \cosh\left(x\right)^{7} + 3 \, b^{2} \cosh\left(x\right)^{5} + 3 \, b^{2} \cosh\left(x\right)^{3} + b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \log\left(\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, a \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + a \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right) + \sqrt{2} {\left({\left(a b + 6 \, b^{2}\right)} \cosh\left(x\right)^{6} + 6 \, {\left(a b + 6 \, b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(a b + 6 \, b^{2}\right)} \sinh\left(x\right)^{6} + {\left(a b - 2 \, b^{2}\right)} \cosh\left(x\right)^{4} + {\left(15 \, {\left(a b + 6 \, b^{2}\right)} \cosh\left(x\right)^{2} + a b - 2 \, b^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, {\left(a b + 6 \, b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a b - 2 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - {\left(a b - 2 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, {\left(a b + 6 \, b^{2}\right)} \cosh\left(x\right)^{4} + 6 \, {\left(a b - 2 \, b^{2}\right)} \cosh\left(x\right)^{2} - a b + 2 \, b^{2}\right)} \sinh\left(x\right)^{2} - a b - 6 \, b^{2} + 2 \, {\left(3 \, {\left(a b + 6 \, b^{2}\right)} \cosh\left(x\right)^{5} + 2 \, {\left(a b - 2 \, b^{2}\right)} \cosh\left(x\right)^{3} - {\left(a b - 2 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{8 \, {\left(b^{2} \cosh\left(x\right)^{8} + 8 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{7} + b^{2} \sinh\left(x\right)^{8} + 4 \, b^{2} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, b^{2} \cosh\left(x\right)^{2} + b^{2}\right)} \sinh\left(x\right)^{6} + 6 \, b^{2} \cosh\left(x\right)^{4} + 8 \, {\left(7 \, b^{2} \cosh\left(x\right)^{3} + 3 \, b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(35 \, b^{2} \cosh\left(x\right)^{4} + 30 \, b^{2} \cosh\left(x\right)^{2} + 3 \, b^{2}\right)} \sinh\left(x\right)^{4} + 4 \, b^{2} \cosh\left(x\right)^{2} + 8 \, {\left(7 \, b^{2} \cosh\left(x\right)^{5} + 10 \, b^{2} \cosh\left(x\right)^{3} + 3 \, b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(7 \, b^{2} \cosh\left(x\right)^{6} + 15 \, b^{2} \cosh\left(x\right)^{4} + 9 \, b^{2} \cosh\left(x\right)^{2} + b^{2}\right)} \sinh\left(x\right)^{2} + b^{2} + 8 \, {\left(b^{2} \cosh\left(x\right)^{7} + 3 \, b^{2} \cosh\left(x\right)^{5} + 3 \, b^{2} \cosh\left(x\right)^{3} + b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}, -\frac{8 \, {\left(b^{2} \cosh\left(x\right)^{8} + 8 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{7} + b^{2} \sinh\left(x\right)^{8} + 4 \, b^{2} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, b^{2} \cosh\left(x\right)^{2} + b^{2}\right)} \sinh\left(x\right)^{6} + 6 \, b^{2} \cosh\left(x\right)^{4} + 8 \, {\left(7 \, b^{2} \cosh\left(x\right)^{3} + 3 \, b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(35 \, b^{2} \cosh\left(x\right)^{4} + 30 \, b^{2} \cosh\left(x\right)^{2} + 3 \, b^{2}\right)} \sinh\left(x\right)^{4} + 4 \, b^{2} \cosh\left(x\right)^{2} + 8 \, {\left(7 \, b^{2} \cosh\left(x\right)^{5} + 10 \, b^{2} \cosh\left(x\right)^{3} + 3 \, b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(7 \, b^{2} \cosh\left(x\right)^{6} + 15 \, b^{2} \cosh\left(x\right)^{4} + 9 \, b^{2} \cosh\left(x\right)^{2} + b^{2}\right)} \sinh\left(x\right)^{2} + b^{2} + 8 \, {\left(b^{2} \cosh\left(x\right)^{7} + 3 \, b^{2} \cosh\left(x\right)^{5} + 3 \, b^{2} \cosh\left(x\right)^{3} + b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} - a - b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a b + b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a b + b^{2}\right)} \sinh\left(x\right)^{4} + {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} - a b - 2 \, b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(2 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + 8 \, {\left(b^{2} \cosh\left(x\right)^{8} + 8 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{7} + b^{2} \sinh\left(x\right)^{8} + 4 \, b^{2} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, b^{2} \cosh\left(x\right)^{2} + b^{2}\right)} \sinh\left(x\right)^{6} + 6 \, b^{2} \cosh\left(x\right)^{4} + 8 \, {\left(7 \, b^{2} \cosh\left(x\right)^{3} + 3 \, b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(35 \, b^{2} \cosh\left(x\right)^{4} + 30 \, b^{2} \cosh\left(x\right)^{2} + 3 \, b^{2}\right)} \sinh\left(x\right)^{4} + 4 \, b^{2} \cosh\left(x\right)^{2} + 8 \, {\left(7 \, b^{2} \cosh\left(x\right)^{5} + 10 \, b^{2} \cosh\left(x\right)^{3} + 3 \, b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(7 \, b^{2} \cosh\left(x\right)^{6} + 15 \, b^{2} \cosh\left(x\right)^{4} + 9 \, b^{2} \cosh\left(x\right)^{2} + b^{2}\right)} \sinh\left(x\right)^{2} + b^{2} + 8 \, {\left(b^{2} \cosh\left(x\right)^{7} + 3 \, b^{2} \cosh\left(x\right)^{5} + 3 \, b^{2} \cosh\left(x\right)^{3} + b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) + {\left({\left(a^{2} - 4 \, a b - 8 \, b^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{2} - 4 \, a b - 8 \, b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{2} - 4 \, a b - 8 \, b^{2}\right)} \sinh\left(x\right)^{8} + 4 \, {\left(a^{2} - 4 \, a b - 8 \, b^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} - 4 \, a b - 8 \, b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} - 4 \, a b - 8 \, b^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} - 4 \, a b - 8 \, b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{2} - 4 \, a b - 8 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 6 \, {\left(a^{2} - 4 \, a b - 8 \, b^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} - 4 \, a b - 8 \, b^{2}\right)} \cosh\left(x\right)^{4} + 30 \, {\left(a^{2} - 4 \, a b - 8 \, b^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} - 12 \, a b - 24 \, b^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} - 4 \, a b - 8 \, b^{2}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(a^{2} - 4 \, a b - 8 \, b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{2} - 4 \, a b - 8 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(a^{2} - 4 \, a b - 8 \, b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} - 4 \, a b - 8 \, b^{2}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(a^{2} - 4 \, a b - 8 \, b^{2}\right)} \cosh\left(x\right)^{4} + 9 \, {\left(a^{2} - 4 \, a b - 8 \, b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} - 4 \, a b - 8 \, b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} - 4 \, a b - 8 \, b^{2} + 8 \, {\left({\left(a^{2} - 4 \, a b - 8 \, b^{2}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(a^{2} - 4 \, a b - 8 \, b^{2}\right)} \cosh\left(x\right)^{5} + 3 \, {\left(a^{2} - 4 \, a b - 8 \, b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{2} - 4 \, a b - 8 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{b} \log\left(-\frac{{\left(a + 2 \, b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + 2 \, b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + a - 2 \, b\right)} \sinh\left(x\right)^{2} - 2 \, \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + 2 \, b\right)} \cosh\left(x\right)^{3} + {\left(a - 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + 2 \, b}{\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) + 2 \, \sqrt{2} {\left({\left(a b + 6 \, b^{2}\right)} \cosh\left(x\right)^{6} + 6 \, {\left(a b + 6 \, b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(a b + 6 \, b^{2}\right)} \sinh\left(x\right)^{6} + {\left(a b - 2 \, b^{2}\right)} \cosh\left(x\right)^{4} + {\left(15 \, {\left(a b + 6 \, b^{2}\right)} \cosh\left(x\right)^{2} + a b - 2 \, b^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, {\left(a b + 6 \, b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a b - 2 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - {\left(a b - 2 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, {\left(a b + 6 \, b^{2}\right)} \cosh\left(x\right)^{4} + 6 \, {\left(a b - 2 \, b^{2}\right)} \cosh\left(x\right)^{2} - a b + 2 \, b^{2}\right)} \sinh\left(x\right)^{2} - a b - 6 \, b^{2} + 2 \, {\left(3 \, {\left(a b + 6 \, b^{2}\right)} \cosh\left(x\right)^{5} + 2 \, {\left(a b - 2 \, b^{2}\right)} \cosh\left(x\right)^{3} - {\left(a b - 2 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{16 \, {\left(b^{2} \cosh\left(x\right)^{8} + 8 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{7} + b^{2} \sinh\left(x\right)^{8} + 4 \, b^{2} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, b^{2} \cosh\left(x\right)^{2} + b^{2}\right)} \sinh\left(x\right)^{6} + 6 \, b^{2} \cosh\left(x\right)^{4} + 8 \, {\left(7 \, b^{2} \cosh\left(x\right)^{3} + 3 \, b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(35 \, b^{2} \cosh\left(x\right)^{4} + 30 \, b^{2} \cosh\left(x\right)^{2} + 3 \, b^{2}\right)} \sinh\left(x\right)^{4} + 4 \, b^{2} \cosh\left(x\right)^{2} + 8 \, {\left(7 \, b^{2} \cosh\left(x\right)^{5} + 10 \, b^{2} \cosh\left(x\right)^{3} + 3 \, b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(7 \, b^{2} \cosh\left(x\right)^{6} + 15 \, b^{2} \cosh\left(x\right)^{4} + 9 \, b^{2} \cosh\left(x\right)^{2} + b^{2}\right)} \sinh\left(x\right)^{2} + b^{2} + 8 \, {\left(b^{2} \cosh\left(x\right)^{7} + 3 \, b^{2} \cosh\left(x\right)^{5} + 3 \, b^{2} \cosh\left(x\right)^{3} + b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}, -\frac{4 \, {\left(b^{2} \cosh\left(x\right)^{8} + 8 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{7} + b^{2} \sinh\left(x\right)^{8} + 4 \, b^{2} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, b^{2} \cosh\left(x\right)^{2} + b^{2}\right)} \sinh\left(x\right)^{6} + 6 \, b^{2} \cosh\left(x\right)^{4} + 8 \, {\left(7 \, b^{2} \cosh\left(x\right)^{3} + 3 \, b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(35 \, b^{2} \cosh\left(x\right)^{4} + 30 \, b^{2} \cosh\left(x\right)^{2} + 3 \, b^{2}\right)} \sinh\left(x\right)^{4} + 4 \, b^{2} \cosh\left(x\right)^{2} + 8 \, {\left(7 \, b^{2} \cosh\left(x\right)^{5} + 10 \, b^{2} \cosh\left(x\right)^{3} + 3 \, b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(7 \, b^{2} \cosh\left(x\right)^{6} + 15 \, b^{2} \cosh\left(x\right)^{4} + 9 \, b^{2} \cosh\left(x\right)^{2} + b^{2}\right)} \sinh\left(x\right)^{2} + b^{2} + 8 \, {\left(b^{2} \cosh\left(x\right)^{7} + 3 \, b^{2} \cosh\left(x\right)^{5} + 3 \, b^{2} \cosh\left(x\right)^{3} + b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} - a - b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a b + b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a b + b^{2}\right)} \sinh\left(x\right)^{4} + {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} - a b - 2 \, b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(2 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + 4 \, {\left(b^{2} \cosh\left(x\right)^{8} + 8 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{7} + b^{2} \sinh\left(x\right)^{8} + 4 \, b^{2} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, b^{2} \cosh\left(x\right)^{2} + b^{2}\right)} \sinh\left(x\right)^{6} + 6 \, b^{2} \cosh\left(x\right)^{4} + 8 \, {\left(7 \, b^{2} \cosh\left(x\right)^{3} + 3 \, b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(35 \, b^{2} \cosh\left(x\right)^{4} + 30 \, b^{2} \cosh\left(x\right)^{2} + 3 \, b^{2}\right)} \sinh\left(x\right)^{4} + 4 \, b^{2} \cosh\left(x\right)^{2} + 8 \, {\left(7 \, b^{2} \cosh\left(x\right)^{5} + 10 \, b^{2} \cosh\left(x\right)^{3} + 3 \, b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(7 \, b^{2} \cosh\left(x\right)^{6} + 15 \, b^{2} \cosh\left(x\right)^{4} + 9 \, b^{2} \cosh\left(x\right)^{2} + b^{2}\right)} \sinh\left(x\right)^{2} + b^{2} + 8 \, {\left(b^{2} \cosh\left(x\right)^{7} + 3 \, b^{2} \cosh\left(x\right)^{5} + 3 \, b^{2} \cosh\left(x\right)^{3} + b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) + {\left({\left(a^{2} - 4 \, a b - 8 \, b^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{2} - 4 \, a b - 8 \, b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{2} - 4 \, a b - 8 \, b^{2}\right)} \sinh\left(x\right)^{8} + 4 \, {\left(a^{2} - 4 \, a b - 8 \, b^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} - 4 \, a b - 8 \, b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} - 4 \, a b - 8 \, b^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} - 4 \, a b - 8 \, b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{2} - 4 \, a b - 8 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 6 \, {\left(a^{2} - 4 \, a b - 8 \, b^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} - 4 \, a b - 8 \, b^{2}\right)} \cosh\left(x\right)^{4} + 30 \, {\left(a^{2} - 4 \, a b - 8 \, b^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} - 12 \, a b - 24 \, b^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} - 4 \, a b - 8 \, b^{2}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(a^{2} - 4 \, a b - 8 \, b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{2} - 4 \, a b - 8 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(a^{2} - 4 \, a b - 8 \, b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} - 4 \, a b - 8 \, b^{2}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(a^{2} - 4 \, a b - 8 \, b^{2}\right)} \cosh\left(x\right)^{4} + 9 \, {\left(a^{2} - 4 \, a b - 8 \, b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} - 4 \, a b - 8 \, b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} - 4 \, a b - 8 \, b^{2} + 8 \, {\left({\left(a^{2} - 4 \, a b - 8 \, b^{2}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(a^{2} - 4 \, a b - 8 \, b^{2}\right)} \cosh\left(x\right)^{5} + 3 \, {\left(a^{2} - 4 \, a b - 8 \, b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{2} - 4 \, a b - 8 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{-b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) + \sqrt{2} {\left({\left(a b + 6 \, b^{2}\right)} \cosh\left(x\right)^{6} + 6 \, {\left(a b + 6 \, b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(a b + 6 \, b^{2}\right)} \sinh\left(x\right)^{6} + {\left(a b - 2 \, b^{2}\right)} \cosh\left(x\right)^{4} + {\left(15 \, {\left(a b + 6 \, b^{2}\right)} \cosh\left(x\right)^{2} + a b - 2 \, b^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, {\left(a b + 6 \, b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a b - 2 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - {\left(a b - 2 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, {\left(a b + 6 \, b^{2}\right)} \cosh\left(x\right)^{4} + 6 \, {\left(a b - 2 \, b^{2}\right)} \cosh\left(x\right)^{2} - a b + 2 \, b^{2}\right)} \sinh\left(x\right)^{2} - a b - 6 \, b^{2} + 2 \, {\left(3 \, {\left(a b + 6 \, b^{2}\right)} \cosh\left(x\right)^{5} + 2 \, {\left(a b - 2 \, b^{2}\right)} \cosh\left(x\right)^{3} - {\left(a b - 2 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{8 \, {\left(b^{2} \cosh\left(x\right)^{8} + 8 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{7} + b^{2} \sinh\left(x\right)^{8} + 4 \, b^{2} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, b^{2} \cosh\left(x\right)^{2} + b^{2}\right)} \sinh\left(x\right)^{6} + 6 \, b^{2} \cosh\left(x\right)^{4} + 8 \, {\left(7 \, b^{2} \cosh\left(x\right)^{3} + 3 \, b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(35 \, b^{2} \cosh\left(x\right)^{4} + 30 \, b^{2} \cosh\left(x\right)^{2} + 3 \, b^{2}\right)} \sinh\left(x\right)^{4} + 4 \, b^{2} \cosh\left(x\right)^{2} + 8 \, {\left(7 \, b^{2} \cosh\left(x\right)^{5} + 10 \, b^{2} \cosh\left(x\right)^{3} + 3 \, b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(7 \, b^{2} \cosh\left(x\right)^{6} + 15 \, b^{2} \cosh\left(x\right)^{4} + 9 \, b^{2} \cosh\left(x\right)^{2} + b^{2}\right)} \sinh\left(x\right)^{2} + b^{2} + 8 \, {\left(b^{2} \cosh\left(x\right)^{7} + 3 \, b^{2} \cosh\left(x\right)^{5} + 3 \, b^{2} \cosh\left(x\right)^{3} + b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}\right]"," ",0,"[1/16*(4*(b^2*cosh(x)^8 + 8*b^2*cosh(x)*sinh(x)^7 + b^2*sinh(x)^8 + 4*b^2*cosh(x)^6 + 4*(7*b^2*cosh(x)^2 + b^2)*sinh(x)^6 + 6*b^2*cosh(x)^4 + 8*(7*b^2*cosh(x)^3 + 3*b^2*cosh(x))*sinh(x)^5 + 2*(35*b^2*cosh(x)^4 + 30*b^2*cosh(x)^2 + 3*b^2)*sinh(x)^4 + 4*b^2*cosh(x)^2 + 8*(7*b^2*cosh(x)^5 + 10*b^2*cosh(x)^3 + 3*b^2*cosh(x))*sinh(x)^3 + 4*(7*b^2*cosh(x)^6 + 15*b^2*cosh(x)^4 + 9*b^2*cosh(x)^2 + b^2)*sinh(x)^2 + b^2 + 8*(b^2*cosh(x)^7 + 3*b^2*cosh(x)^5 + 3*b^2*cosh(x)^3 + b^2*cosh(x))*sinh(x))*sqrt(a + b)*log(-((a*b^2 + b^3)*cosh(x)^8 + 8*(a*b^2 + b^3)*cosh(x)*sinh(x)^7 + (a*b^2 + b^3)*sinh(x)^8 - 2*(a*b^2 + 2*b^3)*cosh(x)^6 - 2*(a*b^2 + 2*b^3 - 14*(a*b^2 + b^3)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a*b^2 + b^3)*cosh(x)^3 - 3*(a*b^2 + 2*b^3)*cosh(x))*sinh(x)^5 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^4 + (70*(a*b^2 + b^3)*cosh(x)^4 + a^3 - a^2*b + 4*a*b^2 + 6*b^3 - 30*(a*b^2 + 2*b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a*b^2 + b^3)*cosh(x)^5 - 10*(a*b^2 + 2*b^3)*cosh(x)^3 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x))*sinh(x)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 + 2*(a^3 - 3*a*b^2 - 2*b^3)*cosh(x)^2 + 2*(14*(a*b^2 + b^3)*cosh(x)^6 - 15*(a*b^2 + 2*b^3)*cosh(x)^4 + a^3 - 3*a*b^2 - 2*b^3 + 3*(a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^2)*sinh(x)^2 + sqrt(2)*(b^2*cosh(x)^6 + 6*b^2*cosh(x)*sinh(x)^5 + b^2*sinh(x)^6 - 3*b^2*cosh(x)^4 + 3*(5*b^2*cosh(x)^2 - b^2)*sinh(x)^4 + 4*(5*b^2*cosh(x)^3 - 3*b^2*cosh(x))*sinh(x)^3 - (a^2 - 2*a*b - 3*b^2)*cosh(x)^2 + (15*b^2*cosh(x)^4 - 18*b^2*cosh(x)^2 - a^2 + 2*a*b + 3*b^2)*sinh(x)^2 - a^2 - 2*a*b - b^2 + 2*(3*b^2*cosh(x)^5 - 6*b^2*cosh(x)^3 - (a^2 - 2*a*b - 3*b^2)*cosh(x))*sinh(x))*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a*b^2 + b^3)*cosh(x)^7 - 3*(a*b^2 + 2*b^3)*cosh(x)^5 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^3 + (a^3 - 3*a*b^2 - 2*b^3)*cosh(x))*sinh(x))/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) - ((a^2 - 4*a*b - 8*b^2)*cosh(x)^8 + 8*(a^2 - 4*a*b - 8*b^2)*cosh(x)*sinh(x)^7 + (a^2 - 4*a*b - 8*b^2)*sinh(x)^8 + 4*(a^2 - 4*a*b - 8*b^2)*cosh(x)^6 + 4*(7*(a^2 - 4*a*b - 8*b^2)*cosh(x)^2 + a^2 - 4*a*b - 8*b^2)*sinh(x)^6 + 8*(7*(a^2 - 4*a*b - 8*b^2)*cosh(x)^3 + 3*(a^2 - 4*a*b - 8*b^2)*cosh(x))*sinh(x)^5 + 6*(a^2 - 4*a*b - 8*b^2)*cosh(x)^4 + 2*(35*(a^2 - 4*a*b - 8*b^2)*cosh(x)^4 + 30*(a^2 - 4*a*b - 8*b^2)*cosh(x)^2 + 3*a^2 - 12*a*b - 24*b^2)*sinh(x)^4 + 8*(7*(a^2 - 4*a*b - 8*b^2)*cosh(x)^5 + 10*(a^2 - 4*a*b - 8*b^2)*cosh(x)^3 + 3*(a^2 - 4*a*b - 8*b^2)*cosh(x))*sinh(x)^3 + 4*(a^2 - 4*a*b - 8*b^2)*cosh(x)^2 + 4*(7*(a^2 - 4*a*b - 8*b^2)*cosh(x)^6 + 15*(a^2 - 4*a*b - 8*b^2)*cosh(x)^4 + 9*(a^2 - 4*a*b - 8*b^2)*cosh(x)^2 + a^2 - 4*a*b - 8*b^2)*sinh(x)^2 + a^2 - 4*a*b - 8*b^2 + 8*((a^2 - 4*a*b - 8*b^2)*cosh(x)^7 + 3*(a^2 - 4*a*b - 8*b^2)*cosh(x)^5 + 3*(a^2 - 4*a*b - 8*b^2)*cosh(x)^3 + (a^2 - 4*a*b - 8*b^2)*cosh(x))*sinh(x))*sqrt(b)*log(-((a + 2*b)*cosh(x)^4 + 4*(a + 2*b)*cosh(x)*sinh(x)^3 + (a + 2*b)*sinh(x)^4 + 2*(a - 2*b)*cosh(x)^2 + 2*(3*(a + 2*b)*cosh(x)^2 + a - 2*b)*sinh(x)^2 - 2*sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + 2*b)*cosh(x)^3 + (a - 2*b)*cosh(x))*sinh(x) + a + 2*b)/(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)) + 4*(b^2*cosh(x)^8 + 8*b^2*cosh(x)*sinh(x)^7 + b^2*sinh(x)^8 + 4*b^2*cosh(x)^6 + 4*(7*b^2*cosh(x)^2 + b^2)*sinh(x)^6 + 6*b^2*cosh(x)^4 + 8*(7*b^2*cosh(x)^3 + 3*b^2*cosh(x))*sinh(x)^5 + 2*(35*b^2*cosh(x)^4 + 30*b^2*cosh(x)^2 + 3*b^2)*sinh(x)^4 + 4*b^2*cosh(x)^2 + 8*(7*b^2*cosh(x)^5 + 10*b^2*cosh(x)^3 + 3*b^2*cosh(x))*sinh(x)^3 + 4*(7*b^2*cosh(x)^6 + 15*b^2*cosh(x)^4 + 9*b^2*cosh(x)^2 + b^2)*sinh(x)^2 + b^2 + 8*(b^2*cosh(x)^7 + 3*b^2*cosh(x)^5 + 3*b^2*cosh(x)^3 + b^2*cosh(x))*sinh(x))*sqrt(a + b)*log(((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*a*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + b)*cosh(x)^3 + a*cosh(x))*sinh(x) + a + b)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) - 2*sqrt(2)*((a*b + 6*b^2)*cosh(x)^6 + 6*(a*b + 6*b^2)*cosh(x)*sinh(x)^5 + (a*b + 6*b^2)*sinh(x)^6 + (a*b - 2*b^2)*cosh(x)^4 + (15*(a*b + 6*b^2)*cosh(x)^2 + a*b - 2*b^2)*sinh(x)^4 + 4*(5*(a*b + 6*b^2)*cosh(x)^3 + (a*b - 2*b^2)*cosh(x))*sinh(x)^3 - (a*b - 2*b^2)*cosh(x)^2 + (15*(a*b + 6*b^2)*cosh(x)^4 + 6*(a*b - 2*b^2)*cosh(x)^2 - a*b + 2*b^2)*sinh(x)^2 - a*b - 6*b^2 + 2*(3*(a*b + 6*b^2)*cosh(x)^5 + 2*(a*b - 2*b^2)*cosh(x)^3 - (a*b - 2*b^2)*cosh(x))*sinh(x))*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(b^2*cosh(x)^8 + 8*b^2*cosh(x)*sinh(x)^7 + b^2*sinh(x)^8 + 4*b^2*cosh(x)^6 + 4*(7*b^2*cosh(x)^2 + b^2)*sinh(x)^6 + 6*b^2*cosh(x)^4 + 8*(7*b^2*cosh(x)^3 + 3*b^2*cosh(x))*sinh(x)^5 + 2*(35*b^2*cosh(x)^4 + 30*b^2*cosh(x)^2 + 3*b^2)*sinh(x)^4 + 4*b^2*cosh(x)^2 + 8*(7*b^2*cosh(x)^5 + 10*b^2*cosh(x)^3 + 3*b^2*cosh(x))*sinh(x)^3 + 4*(7*b^2*cosh(x)^6 + 15*b^2*cosh(x)^4 + 9*b^2*cosh(x)^2 + b^2)*sinh(x)^2 + b^2 + 8*(b^2*cosh(x)^7 + 3*b^2*cosh(x)^5 + 3*b^2*cosh(x)^3 + b^2*cosh(x))*sinh(x)), -1/8*(((a^2 - 4*a*b - 8*b^2)*cosh(x)^8 + 8*(a^2 - 4*a*b - 8*b^2)*cosh(x)*sinh(x)^7 + (a^2 - 4*a*b - 8*b^2)*sinh(x)^8 + 4*(a^2 - 4*a*b - 8*b^2)*cosh(x)^6 + 4*(7*(a^2 - 4*a*b - 8*b^2)*cosh(x)^2 + a^2 - 4*a*b - 8*b^2)*sinh(x)^6 + 8*(7*(a^2 - 4*a*b - 8*b^2)*cosh(x)^3 + 3*(a^2 - 4*a*b - 8*b^2)*cosh(x))*sinh(x)^5 + 6*(a^2 - 4*a*b - 8*b^2)*cosh(x)^4 + 2*(35*(a^2 - 4*a*b - 8*b^2)*cosh(x)^4 + 30*(a^2 - 4*a*b - 8*b^2)*cosh(x)^2 + 3*a^2 - 12*a*b - 24*b^2)*sinh(x)^4 + 8*(7*(a^2 - 4*a*b - 8*b^2)*cosh(x)^5 + 10*(a^2 - 4*a*b - 8*b^2)*cosh(x)^3 + 3*(a^2 - 4*a*b - 8*b^2)*cosh(x))*sinh(x)^3 + 4*(a^2 - 4*a*b - 8*b^2)*cosh(x)^2 + 4*(7*(a^2 - 4*a*b - 8*b^2)*cosh(x)^6 + 15*(a^2 - 4*a*b - 8*b^2)*cosh(x)^4 + 9*(a^2 - 4*a*b - 8*b^2)*cosh(x)^2 + a^2 - 4*a*b - 8*b^2)*sinh(x)^2 + a^2 - 4*a*b - 8*b^2 + 8*((a^2 - 4*a*b - 8*b^2)*cosh(x)^7 + 3*(a^2 - 4*a*b - 8*b^2)*cosh(x)^5 + 3*(a^2 - 4*a*b - 8*b^2)*cosh(x)^3 + (a^2 - 4*a*b - 8*b^2)*cosh(x))*sinh(x))*sqrt(-b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a - b)*cosh(x))*sinh(x) + a + b)) - 2*(b^2*cosh(x)^8 + 8*b^2*cosh(x)*sinh(x)^7 + b^2*sinh(x)^8 + 4*b^2*cosh(x)^6 + 4*(7*b^2*cosh(x)^2 + b^2)*sinh(x)^6 + 6*b^2*cosh(x)^4 + 8*(7*b^2*cosh(x)^3 + 3*b^2*cosh(x))*sinh(x)^5 + 2*(35*b^2*cosh(x)^4 + 30*b^2*cosh(x)^2 + 3*b^2)*sinh(x)^4 + 4*b^2*cosh(x)^2 + 8*(7*b^2*cosh(x)^5 + 10*b^2*cosh(x)^3 + 3*b^2*cosh(x))*sinh(x)^3 + 4*(7*b^2*cosh(x)^6 + 15*b^2*cosh(x)^4 + 9*b^2*cosh(x)^2 + b^2)*sinh(x)^2 + b^2 + 8*(b^2*cosh(x)^7 + 3*b^2*cosh(x)^5 + 3*b^2*cosh(x)^3 + b^2*cosh(x))*sinh(x))*sqrt(a + b)*log(-((a*b^2 + b^3)*cosh(x)^8 + 8*(a*b^2 + b^3)*cosh(x)*sinh(x)^7 + (a*b^2 + b^3)*sinh(x)^8 - 2*(a*b^2 + 2*b^3)*cosh(x)^6 - 2*(a*b^2 + 2*b^3 - 14*(a*b^2 + b^3)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a*b^2 + b^3)*cosh(x)^3 - 3*(a*b^2 + 2*b^3)*cosh(x))*sinh(x)^5 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^4 + (70*(a*b^2 + b^3)*cosh(x)^4 + a^3 - a^2*b + 4*a*b^2 + 6*b^3 - 30*(a*b^2 + 2*b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a*b^2 + b^3)*cosh(x)^5 - 10*(a*b^2 + 2*b^3)*cosh(x)^3 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x))*sinh(x)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 + 2*(a^3 - 3*a*b^2 - 2*b^3)*cosh(x)^2 + 2*(14*(a*b^2 + b^3)*cosh(x)^6 - 15*(a*b^2 + 2*b^3)*cosh(x)^4 + a^3 - 3*a*b^2 - 2*b^3 + 3*(a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^2)*sinh(x)^2 + sqrt(2)*(b^2*cosh(x)^6 + 6*b^2*cosh(x)*sinh(x)^5 + b^2*sinh(x)^6 - 3*b^2*cosh(x)^4 + 3*(5*b^2*cosh(x)^2 - b^2)*sinh(x)^4 + 4*(5*b^2*cosh(x)^3 - 3*b^2*cosh(x))*sinh(x)^3 - (a^2 - 2*a*b - 3*b^2)*cosh(x)^2 + (15*b^2*cosh(x)^4 - 18*b^2*cosh(x)^2 - a^2 + 2*a*b + 3*b^2)*sinh(x)^2 - a^2 - 2*a*b - b^2 + 2*(3*b^2*cosh(x)^5 - 6*b^2*cosh(x)^3 - (a^2 - 2*a*b - 3*b^2)*cosh(x))*sinh(x))*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a*b^2 + b^3)*cosh(x)^7 - 3*(a*b^2 + 2*b^3)*cosh(x)^5 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^3 + (a^3 - 3*a*b^2 - 2*b^3)*cosh(x))*sinh(x))/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) - 2*(b^2*cosh(x)^8 + 8*b^2*cosh(x)*sinh(x)^7 + b^2*sinh(x)^8 + 4*b^2*cosh(x)^6 + 4*(7*b^2*cosh(x)^2 + b^2)*sinh(x)^6 + 6*b^2*cosh(x)^4 + 8*(7*b^2*cosh(x)^3 + 3*b^2*cosh(x))*sinh(x)^5 + 2*(35*b^2*cosh(x)^4 + 30*b^2*cosh(x)^2 + 3*b^2)*sinh(x)^4 + 4*b^2*cosh(x)^2 + 8*(7*b^2*cosh(x)^5 + 10*b^2*cosh(x)^3 + 3*b^2*cosh(x))*sinh(x)^3 + 4*(7*b^2*cosh(x)^6 + 15*b^2*cosh(x)^4 + 9*b^2*cosh(x)^2 + b^2)*sinh(x)^2 + b^2 + 8*(b^2*cosh(x)^7 + 3*b^2*cosh(x)^5 + 3*b^2*cosh(x)^3 + b^2*cosh(x))*sinh(x))*sqrt(a + b)*log(((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*a*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + b)*cosh(x)^3 + a*cosh(x))*sinh(x) + a + b)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) + sqrt(2)*((a*b + 6*b^2)*cosh(x)^6 + 6*(a*b + 6*b^2)*cosh(x)*sinh(x)^5 + (a*b + 6*b^2)*sinh(x)^6 + (a*b - 2*b^2)*cosh(x)^4 + (15*(a*b + 6*b^2)*cosh(x)^2 + a*b - 2*b^2)*sinh(x)^4 + 4*(5*(a*b + 6*b^2)*cosh(x)^3 + (a*b - 2*b^2)*cosh(x))*sinh(x)^3 - (a*b - 2*b^2)*cosh(x)^2 + (15*(a*b + 6*b^2)*cosh(x)^4 + 6*(a*b - 2*b^2)*cosh(x)^2 - a*b + 2*b^2)*sinh(x)^2 - a*b - 6*b^2 + 2*(3*(a*b + 6*b^2)*cosh(x)^5 + 2*(a*b - 2*b^2)*cosh(x)^3 - (a*b - 2*b^2)*cosh(x))*sinh(x))*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(b^2*cosh(x)^8 + 8*b^2*cosh(x)*sinh(x)^7 + b^2*sinh(x)^8 + 4*b^2*cosh(x)^6 + 4*(7*b^2*cosh(x)^2 + b^2)*sinh(x)^6 + 6*b^2*cosh(x)^4 + 8*(7*b^2*cosh(x)^3 + 3*b^2*cosh(x))*sinh(x)^5 + 2*(35*b^2*cosh(x)^4 + 30*b^2*cosh(x)^2 + 3*b^2)*sinh(x)^4 + 4*b^2*cosh(x)^2 + 8*(7*b^2*cosh(x)^5 + 10*b^2*cosh(x)^3 + 3*b^2*cosh(x))*sinh(x)^3 + 4*(7*b^2*cosh(x)^6 + 15*b^2*cosh(x)^4 + 9*b^2*cosh(x)^2 + b^2)*sinh(x)^2 + b^2 + 8*(b^2*cosh(x)^7 + 3*b^2*cosh(x)^5 + 3*b^2*cosh(x)^3 + b^2*cosh(x))*sinh(x)), -1/16*(8*(b^2*cosh(x)^8 + 8*b^2*cosh(x)*sinh(x)^7 + b^2*sinh(x)^8 + 4*b^2*cosh(x)^6 + 4*(7*b^2*cosh(x)^2 + b^2)*sinh(x)^6 + 6*b^2*cosh(x)^4 + 8*(7*b^2*cosh(x)^3 + 3*b^2*cosh(x))*sinh(x)^5 + 2*(35*b^2*cosh(x)^4 + 30*b^2*cosh(x)^2 + 3*b^2)*sinh(x)^4 + 4*b^2*cosh(x)^2 + 8*(7*b^2*cosh(x)^5 + 10*b^2*cosh(x)^3 + 3*b^2*cosh(x))*sinh(x)^3 + 4*(7*b^2*cosh(x)^6 + 15*b^2*cosh(x)^4 + 9*b^2*cosh(x)^2 + b^2)*sinh(x)^2 + b^2 + 8*(b^2*cosh(x)^7 + 3*b^2*cosh(x)^5 + 3*b^2*cosh(x)^3 + b^2*cosh(x))*sinh(x))*sqrt(-a - b)*arctan(sqrt(2)*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 - a - b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a*b + b^2)*cosh(x)^4 + 4*(a*b + b^2)*cosh(x)*sinh(x)^3 + (a*b + b^2)*sinh(x)^4 + (a^2 - a*b - 2*b^2)*cosh(x)^2 + (6*(a*b + b^2)*cosh(x)^2 + a^2 - a*b - 2*b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(2*(a*b + b^2)*cosh(x)^3 + (a^2 - a*b - 2*b^2)*cosh(x))*sinh(x))) + 8*(b^2*cosh(x)^8 + 8*b^2*cosh(x)*sinh(x)^7 + b^2*sinh(x)^8 + 4*b^2*cosh(x)^6 + 4*(7*b^2*cosh(x)^2 + b^2)*sinh(x)^6 + 6*b^2*cosh(x)^4 + 8*(7*b^2*cosh(x)^3 + 3*b^2*cosh(x))*sinh(x)^5 + 2*(35*b^2*cosh(x)^4 + 30*b^2*cosh(x)^2 + 3*b^2)*sinh(x)^4 + 4*b^2*cosh(x)^2 + 8*(7*b^2*cosh(x)^5 + 10*b^2*cosh(x)^3 + 3*b^2*cosh(x))*sinh(x)^3 + 4*(7*b^2*cosh(x)^6 + 15*b^2*cosh(x)^4 + 9*b^2*cosh(x)^2 + b^2)*sinh(x)^2 + b^2 + 8*(b^2*cosh(x)^7 + 3*b^2*cosh(x)^5 + 3*b^2*cosh(x)^3 + b^2*cosh(x))*sinh(x))*sqrt(-a - b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a - b)*cosh(x))*sinh(x) + a + b)) + ((a^2 - 4*a*b - 8*b^2)*cosh(x)^8 + 8*(a^2 - 4*a*b - 8*b^2)*cosh(x)*sinh(x)^7 + (a^2 - 4*a*b - 8*b^2)*sinh(x)^8 + 4*(a^2 - 4*a*b - 8*b^2)*cosh(x)^6 + 4*(7*(a^2 - 4*a*b - 8*b^2)*cosh(x)^2 + a^2 - 4*a*b - 8*b^2)*sinh(x)^6 + 8*(7*(a^2 - 4*a*b - 8*b^2)*cosh(x)^3 + 3*(a^2 - 4*a*b - 8*b^2)*cosh(x))*sinh(x)^5 + 6*(a^2 - 4*a*b - 8*b^2)*cosh(x)^4 + 2*(35*(a^2 - 4*a*b - 8*b^2)*cosh(x)^4 + 30*(a^2 - 4*a*b - 8*b^2)*cosh(x)^2 + 3*a^2 - 12*a*b - 24*b^2)*sinh(x)^4 + 8*(7*(a^2 - 4*a*b - 8*b^2)*cosh(x)^5 + 10*(a^2 - 4*a*b - 8*b^2)*cosh(x)^3 + 3*(a^2 - 4*a*b - 8*b^2)*cosh(x))*sinh(x)^3 + 4*(a^2 - 4*a*b - 8*b^2)*cosh(x)^2 + 4*(7*(a^2 - 4*a*b - 8*b^2)*cosh(x)^6 + 15*(a^2 - 4*a*b - 8*b^2)*cosh(x)^4 + 9*(a^2 - 4*a*b - 8*b^2)*cosh(x)^2 + a^2 - 4*a*b - 8*b^2)*sinh(x)^2 + a^2 - 4*a*b - 8*b^2 + 8*((a^2 - 4*a*b - 8*b^2)*cosh(x)^7 + 3*(a^2 - 4*a*b - 8*b^2)*cosh(x)^5 + 3*(a^2 - 4*a*b - 8*b^2)*cosh(x)^3 + (a^2 - 4*a*b - 8*b^2)*cosh(x))*sinh(x))*sqrt(b)*log(-((a + 2*b)*cosh(x)^4 + 4*(a + 2*b)*cosh(x)*sinh(x)^3 + (a + 2*b)*sinh(x)^4 + 2*(a - 2*b)*cosh(x)^2 + 2*(3*(a + 2*b)*cosh(x)^2 + a - 2*b)*sinh(x)^2 - 2*sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + 2*b)*cosh(x)^3 + (a - 2*b)*cosh(x))*sinh(x) + a + 2*b)/(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)) + 2*sqrt(2)*((a*b + 6*b^2)*cosh(x)^6 + 6*(a*b + 6*b^2)*cosh(x)*sinh(x)^5 + (a*b + 6*b^2)*sinh(x)^6 + (a*b - 2*b^2)*cosh(x)^4 + (15*(a*b + 6*b^2)*cosh(x)^2 + a*b - 2*b^2)*sinh(x)^4 + 4*(5*(a*b + 6*b^2)*cosh(x)^3 + (a*b - 2*b^2)*cosh(x))*sinh(x)^3 - (a*b - 2*b^2)*cosh(x)^2 + (15*(a*b + 6*b^2)*cosh(x)^4 + 6*(a*b - 2*b^2)*cosh(x)^2 - a*b + 2*b^2)*sinh(x)^2 - a*b - 6*b^2 + 2*(3*(a*b + 6*b^2)*cosh(x)^5 + 2*(a*b - 2*b^2)*cosh(x)^3 - (a*b - 2*b^2)*cosh(x))*sinh(x))*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(b^2*cosh(x)^8 + 8*b^2*cosh(x)*sinh(x)^7 + b^2*sinh(x)^8 + 4*b^2*cosh(x)^6 + 4*(7*b^2*cosh(x)^2 + b^2)*sinh(x)^6 + 6*b^2*cosh(x)^4 + 8*(7*b^2*cosh(x)^3 + 3*b^2*cosh(x))*sinh(x)^5 + 2*(35*b^2*cosh(x)^4 + 30*b^2*cosh(x)^2 + 3*b^2)*sinh(x)^4 + 4*b^2*cosh(x)^2 + 8*(7*b^2*cosh(x)^5 + 10*b^2*cosh(x)^3 + 3*b^2*cosh(x))*sinh(x)^3 + 4*(7*b^2*cosh(x)^6 + 15*b^2*cosh(x)^4 + 9*b^2*cosh(x)^2 + b^2)*sinh(x)^2 + b^2 + 8*(b^2*cosh(x)^7 + 3*b^2*cosh(x)^5 + 3*b^2*cosh(x)^3 + b^2*cosh(x))*sinh(x)), -1/8*(4*(b^2*cosh(x)^8 + 8*b^2*cosh(x)*sinh(x)^7 + b^2*sinh(x)^8 + 4*b^2*cosh(x)^6 + 4*(7*b^2*cosh(x)^2 + b^2)*sinh(x)^6 + 6*b^2*cosh(x)^4 + 8*(7*b^2*cosh(x)^3 + 3*b^2*cosh(x))*sinh(x)^5 + 2*(35*b^2*cosh(x)^4 + 30*b^2*cosh(x)^2 + 3*b^2)*sinh(x)^4 + 4*b^2*cosh(x)^2 + 8*(7*b^2*cosh(x)^5 + 10*b^2*cosh(x)^3 + 3*b^2*cosh(x))*sinh(x)^3 + 4*(7*b^2*cosh(x)^6 + 15*b^2*cosh(x)^4 + 9*b^2*cosh(x)^2 + b^2)*sinh(x)^2 + b^2 + 8*(b^2*cosh(x)^7 + 3*b^2*cosh(x)^5 + 3*b^2*cosh(x)^3 + b^2*cosh(x))*sinh(x))*sqrt(-a - b)*arctan(sqrt(2)*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 - a - b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a*b + b^2)*cosh(x)^4 + 4*(a*b + b^2)*cosh(x)*sinh(x)^3 + (a*b + b^2)*sinh(x)^4 + (a^2 - a*b - 2*b^2)*cosh(x)^2 + (6*(a*b + b^2)*cosh(x)^2 + a^2 - a*b - 2*b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(2*(a*b + b^2)*cosh(x)^3 + (a^2 - a*b - 2*b^2)*cosh(x))*sinh(x))) + 4*(b^2*cosh(x)^8 + 8*b^2*cosh(x)*sinh(x)^7 + b^2*sinh(x)^8 + 4*b^2*cosh(x)^6 + 4*(7*b^2*cosh(x)^2 + b^2)*sinh(x)^6 + 6*b^2*cosh(x)^4 + 8*(7*b^2*cosh(x)^3 + 3*b^2*cosh(x))*sinh(x)^5 + 2*(35*b^2*cosh(x)^4 + 30*b^2*cosh(x)^2 + 3*b^2)*sinh(x)^4 + 4*b^2*cosh(x)^2 + 8*(7*b^2*cosh(x)^5 + 10*b^2*cosh(x)^3 + 3*b^2*cosh(x))*sinh(x)^3 + 4*(7*b^2*cosh(x)^6 + 15*b^2*cosh(x)^4 + 9*b^2*cosh(x)^2 + b^2)*sinh(x)^2 + b^2 + 8*(b^2*cosh(x)^7 + 3*b^2*cosh(x)^5 + 3*b^2*cosh(x)^3 + b^2*cosh(x))*sinh(x))*sqrt(-a - b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a - b)*cosh(x))*sinh(x) + a + b)) + ((a^2 - 4*a*b - 8*b^2)*cosh(x)^8 + 8*(a^2 - 4*a*b - 8*b^2)*cosh(x)*sinh(x)^7 + (a^2 - 4*a*b - 8*b^2)*sinh(x)^8 + 4*(a^2 - 4*a*b - 8*b^2)*cosh(x)^6 + 4*(7*(a^2 - 4*a*b - 8*b^2)*cosh(x)^2 + a^2 - 4*a*b - 8*b^2)*sinh(x)^6 + 8*(7*(a^2 - 4*a*b - 8*b^2)*cosh(x)^3 + 3*(a^2 - 4*a*b - 8*b^2)*cosh(x))*sinh(x)^5 + 6*(a^2 - 4*a*b - 8*b^2)*cosh(x)^4 + 2*(35*(a^2 - 4*a*b - 8*b^2)*cosh(x)^4 + 30*(a^2 - 4*a*b - 8*b^2)*cosh(x)^2 + 3*a^2 - 12*a*b - 24*b^2)*sinh(x)^4 + 8*(7*(a^2 - 4*a*b - 8*b^2)*cosh(x)^5 + 10*(a^2 - 4*a*b - 8*b^2)*cosh(x)^3 + 3*(a^2 - 4*a*b - 8*b^2)*cosh(x))*sinh(x)^3 + 4*(a^2 - 4*a*b - 8*b^2)*cosh(x)^2 + 4*(7*(a^2 - 4*a*b - 8*b^2)*cosh(x)^6 + 15*(a^2 - 4*a*b - 8*b^2)*cosh(x)^4 + 9*(a^2 - 4*a*b - 8*b^2)*cosh(x)^2 + a^2 - 4*a*b - 8*b^2)*sinh(x)^2 + a^2 - 4*a*b - 8*b^2 + 8*((a^2 - 4*a*b - 8*b^2)*cosh(x)^7 + 3*(a^2 - 4*a*b - 8*b^2)*cosh(x)^5 + 3*(a^2 - 4*a*b - 8*b^2)*cosh(x)^3 + (a^2 - 4*a*b - 8*b^2)*cosh(x))*sinh(x))*sqrt(-b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a - b)*cosh(x))*sinh(x) + a + b)) + sqrt(2)*((a*b + 6*b^2)*cosh(x)^6 + 6*(a*b + 6*b^2)*cosh(x)*sinh(x)^5 + (a*b + 6*b^2)*sinh(x)^6 + (a*b - 2*b^2)*cosh(x)^4 + (15*(a*b + 6*b^2)*cosh(x)^2 + a*b - 2*b^2)*sinh(x)^4 + 4*(5*(a*b + 6*b^2)*cosh(x)^3 + (a*b - 2*b^2)*cosh(x))*sinh(x)^3 - (a*b - 2*b^2)*cosh(x)^2 + (15*(a*b + 6*b^2)*cosh(x)^4 + 6*(a*b - 2*b^2)*cosh(x)^2 - a*b + 2*b^2)*sinh(x)^2 - a*b - 6*b^2 + 2*(3*(a*b + 6*b^2)*cosh(x)^5 + 2*(a*b - 2*b^2)*cosh(x)^3 - (a*b - 2*b^2)*cosh(x))*sinh(x))*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(b^2*cosh(x)^8 + 8*b^2*cosh(x)*sinh(x)^7 + b^2*sinh(x)^8 + 4*b^2*cosh(x)^6 + 4*(7*b^2*cosh(x)^2 + b^2)*sinh(x)^6 + 6*b^2*cosh(x)^4 + 8*(7*b^2*cosh(x)^3 + 3*b^2*cosh(x))*sinh(x)^5 + 2*(35*b^2*cosh(x)^4 + 30*b^2*cosh(x)^2 + 3*b^2)*sinh(x)^4 + 4*b^2*cosh(x)^2 + 8*(7*b^2*cosh(x)^5 + 10*b^2*cosh(x)^3 + 3*b^2*cosh(x))*sinh(x)^3 + 4*(7*b^2*cosh(x)^6 + 15*b^2*cosh(x)^4 + 9*b^2*cosh(x)^2 + b^2)*sinh(x)^2 + b^2 + 8*(b^2*cosh(x)^7 + 3*b^2*cosh(x)^5 + 3*b^2*cosh(x)^3 + b^2*cosh(x))*sinh(x))]","B",0
210,1,2329,0,0.584035," ","integrate((a+b*tanh(x)^2)^(1/2)*tanh(x)^3,x, algorithm=""fricas"")","\left[\frac{3 \, {\left(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} + 4 \, {\left(5 \, b \cosh\left(x\right)^{3} + 3 \, b \cosh\left(x\right)\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} + b\right)} \sinh\left(x\right)^{2} + 6 \, {\left(b \cosh\left(x\right)^{5} + 2 \, b \cosh\left(x\right)^{3} + b \cosh\left(x\right)\right)} \sinh\left(x\right) + b\right)} \sqrt{a + b} \log\left(\frac{{\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{3} + a^{2} b\right)} \sinh\left(x\right)^{8} + 2 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} + 2 \, {\left(2 \, a^{3} + a^{2} b + 14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} + 3 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3} + 30 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} + 10 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} + 2 \, {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} + 15 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 2 \, a^{3} + 3 \, a^{2} b - b^{3} + 3 \, {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(a^{2} \cosh\left(x\right)^{6} + 6 \, a^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + a^{2} \sinh\left(x\right)^{6} + 3 \, a^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, a^{2} \cosh\left(x\right)^{2} + a^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, a^{2} \cosh\left(x\right)^{3} + 3 \, a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, a^{2} \cosh\left(x\right)^{4} + 18 \, a^{2} \cosh\left(x\right)^{2} + 3 \, a^{2} + 2 \, a b - b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(x\right)^{5} + 6 \, a^{2} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{7} + 3 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) + 3 \, {\left(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} + 4 \, {\left(5 \, b \cosh\left(x\right)^{3} + 3 \, b \cosh\left(x\right)\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} + b\right)} \sinh\left(x\right)^{2} + 6 \, {\left(b \cosh\left(x\right)^{5} + 2 \, b \cosh\left(x\right)^{3} + b \cosh\left(x\right)\right)} \sinh\left(x\right) + b\right)} \sqrt{a + b} \log\left(-\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - b\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - b \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right) - 4 \, \sqrt{2} {\left({\left(a + 4 \, b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + 4 \, b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + 4 \, b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + 4 \, b\right)} \cosh\left(x\right)^{2} + a + 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + 4 \, b\right)} \cosh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + 4 \, b\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{12 \, {\left(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} + 4 \, {\left(5 \, b \cosh\left(x\right)^{3} + 3 \, b \cosh\left(x\right)\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} + b\right)} \sinh\left(x\right)^{2} + 6 \, {\left(b \cosh\left(x\right)^{5} + 2 \, b \cosh\left(x\right)^{3} + b \cosh\left(x\right)\right)} \sinh\left(x\right) + b\right)}}, -\frac{3 \, {\left(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} + 4 \, {\left(5 \, b \cosh\left(x\right)^{3} + 3 \, b \cosh\left(x\right)\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} + b\right)} \sinh\left(x\right)^{2} + 6 \, {\left(b \cosh\left(x\right)^{5} + 2 \, b \cosh\left(x\right)^{3} + b \cosh\left(x\right)\right)} \sinh\left(x\right) + b\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(a \cosh\left(x\right)^{2} + 2 \, a \cosh\left(x\right) \sinh\left(x\right) + a \sinh\left(x\right)^{2} + a + b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a^{2} + a b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{2} + a b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{2} + a b\right)} \sinh\left(x\right)^{4} + {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} + 2 \, a^{2} + a b - b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(2 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + 3 \, {\left(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} + 4 \, {\left(5 \, b \cosh\left(x\right)^{3} + 3 \, b \cosh\left(x\right)\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} + b\right)} \sinh\left(x\right)^{2} + 6 \, {\left(b \cosh\left(x\right)^{5} + 2 \, b \cosh\left(x\right)^{3} + b \cosh\left(x\right)\right)} \sinh\left(x\right) + b\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) + 2 \, \sqrt{2} {\left({\left(a + 4 \, b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + 4 \, b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + 4 \, b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + 4 \, b\right)} \cosh\left(x\right)^{2} + a + 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + 4 \, b\right)} \cosh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + 4 \, b\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{6 \, {\left(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} + 4 \, {\left(5 \, b \cosh\left(x\right)^{3} + 3 \, b \cosh\left(x\right)\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} + b\right)} \sinh\left(x\right)^{2} + 6 \, {\left(b \cosh\left(x\right)^{5} + 2 \, b \cosh\left(x\right)^{3} + b \cosh\left(x\right)\right)} \sinh\left(x\right) + b\right)}}\right]"," ",0,"[1/12*(3*(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 + 4*(5*b*cosh(x)^3 + 3*b*cosh(x))*sinh(x)^3 + 3*b*cosh(x)^2 + 3*(5*b*cosh(x)^4 + 6*b*cosh(x)^2 + b)*sinh(x)^2 + 6*(b*cosh(x)^5 + 2*b*cosh(x)^3 + b*cosh(x))*sinh(x) + b)*sqrt(a + b)*log(((a^3 + a^2*b)*cosh(x)^8 + 8*(a^3 + a^2*b)*cosh(x)*sinh(x)^7 + (a^3 + a^2*b)*sinh(x)^8 + 2*(2*a^3 + a^2*b)*cosh(x)^6 + 2*(2*a^3 + a^2*b + 14*(a^3 + a^2*b)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a^3 + a^2*b)*cosh(x)^3 + 3*(2*a^3 + a^2*b)*cosh(x))*sinh(x)^5 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^4 + (70*(a^3 + a^2*b)*cosh(x)^4 + 6*a^3 + 4*a^2*b - a*b^2 + b^3 + 30*(2*a^3 + a^2*b)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a^3 + a^2*b)*cosh(x)^5 + 10*(2*a^3 + a^2*b)*cosh(x)^3 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x))*sinh(x)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 + 2*(2*a^3 + 3*a^2*b - b^3)*cosh(x)^2 + 2*(14*(a^3 + a^2*b)*cosh(x)^6 + 15*(2*a^3 + a^2*b)*cosh(x)^4 + 2*a^3 + 3*a^2*b - b^3 + 3*(6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^2)*sinh(x)^2 + sqrt(2)*(a^2*cosh(x)^6 + 6*a^2*cosh(x)*sinh(x)^5 + a^2*sinh(x)^6 + 3*a^2*cosh(x)^4 + 3*(5*a^2*cosh(x)^2 + a^2)*sinh(x)^4 + 4*(5*a^2*cosh(x)^3 + 3*a^2*cosh(x))*sinh(x)^3 + (3*a^2 + 2*a*b - b^2)*cosh(x)^2 + (15*a^2*cosh(x)^4 + 18*a^2*cosh(x)^2 + 3*a^2 + 2*a*b - b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(3*a^2*cosh(x)^5 + 6*a^2*cosh(x)^3 + (3*a^2 + 2*a*b - b^2)*cosh(x))*sinh(x))*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a^3 + a^2*b)*cosh(x)^7 + 3*(2*a^3 + a^2*b)*cosh(x)^5 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^3 + (2*a^3 + 3*a^2*b - b^3)*cosh(x))*sinh(x))/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) + 3*(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 + 4*(5*b*cosh(x)^3 + 3*b*cosh(x))*sinh(x)^3 + 3*b*cosh(x)^2 + 3*(5*b*cosh(x)^4 + 6*b*cosh(x)^2 + b)*sinh(x)^2 + 6*(b*cosh(x)^5 + 2*b*cosh(x)^3 + b*cosh(x))*sinh(x) + b)*sqrt(a + b)*log(-((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*b*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + b)*cosh(x)^3 - b*cosh(x))*sinh(x) + a + b)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) - 4*sqrt(2)*((a + 4*b)*cosh(x)^4 + 4*(a + 4*b)*cosh(x)*sinh(x)^3 + (a + 4*b)*sinh(x)^4 + 2*(a + 2*b)*cosh(x)^2 + 2*(3*(a + 4*b)*cosh(x)^2 + a + 2*b)*sinh(x)^2 + 4*((a + 4*b)*cosh(x)^3 + (a + 2*b)*cosh(x))*sinh(x) + a + 4*b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(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 + 4*(5*b*cosh(x)^3 + 3*b*cosh(x))*sinh(x)^3 + 3*b*cosh(x)^2 + 3*(5*b*cosh(x)^4 + 6*b*cosh(x)^2 + b)*sinh(x)^2 + 6*(b*cosh(x)^5 + 2*b*cosh(x)^3 + b*cosh(x))*sinh(x) + b), -1/6*(3*(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 + 4*(5*b*cosh(x)^3 + 3*b*cosh(x))*sinh(x)^3 + 3*b*cosh(x)^2 + 3*(5*b*cosh(x)^4 + 6*b*cosh(x)^2 + b)*sinh(x)^2 + 6*(b*cosh(x)^5 + 2*b*cosh(x)^3 + b*cosh(x))*sinh(x) + b)*sqrt(-a - b)*arctan(sqrt(2)*(a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 + a + b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a^2 + a*b)*cosh(x)^4 + 4*(a^2 + a*b)*cosh(x)*sinh(x)^3 + (a^2 + a*b)*sinh(x)^4 + (2*a^2 + a*b - b^2)*cosh(x)^2 + (6*(a^2 + a*b)*cosh(x)^2 + 2*a^2 + a*b - b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(2*(a^2 + a*b)*cosh(x)^3 + (2*a^2 + a*b - b^2)*cosh(x))*sinh(x))) + 3*(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 + 4*(5*b*cosh(x)^3 + 3*b*cosh(x))*sinh(x)^3 + 3*b*cosh(x)^2 + 3*(5*b*cosh(x)^4 + 6*b*cosh(x)^2 + b)*sinh(x)^2 + 6*(b*cosh(x)^5 + 2*b*cosh(x)^3 + b*cosh(x))*sinh(x) + b)*sqrt(-a - b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a - b)*cosh(x))*sinh(x) + a + b)) + 2*sqrt(2)*((a + 4*b)*cosh(x)^4 + 4*(a + 4*b)*cosh(x)*sinh(x)^3 + (a + 4*b)*sinh(x)^4 + 2*(a + 2*b)*cosh(x)^2 + 2*(3*(a + 4*b)*cosh(x)^2 + a + 2*b)*sinh(x)^2 + 4*((a + 4*b)*cosh(x)^3 + (a + 2*b)*cosh(x))*sinh(x) + a + 4*b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(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 + 4*(5*b*cosh(x)^3 + 3*b*cosh(x))*sinh(x)^3 + 3*b*cosh(x)^2 + 3*(5*b*cosh(x)^4 + 6*b*cosh(x)^2 + b)*sinh(x)^2 + 6*(b*cosh(x)^5 + 2*b*cosh(x)^3 + b*cosh(x))*sinh(x) + b)]","B",0
211,1,4825,0,0.684840," ","integrate((a+b*tanh(x)^2)^(1/2)*tanh(x)^2,x, algorithm=""fricas"")","\left[\frac{{\left(b \cosh\left(x\right)^{4} + 4 \, b \cosh\left(x\right) \sinh\left(x\right)^{3} + b \sinh\left(x\right)^{4} + 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b \cosh\left(x\right)^{2} + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(b \cosh\left(x\right)^{3} + b \cosh\left(x\right)\right)} \sinh\left(x\right) + b\right)} \sqrt{a + b} \log\left(-\frac{{\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a b^{2} + b^{3}\right)} \sinh\left(x\right)^{8} - 2 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{6} - 2 \, {\left(a b^{2} + 2 \, b^{3} - 14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3} - 30 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} + 2 \, {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} - 3 \, a b^{2} - 2 \, b^{3} + 3 \, {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(b^{2} \cosh\left(x\right)^{6} + 6 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + b^{2} \sinh\left(x\right)^{6} - 3 \, b^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, b^{2} \cosh\left(x\right)^{2} - b^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, b^{2} \cosh\left(x\right)^{3} - 3 \, b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, b^{2} \cosh\left(x\right)^{4} - 18 \, b^{2} \cosh\left(x\right)^{2} - a^{2} + 2 \, a b + 3 \, b^{2}\right)} \sinh\left(x\right)^{2} - a^{2} - 2 \, a b - b^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{5} - 6 \, b^{2} \cosh\left(x\right)^{3} - {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{5} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) + {\left({\left(a + 2 \, b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + 2 \, b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + a + 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + 2 \, b\right)} \cosh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + 2 \, b\right)} \sqrt{b} \log\left(-\frac{{\left(a + 2 \, b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + 2 \, b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + a - 2 \, b\right)} \sinh\left(x\right)^{2} - 2 \, \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + 2 \, b\right)} \cosh\left(x\right)^{3} + {\left(a - 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + 2 \, b}{\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) + {\left(b \cosh\left(x\right)^{4} + 4 \, b \cosh\left(x\right) \sinh\left(x\right)^{3} + b \sinh\left(x\right)^{4} + 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b \cosh\left(x\right)^{2} + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(b \cosh\left(x\right)^{3} + b \cosh\left(x\right)\right)} \sinh\left(x\right) + b\right)} \sqrt{a + b} \log\left(\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, a \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + a \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right) - 2 \, \sqrt{2} {\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} - b\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{4 \, {\left(b \cosh\left(x\right)^{4} + 4 \, b \cosh\left(x\right) \sinh\left(x\right)^{3} + b \sinh\left(x\right)^{4} + 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b \cosh\left(x\right)^{2} + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(b \cosh\left(x\right)^{3} + b \cosh\left(x\right)\right)} \sinh\left(x\right) + b\right)}}, \frac{2 \, {\left({\left(a + 2 \, b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + 2 \, b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + a + 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + 2 \, b\right)} \cosh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + 2 \, b\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{-b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) + {\left(b \cosh\left(x\right)^{4} + 4 \, b \cosh\left(x\right) \sinh\left(x\right)^{3} + b \sinh\left(x\right)^{4} + 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b \cosh\left(x\right)^{2} + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(b \cosh\left(x\right)^{3} + b \cosh\left(x\right)\right)} \sinh\left(x\right) + b\right)} \sqrt{a + b} \log\left(-\frac{{\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a b^{2} + b^{3}\right)} \sinh\left(x\right)^{8} - 2 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{6} - 2 \, {\left(a b^{2} + 2 \, b^{3} - 14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3} - 30 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} + 2 \, {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} - 3 \, a b^{2} - 2 \, b^{3} + 3 \, {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(b^{2} \cosh\left(x\right)^{6} + 6 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + b^{2} \sinh\left(x\right)^{6} - 3 \, b^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, b^{2} \cosh\left(x\right)^{2} - b^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, b^{2} \cosh\left(x\right)^{3} - 3 \, b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, b^{2} \cosh\left(x\right)^{4} - 18 \, b^{2} \cosh\left(x\right)^{2} - a^{2} + 2 \, a b + 3 \, b^{2}\right)} \sinh\left(x\right)^{2} - a^{2} - 2 \, a b - b^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{5} - 6 \, b^{2} \cosh\left(x\right)^{3} - {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{5} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) + {\left(b \cosh\left(x\right)^{4} + 4 \, b \cosh\left(x\right) \sinh\left(x\right)^{3} + b \sinh\left(x\right)^{4} + 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b \cosh\left(x\right)^{2} + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(b \cosh\left(x\right)^{3} + b \cosh\left(x\right)\right)} \sinh\left(x\right) + b\right)} \sqrt{a + b} \log\left(\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, a \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + a \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right) - 2 \, \sqrt{2} {\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} - b\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{4 \, {\left(b \cosh\left(x\right)^{4} + 4 \, b \cosh\left(x\right) \sinh\left(x\right)^{3} + b \sinh\left(x\right)^{4} + 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b \cosh\left(x\right)^{2} + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(b \cosh\left(x\right)^{3} + b \cosh\left(x\right)\right)} \sinh\left(x\right) + b\right)}}, -\frac{2 \, {\left(b \cosh\left(x\right)^{4} + 4 \, b \cosh\left(x\right) \sinh\left(x\right)^{3} + b \sinh\left(x\right)^{4} + 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b \cosh\left(x\right)^{2} + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(b \cosh\left(x\right)^{3} + b \cosh\left(x\right)\right)} \sinh\left(x\right) + b\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} - a - b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a b + b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a b + b^{2}\right)} \sinh\left(x\right)^{4} + {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} - a b - 2 \, b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(2 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + 2 \, {\left(b \cosh\left(x\right)^{4} + 4 \, b \cosh\left(x\right) \sinh\left(x\right)^{3} + b \sinh\left(x\right)^{4} + 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b \cosh\left(x\right)^{2} + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(b \cosh\left(x\right)^{3} + b \cosh\left(x\right)\right)} \sinh\left(x\right) + b\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) - {\left({\left(a + 2 \, b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + 2 \, b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + a + 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + 2 \, b\right)} \cosh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + 2 \, b\right)} \sqrt{b} \log\left(-\frac{{\left(a + 2 \, b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + 2 \, b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + a - 2 \, b\right)} \sinh\left(x\right)^{2} - 2 \, \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + 2 \, b\right)} \cosh\left(x\right)^{3} + {\left(a - 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + 2 \, b}{\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) + 2 \, \sqrt{2} {\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} - b\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{4 \, {\left(b \cosh\left(x\right)^{4} + 4 \, b \cosh\left(x\right) \sinh\left(x\right)^{3} + b \sinh\left(x\right)^{4} + 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b \cosh\left(x\right)^{2} + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(b \cosh\left(x\right)^{3} + b \cosh\left(x\right)\right)} \sinh\left(x\right) + b\right)}}, -\frac{{\left(b \cosh\left(x\right)^{4} + 4 \, b \cosh\left(x\right) \sinh\left(x\right)^{3} + b \sinh\left(x\right)^{4} + 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b \cosh\left(x\right)^{2} + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(b \cosh\left(x\right)^{3} + b \cosh\left(x\right)\right)} \sinh\left(x\right) + b\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} - a - b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a b + b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a b + b^{2}\right)} \sinh\left(x\right)^{4} + {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} - a b - 2 \, b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(2 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + {\left(b \cosh\left(x\right)^{4} + 4 \, b \cosh\left(x\right) \sinh\left(x\right)^{3} + b \sinh\left(x\right)^{4} + 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b \cosh\left(x\right)^{2} + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(b \cosh\left(x\right)^{3} + b \cosh\left(x\right)\right)} \sinh\left(x\right) + b\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) - {\left({\left(a + 2 \, b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + 2 \, b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + a + 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + 2 \, b\right)} \cosh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + 2 \, b\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{-b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) + \sqrt{2} {\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} - b\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{2 \, {\left(b \cosh\left(x\right)^{4} + 4 \, b \cosh\left(x\right) \sinh\left(x\right)^{3} + b \sinh\left(x\right)^{4} + 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b \cosh\left(x\right)^{2} + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(b \cosh\left(x\right)^{3} + b \cosh\left(x\right)\right)} \sinh\left(x\right) + b\right)}}\right]"," ",0,"[1/4*((b*cosh(x)^4 + 4*b*cosh(x)*sinh(x)^3 + b*sinh(x)^4 + 2*b*cosh(x)^2 + 2*(3*b*cosh(x)^2 + b)*sinh(x)^2 + 4*(b*cosh(x)^3 + b*cosh(x))*sinh(x) + b)*sqrt(a + b)*log(-((a*b^2 + b^3)*cosh(x)^8 + 8*(a*b^2 + b^3)*cosh(x)*sinh(x)^7 + (a*b^2 + b^3)*sinh(x)^8 - 2*(a*b^2 + 2*b^3)*cosh(x)^6 - 2*(a*b^2 + 2*b^3 - 14*(a*b^2 + b^3)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a*b^2 + b^3)*cosh(x)^3 - 3*(a*b^2 + 2*b^3)*cosh(x))*sinh(x)^5 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^4 + (70*(a*b^2 + b^3)*cosh(x)^4 + a^3 - a^2*b + 4*a*b^2 + 6*b^3 - 30*(a*b^2 + 2*b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a*b^2 + b^3)*cosh(x)^5 - 10*(a*b^2 + 2*b^3)*cosh(x)^3 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x))*sinh(x)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 + 2*(a^3 - 3*a*b^2 - 2*b^3)*cosh(x)^2 + 2*(14*(a*b^2 + b^3)*cosh(x)^6 - 15*(a*b^2 + 2*b^3)*cosh(x)^4 + a^3 - 3*a*b^2 - 2*b^3 + 3*(a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^2)*sinh(x)^2 + sqrt(2)*(b^2*cosh(x)^6 + 6*b^2*cosh(x)*sinh(x)^5 + b^2*sinh(x)^6 - 3*b^2*cosh(x)^4 + 3*(5*b^2*cosh(x)^2 - b^2)*sinh(x)^4 + 4*(5*b^2*cosh(x)^3 - 3*b^2*cosh(x))*sinh(x)^3 - (a^2 - 2*a*b - 3*b^2)*cosh(x)^2 + (15*b^2*cosh(x)^4 - 18*b^2*cosh(x)^2 - a^2 + 2*a*b + 3*b^2)*sinh(x)^2 - a^2 - 2*a*b - b^2 + 2*(3*b^2*cosh(x)^5 - 6*b^2*cosh(x)^3 - (a^2 - 2*a*b - 3*b^2)*cosh(x))*sinh(x))*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a*b^2 + b^3)*cosh(x)^7 - 3*(a*b^2 + 2*b^3)*cosh(x)^5 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^3 + (a^3 - 3*a*b^2 - 2*b^3)*cosh(x))*sinh(x))/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) + ((a + 2*b)*cosh(x)^4 + 4*(a + 2*b)*cosh(x)*sinh(x)^3 + (a + 2*b)*sinh(x)^4 + 2*(a + 2*b)*cosh(x)^2 + 2*(3*(a + 2*b)*cosh(x)^2 + a + 2*b)*sinh(x)^2 + 4*((a + 2*b)*cosh(x)^3 + (a + 2*b)*cosh(x))*sinh(x) + a + 2*b)*sqrt(b)*log(-((a + 2*b)*cosh(x)^4 + 4*(a + 2*b)*cosh(x)*sinh(x)^3 + (a + 2*b)*sinh(x)^4 + 2*(a - 2*b)*cosh(x)^2 + 2*(3*(a + 2*b)*cosh(x)^2 + a - 2*b)*sinh(x)^2 - 2*sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + 2*b)*cosh(x)^3 + (a - 2*b)*cosh(x))*sinh(x) + a + 2*b)/(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)) + (b*cosh(x)^4 + 4*b*cosh(x)*sinh(x)^3 + b*sinh(x)^4 + 2*b*cosh(x)^2 + 2*(3*b*cosh(x)^2 + b)*sinh(x)^2 + 4*(b*cosh(x)^3 + b*cosh(x))*sinh(x) + b)*sqrt(a + b)*log(((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*a*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + b)*cosh(x)^3 + a*cosh(x))*sinh(x) + a + b)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) - 2*sqrt(2)*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(b*cosh(x)^4 + 4*b*cosh(x)*sinh(x)^3 + b*sinh(x)^4 + 2*b*cosh(x)^2 + 2*(3*b*cosh(x)^2 + b)*sinh(x)^2 + 4*(b*cosh(x)^3 + b*cosh(x))*sinh(x) + b), 1/4*(2*((a + 2*b)*cosh(x)^4 + 4*(a + 2*b)*cosh(x)*sinh(x)^3 + (a + 2*b)*sinh(x)^4 + 2*(a + 2*b)*cosh(x)^2 + 2*(3*(a + 2*b)*cosh(x)^2 + a + 2*b)*sinh(x)^2 + 4*((a + 2*b)*cosh(x)^3 + (a + 2*b)*cosh(x))*sinh(x) + a + 2*b)*sqrt(-b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a - b)*cosh(x))*sinh(x) + a + b)) + (b*cosh(x)^4 + 4*b*cosh(x)*sinh(x)^3 + b*sinh(x)^4 + 2*b*cosh(x)^2 + 2*(3*b*cosh(x)^2 + b)*sinh(x)^2 + 4*(b*cosh(x)^3 + b*cosh(x))*sinh(x) + b)*sqrt(a + b)*log(-((a*b^2 + b^3)*cosh(x)^8 + 8*(a*b^2 + b^3)*cosh(x)*sinh(x)^7 + (a*b^2 + b^3)*sinh(x)^8 - 2*(a*b^2 + 2*b^3)*cosh(x)^6 - 2*(a*b^2 + 2*b^3 - 14*(a*b^2 + b^3)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a*b^2 + b^3)*cosh(x)^3 - 3*(a*b^2 + 2*b^3)*cosh(x))*sinh(x)^5 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^4 + (70*(a*b^2 + b^3)*cosh(x)^4 + a^3 - a^2*b + 4*a*b^2 + 6*b^3 - 30*(a*b^2 + 2*b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a*b^2 + b^3)*cosh(x)^5 - 10*(a*b^2 + 2*b^3)*cosh(x)^3 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x))*sinh(x)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 + 2*(a^3 - 3*a*b^2 - 2*b^3)*cosh(x)^2 + 2*(14*(a*b^2 + b^3)*cosh(x)^6 - 15*(a*b^2 + 2*b^3)*cosh(x)^4 + a^3 - 3*a*b^2 - 2*b^3 + 3*(a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^2)*sinh(x)^2 + sqrt(2)*(b^2*cosh(x)^6 + 6*b^2*cosh(x)*sinh(x)^5 + b^2*sinh(x)^6 - 3*b^2*cosh(x)^4 + 3*(5*b^2*cosh(x)^2 - b^2)*sinh(x)^4 + 4*(5*b^2*cosh(x)^3 - 3*b^2*cosh(x))*sinh(x)^3 - (a^2 - 2*a*b - 3*b^2)*cosh(x)^2 + (15*b^2*cosh(x)^4 - 18*b^2*cosh(x)^2 - a^2 + 2*a*b + 3*b^2)*sinh(x)^2 - a^2 - 2*a*b - b^2 + 2*(3*b^2*cosh(x)^5 - 6*b^2*cosh(x)^3 - (a^2 - 2*a*b - 3*b^2)*cosh(x))*sinh(x))*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a*b^2 + b^3)*cosh(x)^7 - 3*(a*b^2 + 2*b^3)*cosh(x)^5 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^3 + (a^3 - 3*a*b^2 - 2*b^3)*cosh(x))*sinh(x))/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) + (b*cosh(x)^4 + 4*b*cosh(x)*sinh(x)^3 + b*sinh(x)^4 + 2*b*cosh(x)^2 + 2*(3*b*cosh(x)^2 + b)*sinh(x)^2 + 4*(b*cosh(x)^3 + b*cosh(x))*sinh(x) + b)*sqrt(a + b)*log(((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*a*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + b)*cosh(x)^3 + a*cosh(x))*sinh(x) + a + b)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) - 2*sqrt(2)*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(b*cosh(x)^4 + 4*b*cosh(x)*sinh(x)^3 + b*sinh(x)^4 + 2*b*cosh(x)^2 + 2*(3*b*cosh(x)^2 + b)*sinh(x)^2 + 4*(b*cosh(x)^3 + b*cosh(x))*sinh(x) + b), -1/4*(2*(b*cosh(x)^4 + 4*b*cosh(x)*sinh(x)^3 + b*sinh(x)^4 + 2*b*cosh(x)^2 + 2*(3*b*cosh(x)^2 + b)*sinh(x)^2 + 4*(b*cosh(x)^3 + b*cosh(x))*sinh(x) + b)*sqrt(-a - b)*arctan(sqrt(2)*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 - a - b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a*b + b^2)*cosh(x)^4 + 4*(a*b + b^2)*cosh(x)*sinh(x)^3 + (a*b + b^2)*sinh(x)^4 + (a^2 - a*b - 2*b^2)*cosh(x)^2 + (6*(a*b + b^2)*cosh(x)^2 + a^2 - a*b - 2*b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(2*(a*b + b^2)*cosh(x)^3 + (a^2 - a*b - 2*b^2)*cosh(x))*sinh(x))) + 2*(b*cosh(x)^4 + 4*b*cosh(x)*sinh(x)^3 + b*sinh(x)^4 + 2*b*cosh(x)^2 + 2*(3*b*cosh(x)^2 + b)*sinh(x)^2 + 4*(b*cosh(x)^3 + b*cosh(x))*sinh(x) + b)*sqrt(-a - b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a - b)*cosh(x))*sinh(x) + a + b)) - ((a + 2*b)*cosh(x)^4 + 4*(a + 2*b)*cosh(x)*sinh(x)^3 + (a + 2*b)*sinh(x)^4 + 2*(a + 2*b)*cosh(x)^2 + 2*(3*(a + 2*b)*cosh(x)^2 + a + 2*b)*sinh(x)^2 + 4*((a + 2*b)*cosh(x)^3 + (a + 2*b)*cosh(x))*sinh(x) + a + 2*b)*sqrt(b)*log(-((a + 2*b)*cosh(x)^4 + 4*(a + 2*b)*cosh(x)*sinh(x)^3 + (a + 2*b)*sinh(x)^4 + 2*(a - 2*b)*cosh(x)^2 + 2*(3*(a + 2*b)*cosh(x)^2 + a - 2*b)*sinh(x)^2 - 2*sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + 2*b)*cosh(x)^3 + (a - 2*b)*cosh(x))*sinh(x) + a + 2*b)/(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)) + 2*sqrt(2)*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(b*cosh(x)^4 + 4*b*cosh(x)*sinh(x)^3 + b*sinh(x)^4 + 2*b*cosh(x)^2 + 2*(3*b*cosh(x)^2 + b)*sinh(x)^2 + 4*(b*cosh(x)^3 + b*cosh(x))*sinh(x) + b), -1/2*((b*cosh(x)^4 + 4*b*cosh(x)*sinh(x)^3 + b*sinh(x)^4 + 2*b*cosh(x)^2 + 2*(3*b*cosh(x)^2 + b)*sinh(x)^2 + 4*(b*cosh(x)^3 + b*cosh(x))*sinh(x) + b)*sqrt(-a - b)*arctan(sqrt(2)*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 - a - b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a*b + b^2)*cosh(x)^4 + 4*(a*b + b^2)*cosh(x)*sinh(x)^3 + (a*b + b^2)*sinh(x)^4 + (a^2 - a*b - 2*b^2)*cosh(x)^2 + (6*(a*b + b^2)*cosh(x)^2 + a^2 - a*b - 2*b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(2*(a*b + b^2)*cosh(x)^3 + (a^2 - a*b - 2*b^2)*cosh(x))*sinh(x))) + (b*cosh(x)^4 + 4*b*cosh(x)*sinh(x)^3 + b*sinh(x)^4 + 2*b*cosh(x)^2 + 2*(3*b*cosh(x)^2 + b)*sinh(x)^2 + 4*(b*cosh(x)^3 + b*cosh(x))*sinh(x) + b)*sqrt(-a - b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a - b)*cosh(x))*sinh(x) + a + b)) - ((a + 2*b)*cosh(x)^4 + 4*(a + 2*b)*cosh(x)*sinh(x)^3 + (a + 2*b)*sinh(x)^4 + 2*(a + 2*b)*cosh(x)^2 + 2*(3*(a + 2*b)*cosh(x)^2 + a + 2*b)*sinh(x)^2 + 4*((a + 2*b)*cosh(x)^3 + (a + 2*b)*cosh(x))*sinh(x) + a + 2*b)*sqrt(-b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a - b)*cosh(x))*sinh(x) + a + b)) + sqrt(2)*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(b*cosh(x)^4 + 4*b*cosh(x)*sinh(x)^3 + b*sinh(x)^4 + 2*b*cosh(x)^2 + 2*(3*b*cosh(x)^2 + b)*sinh(x)^2 + 4*(b*cosh(x)^3 + b*cosh(x))*sinh(x) + b)]","B",0
212,1,1543,0,0.505281," ","integrate((a+b*tanh(x)^2)^(1/2)*tanh(x),x, algorithm=""fricas"")","\left[\frac{{\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{a + b} \log\left(\frac{{\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{3} + a^{2} b\right)} \sinh\left(x\right)^{8} + 2 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} + 2 \, {\left(2 \, a^{3} + a^{2} b + 14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} + 3 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3} + 30 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} + 10 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} + 2 \, {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} + 15 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 2 \, a^{3} + 3 \, a^{2} b - b^{3} + 3 \, {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(a^{2} \cosh\left(x\right)^{6} + 6 \, a^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + a^{2} \sinh\left(x\right)^{6} + 3 \, a^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, a^{2} \cosh\left(x\right)^{2} + a^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, a^{2} \cosh\left(x\right)^{3} + 3 \, a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, a^{2} \cosh\left(x\right)^{4} + 18 \, a^{2} \cosh\left(x\right)^{2} + 3 \, a^{2} + 2 \, a b - b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(x\right)^{5} + 6 \, a^{2} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{7} + 3 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) + {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{a + b} \log\left(-\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - b\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - b \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right) - 4 \, \sqrt{2} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{4 \, {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)}}, -\frac{{\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(a \cosh\left(x\right)^{2} + 2 \, a \cosh\left(x\right) \sinh\left(x\right) + a \sinh\left(x\right)^{2} + a + b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a^{2} + a b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{2} + a b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{2} + a b\right)} \sinh\left(x\right)^{4} + {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} + 2 \, a^{2} + a b - b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(2 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) + 2 \, \sqrt{2} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{2 \, {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)}}\right]"," ",0,"[1/4*((cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a + b)*log(((a^3 + a^2*b)*cosh(x)^8 + 8*(a^3 + a^2*b)*cosh(x)*sinh(x)^7 + (a^3 + a^2*b)*sinh(x)^8 + 2*(2*a^3 + a^2*b)*cosh(x)^6 + 2*(2*a^3 + a^2*b + 14*(a^3 + a^2*b)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a^3 + a^2*b)*cosh(x)^3 + 3*(2*a^3 + a^2*b)*cosh(x))*sinh(x)^5 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^4 + (70*(a^3 + a^2*b)*cosh(x)^4 + 6*a^3 + 4*a^2*b - a*b^2 + b^3 + 30*(2*a^3 + a^2*b)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a^3 + a^2*b)*cosh(x)^5 + 10*(2*a^3 + a^2*b)*cosh(x)^3 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x))*sinh(x)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 + 2*(2*a^3 + 3*a^2*b - b^3)*cosh(x)^2 + 2*(14*(a^3 + a^2*b)*cosh(x)^6 + 15*(2*a^3 + a^2*b)*cosh(x)^4 + 2*a^3 + 3*a^2*b - b^3 + 3*(6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^2)*sinh(x)^2 + sqrt(2)*(a^2*cosh(x)^6 + 6*a^2*cosh(x)*sinh(x)^5 + a^2*sinh(x)^6 + 3*a^2*cosh(x)^4 + 3*(5*a^2*cosh(x)^2 + a^2)*sinh(x)^4 + 4*(5*a^2*cosh(x)^3 + 3*a^2*cosh(x))*sinh(x)^3 + (3*a^2 + 2*a*b - b^2)*cosh(x)^2 + (15*a^2*cosh(x)^4 + 18*a^2*cosh(x)^2 + 3*a^2 + 2*a*b - b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(3*a^2*cosh(x)^5 + 6*a^2*cosh(x)^3 + (3*a^2 + 2*a*b - b^2)*cosh(x))*sinh(x))*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a^3 + a^2*b)*cosh(x)^7 + 3*(2*a^3 + a^2*b)*cosh(x)^5 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^3 + (2*a^3 + 3*a^2*b - b^3)*cosh(x))*sinh(x))/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) + (cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a + b)*log(-((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*b*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + b)*cosh(x)^3 - b*cosh(x))*sinh(x) + a + b)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) - 4*sqrt(2)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1), -1/2*((cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(-a - b)*arctan(sqrt(2)*(a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 + a + b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a^2 + a*b)*cosh(x)^4 + 4*(a^2 + a*b)*cosh(x)*sinh(x)^3 + (a^2 + a*b)*sinh(x)^4 + (2*a^2 + a*b - b^2)*cosh(x)^2 + (6*(a^2 + a*b)*cosh(x)^2 + 2*a^2 + a*b - b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(2*(a^2 + a*b)*cosh(x)^3 + (2*a^2 + a*b - b^2)*cosh(x))*sinh(x))) + (cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(-a - b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a - b)*cosh(x))*sinh(x) + a + b)) + 2*sqrt(2)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)]","B",0
213,1,3443,0,0.571263," ","integrate((a+b*tanh(x)^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{1}{4} \, \sqrt{a + b} \log\left(-\frac{{\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a b^{2} + b^{3}\right)} \sinh\left(x\right)^{8} - 2 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{6} - 2 \, {\left(a b^{2} + 2 \, b^{3} - 14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3} - 30 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} + 2 \, {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} - 3 \, a b^{2} - 2 \, b^{3} + 3 \, {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(b^{2} \cosh\left(x\right)^{6} + 6 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + b^{2} \sinh\left(x\right)^{6} - 3 \, b^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, b^{2} \cosh\left(x\right)^{2} - b^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, b^{2} \cosh\left(x\right)^{3} - 3 \, b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, b^{2} \cosh\left(x\right)^{4} - 18 \, b^{2} \cosh\left(x\right)^{2} - a^{2} + 2 \, a b + 3 \, b^{2}\right)} \sinh\left(x\right)^{2} - a^{2} - 2 \, a b - b^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{5} - 6 \, b^{2} \cosh\left(x\right)^{3} - {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{5} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) + \frac{1}{2} \, \sqrt{b} \log\left(-\frac{{\left(a + 2 \, b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + 2 \, b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + a - 2 \, b\right)} \sinh\left(x\right)^{2} - 2 \, \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + 2 \, b\right)} \cosh\left(x\right)^{3} + {\left(a - 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + 2 \, b}{\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) + \frac{1}{4} \, \sqrt{a + b} \log\left(\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, a \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + a \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right), \sqrt{-b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{-b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) + \frac{1}{4} \, \sqrt{a + b} \log\left(-\frac{{\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a b^{2} + b^{3}\right)} \sinh\left(x\right)^{8} - 2 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{6} - 2 \, {\left(a b^{2} + 2 \, b^{3} - 14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3} - 30 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} + 2 \, {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} - 3 \, a b^{2} - 2 \, b^{3} + 3 \, {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(b^{2} \cosh\left(x\right)^{6} + 6 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + b^{2} \sinh\left(x\right)^{6} - 3 \, b^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, b^{2} \cosh\left(x\right)^{2} - b^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, b^{2} \cosh\left(x\right)^{3} - 3 \, b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, b^{2} \cosh\left(x\right)^{4} - 18 \, b^{2} \cosh\left(x\right)^{2} - a^{2} + 2 \, a b + 3 \, b^{2}\right)} \sinh\left(x\right)^{2} - a^{2} - 2 \, a b - b^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{5} - 6 \, b^{2} \cosh\left(x\right)^{3} - {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{5} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) + \frac{1}{4} \, \sqrt{a + b} \log\left(\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, a \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + a \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right), -\frac{1}{2} \, \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} - a - b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a b + b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a b + b^{2}\right)} \sinh\left(x\right)^{4} + {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} - a b - 2 \, b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(2 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) - \frac{1}{2} \, \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) + \frac{1}{2} \, \sqrt{b} \log\left(-\frac{{\left(a + 2 \, b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + 2 \, b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + a - 2 \, b\right)} \sinh\left(x\right)^{2} - 2 \, \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + 2 \, b\right)} \cosh\left(x\right)^{3} + {\left(a - 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + 2 \, b}{\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), -\frac{1}{2} \, \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} - a - b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a b + b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a b + b^{2}\right)} \sinh\left(x\right)^{4} + {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} - a b - 2 \, b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(2 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) - \frac{1}{2} \, \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) + \sqrt{-b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{-b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right)\right]"," ",0,"[1/4*sqrt(a + b)*log(-((a*b^2 + b^3)*cosh(x)^8 + 8*(a*b^2 + b^3)*cosh(x)*sinh(x)^7 + (a*b^2 + b^3)*sinh(x)^8 - 2*(a*b^2 + 2*b^3)*cosh(x)^6 - 2*(a*b^2 + 2*b^3 - 14*(a*b^2 + b^3)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a*b^2 + b^3)*cosh(x)^3 - 3*(a*b^2 + 2*b^3)*cosh(x))*sinh(x)^5 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^4 + (70*(a*b^2 + b^3)*cosh(x)^4 + a^3 - a^2*b + 4*a*b^2 + 6*b^3 - 30*(a*b^2 + 2*b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a*b^2 + b^3)*cosh(x)^5 - 10*(a*b^2 + 2*b^3)*cosh(x)^3 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x))*sinh(x)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 + 2*(a^3 - 3*a*b^2 - 2*b^3)*cosh(x)^2 + 2*(14*(a*b^2 + b^3)*cosh(x)^6 - 15*(a*b^2 + 2*b^3)*cosh(x)^4 + a^3 - 3*a*b^2 - 2*b^3 + 3*(a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^2)*sinh(x)^2 + sqrt(2)*(b^2*cosh(x)^6 + 6*b^2*cosh(x)*sinh(x)^5 + b^2*sinh(x)^6 - 3*b^2*cosh(x)^4 + 3*(5*b^2*cosh(x)^2 - b^2)*sinh(x)^4 + 4*(5*b^2*cosh(x)^3 - 3*b^2*cosh(x))*sinh(x)^3 - (a^2 - 2*a*b - 3*b^2)*cosh(x)^2 + (15*b^2*cosh(x)^4 - 18*b^2*cosh(x)^2 - a^2 + 2*a*b + 3*b^2)*sinh(x)^2 - a^2 - 2*a*b - b^2 + 2*(3*b^2*cosh(x)^5 - 6*b^2*cosh(x)^3 - (a^2 - 2*a*b - 3*b^2)*cosh(x))*sinh(x))*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a*b^2 + b^3)*cosh(x)^7 - 3*(a*b^2 + 2*b^3)*cosh(x)^5 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^3 + (a^3 - 3*a*b^2 - 2*b^3)*cosh(x))*sinh(x))/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) + 1/2*sqrt(b)*log(-((a + 2*b)*cosh(x)^4 + 4*(a + 2*b)*cosh(x)*sinh(x)^3 + (a + 2*b)*sinh(x)^4 + 2*(a - 2*b)*cosh(x)^2 + 2*(3*(a + 2*b)*cosh(x)^2 + a - 2*b)*sinh(x)^2 - 2*sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + 2*b)*cosh(x)^3 + (a - 2*b)*cosh(x))*sinh(x) + a + 2*b)/(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)) + 1/4*sqrt(a + b)*log(((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*a*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + b)*cosh(x)^3 + a*cosh(x))*sinh(x) + a + b)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)), sqrt(-b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a - b)*cosh(x))*sinh(x) + a + b)) + 1/4*sqrt(a + b)*log(-((a*b^2 + b^3)*cosh(x)^8 + 8*(a*b^2 + b^3)*cosh(x)*sinh(x)^7 + (a*b^2 + b^3)*sinh(x)^8 - 2*(a*b^2 + 2*b^3)*cosh(x)^6 - 2*(a*b^2 + 2*b^3 - 14*(a*b^2 + b^3)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a*b^2 + b^3)*cosh(x)^3 - 3*(a*b^2 + 2*b^3)*cosh(x))*sinh(x)^5 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^4 + (70*(a*b^2 + b^3)*cosh(x)^4 + a^3 - a^2*b + 4*a*b^2 + 6*b^3 - 30*(a*b^2 + 2*b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a*b^2 + b^3)*cosh(x)^5 - 10*(a*b^2 + 2*b^3)*cosh(x)^3 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x))*sinh(x)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 + 2*(a^3 - 3*a*b^2 - 2*b^3)*cosh(x)^2 + 2*(14*(a*b^2 + b^3)*cosh(x)^6 - 15*(a*b^2 + 2*b^3)*cosh(x)^4 + a^3 - 3*a*b^2 - 2*b^3 + 3*(a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^2)*sinh(x)^2 + sqrt(2)*(b^2*cosh(x)^6 + 6*b^2*cosh(x)*sinh(x)^5 + b^2*sinh(x)^6 - 3*b^2*cosh(x)^4 + 3*(5*b^2*cosh(x)^2 - b^2)*sinh(x)^4 + 4*(5*b^2*cosh(x)^3 - 3*b^2*cosh(x))*sinh(x)^3 - (a^2 - 2*a*b - 3*b^2)*cosh(x)^2 + (15*b^2*cosh(x)^4 - 18*b^2*cosh(x)^2 - a^2 + 2*a*b + 3*b^2)*sinh(x)^2 - a^2 - 2*a*b - b^2 + 2*(3*b^2*cosh(x)^5 - 6*b^2*cosh(x)^3 - (a^2 - 2*a*b - 3*b^2)*cosh(x))*sinh(x))*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a*b^2 + b^3)*cosh(x)^7 - 3*(a*b^2 + 2*b^3)*cosh(x)^5 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^3 + (a^3 - 3*a*b^2 - 2*b^3)*cosh(x))*sinh(x))/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) + 1/4*sqrt(a + b)*log(((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*a*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + b)*cosh(x)^3 + a*cosh(x))*sinh(x) + a + b)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)), -1/2*sqrt(-a - b)*arctan(sqrt(2)*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 - a - b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a*b + b^2)*cosh(x)^4 + 4*(a*b + b^2)*cosh(x)*sinh(x)^3 + (a*b + b^2)*sinh(x)^4 + (a^2 - a*b - 2*b^2)*cosh(x)^2 + (6*(a*b + b^2)*cosh(x)^2 + a^2 - a*b - 2*b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(2*(a*b + b^2)*cosh(x)^3 + (a^2 - a*b - 2*b^2)*cosh(x))*sinh(x))) - 1/2*sqrt(-a - b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a - b)*cosh(x))*sinh(x) + a + b)) + 1/2*sqrt(b)*log(-((a + 2*b)*cosh(x)^4 + 4*(a + 2*b)*cosh(x)*sinh(x)^3 + (a + 2*b)*sinh(x)^4 + 2*(a - 2*b)*cosh(x)^2 + 2*(3*(a + 2*b)*cosh(x)^2 + a - 2*b)*sinh(x)^2 - 2*sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + 2*b)*cosh(x)^3 + (a - 2*b)*cosh(x))*sinh(x) + a + 2*b)/(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)), -1/2*sqrt(-a - b)*arctan(sqrt(2)*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 - a - b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a*b + b^2)*cosh(x)^4 + 4*(a*b + b^2)*cosh(x)*sinh(x)^3 + (a*b + b^2)*sinh(x)^4 + (a^2 - a*b - 2*b^2)*cosh(x)^2 + (6*(a*b + b^2)*cosh(x)^2 + a^2 - a*b - 2*b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(2*(a*b + b^2)*cosh(x)^3 + (a^2 - a*b - 2*b^2)*cosh(x))*sinh(x))) - 1/2*sqrt(-a - b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a - b)*cosh(x))*sinh(x) + a + b)) + sqrt(-b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a - b)*cosh(x))*sinh(x) + a + b))]","B",0
214,1,3467,0,0.601899," ","integrate(coth(x)*(a+b*tanh(x)^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{1}{4} \, \sqrt{a + b} \log\left(\frac{{\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{3} + a^{2} b\right)} \sinh\left(x\right)^{8} + 2 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} + 2 \, {\left(2 \, a^{3} + a^{2} b + 14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} + 3 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3} + 30 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} + 10 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} + 2 \, {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} + 15 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 2 \, a^{3} + 3 \, a^{2} b - b^{3} + 3 \, {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(a^{2} \cosh\left(x\right)^{6} + 6 \, a^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + a^{2} \sinh\left(x\right)^{6} + 3 \, a^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, a^{2} \cosh\left(x\right)^{2} + a^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, a^{2} \cosh\left(x\right)^{3} + 3 \, a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, a^{2} \cosh\left(x\right)^{4} + 18 \, a^{2} \cosh\left(x\right)^{2} + 3 \, a^{2} + 2 \, a b - b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(x\right)^{5} + 6 \, a^{2} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{7} + 3 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) + \frac{1}{2} \, \sqrt{a} \log\left(-\frac{{\left(2 \, a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(2 \, a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(2 \, a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(2 \, a + b\right)} \cosh\left(x\right)^{2} + 2 \, a - b\right)} \sinh\left(x\right)^{2} - 2 \, \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{a} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(2 \, a + b\right)} \cosh\left(x\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + 2 \, a + b}{\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) + \frac{1}{4} \, \sqrt{a + b} \log\left(-\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - b\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - b \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right), \sqrt{-a} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{-a} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) + \frac{1}{4} \, \sqrt{a + b} \log\left(\frac{{\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{3} + a^{2} b\right)} \sinh\left(x\right)^{8} + 2 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} + 2 \, {\left(2 \, a^{3} + a^{2} b + 14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} + 3 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3} + 30 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} + 10 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} + 2 \, {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} + 15 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 2 \, a^{3} + 3 \, a^{2} b - b^{3} + 3 \, {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(a^{2} \cosh\left(x\right)^{6} + 6 \, a^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + a^{2} \sinh\left(x\right)^{6} + 3 \, a^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, a^{2} \cosh\left(x\right)^{2} + a^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, a^{2} \cosh\left(x\right)^{3} + 3 \, a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, a^{2} \cosh\left(x\right)^{4} + 18 \, a^{2} \cosh\left(x\right)^{2} + 3 \, a^{2} + 2 \, a b - b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(x\right)^{5} + 6 \, a^{2} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{7} + 3 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) + \frac{1}{4} \, \sqrt{a + b} \log\left(-\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - b\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - b \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right), -\frac{1}{2} \, \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(a \cosh\left(x\right)^{2} + 2 \, a \cosh\left(x\right) \sinh\left(x\right) + a \sinh\left(x\right)^{2} + a + b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a^{2} + a b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{2} + a b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{2} + a b\right)} \sinh\left(x\right)^{4} + {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} + 2 \, a^{2} + a b - b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(2 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) - \frac{1}{2} \, \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) + \frac{1}{2} \, \sqrt{a} \log\left(-\frac{{\left(2 \, a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(2 \, a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(2 \, a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(2 \, a + b\right)} \cosh\left(x\right)^{2} + 2 \, a - b\right)} \sinh\left(x\right)^{2} - 2 \, \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{a} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(2 \, a + b\right)} \cosh\left(x\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + 2 \, a + b}{\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), \sqrt{-a} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{-a} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) - \frac{1}{2} \, \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(a \cosh\left(x\right)^{2} + 2 \, a \cosh\left(x\right) \sinh\left(x\right) + a \sinh\left(x\right)^{2} + a + b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a^{2} + a b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{2} + a b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{2} + a b\right)} \sinh\left(x\right)^{4} + {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} + 2 \, a^{2} + a b - b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(2 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) - \frac{1}{2} \, \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right)\right]"," ",0,"[1/4*sqrt(a + b)*log(((a^3 + a^2*b)*cosh(x)^8 + 8*(a^3 + a^2*b)*cosh(x)*sinh(x)^7 + (a^3 + a^2*b)*sinh(x)^8 + 2*(2*a^3 + a^2*b)*cosh(x)^6 + 2*(2*a^3 + a^2*b + 14*(a^3 + a^2*b)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a^3 + a^2*b)*cosh(x)^3 + 3*(2*a^3 + a^2*b)*cosh(x))*sinh(x)^5 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^4 + (70*(a^3 + a^2*b)*cosh(x)^4 + 6*a^3 + 4*a^2*b - a*b^2 + b^3 + 30*(2*a^3 + a^2*b)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a^3 + a^2*b)*cosh(x)^5 + 10*(2*a^3 + a^2*b)*cosh(x)^3 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x))*sinh(x)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 + 2*(2*a^3 + 3*a^2*b - b^3)*cosh(x)^2 + 2*(14*(a^3 + a^2*b)*cosh(x)^6 + 15*(2*a^3 + a^2*b)*cosh(x)^4 + 2*a^3 + 3*a^2*b - b^3 + 3*(6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^2)*sinh(x)^2 + sqrt(2)*(a^2*cosh(x)^6 + 6*a^2*cosh(x)*sinh(x)^5 + a^2*sinh(x)^6 + 3*a^2*cosh(x)^4 + 3*(5*a^2*cosh(x)^2 + a^2)*sinh(x)^4 + 4*(5*a^2*cosh(x)^3 + 3*a^2*cosh(x))*sinh(x)^3 + (3*a^2 + 2*a*b - b^2)*cosh(x)^2 + (15*a^2*cosh(x)^4 + 18*a^2*cosh(x)^2 + 3*a^2 + 2*a*b - b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(3*a^2*cosh(x)^5 + 6*a^2*cosh(x)^3 + (3*a^2 + 2*a*b - b^2)*cosh(x))*sinh(x))*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a^3 + a^2*b)*cosh(x)^7 + 3*(2*a^3 + a^2*b)*cosh(x)^5 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^3 + (2*a^3 + 3*a^2*b - b^3)*cosh(x))*sinh(x))/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) + 1/2*sqrt(a)*log(-((2*a + b)*cosh(x)^4 + 4*(2*a + b)*cosh(x)*sinh(x)^3 + (2*a + b)*sinh(x)^4 + 2*(2*a - b)*cosh(x)^2 + 2*(3*(2*a + b)*cosh(x)^2 + 2*a - b)*sinh(x)^2 - 2*sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((2*a + b)*cosh(x)^3 + (2*a - b)*cosh(x))*sinh(x) + 2*a + b)/(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)) + 1/4*sqrt(a + b)*log(-((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*b*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + b)*cosh(x)^3 - b*cosh(x))*sinh(x) + a + b)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)), sqrt(-a)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(-a)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a - b)*cosh(x))*sinh(x) + a + b)) + 1/4*sqrt(a + b)*log(((a^3 + a^2*b)*cosh(x)^8 + 8*(a^3 + a^2*b)*cosh(x)*sinh(x)^7 + (a^3 + a^2*b)*sinh(x)^8 + 2*(2*a^3 + a^2*b)*cosh(x)^6 + 2*(2*a^3 + a^2*b + 14*(a^3 + a^2*b)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a^3 + a^2*b)*cosh(x)^3 + 3*(2*a^3 + a^2*b)*cosh(x))*sinh(x)^5 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^4 + (70*(a^3 + a^2*b)*cosh(x)^4 + 6*a^3 + 4*a^2*b - a*b^2 + b^3 + 30*(2*a^3 + a^2*b)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a^3 + a^2*b)*cosh(x)^5 + 10*(2*a^3 + a^2*b)*cosh(x)^3 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x))*sinh(x)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 + 2*(2*a^3 + 3*a^2*b - b^3)*cosh(x)^2 + 2*(14*(a^3 + a^2*b)*cosh(x)^6 + 15*(2*a^3 + a^2*b)*cosh(x)^4 + 2*a^3 + 3*a^2*b - b^3 + 3*(6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^2)*sinh(x)^2 + sqrt(2)*(a^2*cosh(x)^6 + 6*a^2*cosh(x)*sinh(x)^5 + a^2*sinh(x)^6 + 3*a^2*cosh(x)^4 + 3*(5*a^2*cosh(x)^2 + a^2)*sinh(x)^4 + 4*(5*a^2*cosh(x)^3 + 3*a^2*cosh(x))*sinh(x)^3 + (3*a^2 + 2*a*b - b^2)*cosh(x)^2 + (15*a^2*cosh(x)^4 + 18*a^2*cosh(x)^2 + 3*a^2 + 2*a*b - b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(3*a^2*cosh(x)^5 + 6*a^2*cosh(x)^3 + (3*a^2 + 2*a*b - b^2)*cosh(x))*sinh(x))*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a^3 + a^2*b)*cosh(x)^7 + 3*(2*a^3 + a^2*b)*cosh(x)^5 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^3 + (2*a^3 + 3*a^2*b - b^3)*cosh(x))*sinh(x))/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) + 1/4*sqrt(a + b)*log(-((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*b*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + b)*cosh(x)^3 - b*cosh(x))*sinh(x) + a + b)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)), -1/2*sqrt(-a - b)*arctan(sqrt(2)*(a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 + a + b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a^2 + a*b)*cosh(x)^4 + 4*(a^2 + a*b)*cosh(x)*sinh(x)^3 + (a^2 + a*b)*sinh(x)^4 + (2*a^2 + a*b - b^2)*cosh(x)^2 + (6*(a^2 + a*b)*cosh(x)^2 + 2*a^2 + a*b - b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(2*(a^2 + a*b)*cosh(x)^3 + (2*a^2 + a*b - b^2)*cosh(x))*sinh(x))) - 1/2*sqrt(-a - b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a - b)*cosh(x))*sinh(x) + a + b)) + 1/2*sqrt(a)*log(-((2*a + b)*cosh(x)^4 + 4*(2*a + b)*cosh(x)*sinh(x)^3 + (2*a + b)*sinh(x)^4 + 2*(2*a - b)*cosh(x)^2 + 2*(3*(2*a + b)*cosh(x)^2 + 2*a - b)*sinh(x)^2 - 2*sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((2*a + b)*cosh(x)^3 + (2*a - b)*cosh(x))*sinh(x) + 2*a + b)/(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)), sqrt(-a)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(-a)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a - b)*cosh(x))*sinh(x) + a + b)) - 1/2*sqrt(-a - b)*arctan(sqrt(2)*(a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 + a + b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a^2 + a*b)*cosh(x)^4 + 4*(a^2 + a*b)*cosh(x)*sinh(x)^3 + (a^2 + a*b)*sinh(x)^4 + (2*a^2 + a*b - b^2)*cosh(x)^2 + (6*(a^2 + a*b)*cosh(x)^2 + 2*a^2 + a*b - b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(2*(a^2 + a*b)*cosh(x)^3 + (2*a^2 + a*b - b^2)*cosh(x))*sinh(x))) - 1/2*sqrt(-a - b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a - b)*cosh(x))*sinh(x) + a + b))]","B",0
215,1,1539,0,0.505790," ","integrate(coth(x)^2*(a+b*tanh(x)^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{a + b} \log\left(-\frac{{\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a b^{2} + b^{3}\right)} \sinh\left(x\right)^{8} - 2 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{6} - 2 \, {\left(a b^{2} + 2 \, b^{3} - 14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3} - 30 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} + 2 \, {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} - 3 \, a b^{2} - 2 \, b^{3} + 3 \, {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(b^{2} \cosh\left(x\right)^{6} + 6 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + b^{2} \sinh\left(x\right)^{6} - 3 \, b^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, b^{2} \cosh\left(x\right)^{2} - b^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, b^{2} \cosh\left(x\right)^{3} - 3 \, b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, b^{2} \cosh\left(x\right)^{4} - 18 \, b^{2} \cosh\left(x\right)^{2} - a^{2} + 2 \, a b + 3 \, b^{2}\right)} \sinh\left(x\right)^{2} - a^{2} - 2 \, a b - b^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{5} - 6 \, b^{2} \cosh\left(x\right)^{3} - {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{5} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) + {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{a + b} \log\left(\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, a \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + a \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right) - 4 \, \sqrt{2} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{4 \, {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)}}, -\frac{{\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} - a - b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a b + b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a b + b^{2}\right)} \sinh\left(x\right)^{4} + {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} - a b - 2 \, b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(2 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) + 2 \, \sqrt{2} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{2 \, {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)}}\right]"," ",0,"[1/4*((cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(a + b)*log(-((a*b^2 + b^3)*cosh(x)^8 + 8*(a*b^2 + b^3)*cosh(x)*sinh(x)^7 + (a*b^2 + b^3)*sinh(x)^8 - 2*(a*b^2 + 2*b^3)*cosh(x)^6 - 2*(a*b^2 + 2*b^3 - 14*(a*b^2 + b^3)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a*b^2 + b^3)*cosh(x)^3 - 3*(a*b^2 + 2*b^3)*cosh(x))*sinh(x)^5 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^4 + (70*(a*b^2 + b^3)*cosh(x)^4 + a^3 - a^2*b + 4*a*b^2 + 6*b^3 - 30*(a*b^2 + 2*b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a*b^2 + b^3)*cosh(x)^5 - 10*(a*b^2 + 2*b^3)*cosh(x)^3 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x))*sinh(x)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 + 2*(a^3 - 3*a*b^2 - 2*b^3)*cosh(x)^2 + 2*(14*(a*b^2 + b^3)*cosh(x)^6 - 15*(a*b^2 + 2*b^3)*cosh(x)^4 + a^3 - 3*a*b^2 - 2*b^3 + 3*(a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^2)*sinh(x)^2 + sqrt(2)*(b^2*cosh(x)^6 + 6*b^2*cosh(x)*sinh(x)^5 + b^2*sinh(x)^6 - 3*b^2*cosh(x)^4 + 3*(5*b^2*cosh(x)^2 - b^2)*sinh(x)^4 + 4*(5*b^2*cosh(x)^3 - 3*b^2*cosh(x))*sinh(x)^3 - (a^2 - 2*a*b - 3*b^2)*cosh(x)^2 + (15*b^2*cosh(x)^4 - 18*b^2*cosh(x)^2 - a^2 + 2*a*b + 3*b^2)*sinh(x)^2 - a^2 - 2*a*b - b^2 + 2*(3*b^2*cosh(x)^5 - 6*b^2*cosh(x)^3 - (a^2 - 2*a*b - 3*b^2)*cosh(x))*sinh(x))*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a*b^2 + b^3)*cosh(x)^7 - 3*(a*b^2 + 2*b^3)*cosh(x)^5 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^3 + (a^3 - 3*a*b^2 - 2*b^3)*cosh(x))*sinh(x))/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) + (cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(a + b)*log(((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*a*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + b)*cosh(x)^3 + a*cosh(x))*sinh(x) + a + b)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) - 4*sqrt(2)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1), -1/2*((cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-a - b)*arctan(sqrt(2)*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 - a - b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a*b + b^2)*cosh(x)^4 + 4*(a*b + b^2)*cosh(x)*sinh(x)^3 + (a*b + b^2)*sinh(x)^4 + (a^2 - a*b - 2*b^2)*cosh(x)^2 + (6*(a*b + b^2)*cosh(x)^2 + a^2 - a*b - 2*b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(2*(a*b + b^2)*cosh(x)^3 + (a^2 - a*b - 2*b^2)*cosh(x))*sinh(x))) + (cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-a - b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a - b)*cosh(x))*sinh(x) + a + b)) + 2*sqrt(2)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)]","B",0
216,1,4891,0,0.794347," ","integrate(coth(x)^3*(a+b*tanh(x)^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(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\right)} \sqrt{a + b} \log\left(\frac{{\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{3} + a^{2} b\right)} \sinh\left(x\right)^{8} + 2 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} + 2 \, {\left(2 \, a^{3} + a^{2} b + 14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} + 3 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3} + 30 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} + 10 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} + 2 \, {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} + 15 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 2 \, a^{3} + 3 \, a^{2} b - b^{3} + 3 \, {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(a^{2} \cosh\left(x\right)^{6} + 6 \, a^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + a^{2} \sinh\left(x\right)^{6} + 3 \, a^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, a^{2} \cosh\left(x\right)^{2} + a^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, a^{2} \cosh\left(x\right)^{3} + 3 \, a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, a^{2} \cosh\left(x\right)^{4} + 18 \, a^{2} \cosh\left(x\right)^{2} + 3 \, a^{2} + 2 \, a b - b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(x\right)^{5} + 6 \, a^{2} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{7} + 3 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) + {\left({\left(2 \, a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(2 \, a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(2 \, a + b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(2 \, a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(2 \, a + b\right)} \cosh\left(x\right)^{2} - 2 \, a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(2 \, a + b\right)} \cosh\left(x\right)^{3} - {\left(2 \, a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + 2 \, a + b\right)} \sqrt{a} \log\left(-\frac{{\left(2 \, a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(2 \, a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(2 \, a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(2 \, a + b\right)} \cosh\left(x\right)^{2} + 2 \, a - b\right)} \sinh\left(x\right)^{2} - 2 \, \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{a} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(2 \, a + b\right)} \cosh\left(x\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + 2 \, a + b}{\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) + {\left(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\right)} \sqrt{a + b} \log\left(-\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - b\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - b \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right) - 2 \, \sqrt{2} {\left(a \cosh\left(x\right)^{2} + 2 \, a \cosh\left(x\right) \sinh\left(x\right) + a \sinh\left(x\right)^{2} + a\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{4 \, {\left(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\right)}}, \frac{2 \, {\left({\left(2 \, a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(2 \, a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(2 \, a + b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(2 \, a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(2 \, a + b\right)} \cosh\left(x\right)^{2} - 2 \, a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(2 \, a + b\right)} \cosh\left(x\right)^{3} - {\left(2 \, a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + 2 \, a + b\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{-a} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) + {\left(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\right)} \sqrt{a + b} \log\left(\frac{{\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{3} + a^{2} b\right)} \sinh\left(x\right)^{8} + 2 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} + 2 \, {\left(2 \, a^{3} + a^{2} b + 14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} + 3 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3} + 30 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} + 10 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} + 2 \, {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} + 15 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 2 \, a^{3} + 3 \, a^{2} b - b^{3} + 3 \, {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(a^{2} \cosh\left(x\right)^{6} + 6 \, a^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + a^{2} \sinh\left(x\right)^{6} + 3 \, a^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, a^{2} \cosh\left(x\right)^{2} + a^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, a^{2} \cosh\left(x\right)^{3} + 3 \, a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, a^{2} \cosh\left(x\right)^{4} + 18 \, a^{2} \cosh\left(x\right)^{2} + 3 \, a^{2} + 2 \, a b - b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(x\right)^{5} + 6 \, a^{2} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{7} + 3 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) + {\left(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\right)} \sqrt{a + b} \log\left(-\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - b\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - b \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right) - 2 \, \sqrt{2} {\left(a \cosh\left(x\right)^{2} + 2 \, a \cosh\left(x\right) \sinh\left(x\right) + a \sinh\left(x\right)^{2} + a\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{4 \, {\left(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\right)}}, -\frac{2 \, {\left(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\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(a \cosh\left(x\right)^{2} + 2 \, a \cosh\left(x\right) \sinh\left(x\right) + a \sinh\left(x\right)^{2} + a + b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a^{2} + a b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{2} + a b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{2} + a b\right)} \sinh\left(x\right)^{4} + {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} + 2 \, a^{2} + a b - b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(2 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + 2 \, {\left(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\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) - {\left({\left(2 \, a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(2 \, a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(2 \, a + b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(2 \, a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(2 \, a + b\right)} \cosh\left(x\right)^{2} - 2 \, a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(2 \, a + b\right)} \cosh\left(x\right)^{3} - {\left(2 \, a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + 2 \, a + b\right)} \sqrt{a} \log\left(-\frac{{\left(2 \, a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(2 \, a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(2 \, a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(2 \, a + b\right)} \cosh\left(x\right)^{2} + 2 \, a - b\right)} \sinh\left(x\right)^{2} - 2 \, \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{a} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(2 \, a + b\right)} \cosh\left(x\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + 2 \, a + b}{\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) + 2 \, \sqrt{2} {\left(a \cosh\left(x\right)^{2} + 2 \, a \cosh\left(x\right) \sinh\left(x\right) + a \sinh\left(x\right)^{2} + a\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{4 \, {\left(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\right)}}, \frac{{\left({\left(2 \, a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(2 \, a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(2 \, a + b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(2 \, a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(2 \, a + b\right)} \cosh\left(x\right)^{2} - 2 \, a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(2 \, a + b\right)} \cosh\left(x\right)^{3} - {\left(2 \, a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + 2 \, a + b\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{-a} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) - {\left(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\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(a \cosh\left(x\right)^{2} + 2 \, a \cosh\left(x\right) \sinh\left(x\right) + a \sinh\left(x\right)^{2} + a + b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a^{2} + a b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{2} + a b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{2} + a b\right)} \sinh\left(x\right)^{4} + {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} + 2 \, a^{2} + a b - b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(2 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) - {\left(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\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) - \sqrt{2} {\left(a \cosh\left(x\right)^{2} + 2 \, a \cosh\left(x\right) \sinh\left(x\right) + a \sinh\left(x\right)^{2} + a\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{2 \, {\left(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\right)}}\right]"," ",0,"[1/4*((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)*sqrt(a + b)*log(((a^3 + a^2*b)*cosh(x)^8 + 8*(a^3 + a^2*b)*cosh(x)*sinh(x)^7 + (a^3 + a^2*b)*sinh(x)^8 + 2*(2*a^3 + a^2*b)*cosh(x)^6 + 2*(2*a^3 + a^2*b + 14*(a^3 + a^2*b)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a^3 + a^2*b)*cosh(x)^3 + 3*(2*a^3 + a^2*b)*cosh(x))*sinh(x)^5 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^4 + (70*(a^3 + a^2*b)*cosh(x)^4 + 6*a^3 + 4*a^2*b - a*b^2 + b^3 + 30*(2*a^3 + a^2*b)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a^3 + a^2*b)*cosh(x)^5 + 10*(2*a^3 + a^2*b)*cosh(x)^3 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x))*sinh(x)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 + 2*(2*a^3 + 3*a^2*b - b^3)*cosh(x)^2 + 2*(14*(a^3 + a^2*b)*cosh(x)^6 + 15*(2*a^3 + a^2*b)*cosh(x)^4 + 2*a^3 + 3*a^2*b - b^3 + 3*(6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^2)*sinh(x)^2 + sqrt(2)*(a^2*cosh(x)^6 + 6*a^2*cosh(x)*sinh(x)^5 + a^2*sinh(x)^6 + 3*a^2*cosh(x)^4 + 3*(5*a^2*cosh(x)^2 + a^2)*sinh(x)^4 + 4*(5*a^2*cosh(x)^3 + 3*a^2*cosh(x))*sinh(x)^3 + (3*a^2 + 2*a*b - b^2)*cosh(x)^2 + (15*a^2*cosh(x)^4 + 18*a^2*cosh(x)^2 + 3*a^2 + 2*a*b - b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(3*a^2*cosh(x)^5 + 6*a^2*cosh(x)^3 + (3*a^2 + 2*a*b - b^2)*cosh(x))*sinh(x))*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a^3 + a^2*b)*cosh(x)^7 + 3*(2*a^3 + a^2*b)*cosh(x)^5 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^3 + (2*a^3 + 3*a^2*b - b^3)*cosh(x))*sinh(x))/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) + ((2*a + b)*cosh(x)^4 + 4*(2*a + b)*cosh(x)*sinh(x)^3 + (2*a + b)*sinh(x)^4 - 2*(2*a + b)*cosh(x)^2 + 2*(3*(2*a + b)*cosh(x)^2 - 2*a - b)*sinh(x)^2 + 4*((2*a + b)*cosh(x)^3 - (2*a + b)*cosh(x))*sinh(x) + 2*a + b)*sqrt(a)*log(-((2*a + b)*cosh(x)^4 + 4*(2*a + b)*cosh(x)*sinh(x)^3 + (2*a + b)*sinh(x)^4 + 2*(2*a - b)*cosh(x)^2 + 2*(3*(2*a + b)*cosh(x)^2 + 2*a - b)*sinh(x)^2 - 2*sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((2*a + b)*cosh(x)^3 + (2*a - b)*cosh(x))*sinh(x) + 2*a + b)/(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)) + (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)*sqrt(a + b)*log(-((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*b*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + b)*cosh(x)^3 - b*cosh(x))*sinh(x) + a + b)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) - 2*sqrt(2)*(a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 + a)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(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), 1/4*(2*((2*a + b)*cosh(x)^4 + 4*(2*a + b)*cosh(x)*sinh(x)^3 + (2*a + b)*sinh(x)^4 - 2*(2*a + b)*cosh(x)^2 + 2*(3*(2*a + b)*cosh(x)^2 - 2*a - b)*sinh(x)^2 + 4*((2*a + b)*cosh(x)^3 - (2*a + b)*cosh(x))*sinh(x) + 2*a + b)*sqrt(-a)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(-a)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a - b)*cosh(x))*sinh(x) + a + b)) + (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)*sqrt(a + b)*log(((a^3 + a^2*b)*cosh(x)^8 + 8*(a^3 + a^2*b)*cosh(x)*sinh(x)^7 + (a^3 + a^2*b)*sinh(x)^8 + 2*(2*a^3 + a^2*b)*cosh(x)^6 + 2*(2*a^3 + a^2*b + 14*(a^3 + a^2*b)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a^3 + a^2*b)*cosh(x)^3 + 3*(2*a^3 + a^2*b)*cosh(x))*sinh(x)^5 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^4 + (70*(a^3 + a^2*b)*cosh(x)^4 + 6*a^3 + 4*a^2*b - a*b^2 + b^3 + 30*(2*a^3 + a^2*b)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a^3 + a^2*b)*cosh(x)^5 + 10*(2*a^3 + a^2*b)*cosh(x)^3 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x))*sinh(x)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 + 2*(2*a^3 + 3*a^2*b - b^3)*cosh(x)^2 + 2*(14*(a^3 + a^2*b)*cosh(x)^6 + 15*(2*a^3 + a^2*b)*cosh(x)^4 + 2*a^3 + 3*a^2*b - b^3 + 3*(6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^2)*sinh(x)^2 + sqrt(2)*(a^2*cosh(x)^6 + 6*a^2*cosh(x)*sinh(x)^5 + a^2*sinh(x)^6 + 3*a^2*cosh(x)^4 + 3*(5*a^2*cosh(x)^2 + a^2)*sinh(x)^4 + 4*(5*a^2*cosh(x)^3 + 3*a^2*cosh(x))*sinh(x)^3 + (3*a^2 + 2*a*b - b^2)*cosh(x)^2 + (15*a^2*cosh(x)^4 + 18*a^2*cosh(x)^2 + 3*a^2 + 2*a*b - b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(3*a^2*cosh(x)^5 + 6*a^2*cosh(x)^3 + (3*a^2 + 2*a*b - b^2)*cosh(x))*sinh(x))*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a^3 + a^2*b)*cosh(x)^7 + 3*(2*a^3 + a^2*b)*cosh(x)^5 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^3 + (2*a^3 + 3*a^2*b - b^3)*cosh(x))*sinh(x))/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) + (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)*sqrt(a + b)*log(-((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*b*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + b)*cosh(x)^3 - b*cosh(x))*sinh(x) + a + b)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) - 2*sqrt(2)*(a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 + a)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(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), -1/4*(2*(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)*sqrt(-a - b)*arctan(sqrt(2)*(a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 + a + b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a^2 + a*b)*cosh(x)^4 + 4*(a^2 + a*b)*cosh(x)*sinh(x)^3 + (a^2 + a*b)*sinh(x)^4 + (2*a^2 + a*b - b^2)*cosh(x)^2 + (6*(a^2 + a*b)*cosh(x)^2 + 2*a^2 + a*b - b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(2*(a^2 + a*b)*cosh(x)^3 + (2*a^2 + a*b - b^2)*cosh(x))*sinh(x))) + 2*(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)*sqrt(-a - b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a - b)*cosh(x))*sinh(x) + a + b)) - ((2*a + b)*cosh(x)^4 + 4*(2*a + b)*cosh(x)*sinh(x)^3 + (2*a + b)*sinh(x)^4 - 2*(2*a + b)*cosh(x)^2 + 2*(3*(2*a + b)*cosh(x)^2 - 2*a - b)*sinh(x)^2 + 4*((2*a + b)*cosh(x)^3 - (2*a + b)*cosh(x))*sinh(x) + 2*a + b)*sqrt(a)*log(-((2*a + b)*cosh(x)^4 + 4*(2*a + b)*cosh(x)*sinh(x)^3 + (2*a + b)*sinh(x)^4 + 2*(2*a - b)*cosh(x)^2 + 2*(3*(2*a + b)*cosh(x)^2 + 2*a - b)*sinh(x)^2 - 2*sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((2*a + b)*cosh(x)^3 + (2*a - b)*cosh(x))*sinh(x) + 2*a + b)/(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)) + 2*sqrt(2)*(a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 + a)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(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), 1/2*(((2*a + b)*cosh(x)^4 + 4*(2*a + b)*cosh(x)*sinh(x)^3 + (2*a + b)*sinh(x)^4 - 2*(2*a + b)*cosh(x)^2 + 2*(3*(2*a + b)*cosh(x)^2 - 2*a - b)*sinh(x)^2 + 4*((2*a + b)*cosh(x)^3 - (2*a + b)*cosh(x))*sinh(x) + 2*a + b)*sqrt(-a)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(-a)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a - b)*cosh(x))*sinh(x) + a + b)) - (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)*sqrt(-a - b)*arctan(sqrt(2)*(a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 + a + b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a^2 + a*b)*cosh(x)^4 + 4*(a^2 + a*b)*cosh(x)*sinh(x)^3 + (a^2 + a*b)*sinh(x)^4 + (2*a^2 + a*b - b^2)*cosh(x)^2 + (6*(a^2 + a*b)*cosh(x)^2 + 2*a^2 + a*b - b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(2*(a^2 + a*b)*cosh(x)^3 + (2*a^2 + a*b - b^2)*cosh(x))*sinh(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)*sqrt(-a - b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a - b)*cosh(x))*sinh(x) + a + b)) - sqrt(2)*(a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 + a)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(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
217,1,2355,0,0.598975," ","integrate(coth(x)^4*(a+b*tanh(x)^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(a \cosh\left(x\right)^{6} + 6 \, a \cosh\left(x\right) \sinh\left(x\right)^{5} + a \sinh\left(x\right)^{6} - 3 \, a \cosh\left(x\right)^{4} + 3 \, {\left(5 \, a \cosh\left(x\right)^{2} - a\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, a \cosh\left(x\right)^{3} - 3 \, a \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 3 \, a \cosh\left(x\right)^{2} + 3 \, {\left(5 \, a \cosh\left(x\right)^{4} - 6 \, a \cosh\left(x\right)^{2} + a\right)} \sinh\left(x\right)^{2} + 6 \, {\left(a \cosh\left(x\right)^{5} - 2 \, a \cosh\left(x\right)^{3} + a \cosh\left(x\right)\right)} \sinh\left(x\right) - a\right)} \sqrt{a + b} \log\left(-\frac{{\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a b^{2} + b^{3}\right)} \sinh\left(x\right)^{8} - 2 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{6} - 2 \, {\left(a b^{2} + 2 \, b^{3} - 14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3} - 30 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} + 2 \, {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} - 3 \, a b^{2} - 2 \, b^{3} + 3 \, {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(b^{2} \cosh\left(x\right)^{6} + 6 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + b^{2} \sinh\left(x\right)^{6} - 3 \, b^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, b^{2} \cosh\left(x\right)^{2} - b^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, b^{2} \cosh\left(x\right)^{3} - 3 \, b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, b^{2} \cosh\left(x\right)^{4} - 18 \, b^{2} \cosh\left(x\right)^{2} - a^{2} + 2 \, a b + 3 \, b^{2}\right)} \sinh\left(x\right)^{2} - a^{2} - 2 \, a b - b^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{5} - 6 \, b^{2} \cosh\left(x\right)^{3} - {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{5} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) + 3 \, {\left(a \cosh\left(x\right)^{6} + 6 \, a \cosh\left(x\right) \sinh\left(x\right)^{5} + a \sinh\left(x\right)^{6} - 3 \, a \cosh\left(x\right)^{4} + 3 \, {\left(5 \, a \cosh\left(x\right)^{2} - a\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, a \cosh\left(x\right)^{3} - 3 \, a \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 3 \, a \cosh\left(x\right)^{2} + 3 \, {\left(5 \, a \cosh\left(x\right)^{4} - 6 \, a \cosh\left(x\right)^{2} + a\right)} \sinh\left(x\right)^{2} + 6 \, {\left(a \cosh\left(x\right)^{5} - 2 \, a \cosh\left(x\right)^{3} + a \cosh\left(x\right)\right)} \sinh\left(x\right) - a\right)} \sqrt{a + b} \log\left(\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, a \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + a \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right) - 4 \, \sqrt{2} {\left({\left(4 \, a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(4 \, a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(4 \, a + b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(2 \, a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(4 \, a + b\right)} \cosh\left(x\right)^{2} - 2 \, a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(4 \, a + b\right)} \cosh\left(x\right)^{3} - {\left(2 \, a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + 4 \, a + b\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{12 \, {\left(a \cosh\left(x\right)^{6} + 6 \, a \cosh\left(x\right) \sinh\left(x\right)^{5} + a \sinh\left(x\right)^{6} - 3 \, a \cosh\left(x\right)^{4} + 3 \, {\left(5 \, a \cosh\left(x\right)^{2} - a\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, a \cosh\left(x\right)^{3} - 3 \, a \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 3 \, a \cosh\left(x\right)^{2} + 3 \, {\left(5 \, a \cosh\left(x\right)^{4} - 6 \, a \cosh\left(x\right)^{2} + a\right)} \sinh\left(x\right)^{2} + 6 \, {\left(a \cosh\left(x\right)^{5} - 2 \, a \cosh\left(x\right)^{3} + a \cosh\left(x\right)\right)} \sinh\left(x\right) - a\right)}}, -\frac{3 \, {\left(a \cosh\left(x\right)^{6} + 6 \, a \cosh\left(x\right) \sinh\left(x\right)^{5} + a \sinh\left(x\right)^{6} - 3 \, a \cosh\left(x\right)^{4} + 3 \, {\left(5 \, a \cosh\left(x\right)^{2} - a\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, a \cosh\left(x\right)^{3} - 3 \, a \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 3 \, a \cosh\left(x\right)^{2} + 3 \, {\left(5 \, a \cosh\left(x\right)^{4} - 6 \, a \cosh\left(x\right)^{2} + a\right)} \sinh\left(x\right)^{2} + 6 \, {\left(a \cosh\left(x\right)^{5} - 2 \, a \cosh\left(x\right)^{3} + a \cosh\left(x\right)\right)} \sinh\left(x\right) - a\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} - a - b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a b + b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a b + b^{2}\right)} \sinh\left(x\right)^{4} + {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} - a b - 2 \, b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(2 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + 3 \, {\left(a \cosh\left(x\right)^{6} + 6 \, a \cosh\left(x\right) \sinh\left(x\right)^{5} + a \sinh\left(x\right)^{6} - 3 \, a \cosh\left(x\right)^{4} + 3 \, {\left(5 \, a \cosh\left(x\right)^{2} - a\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, a \cosh\left(x\right)^{3} - 3 \, a \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 3 \, a \cosh\left(x\right)^{2} + 3 \, {\left(5 \, a \cosh\left(x\right)^{4} - 6 \, a \cosh\left(x\right)^{2} + a\right)} \sinh\left(x\right)^{2} + 6 \, {\left(a \cosh\left(x\right)^{5} - 2 \, a \cosh\left(x\right)^{3} + a \cosh\left(x\right)\right)} \sinh\left(x\right) - a\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) + 2 \, \sqrt{2} {\left({\left(4 \, a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(4 \, a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(4 \, a + b\right)} \sinh\left(x\right)^{4} - 2 \, {\left(2 \, a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(4 \, a + b\right)} \cosh\left(x\right)^{2} - 2 \, a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(4 \, a + b\right)} \cosh\left(x\right)^{3} - {\left(2 \, a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + 4 \, a + b\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{6 \, {\left(a \cosh\left(x\right)^{6} + 6 \, a \cosh\left(x\right) \sinh\left(x\right)^{5} + a \sinh\left(x\right)^{6} - 3 \, a \cosh\left(x\right)^{4} + 3 \, {\left(5 \, a \cosh\left(x\right)^{2} - a\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, a \cosh\left(x\right)^{3} - 3 \, a \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 3 \, a \cosh\left(x\right)^{2} + 3 \, {\left(5 \, a \cosh\left(x\right)^{4} - 6 \, a \cosh\left(x\right)^{2} + a\right)} \sinh\left(x\right)^{2} + 6 \, {\left(a \cosh\left(x\right)^{5} - 2 \, a \cosh\left(x\right)^{3} + a \cosh\left(x\right)\right)} \sinh\left(x\right) - a\right)}}\right]"," ",0,"[1/12*(3*(a*cosh(x)^6 + 6*a*cosh(x)*sinh(x)^5 + a*sinh(x)^6 - 3*a*cosh(x)^4 + 3*(5*a*cosh(x)^2 - a)*sinh(x)^4 + 4*(5*a*cosh(x)^3 - 3*a*cosh(x))*sinh(x)^3 + 3*a*cosh(x)^2 + 3*(5*a*cosh(x)^4 - 6*a*cosh(x)^2 + a)*sinh(x)^2 + 6*(a*cosh(x)^5 - 2*a*cosh(x)^3 + a*cosh(x))*sinh(x) - a)*sqrt(a + b)*log(-((a*b^2 + b^3)*cosh(x)^8 + 8*(a*b^2 + b^3)*cosh(x)*sinh(x)^7 + (a*b^2 + b^3)*sinh(x)^8 - 2*(a*b^2 + 2*b^3)*cosh(x)^6 - 2*(a*b^2 + 2*b^3 - 14*(a*b^2 + b^3)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a*b^2 + b^3)*cosh(x)^3 - 3*(a*b^2 + 2*b^3)*cosh(x))*sinh(x)^5 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^4 + (70*(a*b^2 + b^3)*cosh(x)^4 + a^3 - a^2*b + 4*a*b^2 + 6*b^3 - 30*(a*b^2 + 2*b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a*b^2 + b^3)*cosh(x)^5 - 10*(a*b^2 + 2*b^3)*cosh(x)^3 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x))*sinh(x)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 + 2*(a^3 - 3*a*b^2 - 2*b^3)*cosh(x)^2 + 2*(14*(a*b^2 + b^3)*cosh(x)^6 - 15*(a*b^2 + 2*b^3)*cosh(x)^4 + a^3 - 3*a*b^2 - 2*b^3 + 3*(a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^2)*sinh(x)^2 + sqrt(2)*(b^2*cosh(x)^6 + 6*b^2*cosh(x)*sinh(x)^5 + b^2*sinh(x)^6 - 3*b^2*cosh(x)^4 + 3*(5*b^2*cosh(x)^2 - b^2)*sinh(x)^4 + 4*(5*b^2*cosh(x)^3 - 3*b^2*cosh(x))*sinh(x)^3 - (a^2 - 2*a*b - 3*b^2)*cosh(x)^2 + (15*b^2*cosh(x)^4 - 18*b^2*cosh(x)^2 - a^2 + 2*a*b + 3*b^2)*sinh(x)^2 - a^2 - 2*a*b - b^2 + 2*(3*b^2*cosh(x)^5 - 6*b^2*cosh(x)^3 - (a^2 - 2*a*b - 3*b^2)*cosh(x))*sinh(x))*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a*b^2 + b^3)*cosh(x)^7 - 3*(a*b^2 + 2*b^3)*cosh(x)^5 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^3 + (a^3 - 3*a*b^2 - 2*b^3)*cosh(x))*sinh(x))/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) + 3*(a*cosh(x)^6 + 6*a*cosh(x)*sinh(x)^5 + a*sinh(x)^6 - 3*a*cosh(x)^4 + 3*(5*a*cosh(x)^2 - a)*sinh(x)^4 + 4*(5*a*cosh(x)^3 - 3*a*cosh(x))*sinh(x)^3 + 3*a*cosh(x)^2 + 3*(5*a*cosh(x)^4 - 6*a*cosh(x)^2 + a)*sinh(x)^2 + 6*(a*cosh(x)^5 - 2*a*cosh(x)^3 + a*cosh(x))*sinh(x) - a)*sqrt(a + b)*log(((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*a*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + b)*cosh(x)^3 + a*cosh(x))*sinh(x) + a + b)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) - 4*sqrt(2)*((4*a + b)*cosh(x)^4 + 4*(4*a + b)*cosh(x)*sinh(x)^3 + (4*a + b)*sinh(x)^4 - 2*(2*a + b)*cosh(x)^2 + 2*(3*(4*a + b)*cosh(x)^2 - 2*a - b)*sinh(x)^2 + 4*((4*a + b)*cosh(x)^3 - (2*a + b)*cosh(x))*sinh(x) + 4*a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(a*cosh(x)^6 + 6*a*cosh(x)*sinh(x)^5 + a*sinh(x)^6 - 3*a*cosh(x)^4 + 3*(5*a*cosh(x)^2 - a)*sinh(x)^4 + 4*(5*a*cosh(x)^3 - 3*a*cosh(x))*sinh(x)^3 + 3*a*cosh(x)^2 + 3*(5*a*cosh(x)^4 - 6*a*cosh(x)^2 + a)*sinh(x)^2 + 6*(a*cosh(x)^5 - 2*a*cosh(x)^3 + a*cosh(x))*sinh(x) - a), -1/6*(3*(a*cosh(x)^6 + 6*a*cosh(x)*sinh(x)^5 + a*sinh(x)^6 - 3*a*cosh(x)^4 + 3*(5*a*cosh(x)^2 - a)*sinh(x)^4 + 4*(5*a*cosh(x)^3 - 3*a*cosh(x))*sinh(x)^3 + 3*a*cosh(x)^2 + 3*(5*a*cosh(x)^4 - 6*a*cosh(x)^2 + a)*sinh(x)^2 + 6*(a*cosh(x)^5 - 2*a*cosh(x)^3 + a*cosh(x))*sinh(x) - a)*sqrt(-a - b)*arctan(sqrt(2)*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 - a - b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a*b + b^2)*cosh(x)^4 + 4*(a*b + b^2)*cosh(x)*sinh(x)^3 + (a*b + b^2)*sinh(x)^4 + (a^2 - a*b - 2*b^2)*cosh(x)^2 + (6*(a*b + b^2)*cosh(x)^2 + a^2 - a*b - 2*b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(2*(a*b + b^2)*cosh(x)^3 + (a^2 - a*b - 2*b^2)*cosh(x))*sinh(x))) + 3*(a*cosh(x)^6 + 6*a*cosh(x)*sinh(x)^5 + a*sinh(x)^6 - 3*a*cosh(x)^4 + 3*(5*a*cosh(x)^2 - a)*sinh(x)^4 + 4*(5*a*cosh(x)^3 - 3*a*cosh(x))*sinh(x)^3 + 3*a*cosh(x)^2 + 3*(5*a*cosh(x)^4 - 6*a*cosh(x)^2 + a)*sinh(x)^2 + 6*(a*cosh(x)^5 - 2*a*cosh(x)^3 + a*cosh(x))*sinh(x) - a)*sqrt(-a - b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a - b)*cosh(x))*sinh(x) + a + b)) + 2*sqrt(2)*((4*a + b)*cosh(x)^4 + 4*(4*a + b)*cosh(x)*sinh(x)^3 + (4*a + b)*sinh(x)^4 - 2*(2*a + b)*cosh(x)^2 + 2*(3*(4*a + b)*cosh(x)^2 - 2*a - b)*sinh(x)^2 + 4*((4*a + b)*cosh(x)^3 - (2*a + b)*cosh(x))*sinh(x) + 4*a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(a*cosh(x)^6 + 6*a*cosh(x)*sinh(x)^5 + a*sinh(x)^6 - 3*a*cosh(x)^4 + 3*(5*a*cosh(x)^2 - a)*sinh(x)^4 + 4*(5*a*cosh(x)^3 - 3*a*cosh(x))*sinh(x)^3 + 3*a*cosh(x)^2 + 3*(5*a*cosh(x)^4 - 6*a*cosh(x)^2 + a)*sinh(x)^2 + 6*(a*cosh(x)^5 - 2*a*cosh(x)^3 + a*cosh(x))*sinh(x) - a)]","B",0
218,1,9642,0,0.961108," ","integrate(coth(x)^5*(a+b*tanh(x)^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{4 \, {\left(a^{2} \cosh\left(x\right)^{8} + 8 \, a^{2} \cosh\left(x\right) \sinh\left(x\right)^{7} + a^{2} \sinh\left(x\right)^{8} - 4 \, a^{2} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, a^{2} \cosh\left(x\right)^{2} - a^{2}\right)} \sinh\left(x\right)^{6} + 6 \, a^{2} \cosh\left(x\right)^{4} + 8 \, {\left(7 \, a^{2} \cosh\left(x\right)^{3} - 3 \, a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(35 \, a^{2} \cosh\left(x\right)^{4} - 30 \, a^{2} \cosh\left(x\right)^{2} + 3 \, a^{2}\right)} \sinh\left(x\right)^{4} - 4 \, a^{2} \cosh\left(x\right)^{2} + 8 \, {\left(7 \, a^{2} \cosh\left(x\right)^{5} - 10 \, a^{2} \cosh\left(x\right)^{3} + 3 \, a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(7 \, a^{2} \cosh\left(x\right)^{6} - 15 \, a^{2} \cosh\left(x\right)^{4} + 9 \, a^{2} \cosh\left(x\right)^{2} - a^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 8 \, {\left(a^{2} \cosh\left(x\right)^{7} - 3 \, a^{2} \cosh\left(x\right)^{5} + 3 \, a^{2} \cosh\left(x\right)^{3} - a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \log\left(\frac{{\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{3} + a^{2} b\right)} \sinh\left(x\right)^{8} + 2 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} + 2 \, {\left(2 \, a^{3} + a^{2} b + 14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} + 3 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3} + 30 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} + 10 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} + 2 \, {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} + 15 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 2 \, a^{3} + 3 \, a^{2} b - b^{3} + 3 \, {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(a^{2} \cosh\left(x\right)^{6} + 6 \, a^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + a^{2} \sinh\left(x\right)^{6} + 3 \, a^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, a^{2} \cosh\left(x\right)^{2} + a^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, a^{2} \cosh\left(x\right)^{3} + 3 \, a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, a^{2} \cosh\left(x\right)^{4} + 18 \, a^{2} \cosh\left(x\right)^{2} + 3 \, a^{2} + 2 \, a b - b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(x\right)^{5} + 6 \, a^{2} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{7} + 3 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) - {\left({\left(8 \, a^{2} + 4 \, a b - b^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(8 \, a^{2} + 4 \, a b - b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(8 \, a^{2} + 4 \, a b - b^{2}\right)} \sinh\left(x\right)^{8} - 4 \, {\left(8 \, a^{2} + 4 \, a b - b^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(8 \, a^{2} + 4 \, a b - b^{2}\right)} \cosh\left(x\right)^{2} - 8 \, a^{2} - 4 \, a b + b^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(8 \, a^{2} + 4 \, a b - b^{2}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(8 \, a^{2} + 4 \, a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 6 \, {\left(8 \, a^{2} + 4 \, a b - b^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(8 \, a^{2} + 4 \, a b - b^{2}\right)} \cosh\left(x\right)^{4} - 30 \, {\left(8 \, a^{2} + 4 \, a b - b^{2}\right)} \cosh\left(x\right)^{2} + 24 \, a^{2} + 12 \, a b - 3 \, b^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(8 \, a^{2} + 4 \, a b - b^{2}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(8 \, a^{2} + 4 \, a b - b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(8 \, a^{2} + 4 \, a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 4 \, {\left(8 \, a^{2} + 4 \, a b - b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(8 \, a^{2} + 4 \, a b - b^{2}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(8 \, a^{2} + 4 \, a b - b^{2}\right)} \cosh\left(x\right)^{4} + 9 \, {\left(8 \, a^{2} + 4 \, a b - b^{2}\right)} \cosh\left(x\right)^{2} - 8 \, a^{2} - 4 \, a b + b^{2}\right)} \sinh\left(x\right)^{2} + 8 \, a^{2} + 4 \, a b - b^{2} + 8 \, {\left({\left(8 \, a^{2} + 4 \, a b - b^{2}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(8 \, a^{2} + 4 \, a b - b^{2}\right)} \cosh\left(x\right)^{5} + 3 \, {\left(8 \, a^{2} + 4 \, a b - b^{2}\right)} \cosh\left(x\right)^{3} - {\left(8 \, a^{2} + 4 \, a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \log\left(-\frac{{\left(2 \, a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(2 \, a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(2 \, a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(2 \, a + b\right)} \cosh\left(x\right)^{2} + 2 \, a - b\right)} \sinh\left(x\right)^{2} + 2 \, \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{a} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(2 \, a + b\right)} \cosh\left(x\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + 2 \, a + b}{\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) + 4 \, {\left(a^{2} \cosh\left(x\right)^{8} + 8 \, a^{2} \cosh\left(x\right) \sinh\left(x\right)^{7} + a^{2} \sinh\left(x\right)^{8} - 4 \, a^{2} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, a^{2} \cosh\left(x\right)^{2} - a^{2}\right)} \sinh\left(x\right)^{6} + 6 \, a^{2} \cosh\left(x\right)^{4} + 8 \, {\left(7 \, a^{2} \cosh\left(x\right)^{3} - 3 \, a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(35 \, a^{2} \cosh\left(x\right)^{4} - 30 \, a^{2} \cosh\left(x\right)^{2} + 3 \, a^{2}\right)} \sinh\left(x\right)^{4} - 4 \, a^{2} \cosh\left(x\right)^{2} + 8 \, {\left(7 \, a^{2} \cosh\left(x\right)^{5} - 10 \, a^{2} \cosh\left(x\right)^{3} + 3 \, a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(7 \, a^{2} \cosh\left(x\right)^{6} - 15 \, a^{2} \cosh\left(x\right)^{4} + 9 \, a^{2} \cosh\left(x\right)^{2} - a^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 8 \, {\left(a^{2} \cosh\left(x\right)^{7} - 3 \, a^{2} \cosh\left(x\right)^{5} + 3 \, a^{2} \cosh\left(x\right)^{3} - a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \log\left(-\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - b\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - b \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right) - 2 \, \sqrt{2} {\left({\left(6 \, a^{2} + a b\right)} \cosh\left(x\right)^{6} + 6 \, {\left(6 \, a^{2} + a b\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(6 \, a^{2} + a b\right)} \sinh\left(x\right)^{6} + {\left(2 \, a^{2} - a b\right)} \cosh\left(x\right)^{4} + {\left(15 \, {\left(6 \, a^{2} + a b\right)} \cosh\left(x\right)^{2} + 2 \, a^{2} - a b\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, {\left(6 \, a^{2} + a b\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{2} - a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(2 \, a^{2} - a b\right)} \cosh\left(x\right)^{2} + {\left(15 \, {\left(6 \, a^{2} + a b\right)} \cosh\left(x\right)^{4} + 6 \, {\left(2 \, a^{2} - a b\right)} \cosh\left(x\right)^{2} + 2 \, a^{2} - a b\right)} \sinh\left(x\right)^{2} + 6 \, a^{2} + a b + 2 \, {\left(3 \, {\left(6 \, a^{2} + a b\right)} \cosh\left(x\right)^{5} + 2 \, {\left(2 \, a^{2} - a b\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{2} - a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{16 \, {\left(a^{2} \cosh\left(x\right)^{8} + 8 \, a^{2} \cosh\left(x\right) \sinh\left(x\right)^{7} + a^{2} \sinh\left(x\right)^{8} - 4 \, a^{2} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, a^{2} \cosh\left(x\right)^{2} - a^{2}\right)} \sinh\left(x\right)^{6} + 6 \, a^{2} \cosh\left(x\right)^{4} + 8 \, {\left(7 \, a^{2} \cosh\left(x\right)^{3} - 3 \, a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(35 \, a^{2} \cosh\left(x\right)^{4} - 30 \, a^{2} \cosh\left(x\right)^{2} + 3 \, a^{2}\right)} \sinh\left(x\right)^{4} - 4 \, a^{2} \cosh\left(x\right)^{2} + 8 \, {\left(7 \, a^{2} \cosh\left(x\right)^{5} - 10 \, a^{2} \cosh\left(x\right)^{3} + 3 \, a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(7 \, a^{2} \cosh\left(x\right)^{6} - 15 \, a^{2} \cosh\left(x\right)^{4} + 9 \, a^{2} \cosh\left(x\right)^{2} - a^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 8 \, {\left(a^{2} \cosh\left(x\right)^{7} - 3 \, a^{2} \cosh\left(x\right)^{5} + 3 \, a^{2} \cosh\left(x\right)^{3} - a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}, \frac{{\left({\left(8 \, a^{2} + 4 \, a b - b^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(8 \, a^{2} + 4 \, a b - b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(8 \, a^{2} + 4 \, a b - b^{2}\right)} \sinh\left(x\right)^{8} - 4 \, {\left(8 \, a^{2} + 4 \, a b - b^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(8 \, a^{2} + 4 \, a b - b^{2}\right)} \cosh\left(x\right)^{2} - 8 \, a^{2} - 4 \, a b + b^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(8 \, a^{2} + 4 \, a b - b^{2}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(8 \, a^{2} + 4 \, a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 6 \, {\left(8 \, a^{2} + 4 \, a b - b^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(8 \, a^{2} + 4 \, a b - b^{2}\right)} \cosh\left(x\right)^{4} - 30 \, {\left(8 \, a^{2} + 4 \, a b - b^{2}\right)} \cosh\left(x\right)^{2} + 24 \, a^{2} + 12 \, a b - 3 \, b^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(8 \, a^{2} + 4 \, a b - b^{2}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(8 \, a^{2} + 4 \, a b - b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(8 \, a^{2} + 4 \, a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 4 \, {\left(8 \, a^{2} + 4 \, a b - b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(8 \, a^{2} + 4 \, a b - b^{2}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(8 \, a^{2} + 4 \, a b - b^{2}\right)} \cosh\left(x\right)^{4} + 9 \, {\left(8 \, a^{2} + 4 \, a b - b^{2}\right)} \cosh\left(x\right)^{2} - 8 \, a^{2} - 4 \, a b + b^{2}\right)} \sinh\left(x\right)^{2} + 8 \, a^{2} + 4 \, a b - b^{2} + 8 \, {\left({\left(8 \, a^{2} + 4 \, a b - b^{2}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(8 \, a^{2} + 4 \, a b - b^{2}\right)} \cosh\left(x\right)^{5} + 3 \, {\left(8 \, a^{2} + 4 \, a b - b^{2}\right)} \cosh\left(x\right)^{3} - {\left(8 \, a^{2} + 4 \, a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{-a} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) + 2 \, {\left(a^{2} \cosh\left(x\right)^{8} + 8 \, a^{2} \cosh\left(x\right) \sinh\left(x\right)^{7} + a^{2} \sinh\left(x\right)^{8} - 4 \, a^{2} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, a^{2} \cosh\left(x\right)^{2} - a^{2}\right)} \sinh\left(x\right)^{6} + 6 \, a^{2} \cosh\left(x\right)^{4} + 8 \, {\left(7 \, a^{2} \cosh\left(x\right)^{3} - 3 \, a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(35 \, a^{2} \cosh\left(x\right)^{4} - 30 \, a^{2} \cosh\left(x\right)^{2} + 3 \, a^{2}\right)} \sinh\left(x\right)^{4} - 4 \, a^{2} \cosh\left(x\right)^{2} + 8 \, {\left(7 \, a^{2} \cosh\left(x\right)^{5} - 10 \, a^{2} \cosh\left(x\right)^{3} + 3 \, a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(7 \, a^{2} \cosh\left(x\right)^{6} - 15 \, a^{2} \cosh\left(x\right)^{4} + 9 \, a^{2} \cosh\left(x\right)^{2} - a^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 8 \, {\left(a^{2} \cosh\left(x\right)^{7} - 3 \, a^{2} \cosh\left(x\right)^{5} + 3 \, a^{2} \cosh\left(x\right)^{3} - a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \log\left(\frac{{\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{3} + a^{2} b\right)} \sinh\left(x\right)^{8} + 2 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} + 2 \, {\left(2 \, a^{3} + a^{2} b + 14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} + 3 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3} + 30 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} + 10 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} + 2 \, {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} + 15 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 2 \, a^{3} + 3 \, a^{2} b - b^{3} + 3 \, {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(a^{2} \cosh\left(x\right)^{6} + 6 \, a^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + a^{2} \sinh\left(x\right)^{6} + 3 \, a^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, a^{2} \cosh\left(x\right)^{2} + a^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, a^{2} \cosh\left(x\right)^{3} + 3 \, a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, a^{2} \cosh\left(x\right)^{4} + 18 \, a^{2} \cosh\left(x\right)^{2} + 3 \, a^{2} + 2 \, a b - b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(x\right)^{5} + 6 \, a^{2} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{7} + 3 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) + 2 \, {\left(a^{2} \cosh\left(x\right)^{8} + 8 \, a^{2} \cosh\left(x\right) \sinh\left(x\right)^{7} + a^{2} \sinh\left(x\right)^{8} - 4 \, a^{2} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, a^{2} \cosh\left(x\right)^{2} - a^{2}\right)} \sinh\left(x\right)^{6} + 6 \, a^{2} \cosh\left(x\right)^{4} + 8 \, {\left(7 \, a^{2} \cosh\left(x\right)^{3} - 3 \, a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(35 \, a^{2} \cosh\left(x\right)^{4} - 30 \, a^{2} \cosh\left(x\right)^{2} + 3 \, a^{2}\right)} \sinh\left(x\right)^{4} - 4 \, a^{2} \cosh\left(x\right)^{2} + 8 \, {\left(7 \, a^{2} \cosh\left(x\right)^{5} - 10 \, a^{2} \cosh\left(x\right)^{3} + 3 \, a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(7 \, a^{2} \cosh\left(x\right)^{6} - 15 \, a^{2} \cosh\left(x\right)^{4} + 9 \, a^{2} \cosh\left(x\right)^{2} - a^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 8 \, {\left(a^{2} \cosh\left(x\right)^{7} - 3 \, a^{2} \cosh\left(x\right)^{5} + 3 \, a^{2} \cosh\left(x\right)^{3} - a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \log\left(-\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - b\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - b \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right) - \sqrt{2} {\left({\left(6 \, a^{2} + a b\right)} \cosh\left(x\right)^{6} + 6 \, {\left(6 \, a^{2} + a b\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(6 \, a^{2} + a b\right)} \sinh\left(x\right)^{6} + {\left(2 \, a^{2} - a b\right)} \cosh\left(x\right)^{4} + {\left(15 \, {\left(6 \, a^{2} + a b\right)} \cosh\left(x\right)^{2} + 2 \, a^{2} - a b\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, {\left(6 \, a^{2} + a b\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{2} - a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(2 \, a^{2} - a b\right)} \cosh\left(x\right)^{2} + {\left(15 \, {\left(6 \, a^{2} + a b\right)} \cosh\left(x\right)^{4} + 6 \, {\left(2 \, a^{2} - a b\right)} \cosh\left(x\right)^{2} + 2 \, a^{2} - a b\right)} \sinh\left(x\right)^{2} + 6 \, a^{2} + a b + 2 \, {\left(3 \, {\left(6 \, a^{2} + a b\right)} \cosh\left(x\right)^{5} + 2 \, {\left(2 \, a^{2} - a b\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{2} - a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{8 \, {\left(a^{2} \cosh\left(x\right)^{8} + 8 \, a^{2} \cosh\left(x\right) \sinh\left(x\right)^{7} + a^{2} \sinh\left(x\right)^{8} - 4 \, a^{2} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, a^{2} \cosh\left(x\right)^{2} - a^{2}\right)} \sinh\left(x\right)^{6} + 6 \, a^{2} \cosh\left(x\right)^{4} + 8 \, {\left(7 \, a^{2} \cosh\left(x\right)^{3} - 3 \, a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(35 \, a^{2} \cosh\left(x\right)^{4} - 30 \, a^{2} \cosh\left(x\right)^{2} + 3 \, a^{2}\right)} \sinh\left(x\right)^{4} - 4 \, a^{2} \cosh\left(x\right)^{2} + 8 \, {\left(7 \, a^{2} \cosh\left(x\right)^{5} - 10 \, a^{2} \cosh\left(x\right)^{3} + 3 \, a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(7 \, a^{2} \cosh\left(x\right)^{6} - 15 \, a^{2} \cosh\left(x\right)^{4} + 9 \, a^{2} \cosh\left(x\right)^{2} - a^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 8 \, {\left(a^{2} \cosh\left(x\right)^{7} - 3 \, a^{2} \cosh\left(x\right)^{5} + 3 \, a^{2} \cosh\left(x\right)^{3} - a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}, -\frac{8 \, {\left(a^{2} \cosh\left(x\right)^{8} + 8 \, a^{2} \cosh\left(x\right) \sinh\left(x\right)^{7} + a^{2} \sinh\left(x\right)^{8} - 4 \, a^{2} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, a^{2} \cosh\left(x\right)^{2} - a^{2}\right)} \sinh\left(x\right)^{6} + 6 \, a^{2} \cosh\left(x\right)^{4} + 8 \, {\left(7 \, a^{2} \cosh\left(x\right)^{3} - 3 \, a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(35 \, a^{2} \cosh\left(x\right)^{4} - 30 \, a^{2} \cosh\left(x\right)^{2} + 3 \, a^{2}\right)} \sinh\left(x\right)^{4} - 4 \, a^{2} \cosh\left(x\right)^{2} + 8 \, {\left(7 \, a^{2} \cosh\left(x\right)^{5} - 10 \, a^{2} \cosh\left(x\right)^{3} + 3 \, a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(7 \, a^{2} \cosh\left(x\right)^{6} - 15 \, a^{2} \cosh\left(x\right)^{4} + 9 \, a^{2} \cosh\left(x\right)^{2} - a^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 8 \, {\left(a^{2} \cosh\left(x\right)^{7} - 3 \, a^{2} \cosh\left(x\right)^{5} + 3 \, a^{2} \cosh\left(x\right)^{3} - a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(a \cosh\left(x\right)^{2} + 2 \, a \cosh\left(x\right) \sinh\left(x\right) + a \sinh\left(x\right)^{2} + a + b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a^{2} + a b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{2} + a b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{2} + a b\right)} \sinh\left(x\right)^{4} + {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} + 2 \, a^{2} + a b - b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(2 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + 8 \, {\left(a^{2} \cosh\left(x\right)^{8} + 8 \, a^{2} \cosh\left(x\right) \sinh\left(x\right)^{7} + a^{2} \sinh\left(x\right)^{8} - 4 \, a^{2} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, a^{2} \cosh\left(x\right)^{2} - a^{2}\right)} \sinh\left(x\right)^{6} + 6 \, a^{2} \cosh\left(x\right)^{4} + 8 \, {\left(7 \, a^{2} \cosh\left(x\right)^{3} - 3 \, a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(35 \, a^{2} \cosh\left(x\right)^{4} - 30 \, a^{2} \cosh\left(x\right)^{2} + 3 \, a^{2}\right)} \sinh\left(x\right)^{4} - 4 \, a^{2} \cosh\left(x\right)^{2} + 8 \, {\left(7 \, a^{2} \cosh\left(x\right)^{5} - 10 \, a^{2} \cosh\left(x\right)^{3} + 3 \, a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(7 \, a^{2} \cosh\left(x\right)^{6} - 15 \, a^{2} \cosh\left(x\right)^{4} + 9 \, a^{2} \cosh\left(x\right)^{2} - a^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 8 \, {\left(a^{2} \cosh\left(x\right)^{7} - 3 \, a^{2} \cosh\left(x\right)^{5} + 3 \, a^{2} \cosh\left(x\right)^{3} - a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) + {\left({\left(8 \, a^{2} + 4 \, a b - b^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(8 \, a^{2} + 4 \, a b - b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(8 \, a^{2} + 4 \, a b - b^{2}\right)} \sinh\left(x\right)^{8} - 4 \, {\left(8 \, a^{2} + 4 \, a b - b^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(8 \, a^{2} + 4 \, a b - b^{2}\right)} \cosh\left(x\right)^{2} - 8 \, a^{2} - 4 \, a b + b^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(8 \, a^{2} + 4 \, a b - b^{2}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(8 \, a^{2} + 4 \, a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 6 \, {\left(8 \, a^{2} + 4 \, a b - b^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(8 \, a^{2} + 4 \, a b - b^{2}\right)} \cosh\left(x\right)^{4} - 30 \, {\left(8 \, a^{2} + 4 \, a b - b^{2}\right)} \cosh\left(x\right)^{2} + 24 \, a^{2} + 12 \, a b - 3 \, b^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(8 \, a^{2} + 4 \, a b - b^{2}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(8 \, a^{2} + 4 \, a b - b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(8 \, a^{2} + 4 \, a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 4 \, {\left(8 \, a^{2} + 4 \, a b - b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(8 \, a^{2} + 4 \, a b - b^{2}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(8 \, a^{2} + 4 \, a b - b^{2}\right)} \cosh\left(x\right)^{4} + 9 \, {\left(8 \, a^{2} + 4 \, a b - b^{2}\right)} \cosh\left(x\right)^{2} - 8 \, a^{2} - 4 \, a b + b^{2}\right)} \sinh\left(x\right)^{2} + 8 \, a^{2} + 4 \, a b - b^{2} + 8 \, {\left({\left(8 \, a^{2} + 4 \, a b - b^{2}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(8 \, a^{2} + 4 \, a b - b^{2}\right)} \cosh\left(x\right)^{5} + 3 \, {\left(8 \, a^{2} + 4 \, a b - b^{2}\right)} \cosh\left(x\right)^{3} - {\left(8 \, a^{2} + 4 \, a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \log\left(-\frac{{\left(2 \, a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(2 \, a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(2 \, a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(2 \, a + b\right)} \cosh\left(x\right)^{2} + 2 \, a - b\right)} \sinh\left(x\right)^{2} + 2 \, \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{a} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(2 \, a + b\right)} \cosh\left(x\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + 2 \, a + b}{\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) + 2 \, \sqrt{2} {\left({\left(6 \, a^{2} + a b\right)} \cosh\left(x\right)^{6} + 6 \, {\left(6 \, a^{2} + a b\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(6 \, a^{2} + a b\right)} \sinh\left(x\right)^{6} + {\left(2 \, a^{2} - a b\right)} \cosh\left(x\right)^{4} + {\left(15 \, {\left(6 \, a^{2} + a b\right)} \cosh\left(x\right)^{2} + 2 \, a^{2} - a b\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, {\left(6 \, a^{2} + a b\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{2} - a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(2 \, a^{2} - a b\right)} \cosh\left(x\right)^{2} + {\left(15 \, {\left(6 \, a^{2} + a b\right)} \cosh\left(x\right)^{4} + 6 \, {\left(2 \, a^{2} - a b\right)} \cosh\left(x\right)^{2} + 2 \, a^{2} - a b\right)} \sinh\left(x\right)^{2} + 6 \, a^{2} + a b + 2 \, {\left(3 \, {\left(6 \, a^{2} + a b\right)} \cosh\left(x\right)^{5} + 2 \, {\left(2 \, a^{2} - a b\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{2} - a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{16 \, {\left(a^{2} \cosh\left(x\right)^{8} + 8 \, a^{2} \cosh\left(x\right) \sinh\left(x\right)^{7} + a^{2} \sinh\left(x\right)^{8} - 4 \, a^{2} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, a^{2} \cosh\left(x\right)^{2} - a^{2}\right)} \sinh\left(x\right)^{6} + 6 \, a^{2} \cosh\left(x\right)^{4} + 8 \, {\left(7 \, a^{2} \cosh\left(x\right)^{3} - 3 \, a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(35 \, a^{2} \cosh\left(x\right)^{4} - 30 \, a^{2} \cosh\left(x\right)^{2} + 3 \, a^{2}\right)} \sinh\left(x\right)^{4} - 4 \, a^{2} \cosh\left(x\right)^{2} + 8 \, {\left(7 \, a^{2} \cosh\left(x\right)^{5} - 10 \, a^{2} \cosh\left(x\right)^{3} + 3 \, a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(7 \, a^{2} \cosh\left(x\right)^{6} - 15 \, a^{2} \cosh\left(x\right)^{4} + 9 \, a^{2} \cosh\left(x\right)^{2} - a^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 8 \, {\left(a^{2} \cosh\left(x\right)^{7} - 3 \, a^{2} \cosh\left(x\right)^{5} + 3 \, a^{2} \cosh\left(x\right)^{3} - a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}, \frac{{\left({\left(8 \, a^{2} + 4 \, a b - b^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(8 \, a^{2} + 4 \, a b - b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(8 \, a^{2} + 4 \, a b - b^{2}\right)} \sinh\left(x\right)^{8} - 4 \, {\left(8 \, a^{2} + 4 \, a b - b^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(8 \, a^{2} + 4 \, a b - b^{2}\right)} \cosh\left(x\right)^{2} - 8 \, a^{2} - 4 \, a b + b^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(8 \, a^{2} + 4 \, a b - b^{2}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(8 \, a^{2} + 4 \, a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 6 \, {\left(8 \, a^{2} + 4 \, a b - b^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(8 \, a^{2} + 4 \, a b - b^{2}\right)} \cosh\left(x\right)^{4} - 30 \, {\left(8 \, a^{2} + 4 \, a b - b^{2}\right)} \cosh\left(x\right)^{2} + 24 \, a^{2} + 12 \, a b - 3 \, b^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(8 \, a^{2} + 4 \, a b - b^{2}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(8 \, a^{2} + 4 \, a b - b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(8 \, a^{2} + 4 \, a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 4 \, {\left(8 \, a^{2} + 4 \, a b - b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(8 \, a^{2} + 4 \, a b - b^{2}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(8 \, a^{2} + 4 \, a b - b^{2}\right)} \cosh\left(x\right)^{4} + 9 \, {\left(8 \, a^{2} + 4 \, a b - b^{2}\right)} \cosh\left(x\right)^{2} - 8 \, a^{2} - 4 \, a b + b^{2}\right)} \sinh\left(x\right)^{2} + 8 \, a^{2} + 4 \, a b - b^{2} + 8 \, {\left({\left(8 \, a^{2} + 4 \, a b - b^{2}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(8 \, a^{2} + 4 \, a b - b^{2}\right)} \cosh\left(x\right)^{5} + 3 \, {\left(8 \, a^{2} + 4 \, a b - b^{2}\right)} \cosh\left(x\right)^{3} - {\left(8 \, a^{2} + 4 \, a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{-a} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) - 4 \, {\left(a^{2} \cosh\left(x\right)^{8} + 8 \, a^{2} \cosh\left(x\right) \sinh\left(x\right)^{7} + a^{2} \sinh\left(x\right)^{8} - 4 \, a^{2} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, a^{2} \cosh\left(x\right)^{2} - a^{2}\right)} \sinh\left(x\right)^{6} + 6 \, a^{2} \cosh\left(x\right)^{4} + 8 \, {\left(7 \, a^{2} \cosh\left(x\right)^{3} - 3 \, a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(35 \, a^{2} \cosh\left(x\right)^{4} - 30 \, a^{2} \cosh\left(x\right)^{2} + 3 \, a^{2}\right)} \sinh\left(x\right)^{4} - 4 \, a^{2} \cosh\left(x\right)^{2} + 8 \, {\left(7 \, a^{2} \cosh\left(x\right)^{5} - 10 \, a^{2} \cosh\left(x\right)^{3} + 3 \, a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(7 \, a^{2} \cosh\left(x\right)^{6} - 15 \, a^{2} \cosh\left(x\right)^{4} + 9 \, a^{2} \cosh\left(x\right)^{2} - a^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 8 \, {\left(a^{2} \cosh\left(x\right)^{7} - 3 \, a^{2} \cosh\left(x\right)^{5} + 3 \, a^{2} \cosh\left(x\right)^{3} - a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(a \cosh\left(x\right)^{2} + 2 \, a \cosh\left(x\right) \sinh\left(x\right) + a \sinh\left(x\right)^{2} + a + b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a^{2} + a b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{2} + a b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{2} + a b\right)} \sinh\left(x\right)^{4} + {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} + 2 \, a^{2} + a b - b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(2 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) - 4 \, {\left(a^{2} \cosh\left(x\right)^{8} + 8 \, a^{2} \cosh\left(x\right) \sinh\left(x\right)^{7} + a^{2} \sinh\left(x\right)^{8} - 4 \, a^{2} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, a^{2} \cosh\left(x\right)^{2} - a^{2}\right)} \sinh\left(x\right)^{6} + 6 \, a^{2} \cosh\left(x\right)^{4} + 8 \, {\left(7 \, a^{2} \cosh\left(x\right)^{3} - 3 \, a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(35 \, a^{2} \cosh\left(x\right)^{4} - 30 \, a^{2} \cosh\left(x\right)^{2} + 3 \, a^{2}\right)} \sinh\left(x\right)^{4} - 4 \, a^{2} \cosh\left(x\right)^{2} + 8 \, {\left(7 \, a^{2} \cosh\left(x\right)^{5} - 10 \, a^{2} \cosh\left(x\right)^{3} + 3 \, a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(7 \, a^{2} \cosh\left(x\right)^{6} - 15 \, a^{2} \cosh\left(x\right)^{4} + 9 \, a^{2} \cosh\left(x\right)^{2} - a^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 8 \, {\left(a^{2} \cosh\left(x\right)^{7} - 3 \, a^{2} \cosh\left(x\right)^{5} + 3 \, a^{2} \cosh\left(x\right)^{3} - a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) - \sqrt{2} {\left({\left(6 \, a^{2} + a b\right)} \cosh\left(x\right)^{6} + 6 \, {\left(6 \, a^{2} + a b\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(6 \, a^{2} + a b\right)} \sinh\left(x\right)^{6} + {\left(2 \, a^{2} - a b\right)} \cosh\left(x\right)^{4} + {\left(15 \, {\left(6 \, a^{2} + a b\right)} \cosh\left(x\right)^{2} + 2 \, a^{2} - a b\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, {\left(6 \, a^{2} + a b\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{2} - a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(2 \, a^{2} - a b\right)} \cosh\left(x\right)^{2} + {\left(15 \, {\left(6 \, a^{2} + a b\right)} \cosh\left(x\right)^{4} + 6 \, {\left(2 \, a^{2} - a b\right)} \cosh\left(x\right)^{2} + 2 \, a^{2} - a b\right)} \sinh\left(x\right)^{2} + 6 \, a^{2} + a b + 2 \, {\left(3 \, {\left(6 \, a^{2} + a b\right)} \cosh\left(x\right)^{5} + 2 \, {\left(2 \, a^{2} - a b\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{2} - a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{8 \, {\left(a^{2} \cosh\left(x\right)^{8} + 8 \, a^{2} \cosh\left(x\right) \sinh\left(x\right)^{7} + a^{2} \sinh\left(x\right)^{8} - 4 \, a^{2} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, a^{2} \cosh\left(x\right)^{2} - a^{2}\right)} \sinh\left(x\right)^{6} + 6 \, a^{2} \cosh\left(x\right)^{4} + 8 \, {\left(7 \, a^{2} \cosh\left(x\right)^{3} - 3 \, a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(35 \, a^{2} \cosh\left(x\right)^{4} - 30 \, a^{2} \cosh\left(x\right)^{2} + 3 \, a^{2}\right)} \sinh\left(x\right)^{4} - 4 \, a^{2} \cosh\left(x\right)^{2} + 8 \, {\left(7 \, a^{2} \cosh\left(x\right)^{5} - 10 \, a^{2} \cosh\left(x\right)^{3} + 3 \, a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(7 \, a^{2} \cosh\left(x\right)^{6} - 15 \, a^{2} \cosh\left(x\right)^{4} + 9 \, a^{2} \cosh\left(x\right)^{2} - a^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 8 \, {\left(a^{2} \cosh\left(x\right)^{7} - 3 \, a^{2} \cosh\left(x\right)^{5} + 3 \, a^{2} \cosh\left(x\right)^{3} - a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}\right]"," ",0,"[1/16*(4*(a^2*cosh(x)^8 + 8*a^2*cosh(x)*sinh(x)^7 + a^2*sinh(x)^8 - 4*a^2*cosh(x)^6 + 4*(7*a^2*cosh(x)^2 - a^2)*sinh(x)^6 + 6*a^2*cosh(x)^4 + 8*(7*a^2*cosh(x)^3 - 3*a^2*cosh(x))*sinh(x)^5 + 2*(35*a^2*cosh(x)^4 - 30*a^2*cosh(x)^2 + 3*a^2)*sinh(x)^4 - 4*a^2*cosh(x)^2 + 8*(7*a^2*cosh(x)^5 - 10*a^2*cosh(x)^3 + 3*a^2*cosh(x))*sinh(x)^3 + 4*(7*a^2*cosh(x)^6 - 15*a^2*cosh(x)^4 + 9*a^2*cosh(x)^2 - a^2)*sinh(x)^2 + a^2 + 8*(a^2*cosh(x)^7 - 3*a^2*cosh(x)^5 + 3*a^2*cosh(x)^3 - a^2*cosh(x))*sinh(x))*sqrt(a + b)*log(((a^3 + a^2*b)*cosh(x)^8 + 8*(a^3 + a^2*b)*cosh(x)*sinh(x)^7 + (a^3 + a^2*b)*sinh(x)^8 + 2*(2*a^3 + a^2*b)*cosh(x)^6 + 2*(2*a^3 + a^2*b + 14*(a^3 + a^2*b)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a^3 + a^2*b)*cosh(x)^3 + 3*(2*a^3 + a^2*b)*cosh(x))*sinh(x)^5 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^4 + (70*(a^3 + a^2*b)*cosh(x)^4 + 6*a^3 + 4*a^2*b - a*b^2 + b^3 + 30*(2*a^3 + a^2*b)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a^3 + a^2*b)*cosh(x)^5 + 10*(2*a^3 + a^2*b)*cosh(x)^3 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x))*sinh(x)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 + 2*(2*a^3 + 3*a^2*b - b^3)*cosh(x)^2 + 2*(14*(a^3 + a^2*b)*cosh(x)^6 + 15*(2*a^3 + a^2*b)*cosh(x)^4 + 2*a^3 + 3*a^2*b - b^3 + 3*(6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^2)*sinh(x)^2 + sqrt(2)*(a^2*cosh(x)^6 + 6*a^2*cosh(x)*sinh(x)^5 + a^2*sinh(x)^6 + 3*a^2*cosh(x)^4 + 3*(5*a^2*cosh(x)^2 + a^2)*sinh(x)^4 + 4*(5*a^2*cosh(x)^3 + 3*a^2*cosh(x))*sinh(x)^3 + (3*a^2 + 2*a*b - b^2)*cosh(x)^2 + (15*a^2*cosh(x)^4 + 18*a^2*cosh(x)^2 + 3*a^2 + 2*a*b - b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(3*a^2*cosh(x)^5 + 6*a^2*cosh(x)^3 + (3*a^2 + 2*a*b - b^2)*cosh(x))*sinh(x))*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a^3 + a^2*b)*cosh(x)^7 + 3*(2*a^3 + a^2*b)*cosh(x)^5 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^3 + (2*a^3 + 3*a^2*b - b^3)*cosh(x))*sinh(x))/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) - ((8*a^2 + 4*a*b - b^2)*cosh(x)^8 + 8*(8*a^2 + 4*a*b - b^2)*cosh(x)*sinh(x)^7 + (8*a^2 + 4*a*b - b^2)*sinh(x)^8 - 4*(8*a^2 + 4*a*b - b^2)*cosh(x)^6 + 4*(7*(8*a^2 + 4*a*b - b^2)*cosh(x)^2 - 8*a^2 - 4*a*b + b^2)*sinh(x)^6 + 8*(7*(8*a^2 + 4*a*b - b^2)*cosh(x)^3 - 3*(8*a^2 + 4*a*b - b^2)*cosh(x))*sinh(x)^5 + 6*(8*a^2 + 4*a*b - b^2)*cosh(x)^4 + 2*(35*(8*a^2 + 4*a*b - b^2)*cosh(x)^4 - 30*(8*a^2 + 4*a*b - b^2)*cosh(x)^2 + 24*a^2 + 12*a*b - 3*b^2)*sinh(x)^4 + 8*(7*(8*a^2 + 4*a*b - b^2)*cosh(x)^5 - 10*(8*a^2 + 4*a*b - b^2)*cosh(x)^3 + 3*(8*a^2 + 4*a*b - b^2)*cosh(x))*sinh(x)^3 - 4*(8*a^2 + 4*a*b - b^2)*cosh(x)^2 + 4*(7*(8*a^2 + 4*a*b - b^2)*cosh(x)^6 - 15*(8*a^2 + 4*a*b - b^2)*cosh(x)^4 + 9*(8*a^2 + 4*a*b - b^2)*cosh(x)^2 - 8*a^2 - 4*a*b + b^2)*sinh(x)^2 + 8*a^2 + 4*a*b - b^2 + 8*((8*a^2 + 4*a*b - b^2)*cosh(x)^7 - 3*(8*a^2 + 4*a*b - b^2)*cosh(x)^5 + 3*(8*a^2 + 4*a*b - b^2)*cosh(x)^3 - (8*a^2 + 4*a*b - b^2)*cosh(x))*sinh(x))*sqrt(a)*log(-((2*a + b)*cosh(x)^4 + 4*(2*a + b)*cosh(x)*sinh(x)^3 + (2*a + b)*sinh(x)^4 + 2*(2*a - b)*cosh(x)^2 + 2*(3*(2*a + b)*cosh(x)^2 + 2*a - b)*sinh(x)^2 + 2*sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((2*a + b)*cosh(x)^3 + (2*a - b)*cosh(x))*sinh(x) + 2*a + b)/(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)) + 4*(a^2*cosh(x)^8 + 8*a^2*cosh(x)*sinh(x)^7 + a^2*sinh(x)^8 - 4*a^2*cosh(x)^6 + 4*(7*a^2*cosh(x)^2 - a^2)*sinh(x)^6 + 6*a^2*cosh(x)^4 + 8*(7*a^2*cosh(x)^3 - 3*a^2*cosh(x))*sinh(x)^5 + 2*(35*a^2*cosh(x)^4 - 30*a^2*cosh(x)^2 + 3*a^2)*sinh(x)^4 - 4*a^2*cosh(x)^2 + 8*(7*a^2*cosh(x)^5 - 10*a^2*cosh(x)^3 + 3*a^2*cosh(x))*sinh(x)^3 + 4*(7*a^2*cosh(x)^6 - 15*a^2*cosh(x)^4 + 9*a^2*cosh(x)^2 - a^2)*sinh(x)^2 + a^2 + 8*(a^2*cosh(x)^7 - 3*a^2*cosh(x)^5 + 3*a^2*cosh(x)^3 - a^2*cosh(x))*sinh(x))*sqrt(a + b)*log(-((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*b*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + b)*cosh(x)^3 - b*cosh(x))*sinh(x) + a + b)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) - 2*sqrt(2)*((6*a^2 + a*b)*cosh(x)^6 + 6*(6*a^2 + a*b)*cosh(x)*sinh(x)^5 + (6*a^2 + a*b)*sinh(x)^6 + (2*a^2 - a*b)*cosh(x)^4 + (15*(6*a^2 + a*b)*cosh(x)^2 + 2*a^2 - a*b)*sinh(x)^4 + 4*(5*(6*a^2 + a*b)*cosh(x)^3 + (2*a^2 - a*b)*cosh(x))*sinh(x)^3 + (2*a^2 - a*b)*cosh(x)^2 + (15*(6*a^2 + a*b)*cosh(x)^4 + 6*(2*a^2 - a*b)*cosh(x)^2 + 2*a^2 - a*b)*sinh(x)^2 + 6*a^2 + a*b + 2*(3*(6*a^2 + a*b)*cosh(x)^5 + 2*(2*a^2 - a*b)*cosh(x)^3 + (2*a^2 - a*b)*cosh(x))*sinh(x))*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(a^2*cosh(x)^8 + 8*a^2*cosh(x)*sinh(x)^7 + a^2*sinh(x)^8 - 4*a^2*cosh(x)^6 + 4*(7*a^2*cosh(x)^2 - a^2)*sinh(x)^6 + 6*a^2*cosh(x)^4 + 8*(7*a^2*cosh(x)^3 - 3*a^2*cosh(x))*sinh(x)^5 + 2*(35*a^2*cosh(x)^4 - 30*a^2*cosh(x)^2 + 3*a^2)*sinh(x)^4 - 4*a^2*cosh(x)^2 + 8*(7*a^2*cosh(x)^5 - 10*a^2*cosh(x)^3 + 3*a^2*cosh(x))*sinh(x)^3 + 4*(7*a^2*cosh(x)^6 - 15*a^2*cosh(x)^4 + 9*a^2*cosh(x)^2 - a^2)*sinh(x)^2 + a^2 + 8*(a^2*cosh(x)^7 - 3*a^2*cosh(x)^5 + 3*a^2*cosh(x)^3 - a^2*cosh(x))*sinh(x)), 1/8*(((8*a^2 + 4*a*b - b^2)*cosh(x)^8 + 8*(8*a^2 + 4*a*b - b^2)*cosh(x)*sinh(x)^7 + (8*a^2 + 4*a*b - b^2)*sinh(x)^8 - 4*(8*a^2 + 4*a*b - b^2)*cosh(x)^6 + 4*(7*(8*a^2 + 4*a*b - b^2)*cosh(x)^2 - 8*a^2 - 4*a*b + b^2)*sinh(x)^6 + 8*(7*(8*a^2 + 4*a*b - b^2)*cosh(x)^3 - 3*(8*a^2 + 4*a*b - b^2)*cosh(x))*sinh(x)^5 + 6*(8*a^2 + 4*a*b - b^2)*cosh(x)^4 + 2*(35*(8*a^2 + 4*a*b - b^2)*cosh(x)^4 - 30*(8*a^2 + 4*a*b - b^2)*cosh(x)^2 + 24*a^2 + 12*a*b - 3*b^2)*sinh(x)^4 + 8*(7*(8*a^2 + 4*a*b - b^2)*cosh(x)^5 - 10*(8*a^2 + 4*a*b - b^2)*cosh(x)^3 + 3*(8*a^2 + 4*a*b - b^2)*cosh(x))*sinh(x)^3 - 4*(8*a^2 + 4*a*b - b^2)*cosh(x)^2 + 4*(7*(8*a^2 + 4*a*b - b^2)*cosh(x)^6 - 15*(8*a^2 + 4*a*b - b^2)*cosh(x)^4 + 9*(8*a^2 + 4*a*b - b^2)*cosh(x)^2 - 8*a^2 - 4*a*b + b^2)*sinh(x)^2 + 8*a^2 + 4*a*b - b^2 + 8*((8*a^2 + 4*a*b - b^2)*cosh(x)^7 - 3*(8*a^2 + 4*a*b - b^2)*cosh(x)^5 + 3*(8*a^2 + 4*a*b - b^2)*cosh(x)^3 - (8*a^2 + 4*a*b - b^2)*cosh(x))*sinh(x))*sqrt(-a)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(-a)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a - b)*cosh(x))*sinh(x) + a + b)) + 2*(a^2*cosh(x)^8 + 8*a^2*cosh(x)*sinh(x)^7 + a^2*sinh(x)^8 - 4*a^2*cosh(x)^6 + 4*(7*a^2*cosh(x)^2 - a^2)*sinh(x)^6 + 6*a^2*cosh(x)^4 + 8*(7*a^2*cosh(x)^3 - 3*a^2*cosh(x))*sinh(x)^5 + 2*(35*a^2*cosh(x)^4 - 30*a^2*cosh(x)^2 + 3*a^2)*sinh(x)^4 - 4*a^2*cosh(x)^2 + 8*(7*a^2*cosh(x)^5 - 10*a^2*cosh(x)^3 + 3*a^2*cosh(x))*sinh(x)^3 + 4*(7*a^2*cosh(x)^6 - 15*a^2*cosh(x)^4 + 9*a^2*cosh(x)^2 - a^2)*sinh(x)^2 + a^2 + 8*(a^2*cosh(x)^7 - 3*a^2*cosh(x)^5 + 3*a^2*cosh(x)^3 - a^2*cosh(x))*sinh(x))*sqrt(a + b)*log(((a^3 + a^2*b)*cosh(x)^8 + 8*(a^3 + a^2*b)*cosh(x)*sinh(x)^7 + (a^3 + a^2*b)*sinh(x)^8 + 2*(2*a^3 + a^2*b)*cosh(x)^6 + 2*(2*a^3 + a^2*b + 14*(a^3 + a^2*b)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a^3 + a^2*b)*cosh(x)^3 + 3*(2*a^3 + a^2*b)*cosh(x))*sinh(x)^5 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^4 + (70*(a^3 + a^2*b)*cosh(x)^4 + 6*a^3 + 4*a^2*b - a*b^2 + b^3 + 30*(2*a^3 + a^2*b)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a^3 + a^2*b)*cosh(x)^5 + 10*(2*a^3 + a^2*b)*cosh(x)^3 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x))*sinh(x)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 + 2*(2*a^3 + 3*a^2*b - b^3)*cosh(x)^2 + 2*(14*(a^3 + a^2*b)*cosh(x)^6 + 15*(2*a^3 + a^2*b)*cosh(x)^4 + 2*a^3 + 3*a^2*b - b^3 + 3*(6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^2)*sinh(x)^2 + sqrt(2)*(a^2*cosh(x)^6 + 6*a^2*cosh(x)*sinh(x)^5 + a^2*sinh(x)^6 + 3*a^2*cosh(x)^4 + 3*(5*a^2*cosh(x)^2 + a^2)*sinh(x)^4 + 4*(5*a^2*cosh(x)^3 + 3*a^2*cosh(x))*sinh(x)^3 + (3*a^2 + 2*a*b - b^2)*cosh(x)^2 + (15*a^2*cosh(x)^4 + 18*a^2*cosh(x)^2 + 3*a^2 + 2*a*b - b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(3*a^2*cosh(x)^5 + 6*a^2*cosh(x)^3 + (3*a^2 + 2*a*b - b^2)*cosh(x))*sinh(x))*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a^3 + a^2*b)*cosh(x)^7 + 3*(2*a^3 + a^2*b)*cosh(x)^5 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^3 + (2*a^3 + 3*a^2*b - b^3)*cosh(x))*sinh(x))/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) + 2*(a^2*cosh(x)^8 + 8*a^2*cosh(x)*sinh(x)^7 + a^2*sinh(x)^8 - 4*a^2*cosh(x)^6 + 4*(7*a^2*cosh(x)^2 - a^2)*sinh(x)^6 + 6*a^2*cosh(x)^4 + 8*(7*a^2*cosh(x)^3 - 3*a^2*cosh(x))*sinh(x)^5 + 2*(35*a^2*cosh(x)^4 - 30*a^2*cosh(x)^2 + 3*a^2)*sinh(x)^4 - 4*a^2*cosh(x)^2 + 8*(7*a^2*cosh(x)^5 - 10*a^2*cosh(x)^3 + 3*a^2*cosh(x))*sinh(x)^3 + 4*(7*a^2*cosh(x)^6 - 15*a^2*cosh(x)^4 + 9*a^2*cosh(x)^2 - a^2)*sinh(x)^2 + a^2 + 8*(a^2*cosh(x)^7 - 3*a^2*cosh(x)^5 + 3*a^2*cosh(x)^3 - a^2*cosh(x))*sinh(x))*sqrt(a + b)*log(-((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*b*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + b)*cosh(x)^3 - b*cosh(x))*sinh(x) + a + b)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) - sqrt(2)*((6*a^2 + a*b)*cosh(x)^6 + 6*(6*a^2 + a*b)*cosh(x)*sinh(x)^5 + (6*a^2 + a*b)*sinh(x)^6 + (2*a^2 - a*b)*cosh(x)^4 + (15*(6*a^2 + a*b)*cosh(x)^2 + 2*a^2 - a*b)*sinh(x)^4 + 4*(5*(6*a^2 + a*b)*cosh(x)^3 + (2*a^2 - a*b)*cosh(x))*sinh(x)^3 + (2*a^2 - a*b)*cosh(x)^2 + (15*(6*a^2 + a*b)*cosh(x)^4 + 6*(2*a^2 - a*b)*cosh(x)^2 + 2*a^2 - a*b)*sinh(x)^2 + 6*a^2 + a*b + 2*(3*(6*a^2 + a*b)*cosh(x)^5 + 2*(2*a^2 - a*b)*cosh(x)^3 + (2*a^2 - a*b)*cosh(x))*sinh(x))*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(a^2*cosh(x)^8 + 8*a^2*cosh(x)*sinh(x)^7 + a^2*sinh(x)^8 - 4*a^2*cosh(x)^6 + 4*(7*a^2*cosh(x)^2 - a^2)*sinh(x)^6 + 6*a^2*cosh(x)^4 + 8*(7*a^2*cosh(x)^3 - 3*a^2*cosh(x))*sinh(x)^5 + 2*(35*a^2*cosh(x)^4 - 30*a^2*cosh(x)^2 + 3*a^2)*sinh(x)^4 - 4*a^2*cosh(x)^2 + 8*(7*a^2*cosh(x)^5 - 10*a^2*cosh(x)^3 + 3*a^2*cosh(x))*sinh(x)^3 + 4*(7*a^2*cosh(x)^6 - 15*a^2*cosh(x)^4 + 9*a^2*cosh(x)^2 - a^2)*sinh(x)^2 + a^2 + 8*(a^2*cosh(x)^7 - 3*a^2*cosh(x)^5 + 3*a^2*cosh(x)^3 - a^2*cosh(x))*sinh(x)), -1/16*(8*(a^2*cosh(x)^8 + 8*a^2*cosh(x)*sinh(x)^7 + a^2*sinh(x)^8 - 4*a^2*cosh(x)^6 + 4*(7*a^2*cosh(x)^2 - a^2)*sinh(x)^6 + 6*a^2*cosh(x)^4 + 8*(7*a^2*cosh(x)^3 - 3*a^2*cosh(x))*sinh(x)^5 + 2*(35*a^2*cosh(x)^4 - 30*a^2*cosh(x)^2 + 3*a^2)*sinh(x)^4 - 4*a^2*cosh(x)^2 + 8*(7*a^2*cosh(x)^5 - 10*a^2*cosh(x)^3 + 3*a^2*cosh(x))*sinh(x)^3 + 4*(7*a^2*cosh(x)^6 - 15*a^2*cosh(x)^4 + 9*a^2*cosh(x)^2 - a^2)*sinh(x)^2 + a^2 + 8*(a^2*cosh(x)^7 - 3*a^2*cosh(x)^5 + 3*a^2*cosh(x)^3 - a^2*cosh(x))*sinh(x))*sqrt(-a - b)*arctan(sqrt(2)*(a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 + a + b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a^2 + a*b)*cosh(x)^4 + 4*(a^2 + a*b)*cosh(x)*sinh(x)^3 + (a^2 + a*b)*sinh(x)^4 + (2*a^2 + a*b - b^2)*cosh(x)^2 + (6*(a^2 + a*b)*cosh(x)^2 + 2*a^2 + a*b - b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(2*(a^2 + a*b)*cosh(x)^3 + (2*a^2 + a*b - b^2)*cosh(x))*sinh(x))) + 8*(a^2*cosh(x)^8 + 8*a^2*cosh(x)*sinh(x)^7 + a^2*sinh(x)^8 - 4*a^2*cosh(x)^6 + 4*(7*a^2*cosh(x)^2 - a^2)*sinh(x)^6 + 6*a^2*cosh(x)^4 + 8*(7*a^2*cosh(x)^3 - 3*a^2*cosh(x))*sinh(x)^5 + 2*(35*a^2*cosh(x)^4 - 30*a^2*cosh(x)^2 + 3*a^2)*sinh(x)^4 - 4*a^2*cosh(x)^2 + 8*(7*a^2*cosh(x)^5 - 10*a^2*cosh(x)^3 + 3*a^2*cosh(x))*sinh(x)^3 + 4*(7*a^2*cosh(x)^6 - 15*a^2*cosh(x)^4 + 9*a^2*cosh(x)^2 - a^2)*sinh(x)^2 + a^2 + 8*(a^2*cosh(x)^7 - 3*a^2*cosh(x)^5 + 3*a^2*cosh(x)^3 - a^2*cosh(x))*sinh(x))*sqrt(-a - b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a - b)*cosh(x))*sinh(x) + a + b)) + ((8*a^2 + 4*a*b - b^2)*cosh(x)^8 + 8*(8*a^2 + 4*a*b - b^2)*cosh(x)*sinh(x)^7 + (8*a^2 + 4*a*b - b^2)*sinh(x)^8 - 4*(8*a^2 + 4*a*b - b^2)*cosh(x)^6 + 4*(7*(8*a^2 + 4*a*b - b^2)*cosh(x)^2 - 8*a^2 - 4*a*b + b^2)*sinh(x)^6 + 8*(7*(8*a^2 + 4*a*b - b^2)*cosh(x)^3 - 3*(8*a^2 + 4*a*b - b^2)*cosh(x))*sinh(x)^5 + 6*(8*a^2 + 4*a*b - b^2)*cosh(x)^4 + 2*(35*(8*a^2 + 4*a*b - b^2)*cosh(x)^4 - 30*(8*a^2 + 4*a*b - b^2)*cosh(x)^2 + 24*a^2 + 12*a*b - 3*b^2)*sinh(x)^4 + 8*(7*(8*a^2 + 4*a*b - b^2)*cosh(x)^5 - 10*(8*a^2 + 4*a*b - b^2)*cosh(x)^3 + 3*(8*a^2 + 4*a*b - b^2)*cosh(x))*sinh(x)^3 - 4*(8*a^2 + 4*a*b - b^2)*cosh(x)^2 + 4*(7*(8*a^2 + 4*a*b - b^2)*cosh(x)^6 - 15*(8*a^2 + 4*a*b - b^2)*cosh(x)^4 + 9*(8*a^2 + 4*a*b - b^2)*cosh(x)^2 - 8*a^2 - 4*a*b + b^2)*sinh(x)^2 + 8*a^2 + 4*a*b - b^2 + 8*((8*a^2 + 4*a*b - b^2)*cosh(x)^7 - 3*(8*a^2 + 4*a*b - b^2)*cosh(x)^5 + 3*(8*a^2 + 4*a*b - b^2)*cosh(x)^3 - (8*a^2 + 4*a*b - b^2)*cosh(x))*sinh(x))*sqrt(a)*log(-((2*a + b)*cosh(x)^4 + 4*(2*a + b)*cosh(x)*sinh(x)^3 + (2*a + b)*sinh(x)^4 + 2*(2*a - b)*cosh(x)^2 + 2*(3*(2*a + b)*cosh(x)^2 + 2*a - b)*sinh(x)^2 + 2*sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((2*a + b)*cosh(x)^3 + (2*a - b)*cosh(x))*sinh(x) + 2*a + b)/(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)) + 2*sqrt(2)*((6*a^2 + a*b)*cosh(x)^6 + 6*(6*a^2 + a*b)*cosh(x)*sinh(x)^5 + (6*a^2 + a*b)*sinh(x)^6 + (2*a^2 - a*b)*cosh(x)^4 + (15*(6*a^2 + a*b)*cosh(x)^2 + 2*a^2 - a*b)*sinh(x)^4 + 4*(5*(6*a^2 + a*b)*cosh(x)^3 + (2*a^2 - a*b)*cosh(x))*sinh(x)^3 + (2*a^2 - a*b)*cosh(x)^2 + (15*(6*a^2 + a*b)*cosh(x)^4 + 6*(2*a^2 - a*b)*cosh(x)^2 + 2*a^2 - a*b)*sinh(x)^2 + 6*a^2 + a*b + 2*(3*(6*a^2 + a*b)*cosh(x)^5 + 2*(2*a^2 - a*b)*cosh(x)^3 + (2*a^2 - a*b)*cosh(x))*sinh(x))*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(a^2*cosh(x)^8 + 8*a^2*cosh(x)*sinh(x)^7 + a^2*sinh(x)^8 - 4*a^2*cosh(x)^6 + 4*(7*a^2*cosh(x)^2 - a^2)*sinh(x)^6 + 6*a^2*cosh(x)^4 + 8*(7*a^2*cosh(x)^3 - 3*a^2*cosh(x))*sinh(x)^5 + 2*(35*a^2*cosh(x)^4 - 30*a^2*cosh(x)^2 + 3*a^2)*sinh(x)^4 - 4*a^2*cosh(x)^2 + 8*(7*a^2*cosh(x)^5 - 10*a^2*cosh(x)^3 + 3*a^2*cosh(x))*sinh(x)^3 + 4*(7*a^2*cosh(x)^6 - 15*a^2*cosh(x)^4 + 9*a^2*cosh(x)^2 - a^2)*sinh(x)^2 + a^2 + 8*(a^2*cosh(x)^7 - 3*a^2*cosh(x)^5 + 3*a^2*cosh(x)^3 - a^2*cosh(x))*sinh(x)), 1/8*(((8*a^2 + 4*a*b - b^2)*cosh(x)^8 + 8*(8*a^2 + 4*a*b - b^2)*cosh(x)*sinh(x)^7 + (8*a^2 + 4*a*b - b^2)*sinh(x)^8 - 4*(8*a^2 + 4*a*b - b^2)*cosh(x)^6 + 4*(7*(8*a^2 + 4*a*b - b^2)*cosh(x)^2 - 8*a^2 - 4*a*b + b^2)*sinh(x)^6 + 8*(7*(8*a^2 + 4*a*b - b^2)*cosh(x)^3 - 3*(8*a^2 + 4*a*b - b^2)*cosh(x))*sinh(x)^5 + 6*(8*a^2 + 4*a*b - b^2)*cosh(x)^4 + 2*(35*(8*a^2 + 4*a*b - b^2)*cosh(x)^4 - 30*(8*a^2 + 4*a*b - b^2)*cosh(x)^2 + 24*a^2 + 12*a*b - 3*b^2)*sinh(x)^4 + 8*(7*(8*a^2 + 4*a*b - b^2)*cosh(x)^5 - 10*(8*a^2 + 4*a*b - b^2)*cosh(x)^3 + 3*(8*a^2 + 4*a*b - b^2)*cosh(x))*sinh(x)^3 - 4*(8*a^2 + 4*a*b - b^2)*cosh(x)^2 + 4*(7*(8*a^2 + 4*a*b - b^2)*cosh(x)^6 - 15*(8*a^2 + 4*a*b - b^2)*cosh(x)^4 + 9*(8*a^2 + 4*a*b - b^2)*cosh(x)^2 - 8*a^2 - 4*a*b + b^2)*sinh(x)^2 + 8*a^2 + 4*a*b - b^2 + 8*((8*a^2 + 4*a*b - b^2)*cosh(x)^7 - 3*(8*a^2 + 4*a*b - b^2)*cosh(x)^5 + 3*(8*a^2 + 4*a*b - b^2)*cosh(x)^3 - (8*a^2 + 4*a*b - b^2)*cosh(x))*sinh(x))*sqrt(-a)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(-a)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a - b)*cosh(x))*sinh(x) + a + b)) - 4*(a^2*cosh(x)^8 + 8*a^2*cosh(x)*sinh(x)^7 + a^2*sinh(x)^8 - 4*a^2*cosh(x)^6 + 4*(7*a^2*cosh(x)^2 - a^2)*sinh(x)^6 + 6*a^2*cosh(x)^4 + 8*(7*a^2*cosh(x)^3 - 3*a^2*cosh(x))*sinh(x)^5 + 2*(35*a^2*cosh(x)^4 - 30*a^2*cosh(x)^2 + 3*a^2)*sinh(x)^4 - 4*a^2*cosh(x)^2 + 8*(7*a^2*cosh(x)^5 - 10*a^2*cosh(x)^3 + 3*a^2*cosh(x))*sinh(x)^3 + 4*(7*a^2*cosh(x)^6 - 15*a^2*cosh(x)^4 + 9*a^2*cosh(x)^2 - a^2)*sinh(x)^2 + a^2 + 8*(a^2*cosh(x)^7 - 3*a^2*cosh(x)^5 + 3*a^2*cosh(x)^3 - a^2*cosh(x))*sinh(x))*sqrt(-a - b)*arctan(sqrt(2)*(a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 + a + b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a^2 + a*b)*cosh(x)^4 + 4*(a^2 + a*b)*cosh(x)*sinh(x)^3 + (a^2 + a*b)*sinh(x)^4 + (2*a^2 + a*b - b^2)*cosh(x)^2 + (6*(a^2 + a*b)*cosh(x)^2 + 2*a^2 + a*b - b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(2*(a^2 + a*b)*cosh(x)^3 + (2*a^2 + a*b - b^2)*cosh(x))*sinh(x))) - 4*(a^2*cosh(x)^8 + 8*a^2*cosh(x)*sinh(x)^7 + a^2*sinh(x)^8 - 4*a^2*cosh(x)^6 + 4*(7*a^2*cosh(x)^2 - a^2)*sinh(x)^6 + 6*a^2*cosh(x)^4 + 8*(7*a^2*cosh(x)^3 - 3*a^2*cosh(x))*sinh(x)^5 + 2*(35*a^2*cosh(x)^4 - 30*a^2*cosh(x)^2 + 3*a^2)*sinh(x)^4 - 4*a^2*cosh(x)^2 + 8*(7*a^2*cosh(x)^5 - 10*a^2*cosh(x)^3 + 3*a^2*cosh(x))*sinh(x)^3 + 4*(7*a^2*cosh(x)^6 - 15*a^2*cosh(x)^4 + 9*a^2*cosh(x)^2 - a^2)*sinh(x)^2 + a^2 + 8*(a^2*cosh(x)^7 - 3*a^2*cosh(x)^5 + 3*a^2*cosh(x)^3 - a^2*cosh(x))*sinh(x))*sqrt(-a - b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a - b)*cosh(x))*sinh(x) + a + b)) - sqrt(2)*((6*a^2 + a*b)*cosh(x)^6 + 6*(6*a^2 + a*b)*cosh(x)*sinh(x)^5 + (6*a^2 + a*b)*sinh(x)^6 + (2*a^2 - a*b)*cosh(x)^4 + (15*(6*a^2 + a*b)*cosh(x)^2 + 2*a^2 - a*b)*sinh(x)^4 + 4*(5*(6*a^2 + a*b)*cosh(x)^3 + (2*a^2 - a*b)*cosh(x))*sinh(x)^3 + (2*a^2 - a*b)*cosh(x)^2 + (15*(6*a^2 + a*b)*cosh(x)^4 + 6*(2*a^2 - a*b)*cosh(x)^2 + 2*a^2 - a*b)*sinh(x)^2 + 6*a^2 + a*b + 2*(3*(6*a^2 + a*b)*cosh(x)^5 + 2*(2*a^2 - a*b)*cosh(x)^3 + (2*a^2 - a*b)*cosh(x))*sinh(x))*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(a^2*cosh(x)^8 + 8*a^2*cosh(x)*sinh(x)^7 + a^2*sinh(x)^8 - 4*a^2*cosh(x)^6 + 4*(7*a^2*cosh(x)^2 - a^2)*sinh(x)^6 + 6*a^2*cosh(x)^4 + 8*(7*a^2*cosh(x)^3 - 3*a^2*cosh(x))*sinh(x)^5 + 2*(35*a^2*cosh(x)^4 - 30*a^2*cosh(x)^2 + 3*a^2)*sinh(x)^4 - 4*a^2*cosh(x)^2 + 8*(7*a^2*cosh(x)^5 - 10*a^2*cosh(x)^3 + 3*a^2*cosh(x))*sinh(x)^3 + 4*(7*a^2*cosh(x)^6 - 15*a^2*cosh(x)^4 + 9*a^2*cosh(x)^2 - a^2)*sinh(x)^2 + a^2 + 8*(a^2*cosh(x)^7 - 3*a^2*cosh(x)^5 + 3*a^2*cosh(x)^3 - a^2*cosh(x))*sinh(x))]","B",0
219,1,4941,0,0.832447," ","integrate(tanh(x)^3*(a+b*tanh(x)^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{15 \, {\left({\left(a b + b^{2}\right)} \cosh\left(x\right)^{10} + 10 \, {\left(a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{9} + {\left(a b + b^{2}\right)} \sinh\left(x\right)^{10} + 5 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{8} + 5 \, {\left(9 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} + a b + b^{2}\right)} \sinh\left(x\right)^{8} + 40 \, {\left(3 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a b + b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{7} + 10 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{6} + 10 \, {\left(21 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{4} + 14 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} + a b + b^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(63 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{5} + 70 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{3} + 15 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 10 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{4} + 10 \, {\left(21 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{6} + 35 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{4} + 15 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} + a b + b^{2}\right)} \sinh\left(x\right)^{4} + 40 \, {\left(3 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{7} + 7 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{5} + 5 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a b + b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 5 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} + 5 \, {\left(9 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{8} + 28 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{6} + 30 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{4} + 12 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} + a b + b^{2}\right)} \sinh\left(x\right)^{2} + a b + b^{2} + 10 \, {\left({\left(a b + b^{2}\right)} \cosh\left(x\right)^{9} + 4 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{7} + 6 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{5} + 4 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a b + b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \log\left(\frac{{\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{3} + a^{2} b\right)} \sinh\left(x\right)^{8} + 2 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} + 2 \, {\left(2 \, a^{3} + a^{2} b + 14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} + 3 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3} + 30 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} + 10 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} + 2 \, {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} + 15 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 2 \, a^{3} + 3 \, a^{2} b - b^{3} + 3 \, {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(a^{2} \cosh\left(x\right)^{6} + 6 \, a^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + a^{2} \sinh\left(x\right)^{6} + 3 \, a^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, a^{2} \cosh\left(x\right)^{2} + a^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, a^{2} \cosh\left(x\right)^{3} + 3 \, a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, a^{2} \cosh\left(x\right)^{4} + 18 \, a^{2} \cosh\left(x\right)^{2} + 3 \, a^{2} + 2 \, a b - b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(x\right)^{5} + 6 \, a^{2} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{7} + 3 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) + 15 \, {\left({\left(a b + b^{2}\right)} \cosh\left(x\right)^{10} + 10 \, {\left(a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{9} + {\left(a b + b^{2}\right)} \sinh\left(x\right)^{10} + 5 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{8} + 5 \, {\left(9 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} + a b + b^{2}\right)} \sinh\left(x\right)^{8} + 40 \, {\left(3 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a b + b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{7} + 10 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{6} + 10 \, {\left(21 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{4} + 14 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} + a b + b^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(63 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{5} + 70 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{3} + 15 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 10 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{4} + 10 \, {\left(21 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{6} + 35 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{4} + 15 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} + a b + b^{2}\right)} \sinh\left(x\right)^{4} + 40 \, {\left(3 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{7} + 7 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{5} + 5 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a b + b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 5 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} + 5 \, {\left(9 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{8} + 28 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{6} + 30 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{4} + 12 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} + a b + b^{2}\right)} \sinh\left(x\right)^{2} + a b + b^{2} + 10 \, {\left({\left(a b + b^{2}\right)} \cosh\left(x\right)^{9} + 4 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{7} + 6 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{5} + 4 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a b + b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \log\left(-\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - b\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - b \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right) - 4 \, \sqrt{2} {\left({\left(3 \, a^{2} + 26 \, a b + 23 \, b^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(3 \, a^{2} + 26 \, a b + 23 \, b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(3 \, a^{2} + 26 \, a b + 23 \, b^{2}\right)} \sinh\left(x\right)^{8} + 4 \, {\left(3 \, a^{2} + 20 \, a b + 12 \, b^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(3 \, a^{2} + 26 \, a b + 23 \, b^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} + 20 \, a b + 12 \, b^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(3 \, a^{2} + 26 \, a b + 23 \, b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(3 \, a^{2} + 20 \, a b + 12 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(9 \, a^{2} + 54 \, a b + 49 \, b^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(3 \, a^{2} + 26 \, a b + 23 \, b^{2}\right)} \cosh\left(x\right)^{4} + 30 \, {\left(3 \, a^{2} + 20 \, a b + 12 \, b^{2}\right)} \cosh\left(x\right)^{2} + 9 \, a^{2} + 54 \, a b + 49 \, b^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(3 \, a^{2} + 26 \, a b + 23 \, b^{2}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(3 \, a^{2} + 20 \, a b + 12 \, b^{2}\right)} \cosh\left(x\right)^{3} + {\left(9 \, a^{2} + 54 \, a b + 49 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(3 \, a^{2} + 20 \, a b + 12 \, b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(3 \, a^{2} + 26 \, a b + 23 \, b^{2}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(3 \, a^{2} + 20 \, a b + 12 \, b^{2}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(9 \, a^{2} + 54 \, a b + 49 \, b^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} + 20 \, a b + 12 \, b^{2}\right)} \sinh\left(x\right)^{2} + 3 \, a^{2} + 26 \, a b + 23 \, b^{2} + 8 \, {\left({\left(3 \, a^{2} + 26 \, a b + 23 \, b^{2}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(3 \, a^{2} + 20 \, a b + 12 \, b^{2}\right)} \cosh\left(x\right)^{5} + {\left(9 \, a^{2} + 54 \, a b + 49 \, b^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 20 \, a b + 12 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{60 \, {\left(b \cosh\left(x\right)^{10} + 10 \, b \cosh\left(x\right) \sinh\left(x\right)^{9} + b \sinh\left(x\right)^{10} + 5 \, b \cosh\left(x\right)^{8} + 5 \, {\left(9 \, b \cosh\left(x\right)^{2} + b\right)} \sinh\left(x\right)^{8} + 40 \, {\left(3 \, b \cosh\left(x\right)^{3} + b \cosh\left(x\right)\right)} \sinh\left(x\right)^{7} + 10 \, b \cosh\left(x\right)^{6} + 10 \, {\left(21 \, b \cosh\left(x\right)^{4} + 14 \, b \cosh\left(x\right)^{2} + b\right)} \sinh\left(x\right)^{6} + 4 \, {\left(63 \, b \cosh\left(x\right)^{5} + 70 \, b \cosh\left(x\right)^{3} + 15 \, b \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 10 \, b \cosh\left(x\right)^{4} + 10 \, {\left(21 \, b \cosh\left(x\right)^{6} + 35 \, b \cosh\left(x\right)^{4} + 15 \, b \cosh\left(x\right)^{2} + b\right)} \sinh\left(x\right)^{4} + 40 \, {\left(3 \, b \cosh\left(x\right)^{7} + 7 \, b \cosh\left(x\right)^{5} + 5 \, b \cosh\left(x\right)^{3} + b \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 5 \, b \cosh\left(x\right)^{2} + 5 \, {\left(9 \, b \cosh\left(x\right)^{8} + 28 \, b \cosh\left(x\right)^{6} + 30 \, b \cosh\left(x\right)^{4} + 12 \, b \cosh\left(x\right)^{2} + b\right)} \sinh\left(x\right)^{2} + 10 \, {\left(b \cosh\left(x\right)^{9} + 4 \, b \cosh\left(x\right)^{7} + 6 \, b \cosh\left(x\right)^{5} + 4 \, b \cosh\left(x\right)^{3} + b \cosh\left(x\right)\right)} \sinh\left(x\right) + b\right)}}, -\frac{15 \, {\left({\left(a b + b^{2}\right)} \cosh\left(x\right)^{10} + 10 \, {\left(a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{9} + {\left(a b + b^{2}\right)} \sinh\left(x\right)^{10} + 5 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{8} + 5 \, {\left(9 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} + a b + b^{2}\right)} \sinh\left(x\right)^{8} + 40 \, {\left(3 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a b + b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{7} + 10 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{6} + 10 \, {\left(21 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{4} + 14 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} + a b + b^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(63 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{5} + 70 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{3} + 15 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 10 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{4} + 10 \, {\left(21 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{6} + 35 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{4} + 15 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} + a b + b^{2}\right)} \sinh\left(x\right)^{4} + 40 \, {\left(3 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{7} + 7 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{5} + 5 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a b + b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 5 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} + 5 \, {\left(9 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{8} + 28 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{6} + 30 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{4} + 12 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} + a b + b^{2}\right)} \sinh\left(x\right)^{2} + a b + b^{2} + 10 \, {\left({\left(a b + b^{2}\right)} \cosh\left(x\right)^{9} + 4 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{7} + 6 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{5} + 4 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a b + b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(a \cosh\left(x\right)^{2} + 2 \, a \cosh\left(x\right) \sinh\left(x\right) + a \sinh\left(x\right)^{2} + a + b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a^{2} + a b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{2} + a b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{2} + a b\right)} \sinh\left(x\right)^{4} + {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} + 2 \, a^{2} + a b - b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(2 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + 15 \, {\left({\left(a b + b^{2}\right)} \cosh\left(x\right)^{10} + 10 \, {\left(a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{9} + {\left(a b + b^{2}\right)} \sinh\left(x\right)^{10} + 5 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{8} + 5 \, {\left(9 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} + a b + b^{2}\right)} \sinh\left(x\right)^{8} + 40 \, {\left(3 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a b + b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{7} + 10 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{6} + 10 \, {\left(21 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{4} + 14 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} + a b + b^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(63 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{5} + 70 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{3} + 15 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 10 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{4} + 10 \, {\left(21 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{6} + 35 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{4} + 15 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} + a b + b^{2}\right)} \sinh\left(x\right)^{4} + 40 \, {\left(3 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{7} + 7 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{5} + 5 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a b + b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 5 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} + 5 \, {\left(9 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{8} + 28 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{6} + 30 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{4} + 12 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} + a b + b^{2}\right)} \sinh\left(x\right)^{2} + a b + b^{2} + 10 \, {\left({\left(a b + b^{2}\right)} \cosh\left(x\right)^{9} + 4 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{7} + 6 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{5} + 4 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a b + b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) + 2 \, \sqrt{2} {\left({\left(3 \, a^{2} + 26 \, a b + 23 \, b^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(3 \, a^{2} + 26 \, a b + 23 \, b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(3 \, a^{2} + 26 \, a b + 23 \, b^{2}\right)} \sinh\left(x\right)^{8} + 4 \, {\left(3 \, a^{2} + 20 \, a b + 12 \, b^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(3 \, a^{2} + 26 \, a b + 23 \, b^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} + 20 \, a b + 12 \, b^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(3 \, a^{2} + 26 \, a b + 23 \, b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(3 \, a^{2} + 20 \, a b + 12 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(9 \, a^{2} + 54 \, a b + 49 \, b^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(3 \, a^{2} + 26 \, a b + 23 \, b^{2}\right)} \cosh\left(x\right)^{4} + 30 \, {\left(3 \, a^{2} + 20 \, a b + 12 \, b^{2}\right)} \cosh\left(x\right)^{2} + 9 \, a^{2} + 54 \, a b + 49 \, b^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(3 \, a^{2} + 26 \, a b + 23 \, b^{2}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(3 \, a^{2} + 20 \, a b + 12 \, b^{2}\right)} \cosh\left(x\right)^{3} + {\left(9 \, a^{2} + 54 \, a b + 49 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(3 \, a^{2} + 20 \, a b + 12 \, b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(3 \, a^{2} + 26 \, a b + 23 \, b^{2}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(3 \, a^{2} + 20 \, a b + 12 \, b^{2}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(9 \, a^{2} + 54 \, a b + 49 \, b^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} + 20 \, a b + 12 \, b^{2}\right)} \sinh\left(x\right)^{2} + 3 \, a^{2} + 26 \, a b + 23 \, b^{2} + 8 \, {\left({\left(3 \, a^{2} + 26 \, a b + 23 \, b^{2}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(3 \, a^{2} + 20 \, a b + 12 \, b^{2}\right)} \cosh\left(x\right)^{5} + {\left(9 \, a^{2} + 54 \, a b + 49 \, b^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 20 \, a b + 12 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{30 \, {\left(b \cosh\left(x\right)^{10} + 10 \, b \cosh\left(x\right) \sinh\left(x\right)^{9} + b \sinh\left(x\right)^{10} + 5 \, b \cosh\left(x\right)^{8} + 5 \, {\left(9 \, b \cosh\left(x\right)^{2} + b\right)} \sinh\left(x\right)^{8} + 40 \, {\left(3 \, b \cosh\left(x\right)^{3} + b \cosh\left(x\right)\right)} \sinh\left(x\right)^{7} + 10 \, b \cosh\left(x\right)^{6} + 10 \, {\left(21 \, b \cosh\left(x\right)^{4} + 14 \, b \cosh\left(x\right)^{2} + b\right)} \sinh\left(x\right)^{6} + 4 \, {\left(63 \, b \cosh\left(x\right)^{5} + 70 \, b \cosh\left(x\right)^{3} + 15 \, b \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 10 \, b \cosh\left(x\right)^{4} + 10 \, {\left(21 \, b \cosh\left(x\right)^{6} + 35 \, b \cosh\left(x\right)^{4} + 15 \, b \cosh\left(x\right)^{2} + b\right)} \sinh\left(x\right)^{4} + 40 \, {\left(3 \, b \cosh\left(x\right)^{7} + 7 \, b \cosh\left(x\right)^{5} + 5 \, b \cosh\left(x\right)^{3} + b \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 5 \, b \cosh\left(x\right)^{2} + 5 \, {\left(9 \, b \cosh\left(x\right)^{8} + 28 \, b \cosh\left(x\right)^{6} + 30 \, b \cosh\left(x\right)^{4} + 12 \, b \cosh\left(x\right)^{2} + b\right)} \sinh\left(x\right)^{2} + 10 \, {\left(b \cosh\left(x\right)^{9} + 4 \, b \cosh\left(x\right)^{7} + 6 \, b \cosh\left(x\right)^{5} + 4 \, b \cosh\left(x\right)^{3} + b \cosh\left(x\right)\right)} \sinh\left(x\right) + b\right)}}\right]"," ",0,"[1/60*(15*((a*b + b^2)*cosh(x)^10 + 10*(a*b + b^2)*cosh(x)*sinh(x)^9 + (a*b + b^2)*sinh(x)^10 + 5*(a*b + b^2)*cosh(x)^8 + 5*(9*(a*b + b^2)*cosh(x)^2 + a*b + b^2)*sinh(x)^8 + 40*(3*(a*b + b^2)*cosh(x)^3 + (a*b + b^2)*cosh(x))*sinh(x)^7 + 10*(a*b + b^2)*cosh(x)^6 + 10*(21*(a*b + b^2)*cosh(x)^4 + 14*(a*b + b^2)*cosh(x)^2 + a*b + b^2)*sinh(x)^6 + 4*(63*(a*b + b^2)*cosh(x)^5 + 70*(a*b + b^2)*cosh(x)^3 + 15*(a*b + b^2)*cosh(x))*sinh(x)^5 + 10*(a*b + b^2)*cosh(x)^4 + 10*(21*(a*b + b^2)*cosh(x)^6 + 35*(a*b + b^2)*cosh(x)^4 + 15*(a*b + b^2)*cosh(x)^2 + a*b + b^2)*sinh(x)^4 + 40*(3*(a*b + b^2)*cosh(x)^7 + 7*(a*b + b^2)*cosh(x)^5 + 5*(a*b + b^2)*cosh(x)^3 + (a*b + b^2)*cosh(x))*sinh(x)^3 + 5*(a*b + b^2)*cosh(x)^2 + 5*(9*(a*b + b^2)*cosh(x)^8 + 28*(a*b + b^2)*cosh(x)^6 + 30*(a*b + b^2)*cosh(x)^4 + 12*(a*b + b^2)*cosh(x)^2 + a*b + b^2)*sinh(x)^2 + a*b + b^2 + 10*((a*b + b^2)*cosh(x)^9 + 4*(a*b + b^2)*cosh(x)^7 + 6*(a*b + b^2)*cosh(x)^5 + 4*(a*b + b^2)*cosh(x)^3 + (a*b + b^2)*cosh(x))*sinh(x))*sqrt(a + b)*log(((a^3 + a^2*b)*cosh(x)^8 + 8*(a^3 + a^2*b)*cosh(x)*sinh(x)^7 + (a^3 + a^2*b)*sinh(x)^8 + 2*(2*a^3 + a^2*b)*cosh(x)^6 + 2*(2*a^3 + a^2*b + 14*(a^3 + a^2*b)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a^3 + a^2*b)*cosh(x)^3 + 3*(2*a^3 + a^2*b)*cosh(x))*sinh(x)^5 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^4 + (70*(a^3 + a^2*b)*cosh(x)^4 + 6*a^3 + 4*a^2*b - a*b^2 + b^3 + 30*(2*a^3 + a^2*b)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a^3 + a^2*b)*cosh(x)^5 + 10*(2*a^3 + a^2*b)*cosh(x)^3 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x))*sinh(x)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 + 2*(2*a^3 + 3*a^2*b - b^3)*cosh(x)^2 + 2*(14*(a^3 + a^2*b)*cosh(x)^6 + 15*(2*a^3 + a^2*b)*cosh(x)^4 + 2*a^3 + 3*a^2*b - b^3 + 3*(6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^2)*sinh(x)^2 + sqrt(2)*(a^2*cosh(x)^6 + 6*a^2*cosh(x)*sinh(x)^5 + a^2*sinh(x)^6 + 3*a^2*cosh(x)^4 + 3*(5*a^2*cosh(x)^2 + a^2)*sinh(x)^4 + 4*(5*a^2*cosh(x)^3 + 3*a^2*cosh(x))*sinh(x)^3 + (3*a^2 + 2*a*b - b^2)*cosh(x)^2 + (15*a^2*cosh(x)^4 + 18*a^2*cosh(x)^2 + 3*a^2 + 2*a*b - b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(3*a^2*cosh(x)^5 + 6*a^2*cosh(x)^3 + (3*a^2 + 2*a*b - b^2)*cosh(x))*sinh(x))*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a^3 + a^2*b)*cosh(x)^7 + 3*(2*a^3 + a^2*b)*cosh(x)^5 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^3 + (2*a^3 + 3*a^2*b - b^3)*cosh(x))*sinh(x))/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) + 15*((a*b + b^2)*cosh(x)^10 + 10*(a*b + b^2)*cosh(x)*sinh(x)^9 + (a*b + b^2)*sinh(x)^10 + 5*(a*b + b^2)*cosh(x)^8 + 5*(9*(a*b + b^2)*cosh(x)^2 + a*b + b^2)*sinh(x)^8 + 40*(3*(a*b + b^2)*cosh(x)^3 + (a*b + b^2)*cosh(x))*sinh(x)^7 + 10*(a*b + b^2)*cosh(x)^6 + 10*(21*(a*b + b^2)*cosh(x)^4 + 14*(a*b + b^2)*cosh(x)^2 + a*b + b^2)*sinh(x)^6 + 4*(63*(a*b + b^2)*cosh(x)^5 + 70*(a*b + b^2)*cosh(x)^3 + 15*(a*b + b^2)*cosh(x))*sinh(x)^5 + 10*(a*b + b^2)*cosh(x)^4 + 10*(21*(a*b + b^2)*cosh(x)^6 + 35*(a*b + b^2)*cosh(x)^4 + 15*(a*b + b^2)*cosh(x)^2 + a*b + b^2)*sinh(x)^4 + 40*(3*(a*b + b^2)*cosh(x)^7 + 7*(a*b + b^2)*cosh(x)^5 + 5*(a*b + b^2)*cosh(x)^3 + (a*b + b^2)*cosh(x))*sinh(x)^3 + 5*(a*b + b^2)*cosh(x)^2 + 5*(9*(a*b + b^2)*cosh(x)^8 + 28*(a*b + b^2)*cosh(x)^6 + 30*(a*b + b^2)*cosh(x)^4 + 12*(a*b + b^2)*cosh(x)^2 + a*b + b^2)*sinh(x)^2 + a*b + b^2 + 10*((a*b + b^2)*cosh(x)^9 + 4*(a*b + b^2)*cosh(x)^7 + 6*(a*b + b^2)*cosh(x)^5 + 4*(a*b + b^2)*cosh(x)^3 + (a*b + b^2)*cosh(x))*sinh(x))*sqrt(a + b)*log(-((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*b*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + b)*cosh(x)^3 - b*cosh(x))*sinh(x) + a + b)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) - 4*sqrt(2)*((3*a^2 + 26*a*b + 23*b^2)*cosh(x)^8 + 8*(3*a^2 + 26*a*b + 23*b^2)*cosh(x)*sinh(x)^7 + (3*a^2 + 26*a*b + 23*b^2)*sinh(x)^8 + 4*(3*a^2 + 20*a*b + 12*b^2)*cosh(x)^6 + 4*(7*(3*a^2 + 26*a*b + 23*b^2)*cosh(x)^2 + 3*a^2 + 20*a*b + 12*b^2)*sinh(x)^6 + 8*(7*(3*a^2 + 26*a*b + 23*b^2)*cosh(x)^3 + 3*(3*a^2 + 20*a*b + 12*b^2)*cosh(x))*sinh(x)^5 + 2*(9*a^2 + 54*a*b + 49*b^2)*cosh(x)^4 + 2*(35*(3*a^2 + 26*a*b + 23*b^2)*cosh(x)^4 + 30*(3*a^2 + 20*a*b + 12*b^2)*cosh(x)^2 + 9*a^2 + 54*a*b + 49*b^2)*sinh(x)^4 + 8*(7*(3*a^2 + 26*a*b + 23*b^2)*cosh(x)^5 + 10*(3*a^2 + 20*a*b + 12*b^2)*cosh(x)^3 + (9*a^2 + 54*a*b + 49*b^2)*cosh(x))*sinh(x)^3 + 4*(3*a^2 + 20*a*b + 12*b^2)*cosh(x)^2 + 4*(7*(3*a^2 + 26*a*b + 23*b^2)*cosh(x)^6 + 15*(3*a^2 + 20*a*b + 12*b^2)*cosh(x)^4 + 3*(9*a^2 + 54*a*b + 49*b^2)*cosh(x)^2 + 3*a^2 + 20*a*b + 12*b^2)*sinh(x)^2 + 3*a^2 + 26*a*b + 23*b^2 + 8*((3*a^2 + 26*a*b + 23*b^2)*cosh(x)^7 + 3*(3*a^2 + 20*a*b + 12*b^2)*cosh(x)^5 + (9*a^2 + 54*a*b + 49*b^2)*cosh(x)^3 + (3*a^2 + 20*a*b + 12*b^2)*cosh(x))*sinh(x))*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(b*cosh(x)^10 + 10*b*cosh(x)*sinh(x)^9 + b*sinh(x)^10 + 5*b*cosh(x)^8 + 5*(9*b*cosh(x)^2 + b)*sinh(x)^8 + 40*(3*b*cosh(x)^3 + b*cosh(x))*sinh(x)^7 + 10*b*cosh(x)^6 + 10*(21*b*cosh(x)^4 + 14*b*cosh(x)^2 + b)*sinh(x)^6 + 4*(63*b*cosh(x)^5 + 70*b*cosh(x)^3 + 15*b*cosh(x))*sinh(x)^5 + 10*b*cosh(x)^4 + 10*(21*b*cosh(x)^6 + 35*b*cosh(x)^4 + 15*b*cosh(x)^2 + b)*sinh(x)^4 + 40*(3*b*cosh(x)^7 + 7*b*cosh(x)^5 + 5*b*cosh(x)^3 + b*cosh(x))*sinh(x)^3 + 5*b*cosh(x)^2 + 5*(9*b*cosh(x)^8 + 28*b*cosh(x)^6 + 30*b*cosh(x)^4 + 12*b*cosh(x)^2 + b)*sinh(x)^2 + 10*(b*cosh(x)^9 + 4*b*cosh(x)^7 + 6*b*cosh(x)^5 + 4*b*cosh(x)^3 + b*cosh(x))*sinh(x) + b), -1/30*(15*((a*b + b^2)*cosh(x)^10 + 10*(a*b + b^2)*cosh(x)*sinh(x)^9 + (a*b + b^2)*sinh(x)^10 + 5*(a*b + b^2)*cosh(x)^8 + 5*(9*(a*b + b^2)*cosh(x)^2 + a*b + b^2)*sinh(x)^8 + 40*(3*(a*b + b^2)*cosh(x)^3 + (a*b + b^2)*cosh(x))*sinh(x)^7 + 10*(a*b + b^2)*cosh(x)^6 + 10*(21*(a*b + b^2)*cosh(x)^4 + 14*(a*b + b^2)*cosh(x)^2 + a*b + b^2)*sinh(x)^6 + 4*(63*(a*b + b^2)*cosh(x)^5 + 70*(a*b + b^2)*cosh(x)^3 + 15*(a*b + b^2)*cosh(x))*sinh(x)^5 + 10*(a*b + b^2)*cosh(x)^4 + 10*(21*(a*b + b^2)*cosh(x)^6 + 35*(a*b + b^2)*cosh(x)^4 + 15*(a*b + b^2)*cosh(x)^2 + a*b + b^2)*sinh(x)^4 + 40*(3*(a*b + b^2)*cosh(x)^7 + 7*(a*b + b^2)*cosh(x)^5 + 5*(a*b + b^2)*cosh(x)^3 + (a*b + b^2)*cosh(x))*sinh(x)^3 + 5*(a*b + b^2)*cosh(x)^2 + 5*(9*(a*b + b^2)*cosh(x)^8 + 28*(a*b + b^2)*cosh(x)^6 + 30*(a*b + b^2)*cosh(x)^4 + 12*(a*b + b^2)*cosh(x)^2 + a*b + b^2)*sinh(x)^2 + a*b + b^2 + 10*((a*b + b^2)*cosh(x)^9 + 4*(a*b + b^2)*cosh(x)^7 + 6*(a*b + b^2)*cosh(x)^5 + 4*(a*b + b^2)*cosh(x)^3 + (a*b + b^2)*cosh(x))*sinh(x))*sqrt(-a - b)*arctan(sqrt(2)*(a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 + a + b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a^2 + a*b)*cosh(x)^4 + 4*(a^2 + a*b)*cosh(x)*sinh(x)^3 + (a^2 + a*b)*sinh(x)^4 + (2*a^2 + a*b - b^2)*cosh(x)^2 + (6*(a^2 + a*b)*cosh(x)^2 + 2*a^2 + a*b - b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(2*(a^2 + a*b)*cosh(x)^3 + (2*a^2 + a*b - b^2)*cosh(x))*sinh(x))) + 15*((a*b + b^2)*cosh(x)^10 + 10*(a*b + b^2)*cosh(x)*sinh(x)^9 + (a*b + b^2)*sinh(x)^10 + 5*(a*b + b^2)*cosh(x)^8 + 5*(9*(a*b + b^2)*cosh(x)^2 + a*b + b^2)*sinh(x)^8 + 40*(3*(a*b + b^2)*cosh(x)^3 + (a*b + b^2)*cosh(x))*sinh(x)^7 + 10*(a*b + b^2)*cosh(x)^6 + 10*(21*(a*b + b^2)*cosh(x)^4 + 14*(a*b + b^2)*cosh(x)^2 + a*b + b^2)*sinh(x)^6 + 4*(63*(a*b + b^2)*cosh(x)^5 + 70*(a*b + b^2)*cosh(x)^3 + 15*(a*b + b^2)*cosh(x))*sinh(x)^5 + 10*(a*b + b^2)*cosh(x)^4 + 10*(21*(a*b + b^2)*cosh(x)^6 + 35*(a*b + b^2)*cosh(x)^4 + 15*(a*b + b^2)*cosh(x)^2 + a*b + b^2)*sinh(x)^4 + 40*(3*(a*b + b^2)*cosh(x)^7 + 7*(a*b + b^2)*cosh(x)^5 + 5*(a*b + b^2)*cosh(x)^3 + (a*b + b^2)*cosh(x))*sinh(x)^3 + 5*(a*b + b^2)*cosh(x)^2 + 5*(9*(a*b + b^2)*cosh(x)^8 + 28*(a*b + b^2)*cosh(x)^6 + 30*(a*b + b^2)*cosh(x)^4 + 12*(a*b + b^2)*cosh(x)^2 + a*b + b^2)*sinh(x)^2 + a*b + b^2 + 10*((a*b + b^2)*cosh(x)^9 + 4*(a*b + b^2)*cosh(x)^7 + 6*(a*b + b^2)*cosh(x)^5 + 4*(a*b + b^2)*cosh(x)^3 + (a*b + b^2)*cosh(x))*sinh(x))*sqrt(-a - b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a - b)*cosh(x))*sinh(x) + a + b)) + 2*sqrt(2)*((3*a^2 + 26*a*b + 23*b^2)*cosh(x)^8 + 8*(3*a^2 + 26*a*b + 23*b^2)*cosh(x)*sinh(x)^7 + (3*a^2 + 26*a*b + 23*b^2)*sinh(x)^8 + 4*(3*a^2 + 20*a*b + 12*b^2)*cosh(x)^6 + 4*(7*(3*a^2 + 26*a*b + 23*b^2)*cosh(x)^2 + 3*a^2 + 20*a*b + 12*b^2)*sinh(x)^6 + 8*(7*(3*a^2 + 26*a*b + 23*b^2)*cosh(x)^3 + 3*(3*a^2 + 20*a*b + 12*b^2)*cosh(x))*sinh(x)^5 + 2*(9*a^2 + 54*a*b + 49*b^2)*cosh(x)^4 + 2*(35*(3*a^2 + 26*a*b + 23*b^2)*cosh(x)^4 + 30*(3*a^2 + 20*a*b + 12*b^2)*cosh(x)^2 + 9*a^2 + 54*a*b + 49*b^2)*sinh(x)^4 + 8*(7*(3*a^2 + 26*a*b + 23*b^2)*cosh(x)^5 + 10*(3*a^2 + 20*a*b + 12*b^2)*cosh(x)^3 + (9*a^2 + 54*a*b + 49*b^2)*cosh(x))*sinh(x)^3 + 4*(3*a^2 + 20*a*b + 12*b^2)*cosh(x)^2 + 4*(7*(3*a^2 + 26*a*b + 23*b^2)*cosh(x)^6 + 15*(3*a^2 + 20*a*b + 12*b^2)*cosh(x)^4 + 3*(9*a^2 + 54*a*b + 49*b^2)*cosh(x)^2 + 3*a^2 + 20*a*b + 12*b^2)*sinh(x)^2 + 3*a^2 + 26*a*b + 23*b^2 + 8*((3*a^2 + 26*a*b + 23*b^2)*cosh(x)^7 + 3*(3*a^2 + 20*a*b + 12*b^2)*cosh(x)^5 + (9*a^2 + 54*a*b + 49*b^2)*cosh(x)^3 + (3*a^2 + 20*a*b + 12*b^2)*cosh(x))*sinh(x))*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(b*cosh(x)^10 + 10*b*cosh(x)*sinh(x)^9 + b*sinh(x)^10 + 5*b*cosh(x)^8 + 5*(9*b*cosh(x)^2 + b)*sinh(x)^8 + 40*(3*b*cosh(x)^3 + b*cosh(x))*sinh(x)^7 + 10*b*cosh(x)^6 + 10*(21*b*cosh(x)^4 + 14*b*cosh(x)^2 + b)*sinh(x)^6 + 4*(63*b*cosh(x)^5 + 70*b*cosh(x)^3 + 15*b*cosh(x))*sinh(x)^5 + 10*b*cosh(x)^4 + 10*(21*b*cosh(x)^6 + 35*b*cosh(x)^4 + 15*b*cosh(x)^2 + b)*sinh(x)^4 + 40*(3*b*cosh(x)^7 + 7*b*cosh(x)^5 + 5*b*cosh(x)^3 + b*cosh(x))*sinh(x)^3 + 5*b*cosh(x)^2 + 5*(9*b*cosh(x)^8 + 28*b*cosh(x)^6 + 30*b*cosh(x)^4 + 12*b*cosh(x)^2 + b)*sinh(x)^2 + 10*(b*cosh(x)^9 + 4*b*cosh(x)^7 + 6*b*cosh(x)^5 + 4*b*cosh(x)^3 + b*cosh(x))*sinh(x) + b)]","B",0
220,-1,0,0,0.000000," ","integrate(tanh(x)^2*(a+b*tanh(x)^2)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
221,1,2385,0,2.123658," ","integrate(tanh(x)*(a+b*tanh(x)^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{6} + 6 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(a + b\right)} \sinh\left(x\right)^{6} + 3 \, {\left(a + b\right)} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a + b\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, {\left(a + b\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + 3 \, {\left(5 \, {\left(a + b\right)} \cosh\left(x\right)^{4} + 6 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a + b\right)} \sinh\left(x\right)^{2} + 6 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{5} + 2 \, {\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b\right)} \sqrt{a + b} \log\left(\frac{{\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{3} + a^{2} b\right)} \sinh\left(x\right)^{8} + 2 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} + 2 \, {\left(2 \, a^{3} + a^{2} b + 14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} + 3 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3} + 30 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} + 10 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} + 2 \, {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} + 15 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 2 \, a^{3} + 3 \, a^{2} b - b^{3} + 3 \, {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(a^{2} \cosh\left(x\right)^{6} + 6 \, a^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + a^{2} \sinh\left(x\right)^{6} + 3 \, a^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, a^{2} \cosh\left(x\right)^{2} + a^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, a^{2} \cosh\left(x\right)^{3} + 3 \, a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, a^{2} \cosh\left(x\right)^{4} + 18 \, a^{2} \cosh\left(x\right)^{2} + 3 \, a^{2} + 2 \, a b - b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(x\right)^{5} + 6 \, a^{2} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{7} + 3 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) + 3 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{6} + 6 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(a + b\right)} \sinh\left(x\right)^{6} + 3 \, {\left(a + b\right)} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a + b\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, {\left(a + b\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + 3 \, {\left(5 \, {\left(a + b\right)} \cosh\left(x\right)^{4} + 6 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a + b\right)} \sinh\left(x\right)^{2} + 6 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{5} + 2 \, {\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b\right)} \sqrt{a + b} \log\left(-\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - b\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - b \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right) - 16 \, \sqrt{2} {\left({\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + {\left(2 \, a + b\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, a + b\right)} \sinh\left(x\right)^{2} + 2 \, {\left(2 \, {\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(2 \, a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{12 \, {\left(\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6} + 3 \, {\left(5 \, \cosh\left(x\right)^{2} + 1\right)} \sinh\left(x\right)^{4} + 3 \, \cosh\left(x\right)^{4} + 4 \, {\left(5 \, \cosh\left(x\right)^{3} + 3 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 3 \, {\left(5 \, \cosh\left(x\right)^{4} + 6 \, \cosh\left(x\right)^{2} + 1\right)} \sinh\left(x\right)^{2} + 3 \, \cosh\left(x\right)^{2} + 6 \, {\left(\cosh\left(x\right)^{5} + 2 \, \cosh\left(x\right)^{3} + \cosh\left(x\right)\right)} \sinh\left(x\right) + 1\right)}}, -\frac{3 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{6} + 6 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(a + b\right)} \sinh\left(x\right)^{6} + 3 \, {\left(a + b\right)} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a + b\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, {\left(a + b\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + 3 \, {\left(5 \, {\left(a + b\right)} \cosh\left(x\right)^{4} + 6 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a + b\right)} \sinh\left(x\right)^{2} + 6 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{5} + 2 \, {\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(a \cosh\left(x\right)^{2} + 2 \, a \cosh\left(x\right) \sinh\left(x\right) + a \sinh\left(x\right)^{2} + a + b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a^{2} + a b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{2} + a b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{2} + a b\right)} \sinh\left(x\right)^{4} + {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} + 2 \, a^{2} + a b - b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(2 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + 3 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{6} + 6 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(a + b\right)} \sinh\left(x\right)^{6} + 3 \, {\left(a + b\right)} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a + b\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, {\left(a + b\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + 3 \, {\left(5 \, {\left(a + b\right)} \cosh\left(x\right)^{4} + 6 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a + b\right)} \sinh\left(x\right)^{2} + 6 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{5} + 2 \, {\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) + 8 \, \sqrt{2} {\left({\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + {\left(2 \, a + b\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, a + b\right)} \sinh\left(x\right)^{2} + 2 \, {\left(2 \, {\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(2 \, a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\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)^{6} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6} + 3 \, {\left(5 \, \cosh\left(x\right)^{2} + 1\right)} \sinh\left(x\right)^{4} + 3 \, \cosh\left(x\right)^{4} + 4 \, {\left(5 \, \cosh\left(x\right)^{3} + 3 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 3 \, {\left(5 \, \cosh\left(x\right)^{4} + 6 \, \cosh\left(x\right)^{2} + 1\right)} \sinh\left(x\right)^{2} + 3 \, \cosh\left(x\right)^{2} + 6 \, {\left(\cosh\left(x\right)^{5} + 2 \, \cosh\left(x\right)^{3} + \cosh\left(x\right)\right)} \sinh\left(x\right) + 1\right)}}\right]"," ",0,"[1/12*(3*((a + b)*cosh(x)^6 + 6*(a + b)*cosh(x)*sinh(x)^5 + (a + b)*sinh(x)^6 + 3*(a + b)*cosh(x)^4 + 3*(5*(a + b)*cosh(x)^2 + a + b)*sinh(x)^4 + 4*(5*(a + b)*cosh(x)^3 + 3*(a + b)*cosh(x))*sinh(x)^3 + 3*(a + b)*cosh(x)^2 + 3*(5*(a + b)*cosh(x)^4 + 6*(a + b)*cosh(x)^2 + a + b)*sinh(x)^2 + 6*((a + b)*cosh(x)^5 + 2*(a + b)*cosh(x)^3 + (a + b)*cosh(x))*sinh(x) + a + b)*sqrt(a + b)*log(((a^3 + a^2*b)*cosh(x)^8 + 8*(a^3 + a^2*b)*cosh(x)*sinh(x)^7 + (a^3 + a^2*b)*sinh(x)^8 + 2*(2*a^3 + a^2*b)*cosh(x)^6 + 2*(2*a^3 + a^2*b + 14*(a^3 + a^2*b)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a^3 + a^2*b)*cosh(x)^3 + 3*(2*a^3 + a^2*b)*cosh(x))*sinh(x)^5 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^4 + (70*(a^3 + a^2*b)*cosh(x)^4 + 6*a^3 + 4*a^2*b - a*b^2 + b^3 + 30*(2*a^3 + a^2*b)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a^3 + a^2*b)*cosh(x)^5 + 10*(2*a^3 + a^2*b)*cosh(x)^3 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x))*sinh(x)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 + 2*(2*a^3 + 3*a^2*b - b^3)*cosh(x)^2 + 2*(14*(a^3 + a^2*b)*cosh(x)^6 + 15*(2*a^3 + a^2*b)*cosh(x)^4 + 2*a^3 + 3*a^2*b - b^3 + 3*(6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^2)*sinh(x)^2 + sqrt(2)*(a^2*cosh(x)^6 + 6*a^2*cosh(x)*sinh(x)^5 + a^2*sinh(x)^6 + 3*a^2*cosh(x)^4 + 3*(5*a^2*cosh(x)^2 + a^2)*sinh(x)^4 + 4*(5*a^2*cosh(x)^3 + 3*a^2*cosh(x))*sinh(x)^3 + (3*a^2 + 2*a*b - b^2)*cosh(x)^2 + (15*a^2*cosh(x)^4 + 18*a^2*cosh(x)^2 + 3*a^2 + 2*a*b - b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(3*a^2*cosh(x)^5 + 6*a^2*cosh(x)^3 + (3*a^2 + 2*a*b - b^2)*cosh(x))*sinh(x))*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a^3 + a^2*b)*cosh(x)^7 + 3*(2*a^3 + a^2*b)*cosh(x)^5 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^3 + (2*a^3 + 3*a^2*b - b^3)*cosh(x))*sinh(x))/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) + 3*((a + b)*cosh(x)^6 + 6*(a + b)*cosh(x)*sinh(x)^5 + (a + b)*sinh(x)^6 + 3*(a + b)*cosh(x)^4 + 3*(5*(a + b)*cosh(x)^2 + a + b)*sinh(x)^4 + 4*(5*(a + b)*cosh(x)^3 + 3*(a + b)*cosh(x))*sinh(x)^3 + 3*(a + b)*cosh(x)^2 + 3*(5*(a + b)*cosh(x)^4 + 6*(a + b)*cosh(x)^2 + a + b)*sinh(x)^2 + 6*((a + b)*cosh(x)^5 + 2*(a + b)*cosh(x)^3 + (a + b)*cosh(x))*sinh(x) + a + b)*sqrt(a + b)*log(-((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*b*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + b)*cosh(x)^3 - b*cosh(x))*sinh(x) + a + b)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) - 16*sqrt(2)*((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + (2*a + b)*cosh(x)^2 + (6*(a + b)*cosh(x)^2 + 2*a + b)*sinh(x)^2 + 2*(2*(a + b)*cosh(x)^3 + (2*a + b)*cosh(x))*sinh(x) + a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(cosh(x)^6 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6 + 3*(5*cosh(x)^2 + 1)*sinh(x)^4 + 3*cosh(x)^4 + 4*(5*cosh(x)^3 + 3*cosh(x))*sinh(x)^3 + 3*(5*cosh(x)^4 + 6*cosh(x)^2 + 1)*sinh(x)^2 + 3*cosh(x)^2 + 6*(cosh(x)^5 + 2*cosh(x)^3 + cosh(x))*sinh(x) + 1), -1/6*(3*((a + b)*cosh(x)^6 + 6*(a + b)*cosh(x)*sinh(x)^5 + (a + b)*sinh(x)^6 + 3*(a + b)*cosh(x)^4 + 3*(5*(a + b)*cosh(x)^2 + a + b)*sinh(x)^4 + 4*(5*(a + b)*cosh(x)^3 + 3*(a + b)*cosh(x))*sinh(x)^3 + 3*(a + b)*cosh(x)^2 + 3*(5*(a + b)*cosh(x)^4 + 6*(a + b)*cosh(x)^2 + a + b)*sinh(x)^2 + 6*((a + b)*cosh(x)^5 + 2*(a + b)*cosh(x)^3 + (a + b)*cosh(x))*sinh(x) + a + b)*sqrt(-a - b)*arctan(sqrt(2)*(a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 + a + b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a^2 + a*b)*cosh(x)^4 + 4*(a^2 + a*b)*cosh(x)*sinh(x)^3 + (a^2 + a*b)*sinh(x)^4 + (2*a^2 + a*b - b^2)*cosh(x)^2 + (6*(a^2 + a*b)*cosh(x)^2 + 2*a^2 + a*b - b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(2*(a^2 + a*b)*cosh(x)^3 + (2*a^2 + a*b - b^2)*cosh(x))*sinh(x))) + 3*((a + b)*cosh(x)^6 + 6*(a + b)*cosh(x)*sinh(x)^5 + (a + b)*sinh(x)^6 + 3*(a + b)*cosh(x)^4 + 3*(5*(a + b)*cosh(x)^2 + a + b)*sinh(x)^4 + 4*(5*(a + b)*cosh(x)^3 + 3*(a + b)*cosh(x))*sinh(x)^3 + 3*(a + b)*cosh(x)^2 + 3*(5*(a + b)*cosh(x)^4 + 6*(a + b)*cosh(x)^2 + a + b)*sinh(x)^2 + 6*((a + b)*cosh(x)^5 + 2*(a + b)*cosh(x)^3 + (a + b)*cosh(x))*sinh(x) + a + b)*sqrt(-a - b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a - b)*cosh(x))*sinh(x) + a + b)) + 8*sqrt(2)*((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + (2*a + b)*cosh(x)^2 + (6*(a + b)*cosh(x)^2 + 2*a + b)*sinh(x)^2 + 2*(2*(a + b)*cosh(x)^3 + (2*a + b)*cosh(x))*sinh(x) + a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(cosh(x)^6 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6 + 3*(5*cosh(x)^2 + 1)*sinh(x)^4 + 3*cosh(x)^4 + 4*(5*cosh(x)^3 + 3*cosh(x))*sinh(x)^3 + 3*(5*cosh(x)^4 + 6*cosh(x)^2 + 1)*sinh(x)^2 + 3*cosh(x)^2 + 6*(cosh(x)^5 + 2*cosh(x)^3 + cosh(x))*sinh(x) + 1)]","B",0
222,1,4841,0,3.054903," ","integrate((a+b*tanh(x)^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b\right)} \sqrt{a + b} \log\left(-\frac{{\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a b^{2} + b^{3}\right)} \sinh\left(x\right)^{8} - 2 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{6} - 2 \, {\left(a b^{2} + 2 \, b^{3} - 14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3} - 30 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} + 2 \, {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} - 3 \, a b^{2} - 2 \, b^{3} + 3 \, {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(b^{2} \cosh\left(x\right)^{6} + 6 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + b^{2} \sinh\left(x\right)^{6} - 3 \, b^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, b^{2} \cosh\left(x\right)^{2} - b^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, b^{2} \cosh\left(x\right)^{3} - 3 \, b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, b^{2} \cosh\left(x\right)^{4} - 18 \, b^{2} \cosh\left(x\right)^{2} - a^{2} + 2 \, a b + 3 \, b^{2}\right)} \sinh\left(x\right)^{2} - a^{2} - 2 \, a b - b^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{5} - 6 \, b^{2} \cosh\left(x\right)^{3} - {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{5} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) + {\left({\left(3 \, a + 2 \, b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(3 \, a + 2 \, b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(3 \, a + 2 \, b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(3 \, a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(3 \, a + 2 \, b\right)} \cosh\left(x\right)^{2} + 3 \, a + 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(3 \, a + 2 \, b\right)} \cosh\left(x\right)^{3} + {\left(3 \, a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + 3 \, a + 2 \, b\right)} \sqrt{b} \log\left(-\frac{{\left(a + 2 \, b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + 2 \, b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + a - 2 \, b\right)} \sinh\left(x\right)^{2} - 2 \, \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + 2 \, b\right)} \cosh\left(x\right)^{3} + {\left(a - 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + 2 \, b}{\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) + {\left({\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b\right)} \sqrt{a + b} \log\left(\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, a \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + a \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right) - 2 \, \sqrt{2} {\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} - b\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{4 \, {\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)}}, \frac{2 \, {\left({\left(3 \, a + 2 \, b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(3 \, a + 2 \, b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(3 \, a + 2 \, b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(3 \, a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(3 \, a + 2 \, b\right)} \cosh\left(x\right)^{2} + 3 \, a + 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(3 \, a + 2 \, b\right)} \cosh\left(x\right)^{3} + {\left(3 \, a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + 3 \, a + 2 \, b\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{-b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) + {\left({\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b\right)} \sqrt{a + b} \log\left(-\frac{{\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a b^{2} + b^{3}\right)} \sinh\left(x\right)^{8} - 2 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{6} - 2 \, {\left(a b^{2} + 2 \, b^{3} - 14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3} - 30 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} + 2 \, {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} - 3 \, a b^{2} - 2 \, b^{3} + 3 \, {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(b^{2} \cosh\left(x\right)^{6} + 6 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + b^{2} \sinh\left(x\right)^{6} - 3 \, b^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, b^{2} \cosh\left(x\right)^{2} - b^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, b^{2} \cosh\left(x\right)^{3} - 3 \, b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, b^{2} \cosh\left(x\right)^{4} - 18 \, b^{2} \cosh\left(x\right)^{2} - a^{2} + 2 \, a b + 3 \, b^{2}\right)} \sinh\left(x\right)^{2} - a^{2} - 2 \, a b - b^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{5} - 6 \, b^{2} \cosh\left(x\right)^{3} - {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{5} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) + {\left({\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b\right)} \sqrt{a + b} \log\left(\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, a \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + a \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right) - 2 \, \sqrt{2} {\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} - b\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{4 \, {\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)}}, -\frac{2 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} - a - b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a b + b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a b + b^{2}\right)} \sinh\left(x\right)^{4} + {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} - a b - 2 \, b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(2 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + 2 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a + b\right)} \sinh\left(x\right)^{2} + a + b}\right) - {\left({\left(3 \, a + 2 \, b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(3 \, a + 2 \, b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(3 \, a + 2 \, b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(3 \, a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(3 \, a + 2 \, b\right)} \cosh\left(x\right)^{2} + 3 \, a + 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(3 \, a + 2 \, b\right)} \cosh\left(x\right)^{3} + {\left(3 \, a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + 3 \, a + 2 \, b\right)} \sqrt{b} \log\left(-\frac{{\left(a + 2 \, b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + 2 \, b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + a - 2 \, b\right)} \sinh\left(x\right)^{2} - 2 \, \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + 2 \, b\right)} \cosh\left(x\right)^{3} + {\left(a - 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + 2 \, b}{\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) + 2 \, \sqrt{2} {\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} - b\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{4 \, {\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)}}, -\frac{{\left({\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} - a - b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a b + b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a b + b^{2}\right)} \sinh\left(x\right)^{4} + {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} - a b - 2 \, b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(2 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) - {\left({\left(3 \, a + 2 \, b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(3 \, a + 2 \, b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(3 \, a + 2 \, b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(3 \, a + 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(3 \, a + 2 \, b\right)} \cosh\left(x\right)^{2} + 3 \, a + 2 \, b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(3 \, a + 2 \, b\right)} \cosh\left(x\right)^{3} + {\left(3 \, a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + 3 \, a + 2 \, b\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{-b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) + {\left({\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a + b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a + b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a + b\right)} \sinh\left(x\right)^{2} + a + b}\right) + \sqrt{2} {\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} - b\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{2 \, {\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)}}\right]"," ",0,"[1/4*(((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a + b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a + b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a + b)*cosh(x))*sinh(x) + a + b)*sqrt(a + b)*log(-((a*b^2 + b^3)*cosh(x)^8 + 8*(a*b^2 + b^3)*cosh(x)*sinh(x)^7 + (a*b^2 + b^3)*sinh(x)^8 - 2*(a*b^2 + 2*b^3)*cosh(x)^6 - 2*(a*b^2 + 2*b^3 - 14*(a*b^2 + b^3)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a*b^2 + b^3)*cosh(x)^3 - 3*(a*b^2 + 2*b^3)*cosh(x))*sinh(x)^5 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^4 + (70*(a*b^2 + b^3)*cosh(x)^4 + a^3 - a^2*b + 4*a*b^2 + 6*b^3 - 30*(a*b^2 + 2*b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a*b^2 + b^3)*cosh(x)^5 - 10*(a*b^2 + 2*b^3)*cosh(x)^3 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x))*sinh(x)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 + 2*(a^3 - 3*a*b^2 - 2*b^3)*cosh(x)^2 + 2*(14*(a*b^2 + b^3)*cosh(x)^6 - 15*(a*b^2 + 2*b^3)*cosh(x)^4 + a^3 - 3*a*b^2 - 2*b^3 + 3*(a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^2)*sinh(x)^2 + sqrt(2)*(b^2*cosh(x)^6 + 6*b^2*cosh(x)*sinh(x)^5 + b^2*sinh(x)^6 - 3*b^2*cosh(x)^4 + 3*(5*b^2*cosh(x)^2 - b^2)*sinh(x)^4 + 4*(5*b^2*cosh(x)^3 - 3*b^2*cosh(x))*sinh(x)^3 - (a^2 - 2*a*b - 3*b^2)*cosh(x)^2 + (15*b^2*cosh(x)^4 - 18*b^2*cosh(x)^2 - a^2 + 2*a*b + 3*b^2)*sinh(x)^2 - a^2 - 2*a*b - b^2 + 2*(3*b^2*cosh(x)^5 - 6*b^2*cosh(x)^3 - (a^2 - 2*a*b - 3*b^2)*cosh(x))*sinh(x))*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a*b^2 + b^3)*cosh(x)^7 - 3*(a*b^2 + 2*b^3)*cosh(x)^5 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^3 + (a^3 - 3*a*b^2 - 2*b^3)*cosh(x))*sinh(x))/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) + ((3*a + 2*b)*cosh(x)^4 + 4*(3*a + 2*b)*cosh(x)*sinh(x)^3 + (3*a + 2*b)*sinh(x)^4 + 2*(3*a + 2*b)*cosh(x)^2 + 2*(3*(3*a + 2*b)*cosh(x)^2 + 3*a + 2*b)*sinh(x)^2 + 4*((3*a + 2*b)*cosh(x)^3 + (3*a + 2*b)*cosh(x))*sinh(x) + 3*a + 2*b)*sqrt(b)*log(-((a + 2*b)*cosh(x)^4 + 4*(a + 2*b)*cosh(x)*sinh(x)^3 + (a + 2*b)*sinh(x)^4 + 2*(a - 2*b)*cosh(x)^2 + 2*(3*(a + 2*b)*cosh(x)^2 + a - 2*b)*sinh(x)^2 - 2*sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + 2*b)*cosh(x)^3 + (a - 2*b)*cosh(x))*sinh(x) + a + 2*b)/(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)) + ((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a + b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a + b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a + b)*cosh(x))*sinh(x) + a + b)*sqrt(a + b)*log(((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*a*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + b)*cosh(x)^3 + a*cosh(x))*sinh(x) + a + b)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) - 2*sqrt(2)*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(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), 1/4*(2*((3*a + 2*b)*cosh(x)^4 + 4*(3*a + 2*b)*cosh(x)*sinh(x)^3 + (3*a + 2*b)*sinh(x)^4 + 2*(3*a + 2*b)*cosh(x)^2 + 2*(3*(3*a + 2*b)*cosh(x)^2 + 3*a + 2*b)*sinh(x)^2 + 4*((3*a + 2*b)*cosh(x)^3 + (3*a + 2*b)*cosh(x))*sinh(x) + 3*a + 2*b)*sqrt(-b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a - b)*cosh(x))*sinh(x) + a + b)) + ((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a + b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a + b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a + b)*cosh(x))*sinh(x) + a + b)*sqrt(a + b)*log(-((a*b^2 + b^3)*cosh(x)^8 + 8*(a*b^2 + b^3)*cosh(x)*sinh(x)^7 + (a*b^2 + b^3)*sinh(x)^8 - 2*(a*b^2 + 2*b^3)*cosh(x)^6 - 2*(a*b^2 + 2*b^3 - 14*(a*b^2 + b^3)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a*b^2 + b^3)*cosh(x)^3 - 3*(a*b^2 + 2*b^3)*cosh(x))*sinh(x)^5 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^4 + (70*(a*b^2 + b^3)*cosh(x)^4 + a^3 - a^2*b + 4*a*b^2 + 6*b^3 - 30*(a*b^2 + 2*b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a*b^2 + b^3)*cosh(x)^5 - 10*(a*b^2 + 2*b^3)*cosh(x)^3 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x))*sinh(x)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 + 2*(a^3 - 3*a*b^2 - 2*b^3)*cosh(x)^2 + 2*(14*(a*b^2 + b^3)*cosh(x)^6 - 15*(a*b^2 + 2*b^3)*cosh(x)^4 + a^3 - 3*a*b^2 - 2*b^3 + 3*(a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^2)*sinh(x)^2 + sqrt(2)*(b^2*cosh(x)^6 + 6*b^2*cosh(x)*sinh(x)^5 + b^2*sinh(x)^6 - 3*b^2*cosh(x)^4 + 3*(5*b^2*cosh(x)^2 - b^2)*sinh(x)^4 + 4*(5*b^2*cosh(x)^3 - 3*b^2*cosh(x))*sinh(x)^3 - (a^2 - 2*a*b - 3*b^2)*cosh(x)^2 + (15*b^2*cosh(x)^4 - 18*b^2*cosh(x)^2 - a^2 + 2*a*b + 3*b^2)*sinh(x)^2 - a^2 - 2*a*b - b^2 + 2*(3*b^2*cosh(x)^5 - 6*b^2*cosh(x)^3 - (a^2 - 2*a*b - 3*b^2)*cosh(x))*sinh(x))*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a*b^2 + b^3)*cosh(x)^7 - 3*(a*b^2 + 2*b^3)*cosh(x)^5 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^3 + (a^3 - 3*a*b^2 - 2*b^3)*cosh(x))*sinh(x))/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) + ((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a + b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a + b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a + b)*cosh(x))*sinh(x) + a + b)*sqrt(a + b)*log(((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*a*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + b)*cosh(x)^3 + a*cosh(x))*sinh(x) + a + b)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) - 2*sqrt(2)*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(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), -1/4*(2*((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a + b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a + b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a + b)*cosh(x))*sinh(x) + a + b)*sqrt(-a - b)*arctan(sqrt(2)*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 - a - b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a*b + b^2)*cosh(x)^4 + 4*(a*b + b^2)*cosh(x)*sinh(x)^3 + (a*b + b^2)*sinh(x)^4 + (a^2 - a*b - 2*b^2)*cosh(x)^2 + (6*(a*b + b^2)*cosh(x)^2 + a^2 - a*b - 2*b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(2*(a*b + b^2)*cosh(x)^3 + (a^2 - a*b - 2*b^2)*cosh(x))*sinh(x))) + 2*((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a + b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a + b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a + b)*cosh(x))*sinh(x) + a + b)*sqrt(-a - b)*arctan(sqrt(2)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 + a + b)) - ((3*a + 2*b)*cosh(x)^4 + 4*(3*a + 2*b)*cosh(x)*sinh(x)^3 + (3*a + 2*b)*sinh(x)^4 + 2*(3*a + 2*b)*cosh(x)^2 + 2*(3*(3*a + 2*b)*cosh(x)^2 + 3*a + 2*b)*sinh(x)^2 + 4*((3*a + 2*b)*cosh(x)^3 + (3*a + 2*b)*cosh(x))*sinh(x) + 3*a + 2*b)*sqrt(b)*log(-((a + 2*b)*cosh(x)^4 + 4*(a + 2*b)*cosh(x)*sinh(x)^3 + (a + 2*b)*sinh(x)^4 + 2*(a - 2*b)*cosh(x)^2 + 2*(3*(a + 2*b)*cosh(x)^2 + a - 2*b)*sinh(x)^2 - 2*sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + 2*b)*cosh(x)^3 + (a - 2*b)*cosh(x))*sinh(x) + a + 2*b)/(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)) + 2*sqrt(2)*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(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), -1/2*(((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a + b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a + b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a + b)*cosh(x))*sinh(x) + a + b)*sqrt(-a - b)*arctan(sqrt(2)*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 - a - b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a*b + b^2)*cosh(x)^4 + 4*(a*b + b^2)*cosh(x)*sinh(x)^3 + (a*b + b^2)*sinh(x)^4 + (a^2 - a*b - 2*b^2)*cosh(x)^2 + (6*(a*b + b^2)*cosh(x)^2 + a^2 - a*b - 2*b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(2*(a*b + b^2)*cosh(x)^3 + (a^2 - a*b - 2*b^2)*cosh(x))*sinh(x))) - ((3*a + 2*b)*cosh(x)^4 + 4*(3*a + 2*b)*cosh(x)*sinh(x)^3 + (3*a + 2*b)*sinh(x)^4 + 2*(3*a + 2*b)*cosh(x)^2 + 2*(3*(3*a + 2*b)*cosh(x)^2 + 3*a + 2*b)*sinh(x)^2 + 4*((3*a + 2*b)*cosh(x)^3 + (3*a + 2*b)*cosh(x))*sinh(x) + 3*a + 2*b)*sqrt(-b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a - b)*cosh(x))*sinh(x) + a + b)) + ((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a + b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a + b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a + b)*cosh(x))*sinh(x) + a + b)*sqrt(-a - b)*arctan(sqrt(2)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 + a + b)) + sqrt(2)*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(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)]","B",0
223,1,4039,0,0.645007," ","integrate(coth(x)*(a+b*tanh(x)^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a + b\right)} \sinh\left(x\right)^{2} + a + b\right)} \sqrt{a + b} \log\left(\frac{{\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{3} + a^{2} b\right)} \sinh\left(x\right)^{8} + 2 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} + 2 \, {\left(2 \, a^{3} + a^{2} b + 14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} + 3 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3} + 30 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} + 10 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} + 2 \, {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} + 15 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 2 \, a^{3} + 3 \, a^{2} b - b^{3} + 3 \, {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(a^{2} \cosh\left(x\right)^{6} + 6 \, a^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + a^{2} \sinh\left(x\right)^{6} + 3 \, a^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, a^{2} \cosh\left(x\right)^{2} + a^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, a^{2} \cosh\left(x\right)^{3} + 3 \, a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, a^{2} \cosh\left(x\right)^{4} + 18 \, a^{2} \cosh\left(x\right)^{2} + 3 \, a^{2} + 2 \, a b - b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(x\right)^{5} + 6 \, a^{2} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{7} + 3 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) + 2 \, {\left(a \cosh\left(x\right)^{2} + 2 \, a \cosh\left(x\right) \sinh\left(x\right) + a \sinh\left(x\right)^{2} + a\right)} \sqrt{a} \log\left(-\frac{{\left(2 \, a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(2 \, a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(2 \, a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(2 \, a + b\right)} \cosh\left(x\right)^{2} + 2 \, a - b\right)} \sinh\left(x\right)^{2} - 2 \, \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{a} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(2 \, a + b\right)} \cosh\left(x\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + 2 \, a + b}{\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) + {\left({\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a + b\right)} \sinh\left(x\right)^{2} + a + b\right)} \sqrt{a + b} \log\left(-\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - b\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - b \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right) - 4 \, \sqrt{2} b \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{4 \, {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)}}, \frac{4 \, {\left(a \cosh\left(x\right)^{2} + 2 \, a \cosh\left(x\right) \sinh\left(x\right) + a \sinh\left(x\right)^{2} + a\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{-a} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) + {\left({\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a + b\right)} \sinh\left(x\right)^{2} + a + b\right)} \sqrt{a + b} \log\left(\frac{{\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{3} + a^{2} b\right)} \sinh\left(x\right)^{8} + 2 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} + 2 \, {\left(2 \, a^{3} + a^{2} b + 14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} + 3 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3} + 30 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} + 10 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} + 2 \, {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} + 15 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 2 \, a^{3} + 3 \, a^{2} b - b^{3} + 3 \, {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(a^{2} \cosh\left(x\right)^{6} + 6 \, a^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + a^{2} \sinh\left(x\right)^{6} + 3 \, a^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, a^{2} \cosh\left(x\right)^{2} + a^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, a^{2} \cosh\left(x\right)^{3} + 3 \, a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, a^{2} \cosh\left(x\right)^{4} + 18 \, a^{2} \cosh\left(x\right)^{2} + 3 \, a^{2} + 2 \, a b - b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(x\right)^{5} + 6 \, a^{2} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{7} + 3 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) + {\left({\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a + b\right)} \sinh\left(x\right)^{2} + a + b\right)} \sqrt{a + b} \log\left(-\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - b\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - b \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right) - 4 \, \sqrt{2} b \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{4 \, {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)}}, -\frac{{\left({\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a + b\right)} \sinh\left(x\right)^{2} + a + b\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(a \cosh\left(x\right)^{2} + 2 \, a \cosh\left(x\right) \sinh\left(x\right) + a \sinh\left(x\right)^{2} + a + b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a^{2} + a b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{2} + a b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{2} + a b\right)} \sinh\left(x\right)^{4} + {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} + 2 \, a^{2} + a b - b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(2 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + {\left({\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a + b\right)} \sinh\left(x\right)^{2} + a + b\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) - {\left(a \cosh\left(x\right)^{2} + 2 \, a \cosh\left(x\right) \sinh\left(x\right) + a \sinh\left(x\right)^{2} + a\right)} \sqrt{a} \log\left(-\frac{{\left(2 \, a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(2 \, a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(2 \, a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(2 \, a + b\right)} \cosh\left(x\right)^{2} + 2 \, a - b\right)} \sinh\left(x\right)^{2} - 2 \, \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{a} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(2 \, a + b\right)} \cosh\left(x\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + 2 \, a + b}{\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) + 2 \, \sqrt{2} b \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{2 \, {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)}}, \frac{2 \, {\left(a \cosh\left(x\right)^{2} + 2 \, a \cosh\left(x\right) \sinh\left(x\right) + a \sinh\left(x\right)^{2} + a\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{-a} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) - {\left({\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a + b\right)} \sinh\left(x\right)^{2} + a + b\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(a \cosh\left(x\right)^{2} + 2 \, a \cosh\left(x\right) \sinh\left(x\right) + a \sinh\left(x\right)^{2} + a + b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a^{2} + a b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{2} + a b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{2} + a b\right)} \sinh\left(x\right)^{4} + {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} + 2 \, a^{2} + a b - b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(2 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) - {\left({\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a + b\right)} \sinh\left(x\right)^{2} + a + b\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) - 2 \, \sqrt{2} b \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{2 \, {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)}}\right]"," ",0,"[1/4*(((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 + a + b)*sqrt(a + b)*log(((a^3 + a^2*b)*cosh(x)^8 + 8*(a^3 + a^2*b)*cosh(x)*sinh(x)^7 + (a^3 + a^2*b)*sinh(x)^8 + 2*(2*a^3 + a^2*b)*cosh(x)^6 + 2*(2*a^3 + a^2*b + 14*(a^3 + a^2*b)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a^3 + a^2*b)*cosh(x)^3 + 3*(2*a^3 + a^2*b)*cosh(x))*sinh(x)^5 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^4 + (70*(a^3 + a^2*b)*cosh(x)^4 + 6*a^3 + 4*a^2*b - a*b^2 + b^3 + 30*(2*a^3 + a^2*b)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a^3 + a^2*b)*cosh(x)^5 + 10*(2*a^3 + a^2*b)*cosh(x)^3 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x))*sinh(x)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 + 2*(2*a^3 + 3*a^2*b - b^3)*cosh(x)^2 + 2*(14*(a^3 + a^2*b)*cosh(x)^6 + 15*(2*a^3 + a^2*b)*cosh(x)^4 + 2*a^3 + 3*a^2*b - b^3 + 3*(6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^2)*sinh(x)^2 + sqrt(2)*(a^2*cosh(x)^6 + 6*a^2*cosh(x)*sinh(x)^5 + a^2*sinh(x)^6 + 3*a^2*cosh(x)^4 + 3*(5*a^2*cosh(x)^2 + a^2)*sinh(x)^4 + 4*(5*a^2*cosh(x)^3 + 3*a^2*cosh(x))*sinh(x)^3 + (3*a^2 + 2*a*b - b^2)*cosh(x)^2 + (15*a^2*cosh(x)^4 + 18*a^2*cosh(x)^2 + 3*a^2 + 2*a*b - b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(3*a^2*cosh(x)^5 + 6*a^2*cosh(x)^3 + (3*a^2 + 2*a*b - b^2)*cosh(x))*sinh(x))*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a^3 + a^2*b)*cosh(x)^7 + 3*(2*a^3 + a^2*b)*cosh(x)^5 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^3 + (2*a^3 + 3*a^2*b - b^3)*cosh(x))*sinh(x))/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) + 2*(a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 + a)*sqrt(a)*log(-((2*a + b)*cosh(x)^4 + 4*(2*a + b)*cosh(x)*sinh(x)^3 + (2*a + b)*sinh(x)^4 + 2*(2*a - b)*cosh(x)^2 + 2*(3*(2*a + b)*cosh(x)^2 + 2*a - b)*sinh(x)^2 - 2*sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((2*a + b)*cosh(x)^3 + (2*a - b)*cosh(x))*sinh(x) + 2*a + b)/(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)) + ((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 + a + b)*sqrt(a + b)*log(-((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*b*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + b)*cosh(x)^3 - b*cosh(x))*sinh(x) + a + b)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) - 4*sqrt(2)*b*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1), 1/4*(4*(a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 + a)*sqrt(-a)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(-a)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a - b)*cosh(x))*sinh(x) + a + b)) + ((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 + a + b)*sqrt(a + b)*log(((a^3 + a^2*b)*cosh(x)^8 + 8*(a^3 + a^2*b)*cosh(x)*sinh(x)^7 + (a^3 + a^2*b)*sinh(x)^8 + 2*(2*a^3 + a^2*b)*cosh(x)^6 + 2*(2*a^3 + a^2*b + 14*(a^3 + a^2*b)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a^3 + a^2*b)*cosh(x)^3 + 3*(2*a^3 + a^2*b)*cosh(x))*sinh(x)^5 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^4 + (70*(a^3 + a^2*b)*cosh(x)^4 + 6*a^3 + 4*a^2*b - a*b^2 + b^3 + 30*(2*a^3 + a^2*b)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a^3 + a^2*b)*cosh(x)^5 + 10*(2*a^3 + a^2*b)*cosh(x)^3 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x))*sinh(x)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 + 2*(2*a^3 + 3*a^2*b - b^3)*cosh(x)^2 + 2*(14*(a^3 + a^2*b)*cosh(x)^6 + 15*(2*a^3 + a^2*b)*cosh(x)^4 + 2*a^3 + 3*a^2*b - b^3 + 3*(6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^2)*sinh(x)^2 + sqrt(2)*(a^2*cosh(x)^6 + 6*a^2*cosh(x)*sinh(x)^5 + a^2*sinh(x)^6 + 3*a^2*cosh(x)^4 + 3*(5*a^2*cosh(x)^2 + a^2)*sinh(x)^4 + 4*(5*a^2*cosh(x)^3 + 3*a^2*cosh(x))*sinh(x)^3 + (3*a^2 + 2*a*b - b^2)*cosh(x)^2 + (15*a^2*cosh(x)^4 + 18*a^2*cosh(x)^2 + 3*a^2 + 2*a*b - b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(3*a^2*cosh(x)^5 + 6*a^2*cosh(x)^3 + (3*a^2 + 2*a*b - b^2)*cosh(x))*sinh(x))*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a^3 + a^2*b)*cosh(x)^7 + 3*(2*a^3 + a^2*b)*cosh(x)^5 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^3 + (2*a^3 + 3*a^2*b - b^3)*cosh(x))*sinh(x))/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) + ((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 + a + b)*sqrt(a + b)*log(-((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*b*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + b)*cosh(x)^3 - b*cosh(x))*sinh(x) + a + b)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) - 4*sqrt(2)*b*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1), -1/2*(((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 + a + b)*sqrt(-a - b)*arctan(sqrt(2)*(a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 + a + b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a^2 + a*b)*cosh(x)^4 + 4*(a^2 + a*b)*cosh(x)*sinh(x)^3 + (a^2 + a*b)*sinh(x)^4 + (2*a^2 + a*b - b^2)*cosh(x)^2 + (6*(a^2 + a*b)*cosh(x)^2 + 2*a^2 + a*b - b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(2*(a^2 + a*b)*cosh(x)^3 + (2*a^2 + a*b - b^2)*cosh(x))*sinh(x))) + ((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 + a + b)*sqrt(-a - b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a - b)*cosh(x))*sinh(x) + a + b)) - (a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 + a)*sqrt(a)*log(-((2*a + b)*cosh(x)^4 + 4*(2*a + b)*cosh(x)*sinh(x)^3 + (2*a + b)*sinh(x)^4 + 2*(2*a - b)*cosh(x)^2 + 2*(3*(2*a + b)*cosh(x)^2 + 2*a - b)*sinh(x)^2 - 2*sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((2*a + b)*cosh(x)^3 + (2*a - b)*cosh(x))*sinh(x) + 2*a + b)/(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)) + 2*sqrt(2)*b*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1), 1/2*(2*(a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 + a)*sqrt(-a)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(-a)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a - b)*cosh(x))*sinh(x) + a + b)) - ((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 + a + b)*sqrt(-a - b)*arctan(sqrt(2)*(a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 + a + b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a^2 + a*b)*cosh(x)^4 + 4*(a^2 + a*b)*cosh(x)*sinh(x)^3 + (a^2 + a*b)*sinh(x)^4 + (2*a^2 + a*b - b^2)*cosh(x)^2 + (6*(a^2 + a*b)*cosh(x)^2 + 2*a^2 + a*b - b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(2*(a^2 + a*b)*cosh(x)^3 + (2*a^2 + a*b - b^2)*cosh(x))*sinh(x))) - ((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 + a + b)*sqrt(-a - b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a - b)*cosh(x))*sinh(x) + a + b)) - 2*sqrt(2)*b*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)]","B",0
224,1,3913,0,0.641168," ","integrate(coth(x)^2*(a+b*tanh(x)^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a + b\right)} \sinh\left(x\right)^{2} - a - b\right)} \sqrt{a + b} \log\left(-\frac{{\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a b^{2} + b^{3}\right)} \sinh\left(x\right)^{8} - 2 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{6} - 2 \, {\left(a b^{2} + 2 \, b^{3} - 14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3} - 30 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} + 2 \, {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} - 3 \, a b^{2} - 2 \, b^{3} + 3 \, {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(b^{2} \cosh\left(x\right)^{6} + 6 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + b^{2} \sinh\left(x\right)^{6} - 3 \, b^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, b^{2} \cosh\left(x\right)^{2} - b^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, b^{2} \cosh\left(x\right)^{3} - 3 \, b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, b^{2} \cosh\left(x\right)^{4} - 18 \, b^{2} \cosh\left(x\right)^{2} - a^{2} + 2 \, a b + 3 \, b^{2}\right)} \sinh\left(x\right)^{2} - a^{2} - 2 \, a b - b^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{5} - 6 \, b^{2} \cosh\left(x\right)^{3} - {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{5} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) + 2 \, {\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} - b\right)} \sqrt{b} \log\left(-\frac{{\left(a + 2 \, b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + 2 \, b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + a - 2 \, b\right)} \sinh\left(x\right)^{2} - 2 \, \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + 2 \, b\right)} \cosh\left(x\right)^{3} + {\left(a - 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + 2 \, b}{\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) + {\left({\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a + b\right)} \sinh\left(x\right)^{2} - a - b\right)} \sqrt{a + b} \log\left(\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, a \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + a \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right) - 4 \, \sqrt{2} a \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{4 \, {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)}}, \frac{4 \, {\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} - b\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{-b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) + {\left({\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a + b\right)} \sinh\left(x\right)^{2} - a - b\right)} \sqrt{a + b} \log\left(-\frac{{\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a b^{2} + b^{3}\right)} \sinh\left(x\right)^{8} - 2 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{6} - 2 \, {\left(a b^{2} + 2 \, b^{3} - 14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3} - 30 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} + 2 \, {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} - 3 \, a b^{2} - 2 \, b^{3} + 3 \, {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(b^{2} \cosh\left(x\right)^{6} + 6 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + b^{2} \sinh\left(x\right)^{6} - 3 \, b^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, b^{2} \cosh\left(x\right)^{2} - b^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, b^{2} \cosh\left(x\right)^{3} - 3 \, b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, b^{2} \cosh\left(x\right)^{4} - 18 \, b^{2} \cosh\left(x\right)^{2} - a^{2} + 2 \, a b + 3 \, b^{2}\right)} \sinh\left(x\right)^{2} - a^{2} - 2 \, a b - b^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{5} - 6 \, b^{2} \cosh\left(x\right)^{3} - {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{5} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) + {\left({\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a + b\right)} \sinh\left(x\right)^{2} - a - b\right)} \sqrt{a + b} \log\left(\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, a \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + a \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right) - 4 \, \sqrt{2} a \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{4 \, {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)}}, -\frac{{\left({\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a + b\right)} \sinh\left(x\right)^{2} - a - b\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} - a - b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a b + b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a b + b^{2}\right)} \sinh\left(x\right)^{4} + {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} - a b - 2 \, b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(2 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + {\left({\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a + b\right)} \sinh\left(x\right)^{2} - a - b\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a + b\right)} \sinh\left(x\right)^{2} + a + b}\right) - {\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} - b\right)} \sqrt{b} \log\left(-\frac{{\left(a + 2 \, b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + 2 \, b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + a - 2 \, b\right)} \sinh\left(x\right)^{2} - 2 \, \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + 2 \, b\right)} \cosh\left(x\right)^{3} + {\left(a - 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + 2 \, b}{\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) + 2 \, \sqrt{2} a \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{2 \, {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)}}, -\frac{{\left({\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a + b\right)} \sinh\left(x\right)^{2} - a - b\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} - a - b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a b + b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a b + b^{2}\right)} \sinh\left(x\right)^{4} + {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} - a b - 2 \, b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(2 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) - 2 \, {\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} - b\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{-b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) + {\left({\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a + b\right)} \sinh\left(x\right)^{2} - a - b\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a + b\right)} \sinh\left(x\right)^{2} + a + b}\right) + 2 \, \sqrt{2} a \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{2 \, {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)}}\right]"," ",0,"[1/4*(((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 - a - b)*sqrt(a + b)*log(-((a*b^2 + b^3)*cosh(x)^8 + 8*(a*b^2 + b^3)*cosh(x)*sinh(x)^7 + (a*b^2 + b^3)*sinh(x)^8 - 2*(a*b^2 + 2*b^3)*cosh(x)^6 - 2*(a*b^2 + 2*b^3 - 14*(a*b^2 + b^3)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a*b^2 + b^3)*cosh(x)^3 - 3*(a*b^2 + 2*b^3)*cosh(x))*sinh(x)^5 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^4 + (70*(a*b^2 + b^3)*cosh(x)^4 + a^3 - a^2*b + 4*a*b^2 + 6*b^3 - 30*(a*b^2 + 2*b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a*b^2 + b^3)*cosh(x)^5 - 10*(a*b^2 + 2*b^3)*cosh(x)^3 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x))*sinh(x)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 + 2*(a^3 - 3*a*b^2 - 2*b^3)*cosh(x)^2 + 2*(14*(a*b^2 + b^3)*cosh(x)^6 - 15*(a*b^2 + 2*b^3)*cosh(x)^4 + a^3 - 3*a*b^2 - 2*b^3 + 3*(a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^2)*sinh(x)^2 + sqrt(2)*(b^2*cosh(x)^6 + 6*b^2*cosh(x)*sinh(x)^5 + b^2*sinh(x)^6 - 3*b^2*cosh(x)^4 + 3*(5*b^2*cosh(x)^2 - b^2)*sinh(x)^4 + 4*(5*b^2*cosh(x)^3 - 3*b^2*cosh(x))*sinh(x)^3 - (a^2 - 2*a*b - 3*b^2)*cosh(x)^2 + (15*b^2*cosh(x)^4 - 18*b^2*cosh(x)^2 - a^2 + 2*a*b + 3*b^2)*sinh(x)^2 - a^2 - 2*a*b - b^2 + 2*(3*b^2*cosh(x)^5 - 6*b^2*cosh(x)^3 - (a^2 - 2*a*b - 3*b^2)*cosh(x))*sinh(x))*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a*b^2 + b^3)*cosh(x)^7 - 3*(a*b^2 + 2*b^3)*cosh(x)^5 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^3 + (a^3 - 3*a*b^2 - 2*b^3)*cosh(x))*sinh(x))/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) + 2*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 - b)*sqrt(b)*log(-((a + 2*b)*cosh(x)^4 + 4*(a + 2*b)*cosh(x)*sinh(x)^3 + (a + 2*b)*sinh(x)^4 + 2*(a - 2*b)*cosh(x)^2 + 2*(3*(a + 2*b)*cosh(x)^2 + a - 2*b)*sinh(x)^2 - 2*sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + 2*b)*cosh(x)^3 + (a - 2*b)*cosh(x))*sinh(x) + a + 2*b)/(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)) + ((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 - a - b)*sqrt(a + b)*log(((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*a*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + b)*cosh(x)^3 + a*cosh(x))*sinh(x) + a + b)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) - 4*sqrt(2)*a*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1), 1/4*(4*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 - b)*sqrt(-b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a - b)*cosh(x))*sinh(x) + a + b)) + ((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 - a - b)*sqrt(a + b)*log(-((a*b^2 + b^3)*cosh(x)^8 + 8*(a*b^2 + b^3)*cosh(x)*sinh(x)^7 + (a*b^2 + b^3)*sinh(x)^8 - 2*(a*b^2 + 2*b^3)*cosh(x)^6 - 2*(a*b^2 + 2*b^3 - 14*(a*b^2 + b^3)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a*b^2 + b^3)*cosh(x)^3 - 3*(a*b^2 + 2*b^3)*cosh(x))*sinh(x)^5 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^4 + (70*(a*b^2 + b^3)*cosh(x)^4 + a^3 - a^2*b + 4*a*b^2 + 6*b^3 - 30*(a*b^2 + 2*b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a*b^2 + b^3)*cosh(x)^5 - 10*(a*b^2 + 2*b^3)*cosh(x)^3 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x))*sinh(x)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 + 2*(a^3 - 3*a*b^2 - 2*b^3)*cosh(x)^2 + 2*(14*(a*b^2 + b^3)*cosh(x)^6 - 15*(a*b^2 + 2*b^3)*cosh(x)^4 + a^3 - 3*a*b^2 - 2*b^3 + 3*(a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^2)*sinh(x)^2 + sqrt(2)*(b^2*cosh(x)^6 + 6*b^2*cosh(x)*sinh(x)^5 + b^2*sinh(x)^6 - 3*b^2*cosh(x)^4 + 3*(5*b^2*cosh(x)^2 - b^2)*sinh(x)^4 + 4*(5*b^2*cosh(x)^3 - 3*b^2*cosh(x))*sinh(x)^3 - (a^2 - 2*a*b - 3*b^2)*cosh(x)^2 + (15*b^2*cosh(x)^4 - 18*b^2*cosh(x)^2 - a^2 + 2*a*b + 3*b^2)*sinh(x)^2 - a^2 - 2*a*b - b^2 + 2*(3*b^2*cosh(x)^5 - 6*b^2*cosh(x)^3 - (a^2 - 2*a*b - 3*b^2)*cosh(x))*sinh(x))*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a*b^2 + b^3)*cosh(x)^7 - 3*(a*b^2 + 2*b^3)*cosh(x)^5 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^3 + (a^3 - 3*a*b^2 - 2*b^3)*cosh(x))*sinh(x))/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) + ((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 - a - b)*sqrt(a + b)*log(((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*a*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + b)*cosh(x)^3 + a*cosh(x))*sinh(x) + a + b)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) - 4*sqrt(2)*a*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1), -1/2*(((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 - a - b)*sqrt(-a - b)*arctan(sqrt(2)*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 - a - b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a*b + b^2)*cosh(x)^4 + 4*(a*b + b^2)*cosh(x)*sinh(x)^3 + (a*b + b^2)*sinh(x)^4 + (a^2 - a*b - 2*b^2)*cosh(x)^2 + (6*(a*b + b^2)*cosh(x)^2 + a^2 - a*b - 2*b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(2*(a*b + b^2)*cosh(x)^3 + (a^2 - a*b - 2*b^2)*cosh(x))*sinh(x))) + ((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 - a - b)*sqrt(-a - b)*arctan(sqrt(2)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 + a + b)) - (b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 - b)*sqrt(b)*log(-((a + 2*b)*cosh(x)^4 + 4*(a + 2*b)*cosh(x)*sinh(x)^3 + (a + 2*b)*sinh(x)^4 + 2*(a - 2*b)*cosh(x)^2 + 2*(3*(a + 2*b)*cosh(x)^2 + a - 2*b)*sinh(x)^2 - 2*sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + 2*b)*cosh(x)^3 + (a - 2*b)*cosh(x))*sinh(x) + a + 2*b)/(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)) + 2*sqrt(2)*a*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1), -1/2*(((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 - a - b)*sqrt(-a - b)*arctan(sqrt(2)*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 - a - b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a*b + b^2)*cosh(x)^4 + 4*(a*b + b^2)*cosh(x)*sinh(x)^3 + (a*b + b^2)*sinh(x)^4 + (a^2 - a*b - 2*b^2)*cosh(x)^2 + (6*(a*b + b^2)*cosh(x)^2 + a^2 - a*b - 2*b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(2*(a*b + b^2)*cosh(x)^3 + (a^2 - a*b - 2*b^2)*cosh(x))*sinh(x))) - 2*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 - b)*sqrt(-b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a - b)*cosh(x))*sinh(x) + a + b)) + ((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 - a - b)*sqrt(-a - b)*arctan(sqrt(2)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 + a + b)) + 2*sqrt(2)*a*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)]","B",0
225,1,679,0,0.457955," ","integrate((1+tanh(x)^2)^(1/2),x, algorithm=""fricas"")","\frac{1}{4} \, \sqrt{2} \log\left(-\frac{2 \, {\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} - 3\right)} \sinh\left(x\right)^{6} - 3 \, \cosh\left(x\right)^{6} + 2 \, {\left(28 \, \cosh\left(x\right)^{3} - 9 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 5 \, {\left(14 \, \cosh\left(x\right)^{4} - 9 \, \cosh\left(x\right)^{2} + 1\right)} \sinh\left(x\right)^{4} + 5 \, \cosh\left(x\right)^{4} + 4 \, {\left(14 \, \cosh\left(x\right)^{5} - 15 \, \cosh\left(x\right)^{3} + 5 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(28 \, \cosh\left(x\right)^{6} - 45 \, \cosh\left(x\right)^{4} + 30 \, \cosh\left(x\right)^{2} - 4\right)} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right)^{2} + 2 \, {\left(4 \, \cosh\left(x\right)^{7} - 9 \, \cosh\left(x\right)^{5} + 10 \, \cosh\left(x\right)^{3} - 4 \, \cosh\left(x\right)\right)} \sinh\left(x\right) + {\left(\sqrt{2} \cosh\left(x\right)^{6} + 6 \, \sqrt{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + \sqrt{2} \sinh\left(x\right)^{6} + 3 \, {\left(5 \, \sqrt{2} \cosh\left(x\right)^{2} - \sqrt{2}\right)} \sinh\left(x\right)^{4} - 3 \, \sqrt{2} \cosh\left(x\right)^{4} + 4 \, {\left(5 \, \sqrt{2} \cosh\left(x\right)^{3} - 3 \, \sqrt{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(15 \, \sqrt{2} \cosh\left(x\right)^{4} - 18 \, \sqrt{2} \cosh\left(x\right)^{2} + 4 \, \sqrt{2}\right)} \sinh\left(x\right)^{2} + 4 \, \sqrt{2} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, \sqrt{2} \cosh\left(x\right)^{5} - 6 \, \sqrt{2} \cosh\left(x\right)^{3} + 4 \, \sqrt{2} \cosh\left(x\right)\right)} \sinh\left(x\right) - 4 \, \sqrt{2}\right)} \sqrt{\frac{\cosh\left(x\right)^{2} + \sinh\left(x\right)^{2}}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4\right)}}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) + \frac{1}{4} \, \sqrt{2} \log\left(\frac{2 \, {\left(\cosh\left(x\right)^{4} + 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4} + {\left(6 \, \cosh\left(x\right)^{2} + 1\right)} \sinh\left(x\right)^{2} + \cosh\left(x\right)^{2} + 2 \, {\left(2 \, \cosh\left(x\right)^{3} + \cosh\left(x\right)\right)} \sinh\left(x\right) + {\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)} \sqrt{\frac{\cosh\left(x\right)^{2} + \sinh\left(x\right)^{2}}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 1\right)}}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right) - \frac{1}{2} \, \log\left(\frac{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 2 \, \sqrt{\frac{\cosh\left(x\right)^{2} + \sinh\left(x\right)^{2}}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} - 1}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right) + \frac{1}{2} \, \log\left(\frac{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 2 \, \sqrt{\frac{\cosh\left(x\right)^{2} + \sinh\left(x\right)^{2}}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} - 1}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right)"," ",0,"1/4*sqrt(2)*log(-2*(cosh(x)^8 + 8*cosh(x)*sinh(x)^7 + sinh(x)^8 + (28*cosh(x)^2 - 3)*sinh(x)^6 - 3*cosh(x)^6 + 2*(28*cosh(x)^3 - 9*cosh(x))*sinh(x)^5 + 5*(14*cosh(x)^4 - 9*cosh(x)^2 + 1)*sinh(x)^4 + 5*cosh(x)^4 + 4*(14*cosh(x)^5 - 15*cosh(x)^3 + 5*cosh(x))*sinh(x)^3 + (28*cosh(x)^6 - 45*cosh(x)^4 + 30*cosh(x)^2 - 4)*sinh(x)^2 - 4*cosh(x)^2 + 2*(4*cosh(x)^7 - 9*cosh(x)^5 + 10*cosh(x)^3 - 4*cosh(x))*sinh(x) + (sqrt(2)*cosh(x)^6 + 6*sqrt(2)*cosh(x)*sinh(x)^5 + sqrt(2)*sinh(x)^6 + 3*(5*sqrt(2)*cosh(x)^2 - sqrt(2))*sinh(x)^4 - 3*sqrt(2)*cosh(x)^4 + 4*(5*sqrt(2)*cosh(x)^3 - 3*sqrt(2)*cosh(x))*sinh(x)^3 + (15*sqrt(2)*cosh(x)^4 - 18*sqrt(2)*cosh(x)^2 + 4*sqrt(2))*sinh(x)^2 + 4*sqrt(2)*cosh(x)^2 + 2*(3*sqrt(2)*cosh(x)^5 - 6*sqrt(2)*cosh(x)^3 + 4*sqrt(2)*cosh(x))*sinh(x) - 4*sqrt(2))*sqrt((cosh(x)^2 + sinh(x)^2)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4)/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) + 1/4*sqrt(2)*log(2*(cosh(x)^4 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4 + (6*cosh(x)^2 + 1)*sinh(x)^2 + cosh(x)^2 + 2*(2*cosh(x)^3 + cosh(x))*sinh(x) + (sqrt(2)*cosh(x)^2 + 2*sqrt(2)*cosh(x)*sinh(x) + sqrt(2)*sinh(x)^2 + sqrt(2))*sqrt((cosh(x)^2 + sinh(x)^2)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 1)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) - 1/2*log((cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 2*sqrt((cosh(x)^2 + sinh(x)^2)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) - 1)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) + 1/2*log((cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 2*sqrt((cosh(x)^2 + sinh(x)^2)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) - 1)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2))","B",0
226,1,228,0,0.426755," ","integrate((-1-tanh(x)^2)^(1/2),x, algorithm=""fricas"")","-\frac{1}{4} \, \sqrt{-2} \log\left(-{\left(\sqrt{-2} \sqrt{-2 \, e^{\left(4 \, x\right)} - 2} + 2 \, e^{\left(2 \, x\right)} + 2\right)} e^{\left(-2 \, x\right)}\right) + \frac{1}{4} \, \sqrt{-2} \log\left({\left(\sqrt{-2} \sqrt{-2 \, e^{\left(4 \, x\right)} - 2} - 2 \, e^{\left(2 \, x\right)} - 2\right)} e^{\left(-2 \, x\right)}\right) + \frac{1}{4} \, \sqrt{-2} \log\left(-2 \, {\left(\sqrt{-2 \, e^{\left(4 \, x\right)} - 2} {\left(e^{\left(2 \, x\right)} - 2\right)} + \sqrt{-2} e^{\left(4 \, x\right)} - \sqrt{-2} e^{\left(2 \, x\right)} + 2 \, \sqrt{-2}\right)} e^{\left(-4 \, x\right)}\right) - \frac{1}{4} \, \sqrt{-2} \log\left(-2 \, {\left(\sqrt{-2 \, e^{\left(4 \, x\right)} - 2} {\left(e^{\left(2 \, x\right)} - 2\right)} - \sqrt{-2} e^{\left(4 \, x\right)} + \sqrt{-2} e^{\left(2 \, x\right)} - 2 \, \sqrt{-2}\right)} e^{\left(-4 \, x\right)}\right) - \frac{1}{2} i \, \log\left({\left(4 i \, \sqrt{-2 \, e^{\left(4 \, x\right)} - 2} - 4 \, e^{\left(2 \, x\right)} + 4\right)} e^{\left(-2 \, x\right)}\right) + \frac{1}{2} i \, \log\left({\left(-4 i \, \sqrt{-2 \, e^{\left(4 \, x\right)} - 2} - 4 \, e^{\left(2 \, x\right)} + 4\right)} e^{\left(-2 \, x\right)}\right)"," ",0,"-1/4*sqrt(-2)*log(-(sqrt(-2)*sqrt(-2*e^(4*x) - 2) + 2*e^(2*x) + 2)*e^(-2*x)) + 1/4*sqrt(-2)*log((sqrt(-2)*sqrt(-2*e^(4*x) - 2) - 2*e^(2*x) - 2)*e^(-2*x)) + 1/4*sqrt(-2)*log(-2*(sqrt(-2*e^(4*x) - 2)*(e^(2*x) - 2) + sqrt(-2)*e^(4*x) - sqrt(-2)*e^(2*x) + 2*sqrt(-2))*e^(-4*x)) - 1/4*sqrt(-2)*log(-2*(sqrt(-2*e^(4*x) - 2)*(e^(2*x) - 2) - sqrt(-2)*e^(4*x) + sqrt(-2)*e^(2*x) - 2*sqrt(-2))*e^(-4*x)) - 1/2*I*log((4*I*sqrt(-2*e^(4*x) - 2) - 4*e^(2*x) + 4)*e^(-2*x)) + 1/2*I*log((-4*I*sqrt(-2*e^(4*x) - 2) - 4*e^(2*x) + 4)*e^(-2*x))","C",0
227,1,1027,0,0.429461," ","integrate((1+tanh(x)^2)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\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} + 2 \, {\left(3 \, \sqrt{2} \cosh\left(x\right)^{2} + \sqrt{2}\right)} \sinh\left(x\right)^{2} + 2 \, \sqrt{2} \cosh\left(x\right)^{2} + 4 \, {\left(\sqrt{2} \cosh\left(x\right)^{3} + \sqrt{2} \cosh\left(x\right)\right)} \sinh\left(x\right) + \sqrt{2}\right)} \log\left(-\frac{2 \, {\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} - 3\right)} \sinh\left(x\right)^{6} - 3 \, \cosh\left(x\right)^{6} + 2 \, {\left(28 \, \cosh\left(x\right)^{3} - 9 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 5 \, {\left(14 \, \cosh\left(x\right)^{4} - 9 \, \cosh\left(x\right)^{2} + 1\right)} \sinh\left(x\right)^{4} + 5 \, \cosh\left(x\right)^{4} + 4 \, {\left(14 \, \cosh\left(x\right)^{5} - 15 \, \cosh\left(x\right)^{3} + 5 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(28 \, \cosh\left(x\right)^{6} - 45 \, \cosh\left(x\right)^{4} + 30 \, \cosh\left(x\right)^{2} - 4\right)} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right)^{2} + 2 \, {\left(4 \, \cosh\left(x\right)^{7} - 9 \, \cosh\left(x\right)^{5} + 10 \, \cosh\left(x\right)^{3} - 4 \, \cosh\left(x\right)\right)} \sinh\left(x\right) + {\left(\sqrt{2} \cosh\left(x\right)^{6} + 6 \, \sqrt{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + \sqrt{2} \sinh\left(x\right)^{6} + 3 \, {\left(5 \, \sqrt{2} \cosh\left(x\right)^{2} - \sqrt{2}\right)} \sinh\left(x\right)^{4} - 3 \, \sqrt{2} \cosh\left(x\right)^{4} + 4 \, {\left(5 \, \sqrt{2} \cosh\left(x\right)^{3} - 3 \, \sqrt{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(15 \, \sqrt{2} \cosh\left(x\right)^{4} - 18 \, \sqrt{2} \cosh\left(x\right)^{2} + 4 \, \sqrt{2}\right)} \sinh\left(x\right)^{2} + 4 \, \sqrt{2} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, \sqrt{2} \cosh\left(x\right)^{5} - 6 \, \sqrt{2} \cosh\left(x\right)^{3} + 4 \, \sqrt{2} \cosh\left(x\right)\right)} \sinh\left(x\right) - 4 \, \sqrt{2}\right)} \sqrt{\frac{\cosh\left(x\right)^{2} + \sinh\left(x\right)^{2}}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4\right)}}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) + 2 \, {\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} + 2 \, {\left(3 \, \sqrt{2} \cosh\left(x\right)^{2} + \sqrt{2}\right)} \sinh\left(x\right)^{2} + 2 \, \sqrt{2} \cosh\left(x\right)^{2} + 4 \, {\left(\sqrt{2} \cosh\left(x\right)^{3} + \sqrt{2} \cosh\left(x\right)\right)} \sinh\left(x\right) + \sqrt{2}\right)} \log\left(\frac{2 \, {\left(\cosh\left(x\right)^{4} + 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4} + {\left(6 \, \cosh\left(x\right)^{2} + 1\right)} \sinh\left(x\right)^{2} + \cosh\left(x\right)^{2} + 2 \, {\left(2 \, \cosh\left(x\right)^{3} + \cosh\left(x\right)\right)} \sinh\left(x\right) + {\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)} \sqrt{\frac{\cosh\left(x\right)^{2} + \sinh\left(x\right)^{2}}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 1\right)}}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right) - 5 \, {\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)} \log\left(\frac{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 2 \, \sqrt{\frac{\cosh\left(x\right)^{2} + \sinh\left(x\right)^{2}}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} - 1}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right) + 5 \, {\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)} \log\left(\frac{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 2 \, \sqrt{\frac{\cosh\left(x\right)^{2} + \sinh\left(x\right)^{2}}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} - 1}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right) - 4 \, {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{\frac{\cosh\left(x\right)^{2} + \sinh\left(x\right)^{2}}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{4 \, {\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)}}"," ",0,"1/4*(2*(sqrt(2)*cosh(x)^4 + 4*sqrt(2)*cosh(x)*sinh(x)^3 + sqrt(2)*sinh(x)^4 + 2*(3*sqrt(2)*cosh(x)^2 + sqrt(2))*sinh(x)^2 + 2*sqrt(2)*cosh(x)^2 + 4*(sqrt(2)*cosh(x)^3 + sqrt(2)*cosh(x))*sinh(x) + sqrt(2))*log(-2*(cosh(x)^8 + 8*cosh(x)*sinh(x)^7 + sinh(x)^8 + (28*cosh(x)^2 - 3)*sinh(x)^6 - 3*cosh(x)^6 + 2*(28*cosh(x)^3 - 9*cosh(x))*sinh(x)^5 + 5*(14*cosh(x)^4 - 9*cosh(x)^2 + 1)*sinh(x)^4 + 5*cosh(x)^4 + 4*(14*cosh(x)^5 - 15*cosh(x)^3 + 5*cosh(x))*sinh(x)^3 + (28*cosh(x)^6 - 45*cosh(x)^4 + 30*cosh(x)^2 - 4)*sinh(x)^2 - 4*cosh(x)^2 + 2*(4*cosh(x)^7 - 9*cosh(x)^5 + 10*cosh(x)^3 - 4*cosh(x))*sinh(x) + (sqrt(2)*cosh(x)^6 + 6*sqrt(2)*cosh(x)*sinh(x)^5 + sqrt(2)*sinh(x)^6 + 3*(5*sqrt(2)*cosh(x)^2 - sqrt(2))*sinh(x)^4 - 3*sqrt(2)*cosh(x)^4 + 4*(5*sqrt(2)*cosh(x)^3 - 3*sqrt(2)*cosh(x))*sinh(x)^3 + (15*sqrt(2)*cosh(x)^4 - 18*sqrt(2)*cosh(x)^2 + 4*sqrt(2))*sinh(x)^2 + 4*sqrt(2)*cosh(x)^2 + 2*(3*sqrt(2)*cosh(x)^5 - 6*sqrt(2)*cosh(x)^3 + 4*sqrt(2)*cosh(x))*sinh(x) - 4*sqrt(2))*sqrt((cosh(x)^2 + sinh(x)^2)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4)/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) + 2*(sqrt(2)*cosh(x)^4 + 4*sqrt(2)*cosh(x)*sinh(x)^3 + sqrt(2)*sinh(x)^4 + 2*(3*sqrt(2)*cosh(x)^2 + sqrt(2))*sinh(x)^2 + 2*sqrt(2)*cosh(x)^2 + 4*(sqrt(2)*cosh(x)^3 + sqrt(2)*cosh(x))*sinh(x) + sqrt(2))*log(2*(cosh(x)^4 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4 + (6*cosh(x)^2 + 1)*sinh(x)^2 + cosh(x)^2 + 2*(2*cosh(x)^3 + cosh(x))*sinh(x) + (sqrt(2)*cosh(x)^2 + 2*sqrt(2)*cosh(x)*sinh(x) + sqrt(2)*sinh(x)^2 + sqrt(2))*sqrt((cosh(x)^2 + sinh(x)^2)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 1)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) - 5*(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)*log((cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 2*sqrt((cosh(x)^2 + sinh(x)^2)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) - 1)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) + 5*(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)*log((cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 2*sqrt((cosh(x)^2 + sinh(x)^2)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) - 1)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) - 4*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt((cosh(x)^2 + sinh(x)^2)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(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)","B",0
228,1,361,0,0.405489," ","integrate((-1-tanh(x)^2)^(3/2),x, algorithm=""fricas"")","\frac{2 \, {\left(\sqrt{-2} e^{\left(4 \, x\right)} + 2 \, \sqrt{-2} e^{\left(2 \, x\right)} + \sqrt{-2}\right)} \log\left(2 \, {\left(\sqrt{-2} \sqrt{-2 \, e^{\left(4 \, x\right)} - 2} + 2 \, e^{\left(2 \, x\right)} + 2\right)} e^{\left(-2 \, x\right)}\right) - 2 \, {\left(\sqrt{-2} e^{\left(4 \, x\right)} + 2 \, \sqrt{-2} e^{\left(2 \, x\right)} + \sqrt{-2}\right)} \log\left(-2 \, {\left(\sqrt{-2} \sqrt{-2 \, e^{\left(4 \, x\right)} - 2} - 2 \, e^{\left(2 \, x\right)} - 2\right)} e^{\left(-2 \, x\right)}\right) + {\left(5 i \, e^{\left(4 \, x\right)} + 10 i \, e^{\left(2 \, x\right)} + 5 i\right)} \log\left({\left(4 i \, \sqrt{-2 \, e^{\left(4 \, x\right)} - 2} - 4 \, e^{\left(2 \, x\right)} + 4\right)} e^{\left(-2 \, x\right)}\right) + {\left(-5 i \, e^{\left(4 \, x\right)} - 10 i \, e^{\left(2 \, x\right)} - 5 i\right)} \log\left({\left(-4 i \, \sqrt{-2 \, e^{\left(4 \, x\right)} - 2} - 4 \, e^{\left(2 \, x\right)} + 4\right)} e^{\left(-2 \, x\right)}\right) - 2 \, {\left(\sqrt{-2} e^{\left(4 \, x\right)} + 2 \, \sqrt{-2} e^{\left(2 \, x\right)} + \sqrt{-2}\right)} \log\left(4 \, {\left(\sqrt{-2 \, e^{\left(4 \, x\right)} - 2} {\left(e^{\left(2 \, x\right)} - 2\right)} + \sqrt{-2} e^{\left(4 \, x\right)} - \sqrt{-2} e^{\left(2 \, x\right)} + 2 \, \sqrt{-2}\right)} e^{\left(-4 \, x\right)}\right) + 2 \, {\left(\sqrt{-2} e^{\left(4 \, x\right)} + 2 \, \sqrt{-2} e^{\left(2 \, x\right)} + \sqrt{-2}\right)} \log\left(4 \, {\left(\sqrt{-2 \, e^{\left(4 \, x\right)} - 2} {\left(e^{\left(2 \, x\right)} - 2\right)} - \sqrt{-2} e^{\left(4 \, x\right)} + \sqrt{-2} e^{\left(2 \, x\right)} - 2 \, \sqrt{-2}\right)} e^{\left(-4 \, x\right)}\right) + 2 \, \sqrt{-2 \, e^{\left(4 \, x\right)} - 2} {\left(e^{\left(2 \, x\right)} - 1\right)}}{4 \, {\left(e^{\left(4 \, x\right)} + 2 \, e^{\left(2 \, x\right)} + 1\right)}}"," ",0,"1/4*(2*(sqrt(-2)*e^(4*x) + 2*sqrt(-2)*e^(2*x) + sqrt(-2))*log(2*(sqrt(-2)*sqrt(-2*e^(4*x) - 2) + 2*e^(2*x) + 2)*e^(-2*x)) - 2*(sqrt(-2)*e^(4*x) + 2*sqrt(-2)*e^(2*x) + sqrt(-2))*log(-2*(sqrt(-2)*sqrt(-2*e^(4*x) - 2) - 2*e^(2*x) - 2)*e^(-2*x)) + (5*I*e^(4*x) + 10*I*e^(2*x) + 5*I)*log((4*I*sqrt(-2*e^(4*x) - 2) - 4*e^(2*x) + 4)*e^(-2*x)) + (-5*I*e^(4*x) - 10*I*e^(2*x) - 5*I)*log((-4*I*sqrt(-2*e^(4*x) - 2) - 4*e^(2*x) + 4)*e^(-2*x)) - 2*(sqrt(-2)*e^(4*x) + 2*sqrt(-2)*e^(2*x) + sqrt(-2))*log(4*(sqrt(-2*e^(4*x) - 2)*(e^(2*x) - 2) + sqrt(-2)*e^(4*x) - sqrt(-2)*e^(2*x) + 2*sqrt(-2))*e^(-4*x)) + 2*(sqrt(-2)*e^(4*x) + 2*sqrt(-2)*e^(2*x) + sqrt(-2))*log(4*(sqrt(-2*e^(4*x) - 2)*(e^(2*x) - 2) - sqrt(-2)*e^(4*x) + sqrt(-2)*e^(2*x) - 2*sqrt(-2))*e^(-4*x)) + 2*sqrt(-2*e^(4*x) - 2)*(e^(2*x) - 1))/(e^(4*x) + 2*e^(2*x) + 1)","C",0
229,1,2827,0,0.673281," ","integrate(tanh(x)^5/(a+b*tanh(x)^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left(b^{2} \cosh\left(x\right)^{6} + 6 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + b^{2} \sinh\left(x\right)^{6} + 3 \, b^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, b^{2} \cosh\left(x\right)^{2} + b^{2}\right)} \sinh\left(x\right)^{4} + 3 \, b^{2} \cosh\left(x\right)^{2} + 4 \, {\left(5 \, b^{2} \cosh\left(x\right)^{3} + 3 \, b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 3 \, {\left(5 \, b^{2} \cosh\left(x\right)^{4} + 6 \, b^{2} \cosh\left(x\right)^{2} + b^{2}\right)} \sinh\left(x\right)^{2} + b^{2} + 6 \, {\left(b^{2} \cosh\left(x\right)^{5} + 2 \, b^{2} \cosh\left(x\right)^{3} + b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \log\left(\frac{{\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{3} + a^{2} b\right)} \sinh\left(x\right)^{8} + 2 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} + 2 \, {\left(2 \, a^{3} + a^{2} b + 14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} + 3 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3} + 30 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} + 10 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} + 2 \, {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} + 15 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 2 \, a^{3} + 3 \, a^{2} b - b^{3} + 3 \, {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(a^{2} \cosh\left(x\right)^{6} + 6 \, a^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + a^{2} \sinh\left(x\right)^{6} + 3 \, a^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, a^{2} \cosh\left(x\right)^{2} + a^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, a^{2} \cosh\left(x\right)^{3} + 3 \, a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, a^{2} \cosh\left(x\right)^{4} + 18 \, a^{2} \cosh\left(x\right)^{2} + 3 \, a^{2} + 2 \, a b - b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(x\right)^{5} + 6 \, a^{2} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{7} + 3 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) + 3 \, {\left(b^{2} \cosh\left(x\right)^{6} + 6 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + b^{2} \sinh\left(x\right)^{6} + 3 \, b^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, b^{2} \cosh\left(x\right)^{2} + b^{2}\right)} \sinh\left(x\right)^{4} + 3 \, b^{2} \cosh\left(x\right)^{2} + 4 \, {\left(5 \, b^{2} \cosh\left(x\right)^{3} + 3 \, b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 3 \, {\left(5 \, b^{2} \cosh\left(x\right)^{4} + 6 \, b^{2} \cosh\left(x\right)^{2} + b^{2}\right)} \sinh\left(x\right)^{2} + b^{2} + 6 \, {\left(b^{2} \cosh\left(x\right)^{5} + 2 \, b^{2} \cosh\left(x\right)^{3} + b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \log\left(-\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - b\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - b \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right) + 8 \, \sqrt{2} {\left({\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{2} - a b - 2 \, b^{2}\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} - a b - 2 \, b^{2} + 4 \, {\left({\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{12 \, {\left({\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{6} + 6 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(a b^{2} + b^{3}\right)} \sinh\left(x\right)^{6} + 3 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(a b^{2} + b^{3} + 5 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a b^{2} + b^{3} + 3 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2} + 3 \, {\left(5 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + a b^{2} + b^{3} + 6 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 6 \, {\left({\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{5} + 2 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}, -\frac{3 \, {\left(b^{2} \cosh\left(x\right)^{6} + 6 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + b^{2} \sinh\left(x\right)^{6} + 3 \, b^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, b^{2} \cosh\left(x\right)^{2} + b^{2}\right)} \sinh\left(x\right)^{4} + 3 \, b^{2} \cosh\left(x\right)^{2} + 4 \, {\left(5 \, b^{2} \cosh\left(x\right)^{3} + 3 \, b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 3 \, {\left(5 \, b^{2} \cosh\left(x\right)^{4} + 6 \, b^{2} \cosh\left(x\right)^{2} + b^{2}\right)} \sinh\left(x\right)^{2} + b^{2} + 6 \, {\left(b^{2} \cosh\left(x\right)^{5} + 2 \, b^{2} \cosh\left(x\right)^{3} + b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(a \cosh\left(x\right)^{2} + 2 \, a \cosh\left(x\right) \sinh\left(x\right) + a \sinh\left(x\right)^{2} + a + b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a^{2} + a b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{2} + a b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{2} + a b\right)} \sinh\left(x\right)^{4} + {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} + 2 \, a^{2} + a b - b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(2 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + 3 \, {\left(b^{2} \cosh\left(x\right)^{6} + 6 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + b^{2} \sinh\left(x\right)^{6} + 3 \, b^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, b^{2} \cosh\left(x\right)^{2} + b^{2}\right)} \sinh\left(x\right)^{4} + 3 \, b^{2} \cosh\left(x\right)^{2} + 4 \, {\left(5 \, b^{2} \cosh\left(x\right)^{3} + 3 \, b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 3 \, {\left(5 \, b^{2} \cosh\left(x\right)^{4} + 6 \, b^{2} \cosh\left(x\right)^{2} + b^{2}\right)} \sinh\left(x\right)^{2} + b^{2} + 6 \, {\left(b^{2} \cosh\left(x\right)^{5} + 2 \, b^{2} \cosh\left(x\right)^{3} + b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) - 4 \, \sqrt{2} {\left({\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{2} - a b - 2 \, b^{2}\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} - a b - 2 \, b^{2} + 4 \, {\left({\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{6 \, {\left({\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{6} + 6 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(a b^{2} + b^{3}\right)} \sinh\left(x\right)^{6} + 3 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(a b^{2} + b^{3} + 5 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a b^{2} + b^{3} + 3 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2} + 3 \, {\left(5 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + a b^{2} + b^{3} + 6 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 6 \, {\left({\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{5} + 2 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}\right]"," ",0,"[1/12*(3*(b^2*cosh(x)^6 + 6*b^2*cosh(x)*sinh(x)^5 + b^2*sinh(x)^6 + 3*b^2*cosh(x)^4 + 3*(5*b^2*cosh(x)^2 + b^2)*sinh(x)^4 + 3*b^2*cosh(x)^2 + 4*(5*b^2*cosh(x)^3 + 3*b^2*cosh(x))*sinh(x)^3 + 3*(5*b^2*cosh(x)^4 + 6*b^2*cosh(x)^2 + b^2)*sinh(x)^2 + b^2 + 6*(b^2*cosh(x)^5 + 2*b^2*cosh(x)^3 + b^2*cosh(x))*sinh(x))*sqrt(a + b)*log(((a^3 + a^2*b)*cosh(x)^8 + 8*(a^3 + a^2*b)*cosh(x)*sinh(x)^7 + (a^3 + a^2*b)*sinh(x)^8 + 2*(2*a^3 + a^2*b)*cosh(x)^6 + 2*(2*a^3 + a^2*b + 14*(a^3 + a^2*b)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a^3 + a^2*b)*cosh(x)^3 + 3*(2*a^3 + a^2*b)*cosh(x))*sinh(x)^5 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^4 + (70*(a^3 + a^2*b)*cosh(x)^4 + 6*a^3 + 4*a^2*b - a*b^2 + b^3 + 30*(2*a^3 + a^2*b)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a^3 + a^2*b)*cosh(x)^5 + 10*(2*a^3 + a^2*b)*cosh(x)^3 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x))*sinh(x)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 + 2*(2*a^3 + 3*a^2*b - b^3)*cosh(x)^2 + 2*(14*(a^3 + a^2*b)*cosh(x)^6 + 15*(2*a^3 + a^2*b)*cosh(x)^4 + 2*a^3 + 3*a^2*b - b^3 + 3*(6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^2)*sinh(x)^2 + sqrt(2)*(a^2*cosh(x)^6 + 6*a^2*cosh(x)*sinh(x)^5 + a^2*sinh(x)^6 + 3*a^2*cosh(x)^4 + 3*(5*a^2*cosh(x)^2 + a^2)*sinh(x)^4 + 4*(5*a^2*cosh(x)^3 + 3*a^2*cosh(x))*sinh(x)^3 + (3*a^2 + 2*a*b - b^2)*cosh(x)^2 + (15*a^2*cosh(x)^4 + 18*a^2*cosh(x)^2 + 3*a^2 + 2*a*b - b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(3*a^2*cosh(x)^5 + 6*a^2*cosh(x)^3 + (3*a^2 + 2*a*b - b^2)*cosh(x))*sinh(x))*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a^3 + a^2*b)*cosh(x)^7 + 3*(2*a^3 + a^2*b)*cosh(x)^5 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^3 + (2*a^3 + 3*a^2*b - b^3)*cosh(x))*sinh(x))/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) + 3*(b^2*cosh(x)^6 + 6*b^2*cosh(x)*sinh(x)^5 + b^2*sinh(x)^6 + 3*b^2*cosh(x)^4 + 3*(5*b^2*cosh(x)^2 + b^2)*sinh(x)^4 + 3*b^2*cosh(x)^2 + 4*(5*b^2*cosh(x)^3 + 3*b^2*cosh(x))*sinh(x)^3 + 3*(5*b^2*cosh(x)^4 + 6*b^2*cosh(x)^2 + b^2)*sinh(x)^2 + b^2 + 6*(b^2*cosh(x)^5 + 2*b^2*cosh(x)^3 + b^2*cosh(x))*sinh(x))*sqrt(a + b)*log(-((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*b*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + b)*cosh(x)^3 - b*cosh(x))*sinh(x) + a + b)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) + 8*sqrt(2)*((a^2 - a*b - 2*b^2)*cosh(x)^4 + 4*(a^2 - a*b - 2*b^2)*cosh(x)*sinh(x)^3 + (a^2 - a*b - 2*b^2)*sinh(x)^4 + 2*(a^2 - b^2)*cosh(x)^2 + 2*(3*(a^2 - a*b - 2*b^2)*cosh(x)^2 + a^2 - b^2)*sinh(x)^2 + a^2 - a*b - 2*b^2 + 4*((a^2 - a*b - 2*b^2)*cosh(x)^3 + (a^2 - b^2)*cosh(x))*sinh(x))*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/((a*b^2 + b^3)*cosh(x)^6 + 6*(a*b^2 + b^3)*cosh(x)*sinh(x)^5 + (a*b^2 + b^3)*sinh(x)^6 + 3*(a*b^2 + b^3)*cosh(x)^4 + 3*(a*b^2 + b^3 + 5*(a*b^2 + b^3)*cosh(x)^2)*sinh(x)^4 + 4*(5*(a*b^2 + b^3)*cosh(x)^3 + 3*(a*b^2 + b^3)*cosh(x))*sinh(x)^3 + a*b^2 + b^3 + 3*(a*b^2 + b^3)*cosh(x)^2 + 3*(5*(a*b^2 + b^3)*cosh(x)^4 + a*b^2 + b^3 + 6*(a*b^2 + b^3)*cosh(x)^2)*sinh(x)^2 + 6*((a*b^2 + b^3)*cosh(x)^5 + 2*(a*b^2 + b^3)*cosh(x)^3 + (a*b^2 + b^3)*cosh(x))*sinh(x)), -1/6*(3*(b^2*cosh(x)^6 + 6*b^2*cosh(x)*sinh(x)^5 + b^2*sinh(x)^6 + 3*b^2*cosh(x)^4 + 3*(5*b^2*cosh(x)^2 + b^2)*sinh(x)^4 + 3*b^2*cosh(x)^2 + 4*(5*b^2*cosh(x)^3 + 3*b^2*cosh(x))*sinh(x)^3 + 3*(5*b^2*cosh(x)^4 + 6*b^2*cosh(x)^2 + b^2)*sinh(x)^2 + b^2 + 6*(b^2*cosh(x)^5 + 2*b^2*cosh(x)^3 + b^2*cosh(x))*sinh(x))*sqrt(-a - b)*arctan(sqrt(2)*(a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 + a + b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a^2 + a*b)*cosh(x)^4 + 4*(a^2 + a*b)*cosh(x)*sinh(x)^3 + (a^2 + a*b)*sinh(x)^4 + (2*a^2 + a*b - b^2)*cosh(x)^2 + (6*(a^2 + a*b)*cosh(x)^2 + 2*a^2 + a*b - b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(2*(a^2 + a*b)*cosh(x)^3 + (2*a^2 + a*b - b^2)*cosh(x))*sinh(x))) + 3*(b^2*cosh(x)^6 + 6*b^2*cosh(x)*sinh(x)^5 + b^2*sinh(x)^6 + 3*b^2*cosh(x)^4 + 3*(5*b^2*cosh(x)^2 + b^2)*sinh(x)^4 + 3*b^2*cosh(x)^2 + 4*(5*b^2*cosh(x)^3 + 3*b^2*cosh(x))*sinh(x)^3 + 3*(5*b^2*cosh(x)^4 + 6*b^2*cosh(x)^2 + b^2)*sinh(x)^2 + b^2 + 6*(b^2*cosh(x)^5 + 2*b^2*cosh(x)^3 + b^2*cosh(x))*sinh(x))*sqrt(-a - b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a - b)*cosh(x))*sinh(x) + a + b)) - 4*sqrt(2)*((a^2 - a*b - 2*b^2)*cosh(x)^4 + 4*(a^2 - a*b - 2*b^2)*cosh(x)*sinh(x)^3 + (a^2 - a*b - 2*b^2)*sinh(x)^4 + 2*(a^2 - b^2)*cosh(x)^2 + 2*(3*(a^2 - a*b - 2*b^2)*cosh(x)^2 + a^2 - b^2)*sinh(x)^2 + a^2 - a*b - 2*b^2 + 4*((a^2 - a*b - 2*b^2)*cosh(x)^3 + (a^2 - b^2)*cosh(x))*sinh(x))*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/((a*b^2 + b^3)*cosh(x)^6 + 6*(a*b^2 + b^3)*cosh(x)*sinh(x)^5 + (a*b^2 + b^3)*sinh(x)^6 + 3*(a*b^2 + b^3)*cosh(x)^4 + 3*(a*b^2 + b^3 + 5*(a*b^2 + b^3)*cosh(x)^2)*sinh(x)^4 + 4*(5*(a*b^2 + b^3)*cosh(x)^3 + 3*(a*b^2 + b^3)*cosh(x))*sinh(x)^3 + a*b^2 + b^3 + 3*(a*b^2 + b^3)*cosh(x)^2 + 3*(5*(a*b^2 + b^3)*cosh(x)^4 + a*b^2 + b^3 + 6*(a*b^2 + b^3)*cosh(x)^2)*sinh(x)^2 + 6*((a*b^2 + b^3)*cosh(x)^5 + 2*(a*b^2 + b^3)*cosh(x)^3 + (a*b^2 + b^3)*cosh(x))*sinh(x))]","B",0
230,1,5494,0,0.769450," ","integrate(tanh(x)^4/(a+b*tanh(x)^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(b^{2} \cosh\left(x\right)^{4} + 4 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{3} + b^{2} \sinh\left(x\right)^{4} + 2 \, b^{2} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{2} + b^{2}\right)} \sinh\left(x\right)^{2} + b^{2} + 4 \, {\left(b^{2} \cosh\left(x\right)^{3} + b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \log\left(-\frac{{\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a b^{2} + b^{3}\right)} \sinh\left(x\right)^{8} - 2 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{6} - 2 \, {\left(a b^{2} + 2 \, b^{3} - 14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3} - 30 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} + 2 \, {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} - 3 \, a b^{2} - 2 \, b^{3} + 3 \, {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(b^{2} \cosh\left(x\right)^{6} + 6 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + b^{2} \sinh\left(x\right)^{6} - 3 \, b^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, b^{2} \cosh\left(x\right)^{2} - b^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, b^{2} \cosh\left(x\right)^{3} - 3 \, b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, b^{2} \cosh\left(x\right)^{4} - 18 \, b^{2} \cosh\left(x\right)^{2} - a^{2} + 2 \, a b + 3 \, b^{2}\right)} \sinh\left(x\right)^{2} - a^{2} - 2 \, a b - b^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{5} - 6 \, b^{2} \cosh\left(x\right)^{3} - {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{5} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) - {\left({\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{2} - a b - 2 \, b^{2}\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} - a b - 2 \, b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} - a b - 2 \, b^{2} + 4 \, {\left({\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{b} \log\left(-\frac{{\left(a + 2 \, b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + 2 \, b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + a - 2 \, b\right)} \sinh\left(x\right)^{2} - 2 \, \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + 2 \, b\right)} \cosh\left(x\right)^{3} + {\left(a - 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + 2 \, b}{\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) + {\left(b^{2} \cosh\left(x\right)^{4} + 4 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{3} + b^{2} \sinh\left(x\right)^{4} + 2 \, b^{2} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{2} + b^{2}\right)} \sinh\left(x\right)^{2} + b^{2} + 4 \, {\left(b^{2} \cosh\left(x\right)^{3} + b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \log\left(\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, a \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + a \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right) - 2 \, \sqrt{2} {\left({\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a b + b^{2}\right)} \sinh\left(x\right)^{2} - a b - b^{2}\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{4 \, {\left({\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a b^{2} + b^{3}\right)} \sinh\left(x\right)^{4} + a b^{2} + b^{3} + 2 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a b^{2} + b^{3} + 3 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}, -\frac{2 \, {\left({\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{2} - a b - 2 \, b^{2}\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} - a b - 2 \, b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} - a b - 2 \, b^{2} + 4 \, {\left({\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{-b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) - {\left(b^{2} \cosh\left(x\right)^{4} + 4 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{3} + b^{2} \sinh\left(x\right)^{4} + 2 \, b^{2} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{2} + b^{2}\right)} \sinh\left(x\right)^{2} + b^{2} + 4 \, {\left(b^{2} \cosh\left(x\right)^{3} + b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \log\left(-\frac{{\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a b^{2} + b^{3}\right)} \sinh\left(x\right)^{8} - 2 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{6} - 2 \, {\left(a b^{2} + 2 \, b^{3} - 14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3} - 30 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} + 2 \, {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} - 3 \, a b^{2} - 2 \, b^{3} + 3 \, {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(b^{2} \cosh\left(x\right)^{6} + 6 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + b^{2} \sinh\left(x\right)^{6} - 3 \, b^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, b^{2} \cosh\left(x\right)^{2} - b^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, b^{2} \cosh\left(x\right)^{3} - 3 \, b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, b^{2} \cosh\left(x\right)^{4} - 18 \, b^{2} \cosh\left(x\right)^{2} - a^{2} + 2 \, a b + 3 \, b^{2}\right)} \sinh\left(x\right)^{2} - a^{2} - 2 \, a b - b^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{5} - 6 \, b^{2} \cosh\left(x\right)^{3} - {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{5} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) - {\left(b^{2} \cosh\left(x\right)^{4} + 4 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{3} + b^{2} \sinh\left(x\right)^{4} + 2 \, b^{2} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{2} + b^{2}\right)} \sinh\left(x\right)^{2} + b^{2} + 4 \, {\left(b^{2} \cosh\left(x\right)^{3} + b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \log\left(\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, a \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + a \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right) + 2 \, \sqrt{2} {\left({\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a b + b^{2}\right)} \sinh\left(x\right)^{2} - a b - b^{2}\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{4 \, {\left({\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a b^{2} + b^{3}\right)} \sinh\left(x\right)^{4} + a b^{2} + b^{3} + 2 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a b^{2} + b^{3} + 3 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}, -\frac{2 \, {\left(b^{2} \cosh\left(x\right)^{4} + 4 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{3} + b^{2} \sinh\left(x\right)^{4} + 2 \, b^{2} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{2} + b^{2}\right)} \sinh\left(x\right)^{2} + b^{2} + 4 \, {\left(b^{2} \cosh\left(x\right)^{3} + b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} - a - b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a b + b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a b + b^{2}\right)} \sinh\left(x\right)^{4} + {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} - a b - 2 \, b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(2 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + 2 \, {\left(b^{2} \cosh\left(x\right)^{4} + 4 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{3} + b^{2} \sinh\left(x\right)^{4} + 2 \, b^{2} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{2} + b^{2}\right)} \sinh\left(x\right)^{2} + b^{2} + 4 \, {\left(b^{2} \cosh\left(x\right)^{3} + b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a + b\right)} \sinh\left(x\right)^{2} + a + b}\right) + {\left({\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{2} - a b - 2 \, b^{2}\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} - a b - 2 \, b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} - a b - 2 \, b^{2} + 4 \, {\left({\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{b} \log\left(-\frac{{\left(a + 2 \, b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + 2 \, b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + a - 2 \, b\right)} \sinh\left(x\right)^{2} - 2 \, \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + 2 \, b\right)} \cosh\left(x\right)^{3} + {\left(a - 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + 2 \, b}{\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) + 2 \, \sqrt{2} {\left({\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a b + b^{2}\right)} \sinh\left(x\right)^{2} - a b - b^{2}\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{4 \, {\left({\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a b^{2} + b^{3}\right)} \sinh\left(x\right)^{4} + a b^{2} + b^{3} + 2 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a b^{2} + b^{3} + 3 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}, -\frac{{\left(b^{2} \cosh\left(x\right)^{4} + 4 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{3} + b^{2} \sinh\left(x\right)^{4} + 2 \, b^{2} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{2} + b^{2}\right)} \sinh\left(x\right)^{2} + b^{2} + 4 \, {\left(b^{2} \cosh\left(x\right)^{3} + b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} - a - b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a b + b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a b + b^{2}\right)} \sinh\left(x\right)^{4} + {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} - a b - 2 \, b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(2 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + {\left({\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{2} - a b - 2 \, b^{2}\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} - a b - 2 \, b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} - a b - 2 \, b^{2} + 4 \, {\left({\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{-b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) + {\left(b^{2} \cosh\left(x\right)^{4} + 4 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{3} + b^{2} \sinh\left(x\right)^{4} + 2 \, b^{2} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{2} + b^{2}\right)} \sinh\left(x\right)^{2} + b^{2} + 4 \, {\left(b^{2} \cosh\left(x\right)^{3} + b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a + b\right)} \sinh\left(x\right)^{2} + a + b}\right) + \sqrt{2} {\left({\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a b + b^{2}\right)} \sinh\left(x\right)^{2} - a b - b^{2}\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{2 \, {\left({\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a b^{2} + b^{3}\right)} \sinh\left(x\right)^{4} + a b^{2} + b^{3} + 2 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a b^{2} + b^{3} + 3 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}\right]"," ",0,"[1/4*((b^2*cosh(x)^4 + 4*b^2*cosh(x)*sinh(x)^3 + b^2*sinh(x)^4 + 2*b^2*cosh(x)^2 + 2*(3*b^2*cosh(x)^2 + b^2)*sinh(x)^2 + b^2 + 4*(b^2*cosh(x)^3 + b^2*cosh(x))*sinh(x))*sqrt(a + b)*log(-((a*b^2 + b^3)*cosh(x)^8 + 8*(a*b^2 + b^3)*cosh(x)*sinh(x)^7 + (a*b^2 + b^3)*sinh(x)^8 - 2*(a*b^2 + 2*b^3)*cosh(x)^6 - 2*(a*b^2 + 2*b^3 - 14*(a*b^2 + b^3)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a*b^2 + b^3)*cosh(x)^3 - 3*(a*b^2 + 2*b^3)*cosh(x))*sinh(x)^5 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^4 + (70*(a*b^2 + b^3)*cosh(x)^4 + a^3 - a^2*b + 4*a*b^2 + 6*b^3 - 30*(a*b^2 + 2*b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a*b^2 + b^3)*cosh(x)^5 - 10*(a*b^2 + 2*b^3)*cosh(x)^3 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x))*sinh(x)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 + 2*(a^3 - 3*a*b^2 - 2*b^3)*cosh(x)^2 + 2*(14*(a*b^2 + b^3)*cosh(x)^6 - 15*(a*b^2 + 2*b^3)*cosh(x)^4 + a^3 - 3*a*b^2 - 2*b^3 + 3*(a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^2)*sinh(x)^2 + sqrt(2)*(b^2*cosh(x)^6 + 6*b^2*cosh(x)*sinh(x)^5 + b^2*sinh(x)^6 - 3*b^2*cosh(x)^4 + 3*(5*b^2*cosh(x)^2 - b^2)*sinh(x)^4 + 4*(5*b^2*cosh(x)^3 - 3*b^2*cosh(x))*sinh(x)^3 - (a^2 - 2*a*b - 3*b^2)*cosh(x)^2 + (15*b^2*cosh(x)^4 - 18*b^2*cosh(x)^2 - a^2 + 2*a*b + 3*b^2)*sinh(x)^2 - a^2 - 2*a*b - b^2 + 2*(3*b^2*cosh(x)^5 - 6*b^2*cosh(x)^3 - (a^2 - 2*a*b - 3*b^2)*cosh(x))*sinh(x))*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a*b^2 + b^3)*cosh(x)^7 - 3*(a*b^2 + 2*b^3)*cosh(x)^5 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^3 + (a^3 - 3*a*b^2 - 2*b^3)*cosh(x))*sinh(x))/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) - ((a^2 - a*b - 2*b^2)*cosh(x)^4 + 4*(a^2 - a*b - 2*b^2)*cosh(x)*sinh(x)^3 + (a^2 - a*b - 2*b^2)*sinh(x)^4 + 2*(a^2 - a*b - 2*b^2)*cosh(x)^2 + 2*(3*(a^2 - a*b - 2*b^2)*cosh(x)^2 + a^2 - a*b - 2*b^2)*sinh(x)^2 + a^2 - a*b - 2*b^2 + 4*((a^2 - a*b - 2*b^2)*cosh(x)^3 + (a^2 - a*b - 2*b^2)*cosh(x))*sinh(x))*sqrt(b)*log(-((a + 2*b)*cosh(x)^4 + 4*(a + 2*b)*cosh(x)*sinh(x)^3 + (a + 2*b)*sinh(x)^4 + 2*(a - 2*b)*cosh(x)^2 + 2*(3*(a + 2*b)*cosh(x)^2 + a - 2*b)*sinh(x)^2 - 2*sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + 2*b)*cosh(x)^3 + (a - 2*b)*cosh(x))*sinh(x) + a + 2*b)/(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)) + (b^2*cosh(x)^4 + 4*b^2*cosh(x)*sinh(x)^3 + b^2*sinh(x)^4 + 2*b^2*cosh(x)^2 + 2*(3*b^2*cosh(x)^2 + b^2)*sinh(x)^2 + b^2 + 4*(b^2*cosh(x)^3 + b^2*cosh(x))*sinh(x))*sqrt(a + b)*log(((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*a*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + b)*cosh(x)^3 + a*cosh(x))*sinh(x) + a + b)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) - 2*sqrt(2)*((a*b + b^2)*cosh(x)^2 + 2*(a*b + b^2)*cosh(x)*sinh(x) + (a*b + b^2)*sinh(x)^2 - a*b - b^2)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/((a*b^2 + b^3)*cosh(x)^4 + 4*(a*b^2 + b^3)*cosh(x)*sinh(x)^3 + (a*b^2 + b^3)*sinh(x)^4 + a*b^2 + b^3 + 2*(a*b^2 + b^3)*cosh(x)^2 + 2*(a*b^2 + b^3 + 3*(a*b^2 + b^3)*cosh(x)^2)*sinh(x)^2 + 4*((a*b^2 + b^3)*cosh(x)^3 + (a*b^2 + b^3)*cosh(x))*sinh(x)), -1/4*(2*((a^2 - a*b - 2*b^2)*cosh(x)^4 + 4*(a^2 - a*b - 2*b^2)*cosh(x)*sinh(x)^3 + (a^2 - a*b - 2*b^2)*sinh(x)^4 + 2*(a^2 - a*b - 2*b^2)*cosh(x)^2 + 2*(3*(a^2 - a*b - 2*b^2)*cosh(x)^2 + a^2 - a*b - 2*b^2)*sinh(x)^2 + a^2 - a*b - 2*b^2 + 4*((a^2 - a*b - 2*b^2)*cosh(x)^3 + (a^2 - a*b - 2*b^2)*cosh(x))*sinh(x))*sqrt(-b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a - b)*cosh(x))*sinh(x) + a + b)) - (b^2*cosh(x)^4 + 4*b^2*cosh(x)*sinh(x)^3 + b^2*sinh(x)^4 + 2*b^2*cosh(x)^2 + 2*(3*b^2*cosh(x)^2 + b^2)*sinh(x)^2 + b^2 + 4*(b^2*cosh(x)^3 + b^2*cosh(x))*sinh(x))*sqrt(a + b)*log(-((a*b^2 + b^3)*cosh(x)^8 + 8*(a*b^2 + b^3)*cosh(x)*sinh(x)^7 + (a*b^2 + b^3)*sinh(x)^8 - 2*(a*b^2 + 2*b^3)*cosh(x)^6 - 2*(a*b^2 + 2*b^3 - 14*(a*b^2 + b^3)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a*b^2 + b^3)*cosh(x)^3 - 3*(a*b^2 + 2*b^3)*cosh(x))*sinh(x)^5 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^4 + (70*(a*b^2 + b^3)*cosh(x)^4 + a^3 - a^2*b + 4*a*b^2 + 6*b^3 - 30*(a*b^2 + 2*b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a*b^2 + b^3)*cosh(x)^5 - 10*(a*b^2 + 2*b^3)*cosh(x)^3 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x))*sinh(x)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 + 2*(a^3 - 3*a*b^2 - 2*b^3)*cosh(x)^2 + 2*(14*(a*b^2 + b^3)*cosh(x)^6 - 15*(a*b^2 + 2*b^3)*cosh(x)^4 + a^3 - 3*a*b^2 - 2*b^3 + 3*(a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^2)*sinh(x)^2 + sqrt(2)*(b^2*cosh(x)^6 + 6*b^2*cosh(x)*sinh(x)^5 + b^2*sinh(x)^6 - 3*b^2*cosh(x)^4 + 3*(5*b^2*cosh(x)^2 - b^2)*sinh(x)^4 + 4*(5*b^2*cosh(x)^3 - 3*b^2*cosh(x))*sinh(x)^3 - (a^2 - 2*a*b - 3*b^2)*cosh(x)^2 + (15*b^2*cosh(x)^4 - 18*b^2*cosh(x)^2 - a^2 + 2*a*b + 3*b^2)*sinh(x)^2 - a^2 - 2*a*b - b^2 + 2*(3*b^2*cosh(x)^5 - 6*b^2*cosh(x)^3 - (a^2 - 2*a*b - 3*b^2)*cosh(x))*sinh(x))*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a*b^2 + b^3)*cosh(x)^7 - 3*(a*b^2 + 2*b^3)*cosh(x)^5 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^3 + (a^3 - 3*a*b^2 - 2*b^3)*cosh(x))*sinh(x))/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) - (b^2*cosh(x)^4 + 4*b^2*cosh(x)*sinh(x)^3 + b^2*sinh(x)^4 + 2*b^2*cosh(x)^2 + 2*(3*b^2*cosh(x)^2 + b^2)*sinh(x)^2 + b^2 + 4*(b^2*cosh(x)^3 + b^2*cosh(x))*sinh(x))*sqrt(a + b)*log(((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*a*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + b)*cosh(x)^3 + a*cosh(x))*sinh(x) + a + b)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) + 2*sqrt(2)*((a*b + b^2)*cosh(x)^2 + 2*(a*b + b^2)*cosh(x)*sinh(x) + (a*b + b^2)*sinh(x)^2 - a*b - b^2)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/((a*b^2 + b^3)*cosh(x)^4 + 4*(a*b^2 + b^3)*cosh(x)*sinh(x)^3 + (a*b^2 + b^3)*sinh(x)^4 + a*b^2 + b^3 + 2*(a*b^2 + b^3)*cosh(x)^2 + 2*(a*b^2 + b^3 + 3*(a*b^2 + b^3)*cosh(x)^2)*sinh(x)^2 + 4*((a*b^2 + b^3)*cosh(x)^3 + (a*b^2 + b^3)*cosh(x))*sinh(x)), -1/4*(2*(b^2*cosh(x)^4 + 4*b^2*cosh(x)*sinh(x)^3 + b^2*sinh(x)^4 + 2*b^2*cosh(x)^2 + 2*(3*b^2*cosh(x)^2 + b^2)*sinh(x)^2 + b^2 + 4*(b^2*cosh(x)^3 + b^2*cosh(x))*sinh(x))*sqrt(-a - b)*arctan(sqrt(2)*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 - a - b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a*b + b^2)*cosh(x)^4 + 4*(a*b + b^2)*cosh(x)*sinh(x)^3 + (a*b + b^2)*sinh(x)^4 + (a^2 - a*b - 2*b^2)*cosh(x)^2 + (6*(a*b + b^2)*cosh(x)^2 + a^2 - a*b - 2*b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(2*(a*b + b^2)*cosh(x)^3 + (a^2 - a*b - 2*b^2)*cosh(x))*sinh(x))) + 2*(b^2*cosh(x)^4 + 4*b^2*cosh(x)*sinh(x)^3 + b^2*sinh(x)^4 + 2*b^2*cosh(x)^2 + 2*(3*b^2*cosh(x)^2 + b^2)*sinh(x)^2 + b^2 + 4*(b^2*cosh(x)^3 + b^2*cosh(x))*sinh(x))*sqrt(-a - b)*arctan(sqrt(2)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 + a + b)) + ((a^2 - a*b - 2*b^2)*cosh(x)^4 + 4*(a^2 - a*b - 2*b^2)*cosh(x)*sinh(x)^3 + (a^2 - a*b - 2*b^2)*sinh(x)^4 + 2*(a^2 - a*b - 2*b^2)*cosh(x)^2 + 2*(3*(a^2 - a*b - 2*b^2)*cosh(x)^2 + a^2 - a*b - 2*b^2)*sinh(x)^2 + a^2 - a*b - 2*b^2 + 4*((a^2 - a*b - 2*b^2)*cosh(x)^3 + (a^2 - a*b - 2*b^2)*cosh(x))*sinh(x))*sqrt(b)*log(-((a + 2*b)*cosh(x)^4 + 4*(a + 2*b)*cosh(x)*sinh(x)^3 + (a + 2*b)*sinh(x)^4 + 2*(a - 2*b)*cosh(x)^2 + 2*(3*(a + 2*b)*cosh(x)^2 + a - 2*b)*sinh(x)^2 - 2*sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + 2*b)*cosh(x)^3 + (a - 2*b)*cosh(x))*sinh(x) + a + 2*b)/(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)) + 2*sqrt(2)*((a*b + b^2)*cosh(x)^2 + 2*(a*b + b^2)*cosh(x)*sinh(x) + (a*b + b^2)*sinh(x)^2 - a*b - b^2)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/((a*b^2 + b^3)*cosh(x)^4 + 4*(a*b^2 + b^3)*cosh(x)*sinh(x)^3 + (a*b^2 + b^3)*sinh(x)^4 + a*b^2 + b^3 + 2*(a*b^2 + b^3)*cosh(x)^2 + 2*(a*b^2 + b^3 + 3*(a*b^2 + b^3)*cosh(x)^2)*sinh(x)^2 + 4*((a*b^2 + b^3)*cosh(x)^3 + (a*b^2 + b^3)*cosh(x))*sinh(x)), -1/2*((b^2*cosh(x)^4 + 4*b^2*cosh(x)*sinh(x)^3 + b^2*sinh(x)^4 + 2*b^2*cosh(x)^2 + 2*(3*b^2*cosh(x)^2 + b^2)*sinh(x)^2 + b^2 + 4*(b^2*cosh(x)^3 + b^2*cosh(x))*sinh(x))*sqrt(-a - b)*arctan(sqrt(2)*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 - a - b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a*b + b^2)*cosh(x)^4 + 4*(a*b + b^2)*cosh(x)*sinh(x)^3 + (a*b + b^2)*sinh(x)^4 + (a^2 - a*b - 2*b^2)*cosh(x)^2 + (6*(a*b + b^2)*cosh(x)^2 + a^2 - a*b - 2*b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(2*(a*b + b^2)*cosh(x)^3 + (a^2 - a*b - 2*b^2)*cosh(x))*sinh(x))) + ((a^2 - a*b - 2*b^2)*cosh(x)^4 + 4*(a^2 - a*b - 2*b^2)*cosh(x)*sinh(x)^3 + (a^2 - a*b - 2*b^2)*sinh(x)^4 + 2*(a^2 - a*b - 2*b^2)*cosh(x)^2 + 2*(3*(a^2 - a*b - 2*b^2)*cosh(x)^2 + a^2 - a*b - 2*b^2)*sinh(x)^2 + a^2 - a*b - 2*b^2 + 4*((a^2 - a*b - 2*b^2)*cosh(x)^3 + (a^2 - a*b - 2*b^2)*cosh(x))*sinh(x))*sqrt(-b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a - b)*cosh(x))*sinh(x) + a + b)) + (b^2*cosh(x)^4 + 4*b^2*cosh(x)*sinh(x)^3 + b^2*sinh(x)^4 + 2*b^2*cosh(x)^2 + 2*(3*b^2*cosh(x)^2 + b^2)*sinh(x)^2 + b^2 + 4*(b^2*cosh(x)^3 + b^2*cosh(x))*sinh(x))*sqrt(-a - b)*arctan(sqrt(2)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 + a + b)) + sqrt(2)*((a*b + b^2)*cosh(x)^2 + 2*(a*b + b^2)*cosh(x)*sinh(x) + (a*b + b^2)*sinh(x)^2 - a*b - b^2)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/((a*b^2 + b^3)*cosh(x)^4 + 4*(a*b^2 + b^3)*cosh(x)*sinh(x)^3 + (a*b^2 + b^3)*sinh(x)^4 + a*b^2 + b^3 + 2*(a*b^2 + b^3)*cosh(x)^2 + 2*(a*b^2 + b^3 + 3*(a*b^2 + b^3)*cosh(x)^2)*sinh(x)^2 + 4*((a*b^2 + b^3)*cosh(x)^3 + (a*b^2 + b^3)*cosh(x))*sinh(x))]","B",0
231,1,1625,0,0.510542," ","integrate(tanh(x)^3/(a+b*tanh(x)^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} + b\right)} \sqrt{a + b} \log\left(\frac{{\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{3} + a^{2} b\right)} \sinh\left(x\right)^{8} + 2 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} + 2 \, {\left(2 \, a^{3} + a^{2} b + 14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} + 3 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3} + 30 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} + 10 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} + 2 \, {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} + 15 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 2 \, a^{3} + 3 \, a^{2} b - b^{3} + 3 \, {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(a^{2} \cosh\left(x\right)^{6} + 6 \, a^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + a^{2} \sinh\left(x\right)^{6} + 3 \, a^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, a^{2} \cosh\left(x\right)^{2} + a^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, a^{2} \cosh\left(x\right)^{3} + 3 \, a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, a^{2} \cosh\left(x\right)^{4} + 18 \, a^{2} \cosh\left(x\right)^{2} + 3 \, a^{2} + 2 \, a b - b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(x\right)^{5} + 6 \, a^{2} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{7} + 3 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) + {\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} + b\right)} \sqrt{a + b} \log\left(-\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - b\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - b \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right) - 4 \, \sqrt{2} {\left(a + b\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{4 \, {\left({\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a b + b^{2}\right)} \sinh\left(x\right)^{2} + a b + b^{2}\right)}}, -\frac{{\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} + b\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(a \cosh\left(x\right)^{2} + 2 \, a \cosh\left(x\right) \sinh\left(x\right) + a \sinh\left(x\right)^{2} + a + b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a^{2} + a b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{2} + a b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{2} + a b\right)} \sinh\left(x\right)^{4} + {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} + 2 \, a^{2} + a b - b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(2 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + {\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} + b\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) + 2 \, \sqrt{2} {\left(a + b\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{2 \, {\left({\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a b + b^{2}\right)} \sinh\left(x\right)^{2} + a b + b^{2}\right)}}\right]"," ",0,"[1/4*((b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 + b)*sqrt(a + b)*log(((a^3 + a^2*b)*cosh(x)^8 + 8*(a^3 + a^2*b)*cosh(x)*sinh(x)^7 + (a^3 + a^2*b)*sinh(x)^8 + 2*(2*a^3 + a^2*b)*cosh(x)^6 + 2*(2*a^3 + a^2*b + 14*(a^3 + a^2*b)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a^3 + a^2*b)*cosh(x)^3 + 3*(2*a^3 + a^2*b)*cosh(x))*sinh(x)^5 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^4 + (70*(a^3 + a^2*b)*cosh(x)^4 + 6*a^3 + 4*a^2*b - a*b^2 + b^3 + 30*(2*a^3 + a^2*b)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a^3 + a^2*b)*cosh(x)^5 + 10*(2*a^3 + a^2*b)*cosh(x)^3 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x))*sinh(x)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 + 2*(2*a^3 + 3*a^2*b - b^3)*cosh(x)^2 + 2*(14*(a^3 + a^2*b)*cosh(x)^6 + 15*(2*a^3 + a^2*b)*cosh(x)^4 + 2*a^3 + 3*a^2*b - b^3 + 3*(6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^2)*sinh(x)^2 + sqrt(2)*(a^2*cosh(x)^6 + 6*a^2*cosh(x)*sinh(x)^5 + a^2*sinh(x)^6 + 3*a^2*cosh(x)^4 + 3*(5*a^2*cosh(x)^2 + a^2)*sinh(x)^4 + 4*(5*a^2*cosh(x)^3 + 3*a^2*cosh(x))*sinh(x)^3 + (3*a^2 + 2*a*b - b^2)*cosh(x)^2 + (15*a^2*cosh(x)^4 + 18*a^2*cosh(x)^2 + 3*a^2 + 2*a*b - b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(3*a^2*cosh(x)^5 + 6*a^2*cosh(x)^3 + (3*a^2 + 2*a*b - b^2)*cosh(x))*sinh(x))*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a^3 + a^2*b)*cosh(x)^7 + 3*(2*a^3 + a^2*b)*cosh(x)^5 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^3 + (2*a^3 + 3*a^2*b - b^3)*cosh(x))*sinh(x))/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) + (b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 + b)*sqrt(a + b)*log(-((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*b*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + b)*cosh(x)^3 - b*cosh(x))*sinh(x) + a + b)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) - 4*sqrt(2)*(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/((a*b + b^2)*cosh(x)^2 + 2*(a*b + b^2)*cosh(x)*sinh(x) + (a*b + b^2)*sinh(x)^2 + a*b + b^2), -1/2*((b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 + b)*sqrt(-a - b)*arctan(sqrt(2)*(a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 + a + b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a^2 + a*b)*cosh(x)^4 + 4*(a^2 + a*b)*cosh(x)*sinh(x)^3 + (a^2 + a*b)*sinh(x)^4 + (2*a^2 + a*b - b^2)*cosh(x)^2 + (6*(a^2 + a*b)*cosh(x)^2 + 2*a^2 + a*b - b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(2*(a^2 + a*b)*cosh(x)^3 + (2*a^2 + a*b - b^2)*cosh(x))*sinh(x))) + (b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 + b)*sqrt(-a - b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a - b)*cosh(x))*sinh(x) + a + b)) + 2*sqrt(2)*(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/((a*b + b^2)*cosh(x)^2 + 2*(a*b + b^2)*cosh(x)*sinh(x) + (a*b + b^2)*sinh(x)^2 + a*b + b^2)]","B",0
232,1,3361,0,0.667964," ","integrate(tanh(x)^2/(a+b*tanh(x)^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{a + b} b \log\left(-\frac{{\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a b^{2} + b^{3}\right)} \sinh\left(x\right)^{8} - 2 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{6} - 2 \, {\left(a b^{2} + 2 \, b^{3} - 14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3} - 30 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} + 2 \, {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} - 3 \, a b^{2} - 2 \, b^{3} + 3 \, {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(b^{2} \cosh\left(x\right)^{6} + 6 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + b^{2} \sinh\left(x\right)^{6} - 3 \, b^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, b^{2} \cosh\left(x\right)^{2} - b^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, b^{2} \cosh\left(x\right)^{3} - 3 \, b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, b^{2} \cosh\left(x\right)^{4} - 18 \, b^{2} \cosh\left(x\right)^{2} - a^{2} + 2 \, a b + 3 \, b^{2}\right)} \sinh\left(x\right)^{2} - a^{2} - 2 \, a b - b^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{5} - 6 \, b^{2} \cosh\left(x\right)^{3} - {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{5} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) + 2 \, {\left(a + b\right)} \sqrt{b} \log\left(-\frac{{\left(a + 2 \, b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + 2 \, b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + a - 2 \, b\right)} \sinh\left(x\right)^{2} - 2 \, \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + 2 \, b\right)} \cosh\left(x\right)^{3} + {\left(a - 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + 2 \, b}{\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) + \sqrt{a + b} b \log\left(\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, a \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + a \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right)}{4 \, {\left(a b + b^{2}\right)}}, \frac{4 \, {\left(a + b\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{-b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) + \sqrt{a + b} b \log\left(-\frac{{\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a b^{2} + b^{3}\right)} \sinh\left(x\right)^{8} - 2 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{6} - 2 \, {\left(a b^{2} + 2 \, b^{3} - 14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3} - 30 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} + 2 \, {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} - 3 \, a b^{2} - 2 \, b^{3} + 3 \, {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(b^{2} \cosh\left(x\right)^{6} + 6 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + b^{2} \sinh\left(x\right)^{6} - 3 \, b^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, b^{2} \cosh\left(x\right)^{2} - b^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, b^{2} \cosh\left(x\right)^{3} - 3 \, b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, b^{2} \cosh\left(x\right)^{4} - 18 \, b^{2} \cosh\left(x\right)^{2} - a^{2} + 2 \, a b + 3 \, b^{2}\right)} \sinh\left(x\right)^{2} - a^{2} - 2 \, a b - b^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{5} - 6 \, b^{2} \cosh\left(x\right)^{3} - {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{5} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) + \sqrt{a + b} b \log\left(\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, a \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + a \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right)}{4 \, {\left(a b + b^{2}\right)}}, -\frac{\sqrt{-a - b} b \arctan\left(\frac{\sqrt{2} {\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} - a - b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a b + b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a b + b^{2}\right)} \sinh\left(x\right)^{4} + {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} - a b - 2 \, b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(2 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + \sqrt{-a - b} b \arctan\left(\frac{\sqrt{2} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a + b\right)} \sinh\left(x\right)^{2} + a + b}\right) - {\left(a + b\right)} \sqrt{b} \log\left(-\frac{{\left(a + 2 \, b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + 2 \, b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + a - 2 \, b\right)} \sinh\left(x\right)^{2} - 2 \, \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + 2 \, b\right)} \cosh\left(x\right)^{3} + {\left(a - 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + 2 \, b}{\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)}{2 \, {\left(a b + b^{2}\right)}}, -\frac{\sqrt{-a - b} b \arctan\left(\frac{\sqrt{2} {\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} - a - b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a b + b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a b + b^{2}\right)} \sinh\left(x\right)^{4} + {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} - a b - 2 \, b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(2 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) - 2 \, {\left(a + b\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{-b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) + \sqrt{-a - b} b \arctan\left(\frac{\sqrt{2} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a + b\right)} \sinh\left(x\right)^{2} + a + b}\right)}{2 \, {\left(a b + b^{2}\right)}}\right]"," ",0,"[1/4*(sqrt(a + b)*b*log(-((a*b^2 + b^3)*cosh(x)^8 + 8*(a*b^2 + b^3)*cosh(x)*sinh(x)^7 + (a*b^2 + b^3)*sinh(x)^8 - 2*(a*b^2 + 2*b^3)*cosh(x)^6 - 2*(a*b^2 + 2*b^3 - 14*(a*b^2 + b^3)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a*b^2 + b^3)*cosh(x)^3 - 3*(a*b^2 + 2*b^3)*cosh(x))*sinh(x)^5 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^4 + (70*(a*b^2 + b^3)*cosh(x)^4 + a^3 - a^2*b + 4*a*b^2 + 6*b^3 - 30*(a*b^2 + 2*b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a*b^2 + b^3)*cosh(x)^5 - 10*(a*b^2 + 2*b^3)*cosh(x)^3 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x))*sinh(x)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 + 2*(a^3 - 3*a*b^2 - 2*b^3)*cosh(x)^2 + 2*(14*(a*b^2 + b^3)*cosh(x)^6 - 15*(a*b^2 + 2*b^3)*cosh(x)^4 + a^3 - 3*a*b^2 - 2*b^3 + 3*(a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^2)*sinh(x)^2 + sqrt(2)*(b^2*cosh(x)^6 + 6*b^2*cosh(x)*sinh(x)^5 + b^2*sinh(x)^6 - 3*b^2*cosh(x)^4 + 3*(5*b^2*cosh(x)^2 - b^2)*sinh(x)^4 + 4*(5*b^2*cosh(x)^3 - 3*b^2*cosh(x))*sinh(x)^3 - (a^2 - 2*a*b - 3*b^2)*cosh(x)^2 + (15*b^2*cosh(x)^4 - 18*b^2*cosh(x)^2 - a^2 + 2*a*b + 3*b^2)*sinh(x)^2 - a^2 - 2*a*b - b^2 + 2*(3*b^2*cosh(x)^5 - 6*b^2*cosh(x)^3 - (a^2 - 2*a*b - 3*b^2)*cosh(x))*sinh(x))*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a*b^2 + b^3)*cosh(x)^7 - 3*(a*b^2 + 2*b^3)*cosh(x)^5 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^3 + (a^3 - 3*a*b^2 - 2*b^3)*cosh(x))*sinh(x))/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) + 2*(a + b)*sqrt(b)*log(-((a + 2*b)*cosh(x)^4 + 4*(a + 2*b)*cosh(x)*sinh(x)^3 + (a + 2*b)*sinh(x)^4 + 2*(a - 2*b)*cosh(x)^2 + 2*(3*(a + 2*b)*cosh(x)^2 + a - 2*b)*sinh(x)^2 - 2*sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + 2*b)*cosh(x)^3 + (a - 2*b)*cosh(x))*sinh(x) + a + 2*b)/(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)) + sqrt(a + b)*b*log(((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*a*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + b)*cosh(x)^3 + a*cosh(x))*sinh(x) + a + b)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)))/(a*b + b^2), 1/4*(4*(a + b)*sqrt(-b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a - b)*cosh(x))*sinh(x) + a + b)) + sqrt(a + b)*b*log(-((a*b^2 + b^3)*cosh(x)^8 + 8*(a*b^2 + b^3)*cosh(x)*sinh(x)^7 + (a*b^2 + b^3)*sinh(x)^8 - 2*(a*b^2 + 2*b^3)*cosh(x)^6 - 2*(a*b^2 + 2*b^3 - 14*(a*b^2 + b^3)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a*b^2 + b^3)*cosh(x)^3 - 3*(a*b^2 + 2*b^3)*cosh(x))*sinh(x)^5 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^4 + (70*(a*b^2 + b^3)*cosh(x)^4 + a^3 - a^2*b + 4*a*b^2 + 6*b^3 - 30*(a*b^2 + 2*b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a*b^2 + b^3)*cosh(x)^5 - 10*(a*b^2 + 2*b^3)*cosh(x)^3 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x))*sinh(x)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 + 2*(a^3 - 3*a*b^2 - 2*b^3)*cosh(x)^2 + 2*(14*(a*b^2 + b^3)*cosh(x)^6 - 15*(a*b^2 + 2*b^3)*cosh(x)^4 + a^3 - 3*a*b^2 - 2*b^3 + 3*(a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^2)*sinh(x)^2 + sqrt(2)*(b^2*cosh(x)^6 + 6*b^2*cosh(x)*sinh(x)^5 + b^2*sinh(x)^6 - 3*b^2*cosh(x)^4 + 3*(5*b^2*cosh(x)^2 - b^2)*sinh(x)^4 + 4*(5*b^2*cosh(x)^3 - 3*b^2*cosh(x))*sinh(x)^3 - (a^2 - 2*a*b - 3*b^2)*cosh(x)^2 + (15*b^2*cosh(x)^4 - 18*b^2*cosh(x)^2 - a^2 + 2*a*b + 3*b^2)*sinh(x)^2 - a^2 - 2*a*b - b^2 + 2*(3*b^2*cosh(x)^5 - 6*b^2*cosh(x)^3 - (a^2 - 2*a*b - 3*b^2)*cosh(x))*sinh(x))*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a*b^2 + b^3)*cosh(x)^7 - 3*(a*b^2 + 2*b^3)*cosh(x)^5 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^3 + (a^3 - 3*a*b^2 - 2*b^3)*cosh(x))*sinh(x))/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) + sqrt(a + b)*b*log(((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*a*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + b)*cosh(x)^3 + a*cosh(x))*sinh(x) + a + b)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)))/(a*b + b^2), -1/2*(sqrt(-a - b)*b*arctan(sqrt(2)*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 - a - b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a*b + b^2)*cosh(x)^4 + 4*(a*b + b^2)*cosh(x)*sinh(x)^3 + (a*b + b^2)*sinh(x)^4 + (a^2 - a*b - 2*b^2)*cosh(x)^2 + (6*(a*b + b^2)*cosh(x)^2 + a^2 - a*b - 2*b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(2*(a*b + b^2)*cosh(x)^3 + (a^2 - a*b - 2*b^2)*cosh(x))*sinh(x))) + sqrt(-a - b)*b*arctan(sqrt(2)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 + a + b)) - (a + b)*sqrt(b)*log(-((a + 2*b)*cosh(x)^4 + 4*(a + 2*b)*cosh(x)*sinh(x)^3 + (a + 2*b)*sinh(x)^4 + 2*(a - 2*b)*cosh(x)^2 + 2*(3*(a + 2*b)*cosh(x)^2 + a - 2*b)*sinh(x)^2 - 2*sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + 2*b)*cosh(x)^3 + (a - 2*b)*cosh(x))*sinh(x) + a + 2*b)/(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)))/(a*b + b^2), -1/2*(sqrt(-a - b)*b*arctan(sqrt(2)*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 - a - b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a*b + b^2)*cosh(x)^4 + 4*(a*b + b^2)*cosh(x)*sinh(x)^3 + (a*b + b^2)*sinh(x)^4 + (a^2 - a*b - 2*b^2)*cosh(x)^2 + (6*(a*b + b^2)*cosh(x)^2 + a^2 - a*b - 2*b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(2*(a*b + b^2)*cosh(x)^3 + (a^2 - a*b - 2*b^2)*cosh(x))*sinh(x))) - 2*(a + b)*sqrt(-b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a - b)*cosh(x))*sinh(x) + a + b)) + sqrt(-a - b)*b*arctan(sqrt(2)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 + a + b)))/(a*b + b^2)]","B",0
233,1,1361,0,0.500248," ","integrate(tanh(x)/(a+b*tanh(x)^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{a + b} \log\left(\frac{{\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{3} + a^{2} b\right)} \sinh\left(x\right)^{8} + 2 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} + 2 \, {\left(2 \, a^{3} + a^{2} b + 14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} + 3 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3} + 30 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} + 10 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} + 2 \, {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} + 15 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 2 \, a^{3} + 3 \, a^{2} b - b^{3} + 3 \, {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(a^{2} \cosh\left(x\right)^{6} + 6 \, a^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + a^{2} \sinh\left(x\right)^{6} + 3 \, a^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, a^{2} \cosh\left(x\right)^{2} + a^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, a^{2} \cosh\left(x\right)^{3} + 3 \, a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, a^{2} \cosh\left(x\right)^{4} + 18 \, a^{2} \cosh\left(x\right)^{2} + 3 \, a^{2} + 2 \, a b - b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(x\right)^{5} + 6 \, a^{2} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{7} + 3 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) + \sqrt{a + b} \log\left(-\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - b\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - b \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right)}{4 \, {\left(a + b\right)}}, -\frac{\sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(a \cosh\left(x\right)^{2} + 2 \, a \cosh\left(x\right) \sinh\left(x\right) + a \sinh\left(x\right)^{2} + a + b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a^{2} + a b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{2} + a b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{2} + a b\right)} \sinh\left(x\right)^{4} + {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} + 2 \, a^{2} + a b - b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(2 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right)}{2 \, {\left(a + b\right)}}\right]"," ",0,"[1/4*(sqrt(a + b)*log(((a^3 + a^2*b)*cosh(x)^8 + 8*(a^3 + a^2*b)*cosh(x)*sinh(x)^7 + (a^3 + a^2*b)*sinh(x)^8 + 2*(2*a^3 + a^2*b)*cosh(x)^6 + 2*(2*a^3 + a^2*b + 14*(a^3 + a^2*b)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a^3 + a^2*b)*cosh(x)^3 + 3*(2*a^3 + a^2*b)*cosh(x))*sinh(x)^5 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^4 + (70*(a^3 + a^2*b)*cosh(x)^4 + 6*a^3 + 4*a^2*b - a*b^2 + b^3 + 30*(2*a^3 + a^2*b)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a^3 + a^2*b)*cosh(x)^5 + 10*(2*a^3 + a^2*b)*cosh(x)^3 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x))*sinh(x)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 + 2*(2*a^3 + 3*a^2*b - b^3)*cosh(x)^2 + 2*(14*(a^3 + a^2*b)*cosh(x)^6 + 15*(2*a^3 + a^2*b)*cosh(x)^4 + 2*a^3 + 3*a^2*b - b^3 + 3*(6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^2)*sinh(x)^2 + sqrt(2)*(a^2*cosh(x)^6 + 6*a^2*cosh(x)*sinh(x)^5 + a^2*sinh(x)^6 + 3*a^2*cosh(x)^4 + 3*(5*a^2*cosh(x)^2 + a^2)*sinh(x)^4 + 4*(5*a^2*cosh(x)^3 + 3*a^2*cosh(x))*sinh(x)^3 + (3*a^2 + 2*a*b - b^2)*cosh(x)^2 + (15*a^2*cosh(x)^4 + 18*a^2*cosh(x)^2 + 3*a^2 + 2*a*b - b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(3*a^2*cosh(x)^5 + 6*a^2*cosh(x)^3 + (3*a^2 + 2*a*b - b^2)*cosh(x))*sinh(x))*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a^3 + a^2*b)*cosh(x)^7 + 3*(2*a^3 + a^2*b)*cosh(x)^5 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^3 + (2*a^3 + 3*a^2*b - b^3)*cosh(x))*sinh(x))/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) + sqrt(a + b)*log(-((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*b*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + b)*cosh(x)^3 - b*cosh(x))*sinh(x) + a + b)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)))/(a + b), -1/2*(sqrt(-a - b)*arctan(sqrt(2)*(a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 + a + b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a^2 + a*b)*cosh(x)^4 + 4*(a^2 + a*b)*cosh(x)*sinh(x)^3 + (a^2 + a*b)*sinh(x)^4 + (2*a^2 + a*b - b^2)*cosh(x)^2 + (6*(a^2 + a*b)*cosh(x)^2 + 2*a^2 + a*b - b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(2*(a^2 + a*b)*cosh(x)^3 + (2*a^2 + a*b - b^2)*cosh(x))*sinh(x))) + sqrt(-a - b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a - b)*cosh(x))*sinh(x) + a + b)))/(a + b)]","B",0
234,1,1287,0,0.481178," ","integrate(1/(a+b*tanh(x)^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{a + b} \log\left(-\frac{{\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a b^{2} + b^{3}\right)} \sinh\left(x\right)^{8} - 2 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{6} - 2 \, {\left(a b^{2} + 2 \, b^{3} - 14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3} - 30 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} + 2 \, {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} - 3 \, a b^{2} - 2 \, b^{3} + 3 \, {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(b^{2} \cosh\left(x\right)^{6} + 6 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + b^{2} \sinh\left(x\right)^{6} - 3 \, b^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, b^{2} \cosh\left(x\right)^{2} - b^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, b^{2} \cosh\left(x\right)^{3} - 3 \, b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, b^{2} \cosh\left(x\right)^{4} - 18 \, b^{2} \cosh\left(x\right)^{2} - a^{2} + 2 \, a b + 3 \, b^{2}\right)} \sinh\left(x\right)^{2} - a^{2} - 2 \, a b - b^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{5} - 6 \, b^{2} \cosh\left(x\right)^{3} - {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{5} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) + \sqrt{a + b} \log\left(\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, a \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + a \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right)}{4 \, {\left(a + b\right)}}, -\frac{\sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} - a - b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a b + b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a b + b^{2}\right)} \sinh\left(x\right)^{4} + {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} - a b - 2 \, b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(2 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a + b\right)} \sinh\left(x\right)^{2} + a + b}\right)}{2 \, {\left(a + b\right)}}\right]"," ",0,"[1/4*(sqrt(a + b)*log(-((a*b^2 + b^3)*cosh(x)^8 + 8*(a*b^2 + b^3)*cosh(x)*sinh(x)^7 + (a*b^2 + b^3)*sinh(x)^8 - 2*(a*b^2 + 2*b^3)*cosh(x)^6 - 2*(a*b^2 + 2*b^3 - 14*(a*b^2 + b^3)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a*b^2 + b^3)*cosh(x)^3 - 3*(a*b^2 + 2*b^3)*cosh(x))*sinh(x)^5 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^4 + (70*(a*b^2 + b^3)*cosh(x)^4 + a^3 - a^2*b + 4*a*b^2 + 6*b^3 - 30*(a*b^2 + 2*b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a*b^2 + b^3)*cosh(x)^5 - 10*(a*b^2 + 2*b^3)*cosh(x)^3 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x))*sinh(x)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 + 2*(a^3 - 3*a*b^2 - 2*b^3)*cosh(x)^2 + 2*(14*(a*b^2 + b^3)*cosh(x)^6 - 15*(a*b^2 + 2*b^3)*cosh(x)^4 + a^3 - 3*a*b^2 - 2*b^3 + 3*(a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^2)*sinh(x)^2 + sqrt(2)*(b^2*cosh(x)^6 + 6*b^2*cosh(x)*sinh(x)^5 + b^2*sinh(x)^6 - 3*b^2*cosh(x)^4 + 3*(5*b^2*cosh(x)^2 - b^2)*sinh(x)^4 + 4*(5*b^2*cosh(x)^3 - 3*b^2*cosh(x))*sinh(x)^3 - (a^2 - 2*a*b - 3*b^2)*cosh(x)^2 + (15*b^2*cosh(x)^4 - 18*b^2*cosh(x)^2 - a^2 + 2*a*b + 3*b^2)*sinh(x)^2 - a^2 - 2*a*b - b^2 + 2*(3*b^2*cosh(x)^5 - 6*b^2*cosh(x)^3 - (a^2 - 2*a*b - 3*b^2)*cosh(x))*sinh(x))*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a*b^2 + b^3)*cosh(x)^7 - 3*(a*b^2 + 2*b^3)*cosh(x)^5 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^3 + (a^3 - 3*a*b^2 - 2*b^3)*cosh(x))*sinh(x))/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) + sqrt(a + b)*log(((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*a*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + b)*cosh(x)^3 + a*cosh(x))*sinh(x) + a + b)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)))/(a + b), -1/2*(sqrt(-a - b)*arctan(sqrt(2)*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 - a - b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a*b + b^2)*cosh(x)^4 + 4*(a*b + b^2)*cosh(x)*sinh(x)^3 + (a*b + b^2)*sinh(x)^4 + (a^2 - a*b - 2*b^2)*cosh(x)^2 + (6*(a*b + b^2)*cosh(x)^2 + a^2 - a*b - 2*b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(2*(a*b + b^2)*cosh(x)^3 + (a^2 - a*b - 2*b^2)*cosh(x))*sinh(x))) + sqrt(-a - b)*arctan(sqrt(2)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 + a + b)))/(a + b)]","B",0
235,1,3527,0,0.610965," ","integrate(coth(x)/(a+b*tanh(x)^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{\sqrt{a + b} a \log\left(\frac{{\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{3} + a^{2} b\right)} \sinh\left(x\right)^{8} + 2 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} + 2 \, {\left(2 \, a^{3} + a^{2} b + 14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} + 3 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3} + 30 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} + 10 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} + 2 \, {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} + 15 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 2 \, a^{3} + 3 \, a^{2} b - b^{3} + 3 \, {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(a^{2} \cosh\left(x\right)^{6} + 6 \, a^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + a^{2} \sinh\left(x\right)^{6} + 3 \, a^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, a^{2} \cosh\left(x\right)^{2} + a^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, a^{2} \cosh\left(x\right)^{3} + 3 \, a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, a^{2} \cosh\left(x\right)^{4} + 18 \, a^{2} \cosh\left(x\right)^{2} + 3 \, a^{2} + 2 \, a b - b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(x\right)^{5} + 6 \, a^{2} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{7} + 3 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) + 2 \, {\left(a + b\right)} \sqrt{a} \log\left(-\frac{{\left(2 \, a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(2 \, a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(2 \, a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(2 \, a + b\right)} \cosh\left(x\right)^{2} + 2 \, a - b\right)} \sinh\left(x\right)^{2} - 2 \, \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{a} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(2 \, a + b\right)} \cosh\left(x\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + 2 \, a + b}{\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) + \sqrt{a + b} a \log\left(-\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - b\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - b \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right)}{4 \, {\left(a^{2} + a b\right)}}, \frac{4 \, \sqrt{-a} {\left(a + b\right)} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{-a} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) + \sqrt{a + b} a \log\left(\frac{{\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{3} + a^{2} b\right)} \sinh\left(x\right)^{8} + 2 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} + 2 \, {\left(2 \, a^{3} + a^{2} b + 14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} + 3 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3} + 30 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} + 10 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} + 2 \, {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} + 15 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 2 \, a^{3} + 3 \, a^{2} b - b^{3} + 3 \, {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(a^{2} \cosh\left(x\right)^{6} + 6 \, a^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + a^{2} \sinh\left(x\right)^{6} + 3 \, a^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, a^{2} \cosh\left(x\right)^{2} + a^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, a^{2} \cosh\left(x\right)^{3} + 3 \, a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, a^{2} \cosh\left(x\right)^{4} + 18 \, a^{2} \cosh\left(x\right)^{2} + 3 \, a^{2} + 2 \, a b - b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(x\right)^{5} + 6 \, a^{2} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{7} + 3 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) + \sqrt{a + b} a \log\left(-\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - b\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - b \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right)}{4 \, {\left(a^{2} + a b\right)}}, -\frac{a \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(a \cosh\left(x\right)^{2} + 2 \, a \cosh\left(x\right) \sinh\left(x\right) + a \sinh\left(x\right)^{2} + a + b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a^{2} + a b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{2} + a b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{2} + a b\right)} \sinh\left(x\right)^{4} + {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} + 2 \, a^{2} + a b - b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(2 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + a \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) - {\left(a + b\right)} \sqrt{a} \log\left(-\frac{{\left(2 \, a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(2 \, a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(2 \, a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(2 \, a + b\right)} \cosh\left(x\right)^{2} + 2 \, a - b\right)} \sinh\left(x\right)^{2} - 2 \, \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{a} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(2 \, a + b\right)} \cosh\left(x\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + 2 \, a + b}{\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)}{2 \, {\left(a^{2} + a b\right)}}, \frac{2 \, \sqrt{-a} {\left(a + b\right)} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{-a} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) - a \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(a \cosh\left(x\right)^{2} + 2 \, a \cosh\left(x\right) \sinh\left(x\right) + a \sinh\left(x\right)^{2} + a + b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a^{2} + a b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{2} + a b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{2} + a b\right)} \sinh\left(x\right)^{4} + {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} + 2 \, a^{2} + a b - b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(2 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) - a \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right)}{2 \, {\left(a^{2} + a b\right)}}\right]"," ",0,"[1/4*(sqrt(a + b)*a*log(((a^3 + a^2*b)*cosh(x)^8 + 8*(a^3 + a^2*b)*cosh(x)*sinh(x)^7 + (a^3 + a^2*b)*sinh(x)^8 + 2*(2*a^3 + a^2*b)*cosh(x)^6 + 2*(2*a^3 + a^2*b + 14*(a^3 + a^2*b)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a^3 + a^2*b)*cosh(x)^3 + 3*(2*a^3 + a^2*b)*cosh(x))*sinh(x)^5 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^4 + (70*(a^3 + a^2*b)*cosh(x)^4 + 6*a^3 + 4*a^2*b - a*b^2 + b^3 + 30*(2*a^3 + a^2*b)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a^3 + a^2*b)*cosh(x)^5 + 10*(2*a^3 + a^2*b)*cosh(x)^3 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x))*sinh(x)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 + 2*(2*a^3 + 3*a^2*b - b^3)*cosh(x)^2 + 2*(14*(a^3 + a^2*b)*cosh(x)^6 + 15*(2*a^3 + a^2*b)*cosh(x)^4 + 2*a^3 + 3*a^2*b - b^3 + 3*(6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^2)*sinh(x)^2 + sqrt(2)*(a^2*cosh(x)^6 + 6*a^2*cosh(x)*sinh(x)^5 + a^2*sinh(x)^6 + 3*a^2*cosh(x)^4 + 3*(5*a^2*cosh(x)^2 + a^2)*sinh(x)^4 + 4*(5*a^2*cosh(x)^3 + 3*a^2*cosh(x))*sinh(x)^3 + (3*a^2 + 2*a*b - b^2)*cosh(x)^2 + (15*a^2*cosh(x)^4 + 18*a^2*cosh(x)^2 + 3*a^2 + 2*a*b - b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(3*a^2*cosh(x)^5 + 6*a^2*cosh(x)^3 + (3*a^2 + 2*a*b - b^2)*cosh(x))*sinh(x))*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a^3 + a^2*b)*cosh(x)^7 + 3*(2*a^3 + a^2*b)*cosh(x)^5 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^3 + (2*a^3 + 3*a^2*b - b^3)*cosh(x))*sinh(x))/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) + 2*(a + b)*sqrt(a)*log(-((2*a + b)*cosh(x)^4 + 4*(2*a + b)*cosh(x)*sinh(x)^3 + (2*a + b)*sinh(x)^4 + 2*(2*a - b)*cosh(x)^2 + 2*(3*(2*a + b)*cosh(x)^2 + 2*a - b)*sinh(x)^2 - 2*sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((2*a + b)*cosh(x)^3 + (2*a - b)*cosh(x))*sinh(x) + 2*a + b)/(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)) + sqrt(a + b)*a*log(-((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*b*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + b)*cosh(x)^3 - b*cosh(x))*sinh(x) + a + b)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)))/(a^2 + a*b), 1/4*(4*sqrt(-a)*(a + b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(-a)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a - b)*cosh(x))*sinh(x) + a + b)) + sqrt(a + b)*a*log(((a^3 + a^2*b)*cosh(x)^8 + 8*(a^3 + a^2*b)*cosh(x)*sinh(x)^7 + (a^3 + a^2*b)*sinh(x)^8 + 2*(2*a^3 + a^2*b)*cosh(x)^6 + 2*(2*a^3 + a^2*b + 14*(a^3 + a^2*b)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a^3 + a^2*b)*cosh(x)^3 + 3*(2*a^3 + a^2*b)*cosh(x))*sinh(x)^5 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^4 + (70*(a^3 + a^2*b)*cosh(x)^4 + 6*a^3 + 4*a^2*b - a*b^2 + b^3 + 30*(2*a^3 + a^2*b)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a^3 + a^2*b)*cosh(x)^5 + 10*(2*a^3 + a^2*b)*cosh(x)^3 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x))*sinh(x)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 + 2*(2*a^3 + 3*a^2*b - b^3)*cosh(x)^2 + 2*(14*(a^3 + a^2*b)*cosh(x)^6 + 15*(2*a^3 + a^2*b)*cosh(x)^4 + 2*a^3 + 3*a^2*b - b^3 + 3*(6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^2)*sinh(x)^2 + sqrt(2)*(a^2*cosh(x)^6 + 6*a^2*cosh(x)*sinh(x)^5 + a^2*sinh(x)^6 + 3*a^2*cosh(x)^4 + 3*(5*a^2*cosh(x)^2 + a^2)*sinh(x)^4 + 4*(5*a^2*cosh(x)^3 + 3*a^2*cosh(x))*sinh(x)^3 + (3*a^2 + 2*a*b - b^2)*cosh(x)^2 + (15*a^2*cosh(x)^4 + 18*a^2*cosh(x)^2 + 3*a^2 + 2*a*b - b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(3*a^2*cosh(x)^5 + 6*a^2*cosh(x)^3 + (3*a^2 + 2*a*b - b^2)*cosh(x))*sinh(x))*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a^3 + a^2*b)*cosh(x)^7 + 3*(2*a^3 + a^2*b)*cosh(x)^5 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^3 + (2*a^3 + 3*a^2*b - b^3)*cosh(x))*sinh(x))/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) + sqrt(a + b)*a*log(-((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*b*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + b)*cosh(x)^3 - b*cosh(x))*sinh(x) + a + b)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)))/(a^2 + a*b), -1/2*(a*sqrt(-a - b)*arctan(sqrt(2)*(a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 + a + b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a^2 + a*b)*cosh(x)^4 + 4*(a^2 + a*b)*cosh(x)*sinh(x)^3 + (a^2 + a*b)*sinh(x)^4 + (2*a^2 + a*b - b^2)*cosh(x)^2 + (6*(a^2 + a*b)*cosh(x)^2 + 2*a^2 + a*b - b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(2*(a^2 + a*b)*cosh(x)^3 + (2*a^2 + a*b - b^2)*cosh(x))*sinh(x))) + a*sqrt(-a - b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a - b)*cosh(x))*sinh(x) + a + b)) - (a + b)*sqrt(a)*log(-((2*a + b)*cosh(x)^4 + 4*(2*a + b)*cosh(x)*sinh(x)^3 + (2*a + b)*sinh(x)^4 + 2*(2*a - b)*cosh(x)^2 + 2*(3*(2*a + b)*cosh(x)^2 + 2*a - b)*sinh(x)^2 - 2*sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((2*a + b)*cosh(x)^3 + (2*a - b)*cosh(x))*sinh(x) + 2*a + b)/(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)))/(a^2 + a*b), 1/2*(2*sqrt(-a)*(a + b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(-a)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a - b)*cosh(x))*sinh(x) + a + b)) - a*sqrt(-a - b)*arctan(sqrt(2)*(a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 + a + b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a^2 + a*b)*cosh(x)^4 + 4*(a^2 + a*b)*cosh(x)*sinh(x)^3 + (a^2 + a*b)*sinh(x)^4 + (2*a^2 + a*b - b^2)*cosh(x)^2 + (6*(a^2 + a*b)*cosh(x)^2 + 2*a^2 + a*b - b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(2*(a^2 + a*b)*cosh(x)^3 + (2*a^2 + a*b - b^2)*cosh(x))*sinh(x))) - a*sqrt(-a - b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a - b)*cosh(x))*sinh(x) + a + b)))/(a^2 + a*b)]","B",0
236,1,1565,0,0.599451," ","integrate(coth(x)^2/(a+b*tanh(x)^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(a \cosh\left(x\right)^{2} + 2 \, a \cosh\left(x\right) \sinh\left(x\right) + a \sinh\left(x\right)^{2} - a\right)} \sqrt{a + b} \log\left(-\frac{{\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a b^{2} + b^{3}\right)} \sinh\left(x\right)^{8} - 2 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{6} - 2 \, {\left(a b^{2} + 2 \, b^{3} - 14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3} - 30 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} + 2 \, {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} - 3 \, a b^{2} - 2 \, b^{3} + 3 \, {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(b^{2} \cosh\left(x\right)^{6} + 6 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + b^{2} \sinh\left(x\right)^{6} - 3 \, b^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, b^{2} \cosh\left(x\right)^{2} - b^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, b^{2} \cosh\left(x\right)^{3} - 3 \, b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, b^{2} \cosh\left(x\right)^{4} - 18 \, b^{2} \cosh\left(x\right)^{2} - a^{2} + 2 \, a b + 3 \, b^{2}\right)} \sinh\left(x\right)^{2} - a^{2} - 2 \, a b - b^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{5} - 6 \, b^{2} \cosh\left(x\right)^{3} - {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{5} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) + {\left(a \cosh\left(x\right)^{2} + 2 \, a \cosh\left(x\right) \sinh\left(x\right) + a \sinh\left(x\right)^{2} - a\right)} \sqrt{a + b} \log\left(\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, a \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + a \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right) - 4 \, \sqrt{2} {\left(a + b\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{4 \, {\left({\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a^{2} + a b\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a^{2} + a b\right)} \sinh\left(x\right)^{2} - a^{2} - a b\right)}}, -\frac{{\left(a \cosh\left(x\right)^{2} + 2 \, a \cosh\left(x\right) \sinh\left(x\right) + a \sinh\left(x\right)^{2} - a\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} - a - b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a b + b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a b + b^{2}\right)} \sinh\left(x\right)^{4} + {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} - a b - 2 \, b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(2 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + {\left(a \cosh\left(x\right)^{2} + 2 \, a \cosh\left(x\right) \sinh\left(x\right) + a \sinh\left(x\right)^{2} - a\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a + b\right)} \sinh\left(x\right)^{2} + a + b}\right) + 2 \, \sqrt{2} {\left(a + b\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{2 \, {\left({\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a^{2} + a b\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a^{2} + a b\right)} \sinh\left(x\right)^{2} - a^{2} - a b\right)}}\right]"," ",0,"[1/4*((a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 - a)*sqrt(a + b)*log(-((a*b^2 + b^3)*cosh(x)^8 + 8*(a*b^2 + b^3)*cosh(x)*sinh(x)^7 + (a*b^2 + b^3)*sinh(x)^8 - 2*(a*b^2 + 2*b^3)*cosh(x)^6 - 2*(a*b^2 + 2*b^3 - 14*(a*b^2 + b^3)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a*b^2 + b^3)*cosh(x)^3 - 3*(a*b^2 + 2*b^3)*cosh(x))*sinh(x)^5 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^4 + (70*(a*b^2 + b^3)*cosh(x)^4 + a^3 - a^2*b + 4*a*b^2 + 6*b^3 - 30*(a*b^2 + 2*b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a*b^2 + b^3)*cosh(x)^5 - 10*(a*b^2 + 2*b^3)*cosh(x)^3 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x))*sinh(x)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 + 2*(a^3 - 3*a*b^2 - 2*b^3)*cosh(x)^2 + 2*(14*(a*b^2 + b^3)*cosh(x)^6 - 15*(a*b^2 + 2*b^3)*cosh(x)^4 + a^3 - 3*a*b^2 - 2*b^3 + 3*(a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^2)*sinh(x)^2 + sqrt(2)*(b^2*cosh(x)^6 + 6*b^2*cosh(x)*sinh(x)^5 + b^2*sinh(x)^6 - 3*b^2*cosh(x)^4 + 3*(5*b^2*cosh(x)^2 - b^2)*sinh(x)^4 + 4*(5*b^2*cosh(x)^3 - 3*b^2*cosh(x))*sinh(x)^3 - (a^2 - 2*a*b - 3*b^2)*cosh(x)^2 + (15*b^2*cosh(x)^4 - 18*b^2*cosh(x)^2 - a^2 + 2*a*b + 3*b^2)*sinh(x)^2 - a^2 - 2*a*b - b^2 + 2*(3*b^2*cosh(x)^5 - 6*b^2*cosh(x)^3 - (a^2 - 2*a*b - 3*b^2)*cosh(x))*sinh(x))*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a*b^2 + b^3)*cosh(x)^7 - 3*(a*b^2 + 2*b^3)*cosh(x)^5 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^3 + (a^3 - 3*a*b^2 - 2*b^3)*cosh(x))*sinh(x))/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) + (a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 - a)*sqrt(a + b)*log(((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*a*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + b)*cosh(x)^3 + a*cosh(x))*sinh(x) + a + b)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) - 4*sqrt(2)*(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/((a^2 + a*b)*cosh(x)^2 + 2*(a^2 + a*b)*cosh(x)*sinh(x) + (a^2 + a*b)*sinh(x)^2 - a^2 - a*b), -1/2*((a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 - a)*sqrt(-a - b)*arctan(sqrt(2)*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 - a - b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a*b + b^2)*cosh(x)^4 + 4*(a*b + b^2)*cosh(x)*sinh(x)^3 + (a*b + b^2)*sinh(x)^4 + (a^2 - a*b - 2*b^2)*cosh(x)^2 + (6*(a*b + b^2)*cosh(x)^2 + a^2 - a*b - 2*b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(2*(a*b + b^2)*cosh(x)^3 + (a^2 - a*b - 2*b^2)*cosh(x))*sinh(x))) + (a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 - a)*sqrt(-a - b)*arctan(sqrt(2)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 + a + b)) + 2*sqrt(2)*(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/((a^2 + a*b)*cosh(x)^2 + 2*(a^2 + a*b)*cosh(x)*sinh(x) + (a^2 + a*b)*sinh(x)^2 - a^2 - a*b)]","B",0
237,1,5711,0,0.986065," ","integrate(coth(x)^3/(a+b*tanh(x)^2)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\left(a^{2} \cosh\left(x\right)^{4} + 4 \, a^{2} \cosh\left(x\right) \sinh\left(x\right)^{3} + a^{2} \sinh\left(x\right)^{4} - 2 \, a^{2} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(x\right)^{2} - a^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 4 \, {\left(a^{2} \cosh\left(x\right)^{3} - a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \log\left(\frac{{\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{3} + a^{2} b\right)} \sinh\left(x\right)^{8} + 2 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} + 2 \, {\left(2 \, a^{3} + a^{2} b + 14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} + 3 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3} + 30 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} + 10 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} + 2 \, {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} + 15 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 2 \, a^{3} + 3 \, a^{2} b - b^{3} + 3 \, {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(a^{2} \cosh\left(x\right)^{6} + 6 \, a^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + a^{2} \sinh\left(x\right)^{6} + 3 \, a^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, a^{2} \cosh\left(x\right)^{2} + a^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, a^{2} \cosh\left(x\right)^{3} + 3 \, a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, a^{2} \cosh\left(x\right)^{4} + 18 \, a^{2} \cosh\left(x\right)^{2} + 3 \, a^{2} + 2 \, a b - b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(x\right)^{5} + 6 \, a^{2} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{7} + 3 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) - {\left({\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(2 \, a^{2} + a b - b^{2}\right)} \sinh\left(x\right)^{4} - 2 \, {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)^{2} - 2 \, a^{2} - a b + b^{2}\right)} \sinh\left(x\right)^{2} + 2 \, a^{2} + a b - b^{2} + 4 \, {\left({\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)^{3} - {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \log\left(-\frac{{\left(2 \, a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(2 \, a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(2 \, a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(2 \, a + b\right)} \cosh\left(x\right)^{2} + 2 \, a - b\right)} \sinh\left(x\right)^{2} + 2 \, \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{a} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(2 \, a + b\right)} \cosh\left(x\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + 2 \, a + b}{\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) + {\left(a^{2} \cosh\left(x\right)^{4} + 4 \, a^{2} \cosh\left(x\right) \sinh\left(x\right)^{3} + a^{2} \sinh\left(x\right)^{4} - 2 \, a^{2} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(x\right)^{2} - a^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 4 \, {\left(a^{2} \cosh\left(x\right)^{3} - a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \log\left(-\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - b\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - b \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right) - 2 \, \sqrt{2} {\left({\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a^{2} + a b\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a^{2} + a b\right)} \sinh\left(x\right)^{2} + a^{2} + a b\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{4 \, {\left({\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{3} + a^{2} b\right)} \sinh\left(x\right)^{4} + a^{3} + a^{2} b - 2 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2} - 2 \, {\left(a^{3} + a^{2} b - 3 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} - {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}, \frac{2 \, {\left({\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(2 \, a^{2} + a b - b^{2}\right)} \sinh\left(x\right)^{4} - 2 \, {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)^{2} - 2 \, a^{2} - a b + b^{2}\right)} \sinh\left(x\right)^{2} + 2 \, a^{2} + a b - b^{2} + 4 \, {\left({\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)^{3} - {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{-a} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) + {\left(a^{2} \cosh\left(x\right)^{4} + 4 \, a^{2} \cosh\left(x\right) \sinh\left(x\right)^{3} + a^{2} \sinh\left(x\right)^{4} - 2 \, a^{2} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(x\right)^{2} - a^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 4 \, {\left(a^{2} \cosh\left(x\right)^{3} - a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \log\left(\frac{{\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{3} + a^{2} b\right)} \sinh\left(x\right)^{8} + 2 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} + 2 \, {\left(2 \, a^{3} + a^{2} b + 14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} + 3 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3} + 30 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} + 10 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} + 2 \, {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} + 15 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 2 \, a^{3} + 3 \, a^{2} b - b^{3} + 3 \, {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(a^{2} \cosh\left(x\right)^{6} + 6 \, a^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + a^{2} \sinh\left(x\right)^{6} + 3 \, a^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, a^{2} \cosh\left(x\right)^{2} + a^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, a^{2} \cosh\left(x\right)^{3} + 3 \, a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, a^{2} \cosh\left(x\right)^{4} + 18 \, a^{2} \cosh\left(x\right)^{2} + 3 \, a^{2} + 2 \, a b - b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(x\right)^{5} + 6 \, a^{2} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{7} + 3 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) + {\left(a^{2} \cosh\left(x\right)^{4} + 4 \, a^{2} \cosh\left(x\right) \sinh\left(x\right)^{3} + a^{2} \sinh\left(x\right)^{4} - 2 \, a^{2} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(x\right)^{2} - a^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 4 \, {\left(a^{2} \cosh\left(x\right)^{3} - a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \log\left(-\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - b\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - b \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right) - 2 \, \sqrt{2} {\left({\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a^{2} + a b\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a^{2} + a b\right)} \sinh\left(x\right)^{2} + a^{2} + a b\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{4 \, {\left({\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{3} + a^{2} b\right)} \sinh\left(x\right)^{4} + a^{3} + a^{2} b - 2 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2} - 2 \, {\left(a^{3} + a^{2} b - 3 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} - {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}, -\frac{2 \, {\left(a^{2} \cosh\left(x\right)^{4} + 4 \, a^{2} \cosh\left(x\right) \sinh\left(x\right)^{3} + a^{2} \sinh\left(x\right)^{4} - 2 \, a^{2} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(x\right)^{2} - a^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 4 \, {\left(a^{2} \cosh\left(x\right)^{3} - a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(a \cosh\left(x\right)^{2} + 2 \, a \cosh\left(x\right) \sinh\left(x\right) + a \sinh\left(x\right)^{2} + a + b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a^{2} + a b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{2} + a b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{2} + a b\right)} \sinh\left(x\right)^{4} + {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} + 2 \, a^{2} + a b - b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(2 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + 2 \, {\left(a^{2} \cosh\left(x\right)^{4} + 4 \, a^{2} \cosh\left(x\right) \sinh\left(x\right)^{3} + a^{2} \sinh\left(x\right)^{4} - 2 \, a^{2} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(x\right)^{2} - a^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 4 \, {\left(a^{2} \cosh\left(x\right)^{3} - a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) + {\left({\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(2 \, a^{2} + a b - b^{2}\right)} \sinh\left(x\right)^{4} - 2 \, {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)^{2} - 2 \, a^{2} - a b + b^{2}\right)} \sinh\left(x\right)^{2} + 2 \, a^{2} + a b - b^{2} + 4 \, {\left({\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)^{3} - {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \log\left(-\frac{{\left(2 \, a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(2 \, a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(2 \, a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(2 \, a + b\right)} \cosh\left(x\right)^{2} + 2 \, a - b\right)} \sinh\left(x\right)^{2} + 2 \, \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{a} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(2 \, a + b\right)} \cosh\left(x\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + 2 \, a + b}{\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) + 2 \, \sqrt{2} {\left({\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a^{2} + a b\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a^{2} + a b\right)} \sinh\left(x\right)^{2} + a^{2} + a b\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{4 \, {\left({\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{3} + a^{2} b\right)} \sinh\left(x\right)^{4} + a^{3} + a^{2} b - 2 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2} - 2 \, {\left(a^{3} + a^{2} b - 3 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} - {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}, \frac{{\left({\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(2 \, a^{2} + a b - b^{2}\right)} \sinh\left(x\right)^{4} - 2 \, {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)^{2} - 2 \, a^{2} - a b + b^{2}\right)} \sinh\left(x\right)^{2} + 2 \, a^{2} + a b - b^{2} + 4 \, {\left({\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)^{3} - {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{-a} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) - {\left(a^{2} \cosh\left(x\right)^{4} + 4 \, a^{2} \cosh\left(x\right) \sinh\left(x\right)^{3} + a^{2} \sinh\left(x\right)^{4} - 2 \, a^{2} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(x\right)^{2} - a^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 4 \, {\left(a^{2} \cosh\left(x\right)^{3} - a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(a \cosh\left(x\right)^{2} + 2 \, a \cosh\left(x\right) \sinh\left(x\right) + a \sinh\left(x\right)^{2} + a + b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a^{2} + a b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{2} + a b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{2} + a b\right)} \sinh\left(x\right)^{4} + {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} + 2 \, a^{2} + a b - b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(2 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) - {\left(a^{2} \cosh\left(x\right)^{4} + 4 \, a^{2} \cosh\left(x\right) \sinh\left(x\right)^{3} + a^{2} \sinh\left(x\right)^{4} - 2 \, a^{2} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(x\right)^{2} - a^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 4 \, {\left(a^{2} \cosh\left(x\right)^{3} - a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) - \sqrt{2} {\left({\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a^{2} + a b\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a^{2} + a b\right)} \sinh\left(x\right)^{2} + a^{2} + a b\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{2 \, {\left({\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{3} + a^{2} b\right)} \sinh\left(x\right)^{4} + a^{3} + a^{2} b - 2 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2} - 2 \, {\left(a^{3} + a^{2} b - 3 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} - {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}\right]"," ",0,"[1/4*((a^2*cosh(x)^4 + 4*a^2*cosh(x)*sinh(x)^3 + a^2*sinh(x)^4 - 2*a^2*cosh(x)^2 + 2*(3*a^2*cosh(x)^2 - a^2)*sinh(x)^2 + a^2 + 4*(a^2*cosh(x)^3 - a^2*cosh(x))*sinh(x))*sqrt(a + b)*log(((a^3 + a^2*b)*cosh(x)^8 + 8*(a^3 + a^2*b)*cosh(x)*sinh(x)^7 + (a^3 + a^2*b)*sinh(x)^8 + 2*(2*a^3 + a^2*b)*cosh(x)^6 + 2*(2*a^3 + a^2*b + 14*(a^3 + a^2*b)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a^3 + a^2*b)*cosh(x)^3 + 3*(2*a^3 + a^2*b)*cosh(x))*sinh(x)^5 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^4 + (70*(a^3 + a^2*b)*cosh(x)^4 + 6*a^3 + 4*a^2*b - a*b^2 + b^3 + 30*(2*a^3 + a^2*b)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a^3 + a^2*b)*cosh(x)^5 + 10*(2*a^3 + a^2*b)*cosh(x)^3 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x))*sinh(x)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 + 2*(2*a^3 + 3*a^2*b - b^3)*cosh(x)^2 + 2*(14*(a^3 + a^2*b)*cosh(x)^6 + 15*(2*a^3 + a^2*b)*cosh(x)^4 + 2*a^3 + 3*a^2*b - b^3 + 3*(6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^2)*sinh(x)^2 + sqrt(2)*(a^2*cosh(x)^6 + 6*a^2*cosh(x)*sinh(x)^5 + a^2*sinh(x)^6 + 3*a^2*cosh(x)^4 + 3*(5*a^2*cosh(x)^2 + a^2)*sinh(x)^4 + 4*(5*a^2*cosh(x)^3 + 3*a^2*cosh(x))*sinh(x)^3 + (3*a^2 + 2*a*b - b^2)*cosh(x)^2 + (15*a^2*cosh(x)^4 + 18*a^2*cosh(x)^2 + 3*a^2 + 2*a*b - b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(3*a^2*cosh(x)^5 + 6*a^2*cosh(x)^3 + (3*a^2 + 2*a*b - b^2)*cosh(x))*sinh(x))*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a^3 + a^2*b)*cosh(x)^7 + 3*(2*a^3 + a^2*b)*cosh(x)^5 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^3 + (2*a^3 + 3*a^2*b - b^3)*cosh(x))*sinh(x))/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) - ((2*a^2 + a*b - b^2)*cosh(x)^4 + 4*(2*a^2 + a*b - b^2)*cosh(x)*sinh(x)^3 + (2*a^2 + a*b - b^2)*sinh(x)^4 - 2*(2*a^2 + a*b - b^2)*cosh(x)^2 + 2*(3*(2*a^2 + a*b - b^2)*cosh(x)^2 - 2*a^2 - a*b + b^2)*sinh(x)^2 + 2*a^2 + a*b - b^2 + 4*((2*a^2 + a*b - b^2)*cosh(x)^3 - (2*a^2 + a*b - b^2)*cosh(x))*sinh(x))*sqrt(a)*log(-((2*a + b)*cosh(x)^4 + 4*(2*a + b)*cosh(x)*sinh(x)^3 + (2*a + b)*sinh(x)^4 + 2*(2*a - b)*cosh(x)^2 + 2*(3*(2*a + b)*cosh(x)^2 + 2*a - b)*sinh(x)^2 + 2*sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((2*a + b)*cosh(x)^3 + (2*a - b)*cosh(x))*sinh(x) + 2*a + b)/(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)) + (a^2*cosh(x)^4 + 4*a^2*cosh(x)*sinh(x)^3 + a^2*sinh(x)^4 - 2*a^2*cosh(x)^2 + 2*(3*a^2*cosh(x)^2 - a^2)*sinh(x)^2 + a^2 + 4*(a^2*cosh(x)^3 - a^2*cosh(x))*sinh(x))*sqrt(a + b)*log(-((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*b*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + b)*cosh(x)^3 - b*cosh(x))*sinh(x) + a + b)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) - 2*sqrt(2)*((a^2 + a*b)*cosh(x)^2 + 2*(a^2 + a*b)*cosh(x)*sinh(x) + (a^2 + a*b)*sinh(x)^2 + a^2 + a*b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/((a^3 + a^2*b)*cosh(x)^4 + 4*(a^3 + a^2*b)*cosh(x)*sinh(x)^3 + (a^3 + a^2*b)*sinh(x)^4 + a^3 + a^2*b - 2*(a^3 + a^2*b)*cosh(x)^2 - 2*(a^3 + a^2*b - 3*(a^3 + a^2*b)*cosh(x)^2)*sinh(x)^2 + 4*((a^3 + a^2*b)*cosh(x)^3 - (a^3 + a^2*b)*cosh(x))*sinh(x)), 1/4*(2*((2*a^2 + a*b - b^2)*cosh(x)^4 + 4*(2*a^2 + a*b - b^2)*cosh(x)*sinh(x)^3 + (2*a^2 + a*b - b^2)*sinh(x)^4 - 2*(2*a^2 + a*b - b^2)*cosh(x)^2 + 2*(3*(2*a^2 + a*b - b^2)*cosh(x)^2 - 2*a^2 - a*b + b^2)*sinh(x)^2 + 2*a^2 + a*b - b^2 + 4*((2*a^2 + a*b - b^2)*cosh(x)^3 - (2*a^2 + a*b - b^2)*cosh(x))*sinh(x))*sqrt(-a)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(-a)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a - b)*cosh(x))*sinh(x) + a + b)) + (a^2*cosh(x)^4 + 4*a^2*cosh(x)*sinh(x)^3 + a^2*sinh(x)^4 - 2*a^2*cosh(x)^2 + 2*(3*a^2*cosh(x)^2 - a^2)*sinh(x)^2 + a^2 + 4*(a^2*cosh(x)^3 - a^2*cosh(x))*sinh(x))*sqrt(a + b)*log(((a^3 + a^2*b)*cosh(x)^8 + 8*(a^3 + a^2*b)*cosh(x)*sinh(x)^7 + (a^3 + a^2*b)*sinh(x)^8 + 2*(2*a^3 + a^2*b)*cosh(x)^6 + 2*(2*a^3 + a^2*b + 14*(a^3 + a^2*b)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a^3 + a^2*b)*cosh(x)^3 + 3*(2*a^3 + a^2*b)*cosh(x))*sinh(x)^5 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^4 + (70*(a^3 + a^2*b)*cosh(x)^4 + 6*a^3 + 4*a^2*b - a*b^2 + b^3 + 30*(2*a^3 + a^2*b)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a^3 + a^2*b)*cosh(x)^5 + 10*(2*a^3 + a^2*b)*cosh(x)^3 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x))*sinh(x)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 + 2*(2*a^3 + 3*a^2*b - b^3)*cosh(x)^2 + 2*(14*(a^3 + a^2*b)*cosh(x)^6 + 15*(2*a^3 + a^2*b)*cosh(x)^4 + 2*a^3 + 3*a^2*b - b^3 + 3*(6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^2)*sinh(x)^2 + sqrt(2)*(a^2*cosh(x)^6 + 6*a^2*cosh(x)*sinh(x)^5 + a^2*sinh(x)^6 + 3*a^2*cosh(x)^4 + 3*(5*a^2*cosh(x)^2 + a^2)*sinh(x)^4 + 4*(5*a^2*cosh(x)^3 + 3*a^2*cosh(x))*sinh(x)^3 + (3*a^2 + 2*a*b - b^2)*cosh(x)^2 + (15*a^2*cosh(x)^4 + 18*a^2*cosh(x)^2 + 3*a^2 + 2*a*b - b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(3*a^2*cosh(x)^5 + 6*a^2*cosh(x)^3 + (3*a^2 + 2*a*b - b^2)*cosh(x))*sinh(x))*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a^3 + a^2*b)*cosh(x)^7 + 3*(2*a^3 + a^2*b)*cosh(x)^5 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^3 + (2*a^3 + 3*a^2*b - b^3)*cosh(x))*sinh(x))/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) + (a^2*cosh(x)^4 + 4*a^2*cosh(x)*sinh(x)^3 + a^2*sinh(x)^4 - 2*a^2*cosh(x)^2 + 2*(3*a^2*cosh(x)^2 - a^2)*sinh(x)^2 + a^2 + 4*(a^2*cosh(x)^3 - a^2*cosh(x))*sinh(x))*sqrt(a + b)*log(-((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*b*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + b)*cosh(x)^3 - b*cosh(x))*sinh(x) + a + b)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) - 2*sqrt(2)*((a^2 + a*b)*cosh(x)^2 + 2*(a^2 + a*b)*cosh(x)*sinh(x) + (a^2 + a*b)*sinh(x)^2 + a^2 + a*b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/((a^3 + a^2*b)*cosh(x)^4 + 4*(a^3 + a^2*b)*cosh(x)*sinh(x)^3 + (a^3 + a^2*b)*sinh(x)^4 + a^3 + a^2*b - 2*(a^3 + a^2*b)*cosh(x)^2 - 2*(a^3 + a^2*b - 3*(a^3 + a^2*b)*cosh(x)^2)*sinh(x)^2 + 4*((a^3 + a^2*b)*cosh(x)^3 - (a^3 + a^2*b)*cosh(x))*sinh(x)), -1/4*(2*(a^2*cosh(x)^4 + 4*a^2*cosh(x)*sinh(x)^3 + a^2*sinh(x)^4 - 2*a^2*cosh(x)^2 + 2*(3*a^2*cosh(x)^2 - a^2)*sinh(x)^2 + a^2 + 4*(a^2*cosh(x)^3 - a^2*cosh(x))*sinh(x))*sqrt(-a - b)*arctan(sqrt(2)*(a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 + a + b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a^2 + a*b)*cosh(x)^4 + 4*(a^2 + a*b)*cosh(x)*sinh(x)^3 + (a^2 + a*b)*sinh(x)^4 + (2*a^2 + a*b - b^2)*cosh(x)^2 + (6*(a^2 + a*b)*cosh(x)^2 + 2*a^2 + a*b - b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(2*(a^2 + a*b)*cosh(x)^3 + (2*a^2 + a*b - b^2)*cosh(x))*sinh(x))) + 2*(a^2*cosh(x)^4 + 4*a^2*cosh(x)*sinh(x)^3 + a^2*sinh(x)^4 - 2*a^2*cosh(x)^2 + 2*(3*a^2*cosh(x)^2 - a^2)*sinh(x)^2 + a^2 + 4*(a^2*cosh(x)^3 - a^2*cosh(x))*sinh(x))*sqrt(-a - b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a - b)*cosh(x))*sinh(x) + a + b)) + ((2*a^2 + a*b - b^2)*cosh(x)^4 + 4*(2*a^2 + a*b - b^2)*cosh(x)*sinh(x)^3 + (2*a^2 + a*b - b^2)*sinh(x)^4 - 2*(2*a^2 + a*b - b^2)*cosh(x)^2 + 2*(3*(2*a^2 + a*b - b^2)*cosh(x)^2 - 2*a^2 - a*b + b^2)*sinh(x)^2 + 2*a^2 + a*b - b^2 + 4*((2*a^2 + a*b - b^2)*cosh(x)^3 - (2*a^2 + a*b - b^2)*cosh(x))*sinh(x))*sqrt(a)*log(-((2*a + b)*cosh(x)^4 + 4*(2*a + b)*cosh(x)*sinh(x)^3 + (2*a + b)*sinh(x)^4 + 2*(2*a - b)*cosh(x)^2 + 2*(3*(2*a + b)*cosh(x)^2 + 2*a - b)*sinh(x)^2 + 2*sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((2*a + b)*cosh(x)^3 + (2*a - b)*cosh(x))*sinh(x) + 2*a + b)/(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)) + 2*sqrt(2)*((a^2 + a*b)*cosh(x)^2 + 2*(a^2 + a*b)*cosh(x)*sinh(x) + (a^2 + a*b)*sinh(x)^2 + a^2 + a*b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/((a^3 + a^2*b)*cosh(x)^4 + 4*(a^3 + a^2*b)*cosh(x)*sinh(x)^3 + (a^3 + a^2*b)*sinh(x)^4 + a^3 + a^2*b - 2*(a^3 + a^2*b)*cosh(x)^2 - 2*(a^3 + a^2*b - 3*(a^3 + a^2*b)*cosh(x)^2)*sinh(x)^2 + 4*((a^3 + a^2*b)*cosh(x)^3 - (a^3 + a^2*b)*cosh(x))*sinh(x)), 1/2*(((2*a^2 + a*b - b^2)*cosh(x)^4 + 4*(2*a^2 + a*b - b^2)*cosh(x)*sinh(x)^3 + (2*a^2 + a*b - b^2)*sinh(x)^4 - 2*(2*a^2 + a*b - b^2)*cosh(x)^2 + 2*(3*(2*a^2 + a*b - b^2)*cosh(x)^2 - 2*a^2 - a*b + b^2)*sinh(x)^2 + 2*a^2 + a*b - b^2 + 4*((2*a^2 + a*b - b^2)*cosh(x)^3 - (2*a^2 + a*b - b^2)*cosh(x))*sinh(x))*sqrt(-a)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(-a)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a - b)*cosh(x))*sinh(x) + a + b)) - (a^2*cosh(x)^4 + 4*a^2*cosh(x)*sinh(x)^3 + a^2*sinh(x)^4 - 2*a^2*cosh(x)^2 + 2*(3*a^2*cosh(x)^2 - a^2)*sinh(x)^2 + a^2 + 4*(a^2*cosh(x)^3 - a^2*cosh(x))*sinh(x))*sqrt(-a - b)*arctan(sqrt(2)*(a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 + a + b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a^2 + a*b)*cosh(x)^4 + 4*(a^2 + a*b)*cosh(x)*sinh(x)^3 + (a^2 + a*b)*sinh(x)^4 + (2*a^2 + a*b - b^2)*cosh(x)^2 + (6*(a^2 + a*b)*cosh(x)^2 + 2*a^2 + a*b - b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(2*(a^2 + a*b)*cosh(x)^3 + (2*a^2 + a*b - b^2)*cosh(x))*sinh(x))) - (a^2*cosh(x)^4 + 4*a^2*cosh(x)*sinh(x)^3 + a^2*sinh(x)^4 - 2*a^2*cosh(x)^2 + 2*(3*a^2*cosh(x)^2 - a^2)*sinh(x)^2 + a^2 + 4*(a^2*cosh(x)^3 - a^2*cosh(x))*sinh(x))*sqrt(-a - b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a - b)*cosh(x))*sinh(x) + a + b)) - sqrt(2)*((a^2 + a*b)*cosh(x)^2 + 2*(a^2 + a*b)*cosh(x)*sinh(x) + (a^2 + a*b)*sinh(x)^2 + a^2 + a*b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/((a^3 + a^2*b)*cosh(x)^4 + 4*(a^3 + a^2*b)*cosh(x)*sinh(x)^3 + (a^3 + a^2*b)*sinh(x)^4 + a^3 + a^2*b - 2*(a^3 + a^2*b)*cosh(x)^2 - 2*(a^3 + a^2*b - 3*(a^3 + a^2*b)*cosh(x)^2)*sinh(x)^2 + 4*((a^3 + a^2*b)*cosh(x)^3 - (a^3 + a^2*b)*cosh(x))*sinh(x))]","B",0
238,1,3991,0,0.864263," ","integrate(tanh(x)^5/(a+b*tanh(x)^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{6} + 6 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(a b^{2} + b^{3}\right)} \sinh\left(x\right)^{6} + {\left(3 \, a b^{2} - b^{3}\right)} \cosh\left(x\right)^{4} + {\left(3 \, a b^{2} - b^{3} + 15 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a b^{2} - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a b^{2} + b^{3} + {\left(3 \, a b^{2} - b^{3}\right)} \cosh\left(x\right)^{2} + {\left(15 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + 3 \, a b^{2} - b^{3} + 6 \, {\left(3 \, a b^{2} - b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{5} + 2 \, {\left(3 \, a b^{2} - b^{3}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a b^{2} - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \log\left(\frac{{\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{3} + a^{2} b\right)} \sinh\left(x\right)^{8} + 2 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} + 2 \, {\left(2 \, a^{3} + a^{2} b + 14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} + 3 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3} + 30 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} + 10 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} + 2 \, {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} + 15 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 2 \, a^{3} + 3 \, a^{2} b - b^{3} + 3 \, {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(a^{2} \cosh\left(x\right)^{6} + 6 \, a^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + a^{2} \sinh\left(x\right)^{6} + 3 \, a^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, a^{2} \cosh\left(x\right)^{2} + a^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, a^{2} \cosh\left(x\right)^{3} + 3 \, a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, a^{2} \cosh\left(x\right)^{4} + 18 \, a^{2} \cosh\left(x\right)^{2} + 3 \, a^{2} + 2 \, a b - b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(x\right)^{5} + 6 \, a^{2} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{7} + 3 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) + {\left({\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{6} + 6 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(a b^{2} + b^{3}\right)} \sinh\left(x\right)^{6} + {\left(3 \, a b^{2} - b^{3}\right)} \cosh\left(x\right)^{4} + {\left(3 \, a b^{2} - b^{3} + 15 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a b^{2} - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a b^{2} + b^{3} + {\left(3 \, a b^{2} - b^{3}\right)} \cosh\left(x\right)^{2} + {\left(15 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + 3 \, a b^{2} - b^{3} + 6 \, {\left(3 \, a b^{2} - b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{5} + 2 \, {\left(3 \, a b^{2} - b^{3}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a b^{2} - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \log\left(-\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - b\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - b \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right) - 4 \, \sqrt{2} {\left({\left(2 \, a^{3} + 4 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(2 \, a^{3} + 4 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(2 \, a^{3} + 4 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \sinh\left(x\right)^{4} + 2 \, a^{3} + 4 \, a^{2} b + 3 \, a b^{2} + b^{3} + 2 \, {\left(2 \, a^{3} + 2 \, a^{2} b - a b^{2} - b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(2 \, a^{3} + 2 \, a^{2} b - a b^{2} - b^{3} + 3 \, {\left(2 \, a^{3} + 4 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(2 \, a^{3} + 4 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{3} + 2 \, a^{2} b - a b^{2} - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{4 \, {\left({\left(a^{3} b^{2} + 3 \, a^{2} b^{3} + 3 \, a b^{4} + b^{5}\right)} \cosh\left(x\right)^{6} + 6 \, {\left(a^{3} b^{2} + 3 \, a^{2} b^{3} + 3 \, a b^{4} + b^{5}\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(a^{3} b^{2} + 3 \, a^{2} b^{3} + 3 \, a b^{4} + b^{5}\right)} \sinh\left(x\right)^{6} + a^{3} b^{2} + 3 \, a^{2} b^{3} + 3 \, a b^{4} + b^{5} + {\left(3 \, a^{3} b^{2} + 5 \, a^{2} b^{3} + a b^{4} - b^{5}\right)} \cosh\left(x\right)^{4} + {\left(3 \, a^{3} b^{2} + 5 \, a^{2} b^{3} + a b^{4} - b^{5} + 15 \, {\left(a^{3} b^{2} + 3 \, a^{2} b^{3} + 3 \, a b^{4} + b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, {\left(a^{3} b^{2} + 3 \, a^{2} b^{3} + 3 \, a b^{4} + b^{5}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{3} b^{2} + 5 \, a^{2} b^{3} + a b^{4} - b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(3 \, a^{3} b^{2} + 5 \, a^{2} b^{3} + a b^{4} - b^{5}\right)} \cosh\left(x\right)^{2} + {\left(3 \, a^{3} b^{2} + 5 \, a^{2} b^{3} + a b^{4} - b^{5} + 15 \, {\left(a^{3} b^{2} + 3 \, a^{2} b^{3} + 3 \, a b^{4} + b^{5}\right)} \cosh\left(x\right)^{4} + 6 \, {\left(3 \, a^{3} b^{2} + 5 \, a^{2} b^{3} + a b^{4} - b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a^{3} b^{2} + 3 \, a^{2} b^{3} + 3 \, a b^{4} + b^{5}\right)} \cosh\left(x\right)^{5} + 2 \, {\left(3 \, a^{3} b^{2} + 5 \, a^{2} b^{3} + a b^{4} - b^{5}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{3} b^{2} + 5 \, a^{2} b^{3} + a b^{4} - b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}, -\frac{{\left({\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{6} + 6 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(a b^{2} + b^{3}\right)} \sinh\left(x\right)^{6} + {\left(3 \, a b^{2} - b^{3}\right)} \cosh\left(x\right)^{4} + {\left(3 \, a b^{2} - b^{3} + 15 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a b^{2} - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a b^{2} + b^{3} + {\left(3 \, a b^{2} - b^{3}\right)} \cosh\left(x\right)^{2} + {\left(15 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + 3 \, a b^{2} - b^{3} + 6 \, {\left(3 \, a b^{2} - b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{5} + 2 \, {\left(3 \, a b^{2} - b^{3}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a b^{2} - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(a \cosh\left(x\right)^{2} + 2 \, a \cosh\left(x\right) \sinh\left(x\right) + a \sinh\left(x\right)^{2} + a + b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a^{2} + a b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{2} + a b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{2} + a b\right)} \sinh\left(x\right)^{4} + {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} + 2 \, a^{2} + a b - b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(2 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + {\left({\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{6} + 6 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(a b^{2} + b^{3}\right)} \sinh\left(x\right)^{6} + {\left(3 \, a b^{2} - b^{3}\right)} \cosh\left(x\right)^{4} + {\left(3 \, a b^{2} - b^{3} + 15 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a b^{2} - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a b^{2} + b^{3} + {\left(3 \, a b^{2} - b^{3}\right)} \cosh\left(x\right)^{2} + {\left(15 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + 3 \, a b^{2} - b^{3} + 6 \, {\left(3 \, a b^{2} - b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{5} + 2 \, {\left(3 \, a b^{2} - b^{3}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a b^{2} - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) + 2 \, \sqrt{2} {\left({\left(2 \, a^{3} + 4 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(2 \, a^{3} + 4 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(2 \, a^{3} + 4 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \sinh\left(x\right)^{4} + 2 \, a^{3} + 4 \, a^{2} b + 3 \, a b^{2} + b^{3} + 2 \, {\left(2 \, a^{3} + 2 \, a^{2} b - a b^{2} - b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(2 \, a^{3} + 2 \, a^{2} b - a b^{2} - b^{3} + 3 \, {\left(2 \, a^{3} + 4 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(2 \, a^{3} + 4 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{3} + 2 \, a^{2} b - a b^{2} - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{2 \, {\left({\left(a^{3} b^{2} + 3 \, a^{2} b^{3} + 3 \, a b^{4} + b^{5}\right)} \cosh\left(x\right)^{6} + 6 \, {\left(a^{3} b^{2} + 3 \, a^{2} b^{3} + 3 \, a b^{4} + b^{5}\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(a^{3} b^{2} + 3 \, a^{2} b^{3} + 3 \, a b^{4} + b^{5}\right)} \sinh\left(x\right)^{6} + a^{3} b^{2} + 3 \, a^{2} b^{3} + 3 \, a b^{4} + b^{5} + {\left(3 \, a^{3} b^{2} + 5 \, a^{2} b^{3} + a b^{4} - b^{5}\right)} \cosh\left(x\right)^{4} + {\left(3 \, a^{3} b^{2} + 5 \, a^{2} b^{3} + a b^{4} - b^{5} + 15 \, {\left(a^{3} b^{2} + 3 \, a^{2} b^{3} + 3 \, a b^{4} + b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, {\left(a^{3} b^{2} + 3 \, a^{2} b^{3} + 3 \, a b^{4} + b^{5}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{3} b^{2} + 5 \, a^{2} b^{3} + a b^{4} - b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(3 \, a^{3} b^{2} + 5 \, a^{2} b^{3} + a b^{4} - b^{5}\right)} \cosh\left(x\right)^{2} + {\left(3 \, a^{3} b^{2} + 5 \, a^{2} b^{3} + a b^{4} - b^{5} + 15 \, {\left(a^{3} b^{2} + 3 \, a^{2} b^{3} + 3 \, a b^{4} + b^{5}\right)} \cosh\left(x\right)^{4} + 6 \, {\left(3 \, a^{3} b^{2} + 5 \, a^{2} b^{3} + a b^{4} - b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a^{3} b^{2} + 3 \, a^{2} b^{3} + 3 \, a b^{4} + b^{5}\right)} \cosh\left(x\right)^{5} + 2 \, {\left(3 \, a^{3} b^{2} + 5 \, a^{2} b^{3} + a b^{4} - b^{5}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{3} b^{2} + 5 \, a^{2} b^{3} + a b^{4} - b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}\right]"," ",0,"[1/4*(((a*b^2 + b^3)*cosh(x)^6 + 6*(a*b^2 + b^3)*cosh(x)*sinh(x)^5 + (a*b^2 + b^3)*sinh(x)^6 + (3*a*b^2 - b^3)*cosh(x)^4 + (3*a*b^2 - b^3 + 15*(a*b^2 + b^3)*cosh(x)^2)*sinh(x)^4 + 4*(5*(a*b^2 + b^3)*cosh(x)^3 + (3*a*b^2 - b^3)*cosh(x))*sinh(x)^3 + a*b^2 + b^3 + (3*a*b^2 - b^3)*cosh(x)^2 + (15*(a*b^2 + b^3)*cosh(x)^4 + 3*a*b^2 - b^3 + 6*(3*a*b^2 - b^3)*cosh(x)^2)*sinh(x)^2 + 2*(3*(a*b^2 + b^3)*cosh(x)^5 + 2*(3*a*b^2 - b^3)*cosh(x)^3 + (3*a*b^2 - b^3)*cosh(x))*sinh(x))*sqrt(a + b)*log(((a^3 + a^2*b)*cosh(x)^8 + 8*(a^3 + a^2*b)*cosh(x)*sinh(x)^7 + (a^3 + a^2*b)*sinh(x)^8 + 2*(2*a^3 + a^2*b)*cosh(x)^6 + 2*(2*a^3 + a^2*b + 14*(a^3 + a^2*b)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a^3 + a^2*b)*cosh(x)^3 + 3*(2*a^3 + a^2*b)*cosh(x))*sinh(x)^5 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^4 + (70*(a^3 + a^2*b)*cosh(x)^4 + 6*a^3 + 4*a^2*b - a*b^2 + b^3 + 30*(2*a^3 + a^2*b)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a^3 + a^2*b)*cosh(x)^5 + 10*(2*a^3 + a^2*b)*cosh(x)^3 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x))*sinh(x)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 + 2*(2*a^3 + 3*a^2*b - b^3)*cosh(x)^2 + 2*(14*(a^3 + a^2*b)*cosh(x)^6 + 15*(2*a^3 + a^2*b)*cosh(x)^4 + 2*a^3 + 3*a^2*b - b^3 + 3*(6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^2)*sinh(x)^2 + sqrt(2)*(a^2*cosh(x)^6 + 6*a^2*cosh(x)*sinh(x)^5 + a^2*sinh(x)^6 + 3*a^2*cosh(x)^4 + 3*(5*a^2*cosh(x)^2 + a^2)*sinh(x)^4 + 4*(5*a^2*cosh(x)^3 + 3*a^2*cosh(x))*sinh(x)^3 + (3*a^2 + 2*a*b - b^2)*cosh(x)^2 + (15*a^2*cosh(x)^4 + 18*a^2*cosh(x)^2 + 3*a^2 + 2*a*b - b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(3*a^2*cosh(x)^5 + 6*a^2*cosh(x)^3 + (3*a^2 + 2*a*b - b^2)*cosh(x))*sinh(x))*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a^3 + a^2*b)*cosh(x)^7 + 3*(2*a^3 + a^2*b)*cosh(x)^5 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^3 + (2*a^3 + 3*a^2*b - b^3)*cosh(x))*sinh(x))/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) + ((a*b^2 + b^3)*cosh(x)^6 + 6*(a*b^2 + b^3)*cosh(x)*sinh(x)^5 + (a*b^2 + b^3)*sinh(x)^6 + (3*a*b^2 - b^3)*cosh(x)^4 + (3*a*b^2 - b^3 + 15*(a*b^2 + b^3)*cosh(x)^2)*sinh(x)^4 + 4*(5*(a*b^2 + b^3)*cosh(x)^3 + (3*a*b^2 - b^3)*cosh(x))*sinh(x)^3 + a*b^2 + b^3 + (3*a*b^2 - b^3)*cosh(x)^2 + (15*(a*b^2 + b^3)*cosh(x)^4 + 3*a*b^2 - b^3 + 6*(3*a*b^2 - b^3)*cosh(x)^2)*sinh(x)^2 + 2*(3*(a*b^2 + b^3)*cosh(x)^5 + 2*(3*a*b^2 - b^3)*cosh(x)^3 + (3*a*b^2 - b^3)*cosh(x))*sinh(x))*sqrt(a + b)*log(-((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*b*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + b)*cosh(x)^3 - b*cosh(x))*sinh(x) + a + b)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) - 4*sqrt(2)*((2*a^3 + 4*a^2*b + 3*a*b^2 + b^3)*cosh(x)^4 + 4*(2*a^3 + 4*a^2*b + 3*a*b^2 + b^3)*cosh(x)*sinh(x)^3 + (2*a^3 + 4*a^2*b + 3*a*b^2 + b^3)*sinh(x)^4 + 2*a^3 + 4*a^2*b + 3*a*b^2 + b^3 + 2*(2*a^3 + 2*a^2*b - a*b^2 - b^3)*cosh(x)^2 + 2*(2*a^3 + 2*a^2*b - a*b^2 - b^3 + 3*(2*a^3 + 4*a^2*b + 3*a*b^2 + b^3)*cosh(x)^2)*sinh(x)^2 + 4*((2*a^3 + 4*a^2*b + 3*a*b^2 + b^3)*cosh(x)^3 + (2*a^3 + 2*a^2*b - a*b^2 - b^3)*cosh(x))*sinh(x))*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/((a^3*b^2 + 3*a^2*b^3 + 3*a*b^4 + b^5)*cosh(x)^6 + 6*(a^3*b^2 + 3*a^2*b^3 + 3*a*b^4 + b^5)*cosh(x)*sinh(x)^5 + (a^3*b^2 + 3*a^2*b^3 + 3*a*b^4 + b^5)*sinh(x)^6 + a^3*b^2 + 3*a^2*b^3 + 3*a*b^4 + b^5 + (3*a^3*b^2 + 5*a^2*b^3 + a*b^4 - b^5)*cosh(x)^4 + (3*a^3*b^2 + 5*a^2*b^3 + a*b^4 - b^5 + 15*(a^3*b^2 + 3*a^2*b^3 + 3*a*b^4 + b^5)*cosh(x)^2)*sinh(x)^4 + 4*(5*(a^3*b^2 + 3*a^2*b^3 + 3*a*b^4 + b^5)*cosh(x)^3 + (3*a^3*b^2 + 5*a^2*b^3 + a*b^4 - b^5)*cosh(x))*sinh(x)^3 + (3*a^3*b^2 + 5*a^2*b^3 + a*b^4 - b^5)*cosh(x)^2 + (3*a^3*b^2 + 5*a^2*b^3 + a*b^4 - b^5 + 15*(a^3*b^2 + 3*a^2*b^3 + 3*a*b^4 + b^5)*cosh(x)^4 + 6*(3*a^3*b^2 + 5*a^2*b^3 + a*b^4 - b^5)*cosh(x)^2)*sinh(x)^2 + 2*(3*(a^3*b^2 + 3*a^2*b^3 + 3*a*b^4 + b^5)*cosh(x)^5 + 2*(3*a^3*b^2 + 5*a^2*b^3 + a*b^4 - b^5)*cosh(x)^3 + (3*a^3*b^2 + 5*a^2*b^3 + a*b^4 - b^5)*cosh(x))*sinh(x)), -1/2*(((a*b^2 + b^3)*cosh(x)^6 + 6*(a*b^2 + b^3)*cosh(x)*sinh(x)^5 + (a*b^2 + b^3)*sinh(x)^6 + (3*a*b^2 - b^3)*cosh(x)^4 + (3*a*b^2 - b^3 + 15*(a*b^2 + b^3)*cosh(x)^2)*sinh(x)^4 + 4*(5*(a*b^2 + b^3)*cosh(x)^3 + (3*a*b^2 - b^3)*cosh(x))*sinh(x)^3 + a*b^2 + b^3 + (3*a*b^2 - b^3)*cosh(x)^2 + (15*(a*b^2 + b^3)*cosh(x)^4 + 3*a*b^2 - b^3 + 6*(3*a*b^2 - b^3)*cosh(x)^2)*sinh(x)^2 + 2*(3*(a*b^2 + b^3)*cosh(x)^5 + 2*(3*a*b^2 - b^3)*cosh(x)^3 + (3*a*b^2 - b^3)*cosh(x))*sinh(x))*sqrt(-a - b)*arctan(sqrt(2)*(a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 + a + b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a^2 + a*b)*cosh(x)^4 + 4*(a^2 + a*b)*cosh(x)*sinh(x)^3 + (a^2 + a*b)*sinh(x)^4 + (2*a^2 + a*b - b^2)*cosh(x)^2 + (6*(a^2 + a*b)*cosh(x)^2 + 2*a^2 + a*b - b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(2*(a^2 + a*b)*cosh(x)^3 + (2*a^2 + a*b - b^2)*cosh(x))*sinh(x))) + ((a*b^2 + b^3)*cosh(x)^6 + 6*(a*b^2 + b^3)*cosh(x)*sinh(x)^5 + (a*b^2 + b^3)*sinh(x)^6 + (3*a*b^2 - b^3)*cosh(x)^4 + (3*a*b^2 - b^3 + 15*(a*b^2 + b^3)*cosh(x)^2)*sinh(x)^4 + 4*(5*(a*b^2 + b^3)*cosh(x)^3 + (3*a*b^2 - b^3)*cosh(x))*sinh(x)^3 + a*b^2 + b^3 + (3*a*b^2 - b^3)*cosh(x)^2 + (15*(a*b^2 + b^3)*cosh(x)^4 + 3*a*b^2 - b^3 + 6*(3*a*b^2 - b^3)*cosh(x)^2)*sinh(x)^2 + 2*(3*(a*b^2 + b^3)*cosh(x)^5 + 2*(3*a*b^2 - b^3)*cosh(x)^3 + (3*a*b^2 - b^3)*cosh(x))*sinh(x))*sqrt(-a - b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a - b)*cosh(x))*sinh(x) + a + b)) + 2*sqrt(2)*((2*a^3 + 4*a^2*b + 3*a*b^2 + b^3)*cosh(x)^4 + 4*(2*a^3 + 4*a^2*b + 3*a*b^2 + b^3)*cosh(x)*sinh(x)^3 + (2*a^3 + 4*a^2*b + 3*a*b^2 + b^3)*sinh(x)^4 + 2*a^3 + 4*a^2*b + 3*a*b^2 + b^3 + 2*(2*a^3 + 2*a^2*b - a*b^2 - b^3)*cosh(x)^2 + 2*(2*a^3 + 2*a^2*b - a*b^2 - b^3 + 3*(2*a^3 + 4*a^2*b + 3*a*b^2 + b^3)*cosh(x)^2)*sinh(x)^2 + 4*((2*a^3 + 4*a^2*b + 3*a*b^2 + b^3)*cosh(x)^3 + (2*a^3 + 2*a^2*b - a*b^2 - b^3)*cosh(x))*sinh(x))*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/((a^3*b^2 + 3*a^2*b^3 + 3*a*b^4 + b^5)*cosh(x)^6 + 6*(a^3*b^2 + 3*a^2*b^3 + 3*a*b^4 + b^5)*cosh(x)*sinh(x)^5 + (a^3*b^2 + 3*a^2*b^3 + 3*a*b^4 + b^5)*sinh(x)^6 + a^3*b^2 + 3*a^2*b^3 + 3*a*b^4 + b^5 + (3*a^3*b^2 + 5*a^2*b^3 + a*b^4 - b^5)*cosh(x)^4 + (3*a^3*b^2 + 5*a^2*b^3 + a*b^4 - b^5 + 15*(a^3*b^2 + 3*a^2*b^3 + 3*a*b^4 + b^5)*cosh(x)^2)*sinh(x)^4 + 4*(5*(a^3*b^2 + 3*a^2*b^3 + 3*a*b^4 + b^5)*cosh(x)^3 + (3*a^3*b^2 + 5*a^2*b^3 + a*b^4 - b^5)*cosh(x))*sinh(x)^3 + (3*a^3*b^2 + 5*a^2*b^3 + a*b^4 - b^5)*cosh(x)^2 + (3*a^3*b^2 + 5*a^2*b^3 + a*b^4 - b^5 + 15*(a^3*b^2 + 3*a^2*b^3 + 3*a*b^4 + b^5)*cosh(x)^4 + 6*(3*a^3*b^2 + 5*a^2*b^3 + a*b^4 - b^5)*cosh(x)^2)*sinh(x)^2 + 2*(3*(a^3*b^2 + 3*a^2*b^3 + 3*a*b^4 + b^5)*cosh(x)^5 + 2*(3*a^3*b^2 + 5*a^2*b^3 + a*b^4 - b^5)*cosh(x)^3 + (3*a^3*b^2 + 5*a^2*b^3 + a*b^4 - b^5)*cosh(x))*sinh(x))]","B",0
239,1,6973,0,0.831924," ","integrate(tanh(x)^4/(a+b*tanh(x)^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a b^{2} + b^{3}\right)} \sinh\left(x\right)^{4} + a b^{2} + b^{3} + 2 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a b^{2} - b^{3} + 3 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \log\left(-\frac{{\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a b^{2} + b^{3}\right)} \sinh\left(x\right)^{8} - 2 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{6} - 2 \, {\left(a b^{2} + 2 \, b^{3} - 14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3} - 30 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} + 2 \, {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} - 3 \, a b^{2} - 2 \, b^{3} + 3 \, {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(b^{2} \cosh\left(x\right)^{6} + 6 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + b^{2} \sinh\left(x\right)^{6} - 3 \, b^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, b^{2} \cosh\left(x\right)^{2} - b^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, b^{2} \cosh\left(x\right)^{3} - 3 \, b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, b^{2} \cosh\left(x\right)^{4} - 18 \, b^{2} \cosh\left(x\right)^{2} - a^{2} + 2 \, a b + 3 \, b^{2}\right)} \sinh\left(x\right)^{2} - a^{2} - 2 \, a b - b^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{5} - 6 \, b^{2} \cosh\left(x\right)^{3} - {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{5} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) + 2 \, {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \sinh\left(x\right)^{4} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} + 2 \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3} + 3 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{b} \log\left(-\frac{{\left(a + 2 \, b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + 2 \, b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + a - 2 \, b\right)} \sinh\left(x\right)^{2} - 2 \, \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + 2 \, b\right)} \cosh\left(x\right)^{3} + {\left(a - 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + 2 \, b}{\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) + {\left({\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a b^{2} + b^{3}\right)} \sinh\left(x\right)^{4} + a b^{2} + b^{3} + 2 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a b^{2} - b^{3} + 3 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \log\left(\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, a \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + a \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right) - 4 \, \sqrt{2} {\left(a^{2} b + a b^{2} - {\left(a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{2} - 2 \, {\left(a^{2} b + a b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right) - {\left(a^{2} b + a b^{2}\right)} \sinh\left(x\right)^{2}\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{4 \, {\left(a^{3} b^{2} + 3 \, a^{2} b^{3} + 3 \, a b^{4} + b^{5} + {\left(a^{3} b^{2} + 3 \, a^{2} b^{3} + 3 \, a b^{4} + b^{5}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{3} b^{2} + 3 \, a^{2} b^{3} + 3 \, a b^{4} + b^{5}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{3} b^{2} + 3 \, a^{2} b^{3} + 3 \, a b^{4} + b^{5}\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a^{3} b^{2} + a^{2} b^{3} - a b^{4} - b^{5}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a^{3} b^{2} + a^{2} b^{3} - a b^{4} - b^{5} + 3 \, {\left(a^{3} b^{2} + 3 \, a^{2} b^{3} + 3 \, a b^{4} + b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{3} b^{2} + 3 \, a^{2} b^{3} + 3 \, a b^{4} + b^{5}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} b^{2} + a^{2} b^{3} - a b^{4} - b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}, \frac{4 \, {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \sinh\left(x\right)^{4} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} + 2 \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3} + 3 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{-b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) + {\left({\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a b^{2} + b^{3}\right)} \sinh\left(x\right)^{4} + a b^{2} + b^{3} + 2 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a b^{2} - b^{3} + 3 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \log\left(-\frac{{\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a b^{2} + b^{3}\right)} \sinh\left(x\right)^{8} - 2 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{6} - 2 \, {\left(a b^{2} + 2 \, b^{3} - 14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3} - 30 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} + 2 \, {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} - 3 \, a b^{2} - 2 \, b^{3} + 3 \, {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(b^{2} \cosh\left(x\right)^{6} + 6 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + b^{2} \sinh\left(x\right)^{6} - 3 \, b^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, b^{2} \cosh\left(x\right)^{2} - b^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, b^{2} \cosh\left(x\right)^{3} - 3 \, b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, b^{2} \cosh\left(x\right)^{4} - 18 \, b^{2} \cosh\left(x\right)^{2} - a^{2} + 2 \, a b + 3 \, b^{2}\right)} \sinh\left(x\right)^{2} - a^{2} - 2 \, a b - b^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{5} - 6 \, b^{2} \cosh\left(x\right)^{3} - {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{5} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) + {\left({\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a b^{2} + b^{3}\right)} \sinh\left(x\right)^{4} + a b^{2} + b^{3} + 2 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a b^{2} - b^{3} + 3 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \log\left(\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, a \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + a \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right) - 4 \, \sqrt{2} {\left(a^{2} b + a b^{2} - {\left(a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{2} - 2 \, {\left(a^{2} b + a b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right) - {\left(a^{2} b + a b^{2}\right)} \sinh\left(x\right)^{2}\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{4 \, {\left(a^{3} b^{2} + 3 \, a^{2} b^{3} + 3 \, a b^{4} + b^{5} + {\left(a^{3} b^{2} + 3 \, a^{2} b^{3} + 3 \, a b^{4} + b^{5}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{3} b^{2} + 3 \, a^{2} b^{3} + 3 \, a b^{4} + b^{5}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{3} b^{2} + 3 \, a^{2} b^{3} + 3 \, a b^{4} + b^{5}\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a^{3} b^{2} + a^{2} b^{3} - a b^{4} - b^{5}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a^{3} b^{2} + a^{2} b^{3} - a b^{4} - b^{5} + 3 \, {\left(a^{3} b^{2} + 3 \, a^{2} b^{3} + 3 \, a b^{4} + b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{3} b^{2} + 3 \, a^{2} b^{3} + 3 \, a b^{4} + b^{5}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} b^{2} + a^{2} b^{3} - a b^{4} - b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}, -\frac{{\left({\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a b^{2} + b^{3}\right)} \sinh\left(x\right)^{4} + a b^{2} + b^{3} + 2 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a b^{2} - b^{3} + 3 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} - a - b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a b + b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a b + b^{2}\right)} \sinh\left(x\right)^{4} + {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} - a b - 2 \, b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(2 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + {\left({\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a b^{2} + b^{3}\right)} \sinh\left(x\right)^{4} + a b^{2} + b^{3} + 2 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a b^{2} - b^{3} + 3 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) - {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \sinh\left(x\right)^{4} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} + 2 \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3} + 3 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{b} \log\left(-\frac{{\left(a + 2 \, b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + 2 \, b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + 2 \, b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - 2 \, b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + a - 2 \, b\right)} \sinh\left(x\right)^{2} - 2 \, \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + 2 \, b\right)} \cosh\left(x\right)^{3} + {\left(a - 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + 2 \, b}{\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) + 2 \, \sqrt{2} {\left(a^{2} b + a b^{2} - {\left(a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{2} - 2 \, {\left(a^{2} b + a b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right) - {\left(a^{2} b + a b^{2}\right)} \sinh\left(x\right)^{2}\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{2 \, {\left(a^{3} b^{2} + 3 \, a^{2} b^{3} + 3 \, a b^{4} + b^{5} + {\left(a^{3} b^{2} + 3 \, a^{2} b^{3} + 3 \, a b^{4} + b^{5}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{3} b^{2} + 3 \, a^{2} b^{3} + 3 \, a b^{4} + b^{5}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{3} b^{2} + 3 \, a^{2} b^{3} + 3 \, a b^{4} + b^{5}\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a^{3} b^{2} + a^{2} b^{3} - a b^{4} - b^{5}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a^{3} b^{2} + a^{2} b^{3} - a b^{4} - b^{5} + 3 \, {\left(a^{3} b^{2} + 3 \, a^{2} b^{3} + 3 \, a b^{4} + b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{3} b^{2} + 3 \, a^{2} b^{3} + 3 \, a b^{4} + b^{5}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} b^{2} + a^{2} b^{3} - a b^{4} - b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}, -\frac{{\left({\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a b^{2} + b^{3}\right)} \sinh\left(x\right)^{4} + a b^{2} + b^{3} + 2 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a b^{2} - b^{3} + 3 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} - a - b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a b + b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a b + b^{2}\right)} \sinh\left(x\right)^{4} + {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} - a b - 2 \, b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(2 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + {\left({\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a b^{2} + b^{3}\right)} \sinh\left(x\right)^{4} + a b^{2} + b^{3} + 2 \, {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a b^{2} - b^{3} + 3 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a b^{2} - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) - 2 \, {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \sinh\left(x\right)^{4} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} + 2 \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3} + 3 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{-b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) + 2 \, \sqrt{2} {\left(a^{2} b + a b^{2} - {\left(a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{2} - 2 \, {\left(a^{2} b + a b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right) - {\left(a^{2} b + a b^{2}\right)} \sinh\left(x\right)^{2}\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{2 \, {\left(a^{3} b^{2} + 3 \, a^{2} b^{3} + 3 \, a b^{4} + b^{5} + {\left(a^{3} b^{2} + 3 \, a^{2} b^{3} + 3 \, a b^{4} + b^{5}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{3} b^{2} + 3 \, a^{2} b^{3} + 3 \, a b^{4} + b^{5}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{3} b^{2} + 3 \, a^{2} b^{3} + 3 \, a b^{4} + b^{5}\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a^{3} b^{2} + a^{2} b^{3} - a b^{4} - b^{5}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a^{3} b^{2} + a^{2} b^{3} - a b^{4} - b^{5} + 3 \, {\left(a^{3} b^{2} + 3 \, a^{2} b^{3} + 3 \, a b^{4} + b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{3} b^{2} + 3 \, a^{2} b^{3} + 3 \, a b^{4} + b^{5}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} b^{2} + a^{2} b^{3} - a b^{4} - b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}\right]"," ",0,"[1/4*(((a*b^2 + b^3)*cosh(x)^4 + 4*(a*b^2 + b^3)*cosh(x)*sinh(x)^3 + (a*b^2 + b^3)*sinh(x)^4 + a*b^2 + b^3 + 2*(a*b^2 - b^3)*cosh(x)^2 + 2*(a*b^2 - b^3 + 3*(a*b^2 + b^3)*cosh(x)^2)*sinh(x)^2 + 4*((a*b^2 + b^3)*cosh(x)^3 + (a*b^2 - b^3)*cosh(x))*sinh(x))*sqrt(a + b)*log(-((a*b^2 + b^3)*cosh(x)^8 + 8*(a*b^2 + b^3)*cosh(x)*sinh(x)^7 + (a*b^2 + b^3)*sinh(x)^8 - 2*(a*b^2 + 2*b^3)*cosh(x)^6 - 2*(a*b^2 + 2*b^3 - 14*(a*b^2 + b^3)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a*b^2 + b^3)*cosh(x)^3 - 3*(a*b^2 + 2*b^3)*cosh(x))*sinh(x)^5 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^4 + (70*(a*b^2 + b^3)*cosh(x)^4 + a^3 - a^2*b + 4*a*b^2 + 6*b^3 - 30*(a*b^2 + 2*b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a*b^2 + b^3)*cosh(x)^5 - 10*(a*b^2 + 2*b^3)*cosh(x)^3 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x))*sinh(x)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 + 2*(a^3 - 3*a*b^2 - 2*b^3)*cosh(x)^2 + 2*(14*(a*b^2 + b^3)*cosh(x)^6 - 15*(a*b^2 + 2*b^3)*cosh(x)^4 + a^3 - 3*a*b^2 - 2*b^3 + 3*(a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^2)*sinh(x)^2 + sqrt(2)*(b^2*cosh(x)^6 + 6*b^2*cosh(x)*sinh(x)^5 + b^2*sinh(x)^6 - 3*b^2*cosh(x)^4 + 3*(5*b^2*cosh(x)^2 - b^2)*sinh(x)^4 + 4*(5*b^2*cosh(x)^3 - 3*b^2*cosh(x))*sinh(x)^3 - (a^2 - 2*a*b - 3*b^2)*cosh(x)^2 + (15*b^2*cosh(x)^4 - 18*b^2*cosh(x)^2 - a^2 + 2*a*b + 3*b^2)*sinh(x)^2 - a^2 - 2*a*b - b^2 + 2*(3*b^2*cosh(x)^5 - 6*b^2*cosh(x)^3 - (a^2 - 2*a*b - 3*b^2)*cosh(x))*sinh(x))*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a*b^2 + b^3)*cosh(x)^7 - 3*(a*b^2 + 2*b^3)*cosh(x)^5 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^3 + (a^3 - 3*a*b^2 - 2*b^3)*cosh(x))*sinh(x))/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) + 2*((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^4 + 4*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)*sinh(x)^3 + (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*sinh(x)^4 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 + 2*(a^3 + a^2*b - a*b^2 - b^3)*cosh(x)^2 + 2*(a^3 + a^2*b - a*b^2 - b^3 + 3*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^2)*sinh(x)^2 + 4*((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^3 + (a^3 + a^2*b - a*b^2 - b^3)*cosh(x))*sinh(x))*sqrt(b)*log(-((a + 2*b)*cosh(x)^4 + 4*(a + 2*b)*cosh(x)*sinh(x)^3 + (a + 2*b)*sinh(x)^4 + 2*(a - 2*b)*cosh(x)^2 + 2*(3*(a + 2*b)*cosh(x)^2 + a - 2*b)*sinh(x)^2 - 2*sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + 2*b)*cosh(x)^3 + (a - 2*b)*cosh(x))*sinh(x) + a + 2*b)/(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)) + ((a*b^2 + b^3)*cosh(x)^4 + 4*(a*b^2 + b^3)*cosh(x)*sinh(x)^3 + (a*b^2 + b^3)*sinh(x)^4 + a*b^2 + b^3 + 2*(a*b^2 - b^3)*cosh(x)^2 + 2*(a*b^2 - b^3 + 3*(a*b^2 + b^3)*cosh(x)^2)*sinh(x)^2 + 4*((a*b^2 + b^3)*cosh(x)^3 + (a*b^2 - b^3)*cosh(x))*sinh(x))*sqrt(a + b)*log(((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*a*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + b)*cosh(x)^3 + a*cosh(x))*sinh(x) + a + b)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) - 4*sqrt(2)*(a^2*b + a*b^2 - (a^2*b + a*b^2)*cosh(x)^2 - 2*(a^2*b + a*b^2)*cosh(x)*sinh(x) - (a^2*b + a*b^2)*sinh(x)^2)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(a^3*b^2 + 3*a^2*b^3 + 3*a*b^4 + b^5 + (a^3*b^2 + 3*a^2*b^3 + 3*a*b^4 + b^5)*cosh(x)^4 + 4*(a^3*b^2 + 3*a^2*b^3 + 3*a*b^4 + b^5)*cosh(x)*sinh(x)^3 + (a^3*b^2 + 3*a^2*b^3 + 3*a*b^4 + b^5)*sinh(x)^4 + 2*(a^3*b^2 + a^2*b^3 - a*b^4 - b^5)*cosh(x)^2 + 2*(a^3*b^2 + a^2*b^3 - a*b^4 - b^5 + 3*(a^3*b^2 + 3*a^2*b^3 + 3*a*b^4 + b^5)*cosh(x)^2)*sinh(x)^2 + 4*((a^3*b^2 + 3*a^2*b^3 + 3*a*b^4 + b^5)*cosh(x)^3 + (a^3*b^2 + a^2*b^3 - a*b^4 - b^5)*cosh(x))*sinh(x)), 1/4*(4*((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^4 + 4*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)*sinh(x)^3 + (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*sinh(x)^4 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 + 2*(a^3 + a^2*b - a*b^2 - b^3)*cosh(x)^2 + 2*(a^3 + a^2*b - a*b^2 - b^3 + 3*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^2)*sinh(x)^2 + 4*((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^3 + (a^3 + a^2*b - a*b^2 - b^3)*cosh(x))*sinh(x))*sqrt(-b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a - b)*cosh(x))*sinh(x) + a + b)) + ((a*b^2 + b^3)*cosh(x)^4 + 4*(a*b^2 + b^3)*cosh(x)*sinh(x)^3 + (a*b^2 + b^3)*sinh(x)^4 + a*b^2 + b^3 + 2*(a*b^2 - b^3)*cosh(x)^2 + 2*(a*b^2 - b^3 + 3*(a*b^2 + b^3)*cosh(x)^2)*sinh(x)^2 + 4*((a*b^2 + b^3)*cosh(x)^3 + (a*b^2 - b^3)*cosh(x))*sinh(x))*sqrt(a + b)*log(-((a*b^2 + b^3)*cosh(x)^8 + 8*(a*b^2 + b^3)*cosh(x)*sinh(x)^7 + (a*b^2 + b^3)*sinh(x)^8 - 2*(a*b^2 + 2*b^3)*cosh(x)^6 - 2*(a*b^2 + 2*b^3 - 14*(a*b^2 + b^3)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a*b^2 + b^3)*cosh(x)^3 - 3*(a*b^2 + 2*b^3)*cosh(x))*sinh(x)^5 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^4 + (70*(a*b^2 + b^3)*cosh(x)^4 + a^3 - a^2*b + 4*a*b^2 + 6*b^3 - 30*(a*b^2 + 2*b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a*b^2 + b^3)*cosh(x)^5 - 10*(a*b^2 + 2*b^3)*cosh(x)^3 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x))*sinh(x)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 + 2*(a^3 - 3*a*b^2 - 2*b^3)*cosh(x)^2 + 2*(14*(a*b^2 + b^3)*cosh(x)^6 - 15*(a*b^2 + 2*b^3)*cosh(x)^4 + a^3 - 3*a*b^2 - 2*b^3 + 3*(a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^2)*sinh(x)^2 + sqrt(2)*(b^2*cosh(x)^6 + 6*b^2*cosh(x)*sinh(x)^5 + b^2*sinh(x)^6 - 3*b^2*cosh(x)^4 + 3*(5*b^2*cosh(x)^2 - b^2)*sinh(x)^4 + 4*(5*b^2*cosh(x)^3 - 3*b^2*cosh(x))*sinh(x)^3 - (a^2 - 2*a*b - 3*b^2)*cosh(x)^2 + (15*b^2*cosh(x)^4 - 18*b^2*cosh(x)^2 - a^2 + 2*a*b + 3*b^2)*sinh(x)^2 - a^2 - 2*a*b - b^2 + 2*(3*b^2*cosh(x)^5 - 6*b^2*cosh(x)^3 - (a^2 - 2*a*b - 3*b^2)*cosh(x))*sinh(x))*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a*b^2 + b^3)*cosh(x)^7 - 3*(a*b^2 + 2*b^3)*cosh(x)^5 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^3 + (a^3 - 3*a*b^2 - 2*b^3)*cosh(x))*sinh(x))/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) + ((a*b^2 + b^3)*cosh(x)^4 + 4*(a*b^2 + b^3)*cosh(x)*sinh(x)^3 + (a*b^2 + b^3)*sinh(x)^4 + a*b^2 + b^3 + 2*(a*b^2 - b^3)*cosh(x)^2 + 2*(a*b^2 - b^3 + 3*(a*b^2 + b^3)*cosh(x)^2)*sinh(x)^2 + 4*((a*b^2 + b^3)*cosh(x)^3 + (a*b^2 - b^3)*cosh(x))*sinh(x))*sqrt(a + b)*log(((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*a*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + b)*cosh(x)^3 + a*cosh(x))*sinh(x) + a + b)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) - 4*sqrt(2)*(a^2*b + a*b^2 - (a^2*b + a*b^2)*cosh(x)^2 - 2*(a^2*b + a*b^2)*cosh(x)*sinh(x) - (a^2*b + a*b^2)*sinh(x)^2)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(a^3*b^2 + 3*a^2*b^3 + 3*a*b^4 + b^5 + (a^3*b^2 + 3*a^2*b^3 + 3*a*b^4 + b^5)*cosh(x)^4 + 4*(a^3*b^2 + 3*a^2*b^3 + 3*a*b^4 + b^5)*cosh(x)*sinh(x)^3 + (a^3*b^2 + 3*a^2*b^3 + 3*a*b^4 + b^5)*sinh(x)^4 + 2*(a^3*b^2 + a^2*b^3 - a*b^4 - b^5)*cosh(x)^2 + 2*(a^3*b^2 + a^2*b^3 - a*b^4 - b^5 + 3*(a^3*b^2 + 3*a^2*b^3 + 3*a*b^4 + b^5)*cosh(x)^2)*sinh(x)^2 + 4*((a^3*b^2 + 3*a^2*b^3 + 3*a*b^4 + b^5)*cosh(x)^3 + (a^3*b^2 + a^2*b^3 - a*b^4 - b^5)*cosh(x))*sinh(x)), -1/2*(((a*b^2 + b^3)*cosh(x)^4 + 4*(a*b^2 + b^3)*cosh(x)*sinh(x)^3 + (a*b^2 + b^3)*sinh(x)^4 + a*b^2 + b^3 + 2*(a*b^2 - b^3)*cosh(x)^2 + 2*(a*b^2 - b^3 + 3*(a*b^2 + b^3)*cosh(x)^2)*sinh(x)^2 + 4*((a*b^2 + b^3)*cosh(x)^3 + (a*b^2 - b^3)*cosh(x))*sinh(x))*sqrt(-a - b)*arctan(sqrt(2)*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 - a - b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a*b + b^2)*cosh(x)^4 + 4*(a*b + b^2)*cosh(x)*sinh(x)^3 + (a*b + b^2)*sinh(x)^4 + (a^2 - a*b - 2*b^2)*cosh(x)^2 + (6*(a*b + b^2)*cosh(x)^2 + a^2 - a*b - 2*b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(2*(a*b + b^2)*cosh(x)^3 + (a^2 - a*b - 2*b^2)*cosh(x))*sinh(x))) + ((a*b^2 + b^3)*cosh(x)^4 + 4*(a*b^2 + b^3)*cosh(x)*sinh(x)^3 + (a*b^2 + b^3)*sinh(x)^4 + a*b^2 + b^3 + 2*(a*b^2 - b^3)*cosh(x)^2 + 2*(a*b^2 - b^3 + 3*(a*b^2 + b^3)*cosh(x)^2)*sinh(x)^2 + 4*((a*b^2 + b^3)*cosh(x)^3 + (a*b^2 - b^3)*cosh(x))*sinh(x))*sqrt(-a - b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a - b)*cosh(x))*sinh(x) + a + b)) - ((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^4 + 4*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)*sinh(x)^3 + (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*sinh(x)^4 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 + 2*(a^3 + a^2*b - a*b^2 - b^3)*cosh(x)^2 + 2*(a^3 + a^2*b - a*b^2 - b^3 + 3*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^2)*sinh(x)^2 + 4*((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^3 + (a^3 + a^2*b - a*b^2 - b^3)*cosh(x))*sinh(x))*sqrt(b)*log(-((a + 2*b)*cosh(x)^4 + 4*(a + 2*b)*cosh(x)*sinh(x)^3 + (a + 2*b)*sinh(x)^4 + 2*(a - 2*b)*cosh(x)^2 + 2*(3*(a + 2*b)*cosh(x)^2 + a - 2*b)*sinh(x)^2 - 2*sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + 2*b)*cosh(x)^3 + (a - 2*b)*cosh(x))*sinh(x) + a + 2*b)/(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)) + 2*sqrt(2)*(a^2*b + a*b^2 - (a^2*b + a*b^2)*cosh(x)^2 - 2*(a^2*b + a*b^2)*cosh(x)*sinh(x) - (a^2*b + a*b^2)*sinh(x)^2)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(a^3*b^2 + 3*a^2*b^3 + 3*a*b^4 + b^5 + (a^3*b^2 + 3*a^2*b^3 + 3*a*b^4 + b^5)*cosh(x)^4 + 4*(a^3*b^2 + 3*a^2*b^3 + 3*a*b^4 + b^5)*cosh(x)*sinh(x)^3 + (a^3*b^2 + 3*a^2*b^3 + 3*a*b^4 + b^5)*sinh(x)^4 + 2*(a^3*b^2 + a^2*b^3 - a*b^4 - b^5)*cosh(x)^2 + 2*(a^3*b^2 + a^2*b^3 - a*b^4 - b^5 + 3*(a^3*b^2 + 3*a^2*b^3 + 3*a*b^4 + b^5)*cosh(x)^2)*sinh(x)^2 + 4*((a^3*b^2 + 3*a^2*b^3 + 3*a*b^4 + b^5)*cosh(x)^3 + (a^3*b^2 + a^2*b^3 - a*b^4 - b^5)*cosh(x))*sinh(x)), -1/2*(((a*b^2 + b^3)*cosh(x)^4 + 4*(a*b^2 + b^3)*cosh(x)*sinh(x)^3 + (a*b^2 + b^3)*sinh(x)^4 + a*b^2 + b^3 + 2*(a*b^2 - b^3)*cosh(x)^2 + 2*(a*b^2 - b^3 + 3*(a*b^2 + b^3)*cosh(x)^2)*sinh(x)^2 + 4*((a*b^2 + b^3)*cosh(x)^3 + (a*b^2 - b^3)*cosh(x))*sinh(x))*sqrt(-a - b)*arctan(sqrt(2)*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 - a - b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a*b + b^2)*cosh(x)^4 + 4*(a*b + b^2)*cosh(x)*sinh(x)^3 + (a*b + b^2)*sinh(x)^4 + (a^2 - a*b - 2*b^2)*cosh(x)^2 + (6*(a*b + b^2)*cosh(x)^2 + a^2 - a*b - 2*b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(2*(a*b + b^2)*cosh(x)^3 + (a^2 - a*b - 2*b^2)*cosh(x))*sinh(x))) + ((a*b^2 + b^3)*cosh(x)^4 + 4*(a*b^2 + b^3)*cosh(x)*sinh(x)^3 + (a*b^2 + b^3)*sinh(x)^4 + a*b^2 + b^3 + 2*(a*b^2 - b^3)*cosh(x)^2 + 2*(a*b^2 - b^3 + 3*(a*b^2 + b^3)*cosh(x)^2)*sinh(x)^2 + 4*((a*b^2 + b^3)*cosh(x)^3 + (a*b^2 - b^3)*cosh(x))*sinh(x))*sqrt(-a - b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a - b)*cosh(x))*sinh(x) + a + b)) - 2*((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^4 + 4*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)*sinh(x)^3 + (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*sinh(x)^4 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 + 2*(a^3 + a^2*b - a*b^2 - b^3)*cosh(x)^2 + 2*(a^3 + a^2*b - a*b^2 - b^3 + 3*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^2)*sinh(x)^2 + 4*((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^3 + (a^3 + a^2*b - a*b^2 - b^3)*cosh(x))*sinh(x))*sqrt(-b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a - b)*cosh(x))*sinh(x) + a + b)) + 2*sqrt(2)*(a^2*b + a*b^2 - (a^2*b + a*b^2)*cosh(x)^2 - 2*(a^2*b + a*b^2)*cosh(x)*sinh(x) - (a^2*b + a*b^2)*sinh(x)^2)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(a^3*b^2 + 3*a^2*b^3 + 3*a*b^4 + b^5 + (a^3*b^2 + 3*a^2*b^3 + 3*a*b^4 + b^5)*cosh(x)^4 + 4*(a^3*b^2 + 3*a^2*b^3 + 3*a*b^4 + b^5)*cosh(x)*sinh(x)^3 + (a^3*b^2 + 3*a^2*b^3 + 3*a*b^4 + b^5)*sinh(x)^4 + 2*(a^3*b^2 + a^2*b^3 - a*b^4 - b^5)*cosh(x)^2 + 2*(a^3*b^2 + a^2*b^3 - a*b^4 - b^5 + 3*(a^3*b^2 + 3*a^2*b^3 + 3*a*b^4 + b^5)*cosh(x)^2)*sinh(x)^2 + 4*((a^3*b^2 + 3*a^2*b^3 + 3*a*b^4 + b^5)*cosh(x)^3 + (a^3*b^2 + a^2*b^3 - a*b^4 - b^5)*cosh(x))*sinh(x))]","B",0
240,1,2525,0,0.535686," ","integrate(tanh(x)^3/(a+b*tanh(x)^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(a b + b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a b + b^{2}\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a b - b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} + a b - b^{2}\right)} \sinh\left(x\right)^{2} + a b + b^{2} + 4 \, {\left({\left(a b + b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \log\left(\frac{{\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{3} + a^{2} b\right)} \sinh\left(x\right)^{8} + 2 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} + 2 \, {\left(2 \, a^{3} + a^{2} b + 14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} + 3 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3} + 30 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} + 10 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} + 2 \, {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} + 15 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 2 \, a^{3} + 3 \, a^{2} b - b^{3} + 3 \, {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(a^{2} \cosh\left(x\right)^{6} + 6 \, a^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + a^{2} \sinh\left(x\right)^{6} + 3 \, a^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, a^{2} \cosh\left(x\right)^{2} + a^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, a^{2} \cosh\left(x\right)^{3} + 3 \, a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, a^{2} \cosh\left(x\right)^{4} + 18 \, a^{2} \cosh\left(x\right)^{2} + 3 \, a^{2} + 2 \, a b - b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(x\right)^{5} + 6 \, a^{2} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{7} + 3 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) + {\left({\left(a b + b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a b + b^{2}\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a b - b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} + a b - b^{2}\right)} \sinh\left(x\right)^{2} + a b + b^{2} + 4 \, {\left({\left(a b + b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \log\left(-\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - b\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - b \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right) + 4 \, \sqrt{2} {\left({\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a^{2} + a b\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a^{2} + a b\right)} \sinh\left(x\right)^{2} + a^{2} + a b\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{4 \, {\left({\left(a^{3} b + 3 \, a^{2} b^{2} + 3 \, a b^{3} + b^{4}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{3} b + 3 \, a^{2} b^{2} + 3 \, a b^{3} + b^{4}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{3} b + 3 \, a^{2} b^{2} + 3 \, a b^{3} + b^{4}\right)} \sinh\left(x\right)^{4} + a^{3} b + 3 \, a^{2} b^{2} + 3 \, a b^{3} + b^{4} + 2 \, {\left(a^{3} b + a^{2} b^{2} - a b^{3} - b^{4}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a^{3} b + a^{2} b^{2} - a b^{3} - b^{4} + 3 \, {\left(a^{3} b + 3 \, a^{2} b^{2} + 3 \, a b^{3} + b^{4}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{3} b + 3 \, a^{2} b^{2} + 3 \, a b^{3} + b^{4}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} b + a^{2} b^{2} - a b^{3} - b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}, -\frac{{\left({\left(a b + b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a b + b^{2}\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a b - b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} + a b - b^{2}\right)} \sinh\left(x\right)^{2} + a b + b^{2} + 4 \, {\left({\left(a b + b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(a \cosh\left(x\right)^{2} + 2 \, a \cosh\left(x\right) \sinh\left(x\right) + a \sinh\left(x\right)^{2} + a + b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a^{2} + a b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{2} + a b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{2} + a b\right)} \sinh\left(x\right)^{4} + {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} + 2 \, a^{2} + a b - b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(2 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + {\left({\left(a b + b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a b + b^{2}\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a b - b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} + a b - b^{2}\right)} \sinh\left(x\right)^{2} + a b + b^{2} + 4 \, {\left({\left(a b + b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) - 2 \, \sqrt{2} {\left({\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a^{2} + a b\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a^{2} + a b\right)} \sinh\left(x\right)^{2} + a^{2} + a b\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{2 \, {\left({\left(a^{3} b + 3 \, a^{2} b^{2} + 3 \, a b^{3} + b^{4}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{3} b + 3 \, a^{2} b^{2} + 3 \, a b^{3} + b^{4}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{3} b + 3 \, a^{2} b^{2} + 3 \, a b^{3} + b^{4}\right)} \sinh\left(x\right)^{4} + a^{3} b + 3 \, a^{2} b^{2} + 3 \, a b^{3} + b^{4} + 2 \, {\left(a^{3} b + a^{2} b^{2} - a b^{3} - b^{4}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a^{3} b + a^{2} b^{2} - a b^{3} - b^{4} + 3 \, {\left(a^{3} b + 3 \, a^{2} b^{2} + 3 \, a b^{3} + b^{4}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{3} b + 3 \, a^{2} b^{2} + 3 \, a b^{3} + b^{4}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} b + a^{2} b^{2} - a b^{3} - b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}\right]"," ",0,"[1/4*(((a*b + b^2)*cosh(x)^4 + 4*(a*b + b^2)*cosh(x)*sinh(x)^3 + (a*b + b^2)*sinh(x)^4 + 2*(a*b - b^2)*cosh(x)^2 + 2*(3*(a*b + b^2)*cosh(x)^2 + a*b - b^2)*sinh(x)^2 + a*b + b^2 + 4*((a*b + b^2)*cosh(x)^3 + (a*b - b^2)*cosh(x))*sinh(x))*sqrt(a + b)*log(((a^3 + a^2*b)*cosh(x)^8 + 8*(a^3 + a^2*b)*cosh(x)*sinh(x)^7 + (a^3 + a^2*b)*sinh(x)^8 + 2*(2*a^3 + a^2*b)*cosh(x)^6 + 2*(2*a^3 + a^2*b + 14*(a^3 + a^2*b)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a^3 + a^2*b)*cosh(x)^3 + 3*(2*a^3 + a^2*b)*cosh(x))*sinh(x)^5 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^4 + (70*(a^3 + a^2*b)*cosh(x)^4 + 6*a^3 + 4*a^2*b - a*b^2 + b^3 + 30*(2*a^3 + a^2*b)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a^3 + a^2*b)*cosh(x)^5 + 10*(2*a^3 + a^2*b)*cosh(x)^3 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x))*sinh(x)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 + 2*(2*a^3 + 3*a^2*b - b^3)*cosh(x)^2 + 2*(14*(a^3 + a^2*b)*cosh(x)^6 + 15*(2*a^3 + a^2*b)*cosh(x)^4 + 2*a^3 + 3*a^2*b - b^3 + 3*(6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^2)*sinh(x)^2 + sqrt(2)*(a^2*cosh(x)^6 + 6*a^2*cosh(x)*sinh(x)^5 + a^2*sinh(x)^6 + 3*a^2*cosh(x)^4 + 3*(5*a^2*cosh(x)^2 + a^2)*sinh(x)^4 + 4*(5*a^2*cosh(x)^3 + 3*a^2*cosh(x))*sinh(x)^3 + (3*a^2 + 2*a*b - b^2)*cosh(x)^2 + (15*a^2*cosh(x)^4 + 18*a^2*cosh(x)^2 + 3*a^2 + 2*a*b - b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(3*a^2*cosh(x)^5 + 6*a^2*cosh(x)^3 + (3*a^2 + 2*a*b - b^2)*cosh(x))*sinh(x))*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a^3 + a^2*b)*cosh(x)^7 + 3*(2*a^3 + a^2*b)*cosh(x)^5 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^3 + (2*a^3 + 3*a^2*b - b^3)*cosh(x))*sinh(x))/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) + ((a*b + b^2)*cosh(x)^4 + 4*(a*b + b^2)*cosh(x)*sinh(x)^3 + (a*b + b^2)*sinh(x)^4 + 2*(a*b - b^2)*cosh(x)^2 + 2*(3*(a*b + b^2)*cosh(x)^2 + a*b - b^2)*sinh(x)^2 + a*b + b^2 + 4*((a*b + b^2)*cosh(x)^3 + (a*b - b^2)*cosh(x))*sinh(x))*sqrt(a + b)*log(-((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*b*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + b)*cosh(x)^3 - b*cosh(x))*sinh(x) + a + b)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*sqrt(2)*((a^2 + a*b)*cosh(x)^2 + 2*(a^2 + a*b)*cosh(x)*sinh(x) + (a^2 + a*b)*sinh(x)^2 + a^2 + a*b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/((a^3*b + 3*a^2*b^2 + 3*a*b^3 + b^4)*cosh(x)^4 + 4*(a^3*b + 3*a^2*b^2 + 3*a*b^3 + b^4)*cosh(x)*sinh(x)^3 + (a^3*b + 3*a^2*b^2 + 3*a*b^3 + b^4)*sinh(x)^4 + a^3*b + 3*a^2*b^2 + 3*a*b^3 + b^4 + 2*(a^3*b + a^2*b^2 - a*b^3 - b^4)*cosh(x)^2 + 2*(a^3*b + a^2*b^2 - a*b^3 - b^4 + 3*(a^3*b + 3*a^2*b^2 + 3*a*b^3 + b^4)*cosh(x)^2)*sinh(x)^2 + 4*((a^3*b + 3*a^2*b^2 + 3*a*b^3 + b^4)*cosh(x)^3 + (a^3*b + a^2*b^2 - a*b^3 - b^4)*cosh(x))*sinh(x)), -1/2*(((a*b + b^2)*cosh(x)^4 + 4*(a*b + b^2)*cosh(x)*sinh(x)^3 + (a*b + b^2)*sinh(x)^4 + 2*(a*b - b^2)*cosh(x)^2 + 2*(3*(a*b + b^2)*cosh(x)^2 + a*b - b^2)*sinh(x)^2 + a*b + b^2 + 4*((a*b + b^2)*cosh(x)^3 + (a*b - b^2)*cosh(x))*sinh(x))*sqrt(-a - b)*arctan(sqrt(2)*(a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 + a + b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a^2 + a*b)*cosh(x)^4 + 4*(a^2 + a*b)*cosh(x)*sinh(x)^3 + (a^2 + a*b)*sinh(x)^4 + (2*a^2 + a*b - b^2)*cosh(x)^2 + (6*(a^2 + a*b)*cosh(x)^2 + 2*a^2 + a*b - b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(2*(a^2 + a*b)*cosh(x)^3 + (2*a^2 + a*b - b^2)*cosh(x))*sinh(x))) + ((a*b + b^2)*cosh(x)^4 + 4*(a*b + b^2)*cosh(x)*sinh(x)^3 + (a*b + b^2)*sinh(x)^4 + 2*(a*b - b^2)*cosh(x)^2 + 2*(3*(a*b + b^2)*cosh(x)^2 + a*b - b^2)*sinh(x)^2 + a*b + b^2 + 4*((a*b + b^2)*cosh(x)^3 + (a*b - b^2)*cosh(x))*sinh(x))*sqrt(-a - b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a - b)*cosh(x))*sinh(x) + a + b)) - 2*sqrt(2)*((a^2 + a*b)*cosh(x)^2 + 2*(a^2 + a*b)*cosh(x)*sinh(x) + (a^2 + a*b)*sinh(x)^2 + a^2 + a*b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/((a^3*b + 3*a^2*b^2 + 3*a*b^3 + b^4)*cosh(x)^4 + 4*(a^3*b + 3*a^2*b^2 + 3*a*b^3 + b^4)*cosh(x)*sinh(x)^3 + (a^3*b + 3*a^2*b^2 + 3*a*b^3 + b^4)*sinh(x)^4 + a^3*b + 3*a^2*b^2 + 3*a*b^3 + b^4 + 2*(a^3*b + a^2*b^2 - a*b^3 - b^4)*cosh(x)^2 + 2*(a^3*b + a^2*b^2 - a*b^3 - b^4 + 3*(a^3*b + 3*a^2*b^2 + 3*a*b^3 + b^4)*cosh(x)^2)*sinh(x)^2 + 4*((a^3*b + 3*a^2*b^2 + 3*a*b^3 + b^4)*cosh(x)^3 + (a^3*b + a^2*b^2 - a*b^3 - b^4)*cosh(x))*sinh(x))]","B",0
241,1,2281,0,0.553042," ","integrate(tanh(x)^2/(a+b*tanh(x)^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b\right)} \sqrt{a + b} \log\left(-\frac{{\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a b^{2} + b^{3}\right)} \sinh\left(x\right)^{8} - 2 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{6} - 2 \, {\left(a b^{2} + 2 \, b^{3} - 14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3} - 30 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} + 2 \, {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} - 3 \, a b^{2} - 2 \, b^{3} + 3 \, {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(b^{2} \cosh\left(x\right)^{6} + 6 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + b^{2} \sinh\left(x\right)^{6} - 3 \, b^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, b^{2} \cosh\left(x\right)^{2} - b^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, b^{2} \cosh\left(x\right)^{3} - 3 \, b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, b^{2} \cosh\left(x\right)^{4} - 18 \, b^{2} \cosh\left(x\right)^{2} - a^{2} + 2 \, a b + 3 \, b^{2}\right)} \sinh\left(x\right)^{2} - a^{2} - 2 \, a b - b^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{5} - 6 \, b^{2} \cosh\left(x\right)^{3} - {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{5} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) + {\left({\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b\right)} \sqrt{a + b} \log\left(\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, a \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + a \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right) - 4 \, \sqrt{2} {\left({\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a + b\right)} \sinh\left(x\right)^{2} - a - b\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{4 \, {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \sinh\left(x\right)^{4} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} + 2 \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3} + 3 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}, -\frac{{\left({\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} - a - b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a b + b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a b + b^{2}\right)} \sinh\left(x\right)^{4} + {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} - a b - 2 \, b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(2 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + {\left({\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) + 2 \, \sqrt{2} {\left({\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a + b\right)} \sinh\left(x\right)^{2} - a - b\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{2 \, {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \sinh\left(x\right)^{4} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} + 2 \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3} + 3 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}\right]"," ",0,"[1/4*(((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a - b)*cosh(x))*sinh(x) + a + b)*sqrt(a + b)*log(-((a*b^2 + b^3)*cosh(x)^8 + 8*(a*b^2 + b^3)*cosh(x)*sinh(x)^7 + (a*b^2 + b^3)*sinh(x)^8 - 2*(a*b^2 + 2*b^3)*cosh(x)^6 - 2*(a*b^2 + 2*b^3 - 14*(a*b^2 + b^3)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a*b^2 + b^3)*cosh(x)^3 - 3*(a*b^2 + 2*b^3)*cosh(x))*sinh(x)^5 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^4 + (70*(a*b^2 + b^3)*cosh(x)^4 + a^3 - a^2*b + 4*a*b^2 + 6*b^3 - 30*(a*b^2 + 2*b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a*b^2 + b^3)*cosh(x)^5 - 10*(a*b^2 + 2*b^3)*cosh(x)^3 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x))*sinh(x)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 + 2*(a^3 - 3*a*b^2 - 2*b^3)*cosh(x)^2 + 2*(14*(a*b^2 + b^3)*cosh(x)^6 - 15*(a*b^2 + 2*b^3)*cosh(x)^4 + a^3 - 3*a*b^2 - 2*b^3 + 3*(a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^2)*sinh(x)^2 + sqrt(2)*(b^2*cosh(x)^6 + 6*b^2*cosh(x)*sinh(x)^5 + b^2*sinh(x)^6 - 3*b^2*cosh(x)^4 + 3*(5*b^2*cosh(x)^2 - b^2)*sinh(x)^4 + 4*(5*b^2*cosh(x)^3 - 3*b^2*cosh(x))*sinh(x)^3 - (a^2 - 2*a*b - 3*b^2)*cosh(x)^2 + (15*b^2*cosh(x)^4 - 18*b^2*cosh(x)^2 - a^2 + 2*a*b + 3*b^2)*sinh(x)^2 - a^2 - 2*a*b - b^2 + 2*(3*b^2*cosh(x)^5 - 6*b^2*cosh(x)^3 - (a^2 - 2*a*b - 3*b^2)*cosh(x))*sinh(x))*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a*b^2 + b^3)*cosh(x)^7 - 3*(a*b^2 + 2*b^3)*cosh(x)^5 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^3 + (a^3 - 3*a*b^2 - 2*b^3)*cosh(x))*sinh(x))/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) + ((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a - b)*cosh(x))*sinh(x) + a + b)*sqrt(a + b)*log(((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*a*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + b)*cosh(x)^3 + a*cosh(x))*sinh(x) + a + b)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) - 4*sqrt(2)*((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 - a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^4 + 4*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)*sinh(x)^3 + (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*sinh(x)^4 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 + 2*(a^3 + a^2*b - a*b^2 - b^3)*cosh(x)^2 + 2*(a^3 + a^2*b - a*b^2 - b^3 + 3*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^2)*sinh(x)^2 + 4*((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^3 + (a^3 + a^2*b - a*b^2 - b^3)*cosh(x))*sinh(x)), -1/2*(((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a - b)*cosh(x))*sinh(x) + a + b)*sqrt(-a - b)*arctan(sqrt(2)*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 - a - b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a*b + b^2)*cosh(x)^4 + 4*(a*b + b^2)*cosh(x)*sinh(x)^3 + (a*b + b^2)*sinh(x)^4 + (a^2 - a*b - 2*b^2)*cosh(x)^2 + (6*(a*b + b^2)*cosh(x)^2 + a^2 - a*b - 2*b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(2*(a*b + b^2)*cosh(x)^3 + (a^2 - a*b - 2*b^2)*cosh(x))*sinh(x))) + ((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a - b)*cosh(x))*sinh(x) + a + b)*sqrt(-a - b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a - b)*cosh(x))*sinh(x) + a + b)) + 2*sqrt(2)*((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 - a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^4 + 4*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)*sinh(x)^3 + (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*sinh(x)^4 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 + 2*(a^3 + a^2*b - a*b^2 - b^3)*cosh(x)^2 + 2*(a^3 + a^2*b - a*b^2 - b^3 + 3*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^2)*sinh(x)^2 + 4*((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^3 + (a^3 + a^2*b - a*b^2 - b^3)*cosh(x))*sinh(x))]","B",0
242,1,2277,0,0.668842," ","integrate(tanh(x)/(a+b*tanh(x)^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b\right)} \sqrt{a + b} \log\left(\frac{{\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{3} + a^{2} b\right)} \sinh\left(x\right)^{8} + 2 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} + 2 \, {\left(2 \, a^{3} + a^{2} b + 14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} + 3 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3} + 30 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} + 10 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} + 2 \, {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} + 15 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 2 \, a^{3} + 3 \, a^{2} b - b^{3} + 3 \, {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(a^{2} \cosh\left(x\right)^{6} + 6 \, a^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + a^{2} \sinh\left(x\right)^{6} + 3 \, a^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, a^{2} \cosh\left(x\right)^{2} + a^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, a^{2} \cosh\left(x\right)^{3} + 3 \, a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, a^{2} \cosh\left(x\right)^{4} + 18 \, a^{2} \cosh\left(x\right)^{2} + 3 \, a^{2} + 2 \, a b - b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(x\right)^{5} + 6 \, a^{2} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{7} + 3 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) + {\left({\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b\right)} \sqrt{a + b} \log\left(-\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - b\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - b \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right) - 4 \, \sqrt{2} {\left({\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a + b\right)} \sinh\left(x\right)^{2} + a + b\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{4 \, {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \sinh\left(x\right)^{4} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} + 2 \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3} + 3 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}, -\frac{{\left({\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(a \cosh\left(x\right)^{2} + 2 \, a \cosh\left(x\right) \sinh\left(x\right) + a \sinh\left(x\right)^{2} + a + b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a^{2} + a b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{2} + a b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{2} + a b\right)} \sinh\left(x\right)^{4} + {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} + 2 \, a^{2} + a b - b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(2 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + {\left({\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) + 2 \, \sqrt{2} {\left({\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a + b\right)} \sinh\left(x\right)^{2} + a + b\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{2 \, {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \sinh\left(x\right)^{4} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} + 2 \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3} + 3 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}\right]"," ",0,"[1/4*(((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a - b)*cosh(x))*sinh(x) + a + b)*sqrt(a + b)*log(((a^3 + a^2*b)*cosh(x)^8 + 8*(a^3 + a^2*b)*cosh(x)*sinh(x)^7 + (a^3 + a^2*b)*sinh(x)^8 + 2*(2*a^3 + a^2*b)*cosh(x)^6 + 2*(2*a^3 + a^2*b + 14*(a^3 + a^2*b)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a^3 + a^2*b)*cosh(x)^3 + 3*(2*a^3 + a^2*b)*cosh(x))*sinh(x)^5 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^4 + (70*(a^3 + a^2*b)*cosh(x)^4 + 6*a^3 + 4*a^2*b - a*b^2 + b^3 + 30*(2*a^3 + a^2*b)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a^3 + a^2*b)*cosh(x)^5 + 10*(2*a^3 + a^2*b)*cosh(x)^3 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x))*sinh(x)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 + 2*(2*a^3 + 3*a^2*b - b^3)*cosh(x)^2 + 2*(14*(a^3 + a^2*b)*cosh(x)^6 + 15*(2*a^3 + a^2*b)*cosh(x)^4 + 2*a^3 + 3*a^2*b - b^3 + 3*(6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^2)*sinh(x)^2 + sqrt(2)*(a^2*cosh(x)^6 + 6*a^2*cosh(x)*sinh(x)^5 + a^2*sinh(x)^6 + 3*a^2*cosh(x)^4 + 3*(5*a^2*cosh(x)^2 + a^2)*sinh(x)^4 + 4*(5*a^2*cosh(x)^3 + 3*a^2*cosh(x))*sinh(x)^3 + (3*a^2 + 2*a*b - b^2)*cosh(x)^2 + (15*a^2*cosh(x)^4 + 18*a^2*cosh(x)^2 + 3*a^2 + 2*a*b - b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(3*a^2*cosh(x)^5 + 6*a^2*cosh(x)^3 + (3*a^2 + 2*a*b - b^2)*cosh(x))*sinh(x))*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a^3 + a^2*b)*cosh(x)^7 + 3*(2*a^3 + a^2*b)*cosh(x)^5 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^3 + (2*a^3 + 3*a^2*b - b^3)*cosh(x))*sinh(x))/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) + ((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a - b)*cosh(x))*sinh(x) + a + b)*sqrt(a + b)*log(-((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*b*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + b)*cosh(x)^3 - b*cosh(x))*sinh(x) + a + b)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) - 4*sqrt(2)*((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 + a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^4 + 4*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)*sinh(x)^3 + (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*sinh(x)^4 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 + 2*(a^3 + a^2*b - a*b^2 - b^3)*cosh(x)^2 + 2*(a^3 + a^2*b - a*b^2 - b^3 + 3*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^2)*sinh(x)^2 + 4*((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^3 + (a^3 + a^2*b - a*b^2 - b^3)*cosh(x))*sinh(x)), -1/2*(((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a - b)*cosh(x))*sinh(x) + a + b)*sqrt(-a - b)*arctan(sqrt(2)*(a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 + a + b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a^2 + a*b)*cosh(x)^4 + 4*(a^2 + a*b)*cosh(x)*sinh(x)^3 + (a^2 + a*b)*sinh(x)^4 + (2*a^2 + a*b - b^2)*cosh(x)^2 + (6*(a^2 + a*b)*cosh(x)^2 + 2*a^2 + a*b - b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(2*(a^2 + a*b)*cosh(x)^3 + (2*a^2 + a*b - b^2)*cosh(x))*sinh(x))) + ((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a - b)*cosh(x))*sinh(x) + a + b)*sqrt(-a - b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a - b)*cosh(x))*sinh(x) + a + b)) + 2*sqrt(2)*((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 + a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^4 + 4*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)*sinh(x)^3 + (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*sinh(x)^4 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 + 2*(a^3 + a^2*b - a*b^2 - b^3)*cosh(x)^2 + 2*(a^3 + a^2*b - a*b^2 - b^3 + 3*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^2)*sinh(x)^2 + 4*((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^3 + (a^3 + a^2*b - a*b^2 - b^3)*cosh(x))*sinh(x))]","B",0
243,1,2509,0,0.715676," ","integrate(1/(a+b*tanh(x)^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(a^{2} + a b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{2} + a b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{2} + a b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a^{2} - a b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} + a^{2} - a b\right)} \sinh\left(x\right)^{2} + a^{2} + a b + 4 \, {\left({\left(a^{2} + a b\right)} \cosh\left(x\right)^{3} + {\left(a^{2} - a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \log\left(-\frac{{\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a b^{2} + b^{3}\right)} \sinh\left(x\right)^{8} - 2 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{6} - 2 \, {\left(a b^{2} + 2 \, b^{3} - 14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3} - 30 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} + 2 \, {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} - 3 \, a b^{2} - 2 \, b^{3} + 3 \, {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(b^{2} \cosh\left(x\right)^{6} + 6 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + b^{2} \sinh\left(x\right)^{6} - 3 \, b^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, b^{2} \cosh\left(x\right)^{2} - b^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, b^{2} \cosh\left(x\right)^{3} - 3 \, b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, b^{2} \cosh\left(x\right)^{4} - 18 \, b^{2} \cosh\left(x\right)^{2} - a^{2} + 2 \, a b + 3 \, b^{2}\right)} \sinh\left(x\right)^{2} - a^{2} - 2 \, a b - b^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{5} - 6 \, b^{2} \cosh\left(x\right)^{3} - {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{5} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) + {\left({\left(a^{2} + a b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{2} + a b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{2} + a b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a^{2} - a b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} + a^{2} - a b\right)} \sinh\left(x\right)^{2} + a^{2} + a b + 4 \, {\left({\left(a^{2} + a b\right)} \cosh\left(x\right)^{3} + {\left(a^{2} - a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \log\left(\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, a \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + a \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right) + 4 \, \sqrt{2} {\left({\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a b + b^{2}\right)} \sinh\left(x\right)^{2} - a b - b^{2}\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{4 \, {\left({\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \sinh\left(x\right)^{4} + a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3} + 2 \, {\left(a^{4} + a^{3} b - a^{2} b^{2} - a b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a^{4} + a^{3} b - a^{2} b^{2} - a b^{3} + 3 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{4} + a^{3} b - a^{2} b^{2} - a b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}, -\frac{{\left({\left(a^{2} + a b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{2} + a b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{2} + a b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a^{2} - a b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} + a^{2} - a b\right)} \sinh\left(x\right)^{2} + a^{2} + a b + 4 \, {\left({\left(a^{2} + a b\right)} \cosh\left(x\right)^{3} + {\left(a^{2} - a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} - a - b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a b + b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a b + b^{2}\right)} \sinh\left(x\right)^{4} + {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} - a b - 2 \, b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(2 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + {\left({\left(a^{2} + a b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{2} + a b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{2} + a b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a^{2} - a b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} + a^{2} - a b\right)} \sinh\left(x\right)^{2} + a^{2} + a b + 4 \, {\left({\left(a^{2} + a b\right)} \cosh\left(x\right)^{3} + {\left(a^{2} - a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) - 2 \, \sqrt{2} {\left({\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a b + b^{2}\right)} \sinh\left(x\right)^{2} - a b - b^{2}\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{2 \, {\left({\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \sinh\left(x\right)^{4} + a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3} + 2 \, {\left(a^{4} + a^{3} b - a^{2} b^{2} - a b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a^{4} + a^{3} b - a^{2} b^{2} - a b^{3} + 3 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{4} + a^{3} b - a^{2} b^{2} - a b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}\right]"," ",0,"[1/4*(((a^2 + a*b)*cosh(x)^4 + 4*(a^2 + a*b)*cosh(x)*sinh(x)^3 + (a^2 + a*b)*sinh(x)^4 + 2*(a^2 - a*b)*cosh(x)^2 + 2*(3*(a^2 + a*b)*cosh(x)^2 + a^2 - a*b)*sinh(x)^2 + a^2 + a*b + 4*((a^2 + a*b)*cosh(x)^3 + (a^2 - a*b)*cosh(x))*sinh(x))*sqrt(a + b)*log(-((a*b^2 + b^3)*cosh(x)^8 + 8*(a*b^2 + b^3)*cosh(x)*sinh(x)^7 + (a*b^2 + b^3)*sinh(x)^8 - 2*(a*b^2 + 2*b^3)*cosh(x)^6 - 2*(a*b^2 + 2*b^3 - 14*(a*b^2 + b^3)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a*b^2 + b^3)*cosh(x)^3 - 3*(a*b^2 + 2*b^3)*cosh(x))*sinh(x)^5 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^4 + (70*(a*b^2 + b^3)*cosh(x)^4 + a^3 - a^2*b + 4*a*b^2 + 6*b^3 - 30*(a*b^2 + 2*b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a*b^2 + b^3)*cosh(x)^5 - 10*(a*b^2 + 2*b^3)*cosh(x)^3 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x))*sinh(x)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 + 2*(a^3 - 3*a*b^2 - 2*b^3)*cosh(x)^2 + 2*(14*(a*b^2 + b^3)*cosh(x)^6 - 15*(a*b^2 + 2*b^3)*cosh(x)^4 + a^3 - 3*a*b^2 - 2*b^3 + 3*(a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^2)*sinh(x)^2 + sqrt(2)*(b^2*cosh(x)^6 + 6*b^2*cosh(x)*sinh(x)^5 + b^2*sinh(x)^6 - 3*b^2*cosh(x)^4 + 3*(5*b^2*cosh(x)^2 - b^2)*sinh(x)^4 + 4*(5*b^2*cosh(x)^3 - 3*b^2*cosh(x))*sinh(x)^3 - (a^2 - 2*a*b - 3*b^2)*cosh(x)^2 + (15*b^2*cosh(x)^4 - 18*b^2*cosh(x)^2 - a^2 + 2*a*b + 3*b^2)*sinh(x)^2 - a^2 - 2*a*b - b^2 + 2*(3*b^2*cosh(x)^5 - 6*b^2*cosh(x)^3 - (a^2 - 2*a*b - 3*b^2)*cosh(x))*sinh(x))*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a*b^2 + b^3)*cosh(x)^7 - 3*(a*b^2 + 2*b^3)*cosh(x)^5 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^3 + (a^3 - 3*a*b^2 - 2*b^3)*cosh(x))*sinh(x))/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) + ((a^2 + a*b)*cosh(x)^4 + 4*(a^2 + a*b)*cosh(x)*sinh(x)^3 + (a^2 + a*b)*sinh(x)^4 + 2*(a^2 - a*b)*cosh(x)^2 + 2*(3*(a^2 + a*b)*cosh(x)^2 + a^2 - a*b)*sinh(x)^2 + a^2 + a*b + 4*((a^2 + a*b)*cosh(x)^3 + (a^2 - a*b)*cosh(x))*sinh(x))*sqrt(a + b)*log(((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*a*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + b)*cosh(x)^3 + a*cosh(x))*sinh(x) + a + b)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*sqrt(2)*((a*b + b^2)*cosh(x)^2 + 2*(a*b + b^2)*cosh(x)*sinh(x) + (a*b + b^2)*sinh(x)^2 - a*b - b^2)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/((a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(x)^4 + 4*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(x)*sinh(x)^3 + (a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*sinh(x)^4 + a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3 + 2*(a^4 + a^3*b - a^2*b^2 - a*b^3)*cosh(x)^2 + 2*(a^4 + a^3*b - a^2*b^2 - a*b^3 + 3*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(x)^2)*sinh(x)^2 + 4*((a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(x)^3 + (a^4 + a^3*b - a^2*b^2 - a*b^3)*cosh(x))*sinh(x)), -1/2*(((a^2 + a*b)*cosh(x)^4 + 4*(a^2 + a*b)*cosh(x)*sinh(x)^3 + (a^2 + a*b)*sinh(x)^4 + 2*(a^2 - a*b)*cosh(x)^2 + 2*(3*(a^2 + a*b)*cosh(x)^2 + a^2 - a*b)*sinh(x)^2 + a^2 + a*b + 4*((a^2 + a*b)*cosh(x)^3 + (a^2 - a*b)*cosh(x))*sinh(x))*sqrt(-a - b)*arctan(sqrt(2)*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 - a - b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a*b + b^2)*cosh(x)^4 + 4*(a*b + b^2)*cosh(x)*sinh(x)^3 + (a*b + b^2)*sinh(x)^4 + (a^2 - a*b - 2*b^2)*cosh(x)^2 + (6*(a*b + b^2)*cosh(x)^2 + a^2 - a*b - 2*b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(2*(a*b + b^2)*cosh(x)^3 + (a^2 - a*b - 2*b^2)*cosh(x))*sinh(x))) + ((a^2 + a*b)*cosh(x)^4 + 4*(a^2 + a*b)*cosh(x)*sinh(x)^3 + (a^2 + a*b)*sinh(x)^4 + 2*(a^2 - a*b)*cosh(x)^2 + 2*(3*(a^2 + a*b)*cosh(x)^2 + a^2 - a*b)*sinh(x)^2 + a^2 + a*b + 4*((a^2 + a*b)*cosh(x)^3 + (a^2 - a*b)*cosh(x))*sinh(x))*sqrt(-a - b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a - b)*cosh(x))*sinh(x) + a + b)) - 2*sqrt(2)*((a*b + b^2)*cosh(x)^2 + 2*(a*b + b^2)*cosh(x)*sinh(x) + (a*b + b^2)*sinh(x)^2 - a*b - b^2)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/((a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(x)^4 + 4*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(x)*sinh(x)^3 + (a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*sinh(x)^4 + a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3 + 2*(a^4 + a^3*b - a^2*b^2 - a*b^3)*cosh(x)^2 + 2*(a^4 + a^3*b - a^2*b^2 - a*b^3 + 3*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(x)^2)*sinh(x)^2 + 4*((a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(x)^3 + (a^4 + a^3*b - a^2*b^2 - a*b^3)*cosh(x))*sinh(x))]","B",0
244,1,6955,0,1.006637," ","integrate(coth(x)/(a+b*tanh(x)^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{3} + a^{2} b\right)} \sinh\left(x\right)^{4} + a^{3} + a^{2} b + 2 \, {\left(a^{3} - a^{2} b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a^{3} - a^{2} b + 3 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} + {\left(a^{3} - a^{2} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \log\left(\frac{{\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{3} + a^{2} b\right)} \sinh\left(x\right)^{8} + 2 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} + 2 \, {\left(2 \, a^{3} + a^{2} b + 14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} + 3 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3} + 30 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} + 10 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} + 2 \, {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} + 15 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 2 \, a^{3} + 3 \, a^{2} b - b^{3} + 3 \, {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(a^{2} \cosh\left(x\right)^{6} + 6 \, a^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + a^{2} \sinh\left(x\right)^{6} + 3 \, a^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, a^{2} \cosh\left(x\right)^{2} + a^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, a^{2} \cosh\left(x\right)^{3} + 3 \, a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, a^{2} \cosh\left(x\right)^{4} + 18 \, a^{2} \cosh\left(x\right)^{2} + 3 \, a^{2} + 2 \, a b - b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(x\right)^{5} + 6 \, a^{2} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{7} + 3 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) + 2 \, {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \sinh\left(x\right)^{4} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} + 2 \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3} + 3 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \log\left(-\frac{{\left(2 \, a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(2 \, a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(2 \, a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(2 \, a + b\right)} \cosh\left(x\right)^{2} + 2 \, a - b\right)} \sinh\left(x\right)^{2} - 2 \, \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{a} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(2 \, a + b\right)} \cosh\left(x\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + 2 \, a + b}{\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) + {\left({\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{3} + a^{2} b\right)} \sinh\left(x\right)^{4} + a^{3} + a^{2} b + 2 \, {\left(a^{3} - a^{2} b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a^{3} - a^{2} b + 3 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} + {\left(a^{3} - a^{2} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \log\left(-\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - b\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - b \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right) + 4 \, \sqrt{2} {\left(a^{2} b + a b^{2} + {\left(a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a^{2} b + a b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a^{2} b + a b^{2}\right)} \sinh\left(x\right)^{2}\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{4 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3} + {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a^{5} + a^{4} b - a^{3} b^{2} - a^{2} b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a^{5} + a^{4} b - a^{3} b^{2} - a^{2} b^{3} + 3 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{5} + a^{4} b - a^{3} b^{2} - a^{2} b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}, \frac{4 \, {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \sinh\left(x\right)^{4} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} + 2 \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3} + 3 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{-a} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) + {\left({\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{3} + a^{2} b\right)} \sinh\left(x\right)^{4} + a^{3} + a^{2} b + 2 \, {\left(a^{3} - a^{2} b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a^{3} - a^{2} b + 3 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} + {\left(a^{3} - a^{2} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \log\left(\frac{{\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{3} + a^{2} b\right)} \sinh\left(x\right)^{8} + 2 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} + 2 \, {\left(2 \, a^{3} + a^{2} b + 14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} + 3 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3} + 30 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} + 10 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} + 2 \, {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} + 15 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 2 \, a^{3} + 3 \, a^{2} b - b^{3} + 3 \, {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(a^{2} \cosh\left(x\right)^{6} + 6 \, a^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + a^{2} \sinh\left(x\right)^{6} + 3 \, a^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, a^{2} \cosh\left(x\right)^{2} + a^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, a^{2} \cosh\left(x\right)^{3} + 3 \, a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, a^{2} \cosh\left(x\right)^{4} + 18 \, a^{2} \cosh\left(x\right)^{2} + 3 \, a^{2} + 2 \, a b - b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(x\right)^{5} + 6 \, a^{2} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{7} + 3 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) + {\left({\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{3} + a^{2} b\right)} \sinh\left(x\right)^{4} + a^{3} + a^{2} b + 2 \, {\left(a^{3} - a^{2} b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a^{3} - a^{2} b + 3 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} + {\left(a^{3} - a^{2} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \log\left(-\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - b\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - b \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right) + 4 \, \sqrt{2} {\left(a^{2} b + a b^{2} + {\left(a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a^{2} b + a b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a^{2} b + a b^{2}\right)} \sinh\left(x\right)^{2}\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{4 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3} + {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a^{5} + a^{4} b - a^{3} b^{2} - a^{2} b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a^{5} + a^{4} b - a^{3} b^{2} - a^{2} b^{3} + 3 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{5} + a^{4} b - a^{3} b^{2} - a^{2} b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}, -\frac{{\left({\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{3} + a^{2} b\right)} \sinh\left(x\right)^{4} + a^{3} + a^{2} b + 2 \, {\left(a^{3} - a^{2} b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a^{3} - a^{2} b + 3 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} + {\left(a^{3} - a^{2} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(a \cosh\left(x\right)^{2} + 2 \, a \cosh\left(x\right) \sinh\left(x\right) + a \sinh\left(x\right)^{2} + a + b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a^{2} + a b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{2} + a b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{2} + a b\right)} \sinh\left(x\right)^{4} + {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} + 2 \, a^{2} + a b - b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(2 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + {\left({\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{3} + a^{2} b\right)} \sinh\left(x\right)^{4} + a^{3} + a^{2} b + 2 \, {\left(a^{3} - a^{2} b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a^{3} - a^{2} b + 3 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} + {\left(a^{3} - a^{2} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) - {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \sinh\left(x\right)^{4} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} + 2 \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3} + 3 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a} \log\left(-\frac{{\left(2 \, a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(2 \, a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(2 \, a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(2 \, a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(2 \, a + b\right)} \cosh\left(x\right)^{2} + 2 \, a - b\right)} \sinh\left(x\right)^{2} - 2 \, \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{a} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(2 \, a + b\right)} \cosh\left(x\right)^{3} + {\left(2 \, a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + 2 \, a + b}{\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) - 2 \, \sqrt{2} {\left(a^{2} b + a b^{2} + {\left(a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a^{2} b + a b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a^{2} b + a b^{2}\right)} \sinh\left(x\right)^{2}\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{2 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3} + {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a^{5} + a^{4} b - a^{3} b^{2} - a^{2} b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a^{5} + a^{4} b - a^{3} b^{2} - a^{2} b^{3} + 3 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{5} + a^{4} b - a^{3} b^{2} - a^{2} b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}, \frac{2 \, {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \sinh\left(x\right)^{4} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} + 2 \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a^{3} + a^{2} b - a b^{2} - b^{3} + 3 \, {\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + a^{2} b - a b^{2} - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{-a} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) - {\left({\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{3} + a^{2} b\right)} \sinh\left(x\right)^{4} + a^{3} + a^{2} b + 2 \, {\left(a^{3} - a^{2} b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a^{3} - a^{2} b + 3 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} + {\left(a^{3} - a^{2} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(a \cosh\left(x\right)^{2} + 2 \, a \cosh\left(x\right) \sinh\left(x\right) + a \sinh\left(x\right)^{2} + a + b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a^{2} + a b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{2} + a b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{2} + a b\right)} \sinh\left(x\right)^{4} + {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} + 2 \, a^{2} + a b - b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(2 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) - {\left({\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{3} + a^{2} b\right)} \sinh\left(x\right)^{4} + a^{3} + a^{2} b + 2 \, {\left(a^{3} - a^{2} b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a^{3} - a^{2} b + 3 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} + {\left(a^{3} - a^{2} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) + 2 \, \sqrt{2} {\left(a^{2} b + a b^{2} + {\left(a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a^{2} b + a b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a^{2} b + a b^{2}\right)} \sinh\left(x\right)^{2}\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{2 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3} + {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a^{5} + a^{4} b - a^{3} b^{2} - a^{2} b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a^{5} + a^{4} b - a^{3} b^{2} - a^{2} b^{3} + 3 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{5} + a^{4} b - a^{3} b^{2} - a^{2} b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}\right]"," ",0,"[1/4*(((a^3 + a^2*b)*cosh(x)^4 + 4*(a^3 + a^2*b)*cosh(x)*sinh(x)^3 + (a^3 + a^2*b)*sinh(x)^4 + a^3 + a^2*b + 2*(a^3 - a^2*b)*cosh(x)^2 + 2*(a^3 - a^2*b + 3*(a^3 + a^2*b)*cosh(x)^2)*sinh(x)^2 + 4*((a^3 + a^2*b)*cosh(x)^3 + (a^3 - a^2*b)*cosh(x))*sinh(x))*sqrt(a + b)*log(((a^3 + a^2*b)*cosh(x)^8 + 8*(a^3 + a^2*b)*cosh(x)*sinh(x)^7 + (a^3 + a^2*b)*sinh(x)^8 + 2*(2*a^3 + a^2*b)*cosh(x)^6 + 2*(2*a^3 + a^2*b + 14*(a^3 + a^2*b)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a^3 + a^2*b)*cosh(x)^3 + 3*(2*a^3 + a^2*b)*cosh(x))*sinh(x)^5 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^4 + (70*(a^3 + a^2*b)*cosh(x)^4 + 6*a^3 + 4*a^2*b - a*b^2 + b^3 + 30*(2*a^3 + a^2*b)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a^3 + a^2*b)*cosh(x)^5 + 10*(2*a^3 + a^2*b)*cosh(x)^3 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x))*sinh(x)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 + 2*(2*a^3 + 3*a^2*b - b^3)*cosh(x)^2 + 2*(14*(a^3 + a^2*b)*cosh(x)^6 + 15*(2*a^3 + a^2*b)*cosh(x)^4 + 2*a^3 + 3*a^2*b - b^3 + 3*(6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^2)*sinh(x)^2 + sqrt(2)*(a^2*cosh(x)^6 + 6*a^2*cosh(x)*sinh(x)^5 + a^2*sinh(x)^6 + 3*a^2*cosh(x)^4 + 3*(5*a^2*cosh(x)^2 + a^2)*sinh(x)^4 + 4*(5*a^2*cosh(x)^3 + 3*a^2*cosh(x))*sinh(x)^3 + (3*a^2 + 2*a*b - b^2)*cosh(x)^2 + (15*a^2*cosh(x)^4 + 18*a^2*cosh(x)^2 + 3*a^2 + 2*a*b - b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(3*a^2*cosh(x)^5 + 6*a^2*cosh(x)^3 + (3*a^2 + 2*a*b - b^2)*cosh(x))*sinh(x))*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a^3 + a^2*b)*cosh(x)^7 + 3*(2*a^3 + a^2*b)*cosh(x)^5 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^3 + (2*a^3 + 3*a^2*b - b^3)*cosh(x))*sinh(x))/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) + 2*((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^4 + 4*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)*sinh(x)^3 + (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*sinh(x)^4 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 + 2*(a^3 + a^2*b - a*b^2 - b^3)*cosh(x)^2 + 2*(a^3 + a^2*b - a*b^2 - b^3 + 3*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^2)*sinh(x)^2 + 4*((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^3 + (a^3 + a^2*b - a*b^2 - b^3)*cosh(x))*sinh(x))*sqrt(a)*log(-((2*a + b)*cosh(x)^4 + 4*(2*a + b)*cosh(x)*sinh(x)^3 + (2*a + b)*sinh(x)^4 + 2*(2*a - b)*cosh(x)^2 + 2*(3*(2*a + b)*cosh(x)^2 + 2*a - b)*sinh(x)^2 - 2*sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((2*a + b)*cosh(x)^3 + (2*a - b)*cosh(x))*sinh(x) + 2*a + b)/(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)) + ((a^3 + a^2*b)*cosh(x)^4 + 4*(a^3 + a^2*b)*cosh(x)*sinh(x)^3 + (a^3 + a^2*b)*sinh(x)^4 + a^3 + a^2*b + 2*(a^3 - a^2*b)*cosh(x)^2 + 2*(a^3 - a^2*b + 3*(a^3 + a^2*b)*cosh(x)^2)*sinh(x)^2 + 4*((a^3 + a^2*b)*cosh(x)^3 + (a^3 - a^2*b)*cosh(x))*sinh(x))*sqrt(a + b)*log(-((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*b*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + b)*cosh(x)^3 - b*cosh(x))*sinh(x) + a + b)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*sqrt(2)*(a^2*b + a*b^2 + (a^2*b + a*b^2)*cosh(x)^2 + 2*(a^2*b + a*b^2)*cosh(x)*sinh(x) + (a^2*b + a*b^2)*sinh(x)^2)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3 + (a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)^4 + 4*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)*sinh(x)^3 + (a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*sinh(x)^4 + 2*(a^5 + a^4*b - a^3*b^2 - a^2*b^3)*cosh(x)^2 + 2*(a^5 + a^4*b - a^3*b^2 - a^2*b^3 + 3*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)^2)*sinh(x)^2 + 4*((a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)^3 + (a^5 + a^4*b - a^3*b^2 - a^2*b^3)*cosh(x))*sinh(x)), 1/4*(4*((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^4 + 4*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)*sinh(x)^3 + (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*sinh(x)^4 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 + 2*(a^3 + a^2*b - a*b^2 - b^3)*cosh(x)^2 + 2*(a^3 + a^2*b - a*b^2 - b^3 + 3*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^2)*sinh(x)^2 + 4*((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^3 + (a^3 + a^2*b - a*b^2 - b^3)*cosh(x))*sinh(x))*sqrt(-a)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(-a)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a - b)*cosh(x))*sinh(x) + a + b)) + ((a^3 + a^2*b)*cosh(x)^4 + 4*(a^3 + a^2*b)*cosh(x)*sinh(x)^3 + (a^3 + a^2*b)*sinh(x)^4 + a^3 + a^2*b + 2*(a^3 - a^2*b)*cosh(x)^2 + 2*(a^3 - a^2*b + 3*(a^3 + a^2*b)*cosh(x)^2)*sinh(x)^2 + 4*((a^3 + a^2*b)*cosh(x)^3 + (a^3 - a^2*b)*cosh(x))*sinh(x))*sqrt(a + b)*log(((a^3 + a^2*b)*cosh(x)^8 + 8*(a^3 + a^2*b)*cosh(x)*sinh(x)^7 + (a^3 + a^2*b)*sinh(x)^8 + 2*(2*a^3 + a^2*b)*cosh(x)^6 + 2*(2*a^3 + a^2*b + 14*(a^3 + a^2*b)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a^3 + a^2*b)*cosh(x)^3 + 3*(2*a^3 + a^2*b)*cosh(x))*sinh(x)^5 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^4 + (70*(a^3 + a^2*b)*cosh(x)^4 + 6*a^3 + 4*a^2*b - a*b^2 + b^3 + 30*(2*a^3 + a^2*b)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a^3 + a^2*b)*cosh(x)^5 + 10*(2*a^3 + a^2*b)*cosh(x)^3 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x))*sinh(x)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 + 2*(2*a^3 + 3*a^2*b - b^3)*cosh(x)^2 + 2*(14*(a^3 + a^2*b)*cosh(x)^6 + 15*(2*a^3 + a^2*b)*cosh(x)^4 + 2*a^3 + 3*a^2*b - b^3 + 3*(6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^2)*sinh(x)^2 + sqrt(2)*(a^2*cosh(x)^6 + 6*a^2*cosh(x)*sinh(x)^5 + a^2*sinh(x)^6 + 3*a^2*cosh(x)^4 + 3*(5*a^2*cosh(x)^2 + a^2)*sinh(x)^4 + 4*(5*a^2*cosh(x)^3 + 3*a^2*cosh(x))*sinh(x)^3 + (3*a^2 + 2*a*b - b^2)*cosh(x)^2 + (15*a^2*cosh(x)^4 + 18*a^2*cosh(x)^2 + 3*a^2 + 2*a*b - b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(3*a^2*cosh(x)^5 + 6*a^2*cosh(x)^3 + (3*a^2 + 2*a*b - b^2)*cosh(x))*sinh(x))*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a^3 + a^2*b)*cosh(x)^7 + 3*(2*a^3 + a^2*b)*cosh(x)^5 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^3 + (2*a^3 + 3*a^2*b - b^3)*cosh(x))*sinh(x))/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) + ((a^3 + a^2*b)*cosh(x)^4 + 4*(a^3 + a^2*b)*cosh(x)*sinh(x)^3 + (a^3 + a^2*b)*sinh(x)^4 + a^3 + a^2*b + 2*(a^3 - a^2*b)*cosh(x)^2 + 2*(a^3 - a^2*b + 3*(a^3 + a^2*b)*cosh(x)^2)*sinh(x)^2 + 4*((a^3 + a^2*b)*cosh(x)^3 + (a^3 - a^2*b)*cosh(x))*sinh(x))*sqrt(a + b)*log(-((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*b*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + b)*cosh(x)^3 - b*cosh(x))*sinh(x) + a + b)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*sqrt(2)*(a^2*b + a*b^2 + (a^2*b + a*b^2)*cosh(x)^2 + 2*(a^2*b + a*b^2)*cosh(x)*sinh(x) + (a^2*b + a*b^2)*sinh(x)^2)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3 + (a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)^4 + 4*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)*sinh(x)^3 + (a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*sinh(x)^4 + 2*(a^5 + a^4*b - a^3*b^2 - a^2*b^3)*cosh(x)^2 + 2*(a^5 + a^4*b - a^3*b^2 - a^2*b^3 + 3*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)^2)*sinh(x)^2 + 4*((a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)^3 + (a^5 + a^4*b - a^3*b^2 - a^2*b^3)*cosh(x))*sinh(x)), -1/2*(((a^3 + a^2*b)*cosh(x)^4 + 4*(a^3 + a^2*b)*cosh(x)*sinh(x)^3 + (a^3 + a^2*b)*sinh(x)^4 + a^3 + a^2*b + 2*(a^3 - a^2*b)*cosh(x)^2 + 2*(a^3 - a^2*b + 3*(a^3 + a^2*b)*cosh(x)^2)*sinh(x)^2 + 4*((a^3 + a^2*b)*cosh(x)^3 + (a^3 - a^2*b)*cosh(x))*sinh(x))*sqrt(-a - b)*arctan(sqrt(2)*(a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 + a + b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a^2 + a*b)*cosh(x)^4 + 4*(a^2 + a*b)*cosh(x)*sinh(x)^3 + (a^2 + a*b)*sinh(x)^4 + (2*a^2 + a*b - b^2)*cosh(x)^2 + (6*(a^2 + a*b)*cosh(x)^2 + 2*a^2 + a*b - b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(2*(a^2 + a*b)*cosh(x)^3 + (2*a^2 + a*b - b^2)*cosh(x))*sinh(x))) + ((a^3 + a^2*b)*cosh(x)^4 + 4*(a^3 + a^2*b)*cosh(x)*sinh(x)^3 + (a^3 + a^2*b)*sinh(x)^4 + a^3 + a^2*b + 2*(a^3 - a^2*b)*cosh(x)^2 + 2*(a^3 - a^2*b + 3*(a^3 + a^2*b)*cosh(x)^2)*sinh(x)^2 + 4*((a^3 + a^2*b)*cosh(x)^3 + (a^3 - a^2*b)*cosh(x))*sinh(x))*sqrt(-a - b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a - b)*cosh(x))*sinh(x) + a + b)) - ((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^4 + 4*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)*sinh(x)^3 + (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*sinh(x)^4 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 + 2*(a^3 + a^2*b - a*b^2 - b^3)*cosh(x)^2 + 2*(a^3 + a^2*b - a*b^2 - b^3 + 3*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^2)*sinh(x)^2 + 4*((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^3 + (a^3 + a^2*b - a*b^2 - b^3)*cosh(x))*sinh(x))*sqrt(a)*log(-((2*a + b)*cosh(x)^4 + 4*(2*a + b)*cosh(x)*sinh(x)^3 + (2*a + b)*sinh(x)^4 + 2*(2*a - b)*cosh(x)^2 + 2*(3*(2*a + b)*cosh(x)^2 + 2*a - b)*sinh(x)^2 - 2*sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((2*a + b)*cosh(x)^3 + (2*a - b)*cosh(x))*sinh(x) + 2*a + b)/(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)) - 2*sqrt(2)*(a^2*b + a*b^2 + (a^2*b + a*b^2)*cosh(x)^2 + 2*(a^2*b + a*b^2)*cosh(x)*sinh(x) + (a^2*b + a*b^2)*sinh(x)^2)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3 + (a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)^4 + 4*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)*sinh(x)^3 + (a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*sinh(x)^4 + 2*(a^5 + a^4*b - a^3*b^2 - a^2*b^3)*cosh(x)^2 + 2*(a^5 + a^4*b - a^3*b^2 - a^2*b^3 + 3*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)^2)*sinh(x)^2 + 4*((a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)^3 + (a^5 + a^4*b - a^3*b^2 - a^2*b^3)*cosh(x))*sinh(x)), 1/2*(2*((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^4 + 4*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)*sinh(x)^3 + (a^3 + 3*a^2*b + 3*a*b^2 + b^3)*sinh(x)^4 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 + 2*(a^3 + a^2*b - a*b^2 - b^3)*cosh(x)^2 + 2*(a^3 + a^2*b - a*b^2 - b^3 + 3*(a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^2)*sinh(x)^2 + 4*((a^3 + 3*a^2*b + 3*a*b^2 + b^3)*cosh(x)^3 + (a^3 + a^2*b - a*b^2 - b^3)*cosh(x))*sinh(x))*sqrt(-a)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(-a)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a - b)*cosh(x))*sinh(x) + a + b)) - ((a^3 + a^2*b)*cosh(x)^4 + 4*(a^3 + a^2*b)*cosh(x)*sinh(x)^3 + (a^3 + a^2*b)*sinh(x)^4 + a^3 + a^2*b + 2*(a^3 - a^2*b)*cosh(x)^2 + 2*(a^3 - a^2*b + 3*(a^3 + a^2*b)*cosh(x)^2)*sinh(x)^2 + 4*((a^3 + a^2*b)*cosh(x)^3 + (a^3 - a^2*b)*cosh(x))*sinh(x))*sqrt(-a - b)*arctan(sqrt(2)*(a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 + a + b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a^2 + a*b)*cosh(x)^4 + 4*(a^2 + a*b)*cosh(x)*sinh(x)^3 + (a^2 + a*b)*sinh(x)^4 + (2*a^2 + a*b - b^2)*cosh(x)^2 + (6*(a^2 + a*b)*cosh(x)^2 + 2*a^2 + a*b - b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(2*(a^2 + a*b)*cosh(x)^3 + (2*a^2 + a*b - b^2)*cosh(x))*sinh(x))) - ((a^3 + a^2*b)*cosh(x)^4 + 4*(a^3 + a^2*b)*cosh(x)*sinh(x)^3 + (a^3 + a^2*b)*sinh(x)^4 + a^3 + a^2*b + 2*(a^3 - a^2*b)*cosh(x)^2 + 2*(a^3 - a^2*b + 3*(a^3 + a^2*b)*cosh(x)^2)*sinh(x)^2 + 4*((a^3 + a^2*b)*cosh(x)^3 + (a^3 - a^2*b)*cosh(x))*sinh(x))*sqrt(-a - b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a - b)*cosh(x))*sinh(x) + a + b)) + 2*sqrt(2)*(a^2*b + a*b^2 + (a^2*b + a*b^2)*cosh(x)^2 + 2*(a^2*b + a*b^2)*cosh(x)*sinh(x) + (a^2*b + a*b^2)*sinh(x)^2)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3 + (a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)^4 + 4*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)*sinh(x)^3 + (a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*sinh(x)^4 + 2*(a^5 + a^4*b - a^3*b^2 - a^2*b^3)*cosh(x)^2 + 2*(a^5 + a^4*b - a^3*b^2 - a^2*b^3 + 3*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)^2)*sinh(x)^2 + 4*((a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)^3 + (a^5 + a^4*b - a^3*b^2 - a^2*b^3)*cosh(x))*sinh(x))]","B",0
245,1,3929,0,0.927192," ","integrate(coth(x)^2/(a+b*tanh(x)^2)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} + 6 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(a^{3} + a^{2} b\right)} \sinh\left(x\right)^{6} + {\left(a^{3} - 3 \, a^{2} b\right)} \cosh\left(x\right)^{4} + {\left(a^{3} - 3 \, a^{2} b + 15 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} + {\left(a^{3} - 3 \, a^{2} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - a^{3} - a^{2} b - {\left(a^{3} - 3 \, a^{2} b\right)} \cosh\left(x\right)^{2} + {\left(15 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} - a^{3} + 3 \, a^{2} b + 6 \, {\left(a^{3} - 3 \, a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} + 2 \, {\left(a^{3} - 3 \, a^{2} b\right)} \cosh\left(x\right)^{3} - {\left(a^{3} - 3 \, a^{2} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \log\left(-\frac{{\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a b^{2} + b^{3}\right)} \sinh\left(x\right)^{8} - 2 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{6} - 2 \, {\left(a b^{2} + 2 \, b^{3} - 14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3} - 30 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} + 2 \, {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} - 3 \, a b^{2} - 2 \, b^{3} + 3 \, {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(b^{2} \cosh\left(x\right)^{6} + 6 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + b^{2} \sinh\left(x\right)^{6} - 3 \, b^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, b^{2} \cosh\left(x\right)^{2} - b^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, b^{2} \cosh\left(x\right)^{3} - 3 \, b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, b^{2} \cosh\left(x\right)^{4} - 18 \, b^{2} \cosh\left(x\right)^{2} - a^{2} + 2 \, a b + 3 \, b^{2}\right)} \sinh\left(x\right)^{2} - a^{2} - 2 \, a b - b^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{5} - 6 \, b^{2} \cosh\left(x\right)^{3} - {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{5} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) + {\left({\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} + 6 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(a^{3} + a^{2} b\right)} \sinh\left(x\right)^{6} + {\left(a^{3} - 3 \, a^{2} b\right)} \cosh\left(x\right)^{4} + {\left(a^{3} - 3 \, a^{2} b + 15 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} + {\left(a^{3} - 3 \, a^{2} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - a^{3} - a^{2} b - {\left(a^{3} - 3 \, a^{2} b\right)} \cosh\left(x\right)^{2} + {\left(15 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} - a^{3} + 3 \, a^{2} b + 6 \, {\left(a^{3} - 3 \, a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} + 2 \, {\left(a^{3} - 3 \, a^{2} b\right)} \cosh\left(x\right)^{3} - {\left(a^{3} - 3 \, a^{2} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \log\left(\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, a \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + a \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right) - 4 \, \sqrt{2} {\left({\left(a^{3} + 3 \, a^{2} b + 4 \, a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{3} + 3 \, a^{2} b + 4 \, a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{3} + 3 \, a^{2} b + 4 \, a b^{2} + 2 \, b^{3}\right)} \sinh\left(x\right)^{4} + a^{3} + 3 \, a^{2} b + 4 \, a b^{2} + 2 \, b^{3} + 2 \, {\left(a^{3} + a^{2} b - 2 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a^{3} + a^{2} b - 2 \, a b^{2} - 2 \, b^{3} + 3 \, {\left(a^{3} + 3 \, a^{2} b + 4 \, a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{3} + 3 \, a^{2} b + 4 \, a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + a^{2} b - 2 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{4 \, {\left({\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right)^{6} + 6 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \sinh\left(x\right)^{6} - a^{5} - 3 \, a^{4} b - 3 \, a^{3} b^{2} - a^{2} b^{3} + {\left(a^{5} - a^{4} b - 5 \, a^{3} b^{2} - 3 \, a^{2} b^{3}\right)} \cosh\left(x\right)^{4} + {\left(a^{5} - a^{4} b - 5 \, a^{3} b^{2} - 3 \, a^{2} b^{3} + 15 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{5} - a^{4} b - 5 \, a^{3} b^{2} - 3 \, a^{2} b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - {\left(a^{5} - a^{4} b - 5 \, a^{3} b^{2} - 3 \, a^{2} b^{3}\right)} \cosh\left(x\right)^{2} - {\left(a^{5} - a^{4} b - 5 \, a^{3} b^{2} - 3 \, a^{2} b^{3} - 15 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right)^{4} - 6 \, {\left(a^{5} - a^{4} b - 5 \, a^{3} b^{2} - 3 \, a^{2} b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right)^{5} + 2 \, {\left(a^{5} - a^{4} b - 5 \, a^{3} b^{2} - 3 \, a^{2} b^{3}\right)} \cosh\left(x\right)^{3} - {\left(a^{5} - a^{4} b - 5 \, a^{3} b^{2} - 3 \, a^{2} b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}, -\frac{{\left({\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} + 6 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(a^{3} + a^{2} b\right)} \sinh\left(x\right)^{6} + {\left(a^{3} - 3 \, a^{2} b\right)} \cosh\left(x\right)^{4} + {\left(a^{3} - 3 \, a^{2} b + 15 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} + {\left(a^{3} - 3 \, a^{2} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - a^{3} - a^{2} b - {\left(a^{3} - 3 \, a^{2} b\right)} \cosh\left(x\right)^{2} + {\left(15 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} - a^{3} + 3 \, a^{2} b + 6 \, {\left(a^{3} - 3 \, a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} + 2 \, {\left(a^{3} - 3 \, a^{2} b\right)} \cosh\left(x\right)^{3} - {\left(a^{3} - 3 \, a^{2} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} - a - b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a b + b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a b + b^{2}\right)} \sinh\left(x\right)^{4} + {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} - a b - 2 \, b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(2 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + {\left({\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} + 6 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(a^{3} + a^{2} b\right)} \sinh\left(x\right)^{6} + {\left(a^{3} - 3 \, a^{2} b\right)} \cosh\left(x\right)^{4} + {\left(a^{3} - 3 \, a^{2} b + 15 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} + {\left(a^{3} - 3 \, a^{2} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - a^{3} - a^{2} b - {\left(a^{3} - 3 \, a^{2} b\right)} \cosh\left(x\right)^{2} + {\left(15 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} - a^{3} + 3 \, a^{2} b + 6 \, {\left(a^{3} - 3 \, a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} + 2 \, {\left(a^{3} - 3 \, a^{2} b\right)} \cosh\left(x\right)^{3} - {\left(a^{3} - 3 \, a^{2} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) + 2 \, \sqrt{2} {\left({\left(a^{3} + 3 \, a^{2} b + 4 \, a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{3} + 3 \, a^{2} b + 4 \, a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{3} + 3 \, a^{2} b + 4 \, a b^{2} + 2 \, b^{3}\right)} \sinh\left(x\right)^{4} + a^{3} + 3 \, a^{2} b + 4 \, a b^{2} + 2 \, b^{3} + 2 \, {\left(a^{3} + a^{2} b - 2 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a^{3} + a^{2} b - 2 \, a b^{2} - 2 \, b^{3} + 3 \, {\left(a^{3} + 3 \, a^{2} b + 4 \, a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a^{3} + 3 \, a^{2} b + 4 \, a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} + a^{2} b - 2 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{2 \, {\left({\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right)^{6} + 6 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \sinh\left(x\right)^{6} - a^{5} - 3 \, a^{4} b - 3 \, a^{3} b^{2} - a^{2} b^{3} + {\left(a^{5} - a^{4} b - 5 \, a^{3} b^{2} - 3 \, a^{2} b^{3}\right)} \cosh\left(x\right)^{4} + {\left(a^{5} - a^{4} b - 5 \, a^{3} b^{2} - 3 \, a^{2} b^{3} + 15 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{5} - a^{4} b - 5 \, a^{3} b^{2} - 3 \, a^{2} b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - {\left(a^{5} - a^{4} b - 5 \, a^{3} b^{2} - 3 \, a^{2} b^{3}\right)} \cosh\left(x\right)^{2} - {\left(a^{5} - a^{4} b - 5 \, a^{3} b^{2} - 3 \, a^{2} b^{3} - 15 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right)^{4} - 6 \, {\left(a^{5} - a^{4} b - 5 \, a^{3} b^{2} - 3 \, a^{2} b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a^{5} + 3 \, a^{4} b + 3 \, a^{3} b^{2} + a^{2} b^{3}\right)} \cosh\left(x\right)^{5} + 2 \, {\left(a^{5} - a^{4} b - 5 \, a^{3} b^{2} - 3 \, a^{2} b^{3}\right)} \cosh\left(x\right)^{3} - {\left(a^{5} - a^{4} b - 5 \, a^{3} b^{2} - 3 \, a^{2} b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}\right]"," ",0,"[1/4*(((a^3 + a^2*b)*cosh(x)^6 + 6*(a^3 + a^2*b)*cosh(x)*sinh(x)^5 + (a^3 + a^2*b)*sinh(x)^6 + (a^3 - 3*a^2*b)*cosh(x)^4 + (a^3 - 3*a^2*b + 15*(a^3 + a^2*b)*cosh(x)^2)*sinh(x)^4 + 4*(5*(a^3 + a^2*b)*cosh(x)^3 + (a^3 - 3*a^2*b)*cosh(x))*sinh(x)^3 - a^3 - a^2*b - (a^3 - 3*a^2*b)*cosh(x)^2 + (15*(a^3 + a^2*b)*cosh(x)^4 - a^3 + 3*a^2*b + 6*(a^3 - 3*a^2*b)*cosh(x)^2)*sinh(x)^2 + 2*(3*(a^3 + a^2*b)*cosh(x)^5 + 2*(a^3 - 3*a^2*b)*cosh(x)^3 - (a^3 - 3*a^2*b)*cosh(x))*sinh(x))*sqrt(a + b)*log(-((a*b^2 + b^3)*cosh(x)^8 + 8*(a*b^2 + b^3)*cosh(x)*sinh(x)^7 + (a*b^2 + b^3)*sinh(x)^8 - 2*(a*b^2 + 2*b^3)*cosh(x)^6 - 2*(a*b^2 + 2*b^3 - 14*(a*b^2 + b^3)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a*b^2 + b^3)*cosh(x)^3 - 3*(a*b^2 + 2*b^3)*cosh(x))*sinh(x)^5 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^4 + (70*(a*b^2 + b^3)*cosh(x)^4 + a^3 - a^2*b + 4*a*b^2 + 6*b^3 - 30*(a*b^2 + 2*b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a*b^2 + b^3)*cosh(x)^5 - 10*(a*b^2 + 2*b^3)*cosh(x)^3 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x))*sinh(x)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 + 2*(a^3 - 3*a*b^2 - 2*b^3)*cosh(x)^2 + 2*(14*(a*b^2 + b^3)*cosh(x)^6 - 15*(a*b^2 + 2*b^3)*cosh(x)^4 + a^3 - 3*a*b^2 - 2*b^3 + 3*(a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^2)*sinh(x)^2 + sqrt(2)*(b^2*cosh(x)^6 + 6*b^2*cosh(x)*sinh(x)^5 + b^2*sinh(x)^6 - 3*b^2*cosh(x)^4 + 3*(5*b^2*cosh(x)^2 - b^2)*sinh(x)^4 + 4*(5*b^2*cosh(x)^3 - 3*b^2*cosh(x))*sinh(x)^3 - (a^2 - 2*a*b - 3*b^2)*cosh(x)^2 + (15*b^2*cosh(x)^4 - 18*b^2*cosh(x)^2 - a^2 + 2*a*b + 3*b^2)*sinh(x)^2 - a^2 - 2*a*b - b^2 + 2*(3*b^2*cosh(x)^5 - 6*b^2*cosh(x)^3 - (a^2 - 2*a*b - 3*b^2)*cosh(x))*sinh(x))*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a*b^2 + b^3)*cosh(x)^7 - 3*(a*b^2 + 2*b^3)*cosh(x)^5 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^3 + (a^3 - 3*a*b^2 - 2*b^3)*cosh(x))*sinh(x))/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) + ((a^3 + a^2*b)*cosh(x)^6 + 6*(a^3 + a^2*b)*cosh(x)*sinh(x)^5 + (a^3 + a^2*b)*sinh(x)^6 + (a^3 - 3*a^2*b)*cosh(x)^4 + (a^3 - 3*a^2*b + 15*(a^3 + a^2*b)*cosh(x)^2)*sinh(x)^4 + 4*(5*(a^3 + a^2*b)*cosh(x)^3 + (a^3 - 3*a^2*b)*cosh(x))*sinh(x)^3 - a^3 - a^2*b - (a^3 - 3*a^2*b)*cosh(x)^2 + (15*(a^3 + a^2*b)*cosh(x)^4 - a^3 + 3*a^2*b + 6*(a^3 - 3*a^2*b)*cosh(x)^2)*sinh(x)^2 + 2*(3*(a^3 + a^2*b)*cosh(x)^5 + 2*(a^3 - 3*a^2*b)*cosh(x)^3 - (a^3 - 3*a^2*b)*cosh(x))*sinh(x))*sqrt(a + b)*log(((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*a*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + b)*cosh(x)^3 + a*cosh(x))*sinh(x) + a + b)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) - 4*sqrt(2)*((a^3 + 3*a^2*b + 4*a*b^2 + 2*b^3)*cosh(x)^4 + 4*(a^3 + 3*a^2*b + 4*a*b^2 + 2*b^3)*cosh(x)*sinh(x)^3 + (a^3 + 3*a^2*b + 4*a*b^2 + 2*b^3)*sinh(x)^4 + a^3 + 3*a^2*b + 4*a*b^2 + 2*b^3 + 2*(a^3 + a^2*b - 2*a*b^2 - 2*b^3)*cosh(x)^2 + 2*(a^3 + a^2*b - 2*a*b^2 - 2*b^3 + 3*(a^3 + 3*a^2*b + 4*a*b^2 + 2*b^3)*cosh(x)^2)*sinh(x)^2 + 4*((a^3 + 3*a^2*b + 4*a*b^2 + 2*b^3)*cosh(x)^3 + (a^3 + a^2*b - 2*a*b^2 - 2*b^3)*cosh(x))*sinh(x))*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/((a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)^6 + 6*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)*sinh(x)^5 + (a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*sinh(x)^6 - a^5 - 3*a^4*b - 3*a^3*b^2 - a^2*b^3 + (a^5 - a^4*b - 5*a^3*b^2 - 3*a^2*b^3)*cosh(x)^4 + (a^5 - a^4*b - 5*a^3*b^2 - 3*a^2*b^3 + 15*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)^2)*sinh(x)^4 + 4*(5*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)^3 + (a^5 - a^4*b - 5*a^3*b^2 - 3*a^2*b^3)*cosh(x))*sinh(x)^3 - (a^5 - a^4*b - 5*a^3*b^2 - 3*a^2*b^3)*cosh(x)^2 - (a^5 - a^4*b - 5*a^3*b^2 - 3*a^2*b^3 - 15*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)^4 - 6*(a^5 - a^4*b - 5*a^3*b^2 - 3*a^2*b^3)*cosh(x)^2)*sinh(x)^2 + 2*(3*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)^5 + 2*(a^5 - a^4*b - 5*a^3*b^2 - 3*a^2*b^3)*cosh(x)^3 - (a^5 - a^4*b - 5*a^3*b^2 - 3*a^2*b^3)*cosh(x))*sinh(x)), -1/2*(((a^3 + a^2*b)*cosh(x)^6 + 6*(a^3 + a^2*b)*cosh(x)*sinh(x)^5 + (a^3 + a^2*b)*sinh(x)^6 + (a^3 - 3*a^2*b)*cosh(x)^4 + (a^3 - 3*a^2*b + 15*(a^3 + a^2*b)*cosh(x)^2)*sinh(x)^4 + 4*(5*(a^3 + a^2*b)*cosh(x)^3 + (a^3 - 3*a^2*b)*cosh(x))*sinh(x)^3 - a^3 - a^2*b - (a^3 - 3*a^2*b)*cosh(x)^2 + (15*(a^3 + a^2*b)*cosh(x)^4 - a^3 + 3*a^2*b + 6*(a^3 - 3*a^2*b)*cosh(x)^2)*sinh(x)^2 + 2*(3*(a^3 + a^2*b)*cosh(x)^5 + 2*(a^3 - 3*a^2*b)*cosh(x)^3 - (a^3 - 3*a^2*b)*cosh(x))*sinh(x))*sqrt(-a - b)*arctan(sqrt(2)*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 - a - b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a*b + b^2)*cosh(x)^4 + 4*(a*b + b^2)*cosh(x)*sinh(x)^3 + (a*b + b^2)*sinh(x)^4 + (a^2 - a*b - 2*b^2)*cosh(x)^2 + (6*(a*b + b^2)*cosh(x)^2 + a^2 - a*b - 2*b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(2*(a*b + b^2)*cosh(x)^3 + (a^2 - a*b - 2*b^2)*cosh(x))*sinh(x))) + ((a^3 + a^2*b)*cosh(x)^6 + 6*(a^3 + a^2*b)*cosh(x)*sinh(x)^5 + (a^3 + a^2*b)*sinh(x)^6 + (a^3 - 3*a^2*b)*cosh(x)^4 + (a^3 - 3*a^2*b + 15*(a^3 + a^2*b)*cosh(x)^2)*sinh(x)^4 + 4*(5*(a^3 + a^2*b)*cosh(x)^3 + (a^3 - 3*a^2*b)*cosh(x))*sinh(x)^3 - a^3 - a^2*b - (a^3 - 3*a^2*b)*cosh(x)^2 + (15*(a^3 + a^2*b)*cosh(x)^4 - a^3 + 3*a^2*b + 6*(a^3 - 3*a^2*b)*cosh(x)^2)*sinh(x)^2 + 2*(3*(a^3 + a^2*b)*cosh(x)^5 + 2*(a^3 - 3*a^2*b)*cosh(x)^3 - (a^3 - 3*a^2*b)*cosh(x))*sinh(x))*sqrt(-a - b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a - b)*cosh(x))*sinh(x) + a + b)) + 2*sqrt(2)*((a^3 + 3*a^2*b + 4*a*b^2 + 2*b^3)*cosh(x)^4 + 4*(a^3 + 3*a^2*b + 4*a*b^2 + 2*b^3)*cosh(x)*sinh(x)^3 + (a^3 + 3*a^2*b + 4*a*b^2 + 2*b^3)*sinh(x)^4 + a^3 + 3*a^2*b + 4*a*b^2 + 2*b^3 + 2*(a^3 + a^2*b - 2*a*b^2 - 2*b^3)*cosh(x)^2 + 2*(a^3 + a^2*b - 2*a*b^2 - 2*b^3 + 3*(a^3 + 3*a^2*b + 4*a*b^2 + 2*b^3)*cosh(x)^2)*sinh(x)^2 + 4*((a^3 + 3*a^2*b + 4*a*b^2 + 2*b^3)*cosh(x)^3 + (a^3 + a^2*b - 2*a*b^2 - 2*b^3)*cosh(x))*sinh(x))*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/((a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)^6 + 6*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)*sinh(x)^5 + (a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*sinh(x)^6 - a^5 - 3*a^4*b - 3*a^3*b^2 - a^2*b^3 + (a^5 - a^4*b - 5*a^3*b^2 - 3*a^2*b^3)*cosh(x)^4 + (a^5 - a^4*b - 5*a^3*b^2 - 3*a^2*b^3 + 15*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)^2)*sinh(x)^4 + 4*(5*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)^3 + (a^5 - a^4*b - 5*a^3*b^2 - 3*a^2*b^3)*cosh(x))*sinh(x)^3 - (a^5 - a^4*b - 5*a^3*b^2 - 3*a^2*b^3)*cosh(x)^2 - (a^5 - a^4*b - 5*a^3*b^2 - 3*a^2*b^3 - 15*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)^4 - 6*(a^5 - a^4*b - 5*a^3*b^2 - 3*a^2*b^3)*cosh(x)^2)*sinh(x)^2 + 2*(3*(a^5 + 3*a^4*b + 3*a^3*b^2 + a^2*b^3)*cosh(x)^5 + 2*(a^5 - a^4*b - 5*a^3*b^2 - 3*a^2*b^3)*cosh(x)^3 - (a^5 - a^4*b - 5*a^3*b^2 - 3*a^2*b^3)*cosh(x))*sinh(x))]","B",0
246,-1,0,0,0.000000," ","integrate(tanh(x)^6/(a+b*tanh(x)^2)^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
247,1,7033,0,1.578957," ","integrate(tanh(x)^5/(a+b*tanh(x)^2)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(a^{2} b^{2} + 2 \, a b^{3} + b^{4}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{2} b^{2} + 2 \, a b^{3} + b^{4}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{2} b^{2} + 2 \, a b^{3} + b^{4}\right)} \sinh\left(x\right)^{8} + 4 \, {\left(a^{2} b^{2} - b^{4}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(a^{2} b^{2} - b^{4} + 7 \, {\left(a^{2} b^{2} + 2 \, a b^{3} + b^{4}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} b^{2} + 2 \, a b^{3} + b^{4}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{2} b^{2} - b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{2} b^{2} - 2 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} b^{2} + 2 \, a b^{3} + b^{4}\right)} \cosh\left(x\right)^{4} + 3 \, a^{2} b^{2} - 2 \, a b^{3} + 3 \, b^{4} + 30 \, {\left(a^{2} b^{2} - b^{4}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\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(x\right)^{5} + 10 \, {\left(a^{2} b^{2} - b^{4}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} b^{2} - 2 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(a^{2} b^{2} - b^{4}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} b^{2} + 2 \, a b^{3} + b^{4}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(a^{2} b^{2} - b^{4}\right)} \cosh\left(x\right)^{4} + a^{2} b^{2} - b^{4} + 3 \, {\left(3 \, a^{2} b^{2} - 2 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 8 \, {\left({\left(a^{2} b^{2} + 2 \, a b^{3} + b^{4}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(a^{2} b^{2} - b^{4}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{2} b^{2} - 2 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(x\right)^{3} + {\left(a^{2} b^{2} - b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \log\left(\frac{{\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{3} + a^{2} b\right)} \sinh\left(x\right)^{8} + 2 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} + 2 \, {\left(2 \, a^{3} + a^{2} b + 14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} + 3 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3} + 30 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} + 10 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} + 2 \, {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} + 15 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 2 \, a^{3} + 3 \, a^{2} b - b^{3} + 3 \, {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(a^{2} \cosh\left(x\right)^{6} + 6 \, a^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + a^{2} \sinh\left(x\right)^{6} + 3 \, a^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, a^{2} \cosh\left(x\right)^{2} + a^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, a^{2} \cosh\left(x\right)^{3} + 3 \, a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, a^{2} \cosh\left(x\right)^{4} + 18 \, a^{2} \cosh\left(x\right)^{2} + 3 \, a^{2} + 2 \, a b - b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(x\right)^{5} + 6 \, a^{2} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{7} + 3 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) + 3 \, {\left({\left(a^{2} b^{2} + 2 \, a b^{3} + b^{4}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{2} b^{2} + 2 \, a b^{3} + b^{4}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{2} b^{2} + 2 \, a b^{3} + b^{4}\right)} \sinh\left(x\right)^{8} + 4 \, {\left(a^{2} b^{2} - b^{4}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(a^{2} b^{2} - b^{4} + 7 \, {\left(a^{2} b^{2} + 2 \, a b^{3} + b^{4}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} b^{2} + 2 \, a b^{3} + b^{4}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{2} b^{2} - b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{2} b^{2} - 2 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} b^{2} + 2 \, a b^{3} + b^{4}\right)} \cosh\left(x\right)^{4} + 3 \, a^{2} b^{2} - 2 \, a b^{3} + 3 \, b^{4} + 30 \, {\left(a^{2} b^{2} - b^{4}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\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(x\right)^{5} + 10 \, {\left(a^{2} b^{2} - b^{4}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} b^{2} - 2 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(a^{2} b^{2} - b^{4}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} b^{2} + 2 \, a b^{3} + b^{4}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(a^{2} b^{2} - b^{4}\right)} \cosh\left(x\right)^{4} + a^{2} b^{2} - b^{4} + 3 \, {\left(3 \, a^{2} b^{2} - 2 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 8 \, {\left({\left(a^{2} b^{2} + 2 \, a b^{3} + b^{4}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(a^{2} b^{2} - b^{4}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{2} b^{2} - 2 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(x\right)^{3} + {\left(a^{2} b^{2} - b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \log\left(-\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - b\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - b \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right) + 8 \, \sqrt{2} {\left({\left(a^{4} + 5 \, a^{3} b + 7 \, a^{2} b^{2} + 3 \, a b^{3}\right)} \cosh\left(x\right)^{6} + 6 \, {\left(a^{4} + 5 \, a^{3} b + 7 \, a^{2} b^{2} + 3 \, a b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(a^{4} + 5 \, a^{3} b + 7 \, a^{2} b^{2} + 3 \, a b^{3}\right)} \sinh\left(x\right)^{6} + 3 \, {\left(a^{4} + 3 \, a^{3} b + a^{2} b^{2} - a b^{3}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(a^{4} + 3 \, a^{3} b + a^{2} b^{2} - a b^{3} + 5 \, {\left(a^{4} + 5 \, a^{3} b + 7 \, a^{2} b^{2} + 3 \, a b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + a^{4} + 5 \, a^{3} b + 7 \, a^{2} b^{2} + 3 \, a b^{3} + 4 \, {\left(5 \, {\left(a^{4} + 5 \, a^{3} b + 7 \, a^{2} b^{2} + 3 \, a b^{3}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{4} + 3 \, a^{3} b + a^{2} b^{2} - a b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 3 \, {\left(a^{4} + 3 \, a^{3} b + a^{2} b^{2} - a b^{3}\right)} \cosh\left(x\right)^{2} + 3 \, {\left(5 \, {\left(a^{4} + 5 \, a^{3} b + 7 \, a^{2} b^{2} + 3 \, a b^{3}\right)} \cosh\left(x\right)^{4} + a^{4} + 3 \, a^{3} b + a^{2} b^{2} - a b^{3} + 6 \, {\left(a^{4} + 3 \, a^{3} b + a^{2} b^{2} - a b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 6 \, {\left({\left(a^{4} + 5 \, a^{3} b + 7 \, a^{2} b^{2} + 3 \, a b^{3}\right)} \cosh\left(x\right)^{5} + 2 \, {\left(a^{4} + 3 \, a^{3} b + a^{2} b^{2} - a b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{4} + 3 \, a^{3} b + a^{2} b^{2} - a b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{12 \, {\left({\left(a^{5} b^{2} + 5 \, a^{4} b^{3} + 10 \, a^{3} b^{4} + 10 \, a^{2} b^{5} + 5 \, a b^{6} + b^{7}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{5} b^{2} + 5 \, a^{4} b^{3} + 10 \, a^{3} b^{4} + 10 \, a^{2} b^{5} + 5 \, a b^{6} + b^{7}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{5} b^{2} + 5 \, a^{4} b^{3} + 10 \, a^{3} b^{4} + 10 \, a^{2} b^{5} + 5 \, a b^{6} + b^{7}\right)} \sinh\left(x\right)^{8} + a^{5} b^{2} + 5 \, a^{4} b^{3} + 10 \, a^{3} b^{4} + 10 \, a^{2} b^{5} + 5 \, a b^{6} + b^{7} + 4 \, {\left(a^{5} b^{2} + 3 \, a^{4} b^{3} + 2 \, a^{3} b^{4} - 2 \, a^{2} b^{5} - 3 \, a b^{6} - b^{7}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(a^{5} b^{2} + 3 \, a^{4} b^{3} + 2 \, a^{3} b^{4} - 2 \, a^{2} b^{5} - 3 \, a b^{6} - b^{7} + 7 \, {\left(a^{5} b^{2} + 5 \, a^{4} b^{3} + 10 \, a^{3} b^{4} + 10 \, a^{2} b^{5} + 5 \, a b^{6} + b^{7}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{5} b^{2} + 5 \, a^{4} b^{3} + 10 \, a^{3} b^{4} + 10 \, a^{2} b^{5} + 5 \, a b^{6} + b^{7}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{5} b^{2} + 3 \, a^{4} b^{3} + 2 \, a^{3} b^{4} - 2 \, a^{2} b^{5} - 3 \, a b^{6} - b^{7}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{5} b^{2} + 7 \, a^{4} b^{3} + 6 \, a^{3} b^{4} + 6 \, a^{2} b^{5} + 7 \, a b^{6} + 3 \, b^{7}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(3 \, a^{5} b^{2} + 7 \, a^{4} b^{3} + 6 \, a^{3} b^{4} + 6 \, a^{2} b^{5} + 7 \, a b^{6} + 3 \, b^{7} + 35 \, {\left(a^{5} b^{2} + 5 \, a^{4} b^{3} + 10 \, a^{3} b^{4} + 10 \, a^{2} b^{5} + 5 \, a b^{6} + b^{7}\right)} \cosh\left(x\right)^{4} + 30 \, {\left(a^{5} b^{2} + 3 \, a^{4} b^{3} + 2 \, a^{3} b^{4} - 2 \, a^{2} b^{5} - 3 \, a b^{6} - b^{7}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{5} b^{2} + 5 \, a^{4} b^{3} + 10 \, a^{3} b^{4} + 10 \, a^{2} b^{5} + 5 \, a b^{6} + b^{7}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(a^{5} b^{2} + 3 \, a^{4} b^{3} + 2 \, a^{3} b^{4} - 2 \, a^{2} b^{5} - 3 \, a b^{6} - b^{7}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{5} b^{2} + 7 \, a^{4} b^{3} + 6 \, a^{3} b^{4} + 6 \, a^{2} b^{5} + 7 \, a b^{6} + 3 \, b^{7}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(a^{5} b^{2} + 3 \, a^{4} b^{3} + 2 \, a^{3} b^{4} - 2 \, a^{2} b^{5} - 3 \, a b^{6} - b^{7}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(a^{5} b^{2} + 3 \, a^{4} b^{3} + 2 \, a^{3} b^{4} - 2 \, a^{2} b^{5} - 3 \, a b^{6} - b^{7} + 7 \, {\left(a^{5} b^{2} + 5 \, a^{4} b^{3} + 10 \, a^{3} b^{4} + 10 \, a^{2} b^{5} + 5 \, a b^{6} + b^{7}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(a^{5} b^{2} + 3 \, a^{4} b^{3} + 2 \, a^{3} b^{4} - 2 \, a^{2} b^{5} - 3 \, a b^{6} - b^{7}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(3 \, a^{5} b^{2} + 7 \, a^{4} b^{3} + 6 \, a^{3} b^{4} + 6 \, a^{2} b^{5} + 7 \, a b^{6} + 3 \, b^{7}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 8 \, {\left({\left(a^{5} b^{2} + 5 \, a^{4} b^{3} + 10 \, a^{3} b^{4} + 10 \, a^{2} b^{5} + 5 \, a b^{6} + b^{7}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(a^{5} b^{2} + 3 \, a^{4} b^{3} + 2 \, a^{3} b^{4} - 2 \, a^{2} b^{5} - 3 \, a b^{6} - b^{7}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{5} b^{2} + 7 \, a^{4} b^{3} + 6 \, a^{3} b^{4} + 6 \, a^{2} b^{5} + 7 \, a b^{6} + 3 \, b^{7}\right)} \cosh\left(x\right)^{3} + {\left(a^{5} b^{2} + 3 \, a^{4} b^{3} + 2 \, a^{3} b^{4} - 2 \, a^{2} b^{5} - 3 \, a b^{6} - b^{7}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}, -\frac{3 \, {\left({\left(a^{2} b^{2} + 2 \, a b^{3} + b^{4}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{2} b^{2} + 2 \, a b^{3} + b^{4}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{2} b^{2} + 2 \, a b^{3} + b^{4}\right)} \sinh\left(x\right)^{8} + 4 \, {\left(a^{2} b^{2} - b^{4}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(a^{2} b^{2} - b^{4} + 7 \, {\left(a^{2} b^{2} + 2 \, a b^{3} + b^{4}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} b^{2} + 2 \, a b^{3} + b^{4}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{2} b^{2} - b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{2} b^{2} - 2 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} b^{2} + 2 \, a b^{3} + b^{4}\right)} \cosh\left(x\right)^{4} + 3 \, a^{2} b^{2} - 2 \, a b^{3} + 3 \, b^{4} + 30 \, {\left(a^{2} b^{2} - b^{4}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\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(x\right)^{5} + 10 \, {\left(a^{2} b^{2} - b^{4}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} b^{2} - 2 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(a^{2} b^{2} - b^{4}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} b^{2} + 2 \, a b^{3} + b^{4}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(a^{2} b^{2} - b^{4}\right)} \cosh\left(x\right)^{4} + a^{2} b^{2} - b^{4} + 3 \, {\left(3 \, a^{2} b^{2} - 2 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 8 \, {\left({\left(a^{2} b^{2} + 2 \, a b^{3} + b^{4}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(a^{2} b^{2} - b^{4}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{2} b^{2} - 2 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(x\right)^{3} + {\left(a^{2} b^{2} - b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(a \cosh\left(x\right)^{2} + 2 \, a \cosh\left(x\right) \sinh\left(x\right) + a \sinh\left(x\right)^{2} + a + b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a^{2} + a b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{2} + a b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{2} + a b\right)} \sinh\left(x\right)^{4} + {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} + 2 \, a^{2} + a b - b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(2 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + 3 \, {\left({\left(a^{2} b^{2} + 2 \, a b^{3} + b^{4}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{2} b^{2} + 2 \, a b^{3} + b^{4}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{2} b^{2} + 2 \, a b^{3} + b^{4}\right)} \sinh\left(x\right)^{8} + 4 \, {\left(a^{2} b^{2} - b^{4}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(a^{2} b^{2} - b^{4} + 7 \, {\left(a^{2} b^{2} + 2 \, a b^{3} + b^{4}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} b^{2} + 2 \, a b^{3} + b^{4}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{2} b^{2} - b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{2} b^{2} - 2 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} b^{2} + 2 \, a b^{3} + b^{4}\right)} \cosh\left(x\right)^{4} + 3 \, a^{2} b^{2} - 2 \, a b^{3} + 3 \, b^{4} + 30 \, {\left(a^{2} b^{2} - b^{4}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\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(x\right)^{5} + 10 \, {\left(a^{2} b^{2} - b^{4}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} b^{2} - 2 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(a^{2} b^{2} - b^{4}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} b^{2} + 2 \, a b^{3} + b^{4}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(a^{2} b^{2} - b^{4}\right)} \cosh\left(x\right)^{4} + a^{2} b^{2} - b^{4} + 3 \, {\left(3 \, a^{2} b^{2} - 2 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 8 \, {\left({\left(a^{2} b^{2} + 2 \, a b^{3} + b^{4}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(a^{2} b^{2} - b^{4}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{2} b^{2} - 2 \, a b^{3} + 3 \, b^{4}\right)} \cosh\left(x\right)^{3} + {\left(a^{2} b^{2} - b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) - 4 \, \sqrt{2} {\left({\left(a^{4} + 5 \, a^{3} b + 7 \, a^{2} b^{2} + 3 \, a b^{3}\right)} \cosh\left(x\right)^{6} + 6 \, {\left(a^{4} + 5 \, a^{3} b + 7 \, a^{2} b^{2} + 3 \, a b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(a^{4} + 5 \, a^{3} b + 7 \, a^{2} b^{2} + 3 \, a b^{3}\right)} \sinh\left(x\right)^{6} + 3 \, {\left(a^{4} + 3 \, a^{3} b + a^{2} b^{2} - a b^{3}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(a^{4} + 3 \, a^{3} b + a^{2} b^{2} - a b^{3} + 5 \, {\left(a^{4} + 5 \, a^{3} b + 7 \, a^{2} b^{2} + 3 \, a b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + a^{4} + 5 \, a^{3} b + 7 \, a^{2} b^{2} + 3 \, a b^{3} + 4 \, {\left(5 \, {\left(a^{4} + 5 \, a^{3} b + 7 \, a^{2} b^{2} + 3 \, a b^{3}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{4} + 3 \, a^{3} b + a^{2} b^{2} - a b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 3 \, {\left(a^{4} + 3 \, a^{3} b + a^{2} b^{2} - a b^{3}\right)} \cosh\left(x\right)^{2} + 3 \, {\left(5 \, {\left(a^{4} + 5 \, a^{3} b + 7 \, a^{2} b^{2} + 3 \, a b^{3}\right)} \cosh\left(x\right)^{4} + a^{4} + 3 \, a^{3} b + a^{2} b^{2} - a b^{3} + 6 \, {\left(a^{4} + 3 \, a^{3} b + a^{2} b^{2} - a b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 6 \, {\left({\left(a^{4} + 5 \, a^{3} b + 7 \, a^{2} b^{2} + 3 \, a b^{3}\right)} \cosh\left(x\right)^{5} + 2 \, {\left(a^{4} + 3 \, a^{3} b + a^{2} b^{2} - a b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{4} + 3 \, a^{3} b + a^{2} b^{2} - a b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{6 \, {\left({\left(a^{5} b^{2} + 5 \, a^{4} b^{3} + 10 \, a^{3} b^{4} + 10 \, a^{2} b^{5} + 5 \, a b^{6} + b^{7}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{5} b^{2} + 5 \, a^{4} b^{3} + 10 \, a^{3} b^{4} + 10 \, a^{2} b^{5} + 5 \, a b^{6} + b^{7}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{5} b^{2} + 5 \, a^{4} b^{3} + 10 \, a^{3} b^{4} + 10 \, a^{2} b^{5} + 5 \, a b^{6} + b^{7}\right)} \sinh\left(x\right)^{8} + a^{5} b^{2} + 5 \, a^{4} b^{3} + 10 \, a^{3} b^{4} + 10 \, a^{2} b^{5} + 5 \, a b^{6} + b^{7} + 4 \, {\left(a^{5} b^{2} + 3 \, a^{4} b^{3} + 2 \, a^{3} b^{4} - 2 \, a^{2} b^{5} - 3 \, a b^{6} - b^{7}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(a^{5} b^{2} + 3 \, a^{4} b^{3} + 2 \, a^{3} b^{4} - 2 \, a^{2} b^{5} - 3 \, a b^{6} - b^{7} + 7 \, {\left(a^{5} b^{2} + 5 \, a^{4} b^{3} + 10 \, a^{3} b^{4} + 10 \, a^{2} b^{5} + 5 \, a b^{6} + b^{7}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{5} b^{2} + 5 \, a^{4} b^{3} + 10 \, a^{3} b^{4} + 10 \, a^{2} b^{5} + 5 \, a b^{6} + b^{7}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{5} b^{2} + 3 \, a^{4} b^{3} + 2 \, a^{3} b^{4} - 2 \, a^{2} b^{5} - 3 \, a b^{6} - b^{7}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{5} b^{2} + 7 \, a^{4} b^{3} + 6 \, a^{3} b^{4} + 6 \, a^{2} b^{5} + 7 \, a b^{6} + 3 \, b^{7}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(3 \, a^{5} b^{2} + 7 \, a^{4} b^{3} + 6 \, a^{3} b^{4} + 6 \, a^{2} b^{5} + 7 \, a b^{6} + 3 \, b^{7} + 35 \, {\left(a^{5} b^{2} + 5 \, a^{4} b^{3} + 10 \, a^{3} b^{4} + 10 \, a^{2} b^{5} + 5 \, a b^{6} + b^{7}\right)} \cosh\left(x\right)^{4} + 30 \, {\left(a^{5} b^{2} + 3 \, a^{4} b^{3} + 2 \, a^{3} b^{4} - 2 \, a^{2} b^{5} - 3 \, a b^{6} - b^{7}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{5} b^{2} + 5 \, a^{4} b^{3} + 10 \, a^{3} b^{4} + 10 \, a^{2} b^{5} + 5 \, a b^{6} + b^{7}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(a^{5} b^{2} + 3 \, a^{4} b^{3} + 2 \, a^{3} b^{4} - 2 \, a^{2} b^{5} - 3 \, a b^{6} - b^{7}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{5} b^{2} + 7 \, a^{4} b^{3} + 6 \, a^{3} b^{4} + 6 \, a^{2} b^{5} + 7 \, a b^{6} + 3 \, b^{7}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(a^{5} b^{2} + 3 \, a^{4} b^{3} + 2 \, a^{3} b^{4} - 2 \, a^{2} b^{5} - 3 \, a b^{6} - b^{7}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(a^{5} b^{2} + 3 \, a^{4} b^{3} + 2 \, a^{3} b^{4} - 2 \, a^{2} b^{5} - 3 \, a b^{6} - b^{7} + 7 \, {\left(a^{5} b^{2} + 5 \, a^{4} b^{3} + 10 \, a^{3} b^{4} + 10 \, a^{2} b^{5} + 5 \, a b^{6} + b^{7}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(a^{5} b^{2} + 3 \, a^{4} b^{3} + 2 \, a^{3} b^{4} - 2 \, a^{2} b^{5} - 3 \, a b^{6} - b^{7}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(3 \, a^{5} b^{2} + 7 \, a^{4} b^{3} + 6 \, a^{3} b^{4} + 6 \, a^{2} b^{5} + 7 \, a b^{6} + 3 \, b^{7}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 8 \, {\left({\left(a^{5} b^{2} + 5 \, a^{4} b^{3} + 10 \, a^{3} b^{4} + 10 \, a^{2} b^{5} + 5 \, a b^{6} + b^{7}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(a^{5} b^{2} + 3 \, a^{4} b^{3} + 2 \, a^{3} b^{4} - 2 \, a^{2} b^{5} - 3 \, a b^{6} - b^{7}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{5} b^{2} + 7 \, a^{4} b^{3} + 6 \, a^{3} b^{4} + 6 \, a^{2} b^{5} + 7 \, a b^{6} + 3 \, b^{7}\right)} \cosh\left(x\right)^{3} + {\left(a^{5} b^{2} + 3 \, a^{4} b^{3} + 2 \, a^{3} b^{4} - 2 \, a^{2} b^{5} - 3 \, a b^{6} - b^{7}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}\right]"," ",0,"[1/12*(3*((a^2*b^2 + 2*a*b^3 + b^4)*cosh(x)^8 + 8*(a^2*b^2 + 2*a*b^3 + b^4)*cosh(x)*sinh(x)^7 + (a^2*b^2 + 2*a*b^3 + b^4)*sinh(x)^8 + 4*(a^2*b^2 - b^4)*cosh(x)^6 + 4*(a^2*b^2 - b^4 + 7*(a^2*b^2 + 2*a*b^3 + b^4)*cosh(x)^2)*sinh(x)^6 + 8*(7*(a^2*b^2 + 2*a*b^3 + b^4)*cosh(x)^3 + 3*(a^2*b^2 - b^4)*cosh(x))*sinh(x)^5 + 2*(3*a^2*b^2 - 2*a*b^3 + 3*b^4)*cosh(x)^4 + 2*(35*(a^2*b^2 + 2*a*b^3 + b^4)*cosh(x)^4 + 3*a^2*b^2 - 2*a*b^3 + 3*b^4 + 30*(a^2*b^2 - b^4)*cosh(x)^2)*sinh(x)^4 + a^2*b^2 + 2*a*b^3 + b^4 + 8*(7*(a^2*b^2 + 2*a*b^3 + b^4)*cosh(x)^5 + 10*(a^2*b^2 - b^4)*cosh(x)^3 + (3*a^2*b^2 - 2*a*b^3 + 3*b^4)*cosh(x))*sinh(x)^3 + 4*(a^2*b^2 - b^4)*cosh(x)^2 + 4*(7*(a^2*b^2 + 2*a*b^3 + b^4)*cosh(x)^6 + 15*(a^2*b^2 - b^4)*cosh(x)^4 + a^2*b^2 - b^4 + 3*(3*a^2*b^2 - 2*a*b^3 + 3*b^4)*cosh(x)^2)*sinh(x)^2 + 8*((a^2*b^2 + 2*a*b^3 + b^4)*cosh(x)^7 + 3*(a^2*b^2 - b^4)*cosh(x)^5 + (3*a^2*b^2 - 2*a*b^3 + 3*b^4)*cosh(x)^3 + (a^2*b^2 - b^4)*cosh(x))*sinh(x))*sqrt(a + b)*log(((a^3 + a^2*b)*cosh(x)^8 + 8*(a^3 + a^2*b)*cosh(x)*sinh(x)^7 + (a^3 + a^2*b)*sinh(x)^8 + 2*(2*a^3 + a^2*b)*cosh(x)^6 + 2*(2*a^3 + a^2*b + 14*(a^3 + a^2*b)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a^3 + a^2*b)*cosh(x)^3 + 3*(2*a^3 + a^2*b)*cosh(x))*sinh(x)^5 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^4 + (70*(a^3 + a^2*b)*cosh(x)^4 + 6*a^3 + 4*a^2*b - a*b^2 + b^3 + 30*(2*a^3 + a^2*b)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a^3 + a^2*b)*cosh(x)^5 + 10*(2*a^3 + a^2*b)*cosh(x)^3 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x))*sinh(x)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 + 2*(2*a^3 + 3*a^2*b - b^3)*cosh(x)^2 + 2*(14*(a^3 + a^2*b)*cosh(x)^6 + 15*(2*a^3 + a^2*b)*cosh(x)^4 + 2*a^3 + 3*a^2*b - b^3 + 3*(6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^2)*sinh(x)^2 + sqrt(2)*(a^2*cosh(x)^6 + 6*a^2*cosh(x)*sinh(x)^5 + a^2*sinh(x)^6 + 3*a^2*cosh(x)^4 + 3*(5*a^2*cosh(x)^2 + a^2)*sinh(x)^4 + 4*(5*a^2*cosh(x)^3 + 3*a^2*cosh(x))*sinh(x)^3 + (3*a^2 + 2*a*b - b^2)*cosh(x)^2 + (15*a^2*cosh(x)^4 + 18*a^2*cosh(x)^2 + 3*a^2 + 2*a*b - b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(3*a^2*cosh(x)^5 + 6*a^2*cosh(x)^3 + (3*a^2 + 2*a*b - b^2)*cosh(x))*sinh(x))*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a^3 + a^2*b)*cosh(x)^7 + 3*(2*a^3 + a^2*b)*cosh(x)^5 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^3 + (2*a^3 + 3*a^2*b - b^3)*cosh(x))*sinh(x))/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) + 3*((a^2*b^2 + 2*a*b^3 + b^4)*cosh(x)^8 + 8*(a^2*b^2 + 2*a*b^3 + b^4)*cosh(x)*sinh(x)^7 + (a^2*b^2 + 2*a*b^3 + b^4)*sinh(x)^8 + 4*(a^2*b^2 - b^4)*cosh(x)^6 + 4*(a^2*b^2 - b^4 + 7*(a^2*b^2 + 2*a*b^3 + b^4)*cosh(x)^2)*sinh(x)^6 + 8*(7*(a^2*b^2 + 2*a*b^3 + b^4)*cosh(x)^3 + 3*(a^2*b^2 - b^4)*cosh(x))*sinh(x)^5 + 2*(3*a^2*b^2 - 2*a*b^3 + 3*b^4)*cosh(x)^4 + 2*(35*(a^2*b^2 + 2*a*b^3 + b^4)*cosh(x)^4 + 3*a^2*b^2 - 2*a*b^3 + 3*b^4 + 30*(a^2*b^2 - b^4)*cosh(x)^2)*sinh(x)^4 + a^2*b^2 + 2*a*b^3 + b^4 + 8*(7*(a^2*b^2 + 2*a*b^3 + b^4)*cosh(x)^5 + 10*(a^2*b^2 - b^4)*cosh(x)^3 + (3*a^2*b^2 - 2*a*b^3 + 3*b^4)*cosh(x))*sinh(x)^3 + 4*(a^2*b^2 - b^4)*cosh(x)^2 + 4*(7*(a^2*b^2 + 2*a*b^3 + b^4)*cosh(x)^6 + 15*(a^2*b^2 - b^4)*cosh(x)^4 + a^2*b^2 - b^4 + 3*(3*a^2*b^2 - 2*a*b^3 + 3*b^4)*cosh(x)^2)*sinh(x)^2 + 8*((a^2*b^2 + 2*a*b^3 + b^4)*cosh(x)^7 + 3*(a^2*b^2 - b^4)*cosh(x)^5 + (3*a^2*b^2 - 2*a*b^3 + 3*b^4)*cosh(x)^3 + (a^2*b^2 - b^4)*cosh(x))*sinh(x))*sqrt(a + b)*log(-((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*b*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + b)*cosh(x)^3 - b*cosh(x))*sinh(x) + a + b)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) + 8*sqrt(2)*((a^4 + 5*a^3*b + 7*a^2*b^2 + 3*a*b^3)*cosh(x)^6 + 6*(a^4 + 5*a^3*b + 7*a^2*b^2 + 3*a*b^3)*cosh(x)*sinh(x)^5 + (a^4 + 5*a^3*b + 7*a^2*b^2 + 3*a*b^3)*sinh(x)^6 + 3*(a^4 + 3*a^3*b + a^2*b^2 - a*b^3)*cosh(x)^4 + 3*(a^4 + 3*a^3*b + a^2*b^2 - a*b^3 + 5*(a^4 + 5*a^3*b + 7*a^2*b^2 + 3*a*b^3)*cosh(x)^2)*sinh(x)^4 + a^4 + 5*a^3*b + 7*a^2*b^2 + 3*a*b^3 + 4*(5*(a^4 + 5*a^3*b + 7*a^2*b^2 + 3*a*b^3)*cosh(x)^3 + 3*(a^4 + 3*a^3*b + a^2*b^2 - a*b^3)*cosh(x))*sinh(x)^3 + 3*(a^4 + 3*a^3*b + a^2*b^2 - a*b^3)*cosh(x)^2 + 3*(5*(a^4 + 5*a^3*b + 7*a^2*b^2 + 3*a*b^3)*cosh(x)^4 + a^4 + 3*a^3*b + a^2*b^2 - a*b^3 + 6*(a^4 + 3*a^3*b + a^2*b^2 - a*b^3)*cosh(x)^2)*sinh(x)^2 + 6*((a^4 + 5*a^3*b + 7*a^2*b^2 + 3*a*b^3)*cosh(x)^5 + 2*(a^4 + 3*a^3*b + a^2*b^2 - a*b^3)*cosh(x)^3 + (a^4 + 3*a^3*b + a^2*b^2 - a*b^3)*cosh(x))*sinh(x))*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/((a^5*b^2 + 5*a^4*b^3 + 10*a^3*b^4 + 10*a^2*b^5 + 5*a*b^6 + b^7)*cosh(x)^8 + 8*(a^5*b^2 + 5*a^4*b^3 + 10*a^3*b^4 + 10*a^2*b^5 + 5*a*b^6 + b^7)*cosh(x)*sinh(x)^7 + (a^5*b^2 + 5*a^4*b^3 + 10*a^3*b^4 + 10*a^2*b^5 + 5*a*b^6 + b^7)*sinh(x)^8 + a^5*b^2 + 5*a^4*b^3 + 10*a^3*b^4 + 10*a^2*b^5 + 5*a*b^6 + b^7 + 4*(a^5*b^2 + 3*a^4*b^3 + 2*a^3*b^4 - 2*a^2*b^5 - 3*a*b^6 - b^7)*cosh(x)^6 + 4*(a^5*b^2 + 3*a^4*b^3 + 2*a^3*b^4 - 2*a^2*b^5 - 3*a*b^6 - b^7 + 7*(a^5*b^2 + 5*a^4*b^3 + 10*a^3*b^4 + 10*a^2*b^5 + 5*a*b^6 + b^7)*cosh(x)^2)*sinh(x)^6 + 8*(7*(a^5*b^2 + 5*a^4*b^3 + 10*a^3*b^4 + 10*a^2*b^5 + 5*a*b^6 + b^7)*cosh(x)^3 + 3*(a^5*b^2 + 3*a^4*b^3 + 2*a^3*b^4 - 2*a^2*b^5 - 3*a*b^6 - b^7)*cosh(x))*sinh(x)^5 + 2*(3*a^5*b^2 + 7*a^4*b^3 + 6*a^3*b^4 + 6*a^2*b^5 + 7*a*b^6 + 3*b^7)*cosh(x)^4 + 2*(3*a^5*b^2 + 7*a^4*b^3 + 6*a^3*b^4 + 6*a^2*b^5 + 7*a*b^6 + 3*b^7 + 35*(a^5*b^2 + 5*a^4*b^3 + 10*a^3*b^4 + 10*a^2*b^5 + 5*a*b^6 + b^7)*cosh(x)^4 + 30*(a^5*b^2 + 3*a^4*b^3 + 2*a^3*b^4 - 2*a^2*b^5 - 3*a*b^6 - b^7)*cosh(x)^2)*sinh(x)^4 + 8*(7*(a^5*b^2 + 5*a^4*b^3 + 10*a^3*b^4 + 10*a^2*b^5 + 5*a*b^6 + b^7)*cosh(x)^5 + 10*(a^5*b^2 + 3*a^4*b^3 + 2*a^3*b^4 - 2*a^2*b^5 - 3*a*b^6 - b^7)*cosh(x)^3 + (3*a^5*b^2 + 7*a^4*b^3 + 6*a^3*b^4 + 6*a^2*b^5 + 7*a*b^6 + 3*b^7)*cosh(x))*sinh(x)^3 + 4*(a^5*b^2 + 3*a^4*b^3 + 2*a^3*b^4 - 2*a^2*b^5 - 3*a*b^6 - b^7)*cosh(x)^2 + 4*(a^5*b^2 + 3*a^4*b^3 + 2*a^3*b^4 - 2*a^2*b^5 - 3*a*b^6 - b^7 + 7*(a^5*b^2 + 5*a^4*b^3 + 10*a^3*b^4 + 10*a^2*b^5 + 5*a*b^6 + b^7)*cosh(x)^6 + 15*(a^5*b^2 + 3*a^4*b^3 + 2*a^3*b^4 - 2*a^2*b^5 - 3*a*b^6 - b^7)*cosh(x)^4 + 3*(3*a^5*b^2 + 7*a^4*b^3 + 6*a^3*b^4 + 6*a^2*b^5 + 7*a*b^6 + 3*b^7)*cosh(x)^2)*sinh(x)^2 + 8*((a^5*b^2 + 5*a^4*b^3 + 10*a^3*b^4 + 10*a^2*b^5 + 5*a*b^6 + b^7)*cosh(x)^7 + 3*(a^5*b^2 + 3*a^4*b^3 + 2*a^3*b^4 - 2*a^2*b^5 - 3*a*b^6 - b^7)*cosh(x)^5 + (3*a^5*b^2 + 7*a^4*b^3 + 6*a^3*b^4 + 6*a^2*b^5 + 7*a*b^6 + 3*b^7)*cosh(x)^3 + (a^5*b^2 + 3*a^4*b^3 + 2*a^3*b^4 - 2*a^2*b^5 - 3*a*b^6 - b^7)*cosh(x))*sinh(x)), -1/6*(3*((a^2*b^2 + 2*a*b^3 + b^4)*cosh(x)^8 + 8*(a^2*b^2 + 2*a*b^3 + b^4)*cosh(x)*sinh(x)^7 + (a^2*b^2 + 2*a*b^3 + b^4)*sinh(x)^8 + 4*(a^2*b^2 - b^4)*cosh(x)^6 + 4*(a^2*b^2 - b^4 + 7*(a^2*b^2 + 2*a*b^3 + b^4)*cosh(x)^2)*sinh(x)^6 + 8*(7*(a^2*b^2 + 2*a*b^3 + b^4)*cosh(x)^3 + 3*(a^2*b^2 - b^4)*cosh(x))*sinh(x)^5 + 2*(3*a^2*b^2 - 2*a*b^3 + 3*b^4)*cosh(x)^4 + 2*(35*(a^2*b^2 + 2*a*b^3 + b^4)*cosh(x)^4 + 3*a^2*b^2 - 2*a*b^3 + 3*b^4 + 30*(a^2*b^2 - b^4)*cosh(x)^2)*sinh(x)^4 + a^2*b^2 + 2*a*b^3 + b^4 + 8*(7*(a^2*b^2 + 2*a*b^3 + b^4)*cosh(x)^5 + 10*(a^2*b^2 - b^4)*cosh(x)^3 + (3*a^2*b^2 - 2*a*b^3 + 3*b^4)*cosh(x))*sinh(x)^3 + 4*(a^2*b^2 - b^4)*cosh(x)^2 + 4*(7*(a^2*b^2 + 2*a*b^3 + b^4)*cosh(x)^6 + 15*(a^2*b^2 - b^4)*cosh(x)^4 + a^2*b^2 - b^4 + 3*(3*a^2*b^2 - 2*a*b^3 + 3*b^4)*cosh(x)^2)*sinh(x)^2 + 8*((a^2*b^2 + 2*a*b^3 + b^4)*cosh(x)^7 + 3*(a^2*b^2 - b^4)*cosh(x)^5 + (3*a^2*b^2 - 2*a*b^3 + 3*b^4)*cosh(x)^3 + (a^2*b^2 - b^4)*cosh(x))*sinh(x))*sqrt(-a - b)*arctan(sqrt(2)*(a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 + a + b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a^2 + a*b)*cosh(x)^4 + 4*(a^2 + a*b)*cosh(x)*sinh(x)^3 + (a^2 + a*b)*sinh(x)^4 + (2*a^2 + a*b - b^2)*cosh(x)^2 + (6*(a^2 + a*b)*cosh(x)^2 + 2*a^2 + a*b - b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(2*(a^2 + a*b)*cosh(x)^3 + (2*a^2 + a*b - b^2)*cosh(x))*sinh(x))) + 3*((a^2*b^2 + 2*a*b^3 + b^4)*cosh(x)^8 + 8*(a^2*b^2 + 2*a*b^3 + b^4)*cosh(x)*sinh(x)^7 + (a^2*b^2 + 2*a*b^3 + b^4)*sinh(x)^8 + 4*(a^2*b^2 - b^4)*cosh(x)^6 + 4*(a^2*b^2 - b^4 + 7*(a^2*b^2 + 2*a*b^3 + b^4)*cosh(x)^2)*sinh(x)^6 + 8*(7*(a^2*b^2 + 2*a*b^3 + b^4)*cosh(x)^3 + 3*(a^2*b^2 - b^4)*cosh(x))*sinh(x)^5 + 2*(3*a^2*b^2 - 2*a*b^3 + 3*b^4)*cosh(x)^4 + 2*(35*(a^2*b^2 + 2*a*b^3 + b^4)*cosh(x)^4 + 3*a^2*b^2 - 2*a*b^3 + 3*b^4 + 30*(a^2*b^2 - b^4)*cosh(x)^2)*sinh(x)^4 + a^2*b^2 + 2*a*b^3 + b^4 + 8*(7*(a^2*b^2 + 2*a*b^3 + b^4)*cosh(x)^5 + 10*(a^2*b^2 - b^4)*cosh(x)^3 + (3*a^2*b^2 - 2*a*b^3 + 3*b^4)*cosh(x))*sinh(x)^3 + 4*(a^2*b^2 - b^4)*cosh(x)^2 + 4*(7*(a^2*b^2 + 2*a*b^3 + b^4)*cosh(x)^6 + 15*(a^2*b^2 - b^4)*cosh(x)^4 + a^2*b^2 - b^4 + 3*(3*a^2*b^2 - 2*a*b^3 + 3*b^4)*cosh(x)^2)*sinh(x)^2 + 8*((a^2*b^2 + 2*a*b^3 + b^4)*cosh(x)^7 + 3*(a^2*b^2 - b^4)*cosh(x)^5 + (3*a^2*b^2 - 2*a*b^3 + 3*b^4)*cosh(x)^3 + (a^2*b^2 - b^4)*cosh(x))*sinh(x))*sqrt(-a - b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a - b)*cosh(x))*sinh(x) + a + b)) - 4*sqrt(2)*((a^4 + 5*a^3*b + 7*a^2*b^2 + 3*a*b^3)*cosh(x)^6 + 6*(a^4 + 5*a^3*b + 7*a^2*b^2 + 3*a*b^3)*cosh(x)*sinh(x)^5 + (a^4 + 5*a^3*b + 7*a^2*b^2 + 3*a*b^3)*sinh(x)^6 + 3*(a^4 + 3*a^3*b + a^2*b^2 - a*b^3)*cosh(x)^4 + 3*(a^4 + 3*a^3*b + a^2*b^2 - a*b^3 + 5*(a^4 + 5*a^3*b + 7*a^2*b^2 + 3*a*b^3)*cosh(x)^2)*sinh(x)^4 + a^4 + 5*a^3*b + 7*a^2*b^2 + 3*a*b^3 + 4*(5*(a^4 + 5*a^3*b + 7*a^2*b^2 + 3*a*b^3)*cosh(x)^3 + 3*(a^4 + 3*a^3*b + a^2*b^2 - a*b^3)*cosh(x))*sinh(x)^3 + 3*(a^4 + 3*a^3*b + a^2*b^2 - a*b^3)*cosh(x)^2 + 3*(5*(a^4 + 5*a^3*b + 7*a^2*b^2 + 3*a*b^3)*cosh(x)^4 + a^4 + 3*a^3*b + a^2*b^2 - a*b^3 + 6*(a^4 + 3*a^3*b + a^2*b^2 - a*b^3)*cosh(x)^2)*sinh(x)^2 + 6*((a^4 + 5*a^3*b + 7*a^2*b^2 + 3*a*b^3)*cosh(x)^5 + 2*(a^4 + 3*a^3*b + a^2*b^2 - a*b^3)*cosh(x)^3 + (a^4 + 3*a^3*b + a^2*b^2 - a*b^3)*cosh(x))*sinh(x))*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/((a^5*b^2 + 5*a^4*b^3 + 10*a^3*b^4 + 10*a^2*b^5 + 5*a*b^6 + b^7)*cosh(x)^8 + 8*(a^5*b^2 + 5*a^4*b^3 + 10*a^3*b^4 + 10*a^2*b^5 + 5*a*b^6 + b^7)*cosh(x)*sinh(x)^7 + (a^5*b^2 + 5*a^4*b^3 + 10*a^3*b^4 + 10*a^2*b^5 + 5*a*b^6 + b^7)*sinh(x)^8 + a^5*b^2 + 5*a^4*b^3 + 10*a^3*b^4 + 10*a^2*b^5 + 5*a*b^6 + b^7 + 4*(a^5*b^2 + 3*a^4*b^3 + 2*a^3*b^4 - 2*a^2*b^5 - 3*a*b^6 - b^7)*cosh(x)^6 + 4*(a^5*b^2 + 3*a^4*b^3 + 2*a^3*b^4 - 2*a^2*b^5 - 3*a*b^6 - b^7 + 7*(a^5*b^2 + 5*a^4*b^3 + 10*a^3*b^4 + 10*a^2*b^5 + 5*a*b^6 + b^7)*cosh(x)^2)*sinh(x)^6 + 8*(7*(a^5*b^2 + 5*a^4*b^3 + 10*a^3*b^4 + 10*a^2*b^5 + 5*a*b^6 + b^7)*cosh(x)^3 + 3*(a^5*b^2 + 3*a^4*b^3 + 2*a^3*b^4 - 2*a^2*b^5 - 3*a*b^6 - b^7)*cosh(x))*sinh(x)^5 + 2*(3*a^5*b^2 + 7*a^4*b^3 + 6*a^3*b^4 + 6*a^2*b^5 + 7*a*b^6 + 3*b^7)*cosh(x)^4 + 2*(3*a^5*b^2 + 7*a^4*b^3 + 6*a^3*b^4 + 6*a^2*b^5 + 7*a*b^6 + 3*b^7 + 35*(a^5*b^2 + 5*a^4*b^3 + 10*a^3*b^4 + 10*a^2*b^5 + 5*a*b^6 + b^7)*cosh(x)^4 + 30*(a^5*b^2 + 3*a^4*b^3 + 2*a^3*b^4 - 2*a^2*b^5 - 3*a*b^6 - b^7)*cosh(x)^2)*sinh(x)^4 + 8*(7*(a^5*b^2 + 5*a^4*b^3 + 10*a^3*b^4 + 10*a^2*b^5 + 5*a*b^6 + b^7)*cosh(x)^5 + 10*(a^5*b^2 + 3*a^4*b^3 + 2*a^3*b^4 - 2*a^2*b^5 - 3*a*b^6 - b^7)*cosh(x)^3 + (3*a^5*b^2 + 7*a^4*b^3 + 6*a^3*b^4 + 6*a^2*b^5 + 7*a*b^6 + 3*b^7)*cosh(x))*sinh(x)^3 + 4*(a^5*b^2 + 3*a^4*b^3 + 2*a^3*b^4 - 2*a^2*b^5 - 3*a*b^6 - b^7)*cosh(x)^2 + 4*(a^5*b^2 + 3*a^4*b^3 + 2*a^3*b^4 - 2*a^2*b^5 - 3*a*b^6 - b^7 + 7*(a^5*b^2 + 5*a^4*b^3 + 10*a^3*b^4 + 10*a^2*b^5 + 5*a*b^6 + b^7)*cosh(x)^6 + 15*(a^5*b^2 + 3*a^4*b^3 + 2*a^3*b^4 - 2*a^2*b^5 - 3*a*b^6 - b^7)*cosh(x)^4 + 3*(3*a^5*b^2 + 7*a^4*b^3 + 6*a^3*b^4 + 6*a^2*b^5 + 7*a*b^6 + 3*b^7)*cosh(x)^2)*sinh(x)^2 + 8*((a^5*b^2 + 5*a^4*b^3 + 10*a^3*b^4 + 10*a^2*b^5 + 5*a*b^6 + b^7)*cosh(x)^7 + 3*(a^5*b^2 + 3*a^4*b^3 + 2*a^3*b^4 - 2*a^2*b^5 - 3*a*b^6 - b^7)*cosh(x)^5 + (3*a^5*b^2 + 7*a^4*b^3 + 6*a^3*b^4 + 6*a^2*b^5 + 7*a*b^6 + 3*b^7)*cosh(x)^3 + (a^5*b^2 + 3*a^4*b^3 + 2*a^3*b^4 - 2*a^2*b^5 - 3*a*b^6 - b^7)*cosh(x))*sinh(x))]","B",0
248,1,5719,0,1.803379," ","integrate(tanh(x)^4/(a+b*tanh(x)^2)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(x\right)^{8} + 4 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{4} + 30 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 8 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \log\left(-\frac{{\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a b^{2} + b^{3}\right)} \sinh\left(x\right)^{8} - 2 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{6} - 2 \, {\left(a b^{2} + 2 \, b^{3} - 14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3} - 30 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} + 2 \, {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} - 3 \, a b^{2} - 2 \, b^{3} + 3 \, {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(b^{2} \cosh\left(x\right)^{6} + 6 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + b^{2} \sinh\left(x\right)^{6} - 3 \, b^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, b^{2} \cosh\left(x\right)^{2} - b^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, b^{2} \cosh\left(x\right)^{3} - 3 \, b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, b^{2} \cosh\left(x\right)^{4} - 18 \, b^{2} \cosh\left(x\right)^{2} - a^{2} + 2 \, a b + 3 \, b^{2}\right)} \sinh\left(x\right)^{2} - a^{2} - 2 \, a b - b^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{5} - 6 \, b^{2} \cosh\left(x\right)^{3} - {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{5} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) + 3 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(x\right)^{8} + 4 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{4} + 30 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 8 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \log\left(\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, a \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + a \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right) - 16 \, \sqrt{2} {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{6} + 6 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(x\right)^{6} - 3 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} - a b - b^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 3 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} + 3 \, {\left(5 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{4} - 6 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} + a b + b^{2}\right)} \sinh\left(x\right)^{2} - a^{2} - 2 \, a b - b^{2} + 6 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{5} - 2 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a b + b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{12 \, {\left({\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} \sinh\left(x\right)^{8} + 4 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5} + 7 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5} + 2 \, {\left(3 \, a^{5} + 7 \, a^{4} b + 6 \, a^{3} b^{2} + 6 \, a^{2} b^{3} + 7 \, a b^{4} + 3 \, b^{5}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(3 \, a^{5} + 7 \, a^{4} b + 6 \, a^{3} b^{2} + 6 \, a^{2} b^{3} + 7 \, a b^{4} + 3 \, b^{5} + 35 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} \cosh\left(x\right)^{4} + 30 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{5} + 7 \, a^{4} b + 6 \, a^{3} b^{2} + 6 \, a^{2} b^{3} + 7 \, a b^{4} + 3 \, b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} \cosh\left(x\right)^{6} + a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5} + 15 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(3 \, a^{5} + 7 \, a^{4} b + 6 \, a^{3} b^{2} + 6 \, a^{2} b^{3} + 7 \, a b^{4} + 3 \, b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 8 \, {\left({\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{5} + 7 \, a^{4} b + 6 \, a^{3} b^{2} + 6 \, a^{2} b^{3} + 7 \, a b^{4} + 3 \, b^{5}\right)} \cosh\left(x\right)^{3} + {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}, -\frac{3 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(x\right)^{8} + 4 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{4} + 30 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 8 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} - a - b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a b + b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a b + b^{2}\right)} \sinh\left(x\right)^{4} + {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} - a b - 2 \, b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(2 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + 3 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(x\right)^{8} + 4 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{4} + 30 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 8 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a + b\right)} \sinh\left(x\right)^{2} + a + b}\right) + 8 \, \sqrt{2} {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{6} + 6 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(x\right)^{6} - 3 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} - a b - b^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 3 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} + 3 \, {\left(5 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{4} - 6 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} + a b + b^{2}\right)} \sinh\left(x\right)^{2} - a^{2} - 2 \, a b - b^{2} + 6 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{5} - 2 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a b + b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{6 \, {\left({\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} \sinh\left(x\right)^{8} + 4 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5} + 7 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5} + 2 \, {\left(3 \, a^{5} + 7 \, a^{4} b + 6 \, a^{3} b^{2} + 6 \, a^{2} b^{3} + 7 \, a b^{4} + 3 \, b^{5}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(3 \, a^{5} + 7 \, a^{4} b + 6 \, a^{3} b^{2} + 6 \, a^{2} b^{3} + 7 \, a b^{4} + 3 \, b^{5} + 35 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} \cosh\left(x\right)^{4} + 30 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{5} + 7 \, a^{4} b + 6 \, a^{3} b^{2} + 6 \, a^{2} b^{3} + 7 \, a b^{4} + 3 \, b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} \cosh\left(x\right)^{6} + a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5} + 15 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(3 \, a^{5} + 7 \, a^{4} b + 6 \, a^{3} b^{2} + 6 \, a^{2} b^{3} + 7 \, a b^{4} + 3 \, b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 8 \, {\left({\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{5} + 7 \, a^{4} b + 6 \, a^{3} b^{2} + 6 \, a^{2} b^{3} + 7 \, a b^{4} + 3 \, b^{5}\right)} \cosh\left(x\right)^{3} + {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}\right]"," ",0,"[1/12*(3*((a^2 + 2*a*b + b^2)*cosh(x)^8 + 8*(a^2 + 2*a*b + b^2)*cosh(x)*sinh(x)^7 + (a^2 + 2*a*b + b^2)*sinh(x)^8 + 4*(a^2 - b^2)*cosh(x)^6 + 4*(7*(a^2 + 2*a*b + b^2)*cosh(x)^2 + a^2 - b^2)*sinh(x)^6 + 8*(7*(a^2 + 2*a*b + b^2)*cosh(x)^3 + 3*(a^2 - b^2)*cosh(x))*sinh(x)^5 + 2*(3*a^2 - 2*a*b + 3*b^2)*cosh(x)^4 + 2*(35*(a^2 + 2*a*b + b^2)*cosh(x)^4 + 30*(a^2 - b^2)*cosh(x)^2 + 3*a^2 - 2*a*b + 3*b^2)*sinh(x)^4 + 8*(7*(a^2 + 2*a*b + b^2)*cosh(x)^5 + 10*(a^2 - b^2)*cosh(x)^3 + (3*a^2 - 2*a*b + 3*b^2)*cosh(x))*sinh(x)^3 + 4*(a^2 - b^2)*cosh(x)^2 + 4*(7*(a^2 + 2*a*b + b^2)*cosh(x)^6 + 15*(a^2 - b^2)*cosh(x)^4 + 3*(3*a^2 - 2*a*b + 3*b^2)*cosh(x)^2 + a^2 - b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 8*((a^2 + 2*a*b + b^2)*cosh(x)^7 + 3*(a^2 - b^2)*cosh(x)^5 + (3*a^2 - 2*a*b + 3*b^2)*cosh(x)^3 + (a^2 - b^2)*cosh(x))*sinh(x))*sqrt(a + b)*log(-((a*b^2 + b^3)*cosh(x)^8 + 8*(a*b^2 + b^3)*cosh(x)*sinh(x)^7 + (a*b^2 + b^3)*sinh(x)^8 - 2*(a*b^2 + 2*b^3)*cosh(x)^6 - 2*(a*b^2 + 2*b^3 - 14*(a*b^2 + b^3)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a*b^2 + b^3)*cosh(x)^3 - 3*(a*b^2 + 2*b^3)*cosh(x))*sinh(x)^5 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^4 + (70*(a*b^2 + b^3)*cosh(x)^4 + a^3 - a^2*b + 4*a*b^2 + 6*b^3 - 30*(a*b^2 + 2*b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a*b^2 + b^3)*cosh(x)^5 - 10*(a*b^2 + 2*b^3)*cosh(x)^3 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x))*sinh(x)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 + 2*(a^3 - 3*a*b^2 - 2*b^3)*cosh(x)^2 + 2*(14*(a*b^2 + b^3)*cosh(x)^6 - 15*(a*b^2 + 2*b^3)*cosh(x)^4 + a^3 - 3*a*b^2 - 2*b^3 + 3*(a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^2)*sinh(x)^2 + sqrt(2)*(b^2*cosh(x)^6 + 6*b^2*cosh(x)*sinh(x)^5 + b^2*sinh(x)^6 - 3*b^2*cosh(x)^4 + 3*(5*b^2*cosh(x)^2 - b^2)*sinh(x)^4 + 4*(5*b^2*cosh(x)^3 - 3*b^2*cosh(x))*sinh(x)^3 - (a^2 - 2*a*b - 3*b^2)*cosh(x)^2 + (15*b^2*cosh(x)^4 - 18*b^2*cosh(x)^2 - a^2 + 2*a*b + 3*b^2)*sinh(x)^2 - a^2 - 2*a*b - b^2 + 2*(3*b^2*cosh(x)^5 - 6*b^2*cosh(x)^3 - (a^2 - 2*a*b - 3*b^2)*cosh(x))*sinh(x))*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a*b^2 + b^3)*cosh(x)^7 - 3*(a*b^2 + 2*b^3)*cosh(x)^5 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^3 + (a^3 - 3*a*b^2 - 2*b^3)*cosh(x))*sinh(x))/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) + 3*((a^2 + 2*a*b + b^2)*cosh(x)^8 + 8*(a^2 + 2*a*b + b^2)*cosh(x)*sinh(x)^7 + (a^2 + 2*a*b + b^2)*sinh(x)^8 + 4*(a^2 - b^2)*cosh(x)^6 + 4*(7*(a^2 + 2*a*b + b^2)*cosh(x)^2 + a^2 - b^2)*sinh(x)^6 + 8*(7*(a^2 + 2*a*b + b^2)*cosh(x)^3 + 3*(a^2 - b^2)*cosh(x))*sinh(x)^5 + 2*(3*a^2 - 2*a*b + 3*b^2)*cosh(x)^4 + 2*(35*(a^2 + 2*a*b + b^2)*cosh(x)^4 + 30*(a^2 - b^2)*cosh(x)^2 + 3*a^2 - 2*a*b + 3*b^2)*sinh(x)^4 + 8*(7*(a^2 + 2*a*b + b^2)*cosh(x)^5 + 10*(a^2 - b^2)*cosh(x)^3 + (3*a^2 - 2*a*b + 3*b^2)*cosh(x))*sinh(x)^3 + 4*(a^2 - b^2)*cosh(x)^2 + 4*(7*(a^2 + 2*a*b + b^2)*cosh(x)^6 + 15*(a^2 - b^2)*cosh(x)^4 + 3*(3*a^2 - 2*a*b + 3*b^2)*cosh(x)^2 + a^2 - b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 8*((a^2 + 2*a*b + b^2)*cosh(x)^7 + 3*(a^2 - b^2)*cosh(x)^5 + (3*a^2 - 2*a*b + 3*b^2)*cosh(x)^3 + (a^2 - b^2)*cosh(x))*sinh(x))*sqrt(a + b)*log(((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*a*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + b)*cosh(x)^3 + a*cosh(x))*sinh(x) + a + b)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) - 16*sqrt(2)*((a^2 + 2*a*b + b^2)*cosh(x)^6 + 6*(a^2 + 2*a*b + b^2)*cosh(x)*sinh(x)^5 + (a^2 + 2*a*b + b^2)*sinh(x)^6 - 3*(a*b + b^2)*cosh(x)^4 + 3*(5*(a^2 + 2*a*b + b^2)*cosh(x)^2 - a*b - b^2)*sinh(x)^4 + 4*(5*(a^2 + 2*a*b + b^2)*cosh(x)^3 - 3*(a*b + b^2)*cosh(x))*sinh(x)^3 + 3*(a*b + b^2)*cosh(x)^2 + 3*(5*(a^2 + 2*a*b + b^2)*cosh(x)^4 - 6*(a*b + b^2)*cosh(x)^2 + a*b + b^2)*sinh(x)^2 - a^2 - 2*a*b - b^2 + 6*((a^2 + 2*a*b + b^2)*cosh(x)^5 - 2*(a*b + b^2)*cosh(x)^3 + (a*b + b^2)*cosh(x))*sinh(x))*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/((a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*cosh(x)^8 + 8*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*cosh(x)*sinh(x)^7 + (a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*sinh(x)^8 + 4*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*cosh(x)^6 + 4*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5 + 7*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*cosh(x)^2)*sinh(x)^6 + 8*(7*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*cosh(x)^3 + 3*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*cosh(x))*sinh(x)^5 + a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5 + 2*(3*a^5 + 7*a^4*b + 6*a^3*b^2 + 6*a^2*b^3 + 7*a*b^4 + 3*b^5)*cosh(x)^4 + 2*(3*a^5 + 7*a^4*b + 6*a^3*b^2 + 6*a^2*b^3 + 7*a*b^4 + 3*b^5 + 35*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*cosh(x)^4 + 30*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*cosh(x)^2)*sinh(x)^4 + 8*(7*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*cosh(x)^5 + 10*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*cosh(x)^3 + (3*a^5 + 7*a^4*b + 6*a^3*b^2 + 6*a^2*b^3 + 7*a*b^4 + 3*b^5)*cosh(x))*sinh(x)^3 + 4*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*cosh(x)^2 + 4*(7*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*cosh(x)^6 + a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5 + 15*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*cosh(x)^4 + 3*(3*a^5 + 7*a^4*b + 6*a^3*b^2 + 6*a^2*b^3 + 7*a*b^4 + 3*b^5)*cosh(x)^2)*sinh(x)^2 + 8*((a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*cosh(x)^7 + 3*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*cosh(x)^5 + (3*a^5 + 7*a^4*b + 6*a^3*b^2 + 6*a^2*b^3 + 7*a*b^4 + 3*b^5)*cosh(x)^3 + (a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*cosh(x))*sinh(x)), -1/6*(3*((a^2 + 2*a*b + b^2)*cosh(x)^8 + 8*(a^2 + 2*a*b + b^2)*cosh(x)*sinh(x)^7 + (a^2 + 2*a*b + b^2)*sinh(x)^8 + 4*(a^2 - b^2)*cosh(x)^6 + 4*(7*(a^2 + 2*a*b + b^2)*cosh(x)^2 + a^2 - b^2)*sinh(x)^6 + 8*(7*(a^2 + 2*a*b + b^2)*cosh(x)^3 + 3*(a^2 - b^2)*cosh(x))*sinh(x)^5 + 2*(3*a^2 - 2*a*b + 3*b^2)*cosh(x)^4 + 2*(35*(a^2 + 2*a*b + b^2)*cosh(x)^4 + 30*(a^2 - b^2)*cosh(x)^2 + 3*a^2 - 2*a*b + 3*b^2)*sinh(x)^4 + 8*(7*(a^2 + 2*a*b + b^2)*cosh(x)^5 + 10*(a^2 - b^2)*cosh(x)^3 + (3*a^2 - 2*a*b + 3*b^2)*cosh(x))*sinh(x)^3 + 4*(a^2 - b^2)*cosh(x)^2 + 4*(7*(a^2 + 2*a*b + b^2)*cosh(x)^6 + 15*(a^2 - b^2)*cosh(x)^4 + 3*(3*a^2 - 2*a*b + 3*b^2)*cosh(x)^2 + a^2 - b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 8*((a^2 + 2*a*b + b^2)*cosh(x)^7 + 3*(a^2 - b^2)*cosh(x)^5 + (3*a^2 - 2*a*b + 3*b^2)*cosh(x)^3 + (a^2 - b^2)*cosh(x))*sinh(x))*sqrt(-a - b)*arctan(sqrt(2)*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 - a - b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a*b + b^2)*cosh(x)^4 + 4*(a*b + b^2)*cosh(x)*sinh(x)^3 + (a*b + b^2)*sinh(x)^4 + (a^2 - a*b - 2*b^2)*cosh(x)^2 + (6*(a*b + b^2)*cosh(x)^2 + a^2 - a*b - 2*b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(2*(a*b + b^2)*cosh(x)^3 + (a^2 - a*b - 2*b^2)*cosh(x))*sinh(x))) + 3*((a^2 + 2*a*b + b^2)*cosh(x)^8 + 8*(a^2 + 2*a*b + b^2)*cosh(x)*sinh(x)^7 + (a^2 + 2*a*b + b^2)*sinh(x)^8 + 4*(a^2 - b^2)*cosh(x)^6 + 4*(7*(a^2 + 2*a*b + b^2)*cosh(x)^2 + a^2 - b^2)*sinh(x)^6 + 8*(7*(a^2 + 2*a*b + b^2)*cosh(x)^3 + 3*(a^2 - b^2)*cosh(x))*sinh(x)^5 + 2*(3*a^2 - 2*a*b + 3*b^2)*cosh(x)^4 + 2*(35*(a^2 + 2*a*b + b^2)*cosh(x)^4 + 30*(a^2 - b^2)*cosh(x)^2 + 3*a^2 - 2*a*b + 3*b^2)*sinh(x)^4 + 8*(7*(a^2 + 2*a*b + b^2)*cosh(x)^5 + 10*(a^2 - b^2)*cosh(x)^3 + (3*a^2 - 2*a*b + 3*b^2)*cosh(x))*sinh(x)^3 + 4*(a^2 - b^2)*cosh(x)^2 + 4*(7*(a^2 + 2*a*b + b^2)*cosh(x)^6 + 15*(a^2 - b^2)*cosh(x)^4 + 3*(3*a^2 - 2*a*b + 3*b^2)*cosh(x)^2 + a^2 - b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 8*((a^2 + 2*a*b + b^2)*cosh(x)^7 + 3*(a^2 - b^2)*cosh(x)^5 + (3*a^2 - 2*a*b + 3*b^2)*cosh(x)^3 + (a^2 - b^2)*cosh(x))*sinh(x))*sqrt(-a - b)*arctan(sqrt(2)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 + a + b)) + 8*sqrt(2)*((a^2 + 2*a*b + b^2)*cosh(x)^6 + 6*(a^2 + 2*a*b + b^2)*cosh(x)*sinh(x)^5 + (a^2 + 2*a*b + b^2)*sinh(x)^6 - 3*(a*b + b^2)*cosh(x)^4 + 3*(5*(a^2 + 2*a*b + b^2)*cosh(x)^2 - a*b - b^2)*sinh(x)^4 + 4*(5*(a^2 + 2*a*b + b^2)*cosh(x)^3 - 3*(a*b + b^2)*cosh(x))*sinh(x)^3 + 3*(a*b + b^2)*cosh(x)^2 + 3*(5*(a^2 + 2*a*b + b^2)*cosh(x)^4 - 6*(a*b + b^2)*cosh(x)^2 + a*b + b^2)*sinh(x)^2 - a^2 - 2*a*b - b^2 + 6*((a^2 + 2*a*b + b^2)*cosh(x)^5 - 2*(a*b + b^2)*cosh(x)^3 + (a*b + b^2)*cosh(x))*sinh(x))*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/((a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*cosh(x)^8 + 8*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*cosh(x)*sinh(x)^7 + (a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*sinh(x)^8 + 4*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*cosh(x)^6 + 4*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5 + 7*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*cosh(x)^2)*sinh(x)^6 + 8*(7*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*cosh(x)^3 + 3*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*cosh(x))*sinh(x)^5 + a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5 + 2*(3*a^5 + 7*a^4*b + 6*a^3*b^2 + 6*a^2*b^3 + 7*a*b^4 + 3*b^5)*cosh(x)^4 + 2*(3*a^5 + 7*a^4*b + 6*a^3*b^2 + 6*a^2*b^3 + 7*a*b^4 + 3*b^5 + 35*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*cosh(x)^4 + 30*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*cosh(x)^2)*sinh(x)^4 + 8*(7*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*cosh(x)^5 + 10*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*cosh(x)^3 + (3*a^5 + 7*a^4*b + 6*a^3*b^2 + 6*a^2*b^3 + 7*a*b^4 + 3*b^5)*cosh(x))*sinh(x)^3 + 4*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*cosh(x)^2 + 4*(7*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*cosh(x)^6 + a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5 + 15*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*cosh(x)^4 + 3*(3*a^5 + 7*a^4*b + 6*a^3*b^2 + 6*a^2*b^3 + 7*a*b^4 + 3*b^5)*cosh(x)^2)*sinh(x)^2 + 8*((a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*cosh(x)^7 + 3*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*cosh(x)^5 + (3*a^5 + 7*a^4*b + 6*a^3*b^2 + 6*a^2*b^3 + 7*a*b^4 + 3*b^5)*cosh(x)^3 + (a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*cosh(x))*sinh(x))]","B",0
249,1,6621,0,1.431266," ","integrate(tanh(x)^3/(a+b*tanh(x)^2)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(a^{2} b + 2 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{2} b + 2 \, a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{2} b + 2 \, a b^{2} + b^{3}\right)} \sinh\left(x\right)^{8} + 4 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(a^{2} b - b^{3} + 7 \, {\left(a^{2} b + 2 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} b + 2 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{2} b - 2 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} b + 2 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + 3 \, a^{2} b - 2 \, a b^{2} + 3 \, b^{3} + 30 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} b + 2 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} b - 2 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{2} b + 2 \, a b^{2} + b^{3} + 4 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} b + 2 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)^{4} + a^{2} b - b^{3} + 3 \, {\left(3 \, a^{2} b - 2 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 8 \, {\left({\left(a^{2} b + 2 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{2} b - 2 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \log\left(\frac{{\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{3} + a^{2} b\right)} \sinh\left(x\right)^{8} + 2 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} + 2 \, {\left(2 \, a^{3} + a^{2} b + 14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} + 3 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3} + 30 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} + 10 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} + 2 \, {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} + 15 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 2 \, a^{3} + 3 \, a^{2} b - b^{3} + 3 \, {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(a^{2} \cosh\left(x\right)^{6} + 6 \, a^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + a^{2} \sinh\left(x\right)^{6} + 3 \, a^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, a^{2} \cosh\left(x\right)^{2} + a^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, a^{2} \cosh\left(x\right)^{3} + 3 \, a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, a^{2} \cosh\left(x\right)^{4} + 18 \, a^{2} \cosh\left(x\right)^{2} + 3 \, a^{2} + 2 \, a b - b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(x\right)^{5} + 6 \, a^{2} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{7} + 3 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) + 3 \, {\left({\left(a^{2} b + 2 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{2} b + 2 \, a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{2} b + 2 \, a b^{2} + b^{3}\right)} \sinh\left(x\right)^{8} + 4 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(a^{2} b - b^{3} + 7 \, {\left(a^{2} b + 2 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} b + 2 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{2} b - 2 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} b + 2 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + 3 \, a^{2} b - 2 \, a b^{2} + 3 \, b^{3} + 30 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} b + 2 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} b - 2 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{2} b + 2 \, a b^{2} + b^{3} + 4 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} b + 2 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)^{4} + a^{2} b - b^{3} + 3 \, {\left(3 \, a^{2} b - 2 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 8 \, {\left({\left(a^{2} b + 2 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{2} b - 2 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \log\left(-\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - b\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - b \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right) + 4 \, \sqrt{2} {\left({\left(a^{3} - a^{2} b - 5 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(x\right)^{6} + 6 \, {\left(a^{3} - a^{2} b - 5 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(a^{3} - a^{2} b - 5 \, a b^{2} - 3 \, b^{3}\right)} \sinh\left(x\right)^{6} + 3 \, {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(a^{3} - a^{2} b - a b^{2} + b^{3} + 5 \, {\left(a^{3} - a^{2} b - 5 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, {\left(a^{3} - a^{2} b - 5 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} - a^{2} b - 5 \, a b^{2} - 3 \, b^{3} + 3 \, {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2} + 3 \, {\left(5 \, {\left(a^{3} - a^{2} b - 5 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} - a^{2} b - a b^{2} + b^{3} + 6 \, {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 6 \, {\left({\left(a^{3} - a^{2} b - 5 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(x\right)^{5} + 2 \, {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{12 \, {\left({\left(a^{5} b + 5 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 10 \, a^{2} b^{4} + 5 \, a b^{5} + b^{6}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{5} b + 5 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 10 \, a^{2} b^{4} + 5 \, a b^{5} + b^{6}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{5} b + 5 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 10 \, a^{2} b^{4} + 5 \, a b^{5} + b^{6}\right)} \sinh\left(x\right)^{8} + 4 \, {\left(a^{5} b + 3 \, a^{4} b^{2} + 2 \, a^{3} b^{3} - 2 \, a^{2} b^{4} - 3 \, a b^{5} - b^{6}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(a^{5} b + 3 \, a^{4} b^{2} + 2 \, a^{3} b^{3} - 2 \, a^{2} b^{4} - 3 \, a b^{5} - b^{6} + 7 \, {\left(a^{5} b + 5 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 10 \, a^{2} b^{4} + 5 \, a b^{5} + b^{6}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + a^{5} b + 5 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 10 \, a^{2} b^{4} + 5 \, a b^{5} + b^{6} + 8 \, {\left(7 \, {\left(a^{5} b + 5 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 10 \, a^{2} b^{4} + 5 \, a b^{5} + b^{6}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{5} b + 3 \, a^{4} b^{2} + 2 \, a^{3} b^{3} - 2 \, a^{2} b^{4} - 3 \, a b^{5} - b^{6}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{5} b + 7 \, a^{4} b^{2} + 6 \, a^{3} b^{3} + 6 \, a^{2} b^{4} + 7 \, a b^{5} + 3 \, b^{6}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(3 \, a^{5} b + 7 \, a^{4} b^{2} + 6 \, a^{3} b^{3} + 6 \, a^{2} b^{4} + 7 \, a b^{5} + 3 \, b^{6} + 35 \, {\left(a^{5} b + 5 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 10 \, a^{2} b^{4} + 5 \, a b^{5} + b^{6}\right)} \cosh\left(x\right)^{4} + 30 \, {\left(a^{5} b + 3 \, a^{4} b^{2} + 2 \, a^{3} b^{3} - 2 \, a^{2} b^{4} - 3 \, a b^{5} - b^{6}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{5} b + 5 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 10 \, a^{2} b^{4} + 5 \, a b^{5} + b^{6}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(a^{5} b + 3 \, a^{4} b^{2} + 2 \, a^{3} b^{3} - 2 \, a^{2} b^{4} - 3 \, a b^{5} - b^{6}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{5} b + 7 \, a^{4} b^{2} + 6 \, a^{3} b^{3} + 6 \, a^{2} b^{4} + 7 \, a b^{5} + 3 \, b^{6}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(a^{5} b + 3 \, a^{4} b^{2} + 2 \, a^{3} b^{3} - 2 \, a^{2} b^{4} - 3 \, a b^{5} - b^{6}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{5} b + 5 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 10 \, a^{2} b^{4} + 5 \, a b^{5} + b^{6}\right)} \cosh\left(x\right)^{6} + a^{5} b + 3 \, a^{4} b^{2} + 2 \, a^{3} b^{3} - 2 \, a^{2} b^{4} - 3 \, a b^{5} - b^{6} + 15 \, {\left(a^{5} b + 3 \, a^{4} b^{2} + 2 \, a^{3} b^{3} - 2 \, a^{2} b^{4} - 3 \, a b^{5} - b^{6}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(3 \, a^{5} b + 7 \, a^{4} b^{2} + 6 \, a^{3} b^{3} + 6 \, a^{2} b^{4} + 7 \, a b^{5} + 3 \, b^{6}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 8 \, {\left({\left(a^{5} b + 5 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 10 \, a^{2} b^{4} + 5 \, a b^{5} + b^{6}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(a^{5} b + 3 \, a^{4} b^{2} + 2 \, a^{3} b^{3} - 2 \, a^{2} b^{4} - 3 \, a b^{5} - b^{6}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{5} b + 7 \, a^{4} b^{2} + 6 \, a^{3} b^{3} + 6 \, a^{2} b^{4} + 7 \, a b^{5} + 3 \, b^{6}\right)} \cosh\left(x\right)^{3} + {\left(a^{5} b + 3 \, a^{4} b^{2} + 2 \, a^{3} b^{3} - 2 \, a^{2} b^{4} - 3 \, a b^{5} - b^{6}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}, -\frac{3 \, {\left({\left(a^{2} b + 2 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{2} b + 2 \, a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{2} b + 2 \, a b^{2} + b^{3}\right)} \sinh\left(x\right)^{8} + 4 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(a^{2} b - b^{3} + 7 \, {\left(a^{2} b + 2 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} b + 2 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{2} b - 2 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} b + 2 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + 3 \, a^{2} b - 2 \, a b^{2} + 3 \, b^{3} + 30 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} b + 2 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} b - 2 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{2} b + 2 \, a b^{2} + b^{3} + 4 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} b + 2 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)^{4} + a^{2} b - b^{3} + 3 \, {\left(3 \, a^{2} b - 2 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 8 \, {\left({\left(a^{2} b + 2 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{2} b - 2 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(a \cosh\left(x\right)^{2} + 2 \, a \cosh\left(x\right) \sinh\left(x\right) + a \sinh\left(x\right)^{2} + a + b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a^{2} + a b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{2} + a b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{2} + a b\right)} \sinh\left(x\right)^{4} + {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} + 2 \, a^{2} + a b - b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(2 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + 3 \, {\left({\left(a^{2} b + 2 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{2} b + 2 \, a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{2} b + 2 \, a b^{2} + b^{3}\right)} \sinh\left(x\right)^{8} + 4 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(a^{2} b - b^{3} + 7 \, {\left(a^{2} b + 2 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} b + 2 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{2} b - 2 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} b + 2 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + 3 \, a^{2} b - 2 \, a b^{2} + 3 \, b^{3} + 30 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} b + 2 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} b - 2 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{2} b + 2 \, a b^{2} + b^{3} + 4 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} b + 2 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)^{4} + a^{2} b - b^{3} + 3 \, {\left(3 \, a^{2} b - 2 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 8 \, {\left({\left(a^{2} b + 2 \, a b^{2} + b^{3}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{2} b - 2 \, a b^{2} + 3 \, b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{2} b - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) - 2 \, \sqrt{2} {\left({\left(a^{3} - a^{2} b - 5 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(x\right)^{6} + 6 \, {\left(a^{3} - a^{2} b - 5 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(a^{3} - a^{2} b - 5 \, a b^{2} - 3 \, b^{3}\right)} \sinh\left(x\right)^{6} + 3 \, {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(a^{3} - a^{2} b - a b^{2} + b^{3} + 5 \, {\left(a^{3} - a^{2} b - 5 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, {\left(a^{3} - a^{2} b - 5 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} - a^{2} b - 5 \, a b^{2} - 3 \, b^{3} + 3 \, {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2} + 3 \, {\left(5 \, {\left(a^{3} - a^{2} b - 5 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} - a^{2} b - a b^{2} + b^{3} + 6 \, {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 6 \, {\left({\left(a^{3} - a^{2} b - 5 \, a b^{2} - 3 \, b^{3}\right)} \cosh\left(x\right)^{5} + 2 \, {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{6 \, {\left({\left(a^{5} b + 5 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 10 \, a^{2} b^{4} + 5 \, a b^{5} + b^{6}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{5} b + 5 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 10 \, a^{2} b^{4} + 5 \, a b^{5} + b^{6}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{5} b + 5 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 10 \, a^{2} b^{4} + 5 \, a b^{5} + b^{6}\right)} \sinh\left(x\right)^{8} + 4 \, {\left(a^{5} b + 3 \, a^{4} b^{2} + 2 \, a^{3} b^{3} - 2 \, a^{2} b^{4} - 3 \, a b^{5} - b^{6}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(a^{5} b + 3 \, a^{4} b^{2} + 2 \, a^{3} b^{3} - 2 \, a^{2} b^{4} - 3 \, a b^{5} - b^{6} + 7 \, {\left(a^{5} b + 5 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 10 \, a^{2} b^{4} + 5 \, a b^{5} + b^{6}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + a^{5} b + 5 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 10 \, a^{2} b^{4} + 5 \, a b^{5} + b^{6} + 8 \, {\left(7 \, {\left(a^{5} b + 5 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 10 \, a^{2} b^{4} + 5 \, a b^{5} + b^{6}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{5} b + 3 \, a^{4} b^{2} + 2 \, a^{3} b^{3} - 2 \, a^{2} b^{4} - 3 \, a b^{5} - b^{6}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{5} b + 7 \, a^{4} b^{2} + 6 \, a^{3} b^{3} + 6 \, a^{2} b^{4} + 7 \, a b^{5} + 3 \, b^{6}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(3 \, a^{5} b + 7 \, a^{4} b^{2} + 6 \, a^{3} b^{3} + 6 \, a^{2} b^{4} + 7 \, a b^{5} + 3 \, b^{6} + 35 \, {\left(a^{5} b + 5 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 10 \, a^{2} b^{4} + 5 \, a b^{5} + b^{6}\right)} \cosh\left(x\right)^{4} + 30 \, {\left(a^{5} b + 3 \, a^{4} b^{2} + 2 \, a^{3} b^{3} - 2 \, a^{2} b^{4} - 3 \, a b^{5} - b^{6}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{5} b + 5 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 10 \, a^{2} b^{4} + 5 \, a b^{5} + b^{6}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(a^{5} b + 3 \, a^{4} b^{2} + 2 \, a^{3} b^{3} - 2 \, a^{2} b^{4} - 3 \, a b^{5} - b^{6}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{5} b + 7 \, a^{4} b^{2} + 6 \, a^{3} b^{3} + 6 \, a^{2} b^{4} + 7 \, a b^{5} + 3 \, b^{6}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(a^{5} b + 3 \, a^{4} b^{2} + 2 \, a^{3} b^{3} - 2 \, a^{2} b^{4} - 3 \, a b^{5} - b^{6}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{5} b + 5 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 10 \, a^{2} b^{4} + 5 \, a b^{5} + b^{6}\right)} \cosh\left(x\right)^{6} + a^{5} b + 3 \, a^{4} b^{2} + 2 \, a^{3} b^{3} - 2 \, a^{2} b^{4} - 3 \, a b^{5} - b^{6} + 15 \, {\left(a^{5} b + 3 \, a^{4} b^{2} + 2 \, a^{3} b^{3} - 2 \, a^{2} b^{4} - 3 \, a b^{5} - b^{6}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(3 \, a^{5} b + 7 \, a^{4} b^{2} + 6 \, a^{3} b^{3} + 6 \, a^{2} b^{4} + 7 \, a b^{5} + 3 \, b^{6}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 8 \, {\left({\left(a^{5} b + 5 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 10 \, a^{2} b^{4} + 5 \, a b^{5} + b^{6}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(a^{5} b + 3 \, a^{4} b^{2} + 2 \, a^{3} b^{3} - 2 \, a^{2} b^{4} - 3 \, a b^{5} - b^{6}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{5} b + 7 \, a^{4} b^{2} + 6 \, a^{3} b^{3} + 6 \, a^{2} b^{4} + 7 \, a b^{5} + 3 \, b^{6}\right)} \cosh\left(x\right)^{3} + {\left(a^{5} b + 3 \, a^{4} b^{2} + 2 \, a^{3} b^{3} - 2 \, a^{2} b^{4} - 3 \, a b^{5} - b^{6}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}\right]"," ",0,"[1/12*(3*((a^2*b + 2*a*b^2 + b^3)*cosh(x)^8 + 8*(a^2*b + 2*a*b^2 + b^3)*cosh(x)*sinh(x)^7 + (a^2*b + 2*a*b^2 + b^3)*sinh(x)^8 + 4*(a^2*b - b^3)*cosh(x)^6 + 4*(a^2*b - b^3 + 7*(a^2*b + 2*a*b^2 + b^3)*cosh(x)^2)*sinh(x)^6 + 8*(7*(a^2*b + 2*a*b^2 + b^3)*cosh(x)^3 + 3*(a^2*b - b^3)*cosh(x))*sinh(x)^5 + 2*(3*a^2*b - 2*a*b^2 + 3*b^3)*cosh(x)^4 + 2*(35*(a^2*b + 2*a*b^2 + b^3)*cosh(x)^4 + 3*a^2*b - 2*a*b^2 + 3*b^3 + 30*(a^2*b - b^3)*cosh(x)^2)*sinh(x)^4 + 8*(7*(a^2*b + 2*a*b^2 + b^3)*cosh(x)^5 + 10*(a^2*b - b^3)*cosh(x)^3 + (3*a^2*b - 2*a*b^2 + 3*b^3)*cosh(x))*sinh(x)^3 + a^2*b + 2*a*b^2 + b^3 + 4*(a^2*b - b^3)*cosh(x)^2 + 4*(7*(a^2*b + 2*a*b^2 + b^3)*cosh(x)^6 + 15*(a^2*b - b^3)*cosh(x)^4 + a^2*b - b^3 + 3*(3*a^2*b - 2*a*b^2 + 3*b^3)*cosh(x)^2)*sinh(x)^2 + 8*((a^2*b + 2*a*b^2 + b^3)*cosh(x)^7 + 3*(a^2*b - b^3)*cosh(x)^5 + (3*a^2*b - 2*a*b^2 + 3*b^3)*cosh(x)^3 + (a^2*b - b^3)*cosh(x))*sinh(x))*sqrt(a + b)*log(((a^3 + a^2*b)*cosh(x)^8 + 8*(a^3 + a^2*b)*cosh(x)*sinh(x)^7 + (a^3 + a^2*b)*sinh(x)^8 + 2*(2*a^3 + a^2*b)*cosh(x)^6 + 2*(2*a^3 + a^2*b + 14*(a^3 + a^2*b)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a^3 + a^2*b)*cosh(x)^3 + 3*(2*a^3 + a^2*b)*cosh(x))*sinh(x)^5 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^4 + (70*(a^3 + a^2*b)*cosh(x)^4 + 6*a^3 + 4*a^2*b - a*b^2 + b^3 + 30*(2*a^3 + a^2*b)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a^3 + a^2*b)*cosh(x)^5 + 10*(2*a^3 + a^2*b)*cosh(x)^3 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x))*sinh(x)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 + 2*(2*a^3 + 3*a^2*b - b^3)*cosh(x)^2 + 2*(14*(a^3 + a^2*b)*cosh(x)^6 + 15*(2*a^3 + a^2*b)*cosh(x)^4 + 2*a^3 + 3*a^2*b - b^3 + 3*(6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^2)*sinh(x)^2 + sqrt(2)*(a^2*cosh(x)^6 + 6*a^2*cosh(x)*sinh(x)^5 + a^2*sinh(x)^6 + 3*a^2*cosh(x)^4 + 3*(5*a^2*cosh(x)^2 + a^2)*sinh(x)^4 + 4*(5*a^2*cosh(x)^3 + 3*a^2*cosh(x))*sinh(x)^3 + (3*a^2 + 2*a*b - b^2)*cosh(x)^2 + (15*a^2*cosh(x)^4 + 18*a^2*cosh(x)^2 + 3*a^2 + 2*a*b - b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(3*a^2*cosh(x)^5 + 6*a^2*cosh(x)^3 + (3*a^2 + 2*a*b - b^2)*cosh(x))*sinh(x))*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a^3 + a^2*b)*cosh(x)^7 + 3*(2*a^3 + a^2*b)*cosh(x)^5 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^3 + (2*a^3 + 3*a^2*b - b^3)*cosh(x))*sinh(x))/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) + 3*((a^2*b + 2*a*b^2 + b^3)*cosh(x)^8 + 8*(a^2*b + 2*a*b^2 + b^3)*cosh(x)*sinh(x)^7 + (a^2*b + 2*a*b^2 + b^3)*sinh(x)^8 + 4*(a^2*b - b^3)*cosh(x)^6 + 4*(a^2*b - b^3 + 7*(a^2*b + 2*a*b^2 + b^3)*cosh(x)^2)*sinh(x)^6 + 8*(7*(a^2*b + 2*a*b^2 + b^3)*cosh(x)^3 + 3*(a^2*b - b^3)*cosh(x))*sinh(x)^5 + 2*(3*a^2*b - 2*a*b^2 + 3*b^3)*cosh(x)^4 + 2*(35*(a^2*b + 2*a*b^2 + b^3)*cosh(x)^4 + 3*a^2*b - 2*a*b^2 + 3*b^3 + 30*(a^2*b - b^3)*cosh(x)^2)*sinh(x)^4 + 8*(7*(a^2*b + 2*a*b^2 + b^3)*cosh(x)^5 + 10*(a^2*b - b^3)*cosh(x)^3 + (3*a^2*b - 2*a*b^2 + 3*b^3)*cosh(x))*sinh(x)^3 + a^2*b + 2*a*b^2 + b^3 + 4*(a^2*b - b^3)*cosh(x)^2 + 4*(7*(a^2*b + 2*a*b^2 + b^3)*cosh(x)^6 + 15*(a^2*b - b^3)*cosh(x)^4 + a^2*b - b^3 + 3*(3*a^2*b - 2*a*b^2 + 3*b^3)*cosh(x)^2)*sinh(x)^2 + 8*((a^2*b + 2*a*b^2 + b^3)*cosh(x)^7 + 3*(a^2*b - b^3)*cosh(x)^5 + (3*a^2*b - 2*a*b^2 + 3*b^3)*cosh(x)^3 + (a^2*b - b^3)*cosh(x))*sinh(x))*sqrt(a + b)*log(-((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*b*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + b)*cosh(x)^3 - b*cosh(x))*sinh(x) + a + b)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*sqrt(2)*((a^3 - a^2*b - 5*a*b^2 - 3*b^3)*cosh(x)^6 + 6*(a^3 - a^2*b - 5*a*b^2 - 3*b^3)*cosh(x)*sinh(x)^5 + (a^3 - a^2*b - 5*a*b^2 - 3*b^3)*sinh(x)^6 + 3*(a^3 - a^2*b - a*b^2 + b^3)*cosh(x)^4 + 3*(a^3 - a^2*b - a*b^2 + b^3 + 5*(a^3 - a^2*b - 5*a*b^2 - 3*b^3)*cosh(x)^2)*sinh(x)^4 + 4*(5*(a^3 - a^2*b - 5*a*b^2 - 3*b^3)*cosh(x)^3 + 3*(a^3 - a^2*b - a*b^2 + b^3)*cosh(x))*sinh(x)^3 + a^3 - a^2*b - 5*a*b^2 - 3*b^3 + 3*(a^3 - a^2*b - a*b^2 + b^3)*cosh(x)^2 + 3*(5*(a^3 - a^2*b - 5*a*b^2 - 3*b^3)*cosh(x)^4 + a^3 - a^2*b - a*b^2 + b^3 + 6*(a^3 - a^2*b - a*b^2 + b^3)*cosh(x)^2)*sinh(x)^2 + 6*((a^3 - a^2*b - 5*a*b^2 - 3*b^3)*cosh(x)^5 + 2*(a^3 - a^2*b - a*b^2 + b^3)*cosh(x)^3 + (a^3 - a^2*b - a*b^2 + b^3)*cosh(x))*sinh(x))*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/((a^5*b + 5*a^4*b^2 + 10*a^3*b^3 + 10*a^2*b^4 + 5*a*b^5 + b^6)*cosh(x)^8 + 8*(a^5*b + 5*a^4*b^2 + 10*a^3*b^3 + 10*a^2*b^4 + 5*a*b^5 + b^6)*cosh(x)*sinh(x)^7 + (a^5*b + 5*a^4*b^2 + 10*a^3*b^3 + 10*a^2*b^4 + 5*a*b^5 + b^6)*sinh(x)^8 + 4*(a^5*b + 3*a^4*b^2 + 2*a^3*b^3 - 2*a^2*b^4 - 3*a*b^5 - b^6)*cosh(x)^6 + 4*(a^5*b + 3*a^4*b^2 + 2*a^3*b^3 - 2*a^2*b^4 - 3*a*b^5 - b^6 + 7*(a^5*b + 5*a^4*b^2 + 10*a^3*b^3 + 10*a^2*b^4 + 5*a*b^5 + b^6)*cosh(x)^2)*sinh(x)^6 + a^5*b + 5*a^4*b^2 + 10*a^3*b^3 + 10*a^2*b^4 + 5*a*b^5 + b^6 + 8*(7*(a^5*b + 5*a^4*b^2 + 10*a^3*b^3 + 10*a^2*b^4 + 5*a*b^5 + b^6)*cosh(x)^3 + 3*(a^5*b + 3*a^4*b^2 + 2*a^3*b^3 - 2*a^2*b^4 - 3*a*b^5 - b^6)*cosh(x))*sinh(x)^5 + 2*(3*a^5*b + 7*a^4*b^2 + 6*a^3*b^3 + 6*a^2*b^4 + 7*a*b^5 + 3*b^6)*cosh(x)^4 + 2*(3*a^5*b + 7*a^4*b^2 + 6*a^3*b^3 + 6*a^2*b^4 + 7*a*b^5 + 3*b^6 + 35*(a^5*b + 5*a^4*b^2 + 10*a^3*b^3 + 10*a^2*b^4 + 5*a*b^5 + b^6)*cosh(x)^4 + 30*(a^5*b + 3*a^4*b^2 + 2*a^3*b^3 - 2*a^2*b^4 - 3*a*b^5 - b^6)*cosh(x)^2)*sinh(x)^4 + 8*(7*(a^5*b + 5*a^4*b^2 + 10*a^3*b^3 + 10*a^2*b^4 + 5*a*b^5 + b^6)*cosh(x)^5 + 10*(a^5*b + 3*a^4*b^2 + 2*a^3*b^3 - 2*a^2*b^4 - 3*a*b^5 - b^6)*cosh(x)^3 + (3*a^5*b + 7*a^4*b^2 + 6*a^3*b^3 + 6*a^2*b^4 + 7*a*b^5 + 3*b^6)*cosh(x))*sinh(x)^3 + 4*(a^5*b + 3*a^4*b^2 + 2*a^3*b^3 - 2*a^2*b^4 - 3*a*b^5 - b^6)*cosh(x)^2 + 4*(7*(a^5*b + 5*a^4*b^2 + 10*a^3*b^3 + 10*a^2*b^4 + 5*a*b^5 + b^6)*cosh(x)^6 + a^5*b + 3*a^4*b^2 + 2*a^3*b^3 - 2*a^2*b^4 - 3*a*b^5 - b^6 + 15*(a^5*b + 3*a^4*b^2 + 2*a^3*b^3 - 2*a^2*b^4 - 3*a*b^5 - b^6)*cosh(x)^4 + 3*(3*a^5*b + 7*a^4*b^2 + 6*a^3*b^3 + 6*a^2*b^4 + 7*a*b^5 + 3*b^6)*cosh(x)^2)*sinh(x)^2 + 8*((a^5*b + 5*a^4*b^2 + 10*a^3*b^3 + 10*a^2*b^4 + 5*a*b^5 + b^6)*cosh(x)^7 + 3*(a^5*b + 3*a^4*b^2 + 2*a^3*b^3 - 2*a^2*b^4 - 3*a*b^5 - b^6)*cosh(x)^5 + (3*a^5*b + 7*a^4*b^2 + 6*a^3*b^3 + 6*a^2*b^4 + 7*a*b^5 + 3*b^6)*cosh(x)^3 + (a^5*b + 3*a^4*b^2 + 2*a^3*b^3 - 2*a^2*b^4 - 3*a*b^5 - b^6)*cosh(x))*sinh(x)), -1/6*(3*((a^2*b + 2*a*b^2 + b^3)*cosh(x)^8 + 8*(a^2*b + 2*a*b^2 + b^3)*cosh(x)*sinh(x)^7 + (a^2*b + 2*a*b^2 + b^3)*sinh(x)^8 + 4*(a^2*b - b^3)*cosh(x)^6 + 4*(a^2*b - b^3 + 7*(a^2*b + 2*a*b^2 + b^3)*cosh(x)^2)*sinh(x)^6 + 8*(7*(a^2*b + 2*a*b^2 + b^3)*cosh(x)^3 + 3*(a^2*b - b^3)*cosh(x))*sinh(x)^5 + 2*(3*a^2*b - 2*a*b^2 + 3*b^3)*cosh(x)^4 + 2*(35*(a^2*b + 2*a*b^2 + b^3)*cosh(x)^4 + 3*a^2*b - 2*a*b^2 + 3*b^3 + 30*(a^2*b - b^3)*cosh(x)^2)*sinh(x)^4 + 8*(7*(a^2*b + 2*a*b^2 + b^3)*cosh(x)^5 + 10*(a^2*b - b^3)*cosh(x)^3 + (3*a^2*b - 2*a*b^2 + 3*b^3)*cosh(x))*sinh(x)^3 + a^2*b + 2*a*b^2 + b^3 + 4*(a^2*b - b^3)*cosh(x)^2 + 4*(7*(a^2*b + 2*a*b^2 + b^3)*cosh(x)^6 + 15*(a^2*b - b^3)*cosh(x)^4 + a^2*b - b^3 + 3*(3*a^2*b - 2*a*b^2 + 3*b^3)*cosh(x)^2)*sinh(x)^2 + 8*((a^2*b + 2*a*b^2 + b^3)*cosh(x)^7 + 3*(a^2*b - b^3)*cosh(x)^5 + (3*a^2*b - 2*a*b^2 + 3*b^3)*cosh(x)^3 + (a^2*b - b^3)*cosh(x))*sinh(x))*sqrt(-a - b)*arctan(sqrt(2)*(a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 + a + b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a^2 + a*b)*cosh(x)^4 + 4*(a^2 + a*b)*cosh(x)*sinh(x)^3 + (a^2 + a*b)*sinh(x)^4 + (2*a^2 + a*b - b^2)*cosh(x)^2 + (6*(a^2 + a*b)*cosh(x)^2 + 2*a^2 + a*b - b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(2*(a^2 + a*b)*cosh(x)^3 + (2*a^2 + a*b - b^2)*cosh(x))*sinh(x))) + 3*((a^2*b + 2*a*b^2 + b^3)*cosh(x)^8 + 8*(a^2*b + 2*a*b^2 + b^3)*cosh(x)*sinh(x)^7 + (a^2*b + 2*a*b^2 + b^3)*sinh(x)^8 + 4*(a^2*b - b^3)*cosh(x)^6 + 4*(a^2*b - b^3 + 7*(a^2*b + 2*a*b^2 + b^3)*cosh(x)^2)*sinh(x)^6 + 8*(7*(a^2*b + 2*a*b^2 + b^3)*cosh(x)^3 + 3*(a^2*b - b^3)*cosh(x))*sinh(x)^5 + 2*(3*a^2*b - 2*a*b^2 + 3*b^3)*cosh(x)^4 + 2*(35*(a^2*b + 2*a*b^2 + b^3)*cosh(x)^4 + 3*a^2*b - 2*a*b^2 + 3*b^3 + 30*(a^2*b - b^3)*cosh(x)^2)*sinh(x)^4 + 8*(7*(a^2*b + 2*a*b^2 + b^3)*cosh(x)^5 + 10*(a^2*b - b^3)*cosh(x)^3 + (3*a^2*b - 2*a*b^2 + 3*b^3)*cosh(x))*sinh(x)^3 + a^2*b + 2*a*b^2 + b^3 + 4*(a^2*b - b^3)*cosh(x)^2 + 4*(7*(a^2*b + 2*a*b^2 + b^3)*cosh(x)^6 + 15*(a^2*b - b^3)*cosh(x)^4 + a^2*b - b^3 + 3*(3*a^2*b - 2*a*b^2 + 3*b^3)*cosh(x)^2)*sinh(x)^2 + 8*((a^2*b + 2*a*b^2 + b^3)*cosh(x)^7 + 3*(a^2*b - b^3)*cosh(x)^5 + (3*a^2*b - 2*a*b^2 + 3*b^3)*cosh(x)^3 + (a^2*b - b^3)*cosh(x))*sinh(x))*sqrt(-a - b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a - b)*cosh(x))*sinh(x) + a + b)) - 2*sqrt(2)*((a^3 - a^2*b - 5*a*b^2 - 3*b^3)*cosh(x)^6 + 6*(a^3 - a^2*b - 5*a*b^2 - 3*b^3)*cosh(x)*sinh(x)^5 + (a^3 - a^2*b - 5*a*b^2 - 3*b^3)*sinh(x)^6 + 3*(a^3 - a^2*b - a*b^2 + b^3)*cosh(x)^4 + 3*(a^3 - a^2*b - a*b^2 + b^3 + 5*(a^3 - a^2*b - 5*a*b^2 - 3*b^3)*cosh(x)^2)*sinh(x)^4 + 4*(5*(a^3 - a^2*b - 5*a*b^2 - 3*b^3)*cosh(x)^3 + 3*(a^3 - a^2*b - a*b^2 + b^3)*cosh(x))*sinh(x)^3 + a^3 - a^2*b - 5*a*b^2 - 3*b^3 + 3*(a^3 - a^2*b - a*b^2 + b^3)*cosh(x)^2 + 3*(5*(a^3 - a^2*b - 5*a*b^2 - 3*b^3)*cosh(x)^4 + a^3 - a^2*b - a*b^2 + b^3 + 6*(a^3 - a^2*b - a*b^2 + b^3)*cosh(x)^2)*sinh(x)^2 + 6*((a^3 - a^2*b - 5*a*b^2 - 3*b^3)*cosh(x)^5 + 2*(a^3 - a^2*b - a*b^2 + b^3)*cosh(x)^3 + (a^3 - a^2*b - a*b^2 + b^3)*cosh(x))*sinh(x))*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/((a^5*b + 5*a^4*b^2 + 10*a^3*b^3 + 10*a^2*b^4 + 5*a*b^5 + b^6)*cosh(x)^8 + 8*(a^5*b + 5*a^4*b^2 + 10*a^3*b^3 + 10*a^2*b^4 + 5*a*b^5 + b^6)*cosh(x)*sinh(x)^7 + (a^5*b + 5*a^4*b^2 + 10*a^3*b^3 + 10*a^2*b^4 + 5*a*b^5 + b^6)*sinh(x)^8 + 4*(a^5*b + 3*a^4*b^2 + 2*a^3*b^3 - 2*a^2*b^4 - 3*a*b^5 - b^6)*cosh(x)^6 + 4*(a^5*b + 3*a^4*b^2 + 2*a^3*b^3 - 2*a^2*b^4 - 3*a*b^5 - b^6 + 7*(a^5*b + 5*a^4*b^2 + 10*a^3*b^3 + 10*a^2*b^4 + 5*a*b^5 + b^6)*cosh(x)^2)*sinh(x)^6 + a^5*b + 5*a^4*b^2 + 10*a^3*b^3 + 10*a^2*b^4 + 5*a*b^5 + b^6 + 8*(7*(a^5*b + 5*a^4*b^2 + 10*a^3*b^3 + 10*a^2*b^4 + 5*a*b^5 + b^6)*cosh(x)^3 + 3*(a^5*b + 3*a^4*b^2 + 2*a^3*b^3 - 2*a^2*b^4 - 3*a*b^5 - b^6)*cosh(x))*sinh(x)^5 + 2*(3*a^5*b + 7*a^4*b^2 + 6*a^3*b^3 + 6*a^2*b^4 + 7*a*b^5 + 3*b^6)*cosh(x)^4 + 2*(3*a^5*b + 7*a^4*b^2 + 6*a^3*b^3 + 6*a^2*b^4 + 7*a*b^5 + 3*b^6 + 35*(a^5*b + 5*a^4*b^2 + 10*a^3*b^3 + 10*a^2*b^4 + 5*a*b^5 + b^6)*cosh(x)^4 + 30*(a^5*b + 3*a^4*b^2 + 2*a^3*b^3 - 2*a^2*b^4 - 3*a*b^5 - b^6)*cosh(x)^2)*sinh(x)^4 + 8*(7*(a^5*b + 5*a^4*b^2 + 10*a^3*b^3 + 10*a^2*b^4 + 5*a*b^5 + b^6)*cosh(x)^5 + 10*(a^5*b + 3*a^4*b^2 + 2*a^3*b^3 - 2*a^2*b^4 - 3*a*b^5 - b^6)*cosh(x)^3 + (3*a^5*b + 7*a^4*b^2 + 6*a^3*b^3 + 6*a^2*b^4 + 7*a*b^5 + 3*b^6)*cosh(x))*sinh(x)^3 + 4*(a^5*b + 3*a^4*b^2 + 2*a^3*b^3 - 2*a^2*b^4 - 3*a*b^5 - b^6)*cosh(x)^2 + 4*(7*(a^5*b + 5*a^4*b^2 + 10*a^3*b^3 + 10*a^2*b^4 + 5*a*b^5 + b^6)*cosh(x)^6 + a^5*b + 3*a^4*b^2 + 2*a^3*b^3 - 2*a^2*b^4 - 3*a*b^5 - b^6 + 15*(a^5*b + 3*a^4*b^2 + 2*a^3*b^3 - 2*a^2*b^4 - 3*a*b^5 - b^6)*cosh(x)^4 + 3*(3*a^5*b + 7*a^4*b^2 + 6*a^3*b^3 + 6*a^2*b^4 + 7*a*b^5 + 3*b^6)*cosh(x)^2)*sinh(x)^2 + 8*((a^5*b + 5*a^4*b^2 + 10*a^3*b^3 + 10*a^2*b^4 + 5*a*b^5 + b^6)*cosh(x)^7 + 3*(a^5*b + 3*a^4*b^2 + 2*a^3*b^3 - 2*a^2*b^4 - 3*a*b^5 - b^6)*cosh(x)^5 + (3*a^5*b + 7*a^4*b^2 + 6*a^3*b^3 + 6*a^2*b^4 + 7*a*b^5 + 3*b^6)*cosh(x)^3 + (a^5*b + 3*a^4*b^2 + 2*a^3*b^3 - 2*a^2*b^4 - 3*a*b^5 - b^6)*cosh(x))*sinh(x))]","B",0
250,1,6507,0,1.597430," ","integrate(tanh(x)^2/(a+b*tanh(x)^2)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \sinh\left(x\right)^{8} + 4 \, {\left(a^{3} - a b^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(a^{3} - a b^{2} + 7 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{3} - a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{3} - 2 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{4} + 3 \, a^{3} - 2 \, a^{2} b + 3 \, a b^{2} + 30 \, {\left(a^{3} - a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(a^{3} - a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{3} - 2 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 2 \, a^{2} b + a b^{2} + 4 \, {\left(a^{3} - a b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(a^{3} - a b^{2}\right)} \cosh\left(x\right)^{4} + a^{3} - a b^{2} + 3 \, {\left(3 \, a^{3} - 2 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 8 \, {\left({\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(a^{3} - a b^{2}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{3} - 2 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} - a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \log\left(-\frac{{\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a b^{2} + b^{3}\right)} \sinh\left(x\right)^{8} - 2 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{6} - 2 \, {\left(a b^{2} + 2 \, b^{3} - 14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3} - 30 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} + 2 \, {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} - 3 \, a b^{2} - 2 \, b^{3} + 3 \, {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(b^{2} \cosh\left(x\right)^{6} + 6 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + b^{2} \sinh\left(x\right)^{6} - 3 \, b^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, b^{2} \cosh\left(x\right)^{2} - b^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, b^{2} \cosh\left(x\right)^{3} - 3 \, b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, b^{2} \cosh\left(x\right)^{4} - 18 \, b^{2} \cosh\left(x\right)^{2} - a^{2} + 2 \, a b + 3 \, b^{2}\right)} \sinh\left(x\right)^{2} - a^{2} - 2 \, a b - b^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{5} - 6 \, b^{2} \cosh\left(x\right)^{3} - {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{5} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) + 3 \, {\left({\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \sinh\left(x\right)^{8} + 4 \, {\left(a^{3} - a b^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(a^{3} - a b^{2} + 7 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{3} - a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{3} - 2 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{4} + 3 \, a^{3} - 2 \, a^{2} b + 3 \, a b^{2} + 30 \, {\left(a^{3} - a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(a^{3} - a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{3} - 2 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 2 \, a^{2} b + a b^{2} + 4 \, {\left(a^{3} - a b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(a^{3} - a b^{2}\right)} \cosh\left(x\right)^{4} + a^{3} - a b^{2} + 3 \, {\left(3 \, a^{3} - 2 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 8 \, {\left({\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(a^{3} - a b^{2}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{3} - 2 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} - a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \log\left(\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, a \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + a \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right) - 4 \, \sqrt{2} {\left({\left(3 \, a^{3} + 5 \, a^{2} b + a b^{2} - b^{3}\right)} \cosh\left(x\right)^{6} + 6 \, {\left(3 \, a^{3} + 5 \, a^{2} b + a b^{2} - b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(3 \, a^{3} + 5 \, a^{2} b + a b^{2} - b^{3}\right)} \sinh\left(x\right)^{6} + 3 \, {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(a^{3} - a^{2} b - a b^{2} + b^{3} + 5 \, {\left(3 \, a^{3} + 5 \, a^{2} b + a b^{2} - b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, {\left(3 \, a^{3} + 5 \, a^{2} b + a b^{2} - b^{3}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 3 \, a^{3} - 5 \, a^{2} b - a b^{2} + b^{3} - 3 \, {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2} + 3 \, {\left(5 \, {\left(3 \, a^{3} + 5 \, a^{2} b + a b^{2} - b^{3}\right)} \cosh\left(x\right)^{4} - a^{3} + a^{2} b + a b^{2} - b^{3} + 6 \, {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 6 \, {\left({\left(3 \, a^{3} + 5 \, a^{2} b + a b^{2} - b^{3}\right)} \cosh\left(x\right)^{5} + 2 \, {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} - {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{12 \, {\left({\left(a^{6} + 5 \, a^{5} b + 10 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 5 \, a^{2} b^{4} + a b^{5}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{6} + 5 \, a^{5} b + 10 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 5 \, a^{2} b^{4} + a b^{5}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{6} + 5 \, a^{5} b + 10 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 5 \, a^{2} b^{4} + a b^{5}\right)} \sinh\left(x\right)^{8} + 4 \, {\left(a^{6} + 3 \, a^{5} b + 2 \, a^{4} b^{2} - 2 \, a^{3} b^{3} - 3 \, a^{2} b^{4} - a b^{5}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(a^{6} + 3 \, a^{5} b + 2 \, a^{4} b^{2} - 2 \, a^{3} b^{3} - 3 \, a^{2} b^{4} - a b^{5} + 7 \, {\left(a^{6} + 5 \, a^{5} b + 10 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 5 \, a^{2} b^{4} + a b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + a^{6} + 5 \, a^{5} b + 10 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 5 \, a^{2} b^{4} + a b^{5} + 8 \, {\left(7 \, {\left(a^{6} + 5 \, a^{5} b + 10 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 5 \, a^{2} b^{4} + a b^{5}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{6} + 3 \, a^{5} b + 2 \, a^{4} b^{2} - 2 \, a^{3} b^{3} - 3 \, a^{2} b^{4} - a b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{6} + 7 \, a^{5} b + 6 \, a^{4} b^{2} + 6 \, a^{3} b^{3} + 7 \, a^{2} b^{4} + 3 \, a b^{5}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(3 \, a^{6} + 7 \, a^{5} b + 6 \, a^{4} b^{2} + 6 \, a^{3} b^{3} + 7 \, a^{2} b^{4} + 3 \, a b^{5} + 35 \, {\left(a^{6} + 5 \, a^{5} b + 10 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 5 \, a^{2} b^{4} + a b^{5}\right)} \cosh\left(x\right)^{4} + 30 \, {\left(a^{6} + 3 \, a^{5} b + 2 \, a^{4} b^{2} - 2 \, a^{3} b^{3} - 3 \, a^{2} b^{4} - a b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{6} + 5 \, a^{5} b + 10 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 5 \, a^{2} b^{4} + a b^{5}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(a^{6} + 3 \, a^{5} b + 2 \, a^{4} b^{2} - 2 \, a^{3} b^{3} - 3 \, a^{2} b^{4} - a b^{5}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{6} + 7 \, a^{5} b + 6 \, a^{4} b^{2} + 6 \, a^{3} b^{3} + 7 \, a^{2} b^{4} + 3 \, a b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(a^{6} + 3 \, a^{5} b + 2 \, a^{4} b^{2} - 2 \, a^{3} b^{3} - 3 \, a^{2} b^{4} - a b^{5}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{6} + 5 \, a^{5} b + 10 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 5 \, a^{2} b^{4} + a b^{5}\right)} \cosh\left(x\right)^{6} + a^{6} + 3 \, a^{5} b + 2 \, a^{4} b^{2} - 2 \, a^{3} b^{3} - 3 \, a^{2} b^{4} - a b^{5} + 15 \, {\left(a^{6} + 3 \, a^{5} b + 2 \, a^{4} b^{2} - 2 \, a^{3} b^{3} - 3 \, a^{2} b^{4} - a b^{5}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(3 \, a^{6} + 7 \, a^{5} b + 6 \, a^{4} b^{2} + 6 \, a^{3} b^{3} + 7 \, a^{2} b^{4} + 3 \, a b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 8 \, {\left({\left(a^{6} + 5 \, a^{5} b + 10 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 5 \, a^{2} b^{4} + a b^{5}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(a^{6} + 3 \, a^{5} b + 2 \, a^{4} b^{2} - 2 \, a^{3} b^{3} - 3 \, a^{2} b^{4} - a b^{5}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{6} + 7 \, a^{5} b + 6 \, a^{4} b^{2} + 6 \, a^{3} b^{3} + 7 \, a^{2} b^{4} + 3 \, a b^{5}\right)} \cosh\left(x\right)^{3} + {\left(a^{6} + 3 \, a^{5} b + 2 \, a^{4} b^{2} - 2 \, a^{3} b^{3} - 3 \, a^{2} b^{4} - a b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}, -\frac{3 \, {\left({\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \sinh\left(x\right)^{8} + 4 \, {\left(a^{3} - a b^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(a^{3} - a b^{2} + 7 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{3} - a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{3} - 2 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{4} + 3 \, a^{3} - 2 \, a^{2} b + 3 \, a b^{2} + 30 \, {\left(a^{3} - a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(a^{3} - a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{3} - 2 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 2 \, a^{2} b + a b^{2} + 4 \, {\left(a^{3} - a b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(a^{3} - a b^{2}\right)} \cosh\left(x\right)^{4} + a^{3} - a b^{2} + 3 \, {\left(3 \, a^{3} - 2 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 8 \, {\left({\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(a^{3} - a b^{2}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{3} - 2 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} - a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} - a - b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a b + b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a b + b^{2}\right)} \sinh\left(x\right)^{4} + {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} - a b - 2 \, b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(2 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + 3 \, {\left({\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \sinh\left(x\right)^{8} + 4 \, {\left(a^{3} - a b^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(a^{3} - a b^{2} + 7 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{3} - a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{3} - 2 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{4} + 3 \, a^{3} - 2 \, a^{2} b + 3 \, a b^{2} + 30 \, {\left(a^{3} - a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(a^{3} - a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{3} - 2 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 2 \, a^{2} b + a b^{2} + 4 \, {\left(a^{3} - a b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(a^{3} - a b^{2}\right)} \cosh\left(x\right)^{4} + a^{3} - a b^{2} + 3 \, {\left(3 \, a^{3} - 2 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 8 \, {\left({\left(a^{3} + 2 \, a^{2} b + a b^{2}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(a^{3} - a b^{2}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{3} - 2 \, a^{2} b + 3 \, a b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} - a b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a + b\right)} \sinh\left(x\right)^{2} + a + b}\right) + 2 \, \sqrt{2} {\left({\left(3 \, a^{3} + 5 \, a^{2} b + a b^{2} - b^{3}\right)} \cosh\left(x\right)^{6} + 6 \, {\left(3 \, a^{3} + 5 \, a^{2} b + a b^{2} - b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(3 \, a^{3} + 5 \, a^{2} b + a b^{2} - b^{3}\right)} \sinh\left(x\right)^{6} + 3 \, {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(a^{3} - a^{2} b - a b^{2} + b^{3} + 5 \, {\left(3 \, a^{3} + 5 \, a^{2} b + a b^{2} - b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, {\left(3 \, a^{3} + 5 \, a^{2} b + a b^{2} - b^{3}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 3 \, a^{3} - 5 \, a^{2} b - a b^{2} + b^{3} - 3 \, {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2} + 3 \, {\left(5 \, {\left(3 \, a^{3} + 5 \, a^{2} b + a b^{2} - b^{3}\right)} \cosh\left(x\right)^{4} - a^{3} + a^{2} b + a b^{2} - b^{3} + 6 \, {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 6 \, {\left({\left(3 \, a^{3} + 5 \, a^{2} b + a b^{2} - b^{3}\right)} \cosh\left(x\right)^{5} + 2 \, {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} - {\left(a^{3} - a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{6 \, {\left({\left(a^{6} + 5 \, a^{5} b + 10 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 5 \, a^{2} b^{4} + a b^{5}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{6} + 5 \, a^{5} b + 10 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 5 \, a^{2} b^{4} + a b^{5}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{6} + 5 \, a^{5} b + 10 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 5 \, a^{2} b^{4} + a b^{5}\right)} \sinh\left(x\right)^{8} + 4 \, {\left(a^{6} + 3 \, a^{5} b + 2 \, a^{4} b^{2} - 2 \, a^{3} b^{3} - 3 \, a^{2} b^{4} - a b^{5}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(a^{6} + 3 \, a^{5} b + 2 \, a^{4} b^{2} - 2 \, a^{3} b^{3} - 3 \, a^{2} b^{4} - a b^{5} + 7 \, {\left(a^{6} + 5 \, a^{5} b + 10 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 5 \, a^{2} b^{4} + a b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + a^{6} + 5 \, a^{5} b + 10 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 5 \, a^{2} b^{4} + a b^{5} + 8 \, {\left(7 \, {\left(a^{6} + 5 \, a^{5} b + 10 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 5 \, a^{2} b^{4} + a b^{5}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{6} + 3 \, a^{5} b + 2 \, a^{4} b^{2} - 2 \, a^{3} b^{3} - 3 \, a^{2} b^{4} - a b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{6} + 7 \, a^{5} b + 6 \, a^{4} b^{2} + 6 \, a^{3} b^{3} + 7 \, a^{2} b^{4} + 3 \, a b^{5}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(3 \, a^{6} + 7 \, a^{5} b + 6 \, a^{4} b^{2} + 6 \, a^{3} b^{3} + 7 \, a^{2} b^{4} + 3 \, a b^{5} + 35 \, {\left(a^{6} + 5 \, a^{5} b + 10 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 5 \, a^{2} b^{4} + a b^{5}\right)} \cosh\left(x\right)^{4} + 30 \, {\left(a^{6} + 3 \, a^{5} b + 2 \, a^{4} b^{2} - 2 \, a^{3} b^{3} - 3 \, a^{2} b^{4} - a b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{6} + 5 \, a^{5} b + 10 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 5 \, a^{2} b^{4} + a b^{5}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(a^{6} + 3 \, a^{5} b + 2 \, a^{4} b^{2} - 2 \, a^{3} b^{3} - 3 \, a^{2} b^{4} - a b^{5}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{6} + 7 \, a^{5} b + 6 \, a^{4} b^{2} + 6 \, a^{3} b^{3} + 7 \, a^{2} b^{4} + 3 \, a b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(a^{6} + 3 \, a^{5} b + 2 \, a^{4} b^{2} - 2 \, a^{3} b^{3} - 3 \, a^{2} b^{4} - a b^{5}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{6} + 5 \, a^{5} b + 10 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 5 \, a^{2} b^{4} + a b^{5}\right)} \cosh\left(x\right)^{6} + a^{6} + 3 \, a^{5} b + 2 \, a^{4} b^{2} - 2 \, a^{3} b^{3} - 3 \, a^{2} b^{4} - a b^{5} + 15 \, {\left(a^{6} + 3 \, a^{5} b + 2 \, a^{4} b^{2} - 2 \, a^{3} b^{3} - 3 \, a^{2} b^{4} - a b^{5}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(3 \, a^{6} + 7 \, a^{5} b + 6 \, a^{4} b^{2} + 6 \, a^{3} b^{3} + 7 \, a^{2} b^{4} + 3 \, a b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 8 \, {\left({\left(a^{6} + 5 \, a^{5} b + 10 \, a^{4} b^{2} + 10 \, a^{3} b^{3} + 5 \, a^{2} b^{4} + a b^{5}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(a^{6} + 3 \, a^{5} b + 2 \, a^{4} b^{2} - 2 \, a^{3} b^{3} - 3 \, a^{2} b^{4} - a b^{5}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{6} + 7 \, a^{5} b + 6 \, a^{4} b^{2} + 6 \, a^{3} b^{3} + 7 \, a^{2} b^{4} + 3 \, a b^{5}\right)} \cosh\left(x\right)^{3} + {\left(a^{6} + 3 \, a^{5} b + 2 \, a^{4} b^{2} - 2 \, a^{3} b^{3} - 3 \, a^{2} b^{4} - a b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}\right]"," ",0,"[1/12*(3*((a^3 + 2*a^2*b + a*b^2)*cosh(x)^8 + 8*(a^3 + 2*a^2*b + a*b^2)*cosh(x)*sinh(x)^7 + (a^3 + 2*a^2*b + a*b^2)*sinh(x)^8 + 4*(a^3 - a*b^2)*cosh(x)^6 + 4*(a^3 - a*b^2 + 7*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^2)*sinh(x)^6 + 8*(7*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^3 + 3*(a^3 - a*b^2)*cosh(x))*sinh(x)^5 + 2*(3*a^3 - 2*a^2*b + 3*a*b^2)*cosh(x)^4 + 2*(35*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^4 + 3*a^3 - 2*a^2*b + 3*a*b^2 + 30*(a^3 - a*b^2)*cosh(x)^2)*sinh(x)^4 + 8*(7*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^5 + 10*(a^3 - a*b^2)*cosh(x)^3 + (3*a^3 - 2*a^2*b + 3*a*b^2)*cosh(x))*sinh(x)^3 + a^3 + 2*a^2*b + a*b^2 + 4*(a^3 - a*b^2)*cosh(x)^2 + 4*(7*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^6 + 15*(a^3 - a*b^2)*cosh(x)^4 + a^3 - a*b^2 + 3*(3*a^3 - 2*a^2*b + 3*a*b^2)*cosh(x)^2)*sinh(x)^2 + 8*((a^3 + 2*a^2*b + a*b^2)*cosh(x)^7 + 3*(a^3 - a*b^2)*cosh(x)^5 + (3*a^3 - 2*a^2*b + 3*a*b^2)*cosh(x)^3 + (a^3 - a*b^2)*cosh(x))*sinh(x))*sqrt(a + b)*log(-((a*b^2 + b^3)*cosh(x)^8 + 8*(a*b^2 + b^3)*cosh(x)*sinh(x)^7 + (a*b^2 + b^3)*sinh(x)^8 - 2*(a*b^2 + 2*b^3)*cosh(x)^6 - 2*(a*b^2 + 2*b^3 - 14*(a*b^2 + b^3)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a*b^2 + b^3)*cosh(x)^3 - 3*(a*b^2 + 2*b^3)*cosh(x))*sinh(x)^5 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^4 + (70*(a*b^2 + b^3)*cosh(x)^4 + a^3 - a^2*b + 4*a*b^2 + 6*b^3 - 30*(a*b^2 + 2*b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a*b^2 + b^3)*cosh(x)^5 - 10*(a*b^2 + 2*b^3)*cosh(x)^3 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x))*sinh(x)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 + 2*(a^3 - 3*a*b^2 - 2*b^3)*cosh(x)^2 + 2*(14*(a*b^2 + b^3)*cosh(x)^6 - 15*(a*b^2 + 2*b^3)*cosh(x)^4 + a^3 - 3*a*b^2 - 2*b^3 + 3*(a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^2)*sinh(x)^2 + sqrt(2)*(b^2*cosh(x)^6 + 6*b^2*cosh(x)*sinh(x)^5 + b^2*sinh(x)^6 - 3*b^2*cosh(x)^4 + 3*(5*b^2*cosh(x)^2 - b^2)*sinh(x)^4 + 4*(5*b^2*cosh(x)^3 - 3*b^2*cosh(x))*sinh(x)^3 - (a^2 - 2*a*b - 3*b^2)*cosh(x)^2 + (15*b^2*cosh(x)^4 - 18*b^2*cosh(x)^2 - a^2 + 2*a*b + 3*b^2)*sinh(x)^2 - a^2 - 2*a*b - b^2 + 2*(3*b^2*cosh(x)^5 - 6*b^2*cosh(x)^3 - (a^2 - 2*a*b - 3*b^2)*cosh(x))*sinh(x))*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a*b^2 + b^3)*cosh(x)^7 - 3*(a*b^2 + 2*b^3)*cosh(x)^5 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^3 + (a^3 - 3*a*b^2 - 2*b^3)*cosh(x))*sinh(x))/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) + 3*((a^3 + 2*a^2*b + a*b^2)*cosh(x)^8 + 8*(a^3 + 2*a^2*b + a*b^2)*cosh(x)*sinh(x)^7 + (a^3 + 2*a^2*b + a*b^2)*sinh(x)^8 + 4*(a^3 - a*b^2)*cosh(x)^6 + 4*(a^3 - a*b^2 + 7*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^2)*sinh(x)^6 + 8*(7*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^3 + 3*(a^3 - a*b^2)*cosh(x))*sinh(x)^5 + 2*(3*a^3 - 2*a^2*b + 3*a*b^2)*cosh(x)^4 + 2*(35*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^4 + 3*a^3 - 2*a^2*b + 3*a*b^2 + 30*(a^3 - a*b^2)*cosh(x)^2)*sinh(x)^4 + 8*(7*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^5 + 10*(a^3 - a*b^2)*cosh(x)^3 + (3*a^3 - 2*a^2*b + 3*a*b^2)*cosh(x))*sinh(x)^3 + a^3 + 2*a^2*b + a*b^2 + 4*(a^3 - a*b^2)*cosh(x)^2 + 4*(7*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^6 + 15*(a^3 - a*b^2)*cosh(x)^4 + a^3 - a*b^2 + 3*(3*a^3 - 2*a^2*b + 3*a*b^2)*cosh(x)^2)*sinh(x)^2 + 8*((a^3 + 2*a^2*b + a*b^2)*cosh(x)^7 + 3*(a^3 - a*b^2)*cosh(x)^5 + (3*a^3 - 2*a^2*b + 3*a*b^2)*cosh(x)^3 + (a^3 - a*b^2)*cosh(x))*sinh(x))*sqrt(a + b)*log(((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*a*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + b)*cosh(x)^3 + a*cosh(x))*sinh(x) + a + b)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) - 4*sqrt(2)*((3*a^3 + 5*a^2*b + a*b^2 - b^3)*cosh(x)^6 + 6*(3*a^3 + 5*a^2*b + a*b^2 - b^3)*cosh(x)*sinh(x)^5 + (3*a^3 + 5*a^2*b + a*b^2 - b^3)*sinh(x)^6 + 3*(a^3 - a^2*b - a*b^2 + b^3)*cosh(x)^4 + 3*(a^3 - a^2*b - a*b^2 + b^3 + 5*(3*a^3 + 5*a^2*b + a*b^2 - b^3)*cosh(x)^2)*sinh(x)^4 + 4*(5*(3*a^3 + 5*a^2*b + a*b^2 - b^3)*cosh(x)^3 + 3*(a^3 - a^2*b - a*b^2 + b^3)*cosh(x))*sinh(x)^3 - 3*a^3 - 5*a^2*b - a*b^2 + b^3 - 3*(a^3 - a^2*b - a*b^2 + b^3)*cosh(x)^2 + 3*(5*(3*a^3 + 5*a^2*b + a*b^2 - b^3)*cosh(x)^4 - a^3 + a^2*b + a*b^2 - b^3 + 6*(a^3 - a^2*b - a*b^2 + b^3)*cosh(x)^2)*sinh(x)^2 + 6*((3*a^3 + 5*a^2*b + a*b^2 - b^3)*cosh(x)^5 + 2*(a^3 - a^2*b - a*b^2 + b^3)*cosh(x)^3 - (a^3 - a^2*b - a*b^2 + b^3)*cosh(x))*sinh(x))*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/((a^6 + 5*a^5*b + 10*a^4*b^2 + 10*a^3*b^3 + 5*a^2*b^4 + a*b^5)*cosh(x)^8 + 8*(a^6 + 5*a^5*b + 10*a^4*b^2 + 10*a^3*b^3 + 5*a^2*b^4 + a*b^5)*cosh(x)*sinh(x)^7 + (a^6 + 5*a^5*b + 10*a^4*b^2 + 10*a^3*b^3 + 5*a^2*b^4 + a*b^5)*sinh(x)^8 + 4*(a^6 + 3*a^5*b + 2*a^4*b^2 - 2*a^3*b^3 - 3*a^2*b^4 - a*b^5)*cosh(x)^6 + 4*(a^6 + 3*a^5*b + 2*a^4*b^2 - 2*a^3*b^3 - 3*a^2*b^4 - a*b^5 + 7*(a^6 + 5*a^5*b + 10*a^4*b^2 + 10*a^3*b^3 + 5*a^2*b^4 + a*b^5)*cosh(x)^2)*sinh(x)^6 + a^6 + 5*a^5*b + 10*a^4*b^2 + 10*a^3*b^3 + 5*a^2*b^4 + a*b^5 + 8*(7*(a^6 + 5*a^5*b + 10*a^4*b^2 + 10*a^3*b^3 + 5*a^2*b^4 + a*b^5)*cosh(x)^3 + 3*(a^6 + 3*a^5*b + 2*a^4*b^2 - 2*a^3*b^3 - 3*a^2*b^4 - a*b^5)*cosh(x))*sinh(x)^5 + 2*(3*a^6 + 7*a^5*b + 6*a^4*b^2 + 6*a^3*b^3 + 7*a^2*b^4 + 3*a*b^5)*cosh(x)^4 + 2*(3*a^6 + 7*a^5*b + 6*a^4*b^2 + 6*a^3*b^3 + 7*a^2*b^4 + 3*a*b^5 + 35*(a^6 + 5*a^5*b + 10*a^4*b^2 + 10*a^3*b^3 + 5*a^2*b^4 + a*b^5)*cosh(x)^4 + 30*(a^6 + 3*a^5*b + 2*a^4*b^2 - 2*a^3*b^3 - 3*a^2*b^4 - a*b^5)*cosh(x)^2)*sinh(x)^4 + 8*(7*(a^6 + 5*a^5*b + 10*a^4*b^2 + 10*a^3*b^3 + 5*a^2*b^4 + a*b^5)*cosh(x)^5 + 10*(a^6 + 3*a^5*b + 2*a^4*b^2 - 2*a^3*b^3 - 3*a^2*b^4 - a*b^5)*cosh(x)^3 + (3*a^6 + 7*a^5*b + 6*a^4*b^2 + 6*a^3*b^3 + 7*a^2*b^4 + 3*a*b^5)*cosh(x))*sinh(x)^3 + 4*(a^6 + 3*a^5*b + 2*a^4*b^2 - 2*a^3*b^3 - 3*a^2*b^4 - a*b^5)*cosh(x)^2 + 4*(7*(a^6 + 5*a^5*b + 10*a^4*b^2 + 10*a^3*b^3 + 5*a^2*b^4 + a*b^5)*cosh(x)^6 + a^6 + 3*a^5*b + 2*a^4*b^2 - 2*a^3*b^3 - 3*a^2*b^4 - a*b^5 + 15*(a^6 + 3*a^5*b + 2*a^4*b^2 - 2*a^3*b^3 - 3*a^2*b^4 - a*b^5)*cosh(x)^4 + 3*(3*a^6 + 7*a^5*b + 6*a^4*b^2 + 6*a^3*b^3 + 7*a^2*b^4 + 3*a*b^5)*cosh(x)^2)*sinh(x)^2 + 8*((a^6 + 5*a^5*b + 10*a^4*b^2 + 10*a^3*b^3 + 5*a^2*b^4 + a*b^5)*cosh(x)^7 + 3*(a^6 + 3*a^5*b + 2*a^4*b^2 - 2*a^3*b^3 - 3*a^2*b^4 - a*b^5)*cosh(x)^5 + (3*a^6 + 7*a^5*b + 6*a^4*b^2 + 6*a^3*b^3 + 7*a^2*b^4 + 3*a*b^5)*cosh(x)^3 + (a^6 + 3*a^5*b + 2*a^4*b^2 - 2*a^3*b^3 - 3*a^2*b^4 - a*b^5)*cosh(x))*sinh(x)), -1/6*(3*((a^3 + 2*a^2*b + a*b^2)*cosh(x)^8 + 8*(a^3 + 2*a^2*b + a*b^2)*cosh(x)*sinh(x)^7 + (a^3 + 2*a^2*b + a*b^2)*sinh(x)^8 + 4*(a^3 - a*b^2)*cosh(x)^6 + 4*(a^3 - a*b^2 + 7*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^2)*sinh(x)^6 + 8*(7*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^3 + 3*(a^3 - a*b^2)*cosh(x))*sinh(x)^5 + 2*(3*a^3 - 2*a^2*b + 3*a*b^2)*cosh(x)^4 + 2*(35*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^4 + 3*a^3 - 2*a^2*b + 3*a*b^2 + 30*(a^3 - a*b^2)*cosh(x)^2)*sinh(x)^4 + 8*(7*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^5 + 10*(a^3 - a*b^2)*cosh(x)^3 + (3*a^3 - 2*a^2*b + 3*a*b^2)*cosh(x))*sinh(x)^3 + a^3 + 2*a^2*b + a*b^2 + 4*(a^3 - a*b^2)*cosh(x)^2 + 4*(7*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^6 + 15*(a^3 - a*b^2)*cosh(x)^4 + a^3 - a*b^2 + 3*(3*a^3 - 2*a^2*b + 3*a*b^2)*cosh(x)^2)*sinh(x)^2 + 8*((a^3 + 2*a^2*b + a*b^2)*cosh(x)^7 + 3*(a^3 - a*b^2)*cosh(x)^5 + (3*a^3 - 2*a^2*b + 3*a*b^2)*cosh(x)^3 + (a^3 - a*b^2)*cosh(x))*sinh(x))*sqrt(-a - b)*arctan(sqrt(2)*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 - a - b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a*b + b^2)*cosh(x)^4 + 4*(a*b + b^2)*cosh(x)*sinh(x)^3 + (a*b + b^2)*sinh(x)^4 + (a^2 - a*b - 2*b^2)*cosh(x)^2 + (6*(a*b + b^2)*cosh(x)^2 + a^2 - a*b - 2*b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(2*(a*b + b^2)*cosh(x)^3 + (a^2 - a*b - 2*b^2)*cosh(x))*sinh(x))) + 3*((a^3 + 2*a^2*b + a*b^2)*cosh(x)^8 + 8*(a^3 + 2*a^2*b + a*b^2)*cosh(x)*sinh(x)^7 + (a^3 + 2*a^2*b + a*b^2)*sinh(x)^8 + 4*(a^3 - a*b^2)*cosh(x)^6 + 4*(a^3 - a*b^2 + 7*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^2)*sinh(x)^6 + 8*(7*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^3 + 3*(a^3 - a*b^2)*cosh(x))*sinh(x)^5 + 2*(3*a^3 - 2*a^2*b + 3*a*b^2)*cosh(x)^4 + 2*(35*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^4 + 3*a^3 - 2*a^2*b + 3*a*b^2 + 30*(a^3 - a*b^2)*cosh(x)^2)*sinh(x)^4 + 8*(7*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^5 + 10*(a^3 - a*b^2)*cosh(x)^3 + (3*a^3 - 2*a^2*b + 3*a*b^2)*cosh(x))*sinh(x)^3 + a^3 + 2*a^2*b + a*b^2 + 4*(a^3 - a*b^2)*cosh(x)^2 + 4*(7*(a^3 + 2*a^2*b + a*b^2)*cosh(x)^6 + 15*(a^3 - a*b^2)*cosh(x)^4 + a^3 - a*b^2 + 3*(3*a^3 - 2*a^2*b + 3*a*b^2)*cosh(x)^2)*sinh(x)^2 + 8*((a^3 + 2*a^2*b + a*b^2)*cosh(x)^7 + 3*(a^3 - a*b^2)*cosh(x)^5 + (3*a^3 - 2*a^2*b + 3*a*b^2)*cosh(x)^3 + (a^3 - a*b^2)*cosh(x))*sinh(x))*sqrt(-a - b)*arctan(sqrt(2)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 + a + b)) + 2*sqrt(2)*((3*a^3 + 5*a^2*b + a*b^2 - b^3)*cosh(x)^6 + 6*(3*a^3 + 5*a^2*b + a*b^2 - b^3)*cosh(x)*sinh(x)^5 + (3*a^3 + 5*a^2*b + a*b^2 - b^3)*sinh(x)^6 + 3*(a^3 - a^2*b - a*b^2 + b^3)*cosh(x)^4 + 3*(a^3 - a^2*b - a*b^2 + b^3 + 5*(3*a^3 + 5*a^2*b + a*b^2 - b^3)*cosh(x)^2)*sinh(x)^4 + 4*(5*(3*a^3 + 5*a^2*b + a*b^2 - b^3)*cosh(x)^3 + 3*(a^3 - a^2*b - a*b^2 + b^3)*cosh(x))*sinh(x)^3 - 3*a^3 - 5*a^2*b - a*b^2 + b^3 - 3*(a^3 - a^2*b - a*b^2 + b^3)*cosh(x)^2 + 3*(5*(3*a^3 + 5*a^2*b + a*b^2 - b^3)*cosh(x)^4 - a^3 + a^2*b + a*b^2 - b^3 + 6*(a^3 - a^2*b - a*b^2 + b^3)*cosh(x)^2)*sinh(x)^2 + 6*((3*a^3 + 5*a^2*b + a*b^2 - b^3)*cosh(x)^5 + 2*(a^3 - a^2*b - a*b^2 + b^3)*cosh(x)^3 - (a^3 - a^2*b - a*b^2 + b^3)*cosh(x))*sinh(x))*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/((a^6 + 5*a^5*b + 10*a^4*b^2 + 10*a^3*b^3 + 5*a^2*b^4 + a*b^5)*cosh(x)^8 + 8*(a^6 + 5*a^5*b + 10*a^4*b^2 + 10*a^3*b^3 + 5*a^2*b^4 + a*b^5)*cosh(x)*sinh(x)^7 + (a^6 + 5*a^5*b + 10*a^4*b^2 + 10*a^3*b^3 + 5*a^2*b^4 + a*b^5)*sinh(x)^8 + 4*(a^6 + 3*a^5*b + 2*a^4*b^2 - 2*a^3*b^3 - 3*a^2*b^4 - a*b^5)*cosh(x)^6 + 4*(a^6 + 3*a^5*b + 2*a^4*b^2 - 2*a^3*b^3 - 3*a^2*b^4 - a*b^5 + 7*(a^6 + 5*a^5*b + 10*a^4*b^2 + 10*a^3*b^3 + 5*a^2*b^4 + a*b^5)*cosh(x)^2)*sinh(x)^6 + a^6 + 5*a^5*b + 10*a^4*b^2 + 10*a^3*b^3 + 5*a^2*b^4 + a*b^5 + 8*(7*(a^6 + 5*a^5*b + 10*a^4*b^2 + 10*a^3*b^3 + 5*a^2*b^4 + a*b^5)*cosh(x)^3 + 3*(a^6 + 3*a^5*b + 2*a^4*b^2 - 2*a^3*b^3 - 3*a^2*b^4 - a*b^5)*cosh(x))*sinh(x)^5 + 2*(3*a^6 + 7*a^5*b + 6*a^4*b^2 + 6*a^3*b^3 + 7*a^2*b^4 + 3*a*b^5)*cosh(x)^4 + 2*(3*a^6 + 7*a^5*b + 6*a^4*b^2 + 6*a^3*b^3 + 7*a^2*b^4 + 3*a*b^5 + 35*(a^6 + 5*a^5*b + 10*a^4*b^2 + 10*a^3*b^3 + 5*a^2*b^4 + a*b^5)*cosh(x)^4 + 30*(a^6 + 3*a^5*b + 2*a^4*b^2 - 2*a^3*b^3 - 3*a^2*b^4 - a*b^5)*cosh(x)^2)*sinh(x)^4 + 8*(7*(a^6 + 5*a^5*b + 10*a^4*b^2 + 10*a^3*b^3 + 5*a^2*b^4 + a*b^5)*cosh(x)^5 + 10*(a^6 + 3*a^5*b + 2*a^4*b^2 - 2*a^3*b^3 - 3*a^2*b^4 - a*b^5)*cosh(x)^3 + (3*a^6 + 7*a^5*b + 6*a^4*b^2 + 6*a^3*b^3 + 7*a^2*b^4 + 3*a*b^5)*cosh(x))*sinh(x)^3 + 4*(a^6 + 3*a^5*b + 2*a^4*b^2 - 2*a^3*b^3 - 3*a^2*b^4 - a*b^5)*cosh(x)^2 + 4*(7*(a^6 + 5*a^5*b + 10*a^4*b^2 + 10*a^3*b^3 + 5*a^2*b^4 + a*b^5)*cosh(x)^6 + a^6 + 3*a^5*b + 2*a^4*b^2 - 2*a^3*b^3 - 3*a^2*b^4 - a*b^5 + 15*(a^6 + 3*a^5*b + 2*a^4*b^2 - 2*a^3*b^3 - 3*a^2*b^4 - a*b^5)*cosh(x)^4 + 3*(3*a^6 + 7*a^5*b + 6*a^4*b^2 + 6*a^3*b^3 + 7*a^2*b^4 + 3*a*b^5)*cosh(x)^2)*sinh(x)^2 + 8*((a^6 + 5*a^5*b + 10*a^4*b^2 + 10*a^3*b^3 + 5*a^2*b^4 + a*b^5)*cosh(x)^7 + 3*(a^6 + 3*a^5*b + 2*a^4*b^2 - 2*a^3*b^3 - 3*a^2*b^4 - a*b^5)*cosh(x)^5 + (3*a^6 + 7*a^5*b + 6*a^4*b^2 + 6*a^3*b^3 + 7*a^2*b^4 + 3*a*b^5)*cosh(x)^3 + (a^6 + 3*a^5*b + 2*a^4*b^2 - 2*a^3*b^3 - 3*a^2*b^4 - a*b^5)*cosh(x))*sinh(x))]","B",0
251,1,5779,0,1.395619," ","integrate(tanh(x)/(a+b*tanh(x)^2)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(x\right)^{8} + 4 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{4} + 30 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 8 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \log\left(\frac{{\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{3} + a^{2} b\right)} \sinh\left(x\right)^{8} + 2 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} + 2 \, {\left(2 \, a^{3} + a^{2} b + 14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} + 3 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3} + 30 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} + 10 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{3} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} + 2 \, {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{6} + 15 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{4} + 2 \, a^{3} + 3 \, a^{2} b - b^{3} + 3 \, {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(a^{2} \cosh\left(x\right)^{6} + 6 \, a^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + a^{2} \sinh\left(x\right)^{6} + 3 \, a^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, a^{2} \cosh\left(x\right)^{2} + a^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, a^{2} \cosh\left(x\right)^{3} + 3 \, a^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, a^{2} \cosh\left(x\right)^{4} + 18 \, a^{2} \cosh\left(x\right)^{2} + 3 \, a^{2} + 2 \, a b - b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(3 \, a^{2} \cosh\left(x\right)^{5} + 6 \, a^{2} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, {\left(a^{3} + a^{2} b\right)} \cosh\left(x\right)^{7} + 3 \, {\left(2 \, a^{3} + a^{2} b\right)} \cosh\left(x\right)^{5} + {\left(6 \, a^{3} + 4 \, a^{2} b - a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{3} + 3 \, a^{2} b - b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) + 3 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(x\right)^{8} + 4 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{4} + 30 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 8 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \log\left(-\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} - 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} - b\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} - b \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right) - 16 \, \sqrt{2} {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{6} + 6 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(x\right)^{6} + 3 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} + a b\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 3 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} + 3 \, {\left(5 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{4} + 6 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} + a^{2} + a b\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 6 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{5} + 2 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{3} + {\left(a^{2} + a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{12 \, {\left({\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} \sinh\left(x\right)^{8} + 4 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5} + 7 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5} + 2 \, {\left(3 \, a^{5} + 7 \, a^{4} b + 6 \, a^{3} b^{2} + 6 \, a^{2} b^{3} + 7 \, a b^{4} + 3 \, b^{5}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(3 \, a^{5} + 7 \, a^{4} b + 6 \, a^{3} b^{2} + 6 \, a^{2} b^{3} + 7 \, a b^{4} + 3 \, b^{5} + 35 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} \cosh\left(x\right)^{4} + 30 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{5} + 7 \, a^{4} b + 6 \, a^{3} b^{2} + 6 \, a^{2} b^{3} + 7 \, a b^{4} + 3 \, b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} \cosh\left(x\right)^{6} + a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5} + 15 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(3 \, a^{5} + 7 \, a^{4} b + 6 \, a^{3} b^{2} + 6 \, a^{2} b^{3} + 7 \, a b^{4} + 3 \, b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 8 \, {\left({\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{5} + 7 \, a^{4} b + 6 \, a^{3} b^{2} + 6 \, a^{2} b^{3} + 7 \, a b^{4} + 3 \, b^{5}\right)} \cosh\left(x\right)^{3} + {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}, -\frac{3 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(x\right)^{8} + 4 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{4} + 30 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 8 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(a \cosh\left(x\right)^{2} + 2 \, a \cosh\left(x\right) \sinh\left(x\right) + a \sinh\left(x\right)^{2} + a + b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a^{2} + a b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{2} + a b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{2} + a b\right)} \sinh\left(x\right)^{4} + {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} + 2 \, a^{2} + a b - b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(2 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{3} + {\left(2 \, a^{2} + a b - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + 3 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(x\right)^{8} + 4 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{4} + 30 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 8 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{2} - 2 \, a b + 3 \, b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} - 1\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}\right) + 8 \, \sqrt{2} {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{6} + 6 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(x\right)^{6} + 3 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} + a b\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 3 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} + 3 \, {\left(5 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{4} + 6 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} + a^{2} + a b\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 6 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{5} + 2 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{3} + {\left(a^{2} + a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{6 \, {\left({\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} \sinh\left(x\right)^{8} + 4 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5} + 7 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5} + 2 \, {\left(3 \, a^{5} + 7 \, a^{4} b + 6 \, a^{3} b^{2} + 6 \, a^{2} b^{3} + 7 \, a b^{4} + 3 \, b^{5}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(3 \, a^{5} + 7 \, a^{4} b + 6 \, a^{3} b^{2} + 6 \, a^{2} b^{3} + 7 \, a b^{4} + 3 \, b^{5} + 35 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} \cosh\left(x\right)^{4} + 30 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{5} + 7 \, a^{4} b + 6 \, a^{3} b^{2} + 6 \, a^{2} b^{3} + 7 \, a b^{4} + 3 \, b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} \cosh\left(x\right)^{6} + a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5} + 15 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(3 \, a^{5} + 7 \, a^{4} b + 6 \, a^{3} b^{2} + 6 \, a^{2} b^{3} + 7 \, a b^{4} + 3 \, b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 8 \, {\left({\left(a^{5} + 5 \, a^{4} b + 10 \, a^{3} b^{2} + 10 \, a^{2} b^{3} + 5 \, a b^{4} + b^{5}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{5} + 7 \, a^{4} b + 6 \, a^{3} b^{2} + 6 \, a^{2} b^{3} + 7 \, a b^{4} + 3 \, b^{5}\right)} \cosh\left(x\right)^{3} + {\left(a^{5} + 3 \, a^{4} b + 2 \, a^{3} b^{2} - 2 \, a^{2} b^{3} - 3 \, a b^{4} - b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}\right]"," ",0,"[1/12*(3*((a^2 + 2*a*b + b^2)*cosh(x)^8 + 8*(a^2 + 2*a*b + b^2)*cosh(x)*sinh(x)^7 + (a^2 + 2*a*b + b^2)*sinh(x)^8 + 4*(a^2 - b^2)*cosh(x)^6 + 4*(7*(a^2 + 2*a*b + b^2)*cosh(x)^2 + a^2 - b^2)*sinh(x)^6 + 8*(7*(a^2 + 2*a*b + b^2)*cosh(x)^3 + 3*(a^2 - b^2)*cosh(x))*sinh(x)^5 + 2*(3*a^2 - 2*a*b + 3*b^2)*cosh(x)^4 + 2*(35*(a^2 + 2*a*b + b^2)*cosh(x)^4 + 30*(a^2 - b^2)*cosh(x)^2 + 3*a^2 - 2*a*b + 3*b^2)*sinh(x)^4 + 8*(7*(a^2 + 2*a*b + b^2)*cosh(x)^5 + 10*(a^2 - b^2)*cosh(x)^3 + (3*a^2 - 2*a*b + 3*b^2)*cosh(x))*sinh(x)^3 + 4*(a^2 - b^2)*cosh(x)^2 + 4*(7*(a^2 + 2*a*b + b^2)*cosh(x)^6 + 15*(a^2 - b^2)*cosh(x)^4 + 3*(3*a^2 - 2*a*b + 3*b^2)*cosh(x)^2 + a^2 - b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 8*((a^2 + 2*a*b + b^2)*cosh(x)^7 + 3*(a^2 - b^2)*cosh(x)^5 + (3*a^2 - 2*a*b + 3*b^2)*cosh(x)^3 + (a^2 - b^2)*cosh(x))*sinh(x))*sqrt(a + b)*log(((a^3 + a^2*b)*cosh(x)^8 + 8*(a^3 + a^2*b)*cosh(x)*sinh(x)^7 + (a^3 + a^2*b)*sinh(x)^8 + 2*(2*a^3 + a^2*b)*cosh(x)^6 + 2*(2*a^3 + a^2*b + 14*(a^3 + a^2*b)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a^3 + a^2*b)*cosh(x)^3 + 3*(2*a^3 + a^2*b)*cosh(x))*sinh(x)^5 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^4 + (70*(a^3 + a^2*b)*cosh(x)^4 + 6*a^3 + 4*a^2*b - a*b^2 + b^3 + 30*(2*a^3 + a^2*b)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a^3 + a^2*b)*cosh(x)^5 + 10*(2*a^3 + a^2*b)*cosh(x)^3 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x))*sinh(x)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 + 2*(2*a^3 + 3*a^2*b - b^3)*cosh(x)^2 + 2*(14*(a^3 + a^2*b)*cosh(x)^6 + 15*(2*a^3 + a^2*b)*cosh(x)^4 + 2*a^3 + 3*a^2*b - b^3 + 3*(6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^2)*sinh(x)^2 + sqrt(2)*(a^2*cosh(x)^6 + 6*a^2*cosh(x)*sinh(x)^5 + a^2*sinh(x)^6 + 3*a^2*cosh(x)^4 + 3*(5*a^2*cosh(x)^2 + a^2)*sinh(x)^4 + 4*(5*a^2*cosh(x)^3 + 3*a^2*cosh(x))*sinh(x)^3 + (3*a^2 + 2*a*b - b^2)*cosh(x)^2 + (15*a^2*cosh(x)^4 + 18*a^2*cosh(x)^2 + 3*a^2 + 2*a*b - b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(3*a^2*cosh(x)^5 + 6*a^2*cosh(x)^3 + (3*a^2 + 2*a*b - b^2)*cosh(x))*sinh(x))*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a^3 + a^2*b)*cosh(x)^7 + 3*(2*a^3 + a^2*b)*cosh(x)^5 + (6*a^3 + 4*a^2*b - a*b^2 + b^3)*cosh(x)^3 + (2*a^3 + 3*a^2*b - b^3)*cosh(x))*sinh(x))/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) + 3*((a^2 + 2*a*b + b^2)*cosh(x)^8 + 8*(a^2 + 2*a*b + b^2)*cosh(x)*sinh(x)^7 + (a^2 + 2*a*b + b^2)*sinh(x)^8 + 4*(a^2 - b^2)*cosh(x)^6 + 4*(7*(a^2 + 2*a*b + b^2)*cosh(x)^2 + a^2 - b^2)*sinh(x)^6 + 8*(7*(a^2 + 2*a*b + b^2)*cosh(x)^3 + 3*(a^2 - b^2)*cosh(x))*sinh(x)^5 + 2*(3*a^2 - 2*a*b + 3*b^2)*cosh(x)^4 + 2*(35*(a^2 + 2*a*b + b^2)*cosh(x)^4 + 30*(a^2 - b^2)*cosh(x)^2 + 3*a^2 - 2*a*b + 3*b^2)*sinh(x)^4 + 8*(7*(a^2 + 2*a*b + b^2)*cosh(x)^5 + 10*(a^2 - b^2)*cosh(x)^3 + (3*a^2 - 2*a*b + 3*b^2)*cosh(x))*sinh(x)^3 + 4*(a^2 - b^2)*cosh(x)^2 + 4*(7*(a^2 + 2*a*b + b^2)*cosh(x)^6 + 15*(a^2 - b^2)*cosh(x)^4 + 3*(3*a^2 - 2*a*b + 3*b^2)*cosh(x)^2 + a^2 - b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 8*((a^2 + 2*a*b + b^2)*cosh(x)^7 + 3*(a^2 - b^2)*cosh(x)^5 + (3*a^2 - 2*a*b + 3*b^2)*cosh(x)^3 + (a^2 - b^2)*cosh(x))*sinh(x))*sqrt(a + b)*log(-((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 - 2*b*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 - b)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + b)*cosh(x)^3 - b*cosh(x))*sinh(x) + a + b)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) - 16*sqrt(2)*((a^2 + 2*a*b + b^2)*cosh(x)^6 + 6*(a^2 + 2*a*b + b^2)*cosh(x)*sinh(x)^5 + (a^2 + 2*a*b + b^2)*sinh(x)^6 + 3*(a^2 + a*b)*cosh(x)^4 + 3*(5*(a^2 + 2*a*b + b^2)*cosh(x)^2 + a^2 + a*b)*sinh(x)^4 + 4*(5*(a^2 + 2*a*b + b^2)*cosh(x)^3 + 3*(a^2 + a*b)*cosh(x))*sinh(x)^3 + 3*(a^2 + a*b)*cosh(x)^2 + 3*(5*(a^2 + 2*a*b + b^2)*cosh(x)^4 + 6*(a^2 + a*b)*cosh(x)^2 + a^2 + a*b)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 6*((a^2 + 2*a*b + b^2)*cosh(x)^5 + 2*(a^2 + a*b)*cosh(x)^3 + (a^2 + a*b)*cosh(x))*sinh(x))*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/((a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*cosh(x)^8 + 8*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*cosh(x)*sinh(x)^7 + (a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*sinh(x)^8 + 4*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*cosh(x)^6 + 4*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5 + 7*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*cosh(x)^2)*sinh(x)^6 + 8*(7*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*cosh(x)^3 + 3*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*cosh(x))*sinh(x)^5 + a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5 + 2*(3*a^5 + 7*a^4*b + 6*a^3*b^2 + 6*a^2*b^3 + 7*a*b^4 + 3*b^5)*cosh(x)^4 + 2*(3*a^5 + 7*a^4*b + 6*a^3*b^2 + 6*a^2*b^3 + 7*a*b^4 + 3*b^5 + 35*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*cosh(x)^4 + 30*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*cosh(x)^2)*sinh(x)^4 + 8*(7*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*cosh(x)^5 + 10*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*cosh(x)^3 + (3*a^5 + 7*a^4*b + 6*a^3*b^2 + 6*a^2*b^3 + 7*a*b^4 + 3*b^5)*cosh(x))*sinh(x)^3 + 4*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*cosh(x)^2 + 4*(7*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*cosh(x)^6 + a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5 + 15*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*cosh(x)^4 + 3*(3*a^5 + 7*a^4*b + 6*a^3*b^2 + 6*a^2*b^3 + 7*a*b^4 + 3*b^5)*cosh(x)^2)*sinh(x)^2 + 8*((a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*cosh(x)^7 + 3*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*cosh(x)^5 + (3*a^5 + 7*a^4*b + 6*a^3*b^2 + 6*a^2*b^3 + 7*a*b^4 + 3*b^5)*cosh(x)^3 + (a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*cosh(x))*sinh(x)), -1/6*(3*((a^2 + 2*a*b + b^2)*cosh(x)^8 + 8*(a^2 + 2*a*b + b^2)*cosh(x)*sinh(x)^7 + (a^2 + 2*a*b + b^2)*sinh(x)^8 + 4*(a^2 - b^2)*cosh(x)^6 + 4*(7*(a^2 + 2*a*b + b^2)*cosh(x)^2 + a^2 - b^2)*sinh(x)^6 + 8*(7*(a^2 + 2*a*b + b^2)*cosh(x)^3 + 3*(a^2 - b^2)*cosh(x))*sinh(x)^5 + 2*(3*a^2 - 2*a*b + 3*b^2)*cosh(x)^4 + 2*(35*(a^2 + 2*a*b + b^2)*cosh(x)^4 + 30*(a^2 - b^2)*cosh(x)^2 + 3*a^2 - 2*a*b + 3*b^2)*sinh(x)^4 + 8*(7*(a^2 + 2*a*b + b^2)*cosh(x)^5 + 10*(a^2 - b^2)*cosh(x)^3 + (3*a^2 - 2*a*b + 3*b^2)*cosh(x))*sinh(x)^3 + 4*(a^2 - b^2)*cosh(x)^2 + 4*(7*(a^2 + 2*a*b + b^2)*cosh(x)^6 + 15*(a^2 - b^2)*cosh(x)^4 + 3*(3*a^2 - 2*a*b + 3*b^2)*cosh(x)^2 + a^2 - b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 8*((a^2 + 2*a*b + b^2)*cosh(x)^7 + 3*(a^2 - b^2)*cosh(x)^5 + (3*a^2 - 2*a*b + 3*b^2)*cosh(x)^3 + (a^2 - b^2)*cosh(x))*sinh(x))*sqrt(-a - b)*arctan(sqrt(2)*(a*cosh(x)^2 + 2*a*cosh(x)*sinh(x) + a*sinh(x)^2 + a + b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a^2 + a*b)*cosh(x)^4 + 4*(a^2 + a*b)*cosh(x)*sinh(x)^3 + (a^2 + a*b)*sinh(x)^4 + (2*a^2 + a*b - b^2)*cosh(x)^2 + (6*(a^2 + a*b)*cosh(x)^2 + 2*a^2 + a*b - b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(2*(a^2 + a*b)*cosh(x)^3 + (2*a^2 + a*b - b^2)*cosh(x))*sinh(x))) + 3*((a^2 + 2*a*b + b^2)*cosh(x)^8 + 8*(a^2 + 2*a*b + b^2)*cosh(x)*sinh(x)^7 + (a^2 + 2*a*b + b^2)*sinh(x)^8 + 4*(a^2 - b^2)*cosh(x)^6 + 4*(7*(a^2 + 2*a*b + b^2)*cosh(x)^2 + a^2 - b^2)*sinh(x)^6 + 8*(7*(a^2 + 2*a*b + b^2)*cosh(x)^3 + 3*(a^2 - b^2)*cosh(x))*sinh(x)^5 + 2*(3*a^2 - 2*a*b + 3*b^2)*cosh(x)^4 + 2*(35*(a^2 + 2*a*b + b^2)*cosh(x)^4 + 30*(a^2 - b^2)*cosh(x)^2 + 3*a^2 - 2*a*b + 3*b^2)*sinh(x)^4 + 8*(7*(a^2 + 2*a*b + b^2)*cosh(x)^5 + 10*(a^2 - b^2)*cosh(x)^3 + (3*a^2 - 2*a*b + 3*b^2)*cosh(x))*sinh(x)^3 + 4*(a^2 - b^2)*cosh(x)^2 + 4*(7*(a^2 + 2*a*b + b^2)*cosh(x)^6 + 15*(a^2 - b^2)*cosh(x)^4 + 3*(3*a^2 - 2*a*b + 3*b^2)*cosh(x)^2 + a^2 - b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 8*((a^2 + 2*a*b + b^2)*cosh(x)^7 + 3*(a^2 - b^2)*cosh(x)^5 + (3*a^2 - 2*a*b + 3*b^2)*cosh(x)^3 + (a^2 - b^2)*cosh(x))*sinh(x))*sqrt(-a - b)*arctan(sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 - 1)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a - b)*cosh(x))*sinh(x) + a + b)) + 8*sqrt(2)*((a^2 + 2*a*b + b^2)*cosh(x)^6 + 6*(a^2 + 2*a*b + b^2)*cosh(x)*sinh(x)^5 + (a^2 + 2*a*b + b^2)*sinh(x)^6 + 3*(a^2 + a*b)*cosh(x)^4 + 3*(5*(a^2 + 2*a*b + b^2)*cosh(x)^2 + a^2 + a*b)*sinh(x)^4 + 4*(5*(a^2 + 2*a*b + b^2)*cosh(x)^3 + 3*(a^2 + a*b)*cosh(x))*sinh(x)^3 + 3*(a^2 + a*b)*cosh(x)^2 + 3*(5*(a^2 + 2*a*b + b^2)*cosh(x)^4 + 6*(a^2 + a*b)*cosh(x)^2 + a^2 + a*b)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 6*((a^2 + 2*a*b + b^2)*cosh(x)^5 + 2*(a^2 + a*b)*cosh(x)^3 + (a^2 + a*b)*cosh(x))*sinh(x))*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/((a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*cosh(x)^8 + 8*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*cosh(x)*sinh(x)^7 + (a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*sinh(x)^8 + 4*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*cosh(x)^6 + 4*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5 + 7*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*cosh(x)^2)*sinh(x)^6 + 8*(7*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*cosh(x)^3 + 3*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*cosh(x))*sinh(x)^5 + a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5 + 2*(3*a^5 + 7*a^4*b + 6*a^3*b^2 + 6*a^2*b^3 + 7*a*b^4 + 3*b^5)*cosh(x)^4 + 2*(3*a^5 + 7*a^4*b + 6*a^3*b^2 + 6*a^2*b^3 + 7*a*b^4 + 3*b^5 + 35*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*cosh(x)^4 + 30*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*cosh(x)^2)*sinh(x)^4 + 8*(7*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*cosh(x)^5 + 10*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*cosh(x)^3 + (3*a^5 + 7*a^4*b + 6*a^3*b^2 + 6*a^2*b^3 + 7*a*b^4 + 3*b^5)*cosh(x))*sinh(x)^3 + 4*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*cosh(x)^2 + 4*(7*(a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*cosh(x)^6 + a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5 + 15*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*cosh(x)^4 + 3*(3*a^5 + 7*a^4*b + 6*a^3*b^2 + 6*a^2*b^3 + 7*a*b^4 + 3*b^5)*cosh(x)^2)*sinh(x)^2 + 8*((a^5 + 5*a^4*b + 10*a^3*b^2 + 10*a^2*b^3 + 5*a*b^4 + b^5)*cosh(x)^7 + 3*(a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*cosh(x)^5 + (3*a^5 + 7*a^4*b + 6*a^3*b^2 + 6*a^2*b^3 + 7*a*b^4 + 3*b^5)*cosh(x)^3 + (a^5 + 3*a^4*b + 2*a^3*b^2 - 2*a^2*b^3 - 3*a*b^4 - b^5)*cosh(x))*sinh(x))]","B",0
252,1,6933,0,1.481534," ","integrate(1/(a+b*tanh(x)^2)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} \sinh\left(x\right)^{8} + 4 \, {\left(a^{4} - a^{2} b^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(a^{4} - a^{2} b^{2} + 7 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{4} - a^{2} b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{4} - 2 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(x\right)^{4} + 3 \, a^{4} - 2 \, a^{3} b + 3 \, a^{2} b^{2} + 30 \, {\left(a^{4} - a^{2} b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + a^{4} + 2 \, a^{3} b + a^{2} b^{2} + 8 \, {\left(7 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(a^{4} - a^{2} b^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{4} - 2 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(a^{4} - a^{2} b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(a^{4} - a^{2} b^{2}\right)} \cosh\left(x\right)^{4} + a^{4} - a^{2} b^{2} + 3 \, {\left(3 \, a^{4} - 2 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 8 \, {\left({\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(a^{4} - a^{2} b^{2}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{4} - 2 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{4} - a^{2} b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \log\left(-\frac{{\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a b^{2} + b^{3}\right)} \sinh\left(x\right)^{8} - 2 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{6} - 2 \, {\left(a b^{2} + 2 \, b^{3} - 14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3} - 30 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} + 2 \, {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} - 3 \, a b^{2} - 2 \, b^{3} + 3 \, {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(b^{2} \cosh\left(x\right)^{6} + 6 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + b^{2} \sinh\left(x\right)^{6} - 3 \, b^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, b^{2} \cosh\left(x\right)^{2} - b^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, b^{2} \cosh\left(x\right)^{3} - 3 \, b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, b^{2} \cosh\left(x\right)^{4} - 18 \, b^{2} \cosh\left(x\right)^{2} - a^{2} + 2 \, a b + 3 \, b^{2}\right)} \sinh\left(x\right)^{2} - a^{2} - 2 \, a b - b^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{5} - 6 \, b^{2} \cosh\left(x\right)^{3} - {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{5} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) + 3 \, {\left({\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} \sinh\left(x\right)^{8} + 4 \, {\left(a^{4} - a^{2} b^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(a^{4} - a^{2} b^{2} + 7 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{4} - a^{2} b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{4} - 2 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(x\right)^{4} + 3 \, a^{4} - 2 \, a^{3} b + 3 \, a^{2} b^{2} + 30 \, {\left(a^{4} - a^{2} b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + a^{4} + 2 \, a^{3} b + a^{2} b^{2} + 8 \, {\left(7 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(a^{4} - a^{2} b^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{4} - 2 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(a^{4} - a^{2} b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(a^{4} - a^{2} b^{2}\right)} \cosh\left(x\right)^{4} + a^{4} - a^{2} b^{2} + 3 \, {\left(3 \, a^{4} - 2 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 8 \, {\left({\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(a^{4} - a^{2} b^{2}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{4} - 2 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{4} - a^{2} b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \log\left(\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, a \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + a \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right) + 8 \, \sqrt{2} {\left({\left(3 \, a^{3} b + 7 \, a^{2} b^{2} + 5 \, a b^{3} + b^{4}\right)} \cosh\left(x\right)^{6} + 6 \, {\left(3 \, a^{3} b + 7 \, a^{2} b^{2} + 5 \, a b^{3} + b^{4}\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(3 \, a^{3} b + 7 \, a^{2} b^{2} + 5 \, a b^{3} + b^{4}\right)} \sinh\left(x\right)^{6} + 3 \, {\left(a^{3} b - a^{2} b^{2} - 3 \, a b^{3} - b^{4}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(a^{3} b - a^{2} b^{2} - 3 \, a b^{3} - b^{4} + 5 \, {\left(3 \, a^{3} b + 7 \, a^{2} b^{2} + 5 \, a b^{3} + b^{4}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} - 3 \, a^{3} b - 7 \, a^{2} b^{2} - 5 \, a b^{3} - b^{4} + 4 \, {\left(5 \, {\left(3 \, a^{3} b + 7 \, a^{2} b^{2} + 5 \, a b^{3} + b^{4}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{3} b - a^{2} b^{2} - 3 \, a b^{3} - b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 3 \, {\left(a^{3} b - a^{2} b^{2} - 3 \, a b^{3} - b^{4}\right)} \cosh\left(x\right)^{2} + 3 \, {\left(5 \, {\left(3 \, a^{3} b + 7 \, a^{2} b^{2} + 5 \, a b^{3} + b^{4}\right)} \cosh\left(x\right)^{4} - a^{3} b + a^{2} b^{2} + 3 \, a b^{3} + b^{4} + 6 \, {\left(a^{3} b - a^{2} b^{2} - 3 \, a b^{3} - b^{4}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 6 \, {\left({\left(3 \, a^{3} b + 7 \, a^{2} b^{2} + 5 \, a b^{3} + b^{4}\right)} \cosh\left(x\right)^{5} + 2 \, {\left(a^{3} b - a^{2} b^{2} - 3 \, a b^{3} - b^{4}\right)} \cosh\left(x\right)^{3} - {\left(a^{3} b - a^{2} b^{2} - 3 \, a b^{3} - b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{12 \, {\left({\left(a^{7} + 5 \, a^{6} b + 10 \, a^{5} b^{2} + 10 \, a^{4} b^{3} + 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{7} + 5 \, a^{6} b + 10 \, a^{5} b^{2} + 10 \, a^{4} b^{3} + 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{7} + 5 \, a^{6} b + 10 \, a^{5} b^{2} + 10 \, a^{4} b^{3} + 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} \sinh\left(x\right)^{8} + a^{7} + 5 \, a^{6} b + 10 \, a^{5} b^{2} + 10 \, a^{4} b^{3} + 5 \, a^{3} b^{4} + a^{2} b^{5} + 4 \, {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2} - 2 \, a^{4} b^{3} - 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2} - 2 \, a^{4} b^{3} - 3 \, a^{3} b^{4} - a^{2} b^{5} + 7 \, {\left(a^{7} + 5 \, a^{6} b + 10 \, a^{5} b^{2} + 10 \, a^{4} b^{3} + 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{7} + 5 \, a^{6} b + 10 \, a^{5} b^{2} + 10 \, a^{4} b^{3} + 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2} - 2 \, a^{4} b^{3} - 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{7} + 7 \, a^{6} b + 6 \, a^{5} b^{2} + 6 \, a^{4} b^{3} + 7 \, a^{3} b^{4} + 3 \, a^{2} b^{5}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(3 \, a^{7} + 7 \, a^{6} b + 6 \, a^{5} b^{2} + 6 \, a^{4} b^{3} + 7 \, a^{3} b^{4} + 3 \, a^{2} b^{5} + 35 \, {\left(a^{7} + 5 \, a^{6} b + 10 \, a^{5} b^{2} + 10 \, a^{4} b^{3} + 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} \cosh\left(x\right)^{4} + 30 \, {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2} - 2 \, a^{4} b^{3} - 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{7} + 5 \, a^{6} b + 10 \, a^{5} b^{2} + 10 \, a^{4} b^{3} + 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2} - 2 \, a^{4} b^{3} - 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{7} + 7 \, a^{6} b + 6 \, a^{5} b^{2} + 6 \, a^{4} b^{3} + 7 \, a^{3} b^{4} + 3 \, a^{2} b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2} - 2 \, a^{4} b^{3} - 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2} - 2 \, a^{4} b^{3} - 3 \, a^{3} b^{4} - a^{2} b^{5} + 7 \, {\left(a^{7} + 5 \, a^{6} b + 10 \, a^{5} b^{2} + 10 \, a^{4} b^{3} + 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2} - 2 \, a^{4} b^{3} - 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(3 \, a^{7} + 7 \, a^{6} b + 6 \, a^{5} b^{2} + 6 \, a^{4} b^{3} + 7 \, a^{3} b^{4} + 3 \, a^{2} b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 8 \, {\left({\left(a^{7} + 5 \, a^{6} b + 10 \, a^{5} b^{2} + 10 \, a^{4} b^{3} + 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2} - 2 \, a^{4} b^{3} - 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{7} + 7 \, a^{6} b + 6 \, a^{5} b^{2} + 6 \, a^{4} b^{3} + 7 \, a^{3} b^{4} + 3 \, a^{2} b^{5}\right)} \cosh\left(x\right)^{3} + {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2} - 2 \, a^{4} b^{3} - 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}, -\frac{3 \, {\left({\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} \sinh\left(x\right)^{8} + 4 \, {\left(a^{4} - a^{2} b^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(a^{4} - a^{2} b^{2} + 7 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{4} - a^{2} b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{4} - 2 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(x\right)^{4} + 3 \, a^{4} - 2 \, a^{3} b + 3 \, a^{2} b^{2} + 30 \, {\left(a^{4} - a^{2} b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + a^{4} + 2 \, a^{3} b + a^{2} b^{2} + 8 \, {\left(7 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(a^{4} - a^{2} b^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{4} - 2 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(a^{4} - a^{2} b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(a^{4} - a^{2} b^{2}\right)} \cosh\left(x\right)^{4} + a^{4} - a^{2} b^{2} + 3 \, {\left(3 \, a^{4} - 2 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 8 \, {\left({\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(a^{4} - a^{2} b^{2}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{4} - 2 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{4} - a^{2} b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} - a - b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a b + b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a b + b^{2}\right)} \sinh\left(x\right)^{4} + {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} - a b - 2 \, b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(2 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + 3 \, {\left({\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} \sinh\left(x\right)^{8} + 4 \, {\left(a^{4} - a^{2} b^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(a^{4} - a^{2} b^{2} + 7 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{4} - a^{2} b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{4} - 2 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(x\right)^{4} + 3 \, a^{4} - 2 \, a^{3} b + 3 \, a^{2} b^{2} + 30 \, {\left(a^{4} - a^{2} b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + a^{4} + 2 \, a^{3} b + a^{2} b^{2} + 8 \, {\left(7 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(a^{4} - a^{2} b^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{4} - 2 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(a^{4} - a^{2} b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(a^{4} - a^{2} b^{2}\right)} \cosh\left(x\right)^{4} + a^{4} - a^{2} b^{2} + 3 \, {\left(3 \, a^{4} - 2 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 8 \, {\left({\left(a^{4} + 2 \, a^{3} b + a^{2} b^{2}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(a^{4} - a^{2} b^{2}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{4} - 2 \, a^{3} b + 3 \, a^{2} b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{4} - a^{2} b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a + b\right)} \sinh\left(x\right)^{2} + a + b}\right) - 4 \, \sqrt{2} {\left({\left(3 \, a^{3} b + 7 \, a^{2} b^{2} + 5 \, a b^{3} + b^{4}\right)} \cosh\left(x\right)^{6} + 6 \, {\left(3 \, a^{3} b + 7 \, a^{2} b^{2} + 5 \, a b^{3} + b^{4}\right)} \cosh\left(x\right) \sinh\left(x\right)^{5} + {\left(3 \, a^{3} b + 7 \, a^{2} b^{2} + 5 \, a b^{3} + b^{4}\right)} \sinh\left(x\right)^{6} + 3 \, {\left(a^{3} b - a^{2} b^{2} - 3 \, a b^{3} - b^{4}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(a^{3} b - a^{2} b^{2} - 3 \, a b^{3} - b^{4} + 5 \, {\left(3 \, a^{3} b + 7 \, a^{2} b^{2} + 5 \, a b^{3} + b^{4}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} - 3 \, a^{3} b - 7 \, a^{2} b^{2} - 5 \, a b^{3} - b^{4} + 4 \, {\left(5 \, {\left(3 \, a^{3} b + 7 \, a^{2} b^{2} + 5 \, a b^{3} + b^{4}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{3} b - a^{2} b^{2} - 3 \, a b^{3} - b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - 3 \, {\left(a^{3} b - a^{2} b^{2} - 3 \, a b^{3} - b^{4}\right)} \cosh\left(x\right)^{2} + 3 \, {\left(5 \, {\left(3 \, a^{3} b + 7 \, a^{2} b^{2} + 5 \, a b^{3} + b^{4}\right)} \cosh\left(x\right)^{4} - a^{3} b + a^{2} b^{2} + 3 \, a b^{3} + b^{4} + 6 \, {\left(a^{3} b - a^{2} b^{2} - 3 \, a b^{3} - b^{4}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 6 \, {\left({\left(3 \, a^{3} b + 7 \, a^{2} b^{2} + 5 \, a b^{3} + b^{4}\right)} \cosh\left(x\right)^{5} + 2 \, {\left(a^{3} b - a^{2} b^{2} - 3 \, a b^{3} - b^{4}\right)} \cosh\left(x\right)^{3} - {\left(a^{3} b - a^{2} b^{2} - 3 \, a b^{3} - b^{4}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{6 \, {\left({\left(a^{7} + 5 \, a^{6} b + 10 \, a^{5} b^{2} + 10 \, a^{4} b^{3} + 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{7} + 5 \, a^{6} b + 10 \, a^{5} b^{2} + 10 \, a^{4} b^{3} + 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{7} + 5 \, a^{6} b + 10 \, a^{5} b^{2} + 10 \, a^{4} b^{3} + 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} \sinh\left(x\right)^{8} + a^{7} + 5 \, a^{6} b + 10 \, a^{5} b^{2} + 10 \, a^{4} b^{3} + 5 \, a^{3} b^{4} + a^{2} b^{5} + 4 \, {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2} - 2 \, a^{4} b^{3} - 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2} - 2 \, a^{4} b^{3} - 3 \, a^{3} b^{4} - a^{2} b^{5} + 7 \, {\left(a^{7} + 5 \, a^{6} b + 10 \, a^{5} b^{2} + 10 \, a^{4} b^{3} + 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{7} + 5 \, a^{6} b + 10 \, a^{5} b^{2} + 10 \, a^{4} b^{3} + 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2} - 2 \, a^{4} b^{3} - 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{7} + 7 \, a^{6} b + 6 \, a^{5} b^{2} + 6 \, a^{4} b^{3} + 7 \, a^{3} b^{4} + 3 \, a^{2} b^{5}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(3 \, a^{7} + 7 \, a^{6} b + 6 \, a^{5} b^{2} + 6 \, a^{4} b^{3} + 7 \, a^{3} b^{4} + 3 \, a^{2} b^{5} + 35 \, {\left(a^{7} + 5 \, a^{6} b + 10 \, a^{5} b^{2} + 10 \, a^{4} b^{3} + 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} \cosh\left(x\right)^{4} + 30 \, {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2} - 2 \, a^{4} b^{3} - 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{7} + 5 \, a^{6} b + 10 \, a^{5} b^{2} + 10 \, a^{4} b^{3} + 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2} - 2 \, a^{4} b^{3} - 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{7} + 7 \, a^{6} b + 6 \, a^{5} b^{2} + 6 \, a^{4} b^{3} + 7 \, a^{3} b^{4} + 3 \, a^{2} b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2} - 2 \, a^{4} b^{3} - 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2} - 2 \, a^{4} b^{3} - 3 \, a^{3} b^{4} - a^{2} b^{5} + 7 \, {\left(a^{7} + 5 \, a^{6} b + 10 \, a^{5} b^{2} + 10 \, a^{4} b^{3} + 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2} - 2 \, a^{4} b^{3} - 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(3 \, a^{7} + 7 \, a^{6} b + 6 \, a^{5} b^{2} + 6 \, a^{4} b^{3} + 7 \, a^{3} b^{4} + 3 \, a^{2} b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 8 \, {\left({\left(a^{7} + 5 \, a^{6} b + 10 \, a^{5} b^{2} + 10 \, a^{4} b^{3} + 5 \, a^{3} b^{4} + a^{2} b^{5}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2} - 2 \, a^{4} b^{3} - 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{7} + 7 \, a^{6} b + 6 \, a^{5} b^{2} + 6 \, a^{4} b^{3} + 7 \, a^{3} b^{4} + 3 \, a^{2} b^{5}\right)} \cosh\left(x\right)^{3} + {\left(a^{7} + 3 \, a^{6} b + 2 \, a^{5} b^{2} - 2 \, a^{4} b^{3} - 3 \, a^{3} b^{4} - a^{2} b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}\right]"," ",0,"[1/12*(3*((a^4 + 2*a^3*b + a^2*b^2)*cosh(x)^8 + 8*(a^4 + 2*a^3*b + a^2*b^2)*cosh(x)*sinh(x)^7 + (a^4 + 2*a^3*b + a^2*b^2)*sinh(x)^8 + 4*(a^4 - a^2*b^2)*cosh(x)^6 + 4*(a^4 - a^2*b^2 + 7*(a^4 + 2*a^3*b + a^2*b^2)*cosh(x)^2)*sinh(x)^6 + 8*(7*(a^4 + 2*a^3*b + a^2*b^2)*cosh(x)^3 + 3*(a^4 - a^2*b^2)*cosh(x))*sinh(x)^5 + 2*(3*a^4 - 2*a^3*b + 3*a^2*b^2)*cosh(x)^4 + 2*(35*(a^4 + 2*a^3*b + a^2*b^2)*cosh(x)^4 + 3*a^4 - 2*a^3*b + 3*a^2*b^2 + 30*(a^4 - a^2*b^2)*cosh(x)^2)*sinh(x)^4 + a^4 + 2*a^3*b + a^2*b^2 + 8*(7*(a^4 + 2*a^3*b + a^2*b^2)*cosh(x)^5 + 10*(a^4 - a^2*b^2)*cosh(x)^3 + (3*a^4 - 2*a^3*b + 3*a^2*b^2)*cosh(x))*sinh(x)^3 + 4*(a^4 - a^2*b^2)*cosh(x)^2 + 4*(7*(a^4 + 2*a^3*b + a^2*b^2)*cosh(x)^6 + 15*(a^4 - a^2*b^2)*cosh(x)^4 + a^4 - a^2*b^2 + 3*(3*a^4 - 2*a^3*b + 3*a^2*b^2)*cosh(x)^2)*sinh(x)^2 + 8*((a^4 + 2*a^3*b + a^2*b^2)*cosh(x)^7 + 3*(a^4 - a^2*b^2)*cosh(x)^5 + (3*a^4 - 2*a^3*b + 3*a^2*b^2)*cosh(x)^3 + (a^4 - a^2*b^2)*cosh(x))*sinh(x))*sqrt(a + b)*log(-((a*b^2 + b^3)*cosh(x)^8 + 8*(a*b^2 + b^3)*cosh(x)*sinh(x)^7 + (a*b^2 + b^3)*sinh(x)^8 - 2*(a*b^2 + 2*b^3)*cosh(x)^6 - 2*(a*b^2 + 2*b^3 - 14*(a*b^2 + b^3)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a*b^2 + b^3)*cosh(x)^3 - 3*(a*b^2 + 2*b^3)*cosh(x))*sinh(x)^5 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^4 + (70*(a*b^2 + b^3)*cosh(x)^4 + a^3 - a^2*b + 4*a*b^2 + 6*b^3 - 30*(a*b^2 + 2*b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a*b^2 + b^3)*cosh(x)^5 - 10*(a*b^2 + 2*b^3)*cosh(x)^3 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x))*sinh(x)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 + 2*(a^3 - 3*a*b^2 - 2*b^3)*cosh(x)^2 + 2*(14*(a*b^2 + b^3)*cosh(x)^6 - 15*(a*b^2 + 2*b^3)*cosh(x)^4 + a^3 - 3*a*b^2 - 2*b^3 + 3*(a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^2)*sinh(x)^2 + sqrt(2)*(b^2*cosh(x)^6 + 6*b^2*cosh(x)*sinh(x)^5 + b^2*sinh(x)^6 - 3*b^2*cosh(x)^4 + 3*(5*b^2*cosh(x)^2 - b^2)*sinh(x)^4 + 4*(5*b^2*cosh(x)^3 - 3*b^2*cosh(x))*sinh(x)^3 - (a^2 - 2*a*b - 3*b^2)*cosh(x)^2 + (15*b^2*cosh(x)^4 - 18*b^2*cosh(x)^2 - a^2 + 2*a*b + 3*b^2)*sinh(x)^2 - a^2 - 2*a*b - b^2 + 2*(3*b^2*cosh(x)^5 - 6*b^2*cosh(x)^3 - (a^2 - 2*a*b - 3*b^2)*cosh(x))*sinh(x))*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a*b^2 + b^3)*cosh(x)^7 - 3*(a*b^2 + 2*b^3)*cosh(x)^5 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^3 + (a^3 - 3*a*b^2 - 2*b^3)*cosh(x))*sinh(x))/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) + 3*((a^4 + 2*a^3*b + a^2*b^2)*cosh(x)^8 + 8*(a^4 + 2*a^3*b + a^2*b^2)*cosh(x)*sinh(x)^7 + (a^4 + 2*a^3*b + a^2*b^2)*sinh(x)^8 + 4*(a^4 - a^2*b^2)*cosh(x)^6 + 4*(a^4 - a^2*b^2 + 7*(a^4 + 2*a^3*b + a^2*b^2)*cosh(x)^2)*sinh(x)^6 + 8*(7*(a^4 + 2*a^3*b + a^2*b^2)*cosh(x)^3 + 3*(a^4 - a^2*b^2)*cosh(x))*sinh(x)^5 + 2*(3*a^4 - 2*a^3*b + 3*a^2*b^2)*cosh(x)^4 + 2*(35*(a^4 + 2*a^3*b + a^2*b^2)*cosh(x)^4 + 3*a^4 - 2*a^3*b + 3*a^2*b^2 + 30*(a^4 - a^2*b^2)*cosh(x)^2)*sinh(x)^4 + a^4 + 2*a^3*b + a^2*b^2 + 8*(7*(a^4 + 2*a^3*b + a^2*b^2)*cosh(x)^5 + 10*(a^4 - a^2*b^2)*cosh(x)^3 + (3*a^4 - 2*a^3*b + 3*a^2*b^2)*cosh(x))*sinh(x)^3 + 4*(a^4 - a^2*b^2)*cosh(x)^2 + 4*(7*(a^4 + 2*a^3*b + a^2*b^2)*cosh(x)^6 + 15*(a^4 - a^2*b^2)*cosh(x)^4 + a^4 - a^2*b^2 + 3*(3*a^4 - 2*a^3*b + 3*a^2*b^2)*cosh(x)^2)*sinh(x)^2 + 8*((a^4 + 2*a^3*b + a^2*b^2)*cosh(x)^7 + 3*(a^4 - a^2*b^2)*cosh(x)^5 + (3*a^4 - 2*a^3*b + 3*a^2*b^2)*cosh(x)^3 + (a^4 - a^2*b^2)*cosh(x))*sinh(x))*sqrt(a + b)*log(((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*a*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + b)*cosh(x)^3 + a*cosh(x))*sinh(x) + a + b)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) + 8*sqrt(2)*((3*a^3*b + 7*a^2*b^2 + 5*a*b^3 + b^4)*cosh(x)^6 + 6*(3*a^3*b + 7*a^2*b^2 + 5*a*b^3 + b^4)*cosh(x)*sinh(x)^5 + (3*a^3*b + 7*a^2*b^2 + 5*a*b^3 + b^4)*sinh(x)^6 + 3*(a^3*b - a^2*b^2 - 3*a*b^3 - b^4)*cosh(x)^4 + 3*(a^3*b - a^2*b^2 - 3*a*b^3 - b^4 + 5*(3*a^3*b + 7*a^2*b^2 + 5*a*b^3 + b^4)*cosh(x)^2)*sinh(x)^4 - 3*a^3*b - 7*a^2*b^2 - 5*a*b^3 - b^4 + 4*(5*(3*a^3*b + 7*a^2*b^2 + 5*a*b^3 + b^4)*cosh(x)^3 + 3*(a^3*b - a^2*b^2 - 3*a*b^3 - b^4)*cosh(x))*sinh(x)^3 - 3*(a^3*b - a^2*b^2 - 3*a*b^3 - b^4)*cosh(x)^2 + 3*(5*(3*a^3*b + 7*a^2*b^2 + 5*a*b^3 + b^4)*cosh(x)^4 - a^3*b + a^2*b^2 + 3*a*b^3 + b^4 + 6*(a^3*b - a^2*b^2 - 3*a*b^3 - b^4)*cosh(x)^2)*sinh(x)^2 + 6*((3*a^3*b + 7*a^2*b^2 + 5*a*b^3 + b^4)*cosh(x)^5 + 2*(a^3*b - a^2*b^2 - 3*a*b^3 - b^4)*cosh(x)^3 - (a^3*b - a^2*b^2 - 3*a*b^3 - b^4)*cosh(x))*sinh(x))*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/((a^7 + 5*a^6*b + 10*a^5*b^2 + 10*a^4*b^3 + 5*a^3*b^4 + a^2*b^5)*cosh(x)^8 + 8*(a^7 + 5*a^6*b + 10*a^5*b^2 + 10*a^4*b^3 + 5*a^3*b^4 + a^2*b^5)*cosh(x)*sinh(x)^7 + (a^7 + 5*a^6*b + 10*a^5*b^2 + 10*a^4*b^3 + 5*a^3*b^4 + a^2*b^5)*sinh(x)^8 + a^7 + 5*a^6*b + 10*a^5*b^2 + 10*a^4*b^3 + 5*a^3*b^4 + a^2*b^5 + 4*(a^7 + 3*a^6*b + 2*a^5*b^2 - 2*a^4*b^3 - 3*a^3*b^4 - a^2*b^5)*cosh(x)^6 + 4*(a^7 + 3*a^6*b + 2*a^5*b^2 - 2*a^4*b^3 - 3*a^3*b^4 - a^2*b^5 + 7*(a^7 + 5*a^6*b + 10*a^5*b^2 + 10*a^4*b^3 + 5*a^3*b^4 + a^2*b^5)*cosh(x)^2)*sinh(x)^6 + 8*(7*(a^7 + 5*a^6*b + 10*a^5*b^2 + 10*a^4*b^3 + 5*a^3*b^4 + a^2*b^5)*cosh(x)^3 + 3*(a^7 + 3*a^6*b + 2*a^5*b^2 - 2*a^4*b^3 - 3*a^3*b^4 - a^2*b^5)*cosh(x))*sinh(x)^5 + 2*(3*a^7 + 7*a^6*b + 6*a^5*b^2 + 6*a^4*b^3 + 7*a^3*b^4 + 3*a^2*b^5)*cosh(x)^4 + 2*(3*a^7 + 7*a^6*b + 6*a^5*b^2 + 6*a^4*b^3 + 7*a^3*b^4 + 3*a^2*b^5 + 35*(a^7 + 5*a^6*b + 10*a^5*b^2 + 10*a^4*b^3 + 5*a^3*b^4 + a^2*b^5)*cosh(x)^4 + 30*(a^7 + 3*a^6*b + 2*a^5*b^2 - 2*a^4*b^3 - 3*a^3*b^4 - a^2*b^5)*cosh(x)^2)*sinh(x)^4 + 8*(7*(a^7 + 5*a^6*b + 10*a^5*b^2 + 10*a^4*b^3 + 5*a^3*b^4 + a^2*b^5)*cosh(x)^5 + 10*(a^7 + 3*a^6*b + 2*a^5*b^2 - 2*a^4*b^3 - 3*a^3*b^4 - a^2*b^5)*cosh(x)^3 + (3*a^7 + 7*a^6*b + 6*a^5*b^2 + 6*a^4*b^3 + 7*a^3*b^4 + 3*a^2*b^5)*cosh(x))*sinh(x)^3 + 4*(a^7 + 3*a^6*b + 2*a^5*b^2 - 2*a^4*b^3 - 3*a^3*b^4 - a^2*b^5)*cosh(x)^2 + 4*(a^7 + 3*a^6*b + 2*a^5*b^2 - 2*a^4*b^3 - 3*a^3*b^4 - a^2*b^5 + 7*(a^7 + 5*a^6*b + 10*a^5*b^2 + 10*a^4*b^3 + 5*a^3*b^4 + a^2*b^5)*cosh(x)^6 + 15*(a^7 + 3*a^6*b + 2*a^5*b^2 - 2*a^4*b^3 - 3*a^3*b^4 - a^2*b^5)*cosh(x)^4 + 3*(3*a^7 + 7*a^6*b + 6*a^5*b^2 + 6*a^4*b^3 + 7*a^3*b^4 + 3*a^2*b^5)*cosh(x)^2)*sinh(x)^2 + 8*((a^7 + 5*a^6*b + 10*a^5*b^2 + 10*a^4*b^3 + 5*a^3*b^4 + a^2*b^5)*cosh(x)^7 + 3*(a^7 + 3*a^6*b + 2*a^5*b^2 - 2*a^4*b^3 - 3*a^3*b^4 - a^2*b^5)*cosh(x)^5 + (3*a^7 + 7*a^6*b + 6*a^5*b^2 + 6*a^4*b^3 + 7*a^3*b^4 + 3*a^2*b^5)*cosh(x)^3 + (a^7 + 3*a^6*b + 2*a^5*b^2 - 2*a^4*b^3 - 3*a^3*b^4 - a^2*b^5)*cosh(x))*sinh(x)), -1/6*(3*((a^4 + 2*a^3*b + a^2*b^2)*cosh(x)^8 + 8*(a^4 + 2*a^3*b + a^2*b^2)*cosh(x)*sinh(x)^7 + (a^4 + 2*a^3*b + a^2*b^2)*sinh(x)^8 + 4*(a^4 - a^2*b^2)*cosh(x)^6 + 4*(a^4 - a^2*b^2 + 7*(a^4 + 2*a^3*b + a^2*b^2)*cosh(x)^2)*sinh(x)^6 + 8*(7*(a^4 + 2*a^3*b + a^2*b^2)*cosh(x)^3 + 3*(a^4 - a^2*b^2)*cosh(x))*sinh(x)^5 + 2*(3*a^4 - 2*a^3*b + 3*a^2*b^2)*cosh(x)^4 + 2*(35*(a^4 + 2*a^3*b + a^2*b^2)*cosh(x)^4 + 3*a^4 - 2*a^3*b + 3*a^2*b^2 + 30*(a^4 - a^2*b^2)*cosh(x)^2)*sinh(x)^4 + a^4 + 2*a^3*b + a^2*b^2 + 8*(7*(a^4 + 2*a^3*b + a^2*b^2)*cosh(x)^5 + 10*(a^4 - a^2*b^2)*cosh(x)^3 + (3*a^4 - 2*a^3*b + 3*a^2*b^2)*cosh(x))*sinh(x)^3 + 4*(a^4 - a^2*b^2)*cosh(x)^2 + 4*(7*(a^4 + 2*a^3*b + a^2*b^2)*cosh(x)^6 + 15*(a^4 - a^2*b^2)*cosh(x)^4 + a^4 - a^2*b^2 + 3*(3*a^4 - 2*a^3*b + 3*a^2*b^2)*cosh(x)^2)*sinh(x)^2 + 8*((a^4 + 2*a^3*b + a^2*b^2)*cosh(x)^7 + 3*(a^4 - a^2*b^2)*cosh(x)^5 + (3*a^4 - 2*a^3*b + 3*a^2*b^2)*cosh(x)^3 + (a^4 - a^2*b^2)*cosh(x))*sinh(x))*sqrt(-a - b)*arctan(sqrt(2)*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 - a - b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a*b + b^2)*cosh(x)^4 + 4*(a*b + b^2)*cosh(x)*sinh(x)^3 + (a*b + b^2)*sinh(x)^4 + (a^2 - a*b - 2*b^2)*cosh(x)^2 + (6*(a*b + b^2)*cosh(x)^2 + a^2 - a*b - 2*b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(2*(a*b + b^2)*cosh(x)^3 + (a^2 - a*b - 2*b^2)*cosh(x))*sinh(x))) + 3*((a^4 + 2*a^3*b + a^2*b^2)*cosh(x)^8 + 8*(a^4 + 2*a^3*b + a^2*b^2)*cosh(x)*sinh(x)^7 + (a^4 + 2*a^3*b + a^2*b^2)*sinh(x)^8 + 4*(a^4 - a^2*b^2)*cosh(x)^6 + 4*(a^4 - a^2*b^2 + 7*(a^4 + 2*a^3*b + a^2*b^2)*cosh(x)^2)*sinh(x)^6 + 8*(7*(a^4 + 2*a^3*b + a^2*b^2)*cosh(x)^3 + 3*(a^4 - a^2*b^2)*cosh(x))*sinh(x)^5 + 2*(3*a^4 - 2*a^3*b + 3*a^2*b^2)*cosh(x)^4 + 2*(35*(a^4 + 2*a^3*b + a^2*b^2)*cosh(x)^4 + 3*a^4 - 2*a^3*b + 3*a^2*b^2 + 30*(a^4 - a^2*b^2)*cosh(x)^2)*sinh(x)^4 + a^4 + 2*a^3*b + a^2*b^2 + 8*(7*(a^4 + 2*a^3*b + a^2*b^2)*cosh(x)^5 + 10*(a^4 - a^2*b^2)*cosh(x)^3 + (3*a^4 - 2*a^3*b + 3*a^2*b^2)*cosh(x))*sinh(x)^3 + 4*(a^4 - a^2*b^2)*cosh(x)^2 + 4*(7*(a^4 + 2*a^3*b + a^2*b^2)*cosh(x)^6 + 15*(a^4 - a^2*b^2)*cosh(x)^4 + a^4 - a^2*b^2 + 3*(3*a^4 - 2*a^3*b + 3*a^2*b^2)*cosh(x)^2)*sinh(x)^2 + 8*((a^4 + 2*a^3*b + a^2*b^2)*cosh(x)^7 + 3*(a^4 - a^2*b^2)*cosh(x)^5 + (3*a^4 - 2*a^3*b + 3*a^2*b^2)*cosh(x)^3 + (a^4 - a^2*b^2)*cosh(x))*sinh(x))*sqrt(-a - b)*arctan(sqrt(2)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 + a + b)) - 4*sqrt(2)*((3*a^3*b + 7*a^2*b^2 + 5*a*b^3 + b^4)*cosh(x)^6 + 6*(3*a^3*b + 7*a^2*b^2 + 5*a*b^3 + b^4)*cosh(x)*sinh(x)^5 + (3*a^3*b + 7*a^2*b^2 + 5*a*b^3 + b^4)*sinh(x)^6 + 3*(a^3*b - a^2*b^2 - 3*a*b^3 - b^4)*cosh(x)^4 + 3*(a^3*b - a^2*b^2 - 3*a*b^3 - b^4 + 5*(3*a^3*b + 7*a^2*b^2 + 5*a*b^3 + b^4)*cosh(x)^2)*sinh(x)^4 - 3*a^3*b - 7*a^2*b^2 - 5*a*b^3 - b^4 + 4*(5*(3*a^3*b + 7*a^2*b^2 + 5*a*b^3 + b^4)*cosh(x)^3 + 3*(a^3*b - a^2*b^2 - 3*a*b^3 - b^4)*cosh(x))*sinh(x)^3 - 3*(a^3*b - a^2*b^2 - 3*a*b^3 - b^4)*cosh(x)^2 + 3*(5*(3*a^3*b + 7*a^2*b^2 + 5*a*b^3 + b^4)*cosh(x)^4 - a^3*b + a^2*b^2 + 3*a*b^3 + b^4 + 6*(a^3*b - a^2*b^2 - 3*a*b^3 - b^4)*cosh(x)^2)*sinh(x)^2 + 6*((3*a^3*b + 7*a^2*b^2 + 5*a*b^3 + b^4)*cosh(x)^5 + 2*(a^3*b - a^2*b^2 - 3*a*b^3 - b^4)*cosh(x)^3 - (a^3*b - a^2*b^2 - 3*a*b^3 - b^4)*cosh(x))*sinh(x))*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/((a^7 + 5*a^6*b + 10*a^5*b^2 + 10*a^4*b^3 + 5*a^3*b^4 + a^2*b^5)*cosh(x)^8 + 8*(a^7 + 5*a^6*b + 10*a^5*b^2 + 10*a^4*b^3 + 5*a^3*b^4 + a^2*b^5)*cosh(x)*sinh(x)^7 + (a^7 + 5*a^6*b + 10*a^5*b^2 + 10*a^4*b^3 + 5*a^3*b^4 + a^2*b^5)*sinh(x)^8 + a^7 + 5*a^6*b + 10*a^5*b^2 + 10*a^4*b^3 + 5*a^3*b^4 + a^2*b^5 + 4*(a^7 + 3*a^6*b + 2*a^5*b^2 - 2*a^4*b^3 - 3*a^3*b^4 - a^2*b^5)*cosh(x)^6 + 4*(a^7 + 3*a^6*b + 2*a^5*b^2 - 2*a^4*b^3 - 3*a^3*b^4 - a^2*b^5 + 7*(a^7 + 5*a^6*b + 10*a^5*b^2 + 10*a^4*b^3 + 5*a^3*b^4 + a^2*b^5)*cosh(x)^2)*sinh(x)^6 + 8*(7*(a^7 + 5*a^6*b + 10*a^5*b^2 + 10*a^4*b^3 + 5*a^3*b^4 + a^2*b^5)*cosh(x)^3 + 3*(a^7 + 3*a^6*b + 2*a^5*b^2 - 2*a^4*b^3 - 3*a^3*b^4 - a^2*b^5)*cosh(x))*sinh(x)^5 + 2*(3*a^7 + 7*a^6*b + 6*a^5*b^2 + 6*a^4*b^3 + 7*a^3*b^4 + 3*a^2*b^5)*cosh(x)^4 + 2*(3*a^7 + 7*a^6*b + 6*a^5*b^2 + 6*a^4*b^3 + 7*a^3*b^4 + 3*a^2*b^5 + 35*(a^7 + 5*a^6*b + 10*a^5*b^2 + 10*a^4*b^3 + 5*a^3*b^4 + a^2*b^5)*cosh(x)^4 + 30*(a^7 + 3*a^6*b + 2*a^5*b^2 - 2*a^4*b^3 - 3*a^3*b^4 - a^2*b^5)*cosh(x)^2)*sinh(x)^4 + 8*(7*(a^7 + 5*a^6*b + 10*a^5*b^2 + 10*a^4*b^3 + 5*a^3*b^4 + a^2*b^5)*cosh(x)^5 + 10*(a^7 + 3*a^6*b + 2*a^5*b^2 - 2*a^4*b^3 - 3*a^3*b^4 - a^2*b^5)*cosh(x)^3 + (3*a^7 + 7*a^6*b + 6*a^5*b^2 + 6*a^4*b^3 + 7*a^3*b^4 + 3*a^2*b^5)*cosh(x))*sinh(x)^3 + 4*(a^7 + 3*a^6*b + 2*a^5*b^2 - 2*a^4*b^3 - 3*a^3*b^4 - a^2*b^5)*cosh(x)^2 + 4*(a^7 + 3*a^6*b + 2*a^5*b^2 - 2*a^4*b^3 - 3*a^3*b^4 - a^2*b^5 + 7*(a^7 + 5*a^6*b + 10*a^5*b^2 + 10*a^4*b^3 + 5*a^3*b^4 + a^2*b^5)*cosh(x)^6 + 15*(a^7 + 3*a^6*b + 2*a^5*b^2 - 2*a^4*b^3 - 3*a^3*b^4 - a^2*b^5)*cosh(x)^4 + 3*(3*a^7 + 7*a^6*b + 6*a^5*b^2 + 6*a^4*b^3 + 7*a^3*b^4 + 3*a^2*b^5)*cosh(x)^2)*sinh(x)^2 + 8*((a^7 + 5*a^6*b + 10*a^5*b^2 + 10*a^4*b^3 + 5*a^3*b^4 + a^2*b^5)*cosh(x)^7 + 3*(a^7 + 3*a^6*b + 2*a^5*b^2 - 2*a^4*b^3 - 3*a^3*b^4 - a^2*b^5)*cosh(x)^5 + (3*a^7 + 7*a^6*b + 6*a^5*b^2 + 6*a^4*b^3 + 7*a^3*b^4 + 3*a^2*b^5)*cosh(x)^3 + (a^7 + 3*a^6*b + 2*a^5*b^2 - 2*a^4*b^3 - 3*a^3*b^4 - a^2*b^5)*cosh(x))*sinh(x))]","B",0
253,-1,0,0,0.000000," ","integrate(coth(x)/(a+b*tanh(x)^2)^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
254,1,10671,0,2.490933," ","integrate(coth(x)^2/(a+b*tanh(x)^2)^(5/2),x, algorithm=""fricas"")","\left[\frac{3 \, {\left({\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right)^{10} + 10 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{9} + {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \sinh\left(x\right)^{10} + {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{8} + {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2} + 45 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{8} + 8 \, {\left(15 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{7} + 2 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{6} + 2 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2} + 105 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right)^{4} + 14 \, {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(63 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right)^{5} + 14 \, {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} - a^{5} - 2 \, a^{4} b - a^{3} b^{2} - 2 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(105 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right)^{6} - a^{5} + 2 \, a^{4} b - 5 \, a^{3} b^{2} + 35 \, {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{4} + 15 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(15 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right)^{7} + 7 \, {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{5} + 5 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{3} - {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{2} + {\left(45 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right)^{8} + 28 \, {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{6} - 3 \, a^{5} + 2 \, a^{4} b + 5 \, a^{3} b^{2} + 30 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{4} - 12 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 2 \, {\left(5 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right)^{9} + 4 \, {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{7} + 6 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{5} - 4 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{3} - {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \log\left(-\frac{{\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a b^{2} + b^{3}\right)} \sinh\left(x\right)^{8} - 2 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{6} - 2 \, {\left(a b^{2} + 2 \, b^{3} - 14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{3} - 3 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{4} + {\left(70 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3} - 30 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{5} - 10 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + a^{3} + 3 \, a^{2} b + 3 \, a b^{2} + b^{3} + 2 \, {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(14 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{6} - 15 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{4} + a^{3} - 3 \, a b^{2} - 2 \, b^{3} + 3 \, {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(b^{2} \cosh\left(x\right)^{6} + 6 \, b^{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + b^{2} \sinh\left(x\right)^{6} - 3 \, b^{2} \cosh\left(x\right)^{4} + 3 \, {\left(5 \, b^{2} \cosh\left(x\right)^{2} - b^{2}\right)} \sinh\left(x\right)^{4} + 4 \, {\left(5 \, b^{2} \cosh\left(x\right)^{3} - 3 \, b^{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(15 \, b^{2} \cosh\left(x\right)^{4} - 18 \, b^{2} \cosh\left(x\right)^{2} - a^{2} + 2 \, a b + 3 \, b^{2}\right)} \sinh\left(x\right)^{2} - a^{2} - 2 \, a b - b^{2} + 2 \, {\left(3 \, b^{2} \cosh\left(x\right)^{5} - 6 \, b^{2} \cosh\left(x\right)^{3} - {\left(a^{2} - 2 \, a b - 3 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left(2 \, {\left(a b^{2} + b^{3}\right)} \cosh\left(x\right)^{7} - 3 \, {\left(a b^{2} + 2 \, b^{3}\right)} \cosh\left(x\right)^{5} + {\left(a^{3} - a^{2} b + 4 \, a b^{2} + 6 \, b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{3} - 3 \, a b^{2} - 2 \, b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) + 3 \, {\left({\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right)^{10} + 10 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{9} + {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \sinh\left(x\right)^{10} + {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{8} + {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2} + 45 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{8} + 8 \, {\left(15 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{7} + 2 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{6} + 2 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2} + 105 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right)^{4} + 14 \, {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(63 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right)^{5} + 14 \, {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} - a^{5} - 2 \, a^{4} b - a^{3} b^{2} - 2 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(105 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right)^{6} - a^{5} + 2 \, a^{4} b - 5 \, a^{3} b^{2} + 35 \, {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{4} + 15 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(15 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right)^{7} + 7 \, {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{5} + 5 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{3} - {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{2} + {\left(45 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right)^{8} + 28 \, {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{6} - 3 \, a^{5} + 2 \, a^{4} b + 5 \, a^{3} b^{2} + 30 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{4} - 12 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 2 \, {\left(5 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right)^{9} + 4 \, {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{7} + 6 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{5} - 4 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{3} - {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \log\left(\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, a \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2} + 1\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + a \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right) - 4 \, \sqrt{2} {\left({\left(3 \, a^{5} + 15 \, a^{4} b + 39 \, a^{3} b^{2} + 53 \, a^{2} b^{3} + 34 \, a b^{4} + 8 \, b^{5}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(3 \, a^{5} + 15 \, a^{4} b + 39 \, a^{3} b^{2} + 53 \, a^{2} b^{3} + 34 \, a b^{4} + 8 \, b^{5}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(3 \, a^{5} + 15 \, a^{4} b + 39 \, a^{3} b^{2} + 53 \, a^{2} b^{3} + 34 \, a b^{4} + 8 \, b^{5}\right)} \sinh\left(x\right)^{8} + 4 \, {\left(3 \, a^{5} + 9 \, a^{4} b + 6 \, a^{3} b^{2} - 14 \, a^{2} b^{3} - 22 \, a b^{4} - 8 \, b^{5}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(3 \, a^{5} + 9 \, a^{4} b + 6 \, a^{3} b^{2} - 14 \, a^{2} b^{3} - 22 \, a b^{4} - 8 \, b^{5} + 7 \, {\left(3 \, a^{5} + 15 \, a^{4} b + 39 \, a^{3} b^{2} + 53 \, a^{2} b^{3} + 34 \, a b^{4} + 8 \, b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(3 \, a^{5} + 15 \, a^{4} b + 39 \, a^{3} b^{2} + 53 \, a^{2} b^{3} + 34 \, a b^{4} + 8 \, b^{5}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(3 \, a^{5} + 9 \, a^{4} b + 6 \, a^{3} b^{2} - 14 \, a^{2} b^{3} - 22 \, a b^{4} - 8 \, b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 3 \, a^{5} + 15 \, a^{4} b + 39 \, a^{3} b^{2} + 53 \, a^{2} b^{3} + 34 \, a b^{4} + 8 \, b^{5} + 6 \, {\left(3 \, a^{5} + 7 \, a^{4} b + 3 \, a^{3} b^{2} + 9 \, a^{2} b^{3} + 18 \, a b^{4} + 8 \, b^{5}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(9 \, a^{5} + 21 \, a^{4} b + 9 \, a^{3} b^{2} + 27 \, a^{2} b^{3} + 54 \, a b^{4} + 24 \, b^{5} + 35 \, {\left(3 \, a^{5} + 15 \, a^{4} b + 39 \, a^{3} b^{2} + 53 \, a^{2} b^{3} + 34 \, a b^{4} + 8 \, b^{5}\right)} \cosh\left(x\right)^{4} + 30 \, {\left(3 \, a^{5} + 9 \, a^{4} b + 6 \, a^{3} b^{2} - 14 \, a^{2} b^{3} - 22 \, a b^{4} - 8 \, b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(3 \, a^{5} + 15 \, a^{4} b + 39 \, a^{3} b^{2} + 53 \, a^{2} b^{3} + 34 \, a b^{4} + 8 \, b^{5}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(3 \, a^{5} + 9 \, a^{4} b + 6 \, a^{3} b^{2} - 14 \, a^{2} b^{3} - 22 \, a b^{4} - 8 \, b^{5}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(3 \, a^{5} + 7 \, a^{4} b + 3 \, a^{3} b^{2} + 9 \, a^{2} b^{3} + 18 \, a b^{4} + 8 \, b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(3 \, a^{5} + 9 \, a^{4} b + 6 \, a^{3} b^{2} - 14 \, a^{2} b^{3} - 22 \, a b^{4} - 8 \, b^{5}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(3 \, a^{5} + 15 \, a^{4} b + 39 \, a^{3} b^{2} + 53 \, a^{2} b^{3} + 34 \, a b^{4} + 8 \, b^{5}\right)} \cosh\left(x\right)^{6} + 3 \, a^{5} + 9 \, a^{4} b + 6 \, a^{3} b^{2} - 14 \, a^{2} b^{3} - 22 \, a b^{4} - 8 \, b^{5} + 15 \, {\left(3 \, a^{5} + 9 \, a^{4} b + 6 \, a^{3} b^{2} - 14 \, a^{2} b^{3} - 22 \, a b^{4} - 8 \, b^{5}\right)} \cosh\left(x\right)^{4} + 9 \, {\left(3 \, a^{5} + 7 \, a^{4} b + 3 \, a^{3} b^{2} + 9 \, a^{2} b^{3} + 18 \, a b^{4} + 8 \, b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 8 \, {\left({\left(3 \, a^{5} + 15 \, a^{4} b + 39 \, a^{3} b^{2} + 53 \, a^{2} b^{3} + 34 \, a b^{4} + 8 \, b^{5}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(3 \, a^{5} + 9 \, a^{4} b + 6 \, a^{3} b^{2} - 14 \, a^{2} b^{3} - 22 \, a b^{4} - 8 \, b^{5}\right)} \cosh\left(x\right)^{5} + 3 \, {\left(3 \, a^{5} + 7 \, a^{4} b + 3 \, a^{3} b^{2} + 9 \, a^{2} b^{3} + 18 \, a b^{4} + 8 \, b^{5}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{5} + 9 \, a^{4} b + 6 \, a^{3} b^{2} - 14 \, a^{2} b^{3} - 22 \, a b^{4} - 8 \, b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{12 \, {\left({\left(a^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} \cosh\left(x\right)^{10} + 10 \, {\left(a^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} \cosh\left(x\right) \sinh\left(x\right)^{9} + {\left(a^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} \sinh\left(x\right)^{10} + {\left(3 \, a^{8} + 7 \, a^{7} b - 2 \, a^{6} b^{2} - 18 \, a^{5} b^{3} - 17 \, a^{4} b^{4} - 5 \, a^{3} b^{5}\right)} \cosh\left(x\right)^{8} + {\left(3 \, a^{8} + 7 \, a^{7} b - 2 \, a^{6} b^{2} - 18 \, a^{5} b^{3} - 17 \, a^{4} b^{4} - 5 \, a^{3} b^{5} + 45 \, {\left(a^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{8} - a^{8} - 5 \, a^{7} b - 10 \, a^{6} b^{2} - 10 \, a^{5} b^{3} - 5 \, a^{4} b^{4} - a^{3} b^{5} + 8 \, {\left(15 \, {\left(a^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{8} + 7 \, a^{7} b - 2 \, a^{6} b^{2} - 18 \, a^{5} b^{3} - 17 \, a^{4} b^{4} - 5 \, a^{3} b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{7} + 2 \, {\left(a^{8} + a^{7} b + 2 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 5 \, a^{3} b^{5}\right)} \cosh\left(x\right)^{6} + 2 \, {\left(a^{8} + a^{7} b + 2 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 5 \, a^{3} b^{5} + 105 \, {\left(a^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} \cosh\left(x\right)^{4} + 14 \, {\left(3 \, a^{8} + 7 \, a^{7} b - 2 \, a^{6} b^{2} - 18 \, a^{5} b^{3} - 17 \, a^{4} b^{4} - 5 \, a^{3} b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(63 \, {\left(a^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} \cosh\left(x\right)^{5} + 14 \, {\left(3 \, a^{8} + 7 \, a^{7} b - 2 \, a^{6} b^{2} - 18 \, a^{5} b^{3} - 17 \, a^{4} b^{4} - 5 \, a^{3} b^{5}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{8} + a^{7} b + 2 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 5 \, a^{3} b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} - 2 \, {\left(a^{8} + a^{7} b + 2 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 5 \, a^{3} b^{5}\right)} \cosh\left(x\right)^{4} - 2 \, {\left(a^{8} + a^{7} b + 2 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 5 \, a^{3} b^{5} - 105 \, {\left(a^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} \cosh\left(x\right)^{6} - 35 \, {\left(3 \, a^{8} + 7 \, a^{7} b - 2 \, a^{6} b^{2} - 18 \, a^{5} b^{3} - 17 \, a^{4} b^{4} - 5 \, a^{3} b^{5}\right)} \cosh\left(x\right)^{4} - 15 \, {\left(a^{8} + a^{7} b + 2 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 5 \, a^{3} b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(15 \, {\left(a^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} \cosh\left(x\right)^{7} + 7 \, {\left(3 \, a^{8} + 7 \, a^{7} b - 2 \, a^{6} b^{2} - 18 \, a^{5} b^{3} - 17 \, a^{4} b^{4} - 5 \, a^{3} b^{5}\right)} \cosh\left(x\right)^{5} + 5 \, {\left(a^{8} + a^{7} b + 2 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 5 \, a^{3} b^{5}\right)} \cosh\left(x\right)^{3} - {\left(a^{8} + a^{7} b + 2 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 5 \, a^{3} b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - {\left(3 \, a^{8} + 7 \, a^{7} b - 2 \, a^{6} b^{2} - 18 \, a^{5} b^{3} - 17 \, a^{4} b^{4} - 5 \, a^{3} b^{5}\right)} \cosh\left(x\right)^{2} + {\left(45 \, {\left(a^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} \cosh\left(x\right)^{8} - 3 \, a^{8} - 7 \, a^{7} b + 2 \, a^{6} b^{2} + 18 \, a^{5} b^{3} + 17 \, a^{4} b^{4} + 5 \, a^{3} b^{5} + 28 \, {\left(3 \, a^{8} + 7 \, a^{7} b - 2 \, a^{6} b^{2} - 18 \, a^{5} b^{3} - 17 \, a^{4} b^{4} - 5 \, a^{3} b^{5}\right)} \cosh\left(x\right)^{6} + 30 \, {\left(a^{8} + a^{7} b + 2 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 5 \, a^{3} b^{5}\right)} \cosh\left(x\right)^{4} - 12 \, {\left(a^{8} + a^{7} b + 2 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 5 \, a^{3} b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 2 \, {\left(5 \, {\left(a^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} \cosh\left(x\right)^{9} + 4 \, {\left(3 \, a^{8} + 7 \, a^{7} b - 2 \, a^{6} b^{2} - 18 \, a^{5} b^{3} - 17 \, a^{4} b^{4} - 5 \, a^{3} b^{5}\right)} \cosh\left(x\right)^{7} + 6 \, {\left(a^{8} + a^{7} b + 2 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 5 \, a^{3} b^{5}\right)} \cosh\left(x\right)^{5} - 4 \, {\left(a^{8} + a^{7} b + 2 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 5 \, a^{3} b^{5}\right)} \cosh\left(x\right)^{3} - {\left(3 \, a^{8} + 7 \, a^{7} b - 2 \, a^{6} b^{2} - 18 \, a^{5} b^{3} - 17 \, a^{4} b^{4} - 5 \, a^{3} b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}, -\frac{3 \, {\left({\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right)^{10} + 10 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{9} + {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \sinh\left(x\right)^{10} + {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{8} + {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2} + 45 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{8} + 8 \, {\left(15 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{7} + 2 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{6} + 2 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2} + 105 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right)^{4} + 14 \, {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(63 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right)^{5} + 14 \, {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} - a^{5} - 2 \, a^{4} b - a^{3} b^{2} - 2 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(105 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right)^{6} - a^{5} + 2 \, a^{4} b - 5 \, a^{3} b^{2} + 35 \, {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{4} + 15 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(15 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right)^{7} + 7 \, {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{5} + 5 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{3} - {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{2} + {\left(45 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right)^{8} + 28 \, {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{6} - 3 \, a^{5} + 2 \, a^{4} b + 5 \, a^{3} b^{2} + 30 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{4} - 12 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 2 \, {\left(5 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right)^{9} + 4 \, {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{7} + 6 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{5} - 4 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{3} - {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left(b \cosh\left(x\right)^{2} + 2 \, b \cosh\left(x\right) \sinh\left(x\right) + b \sinh\left(x\right)^{2} - a - b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a b + b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a b + b^{2}\right)} \sinh\left(x\right)^{4} + {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)^{2} + {\left(6 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} - a b - 2 \, b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 2 \, {\left(2 \, {\left(a b + b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{2} - a b - 2 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + 3 \, {\left({\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right)^{10} + 10 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{9} + {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \sinh\left(x\right)^{10} + {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{8} + {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2} + 45 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{8} + 8 \, {\left(15 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{7} + 2 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{6} + 2 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2} + 105 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right)^{4} + 14 \, {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(63 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right)^{5} + 14 \, {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} - a^{5} - 2 \, a^{4} b - a^{3} b^{2} - 2 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(105 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right)^{6} - a^{5} + 2 \, a^{4} b - 5 \, a^{3} b^{2} + 35 \, {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{4} + 15 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(15 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right)^{7} + 7 \, {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{5} + 5 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{3} - {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{2} + {\left(45 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right)^{8} + 28 \, {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{6} - 3 \, a^{5} + 2 \, a^{4} b + 5 \, a^{3} b^{2} + 30 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{4} - 12 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 2 \, {\left(5 \, {\left(a^{5} + 2 \, a^{4} b + a^{3} b^{2}\right)} \cosh\left(x\right)^{9} + 4 \, {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{7} + 6 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{5} - 4 \, {\left(a^{5} - 2 \, a^{4} b + 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)^{3} - {\left(3 \, a^{5} - 2 \, a^{4} b - 5 \, a^{3} b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{{\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right) + {\left(a + b\right)} \sinh\left(x\right)^{2} + a + b}\right) + 2 \, \sqrt{2} {\left({\left(3 \, a^{5} + 15 \, a^{4} b + 39 \, a^{3} b^{2} + 53 \, a^{2} b^{3} + 34 \, a b^{4} + 8 \, b^{5}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(3 \, a^{5} + 15 \, a^{4} b + 39 \, a^{3} b^{2} + 53 \, a^{2} b^{3} + 34 \, a b^{4} + 8 \, b^{5}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(3 \, a^{5} + 15 \, a^{4} b + 39 \, a^{3} b^{2} + 53 \, a^{2} b^{3} + 34 \, a b^{4} + 8 \, b^{5}\right)} \sinh\left(x\right)^{8} + 4 \, {\left(3 \, a^{5} + 9 \, a^{4} b + 6 \, a^{3} b^{2} - 14 \, a^{2} b^{3} - 22 \, a b^{4} - 8 \, b^{5}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(3 \, a^{5} + 9 \, a^{4} b + 6 \, a^{3} b^{2} - 14 \, a^{2} b^{3} - 22 \, a b^{4} - 8 \, b^{5} + 7 \, {\left(3 \, a^{5} + 15 \, a^{4} b + 39 \, a^{3} b^{2} + 53 \, a^{2} b^{3} + 34 \, a b^{4} + 8 \, b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(3 \, a^{5} + 15 \, a^{4} b + 39 \, a^{3} b^{2} + 53 \, a^{2} b^{3} + 34 \, a b^{4} + 8 \, b^{5}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(3 \, a^{5} + 9 \, a^{4} b + 6 \, a^{3} b^{2} - 14 \, a^{2} b^{3} - 22 \, a b^{4} - 8 \, b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 3 \, a^{5} + 15 \, a^{4} b + 39 \, a^{3} b^{2} + 53 \, a^{2} b^{3} + 34 \, a b^{4} + 8 \, b^{5} + 6 \, {\left(3 \, a^{5} + 7 \, a^{4} b + 3 \, a^{3} b^{2} + 9 \, a^{2} b^{3} + 18 \, a b^{4} + 8 \, b^{5}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(9 \, a^{5} + 21 \, a^{4} b + 9 \, a^{3} b^{2} + 27 \, a^{2} b^{3} + 54 \, a b^{4} + 24 \, b^{5} + 35 \, {\left(3 \, a^{5} + 15 \, a^{4} b + 39 \, a^{3} b^{2} + 53 \, a^{2} b^{3} + 34 \, a b^{4} + 8 \, b^{5}\right)} \cosh\left(x\right)^{4} + 30 \, {\left(3 \, a^{5} + 9 \, a^{4} b + 6 \, a^{3} b^{2} - 14 \, a^{2} b^{3} - 22 \, a b^{4} - 8 \, b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(3 \, a^{5} + 15 \, a^{4} b + 39 \, a^{3} b^{2} + 53 \, a^{2} b^{3} + 34 \, a b^{4} + 8 \, b^{5}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(3 \, a^{5} + 9 \, a^{4} b + 6 \, a^{3} b^{2} - 14 \, a^{2} b^{3} - 22 \, a b^{4} - 8 \, b^{5}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(3 \, a^{5} + 7 \, a^{4} b + 3 \, a^{3} b^{2} + 9 \, a^{2} b^{3} + 18 \, a b^{4} + 8 \, b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(3 \, a^{5} + 9 \, a^{4} b + 6 \, a^{3} b^{2} - 14 \, a^{2} b^{3} - 22 \, a b^{4} - 8 \, b^{5}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(3 \, a^{5} + 15 \, a^{4} b + 39 \, a^{3} b^{2} + 53 \, a^{2} b^{3} + 34 \, a b^{4} + 8 \, b^{5}\right)} \cosh\left(x\right)^{6} + 3 \, a^{5} + 9 \, a^{4} b + 6 \, a^{3} b^{2} - 14 \, a^{2} b^{3} - 22 \, a b^{4} - 8 \, b^{5} + 15 \, {\left(3 \, a^{5} + 9 \, a^{4} b + 6 \, a^{3} b^{2} - 14 \, a^{2} b^{3} - 22 \, a b^{4} - 8 \, b^{5}\right)} \cosh\left(x\right)^{4} + 9 \, {\left(3 \, a^{5} + 7 \, a^{4} b + 3 \, a^{3} b^{2} + 9 \, a^{2} b^{3} + 18 \, a b^{4} + 8 \, b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 8 \, {\left({\left(3 \, a^{5} + 15 \, a^{4} b + 39 \, a^{3} b^{2} + 53 \, a^{2} b^{3} + 34 \, a b^{4} + 8 \, b^{5}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(3 \, a^{5} + 9 \, a^{4} b + 6 \, a^{3} b^{2} - 14 \, a^{2} b^{3} - 22 \, a b^{4} - 8 \, b^{5}\right)} \cosh\left(x\right)^{5} + 3 \, {\left(3 \, a^{5} + 7 \, a^{4} b + 3 \, a^{3} b^{2} + 9 \, a^{2} b^{3} + 18 \, a b^{4} + 8 \, b^{5}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{5} + 9 \, a^{4} b + 6 \, a^{3} b^{2} - 14 \, a^{2} b^{3} - 22 \, a b^{4} - 8 \, b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{2} + {\left(a + b\right)} \sinh\left(x\right)^{2} + a - b}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}}}{6 \, {\left({\left(a^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} \cosh\left(x\right)^{10} + 10 \, {\left(a^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} \cosh\left(x\right) \sinh\left(x\right)^{9} + {\left(a^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} \sinh\left(x\right)^{10} + {\left(3 \, a^{8} + 7 \, a^{7} b - 2 \, a^{6} b^{2} - 18 \, a^{5} b^{3} - 17 \, a^{4} b^{4} - 5 \, a^{3} b^{5}\right)} \cosh\left(x\right)^{8} + {\left(3 \, a^{8} + 7 \, a^{7} b - 2 \, a^{6} b^{2} - 18 \, a^{5} b^{3} - 17 \, a^{4} b^{4} - 5 \, a^{3} b^{5} + 45 \, {\left(a^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{8} - a^{8} - 5 \, a^{7} b - 10 \, a^{6} b^{2} - 10 \, a^{5} b^{3} - 5 \, a^{4} b^{4} - a^{3} b^{5} + 8 \, {\left(15 \, {\left(a^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{8} + 7 \, a^{7} b - 2 \, a^{6} b^{2} - 18 \, a^{5} b^{3} - 17 \, a^{4} b^{4} - 5 \, a^{3} b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{7} + 2 \, {\left(a^{8} + a^{7} b + 2 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 5 \, a^{3} b^{5}\right)} \cosh\left(x\right)^{6} + 2 \, {\left(a^{8} + a^{7} b + 2 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 5 \, a^{3} b^{5} + 105 \, {\left(a^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} \cosh\left(x\right)^{4} + 14 \, {\left(3 \, a^{8} + 7 \, a^{7} b - 2 \, a^{6} b^{2} - 18 \, a^{5} b^{3} - 17 \, a^{4} b^{4} - 5 \, a^{3} b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 4 \, {\left(63 \, {\left(a^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} \cosh\left(x\right)^{5} + 14 \, {\left(3 \, a^{8} + 7 \, a^{7} b - 2 \, a^{6} b^{2} - 18 \, a^{5} b^{3} - 17 \, a^{4} b^{4} - 5 \, a^{3} b^{5}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{8} + a^{7} b + 2 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 5 \, a^{3} b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} - 2 \, {\left(a^{8} + a^{7} b + 2 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 5 \, a^{3} b^{5}\right)} \cosh\left(x\right)^{4} - 2 \, {\left(a^{8} + a^{7} b + 2 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 5 \, a^{3} b^{5} - 105 \, {\left(a^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} \cosh\left(x\right)^{6} - 35 \, {\left(3 \, a^{8} + 7 \, a^{7} b - 2 \, a^{6} b^{2} - 18 \, a^{5} b^{3} - 17 \, a^{4} b^{4} - 5 \, a^{3} b^{5}\right)} \cosh\left(x\right)^{4} - 15 \, {\left(a^{8} + a^{7} b + 2 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 5 \, a^{3} b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(15 \, {\left(a^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} \cosh\left(x\right)^{7} + 7 \, {\left(3 \, a^{8} + 7 \, a^{7} b - 2 \, a^{6} b^{2} - 18 \, a^{5} b^{3} - 17 \, a^{4} b^{4} - 5 \, a^{3} b^{5}\right)} \cosh\left(x\right)^{5} + 5 \, {\left(a^{8} + a^{7} b + 2 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 5 \, a^{3} b^{5}\right)} \cosh\left(x\right)^{3} - {\left(a^{8} + a^{7} b + 2 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 5 \, a^{3} b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} - {\left(3 \, a^{8} + 7 \, a^{7} b - 2 \, a^{6} b^{2} - 18 \, a^{5} b^{3} - 17 \, a^{4} b^{4} - 5 \, a^{3} b^{5}\right)} \cosh\left(x\right)^{2} + {\left(45 \, {\left(a^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} \cosh\left(x\right)^{8} - 3 \, a^{8} - 7 \, a^{7} b + 2 \, a^{6} b^{2} + 18 \, a^{5} b^{3} + 17 \, a^{4} b^{4} + 5 \, a^{3} b^{5} + 28 \, {\left(3 \, a^{8} + 7 \, a^{7} b - 2 \, a^{6} b^{2} - 18 \, a^{5} b^{3} - 17 \, a^{4} b^{4} - 5 \, a^{3} b^{5}\right)} \cosh\left(x\right)^{6} + 30 \, {\left(a^{8} + a^{7} b + 2 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 5 \, a^{3} b^{5}\right)} \cosh\left(x\right)^{4} - 12 \, {\left(a^{8} + a^{7} b + 2 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 5 \, a^{3} b^{5}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 2 \, {\left(5 \, {\left(a^{8} + 5 \, a^{7} b + 10 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 5 \, a^{4} b^{4} + a^{3} b^{5}\right)} \cosh\left(x\right)^{9} + 4 \, {\left(3 \, a^{8} + 7 \, a^{7} b - 2 \, a^{6} b^{2} - 18 \, a^{5} b^{3} - 17 \, a^{4} b^{4} - 5 \, a^{3} b^{5}\right)} \cosh\left(x\right)^{7} + 6 \, {\left(a^{8} + a^{7} b + 2 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 5 \, a^{3} b^{5}\right)} \cosh\left(x\right)^{5} - 4 \, {\left(a^{8} + a^{7} b + 2 \, a^{6} b^{2} + 10 \, a^{5} b^{3} + 13 \, a^{4} b^{4} + 5 \, a^{3} b^{5}\right)} \cosh\left(x\right)^{3} - {\left(3 \, a^{8} + 7 \, a^{7} b - 2 \, a^{6} b^{2} - 18 \, a^{5} b^{3} - 17 \, a^{4} b^{4} - 5 \, a^{3} b^{5}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}\right]"," ",0,"[1/12*(3*((a^5 + 2*a^4*b + a^3*b^2)*cosh(x)^10 + 10*(a^5 + 2*a^4*b + a^3*b^2)*cosh(x)*sinh(x)^9 + (a^5 + 2*a^4*b + a^3*b^2)*sinh(x)^10 + (3*a^5 - 2*a^4*b - 5*a^3*b^2)*cosh(x)^8 + (3*a^5 - 2*a^4*b - 5*a^3*b^2 + 45*(a^5 + 2*a^4*b + a^3*b^2)*cosh(x)^2)*sinh(x)^8 + 8*(15*(a^5 + 2*a^4*b + a^3*b^2)*cosh(x)^3 + (3*a^5 - 2*a^4*b - 5*a^3*b^2)*cosh(x))*sinh(x)^7 + 2*(a^5 - 2*a^4*b + 5*a^3*b^2)*cosh(x)^6 + 2*(a^5 - 2*a^4*b + 5*a^3*b^2 + 105*(a^5 + 2*a^4*b + a^3*b^2)*cosh(x)^4 + 14*(3*a^5 - 2*a^4*b - 5*a^3*b^2)*cosh(x)^2)*sinh(x)^6 + 4*(63*(a^5 + 2*a^4*b + a^3*b^2)*cosh(x)^5 + 14*(3*a^5 - 2*a^4*b - 5*a^3*b^2)*cosh(x)^3 + 3*(a^5 - 2*a^4*b + 5*a^3*b^2)*cosh(x))*sinh(x)^5 - a^5 - 2*a^4*b - a^3*b^2 - 2*(a^5 - 2*a^4*b + 5*a^3*b^2)*cosh(x)^4 + 2*(105*(a^5 + 2*a^4*b + a^3*b^2)*cosh(x)^6 - a^5 + 2*a^4*b - 5*a^3*b^2 + 35*(3*a^5 - 2*a^4*b - 5*a^3*b^2)*cosh(x)^4 + 15*(a^5 - 2*a^4*b + 5*a^3*b^2)*cosh(x)^2)*sinh(x)^4 + 8*(15*(a^5 + 2*a^4*b + a^3*b^2)*cosh(x)^7 + 7*(3*a^5 - 2*a^4*b - 5*a^3*b^2)*cosh(x)^5 + 5*(a^5 - 2*a^4*b + 5*a^3*b^2)*cosh(x)^3 - (a^5 - 2*a^4*b + 5*a^3*b^2)*cosh(x))*sinh(x)^3 - (3*a^5 - 2*a^4*b - 5*a^3*b^2)*cosh(x)^2 + (45*(a^5 + 2*a^4*b + a^3*b^2)*cosh(x)^8 + 28*(3*a^5 - 2*a^4*b - 5*a^3*b^2)*cosh(x)^6 - 3*a^5 + 2*a^4*b + 5*a^3*b^2 + 30*(a^5 - 2*a^4*b + 5*a^3*b^2)*cosh(x)^4 - 12*(a^5 - 2*a^4*b + 5*a^3*b^2)*cosh(x)^2)*sinh(x)^2 + 2*(5*(a^5 + 2*a^4*b + a^3*b^2)*cosh(x)^9 + 4*(3*a^5 - 2*a^4*b - 5*a^3*b^2)*cosh(x)^7 + 6*(a^5 - 2*a^4*b + 5*a^3*b^2)*cosh(x)^5 - 4*(a^5 - 2*a^4*b + 5*a^3*b^2)*cosh(x)^3 - (3*a^5 - 2*a^4*b - 5*a^3*b^2)*cosh(x))*sinh(x))*sqrt(a + b)*log(-((a*b^2 + b^3)*cosh(x)^8 + 8*(a*b^2 + b^3)*cosh(x)*sinh(x)^7 + (a*b^2 + b^3)*sinh(x)^8 - 2*(a*b^2 + 2*b^3)*cosh(x)^6 - 2*(a*b^2 + 2*b^3 - 14*(a*b^2 + b^3)*cosh(x)^2)*sinh(x)^6 + 4*(14*(a*b^2 + b^3)*cosh(x)^3 - 3*(a*b^2 + 2*b^3)*cosh(x))*sinh(x)^5 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^4 + (70*(a*b^2 + b^3)*cosh(x)^4 + a^3 - a^2*b + 4*a*b^2 + 6*b^3 - 30*(a*b^2 + 2*b^3)*cosh(x)^2)*sinh(x)^4 + 4*(14*(a*b^2 + b^3)*cosh(x)^5 - 10*(a*b^2 + 2*b^3)*cosh(x)^3 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x))*sinh(x)^3 + a^3 + 3*a^2*b + 3*a*b^2 + b^3 + 2*(a^3 - 3*a*b^2 - 2*b^3)*cosh(x)^2 + 2*(14*(a*b^2 + b^3)*cosh(x)^6 - 15*(a*b^2 + 2*b^3)*cosh(x)^4 + a^3 - 3*a*b^2 - 2*b^3 + 3*(a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^2)*sinh(x)^2 + sqrt(2)*(b^2*cosh(x)^6 + 6*b^2*cosh(x)*sinh(x)^5 + b^2*sinh(x)^6 - 3*b^2*cosh(x)^4 + 3*(5*b^2*cosh(x)^2 - b^2)*sinh(x)^4 + 4*(5*b^2*cosh(x)^3 - 3*b^2*cosh(x))*sinh(x)^3 - (a^2 - 2*a*b - 3*b^2)*cosh(x)^2 + (15*b^2*cosh(x)^4 - 18*b^2*cosh(x)^2 - a^2 + 2*a*b + 3*b^2)*sinh(x)^2 - a^2 - 2*a*b - b^2 + 2*(3*b^2*cosh(x)^5 - 6*b^2*cosh(x)^3 - (a^2 - 2*a*b - 3*b^2)*cosh(x))*sinh(x))*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*(2*(a*b^2 + b^3)*cosh(x)^7 - 3*(a*b^2 + 2*b^3)*cosh(x)^5 + (a^3 - a^2*b + 4*a*b^2 + 6*b^3)*cosh(x)^3 + (a^3 - 3*a*b^2 - 2*b^3)*cosh(x))*sinh(x))/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) + 3*((a^5 + 2*a^4*b + a^3*b^2)*cosh(x)^10 + 10*(a^5 + 2*a^4*b + a^3*b^2)*cosh(x)*sinh(x)^9 + (a^5 + 2*a^4*b + a^3*b^2)*sinh(x)^10 + (3*a^5 - 2*a^4*b - 5*a^3*b^2)*cosh(x)^8 + (3*a^5 - 2*a^4*b - 5*a^3*b^2 + 45*(a^5 + 2*a^4*b + a^3*b^2)*cosh(x)^2)*sinh(x)^8 + 8*(15*(a^5 + 2*a^4*b + a^3*b^2)*cosh(x)^3 + (3*a^5 - 2*a^4*b - 5*a^3*b^2)*cosh(x))*sinh(x)^7 + 2*(a^5 - 2*a^4*b + 5*a^3*b^2)*cosh(x)^6 + 2*(a^5 - 2*a^4*b + 5*a^3*b^2 + 105*(a^5 + 2*a^4*b + a^3*b^2)*cosh(x)^4 + 14*(3*a^5 - 2*a^4*b - 5*a^3*b^2)*cosh(x)^2)*sinh(x)^6 + 4*(63*(a^5 + 2*a^4*b + a^3*b^2)*cosh(x)^5 + 14*(3*a^5 - 2*a^4*b - 5*a^3*b^2)*cosh(x)^3 + 3*(a^5 - 2*a^4*b + 5*a^3*b^2)*cosh(x))*sinh(x)^5 - a^5 - 2*a^4*b - a^3*b^2 - 2*(a^5 - 2*a^4*b + 5*a^3*b^2)*cosh(x)^4 + 2*(105*(a^5 + 2*a^4*b + a^3*b^2)*cosh(x)^6 - a^5 + 2*a^4*b - 5*a^3*b^2 + 35*(3*a^5 - 2*a^4*b - 5*a^3*b^2)*cosh(x)^4 + 15*(a^5 - 2*a^4*b + 5*a^3*b^2)*cosh(x)^2)*sinh(x)^4 + 8*(15*(a^5 + 2*a^4*b + a^3*b^2)*cosh(x)^7 + 7*(3*a^5 - 2*a^4*b - 5*a^3*b^2)*cosh(x)^5 + 5*(a^5 - 2*a^4*b + 5*a^3*b^2)*cosh(x)^3 - (a^5 - 2*a^4*b + 5*a^3*b^2)*cosh(x))*sinh(x)^3 - (3*a^5 - 2*a^4*b - 5*a^3*b^2)*cosh(x)^2 + (45*(a^5 + 2*a^4*b + a^3*b^2)*cosh(x)^8 + 28*(3*a^5 - 2*a^4*b - 5*a^3*b^2)*cosh(x)^6 - 3*a^5 + 2*a^4*b + 5*a^3*b^2 + 30*(a^5 - 2*a^4*b + 5*a^3*b^2)*cosh(x)^4 - 12*(a^5 - 2*a^4*b + 5*a^3*b^2)*cosh(x)^2)*sinh(x)^2 + 2*(5*(a^5 + 2*a^4*b + a^3*b^2)*cosh(x)^9 + 4*(3*a^5 - 2*a^4*b - 5*a^3*b^2)*cosh(x)^7 + 6*(a^5 - 2*a^4*b + 5*a^3*b^2)*cosh(x)^5 - 4*(a^5 - 2*a^4*b + 5*a^3*b^2)*cosh(x)^3 - (3*a^5 - 2*a^4*b - 5*a^3*b^2)*cosh(x))*sinh(x))*sqrt(a + b)*log(((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*a*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a)*sinh(x)^2 + sqrt(2)*(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2 + 1)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4*((a + b)*cosh(x)^3 + a*cosh(x))*sinh(x) + a + b)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)) - 4*sqrt(2)*((3*a^5 + 15*a^4*b + 39*a^3*b^2 + 53*a^2*b^3 + 34*a*b^4 + 8*b^5)*cosh(x)^8 + 8*(3*a^5 + 15*a^4*b + 39*a^3*b^2 + 53*a^2*b^3 + 34*a*b^4 + 8*b^5)*cosh(x)*sinh(x)^7 + (3*a^5 + 15*a^4*b + 39*a^3*b^2 + 53*a^2*b^3 + 34*a*b^4 + 8*b^5)*sinh(x)^8 + 4*(3*a^5 + 9*a^4*b + 6*a^3*b^2 - 14*a^2*b^3 - 22*a*b^4 - 8*b^5)*cosh(x)^6 + 4*(3*a^5 + 9*a^4*b + 6*a^3*b^2 - 14*a^2*b^3 - 22*a*b^4 - 8*b^5 + 7*(3*a^5 + 15*a^4*b + 39*a^3*b^2 + 53*a^2*b^3 + 34*a*b^4 + 8*b^5)*cosh(x)^2)*sinh(x)^6 + 8*(7*(3*a^5 + 15*a^4*b + 39*a^3*b^2 + 53*a^2*b^3 + 34*a*b^4 + 8*b^5)*cosh(x)^3 + 3*(3*a^5 + 9*a^4*b + 6*a^3*b^2 - 14*a^2*b^3 - 22*a*b^4 - 8*b^5)*cosh(x))*sinh(x)^5 + 3*a^5 + 15*a^4*b + 39*a^3*b^2 + 53*a^2*b^3 + 34*a*b^4 + 8*b^5 + 6*(3*a^5 + 7*a^4*b + 3*a^3*b^2 + 9*a^2*b^3 + 18*a*b^4 + 8*b^5)*cosh(x)^4 + 2*(9*a^5 + 21*a^4*b + 9*a^3*b^2 + 27*a^2*b^3 + 54*a*b^4 + 24*b^5 + 35*(3*a^5 + 15*a^4*b + 39*a^3*b^2 + 53*a^2*b^3 + 34*a*b^4 + 8*b^5)*cosh(x)^4 + 30*(3*a^5 + 9*a^4*b + 6*a^3*b^2 - 14*a^2*b^3 - 22*a*b^4 - 8*b^5)*cosh(x)^2)*sinh(x)^4 + 8*(7*(3*a^5 + 15*a^4*b + 39*a^3*b^2 + 53*a^2*b^3 + 34*a*b^4 + 8*b^5)*cosh(x)^5 + 10*(3*a^5 + 9*a^4*b + 6*a^3*b^2 - 14*a^2*b^3 - 22*a*b^4 - 8*b^5)*cosh(x)^3 + 3*(3*a^5 + 7*a^4*b + 3*a^3*b^2 + 9*a^2*b^3 + 18*a*b^4 + 8*b^5)*cosh(x))*sinh(x)^3 + 4*(3*a^5 + 9*a^4*b + 6*a^3*b^2 - 14*a^2*b^3 - 22*a*b^4 - 8*b^5)*cosh(x)^2 + 4*(7*(3*a^5 + 15*a^4*b + 39*a^3*b^2 + 53*a^2*b^3 + 34*a*b^4 + 8*b^5)*cosh(x)^6 + 3*a^5 + 9*a^4*b + 6*a^3*b^2 - 14*a^2*b^3 - 22*a*b^4 - 8*b^5 + 15*(3*a^5 + 9*a^4*b + 6*a^3*b^2 - 14*a^2*b^3 - 22*a*b^4 - 8*b^5)*cosh(x)^4 + 9*(3*a^5 + 7*a^4*b + 3*a^3*b^2 + 9*a^2*b^3 + 18*a*b^4 + 8*b^5)*cosh(x)^2)*sinh(x)^2 + 8*((3*a^5 + 15*a^4*b + 39*a^3*b^2 + 53*a^2*b^3 + 34*a*b^4 + 8*b^5)*cosh(x)^7 + 3*(3*a^5 + 9*a^4*b + 6*a^3*b^2 - 14*a^2*b^3 - 22*a*b^4 - 8*b^5)*cosh(x)^5 + 3*(3*a^5 + 7*a^4*b + 3*a^3*b^2 + 9*a^2*b^3 + 18*a*b^4 + 8*b^5)*cosh(x)^3 + (3*a^5 + 9*a^4*b + 6*a^3*b^2 - 14*a^2*b^3 - 22*a*b^4 - 8*b^5)*cosh(x))*sinh(x))*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/((a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*cosh(x)^10 + 10*(a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*cosh(x)*sinh(x)^9 + (a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*sinh(x)^10 + (3*a^8 + 7*a^7*b - 2*a^6*b^2 - 18*a^5*b^3 - 17*a^4*b^4 - 5*a^3*b^5)*cosh(x)^8 + (3*a^8 + 7*a^7*b - 2*a^6*b^2 - 18*a^5*b^3 - 17*a^4*b^4 - 5*a^3*b^5 + 45*(a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*cosh(x)^2)*sinh(x)^8 - a^8 - 5*a^7*b - 10*a^6*b^2 - 10*a^5*b^3 - 5*a^4*b^4 - a^3*b^5 + 8*(15*(a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*cosh(x)^3 + (3*a^8 + 7*a^7*b - 2*a^6*b^2 - 18*a^5*b^3 - 17*a^4*b^4 - 5*a^3*b^5)*cosh(x))*sinh(x)^7 + 2*(a^8 + a^7*b + 2*a^6*b^2 + 10*a^5*b^3 + 13*a^4*b^4 + 5*a^3*b^5)*cosh(x)^6 + 2*(a^8 + a^7*b + 2*a^6*b^2 + 10*a^5*b^3 + 13*a^4*b^4 + 5*a^3*b^5 + 105*(a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*cosh(x)^4 + 14*(3*a^8 + 7*a^7*b - 2*a^6*b^2 - 18*a^5*b^3 - 17*a^4*b^4 - 5*a^3*b^5)*cosh(x)^2)*sinh(x)^6 + 4*(63*(a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*cosh(x)^5 + 14*(3*a^8 + 7*a^7*b - 2*a^6*b^2 - 18*a^5*b^3 - 17*a^4*b^4 - 5*a^3*b^5)*cosh(x)^3 + 3*(a^8 + a^7*b + 2*a^6*b^2 + 10*a^5*b^3 + 13*a^4*b^4 + 5*a^3*b^5)*cosh(x))*sinh(x)^5 - 2*(a^8 + a^7*b + 2*a^6*b^2 + 10*a^5*b^3 + 13*a^4*b^4 + 5*a^3*b^5)*cosh(x)^4 - 2*(a^8 + a^7*b + 2*a^6*b^2 + 10*a^5*b^3 + 13*a^4*b^4 + 5*a^3*b^5 - 105*(a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*cosh(x)^6 - 35*(3*a^8 + 7*a^7*b - 2*a^6*b^2 - 18*a^5*b^3 - 17*a^4*b^4 - 5*a^3*b^5)*cosh(x)^4 - 15*(a^8 + a^7*b + 2*a^6*b^2 + 10*a^5*b^3 + 13*a^4*b^4 + 5*a^3*b^5)*cosh(x)^2)*sinh(x)^4 + 8*(15*(a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*cosh(x)^7 + 7*(3*a^8 + 7*a^7*b - 2*a^6*b^2 - 18*a^5*b^3 - 17*a^4*b^4 - 5*a^3*b^5)*cosh(x)^5 + 5*(a^8 + a^7*b + 2*a^6*b^2 + 10*a^5*b^3 + 13*a^4*b^4 + 5*a^3*b^5)*cosh(x)^3 - (a^8 + a^7*b + 2*a^6*b^2 + 10*a^5*b^3 + 13*a^4*b^4 + 5*a^3*b^5)*cosh(x))*sinh(x)^3 - (3*a^8 + 7*a^7*b - 2*a^6*b^2 - 18*a^5*b^3 - 17*a^4*b^4 - 5*a^3*b^5)*cosh(x)^2 + (45*(a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*cosh(x)^8 - 3*a^8 - 7*a^7*b + 2*a^6*b^2 + 18*a^5*b^3 + 17*a^4*b^4 + 5*a^3*b^5 + 28*(3*a^8 + 7*a^7*b - 2*a^6*b^2 - 18*a^5*b^3 - 17*a^4*b^4 - 5*a^3*b^5)*cosh(x)^6 + 30*(a^8 + a^7*b + 2*a^6*b^2 + 10*a^5*b^3 + 13*a^4*b^4 + 5*a^3*b^5)*cosh(x)^4 - 12*(a^8 + a^7*b + 2*a^6*b^2 + 10*a^5*b^3 + 13*a^4*b^4 + 5*a^3*b^5)*cosh(x)^2)*sinh(x)^2 + 2*(5*(a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*cosh(x)^9 + 4*(3*a^8 + 7*a^7*b - 2*a^6*b^2 - 18*a^5*b^3 - 17*a^4*b^4 - 5*a^3*b^5)*cosh(x)^7 + 6*(a^8 + a^7*b + 2*a^6*b^2 + 10*a^5*b^3 + 13*a^4*b^4 + 5*a^3*b^5)*cosh(x)^5 - 4*(a^8 + a^7*b + 2*a^6*b^2 + 10*a^5*b^3 + 13*a^4*b^4 + 5*a^3*b^5)*cosh(x)^3 - (3*a^8 + 7*a^7*b - 2*a^6*b^2 - 18*a^5*b^3 - 17*a^4*b^4 - 5*a^3*b^5)*cosh(x))*sinh(x)), -1/6*(3*((a^5 + 2*a^4*b + a^3*b^2)*cosh(x)^10 + 10*(a^5 + 2*a^4*b + a^3*b^2)*cosh(x)*sinh(x)^9 + (a^5 + 2*a^4*b + a^3*b^2)*sinh(x)^10 + (3*a^5 - 2*a^4*b - 5*a^3*b^2)*cosh(x)^8 + (3*a^5 - 2*a^4*b - 5*a^3*b^2 + 45*(a^5 + 2*a^4*b + a^3*b^2)*cosh(x)^2)*sinh(x)^8 + 8*(15*(a^5 + 2*a^4*b + a^3*b^2)*cosh(x)^3 + (3*a^5 - 2*a^4*b - 5*a^3*b^2)*cosh(x))*sinh(x)^7 + 2*(a^5 - 2*a^4*b + 5*a^3*b^2)*cosh(x)^6 + 2*(a^5 - 2*a^4*b + 5*a^3*b^2 + 105*(a^5 + 2*a^4*b + a^3*b^2)*cosh(x)^4 + 14*(3*a^5 - 2*a^4*b - 5*a^3*b^2)*cosh(x)^2)*sinh(x)^6 + 4*(63*(a^5 + 2*a^4*b + a^3*b^2)*cosh(x)^5 + 14*(3*a^5 - 2*a^4*b - 5*a^3*b^2)*cosh(x)^3 + 3*(a^5 - 2*a^4*b + 5*a^3*b^2)*cosh(x))*sinh(x)^5 - a^5 - 2*a^4*b - a^3*b^2 - 2*(a^5 - 2*a^4*b + 5*a^3*b^2)*cosh(x)^4 + 2*(105*(a^5 + 2*a^4*b + a^3*b^2)*cosh(x)^6 - a^5 + 2*a^4*b - 5*a^3*b^2 + 35*(3*a^5 - 2*a^4*b - 5*a^3*b^2)*cosh(x)^4 + 15*(a^5 - 2*a^4*b + 5*a^3*b^2)*cosh(x)^2)*sinh(x)^4 + 8*(15*(a^5 + 2*a^4*b + a^3*b^2)*cosh(x)^7 + 7*(3*a^5 - 2*a^4*b - 5*a^3*b^2)*cosh(x)^5 + 5*(a^5 - 2*a^4*b + 5*a^3*b^2)*cosh(x)^3 - (a^5 - 2*a^4*b + 5*a^3*b^2)*cosh(x))*sinh(x)^3 - (3*a^5 - 2*a^4*b - 5*a^3*b^2)*cosh(x)^2 + (45*(a^5 + 2*a^4*b + a^3*b^2)*cosh(x)^8 + 28*(3*a^5 - 2*a^4*b - 5*a^3*b^2)*cosh(x)^6 - 3*a^5 + 2*a^4*b + 5*a^3*b^2 + 30*(a^5 - 2*a^4*b + 5*a^3*b^2)*cosh(x)^4 - 12*(a^5 - 2*a^4*b + 5*a^3*b^2)*cosh(x)^2)*sinh(x)^2 + 2*(5*(a^5 + 2*a^4*b + a^3*b^2)*cosh(x)^9 + 4*(3*a^5 - 2*a^4*b - 5*a^3*b^2)*cosh(x)^7 + 6*(a^5 - 2*a^4*b + 5*a^3*b^2)*cosh(x)^5 - 4*(a^5 - 2*a^4*b + 5*a^3*b^2)*cosh(x)^3 - (3*a^5 - 2*a^4*b - 5*a^3*b^2)*cosh(x))*sinh(x))*sqrt(-a - b)*arctan(sqrt(2)*(b*cosh(x)^2 + 2*b*cosh(x)*sinh(x) + b*sinh(x)^2 - a - b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a*b + b^2)*cosh(x)^4 + 4*(a*b + b^2)*cosh(x)*sinh(x)^3 + (a*b + b^2)*sinh(x)^4 + (a^2 - a*b - 2*b^2)*cosh(x)^2 + (6*(a*b + b^2)*cosh(x)^2 + a^2 - a*b - 2*b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 2*(2*(a*b + b^2)*cosh(x)^3 + (a^2 - a*b - 2*b^2)*cosh(x))*sinh(x))) + 3*((a^5 + 2*a^4*b + a^3*b^2)*cosh(x)^10 + 10*(a^5 + 2*a^4*b + a^3*b^2)*cosh(x)*sinh(x)^9 + (a^5 + 2*a^4*b + a^3*b^2)*sinh(x)^10 + (3*a^5 - 2*a^4*b - 5*a^3*b^2)*cosh(x)^8 + (3*a^5 - 2*a^4*b - 5*a^3*b^2 + 45*(a^5 + 2*a^4*b + a^3*b^2)*cosh(x)^2)*sinh(x)^8 + 8*(15*(a^5 + 2*a^4*b + a^3*b^2)*cosh(x)^3 + (3*a^5 - 2*a^4*b - 5*a^3*b^2)*cosh(x))*sinh(x)^7 + 2*(a^5 - 2*a^4*b + 5*a^3*b^2)*cosh(x)^6 + 2*(a^5 - 2*a^4*b + 5*a^3*b^2 + 105*(a^5 + 2*a^4*b + a^3*b^2)*cosh(x)^4 + 14*(3*a^5 - 2*a^4*b - 5*a^3*b^2)*cosh(x)^2)*sinh(x)^6 + 4*(63*(a^5 + 2*a^4*b + a^3*b^2)*cosh(x)^5 + 14*(3*a^5 - 2*a^4*b - 5*a^3*b^2)*cosh(x)^3 + 3*(a^5 - 2*a^4*b + 5*a^3*b^2)*cosh(x))*sinh(x)^5 - a^5 - 2*a^4*b - a^3*b^2 - 2*(a^5 - 2*a^4*b + 5*a^3*b^2)*cosh(x)^4 + 2*(105*(a^5 + 2*a^4*b + a^3*b^2)*cosh(x)^6 - a^5 + 2*a^4*b - 5*a^3*b^2 + 35*(3*a^5 - 2*a^4*b - 5*a^3*b^2)*cosh(x)^4 + 15*(a^5 - 2*a^4*b + 5*a^3*b^2)*cosh(x)^2)*sinh(x)^4 + 8*(15*(a^5 + 2*a^4*b + a^3*b^2)*cosh(x)^7 + 7*(3*a^5 - 2*a^4*b - 5*a^3*b^2)*cosh(x)^5 + 5*(a^5 - 2*a^4*b + 5*a^3*b^2)*cosh(x)^3 - (a^5 - 2*a^4*b + 5*a^3*b^2)*cosh(x))*sinh(x)^3 - (3*a^5 - 2*a^4*b - 5*a^3*b^2)*cosh(x)^2 + (45*(a^5 + 2*a^4*b + a^3*b^2)*cosh(x)^8 + 28*(3*a^5 - 2*a^4*b - 5*a^3*b^2)*cosh(x)^6 - 3*a^5 + 2*a^4*b + 5*a^3*b^2 + 30*(a^5 - 2*a^4*b + 5*a^3*b^2)*cosh(x)^4 - 12*(a^5 - 2*a^4*b + 5*a^3*b^2)*cosh(x)^2)*sinh(x)^2 + 2*(5*(a^5 + 2*a^4*b + a^3*b^2)*cosh(x)^9 + 4*(3*a^5 - 2*a^4*b - 5*a^3*b^2)*cosh(x)^7 + 6*(a^5 - 2*a^4*b + 5*a^3*b^2)*cosh(x)^5 - 4*(a^5 - 2*a^4*b + 5*a^3*b^2)*cosh(x)^3 - (3*a^5 - 2*a^4*b - 5*a^3*b^2)*cosh(x))*sinh(x))*sqrt(-a - b)*arctan(sqrt(2)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2))/((a + b)*cosh(x)^2 + 2*(a + b)*cosh(x)*sinh(x) + (a + b)*sinh(x)^2 + a + b)) + 2*sqrt(2)*((3*a^5 + 15*a^4*b + 39*a^3*b^2 + 53*a^2*b^3 + 34*a*b^4 + 8*b^5)*cosh(x)^8 + 8*(3*a^5 + 15*a^4*b + 39*a^3*b^2 + 53*a^2*b^3 + 34*a*b^4 + 8*b^5)*cosh(x)*sinh(x)^7 + (3*a^5 + 15*a^4*b + 39*a^3*b^2 + 53*a^2*b^3 + 34*a*b^4 + 8*b^5)*sinh(x)^8 + 4*(3*a^5 + 9*a^4*b + 6*a^3*b^2 - 14*a^2*b^3 - 22*a*b^4 - 8*b^5)*cosh(x)^6 + 4*(3*a^5 + 9*a^4*b + 6*a^3*b^2 - 14*a^2*b^3 - 22*a*b^4 - 8*b^5 + 7*(3*a^5 + 15*a^4*b + 39*a^3*b^2 + 53*a^2*b^3 + 34*a*b^4 + 8*b^5)*cosh(x)^2)*sinh(x)^6 + 8*(7*(3*a^5 + 15*a^4*b + 39*a^3*b^2 + 53*a^2*b^3 + 34*a*b^4 + 8*b^5)*cosh(x)^3 + 3*(3*a^5 + 9*a^4*b + 6*a^3*b^2 - 14*a^2*b^3 - 22*a*b^4 - 8*b^5)*cosh(x))*sinh(x)^5 + 3*a^5 + 15*a^4*b + 39*a^3*b^2 + 53*a^2*b^3 + 34*a*b^4 + 8*b^5 + 6*(3*a^5 + 7*a^4*b + 3*a^3*b^2 + 9*a^2*b^3 + 18*a*b^4 + 8*b^5)*cosh(x)^4 + 2*(9*a^5 + 21*a^4*b + 9*a^3*b^2 + 27*a^2*b^3 + 54*a*b^4 + 24*b^5 + 35*(3*a^5 + 15*a^4*b + 39*a^3*b^2 + 53*a^2*b^3 + 34*a*b^4 + 8*b^5)*cosh(x)^4 + 30*(3*a^5 + 9*a^4*b + 6*a^3*b^2 - 14*a^2*b^3 - 22*a*b^4 - 8*b^5)*cosh(x)^2)*sinh(x)^4 + 8*(7*(3*a^5 + 15*a^4*b + 39*a^3*b^2 + 53*a^2*b^3 + 34*a*b^4 + 8*b^5)*cosh(x)^5 + 10*(3*a^5 + 9*a^4*b + 6*a^3*b^2 - 14*a^2*b^3 - 22*a*b^4 - 8*b^5)*cosh(x)^3 + 3*(3*a^5 + 7*a^4*b + 3*a^3*b^2 + 9*a^2*b^3 + 18*a*b^4 + 8*b^5)*cosh(x))*sinh(x)^3 + 4*(3*a^5 + 9*a^4*b + 6*a^3*b^2 - 14*a^2*b^3 - 22*a*b^4 - 8*b^5)*cosh(x)^2 + 4*(7*(3*a^5 + 15*a^4*b + 39*a^3*b^2 + 53*a^2*b^3 + 34*a*b^4 + 8*b^5)*cosh(x)^6 + 3*a^5 + 9*a^4*b + 6*a^3*b^2 - 14*a^2*b^3 - 22*a*b^4 - 8*b^5 + 15*(3*a^5 + 9*a^4*b + 6*a^3*b^2 - 14*a^2*b^3 - 22*a*b^4 - 8*b^5)*cosh(x)^4 + 9*(3*a^5 + 7*a^4*b + 3*a^3*b^2 + 9*a^2*b^3 + 18*a*b^4 + 8*b^5)*cosh(x)^2)*sinh(x)^2 + 8*((3*a^5 + 15*a^4*b + 39*a^3*b^2 + 53*a^2*b^3 + 34*a*b^4 + 8*b^5)*cosh(x)^7 + 3*(3*a^5 + 9*a^4*b + 6*a^3*b^2 - 14*a^2*b^3 - 22*a*b^4 - 8*b^5)*cosh(x)^5 + 3*(3*a^5 + 7*a^4*b + 3*a^3*b^2 + 9*a^2*b^3 + 18*a*b^4 + 8*b^5)*cosh(x)^3 + (3*a^5 + 9*a^4*b + 6*a^3*b^2 - 14*a^2*b^3 - 22*a*b^4 - 8*b^5)*cosh(x))*sinh(x))*sqrt(((a + b)*cosh(x)^2 + (a + b)*sinh(x)^2 + a - b)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)))/((a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*cosh(x)^10 + 10*(a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*cosh(x)*sinh(x)^9 + (a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*sinh(x)^10 + (3*a^8 + 7*a^7*b - 2*a^6*b^2 - 18*a^5*b^3 - 17*a^4*b^4 - 5*a^3*b^5)*cosh(x)^8 + (3*a^8 + 7*a^7*b - 2*a^6*b^2 - 18*a^5*b^3 - 17*a^4*b^4 - 5*a^3*b^5 + 45*(a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*cosh(x)^2)*sinh(x)^8 - a^8 - 5*a^7*b - 10*a^6*b^2 - 10*a^5*b^3 - 5*a^4*b^4 - a^3*b^5 + 8*(15*(a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*cosh(x)^3 + (3*a^8 + 7*a^7*b - 2*a^6*b^2 - 18*a^5*b^3 - 17*a^4*b^4 - 5*a^3*b^5)*cosh(x))*sinh(x)^7 + 2*(a^8 + a^7*b + 2*a^6*b^2 + 10*a^5*b^3 + 13*a^4*b^4 + 5*a^3*b^5)*cosh(x)^6 + 2*(a^8 + a^7*b + 2*a^6*b^2 + 10*a^5*b^3 + 13*a^4*b^4 + 5*a^3*b^5 + 105*(a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*cosh(x)^4 + 14*(3*a^8 + 7*a^7*b - 2*a^6*b^2 - 18*a^5*b^3 - 17*a^4*b^4 - 5*a^3*b^5)*cosh(x)^2)*sinh(x)^6 + 4*(63*(a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*cosh(x)^5 + 14*(3*a^8 + 7*a^7*b - 2*a^6*b^2 - 18*a^5*b^3 - 17*a^4*b^4 - 5*a^3*b^5)*cosh(x)^3 + 3*(a^8 + a^7*b + 2*a^6*b^2 + 10*a^5*b^3 + 13*a^4*b^4 + 5*a^3*b^5)*cosh(x))*sinh(x)^5 - 2*(a^8 + a^7*b + 2*a^6*b^2 + 10*a^5*b^3 + 13*a^4*b^4 + 5*a^3*b^5)*cosh(x)^4 - 2*(a^8 + a^7*b + 2*a^6*b^2 + 10*a^5*b^3 + 13*a^4*b^4 + 5*a^3*b^5 - 105*(a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*cosh(x)^6 - 35*(3*a^8 + 7*a^7*b - 2*a^6*b^2 - 18*a^5*b^3 - 17*a^4*b^4 - 5*a^3*b^5)*cosh(x)^4 - 15*(a^8 + a^7*b + 2*a^6*b^2 + 10*a^5*b^3 + 13*a^4*b^4 + 5*a^3*b^5)*cosh(x)^2)*sinh(x)^4 + 8*(15*(a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*cosh(x)^7 + 7*(3*a^8 + 7*a^7*b - 2*a^6*b^2 - 18*a^5*b^3 - 17*a^4*b^4 - 5*a^3*b^5)*cosh(x)^5 + 5*(a^8 + a^7*b + 2*a^6*b^2 + 10*a^5*b^3 + 13*a^4*b^4 + 5*a^3*b^5)*cosh(x)^3 - (a^8 + a^7*b + 2*a^6*b^2 + 10*a^5*b^3 + 13*a^4*b^4 + 5*a^3*b^5)*cosh(x))*sinh(x)^3 - (3*a^8 + 7*a^7*b - 2*a^6*b^2 - 18*a^5*b^3 - 17*a^4*b^4 - 5*a^3*b^5)*cosh(x)^2 + (45*(a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*cosh(x)^8 - 3*a^8 - 7*a^7*b + 2*a^6*b^2 + 18*a^5*b^3 + 17*a^4*b^4 + 5*a^3*b^5 + 28*(3*a^8 + 7*a^7*b - 2*a^6*b^2 - 18*a^5*b^3 - 17*a^4*b^4 - 5*a^3*b^5)*cosh(x)^6 + 30*(a^8 + a^7*b + 2*a^6*b^2 + 10*a^5*b^3 + 13*a^4*b^4 + 5*a^3*b^5)*cosh(x)^4 - 12*(a^8 + a^7*b + 2*a^6*b^2 + 10*a^5*b^3 + 13*a^4*b^4 + 5*a^3*b^5)*cosh(x)^2)*sinh(x)^2 + 2*(5*(a^8 + 5*a^7*b + 10*a^6*b^2 + 10*a^5*b^3 + 5*a^4*b^4 + a^3*b^5)*cosh(x)^9 + 4*(3*a^8 + 7*a^7*b - 2*a^6*b^2 - 18*a^5*b^3 - 17*a^4*b^4 - 5*a^3*b^5)*cosh(x)^7 + 6*(a^8 + a^7*b + 2*a^6*b^2 + 10*a^5*b^3 + 13*a^4*b^4 + 5*a^3*b^5)*cosh(x)^5 - 4*(a^8 + a^7*b + 2*a^6*b^2 + 10*a^5*b^3 + 13*a^4*b^4 + 5*a^3*b^5)*cosh(x)^3 - (3*a^8 + 7*a^7*b - 2*a^6*b^2 - 18*a^5*b^3 - 17*a^4*b^4 - 5*a^3*b^5)*cosh(x))*sinh(x))]","B",0
255,1,543,0,0.445814," ","integrate(1/(1+tanh(x)^2)^(1/2),x, algorithm=""fricas"")","\frac{1}{8} \, \sqrt{2} \log\left(-\frac{2 \, {\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} - 3\right)} \sinh\left(x\right)^{6} - 3 \, \cosh\left(x\right)^{6} + 2 \, {\left(28 \, \cosh\left(x\right)^{3} - 9 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 5 \, {\left(14 \, \cosh\left(x\right)^{4} - 9 \, \cosh\left(x\right)^{2} + 1\right)} \sinh\left(x\right)^{4} + 5 \, \cosh\left(x\right)^{4} + 4 \, {\left(14 \, \cosh\left(x\right)^{5} - 15 \, \cosh\left(x\right)^{3} + 5 \, \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(28 \, \cosh\left(x\right)^{6} - 45 \, \cosh\left(x\right)^{4} + 30 \, \cosh\left(x\right)^{2} - 4\right)} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right)^{2} + 2 \, {\left(4 \, \cosh\left(x\right)^{7} - 9 \, \cosh\left(x\right)^{5} + 10 \, \cosh\left(x\right)^{3} - 4 \, \cosh\left(x\right)\right)} \sinh\left(x\right) + {\left(\sqrt{2} \cosh\left(x\right)^{6} + 6 \, \sqrt{2} \cosh\left(x\right) \sinh\left(x\right)^{5} + \sqrt{2} \sinh\left(x\right)^{6} + 3 \, {\left(5 \, \sqrt{2} \cosh\left(x\right)^{2} - \sqrt{2}\right)} \sinh\left(x\right)^{4} - 3 \, \sqrt{2} \cosh\left(x\right)^{4} + 4 \, {\left(5 \, \sqrt{2} \cosh\left(x\right)^{3} - 3 \, \sqrt{2} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + {\left(15 \, \sqrt{2} \cosh\left(x\right)^{4} - 18 \, \sqrt{2} \cosh\left(x\right)^{2} + 4 \, \sqrt{2}\right)} \sinh\left(x\right)^{2} + 4 \, \sqrt{2} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, \sqrt{2} \cosh\left(x\right)^{5} - 6 \, \sqrt{2} \cosh\left(x\right)^{3} + 4 \, \sqrt{2} \cosh\left(x\right)\right)} \sinh\left(x\right) - 4 \, \sqrt{2}\right)} \sqrt{\frac{\cosh\left(x\right)^{2} + \sinh\left(x\right)^{2}}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 4\right)}}{\cosh\left(x\right)^{6} + 6 \, \cosh\left(x\right)^{5} \sinh\left(x\right) + 15 \, \cosh\left(x\right)^{4} \sinh\left(x\right)^{2} + 20 \, \cosh\left(x\right)^{3} \sinh\left(x\right)^{3} + 15 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{4} + 6 \, \cosh\left(x\right) \sinh\left(x\right)^{5} + \sinh\left(x\right)^{6}}\right) + \frac{1}{8} \, \sqrt{2} \log\left(\frac{2 \, {\left(\cosh\left(x\right)^{4} + 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4} + {\left(6 \, \cosh\left(x\right)^{2} + 1\right)} \sinh\left(x\right)^{2} + \cosh\left(x\right)^{2} + 2 \, {\left(2 \, \cosh\left(x\right)^{3} + \cosh\left(x\right)\right)} \sinh\left(x\right) + {\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)} \sqrt{\frac{\cosh\left(x\right)^{2} + \sinh\left(x\right)^{2}}{\cosh\left(x\right)^{2} - 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}} + 1\right)}}{\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}}\right)"," ",0,"1/8*sqrt(2)*log(-2*(cosh(x)^8 + 8*cosh(x)*sinh(x)^7 + sinh(x)^8 + (28*cosh(x)^2 - 3)*sinh(x)^6 - 3*cosh(x)^6 + 2*(28*cosh(x)^3 - 9*cosh(x))*sinh(x)^5 + 5*(14*cosh(x)^4 - 9*cosh(x)^2 + 1)*sinh(x)^4 + 5*cosh(x)^4 + 4*(14*cosh(x)^5 - 15*cosh(x)^3 + 5*cosh(x))*sinh(x)^3 + (28*cosh(x)^6 - 45*cosh(x)^4 + 30*cosh(x)^2 - 4)*sinh(x)^2 - 4*cosh(x)^2 + 2*(4*cosh(x)^7 - 9*cosh(x)^5 + 10*cosh(x)^3 - 4*cosh(x))*sinh(x) + (sqrt(2)*cosh(x)^6 + 6*sqrt(2)*cosh(x)*sinh(x)^5 + sqrt(2)*sinh(x)^6 + 3*(5*sqrt(2)*cosh(x)^2 - sqrt(2))*sinh(x)^4 - 3*sqrt(2)*cosh(x)^4 + 4*(5*sqrt(2)*cosh(x)^3 - 3*sqrt(2)*cosh(x))*sinh(x)^3 + (15*sqrt(2)*cosh(x)^4 - 18*sqrt(2)*cosh(x)^2 + 4*sqrt(2))*sinh(x)^2 + 4*sqrt(2)*cosh(x)^2 + 2*(3*sqrt(2)*cosh(x)^5 - 6*sqrt(2)*cosh(x)^3 + 4*sqrt(2)*cosh(x))*sinh(x) - 4*sqrt(2))*sqrt((cosh(x)^2 + sinh(x)^2)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 4)/(cosh(x)^6 + 6*cosh(x)^5*sinh(x) + 15*cosh(x)^4*sinh(x)^2 + 20*cosh(x)^3*sinh(x)^3 + 15*cosh(x)^2*sinh(x)^4 + 6*cosh(x)*sinh(x)^5 + sinh(x)^6)) + 1/8*sqrt(2)*log(2*(cosh(x)^4 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4 + (6*cosh(x)^2 + 1)*sinh(x)^2 + cosh(x)^2 + 2*(2*cosh(x)^3 + cosh(x))*sinh(x) + (sqrt(2)*cosh(x)^2 + 2*sqrt(2)*cosh(x)*sinh(x) + sqrt(2)*sinh(x)^2 + sqrt(2))*sqrt((cosh(x)^2 + sinh(x)^2)/(cosh(x)^2 - 2*cosh(x)*sinh(x) + sinh(x)^2)) + 1)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2))","B",0
256,1,175,0,0.406695," ","integrate(1/(-1-tanh(x)^2)^(1/2),x, algorithm=""fricas"")","\frac{1}{8} i \, \sqrt{2} \log\left(\frac{1}{2} \, {\left(i \, \sqrt{2} \sqrt{-2 \, e^{\left(4 \, x\right)} - 2} + 2 \, e^{\left(2 \, x\right)} + 2\right)} e^{\left(-2 \, x\right)}\right) - \frac{1}{8} i \, \sqrt{2} \log\left(\frac{1}{2} \, {\left(-i \, \sqrt{2} \sqrt{-2 \, e^{\left(4 \, x\right)} - 2} + 2 \, e^{\left(2 \, x\right)} + 2\right)} e^{\left(-2 \, x\right)}\right) - \frac{1}{8} i \, \sqrt{2} \log\left({\left(\sqrt{-2 \, e^{\left(4 \, x\right)} - 2} {\left(e^{\left(2 \, x\right)} - 2\right)} + i \, \sqrt{2} e^{\left(4 \, x\right)} - i \, \sqrt{2} e^{\left(2 \, x\right)} + 2 i \, \sqrt{2}\right)} e^{\left(-4 \, x\right)}\right) + \frac{1}{8} i \, \sqrt{2} \log\left({\left(\sqrt{-2 \, e^{\left(4 \, x\right)} - 2} {\left(e^{\left(2 \, x\right)} - 2\right)} - i \, \sqrt{2} e^{\left(4 \, x\right)} + i \, \sqrt{2} e^{\left(2 \, x\right)} - 2 i \, \sqrt{2}\right)} e^{\left(-4 \, x\right)}\right)"," ",0,"1/8*I*sqrt(2)*log(1/2*(I*sqrt(2)*sqrt(-2*e^(4*x) - 2) + 2*e^(2*x) + 2)*e^(-2*x)) - 1/8*I*sqrt(2)*log(1/2*(-I*sqrt(2)*sqrt(-2*e^(4*x) - 2) + 2*e^(2*x) + 2)*e^(-2*x)) - 1/8*I*sqrt(2)*log((sqrt(-2*e^(4*x) - 2)*(e^(2*x) - 2) + I*sqrt(2)*e^(4*x) - I*sqrt(2)*e^(2*x) + 2*I*sqrt(2))*e^(-4*x)) + 1/8*I*sqrt(2)*log((sqrt(-2*e^(4*x) - 2)*(e^(2*x) - 2) - I*sqrt(2)*e^(4*x) + I*sqrt(2)*e^(2*x) - 2*I*sqrt(2))*e^(-4*x))","C",0
257,1,2074,0,0.430263," ","integrate((a+b*tanh(d*x+c)^3)^2,x, algorithm=""fricas"")","\frac{15 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} d x \cosh\left(d x + c\right)^{10} + 150 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} d x \cosh\left(d x + c\right) \sinh\left(d x + c\right)^{9} + 15 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} d x \sinh\left(d x + c\right)^{10} + 15 \, {\left(5 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} d x + 4 \, a b + 6 \, b^{2}\right)} \cosh\left(d x + c\right)^{8} + 15 \, {\left(45 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} d x \cosh\left(d x + c\right)^{2} + 5 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} d x + 4 \, a b + 6 \, b^{2}\right)} \sinh\left(d x + c\right)^{8} + 120 \, {\left(15 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} d x \cosh\left(d x + c\right)^{3} + {\left(5 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} d x + 4 \, a b + 6 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{7} + 30 \, {\left(5 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} d x + 6 \, a b + 6 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 30 \, {\left(105 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} d x \cosh\left(d x + c\right)^{4} + 5 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} d x + 14 \, {\left(5 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} d x + 4 \, a b + 6 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 6 \, a b + 6 \, b^{2}\right)} \sinh\left(d x + c\right)^{6} + 60 \, {\left(63 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} d x \cosh\left(d x + c\right)^{5} + 14 \, {\left(5 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} d x + 4 \, a b + 6 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + 3 \, {\left(5 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} d x + 6 \, a b + 6 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{5} + 10 \, {\left(15 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} d x + 18 \, a b + 28 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 10 \, {\left(315 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} d x \cosh\left(d x + c\right)^{6} + 105 \, {\left(5 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} d x + 4 \, a b + 6 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 15 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} d x + 45 \, {\left(5 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} d x + 6 \, a b + 6 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 18 \, a b + 28 \, b^{2}\right)} \sinh\left(d x + c\right)^{4} + 40 \, {\left(45 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} d x \cosh\left(d x + c\right)^{7} + 21 \, {\left(5 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} d x + 4 \, a b + 6 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 15 \, {\left(5 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} d x + 6 \, a b + 6 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(15 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} d x + 18 \, a b + 28 \, b^{2}\right)} \cosh\left(d x + c\right)\right)} \sinh\left(d x + c\right)^{3} + 15 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} d x + 5 \, {\left(15 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} d x + 12 \, a b + 28 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 5 \, {\left(135 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} d x \cosh\left(d x + c\right)^{8} + 84 \, {\left(5 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} d x + 4 \, a b + 6 \, b^{2}\right)} \cosh\left(d x + c\right)^{6} + 90 \, {\left(5 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} d x + 6 \, a b + 6 \, b^{2}\right)} \cosh\left(d x + c\right)^{4} + 15 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} d x + 12 \, {\left(15 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} d x + 18 \, a b + 28 \, b^{2}\right)} \cosh\left(d x + c\right)^{2} + 12 \, a b + 28 \, b^{2}\right)} \sinh\left(d x + c\right)^{2} + 46 \, b^{2} + 30 \, {\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(\frac{2 \, \cosh\left(d x + c\right)}{\cosh\left(d x + c\right) - \sinh\left(d x + c\right)}\right) + 10 \, {\left(15 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} d x \cosh\left(d x + c\right)^{9} + 12 \, {\left(5 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} d x + 4 \, a b + 6 \, b^{2}\right)} \cosh\left(d x + c\right)^{7} + 18 \, {\left(5 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} d x + 6 \, a b + 6 \, b^{2}\right)} \cosh\left(d x + c\right)^{5} + 4 \, {\left(15 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} d x + 18 \, a b + 28 \, b^{2}\right)} \cosh\left(d x + c\right)^{3} + {\left(15 \, {\left(a^{2} - 2 \, a b + b^{2}\right)} d x + 12 \, a b + 28 \, b^{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*(a^2 - 2*a*b + b^2)*d*x*cosh(d*x + c)^10 + 150*(a^2 - 2*a*b + b^2)*d*x*cosh(d*x + c)*sinh(d*x + c)^9 + 15*(a^2 - 2*a*b + b^2)*d*x*sinh(d*x + c)^10 + 15*(5*(a^2 - 2*a*b + b^2)*d*x + 4*a*b + 6*b^2)*cosh(d*x + c)^8 + 15*(45*(a^2 - 2*a*b + b^2)*d*x*cosh(d*x + c)^2 + 5*(a^2 - 2*a*b + b^2)*d*x + 4*a*b + 6*b^2)*sinh(d*x + c)^8 + 120*(15*(a^2 - 2*a*b + b^2)*d*x*cosh(d*x + c)^3 + (5*(a^2 - 2*a*b + b^2)*d*x + 4*a*b + 6*b^2)*cosh(d*x + c))*sinh(d*x + c)^7 + 30*(5*(a^2 - 2*a*b + b^2)*d*x + 6*a*b + 6*b^2)*cosh(d*x + c)^6 + 30*(105*(a^2 - 2*a*b + b^2)*d*x*cosh(d*x + c)^4 + 5*(a^2 - 2*a*b + b^2)*d*x + 14*(5*(a^2 - 2*a*b + b^2)*d*x + 4*a*b + 6*b^2)*cosh(d*x + c)^2 + 6*a*b + 6*b^2)*sinh(d*x + c)^6 + 60*(63*(a^2 - 2*a*b + b^2)*d*x*cosh(d*x + c)^5 + 14*(5*(a^2 - 2*a*b + b^2)*d*x + 4*a*b + 6*b^2)*cosh(d*x + c)^3 + 3*(5*(a^2 - 2*a*b + b^2)*d*x + 6*a*b + 6*b^2)*cosh(d*x + c))*sinh(d*x + c)^5 + 10*(15*(a^2 - 2*a*b + b^2)*d*x + 18*a*b + 28*b^2)*cosh(d*x + c)^4 + 10*(315*(a^2 - 2*a*b + b^2)*d*x*cosh(d*x + c)^6 + 105*(5*(a^2 - 2*a*b + b^2)*d*x + 4*a*b + 6*b^2)*cosh(d*x + c)^4 + 15*(a^2 - 2*a*b + b^2)*d*x + 45*(5*(a^2 - 2*a*b + b^2)*d*x + 6*a*b + 6*b^2)*cosh(d*x + c)^2 + 18*a*b + 28*b^2)*sinh(d*x + c)^4 + 40*(45*(a^2 - 2*a*b + b^2)*d*x*cosh(d*x + c)^7 + 21*(5*(a^2 - 2*a*b + b^2)*d*x + 4*a*b + 6*b^2)*cosh(d*x + c)^5 + 15*(5*(a^2 - 2*a*b + b^2)*d*x + 6*a*b + 6*b^2)*cosh(d*x + c)^3 + (15*(a^2 - 2*a*b + b^2)*d*x + 18*a*b + 28*b^2)*cosh(d*x + c))*sinh(d*x + c)^3 + 15*(a^2 - 2*a*b + b^2)*d*x + 5*(15*(a^2 - 2*a*b + b^2)*d*x + 12*a*b + 28*b^2)*cosh(d*x + c)^2 + 5*(135*(a^2 - 2*a*b + b^2)*d*x*cosh(d*x + c)^8 + 84*(5*(a^2 - 2*a*b + b^2)*d*x + 4*a*b + 6*b^2)*cosh(d*x + c)^6 + 90*(5*(a^2 - 2*a*b + b^2)*d*x + 6*a*b + 6*b^2)*cosh(d*x + c)^4 + 15*(a^2 - 2*a*b + b^2)*d*x + 12*(15*(a^2 - 2*a*b + b^2)*d*x + 18*a*b + 28*b^2)*cosh(d*x + c)^2 + 12*a*b + 28*b^2)*sinh(d*x + c)^2 + 46*b^2 + 30*(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(2*cosh(d*x + c)/(cosh(d*x + c) - sinh(d*x + c))) + 10*(15*(a^2 - 2*a*b + b^2)*d*x*cosh(d*x + c)^9 + 12*(5*(a^2 - 2*a*b + b^2)*d*x + 4*a*b + 6*b^2)*cosh(d*x + c)^7 + 18*(5*(a^2 - 2*a*b + b^2)*d*x + 6*a*b + 6*b^2)*cosh(d*x + c)^5 + 4*(15*(a^2 - 2*a*b + b^2)*d*x + 18*a*b + 28*b^2)*cosh(d*x + c)^3 + (15*(a^2 - 2*a*b + b^2)*d*x + 12*a*b + 28*b^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
258,1,95,0,0.527060," ","integrate(1/(1+tanh(x)^3),x, algorithm=""fricas"")","\frac{18 \, x \cosh\left(x\right)^{2} + 36 \, x \cosh\left(x\right) \sinh\left(x\right) + 18 \, x \sinh\left(x\right)^{2} - 8 \, {\left(\sqrt{3} \cosh\left(x\right)^{2} + 2 \, \sqrt{3} \cosh\left(x\right) \sinh\left(x\right) + \sqrt{3} \sinh\left(x\right)^{2}\right)} \arctan\left(-\frac{\sqrt{3} \cosh\left(x\right) + \sqrt{3} \sinh\left(x\right)}{3 \, {\left(\cosh\left(x\right) - \sinh\left(x\right)\right)}}\right) - 3}{36 \, {\left(\cosh\left(x\right)^{2} + 2 \, \cosh\left(x\right) \sinh\left(x\right) + \sinh\left(x\right)^{2}\right)}}"," ",0,"1/36*(18*x*cosh(x)^2 + 36*x*cosh(x)*sinh(x) + 18*x*sinh(x)^2 - 8*(sqrt(3)*cosh(x)^2 + 2*sqrt(3)*cosh(x)*sinh(x) + sqrt(3)*sinh(x)^2)*arctan(-1/3*(sqrt(3)*cosh(x) + sqrt(3)*sinh(x))/(cosh(x) - sinh(x))) - 3)/(cosh(x)^2 + 2*cosh(x)*sinh(x) + sinh(x)^2)","B",0
259,-1,0,0,0.000000," ","integrate(tanh(x)*(a+b*tanh(x)^4)^(3/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
260,1,5136,0,0.649134," ","integrate(tanh(x)*(a+b*tanh(x)^4)^(1/2),x, algorithm=""fricas"")","\left[\frac{{\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)} \sqrt{b} \log\left(-\frac{{\left(a + 2 \, b\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a + 2 \, b\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a + 2 \, b\right)} \sinh\left(x\right)^{8} + 4 \, {\left(a - 2 \, b\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + a - 2 \, b\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a - 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 6 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{4} + 30 \, {\left(a - 2 \, b\right)} \cosh\left(x\right)^{2} + 3 \, a + 6 \, b\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{5} + 10 \, {\left(a - 2 \, b\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(a - 2 \, b\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{6} + 15 \, {\left(a - 2 \, b\right)} \cosh\left(x\right)^{4} + 9 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + a - 2 \, b\right)} \sinh\left(x\right)^{2} - 2 \, \sqrt{2} {\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)} \sqrt{b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 4 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, a - 2 \, b\right)} \sinh\left(x\right)^{2} + 3 \, a + 3 \, b}{\cosh\left(x\right)^{4} - 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}} + 8 \, {\left({\left(a + 2 \, b\right)} \cosh\left(x\right)^{7} + 3 \, {\left(a - 2 \, b\right)} \cosh\left(x\right)^{5} + 3 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{3} + {\left(a - 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + 2 \, b}{\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) + {\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)} \sqrt{a + b} \log\left(\frac{{\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(x\right)^{8} + 4 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{2} + 2 \, a b + 3 \, b^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{4} + 30 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} + 2 \, a b + 3 \, b^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b + 3 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(3 \, a^{2} + 2 \, a b + 3 \, b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left({\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 4 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, a - 2 \, b\right)} \sinh\left(x\right)^{2} + 3 \, a + 3 \, b}{\cosh\left(x\right)^{4} - 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}} + a^{2} + 2 \, a b + b^{2} + 8 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{2} + 2 \, a b + 3 \, b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{4} + 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} + 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}\right) - 2 \, \sqrt{2} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 4 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, a - 2 \, b\right)} \sinh\left(x\right)^{2} + 3 \, a + 3 \, b}{\cosh\left(x\right)^{4} - 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}}}{4 \, {\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)}}, -\frac{2 \, {\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)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left({\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 4 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, a - 2 \, b\right)} \sinh\left(x\right)^{2} + 3 \, a + 3 \, b}{\cosh\left(x\right)^{4} - 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}}}{{\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(x\right)^{8} + 4 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 6 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{4} + 30 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} + 6 \, a b + 3 \, b^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{4} + 9 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 8 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{5} + 3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) - {\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)} \sqrt{b} \log\left(-\frac{{\left(a + 2 \, b\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a + 2 \, b\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a + 2 \, b\right)} \sinh\left(x\right)^{8} + 4 \, {\left(a - 2 \, b\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + a - 2 \, b\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a - 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 6 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{4} + 30 \, {\left(a - 2 \, b\right)} \cosh\left(x\right)^{2} + 3 \, a + 6 \, b\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{5} + 10 \, {\left(a - 2 \, b\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(a - 2 \, b\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{6} + 15 \, {\left(a - 2 \, b\right)} \cosh\left(x\right)^{4} + 9 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{2} + a - 2 \, b\right)} \sinh\left(x\right)^{2} - 2 \, \sqrt{2} {\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)} \sqrt{b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 4 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, a - 2 \, b\right)} \sinh\left(x\right)^{2} + 3 \, a + 3 \, b}{\cosh\left(x\right)^{4} - 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}} + 8 \, {\left({\left(a + 2 \, b\right)} \cosh\left(x\right)^{7} + 3 \, {\left(a - 2 \, b\right)} \cosh\left(x\right)^{5} + 3 \, {\left(a + 2 \, b\right)} \cosh\left(x\right)^{3} + {\left(a - 2 \, b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + 2 \, b}{\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) + 2 \, \sqrt{2} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 4 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, a - 2 \, b\right)} \sinh\left(x\right)^{2} + 3 \, a + 3 \, b}{\cosh\left(x\right)^{4} - 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}}}{4 \, {\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)}}, \frac{2 \, {\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)} \sqrt{-b} \arctan\left(\frac{\sqrt{2} \sqrt{-b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 4 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, a - 2 \, b\right)} \sinh\left(x\right)^{2} + 3 \, a + 3 \, b}{\cosh\left(x\right)^{4} - 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}}}{b \cosh\left(x\right)^{4} + 4 \, b \cosh\left(x\right) \sinh\left(x\right)^{3} + b \sinh\left(x\right)^{4} - 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b \cosh\left(x\right)^{2} - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(b \cosh\left(x\right)^{3} - b \cosh\left(x\right)\right)} \sinh\left(x\right) + b}\right) + {\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)} \sqrt{a + b} \log\left(\frac{{\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(x\right)^{8} + 4 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{2} + 2 \, a b + 3 \, b^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{4} + 30 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} + 2 \, a b + 3 \, b^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b + 3 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(3 \, a^{2} + 2 \, a b + 3 \, b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left({\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 4 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, a - 2 \, b\right)} \sinh\left(x\right)^{2} + 3 \, a + 3 \, b}{\cosh\left(x\right)^{4} - 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}} + a^{2} + 2 \, a b + b^{2} + 8 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{2} + 2 \, a b + 3 \, b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{4} + 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} + 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}\right) - 2 \, \sqrt{2} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 4 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, a - 2 \, b\right)} \sinh\left(x\right)^{2} + 3 \, a + 3 \, b}{\cosh\left(x\right)^{4} - 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}}}{4 \, {\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)}}, -\frac{{\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)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left({\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 4 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, a - 2 \, b\right)} \sinh\left(x\right)^{2} + 3 \, a + 3 \, b}{\cosh\left(x\right)^{4} - 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}}}{{\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(x\right)^{8} + 4 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 6 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{4} + 30 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} + 6 \, a b + 3 \, b^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{4} + 9 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 8 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{5} + 3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) - {\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)} \sqrt{-b} \arctan\left(\frac{\sqrt{2} \sqrt{-b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 4 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, a - 2 \, b\right)} \sinh\left(x\right)^{2} + 3 \, a + 3 \, b}{\cosh\left(x\right)^{4} - 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}}}{b \cosh\left(x\right)^{4} + 4 \, b \cosh\left(x\right) \sinh\left(x\right)^{3} + b \sinh\left(x\right)^{4} - 2 \, b \cosh\left(x\right)^{2} + 2 \, {\left(3 \, b \cosh\left(x\right)^{2} - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left(b \cosh\left(x\right)^{3} - b \cosh\left(x\right)\right)} \sinh\left(x\right) + b}\right) + \sqrt{2} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 4 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, a - 2 \, b\right)} \sinh\left(x\right)^{2} + 3 \, a + 3 \, b}{\cosh\left(x\right)^{4} - 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}}}{2 \, {\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)}}\right]"," ",0,"[1/4*((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)*sqrt(b)*log(-((a + 2*b)*cosh(x)^8 + 8*(a + 2*b)*cosh(x)*sinh(x)^7 + (a + 2*b)*sinh(x)^8 + 4*(a - 2*b)*cosh(x)^6 + 4*(7*(a + 2*b)*cosh(x)^2 + a - 2*b)*sinh(x)^6 + 8*(7*(a + 2*b)*cosh(x)^3 + 3*(a - 2*b)*cosh(x))*sinh(x)^5 + 6*(a + 2*b)*cosh(x)^4 + 2*(35*(a + 2*b)*cosh(x)^4 + 30*(a - 2*b)*cosh(x)^2 + 3*a + 6*b)*sinh(x)^4 + 8*(7*(a + 2*b)*cosh(x)^5 + 10*(a - 2*b)*cosh(x)^3 + 3*(a + 2*b)*cosh(x))*sinh(x)^3 + 4*(a - 2*b)*cosh(x)^2 + 4*(7*(a + 2*b)*cosh(x)^6 + 15*(a - 2*b)*cosh(x)^4 + 9*(a + 2*b)*cosh(x)^2 + a - 2*b)*sinh(x)^2 - 2*sqrt(2)*(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)*sqrt(b)*sqrt(((a + b)*cosh(x)^4 + (a + b)*sinh(x)^4 + 4*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + 2*a - 2*b)*sinh(x)^2 + 3*a + 3*b)/(cosh(x)^4 - 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 - 4*cosh(x)*sinh(x)^3 + sinh(x)^4)) + 8*((a + 2*b)*cosh(x)^7 + 3*(a - 2*b)*cosh(x)^5 + 3*(a + 2*b)*cosh(x)^3 + (a - 2*b)*cosh(x))*sinh(x) + a + 2*b)/(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)) + (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)*sqrt(a + b)*log(((a^2 + 2*a*b + b^2)*cosh(x)^8 + 8*(a^2 + 2*a*b + b^2)*cosh(x)*sinh(x)^7 + (a^2 + 2*a*b + b^2)*sinh(x)^8 + 4*(a^2 - b^2)*cosh(x)^6 + 4*(7*(a^2 + 2*a*b + b^2)*cosh(x)^2 + a^2 - b^2)*sinh(x)^6 + 8*(7*(a^2 + 2*a*b + b^2)*cosh(x)^3 + 3*(a^2 - b^2)*cosh(x))*sinh(x)^5 + 2*(3*a^2 + 2*a*b + 3*b^2)*cosh(x)^4 + 2*(35*(a^2 + 2*a*b + b^2)*cosh(x)^4 + 30*(a^2 - b^2)*cosh(x)^2 + 3*a^2 + 2*a*b + 3*b^2)*sinh(x)^4 + 8*(7*(a^2 + 2*a*b + b^2)*cosh(x)^5 + 10*(a^2 - b^2)*cosh(x)^3 + (3*a^2 + 2*a*b + 3*b^2)*cosh(x))*sinh(x)^3 + 4*(a^2 - b^2)*cosh(x)^2 + 4*(7*(a^2 + 2*a*b + b^2)*cosh(x)^6 + 15*(a^2 - b^2)*cosh(x)^4 + 3*(3*a^2 + 2*a*b + 3*b^2)*cosh(x)^2 + a^2 - b^2)*sinh(x)^2 + sqrt(2)*((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a - b)*cosh(x))*sinh(x) + a + b)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^4 + (a + b)*sinh(x)^4 + 4*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + 2*a - 2*b)*sinh(x)^2 + 3*a + 3*b)/(cosh(x)^4 - 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 - 4*cosh(x)*sinh(x)^3 + sinh(x)^4)) + a^2 + 2*a*b + b^2 + 8*((a^2 + 2*a*b + b^2)*cosh(x)^7 + 3*(a^2 - b^2)*cosh(x)^5 + (3*a^2 + 2*a*b + 3*b^2)*cosh(x)^3 + (a^2 - b^2)*cosh(x))*sinh(x))/(cosh(x)^4 + 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4)) - 2*sqrt(2)*sqrt(((a + b)*cosh(x)^4 + (a + b)*sinh(x)^4 + 4*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + 2*a - 2*b)*sinh(x)^2 + 3*a + 3*b)/(cosh(x)^4 - 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 - 4*cosh(x)*sinh(x)^3 + sinh(x)^4)))/(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), -1/4*(2*(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)*sqrt(-a - b)*arctan(sqrt(2)*((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a - b)*cosh(x))*sinh(x) + a + b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^4 + (a + b)*sinh(x)^4 + 4*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + 2*a - 2*b)*sinh(x)^2 + 3*a + 3*b)/(cosh(x)^4 - 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 - 4*cosh(x)*sinh(x)^3 + sinh(x)^4))/((a^2 + 2*a*b + b^2)*cosh(x)^8 + 8*(a^2 + 2*a*b + b^2)*cosh(x)*sinh(x)^7 + (a^2 + 2*a*b + b^2)*sinh(x)^8 + 4*(a^2 - b^2)*cosh(x)^6 + 4*(7*(a^2 + 2*a*b + b^2)*cosh(x)^2 + a^2 - b^2)*sinh(x)^6 + 8*(7*(a^2 + 2*a*b + b^2)*cosh(x)^3 + 3*(a^2 - b^2)*cosh(x))*sinh(x)^5 + 6*(a^2 + 2*a*b + b^2)*cosh(x)^4 + 2*(35*(a^2 + 2*a*b + b^2)*cosh(x)^4 + 30*(a^2 - b^2)*cosh(x)^2 + 3*a^2 + 6*a*b + 3*b^2)*sinh(x)^4 + 8*(7*(a^2 + 2*a*b + b^2)*cosh(x)^5 + 10*(a^2 - b^2)*cosh(x)^3 + 3*(a^2 + 2*a*b + b^2)*cosh(x))*sinh(x)^3 + 4*(a^2 - b^2)*cosh(x)^2 + 4*(7*(a^2 + 2*a*b + b^2)*cosh(x)^6 + 15*(a^2 - b^2)*cosh(x)^4 + 9*(a^2 + 2*a*b + b^2)*cosh(x)^2 + a^2 - b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 8*((a^2 + 2*a*b + b^2)*cosh(x)^7 + 3*(a^2 - b^2)*cosh(x)^5 + 3*(a^2 + 2*a*b + b^2)*cosh(x)^3 + (a^2 - b^2)*cosh(x))*sinh(x))) - (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)*sqrt(b)*log(-((a + 2*b)*cosh(x)^8 + 8*(a + 2*b)*cosh(x)*sinh(x)^7 + (a + 2*b)*sinh(x)^8 + 4*(a - 2*b)*cosh(x)^6 + 4*(7*(a + 2*b)*cosh(x)^2 + a - 2*b)*sinh(x)^6 + 8*(7*(a + 2*b)*cosh(x)^3 + 3*(a - 2*b)*cosh(x))*sinh(x)^5 + 6*(a + 2*b)*cosh(x)^4 + 2*(35*(a + 2*b)*cosh(x)^4 + 30*(a - 2*b)*cosh(x)^2 + 3*a + 6*b)*sinh(x)^4 + 8*(7*(a + 2*b)*cosh(x)^5 + 10*(a - 2*b)*cosh(x)^3 + 3*(a + 2*b)*cosh(x))*sinh(x)^3 + 4*(a - 2*b)*cosh(x)^2 + 4*(7*(a + 2*b)*cosh(x)^6 + 15*(a - 2*b)*cosh(x)^4 + 9*(a + 2*b)*cosh(x)^2 + a - 2*b)*sinh(x)^2 - 2*sqrt(2)*(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)*sqrt(b)*sqrt(((a + b)*cosh(x)^4 + (a + b)*sinh(x)^4 + 4*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + 2*a - 2*b)*sinh(x)^2 + 3*a + 3*b)/(cosh(x)^4 - 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 - 4*cosh(x)*sinh(x)^3 + sinh(x)^4)) + 8*((a + 2*b)*cosh(x)^7 + 3*(a - 2*b)*cosh(x)^5 + 3*(a + 2*b)*cosh(x)^3 + (a - 2*b)*cosh(x))*sinh(x) + a + 2*b)/(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)) + 2*sqrt(2)*sqrt(((a + b)*cosh(x)^4 + (a + b)*sinh(x)^4 + 4*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + 2*a - 2*b)*sinh(x)^2 + 3*a + 3*b)/(cosh(x)^4 - 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 - 4*cosh(x)*sinh(x)^3 + sinh(x)^4)))/(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), 1/4*(2*(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)*sqrt(-b)*arctan(sqrt(2)*sqrt(-b)*sqrt(((a + b)*cosh(x)^4 + (a + b)*sinh(x)^4 + 4*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + 2*a - 2*b)*sinh(x)^2 + 3*a + 3*b)/(cosh(x)^4 - 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 - 4*cosh(x)*sinh(x)^3 + sinh(x)^4))/(b*cosh(x)^4 + 4*b*cosh(x)*sinh(x)^3 + b*sinh(x)^4 - 2*b*cosh(x)^2 + 2*(3*b*cosh(x)^2 - b)*sinh(x)^2 + 4*(b*cosh(x)^3 - b*cosh(x))*sinh(x) + b)) + (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)*sqrt(a + b)*log(((a^2 + 2*a*b + b^2)*cosh(x)^8 + 8*(a^2 + 2*a*b + b^2)*cosh(x)*sinh(x)^7 + (a^2 + 2*a*b + b^2)*sinh(x)^8 + 4*(a^2 - b^2)*cosh(x)^6 + 4*(7*(a^2 + 2*a*b + b^2)*cosh(x)^2 + a^2 - b^2)*sinh(x)^6 + 8*(7*(a^2 + 2*a*b + b^2)*cosh(x)^3 + 3*(a^2 - b^2)*cosh(x))*sinh(x)^5 + 2*(3*a^2 + 2*a*b + 3*b^2)*cosh(x)^4 + 2*(35*(a^2 + 2*a*b + b^2)*cosh(x)^4 + 30*(a^2 - b^2)*cosh(x)^2 + 3*a^2 + 2*a*b + 3*b^2)*sinh(x)^4 + 8*(7*(a^2 + 2*a*b + b^2)*cosh(x)^5 + 10*(a^2 - b^2)*cosh(x)^3 + (3*a^2 + 2*a*b + 3*b^2)*cosh(x))*sinh(x)^3 + 4*(a^2 - b^2)*cosh(x)^2 + 4*(7*(a^2 + 2*a*b + b^2)*cosh(x)^6 + 15*(a^2 - b^2)*cosh(x)^4 + 3*(3*a^2 + 2*a*b + 3*b^2)*cosh(x)^2 + a^2 - b^2)*sinh(x)^2 + sqrt(2)*((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a - b)*cosh(x))*sinh(x) + a + b)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^4 + (a + b)*sinh(x)^4 + 4*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + 2*a - 2*b)*sinh(x)^2 + 3*a + 3*b)/(cosh(x)^4 - 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 - 4*cosh(x)*sinh(x)^3 + sinh(x)^4)) + a^2 + 2*a*b + b^2 + 8*((a^2 + 2*a*b + b^2)*cosh(x)^7 + 3*(a^2 - b^2)*cosh(x)^5 + (3*a^2 + 2*a*b + 3*b^2)*cosh(x)^3 + (a^2 - b^2)*cosh(x))*sinh(x))/(cosh(x)^4 + 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4)) - 2*sqrt(2)*sqrt(((a + b)*cosh(x)^4 + (a + b)*sinh(x)^4 + 4*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + 2*a - 2*b)*sinh(x)^2 + 3*a + 3*b)/(cosh(x)^4 - 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 - 4*cosh(x)*sinh(x)^3 + sinh(x)^4)))/(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), -1/2*((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)*sqrt(-a - b)*arctan(sqrt(2)*((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a - b)*cosh(x))*sinh(x) + a + b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^4 + (a + b)*sinh(x)^4 + 4*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + 2*a - 2*b)*sinh(x)^2 + 3*a + 3*b)/(cosh(x)^4 - 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 - 4*cosh(x)*sinh(x)^3 + sinh(x)^4))/((a^2 + 2*a*b + b^2)*cosh(x)^8 + 8*(a^2 + 2*a*b + b^2)*cosh(x)*sinh(x)^7 + (a^2 + 2*a*b + b^2)*sinh(x)^8 + 4*(a^2 - b^2)*cosh(x)^6 + 4*(7*(a^2 + 2*a*b + b^2)*cosh(x)^2 + a^2 - b^2)*sinh(x)^6 + 8*(7*(a^2 + 2*a*b + b^2)*cosh(x)^3 + 3*(a^2 - b^2)*cosh(x))*sinh(x)^5 + 6*(a^2 + 2*a*b + b^2)*cosh(x)^4 + 2*(35*(a^2 + 2*a*b + b^2)*cosh(x)^4 + 30*(a^2 - b^2)*cosh(x)^2 + 3*a^2 + 6*a*b + 3*b^2)*sinh(x)^4 + 8*(7*(a^2 + 2*a*b + b^2)*cosh(x)^5 + 10*(a^2 - b^2)*cosh(x)^3 + 3*(a^2 + 2*a*b + b^2)*cosh(x))*sinh(x)^3 + 4*(a^2 - b^2)*cosh(x)^2 + 4*(7*(a^2 + 2*a*b + b^2)*cosh(x)^6 + 15*(a^2 - b^2)*cosh(x)^4 + 9*(a^2 + 2*a*b + b^2)*cosh(x)^2 + a^2 - b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 8*((a^2 + 2*a*b + b^2)*cosh(x)^7 + 3*(a^2 - b^2)*cosh(x)^5 + 3*(a^2 + 2*a*b + b^2)*cosh(x)^3 + (a^2 - b^2)*cosh(x))*sinh(x))) - (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)*sqrt(-b)*arctan(sqrt(2)*sqrt(-b)*sqrt(((a + b)*cosh(x)^4 + (a + b)*sinh(x)^4 + 4*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + 2*a - 2*b)*sinh(x)^2 + 3*a + 3*b)/(cosh(x)^4 - 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 - 4*cosh(x)*sinh(x)^3 + sinh(x)^4))/(b*cosh(x)^4 + 4*b*cosh(x)*sinh(x)^3 + b*sinh(x)^4 - 2*b*cosh(x)^2 + 2*(3*b*cosh(x)^2 - b)*sinh(x)^2 + 4*(b*cosh(x)^3 - b*cosh(x))*sinh(x) + b)) + sqrt(2)*sqrt(((a + b)*cosh(x)^4 + (a + b)*sinh(x)^4 + 4*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + 2*a - 2*b)*sinh(x)^2 + 3*a + 3*b)/(cosh(x)^4 - 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 - 4*cosh(x)*sinh(x)^3 + sinh(x)^4)))/(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)]","B",0
261,1,1286,0,0.638742," ","integrate(tanh(x)/(a+b*tanh(x)^4)^(1/2),x, algorithm=""fricas"")","\left[\frac{\log\left(\frac{{\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(x\right)^{8} + 4 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{2} + 2 \, a b + 3 \, b^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{4} + 30 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} + 2 \, a b + 3 \, b^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b + 3 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(3 \, a^{2} + 2 \, a b + 3 \, b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left({\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 4 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, a - 2 \, b\right)} \sinh\left(x\right)^{2} + 3 \, a + 3 \, b}{\cosh\left(x\right)^{4} - 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}} + a^{2} + 2 \, a b + b^{2} + 8 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{2} + 2 \, a b + 3 \, b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{4} + 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} + 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}\right)}{4 \, \sqrt{a + b}}, -\frac{\sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left({\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 4 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, a - 2 \, b\right)} \sinh\left(x\right)^{2} + 3 \, a + 3 \, b}{\cosh\left(x\right)^{4} - 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}}}{{\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(x\right)^{8} + 4 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 6 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{4} + 30 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} + 6 \, a b + 3 \, b^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{4} + 9 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 8 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{5} + 3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right)}{2 \, {\left(a + b\right)}}\right]"," ",0,"[1/4*log(((a^2 + 2*a*b + b^2)*cosh(x)^8 + 8*(a^2 + 2*a*b + b^2)*cosh(x)*sinh(x)^7 + (a^2 + 2*a*b + b^2)*sinh(x)^8 + 4*(a^2 - b^2)*cosh(x)^6 + 4*(7*(a^2 + 2*a*b + b^2)*cosh(x)^2 + a^2 - b^2)*sinh(x)^6 + 8*(7*(a^2 + 2*a*b + b^2)*cosh(x)^3 + 3*(a^2 - b^2)*cosh(x))*sinh(x)^5 + 2*(3*a^2 + 2*a*b + 3*b^2)*cosh(x)^4 + 2*(35*(a^2 + 2*a*b + b^2)*cosh(x)^4 + 30*(a^2 - b^2)*cosh(x)^2 + 3*a^2 + 2*a*b + 3*b^2)*sinh(x)^4 + 8*(7*(a^2 + 2*a*b + b^2)*cosh(x)^5 + 10*(a^2 - b^2)*cosh(x)^3 + (3*a^2 + 2*a*b + 3*b^2)*cosh(x))*sinh(x)^3 + 4*(a^2 - b^2)*cosh(x)^2 + 4*(7*(a^2 + 2*a*b + b^2)*cosh(x)^6 + 15*(a^2 - b^2)*cosh(x)^4 + 3*(3*a^2 + 2*a*b + 3*b^2)*cosh(x)^2 + a^2 - b^2)*sinh(x)^2 + sqrt(2)*((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a - b)*cosh(x))*sinh(x) + a + b)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^4 + (a + b)*sinh(x)^4 + 4*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + 2*a - 2*b)*sinh(x)^2 + 3*a + 3*b)/(cosh(x)^4 - 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 - 4*cosh(x)*sinh(x)^3 + sinh(x)^4)) + a^2 + 2*a*b + b^2 + 8*((a^2 + 2*a*b + b^2)*cosh(x)^7 + 3*(a^2 - b^2)*cosh(x)^5 + (3*a^2 + 2*a*b + 3*b^2)*cosh(x)^3 + (a^2 - b^2)*cosh(x))*sinh(x))/(cosh(x)^4 + 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4))/sqrt(a + b), -1/2*sqrt(-a - b)*arctan(sqrt(2)*((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a - b)*cosh(x))*sinh(x) + a + b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^4 + (a + b)*sinh(x)^4 + 4*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + 2*a - 2*b)*sinh(x)^2 + 3*a + 3*b)/(cosh(x)^4 - 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 - 4*cosh(x)*sinh(x)^3 + sinh(x)^4))/((a^2 + 2*a*b + b^2)*cosh(x)^8 + 8*(a^2 + 2*a*b + b^2)*cosh(x)*sinh(x)^7 + (a^2 + 2*a*b + b^2)*sinh(x)^8 + 4*(a^2 - b^2)*cosh(x)^6 + 4*(7*(a^2 + 2*a*b + b^2)*cosh(x)^2 + a^2 - b^2)*sinh(x)^6 + 8*(7*(a^2 + 2*a*b + b^2)*cosh(x)^3 + 3*(a^2 - b^2)*cosh(x))*sinh(x)^5 + 6*(a^2 + 2*a*b + b^2)*cosh(x)^4 + 2*(35*(a^2 + 2*a*b + b^2)*cosh(x)^4 + 30*(a^2 - b^2)*cosh(x)^2 + 3*a^2 + 6*a*b + 3*b^2)*sinh(x)^4 + 8*(7*(a^2 + 2*a*b + b^2)*cosh(x)^5 + 10*(a^2 - b^2)*cosh(x)^3 + 3*(a^2 + 2*a*b + b^2)*cosh(x))*sinh(x)^3 + 4*(a^2 - b^2)*cosh(x)^2 + 4*(7*(a^2 + 2*a*b + b^2)*cosh(x)^6 + 15*(a^2 - b^2)*cosh(x)^4 + 9*(a^2 + 2*a*b + b^2)*cosh(x)^2 + a^2 - b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 8*((a^2 + 2*a*b + b^2)*cosh(x)^7 + 3*(a^2 - b^2)*cosh(x)^5 + 3*(a^2 + 2*a*b + b^2)*cosh(x)^3 + (a^2 - b^2)*cosh(x))*sinh(x)))/(a + b)]","B",0
262,1,3914,0,0.807499," ","integrate(tanh(x)/(a+b*tanh(x)^4)^(3/2),x, algorithm=""fricas"")","\left[\frac{{\left({\left(a^{2} + a b\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{2} + a b\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{2} + a b\right)} \sinh\left(x\right)^{8} + 4 \, {\left(a^{2} - a b\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} + a^{2} - a b\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{2} - a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 6 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{4} + 30 \, {\left(a^{2} - a b\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} + 3 \, a b\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{5} + 10 \, {\left(a^{2} - a b\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(a^{2} - a b\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{6} + 15 \, {\left(a^{2} - a b\right)} \cosh\left(x\right)^{4} + 9 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} + a^{2} - a b\right)} \sinh\left(x\right)^{2} + a^{2} + a b + 8 \, {\left({\left(a^{2} + a b\right)} \cosh\left(x\right)^{7} + 3 \, {\left(a^{2} - a b\right)} \cosh\left(x\right)^{5} + 3 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{3} + {\left(a^{2} - a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{a + b} \log\left(\frac{{\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(x\right)^{8} + 4 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 2 \, {\left(3 \, a^{2} + 2 \, a b + 3 \, b^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{4} + 30 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} + 2 \, a b + 3 \, b^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{3} + {\left(3 \, a^{2} + 2 \, a b + 3 \, b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{4} + 3 \, {\left(3 \, a^{2} + 2 \, a b + 3 \, b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(x\right)^{2} + \sqrt{2} {\left({\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b\right)} \sqrt{a + b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 4 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, a - 2 \, b\right)} \sinh\left(x\right)^{2} + 3 \, a + 3 \, b}{\cosh\left(x\right)^{4} - 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}} + a^{2} + 2 \, a b + b^{2} + 8 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{5} + {\left(3 \, a^{2} + 2 \, a b + 3 \, b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}{\cosh\left(x\right)^{4} + 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} + 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}\right) - 2 \, \sqrt{2} {\left({\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{2} - b^{2}\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} - b^{2} + 4 \, {\left({\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 4 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, a - 2 \, b\right)} \sinh\left(x\right)^{2} + 3 \, a + 3 \, b}{\cosh\left(x\right)^{4} - 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}}}{4 \, {\left({\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \sinh\left(x\right)^{8} + 4 \, {\left(a^{4} + a^{3} b - a^{2} b^{2} - a b^{3}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(a^{4} + a^{3} b - a^{2} b^{2} - a b^{3} + 7 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{4} + a^{3} b - a^{2} b^{2} - a b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 6 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right)^{4} + 3 \, a^{4} + 9 \, a^{3} b + 9 \, a^{2} b^{2} + 3 \, a b^{3} + 30 \, {\left(a^{4} + a^{3} b - a^{2} b^{2} - a b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3} + 8 \, {\left(7 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(a^{4} + a^{3} b - a^{2} b^{2} - a b^{3}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(a^{4} + a^{3} b - a^{2} b^{2} - a b^{3}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(a^{4} + a^{3} b - a^{2} b^{2} - a b^{3}\right)} \cosh\left(x\right)^{4} + a^{4} + a^{3} b - a^{2} b^{2} - a b^{3} + 9 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 8 \, {\left({\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(a^{4} + a^{3} b - a^{2} b^{2} - a b^{3}\right)} \cosh\left(x\right)^{5} + 3 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{4} + a^{3} b - a^{2} b^{2} - a b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}, -\frac{{\left({\left(a^{2} + a b\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{2} + a b\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{2} + a b\right)} \sinh\left(x\right)^{8} + 4 \, {\left(a^{2} - a b\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} + a^{2} - a b\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{2} - a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 6 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{4} + 30 \, {\left(a^{2} - a b\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} + 3 \, a b\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{5} + 10 \, {\left(a^{2} - a b\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(a^{2} - a b\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{6} + 15 \, {\left(a^{2} - a b\right)} \cosh\left(x\right)^{4} + 9 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{2} + a^{2} - a b\right)} \sinh\left(x\right)^{2} + a^{2} + a b + 8 \, {\left({\left(a^{2} + a b\right)} \cosh\left(x\right)^{7} + 3 \, {\left(a^{2} - a b\right)} \cosh\left(x\right)^{5} + 3 \, {\left(a^{2} + a b\right)} \cosh\left(x\right)^{3} + {\left(a^{2} - a b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{-a - b} \arctan\left(\frac{\sqrt{2} {\left({\left(a + b\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a + b\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + a - b\right)} \sinh\left(x\right)^{2} + 4 \, {\left({\left(a + b\right)} \cosh\left(x\right)^{3} + {\left(a - b\right)} \cosh\left(x\right)\right)} \sinh\left(x\right) + a + b\right)} \sqrt{-a - b} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 4 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, a - 2 \, b\right)} \sinh\left(x\right)^{2} + 3 \, a + 3 \, b}{\cosh\left(x\right)^{4} - 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}}}{{\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(x\right)^{8} + 4 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 6 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{4} + 30 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{2} + 3 \, a^{2} + 6 \, a b + 3 \, b^{2}\right)} \sinh\left(x\right)^{4} + 8 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{4} + 9 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} - b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2} + 8 \, {\left({\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{5} + 3 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)}\right) + \sqrt{2} {\left({\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{4} + 4 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right) \sinh\left(x\right)^{3} + {\left(a^{2} - b^{2}\right)} \sinh\left(x\right)^{4} + 2 \, {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{2} + a^{2} + 2 \, a b + b^{2}\right)} \sinh\left(x\right)^{2} + a^{2} - b^{2} + 4 \, {\left({\left(a^{2} - b^{2}\right)} \cosh\left(x\right)^{3} + {\left(a^{2} + 2 \, a b + b^{2}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)} \sqrt{\frac{{\left(a + b\right)} \cosh\left(x\right)^{4} + {\left(a + b\right)} \sinh\left(x\right)^{4} + 4 \, {\left(a - b\right)} \cosh\left(x\right)^{2} + 2 \, {\left(3 \, {\left(a + b\right)} \cosh\left(x\right)^{2} + 2 \, a - 2 \, b\right)} \sinh\left(x\right)^{2} + 3 \, a + 3 \, b}{\cosh\left(x\right)^{4} - 4 \, \cosh\left(x\right)^{3} \sinh\left(x\right) + 6 \, \cosh\left(x\right)^{2} \sinh\left(x\right)^{2} - 4 \, \cosh\left(x\right) \sinh\left(x\right)^{3} + \sinh\left(x\right)^{4}}}}{2 \, {\left({\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right)^{8} + 8 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right) \sinh\left(x\right)^{7} + {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \sinh\left(x\right)^{8} + 4 \, {\left(a^{4} + a^{3} b - a^{2} b^{2} - a b^{3}\right)} \cosh\left(x\right)^{6} + 4 \, {\left(a^{4} + a^{3} b - a^{2} b^{2} - a b^{3} + 7 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{6} + 8 \, {\left(7 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{4} + a^{3} b - a^{2} b^{2} - a b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{5} + 6 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right)^{4} + 2 \, {\left(35 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right)^{4} + 3 \, a^{4} + 9 \, a^{3} b + 9 \, a^{2} b^{2} + 3 \, a b^{3} + 30 \, {\left(a^{4} + a^{3} b - a^{2} b^{2} - a b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{4} + a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3} + 8 \, {\left(7 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right)^{5} + 10 \, {\left(a^{4} + a^{3} b - a^{2} b^{2} - a b^{3}\right)} \cosh\left(x\right)^{3} + 3 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)^{3} + 4 \, {\left(a^{4} + a^{3} b - a^{2} b^{2} - a b^{3}\right)} \cosh\left(x\right)^{2} + 4 \, {\left(7 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right)^{6} + 15 \, {\left(a^{4} + a^{3} b - a^{2} b^{2} - a b^{3}\right)} \cosh\left(x\right)^{4} + a^{4} + a^{3} b - a^{2} b^{2} - a b^{3} + 9 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right)^{2}\right)} \sinh\left(x\right)^{2} + 8 \, {\left({\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right)^{7} + 3 \, {\left(a^{4} + a^{3} b - a^{2} b^{2} - a b^{3}\right)} \cosh\left(x\right)^{5} + 3 \, {\left(a^{4} + 3 \, a^{3} b + 3 \, a^{2} b^{2} + a b^{3}\right)} \cosh\left(x\right)^{3} + {\left(a^{4} + a^{3} b - a^{2} b^{2} - a b^{3}\right)} \cosh\left(x\right)\right)} \sinh\left(x\right)\right)}}\right]"," ",0,"[1/4*(((a^2 + a*b)*cosh(x)^8 + 8*(a^2 + a*b)*cosh(x)*sinh(x)^7 + (a^2 + a*b)*sinh(x)^8 + 4*(a^2 - a*b)*cosh(x)^6 + 4*(7*(a^2 + a*b)*cosh(x)^2 + a^2 - a*b)*sinh(x)^6 + 8*(7*(a^2 + a*b)*cosh(x)^3 + 3*(a^2 - a*b)*cosh(x))*sinh(x)^5 + 6*(a^2 + a*b)*cosh(x)^4 + 2*(35*(a^2 + a*b)*cosh(x)^4 + 30*(a^2 - a*b)*cosh(x)^2 + 3*a^2 + 3*a*b)*sinh(x)^4 + 8*(7*(a^2 + a*b)*cosh(x)^5 + 10*(a^2 - a*b)*cosh(x)^3 + 3*(a^2 + a*b)*cosh(x))*sinh(x)^3 + 4*(a^2 - a*b)*cosh(x)^2 + 4*(7*(a^2 + a*b)*cosh(x)^6 + 15*(a^2 - a*b)*cosh(x)^4 + 9*(a^2 + a*b)*cosh(x)^2 + a^2 - a*b)*sinh(x)^2 + a^2 + a*b + 8*((a^2 + a*b)*cosh(x)^7 + 3*(a^2 - a*b)*cosh(x)^5 + 3*(a^2 + a*b)*cosh(x)^3 + (a^2 - a*b)*cosh(x))*sinh(x))*sqrt(a + b)*log(((a^2 + 2*a*b + b^2)*cosh(x)^8 + 8*(a^2 + 2*a*b + b^2)*cosh(x)*sinh(x)^7 + (a^2 + 2*a*b + b^2)*sinh(x)^8 + 4*(a^2 - b^2)*cosh(x)^6 + 4*(7*(a^2 + 2*a*b + b^2)*cosh(x)^2 + a^2 - b^2)*sinh(x)^6 + 8*(7*(a^2 + 2*a*b + b^2)*cosh(x)^3 + 3*(a^2 - b^2)*cosh(x))*sinh(x)^5 + 2*(3*a^2 + 2*a*b + 3*b^2)*cosh(x)^4 + 2*(35*(a^2 + 2*a*b + b^2)*cosh(x)^4 + 30*(a^2 - b^2)*cosh(x)^2 + 3*a^2 + 2*a*b + 3*b^2)*sinh(x)^4 + 8*(7*(a^2 + 2*a*b + b^2)*cosh(x)^5 + 10*(a^2 - b^2)*cosh(x)^3 + (3*a^2 + 2*a*b + 3*b^2)*cosh(x))*sinh(x)^3 + 4*(a^2 - b^2)*cosh(x)^2 + 4*(7*(a^2 + 2*a*b + b^2)*cosh(x)^6 + 15*(a^2 - b^2)*cosh(x)^4 + 3*(3*a^2 + 2*a*b + 3*b^2)*cosh(x)^2 + a^2 - b^2)*sinh(x)^2 + sqrt(2)*((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a - b)*cosh(x))*sinh(x) + a + b)*sqrt(a + b)*sqrt(((a + b)*cosh(x)^4 + (a + b)*sinh(x)^4 + 4*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + 2*a - 2*b)*sinh(x)^2 + 3*a + 3*b)/(cosh(x)^4 - 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 - 4*cosh(x)*sinh(x)^3 + sinh(x)^4)) + a^2 + 2*a*b + b^2 + 8*((a^2 + 2*a*b + b^2)*cosh(x)^7 + 3*(a^2 - b^2)*cosh(x)^5 + (3*a^2 + 2*a*b + 3*b^2)*cosh(x)^3 + (a^2 - b^2)*cosh(x))*sinh(x))/(cosh(x)^4 + 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 + 4*cosh(x)*sinh(x)^3 + sinh(x)^4)) - 2*sqrt(2)*((a^2 - b^2)*cosh(x)^4 + 4*(a^2 - b^2)*cosh(x)*sinh(x)^3 + (a^2 - b^2)*sinh(x)^4 + 2*(a^2 + 2*a*b + b^2)*cosh(x)^2 + 2*(3*(a^2 - b^2)*cosh(x)^2 + a^2 + 2*a*b + b^2)*sinh(x)^2 + a^2 - b^2 + 4*((a^2 - b^2)*cosh(x)^3 + (a^2 + 2*a*b + b^2)*cosh(x))*sinh(x))*sqrt(((a + b)*cosh(x)^4 + (a + b)*sinh(x)^4 + 4*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + 2*a - 2*b)*sinh(x)^2 + 3*a + 3*b)/(cosh(x)^4 - 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 - 4*cosh(x)*sinh(x)^3 + sinh(x)^4)))/((a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(x)^8 + 8*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(x)*sinh(x)^7 + (a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*sinh(x)^8 + 4*(a^4 + a^3*b - a^2*b^2 - a*b^3)*cosh(x)^6 + 4*(a^4 + a^3*b - a^2*b^2 - a*b^3 + 7*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(x)^2)*sinh(x)^6 + 8*(7*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(x)^3 + 3*(a^4 + a^3*b - a^2*b^2 - a*b^3)*cosh(x))*sinh(x)^5 + 6*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(x)^4 + 2*(35*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(x)^4 + 3*a^4 + 9*a^3*b + 9*a^2*b^2 + 3*a*b^3 + 30*(a^4 + a^3*b - a^2*b^2 - a*b^3)*cosh(x)^2)*sinh(x)^4 + a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3 + 8*(7*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(x)^5 + 10*(a^4 + a^3*b - a^2*b^2 - a*b^3)*cosh(x)^3 + 3*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(x))*sinh(x)^3 + 4*(a^4 + a^3*b - a^2*b^2 - a*b^3)*cosh(x)^2 + 4*(7*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(x)^6 + 15*(a^4 + a^3*b - a^2*b^2 - a*b^3)*cosh(x)^4 + a^4 + a^3*b - a^2*b^2 - a*b^3 + 9*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(x)^2)*sinh(x)^2 + 8*((a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(x)^7 + 3*(a^4 + a^3*b - a^2*b^2 - a*b^3)*cosh(x)^5 + 3*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(x)^3 + (a^4 + a^3*b - a^2*b^2 - a*b^3)*cosh(x))*sinh(x)), -1/2*(((a^2 + a*b)*cosh(x)^8 + 8*(a^2 + a*b)*cosh(x)*sinh(x)^7 + (a^2 + a*b)*sinh(x)^8 + 4*(a^2 - a*b)*cosh(x)^6 + 4*(7*(a^2 + a*b)*cosh(x)^2 + a^2 - a*b)*sinh(x)^6 + 8*(7*(a^2 + a*b)*cosh(x)^3 + 3*(a^2 - a*b)*cosh(x))*sinh(x)^5 + 6*(a^2 + a*b)*cosh(x)^4 + 2*(35*(a^2 + a*b)*cosh(x)^4 + 30*(a^2 - a*b)*cosh(x)^2 + 3*a^2 + 3*a*b)*sinh(x)^4 + 8*(7*(a^2 + a*b)*cosh(x)^5 + 10*(a^2 - a*b)*cosh(x)^3 + 3*(a^2 + a*b)*cosh(x))*sinh(x)^3 + 4*(a^2 - a*b)*cosh(x)^2 + 4*(7*(a^2 + a*b)*cosh(x)^6 + 15*(a^2 - a*b)*cosh(x)^4 + 9*(a^2 + a*b)*cosh(x)^2 + a^2 - a*b)*sinh(x)^2 + a^2 + a*b + 8*((a^2 + a*b)*cosh(x)^7 + 3*(a^2 - a*b)*cosh(x)^5 + 3*(a^2 + a*b)*cosh(x)^3 + (a^2 - a*b)*cosh(x))*sinh(x))*sqrt(-a - b)*arctan(sqrt(2)*((a + b)*cosh(x)^4 + 4*(a + b)*cosh(x)*sinh(x)^3 + (a + b)*sinh(x)^4 + 2*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + a - b)*sinh(x)^2 + 4*((a + b)*cosh(x)^3 + (a - b)*cosh(x))*sinh(x) + a + b)*sqrt(-a - b)*sqrt(((a + b)*cosh(x)^4 + (a + b)*sinh(x)^4 + 4*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + 2*a - 2*b)*sinh(x)^2 + 3*a + 3*b)/(cosh(x)^4 - 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 - 4*cosh(x)*sinh(x)^3 + sinh(x)^4))/((a^2 + 2*a*b + b^2)*cosh(x)^8 + 8*(a^2 + 2*a*b + b^2)*cosh(x)*sinh(x)^7 + (a^2 + 2*a*b + b^2)*sinh(x)^8 + 4*(a^2 - b^2)*cosh(x)^6 + 4*(7*(a^2 + 2*a*b + b^2)*cosh(x)^2 + a^2 - b^2)*sinh(x)^6 + 8*(7*(a^2 + 2*a*b + b^2)*cosh(x)^3 + 3*(a^2 - b^2)*cosh(x))*sinh(x)^5 + 6*(a^2 + 2*a*b + b^2)*cosh(x)^4 + 2*(35*(a^2 + 2*a*b + b^2)*cosh(x)^4 + 30*(a^2 - b^2)*cosh(x)^2 + 3*a^2 + 6*a*b + 3*b^2)*sinh(x)^4 + 8*(7*(a^2 + 2*a*b + b^2)*cosh(x)^5 + 10*(a^2 - b^2)*cosh(x)^3 + 3*(a^2 + 2*a*b + b^2)*cosh(x))*sinh(x)^3 + 4*(a^2 - b^2)*cosh(x)^2 + 4*(7*(a^2 + 2*a*b + b^2)*cosh(x)^6 + 15*(a^2 - b^2)*cosh(x)^4 + 9*(a^2 + 2*a*b + b^2)*cosh(x)^2 + a^2 - b^2)*sinh(x)^2 + a^2 + 2*a*b + b^2 + 8*((a^2 + 2*a*b + b^2)*cosh(x)^7 + 3*(a^2 - b^2)*cosh(x)^5 + 3*(a^2 + 2*a*b + b^2)*cosh(x)^3 + (a^2 - b^2)*cosh(x))*sinh(x))) + sqrt(2)*((a^2 - b^2)*cosh(x)^4 + 4*(a^2 - b^2)*cosh(x)*sinh(x)^3 + (a^2 - b^2)*sinh(x)^4 + 2*(a^2 + 2*a*b + b^2)*cosh(x)^2 + 2*(3*(a^2 - b^2)*cosh(x)^2 + a^2 + 2*a*b + b^2)*sinh(x)^2 + a^2 - b^2 + 4*((a^2 - b^2)*cosh(x)^3 + (a^2 + 2*a*b + b^2)*cosh(x))*sinh(x))*sqrt(((a + b)*cosh(x)^4 + (a + b)*sinh(x)^4 + 4*(a - b)*cosh(x)^2 + 2*(3*(a + b)*cosh(x)^2 + 2*a - 2*b)*sinh(x)^2 + 3*a + 3*b)/(cosh(x)^4 - 4*cosh(x)^3*sinh(x) + 6*cosh(x)^2*sinh(x)^2 - 4*cosh(x)*sinh(x)^3 + sinh(x)^4)))/((a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(x)^8 + 8*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(x)*sinh(x)^7 + (a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*sinh(x)^8 + 4*(a^4 + a^3*b - a^2*b^2 - a*b^3)*cosh(x)^6 + 4*(a^4 + a^3*b - a^2*b^2 - a*b^3 + 7*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(x)^2)*sinh(x)^6 + 8*(7*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(x)^3 + 3*(a^4 + a^3*b - a^2*b^2 - a*b^3)*cosh(x))*sinh(x)^5 + 6*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(x)^4 + 2*(35*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(x)^4 + 3*a^4 + 9*a^3*b + 9*a^2*b^2 + 3*a*b^3 + 30*(a^4 + a^3*b - a^2*b^2 - a*b^3)*cosh(x)^2)*sinh(x)^4 + a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3 + 8*(7*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(x)^5 + 10*(a^4 + a^3*b - a^2*b^2 - a*b^3)*cosh(x)^3 + 3*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(x))*sinh(x)^3 + 4*(a^4 + a^3*b - a^2*b^2 - a*b^3)*cosh(x)^2 + 4*(7*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(x)^6 + 15*(a^4 + a^3*b - a^2*b^2 - a*b^3)*cosh(x)^4 + a^4 + a^3*b - a^2*b^2 - a*b^3 + 9*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(x)^2)*sinh(x)^2 + 8*((a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(x)^7 + 3*(a^4 + a^3*b - a^2*b^2 - a*b^3)*cosh(x)^5 + 3*(a^4 + 3*a^3*b + 3*a^2*b^2 + a*b^3)*cosh(x)^3 + (a^4 + a^3*b - a^2*b^2 - a*b^3)*cosh(x))*sinh(x))]","B",0
263,-1,0,0,0.000000," ","integrate(tanh(x)/(a+b*tanh(x)^4)^(5/2),x, algorithm=""fricas"")","\text{Timed out}"," ",0,"Timed out","F(-1)",0
